LMFDB - Embedded newform 819.2.s.f.802.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(289,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

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

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

chi := DirichletCharacter("819.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.s (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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 $ x^20 + 18x^18 - 4x^17 + 211x^16 - 59x^15 + 1458x^14 - 526x^13 + 7324x^12 - 2645x^11 + 23428x^10 - 8506x^9 + 54235x^8 - 18801x^7 + 74141x^6 - 25533x^5 + 68867x^4 - 16327x^3 + 16588x^2 + 2997x + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			802.3
Root			$0.904928 - 1.56738i$ of defining polynomial
Character	$\chi$	$=$	819.802
Dual form			819.2.s.f.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.80986 q^{2} +1.27558 q^{4} +(-1.98776 - 3.44291i) q^{5} +(1.70815 - 2.02045i) q^{7} +1.31110 q^{8} +O(q^{10})$	\(q-1.80986 q^{2} +1.27558 q^{4} +(-1.98776 - 3.44291i) q^{5} +(1.70815 - 2.02045i) q^{7} +1.31110 q^{8} +(3.59756 + 6.23116i) q^{10} +(-0.143327 - 0.248250i) q^{11} +(3.60075 - 0.185985i) q^{13} +(-3.09151 + 3.65672i) q^{14} -4.92406 q^{16} +4.60182 q^{17} +(3.48374 - 6.03402i) q^{19} +(-2.53555 - 4.39170i) q^{20} +(0.259402 + 0.449297i) q^{22} +7.23857 q^{23} +(-5.40240 + 9.35723i) q^{25} +(-6.51684 + 0.336606i) q^{26} +(2.17888 - 2.57724i) q^{28} +(-0.421754 + 0.730500i) q^{29} +(-0.212854 + 0.368675i) q^{31} +6.28963 q^{32} -8.32864 q^{34} +(-10.3516 - 1.86483i) q^{35} -4.36416 q^{37} +(-6.30507 + 10.9207i) q^{38} +(-2.60615 - 4.51399i) q^{40} +(0.509885 - 0.883147i) q^{41} +(0.585291 + 1.01375i) q^{43} +(-0.182825 - 0.316662i) q^{44} -13.1008 q^{46} +(-2.71264 - 4.69843i) q^{47} +(-1.16444 - 6.90247i) q^{49} +(9.77756 - 16.9352i) q^{50} +(4.59304 - 0.237238i) q^{52} +(0.574226 - 0.994589i) q^{53} +(-0.569801 + 0.986924i) q^{55} +(2.23956 - 2.64901i) q^{56} +(0.763315 - 1.32210i) q^{58} +4.85854 q^{59} +(-4.08424 + 7.07411i) q^{61} +(0.385236 - 0.667248i) q^{62} -1.53522 q^{64} +(-7.79777 - 12.0274i) q^{65} +(-0.786937 - 1.36302i) q^{67} +5.86999 q^{68} +(18.7349 + 3.37507i) q^{70} +(3.22369 + 5.58359i) q^{71} +(8.24845 - 14.2867i) q^{73} +7.89851 q^{74} +(4.44379 - 7.69686i) q^{76} +(-0.746401 - 0.134463i) q^{77} +(-3.84412 - 6.65821i) q^{79} +(9.78785 + 16.9531i) q^{80} +(-0.922819 + 1.59837i) q^{82} -13.3888 q^{83} +(-9.14733 - 15.8436i) q^{85} +(-1.05929 - 1.83475i) q^{86} +(-0.187916 - 0.325480i) q^{88} +2.21571 q^{89} +(5.77486 - 7.59283i) q^{91} +9.23336 q^{92} +(4.90949 + 8.50349i) q^{94} -27.6994 q^{95} +(9.52241 + 16.4933i) q^{97} +(2.10746 + 12.4925i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 32 q^{4} + 3 q^{7} + 12 q^{8}+O(q^{10}) $ 20 * q + 32 * q^4 + 3 * q^7 + 12 * q^8	$ 20 q + 32 q^{4} + 3 q^{7} + 12 q^{8} - 4 q^{10} + 8 q^{11} - 5 q^{13} + 9 q^{14} + 40 q^{16} + 7 q^{19} - 12 q^{20} - 9 q^{22} - 28 q^{23} - 32 q^{25} - 13 q^{26} - 23 q^{28} + 9 q^{29} - 9 q^{31} + 34 q^{32} + 12 q^{34} - 10 q^{35} - 36 q^{37} - 22 q^{38} - 9 q^{40} + q^{41} - 11 q^{43} - 8 q^{44} + 20 q^{46} - 13 q^{47} - 3 q^{49} - 5 q^{50} - 44 q^{52} + 6 q^{53} - 19 q^{55} + 23 q^{56} - 30 q^{59} - 22 q^{62} + 72 q^{64} + 6 q^{65} - 22 q^{67} + 78 q^{68} + 30 q^{70} + 11 q^{71} - 6 q^{74} + 6 q^{76} - 56 q^{77} - 36 q^{79} - 48 q^{80} - 13 q^{82} - 40 q^{83} - 16 q^{85} - 4 q^{86} - 12 q^{88} + 4 q^{89} + 30 q^{91} - 66 q^{92} - 44 q^{94} - 72 q^{95} + 21 q^{97} + 76 q^{98}+O(q^{100}) $ 20 * q + 32 * q^4 + 3 * q^7 + 12 * q^8 - 4 * q^10 + 8 * q^11 - 5 * q^13 + 9 * q^14 + 40 * q^16 + 7 * q^19 - 12 * q^20 - 9 * q^22 - 28 * q^23 - 32 * q^25 - 13 * q^26 - 23 * q^28 + 9 * q^29 - 9 * q^31 + 34 * q^32 + 12 * q^34 - 10 * q^35 - 36 * q^37 - 22 * q^38 - 9 * q^40 + q^41 - 11 * q^43 - 8 * q^44 + 20 * q^46 - 13 * q^47 - 3 * q^49 - 5 * q^50 - 44 * q^52 + 6 * q^53 - 19 * q^55 + 23 * q^56 - 30 * q^59 - 22 * q^62 + 72 * q^64 + 6 * q^65 - 22 * q^67 + 78 * q^68 + 30 * q^70 + 11 * q^71 - 6 * q^74 + 6 * q^76 - 56 * q^77 - 36 * q^79 - 48 * q^80 - 13 * q^82 - 40 * q^83 - 16 * q^85 - 4 * q^86 - 12 * q^88 + 4 * q^89 + 30 * q^91 - 66 * q^92 - 44 * q^94 - 72 * q^95 + 21 * q^97 + 76 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.80986			−1.27976			−0.639881	−	0.768474i	$-0.721016\pi$
$2$	−1.80986			−1.27976			−0.639881	+	0.768474i	$0.721016\pi$
$3$		0			0
$3$		0			0
$4$	1.27558			0.637789
$5$	−1.98776	−	3.44291i	−0.888954	−	1.53971i	−0.841113	−	0.540859i	$-0.818099\pi$
$5$	−1.98776	−	3.44291i	−0.888954	−	1.53971i	−0.0478412	−	0.998855i	$-0.515234\pi$
$6$		0			0
$7$	1.70815	−	2.02045i	0.645621	−	0.763658i
$7$	1.70815	−	2.02045i	0.645621	−	0.763658i
$8$	1.31110			0.463543
$9$		0			0
$10$	3.59756	+	6.23116i	1.13765	+	1.97047i
$11$	−0.143327	−	0.248250i	−0.0432148	−	0.0748502i	0.843609	−	0.536958i	$-0.180427\pi$
$11$	−0.143327	−	0.248250i	−0.0432148	−	0.0748502i	−0.886824	+	0.462108i	$0.847093\pi$
$12$		0			0
$13$	3.60075	−	0.185985i	0.998669	−	0.0515830i
$13$	3.60075	−	0.185985i	0.998669	−	0.0515830i
$14$	−3.09151	+	3.65672i	−0.826240	+	0.977300i
$15$		0			0
$16$	−4.92406			−1.23101
$17$	4.60182			1.11611			0.558053	−	0.829805i	$-0.311548\pi$
$17$	4.60182			1.11611			0.558053	+	0.829805i	$0.311548\pi$
$18$		0			0
$19$	3.48374	−	6.03402i	0.799225	−	1.38430i	−0.120896	−	0.992665i	$-0.538577\pi$
$19$	3.48374	−	6.03402i	0.799225	−	1.38430i	0.920121	−	0.391634i	$-0.128090\pi$
$20$	−2.53555	−	4.39170i	−0.566965	−	0.982013i
$21$		0			0
$22$	0.259402	+	0.449297i	0.0553046	+	0.0957904i
$23$	7.23857			1.50935			0.754673	−	0.656101i	$-0.227795\pi$
$23$	7.23857			1.50935			0.754673	+	0.656101i	$0.227795\pi$
$24$		0			0
$25$	−5.40240	+	9.35723i	−1.08048	+	1.87145i
$26$	−6.51684	+	0.336606i	−1.27806	+	0.0660139i
$27$		0			0
$28$	2.17888	−	2.57724i	0.411770	−	0.487053i
$29$	−0.421754	+	0.730500i	−0.0783178	+	0.135650i	−0.902524	−	0.430639i	$-0.858288\pi$
$29$	−0.421754	+	0.730500i	−0.0783178	+	0.135650i	0.824206	+	0.566289i	$0.191622\pi$
$30$		0			0
$31$	−0.212854	+	0.368675i	−0.0382298	+	0.0662159i	−0.884507	−	0.466527i	$-0.845505\pi$
$31$	−0.212854	+	0.368675i	−0.0382298	+	0.0662159i	0.846277	+	0.532742i	$0.178839\pi$
$32$	6.28963			1.11186
$33$		0			0
$34$	−8.32864			−1.42835
$35$	−10.3516	−	1.86483i	−1.74974	−	0.315214i
$36$		0			0
$37$	−4.36416			−0.717464			−0.358732	−	0.933441i	$-0.616791\pi$
$37$	−4.36416			−0.717464			−0.358732	+	0.933441i	$0.616791\pi$
$38$	−6.30507	+	10.9207i	−1.02282	+	1.77157i
$39$		0			0
$40$	−2.60615	−	4.51399i	−0.412069	−	0.713724i
$41$	0.509885	−	0.883147i	0.0796307	−	0.137924i	−0.823460	−	0.567374i	$-0.807959\pi$
$41$	0.509885	−	0.883147i	0.0796307	−	0.137924i	0.903091	+	0.429450i	$0.141293\pi$
$42$		0			0
$43$	0.585291	+	1.01375i	0.0892560	+	0.154596i	0.907197	−	0.420706i	$-0.138218\pi$
$43$	0.585291	+	1.01375i	0.0892560	+	0.154596i	−0.817941	+	0.575302i	$0.804884\pi$
$44$	−0.182825	−	0.316662i	−0.0275619	−	0.0477386i
$45$		0			0
$46$	−13.1008			−1.93160
$47$	−2.71264	−	4.69843i	−0.395680	−	0.685337i	0.597508	−	0.801863i	$-0.296158\pi$
$47$	−2.71264	−	4.69843i	−0.395680	−	0.685337i	−0.993188	+	0.116526i	$0.962824\pi$
$48$		0			0
$49$	−1.16444	−	6.90247i	−0.166348	−	0.986067i
$50$	9.77756	−	16.9352i	1.38276	−	2.39500i
$51$		0			0
$52$	4.59304	−	0.237238i	0.636940	−	0.0328991i
$53$	0.574226	−	0.994589i	0.0788760	−	0.136617i	−0.823889	−	0.566751i	$-0.808200\pi$
