LMFDB - Embedded newform 912.2.bo.d.289.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [912,2,Mod(289,912)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("912.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(912, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bo (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			289.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	912.289
Dual form			912.2.bo.d.385.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.173648 + 0.984808i) q^{3} +(-0.0923963 + 0.0775297i) q^{5} +(-2.14543 + 3.71599i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(1.28699 + 2.22913i) q^{11} +(0.141559 - 0.802823i) q^{13} +(-0.0923963 - 0.0775297i) q^{15} +(0.439693 + 0.160035i) q^{17} +(-3.16637 - 2.99568i) q^{19} +(-4.03209 - 1.46756i) q^{21} +(-4.25490 - 3.57029i) q^{23} +(-0.865715 + 4.90971i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(-2.20574 + 0.802823i) q^{29} +(2.67365 - 4.63089i) q^{31} +(-1.97178 + 1.65452i) q^{33} +(-0.0898700 - 0.509678i) q^{35} -8.51754 q^{37} +0.815207 q^{39} +(0.666374 + 3.77920i) q^{41} +(-7.14930 + 5.99898i) q^{43} +(0.0603074 - 0.104455i) q^{45} +(-8.90420 + 3.24086i) q^{47} +(-5.70574 - 9.88263i) q^{49} +(-0.0812519 + 0.460802i) q^{51} +(9.77379 + 8.20118i) q^{53} +(-0.291737 - 0.106183i) q^{55} +(2.40033 - 3.63846i) q^{57} +(14.1420 + 5.14728i) q^{59} +(-1.31521 - 1.10359i) q^{61} +(0.745100 - 4.22567i) q^{63} +(0.0491630 + 0.0851529i) q^{65} +(10.7652 - 3.91820i) q^{67} +(2.77719 - 4.81023i) q^{69} +(-10.2135 + 8.57013i) q^{71} +(0.396459 + 2.24843i) q^{73} -4.98545 q^{75} -11.0446 q^{77} +(-0.843426 - 4.78331i) q^{79} +(0.766044 - 0.642788i) q^{81} +(1.62449 - 2.81369i) q^{83} +(-0.0530334 + 0.0193026i) q^{85} +(-1.17365 - 2.03282i) q^{87} +(0.595800 - 3.37895i) q^{89} +(2.67958 + 2.24843i) q^{91} +(5.02481 + 1.82888i) q^{93} +(0.524815 + 0.0313013i) q^{95} +(-2.91400 - 1.06061i) q^{97} +(-1.97178 - 1.65452i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} + 3 q^{7} + 9 q^{13} + 3 q^{15} - 3 q^{17} - 15 q^{21} - 27 q^{23} - 15 q^{25} - 3 q^{27} - 3 q^{29} + 15 q^{31} + 3 q^{33} - 12 q^{35} - 6 q^{37} + 12 q^{39} - 15 q^{41} - 3 q^{43} + 6 q^{45}+ \cdots + 3 q^{99}+O(q^{100}) $ 6 * q + 3 * q^5 + 3 * q^7 + 9 * q^13 + 3 * q^15 - 3 * q^17 - 15 * q^21 - 27 * q^23 - 15 * q^25 - 3 * q^27 - 3 * q^29 + 15 * q^31 + 3 * q^33 - 12 * q^35 - 6 * q^37 + 12 * q^39 - 15 * q^41 - 3 * q^43 + 6 * q^45 - 15 * q^47 - 24 * q^49 - 3 * q^51 + 6 * q^53 - 27 * q^55 + 27 * q^59 - 15 * q^61 + 3 * q^63 + 12 * q^65 + 3 * q^67 + 6 * q^69 - 3 * q^71 + 12 * q^73 + 6 * q^75 - 42 * q^77 - 27 * q^79 - 3 * q^83 + 12 * q^85 - 6 * q^87 + 42 * q^89 + 42 * q^91 + 3 * q^93 - 24 * q^95 + 18 * q^97 + 3 * q^99

Character values

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

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$	$1$	$1$

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
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$4$		0			0
$5$	−0.0923963	+	0.0775297i	−0.0413209	+	0.0346723i	−0.663214	−	0.748430i	$-0.730808\pi$
$5$	−0.0923963	+	0.0775297i	−0.0413209	+	0.0346723i	0.621893	+	0.783102i	$0.286364\pi$
$6$		0			0
$7$	−2.14543	+	3.71599i	−0.810896	+	1.40451i	0.101341	+	0.994852i	$0.467687\pi$
$7$	−2.14543	+	3.71599i	−0.810896	+	1.40451i	−0.912238	+	0.409662i	$0.865647\pi$
$8$		0			0
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$		0			0
$11$	1.28699	+	2.22913i	0.388042	+	0.672108i	0.992186	−	0.124767i	$-0.0398183\pi$
$11$	1.28699	+	2.22913i	0.388042	+	0.672108i	−0.604144	+	0.796875i	$0.706485\pi$
$12$		0			0
$13$	0.141559	−	0.802823i	0.0392615	−	0.222663i	−0.958864	−	0.283866i	$-0.908383\pi$
$13$	0.141559	−	0.802823i	0.0392615	−	0.222663i	0.998125	+	0.0612035i	$0.0194939\pi$
$14$		0			0
$15$	−0.0923963	−	0.0775297i	−0.0238566	−	0.0200181i
$16$		0			0
$17$	0.439693	+	0.160035i	0.106641	+	0.0388142i	0.394790	−	0.918772i	$-0.370817\pi$
$17$	0.439693	+	0.160035i	0.106641	+	0.0388142i	−0.288149	+	0.957586i	$0.593040\pi$
$18$		0			0
$19$	−3.16637	−	2.99568i	−0.726416	−	0.687255i
$19$	−3.16637	−	2.99568i	−0.726416	−	0.687255i
$20$		0			0
$21$	−4.03209	−	1.46756i	−0.879874	−	0.320248i
$22$		0			0
$23$	−4.25490	−	3.57029i	−0.887208	−	0.744456i	0.0804401	−	0.996759i	$-0.474367\pi$
$23$	−4.25490	−	3.57029i	−0.887208	−	0.744456i	−0.967648	+	0.252304i	$0.918812\pi$
$24$		0			0
$25$	−0.865715	+	4.90971i	−0.173143	+	0.981942i
$26$		0			0
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$		0			0
$29$	−2.20574	+	0.802823i	−0.409595	+	0.149080i	−0.538596	−	0.842564i	$-0.681045\pi$
$29$	−2.20574	+	0.802823i	−0.409595	+	0.149080i	0.129001	+	0.991644i	$0.458823\pi$
$30$		0			0
$31$	2.67365	−	4.63089i	0.480201	−	0.831733i	−0.519541	−	0.854446i	$-0.673897\pi$
$31$	2.67365	−	4.63089i	0.480201	−	0.831733i	0.999742	+	0.0227125i	$0.00723025\pi$
$32$		0			0
$33$	−1.97178	+	1.65452i	−0.343243	+	0.288015i
$34$		0			0
$35$	−0.0898700	−	0.509678i	−0.0151908	−	0.0861514i
$36$		0			0
$37$	−8.51754			−1.40028			−0.700138	−	0.714008i	$-0.746878\pi$
$37$	−8.51754			−1.40028			−0.700138	+	0.714008i	$0.746878\pi$
$38$		0			0
$39$	0.815207			0.130538
$40$		0			0
$41$	0.666374	+	3.77920i	0.104070	+	0.590211i	0.991588	+	0.129437i	$0.0413171\pi$
$41$	0.666374	+	3.77920i	0.104070	+	0.590211i	−0.887517	+	0.460774i	$0.847572\pi$
$42$		0			0
$43$	−7.14930	+	5.99898i	−1.09026	+	0.914835i	−0.996732	−	0.0807817i	$-0.974258\pi$
$43$	−7.14930	+	5.99898i	−1.09026	+	0.914835i	−0.0935262	+	0.995617i	$0.529814\pi$
$44$		0			0
$45$	0.0603074	−	0.104455i	0.00899009	−	0.0155713i
$46$		0			0
$47$	−8.90420	+	3.24086i	−1.29881	+	0.472729i	−0.896609	−	0.442822i	$-0.853977\pi$
$47$	−8.90420	+	3.24086i	−1.29881	+	0.472729i	−0.402202	+	0.915551i	$0.631755\pi$
$48$		0			0
$49$	−5.70574	−	9.88263i	−0.815105	−	1.41180i
$50$		0			0
$51$	−0.0812519	+	0.460802i	−0.0113775	+	0.0645253i
$52$		0			0
$53$	9.77379	+	8.20118i	1.34253	+	1.12652i	0.980968	+	0.194172i	$0.0622019\pi$
$53$	9.77379	+	8.20118i	1.34253	+	1.12652i	0.361565	+	0.932347i	$0.382243\pi$
$54$		0			0
$55$	−0.291737	−	0.106183i	−0.0393378	−	0.0143178i
$56$		0			0
$57$	2.40033	−	3.63846i	0.317931	−	0.481926i
$58$		0			0
$59$	14.1420	+	5.14728i	1.84113	+	0.670118i	0.989220	+	0.146439i	$0.0467811\pi$
$59$	14.1420	+	5.14728i	1.84113	+	0.670118i	0.851915	+	0.523680i	$0.175441\pi$
$60$		0			0
$61$	−1.31521	−	1.10359i	−0.168395	−	0.141300i	0.554696	−	0.832053i	$-0.312835\pi$
$61$	−1.31521	−	1.10359i	−0.168395	−	0.141300i	−0.723091	+	0.690753i	$0.757279\pi$
$62$		0			0
$63$	0.745100	−	4.22567i	0.0938738	−	0.532385i
$64$		0			0
$65$	0.0491630	+	0.0851529i	0.00609792	+	0.0105619i
$66$		0			0
$67$	10.7652	−	3.91820i	1.31517	−	0.478684i	0.413266	−	0.910611i	$-0.364388\pi$
$67$	10.7652	−	3.91820i	1.31517	−	0.478684i	0.901909	+	0.431926i	$0.142166\pi$
$68$		0			0
$69$	2.77719	−	4.81023i	0.334334	−	0.579084i
$70$		0			0
