LMFDB - Embedded newform 1638.2.bj.g.1135.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1135.5
Root			$0.500000 + 0.613147i$ of defining polynomial
Character	$\chi$	$=$	1638.1135
Dual form			1638.2.bj.g.127.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.14776i q^{5} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.14776i q^{5} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(0.573878 - 0.993985i) q^{10} +(-3.84935 - 2.22243i) q^{11} +(-3.54343 + 0.666437i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.35488 - 2.34672i) q^{17} +(5.68371 - 3.28149i) q^{19} +(0.993985 - 0.573878i) q^{20} +(-2.22243 - 3.84935i) q^{22} +(1.04000 - 1.80133i) q^{23} +3.68266 q^{25} +(-3.40191 - 1.19456i) q^{26} +(-0.866025 - 0.500000i) q^{28} +(3.59960 - 6.23469i) q^{29} -7.90895i q^{31} +(-0.866025 + 0.500000i) q^{32} -2.70976i q^{34} +(0.573878 + 0.993985i) q^{35} +(-8.35199 - 4.82202i) q^{37} +6.56298 q^{38} +1.14776 q^{40} +(8.22266 + 4.74735i) q^{41} +(-1.70160 - 2.94725i) q^{43} -4.44485i q^{44} +(1.80133 - 1.04000i) q^{46} -1.67435i q^{47} +(0.500000 - 0.866025i) q^{49} +(3.18927 + 1.84133i) q^{50} +(-2.34886 - 2.73548i) q^{52} -13.2815 q^{53} +(-2.55080 + 4.41812i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(6.23469 - 3.59960i) q^{58} +(-0.0586805 + 0.0338792i) q^{59} +(-4.05023 - 7.01521i) q^{61} +(3.95448 - 6.84935i) q^{62} -1.00000 q^{64} +(0.764907 + 4.06699i) q^{65} +(-0.444700 - 0.256747i) q^{67} +(1.35488 - 2.34672i) q^{68} +1.14776i q^{70} +(-9.34208 + 5.39365i) q^{71} +8.02452i q^{73} +(-4.82202 - 8.35199i) q^{74} +(5.68371 + 3.28149i) q^{76} +4.44485 q^{77} +10.7404 q^{79} +(0.993985 + 0.573878i) q^{80} +(4.74735 + 8.22266i) q^{82} +15.3479i q^{83} +(-2.69346 + 1.55507i) q^{85} -3.40320i q^{86} +(2.22243 - 3.84935i) q^{88} +(-9.40465 - 5.42978i) q^{89} +(2.73548 - 2.34886i) q^{91} +2.08000 q^{92} +(0.837173 - 1.45003i) q^{94} +(-3.76635 - 6.52351i) q^{95} +(1.84198 - 1.06347i) q^{97} +(0.866025 - 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4}+O(q^{10}) $ 12 * q + 6 * q^4	$ 12 q + 6 q^{4} - 2 q^{10} + 18 q^{11} - 8 q^{13} - 12 q^{14} - 6 q^{16} - 4 q^{17} + 12 q^{19} - 2 q^{22} + 6 q^{23} - 24 q^{25} + 14 q^{26} + 10 q^{29} - 2 q^{35} - 6 q^{37} - 8 q^{38} - 4 q^{40} + 24 q^{41} + 26 q^{43} - 6 q^{46} + 6 q^{49} + 12 q^{50} - 4 q^{52} - 36 q^{53} - 6 q^{55} - 6 q^{56} + 24 q^{58} - 6 q^{59} - 28 q^{61} + 2 q^{62} - 12 q^{64} + 34 q^{65} - 42 q^{67} + 4 q^{68} - 48 q^{71} + 12 q^{76} + 4 q^{77} + 44 q^{79} + 6 q^{82} + 54 q^{85} + 2 q^{88} - 12 q^{89} - 16 q^{91} + 12 q^{92} + 8 q^{94} - 32 q^{95} + 60 q^{97}+O(q^{100}) $ 12 * q + 6 * q^4 - 2 * q^10 + 18 * q^11 - 8 * q^13 - 12 * q^14 - 6 * q^16 - 4 * q^17 + 12 * q^19 - 2 * q^22 + 6 * q^23 - 24 * q^25 + 14 * q^26 + 10 * q^29 - 2 * q^35 - 6 * q^37 - 8 * q^38 - 4 * q^40 + 24 * q^41 + 26 * q^43 - 6 * q^46 + 6 * q^49 + 12 * q^50 - 4 * q^52 - 36 * q^53 - 6 * q^55 - 6 * q^56 + 24 * q^58 - 6 * q^59 - 28 * q^61 + 2 * q^62 - 12 * q^64 + 34 * q^65 - 42 * q^67 + 4 * q^68 - 48 * q^71 + 12 * q^76 + 4 * q^77 + 44 * q^79 + 6 * q^82 + 54 * q^85 + 2 * q^88 - 12 * q^89 - 16 * q^91 + 12 * q^92 + 8 * q^94 - 32 * q^95 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		−	1.14776i		−	0.513292i	−0.966505	−	0.256646i	$-0.917383\pi$
$5$		−	1.14776i		−	0.513292i	0.966505	−	0.256646i	$-0.0826174\pi$
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.573878	−	0.993985i	0.181476	−	0.314326i
$11$	−3.84935	−	2.22243i	−1.16062	−	0.670086i	−0.209170	−	0.977879i	$-0.567076\pi$
$11$	−3.84935	−	2.22243i	−1.16062	−	0.670086i	−0.951453	+	0.307793i	$0.900410\pi$
$12$		0			0
$13$	−3.54343	+	0.666437i	−0.982769	+	0.184837i
$13$	−3.54343	+	0.666437i	−0.982769	+	0.184837i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.35488	−	2.34672i	−0.328606	−	0.569163i	0.653629	−	0.756815i	$-0.273246\pi$
$17$	−1.35488	−	2.34672i	−0.328606	−	0.569163i	−0.982236	+	0.187652i	$0.939912\pi$
$18$		0			0
$19$	5.68371	−	3.28149i	1.30393	−	0.752826i	0.322856	−	0.946448i	$-0.395357\pi$
$19$	5.68371	−	3.28149i	1.30393	−	0.752826i	0.981076	+	0.193623i	$0.0620237\pi$
$20$	0.993985	−	0.573878i	0.222262	−	0.128323i
$21$		0			0
$22$	−2.22243	−	3.84935i	−0.473823	−	0.820685i
$23$	1.04000	−	1.80133i	0.216855	−	0.375603i	−0.736990	−	0.675904i	$-0.763754\pi$
$23$	1.04000	−	1.80133i	0.216855	−	0.375603i	0.953845	+	0.300300i	$0.0970869\pi$
$24$		0			0
$25$	3.68266			0.736531
$26$	−3.40191	−	1.19456i	−0.667170	−	0.234273i
$27$		0			0
$28$	−0.866025	−	0.500000i	−0.163663	−	0.0944911i
$29$	3.59960	−	6.23469i	0.668428	−	1.15775i	−0.309915	−	0.950764i	$-0.600301\pi$
$29$	3.59960	−	6.23469i	0.668428	−	1.15775i	0.978344	−	0.206988i	$-0.0663660\pi$
$30$		0			0
$31$		−	7.90895i		−	1.42049i	−0.703955	−	0.710245i	$-0.748584\pi$
$31$		−	7.90895i		−	1.42049i	0.703955	−	0.710245i	$-0.251416\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$		−	2.70976i		−	0.464720i
$35$	0.573878	+	0.993985i	0.0970030	+	0.168014i
$36$		0			0
$37$	−8.35199	−	4.82202i	−1.37306	−	0.792736i	−0.381746	−	0.924267i	$-0.624677\pi$
$37$	−8.35199	−	4.82202i	−1.37306	−	0.792736i	−0.991312	+	0.131532i	$0.958011\pi$
$38$	6.56298			1.06466
$39$		0			0
$40$	1.14776			0.181476
$41$	8.22266	+	4.74735i	1.28416	+	0.741412i	0.977607	−	0.210441i	$-0.0674898\pi$
$41$	8.22266	+	4.74735i	1.28416	+	0.741412i	0.306556	+	0.951852i	$0.400823\pi$
$42$		0			0
$43$	−1.70160	−	2.94725i	−0.259491	−	0.449452i	0.706614	−	0.707599i	$-0.250222\pi$
$43$	−1.70160	−	2.94725i	−0.259491	−	0.449452i	−0.966106	+	0.258147i	$0.916888\pi$
$44$		−	4.44485i		−	0.670086i
$45$		0			0
$46$	1.80133	−	1.04000i	0.265592	−	0.153339i
$47$		−	1.67435i		−	0.244229i	−0.992516	−	0.122114i	$-0.961033\pi$
$47$		−	1.67435i		−	0.244229i	0.992516	−	0.122114i	$-0.0389674\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	3.18927	+	1.84133i	0.451032	+	0.260403i
$51$		0			0
$52$	−2.34886	−	2.73548i	−0.325729	−	0.379342i
$53$	−13.2815			−1.82436			−0.912180	−	0.409789i	$-0.865602\pi$
$53$	−13.2815			−1.82436			−0.912180	+	0.409789i	$0.865602\pi$
$54$		0			0
$55$	−2.55080	+	4.41812i	−0.343950	+	0.595739i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$		0			0
$58$	6.23469	−	3.59960i	0.818654	−	0.472650i
$59$	−0.0586805	+	0.0338792i	−0.00763956	+	0.00441070i	−0.503815	−	0.863812i	$-0.668071\pi$
$59$	−0.0586805	+	0.0338792i	−0.00763956	+	0.00441070i	0.496175	+	0.868222i	$0.334737\pi$
$60$		0			0
$61$	−4.05023	−	7.01521i	−0.518579	−	0.898205i	−0.999767	−	0.0215878i	$-0.993128\pi$
$61$	−4.05023	−	7.01521i	−0.518579	−	0.898205i	0.481188	−	0.876617i	$-0.340205\pi$
$62$	3.95448	−	6.84935i	0.502219	−	0.869869i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.764907	+	4.06699i	0.0948751	+	0.504447i
$66$		0			0
$67$	−0.444700	−	0.256747i	−0.0543287	−	0.0313667i	0.472590	−	0.881283i	$-0.343319\pi$
$67$	−0.444700	−	0.256747i	−0.0543287	−	0.0313667i	−0.526918	+	0.849916i	$0.676653\pi$
$68$	1.35488	−	2.34672i	0.164303	−	0.284582i
$69$		0			0
$70$			1.14776i			0.137183i
$71$	−9.34208	+	5.39365i	−1.10870	+	0.640109i	−0.938493	−	0.345300i	$-0.887777\pi$
$71$	−9.34208	+	5.39365i	−1.10870	+	0.640109i	−0.170208	+	0.985408i	$0.554444\pi$
$72$		0			0
$73$			8.02452i			0.939199i	0.882880	+	0.469599i	$0.155602\pi$
$73$			8.02452i			0.939199i	−0.882880	+	0.469599i	$0.844398\pi$