$53$	0.574226	−	0.994589i	0.0788760	−	0.136617i	0.902765	+	0.430134i	$0.141534\pi$
$54$		0			0
$55$	−0.569801	+	0.986924i	−0.0768319	+	0.133077i
$56$	2.23956	−	2.64901i	0.299273	−	0.353989i
$57$		0			0
$58$	0.763315	−	1.32210i	0.100228	−	0.173600i
$59$	4.85854			0.632528			0.316264	−	0.948671i	$-0.397571\pi$
$59$	4.85854			0.632528			0.316264	+	0.948671i	$0.397571\pi$
$60$		0			0
$61$	−4.08424	+	7.07411i	−0.522933	+	0.905747i	0.476710	+	0.879060i	$0.341829\pi$
$61$	−4.08424	+	7.07411i	−0.522933	+	0.905747i	−0.999644	+	0.0266869i	$0.991504\pi$
$62$	0.385236	−	0.667248i	0.0489250	−	0.0847406i
$63$		0			0
$64$	−1.53522			−0.191902
$65$	−7.79777	−	12.0274i	−0.967194	−	1.49181i
$66$		0			0
$67$	−0.786937	−	1.36302i	−0.0961397	−	0.166519i	0.813944	−	0.580943i	$-0.197316\pi$
$67$	−0.786937	−	1.36302i	−0.0961397	−	0.166519i	−0.910084	+	0.414425i	$0.863983\pi$
$68$	5.86999			0.711841
$69$		0			0
$70$	18.7349	+	3.37507i	2.23925	+	0.403399i
$71$	3.22369	+	5.58359i	0.382581	+	0.662650i	0.991430	−	0.130636i	$-0.0417019\pi$
$71$	3.22369	+	5.58359i	0.382581	+	0.662650i	−0.608849	+	0.793286i	$0.708369\pi$
$72$		0			0
$73$	8.24845	−	14.2867i	0.965408	−	1.67214i	0.256893	−	0.966440i	$-0.417301\pi$
$73$	8.24845	−	14.2867i	0.965408	−	1.67214i	0.708515	−	0.705696i	$-0.249365\pi$
$74$	7.89851			0.918183
$75$		0			0
$76$	4.44379	−	7.69686i	0.509737	−	0.882891i
$77$	−0.746401	−	0.134463i	−0.0850603	−	0.0153235i
$78$		0			0
$79$	−3.84412	−	6.65821i	−0.432497	−	0.749107i	0.564590	−	0.825371i	$-0.309034\pi$
$79$	−3.84412	−	6.65821i	−0.432497	−	0.749107i	−0.997088	+	0.0762639i	$0.975701\pi$
$80$	9.78785	+	16.9531i	1.09432	+	1.89541i
$81$		0			0
$82$	−0.922819	+	1.59837i	−0.101908	+	0.176510i
$83$	−13.3888			−1.46961			−0.734805	−	0.678279i	$-0.762726\pi$
$83$	−13.3888			−1.46961			−0.734805	+	0.678279i	$0.762726\pi$
$84$		0			0
$85$	−9.14733	−	15.8436i	−0.992168	−	1.71848i
$86$	−1.05929	−	1.83475i	−0.114226	−	0.197846i
$87$		0			0
$88$	−0.187916	−	0.325480i	−0.0200319	−	0.0346963i
$89$	2.21571			0.234865			0.117433	−	0.993081i	$-0.462534\pi$
$89$	2.21571			0.234865			0.117433	+	0.993081i	$0.462534\pi$
$90$		0			0
$91$	5.77486	−	7.59283i	0.605369	−	0.795945i
$92$	9.23336			0.962645
$93$		0			0
$94$	4.90949	+	8.50349i	0.506375	+	0.877068i
$95$	−27.6994			−2.84190
$96$		0			0
$97$	9.52241	+	16.4933i	0.966854	+	1.67464i	0.704549	+	0.709656i	$0.251150\pi$
$97$	9.52241	+	16.4933i	0.966854	+	1.67464i	0.262306	+	0.964985i	$0.415517\pi$
$98$	2.10746	+	12.4925i	0.212886	+	1.26193i
$99$		0			0
$100$	−6.89118	+	11.9359i	−0.689118	+	1.19359i
$101$	−4.54427	−	7.87091i	−0.452172	−	0.783185i	0.546348	−	0.837558i	$-0.316017\pi$
$101$	−4.54427	−	7.87091i	−0.452172	−	0.783185i	−0.998521	+	0.0543727i	$0.982684\pi$
$102$		0			0
$103$	2.34421	+	4.06029i	0.230982	+	0.400072i	0.958097	−	0.286443i	$-0.0924729\pi$
$103$	2.34421	+	4.06029i	0.230982	+	0.400072i	−0.727116	+	0.686515i	$0.759140\pi$
$104$	4.72094	−	0.243845i	0.462926	−	0.0239109i
$105$		0			0
$106$	−1.03927	+	1.80006i	−0.100943	+	0.174838i
$107$	−14.5056			−1.40231			−0.701154	−	0.713010i	$-0.747331\pi$
$107$	−14.5056			−1.40231			−0.701154	+	0.713010i	$0.747331\pi$
$108$		0			0
$109$	2.09694	−	3.63200i	0.200850	−	0.347883i	−0.747952	−	0.663752i	$-0.768963\pi$
$109$	2.09694	−	3.63200i	0.200850	−	0.347883i	0.948803	+	0.315870i	$0.102296\pi$
$110$	1.03126	−	1.78619i	0.0983265	−	0.170307i
$111$		0			0
$112$	−8.41104	+	9.94881i	−0.794768	+	0.940074i
$113$	−4.12305	−	7.14133i	−0.387864	−	0.671800i	0.604298	−	0.796758i	$-0.293454\pi$
$113$	−4.12305	−	7.14133i	−0.387864	−	0.671800i	−0.992162	+	0.124958i	$0.960120\pi$
$114$		0			0
$115$	−14.3886	−	24.9217i	−1.34174	−	2.32396i
$116$	−0.537981	+	0.931810i	−0.0499503	+	0.0865164i
$117$		0			0
$118$	−8.79326			−0.809485
$119$	7.86061	−	9.29776i	0.720581	−	0.852324i
$120$		0			0
$121$	5.45891	−	9.45512i	0.496265	−	0.859556i
$122$	7.39189	−	12.8031i	0.669230	−	1.15914i
$123$		0			0
$124$	−0.271512	+	0.470273i	−0.0243825	+	0.0422318i
$125$	23.0771			2.06408
$126$		0			0
$127$	−3.92173	+	6.79263i	−0.347997	+	0.602748i	−0.985894	−	0.167374i	$-0.946471\pi$
$127$	−3.92173	+	6.79263i	−0.347997	+	0.602748i	0.637897	+	0.770122i	$0.279805\pi$
$128$	−9.80074			−0.866272
$129$		0			0
$130$	14.1128	+	21.7678i	1.23778	+	1.90916i
$131$	4.04277	+	7.00228i	0.353218	+	0.611792i	0.986811	−	0.161874i	$-0.0517540\pi$
$131$	4.04277	+	7.00228i	0.353218	+	0.611792i	−0.633593	+	0.773666i	$0.718421\pi$
$132$		0			0
$133$	−6.24067	−	17.3457i	−0.541135	−	1.50407i
$134$	1.42424	+	2.46686i	0.123036	+	0.213104i
$135$		0			0
$136$	6.03345			0.517364
$137$	−1.50968			−0.128981			−0.0644904	−	0.997918i	$-0.520542\pi$
$137$	−1.50968			−0.128981			−0.0644904	+	0.997918i	$0.520542\pi$
$138$		0			0
$139$	2.02132	+	3.50104i	0.171446	+	0.296954i	0.938926	−	0.344120i	$-0.111823\pi$
$139$	2.02132	+	3.50104i	0.171446	+	0.296954i	−0.767479	+	0.641074i	$0.778489\pi$
$140$	−13.2043	−	2.37874i	−1.11597	−	0.201040i
$141$		0			0
$142$	−5.83441	−	10.1055i	−0.489613	−	0.848034i
$143$	−0.562256	−	0.867230i	−0.0470182	−	0.0725214i
$144$		0			0
$145$	3.35339			0.278484
$146$	−14.9285	+	25.8569i	−1.23549	+	2.13993i
$147$		0			0
$148$	−5.56683			−0.457591
$149$	−9.59737	+	16.6231i	−0.786247	+	1.36182i	0.142004	+	0.989866i	$0.454645\pi$
$149$	−9.59737	+	16.6231i	−0.786247	+	1.36182i	−0.928251	+	0.371954i	$0.878688\pi$
$150$		0			0
$151$	−9.47334	+	16.4083i	−0.770929	+	1.33529i	0.166125	+	0.986105i	$0.446874\pi$
$151$	−9.47334	+	16.4083i	−0.770929	+	1.33529i	−0.937054	+	0.349184i	$0.886459\pi$
$152$	4.56753	−	7.91120i	0.370476	−	0.641683i
$153$		0			0
$154$	1.35088	+	0.243359i	0.108857	+	0.0196104i
$155$	1.69242			0.135938
$156$		0			0
$157$	−9.31770	+	16.1387i	−0.743633	+	1.28801i	0.207197	+	0.978299i	$0.433566\pi$
$157$	−9.31770	+	16.1387i	−0.743633	+	1.28801i	−0.950831	+	0.309711i	$0.899768\pi$
$158$	6.95730	+	12.0504i	0.553493	+	0.958679i
$159$		0			0
$160$	−12.5023	−	21.6546i	−0.988394	−	1.71195i
$161$	12.3646	−	14.6252i	0.974465	−	1.15262i
$162$		0			0
$163$	−5.35262	+	9.27102i	−0.419250	+	0.726162i	−0.995864	−	0.0908544i	$-0.971040\pi$
$163$	−5.35262	+	9.27102i	−0.419250	+	0.726162i	0.576614	+	0.817016i	$0.304374\pi$
$164$	0.650398	−	1.12652i	0.0507876	−	0.0879667i
$165$		0			0
$166$	24.2318			1.88075
$167$	−0.0240620	+	0.0416766i	−0.00186197	+	0.00322503i	−0.866955	−	0.498387i	$-0.833926\pi$
$167$	−0.0240620	+	0.0416766i	−0.00186197	+	0.00322503i	0.865093	+	0.501612i	$0.167259\pi$
$168$		0			0
$169$	12.9308	−	1.33937i	0.994678	−	0.103029i
$170$	16.5554	+	28.6747i	1.26974	+	2.19925i
$171$		0			0
$172$	0.746584	+	1.29312i	0.0569265	+	0.0985996i
$173$	−7.01486	+	12.1501i	−0.533330	+	0.923755i	0.465912	+	0.884831i	$0.345726\pi$
$173$	−7.01486	+	12.1501i	−0.533330	+	0.923755i	−0.999242	+	0.0389240i	$0.987607\pi$
$174$		0			0
$175$	9.67770	+	26.8988i	0.731565	+	2.03336i
$176$	0.705751	+	1.22240i	0.0531980	+	0.0921416i
$177$		0			0
$178$	−4.01012			−0.300571
$179$	2.34931	+	4.06913i	0.175596	+	0.304141i	0.940367	−	0.340161i	$-0.110481\pi$
$179$	2.34931	+	4.06913i	0.175596	+	0.304141i	−0.764771	+	0.644302i	$0.777148\pi$
$180$		0			0
$181$	−22.0382			−1.63809			−0.819044	−	0.573730i	$-0.805496\pi$
$181$	−22.0382			−1.63809			−0.819044	+	0.573730i	$0.805496\pi$
$182$	−10.4517	+	13.7419i	−0.774728	+	1.01862i
$183$		0			0
$184$	9.49048			0.699648
$185$	8.67492	+	15.0254i	0.637793	+	1.10469i
$186$		0			0
$187$	−0.659567	−	1.14240i	−0.0482323	−	0.0835408i
$188$	−3.46019	−	5.99322i	−0.252360	−	0.437101i
