LMFDB - Embedded newform 912.2.ci.b.127.1

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:	$0$
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			127.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	912.127
Dual form			912.2.ci.b.79.1

$q$-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 $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$1$	$-1$

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	−0.991368	−	0.131107i	$-0.958147\pi$
$5$	−0.233956	−	1.32683i	−0.104628	−	0.593375i	0.886740	−	0.462268i	$-0.152964\pi$
$6$		0			0
$7$	3.20574	+	1.85083i	1.21165	+	0.699549i	0.963120	−	0.269074i	$-0.0867175\pi$
$7$	3.20574	+	1.85083i	1.21165	+	0.699549i	0.248535	+	0.968623i	$0.420051\pi$
$8$		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	$-0.740416\pi$
$11$	−1.31908	+	0.761570i	−0.397717	+	0.229622i	0.287781	+	0.957696i	$0.407082\pi$
$12$		0			0
$13$	0.286989	+	0.788496i	0.0795964	+	0.218689i	0.973107	−	0.230352i	$-0.0739878\pi$
$13$	0.286989	+	0.788496i	0.0795964	+	0.218689i	−0.893511	+	0.449041i	$0.851766\pi$
$14$		0			0
$15$	0.233956	−	1.32683i	0.0604071	−	0.342585i
$16$		0			0
$17$	0.124485	−	0.104455i	0.0301921	−	0.0253342i	−0.627567	−	0.778563i	$-0.715949\pi$
$17$	0.124485	−	0.104455i	0.0301921	−	0.0253342i	0.657759	+	0.753229i	$0.271505\pi$
$18$		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	$-0.381407\pi$
$23$	1.85844	+	0.327693i	0.387512	+	0.0683288i	0.0235017	+	0.999724i	$0.492519\pi$
$24$		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	−0.457390	+	0.889266i	$0.651216\pi$
$29$	−6.75150	+	8.04612i	−1.25372	+	1.49413i	−0.796331	+	0.604861i	$0.793229\pi$
$30$		0			0
$31$	2.95084	−	5.11100i	0.529986	−	0.917963i	−0.469402	−	0.882985i	$-0.655531\pi$
$31$	2.95084	−	5.11100i	0.529986	−	0.917963i	0.999388	−	0.0349781i	$-0.0111361\pi$
$32$		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	$0.0976275\pi$
$37$			3.67301i			0.603840i	−0.953333	+	0.301920i	$0.902373\pi$
$38$		0			0
$39$			0.839100i			0.134363i
$40$		0			0
$41$	0.788333	−	2.16593i	0.123117	−	0.338261i	−0.862788	−	0.505565i	$-0.831284\pi$
$41$	0.788333	−	2.16593i	0.123117	−	0.338261i	0.985905	+	0.167304i	$0.0535062\pi$
$42$		0			0
$43$	−2.89053	+	0.509678i	−0.440802	+	0.0777252i	−0.389644	−	0.920965i	$-0.627402\pi$
$43$	−2.89053	+	0.509678i	−0.440802	+	0.0777252i	−0.0511572	+	0.998691i	$0.516291\pi$
$44$		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	$-0.557128\pi$
$47$	5.63176	−	6.71167i	0.821476	−	0.978998i	0.999988	+	0.00494030i	$0.00157255\pi$
$48$		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	−0.306516	−	0.951865i	$-0.599163\pi$
$53$	−6.69846	−	1.18112i	−0.920105	−	0.162239i	−0.613588	+	0.789626i	$0.710275\pi$
$54$		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	0.180584	−	0.983560i	$-0.442201\pi$
$59$	9.06805	−	7.60900i	1.18056	−	0.990607i	0.999975	−	0.00704735i	$-0.00224326\pi$
$60$		0			0
$61$	0.741230	−	4.20372i	0.0949047	−	0.538231i	−0.899872	−	0.436154i	$-0.856340\pi$
$61$	0.741230	−	4.20372i	0.0949047	−	0.538231i	0.994777	−	0.102077i	$-0.0325488\pi$
$62$		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	$-0.0381506\pi$
$67$	8.57398	+	7.19442i	1.04748	+	0.878939i	0.0546520	+	0.998505i	$0.482595\pi$
$68$		0			0
$69$	1.63429	+	0.943555i	0.196745	+	0.113591i
$70$		0			0
$71$	1.29426	+	7.34013i	0.153601	+	0.871113i	0.960054	+	0.279815i	$0.0902732\pi$
$71$	1.29426	+	7.34013i	0.153601	+	0.871113i	−0.806453	+	0.591298i	$0.798616\pi$
$72$		0			0
$73$	6.53849	+	2.37981i	0.765272	+	0.278536i	0.695017	−	0.718993i	$-0.255397\pi$
$73$	6.53849	+	2.37981i	0.765272	+	0.278536i	0.0702545	+	0.997529i	$0.477619\pi$
$74$		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	$-0.672453\pi$