$74$	−4.82202	−	8.35199i	−0.560549	−	0.970899i
$75$		0			0
$76$	5.68371	+	3.28149i	0.651966	+	0.376413i
$77$	4.44485			0.506538
$78$		0			0
$79$	10.7404			1.20839			0.604193	−	0.796838i	$-0.293496\pi$
$79$	10.7404			1.20839			0.604193	+	0.796838i	$0.293496\pi$
$80$	0.993985	+	0.573878i	0.111131	+	0.0641615i
$81$		0			0
$82$	4.74735	+	8.22266i	0.524257	+	0.908040i
$83$			15.3479i			1.68465i	0.538967	+	0.842327i	$0.318815\pi$
$83$			15.3479i			1.68465i	−0.538967	+	0.842327i	$0.681185\pi$
$84$		0			0
$85$	−2.69346	+	1.55507i	−0.292147	+	0.168671i
$86$		−	3.40320i		−	0.366976i
$87$		0			0
$88$	2.22243	−	3.84935i	0.236911	−	0.410342i
$89$	−9.40465	−	5.42978i	−0.996891	−	0.575555i	−0.0895643	−	0.995981i	$-0.528547\pi$
$89$	−9.40465	−	5.42978i	−0.996891	−	0.575555i	−0.907327	+	0.420426i	$0.861881\pi$
$90$		0			0
$91$	2.73548	−	2.34886i	0.286756	−	0.246228i
$92$	2.08000			0.216855
$93$		0			0
$94$	0.837173	−	1.45003i	0.0863478	−	0.149559i
$95$	−3.76635	−	6.52351i	−0.386419	−	0.669298i
$96$		0			0
$97$	1.84198	−	1.06347i	0.187025	−	0.107979i	−0.403564	−	0.914951i	$-0.632229\pi$
$97$	1.84198	−	1.06347i	0.187025	−	0.107979i	0.590589	+	0.806973i	$0.298895\pi$
$98$	0.866025	−	0.500000i	0.0874818	−	0.0505076i
$99$		0			0
$100$	1.84133	+	3.18927i	0.184133	+	0.318927i
$101$	3.00944	−	5.21251i	0.299451	−	0.518664i	−0.676560	−	0.736388i	$-0.736530\pi$
$101$	3.00944	−	5.21251i	0.299451	−	0.518664i	0.976010	+	0.217724i	$0.0698633\pi$
$102$		0			0
$103$	5.75670			0.567224			0.283612	−	0.958939i	$-0.408467\pi$
$103$	5.75670			0.567224			0.283612	+	0.958939i	$0.408467\pi$
$104$	−0.666437	−	3.54343i	−0.0653496	−	0.347461i
$105$		0			0
$106$	−11.5022	−	6.64077i	−1.11719	−	0.645009i
$107$	−2.77468	+	4.80589i	−0.268239	+	0.464603i	−0.968407	−	0.249375i	$-0.919775\pi$
$107$	−2.77468	+	4.80589i	−0.268239	+	0.464603i	0.700168	+	0.713978i	$0.253108\pi$
$108$		0			0
$109$		−	7.96986i		−	0.763374i	−0.924292	−	0.381687i	$-0.875343\pi$
$109$		−	7.96986i		−	0.763374i	0.924292	−	0.381687i	$-0.124657\pi$
$110$	−4.41812	+	2.55080i	−0.421251	+	0.243209i
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$	−2.18535	−	3.78514i	−0.205580	−	0.356076i	0.744737	−	0.667358i	$-0.232575\pi$
$113$	−2.18535	−	3.78514i	−0.205580	−	0.356076i	−0.950318	+	0.311282i	$0.899242\pi$
$114$		0			0
$115$	−2.06749	−	1.19366i	−0.192794	−	0.111310i
$116$	7.19919			0.668428
$117$		0			0
$118$	−0.0677585			−0.00623767
$119$	2.34672	+	1.35488i	0.215123	+	0.124202i
$120$		0			0
$121$	4.37835	+	7.58352i	0.398032	+	0.689411i
$122$		−	8.10046i		−	0.733382i
$123$		0			0
$124$	6.84935	−	3.95448i	0.615090	−	0.355122i
$125$		−	9.96557i		−	0.891347i
$126$		0			0
$127$	3.43247	−	5.94522i	0.304583	−	0.527553i	−0.672586	−	0.740019i	$-0.734816\pi$
$127$	3.43247	−	5.94522i	0.304583	−	0.527553i	0.977168	+	0.212467i	$0.0681497\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−1.37106	+	3.90457i	−0.120250	+	0.342453i
$131$	16.1996			1.41537			0.707683	−	0.706530i	$-0.249741\pi$
$131$	16.1996			1.41537			0.707683	+	0.706530i	$0.249741\pi$
$132$		0			0
$133$	−3.28149	+	5.68371i	−0.284541	+	0.492840i
$134$	−0.256747	−	0.444700i	−0.0221796	−	0.0384162i
$135$		0			0
$136$	2.34672	−	1.35488i	0.201230	−	0.116180i
$137$	−4.50527	+	2.60112i	−0.384911	+	0.222229i	−0.679953	−	0.733256i	$-0.738000\pi$
$137$	−4.50527	+	2.60112i	−0.384911	+	0.222229i	0.295042	+	0.955484i	$0.404666\pi$
$138$		0			0
$139$	−2.87013	−	4.97122i	−0.243442	−	0.421653i	0.718251	−	0.695784i	$-0.244943\pi$
$139$	−2.87013	−	4.97122i	−0.243442	−	0.421653i	−0.961692	+	0.274131i	$0.911610\pi$
$140$	−0.573878	+	0.993985i	−0.0485015	+	0.0840071i
$141$		0			0
$142$	−10.7873			−0.905250
$143$	15.1210	+	5.30964i	1.26448	+	0.444015i
$144$		0			0
$145$	−7.15589	−	4.13146i	−0.594265	−	0.343099i
$146$	−4.01226	+	6.94944i	−0.332057	+	0.575140i
$147$		0			0
$148$		−	9.64405i		−	0.792736i
$149$	−2.62042	+	1.51290i	−0.214673	+	0.123941i	−0.603481	−	0.797377i	$-0.706220\pi$
$149$	−2.62042	+	1.51290i	−0.214673	+	0.123941i	0.388808	+	0.921319i	$0.372887\pi$
$150$		0			0
$151$			1.27030i			0.103376i	0.998663	+	0.0516879i	$0.0164601\pi$
$151$			1.27030i			0.103376i	−0.998663	+	0.0516879i	$0.983540\pi$
$152$	3.28149	+	5.68371i	0.266164	+	0.461010i
$153$		0			0
$154$	3.84935	+	2.22243i	0.310190	+	0.179088i
$155$	−9.07754			−0.729126
$156$		0			0
$157$	−4.11859			−0.328699			−0.164350	−	0.986402i	$-0.552553\pi$
$157$	−4.11859			−0.328699			−0.164350	+	0.986402i	$0.552553\pi$
$158$	9.30143	+	5.37018i	0.739982	+	0.427229i
$159$		0			0
$160$	0.573878	+	0.993985i	0.0453690	+	0.0785814i
$161$			2.08000i			0.163927i
$162$		0			0
$163$	−9.71606	+	5.60957i	−0.761021	+	0.439376i	−0.829662	−	0.558266i	$-0.811467\pi$
$163$	−9.71606	+	5.60957i	−0.761021	+	0.439376i	0.0686413	+	0.997641i	$0.478134\pi$
$164$			9.49471i			0.741412i
$165$		0			0
$166$	−7.67396	+	13.2917i	−0.595615	+	1.03164i
$167$	3.46184	+	1.99869i	0.267885	+	0.154664i	0.627926	−	0.778273i	$-0.283904\pi$
$167$	3.46184	+	1.99869i	0.267885	+	0.154664i	−0.360041	+	0.932936i	$0.617237\pi$
$168$		0			0
$169$	12.1117	−	4.72294i	0.931671	−	0.363303i
$170$	−3.11014			−0.238537
$171$		0			0
$172$	1.70160	−	2.94725i	0.129746	−	0.224726i
$173$	6.08396	+	10.5377i	0.462555	+	0.801168i	0.999087	−	0.0427113i	$-0.0135996\pi$
$173$	6.08396	+	10.5377i	0.462555	+	0.801168i	−0.536533	+	0.843879i	$0.680266\pi$
$174$		0			0
$175$	−3.18927	+	1.84133i	−0.241087	+	0.139191i
$176$	3.84935	−	2.22243i	0.290156	−	0.167522i
$177$		0			0
$178$	−5.42978	−	9.40465i	−0.406979	−	0.704909i
$179$	5.93554	−	10.2806i	0.443643	−	0.768412i	−0.554314	−	0.832308i	$-0.687019\pi$
$179$	5.93554	−	10.2806i	0.443643	−	0.768412i	0.997957	+	0.0638960i	$0.0203526\pi$
$180$		0			0
$181$	−4.79134			−0.356137			−0.178069	−	0.984018i	$-0.556985\pi$
$181$	−4.79134			−0.356137			−0.178069	+	0.984018i	$0.556985\pi$
$182$	3.54343	−	0.666437i	0.262656	−	0.0493996i
$183$		0			0
$184$	1.80133	+	1.04000i	0.132796	+	0.0766697i
$185$	−5.53450	+	9.58604i	−0.406905	+	0.704780i
$186$		0			0
$187$			12.0445i			0.880779i
$188$	1.45003	−	0.837173i	0.105754	−	0.0610571i
$189$		0			0
$190$		−	7.53270i		−	0.546479i
$191$	7.79263	+	13.4972i	0.563855	+	0.976625i	0.997155	+	0.0753756i	$0.0240156\pi$
$191$	7.79263	+	13.4972i	0.563855	+	0.976625i	−0.433300	+	0.901250i	$0.642651\pi$
$192$		0			0
$193$	−15.2295	−	8.79275i	−1.09624	−	0.632916i	−0.161011	−	0.986953i	$-0.551475\pi$
$193$	−15.2295	−	8.79275i	−1.09624	−	0.632916i	−0.935231	+	0.354037i	$0.884809\pi$
$194$	2.12694			0.152705
$195$		0			0
$196$	1.00000			0.0714286
$197$	0.458833	+	0.264907i	0.0326905	+	0.0188739i	0.516256	−	0.856434i	$-0.327325\pi$
$197$	0.458833	+	0.264907i	0.0326905	+	0.0188739i	−0.483566	+	0.875308i	$0.660659\pi$
$198$		0			0
$199$	12.5732	+	21.7775i	0.891294	+	1.54377i	0.838326	+	0.545170i	$0.183535\pi$
$199$	12.5732	+	21.7775i	0.891294	+	1.54377i	0.0529680	+	0.998596i	$0.483132\pi$
$200$			3.68266i			0.260403i
$201$		0			0
$202$	5.21251	−	3.00944i	0.366751	−	0.211744i
$203$			7.19919i			0.505284i
$204$		0			0
$205$	5.44880	−	9.43760i	0.380561	−	0.659150i
$206$	4.98545	+	2.87835i	0.347352	+	0.200544i
$207$		0			0
$208$	1.19456	−	3.40191i	0.0828279	−	0.235880i
$209$	−29.1715			−2.01783
$210$		0			0
$211$	−2.72085	+	4.71265i	−0.187311	+	0.324432i	−0.944353	−	0.328934i	$-0.893311\pi$
