LMFDB - Embedded newform 912.2.ci.a.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(79,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))

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

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

chi := DirichletCharacter("912.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.ci (of order $18$, degree $6$, 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:	$7.28235666434$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			79.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	912.79
Dual form			912.2.ci.a.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{3} +(-0.233956 + 1.32683i) q^{5} +(-3.20574 + 1.85083i) q^{7} +(0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{3} +(-0.233956 + 1.32683i) q^{5} +(-3.20574 + 1.85083i) q^{7} +(0.766044 - 0.642788i) q^{9} +(1.31908 + 0.761570i) q^{11} +(0.286989 - 0.788496i) q^{13} +(-0.233956 - 1.32683i) q^{15} +(0.124485 + 0.104455i) q^{17} +(-4.35844 + 0.0632028i) q^{19} +(2.37939 - 2.83564i) q^{21} +(-1.85844 + 0.327693i) q^{23} +(2.99273 + 1.08926i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-6.75150 - 8.04612i) q^{29} +(-2.95084 - 5.11100i) q^{31} +(-1.50000 - 0.264490i) q^{33} +(-1.70574 - 4.68647i) q^{35} -3.67301i q^{37} +0.839100i q^{39} +(0.788333 + 2.16593i) q^{41} +(2.89053 + 0.509678i) q^{43} +(0.673648 + 1.16679i) q^{45} +(-5.63176 - 6.71167i) q^{47} +(3.35117 - 5.80439i) q^{49} +(-0.152704 - 0.0555796i) q^{51} +(-6.69846 + 1.18112i) q^{53} +(-1.31908 + 1.57202i) q^{55} +(4.07398 - 1.55007i) q^{57} +(-9.06805 - 7.60900i) q^{59} +(0.741230 + 4.20372i) q^{61} +(-1.26604 + 3.47843i) q^{63} +(0.979055 + 0.565258i) q^{65} +(-8.57398 + 7.19442i) q^{67} +(1.63429 - 0.943555i) q^{69} +(-1.29426 + 7.34013i) q^{71} +(6.53849 - 2.37981i) q^{73} -3.18479 q^{75} -5.63816 q^{77} +(12.9893 - 4.72773i) q^{79} +(0.173648 - 0.984808i) q^{81} +(-0.134285 + 0.0775297i) q^{83} +(-0.167718 + 0.140732i) q^{85} +(9.09627 + 5.25173i) q^{87} +(1.92989 - 5.30234i) q^{89} +(0.539363 + 3.05888i) q^{91} +(4.52094 + 3.79352i) q^{93} +(0.935822 - 5.79769i) q^{95} +(-5.19846 + 6.19529i) q^{97} +(1.50000 - 0.264490i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{5} - 9 q^{7}+O(q^{10}) $ 6 * q - 6 * q^5 - 9 * q^7	$ 6 q - 6 q^{5} - 9 q^{7} - 9 q^{11} - 6 q^{13} - 6 q^{15} - 12 q^{17} - 18 q^{19} + 3 q^{21} - 3 q^{23} - 3 q^{27} - 6 q^{31} - 9 q^{33} - 12 q^{41} + 3 q^{45} - 39 q^{47} - 6 q^{49} - 3 q^{51} - 12 q^{53} + 9 q^{55} + 9 q^{57} - 12 q^{59} + 27 q^{61} - 3 q^{63} + 9 q^{65} - 36 q^{67} - 18 q^{71} - 9 q^{73} - 12 q^{75} + 18 q^{79} + 9 q^{83} + 27 q^{85} + 27 q^{87} + 3 q^{89} + 12 q^{91} + 24 q^{93} + 24 q^{95} - 3 q^{97} + 9 q^{99}+O(q^{100}) $ 6 * q - 6 * q^5 - 9 * q^7 - 9 * q^11 - 6 * q^13 - 6 * q^15 - 12 * q^17 - 18 * q^19 + 3 * q^21 - 3 * q^23 - 3 * q^27 - 6 * q^31 - 9 * q^33 - 12 * q^41 + 3 * q^45 - 39 * q^47 - 6 * q^49 - 3 * q^51 - 12 * q^53 + 9 * q^55 + 9 * q^57 - 12 * q^59 + 27 * q^61 - 3 * q^63 + 9 * q^65 - 36 * q^67 - 18 * q^71 - 9 * q^73 - 12 * q^75 + 18 * q^79 + 9 * q^83 + 27 * q^85 + 27 * q^87 + 3 * q^89 + 12 * q^91 + 24 * q^93 + 24 * q^95 - 3 * q^97 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$	$1$	$-1$

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			0
$2$		0			0
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$4$		0			0
$5$	−0.233956	+	1.32683i	−0.104628	+	0.593375i	0.886740	+	0.462268i	$0.152964\pi$
$5$	−0.233956	+	1.32683i	−0.104628	+	0.593375i	−0.991368	+	0.131107i	$0.958147\pi$
$6$		0			0
$7$	−3.20574	+	1.85083i	−1.21165	+	0.699549i	−0.963120	−	0.269074i	$-0.913282\pi$
$7$	−3.20574	+	1.85083i	−1.21165	+	0.699549i	−0.248535	+	0.968623i	$0.579949\pi$
$8$		0			0
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$		0			0
$11$	1.31908	+	0.761570i	0.397717	+	0.229622i	0.685498	−	0.728074i	$-0.259584\pi$
$11$	1.31908	+	0.761570i	0.397717	+	0.229622i	−0.287781	+	0.957696i	$0.592918\pi$
$12$		0			0
$13$	0.286989	−	0.788496i	0.0795964	−	0.218689i	−0.893511	−	0.449041i	$-0.851766\pi$
$13$	0.286989	−	0.788496i	0.0795964	−	0.218689i	0.973107	+	0.230352i	$0.0739878\pi$
$14$		0			0
$15$	−0.233956	−	1.32683i	−0.0604071	−	0.342585i
$16$		0			0
$17$	0.124485	+	0.104455i	0.0301921	+	0.0253342i	0.657759	−	0.753229i	$-0.271505\pi$
$17$	0.124485	+	0.104455i	0.0301921	+	0.0253342i	−0.627567	+	0.778563i	$0.715949\pi$
$18$		0			0
$19$	−4.35844	+	0.0632028i	−0.999895	+	0.0144997i
$19$	−4.35844	+	0.0632028i	−0.999895	+	0.0144997i
$20$		0			0
$21$	2.37939	−	2.83564i	0.519224	−	0.618788i
$22$		0			0
$23$	−1.85844	+	0.327693i	−0.387512	+	0.0683288i	−0.364010	−	0.931395i	$-0.618593\pi$
$23$	−1.85844	+	0.327693i	−0.387512	+	0.0683288i	−0.0235017	+	0.999724i	$0.507481\pi$
$24$		0			0
$25$	2.99273	+	1.08926i	0.598545	+	0.217853i
$26$		0			0
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$		0			0
$29$	−6.75150	−	8.04612i	−1.25372	−	1.49413i	−0.796331	−	0.604861i	$-0.793229\pi$
$29$	−6.75150	−	8.04612i	−1.25372	−	1.49413i	−0.457390	−	0.889266i	$-0.651216\pi$
$30$		0			0
$31$	−2.95084	−	5.11100i	−0.529986	−	0.917963i	−0.999388	−	0.0349781i	$-0.988864\pi$
$31$	−2.95084	−	5.11100i	−0.529986	−	0.917963i	0.469402	−	0.882985i	$-0.344469\pi$
$32$		0			0
$33$	−1.50000	−	0.264490i	−0.261116	−	0.0460419i
$34$		0			0
$35$	−1.70574	−	4.68647i	−0.288322	−	0.792159i
$36$		0			0
$37$		−	3.67301i		−	0.603840i	−0.953333	−	0.301920i	$-0.902373\pi$
$37$		−	3.67301i		−	0.603840i	0.953333	−	0.301920i	$-0.0976275\pi$
$38$		0			0
$39$			0.839100i			0.134363i
$40$		0			0
$41$	0.788333	+	2.16593i	0.123117	+	0.338261i	0.985905	−	0.167304i	$-0.0535062\pi$
$41$	0.788333	+	2.16593i	0.123117	+	0.338261i	−0.862788	+	0.505565i	$0.831284\pi$
$42$		0			0
$43$	2.89053	+	0.509678i	0.440802	+	0.0777252i	0.389644	−	0.920965i	$-0.372598\pi$
$43$	2.89053	+	0.509678i	0.440802	+	0.0777252i	0.0511572	+	0.998691i	$0.483709\pi$
$44$		0			0
$45$	0.673648	+	1.16679i	0.100422	+	0.173935i
$46$		0			0
$47$	−5.63176	−	6.71167i	−0.821476	−	0.978998i	0.178511	−	0.983938i	$-0.442872\pi$
$47$	−5.63176	−	6.71167i	−0.821476	−	0.978998i	−0.999988	+	0.00494030i	$0.998427\pi$
$48$		0			0
$49$	3.35117	−	5.80439i	0.478738	−	0.829199i
$50$		0			0
$51$	−0.152704	−	0.0555796i	−0.0213828	−	0.00778270i
$52$		0			0
$53$	−6.69846	+	1.18112i	−0.920105	+	0.162239i	−0.613588	−	0.789626i	$-0.710275\pi$
$53$	−6.69846	+	1.18112i	−0.920105	+	0.162239i	−0.306516	+	0.951865i	$0.599163\pi$
$54$		0			0
$55$	−1.31908	+	1.57202i	−0.177864	+	0.211971i
$56$		0			0
$57$	4.07398	−	1.55007i	0.539612	−	0.205311i
$58$		0			0
$59$	−9.06805	−	7.60900i	−1.18056	−	0.990607i	−0.999975	−	0.00704735i	$-0.997757\pi$
$59$	−9.06805	−	7.60900i	−1.18056	−	0.990607i	−0.180584	−	0.983560i	$-0.557799\pi$
$60$		0			0
$61$	0.741230	+	4.20372i	0.0949047	+	0.538231i	0.994777	+	0.102077i	$0.0325488\pi$
$61$	0.741230	+	4.20372i	0.0949047	+	0.538231i	−0.899872	+	0.436154i	$0.856340\pi$
$62$		0			0
