LMFDB - Embedded newform 931.2.x.d.226.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(226,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([6, 10]))

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

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

chi := DirichletCharacter("931.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.x (of order $9$, degree $6$, not 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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 133)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			226.4
Character	$\chi$	$=$	931.226
Dual form			931.2.x.d.655.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24615 + 1.04564i) q^{2} +(-0.186827 + 1.05955i) q^{3} +(0.112220 + 0.636434i) q^{4} +(-0.0122200 + 0.0693033i) q^{5} +(-1.34072 + 1.12500i) q^{6} +(1.10109 - 1.90715i) q^{8} +(1.73134 + 0.630158i) q^{9} +O(q^{10})$	\(q+(1.24615 + 1.04564i) q^{2} +(-0.186827 + 1.05955i) q^{3} +(0.112220 + 0.636434i) q^{4} +(-0.0122200 + 0.0693033i) q^{5} +(-1.34072 + 1.12500i) q^{6} +(1.10109 - 1.90715i) q^{8} +(1.73134 + 0.630158i) q^{9} +(-0.0876945 + 0.0735844i) q^{10} +1.79123 q^{11} -0.695297 q^{12} +(2.27346 - 1.90766i) q^{13} +(-0.0711470 - 0.0258954i) q^{15} +(4.58087 - 1.66730i) q^{16} +(-0.591642 + 0.215340i) q^{17} +(1.49859 + 2.59564i) q^{18} +(0.791993 + 4.28634i) q^{19} -0.0454783 q^{20} +(2.23214 + 1.87299i) q^{22} +(-1.14928 + 0.964356i) q^{23} +(1.81500 + 1.52296i) q^{24} +(4.69381 + 1.70841i) q^{25} +4.82780 q^{26} +(-2.60498 + 4.51196i) q^{27} +(-0.942253 - 5.34378i) q^{29} +(-0.0615824 - 0.106664i) q^{30} +(-3.26526 + 5.65559i) q^{31} +(3.31309 + 1.20587i) q^{32} +(-0.334650 + 1.89789i) q^{33} +(-0.962442 - 0.350300i) q^{34} +(-0.206761 + 1.17260i) q^{36} +(-0.345571 + 0.598546i) q^{37} +(-3.49504 + 6.16956i) q^{38} +(1.59651 + 2.76524i) q^{39} +(0.118716 + 0.0996148i) q^{40} +(-5.15375 - 4.32451i) q^{41} +(-1.77256 + 0.645159i) q^{43} +(0.201013 + 1.14000i) q^{44} +(-0.0648291 + 0.112287i) q^{45} -2.44054 q^{46} +(-1.30673 - 0.475610i) q^{47} +(0.910754 + 5.16514i) q^{48} +(4.06280 + 7.03697i) q^{50} +(-0.117628 - 0.667103i) q^{51} +(1.46923 + 1.23283i) q^{52} +(1.28138 + 7.26708i) q^{53} +(-7.96408 + 2.89869i) q^{54} +(-0.0218890 + 0.124138i) q^{55} +(-4.68954 + 0.0383506i) q^{57} +(4.41350 - 7.64440i) q^{58} +(13.0307 - 4.74278i) q^{59} +(0.00849656 - 0.0481864i) q^{60} +(0.128760 - 0.108043i) q^{61} +(-9.98271 + 3.63341i) q^{62} +(-2.00716 - 3.47651i) q^{64} +(0.104426 + 0.180870i) q^{65} +(-2.40154 + 2.01513i) q^{66} +(-7.07640 + 5.93781i) q^{67} +(-0.203444 - 0.352375i) q^{68} +(-0.807065 - 1.39788i) q^{69} +(11.0779 - 4.03202i) q^{71} +(3.10817 - 2.60807i) q^{72} +(1.94927 - 11.0549i) q^{73} +(-1.05650 + 0.384533i) q^{74} +(-2.68706 + 4.65413i) q^{75} +(-2.63910 + 0.985067i) q^{76} +(-0.901962 + 5.11528i) q^{78} +(-9.84833 + 3.58450i) q^{79} +(0.0595710 + 0.337844i) q^{80} +(-0.0597313 - 0.0501205i) q^{81} +(-1.90045 - 10.7780i) q^{82} +(-3.37852 - 5.85176i) q^{83} +(-0.00769389 - 0.0436342i) q^{85} +(-2.88348 - 1.04950i) q^{86} +5.83802 q^{87} +(1.97231 - 3.41615i) q^{88} +(0.716785 + 4.06509i) q^{89} +(-0.198199 + 0.0721386i) q^{90} +(-0.742721 - 0.623217i) q^{92} +(-5.38232 - 4.51630i) q^{93} +(-1.13106 - 1.95905i) q^{94} +(-0.306736 + 0.00250846i) q^{95} +(-1.89665 + 3.28509i) q^{96} +(0.928436 - 5.26542i) q^{97} +(3.10124 + 1.12876i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{3} - 6 q^{4} + 6 q^{5} + 9 q^{6} + 9 q^{8} + 24 q^{9}+O(q^{10}) $ 30 * q - 6 * q^3 - 6 * q^4 + 6 * q^5 + 9 * q^6 + 9 * q^8 + 24 * q^9	$ 30 q - 6 q^{3} - 6 q^{4} + 6 q^{5} + 9 q^{6} + 9 q^{8} + 24 q^{9} + 36 q^{12} - 30 q^{15} - 18 q^{16} - 3 q^{17} + 15 q^{18} + 12 q^{19} + 30 q^{20} + 12 q^{22} + 3 q^{23} - 18 q^{24} - 42 q^{25} - 90 q^{26} - 27 q^{27} + 21 q^{30} - 12 q^{31} + 15 q^{32} + 27 q^{33} + 42 q^{34} - 21 q^{36} + 18 q^{37} - 3 q^{38} + 12 q^{39} + 48 q^{40} - 3 q^{41} - 12 q^{43} - 27 q^{45} - 12 q^{46} - 9 q^{47} - 18 q^{48} - 3 q^{50} + 27 q^{51} - 30 q^{52} + 30 q^{53} - 78 q^{54} - 33 q^{55} - 12 q^{57} + 30 q^{58} - 42 q^{59} - 87 q^{60} - 33 q^{61} - 96 q^{62} + 3 q^{64} + 45 q^{65} + 117 q^{66} - 69 q^{67} - 51 q^{68} - 15 q^{69} + 30 q^{71} + 18 q^{72} + 3 q^{73} + 33 q^{74} - 72 q^{75} - 84 q^{76} + 6 q^{78} - 15 q^{79} - 87 q^{80} + 21 q^{81} - 3 q^{82} - 12 q^{83} + 42 q^{85} + 6 q^{86} + 48 q^{87} + 36 q^{88} - 42 q^{89} - 180 q^{90} - 75 q^{92} - 42 q^{93} - 21 q^{94} - 15 q^{95} + 33 q^{96} + 63 q^{97} + 45 q^{99}+O(q^{100}) $ 30 * q - 6 * q^3 - 6 * q^4 + 6 * q^5 + 9 * q^6 + 9 * q^8 + 24 * q^9 + 36 * q^12 - 30 * q^15 - 18 * q^16 - 3 * q^17 + 15 * q^18 + 12 * q^19 + 30 * q^20 + 12 * q^22 + 3 * q^23 - 18 * q^24 - 42 * q^25 - 90 * q^26 - 27 * q^27 + 21 * q^30 - 12 * q^31 + 15 * q^32 + 27 * q^33 + 42 * q^34 - 21 * q^36 + 18 * q^37 - 3 * q^38 + 12 * q^39 + 48 * q^40 - 3 * q^41 - 12 * q^43 - 27 * q^45 - 12 * q^46 - 9 * q^47 - 18 * q^48 - 3 * q^50 + 27 * q^51 - 30 * q^52 + 30 * q^53 - 78 * q^54 - 33 * q^55 - 12 * q^57 + 30 * q^58 - 42 * q^59 - 87 * q^60 - 33 * q^61 - 96 * q^62 + 3 * q^64 + 45 * q^65 + 117 * q^66 - 69 * q^67 - 51 * q^68 - 15 * q^69 + 30 * q^71 + 18 * q^72 + 3 * q^73 + 33 * q^74 - 72 * q^75 - 84 * q^76 + 6 * q^78 - 15 * q^79 - 87 * q^80 + 21 * q^81 - 3 * q^82 - 12 * q^83 + 42 * q^85 + 6 * q^86 + 48 * q^87 + 36 * q^88 - 42 * q^89 - 180 * q^90 - 75 * q^92 - 42 * q^93 - 21 * q^94 - 15 * q^95 + 33 * q^96 + 63 * q^97 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	1.24615	+	1.04564i	0.881160	+	0.739381i	0.966417	−	0.256978i	$-0.0827269\pi$
$2$	1.24615	+	1.04564i	0.881160	+	0.739381i	−0.0852576	+	0.996359i	$0.527171\pi$
$3$	−0.186827	+	1.05955i	−0.107864	+	0.611729i	0.882173	+	0.470925i	$0.156080\pi$
$3$	−0.186827	+	1.05955i	−0.107864	+	0.611729i	−0.990037	+	0.140804i	$0.955031\pi$
$4$	0.112220	+	0.636434i	0.0561102	+	0.318217i
$5$	−0.0122200	+	0.0693033i	−0.00546497	+	0.0309934i	−0.987418	−	0.158130i	$-0.949453\pi$
$5$	−0.0122200	+	0.0693033i	−0.00546497	+	0.0309934i	0.981953	+	0.189123i	$0.0605646\pi$
$6$	−1.34072	+	1.12500i	−0.547346	+	0.459278i
$7$		0			0
$7$		0			0
$8$	1.10109	−	1.90715i	0.389295	−	0.674278i
$9$	1.73134	+	0.630158i	0.577115	+	0.210053i
$10$	−0.0876945	+	0.0735844i	−0.0277314	+	0.0232694i
$11$	1.79123			0.540077			0.270039	−	0.962849i	$-0.412964\pi$
$11$	1.79123			0.540077			0.270039	+	0.962849i	$0.412964\pi$
$12$	−0.695297			−0.200715
$13$	2.27346	−	1.90766i	0.630545	−	0.529090i	−0.270553	−	0.962705i	$-0.587207\pi$
$13$	2.27346	−	1.90766i	0.630545	−	0.529090i	0.901098	+	0.433615i	$0.142762\pi$
$14$		0			0
$15$	−0.0711470	−	0.0258954i	−0.0183701	−	0.00668616i
$16$	4.58087	−	1.66730i	1.14522	−	0.416825i
$17$	−0.591642	+	0.215340i	−0.143494	+	0.0522276i	−0.412769	−	0.910836i	$-0.635438\pi$
$17$	−0.591642	+	0.215340i	−0.143494	+	0.0522276i	0.269275	+	0.963063i	$0.413216\pi$
$18$	1.49859	+	2.59564i	0.353221	+	0.611797i
$19$	0.791993	+	4.28634i	0.181696	+	0.983355i
$19$	0.791993	+	4.28634i	0.181696	+	0.983355i
$20$	−0.0454783			−0.0101693
$21$		0			0
$22$	2.23214	+	1.87299i	0.475894	+	0.399323i
$23$	−1.14928	+	0.964356i	−0.239640	+	0.201082i	−0.754696	−	0.656075i	$-0.772216\pi$
$23$	−1.14928	+	0.964356i	−0.239640	+	0.201082i	0.515056	+	0.857157i	$0.327771\pi$
$24$	1.81500	+	1.52296i	0.370485	+	0.310874i
$25$	4.69381	+	1.70841i	0.938762	+	0.341681i
$26$	4.82780			0.946810
$27$	−2.60498	+	4.51196i	−0.501328	+	0.868326i
$28$		0			0
$29$	−0.942253	−	5.34378i	−0.174972	−	0.992316i	−0.938176	−	0.346158i	$-0.887486\pi$
$29$	−0.942253	−	5.34378i	−0.174972	−	0.992316i	0.763204	−	0.646157i	$-0.223625\pi$
$30$	−0.0615824	−	0.106664i	−0.0112434	−	0.0194741i
$31$	−3.26526	+	5.65559i	−0.586457	+	1.01577i	0.408235	+	0.912877i	$0.366144\pi$
$31$	−3.26526	+	5.65559i	−0.586457	+	1.01577i	−0.994692	+	0.102897i	$0.967189\pi$
$32$	3.31309	+	1.20587i	0.585678	+	0.213169i
$33$	−0.334650	+	1.89789i	−0.0582551	+	0.330381i
$34$	−0.962442	−	0.350300i	−0.165057	−	0.0600760i
$35$		0			0
$36$	−0.206761	+	1.17260i	−0.0344602	+	0.195434i
$37$	−0.345571	+	0.598546i	−0.0568115	+	0.0984003i	−0.893032	−	0.449992i	$-0.851427\pi$
$37$	−0.345571	+	0.598546i	−0.0568115	+	0.0984003i	0.836221	+	0.548393i	$0.184760\pi$
$38$	−3.49504	+	6.16956i	−0.566971	+	1.00083i
$39$	1.59651	+	2.76524i	0.255647	+	0.442793i
$40$	0.118716	+	0.0996148i	0.0187707	+	0.0157505i
$41$	−5.15375	−	4.32451i	−0.804881	−	0.675376i	0.144499	−	0.989505i	$-0.453843\pi$
$41$	−5.15375	−	4.32451i	−0.804881	−	0.675376i	−0.949380	+	0.314129i	$0.898287\pi$
$42$		0			0
$43$	−1.77256	+	0.645159i	−0.270313	+	0.0983859i	−0.473620	−	0.880729i	$-0.657053\pi$
$43$	−1.77256	+	0.645159i	−0.270313	+	0.0983859i	0.203307	+	0.979115i	$0.434831\pi$
$44$	0.201013	+	1.14000i	0.0303039	+	0.171862i
$45$	−0.0648291	+	0.112287i	−0.00966416	+	0.0167388i
$46$	−2.44054			−0.359838
$47$	−1.30673	−	0.475610i	−0.190606	−	0.0693748i	0.244954	−	0.969535i	$-0.421227\pi$
$47$	−1.30673	−	0.475610i	−0.190606	−	0.0693748i	−0.435559	+	0.900160i	$0.643449\pi$
$48$	0.910754	+	5.16514i	0.131456	+	0.745524i
$49$		0			0
$50$	4.06280	+	7.03697i	0.574566	+	0.995178i