$211$	−2.72085	+	4.71265i	−0.187311	+	0.324432i	0.757042	+	0.653366i	$0.226644\pi$
$212$	−6.64077	−	11.5022i	−0.456090	−	0.789971i
$213$		0			0
$214$	−4.80589	+	2.77468i	−0.328524	+	0.189673i
$215$	−3.38273	+	1.95302i	−0.230700	+	0.133195i
$216$		0			0
$217$	3.95448	+	6.84935i	0.268447	+	0.464964i
$218$	3.98493	−	6.90210i	0.269893	−	0.467469i
$219$		0			0
$220$	−5.10160			−0.343950
$221$	6.36485	+	7.41248i	0.428146	+	0.498617i
$222$		0			0
$223$	8.00684	+	4.62275i	0.536177	+	0.309562i	0.743528	−	0.668704i	$-0.233151\pi$
$223$	8.00684	+	4.62275i	0.536177	+	0.309562i	−0.207351	+	0.978267i	$0.566484\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$		0			0
$226$		−	4.37070i		−	0.290735i
$227$	1.30318	−	0.752389i	0.0864948	−	0.0499378i	−0.456129	−	0.889914i	$-0.650764\pi$
$227$	1.30318	−	0.752389i	0.0864948	−	0.0499378i	0.542624	+	0.839976i	$0.317431\pi$
$228$		0			0
$229$			25.4380i			1.68099i	0.541818	+	0.840496i	$0.317736\pi$
$229$			25.4380i			1.68099i	−0.541818	+	0.840496i	$0.682264\pi$
$230$	−1.19366	−	2.06749i	−0.0787079	−	0.136326i
$231$		0			0
$232$	6.23469	+	3.59960i	0.409327	+	0.236325i
$233$	−12.1004			−0.792724			−0.396362	−	0.918094i	$-0.629727\pi$
$233$	−12.1004			−0.792724			−0.396362	+	0.918094i	$0.629727\pi$
$234$		0			0
$235$	−1.92174			−0.125361
$236$	−0.0586805	−	0.0338792i	−0.00381978	−	0.00220535i
$237$		0			0
$238$	1.35488	+	2.34672i	0.0878238	+	0.152115i
$239$		−	5.57964i		−	0.360917i	−0.983583	−	0.180458i	$-0.942242\pi$
$239$		−	5.57964i		−	0.360917i	0.983583	−	0.180458i	$-0.0577581\pi$
$240$		0			0
$241$	20.1291	−	11.6215i	1.29663	−	0.748608i	0.316807	−	0.948490i	$-0.397389\pi$
$241$	20.1291	−	11.6215i	1.29663	−	0.748608i	0.979820	+	0.199882i	$0.0640559\pi$
$242$			8.75670i			0.562902i
$243$		0			0
$244$	4.05023	−	7.01521i	0.259290	−	0.449103i
$245$	−0.993985	−	0.573878i	−0.0635034	−	0.0366637i
$246$		0			0
$247$	−17.9529	+	15.4156i	−1.14231	+	0.980868i
$248$	7.90895			0.502219
$249$		0			0
$250$	4.98278	−	8.63043i	0.315139	−	0.545837i
$251$	11.8707	+	20.5607i	0.749273	+	1.29778i	0.948171	+	0.317760i	$0.102930\pi$
$251$	11.8707	+	20.5607i	0.749273	+	1.29778i	−0.198898	+	0.980020i	$0.563736\pi$
$252$		0			0
$253$	−8.00664	+	4.62264i	−0.503373	+	0.290623i
$254$	5.94522	−	3.43247i	0.373036	−	0.215372i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.50520	+	6.07118i	−0.218648	+	0.378710i	−0.954395	−	0.298547i	$-0.903498\pi$
$257$	−3.50520	+	6.07118i	−0.218648	+	0.378710i	0.735747	+	0.677257i	$0.236831\pi$
$258$		0			0
$259$	9.64405			0.599252
$260$	−3.13966	+	2.69592i	−0.194713	+	0.167194i
$261$		0			0
$262$	14.0293	+	8.09980i	0.866731	+	0.500407i
$263$	15.4226	−	26.7127i	0.950998	−	1.64718i	0.207728	−	0.978187i	$-0.433393\pi$
$263$	15.4226	−	26.7127i	0.950998	−	1.64718i	0.743270	−	0.668991i	$-0.233274\pi$
$264$		0			0
$265$			15.2440i			0.936429i
$266$	−5.68371	+	3.28149i	−0.348491	+	0.201201i
$267$		0			0
$268$		−	0.513495i		−	0.0313667i
$269$	−2.81595	−	4.87737i	−0.171692	−	0.297379i	0.767320	−	0.641265i	$-0.221590\pi$
$269$	−2.81595	−	4.87737i	−0.171692	−	0.297379i	−0.939011	+	0.343886i	$0.888257\pi$
$270$		0			0
$271$	−2.60224	−	1.50240i	−0.158075	−	0.0912645i	0.418876	−	0.908043i	$-0.362424\pi$
$271$	−2.60224	−	1.50240i	−0.158075	−	0.0912645i	−0.576951	+	0.816779i	$0.695758\pi$
$272$	2.70976			0.164303
$273$		0			0
$274$	−5.20224			−0.314279
$275$	−14.1759	−	8.18443i	−0.854836	−	0.493540i
$276$		0			0
$277$	−12.0866	−	20.9346i	−0.726214	−	1.25784i	−0.958473	−	0.285185i	$-0.907945\pi$
$277$	−12.0866	−	20.9346i	−0.726214	−	1.25784i	0.232259	−	0.972654i	$-0.425388\pi$
$278$		−	5.74027i		−	0.344278i
$279$		0			0
$280$	−0.993985	+	0.573878i	−0.0594020	+	0.0342958i
$281$			1.74575i			0.104143i	0.998643	+	0.0520713i	$0.0165823\pi$
$281$			1.74575i			0.104143i	−0.998643	+	0.0520713i	$0.983418\pi$
$282$		0			0
$283$	13.0572	−	22.6156i	0.776167	−	1.34436i	−0.157969	−	0.987444i	$-0.550495\pi$
$283$	13.0572	−	22.6156i	0.776167	−	1.34436i	0.934136	−	0.356917i	$-0.116172\pi$
$284$	−9.34208	−	5.39365i	−0.554350	−	0.320054i
$285$		0			0
$286$	10.4404	+	12.1588i	0.617351	+	0.718964i
$287$	−9.49471			−0.560455
$288$		0			0
$289$	4.82861	−	8.36339i	0.284036	−	0.491964i
$290$	−4.13146	−	7.15589i	−0.242608	−	0.420209i
$291$		0			0
$292$	−6.94944	+	4.01226i	−0.406685	+	0.234800i
$293$	4.89767	−	2.82767i	0.286125	−	0.165194i	−0.350068	−	0.936724i	$-0.613841\pi$
$293$	4.89767	−	2.82767i	0.286125	−	0.165194i	0.636193	+	0.771530i	$0.280508\pi$
$294$		0			0
$295$	0.0388851	+	0.0673509i	0.00226398	+	0.00392132i
$296$	4.82202	−	8.35199i	0.280274	−	0.485449i
$297$		0			0
$298$	−3.02580			−0.175280
$299$	−2.48468	+	7.07597i	−0.143693	+	0.409214i
$300$		0			0
$301$	2.94725	+	1.70160i	0.169877	+	0.0980785i
$302$	−0.635151	+	1.10011i	−0.0365489	+	0.0633045i
$303$		0			0
$304$			6.56298i			0.376413i
$305$	−8.05174	+	4.64868i	−0.461041	+	0.266182i
$306$		0			0
$307$			20.4767i			1.16867i	0.811514	+	0.584333i	$0.198644\pi$
$307$			20.4767i			1.16867i	−0.811514	+	0.584333i	$0.801356\pi$
$308$	2.22243	+	3.84935i	0.126634	+	0.219337i
$309$		0			0
$310$	−7.86138	−	4.53877i	−0.446497	−	0.257785i
$311$	−1.23712			−0.0701506			−0.0350753	−	0.999385i	$-0.511167\pi$
$311$	−1.23712			−0.0701506			−0.0350753	+	0.999385i	$0.511167\pi$
$312$		0			0
$313$	−9.01151			−0.509361			−0.254680	−	0.967025i	$-0.581970\pi$
$313$	−9.01151			−0.509361			−0.254680	+	0.967025i	$0.581970\pi$
$314$	−3.56680	−	2.05930i	−0.201286	−	0.116213i
$315$		0			0
$316$	5.37018	+	9.30143i	0.302096	+	0.523246i
$317$		−	0.580644i		−	0.0326122i	−0.999867	−	0.0163061i	$-0.994809\pi$
$317$		−	0.580644i		−	0.0326122i	0.999867	−	0.0163061i	$-0.00519062\pi$
$318$		0			0
$319$	−27.7122	+	15.9997i	−1.55159	+	0.895810i
$320$			1.14776i			0.0641615i
$321$		0			0
$322$	−1.04000	+	1.80133i	−0.0579569	+	0.100384i
$323$	−15.4015	−	8.89204i	−0.856961	−	0.494767i
$324$		0			0
$325$	−13.0492	+	2.45426i	−0.723841	+	0.136138i
$326$	−11.2191			−0.621371
$327$		0			0
$328$	−4.74735	+	8.22266i	−0.262129	+	0.454020i
$329$	0.837173	+	1.45003i	0.0461549	+	0.0799426i
$330$		0			0
$331$	−27.1632	+	15.6827i	−1.49303	+	0.861999i	−0.999968	−	0.00799735i	$-0.997454\pi$
$331$	−27.1632	+	15.6827i	−1.49303	+	0.861999i	−0.493058	+	0.869996i	$0.664121\pi$
$332$	−13.2917	+	7.67396i	−0.729477	+	0.421163i
$333$		0			0
$334$	1.99869	+	3.46184i	0.109364	+	0.189423i
$335$	−0.294683	+	0.510406i	−0.0161003	+	0.0278865i
$336$		0			0
$337$	9.43033			0.513703			0.256851	−	0.966451i	$-0.417315\pi$
$337$	9.43033			0.513703			0.256851	+	0.966451i	$0.417315\pi$
$338$	12.8505	+	1.96567i	0.698977	+	0.106919i
$339$		0			0
$340$	−2.69346	−	1.55507i	−0.146073	−	0.0843355i
$341$	−17.5771	+	30.4444i	−0.951851	+	1.64865i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	2.94725	−	1.70160i	0.158905	−	0.0917440i
$345$		0			0
$346$			12.1679i			0.654151i
$347$	3.23650	+	5.60578i	0.173744	+	0.300934i	0.939726	−	0.341928i	$-0.111080\pi$
$347$	3.23650	+	5.60578i	0.173744	+	0.300934i	−0.765982	+	0.642862i	$0.777747\pi$
$348$		0			0
$349$	8.57811	+	4.95258i	0.459176	+	0.265105i	0.711698	−	0.702486i	$-0.247927\pi$
$349$	8.57811	+	4.95258i	0.459176	+	0.265105i	−0.252522	+	0.967591i	$0.581260\pi$
$350$	−3.68266			−0.196846
$351$		0			0
$352$	4.44485			0.236911
$353$	−24.9206	−	14.3879i	−1.32639	−	0.765790i	−0.341649	−	0.939828i	$-0.610985\pi$