$71$	−10.2135	+	8.57013i	−1.21212	+	1.01709i	−0.212918	+	0.977070i	$0.568297\pi$
$71$	−10.2135	+	8.57013i	−1.21212	+	1.01709i	−0.999199	+	0.0400167i	$0.987259\pi$
$72$		0			0
$73$	0.396459	+	2.24843i	0.0464021	+	0.263159i	0.999179	−	0.0405117i	$-0.0128988\pi$
$73$	0.396459	+	2.24843i	0.0464021	+	0.263159i	−0.952777	+	0.303671i	$0.901788\pi$
$74$		0			0
$75$	−4.98545			−0.575670
$76$		0			0
$77$	−11.0446			−1.25865
$78$		0			0
$79$	−0.843426	−	4.78331i	−0.0948928	−	0.538164i	−0.994780	−	0.102042i	$-0.967463\pi$
$79$	−0.843426	−	4.78331i	−0.0948928	−	0.538164i	0.899887	−	0.436122i	$-0.143649\pi$
$80$		0			0
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$		0			0
$83$	1.62449	−	2.81369i	0.178310	−	0.308843i	−0.762992	−	0.646408i	$-0.776270\pi$
$83$	1.62449	−	2.81369i	0.178310	−	0.308843i	0.941302	+	0.337566i	$0.109604\pi$
$84$		0			0
$85$	−0.0530334	+	0.0193026i	−0.00575228	+	0.00209366i
$86$		0			0
$87$	−1.17365	−	2.03282i	−0.125828	−	0.217941i
$88$		0			0
$89$	0.595800	−	3.37895i	0.0631547	−	0.358168i	−0.936811	−	0.349837i	$-0.886237\pi$
$89$	0.595800	−	3.37895i	0.0631547	−	0.358168i	0.999965	−	0.00833100i	$-0.00265187\pi$
$90$		0			0
$91$	2.67958	+	2.24843i	0.280896	+	0.235700i
$92$		0			0
$93$	5.02481	+	1.82888i	0.521049	+	0.189646i
$94$		0			0
$95$	0.524815	+	0.0313013i	0.0538449	+	0.00321145i
$96$		0			0
$97$	−2.91400	−	1.06061i	−0.295872	−	0.107689i	0.189819	−	0.981819i	$-0.439210\pi$
$97$	−2.91400	−	1.06061i	−0.295872	−	0.107689i	−0.485691	+	0.874130i	$0.661432\pi$
$98$		0			0
$99$	−1.97178	−	1.65452i	−0.198171	−	0.166286i
$100$		0			0
$101$	−2.90508	+	16.4755i	−0.289066	+	1.63937i	0.401323	+	0.915937i	$0.368550\pi$
$101$	−2.90508	+	16.4755i	−0.289066	+	1.63937i	−0.690389	+	0.723438i	$0.742561\pi$
$102$		0			0
$103$	−5.19846	−	9.00400i	−0.512220	−	0.887191i	−0.999900	−	0.0141681i	$-0.995490\pi$
$103$	−5.19846	−	9.00400i	−0.512220	−	0.887191i	0.487680	−	0.873023i	$-0.337843\pi$
$104$		0			0
$105$	0.486329	−	0.177009i	0.0474609	−	0.0172744i
$106$		0			0
$107$	−4.55690	+	7.89279i	−0.440533	+	0.763025i	−0.997729	−	0.0673560i	$-0.978544\pi$
$107$	−4.55690	+	7.89279i	−0.440533	+	0.763025i	0.557196	+	0.830381i	$0.311877\pi$
$108$		0			0
$109$	2.93376	−	2.46172i	0.281004	−	0.235790i	−0.491382	−	0.870944i	$-0.663508\pi$
$109$	2.93376	−	2.46172i	0.281004	−	0.235790i	0.772385	+	0.635154i	$0.219064\pi$
$110$		0			0
$111$	−1.47906	−	8.38814i	−0.140386	−	0.796167i
$112$		0			0
$113$	5.41147			0.509069			0.254534	−	0.967064i	$-0.418078\pi$
$113$	5.41147			0.509069			0.254534	+	0.967064i	$0.418078\pi$
$114$		0			0
$115$	0.669940			0.0624722
$116$		0			0
$117$	0.141559	+	0.802823i	0.0130872	+	0.0742210i
$118$		0			0
$119$	−1.53802	+	1.29055i	−0.140990	+	0.118305i
$120$		0			0
$121$	2.18732	−	3.78855i	0.198847	−	0.344413i
$122$		0			0
$123$	−3.60607	+	1.31250i	−0.325148	+	0.118344i
$124$		0			0
$125$	−0.602196	−	1.04303i	−0.0538621	−	0.0932919i
$126$		0			0
$127$	−0.736482	+	4.17680i	−0.0653522	+	0.370631i	0.934539	+	0.355861i	$0.115812\pi$
$127$	−0.736482	+	4.17680i	−0.0653522	+	0.370631i	−0.999891	+	0.0147693i	$0.995299\pi$
$128$		0			0
$129$	−7.14930	−	5.99898i	−0.629461	−	0.528180i
$130$		0			0
$131$	19.7738	+	7.19707i	1.72764	+	0.628811i	0.998458	−	0.0555055i	$-0.0176770\pi$
$131$	19.7738	+	7.19707i	1.72764	+	0.628811i	0.729185	+	0.684316i	$0.239899\pi$
$132$		0			0
$133$	17.9251	−	5.33921i	1.55431	−	0.462968i
$134$		0			0
$135$	0.113341	+	0.0412527i	0.00975482	+	0.00355047i
$136$		0			0
$137$	−9.43835	−	7.91971i	−0.806373	−	0.676627i	0.143367	−	0.989670i	$-0.454207\pi$
$137$	−9.43835	−	7.91971i	−0.806373	−	0.676627i	−0.949739	+	0.313043i	$0.898652\pi$
$138$		0			0
$139$	0.970437	−	5.50362i	0.0823114	−	0.466811i	−0.915593	−	0.402106i	$-0.868278\pi$
$139$	0.970437	−	5.50362i	0.0823114	−	0.466811i	0.997904	−	0.0647050i	$-0.0206106\pi$
$140$		0			0
$141$	−4.73783	−	8.20616i	−0.398997	−	0.691083i
$142$		0			0
$143$	1.97178	−	0.717670i	0.164889	−	0.0600146i
$144$		0			0
$145$	0.141559	−	0.245188i	0.0117559	−	0.0203617i
$146$		0			0
$147$	8.74170	−	7.33515i	0.721003	−	0.604993i
$148$		0			0
$149$	1.92649	+	10.9257i	0.157824	+	0.895065i	0.956158	+	0.292850i	$0.0946038\pi$
$149$	1.92649	+	10.9257i	0.157824	+	0.895065i	−0.798334	+	0.602215i	$0.794285\pi$
$150$		0			0
$151$	−12.5963			−1.02507			−0.512535	−	0.858666i	$-0.671293\pi$
$151$	−12.5963			−1.02507			−0.512535	+	0.858666i	$0.671293\pi$
$152$		0			0
$153$	−0.467911			−0.0378284
$154$		0			0
$155$	0.111997	+	0.635164i	0.00899579	+	0.0510176i
$156$		0			0
$157$	−3.04710	+	2.55682i	−0.243185	+	0.204057i	−0.756231	−	0.654304i	$-0.772962\pi$
$157$	−3.04710	+	2.55682i	−0.243185	+	0.204057i	0.513046	+	0.858361i	$0.328517\pi$
$158$		0			0
$159$	−6.37939	+	11.0494i	−0.505918	+	0.876276i
$160$		0			0
$161$	22.3957	−	8.15138i	1.76503	−	0.642419i
$162$		0			0
$163$	9.60014	+	16.6279i	0.751941	+	1.30240i	0.946881	+	0.321584i	$0.104215\pi$
$163$	9.60014	+	16.6279i	0.751941	+	1.30240i	−0.194940	+	0.980815i	$0.562451\pi$
$164$		0			0
$165$	0.0539108	−	0.305743i	0.00419695	−	0.0238021i
$166$		0			0
$167$	11.7777	+	9.88263i	0.911382	+	0.764741i	0.972381	−	0.233397i	$-0.0749842\pi$
$167$	11.7777	+	9.88263i	0.911382	+	0.764741i	−0.0609991	+	0.998138i	$0.519429\pi$
$168$		0			0
$169$	11.5915	+	4.21897i	0.891655	+	0.324536i
$170$		0			0
$171$	4.00000	+	1.73205i	0.305888	+	0.132453i
$172$		0			0
$173$	6.19594	+	2.25514i	0.471068	+	0.171455i	0.566636	−	0.823968i	$-0.308244\pi$
$173$	6.19594	+	2.25514i	0.471068	+	0.171455i	−0.0955679	+	0.995423i	$0.530467\pi$
$174$		0			0
$175$	−16.3871	−	13.7504i	−1.23875	−	1.03943i
$176$		0			0
$177$	−2.61334	+	14.8210i	−0.196431	+	1.11401i
$178$		0			0
$179$	0.620615	+	1.07494i	0.0463869	+	0.0803445i	0.888287	−	0.459290i	$-0.151896\pi$
$179$	0.620615	+	1.07494i	0.0463869	+	0.0803445i	−0.841900	+	0.539634i	$0.818563\pi$
$180$		0			0
$181$	−3.78699	+	1.37835i	−0.281485	+	0.102452i	−0.478905	−	0.877867i	$-0.658966\pi$
$181$	−3.78699	+	1.37835i	−0.281485	+	0.102452i	0.197420	+	0.980319i	$0.436744\pi$
$182$		0			0
$183$	0.858441	−	1.48686i	0.0634578	−	0.109912i
$184$		0			0
$185$	0.786989	−	0.660362i	0.0578606	−	0.0485508i
$186$		0			0
$187$	0.209141	+	1.18610i	0.0152939	+	0.0867359i
$188$		0			0
$189$	4.29086			0.312114
$190$		0			0
$191$	24.0847			1.74271			0.871354	−	0.490654i	$-0.163242\pi$
$191$	24.0847			1.74271			0.871354	+	0.490654i	$0.163242\pi$
$192$		0			0
$193$	−1.71213	−	9.70999i	−0.123242	−	0.698941i	−0.982336	−	0.187123i	$-0.940084\pi$
$193$	−1.71213	−	9.70999i	−0.123242	−	0.698941i	0.859094	−	0.511817i	$-0.171028\pi$
$194$		0			0
$195$	−0.0753221	+	0.0632028i	−0.00539393	+	0.00452604i
$196$		0			0
$197$	3.22803	−	5.59110i	0.229987	−	0.398350i	−0.727817	−	0.685772i	$-0.759465\pi$
$197$	3.22803	−	5.59110i	0.229987	−	0.398350i	0.957804	+	0.287422i	$0.0927982\pi$
$198$		0			0
$199$	23.2777	−	8.47237i	1.65011	−	0.600591i	0.661346	−	0.750081i	$-0.269985\pi$
