LMFDB - Embedded newform 1320.2.bw.i.961.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1320,2,Mod(361,1320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1320, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 6]))

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

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

chi := DirichletCharacter("1320.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1320.bw (of order $5$, degree $4$, 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:	$10.5402530668$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 26 x^{14} - 64 x^{13} + 486 x^{12} - 10 x^{11} + 6075 x^{10} + 9130 x^{9} + \cdots + 50410000 $ x^16 - 4x^15 + 26x^14 - 64x^13 + 486x^12 - 10x^11 + 6075x^10 + 9130x^9 + 72165x^8 + 32200x^7 + 420125x^6 + 573200x^5 + 3577025x^4 + 5167000x^3 + 17399000x^2 + 15265000*x + 50410000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			961.2
Root			$-0.725441 - 2.23268i$ of defining polynomial
Character	$\chi$	$=$	1320.961
Dual form			1320.2.bw.i.1081.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{5} +(-0.725441 - 2.23268i) q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{5} +(-0.725441 - 2.23268i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(0.594072 + 3.26299i) q^{11} +(3.20518 + 2.32870i) q^{13} +(0.309017 + 0.951057i) q^{15} +(5.31826 - 3.86394i) q^{17} +(-1.59260 + 4.90151i) q^{19} -2.34758 q^{21} +4.96182 q^{23} +(0.309017 - 0.951057i) q^{25} +(-0.809017 + 0.587785i) q^{27} +(-2.43543 - 7.49547i) q^{29} +(0.285055 + 0.207104i) q^{31} +(3.28686 + 0.443322i) q^{33} +(1.89923 + 1.37987i) q^{35} +(0.213276 + 0.656397i) q^{37} +(3.20518 - 2.32870i) q^{39} +(3.23638 - 9.96055i) q^{41} +3.22751 q^{43} +1.00000 q^{45} +(2.61497 - 8.04805i) q^{47} +(1.20454 - 0.875146i) q^{49} +(-2.03139 - 6.25198i) q^{51} +(-0.889413 - 0.646196i) q^{53} +(-2.39855 - 2.29062i) q^{55} +(4.16947 + 3.02930i) q^{57} +(-1.15025 - 3.54009i) q^{59} +(5.55086 - 4.03294i) q^{61} +(-0.725441 + 2.23268i) q^{63} -3.96182 q^{65} -0.807017 q^{67} +(1.53329 - 4.71897i) q^{69} +(-3.64814 + 2.65053i) q^{71} +(1.97283 + 6.07176i) q^{73} +(-0.809017 - 0.587785i) q^{75} +(6.85423 - 3.69347i) q^{77} +(3.78512 + 2.75005i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-10.7967 + 7.84430i) q^{83} +(-2.03139 + 6.25198i) q^{85} -7.88121 q^{87} +10.9841 q^{89} +(2.87407 - 8.84547i) q^{91} +(0.285055 - 0.207104i) q^{93} +(-1.59260 - 4.90151i) q^{95} +(5.76828 + 4.19090i) q^{97} +(1.43732 - 2.98900i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 16 q - 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} - q^{11} + q^{13} - 4 q^{15} - 3 q^{17} - 2 q^{19} - 6 q^{21} + 10 q^{23} - 4 q^{25} - 4 q^{27} - 5 q^{29} + 3 q^{31} - q^{33} - q^{35} - 25 q^{37} + q^{39} - 2 q^{41} - 2 q^{43} + 16 q^{45} + 14 q^{47} - 8 q^{49} + 2 q^{51} - 11 q^{53} + 4 q^{55} + 8 q^{57} - 7 q^{59} - 3 q^{61} + 4 q^{63} + 6 q^{65} + 32 q^{67} - 15 q^{71} - q^{73} - 4 q^{75} + 9 q^{77} - 15 q^{79} - 4 q^{81} - 17 q^{83} + 2 q^{85} + 26 q^{89} + 36 q^{91} + 3 q^{93} - 2 q^{95} - 45 q^{97} - q^{99}+O(q^{100}) $ 16 * q - 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 - q^11 + q^13 - 4 * q^15 - 3 * q^17 - 2 * q^19 - 6 * q^21 + 10 * q^23 - 4 * q^25 - 4 * q^27 - 5 * q^29 + 3 * q^31 - q^33 - q^35 - 25 * q^37 + q^39 - 2 * q^41 - 2 * q^43 + 16 * q^45 + 14 * q^47 - 8 * q^49 + 2 * q^51 - 11 * q^53 + 4 * q^55 + 8 * q^57 - 7 * q^59 - 3 * q^61 + 4 * q^63 + 6 * q^65 + 32 * q^67 - 15 * q^71 - q^73 - 4 * q^75 + 9 * q^77 - 15 * q^79 - 4 * q^81 - 17 * q^83 + 2 * q^85 + 26 * q^89 + 36 * q^91 + 3 * q^93 - 2 * q^95 - 45 * q^97 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times$.

$n$	$661$	$881$	$991$	$1057$	$1201$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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			0
$2$		0			0
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$		0			0
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$6$		0			0
$7$	−0.725441	−	2.23268i	−0.274191	−	0.843873i	−0.989432	−	0.144995i	$-0.953683\pi$
$7$	−0.725441	−	2.23268i	−0.274191	−	0.843873i	0.715241	−	0.698877i	$-0.246317\pi$
$8$		0			0
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	0.594072	+	3.26299i	0.179119	+	0.983827i
$11$	0.594072	+	3.26299i	0.179119	+	0.983827i
$12$		0			0
$13$	3.20518	+	2.32870i	0.888957	+	0.645865i	0.935606	−	0.353046i	$-0.114854\pi$
$13$	3.20518	+	2.32870i	0.888957	+	0.645865i	−0.0466487	+	0.998911i	$0.514854\pi$
$14$		0			0
$15$	0.309017	+	0.951057i	0.0797878	+	0.245562i
$16$		0			0
$17$	5.31826	−	3.86394i	1.28987	−	0.937143i	0.290064	−	0.957007i	$-0.406324\pi$
$17$	5.31826	−	3.86394i	1.28987	−	0.937143i	0.999803	+	0.0198646i	$0.00632351\pi$
$18$		0			0
$19$	−1.59260	+	4.90151i	−0.365367	+	1.12448i	0.584384	+	0.811477i	$0.301336\pi$
$19$	−1.59260	+	4.90151i	−0.365367	+	1.12448i	−0.949751	+	0.313006i	$0.898664\pi$
$20$		0			0
$21$	−2.34758			−0.512283
$22$		0			0
$23$	4.96182			1.03461			0.517306	−	0.855801i	$-0.326935\pi$
$23$	4.96182			1.03461			0.517306	+	0.855801i	$0.326935\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$		0			0
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$		0			0
$29$	−2.43543	−	7.49547i	−0.452247	−	1.39187i	−0.874337	−	0.485320i	$-0.838703\pi$
$29$	−2.43543	−	7.49547i	−0.452247	−	1.39187i	0.422089	−	0.906554i	$-0.361297\pi$
$30$		0			0
$31$	0.285055	+	0.207104i	0.0511973	+	0.0371970i	0.613090	−	0.790013i	$-0.289926\pi$
$31$	0.285055	+	0.207104i	0.0511973	+	0.0371970i	−0.561892	+	0.827210i	$0.689926\pi$
$32$		0			0
$33$	3.28686	+	0.443322i	0.572169	+	0.0771725i
$34$		0			0
$35$	1.89923	+	1.37987i	0.321028	+	0.233241i
$36$		0			0
$37$	0.213276	+	0.656397i	0.0350624	+	0.107911i	0.967056	−	0.254564i	$-0.0819319\pi$
$37$	0.213276	+	0.656397i	0.0350624	+	0.107911i	−0.931994	+	0.362475i	$0.881932\pi$
$38$		0			0
$39$	3.20518	−	2.32870i	0.513240	−	0.372890i
$40$		0			0
$41$	3.23638	−	9.96055i	0.505438	−	1.55558i	−0.294596	−	0.955622i	$-0.595185\pi$
$41$	3.23638	−	9.96055i	0.505438	−	1.55558i	0.800034	−	0.599955i	$-0.204815\pi$
$42$		0			0
$43$	3.22751			0.492190			0.246095	−	0.969246i	$-0.420852\pi$
$43$	3.22751			0.492190			0.246095	+	0.969246i	$0.420852\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	2.61497	−	8.04805i	0.381432	−	1.17393i	−0.557603	−	0.830108i	$-0.688279\pi$
$47$	2.61497	−	8.04805i	0.381432	−	1.17393i	0.939035	−	0.343820i	$-0.111721\pi$
$48$		0			0
$49$	1.20454	−	0.875146i	0.172076	−	0.125021i
$50$		0			0
$51$	−2.03139	−	6.25198i	−0.284452	−	0.875453i
$52$		0			0
$53$	−0.889413	−	0.646196i	−0.122170	−	0.0887619i	0.525022	−	0.851089i	$-0.324057\pi$
$53$	−0.889413	−	0.646196i	−0.122170	−	0.0887619i	−0.647192	+	0.762327i	$0.724057\pi$
$54$		0			0
$55$	−2.39855	−	2.29062i	−0.323420	−	0.308868i
$56$		0			0
