LMFDB - Embedded newform 931.2.w.b.834.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(99,931)]

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([0, 2]))

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

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

chi := DirichletCharacter("931.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.w (of order $9$, degree $6$, 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			834.4
Character	$\chi$	$=$	931.834
Dual form			931.2.w.b.883.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.282479 - 1.60202i) q^{2} +(-0.824180 - 0.691570i) q^{3} +(-0.607278 - 0.221031i) q^{4} +(0.0661285 - 0.0240688i) q^{5} +(-1.34072 + 1.12500i) q^{6} +(1.10109 - 1.90715i) q^{8} +(-0.319939 - 1.81447i) q^{9} +O(q^{10})$	\(q+(0.282479 - 1.60202i) q^{2} +(-0.824180 - 0.691570i) q^{3} +(-0.607278 - 0.221031i) q^{4} +(0.0661285 - 0.0240688i) q^{5} +(-1.34072 + 1.12500i) q^{6} +(1.10109 - 1.90715i) q^{8} +(-0.319939 - 1.81447i) q^{9} +(-0.0198787 - 0.112738i) q^{10} +(-0.895617 + 1.55125i) q^{11} +(0.347648 + 0.602145i) q^{12} +(2.27346 - 1.90766i) q^{13} +(-0.0711470 - 0.0258954i) q^{15} +(-3.73436 - 3.13350i) q^{16} +(0.109331 - 0.620047i) q^{17} -2.99718 q^{18} +(3.31609 - 2.82906i) q^{19} -0.0454783 q^{20} +(2.23214 + 1.87299i) q^{22} +(1.40979 + 0.513123i) q^{23} +(-2.22642 + 0.810352i) q^{24} +(-3.82643 + 3.21075i) q^{25} +(-2.41390 - 4.18100i) 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} +(-2.70086 + 2.26629i) q^{32} +(1.81095 - 0.659132i) q^{33} +(-0.962442 - 0.350300i) q^{34} +(-0.206761 + 1.17260i) q^{36} +0.691141 q^{37} +(-3.59548 - 6.11157i) q^{38} -3.19303 q^{39} +(0.0269108 - 0.152619i) q^{40} +(-5.15375 - 4.32451i) q^{41} +(-1.77256 + 0.645159i) q^{43} +(0.886764 - 0.744083i) q^{44} +(-0.0648291 - 0.112287i) q^{45} +(1.22027 - 2.11357i) q^{46} +(0.241473 + 1.36946i) q^{47} +(0.910754 + 5.16514i) q^{48} +(4.06280 + 7.03697i) q^{50} +(-0.518914 + 0.435420i) q^{51} +(-1.80228 + 0.655975i) q^{52} +(-6.93416 - 2.52383i) q^{53} +(6.49238 + 5.44775i) q^{54} +(-0.0218890 + 0.124138i) q^{55} +(-4.68954 + 0.0383506i) q^{57} -8.82700 q^{58} +(-2.40797 + 13.6563i) q^{59} +(0.0374823 + 0.0314514i) q^{60} +(-0.157948 - 0.0574884i) q^{61} +(-9.98271 + 3.63341i) q^{62} +(-2.00716 - 3.47651i) q^{64} +(0.104426 - 0.180870i) q^{65} +(-0.544385 - 3.08736i) q^{66} +(-1.60409 - 9.09725i) q^{67} +(-0.203444 + 0.352375i) q^{68} +(-0.807065 - 1.39788i) q^{69} +(11.0779 - 4.03202i) q^{71} +(-3.81274 - 1.38772i) q^{72} +(8.59917 + 7.21556i) q^{73} +(0.195233 - 1.10722i) q^{74} +5.37413 q^{75} +(-2.63910 + 0.985067i) q^{76} +(-0.901962 + 5.11528i) q^{78} +(8.02843 + 6.73665i) q^{79} +(-0.322367 - 0.117332i) q^{80} +(0.0732713 - 0.0266686i) q^{81} +(-8.38377 + 7.03482i) q^{82} +(-3.37852 - 5.85176i) q^{83} +(-0.00769389 - 0.0436342i) q^{85} +(0.532845 + 3.02192i) q^{86} +(-2.91901 + 5.05588i) q^{87} +(1.97231 + 3.41615i) q^{88} +(3.16208 - 2.65330i) q^{89} +(-0.198199 + 0.0721386i) q^{90} +(-0.742721 - 0.623217i) q^{92} +(-1.22007 + 6.91938i) q^{93} +2.26212 q^{94} +(0.151196 - 0.266896i) q^{95} +3.79329 q^{96} +(0.928436 - 5.26542i) q^{97} +(3.10124 + 1.12876i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} - 6 q^{4} - 3 q^{5} + 9 q^{6} + 9 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 - 6 * q^4 - 3 * q^5 + 9 * q^6 + 9 * q^8 - 3 * q^9	$ 30 q + 3 q^{3} - 6 q^{4} - 3 q^{5} + 9 q^{6} + 9 q^{8} - 3 q^{9} + 36 q^{10} - 18 q^{12} - 30 q^{15} + 18 q^{16} - 12 q^{17} - 30 q^{18} - 6 q^{19} + 30 q^{20} + 12 q^{22} - 15 q^{23} - 45 q^{24} + 21 q^{25} + 45 q^{26} - 27 q^{27} + 21 q^{30} - 12 q^{31} - 75 q^{32} - 18 q^{33} + 42 q^{34} - 21 q^{36} - 36 q^{37} - 57 q^{38} - 24 q^{39} + 39 q^{40} - 3 q^{41} - 12 q^{43} + 72 q^{44} - 27 q^{45} + 6 q^{46} - 27 q^{47} - 18 q^{48} - 3 q^{50} - 27 q^{51} + 15 q^{52} - 15 q^{53} + 57 q^{54} - 33 q^{55} - 12 q^{57} - 60 q^{58} + 84 q^{59} + 75 q^{60} - 42 q^{61} - 96 q^{62} + 3 q^{64} + 45 q^{65} - 99 q^{66} + 39 q^{67} - 51 q^{68} - 15 q^{69} + 30 q^{71} - 117 q^{72} - 15 q^{73} + 24 q^{74} + 144 q^{75} - 84 q^{76} + 6 q^{78} + 12 q^{79} + 165 q^{80} - 15 q^{81} - 3 q^{82} - 12 q^{83} + 42 q^{85} - 48 q^{86} - 24 q^{87} + 36 q^{88} + 66 q^{89} - 180 q^{90} - 75 q^{92} + 30 q^{93} + 42 q^{94} - 15 q^{95} - 66 q^{96} + 63 q^{97} + 45 q^{99}+O(q^{100}) $ 30 * q + 3 * q^3 - 6 * q^4 - 3 * q^5 + 9 * q^6 + 9 * q^8 - 3 * q^9 + 36 * q^10 - 18 * q^12 - 30 * q^15 + 18 * q^16 - 12 * q^17 - 30 * q^18 - 6 * q^19 + 30 * q^20 + 12 * q^22 - 15 * q^23 - 45 * q^24 + 21 * q^25 + 45 * q^26 - 27 * q^27 + 21 * q^30 - 12 * q^31 - 75 * q^32 - 18 * q^33 + 42 * q^34 - 21 * q^36 - 36 * q^37 - 57 * q^38 - 24 * q^39 + 39 * q^40 - 3 * q^41 - 12 * q^43 + 72 * q^44 - 27 * q^45 + 6 * q^46 - 27 * q^47 - 18 * q^48 - 3 * q^50 - 27 * q^51 + 15 * q^52 - 15 * q^53 + 57 * q^54 - 33 * q^55 - 12 * q^57 - 60 * q^58 + 84 * q^59 + 75 * q^60 - 42 * q^61 - 96 * q^62 + 3 * q^64 + 45 * q^65 - 99 * q^66 + 39 * q^67 - 51 * q^68 - 15 * q^69 + 30 * q^71 - 117 * q^72 - 15 * q^73 + 24 * q^74 + 144 * q^75 - 84 * q^76 + 6 * q^78 + 12 * q^79 + 165 * q^80 - 15 * q^81 - 3 * q^82 - 12 * q^83 + 42 * q^85 - 48 * q^86 - 24 * q^87 + 36 * q^88 + 66 * q^89 - 180 * q^90 - 75 * q^92 + 30 * q^93 + 42 * q^94 - 15 * q^95 - 66 * q^96 + 63 * q^97 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.282479	−	1.60202i	0.199743	−	1.13280i	−0.705758	−	0.708453i	$-0.749394\pi$
$2$	0.282479	−	1.60202i	0.199743	−	1.13280i	0.905501	−	0.424344i	$-0.139495\pi$
$3$	−0.824180	−	0.691570i	−0.475841	−	0.399278i	0.373079	−	0.927800i	$-0.378302\pi$
$3$	−0.824180	−	0.691570i	−0.475841	−	0.399278i	−0.848920	+	0.528522i	$0.822747\pi$
$4$	−0.607278	−	0.221031i	−0.303639	−	0.110516i
$5$	0.0661285	−	0.0240688i	0.0295736	−	0.0107639i	−0.327191	−	0.944958i	$-0.606102\pi$
$5$	0.0661285	−	0.0240688i	0.0295736	−	0.0107639i	0.356765	+	0.934194i	$0.383880\pi$
$6$	−1.34072	+	1.12500i	−0.547346	+	0.459278i
$7$		0			0
$7$		0			0
$8$	1.10109	−	1.90715i	0.389295	−	0.674278i
$9$	−0.319939	−	1.81447i	−0.106646	−	0.604822i
$10$	−0.0198787	−	0.112738i	−0.00628620	−	0.0356508i
$11$	−0.895617	+	1.55125i	−0.270039	+	0.467721i	−0.968871	−	0.247564i	$-0.920370\pi$
$11$	−0.895617	+	1.55125i	−0.270039	+	0.467721i	0.698833	+	0.715285i	$0.253703\pi$
$12$	0.347648	+	0.602145i	0.100357	+	0.173824i
$13$	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
$16$	−3.73436	−	3.13350i	−0.933590	−	0.783375i
$17$	0.109331	−	0.620047i	0.0265167	−	0.150383i	−0.968675	−	0.248333i	$-0.920117\pi$
$17$	0.109331	−	0.620047i	0.0265167	−	0.150383i	0.995191	+	0.0979496i	$0.0312284\pi$
$18$	−2.99718			−0.706443
$19$	3.31609	−	2.82906i	0.760762	−	0.649031i
$19$	3.31609	−	2.82906i	0.760762	−	0.649031i
$20$	−0.0454783			−0.0101693
$21$		0			0
$22$	2.23214	+	1.87299i	0.475894	+	0.399323i
$23$	1.40979	+	0.513123i	0.293963	+	0.106994i	0.484792	−	0.874630i	$-0.338895\pi$
$23$	1.40979	+	0.513123i	0.293963	+	0.106994i	−0.190829	+	0.981623i	$0.561118\pi$
$24$	−2.22642	+	0.810352i	−0.454467	+	0.165412i
$25$	−3.82643	+	3.21075i	−0.765286	+	0.642151i
$26$	−2.41390	−	4.18100i	−0.473405	−	0.819962i
$27$	−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	−0.994692	−	0.102897i	$-0.967189\pi$
$31$	−3.26526	−	5.65559i	−0.586457	−	1.01577i	0.408235	−	0.912877i	$-0.366144\pi$
$32$	−2.70086	+	2.26629i	−0.477449	+	0.400627i
$33$	1.81095	−	0.659132i	0.315246	−	0.114740i
$34$	−0.962442	−	0.350300i	−0.165057	−	0.0600760i
$35$		0			0
$36$	−0.206761	+	1.17260i	−0.0344602	+	0.195434i
$37$	0.691141			0.113623			0.0568115	−	0.998385i	$-0.481907\pi$
$37$	0.691141			0.113623			0.0568115	+	0.998385i	$0.481907\pi$
$38$	−3.59548	−	6.11157i	−0.583263	−	0.991428i
