LMFDB - Embedded newform 855.2.k.i.406.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(406,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("855.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.k (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 9x^{8} - 2x^{7} + 56x^{6} - 18x^{5} + 125x^{4} + x^{3} + 189x^{2} - 52x + 16 $ x^10 - x^9 + 9x^8 - 2x^7 + 56x^6 - 18x^5 + 125x^4 + x^3 + 189x^2 - 52*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 285)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			406.3
Root			$0.145349 - 0.251751i$ of defining polynomial
Character	$\chi$	$=$	855.406
Dual form			855.2.k.i.676.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.145349 - 0.251751i) q^{2} +(0.957748 - 1.65887i) q^{4} +(0.500000 + 0.866025i) q^{5} -0.486575 q^{7} -1.13822 q^{8} +(0.145349 - 0.251751i) q^{10} -5.34764 q^{11} +(1.24329 - 2.15344i) q^{13} +(0.0707229 + 0.122496i) q^{14} +(-1.75006 - 3.03119i) q^{16} +(-1.70780 - 2.95800i) q^{17} +(-2.46291 - 3.59640i) q^{19} +1.91550 q^{20} +(0.777272 + 1.34627i) q^{22} +(3.20619 - 5.55329i) q^{23} +(-0.500000 + 0.866025i) q^{25} -0.722840 q^{26} +(-0.466016 + 0.807163i) q^{28} +(1.38312 - 2.39564i) q^{29} +4.83099 q^{31} +(-1.64696 + 2.85262i) q^{32} +(-0.496454 + 0.859883i) q^{34} +(-0.243287 - 0.421386i) q^{35} -6.31756 q^{37} +(-0.547418 + 1.14277i) q^{38} +(-0.569112 - 0.985730i) q^{40} +(1.29070 + 2.23555i) q^{41} +(1.24329 + 2.15344i) q^{43} +(-5.12169 + 8.87102i) q^{44} -1.86406 q^{46} +(5.55533 - 9.62211i) q^{47} -6.76325 q^{49} +0.290697 q^{50} +(-2.38151 - 4.12490i) q^{52} +(1.49839 - 2.59529i) q^{53} +(-2.67382 - 4.63119i) q^{55} +0.553831 q^{56} -0.804139 q^{58} +(6.36659 + 11.0273i) q^{59} +(-5.92742 + 10.2666i) q^{61} +(-0.702178 - 1.21621i) q^{62} -6.04269 q^{64} +2.48657 q^{65} +(7.58770 - 13.1423i) q^{67} -6.54258 q^{68} +(-0.0707229 + 0.122496i) q^{70} +(-4.96452 - 8.59879i) q^{71} +(5.50642 + 9.53740i) q^{73} +(0.918249 + 1.59045i) q^{74} +(-8.32479 + 0.641189i) q^{76} +2.60202 q^{77} +(-4.06636 - 7.04314i) q^{79} +(1.75006 - 3.03119i) q^{80} +(0.375202 - 0.649869i) q^{82} +5.86106 q^{83} +(1.70780 - 2.95800i) q^{85} +(0.361420 - 0.625998i) q^{86} +6.08681 q^{88} +(-3.25521 + 5.63820i) q^{89} +(-0.604952 + 1.04781i) q^{91} +(-6.14145 - 10.6373i) q^{92} -3.22984 q^{94} +(1.88312 - 3.93114i) q^{95} +(-1.00000 - 1.73205i) q^{97} +(0.983028 + 1.70265i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 7 q^{4} + 5 q^{5} + 4 q^{7} + 12 q^{8} + q^{10} - 10 q^{11} + 8 q^{13} - 4 q^{14} - 7 q^{16} + 10 q^{17} + 5 q^{19} - 14 q^{20} - 2 q^{22} - 2 q^{23} - 5 q^{25} + 4 q^{26} - 10 q^{28} - 7 q^{29}+ \cdots + 21 q^{98}+O(q^{100}) $ 10 * q - q^2 - 7 * q^4 + 5 * q^5 + 4 * q^7 + 12 * q^8 + q^10 - 10 * q^11 + 8 * q^13 - 4 * q^14 - 7 * q^16 + 10 * q^17 + 5 * q^19 - 14 * q^20 - 2 * q^22 - 2 * q^23 - 5 * q^25 + 4 * q^26 - 10 * q^28 - 7 * q^29 - 18 * q^31 - 23 * q^32 - 25 * q^34 + 2 * q^35 + 12 * q^37 + 37 * q^38 + 6 * q^40 + 12 * q^41 + 8 * q^43 + 16 * q^44 - 40 * q^46 + 6 * q^47 + 30 * q^49 + 2 * q^50 + 4 * q^52 + 8 * q^53 - 5 * q^55 - 72 * q^56 + 76 * q^58 - q^59 - 7 * q^61 + 15 * q^62 + 28 * q^64 + 16 * q^65 + 14 * q^67 + 2 * q^68 + 4 * q^70 - 27 * q^71 - 26 * q^73 - 18 * q^74 - 56 * q^76 - 28 * q^77 - 23 * q^79 + 7 * q^80 + 36 * q^82 + 24 * q^83 - 10 * q^85 - 2 * q^86 - 9 * q^89 - 46 * q^91 - 52 * q^92 + 90 * q^94 - 2 * q^95 - 10 * q^97 + 21 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.145349	−	0.251751i	−0.102777	−	0.178015i	0.810051	−	0.586360i	$-0.199439\pi$
$2$	−0.145349	−	0.251751i	−0.102777	−	0.178015i	−0.912828	+	0.408345i	$0.866106\pi$
$3$		0			0
$3$		0			0
$4$	0.957748	−	1.65887i	0.478874	−	0.829434i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−0.486575			−0.183908			−0.0919539	−	0.995763i	$-0.529311\pi$
$7$	−0.486575			−0.183908			−0.0919539	+	0.995763i	$0.529311\pi$
$8$	−1.13822			−0.402423
$9$		0			0
$10$	0.145349	−	0.251751i	0.0459633	−	0.0796107i
$11$	−5.34764			−1.61237			−0.806187	−	0.591661i	$-0.798472\pi$
$11$	−5.34764			−1.61237			−0.806187	+	0.591661i	$0.798472\pi$
$12$		0			0
$13$	1.24329	−	2.15344i	0.344826	−	0.597256i	−0.640496	−	0.767961i	$-0.721271\pi$
$13$	1.24329	−	2.15344i	0.344826	−	0.597256i	0.985322	+	0.170705i	$0.0546046\pi$
$14$	0.0707229	+	0.122496i	0.0189015	+	0.0327384i
$15$		0			0
$16$	−1.75006	−	3.03119i	−0.437514	−	0.757796i
$17$	−1.70780	−	2.95800i	−0.414203	−	0.717421i	0.581141	−	0.813803i	$-0.302606\pi$
$17$	−1.70780	−	2.95800i	−0.414203	−	0.717421i	−0.995344	+	0.0963817i	$0.969273\pi$
$18$		0			0
$19$	−2.46291	−	3.59640i	−0.565029	−	0.825071i
$19$	−2.46291	−	3.59640i	−0.565029	−	0.825071i
$20$	1.91550			0.428318
$21$		0			0
$22$	0.777272	+	1.34627i	0.165715	+	0.287027i
$23$	3.20619	−	5.55329i	0.668537	−	1.15794i	−0.309776	−	0.950810i	$-0.600254\pi$
$23$	3.20619	−	5.55329i	0.668537	−	1.15794i	0.978313	−	0.207131i	$-0.0664126\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.722840			−0.141761
$27$		0			0
$28$	−0.466016	+	0.807163i	−0.0880687	+	0.152539i
$29$	1.38312	−	2.39564i	0.256839	−	0.444859i	−0.708554	−	0.705656i	$-0.750652\pi$
$29$	1.38312	−	2.39564i	0.256839	−	0.444859i	0.965393	+	0.260798i	$0.0839856\pi$
$30$		0			0
$31$	4.83099			0.867671			0.433836	−	0.900992i	$-0.357160\pi$
$31$	4.83099			0.867671			0.433836	+	0.900992i	$0.357160\pi$
$32$	−1.64696	+	2.85262i	−0.291144	+	0.504276i
$33$		0			0
$34$	−0.496454	+	0.859883i	−0.0851411	+	0.147469i
$35$	−0.243287	−	0.421386i	−0.0411231	−	0.0712272i
$36$		0			0
$37$	−6.31756			−1.03860			−0.519301	−	0.854592i	$-0.673808\pi$
$37$	−6.31756			−1.03860			−0.519301	+	0.854592i	$0.673808\pi$
$38$	−0.547418	+	1.14277i	−0.0888030	+	0.185382i
$39$		0			0
$40$	−0.569112	−	0.985730i	−0.0899845	−	0.155858i
$41$	1.29070	+	2.23555i	0.201573	+	0.349135i	0.949035	−	0.315169i	$-0.102061\pi$
$41$	1.29070	+	2.23555i	0.201573	+	0.349135i	−0.747462	+	0.664304i	$0.768728\pi$
$42$		0			0
$43$	1.24329	+	2.15344i	0.189600	+	0.328396i	0.945117	−	0.326733i	$-0.105948\pi$
$43$	1.24329	+	2.15344i	0.189600	+	0.328396i	−0.755517	+	0.655129i	$0.772614\pi$
$44$	−5.12169	+	8.87102i	−0.772123	+	1.33736i
$45$		0			0
$46$	−1.86406			−0.274841
$47$	5.55533	−	9.62211i	0.810328	−	1.40353i	−0.102306	−	0.994753i	$-0.532622\pi$
$47$	5.55533	−	9.62211i	0.810328	−	1.40353i	0.912634	−	0.408777i	$-0.134044\pi$
$48$		0			0
$49$	−6.76325			−0.966178
$50$	0.290697			0.0411108
$51$		0			0
$52$	−2.38151	−	4.12490i	−0.330256	−	0.572020i
$53$	1.49839	−	2.59529i	0.205820	−	0.356490i	−0.744574	−	0.667540i	$-0.767347\pi$
$53$	1.49839	−	2.59529i	0.205820	−	0.356490i	0.950394	+	0.311050i	$0.100681\pi$
$54$		0			0
$55$	−2.67382	−	4.63119i	−0.360538	−	0.624470i
$56$	0.553831			0.0740087
$57$		0			0
$58$	−0.804139			−0.105589
$59$	6.36659	+	11.0273i	0.828859	+	1.43563i	0.898934	+	0.438084i	$0.144343\pi$
$59$	6.36659	+	11.0273i	0.828859	+	1.43563i	−0.0700752	+	0.997542i	$0.522324\pi$
$60$		0			0
$61$	−5.92742	+	10.2666i	−0.758929	+	1.31450i	0.184469	+	0.982838i	$0.440944\pi$
$61$	−5.92742	+	10.2666i	−0.758929	+	1.31450i	−0.943397	+	0.331664i	$0.892390\pi$
$62$	−0.702178	−	1.21621i	−0.0891767	−	0.154458i
$63$		0			0
$64$	−6.04269			−0.755336