$79$	−12.9893	−	4.72773i	−1.46141	−	0.531911i	−0.945754	+	0.324883i	$0.894675\pi$
$80$		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	$-0.330624\pi$
$83$	0.134285	+	0.0775297i	0.0147397	+	0.00850999i	−0.492612	+	0.870249i	$0.663958\pi$
$84$		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	0.998971	−	0.0453443i	$-0.0144385\pi$
$89$	1.92989	+	5.30234i	0.204568	+	0.562046i	−0.794403	+	0.607391i	$0.792216\pi$
$90$		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	0.434588	−	0.900629i	$-0.356894\pi$
$97$	−5.19846	−	6.19529i	−0.527824	−	0.629036i	−0.962412	+	0.271593i	$0.912449\pi$
$98$		0			0
$99$	−1.50000	−	0.264490i	−0.150756	−	0.0265823i
$100$		0			0
$101$	−16.4153	+	5.97470i	−1.63339	+	0.594505i	−0.985865	−	0.167542i	$-0.946417\pi$
$101$	−16.4153	+	5.97470i	−1.63339	+	0.594505i	−0.647523	+	0.762046i	$0.724195\pi$
$102$		0			0
$103$	3.09240	+	5.35619i	0.304703	+	0.527761i	0.977195	−	0.212343i	$-0.0681095\pi$
$103$	3.09240	+	5.35619i	0.304703	+	0.527761i	−0.672492	+	0.740104i	$0.734776\pi$
$104$		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	$-0.739671\pi$
$107$	3.00000	−	5.19615i	0.290021	−	0.502331i	0.973814	+	0.227345i	$0.0730044\pi$
$108$		0			0
$109$	−7.19459	+	1.26860i	−0.689117	+	0.121510i	−0.507232	−	0.861810i	$-0.669331\pi$
$109$	−7.19459	+	1.26860i	−0.689117	+	0.121510i	−0.181885	+	0.983320i	$0.558220\pi$
$110$		0			0
$111$	−1.25624	+	3.45150i	−0.119237	+	0.327602i
$112$		0			0
$113$			1.51319i			0.142349i	0.997464	+	0.0711744i	$0.0226747\pi$
$113$			1.51319i			0.142349i	−0.997464	+	0.0711744i	$0.977325\pi$
$114$		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	$-0.802021\pi$
$127$	−11.9547	+	4.35116i	−1.06081	+	0.386103i	−0.248077	+	0.968740i	$0.579798\pi$
$128$		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	$-0.353328\pi$
$131$	−5.89053	−	7.02006i	−0.514658	−	0.613345i	−0.959309	+	0.282358i	$0.908883\pi$
$132$		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	−0.674574	−	0.738207i	$-0.735673\pi$
$137$	2.47906	−	14.0594i	0.211800	−	1.20118i	0.886374	−	0.462970i	$-0.153216\pi$
$138$		0			0
$139$	−0.137689	−	0.378297i	−0.0116786	−	0.0320867i	0.933716	−	0.358014i	$-0.116546\pi$
$139$	−0.137689	−	0.378297i	−0.0116786	−	0.0320867i	−0.945395	+	0.325927i	$0.894324\pi$
$140$		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	−0.125839	−	0.992051i	$-0.540162\pi$
$149$	−10.4966	−	3.82045i	−0.859915	−	0.312983i	−0.734076	+	0.679067i	$0.762384\pi$
$150$		0			0
$151$	−7.18984			−0.585101			−0.292551	−	0.956250i	$-0.594504\pi$
$151$	−7.18984			−0.585101			−0.292551	+	0.956250i	$0.594504\pi$
$152$		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	−0.919775	−	0.392447i	$-0.871629\pi$
$157$	−2.37686	−	13.4798i	−0.189694	−	1.07581i	0.730081	−	0.683361i	$-0.239482\pi$
$158$		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	$-0.882136\pi$
$163$	−13.8516	+	7.99724i	−1.08494	+	0.626393i	−0.152718	+	0.988270i	$0.548803\pi$
$164$		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	$-0.977691\pi$
$167$	−0.467911	+	2.65366i	−0.0362080	+	0.205346i	0.961337	+	0.275375i	$0.0888020\pi$
$168$		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	−0.986436	−	0.164148i	$-0.947512\pi$
$173$	−12.8478	−	15.3114i	−0.976797	−	1.16410i	0.00963834	−	0.999954i	$-0.496932\pi$
$174$		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	$-0.216056\pi$
$179$	−2.06758	−	3.58116i	−0.154538	−	0.267668i	−0.932891	+	0.360159i	$0.882722\pi$
$180$		0			0
$181$	−0.816552	+	0.973128i	−0.0606938	+	0.0723321i	−0.795537	−	0.605905i	$-0.792811\pi$
$181$	−0.816552	+	0.973128i	−0.0606938	+	0.0723321i	0.734843	+	0.678237i	$0.237256\pi$