$39$	−3.19303			−0.511293
$40$	0.0269108	−	0.152619i	0.00425497	−	0.0241311i
$41$	−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	$0.434831\pi$
$44$	0.886764	−	0.744083i	0.133685	−	0.112175i
$45$	−0.0648291	−	0.112287i	−0.00966416	−	0.0167388i
$46$	1.22027	−	2.11357i	0.179919	−	0.311629i
$47$	0.241473	+	1.36946i	0.0352225	+	0.199757i	0.997341	−	0.0728744i	$-0.0232172\pi$
$47$	0.241473	+	1.36946i	0.0352225	+	0.199757i	−0.962119	+	0.272631i	$0.912106\pi$
$48$	0.910754	+	5.16514i	0.131456	+	0.745524i
$49$		0			0
$50$	4.06280	+	7.03697i	0.574566	+	0.995178i
$51$	−0.518914	+	0.435420i	−0.0726625	+	0.0609711i
$52$	−1.80228	+	0.655975i	−0.249931	+	0.0909674i
$53$	−6.93416	−	2.52383i	−0.952481	−	0.346675i	−0.181398	−	0.983410i	$-0.558062\pi$
$53$	−6.93416	−	2.52383i	−0.952481	−	0.346675i	−0.771083	+	0.636735i	$0.780284\pi$
$54$	6.49238	+	5.44775i	0.883501	+	0.741345i
$55$	−0.0218890	+	0.124138i	−0.00295151	+	0.0167388i
$56$		0			0
$57$	−4.68954	+	0.0383506i	−0.621145	+	0.00507966i
$58$	−8.82700			−1.15904
$59$	−2.40797	+	13.6563i	−0.313491	+	1.77790i	0.267066	+	0.963678i	$0.413946\pi$
$59$	−2.40797	+	13.6563i	−0.313491	+	1.77790i	−0.580558	+	0.814219i	$0.697165\pi$
$60$	0.0374823	+	0.0314514i	0.00483895	+	0.00406036i
$61$	−0.157948	−	0.0574884i	−0.0202232	−	0.00736064i	0.331889	−	0.943319i	$-0.392314\pi$
$61$	−0.157948	−	0.0574884i	−0.0202232	−	0.00736064i	−0.352112	+	0.935958i	$0.614536\pi$
$62$	−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
$66$	−0.544385	−	3.08736i	−0.0670092	−	0.380028i
$67$	−1.60409	−	9.09725i	−0.195971	−	1.11141i	−0.911029	−	0.412341i	$-0.864711\pi$
$67$	−1.60409	−	9.09725i	−0.195971	−	1.11141i	0.715059	−	0.699065i	$-0.246400\pi$
$68$	−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	$0.142277\pi$
$72$	−3.81274	−	1.38772i	−0.449335	−	0.163545i
$73$	8.59917	+	7.21556i	1.00646	+	0.844517i	0.987866	−	0.155310i	$-0.0496376\pi$
$73$	8.59917	+	7.21556i	1.00646	+	0.844517i	0.0185909	+	0.999827i	$0.494082\pi$
$74$	0.195233	−	1.10722i	0.0226953	−	0.128712i
$75$	5.37413			0.620551
$76$	−2.63910	+	0.985067i	−0.302725	+	0.112995i
$77$		0			0
$78$	−0.901962	+	5.11528i	−0.102127	+	0.579191i
$79$	8.02843	+	6.73665i	0.903269	+	0.757933i	0.970827	−	0.239783i	$-0.0770762\pi$
$79$	8.02843	+	6.73665i	0.903269	+	0.757933i	−0.0675578	+	0.997715i	$0.521521\pi$
$80$	−0.322367	−	0.117332i	−0.0360417	−	0.0131181i
$81$	0.0732713	−	0.0266686i	0.00814126	−	0.00296318i
$82$	−8.38377	+	7.03482i	−0.925832	+	0.776866i
$83$	−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
$86$	0.532845	+	3.02192i	0.0574582	+	0.325862i
$87$	−2.91901	+	5.05588i	−0.312951	+	0.542047i
$88$	1.97231	+	3.41615i	0.210249	+	0.364162i
$89$	3.16208	−	2.65330i	0.335180	−	0.281249i	−0.459627	−	0.888112i	$-0.652017\pi$
$89$	3.16208	−	2.65330i	0.335180	−	0.281249i	0.794806	+	0.606863i	$0.207572\pi$
$90$	−0.198199	+	0.0721386i	−0.0208920	+	0.00760407i
$91$		0			0
$92$	−0.742721	−	0.623217i	−0.0774340	−	0.0649749i
$93$	−1.22007	+	6.91938i	−0.126516	+	0.717506i
$94$	2.26212			0.233319
$95$	0.151196	−	0.266896i	0.0155124	−	0.0273829i
$96$	3.79329			0.387151
$97$	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
$100$	3.03338	−	1.10406i	0.303338	−	0.110406i
$101$	−3.82000	+	3.20536i	−0.380104	+	0.318945i	−0.812743	−	0.582622i	$-0.802027\pi$
$101$	−3.82000	+	3.20536i	−0.380104	+	0.318945i	0.432639	+	0.901567i	$0.357582\pi$
$102$	0.550969	+	0.954306i	0.0545540	+	0.0944904i
$103$	−1.50069	+	2.59928i	−0.147868	+	0.256115i	−0.930439	−	0.366446i	$-0.880574\pi$
$103$	−1.50069	+	2.59928i	−0.147868	+	0.256115i	0.782571	+	0.622561i	$0.213908\pi$
$104$	−1.13490	−	6.43634i	−0.111286	−	0.631135i
$105$		0			0
$106$	−6.00197	+	10.3957i	−0.582963	+	1.00972i
$107$	6.25942	+	10.8416i	0.605121	+	1.04810i	0.992032	+	0.125983i	$0.0402086\pi$
$107$	6.25942	+	10.8416i	0.605121	+	1.04810i	−0.386912	+	0.922117i	$0.626458\pi$
$108$	2.57923	−	2.16423i	0.248186	−	0.208253i
$109$	13.1915	−	4.80133i	1.26352	−	0.459884i	0.378572	−	0.925572i	$-0.376415\pi$
$109$	13.1915	−	4.80133i	1.26352	−	0.459884i	0.884949	+	0.465688i	$0.154193\pi$
$110$	0.192689	+	0.0701330i	0.0183722	+	0.00668692i
$111$	−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	$0.506296\pi$
$114$	−1.26326	+	7.52356i	−0.118315	+	0.704646i
$115$	0.105578			0.00984518
$116$	−0.608933	+	3.45343i	−0.0565380	+	0.320643i
$117$	−4.18876	−	3.51479i	−0.387251	−	0.324942i
$118$	21.1974	+	7.71522i	1.95138	+	0.710244i
$119$		0			0
$120$	−0.127726	+	0.107175i	−0.0116597	+	0.00978366i
$121$	3.89574	+	6.74762i	0.354158	+	0.613420i
$122$	−0.136714	+	0.236796i	−0.0123775	+	0.0214385i
$123$	1.25692	+	7.12836i	0.113333	+	0.642743i
$124$	0.732857	+	4.15624i	0.0658125	+	0.373241i
$125$	−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	$0.0933852\pi$
$128$	−12.7626	+	4.64520i	−1.12806	+	0.410582i
$129$	1.90708	+	0.694121i	0.167909	+	0.0611140i
$130$	−0.260259	−	0.218383i	−0.0228263	−	0.0191535i
$131$	−0.518798	+	2.94225i	−0.0453276	+	0.257066i	−0.999048	−	0.0436300i	$-0.986108\pi$
$131$	−0.518798	+	2.94225i	−0.0453276	+	0.257066i	0.953720	+	0.300696i	$0.0972188\pi$
$132$	−1.24544			−0.108402
$133$		0			0
$134$	−15.0271			−1.29814
$135$	−0.0636659	+	0.361067i	−0.00547949	+	0.0310757i
$136$	−1.06214	−	0.891239i	−0.0910775	−	0.0764231i
$137$	−20.0563	−	7.29991i	−1.71353	−	0.623673i	−0.716280	−	0.697813i	$-0.754157\pi$
$137$	−20.0563	−	7.29991i	−1.71353	−	0.623673i	−0.997248	+	0.0741400i	$0.976379\pi$
$138$	−2.46740	+	0.898061i	−0.210039	+	0.0764480i
$139$	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
$142$	−3.33010	−	18.8859i	−0.279456	−	1.58487i
$143$	0.923117	+	5.23525i	0.0771949	+	0.437794i
$144$	−4.49086	+	7.77841i	−0.374239	+	0.648200i
$145$	−0.190928	−	0.330697i	−0.0158557	−	0.0274629i
$146$	13.9885	−	11.7378i	1.15770	−	0.971425i
$147$		0			0
$148$	−0.419715	−	0.152764i	−0.0345003	−	0.0125571i
$149$	6.17610	+	5.18236i	0.505965	+	0.424555i	0.859707	−	0.510788i	$-0.170646\pi$
$149$	6.17610	+	5.18236i	0.505965	+	0.424555i	−0.353741	+	0.935343i	$0.615091\pi$
$150$	1.51808	−	8.60944i	0.123950	−	0.702958i
$151$	20.2208			1.64555			0.822773	−	0.568369i	$-0.192426\pi$
$151$	20.2208			1.64555			0.822773	+	0.568369i	$0.192426\pi$
$152$	−1.74411	−	9.43932i	−0.141466	−	0.765630i
$153$	−1.16003			−0.0937832
$154$		0			0
$155$	−0.352050	−	0.295405i	−0.0282773	−	0.0237275i
$156$	1.93905	+	0.705758i	0.155249	+	0.0565059i
$157$	21.5853	−	7.85640i	1.72269	−	0.627009i	0.724625	−	0.689143i	$-0.242013\pi$
$157$	21.5853	−	7.85640i	1.72269	−	0.627009i	0.998068	+	0.0621344i	$0.0197907\pi$
$158$	13.0601	−	10.9587i	1.03900	−	0.871829i
$159$	3.96960	+	6.87555i	0.314810	+	0.545266i
$160$	−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	−0.260439	−	0.965490i	$-0.583867\pi$
$163$	9.01257	−	15.6102i	0.705919	−	1.22269i	0.966359	−	0.257198i	$-0.0827992\pi$
$164$	2.17391	+	3.76532i	0.169754	+	0.294022i
$165$	0.103891	−	0.0871748i	0.00808789	−	0.00678655i
$166$	−10.3290	+	3.75944i	−0.801685	+	0.291789i
$167$	−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
$170$	−0.0720761			−0.00552798
$171$	−6.19418	−	5.11180i	−0.473681	−	0.390909i
$172$	1.21904			0.0929507
$173$	1.87596	−	10.6391i	0.142626	−	0.808874i	−0.826616	−	0.562766i	$-0.809737\pi$
$173$	1.87596	−	10.6391i	0.142626	−	0.808874i	0.969242	−	0.246108i	$-0.0791517\pi$
$174$	7.27504	+	6.10448i	0.551519	+	0.462780i
$175$		0			0
$176$	8.20541	−	2.98653i	0.618506	−	0.225118i
$177$	11.4289	−	9.58997i	0.859047	−	0.720826i
$178$	−3.35741	−	5.81521i	−0.251649	−	0.435868i
$179$	1.03576	−	1.79399i	0.0774165	−	0.134089i	−0.824718	−	0.565544i	$-0.808666\pi$
$179$	1.03576	−	1.79399i	0.0774165	−	0.134089i	0.902135	+	0.431455i	$0.142000\pi$