$65$	2.48657			0.308422
$66$		0			0
$67$	7.58770	−	13.1423i	0.926985	−	1.60559i	0.138649	−	0.990342i	$-0.455724\pi$
$67$	7.58770	−	13.1423i	0.926985	−	1.60559i	0.788336	−	0.615244i	$-0.210943\pi$
$68$	−6.54258			−0.793404
$69$		0			0
$70$	−0.0707229	+	0.122496i	−0.00845301	+	0.0146410i
$71$	−4.96452	−	8.59879i	−0.589180	−	1.02049i	−0.994340	−	0.106244i	$-0.966118\pi$
$71$	−4.96452	−	8.59879i	−0.589180	−	1.02049i	0.405160	−	0.914246i	$-0.367216\pi$
$72$		0			0
$73$	5.50642	+	9.53740i	0.644478	+	1.11627i	0.984422	+	0.175823i	$0.0562585\pi$
$73$	5.50642	+	9.53740i	0.644478	+	1.11627i	−0.339944	+	0.940446i	$0.610408\pi$
$74$	0.918249	+	1.59045i	0.106744	+	0.184887i
$75$		0			0
$76$	−8.32479	+	0.641189i	−0.954919	+	0.0735494i
$77$	2.60202			0.296528
$78$		0			0
$79$	−4.06636	−	7.04314i	−0.457501	−	0.792415i	0.541327	−	0.840812i	$-0.317922\pi$
$79$	−4.06636	−	7.04314i	−0.457501	−	0.792415i	−0.998828	+	0.0483971i	$0.984589\pi$
$80$	1.75006	−	3.03119i	0.195662	−	0.338897i
$81$		0			0
$82$	0.375202	−	0.649869i	0.0414341	−	0.0717660i
$83$	5.86106			0.643335			0.321668	−	0.946853i	$-0.395757\pi$
$83$	5.86106			0.643335			0.321668	+	0.946853i	$0.395757\pi$
$84$		0			0
$85$	1.70780	−	2.95800i	0.185237	−	0.320840i
$86$	0.361420	−	0.625998i	0.0389729	−	0.0675031i
$87$		0			0
$88$	6.08681			0.648856
$89$	−3.25521	+	5.63820i	−0.345052	+	0.597647i	−0.985363	−	0.170468i	$-0.945472\pi$
$89$	−3.25521	+	5.63820i	−0.345052	+	0.597647i	0.640311	+	0.768116i	$0.278805\pi$
$90$		0			0
$91$	−0.604952	+	1.04781i	−0.0634162	+	0.109840i
$92$	−6.14145	−	10.6373i	−0.640290	−	1.10901i
$93$		0			0
$94$	−3.22984			−0.333132
$95$	1.88312	−	3.93114i	0.193204	−	0.403326i
$96$		0			0
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	0.983028	+	1.70265i	0.0993008	+	0.171994i
$99$		0			0
$100$	0.957748	+	1.65887i	0.0957748	+	0.165887i
$101$	0.758324	−	1.31346i	0.0754561	−	0.130694i	−0.825828	−	0.563921i	$-0.809292\pi$
$101$	0.758324	−	1.31346i	0.0754561	−	0.130694i	0.901285	+	0.433228i	$0.142625\pi$
$102$		0			0
$103$	−9.15478			−0.902047			−0.451023	−	0.892512i	$-0.648941\pi$
$103$	−9.15478			−0.902047			−0.451023	+	0.892512i	$0.648941\pi$
$104$	−1.41514	+	2.45109i	−0.138766	+	0.240349i
$105$		0			0
$106$	−0.871155			−0.0846140
$107$	−0.138936			−0.0134315			−0.00671574	−	0.999977i	$-0.502138\pi$
$107$	−0.138936			−0.0134315			−0.00671574	+	0.999977i	$0.502138\pi$
$108$		0			0
$109$	7.86497	+	13.6225i	0.753328	+	1.30480i	0.946201	+	0.323579i	$0.104886\pi$
$109$	7.86497	+	13.6225i	0.753328	+	1.30480i	−0.192873	+	0.981224i	$0.561781\pi$
$110$	−0.777272	+	1.34627i	−0.0741099	+	0.128362i
$111$		0			0
$112$	0.851533	+	1.47490i	0.0804623	+	0.139365i
$113$	−14.8011			−1.39237			−0.696187	−	0.717860i	$-0.745122\pi$
$113$	−14.8011			−1.39237			−0.696187	+	0.717860i	$0.745122\pi$
$114$		0			0
$115$	6.41238			0.597958
$116$	−2.64936	−	4.58883i	−0.245987	−	0.426062i
$117$		0			0
$118$	1.85075	−	3.20559i	0.170375	−	0.295099i
$119$	0.830974	+	1.43929i	0.0761752	+	0.131939i
$120$		0			0
$121$	17.5972			1.59975
$122$	3.44617			0.312002
$123$		0			0
$124$	4.62687	−	8.01397i	0.415505	−	0.719676i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	4.91550	−	8.51389i	0.436180	−	0.755485i	−0.561211	−	0.827672i	$-0.689665\pi$
$127$	4.91550	−	8.51389i	0.436180	−	0.755485i	0.997391	+	0.0721871i	$0.0229979\pi$
$128$	4.17222	+	7.22649i	0.368775	+	0.638738i
$129$		0			0
$130$	−0.361420	−	0.625998i	−0.0316986	−	0.0549037i
$131$	7.11459	+	12.3228i	0.621605	+	1.07665i	0.989187	+	0.146660i	$0.0468524\pi$
$131$	7.11459	+	12.3228i	0.621605	+	1.07665i	−0.367582	+	0.929991i	$0.619814\pi$
$132$		0			0
$133$	1.19839	+	1.74992i	0.103913	+	0.151737i
$134$	−4.41145			−0.381091
$135$		0			0
$136$	1.94386	+	3.36687i	0.166685	+	0.288707i
$137$	3.29220	−	5.70225i	0.281271	−	0.487176i	−0.690427	−	0.723402i	$-0.742577\pi$
$137$	3.29220	−	5.70225i	0.281271	−	0.487176i	0.971698	+	0.236226i	$0.0759106\pi$
$138$		0			0
$139$	−0.116878	+	0.202439i	−0.00991347	+	0.0171706i	−0.870940	−	0.491390i	$-0.836489\pi$
$139$	−0.116878	+	0.202439i	−0.00991347	+	0.0171706i	0.861026	+	0.508561i	$0.169822\pi$
$140$	−0.932031			−0.0787710
$141$		0			0
$142$	−1.44317	+	2.49965i	−0.121108	+	0.209766i
$143$	−6.64865	+	11.5158i	−0.555988	+	0.963000i
$144$		0			0
$145$	2.76624			0.229724
$146$	1.60070	−	2.77250i	0.132475	−	0.229453i
$147$		0			0
$148$	−6.05063	+	10.4800i	−0.497359	+	0.861451i
$149$	−1.33650	−	2.31488i	−0.109490	−	0.189642i	0.806074	−	0.591815i	$-0.201588\pi$
$149$	−1.33650	−	2.31488i	−0.109490	−	0.189642i	−0.915564	+	0.402173i	$0.868255\pi$
$150$		0			0
$151$	5.95266			0.484421			0.242210	−	0.970224i	$-0.422128\pi$
$151$	5.95266			0.484421			0.242210	+	0.970224i	$0.422128\pi$
$152$	2.80334	+	4.09351i	0.227381	+	0.332027i
$153$		0			0
$154$	−0.378201	−	0.655063i	−0.0304763	−	0.0527865i
$155$	2.41550	+	4.18376i	0.194017	+	0.336048i
$156$		0			0
$157$	3.60424	+	6.24273i	0.287650	+	0.498224i	0.973248	−	0.229756i	$-0.0737928\pi$
$157$	3.60424	+	6.24273i	0.287650	+	0.498224i	−0.685599	+	0.727980i	$0.740459\pi$
$158$	−1.18208	+	2.04742i	−0.0940411	+	0.162884i
$159$		0			0
$160$	−3.29392			−0.260407
$161$	−1.56005	+	2.70209i	−0.122949	+	0.212954i
$162$		0			0
$163$	14.1756			1.11032			0.555161	−	0.831743i	$-0.312657\pi$
$163$	14.1756			1.11032			0.555161	+	0.831743i	$0.312657\pi$
$164$	4.94465			0.386112
$165$		0			0
$166$	−0.851897	−	1.47553i	−0.0661201	−	0.114523i
$167$	6.27817	−	10.8741i	0.485819	−	0.841464i	−0.514048	−	0.857762i	$-0.671855\pi$
$167$	6.27817	−	10.8741i	0.485819	−	0.841464i	0.999867	+	0.0162977i	$0.00518794\pi$
$168$		0			0
$169$	3.40847	+	5.90365i	0.262190	+	0.454127i
$170$	−0.992907			−0.0761525
$171$		0			0
$172$	4.76302			0.363177
$173$	1.09482	+	1.89628i	0.0832376	+	0.144172i	0.904639	−	0.426179i	$-0.140141\pi$
$173$	1.09482	+	1.89628i	0.0832376	+	0.144172i	−0.821401	+	0.570351i	$0.806807\pi$
$174$		0			0
$175$	0.243287	−	0.421386i	0.0183908	−	0.0318538i
$176$	9.35867	+	16.2097i	0.705436	+	1.22185i
$177$		0			0
$178$	1.89256			0.141854
$179$	−7.50421			−0.560891			−0.280445	−	0.959870i	$-0.590482\pi$
$179$	−7.50421			−0.560891			−0.280445	+	0.959870i	$0.590482\pi$
$180$		0			0
$181$	6.33260	−	10.9684i	0.470699	−	0.815274i	−0.528740	−	0.848784i	$-0.677335\pi$
$181$	6.33260	−	10.9684i	0.470699	−	0.815274i	0.999438	+	0.0335101i	$0.0106686\pi$
$182$	0.351716			0.0260709
$183$		0			0
$184$	−3.64936	+	6.32088i	−0.269035	+	0.465982i
$185$	−3.15878	−	5.47117i	−0.232238	−	0.402249i
$186$		0			0
$187$	9.13272	+	15.8183i	0.667850	+	1.15675i
$188$	−10.6412	−	18.4311i	−0.776090	−	1.34423i
$189$		0			0
$190$	−1.26338	+	0.0973074i	−0.0916551	+	0.00705942i
$191$	−8.15777			−0.590276			−0.295138	−	0.955455i	$-0.595366\pi$
$191$	−8.15777			−0.590276			−0.295138	+	0.955455i	$0.595366\pi$
$192$		0			0
$193$	1.68252	+	2.91422i	0.121111	+	0.209770i	0.920206	−	0.391435i	$-0.128021\pi$
$193$	1.68252	+	2.91422i	0.121111	+	0.209770i	−0.799095	+	0.601204i	$0.794688\pi$
$194$	−0.290697	+	0.503502i	−0.0208708	+	0.0361494i
$195$		0			0
$196$	−6.47748	+	11.2193i	−0.462677	+	0.801381i
$197$	−3.83399			−0.273160			−0.136580	−	0.990629i	$-0.543611\pi$
$197$	−3.83399			−0.273160			−0.136580	+	0.990629i	$0.543611\pi$