$199$	23.2777	−	8.47237i	1.65011	−	0.600591i	0.988763	+	0.149490i	$0.0477633\pi$
$200$		0			0
$201$	5.72803	+	9.92123i	0.404024	+	0.699790i
$202$		0			0
$203$	1.74897	−	9.91890i	0.122754	−	0.696171i
$204$		0			0
$205$	−0.354570	−	0.297520i	−0.0247643	−	0.0207797i
$206$		0			0
$207$	5.21941	+	1.89971i	0.362774	+	0.132039i
$208$		0			0
$209$	2.60266	−	10.9137i	0.180030	−	0.754914i
$210$		0			0
$211$	−1.30066	−	0.473401i	−0.0895411	−	0.0325903i	0.296861	−	0.954921i	$-0.404060\pi$
$211$	−1.30066	−	0.473401i	−0.0895411	−	0.0325903i	−0.386402	+	0.922330i	$0.626282\pi$
$212$		0			0
$213$	−10.2135	−	8.57013i	−0.699816	−	0.587215i
$214$		0			0
$215$	0.195470	−	1.10857i	0.0133309	−	0.0756036i
$216$		0			0
$217$	11.4722	+	19.8705i	0.778787	+	1.34890i
$218$		0			0
$219$	−2.14543	+	0.780873i	−0.144975	+	0.0527665i
$220$		0			0
$221$	0.190722	−	0.330341i	0.0128294	−	0.0222211i
$222$		0			0
$223$	−17.0929	+	14.3426i	−1.14462	+	0.960453i	−0.999580	−	0.0289729i	$-0.990776\pi$
$223$	−17.0929	+	14.3426i	−1.14462	+	0.960453i	−0.145043	+	0.989425i	$0.546332\pi$
$224$		0			0
$225$	−0.865715	−	4.90971i	−0.0577143	−	0.327314i
$226$		0			0
$227$	20.7665			1.37832			0.689161	−	0.724608i	$-0.257979\pi$
$227$	20.7665			1.37832			0.689161	+	0.724608i	$0.257979\pi$
$228$		0			0
$229$	5.51754			0.364609			0.182305	−	0.983242i	$-0.441644\pi$
$229$	5.51754			0.364609			0.182305	+	0.983242i	$0.441644\pi$
$230$		0			0
$231$	−1.91787	−	10.8768i	−0.126187	−	0.715640i
$232$		0			0
$233$	−11.5569	+	9.69739i	−0.757118	+	0.635297i	−0.937375	−	0.348322i	$-0.886752\pi$
$233$	−11.5569	+	9.69739i	−0.757118	+	0.635297i	0.180257	+	0.983620i	$0.442307\pi$
$234$		0			0
$235$	0.571452	−	0.989783i	0.0372774	−	0.0645664i
$236$		0			0
$237$	4.56418	−	1.66122i	0.296475	−	0.107908i
$238$		0			0
$239$	−14.4757	−	25.0726i	−0.936352	−	1.62181i	−0.772205	−	0.635374i	$-0.780846\pi$
$239$	−14.4757	−	25.0726i	−0.936352	−	1.62181i	−0.164147	−	0.986436i	$-0.552487\pi$
$240$		0			0
$241$	−3.36349	+	19.0753i	−0.216662	+	1.22875i	0.661338	+	0.750088i	$0.269989\pi$
$241$	−3.36349	+	19.0753i	−0.216662	+	1.22875i	−0.878000	+	0.478661i	$0.841122\pi$
$242$		0			0
$243$	0.766044	+	0.642788i	0.0491418	+	0.0412348i
$244$		0			0
$245$	1.29339	+	0.470754i	0.0826314	+	0.0300754i
$246$		0			0
$247$	−2.85323	+	2.11797i	−0.181546	+	0.134763i
$248$		0			0
$249$	3.05303	+	1.11121i	0.193478	+	0.0704203i
$250$		0			0
$251$	3.32635	+	2.79114i	0.209957	+	0.176175i	0.741702	−	0.670730i	$-0.234019\pi$
$251$	3.32635	+	2.79114i	0.209957	+	0.176175i	−0.531745	+	0.846905i	$0.678463\pi$
$252$		0			0
$253$	2.48262	−	14.0796i	0.156081	−	0.885180i
$254$		0			0
$255$	−0.0282185	−	0.0488759i	−0.00176711	−	0.00306073i
$256$		0			0
$257$	−16.6951	+	6.07650i	−1.04141	+	0.379042i	−0.805414	−	0.592712i	$-0.798057\pi$
$257$	−16.6951	+	6.07650i	−1.04141	+	0.379042i	−0.235995	+	0.971754i	$0.575835\pi$
$258$		0			0
$259$	18.2738	−	31.6511i	1.13548	−	1.96671i
$260$		0			0
$261$	1.79813	−	1.50881i	0.111302	−	0.0933932i
$262$		0			0
$263$	0.401674	+	2.27801i	0.0247683	+	0.140468i	0.994684	−	0.102972i	$-0.0328352\pi$
$263$	0.401674	+	2.27801i	0.0247683	+	0.140468i	−0.969916	+	0.243440i	$0.921724\pi$
$264$		0			0
$265$	−1.53890			−0.0945336
$266$		0			0
$267$	3.43107			0.209978
$268$		0			0
$269$	−0.489322	−	2.77509i	−0.0298345	−	0.169200i	0.966250	−	0.257606i	$-0.0829337\pi$
$269$	−0.489322	−	2.77509i	−0.0298345	−	0.169200i	−0.996084	+	0.0884063i	$0.971823\pi$
$270$		0			0
$271$	5.12449	−	4.29995i	0.311290	−	0.261204i	−0.473735	−	0.880668i	$-0.657094\pi$
$271$	5.12449	−	4.29995i	0.311290	−	0.261204i	0.785025	+	0.619464i	$0.212650\pi$
$272$		0			0
$273$	−1.74897	+	3.02931i	−0.105852	+	0.183342i
$274$		0			0
$275$	−12.0586	+	4.38895i	−0.727158	+	0.264664i
$276$		0			0
$277$	−4.12583	−	7.14615i	−0.247897	−	0.429370i	0.715045	−	0.699078i	$-0.246406\pi$
$277$	−4.12583	−	7.14615i	−0.247897	−	0.429370i	−0.962942	+	0.269708i	$0.913073\pi$
$278$		0			0
$279$	−0.928548	+	5.26606i	−0.0555907	+	0.315271i
$280$		0			0
$281$	21.4008	+	17.9574i	1.27666	+	1.07125i	0.993695	+	0.112120i	$0.0357641\pi$
$281$	21.4008	+	17.9574i	1.27666	+	1.07125i	0.282970	+	0.959129i	$0.408680\pi$
$282$		0			0
$283$	2.27972	+	0.829748i	0.135515	+	0.0493234i	0.408887	−	0.912585i	$-0.365917\pi$
$283$	2.27972	+	0.829748i	0.135515	+	0.0493234i	−0.273372	+	0.961908i	$0.588139\pi$
$284$		0			0
$285$	0.0603074	+	0.522277i	0.00357230	+	0.0309370i
$286$		0			0
$287$	−15.4731	−	5.63176i	−0.913350	−	0.332432i
$288$		0			0
$289$	−12.8550	−	10.7867i	−0.756179	−	0.634509i
$290$		0			0
$291$	0.538485	−	3.05390i	0.0315666	−	0.179023i
$292$		0			0
$293$	7.05051	+	12.2118i	0.411895	+	0.713423i	0.995097	−	0.0989041i	$-0.0315337\pi$
$293$	7.05051	+	12.2118i	0.411895	+	0.713423i	−0.583202	+	0.812327i	$0.698200\pi$
$294$		0			0
$295$	−1.70574	+	0.620838i	−0.0993119	+	0.0361466i
$296$		0			0
$297$	1.28699	−	2.22913i	0.0746787	−	0.129347i
$298$		0			0
$299$	−3.46863	+	2.91052i	−0.200596	+	0.168320i
$300$		0			0
$301$	−6.95383	−	39.4371i	−0.400812	−	2.27312i
$302$		0			0
$303$	−16.7297			−0.961095
$304$		0			0
$305$	0.207081			0.0118574
$306$		0			0
$307$	3.50892	+	19.9001i	0.200265	+	1.13576i	0.904719	+	0.426009i	$0.140081\pi$
$307$	3.50892	+	19.9001i	0.200265	+	1.13576i	−0.704454	+	0.709749i	$0.748808\pi$
$308$		0			0
$309$	7.96451	−	6.68302i	0.453085	−	0.380183i
$310$		0			0
$311$	4.80928	−	8.32991i	0.272709	−	0.472346i	−0.696845	−	0.717221i	$-0.745414\pi$
$311$	4.80928	−	8.32991i	0.272709	−	0.472346i	0.969555	+	0.244875i	$0.0787470\pi$
$312$		0			0
$313$	−23.3871	+	8.51222i	−1.32192	+	0.481139i	−0.904073	−	0.427379i	$-0.859437\pi$
$313$	−23.3871	+	8.51222i	−1.32192	+	0.481139i	−0.417846	+	0.908518i	$0.637215\pi$
$314$		0			0
$315$	0.258770	+	0.448204i	0.0145801	+	0.0252534i
$316$		0			0
$317$	2.99778	−	17.0012i	0.168372	−	0.954885i	−0.777147	−	0.629319i	$-0.783334\pi$
$317$	2.99778	−	17.0012i	0.168372	−	0.954885i	0.945519	−	0.325566i	$-0.105555\pi$
$318$		0			0
$319$	−4.62836	−	3.88365i	−0.259138	−	0.217443i
$320$		0			0
$321$	−8.56418	−	3.11711i	−0.478006	−	0.173980i
$322$		0			0
$323$	−0.912818	−	1.82391i	−0.0507906	−	0.101485i
$324$		0			0
$325$	3.81908	+	1.39003i	0.211844	+	0.0771050i
$326$		0			0
$327$	2.93376	+	2.46172i	0.162237	+	0.136133i
$328$		0			0
$329$	7.06031	−	40.0410i	0.389247	−	2.20753i
$330$		0			0
$331$	4.99525	+	8.65203i	0.274564	+	0.475559i	0.970025	−	0.243005i	$-0.0781332\pi$
$331$	4.99525	+	8.65203i	0.274564	+	0.475559i	−0.695461	+	0.718564i	$0.744800\pi$
$332$		0			0
$333$	8.00387	−	2.91317i	0.438609	−	0.159641i
$334$		0			0
$335$	−0.690884	+	1.19665i	−0.0377470	+	0.0653798i
$336$		0			0
$337$	5.18139	−	4.34770i	0.282248	−	0.236834i	−0.490662	−	0.871350i	$-0.663245\pi$
$337$	5.18139	−	4.34770i	0.282248	−	0.236834i	0.772910	+	0.634516i	$0.218800\pi$
$338$		0			0
$339$	0.939693	+	5.32926i	0.0510371	+	0.289446i
$340$		0			0
$341$	13.7638			0.745353
$342$		0			0