$180$	0.0145503	+	0.0825189i	0.00108452	+	0.00615060i
$181$	−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
$184$	2.53091	−	2.12369i	0.186582	−	0.156560i
$185$	0.0457041	−	0.0166349i	0.00336023	−	0.00122302i
$186$	10.7403	+	3.90915i	0.787518	+	0.286633i
$187$	0.863931	+	0.724925i	0.0631769	+	0.0530117i
$188$	0.156053	−	0.885019i	0.0113813	−	0.0645466i
$189$		0			0
$190$	−0.384862	−	0.317610i	−0.0279208	−	0.0230419i
$191$	−0.301438			−0.0218113			−0.0109056	−	0.999941i	$-0.503471\pi$
$191$	−0.301438			−0.0218113			−0.0109056	+	0.999941i	$0.503471\pi$
$192$	−0.749983	+	4.25337i	−0.0541254	+	0.306960i
$193$	2.36234	+	1.98224i	0.170045	+	0.142684i	0.723839	−	0.689969i	$-0.242376\pi$
$193$	2.36234	+	1.98224i	0.170045	+	0.142684i	−0.553794	+	0.832654i	$0.686820\pi$
$194$	−8.17303	−	2.97474i	−0.586789	−	0.213574i
$195$	−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
$199$	0.256896	+	1.45693i	0.0182108	+	0.103279i	0.992558	−	0.121770i	$-0.0388570\pi$
$199$	0.256896	+	1.45693i	0.0182108	+	0.103279i	−0.974348	+	0.225049i	$0.927746\pi$
$200$	1.91013	+	10.8329i	0.135067	+	0.766001i
$201$	−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
$205$	−0.444896	−	0.161929i	−0.0310729	−	0.0113096i
$206$	3.74018	+	3.13838i	0.260590	+	0.218661i
$207$	0.479996	−	2.72219i	0.0333621	−	0.189206i
$208$	−14.4676			−1.00315
$209$	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	$0.657152\pi$
$212$	3.65312	+	3.06533i	0.250897	+	0.210528i
$213$	−11.9186	−	4.33802i	−0.816650	−	0.297236i
$214$	19.1366	−	6.96516i	1.30815	−	0.476129i
$215$	−0.101689	+	0.0853268i	−0.00693510	+	0.00581924i
$216$	5.73664	+	9.93615i	0.390329	+	0.676070i
$217$		0			0
$218$	−3.96548	−	22.4894i	−0.268576	−	1.52317i
$219$	−2.09721	−	11.8938i	−0.141716	−	0.803712i
$220$	0.0407312	−	0.0705484i	0.00274609	−	0.00475637i
$221$	−0.934280	−	1.61822i	−0.0628465	−	0.108853i
$222$	−0.926626	+	0.777532i	−0.0621911	+	0.0521845i
$223$	−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
$226$	−0.118785	+	0.673664i	−0.00790147	+	0.0448115i
$227$	25.3449			1.68220			0.841101	−	0.540878i	$-0.181908\pi$
$227$	25.3449			1.68220			0.841101	+	0.540878i	$0.181908\pi$
$228$	2.85633	+	1.01325i	0.189165	+	0.0671038i
$229$	−24.8429			−1.64167			−0.820834	−	0.571167i	$-0.806491\pi$
$229$	−24.8429			−1.64167			−0.820834	+	0.571167i	$0.806491\pi$
$230$	0.0298235	−	0.169137i	0.00196650	−	0.0111526i
$231$		0			0
$232$	−11.2289	−	4.08698i	−0.737213	−	0.268323i
$233$	−14.8648	+	5.41034i	−0.973825	+	0.354443i	−0.779437	−	0.626481i	$-0.784495\pi$
$233$	−14.8648	+	5.41034i	−0.973825	+	0.354443i	−0.194389	+	0.980925i	$0.562272\pi$
$234$	−6.81399	+	5.71761i	−0.445444	+	0.373772i
$235$	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	$0.208042\pi$
$240$	0.184545	+	0.319642i	0.0119124	+	0.0206328i
$241$	17.3490	−	14.5575i	1.11755	−	0.937733i	0.119068	−	0.992886i	$-0.462009\pi$
$241$	17.3490	−	14.5575i	1.11755	−	0.937733i	0.998478	+	0.0551533i	$0.0175648\pi$
$242$	11.9103	−	4.33498i	0.765621	−	0.278663i
$243$	14.6084	+	5.31704i	0.937132	+	0.341088i
$244$	0.0832117	+	0.0698229i	0.00532708	+	0.00446995i
$245$		0			0
$246$	11.7748			0.750734
$247$	2.14211	−	12.7577i	0.136299	−	0.811755i
$248$	−14.3814			−0.913219
$249$	−1.26239	+	7.15939i	−0.0800009	+	0.453708i
$250$	0.876510	+	0.735480i	0.0554354	+	0.0465158i
$251$	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
$254$	−10.0356	−	17.3822i	−0.629690	−	1.09065i
$255$	−0.0238349	+	0.0412833i	−0.00149260	+	0.00258526i
$256$	2.44237	+	13.8514i	0.152648	+	0.865711i
$257$	−2.18071	−	12.3674i	−0.136029	−	0.771459i	−0.974138	−	0.225956i	$-0.927450\pi$
$257$	−2.18071	−	12.3674i	−0.136029	−	0.771459i	0.838109	−	0.545503i	$-0.183662\pi$
$258$	1.65070	−	2.85910i	0.102768	−	0.178000i
$259$		0			0
$260$	−0.103393	+	0.0867573i	−0.00641218	+	0.00538046i
$261$	−9.39465	+	3.41937i	−0.581515	+	0.211654i
$262$	4.56698	+	1.66225i	0.282149	+	0.102694i
$263$	12.6620	+	10.6247i	0.780774	+	0.655147i	0.943443	−	0.331533i	$-0.107566\pi$
$263$	12.6620	+	10.6247i	0.780774	+	0.655147i	−0.162669	+	0.986681i	$0.552010\pi$
$264$	0.736961	−	4.17951i	0.0453568	−	0.257231i
$265$	−0.519291			−0.0318998
$266$		0			0
$267$	−4.44107			−0.271789
$268$	−1.03665	+	5.87911i	−0.0633233	+	0.359124i
$269$	22.4497	+	18.8376i	1.36879	+	1.14855i	0.973158	+	0.230136i	$0.0739171\pi$
$269$	22.4497	+	18.8376i	1.36879	+	1.14855i	0.395627	+	0.918411i	$0.370527\pi$
$270$	0.560452	+	0.203988i	0.0341080	+	0.0124143i
$271$	26.1830	−	9.52983i	1.59050	−	0.578896i	0.613049	−	0.790045i	$-0.289943\pi$
$271$	26.1830	−	9.52983i	1.59050	−	0.578896i	0.977454	+	0.211149i	$0.0677205\pi$
$272$	−2.35120	+	1.97289i	−0.142562	+	0.119624i
$273$		0			0
$274$	−17.3601	+	30.0685i	−1.04876	+	1.81650i
$275$	−1.55368	−	8.81137i	−0.0936906	−	0.531346i
$276$	0.181138	+	1.02729i	0.0109032	+	0.0618354i
$277$	−3.20279	+	5.54740i	−0.192437	+	0.333311i	−0.946057	−	0.323999i	$-0.894972\pi$
$277$	−3.20279	+	5.54740i	−0.192437	+	0.333311i	0.753620	+	0.657310i	$0.228306\pi$
$278$	−5.71481	−	9.89834i	−0.342752	−	0.593663i
$279$	−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	$0.615726\pi$
$282$	−1.86439	−	1.56441i	−0.111023	−	0.0931593i
$283$	4.57468	−	25.9443i	0.271936	−	1.54223i	−0.476592	−	0.879125i	$-0.658128\pi$
$283$	4.57468	−	25.9443i	0.271936	−	1.54223i	0.748528	−	0.663103i	$-0.230761\pi$
$284$	−7.61856			−0.452079
$285$	−0.309189	+	0.115408i	−0.0183148	+	0.00683616i
$286$	8.64773			0.511351
$287$		0			0
$288$	4.97622	+	4.17554i	0.293226	+	0.246046i
$289$	15.6023	+	5.67876i	0.917781	+	0.334045i
$290$	−0.583716	+	0.212455i	−0.0342770	+	0.0124758i
$291$	−4.40660	+	3.69758i	−0.258320	+	0.216756i
$292$	−3.62722	−	6.28254i	−0.212267	−	0.367658i
$293$	−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
$298$	10.0468	−	8.43030i	0.581998	−	0.488354i
$299$	4.18398	−	1.52285i	0.241966	−	0.0880684i
$300$	−3.26359	−	1.18785i	−0.188423	−	0.0685805i
$301$		0			0
$302$	5.71195	−	32.3941i	0.328686	−	1.86407i
$303$	5.36510			0.308217
$304$	−21.2483	+	0.173766i	−1.21867	+	0.00996619i
$305$	−0.0118285			−0.000677300
$306$	−0.327685	+	1.85839i	−0.0187325	+	0.106237i
$307$	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
$310$	−0.572690	+	0.480544i	−0.0325266	+	0.0272930i
$311$	−14.3737	−	24.8960i	−0.815058	−	1.41172i	−0.909286	−	0.416172i	$-0.863371\pi$
$311$	−14.3737	−	24.8960i	−0.815058	−	1.41172i	0.0942276	−	0.995551i	$-0.469962\pi$
$312$	−3.51581	+	6.08957i	−0.199044	+	0.344754i
$313$	1.22739	+	6.96090i	0.0693764	+	0.393453i	0.999647	+	0.0265784i	$0.00846115\pi$
$313$	1.22739	+	6.96090i	0.0693764	+	0.393453i	−0.930270	+	0.366875i	$0.880428\pi$
$314$	−6.48870	−	36.7992i	−0.366179	−	2.07670i
$315$		0			0
$316$	−3.38648	−	5.86555i	−0.190504	−	0.329963i
$317$	−4.84236	+	4.06322i	−0.271974	+	0.228213i	−0.768565	−	0.639771i	$-0.779029\pi$
$317$	−4.84236	+	4.06322i	−0.271974	+	0.228213i	0.496592	+	0.867984i	$0.334585\pi$
$318$	12.1361	−	4.41717i	0.680557	−	0.247702i
$319$	9.13346	+	3.32431i	0.511376	+	0.186126i
$320$	−0.216406	−	0.181586i	−0.0120975	−	0.0101510i
$321$	2.33885	−	13.2643i	0.130542	−	0.740340i
$322$		0			0
$323$	−1.39160	−	2.36543i	−0.0774306	−	0.131616i
$324$	−0.0503906			−0.00279948
$325$	−2.57421	+	14.5991i	−0.142791	+	0.809811i
$326$	−22.4620	−	18.8479i	−1.24406	−	1.04389i
$327$	−14.1927	−	5.16571i	−0.784857	−	0.285664i
$328$	−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	−0.996864	−	0.0791297i	$-0.974786\pi$
$331$	−7.82141	+	13.5471i	−0.429904	+	0.744615i	0.566960	+	0.823745i	$0.308119\pi$
$332$	0.758277	+	4.30041i	0.0416159	+	0.236015i
$333$	−0.221123	−	1.25405i	−0.0121175	−	0.0687217i
$334$	−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	$0.454328\pi$
