LMFDB - Embedded newform 912.2.ci.f.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("912.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 3 x^{16} + 100 x^{15} - 171 x^{14} - 471 x^{13} + 1537 x^{12} + 321 x^{11} + \cdots + 1367631 $ x^18 - 6x^17 - 3x^16 + 100x^15 - 171x^14 - 471x^13 + 1537x^12 + 321x^11 - 3936x^10 - 1317x^9 + 4941x^8 + 21078x^7 - 14829x^6 - 68589x^5 - 45711x^4 + 421452x^3 - 61938x^2 - 1219779*x + 1367631
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			127.3
Root			$-1.33811 - 1.29514i$ of defining polynomial
Character	$\chi$	$=$	912.127
Dual form			912.2.ci.f.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{3} +(0.590533 + 3.34908i) q^{5} +(1.12990 + 0.652348i) q^{7} +(0.766044 + 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{3} +(0.590533 + 3.34908i) q^{5} +(1.12990 + 0.652348i) q^{7} +(0.766044 + 0.642788i) q^{9} +(0.186673 - 0.107776i) q^{11} +(0.942124 + 2.58846i) q^{13} +(0.590533 - 3.34908i) q^{15} +(0.590917 - 0.495838i) q^{17} +(4.01355 - 1.70041i) q^{19} +(-0.838643 - 0.999456i) q^{21} +(-7.01342 - 1.23665i) q^{23} +(-6.16915 + 2.24539i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(-5.04054 + 6.00708i) q^{29} +(-2.21389 + 3.83458i) q^{31} +(-0.212277 + 0.0374302i) q^{33} +(-1.51752 + 4.16936i) q^{35} +7.08565i q^{37} -2.75459i q^{39} +(0.000924119 - 0.00253900i) q^{41} +(10.0894 - 1.77904i) q^{43} +(-1.70037 + 2.94513i) q^{45} +(0.0760659 - 0.0906519i) q^{47} +(-2.64888 - 4.58800i) q^{49} +(-0.724867 + 0.263830i) q^{51} +(2.58096 + 0.455092i) q^{53} +(0.471187 + 0.561539i) q^{55} +(-4.35308 + 0.225148i) q^{57} +(-4.17909 + 3.50668i) q^{59} +(-0.475045 + 2.69412i) q^{61} +(0.446233 + 1.22601i) q^{63} +(-8.11262 + 4.68382i) q^{65} +(0.399902 + 0.335557i) q^{67} +(6.16750 + 3.56081i) q^{69} +(2.74891 + 15.5898i) q^{71} +(5.35744 + 1.94995i) q^{73} +6.56507 q^{75} +0.281230 q^{77} +(-8.45229 - 3.07638i) q^{79} +(0.173648 + 0.984808i) q^{81} +(-7.27592 - 4.20076i) q^{83} +(2.00956 + 1.68622i) q^{85} +(6.79110 - 3.92084i) q^{87} +(2.20424 + 6.05611i) q^{89} +(-0.624074 + 3.53930i) q^{91} +(3.39188 - 2.84613i) q^{93} +(8.06495 + 12.4376i) q^{95} +(1.39110 + 1.65785i) q^{97} +(0.212277 + 0.0374302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q+O(q^{10}) $ 18 * q	$ 18 q + 3 q^{13} + 12 q^{17} + 3 q^{19} + 15 q^{21} + 6 q^{23} + 24 q^{25} - 9 q^{27} + 12 q^{29} + 12 q^{31} + 6 q^{33} - 36 q^{35} + 12 q^{41} + 21 q^{43} - 6 q^{45} - 24 q^{47} - 3 q^{49} - 6 q^{51} + 6 q^{53} + 12 q^{55} + 54 q^{59} - 24 q^{61} + 12 q^{63} + 36 q^{65} - 21 q^{67} + 15 q^{73} + 18 q^{75} - 60 q^{79} + 54 q^{85} + 18 q^{87} + 36 q^{89} + 24 q^{91} + 24 