$182$		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	−0.767213	−	0.641392i	$-0.778357\pi$
$193$	3.23396	−	8.88522i	0.232785	−	0.639572i	0.999998	+	0.00182013i	$0.000579365\pi$
$194$		0			0
$195$	1.11334	−	0.196312i	0.0797280	−	0.0140582i
$196$		0			0
$197$	6.70708	−	11.6170i	0.477860	−	0.827677i	−0.521818	−	0.853057i	$-0.674746\pi$
$197$	6.70708	−	11.6170i	0.477860	−	0.827677i	0.999678	+	0.0253794i	$0.00807938\pi$
$198$		0			0
$199$	−0.370462	+	0.441500i	−0.0262614	+	0.0312971i	−0.779015	−	0.627005i	$-0.784281\pi$
$199$	−0.370462	+	0.441500i	−0.0262614	+	0.0312971i	0.752754	+	0.658302i	$0.228725\pi$
$200$		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	$-0.638401\pi$
$211$	5.79292	−	4.86084i	0.398801	−	0.334634i	0.820030	+	0.572321i	$0.193957\pi$
$212$		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	−0.999299	−	0.0374482i	$-0.988077\pi$
$223$	−1.09121	−	6.18858i	−0.0730731	−	0.414418i	0.926225	−	0.376970i	$-0.123034\pi$
$224$		0			0
$225$	2.99273	+	1.08926i	0.199515	+	0.0726175i
$226$		0			0
$227$	−13.1480			−0.872660			−0.436330	−	0.899787i	$-0.643722\pi$
$227$	−13.1480			−0.872660			−0.436330	+	0.899787i	$0.643722\pi$
$228$		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	−0.767794	−	0.640697i	$-0.778645\pi$
$233$	−4.05169	−	22.9783i	−0.265435	−	1.50536i	0.502359	−	0.864659i	$-0.332466\pi$
$234$		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	$-0.605299\pi$
$239$	5.13041	−	2.96205i	0.331859	−	0.191599i	0.656666	+	0.754181i	$0.271966\pi$
$240$		0			0
$241$	−3.39187	−	9.31910i	−0.218490	−	0.600296i	0.781223	−	0.624252i	$-0.214596\pi$
$241$	−3.39187	−	9.31910i	−0.218490	−	0.600296i	−0.999713	+	0.0239560i	$0.992374\pi$
$242$		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	$-0.575685\pi$
$251$	−12.5043	−	2.20485i	−0.789267	−	0.139169i	−0.553730	+	0.832696i	$0.686796\pi$
$252$		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	−0.316039	+	0.948746i	$0.602353\pi$
$257$	−19.1652	+	22.8402i	−1.19549	+	1.42473i	−0.879453	+	0.475985i	$0.842092\pi$
$258$		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	−0.719493	−	0.694499i	$-0.755626\pi$
$263$	4.50980	−	12.3906i	0.278086	−	0.764036i	0.997579	−	0.0695361i	$-0.0221519\pi$
$264$		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	0.578933	+	0.815375i	$0.303469\pi$
$269$	−6.37464	+	17.5142i	−0.388669	+	1.06786i	−0.967601	+	0.252483i	$0.918753\pi$
$270$		0			0
$271$	−7.01707	+	1.23730i	−0.426257	+	0.0751606i	−0.382661	−	0.923889i	$-0.624992\pi$
$271$	−7.01707	+	1.23730i	−0.426257	+	0.0751606i	−0.0435955	+	0.999049i	$0.513881\pi$
$272$		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	0.976319	−	0.216338i	$-0.0694113\pi$
$277$	5.00640	+	8.67133i	0.300805	+	0.521010i	−0.675513	+	0.737348i	$0.736078\pi$
$278$		0			0
$279$	5.54576	−	2.01849i	0.332016	−	0.120844i
$280$		0			0
$281$	−19.5981	−	3.45567i	−1.16912	−	0.206148i	−0.444814	−	0.895623i	$-0.646730\pi$
$281$	−19.5981	−	3.45567i	−1.16912	−	0.206148i	−0.724309	+	0.689475i	$0.757841\pi$
$282$		0			0
$283$	16.1370	+	19.2313i	0.959244	+	1.14318i	0.989629	+	0.143644i	$0.0458819\pi$
$283$	16.1370	+	19.2313i	0.959244	+	1.14318i	−0.0303860	+	0.999538i	$0.509674\pi$
$284$		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	−0.484960	−	0.874536i	$-0.661166\pi$
$293$	0.512326	−	0.295792i	0.0299304	−	0.0172803i	0.514891	+	0.857256i	$0.327833\pi$
$294$		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	$-0.479116\pi$
$307$	−9.20961	−	3.35202i	−0.525620	−	0.191310i	−0.591182	+	0.806538i	$0.701338\pi$
$308$		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	$-0.234322\pi$
$311$	9.34864	+	5.39744i	0.530113	+	0.306061i	−0.210950	+	0.977497i	$0.567656\pi$