$353$	−24.9206	−	14.3879i	−1.32639	−	0.765790i	−0.984739	+	0.174037i	$0.944319\pi$
$354$		0			0
$355$	6.19059	+	10.7224i	0.328562	+	0.569087i
$356$		−	10.8596i		−	0.575555i
$357$		0			0
$358$	10.2806	−	5.93554i	0.543349	−	0.313703i
$359$			12.1382i			0.640631i	0.947311	+	0.320315i	$0.103789\pi$
$359$			12.1382i			0.640631i	−0.947311	+	0.320315i	$0.896211\pi$
$360$		0			0
$361$	12.0364	−	20.8476i	0.633493	−	1.09724i
$362$	−4.14942	−	2.39567i	−0.218089	−	0.125914i
$363$		0			0
$364$	3.40191	+	1.19456i	0.178309	+	0.0626120i
$365$	9.21019			0.482083
$366$		0			0
$367$	13.5388	−	23.4498i	0.706717	−	1.22407i	−0.259351	−	0.965783i	$-0.583509\pi$
$367$	13.5388	−	23.4498i	0.706717	−	1.22407i	0.966068	−	0.258287i	$-0.0831580\pi$
$368$	1.04000	+	1.80133i	0.0542137	+	0.0939008i
$369$		0			0
$370$	−9.58604	+	5.53450i	−0.498354	+	0.287725i
$371$	11.5022	−	6.64077i	0.597162	−	0.344772i
$372$		0			0
$373$	7.81661	+	13.5388i	0.404729	+	0.701010i	0.994290	−	0.106713i	$-0.0340327\pi$
$373$	7.81661	+	13.5388i	0.404729	+	0.701010i	−0.589561	+	0.807724i	$0.700699\pi$
$374$	−6.02223	+	10.4308i	−0.311402	+	0.539365i
$375$		0			0
$376$	1.67435			0.0863478
$377$	−8.59987	+	24.4910i	−0.442916	+	1.26135i
$378$		0			0
$379$	−32.3295	−	18.6654i	−1.66065	−	0.958778i	−0.972404	−	0.233304i	$-0.925046\pi$
$379$	−32.3295	−	18.6654i	−1.66065	−	0.958778i	−0.688249	−	0.725475i	$-0.741620\pi$
$380$	3.76635	−	6.52351i	0.193210	−	0.334649i
$381$		0			0
$382$			15.5853i			0.797411i
$383$	32.8193	−	18.9482i	1.67699	−	0.968209i	0.713421	−	0.700736i	$-0.247145\pi$
$383$	32.8193	−	18.9482i	1.67699	−	0.968209i	0.963565	−	0.267473i	$-0.0861886\pi$
$384$		0			0
$385$		−	5.10160i		−	0.260002i
$386$	−8.79275	−	15.2295i	−0.447539	−	0.775160i
$387$		0			0
$388$	1.84198	+	1.06347i	0.0935124	+	0.0539894i
$389$	10.1053			0.512361			0.256180	−	0.966629i	$-0.417536\pi$
$389$	10.1053			0.512361			0.256180	+	0.966629i	$0.417536\pi$
$390$		0			0
$391$	−5.63629			−0.285039
$392$	0.866025	+	0.500000i	0.0437409	+	0.0252538i
$393$		0			0
$394$	0.264907	+	0.458833i	0.0133458	+	0.0231157i
$395$		−	12.3273i		−	0.620254i
$396$		0			0
$397$	4.77041	−	2.75419i	0.239420	−	0.138229i	−0.375490	−	0.926826i	$-0.622526\pi$
$397$	4.77041	−	2.75419i	0.239420	−	0.138229i	0.614910	+	0.788597i	$0.289192\pi$
$398$			25.1465i			1.26048i
$399$		0			0
$400$	−1.84133	+	3.18927i	−0.0920664	+	0.159464i
$401$	23.1657	+	13.3747i	1.15684	+	0.667903i	0.950545	−	0.310587i	$-0.100526\pi$
$401$	23.1657	+	13.3747i	1.15684	+	0.667903i	0.206296	+	0.978490i	$0.433859\pi$
$402$		0			0
$403$	5.27082	+	28.0248i	0.262558	+	1.39601i
$404$	6.01888			0.299451
$405$		0			0
$406$	−3.59960	+	6.23469i	−0.178645	+	0.309422i
$407$	21.4332	+	37.1233i	1.06240	+	1.84014i
$408$		0			0
$409$	−27.7124	+	15.9998i	−1.37029	+	0.791137i	−0.990964	−	0.134127i	$-0.957177\pi$
$409$	−27.7124	+	15.9998i	−1.37029	+	0.791137i	−0.379325	+	0.925264i	$0.623844\pi$
$410$	9.43760	−	5.44880i	0.466090	−	0.269097i
$411$		0			0
$412$	2.87835	+	4.98545i	0.141806	+	0.245615i
$413$	0.0338792	−	0.0586805i	0.00166709	−	0.00288748i
$414$		0			0
$415$	17.6157			0.864719
$416$	2.73548	−	2.34886i	0.134118	−	0.115163i
$417$		0			0
$418$	−25.2632	−	14.5857i	−1.23567	−	0.713412i
$419$	5.84782	−	10.1287i	0.285685	−	0.494821i	−0.687090	−	0.726572i	$-0.741112\pi$
$419$	5.84782	−	10.1287i	0.285685	−	0.494821i	0.972775	+	0.231751i	$0.0744456\pi$
$420$		0			0
$421$		−	25.8565i		−	1.26017i	−0.776527	−	0.630084i	$-0.783021\pi$
$421$		−	25.8565i		−	1.26017i	0.776527	−	0.630084i	$-0.216979\pi$
$422$	−4.71265	+	2.72085i	−0.229408	+	0.132449i
$423$		0			0
$424$		−	13.2815i		−	0.645009i
$425$	−4.98956	−	8.64216i	−0.242029	−	0.419206i
$426$		0			0
$427$	7.01521	+	4.05023i	0.339490	+	0.196004i
$428$	−5.54937			−0.268239
$429$		0			0
$430$	−3.90604			−0.188366
$431$	−9.27186	−	5.35311i	−0.446610	−	0.257850i	0.259788	−	0.965666i	$-0.416347\pi$
$431$	−9.27186	−	5.35311i	−0.446610	−	0.257850i	−0.706397	+	0.707816i	$0.749681\pi$
$432$		0			0
$433$	11.2150	+	19.4249i	0.538956	+	0.933500i	0.998961	+	0.0455830i	$0.0145146\pi$
$433$	11.2150	+	19.4249i	0.538956	+	0.933500i	−0.460004	+	0.887917i	$0.652152\pi$
$434$			7.90895i			0.379642i
$435$		0			0
$436$	6.90210	−	3.98493i	0.330551	−	0.190843i
$437$		−	13.6510i		−	0.653015i
$438$		0			0
$439$	−6.35913	+	11.0143i	−0.303505	+	0.525686i	−0.976927	−	0.213572i	$-0.931490\pi$
$439$	−6.35913	+	11.0143i	−0.303505	+	0.525686i	0.673423	+	0.739258i	$0.264823\pi$
$440$	−4.41812	−	2.55080i	−0.210625	−	0.121605i
$441$		0			0
$442$	1.80588	+	9.60182i	0.0858972	+	0.456712i
$443$	7.86448			0.373653			0.186826	−	0.982393i	$-0.440180\pi$
$443$	7.86448			0.373653			0.186826	+	0.982393i	$0.440180\pi$
$444$		0			0
$445$	−6.23206	+	10.7942i	−0.295428	+	0.511696i
$446$	4.62275	+	8.00684i	0.218893	+	0.379135i
$447$		0			0
$448$	0.866025	−	0.500000i	0.0409159	−	0.0236228i
$449$	14.5815	−	8.41864i	0.688144	−	0.397300i	−0.114772	−	0.993392i	$-0.536614\pi$
$449$	14.5815	−	8.41864i	0.688144	−	0.397300i	0.802916	+	0.596092i	$0.203280\pi$
$450$		0			0
$451$	−21.1013	−	36.5485i	−0.993620	−	1.72100i
$452$	2.18535	−	3.78514i	0.102790	−	0.178038i
$453$		0			0
$454$	1.50478			0.0706227
$455$	−2.69592	−	3.13966i	−0.126387	−	0.147189i
$456$		0			0
$457$	7.96539	+	4.59882i	0.372605	+	0.215124i	0.674596	−	0.738187i	$-0.264318\pi$
$457$	7.96539	+	4.59882i	0.372605	+	0.215124i	−0.301991	+	0.953311i	$0.597651\pi$
$458$	−12.7190	+	22.0300i	−0.594320	+	1.02939i
$459$		0			0
$460$		−	2.38733i		−	0.111310i
$461$	18.8812	−	10.9010i	0.879383	−	0.507712i	0.00892828	−	0.999960i	$-0.497158\pi$
$461$	18.8812	−	10.9010i	0.879383	−	0.507712i	0.870455	+	0.492248i	$0.163825\pi$
$462$		0			0
$463$		−	26.0636i		−	1.21128i	−0.795740	−	0.605638i	$-0.792918\pi$
$463$		−	26.0636i		−	1.21128i	0.795740	−	0.605638i	$-0.207082\pi$
$464$	3.59960	+	6.23469i	0.167107	+	0.289438i
$465$		0			0
$466$	−10.4793	−	6.05020i	−0.485442	−	0.280270i
$467$	−28.6668			−1.32654			−0.663271	−	0.748379i	$-0.730832\pi$
$467$	−28.6668			−1.32654			−0.663271	+	0.748379i	$0.730832\pi$
$468$		0			0
$469$	0.513495			0.0237110
$470$	−1.66428	−	0.960870i	−0.0767673	−	0.0443216i
$471$		0			0
$472$	−0.0338792	−	0.0586805i	−0.00155942	−	0.00270099i
$473$			15.1267i			0.695526i
$474$		0			0
$475$	20.9312	−	12.0846i	0.960387	−	0.554480i
$476$			2.70976i			0.124202i
$477$		0			0
$478$	2.78982	−	4.83211i	0.127603	−	0.221015i
$479$	15.5679	+	8.98812i	0.711315	+	0.410678i	0.811548	−	0.584286i	$-0.198625\pi$
$479$	15.5679	+	8.98812i	0.711315	+	0.410678i	−0.100233	+	0.994964i	$0.531959\pi$
$480$		0			0
$481$	32.8082	+	11.5204i	1.49593	+	0.525285i
$482$	23.2430			1.05869
$483$		0			0
$484$	−4.37835	+	7.58352i	−0.199016	+	0.344706i
$485$	−1.22060	−	2.11414i	−0.0554247	−	0.0959983i
$486$		0			0
$487$	18.9847	−	10.9608i	0.860278	−	0.496681i	−0.00382768	−	0.999993i	$-0.501218\pi$
$487$	18.9847	−	10.9608i	0.860278	−	0.496681i	0.864105	+	0.503311i	$0.167885\pi$
$488$	7.01521	−	4.05023i	0.317564	−	0.183345i
$489$		0			0
$490$	−0.573878	−	0.993985i	−0.0259252	−	0.0449037i
$491$	10.8003	−	18.7067i	0.487411	−	0.844221i	−0.512484	−	0.858697i	$-0.671275\pi$
$491$	10.8003	−	18.7067i	0.487411	−	0.844221i	0.999895	+	0.0144759i	$0.00460798\pi$
$492$		0			0
$493$	−19.5081			−0.878599
$494$	−23.2554	+	4.37382i	−1.04631	+	0.196787i