$57$	4.16947	+	3.02930i	0.552260	+	0.401241i
$58$		0			0
$59$	−1.15025	−	3.54009i	−0.149749	−	0.460881i	0.847842	−	0.530249i	$-0.177902\pi$
$59$	−1.15025	−	3.54009i	−0.149749	−	0.460881i	−0.997591	+	0.0693684i	$0.977902\pi$
$60$		0			0
$61$	5.55086	−	4.03294i	0.710715	−	0.516365i	−0.172689	−	0.984976i	$-0.555246\pi$
$61$	5.55086	−	4.03294i	0.710715	−	0.516365i	0.883404	+	0.468612i	$0.155246\pi$
$62$		0			0
$63$	−0.725441	+	2.23268i	−0.0913970	+	0.281291i
$64$		0			0
$65$	−3.96182			−0.491403
$66$		0			0
$67$	−0.807017			−0.0985929			−0.0492964	−	0.998784i	$-0.515698\pi$
$67$	−0.807017			−0.0985929			−0.0492964	+	0.998784i	$0.515698\pi$
$68$		0			0
$69$	1.53329	−	4.71897i	0.184586	−	0.568098i
$70$		0			0
$71$	−3.64814	+	2.65053i	−0.432955	+	0.314560i	−0.782829	−	0.622237i	$-0.786224\pi$
$71$	−3.64814	+	2.65053i	−0.432955	+	0.314560i	0.349875	+	0.936797i	$0.386224\pi$
$72$		0			0
$73$	1.97283	+	6.07176i	0.230903	+	0.710645i	0.997639	+	0.0686827i	$0.0218796\pi$
$73$	1.97283	+	6.07176i	0.230903	+	0.710645i	−0.766736	+	0.641963i	$0.778120\pi$
$74$		0			0
$75$	−0.809017	−	0.587785i	−0.0934172	−	0.0678716i
$76$		0			0
$77$	6.85423	−	3.69347i	0.781112	−	0.420910i
$78$		0			0
$79$	3.78512	+	2.75005i	0.425860	+	0.309405i	0.779991	−	0.625791i	$-0.215224\pi$
$79$	3.78512	+	2.75005i	0.425860	+	0.309405i	−0.354132	+	0.935196i	$0.615224\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	−10.7967	+	7.84430i	−1.18510	+	0.861023i	−0.992737	−	0.120301i	$-0.961614\pi$
$83$	−10.7967	+	7.84430i	−1.18510	+	0.861023i	−0.192359	+	0.981325i	$0.561614\pi$
$84$		0			0
$85$	−2.03139	+	6.25198i	−0.220335	+	0.678123i
$86$		0			0
$87$	−7.88121			−0.844954
$88$		0			0
$89$	10.9841			1.16431			0.582156	−	0.813077i	$-0.302209\pi$
$89$	10.9841			1.16431			0.582156	+	0.813077i	$0.302209\pi$
$90$		0			0
$91$	2.87407	−	8.84547i	0.301284	−	0.927257i
$92$		0			0
$93$	0.285055	−	0.207104i	0.0295588	−	0.0214757i
$94$		0			0
$95$	−1.59260	−	4.90151i	−0.163397	−	0.502884i
$96$		0			0
$97$	5.76828	+	4.19090i	0.585680	+	0.425521i	0.840767	−	0.541397i	$-0.182104\pi$
$97$	5.76828	+	4.19090i	0.585680	+	0.425521i	−0.255087	+	0.966918i	$0.582104\pi$
$98$		0			0
$99$	1.43732	−	2.98900i	0.144456	−	0.300406i
$100$		0			0
$101$	−3.72133	−	2.70371i	−0.370286	−	0.269029i	0.387043	−	0.922062i	$-0.373496\pi$
$101$	−3.72133	−	2.70371i	−0.370286	−	0.269029i	−0.757330	+	0.653033i	$0.773496\pi$
$102$		0			0
$103$	−0.356529	−	1.09728i	−0.0351299	−	0.108119i	0.931954	−	0.362577i	$-0.118103\pi$
$103$	−0.356529	−	1.09728i	−0.0351299	−	0.108119i	−0.967084	+	0.254458i	$0.918103\pi$
$104$		0			0
$105$	1.89923	−	1.37987i	0.185346	−	0.134662i
$106$		0			0
$107$	−2.65950	+	8.18511i	−0.257104	+	0.791285i	0.736304	+	0.676651i	$0.236569\pi$
$107$	−2.65950	+	8.18511i	−0.257104	+	0.791285i	−0.993408	+	0.114634i	$0.963431\pi$
$108$		0			0
$109$	17.5660			1.68251			0.841257	−	0.540636i	$-0.181816\pi$
$109$	17.5660			1.68251			0.841257	+	0.540636i	$0.181816\pi$
$110$		0			0
$111$	0.690177			0.0655087
$112$		0			0
$113$	−3.96740	+	12.2104i	−0.373221	+	1.14866i	0.571450	+	0.820637i	$0.306381\pi$
$113$	−3.96740	+	12.2104i	−0.373221	+	1.14866i	−0.944671	+	0.328020i	$0.893619\pi$
$114$		0			0
$115$	−4.01420	+	2.91649i	−0.374326	+	0.271964i
$116$		0			0
$117$	−1.22427	−	3.76792i	−0.113184	−	0.348344i
$118$		0			0
$119$	−12.4850	−	9.07089i	−1.14450	−	0.831527i
$120$		0			0
$121$	−10.2942	+	3.87690i	−0.935833	+	0.352445i
$122$		0			0
$123$	−8.47295	−	6.15596i	−0.763981	−	0.555064i
$124$		0			0
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$		0			0
$127$	5.30945	−	3.85754i	0.471137	−	0.342301i	−0.326747	−	0.945112i	$-0.605952\pi$
$127$	5.30945	−	3.85754i	0.471137	−	0.342301i	0.797884	+	0.602810i	$0.205952\pi$
$128$		0			0
$129$	0.997355	−	3.06954i	0.0878122	−	0.270258i
$130$		0			0
$131$	8.64022			0.754900			0.377450	−	0.926030i	$-0.376801\pi$
$131$	8.64022			0.754900			0.377450	+	0.926030i	$0.376801\pi$
$132$		0			0
$133$	12.0988			1.04910
$134$		0			0
$135$	0.309017	−	0.951057i	0.0265959	−	0.0818539i
$136$		0			0
$137$	9.47709	−	6.88551i	0.809683	−	0.588269i	−0.104056	−	0.994571i	$-0.533182\pi$
$137$	9.47709	−	6.88551i	0.809683	−	0.588269i	0.913739	+	0.406302i	$0.133182\pi$
$138$		0			0
$139$	3.95475	+	12.1715i	0.335437	+	1.03237i	0.966506	+	0.256643i	$0.0826165\pi$
$139$	3.95475	+	12.1715i	0.335437	+	1.03237i	−0.631069	+	0.775727i	$0.717384\pi$
$140$		0			0
$141$	−6.84608	−	4.97397i	−0.576544	−	0.418884i
$142$		0			0
$143$	−5.69441	+	11.8419i	−0.476190	+	0.990267i
$144$		0			0
$145$	6.37603	+	4.63246i	0.529500	+	0.384705i
$146$		0			0
$147$	−0.460092	−	1.41602i	−0.0379477	−	0.116791i
$148$		0			0
$149$	−10.0604	+	7.30930i	−0.824179	+	0.598801i	−0.917906	−	0.396797i	$-0.870122\pi$
$149$	−10.0604	+	7.30930i	−0.824179	+	0.598801i	0.0937277	+	0.995598i	$0.470122\pi$
$150$		0			0
$151$	2.37243	−	7.30158i	0.193065	−	0.594194i	−0.806928	−	0.590649i	$-0.798872\pi$
$151$	2.37243	−	7.30158i	0.193065	−	0.594194i	0.999994	−	0.00354490i	$-0.00112838\pi$
$152$		0			0
$153$	−6.57373			−0.531454
$154$		0			0
$155$	−0.352347			−0.0283012
$156$		0			0
$157$	2.01896	−	6.21372i	0.161130	−	0.495909i	−0.837600	−	0.546284i	$-0.816042\pi$
$157$	2.01896	−	6.21372i	0.161130	−	0.495909i	0.998730	+	0.0503756i	$0.0160419\pi$
$158$		0			0
$159$	−0.889413	+	0.646196i	−0.0705350	+	0.0512467i
$160$		0			0
$161$	−3.59951	−	11.0781i	−0.283681	−	0.873080i
$162$		0			0
$163$	−1.91904	−	1.39426i	−0.150311	−	0.109207i	0.510088	−	0.860122i	$-0.329613\pi$
$163$	−1.91904	−	1.39426i	−0.150311	−	0.109207i	−0.660399	+	0.750915i	$0.729613\pi$
$164$		0			0
$165$	−2.91971	+	1.57331i	−0.227299	+	0.122482i
$166$		0			0
$167$	−14.9399	−	10.8545i	−1.15608	−	0.839943i	−0.166804	−	0.985990i	$-0.553345\pi$
$167$	−14.9399	−	10.8545i	−1.15608	−	0.839943i	−0.989278	+	0.146047i	$0.953345\pi$
$168$		0			0
$169$	0.833118	+	2.56407i	0.0640860	+	0.197236i
$170$		0			0
$171$	4.16947	−	3.02930i	0.318848	−	0.231656i
$172$		0			0
$173$	6.63296	−	20.4142i	0.504295	−	1.55206i	−0.297658	−	0.954673i	$-0.596205\pi$
$173$	6.63296	−	20.4142i	0.504295	−	1.55206i	0.801953	−	0.597388i	$-0.203795\pi$
$174$		0			0
$175$	−2.34758			−0.177460
$176$		0			0
$177$	−3.72227			−0.279783
$178$		0			0
$179$	0.803647	−	2.47337i	0.0600674	−	0.184869i	−0.916520	−	0.399988i	$-0.869014\pi$
$179$	0.803647	−	2.47337i	0.0600674	−	0.184869i	0.976588	+	0.215120i	$0.0690142\pi$
$180$		0			0
$181$	−17.9803	+	13.0635i	−1.33647	+	0.971001i	−0.336902	+	0.941540i	$0.609379\pi$
$181$	−17.9803	+	13.0635i	−1.33647	+	0.971001i	−0.999566	+	0.0294615i	$0.990621\pi$
$182$		0			0
$183$	−2.12024	−	6.52543i	−0.156733	−	0.482374i
$184$		0			0
$185$	−0.558365	−	0.405676i	−0.0410518	−	0.0298259i
$186$		0			0
$187$	15.7674	+	15.0579i	1.15303	+	1.10115i
$188$		0			0
$189$	1.89923	+	1.37987i	0.138149	+	0.100371i