$189$		0			0
$190$	50.1319			3.63695
$191$	5.54871	−	9.61065i	0.401491	−	0.695402i	−0.592415	−	0.805633i	$-0.701826\pi$
$191$	5.54871	−	9.61065i	0.401491	−	0.695402i	0.993906	+	0.110230i	$0.0351588\pi$
$192$		0			0
$193$	0.243115	+	0.421088i	0.0174998	+	0.0303106i	0.874643	−	0.484768i	$-0.161096\pi$
$193$	0.243115	+	0.421088i	0.0174998	+	0.0303106i	−0.857143	+	0.515079i	$0.827763\pi$
$194$	−17.2342	−	29.8505i	−1.23734	−	2.14314i
$195$		0			0
$196$	−1.48533	−	8.80464i	−0.106095	−	0.628903i
$197$	8.53814	−	14.7885i	0.608317	−	1.05364i	−0.383200	−	0.923665i	$-0.625178\pi$
$197$	8.53814	−	14.7885i	0.608317	−	1.05364i	0.991518	−	0.129971i	$-0.0414886\pi$
$198$		0			0
$199$	23.1698			1.64246			0.821230	−	0.570597i	$-0.193288\pi$
$199$	23.1698			1.64246			0.821230	+	0.570597i	$0.193288\pi$
$200$	−7.08308	+	12.2683i	−0.500849	+	0.867497i
$201$		0			0
$202$	8.22448	+	14.2452i	0.578673	+	1.00229i
$203$	0.755518	+	2.09994i	0.0530270	+	0.147387i
$204$		0			0
$205$	−4.05412			−0.283152
$206$	−4.24268	−	7.34853i	−0.295601	−	0.511997i
$207$		0			0
$208$	−17.7303	+	0.915801i	−1.22938	+	0.0634994i
$209$	−1.99726			−0.138153
$210$		0			0
$211$	1.40788	−	2.43852i	0.0969224	−	0.167874i	−0.813487	−	0.581583i	$-0.802433\pi$
$211$	1.40788	−	2.43852i	0.0969224	−	0.167874i	0.910409	+	0.413709i	$0.135767\pi$
$212$	0.732470	−	1.26868i	0.0503063	−	0.0871330i
$213$		0			0
$214$	26.2530			1.79462
$215$	2.32684	−	4.03020i	0.158689	−	0.274857i
$216$		0			0
$217$	0.381301	+	1.05981i	0.0258844	+	0.0719449i
$218$	−3.79515	+	6.57340i	−0.257040	+	0.445207i
$219$		0			0
$220$	−0.726825	+	1.25890i	−0.0490026	+	0.0848749i
$221$	16.5700	−	0.855871i	1.11462	−	0.0575721i
$222$		0			0
$223$	−8.16232	+	14.1375i	−0.546589	+	0.946720i	0.451916	+	0.892061i	$0.350741\pi$
$223$	−8.16232	+	14.1375i	−0.546589	+	0.946720i	−0.998505	+	0.0546597i	$0.982593\pi$
$224$	10.7437	−	12.7079i	0.717840	−	0.849082i
$225$		0			0
$226$	7.46213	+	12.9248i	0.496373	+	0.859744i
$227$	6.20577			0.411892			0.205946	−	0.978563i	$-0.433973\pi$
$227$	6.20577			0.411892			0.205946	+	0.978563i	$0.433973\pi$
$228$		0			0
$229$	0.261463	+	0.452867i	0.0172779	+	0.0299263i	0.874535	−	0.484962i	$-0.161167\pi$
$229$	0.261463	+	0.452867i	0.0172779	+	0.0299263i	−0.857257	+	0.514889i	$0.827833\pi$
$230$	26.0412	+	45.1047i	1.71711	+	2.97412i
$231$		0			0
$232$	−0.552962	+	0.957758i	−0.0363037	+	0.0628799i
$233$	6.48273	+	11.2284i	0.424697	+	0.735598i	0.996392	−	0.0848689i	$-0.0270471\pi$
$233$	6.48273	+	11.2284i	0.424697	+	0.735598i	−0.571695	+	0.820466i	$0.693714\pi$
$234$		0			0
$235$	−10.7842	+	18.6787i	−0.703482	+	1.21847i
$236$	6.19745			0.403419
$237$		0			0
$238$	−14.2266	+	16.8276i	−0.922172	+	1.09077i
$239$	4.79605			0.310231			0.155116	−	0.987896i	$-0.450425\pi$
$239$	4.79605			0.310231			0.155116	+	0.987896i	$0.450425\pi$
$240$		0			0
$241$	10.4195			0.671179			0.335589	−	0.942008i	$-0.391065\pi$
$241$	10.4195			0.671179			0.335589	+	0.942008i	$0.391065\pi$
$242$	−9.87985	+	17.1124i	−0.635101	+	1.10003i
$243$		0			0
$244$	−5.20977	+	9.02358i	−0.333521	+	0.577676i
$245$	−21.4499	+	17.7295i	−1.37039	+	1.13270i
$246$		0			0
$247$	11.4219	−	22.3749i	0.726755	−	1.42368i
$248$	−0.279073	+	0.483369i	−0.0177212	+	0.0306940i
$249$		0			0
$250$	−41.7663			−2.64153
$251$	5.10645	+	8.84463i	0.322316	+	0.558268i	0.980966	−	0.194182i	$-0.0622052\pi$
$251$	5.10645	+	8.84463i	0.322316	+	0.558268i	−0.658649	+	0.752450i	$0.728872\pi$
$252$		0			0
$253$	−1.03748	−	1.79698i	−0.0652261	−	0.112975i
$254$	7.09776	−	12.2937i	0.445353	−	0.771374i
$255$		0			0
$256$	20.8084			1.30052
$257$	6.36280			0.396901			0.198450	−	0.980111i	$-0.436409\pi$
$257$	6.36280			0.396901			0.198450	+	0.980111i	$0.436409\pi$
$258$		0			0
$259$	−7.45466	+	8.81758i	−0.463210	+	0.547898i
$260$	−9.94666	−	15.3418i	−0.616866	−	0.951460i
$261$		0			0
$262$	−7.31683	−	12.6731i	−0.452035	−	0.782948i
$263$	−8.50677	−	14.7342i	−0.524550	−	0.908547i	−0.999591	−	0.0285838i	$-0.990900\pi$
$263$	−8.50677	−	14.7342i	−0.524550	−	0.908547i	0.475041	−	0.879963i	$-0.342433\pi$
$264$		0			0
$265$	−4.56570			−0.280469
$266$	11.2947	+	31.3933i	0.692524	+	1.92485i
$267$		0			0
$268$	−1.00380	−	1.73863i	−0.0613168	−	0.106204i
$269$	9.06039			0.552422			0.276211	−	0.961097i	$-0.410921\pi$
$269$	9.06039			0.552422			0.276211	+	0.961097i	$0.410921\pi$
$270$		0			0
$271$	2.22796			0.135339			0.0676696	−	0.997708i	$-0.478444\pi$
$271$	2.22796			0.135339			0.0676696	+	0.997708i	$0.478444\pi$
$272$	−22.6596			−1.37394
$273$		0			0
$274$	2.73231			0.165065
$275$	3.09724			0.186771
$276$		0			0
$277$	−7.80754			−0.469110			−0.234555	−	0.972103i	$-0.575363\pi$
$277$	−7.80754			−0.469110			−0.234555	+	0.972103i	$0.575363\pi$
$278$	−3.65830	−	6.33637i	−0.219411	−	0.380030i
$279$		0			0
$280$	−13.5720	−	2.44498i	−0.811082	−	0.146115i
$281$	12.7531			0.760789			0.380394	−	0.924824i	$-0.375788\pi$
$281$	12.7531			0.760789			0.380394	+	0.924824i	$0.375788\pi$
$282$		0			0
$283$	−8.17193	−	14.1542i	−0.485771	−	0.841380i	0.514095	−	0.857733i	$-0.328128\pi$
$283$	−8.17193	−	14.1542i	−0.485771	−	0.841380i	−0.999866	+	0.0163530i	$0.994794\pi$
$284$	4.11206	+	7.12230i	0.244006	+	0.422631i
$285$		0			0
$286$	1.01760	+	1.56956i	0.0601721	+	0.0928101i
$287$	−0.913393	−	2.53875i	−0.0539159	−	0.149857i
$288$		0			0
$289$	4.17679			0.245694
$290$	−6.06915			−0.356393
$291$		0			0
$292$	10.5215	−	18.2238i	0.615727	−	1.06647i
$293$	−11.8319	−	20.4935i	−0.691227	−	1.19724i	−0.971436	−	0.237302i	$-0.923737\pi$
$293$	−11.8319	−	20.4935i	−0.691227	−	1.19724i	0.280209	−	0.959939i	$-0.409596\pi$
$294$		0			0
$295$	−9.65762	−	16.7275i	−0.562288	−	0.973912i
$296$	−5.72185			−0.332576
$297$		0			0
$298$	17.3699	−	30.0855i	1.00621	−	1.74280i
$299$	26.0643	−	1.34627i	1.50734	−	0.0778566i
$300$		0			0
$301$	3.04800	+	0.549094i	0.175684	+	0.0316492i
$302$	17.1454	−	29.6967i	0.986605	−	1.70885i
$303$		0			0
$304$	−17.1541	+	29.7119i	−0.983858	+	1.70409i
$305$	32.4740			1.85946
$306$		0			0
$307$	8.99691			0.513481			0.256740	−	0.966480i	$-0.417351\pi$
$307$	8.99691			0.513481			0.256740	+	0.966480i	$0.417351\pi$
$308$	−0.952093	−	0.171518i	−0.0542505	−	0.00977316i
$309$		0			0
$310$	−3.06303			−0.173968
$311$	−15.4498	+	26.7598i	−0.876077	+	1.51741i	−0.0204655	+	0.999791i	$0.506515\pi$
$311$	−15.4498	+	26.7598i	−0.876077	+	1.51741i	−0.855611	+	0.517619i	$0.826819\pi$
$312$		0			0
$313$	3.74574	+	6.48782i	0.211722	+	0.366713i	0.952254	−	0.305308i	$-0.0987595\pi$
$313$	3.74574	+	6.48782i	0.211722	+	0.366713i	−0.740532	+	0.672022i	$0.765426\pi$
$314$	16.8637	−	29.2088i	0.951673	−	1.64835i
$315$		0			0
$316$	−4.90348	−	8.49307i	−0.275842	−	0.477773i
$317$	−8.11402	−	14.0539i	−0.455729	−	0.789346i	0.543001	−	0.839732i	$-0.317288\pi$
$317$	−8.11402	−	14.0539i	−0.455729	−	0.789346i	−0.998730	+	0.0503864i	$0.983955\pi$
$318$		0			0
$319$	0.241796			0.0135379
$320$	3.05165	+	5.28562i	0.170593	+	0.295475i
$321$		0			0
$322$	−22.3781	+	26.4695i	−1.24708	+	1.47508i
$323$	16.0316	−	27.7675i	0.892021	−	1.54503i
$324$		0			0
$325$	−17.7124	+	34.6978i	−0.982507	+	1.92469i
$326$	9.68748	−	16.7792i	0.536540	−	0.929314i
$327$		0			0
$328$	0.668510	−	1.15789i	0.0369123	−	0.0639340i
$329$	−14.1266	−	2.54488i	−0.778822	−	0.140304i
$330$		0			0
$331$	−2.79217	+	4.83618i	−0.153472	+	0.265821i	−0.932501	−	0.361166i	$-0.882379\pi$
$331$	−2.79217	+	4.83618i	−0.153472	+	0.265821i	0.779030	+	0.626987i	$0.215712\pi$
$332$	−17.0784			−0.937301
$333$		0			0
