LMFDB - Embedded newform 912.2.bo.a.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(289,912)]

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([0, 0, 0, 2]))

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

//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);

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

Embedding invariants

Embedding label			529.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	912.529
Dual form			912.2.bo.a.481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{3} +(-0.386659 + 2.19285i) q^{5} +(-1.32635 - 2.29731i) q^{7} +(0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{3} +(-0.386659 + 2.19285i) q^{5} +(-1.32635 - 2.29731i) q^{7} +(0.766044 - 0.642788i) q^{9} +(1.11334 - 1.92836i) q^{11} +(4.97178 + 1.80958i) q^{13} +(0.386659 + 2.19285i) q^{15} +(-2.61334 - 2.19285i) q^{17} +(4.29813 + 0.725293i) q^{19} +(-2.03209 - 1.70513i) q^{21} +(-0.386659 - 2.19285i) q^{23} +(0.0393628 + 0.0143269i) q^{25} +(0.500000 - 0.866025i) q^{27} +(3.68866 - 3.09516i) q^{29} +(5.15657 + 8.93145i) q^{31} +(0.386659 - 2.19285i) q^{33} +(5.55051 - 2.02022i) q^{35} +2.30541 q^{37} +5.29086 q^{39} +(6.79813 - 2.47432i) q^{41} +(1.02822 - 5.83132i) q^{43} +(1.11334 + 1.92836i) q^{45} +(-8.43242 + 7.07564i) q^{47} +(-0.0184183 + 0.0319015i) q^{49} +(-3.20574 - 1.16679i) q^{51} +(1.70574 + 9.67372i) q^{53} +(3.79813 + 3.18701i) q^{55} +(4.28699 - 0.788496i) q^{57} +(-3.79813 - 3.18701i) q^{59} +(-0.990200 - 5.61570i) q^{61} +(-2.49273 - 0.907278i) q^{63} +(-5.89053 + 10.2027i) q^{65} +(-6.56805 + 5.51125i) q^{67} +(-1.11334 - 1.92836i) q^{69} +(-0.764700 + 4.33683i) q^{71} +(2.62701 - 0.956154i) q^{73} +0.0418891 q^{75} -5.90673 q^{77} +(12.9684 - 4.72010i) q^{79} +(0.173648 - 0.984808i) q^{81} +(-5.25150 - 9.09586i) q^{83} +(5.81908 - 4.88279i) q^{85} +(2.40760 - 4.17009i) q^{87} +(-7.34389 - 2.67296i) q^{89} +(-2.43717 - 13.8219i) q^{91} +(7.90033 + 6.62916i) q^{93} +(-3.25237 + 9.14473i) q^{95} +(-13.6270 - 11.4344i) q^{97} +(-0.386659 - 2.19285i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{5} - 9 q^{7}+O(q^{10}) $ 6 * q - 9 * q^5 - 9 * q^7	$ 6 q - 9 q^{5} - 9 q^{7} + 15 q^{13} + 9 q^{15} - 9 q^{17} + 12 q^{19} - 3 q^{21} - 9 q^{23} + 9 q^{25} + 3 q^{27} - 9 q^{29} + 9 q^{31} + 9 q^{33} + 36 q^{35} + 18 q^{37} + 27 q^{41} + 21 q^{43} - 27 q^{47} - 12 q^{49} - 9 q^{51} + 9 q^{55} + 18 q^{57} - 9 q^{59} - 3 q^{61} + 3 q^{63} - 18 q^{65} + 3 q^{67} - 9 q^{71} - 12 q^{73} - 6 q^{75} + 18 q^{77} + 21 q^{79} + 9 q^{83} + 18 q^{85} + 18 q^{87} - 24 q^{91} + 33 q^{93} - 36 q^{95} - 54 q^{97} - 9 q^{99}+O(q^{100}) $ 6 * q - 9 * q^5 - 9 * q^7 + 15 * q^13 + 9 * q^15 - 9 * q^17 + 12 * q^19 - 3 * q^21 - 9 * q^23 + 9 * q^25 + 3 * q^27 - 9 * q^29 + 9 * q^31 + 9 * q^33 + 36 * q^35 + 18 * q^37 + 27 * q^41 + 21 * q^43 - 27 * q^47 - 12 * q^49 - 9 * q^51 + 9 * q^55 + 18 * q^57 - 9 * q^59 - 3 * q^61 + 3 * q^63 - 18 * q^65 + 3 * q^67 - 9 * q^71 - 12 * q^73 - 6 * q^75 + 18 * q^77 + 21 * q^79 + 9 * q^83 + 18 * q^85 + 18 * q^87 - 24 * q^91 + 33 * q^93 - 36 * q^95 - 54 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$	$1$	$1$

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
$3$	0.939693	−	0.342020i	0.542532	−	0.197465i
$3$	0.939693	−	0.342020i	0.542532	−	0.197465i
$4$		0			0
$5$	−0.386659	+	2.19285i	−0.172919	+	0.980674i	0.767599	+	0.640930i	$0.221451\pi$
$5$	−0.386659	+	2.19285i	−0.172919	+	0.980674i	−0.940518	+	0.339743i	$0.889660\pi$
$6$		0			0
$7$	−1.32635	−	2.29731i	−0.501314	−	0.868301i	−0.999999	−	0.00151779i	$-0.999517\pi$
$7$	−1.32635	−	2.29731i	−0.501314	−	0.868301i	0.498685	−	0.866783i	$-0.333816\pi$
$8$		0			0
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$		0			0
$11$	1.11334	−	1.92836i	0.335685	−	0.581423i	−0.647931	−	0.761699i	$-0.724366\pi$
$11$	1.11334	−	1.92836i	0.335685	−	0.581423i	0.983616	+	0.180276i	$0.0576989\pi$
$12$		0			0
$13$	4.97178	+	1.80958i	1.37892	+	0.501887i	0.921852	−	0.387542i	$-0.126676\pi$
$13$	4.97178	+	1.80958i	1.37892	+	0.501887i	0.457072	+	0.889430i	$0.348898\pi$
$14$		0			0
$15$	0.386659	+	2.19285i	0.0998350	+	0.566192i
$16$		0			0
$17$	−2.61334	−	2.19285i	−0.633828	−	0.531845i	0.268288	−	0.963339i	$-0.413542\pi$
$17$	−2.61334	−	2.19285i	−0.633828	−	0.531845i	−0.902116	+	0.431494i	$0.857987\pi$
$18$		0			0
$19$	4.29813	+	0.725293i	0.986059	+	0.166394i
$19$	4.29813	+	0.725293i	0.986059	+	0.166394i
$20$		0			0
$21$	−2.03209	−	1.70513i	−0.443438	−	0.372089i
$22$		0			0
$23$	−0.386659	−	2.19285i	−0.0806240	−	0.457242i	−0.998215	−	0.0597166i	$-0.980980\pi$
$23$	−0.386659	−	2.19285i	−0.0806240	−	0.457242i	0.917591	−	0.397525i	$-0.130131\pi$
$24$		0			0
$25$	0.0393628	+	0.0143269i	0.00787257	+	0.00286538i
$26$		0			0
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$		0			0
$29$	3.68866	−	3.09516i	0.684968	−	0.574756i	−0.232486	−	0.972600i	$-0.574686\pi$
$29$	3.68866	−	3.09516i	0.684968	−	0.574756i	0.917453	+	0.397844i	$0.130241\pi$
$30$		0			0
$31$	5.15657	+	8.93145i	0.926148	+	1.60414i	0.789704	+	0.613488i	$0.210234\pi$
$31$	5.15657	+	8.93145i	0.926148	+	1.60414i	0.136444	+	0.990648i	$0.456433\pi$
$32$		0			0
$33$	0.386659	−	2.19285i	0.0673087	−	0.381727i
$34$		0			0
$35$	5.55051	−	2.02022i	0.938207	−	0.341479i
$36$		0			0
$37$	2.30541			0.379007			0.189503	−	0.981880i	$-0.439312\pi$
$37$	2.30541			0.379007			0.189503	+	0.981880i	$0.439312\pi$
$38$		0			0
$39$	5.29086			0.847216
$40$		0			0
$41$	6.79813	−	2.47432i	1.06169	−	0.386424i	0.248627	−	0.968599i	$-0.420021\pi$
$41$	6.79813	−	2.47432i	1.06169	−	0.386424i	0.813063	+	0.582176i	$0.197798\pi$
$42$		0			0
$43$	1.02822	−	5.83132i	0.156802	−	0.889267i	−0.800318	−	0.599576i	$-0.795336\pi$
$43$	1.02822	−	5.83132i	0.156802	−	0.889267i	0.957120	−	0.289692i	$-0.0935528\pi$
$44$		0			0
$45$	1.11334	+	1.92836i	0.165967	+	0.287463i
$46$		0			0
$47$	−8.43242	+	7.07564i	−1.22999	+	1.03209i	−0.231755	+	0.972774i	$0.574447\pi$
$47$	−8.43242	+	7.07564i	−1.22999	+	1.03209i	−0.998239	+	0.0593140i	$0.981109\pi$
$48$		0			0
$49$	−0.0184183	+	0.0319015i	−0.00263119	+	0.00455735i
$50$		0			0
$51$	−3.20574	−	1.16679i	−0.448893	−	0.163384i
$52$		0			0
$53$	1.70574	+	9.67372i	0.234301	+	1.32879i	0.844081	+	0.536216i	$0.180147\pi$
$53$	1.70574	+	9.67372i	0.234301	+	1.32879i	−0.609780	+	0.792571i	$0.708742\pi$
$54$		0			0
$55$	3.79813	+	3.18701i	0.512140	+	0.429737i
$56$		0			0
$57$	4.28699	−	0.788496i	0.567826	−	0.104439i
$58$		0			0
$59$	−3.79813	−	3.18701i	−0.494475	−	0.414914i	0.361152	−	0.932507i	$-0.382384\pi$
$59$	−3.79813	−	3.18701i	−0.494475	−	0.414914i	−0.855627	+	0.517593i	$0.826828\pi$
$60$		0			0
$61$	−0.990200	−	5.61570i	−0.126782	−	0.719017i	−0.980233	−	0.197844i	$-0.936606\pi$
$61$	−0.990200	−	5.61570i	−0.126782	−	0.719017i	0.853451	−	0.521173i	$-0.174505\pi$
$62$		0			0
$63$	−2.49273	−	0.907278i	−0.314054	−	0.114306i
$64$		0			0
$65$	−5.89053	+	10.2027i	−0.730630	+	1.26549i
$66$		0			0