$51$	−0.117628	−	0.667103i	−0.0164712	−	0.0934131i
$52$	1.46923	+	1.23283i	0.203746	+	0.170963i
$53$	1.28138	+	7.26708i	0.176011	+	0.998210i	0.936970	+	0.349410i	$0.113618\pi$
$53$	1.28138	+	7.26708i	0.176011	+	0.998210i	−0.760959	+	0.648800i	$0.775271\pi$
$54$	−7.96408	+	2.89869i	−1.08377	+	0.394461i
$55$	−0.0218890	+	0.124138i	−0.00295151	+	0.0167388i
$56$		0			0
$57$	−4.68954	+	0.0383506i	−0.621145	+	0.00507966i
$58$	4.41350	−	7.64440i	0.579521	−	1.00376i
$59$	13.0307	−	4.74278i	1.69645	−	0.617457i	0.701037	−	0.713125i	$-0.252721\pi$
$59$	13.0307	−	4.74278i	1.69645	−	0.617457i	0.995413	+	0.0956681i	$0.0304987\pi$
$60$	0.00849656	−	0.0481864i	0.00109690	−	0.00622083i
$61$	0.128760	−	0.108043i	0.0164861	−	0.0138335i	−0.634507	−	0.772917i	$-0.718797\pi$
$61$	0.128760	−	0.108043i	0.0164861	−	0.0138335i	0.650993	+	0.759083i	$0.274353\pi$
$62$	−9.98271	+	3.63341i	−1.26781	+	0.461444i
$63$		0			0
$64$	−2.00716	−	3.47651i	−0.250896	−	0.434564i
$65$	0.104426	+	0.180870i	0.0129524	+	0.0224342i
$66$	−2.40154	+	2.01513i	−0.295609	+	0.248046i
$67$	−7.07640	+	5.93781i	−0.864520	+	0.725419i	−0.962937	−	0.269727i	$-0.913067\pi$
$67$	−7.07640	+	5.93781i	−0.864520	+	0.725419i	0.0984165	+	0.995145i	$0.468622\pi$
$68$	−0.203444	−	0.352375i	−0.0246712	−	0.0427318i
$69$	−0.807065	−	1.39788i	−0.0971592	−	0.168285i
$70$		0			0
$71$	11.0779	−	4.03202i	1.31470	−	0.478513i	0.412947	−	0.910755i	$-0.364500\pi$
$71$	11.0779	−	4.03202i	1.31470	−	0.478513i	0.901758	+	0.432242i	$0.142277\pi$
$72$	3.10817	−	2.60807i	0.366302	−	0.307364i
$73$	1.94927	−	11.0549i	0.228145	−	1.29388i	−0.628435	−	0.777862i	$-0.716304\pi$
$73$	1.94927	−	11.0549i	0.228145	−	1.29388i	0.856580	−	0.516014i	$-0.172585\pi$
$74$	−1.05650	+	0.384533i	−0.122815	+	0.0447011i
$75$	−2.68706	+	4.65413i	−0.310275	+	0.537413i
$76$	−2.63910	+	0.985067i	−0.302725	+	0.112995i
$77$		0			0
$78$	−0.901962	+	5.11528i	−0.102127	+	0.579191i
$79$	−9.84833	+	3.58450i	−1.10802	+	0.403287i	−0.830268	−	0.557364i	$-0.811813\pi$
$79$	−9.84833	+	3.58450i	−1.10802	+	0.403287i	−0.277755	+	0.960652i	$0.589590\pi$
$80$	0.0595710	+	0.337844i	0.00666025	+	0.0377721i
$81$	−0.0597313	−	0.0501205i	−0.00663681	−	0.00556895i
$82$	−1.90045	−	10.7780i	−0.209869	−	1.19023i
$83$	−3.37852	−	5.85176i	−0.370840	−	0.642315i	0.618855	−	0.785506i	$-0.287597\pi$
$83$	−3.37852	−	5.85176i	−0.370840	−	0.642315i	−0.989695	+	0.143191i	$0.954264\pi$
$84$		0			0
$85$	−0.00769389	−	0.0436342i	−0.000834519	−	0.00473279i
$86$	−2.88348	−	1.04950i	−0.310933	−	0.113171i
$87$	5.83802			0.625902
$88$	1.97231	−	3.41615i	0.210249	−	0.364162i
$89$	0.716785	+	4.06509i	0.0759791	+	0.430899i	0.998941	+	0.0460077i	$0.0146499\pi$
$89$	0.716785	+	4.06509i	0.0759791	+	0.430899i	−0.922962	+	0.384891i	$0.874239\pi$
$90$	−0.198199	+	0.0721386i	−0.0208920	+	0.00760407i
$91$		0			0
$92$	−0.742721	−	0.623217i	−0.0774340	−	0.0649749i
$93$	−5.38232	−	4.51630i	−0.558120	−	0.468319i
$94$	−1.13106	−	1.95905i	−0.116660	−	0.202061i
$95$	−0.306736	+	0.00250846i	−0.0314705	+	0.000257362i
$96$	−1.89665	+	3.28509i	−0.193576	+	0.335283i
$97$	0.928436	−	5.26542i	0.0942684	−	0.534623i	−0.900701	−	0.434440i	$-0.856946\pi$
$97$	0.928436	−	5.26542i	0.0942684	−	0.534623i	0.994969	−	0.100182i	$-0.0319427\pi$
$98$		0			0
$99$	3.10124	+	1.12876i	0.311687	+	0.113445i
$100$	−0.560546	+	3.17902i	−0.0560546	+	0.317902i
$101$	4.68592	+	1.70554i	0.466267	+	0.169707i	0.564461	−	0.825460i	$-0.309084\pi$
$101$	4.68592	+	1.70554i	0.466267	+	0.169707i	−0.0981936	+	0.995167i	$0.531306\pi$
$102$	0.550969	−	0.954306i	0.0545540	−	0.0944904i
$103$	−1.50069	−	2.59928i	−0.147868	−	0.256115i	0.782571	−	0.622561i	$-0.213908\pi$
$103$	−1.50069	−	2.59928i	−0.147868	−	0.256115i	−0.930439	+	0.366446i	$0.880574\pi$
$104$	−1.13490	−	6.43634i	−0.111286	−	0.631135i
$105$		0			0
$106$	−6.00197	+	10.3957i	−0.582963	+	1.00972i
$107$	−12.5188			−1.21024			−0.605121	−	0.796134i	$-0.706875\pi$
$107$	−12.5188			−1.21024			−0.605121	+	0.796134i	$0.706875\pi$
$108$	−3.16389	−	1.15156i	−0.304446	−	0.110809i
$109$	−10.7539	−	9.02355i	−1.03003	−	0.864299i	−0.0391773	−	0.999232i	$-0.512474\pi$
$109$	−10.7539	−	9.02355i	−1.03003	−	0.864299i	−0.990855	+	0.134933i	$0.956918\pi$
$110$	−0.157081	+	0.131807i	−0.0149771	+	0.0125673i
$111$	−0.569625	−	0.477972i	−0.0540664	−	0.0453671i
$112$		0			0
$113$	−0.420510			−0.0395583			−0.0197791	−	0.999804i	$-0.506296\pi$
$113$	−0.420510			−0.0395583			−0.0197791	+	0.999804i	$0.506296\pi$
$114$	−5.88397	−	4.85579i	−0.551084	−	0.454787i
$115$	−0.0527889	−	0.0914331i	−0.00492259	−	0.00852618i
$116$	3.29522	−	1.19936i	0.305954	−	0.111358i
$117$	5.13828	−	1.87018i	0.475034	−	0.172898i
$118$	21.1974	+	7.71522i	1.95138	+	0.710244i
$119$		0			0
$120$	−0.127726	+	0.107175i	−0.0116597	+	0.00978366i
$121$	−7.79148			−0.708316
$122$	0.273429			0.0247551
$123$	5.54488	−	4.65271i	0.499965	−	0.419520i
$124$	−3.96584	−	1.44345i	−0.356143	−	0.129625i
$125$	−0.351688	+	0.609141i	−0.0314559	+	0.0544833i
$126$		0			0
$127$	9.45174	−	7.93095i	0.838707	−	0.703758i	−0.118566	−	0.992946i	$-0.537830\pi$
$127$	9.45174	−	7.93095i	0.838707	−	0.703758i	0.957272	+	0.289188i	$0.0933852\pi$
$128$	2.35843	−	13.3753i	0.208458	−	1.18222i
$129$	−0.352415	−	1.99864i	−0.0310284	−	0.175971i
$130$	−0.0589960	+	0.334583i	−0.00517429	+	0.0293449i
$131$	−2.28866	−	1.92042i	−0.199962	−	0.167788i	0.537309	−	0.843386i	$-0.319441\pi$
$131$	−2.28866	−	1.92042i	−0.199962	−	0.167788i	−0.737270	+	0.675598i	$0.763885\pi$
$132$	−1.24544			−0.108402
$133$		0			0
$134$	−15.0271			−1.29814
$135$	−0.280861	−	0.235670i	−0.0241726	−	0.0202832i
$136$	−0.240767	+	1.36546i	−0.0206456	+	0.117087i
$137$	3.70626	+	21.0192i	0.316647	+	1.79580i	0.562831	+	0.826572i	$0.309712\pi$
$137$	3.70626	+	21.0192i	0.316647	+	1.79580i	−0.246184	+	0.969223i	$0.579177\pi$
$138$	0.455957	−	2.58586i	0.0388137	−	0.220123i
$139$	5.38233	−	4.51631i	0.456523	−	0.383068i	−0.385327	−	0.922780i	$-0.625911\pi$
$139$	5.38233	−	4.51631i	0.456523	−	0.383068i	0.841850	+	0.539712i	$0.181467\pi$
$140$		0			0
$141$	0.748062	−	1.29568i	0.0629982	−	0.109116i
$142$	18.0207	+	6.55902i	1.51227	+	0.550420i
$143$	4.07231	−	3.41707i	0.340543	−	0.285750i
$144$	8.98173			0.748477
$145$	0.381856			0.0317114
$146$	13.9885	−	11.7378i	1.15770	−	0.971425i
$147$		0			0
$148$	−0.419715	−	0.152764i	−0.0345003	−	0.0125571i
$149$	−7.57610	+	2.75748i	−0.620659	+	0.225901i	−0.633160	−	0.774021i	$-0.718243\pi$
$149$	−7.57610	+	2.75748i	−0.620659	+	0.225901i	0.0125018	+	0.999922i	$0.496020\pi$
$150$	−8.21503	+	2.99003i	−0.670755	+	0.244135i
$151$	−10.1104	−	17.5117i	−0.822773	−	1.42509i	−0.903609	−	0.428358i	$-0.859092\pi$
$151$	−10.1104	−	17.5117i	−0.822773	−	1.42509i	0.0808356	−	0.996727i	$-0.474241\pi$
$152$	9.04674	+	3.20921i	0.733788	+	0.260301i
$153$	−1.16003			−0.0937832
$154$		0			0
$155$	−0.352050	−	0.295405i	−0.0282773	−	0.0237275i
$156$	−1.58073	+	1.32639i	−0.126560	+	0.106196i
$157$	−17.5965	−	14.7652i	−1.40435	−	1.17839i	−0.959128	−	0.282972i	$-0.908680\pi$
$157$	−17.5965	−	14.7652i	−1.40435	−	1.17839i	−0.445224	−	0.895419i	$-0.646876\pi$
$158$	−16.0206	−	5.83101i	−1.27453	−	0.463890i
$159$	−7.93920			−0.629619
$160$	−0.124057	+	0.214873i	−0.00980755	+	0.0169872i
$161$		0			0
$162$	−0.0220259	−	0.124915i	−0.00173052	−	0.00981426i
$163$	9.01257	+	15.6102i	0.705919	+	1.22269i	0.966359	+	0.257198i	$0.0827992\pi$
$163$	9.01257	+	15.6102i	0.705919	+	1.22269i	−0.260439	+	0.965490i	$0.583867\pi$
$164$	2.17391	−	3.76532i	0.169754	−	0.294022i
$165$	−0.127441	−	0.0463847i	−0.00992127	−	0.00361105i
$166$	1.90872	−	10.8249i	0.148145	−	0.840174i
$167$	−3.45416	−	1.25721i	−0.267291	−	0.0972860i	0.204898	−	0.978783i	$-0.434314\pi$
$167$	−3.45416	−	1.25721i	−0.267291	−	0.0972860i	−0.472189	+	0.881497i	$0.656536\pi$
$168$		0			0
$169$	−0.727966	+	4.12850i	−0.0559974	+	0.317577i
$170$	0.0360380	−	0.0624197i	0.00276399	−	0.00478737i
$171$	−1.32986	+	7.92022i	−0.101697	+	0.605674i
$172$	−0.609519	−	1.05572i	−0.0464754	−	0.0804977i
$173$	8.27573	+	6.94416i	0.629192	+	0.527955i	0.900678	−	0.434488i	$-0.143071\pi$
$173$	8.27573	+	6.94416i	0.629192	+	0.527955i	−0.271486	+	0.962442i	$0.587515\pi$
$174$	7.27504	+	6.10448i	0.551519	+	0.462780i
$175$		0			0
$176$	8.20541	−	2.98653i	0.618506	−	0.225118i
$177$	2.59072	+	14.6927i	0.194730	+	1.10437i
$178$	−3.35741	+	5.81521i	−0.251649	+	0.435868i
$179$	−2.07152			−0.154833			−0.0774165	−	0.996999i	$-0.524667\pi$
$179$	−2.07152			−0.154833			−0.0774165	+	0.996999i	$0.524667\pi$
$180$	−0.0787386	−	0.0286585i	−0.00586883	−	0.00213608i
$181$	−0.196089	−	1.11208i	−0.0145752	−	0.0826601i	0.976653	−	0.214825i	$-0.0689182\pi$
$181$	−0.196089	−	1.11208i	−0.0145752	−	0.0826601i	−0.991228	+	0.132165i	$0.957807\pi$
$182$		0			0
$183$	0.0904205	+	0.156613i	0.00668408	+	0.0115772i
$184$	0.573712	+	3.25368i	0.0422946	+	0.239865i
$185$	−0.0372583	−	0.0312635i	−0.00273929	−	0.00229853i
$186$	−1.98473	−	11.2560i	−0.145527	−	0.825327i
$187$	−1.05977	+	0.385724i	−0.0774980	+	0.0282070i
$188$	0.156053	−	0.885019i	0.0113813	−	0.0645466i
$189$		0			0
$190$	−0.384862	−	0.317610i	−0.0279208	−	0.0230419i
$191$	0.150719	−	0.261053i	0.0109056	−	0.0188891i	−0.860521	−	0.509415i	$-0.829862\pi$