$190$		0			0
$191$	−4.89308	−	15.0593i	−0.354051	−	1.08966i	−0.956558	−	0.291543i	$-0.905831\pi$
$191$	−4.89308	−	15.0593i	−0.354051	−	1.08966i	0.602507	−	0.798114i	$-0.294169\pi$
$192$		0			0
$193$	−20.1524	+	14.6416i	−1.45060	+	1.05393i	−0.464914	+	0.885356i	$0.653915\pi$
$193$	−20.1524	+	14.6416i	−1.45060	+	1.05393i	−0.985690	+	0.168569i	$0.946085\pi$
$194$		0			0
$195$	−1.22427	+	3.76792i	−0.0876718	+	0.269826i
$196$		0			0
$197$	22.0645			1.57203			0.786016	−	0.618206i	$-0.212140\pi$
$197$	22.0645			1.57203			0.786016	+	0.618206i	$0.212140\pi$
$198$		0			0
$199$	−16.2638			−1.15291			−0.576454	−	0.817130i	$-0.695564\pi$
$199$	−16.2638			−1.15291			−0.576454	+	0.817130i	$0.695564\pi$
$200$		0			0
$201$	−0.249382	+	0.767519i	−0.0175901	+	0.0541366i
$202$		0			0
$203$	−14.9682	+	10.8750i	−1.05056	+	0.763278i
$204$		0			0
$205$	3.23638	+	9.96055i	0.226039	+	0.695675i
$206$		0			0
$207$	−4.01420	−	2.91649i	−0.279006	−	0.202710i
$208$		0			0
$209$	−16.9397	−	2.28477i	−1.17174	−	0.158041i
$210$		0			0
$211$	8.18267	+	5.94506i	0.563319	+	0.409275i	0.832672	−	0.553767i	$-0.186810\pi$
$211$	8.18267	+	5.94506i	0.563319	+	0.409275i	−0.269353	+	0.963041i	$0.586810\pi$
$212$		0			0
$213$	1.39347	+	4.28865i	0.0954787	+	0.293853i
$214$		0			0
$215$	−2.61111	+	1.89708i	−0.178076	+	0.129380i
$216$		0			0
$217$	0.255607	−	0.786677i	0.0173517	−	0.0534031i
$218$		0			0
$219$	6.38422			0.431406
$220$		0			0
$221$	26.0439			1.75190
$222$		0			0
$223$	−2.41529	+	7.43351i	−0.161740	+	0.497785i	−0.998781	−	0.0493550i	$-0.984283\pi$
$223$	−2.41529	+	7.43351i	−0.161740	+	0.497785i	0.837041	+	0.547140i	$0.184283\pi$
$224$		0			0
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$		0			0
$227$	4.94069	+	15.2059i	0.327925	+	1.00925i	0.970103	+	0.242694i	$0.0780311\pi$
$227$	4.94069	+	15.2059i	0.327925	+	1.00925i	−0.642178	+	0.766556i	$0.721969\pi$
$228$		0			0
$229$	−0.336254	−	0.244303i	−0.0222203	−	0.0161440i	0.576620	−	0.817013i	$-0.304371\pi$
$229$	−0.336254	−	0.244303i	−0.0222203	−	0.0161440i	−0.598840	+	0.800869i	$0.704371\pi$
$230$		0			0
$231$	−1.39463	−	7.66011i	−0.0917598	−	0.503998i
$232$		0			0
$233$	11.7651	+	8.54786i	0.770759	+	0.559989i	0.902191	−	0.431336i	$-0.141958\pi$
$233$	11.7651	+	8.54786i	0.770759	+	0.559989i	−0.131433	+	0.991325i	$0.541958\pi$
$234$		0			0
$235$	2.61497	+	8.04805i	0.170582	+	0.524997i
$236$		0			0
$237$	3.78512	−	2.75005i	0.245870	−	0.178635i
$238$		0			0
$239$	−7.59420	+	23.3725i	−0.491228	+	1.51184i	0.331526	+	0.943446i	$0.392436\pi$
$239$	−7.59420	+	23.3725i	−0.491228	+	1.51184i	−0.822754	+	0.568398i	$0.807564\pi$
$240$		0			0
$241$	15.7211			1.01269			0.506343	−	0.862332i	$-0.330997\pi$
$241$	15.7211			1.01269			0.506343	+	0.862332i	$0.330997\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−0.460092	+	1.41602i	−0.0293942	+	0.0904660i
$246$		0			0
$247$	−16.5187	+	12.0015i	−1.05106	+	0.763640i
$248$		0			0
$249$	4.12399	+	12.6923i	0.261347	+	0.804344i
$250$		0			0
$251$	−6.68830	−	4.85934i	−0.422162	−	0.306719i	0.356345	−	0.934354i	$-0.384023\pi$
$251$	−6.68830	−	4.85934i	−0.422162	−	0.306719i	−0.778507	+	0.627636i	$0.784023\pi$
$252$		0			0
$253$	2.94768	+	16.1904i	0.185319	+	1.01788i
$254$		0			0
$255$	5.31826	+	3.86394i	0.333042	+	0.241969i
$256$		0			0
$257$	−2.98436	−	9.18492i	−0.186159	−	0.572939i	0.813807	−	0.581135i	$-0.197391\pi$
$257$	−2.98436	−	9.18492i	−0.186159	−	0.572939i	−0.999966	+	0.00819566i	$0.997391\pi$
$258$		0			0
$259$	1.31080	−	0.952355i	0.0814494	−	0.0591764i
$260$		0			0
$261$	−2.43543	+	7.49547i	−0.150749	+	0.463958i
$262$		0			0
$263$	23.3379			1.43907			0.719537	−	0.694454i	$-0.244354\pi$
$263$	23.3379			1.43907			0.719537	+	0.694454i	$0.244354\pi$
$264$		0			0
$265$	1.09937			0.0675341
$266$		0			0
$267$	3.39427	−	10.4465i	0.207726	−	0.639316i
$268$		0			0
$269$	6.30967	−	4.58424i	0.384707	−	0.279506i	−0.378576	−	0.925570i	$-0.623586\pi$
$269$	6.30967	−	4.58424i	0.384707	−	0.279506i	0.763283	+	0.646064i	$0.223586\pi$
$270$		0			0
$271$	−2.43791	−	7.50310i	−0.148092	−	0.455781i	0.849303	−	0.527905i	$-0.177022\pi$
$271$	−2.43791	−	7.50310i	−0.148092	−	0.455781i	−0.997396	+	0.0721240i	$0.977022\pi$
$272$		0			0
$273$	−7.52440	−	5.46680i	−0.455398	−	0.330866i
$274$		0			0
$275$	3.28686	+	0.443322i	0.198205	+	0.0267334i
$276$		0			0
$277$	−1.23903	−	0.900208i	−0.0744461	−	0.0540882i	0.549940	−	0.835204i	$-0.314651\pi$
$277$	−1.23903	−	0.900208i	−0.0744461	−	0.0540882i	−0.624386	+	0.781116i	$0.714651\pi$
$278$		0			0
$279$	−0.108881	−	0.335102i	−0.00651855	−	0.0200620i
$280$		0			0
$281$	−20.8986	+	15.1838i	−1.24671	+	0.905787i	−0.998026	−	0.0627981i	$-0.979998\pi$
$281$	−20.8986	+	15.1838i	−1.24671	+	0.905787i	−0.248683	+	0.968585i	$0.579998\pi$
$282$		0			0
$283$	−7.87944	+	24.2504i	−0.468384	+	1.44154i	0.386292	+	0.922377i	$0.373756\pi$
$283$	−7.87944	+	24.2504i	−0.468384	+	1.44154i	−0.854676	+	0.519161i	$0.826244\pi$
$284$		0			0
$285$	−5.15375			−0.305282
$286$		0			0
$287$	−24.5865			−1.45130
$288$		0			0
$289$	8.10053	−	24.9309i	0.476502	−	1.46652i
$290$		0			0
$291$	5.76828	−	4.19090i	0.338142	−	0.245675i
$292$		0			0
$293$	3.23404	+	9.95334i	0.188934	+	0.581480i	0.999994	−	0.00348337i	$-0.00110879\pi$
$293$	3.23404	+	9.95334i	0.188934	+	0.581480i	−0.811060	+	0.584964i	$0.801109\pi$
$294$		0			0
$295$	3.01138	+	2.18790i	0.175329	+	0.127384i
$296$		0			0
$297$	−2.39855	−	2.29062i	−0.139178	−	0.132916i
$298$		0			0
$299$	15.9035	+	11.5546i	0.919725	+	0.668219i
$300$		0			0
$301$	−2.34137	−	7.20598i	−0.134954	−	0.415346i
$302$		0			0
$303$	−3.72133	+	2.70371i	−0.213785	+	0.155324i
$304$		0			0
$305$	−2.12024	+	6.52543i	−0.121405	+	0.373645i
$306$		0			0
$307$	−18.6666			−1.06536			−0.532681	−	0.846316i	$-0.678815\pi$
$307$	−18.6666			−1.06536			−0.532681	+	0.846316i	$0.678815\pi$
$308$		0			0
$309$	−1.15375			−0.0656347
$310$		0			0
$311$	7.61669	−	23.4418i	0.431903	−	1.32926i	−0.464324	−	0.885665i	$-0.653703\pi$
$311$	7.61669	−	23.4418i	0.431903	−	1.32926i	0.896227	−	0.443596i	$-0.146297\pi$
$312$		0			0
$313$	−17.8976	+	13.0034i	−1.01163	+	0.734993i	−0.964551	−	0.263898i	$-0.914992\pi$
$313$	−17.8976	+	13.0034i	−1.01163	+	0.734993i	−0.0470806	+	0.998891i	$0.514992\pi$
$314$		0			0
$315$	−0.725441	−	2.23268i	−0.0408740	−	0.125797i
$316$		0			0
$317$	−21.1127	−	15.3393i	−1.18581	−	0.861541i	−0.192994	−	0.981200i	$-0.561820\pi$
$317$	−21.1127	−	15.3393i	−1.18581	−	0.861541i	−0.992815	+	0.119659i	$0.961820\pi$
$318$		0			0
$319$	23.0108	−	12.3996i	1.28836	−	0.694245i
$320$		0			0
$321$	6.96267	+	5.05868i	0.388618	+	0.282348i
$322$		0			0
$323$	10.4693	+	32.2212i	0.582527	+	1.79283i
$324$		0			0
$325$	3.20518	−	2.32870i	0.177791	−	0.129173i
$326$		0			0
$327$	5.42818	−	16.7062i	0.300179	−	0.923856i
$328$		0			0
$329$	−19.8657			−1.09523
$330$		0			0