$198$		0			0
$199$	−6.34925	+	10.9972i	−0.450086	+	0.779572i	−0.998391	−	0.0567063i	$-0.981940\pi$
$199$	−6.34925	+	10.9972i	−0.450086	+	0.779572i	0.548305	+	0.836279i	$0.315273\pi$
$200$	0.569112	−	0.985730i	0.0402423	−	0.0697017i
$201$		0			0
$202$	−0.440885			−0.0310206
$203$	−0.672992	+	1.16566i	−0.0472348	+	0.0818130i
$204$		0			0
$205$	−1.29070	+	2.23555i	−0.0901462	+	0.156138i
$206$	1.33063	+	2.30473i	0.0927097	+	0.160578i
$207$		0			0
$208$	−8.70329			−0.603465
$209$	13.1707	+	19.2323i	0.911038	+	1.33032i
$210$		0			0
$211$	4.57828	+	7.92982i	0.315182	+	0.545911i	0.979476	−	0.201560i	$-0.0646011\pi$
$211$	4.57828	+	7.92982i	0.315182	+	0.545911i	−0.664294	+	0.747471i	$0.731268\pi$
$212$	−2.87016	−	4.97126i	−0.197123	−	0.341427i
$213$		0			0
$214$	0.0201942	+	0.0349774i	0.00138045	+	0.00239100i
$215$	−1.24329	+	2.15344i	−0.0847915	+	0.146863i
$216$		0			0
$217$	−2.35064			−0.159572
$218$	2.28633	−	3.96003i	0.154850	−	0.268207i
$219$		0			0
$220$	−10.2434			−0.690608
$221$	−8.49316			−0.571312
$222$		0			0
$223$	−5.44877	−	9.43754i	−0.364876	−	0.631984i	0.623880	−	0.781520i	$-0.285555\pi$
$223$	−5.44877	−	9.43754i	−0.364876	−	0.631984i	−0.988756	+	0.149536i	$0.952222\pi$
$224$	0.801369	−	1.38801i	0.0535437	−	0.0927404i
$225$		0			0
$226$	2.15133	+	3.72620i	0.143104	+	0.247863i
$227$	24.6351			1.63509			0.817545	−	0.575864i	$-0.195334\pi$
$227$	24.6351			1.63509			0.817545	+	0.575864i	$0.195334\pi$
$228$		0			0
$229$	17.1676			1.13447			0.567234	−	0.823557i	$-0.308013\pi$
$229$	17.1676			1.13447			0.567234	+	0.823557i	$0.308013\pi$
$230$	−0.932031	−	1.61433i	−0.0614563	−	0.106445i
$231$		0			0
$232$	−1.57430	+	2.72677i	−0.103358	+	0.179021i
$233$	14.2316	+	24.6498i	0.932341	+	1.61486i	0.779309	+	0.626640i	$0.215570\pi$
$233$	14.2316	+	24.6498i	0.932341	+	1.61486i	0.153032	+	0.988221i	$0.451096\pi$
$234$		0			0
$235$	11.1107			0.724780
$236$	24.3903			1.58768
$237$		0			0
$238$	0.241562	−	0.418397i	0.0156581	−	0.0271207i
$239$	−4.07741			−0.263746			−0.131873	−	0.991267i	$-0.542099\pi$
$239$	−4.07741			−0.263746			−0.131873	+	0.991267i	$0.542099\pi$
$240$		0			0
$241$	6.33421	−	10.9712i	0.408023	−	0.706716i	−0.586646	−	0.809844i	$-0.699552\pi$
$241$	6.33421	−	10.9712i	0.408023	−	0.706716i	0.994668	+	0.103128i	$0.0328852\pi$
$242$	−2.55773	−	4.43012i	−0.164417	−	0.284779i
$243$		0			0
$244$	11.3539	+	19.6656i	0.726862	+	1.25896i
$245$	−3.38162	−	5.85714i	−0.216044	−	0.374199i
$246$		0			0
$247$	−10.8067	+	0.832351i	−0.687615	+	0.0529612i
$248$	−5.49875			−0.349171
$249$		0			0
$250$	0.145349	+	0.251751i	0.00919265	+	0.0159221i
$251$	−5.81204	+	10.0668i	−0.366853	+	0.635408i	−0.989072	−	0.147436i	$-0.952898\pi$
$251$	−5.81204	+	10.0668i	−0.366853	+	0.635408i	0.622219	+	0.782843i	$0.286231\pi$
$252$		0			0
$253$	−17.1456	+	29.6970i	−1.07793	+	1.86703i
$254$	−2.85784			−0.179317
$255$		0			0
$256$	−4.82984	+	8.36553i	−0.301865	+	0.522845i
$257$	5.27416	−	9.13512i	0.328993	−	0.569833i	−0.653319	−	0.757083i	$-0.726624\pi$
$257$	5.27416	−	9.13512i	0.328993	−	0.569833i	0.982312	+	0.187250i	$0.0599574\pi$
$258$		0			0
$259$	3.07397			0.191007
$260$	2.38151	−	4.12490i	0.147695	−	0.255815i
$261$		0			0
$262$	2.06819	−	3.58221i	0.127773	−	0.221310i
$263$	11.8967	+	20.6058i	0.733585	+	1.27061i	0.955341	+	0.295504i	$0.0954876\pi$
$263$	11.8967	+	20.6058i	0.733585	+	1.27061i	−0.221757	+	0.975102i	$0.571179\pi$
$264$		0			0
$265$	2.99678			0.184091
$266$	0.266360	−	0.556043i	0.0163316	−	0.0340932i
$267$		0			0
$268$	−14.5342	−	25.1740i	−0.887818	−	1.53775i
$269$	−2.11377	−	3.66115i	−0.128879	−	0.223224i	0.794364	−	0.607442i	$-0.207804\pi$
$269$	−2.11377	−	3.66115i	−0.128879	−	0.223224i	−0.923242	+	0.384218i	$0.874471\pi$
$270$		0			0
$271$	−15.5736	−	26.9742i	−0.946027	−	1.63857i	−0.753682	−	0.657239i	$-0.771724\pi$
$271$	−15.5736	−	26.9742i	−0.946027	−	1.63857i	−0.192344	−	0.981328i	$-0.561609\pi$
$272$	−5.97750	+	10.3533i	−0.362439	+	0.627763i
$273$		0			0
$274$	−1.91406			−0.115633
$275$	2.67382	−	4.63119i	0.161237	−	0.279271i
$276$		0			0
$277$	1.05393			0.0633243			0.0316621	−	0.999499i	$-0.489920\pi$
$277$	1.05393			0.0633243			0.0316621	+	0.999499i	$0.489920\pi$
$278$	0.0679523			0.00407551
$279$		0			0
$280$	0.276915	+	0.479631i	0.0165489	+	0.0286635i
$281$	12.8177	−	22.2009i	0.764638	−	1.32439i	−0.175799	−	0.984426i	$-0.556251\pi$
$281$	12.8177	−	22.2009i	0.764638	−	1.32439i	0.940437	−	0.339967i	$-0.110416\pi$
$282$		0			0
$283$	−14.7056	−	25.4708i	−0.874157	−	1.51408i	−0.857658	−	0.514220i	$-0.828082\pi$
$283$	−14.7056	−	25.4708i	−0.874157	−	1.51408i	−0.0164983	−	0.999864i	$-0.505252\pi$
$284$	−19.0190			−1.12857
$285$		0			0
$286$	3.86549			0.228571
$287$	−0.628020	−	1.08776i	−0.0370709	−	0.0642086i
$288$		0			0
$289$	2.66681	−	4.61906i	0.156871	−	0.271709i
$290$	−0.402070	−	0.696405i	−0.0236103	−	0.0408943i
$291$		0			0
$292$	21.0950			1.23449
$293$	10.8548			0.634147			0.317073	−	0.948401i	$-0.397300\pi$
$293$	10.8548			0.634147			0.317073	+	0.948401i	$0.397300\pi$
$294$		0			0
$295$	−6.36659	+	11.0273i	−0.370677	+	0.642031i
$296$	7.19080			0.417957
$297$		0			0
$298$	−0.388516	+	0.672929i	−0.0225061	+	0.0389817i
$299$	−7.97244	−	13.8087i	−0.461058	−	0.798576i
$300$		0			0
$301$	−0.604952	−	1.04781i	−0.0348688	−	0.0603946i
$302$	−0.865211	−	1.49859i	−0.0497873	−	0.0862341i
$303$		0			0
$304$	−6.59114	+	13.7594i	−0.378028	+	0.789157i
$305$	−11.8548			−0.678806
$306$		0			0
$307$	−16.8445	−	29.1756i	−0.961368	−	1.66514i	−0.719072	−	0.694936i	$-0.755433\pi$
$307$	−16.8445	−	29.1756i	−0.961368	−	1.66514i	−0.242296	−	0.970202i	$-0.577901\pi$
$308$	2.49208	−	4.31641i	0.142000	−	0.245950i
$309$		0			0
$310$	0.702178	−	1.21621i	0.0398810	−	0.0690759i
$311$	11.7221			0.664701			0.332350	−	0.943156i	$-0.392158\pi$
$311$	11.7221			0.664701			0.332350	+	0.943156i	$0.392158\pi$
$312$		0			0
$313$	−2.23928	+	3.87855i	−0.126572	+	0.219229i	−0.922346	−	0.386364i	$-0.873731\pi$
$313$	−2.23928	+	3.87855i	−0.126572	+	0.219229i	0.795775	+	0.605593i	$0.207064\pi$
$314$	1.04774	−	1.81474i	0.0591275	−	0.102412i
$315$		0			0
$316$	−15.5782			−0.876341
$317$	6.19367	−	10.7277i	0.347871	−	0.602530i	−0.638000	−	0.770036i	$-0.720238\pi$
$317$	6.19367	−	10.7277i	0.347871	−	0.602530i	0.985871	+	0.167506i	$0.0535714\pi$
$318$		0			0
$319$	−7.39644	+	12.8110i	−0.414121	+	0.717278i
$320$	−3.02135	−	5.23312i	−0.168898	−	0.292541i
$321$		0			0
$322$	0.907005			0.0505454
$323$	−6.43200	+	13.4272i	−0.357886	+	0.747111i
$324$		0			0
$325$	1.24329	+	2.15344i	0.0689652	+	0.119451i
$326$	−2.06041	−	3.56873i	−0.114115	−	0.197654i
$327$		0			0
$328$	−1.46910	−	2.54456i	−0.0811176	−	0.140500i
$329$	−2.70308	+	4.68188i	−0.149026	+	0.258120i
$330$		0			0
$331$	24.5058			1.34696			0.673480	−	0.739206i	$-0.264799\pi$
$331$	24.5058			1.34696			0.673480	+	0.739206i	$0.264799\pi$
$332$	5.61342	−	9.72273i	0.308076	−	0.533604i
$333$		0			0
$334$	−3.65009			−0.199724
$335$	15.1754			0.829121
$336$		0			0
$337$	−5.25038	−	9.09392i	−0.286006	−	0.495378i	0.686846	−	0.726803i	$-0.258995\pi$
$337$	−5.25038	−	9.09392i	−0.286006	−	0.495378i	−0.972853	+	0.231425i	$0.925661\pi$
$338$	0.990834	−	1.71617i	0.0538942	−	0.0933476i