$191$	0.150719	−	0.261053i	0.0109056	−	0.0188891i	0.871427	+	0.490526i	$0.163195\pi$
$192$	4.05851	−	1.47718i	0.292898	−	0.106606i
$193$	0.535498	−	3.03696i	0.0385460	−	0.218605i	−0.959450	−	0.281878i	$-0.909043\pi$
$193$	0.535498	−	3.03696i	0.0385460	−	0.218605i	0.997996	+	0.0632727i	$0.0201538\pi$
$194$	6.66272	−	5.59068i	0.478355	−	0.401388i
$195$	−0.211150	+	0.0768523i	−0.0151208	+	0.00550351i
$196$		0			0
$197$	−13.9602	−	24.1797i	−0.994620	−	1.72273i	−0.587025	−	0.809569i	$-0.699701\pi$
$197$	−13.9602	−	24.1797i	−0.994620	−	1.72273i	−0.407595	−	0.913163i	$-0.633632\pi$
$198$	2.68433	+	4.64939i	0.190767	+	0.330418i
$199$	1.13329	−	0.950941i	0.0803367	−	0.0674105i	−0.601735	−	0.798696i	$-0.705524\pi$
$199$	1.13329	−	0.950941i	0.0803367	−	0.0674105i	0.682072	+	0.731285i	$0.261079\pi$
$200$	8.42650	−	7.07067i	0.595843	−	0.499972i
$201$	−4.96932	−	8.60712i	−0.350509	−	0.607099i
$202$	4.05597	+	7.02515i	0.285377	+	0.494288i
$203$		0			0
$204$	0.411367	−	0.149725i	0.0288014	−	0.0104829i
$205$	0.362682	−	0.304327i	0.0253308	−	0.0212551i
$206$	0.847829	−	4.80828i	0.0590710	−	0.335008i
$207$	−2.59749	+	0.945408i	−0.180538	+	0.0657104i
$208$	7.23380	−	12.5293i	0.501574	−	0.868751i
$209$	1.41865	+	7.67785i	0.0981298	+	0.531088i
$210$		0			0
$211$	−4.78998	+	27.1653i	−0.329756	+	1.87014i	0.144137	+	0.989558i	$0.453959\pi$
$211$	−4.78998	+	27.1653i	−0.329756	+	1.87014i	−0.473894	+	0.880582i	$0.657152\pi$
$212$	−4.48122	+	1.63103i	−0.307771	+	0.112020i
$213$	2.20247	+	12.4908i	0.150911	+	0.855857i
$214$	−15.6003	−	13.0902i	−1.06642	−	0.894829i
$215$	−0.0230509	−	0.130728i	−0.00157206	−	0.00891559i
$216$	5.73664	+	9.93615i	0.390329	+	0.676070i
$217$		0			0
$218$	−3.96548	−	22.4894i	−0.268576	−	1.52317i
$219$	11.3490	+	4.13069i	0.766893	+	0.279126i
$220$	−0.0814623			−0.00549219
$221$	−0.934280	+	1.61822i	−0.0628465	+	0.108853i
$222$	−0.210049	−	1.19125i	−0.0140976	−	0.0799513i
$223$	−8.38245	+	3.05096i	−0.561331	+	0.204308i	−0.607074	−	0.794646i	$-0.707657\pi$
$223$	−8.38245	+	3.05096i	−0.561331	+	0.204308i	0.0457430	+	0.998953i	$0.485434\pi$
$224$		0			0
$225$	7.05003	+	5.91568i	0.470002	+	0.394379i
$226$	−0.524018	−	0.439703i	−0.0348571	−	0.0292486i
$227$	−12.6725	−	21.9493i	−0.841101	−	1.45683i	−0.888965	−	0.457975i	$-0.848575\pi$
$227$	−12.6725	−	21.9493i	−0.841101	−	1.45683i	0.0478641	−	0.998854i	$-0.484759\pi$
$228$	−0.550670	−	2.98028i	−0.0364690	−	0.197374i
$229$	12.4215	−	21.5146i	0.820834	−	1.42173i	−0.0842287	−	0.996446i	$-0.526843\pi$
$229$	12.4215	−	21.5146i	0.820834	−	1.42173i	0.905062	−	0.425279i	$-0.139824\pi$
$230$	0.0298235	−	0.169137i	0.00196650	−	0.0111526i
$231$		0			0
$232$	−11.2289	−	4.08698i	−0.737213	−	0.268323i
$233$	2.74690	−	15.5785i	0.179956	−	1.02058i	−0.752311	−	0.658808i	$-0.771061\pi$
$233$	2.74690	−	15.5785i	0.179956	−	1.02058i	0.932267	−	0.361771i	$-0.117828\pi$
$234$	8.35859	+	3.04228i	0.546418	+	0.198880i
$235$	0.0489296	−	0.0847486i	0.00319182	−	0.00552839i
$236$	4.48077	+	7.76093i	0.291674	+	0.505193i
$237$	−1.95801	−	11.1044i	−0.127186	−	0.721310i
$238$		0			0
$239$	−2.00385	+	3.47078i	−0.129619	+	0.224506i	−0.923529	−	0.383529i	$-0.874709\pi$
$239$	−2.00385	+	3.47078i	−0.129619	+	0.224506i	0.793910	+	0.608035i	$0.208042\pi$
$240$	−0.369091			−0.0238247
$241$	−21.2817	−	7.74590i	−1.37087	−	0.498957i	−0.451475	−	0.892284i	$-0.649102\pi$
$241$	−21.2817	−	7.74590i	−1.37087	−	0.498957i	−0.919399	+	0.393327i	$0.871324\pi$
$242$	−9.70934	−	8.14710i	−0.624140	−	0.523715i
$243$	−11.9089	+	9.99277i	−0.763957	+	0.641036i
$244$	0.0832117	+	0.0698229i	0.00532708	+	0.00446995i
$245$		0			0
$246$	11.7748			0.750734
$247$	9.97747	+	8.23399i	0.634851	+	0.523916i
$248$	7.19069	+	12.4546i	0.456609	+	0.790871i
$249$	6.83141	−	2.48643i	0.432923	−	0.157571i
$250$	−1.07520	+	0.391341i	−0.0680016	+	0.0247505i
$251$	25.6565	+	9.33821i	1.61942	+	0.589422i	0.983272	−	0.182141i	$-0.0583027\pi$
$251$	25.6565	+	9.33821i	1.61942	+	0.589422i	0.636152	+	0.771563i	$0.280525\pi$
$252$		0			0
$253$	−2.05862	+	1.72739i	−0.129424	+	0.108600i
$254$	20.0712			1.25938
$255$	0.0476699			0.00298520
$256$	10.7745	−	9.04085i	0.673404	−	0.565053i
$257$	11.8009	+	4.29516i	0.736118	+	0.267925i	0.682752	−	0.730650i	$-0.260783\pi$
$257$	11.8009	+	4.29516i	0.736118	+	0.267925i	0.0533655	+	0.998575i	$0.483005\pi$
$258$	1.65070	−	2.85910i	0.102768	−	0.178000i
$259$		0			0
$260$	−0.103393	+	0.0867573i	−0.00641218	+	0.00538046i
$261$	1.73606	−	9.84570i	0.107460	−	0.609433i
$262$	−0.843945	−	4.78625i	−0.0521391	−	0.295695i
$263$	2.87025	−	16.2780i	0.176987	−	1.00374i	−0.758838	−	0.651279i	$-0.774233\pi$
$263$	2.87025	−	16.2780i	0.176987	−	1.00374i	0.935825	−	0.352464i	$-0.114656\pi$
$264$	3.25108	+	2.72798i	0.200090	+	0.167896i
$265$	−0.519291			−0.0318998
$266$		0			0
$267$	−4.44107			−0.271789
$268$	−4.57314	−	3.83732i	−0.279349	−	0.234402i
$269$	5.08894	−	28.8608i	0.310278	−	1.75968i	−0.287276	−	0.957848i	$-0.592750\pi$
$269$	5.08894	−	28.8608i	0.310278	−	1.75968i	0.597554	−	0.801829i	$-0.296139\pi$
$270$	−0.103567	−	0.587359i	−0.00630291	−	0.0357456i
$271$	−4.83842	+	27.4400i	−0.293913	+	1.66686i	0.377674	+	0.925939i	$0.376724\pi$
$271$	−4.83842	+	27.4400i	−0.293913	+	1.66686i	−0.671587	+	0.740926i	$0.734387\pi$
$272$	−2.35120	+	1.97289i	−0.142562	+	0.119624i
$273$		0			0
$274$	−17.3601	+	30.0685i	−1.04876	+	1.81650i
$275$	8.40771	+	3.06016i	0.507004	+	0.184534i
$276$	0.799087	−	0.670514i	0.0480994	−	0.0403602i
$277$	6.40558			0.384874			0.192437	−	0.981309i	$-0.438361\pi$
$277$	6.40558			0.384874			0.192437	+	0.981309i	$0.438361\pi$
$278$	11.4296			0.685503
$279$	−9.21719	+	7.73414i	−0.551819	+	0.463031i
$280$		0			0
$281$	−0.456698	−	0.166224i	−0.0272443	−	0.00991612i	0.328362	−	0.944552i	$-0.393503\pi$
$281$	−0.456698	−	0.166224i	−0.0272443	−	0.00991612i	−0.355606	+	0.934636i	$0.615726\pi$
$282$	2.28701	−	0.832405i	0.136190	−	0.0495690i
$283$	−24.7557	+	9.01035i	−1.47158	+	0.535610i	−0.948528	−	0.316693i	$-0.897427\pi$
$283$	−24.7557	+	9.01035i	−1.47158	+	0.535610i	−0.523048	+	0.852303i	$0.675205\pi$
$284$	3.80928	+	6.59787i	0.226039	+	0.391512i
$285$	0.0546486	−	0.325470i	0.00323711	−	0.0192792i
$286$	8.64773			0.511351
$287$		0			0
$288$	4.97622	+	4.17554i	0.293226	+	0.246046i
$289$	−12.7191	+	10.6726i	−0.748182	+	0.627799i
$290$	0.475850	+	0.399285i	0.0279428	+	0.0234468i
$291$	5.40550	+	1.96744i	0.316876	+	0.115333i
$292$	7.25445			0.424534
$293$	−15.7393	+	27.2613i	−0.919500	+	1.59262i	−0.119324	+	0.992855i	$0.538073\pi$
$293$	−15.7393	+	27.2613i	−0.919500	+	1.59262i	−0.800176	+	0.599765i	$0.795261\pi$
$294$		0			0
$295$	0.169455	+	0.961026i	0.00986605	+	0.0559531i
$296$	0.761010	+	1.31811i	0.0442328	+	0.0766135i
$297$	−4.66613	+	8.08197i	−0.270756	+	0.468963i
$298$	−12.3243	−	4.48567i	−0.713926	−	0.259848i
$299$	−0.773169	+	4.38486i	−0.0447135	+	0.253583i
$300$	−3.26359	−	1.18785i	−0.188423	−	0.0685805i
$301$		0			0
$302$	5.71195	−	32.3941i	0.328686	−	1.86407i
$303$	−2.68255	+	4.64631i	−0.154108	+	0.266924i
$304$	10.7746	+	18.3147i	0.617968	+	1.05042i
$305$	0.00591427	+	0.0102438i	0.000338650	+	0.000586559i
$306$	−1.44557	−	1.21298i	−0.0826379	−	0.0693415i
$307$	13.1843	+	11.0629i	0.752468	+	0.631395i	0.936154	−	0.351589i	$-0.114359\pi$
$307$	13.1843	+	11.0629i	0.752468	+	0.631395i	−0.183687	+	0.982985i	$0.558803\pi$
$308$		0			0
$309$	3.03443	−	1.10444i	0.172622	−	0.0628294i
$310$	−0.129818	−	0.736236i	−0.00737318	−	0.0418154i
$311$	−14.3737	+	24.8960i	−0.815058	+	1.41172i	0.0942276	+	0.995551i	$0.469962\pi$
$311$	−14.3737	+	24.8960i	−0.815058	+	1.41172i	−0.909286	+	0.416172i	$0.863371\pi$
$312$	7.03163			0.398088
$313$	−6.64201	−	2.41749i	−0.375429	−	0.136645i	0.147412	−	0.989075i	$-0.452906\pi$
$313$	−6.64201	−	2.41749i	−0.375429	−	0.136645i	−0.522841	+	0.852430i	$0.675128\pi$
$314$	−6.48870	−	36.7992i	−0.366179	−	2.07670i
$315$		0			0
$316$	−3.38648	−	5.86555i	−0.190504	−	0.329963i
$317$	−1.09767	−	6.22521i	−0.0616515	−	0.349643i	−0.999992	−	0.00393122i	$-0.998749\pi$
$317$	−1.09767	−	6.22521i	−0.0616515	−	0.349643i	0.938341	−	0.345712i	$-0.112362\pi$
$318$	−9.89341	−	8.30156i	−0.554795	−	0.465528i
$319$	−1.68780	−	9.57197i	−0.0944984	−	0.535927i
$320$	0.265461	−	0.0966201i	0.0148397	−	0.00540123i
$321$	2.33885	−	13.2643i	0.130542	−	0.740340i
$322$		0			0
$323$	−1.39160	−	2.36543i	−0.0774306	−	0.131616i
$324$	0.0251953	−	0.0436396i	0.00139974	−	0.00242442i
$325$	13.9303	−	5.07020i	0.772712	−	0.281244i
$326$	−5.09172	+	28.8766i	−0.282004	+	1.59933i
$327$	11.5700	−	9.70836i	0.639821	−	0.536874i
$328$	−13.9222	+	5.06728i	−0.768727	+	0.279794i
$329$		0			0
$330$	−0.110308	−	0.191060i	−0.00607228	−	0.0105175i
$331$	−7.82141	−	13.5471i	−0.429904	−	0.744615i	0.566960	−	0.823745i	$-0.308119\pi$
$331$	−7.82141	−	13.5471i	−0.429904	−	0.744615i	−0.996864	+	0.0791297i	$0.974786\pi$
$332$	3.34512	−	2.80689i	0.183587	−	0.154048i
$333$	−0.975480	+	0.818525i	−0.0534560	+	0.0448549i
$334$	−2.98980	−	5.17849i	−0.163595	−	0.283354i
$335$	−0.325036	−	0.562979i	−0.0177586	−	0.0307588i
$336$		0			0
$337$	−7.04290	+	2.56341i	−0.383651	+	0.139638i	−0.526644	−	0.850086i	$-0.676550\pi$