$338$	6.40829	+	2.33243i	0.348565	+	0.126867i
$339$	0.346576	+	0.290812i	0.0188234	+	0.0157947i
$340$	−0.00497219	+	0.0281987i	−0.000269655	+	0.00152929i
$341$	11.6977			0.633464
$342$	−9.93892	+	8.47921i	−0.537435	+	0.458503i
$343$		0			0
$344$	−0.721338	+	4.09091i	−0.0388920	+	0.220567i
$345$	−0.0870152	−	0.0730144i	−0.00468474	−	0.00393096i
$346$	−16.5141	−	6.01062i	−0.887801	−	0.323133i
$347$	−7.98342	+	2.90573i	−0.428572	+	0.155988i	−0.547295	−	0.836940i	$-0.684342\pi$
$347$	−7.98342	+	2.90573i	−0.428572	+	0.155988i	0.118723	+	0.992927i	$0.462120\pi$
$348$	2.89016	−	2.42513i	0.154929	−	0.130001i
$349$	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
$352$	−1.09666	−	6.21944i	−0.0584520	−	0.331497i
$353$	−13.1627	+	22.7985i	−0.700580	+	1.21344i	0.267683	+	0.963507i	$0.413742\pi$
$353$	−13.1627	+	22.7985i	−0.700580	+	1.21344i	−0.968263	+	0.249933i	$0.919591\pi$
$354$	−12.1349	−	21.0182i	−0.644961	−	1.11711i
$355$	0.635518	−	0.533263i	0.0337298	−	0.0283027i
$356$	−2.50672	+	0.912373i	−0.132856	+	0.0483557i
$357$		0			0
$358$	−2.58142	−	2.16607i	−0.136433	−	0.114480i
$359$	−1.51662	+	8.60116i	−0.0800440	+	0.453952i	0.918272	+	0.395949i	$0.129584\pi$
$359$	−1.51662	+	8.60116i	−0.0800440	+	0.453952i	−0.998316	+	0.0580028i	$0.981527\pi$
$360$	−0.285531			−0.0150488
$361$	2.99286	−	18.7628i	0.157519	−	0.987516i
$362$	−1.83696			−0.0965484
$363$	1.45566	−	8.25543i	0.0764021	−	0.433298i
$364$		0			0
$365$	0.742320	+	0.270182i	0.0388548	+	0.0141420i
$366$	0.276438	−	0.100615i	0.0144497	−	0.00525925i
$367$	−6.48617	+	5.44254i	−0.338575	+	0.284098i	−0.796183	−	0.605056i	$-0.793151\pi$
$367$	−6.48617	+	5.44254i	−0.338575	+	0.284098i	0.457608	+	0.889154i	$0.348706\pi$
$368$	−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
$373$	11.8749	+	20.5679i	0.614859	+	1.06497i	0.990409	+	0.138165i	$0.0441205\pi$
$373$	11.8749	+	20.5679i	0.614859	+	1.06497i	−0.375550	+	0.926802i	$0.622546\pi$
$374$	1.40538	−	1.17926i	0.0726707	−	0.0609779i
$375$	0.711118	−	0.258826i	0.0367220	−	0.0133657i
$376$	2.87765	+	1.04738i	0.148404	+	0.0540145i
$377$	−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	$0.340092\pi$
$380$	−0.150810	+	0.128661i	−0.00773639	+	0.00660016i
$381$	−13.2747			−0.680086
$382$	−0.0851498	+	0.482908i	−0.00435664	+	0.0247077i
$383$	10.1179	+	8.48991i	0.516999	+	0.433814i	0.863584	−	0.504205i	$-0.168214\pi$
$383$	10.1179	+	8.48991i	0.516999	+	0.433814i	−0.346585	+	0.938019i	$0.612659\pi$
$384$	13.7312	+	4.99774i	0.700716	+	0.255040i
$385$		0			0
$386$	3.84288	−	3.22456i	0.195598	−	0.164126i
$387$	1.73773	+	3.00984i	0.0883339	+	0.152999i
$388$	−1.72764	+	2.99236i	−0.0877077	+	0.151914i
$389$	1.66371	+	9.43539i	0.0843537	+	0.478393i	0.997494	+	0.0707485i	$0.0225388\pi$
$389$	1.66371	+	9.43539i	0.0843537	+	0.478393i	−0.913141	+	0.407645i	$0.866350\pi$
$390$	0.0634733	+	0.359975i	0.00321409	+	0.0182280i
$391$	0.472295	−	0.818038i	0.0238850	−	0.0413700i
$392$		0			0
$393$	2.46235	−	2.06616i	0.124209	−	0.104224i
$394$	−42.6797	+	15.5341i	−2.15017	+	0.782599i
$395$	0.693051	+	0.252250i	0.0348712	+	0.0126921i
$396$	−1.63383	−	1.37094i	−0.0821028	−	0.0688924i
$397$	−2.89344	+	16.4095i	−0.145218	+	0.823571i	0.821974	+	0.569524i	$0.192873\pi$
$397$	−2.89344	+	16.4095i	−0.145218	+	0.823571i	−0.967192	+	0.254046i	$0.918238\pi$
$398$	2.40659			0.120631
$399$		0			0
$400$	24.3502			1.21751
$401$	3.48930	−	19.7888i	0.174247	−	0.988206i	−0.764761	−	0.644314i	$-0.777143\pi$
$401$	3.48930	−	19.7888i	0.174247	−	0.988206i	0.939009	−	0.343893i	$-0.111746\pi$
$402$	12.3850	+	10.3923i	0.617709	+	0.518319i
$403$	−18.2124	−	6.62877i	−0.907224	−	0.330202i
$404$	3.02829	−	1.10221i	0.150663	−	0.0548368i
$405$	0.00420344	−	0.00352710i	0.000208871	−	0.000175263i
$406$		0			0
$407$	−0.618998	+	1.07214i	−0.0306826	+	0.0531438i
$408$	0.259039	+	1.46908i	0.0128243	+	0.0727304i
$409$	1.82074	+	10.3259i	0.0900298	+	0.510585i	0.996157	+	0.0875802i	$0.0279134\pi$
$409$	1.82074	+	10.3259i	0.0900298	+	0.510585i	−0.906128	+	0.423004i	$0.860975\pi$
$410$	−0.385086	+	0.666989i	−0.0190181	+	0.0329402i
$411$	11.4816	+	19.8868i	0.566348	+	0.980943i
$412$	1.48586	−	1.24679i	0.0732031	−	0.0614247i
$413$		0			0
$414$	−4.22541	−	1.53792i	−0.207668	−	0.0755849i
$415$	−0.364261	−	0.305651i	−0.0178809	−	0.0150038i
$416$	−1.81699	+	10.3047i	−0.0890852	+	0.505227i
$417$	−7.55935			−0.370183
$418$	12.7008	−	0.103866i	0.621215	−	0.00508023i
$419$	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	$0.526413\pi$
$422$	42.1663	+	15.3473i	2.05262	+	0.747093i
$423$	2.40759	−	0.876291i	0.117061	−	0.0426067i
$424$	−12.4485	+	10.4455i	−0.604551	+	0.507278i
$425$	1.57247	+	2.72360i	0.0762760	+	0.132114i
$426$	−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
$431$	−5.65367	+	4.74399i	−0.272328	+	0.228510i	−0.768716	−	0.639591i	$-0.779104\pi$
$431$	−5.65367	+	4.74399i	−0.272328	+	0.228510i	0.496388	+	0.868101i	$0.334659\pi$
$432$	23.8662	−	8.68657i	1.14826	−	0.417933i
$433$	−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
$436$	−9.07218			−0.434479
$437$	6.12666	−	2.28683i	0.293078	−	0.109394i
$438$	−19.6466			−0.938749
$439$	−5.60590	+	31.7926i	−0.267555	+	1.51738i	0.494104	+	0.869403i	$0.335496\pi$
$439$	−5.60590	+	31.7926i	−0.267555	+	1.51738i	−0.761659	+	0.647978i	$0.775615\pi$
$440$	0.212649	+	0.178433i	0.0101376	+	0.00850647i
$441$		0			0
$442$	−2.85633	+	1.03962i	−0.135862	+	0.0494496i
$443$	−12.6732	+	10.6341i	−0.602121	+	0.505239i	−0.892127	−	0.451786i	$-0.850787\pi$
$443$	−12.6732	+	10.6341i	−0.602121	+	0.505239i	0.290006	+	0.957025i	$0.406343\pi$
$444$	0.240274	+	0.416167i	0.0114029	+	0.0197504i
$445$	0.145242	−	0.251566i	0.00688512	−	0.0119254i
$446$	2.51983	+	14.2907i	0.119317	+	0.676682i
$447$	−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	$-0.494588\pi$
$450$	11.4685	−	9.62322i	0.540631	−	0.453643i
$451$	11.3242	−	4.12168i	0.533236	−	0.194082i
$452$	0.255367	+	0.0929458i	0.0120114	+	0.00437180i
$453$	−16.6656	−	13.9841i	−0.783018	−	0.657030i
$454$	7.15940	−	40.6030i	0.336007	−	1.90559i
$455$		0			0
$456$	−5.09048	+	8.98588i	−0.238383	+	0.420802i
$457$	26.6017			1.24438			0.622188	−	0.782868i	$-0.286244\pi$
$457$	26.6017			1.24438			0.622188	+	0.782868i	$0.286244\pi$
$458$	−7.01760	+	39.7988i	−0.327911	+	1.85968i
$459$	2.51282	+	2.10851i	0.117288	+	0.0984166i
$460$	−0.0641151	−	0.0233360i	−0.00298938	−	0.00108805i
$461$	−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
$465$	0.0858595	+	0.486933i	0.00398164	+	0.0225810i
$466$	4.46847	+	25.3420i	0.206998	+	1.17394i
$467$	7.77568	−	13.4679i	0.359815	−	0.623219i	−0.628114	−	0.778121i	$-0.716173\pi$
$467$	7.77568	−	13.4679i	0.359815	−	0.623219i	0.987930	+	0.154902i	$0.0495063\pi$
$468$	1.76687	+	3.06030i	0.0816734	+	0.141462i
$469$		0			0
$470$	0.149590	−	0.0544464i	0.00690008	−	0.00251142i
$471$	−23.2234	−	8.45263i	−1.07008	−	0.389477i
$472$	23.3931	+	19.6292i	1.07676	+	0.903506i
$473$	0.586729	−	3.32751i	0.0269778	−	0.152999i
$474$	−18.3426			−0.842503
$475$	−3.60535	+	21.4723i	−0.165425	+	0.985218i
$476$		0			0
$477$	−2.36089	+	13.3893i	−0.108098	+	0.613053i
$478$	4.99420	+	4.19063i	0.228429	+	0.191675i
$479$	−28.2468	−	10.2810i	−1.29063	−	0.469751i	−0.396696	−	0.917950i	$-0.629843\pi$
$479$	−28.2468	−	10.2810i	−1.29063	−	0.469751i	−0.893934	+	0.448199i	$0.852066\pi$
$480$	0.250845	−	0.0912999i	0.0114494	−	0.00416725i
$481$	1.57128	−	1.31846i	0.0716444	−	0.0601168i
$482$	−18.4207	−	31.9056i	−0.839039	−	1.45326i
$483$		0			0
$484$	−0.874363	−	4.95876i	−0.0397438	−	0.225398i
$485$	−0.0653363	−	0.370541i	−0.00296677	−	0.0168254i
$486$	12.6446	−	21.9010i	0.573569	−	0.993451i
$487$	−6.20455	−	10.7466i	−0.281155	−	0.486975i	0.690515	−	0.723319i	$-0.257384\pi$
