LMFDB - Embedded newform 1040.2.da.f.641.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(641,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

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

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

chi := DirichletCharacter("1040.641");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.da (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} + 22x^{14} + 183x^{12} + 730x^{10} + 1485x^{8} + 1552x^{6} + 812x^{4} + 192x^{2} + 16 $ x^16 + 22x^14 + 183x^12 + 730x^10 + 1485x^8 + 1552x^6 + 812x^4 + 192*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 520)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			641.8
Root			$-0.551543i$ of defining polynomial
Character	$\chi$	$=$	1040.641
Dual form			1040.2.da.f.881.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.62367 - 2.81228i) q^{3} -1.00000i q^{5} +(-4.00640 + 2.31309i) q^{7} +(-3.77262 - 6.53437i) q^{9} +O(q^{10})$	\(q+(1.62367 - 2.81228i) q^{3} -1.00000i q^{5} +(-4.00640 + 2.31309i) q^{7} +(-3.77262 - 6.53437i) q^{9} +(2.79680 + 1.61473i) q^{11} +(-1.42742 - 3.31096i) q^{13} +(-2.81228 - 1.62367i) q^{15} +(-2.77825 - 4.81207i) q^{17} +(-1.72537 + 0.996140i) q^{19} +15.0228i q^{21} +(-2.20224 + 3.81440i) q^{23} -1.00000 q^{25} -14.7599 q^{27} +(-0.197974 + 0.342902i) q^{29} -7.20020i q^{31} +(9.08216 - 5.24359i) q^{33} +(2.31309 + 4.00640i) q^{35} +(0.708052 + 0.408794i) q^{37} +(-11.6290 - 1.36160i) q^{39} +(-2.79170 - 1.61179i) q^{41} +(-3.42488 - 5.93207i) q^{43} +(-6.53437 + 3.77262i) q^{45} +6.19979i q^{47} +(7.20081 - 12.4722i) q^{49} -18.0439 q^{51} -0.512700 q^{53} +(1.61473 - 2.79680i) q^{55} +6.46962i q^{57} +(6.82230 - 3.93886i) q^{59} +(3.08672 + 5.34635i) q^{61} +(30.2292 + 17.4528i) q^{63} +(-3.31096 + 1.42742i) q^{65} +(7.58286 + 4.37797i) q^{67} +(7.15144 + 12.3867i) q^{69} +(2.43415 - 1.40535i) q^{71} -5.03482i q^{73} +(-1.62367 + 2.81228i) q^{75} -14.9401 q^{77} +8.25143 q^{79} +(-12.6475 + 21.9060i) q^{81} -1.49741i q^{83} +(-4.81207 + 2.77825i) q^{85} +(0.642891 + 1.11352i) q^{87} +(14.1316 + 8.15887i) q^{89} +(13.3774 + 9.96326i) q^{91} +(-20.2490 - 11.6908i) q^{93} +(0.996140 + 1.72537i) q^{95} +(4.84132 - 2.79514i) q^{97} -24.3671i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9}+O(q^{10}) $ 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9	$ 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{17} - 30 q^{19} - 6 q^{23} - 16 q^{25} - 44 q^{27} - 16 q^{29} + 24 q^{33} + 6 q^{35} - 24 q^{37} + 8 q^{39} - 24 q^{41} - 6 q^{43} + 12 q^{45} - 4 q^{49} + 40 q^{51} + 4 q^{53} + 6 q^{55} - 12 q^{59} - 2 q^{61} + 60 q^{63} - 10 q^{65} + 6 q^{67} + 52 q^{69} - 72 q^{71} - 4 q^{75} + 32 q^{77} - 36 q^{79} - 28 q^{81} + 22 q^{87} + 24 q^{89} + 22 q^{91} - 96 q^{93} - 10 q^{95} + 60 q^{97}+O(q^{100}) $ 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9 + 6 * q^11 - 2 * q^13 + 4 * q^17 - 30 * q^19 - 6 * q^23 - 16 * q^25 - 44 * q^27 - 16 * q^29 + 24 * q^33 + 6 * q^35 - 24 * q^37 + 8 * q^39 - 24 * q^41 - 6 * q^43 + 12 * q^45 - 4 * q^49 + 40 * q^51 + 4 * q^53 + 6 * q^55 - 12 * q^59 - 2 * q^61 + 60 * q^63 - 10 * q^65 + 6 * q^67 + 52 * q^69 - 72 * q^71 - 4 * q^75 + 32 * q^77 - 36 * q^79 - 28 * q^81 + 22 * q^87 + 24 * q^89 + 22 * q^91 - 96 * q^93 - 10 * q^95 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	1.62367	−	2.81228i	0.937427	−	1.62367i	0.167180	−	0.985926i	$-0.446534\pi$
$3$	1.62367	−	2.81228i	0.937427	−	1.62367i	0.770247	−	0.637745i	$-0.220133\pi$
$4$		0			0
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	−4.00640	+	2.31309i	−1.51428	+	0.874267i	−0.514415	+	0.857541i	$0.671991\pi$
$7$	−4.00640	+	2.31309i	−1.51428	+	0.874267i	−0.999860	+	0.0167263i	$0.994676\pi$
$8$		0			0
$9$	−3.77262	−	6.53437i	−1.25754	−	2.17812i
$10$		0			0
$11$	2.79680	+	1.61473i	0.843266	+	0.486860i	0.858373	−	0.513026i	$-0.171476\pi$
$11$	2.79680	+	1.61473i	0.843266	+	0.486860i	−0.0151073	+	0.999886i	$0.504809\pi$
$12$		0			0
$13$	−1.42742	−	3.31096i	−0.395896	−	0.918295i
$13$	−1.42742	−	3.31096i	−0.395896	−	0.918295i
$14$		0			0
$15$	−2.81228	−	1.62367i	−0.726128	−	0.419230i
$16$		0			0
$17$	−2.77825	−	4.81207i	−0.673825	−	1.16710i	−0.976811	−	0.214104i	$-0.931317\pi$
$17$	−2.77825	−	4.81207i	−0.673825	−	1.16710i	0.302986	−	0.952995i	$-0.402016\pi$
$18$		0			0
$19$	−1.72537	+	0.996140i	−0.395826	+	0.228530i	−0.684681	−	0.728842i	$-0.740059\pi$
$19$	−1.72537	+	0.996140i	−0.395826	+	0.228530i	0.288855	+	0.957373i	$0.406725\pi$
$20$		0			0
$21$			15.0228i			3.27825i
$22$		0			0
$23$	−2.20224	+	3.81440i	−0.459199	+	0.795357i	−0.998919	−	0.0464882i	$-0.985197\pi$
$23$	−2.20224	+	3.81440i	−0.459199	+	0.795357i	0.539719	+	0.841845i	$0.318530\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−14.7599			−2.84055
$28$		0			0
$29$	−0.197974	+	0.342902i	−0.0367629	+	0.0636753i	−0.883821	−	0.467824i	$-0.845038\pi$
$29$	−0.197974	+	0.342902i	−0.0367629	+	0.0636753i	0.847059	+	0.531500i	$0.178371\pi$
$30$		0			0
$31$		−	7.20020i		−	1.29319i	−0.762832	−	0.646597i	$-0.776192\pi$
$31$		−	7.20020i		−	1.29319i	0.762832	−	0.646597i	$-0.223808\pi$
$32$		0			0
$33$	9.08216	−	5.24359i	1.58100	−	0.912791i
$34$		0			0
$35$	2.31309	+	4.00640i	0.390984	+	0.677205i
$36$		0			0
$37$	0.708052	+	0.408794i	0.116403	+	0.0672053i	0.557071	−	0.830465i	$-0.311925\pi$
$37$	0.708052	+	0.408794i	0.116403	+	0.0672053i	−0.440668	+	0.897670i	$0.645258\pi$
$38$		0			0
$39$	−11.6290	−	1.36160i	−1.86213	−	0.218030i
$40$		0			0
$41$	−2.79170	−	1.61179i	−0.435991	−	0.251719i	0.265905	−	0.963999i	$-0.414329\pi$
$41$	−2.79170	−	1.61179i	−0.435991	−	0.251719i	−0.701896	+	0.712280i	$0.747663\pi$
$42$		0			0
$43$	−3.42488	−	5.93207i	−0.522290	−	0.904633i	−0.999664	−	0.0259325i	$-0.991745\pi$
$43$	−3.42488	−	5.93207i	−0.522290	−	0.904633i	0.477374	−	0.878700i	$-0.341589\pi$
$44$		0			0
$45$	−6.53437	+	3.77262i	−0.974086	+	0.562389i
$46$		0			0
$47$			6.19979i			0.904333i	0.891934	+	0.452166i	$0.149349\pi$
$47$			6.19979i			0.904333i	−0.891934	+	0.452166i	$0.850651\pi$
$48$		0			0
$49$	7.20081	−	12.4722i	1.02869	−	1.78174i
$50$		0			0
$51$	−18.0439			−2.52665
$52$		0			0
$53$	−0.512700			−0.0704247			−0.0352124	−	0.999380i	$-0.511211\pi$
$53$	−0.512700			−0.0704247			−0.0352124	+	0.999380i	$0.511211\pi$
$54$		0			0
$55$	1.61473	−	2.79680i	0.217730	−	0.377120i
$56$		0			0
$57$			6.46962i			0.856922i
$58$		0			0
$59$	6.82230	−	3.93886i	0.888188	−	0.512795i	0.0148385	−	0.999890i	$-0.495277\pi$
$59$	6.82230	−	3.93886i	0.888188	−	0.512795i	0.873349	+	0.487094i	$0.161943\pi$
$60$		0			0