$63$	−1.26604	+	3.47843i	−0.159507	+	0.438241i
$64$		0			0
$65$	0.979055	+	0.565258i	0.121437	+	0.0701116i
$66$		0			0
$67$	−8.57398	+	7.19442i	−1.04748	+	0.878939i	−0.992826	−	0.119567i	$-0.961849\pi$
$67$	−8.57398	+	7.19442i	−1.04748	+	0.878939i	−0.0546520	+	0.998505i	$0.517405\pi$
$68$		0			0
$69$	1.63429	−	0.943555i	0.196745	−	0.113591i
$70$		0			0
$71$	−1.29426	+	7.34013i	−0.153601	+	0.871113i	0.806453	+	0.591298i	$0.201384\pi$
$71$	−1.29426	+	7.34013i	−0.153601	+	0.871113i	−0.960054	+	0.279815i	$0.909727\pi$
$72$		0			0
$73$	6.53849	−	2.37981i	0.765272	−	0.278536i	0.0702545	−	0.997529i	$-0.477619\pi$
$73$	6.53849	−	2.37981i	0.765272	−	0.278536i	0.695017	+	0.718993i	$0.255397\pi$
$74$		0			0
$75$	−3.18479			−0.367748
$76$		0			0
$77$	−5.63816			−0.642527
$78$		0			0
$79$	12.9893	−	4.72773i	1.46141	−	0.531911i	0.515659	−	0.856794i	$-0.327547\pi$
$79$	12.9893	−	4.72773i	1.46141	−	0.531911i	0.945754	+	0.324883i	$0.105325\pi$
$80$		0			0
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$		0			0
$83$	−0.134285	+	0.0775297i	−0.0147397	+	0.00850999i	−0.507352	−	0.861739i	$-0.669376\pi$
$83$	−0.134285	+	0.0775297i	−0.0147397	+	0.00850999i	0.492612	+	0.870249i	$0.336042\pi$
$84$		0			0
$85$	−0.167718	+	0.140732i	−0.0181916	+	0.0152646i
$86$		0			0
$87$	9.09627	+	5.25173i	0.975222	+	0.563045i
$88$		0			0
$89$	1.92989	−	5.30234i	0.204568	−	0.562046i	−0.794403	−	0.607391i	$-0.792216\pi$
$89$	1.92989	−	5.30234i	0.204568	−	0.562046i	0.998971	+	0.0453443i	$0.0144385\pi$
$90$		0			0
$91$	0.539363	+	3.05888i	0.0565406	+	0.320658i
$92$		0			0
$93$	4.52094	+	3.79352i	0.468800	+	0.393370i
$94$		0			0
$95$	0.935822	−	5.79769i	0.0960133	−	0.594830i
$96$		0			0
$97$	−5.19846	+	6.19529i	−0.527824	+	0.629036i	−0.962412	−	0.271593i	$-0.912449\pi$
$97$	−5.19846	+	6.19529i	−0.527824	+	0.629036i	0.434588	+	0.900629i	$0.356894\pi$
$98$		0			0
$99$	1.50000	−	0.264490i	0.150756	−	0.0265823i
$100$		0			0
$101$	−16.4153	−	5.97470i	−1.63339	−	0.594505i	−0.647523	−	0.762046i	$-0.724195\pi$
$101$	−16.4153	−	5.97470i	−1.63339	−	0.594505i	−0.985865	+	0.167542i	$0.946417\pi$
$102$		0			0
$103$	−3.09240	+	5.35619i	−0.304703	+	0.527761i	−0.977195	−	0.212343i	$-0.931890\pi$
$103$	−3.09240	+	5.35619i	−0.304703	+	0.527761i	0.672492	+	0.740104i	$0.265224\pi$
$104$		0			0
$105$	3.20574	+	3.82045i	0.312848	+	0.372838i
$106$		0			0
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	0.683793	−	0.729676i	$-0.260329\pi$
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	−0.973814	+	0.227345i	$0.926996\pi$
$108$		0			0
$109$	−7.19459	−	1.26860i	−0.689117	−	0.121510i	−0.181885	−	0.983320i	$-0.558220\pi$
$109$	−7.19459	−	1.26860i	−0.689117	−	0.121510i	−0.507232	+	0.861810i	$0.669331\pi$
$110$		0			0
$111$	1.25624	+	3.45150i	0.119237	+	0.327602i
$112$		0			0
$113$		−	1.51319i		−	0.142349i	−0.997464	−	0.0711744i	$-0.977325\pi$
$113$		−	1.51319i		−	0.142349i	0.997464	−	0.0711744i	$-0.0226747\pi$
$114$		0			0
$115$		−	2.54250i		−	0.237089i
$116$		0			0
$117$	−0.286989	−	0.788496i	−0.0265321	−	0.0728965i
$118$		0			0
$119$	−0.592396	−	0.104455i	−0.0543049	−	0.00957541i
$120$		0			0
$121$	−4.34002	−	7.51714i	−0.394547	−	0.683376i
$122$		0			0
$123$	−1.48158	−	1.76568i	−0.133590	−	0.159206i
$124$		0			0
$125$	−5.51367	+	9.54996i	−0.493158	+	0.854174i
$126$		0			0
$127$	11.9547	+	4.35116i	1.06081	+	0.386103i	0.812732	−	0.582638i	$-0.197979\pi$
$127$	11.9547	+	4.35116i	1.06081	+	0.386103i	0.248077	+	0.968740i	$0.420202\pi$
$128$		0			0
$129$	−2.89053	+	0.509678i	−0.254497	+	0.0448747i
$130$		0			0
$131$	5.89053	−	7.02006i	0.514658	−	0.613345i	−0.444651	−	0.895704i	$-0.646672\pi$
$131$	5.89053	−	7.02006i	0.514658	−	0.613345i	0.959309	+	0.282358i	$0.0911167\pi$
$132$		0			0
$133$	13.8550	−	8.26936i	1.20138	−	0.717044i
$134$		0			0
$135$	−1.03209	−	0.866025i	−0.0888281	−	0.0745356i
$136$		0			0
$137$	2.47906	+	14.0594i	0.211800	+	1.20118i	0.886374	+	0.462970i	$0.153216\pi$
$137$	2.47906	+	14.0594i	0.211800	+	1.20118i	−0.674574	+	0.738207i	$0.735673\pi$
$138$		0			0
$139$	0.137689	−	0.378297i	0.0116786	−	0.0320867i	−0.933716	−	0.358014i	$-0.883454\pi$
$139$	0.137689	−	0.378297i	0.0116786	−	0.0320867i	0.945395	+	0.325927i	$0.105676\pi$
$140$		0			0
$141$	7.58765	+	4.38073i	0.638995	+	0.368924i
$142$		0			0
$143$	0.979055	−	0.821525i	0.0818727	−	0.0686994i
$144$		0			0
$145$	12.2554	−	7.07564i	1.01775	−	0.587600i
$146$		0			0
$147$	−1.16385	+	6.60051i	−0.0959926	+	0.544401i
$148$		0			0
$149$	−10.4966	+	3.82045i	−0.859915	+	0.312983i	−0.734076	−	0.679067i	$-0.762384\pi$
$149$	−10.4966	+	3.82045i	−0.859915	+	0.312983i	−0.125839	+	0.992051i	$0.540162\pi$
$150$		0			0
$151$	7.18984			0.585101			0.292551	−	0.956250i	$-0.405496\pi$
$151$	7.18984			0.585101			0.292551	+	0.956250i	$0.405496\pi$
$152$		0			0
$153$	0.162504			0.0131377
$154$		0			0
$155$	7.47178	−	2.71951i	0.600148	−	0.218436i
$156$		0			0
$157$	−2.37686	+	13.4798i	−0.189694	+	1.07581i	0.730081	+	0.683361i	$0.239482\pi$
$157$	−2.37686	+	13.4798i	−0.189694	+	1.07581i	−0.919775	+	0.392447i	$0.871629\pi$
$158$		0			0
$159$	5.89053	−	3.40090i	0.467149	−	0.269709i
$160$		0			0
$161$	5.35117	−	4.49016i	0.421731	−	0.353874i
$162$		0			0
$163$	13.8516	+	7.99724i	1.08494	+	0.626393i	0.932226	−	0.361877i	$-0.117864\pi$
$163$	13.8516	+	7.99724i	1.08494	+	0.626393i	0.152718	+	0.988270i	$0.451197\pi$
$164$		0			0
$165$	0.701867	−	1.92836i	0.0546402	−	0.150123i
$166$		0			0
$167$	0.467911	+	2.65366i	0.0362080	+	0.205346i	0.997545	−	0.0700288i	$-0.0223091\pi$
$167$	0.467911	+	2.65366i	0.0362080	+	0.205346i	−0.961337	+	0.275375i	$0.911198\pi$
$168$		0			0
$169$	9.41921	+	7.90366i	0.724555	+	0.607974i
$170$		0			0
$171$	−3.29813	+	2.84997i	−0.252215	+	0.217942i
$172$		0			0
$173$	−12.8478	+	15.3114i	−0.976797	+	1.16410i	0.00963834	+	0.999954i	$0.496932\pi$
$173$	−12.8478	+	15.3114i	−0.976797	+	1.16410i	−0.986436	+	0.164148i	$0.947512\pi$
$174$		0			0
$175$	−11.6099	+	2.04715i	−0.877629	+	0.154750i
$176$		0			0
$177$	11.1236	+	4.04866i	0.836102	+	0.304316i
$178$		0			0
$179$	2.06758	−	3.58116i	0.154538	−	0.267668i	−0.778353	−	0.627827i	$-0.783944\pi$
$179$	2.06758	−	3.58116i	0.154538	−	0.267668i	0.932891	+	0.360159i	$0.117278\pi$
$180$		0			0
$181$	−0.816552	−	0.973128i	−0.0606938	−	0.0723321i	0.734843	−	0.678237i	$-0.237256\pi$
$181$	−0.816552	−	0.973128i	−0.0606938	−	0.0723321i	−0.795537	+	0.605905i	$0.792811\pi$
$182$		0			0
$183$	−2.13429	−	3.69669i	−0.157771	−	0.273267i
$184$		0			0
$185$	4.87346	+	0.859322i	0.358304	+	0.0631786i
$186$		0			0
$187$	0.0846555	+	0.232589i	0.00619062	+	0.0170086i
$188$		0			0
$189$		−	3.70167i		−	0.269257i
$190$		0			0
$191$			5.95275i			0.430726i	0.976534	+	0.215363i	$0.0690934\pi$
$191$			5.95275i			0.430726i	−0.976534	+	0.215363i	$0.930907\pi$
$192$		0			0
$193$	3.23396	+	8.88522i	0.232785	+	0.639572i	0.999998	−	0.00182013i	$-0.000579365\pi$
$193$	3.23396	+	8.88522i	0.232785	+	0.639572i	−0.767213	+	0.641392i	$0.778357\pi$