$339$		0			0
$340$	−3.27129	−	5.66604i	−0.177411	−	0.307284i
$341$	−25.8344			−1.39901
$342$		0			0
$343$	6.69684			0.361596
$344$	−1.41514	−	2.45109i	−0.0762992	−	0.132154i
$345$		0			0
$346$	0.318261	−	0.551244i	0.0171098	−	0.0296351i
$347$	−0.727562	−	1.26017i	−0.0390576	−	0.0676497i	0.845836	−	0.533443i	$-0.179102\pi$
$347$	−0.727562	−	1.26017i	−0.0390576	−	0.0676497i	−0.884893	+	0.465794i	$0.845769\pi$
$348$		0			0
$349$	23.7332			1.27041			0.635204	−	0.772345i	$-0.280916\pi$
$349$	23.7332			1.27041			0.635204	+	0.772345i	$0.280916\pi$
$350$	−0.141446			−0.00756060
$351$		0			0
$352$	8.80735	−	15.2548i	0.469433	−	0.813082i
$353$	7.39055			0.393359			0.196680	−	0.980468i	$-0.436984\pi$
$353$	7.39055			0.393359			0.196680	+	0.980468i	$0.436984\pi$
$354$		0			0
$355$	4.96452	−	8.59879i	0.263489	−	0.456377i
$356$	6.23535	+	10.7999i	0.330473	+	0.572395i
$357$		0			0
$358$	1.09073	+	1.88919i	0.0576467	+	0.0998469i
$359$	1.17934	+	2.04268i	0.0622433	+	0.107808i	0.895468	−	0.445126i	$-0.146841\pi$
$359$	1.17934	+	2.04268i	0.0622433	+	0.107808i	−0.833225	+	0.552935i	$0.813508\pi$
$360$		0			0
$361$	−6.86820	+	17.7152i	−0.361484	+	0.932378i
$362$	−3.68174			−0.193508
$363$		0			0
$364$	1.15878	+	2.00707i	0.0607367	+	0.105199i
$365$	−5.50642	+	9.53740i	−0.288219	+	0.499210i
$366$		0			0
$367$	11.0743	−	19.1812i	0.578073	−	1.00125i	−0.417628	−	0.908618i	$-0.637138\pi$
$367$	11.0743	−	19.1812i	0.578073	−	1.00125i	0.995700	−	0.0926329i	$-0.0295283\pi$
$368$	−22.4441			−1.16998
$369$		0			0
$370$	−0.918249	+	1.59045i	−0.0477375	+	0.0826838i
$371$	−0.729078	+	1.26280i	−0.0378518	+	0.0655613i
$372$		0			0
$373$	31.1738			1.61412			0.807060	−	0.590469i	$-0.201057\pi$
$373$	31.1738			1.61412			0.807060	+	0.590469i	$0.201057\pi$
$374$	2.65485	−	4.59834i	0.137279	−	0.237775i
$375$		0			0
$376$	−6.32321	+	10.9521i	−0.326094	+	0.564812i
$377$	−3.43924	−	5.95693i	−0.177130	−	0.306798i
$378$		0			0
$379$	−26.0349			−1.33732			−0.668662	−	0.743567i	$-0.733132\pi$
$379$	−26.0349			−1.33732			−0.668662	+	0.743567i	$0.733132\pi$
$380$	−4.71768	−	6.88889i	−0.242012	−	0.353393i
$381$		0			0
$382$	1.18572	+	2.05373i	0.0606668	+	0.105078i
$383$	−1.06647	−	1.84718i	−0.0544941	−	0.0943865i	0.837492	−	0.546450i	$-0.184021\pi$
$383$	−1.06647	−	1.84718i	−0.0544941	−	0.0943865i	−0.891986	+	0.452064i	$0.850688\pi$
$384$		0			0
$385$	1.30101	+	2.25342i	0.0663057	+	0.114845i
$386$	0.489105	−	0.847154i	0.0248948	−	0.0431190i
$387$		0			0
$388$	−3.83099			−0.194489
$389$	−6.52135	+	11.2953i	−0.330645	+	0.572695i	−0.982639	−	0.185530i	$-0.940600\pi$
$389$	−6.52135	+	11.2953i	−0.330645	+	0.572695i	0.651993	+	0.758225i	$0.273933\pi$
$390$		0			0
$391$	−21.9022			−1.10764
$392$	7.69808			0.388812
$393$		0			0
$394$	0.557265	+	0.965211i	0.0280746	+	0.0486266i
$395$	4.06636	−	7.04314i	0.204601	−	0.354379i
$396$		0			0
$397$	−0.0143214	−	0.0248054i	−0.000718770	−	0.00124495i	0.865666	−	0.500622i	$-0.166895\pi$
$397$	−0.0143214	−	0.0248054i	−0.000718770	−	0.00124495i	−0.866385	+	0.499377i	$0.833562\pi$
$398$	3.69142			0.185034
$399$		0			0
$400$	3.50011			0.175006
$401$	−13.6596	−	23.6591i	−0.682126	−	1.18148i	−0.974331	−	0.225122i	$-0.927722\pi$
$401$	−13.6596	−	23.6591i	−0.682126	−	1.18148i	0.292204	−	0.956356i	$-0.405611\pi$
$402$		0			0
$403$	6.00631	−	10.4032i	0.299196	−	0.518222i
$404$	−1.45257	−	2.51592i	−0.0722679	−	0.125172i
$405$		0			0
$406$	0.391274			0.0194186
$407$	33.7841			1.67461
$408$		0			0
$409$	3.36958	−	5.83629i	0.166615	−	0.288586i	−0.770612	−	0.637304i	$-0.780050\pi$
$409$	3.36958	−	5.83629i	0.166615	−	0.288586i	0.937228	+	0.348718i	$0.113383\pi$
$410$	0.750404			0.0370598
$411$		0			0
$412$	−8.76796	+	15.1866i	−0.431967	+	0.748188i
$413$	−3.09782	−	5.36558i	−0.152434	−	0.264023i
$414$		0			0
$415$	2.93053	+	5.07583i	0.143854	+	0.249163i
$416$	4.09529	+	7.09325i	0.200788	+	0.347775i
$417$		0			0
$418$	2.92739	−	6.11113i	0.143184	−	0.298905i
$419$	−26.4076			−1.29010			−0.645048	−	0.764142i	$-0.723163\pi$
$419$	−26.4076			−1.29010			−0.645048	+	0.764142i	$0.723163\pi$
$420$		0			0
$421$	−18.9448	−	32.8133i	−0.923311	−	1.59922i	−0.794255	−	0.607584i	$-0.792139\pi$
$421$	−18.9448	−	32.8133i	−0.923311	−	1.59922i	−0.129056	−	0.991637i	$-0.541195\pi$
$422$	1.33089	−	2.30518i	0.0647869	−	0.112214i
$423$		0			0
$424$	−1.70550	+	2.95401i	−0.0828265	+	0.143460i
$425$	3.41561			0.165681
$426$		0			0
$427$	2.88413	−	4.99546i	0.139573	−	0.241747i
$428$	−0.133066	+	0.230477i	−0.00643198	+	0.0111405i
$429$		0			0
$430$	0.722840			0.0348585
$431$	−9.60285	+	16.6326i	−0.462553	+	0.801165i	−0.999087	−	0.0427131i	$-0.986400\pi$
$431$	−9.60285	+	16.6326i	−0.462553	+	0.801165i	0.536534	+	0.843879i	$0.319733\pi$
$432$		0			0
$433$	−8.47562	+	14.6802i	−0.407312	+	0.705485i	−0.994588	−	0.103902i	$-0.966867\pi$
$433$	−8.47562	+	14.6802i	−0.407312	+	0.705485i	0.587275	+	0.809387i	$0.300201\pi$
$434$	0.341662	+	0.591776i	0.0164003	+	0.0284061i
$435$		0			0
$436$	30.1306			1.44300
$437$	−27.8684	+	2.14647i	−1.33313	+	0.102680i
$438$		0			0
$439$	−5.55143	−	9.61536i	−0.264955	−	0.458916i	0.702597	−	0.711588i	$-0.252024\pi$
$439$	−5.55143	−	9.61536i	−0.264955	−	0.458916i	−0.967552	+	0.252672i	$0.918691\pi$
$440$	3.04340	+	5.27133i	0.145089	+	0.251301i
$441$		0			0
$442$	1.23447	+	2.13816i	0.0587177	+	0.101702i
$443$	−6.94708	+	12.0327i	−0.330066	+	0.571691i	−0.982524	−	0.186133i	$-0.940404\pi$
$443$	−6.94708	+	12.0327i	−0.330066	+	0.571691i	0.652459	+	0.757824i	$0.273738\pi$
$444$		0			0
$445$	−6.51043			−0.308624
$446$	−1.58394	+	2.74347i	−0.0750018	+	0.129907i
$447$		0			0
$448$	2.94022			0.138912
$449$	−27.8675			−1.31515			−0.657573	−	0.753391i	$-0.728417\pi$
$449$	−27.8675			−1.31515			−0.657573	+	0.753391i	$0.728417\pi$
$450$		0			0
$451$	−6.90218	−	11.9549i	−0.325011	−	0.562936i
$452$	−14.1758	+	24.5531i	−0.666772	+	1.15488i
$453$		0			0
$454$	−3.58068	−	6.20192i	−0.168050	−	0.291071i
$455$	−1.20990			−0.0567212
$456$		0			0
$457$	−36.5660			−1.71048			−0.855242	−	0.518229i	$-0.826591\pi$
$457$	−36.5660			−1.71048			−0.855242	+	0.518229i	$0.826591\pi$
$458$	−2.49529	−	4.32197i	−0.116597	−	0.201952i
$459$		0			0
$460$	6.14145	−	10.6373i	0.286346	−	0.495966i
$461$	10.9590	+	18.9816i	0.510412	+	0.884059i	0.999927	+	0.0120646i	$0.00384039\pi$
$461$	10.9590	+	18.9816i	0.510412	+	0.884059i	−0.489515	+	0.871995i	$0.662826\pi$
$462$		0			0
$463$	−14.0255			−0.651821			−0.325910	−	0.945401i	$-0.605671\pi$
$463$	−14.0255			−0.651821			−0.325910	+	0.945401i	$0.605671\pi$
$464$	−9.68216			−0.449483
$465$		0			0
$466$	4.13707	−	7.16562i	0.191646	−	0.331941i
$467$	−33.9294			−1.57007			−0.785033	−	0.619453i	$-0.787354\pi$
$467$	−33.9294			−1.57007			−0.785033	+	0.619453i	$0.787354\pi$
$468$		0			0
$469$	−3.69198	+	6.39470i	−0.170480	+	0.295280i
$470$	−1.61492	−	2.79712i	−0.0744906	−	0.129022i
$471$		0			0
$472$	−7.24660	−	12.5515i	−0.333552	−	0.577728i
$473$	−6.64865	−	11.5158i	−0.305705	−	0.529497i
$474$		0			0
$475$	4.34603	−	0.334738i	0.199409	−	0.0153588i
$476$	3.18345			0.145913
$477$		0			0
$478$	0.592646	+	1.02649i	0.0271070	+	0.0469507i
$479$	15.9748	−	27.6692i	0.729909	−	1.26424i	−0.227012	−	0.973892i	$-0.572896\pi$