$495$		0			0
$496$	6.84935	+	3.95448i	0.307545	+	0.177561i
$497$	5.39365	−	9.34208i	0.241938	−	0.419049i
$498$		0			0
$499$			38.6105i			1.72844i	0.503112	+	0.864221i	$0.332188\pi$
$499$			38.6105i			1.72844i	−0.503112	+	0.864221i	$0.667812\pi$
$500$	8.63043	−	4.98278i	0.385965	−	0.222837i
$501$		0			0
$502$			23.7414i			1.05963i
$503$	−4.73503	−	8.20132i	−0.211125	−	0.365679i	0.740942	−	0.671569i	$-0.234379\pi$
$503$	−4.73503	−	8.20132i	−0.211125	−	0.365679i	−0.952067	+	0.305890i	$0.901046\pi$
$504$		0			0
$505$	−5.98268	−	3.45410i	−0.266226	−	0.153706i
$506$	−9.24528			−0.411003
$507$		0			0
$508$	6.86494			0.304583
$509$	−11.3043	−	6.52651i	−0.501052	−	0.289283i	0.228096	−	0.973639i	$-0.426750\pi$
$509$	−11.3043	−	6.52651i	−0.501052	−	0.289283i	−0.729148	+	0.684356i	$0.760083\pi$
$510$		0			0
$511$	−4.01226	−	6.94944i	−0.177492	−	0.307425i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−6.07118	+	3.50520i	−0.267788	+	0.154608i
$515$		−	6.60728i		−	0.291152i
$516$		0			0
$517$	−3.72111	+	6.44515i	−0.163654	+	0.283457i
$518$	8.35199	+	4.82202i	0.366965	+	0.211868i
$519$		0			0
$520$	−4.06699	+	0.764907i	−0.178349	+	0.0335434i
$521$	−10.3444			−0.453196			−0.226598	−	0.973988i	$-0.572760\pi$
$521$	−10.3444			−0.453196			−0.226598	+	0.973988i	$0.572760\pi$
$522$		0			0
$523$	1.06684	−	1.84782i	0.0466497	−	0.0807996i	−0.841758	−	0.539855i	$-0.818479\pi$
$523$	1.06684	−	1.84782i	0.0466497	−	0.0807996i	0.888407	+	0.459056i	$0.151812\pi$
$524$	8.09980	+	14.0293i	0.353841	+	0.612871i
$525$		0			0
$526$	26.7127	−	15.4226i	1.16473	−	0.672457i
$527$	−18.5601	+	10.7157i	−0.808490	+	0.466782i
$528$		0			0
$529$	9.33681	+	16.1718i	0.405948	+	0.703123i
$530$	−7.62198	+	13.2017i	−0.331078	+	0.573444i
$531$		0			0
$532$	−6.56298			−0.284541
$533$	−32.3002	−	11.3420i	−1.39908	−	0.491277i
$534$		0			0
$535$	5.51599	+	3.18466i	0.238477	+	0.137685i
$536$	0.256747	−	0.444700i	0.0110898	−	0.0192081i
$537$		0			0
$538$		−	5.63191i		−	0.242809i
$539$	−3.84935	+	2.22243i	−0.165803	+	0.0957266i
$540$		0			0
$541$		−	8.41225i		−	0.361671i	−0.983513	−	0.180836i	$-0.942120\pi$
$541$		−	8.41225i		−	0.361671i	0.983513	−	0.180836i	$-0.0578802\pi$
$542$	−1.50240	−	2.60224i	−0.0645338	−	0.111776i
$543$		0			0
$544$	2.34672	+	1.35488i	0.100615	+	0.0580900i
$545$	−9.14745			−0.391834
$546$		0			0
$547$	−1.00730			−0.0430692			−0.0215346	−	0.999768i	$-0.506855\pi$
$547$	−1.00730			−0.0430692			−0.0215346	+	0.999768i	$0.506855\pi$
$548$	−4.50527	−	2.60112i	−0.192456	−	0.111114i
$549$		0			0
$550$	−8.18443	−	14.1759i	−0.348985	−	0.604460i
$551$		−	47.2482i		−	2.01284i
$552$		0			0
$553$	−9.30143	+	5.37018i	−0.395537	+	0.228363i
$554$		−	24.1732i		−	1.02702i
$555$		0			0
$556$	2.87013	−	4.97122i	0.121721	−	0.210827i
$557$	−37.9237	−	21.8953i	−1.60688	−	0.927732i	−0.990063	−	0.140624i	$-0.955089\pi$
$557$	−37.9237	−	21.8953i	−1.60688	−	0.927732i	−0.616816	−	0.787108i	$-0.711578\pi$
$558$		0			0
$559$	7.99365	+	9.30937i	0.338095	+	0.393744i
$560$	−1.14776			−0.0485015
$561$		0			0
$562$	−0.872873	+	1.51186i	−0.0368199	+	0.0637740i
$563$	−2.11334	−	3.66041i	−0.0890665	−	0.154268i	0.818050	−	0.575147i	$-0.195055\pi$
$563$	−2.11334	−	3.66041i	−0.0890665	−	0.154268i	−0.907117	+	0.420879i	$0.861722\pi$
$564$		0			0
$565$	−4.34441	+	2.50825i	−0.182771	+	0.105523i
$566$	22.6156	−	13.0572i	0.950607	−	0.548833i
$567$		0			0
$568$	−5.39365	−	9.34208i	−0.226313	−	0.391985i
$569$	−4.71320	+	8.16349i	−0.197587	+	0.342231i	−0.947746	−	0.319027i	$-0.896644\pi$
$569$	−4.71320	+	8.16349i	−0.197587	+	0.342231i	0.750158	+	0.661258i	$0.229977\pi$
$570$		0			0
$571$	25.5304			1.06842			0.534208	−	0.845353i	$-0.320610\pi$
$571$	25.5304			1.06842			0.534208	+	0.845353i	$0.320610\pi$
$572$	2.96222	+	15.7500i	0.123856	+	0.658540i
$573$		0			0
$574$	−8.22266	−	4.74735i	−0.343207	−	0.198151i
$575$	3.82996	−	6.63368i	0.159720	−	0.276644i
$576$		0			0
$577$			31.7623i			1.32228i	0.750262	+	0.661141i	$0.229927\pi$
$577$			31.7623i			1.32228i	−0.750262	+	0.661141i	$0.770073\pi$
$578$	8.36339	−	4.82861i	0.347871	−	0.200844i
$579$		0			0
$580$		−	8.26291i		−	0.343099i
$581$	−7.67396	−	13.2917i	−0.318370	−	0.551432i
$582$		0			0
$583$	51.1254	+	29.5172i	2.11740	+	1.22248i
$584$	−8.02452			−0.332057
$585$		0			0
$586$	5.65535			0.233620
$587$	29.7429	+	17.1721i	1.22762	+	0.708768i	0.966532	−	0.256546i	$-0.0825846\pi$
$587$	29.7429	+	17.1721i	1.22762	+	0.708768i	0.261090	+	0.965314i	$0.415918\pi$
$588$		0			0
$589$	−25.9532	−	44.9522i	−1.06938	−	1.85222i
$590$			0.0777701i			0.00320175i
$591$		0			0
$592$	8.35199	−	4.82202i	0.343265	−	0.198184i
$593$		−	15.1751i		−	0.623168i	−0.950219	−	0.311584i	$-0.899140\pi$
$593$		−	15.1751i		−	0.623168i	0.950219	−	0.311584i	$-0.100860\pi$
$594$		0			0
$595$	1.55507	−	2.69346i	0.0637516	−	0.110421i
$596$	−2.62042	−	1.51290i	−0.107336	−	0.0619707i
$597$		0			0
$598$	−5.68978	+	4.88563i	−0.232673	+	0.199788i
$599$	−7.48641			−0.305886			−0.152943	−	0.988235i	$-0.548875\pi$
$599$	−7.48641			−0.305886			−0.152943	+	0.988235i	$0.548875\pi$
$600$		0			0
$601$	−18.2071	+	31.5356i	−0.742683	+	1.28637i	0.208586	+	0.978004i	$0.433114\pi$
$601$	−18.2071	+	31.5356i	−0.742683	+	1.28637i	−0.951269	+	0.308361i	$0.900219\pi$
$602$	1.70160	+	2.94725i	0.0693520	+	0.120121i
$603$		0			0
$604$	−1.10011	+	0.635151i	−0.0447630	+	0.0258439i
$605$	8.70403	−	5.02527i	0.353869	−	0.204306i
$606$		0			0
$607$	−2.26168	−	3.91735i	−0.0917989	−	0.159000i	0.816469	−	0.577389i	$-0.195928\pi$
$607$	−2.26168	−	3.91735i	−0.0917989	−	0.159000i	−0.908268	+	0.418389i	$0.862595\pi$
$608$	−3.28149	+	5.68371i	−0.133082	+	0.230505i
$609$		0			0
$610$	−9.29735			−0.376439
$611$	1.11585	+	5.93292i	0.0451424	+	0.240020i
$612$		0			0
$613$	−34.8434	−	20.1168i	−1.40731	−	0.812512i	−0.412183	−	0.911101i	$-0.635234\pi$
$613$	−34.8434	−	20.1168i	−1.40731	−	0.812512i	−0.995128	+	0.0985892i	$0.968567\pi$
$614$	−10.2383	+	17.7333i	−0.413186	+	0.715659i
$615$		0			0
$616$			4.44485i			0.179088i
$617$	34.2107	−	19.7516i	1.37727	−	0.795168i	0.385440	−	0.922733i	$-0.374050\pi$
$617$	34.2107	−	19.7516i	1.37727	−	0.795168i	0.991830	+	0.127565i	$0.0407162\pi$
$618$		0			0
$619$		−	22.9229i		−	0.921348i	−0.887569	−	0.460674i	$-0.847608\pi$
$619$		−	22.9229i		−	0.921348i	0.887569	−	0.460674i	$-0.152392\pi$
$620$	−4.53877	−	7.86138i	−0.182281	−	0.315721i
$621$		0			0
$622$	−1.07138	−	0.618559i	−0.0429583	−	0.0248020i
$623$	10.8596			0.435079
$624$		0			0
$625$	6.97525			0.279010
$626$	−7.80420	−	4.50576i	−0.311918	−	0.180086i
$627$		0			0
$628$	−2.05930	−	3.56680i	−0.0821748	−	0.142331i
$629$			26.1330i			1.04199i
$630$		0			0
$631$	3.11897	−	1.80074i	0.124164	−	0.0716862i	−0.436632	−	0.899640i	$-0.643829\pi$
$631$	3.11897	−	1.80074i	0.124164	−	0.0716862i	0.560796	+	0.827954i	$0.310495\pi$
$632$			10.7404i			0.427229i
$633$		0			0
$634$	0.290322	−	0.502852i	0.0115302	−	0.0199708i
$635$	−6.82365	−	3.93964i	−0.270788	−	0.156340i
$636$		0			0
$637$	−1.19456	+	3.40191i	−0.0473302	+	0.134789i
$638$	−31.9993			−1.26687
$639$		0			0
$640$	−0.573878	+	0.993985i	−0.0226845	+	0.0392907i
$641$	−2.60928	−	4.51940i	−0.103060	−	0.178506i	0.809884	−	0.586590i	$-0.199530\pi$
$641$	−2.60928	−	4.51940i	−0.103060	−	0.178506i	−0.912944	+	0.408085i	$0.866197\pi$
$642$		0			0