$61$	3.08672	+	5.34635i	0.395214	+	0.684530i	0.993128	−	0.117029i	$-0.0373371\pi$
$61$	3.08672	+	5.34635i	0.395214	+	0.684530i	−0.597915	+	0.801560i	$0.704004\pi$
$62$		0			0
$63$	30.2292	+	17.4528i	3.80852	+	2.19885i
$64$		0			0
$65$	−3.31096	+	1.42742i	−0.410674	+	0.177050i
$66$		0			0
$67$	7.58286	+	4.37797i	0.926394	+	0.534854i	0.885669	−	0.464317i	$-0.153700\pi$
$67$	7.58286	+	4.37797i	0.926394	+	0.534854i	0.0407246	+	0.999170i	$0.487033\pi$
$68$		0			0
$69$	7.15144	+	12.3867i	0.860932	+	1.49118i
$70$		0			0
$71$	2.43415	−	1.40535i	0.288880	−	0.166785i	−0.348557	−	0.937288i	$-0.613328\pi$
$71$	2.43415	−	1.40535i	0.288880	−	0.166785i	0.637437	+	0.770503i	$0.279995\pi$
$72$		0			0
$73$		−	5.03482i		−	0.589281i	−0.955608	−	0.294640i	$-0.904800\pi$
$73$		−	5.03482i		−	0.589281i	0.955608	−	0.294640i	$-0.0951998\pi$
$74$		0			0
$75$	−1.62367	+	2.81228i	−0.187485	+	0.324734i
$76$		0			0
$77$	−14.9401			−1.70258
$78$		0			0
$79$	8.25143			0.928358			0.464179	−	0.885741i	$-0.346349\pi$
$79$	8.25143			0.928358			0.464179	+	0.885741i	$0.346349\pi$
$80$		0			0
$81$	−12.6475	+	21.9060i	−1.40527	+	2.43400i
$82$		0			0
$83$		−	1.49741i		−	0.164362i	−0.996617	−	0.0821811i	$-0.973811\pi$
$83$		−	1.49741i		−	0.164362i	0.996617	−	0.0821811i	$-0.0261886\pi$
$84$		0			0
$85$	−4.81207	+	2.77825i	−0.521942	+	0.301344i
$86$		0			0
$87$	0.642891	+	1.11352i	0.0689251	+	0.119382i
$88$		0			0
$89$	14.1316	+	8.15887i	1.49794	+	0.864838i	0.999997	−	0.00236896i	$-0.000754063\pi$
$89$	14.1316	+	8.15887i	1.49794	+	0.864838i	0.497947	+	0.867207i	$0.334087\pi$
$90$		0			0
$91$	13.3774	+	9.96326i	1.40233	+	1.04443i
$92$		0			0
$93$	−20.2490	−	11.6908i	−2.09972	−	1.21228i
$94$		0			0
$95$	0.996140	+	1.72537i	0.102202	+	0.177019i
$96$		0			0
$97$	4.84132	−	2.79514i	0.491561	−	0.283803i	−0.233661	−	0.972318i	$-0.575070\pi$
$97$	4.84132	−	2.79514i	0.491561	−	0.283803i	0.725222	+	0.688515i	$0.241737\pi$
$98$		0			0
$99$		−	24.3671i		−	2.44898i
$100$		0			0
$101$	8.14688	−	14.1108i	0.810645	−	1.40408i	−0.101769	−	0.994808i	$-0.532450\pi$
$101$	8.14688	−	14.1108i	0.810645	−	1.40408i	0.912413	−	0.409270i	$-0.134217\pi$
$102$		0			0
$103$	−17.2764			−1.70229			−0.851146	−	0.524928i	$-0.824092\pi$
$103$	−17.2764			−1.70229			−0.851146	+	0.524928i	$0.824092\pi$
$104$		0			0
$105$	15.0228			1.46608
$106$		0			0
$107$	2.79797	−	4.84622i	0.270490	−	0.468502i	−0.698498	−	0.715612i	$-0.746148\pi$
$107$	2.79797	−	4.84622i	0.270490	−	0.468502i	0.968987	+	0.247110i	$0.0794810\pi$
$108$		0			0
$109$		−	7.58276i		−	0.726296i	−0.931731	−	0.363148i	$-0.881702\pi$
$109$		−	7.58276i		−	0.726296i	0.931731	−	0.363148i	$-0.118298\pi$
$110$		0			0
$111$	2.29929	−	1.32749i	0.218239	−	0.126000i
$112$		0			0
$113$	−6.15234	−	10.6562i	−0.578764	−	1.00245i	−0.995622	−	0.0934763i	$-0.970202\pi$
$113$	−6.15234	−	10.6562i	−0.578764	−	1.00245i	0.416858	−	0.908972i	$-0.363131\pi$
$114$		0			0
$115$	3.81440	+	2.20224i	0.355694	+	0.205360i
$116$		0			0
$117$	−16.2499	+	21.8183i	−1.50230	+	2.01710i
$118$		0			0
$119$	22.2615	+	12.8527i	2.04071	+	1.17821i
$120$		0			0
$121$	−0.285288	−	0.494134i	−0.0259353	−	0.0449213i
$122$		0			0
$123$	−9.06562	+	5.23404i	−0.817419	+	0.471937i
$124$		0			0
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	−1.91541	+	3.31759i	−0.169965	+	0.294389i	−0.938407	−	0.345531i	$-0.887699\pi$
$127$	−1.91541	+	3.31759i	−0.169965	+	0.294389i	0.768442	+	0.639919i	$0.221032\pi$
$128$		0			0
$129$	−22.2436			−1.95844
$130$		0			0
$131$	−12.2733			−1.07233			−0.536163	−	0.844115i	$-0.680127\pi$
$131$	−12.2733			−1.07233			−0.536163	+	0.844115i	$0.680127\pi$
$132$		0			0
$133$	4.60833	−	7.98187i	0.399593	−	0.692116i
$134$		0			0
$135$			14.7599i			1.27033i
$136$		0			0
$137$	7.83794	−	4.52523i	0.669640	−	0.386617i	−0.126300	−	0.991992i	$-0.540310\pi$
$137$	7.83794	−	4.52523i	0.669640	−	0.386617i	0.795940	+	0.605375i	$0.206977\pi$
$138$		0			0
$139$	2.60293	+	4.50840i	0.220777	+	0.382398i	0.955044	−	0.296463i	$-0.0958072\pi$
$139$	2.60293	+	4.50840i	0.220777	+	0.382398i	−0.734267	+	0.678861i	$0.762474\pi$
$140$		0			0
$141$	17.4356	+	10.0664i	1.46834	+	0.847746i
$142$		0			0
$143$	1.35410	−	11.5650i	0.113235	−	0.967113i
$144$		0			0
$145$	0.342902	+	0.197974i	0.0284764	+	0.0164409i
$146$		0			0
$147$	−23.3835	−	40.5014i	−1.92864	−	3.34050i
$148$		0			0
$149$	−11.0988	+	6.40790i	−0.909250	+	0.524956i	−0.880190	−	0.474622i	$-0.842585\pi$
$149$	−11.0988	+	6.40790i	−0.909250	+	0.524956i	−0.0290603	+	0.999578i	$0.509251\pi$
$150$		0			0
$151$		−	17.8652i		−	1.45385i	−0.686719	−	0.726923i	$-0.740950\pi$
$151$		−	17.8652i		−	1.45385i	0.686719	−	0.726923i	$-0.259050\pi$
$152$		0			0
$153$	−20.9626	+	36.3082i	−1.69472	+	2.93535i
$154$		0			0
$155$	−7.20020			−0.578334
$156$		0			0
$157$	13.7462			1.09707			0.548533	−	0.836129i	$-0.315186\pi$
$157$	13.7462			1.09707			0.548533	+	0.836129i	$0.315186\pi$
$158$		0			0
$159$	−0.832456	+	1.44186i	−0.0660180	+	0.114347i
$160$		0			0
$161$		−	20.3760i		−	1.60585i
$162$		0			0
$163$	−4.26051	+	2.45980i	−0.333709	+	0.192667i	−0.657486	−	0.753466i	$-0.728380\pi$
$163$	−4.26051	+	2.45980i	−0.333709	+	0.192667i	0.323778	+	0.946133i	$0.395047\pi$
$164$		0			0
$165$	−5.24359	−	9.08216i	−0.408213	−	0.707045i
$166$		0			0
$167$	−17.3879	−	10.0389i	−1.34552	−	0.776834i	−0.357905	−	0.933758i	$-0.616509\pi$
$167$	−17.3879	−	10.0389i	−1.34552	−	0.776834i	−0.987611	+	0.156924i	$0.949842\pi$
$168$		0			0
$169$	−8.92492	+	9.45229i	−0.686533	+	0.727099i
$170$		0			0
$171$	13.0183	+	7.51612i	0.995534	+	0.574772i
$172$		0			0
$173$	−1.48256	−	2.56787i	−0.112717	−	0.195231i	0.804148	−	0.594429i	$-0.202622\pi$
$173$	−1.48256	−	2.56787i	−0.112717	−	0.195231i	−0.916865	+	0.399198i	$0.869289\pi$
$174$		0			0
$175$	4.00640	−	2.31309i	0.302855	−	0.174853i
$176$		0			0
$177$		−	25.5816i		−	1.92283i
$178$		0			0
$179$	13.0457	−	22.5958i	0.975079	−	1.68889i	0.295404	−	0.955372i	$-0.404546\pi$
$179$	13.0457	−	22.5958i	0.975079	−	1.68889i	0.679674	−	0.733514i	$-0.262121\pi$
$180$		0			0
$181$	16.3302			1.21382			0.606909	−	0.794772i	$-0.292409\pi$
$181$	16.3302			1.21382			0.606909	+	0.794772i	$0.292409\pi$
$182$		0			0
$183$	20.0473			1.48194
$184$		0			0
$185$	0.408794	−	0.708052i	0.0300551	−	0.0520570i
$186$		0			0
$187$		−	17.9445i		−	1.31223i
$188$		0			0
$189$	59.1342	−	34.1412i	4.30138	−	2.48340i
$190$		0			0
$191$	−5.06878	−	8.77939i	−0.366764	−	0.635254i	0.622293	−	0.782784i	$-0.286201\pi$
$191$	−5.06878	−	8.77939i	−0.366764	−	0.635254i	−0.989058	+	0.147530i	$0.952868\pi$
$192$		0			0
$193$	9.74200	+	5.62455i	0.701244	+	0.404864i	0.807811	−	0.589442i	$-0.200652\pi$