$312$		0			0
$313$	−17.7285	−	14.8760i	−1.00207	−	0.840840i	−0.0148032	−	0.999890i	$-0.504712\pi$
$313$	−17.7285	−	14.8760i	−1.00207	−	0.840840i	−0.987270	+	0.159051i	$0.949157\pi$
$314$		0			0
$315$	4.31908	−	2.49362i	0.243352	−	0.140500i
$316$		0			0
$317$	8.54829	+	23.4862i	0.480120	+	1.31912i	0.909391	+	0.415942i	$0.136548\pi$
$317$	8.54829	+	23.4862i	0.480120	+	1.31912i	−0.429272	+	0.903175i	$0.641230\pi$
$318$		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	$-0.228051\pi$
$331$	−3.48680	−	6.03931i	−0.191652	−	0.331950i	−0.945798	+	0.324756i	$0.894718\pi$
$332$		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	0.123825	−	0.992304i	$-0.460484\pi$
$337$	10.6395	−	1.87603i	0.579570	−	0.102194i	0.455745	+	0.890110i	$0.349373\pi$
$338$		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	$-0.340489\pi$
$347$	22.9461	−	4.04601i	1.23181	−	0.217201i	0.751403	+	0.659844i	$0.229378\pi$
$348$		0			0
$349$	9.64590	−	16.7072i	0.516333	−	0.894315i	−0.483487	−	0.875351i	$-0.660630\pi$
$349$	9.64590	−	16.7072i	0.516333	−	0.894315i	0.999820	−	0.0189635i	$-0.00603665\pi$
$350$		0			0
$351$	−0.539363	+	0.642788i	−0.0287891	+	0.0343095i
$352$		0			0
$353$	13.4119	+	23.2302i	0.713846	+	1.23642i	0.963403	+	0.268057i	$0.0863815\pi$
$353$	13.4119	+	23.2302i	0.713846	+	1.23642i	−0.249558	+	0.968360i	$0.580285\pi$
$354$		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	0.979721	+	0.200364i	$0.0642126\pi$
$359$	19.0783	+	22.7367i	1.00691	+	1.19999i	0.0271935	+	0.999630i	$0.491343\pi$
$360$		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	0.949106	+	0.314956i	$0.101990\pi$
$367$	8.13223	+	22.3431i	0.424499	+	1.16630i	−0.524607	+	0.851344i	$0.675788\pi$
$368$		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	−0.999621	−	0.0275252i	$-0.991237\pi$
$373$	−29.4192	−	16.9852i	−1.52327	−	0.879460i	−0.523648	−	0.851935i	$-0.675429\pi$
$374$		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	$-0.293234\pi$
$379$	23.5503			1.20970			0.604848	+	0.796341i	$0.293234\pi$
$380$		0			0
$381$	−12.7219			−0.651764
$382$		0			0
$383$	34.7422	+	12.6451i	1.77524	+	0.646135i	0.999893	+	0.0146011i	$0.00464785\pi$
$383$	34.7422	+	12.6451i	1.77524	+	0.646135i	0.775348	+	0.631534i	$0.217574\pi$
$384$		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	0.996025	+	0.0890763i	$0.0283915\pi$
$389$	24.7861	+	20.7980i	1.25671	+	1.05450i	0.260681	+	0.965425i	$0.416053\pi$
$390$		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	−0.471415	−	0.881911i	$-0.656257\pi$
$397$	6.28106	−	5.27043i	0.315237	−	0.264516i	0.786653	+	0.617396i	$0.211812\pi$
$398$		0			0
$399$	10.1912	+	12.5094i	0.510198	+	0.626251i
$400$		0			0
$401$	−11.9500	−	14.2414i	−0.596753	−	0.711182i	0.380136	−	0.924931i	$-0.375877\pi$
$401$	−11.9500	−	14.2414i	−0.596753	−	0.711182i	−0.976889	+	0.213749i	$0.931433\pi$
$402$		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	−0.742752	−	0.669567i	$-0.766480\pi$
$409$	0.922618	−	1.09953i	0.0456205	−	0.0543685i	0.788372	+	0.615199i	$0.210924\pi$
$410$		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	0.301083	+	0.953598i	$0.402652\pi$
$421$	−11.1316	+	30.5838i	−0.542521	+	1.49056i	−0.843604	+	0.536966i	$0.819570\pi$
$422$		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	$-0.799131\pi$
$431$	−21.7297	+	7.90895i	−1.04668	+	0.380961i	−0.239272	+	0.970953i	$0.576909\pi$
$432$		0			0
$433$	11.5869	+	2.04309i	0.556832	+	0.0981846i	0.444980	−	0.895540i	$-0.353211\pi$
$433$	11.5869	+	2.04309i	0.556832	+	0.0981846i	0.111852	+	0.993725i	$0.464322\pi$
$434$		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	$-0.541200\pi$
$439$	17.2875	−	14.5059i	0.825085	−	0.692329i	0.954157	+	0.299307i	$0.0967553\pi$