$487$	−6.20455	−	10.7466i	−0.281155	−	0.486975i	−0.971669	+	0.236344i	$0.924051\pi$
$488$	−0.283554	+	0.237930i	−0.0128359	+	0.0107706i
$489$	−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	$0.346355\pi$
$492$	0.812288	−	4.60672i	0.0366208	−	0.207687i
$493$	−3.41641			−0.153868
$494$	−19.8330	−	7.03549i	−0.892329	−	0.316542i
$495$	0.232248			0.0104388
$496$	−5.52815	+	31.3517i	−0.248221	+	1.40773i
$497$		0			0
$498$	11.1129	+	4.04475i	0.497979	+	0.181250i
$499$	−6.97547	+	2.53886i	−0.312265	+	0.113655i	−0.493399	−	0.869803i	$-0.664246\pi$
$499$	−6.97547	+	2.53886i	−0.312265	+	0.113655i	0.181134	+	0.983459i	$0.442023\pi$
$500$	0.348212	−	0.292184i	0.0155725	−	0.0130669i
$501$	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
$506$	2.18579	+	3.78590i	0.0971701	+	0.168304i
$507$	3.45512	−	2.89919i	0.153447	−	0.128757i
$508$	−7.49282	+	2.72716i	−0.332440	+	0.120998i
$509$	−3.22212	−	1.17276i	−0.142818	−	0.0519815i	0.269622	−	0.962966i	$-0.413101\pi$
$509$	−3.22212	−	1.17276i	−0.142818	−	0.0519815i	−0.412440	+	0.910985i	$0.635323\pi$
$510$	0.0594037	+	0.0498456i	0.00263044	+	0.00220720i
$511$		0			0
$512$	−4.28328			−0.189296
$513$	4.12625	+	22.3317i	0.182179	+	0.985967i
$514$	−20.4288			−0.901077
$515$	−0.0366771	+	0.208006i	−0.00161619	+	0.00916585i
$516$	−1.00471	−	0.843049i	−0.0442298	−	0.0371132i
$517$	−2.34065	−	0.851929i	−0.102942	−	0.0374678i
$518$		0			0
$519$	−8.90378	+	7.47116i	−0.390833	+	0.327948i
$520$	−0.229964	−	0.398310i	−0.0100846	−	0.0174670i
$521$	−6.37820	+	11.0474i	−0.279434	+	0.483994i	−0.971244	−	0.238085i	$-0.923480\pi$
$521$	−6.37820	+	11.0474i	−0.279434	+	0.483994i	0.691810	+	0.722079i	$0.256814\pi$
$522$	2.82410	+	16.0163i	0.123608	+	0.701014i
$523$	3.26971	+	18.5435i	0.142975	+	0.810849i	0.968971	+	0.247174i	$0.0795019\pi$
$523$	3.26971	+	18.5435i	0.142975	+	0.810849i	−0.825997	+	0.563675i	$0.809387\pi$
$524$	0.965384	−	1.67209i	0.0421730	−	0.0730457i
$525$		0			0
$526$	20.5977	−	17.2835i	0.898103	−	0.753597i
$527$	−3.86372	+	1.40628i	−0.168306	+	0.0612585i
$528$	−8.82813	−	3.21318i	−0.384195	−	0.139836i
$529$	−15.8948	−	13.3373i	−0.691078	−	0.579883i
$530$	−0.146689	+	0.831913i	−0.00637175	+	0.0361360i
$531$	25.5493			1.10874
$532$		0			0
$533$	−19.9666			−0.864849
$534$	−1.25451	+	7.11466i	−0.0542878	+	0.307882i
$535$	0.674871	+	0.566284i	0.0291772	+	0.0244826i
$536$	−19.1160	−	6.95767i	−0.825687	−	0.300526i
$537$	−2.09433	+	0.762272i	−0.0903768	+	0.0328945i
$538$	36.5197	−	30.6437i	1.57448	−	1.32114i
$539$		0			0
$540$	0.118470	−	0.205196i	0.00509814	−	0.00883024i
$541$	−5.35002	−	30.3415i	−0.230015	−	1.30448i	−0.852861	−	0.522138i	$-0.825135\pi$
$541$	−5.35002	−	30.3415i	−0.230015	−	1.30448i	0.622846	−	0.782345i	$-0.285976\pi$
$542$	−7.87081	−	44.6376i	−0.338080	−	1.91735i
$543$	−0.607466	+	1.05216i	−0.0260689	+	0.0451526i
$544$	1.10992	+	1.92243i	0.0475873	+	0.0824237i
$545$	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	$0.681985\pi$
$548$	10.5663	+	8.86615i	0.451368	+	0.378743i
$549$	−0.0537770	+	0.304984i	−0.00229515	+	0.0130164i
$550$	−14.5548			−0.620621
$551$	−18.2425	−	15.0548i	−0.777155	−	0.641354i
$552$	−3.55461			−0.151294
$553$		0			0
$554$	7.98230	+	6.69794i	0.339135	+	0.284568i
$555$	−0.0491727	−	0.0178974i	−0.00208726	−	0.000759702i
$556$	−4.26681	+	1.55299i	−0.180953	+	0.0658616i
$557$	−15.9403	+	13.3755i	−0.675413	+	0.566739i	−0.914662	−	0.404220i	$-0.867543\pi$
$557$	−15.9403	+	13.3755i	−0.675413	+	0.566739i	0.239249	+	0.970958i	$0.423099\pi$
$558$	9.78657	+	16.9508i	0.414298	+	0.717586i
$559$	−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	0.626657	−	0.779295i	$-0.284423\pi$
$563$	−8.57899	−	14.8592i	−0.361561	−	0.626242i	−0.988218	+	0.153053i	$0.951089\pi$
$564$	−0.740667	+	0.621494i	−0.0311877	+	0.0261696i
$565$	−0.0278077	+	0.0101212i	−0.00116988	+	0.000425801i
$566$	−40.2709	−	14.6574i	−1.69271	−	0.616097i
$567$		0			0
$568$	4.50812	−	25.5668i	0.189156	−	1.07276i
$569$	−23.7998			−0.997738			−0.498869	−	0.866678i	$-0.666251\pi$
$569$	−23.7998			−0.997738			−0.498869	+	0.866678i	$0.666251\pi$
$570$	0.0975457	+	0.527927i	0.00408574	+	0.0221124i
$571$	−10.6996			−0.447766			−0.223883	−	0.974616i	$-0.571873\pi$
$571$	−10.6996			−0.447766			−0.223883	+	0.974616i	$0.571873\pi$
$572$	0.596566	−	3.38329i	0.0249437	−	0.141463i
$573$	0.248439	+	0.208465i	0.0103787	+	0.00870876i
$574$		0			0
$575$	−7.04199	+	2.56308i	−0.293671	+	0.106888i
$576$	−5.66584	+	4.75421i	−0.236077	+	0.198092i
$577$	−10.8671	−	18.8224i	−0.452404	−	0.783586i	0.546131	−	0.837700i	$-0.316100\pi$
$577$	−10.8671	−	18.8224i	−0.452404	−	0.783586i	−0.998535	+	0.0541136i	$0.982767\pi$
$578$	13.5048	−	23.3910i	0.561725	−	0.972936i
$579$	−0.576138	−	3.26744i	−0.0239435	−	0.135790i
$580$	0.0428521	+	0.243026i	0.00177934	+	0.0100911i
$581$		0			0
$582$	4.67881	+	8.10394i	0.193943	+	0.335919i
$583$	10.1255	−	8.49627i	0.419354	−	0.351879i
$584$	23.2296	−	8.45489i	0.961248	−	0.349866i
$585$	−0.361593	−	0.131609i	−0.0149500	−	0.00544137i
$586$	39.2270	+	32.9154i	1.62045	+	1.35972i
$587$	−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
$590$	1.58745			0.0653542
$591$	−5.21625	+	29.5828i	−0.214568	+	1.21688i
$592$	−2.58097	−	2.16569i	−0.106077	−	0.0890094i
$593$	−31.7666	−	11.5621i	−1.30450	−	0.474798i	−0.406038	−	0.913856i	$-0.633090\pi$
$593$	−31.7666	−	11.5621i	−1.30450	−	0.474798i	−0.898459	+	0.439058i	$0.855312\pi$
$594$	−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
$598$	−1.25774	−	7.13298i	−0.0514327	−	0.291689i
$599$	0.481938	+	2.73321i	0.0196915	+	0.111676i	0.993069	−	0.117531i	$-0.0374979\pi$
$599$	0.481938	+	2.73321i	0.0196915	+	0.111676i	−0.973378	+	0.229207i	$0.926387\pi$
$600$	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
$604$	−12.2797	−	4.46943i	−0.499652	−	0.181859i
$605$	0.420026	+	0.352444i	0.0170765	+	0.0143289i
$606$	1.51553	−	8.59498i	0.0615641	−	0.349147i
$607$	38.2873			1.55403			0.777016	−	0.629481i	$-0.216732\pi$
$607$	38.2873			1.55403			0.777016	+	0.629481i	$0.216732\pi$
$608$	−2.54481	+	15.1561i	−0.103206	+	0.614661i
$609$		0			0
$610$	−0.00334131	+	0.0189495i	−0.000135286	+	0.000767244i
$611$	3.16146	+	2.65278i	0.127899	+	0.107320i
$612$	0.704463	+	0.256404i	0.0284762	+	0.0103645i
$613$	−17.9570	+	6.53583i	−0.725278	+	0.263980i	−0.678165	−	0.734910i	$-0.737224\pi$
$613$	−17.9570	+	6.53583i	−0.725278	+	0.263980i	−0.0471132	+	0.998890i	$0.515002\pi$
$614$	21.4473	−	17.9964i	0.865543	−	0.726277i
$615$	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	$0.953391\pi$
$618$	−0.912172	−	5.17318i	−0.0366929	−	0.208096i
$619$	−18.1490	+	31.4350i	−0.729469	+	1.26348i	0.227638	+	0.973746i	$0.426900\pi$
$619$	−18.1490	+	31.4350i	−0.729469	+	1.26348i	−0.957108	+	0.289732i	$0.906434\pi$
$620$	0.148498	+	0.257207i	0.00596384	+	0.0103297i
$621$	−5.98768	+	5.02426i	−0.240277	+	0.201616i
$622$	−43.9441	+	15.9943i	−1.76200	+	0.641314i
$623$		0			0
$624$	11.9239	+	10.0053i	0.477338	+	0.400535i
$625$	4.32831	−	24.5471i	0.173132	−	0.981882i
$626$	11.4982			0.459560
$627$	4.14054	−	7.30902i	0.165357	−	0.291894i
$628$	−14.8448			−0.592371
$629$	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	$0.507490\pi$
$632$	21.6878	−	7.89372i	0.862695	−	0.313995i
$633$	22.7345	−	19.0765i	0.903617	−	0.758225i
$634$	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
$639$	−10.8602	−	18.8105i	−0.429624	−	0.744131i
$640$	−0.732166	+	0.614361i	−0.0289414	+	0.0242847i
$641$	36.5569	−	13.3056i	1.44391	−	0.525540i	0.503026	−	0.864271i	$-0.332220\pi$
$641$	36.5569	−	13.3056i	1.44391	−	0.525540i	0.940883	+	0.338731i	$0.109998\pi$
$642$	−20.5889	−	7.49376i	−0.812580	−	0.295755i
$643$	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