$193$	9.74200	+	5.62455i	0.701244	+	0.404864i	−0.106566	+	0.994306i	$0.533986\pi$
$194$		0			0
$195$	−1.36160	+	11.6290i	−0.0975059	+	0.832772i
$196$		0			0
$197$	−15.4235	−	8.90475i	−1.09888	−	0.634437i	−0.162951	−	0.986634i	$-0.552101\pi$
$197$	−15.4235	−	8.90475i	−1.09888	−	0.634437i	−0.935926	+	0.352197i	$0.885435\pi$
$198$		0			0
$199$	1.27617	+	2.21039i	0.0904652	+	0.156690i	0.907707	−	0.419605i	$-0.137831\pi$
$199$	1.27617	+	2.21039i	0.0904652	+	0.156690i	−0.817242	+	0.576295i	$0.804498\pi$
$200$		0			0
$201$	24.6242	−	14.2168i	1.73685	−	1.00277i
$202$		0			0
$203$		−	1.83173i		−	0.128562i
$204$		0			0
$205$	−1.61179	+	2.79170i	−0.112572	+	0.194981i
$206$		0			0
$207$	33.2329			2.30985
$208$		0			0
$209$	−6.43399			−0.445049
$210$		0			0
$211$	−8.82052	+	15.2776i	−0.607230	+	1.05175i	0.384465	+	0.923140i	$0.374386\pi$
$211$	−8.82052	+	15.2776i	−0.607230	+	1.05175i	−0.991695	+	0.128613i	$0.958947\pi$
$212$		0			0
$213$		−	9.12734i		−	0.625395i
$214$		0			0
$215$	−5.93207	+	3.42488i	−0.404564	+	0.233575i
$216$		0			0
$217$	16.6547	+	28.8469i	1.13060	+	1.95825i
$218$		0			0
$219$	−14.1593	−	8.17489i	−0.956798	−	0.552408i
$220$		0			0
$221$	−11.9668	+	16.0675i	−0.804977	+	1.08082i
$222$		0			0
$223$	2.63584	+	1.52181i	0.176509	+	0.101908i	0.585652	−	0.810563i	$-0.300839\pi$
$223$	2.63584	+	1.52181i	0.176509	+	0.101908i	−0.409142	+	0.912471i	$0.634172\pi$
$224$		0			0
$225$	3.77262	+	6.53437i	0.251508	+	0.435625i
$226$		0			0
$227$	−3.09823	+	1.78877i	−0.205637	+	0.118725i	−0.599282	−	0.800538i	$-0.704547\pi$
$227$	−3.09823	+	1.78877i	−0.205637	+	0.118725i	0.393645	+	0.919262i	$0.371214\pi$
$228$		0			0
$229$		−	4.44560i		−	0.293774i	−0.989153	−	0.146887i	$-0.953075\pi$
$229$		−	4.44560i		−	0.293774i	0.989153	−	0.146887i	$-0.0469253\pi$
$230$		0			0
$231$	−24.2578	+	42.0158i	−1.59605	+	2.76443i
$232$		0			0
$233$	−1.11772			−0.0732245			−0.0366122	−	0.999330i	$-0.511657\pi$
$233$	−1.11772			−0.0732245			−0.0366122	+	0.999330i	$0.511657\pi$
$234$		0			0
$235$	6.19979			0.404430
$236$		0			0
$237$	13.3976	−	23.2053i	0.870268	−	1.50735i
$238$		0			0
$239$			1.69362i			0.109551i	0.998499	+	0.0547755i	$0.0174443\pi$
$239$			1.69362i			0.109551i	−0.998499	+	0.0547755i	$0.982556\pi$
$240$		0			0
$241$	−21.0402	+	12.1476i	−1.35532	+	0.782494i	−0.988989	−	0.147991i	$-0.952719\pi$
$241$	−21.0402	+	12.1476i	−1.35532	+	0.782494i	−0.366331	+	0.930485i	$0.619386\pi$
$242$		0			0
$243$	18.9307	+	32.7889i	1.21440	+	2.10341i
$244$		0			0
$245$	−12.4722	−	7.20081i	−0.796817	−	0.460043i
$246$		0			0
$247$	5.76101	+	4.29070i	0.366564	+	0.273011i
$248$		0			0
$249$	−4.21114	−	2.43130i	−0.266870	−	0.154078i
$250$		0			0
$251$	6.39028	+	11.0683i	0.403351	+	0.698624i	0.994128	−	0.108211i	$-0.0345122\pi$
$251$	6.39028	+	11.0683i	0.403351	+	0.698624i	−0.590777	+	0.806835i	$0.701179\pi$
$252$		0			0
$253$	−12.3184	+	7.11206i	−0.774454	+	0.447131i
$254$		0			0
$255$			18.0439i			1.12995i
$256$		0			0
$257$	−0.350393	+	0.606898i	−0.0218569	+	0.0378573i	−0.876747	−	0.480952i	$-0.840291\pi$
$257$	−0.350393	+	0.606898i	−0.0218569	+	0.0378573i	0.854890	+	0.518809i	$0.173624\pi$
$258$		0			0
$259$	−3.78232			−0.235022
$260$		0			0
$261$	2.98753			0.184923
$262$		0			0
$263$	−2.97697	+	5.15626i	−0.183568	+	0.317948i	−0.943093	−	0.332529i	$-0.892098\pi$
$263$	−2.97697	+	5.15626i	−0.183568	+	0.317948i	0.759525	+	0.650478i	$0.225431\pi$
$264$		0			0
$265$			0.512700i			0.0314949i
$266$		0			0
$267$	45.8901	−	26.4947i	2.80843	−	1.62145i
$268$		0			0
$269$	−9.77151	−	16.9247i	−0.595779	−	1.03192i	−0.993436	−	0.114386i	$-0.963510\pi$
$269$	−9.77151	−	16.9247i	−0.595779	−	1.03192i	0.397657	−	0.917534i	$-0.369823\pi$
$270$		0			0
$271$	20.1091	+	11.6100i	1.22154	+	0.705257i	0.965246	−	0.261342i	$-0.0841650\pi$
$271$	20.1091	+	11.6100i	1.22154	+	0.705257i	0.256294	+	0.966599i	$0.417498\pi$
$272$		0			0
$273$	49.7400	−	21.4439i	3.01040	−	1.29785i
$274$		0			0
$275$	−2.79680	−	1.61473i	−0.168653	−	0.0973719i
$276$		0			0
$277$	8.96861	+	15.5341i	0.538872	+	0.933353i	0.998965	+	0.0454825i	$0.0144825\pi$
$277$	8.96861	+	15.5341i	0.538872	+	0.933353i	−0.460094	+	0.887870i	$0.652184\pi$
$278$		0			0
$279$	−47.0488	+	27.1636i	−2.81674	+	1.62624i
$280$		0			0
$281$			28.0370i			1.67254i	0.548314	+	0.836272i	$0.315270\pi$
$281$			28.0370i			1.67254i	−0.548314	+	0.836272i	$0.684730\pi$
$282$		0			0
$283$	4.04936	−	7.01370i	0.240709	−	0.416921i	−0.720207	−	0.693759i	$-0.755953\pi$
$283$	4.04936	−	7.01370i	0.240709	−	0.416921i	0.960917	+	0.276838i	$0.0892866\pi$
$284$		0			0
$285$	6.46962			0.383227
$286$		0			0
$287$	14.9129			0.880280
$288$		0			0
$289$	−6.93735	+	12.0158i	−0.408079	+	0.706814i
$290$		0			0
$291$		−	18.1535i		−	1.06418i
$292$		0			0
$293$	6.35415	−	3.66857i	0.371213	−	0.214320i	−0.302775	−	0.953062i	$-0.597913\pi$
$293$	6.35415	−	3.66857i	0.371213	−	0.214320i	0.673988	+	0.738742i	$0.264580\pi$
$294$		0			0
$295$	−3.93886	−	6.82230i	−0.229329	−	0.397210i
$296$		0			0
$297$	−41.2806	−	23.8333i	−2.39534	−	1.38295i
$298$		0			0
$299$	15.7729	+	1.84678i	0.912168	+	0.106802i
$300$		0			0
$301$	27.4429	+	15.8442i	1.58178	+	0.913242i
$302$		0			0
$303$	−26.4557	−	45.8226i	−1.51984	−	2.63244i
$304$		0			0
$305$	5.34635	−	3.08672i	0.306131	−	0.176745i
$306$		0			0
$307$			19.4266i			1.10874i	0.832271	+	0.554369i	$0.187040\pi$
$307$			19.4266i			1.10874i	−0.832271	+	0.554369i	$0.812960\pi$
$308$		0			0
$309$	−28.0512	+	48.5861i	−1.59578	+	2.76396i
$310$		0			0
$311$	5.69920			0.323172			0.161586	−	0.986859i	$-0.448339\pi$
$311$	5.69920			0.323172			0.161586	+	0.986859i	$0.448339\pi$
$312$		0			0
$313$	26.8426			1.51724			0.758618	−	0.651536i	$-0.225875\pi$
$313$	26.8426			1.51724			0.758618	+	0.651536i	$0.225875\pi$
$314$		0			0
$315$	17.4528	−	30.2292i	0.983356	−	1.70322i
$316$		0			0
$317$		−	10.2434i		−	0.575326i	−0.957732	−	0.287663i	$-0.907122\pi$
$317$		−	10.2434i		−	0.575326i	0.957732	−	0.287663i	$-0.0928782\pi$
$318$		0			0
$319$	−1.10739	+	0.639351i	−0.0620018	+	0.0357968i
$320$		0			0
$321$	−9.08596	−	15.7373i	−0.507129	−	0.878373i
$322$		0			0
$323$	9.58699	+	5.53505i	0.533435	+	0.307979i
$324$		0			0
$325$	1.42742	+	3.31096i	0.0791792	+	0.183659i
$326$		0			0
$327$	−21.3248	−	12.3119i	−1.17927	−	0.680850i
$328$		0			0
$329$	−14.3407	−	24.8388i	−0.790629	−	1.36941i
$330$		0			0
$331$	−19.9111	+	11.4957i	−1.09441	+	0.631861i	−0.934748	−	0.355310i	$-0.884375\pi$
$331$	−19.9111	+	11.4957i	−1.09441	+	0.631861i	−0.159666	+	0.987171i	$0.551042\pi$
$332$		0			0
$333$		−	6.16890i		−	0.338053i
$334$		0			0