$440$		0			0
$441$	−1.16385	+	6.60051i	−0.0554213	+	0.314310i
$442$		0			0
$443$	7.23601	+	19.8808i	0.343793	+	0.944565i	0.984283	+	0.176598i	$0.0565092\pi$
$443$	7.23601	+	19.8808i	0.343793	+	0.944565i	−0.640490	+	0.767967i	$0.721269\pi$
$444$		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	0.999552	−	0.0299162i	$-0.00952405\pi$
$449$	31.2212	+	18.0256i	1.47342	+	0.850680i	0.473868	+	0.880596i	$0.342857\pi$
$450$		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	−0.807601	−	0.589729i	$-0.799235\pi$
$461$	−5.37639	−	30.4910i	−0.250404	−	1.42011i	0.557198	−	0.830380i	$-0.311877\pi$
$462$		0			0
$463$	−32.8919	−	18.9902i	−1.52862	−	0.882548i	−0.999420	−	0.0340491i	$-0.989160\pi$
$463$	−32.8919	−	18.9902i	−1.52862	−	0.882548i	−0.529197	−	0.848499i	$-0.677507\pi$
$464$		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	$-0.403890\pi$
$467$	27.5077	−	15.8816i	1.27291	−	0.734913i	0.975534	+	0.219849i	$0.0705564\pi$
$468$		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	$-0.0934343\pi$
$479$	38.4707	+	6.78341i	1.75777	+	0.309942i	0.800541	+	0.599278i	$0.204545\pi$
$480$		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	$-0.990679\pi$
$487$	−10.4697	+	18.1341i	−0.474428	+	0.821734i	0.525143	+	0.851014i	$0.324012\pi$
$488$		0			0
$489$	−15.7515	+	2.77741i	−0.712307	+	0.125599i
$490$		0			0
$491$	−13.7144	+	37.6799i	−0.618920	+	1.70047i	0.0906940	+	0.995879i	$0.471091\pi$
$491$	−13.7144	+	37.6799i	−0.618920	+	1.70047i	−0.709614	+	0.704590i	$0.751131\pi$
$492$		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	$-0.363304\pi$
$499$	24.9873	−	4.40593i	1.11858	−	0.197236i	0.702219	+	0.711961i	$0.252193\pi$
$500$		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	$-0.797481\pi$
$503$	−1.78359	+	2.12559i	−0.0795261	+	0.0947756i	0.724814	+	0.688944i	$0.241926\pi$
$504$		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	0.696712	−	0.717351i	$-0.254645\pi$
$509$	24.9538	+	4.40003i	1.10606	+	0.195028i	0.409347	+	0.912379i	$0.365757\pi$
$510$		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	−0.397691	−	0.917520i	$-0.630188\pi$
$521$	4.52078	−	2.61007i	0.198059	−	0.114349i	0.595750	+	0.803170i	$0.296855\pi$
$522$		0			0
$523$	0.657289	+	0.551531i	0.0287413	+	0.0241168i	0.657045	−	0.753851i	$-0.271806\pi$
$523$	0.657289	+	0.551531i	0.0287413	+	0.0241168i	−0.628304	+	0.777968i	$0.716251\pi$
$524$		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	0.774601	−	0.632451i	$-0.217951\pi$
$541$	6.65839	+	5.58705i	0.286266	+	0.240206i	−0.488334	+	0.872657i	$0.662395\pi$
$542$		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	−0.571827	−	0.820375i	$-0.693765\pi$
$547$	5.75578	−	32.6426i	0.246099	−	1.39570i	0.817926	−	0.575324i	$-0.195124\pi$
$548$		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	−0.621966	−	0.783044i	$-0.713666\pi$
$557$	−14.0446	+	5.11181i	−0.595088	+	0.216594i	0.0268779	+	0.999639i	$0.491443\pi$
$558$		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	$-0.957263\pi$
$563$	−9.00640	+	15.5995i	−0.379574	+	0.657442i	0.611426	+	0.791302i	$0.290596\pi$
$564$		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	$-0.866134\pi$
$569$		−	19.4773i		−	0.816531i	0.912863	−	0.408265i	$-0.133866\pi$
$570$		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	0.0505517	+	0.998721i	$0.483902\pi$
$577$	−20.1689	+	34.9336i	−0.839642	+	1.45430i	−0.890194	+	0.455582i	$0.849431\pi$
$578$		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	$-0.258313\pi$
$587$	−3.52394	−	4.19967i	−0.145448	−	0.173339i	−0.833850	+	0.551991i	$0.813868\pi$
$588$		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	0.914268	+	0.405110i	$0.132767\pi$