$331$	−22.9764			−1.26290			−0.631448	−	0.775418i	$-0.717539\pi$
$331$	−22.9764			−1.26290			−0.631448	+	0.775418i	$0.717539\pi$
$332$		0			0
$333$	0.213276	−	0.656397i	0.0116875	−	0.0359703i
$334$		0			0
$335$	0.652891	−	0.474353i	0.0356712	−	0.0259167i
$336$		0			0
$337$	−0.834511	−	2.56836i	−0.0454587	−	0.139908i	0.925751	−	0.378134i	$-0.123434\pi$
$337$	−0.834511	−	2.56836i	−0.0454587	−	0.139908i	−0.971210	+	0.238226i	$0.923434\pi$
$338$		0			0
$339$	10.3868	+	7.54644i	0.564132	+	0.409866i
$340$		0			0
$341$	−0.506436	+	1.05316i	−0.0274250	+	0.0570320i
$342$		0			0
$343$	−16.1223	−	11.7136i	−0.870525	−	0.632473i
$344$		0			0
$345$	1.53329	+	4.71897i	0.0825494	+	0.254061i
$346$		0			0
$347$	−21.1671	+	15.3788i	−1.13631	+	0.825578i	−0.986601	−	0.163152i	$-0.947834\pi$
$347$	−21.1671	+	15.3788i	−1.13631	+	0.825578i	−0.149709	+	0.988730i	$0.547834\pi$
$348$		0			0
$349$	−10.7228	+	33.0015i	−0.573981	+	1.76653i	0.0656441	+	0.997843i	$0.479090\pi$
$349$	−10.7228	+	33.0015i	−0.573981	+	1.76653i	−0.639625	+	0.768687i	$0.720910\pi$
$350$		0			0
$351$	−3.96182			−0.211466
$352$		0			0
$353$	−12.4071			−0.660361			−0.330180	−	0.943918i	$-0.607110\pi$
$353$	−12.4071			−0.660361			−0.330180	+	0.943918i	$0.607110\pi$
$354$		0			0
$355$	1.39347	−	4.28865i	0.0739575	−	0.227618i
$356$		0			0
$357$	−12.4850	+	9.07089i	−0.660777	+	0.480082i
$358$		0			0
$359$	−5.12164	−	15.7628i	−0.270310	−	0.831928i	−0.990422	−	0.138071i	$-0.955910\pi$
$359$	−5.12164	−	15.7628i	−0.270310	−	0.831928i	0.720113	−	0.693857i	$-0.244090\pi$
$360$		0			0
$361$	−6.11712	−	4.44435i	−0.321953	−	0.233913i
$362$		0			0
$363$	0.506077	+	10.9884i	0.0265621	+	0.576739i
$364$		0			0
$365$	−5.16494	−	3.75255i	−0.270346	−	0.196418i
$366$		0			0
$367$	2.39151	+	7.36031i	0.124836	+	0.384205i	0.993871	−	0.110545i	$-0.0352596\pi$
$367$	2.39151	+	7.36031i	0.124836	+	0.384205i	−0.869035	+	0.494750i	$0.835260\pi$
$368$		0			0
$369$	−8.47295	+	6.15596i	−0.441084	+	0.320467i
$370$		0			0
$371$	−0.797531	+	2.45455i	−0.0414058	+	0.127434i
$372$		0			0
$373$	−8.37280			−0.433527			−0.216764	−	0.976224i	$-0.569550\pi$
$373$	−8.37280			−0.433527			−0.216764	+	0.976224i	$0.569550\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	9.64873	−	29.6957i	0.496935	−	1.52941i
$378$		0			0
$379$	12.0711	−	8.77015i	0.620049	−	0.450492i	−0.232889	−	0.972503i	$-0.574818\pi$
$379$	12.0711	−	8.77015i	0.620049	−	0.450492i	0.852939	+	0.522011i	$0.174818\pi$
$380$		0			0
$381$	−2.02803	−	6.24163i	−0.103899	−	0.319768i
$382$		0			0
$383$	29.3770	+	21.3436i	1.50109	+	1.09061i	0.969944	+	0.243330i	$0.0782398\pi$
$383$	29.3770	+	21.3436i	1.50109	+	1.09061i	0.531150	+	0.847278i	$0.321760\pi$
$384$		0			0
$385$	−3.37422	+	7.01690i	−0.171966	+	0.357614i
$386$		0			0
$387$	−2.61111	−	1.89708i	−0.132730	−	0.0964341i
$388$		0			0
$389$	−11.9878	−	36.8946i	−0.607804	−	1.87063i	−0.476223	−	0.879324i	$-0.657995\pi$
$389$	−11.9878	−	36.8946i	−0.607804	−	1.87063i	−0.131581	−	0.991305i	$-0.542005\pi$
$390$		0			0
$391$	26.3882	−	19.1722i	1.33451	−	0.969578i
$392$		0			0
$393$	2.66998	−	8.21734i	0.134682	−	0.414510i
$394$		0			0
$395$	−4.67867			−0.235409
$396$		0			0
$397$	−0.0482861			−0.00242341			−0.00121170	−	0.999999i	$-0.500386\pi$
$397$	−0.0482861			−0.00242341			−0.00121170	+	0.999999i	$0.500386\pi$
$398$		0			0
$399$	3.73874	−	11.5067i	0.187171	−	0.576054i
$400$		0			0
$401$	−19.5548	+	14.2074i	−0.976519	+	0.709482i	−0.956928	−	0.290326i	$-0.906236\pi$
$401$	−19.5548	+	14.2074i	−0.976519	+	0.709482i	−0.0195909	+	0.999808i	$0.506236\pi$
$402$		0			0
$403$	0.431368	+	1.32761i	0.0214880	+	0.0661331i
$404$		0			0
$405$	−0.809017	−	0.587785i	−0.0402004	−	0.0292073i
$406$		0			0
$407$	−2.01511	+	1.08586i	−0.0998855	+	0.0538243i
$408$		0			0
$409$	12.6907	+	9.22030i	0.627513	+	0.455915i	0.855538	−	0.517741i	$-0.173227\pi$
$409$	12.6907	+	9.22030i	0.627513	+	0.455915i	−0.228025	+	0.973655i	$0.573227\pi$
$410$		0			0
$411$	−3.61993	−	11.1410i	−0.178558	−	0.549545i
$412$		0			0
$413$	−7.06945	+	5.13625i	−0.347865	+	0.252739i
$414$		0			0
$415$	4.12399	−	12.6923i	0.202439	−	0.623042i
$416$		0			0
$417$	12.7978			0.626712
$418$		0			0
$419$	−28.2344			−1.37934			−0.689670	−	0.724124i	$-0.742245\pi$
$419$	−28.2344			−1.37934			−0.689670	+	0.724124i	$0.742245\pi$
$420$		0			0
$421$	−0.837966	+	2.57900i	−0.0408400	+	0.125693i	−0.969398	−	0.245495i	$-0.921049\pi$
$421$	−0.837966	+	2.57900i	−0.0408400	+	0.125693i	0.928558	+	0.371188i	$0.121049\pi$
$422$		0			0
$423$	−6.84608	+	4.97397i	−0.332868	+	0.241843i
$424$		0			0
$425$	−2.03139	−	6.25198i	−0.0985370	−	0.303266i
$426$		0			0
$427$	−13.0311	−	9.46763i	−0.630618	−	0.458171i
$428$		0			0
$429$	9.50262	+	9.07505i	0.458791	+	0.438147i
$430$		0			0
$431$	−1.16938	−	0.849605i	−0.0563271	−	0.0409240i	0.559265	−	0.828989i	$-0.311083\pi$
$431$	−1.16938	−	0.849605i	−0.0563271	−	0.0409240i	−0.615593	+	0.788065i	$0.711083\pi$
$432$		0			0
$433$	9.64008	+	29.6691i	0.463273	+	1.42581i	0.861142	+	0.508364i	$0.169750\pi$
$433$	9.64008	+	29.6691i	0.463273	+	1.42581i	−0.397870	+	0.917442i	$0.630250\pi$
$434$		0			0
$435$	6.37603	−	4.63246i	0.305707	−	0.222109i
$436$		0			0
$437$	−7.90218	+	24.3204i	−0.378013	+	1.16340i
$438$		0			0
$439$	−32.0634			−1.53030			−0.765152	−	0.643849i	$-0.777336\pi$
$439$	−32.0634			−1.53030			−0.765152	+	0.643849i	$0.777336\pi$
$440$		0			0
$441$	−1.48889			−0.0708994
$442$		0			0
$443$	8.27554	−	25.4695i	0.393183	−	1.21009i	−0.537185	−	0.843465i	$-0.680512\pi$
$443$	8.27554	−	25.4695i	0.393183	−	1.21009i	0.930368	−	0.366628i	$-0.119488\pi$
$444$		0			0
$445$	−8.88633	+	6.45629i	−0.421252	+	0.306058i
$446$		0			0
$447$	3.84272	+	11.8267i	0.181755	+	0.559383i
$448$		0			0
$449$	−16.1329	−	11.7212i	−0.761358	−	0.553159i	0.137968	−	0.990437i	$-0.455943\pi$
$449$	−16.1329	−	11.7212i	−0.761358	−	0.553159i	−0.899327	+	0.437277i	$0.855943\pi$
$450$		0			0
$451$	34.4238	+	4.64298i	1.62095	+	0.218629i
$452$		0			0
$453$	−6.21110	−	4.51263i	−0.291823	−	0.212022i
$454$		0			0
$455$	2.87407	+	8.84547i	0.134738	+	0.414682i
$456$		0			0
$457$	−2.36256	+	1.71650i	−0.110516	+	0.0802944i	−0.641670	−	0.766980i	$-0.721758\pi$
$457$	−2.36256	+	1.71650i	−0.110516	+	0.0802944i	0.531155	+	0.847275i	$0.321758\pi$
$458$		0			0
$459$	−2.03139	+	6.25198i	−0.0948173	+	0.291818i
$460$		0			0
$461$	30.6204			1.42614			0.713068	−	0.701095i	$-0.247305\pi$
$461$	30.6204			1.42614			0.713068	+	0.701095i	$0.247305\pi$
$462$		0			0
$463$	1.01879			0.0473473			0.0236737	−	0.999720i	$-0.492464\pi$
$463$	1.01879			0.0473473			0.0236737	+	0.999720i	$0.492464\pi$
$464$		0			0
$465$	−0.108881	+	0.335102i	−0.00504924	+	0.0155400i
$466$		0			0
$467$	31.5791	−	22.9435i	1.46130	−	1.06170i	0.478284	−	0.878205i	$-0.341259\pi$
$467$	31.5791	−	22.9435i	1.46130	−	1.06170i	0.983021	−	0.183494i	$-0.0587409\pi$