$479$	15.9748	−	27.6692i	0.729909	−	1.26424i	0.956921	−	0.290348i	$-0.0937711\pi$
$480$		0			0
$481$	−7.85455	+	13.6045i	−0.358137	+	0.620311i
$482$	−3.68268			−0.167741
$483$		0			0
$484$	16.8537	−	29.1915i	0.766078	−	1.32689i
$485$	1.00000	−	1.73205i	0.0454077	−	0.0786484i
$486$		0			0
$487$	37.6229			1.70486			0.852428	−	0.522844i	$-0.175129\pi$
$487$	37.6229			1.70486			0.852428	+	0.522844i	$0.175129\pi$
$488$	6.74673	−	11.6857i	0.305410	−	0.528986i
$489$		0			0
$490$	−0.983028	+	1.70265i	−0.0444087	+	0.0769181i
$491$	−20.0421	−	34.7139i	−0.904487	−	1.56662i	−0.821604	−	0.570059i	$-0.806920\pi$
$491$	−20.0421	−	34.7139i	−0.904487	−	1.56662i	−0.0828838	−	0.996559i	$-0.526413\pi$
$492$		0			0
$493$	−9.44840			−0.425535
$494$	1.78029	+	2.59962i	0.0800989	+	0.116963i
$495$		0			0
$496$	−8.45450	−	14.6436i	−0.379618	−	0.657518i
$497$	2.41561	+	4.18395i	0.108355	+	0.187676i
$498$		0			0
$499$	15.1533	+	26.2464i	0.678357	+	1.17495i	0.975475	+	0.220108i	$0.0706410\pi$
$499$	15.1533	+	26.2464i	0.678357	+	1.17495i	−0.297118	+	0.954841i	$0.596026\pi$
$500$	−0.957748	+	1.65887i	−0.0428318	+	0.0741868i
$501$		0			0
$502$	3.37909			0.150816
$503$	−8.64393	+	14.9717i	−0.385414	+	0.667556i	−0.991827	−	0.127594i	$-0.959275\pi$
$503$	−8.64393	+	14.9717i	−0.385414	+	0.667556i	0.606413	+	0.795150i	$0.292608\pi$
$504$		0			0
$505$	1.51665			0.0674899
$506$	9.96833			0.443146
$507$		0			0
$508$	−9.41561	−	16.3083i	−0.417750	−	0.723564i
$509$	2.80412	−	4.85688i	0.124291	−	0.215278i	−0.797165	−	0.603762i	$-0.793668\pi$
$509$	2.80412	−	4.85688i	0.124291	−	0.215278i	0.921455	+	0.388484i	$0.127001\pi$
$510$		0			0
$511$	−2.67928	−	4.64066i	−0.118525	−	0.205291i
$512$	19.4969			0.861650
$513$		0			0
$514$	−3.06637			−0.135252
$515$	−4.57739	−	7.92827i	−0.201704	−	0.349361i
$516$		0			0
$517$	−29.7079	+	51.4556i	−1.30655	+	2.26301i
$518$	−0.446797	−	0.773874i	−0.0196311	−	0.0340021i
$519$		0			0
$520$	−2.83028			−0.124116
$521$	−13.7128			−0.600767			−0.300384	−	0.953818i	$-0.597115\pi$
$521$	−13.7128			−0.600767			−0.300384	+	0.953818i	$0.597115\pi$
$522$		0			0
$523$	17.6171	−	30.5137i	0.770341	−	1.33427i	−0.167035	−	0.985951i	$-0.553419\pi$
$523$	17.6171	−	30.5137i	0.770341	−	1.33427i	0.937376	−	0.348319i	$-0.113247\pi$
$524$	27.2559			1.19068
$525$		0			0
$526$	3.45835	−	5.99004i	0.150791	−	0.261178i
$527$	−8.25038	−	14.2901i	−0.359392	−	0.622486i
$528$		0			0
$529$	−9.05934	−	15.6912i	−0.393884	−	0.682228i
$530$	−0.435577	−	0.754442i	−0.0189203	−	0.0327709i
$531$		0			0
$532$	4.05063	−	0.311986i	0.175617	−	0.0135263i
$533$	6.41883			0.278030
$534$		0			0
$535$	−0.0694682	−	0.120322i	−0.00300337	−	0.00520199i
$536$	−8.63650	+	14.9589i	−0.373040	+	0.646124i
$537$		0			0
$538$	−0.614466	+	1.06429i	−0.0264915	+	0.0458847i
$539$	36.1674			1.55784
$540$		0			0
$541$	−15.1179	+	26.1849i	−0.649968	+	1.12578i	0.333162	+	0.942869i	$0.391884\pi$
$541$	−15.1179	+	26.1849i	−0.649968	+	1.12578i	−0.983130	+	0.182908i	$0.941449\pi$
$542$	−4.52719	+	7.84133i	−0.194460	+	0.336814i
$543$		0			0
$544$	11.2507			0.482371
$545$	−7.86497	+	13.6225i	−0.336899	+	0.583525i
$546$		0			0
$547$	−17.4766	+	30.2703i	−0.747244	+	1.29426i	0.201895	+	0.979407i	$0.435290\pi$
$547$	−17.4766	+	30.2703i	−0.747244	+	1.29426i	−0.949139	+	0.314858i	$0.898043\pi$
$548$	−6.30619	−	10.9226i	−0.269387	−	0.466592i
$549$		0			0
$550$	−1.55454			−0.0662860
$551$	−12.0222	+	0.925967i	−0.512162	+	0.0394475i
$552$		0			0
$553$	1.97859	+	3.42701i	0.0841380	+	0.145731i
$554$	−0.153187	−	0.265327i	−0.00650828	−	0.0112727i
$555$		0			0
$556$	0.223879	+	0.387771i	0.00949460	+	0.0164451i
$557$	1.58139	−	2.73906i	0.0670058	−	0.116058i	−0.830576	−	0.556905i	$-0.811989\pi$
$557$	1.58139	−	2.73906i	0.0670058	−	0.116058i	0.897582	+	0.440848i	$0.145322\pi$
$558$		0			0
$559$	6.18305			0.261515
$560$	−0.851533	+	1.47490i	−0.0359838	+	0.0623258i
$561$		0			0
$562$	−7.45213			−0.314349
$563$	29.0570			1.22460			0.612302	−	0.790624i	$-0.290244\pi$
$563$	29.0570			1.22460			0.612302	+	0.790624i	$0.290244\pi$
$564$		0			0
$565$	−7.40057	−	12.8182i	−0.311344	−	0.539264i
$566$	−4.27487	+	7.40430i	−0.179686	+	0.311226i
$567$		0			0
$568$	5.65073	+	9.78735i	0.237099	+	0.410668i
$569$	31.3398			1.31383			0.656916	−	0.753964i	$-0.271861\pi$
$569$	31.3398			1.31383			0.656916	+	0.753964i	$0.271861\pi$
$570$		0			0
$571$	2.56556			0.107365			0.0536827	−	0.998558i	$-0.482904\pi$
$571$	2.56556			0.107365			0.0536827	+	0.998558i	$0.482904\pi$
$572$	12.7355	+	22.0585i	0.532496	+	0.922311i
$573$		0			0
$574$	−0.182564	+	0.316210i	−0.00762006	+	0.0131983i
$575$	3.20619	+	5.55329i	0.133707	+	0.231588i
$576$		0			0
$577$	3.12153			0.129951			0.0649755	−	0.997887i	$-0.479303\pi$
$577$	3.12153			0.129951			0.0649755	+	0.997887i	$0.479303\pi$
$578$	−1.55047			−0.0644911
$579$		0			0
$580$	2.64936	−	4.58883i	0.110009	−	0.190541i
$581$	−2.85184			−0.118314
$582$		0			0
$583$	−8.01284	+	13.8786i	−0.331858	+	0.574795i
$584$	−6.26754	−	10.8557i	−0.259353	−	0.449212i
$585$		0			0
$586$	−1.57774	−	2.73272i	−0.0651757	−	0.112888i
$587$	−4.63985	−	8.03646i	−0.191507	−	0.331700i	0.754243	−	0.656596i	$-0.228004\pi$
$587$	−4.63985	−	8.03646i	−0.191507	−	0.331700i	−0.945750	+	0.324896i	$0.894671\pi$
$588$		0			0
$589$	−11.8983	−	17.3742i	−0.490260	−	0.715891i
$590$	3.70150			0.152388
$591$		0			0
$592$	11.0561	+	19.1497i	0.454403	+	0.787048i
$593$	17.0224	−	29.4836i	0.699025	−	1.21075i	−0.269780	−	0.962922i	$-0.586951\pi$
$593$	17.0224	−	29.4836i	0.699025	−	1.21075i	0.968805	−	0.247825i	$-0.0797157\pi$
$594$		0			0
$595$	−0.830974	+	1.43929i	−0.0340666	+	0.0590051i
$596$	−5.12010			−0.209728
$597$		0			0
$598$	−2.31756	+	4.01414i	−0.0947723	+	0.164150i
$599$	12.5366	−	21.7140i	0.512231	−	0.887210i	−0.487669	−	0.873029i	$-0.662153\pi$
$599$	12.5366	−	21.7140i	0.512231	−	0.887210i	0.999899	−	0.0141810i	$-0.00451411\pi$
$600$		0			0
$601$	−26.0225			−1.06148			−0.530739	−	0.847535i	$-0.678086\pi$
$601$	−26.0225			−1.06148			−0.530739	+	0.847535i	$0.678086\pi$
$602$	−0.175858	+	0.304595i	−0.00716743	+	0.0124144i
$603$		0			0
$604$	5.70115	−	9.87468i	0.231976	−	0.401795i
$605$	8.79862	+	15.2397i	0.357715	+	0.619580i
$606$		0			0
$607$	−7.54650			−0.306303			−0.153151	−	0.988203i	$-0.548942\pi$
$607$	−7.54650			−0.306303			−0.153151	+	0.988203i	$0.548942\pi$
$608$	14.3155	−	1.10260i	0.580569	−	0.0447163i
$609$		0			0
$610$	1.72308	+	2.98447i	0.0697657	+	0.120838i
$611$	−13.8137	−	23.9261i	−0.558844	−	0.967946i
$612$		0			0
$613$	19.1345	+	33.1419i	0.772836	+	1.33859i	0.936003	+	0.351992i	$0.114496\pi$
$613$	19.1345	+	33.1419i	0.772836	+	1.33859i	−0.163167	+	0.986598i	$0.552171\pi$
$614$	−4.89666	+	8.48126i	−0.197613	+	0.342276i
$615$		0			0
$616$	−2.96169			−0.119330
$617$	−5.82540	+	10.0899i	−0.234522	+	0.406203i	−0.959134	−	0.282954i	$-0.908686\pi$
$617$	−5.82540	+	10.0899i	−0.234522	+	0.406203i	0.724612	+	0.689157i	$0.242019\pi$
$618$		0			0
$619$	−2.47710			−0.0995630			−0.0497815	−	0.998760i	$-0.515852\pi$
$619$	−2.47710			−0.0995630			−0.0497815	+	0.998760i	$0.515852\pi$
$620$	9.25374			0.371639
$621$		0			0
$622$	−1.70379	−	2.95106i	−0.0683159	−	0.118327i