$593$	−2.03137	+	11.5205i	−0.0834185	+	0.473090i	−0.997687	+	0.0679804i	$0.978344\pi$
$594$		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	$-0.250968\pi$
$599$	3.15451	+	2.64695i	0.128890	+	0.108152i	−0.576064	+	0.817405i	$0.695412\pi$
$600$		0			0
$601$	6.24376	+	3.60483i	0.254688	+	0.147044i	0.621909	−	0.783090i	$-0.286357\pi$
$601$	6.24376	+	3.60483i	0.254688	+	0.147044i	−0.367221	+	0.930134i	$0.619691\pi$
$602$		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	$-0.601826\pi$
$607$	−15.4953			−0.628933			−0.314466	+	0.949269i	$0.601826\pi$
$608$		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	−0.938528	−	0.345203i	$-0.887810\pi$
$613$	−4.32454	−	24.5257i	−0.174667	−	0.990583i	0.763861	−	0.645380i	$-0.223301\pi$
$614$		0			0
$615$	−2.68938	−	1.55271i	−0.108446	−	0.0626114i
$616$		0			0
$617$	7.19119	+	6.03412i	0.289506	+	0.242925i	0.775961	−	0.630781i	$-0.217266\pi$
$617$	7.19119	+	6.03412i	0.289506	+	0.242925i	−0.486454	+	0.873706i	$0.661710\pi$
$618$		0			0
$619$	23.1318	−	13.3552i	0.929746	−	0.536789i	0.0430149	−	0.999074i	$-0.486304\pi$
$619$	23.1318	−	13.3552i	0.929746	−	0.536789i	0.886731	+	0.462285i	$0.152970\pi$
$620$		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	$-0.428544\pi$
$631$	2.47044	+	0.435605i	0.0983466	+	0.0173412i	−0.124258	+	0.992250i	$0.539655\pi$
$632$		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	0.505419	−	0.862874i	$-0.331338\pi$
$641$	32.2925	−	5.69404i	1.27548	−	0.224901i	0.770059	+	0.637973i	$0.220227\pi$
$642$		0			0
$643$	−5.22028	+	14.3426i	−0.205868	+	0.565618i	−0.999060	−	0.0433543i	$-0.986196\pi$
$643$	−5.22028	+	14.3426i	−0.205868	+	0.565618i	0.793192	+	0.608972i	$0.208418\pi$
$644$		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	−0.653716	−	0.756740i	$-0.726791\pi$
$653$	8.39440	−	14.5395i	0.328498	−	0.568976i	0.982214	+	0.187764i	$0.0601242\pi$
$654$		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	$-0.596330\pi$
$659$	2.23947	−	0.815102i	0.0872376	−	0.0317519i	0.385270	+	0.922804i	$0.374108\pi$
$660$		0			0
$661$	−5.44104	−	0.959402i	−0.211632	−	0.0373164i	0.0668270	−	0.997765i	$-0.478712\pi$
$661$	−5.44104	−	0.959402i	−0.211632	−	0.0373164i	−0.278459	+	0.960448i	$0.589824\pi$
$662$		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	−0.501434	−	0.865196i	$-0.667194\pi$
$673$	−0.0744448	+	0.0429807i	−0.00286964	+	0.00165678i	0.498564	+	0.866853i	$0.333861\pi$
$674$		0			0
$675$	2.43969	+	2.04715i	0.0939038	+	0.0787947i
$676$		0			0
$677$	9.80113	+	5.65868i	0.376688	+	0.217481i	0.676376	−	0.736556i	$-0.263549\pi$
$677$	9.80113	+	5.65868i	0.376688	+	0.217481i	−0.299688	+	0.954037i	$0.596883\pi$
$678$		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	$-0.844372\pi$
$683$	−46.1448			−1.76568			−0.882840	+	0.469673i	$0.844372\pi$
$684$		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	$-0.185918\pi$
$691$	20.3402	+	11.7434i	0.773777	+	0.446740i	−0.0604433	+	0.998172i	$0.519251\pi$
$692$		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	−0.0588912	−	0.998264i	$-0.518757\pi$
$701$	24.1989	−	20.3053i	0.913981	−	0.766921i	0.972872	+	0.231343i	$0.0743121\pi$
$702$		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	0.446738	−	0.894665i	$-0.352586\pi$
$709$	36.3203	−	13.2195i	1.36404	−	0.496469i	0.917300	+	0.398196i	$0.130364\pi$
$710$		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	−0.621084	−	0.783744i	$-0.713307\pi$
$719$	9.61222	−	26.4093i	0.358475	−	0.984902i	0.979559	−	0.201158i	$-0.0644705\pi$
$720$		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	$-0.540978\pi$
$727$	2.43124	−	0.428693i	0.0901696	−	0.0158993i	0.218551	+	0.975826i	$0.429867\pi$