$334$	0.0435488	−	0.0754287i	0.00238288	−	0.00412727i
$335$	−3.12849	+	5.41870i	−0.170928	+	0.296055i
$336$		0			0
$337$	−0.504097			−0.0274599			−0.0137299	−	0.999906i	$-0.504371\pi$
$337$	−0.504097			−0.0274599			−0.0137299	+	0.999906i	$0.504371\pi$
$338$	−23.4029	+	2.42407i	−1.27295	+	0.131852i
$339$		0			0
$340$	−11.6681	−	20.2098i	−0.632794	−	1.09603i
$341$	0.122031			0.00660836
$342$		0			0
$343$	−15.9351	−	9.43778i	−0.860416	−	0.509592i
$344$	0.767374	+	1.32913i	0.0413740	+	0.0716619i
$345$		0			0
$346$	12.6959	−	21.9899i	0.682535	−	1.18219i
$347$	12.1334			0.651357			0.325678	−	0.945481i	$-0.394407\pi$
$347$	12.1334			0.651357			0.325678	+	0.945481i	$0.394407\pi$
$348$		0			0
$349$	10.9086	−	18.8943i	0.583924	−	1.01139i	−0.411084	−	0.911597i	$-0.634850\pi$
$349$	10.9086	−	18.8943i	0.583924	−	1.01139i	0.995009	−	0.0997893i	$-0.0318169\pi$
$350$	−17.5152	−	48.6830i	−0.936229	−	2.60222i
$351$		0			0
$352$	−0.901476	−	1.56140i	−0.0480488	−	0.0832230i
$353$	−6.04396	−	10.4684i	−0.321688	−	0.557179i	0.659149	−	0.752013i	$-0.270917\pi$
$353$	−6.04396	−	10.4684i	−0.321688	−	0.557179i	−0.980836	+	0.194833i	$0.937583\pi$
$354$		0			0
$355$	12.8158	−	22.1977i	0.680194	−	1.17813i
$356$	2.82631			0.149794
$357$		0			0
$358$	−4.25192	−	7.36454i	−0.224721	−	0.389228i
$359$	7.22027	+	12.5059i	0.381071	+	0.660035i	0.991216	−	0.132255i	$-0.0422218\pi$
$359$	7.22027	+	12.5059i	0.381071	+	0.660035i	−0.610144	+	0.792290i	$0.708889\pi$
$360$		0			0
$361$	−14.7729	−	25.5875i	−0.777523	−	1.34671i
$362$	39.8860			2.09636
$363$		0			0
$364$	7.36628	−	9.68525i	0.386098	−	0.507645i
$365$	−65.5838			−3.43281
$366$		0			0
$367$	−12.1894	−	21.1126i	−0.636280	−	1.10207i	−0.986242	−	0.165305i	$-0.947139\pi$
$367$	−12.1894	−	21.1126i	−0.636280	−	1.10207i	0.349963	−	0.936764i	$-0.386194\pi$
$368$	−35.6431			−1.85803
$369$		0			0
$370$	−15.7004	−	27.1938i	−0.816223	−	1.41374i
$371$	−1.02865	−	2.85910i	−0.0534049	−	0.148437i
$372$		0			0
$373$	4.20017	−	7.27490i	0.217476	−	0.376680i	−0.736559	−	0.676373i	$-0.763551\pi$
$373$	4.20017	−	7.27490i	0.217476	−	0.376680i	0.954036	+	0.299693i	$0.0968842\pi$
$374$	1.19372	+	2.06758i	0.0617258	+	0.106912i
$375$		0			0
$376$	−3.55654	−	6.16011i	−0.183415	−	0.317684i
$377$	−1.38277	+	2.70879i	−0.0712163	+	0.139510i
$378$		0			0
$379$	−1.82895	+	3.16783i	−0.0939467	+	0.162720i	−0.909169	−	0.416428i	$-0.863282\pi$
$379$	−1.82895	+	3.16783i	−0.0939467	+	0.162720i	0.815222	+	0.579149i	$0.196615\pi$
$380$	−35.3328			−1.81253
$381$		0			0
$382$	−10.0424	+	17.3939i	−0.513812	+	0.889949i
$383$	−15.3526	+	26.5915i	−0.784481	+	1.35876i	0.144827	+	0.989457i	$0.453737\pi$
$383$	−15.3526	+	26.5915i	−0.784481	+	1.35876i	−0.929308	+	0.369305i	$0.879596\pi$
$384$		0			0
$385$	1.02072	+	2.83707i	0.0520209	+	0.144590i
$386$	−0.440003	−	0.762108i	−0.0223956	−	0.0387903i
$387$		0			0
$388$	12.1466	+	21.0385i	0.616649	+	1.06807i
$389$	9.21889	−	15.9676i	0.467416	−	0.809589i	−0.531890	−	0.846813i	$-0.678518\pi$
$389$	9.21889	−	15.9676i	0.467416	−	0.809589i	0.999307	+	0.0372241i	$0.0118515\pi$
$390$		0			0
$391$	33.3106			1.68459
$392$	−1.52669	−	9.04982i	−0.0771095	−	0.457085i
$393$		0			0
$394$	−15.4528	+	26.7650i	−0.778501	+	1.34840i
$395$	−15.2824	+	26.4699i	−0.768941	+	1.33184i
$396$		0			0
$397$	1.13032	−	1.95777i	0.0567290	−	0.0982576i	−0.836266	−	0.548324i	$-0.815266\pi$
$397$	1.13032	−	1.95777i	0.0567290	−	0.0982576i	0.892995	+	0.450066i	$0.148600\pi$
$398$	−41.9339			−2.10196
$399$		0			0
$400$	26.6017	−	46.0755i	1.33009	−	2.30378i
$401$	−28.5217			−1.42431			−0.712153	−	0.702024i	$-0.752280\pi$
$401$	−28.5217			−1.42431			−0.712153	+	0.702024i	$0.752280\pi$
$402$		0			0
$403$	−0.697868	+	1.36709i	−0.0347633	+	0.0680998i
$404$	−5.79658	−	10.0400i	−0.288391	−	0.499507i
$405$		0			0
$406$	−1.36738	−	3.80059i	−0.0678619	−	0.188620i
$407$	0.625503	+	1.08340i	0.0310051	+	0.0537023i
$408$		0			0
$409$	10.8540			0.536695			0.268348	−	0.963322i	$-0.413522\pi$
$409$	10.8540			0.536695			0.268348	+	0.963322i	$0.413522\pi$
$410$	7.33738			0.362367
$411$		0			0
$412$	2.99022	+	5.17921i	0.147318	+	0.255162i
$413$	8.29912	−	9.81643i	0.408373	−	0.483035i
$414$		0			0
$415$	26.6137	+	46.0963i	1.30642	+	2.26278i
$416$	22.6474	−	1.16978i	1.11038	−	0.0573531i
$417$		0			0
$418$	3.61475			0.176803
$419$	7.68279	−	13.3070i	0.375329	−	0.650089i	−0.615047	−	0.788490i	$-0.710863\pi$
$419$	7.68279	−	13.3070i	0.375329	−	0.650089i	0.990376	+	0.138401i	$0.0441964\pi$
$420$		0			0
$421$	−3.33695			−0.162633			−0.0813166	−	0.996688i	$-0.525912\pi$
$421$	−3.33695			−0.162633			−0.0813166	+	0.996688i	$0.525912\pi$
$422$	−2.54806	+	4.41337i	−0.124038	+	0.214839i
$423$		0			0
$424$	0.752867	−	1.30400i	0.0365625	−	0.0633281i
$425$	−24.8609	+	43.0603i	−1.20593	+	2.08873i
$426$		0			0
$427$	7.31639	+	20.3357i	0.354065	+	0.984112i
$428$	−18.5030			−0.894377
$429$		0			0
$430$	−4.21124	+	7.29408i	−0.203084	+	0.351752i
$431$	−2.13047	−	3.69008i	−0.102621	−	0.177745i	0.810143	−	0.586233i	$-0.199390\pi$
$431$	−2.13047	−	3.69008i	−0.102621	−	0.177745i	−0.912764	+	0.408488i	$0.866056\pi$
$432$		0			0
$433$	−5.56416	−	9.63741i	−0.267396	−	0.463144i	0.700792	−	0.713365i	$-0.252830\pi$
$433$	−5.56416	−	9.63741i	−0.267396	−	0.463144i	−0.968189	+	0.250221i	$0.919497\pi$
$434$	−0.690100	−	1.91811i	−0.0331259	−	0.0920722i
$435$		0			0
$436$	2.67481	−	4.63290i	0.128100	−	0.221876i
$437$	25.2173	−	43.6777i	1.20631	−	2.08939i
$438$		0			0
$439$	41.0024			1.95694			0.978470	−	0.206389i	$-0.0661712\pi$
$439$	41.0024			1.95694			0.978470	+	0.206389i	$0.0661712\pi$
$440$	−0.747065	+	1.29395i	−0.0356149	+	0.0616869i
$441$		0			0
$442$	−29.9894	+	1.54900i	−1.42645	+	0.0736785i
$443$	7.92693	+	13.7298i	0.376620	+	0.652325i	0.990568	−	0.137022i	$-0.0437530\pi$
$443$	7.92693	+	13.7298i	0.376620	+	0.652325i	−0.613948	+	0.789346i	$0.710420\pi$
$444$		0			0
$445$	−4.40431	−	7.62849i	−0.208784	−	0.361625i
$446$	14.7726	−	25.5869i	0.699504	−	1.21158i
$447$		0			0
$448$	−2.62239	+	3.10183i	−0.123896	+	0.146548i
$449$	7.54997	+	13.0769i	0.356305	+	0.617139i	0.987340	−	0.158616i	$-0.0507030\pi$
$449$	7.54997	+	13.0769i	0.356305	+	0.617139i	−0.631035	+	0.775754i	$0.717370\pi$
$450$		0			0
$451$	−0.292322			−0.0137649
$452$	−5.25927	−	9.10933i	−0.247375	−	0.428467i
$453$		0			0
$454$	−11.2316			−0.527123
$455$	−37.6204	−	4.78954i	−1.76367	−	0.224537i
$456$		0			0
$457$	−0.0278479			−0.00130267			−0.000651335	−	1.00000i	$-0.500207\pi$
$457$	−0.0278479			−0.00130267			−0.000651335		1.00000i	$0.500207\pi$
$458$	−0.473210	−	0.819624i	−0.0221116	−	0.0382985i
$459$		0			0
$460$	−18.3537	−	31.7896i	−0.855747	−	1.48220i
$461$	−14.0543	−	24.3428i	−0.654575	−	1.13376i	−0.982000	−	0.188880i	$-0.939514\pi$
$461$	−14.0543	−	24.3428i	−0.654575	−	1.13376i	0.327425	−	0.944877i	$-0.393819\pi$
$462$		0			0
$463$	−0.266538			−0.0123871			−0.00619354	−	0.999981i	$-0.501971\pi$
$463$	−0.266538			−0.0123871			−0.00619354	+	0.999981i	$0.501971\pi$
$464$	2.07674	−	3.59702i	0.0964104	−	0.166988i
$465$		0			0
$466$	−11.7328	−	20.3218i	−0.543511	−	0.941389i
$467$	18.5400	+	32.1123i	0.857931	+	1.48598i	0.873899	+	0.486107i	$0.161583\pi$
$467$	18.5400	+	32.1123i	0.857931	+	1.48598i	−0.0159687	+	0.999872i	$0.505083\pi$
$468$		0			0
$469$	−4.09811	−	0.738270i	−0.189233	−	0.0340901i
$470$	19.5178	−	33.8058i	0.900289	−	1.55935i
$471$		0			0
$472$	6.37002			0.293204
$473$	0.167776	−	0.290597i	0.00771436	−	0.0133617i
$474$		0			0
$475$	37.6411	+	65.1964i	1.72709	+	2.99141i