$468$		0			0
$469$	0.585443	+	1.80181i	0.0270333	+	0.0831998i
$470$		0			0
$471$	−5.28570	−	3.84029i	−0.243552	−	0.176951i
$472$		0			0
$473$	1.91737	+	10.5313i	0.0881608	+	0.484230i
$474$		0			0
$475$	4.16947	+	3.02930i	0.191309	+	0.138994i
$476$		0			0
$477$	0.339725	+	1.04557i	0.0155550	+	0.0478732i
$478$		0			0
$479$	−10.5829	+	7.68893i	−0.483545	+	0.351316i	−0.802697	−	0.596388i	$-0.796602\pi$
$479$	−10.5829	+	7.68893i	−0.483545	+	0.351316i	0.319151	+	0.947704i	$0.396602\pi$
$480$		0			0
$481$	−0.844963	+	2.60053i	−0.0385270	+	0.118574i
$482$		0			0
$483$	−11.6483			−0.530014
$484$		0			0
$485$	−7.12998			−0.323756
$486$		0			0
$487$	−4.02930	+	12.4009i	−0.182585	+	0.561940i	−0.999898	−	0.0142541i	$-0.995463\pi$
$487$	−4.02930	+	12.4009i	−0.182585	+	0.561940i	0.817313	+	0.576194i	$0.195463\pi$
$488$		0			0
$489$	−1.91904	+	1.39426i	−0.0867820	+	0.0630508i
$490$		0			0
$491$	−0.878881	−	2.70492i	−0.0396633	−	0.122071i	0.929264	−	0.369416i	$-0.120442\pi$
$491$	−0.878881	−	2.70492i	−0.0396633	−	0.122071i	−0.968928	+	0.247344i	$0.920442\pi$
$492$		0			0
$493$	−41.9143	−	30.4525i	−1.88772	−	1.37151i
$494$		0			0
$495$	0.594072	+	3.26299i	0.0267015	+	0.146660i
$496$		0			0
$497$	8.56429	+	6.22232i	0.384161	+	0.279109i
$498$		0			0
$499$	5.16772	+	15.9046i	0.231339	+	0.711987i	0.997586	+	0.0694416i	$0.0221218\pi$
$499$	5.16772	+	15.9046i	0.231339	+	0.711987i	−0.766247	+	0.642546i	$0.777878\pi$
$500$		0			0
$501$	−14.9399	+	10.8545i	−0.667464	+	0.484941i
$502$		0			0
$503$	−5.90309	+	18.1679i	−0.263206	+	0.810064i	0.728895	+	0.684625i	$0.240034\pi$
$503$	−5.90309	+	18.1679i	−0.263206	+	0.810064i	−0.992101	+	0.125439i	$0.959966\pi$
$504$		0			0
$505$	4.59982			0.204689
$506$		0			0
$507$	2.69603			0.119735
$508$		0			0
$509$	9.96021	−	30.6544i	0.441478	−	1.35873i	−0.444822	−	0.895619i	$-0.646733\pi$
$509$	9.96021	−	30.6544i	0.441478	−	1.35873i	0.886300	−	0.463112i	$-0.153267\pi$
$510$		0			0
$511$	12.1251	−	8.80940i	0.536383	−	0.389705i
$512$		0			0
$513$	−1.59260	−	4.90151i	−0.0703149	−	0.216407i
$514$		0			0
$515$	0.933406	+	0.678159i	0.0411308	+	0.0298833i
$516$		0			0
$517$	27.8141	+	3.75149i	1.22326	+	0.164990i
$518$		0			0
$519$	−17.3653	−	12.6166i	−0.762253	−	0.553809i
$520$		0			0
$521$	−9.79895	−	30.1581i	−0.429300	−	1.32125i	−0.898816	−	0.438325i	$-0.855572\pi$
$521$	−9.79895	−	30.1581i	−0.429300	−	1.32125i	0.469517	−	0.882924i	$-0.344428\pi$
$522$		0			0
$523$	−4.08497	+	2.96790i	−0.178623	+	0.129777i	−0.673504	−	0.739183i	$-0.735212\pi$
$523$	−4.08497	+	2.96790i	−0.178623	+	0.129777i	0.494881	+	0.868961i	$0.335212\pi$
$524$		0			0
$525$	−0.725441	+	2.23268i	−0.0316608	+	0.0974420i
$526$		0			0
$527$	2.31623			0.100897
$528$		0			0
$529$	1.61967			0.0704204
$530$		0			0
$531$	−1.15025	+	3.54009i	−0.0499164	+	0.153627i
$532$		0			0
$533$	33.5683	−	24.3888i	1.45401	−	1.05640i
$534$		0			0
$535$	−2.65950	−	8.18511i	−0.114980	−	0.353873i
$536$		0			0
$537$	−2.10398	−	1.52863i	−0.0907933	−	0.0659652i
$538$		0			0
$539$	3.57117	+	3.41048i	0.153821	+	0.146900i
$540$		0			0
$541$	−27.2811	−	19.8209i	−1.17291	−	0.852166i	−0.181552	−	0.983381i	$-0.558112\pi$
$541$	−27.2811	−	19.8209i	−1.17291	−	0.852166i	−0.991354	+	0.131215i	$0.958112\pi$
$542$		0			0
$543$	6.86788	+	21.1372i	0.294729	+	0.907082i
$544$		0			0
$545$	−14.2112	+	10.3250i	−0.608739	+	0.442275i
$546$		0			0
$547$	10.7989	−	33.2355i	0.461726	−	1.42105i	−0.401327	−	0.915935i	$-0.631451\pi$
$547$	10.7989	−	33.2355i	0.461726	−	1.42105i	0.863053	−	0.505113i	$-0.168549\pi$
$548$		0			0
$549$	−6.86124			−0.292831
$550$		0			0
$551$	40.6178			1.73038
$552$		0			0
$553$	3.39410	−	10.4460i	0.144332	−	0.444207i
$554$		0			0
$555$	−0.558365	+	0.405676i	−0.0237013	+	0.0172200i
$556$		0			0
$557$	1.27401	+	3.92099i	0.0539814	+	0.166138i	0.974412	−	0.224767i	$-0.0721622\pi$
$557$	1.27401	+	3.92099i	0.0539814	+	0.166138i	−0.920431	+	0.390905i	$0.872162\pi$
$558$		0			0
$559$	10.3447	+	7.51590i	0.437536	+	0.317889i
$560$		0			0
$561$	19.1933	−	10.3425i	0.810344	−	0.436662i
$562$		0			0
$563$	35.7785	+	25.9946i	1.50788	+	1.09554i	0.967106	+	0.254374i	$0.0818693\pi$
$563$	35.7785	+	25.9946i	1.50788	+	1.09554i	0.540776	+	0.841167i	$0.318131\pi$
$564$		0			0
$565$	−3.96740	−	12.2104i	−0.166910	−	0.513695i
$566$		0			0
$567$	1.89923	−	1.37987i	0.0797601	−	0.0579491i
$568$		0			0
$569$	7.69775	−	23.6912i	0.322707	−	0.993189i	−0.649759	−	0.760141i	$-0.725130\pi$
$569$	7.69775	−	23.6912i	0.322707	−	0.993189i	0.972465	−	0.233048i	$-0.0748699\pi$
$570$		0			0
$571$	40.8059			1.70767			0.853837	−	0.520540i	$-0.174269\pi$
$571$	40.8059			1.70767			0.853837	+	0.520540i	$0.174269\pi$
$572$		0			0
$573$	−15.8343			−0.661489
$574$		0			0
$575$	1.53329	−	4.71897i	0.0639425	−	0.196795i
$576$		0			0
$577$	21.0300	−	15.2792i	0.875489	−	0.636080i	−0.0565650	−	0.998399i	$-0.518015\pi$
$577$	21.0300	−	15.2792i	0.875489	−	0.636080i	0.932054	+	0.362319i	$0.118015\pi$
$578$		0			0
$579$	7.69754	+	23.6906i	0.319899	+	0.984548i
$580$		0			0
$581$	25.3462	+	18.4151i	1.05154	+	0.763986i
$582$		0			0
$583$	1.58015	−	3.28603i	0.0654433	−	0.136093i
$584$		0			0
$585$	3.20518	+	2.32870i	0.132518	+	0.0962799i
$586$		0			0
$587$	11.2440	+	34.6053i	0.464088	+	1.42831i	0.860126	+	0.510081i	$0.170385\pi$
$587$	11.2440	+	34.6053i	0.464088	+	1.42831i	−0.396039	+	0.918234i	$0.629615\pi$
$588$		0			0
$589$	−1.46910	+	1.06736i	−0.0605333	+	0.0439800i
$590$		0			0
$591$	6.81831	−	20.9846i	0.280468	−	0.863192i
$592$		0			0
$593$	5.95321			0.244469			0.122234	−	0.992501i	$-0.460994\pi$
$593$	5.95321			0.244469			0.122234	+	0.992501i	$0.460994\pi$
$594$		0			0
$595$	15.4323			0.632663
$596$		0			0
$597$	−5.02578	+	15.4678i	−0.205691	+	0.633053i
$598$		0			0
$599$	−21.9579	+	15.9533i	−0.897174	+	0.651835i	−0.937739	−	0.347342i	$-0.887084\pi$
$599$	−21.9579	+	15.9533i	−0.897174	+	0.651835i	0.0405645	+	0.999177i	$0.487084\pi$
$600$		0			0
$601$	−8.30404	−	25.5572i	−0.338729	−	1.04250i	−0.964856	−	0.262779i	$-0.915361\pi$
$601$	−8.30404	−	25.5572i	−0.338729	−	1.04250i	0.626127	−	0.779721i	$-0.284639\pi$
$602$		0			0
$603$	0.652891	+	0.474353i	0.0265878	+	0.0193171i
$604$		0			0
$605$	6.04937	−	9.18723i	0.245942	−	0.373514i
$606$		0			0
$607$	−3.75411	−	2.72752i	−0.152375	−	0.110707i	0.508986	−	0.860775i	$-0.330021\pi$
$607$	−3.75411	−	2.72752i	−0.152375	−	0.110707i	−0.661360	+	0.750068i	$0.730021\pi$
$608$		0			0
$609$	5.71735	+	17.5962i	0.231679	+	0.713034i
$610$		0			0
$611$	27.1229	−	19.7060i	1.09728	−	0.797218i
$612$		0			0
$613$	4.83913	−	14.8933i	0.195451	−	0.601535i	−0.804520	−	0.593925i	$-0.797578\pi$
$613$	4.83913	−	14.8933i	0.195451	−	0.601535i	0.999971	−	0.00761031i	$-0.00242246\pi$
$614$		0			0
$615$	10.4731			0.422318
$616$		0			0
$617$	−5.62586			−0.226489			−0.113244	−	0.993567i	$-0.536124\pi$