q^{93} - 6 q^{95} - 6 q^{97} - 6 q^{99}+O(q^{100}) $ 18 * q + 3 * q^13 + 12 * q^17 + 3 * q^19 + 15 * q^21 + 6 * q^23 + 24 * q^25 - 9 * q^27 + 12 * q^29 + 12 * q^31 + 6 * q^33 - 36 * q^35 + 12 * q^41 + 21 * q^43 - 6 * q^45 - 24 * q^47 - 3 * q^49 - 6 * q^51 + 6 * q^53 + 12 * q^55 + 54 * q^59 - 24 * q^61 + 12 * q^63 + 36 * q^65 - 21 * q^67 + 15 * q^73 + 18 * q^75 - 60 * q^79 + 54 * q^85 + 18 * q^87 + 36 * q^89 + 24 * q^91 + 24 * q^93 - 6 * q^95 - 6 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$4$		0			0
$5$	0.590533	+	3.34908i	0.264095	+	1.49775i	0.771601	+	0.636107i	$0.219456\pi$
$5$	0.590533	+	3.34908i	0.264095	+	1.49775i	−0.507507	+	0.861648i	$0.669433\pi$
$6$		0			0
$7$	1.12990	+	0.652348i	0.427062	+	0.246565i	0.698094	−	0.716006i	$-0.254032\pi$
$7$	1.12990	+	0.652348i	0.427062	+	0.246565i	−0.271032	+	0.962570i	$0.587365\pi$
$8$		0			0
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$		0			0
$11$	0.186673	−	0.107776i	0.0562841	−	0.0324957i	−0.471594	−	0.881816i	$-0.656321\pi$
$11$	0.186673	−	0.107776i	0.0562841	−	0.0324957i	0.527878	+	0.849320i	$0.322988\pi$
$12$		0			0
$13$	0.942124	+	2.58846i	0.261298	+	0.717911i	0.999081	+	0.0428722i	$0.0136508\pi$
$13$	0.942124	+	2.58846i	0.261298	+	0.717911i	−0.737782	+	0.675039i	$0.764127\pi$
$14$		0			0
$15$	0.590533	−	3.34908i	0.152475	−	0.864729i
$16$		0			0
$17$	0.590917	−	0.495838i	0.143318	−	0.120258i	−0.568310	−	0.822815i	$-0.692403\pi$
$17$	0.590917	−	0.495838i	0.143318	−	0.120258i	0.711628	+	0.702556i	$0.247958\pi$
$18$		0			0
$19$	4.01355	−	1.70041i	0.920772	−	0.390101i
$19$	4.01355	−	1.70041i	0.920772	−	0.390101i
$20$		0			0
$21$	−0.838643	−	0.999456i	−0.183007	−	0.218099i
$22$		0			0
$23$	−7.01342	−	1.23665i	−1.46240	−	0.257860i	−0.614878	−	0.788622i	$-0.710795\pi$
$23$	−7.01342	−	1.23665i	−1.46240	−	0.257860i	−0.847521	+	0.530762i	$0.821906\pi$
$24$		0			0
$25$	−6.16915	+	2.24539i	−1.23383	+	0.449078i
$26$		0			0
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$		0			0
$29$	−5.04054	+	6.00708i	−0.936005	+	1.11549i	0.0571130	+	0.998368i	$0.481810\pi$
$29$	−5.04054	+	6.00708i	−0.936005	+	1.11549i	−0.993118	+	0.117119i	$0.962634\pi$
$30$		0			0
$31$	−2.21389	+	3.83458i	−0.397627	+	0.688710i	−0.993433	−	0.114418i	$-0.963500\pi$
$31$	−2.21389	+	3.83458i	−0.397627	+	0.688710i	0.595806	+	0.803129i	$0.296833\pi$
$32$		0			0
$33$	−0.212277	+	0.0374302i	−0.0369527	+	0.00651576i
$34$		0			0
$35$	−1.51752	+	4.16936i	−0.256508	+	0.704751i
$36$		0			0
$37$			7.08565i			1.16487i	0.812876	+	0.582437i	$0.197901\pi$
$37$			7.08565i			1.16487i	−0.812876	+	0.582437i	$0.802099\pi$
$38$		0			0
$39$		−	2.75459i		−	0.441087i
$40$		0			0