$337$	−7.04290	+	2.56341i	−0.383651	+	0.139638i	0.142992	+	0.989724i	$0.454328\pi$
$338$	−5.22408	+	4.38353i	−0.284153	+	0.238432i
$339$	0.0785624	−	0.445550i	0.00426693	−	0.0241989i
$340$	0.0269069	−	0.00979330i	0.00145923	−	0.000531116i
$341$	−5.84884	+	10.1305i	−0.316732	+	0.548596i
$342$	−9.93892	+	8.47921i	−0.537435	+	0.458503i
$343$		0			0
$344$	−0.721338	+	4.09091i	−0.0388920	+	0.220567i
$345$	0.106740	−	0.0388502i	0.00574669	−	0.00209162i
$346$	3.05167	+	17.3069i	0.164059	+	0.930425i
$347$	6.50814	+	5.46098i	0.349375	+	0.293161i	0.800539	−	0.599280i	$-0.204547\pi$
$347$	6.50814	+	5.46098i	0.349375	+	0.293161i	−0.451164	+	0.892441i	$0.648991\pi$
$348$	0.655145	+	3.71551i	0.0351195	+	0.199172i
$349$	0.310773	+	0.538275i	0.0166353	+	0.0288132i	0.874223	−	0.485524i	$-0.161371\pi$
$349$	0.310773	+	0.538275i	0.0166353	+	0.0288132i	−0.857588	+	0.514337i	$0.828038\pi$
$350$		0			0
$351$	2.68496	+	15.2272i	0.143313	+	0.812767i
$352$	5.93452	+	2.15999i	0.316311	+	0.115128i
$353$	26.3254			1.40116			0.700580	−	0.713574i	$-0.252925\pi$
$353$	26.3254			1.40116			0.700580	+	0.713574i	$0.252925\pi$
$354$	−12.1349	+	21.0182i	−0.644961	+	1.11711i
$355$	0.144060	+	0.817007i	0.00764593	+	0.0433622i
$356$	−2.50672	+	0.912373i	−0.132856	+	0.0483557i
$357$		0			0
$358$	−2.58142	−	2.16607i	−0.136433	−	0.114480i
$359$	−6.69052	−	5.61401i	−0.353112	−	0.296296i	0.448926	−	0.893569i	$-0.351807\pi$
$359$	−6.69052	−	5.61401i	−0.353112	−	0.296296i	−0.802038	+	0.597273i	$0.796251\pi$
$360$	0.142766	+	0.247277i	0.00752441	+	0.0130327i
$361$	−17.7455	+	6.78951i	−0.933973	+	0.357343i
$362$	0.918479	−	1.59085i	0.0482742	−	0.0836134i
$363$	1.45566	−	8.25543i	0.0764021	−	0.433298i
$364$		0			0
$365$	0.742320	+	0.270182i	0.0388548	+	0.0141420i
$366$	−0.0510837	+	0.289710i	−0.00267019	+	0.0151434i
$367$	7.95647	+	2.89592i	0.415324	+	0.151166i	0.541226	−	0.840877i	$-0.317960\pi$
$367$	7.95647	+	2.89592i	0.415324	+	0.151166i	−0.125902	+	0.992043i	$0.540182\pi$
$368$	−3.65681	+	6.33378i	−0.190624	+	0.330171i
$369$	−6.19780	−	10.7349i	−0.322644	−	0.558837i
$370$	−0.0137390	−	0.0779178i	−0.000714257	−	0.00405075i
$371$		0			0
$372$	2.27032	−	3.93231i	0.117711	−	0.203881i
$373$	−23.7498			−1.22972			−0.614859	−	0.788637i	$-0.710787\pi$
$373$	−23.7498			−1.22972			−0.614859	+	0.788637i	$0.710787\pi$
$374$	−1.72396	−	0.627469i	−0.0891438	−	0.0324457i
$375$	−0.579709	−	0.486433i	−0.0299360	−	0.0251193i
$376$	−2.34588	+	1.96843i	−0.120980	+	0.101514i
$377$	−12.3363	−	10.3514i	−0.635352	−	0.533124i
$378$		0			0
$379$	18.7476			0.962999			0.481500	−	0.876446i	$-0.340092\pi$
$379$	18.7476			0.962999			0.481500	+	0.876446i	$0.340092\pi$
$380$	−0.0360185	−	0.194936i	−0.00184771	−	0.00999999i
$381$	6.63737	+	11.4963i	0.340043	+	0.588972i
$382$	0.460786	−	0.167712i	0.0235758	−	0.00858091i
$383$	−12.4114	+	4.51739i	−0.634194	+	0.230828i	−0.639056	−	0.769161i	$-0.720675\pi$
$383$	−12.4114	+	4.51739i	−0.634194	+	0.230828i	0.00486193	+	0.999988i	$0.498452\pi$
$384$	13.7312	+	4.99774i	0.700716	+	0.255040i
$385$		0			0
$386$	3.84288	−	3.22456i	0.195598	−	0.164126i
$387$	−3.47546			−0.176668
$388$	3.45528			0.175415
$389$	7.33943	−	6.15852i	0.372124	−	0.312249i	−0.437477	−	0.899230i	$-0.644128\pi$
$389$	7.33943	−	6.15852i	0.372124	−	0.312249i	0.809601	+	0.586980i	$0.199683\pi$
$390$	−0.343484	−	0.125018i	−0.0173930	−	0.00633053i
$391$	0.472295	−	0.818038i	0.0238850	−	0.0413700i
$392$		0			0
$393$	2.46235	−	2.06616i	0.124209	−	0.104224i
$394$	7.88689	−	44.7288i	0.397336	−	2.25340i
$395$	−0.128071	−	0.726325i	−0.00644393	−	0.0365454i
$396$	−0.370358	+	2.10041i	−0.0186112	+	0.105549i
$397$	−12.7643	−	10.7106i	−0.640624	−	0.537548i	0.263586	−	0.964636i	$-0.415095\pi$
$397$	−12.7643	−	10.7106i	−0.640624	−	0.537548i	−0.904210	+	0.427088i	$0.859539\pi$
$398$	2.40659			0.120631
$399$		0			0
$400$	24.3502			1.21751
$401$	15.3930	+	12.9162i	0.768688	+	0.645006i	0.940373	−	0.340146i	$-0.110477\pi$
$401$	15.3930	+	12.9162i	0.768688	+	0.645006i	−0.171685	+	0.985152i	$0.554921\pi$
$402$	2.80746	−	15.9219i	0.140023	−	0.794111i
$403$	3.36551	+	19.0868i	0.167648	+	0.950780i
$404$	−0.559605	+	3.17368i	−0.0278414	+	0.157896i
$405$	0.00420344	−	0.00352710i	0.000208871	−	0.000175263i
$406$		0			0
$407$	−0.618998	+	1.07214i	−0.0306826	+	0.0531438i
$408$	−1.40178	−	0.510207i	−0.0693986	−	0.0252590i
$409$	8.03215	−	6.73977i	0.397164	−	0.333260i	−0.422232	−	0.906488i	$-0.638753\pi$
$409$	8.03215	−	6.73977i	0.397164	−	0.333260i	0.819396	+	0.573227i	$0.194309\pi$
$410$	0.770173			0.0380361
$411$	−22.9633			−1.13270
$412$	1.48586	−	1.24679i	0.0732031	−	0.0614247i
$413$		0			0
$414$	−4.22541	−	1.53792i	−0.207668	−	0.0755849i
$415$	0.446832	−	0.162634i	0.0219341	−	0.00798337i
$416$	9.83258	−	3.57877i	0.482082	−	0.175464i
$417$	3.77968	+	6.54659i	0.185092	+	0.320588i
$418$	−6.26044	+	11.0511i	−0.306208	+	0.540528i
$419$	13.0830			0.639145			0.319573	−	0.947562i	$-0.396461\pi$
$419$	13.0830			0.639145			0.319573	+	0.947562i	$0.396461\pi$
$420$		0			0
$421$	18.1411	+	15.2222i	0.884144	+	0.741885i	0.967027	−	0.254674i	$-0.0819682\pi$
$421$	18.1411	+	15.2222i	0.884144	+	0.741885i	−0.0828825	+	0.996559i	$0.526413\pi$
$422$	−34.3743	+	28.8434i	−1.67331	+	1.40408i
$423$	−1.96269	−	1.64689i	−0.0954290	−	0.0800745i
$424$	15.2703	+	5.55794i	0.741591	+	0.269917i
$425$	−3.14494			−0.152552
$426$	−10.3163	+	17.8684i	−0.499828	+	0.865727i
$427$		0			0
$428$	−1.40487	−	7.96741i	−0.0679069	−	0.385119i
$429$	2.85973	+	4.95319i	0.138069	+	0.239142i
$430$	0.107970	−	0.187010i	0.00520678	−	0.00901841i
$431$	6.93525	+	2.52422i	0.334059	+	0.121588i	0.503603	−	0.863935i	$-0.332007\pi$
$431$	6.93525	+	2.52422i	0.334059	+	0.121588i	−0.169544	+	0.985523i	$0.554230\pi$
$432$	−4.41029	+	25.0120i	−0.212190	+	1.20339i
$433$	−32.5494	−	11.8470i	−1.56423	−	0.569331i	−0.592526	−	0.805551i	$-0.701869\pi$
$433$	−32.5494	−	11.8470i	−1.56423	−	0.569331i	−0.971700	+	0.236220i	$0.924091\pi$
$434$		0			0
$435$	−0.0713409	+	0.404594i	−0.00342053	+	0.0193988i
$436$	4.53609	−	7.85674i	0.217239	−	0.376270i
$437$	−5.04378	−	4.16243i	−0.241277	−	0.199116i
$438$	9.82328	+	17.0144i	0.469374	+	0.812980i
$439$	−24.7303	−	20.7512i	−1.18031	−	0.990400i	−0.999977	−	0.00679434i	$-0.997837\pi$
$439$	−24.7303	−	20.7512i	−1.18031	−	0.990400i	−0.180335	−	0.983605i	$-0.557718\pi$
$440$	0.212649	+	0.178433i	0.0101376	+	0.00850647i
$441$		0			0
$442$	−2.85633	+	1.03962i	−0.135862	+	0.0494496i
$443$	−2.87278	−	16.2923i	−0.136490	−	0.774071i	−0.973811	−	0.227360i	$-0.926991\pi$
$443$	−2.87278	−	16.2923i	−0.136490	−	0.774071i	0.837321	−	0.546711i	$-0.184121\pi$
$444$	0.240274	−	0.416167i	0.0114029	−	0.0197504i
$445$	−0.290484			−0.0137702
$446$	−13.6360	−	4.96309i	−0.645683	−	0.235009i
$447$	−1.50626	−	8.54240i	−0.0712434	−	0.404042i
$448$		0			0
$449$	−18.1680	−	31.4678i	−0.857399	−	1.48506i	−0.874401	−	0.485204i	$-0.838746\pi$
$449$	−18.1680	−	31.4678i	−0.857399	−	1.48506i	0.0170021	−	0.999855i	$-0.494588\pi$
$450$	2.59970	+	14.7436i	0.122551	+	0.695021i
$451$	−9.23158	−	7.74622i	−0.434698	−	0.364755i
$452$	−0.0471898	−	0.267627i	−0.00221962	−	0.0125881i
$453$	20.4434	−	7.44079i	0.960514	−	0.349599i
$454$	7.15940	−	40.6030i	0.336007	−	1.90559i
$455$		0			0
$456$	−5.09048	+	8.98588i	−0.238383	+	0.420802i
$457$	−13.3009	+	23.0378i	−0.622188	+	1.07766i	0.366889	+	0.930265i	$0.380423\pi$
$457$	−13.3009	+	23.0378i	−0.622188	+	1.07766i	−0.989077	+	0.147397i	$0.952911\pi$
$458$	37.9756	−	13.8220i	1.77448	−	0.645858i
$459$	0.569610	−	3.23042i	0.0265871	−	0.150783i
$460$	0.0522671	−	0.0438573i	0.00243697	−	0.00204486i
$461$	−0.0577102	+	0.0210048i	−0.00268783	+	0.000978292i	−0.343364	−	0.939203i	$-0.611566\pi$
$461$	−0.0577102	+	0.0210048i	−0.00268783	+	0.000978292i	0.340676	+	0.940181i	$0.389344\pi$
$462$		0			0
$463$	6.51380	+	11.2822i	0.302722	+	0.524329i	0.976751	−	0.214375i	$-0.0687714\pi$
$463$	6.51380	+	11.2822i	0.302722	+	0.524329i	−0.674030	+	0.738704i	$0.735438\pi$
$464$	−13.2260	−	22.9082i	−0.614003	−	1.06349i
$465$	0.378767	−	0.317823i	0.0175649	−	0.0147387i
$466$	19.7125	−	16.5408i	0.913166	−	0.766237i
$467$	7.77568	+	13.4679i	0.359815	+	0.623219i	0.987930	−	0.154902i	$-0.0495063\pi$
$467$	7.77568	+	13.4679i	0.359815	+	0.623219i	−0.628114	+	0.778121i	$0.716173\pi$
$468$	1.76687	+	3.06030i	0.0816734	+	0.141462i
$469$		0			0
$470$	0.149590	−	0.0544464i	0.00690008	−	0.00251142i
$471$	18.9319	−	15.8857i	0.872336	−	0.731977i
$472$	5.30280	−	30.0737i	0.244081	−	1.38425i
$473$	−3.17507	+	1.15563i	−0.145990	+	0.0531360i
$474$	9.17129	−	15.8851i	0.421251	−	0.729629i
$475$	−3.60535	+	21.4723i	−0.165425	+	0.985218i
$476$		0			0
$477$	−2.36089	+	13.3893i	−0.108098	+	0.613053i
$478$	−6.12629	+	2.22979i	−0.280210	+	0.101988i
$479$	5.21980	+	29.6030i	0.238499	+	1.35259i	0.835119	+	0.550070i	$0.185399\pi$
$479$	5.21980	+	29.6030i	0.238499	+	1.35259i	−0.596620	+	0.802524i	$0.703490\pi$
$480$	−0.204490	−	0.171588i	−0.00933366	−	0.00783187i
$481$	0.356181	+	2.02000i	0.0162405	+	0.0921043i
$482$	−18.4207	−	31.9056i	−0.839039	−	1.45326i
$483$		0			0
$484$	−0.874363	−	4.95876i	−0.0397438	−	0.225398i
$485$	0.353566	+	0.128687i	0.0160546	+	0.00584340i