$623$	1.58390	−	2.74340i	0.0634578	−	0.109912i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	1.30191			0.0520346
$627$		0			0
$628$	13.8078			0.550991
$629$	10.7892	+	18.6874i	0.430192	+	0.745114i
$630$		0			0
$631$	21.8279	−	37.8070i	0.868954	−	1.50507i	0.00588756	−	0.999983i	$-0.498126\pi$
$631$	21.8279	−	37.8070i	0.868954	−	1.50507i	0.863067	−	0.505090i	$-0.168541\pi$
$632$	4.62842	+	8.01666i	0.184109	+	0.318886i
$633$		0			0
$634$	−3.60096			−0.143012
$635$	9.83099			0.390131
$636$		0			0
$637$	−8.40866	+	14.5642i	−0.333163	+	0.577055i
$638$	4.30025			0.170248
$639$		0			0
$640$	−4.17222	+	7.22649i	−0.164921	+	0.285652i
$641$	12.1163	+	20.9860i	0.478564	+	0.828897i	0.999698	−	0.0245776i	$-0.00782407\pi$
$641$	12.1163	+	20.9860i	0.478564	+	0.828897i	−0.521134	+	0.853475i	$0.674491\pi$
$642$		0			0
$643$	−4.15878	−	7.20322i	−0.164006	−	0.284067i	0.772296	−	0.635263i	$-0.219108\pi$
$643$	−4.15878	−	7.20322i	−0.164006	−	0.284067i	−0.936302	+	0.351196i	$0.885775\pi$
$644$	2.98827	+	5.17584i	0.117754	+	0.203957i
$645$		0			0
$646$	4.31520	−	0.332364i	0.169779	−	0.0130767i
$647$	10.9164			0.429170			0.214585	−	0.976705i	$-0.431160\pi$
$647$	10.9164			0.429170			0.214585	+	0.976705i	$0.431160\pi$
$648$		0			0
$649$	−34.0462	−	58.9697i	−1.33643	−	2.31476i
$650$	0.361420	−	0.625998i	0.0141761	−	0.0245537i
$651$		0			0
$652$	13.5767	−	23.5155i	0.531704	−	0.920938i
$653$	21.8452			0.854868			0.427434	−	0.904047i	$-0.359418\pi$
$653$	21.8452			0.854868			0.427434	+	0.904047i	$0.359418\pi$
$654$		0			0
$655$	−7.11459	+	12.3228i	−0.277990	+	0.481493i
$656$	4.51758	−	7.82469i	0.176382	−	0.305503i
$657$		0			0
$658$	1.57156			0.0612657
$659$	−13.2094	+	22.8794i	−0.514566	+	0.891254i	0.485291	+	0.874352i	$0.338714\pi$
$659$	−13.2094	+	22.8794i	−0.514566	+	0.891254i	−0.999857	+	0.0169015i	$0.994620\pi$
$660$		0			0
$661$	−9.30721	+	16.1206i	−0.362008	+	0.627017i	−0.988291	−	0.152579i	$-0.951242\pi$
$661$	−9.30721	+	16.1206i	−0.362008	+	0.627017i	0.626283	+	0.779596i	$0.284576\pi$
$662$	−3.56188	−	6.16936i	−0.138436	−	0.239779i
$663$		0			0
$664$	−6.67120			−0.258893
$665$	−0.916279	+	1.91279i	−0.0355318	+	0.0741749i
$666$		0			0
$667$	−8.86911	−	15.3617i	−0.343413	−	0.594809i
$668$	−12.0258	−	20.8293i	−0.465292	−	0.805910i
$669$		0			0
$670$	−2.20572	−	3.82043i	−0.0852146	−	0.147596i
$671$	31.6977	−	54.9020i	1.22368	−	2.11947i
$672$		0			0
$673$	5.98693			0.230779			0.115390	−	0.993320i	$-0.463188\pi$
$673$	5.98693			0.230779			0.115390	+	0.993320i	$0.463188\pi$
$674$	−1.52627	+	2.64358i	−0.0587898	+	0.101827i
$675$		0			0
$676$	13.0578			0.502224
$677$	−33.7287			−1.29630			−0.648150	−	0.761512i	$-0.724457\pi$
$677$	−33.7287			−1.29630			−0.648150	+	0.761512i	$0.724457\pi$
$678$		0			0
$679$	0.486575	+	0.842772i	0.0186730	+	0.0323426i
$680$	−1.94386	+	3.36687i	−0.0745437	+	0.129113i
$681$		0			0
$682$	3.75499	+	6.50384i	0.143786	+	0.249045i
$683$	−11.4959			−0.439880			−0.219940	−	0.975513i	$-0.570586\pi$
$683$	−11.4959			−0.439880			−0.219940	+	0.975513i	$0.570586\pi$
$684$		0			0
$685$	6.58439			0.251577
$686$	−0.973377	−	1.68594i	−0.0371637	−	0.0643694i
$687$		0			0
$688$	4.35164	−	7.53727i	0.165905	−	0.287356i
$689$	−3.72586	−	6.45337i	−0.141944	−	0.245854i
$690$		0			0
$691$	36.3039			1.38107			0.690533	−	0.723301i	$-0.257376\pi$
$691$	36.3039			1.38107			0.690533	+	0.723301i	$0.257376\pi$
$692$	4.19424			0.159441
$693$		0			0
$694$	−0.211500	+	0.366329i	−0.00802844	+	0.0139057i
$695$	−0.233756			−0.00886688
$696$		0			0
$697$	4.40851	−	7.63577i	0.166984	−	0.289225i
$698$	−3.44958	−	5.97485i	−0.130569	−	0.226152i
$699$		0			0
$700$	−0.466016	−	0.807163i	−0.0176137	−	0.0305079i
$701$	6.76373	+	11.7151i	0.255463	+	0.442474i	0.965021	−	0.262172i	$-0.0844389\pi$
$701$	6.76373	+	11.7151i	0.255463	+	0.442474i	−0.709558	+	0.704647i	$0.751106\pi$
$702$		0			0
$703$	15.5596	+	22.7205i	0.586840	+	0.856920i
$704$	32.3141			1.21788
$705$		0			0
$706$	−1.07421	−	1.86058i	−0.0404283	−	0.0700239i
$707$	−0.368981	+	0.639094i	−0.0138770	+	0.0240356i
$708$		0			0
$709$	0.496778	−	0.860444i	0.0186569	−	0.0323147i	−0.856546	−	0.516070i	$-0.827394\pi$
$709$	0.496778	−	0.860444i	0.0186569	−	0.0323147i	0.875203	+	0.483756i	$0.160728\pi$
$710$	−2.88634			−0.108322
$711$		0			0
$712$	3.70516	−	6.41753i	0.138857	−	0.240507i
$713$	15.4891	−	26.8279i	0.580071	−	1.00471i
$714$		0			0
$715$	−13.2973			−0.497291
$716$	−7.18714	+	12.4485i	−0.268596	+	0.465222i
$717$		0			0
$718$	0.342831	−	0.593801i	0.0127943	−	0.0221605i
$719$	−0.700670	−	1.21360i	−0.0261306	−	0.0452595i	0.852664	−	0.522459i	$-0.174985\pi$
$719$	−0.700670	−	1.21360i	−0.0261306	−	0.0452595i	−0.878795	+	0.477200i	$0.841652\pi$
$720$		0			0
$721$	4.45448			0.165894
$722$	5.45810	−	0.845801i	0.203130	−	0.0314775i
$723$		0			0
$724$	−12.1301	−	21.0099i	−0.450810	−	0.780827i
$725$	1.38312	+	2.39564i	0.0513679	+	0.0889717i
$726$		0			0
$727$	23.4834	+	40.6745i	0.870953	+	1.50853i	0.861013	+	0.508584i	$0.169831\pi$
$727$	23.4834	+	40.6745i	0.870953	+	1.50853i	0.00993990	+	0.999951i	$0.496836\pi$
$728$	0.688570	−	1.19264i	0.0255201	−	0.0442021i
$729$		0			0
$730$	3.20140			0.118489
$731$	4.24658	−	7.35529i	0.157065	−	0.272045i
$732$		0			0
$733$	−21.6068			−0.798066			−0.399033	−	0.916937i	$-0.630654\pi$
$733$	−21.6068			−0.798066			−0.399033	+	0.916937i	$0.630654\pi$
$734$	−6.43852			−0.237650
$735$		0			0
$736$	10.5609	+	18.2921i	0.389281	+	0.674255i
$737$	−40.5763	+	70.2802i	−1.49465	+	2.58880i
$738$		0			0
$739$	15.4063	+	26.6845i	0.566729	+	0.981603i	0.996887	+	0.0788496i	$0.0251247\pi$
$739$	15.4063	+	26.6845i	0.566729	+	0.981603i	−0.430158	+	0.902754i	$0.641542\pi$
$740$	−12.1013			−0.444851
$741$		0			0
$742$	0.423882			0.0155612
$743$	22.2143	+	38.4763i	0.814964	+	1.41156i	0.909354	+	0.416024i	$0.136577\pi$
$743$	22.2143	+	38.4763i	0.814964	+	1.41156i	−0.0943897	+	0.995535i	$0.530090\pi$
$744$		0			0
$745$	1.33650	−	2.31488i	0.0489654	−	0.0848106i
$746$	−4.53107	−	7.84805i	−0.165894	−	0.287338i
$747$		0			0
$748$	34.9873			1.27926
$749$	0.0676029			0.00247016
$750$		0			0
$751$	−7.43935	+	12.8853i	−0.271466	+	0.470192i	−0.969237	−	0.246128i	$-0.920842\pi$
$751$	−7.43935	+	12.8853i	−0.271466	+	0.470192i	0.697772	+	0.716320i	$0.254175\pi$
$752$	−38.8886			−1.41812
$753$		0			0
$754$	−0.999776	+	1.73166i	−0.0364097	+	0.0630634i
$755$	2.97633	+	5.15516i	0.108320	+	0.187615i
$756$		0			0
$757$	−11.7204	−	20.3004i	−0.425986	−	0.737829i	0.570526	−	0.821279i	$-0.306739\pi$
$757$	−11.7204	−	20.3004i	−0.425986	−	0.737829i	−0.996512	+	0.0834503i	$0.973406\pi$
$758$	3.78414	+	6.55432i	0.137446	+	0.238063i
$759$		0			0
$760$	−2.14341	+	4.47451i	−0.0777498	+	0.162308i
$761$	−36.3224			−1.31669			−0.658344	−	0.752717i	$-0.728743\pi$
$761$	−36.3224			−1.31669			−0.658344	+	0.752717i	$0.728743\pi$
$762$		0			0
$763$	−3.82690	−	6.62838i	−0.138543	−	0.239963i
$764$	−7.81309	+	13.5327i	−0.282668	+	0.489595i
$765$		0			0
$766$	−0.310020	+	0.536970i	−0.0112015	+	0.0194015i
$767$	31.6620			1.14325
$768$		0			0
$769$	−10.4052	+	18.0223i	−0.375220	+	0.649901i	−0.990360	−	0.138517i	$-0.955766\pi$
$769$	−10.4052	+	18.0223i	−0.375220	+	0.649901i	0.615140	+	0.788418i	$0.289100\pi$