$643$	18.1006	−	10.4504i	0.713820	−	0.412124i	−0.0986540	−	0.995122i	$-0.531454\pi$
$643$	18.1006	−	10.4504i	0.713820	−	0.412124i	0.812474	+	0.582998i	$0.198120\pi$
$644$	−1.80133	+	1.04000i	−0.0709824	+	0.0409817i
$645$		0			0
$646$	−8.89204	−	15.4015i	−0.349853	−	0.605963i
$647$	3.81055	−	6.60007i	0.149808	−	0.259476i	−0.781348	−	0.624095i	$-0.785468\pi$
$647$	3.81055	−	6.60007i	0.149808	−	0.259476i	0.931156	+	0.364620i	$0.118801\pi$
$648$		0			0
$649$	0.301176			0.0118222
$650$	−12.5281	−	4.39916i	−0.491392	−	0.172549i
$651$		0			0
$652$	−9.71606	−	5.60957i	−0.380510	−	0.219688i
$653$	−12.8910	+	22.3278i	−0.504462	+	0.873755i	0.495524	+	0.868594i	$0.334976\pi$
$653$	−12.8910	+	22.3278i	−0.504462	+	0.873755i	−0.999987	+	0.00516051i	$0.998357\pi$
$654$		0			0
$655$		−	18.5932i		−	0.726495i
$656$	−8.22266	+	4.74735i	−0.321041	+	0.185353i
$657$		0			0
$658$			1.67435i			0.0652728i
$659$	7.82964	+	13.5613i	0.305000	+	0.528275i	0.977261	−	0.212039i	$-0.0680103\pi$
$659$	7.82964	+	13.5613i	0.305000	+	0.528275i	−0.672262	+	0.740314i	$0.734677\pi$
$660$		0			0
$661$	−27.4434	−	15.8444i	−1.06742	−	0.616277i	−0.139947	−	0.990159i	$-0.544693\pi$
$661$	−27.4434	−	15.8444i	−1.06742	−	0.616277i	−0.927476	+	0.373881i	$0.878027\pi$
$662$	−31.3654			−1.21905
$663$		0			0
$664$	−15.3479			−0.595615
$665$	6.52351	+	3.76635i	0.252971	+	0.146053i
$666$		0			0
$667$	−7.48715	−	12.9681i	−0.289904	−	0.502128i
$668$			3.99739i			0.154664i
$669$		0			0
$670$	−0.510406	+	0.294683i	−0.0197187	+	0.0113846i
$671$			36.0054i			1.38997i
$672$		0			0
$673$	8.38642	−	14.5257i	0.323273	−	0.559925i	−0.657889	−	0.753115i	$-0.728550\pi$
$673$	8.38642	−	14.5257i	0.323273	−	0.559925i	0.981161	+	0.193190i	$0.0618835\pi$
$674$	8.16690	+	4.71516i	0.314577	+	0.181621i
$675$		0			0
$676$	10.1460	+	8.12759i	0.390233	+	0.312600i
$677$	8.34791			0.320836			0.160418	−	0.987049i	$-0.448716\pi$
$677$	8.34791			0.320836			0.160418	+	0.987049i	$0.448716\pi$
$678$		0			0
$679$	−1.06347	+	1.84198i	−0.0408122	+	0.0706887i
$680$	−1.55507	−	2.69346i	−0.0596342	−	0.103289i
$681$		0			0
$682$	−30.4444	+	17.5771i	−1.16577	+	0.673060i
$683$	23.5376	−	13.5895i	0.900642	−	0.519986i	0.0232337	−	0.999730i	$-0.492604\pi$
$683$	23.5376	−	13.5895i	0.900642	−	0.519986i	0.877408	+	0.479744i	$0.159270\pi$
$684$		0			0
$685$	2.98545	+	5.17095i	0.114068	+	0.197572i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$		0			0
$688$	3.40320			0.129746
$689$	47.0622	−	8.85132i	1.79293	−	0.337208i
$690$		0			0
$691$	22.7403	+	13.1291i	0.865080	+	0.499454i	0.865710	−	0.500545i	$-0.166867\pi$
$691$	22.7403	+	13.1291i	0.865080	+	0.499454i	−0.000629844		1.00000i	$0.500200\pi$
$692$	−6.08396	+	10.5377i	−0.231277	+	0.400584i
$693$		0			0
$694$			6.47300i			0.245712i
$695$	−5.70574	+	3.29421i	−0.216431	+	0.124957i
$696$		0			0
$697$		−	25.7284i		−	0.974531i
$698$	4.95258	+	8.57811i	0.187458	+	0.324686i
$699$		0			0
$700$	−3.18927	−	1.84133i	−0.120543	−	0.0695957i
$701$	26.4443			0.998786			0.499393	−	0.866376i	$-0.333556\pi$
$701$	26.4443			0.998786			0.499393	+	0.866376i	$0.333556\pi$
$702$		0			0
$703$	−63.2937			−2.38717
$704$	3.84935	+	2.22243i	0.145078	+	0.0837608i
$705$		0			0
$706$	−14.3879	−	24.9206i	−0.541496	−	0.937898i
$707$			6.01888i			0.226363i
$708$		0			0
$709$	10.0688	−	5.81322i	0.378141	−	0.218320i	−0.298868	−	0.954294i	$-0.596609\pi$
$709$	10.0688	−	5.81322i	0.378141	−	0.218320i	0.677009	+	0.735975i	$0.263276\pi$
$710$			12.3812i			0.464658i
$711$		0			0
$712$	5.42978	−	9.40465i	0.203490	−	0.352454i
$713$	−14.2466	−	8.22530i	−0.533541	−	0.308040i
$714$		0			0
$715$	6.09417	−	17.3552i	0.227909	−	0.649048i
$716$	11.8711			0.443643
$717$		0			0
$718$	−6.06911	+	10.5120i	−0.226497	+	0.392305i
$719$	22.4379	+	38.8636i	0.836793	+	1.44937i	0.892562	+	0.450925i	$0.148906\pi$
$719$	22.4379	+	38.8636i	0.836793	+	1.44937i	−0.0557687	+	0.998444i	$0.517761\pi$
$720$		0			0
$721$	−4.98545	+	2.87835i	−0.185668	+	0.107195i
$722$	20.8476	−	12.0364i	0.775867	−	0.447947i
$723$		0			0
$724$	−2.39567	−	4.14942i	−0.0890344	−	0.154212i
$725$	13.2561	−	22.9602i	0.492319	−	0.852721i
$726$		0			0
$727$	19.5156			0.723793			0.361896	−	0.932218i	$-0.382129\pi$
$727$	19.5156			0.723793			0.361896	+	0.932218i	$0.382129\pi$
$728$	2.34886	+	2.73548i	0.0870547	+	0.101384i
$729$		0			0
$730$	7.97626	+	4.60509i	0.295214	+	0.170442i
$731$	−4.61092	+	7.98635i	−0.170541	+	0.295386i
$732$		0			0
$733$			10.7037i			0.395349i	0.980268	+	0.197675i	$0.0633390\pi$
$733$			10.7037i			0.395349i	−0.980268	+	0.197675i	$0.936661\pi$
$734$	23.4498	−	13.5388i	0.865548	−	0.499725i
$735$		0			0
$736$			2.08000i			0.0766697i
$737$	1.14120	+	1.97662i	0.0420368	+	0.0728099i
$738$		0			0
$739$	0.413619	+	0.238803i	0.0152152	+	0.00878452i	0.507588	−	0.861600i	$-0.330537\pi$
$739$	0.413619	+	0.238803i	0.0152152	+	0.00878452i	−0.492373	+	0.870384i	$0.663870\pi$
$740$	−11.0690			−0.406905
$741$		0			0
$742$	13.2815			0.487581
$743$	−8.43019	−	4.86717i	−0.309274	−	0.178559i	0.337328	−	0.941387i	$-0.390477\pi$
$743$	−8.43019	−	4.86717i	−0.309274	−	0.178559i	−0.646601	+	0.762828i	$0.723810\pi$
$744$		0			0
$745$	1.73644	+	3.00760i	0.0636181	+	0.110190i
$746$			15.6332i			0.572373i
$747$		0			0
$748$	−10.4308	+	6.02223i	−0.381388	+	0.220195i
$749$		−	5.54937i		−	0.202769i
$750$		0			0
$751$	18.1084	−	31.3646i	0.660784	−	1.14451i	−0.319626	−	0.947544i	$-0.603557\pi$
$751$	18.1084	−	31.3646i	0.660784	−	1.14451i	0.980410	−	0.196967i	$-0.0631093\pi$
$752$	1.45003	+	0.837173i	0.0528770	+	0.0305286i
$753$		0			0
$754$	−19.6932	+	16.9099i	−0.717185	+	0.615823i
$755$	1.45800			0.0530619
$756$		0			0
$757$	−23.2347	+	40.2436i	−0.844479	+	1.46268i	0.0415945	+	0.999135i	$0.486756\pi$
$757$	−23.2347	+	40.2436i	−0.844479	+	1.46268i	−0.886073	+	0.463545i	$0.846577\pi$
$758$	−18.6654	−	32.3295i	−0.677959	−	1.17426i
$759$		0			0
$760$	6.52351	−	3.76635i	0.236632	−	0.136620i
$761$	−18.5037	+	10.6831i	−0.670760	+	0.387263i	−0.796365	−	0.604817i	$-0.793246\pi$
$761$	−18.5037	+	10.6831i	−0.670760	+	0.387263i	0.125605	+	0.992080i	$0.459913\pi$
$762$		0			0
$763$	3.98493	+	6.90210i	0.144264	+	0.249873i
$764$	−7.79263	+	13.4972i	−0.281927	+	0.488313i
$765$		0			0
$766$	37.8964			1.36925
$767$	0.185352	−	0.159155i	0.00669266	−	0.00574677i
$768$		0			0
$769$	−39.8297	−	22.9957i	−1.43630	−	0.829246i	−0.438706	−	0.898631i	$-0.644563\pi$
$769$	−39.8297	−	22.9957i	−1.43630	−	0.829246i	−0.997590	+	0.0693848i	$0.977896\pi$
$770$	2.55080	−	4.41812i	0.0919245	−	0.159218i
$771$		0			0
$772$		−	17.5855i		−	0.632916i
$773$	−17.2754	+	9.97393i	−0.621351	+	0.358737i	−0.777395	−	0.629013i	$-0.783459\pi$
$773$	−17.2754	+	9.97393i	−0.621351	+	0.358737i	0.156044	+	0.987750i	$0.450126\pi$
$774$		0			0
$775$		−	29.1260i		−	1.04624i
$776$	1.06347	+	1.84198i	0.0381763	+	0.0661233i
$777$		0			0
$778$	8.75147	+	5.05267i	0.313756	+	0.181147i
$779$	62.3136			2.23262
$780$		0			0
$781$	47.9479			1.71571
$782$	−4.88117	−	2.81814i	−0.174550	−	0.100777i
$783$		0			0
$784$	0.500000	+	0.866025i	0.0178571	+	0.0309295i
$785$			4.72714i			0.168719i
$786$		0			0
$787$	38.0726	−	21.9812i	1.35714	−	0.783546i	0.367904	−	0.929864i	$-0.380075\pi$
$787$	38.0726	−	21.9812i	1.35714	−	0.783546i	0.989238	+	0.146318i	$0.0467421\pi$
$788$			0.529815i			0.0188739i
$789$		0			0
$790$	6.16365	−	10.6758i	0.219293	−	0.379827i