$486$	−25.2891			−1.14714
$487$	−6.20455	+	10.7466i	−0.281155	+	0.486975i	−0.971669	−	0.236344i	$-0.924051\pi$
$487$	−6.20455	+	10.7466i	−0.281155	+	0.486975i	0.690515	+	0.723319i	$0.257384\pi$
$488$	−0.0642765	−	0.364530i	−0.00290966	−	0.0165015i
$489$	−18.2236	+	6.63283i	−0.824097	+	0.299947i
$490$		0			0
$491$	31.3999	+	26.3477i	1.41706	+	1.18905i	0.952894	+	0.303304i	$0.0980898\pi$
$491$	31.3999	+	26.3477i	1.41706	+	1.18905i	0.464165	+	0.885749i	$0.346355\pi$
$492$	3.58339	+	3.00682i	0.161552	+	0.135558i
$493$	1.70821	+	2.95870i	0.0769338	+	0.133253i
$494$	3.82359	+	20.6936i	0.172031	+	0.931050i
$495$	−0.116124	+	0.201133i	−0.00521939	+	0.00904025i
$496$	−5.52815	+	31.3517i	−0.248221	+	1.40773i
$497$		0			0
$498$	11.1129	+	4.04475i	0.497979	+	0.181250i
$499$	1.28902	−	7.31037i	0.0577042	−	0.327257i	−0.942267	−	0.334863i	$-0.891310\pi$
$499$	1.28902	−	7.31037i	0.0577042	−	0.327257i	0.999971	+	0.00760595i	$0.00242107\pi$
$500$	−0.427145	−	0.155468i	−0.0191025	−	0.00695274i
$501$	1.97740	−	3.42496i	0.0883439	−	0.153016i
$502$	22.2074	+	38.4643i	0.991164	+	1.71675i
$503$	−3.81927	−	21.6602i	−0.170293	−	0.965779i	−0.943438	−	0.331549i	$-0.892429\pi$
$503$	−3.81927	−	21.6602i	−0.170293	−	0.965779i	0.773145	−	0.634229i	$-0.218682\pi$
$504$		0			0
$505$	−0.175462	+	0.303908i	−0.00780794	+	0.0135237i
$506$	−4.37158			−0.194340
$507$	−4.23833	−	1.54263i	−0.188231	−	0.0685104i
$508$	6.10821	+	5.12539i	0.271008	+	0.227403i
$509$	2.62670	−	2.20406i	0.116426	−	0.0976933i	−0.582716	−	0.812676i	$-0.698010\pi$
$509$	2.62670	−	2.20406i	0.116426	−	0.0976933i	0.699142	+	0.714983i	$0.253565\pi$
$510$	0.0594037	+	0.0498456i	0.00263044	+	0.00220720i
$511$		0			0
$512$	−4.28328			−0.189296
$513$	−21.4029	−	7.59240i	−0.944962	−	0.335213i
$514$	10.2144	+	17.6919i	0.450539	+	0.780356i
$515$	0.198477	−	0.0722398i	0.00874596	−	0.00318327i
$516$	1.23246	−	0.448577i	0.0542558	−	0.0197475i
$517$	−2.34065	−	0.851929i	−0.102942	−	0.0374678i
$518$		0			0
$519$	−8.90378	+	7.47116i	−0.390833	+	0.327948i
$520$	0.459928			0.0201692
$521$	12.7564			0.558868			0.279434	−	0.960165i	$-0.409853\pi$
$521$	12.7564			0.558868			0.279434	+	0.960165i	$0.409853\pi$
$522$	12.4585	−	10.4539i	0.545292	−	0.457555i
$523$	−17.6940	−	6.44008i	−0.773703	−	0.281605i	−0.0751586	−	0.997172i	$-0.523946\pi$
$523$	−17.6940	−	6.44008i	−0.773703	−	0.281605i	−0.698544	+	0.715567i	$0.746169\pi$
$524$	0.965384	−	1.67209i	0.0421730	−	0.0730457i
$525$		0			0
$526$	20.5977	−	17.2835i	0.898103	−	0.753597i
$527$	0.713987	−	4.04922i	0.0311018	−	0.176387i
$528$	1.63137	+	9.25198i	0.0709964	+	0.402641i
$529$	−3.60306	+	20.4340i	−0.156655	+	0.888433i
$530$	−0.647114	−	0.542993i	−0.0281088	−	0.0235861i
$531$	25.5493			1.10874
$532$		0			0
$533$	−19.9666			−0.864849
$534$	−5.53422	−	4.64377i	−0.239489	−	0.200955i
$535$	0.152981	−	0.867597i	0.00661394	−	0.0375095i
$536$	3.53250	+	20.0338i	0.152581	+	0.865329i
$537$	0.387016	−	2.19487i	0.0167010	−	0.0947158i
$538$	36.5197	−	30.6437i	1.57448	−	1.32114i
$539$		0			0
$540$	0.118470	−	0.205196i	0.00509814	−	0.00883024i
$541$	28.9515	+	10.5375i	1.24472	+	0.453042i	0.878615	−	0.477531i	$-0.158468\pi$
$541$	28.9515	+	10.5375i	1.24472	+	0.453042i	0.366107	+	0.930573i	$0.380690\pi$
$542$	−34.7219	+	29.1351i	−1.49143	+	1.25146i
$543$	1.21493			0.0521377
$544$	−2.21984			−0.0951747
$545$	0.756775	−	0.635009i	0.0324167	−	0.0272008i
$546$		0			0
$547$	−9.70626	−	3.53279i	−0.415010	−	0.151051i	0.126072	−	0.992021i	$-0.459763\pi$
$547$	−9.70626	−	3.53279i	−0.415010	−	0.151051i	−0.541082	+	0.840970i	$0.681985\pi$
$548$	−12.9614	+	4.71758i	−0.553685	+	0.201525i
$549$	0.291013	−	0.105920i	0.0124201	−	0.00452055i
$550$	7.27742	+	12.6049i	0.310310	+	0.537473i
$551$	22.1590	−	8.27106i	0.944007	−	0.352359i
$552$	−3.55461			−0.151294
$553$		0			0
$554$	7.98230	+	6.69794i	0.339135	+	0.284568i
$555$	0.0400859	−	0.0336361i	0.00170155	−	0.00142777i
$556$	3.47834	+	2.91867i	0.147514	+	0.123779i
$557$	19.5537	+	7.11696i	0.828516	+	0.301555i	0.721250	−	0.692675i	$-0.243568\pi$
$557$	19.5537	+	7.11696i	0.828516	+	0.301555i	0.107267	+	0.994230i	$0.465790\pi$
$558$	−19.5731			−0.828597
$559$	−2.79911	+	4.84819i	−0.118390	+	0.205057i
$560$		0			0
$561$	−0.210700	−	1.19494i	−0.00889575	−	0.0504503i
$562$	−0.395302	−	0.684683i	−0.0166748	−	0.0288816i
$563$	−8.57899	+	14.8592i	−0.361561	+	0.626242i	−0.988218	−	0.153053i	$-0.951089\pi$
$563$	−8.57899	+	14.8592i	−0.361561	+	0.626242i	0.626657	+	0.779295i	$0.284423\pi$
$564$	0.908563	+	0.330690i	0.0382574	+	0.0139246i
$565$	0.00513865	−	0.0291428i	0.000216185	−	0.00122604i
$566$	−40.2709	−	14.6574i	−1.69271	−	0.616097i
$567$		0			0
$568$	4.50812	−	25.5668i	0.189156	−	1.07276i
$569$	11.8999	−	20.6112i	0.498869	−	0.864066i	−0.501130	−	0.865372i	$-0.667082\pi$
$569$	11.8999	−	20.6112i	0.498869	−	0.864066i	0.999999	+	0.00130568i	$0.000415612\pi$
$570$	0.408425	−	0.348440i	0.0171070	−	0.0145946i
$571$	5.34982	+	9.26617i	0.223883	+	0.387777i	0.955984	−	0.293419i	$-0.0947933\pi$
$571$	5.34982	+	9.26617i	0.223883	+	0.387777i	−0.732101	+	0.681196i	$0.761460\pi$
$572$	2.63173	+	2.20829i	0.110038	+	0.0923331i
$573$	0.248439	+	0.208465i	0.0103787	+	0.00870876i
$574$		0			0
$575$	−7.04199	+	2.56308i	−0.293671	+	0.106888i
$576$	−1.28434	−	7.28387i	−0.0535143	−	0.303494i
$577$	−10.8671	+	18.8224i	−0.452404	+	0.783586i	−0.998535	−	0.0541136i	$-0.982767\pi$
$577$	−10.8671	+	18.8224i	−0.452404	+	0.783586i	0.546131	+	0.837700i	$0.316100\pi$
$578$	−27.0096			−1.12345
$579$	3.11775	+	1.13477i	0.129569	+	0.0471594i
$580$	0.0428521	+	0.243026i	0.00177934	+	0.0100911i
$581$		0			0
$582$	4.67881	+	8.10394i	0.193943	+	0.335919i
$583$	2.29525	+	13.0170i	0.0950597	+	0.539111i
$584$	−18.9369	−	15.8900i	−0.783616	−	0.657532i
$585$	0.0668197	+	0.378953i	0.00276265	+	0.0156678i
$586$	−48.1190	+	17.5139i	−1.98778	+	0.723492i
$587$	−4.64746	+	26.3570i	−0.191821	+	1.08787i	0.725052	+	0.688694i	$0.241816\pi$
$587$	−4.64746	+	26.3570i	−0.191821	+	1.08787i	−0.916873	+	0.399178i	$0.869296\pi$
$588$		0			0
$589$	−26.8279	−	9.51682i	−1.10542	−	0.392134i
$590$	−0.793724	+	1.37477i	−0.0326771	+	0.0565984i
$591$	28.2276	−	10.2740i	1.16113	−	0.422616i
$592$	−0.585059	+	3.31803i	−0.0240458	+	0.136370i
$593$	25.8963	−	21.7296i	1.06344	−	0.892328i	0.0689937	−	0.997617i	$-0.478021\pi$
$593$	25.8963	−	21.7296i	1.06344	−	0.892328i	0.994442	+	0.105289i	$0.0335767\pi$
$594$	−14.2655	+	5.19223i	−0.585322	+	0.213040i
$595$		0			0
$596$	−2.60514	−	4.51224i	−0.106711	−	0.184829i
$597$	0.795838	+	1.37843i	0.0325715	+	0.0564155i
$598$	−5.54848	+	4.65572i	−0.226894	+	0.190387i
$599$	2.12606	−	1.78397i	0.0868684	−	0.0728912i	−0.598319	−	0.801258i	$-0.704165\pi$
$599$	2.12606	−	1.78397i	0.0868684	−	0.0728912i	0.685188	+	0.728366i	$0.259720\pi$
$600$	5.91741	+	10.2493i	0.241577	+	0.418424i
$601$	18.6256	+	32.2605i	0.759755	+	1.31594i	0.942975	+	0.332863i	$0.108015\pi$
$601$	18.6256	+	32.2605i	0.759755	+	1.31594i	−0.183220	+	0.983072i	$0.558652\pi$
$602$		0			0
$603$	−15.9934	+	5.82114i	−0.651304	+	0.237055i
$604$	10.0105	−	8.39978i	0.407320	−	0.341782i
$605$	0.0952123	−	0.539976i	0.00387093	−	0.0219531i
$606$	−8.20123	+	2.98501i	−0.333152	+	0.121258i
$607$	−19.1436	+	33.1578i	−0.777016	+	1.34583i	0.156638	+	0.987656i	$0.449934\pi$
$607$	−19.1436	+	33.1578i	−0.777016	+	1.34583i	−0.933654	+	0.358176i	$0.883399\pi$
$608$	−2.54481	+	15.1561i	−0.103206	+	0.614661i
$609$		0			0
$610$	−0.00334131	+	0.0189495i	−0.000135286	+	0.000767244i
$611$	−3.87810	+	1.41151i	−0.156891	+	0.0571037i
$612$	−0.130180	−	0.738285i	−0.00526219	−	0.0298434i
$613$	14.6387	+	12.2833i	0.591252	+	0.496119i	0.888620	−	0.458644i	$-0.151665\pi$
$613$	14.6387	+	12.2833i	0.591252	+	0.496119i	−0.297368	+	0.954763i	$0.596109\pi$
$614$	4.86171	+	27.5721i	0.196203	+	1.11272i
$615$	0.254689	+	0.441135i	0.0102701	+	0.0177883i
$616$		0			0
$617$	−0.242442	−	1.37496i	−0.00976036	−	0.0553538i	0.979539	−	0.201256i	$-0.0645025\pi$
$617$	−0.242442	−	1.37496i	−0.00976036	−	0.0553538i	−0.989299	+	0.145903i	$0.953391\pi$
$618$	4.93619	+	1.79663i	0.198563	+	0.0722710i
$619$	36.2980			1.45894			0.729469	−	0.684013i	$-0.239767\pi$
$619$	36.2980			1.45894			0.729469	+	0.684013i	$0.239767\pi$
$620$	0.148498	−	0.257207i	0.00596384	−	0.0103297i
$621$	−1.35730	−	7.69761i	−0.0544664	−	0.308894i
$622$	−43.9441	+	15.9943i	−1.76200	+	0.641314i
$623$		0			0
$624$	11.9239	+	10.0053i	0.477338	+	0.400535i
$625$	19.0942	+	16.0220i	0.763769	+	0.640878i
$626$	−5.74909	−	9.95772i	−0.229780	−	0.397991i
$627$	−8.40007	+	0.0686949i	−0.335467	+	0.00274341i
$628$	7.42239	−	12.8560i	0.296186	−	0.513008i
$629$	0.0755631	−	0.428540i	0.00301290	−	0.0170870i
$630$		0			0
$631$	15.0984	+	5.49536i	0.601057	+	0.218767i	0.624586	−	0.780956i	$-0.285268\pi$
$631$	15.0984	+	5.49536i	0.601057	+	0.218767i	−0.0235288	+	0.999723i	$0.507490\pi$
$632$	−4.00775	+	22.7291i	−0.159420	+	0.904114i
$633$	−27.8880	−	10.1504i	−1.10845	−	0.403443i
$634$	5.14148	−	8.90531i	0.204194	−	0.353675i
$635$	0.434141	+	0.751954i	0.0172284	+	0.0298404i
$636$	−0.890940	−	5.05277i	−0.0353281	−	0.200356i
$637$		0			0
$638$	7.90561	−	13.6929i	0.312986	−	0.542108i