$41$	0.000924119	−	0.00253900i	0.000144323	−	0.000396525i	−0.939620	−	0.342218i	$-0.888822\pi$
$41$	0.000924119	−	0.00253900i	0.000144323	−	0.000396525i	0.939765	+	0.341822i	$0.111044\pi$
$42$		0			0
$43$	10.0894	−	1.77904i	1.53863	−	0.271301i	0.660904	−	0.750471i	$-0.270173\pi$
$43$	10.0894	−	1.77904i	1.53863	−	0.271301i	0.877722	+	0.479169i	$0.159062\pi$
$44$		0			0
$45$	−1.70037	+	2.94513i	−0.253477	+	0.439034i
$46$		0			0
$47$	0.0760659	−	0.0906519i	0.0110954	−	0.0132229i	−0.760468	−	0.649375i	$-0.775031\pi$
$47$	0.0760659	−	0.0906519i	0.0110954	−	0.0132229i	0.771564	+	0.636152i	$0.219475\pi$
$48$		0			0
$49$	−2.64888	−	4.58800i	−0.378412	−	0.655429i
$50$		0			0
$51$	−0.724867	+	0.263830i	−0.101502	+	0.0369436i
$52$		0			0
$53$	2.58096	+	0.455092i	0.354522	+	0.0625117i	0.348073	−	0.937467i	$-0.386836\pi$
$53$	2.58096	+	0.455092i	0.354522	+	0.0625117i	0.00644875	+	0.999979i	$0.497947\pi$
$54$		0			0
$55$	0.471187	+	0.561539i	0.0635348	+	0.0757179i
$56$		0			0
$57$	−4.35308	+	0.225148i	−0.576580	+	0.0298216i
$58$		0			0
$59$	−4.17909	+	3.50668i	−0.544072	+	0.456530i	−0.872928	−	0.487850i	$-0.837781\pi$
$59$	−4.17909	+	3.50668i	−0.544072	+	0.456530i	0.328856	+	0.944380i	$0.393337\pi$
$60$		0			0
$61$	−0.475045	+	2.69412i	−0.0608233	+	0.344946i	0.939176	+	0.343437i	$0.111591\pi$
$61$	−0.475045	+	2.69412i	−0.0608233	+	0.344946i	−0.999999	+	0.00150871i	$0.999520\pi$
$62$		0			0
$63$	0.446233	+	1.22601i	0.0562200	+	0.154463i
$64$		0			0
$65$	−8.11262	+	4.68382i	−1.00625	+	0.580957i
$66$		0			0
$67$	0.399902	+	0.335557i	0.0488558	+	0.0409949i	0.666889	−	0.745157i	$-0.267626\pi$
$67$	0.399902	+	0.335557i	0.0488558	+	0.0409949i	−0.618033	+	0.786152i	$0.712070\pi$
$68$		0			0
$69$	6.16750	+	3.56081i	0.742479	+	0.428671i
$70$		0			0
$71$	2.74891	+	15.5898i	0.326235	+	1.85017i	0.500848	+	0.865535i	$0.333021\pi$
$71$	2.74891	+	15.5898i	0.326235	+	1.85017i	−0.174613	+	0.984637i	$0.555867\pi$
$72$		0			0
$73$	5.35744	+	1.94995i	0.627040	+	0.228224i	0.635943	−	0.771736i	$-0.280611\pi$
$73$	5.35744	+	1.94995i	0.627040	+	0.228224i	−0.00890224	+	0.999960i	$0.502834\pi$
$74$		0			0
$75$	6.56507			0.758069
$76$		0			0
$77$	0.281230			0.0320491
$78$		0			0
$79$	−8.45229	−	3.07638i	−0.950957	−	0.346120i	−0.180474	−	0.983580i	$-0.557763\pi$
$79$	−8.45229	−	3.07638i	−0.950957	−	0.346120i	−0.770484	+	0.637460i	$0.779985\pi$
$80$		0			0
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$		0			0
$83$	−7.27592	−	4.20076i	−0.798636	−	0.461093i	0.0443579	−	0.999016i	$-0.485876\pi$
$83$	−7.27592	−	4.20076i	−0.798636	−	0.461093i	−0.842994	+	0.537923i	$0.819209\pi$
$84$		0			0
$85$	2.00956	+	1.68622i	0.217967	+	0.182896i
$86$		0			0