$335$	4.37797	−	7.58286i	0.239194	−	0.414296i
$336$		0			0
$337$	−1.35010			−0.0735446			−0.0367723	−	0.999324i	$-0.511708\pi$
$337$	−1.35010			−0.0735446			−0.0367723	+	0.999324i	$0.511708\pi$
$338$		0			0
$339$	−39.9575			−2.17020
$340$		0			0
$341$	11.6264	−	20.1375i	0.629604	−	1.09051i
$342$		0			0
$343$			34.2413i			1.84885i
$344$		0			0
$345$	12.3867	−	7.15144i	0.666875	−	0.385021i
$346$		0			0
$347$	0.904069	+	1.56589i	0.0485330	+	0.0840615i	0.889271	−	0.457380i	$-0.151212\pi$
$347$	0.904069	+	1.56589i	0.0485330	+	0.0840615i	−0.840738	+	0.541442i	$0.817879\pi$
$348$		0			0
$349$	11.5909	+	6.69200i	0.620446	+	0.358215i	0.777043	−	0.629448i	$-0.216719\pi$
$349$	11.5909	+	6.69200i	0.620446	+	0.358215i	−0.156597	+	0.987663i	$0.550052\pi$
$350$		0			0
$351$	21.0687	+	48.8696i	1.12456	+	2.60847i
$352$		0			0
$353$	7.29102	+	4.20948i	0.388062	+	0.224048i	0.681320	−	0.731986i	$-0.261406\pi$
$353$	7.29102	+	4.20948i	0.388062	+	0.224048i	−0.293258	+	0.956033i	$0.594740\pi$
$354$		0			0
$355$	−1.40535	−	2.43415i	−0.0745885	−	0.129191i
$356$		0			0
$357$	72.2909	−	41.7372i	3.82604	−	2.20896i
$358$		0			0
$359$		−	9.35788i		−	0.493890i	−0.969029	−	0.246945i	$-0.920573\pi$
$359$		−	9.35788i		−	0.493890i	0.969029	−	0.246945i	$-0.0794267\pi$
$360$		0			0
$361$	−7.51541	+	13.0171i	−0.395548	+	0.685109i
$362$		0			0
$363$	−1.85286			−0.0972499
$364$		0			0
$365$	−5.03482			−0.263534
$366$		0			0
$367$	14.4871	−	25.0924i	0.756219	−	1.30981i	−0.188547	−	0.982064i	$-0.560378\pi$
$367$	14.4871	−	25.0924i	0.756219	−	1.30981i	0.944766	−	0.327746i	$-0.106289\pi$
$368$		0			0
$369$			24.3227i			1.26619i
$370$		0			0
$371$	2.05408	−	1.18592i	0.106642	−	0.0615700i
$372$		0			0
$373$	−8.76329	−	15.1785i	−0.453746	−	0.785911i	0.544869	−	0.838521i	$-0.316579\pi$
$373$	−8.76329	−	15.1785i	−0.453746	−	0.785911i	−0.998615	+	0.0526100i	$0.983246\pi$
$374$		0			0
$375$	2.81228	+	1.62367i	0.145226	+	0.0838460i
$376$		0			0
$377$	1.41793	+	0.166019i	0.0730270	+	0.00855044i
$378$		0			0
$379$	−10.5841	−	6.11073i	−0.543669	−	0.313887i	0.202896	−	0.979200i	$-0.434965\pi$
$379$	−10.5841	−	6.11073i	−0.543669	−	0.313887i	−0.746564	+	0.665313i	$0.768298\pi$
$380$		0			0
$381$	6.22000	+	10.7734i	0.318660	+	0.551936i
$382$		0			0
$383$	4.41450	−	2.54871i	0.225570	−	0.130233i	−0.382957	−	0.923766i	$-0.625094\pi$
$383$	4.41450	−	2.54871i	0.225570	−	0.130233i	0.608527	+	0.793533i	$0.291761\pi$
$384$		0			0
$385$			14.9401i			0.761418i
$386$		0			0
$387$	−25.8416	+	44.7589i	−1.31360	+	2.27522i
$388$		0			0
$389$	−15.3931			−0.780461			−0.390231	−	0.920717i	$-0.627605\pi$
$389$	−15.3931			−0.780461			−0.390231	+	0.920717i	$0.627605\pi$
$390$		0			0
$391$	24.4735			1.23768
$392$		0			0
$393$	−19.9279	+	34.5161i	−1.00523	+	1.74110i
$394$		0			0
$395$		−	8.25143i		−	0.415174i
$396$		0			0
$397$	8.37393	−	4.83469i	0.420276	−	0.242646i	−0.274920	−	0.961467i	$-0.588651\pi$
$397$	8.37393	−	4.83469i	0.420276	−	0.242646i	0.695195	+	0.718821i	$0.255318\pi$
$398$		0			0
$399$	−14.9648	−	25.9199i	−0.749179	−	1.29762i
$400$		0			0
$401$	24.7662	+	14.2988i	1.23676	+	0.714046i	0.968431	−	0.249281i	$-0.0801941\pi$
$401$	24.7662	+	14.2988i	1.23676	+	0.714046i	0.268332	+	0.963326i	$0.413527\pi$
$402$		0			0
$403$	−23.8396	+	10.2777i	−1.18753	+	0.511970i
$404$		0			0
$405$	21.9060	+	12.6475i	1.08852	+	0.628457i
$406$		0			0
$407$	1.32018	+	2.28663i	0.0654391	+	0.113344i
$408$		0			0
$409$	5.76401	−	3.32785i	0.285012	−	0.164552i	−0.350678	−	0.936496i	$-0.614049\pi$
$409$	5.76401	−	3.32785i	0.285012	−	0.164552i	0.635690	+	0.771944i	$0.280716\pi$
$410$		0			0
$411$		−	29.3900i		−	1.44970i
$412$		0			0
$413$	−18.2219	+	31.5612i	−0.896641	+	1.55303i
$414$		0			0
$415$	−1.49741			−0.0735050
$416$		0			0
$417$	16.9052			0.827851
$418$		0			0
$419$	8.57883	−	14.8590i	0.419103	−	0.725909i	−0.576746	−	0.816923i	$-0.695678\pi$
$419$	8.57883	−	14.8590i	0.419103	−	0.725909i	0.995850	+	0.0910150i	$0.0290111\pi$
$420$		0			0
$421$			18.9638i			0.924237i	0.886818	+	0.462119i	$0.152911\pi$
$421$			18.9638i			0.924237i	−0.886818	+	0.462119i	$0.847089\pi$
$422$		0			0
$423$	40.5117	−	23.3895i	1.96975	−	1.13723i
$424$		0			0
$425$	2.77825	+	4.81207i	0.134765	+	0.233420i
$426$		0			0
$427$	−24.7332	−	14.2797i	−1.19693	−	0.691045i
$428$		0			0
$429$	−30.3254	−	22.5858i	−1.46412	−	1.09045i
$430$		0			0
$431$	7.90265	+	4.56260i	0.380657	+	0.219773i	0.678104	−	0.734966i	$-0.262802\pi$
$431$	7.90265	+	4.56260i	0.380657	+	0.219773i	−0.297447	+	0.954738i	$0.596135\pi$
$432$		0			0
$433$	15.0774	+	26.1149i	0.724575	+	1.25500i	0.959149	+	0.282902i	$0.0912970\pi$
$433$	15.0774	+	26.1149i	0.724575	+	1.25500i	−0.234574	+	0.972098i	$0.575370\pi$
$434$		0			0
$435$	1.11352	−	0.642891i	0.0533892	−	0.0308243i
$436$		0			0
$437$		−	8.77497i		−	0.419764i
$438$		0			0
$439$	−2.07643	+	3.59649i	−0.0991028	+	0.171651i	−0.911314	−	0.411713i	$-0.864931\pi$
$439$	−2.07643	+	3.59649i	−0.0991028	+	0.171651i	0.812211	+	0.583364i	$0.198264\pi$
$440$		0			0
$441$	−108.664			−5.17446
$442$		0			0
$443$	−33.0164			−1.56866			−0.784329	−	0.620345i	$-0.786993\pi$
$443$	−33.0164			−1.56866			−0.784329	+	0.620345i	$0.786993\pi$
$444$		0			0
$445$	8.15887	−	14.1316i	0.386768	−	0.669901i
$446$		0			0
$447$			41.6173i			1.96843i
$448$		0			0
$449$	17.9151	−	10.3433i	0.845466	−	0.488130i	−0.0136523	−	0.999907i	$-0.504346\pi$
$449$	17.9151	−	10.3433i	0.845466	−	0.488130i	0.859119	+	0.511777i	$0.171012\pi$
$450$		0			0
$451$	−5.20522	−	9.01570i	−0.245104	−	0.424533i
$452$		0			0
$453$	−50.2419	−	29.0072i	−2.36057	−	1.36287i
$454$		0			0
$455$	9.96326	−	13.3774i	0.467085	−	0.627142i
$456$		0			0
$457$	−3.88255	−	2.24159i	−0.181618	−	0.104857i	0.406435	−	0.913680i	$-0.366772\pi$
$457$	−3.88255	−	2.24159i	−0.181618	−	0.104857i	−0.588053	+	0.808823i	$0.700105\pi$
$458$		0			0
$459$	41.0068	+	71.0259i	1.91403	+	3.31521i
$460$		0			0
$461$	−19.8427	+	11.4562i	−0.924167	+	0.533568i	−0.884962	−	0.465663i	$-0.845816\pi$
$461$	−19.8427	+	11.4562i	−0.924167	+	0.533568i	−0.0392048	+	0.999231i	$0.512482\pi$
$462$		0			0
$463$		−	19.4119i		−	0.902148i	−0.892486	−	0.451074i	$-0.851041\pi$
$463$		−	19.4119i		−	0.902148i	0.892486	−	0.451074i	$-0.148959\pi$
$464$		0			0
$465$	−11.6908	+	20.2490i	−0.542146	+	0.939024i
$466$		0			0
$467$	2.90247			0.134310			0.0671552	−	0.997743i	$-0.478608\pi$
$467$	2.90247			0.134310			0.0671552	+	0.997743i	$0.478608\pi$
$468$		0			0
$469$	−40.5066			−1.87042
$470$		0			0
$471$	22.3193	−	38.6582i	1.02842	−	1.78128i
$472$		0			0
$473$		−	22.1211i		−	1.01713i
$474$		0			0
$475$	1.72537	−	0.996140i	0.0791652	−	0.0457061i