$639$	21.7205			0.859248
$640$	0.898135	+	0.326894i	0.0355019	+	0.0129216i
$641$	−29.8014	−	25.0064i	−1.17709	−	0.987692i	−0.999994	−	0.00349805i	$-0.998887\pi$
$641$	−29.8014	−	25.0064i	−1.17709	−	0.987692i	−0.177092	−	0.984194i	$-0.556669\pi$
$642$	16.7842	−	14.0837i	0.662421	−	0.555838i
$643$	12.2408	+	10.2712i	0.482729	+	0.405058i	0.851412	−	0.524498i	$-0.175747\pi$
$643$	12.2408	+	10.2712i	0.482729	+	0.405058i	−0.368683	+	0.929555i	$0.620191\pi$
$644$		0			0
$645$	0.142819			0.00562350
$646$	0.739259	−	4.40279i	0.0290858	−	0.173226i
$647$	0.912483	+	1.58047i	0.0358734	+	0.0621346i	0.883405	−	0.468611i	$-0.155245\pi$
$647$	0.912483	+	1.58047i	0.0358734	+	0.0621346i	−0.847531	+	0.530745i	$0.821912\pi$
$648$	−0.161357	+	0.0587291i	−0.00633870	+	0.00230710i
$649$	23.3410	−	8.49543i	0.916214	−	0.333475i
$650$	22.6608	+	8.24785i	0.888829	+	0.323507i
$651$		0			0
$652$	−8.92349	+	7.48769i	−0.349471	+	0.293241i
$653$	21.7882			0.852639			0.426320	−	0.904573i	$-0.359810\pi$
$653$	21.7882			0.852639			0.426320	+	0.904573i	$0.359810\pi$
$654$	24.5694			0.960738
$655$	0.161059	−	0.135144i	0.00629309	−	0.00528053i
$656$	−30.8190	−	11.2172i	−1.20328	−	0.437957i
$657$	10.3412	−	17.9115i	0.403448	−	0.698792i
$658$		0			0
$659$	13.3023	−	11.1620i	0.518186	−	0.434810i	−0.345813	−	0.938303i	$-0.612397\pi$
$659$	13.3023	−	11.1620i	0.518186	−	0.434810i	0.863999	+	0.503494i	$0.167952\pi$
$660$	0.0152193	−	0.0863131i	0.000592411	−	0.00335973i
$661$	5.18450	+	29.4028i	0.201654	+	1.14364i	0.902619	+	0.430440i	$0.141642\pi$
$661$	5.18450	+	29.4028i	0.201654	+	1.14364i	−0.700966	+	0.713195i	$0.747247\pi$
$662$	4.41877	−	25.0601i	0.171740	−	0.973987i
$663$	−1.54003	−	1.29224i	−0.0598098	−	0.0501864i
$664$	−14.8802			−0.577465
$665$		0			0
$666$	−2.07148			−0.0802681
$667$	6.23622	+	5.23281i	0.241467	+	0.202615i
$668$	0.412505	−	2.33943i	0.0159603	−	0.0905153i
$669$	−1.66657	−	9.45159i	−0.0644334	−	0.365420i
$670$	0.183632	−	1.04143i	0.00709430	−	0.0402338i
$671$	0.230640	−	0.193530i	0.00890376	−	0.00747114i
$672$		0			0
$673$	5.12496	−	8.87669i	0.197553	−	0.342171i	−0.750182	−	0.661232i	$-0.770034\pi$
$673$	5.12496	−	8.87669i	0.197553	−	0.342171i	0.947734	+	0.319061i	$0.103367\pi$
$674$	−11.4569	−	4.16997i	−0.441303	−	0.160621i
$675$	−19.9355	+	16.7279i	−0.767319	+	0.643857i
$676$	−2.70921			−0.104200
$677$	27.8896			1.07189			0.535943	−	0.844254i	$-0.319956\pi$
$677$	27.8896			1.07189			0.535943	+	0.844254i	$0.319956\pi$
$678$	0.563786	−	0.473073i	0.0216521	−	0.0181682i
$679$		0			0
$680$	−0.0916885	−	0.0333719i	−0.00351609	−	0.00127975i
$681$	25.6239	−	9.32633i	0.981910	−	0.357386i
$682$	−17.8814	+	6.50829i	−0.684713	+	0.249215i
$683$	−6.44497	−	11.1630i	−0.246610	−	0.427141i	0.715973	−	0.698128i	$-0.245983\pi$
$683$	−6.44497	−	11.1630i	−0.246610	−	0.427141i	−0.962583	+	0.270987i	$0.912650\pi$
$684$	−5.18993	+	0.0424427i	−0.198442	+	0.00162284i
$685$	−1.50199			−0.0573883
$686$		0			0
$687$	20.4751	+	17.1806i	0.781172	+	0.655481i
$688$	−7.04420	+	5.91078i	−0.268558	+	0.225347i
$689$	16.7763	+	14.0770i	0.639126	+	0.536291i
$690$	0.173637	+	0.0631987i	0.00661025	+	0.00240593i
$691$	7.93990			0.302048			0.151024	−	0.988530i	$-0.451743\pi$
$691$	7.93990			0.302048			0.151024	+	0.988530i	$0.451743\pi$
$692$	−3.49079	+	6.04623i	−0.132700	+	0.229843i
$693$		0			0
$694$	2.39988	+	13.6104i	0.0910980	+	0.516643i
$695$	0.247223	+	0.428203i	0.00937770	+	0.0162427i
$696$	6.42820	−	11.1340i	0.243660	−	0.422032i
$697$	3.98042	+	1.44875i	0.150769	+	0.0548755i
$698$	−0.175574	+	0.995728i	−0.00664557	+	0.0376889i
$699$	15.9929	+	5.82094i	0.604907	+	0.220168i
$700$		0			0
$701$	4.73725	−	26.8663i	0.178924	−	1.01473i	−0.754593	−	0.656193i	$-0.772166\pi$
$701$	4.73725	−	26.8663i	0.178924	−	1.01473i	0.933517	−	0.358533i	$-0.116723\pi$
$702$	−12.5763	+	21.7828i	−0.474663	+	0.822140i
$703$	−2.83926	−	1.00719i	−0.107085	−	0.0379869i
$704$	−3.59530	−	6.22724i	−0.135503	−	0.234698i
$705$	0.0806537	+	0.0676765i	0.00303759	+	0.00254884i
$706$	32.8053	+	27.5269i	1.23464	+	1.03599i
$707$		0			0
$708$	−9.06019	+	3.29764i	−0.340503	+	0.123933i
$709$	−4.02231	−	22.8117i	−0.151061	−	0.856710i	−0.962299	−	0.271994i	$-0.912317\pi$
$709$	−4.02231	−	22.8117i	−0.151061	−	0.856710i	0.811238	−	0.584716i	$-0.198794\pi$
$710$	−0.674776	+	1.16875i	−0.0253239	+	0.0438623i
$711$	−19.3096			−0.724168
$712$	8.54197	+	3.10902i	0.320124	+	0.116516i
$713$	−1.70133	−	9.64870i	−0.0637151	−	0.361347i
$714$		0			0
$715$	0.187051	+	0.323981i	0.00699529	+	0.0121162i
$716$	−0.232467	−	1.31839i	−0.00868771	−	0.0492705i
$717$	−3.30307	−	2.77161i	−0.123356	−	0.103508i
$718$	−2.46713	−	13.9918i	−0.0920724	−	0.522168i
$719$	44.9655	−	16.3661i	1.67693	−	0.610353i	0.684046	−	0.729438i	$-0.260219\pi$
$719$	44.9655	−	16.3661i	1.67693	−	0.610353i	0.992884	+	0.119086i	$0.0379963\pi$
$720$	−0.109757	+	0.622464i	−0.00409041	+	0.0231979i
$721$		0			0
$722$	−29.2129	−	10.0947i	−1.08719	−	0.375686i
$723$	12.1831	−	21.1018i	0.453095	−	0.784784i
$724$	0.685759	−	0.249596i	0.0254860	−	0.00927615i
$725$	4.70660	−	26.6925i	0.174799	−	0.991333i
$726$	10.4462	−	8.76539i	0.387694	−	0.325314i
$727$	−24.2763	+	8.83586i	−0.900359	+	0.327704i	−0.750397	−	0.660988i	$-0.770138\pi$
$727$	−24.2763	+	8.83586i	−0.900359	+	0.327704i	−0.149963	+	0.988692i	$0.547915\pi$
$728$		0			0
$729$	−8.47985	−	14.6875i	−0.314069	−	0.543983i
$730$	0.642526	+	1.11289i	0.0237810	+	0.0411898i
$731$	0.909792	−	0.763406i	0.0336499	−	0.0282356i
$732$	−0.0895267	+	0.0751218i	−0.00330900	+	0.00277658i
$733$	12.6849	+	21.9708i	0.468526	+	0.811511i	0.999353	−	0.0359690i	$-0.0114518\pi$
$733$	12.6849	+	21.9708i	0.468526	+	0.811511i	−0.530827	+	0.847480i	$0.678118\pi$
$734$	6.88684	+	11.9284i	0.254198	+	0.440284i
$735$		0			0
$736$	−4.97054	+	1.80913i	−0.183217	+	0.0666854i
$737$	−12.6755	+	10.6360i	−0.466908	+	0.391782i
$738$	3.50149	−	19.8580i	0.128892	−	0.730981i
$739$	31.9783	−	11.6392i	1.17634	−	0.428154i	0.321434	−	0.946932i	$-0.395835\pi$
$739$	31.9783	−	11.6392i	1.17634	−	0.428154i	0.854909	+	0.518779i	$0.173613\pi$
$740$	0.0157160	−	0.0272209i	0.000577731	−	0.00100066i
$741$	−10.5883	+	9.03326i	−0.388973	+	0.331845i
$742$		0			0
$743$	−0.791920	+	4.49120i	−0.0290527	+	0.164766i	−0.995882	−	0.0906564i	$-0.971103\pi$
$743$	−0.791920	+	4.49120i	−0.0290527	+	0.164766i	0.966830	+	0.255423i	$0.0822146\pi$
$744$	−14.5397	+	5.29201i	−0.533050	+	0.194014i
$745$	−0.0985219	−	0.558746i	−0.00360956	−	0.0204709i
$746$	−29.5958	−	24.8338i	−1.08358	−	0.909230i
$747$	−2.16184	−	12.2604i	−0.0790977	−	0.448585i
$748$	−0.364416	−	0.631187i	−0.0133244	−	0.0230785i
$749$		0			0
$750$	−0.213768	−	1.21234i	−0.00780569	−	0.0442682i
$751$	13.7211	+	4.99406i	0.500689	+	0.182236i	0.580004	−	0.814614i	$-0.303051\pi$
$751$	13.7211	+	4.99406i	0.500689	+	0.182236i	−0.0793150	+	0.996850i	$0.525273\pi$
$752$	−6.77894			−0.247202
$753$	−14.6876	+	25.4396i	−0.535245	+	0.927072i
$754$	−4.54901	−	25.7987i	−0.165665	−	0.939535i
$755$	1.33717	−	0.486691i	0.0486647	−	0.0177125i
$756$		0			0
$757$	−19.1043	−	16.0304i	−0.694358	−	0.582636i	0.225804	−	0.974173i	$-0.427499\pi$
$757$	−19.1043	−	16.0304i	−0.694358	−	0.582636i	−0.920162	+	0.391537i	$0.871943\pi$
$758$	23.3623	+	19.6033i	0.848556	+	0.712023i
$759$	−1.44564	−	2.50393i	−0.0524735	−	0.0908867i
$760$	−0.332961	+	0.587753i	−0.0120778	+	0.0213200i
$761$	−22.6403	+	39.2142i	−0.820711	+	1.42151i	0.0844426	+	0.996428i	$0.473089\pi$
$761$	−22.6403	+	39.2142i	−0.820711	+	1.42151i	−0.905154	+	0.425085i	$0.860244\pi$
$762$	−3.74983	+	21.2664i	−0.135842	+	0.770399i
$763$		0			0
$764$	0.183057	+	0.0666271i	0.00662275	+	0.00241048i
$765$	0.0141757	−	0.0803942i	0.000512522	−	0.00290666i
$766$	−20.1900	−	7.34857i	−0.729495	−	0.265515i
$767$	20.5772	−	35.6407i	0.742998	−	1.28691i
$768$	7.56624	+	13.1051i	0.273023	+	0.472890i
$769$	−8.35448	−	47.3806i	−0.301270	−	1.70859i	−0.640561	−	0.767907i	$-0.721298\pi$
$769$	−8.35448	−	47.3806i	−0.301270	−	1.70859i	0.339291	−	0.940682i	$-0.389813\pi$
$770$		0			0
$771$	−6.75564	+	11.7011i	−0.243298	+	0.421405i
$772$	1.99292			0.0717267
$773$	−23.0632	−	8.39434i	−0.829527	−	0.301923i	−0.107862	−	0.994166i	$-0.534401\pi$
$773$	−23.0632	−	8.39434i	−0.829527	−	0.301923i	−0.721665	+	0.692243i	$0.756623\pi$
$774$	−4.33094	−	3.63409i	−0.155673	−	0.130625i
$775$	−24.9885	+	20.9679i	−0.897615	+	0.753188i
$776$	−9.01964	−	7.56838i	−0.323786	−	0.271689i
$777$		0			0
$778$	15.5856			0.558772
$779$	14.4546	−	25.5158i	0.517890	−	0.914197i
$780$	−0.0726067	−	0.125759i	−0.00259974	−	0.00450288i
$781$	19.8431	−	7.22230i	0.710042	−	0.258434i
$782$	1.44392	−	0.525546i	0.0516346	−	0.0187935i
$783$	26.5655	+	9.66904i	0.949372	+	0.345543i
$784$		0			0
$785$	1.23831	−	1.03906i	0.0441971	−	0.0370858i
$786$	5.22892			0.186509
$787$	−9.19502			−0.327767			−0.163884	−	0.986480i	$-0.552402\pi$
$787$	−9.19502			−0.327767			−0.163884	+	0.986480i	$0.552402\pi$
$788$	13.8222	−	11.5982i	0.492394	−	0.413168i
$789$	16.7110	+	6.08232i	0.594929	+	0.216536i
$790$	0.599881	−	1.03902i	0.0213428	−	0.0369668i
$791$		0			0
$792$	5.56746	−	4.67166i	0.197831	−	0.166000i