$791$	3.78514	+	2.18535i	0.134584	+	0.0777021i
$792$		0			0
$793$	19.0269	+	22.1586i	0.675665	+	0.786876i
$794$	5.50839			0.195485
$795$		0			0
$796$	−12.5732	+	21.7775i	−0.445647	+	0.771883i
$797$	−15.9862	−	27.6889i	−0.566260	−	0.980792i	−0.996931	−	0.0782827i	$-0.975056\pi$
$797$	−15.9862	−	27.6889i	−0.566260	−	0.980792i	0.430671	−	0.902509i	$-0.358277\pi$
$798$		0			0
$799$	−3.92922	+	2.26854i	−0.139006	+	0.0802551i
$800$	−3.18927	+	1.84133i	−0.112758	+	0.0651008i
$801$		0			0
$802$	13.3747	+	23.1657i	0.472278	+	0.818010i
$803$	17.8339	−	30.8892i	0.629345	−	1.09006i
$804$		0			0
$805$	2.38733			0.0841423
$806$	−9.44772	+	26.9056i	−0.332782	+	0.947709i
$807$		0			0
$808$	5.21251	+	3.00944i	0.183375	+	0.105872i
$809$	−14.0866	+	24.3986i	−0.495257	+	0.857811i	−0.999985	−	0.00546789i	$-0.998260\pi$
$809$	−14.0866	+	24.3986i	−0.495257	+	0.857811i	0.504728	+	0.863279i	$0.331593\pi$
$810$		0			0
$811$		−	39.0534i		−	1.37135i	−0.727908	−	0.685675i	$-0.759507\pi$
$811$		−	39.0534i		−	1.37135i	0.727908	−	0.685675i	$-0.240493\pi$
$812$	−6.23469	+	3.59960i	−0.218795	+	0.126321i
$813$		0			0
$814$			42.8663i			1.50246i
$815$	6.43842	+	11.1517i	0.225528	+	0.390626i
$816$		0			0
$817$	−19.3428	−	11.1676i	−0.676718	−	0.390703i
$818$	−31.9995			−1.11884
$819$		0			0
$820$	10.8976			0.380561
$821$	−20.4243	−	11.7920i	−0.712812	−	0.411542i	0.0992893	−	0.995059i	$-0.468343\pi$
$821$	−20.4243	−	11.7920i	−0.712812	−	0.411542i	−0.812101	+	0.583516i	$0.801676\pi$
$822$		0			0
$823$	12.3566	+	21.4023i	0.430725	+	0.746038i	0.996936	−	0.0782228i	$-0.0249245\pi$
$823$	12.3566	+	21.4023i	0.430725	+	0.746038i	−0.566211	+	0.824260i	$0.691591\pi$
$824$			5.75670i			0.200544i
$825$		0			0
$826$	0.0586805	−	0.0338792i	0.00204176	−	0.00117881i
$827$			45.2456i			1.57334i	0.617371	+	0.786672i	$0.288198\pi$
$827$			45.2456i			1.57334i	−0.617371	+	0.786672i	$0.711802\pi$
$828$		0			0
$829$	22.4064	−	38.8091i	0.778208	−	1.34790i	−0.154765	−	0.987951i	$-0.549462\pi$
$829$	22.4064	−	38.8091i	0.778208	−	1.34790i	0.932974	−	0.359945i	$-0.117204\pi$
$830$	15.2556	+	8.80783i	0.529530	+	0.305724i
$831$		0			0
$832$	3.54343	−	0.666437i	0.122846	−	0.0231046i
$833$	−2.70976			−0.0938875
$834$		0			0
$835$	2.29401	−	3.97334i	0.0793875	−	0.137503i
$836$	−14.5857	−	25.2632i	−0.504458	−	0.873747i
$837$		0			0
$838$	10.1287	−	5.84782i	0.349891	−	0.202010i
$839$	26.7511	−	15.4447i	0.923550	−	0.533212i	0.0387839	−	0.999248i	$-0.487652\pi$
$839$	26.7511	−	15.4447i	0.923550	−	0.533212i	0.884766	+	0.466036i	$0.154318\pi$
$840$		0			0
$841$	−11.4142	−	19.7700i	−0.393593	−	0.681723i
$842$	12.9282	−	22.3924i	0.445536	−	0.771692i
$843$		0			0
$844$	−5.44170			−0.187311
$845$	−5.42078	−	13.9013i	−0.186481	−	0.478219i
$846$		0			0
$847$	−7.58352	−	4.37835i	−0.260573	−	0.150442i
$848$	6.64077	−	11.5022i	0.228045	−	0.394986i
$849$		0			0
$850$		−	9.97911i		−	0.342281i
$851$	−17.3721	+	10.0298i	−0.595508	+	0.343817i
$852$		0			0
$853$			27.9201i			0.955965i	0.878369	+	0.477982i	$0.158632\pi$
$853$			27.9201i			0.955965i	−0.878369	+	0.477982i	$0.841368\pi$
$854$	4.05023	+	7.01521i	0.138596	+	0.240055i
$855$		0			0
$856$	−4.80589	−	2.77468i	−0.164262	−	0.0948367i
$857$	17.5921			0.600935			0.300468	−	0.953792i	$-0.402857\pi$
$857$	17.5921			0.600935			0.300468	+	0.953792i	$0.402857\pi$
$858$		0			0
$859$	22.1337			0.755193			0.377596	−	0.925970i	$-0.376751\pi$
$859$	22.1337			0.755193			0.377596	+	0.925970i	$0.376751\pi$
$860$	−3.38273	−	1.95302i	−0.115350	−	0.0665974i
$861$		0			0
$862$	−5.35311	−	9.27186i	−0.182328	−	0.315801i
$863$		−	4.58867i		−	0.156200i	−0.996946	−	0.0781000i	$-0.975115\pi$
$863$		−	4.58867i		−	0.156200i	0.996946	−	0.0781000i	$-0.0248854\pi$
$864$		0			0
$865$	12.0947	−	6.98289i	0.411233	−	0.237426i
$866$			22.4299i			0.762199i
$867$		0			0
$868$	−3.95448	+	6.84935i	−0.134224	+	0.232482i
$869$	−41.3434	−	23.8697i	−1.40248	−	0.809722i
$870$		0			0
$871$	1.74687	+	0.613401i	0.0591903	+	0.0207843i
$872$	7.96986			0.269893
$873$		0			0
$874$	6.82549	−	11.8221i	0.230876	−	0.399888i
$875$	4.98278	+	8.63043i	0.168449	+	0.291762i
$876$		0			0
$877$	−34.6248	+	19.9906i	−1.16920	+	0.675035i	−0.953490	−	0.301423i	$-0.902538\pi$
$877$	−34.6248	+	19.9906i	−1.16920	+	0.675035i	−0.215705	+	0.976459i	$0.569205\pi$
$878$	−11.0143	+	6.35913i	−0.371716	+	0.214610i
$879$		0			0
$880$	−2.55080	−	4.41812i	−0.0859875	−	0.148935i
$881$	23.9548	−	41.4910i	0.807058	−	1.39787i	−0.107834	−	0.994169i	$-0.534392\pi$
$881$	23.9548	−	41.4910i	0.807058	−	1.39787i	0.914893	−	0.403697i	$-0.132275\pi$
$882$		0			0
$883$	34.0091			1.14450			0.572248	−	0.820080i	$-0.306071\pi$
$883$	34.0091			1.14450			0.572248	+	0.820080i	$0.306071\pi$
$884$	−3.23697	+	9.21837i	−0.108871	+	0.310047i
$885$		0			0
$886$	6.81084	+	3.93224i	0.228815	+	0.132106i
$887$	1.88672	−	3.26789i	0.0633497	−	0.109725i	−0.832611	−	0.553858i	$-0.813155\pi$
$887$	1.88672	−	3.26789i	0.0633497	−	0.109725i	0.895961	+	0.444133i	$0.146488\pi$
$888$		0			0
$889$			6.86494i			0.230243i
$890$	−10.7942	+	6.23206i	−0.361824	+	0.208899i
$891$		0			0
$892$			9.24550i			0.309562i
$893$	−5.49435	−	9.51650i	−0.183862	−	0.318457i
$894$		0			0
$895$	−11.7997	−	6.81254i	−0.394419	−	0.227718i
$896$	1.00000			0.0334077
$897$		0			0
$898$	16.8373			0.561867
$899$	−49.3098	−	28.4690i	−1.64457	−	0.949496i
$900$		0			0
$901$	17.9949	+	31.1681i	0.599497	+	1.03836i
$902$		−	42.2025i		−	1.40519i
$903$		0			0
$904$	3.78514	−	2.18535i	0.125892	−	0.0726837i
$905$			5.49929i			0.182802i
$906$		0			0
$907$	7.13753	−	12.3626i	0.236998	−	0.410492i	−0.722854	−	0.691001i	$-0.757170\pi$
$907$	7.13753	−	12.3626i	0.236998	−	0.410492i	0.959851	+	0.280509i	$0.0905032\pi$
$908$	1.30318	+	0.752389i	0.0432474	+	0.0249689i
$909$		0			0
$910$	−0.764907	−	4.06699i	−0.0253564	−	0.134819i
$911$	−17.4161			−0.577020			−0.288510	−	0.957477i	$-0.593160\pi$
$911$	−17.4161			−0.577020			−0.288510	+	0.957477i	$0.593160\pi$
$912$		0			0
$913$	34.1096	−	59.0796i	1.12886	−	1.95525i
$914$	4.59882	+	7.96539i	0.152115	+	0.263472i
$915$		0			0
$916$	−22.0300	+	12.7190i	−0.727891	+	0.420248i
$917$	−14.0293	+	8.09980i	−0.463287	+	0.267479i
$918$		0			0
$919$	−18.1179	−	31.3811i	−0.597654	−	1.03517i	−0.993166	−	0.116707i	$-0.962766\pi$
$919$	−18.1179	−	31.3811i	−0.597654	−	1.03517i	0.395512	−	0.918461i	$-0.370567\pi$
$920$	1.19366	−	2.06749i	0.0393539	−	0.0681630i
$921$		0			0
$922$	21.8021			0.718013
$923$	29.5084	−	25.3379i	0.971281	−	0.834007i
$924$		0			0
$925$	−30.7575	−	17.7579i	−1.01130	−	0.583875i
$926$	13.0318	−	22.5717i	0.428251	−	0.741752i
$927$		0			0
$928$			7.19919i			0.236325i
$929$	12.4656	−	7.19701i	0.408983	−	0.236126i	−0.281370	−	0.959599i	$-0.590789\pi$
$929$	12.4656	−	7.19701i	0.408983	−	0.236126i	0.690353	+	0.723473i	$0.257455\pi$
$930$		0			0
$931$		−	6.56298i		−	0.215093i
$932$	−6.05020	−	10.4793i	−0.198181	−	0.343260i
$933$		0			0
$934$	−24.8262	−	14.3334i	−0.812338	−	0.469004i
$935$	13.8241			0.452097
$936$		0			0
$937$	−6.25633			−0.204385			−0.102193	−	0.994765i	$-0.532586\pi$
$937$	−6.25633			−0.204385			−0.102193	+	0.994765i	$0.532586\pi$
$938$	0.444700	+	0.256747i	0.0145200	+	0.00838310i
$939$		0			0
$940$	−0.960870	−	1.66428i	−0.0313401	−	0.0542827i
$941$		−	29.1506i		−	0.950284i	−0.879909	−	0.475142i	$-0.842397\pi$
$941$		−	29.1506i		−	0.950284i	0.879909	−	0.475142i	$-0.157603\pi$