$67$	−6.56805	+	5.51125i	−0.802415	+	0.673306i	−0.948784	−	0.315924i	$-0.897686\pi$
$67$	−6.56805	+	5.51125i	−0.802415	+	0.673306i	0.146370	+	0.989230i	$0.453241\pi$
$68$		0			0
$69$	−1.11334	−	1.92836i	−0.134030	−	0.232148i
$70$		0			0
$71$	−0.764700	+	4.33683i	−0.0907532	+	0.514687i	0.905213	+	0.424958i	$0.139711\pi$
$71$	−0.764700	+	4.33683i	−0.0907532	+	0.514687i	−0.995966	+	0.0897290i	$0.971400\pi$
$72$		0			0
$73$	2.62701	−	0.956154i	0.307468	−	0.111909i	−0.183678	−	0.982987i	$-0.558800\pi$
$73$	2.62701	−	0.956154i	0.307468	−	0.111909i	0.491146	+	0.871077i	$0.336578\pi$
$74$		0			0
$75$	0.0418891			0.00483693
$76$		0			0
$77$	−5.90673			−0.673134
$78$		0			0
$79$	12.9684	−	4.72010i	1.45906	−	0.531053i	0.513951	−	0.857819i	$-0.328181\pi$
$79$	12.9684	−	4.72010i	1.45906	−	0.531053i	0.945105	+	0.326766i	$0.105959\pi$
$80$		0			0
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$		0			0
$83$	−5.25150	−	9.09586i	−0.576427	−	0.998400i	−0.995885	−	0.0906256i	$-0.971113\pi$
$83$	−5.25150	−	9.09586i	−0.576427	−	0.998400i	0.419458	−	0.907775i	$-0.362220\pi$
$84$		0			0
$85$	5.81908	−	4.88279i	0.631168	−	0.529613i
$86$		0			0
$87$	2.40760	−	4.17009i	0.258122	−	0.447081i
$88$		0			0
$89$	−7.34389	−	2.67296i	−0.778451	−	0.283333i	−0.0779244	−	0.996959i	$-0.524829\pi$
$89$	−7.34389	−	2.67296i	−0.778451	−	0.283333i	−0.700527	+	0.713626i	$0.747052\pi$
$90$		0			0
$91$	−2.43717	−	13.8219i	−0.255484	−	1.44892i
$92$		0			0
$93$	7.90033	+	6.62916i	0.819226	+	0.687412i
$94$		0			0
$95$	−3.25237	+	9.14473i	−0.333687	+	0.938230i
$96$		0			0
$97$	−13.6270	−	11.4344i	−1.38361	−	1.16099i	−0.967853	−	0.251515i	$-0.919071\pi$
$97$	−13.6270	−	11.4344i	−1.38361	−	1.16099i	−0.415760	−	0.909474i	$-0.636484\pi$
$98$		0			0
$99$	−0.386659	−	2.19285i	−0.0388607	−	0.220390i
$100$		0			0
$101$	−16.8268	−	6.12446i	−1.67433	−	0.609407i	−0.681815	−	0.731524i	$-0.738809\pi$
$101$	−16.8268	−	6.12446i	−1.67433	−	0.609407i	−0.992516	+	0.122118i	$0.961031\pi$
$102$		0			0
$103$	2.12314	−	3.67739i	0.209199	−	0.362344i	−0.742263	−	0.670108i	$-0.766248\pi$
$103$	2.12314	−	3.67739i	0.209199	−	0.362344i	0.951463	+	0.307765i	$0.0995809\pi$
$104$		0			0
$105$	4.52481	−	3.79677i	0.441577	−	0.370527i
$106$		0			0
$107$	7.80200	+	13.5135i	0.754248	+	1.30640i	0.945747	+	0.324903i	$0.105332\pi$
$107$	7.80200	+	13.5135i	0.754248	+	1.30640i	−0.191499	+	0.981493i	$0.561335\pi$
$108$		0			0
$109$	−0.236482	+	1.34115i	−0.0226508	+	0.128459i	−0.994036	−	0.109049i	$-0.965220\pi$
$109$	−0.236482	+	1.34115i	−0.0226508	+	0.128459i	0.971386	+	0.237508i	$0.0763306\pi$
$110$		0			0
$111$	2.16637	−	0.788496i	0.205623	−	0.0748407i
$112$		0			0
$113$	17.2003			1.61807			0.809033	−	0.587763i	$-0.199991\pi$
$113$	17.2003			1.61807			0.809033	+	0.587763i	$0.199991\pi$
$114$		0			0
$115$	4.95811			0.462346
$116$		0			0
$117$	4.97178	−	1.80958i	0.459641	−	0.167296i
$118$		0			0
$119$	−1.57145	+	8.91215i	−0.144055	+	0.816975i
$120$		0			0
$121$	3.02094	+	5.23243i	0.274631	+	0.475675i
$122$		0			0
$123$	5.54189	−	4.65020i	0.499695	−	0.419294i
$124$		0			0
$125$	−5.61334	+	9.72259i	−0.502072	+	0.869615i
$126$		0			0
$127$	−12.3969	−	4.51211i	−1.10005	−	0.400385i	−0.272715	−	0.962095i	$-0.587922\pi$
$127$	−12.3969	−	4.51211i	−1.10005	−	0.400385i	−0.827334	+	0.561710i	$0.810144\pi$
$128$		0			0
$129$	−1.02822	−	5.83132i	−0.0905296	−	0.513419i
$130$		0			0
$131$	−5.74763	−	4.82283i	−0.502172	−	0.421373i	0.356192	−	0.934413i	$-0.384075\pi$
$131$	−5.74763	−	4.82283i	−0.502172	−	0.421373i	−0.858365	+	0.513040i	$0.828519\pi$
$132$		0			0
$133$	−4.03462	−	10.8361i	−0.349845	−	0.939612i
$134$		0			0
$135$	1.70574	+	1.43128i	0.146806	+	0.123185i
$136$		0			0
$137$	1.15136	+	6.52968i	0.0983673	+	0.557869i	0.993663	+	0.112397i	$0.0358528\pi$
$137$	1.15136	+	6.52968i	0.0983673	+	0.557869i	−0.895296	+	0.445472i	$0.853036\pi$
$138$		0			0
$139$	−7.99660	−	2.91052i	−0.678262	−	0.246867i	−0.0201612	−	0.999797i	$-0.506418\pi$
$139$	−7.99660	−	2.91052i	−0.678262	−	0.246867i	−0.658101	+	0.752929i	$0.728640\pi$
$140$		0			0
$141$	−5.50387	+	9.53298i	−0.463510	+	0.802822i
$142$		0			0
$143$	9.02481	−	7.57272i	0.754693	−	0.633263i
$144$		0			0
$145$	5.36097	+	9.28547i	0.445204	+	0.771116i
$146$		0			0
$147$	−0.00639661	+	0.0362770i	−0.000527584	+	0.00299208i
$148$		0			0
$149$	3.20574	−	1.16679i	0.262624	−	0.0955874i	−0.207352	−	0.978266i	$-0.566485\pi$
$149$	3.20574	−	1.16679i	0.262624	−	0.0955874i	0.469976	+	0.882679i	$0.344262\pi$
$150$		0			0
$151$	−3.04189			−0.247545			−0.123773	−	0.992311i	$-0.539499\pi$
$151$	−3.04189			−0.247545			−0.123773	+	0.992311i	$0.539499\pi$
$152$		0			0
$153$	−3.41147			−0.275801
$154$		0			0
$155$	−21.5792	+	7.85418i	−1.73328	+	0.630863i
$156$		0			0
$157$	−2.69594	+	15.2894i	−0.215159	+	1.22023i	0.665471	+	0.746424i	$0.268231\pi$
$157$	−2.69594	+	15.2894i	−0.215159	+	1.22023i	−0.880630	+	0.473805i	$0.842880\pi$
$158$		0			0
$159$	4.91147	+	8.50692i	0.389505	+	0.674643i
$160$		0			0
$161$	−4.52481	+	3.79677i	−0.356605	+	0.299227i
$162$		0			0
$163$	2.21941	−	3.84413i	0.173837	−	0.301095i	−0.765921	−	0.642935i	$-0.777717\pi$
$163$	2.21941	−	3.84413i	0.173837	−	0.301095i	0.939758	+	0.341840i	$0.111050\pi$
$164$		0			0
$165$	4.65910	+	1.69577i	0.362710	+	0.132016i
$166$		0			0
$167$	1.41534	+	8.02682i	0.109523	+	0.621134i	0.989317	+	0.145779i	$0.0465690\pi$
$167$	1.41534	+	8.02682i	0.109523	+	0.621134i	−0.879794	+	0.475354i	$0.842320\pi$
$168$		0			0
$169$	11.4855	+	9.63744i	0.883496	+	0.741341i
$170$		0			0
$171$	3.75877	−	2.20718i	0.287440	−	0.168787i
$172$		0			0
$173$	−12.2306	−	10.2627i	−0.929872	−	0.780255i	0.0459227	−	0.998945i	$-0.485377\pi$
$173$	−12.2306	−	10.2627i	−0.929872	−	0.780255i	−0.975794	+	0.218690i	$0.929822\pi$
$174$		0			0
$175$	−0.0192957	−	0.109431i	−0.00145861	−	0.00827222i
$176$		0			0
$177$	−4.65910	−	1.69577i	−0.350199	−	0.127462i
$178$		0			0
$179$	0.726682	−	1.25865i	0.0543147	−	0.0940759i	−0.837590	−	0.546300i	$-0.816036\pi$
$179$	0.726682	−	1.25865i	0.0543147	−	0.0940759i	0.891904	+	0.452224i	$0.149369\pi$
$180$		0			0
$181$	−0.862311	+	0.723565i	−0.0640951	+	0.0537822i	−0.674272	−	0.738483i	$-0.735543\pi$
$181$	−0.862311	+	0.723565i	−0.0640951	+	0.0537822i	0.610177	+	0.792265i	$0.291098\pi$
$182$		0			0
$183$	−2.85117	−	4.93837i	−0.210764	−	0.365054i
$184$		0			0
$185$	−0.891407	+	5.05542i	−0.0655375	+	0.371682i
$186$		0			0
$187$	−7.13816	+	2.59808i	−0.521994	+	0.189990i
$188$		0			0
$189$	−2.65270			−0.192956
$190$		0			0
$191$	1.32770			0.0960687			0.0480344	−	0.998846i	$-0.484704\pi$
$191$	1.32770			0.0960687			0.0480344	+	0.998846i	$0.484704\pi$
$192$		0			0
$193$	−14.0817	+	5.12533i	−1.01362	+	0.368929i	−0.794824	−	0.606841i	$-0.792437\pi$
$193$	−14.0817	+	5.12533i	−1.01362	+	0.368929i	−0.218801	+	0.975770i	$0.570214\pi$
$194$		0			0
$195$	−2.04576	+	11.6021i	−0.146500	+	0.830842i
$196$		0			0
$197$	−11.5039	−	19.9253i	−0.819617	−	1.41962i	−0.905965	−	0.423353i	$-0.860853\pi$