$617$	−5.62586			−0.226489			−0.113244	+	0.993567i	$0.536124\pi$
$618$		0			0
$619$	0.118581	−	0.364953i	0.00476615	−	0.0146687i	−0.948645	−	0.316342i	$-0.897545\pi$
$619$	0.118581	−	0.364953i	0.00476615	−	0.0146687i	0.953411	+	0.301673i	$0.0975452\pi$
$620$		0			0
$621$	−4.01420	+	2.91649i	−0.161084	+	0.117035i
$622$		0			0
$623$	−7.96832	−	24.5240i	−0.319244	−	0.982532i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$		0			0
$627$	−7.40760	+	15.4046i	−0.295831	+	0.615199i
$628$		0			0
$629$	3.67054	+	2.66680i	0.146354	+	0.106332i
$630$		0			0
$631$	7.63387	+	23.4946i	0.303899	+	0.935306i	0.980086	+	0.198576i	$0.0636315\pi$
$631$	7.63387	+	23.4946i	0.303899	+	0.935306i	−0.676186	+	0.736731i	$0.736368\pi$
$632$		0			0
$633$	8.18267	−	5.94506i	0.325232	−	0.236295i
$634$		0			0
$635$	−2.02803	+	6.24163i	−0.0804799	+	0.247692i
$636$		0			0
$637$	5.89871			0.233715
$638$		0			0
$639$	4.50935			0.178387
$640$		0			0
$641$	−6.09967	+	18.7729i	−0.240923	+	0.741483i	0.755358	+	0.655313i	$0.227463\pi$
$641$	−6.09967	+	18.7729i	−0.240923	+	0.741483i	−0.996280	+	0.0861709i	$0.972537\pi$
$642$		0			0
$643$	18.7262	−	13.6054i	0.738491	−	0.536545i	−0.153747	−	0.988110i	$-0.549134\pi$
$643$	18.7262	−	13.6054i	0.738491	−	0.536545i	0.892238	+	0.451565i	$0.149134\pi$
$644$		0			0
$645$	0.997355	+	3.06954i	0.0392708	+	0.120863i
$646$		0			0
$647$	2.97622	+	2.16235i	0.117007	+	0.0850108i	0.644750	−	0.764393i	$-0.276961\pi$
$647$	2.97622	+	2.16235i	0.117007	+	0.0850108i	−0.527743	+	0.849404i	$0.676961\pi$
$648$		0			0
$649$	10.8679	−	5.85630i	0.426604	−	0.229880i
$650$		0			0
$651$	−0.669187	−	0.486193i	−0.0262275	−	0.0190554i
$652$		0			0
$653$	3.45565	+	10.6354i	0.135230	+	0.416195i	0.995626	−	0.0934314i	$-0.0297836\pi$
$653$	3.45565	+	10.6354i	0.135230	+	0.416195i	−0.860396	+	0.509627i	$0.829784\pi$
$654$		0			0
$655$	−6.99009	+	5.07859i	−0.273125	+	0.198437i
$656$		0			0
$657$	1.97283	−	6.07176i	0.0769676	−	0.236882i
$658$		0			0
$659$	−21.6618			−0.843823			−0.421911	−	0.906637i	$-0.638641\pi$
$659$	−21.6618			−0.843823			−0.421911	+	0.906637i	$0.638641\pi$
$660$		0			0
$661$	−32.3120			−1.25679			−0.628395	−	0.777895i	$-0.716288\pi$
$661$	−32.3120			−1.25679			−0.628395	+	0.777895i	$0.716288\pi$
$662$		0			0
$663$	8.04801	−	24.7692i	0.312559	−	0.961958i
$664$		0			0
$665$	−9.78816	+	7.11151i	−0.379568	+	0.275773i
$666$		0			0
$667$	−12.0842	−	37.1912i	−0.467900	−	1.44005i
$668$		0			0
$669$	6.32332	+	4.59416i	0.244474	+	0.177621i
$670$		0			0
$671$	16.4570	+	15.7165i	0.635317	+	0.606730i
$672$		0			0
$673$	29.5469	+	21.4671i	1.13895	+	0.827496i	0.986973	−	0.160888i	$-0.0514358\pi$
$673$	29.5469	+	21.4671i	1.13895	+	0.827496i	0.151978	+	0.988384i	$0.451436\pi$
$674$		0			0
$675$	0.309017	+	0.951057i	0.0118941	+	0.0366062i
$676$		0			0
$677$	−28.7065	+	20.8565i	−1.10328	+	0.801579i	−0.981592	−	0.190989i	$-0.938831\pi$
$677$	−28.7065	+	20.8565i	−1.10328	+	0.801579i	−0.121687	+	0.992568i	$0.538831\pi$
$678$		0			0
$679$	5.17238	−	15.9190i	0.198498	−	0.610913i
$680$		0			0
$681$	15.9884			0.612677
$682$		0			0
$683$	−10.5455			−0.403514			−0.201757	−	0.979436i	$-0.564665\pi$
$683$	−10.5455			−0.403514			−0.201757	+	0.979436i	$0.564665\pi$
$684$		0			0
$685$	−3.61993	+	11.1410i	−0.138310	+	0.425675i
$686$		0			0
$687$	−0.336254	+	0.244303i	−0.0128289	+	0.00932074i
$688$		0			0
$689$	−1.34593	−	4.14235i	−0.0512759	−	0.157811i
$690$		0			0
$691$	−28.5673	−	20.7554i	−1.08675	−	0.789571i	−0.107903	−	0.994161i	$-0.534414\pi$
$691$	−28.5673	−	20.7554i	−1.08675	−	0.789571i	−0.978848	+	0.204590i	$0.934414\pi$
$692$		0			0
$693$	−7.71616	−	1.04073i	−0.293113	−	0.0395342i
$694$		0			0
$695$	−10.3537	−	7.52238i	−0.392737	−	0.285340i
$696$		0			0
$697$	−21.2751	−	65.4779i	−0.805851	−	2.48015i
$698$		0			0
$699$	11.7651	−	8.54786i	0.444998	−	0.323310i
$700$		0			0
$701$	−9.98217	+	30.7220i	−0.377021	+	1.16035i	0.565083	+	0.825034i	$0.308844\pi$
$701$	−9.98217	+	30.7220i	−0.377021	+	1.16035i	−0.942105	+	0.335319i	$0.891156\pi$
$702$		0			0
$703$	−3.55700			−0.134155
$704$		0			0
$705$	8.46222			0.318706
$706$		0			0
$707$	−3.33690	+	10.2699i	−0.125497	+	0.386240i
$708$		0			0
$709$	0.553367	−	0.402044i	0.0207821	−	0.0150991i	−0.577346	−	0.816500i	$-0.695911\pi$
$709$	0.553367	−	0.402044i	0.0207821	−	0.0150991i	0.598128	+	0.801401i	$0.295911\pi$
$710$		0			0
$711$	−1.44579	−	4.44968i	−0.0542213	−	0.166876i
$712$		0			0
$713$	1.41439	+	1.02761i	0.0529693	+	0.0384845i
$714$		0			0
$715$	−2.35361	−	12.9274i	−0.0880199	−	0.483456i
$716$		0			0
$717$	19.8819	+	14.4450i	0.742502	+	0.539459i
$718$		0			0
$719$	−14.3916	−	44.2926i	−0.536714	−	1.65184i	−0.739915	−	0.672700i	$-0.765134\pi$
$719$	−14.3916	−	44.2926i	−0.536714	−	1.65184i	0.203201	−	0.979137i	$-0.434866\pi$
$720$		0			0
$721$	−2.19124	+	1.59203i	−0.0816061	+	0.0592903i
$722$		0			0
$723$	4.85810	−	14.9517i	0.180675	−	0.556059i
$724$		0			0
$725$	−7.88121			−0.292701
$726$		0			0
$727$	23.5526			0.873519			0.436759	−	0.899578i	$-0.356126\pi$
$727$	23.5526			0.873519			0.436759	+	0.899578i	$0.356126\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	17.1647	−	12.4709i	0.634860	−	0.461253i
$732$		0			0
$733$	7.32752	+	22.5518i	0.270648	+	0.832969i	0.990338	+	0.138674i	$0.0442839\pi$
$733$	7.32752	+	22.5518i	0.270648	+	0.832969i	−0.719690	+	0.694296i	$0.755716\pi$
$734$		0			0
$735$	1.20454	+	0.875146i	0.0444300	+	0.0322803i
$736$		0			0
$737$	−0.479426	−	2.63329i	−0.0176599	−	0.0969983i
$738$		0			0
$739$	28.1920	+	20.4827i	1.03706	+	0.753468i	0.969710	−	0.244261i	$-0.0785454\pi$
$739$	28.1920	+	20.4827i	1.03706	+	0.753468i	0.0673506	+	0.997729i	$0.478545\pi$
$740$		0			0
$741$	6.30959	+	19.4189i	0.231788	+	0.713371i
$742$		0			0
$743$	−13.6435	+	9.91261i	−0.500533	+	0.363658i	−0.809220	−	0.587505i	$-0.800110\pi$
$743$	−13.6435	+	9.91261i	−0.500533	+	0.363658i	0.308688	+	0.951163i	$0.400110\pi$
$744$		0			0
$745$	3.84272	−	11.8267i	0.140787	−	0.433296i
$746$		0			0
$747$	13.3455			0.488287
$748$		0			0
$749$	20.2040			0.738239
$750$		0			0
$751$	10.4193	−	32.0672i	0.380205	−	1.17015i	−0.559695	−	0.828699i	$-0.689082\pi$
$751$	10.4193	−	32.0672i	0.380205	−	1.17015i	0.939900	−	0.341451i	$-0.110918\pi$
$752$		0			0
$753$	−6.68830	+	4.85934i	−0.243735	+	0.177084i
$754$		0			0
$755$	2.37243	+	7.30158i	0.0863415	+	0.265732i
$756$		0			0
$757$	−39.2854	−	28.5425i	−1.42785	−	1.03740i	−0.990412	−	0.138148i	$-0.955885\pi$
$757$	−39.2854	−	28.5425i	−1.42785	−	1.03740i	−0.437441	−	0.899247i	$-0.644115\pi$
$758$		0			0
$759$	16.3088	+	2.19969i	0.591973	+	0.0798436i
$760$		0			0
$761$	25.9095	+	18.8244i	0.939219	+	0.682382i	0.948232	−	0.317577i	$-0.102869\pi$
$761$	25.9095	+	18.8244i	0.939219	+	0.682382i	−0.00901374	+	0.999959i	$0.502869\pi$
$762$		0			0