$343$	18.9290			1.02207
$344$		0			0
$345$	0.116334	+	0.659762i	0.00626320	+	0.0355204i
$346$		0			0
$347$	−18.8457	+	15.8134i	−1.01169	+	0.848909i	−0.988561	−	0.150823i	$-0.951808\pi$
$347$	−18.8457	+	15.8134i	−1.01169	+	0.848909i	−0.0231297	+	0.999732i	$0.507363\pi$
$348$		0			0
$349$	3.41740	−	5.91912i	0.182929	−	0.316843i	−0.759947	−	0.649985i	$-0.774775\pi$
$349$	3.41740	−	5.91912i	0.182929	−	0.316843i	0.942877	+	0.333141i	$0.108109\pi$
$350$		0			0
$351$	−0.766044	+	0.278817i	−0.0408884	+	0.0148822i
$352$		0			0
$353$	2.54189	+	4.40268i	0.135291	+	0.234331i	0.925709	−	0.378237i	$-0.123470\pi$
$353$	2.54189	+	4.40268i	0.135291	+	0.234331i	−0.790418	+	0.612568i	$0.790136\pi$
$354$		0			0
$355$	0.279248	−	1.58370i	0.0148210	−	0.0840538i
$356$		0			0
$357$	−1.53802	−	1.29055i	−0.0814006	−	0.0683032i
$358$		0			0
$359$	−2.69459	−	0.980752i	−0.142215	−	0.0517621i	0.269932	−	0.962879i	$-0.412999\pi$
$359$	−2.69459	−	0.980752i	−0.142215	−	0.0517621i	−0.412147	+	0.911117i	$0.635221\pi$
$360$		0			0
$361$	1.05185	+	18.9709i	0.0553606	+	0.998466i
$362$		0			0
$363$	4.11081	+	1.49621i	0.215762	+	0.0785309i
$364$		0			0
$365$	−0.210952	−	0.177009i	−0.0110417	−	0.00926510i
$366$		0			0
$367$	−3.84507	+	21.8065i	−0.200711	+	1.13829i	0.703336	+	0.710858i	$0.251693\pi$
$367$	−3.84507	+	21.8065i	−0.200711	+	1.13829i	−0.904047	+	0.427433i	$0.859418\pi$
$368$		0			0
$369$	−1.91875	−	3.32337i	−0.0998860	−	0.173008i
$370$		0			0
$371$	−51.4445	+	18.7243i	−2.67087	+	0.972115i
$372$		0			0
$373$	−8.83662	+	15.3055i	−0.457543	+	0.792487i	−0.998830	−	0.0483501i	$-0.984604\pi$
$373$	−8.83662	+	15.3055i	−0.457543	+	0.792487i	0.541288	+	0.840837i	$0.317937\pi$
$374$		0			0
$375$	0.922618	−	0.774169i	0.0476438	−	0.0399779i
$376$		0			0
$377$	0.332282	+	1.88446i	0.0171134	+	0.0970548i
$378$		0			0
$379$	9.75970			0.501322			0.250661	−	0.968075i	$-0.419352\pi$
$379$	9.75970			0.501322			0.250661	+	0.968075i	$0.419352\pi$
$380$		0			0
$381$	−4.24123			−0.217285
$382$		0			0
$383$	3.87505	+	21.9765i	0.198006	+	1.12295i	0.908073	+	0.418812i	$0.137553\pi$
$383$	3.87505	+	21.9765i	0.198006	+	1.12295i	−0.710067	+	0.704134i	$0.751335\pi$
$384$		0			0
$385$	1.02048	−	0.856282i	0.0520084	−	0.0436402i
$386$		0			0
$387$	4.66637	−	8.08240i	0.237205	−	0.410851i
$388$		0			0
$389$	−6.59879	+	2.40176i	−0.334572	+	0.121774i	−0.503843	−	0.863795i	$-0.668081\pi$
$389$	−6.59879	+	2.40176i	−0.334572	+	0.121774i	0.169271	+	0.985570i	$0.445859\pi$
$390$		0			0
$391$	−1.29948	−	2.25076i	−0.0657174	−	0.113826i
$392$		0			0
$393$	−3.65405	+	20.7231i	−0.184322	+	1.04534i
$394$		0			0
$395$	0.448778	+	0.376569i	0.0225805	+	0.0189472i
$396$		0			0
$397$	18.7738	+	6.83310i	0.942229	+	0.342943i	0.767046	−	0.641592i	$-0.221726\pi$
$397$	18.7738	+	6.83310i	0.942229	+	0.342943i	0.175184	+	0.984536i	$0.443948\pi$
$398$		0			0
$399$	8.37077	+	16.7257i	0.419063	+	0.837331i
$400$		0			0
$401$	1.11809	+	0.406951i	0.0558347	+	0.0203222i	0.369787	−	0.929117i	$-0.379431\pi$
$401$	1.11809	+	0.406951i	0.0558347	+	0.0203222i	−0.313952	+	0.949439i	$0.601653\pi$
$402$		0			0
$403$	−3.33931	−	2.80201i	−0.166343	−	0.139578i
$404$		0			0
$405$	−0.0209445	+	0.118782i	−0.00104074	+	0.00590234i
$406$		0			0
$407$	−10.9620	−	18.9867i	−0.543365	−	0.941136i
$408$		0			0
$409$	−8.91622	+	3.24524i	−0.440879	+	0.160467i	−0.552916	−	0.833237i	$-0.686485\pi$
$409$	−8.91622	+	3.24524i	−0.440879	+	0.160467i	0.112037	+	0.993704i	$0.464263\pi$
$410$		0			0
$411$	6.16044	−	10.6702i	0.303872	−	0.526322i
$412$		0			0
$413$	−49.4680	+	41.5086i	−2.43416	+	2.04250i
$414$		0			0
$415$	0.0680482	+	0.385920i	0.00334035	+	0.0189441i
$416$		0			0
$417$	5.58853			0.273671
$418$		0			0
$419$	−4.72638			−0.230899			−0.115449	−	0.993313i	$-0.536831\pi$
$419$	−4.72638			−0.230899			−0.115449	+	0.993313i	$0.536831\pi$
$420$		0			0
$421$	0.240819	+	1.36575i	0.0117368	+	0.0665627i	0.990114	−	0.140268i	$-0.0447963\pi$
$421$	0.240819	+	1.36575i	0.0117368	+	0.0665627i	−0.978377	+	0.206830i	$0.933685\pi$
$422$		0			0
$423$	7.25877	−	6.09083i	0.352933	−	0.296146i
$424$		0			0
$425$	−1.16637	+	2.02022i	−0.0565775	+	0.0979950i
$426$		0			0
$427$	6.92262	−	2.51963i	0.335009	−	0.121933i
$428$		0			0
$429$	1.04916	+	1.81720i	0.0506541	+	0.0877354i
$430$		0			0
$431$	−0.470904	+	2.67063i	−0.0226827	+	0.128640i	−0.994046	−	0.108958i	$-0.965249\pi$
$431$	−0.470904	+	2.67063i	−0.0226827	+	0.128640i	0.971364	+	0.237597i	$0.0763599\pi$
$432$		0			0
$433$	−15.5057	−	13.0108i	−0.745155	−	0.625260i	0.189061	−	0.981965i	$-0.439455\pi$
$433$	−15.5057	−	13.0108i	−0.745155	−	0.625260i	−0.934217	+	0.356706i	$0.883900\pi$
$434$		0			0
$435$	0.266044	+	0.0968323i	0.0127559	+	0.00464275i
$436$		0			0
$437$	2.77719	+	24.0512i	0.132851	+	1.15052i
$438$		0			0
$439$	−17.1027	−	6.22486i	−0.816266	−	0.297096i	−0.100056	−	0.994982i	$-0.531902\pi$
$439$	−17.1027	−	6.22486i	−0.816266	−	0.297096i	−0.716209	+	0.697885i	$0.754124\pi$
$440$		0			0
$441$	8.74170	+	7.33515i	0.416271	+	0.349293i
$442$		0			0
$443$	6.20661	−	35.1995i	0.294885	−	1.67238i	−0.372784	−	0.927918i	$-0.621597\pi$
$443$	6.20661	−	35.1995i	0.294885	−	1.67238i	0.667669	−	0.744458i	$-0.267292\pi$
$444$		0			0
$445$	0.206919	+	0.358394i	0.00980891	+	0.0169895i
$446$		0			0
$447$	−10.4251	+	3.79444i	−0.493092	+	0.179471i
$448$		0			0
$449$	9.49525	−	16.4463i	0.448109	−	0.776147i	−0.550154	−	0.835063i	$-0.685431\pi$
$449$	9.49525	−	16.4463i	0.448109	−	0.776147i	0.998263	+	0.0589161i	$0.0187644\pi$
$450$		0			0
$451$	−7.56670	+	6.34922i	−0.356302	+	0.298973i
$452$		0			0
$453$	−2.18732	−	12.4049i	−0.102769	−	0.582833i
$454$		0			0
$455$	−0.421903			−0.0197791
$456$		0			0
$457$	25.9632			1.21451			0.607253	−	0.794509i	$-0.292272\pi$
$457$	25.9632			1.21451			0.607253	+	0.794509i	$0.292272\pi$
$458$		0			0
$459$	−0.0812519	−	0.460802i	−0.00379251	−	0.0215084i
$460$		0			0
$461$	−22.3949	+	18.7915i	−1.04303	+	0.875209i	−0.992344	−	0.123506i	$-0.960586\pi$
$461$	−22.3949	+	18.7915i	−1.04303	+	0.875209i	−0.0506891	+	0.998714i	$0.516142\pi$
$462$		0			0
$463$	−10.5954	+	18.3518i	−0.492410	+	0.852878i	−0.999962	−	0.00874269i	$-0.997217\pi$
$463$	−10.5954	+	18.3518i	−0.492410	+	0.852878i	0.507552	+	0.861621i	$0.330550\pi$
$464$		0			0
$465$	−0.606067	+	0.220590i	−0.0281057	+	0.0102296i
$466$		0			0
$467$	−1.07263	−	1.85786i	−0.0496356	−	0.0859713i	0.840140	−	0.542369i	$-0.182473\pi$
$467$	−1.07263	−	1.85786i	−0.0496356	−	0.0859713i	−0.889776	+	0.456398i	$0.849139\pi$
$468$		0			0
$469$	−8.53590	+	48.4095i	−0.394151	+	2.23534i
$470$		0			0
$471$	−3.04710	−	2.55682i	−0.140403	−	0.117812i
$472$		0			0
$473$	−22.5736	−	8.21611i	−1.03793	−	0.377777i
$474$		0			0
$475$	17.4491	−	12.9526i	0.800619	−	0.594305i
$476$		0			0
$477$	−11.9893	−	4.36376i	−0.548953	−	0.199803i
$478$		0			0
$479$	2.60220	+	2.18350i	0.118897	+	0.0997668i	0.700298	−	0.713851i	$-0.253051\pi$