$770$	0.378201	−	0.655063i	0.0136294	−	0.0236068i
$771$		0			0
$772$	6.44573			0.231987
$773$	1.78351	−	3.08913i	0.0641484	−	0.111108i	−0.832168	−	0.554524i	$-0.812900\pi$
$773$	1.78351	−	3.08913i	0.0641484	−	0.111108i	0.896316	+	0.443416i	$0.146234\pi$
$774$		0			0
$775$	−2.41550	+	4.18376i	−0.0867671	+	0.150285i
$776$	1.13822	+	1.97146i	0.0408598	+	0.0707713i
$777$		0			0
$778$	3.79147			0.135931
$779$	4.86108	−	10.1478i	0.174166	−	0.363583i
$780$		0			0
$781$	26.5484	+	45.9832i	0.949978	+	1.64541i
$782$	3.18345	+	5.51390i	0.113840	+	0.197177i
$783$		0			0
$784$	11.8361	+	20.5007i	0.422716	+	0.732166i
$785$	−3.60424	+	6.24273i	−0.128641	+	0.222812i
$786$		0			0
$787$	44.5660			1.58860			0.794302	−	0.607523i	$-0.207837\pi$
$787$	44.5660			1.58860			0.794302	+	0.607523i	$0.207837\pi$
$788$	−3.67199	+	6.36008i	−0.130809	+	0.226568i
$789$		0			0
$790$	−2.36416			−0.0841129
$791$	7.20186			0.256069
$792$		0			0
$793$	14.7390	+	25.5287i	0.523396	+	0.906549i
$794$	−0.00416319	+	0.00721085i	−0.000147746	+	0.000255904i
$795$		0			0
$796$	12.1620	+	21.0651i	0.431069	+	0.746634i
$797$	44.7396			1.58476			0.792378	−	0.610030i	$-0.208843\pi$
$797$	44.7396			1.58476			0.792378	+	0.610030i	$0.208843\pi$
$798$		0			0
$799$	−37.9496			−1.34256
$800$	−1.64696	−	2.85262i	−0.0582288	−	0.100855i
$801$		0			0
$802$	−3.97080	+	6.87762i	−0.140214	+	0.242857i
$803$	−29.4463	−	51.0026i	−1.03914	−	1.79984i
$804$		0			0
$805$	−3.12010			−0.109969
$806$	−3.49203			−0.123002
$807$		0			0
$808$	−0.863142	+	1.49501i	−0.0303652	+	0.0525941i
$809$	−8.67442			−0.304976			−0.152488	−	0.988305i	$-0.548729\pi$
$809$	−8.67442			−0.304976			−0.152488	+	0.988305i	$0.548729\pi$
$810$		0			0
$811$	−13.3651	+	23.1490i	−0.469312	+	0.812872i	−0.999384	−	0.0350805i	$-0.988831\pi$
$811$	−13.3651	+	23.1490i	−0.469312	+	0.812872i	0.530073	+	0.847952i	$0.322165\pi$
$812$	1.28911	+	2.23281i	0.0452390	+	0.0783562i
$813$		0			0
$814$	−4.91046	−	8.50517i	−0.172112	−	0.298106i
$815$	7.08781	+	12.2765i	0.248275	+	0.430025i
$816$		0			0
$817$	4.68252	−	9.77507i	0.163821	−	0.341986i
$818$	−1.95906			−0.0684968
$819$		0			0
$820$	2.47232	+	4.28219i	0.0863373	+	0.149541i
$821$	−4.72432	+	8.18275i	−0.164880	+	0.285580i	−0.936613	−	0.350367i	$-0.886057\pi$
$821$	−4.72432	+	8.18275i	−0.164880	+	0.285580i	0.771733	+	0.635947i	$0.219390\pi$
$822$		0			0
$823$	9.73340	−	16.8587i	0.339285	−	0.587659i	−0.645014	−	0.764171i	$-0.723148\pi$
$823$	9.73340	−	16.8587i	0.339285	−	0.587659i	0.984298	+	0.176513i	$0.0564816\pi$
$824$	10.4202			0.363004
$825$		0			0
$826$	−0.900527	+	1.55976i	−0.0313333	+	0.0542709i
$827$	−18.5009	+	32.0445i	−0.643340	+	1.11430i	0.341342	+	0.939939i	$0.389118\pi$
$827$	−18.5009	+	32.0445i	−0.643340	+	1.11430i	−0.984682	+	0.174358i	$0.944215\pi$
$828$		0			0
$829$	20.5418			0.713448			0.356724	−	0.934210i	$-0.383894\pi$
$829$	20.5418			0.713448			0.356724	+	0.934210i	$0.383894\pi$
$830$	0.851897	−	1.47553i	0.0295698	−	0.0512164i
$831$		0			0
$832$	−7.51280	+	13.0126i	−0.260459	+	0.451129i
$833$	11.5503	+	20.0057i	0.400194	+	0.693156i
$834$		0			0
$835$	12.5563			0.434530
$836$	44.5180	−	3.42885i	1.53969	−	0.118589i
$837$		0			0
$838$	3.83831	+	6.64814i	0.132592	+	0.229656i
$839$	−23.8946	−	41.3866i	−0.824932	−	1.42882i	−0.901972	−	0.431795i	$-0.857880\pi$
$839$	−23.8946	−	41.3866i	−0.824932	−	1.42882i	0.0770401	−	0.997028i	$-0.475453\pi$
$840$		0			0
$841$	10.6739	+	18.4878i	0.368067	+	0.637511i
$842$	−5.50719	+	9.53873i	−0.189790	+	0.328726i
$843$		0			0
$844$	17.5394			0.603730
$845$	−3.40847	+	5.90365i	−0.117255	+	0.203092i
$846$		0			0
$847$	−8.56237			−0.294206
$848$	−10.4891			−0.360196
$849$		0			0
$850$	−0.496454	−	0.859883i	−0.0170282	−	0.0294937i
$851$	−20.2553	+	35.0833i	−0.694344	+	1.20264i
$852$		0			0
$853$	−5.71632	−	9.90096i	−0.195723	−	0.339003i	0.751414	−	0.659831i	$-0.229372\pi$
$853$	−5.71632	−	9.90096i	−0.195723	−	0.339003i	−0.947137	+	0.320828i	$0.896039\pi$
$854$	−1.67682			−0.0573795
$855$		0			0
$856$	0.158141			0.00540513
$857$	2.78522	+	4.82414i	0.0951412	+	0.164789i	0.909668	−	0.415337i	$-0.136336\pi$
$857$	2.78522	+	4.82414i	0.0951412	+	0.164789i	−0.814526	+	0.580127i	$0.803003\pi$
$858$		0			0
$859$	8.50709	−	14.7347i	0.290258	−	0.502742i	−0.683612	−	0.729845i	$-0.739592\pi$
$859$	8.50709	−	14.7347i	0.290258	−	0.502742i	0.973871	+	0.227103i	$0.0729255\pi$
$860$	2.38151	+	4.12490i	0.0812088	+	0.140658i
$861$		0			0
$862$	5.58304			0.190159
$863$	−46.8850			−1.59598			−0.797992	−	0.602668i	$-0.794104\pi$
$863$	−46.8850			−1.59598			−0.797992	+	0.602668i	$0.794104\pi$
$864$		0			0
$865$	−1.09482	+	1.89628i	−0.0372250	+	0.0644756i
$866$	4.92768			0.167449
$867$		0			0
$868$	−2.25132	+	3.89939i	−0.0764147	+	0.132354i
$869$	21.7454	+	37.6642i	0.737662	+	1.27767i
$870$		0			0
$871$	−18.8674	−	32.6793i	−0.639297	−	1.10730i
$872$	−8.95210	−	15.5055i	−0.303156	−	0.525082i
$873$		0			0
$874$	4.59101	+	6.70391i	0.155293	+	0.226763i
$875$	0.486575			0.0164492
$876$		0			0
$877$	14.8922	+	25.7940i	0.502873	+	0.871002i	0.999994	+	0.00332078i	$0.00105704\pi$
$877$	14.8922	+	25.7940i	0.502873	+	0.871002i	−0.497121	+	0.867681i	$0.665610\pi$
$878$	−1.61379	+	2.79516i	−0.0544626	+	0.0943321i
$879$		0			0
$880$	−9.35867	+	16.2097i	−0.315481	+	0.546428i
$881$	20.4884			0.690271			0.345135	−	0.938553i	$-0.387833\pi$
$881$	20.4884			0.690271			0.345135	+	0.938553i	$0.387833\pi$
$882$		0			0
$883$	−15.7402	+	27.2628i	−0.529699	+	0.917466i	0.469701	+	0.882826i	$0.344362\pi$
$883$	−15.7402	+	27.2628i	−0.529699	+	0.917466i	−0.999400	+	0.0346401i	$0.988972\pi$
$884$	−8.13430	+	14.0890i	−0.273586	+	0.473865i
$885$		0			0
$886$	4.03900			0.135693
$887$	−16.8051	+	29.1074i	−0.564262	+	0.977330i	0.432856	+	0.901463i	$0.357506\pi$
$887$	−16.8051	+	29.1074i	−0.564262	+	0.977330i	−0.997118	+	0.0758670i	$0.975828\pi$
$888$		0			0
$889$	−2.39175	+	4.14264i	−0.0802169	+	0.138940i
$890$	0.946281	+	1.63901i	0.0317194	+	0.0549397i
$891$		0			0
$892$	−20.8742			−0.698919
$893$	−48.2872	+	3.71916i	−1.61587	+	0.124457i
$894$		0			0
$895$	−3.75210	−	6.49883i	−0.125419	−	0.217232i
$896$	−2.03009	−	3.51623i	−0.0678207	−	0.117469i
$897$		0			0
$898$	4.05050	+	7.01567i	0.135167	+	0.234116i
$899$	6.68185	−	11.5733i	0.222852	−	0.385991i
$900$		0			0
$901$	−10.2358			−0.341004
$902$	−2.00644	+	3.47526i	−0.0668073	+	0.115714i
$903$		0			0
$904$	16.8470			0.560323
$905$	12.6652			0.421006
$906$		0			0
$907$	−10.9747	−	19.0088i	−0.364410	−	0.631176i	0.624272	−	0.781207i	$-0.285396\pi$
$907$	−10.9747	−	19.0088i	−0.364410	−	0.631176i	−0.988681	+	0.150031i	$0.952063\pi$
$908$	23.5942	−	40.8664i	0.783002	−	1.35620i
$909$		0			0
$910$	0.175858	+	0.304595i	0.00582963	+	0.0100972i
$911$	−21.2865			−0.705253			−0.352626	−	0.935764i	$-0.614711\pi$
$911$	−21.2865			−0.705253			−0.352626	+	0.935764i	$0.614711\pi$
$912$		0			0
$913$	−31.3428			−1.03730
$914$	5.31481	+	9.20552i	0.175798	+	0.304492i
$915$		0			0
$916$	16.4422	−	28.4788i	0.543267	−	0.940966i
$917$	−3.46178	−	5.99598i	−0.114318	−	0.198005i
$918$		0			0
$919$	−2.61948			−0.0864087			−0.0432043	−	0.999066i	$-0.513757\pi$
$919$	−2.61948			−0.0864087			−0.0432043	+	0.999066i	$0.513757\pi$
$920$	−7.29873			−0.240632