$87$	6.79110	−	3.92084i	0.728083	−	0.420359i
$88$		0			0
$89$	2.20424	+	6.05611i	0.233649	+	0.641946i	1.00000		0.000476371i	$-0.000151634\pi$
$89$	2.20424	+	6.05611i	0.233649	+	0.641946i	−0.766351	+	0.642423i	$0.777929\pi$
$90$		0			0
$91$	−0.624074	+	3.53930i	−0.0654208	+	0.371020i
$92$		0			0
$93$	3.39188	−	2.84613i	0.351722	−	0.295130i
$94$		0			0
$95$	8.06495	+	12.4376i	0.827447	+	1.27607i
$96$		0			0
$97$	1.39110	+	1.65785i	0.141245	+	0.168330i	0.832029	−	0.554731i	$-0.187179\pi$
$97$	1.39110	+	1.65785i	0.141245	+	0.168330i	−0.690784	+	0.723061i	$0.742735\pi$
$98$		0			0
$99$	0.212277	+	0.0374302i	0.0213346	+	0.00376187i
$100$		0			0
$101$	13.5308	−	4.92482i	1.34637	−	0.490038i	0.434555	−	0.900645i	$-0.356905\pi$
$101$	13.5308	−	4.92482i	1.34637	−	0.490038i	0.911812	+	0.410607i	$0.134683\pi$
$102$		0			0
$103$	−9.48394	−	16.4267i	−0.934481	−	1.61857i	−0.775557	−	0.631277i	$-0.782531\pi$
$103$	−9.48394	−	16.4267i	−0.934481	−	1.61857i	−0.158923	−	0.987291i	$-0.550802\pi$
$104$		0			0
$105$	2.85201	−	3.39890i	0.278328	−	0.331698i
$106$		0			0
$107$	−8.01827	+	13.8880i	−0.775155	+	1.34261i	0.159552	+	0.987190i	$0.448995\pi$
$107$	−8.01827	+	13.8880i	−0.775155	+	1.34261i	−0.934707	+	0.355419i	$0.884338\pi$
$108$		0			0
$109$	9.74537	−	1.71837i	0.933437	−	0.164590i	0.313810	−	0.949486i	$-0.398395\pi$
$109$	9.74537	−	1.71837i	0.933437	−	0.164590i	0.619628	+	0.784896i	$0.287284\pi$
$110$		0			0
$111$	2.42344	−	6.65834i	0.230022	−	0.631981i
$112$		0			0
$113$		−	9.15578i		−	0.861303i	−0.902518	−	0.430651i	$-0.858284\pi$
$113$		−	9.15578i		−	0.861303i	0.902518	−	0.430651i	$-0.141716\pi$
$114$		0			0
$115$		−	24.2188i		−	2.25841i
$116$		0			0
$117$	−0.942124	+	2.58846i	−0.0870994	+	0.239304i
$118$		0			0
$119$	0.991137	−	0.174764i	0.0908574	−	0.0160206i
$120$		0			0
$121$	−5.47677	+	9.48604i	−0.497888	+	0.862367i
$122$		0			0
$123$	−0.00173678	+	0.00206981i	−0.000156600	+	0.000186628i
$124$		0			0
$125$	−2.66121	−	4.60935i	−0.238026	−	0.412273i
$126$		0			0
$127$	7.94075	−	2.89020i	0.704628	−	0.256464i	0.0352424	−	0.999379i	$-0.488780\pi$
$127$	7.94075	−	2.89020i	0.704628	−	0.256464i	0.669386	+	0.742915i	$0.266557\pi$
$128$		0			0
$129$	−10.0894	−	1.77904i	−0.888326	−	0.156636i
$130$		0			0
$131$	3.85490	+	4.59409i	0.336804	+	0.401387i	0.907690	−	0.419642i	$-0.137844\pi$
$131$	3.85490	+	4.59409i	0.336804	+	0.401387i	−0.570886	+	0.821030i	$0.693400\pi$
$132$		0			0
$133$	5.64418	+	0.696939i	0.489412	+	0.0604322i
$134$		0			0
$135$	2.60512	−	2.18596i	0.224213	−	0.188137i
$136$		0			0
$137$	1.67623	−	9.50637i	0.143210	−	0.812184i	−0.825577	−	0.564289i	$-0.809150\pi$