$793$	0.0866229	−	0.491263i	0.00307607	−	0.0174453i
$794$	−4.70685	−	26.6939i	−0.167040	−	0.947330i
$795$	0.0970174	−	0.550213i	0.00344085	−	0.0195140i
$796$	0.732389	+	0.614548i	0.0259589	+	0.0217821i
$797$	50.7437			1.79743			0.898716	−	0.438530i	$-0.144501\pi$
$797$	50.7437			1.79743			0.898716	+	0.438530i	$0.144501\pi$
$798$		0			0
$799$	0.875532			0.0309741
$800$	13.4909	+	11.3202i	0.476976	+	0.400230i
$801$	−1.32065	+	7.48976i	−0.0466628	+	0.264638i
$802$	5.67615	+	32.1911i	0.200432	+	1.13671i
$803$	3.49160	−	19.8019i	0.123216	−	0.698793i
$804$	4.92020	−	4.12854i	0.173522	−	0.145602i
$805$		0			0
$806$	−15.7640	+	27.3041i	−0.555264	+	0.961745i
$807$	29.6286	+	10.7839i	1.04298	+	0.379613i
$808$	8.41234	−	7.05879i	0.295945	−	0.248327i
$809$	−2.23136			−0.0784504			−0.0392252	−	0.999230i	$-0.512489\pi$
$809$	−2.23136			−0.0784504			−0.0392252	+	0.999230i	$0.512489\pi$
$810$	0.00892620			0.000313635
$811$	9.48231	−	7.95660i	0.332969	−	0.279394i	−0.460939	−	0.887432i	$-0.652487\pi$
$811$	9.48231	−	7.95660i	0.332969	−	0.279394i	0.793908	+	0.608038i	$0.208043\pi$
$812$		0			0
$813$	−28.1700	−	10.2531i	−0.987967	−	0.359590i
$814$	−1.89243	+	0.688789i	−0.0663297	+	0.0241421i
$815$	−1.19198	+	0.433844i	−0.0417531	+	0.0151969i
$816$	−1.65110	−	2.85979i	−0.0578001	−	0.100113i
$817$	−4.16923	−	7.08684i	−0.145863	−	0.247937i
$818$	17.0566			0.596371
$819$		0			0
$820$	0.234384	+	0.196672i	0.00818505	+	0.00686807i
$821$	−34.5912	+	29.0255i	−1.20724	+	1.01300i	−0.207850	+	0.978161i	$0.566646\pi$
$821$	−34.5912	+	29.0255i	−1.20724	+	1.01300i	−0.999393	+	0.0348360i	$0.988909\pi$
$822$	−28.6156	−	24.0114i	−0.998085	−	0.837493i
$823$	8.49574	+	3.09220i	0.296143	+	0.107787i	0.485819	−	0.874060i	$-0.338521\pi$
$823$	8.49574	+	3.09220i	0.296143	+	0.107787i	−0.189676	+	0.981847i	$0.560744\pi$
$824$	−6.60961			−0.230257
$825$	−4.81316	+	8.33664i	−0.167573	+	0.290244i
$826$		0			0
$827$	−4.71598	−	26.7457i	−0.163991	−	0.930037i	−0.950099	−	0.311949i	$-0.899018\pi$
$827$	−4.71598	−	26.7457i	−0.163991	−	0.930037i	0.786108	−	0.618089i	$-0.212093\pi$
$828$	−0.893181	−	1.54703i	−0.0310402	−	0.0537632i
$829$	12.3864	−	21.4539i	0.430197	−	0.745123i	−0.566693	−	0.823929i	$-0.691777\pi$
$829$	12.3864	−	21.4539i	0.430197	−	0.745123i	0.996890	+	0.0788058i	$0.0251107\pi$
$830$	0.726876	+	0.264561i	0.0252302	+	0.00918305i
$831$	−1.19673	+	6.78701i	−0.0415142	+	0.235439i
$832$	−11.1952	−	4.07473i	−0.388125	−	0.141266i
$833$		0			0
$834$	−2.13536	+	12.1102i	−0.0739413	+	0.419342i
$835$	0.129339	−	0.224022i	0.00447596	−	0.00775260i
$836$	−4.72724	+	1.76449i	−0.163495	+	0.0610260i
$837$	−17.0118	−	29.4654i	−0.588015	−	1.01847i
$838$	16.3033	+	13.6801i	0.563189	+	0.472572i
$839$	23.9268	+	20.0769i	0.826043	+	0.693133i	0.954379	−	0.298598i	$-0.0965191\pi$
$839$	23.9268	+	20.0769i	0.826043	+	0.693133i	−0.128336	+	0.991731i	$0.540964\pi$
$840$		0			0
$841$	−0.417095	+	0.151810i	−0.0143826	+	0.00523483i
$842$	6.68954	+	37.9383i	0.230537	+	1.30744i
$843$	0.261446	−	0.452837i	0.00900467	−	0.0155965i
$844$	−17.8265			−0.613613
$845$	−0.277223	−	0.100901i	−0.00953676	−	0.00347110i
$846$	−0.723740	−	4.10453i	−0.0248827	−	0.141117i
$847$		0			0
$848$	17.9863	+	31.1531i	0.617650	+	1.06980i
$849$	−4.92185	−	27.9132i	−0.168918	−	0.957979i
$850$	−3.91906	−	3.28848i	−0.134423	−	0.112794i
$851$	−0.180056	−	1.02115i	−0.00617223	−	0.0350045i
$852$	−7.70242	+	2.80345i	−0.263881	+	0.0960447i
$853$	5.23367	−	29.6816i	0.179197	−	1.01628i	−0.753989	−	0.656887i	$-0.771873\pi$
$853$	5.23367	−	29.6816i	0.179197	−	1.01628i	0.933187	−	0.359392i	$-0.117016\pi$
$854$		0			0
$855$	−0.532647	−	0.188949i	−0.0182161	−	0.00646193i
$856$	−13.7844	+	23.8753i	−0.471141	+	0.816040i
$857$	−24.6035	+	8.95494i	−0.840440	+	0.305895i	−0.726136	−	0.687551i	$-0.758686\pi$
$857$	−24.6035	+	8.95494i	−0.840440	+	0.305895i	−0.114303	+	0.993446i	$0.536464\pi$
$858$	−1.61562	+	9.16266i	−0.0551565	+	0.312808i
$859$	16.5886	−	13.9195i	0.565995	−	0.474926i	−0.314319	−	0.949317i	$-0.601776\pi$
$859$	16.5886	−	13.9195i	0.565995	−	0.474926i	0.880314	+	0.474391i	$0.157332\pi$
$860$	0.0806131	−	0.0293408i	0.00274888	−	0.00100051i
$861$		0			0
$862$	6.00291	+	10.3973i	0.204460	+	0.354135i
$863$	−21.6234	−	37.4528i	−0.736068	−	1.27491i	−0.954253	−	0.299000i	$-0.903347\pi$
$863$	−21.6234	−	37.4528i	−0.736068	−	1.27491i	0.218185	−	0.975907i	$-0.429986\pi$
$864$	−14.0714	+	11.8073i	−0.478717	+	0.401692i
$865$	−0.582383	+	0.488678i	−0.0198016	+	0.0166155i
$866$	−28.1736	−	48.7982i	−0.957379	−	1.65823i
$867$	−8.93183	−	15.4704i	−0.303341	−	0.525402i
$868$		0			0
$869$	−17.6407	+	6.42067i	−0.598418	+	0.217806i
$870$	−0.511962	+	0.429587i	−0.0173571	+	0.0145644i
$871$	−4.76061	+	26.9988i	−0.161307	+	0.914819i
$872$	−29.0502	+	10.5734i	−0.983764	+	0.358061i
$873$	4.92549	−	8.53120i	0.166703	−	0.288737i
$874$	−1.93289	−	10.4610i	−0.0653810	−	0.353848i
$875$		0			0
$876$	−1.35532	+	7.68642i	−0.0457921	+	0.259700i
$877$	−17.6616	+	6.42831i	−0.596391	+	0.217069i	−0.622538	−	0.782590i	$-0.713898\pi$
$877$	−17.6616	+	6.42831i	−0.596391	+	0.217069i	0.0261470	+	0.999658i	$0.491676\pi$
$878$	−9.11929	−	51.7181i	−0.307761	−	1.74540i
$879$	−25.9441	−	21.7696i	−0.875071	−	0.734272i
$880$	0.106706	+	0.605158i	0.00359705	+	0.0203999i
$881$	−4.57192	−	7.91881i	−0.154032	−	0.266791i	0.778674	−	0.627429i	$-0.215893\pi$
$881$	−4.57192	−	7.91881i	−0.154032	−	0.266791i	−0.932706	+	0.360637i	$0.882559\pi$
$882$		0			0
$883$	3.57800	+	20.2918i	0.120409	+	0.682874i	0.983929	+	0.178560i	$0.0571437\pi$
$883$	3.57800	+	20.2918i	0.120409	+	0.682874i	−0.863520	+	0.504315i	$0.831745\pi$
$884$	−1.13474	−	0.413010i	−0.0381653	−	0.0138910i
$885$	−1.04991			−0.0352924
$886$	13.4560	−	23.3065i	0.452064	−	0.782998i
$887$	−5.03997	−	28.5831i	−0.169225	−	0.959725i	−0.944600	−	0.328224i	$-0.893550\pi$
$887$	−5.03997	−	28.5831i	−0.169225	−	0.959725i	0.775374	−	0.631502i	$-0.217561\pi$
$888$	−1.53877	+	0.560067i	−0.0516378	+	0.0187946i
$889$		0			0
$890$	−0.361985	−	0.303742i	−0.0121338	−	0.0101814i
$891$	−0.106993	−	0.0897776i	−0.00358439	−	0.00300766i
$892$	−2.88242	−	4.99250i	−0.0965105	−	0.167161i
$893$	1.00371	−	5.97776i	0.0335878	−	0.200038i
$894$	7.05528	−	12.2201i	0.235964	−	0.408701i
$895$	0.0253141	−	0.143564i	0.000846158	−	0.00479880i
$896$		0			0
$897$	−4.50151	−	1.63842i	−0.150301	−	0.0547051i
$898$	10.2641	−	58.2108i	0.342518	−	1.94252i
$899$	33.2989	+	12.1198i	1.11058	+	0.404219i
$900$	−2.97378	+	5.15074i	−0.0991260	+	0.171691i
$901$	−2.32301	−	4.02357i	−0.0773907	−	0.134045i
$902$	−3.40414	−	19.3059i	−0.113346	−	0.642815i
$903$		0			0
$904$	−0.463020	+	0.801974i	−0.0153998	+	0.0266733i
$905$	0.0794669			0.00264157
$906$	33.2559	+	12.1042i	1.10485	+	0.402134i
$907$	12.6132	+	10.5837i	0.418813	+	0.351426i	0.827711	−	0.561154i	$-0.189643\pi$
$907$	12.6132	+	10.5837i	0.418813	+	0.351426i	−0.408898	+	0.912580i	$0.634087\pi$
$908$	12.5472	−	10.5283i	0.416393	−	0.349395i
$909$	7.03819	+	5.90574i	0.233442	+	0.195881i
$910$		0			0
$911$	28.9644			0.959634			0.479817	−	0.877368i	$-0.340703\pi$
$911$	28.9644			0.959634			0.479817	+	0.877368i	$0.340703\pi$
$912$	−21.4183	+	7.99456i	−0.709229	+	0.264726i
$913$	−6.05171	−	10.4819i	−0.200283	−	0.346900i
$914$	−40.6641	+	14.8005i	−1.34505	+	0.489558i
$915$	−0.0119587	+	0.00435263i	−0.000395344	+	0.000143893i
$916$	15.0866	+	5.49106i	0.498474	+	0.181430i
$917$		0			0
$918$	4.08768	−	3.42997i	0.134914	−	0.113206i
$919$	−21.6498			−0.714162			−0.357081	−	0.934073i	$-0.616228\pi$
$919$	−21.6498			−0.714162			−0.357081	+	0.934073i	$0.616228\pi$
$920$	−0.232502			−0.00766536
$921$	−14.1849	+	11.9025i	−0.467407	+	0.392201i
$922$	−0.0938790	−	0.0341692i	−0.00309174	−	0.00112530i
$923$	17.4934	−	30.2995i	0.575804	−	0.997322i
$924$		0			0
$925$	−2.64460	+	2.21908i	−0.0869540	+	0.0729631i
$926$	−3.68002	+	20.8704i	−0.120933	+	0.685845i
$927$	−0.960263	−	5.44592i	−0.0315392	−	0.178868i
$928$	3.32212	−	18.8407i	0.109054	−	0.618476i
$929$	−13.2050	−	11.0803i	−0.433243	−	0.363534i	0.399931	−	0.916545i	$-0.369034\pi$
$929$	−13.2050	−	11.0803i	−0.433243	−	0.363534i	−0.833174	+	0.553012i	$0.813479\pi$
$930$	0.804329			0.0263750
$931$		0			0
$932$	10.2229			0.334863
$933$	−23.6931	−	19.8808i	−0.775676	−	0.650870i
$934$	−4.39293	+	24.9135i	−0.143741	+	0.815196i
$935$	−0.0137816	−	0.0781591i	−0.000450705	−	0.00255608i
$936$	2.09101	−	11.8587i	0.0683467	−	0.387613i
$937$	−10.5786	+	8.87649i	−0.345588	+	0.289982i	−0.799015	−	0.601311i	$-0.794645\pi$
$937$	−10.5786	+	8.87649i	−0.345588	+	0.289982i	0.453428	+	0.891293i	$0.350201\pi$
$938$		0			0
$939$	3.80235	−	6.58586i	0.124085	−	0.214922i
$940$	0.0594278	+	0.0216299i	0.00193832	+	0.000705491i
$941$	33.3859	−	28.0141i	1.08835	−	0.913233i	0.0917615	−	0.995781i	$-0.470750\pi$
$941$	33.3859	−	28.0141i	1.08835	−	0.913233i	0.996587	+	0.0825481i	$0.0263058\pi$
$942$	40.2028			1.30988
$943$	10.0935			0.328688
$944$	51.7842	−	43.4521i	1.68543	−	1.41425i
$945$		0			0
$946$	−5.16498	−	1.87990i	−0.167928	−	0.0611208i
$947$	−14.1396	+	5.14641i	−0.459476	+	0.167236i	−0.561379	−	0.827559i	$-0.689729\pi$
$947$	−14.1396	+	5.14641i	−0.459476	+	0.167236i	0.101903	+	0.994794i	$0.467507\pi$