$476$	10.0268	−	11.8600i	0.459579	−	0.543603i
$477$		0			0
$478$	−8.68017			−0.397022
$479$	14.3993	+	24.9404i	0.657922	+	1.13955i	0.981153	+	0.193234i	$0.0618976\pi$
$479$	14.3993	+	24.9404i	0.657922	+	1.13955i	−0.323231	+	0.946320i	$0.604769\pi$
$480$		0			0
$481$	−15.7143	+	0.811669i	−0.716509	+	0.0370089i
$482$	−18.8578			−0.858949
$483$		0			0
$484$	6.96327	−	12.0607i	0.316512	−	0.548216i
$485$	37.8566	−	65.5695i	1.71898	−	2.97736i
$486$		0			0
$487$	−13.7303			−0.622181			−0.311090	−	0.950380i	$-0.600694\pi$
$487$	−13.7303			−0.622181			−0.311090	+	0.950380i	$0.600694\pi$
$488$	−5.35484	+	9.27486i	−0.242402	+	0.419853i
$489$		0			0
$490$	38.8213	−	32.0879i	1.75377	−	1.44958i
$491$	−13.7632	+	23.8386i	−0.621126	+	1.07582i	0.368150	+	0.929766i	$0.379991\pi$
$491$	−13.7632	+	23.8386i	−0.621126	+	1.07582i	−0.989276	+	0.146056i	$0.953342\pi$
$492$		0			0
$493$	−1.94084	+	3.36163i	−0.0874110	+	0.151400i
$494$	−20.6719	+	40.4954i	−0.930073	+	1.82197i
$495$		0			0
$496$	1.04811	−	1.81537i	0.0470614	−	0.0815127i
$497$	16.7879	+	3.02432i	0.753041	+	0.135659i
$498$		0			0
$499$	1.94567	+	3.37000i	0.0871001	+	0.150862i	0.906284	−	0.422669i	$-0.138907\pi$
$499$	1.94567	+	3.37000i	0.0871001	+	0.150862i	−0.819184	+	0.573531i	$0.805573\pi$
$500$	29.4367			1.31645
$501$		0			0
$502$	−9.24194	−	16.0075i	−0.412488	−	0.714450i
$503$	1.87991	+	3.25610i	0.0838212	+	0.145183i	0.904888	−	0.425649i	$-0.139954\pi$
$503$	1.87991	+	3.25610i	0.0838212	+	0.145183i	−0.821067	+	0.570832i	$0.806621\pi$
$504$		0			0
$505$	−18.0659	+	31.2910i	−0.803921	+	1.39243i
$506$	1.87770	+	3.25227i	0.0834738	+	0.144581i
$507$		0			0
$508$	−5.00247	+	8.66453i	−0.221949	+	0.384426i
$509$	38.5481			1.70861			0.854307	−	0.519769i	$-0.173982\pi$
$509$	38.5481			1.70861			0.854307	+	0.519769i	$0.173982\pi$
$510$		0			0
$511$	−14.7760	−	41.0695i	−0.653653	−	1.81681i
$512$	−18.0587			−0.798088
$513$		0			0
$514$	−11.5158			−0.507938
$515$	9.31946	−	16.1418i	0.410664	−	0.711291i
$516$		0			0
$517$	−0.777591	+	1.34683i	−0.0341984	+	0.0592334i
$518$	13.4919	−	15.9585i	0.592798	−	0.701178i
$519$		0			0
$520$	−10.2236	−	15.7690i	−0.448336	−	0.691519i
$521$	6.92277	−	11.9906i	0.303292	−	0.525318i	−0.673587	−	0.739108i	$-0.735247\pi$
$521$	6.92277	−	11.9906i	0.303292	−	0.525318i	0.976880	+	0.213790i	$0.0685808\pi$
$522$		0			0
$523$	20.0671			0.877472			0.438736	−	0.898616i	$-0.355426\pi$
$523$	20.0671			0.877472			0.438736	+	0.898616i	$0.355426\pi$
$524$	5.15687	+	8.93196i	0.225279	+	0.390194i
$525$		0			0
$526$	15.3960	+	26.6667i	0.671299	+	1.16272i
$527$	−0.979519	+	1.69658i	−0.0426685	+	0.0739040i
$528$		0			0
$529$	29.3969			1.27813
$530$	8.26326			0.358933
$531$		0			0
$532$	−7.96047	−	22.1259i	−0.345130	−	0.959278i
$533$	1.67172	−	3.27482i	0.0724101	−	0.141848i
$534$		0			0
$535$	28.8337	+	49.9414i	1.24659	+	2.15915i
$536$	−1.03175	−	1.78705i	−0.0445649	−	0.0771887i
$537$		0			0
$538$	−16.3980			−0.706968
$539$	−1.54664	+	1.27838i	−0.0666186	+	0.0550638i
$540$		0			0
$541$	−18.9415	−	32.8076i	−0.814357	−	1.41051i	−0.909788	−	0.415072i	$-0.863756\pi$
$541$	−18.9415	−	32.8076i	−0.814357	−	1.41051i	0.0954310	−	0.995436i	$-0.469577\pi$
$542$	−4.03229			−0.173202
$543$		0			0
$544$	28.9438			1.24096
$545$	−16.6728			−0.714186
$546$		0			0
$547$	29.3783			1.25613			0.628063	−	0.778162i	$-0.283848\pi$
$547$	29.3783			1.25613			0.628063	+	0.778162i	$0.283848\pi$
$548$	−1.92572			−0.0822625
$549$		0			0
$550$	−5.60556			−0.239022
$551$	2.93857	+	5.08975i	0.125187	+	0.216831i
$552$		0			0
$553$	−20.0189	−	3.60638i	−0.851291	−	0.153359i
$554$	14.1305			0.600349
$555$		0			0
$556$	2.57836	+	4.46584i	0.109347	+	0.189394i
$557$	0.513038	+	0.888609i	0.0217381	+	0.0376516i	0.876690	−	0.481056i	$-0.159747\pi$
$557$	0.513038	+	0.888609i	0.0217381	+	0.0376516i	−0.854952	+	0.518708i	$0.826413\pi$
$558$		0			0
$559$	2.29603	+	3.54142i	0.0971117	+	0.149786i
$560$	50.9720	+	9.18253i	2.15396	+	0.388033i
$561$		0			0
$562$	−23.0814			−0.973628
$563$	36.2249			1.52670			0.763348	−	0.645988i	$-0.223554\pi$
$563$	36.2249			1.52670			0.763348	+	0.645988i	$0.223554\pi$
$564$		0			0
$565$	−16.3913	+	28.3905i	−0.689587	+	1.19440i
$566$	14.7900	+	25.6171i	0.621671	+	1.07677i
$567$		0			0
$568$	4.22657	+	7.32064i	0.177343	+	0.307167i
$569$	−2.83671			−0.118921			−0.0594605	−	0.998231i	$-0.518938\pi$
$569$	−2.83671			−0.118921			−0.0594605	+	0.998231i	$0.518938\pi$
$570$		0			0
$571$	2.29825	−	3.98069i	0.0961789	−	0.166587i	−0.813921	−	0.580975i	$-0.802671\pi$
$571$	2.29825	−	3.98069i	0.0961789	−	0.166587i	0.910100	+	0.414389i	$0.136005\pi$
$572$	−0.717202	−	1.10622i	−0.0299877	−	0.0462534i
$573$		0			0
$574$	1.65311	+	4.59477i	0.0689995	+	0.191782i
$575$	−39.1057	+	67.7330i	−1.63082	+	2.82466i
$576$		0			0
$577$	8.75176	−	15.1585i	0.364341	−	0.631056i	−0.624329	−	0.781161i	$-0.714628\pi$
$577$	8.75176	−	15.1585i	0.364341	−	0.631056i	0.988670	+	0.150105i	$0.0479611\pi$
$578$	−7.55939			−0.314429
$579$		0			0
$580$	4.27751			0.177614
$581$	−22.8701	+	27.0514i	−0.948810	+	1.12228i
$582$		0			0
$583$	−0.329209			−0.0136344
$584$	10.8145	−	18.7313i	0.447509	−	0.775108i
$585$		0			0
$586$	21.4140	+	37.0902i	0.884606	+	1.53218i
$587$	0.671155	−	1.16247i	0.0277015	−	0.0479805i	−0.851842	−	0.523798i	$-0.824515\pi$
$587$	0.671155	−	1.16247i	0.0277015	−	0.0479805i	0.879544	+	0.475818i	$0.157848\pi$
$588$		0			0
$589$	1.48306	+	2.56874i	0.0611084	+	0.105843i
$590$	17.4789	+	30.2743i	0.719595	+	1.24638i
$591$		0			0
$592$	21.4894			0.883209
$593$	−22.0843	−	38.2512i	−0.906895	−	1.57079i	−0.818353	−	0.574716i	$-0.805112\pi$
$593$	−22.0843	−	38.2512i	−0.906895	−	1.57079i	−0.0885427	−	0.996072i	$-0.528221\pi$
$594$		0			0
$595$	−47.6363	−	8.58162i	−1.95290	−	0.351812i
$596$	−12.2422	+	21.2041i	−0.501460	+	0.868554i
$597$		0			0
$598$	−47.1726	+	2.43655i	−1.92903	+	0.0996378i
$599$	−8.46583	+	14.6632i	−0.345904	+	0.599124i	−0.985518	−	0.169573i	$-0.945761\pi$
$599$	−8.46583	+	14.6632i	−0.345904	+	0.599124i	0.639613	+	0.768697i	$0.279095\pi$
$600$		0			0
$601$	7.56311	−	13.0997i	0.308506	−	0.534348i	−0.669530	−	0.742785i	$-0.733504\pi$
$601$	7.56311	−	13.0997i	0.308506	−	0.534348i	0.978036	+	0.208437i	$0.0668378\pi$
$602$	−5.51645	−	0.993781i	−0.224834	−	0.0405035i
$603$		0			0
$604$	−12.0840	+	20.9301i	−0.491690	+	0.851633i
$605$	−43.4041			−1.76463
$606$		0			0
$607$	−23.8620	+	41.3301i	−0.968527	+	1.67754i	−0.268701	+	0.963224i	$0.586594\pi$
$607$	−23.8620	+	41.3301i	−0.968527	+	1.67754i	−0.699825	+	0.714314i	$0.746739\pi$
$608$	21.9115	−	37.9518i	0.888628	−	1.53915i
$609$		0			0
$610$	−58.7733			−2.37966
$611$	−10.6414	−	16.4134i	−0.430505	−	0.664014i
$612$		0			0
$613$	−11.9854	−	20.7593i	−0.484086	−	0.838462i	0.515747	−	0.856741i	$-0.327515\pi$
$613$	−11.9854	−	20.7593i	−0.484086	−	0.838462i	−0.999833	+	0.0182791i	$0.994181\pi$
$614$	−16.2831			−0.657133
$615$		0			0
$616$	−0.978606	−	0.176295i	−0.0394292	−	0.00710311i
$617$	1.41810	+	2.45623i	0.0570907	+	0.0988839i	0.893158	−	0.449743i	$-0.148484\pi$
$617$	1.41810	+	2.45623i	0.0570907	+	0.0988839i	−0.836068	+	0.548626i	$0.815151\pi$
$618$		0			0
$619$	0.658494	−	1.14055i	0.0264671	−	0.0458424i	−0.852488	−	0.522746i	$-0.824908\pi$
$619$	0.658494	−	1.14055i	0.0264671	−	0.0458424i	0.878956	+	0.476904i	$0.158241\pi$
$620$	2.15881			0.0866999
$621$		0			0
$622$	27.9619	−	48.4314i	1.12117	−	1.94192i
$623$	3.78477	−	4.47674i	0.151634	−	0.179357i
$624$		0			0
$625$	−18.8598	−	32.6662i	−0.754393	−	1.30665i