$476$		0			0
$477$	1.93422	+	3.35017i	0.0885619	+	0.153394i
$478$		0			0
$479$	12.9896	+	7.49954i	0.593509	+	0.342663i	0.766484	−	0.642264i	$-0.222005\pi$
$479$	12.9896	+	7.49954i	0.593509	+	0.342663i	−0.172975	+	0.984926i	$0.555338\pi$
$480$		0			0
$481$	0.342811	−	2.92786i	0.0156308	−	0.133499i
$482$		0			0
$483$	−57.3030	−	33.0839i	−2.60738	−	1.50537i
$484$		0			0
$485$	−2.79514	−	4.84132i	−0.126921	−	0.219833i
$486$		0			0
$487$	32.1131	−	18.5405i	1.45518	−	0.840149i	0.456413	−	0.889768i	$-0.349134\pi$
$487$	32.1131	−	18.5405i	1.45518	−	0.840149i	0.998768	+	0.0496185i	$0.0158006\pi$
$488$		0			0
$489$			15.9757i			0.722444i
$490$		0			0
$491$	4.83319	−	8.37133i	0.218119	−	0.377793i	−0.736114	−	0.676857i	$-0.763341\pi$
$491$	4.83319	−	8.37133i	0.218119	−	0.377793i	0.954233	+	0.299065i	$0.0966747\pi$
$492$		0			0
$493$	2.20009			0.0990871
$494$		0			0
$495$	−24.3671			−1.09522
$496$		0			0
$497$	−6.50143	+	11.2608i	−0.291629	+	0.505117i
$498$		0			0
$499$			38.0637i			1.70397i	0.523570	+	0.851983i	$0.324600\pi$
$499$			38.0637i			1.70397i	−0.523570	+	0.851983i	$0.675400\pi$
$500$		0			0
$501$	−56.4645	+	32.5998i	−2.52265	+	1.45645i
$502$		0			0
$503$	1.09655	+	1.89928i	0.0488927	+	0.0846846i	0.889436	−	0.457060i	$-0.151097\pi$
$503$	1.09655	+	1.89928i	0.0488927	+	0.0846846i	−0.840543	+	0.541744i	$0.817764\pi$
$504$		0			0
$505$	−14.1108	−	8.14688i	−0.627923	−	0.362531i
$506$		0			0
$507$	12.0914	+	40.4468i	0.536996	+	1.79631i
$508$		0			0
$509$	21.5682	+	12.4524i	0.955992	+	0.551942i	0.894937	−	0.446192i	$-0.147220\pi$
$509$	21.5682	+	12.4524i	0.955992	+	0.551942i	0.0610551	+	0.998134i	$0.480553\pi$
$510$		0			0
$511$	11.6460	+	20.1715i	0.515189	+	0.892333i
$512$		0			0
$513$	25.4663	−	14.7030i	1.12436	−	0.649152i
$514$		0			0
$515$			17.2764i			0.761288i
$516$		0			0
$517$	−10.0110	+	17.3396i	−0.440283	+	0.762593i
$518$		0			0
$519$	−9.62875			−0.422655
$520$		0			0
$521$	21.2273			0.929984			0.464992	−	0.885315i	$-0.346057\pi$
$521$	21.2273			0.929984			0.464992	+	0.885315i	$0.346057\pi$
$522$		0			0
$523$	−11.1474	+	19.3079i	−0.487444	+	0.844278i	−0.999896	−	0.0144383i	$-0.995404\pi$
$523$	−11.1474	+	19.3079i	−0.487444	+	0.844278i	0.512452	+	0.858716i	$0.328737\pi$
$524$		0			0
$525$		−	15.0228i		−	0.655650i
$526$		0			0
$527$	−34.6479	+	20.0040i	−1.50928	+	0.871386i
$528$		0			0
$529$	1.80025	+	3.11812i	0.0782717	+	0.135571i
$530$		0			0
$531$	−51.4759	−	29.7196i	−2.23386	−	1.28972i
$532$		0			0
$533$	−1.35163	+	11.5439i	−0.0585457	+	0.500023i
$534$		0			0
$535$	−4.84622	−	2.79797i	−0.209520	−	0.120967i
$536$		0			0
$537$	−42.3638	−	73.3762i	−1.82813	−	3.16642i
$538$		0			0
$539$	40.2784	−	23.2547i	1.73491	−	1.00165i
$540$		0			0
$541$		−	24.1110i		−	1.03661i	−0.855194	−	0.518307i	$-0.826562\pi$
$541$		−	24.1110i		−	1.03661i	0.855194	−	0.518307i	$-0.173438\pi$
$542$		0			0
$543$	26.5150	−	45.9252i	1.13787	−	1.97084i
$544$		0			0
$545$	−7.58276			−0.324810
$546$		0			0
$547$	44.9078			1.92012			0.960060	−	0.279794i	$-0.0902662\pi$
$547$	44.9078			1.92012			0.960060	+	0.279794i	$0.0902662\pi$
$548$		0			0
$549$	23.2900	−	40.3395i	0.993994	−	1.72165i
$550$		0			0
$551$		−	0.788841i		−	0.0336058i
$552$		0			0
$553$	−33.0585	+	19.0863i	−1.40579	+	0.811633i
$554$		0			0
$555$	−1.32749	−	2.29929i	−0.0563490	−	0.0975993i
$556$		0			0
$557$	10.9799	+	6.33924i	0.465233	+	0.268602i	0.714242	−	0.699899i	$-0.246772\pi$
$557$	10.9799	+	6.33924i	0.465233	+	0.268602i	−0.249009	+	0.968501i	$0.580105\pi$
$558$		0			0
$559$	−14.7521	+	19.8072i	−0.623948	+	0.837757i
$560$		0			0
$561$	−50.4650	−	29.1360i	−2.13063	−	1.23012i
$562$		0			0
$563$	−8.99769	−	15.5845i	−0.379208	−	0.656807i	0.611740	−	0.791059i	$-0.290470\pi$
$563$	−8.99769	−	15.5845i	−0.379208	−	0.656807i	−0.990947	+	0.134252i	$0.957137\pi$
$564$		0			0
$565$	−10.6562	+	6.15234i	−0.448308	+	0.258831i
$566$		0			0
$567$		−	117.019i		−	4.91434i
$568$		0			0
$569$	3.59418	−	6.22530i	0.150676	−	0.260978i	−0.780800	−	0.624781i	$-0.785188\pi$
$569$	3.59418	−	6.22530i	0.150676	−	0.260978i	0.931476	+	0.363803i	$0.118522\pi$
$570$		0			0
$571$	−36.5611			−1.53003			−0.765016	−	0.644011i	$-0.777269\pi$
$571$	−36.5611			−1.53003			−0.765016	+	0.644011i	$0.777269\pi$
$572$		0			0
$573$	−32.9202			−1.37526
$574$		0			0
$575$	2.20224	−	3.81440i	0.0918399	−	0.159071i
$576$		0			0
$577$		−	6.37212i		−	0.265275i	−0.991165	−	0.132637i	$-0.957655\pi$
$577$		−	6.37212i		−	0.265275i	0.991165	−	0.132637i	$-0.0423446\pi$
$578$		0			0
$579$	31.6356	−	18.2648i	1.31473	−	0.759060i
$580$		0			0
$581$	3.46365	+	5.99922i	0.143697	+	0.248890i
$582$		0			0
$583$	−1.43392	−	0.827872i	−0.0593867	−	0.0342870i
$584$		0			0
$585$	21.8183	+	16.2499i	0.902076	+	0.671851i
$586$		0			0
$587$	−15.1127	−	8.72530i	−0.623767	−	0.360132i	0.154567	−	0.987982i	$-0.450602\pi$
$587$	−15.1127	−	8.72530i	−0.623767	−	0.360132i	−0.778334	+	0.627850i	$0.783935\pi$
$588$		0			0
$589$	7.17241	+	12.4230i	0.295534	+	0.511880i
$590$		0			0
$591$	−50.0853	+	28.9168i	−2.06023	+	1.18948i
$592$		0			0
$593$		−	27.2584i		−	1.11937i	−0.828705	−	0.559685i	$-0.810922\pi$
$593$		−	27.2584i		−	1.11937i	0.828705	−	0.559685i	$-0.189078\pi$
$594$		0			0
$595$	12.8527	−	22.2615i	0.526910	−	0.912634i
$596$		0			0
$597$	8.28832			0.339218
$598$		0			0
$599$	−39.1965			−1.60152			−0.800762	−	0.598982i	$-0.795572\pi$
$599$	−39.1965			−1.60152			−0.800762	+	0.598982i	$0.795572\pi$
$600$		0			0
$601$	19.8891	−	34.4489i	0.811294	−	1.40520i	−0.100665	−	0.994920i	$-0.532097\pi$
$601$	19.8891	−	34.4489i	0.811294	−	1.40520i	0.911959	−	0.410282i	$-0.134570\pi$
$602$		0			0
$603$		−	66.0656i		−	2.69040i
$604$		0			0
$605$	−0.494134	+	0.285288i	−0.0200894	+	0.0115986i
$606$		0			0
$607$	11.7281	+	20.3137i	0.476031	+	0.824509i	0.999623	−	0.0274598i	$-0.00874181\pi$
$607$	11.7281	+	20.3137i	0.476031	+	0.824509i	−0.523592	+	0.851969i	$0.675408\pi$
$608$		0			0
$609$	−5.15135	−	2.97413i	−0.208743	−	0.120518i
$610$		0			0
$611$	20.5273	−	8.84973i	0.830444	−	0.358022i
$612$		0			0
$613$	7.81755	+	4.51346i	0.315748	+	0.182297i	0.649496	−	0.760365i	$-0.274980\pi$
$613$	7.81755	+	4.51346i	0.315748	+	0.182297i	−0.333748	+	0.942662i	$0.608313\pi$
$614$		0			0
$615$	5.23404	+	9.06562i	0.211057	+	0.365561i
$616$		0			0
$617$	−10.3281	+	5.96295i	−0.415795	+	0.240060i	−0.693277	−	0.720671i	$-0.743834\pi$
$617$	−10.3281	+	5.96295i	−0.415795	+	0.240060i	0.277481	+	0.960731i	$0.410500\pi$
$618$		0			0
$619$		−	3.10815i		−	0.124927i	−0.998047	−	0.0624636i	$-0.980104\pi$
$619$		−	3.10815i		−	0.124927i	0.998047	−	0.0624636i	$-0.0198957\pi$