$194$		0			0
$195$	−1.11334	−	0.196312i	−0.0797280	−	0.0140582i
$196$		0			0
$197$	6.70708	+	11.6170i	0.477860	+	0.827677i	0.999678	−	0.0253794i	$-0.00807938\pi$
$197$	6.70708	+	11.6170i	0.477860	+	0.827677i	−0.521818	+	0.853057i	$0.674746\pi$
$198$		0			0
$199$	0.370462	+	0.441500i	0.0262614	+	0.0312971i	0.779015	−	0.627005i	$-0.215719\pi$
$199$	0.370462	+	0.441500i	0.0262614	+	0.0312971i	−0.752754	+	0.658302i	$0.771275\pi$
$200$		0			0
$201$	5.59627	−	9.69302i	0.394730	−	0.683693i
$202$		0			0
$203$	36.5355	+	13.2979i	2.56429	+	0.933326i
$204$		0			0
$205$	−3.05825	+	0.539252i	−0.213597	+	0.0376630i
$206$		0			0
$207$	−1.21301	+	1.44561i	−0.0843101	+	0.100477i
$208$		0			0
$209$	−5.79726	−	3.23589i	−0.401005	−	0.223831i
$210$		0			0
$211$	−5.79292	−	4.86084i	−0.398801	−	0.334634i	0.421229	−	0.906954i	$-0.361599\pi$
$211$	−5.79292	−	4.86084i	−0.398801	−	0.334634i	−0.820030	+	0.572321i	$0.806043\pi$
$212$		0			0
$213$	−1.29426	−	7.34013i	−0.0886814	−	0.502937i
$214$		0			0
$215$	−1.35251	+	3.71599i	−0.0922405	+	0.253429i
$216$		0			0
$217$	18.9192	+	10.9230i	1.28432	+	0.741502i
$218$		0			0
$219$	−5.33022	+	4.47259i	−0.360183	+	0.302229i
$220$		0			0
$221$	0.118089	−	0.0681784i	0.00794349	−	0.00458618i
$222$		0			0
$223$	1.09121	−	6.18858i	0.0730731	−	0.414418i	−0.926225	−	0.376970i	$-0.876966\pi$
$223$	1.09121	−	6.18858i	0.0730731	−	0.414418i	0.999299	−	0.0374482i	$-0.0119229\pi$
$224$		0			0
$225$	2.99273	−	1.08926i	0.199515	−	0.0726175i
$226$		0			0
$227$	13.1480			0.872660			0.436330	−	0.899787i	$-0.356278\pi$
$227$	13.1480			0.872660			0.436330	+	0.899787i	$0.356278\pi$
$228$		0			0
$229$	−19.3851			−1.28100			−0.640501	−	0.767958i	$-0.721273\pi$
$229$	−19.3851			−1.28100			−0.640501	+	0.767958i	$0.721273\pi$
$230$		0			0
$231$	5.29813	−	1.92836i	0.348592	−	0.126877i
$232$		0			0
$233$	−4.05169	+	22.9783i	−0.265435	+	1.50536i	0.502359	+	0.864659i	$0.332466\pi$
$233$	−4.05169	+	22.9783i	−0.265435	+	1.50536i	−0.767794	+	0.640697i	$0.778645\pi$
$234$		0			0
$235$	10.2228	−	5.90214i	0.666863	−	0.385013i
$236$		0			0
$237$	−10.5890	+	8.88522i	−0.687829	+	0.577157i
$238$		0			0
$239$	−5.13041	−	2.96205i	−0.331859	−	0.191599i	0.324807	−	0.945780i	$-0.394701\pi$
$239$	−5.13041	−	2.96205i	−0.331859	−	0.191599i	−0.656666	+	0.754181i	$0.728034\pi$
$240$		0			0
$241$	−3.39187	+	9.31910i	−0.218490	+	0.600296i	−0.999713	−	0.0239560i	$-0.992374\pi$
$241$	−3.39187	+	9.31910i	−0.218490	+	0.600296i	0.781223	+	0.624252i	$0.214596\pi$
$242$		0			0
$243$	0.173648	+	0.984808i	0.0111395	+	0.0631754i
$244$		0			0
$245$	6.91740	+	5.80439i	0.441937	+	0.370829i
$246$		0			0
$247$	−1.20099	+	3.45475i	−0.0764171	+	0.219821i
$248$		0			0
$249$	0.0996702	−	0.118782i	0.00631634	−	0.00752753i
$250$		0			0
$251$	12.5043	−	2.20485i	0.789267	−	0.139169i	0.235537	−	0.971865i	$-0.424315\pi$
$251$	12.5043	−	2.20485i	0.789267	−	0.139169i	0.553730	+	0.832696i	$0.313204\pi$
$252$		0			0
$253$	−2.70099	−	0.983080i	−0.169810	−	0.0618057i
$254$		0			0
$255$	0.109470	−	0.189608i	0.00685530	−	0.0118737i
$256$		0			0
$257$	−19.1652	−	22.8402i	−1.19549	−	1.42473i	−0.879453	−	0.475985i	$-0.842092\pi$
$257$	−19.1652	−	22.8402i	−1.19549	−	1.42473i	−0.316039	−	0.948746i	$-0.602353\pi$
$258$		0			0
$259$	6.79813	+	11.7747i	0.422415	+	0.731645i
$260$		0			0
$261$	−10.3439	−	1.82391i	−0.640271	−	0.112897i
$262$		0			0
$263$	−4.50980	−	12.3906i	−0.278086	−	0.764036i	−0.997579	−	0.0695361i	$-0.977848\pi$
$263$	−4.50980	−	12.3906i	−0.278086	−	0.764036i	0.719493	−	0.694499i	$-0.244374\pi$
$264$		0			0
$265$		−	9.16404i		−	0.562942i
$266$		0			0
$267$			5.64263i			0.345323i
$268$		0			0
$269$	−6.37464	−	17.5142i	−0.388669	−	1.06786i	−0.967601	−	0.252483i	$-0.918753\pi$
$269$	−6.37464	−	17.5142i	−0.388669	−	1.06786i	0.578933	−	0.815375i	$-0.303469\pi$
$270$		0			0
$271$	7.01707	+	1.23730i	0.426257	+	0.0751606i	0.382661	−	0.923889i	$-0.375008\pi$
$271$	7.01707	+	1.23730i	0.426257	+	0.0751606i	0.0435955	+	0.999049i	$0.486119\pi$
$272$		0			0
$273$	−1.55303	−	2.68993i	−0.0939939	−	0.162802i
$274$		0			0
$275$	3.11809	+	3.71599i	0.188028	+	0.224083i
$276$		0			0
$277$	5.00640	−	8.67133i	0.300805	−	0.521010i	−0.675513	−	0.737348i	$-0.736078\pi$
$277$	5.00640	−	8.67133i	0.300805	−	0.521010i	0.976319	+	0.216338i	$0.0694113\pi$
$278$		0			0
$279$	−5.54576	−	2.01849i	−0.332016	−	0.120844i
$280$		0			0
$281$	−19.5981	+	3.45567i	−1.16912	+	0.206148i	−0.724309	−	0.689475i	$-0.757841\pi$
$281$	−19.5981	+	3.45567i	−1.16912	+	0.206148i	−0.444814	+	0.895623i	$0.646730\pi$
$282$		0			0
$283$	−16.1370	+	19.2313i	−0.959244	+	1.14318i	0.0303860	+	0.999538i	$0.490326\pi$
$283$	−16.1370	+	19.2313i	−0.959244	+	1.14318i	−0.989629	+	0.143644i	$0.954118\pi$
$284$		0			0
$285$	1.10354	+	5.76811i	0.0653681	+	0.341674i
$286$		0			0
$287$	−6.53596	−	5.48432i	−0.385805	−	0.323729i
$288$		0			0
$289$	−2.94743	−	16.7157i	−0.173378	−	0.983278i
$290$		0			0
$291$	2.76604	−	7.59964i	0.162148	−	0.445499i
$292$		0			0
$293$	0.512326	+	0.295792i	0.0299304	+	0.0172803i	0.514891	−	0.857256i	$-0.327833\pi$
$293$	0.512326	+	0.295792i	0.0299304	+	0.0172803i	−0.484960	+	0.874536i	$0.661166\pi$
$294$		0			0
$295$	12.2173	−	10.2516i	0.711322	−	0.596870i
$296$		0			0
$297$	−1.31908	+	0.761570i	−0.0765407	+	0.0441908i
$298$		0			0
$299$	−0.274967	+	1.55942i	−0.0159018	+	0.0901834i
$300$		0			0
$301$	−10.2096	+	3.71599i	−0.588472	+	0.214186i
$302$		0			0
$303$	17.4688			1.00356
$304$		0			0
$305$	−5.75103			−0.329303
$306$		0			0
$307$	9.20961	−	3.35202i	0.525620	−	0.191310i	−0.0655615	−	0.997849i	$-0.520884\pi$
$307$	9.20961	−	3.35202i	0.525620	−	0.191310i	0.591182	+	0.806538i	$0.298662\pi$
$308$		0			0
$309$	1.07398	−	6.09083i	0.0610965	−	0.346495i
$310$		0			0
$311$	−9.34864	+	5.39744i	−0.530113	+	0.306061i	−0.741062	−	0.671436i	$-0.765678\pi$
$311$	−9.34864	+	5.39744i	−0.530113	+	0.306061i	0.210950	+	0.977497i	$0.432344\pi$
$312$		0			0
$313$	−17.7285	+	14.8760i	−1.00207	+	0.840840i	−0.987270	−	0.159051i	$-0.949157\pi$
$313$	−17.7285	+	14.8760i	−1.00207	+	0.840840i	−0.0148032	+	0.999890i	$0.504712\pi$
$314$		0			0
$315$	−4.31908	−	2.49362i	−0.243352	−	0.140500i
$316$		0			0
$317$	8.54829	−	23.4862i	0.480120	−	1.31912i	−0.429272	−	0.903175i	$-0.641230\pi$
$317$	8.54829	−	23.4862i	0.480120	−	1.31912i	0.909391	−	0.415942i	$-0.136548\pi$
$318$		0			0
$319$	−2.77807	−	15.7552i	−0.155542	−	0.882122i
$320$		0			0
$321$	4.59627	+	3.85673i	0.256539	+	0.215261i
$322$		0			0
$323$	−0.549163	−	0.447395i	−0.0305562	−	0.0248937i
$324$		0			0
$325$	1.71776	−	2.04715i	0.0952841	−	0.113555i
$326$		0			0
$327$	7.19459	−	1.26860i	0.397862	−	0.0701538i
$328$		0			0
$329$	30.4761	+	11.0924i	1.68020	+	0.611544i
$330$		0			0
$331$	3.48680	−	6.03931i	0.191652	−	0.331950i	−0.754146	−	0.656707i	$-0.771949\pi$
$331$	3.48680	−	6.03931i	0.191652	−	0.331950i	0.945798	+	0.324756i	$0.105282\pi$
$332$		0			0
$333$	−2.36097	−	2.81369i	−0.129380	−	0.154189i
$334$		0			0