$137$	1.67623	−	9.50637i	0.143210	−	0.812184i	0.968787	−	0.247894i	$-0.0797386\pi$
$138$		0			0
$139$	1.86551	+	5.12544i	0.158230	+	0.434734i	0.993322	−	0.115377i	$-0.0368076\pi$
$139$	1.86551	+	5.12544i	0.158230	+	0.434734i	−0.835092	+	0.550111i	$0.814585\pi$
$140$		0			0
$141$	−0.102483	+	0.0591688i	−0.00863066	+	0.00498291i
$142$		0			0
$143$	0.454843	+	0.381659i	0.0380359	+	0.0319159i
$144$		0			0
$145$	−23.0948	−	13.3338i	−1.91792	−	1.10731i
$146$		0			0
$147$	0.919947	+	5.21728i	0.0758760	+	0.430314i
$148$		0			0
$149$	9.68294	+	3.52430i	0.793257	+	0.288722i	0.706689	−	0.707524i	$-0.250188\pi$
$149$	9.68294	+	3.52430i	0.793257	+	0.288722i	0.0865680	+	0.996246i	$0.472410\pi$
$150$		0			0
$151$	−7.96039			−0.647807			−0.323904	−	0.946090i	$-0.604995\pi$
$151$	−7.96039			−0.647807			−0.323904	+	0.946090i	$0.604995\pi$
$152$		0			0
$153$	0.771387			0.0623630
$154$		0			0
$155$	−14.1497	−	5.15007i	−1.13653	−	0.413663i
$156$		0			0
$157$	−3.61141	−	20.4813i	−0.288222	−	1.63459i	−0.693544	−	0.720415i	$-0.743952\pi$
$157$	−3.61141	−	20.4813i	−0.288222	−	1.63459i	0.405322	−	0.914174i	$-0.367160\pi$
$158$		0			0
$159$	−2.26965	−	1.31039i	−0.179995	−	0.103920i
$160$		0			0
$161$	−7.11774	−	5.97249i	−0.560956	−	0.470698i
$162$		0			0
$163$	7.91760	−	4.57123i	0.620154	−	0.358046i	−0.156775	−	0.987634i	$-0.550110\pi$
$163$	7.91760	−	4.57123i	0.620154	−	0.358046i	0.776929	+	0.629588i	$0.216776\pi$
$164$		0			0
$165$	−0.250713	−	0.688829i	−0.0195180	−	0.0536253i
$166$		0			0
$167$	−1.51671	+	8.60169i	−0.117367	+	0.665619i	0.868185	+	0.496241i	$0.165287\pi$
$167$	−1.51671	+	8.60169i	−0.117367	+	0.665619i	−0.985551	+	0.169378i	$0.945824\pi$
$168$		0			0
$169$	4.14603	−	3.47893i	0.318925	−	0.267610i
$170$		0			0
$171$	4.16756	+	1.27727i	0.318701	+	0.0976754i
$172$		0			0
$173$	−4.25114	−	5.06632i	−0.323209	−	0.385185i	0.579835	−	0.814734i	$-0.303117\pi$
$173$	−4.25114	−	5.06632i	−0.323209	−	0.385185i	−0.903044	+	0.429549i	$0.858673\pi$
$174$		0			0
$175$	−8.43530	−	1.48737i	−0.637649	−	0.112435i
$176$		0			0
$177$	5.12642	−	1.86586i	0.385325	−	0.140247i
$178$		0			0
$179$	0.936849	+	1.62267i	0.0700234	+	0.121284i	0.898911	−	0.438131i	$-0.144359\pi$
$179$	0.936849	+	1.62267i	0.0700234	+	0.121284i	−0.828888	+	0.559415i	$0.811026\pi$
$180$		0			0
$181$	6.92080	−	8.24789i	0.514419	−	0.613061i	−0.444832	−	0.895614i	$-0.646737\pi$
$181$	6.92080	−	8.24789i	0.514419	−	0.613061i	0.959252	+	0.282553i	$0.0911812\pi$
$182$		0			0
$183$	1.36784	−	2.36917i	0.101114	−	0.175134i
$184$		0			0
$185$	−23.7304	+	4.18432i	−1.74470	+	0.307637i
$186$		0			0
$187$	0.0568690	−	0.156246i	0.00415868	−	0.0114259i
$188$		0			0
$189$		−	1.30470i		−	0.0949027i
$190$		0			0