$921$		0			0
$922$	3.18575	−	5.51789i	0.104917	−	0.181722i
$923$	−24.6893			−0.812658
$924$		0			0
$925$	3.15878	−	5.47117i	0.103860	−	0.179891i
$926$	2.03859	+	3.53094i	0.0669921	+	0.116034i
$927$		0			0
$928$	4.55589	+	7.89104i	0.149554	+	0.259036i
$929$	1.91237	+	3.31232i	0.0627428	+	0.108674i	0.895691	−	0.444678i	$-0.146682\pi$
$929$	1.91237	+	3.31232i	0.0627428	+	0.108674i	−0.832948	+	0.553352i	$0.813349\pi$
$930$		0			0
$931$	16.6572	+	24.3233i	0.545919	+	0.797165i
$932$	54.5210			1.78589
$933$		0			0
$934$	4.93160	+	8.54177i	0.161367	+	0.279495i
$935$	−9.13272	+	15.8183i	−0.298672	+	0.517315i
$936$		0			0
$937$	3.69584	−	6.40138i	0.120738	−	0.209124i	−0.799321	−	0.600904i	$-0.794807\pi$
$937$	3.69584	−	6.40138i	0.120738	−	0.209124i	0.920059	+	0.391780i	$0.128141\pi$
$938$	2.14650			0.0700856
$939$		0			0
$940$	10.6412	−	18.4311i	0.347078	−	0.601157i
$941$	24.3057	−	42.0988i	0.792344	−	1.37238i	−0.132168	−	0.991227i	$-0.542194\pi$
$941$	24.3057	−	42.0988i	0.792344	−	1.37238i	0.924512	−	0.381153i	$-0.124473\pi$
$942$		0			0
$943$	16.5529			0.539036
$944$	22.2838	−	38.5966i	0.725275	−	1.25621i
$945$		0			0
$946$	−1.93274	+	3.34761i	−0.0628389	+	0.108840i
$947$	−18.0103	−	31.1948i	−0.585257	−	1.01370i	−0.994843	−	0.101424i	$-0.967660\pi$
$947$	−18.0103	−	31.1948i	−0.585257	−	1.01370i	0.409586	−	0.912271i	$-0.365673\pi$
$948$		0			0
$949$	27.3843			0.888930
$950$	−0.715960	−	1.04546i	−0.0232288	−	0.0339193i
$951$		0			0
$952$	−0.945834	−	1.63823i	−0.0306546	−	0.0530954i
$953$	5.60605	+	9.70996i	0.181598	+	0.314537i	0.942425	−	0.334418i	$-0.108540\pi$
$953$	5.60605	+	9.70996i	0.181598	+	0.314537i	−0.760827	+	0.648955i	$0.775206\pi$
$954$		0			0
$955$	−4.07889	−	7.06484i	−0.131990	−	0.228613i
$956$	−3.90513	+	6.76389i	−0.126301	+	0.218760i
$957$		0			0
$958$	−9.28769			−0.300072
$959$	−1.60190	+	2.77457i	−0.0517280	+	0.0895955i
$960$		0			0
$961$	−7.66153			−0.247146
$962$	4.56659			0.147233
$963$		0			0
$964$	−12.1332	−	21.0152i	−0.390783	−	0.676855i
$965$	−1.68252	+	2.91422i	−0.0541623	+	0.0938119i
$966$		0			0
$967$	5.02307	+	8.70021i	0.161531	+	0.279780i	0.935418	−	0.353544i	$-0.115023\pi$
$967$	5.02307	+	8.70021i	0.161531	+	0.279780i	−0.773887	+	0.633324i	$0.781690\pi$
$968$	−20.0296			−0.643775
$969$		0			0
$970$	−0.581394			−0.0186674
$971$	−18.9495	−	32.8214i	−0.608117	−	1.05329i	−0.991551	−	0.129721i	$-0.958592\pi$
$971$	−18.9495	−	32.8214i	−0.608117	−	1.05329i	0.383434	−	0.923568i	$-0.374742\pi$
$972$		0			0
$973$	0.0568699	−	0.0985016i	0.00182317	−	0.00315782i
$974$	−5.46844	−	9.47161i	−0.175220	−	0.303490i
$975$		0			0
$976$	41.4933			1.32817
$977$	−44.6435			−1.42827			−0.714135	−	0.700008i	$-0.753180\pi$
$977$	−44.6435			−1.42827			−0.714135	+	0.700008i	$0.753180\pi$
$978$		0			0
$979$	17.4077	−	30.1510i	0.556353	−	0.963631i
$980$	−12.9550			−0.413831
$981$		0			0
$982$	−5.82618	+	10.0912i	−0.185921	+	0.322025i
$983$	−6.25454	−	10.8332i	−0.199489	−	0.345525i	0.748874	−	0.662712i	$-0.230595\pi$
$983$	−6.25454	−	10.8332i	−0.199489	−	0.345525i	−0.948363	+	0.317188i	$0.897262\pi$
$984$		0			0
$985$	−1.91699	−	3.32033i	−0.0610805	−	0.105795i
$986$	1.37331	+	2.37865i	0.0437352	+	0.0757515i
$987$		0			0
$988$	−8.96935	+	18.7241i	−0.285353	+	0.595693i
$989$	15.9449			0.507017
$990$		0			0
$991$	−25.1503	−	43.5617i	−0.798927	−	1.38378i	−0.920315	−	0.391177i	$-0.872068\pi$
$991$	−25.1503	−	43.5617i	−0.798927	−	1.38378i	0.121388	−	0.992605i	$-0.461265\pi$
$992$	−7.95645	+	13.7810i	−0.252617	+	0.437546i
$993$		0			0
$994$	0.702210	−	1.21626i	0.0222728	−	0.0385775i
$995$	−12.6985			−0.402569
$996$		0			0
$997$	−6.46875	+	11.2042i	−0.204867	+	0.354841i	−0.950090	−	0.311975i	$-0.899010\pi$
$997$	−6.46875	+	11.2042i	−0.204867	+	0.354841i	0.745223	+	0.666815i	$0.232343\pi$
$998$	4.40504	−	7.62975i	0.139439	−	0.241515i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.k.i.406.3		10
3.2	odd	2		285.2.i.f.121.3	yes	10
19.11	even	3	inner	855.2.k.i.676.3		10
57.11	odd	6		285.2.i.f.106.3	✓	10
57.26	odd	6		5415.2.a.y.1.3		5
57.50	even	6		5415.2.a.z.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.f.106.3	✓	10	57.11	odd	6
285.2.i.f.121.3	yes	10	3.2	odd	2
855.2.k.i.406.3		10	1.1	even	1	trivial
855.2.k.i.676.3		10	19.11	even	3	inner
5415.2.a.y.1.3		5	57.26	odd	6
5415.2.a.z.1.3		5	57.50	even	6

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.145349 - 0.251751i) q^{2} +(0.957748 - 1.65887i) q^{4} +(0.500000 + 0.866025i) q^{5} -0.486575 q^{7} -1.13822 q^{8} +(0.145349 - 0.251751i) q^{10} -5.34764 q^{11} +(1.24329 - 2.15344i) q^{13} +(0.0707229 + 0.122496i) q^{14} +(-1.75006 - 3.03119i) q^{16} +(-1.70780 - 2.95800i) q^{17} +(-2.46291 - 3.59640i) q^{19} +1.91550 q^{20} +(0.777272 + 1.34627i) q^{22} +(3.20619 - 5.55329i) q^{23} +(-0.500000 + 0.866025i) q^{25} -0.722840 q^{26} +(-0.466016 + 0.807163i) q^{28} +(1.38312 - 2.39564i) q^{29} +4.83099 q^{31} +(-1.64696 + 2.85262i) q^{32} +(-0.496454 + 0.859883i) q^{34} +(-0.243287 - 0.421386i) q^{35} -6.31756 q^{37} +(-0.547418 + 1.14277i) q^{38} +(-0.569112 - 0.985730i) q^{40} +(1.29070 + 2.23555i) q^{41} +(1.24329 + 2.15344i) q^{43} +(-5.12169 + 8.87102i) q^{44} -1.86406 q^{46} +(5.55533 - 9.62211i) q^{47} -6.76325 q^{49} +0.290697 q^{50} +(-2.38151 - 4.12490i) q^{52} +(1.49839 - 2.59529i) q^{53} +(-2.67382 - 4.63119i) q^{55} +0.553831 q^{56} -0.804139 q^{58} +(6.36659 + 11.0273i) q^{59} +(-5.92742 + 10.2666i) q^{61} +(-0.702178 - 1.21621i) q^{62} -6.04269 q^{64} +2.48657 q^{65} +(7.58770 - 13.1423i) q^{67} -6.54258 q^{68} +(-0.0707229 + 0.122496i) q^{70} +(-4.96452 - 8.59879i) q^{71} +(5.50642 + 9.53740i) q^{73} +(0.918249 + 1.59045i) q^{74} +(-8.32479 + 0.641189i) q^{76} +2.60202 q^{77} +(-4.06636 - 7.04314i) q^{79} +(1.75006 - 3.03119i) q^{80} +(0.375202 - 0.649869i) q^{82} +5.86106 q^{83} +(1.70780 - 2.95800i) q^{85} +(0.361420 - 0.625998i) q^{86} +6.08681 q^{88} +(-3.25521 + 5.63820i) q^{89} +(-0.604952 + 1.04781i) q^{91} +(-6.14145 - 10.6373i) q^{92} -3.22984 q^{94} +(1.88312 - 3.93114i) q^{95} +(-1.00000 - 1.73205i) q^{97} +(0.983028 + 1.70265i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 7 q^{4} + 5 q^{5} + 4 q^{7} + 12 q^{8} + q^{10} - 10 q^{11} + 8 q^{13} - 4 q^{14} - 7 q^{16} + 10 q^{17} + 5 q^{19} - 14 q^{20} - 2 q^{22} - 2 q^{23} - 5 q^{25} + 4 q^{26} - 10 q^{28} - 7 q^{29}+ \cdots + 21 q^{98}+O(q^{100}) \) 10 * q - q^2 - 7 * q^4 + 5 * q^5 + 4 * q^7 + 12 * q^8 + q^10 - 10 * q^11 + 8 * q^13 - 4 * q^14 - 7 * q^16 + 10 * q^17 + 5 * q^19 - 14 * q^20 - 2 * q^22 - 2 * q^23 - 5 * q^25 + 4 * q^26 - 10 * q^28 - 7 * q^29 - 18 * q^31 - 23 * q^32 - 25 * q^34 + 2 * q^35 + 12 * q^37 + 37 * q^38 + 6 * q^40 + 12 * q^41 + 8 * q^43 + 16 * q^44 - 40 * q^46 + 6 * q^47 + 30 * q^49 + 2 * q^50 + 4 * q^52 + 8 * q^53 - 5 * q^55 - 72 * q^56 + 76 * q^58 - q^59 - 7 * q^61 + 15 * q^62 + 28 * q^64 + 16 * q^65 + 14 * q^67 + 2 * q^68 + 4 * q^70 - 27 * q^71 - 26 * q^73 - 18 * q^74 - 56 * q^76 - 28 * q^77 - 23 * q^79 + 7 * q^80 + 36 * q^82 + 24 * q^83 - 10 * q^85 - 2 * q^86 - 9 * q^89 - 46 * q^91 - 52 * q^92 + 90 * q^94 - 2 * q^95 - 10 * q^97 + 21 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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