$197$	−11.5039	−	19.9253i	−0.819617	−	1.41962i	0.0863480	−	0.996265i	$-0.472480\pi$
$198$		0			0
$199$	−7.41740	+	6.22394i	−0.525806	+	0.441203i	−0.866650	−	0.498916i	$-0.833732\pi$
$199$	−7.41740	+	6.22394i	−0.525806	+	0.441203i	0.340844	+	0.940120i	$0.389287\pi$
$200$		0			0
$201$	−4.28699	+	7.42528i	−0.302381	+	0.523739i
$202$		0			0
$203$	−12.0030	−	4.36873i	−0.842445	−	0.306625i
$204$		0			0
$205$	2.79726	+	15.8640i	0.195369	+	1.10799i
$206$		0			0
$207$	−1.70574	−	1.43128i	−0.118557	−	0.0994811i
$208$		0			0
$209$	6.18392	−	7.48086i	0.427750	−	0.517462i
$210$		0			0
$211$	0.847296	+	0.710966i	0.0583303	+	0.0489449i	0.671487	−	0.741017i	$-0.265656\pi$
$211$	0.847296	+	0.710966i	0.0583303	+	0.0489449i	−0.613156	+	0.789962i	$0.710100\pi$
$212$		0			0
$213$	0.764700	+	4.33683i	0.0523964	+	0.297155i
$214$		0			0
$215$	12.3897	+	4.50946i	0.844967	+	0.307543i
$216$		0			0
$217$	13.6789	−	23.6925i	0.928582	−	1.60835i
$218$		0			0
$219$	2.14156	−	1.79698i	0.144713	−	0.121429i
$220$		0			0
$221$	−9.02481	−	15.6314i	−0.607075	−	1.05148i
$222$		0			0
$223$	−4.39100	+	24.9026i	−0.294043	+	1.66760i	0.377024	+	0.926203i	$0.376947\pi$
$223$	−4.39100	+	24.9026i	−0.294043	+	1.66760i	−0.671067	+	0.741397i	$0.734164\pi$
$224$		0			0
$225$	0.0393628	−	0.0143269i	0.00262419	−	0.000955127i
$226$		0			0
$227$	−3.42871			−0.227572			−0.113786	−	0.993505i	$-0.536298\pi$
$227$	−3.42871			−0.227572			−0.113786	+	0.993505i	$0.536298\pi$
$228$		0			0
$229$	29.9418			1.97861			0.989305	−	0.145860i	$-0.0465950\pi$
$229$	29.9418			1.97861			0.989305	+	0.145860i	$0.0465950\pi$
$230$		0			0
$231$	−5.55051	+	2.02022i	−0.365197	+	0.132921i
$232$		0			0
$233$	−1.80200	+	10.2197i	−0.118053	+	0.669513i	0.867140	+	0.498065i	$0.165956\pi$
$233$	−1.80200	+	10.2197i	−0.118053	+	0.669513i	−0.985193	+	0.171448i	$0.945155\pi$
$234$		0			0
$235$	−12.2554	−	21.2269i	−0.799452	−	1.38469i
$236$		0			0
$237$	10.5719	−	8.87089i	0.686720	−	0.576226i
$238$		0			0
$239$	−8.00774	+	13.8698i	−0.517978	+	0.897164i	0.481804	+	0.876279i	$0.339982\pi$
$239$	−8.00774	+	13.8698i	−0.517978	+	0.897164i	−0.999782	+	0.0208848i	$0.993352\pi$
$240$		0			0
$241$	−24.0390	−	8.74946i	−1.54849	−	0.563602i	−0.580423	−	0.814315i	$-0.697113\pi$
$241$	−24.0390	−	8.74946i	−1.54849	−	0.563602i	−0.968062	+	0.250712i	$0.919335\pi$
$242$		0			0
$243$	−0.173648	−	0.984808i	−0.0111395	−	0.0631754i
$244$		0			0
$245$	−0.0628336	−	0.0527236i	−0.00401429	−	0.00336839i
$246$		0			0
$247$	20.0569	+	11.3838i	1.27619	+	0.724335i
$248$		0			0
$249$	−8.04576	−	6.75119i	−0.509879	−	0.427840i
$250$		0			0
$251$	−1.85622	−	10.5271i	−0.117164	−	0.664467i	−0.985656	−	0.168765i	$-0.946022\pi$
$251$	−1.85622	−	10.5271i	−0.117164	−	0.664467i	0.868493	−	0.495702i	$-0.165089\pi$
$252$		0			0
$253$	−4.65910	−	1.69577i	−0.292915	−	0.106612i
$254$		0			0
$255$	3.79813	−	6.57856i	0.237848	−	0.411965i
$256$		0			0
$257$	−23.5783	+	19.7846i	−1.47077	+	1.23413i	−0.555363	+	0.831608i	$0.687421\pi$
$257$	−23.5783	+	19.7846i	−1.47077	+	1.23413i	−0.915412	+	0.402519i	$0.868135\pi$
$258$		0			0
$259$	−3.05778	−	5.29623i	−0.190001	−	0.329092i
$260$		0			0
$261$	0.836152	−	4.74205i	0.0517565	−	0.293526i
$262$		0			0
$263$	2.95336	−	1.07494i	0.182112	−	0.0662834i	−0.249355	−	0.968412i	$-0.580218\pi$
$263$	2.95336	−	1.07494i	0.182112	−	0.0662834i	0.431467	+	0.902129i	$0.357996\pi$
$264$		0			0
$265$	−21.8726			−1.34362
$266$		0			0
$267$	−7.81521			−0.478283
$268$		0			0
$269$	−13.9829	+	5.08937i	−0.852554	+	0.310304i	−0.731081	−	0.682290i	$-0.760984\pi$
$269$	−13.9829	+	5.08937i	−0.852554	+	0.310304i	−0.121473	+	0.992595i	$0.538762\pi$
$270$		0			0
$271$	−2.64543	+	15.0030i	−0.160698	+	0.911366i	0.792691	+	0.609624i	$0.208679\pi$
$271$	−2.64543	+	15.0030i	−0.160698	+	0.911366i	−0.953389	+	0.301742i	$0.902432\pi$
$272$		0			0
$273$	−7.01754	−	12.1547i	−0.424721	−	0.735638i
$274$		0			0
$275$	0.0714517	−	0.0599551i	0.00430870	−	0.00361543i
$276$		0			0
$277$	6.10472	−	10.5737i	0.366797	−	0.635311i	−0.622266	−	0.782806i	$-0.713788\pi$
$277$	6.10472	−	10.5737i	0.366797	−	0.635311i	0.989063	+	0.147495i	$0.0471209\pi$
$278$		0			0
$279$	9.69119	+	3.52730i	0.580196	+	0.211174i
$280$		0			0
$281$	−0.389652	−	2.20983i	−0.0232447	−	0.131827i	0.970977	−	0.239172i	$-0.0768761\pi$
$281$	−0.389652	−	2.20983i	−0.0232447	−	0.131827i	−0.994222	+	0.107345i	$0.965765\pi$
$282$		0			0
$283$	11.3289	+	9.50606i	0.673432	+	0.565076i	0.914079	−	0.405536i	$-0.132915\pi$
$283$	11.3289	+	9.50606i	0.673432	+	0.565076i	−0.240647	+	0.970613i	$0.577360\pi$
$284$		0			0
$285$	0.0714517	+	9.70562i	0.00423244	+	0.574911i
$286$		0			0
$287$	−14.7010	−	12.3356i	−0.867772	−	0.728147i
$288$		0			0
$289$	−0.931074	−	5.28039i	−0.0547691	−	0.310611i
$290$		0			0
$291$	−16.7160	−	6.08413i	−0.979910	−	0.356658i
$292$		0			0
$293$	6.02481	−	10.4353i	0.351973	−	0.609636i	−0.634622	−	0.772823i	$-0.718844\pi$
$293$	6.02481	−	10.4353i	0.351973	−	0.609636i	0.986595	+	0.163187i	$0.0521774\pi$
$294$		0			0
$295$	8.45723	−	7.09646i	0.492399	−	0.413172i
$296$		0			0
$297$	−1.11334	−	1.92836i	−0.0646026	−	0.111895i
$298$		0			0
$299$	2.04576	−	11.6021i	0.118309	−	0.670966i
$300$		0			0
$301$	−14.7601	+	5.37224i	−0.850759	+	0.309651i
$302$		0			0
$303$	−17.9067			−1.02871
$304$		0			0
$305$	12.6973			0.727044
$306$		0			0
$307$	21.2319	−	7.72778i	1.21177	−	0.441048i	0.344452	−	0.938804i	$-0.388065\pi$
$307$	21.2319	−	7.72778i	1.21177	−	0.441048i	0.867317	+	0.497757i	$0.165843\pi$
$308$		0			0
$309$	0.737359	−	4.18177i	0.0419469	−	0.237893i
$310$		0			0
$311$	−5.66297	−	9.80855i	−0.321118	−	0.556192i	0.659601	−	0.751616i	$-0.270725\pi$
$311$	−5.66297	−	9.80855i	−0.321118	−	0.556192i	−0.980719	+	0.195424i	$0.937392\pi$
$312$		0			0
$313$	−4.56418	+	3.82980i	−0.257983	+	0.216473i	−0.762601	−	0.646870i	$-0.776078\pi$
$313$	−4.56418	+	3.82980i	−0.257983	+	0.216473i	0.504618	+	0.863343i	$0.331633\pi$
$314$		0			0
$315$	2.95336	−	5.11538i	0.166403	−	0.288219i
$316$		0			0
$317$	8.38578	+	3.05217i	0.470992	+	0.171427i	0.566602	−	0.823992i	$-0.308258\pi$
$317$	8.38578	+	3.05217i	0.470992	+	0.171427i	−0.0956094	+	0.995419i	$0.530480\pi$
$318$		0			0
$319$	−1.86184	−	10.5590i	−0.104243	−	0.591193i
$320$		0			0
$321$	11.9534	+	10.0301i	0.667172	+	0.559824i
$322$		0			0
$323$	−9.64203	−	11.3206i	−0.536497	−	0.629896i
$324$		0			0
$325$	0.169778	+	0.142460i	0.00941758	+	0.00790229i
$326$		0			0
$327$	0.236482	+	1.34115i	0.0130775	+	0.0741660i
$328$		0			0
$329$	27.4393	+	9.98708i	1.51278	+	0.550606i
$330$		0			0
$331$	3.32976	−	5.76731i	0.183020	−	0.317000i	−0.759888	−	0.650054i	$-0.774746\pi$
$331$	3.32976	−	5.76731i	0.183020	−	0.317000i	0.942908	+	0.333055i	$0.108079\pi$
$332$		0			0
$333$	1.76604	−	1.48189i	0.0967786	−	0.0812069i
$334$		0			0
$335$	−9.54576	−	16.5337i	−0.521541	−	0.903335i
$336$		0			0
$337$	−1.88057	+	10.6652i	−0.102441	+	0.580972i	0.889771	+	0.456408i	$0.150864\pi$
$337$	−1.88057	+	10.6652i	−0.102441	+	0.580972i	−0.992212	+	0.124564i	$0.960247\pi$