$948$	6.84751	−	2.49229i	0.222397	−	0.0809458i
$949$	−16.6574	−	28.8514i	−0.540721	−	0.936557i
$950$	−26.9452	+	22.9878i	−0.874217	+	0.745822i
$951$	6.80098			0.220537
$952$		0			0
$953$	−27.9792	−	23.4774i	−0.906336	−	0.760506i	0.0650825	−	0.997880i	$-0.479269\pi$
$953$	−27.9792	−	23.4774i	−0.906336	−	0.760506i	−0.971418	+	0.237374i	$0.923713\pi$
$954$	−16.9424	+	14.2164i	−0.548531	+	0.460272i
$955$	0.0162500	+	0.0136354i	0.000525839	+	0.000441231i
$956$	−2.43379	−	0.885828i	−0.0787145	−	0.0286497i
$957$	10.4573			0.338035
$958$	−24.4495	+	42.3477i	−0.789926	+	1.36819i
$959$		0			0
$960$	0.0527782	+	0.299320i	0.00170341	+	0.00966050i
$961$	−5.82378	−	10.0871i	−0.187864	−	0.325390i
$962$	−1.66835	+	2.88966i	−0.0537897	+	0.0931664i
$963$	−21.6744	−	7.88884i	−0.698448	−	0.254214i
$964$	2.54151	−	14.4136i	0.0818566	−	0.464232i
$965$	0.203928	+	0.0742236i	0.00656467	+	0.00238934i
$966$		0			0
$967$	2.76506	−	15.6814i	0.0889184	−	0.504281i	−0.907524	−	0.420001i	$-0.862030\pi$
$967$	2.76506	−	15.6814i	0.0889184	−	0.504281i	0.996442	−	0.0842804i	$-0.0268592\pi$
$968$	−8.57913	+	14.8595i	−0.275744	+	0.477602i
$969$	2.76627	−	1.03254i	0.0888655	−	0.0331698i
$970$	0.306034	+	0.530067i	0.00982617	+	0.0170194i
$971$	0.724478	+	0.607909i	0.0232496	+	0.0195087i	0.654338	−	0.756202i	$-0.272947\pi$
$971$	0.724478	+	0.607909i	0.0232496	+	0.0195087i	−0.631089	+	0.775711i	$0.717392\pi$
$972$	−7.69616	−	6.45784i	−0.246854	−	0.207135i
$973$		0			0
$974$	−18.9689	+	6.90411i	−0.607802	+	0.221222i
$975$	2.76957	+	15.7070i	0.0886972	+	0.503027i
$976$	0.409695	−	0.709613i	0.0131140	−	0.0227142i
$977$	−2.65305			−0.0848785			−0.0424392	−	0.999099i	$-0.513513\pi$
$977$	−2.65305			−0.0848785			−0.0424392	+	0.999099i	$0.513513\pi$
$978$	−29.6448	−	10.7898i	−0.947936	−	0.345021i
$979$	1.28393	+	7.28153i	0.0410346	+	0.232719i
$980$		0			0
$981$	−12.9324	−	22.3995i	−0.412898	−	0.715161i
$982$	11.5787	+	65.6662i	0.369492	+	2.09549i
$983$	25.7255	+	21.5862i	0.820515	+	0.688494i	0.953093	−	0.302679i	$-0.0978809\pi$
$983$	25.7255	+	21.5862i	0.820515	+	0.688494i	−0.132577	+	0.991173i	$0.542325\pi$
$984$	−2.76797	−	15.6980i	−0.0882398	−	0.500433i
$985$	1.84633	−	0.672008i	0.0588289	−	0.0214120i
$986$	−0.965064	+	5.47315i	−0.0307339	+	0.174301i
$987$		0			0
$988$	−4.12071	+	7.27402i	−0.131097	+	0.231417i
$989$	1.41500	−	2.45085i	0.0449943	−	0.0779324i
$990$	−0.355021	+	0.129217i	−0.0112833	+	0.00410679i
$991$	−5.48700	+	31.1183i	−0.174300	+	0.988506i	0.764648	+	0.644448i	$0.222913\pi$
$991$	−5.48700	+	31.1183i	−0.174300	+	0.988506i	−0.938948	+	0.344058i	$0.888198\pi$
$992$	−17.6380	+	14.8000i	−0.560006	+	0.469901i
$993$	15.8150	−	5.75619i	0.501874	−	0.182667i
$994$		0			0
$995$	0.0520546	+	0.0901612i	0.00165024	+	0.00285830i
$996$	2.34907	+	4.06871i	0.0744332	+	0.128922i
$997$	26.1003	−	21.9008i	0.826606	−	0.693605i	−0.127903	−	0.991787i	$-0.540825\pi$
$997$	26.1003	−	21.9008i	0.826606	−	0.693605i	0.954509	+	0.298182i	$0.0963801\pi$
$998$	9.25033	−	7.76195i	0.292814	−	0.245700i
$999$	−1.80041	−	3.11840i	−0.0569624	−	0.0986618i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.x.d.226.4		30
7.2	even	3		931.2.w.b.834.4		30
7.3	odd	6		931.2.v.d.606.2		30
7.4	even	3		931.2.v.e.606.2		30
7.5	odd	6		133.2.v.b.36.4	✓	30
7.6	odd	2		931.2.x.e.226.4		30
19.9	even	9		931.2.v.e.275.2		30
133.9	even	9		931.2.w.b.883.4		30
133.47	odd	18		133.2.v.b.85.4	yes	30
133.54	odd	18		2527.2.a.r.1.11		15
133.66	odd	18		931.2.x.e.655.4		30
133.104	odd	18		931.2.v.d.275.2		30
133.117	even	18		2527.2.a.s.1.5		15
133.123	even	9	inner	931.2.x.d.655.4		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.v.b.36.4	✓	30	7.5	odd	6
133.2.v.b.85.4	yes	30	133.47	odd	18
931.2.v.d.275.2		30	133.104	odd	18
931.2.v.d.606.2		30	7.3	odd	6
931.2.v.e.275.2		30	19.9	even	9
931.2.v.e.606.2		30	7.4	even	3
931.2.w.b.834.4		30	7.2	even	3
931.2.w.b.883.4		30	133.9	even	9
931.2.x.d.226.4		30	1.1	even	1	trivial
931.2.x.d.655.4		30	133.123	even	9	inner
931.2.x.e.226.4		30	7.6	odd	2
931.2.x.e.655.4		30	133.66	odd	18
2527.2.a.r.1.11		15	133.54	odd	18
2527.2.a.s.1.5		15	133.117	even	18

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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.x (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.24615 + 1.04564i) q^{2} +(-0.186827 + 1.05955i) q^{3} +(0.112220 + 0.636434i) q^{4} +(-0.0122200 + 0.0693033i) q^{5} +(-1.34072 + 1.12500i) q^{6} +(1.10109 - 1.90715i) q^{8} +(1.73134 + 0.630158i) q^{9} +O(q^{10})\)	\(q+(1.24615 + 1.04564i) q^{2} +(-0.186827 + 1.05955i) q^{3} +(0.112220 + 0.636434i) q^{4} +(-0.0122200 + 0.0693033i) q^{5} +(-1.34072 + 1.12500i) q^{6} +(1.10109 - 1.90715i) q^{8} +(1.73134 + 0.630158i) q^{9} +(-0.0876945 + 0.0735844i) q^{10} +1.79123 q^{11} -0.695297 q^{12} +(2.27346 - 1.90766i) q^{13} +(-0.0711470 - 0.0258954i) q^{15} +(4.58087 - 1.66730i) q^{16} +(-0.591642 + 0.215340i) q^{17} +(1.49859 + 2.59564i) q^{18} +(0.791993 + 4.28634i) q^{19} -0.0454783 q^{20} +(2.23214 + 1.87299i) q^{22} +(-1.14928 + 0.964356i) q^{23} +(1.81500 + 1.52296i) q^{24} +(4.69381 + 1.70841i) q^{25} +4.82780 q^{26} +(-2.60498 + 4.51196i) q^{27} +(-0.942253 - 5.34378i) q^{29} +(-0.0615824 - 0.106664i) q^{30} +(-3.26526 + 5.65559i) q^{31} +(3.31309 + 1.20587i) q^{32} +(-0.334650 + 1.89789i) q^{33} +(-0.962442 - 0.350300i) q^{34} +(-0.206761 + 1.17260i) q^{36} +(-0.345571 + 0.598546i) q^{37} +(-3.49504 + 6.16956i) q^{38} +(1.59651 + 2.76524i) q^{39} +(0.118716 + 0.0996148i) q^{40} +(-5.15375 - 4.32451i) q^{41} +(-1.77256 + 0.645159i) q^{43} +(0.201013 + 1.14000i) q^{44} +(-0.0648291 + 0.112287i) q^{45} -2.44054 q^{46} +(-1.30673 - 0.475610i) q^{47} +(0.910754 + 5.16514i) q^{48} +(4.06280 + 7.03697i) q^{50} +(-0.117628 - 0.667103i) q^{51} +(1.46923 + 1.23283i) q^{52} +(1.28138 + 7.26708i) q^{53} +(-7.96408 + 2.89869i) q^{54} +(-0.0218890 + 0.124138i) q^{55} +(-4.68954 + 0.0383506i) q^{57} +(4.41350 - 7.64440i) q^{58} +(13.0307 - 4.74278i) q^{59} +(0.00849656 - 0.0481864i) q^{60} +(0.128760 - 0.108043i) q^{61} +(-9.98271 + 3.63341i) q^{62} +(-2.00716 - 3.47651i) q^{64} +(0.104426 + 0.180870i) q^{65} +(-2.40154 + 2.01513i) q^{66} +(-7.07640 + 5.93781i) q^{67} +(-0.203444 - 0.352375i) q^{68} +(-0.807065 - 1.39788i) q^{69} +(11.0779 - 4.03202i) q^{71} +(3.10817 - 2.60807i) q^{72} +(1.94927 - 11.0549i) q^{73} +(-1.05650 + 0.384533i) q^{74} +(-2.68706 + 4.65413i) q^{75} +(-2.63910 + 0.985067i) q^{76} +(-0.901962 + 5.11528i) q^{78} +(-9.84833 + 3.58450i) q^{79} +(0.0595710 + 0.337844i) q^{80} +(-0.0597313 - 0.0501205i) q^{81} +(-1.90045 - 10.7780i) q^{82} +(-3.37852 - 5.85176i) q^{83} +(-0.00769389 - 0.0436342i) q^{85} +(-2.88348 - 1.04950i) q^{86} +5.83802 q^{87} +(1.97231 - 3.41615i) q^{88} +(0.716785 + 4.06509i) q^{89} +(-0.198199 + 0.0721386i) q^{90} +(-0.742721 - 0.623217i) q^{92} +(-5.38232 - 4.51630i) q^{93} +(-1.13106 - 1.95905i) q^{94} +(-0.306736 + 0.00250846i) q^{95} +(-1.89665 + 3.28509i) q^{96} +(0.928436 - 5.26542i) q^{97} +(3.10124 + 1.12876i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{3} - 6 q^{4} + 6 q^{5} + 9 q^{6} + 9 q^{8} + 24 q^{9}+O(q^{10}) \) 30 * q - 6 * q^3 - 6 * q^4 + 6 * q^5 + 9 * q^6 + 9 * q^8 + 24 * q^9	\( 30 q - 6 q^{3} - 6 q^{4} + 6 q^{5} + 9 q^{6} + 9 q^{8} + 24 q^{9} + 36 q^{12} - 30 q^{15} - 18 q^{16} - 3 q^{17} + 15 q^{18} + 12 q^{19} + 30 q^{20} + 12 q^{22} + 3 q^{23} - 18 q^{24} - 42 q^{25} - 90 q^{26} - 27 q^{27} + 21 q^{30} - 12 q^{31} + 15 q^{32} + 27 q^{33} + 42 q^{34} - 21 q^{36} + 18 q^{37} - 3 q^{38} + 12 q^{39} + 48 q^{40} - 3 q^{41} - 12 q^{43} - 27 q^{45} - 12 q^{46} - 9 q^{47} - 18 q^{48} - 3 q^{50} + 27 q^{51} - 30 q^{52} + 30 q^{53} - 78 q^{54} - 33 q^{55} - 12 q^{57} + 30 q^{58} - 42 q^{59} - 87 q^{60} - 33 q^{61} - 96 q^{62} + 3 q^{64} + 45 q^{65} + 117 q^{66} - 69 q^{67} - 51 q^{68} - 15 q^{69} + 30 q^{71} + 18 q^{72} + 3 q^{73} + 33 q^{74} - 72 q^{75} - 84 q^{76} + 6 q^{78} - 15 q^{79} - 87 q^{80} + 21 q^{81} - 3 q^{82} - 12 q^{83} + 42 q^{85} + 6 q^{86} + 48 q^{87} + 36 q^{88} - 42 q^{89} - 180 q^{90} - 75 q^{92} - 42 q^{93} - 21 q^{94} - 15 q^{95} + 33 q^{96} + 63 q^{97} + 45 q^{99}+O(q^{100}) \) 30 * q - 6 * q^3 - 6 * q^4 + 6 * q^5 + 9 * q^6 + 9 * q^8 + 24 * q^9 + 36 * q^12 - 30 * q^15 - 18 * q^16 - 3 * q^17 + 15 * q^18 + 12 * q^19 + 30 * q^20 + 12 * q^22 + 3 * q^23 - 18 * q^24 - 42 * q^25 - 90 * q^26 - 27 * q^27 + 21 * q^30 - 12 * q^31 + 15 * q^32 + 27 * q^33 + 42 * q^34 - 21 * q^36 + 18 * q^37 - 3 * q^38 + 12 * q^39 + 48 * q^40 - 3 * q^41 - 12 * q^43 - 27 * q^45 - 12 * q^46 - 9 * q^47 - 18 * q^48 - 3 * q^50 + 27 * q^51 - 30 * q^52 + 30 * q^53 - 78 * q^54 - 33 * q^55 - 12 * q^57 + 30 * q^58 - 42 * q^59 - 87 * q^60 - 33 * q^61 - 96 * q^62 + 3 * q^64 + 45 * q^65 + 117 * q^66 - 69 * q^67 - 51 * q^68 - 15 * q^69 + 30 * q^71 + 18 * q^72 + 3 * q^73 + 33 * q^74 - 72 * q^75 - 84 * q^76 + 6 * q^78 - 15 * q^79 - 87 * q^80 + 21 * q^81 - 3 * q^82 - 12 * q^83 + 42 * q^85 + 6 * q^86 + 48 * q^87 + 36 * q^88 - 42 * q^89 - 180 * q^90 - 75 * q^92 - 42 * q^93 - 21 * q^94 - 15 * q^95 + 33 * q^96 + 63 * q^97 + 45 * q^99

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