$335$	−7.53983	−	13.0594i	−0.411945	−	0.713509i
$336$		0			0
$337$	10.6395	+	1.87603i	0.579570	+	0.102194i	0.455745	−	0.890110i	$-0.349373\pi$
$337$	10.6395	+	1.87603i	0.579570	+	0.102194i	0.123825	+	0.992304i	$0.460484\pi$
$338$		0			0
$339$	0.517541	+	1.42193i	0.0281090	+	0.0772288i
$340$		0			0
$341$		−	8.98908i		−	0.486786i
$342$		0			0
$343$		−	1.10186i		−	0.0594950i
$344$		0			0
$345$	0.869585	+	2.38917i	0.0468169	+	0.128628i
$346$		0			0
$347$	−22.9461	−	4.04601i	−1.23181	−	0.217201i	−0.480408	−	0.877045i	$-0.659511\pi$
$347$	−22.9461	−	4.04601i	−1.23181	−	0.217201i	−0.751403	+	0.659844i	$0.770622\pi$
$348$		0			0
$349$	9.64590	+	16.7072i	0.516333	+	0.894315i	0.999820	+	0.0189635i	$0.00603665\pi$
$349$	9.64590	+	16.7072i	0.516333	+	0.894315i	−0.483487	+	0.875351i	$0.660630\pi$
$350$		0			0
$351$	0.539363	+	0.642788i	0.0287891	+	0.0343095i
$352$		0			0
$353$	13.4119	−	23.2302i	0.713846	−	1.23642i	−0.249558	−	0.968360i	$-0.580285\pi$
$353$	13.4119	−	23.2302i	0.713846	−	1.23642i	0.963403	−	0.268057i	$-0.0863815\pi$
$354$		0			0
$355$	−9.43629	−	3.43453i	−0.500826	−	0.182286i
$356$		0			0
$357$	0.592396	−	0.104455i	0.0313529	−	0.00552837i
$358$		0			0
$359$	−19.0783	+	22.7367i	−1.00691	+	1.19999i	−0.0271935	+	0.999630i	$0.508657\pi$
$359$	−19.0783	+	22.7367i	−1.00691	+	1.19999i	−0.979721	+	0.200364i	$0.935787\pi$
$360$		0			0
$361$	18.9920	−	0.550931i	0.999580	−	0.0289964i
$362$		0			0
$363$	6.64930	+	5.57943i	0.348998	+	0.292844i
$364$		0			0
$365$	1.62789	+	9.23222i	0.0852076	+	0.483236i
$366$		0			0
$367$	−8.13223	+	22.3431i	−0.424499	+	1.16630i	0.524607	+	0.851344i	$0.324212\pi$
$367$	−8.13223	+	22.3431i	−0.424499	+	1.16630i	−0.949106	+	0.314956i	$0.898010\pi$
$368$		0			0
$369$	1.99613	+	1.15247i	0.103914	+	0.0599950i
$370$		0			0
$371$	19.2875	−	16.1841i	1.00135	−	0.840236i
$372$		0			0
$373$	−29.4192	+	16.9852i	−1.52327	+	0.879460i	−0.523648	+	0.851935i	$0.675429\pi$
$373$	−29.4192	+	16.9852i	−1.52327	+	0.879460i	−0.999621	+	0.0275252i	$0.991237\pi$
$374$		0			0
$375$	1.91488	−	10.8598i	0.0988839	−	0.560798i
$376$		0			0
$377$	−8.28194	+	3.01438i	−0.426541	+	0.155248i
$378$		0			0
$379$	−23.5503			−1.20970			−0.604848	−	0.796341i	$-0.706766\pi$
$379$	−23.5503			−1.20970			−0.604848	+	0.796341i	$0.706766\pi$
$380$		0			0
$381$	−12.7219			−0.651764
$382$		0			0
$383$	−34.7422	+	12.6451i	−1.77524	+	0.646135i	−0.775348	+	0.631534i	$0.782426\pi$
$383$	−34.7422	+	12.6451i	−1.77524	+	0.646135i	−0.999893	+	0.0146011i	$0.995352\pi$
$384$		0			0
$385$	1.31908	−	7.48086i	0.0672264	−	0.381260i
$386$		0			0
$387$	2.54189	−	1.46756i	0.129211	−	0.0746003i
$388$		0			0
$389$	24.7861	−	20.7980i	1.25671	−	1.05450i	0.260681	−	0.965425i	$-0.416053\pi$
$389$	24.7861	−	20.7980i	1.25671	−	1.05450i	0.996025	−	0.0890763i	$-0.0283915\pi$
$390$		0			0
$391$	−0.265578	−	0.153331i	−0.0134308	−	0.00775430i
$392$		0			0
$393$	−3.13429	+	8.61138i	−0.158104	+	0.434387i
$394$		0			0
$395$	3.23396	+	18.3407i	0.162718	+	0.922819i
$396$		0			0
$397$	6.28106	+	5.27043i	0.315237	+	0.264516i	0.786653	−	0.617396i	$-0.211812\pi$
$397$	6.28106	+	5.27043i	0.315237	+	0.264516i	−0.471415	+	0.881911i	$0.656257\pi$
$398$		0			0
$399$	−10.1912	+	12.5094i	−0.510198	+	0.626251i
$400$		0			0
$401$	−11.9500	+	14.2414i	−0.596753	+	0.711182i	−0.976889	−	0.213749i	$-0.931433\pi$
$401$	−11.9500	+	14.2414i	−0.596753	+	0.711182i	0.380136	+	0.924931i	$0.375877\pi$
$402$		0			0
$403$	−4.87686	+	0.859922i	−0.242934	+	0.0428358i
$404$		0			0
$405$	1.26604	+	0.460802i	0.0629103	+	0.0228975i
$406$		0			0
$407$	2.79726	−	4.84499i	0.138655	−	0.240157i
$408$		0			0
$409$	0.922618	+	1.09953i	0.0456205	+	0.0543685i	0.788372	−	0.615199i	$-0.210924\pi$
$409$	0.922618	+	1.09953i	0.0456205	+	0.0543685i	−0.742752	+	0.669567i	$0.766480\pi$
$410$		0			0
$411$	−7.13816	−	12.3636i	−0.352099	−	0.609854i
$412$		0			0
$413$	43.1528	+	7.60900i	2.12341	+	0.374414i
$414$		0			0
$415$	−0.0714517	−	0.196312i	−0.00350743	−	0.00963658i
$416$		0			0
$417$			0.402575i			0.0197142i
$418$		0			0
$419$		−	35.0031i		−	1.71002i	−0.518615	−	0.855008i	$-0.673552\pi$
$419$		−	35.0031i		−	1.71002i	0.518615	−	0.855008i	$-0.326448\pi$
$420$		0			0
$421$	−11.1316	−	30.5838i	−0.542521	−	1.49056i	−0.843604	−	0.536966i	$-0.819570\pi$
$421$	−11.1316	−	30.5838i	−0.542521	−	1.49056i	0.301083	−	0.953598i	$-0.402652\pi$
$422$		0			0
$423$	−8.62836	−	1.52141i	−0.419525	−	0.0739736i
$424$		0			0
$425$	0.258770	+	0.448204i	0.0125522	+	0.0217411i
$426$		0			0
$427$	−10.1566	−	12.1041i	−0.491511	−	0.585760i
$428$		0			0
$429$	−0.639033	+	1.10684i	−0.0308528	+	0.0534386i
$430$		0			0
$431$	21.7297	+	7.90895i	1.04668	+	0.380961i	0.807409	−	0.589992i	$-0.200869\pi$
$431$	21.7297	+	7.90895i	1.04668	+	0.380961i	0.239272	+	0.970953i	$0.423091\pi$
$432$		0			0
$433$	11.5869	−	2.04309i	0.556832	−	0.0981846i	0.111852	−	0.993725i	$-0.464322\pi$
$433$	11.5869	−	2.04309i	0.556832	−	0.0981846i	0.444980	+	0.895540i	$0.353211\pi$
$434$		0			0
$435$	−9.09627	+	10.8405i	−0.436133	+	0.519763i
$436$		0			0
$437$	8.07919	−	1.54569i	0.386480	−	0.0739404i
$438$		0			0
$439$	−17.2875	−	14.5059i	−0.825085	−	0.692329i	0.129072	−	0.991635i	$-0.458800\pi$
$439$	−17.2875	−	14.5059i	−0.825085	−	0.692329i	−0.954157	+	0.299307i	$0.903245\pi$
$440$		0			0
$441$	−1.16385	−	6.60051i	−0.0554213	−	0.314310i
$442$		0			0
$443$	−7.23601	+	19.8808i	−0.343793	+	0.944565i	0.640490	+	0.767967i	$0.278731\pi$
$443$	−7.23601	+	19.8808i	−0.343793	+	0.944565i	−0.984283	+	0.176598i	$0.943491\pi$
$444$		0			0
$445$	6.58378	+	3.80115i	0.312101	+	0.180192i
$446$		0			0
$447$	8.55690	−	7.18009i	0.404728	−	0.339607i
$448$		0			0
$449$	31.2212	−	18.0256i	1.47342	−	0.850680i	0.473868	−	0.880596i	$-0.342857\pi$
$449$	31.2212	−	18.0256i	1.47342	−	0.850680i	0.999552	+	0.0299162i	$0.00952405\pi$
$450$		0			0
$451$	−0.609633	+	3.45740i	−0.0287065	+	0.162803i
$452$		0			0
$453$	−6.75624	+	2.45907i	−0.317436	+	0.115537i
$454$		0			0
$455$	−4.18479			−0.196186
$456$		0			0
$457$	−39.1908			−1.83327			−0.916634	−	0.399728i	$-0.869104\pi$
$457$	−39.1908			−1.83327			−0.916634	+	0.399728i	$0.869104\pi$
$458$		0			0
$459$	−0.152704	+	0.0555796i	−0.00712760	+	0.00259423i
$460$		0			0
$461$	−5.37639	+	30.4910i	−0.250404	+	1.42011i	0.557198	+	0.830380i	$0.311877\pi$
$461$	−5.37639	+	30.4910i	−0.250404	+	1.42011i	−0.807601	+	0.589729i	$0.799235\pi$
$462$		0			0
$463$	32.8919	−	18.9902i	1.52862	−	0.882548i	0.529197	−	0.848499i	$-0.322493\pi$
$463$	32.8919	−	18.9902i	1.52862	−	0.882548i	0.999420	−	0.0340491i	$-0.0108403\pi$
$464$		0			0
$465$	−6.09105	+	5.11100i	−0.282466	+	0.237017i
$466$		0			0
$467$	−27.5077	−	15.8816i	−1.27291	−	0.734913i	−0.297372	−	0.954762i	$-0.596110\pi$
$467$	−27.5077	−	15.8816i	−1.27291	−	0.734913i	−0.975534	+	0.219849i	$0.929444\pi$
$468$		0			0
$469$	14.1702	−	38.9324i	0.654321	−	1.79773i
$470$		0			0
$471$	−2.37686	−	13.4798i	−0.109520	−	0.621118i
$472$		0			0
$473$	3.42468	+	2.87365i	0.157467	+	0.132130i