$728$		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	0.638998	−	0.769208i	$-0.279349\pi$
$733$	−9.38532	−	16.2558i	−0.346655	−	0.600423i	−0.985653	+	0.168785i	$0.946016\pi$
$734$		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	$-0.0381239\pi$
$739$	19.1043	+	22.7676i	0.702763	+	0.837521i	−0.290073	+	0.957005i	$0.593679\pi$
$740$		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	$-0.693233\pi$
$743$	3.79813	−	3.18701i	0.139340	−	0.116920i	0.709794	+	0.704410i	$0.248788\pi$
$744$		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	$-0.437406\pi$
$751$	−20.1839	−	16.9363i	−0.736522	−	0.618015i	−0.931901	+	0.362713i	$0.881851\pi$
$752$		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	0.397109	−	0.917771i	$-0.370013\pi$
$757$	3.06448	+	1.11538i	0.111381	+	0.0405392i	−0.285729	+	0.958311i	$0.592236\pi$
$758$		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	−0.946333	−	0.323195i	$-0.895243\pi$
$769$	−39.6259	−	33.2501i	−1.42895	−	1.19903i	−0.482613	−	0.875833i	$-0.660312\pi$
$770$		0			0
$771$	−25.8212	+	14.9079i	−0.929928	+	0.536894i
$772$		0			0
$773$	4.76975	+	13.1048i	0.171556	+	0.471346i	0.995438	−	0.0954157i	$-0.0304180\pi$
$773$	4.76975	+	13.1048i	0.171556	+	0.471346i	−0.823881	+	0.566762i	$0.808196\pi$
$774$		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	$-0.256916\pi$
$787$	−7.84776	−	13.5927i	−0.279743	−	0.484528i	−0.971321	+	0.237773i	$0.923582\pi$
$788$		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	$0.157598\pi$
$797$			26.8268i			0.950253i	−0.879917	+	0.475127i	$0.842402\pi$
$798$		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	0.997638	−	0.0686963i	$-0.0218839\pi$
$809$	12.4957	+	21.6432i	0.439326	+	0.760935i	−0.558312	+	0.829631i	$0.688551\pi$
$810$		0			0
$811$	−22.2785	+	8.10872i	−0.782305	+	0.284736i	−0.702134	−	0.712045i	$-0.747769\pi$
$811$	−22.2785	+	8.10872i	−0.782305	+	0.284736i	−0.0801716	+	0.996781i	$0.525547\pi$
$812$		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	−0.992745	−	0.120237i	$-0.961635\pi$
$821$	−0.537141	+	3.04628i	−0.0187464	+	0.106316i	0.973999	+	0.226553i	$0.0727456\pi$
$822$		0			0
$823$	−7.49660	−	20.5967i	−0.261315	−	0.717957i	−0.999079	−	0.0428987i	$-0.986341\pi$
$823$	−7.49660	−	20.5967i	−0.261315	−	0.717957i	0.737765	−	0.675058i	$-0.235881\pi$
$824$		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	$-0.294126\pi$
$827$	−2.26193	−	1.89798i	−0.0786549	−	0.0659993i	−0.681267	+	0.732035i	$0.738571\pi$
$828$		0			0
$829$	31.0241	+	17.9118i	1.07751	+	0.622102i	0.930224	−	0.366992i	$-0.119612\pi$
$829$	31.0241	+	17.9118i	1.07751	+	0.622102i	0.147287	+	0.989094i	$0.452946\pi$
$830$		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	$-0.275319\pi$
$839$	19.0133	+	6.92026i	0.656411	+	0.238914i	0.00772472	+	0.999970i	$0.497541\pi$
$840$		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	−0.311531	−	0.950236i	$-0.600842\pi$
$853$	16.6525	−	13.9731i	0.570172	−	0.478431i	0.881703	+	0.471805i	$0.156397\pi$
$854$		0			0
$855$	3.00980	−	5.04282i	0.102933	−	0.172461i
$856$		0			0
$857$	−7.93289	−	9.45404i	−0.270982	−	0.322944i	0.613342	−	0.789818i	$-0.289825\pi$
$857$	−7.93289	−	9.45404i	−0.270982	−	0.322944i	−0.884324	+	0.466873i	$0.845380\pi$
$858$		0			0
$859$	−28.9231	−	5.09992i	−0.986843	−	0.174007i	−0.343141	−	0.939284i	$-0.611491\pi$
$859$	−28.9231	−	5.09992i	−0.986843	−	0.174007i	−0.643701	+	0.765277i	$0.722602\pi$
$860$		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	$-0.116729\pi$
$863$	4.58987	+	7.94989i	0.156241	+	0.270617i	−0.777269	+	0.629168i	$0.783396\pi$
$864$		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	−0.365662	−	0.930748i	$-0.619157\pi$