$626$	−6.77926	−	11.7420i	−0.270954	−	0.469305i
$627$		0			0
$628$	−11.8855	+	20.5862i	−0.474281	+	0.821479i
$629$	−20.0831			−0.800766
$630$		0			0
$631$	−11.5676	−	20.0356i	−0.460497	−	0.797604i	0.538489	−	0.842633i	$-0.318995\pi$
$631$	−11.5676	−	20.0356i	−0.460497	−	0.797604i	−0.998986	+	0.0450286i	$0.985662\pi$
$632$	−5.04002	−	8.72957i	−0.200481	−	0.347244i
$633$		0			0
$634$	14.6852	+	25.4355i	0.583224	+	1.01017i
$635$	31.1818			1.23741
$636$		0			0
$637$	−5.47660	−	24.6375i	−0.216991	−	0.976174i
$638$	−0.437615			−0.0173253
$639$		0			0
$640$	19.4816	+	33.7430i	0.770076	+	1.33381i
$641$	36.6525			1.44769			0.723843	−	0.689965i	$-0.242374\pi$
$641$	36.6525			1.44769			0.723843	+	0.689965i	$0.242374\pi$
$642$		0			0
$643$	−1.86917	−	3.23749i	−0.0737127	−	0.127674i	0.826813	−	0.562477i	$-0.190151\pi$
$643$	−1.86917	−	3.23749i	−0.0737127	−	0.127674i	−0.900526	+	0.434803i	$0.856818\pi$
$644$	15.7720	−	18.6556i	0.621503	−	0.735132i
$645$		0			0
$646$	−29.0148	+	50.2552i	−1.14157	+	1.97726i
$647$	−0.763093	−	1.32172i	−0.0300003	−	0.0519620i	0.850635	−	0.525756i	$-0.176217\pi$
$647$	−0.763093	−	1.32172i	−0.0300003	−	0.0519620i	−0.880636	+	0.473794i	$0.842884\pi$
$648$		0			0
$649$	−0.696361	−	1.20613i	−0.0273345	−	0.0473448i
$650$	32.0569	−	62.7981i	1.25737	−	2.46314i
$651$		0			0
$652$	−6.82769	+	11.8259i	−0.267393	+	0.463138i
$653$	−8.95092			−0.350277			−0.175138	−	0.984544i	$-0.556037\pi$
$653$	−8.95092			−0.350277			−0.175138	+	0.984544i	$0.556037\pi$
$654$		0			0
$655$	16.0721	−	27.8377i	0.627990	−	1.08771i
$656$	−2.51070	+	4.34867i	−0.0980265	+	0.169787i
$657$		0			0
$658$	25.5670	+	4.60587i	0.996707	+	0.179555i
$659$	−4.30599	−	7.45819i	−0.167737	−	0.290530i	0.769887	−	0.638181i	$-0.220313\pi$
$659$	−4.30599	−	7.45819i	−0.167737	−	0.290530i	−0.937624	+	0.347651i	$0.886979\pi$
$660$		0			0
$661$	20.0392	+	34.7088i	0.779433	+	1.35002i	0.932269	+	0.361765i	$0.117826\pi$
$661$	20.0392	+	34.7088i	0.779433	+	1.35002i	−0.152837	+	0.988251i	$0.548841\pi$
$662$	5.05343	−	8.75279i	0.196407	−	0.340187i
$663$		0			0
$664$	−17.5540			−0.681228
$665$	−47.3148	+	55.9653i	−1.83479	+	2.17024i
$666$		0			0
$667$	−3.05290	+	5.28778i	−0.118209	+	0.204744i
$668$	−0.0306930	+	0.0531618i	−0.00118755	+	0.00205689i
$669$		0			0
$670$	5.66211	−	9.80707i	0.218747	−	0.378880i
$671$	2.34153			0.0903938
$672$		0			0
$673$	−22.0131	+	38.1277i	−0.848541	+	1.46972i	0.0339689	+	0.999423i	$0.489185\pi$
$673$	−22.0131	+	38.1277i	−0.848541	+	1.46972i	−0.882510	+	0.470294i	$0.844148\pi$
$674$	0.912342			0.0351421
$675$		0			0
$676$	16.4943	−	1.70847i	0.634395	−	0.0657105i
$677$	12.0556	+	20.8809i	0.463334	+	0.802518i	0.999125	−	0.0418328i	$-0.0133197\pi$
$677$	12.0556	+	20.8809i	0.463334	+	0.802518i	−0.535791	+	0.844351i	$0.679986\pi$
$678$		0			0
$679$	49.5896	+	8.93350i	1.90307	+	0.342836i
$680$	−11.9931	−	20.7726i	−0.459913	−	0.796592i
$681$		0			0
$682$	−0.220859			−0.00845713
$683$	18.5855			0.711155			0.355578	−	0.934647i	$-0.384284\pi$
$683$	18.5855			0.711155			0.355578	+	0.934647i	$0.384284\pi$
$684$		0			0
$685$	3.00089	+	5.19769i	0.114658	+	0.198594i
$686$	28.8403	+	17.0810i	1.10113	+	0.652157i
$687$		0			0
$688$	−2.88201	−	4.99178i	−0.109875	−	0.190310i
$689$	1.88267	−	3.68807i	0.0717239	−	0.140504i
$690$		0			0
$691$	−22.6374			−0.861166			−0.430583	−	0.902551i	$-0.641692\pi$
$691$	−22.6374			−0.861166			−0.430583	+	0.902551i	$0.641692\pi$
$692$	−8.94801	+	15.4984i	−0.340152	+	0.589161i
$693$		0			0
$694$	−21.9598			−0.833581
$695$	8.03582	−	13.9185i	0.304816	−	0.527957i
$696$		0			0
$697$	2.34640	−	4.06409i	0.0888763	−	0.153938i
$698$	−19.7430	+	34.1959i	−0.747284	+	1.29433i
$699$		0			0
$700$	12.3447	+	34.3116i	0.466584	+	1.29686i
$701$	−50.1432			−1.89388			−0.946941	−	0.321407i	$-0.895844\pi$
$701$	−50.1432			−1.89388			−0.946941	+	0.321407i	$0.895844\pi$
$702$		0			0
$703$	−15.2036	+	26.3335i	−0.573416	+	0.993185i
$704$	0.220039	+	0.381118i	0.00829302	+	0.0143639i
$705$		0			0
$706$	10.9387	+	18.9464i	0.411683	+	0.713056i
$707$	−23.6651	−	4.26324i	−0.890018	−	0.160336i
$708$		0			0
$709$	14.8556	−	25.7306i	0.557913	−	0.966334i	−0.439757	−	0.898117i	$-0.644936\pi$
$709$	14.8556	−	25.7306i	0.557913	−	0.966334i	0.997670	−	0.0682172i	$-0.0217311\pi$
$710$	−23.1948	+	40.1746i	−0.870487	+	1.50773i
$711$		0			0
$712$	2.90502			0.108870
$713$	−1.54076	+	2.66868i	−0.0577020	+	0.0999428i
$714$		0			0
$715$	−1.86816	+	3.65964i	−0.0698651	+	0.136863i
$716$	2.99673	+	5.19049i	0.111993	+	0.193978i
$717$		0			0
$718$	−13.0677	−	22.6338i	−0.487681	−	0.844687i
$719$	−14.9346	+	25.8675i	−0.556968	+	0.964697i	0.440780	+	0.897615i	$0.354702\pi$
$719$	−14.9346	+	25.8675i	−0.556968	+	0.964697i	−0.997748	+	0.0670813i	$0.978631\pi$
$720$		0			0
$721$	12.2079	+	2.19923i	0.454645	+	0.0819037i
$722$	26.7369	+	46.3096i	0.995044	+	1.72347i
$723$		0			0
$724$	−28.1115			−1.04476
$725$	−4.55697	−	7.89291i	−0.169242	−	0.293135i
$726$		0			0
$727$	36.0210			1.33594			0.667972	−	0.744186i	$-0.267163\pi$
$727$	36.0210			1.33594			0.667972	+	0.744186i	$0.267163\pi$
$728$	7.57141	−	9.95495i	0.280615	−	0.368955i
$729$		0			0
$730$	118.697			4.39318
$731$	2.69341	+	4.66512i	0.0996192	+	0.172546i
$732$		0			0
$733$	8.97642	+	15.5476i	0.331552	+	0.574265i	0.982816	−	0.184586i	$-0.0590945\pi$
$733$	8.97642	+	15.5476i	0.331552	+	0.574265i	−0.651265	+	0.758851i	$0.725761\pi$
$734$	22.0610	+	38.2108i	0.814286	+	1.41038i
$735$		0			0
$736$	45.5280			1.67818
$737$	−0.225579	+	0.390714i	−0.00830931	+	0.0143921i
$738$		0			0
$739$	−22.2469	−	38.5328i	−0.818366	−	1.41745i	−0.906886	−	0.421377i	$-0.861547\pi$
$739$	−22.2469	−	38.5328i	−0.818366	−	1.41745i	0.0885201	−	0.996074i	$-0.471786\pi$
$740$	11.0655	+	19.1661i	0.406777	+	0.704559i
$741$		0			0
$742$	1.86171	+	5.17457i	0.0683456	+	0.189964i
$743$	10.7390	−	18.6004i	0.393975	−	0.682384i	−0.598995	−	0.800753i	$-0.704433\pi$
$743$	10.7390	−	18.6004i	0.393975	−	0.682384i	0.992970	+	0.118368i	$0.0377664\pi$
$744$		0			0
$745$	76.3092			2.79575
$746$	−7.60169	+	13.1665i	−0.278318	+	0.482061i
$747$		0			0
$748$	−0.841329	−	1.45722i	−0.0307620	−	0.0532814i
$749$	−24.7777	+	29.3078i	−0.905359	+	1.07088i
$750$		0			0
$751$	3.20035			0.116783			0.0583913	−	0.998294i	$-0.481403\pi$
$751$	3.20035			0.116783			0.0583913	+	0.998294i	$0.481403\pi$
$752$	13.3572	+	23.1354i	0.487087	+	0.843660i
$753$		0			0
$754$	2.50262	−	4.90252i	0.0911399	−	0.178539i
$755$	75.3230			2.74128
$756$		0			0
$757$	−12.8640	+	22.2811i	−0.467550	+	0.809821i	−0.999313	−	0.0370727i	$-0.988197\pi$
$757$	−12.8640	+	22.2811i	−0.467550	+	0.809821i	0.531762	+	0.846894i	$0.321530\pi$
$758$	3.31013	−	5.73331i	0.120229	−	0.208243i
$759$		0			0
$760$	−36.3167			−1.31734
$761$	14.3748	−	24.8979i	0.521087	−	0.902548i	−0.478613	−	0.878026i	$-0.658860\pi$
$761$	14.3748	−	24.8979i	0.521087	−	0.902548i	0.999699	−	0.0245222i	$-0.00780645\pi$
$762$		0			0
$763$	−3.75639	−	10.4408i	−0.135990	−	0.377981i
$764$	7.07782	−	12.2591i	0.256066	−	0.443520i
$765$		0			0
$766$	27.7860	−	48.1268i	1.00395	−	1.73889i
$767$	17.4944	−	0.903616i	0.631686	−	0.0326277i
$768$		0			0
$769$	8.98213	−	15.5575i	0.323904	−	0.561018i	−0.657386	−	0.753554i	$-0.728338\pi$
$769$	8.98213	−	15.5575i	0.323904	−	0.561018i	0.981290	+	0.192536i	$0.0616712\pi$
$770$	−1.84736	−	5.13469i	−0.0665744	−	0.185041i
$771$		0			0
$772$	0.310112	+	0.537131i	0.0111612	+	0.0193318i
$773$	−39.6652			−1.42666			−0.713329	−	0.700829i	$-0.752813\pi$