$620$		0			0
$621$	32.5050	−	56.3003i	1.30438	−	2.25925i
$622$		0			0
$623$	−75.4889			−3.02440
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−10.4467	+	18.0942i	−0.417201	+	0.722613i
$628$		0			0
$629$		−	4.54293i		−	0.181138i
$630$		0			0
$631$	−37.6497	+	21.7371i	−1.49881	+	0.865340i	−0.999999	−	0.00136957i	$-0.999564\pi$
$631$	−37.6497	+	21.7371i	−1.49881	+	0.865340i	−0.498813	+	0.866709i	$0.666231\pi$
$632$		0			0
$633$	28.6433	+	49.6116i	1.13847	+	1.97188i
$634$		0			0
$635$	3.31759	+	1.91541i	0.131655	+	0.0760108i
$636$		0			0
$637$	−51.5735	−	6.03853i	−2.04341	−	0.239255i
$638$		0			0
$639$	−18.3662	−	10.6037i	−0.726556	−	0.419477i
$640$		0			0
$641$	10.9222	+	18.9178i	0.431401	+	0.747208i	0.996994	−	0.0774765i	$-0.0246863\pi$
$641$	10.9222	+	18.9178i	0.431401	+	0.747208i	−0.565594	+	0.824684i	$0.691353\pi$
$642$		0			0
$643$	5.65668	−	3.26589i	0.223078	−	0.128794i	−0.384297	−	0.923210i	$-0.625556\pi$
$643$	5.65668	−	3.26589i	0.223078	−	0.128794i	0.607375	+	0.794416i	$0.292223\pi$
$644$		0			0
$645$			22.2436i			0.875839i
$646$		0			0
$647$	−4.78738	+	8.29199i	−0.188211	+	0.325992i	−0.944654	−	0.328068i	$-0.893602\pi$
$647$	−4.78738	+	8.29199i	−0.188211	+	0.325992i	0.756442	+	0.654060i	$0.226936\pi$
$648$		0			0
$649$	25.4408			0.998638
$650$		0			0
$651$	108.167			4.23941
$652$		0			0
$653$	−15.9175	+	27.5699i	−0.622900	+	1.07889i	0.366043	+	0.930598i	$0.380712\pi$
$653$	−15.9175	+	27.5699i	−0.622900	+	1.07889i	−0.988943	+	0.148296i	$0.952621\pi$
$654$		0			0
$655$			12.2733i			0.479559i
$656$		0			0
$657$	−32.8993	+	18.9944i	−1.28353	+	0.741044i
$658$		0			0
$659$	2.84117	+	4.92106i	0.110676	+	0.191697i	0.916043	−	0.401080i	$-0.131365\pi$
$659$	2.84117	+	4.92106i	0.110676	+	0.191697i	−0.805367	+	0.592777i	$0.798032\pi$
$660$		0			0
$661$	9.56664	+	5.52330i	0.372099	+	0.214832i	0.674375	−	0.738389i	$-0.264413\pi$
$661$	9.56664	+	5.52330i	0.372099	+	0.214832i	−0.302276	+	0.953220i	$0.597746\pi$
$662$		0			0
$663$	25.7562	+	59.7425i	1.00029	+	2.32021i
$664$		0			0
$665$	−7.98187	−	4.60833i	−0.309523	−	0.178703i
$666$		0			0
$667$	−0.871976	−	1.51031i	−0.0337630	−	0.0584793i
$668$		0			0
$669$	8.55949	−	4.94182i	0.330929	−	0.191062i
$670$		0			0
$671$			19.9369i			0.769655i
$672$		0			0
$673$	12.0476	−	20.8671i	0.464403	−	0.804369i	−0.534772	−	0.844997i	$-0.679602\pi$
$673$	12.0476	−	20.8671i	0.464403	−	0.804369i	0.999174	+	0.0406276i	$0.0129357\pi$
$674$		0			0
$675$	14.7599			0.568111
$676$		0			0
$677$	−16.1944			−0.622403			−0.311201	−	0.950344i	$-0.600731\pi$
$677$	−16.1944			−0.622403			−0.311201	+	0.950344i	$0.600731\pi$
$678$		0			0
$679$	−12.9308	+	22.3968i	−0.496240	+	0.859512i
$680$		0			0
$681$			11.6175i			0.445183i
$682$		0			0
$683$	−30.8212	+	17.7946i	−1.17934	+	0.680892i	−0.955862	−	0.293817i	$-0.905074\pi$
$683$	−30.8212	+	17.7946i	−1.17934	+	0.680892i	−0.223478	+	0.974709i	$0.571741\pi$
$684$		0			0
$685$	−4.52523	−	7.83794i	−0.172900	−	0.299472i
$686$		0			0
$687$	−12.5023	−	7.21820i	−0.476992	−	0.275391i
$688$		0			0
$689$	0.731840	+	1.69753i	0.0278809	+	0.0646707i
$690$		0			0
$691$	33.0084	+	19.0574i	1.25570	+	0.724977i	0.972235	−	0.234006i	$-0.0751835\pi$
$691$	33.0084	+	19.0574i	1.25570	+	0.724977i	0.283463	+	0.958983i	$0.408517\pi$
$692$		0			0
$693$	56.3633	+	97.6241i	2.14106	+	3.70843i
$694$		0			0
$695$	4.50840	−	2.60293i	0.171013	−	0.0987347i
$696$		0			0
$697$			17.9118i			0.678459i
$698$		0			0
$699$	−1.81482	+	3.14335i	−0.0686426	+	0.118893i
$700$		0			0
$701$	−10.5042			−0.396740			−0.198370	−	0.980127i	$-0.563565\pi$
$701$	−10.5042			−0.396740			−0.198370	+	0.980127i	$0.563565\pi$
$702$		0			0
$703$	−1.62886			−0.0614338
$704$		0			0
$705$	10.0664	−	17.4356i	0.379124	−	0.656661i
$706$		0			0
$707$			75.3780i			2.83488i
$708$		0			0
$709$	−36.0124	+	20.7918i	−1.35247	+	0.780851i	−0.988595	−	0.150596i	$-0.951881\pi$
$709$	−36.0124	+	20.7918i	−1.35247	+	0.780851i	−0.363878	+	0.931447i	$0.618548\pi$
$710$		0			0
$711$	−31.1295	−	53.9179i	−1.16745	−	2.02208i
$712$		0			0
$713$	27.4644	+	15.8566i	1.02855	+	0.593834i
$714$		0			0
$715$	−11.5650	−	1.35410i	−0.432506	−	0.0506404i
$716$		0			0
$717$	4.76293	+	2.74988i	0.177875	+	0.102696i
$718$		0			0
$719$	−21.3994	−	37.0649i	−0.798063	−	1.38229i	−0.920876	−	0.389856i	$-0.872525\pi$
$719$	−21.3994	−	37.0649i	−0.798063	−	1.38229i	0.122813	−	0.992430i	$-0.460809\pi$
$720$		0			0
$721$	69.2160	−	39.9619i	2.57774	−	1.48826i
$722$		0			0
$723$			78.8947i			2.93412i
$724$		0			0
$725$	0.197974	−	0.342902i	0.00735258	−	0.0127351i
$726$		0			0
$727$	−1.06263			−0.0394108			−0.0197054	−	0.999806i	$-0.506273\pi$
$727$	−1.06263			−0.0394108			−0.0197054	+	0.999806i	$0.506273\pi$
$728$		0			0
$729$	47.0642			1.74312
$730$		0			0
$731$	−19.0304	+	32.9616i	−0.703864	+	1.21913i
$732$		0			0
$733$		−	20.7272i		−	0.765577i	−0.923836	−	0.382789i	$-0.874964\pi$
$733$		−	20.7272i		−	0.765577i	0.923836	−	0.382789i	$-0.125036\pi$
$734$		0			0
$735$	−40.5014	+	23.3835i	−1.49392	+	0.862513i
$736$		0			0
$737$	14.1385	+	24.4886i	0.520797	+	0.902048i
$738$		0			0
$739$	11.5583	+	6.67319i	0.425179	+	0.245477i	0.697291	−	0.716788i	$-0.254389\pi$
$739$	11.5583	+	6.67319i	0.425179	+	0.245477i	−0.272112	+	0.962266i	$0.587722\pi$
$740$		0			0
$741$	21.4207	−	9.23489i	0.786907	−	0.339252i
$742$		0			0
$743$	0.346740	+	0.200191i	0.0127207	+	0.00734428i	0.506347	−	0.862330i	$-0.330996\pi$
$743$	0.346740	+	0.200191i	0.0127207	+	0.00734428i	−0.493626	+	0.869674i	$0.664329\pi$
$744$		0			0
$745$	6.40790	+	11.0988i	0.234767	+	0.406629i
$746$		0			0
$747$	−9.78463	+	5.64916i	−0.358001	+	0.206692i
$748$		0			0
$749$			25.8878i			0.945921i
$750$		0			0
$751$	25.0742	−	43.4298i	0.914971	−	1.58478i	0.108027	−	0.994148i	$-0.465547\pi$
$751$	25.0742	−	43.4298i	0.914971	−	1.58478i	0.806944	−	0.590628i	$-0.201120\pi$
$752$		0			0
$753$	41.5028			1.51245
$754$		0			0
$755$	−17.8652			−0.650180
$756$		0			0
$757$	1.11832	−	1.93698i	0.0406459	−	0.0704008i	−0.844987	−	0.534787i	$-0.820392\pi$
$757$	1.11832	−	1.93698i	0.0406459	−	0.0704008i	0.885633	+	0.464386i	$0.153725\pi$
$758$		0			0
$759$			46.1906i			1.67661i
$760$		0			0
$761$	−16.3704	+	9.45146i	−0.593427	+	0.342615i	−0.766451	−	0.642303i	$-0.777979\pi$
$761$	−16.3704	+	9.45146i	−0.593427	+	0.342615i	0.173025	+	0.984917i	$0.444646\pi$
$762$		0			0
$763$	17.5396	+	30.3795i	0.634977	+	1.09981i
$764$		0			0
$765$	36.3082	+	20.9626i	1.31273	+	0.757903i
$766$		0			0
$767$	−22.7797	−	16.9659i	−0.822528	−	0.612605i
$768$		0			0
$769$	−10.3046	−	5.94934i	−0.371592	−	0.214539i	0.302562	−	0.953130i	$-0.402158\pi$