$646$	−4.18256	+	1.56118i	−0.164561	+	0.0614237i
$647$	−1.82497			−0.0717468			−0.0358734	−	0.999356i	$-0.511421\pi$
$647$	−1.82497			−0.0717468			−0.0358734	+	0.999356i	$0.511421\pi$
$648$	0.0298175	−	0.169104i	0.00117134	−	0.00664302i
$649$	−19.0278	−	15.9662i	−0.746905	−	0.626727i
$650$	22.6608	+	8.24785i	0.888829	+	0.323507i
$651$		0			0
$652$	−8.92349	+	7.48769i	−0.349471	+	0.293241i
$653$	−10.8941	−	18.8692i	−0.426320	−	0.738407i	0.570223	−	0.821490i	$-0.306857\pi$
$653$	−10.8941	−	18.8692i	−0.426320	−	0.738407i	−0.996543	+	0.0830827i	$0.973523\pi$
$654$	−12.2847	+	21.2777i	−0.480369	+	0.832024i
$655$	0.0365091	+	0.207053i	0.00142653	+	0.00809024i
$656$	5.69511	+	32.2986i	0.222357	+	1.26105i
$657$	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	$0.167952\pi$
$660$	−0.0823590	+	0.0299762i	−0.00320582	+	0.00116682i
$661$	−28.0558	−	10.2115i	−1.09124	−	0.397180i	−0.267162	−	0.963652i	$-0.586086\pi$
$661$	−28.0558	−	10.2115i	−1.09124	−	0.397180i	−0.824082	+	0.566471i	$0.808308\pi$
$662$	19.4933	+	16.3568i	0.757628	+	0.635725i
$663$	−0.349097	+	1.97983i	−0.0135578	+	0.0768900i
$664$	−14.8802			−0.577465
$665$		0			0
$666$	−2.07148			−0.0802681
$667$	1.41364	−	8.01713i	0.0547362	−	0.310425i
$668$	1.81975	+	1.52696i	0.0704084	+	0.0590797i
$669$	9.01861	+	3.28250i	0.348679	+	0.126909i
$670$	−0.993717	+	0.361683i	−0.0383906	+	0.0139731i
$671$	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	$0.103367\pi$
$674$	2.11715	+	12.0070i	0.0815496	+	0.462491i
$675$	−4.51902	−	25.6286i	−0.173937	−	0.986446i
$676$	1.35460	−	2.34624i	0.0521002	−	0.0902401i
$677$	−13.9448	−	24.1531i	−0.535943	−	0.928280i	−0.999117	−	0.0420130i	$-0.986623\pi$
$677$	−13.9448	−	24.1531i	−0.535943	−	0.928280i	0.463174	−	0.886267i	$-0.346710\pi$
$678$	0.563786	−	0.473073i	0.0216521	−	0.0181682i
$679$		0			0
$680$	−0.0916885	−	0.0333719i	−0.00351609	−	0.00127975i
$681$	−20.8888	−	17.5278i	−0.800460	−	0.671666i
$682$	3.30434	−	18.7399i	0.126530	−	0.717587i
$683$	12.8899			0.493220			0.246610	−	0.969115i	$-0.420683\pi$
$683$	12.8899			0.493220			0.246610	+	0.969115i	$0.420683\pi$
$684$	2.63172	+	4.47339i	0.100626	+	0.171044i
$685$	−1.50199			−0.0573883
$686$		0			0
$687$	20.4751	+	17.1806i	0.781172	+	0.655481i
$688$	8.64099	+	3.14506i	0.329435	+	0.119904i
$689$	−20.5792	+	7.49021i	−0.784005	+	0.285354i
$690$	−0.141550	+	0.118775i	−0.00538873	+	0.00452168i
$691$	−3.96995	−	6.87616i	−0.151024	−	0.261581i	0.780580	−	0.625056i	$-0.214924\pi$
$691$	−3.96995	−	6.87616i	−0.151024	−	0.261581i	−0.931604	+	0.363474i	$0.881590\pi$
$692$	−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
$697$	−3.24487	+	2.72277i	−0.122908	+	0.103132i
$698$	0.950113	−	0.345813i	0.0359623	−	0.0130892i
$699$	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	$-0.116723\pi$
$702$	25.1527			0.949326
$703$	2.29188	−	1.95528i	0.0864400	−	0.0737447i
$704$	7.19060			0.271006
$705$	0.0182827	−	0.103686i	0.000688566	−	0.00390505i
$706$	32.8053	+	27.5269i	1.23464	+	1.03599i
$707$		0			0
$708$	−9.06019	+	3.29764i	−0.340503	+	0.123933i
$709$	−17.7443	+	14.8893i	−0.666402	+	0.559178i	−0.911998	−	0.410195i	$-0.865461\pi$
$709$	−17.7443	+	14.8893i	−0.666402	+	0.559178i	0.245596	+	0.969372i	$0.421016\pi$
$710$	−0.674776	−	1.16875i	−0.0253239	−	0.0438623i
$711$	9.65482	−	16.7226i	0.362084	−	0.627148i
$712$	−1.57849	−	8.95208i	−0.0591565	−	0.335493i
$713$	−1.70133	−	9.64870i	−0.0637151	−	0.361347i
$714$		0			0
$715$	0.187051	+	0.323981i	0.00699529	+	0.0121162i
$716$	−1.02552	+	0.860516i	−0.0383256	+	0.0321590i
$717$	4.05182	−	1.47474i	0.151318	−	0.0550752i
$718$	13.3508	+	4.85929i	0.498247	+	0.181347i
$719$	−36.6562	−	30.7582i	−1.36705	−	1.14709i	−0.973735	−	0.227682i	$-0.926885\pi$
$719$	−36.6562	−	30.7582i	−1.36705	−	1.14709i	−0.393311	−	0.919406i	$-0.628670\pi$
$720$	−0.109757	+	0.622464i	−0.00409041	+	0.0231979i
$721$		0			0
$722$	−29.2129	−	10.0947i	−1.08719	−	0.375686i
$723$	−24.3662			−0.906190
$724$	−0.126723	+	0.718682i	−0.00470963	+	0.0267096i
$725$	20.7630	+	17.4223i	0.771120	+	0.647047i
$726$	−12.8141	−	4.66397i	−0.475578	−	0.173096i
$727$	−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
$731$	0.206233	+	1.16961i	0.00762781	+	0.0432595i
$732$	−0.0202941	−	0.115093i	−0.000750090	−	0.00425397i
$733$	12.6849	−	21.9708i	0.468526	−	0.811511i	−0.530827	−	0.847480i	$-0.678118\pi$
$733$	12.6849	−	21.9708i	0.468526	−	0.811511i	0.999353	+	0.0359690i	$0.0114518\pi$
$734$	6.88684	+	11.9284i	0.254198	+	0.440284i
$735$		0			0
$736$	−4.97054	+	1.80913i	−0.183217	+	0.0666854i
$737$	15.5488	+	5.65930i	0.572747	+	0.208463i
$738$	15.4467	+	12.9614i	0.568603	+	0.477114i
$739$	−5.90936	+	33.5136i	−0.217379	+	1.23282i	0.659350	+	0.751836i	$0.270831\pi$
$739$	−5.90936	+	33.5136i	−0.217379	+	1.23282i	−0.876730	+	0.480983i	$0.840280\pi$
$740$	−0.0314319			−0.00115546
$741$	−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	$0.0822146\pi$
$744$	11.8529	+	9.94572i	0.434547	+	0.364628i
$745$	0.533149	+	0.194050i	0.0195331	+	0.00710945i
$746$	36.3046	−	13.2138i	1.32921	−	0.483791i
$747$	−9.53691	+	8.00242i	−0.348937	+	0.292793i
$748$	−0.364416	−	0.631187i	−0.0133244	−	0.0230785i
$749$		0			0
$750$	−0.213768	−	1.21234i	−0.00780569	−	0.0442682i
$751$	−2.53555	−	14.3798i	−0.0925236	−	0.524727i	−0.995478	−	0.0949911i	$-0.969718\pi$
$751$	−2.53555	−	14.3798i	−0.0925236	−	0.524727i	0.902955	−	0.429736i	$-0.141393\pi$
$752$	3.38947	−	5.87073i	0.123601	−	0.214084i
$753$	−14.6876	−	25.4396i	−0.535245	−	0.927072i
$754$	−20.0679	+	16.8389i	−0.730828	+	0.613238i
$755$	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	$0.871943\pi$
$758$	5.29580	−	30.0340i	0.192352	−	1.09088i
$759$	2.89128			0.104947
$760$	−0.342529	−	0.582229i	−0.0124248	−	0.0211197i
$761$	45.2806			1.64142			0.820711	−	0.571344i	$-0.193578\pi$
$761$	45.2806			1.64142			0.820711	+	0.571344i	$0.193578\pi$
$762$	−3.74983	+	21.2664i	−0.135842	+	0.770399i
$763$		0			0
$764$	0.183057	+	0.0666271i	0.00662275	+	0.00241048i
$765$	−0.0767113	+	0.0279206i	−0.00277350	+	0.00100947i
$766$	16.4591	−	13.8108i	0.594690	−	0.499004i
$767$	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
$772$	−0.996459	−	1.72592i	−0.0358634	−	0.0621171i
$773$	18.8013	−	15.7762i	0.676237	−	0.567430i	−0.238667	−	0.971101i	$-0.576710\pi$
$773$	18.8013	−	15.7762i	0.676237	−	0.567430i	0.914904	+	0.403671i	$0.132266\pi$
$774$	5.31269	−	1.93366i	0.190961	−	0.0695040i
$775$	30.6530	+	11.1568i	1.10109	+	0.400763i
$776$	−9.01964	−	7.56838i	−0.323786	−	0.271689i
$777$		0			0
$778$	15.5856			0.558772
$779$	−29.3246	+	0.239813i	−1.05066	+	0.00859221i
$780$	0.145213			0.00519948
$781$	−3.66686	+	20.7958i	−0.131210	+	0.744131i
$782$	−1.17710	−	0.987703i	−0.0420929	−	0.0353202i
$783$	26.5655	+	9.66904i	0.949372	+	0.345543i
$784$		0			0
$785$	1.23831	−	1.03906i	0.0441971	−	0.0370858i
$786$	−2.61446	−	4.52838i	−0.0932547	−	0.161522i
$787$	4.59751	−	7.96312i	0.163884	−	0.283855i	−0.772375	−	0.635167i	$-0.780931\pi$
$787$	4.59751	−	7.96312i	0.163884	−	0.283855i	0.936258	+	0.351313i	$0.114265\pi$
$788$	3.13323	+	17.7694i	0.111617	+	0.633010i
$789$	−3.08807	−	17.5133i	−0.109938	−	0.623492i
$790$	0.599881	−	1.03902i	0.0213428	−	0.0369668i
$791$		0			0
$792$	5.56746	−	4.67166i	0.197831	−	0.166000i
$793$	−0.468758	+	0.170614i	−0.0166461	+	0.00605868i
$794$	25.4710	+	9.27069i	0.903932	+	0.329004i
$795$	0.427990	+	0.359126i	0.0151792	+	0.0127369i
$796$	0.166019	−	0.941542i	0.00588439	−	0.0333721i
$797$	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
$800$	3.05814	−	17.3436i	0.108122	−	0.613188i
$801$	−5.82600	−	4.88859i	−0.205852	−	0.172730i
$802$	−30.7164	−	11.1798i	−1.08463	−	0.394774i
$803$	−18.8947	+	6.87712i	−0.666781	+	0.242688i