$474$		0			0
$475$	−13.1125	−	4.55834i	−0.601641	−	0.209151i
$476$		0			0
$477$	−4.37211	+	5.21048i	−0.200185	+	0.238571i
$478$		0			0
$479$	−38.4707	+	6.78341i	−1.75777	+	0.309942i	−0.957228	−	0.289335i	$-0.906566\pi$
$479$	−38.4707	+	6.78341i	−1.75777	+	0.309942i	−0.800541	+	0.599278i	$0.795455\pi$
$480$		0			0
$481$	−2.89615	−	1.05411i	−0.132053	−	0.0480635i
$482$		0			0
$483$	−3.49273	+	6.04958i	−0.158925	+	0.275265i
$484$		0			0
$485$	−7.00387	−	8.34689i	−0.318029	−	0.379013i
$486$		0			0
$487$	10.4697	+	18.1341i	0.474428	+	0.821734i	0.999571	−	0.0292800i	$-0.00932145\pi$
$487$	10.4697	+	18.1341i	0.474428	+	0.821734i	−0.525143	+	0.851014i	$0.675988\pi$
$488$		0			0
$489$	−15.7515	−	2.77741i	−0.712307	−	0.125599i
$490$		0			0
$491$	13.7144	+	37.6799i	0.618920	+	1.70047i	0.709614	+	0.704590i	$0.248869\pi$
$491$	13.7144	+	37.6799i	0.618920	+	1.70047i	−0.0906940	+	0.995879i	$0.528909\pi$
$492$		0			0
$493$		−	1.70685i		−	0.0768728i
$494$		0			0
$495$			2.05212i			0.0922360i
$496$		0			0
$497$	−9.43629	−	25.9260i	−0.423275	−	1.16294i
$498$		0			0
$499$	−24.9873	−	4.40593i	−1.11858	−	0.197236i	−0.416365	−	0.909198i	$-0.636696\pi$
$499$	−24.9873	−	4.40593i	−1.11858	−	0.197236i	−0.702219	+	0.711961i	$0.747807\pi$
$500$		0			0
$501$	−1.34730	−	2.33359i	−0.0601928	−	0.104257i
$502$		0			0
$503$	1.78359	+	2.12559i	0.0795261	+	0.0947756i	0.804340	−	0.594169i	$-0.202519\pi$
$503$	1.78359	+	2.12559i	0.0795261	+	0.0947756i	−0.724814	+	0.688944i	$0.758074\pi$
$504$		0			0
$505$	11.7679	−	20.3825i	0.523663	−	0.907010i
$506$		0			0
$507$	−11.5544	−	4.20545i	−0.513148	−	0.186771i
$508$		0			0
$509$	24.9538	−	4.40003i	1.10606	−	0.195028i	0.409347	−	0.912379i	$-0.365757\pi$
$509$	24.9538	−	4.40003i	1.10606	−	0.195028i	0.696712	+	0.717351i	$0.254645\pi$
$510$		0			0
$511$	−16.5560	+	19.7307i	−0.732395	+	0.872835i
$512$		0			0
$513$	2.12449	−	3.80612i	0.0937983	−	0.168044i
$514$		0			0
$515$	−6.38326	−	5.35619i	−0.281280	−	0.236022i
$516$		0			0
$517$	−2.31732	−	13.1422i	−0.101916	−	0.577993i
$518$		0			0
$519$	6.83615	−	18.7822i	0.300074	−	0.824446i
$520$		0			0
$521$	4.52078	+	2.61007i	0.198059	+	0.114349i	0.595750	−	0.803170i	$-0.296855\pi$
$521$	4.52078	+	2.61007i	0.198059	+	0.114349i	−0.397691	+	0.917520i	$0.630188\pi$
$522$		0			0
$523$	−0.657289	+	0.551531i	−0.0287413	+	0.0241168i	−0.657045	−	0.753851i	$-0.728194\pi$
$523$	−0.657289	+	0.551531i	−0.0287413	+	0.0241168i	0.628304	+	0.777968i	$0.283749\pi$
$524$		0			0
$525$	10.2096	−	5.89452i	0.445584	−	0.257258i
$526$		0			0
$527$	0.166536	−	0.944475i	0.00725444	−	0.0411420i
$528$		0			0
$529$	−18.2665	+	6.64847i	−0.794196	+	0.289064i
$530$		0			0
$531$	−11.8375			−0.513704
$532$		0			0
$533$	1.93407			0.0837738
$534$		0			0
$535$	7.59627	−	2.76481i	0.328415	−	0.119533i
$536$		0			0
$537$	−0.718063	+	4.07234i	−0.0309867	+	0.175734i
$538$		0			0
$539$	8.84090	−	5.10430i	0.380805	−	0.219858i
$540$		0			0
$541$	6.65839	−	5.58705i	0.286266	−	0.240206i	−0.488334	−	0.872657i	$-0.662395\pi$
$541$	6.65839	−	5.58705i	0.286266	−	0.240206i	0.774601	+	0.632451i	$0.217951\pi$
$542$		0			0
$543$	1.10014	+	0.635164i	0.0472114	+	0.0272575i
$544$		0			0
$545$	3.36643	−	9.24919i	0.144202	−	0.396192i
$546$		0			0
$547$	−5.75578	−	32.6426i	−0.246099	−	1.39570i	−0.817926	−	0.575324i	$-0.804876\pi$
$547$	−5.75578	−	32.6426i	−0.246099	−	1.39570i	0.571827	−	0.820375i	$-0.306235\pi$
$548$		0			0
$549$	3.26991	+	2.74378i	0.139557	+	0.117102i
$550$		0			0
$551$	29.9345	+	34.6418i	1.27525	+	1.47579i
$552$		0			0
$553$	−32.8901	+	39.1969i	−1.39863	+	1.66682i
$554$		0			0
$555$	−4.87346	+	0.859322i	−0.206867	+	0.0364762i
$556$		0			0
$557$	−14.0446	−	5.11181i	−0.595088	−	0.216594i	0.0268779	−	0.999639i	$-0.491443\pi$
$557$	−14.0446	−	5.11181i	−0.595088	−	0.216594i	−0.621966	+	0.783044i	$0.713666\pi$
$558$		0			0
$559$	1.23143	−	2.13290i	0.0520839	−	0.0902120i
$560$		0			0
$561$	−0.159100	−	0.189608i	−0.00671722	−	0.00800527i
$562$		0			0
$563$	9.00640	+	15.5995i	0.379574	+	0.657442i	0.991000	−	0.133860i	$-0.0427371\pi$
$563$	9.00640	+	15.5995i	0.379574	+	0.657442i	−0.611426	+	0.791302i	$0.709404\pi$
$564$		0			0
$565$	2.00774	+	0.354019i	0.0844663	+	0.0148937i
$566$		0			0
$567$	1.26604	+	3.47843i	0.0531689	+	0.146080i
$568$		0			0
$569$			19.4773i			0.816531i	0.912863	+	0.408265i	$0.133866\pi$
$569$			19.4773i			0.816531i	−0.912863	+	0.408265i	$0.866134\pi$
$570$		0			0
$571$		−	24.2575i		−	1.01514i	−0.861610	−	0.507572i	$-0.830543\pi$
$571$		−	24.2575i		−	1.01514i	0.861610	−	0.507572i	$-0.169457\pi$
$572$		0			0
$573$	−2.03596	−	5.59375i	−0.0850534	−	0.233682i
$574$		0			0
$575$	−5.91875	−	1.04363i	−0.246829	−	0.0435226i
$576$		0			0
$577$	−20.1689	−	34.9336i	−0.839642	−	1.45430i	−0.890194	−	0.455582i	$-0.849431\pi$
$577$	−20.1689	−	34.9336i	−0.839642	−	1.45430i	0.0505517	−	0.998721i	$-0.483902\pi$
$578$		0			0
$579$	−6.07785	−	7.24330i	−0.252587	−	0.301021i
$580$		0			0
$581$	0.286989	−	0.497079i	0.0119063	−	0.0206223i
$582$		0			0
$583$	−9.73530	−	3.54336i	−0.403195	−	0.146751i
$584$		0			0
$585$	1.11334	−	0.196312i	0.0460310	−	0.00811650i
$586$		0			0
$587$	3.52394	−	4.19967i	0.145448	−	0.173339i	−0.688402	−	0.725330i	$-0.741687\pi$
$587$	3.52394	−	4.19967i	0.145448	−	0.173339i	0.833850	+	0.551991i	$0.186132\pi$
$588$		0			0
$589$	13.1841	+	22.0895i	0.543240	+	0.910181i
$590$		0			0
$591$	−10.2758	−	8.62246i	−0.422692	−	0.354681i
$592$		0			0
$593$	−2.03137	−	11.5205i	−0.0834185	−	0.473090i	−0.997687	−	0.0679804i	$-0.978344\pi$
$593$	−2.03137	−	11.5205i	−0.0834185	−	0.473090i	0.914268	−	0.405110i	$-0.132767\pi$
$594$		0			0
$595$	0.277189	−	0.761570i	0.0113636	−	0.0312213i
$596$		0			0
$597$	−0.499123	−	0.288169i	−0.0204277	−	0.0117940i
$598$		0			0
$599$	−3.15451	+	2.64695i	−0.128890	+	0.108152i	−0.704954	−	0.709253i	$-0.749032\pi$
$599$	−3.15451	+	2.64695i	−0.128890	+	0.108152i	0.576064	+	0.817405i	$0.304588\pi$
$600$		0			0
$601$	6.24376	−	3.60483i	0.254688	−	0.147044i	−0.367221	−	0.930134i	$-0.619691\pi$
$601$	6.24376	−	3.60483i	0.254688	−	0.147044i	0.621909	+	0.783090i	$0.286357\pi$
$602$		0			0
$603$	−1.94356	+	11.0225i	−0.0791480	+	0.448871i
$604$		0			0
$605$	10.9893	−	3.99979i	0.446779	−	0.162614i
$606$		0			0
$607$	15.4953			0.628933			0.314466	−	0.949269i	$-0.398174\pi$
$607$	15.4953			0.628933			0.314466	+	0.949269i	$0.398174\pi$
$608$		0			0
$609$	−38.8803			−1.57551
$610$		0			0
$611$	−6.90838	+	2.51444i	−0.279483	+	0.101723i
$612$		0			0
$613$	−4.32454	+	24.5257i	−0.174667	+	0.990583i	0.763861	+	0.645380i	$0.223301\pi$
$613$	−4.32454	+	24.5257i	−0.174667	+	0.990583i	−0.938528	+	0.345203i	$0.887810\pi$
$614$		0			0
$615$	2.68938	−	1.55271i	0.108446	−	0.0626114i
$616$		0			0
$617$	7.19119	−	6.03412i	0.289506	−	0.242925i	−0.486454	−	0.873706i	$-0.661710\pi$
$617$	7.19119	−	6.03412i	0.289506	−	0.242925i	0.775961	+	0.630781i	$0.217266\pi$
$618$		0			0