$769$	−10.3046	−	5.94934i	−0.371592	−	0.214539i	−0.674154	+	0.738591i	$0.735491\pi$
$770$		0			0
$771$	1.13785	+	1.97081i	0.0409785	+	0.0709768i
$772$		0			0
$773$	−12.3557	+	7.13356i	−0.444403	+	0.256576i	−0.705464	−	0.708746i	$-0.749261\pi$
$773$	−12.3557	+	7.13356i	−0.444403	+	0.256576i	0.261060	+	0.965322i	$0.415928\pi$
$774$		0			0
$775$			7.20020i			0.258639i
$776$		0			0
$777$	−6.14124	+	10.6369i	−0.220316	+	0.381598i
$778$		0			0
$779$	6.42228			0.230102
$780$		0			0
$781$	9.07708			0.324803
$782$		0			0
$783$	2.92209	−	5.06121i	0.104427	−	0.180873i
$784$		0			0
$785$		−	13.7462i		−	0.490623i
$786$		0			0
$787$	30.7475	−	17.7521i	1.09603	−	0.632792i	0.160853	−	0.986978i	$-0.448575\pi$
$787$	30.7475	−	17.7521i	1.09603	−	0.632792i	0.935175	+	0.354186i	$0.115242\pi$
$788$		0			0
$789$	9.66723	+	16.7441i	0.344162	+	0.596107i
$790$		0			0
$791$	49.2974	+	28.4619i	1.75282	+	1.01199i
$792$		0			0
$793$	13.2955	−	17.8515i	0.472138	−	0.633926i
$794$		0			0
$795$	1.44186	+	0.832456i	0.0511374	+	0.0295242i
$796$		0			0
$797$	11.4801	+	19.8841i	0.406647	+	0.704333i	0.994512	−	0.104626i	$-0.0333647\pi$
$797$	11.4801	+	19.8841i	0.406647	+	0.704333i	−0.587865	+	0.808959i	$0.700031\pi$
$798$		0			0
$799$	29.8338	−	17.2246i	1.05545	−	0.609362i
$800$		0			0
$801$		−	123.121i		−	4.35028i
$802$		0			0
$803$	8.12987	−	14.0814i	0.286897	−	0.496920i
$804$		0			0
$805$	−20.3760			−0.718159
$806$		0			0
$807$	−63.4629			−2.23400
$808$		0			0
$809$	−3.47413	+	6.01737i	−0.122144	+	0.211560i	−0.920613	−	0.390476i	$-0.872310\pi$
$809$	−3.47413	+	6.01737i	−0.122144	+	0.211560i	0.798469	+	0.602036i	$0.205644\pi$
$810$		0			0
$811$			53.7587i			1.88772i	0.330342	+	0.943861i	$0.392836\pi$
$811$			53.7587i			1.88772i	−0.330342	+	0.943861i	$0.607164\pi$
$812$		0			0
$813$	65.3011	−	37.7016i	2.29021	−	1.32225i
$814$		0			0
$815$	2.45980	+	4.26051i	0.0861632	+	0.149239i
$816$		0			0
$817$	11.8184	+	6.82333i	0.413472	+	0.238718i
$818$		0			0
$819$	14.6358	−	125.000i	0.511416	−	4.36787i
$820$		0			0
$821$	−40.7388	−	23.5205i	−1.42179	−	0.820873i	−0.425341	−	0.905033i	$-0.639846\pi$
$821$	−40.7388	−	23.5205i	−1.42179	−	0.820873i	−0.996452	+	0.0841607i	$0.973179\pi$
$822$		0			0
$823$	−17.8087	−	30.8457i	−0.620774	−	1.07521i	−0.989342	−	0.145611i	$-0.953485\pi$
$823$	−17.8087	−	30.8457i	−0.620774	−	1.07521i	0.368568	−	0.929601i	$-0.379848\pi$
$824$		0			0
$825$	−9.08216	+	5.24359i	−0.316200	+	0.182558i
$826$		0			0
$827$		−	11.2270i		−	0.390399i	−0.980764	−	0.195200i	$-0.937465\pi$
$827$		−	11.2270i		−	0.390399i	0.980764	−	0.195200i	$-0.0625355\pi$
$828$		0			0
$829$	13.2468	−	22.9442i	0.460081	−	0.796884i	−0.538884	−	0.842380i	$-0.681154\pi$
$829$	13.2468	−	22.9442i	0.460081	−	0.796884i	0.998964	+	0.0454967i	$0.0144871\pi$
$830$		0			0
$831$	58.2483			2.02061
$832$		0			0
$833$	−80.0226			−2.77262
$834$		0			0
$835$	−10.0389	+	17.3879i	−0.347411	+	0.601733i
$836$		0			0
$837$			106.275i			3.67339i
$838$		0			0
$839$	28.4785	−	16.4421i	0.983189	−	0.567644i	0.0799573	−	0.996798i	$-0.474522\pi$
$839$	28.4785	−	16.4421i	0.983189	−	0.567644i	0.903231	+	0.429154i	$0.141188\pi$
$840$		0			0
$841$	14.4216	+	24.9790i	0.497297	+	0.861344i
$842$		0			0
$843$	78.8478	+	45.5228i	2.71566	+	1.56789i
$844$		0			0
$845$	9.45229	+	8.92492i	0.325169	+	0.307027i
$846$		0			0
$847$	2.28596	+	1.31980i	0.0785464	+	0.0453488i
$848$		0			0
$849$	−13.1497	−	22.7759i	−0.451295	−	0.781666i
$850$		0			0
$851$	−3.11861	+	1.80053i	−0.106904	+	0.0617213i
$852$		0			0
$853$		−	10.1806i		−	0.348578i	−0.984695	−	0.174289i	$-0.944237\pi$
$853$		−	10.1806i		−	0.348578i	0.984695	−	0.174289i	$-0.0557627\pi$
$854$		0			0
$855$	7.51612	−	13.0183i	0.257046	−	0.445216i
$856$		0			0
$857$	48.5596			1.65877			0.829383	−	0.558681i	$-0.188692\pi$
$857$	48.5596			1.65877			0.829383	+	0.558681i	$0.188692\pi$
$858$		0			0
$859$	−25.0502			−0.854703			−0.427351	−	0.904086i	$-0.640553\pi$
$859$	−25.0502			−0.854703			−0.427351	+	0.904086i	$0.640553\pi$
$860$		0			0
$861$	24.2136	−	41.9393i	0.825199	−	1.42929i
$862$		0			0
$863$			3.15537i			0.107410i	0.998557	+	0.0537050i	$0.0171031\pi$
$863$			3.15537i			0.107410i	−0.998557	+	0.0537050i	$0.982897\pi$
$864$		0			0
$865$	−2.56787	+	1.48256i	−0.0873101	+	0.0504085i
$866$		0			0
$867$	22.5279	+	39.0196i	0.765089	+	1.32517i
$868$		0			0
$869$	23.0776	+	13.3238i	0.782853	+	0.451980i
$870$		0			0
$871$	3.67132	−	31.3558i	0.124398	−	1.06245i
$872$		0			0
$873$	−36.5289	−	21.0900i	−1.23632	−	0.713787i
$874$		0			0
$875$	−2.31309	−	4.00640i	−0.0781969	−	0.135441i
$876$		0			0
$877$	−43.4272	+	25.0727i	−1.46643	+	0.846645i	−0.999295	−	0.0375405i	$-0.988048\pi$
$877$	−43.4272	+	25.0727i	−1.46643	+	0.846645i	−0.467137	+	0.884185i	$0.654714\pi$
$878$		0			0
$879$		−	23.8262i		−	0.803638i
$880$		0			0
$881$	23.3359	−	40.4190i	0.786208	−	1.36175i	−0.142067	−	0.989857i	$-0.545375\pi$
$881$	23.3359	−	40.4190i	0.786208	−	1.36175i	0.928275	−	0.371895i	$-0.121292\pi$
$882$		0			0
$883$	34.2630			1.15304			0.576521	−	0.817083i	$-0.304410\pi$
$883$	34.2630			1.15304			0.576521	+	0.817083i	$0.304410\pi$
$884$		0			0
$885$	−25.5816			−0.859917
$886$		0			0
$887$	−9.00525	+	15.5975i	−0.302367	+	0.523714i	−0.976672	−	0.214739i	$-0.931110\pi$
$887$	−9.00525	+	15.5975i	−0.302367	+	0.523714i	0.674305	+	0.738453i	$0.264443\pi$
$888$		0			0
$889$		−	17.7221i		−	0.594381i
$890$		0			0
$891$	−70.7447	+	40.8445i	−2.37004	+	1.36834i
$892$		0			0
$893$	−6.17586	−	10.6969i	−0.206667	−	0.357958i
$894$		0			0
$895$	−22.5958	−	13.0457i	−0.755293	−	0.436069i
$896$		0			0
$897$	30.8036	−	41.3591i	1.02850	−	1.38094i
$898$		0			0
$899$	2.46896	+	1.42546i	0.0823445	+	0.0475416i
$900$		0			0
$901$	1.42441	+	2.46715i	0.0474539	+	0.0821926i
$902$		0			0
$903$	89.1165	−	51.4514i	2.96561	−	1.71220i
$904$		0			0
$905$		−	16.3302i		−	0.542836i
$906$		0			0
$907$	8.56587	−	14.8365i	0.284425	−	0.492639i	−0.688044	−	0.725669i	$-0.741531\pi$
$907$	8.56587	−	14.8365i	0.284425	−	0.492639i	0.972470	+	0.233030i	$0.0748640\pi$
$908$		0			0
$909$	−122.940			−4.07767
$910$		0			0
$911$	−51.2138			−1.69679			−0.848395	−	0.529364i	$-0.822430\pi$
$911$	−51.2138			−1.69679			−0.848395	+	0.529364i	$0.822430\pi$
$912$		0			0
$913$	2.41792	−	4.18795i	0.0800213	−	0.138601i
$914$		0			0
$915$		−	20.0473i		−	0.662742i
$916$		0			0
$917$	49.1718	−	28.3894i	1.62380	−	0.937499i
$918$		0			0
$919$	27.2238	+	47.1529i	0.898029	+	1.55543i	0.830011	+	0.557747i	$0.188334\pi$
$919$	27.2238	+	47.1529i	0.898029	+	1.55543i	0.0680179	+	0.997684i	$0.478333\pi$
$920$		0			0
$921$	54.6332	+	31.5425i	1.80023	+	1.03936i