$942$		0			0
$943$	17.1031	−	9.87448i	0.556954	−	0.321557i
$944$		−	0.0677585i		−	0.00220535i
$945$		0			0
$946$	−7.56335	+	13.1001i	−0.245906	+	0.425921i
$947$	9.43915	+	5.44970i	0.306731	+	0.177091i	0.645463	−	0.763792i	$-0.276665\pi$
$947$	9.43915	+	5.44970i	0.306731	+	0.177091i	−0.338732	+	0.940883i	$0.609998\pi$
$948$		0			0
$949$	−5.34784	−	28.4343i	−0.173598	−	0.923016i
$950$	24.1692			0.784153
$951$		0			0
$952$	−1.35488	+	2.34672i	−0.0439119	+	0.0760576i
$953$	−13.7652	−	23.8421i	−0.445900	−	0.772321i	0.552215	−	0.833702i	$-0.313783\pi$
$953$	−13.7652	−	23.8421i	−0.445900	−	0.772321i	−0.998114	+	0.0613812i	$0.980449\pi$
$954$		0			0
$955$	15.4915	−	8.94403i	0.501294	−	0.289422i
$956$	4.83211	−	2.78982i	0.156282	−	0.0902292i
$957$		0			0
$958$	8.98812	+	15.5679i	0.290393	+	0.502975i
$959$	2.60112	−	4.50527i	0.0839945	−	0.145483i
$960$		0			0
$961$	−31.5515			−1.01779
$962$	22.6526	+	26.3811i	0.730348	+	0.850560i
$963$		0			0
$964$	20.1291	+	11.6215i	0.648314	+	0.374304i
$965$	−10.0919	+	17.4797i	−0.324870	+	0.562692i
$966$		0			0
$967$			21.0297i			0.676271i	0.941097	+	0.338135i	$0.109796\pi$
$967$			21.0297i			0.676271i	−0.941097	+	0.338135i	$0.890204\pi$
$968$	−7.58352	+	4.37835i	−0.243744	+	0.140725i
$969$		0			0
$970$		−	2.44120i		−	0.0783823i
$971$	2.18410	+	3.78297i	0.0700911	+	0.121401i	0.898941	−	0.438070i	$-0.144338\pi$
$971$	2.18410	+	3.78297i	0.0700911	+	0.121401i	−0.828850	+	0.559471i	$0.811004\pi$
$972$		0			0
$973$	4.97122	+	2.87013i	0.159370	+	0.0920123i
$974$	21.9216			0.702414
$975$		0			0
$976$	8.10046			0.259290
$977$	46.8829	+	27.0679i	1.49992	+	0.865978i	1.00000		9.46999e-5i	$-3.01439e-5\pi$
$977$	46.8829	+	27.0679i	1.49992	+	0.865978i	0.499918	+	0.866073i	$0.333363\pi$
$978$		0			0
$979$	24.1346	+	41.8023i	0.771344	+	1.33601i
$980$		−	1.14776i		−	0.0366637i
$981$		0			0
$982$	18.7067	−	10.8003i	0.596954	−	0.344652i
$983$		−	44.3574i		−	1.41478i	−0.706823	−	0.707391i	$-0.749872\pi$
$983$		−	44.3574i		−	1.41478i	0.706823	−	0.707391i	$-0.250128\pi$
$984$		0			0
$985$	0.304049	−	0.526628i	0.00968780	−	0.0167798i
$986$	−16.8945	−	9.75404i	−0.538030	−	0.310632i
$987$		0			0
$988$	−22.3267	−	7.83988i	−0.710307	−	0.249420i
$989$	−7.07864			−0.225088
$990$		0			0
$991$	−13.6936	+	23.7181i	−0.434992	+	0.753429i	−0.997295	−	0.0735026i	$-0.976582\pi$
$991$	−13.6936	+	23.7181i	−0.434992	+	0.753429i	0.562303	+	0.826932i	$0.309916\pi$
$992$	3.95448	+	6.84935i	0.125555	+	0.217467i
$993$		0			0
$994$	9.34208	−	5.39365i	0.296313	−	0.171076i
$995$	24.9952	−	14.4310i	0.792402	−	0.457494i
$996$		0			0
$997$	22.9017	+	39.6669i	0.725303	+	1.25626i	0.958849	+	0.283916i	$0.0916338\pi$
$997$	22.9017	+	39.6669i	0.725303	+	1.25626i	−0.233546	+	0.972346i	$0.575033\pi$
$998$	−19.3052	+	33.4377i	−0.611097	+	1.05845i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.bj.g.1135.5		12
3.2	odd	2		182.2.m.b.43.2	✓	12
12.11	even	2		1456.2.cc.d.225.4		12
13.10	even	6	inner	1638.2.bj.g.127.5		12
21.2	odd	6		1274.2.o.d.459.5		12
21.5	even	6		1274.2.o.e.459.5		12
21.11	odd	6		1274.2.v.e.667.5		12
21.17	even	6		1274.2.v.d.667.5		12
21.20	even	2		1274.2.m.c.589.2		12
39.17	odd	6		2366.2.d.r.337.4		12
39.20	even	12		2366.2.a.bf.1.4		6
39.23	odd	6		182.2.m.b.127.2	yes	12
39.32	even	12		2366.2.a.bh.1.4		6
39.35	odd	6		2366.2.d.r.337.10		12
156.23	even	6		1456.2.cc.d.673.4		12
273.23	odd	6		1274.2.v.e.361.5		12
273.62	even	6		1274.2.m.c.491.2		12
273.101	even	6		1274.2.o.e.569.2		12
273.179	odd	6		1274.2.o.d.569.2		12
273.257	even	6		1274.2.v.d.361.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.2	✓	12	3.2	odd	2
182.2.m.b.127.2	yes	12	39.23	odd	6
1274.2.m.c.491.2		12	273.62	even	6
1274.2.m.c.589.2		12	21.20	even	2
1274.2.o.d.459.5		12	21.2	odd	6
1274.2.o.d.569.2		12	273.179	odd	6
1274.2.o.e.459.5		12	21.5	even	6
1274.2.o.e.569.2		12	273.101	even	6
1274.2.v.d.361.5		12	273.257	even	6
1274.2.v.d.667.5		12	21.17	even	6
1274.2.v.e.361.5		12	273.23	odd	6
1274.2.v.e.667.5		12	21.11	odd	6
1456.2.cc.d.225.4		12	12.11	even	2
1456.2.cc.d.673.4		12	156.23	even	6
1638.2.bj.g.127.5		12	13.10	even	6	inner
1638.2.bj.g.1135.5		12	1.1	even	1	trivial
2366.2.a.bf.1.4		6	39.20	even	12
2366.2.a.bh.1.4		6	39.32	even	12
2366.2.d.r.337.4		12	39.17	odd	6
2366.2.d.r.337.10		12	39.35	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.14776i q^{5} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.14776i q^{5} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(0.573878 - 0.993985i) q^{10} +(-3.84935 - 2.22243i) q^{11} +(-3.54343 + 0.666437i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.35488 - 2.34672i) q^{17} +(5.68371 - 3.28149i) q^{19} +(0.993985 - 0.573878i) q^{20} +(-2.22243 - 3.84935i) q^{22} +(1.04000 - 1.80133i) q^{23} +3.68266 q^{25} +(-3.40191 - 1.19456i) q^{26} +(-0.866025 - 0.500000i) q^{28} +(3.59960 - 6.23469i) q^{29} -7.90895i q^{31} +(-0.866025 + 0.500000i) q^{32} -2.70976i q^{34} +(0.573878 + 0.993985i) q^{35} +(-8.35199 - 4.82202i) q^{37} +6.56298 q^{38} +1.14776 q^{40} +(8.22266 + 4.74735i) q^{41} +(-1.70160 - 2.94725i) q^{43} -4.44485i q^{44} +(1.80133 - 1.04000i) q^{46} -1.67435i q^{47} +(0.500000 - 0.866025i) q^{49} +(3.18927 + 1.84133i) q^{50} +(-2.34886 - 2.73548i) q^{52} -13.2815 q^{53} +(-2.55080 + 4.41812i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(6.23469 - 3.59960i) q^{58} +(-0.0586805 + 0.0338792i) q^{59} +(-4.05023 - 7.01521i) q^{61} +(3.95448 - 6.84935i) q^{62} -1.00000 q^{64} +(0.764907 + 4.06699i) q^{65} +(-0.444700 - 0.256747i) q^{67} +(1.35488 - 2.34672i) q^{68} +1.14776i q^{70} +(-9.34208 + 5.39365i) q^{71} +8.02452i q^{73} +(-4.82202 - 8.35199i) q^{74} +(5.68371 + 3.28149i) q^{76} +4.44485 q^{77} +10.7404 q^{79} +(0.993985 + 0.573878i) q^{80} +(4.74735 + 8.22266i) q^{82} +15.3479i q^{83} +(-2.69346 + 1.55507i) q^{85} -3.40320i q^{86} +(2.22243 - 3.84935i) q^{88} +(-9.40465 - 5.42978i) q^{89} +(2.73548 - 2.34886i) q^{91} +2.08000 q^{92} +(0.837173 - 1.45003i) q^{94} +(-3.76635 - 6.52351i) q^{95} +(1.84198 - 1.06347i) q^{97} +(0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4}+O(q^{10}) \) 12 * q + 6 * q^4	\( 12 q + 6 q^{4} - 2 q^{10} + 18 q^{11} - 8 q^{13} - 12 q^{14} - 6 q^{16} - 4 q^{17} + 12 q^{19} - 2 q^{22} + 6 q^{23} - 24 q^{25} + 14 q^{26} + 10 q^{29} - 2 q^{35} - 6 q^{37} - 8 q^{38} - 4 q^{40} + 24 q^{41} + 26 q^{43} - 6 q^{46} + 6 q^{49} + 12 q^{50} - 4 q^{52} - 36 q^{53} - 6 q^{55} - 6 q^{56} + 24 q^{58} - 6 q^{59} - 28 q^{61} + 2 q^{62} - 12 q^{64} + 34 q^{65} - 42 q^{67} + 4 q^{68} - 48 q^{71} + 12 q^{76} + 4 q^{77} + 44 q^{79} + 6 q^{82} + 54 q^{85} + 2 q^{88} - 12 q^{89} - 16 q^{91} + 12 q^{92} + 8 q^{94} - 32 q^{95} + 60 q^{97}+O(q^{100}) \) 12 * q + 6 * q^4 - 2 * q^10 + 18 * q^11 - 8 * q^13 - 12 * q^14 - 6 * q^16 - 4 * q^17 + 12 * q^19 - 2 * q^22 + 6 * q^23 - 24 * q^25 + 14 * q^26 + 10 * q^29 - 2 * q^35 - 6 * q^37 - 8 * q^38 - 4 * q^40 + 24 * q^41 + 26 * q^43 - 6 * q^46 + 6 * q^49 + 12 * q^50 - 4 * q^52 - 36 * q^53 - 6 * q^55 - 6 * q^56 + 24 * q^58 - 6 * q^59 - 28 * q^61 + 2 * q^62 - 12 * q^64 + 34 * q^65 - 42 * q^67 + 4 * q^68 - 48 * q^71 + 12 * q^76 + 4 * q^77 + 44 * q^79 + 6 * q^82 + 54 * q^85 + 2 * q^88 - 12 * q^89 - 16 * q^91 + 12 * q^92 + 8 * q^94 - 32 * q^95 + 60 * q^97

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