$877$	15.1839	−	41.7175i	0.512724	−	1.40870i	0.878386	−	0.477951i	$-0.158620\pi$
$878$		0			0
$879$	0.582596	−	0.102727i	0.0196505	−	0.00346491i
$880$		0			0
$881$	−9.03802	+	15.6543i	−0.304499	+	0.527407i	−0.977150	−	0.212553i	$-0.931822\pi$
$881$	−9.03802	+	15.6543i	−0.304499	+	0.527407i	0.672651	+	0.739960i	$0.265156\pi$
$882$		0			0
$883$	−34.7271	+	41.3862i	−1.16866	+	1.39276i	−0.265142	+	0.964209i	$0.585419\pi$
$883$	−34.7271	+	41.3862i	−1.16866	+	1.39276i	−0.903519	+	0.428547i	$0.859026\pi$
$884$		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	$-0.886313\pi$
$887$	−42.5852	+	15.4997i	−1.42987	+	0.520430i	−0.492976	+	0.870043i	$0.664091\pi$
$888$		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	0.948240	+	0.317556i	$0.102862\pi$
$907$	4.99319	+	28.3178i	0.165796	+	0.940277i	−0.782443	+	0.622722i	$0.786027\pi$
$908$		0			0
$909$	−16.4153	−	5.97470i	−0.544463	−	0.198168i
$910$		0			0
$911$	−8.61856			−0.285545			−0.142773	−	0.989755i	$-0.545602\pi$
$911$	−8.61856			−0.285545			−0.142773	+	0.989755i	$0.545602\pi$
$912$		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	$-0.101669\pi$
$919$	34.9291	+	20.1663i	1.15220	+	0.665225i	0.202780	+	0.979224i	$0.435002\pi$
$920$		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	0.549089	−	0.835764i	$-0.314975\pi$
$929$	44.7288	−	37.5319i	1.46750	−	1.23138i	0.918415	−	0.395619i	$-0.129470\pi$
$930$		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	0.823976	−	0.566625i	$-0.191751\pi$
$937$	55.6926	−	20.2704i	1.81940	−	0.662207i	0.995422	−	0.0955819i	$-0.0304712\pi$
$938$		0			0
$939$	−11.5715	−	20.0423i	−0.377620	−	0.654057i
$940$		0			0
$941$	−15.4765	+	18.4442i	−0.504520	+	0.601264i	−0.956848	−	0.290588i	$-0.906149\pi$
$941$	−15.4765	+	18.4442i	−0.504520	+	0.601264i	0.452328	+	0.891852i	$0.350594\pi$
$942$		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	−0.475439	−	0.879749i	$-0.657711\pi$
$947$	13.9791	−	38.4073i	0.454260	−	1.24807i	0.929699	−	0.368321i	$-0.120067\pi$
$948$		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	0.665983	+	0.745967i	$0.268012\pi$
$953$	−9.99248	+	27.4541i	−0.323688	+	0.889326i	−0.989671	+	0.143359i	$0.954210\pi$
$954$		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	$-0.361903\pi$
$967$	−16.9851	−	20.2421i	−0.546206	−	0.650942i	−0.966567	+	0.256414i	$0.917459\pi$
$968$		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	$-0.671090\pi$
$971$	7.63610	−	6.40745i	0.245054	−	0.205625i	0.757039	+	0.653370i	$0.226645\pi$
$972$		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	−0.632427	−	0.774620i	$-0.717941\pi$
$977$	−8.68320	+	5.01325i	−0.277800	+	0.160388i	0.354627	+	0.935008i	$0.384608\pi$
$978$		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	0.884686	+	0.466187i	$0.154373\pi$
$983$	6.67184	+	37.8379i	0.212799	+	1.20684i	−0.671887	+	0.740653i	$0.734516\pi$
$984$		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	$-0.722163\pi$
$991$	−51.2315	−	18.6467i	−1.62742	−	0.592333i	−0.984776	+	0.173830i	$0.944386\pi$
$992$		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	0.873846	−	0.486203i	$-0.161619\pi$
$997$	17.2645	+	14.4866i	0.546771	+	0.458795i	−0.327075	+	0.944998i	$0.606063\pi$
$998$		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.b.127.1	yes	6
4.3	odd	2		912.2.ci.a.127.1	yes	6
19.3	odd	18		912.2.ci.a.79.1	✓	6
76.3	even	18	inner	912.2.ci.b.79.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.a.79.1	✓	6	19.3	odd	18
912.2.ci.a.127.1	yes	6	4.3	odd	2
912.2.ci.b.79.1	yes	6	76.3	even	18	inner
912.2.ci.b.127.1	yes	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
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

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