$763$	−12.7431	−	39.2191i	−0.461330	−	1.41983i
$764$		0			0
$765$	5.31826	−	3.86394i	0.192282	−	0.139701i
$766$		0			0
$767$	4.55707	−	14.0252i	0.164546	−	0.506421i
$768$		0			0
$769$	11.2576			0.405961			0.202980	−	0.979183i	$-0.434937\pi$
$769$	11.2576			0.405961			0.202980	+	0.979183i	$0.434937\pi$
$770$		0			0
$771$	−9.65759			−0.347810
$772$		0			0
$773$	1.65468	−	5.09259i	0.0595148	−	0.183168i	−0.916879	−	0.399165i	$-0.869300\pi$
$773$	1.65468	−	5.09259i	0.0595148	−	0.183168i	0.976394	+	0.215997i	$0.0693002\pi$
$774$		0			0
$775$	0.285055	−	0.207104i	0.0102395	−	0.00743941i
$776$		0			0
$777$	−0.500683	−	1.54094i	−0.0179619	−	0.0552810i
$778$		0			0
$779$	43.6675	+	31.7263i	1.56455	+	1.13671i
$780$		0			0
$781$	−10.8159	−	10.3292i	−0.387023	−	0.369609i
$782$		0			0
$783$	6.37603	+	4.63246i	0.227861	+	0.165551i
$784$		0			0
$785$	2.01896	+	6.21372i	0.0720597	+	0.221777i
$786$		0			0
$787$	−25.6524	+	18.6376i	−0.914411	+	0.664358i	−0.942127	−	0.335257i	$-0.891177\pi$
$787$	−25.6524	+	18.6376i	−0.914411	+	0.664358i	0.0277156	+	0.999616i	$0.491177\pi$
$788$		0			0
$789$	7.21180	−	22.1956i	0.256747	−	0.790185i
$790$		0			0
$791$	30.1400			1.07165
$792$		0			0
$793$	27.1830			0.965297
$794$		0			0
$795$	0.339725	−	1.04557i	0.0120488	−	0.0370825i
$796$		0			0
$797$	1.50188	−	1.09118i	0.0531992	−	0.0386515i	−0.560868	−	0.827905i	$-0.689532\pi$
$797$	1.50188	−	1.09118i	0.0531992	−	0.0386515i	0.614067	+	0.789254i	$0.289532\pi$
$798$		0			0
$799$	−17.1901	−	52.9056i	−0.608142	−	1.87167i
$800$		0			0
$801$	−8.88633	−	6.45629i	−0.313983	−	0.228122i
$802$		0			0
$803$	−18.6401	+	10.0444i	−0.657793	+	0.354459i
$804$		0			0
$805$	9.42363	+	6.84667i	0.332139	+	0.241313i
$806$		0			0
$807$	−2.41008	−	7.41746i	−0.0848388	−	0.261107i
$808$		0			0
$809$	4.53632	−	3.29583i	0.159489	−	0.115875i	−0.505179	−	0.863015i	$-0.668573\pi$
$809$	4.53632	−	3.29583i	0.159489	−	0.115875i	0.664667	+	0.747140i	$0.268573\pi$
$810$		0			0
$811$	−11.7458	+	36.1498i	−0.412450	+	1.26939i	0.502062	+	0.864831i	$0.332575\pi$
$811$	−11.7458	+	36.1498i	−0.412450	+	1.26939i	−0.914512	+	0.404559i	$0.867425\pi$
$812$		0			0
$813$	−7.88923			−0.276687
$814$		0			0
$815$	2.37206			0.0830898
$816$		0			0
$817$	−5.14012	+	15.8197i	−0.179830	+	0.553460i
$818$		0			0
$819$	−7.52440	+	5.46680i	−0.262924	+	0.191025i
$820$		0			0
$821$	−7.39181	−	22.7497i	−0.257976	−	0.793969i	−0.993229	−	0.116176i	$-0.962936\pi$
$821$	−7.39181	−	22.7497i	−0.257976	−	0.793969i	0.735253	−	0.677793i	$-0.237064\pi$
$822$		0			0
$823$	−37.2340	−	27.0521i	−1.29790	−	0.942978i	−0.297965	−	0.954577i	$-0.596308\pi$
$823$	−37.2340	−	27.0521i	−1.29790	−	0.942978i	−0.999933	+	0.0115993i	$0.996308\pi$
$824$		0			0
$825$	1.43732	−	2.98900i	0.0500411	−	0.104064i
$826$		0			0
$827$	19.8496	+	14.4215i	0.690237	+	0.501486i	0.876738	−	0.480968i	$-0.159715\pi$
$827$	19.8496	+	14.4215i	0.690237	+	0.501486i	−0.186501	+	0.982455i	$0.559715\pi$
$828$		0			0
$829$	−1.85470	−	5.70818i	−0.0644164	−	0.198253i	0.913668	−	0.406461i	$-0.133237\pi$
$829$	−1.85470	−	5.70818i	−0.0644164	−	0.198253i	−0.978085	+	0.208207i	$0.933237\pi$
$830$		0			0
$831$	−1.23903	+	0.900208i	−0.0429815	+	0.0312279i
$832$		0			0
$833$	3.02452	−	9.30850i	0.104793	−	0.322520i
$834$		0			0
$835$	18.4667			0.639066
$836$		0			0
$837$	−0.352347			−0.0121789
$838$		0			0
$839$	15.4492	−	47.5476i	0.533364	−	1.64153i	−0.213794	−	0.976879i	$-0.568582\pi$
$839$	15.4492	−	47.5476i	0.533364	−	1.64153i	0.747158	−	0.664647i	$-0.231418\pi$
$840$		0			0
$841$	−26.7893	+	19.4636i	−0.923770	+	0.671158i
$842$		0			0
$843$	7.98257	+	24.5678i	0.274934	+	0.846161i
$844$		0			0
$845$	−2.18113	−	1.58469i	−0.0750332	−	0.0545148i
$846$		0			0
$847$	16.1237	+	20.1711i	0.554015	+	0.693086i
$848$		0			0
$849$	20.6286	+	14.9876i	0.707973	+	0.514373i
$850$		0			0
$851$	1.05824	+	3.25693i	0.0362760	+	0.111646i
$852$		0			0
$853$	−34.8388	+	25.3119i	−1.19286	+	0.866662i	−0.993563	−	0.113278i	$-0.963865\pi$
$853$	−34.8388	+	25.3119i	−1.19286	+	0.866662i	−0.199295	+	0.979940i	$0.563865\pi$
$854$		0			0
$855$	−1.59260	+	4.90151i	−0.0544657	+	0.167628i
$856$		0			0
$857$	24.1719			0.825696			0.412848	−	0.910800i	$-0.364534\pi$
$857$	24.1719			0.825696			0.412848	+	0.910800i	$0.364534\pi$
$858$		0			0
$859$	18.7771			0.640667			0.320333	−	0.947305i	$-0.396205\pi$
$859$	18.7771			0.640667			0.320333	+	0.947305i	$0.396205\pi$
$860$		0			0
$861$	−7.59765	+	23.3832i	−0.258927	+	0.796896i
$862$		0			0
$863$	11.9725	−	8.69857i	0.407550	−	0.296103i	−0.365059	−	0.930984i	$-0.618951\pi$
$863$	11.9725	−	8.69857i	0.407550	−	0.296103i	0.772609	+	0.634882i	$0.218951\pi$
$864$		0			0
$865$	6.63296	+	20.4142i	0.225528	+	0.694102i
$866$		0			0
$867$	−21.2075	−	15.4081i	−0.720243	−	0.523287i
$868$		0			0
$869$	−6.72475	+	13.9845i	−0.228121	+	0.474393i
$870$		0			0
$871$	−2.58664	−	1.87930i	−0.0876448	−	0.0636777i
$872$		0			0
$873$	−2.20329	−	6.78102i	−0.0745699	−	0.229503i
$874$		0			0
$875$	1.89923	−	1.37987i	0.0642057	−	0.0466481i
$876$		0			0
$877$	7.27159	−	22.3797i	0.245544	−	0.755707i	−0.750002	−	0.661435i	$-0.769948\pi$
$877$	7.27159	−	22.3797i	0.245544	−	0.755707i	0.995546	−	0.0942721i	$-0.0300524\pi$
$878$		0			0
$879$	10.4656			0.352995
$880$		0			0
$881$	−52.5174			−1.76936			−0.884678	−	0.466202i	$-0.845622\pi$
$881$	−52.5174			−1.76936			−0.884678	+	0.466202i	$0.845622\pi$
$882$		0			0
$883$	14.0454	−	43.2272i	0.472665	−	1.45471i	−0.376417	−	0.926450i	$-0.622844\pi$
$883$	14.0454	−	43.2272i	0.472665	−	1.45471i	0.849082	−	0.528262i	$-0.177156\pi$
$884$		0			0
$885$	3.01138	−	2.18790i	0.101226	−	0.0735454i
$886$		0			0
$887$	6.73001	+	20.7128i	0.225972	+	0.695469i	0.998192	+	0.0601136i	$0.0191463\pi$
$887$	6.73001	+	20.7128i	0.225972	+	0.695469i	−0.772220	+	0.635355i	$0.780854\pi$
$888$		0			0
$889$	−12.4643	−	9.05587i	−0.418040	−	0.303724i
$890$		0			0
$891$	−2.91971	+	1.57331i	−0.0978138	+	0.0527080i
$892$		0			0
$893$	35.2830	+	25.6346i	1.18070	+	0.857829i
$894$		0			0
$895$	0.803647	+	2.47337i	0.0268630	+	0.0826757i
$896$		0			0
$897$	15.9035	−	11.5546i	0.531004	−	0.385797i
$898$		0			0
$899$	0.858115	−	2.64101i	0.0286197	−	0.0880825i
$900$		0			0
$901$	−7.22699			−0.240766
$902$		0			0
$903$	−7.57682			−0.252141
$904$		0			0
$905$	6.86788	−	21.1372i	0.228296	−	0.702623i
$906$		0			0
$907$	−31.3302	+	22.7627i	−1.04030	+	0.755823i	−0.970344	−	0.241727i	$-0.922286\pi$
$907$	−31.3302	+	22.7627i	−1.04030	+	0.755823i	−0.0699566	+	0.997550i	$0.522286\pi$
$908$		0			0
$909$	1.42142	+	4.37469i	0.0471456	+	0.145099i
$910$		0			0
$911$	−3.39630	−	2.46755i	−0.112524	−	0.0817537i	0.530100	−	0.847935i	$-0.322154\pi$
$911$	−3.39630	−	2.46755i	−0.112524	−	0.0817537i	−0.642624	+	0.766181i	$0.722154\pi$
$912$		0			0
$913$	−32.0099	−	30.5696i	−1.05937	−	1.01170i
$914$		0			0
$915$	5.55086	+	4.03294i	0.183506	+	0.133325i