$479$	2.60220	+	2.18350i	0.118897	+	0.0997668i	−0.581400	+	0.813618i	$0.697495\pi$
$480$		0			0
$481$	−1.20574	+	6.83807i	−0.0549769	+	0.311789i
$482$		0			0
$483$	11.9165	+	20.6400i	0.542221	+	0.939154i
$484$		0			0
$485$	0.351471	−	0.127925i	0.0159595	−	0.00580878i
$486$		0			0
$487$	9.89306	−	17.1353i	0.448297	−	0.776473i	−0.549978	−	0.835179i	$-0.685364\pi$
$487$	9.89306	−	17.1353i	0.448297	−	0.776473i	0.998275	+	0.0587056i	$0.0186973\pi$
$488$		0			0
$489$	−14.7083	+	12.3417i	−0.665131	+	0.558111i
$490$		0			0
$491$	−4.36618	−	24.7618i	−0.197043	−	1.11749i	−0.909479	−	0.415750i	$-0.863519\pi$
$491$	−4.36618	−	24.7618i	−0.197043	−	1.11749i	0.712436	−	0.701737i	$-0.247592\pi$
$492$		0			0
$493$	−1.09833			−0.0494661
$494$		0			0
$495$	0.310460			0.0139541
$496$		0			0
$497$	−9.93423	−	56.3398i	−0.445611	−	2.52719i
$498$		0			0
$499$	−26.9329	+	22.5994i	−1.20568	+	1.01169i	−0.206232	+	0.978503i	$0.566120\pi$
$499$	−26.9329	+	22.5994i	−1.20568	+	1.01169i	−0.999449	+	0.0331839i	$0.989435\pi$
$500$		0			0
$501$	−7.68732	+	13.3148i	−0.343444	+	0.594863i
$502$		0			0
$503$	19.1186	−	6.95859i	0.852454	−	0.310268i	0.121414	−	0.992602i	$-0.461257\pi$
$503$	19.1186	−	6.95859i	0.852454	−	0.310268i	0.731041	+	0.682334i	$0.239035\pi$
$504$		0			0
$505$	−1.00892	−	1.74751i	−0.0448965	−	0.0777630i
$506$		0			0
$507$	−2.14203	+	12.1480i	−0.0951307	+	0.539513i
$508$		0			0
$509$	−10.0851	−	8.46242i	−0.447015	−	0.375090i	0.391312	−	0.920258i	$-0.372021\pi$
$509$	−10.0851	−	8.46242i	−0.447015	−	0.375090i	−0.838327	+	0.545168i	$0.816466\pi$
$510$		0			0
$511$	−9.20574	−	3.35061i	−0.407238	−	0.148222i
$512$		0			0
$513$	−1.01114	+	4.24000i	−0.0446431	+	0.187201i
$514$		0			0
$515$	1.17840	+	0.428901i	0.0519263	+	0.0188996i
$516$		0			0
$517$	−18.6839	−	15.6777i	−0.821718	−	0.689503i
$518$		0			0
$519$	−1.14496	+	6.49341i	−0.0502583	+	0.285029i
$520$		0			0
$521$	−10.2456	−	17.7458i	−0.448866	−	0.777459i	0.549446	−	0.835529i	$-0.314839\pi$
$521$	−10.2456	−	17.7458i	−0.448866	−	0.777459i	−0.998313	+	0.0580697i	$0.981505\pi$
$522$		0			0
$523$	−40.3312	+	14.6793i	−1.76356	+	0.641883i	−0.999993	−	0.00384740i	$-0.998775\pi$
$523$	−40.3312	+	14.6793i	−1.76356	+	0.641883i	−0.763566	+	0.645730i	$0.776553\pi$
$524$		0			0
$525$	10.6959	−	18.5259i	0.466809	−	0.808537i
$526$		0			0
$527$	1.91669	−	1.60829i	0.0834923	−	0.0700583i
$528$		0			0
$529$	1.36333	+	7.73183i	0.0592753	+	0.336167i
$530$		0			0
$531$	−15.0496			−0.653098
$532$		0			0
$533$	3.12836			0.135504
$534$		0			0
$535$	−0.190884	−	1.08256i	−0.00825265	−	0.0468031i
$536$		0			0
$537$	−0.950837	+	0.797847i	−0.0410316	+	0.0344296i
$538$		0			0
$539$	14.6864	−	25.4377i	0.632590	−	1.09568i
$540$		0			0
$541$	13.6976	−	4.98551i	0.588905	−	0.214344i	−0.0303426	−	0.999540i	$-0.509660\pi$
$541$	13.6976	−	4.98551i	0.588905	−	0.214344i	0.619248	+	0.785196i	$0.287438\pi$
$542$		0			0
$543$	−2.01501	−	3.49011i	−0.0864726	−	0.149775i
$544$		0			0
$545$	−0.0802124	+	0.454907i	−0.00343592	+	0.0194861i
$546$		0			0
$547$	−14.2246	−	11.9359i	−0.608201	−	0.510341i	0.285869	−	0.958269i	$-0.407718\pi$
$547$	−14.2246	−	11.9359i	−0.608201	−	0.510341i	−0.894070	+	0.447928i	$0.852162\pi$
$548$		0			0
$549$	1.61334	+	0.587208i	0.0688557	+	0.0250614i
$550$		0			0
$551$	9.38919	+	4.06564i	0.399993	+	0.173202i
$552$		0			0
$553$	19.5842	+	7.12808i	0.832807	+	0.303117i
$554$		0			0
$555$	0.786989	+	0.660362i	0.0334058	+	0.0280308i
$556$		0			0
$557$	2.69816	−	15.3020i	0.114325	−	0.648367i	−0.872758	−	0.488154i	$-0.837671\pi$
$557$	2.69816	−	15.3020i	0.114325	−	0.648367i	0.987082	−	0.160214i	$-0.0512183\pi$
$558$		0			0
$559$	3.80406	+	6.58883i	0.160895	+	0.278678i
$560$		0			0
$561$	−1.13176	+	0.411927i	−0.0477829	+	0.0173916i
$562$		0			0
$563$	−6.07785	+	10.5271i	−0.256151	+	0.443666i	−0.965207	−	0.261485i	$-0.915788\pi$
$563$	−6.07785	+	10.5271i	−0.256151	+	0.443666i	0.709057	+	0.705151i	$0.249121\pi$
$564$		0			0
$565$	−0.500000	+	0.419550i	−0.0210352	+	0.0176506i
$566$		0			0
$567$	0.745100	+	4.22567i	0.0312913	+	0.177462i
$568$		0			0
$569$	13.6709			0.573113			0.286556	−	0.958063i	$-0.407489\pi$
$569$	13.6709			0.573113			0.286556	+	0.958063i	$0.407489\pi$
$570$		0			0
$571$	−28.2003			−1.18014			−0.590072	−	0.807350i	$-0.700901\pi$
$571$	−28.2003			−1.18014			−0.590072	+	0.807350i	$0.700901\pi$
$572$		0			0
$573$	4.18227	+	23.7188i	0.174717	+	0.990868i
$574$		0			0
$575$	21.2126	−	17.7995i	0.884627	−	0.742290i
$576$		0			0
$577$	−10.1095	+	17.5101i	−0.420863	+	0.728956i	−0.996024	−	0.0890843i	$-0.971606\pi$
$577$	−10.1095	+	17.5101i	−0.420863	+	0.728956i	0.575161	+	0.818040i	$0.304939\pi$
$578$		0			0
$579$	9.26517	−	3.37225i	0.385047	−	0.140146i
$580$		0			0
$581$	6.97044	+	12.0732i	0.289182	+	0.500879i
$582$		0			0
$583$	−5.70274	+	32.3419i	−0.236184	+	1.33946i
$584$		0			0
$585$	−0.0753221	−	0.0632028i	−0.00311419	−	0.00261311i
$586$		0			0
$587$	−4.89306	−	1.78093i	−0.201958	−	0.0735067i	0.239061	−	0.971005i	$-0.423161\pi$
$587$	−4.89306	−	1.78093i	−0.201958	−	0.0735067i	−0.441019	+	0.897498i	$0.645383\pi$
$588$		0			0
$589$	−22.3384	+	6.65376i	−0.920439	+	0.274163i
$590$		0			0
$591$	6.06670	+	2.20810i	0.249551	+	0.0908291i
$592$		0			0
$593$	−33.3573	−	27.9901i	−1.36982	−	1.14942i	−0.972811	−	0.231602i	$-0.925603\pi$
$593$	−33.3573	−	27.9901i	−1.36982	−	1.14942i	−0.397010	−	0.917814i	$-0.629952\pi$
$594$		0			0
$595$	0.0420512	−	0.238484i	0.00172393	−	0.00977690i
$596$		0			0
$597$	12.3858	+	21.4528i	0.506916	+	0.878005i
$598$		0			0
$599$	−30.7511	+	11.1925i	−1.25646	+	0.457312i	−0.882578	−	0.470166i	$-0.844194\pi$
$599$	−30.7511	+	11.1925i	−1.25646	+	0.457312i	−0.373877	+	0.927478i	$0.621972\pi$
$600$		0			0
$601$	10.3867	−	17.9902i	0.423681	−	0.733836i	−0.572616	−	0.819824i	$-0.694071\pi$
$601$	10.3867	−	17.9902i	0.423681	−	0.733836i	0.996296	+	0.0859876i	$0.0274045\pi$
$602$		0			0
$603$	−8.77584	+	7.36381i	−0.357380	+	0.299877i
$604$		0			0
$605$	0.0916247	+	0.519630i	0.00372508	+	0.0211260i
$606$		0			0
$607$	23.0419			0.935241			0.467621	−	0.883929i	$-0.345111\pi$
$607$	23.0419			0.935241			0.467621	+	0.883929i	$0.345111\pi$
$608$		0			0
$609$	10.0719			0.408135
$610$		0			0
$611$	1.34137	+	7.60727i	0.0542659	+	0.307757i
$612$		0			0
$613$	16.2404	−	13.6273i	0.655942	−	0.550400i	−0.252926	−	0.967486i	$-0.581393\pi$
$613$	16.2404	−	13.6273i	0.655942	−	0.550400i	0.908867	+	0.417085i	$0.136948\pi$
$614$		0			0
$615$	0.231429	−	0.400847i	0.00933213	−	0.0161637i
$616$		0			0
$617$	19.2472	−	7.00541i	0.774864	−	0.282027i	0.0758345	−	0.997120i	$-0.475838\pi$
$617$	19.2472	−	7.00541i	0.774864	−	0.282027i	0.699029	+	0.715093i	$0.253616\pi$
$618$		0			0
$619$	−7.87258	−	13.6357i	−0.316426	−	0.548065i	0.663314	−	0.748341i	$-0.269149\pi$
$619$	−7.87258	−	13.6357i	−0.316426	−	0.548065i	−0.979740	+	0.200276i	$0.935816\pi$
$620$		0			0
$621$	−0.964508	+	5.46999i	−0.0387044	+	0.219503i
$622$		0			0
$623$	11.2779	+	9.46329i	0.451840	+	0.379139i