$804$	4.92020	−	4.12854i	0.173522	−	0.145602i
$805$		0			0
$806$	−15.7640	+	27.3041i	−0.555264	+	0.961745i
$807$	−5.47515	−	31.0511i	−0.192734	−	1.09305i
$808$	1.90692	+	10.8147i	0.0670853	+	0.380460i
$809$	1.11568	−	1.93241i	0.0392252	−	0.0679400i	−0.845746	−	0.533585i	$-0.820844\pi$
$809$	1.11568	−	1.93241i	0.0392252	−	0.0679400i	0.884972	+	0.465645i	$0.154178\pi$
$810$	−0.00446310	−	0.00773031i	−0.000156817	−	0.000271615i
$811$	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
$814$	1.54273	+	1.29450i	0.0540725	+	0.0453722i
$815$	0.220268	−	1.24920i	0.00771566	−	0.0437577i
$816$	3.30220			0.115600
$817$	−4.05277	+	7.15408i	−0.141788	+	0.250290i
$818$	17.0566			0.596371
$819$		0			0
$820$	0.234384	+	0.196672i	0.00818505	+	0.00686807i
$821$	42.4324	+	15.4441i	1.48090	+	0.539004i	0.951037	−	0.309077i	$-0.100020\pi$
$821$	42.4324	+	15.4441i	1.48090	+	0.539004i	0.529865	+	0.848082i	$0.322242\pi$
$822$	35.1023	−	12.7762i	1.22433	−	0.445621i
$823$	−6.92579	+	5.81143i	−0.241418	+	0.202574i	−0.755466	−	0.655187i	$-0.772590\pi$
$823$	−6.92579	+	5.81143i	−0.241418	+	0.202574i	0.514048	+	0.857761i	$0.328145\pi$
$824$	3.30481	+	5.72409i	0.115128	+	0.199408i
$825$	−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	0.996890	−	0.0788058i	$-0.0251107\pi$
$829$	12.3864	+	21.4539i	0.430197	+	0.745123i	−0.566693	+	0.823929i	$0.691777\pi$
$830$	−0.592555	+	0.497212i	−0.0205679	+	0.0172585i
$831$	6.47609	−	2.35710i	0.224653	−	0.0817670i
$832$	−11.1952	−	4.07473i	−0.388125	−	0.141266i
$833$		0			0
$834$	−2.13536	+	12.1102i	−0.0739413	+	0.419342i
$835$	−0.258678			−0.00895193
$836$	0.835531	−	4.97615i	0.0288974	−	0.172104i
$837$	34.0237			1.17603
$838$	3.69566	−	20.9591i	0.127665	−	0.724022i
$839$	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
$842$	29.5107	−	24.7624i	1.01701	−	0.853370i
$843$	0.261446	+	0.452837i	0.00900467	+	0.0155965i
$844$	8.91324	−	15.4382i	0.306806	−	0.531404i
$845$	0.0512287	+	0.290533i	0.00176232	+	0.00999462i
$846$	−0.723740	−	4.10453i	−0.0248827	−	0.141117i
$847$		0			0
$848$	17.9863	+	31.1531i	0.617650	+	1.06980i
$849$	−21.7126	+	18.2191i	−0.745176	+	0.625277i
$850$	4.80744	−	1.74977i	0.164894	−	0.0600165i
$851$	0.974367	+	0.354641i	0.0334009	+	0.0121569i
$852$	6.27907	+	5.26877i	0.215117	+	0.180505i
$853$	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
$856$	27.5688			0.942281
$857$	4.54654	−	25.7847i	0.155307	−	0.880789i	−0.803198	−	0.595713i	$-0.796870\pi$
$857$	4.54654	−	25.7847i	0.155307	−	0.880789i	0.958505	−	0.285077i	$-0.0920191\pi$
$858$	−7.12729	−	5.98050i	−0.243322	−	0.204171i
$859$	−20.3489	−	7.40639i	−0.694295	−	0.252703i	−0.0293222	−	0.999570i	$-0.509335\pi$
$859$	−20.3489	−	7.40639i	−0.694295	−	0.252703i	−0.664973	+	0.746867i	$0.731557\pi$
$860$	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	0.218185	+	0.975907i	$0.429986\pi$
$863$	−21.6234	+	37.4528i	−0.736068	+	1.27491i	−0.954253	+	0.299000i	$0.903347\pi$
$864$	−3.18972	−	18.0898i	−0.108516	−	0.615427i
$865$	−0.132016	−	0.748698i	−0.00448866	−	0.0254565i
$866$	−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
$870$	0.628015	+	0.228579i	0.0212917	+	0.00774954i
$871$	−21.0013	−	17.6222i	−0.711603	−	0.597106i
$872$	5.36826	−	30.4449i	0.181792	−	1.03100i
$873$	−9.85098			−0.333405
$874$	−1.93289	−	10.4610i	−0.0653810	−	0.353848i
$875$		0			0
$876$	−1.35532	+	7.68642i	−0.0457921	+	0.259700i
$877$	14.3979	+	12.0813i	0.486182	+	0.407956i	0.852656	−	0.522473i	$-0.174990\pi$
$877$	14.3979	+	12.0813i	0.486182	+	0.407956i	−0.366473	+	0.930429i	$0.619435\pi$
$878$	49.3488	+	17.9615i	1.66544	+	0.606171i
$879$	31.8251	−	11.5834i	1.07343	−	0.390698i
$880$	0.470729	−	0.394989i	0.0158683	−	0.0133151i
$881$	−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	$0.831745\pi$
$884$	0.209691	+	1.18921i	0.00705266	+	0.0399976i
$885$	0.524955	−	0.909249i	0.0176462	−	0.0305641i
$886$	13.4560	+	23.3065i	0.452064	+	0.782998i
$887$	−22.2337	+	18.6563i	−0.746534	+	0.626416i	−0.934584	−	0.355743i	$-0.884228\pi$
$887$	−22.2337	+	18.6563i	−0.746534	+	0.626416i	0.188050	+	0.982159i	$0.439783\pi$
$888$	−1.53877	+	0.560067i	−0.0516378	+	0.0187946i
$889$		0			0
$890$	−0.361985	−	0.303742i	−0.0121338	−	0.0101814i
$891$	−0.0242533	+	0.137547i	−0.000812516	+	0.00460801i
$892$	5.76484			0.193021
$893$	4.67504	+	3.85812i	0.156444	+	0.129107i
$894$	−14.1106			−0.471927
$895$	0.0253141	−	0.143564i	0.000846158	−	0.00479880i
$896$		0			0
$897$	−4.50151	−	1.63842i	−0.150301	−	0.0547051i
$898$	−55.5441	+	20.2164i	−1.85353	+	0.674630i
$899$	−27.1455	+	22.7778i	−0.905354	+	0.759683i
$900$	−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
$905$	−0.0397335	−	0.0688204i	−0.00132078	−	0.00228767i
$906$	−27.1104	+	22.7484i	−0.900684	+	0.755764i
$907$	−15.4723	+	5.63147i	−0.513750	+	0.186990i	−0.585868	−	0.810406i	$-0.699246\pi$
$907$	−15.4723	+	5.63147i	−0.513750	+	0.186990i	0.0721181	+	0.997396i	$0.477024\pi$
$908$	−15.3914	−	5.60202i	−0.510782	−	0.185909i
$909$	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	$0.340703\pi$
$912$	17.6326	+	14.5515i	0.583874	+	0.481848i
$913$	12.1034			0.400565
$914$	7.51442	−	42.6164i	0.248555	−	1.40963i
$915$	0.00974885	+	0.00818026i	0.000322287	+	0.000270431i
$916$	15.0866	+	5.49106i	0.498474	+	0.181430i
$917$		0			0
$918$	4.08768	−	3.42997i	0.134914	−	0.113206i
$919$	10.8249	+	18.7493i	0.357081	+	0.618482i	0.987472	−	0.157796i	$-0.0504387\pi$
$919$	10.8249	+	18.7493i	0.357081	+	0.618482i	−0.630391	+	0.776278i	$0.717105\pi$
$920$	0.116251	−	0.201352i	0.00383268	−	0.00663839i
$921$	−3.21545	−	18.2357i	−0.105953	−	0.600887i
$922$	0.0173481	+	0.0983862i	0.000571331	+	0.00324018i
$923$	17.4934	−	30.2995i	0.575804	−	0.997322i
$924$		0			0
$925$	−2.64460	+	2.21908i	−0.0869540	+	0.0729631i
$926$	19.9143	−	7.24822i	0.654425	−	0.238191i
$927$	5.19644	+	1.89135i	0.170673	+	0.0621201i
$928$	14.6555	+	12.2974i	0.481089	+	0.403681i
$929$	−2.99333	+	16.9760i	−0.0982081	+	0.556966i	0.895509	+	0.445044i	$0.146812\pi$
$929$	−2.99333	+	16.9760i	−0.0982081	+	0.556966i	−0.993717	+	0.111922i	$0.964299\pi$
$930$	0.804329			0.0263750
$931$		0			0
$932$	10.2229			0.334863
$933$	−5.37078	+	30.4592i	−0.175831	+	0.997190i
$934$	−19.3793	−	16.2612i	−0.634110	−	0.532081i
$935$	0.0745785	+	0.0271444i	0.00243898	+	0.000887716i
$936$	−11.3154	+	4.11848i	−0.369856	+	0.134617i
$937$	−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
$940$	−0.0109818	−	0.0622809i	−0.000358187	−	0.00203138i
$941$	7.56796	+	42.9201i	0.246709	+	1.39915i	0.816491	+	0.577358i	$0.195916\pi$
$941$	7.56796	+	42.9201i	0.246709	+	1.39915i	−0.569782	+	0.821796i	$0.692972\pi$
$942$	−20.1014	+	34.8166i	−0.654938	+	1.13439i
$943$	−5.04673	−	8.74119i	−0.164344	−	0.284652i
$944$	51.7842	−	43.4521i	1.68543	−	1.41425i
$945$		0			0
$946$	−5.16498	−	1.87990i	−0.167928	−	0.0611208i
$947$	11.5267	+	9.67208i	0.374569	+	0.314300i	0.810566	−	0.585648i	$-0.199160\pi$
$947$	11.5267	+	9.67208i	0.374569	+	0.314300i	−0.435997	+	0.899948i	$0.643604\pi$
$948$	−1.26537	+	7.17626i	−0.0410973	+	0.233074i
$949$	33.3148			1.08144
$950$	33.3806	+	11.8413i	1.08301	+	0.384183i
$951$	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	$0.923713\pi$
$954$	20.7830	+	7.56438i	0.672873	+	0.244906i
$955$	−0.0199336	+	0.00725524i	−0.000645037	+	0.000234774i
$956$	1.98405	−	1.66481i	0.0641686	−	0.0538439i
$957$	−5.22863	−	9.05626i	−0.169018	−	0.292747i
$958$	−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
$963$	17.6691	−	14.8262i	0.569380	−	0.477767i
$964$	−13.7533	+	5.00580i	−0.442965	+	0.161226i
$965$	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	$-0.0268592\pi$
$968$	17.1583			0.551488
$969$	−0.488933	+	2.91193i	−0.0157068	+	0.0935447i