$619$	−23.1318	−	13.3552i	−0.929746	−	0.536789i	−0.0430149	−	0.999074i	$-0.513696\pi$
$619$	−23.1318	−	13.3552i	−0.929746	−	0.536789i	−0.886731	+	0.462285i	$0.847030\pi$
$620$		0			0
$621$	0.645430	−	1.77330i	0.0259002	−	0.0711602i
$622$		0			0
$623$	3.62701	+	20.5698i	0.145313	+	0.824112i
$624$		0			0
$625$	0.817267	+	0.685768i	0.0326907	+	0.0274307i
$626$		0			0
$627$	6.55438	+	1.05796i	0.261757	+	0.0422509i
$628$		0			0
$629$	0.383666	−	0.457236i	0.0152978	−	0.0182312i
$630$		0			0
$631$	−2.47044	+	0.435605i	−0.0983466	+	0.0173412i	−0.222605	−	0.974909i	$-0.571456\pi$
$631$	−2.47044	+	0.435605i	−0.0983466	+	0.0173412i	0.124258	+	0.992250i	$0.460345\pi$
$632$		0			0
$633$	7.10607	+	2.58640i	0.282441	+	0.102800i
$634$		0			0
$635$	−8.57011	+	14.8439i	−0.340094	+	0.589061i
$636$		0			0
$637$	−3.61499	−	4.30818i	−0.143231	−	0.170696i
$638$		0			0
$639$	3.72668	+	6.45480i	0.147425	+	0.255348i
$640$		0			0
$641$	32.2925	+	5.69404i	1.27548	+	0.224901i	0.770059	−	0.637973i	$-0.220227\pi$
$641$	32.2925	+	5.69404i	1.27548	+	0.224901i	0.505419	+	0.862874i	$0.331338\pi$
$642$		0			0
$643$	5.22028	+	14.3426i	0.205868	+	0.565618i	0.999060	−	0.0433543i	$-0.0138044\pi$
$643$	5.22028	+	14.3426i	0.205868	+	0.565618i	−0.793192	+	0.608972i	$0.791582\pi$
$644$		0			0
$645$		−	3.95448i		−	0.155707i
$646$		0			0
$647$		−	13.8107i		−	0.542953i	−0.962445	−	0.271477i	$-0.912488\pi$
$647$		−	13.8107i		−	0.542953i	0.962445	−	0.271477i	$-0.0875120\pi$
$648$		0			0
$649$	−6.16668	−	16.9428i	−0.242063	−	0.665064i
$650$		0			0
$651$	−21.5141	−	3.79352i	−0.843206	−	0.148680i
$652$		0			0
$653$	8.39440	+	14.5395i	0.328498	+	0.568976i	0.982214	−	0.187764i	$-0.0601242\pi$
$653$	8.39440	+	14.5395i	0.328498	+	0.568976i	−0.653716	+	0.756740i	$0.726791\pi$
$654$		0			0
$655$	7.93629	+	9.45810i	0.310096	+	0.369559i
$656$		0			0
$657$	3.47906	−	6.02590i	0.135731	−	0.235093i
$658$		0			0
$659$	−2.23947	−	0.815102i	−0.0872376	−	0.0317519i	0.298033	−	0.954556i	$-0.403670\pi$
$659$	−2.23947	−	0.815102i	−0.0872376	−	0.0317519i	−0.385270	+	0.922804i	$0.625892\pi$
$660$		0			0
$661$	−5.44104	+	0.959402i	−0.211632	+	0.0373164i	−0.278459	−	0.960448i	$-0.589824\pi$
$661$	−5.44104	+	0.959402i	−0.211632	+	0.0373164i	0.0668270	+	0.997765i	$0.478712\pi$
$662$		0			0
$663$	−0.0876485	+	0.104455i	−0.00340399	+	0.00405671i
$664$		0			0
$665$	7.73055	+	20.3179i	0.299778	+	0.787895i
$666$		0			0
$667$	15.1839	+	12.7408i	0.587924	+	0.493326i
$668$		0			0
$669$	1.09121	+	6.18858i	0.0421888	+	0.239264i
$670$		0			0
$671$	−2.22369	+	6.10953i	−0.0858445	+	0.235856i
$672$		0			0
$673$	−0.0744448	−	0.0429807i	−0.00286964	−	0.00165678i	0.498564	−	0.866853i	$-0.333861\pi$
$673$	−0.0744448	−	0.0429807i	−0.00286964	−	0.00165678i	−0.501434	+	0.865196i	$0.667194\pi$
$674$		0			0
$675$	−2.43969	+	2.04715i	−0.0939038	+	0.0787947i
$676$		0			0
$677$	9.80113	−	5.65868i	0.376688	−	0.217481i	−0.299688	−	0.954037i	$-0.596883\pi$
$677$	9.80113	−	5.65868i	0.376688	−	0.217481i	0.676376	+	0.736556i	$0.263549\pi$
$678$		0			0
$679$	5.19846	−	29.4819i	0.199499	−	1.13141i
$680$		0			0
$681$	−12.3550	+	4.49687i	−0.473446	+	0.172320i
$682$		0			0
$683$	46.1448			1.76568			0.882840	−	0.469673i	$-0.155628\pi$
$683$	46.1448			1.76568			0.882840	+	0.469673i	$0.155628\pi$
$684$		0			0
$685$	−19.2344			−0.734910
$686$		0			0
$687$	18.2160	−	6.63008i	0.694984	−	0.252953i
$688$		0			0
$689$	−0.991077	+	5.62068i	−0.0377570	+	0.214131i
$690$		0			0
$691$	−20.3402	+	11.7434i	−0.773777	+	0.446740i	−0.834220	−	0.551431i	$-0.814082\pi$
$691$	−20.3402	+	11.7434i	−0.773777	+	0.446740i	0.0604433	+	0.998172i	$0.480749\pi$
$692$		0			0
$693$	−4.31908	+	3.62414i	−0.164068	+	0.137670i
$694$		0			0
$695$	0.469722	+	0.271194i	0.0178176	+	0.0102870i
$696$		0			0
$697$	−0.128107	+	0.351972i	−0.00485240	+	0.0133319i
$698$		0			0
$699$	−4.05169	−	22.9783i	−0.153249	−	0.869118i
$700$		0			0
$701$	24.1989	+	20.3053i	0.913981	+	0.766921i	0.972872	−	0.231343i	$-0.0743121\pi$
$701$	24.1989	+	20.3053i	0.913981	+	0.766921i	−0.0588912	+	0.998264i	$0.518757\pi$
$702$		0			0
$703$	0.232145	+	16.0086i	0.00875550	+	0.603776i
$704$		0			0
$705$	−7.58765	+	9.04261i	−0.285767	+	0.340564i
$706$		0			0
$707$	63.6814	−	11.2288i	2.39499	−	0.422301i
$708$		0			0
$709$	36.3203	+	13.2195i	1.36404	+	0.496469i	0.917300	−	0.398196i	$-0.130364\pi$
$709$	36.3203	+	13.2195i	1.36404	+	0.496469i	0.446738	+	0.894665i	$0.352586\pi$
$710$		0			0
$711$	6.91147	−	11.9710i	0.259201	−	0.448948i
$712$		0			0
$713$	7.15880	+	8.53152i	0.268099	+	0.319508i
$714$		0			0
$715$	0.860967	+	1.49124i	0.0321983	+	0.0557692i
$716$		0			0
$717$	5.83409	+	1.02871i	0.217878	+	0.0384178i
$718$		0			0
$719$	−9.61222	−	26.4093i	−0.358475	−	0.984902i	−0.979559	−	0.201158i	$-0.935530\pi$
$719$	−9.61222	−	26.4093i	−0.358475	−	0.984902i	0.621084	−	0.783744i	$-0.286693\pi$
$720$		0			0
$721$		−	22.8940i		−	0.852619i
$722$		0			0
$723$		−	9.91718i		−	0.368824i
$724$		0			0
$725$	−11.4410	−	31.4340i	−0.424909	−	1.16743i
$726$		0			0
$727$	−2.43124	−	0.428693i	−0.0901696	−	0.0158993i	0.128381	−	0.991725i	$-0.459022\pi$
$727$	−2.43124	−	0.428693i	−0.0901696	−	0.0158993i	−0.218551	+	0.975826i	$0.570133\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	0.306589	+	0.365379i	0.0113396	+	0.0135140i
$732$		0			0
$733$	−9.38532	+	16.2558i	−0.346655	+	0.600423i	−0.985653	−	0.168785i	$-0.946016\pi$
$733$	−9.38532	+	16.2558i	−0.346655	+	0.600423i	0.638998	+	0.769208i	$0.279349\pi$
$734$		0			0
$735$	−8.48545	−	3.08845i	−0.312991	−	0.113919i
$736$		0			0
$737$	−16.7888	+	2.96032i	−0.618423	+	0.109045i
$738$		0			0
$739$	−19.1043	+	22.7676i	−0.702763	+	0.837521i	−0.992836	−	0.119484i	$-0.961876\pi$
$739$	−19.1043	+	22.7676i	−0.702763	+	0.837521i	0.290073	+	0.957005i	$0.406321\pi$
$740$		0			0
$741$	−0.0530334	−	3.65717i	−0.00194823	−	0.134349i
$742$		0			0
$743$	−3.79813	−	3.18701i	−0.139340	−	0.116920i	0.570454	−	0.821330i	$-0.306767\pi$
$743$	−3.79813	−	3.18701i	−0.139340	−	0.116920i	−0.709794	+	0.704410i	$0.751212\pi$
$744$		0			0
$745$	−2.61334	−	14.8210i	−0.0957454	−	0.542999i
$746$		0			0
$747$	−0.0530334	+	0.145708i	−0.00194039	+	0.00533118i
$748$		0			0
$749$	19.2344	+	11.1050i	0.702810	+	0.405768i
$750$		0			0
$751$	20.1839	−	16.9363i	0.736522	−	0.618015i	−0.195379	−	0.980728i	$-0.562594\pi$
$751$	20.1839	−	16.9363i	0.736522	−	0.618015i	0.931901	+	0.362713i	$0.118149\pi$
$752$		0			0
$753$	−10.9961	+	6.34862i	−0.400721	+	0.231357i
$754$		0			0
$755$	−1.68210	+	9.53969i	−0.0612180	+	0.347185i
$756$		0			0
$757$	3.06448	−	1.11538i	0.111381	−	0.0405392i	−0.285729	−	0.958311i	$-0.592236\pi$
$757$	3.06448	−	1.11538i	0.111381	−	0.0405392i	0.397109	+	0.917771i	$0.370013\pi$
$758$		0			0
$759$	2.87433			0.104332
$760$		0			0
$761$	−20.0205			−0.725744			−0.362872	−	0.931839i	$-0.618204\pi$
$761$	−20.0205			−0.725744			−0.362872	+	0.931839i	$0.618204\pi$
$762$		0			0
$763$	25.4119	−	9.24919i	0.919974	−	0.334843i
$764$		0			0
$765$	−0.0380187	+	0.215615i	−0.00137457	+	0.00779556i