$338$		0			0
$339$	16.1630	−	5.88284i	0.877852	−	0.319512i
$340$		0			0
$341$	22.9641			1.24358
$342$		0			0
$343$	−18.4712			−0.997352
$344$		0			0
$345$	4.65910	−	1.69577i	0.250838	−	0.0912974i
$346$		0			0
$347$	−3.58781	+	20.3475i	−0.192604	+	1.09231i	0.723186	+	0.690653i	$0.242677\pi$
$347$	−3.58781	+	20.3475i	−0.192604	+	1.09231i	−0.915790	+	0.401657i	$0.868434\pi$
$348$		0			0
$349$	1.01976	+	1.76628i	0.0545866	+	0.0945468i	0.892028	−	0.451981i	$-0.149283\pi$
$349$	1.01976	+	1.76628i	0.0545866	+	0.0945468i	−0.837441	+	0.546528i	$0.815949\pi$
$350$		0			0
$351$	4.05303	−	3.40090i	0.216335	−	0.181527i
$352$		0			0
$353$	−15.6506	+	27.1077i	−0.833000	+	1.44280i	0.0626489	+	0.998036i	$0.480045\pi$
$353$	−15.6506	+	27.1077i	−0.833000	+	1.44280i	−0.895649	+	0.444762i	$0.853288\pi$
$354$		0			0
$355$	−9.21436	−	3.35375i	−0.489047	−	0.177999i
$356$		0			0
$357$	1.57145	+	8.91215i	0.0831700	+	0.471681i
$358$		0			0
$359$	6.82295	+	5.72513i	0.360101	+	0.302161i	0.804831	−	0.593504i	$-0.202256\pi$
$359$	6.82295	+	5.72513i	0.360101	+	0.302161i	−0.444730	+	0.895665i	$0.646700\pi$
$360$		0			0
$361$	17.9479	+	6.23481i	0.944626	+	0.328148i
$362$		0			0
$363$	4.62836	+	3.88365i	0.242926	+	0.203839i
$364$		0			0
$365$	1.08095	+	6.13036i	0.0565794	+	0.320878i
$366$		0			0
$367$	3.23308	+	1.17674i	0.168765	+	0.0614255i	0.425021	−	0.905183i	$-0.360267\pi$
$367$	3.23308	+	1.17674i	0.168765	+	0.0614255i	−0.256256	+	0.966609i	$0.582489\pi$
$368$		0			0
$369$	3.61721	−	6.26519i	0.188304	−	0.326153i
$370$		0			0
$371$	19.9611	−	16.7494i	1.03633	−	0.869583i
$372$		0			0
$373$	3.15998	+	5.47324i	0.163617	+	0.283394i	0.936163	−	0.351565i	$-0.114350\pi$
$373$	3.15998	+	5.47324i	0.163617	+	0.283394i	−0.772546	+	0.634959i	$0.781017\pi$
$374$		0			0
$375$	−1.94949	+	11.0561i	−0.100671	+	0.570936i
$376$		0			0
$377$	23.9402	−	8.71351i	1.23298	−	0.448768i
$378$		0			0
$379$	14.4074			0.740056			0.370028	−	0.929021i	$-0.379348\pi$
$379$	14.4074			0.740056			0.370028	+	0.929021i	$0.379348\pi$
$380$		0			0
$381$	−13.1925			−0.675874
$382$		0			0
$383$	−1.77719	+	0.646844i	−0.0908101	+	0.0330522i	−0.387026	−	0.922069i	$-0.626498\pi$
$383$	−1.77719	+	0.646844i	−0.0908101	+	0.0330522i	0.296216	+	0.955121i	$0.404275\pi$
$384$		0			0
$385$	2.28389	−	12.9526i	0.116398	−	0.660125i
$386$		0			0
$387$	−2.96064	−	5.12797i	−0.150498	−	0.260670i
$388$		0			0
$389$	−5.65136	+	4.74205i	−0.286535	+	0.240432i	−0.774714	−	0.632312i	$-0.782106\pi$
$389$	−5.65136	+	4.74205i	−0.286535	+	0.240432i	0.488178	+	0.872744i	$0.337662\pi$
$390$		0			0
$391$	−3.79813	+	6.57856i	−0.192080	+	0.332692i
$392$		0			0
$393$	−7.05051	−	2.56617i	−0.355651	−	0.129446i
$394$		0			0
$395$	5.33615	+	30.2628i	0.268491	+	1.52269i
$396$		0			0
$397$	−8.86824	−	7.44134i	−0.445084	−	0.373470i	0.392524	−	0.919742i	$-0.371602\pi$
$397$	−8.86824	−	7.44134i	−0.445084	−	0.373470i	−0.837608	+	0.546272i	$0.816047\pi$
$398$		0			0
$399$	−7.49747	−	8.80271i	−0.375343	−	0.440687i
$400$		0			0
$401$	11.6514	+	9.77665i	0.581841	+	0.488223i	0.885551	−	0.464542i	$-0.153781\pi$
$401$	11.6514	+	9.77665i	0.581841	+	0.488223i	−0.303710	+	0.952765i	$0.598225\pi$
$402$		0			0
$403$	9.47519	+	53.7364i	0.471993	+	2.67680i
$404$		0			0
$405$	2.09240	+	0.761570i	0.103972	+	0.0378427i
$406$		0			0
$407$	2.56670	−	4.44566i	0.127227	−	0.220363i
$408$		0			0
$409$	−1.17293	+	0.984208i	−0.0579978	+	0.0486659i	−0.671326	−	0.741162i	$-0.734275\pi$
$409$	−1.17293	+	0.984208i	−0.0579978	+	0.0486659i	0.613328	+	0.789828i	$0.289830\pi$
$410$		0			0
$411$	3.31521	+	5.74211i	0.163527	+	0.283237i
$412$		0			0
$413$	−2.28389	+	12.9526i	−0.112383	+	0.637355i
$414$		0			0
$415$	21.9764	−	7.99876i	1.07878	−	0.392644i
$416$		0			0
$417$	−8.50980			−0.416727
$418$		0			0
$419$	26.7374			1.30621			0.653104	−	0.757268i	$-0.273466\pi$
$419$	26.7374			1.30621			0.653104	+	0.757268i	$0.273466\pi$
$420$		0			0
$421$	−22.4329	+	8.16490i	−1.09331	+	0.397933i	−0.824847	−	0.565356i	$-0.808739\pi$
$421$	−22.4329	+	8.16490i	−1.09331	+	0.397933i	−0.268465	+	0.963289i	$0.586516\pi$
$422$		0			0
$423$	−1.91147	+	10.8405i	−0.0929391	+	0.527084i
$424$		0			0
$425$	−0.0714517	−	0.123758i	−0.00346592	−	0.00600315i
$426$		0			0
$427$	−11.5876	+	9.72319i	−0.560766	+	0.470538i
$428$		0			0
$429$	5.89053	−	10.2027i	0.284397	−	0.492591i
$430$		0			0
$431$	14.8277	+	5.39684i	0.714225	+	0.259957i	0.673472	−	0.739213i	$-0.264802\pi$
$431$	14.8277	+	5.39684i	0.714225	+	0.259957i	0.0407529	+	0.999169i	$0.487024\pi$
$432$		0			0
$433$	−2.33006	−	13.2144i	−0.111976	−	0.635045i	−0.988203	−	0.153148i	$-0.951059\pi$
$433$	−2.33006	−	13.2144i	−0.111976	−	0.635045i	0.876228	−	0.481897i	$-0.160052\pi$
$434$		0			0
$435$	8.21348	+	6.89193i	0.393806	+	0.330443i
$436$		0			0
$437$	−0.0714517	−	9.70562i	−0.00341800	−	0.464283i
$438$		0			0
$439$	−14.4795	−	12.1498i	−0.691070	−	0.579876i	0.228148	−	0.973627i	$-0.426733\pi$
$439$	−14.4795	−	12.1498i	−0.691070	−	0.579876i	−0.919218	+	0.393750i	$0.871178\pi$
$440$		0			0
$441$	0.00639661	+	0.0362770i	0.000304601	+	0.00172748i
$442$		0			0
$443$	−10.6125	−	3.86262i	−0.504213	−	0.183519i	0.0773747	−	0.997002i	$-0.475346\pi$
$443$	−10.6125	−	3.86262i	−0.504213	−	0.183519i	−0.581588	+	0.813483i	$0.697568\pi$
$444$		0			0
$445$	8.70099	−	15.0706i	0.412466	−	0.714413i
$446$		0			0
$447$	2.61334	−	2.19285i	0.123607	−	0.103718i
$448$		0			0
$449$	4.37733	+	7.58175i	0.206579	+	0.357805i	0.950635	−	0.310313i	$-0.100434\pi$
$449$	4.37733	+	7.58175i	0.206579	+	0.357805i	−0.744056	+	0.668117i	$0.767100\pi$
$450$		0			0
$451$	2.79726	−	15.8640i	0.131718	−	0.747008i
$452$		0			0
$453$	−2.85844	+	1.04039i	−0.134301	+	0.0488817i
$454$		0			0
$455$	31.2517			1.46510
$456$		0			0
$457$	23.8334			1.11488			0.557439	−	0.830218i	$-0.311784\pi$
$457$	23.8334			1.11488			0.557439	+	0.830218i	$0.311784\pi$
$458$		0			0
$459$	−3.20574	+	1.16679i	−0.149631	+	0.0544612i
$460$		0			0
$461$	2.73442	−	15.5077i	0.127355	−	0.722265i	−0.852527	−	0.522684i	$-0.824931\pi$
$461$	2.73442	−	15.5077i	0.127355	−	0.722265i	0.979881	−	0.199581i	$-0.0639581\pi$
$462$		0			0
$463$	−2.18732	−	3.78855i	−0.101653	−	0.176069i	0.810713	−	0.585444i	$-0.199080\pi$
$463$	−2.18732	−	3.78855i	−0.101653	−	0.176069i	−0.912366	+	0.409376i	$0.865747\pi$
$464$		0			0
$465$	−17.5915	+	14.7610i	−0.815787	+	0.684527i
$466$		0			0
$467$	13.0535	−	22.6093i	0.604044	−	1.04623i	−0.388158	−	0.921593i	$-0.626888\pi$
$467$	13.0535	−	22.6093i	0.604044	−	1.04623i	0.992202	−	0.124642i	$-0.0397782\pi$
$468$		0			0
$469$	21.3726	+	7.77898i	0.986894	+	0.359200i
$470$		0			0
$471$	2.69594	+	15.2894i	0.124222	+	0.704499i
$472$		0			0
$473$	−10.1001	−	8.47502i	−0.464405	−	0.389682i
$474$		0			0
$475$	0.158796	+	0.0901285i	0.00728604	+	0.00413538i
$476$		0			0
$477$	7.52481	+	6.31407i	0.344538	+	0.289101i
$478$		0			0
$479$	5.92556	+	33.6055i	0.270746	+	1.53547i	0.752160	+	0.658981i	$0.229012\pi$
$479$	5.92556	+	33.6055i	0.270746	+	1.53547i	−0.481414	+	0.876493i	$0.659877\pi$