$773$	−39.6652			−1.42666			−0.713329	+	0.700829i	$0.752813\pi$
$774$		0			0
$775$	−2.29985	−	3.98345i	−0.0826130	−	0.143090i
$776$	12.4848	+	21.6243i	0.448179	+	0.776269i
$777$		0			0
$778$	−16.6849	+	28.8990i	−0.598182	+	1.03608i
$779$	−3.55262	−	6.15331i	−0.127286	−	0.220465i
$780$		0			0
$781$	0.924084	−	1.60056i	0.0330663	−	0.0572725i
$782$	−60.2875			−2.15587
$783$		0			0
$784$	5.73375	+	33.9882i	0.204777	+	1.21386i
$785$	74.0855			2.64422
$786$		0			0
$787$	−39.5666			−1.41040			−0.705199	−	0.709010i	$-0.749142\pi$
$787$	−39.5666			−1.41040			−0.705199	+	0.709010i	$0.749142\pi$
$788$	10.8911	−	18.8639i	0.387978	−	0.671998i
$789$		0			0
$790$	27.6589	−	47.9067i	0.984061	−	1.70444i
$791$	−21.4715	−	3.86806i	−0.763439	−	0.137533i
$792$		0			0
$793$	−13.3907	+	26.2317i	−0.475516	+	0.931516i
$794$	−2.04571	+	3.54328i	−0.0725996	+	0.125746i
$795$		0			0
$796$	29.5548			1.04754
$797$	9.72309	+	16.8409i	0.344409	+	0.596535i	0.985246	−	0.171142i	$-0.0547458\pi$
$797$	9.72309	+	16.8409i	0.344409	+	0.596535i	−0.640837	+	0.767677i	$0.721412\pi$
$798$		0			0
$799$	−12.4831	−	21.6214i	−0.441621	−	0.764909i
$800$	−33.9791	+	58.8536i	−1.20134	+	2.08079i
$801$		0			0
$802$	51.6202			1.82277
$803$	−4.72891			−0.166880
$804$		0			0
$805$	−74.9309	−	13.4987i	−2.64097	−	0.475767i
$806$	1.26304	−	2.47424i	0.0444887	−	0.0871515i
$807$		0			0
$808$	−5.95799	−	10.3195i	−0.209601	−	0.363040i
$809$	−8.65420	−	14.9895i	−0.304265	−	0.527003i	0.672832	−	0.739795i	$-0.265078\pi$
$809$	−8.65420	−	14.9895i	−0.304265	−	0.527003i	−0.977098	+	0.212792i	$0.931744\pi$
$810$		0			0
$811$	−2.62646			−0.0922275			−0.0461138	−	0.998936i	$-0.514684\pi$
$811$	−2.62646			−0.0922275			−0.0461138	+	0.998936i	$0.514684\pi$
$812$	0.963723	+	2.67864i	0.0338200	+	0.0940017i
$813$		0			0
$814$	−1.13207	−	1.96080i	−0.0396791	−	0.0687262i
$815$	42.5590			1.49078
$816$		0			0
$817$	8.15601			0.285343
$818$	−19.6442			−0.686842
$819$		0			0
$820$	−5.17135			−0.180591
$821$	32.3955			1.13061			0.565305	−	0.824882i	$-0.308758\pi$
$821$	32.3955			1.13061			0.565305	+	0.824882i	$0.308758\pi$
$822$		0			0
$823$	−41.0161			−1.42973			−0.714866	−	0.699261i	$-0.753512\pi$
$823$	−41.0161			−1.42973			−0.714866	+	0.699261i	$0.753512\pi$
$824$	3.07349	+	5.32344i	0.107070	+	0.185451i
$825$		0			0
$826$	−15.0202	+	17.7663i	−0.522620	+	0.618170i
$827$	44.2260			1.53789			0.768944	−	0.639316i	$-0.220782\pi$
$827$	44.2260			1.53789			0.768944	+	0.639316i	$0.220782\pi$
$828$		0			0
$829$	2.74781	+	4.75935i	0.0954354	+	0.165299i	0.909790	−	0.415068i	$-0.136242\pi$
$829$	2.74781	+	4.75935i	0.0954354	+	0.165299i	−0.814355	+	0.580367i	$0.802909\pi$
$830$	−48.1670	−	83.4276i	−1.67190	−	2.89582i
$831$		0			0
$832$	−5.52794	+	0.285528i	−0.191647	+	0.00989890i
$833$	−5.35853	−	31.7640i	−0.185662	−	1.10056i
$834$		0			0
$835$	0.191318			0.00662084
$836$	−2.54766			−0.0881127
$837$		0			0
$838$	−13.9047	+	24.0837i	−0.480332	+	0.831959i
$839$	21.4269	+	37.1125i	0.739739	+	1.28127i	0.952612	+	0.304186i	$0.0983846\pi$
$839$	21.4269	+	37.1125i	0.739739	+	1.28127i	−0.212873	+	0.977080i	$0.568282\pi$
$840$		0			0
$841$	14.1442	+	24.4986i	0.487733	+	0.844778i
$842$	6.03941			0.208132
$843$		0			0
$844$	1.79586	−	3.11052i	0.0618160	−	0.107069i
$845$	−30.3147	−	41.8572i	−1.04286	−	1.43993i
$846$		0			0
$847$	−9.77894	−	27.1802i	−0.336008	−	0.933924i
$848$	−2.82752	+	4.89741i	−0.0970975	+	0.168178i
$849$		0			0
$850$	44.9946	−	77.9330i	1.54330	−	2.67308i
$851$	−31.5903			−1.08290
$852$		0			0
$853$	−46.0876			−1.57801			−0.789004	−	0.614388i	$-0.789403\pi$
$853$	−46.0876			−1.57801			−0.789004	+	0.614388i	$0.789403\pi$
$854$	−13.2416	−	36.8046i	−0.453118	−	1.25943i
$855$		0			0
$856$	−19.0183			−0.650031
$857$	−3.33662	+	5.77919i	−0.113977	+	0.197413i	−0.917370	−	0.398035i	$-0.869692\pi$
$857$	−3.33662	+	5.77919i	−0.113977	+	0.197413i	0.803394	+	0.595448i	$0.203026\pi$
$858$		0			0
$859$	8.20940	+	14.2191i	0.280101	+	0.485149i	0.971409	−	0.237411i	$-0.0762987\pi$
$859$	8.20940	+	14.2191i	0.280101	+	0.485149i	−0.691308	+	0.722560i	$0.742965\pi$
$860$	2.96806	−	5.14084i	0.101210	−	0.175301i
$861$		0			0
$862$	3.85584	+	6.67851i	0.131330	+	0.227471i
$863$	−4.92500	−	8.53035i	−0.167649	−	0.290377i	0.769944	−	0.638112i	$-0.220284\pi$
$863$	−4.92500	−	8.53035i	−0.167649	−	0.290377i	−0.937593	+	0.347735i	$0.886951\pi$
$864$		0			0
$865$	55.7755			1.89643
$866$	10.0703	+	17.4423i	0.342204	+	0.592714i
$867$		0			0
$868$	0.486379	+	1.35188i	0.0165088	+	0.0458856i
$869$	−1.10193	+	1.90861i	−0.0373805	+	0.0647450i
$870$		0			0
$871$	−3.08707	−	4.76152i	−0.104601	−	0.161338i
$872$	2.74929	−	4.76191i	0.0931027	−	0.161259i
$873$		0			0
$874$	−45.6397	+	79.0503i	−1.54379	+	2.67392i
$875$	39.4192	−	46.6262i	1.33261	−	1.57625i
$876$		0			0
$877$	−3.02056	+	5.23177i	−0.101997	+	0.176664i	−0.912507	−	0.409060i	$-0.865857\pi$
$877$	−3.02056	+	5.23177i	−0.101997	+	0.176664i	0.810510	+	0.585724i	$0.199190\pi$
$878$	−74.2085			−2.50442
$879$		0			0
$880$	2.80573	−	4.85967i	0.0945812	−	0.163819i
$881$	−15.5861	+	26.9959i	−0.525109	+	0.909516i	0.474463	+	0.880275i	$0.342642\pi$
$881$	−15.5861	+	26.9959i	−0.525109	+	0.909516i	−0.999572	+	0.0292404i	$0.990691\pi$
$882$		0			0
$883$	−18.2205			−0.613169			−0.306584	−	0.951844i	$-0.599186\pi$
$883$	−18.2205			−0.613169			−0.306584	+	0.951844i	$0.599186\pi$
$884$	21.1364	−	1.09173i	0.710893	−	0.0367189i
$885$		0			0
$886$	−14.3466	−	24.8490i	−0.481984	−	0.834820i
$887$	−7.41684			−0.249033			−0.124517	−	0.992218i	$-0.539738\pi$
$887$	−7.41684			−0.249033			−0.124517	+	0.992218i	$0.539738\pi$
$888$		0			0
$889$	7.02526	+	19.5265i	0.235620	+	0.654898i
$890$	7.97117	+	13.8065i	0.267194	+	0.462794i
$891$		0			0
$892$	−10.4117	+	18.0336i	−0.348609	+	0.603808i
$893$	−37.8006			−1.26495
$894$		0			0
$895$	9.33975	−	16.1769i	0.312194	−	0.540735i
$896$	−16.7412	+	19.8019i	−0.559283	+	0.661535i
$897$		0			0
$898$	−13.6644	−	23.6674i	−0.455986	−	0.789790i
$899$	−0.179545	−	0.310980i	−0.00598815	−	0.0103718i
$900$		0			0
$901$	2.64249	−	4.57692i	0.0880341	−	0.152479i
$902$	0.529060			0.0176158
$903$		0			0
$904$	−5.40573	−	9.36299i	−0.179792	−	0.311409i
$905$	43.8068	+	75.8756i	1.45619	+	2.52219i
$906$		0			0
$907$	8.70718	+	15.0813i	0.289117	+	0.500766i	0.973599	−	0.228264i	$-0.0733049\pi$
$907$	8.70718	+	15.0813i	0.289117	+	0.500766i	−0.684482	+	0.729030i	$0.739972\pi$
$908$	7.91595			0.262700
$909$		0			0
$910$	68.0876	+	8.66839i	2.25708	+	0.287354i
$911$	40.5753			1.34432			0.672159	−	0.740407i	$-0.265367\pi$
$911$	40.5753			1.34432			0.672159	+	0.740407i	$0.265367\pi$
$912$		0			0
$913$	1.91898	+	3.32376i	0.0635088	+	0.110001i
$914$	0.0504007			0.00166711
$915$		0			0
$916$	0.333516	+	0.577667i	0.0110197	+	0.0190867i
$917$	21.0534	+	3.79275i	0.695245	+	0.125247i
$918$		0			0
$919$	24.2733	−	42.0426i	0.800702	−	1.38686i	−0.118452	−	0.992960i	$-0.537793\pi$
$919$	24.2733	−	42.0426i	0.800702	−	1.38686i	0.919154	−	0.393898i	$-0.128874\pi$
$920$	−18.8648	−	32.6748i	−0.621955	−	1.07726i
$921$		0			0
$922$	25.4363	+	44.0570i	0.837700	+	1.45094i
$923$	12.6462	+	19.5056i	0.416253	+	0.642033i
$924$		0			0
$925$	23.5770	−	40.8365i	0.775206	−	1.34270i
$926$	0.482395			0.0158525
$927$		0			0
$928$	−2.65268	+	4.59458i	−0.0870785	+	0.150824i
$929$	−4.06964	+	7.04883i	−0.133521	+	0.231264i	−0.925031	−	0.379891i	$-0.875962\pi$
$929$	−4.06964	+	7.04883i	−0.133521	+	0.231264i	0.791511	+	0.611155i	$0.209295\pi$
$930$		0			0