$970$	−0.612069			−0.0196523
$971$	0.164226	−	0.931371i	0.00527026	−	0.0298891i	−0.982059	−	0.188573i	$-0.939614\pi$
$971$	0.164226	−	0.931371i	0.00527026	−	0.0298891i	0.987329	+	0.158684i	$0.0507250\pi$
$972$	−7.69616	−	6.45784i	−0.246854	−	0.207135i
$973$		0			0
$974$	−18.9689	+	6.90411i	−0.607802	+	0.221222i
$975$	12.2179	−	10.2520i	0.391285	−	0.328327i
$976$	0.409695	+	0.709613i	0.0131140	+	0.0227142i
$977$	1.32652	−	2.29761i	0.0424392	−	0.0735069i	−0.844026	−	0.536303i	$-0.819820\pi$
$977$	1.32652	−	2.29761i	0.0424392	−	0.0735069i	0.886465	+	0.462796i	$0.153154\pi$
$978$	5.47814	+	31.0681i	0.175172	+	0.993447i
$979$	1.28393	+	7.28153i	0.0410346	+	0.232719i
$980$		0			0
$981$	−12.9324	−	22.3995i	−0.412898	−	0.715161i
$982$	51.0792	−	42.8605i	1.63000	−	1.36773i
$983$	−31.5570	+	11.4858i	−1.00651	+	0.366340i	−0.792092	−	0.610402i	$-0.791008\pi$
$983$	−31.5570	+	11.4858i	−1.00651	+	0.366340i	−0.214419	+	0.976742i	$0.568786\pi$
$984$	14.9788	+	5.45184i	0.477507	+	0.173798i
$985$	−1.50514	−	1.26296i	−0.0479577	−	0.0402413i
$986$	−0.965064	+	5.47315i	−0.0307339	+	0.174301i
$987$		0			0
$988$	−4.12071	+	7.27402i	−0.131097	+	0.231417i
$989$	−2.82999			−0.0899885
$990$	0.0656052	−	0.372066i	0.00208507	−	0.0118250i
$991$	−24.2057	−	20.3110i	−0.768921	−	0.645201i	0.171511	−	0.985182i	$-0.445135\pi$
$991$	−24.2057	−	20.3110i	−0.768921	−	0.645201i	−0.940432	+	0.339981i	$0.889579\pi$
$992$	21.6362	+	7.87493i	0.686950	+	0.250029i
$993$	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
$997$	5.91647	+	33.5540i	0.187376	+	1.06266i	0.922864	+	0.385126i	$0.125842\pi$
$997$	5.91647	+	33.5540i	0.187376	+	1.06266i	−0.735488	+	0.677538i	$0.763047\pi$
$998$	2.09688	+	11.8920i	0.0663756	+	0.376435i
$999$	−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.w.b.834.4		30
7.2	even	3		931.2.v.e.606.2		30
7.3	odd	6		931.2.x.e.226.4		30
7.4	even	3		931.2.x.d.226.4		30
7.5	odd	6		931.2.v.d.606.2		30
7.6	odd	2		133.2.v.b.36.4	✓	30
19.9	even	9	inner	931.2.w.b.883.4		30
133.9	even	9		931.2.x.d.655.4		30
133.41	even	18		2527.2.a.s.1.5		15
133.47	odd	18		931.2.x.e.655.4		30
133.66	odd	18		931.2.v.d.275.2		30
133.104	odd	18		133.2.v.b.85.4	yes	30
133.111	odd	18		2527.2.a.r.1.11		15
133.123	even	9		931.2.v.e.275.2		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.v.b.36.4	✓	30	7.6	odd	2
133.2.v.b.85.4	yes	30	133.104	odd	18
931.2.v.d.275.2		30	133.66	odd	18
931.2.v.d.606.2		30	7.5	odd	6
931.2.v.e.275.2		30	133.123	even	9
931.2.v.e.606.2		30	7.2	even	3
931.2.w.b.834.4		30	1.1	even	1	trivial
931.2.w.b.883.4		30	19.9	even	9	inner
931.2.x.d.226.4		30	7.4	even	3
931.2.x.d.655.4		30	133.9	even	9
931.2.x.e.226.4		30	7.3	odd	6
931.2.x.e.655.4		30	133.47	odd	18
2527.2.a.r.1.11		15	133.111	odd	18
2527.2.a.s.1.5		15	133.41	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.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.282479 - 1.60202i) q^{2} +(-0.824180 - 0.691570i) q^{3} +(-0.607278 - 0.221031i) q^{4} +(0.0661285 - 0.0240688i) q^{5} +(-1.34072 + 1.12500i) q^{6} +(1.10109 - 1.90715i) q^{8} +(-0.319939 - 1.81447i) q^{9} +O(q^{10})\)	\(q+(0.282479 - 1.60202i) q^{2} +(-0.824180 - 0.691570i) q^{3} +(-0.607278 - 0.221031i) q^{4} +(0.0661285 - 0.0240688i) q^{5} +(-1.34072 + 1.12500i) q^{6} +(1.10109 - 1.90715i) q^{8} +(-0.319939 - 1.81447i) q^{9} +(-0.0198787 - 0.112738i) q^{10} +(-0.895617 + 1.55125i) q^{11} +(0.347648 + 0.602145i) q^{12} +(2.27346 - 1.90766i) q^{13} +(-0.0711470 - 0.0258954i) q^{15} +(-3.73436 - 3.13350i) q^{16} +(0.109331 - 0.620047i) q^{17} -2.99718 q^{18} +(3.31609 - 2.82906i) q^{19} -0.0454783 q^{20} +(2.23214 + 1.87299i) q^{22} +(1.40979 + 0.513123i) q^{23} +(-2.22642 + 0.810352i) q^{24} +(-3.82643 + 3.21075i) q^{25} +(-2.41390 - 4.18100i) 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} +(-2.70086 + 2.26629i) q^{32} +(1.81095 - 0.659132i) q^{33} +(-0.962442 - 0.350300i) q^{34} +(-0.206761 + 1.17260i) q^{36} +0.691141 q^{37} +(-3.59548 - 6.11157i) q^{38} -3.19303 q^{39} +(0.0269108 - 0.152619i) q^{40} +(-5.15375 - 4.32451i) q^{41} +(-1.77256 + 0.645159i) q^{43} +(0.886764 - 0.744083i) q^{44} +(-0.0648291 - 0.112287i) q^{45} +(1.22027 - 2.11357i) q^{46} +(0.241473 + 1.36946i) q^{47} +(0.910754 + 5.16514i) q^{48} +(4.06280 + 7.03697i) q^{50} +(-0.518914 + 0.435420i) q^{51} +(-1.80228 + 0.655975i) q^{52} +(-6.93416 - 2.52383i) q^{53} +(6.49238 + 5.44775i) q^{54} +(-0.0218890 + 0.124138i) q^{55} +(-4.68954 + 0.0383506i) q^{57} -8.82700 q^{58} +(-2.40797 + 13.6563i) q^{59} +(0.0374823 + 0.0314514i) q^{60} +(-0.157948 - 0.0574884i) q^{61} +(-9.98271 + 3.63341i) q^{62} +(-2.00716 - 3.47651i) q^{64} +(0.104426 - 0.180870i) q^{65} +(-0.544385 - 3.08736i) q^{66} +(-1.60409 - 9.09725i) q^{67} +(-0.203444 + 0.352375i) q^{68} +(-0.807065 - 1.39788i) q^{69} +(11.0779 - 4.03202i) q^{71} +(-3.81274 - 1.38772i) q^{72} +(8.59917 + 7.21556i) q^{73} +(0.195233 - 1.10722i) q^{74} +5.37413 q^{75} +(-2.63910 + 0.985067i) q^{76} +(-0.901962 + 5.11528i) q^{78} +(8.02843 + 6.73665i) q^{79} +(-0.322367 - 0.117332i) q^{80} +(0.0732713 - 0.0266686i) q^{81} +(-8.38377 + 7.03482i) q^{82} +(-3.37852 - 5.85176i) q^{83} +(-0.00769389 - 0.0436342i) q^{85} +(0.532845 + 3.02192i) q^{86} +(-2.91901 + 5.05588i) q^{87} +(1.97231 + 3.41615i) q^{88} +(3.16208 - 2.65330i) q^{89} +(-0.198199 + 0.0721386i) q^{90} +(-0.742721 - 0.623217i) q^{92} +(-1.22007 + 6.91938i) q^{93} +2.26212 q^{94} +(0.151196 - 0.266896i) q^{95} +3.79329 q^{96} +(0.928436 - 5.26542i) q^{97} +(3.10124 + 1.12876i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} - 6 q^{4} - 3 q^{5} + 9 q^{6} + 9 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 - 6 * q^4 - 3 * q^5 + 9 * q^6 + 9 * q^8 - 3 * q^9	\( 30 q + 3 q^{3} - 6 q^{4} - 3 q^{5} + 9 q^{6} + 9 q^{8} - 3 q^{9} + 36 q^{10} - 18 q^{12} - 30 q^{15} + 18 q^{16} - 12 q^{17} - 30 q^{18} - 6 q^{19} + 30 q^{20} + 12 q^{22} - 15 q^{23} - 45 q^{24} + 21 q^{25} + 45 q^{26} - 27 q^{27} + 21 q^{30} - 12 q^{31} - 75 q^{32} - 18 q^{33} + 42 q^{34} - 21 q^{36} - 36 q^{37} - 57 q^{38} - 24 q^{39} + 39 q^{40} - 3 q^{41} - 12 q^{43} + 72 q^{44} - 27 q^{45} + 6 q^{46} - 27 q^{47} - 18 q^{48} - 3 q^{50} - 27 q^{51} + 15 q^{52} - 15 q^{53} + 57 q^{54} - 33 q^{55} - 12 q^{57} - 60 q^{58} + 84 q^{59} + 75 q^{60} - 42 q^{61} - 96 q^{62} + 3 q^{64} + 45 q^{65} - 99 q^{66} + 39 q^{67} - 51 q^{68} - 15 q^{69} + 30 q^{71} - 117 q^{72} - 15 q^{73} + 24 q^{74} + 144 q^{75} - 84 q^{76} + 6 q^{78} + 12 q^{79} + 165 q^{80} - 15 q^{81} - 3 q^{82} - 12 q^{83} + 42 q^{85} - 48 q^{86} - 24 q^{87} + 36 q^{88} + 66 q^{89} - 180 q^{90} - 75 q^{92} + 30 q^{93} + 42 q^{94} - 15 q^{95} - 66 q^{96} + 63 q^{97} + 45 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 - 6 * q^4 - 3 * q^5 + 9 * q^6 + 9 * q^8 - 3 * q^9 + 36 * q^10 - 18 * q^12 - 30 * q^15 + 18 * q^16 - 12 * q^17 - 30 * q^18 - 6 * q^19 + 30 * q^20 + 12 * q^22 - 15 * q^23 - 45 * q^24 + 21 * q^25 + 45 * q^26 - 27 * q^27 + 21 * q^30 - 12 * q^31 - 75 * q^32 - 18 * q^33 + 42 * q^34 - 21 * q^36 - 36 * q^37 - 57 * q^38 - 24 * q^39 + 39 * q^40 - 3 * q^41 - 12 * q^43 + 72 * q^44 - 27 * q^45 + 6 * q^46 - 27 * q^47 - 18 * q^48 - 3 * q^50 - 27 * q^51 + 15 * q^52 - 15 * q^53 + 57 * q^54 - 33 * q^55 - 12 * q^57 - 60 * q^58 + 84 * q^59 + 75 * q^60 - 42 * q^61 - 96 * q^62 + 3 * q^64 + 45 * q^65 - 99 * q^66 + 39 * q^67 - 51 * q^68 - 15 * q^69 + 30 * q^71 - 117 * q^72 - 15 * q^73 + 24 * q^74 + 144 * q^75 - 84 * q^76 + 6 * q^78 + 12 * q^79 + 165 * q^80 - 15 * q^81 - 3 * q^82 - 12 * q^83 + 42 * q^85 - 48 * q^86 - 24 * q^87 + 36 * q^88 + 66 * q^89 - 180 * q^90 - 75 * q^92 + 30 * q^93 + 42 * q^94 - 15 * q^95 - 66 * q^96 + 63 * q^97 + 45 * q^99

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