$480$		0			0
$481$	11.4620	+	4.17182i	0.522621	+	0.190219i
$482$		0			0
$483$	−2.95336	+	5.11538i	−0.134383	+	0.232758i
$484$		0			0
$485$	30.3430	−	25.4608i	1.37781	−	1.15612i
$486$		0			0
$487$	−7.88191	−	13.6519i	−0.357164	−	0.618625i	0.630322	−	0.776334i	$-0.282923\pi$
$487$	−7.88191	−	13.6519i	−0.357164	−	0.618625i	−0.987486	+	0.157708i	$0.949589\pi$
$488$		0			0
$489$	0.770792	−	4.37138i	0.0348564	−	0.197681i
$490$		0			0
$491$	13.0039	−	4.73302i	0.586856	−	0.213598i	−0.0314898	−	0.999504i	$-0.510025\pi$
$491$	13.0039	−	4.73302i	0.586856	−	0.213598i	0.618346	+	0.785906i	$0.287803\pi$
$492$		0			0
$493$	−16.4270			−0.739833
$494$		0			0
$495$	4.95811			0.222851
$496$		0			0
$497$	10.9773	−	3.99541i	0.492399	−	0.179219i
$498$		0			0
$499$	3.46064	−	19.6262i	0.154919	−	0.878592i	−0.803940	−	0.594710i	$-0.797267\pi$
$499$	3.46064	−	19.6262i	0.154919	−	0.878592i	0.958859	−	0.283881i	$-0.0916221\pi$
$500$		0			0
$501$	4.07532	+	7.05866i	0.182072	+	0.315358i
$502$		0			0
$503$	11.3990	−	9.56488i	0.508256	−	0.426477i	−0.352259	−	0.935902i	$-0.614586\pi$
$503$	11.3990	−	9.56488i	0.508256	−	0.426477i	0.860515	+	0.509425i	$0.170142\pi$
$504$		0			0
$505$	19.9363	−	34.5307i	0.887153	−	1.53659i
$506$		0			0
$507$	14.0890	+	5.12797i	0.625714	+	0.227741i
$508$		0			0
$509$	−6.37046	−	36.1287i	−0.282366	−	1.60138i	−0.714546	−	0.699589i	$-0.753367\pi$
$509$	−6.37046	−	36.1287i	−0.282366	−	1.60138i	0.432180	−	0.901787i	$-0.357744\pi$
$510$		0			0
$511$	−5.68092	−	4.76686i	−0.251309	−	0.210873i
$512$		0			0
$513$	2.77719	−	3.35965i	0.122616	−	0.148332i
$514$		0			0
$515$	7.24304	+	6.07763i	0.319166	+	0.267812i
$516$		0			0
$517$	4.25624	+	24.1384i	0.187189	+	1.06160i
$518$		0			0
$519$	−15.0030	−	5.46064i	−0.658558	−	0.239696i
$520$		0			0
$521$	18.7677	−	32.5066i	0.822228	−	1.42414i	−0.0817923	−	0.996649i	$-0.526064\pi$
$521$	18.7677	−	32.5066i	0.822228	−	1.42414i	0.904020	−	0.427491i	$-0.140602\pi$
$522$		0			0
$523$	−0.304063	+	0.255139i	−0.0132958	+	0.0111565i	−0.649411	−	0.760437i	$-0.724985\pi$
$523$	−0.304063	+	0.255139i	−0.0132958	+	0.0111565i	0.636116	+	0.771594i	$0.280540\pi$
$524$		0			0
$525$	−0.0555596	−	0.0962321i	−0.00242482	−	0.00419991i
$526$		0			0
$527$	6.10947	−	34.6485i	0.266133	−	1.50931i
$528$		0			0
$529$	16.9538	−	6.17069i	0.737123	−	0.268291i
$530$		0			0
$531$	−4.95811			−0.215164
$532$		0			0
$533$	38.2763			1.65793
$534$		0			0
$535$	−32.6498	+	11.8835i	−1.41157	+	0.513770i
$536$		0			0
$537$	0.252374	−	1.43128i	0.0108907	−	0.0617644i
$538$		0			0
$539$	0.0410117	+	0.0710344i	0.00176650	+	0.00305967i
$540$		0			0
$541$	−15.9730	+	13.4029i	−0.686731	+	0.576236i	−0.917965	−	0.396662i	$-0.870168\pi$
$541$	−15.9730	+	13.4029i	−0.686731	+	0.576236i	0.231233	+	0.972898i	$0.425724\pi$
$542$		0			0
$543$	−0.562834	+	0.974856i	−0.0241535	+	0.0418351i
$544$		0			0
$545$	−2.84952	−	1.03714i	−0.122060	−	0.0444262i
$546$		0			0
$547$	0.896926	+	5.08672i	0.0383498	+	0.217492i	0.997960	−	0.0638400i	$-0.0203347\pi$
$547$	0.896926	+	5.08672i	0.0383498	+	0.217492i	−0.959610	+	0.281332i	$0.909224\pi$
$548$		0			0
$549$	−4.36824	−	3.66539i	−0.186432	−	0.156435i
$550$		0			0
$551$	18.0993	−	10.6280i	0.771054	−	0.452769i
$552$		0			0
$553$	−28.0442	−	23.5319i	−1.19256	−	1.00068i
$554$		0			0
$555$	0.891407	+	5.05542i	0.0378381	+	0.214591i
$556$		0			0
$557$	−27.2173	−	9.90630i	−1.15324	−	0.419744i	−0.306560	−	0.951851i	$-0.599178\pi$
$557$	−27.2173	−	9.90630i	−1.15324	−	0.419744i	−0.846677	+	0.532108i	$0.821400\pi$
$558$		0			0
$559$	15.6643	−	27.1314i	0.662530	−	1.14754i
$560$		0			0
$561$	−5.81908	+	4.88279i	−0.245682	+	0.206151i
$562$		0			0
$563$	−4.37892	−	7.58451i	−0.184549	−	0.319649i	0.758875	−	0.651236i	$-0.225749\pi$
$563$	−4.37892	−	7.58451i	−0.184549	−	0.319649i	−0.943425	+	0.331587i	$0.892416\pi$
$564$		0			0
$565$	−6.65064	+	37.7177i	−0.279795	+	1.58679i
$566$		0			0
$567$	−2.49273	+	0.907278i	−0.104685	+	0.0381021i
$568$		0			0
$569$	11.3696			0.476638			0.238319	−	0.971187i	$-0.423404\pi$
$569$	11.3696			0.476638			0.238319	+	0.971187i	$0.423404\pi$
$570$		0			0
$571$	−2.98545			−0.124937			−0.0624686	−	0.998047i	$-0.519897\pi$
$571$	−2.98545			−0.124937			−0.0624686	+	0.998047i	$0.519897\pi$
$572$		0			0
$573$	1.24763	−	0.454099i	0.0521203	−	0.0189702i
$574$		0			0
$575$	0.0161968	−	0.0918566i	0.000675453	−	0.00383068i
$576$		0			0
$577$	11.3735	+	19.6994i	0.473483	+	0.820097i	0.999539	−	0.0303530i	$-0.00966315\pi$
$577$	11.3735	+	19.6994i	0.473483	+	0.820097i	−0.526056	+	0.850450i	$0.676330\pi$
$578$		0			0
$579$	−11.4795	+	9.63246i	−0.477073	+	0.400311i
$580$		0			0
$581$	−13.9307	+	24.1286i	−0.577941	+	1.00102i
$582$		0			0
$583$	20.5535	+	7.48086i	0.851239	+	0.309826i
$584$		0			0
$585$	2.04576	+	11.6021i	0.0845817	+	0.479687i
$586$		0			0
$587$	12.6552	+	10.6190i	0.522337	+	0.438293i	0.865446	−	0.501003i	$-0.167035\pi$
$587$	12.6552	+	10.6190i	0.522337	+	0.438293i	−0.343108	+	0.939296i	$0.611480\pi$
$588$		0			0
$589$	15.6857	+	42.1286i	0.646319	+	1.73588i
$590$		0			0
$591$	−17.6250	−	14.7891i	−0.724994	−	0.608342i
$592$		0			0
$593$	2.62355	+	14.8789i	0.107736	+	0.611003i	0.990092	+	0.140420i	$0.0448453\pi$
$593$	2.62355	+	14.8789i	0.107736	+	0.611003i	−0.882356	+	0.470583i	$0.844044\pi$
$594$		0			0
$595$	−18.9354	−	6.89193i	−0.776276	−	0.282541i
$596$		0			0
$597$	−4.84137	+	8.38549i	−0.198144	+	0.343195i
$598$		0			0
$599$	14.0326	−	11.7747i	0.573355	−	0.481102i	−0.309403	−	0.950931i	$-0.600129\pi$
$599$	14.0326	−	11.7747i	0.573355	−	0.481102i	0.882757	+	0.469829i	$0.155685\pi$
$600$		0			0
$601$	1.78746	+	3.09596i	0.0729118	+	0.126287i	0.900176	−	0.435526i	$-0.143437\pi$
$601$	1.78746	+	3.09596i	0.0729118	+	0.126287i	−0.827264	+	0.561813i	$0.810104\pi$
$602$		0			0
$603$	−1.48886	+	8.44372i	−0.0606309	+	0.343855i
$604$		0			0
$605$	−12.6420	+	4.60132i	−0.513971	+	0.187070i
$606$		0			0
$607$	−10.9436			−0.444186			−0.222093	−	0.975026i	$-0.571289\pi$
$607$	−10.9436			−0.444186			−0.222093	+	0.975026i	$0.571289\pi$
$608$		0			0
$609$	−12.7733			−0.517601
$610$		0			0
$611$	−54.7281	+	19.9194i	−2.21406	+	0.805852i
$612$		0			0
$613$	7.74345	−	43.9153i	0.312755	−	1.77372i	−0.271786	−	0.962358i	$-0.587614\pi$
$613$	7.74345	−	43.9153i	0.312755	−	1.77372i	0.584541	−	0.811364i	$-0.301275\pi$
$614$		0			0
$615$	8.05438	+	13.9506i	0.324784	+	0.562542i
$616$		0			0
$617$	−1.10876	+	0.930356i	−0.0446368	+	0.0374547i	−0.664833	−	0.746992i	$-0.731497\pi$
$617$	−1.10876	+	0.930356i	−0.0446368	+	0.0374547i	0.620196	+	0.784447i	$0.287053\pi$
$618$		0			0
$619$	−23.6236	+	40.9173i	−0.949513	+	1.64460i	−0.203060	+	0.979166i	$0.565089\pi$
$619$	−23.6236	+	40.9173i	−0.949513	+	1.64460i	−0.746453	+	0.665438i	$0.768245\pi$
$620$		0			0
$621$	−2.09240	−	0.761570i	−0.0839650	−	0.0305607i
$622$		0			0
$623$	3.59997	+	20.4165i	0.144230	+	0.817969i
$624$		0			0
$625$	−18.9893	−	15.9339i	−0.759573	−	0.637357i
$626$		0			0