$922$		0			0
$923$	−8.12763	−	6.05332i	−0.267524	−	0.199248i
$924$		0			0
$925$	−0.708052	−	0.408794i	−0.0232806	−	0.0134411i
$926$		0			0
$927$	65.1772	+	112.890i	2.14070	+	3.70780i
$928$		0			0
$929$	5.77311	−	3.33311i	0.189410	−	0.109356i	−0.402297	−	0.915509i	$-0.631788\pi$
$929$	5.77311	−	3.33311i	0.189410	−	0.109356i	0.591706	+	0.806154i	$0.298455\pi$
$930$		0			0
$931$			28.6921i			0.940344i
$932$		0			0
$933$	9.25362	−	16.0277i	0.302950	−	0.524725i
$934$		0			0
$935$	−17.9445			−0.586848
$936$		0			0
$937$	−38.3341			−1.25232			−0.626160	−	0.779694i	$-0.715375\pi$
$937$	−38.3341			−1.25232			−0.626160	+	0.779694i	$0.715375\pi$
$938$		0			0
$939$	43.5836	−	75.4891i	1.42230	−	2.46349i
$940$		0			0
$941$			14.2511i			0.464574i	0.972647	+	0.232287i	$0.0746208\pi$
$941$			14.2511i			0.464574i	−0.972647	+	0.232287i	$0.925379\pi$
$942$		0			0
$943$	12.2960	−	7.09911i	0.400414	−	0.231179i
$944$		0			0
$945$	−34.1412	−	59.1342i	−1.11061	−	1.92364i
$946$		0			0
$947$	−2.93761	−	1.69603i	−0.0954594	−	0.0551135i	0.451510	−	0.892266i	$-0.350885\pi$
$947$	−2.93761	−	1.69603i	−0.0954594	−	0.0551135i	−0.546970	+	0.837152i	$0.684219\pi$
$948$		0			0
$949$	−16.6701	+	7.18681i	−0.541134	+	0.233294i
$950$		0			0
$951$	−28.8073	−	16.6319i	−0.934140	−	0.539326i
$952$		0			0
$953$	−24.9642	−	43.2393i	−0.808670	−	1.40066i	−0.913786	−	0.406197i	$-0.866855\pi$
$953$	−24.9642	−	43.2393i	−0.808670	−	1.40066i	0.105116	−	0.994460i	$-0.466479\pi$
$954$		0			0
$955$	−8.77939	+	5.06878i	−0.284094	+	0.164022i
$956$		0			0
$957$			4.15238i			0.134227i
$958$		0			0
$959$	−20.9346	+	36.2598i	−0.676013	+	1.17089i
$960$		0			0
$961$	−20.8429			−0.672351
$962$		0			0
$963$	−42.2227			−1.36061
$964$		0			0
$965$	5.62455	−	9.74200i	0.181061	−	0.313606i
$966$		0			0
$967$		−	49.5568i		−	1.59364i	−0.604218	−	0.796819i	$-0.706514\pi$
$967$		−	49.5568i		−	1.59364i	0.604218	−	0.796819i	$-0.293486\pi$
$968$		0			0
$969$	31.1323	−	17.9742i	1.00011	−	0.577415i
$970$		0			0
$971$	−17.9858	−	31.1523i	−0.577192	−	0.999726i	−0.995800	−	0.0915584i	$-0.970815\pi$
$971$	−17.9858	−	31.1523i	−0.577192	−	0.999726i	0.418608	−	0.908167i	$-0.362518\pi$
$972$		0			0
$973$	−20.8567	−	12.0416i	−0.668636	−	0.386037i
$974$		0			0
$975$	11.6290	+	1.36160i	0.372427	+	0.0436060i
$976$		0			0
$977$	−43.6460	−	25.1990i	−1.39636	−	0.806188i	−0.402349	−	0.915486i	$-0.631806\pi$
$977$	−43.6460	−	25.1990i	−1.39636	−	0.806188i	−0.994009	+	0.109298i	$0.965140\pi$
$978$		0			0
$979$	26.3488	+	45.6374i	0.842110	+	1.45858i
$980$		0			0
$981$	−49.5485	+	28.6069i	−1.58196	+	0.913347i
$982$		0			0
$983$			18.8159i			0.600133i	0.953918	+	0.300067i	$0.0970089\pi$
$983$			18.8159i			0.600133i	−0.953918	+	0.300067i	$0.902991\pi$
$984$		0			0
$985$	−8.90475	+	15.4235i	−0.283729	+	0.491433i
$986$		0			0
$987$	−93.1384			−2.96463
$988$		0			0
$989$	30.1697			0.959341
$990$		0			0
$991$	−0.387825	+	0.671733i	−0.0123197	+	0.0213383i	−0.872120	−	0.489293i	$-0.837255\pi$
$991$	−0.387825	+	0.671733i	−0.0123197	+	0.0213383i	0.859800	+	0.510631i	$0.170588\pi$
$992$		0			0
$993$			74.6609i			2.36929i
$994$		0			0
$995$	2.21039	−	1.27617i	0.0700741	−	0.0404573i
$996$		0			0
$997$	29.2347	+	50.6361i	0.925874	+	1.60366i	0.790150	+	0.612913i	$0.210003\pi$
$997$	29.2347	+	50.6361i	0.925874	+	1.60366i	0.135724	+	0.990747i	$0.456664\pi$
$998$		0			0
$999$	−10.4508	−	6.03378i	−0.330649	−	0.190900i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.da.f.641.8		16
4.3	odd	2		520.2.bu.b.121.1	✓	16
13.10	even	6	inner	1040.2.da.f.881.8		16
52.7	even	12		6760.2.a.bl.1.8		8
52.19	even	12		6760.2.a.bk.1.8		8
52.23	odd	6		520.2.bu.b.361.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.bu.b.121.1	✓	16	4.3	odd	2
520.2.bu.b.361.1	yes	16	52.23	odd	6
1040.2.da.f.641.8		16	1.1	even	1	trivial
1040.2.da.f.881.8		16	13.10	even	6	inner
6760.2.a.bk.1.8		8	52.19	even	12
6760.2.a.bl.1.8		8	52.7	even	12

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.da (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.62367 - 2.81228i) q^{3} -1.00000i q^{5} +(-4.00640 + 2.31309i) q^{7} +(-3.77262 - 6.53437i) q^{9} +O(q^{10})\)	\(q+(1.62367 - 2.81228i) q^{3} -1.00000i q^{5} +(-4.00640 + 2.31309i) q^{7} +(-3.77262 - 6.53437i) q^{9} +(2.79680 + 1.61473i) q^{11} +(-1.42742 - 3.31096i) q^{13} +(-2.81228 - 1.62367i) q^{15} +(-2.77825 - 4.81207i) q^{17} +(-1.72537 + 0.996140i) q^{19} +15.0228i q^{21} +(-2.20224 + 3.81440i) q^{23} -1.00000 q^{25} -14.7599 q^{27} +(-0.197974 + 0.342902i) q^{29} -7.20020i q^{31} +(9.08216 - 5.24359i) q^{33} +(2.31309 + 4.00640i) q^{35} +(0.708052 + 0.408794i) q^{37} +(-11.6290 - 1.36160i) q^{39} +(-2.79170 - 1.61179i) q^{41} +(-3.42488 - 5.93207i) q^{43} +(-6.53437 + 3.77262i) q^{45} +6.19979i q^{47} +(7.20081 - 12.4722i) q^{49} -18.0439 q^{51} -0.512700 q^{53} +(1.61473 - 2.79680i) q^{55} +6.46962i q^{57} +(6.82230 - 3.93886i) q^{59} +(3.08672 + 5.34635i) q^{61} +(30.2292 + 17.4528i) q^{63} +(-3.31096 + 1.42742i) q^{65} +(7.58286 + 4.37797i) q^{67} +(7.15144 + 12.3867i) q^{69} +(2.43415 - 1.40535i) q^{71} -5.03482i q^{73} +(-1.62367 + 2.81228i) q^{75} -14.9401 q^{77} +8.25143 q^{79} +(-12.6475 + 21.9060i) q^{81} -1.49741i q^{83} +(-4.81207 + 2.77825i) q^{85} +(0.642891 + 1.11352i) q^{87} +(14.1316 + 8.15887i) q^{89} +(13.3774 + 9.96326i) q^{91} +(-20.2490 - 11.6908i) q^{93} +(0.996140 + 1.72537i) q^{95} +(4.84132 - 2.79514i) q^{97} -24.3671i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9}+O(q^{10}) \) 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9	\( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{17} - 30 q^{19} - 6 q^{23} - 16 q^{25} - 44 q^{27} - 16 q^{29} + 24 q^{33} + 6 q^{35} - 24 q^{37} + 8 q^{39} - 24 q^{41} - 6 q^{43} + 12 q^{45} - 4 q^{49} + 40 q^{51} + 4 q^{53} + 6 q^{55} - 12 q^{59} - 2 q^{61} + 60 q^{63} - 10 q^{65} + 6 q^{67} + 52 q^{69} - 72 q^{71} - 4 q^{75} + 32 q^{77} - 36 q^{79} - 28 q^{81} + 22 q^{87} + 24 q^{89} + 22 q^{91} - 96 q^{93} - 10 q^{95} + 60 q^{97}+O(q^{100}) \) 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9 + 6 * q^11 - 2 * q^13 + 4 * q^17 - 30 * q^19 - 6 * q^23 - 16 * q^25 - 44 * q^27 - 16 * q^29 + 24 * q^33 + 6 * q^35 - 24 * q^37 + 8 * q^39 - 24 * q^41 - 6 * q^43 + 12 * q^45 - 4 * q^49 + 40 * q^51 + 4 * q^53 + 6 * q^55 - 12 * q^59 - 2 * q^61 + 60 * q^63 - 10 * q^65 + 6 * q^67 + 52 * q^69 - 72 * q^71 - 4 * q^75 + 32 * q^77 - 36 * q^79 - 28 * q^81 + 22 * q^87 + 24 * q^89 + 22 * q^91 - 96 * q^93 - 10 * q^95 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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