$191$		−	26.3388i		−	1.90581i	−0.303269	−	0.952905i	$-0.598078\pi$
$191$		−	26.3388i		−	1.90581i	0.303269	−	0.952905i	$-0.401922\pi$
$192$		0			0
$193$	5.76966	−	15.8520i	0.415309	−	1.14105i	−0.539020	−	0.842293i	$-0.681205\pi$
$193$	5.76966	−	15.8520i	0.415309	−	1.14105i	0.954329	−	0.298759i	$-0.0965726\pi$
$194$		0			0
$195$	9.22533	−	1.62668i	0.660640	−	0.116489i
$196$		0			0
$197$	4.62213	−	8.00577i	0.329313	−	0.570388i	−0.653062	−	0.757304i	$-0.726516\pi$
$197$	4.62213	−	8.00577i	0.329313	−	0.570388i	0.982376	+	0.186917i	$0.0598494\pi$
$198$		0			0
$199$	3.74033	−	4.45755i	0.265145	−	0.315987i	−0.617002	−	0.786961i	$-0.711653\pi$
$199$	3.74033	−	4.45755i	0.265145	−	0.315987i	0.882147	+	0.470974i	$0.156098\pi$
$200$		0			0
$201$	−0.261017	−	0.452095i	−0.0184107	−	0.0318883i
$202$		0			0
$203$	−9.61402	+	3.49922i	−0.674772	+	0.245597i
$204$		0			0
$205$	0.00904903	+	0.00159559i	0.000632011	+	0.000111441i
$206$		0			0
$207$	−4.57768	−	5.45547i	−0.318171	−	0.379181i
$208$		0			0
$209$	0.565960	−	0.749986i	0.0391483	−	0.0518776i
$210$		0			0
$211$	7.21596	−	6.05491i	0.496767	−	0.416837i	−0.359677	−	0.933077i	$-0.617113\pi$
$211$	7.21596	−	6.05491i	0.496767	−	0.416837i	0.856444	+	0.516240i	$0.172669\pi$
$212$		0			0
$213$	2.74891	−	15.5898i	0.188352	−	1.06820i
$214$		0			0
$215$	11.9163	+	32.7398i	0.812686	+	2.23284i
$216$		0			0
$217$	−5.00296	+	2.88846i	−0.339623	+	0.196081i
$218$		0			0
$219$	−4.36742	−	3.66470i	−0.295123	−	0.247638i
$220$		0			0
$221$	1.84018	+	1.06243i	0.123784	+	0.0714665i
$222$		0			0
$223$	4.29828	+	24.3768i	0.287834	+	1.63239i	0.694982	+	0.719027i	$0.255412\pi$
$223$	4.29828	+	24.3768i	0.287834	+	1.63239i	−0.407148	+	0.913362i	$0.633477\pi$
$224$		0			0
$225$	−6.16915	−	2.24539i	−0.411277	−	0.149693i
$226$		0			0
$227$	−3.56994			−0.236945			−0.118473	−	0.992957i	$-0.537800\pi$
$227$	−3.56994			−0.236945			−0.118473	+	0.992957i	$0.537800\pi$
$228$		0			0
$229$	19.5420			1.29137			0.645685	−	0.763604i	$-0.276572\pi$
$229$	19.5420			1.29137			0.645685	+	0.763604i	$0.276572\pi$
$230$		0			0
$231$	−0.264270	−	0.0961862i	−0.0173877	−	0.00632859i
$232$		0			0
$233$	2.10353	+	11.9297i	0.137807	+	0.781540i	0.972864	+	0.231377i	$0.0743232\pi$
$233$	2.10353	+	11.9297i	0.137807	+	0.781540i	−0.835058	+	0.550163i	$0.814566\pi$
$234$		0			0
$235$	0.348520	+	0.201218i	0.0227349	+	0.0131260i
$236$		0			0
$237$	6.89037	+	5.78171i	0.447578	+	0.375562i
$238$		0			0
$239$	−0.891786	+	0.514873i	−0.0576848	+	0.0333044i	−0.528565	−	0.848893i	$-0.677270\pi$
$239$	−0.891786	+	0.514873i	−0.0576848	+	0.0333044i	0.470880	+	0.882197i	$0.343936\pi$
$240$		0			0
$241$	−4.42082	−	12.1461i	−0.284770	−	0.782400i	−0.996777	−	0.0802267i	$-0.974436\pi$