$627$	3.25237	−	9.14473i	0.129887	−	0.365206i
$628$		0			0
$629$	−6.02481	−	5.05542i	−0.240225	−	0.201573i
$630$		0			0
$631$	−6.05010	−	34.3118i	−0.240851	−	1.36593i	−0.829935	−	0.557860i	$-0.811623\pi$
$631$	−6.05010	−	34.3118i	−0.240851	−	1.36593i	0.589085	−	0.808071i	$-0.299488\pi$
$632$		0			0
$633$	1.03936	+	0.378297i	0.0413110	+	0.0150360i
$634$		0			0
$635$	14.6878	−	25.4400i	0.582867	−	1.00956i
$636$		0			0
$637$	−0.149300	+	0.125278i	−0.00591548	+	0.00496368i
$638$		0			0
$639$	2.20187	+	3.81374i	0.0871045	+	0.150869i
$640$		0			0
$641$	1.90286	−	10.7916i	0.0751583	−	0.426244i	−0.923891	−	0.382655i	$-0.875010\pi$
$641$	1.90286	−	10.7916i	0.0751583	−	0.426244i	0.999050	−	0.0435888i	$-0.0138791\pi$
$642$		0			0
$643$	3.47683	−	1.26546i	0.137113	−	0.0499050i	−0.272552	−	0.962141i	$-0.587868\pi$
$643$	3.47683	−	1.26546i	0.137113	−	0.0499050i	0.409665	+	0.912236i	$0.365646\pi$
$644$		0			0
$645$	13.1848			0.519151
$646$		0			0
$647$	−26.2671			−1.03267			−0.516334	−	0.856387i	$-0.672704\pi$
$647$	−26.2671			−1.03267			−0.516334	+	0.856387i	$0.672704\pi$
$648$		0			0
$649$	−10.3743	+	3.77595i	−0.407228	+	0.148219i
$650$		0			0
$651$	4.75062	−	26.9421i	0.186191	−	1.05594i
$652$		0			0
$653$	−13.0783	−	22.6523i	−0.511794	−	0.886453i	−0.999907	−	0.0136725i	$-0.995648\pi$
$653$	−13.0783	−	22.6523i	−0.511794	−	0.886453i	0.488113	−	0.872781i	$-0.337686\pi$
$654$		0			0
$655$	12.7981	−	10.7389i	0.500064	−	0.419604i
$656$		0			0
$657$	1.39780	−	2.42107i	0.0545335	−	0.0944548i
$658$		0			0
$659$	25.2592	+	9.19361i	0.983960	+	0.358132i	0.783379	−	0.621545i	$-0.213495\pi$
$659$	25.2592	+	9.19361i	0.983960	+	0.358132i	0.200582	+	0.979677i	$0.435717\pi$
$660$		0			0
$661$	0.972086	+	5.51297i	0.0378098	+	0.214430i	0.997859	−	0.0654011i	$-0.0208327\pi$
$661$	0.972086	+	5.51297i	0.0378098	+	0.214430i	−0.960049	+	0.279831i	$0.909722\pi$
$662$		0			0
$663$	−13.8268	−	11.6021i	−0.536989	−	0.450587i
$664$		0			0
$665$	25.3221	−	4.65743i	0.981948	−	0.180607i
$666$		0			0
$667$	−8.21348	−	6.89193i	−0.318027	−	0.266856i
$668$		0			0
$669$	4.39100	+	24.9026i	0.169766	+	0.962789i
$670$		0			0
$671$	−11.9315	−	4.34273i	−0.460612	−	0.167649i
$672$		0			0
$673$	−11.4966	+	19.9127i	−0.443161	+	0.767578i	−0.997922	−	0.0644321i	$-0.979476\pi$
$673$	−11.4966	+	19.9127i	−0.443161	+	0.767578i	0.554761	+	0.832010i	$0.312810\pi$
$674$		0			0
$675$	0.0320889	−	0.0269258i	0.00123510	−	0.00103637i
$676$		0			0
$677$	−7.66772	−	13.2809i	−0.294694	−	0.510426i	0.680219	−	0.733009i	$-0.261885\pi$
$677$	−7.66772	−	13.2809i	−0.294694	−	0.510426i	−0.974914	+	0.222583i	$0.928551\pi$
$678$		0			0
$679$	−8.19418	+	46.4715i	−0.314464	+	1.78341i
$680$		0			0
$681$	−3.22193	+	1.17269i	−0.123465	+	0.0449375i
$682$		0			0
$683$	19.6459			0.751729			0.375865	−	0.926675i	$-0.377346\pi$
$683$	19.6459			0.751729			0.375865	+	0.926675i	$0.377346\pi$
$684$		0			0
$685$	−14.7638			−0.564097
$686$		0			0
$687$	28.1361	−	10.2407i	1.07346	−	0.390707i
$688$		0			0
$689$	−9.02481	+	51.1823i	−0.343818	+	1.94989i
$690$		0			0
$691$	9.73442	+	16.8605i	0.370315	+	0.641404i	0.989614	−	0.143751i	$-0.0459165\pi$
$691$	9.73442	+	16.8605i	0.370315	+	0.641404i	−0.619299	+	0.785155i	$0.712583\pi$
$692$		0			0
$693$	−4.52481	+	3.79677i	−0.171884	+	0.144227i
$694$		0			0
$695$	9.47431	−	16.4100i	0.359381	−	0.622466i
$696$		0			0
$697$	−23.1917	−	8.44107i	−0.878447	−	0.319728i
$698$		0			0
$699$	1.80200	+	10.2197i	0.0681580	+	0.386543i
$700$		0			0
$701$	16.9433	+	14.2171i	0.639940	+	0.536974i	0.904000	−	0.427533i	$-0.140617\pi$
$701$	16.9433	+	14.2171i	0.639940	+	0.536974i	−0.264060	+	0.964506i	$0.585062\pi$
$702$		0			0
$703$	9.90895	+	1.67210i	0.373723	+	0.0630643i
$704$		0			0
$705$	−18.7763	−	15.7552i	−0.707157	−	0.593375i
$706$		0			0
$707$	8.24850	+	46.7796i	0.310217	+	1.75933i
$708$		0			0
$709$	−8.96451	−	3.26281i	−0.336669	−	0.122538i	0.168153	−	0.985761i	$-0.446220\pi$
$709$	−8.96451	−	3.26281i	−0.336669	−	0.122538i	−0.504822	+	0.863223i	$0.668442\pi$
$710$		0			0
$711$	6.90033	−	11.9517i	0.258783	−	0.448225i
$712$		0			0
$713$	17.5915	−	14.7610i	0.658808	−	0.552805i
$714$		0			0
$715$	13.1163	+	22.7182i	0.490523	+	0.849611i
$716$		0			0
$717$	−2.78106	+	15.7722i	−0.103861	+	0.589022i
$718$		0			0
$719$	−36.4479	+	13.2660i	−1.35928	+	0.494736i	−0.915831	−	0.401564i	$-0.868467\pi$
$719$	−36.4479	+	13.2660i	−1.35928	+	0.494736i	−0.443447	+	0.896301i	$0.646244\pi$
$720$		0			0
$721$	−11.2641			−0.419498
$722$		0			0
$723$	−25.5817			−0.951394
$724$		0			0
$725$	0.189540	−	0.0689870i	0.00703935	−	0.00256211i
$726$		0			0
$727$	6.22446	−	35.3007i	0.230852	−	1.30923i	−0.620322	−	0.784347i	$-0.712998\pi$
$727$	6.22446	−	35.3007i	0.230852	−	1.30923i	0.851175	−	0.524882i	$-0.175891\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	−15.4743	+	12.9845i	−0.572338	+	0.480249i
$732$		0			0
$733$	−0.201867	+	0.349643i	−0.00745612	+	0.0129144i	−0.869729	−	0.493529i	$-0.835707\pi$
$733$	−0.201867	+	0.349643i	−0.00745612	+	0.0129144i	0.862273	+	0.506443i	$0.169040\pi$
$734$		0			0
$735$	−0.0770768	−	0.0280537i	−0.00284302	−	0.00103478i
$736$		0			0
$737$	3.31521	+	18.8015i	0.122117	+	0.692561i
$738$		0			0
$739$	0.456052	+	0.382673i	0.0167761	+	0.0140768i	0.651137	−	0.758960i	$-0.274292\pi$
$739$	0.456052	+	0.382673i	0.0167761	+	0.0140768i	−0.634361	+	0.773037i	$0.718737\pi$
$740$		0			0
$741$	22.7408	+	3.83742i	0.835405	+	0.140971i
$742$		0			0
$743$	−9.09627	−	7.63267i	−0.333710	−	0.280016i	0.460500	−	0.887660i	$-0.347670\pi$
$743$	−9.09627	−	7.63267i	−0.333710	−	0.280016i	−0.794209	+	0.607644i	$0.792115\pi$
$744$		0			0
$745$	1.31908	+	7.48086i	0.0483273	+	0.274078i
$746$		0			0
$747$	−9.86959	−	3.59224i	−0.361109	−	0.131433i
$748$		0			0
$749$	20.6964	−	35.8472i	0.756230	−	1.30983i
$750$		0			0
$751$	−4.18067	+	3.50800i	−0.152555	+	0.128009i	−0.715871	−	0.698233i	$-0.753970\pi$
$751$	−4.18067	+	3.50800i	−0.152555	+	0.128009i	0.563316	+	0.826242i	$0.309526\pi$
$752$		0			0
$753$	−5.34477	−	9.25741i	−0.194774	−	0.337359i
$754$		0			0
$755$	1.17617	−	6.67042i	0.0428054	−	0.242761i
$756$		0			0
$757$	−11.3645	+	4.13635i	−0.413051	+	0.150338i	−0.540183	−	0.841548i	$-0.681645\pi$
$757$	−11.3645	+	4.13635i	−0.413051	+	0.150338i	0.127132	+	0.991886i	$0.459423\pi$
$758$		0			0
$759$	−4.95811			−0.179968
$760$		0			0
$761$	−18.8726			−0.684130			−0.342065	−	0.939676i	$-0.611126\pi$
$761$	−18.8726			−0.684130			−0.342065	+	0.939676i	$0.611126\pi$
$762$		0			0
$763$	3.39470	−	1.23557i	0.122897	−	0.0447307i
$764$		0			0
$765$	1.31908	−	7.48086i	0.0476914	−	0.270471i
$766$		0			0
$767$	−13.1163	−	22.7182i	−0.473603	−	0.820305i
$768$		0			0
$769$	−38.5094	+	32.3132i	−1.38868	+	1.16524i	−0.422814	+	0.906216i	$0.638958\pi$
$769$	−38.5094	+	32.3132i	−1.38868	+	1.16524i	−0.965870	+	0.259028i	$0.916598\pi$
$770$		0			0
$771$	−15.3897	+	26.6557i	−0.554245	+	0.959980i
$772$		0			0
$773$	20.1887	+	7.34807i	0.726136	+	0.264292i	0.678528	−	0.734574i	$-0.262618\pi$