$766$		0			0
$767$	−8.60209	+	4.96642i	−0.310603	+	0.179327i
$768$		0			0
$769$	−39.6259	+	33.2501i	−1.42895	+	1.19903i	−0.482613	+	0.875833i	$0.660312\pi$
$769$	−39.6259	+	33.2501i	−1.42895	+	1.19903i	−0.946333	+	0.323195i	$0.895243\pi$
$770$		0			0
$771$	25.8212	+	14.9079i	0.929928	+	0.536894i
$772$		0			0
$773$	4.76975	−	13.1048i	0.171556	−	0.471346i	−0.823881	−	0.566762i	$-0.808196\pi$
$773$	4.76975	−	13.1048i	0.171556	−	0.471346i	0.995438	+	0.0954157i	$0.0304180\pi$
$774$		0			0
$775$	−3.26382	−	18.5101i	−0.117240	−	0.664901i
$776$		0			0
$777$	−10.4153	−	8.73951i	−0.373648	−	0.313528i
$778$		0			0
$779$	−3.57280	−	9.39024i	−0.128009	−	0.336440i
$780$		0			0
$781$	−7.29726	+	8.69653i	−0.261116	+	0.311186i
$782$		0			0
$783$	10.3439	−	1.82391i	0.369661	−	0.0651811i
$784$		0			0
$785$	−17.3293	−	6.30737i	−0.618511	−	0.225120i
$786$		0			0
$787$	7.84776	−	13.5927i	0.279743	−	0.484528i	−0.691578	−	0.722302i	$-0.743084\pi$
$787$	7.84776	−	13.5927i	0.279743	−	0.484528i	0.971321	+	0.237773i	$0.0764176\pi$
$788$		0			0
$789$	8.47565	+	10.1009i	0.301741	+	0.359601i
$790$		0			0
$791$	2.80066	+	4.85088i	0.0995800	+	0.172478i
$792$		0			0
$793$	3.52734	+	0.621965i	0.125260	+	0.0220866i
$794$		0			0
$795$	3.13429	+	8.61138i	0.111162	+	0.305414i
$796$		0			0
$797$		−	26.8268i		−	0.950253i	−0.879917	−	0.475127i	$-0.842402\pi$
$797$		−	26.8268i		−	0.950253i	0.879917	−	0.475127i	$-0.157598\pi$
$798$		0			0
$799$		−	1.42377i		−	0.0503694i
$800$		0			0
$801$	−1.92989	−	5.30234i	−0.0681894	−	0.187349i
$802$		0			0
$803$	10.4372	+	1.84035i	0.368320	+	0.0649447i
$804$		0			0
$805$	4.70574	+	8.15058i	0.165855	+	0.287270i
$806$		0			0
$807$	11.9804	+	14.2777i	0.421730	+	0.502598i
$808$		0			0
$809$	12.4957	−	21.6432i	0.439326	−	0.760935i	−0.558312	−	0.829631i	$-0.688551\pi$
$809$	12.4957	−	21.6432i	0.439326	−	0.760935i	0.997638	+	0.0686963i	$0.0218839\pi$
$810$		0			0
$811$	22.2785	+	8.10872i	0.782305	+	0.284736i	0.702134	−	0.712045i	$-0.252231\pi$
$811$	22.2785	+	8.10872i	0.782305	+	0.284736i	0.0801716	+	0.996781i	$0.474453\pi$
$812$		0			0
$813$	−7.01707	+	1.23730i	−0.246100	+	0.0433940i
$814$		0			0
$815$	−13.8516	+	16.5077i	−0.485202	+	0.578241i
$816$		0			0
$817$	−12.6304	−	2.03871i	−0.441882	−	0.0713256i
$818$		0			0
$819$	2.37939	+	1.99654i	0.0831424	+	0.0697648i
$820$		0			0
$821$	−0.537141	−	3.04628i	−0.0187464	−	0.106316i	0.973999	−	0.226553i	$-0.0727456\pi$
$821$	−0.537141	−	3.04628i	−0.0187464	−	0.106316i	−0.992745	+	0.120237i	$0.961635\pi$
$822$		0			0
$823$	7.49660	−	20.5967i	0.261315	−	0.717957i	−0.737765	−	0.675058i	$-0.764119\pi$
$823$	7.49660	−	20.5967i	0.261315	−	0.717957i	0.999079	−	0.0428987i	$-0.0136593\pi$
$824$		0			0
$825$	−4.20099	−	2.42544i	−0.146260	−	0.0844431i
$826$		0			0
$827$	2.26193	−	1.89798i	0.0786549	−	0.0659993i	−0.602613	−	0.798034i	$-0.705874\pi$
$827$	2.26193	−	1.89798i	0.0786549	−	0.0659993i	0.681267	+	0.732035i	$0.261429\pi$
$828$		0			0
$829$	31.0241	−	17.9118i	1.07751	−	0.622102i	0.147287	−	0.989094i	$-0.452946\pi$
$829$	31.0241	−	17.9118i	1.07751	−	0.622102i	0.930224	+	0.366992i	$0.119612\pi$
$830$		0			0
$831$	−1.73870	+	9.86068i	−0.0603149	+	0.342063i
$832$		0			0
$833$	1.02347	−	0.372513i	0.0354612	−	0.0129068i
$834$		0			0
$835$	−3.63041			−0.125636
$836$		0			0
$837$	5.90167			0.203992
$838$		0			0
$839$	−19.0133	+	6.92026i	−0.656411	+	0.238914i	−0.648686	−	0.761056i	$-0.724681\pi$
$839$	−19.0133	+	6.92026i	−0.656411	+	0.238914i	−0.00772472	+	0.999970i	$0.502459\pi$
$840$		0			0
$841$	−14.1215	+	80.0873i	−0.486950	+	2.76163i
$842$		0			0
$843$	17.2343	−	9.95020i	0.593579	−	0.342703i
$844$		0			0
$845$	−12.6905	+	10.6486i	−0.436566	+	0.366322i
$846$		0			0
$847$	27.8259	+	16.0653i	0.956111	+	0.552011i
$848$		0			0
$849$	8.58630	−	23.5907i	0.294681	−	0.809630i
$850$		0			0
$851$	1.20362	+	6.82608i	0.0412596	+	0.233995i
$852$		0			0
$853$	16.6525	+	13.9731i	0.570172	+	0.478431i	0.881703	−	0.471805i	$-0.156397\pi$
$853$	16.6525	+	13.9731i	0.570172	+	0.478431i	−0.311531	+	0.950236i	$0.600842\pi$
$854$		0			0
$855$	−3.00980	−	5.04282i	−0.102933	−	0.172461i
$856$		0			0
$857$	−7.93289	+	9.45404i	−0.270982	+	0.322944i	−0.884324	−	0.466873i	$-0.845380\pi$
$857$	−7.93289	+	9.45404i	−0.270982	+	0.322944i	0.613342	+	0.789818i	$0.289825\pi$
$858$		0			0
$859$	28.9231	−	5.09992i	0.986843	−	0.174007i	0.343141	−	0.939284i	$-0.388509\pi$
$859$	28.9231	−	5.09992i	0.986843	−	0.174007i	0.643701	+	0.765277i	$0.277398\pi$
$860$		0			0
$861$	8.01754	+	2.91815i	0.273237	+	0.0994502i
$862$		0			0
$863$	−4.58987	+	7.94989i	−0.156241	+	0.270617i	−0.933510	−	0.358551i	$-0.883271\pi$
$863$	−4.58987	+	7.94989i	−0.156241	+	0.270617i	0.777269	+	0.629168i	$0.216604\pi$
$864$		0			0
$865$	−17.3097	−	20.6290i	−0.588549	−	0.701405i
$866$		0			0
$867$	8.48680	+	14.6996i	0.288227	+	0.499223i
$868$		0			0
$869$	20.7344	+	3.65604i	0.703367	+	0.124023i
$870$		0			0
$871$	3.21213	+	8.82526i	0.108839	+	0.299033i
$872$		0			0
$873$			8.08737i			0.273716i
$874$		0			0
$875$		−	40.8195i		−	1.37995i
$876$		0			0
$877$	15.1839	+	41.7175i	0.512724	+	1.40870i	0.878386	+	0.477951i	$0.158620\pi$
$877$	15.1839	+	41.7175i	0.512724	+	1.40870i	−0.365662	+	0.930748i	$0.619157\pi$
$878$		0			0
$879$	−0.582596	−	0.102727i	−0.0196505	−	0.00346491i
$880$		0			0
$881$	−9.03802	−	15.6543i	−0.304499	−	0.527407i	0.672651	−	0.739960i	$-0.265156\pi$
$881$	−9.03802	−	15.6543i	−0.304499	−	0.527407i	−0.977150	+	0.212553i	$0.931822\pi$
$882$		0			0
$883$	34.7271	+	41.3862i	1.16866	+	1.39276i	0.903519	+	0.428547i	$0.140974\pi$
$883$	34.7271	+	41.3862i	1.16866	+	1.39276i	0.265142	+	0.964209i	$0.414581\pi$
$884$		0			0
$885$	−7.97431	+	13.8119i	−0.268053	+	0.464282i
$886$		0			0
$887$	42.5852	+	15.4997i	1.42987	+	0.520430i	0.936894	−	0.349613i	$-0.113687\pi$
$887$	42.5852	+	15.4997i	1.42987	+	0.520430i	0.492976	+	0.870043i	$0.335909\pi$
$888$		0			0
$889$	−46.3769	+	8.17750i	−1.55543	+	0.274265i
$890$		0			0
$891$	0.979055	−	1.16679i	0.0327996	−	0.0390890i
$892$		0			0
$893$	24.9699	+	28.8965i	0.835585	+	0.966983i
$894$		0			0
$895$	4.26786	+	3.58116i	0.142659	+	0.119705i
$896$		0			0
$897$	−0.274967	−	1.55942i	−0.00918089	−	0.0520674i
$898$		0			0
$899$	−21.2012	+	58.2497i	−0.707098	+	1.94274i
$900$		0			0
$901$	−0.957234	−	0.552659i	−0.0318901	−	0.0184117i
$902$		0			0
$903$	8.32295	−	6.98378i	0.276970	−	0.232406i
$904$		0			0
$905$	1.48221	−	0.855755i	0.0492703	−	0.0284462i
$906$		0			0
$907$	−4.99319	+	28.3178i	−0.165796	+	0.940277i	0.782443	+	0.622722i	$0.213973\pi$
$907$	−4.99319	+	28.3178i	−0.165796	+	0.940277i	−0.948240	+	0.317556i	$0.897138\pi$
$908$		0			0
$909$	−16.4153	+	5.97470i	−0.544463	+	0.198168i
$910$		0			0
$911$	8.61856			0.285545			0.142773	−	0.989755i	$-0.454398\pi$
$911$	8.61856			0.285545			0.142773	+	0.989755i	$0.454398\pi$
$912$		0			0
$913$	−0.236177			−0.00781632
$914$		0			0
$915$	5.40420	−	1.96697i	0.178657	−	0.0650260i
$916$		0			0