$624$		0			0
$625$	−23.2875	−	8.47594i	−0.931498	−	0.339038i
$626$		0			0
$627$	11.1998	+	0.667985i	0.447277	+	0.0266768i
$628$		0			0
$629$	−3.74510	−	1.36310i	−0.149327	−	0.0543506i
$630$		0			0
$631$	16.2041	+	13.5969i	0.645077	+	0.541284i	0.905573	−	0.424191i	$-0.139442\pi$
$631$	16.2041	+	13.5969i	0.645077	+	0.541284i	−0.260496	+	0.965475i	$0.583886\pi$
$632$		0			0
$633$	0.240352	−	1.36310i	0.00955314	−	0.0541786i
$634$		0			0
$635$	−0.255777	−	0.443020i	−0.0101502	−	0.0175807i
$636$		0			0
$637$	−8.74170	+	3.18172i	−0.346359	+	0.126064i
$638$		0			0
$639$	6.66637	−	11.5465i	0.263718	−	0.456772i
$640$		0			0
$641$	6.30200	−	5.28801i	0.248914	−	0.208864i	−0.509790	−	0.860299i	$-0.670277\pi$
$641$	6.30200	−	5.28801i	0.248914	−	0.208864i	0.758705	+	0.651435i	$0.225833\pi$
$642$		0			0
$643$	0.742574	+	4.21134i	0.0292842	+	0.166079i	0.995943	−	0.0899901i	$-0.0286836\pi$
$643$	0.742574	+	4.21134i	0.0292842	+	0.166079i	−0.966658	+	0.256069i	$0.917572\pi$
$644$		0			0
$645$	1.12567			0.0443231
$646$		0			0
$647$	−0.947682			−0.0372572			−0.0186286	−	0.999826i	$-0.505930\pi$
$647$	−0.947682			−0.0372572			−0.0186286	+	0.999826i	$0.505930\pi$
$648$		0			0
$649$	6.72668	+	38.1489i	0.264045	+	1.49748i
$650$		0			0
$651$	−17.5765	+	14.7484i	−0.688878	+	0.578037i
$652$		0			0
$653$	16.4217	−	28.4433i	0.642632	−	1.11307i	−0.342211	−	0.939623i	$-0.611176\pi$
$653$	16.4217	−	28.4433i	0.642632	−	1.11307i	0.984843	−	0.173449i	$-0.0554911\pi$
$654$		0			0
$655$	−2.38501	+	0.868073i	−0.0931901	+	0.0339184i
$656$		0			0
$657$	−1.14156	−	1.97724i	−0.0445365	−	0.0771394i
$658$		0			0
$659$	−0.823826	+	4.67215i	−0.0320917	+	0.182001i	−0.996640	−	0.0819047i	$-0.973900\pi$
$659$	−0.823826	+	4.67215i	−0.0320917	+	0.182001i	0.964548	+	0.263906i	$0.0850108\pi$
$660$		0			0
$661$	30.1864	+	25.3294i	1.17412	+	0.985201i	1.00000		0.000475674i	$0.000151412\pi$
$661$	30.1864	+	25.3294i	1.17412	+	0.985201i	0.174117	+	0.984725i	$0.444293\pi$
$662$		0			0
$663$	0.358441	+	0.130462i	0.0139207	+	0.00506671i
$664$		0			0
$665$	−1.24227	+	1.88305i	−0.0481731	+	0.0730217i
$666$		0			0
$667$	12.2515	+	4.45918i	0.474380	+	0.172660i
$668$		0			0
$669$	−17.0929	−	14.3426i	−0.660848	−	0.554518i
$670$		0			0
$671$	0.767389	−	4.35208i	0.0296247	−	0.168010i
$672$		0			0
$673$	−8.57145	−	14.8462i	−0.330405	−	0.572279i	0.652186	−	0.758059i	$-0.273852\pi$
$673$	−8.57145	−	14.8462i	−0.330405	−	0.572279i	−0.982591	+	0.185780i	$0.940519\pi$
$674$		0			0
$675$	4.68479	−	1.70513i	0.180318	−	0.0656303i
$676$		0			0
$677$	−3.56506	+	6.17486i	−0.137016	+	0.237319i	−0.926366	−	0.376625i	$-0.877085\pi$
$677$	−3.56506	+	6.17486i	−0.137016	+	0.237319i	0.789350	+	0.613944i	$0.210418\pi$
$678$		0			0
$679$	10.1930	−	8.55294i	0.391171	−	0.328232i
$680$		0			0
$681$	3.60607	+	20.4510i	0.138185	+	0.783685i
$682$		0			0
$683$	26.0000			0.994862			0.497431	−	0.867503i	$-0.334277\pi$
$683$	26.0000			0.994862			0.497431	+	0.867503i	$0.334277\pi$
$684$		0			0
$685$	1.48608			0.0567802
$686$		0			0
$687$	0.958111	+	5.43372i	0.0365542	+	0.207309i
$688$		0			0
$689$	7.96766	−	6.68566i	0.303544	−	0.254703i
$690$		0			0
$691$	19.6857	−	34.0967i	0.748880	−	1.29710i	−0.199479	−	0.979902i	$-0.563925\pi$
$691$	19.6857	−	34.0967i	0.748880	−	1.29710i	0.948360	−	0.317197i	$-0.102742\pi$
$692$		0			0
$693$	10.3785	−	3.77747i	0.394247	−	0.143494i
$694$		0			0
$695$	0.337029	+	0.583752i	0.0127843	+	0.0221430i
$696$		0			0
$697$	−0.311804	+	1.76833i	−0.0118104	+	0.0669802i
$698$		0			0
$699$	−11.5569	−	9.69739i	−0.437122	−	0.366789i
$700$		0			0
$701$	−5.29426	−	1.92695i	−0.199962	−	0.0727801i	0.240098	−	0.970749i	$-0.422820\pi$
$701$	−5.29426	−	1.92695i	−0.199962	−	0.0727801i	−0.440060	+	0.897969i	$0.645043\pi$
$702$		0			0
$703$	26.9697	+	25.5158i	1.01718	+	0.962346i
$704$		0			0
$705$	1.07398	+	0.390896i	0.0404483	+	0.0147220i
$706$		0			0
$707$	−54.9903	−	46.1423i	−2.06812	−	1.73536i
$708$		0			0
$709$	5.32517	−	30.2005i	0.199991	−	1.13421i	−0.705139	−	0.709069i	$-0.749115\pi$
$709$	5.32517	−	30.2005i	0.199991	−	1.13421i	0.905130	−	0.425136i	$-0.139774\pi$
$710$		0			0
$711$	2.42855	+	4.20637i	0.0910777	+	0.157751i
$712$		0			0
$713$	−27.9097	+	10.1583i	−1.04523	+	0.380432i
$714$		0			0
$715$	−0.126545	+	0.219182i	−0.00473250	+	0.00819693i
$716$		0			0
$717$	22.1780	−	18.6095i	0.828252	−	0.694986i
$718$		0			0
$719$	−1.10085	−	6.24324i	−0.0410549	−	0.232834i	0.957375	−	0.288847i	$-0.0932720\pi$
$719$	−1.10085	−	6.24324i	−0.0410549	−	0.232834i	−0.998430	+	0.0560138i	$0.982161\pi$
$720$		0			0
$721$	44.6117			1.66143
$722$		0			0
$723$	−19.3696			−0.720363
$724$		0			0
$725$	−2.03209	−	11.5245i	−0.0754699	−	0.428011i
$726$		0			0
$727$	17.8806	−	15.0036i	0.663154	−	0.556452i	−0.247877	−	0.968792i	$-0.579733\pi$
$727$	17.8806	−	15.0036i	0.663154	−	0.556452i	0.911030	+	0.412340i	$0.135288\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	−4.10354	+	1.49357i	−0.151775	+	0.0552416i
$732$		0			0
$733$	−0.794730	−	1.37651i	−0.0293540	−	0.0508426i	0.850975	−	0.525206i	$-0.176012\pi$
$733$	−0.794730	−	1.37651i	−0.0293540	−	0.0508426i	−0.880329	+	0.474363i	$0.842678\pi$
$734$		0			0
$735$	−0.239008	+	1.35548i	−0.00881594	+	0.0499977i
$736$		0			0
$737$	22.5888	+	18.9543i	0.832070	+	0.698190i
$738$		0			0
$739$	3.43882	+	1.25163i	0.126499	+	0.0460418i	0.404494	−	0.914541i	$-0.367448\pi$
$739$	3.43882	+	1.25163i	0.126499	+	0.0460418i	−0.277995	+	0.960582i	$0.589670\pi$
$740$		0			0
$741$	−2.58125	−	2.44210i	−0.0948247	−	0.0897127i
$742$		0			0
$743$	−17.2716	−	6.28634i	−0.633632	−	0.230623i	0.00517924	−	0.999987i	$-0.498351\pi$
$743$	−17.2716	−	6.28634i	−0.633632	−	0.230623i	−0.638811	+	0.769363i	$0.720574\pi$
$744$		0			0
$745$	−1.02506	−	0.860130i	−0.0375554	−	0.0315127i
$746$		0			0
$747$	−0.564178	+	3.19961i	−0.0206422	+	0.117068i
$748$		0			0
$749$	−19.5530	−	33.8668i	−0.714452	−	1.23747i
$750$		0			0
$751$	28.8161	−	10.4882i	1.05152	−	0.382720i	0.242281	−	0.970206i	$-0.422104\pi$
$751$	28.8161	−	10.4882i	1.05152	−	0.382720i	0.809235	+	0.587486i	$0.199882\pi$
$752$		0			0
$753$	−2.17112	+	3.76049i	−0.0791201	+	0.137040i
$754$		0			0
$755$	1.16385	−	0.976584i	0.0423568	−	0.0355415i
$756$		0			0
$757$	−1.35235	−	7.66955i	−0.0491520	−	0.278755i	0.950319	−	0.311278i	$-0.100757\pi$
$757$	−1.35235	−	7.66955i	−0.0491520	−	0.278755i	−0.999471	+	0.0325230i	$0.989646\pi$
$758$		0			0
$759$	14.2968			0.518943
$760$		0			0
$761$	28.3969			1.02939			0.514694	−	0.857374i	$-0.327906\pi$
$761$	28.3969			1.02939			0.514694	+	0.857374i	$0.327906\pi$
$762$		0			0
$763$	2.85355	+	16.1833i	0.103305	+	0.585874i
$764$		0			0
$765$	0.0432332	−	0.0362770i	0.00156310	−	0.00131160i
$766$		0			0
$767$	6.13429	−	10.6249i	0.221496	−	0.383643i
$768$		0			0
$769$	−33.1095	+	12.0509i	−1.19396	+	0.434566i	−0.861112	−	0.508415i	$-0.830232\pi$
$769$	−33.1095	+	12.0509i	−1.19396	+	0.434566i	−0.332848	+	0.942981i	$0.608010\pi$