$773$	20.1887	+	7.34807i	0.726136	+	0.264292i	0.0476075	+	0.998866i	$0.484840\pi$
$774$		0			0
$775$	0.0750174	+	0.425445i	0.00269471	+	0.0152824i
$776$		0			0
$777$	−4.68479	−	3.93101i	−0.168066	−	0.141024i
$778$		0			0
$779$	31.0139	−	5.70431i	1.11119	−	0.204378i
$780$		0			0
$781$	7.51161	+	6.30299i	0.268787	+	0.225539i
$782$		0			0
$783$	−0.836152	−	4.74205i	−0.0298816	−	0.169467i
$784$		0			0
$785$	−32.4850	−	11.8236i	−1.15944	−	0.422002i
$786$		0			0
$787$	−11.2750	+	19.5288i	−0.401909	+	0.696127i	−0.993956	−	0.109776i	$-0.964987\pi$
$787$	−11.2750	+	19.5288i	−0.401909	+	0.696127i	0.592047	+	0.805903i	$0.298320\pi$
$788$		0			0
$789$	2.40760	−	2.02022i	0.0857130	−	0.0719217i
$790$		0			0
$791$	−22.8136	−	39.5143i	−0.811159	−	1.40497i
$792$		0			0
$793$	5.23901	−	29.7119i	0.186043	−	1.05510i
$794$		0			0
$795$	−20.5535	+	7.48086i	−0.728958	+	0.265319i
$796$		0			0
$797$	−27.2098			−0.963819			−0.481910	−	0.876221i	$-0.660057\pi$
$797$	−27.2098			−0.963819			−0.481910	+	0.876221i	$0.660057\pi$
$798$		0			0
$799$	37.5526			1.32852
$800$		0			0
$801$	−7.34389	+	2.67296i	−0.259484	+	0.0944443i
$802$		0			0
$803$	1.08095	−	6.13036i	0.0381458	−	0.216336i
$804$		0			0
$805$	−6.57620	−	11.3903i	−0.231781	−	0.401456i
$806$		0			0
$807$	−11.3990	+	9.56488i	−0.401263	+	0.336700i
$808$		0			0
$809$	14.6762	−	25.4199i	0.515987	−	0.893715i	−0.483841	−	0.875156i	$-0.660759\pi$
$809$	14.6762	−	25.4199i	0.515987	−	0.893715i	0.999828	−	0.0185594i	$-0.00590799\pi$
$810$		0			0
$811$	17.9547	+	6.53498i	0.630475	+	0.229474i	0.637438	−	0.770502i	$-0.279994\pi$
$811$	17.9547	+	6.53498i	0.630475	+	0.229474i	−0.00696301	+	0.999976i	$0.502216\pi$
$812$		0			0
$813$	2.64543	+	15.0030i	0.0927793	+	0.526177i
$814$		0			0
$815$	7.57145	+	6.35320i	0.265216	+	0.222543i
$816$		0			0
$817$	8.64883	−	24.3180i	0.302584	−	0.850780i
$818$		0			0
$819$	−10.7515	−	9.02158i	−0.375688	−	0.315239i
$820$		0			0
$821$	0.0730443	+	0.414255i	0.00254926	+	0.0144576i	0.986056	−	0.166415i	$-0.0532190\pi$
$821$	0.0730443	+	0.414255i	0.00254926	+	0.0144576i	−0.983507	+	0.180872i	$0.942108\pi$
$822$		0			0
$823$	−34.4286	−	12.5310i	−1.20011	−	0.436803i	−0.336845	−	0.941560i	$-0.609360\pi$
$823$	−34.4286	−	12.5310i	−1.20011	−	0.436803i	−0.863261	+	0.504758i	$0.831582\pi$
$824$		0			0
$825$	0.0466368	−	0.0807773i	0.00162369	−	0.00281231i
$826$		0			0
$827$	−22.5876	+	18.9533i	−0.785449	+	0.659070i	−0.944615	−	0.328182i	$-0.893564\pi$
$827$	−22.5876	+	18.9533i	−0.785449	+	0.659070i	0.159165	+	0.987252i	$0.449120\pi$
$828$		0			0
$829$	2.81315	+	4.87252i	0.0977047	+	0.169229i	0.910734	−	0.412993i	$-0.135517\pi$
$829$	2.81315	+	4.87252i	0.0977047	+	0.169229i	−0.813030	+	0.582222i	$0.802183\pi$
$830$		0			0
$831$	2.12015	−	12.0240i	0.0735471	−	0.417106i
$832$		0			0
$833$	0.118089	−	0.0429807i	0.00409153	−	0.00148919i
$834$		0			0
$835$	−18.1489			−0.628068
$836$		0			0
$837$	10.3131			0.356475
$838$		0			0
$839$	40.4213	−	14.7122i	1.39550	−	0.507920i	0.468660	−	0.883379i	$-0.344737\pi$
$839$	40.4213	−	14.7122i	1.39550	−	0.507920i	0.926839	+	0.375458i	$0.122515\pi$
$840$		0			0
$841$	−1.00955	+	5.72545i	−0.0348121	+	0.197429i
$842$		0			0
$843$	−1.12196	−	1.94329i	−0.0386423	−	0.0669305i
$844$		0			0
$845$	−25.5744	+	21.4595i	−0.879788	+	0.738229i
$846$		0			0
$847$	8.01367	−	13.8801i	0.275353	−	0.476925i
$848$		0			0
$849$	13.8969	+	5.05807i	0.476941	+	0.173592i
$850$		0			0
$851$	−0.891407	−	5.05542i	−0.0305570	−	0.173298i
$852$		0			0
$853$	18.1480	+	15.2279i	0.621374	+	0.521395i	0.898235	−	0.439515i	$-0.144850\pi$
$853$	18.1480	+	15.2279i	0.621374	+	0.521395i	−0.276861	+	0.960910i	$0.589294\pi$
$854$		0			0
$855$	3.38666	+	9.09586i	0.115821	+	0.311072i
$856$		0			0
$857$	38.6862	+	32.4616i	1.32150	+	1.10887i	0.985986	+	0.166829i	$0.0533529\pi$
$857$	38.6862	+	32.4616i	1.32150	+	1.10887i	0.335509	+	0.942037i	$0.391092\pi$
$858$		0			0
$859$	−0.864066	−	4.90036i	−0.0294815	−	0.167198i	0.966512	−	0.256620i	$-0.0826090\pi$
$859$	−0.864066	−	4.90036i	−0.0294815	−	0.167198i	−0.995994	+	0.0894223i	$0.971498\pi$
$860$		0			0
$861$	−18.0334	−	6.56363i	−0.614578	−	0.223688i
$862$		0			0
$863$	−3.95424	+	6.84895i	−0.134604	+	0.233141i	−0.925446	−	0.378879i	$-0.876310\pi$
$863$	−3.95424	+	6.84895i	−0.134604	+	0.233141i	0.790842	+	0.612020i	$0.209643\pi$
$864$		0			0
$865$	27.2335	−	22.8517i	0.925968	−	0.776980i
$866$		0			0
$867$	−2.68092	−	4.64349i	−0.0910489	−	0.157701i
$868$		0			0
$869$	5.33615	−	30.2628i	0.181017	−	1.02660i
$870$		0			0
$871$	−42.6279	+	15.5153i	−1.44439	+	0.525716i
$872$		0			0
$873$	−17.7888			−0.602060
$874$		0			0
$875$	29.7811			1.00678
$876$		0			0
$877$	7.17664	−	2.61208i	0.242338	−	0.0882038i	−0.217996	−	0.975950i	$-0.569952\pi$
$877$	7.17664	−	2.61208i	0.242338	−	0.0882038i	0.460334	+	0.887746i	$0.347730\pi$
$878$		0			0
$879$	2.09240	−	11.8666i	0.0705748	−	0.400249i
$880$		0			0
$881$	−9.44491	−	16.3591i	−0.318207	−	0.551151i	0.661907	−	0.749586i	$-0.269747\pi$
$881$	−9.44491	−	16.3591i	−0.318207	−	0.551151i	−0.980114	+	0.198435i	$0.936414\pi$
$882$		0			0
$883$	−41.1339	+	34.5154i	−1.38427	+	1.16154i	−0.416662	+	0.909062i	$0.636800\pi$
$883$	−41.1339	+	34.5154i	−1.38427	+	1.16154i	−0.967604	+	0.252475i	$0.918756\pi$
$884$		0			0
$885$	5.52007	−	9.56104i	0.185555	−	0.321391i
$886$		0			0
$887$	−45.8680	−	16.6946i	−1.54010	−	0.560549i	−0.574028	−	0.818836i	$-0.694620\pi$
$887$	−45.8680	−	16.6946i	−1.54010	−	0.560549i	−0.966068	+	0.258286i	$0.916842\pi$
$888$		0			0
$889$	6.07697	+	34.4642i	0.203815	+	1.15589i
$890$		0			0
$891$	−1.70574	−	1.43128i	−0.0571443	−	0.0479498i
$892$		0			0
$893$	−41.3756	+	24.2961i	−1.38458	+	0.813037i
$894$		0			0
$895$	2.47906	+	2.08017i	0.0828657	+	0.0695326i
$896$		0			0
$897$	−2.04576	−	11.6021i	−0.0683059	−	0.387382i
$898$		0			0
$899$	46.6651	+	16.9847i	1.55637	+	0.566472i
$900$		0			0
$901$	16.7554	−	29.0211i	0.558202	−	0.966835i
$902$		0			0
$903$	−12.0326	+	10.0965i	−0.400418	+	0.335991i
$904$		0			0
$905$	−1.25325	−	2.17069i	−0.0416595	−	0.0721563i
$906$		0			0
$907$	7.04623	−	39.9611i	0.233966	−	1.32689i	−0.610814	−	0.791774i	$-0.709158\pi$
$907$	7.04623	−	39.9611i	0.233966	−	1.32689i	0.844780	−	0.535114i	$-0.179731\pi$
$908$		0			0
$909$	−16.8268	+	6.12446i	−0.558110	+	0.203136i
$910$		0			0
$911$	−36.0384			−1.19400			−0.597002	−	0.802239i	$-0.703642\pi$
$911$	−36.0384			−1.19400			−0.597002	+	0.802239i	$0.703642\pi$
$912$		0			0
$913$	−23.3868			−0.773991
$914$		0			0
$915$	11.9315	−	4.34273i	0.394445	−	0.143566i
$916$		0			0
$917$	−3.45616	+	19.6008i	−0.114132	+	0.647277i
$918$		0			0
$919$	13.0959	+	22.6827i	0.431992	+	0.748233i	0.997045	−	0.0768222i	$-0.0244774\pi$
$919$	13.0959	+	22.6827i	0.431992	+	0.748233i	−0.565052	+	0.825055i	$0.691144\pi$
$920$		0			0
$921$	17.3084	−	14.5235i	0.570331	−	0.478565i
$922$		0			0
$923$	−11.6498	+	20.1780i	−0.383457	+	0.664167i
$924$		0			0
$925$	0.0907474	+	0.0330293i	0.00298376	+	0.00108600i
$926$		0			0