$916$		0			0
$917$	−6.26797	−	19.2908i	−0.206987	−	0.637039i
$918$		0			0
$919$	−18.5810	+	13.4999i	−0.612930	+	0.445320i	−0.850445	−	0.526064i	$-0.823667\pi$
$919$	−18.5810	+	13.4999i	−0.612930	+	0.445320i	0.237515	+	0.971384i	$0.423667\pi$
$920$		0			0
$921$	−5.76831	+	17.7530i	−0.190072	+	0.584982i
$922$		0			0
$923$	−17.8652			−0.588041
$924$		0			0
$925$	0.690177			0.0226929
$926$		0			0
$927$	−0.356529	+	1.09728i	−0.0117100	+	0.0360396i
$928$		0			0
$929$	−46.7142	+	33.9399i	−1.53264	+	1.11353i	−0.577898	+	0.816109i	$0.696127\pi$
$929$	−46.7142	+	33.9399i	−1.53264	+	1.11353i	−0.954746	+	0.297423i	$0.903873\pi$
$930$		0			0
$931$	2.37120	+	7.29780i	0.0777129	+	0.239176i
$932$		0			0
$933$	−19.9408	−	14.4878i	−0.652831	−	0.474310i
$934$		0			0
$935$	−21.6069	−	2.91428i	−0.706622	−	0.0953071i
$936$		0			0
$937$	16.5020	+	11.9894i	0.539096	+	0.391676i	0.823749	−	0.566954i	$-0.191878\pi$
$937$	16.5020	+	11.9894i	0.539096	+	0.391676i	−0.284653	+	0.958631i	$0.591878\pi$
$938$		0			0
$939$	6.83627	+	21.0399i	0.223093	+	0.686610i
$940$		0			0
$941$	−38.5886	+	28.0362i	−1.25795	+	0.913955i	−0.998655	−	0.0518431i	$-0.983490\pi$
$941$	−38.5886	+	28.0362i	−1.25795	+	0.913955i	−0.259296	+	0.965798i	$0.583490\pi$
$942$		0			0
$943$	16.0583	−	49.4225i	0.522932	−	1.60942i
$944$		0			0
$945$	−2.34758			−0.0763666
$946$		0			0
$947$	−24.6026			−0.799476			−0.399738	−	0.916629i	$-0.630899\pi$
$947$	−24.6026			−0.799476			−0.399738	+	0.916629i	$0.630899\pi$
$948$		0			0
$949$	−7.81601	+	24.0552i	−0.253719	+	0.780865i
$950$		0			0
$951$	−21.1127	+	15.3393i	−0.684627	+	0.497411i
$952$		0			0
$953$	−7.14406	−	21.9871i	−0.231419	−	0.712234i	−0.997576	−	0.0695809i	$-0.977834\pi$
$953$	−7.14406	−	21.9871i	−0.231419	−	0.712234i	0.766158	−	0.642653i	$-0.222166\pi$
$954$		0			0
$955$	12.8102	+	9.30719i	0.414530	+	0.301174i
$956$		0			0
$957$	−4.68200	−	25.7163i	−0.151348	−	0.831289i
$958$		0			0
$959$	−22.2482	−	16.1643i	−0.718432	−	0.521971i
$960$		0			0
$961$	−9.54116	−	29.3647i	−0.307779	−	0.947248i
$962$		0			0
$963$	6.96267	−	5.05868i	0.224369	−	0.163014i
$964$		0			0
$965$	7.69754	−	23.6906i	0.247793	−	0.762627i
$966$		0			0
$967$	6.07084			0.195225			0.0976126	−	0.995224i	$-0.468879\pi$
$967$	6.07084			0.195225			0.0976126	+	0.995224i	$0.468879\pi$
$968$		0			0
$969$	33.8794			1.08836
$970$		0			0
$971$	−2.04987	+	6.30885i	−0.0657834	+	0.202460i	−0.978545	−	0.206031i	$-0.933945\pi$
$971$	−2.04987	+	6.30885i	−0.0657834	+	0.202460i	0.912762	+	0.408492i	$0.133945\pi$
$972$		0			0
$973$	24.3060	−	17.6593i	0.779215	−	0.566133i
$974$		0			0
$975$	−1.22427	−	3.76792i	−0.0392080	−	0.120670i
$976$		0			0
$977$	16.7870	+	12.1965i	0.537064	+	0.390200i	0.822993	−	0.568051i	$-0.192302\pi$
$977$	16.7870	+	12.1965i	0.537064	+	0.390200i	−0.285929	+	0.958251i	$0.592302\pi$
$978$		0			0
$979$	6.52534	+	35.8410i	0.208551	+	1.14548i
$980$		0			0
$981$	−14.2112	−	10.3250i	−0.453727	−	0.329652i
$982$		0			0
$983$	12.6344	+	38.8846i	0.402974	+	1.24023i	0.922575	+	0.385817i	$0.126080\pi$
$983$	12.6344	+	38.8846i	0.402974	+	1.24023i	−0.519602	+	0.854409i	$0.673920\pi$
$984$		0			0
$985$	−17.8506	+	12.9692i	−0.568767	+	0.413233i
$986$		0			0
$987$	−6.13884	+	18.8934i	−0.195401	+	0.601384i
$988$		0			0
$989$	16.0143			0.509226
$990$		0			0
$991$	−58.4881			−1.85794			−0.928969	−	0.370159i	$-0.879303\pi$
$991$	−58.4881			−1.85794			−0.928969	+	0.370159i	$0.879303\pi$
$992$		0			0
$993$	−7.10009	+	21.8518i	−0.225315	+	0.693447i
$994$		0			0
$995$	13.1577	−	9.55960i	0.417126	−	0.303060i
$996$		0			0
$997$	8.98655	+	27.6578i	0.284607	+	0.875930i	0.986516	+	0.163664i	$0.0523312\pi$
$997$	8.98655	+	27.6578i	0.284607	+	0.875930i	−0.701909	+	0.712266i	$0.747669\pi$
$998$		0			0
$999$	−0.558365	−	0.405676i	−0.0176659	−	0.0128350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1320.2.bw.i.961.2	✓	16
11.3	even	5	inner	1320.2.bw.i.1081.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1320.2.bw.i.961.2	✓	16	1.1	even	1	trivial
1320.2.bw.i.1081.2	yes	16	11.3	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.bw (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{5} +(-0.725441 - 2.23268i) q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{5} +(-0.725441 - 2.23268i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(0.594072 + 3.26299i) q^{11} +(3.20518 + 2.32870i) q^{13} +(0.309017 + 0.951057i) q^{15} +(5.31826 - 3.86394i) q^{17} +(-1.59260 + 4.90151i) q^{19} -2.34758 q^{21} +4.96182 q^{23} +(0.309017 - 0.951057i) q^{25} +(-0.809017 + 0.587785i) q^{27} +(-2.43543 - 7.49547i) q^{29} +(0.285055 + 0.207104i) q^{31} +(3.28686 + 0.443322i) q^{33} +(1.89923 + 1.37987i) q^{35} +(0.213276 + 0.656397i) q^{37} +(3.20518 - 2.32870i) q^{39} +(3.23638 - 9.96055i) q^{41} +3.22751 q^{43} +1.00000 q^{45} +(2.61497 - 8.04805i) q^{47} +(1.20454 - 0.875146i) q^{49} +(-2.03139 - 6.25198i) q^{51} +(-0.889413 - 0.646196i) q^{53} +(-2.39855 - 2.29062i) q^{55} +(4.16947 + 3.02930i) q^{57} +(-1.15025 - 3.54009i) q^{59} +(5.55086 - 4.03294i) q^{61} +(-0.725441 + 2.23268i) q^{63} -3.96182 q^{65} -0.807017 q^{67} +(1.53329 - 4.71897i) q^{69} +(-3.64814 + 2.65053i) q^{71} +(1.97283 + 6.07176i) q^{73} +(-0.809017 - 0.587785i) q^{75} +(6.85423 - 3.69347i) q^{77} +(3.78512 + 2.75005i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-10.7967 + 7.84430i) q^{83} +(-2.03139 + 6.25198i) q^{85} -7.88121 q^{87} +10.9841 q^{89} +(2.87407 - 8.84547i) q^{91} +(0.285055 - 0.207104i) q^{93} +(-1.59260 - 4.90151i) q^{95} +(5.76828 + 4.19090i) q^{97} +(1.43732 - 2.98900i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 16 q - 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} - q^{11} + q^{13} - 4 q^{15} - 3 q^{17} - 2 q^{19} - 6 q^{21} + 10 q^{23} - 4 q^{25} - 4 q^{27} - 5 q^{29} + 3 q^{31} - q^{33} - q^{35} - 25 q^{37} + q^{39} - 2 q^{41} - 2 q^{43} + 16 q^{45} + 14 q^{47} - 8 q^{49} + 2 q^{51} - 11 q^{53} + 4 q^{55} + 8 q^{57} - 7 q^{59} - 3 q^{61} + 4 q^{63} + 6 q^{65} + 32 q^{67} - 15 q^{71} - q^{73} - 4 q^{75} + 9 q^{77} - 15 q^{79} - 4 q^{81} - 17 q^{83} + 2 q^{85} + 26 q^{89} + 36 q^{91} + 3 q^{93} - 2 q^{95} - 45 q^{97} - q^{99}+O(q^{100}) \) 16 * q - 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 - q^11 + q^13 - 4 * q^15 - 3 * q^17 - 2 * q^19 - 6 * q^21 + 10 * q^23 - 4 * q^25 - 4 * q^27 - 5 * q^29 + 3 * q^31 - q^33 - q^35 - 25 * q^37 + q^39 - 2 * q^41 - 2 * q^43 + 16 * q^45 + 14 * q^47 - 8 * q^49 + 2 * q^51 - 11 * q^53 + 4 * q^55 + 8 * q^57 - 7 * q^59 - 3 * q^61 + 4 * q^63 + 6 * q^65 + 32 * q^67 - 15 * q^71 - q^73 - 4 * q^75 + 9 * q^77 - 15 * q^79 - 4 * q^81 - 17 * q^83 + 2 * q^85 + 26 * q^89 + 36 * q^91 + 3 * q^93 - 2 * q^95 - 45 * q^97 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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