$770$		0			0
$771$	−8.88326	−	15.3863i	−0.319923	−	0.554122i
$772$		0			0
$773$	−3.49092	+	19.7980i	−0.125559	+	0.712083i	0.855415	+	0.517944i	$0.173302\pi$
$773$	−3.49092	+	19.7980i	−0.125559	+	0.712083i	−0.980974	+	0.194139i	$0.937809\pi$
$774$		0			0
$775$	20.4217	+	17.1359i	0.733571	+	0.615539i
$776$		0			0
$777$	34.3435	+	12.5000i	1.23207	+	0.448435i
$778$		0			0
$779$	9.21126	−	13.9626i	0.330028	−	0.500262i
$780$		0			0
$781$	−32.2486	−	11.7375i	−1.15394	−	0.420001i
$782$		0			0
$783$	1.79813	+	1.50881i	0.0642600	+	0.0539206i
$784$		0			0
$785$	0.0833113	−	0.472482i	0.00297351	−	0.0168636i
$786$		0			0
$787$	−11.9265	−	20.6573i	−0.425133	−	0.736353i	0.571299	−	0.820742i	$-0.306439\pi$
$787$	−11.9265	−	20.6573i	−0.425133	−	0.736353i	−0.996433	+	0.0843890i	$0.973106\pi$
$788$		0			0
$789$	−2.17365	+	0.791143i	−0.0773839	+	0.0281654i
$790$		0			0
$791$	−11.6099	+	20.1090i	−0.412802	+	0.714994i
$792$		0			0
$793$	−1.07217	+	0.899655i	−0.0380738	+	0.0319477i
$794$		0			0
$795$	−0.267226	−	1.51552i	−0.00947755	−	0.0537498i
$796$		0			0
$797$	−28.5262			−1.01045			−0.505225	−	0.862988i	$-0.668591\pi$
$797$	−28.5262			−1.01045			−0.505225	+	0.862988i	$0.668591\pi$
$798$		0			0
$799$	−4.43376			−0.156855
$800$		0			0
$801$	0.595800	+	3.37895i	0.0210516	+	0.119389i
$802$		0			0
$803$	−4.50181	+	3.77747i	−0.158865	+	0.133304i
$804$		0			0
$805$	−1.43731	+	2.48949i	−0.0506585	+	0.0877431i
$806$		0			0
$807$	2.64796	−	0.963777i	0.0932125	−	0.0339266i
$808$		0			0
$809$	−12.4645	−	21.5892i	−0.438229	−	0.759034i	0.559324	−	0.828949i	$-0.311061\pi$
$809$	−12.4645	−	21.5892i	−0.438229	−	0.759034i	−0.997553	+	0.0699145i	$0.977727\pi$
$810$		0			0
$811$	−3.21672	+	18.2429i	−0.112954	+	0.640596i	0.874788	+	0.484505i	$0.161000\pi$
$811$	−3.21672	+	18.2429i	−0.112954	+	0.640596i	−0.987743	+	0.156091i	$0.950111\pi$
$812$		0			0
$813$	5.12449	+	4.29995i	0.179724	+	0.150806i
$814$		0			0
$815$	−2.17617	−	0.792063i	−0.0762281	−	0.0277447i
$816$		0			0
$817$	40.6083	+	2.42199i	1.42071	+	0.0847346i
$818$		0			0
$819$	−3.28699	−	1.19637i	−0.114857	−	0.0418044i
$820$		0			0
$821$	27.2415	+	22.8584i	0.950736	+	0.797762i	0.979421	−	0.201826i	$-0.0646876\pi$
$821$	27.2415	+	22.8584i	0.950736	+	0.797762i	−0.0286853	+	0.999588i	$0.509132\pi$
$822$		0			0
$823$	3.21167	−	18.2143i	0.111952	−	0.634909i	−0.876263	−	0.481834i	$-0.839971\pi$
$823$	3.21167	−	18.2143i	0.111952	−	0.634909i	0.988214	−	0.153076i	$-0.0489179\pi$
$824$		0			0
$825$	−6.41622	−	11.1132i	−0.223384	−	0.386913i
$826$		0			0
$827$	29.6891	−	10.8060i	1.03239	−	0.375760i	0.230401	−	0.973096i	$-0.425996\pi$
$827$	29.6891	−	10.8060i	1.03239	−	0.375760i	0.801991	+	0.597336i	$0.203774\pi$
$828$		0			0
$829$	20.5719	−	35.6316i	0.714492	−	1.23754i	−0.248663	−	0.968590i	$-0.579991\pi$
$829$	20.5719	−	35.6316i	0.714492	−	1.23754i	0.963155	−	0.268947i	$-0.0866756\pi$
$830$		0			0
$831$	6.32114	−	5.30406i	0.219278	−	0.183996i
$832$		0			0
$833$	−0.927204	−	5.25844i	−0.0321257	−	0.182194i
$834$		0			0
$835$	−1.85441			−0.0641744
$836$		0			0
$837$	−5.34730			−0.184830
$838$		0			0
$839$	−3.46956	−	19.6769i	−0.119783	−	0.679320i	−0.984271	−	0.176667i	$-0.943468\pi$
$839$	−3.46956	−	19.6769i	−0.119783	−	0.679320i	0.864488	−	0.502653i	$-0.167643\pi$
$840$		0			0
$841$	−17.9945	+	15.0992i	−0.620501	+	0.520662i
$842$		0			0
$843$	−13.9684	+	24.1939i	−0.481096	+	0.833284i
$844$		0			0
$845$	−1.39811	+	0.508870i	−0.0480964	+	0.0175057i
$846$		0			0
$847$	9.38548	+	16.2561i	0.322489	+	0.558567i
$848$		0			0
$849$	−0.421274	+	2.38917i	−0.0144581	+	0.0819959i
$850$		0			0
$851$	36.2413	+	30.4100i	1.24234	+	1.04244i
$852$		0			0
$853$	17.7939	+	6.47643i	0.609250	+	0.221749i	0.628175	−	0.778072i	$-0.283802\pi$
$853$	17.7939	+	6.47643i	0.609250	+	0.221749i	−0.0189251	+	0.999821i	$0.506024\pi$
$854$		0			0
$855$	−0.503870	+	0.150084i	−0.0172320	+	0.00513275i
$856$		0			0
$857$	20.0532	+	7.29877i	0.685004	+	0.249321i	0.660995	−	0.750391i	$-0.270135\pi$
$857$	20.0532	+	7.29877i	0.685004	+	0.249321i	0.0240095	+	0.999712i	$0.492357\pi$
$858$		0			0
$859$	−35.1129	−	29.4632i	−1.19804	−	1.00527i	−0.999684	−	0.0251425i	$-0.991996\pi$
$859$	−35.1129	−	29.4632i	−1.19804	−	1.00527i	−0.198354	−	0.980130i	$-0.563560\pi$
$860$		0			0
$861$	2.85932	−	16.2160i	0.0974453	−	0.552640i
$862$		0			0
$863$	7.62970	+	13.2150i	0.259718	+	0.449845i	0.966166	−	0.257920i	$-0.0830371\pi$
$863$	7.62970	+	13.2150i	0.259718	+	0.449845i	−0.706448	+	0.707765i	$0.749704\pi$
$864$		0			0
$865$	−0.747321	+	0.272003i	−0.0254097	+	0.00924837i
$866$		0			0
$867$	8.39053	−	14.5328i	0.284957	−	0.493561i
$868$		0			0
$869$	9.57713	−	8.03617i	0.324882	−	0.272608i
$870$		0			0
$871$	−1.62171	−	9.19718i	−0.0549496	−	0.311634i
$872$		0			0
$873$	3.10101			0.104953
$874$		0			0
$875$	5.16788			0.174706
$876$		0			0
$877$	3.88635	+	22.0406i	0.131233	+	0.744259i	0.977409	+	0.211356i	$0.0677878\pi$
$877$	3.88635	+	22.0406i	0.131233	+	0.744259i	−0.846176	+	0.532903i	$0.821101\pi$
$878$		0			0
$879$	−10.8020	+	9.06396i	−0.364343	+	0.305720i
$880$		0			0
$881$	13.5052	−	23.3917i	0.455002	−	0.788087i	−0.543686	−	0.839289i	$-0.682972\pi$
$881$	13.5052	−	23.3917i	0.455002	−	0.788087i	0.998688	+	0.0512016i	$0.0163051\pi$
$882$		0			0
$883$	16.3640	−	5.95599i	0.550691	−	0.200435i	−0.0516624	−	0.998665i	$-0.516452\pi$
$883$	16.3640	−	5.95599i	0.550691	−	0.200435i	0.602354	+	0.798229i	$0.294230\pi$
$884$		0			0
$885$	−0.907604	−	1.57202i	−0.0305088	−	0.0528427i
$886$		0			0
$887$	−10.1718	+	57.6869i	−0.341534	+	1.93694i	0.00788527	+	0.999969i	$0.497490\pi$
$887$	−10.1718	+	57.6869i	−0.341534	+	1.93694i	−0.349419	+	0.936966i	$0.613621\pi$
$888$		0			0
$889$	−13.9409	−	11.6978i	−0.467562	−	0.392331i
$890$		0			0
$891$	2.41875	+	0.880352i	0.0810311	+	0.0294929i
$892$		0			0
$893$	37.9026	+	16.4123i	1.26836	+	0.549217i
$894$		0			0
$895$	−0.140682	−	0.0512040i	−0.00470248	−	0.00171156i
$896$		0			0
$897$	−3.46863	−	2.91052i	−0.115814	−	0.0971795i
$898$		0			0
$899$	−2.17958	+	12.3610i	−0.0726930	+	0.412262i
$900$		0			0
$901$	2.98499	+	5.17015i	0.0994443	+	0.172243i
$902$		0			0
$903$	37.6305	−	13.6964i	1.25226	−	0.455787i
$904$		0			0
$905$	0.243041	−	0.420959i	0.00807894	−	0.0139931i
$906$		0			0
$907$	7.55896	−	6.34272i	0.250991	−	0.210607i	−0.508608	−	0.860998i	$-0.669840\pi$
$907$	7.55896	−	6.34272i	0.250991	−	0.210607i	0.759599	+	0.650392i	$0.225395\pi$
$908$		0			0
$909$	−2.90508	−	16.4755i	−0.0963553	−	0.546458i
$910$		0			0
$911$	13.9813			0.463222			0.231611	−	0.972808i	$-0.425600\pi$
$911$	13.9813			0.463222			0.231611	+	0.972808i	$0.425600\pi$
$912$		0			0
$913$	8.36278			0.276768
$914$		0			0
$915$	0.0359593	+	0.203935i	0.00118878	+	0.00674189i
$916$		0			0
$917$	−69.1675	+	58.0384i	−2.28411	+	1.91660i
$918$		0			0
$919$	−6.36231	+	11.0198i	−0.209873	+	0.363511i	−0.951674	−	0.307109i	$-0.900638\pi$
$919$	−6.36231	+	11.0198i	−0.209873	+	0.363511i	0.741801	+	0.670620i	$0.233972\pi$