$927$	−0.737359	−	4.18177i	−0.0242181	−	0.137347i
$928$		0			0
$929$	37.0185	+	31.0622i	1.21454	+	1.01912i	0.999092	+	0.0426013i	$0.0135645\pi$
$929$	37.0185	+	31.0622i	1.21454	+	1.01912i	0.215445	+	0.976516i	$0.430880\pi$
$930$		0			0
$931$	−0.102302	+	0.123758i	−0.00335282	+	0.00405601i
$932$		0			0
$933$	−8.67617	−	7.28017i	−0.284045	−	0.238342i
$934$		0			0
$935$	−2.93717	−	16.6575i	−0.0960556	−	0.544758i
$936$		0			0
$937$	−55.6220	−	20.2448i	−1.81709	−	0.661367i	−0.995873	−	0.0907538i	$-0.971072\pi$
$937$	−55.6220	−	20.2448i	−1.81709	−	0.661367i	−0.821219	−	0.570614i	$-0.806705\pi$
$938$		0			0
$939$	−2.97906	+	5.15988i	−0.0972178	+	0.168386i
$940$		0			0
$941$	4.43557	−	3.72189i	0.144596	−	0.121330i	−0.567621	−	0.823290i	$-0.692136\pi$
$941$	4.43557	−	3.72189i	0.144596	−	0.121330i	0.712216	+	0.701960i	$0.247692\pi$
$942$		0			0
$943$	−8.05438	−	13.9506i	−0.262287	−	0.454294i
$944$		0			0
$945$	1.02569	−	5.81699i	0.0333658	−	0.189227i
$946$		0			0
$947$	−43.1441	+	15.7032i	−1.40200	+	0.510285i	−0.928770	−	0.370656i	$-0.879133\pi$
$947$	−43.1441	+	15.7032i	−1.40200	+	0.510285i	−0.473226	+	0.880941i	$0.656911\pi$
$948$		0			0
$949$	14.7912			0.480142
$950$		0			0
$951$	8.92396			0.289379
$952$		0			0
$953$	−26.8307	+	9.76557i	−0.869131	+	0.316338i	−0.737815	−	0.675003i	$-0.764142\pi$
$953$	−26.8307	+	9.76557i	−0.869131	+	0.316338i	−0.131316	+	0.991341i	$0.541920\pi$
$954$		0			0
$955$	−0.513366	+	2.91144i	−0.0166121	+	0.0942121i
$956$		0			0
$957$	−5.36097	−	9.28547i	−0.173295	−	0.300157i
$958$		0			0
$959$	13.4736	−	11.3057i	0.435085	−	0.365080i
$960$		0			0
$961$	−37.6805	+	65.2646i	−1.21550	+	2.10531i
$962$		0			0
$963$	14.6630	+	5.33688i	0.472508	+	0.171979i
$964$		0			0
$965$	−5.79426	−	32.8609i	−0.186524	−	1.05783i
$966$		0			0
$967$	16.9140	+	14.1925i	0.543918	+	0.456401i	0.872875	−	0.487944i	$-0.162253\pi$
$967$	16.9140	+	14.1925i	0.543918	+	0.456401i	−0.328958	+	0.944345i	$0.606697\pi$
$968$		0			0
$969$	−12.9324	−	7.34013i	−0.415449	−	0.235799i
$970$		0			0
$971$	9.70645	+	8.14468i	0.311495	+	0.261375i	0.785110	−	0.619357i	$-0.212607\pi$
$971$	9.70645	+	8.14468i	0.311495	+	0.261375i	−0.473615	+	0.880732i	$0.657051\pi$
$972$		0			0
$973$	3.91993	+	22.2310i	0.125667	+	0.712694i
$974$		0			0
$975$	0.208263	+	0.0758016i	0.00666976	+	0.00242760i
$976$		0			0
$977$	8.62495	−	14.9389i	0.275937	−	0.477936i	−0.694434	−	0.719556i	$-0.744345\pi$
$977$	8.62495	−	14.9389i	0.275937	−	0.477936i	0.970371	+	0.241620i	$0.0776787\pi$
$978$		0			0
$979$	−13.3307	+	11.1858i	−0.426051	+	0.357499i
$980$		0			0
$981$	0.680922	+	1.17939i	0.0217402	+	0.0376551i
$982$		0			0
$983$	1.05509	−	5.98373i	0.0336522	−	0.190851i	−0.963347	−	0.268257i	$-0.913552\pi$
$983$	1.05509	−	5.98373i	0.0336522	−	0.190851i	0.997000	+	0.0774054i	$0.0246636\pi$
$984$		0			0
$985$	48.1413	−	17.5220i	1.53391	−	0.558297i
$986$		0			0
$987$	29.2003			0.929455
$988$		0			0
$989$	−13.1848			−0.419252
$990$		0			0
$991$	−9.37851	+	3.41350i	−0.297918	+	0.108433i	−0.486655	−	0.873594i	$-0.661783\pi$
$991$	−9.37851	+	3.41350i	−0.297918	+	0.108433i	0.188737	+	0.982028i	$0.439561\pi$
$992$		0			0
$993$	1.15641	−	6.55834i	0.0366976	−	0.208123i
$994$		0			0
$995$	−10.7802	−	18.6718i	−0.341755	−	0.591937i
$996$		0			0
$997$	19.3840	−	16.2651i	0.613897	−	0.515120i	−0.281982	−	0.959420i	$-0.590992\pi$
$997$	19.3840	−	16.2651i	0.613897	−	0.515120i	0.895878	+	0.444299i	$0.146547\pi$
$998$		0			0
$999$	1.15270	−	1.99654i	0.0364699	−	0.0631678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bo.a.529.1		6
4.3	odd	2		114.2.i.a.73.1	yes	6
12.11	even	2		342.2.u.e.73.1		6
19.6	even	9	inner	912.2.bo.a.481.1		6
76.43	odd	18		2166.2.a.q.1.1		3
76.63	odd	18		114.2.i.a.25.1	✓	6
76.71	even	18		2166.2.a.s.1.1		3
228.71	odd	18		6498.2.a.bm.1.3		3
228.119	even	18		6498.2.a.br.1.3		3
228.215	even	18		342.2.u.e.253.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.a.25.1	✓	6	76.63	odd	18
114.2.i.a.73.1	yes	6	4.3	odd	2
342.2.u.e.73.1		6	12.11	even	2
342.2.u.e.253.1		6	228.215	even	18
912.2.bo.a.481.1		6	19.6	even	9	inner
912.2.bo.a.529.1		6	1.1	even	1	trivial
2166.2.a.q.1.1		3	76.43	odd	18
2166.2.a.s.1.1		3	76.71	even	18
6498.2.a.bm.1.3		3	228.71	odd	18
6498.2.a.br.1.3		3	228.119	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{3} +(-0.386659 + 2.19285i) q^{5} +(-1.32635 - 2.29731i) q^{7} +(0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{3} +(-0.386659 + 2.19285i) q^{5} +(-1.32635 - 2.29731i) q^{7} +(0.766044 - 0.642788i) q^{9} +(1.11334 - 1.92836i) q^{11} +(4.97178 + 1.80958i) q^{13} +(0.386659 + 2.19285i) q^{15} +(-2.61334 - 2.19285i) q^{17} +(4.29813 + 0.725293i) q^{19} +(-2.03209 - 1.70513i) q^{21} +(-0.386659 - 2.19285i) q^{23} +(0.0393628 + 0.0143269i) q^{25} +(0.500000 - 0.866025i) q^{27} +(3.68866 - 3.09516i) q^{29} +(5.15657 + 8.93145i) q^{31} +(0.386659 - 2.19285i) q^{33} +(5.55051 - 2.02022i) q^{35} +2.30541 q^{37} +5.29086 q^{39} +(6.79813 - 2.47432i) q^{41} +(1.02822 - 5.83132i) q^{43} +(1.11334 + 1.92836i) q^{45} +(-8.43242 + 7.07564i) q^{47} +(-0.0184183 + 0.0319015i) q^{49} +(-3.20574 - 1.16679i) q^{51} +(1.70574 + 9.67372i) q^{53} +(3.79813 + 3.18701i) q^{55} +(4.28699 - 0.788496i) q^{57} +(-3.79813 - 3.18701i) q^{59} +(-0.990200 - 5.61570i) q^{61} +(-2.49273 - 0.907278i) q^{63} +(-5.89053 + 10.2027i) q^{65} +(-6.56805 + 5.51125i) q^{67} +(-1.11334 - 1.92836i) q^{69} +(-0.764700 + 4.33683i) q^{71} +(2.62701 - 0.956154i) q^{73} +0.0418891 q^{75} -5.90673 q^{77} +(12.9684 - 4.72010i) q^{79} +(0.173648 - 0.984808i) q^{81} +(-5.25150 - 9.09586i) q^{83} +(5.81908 - 4.88279i) q^{85} +(2.40760 - 4.17009i) q^{87} +(-7.34389 - 2.67296i) q^{89} +(-2.43717 - 13.8219i) q^{91} +(7.90033 + 6.62916i) q^{93} +(-3.25237 + 9.14473i) q^{95} +(-13.6270 - 11.4344i) q^{97} +(-0.386659 - 2.19285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{5} - 9 q^{7}+O(q^{10}) \) 6 * q - 9 * q^5 - 9 * q^7	\( 6 q - 9 q^{5} - 9 q^{7} + 15 q^{13} + 9 q^{15} - 9 q^{17} + 12 q^{19} - 3 q^{21} - 9 q^{23} + 9 q^{25} + 3 q^{27} - 9 q^{29} + 9 q^{31} + 9 q^{33} + 36 q^{35} + 18 q^{37} + 27 q^{41} + 21 q^{43} - 27 q^{47} - 12 q^{49} - 9 q^{51} + 9 q^{55} + 18 q^{57} - 9 q^{59} - 3 q^{61} + 3 q^{63} - 18 q^{65} + 3 q^{67} - 9 q^{71} - 12 q^{73} - 6 q^{75} + 18 q^{77} + 21 q^{79} + 9 q^{83} + 18 q^{85} + 18 q^{87} - 24 q^{91} + 33 q^{93} - 36 q^{95} - 54 q^{97} - 9 q^{99}+O(q^{100}) \) 6 * q - 9 * q^5 - 9 * q^7 + 15 * q^13 + 9 * q^15 - 9 * q^17 + 12 * q^19 - 3 * q^21 - 9 * q^23 + 9 * q^25 + 3 * q^27 - 9 * q^29 + 9 * q^31 + 9 * q^33 + 36 * q^35 + 18 * q^37 + 27 * q^41 + 21 * q^43 - 27 * q^47 - 12 * q^49 - 9 * q^51 + 9 * q^55 + 18 * q^57 - 9 * q^59 - 3 * q^61 + 3 * q^63 - 18 * q^65 + 3 * q^67 - 9 * q^71 - 12 * q^73 - 6 * q^75 + 18 * q^77 + 21 * q^79 + 9 * q^83 + 18 * q^85 + 18 * q^87 - 24 * q^91 + 33 * q^93 - 36 * q^95 - 54 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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