$917$	−5.89053	+	33.4069i	−0.194522	+	1.10319i
$918$		0			0
$919$	−34.9291	+	20.1663i	−1.15220	+	0.665225i	−0.949423	−	0.313999i	$-0.898331\pi$
$919$	−34.9291	+	20.1663i	−1.15220	+	0.665225i	−0.202780	+	0.979224i	$0.564998\pi$
$920$		0			0
$921$	−7.50774	+	6.29974i	−0.247388	+	0.207584i
$922$		0			0
$923$	5.41622	+	3.12706i	0.178277	+	0.102928i
$924$		0			0
$925$	4.00088	−	10.9923i	0.131548	−	0.361425i
$926$		0			0
$927$	1.07398	+	6.09083i	0.0352741	+	0.200049i
$928$		0			0
$929$	44.7288	+	37.5319i	1.46750	+	1.23138i	0.918415	+	0.395619i	$0.129470\pi$
$929$	44.7288	+	37.5319i	1.46750	+	1.23138i	0.549089	+	0.835764i	$0.314975\pi$
$930$		0			0
$931$	−14.2390	+	25.5099i	−0.466665	+	0.836053i
$932$		0			0
$933$	6.93882	−	8.26936i	0.227167	−	0.270727i
$934$		0			0
$935$	−0.328411	+	0.0579078i	−0.0107402	+	0.00189379i
$936$		0			0
$937$	55.6926	+	20.2704i	1.81940	+	0.662207i	0.995422	+	0.0955819i	$0.0304712\pi$
$937$	55.6926	+	20.2704i	1.81940	+	0.662207i	0.823976	+	0.566625i	$0.191751\pi$
$938$		0			0
$939$	11.5715	−	20.0423i	0.377620	−	0.654057i
$940$		0			0
$941$	−15.4765	−	18.4442i	−0.504520	−	0.601264i	0.452328	−	0.891852i	$-0.350594\pi$
$941$	−15.4765	−	18.4442i	−0.504520	−	0.601264i	−0.956848	+	0.290588i	$0.906149\pi$
$942$		0			0
$943$	−2.17483	−	3.76692i	−0.0708222	−	0.122668i
$944$		0			0
$945$	4.91147	+	0.866025i	0.159770	+	0.0281718i
$946$		0			0
$947$	−13.9791	−	38.4073i	−0.454260	−	1.24807i	−0.929699	−	0.368321i	$-0.879933\pi$
$947$	−13.9791	−	38.4073i	−0.454260	−	1.24807i	0.475439	−	0.879749i	$-0.342289\pi$
$948$		0			0
$949$		−	5.83855i		−	0.189527i
$950$		0			0
$951$			24.9935i			0.810470i
$952$		0			0
$953$	−9.99248	−	27.4541i	−0.323688	−	0.889326i	−0.989671	−	0.143359i	$-0.954210\pi$
$953$	−9.99248	−	27.4541i	−0.323688	−	0.889326i	0.665983	−	0.745967i	$-0.268012\pi$
$954$		0			0
$955$	−7.89827	−	1.39268i	−0.255582	−	0.0450660i
$956$		0			0
$957$	7.99912	+	13.8549i	0.258575	+	0.447865i
$958$		0			0
$959$	−33.9688	−	40.4825i	−1.09691	−	1.30725i
$960$		0			0
$961$	−1.91488	+	3.31667i	−0.0617702	+	0.106989i
$962$		0			0
$963$	−5.63816	−	2.05212i	−0.181687	−	0.0661287i
$964$		0			0
$965$	−12.5458	+	2.21216i	−0.403862	+	0.0712118i
$966$		0			0
$967$	16.9851	−	20.2421i	0.546206	−	0.650942i	−0.420361	−	0.907357i	$-0.638097\pi$
$967$	16.9851	−	20.2421i	0.546206	−	0.650942i	0.966567	+	0.256414i	$0.0825412\pi$
$968$		0			0
$969$	0.669063	+	0.232589i	0.0214934	+	0.00747184i
$970$		0			0
$971$	−7.63610	−	6.40745i	−0.245054	−	0.205625i	0.511985	−	0.858994i	$-0.328910\pi$
$971$	−7.63610	−	6.40745i	−0.245054	−	0.205625i	−0.757039	+	0.653370i	$0.773355\pi$
$972$		0			0
$973$	0.258770	+	1.46756i	0.00829580	+	0.0470478i
$974$		0			0
$975$	−0.914000	+	2.51120i	−0.0292714	+	0.0804226i
$976$		0			0
$977$	−8.68320	−	5.01325i	−0.277800	−	0.160388i	0.354627	−	0.935008i	$-0.384608\pi$
$977$	−8.68320	−	5.01325i	−0.277800	−	0.160388i	−0.632427	+	0.774620i	$0.717941\pi$
$978$		0			0
$979$	6.58378	−	5.52445i	0.210418	−	0.176562i
$980$		0			0
$981$	−6.32682	+	3.65279i	−0.202000	+	0.116625i
$982$		0			0
$983$	−6.67184	+	37.8379i	−0.212799	+	1.20684i	0.671887	+	0.740653i	$0.265484\pi$
$983$	−6.67184	+	37.8379i	−0.212799	+	1.20684i	−0.884686	+	0.466187i	$0.845627\pi$
$984$		0			0
$985$	−16.9829	+	6.18128i	−0.541121	+	0.196952i
$986$		0			0
$987$	−32.4320			−1.03232
$988$		0			0
$989$	−5.53890			−0.176127
$990$		0			0
$991$	51.2315	−	18.6467i	1.62742	−	0.592333i	0.642646	−	0.766163i	$-0.277837\pi$
$991$	51.2315	−	18.6467i	1.62742	−	0.592333i	0.984776	+	0.173830i	$0.0556143\pi$
$992$		0			0
$993$	−1.21095	+	6.86765i	−0.0384284	+	0.217938i
$994$		0			0
$995$	−0.672466	+	0.388249i	−0.0213186	+	0.0123083i
$996$		0			0
$997$	17.2645	−	14.4866i	0.546771	−	0.458795i	−0.327075	−	0.944998i	$-0.606063\pi$
$997$	17.2645	−	14.4866i	0.546771	−	0.458795i	0.873846	+	0.486203i	$0.161619\pi$
$998$		0			0
$999$	3.18092	+	1.83651i	0.100640	+	0.0581045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.a.79.1	✓	6
4.3	odd	2		912.2.ci.b.79.1	yes	6
19.13	odd	18		912.2.ci.b.127.1	yes	6
76.51	even	18	inner	912.2.ci.a.127.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.a.79.1	✓	6	1.1	even	1	trivial
912.2.ci.a.127.1	yes	6	76.51	even	18	inner
912.2.ci.b.79.1	yes	6	4.3	odd	2
912.2.ci.b.127.1	yes	6	19.13	odd	18

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{3} +(-0.233956 + 1.32683i) q^{5} +(-3.20574 + 1.85083i) q^{7} +(0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{3} +(-0.233956 + 1.32683i) q^{5} +(-3.20574 + 1.85083i) q^{7} +(0.766044 - 0.642788i) q^{9} +(1.31908 + 0.761570i) q^{11} +(0.286989 - 0.788496i) q^{13} +(-0.233956 - 1.32683i) q^{15} +(0.124485 + 0.104455i) q^{17} +(-4.35844 + 0.0632028i) q^{19} +(2.37939 - 2.83564i) q^{21} +(-1.85844 + 0.327693i) q^{23} +(2.99273 + 1.08926i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-6.75150 - 8.04612i) q^{29} +(-2.95084 - 5.11100i) q^{31} +(-1.50000 - 0.264490i) q^{33} +(-1.70574 - 4.68647i) q^{35} -3.67301i q^{37} +0.839100i q^{39} +(0.788333 + 2.16593i) q^{41} +(2.89053 + 0.509678i) q^{43} +(0.673648 + 1.16679i) q^{45} +(-5.63176 - 6.71167i) q^{47} +(3.35117 - 5.80439i) q^{49} +(-0.152704 - 0.0555796i) q^{51} +(-6.69846 + 1.18112i) q^{53} +(-1.31908 + 1.57202i) q^{55} +(4.07398 - 1.55007i) q^{57} +(-9.06805 - 7.60900i) q^{59} +(0.741230 + 4.20372i) q^{61} +(-1.26604 + 3.47843i) q^{63} +(0.979055 + 0.565258i) q^{65} +(-8.57398 + 7.19442i) q^{67} +(1.63429 - 0.943555i) q^{69} +(-1.29426 + 7.34013i) q^{71} +(6.53849 - 2.37981i) q^{73} -3.18479 q^{75} -5.63816 q^{77} +(12.9893 - 4.72773i) q^{79} +(0.173648 - 0.984808i) q^{81} +(-0.134285 + 0.0775297i) q^{83} +(-0.167718 + 0.140732i) q^{85} +(9.09627 + 5.25173i) q^{87} +(1.92989 - 5.30234i) q^{89} +(0.539363 + 3.05888i) q^{91} +(4.52094 + 3.79352i) q^{93} +(0.935822 - 5.79769i) q^{95} +(-5.19846 + 6.19529i) q^{97} +(1.50000 - 0.264490i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{5} - 9 q^{7}+O(q^{10}) \) 6 * q - 6 * q^5 - 9 * q^7	\( 6 q - 6 q^{5} - 9 q^{7} - 9 q^{11} - 6 q^{13} - 6 q^{15} - 12 q^{17} - 18 q^{19} + 3 q^{21} - 3 q^{23} - 3 q^{27} - 6 q^{31} - 9 q^{33} - 12 q^{41} + 3 q^{45} - 39 q^{47} - 6 q^{49} - 3 q^{51} - 12 q^{53} + 9 q^{55} + 9 q^{57} - 12 q^{59} + 27 q^{61} - 3 q^{63} + 9 q^{65} - 36 q^{67} - 18 q^{71} - 9 q^{73} - 12 q^{75} + 18 q^{79} + 9 q^{83} + 27 q^{85} + 27 q^{87} + 3 q^{89} + 12 q^{91} + 24 q^{93} + 24 q^{95} - 3 q^{97} + 9 q^{99}+O(q^{100}) \) 6 * q - 6 * q^5 - 9 * q^7 - 9 * q^11 - 6 * q^13 - 6 * q^15 - 12 * q^17 - 18 * q^19 + 3 * q^21 - 3 * q^23 - 3 * q^27 - 6 * q^31 - 9 * q^33 - 12 * q^41 + 3 * q^45 - 39 * q^47 - 6 * q^49 - 3 * q^51 - 12 * q^53 + 9 * q^55 + 9 * q^57 - 12 * q^59 + 27 * q^61 - 3 * q^63 + 9 * q^65 - 36 * q^67 - 18 * q^71 - 9 * q^73 - 12 * q^75 + 18 * q^79 + 9 * q^83 + 27 * q^85 + 27 * q^87 + 3 * q^89 + 12 * q^91 + 24 * q^93 + 24 * q^95 - 3 * q^97 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more