$920$		0			0
$921$	−18.9884	+	6.91123i	−0.625691	+	0.227733i
$922$		0			0
$923$	5.43448	+	9.41279i	0.178878	+	0.309826i
$924$		0			0
$925$	7.37376	−	41.8187i	0.242448	−	1.37499i
$926$		0			0
$927$	7.96451	+	6.68302i	0.261589	+	0.219499i
$928$		0			0
$929$	−19.6830	−	7.16404i	−0.645780	−	0.235045i	−0.00169466	−	0.999999i	$-0.500539\pi$
$929$	−19.6830	−	7.16404i	−0.645780	−	0.235045i	−0.644085	+	0.764954i	$0.722762\pi$
$930$		0			0
$931$	−11.5386	+	48.3846i	−0.378164	+	1.58574i
$932$		0			0
$933$	9.03849	+	3.28974i	0.295907	+	0.107701i
$934$		0			0
$935$	−0.111281	−	0.0933762i	−0.00363929	−	0.00305373i
$936$		0			0
$937$	−1.68866	+	9.57688i	−0.0551662	+	0.312863i	−0.999887	−	0.0150119i	$-0.995221\pi$
$937$	−1.68866	+	9.57688i	−0.0551662	+	0.312863i	0.944721	+	0.327875i	$0.106332\pi$
$938$		0			0
$939$	−12.4440	−	21.5537i	−0.406096	−	0.703378i
$940$		0			0
$941$	21.7875	−	7.92999i	0.710251	−	0.258510i	0.0384696	−	0.999260i	$-0.487752\pi$
$941$	21.7875	−	7.92999i	0.710251	−	0.258510i	0.671781	+	0.740750i	$0.265530\pi$
$942$		0			0
$943$	10.6575	−	18.4592i	0.347054	−	0.601116i
$944$		0			0
$945$	−0.396459	+	0.332669i	−0.0128968	+	0.0108217i
$946$		0			0
$947$	−4.77900	−	27.1031i	−0.155297	−	0.880731i	−0.958514	−	0.285045i	$-0.907991\pi$
$947$	−4.77900	−	27.1031i	−0.155297	−	0.880731i	0.803217	−	0.595686i	$-0.203120\pi$
$948$		0			0
$949$	1.86122			0.0604176
$950$		0			0
$951$	17.2635			0.559808
$952$		0			0
$953$	8.75608	+	49.6582i	0.283637	+	1.60859i	0.710113	+	0.704088i	$0.248644\pi$
$953$	8.75608	+	49.6582i	0.283637	+	1.60859i	−0.426475	+	0.904499i	$0.640245\pi$
$954$		0			0
$955$	−2.22534	+	1.86728i	−0.0720102	+	0.0604238i
$956$		0			0
$957$	3.02094	−	5.23243i	0.0976533	−	0.169140i
$958$		0			0
$959$	49.6789	−	18.0816i	1.60422	−	0.583887i
$960$		0			0
$961$	1.20321	+	2.08402i	0.0388133	+	0.0672265i
$962$		0			0
$963$	1.58260	−	8.97535i	0.0509984	−	0.289227i
$964$		0			0
$965$	0.911007	+	0.764426i	0.0293264	+	0.0246077i
$966$		0			0
$967$	29.9424	+	10.8981i	0.962882	+	0.350460i	0.775162	−	0.631762i	$-0.217668\pi$
$967$	29.9424	+	10.8981i	0.962882	+	0.350460i	0.187720	+	0.982223i	$0.439890\pi$
$968$		0			0
$969$	1.63769	−	1.21567i	0.0526101	−	0.0390529i
$970$		0			0
$971$	−2.10607	−	0.766546i	−0.0675869	−	0.0245996i	0.308005	−	0.951385i	$-0.400338\pi$
$971$	−2.10607	−	0.766546i	−0.0675869	−	0.0245996i	−0.375592	+	0.926785i	$0.622561\pi$
$972$		0			0
$973$	18.3694	+	15.4138i	0.588897	+	0.494143i
$974$		0			0
$975$	−0.705737	+	4.00243i	−0.0226017	+	0.128180i
$976$		0			0
$977$	0.733956	+	1.27125i	0.0234813	+	0.0406708i	0.877527	−	0.479527i	$-0.159192\pi$
$977$	0.733956	+	1.27125i	0.0234813	+	0.0406708i	−0.854046	+	0.520198i	$0.825858\pi$
$978$		0			0
$979$	8.29890	−	3.02055i	0.265234	−	0.0965373i
$980$		0			0
$981$	−1.91488	+	3.31667i	−0.0611373	+	0.105893i
$982$		0			0
$983$	−22.9957	+	19.2957i	−0.733450	+	0.615437i	−0.931070	−	0.364841i	$-0.881123\pi$
$983$	−22.9957	+	19.2957i	−0.733450	+	0.615437i	0.197620	+	0.980279i	$0.436679\pi$
$984$		0			0
$985$	0.135219	+	0.766865i	0.00430844	+	0.0244343i
$986$		0			0
$987$	40.6587			1.29418
$988$		0			0
$989$	51.8376			1.64834
$990$		0			0
$991$	−9.50464	−	53.9035i	−0.301925	−	1.71230i	−0.637637	−	0.770337i	$-0.720088\pi$
$991$	−9.50464	−	53.9035i	−0.301925	−	1.71230i	0.335712	−	0.941965i	$-0.391023\pi$
$992$		0			0
$993$	−7.65317	+	6.42177i	−0.242866	+	0.203789i
$994$		0			0
$995$	−1.49391	+	2.58752i	−0.0473601	+	0.0820300i
$996$		0			0
$997$	45.6896	−	16.6297i	1.44700	−	0.526666i	0.505251	−	0.862972i	$-0.331400\pi$
$997$	45.6896	−	16.6297i	1.44700	−	0.526666i	0.941753	+	0.336306i	$0.109178\pi$
$998$		0			0
$999$	4.25877	+	7.37641i	0.134742	+	0.233379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bo.d.289.1		6
4.3	odd	2		114.2.i.c.61.1	yes	6
12.11	even	2		342.2.u.b.289.1		6
19.5	even	9	inner	912.2.bo.d.385.1		6
76.43	odd	18		114.2.i.c.43.1	✓	6
76.47	odd	18		2166.2.a.r.1.3		3
76.67	even	18		2166.2.a.p.1.3		3
228.47	even	18		6498.2.a.bp.1.1		3
228.119	even	18		342.2.u.b.271.1		6
228.143	odd	18		6498.2.a.bu.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.c.43.1	✓	6	76.43	odd	18
114.2.i.c.61.1	yes	6	4.3	odd	2
342.2.u.b.271.1		6	228.119	even	18
342.2.u.b.289.1		6	12.11	even	2
912.2.bo.d.289.1		6	1.1	even	1	trivial
912.2.bo.d.385.1		6	19.5	even	9	inner
2166.2.a.p.1.3		3	76.67	even	18
2166.2.a.r.1.3		3	76.47	odd	18
6498.2.a.bp.1.1		3	228.47	even	18
6498.2.a.bu.1.1		3	228.143	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bo (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{3} +(-0.0923963 + 0.0775297i) q^{5} +(-2.14543 + 3.71599i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(1.28699 + 2.22913i) q^{11} +(0.141559 - 0.802823i) q^{13} +(-0.0923963 - 0.0775297i) q^{15} +(0.439693 + 0.160035i) q^{17} +(-3.16637 - 2.99568i) q^{19} +(-4.03209 - 1.46756i) q^{21} +(-4.25490 - 3.57029i) q^{23} +(-0.865715 + 4.90971i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(-2.20574 + 0.802823i) q^{29} +(2.67365 - 4.63089i) q^{31} +(-1.97178 + 1.65452i) q^{33} +(-0.0898700 - 0.509678i) q^{35} -8.51754 q^{37} +0.815207 q^{39} +(0.666374 + 3.77920i) q^{41} +(-7.14930 + 5.99898i) q^{43} +(0.0603074 - 0.104455i) q^{45} +(-8.90420 + 3.24086i) q^{47} +(-5.70574 - 9.88263i) q^{49} +(-0.0812519 + 0.460802i) q^{51} +(9.77379 + 8.20118i) q^{53} +(-0.291737 - 0.106183i) q^{55} +(2.40033 - 3.63846i) q^{57} +(14.1420 + 5.14728i) q^{59} +(-1.31521 - 1.10359i) q^{61} +(0.745100 - 4.22567i) q^{63} +(0.0491630 + 0.0851529i) q^{65} +(10.7652 - 3.91820i) q^{67} +(2.77719 - 4.81023i) q^{69} +(-10.2135 + 8.57013i) q^{71} +(0.396459 + 2.24843i) q^{73} -4.98545 q^{75} -11.0446 q^{77} +(-0.843426 - 4.78331i) q^{79} +(0.766044 - 0.642788i) q^{81} +(1.62449 - 2.81369i) q^{83} +(-0.0530334 + 0.0193026i) q^{85} +(-1.17365 - 2.03282i) q^{87} +(0.595800 - 3.37895i) q^{89} +(2.67958 + 2.24843i) q^{91} +(5.02481 + 1.82888i) q^{93} +(0.524815 + 0.0313013i) q^{95} +(-2.91400 - 1.06061i) q^{97} +(-1.97178 - 1.65452i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} + 3 q^{7} + 9 q^{13} + 3 q^{15} - 3 q^{17} - 15 q^{21} - 27 q^{23} - 15 q^{25} - 3 q^{27} - 3 q^{29} + 15 q^{31} + 3 q^{33} - 12 q^{35} - 6 q^{37} + 12 q^{39} - 15 q^{41} - 3 q^{43} + 6 q^{45}+ \cdots + 3 q^{99}+O(q^{100}) \) 6 * q + 3 * q^5 + 3 * q^7 + 9 * q^13 + 3 * q^15 - 3 * q^17 - 15 * q^21 - 27 * q^23 - 15 * q^25 - 3 * q^27 - 3 * q^29 + 15 * q^31 + 3 * q^33 - 12 * q^35 - 6 * q^37 + 12 * q^39 - 15 * q^41 - 3 * q^43 + 6 * q^45 - 15 * q^47 - 24 * q^49 - 3 * q^51 + 6 * q^53 - 27 * q^55 + 27 * q^59 - 15 * q^61 + 3 * q^63 + 12 * q^65 + 3 * q^67 + 6 * q^69 - 3 * q^71 + 12 * q^73 + 6 * q^75 - 42 * q^77 - 27 * q^79 - 3 * q^83 + 12 * q^85 - 6 * q^87 + 42 * q^89 + 42 * q^91 + 3 * q^93 - 24 * q^95 + 18 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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