$931$	−45.7062	−	17.0202i	−1.49796	−	0.557815i
$932$	8.26922	+	14.3227i	0.270867	+	0.469156i
$933$		0			0
$934$	−33.5548	−	58.1186i	−1.09795	−	1.90170i
$935$	−2.62212	+	4.54165i	−0.0857526	+	0.148528i
$936$		0			0
$937$	30.6536			1.00141			0.500705	−	0.865618i	$-0.333074\pi$
$937$	30.6536			1.00141			0.500705	+	0.865618i	$0.333074\pi$
$938$	7.41699	+	1.33616i	0.242173	+	0.0436272i
$939$		0			0
$940$	−13.7561	+	23.8262i	−0.448673	+	0.777125i
$941$	−4.34815	+	7.53122i	−0.141746	+	0.245511i	−0.928154	−	0.372196i	$-0.878605\pi$
$941$	−4.34815	+	7.53122i	−0.141746	+	0.245511i	0.786408	+	0.617707i	$0.211938\pi$
$942$		0			0
$943$	3.69084	−	6.39272i	0.120190	−	0.208176i
$944$	−23.9237			−0.778651
$945$		0			0
$946$	−0.303651	+	0.525938i	−0.00987254	+	0.0170997i
$947$	11.4722			0.372796			0.186398	−	0.982474i	$-0.440319\pi$
$947$	11.4722			0.372796			0.186398	+	0.982474i	$0.440319\pi$
$948$		0			0
$949$	27.0435	−	52.9771i	0.877869	−	1.71971i
$950$	−68.1250	−	117.996i	−2.21027	−	3.82830i
$951$		0			0
$952$	10.3060	−	12.1903i	0.334021	−	0.395089i
$953$	23.1731	+	40.1370i	0.750650	+	1.30016i	0.947508	+	0.319731i	$0.103593\pi$
$953$	23.1731	+	40.1370i	0.750650	+	1.30016i	−0.196859	+	0.980432i	$0.563074\pi$
$954$		0			0
$955$	−44.1181			−1.42763
$956$	6.11774			0.197862
$957$		0			0
$958$	−26.0607	−	45.1384i	−0.841983	−	1.45836i
$959$	−2.57876	+	3.05024i	−0.0832727	+	0.0984972i
$960$		0			0
$961$	15.4094	+	26.6898i	0.497077	+	0.860963i
$962$	28.4406	−	1.46900i	0.916961	−	0.0473626i
$963$		0			0
$964$	13.2909			0.428071
$965$	0.966511	−	1.67405i	0.0311131	−	0.0538894i
$966$		0			0
$967$	8.71419			0.280229			0.140115	−	0.990135i	$-0.455253\pi$
$967$	8.71419			0.280229			0.140115	+	0.990135i	$0.455253\pi$
$968$	7.15718	−	12.3966i	0.230040	−	0.398442i
$969$		0			0
$970$	−68.5149	+	118.671i	−2.19988	+	3.81031i
$971$	20.0281	−	34.6897i	0.642733	−	1.11325i	−0.342087	−	0.939668i	$-0.611134\pi$
$971$	20.0281	−	34.6897i	0.642733	−	1.11325i	0.984820	−	0.173578i	$-0.0555330\pi$
$972$		0			0
$973$	10.5264	+	1.89632i	0.337461	+	0.0607931i
$974$	24.8499			0.796243
$975$		0			0
$976$	20.1110	−	34.8333i	0.643738	−	1.11499i
$977$	−21.1533	−	36.6387i	−0.676755	−	1.17217i	−0.975953	−	0.217983i	$-0.930052\pi$
$977$	−21.1533	−	36.6387i	−0.676755	−	1.17217i	0.299197	−	0.954191i	$-0.403281\pi$
$978$		0			0
$979$	−0.317572	−	0.550050i	−0.0101496	−	0.0175797i
$980$	−27.3611	+	22.6154i	−0.874017	+	0.722422i
$981$		0			0
$982$	24.9095	−	43.1445i	0.794893	−	1.37680i
$983$	−2.44395	+	4.23305i	−0.0779501	+	0.135013i	−0.902365	−	0.430972i	$-0.858171\pi$
$983$	−2.44395	+	4.23305i	−0.0779501	+	0.135013i	0.824415	+	0.565985i	$0.191504\pi$
$984$		0			0
$985$	−67.8872			−2.16307
$986$	3.51264	−	6.08407i	0.111865	−	0.193756i
$987$		0			0
$988$	14.5695	−	28.5410i	0.463517	−	0.908009i
$989$	4.23667	+	7.33813i	0.134718	+	0.233339i
$990$		0			0
$991$	9.29795	+	16.1045i	0.295359	+	0.511577i	0.975068	−	0.221905i	$-0.0712273\pi$
$991$	9.29795	+	16.1045i	0.295359	+	0.511577i	−0.679709	+	0.733482i	$0.737894\pi$
$992$	−1.33878	+	2.31883i	−0.0425062	+	0.0736229i
$993$		0			0
$994$	−30.3837	−	5.47358i	−0.963712	−	0.173612i
$995$	−46.0560	−	79.7713i	−1.46007	−	2.52892i
$996$		0			0
$997$	−25.6363			−0.811909			−0.405954	−	0.913893i	$-0.633061\pi$
$997$	−25.6363			−0.811909			−0.405954	+	0.913893i	$0.633061\pi$
$998$	−3.52138	−	6.09921i	−0.111467	−	0.193067i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.s.f.802.3		20
3.2	odd	2		273.2.l.c.256.8	yes	20
7.2	even	3		819.2.n.f.100.8		20
13.3	even	3		819.2.n.f.172.8		20
21.2	odd	6		273.2.j.c.100.3	✓	20
39.29	odd	6		273.2.j.c.172.3	yes	20
91.16	even	3	inner	819.2.s.f.289.3		20
273.107	odd	6		273.2.l.c.16.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.3	✓	20	21.2	odd	6
273.2.j.c.172.3	yes	20	39.29	odd	6
273.2.l.c.16.8	yes	20	273.107	odd	6
273.2.l.c.256.8	yes	20	3.2	odd	2
819.2.n.f.100.8		20	7.2	even	3
819.2.n.f.172.8		20	13.3	even	3
819.2.s.f.289.3		20	91.16	even	3	inner
819.2.s.f.802.3		20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.80986 q^{2} +1.27558 q^{4} +(-1.98776 - 3.44291i) q^{5} +(1.70815 - 2.02045i) q^{7} +1.31110 q^{8} +O(q^{10})\)	\(q-1.80986 q^{2} +1.27558 q^{4} +(-1.98776 - 3.44291i) q^{5} +(1.70815 - 2.02045i) q^{7} +1.31110 q^{8} +(3.59756 + 6.23116i) q^{10} +(-0.143327 - 0.248250i) q^{11} +(3.60075 - 0.185985i) q^{13} +(-3.09151 + 3.65672i) q^{14} -4.92406 q^{16} +4.60182 q^{17} +(3.48374 - 6.03402i) q^{19} +(-2.53555 - 4.39170i) q^{20} +(0.259402 + 0.449297i) q^{22} +7.23857 q^{23} +(-5.40240 + 9.35723i) q^{25} +(-6.51684 + 0.336606i) q^{26} +(2.17888 - 2.57724i) q^{28} +(-0.421754 + 0.730500i) q^{29} +(-0.212854 + 0.368675i) q^{31} +6.28963 q^{32} -8.32864 q^{34} +(-10.3516 - 1.86483i) q^{35} -4.36416 q^{37} +(-6.30507 + 10.9207i) q^{38} +(-2.60615 - 4.51399i) q^{40} +(0.509885 - 0.883147i) q^{41} +(0.585291 + 1.01375i) q^{43} +(-0.182825 - 0.316662i) q^{44} -13.1008 q^{46} +(-2.71264 - 4.69843i) q^{47} +(-1.16444 - 6.90247i) q^{49} +(9.77756 - 16.9352i) q^{50} +(4.59304 - 0.237238i) q^{52} +(0.574226 - 0.994589i) q^{53} +(-0.569801 + 0.986924i) q^{55} +(2.23956 - 2.64901i) q^{56} +(0.763315 - 1.32210i) q^{58} +4.85854 q^{59} +(-4.08424 + 7.07411i) q^{61} +(0.385236 - 0.667248i) q^{62} -1.53522 q^{64} +(-7.79777 - 12.0274i) q^{65} +(-0.786937 - 1.36302i) q^{67} +5.86999 q^{68} +(18.7349 + 3.37507i) q^{70} +(3.22369 + 5.58359i) q^{71} +(8.24845 - 14.2867i) q^{73} +7.89851 q^{74} +(4.44379 - 7.69686i) q^{76} +(-0.746401 - 0.134463i) q^{77} +(-3.84412 - 6.65821i) q^{79} +(9.78785 + 16.9531i) q^{80} +(-0.922819 + 1.59837i) q^{82} -13.3888 q^{83} +(-9.14733 - 15.8436i) q^{85} +(-1.05929 - 1.83475i) q^{86} +(-0.187916 - 0.325480i) q^{88} +2.21571 q^{89} +(5.77486 - 7.59283i) q^{91} +9.23336 q^{92} +(4.90949 + 8.50349i) q^{94} -27.6994 q^{95} +(9.52241 + 16.4933i) q^{97} +(2.10746 + 12.4925i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 32 q^{4} + 3 q^{7} + 12 q^{8}+O(q^{10}) \) 20 * q + 32 * q^4 + 3 * q^7 + 12 * q^8	\( 20 q + 32 q^{4} + 3 q^{7} + 12 q^{8} - 4 q^{10} + 8 q^{11} - 5 q^{13} + 9 q^{14} + 40 q^{16} + 7 q^{19} - 12 q^{20} - 9 q^{22} - 28 q^{23} - 32 q^{25} - 13 q^{26} - 23 q^{28} + 9 q^{29} - 9 q^{31} + 34 q^{32} + 12 q^{34} - 10 q^{35} - 36 q^{37} - 22 q^{38} - 9 q^{40} + q^{41} - 11 q^{43} - 8 q^{44} + 20 q^{46} - 13 q^{47} - 3 q^{49} - 5 q^{50} - 44 q^{52} + 6 q^{53} - 19 q^{55} + 23 q^{56} - 30 q^{59} - 22 q^{62} + 72 q^{64} + 6 q^{65} - 22 q^{67} + 78 q^{68} + 30 q^{70} + 11 q^{71} - 6 q^{74} + 6 q^{76} - 56 q^{77} - 36 q^{79} - 48 q^{80} - 13 q^{82} - 40 q^{83} - 16 q^{85} - 4 q^{86} - 12 q^{88} + 4 q^{89} + 30 q^{91} - 66 q^{92} - 44 q^{94} - 72 q^{95} + 21 q^{97} + 76 q^{98}+O(q^{100}) \) 20 * q + 32 * q^4 + 3 * q^7 + 12 * q^8 - 4 * q^10 + 8 * q^11 - 5 * q^13 + 9 * q^14 + 40 * q^16 + 7 * q^19 - 12 * q^20 - 9 * q^22 - 28 * q^23 - 32 * q^25 - 13 * q^26 - 23 * q^28 + 9 * q^29 - 9 * q^31 + 34 * q^32 + 12 * q^34 - 10 * q^35 - 36 * q^37 - 22 * q^38 - 9 * q^40 + q^41 - 11 * q^43 - 8 * q^44 + 20 * q^46 - 13 * q^47 - 3 * q^49 - 5 * q^50 - 44 * q^52 + 6 * q^53 - 19 * q^55 + 23 * q^56 - 30 * q^59 - 22 * q^62 + 72 * q^64 + 6 * q^65 - 22 * q^67 + 78 * q^68 + 30 * q^70 + 11 * q^71 - 6 * q^74 + 6 * q^76 - 56 * q^77 - 36 * q^79 - 48 * q^80 - 13 * q^82 - 40 * q^83 - 16 * q^85 - 4 * q^86 - 12 * q^88 + 4 * q^89 + 30 * q^91 - 66 * q^92 - 44 * q^94 - 72 * q^95 + 21 * q^97 + 76 * q^98

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