$241$	−4.42082	−	12.1461i	−0.284770	−	0.782400i	0.712006	−	0.702173i	$-0.247787\pi$
$242$		0			0
$243$	0.173648	−	0.984808i	0.0111395	−	0.0631754i
$244$		0			0
$245$	13.8013	−	11.5807i	0.881735	−	0.739863i
$246$		0			0
$247$	8.18272	+	8.78694i	0.520654	+	0.559100i
$248$		0			0
$249$	5.40039	+	6.43593i	0.342236	+	0.407861i
$250$		0			0
$251$	−23.7545	−	4.18856i	−1.49937	−	0.264379i	−0.637081	−	0.770797i	$-0.719858\pi$
$251$	−23.7545	−	4.18856i	−1.49937	−	0.264379i	−0.862288	+	0.506418i	$0.830969\pi$
$252$		0			0
$253$	−1.44250	+	0.525027i	−0.0906892	+	0.0330082i
$254$		0			0
$255$	−1.31165	−	2.27184i	−0.0821385	−	0.142268i
$256$		0			0
$257$	17.3142	−	20.6343i	1.08003	−	1.28713i	0.124506	−	0.992219i	$-0.460265\pi$
$257$	17.3142	−	20.6343i	1.08003	−	1.28713i	0.955524	−	0.294912i	$-0.0952903\pi$
$258$		0			0
$259$	−4.62232	+	8.00609i	−0.287217	+	0.497474i
$260$		0			0
$261$	−7.72256	+	1.36169i	−0.478014	+	0.0842868i
$262$		0			0
$263$	2.22496	−	6.11303i	0.137197	−	0.376946i	−0.851999	−	0.523543i	$-0.824610\pi$
$263$	2.22496	−	6.11303i	0.137197	−	0.376946i	0.989196	+	0.146597i	$0.0468321\pi$
$264$		0			0
$265$			8.91258i			0.547495i
$266$		0			0
$267$		−	6.44478i		−	0.394414i
$268$		0			0
$269$	−0.779349	+	2.14124i	−0.0475178	+	0.130554i	−0.961181	−	0.275917i	$-0.911019\pi$
$269$	−0.779349	+	2.14124i	−0.0475178	+	0.130554i	0.913664	+	0.406471i	$0.133241\pi$
$270$		0			0
$271$	24.1929	−	4.26585i	1.46961	−	0.259132i	0.619193	−	0.785239i	$-0.287460\pi$
$271$	24.1929	−	4.26585i	1.46961	−	0.259132i	0.850419	+	0.526107i	$0.176349\pi$
$272$		0			0
$273$	1.79695	−	3.11241i	0.108756	−	0.188372i
$274$		0			0
$275$	−0.909617	+	1.08404i	−0.0548520	+	0.0653701i
$276$		0			0
$277$	6.50279	+	11.2632i	0.390715	+	0.676738i	0.992544	−	0.121887i	$-0.0388946\pi$
$277$	6.50279	+	11.2632i	0.390715	+	0.676738i	−0.601829	+	0.798625i	$0.705561\pi$
$278$		0			0
$279$	−4.16076	+	1.51439i	−0.249098	+	0.0906643i
$280$		0			0
$281$	6.23948	+	1.10019i	0.372216	+	0.0656317i	0.356627	−	0.934247i	$-0.383927\pi$
$281$	6.23948	+	1.10019i	0.372216	+	0.0656317i	0.0155887	+	0.999878i	$0.495038\pi$
$282$		0			0
$283$	12.8267	+	15.2863i	0.762468	+	0.908673i	0.998001	−	0.0631928i	$-0.0201283\pi$
$283$	12.8267	+	15.2863i	0.762468	+	0.908673i	−0.235534	+	0.971866i	$0.575684\pi$
$284$		0			0
$285$	−3.32468	−	14.4459i	−0.196937	−	0.855699i
$286$		0			0
$287$	0.00270047	−	0.00226597i	0.000159404	−	0.000133756i
$288$		0			0
$289$	−2.84869	+	16.1557i	−0.167570	+	0.950337i
$290$		0			0
$291$	−0.740191	−	2.03366i	−0.0433908	−	0.119215i
$292$		0			0
$293$	2.46724	−	1.42446i	0.144138	−	0.0832180i	−0.426197	−	0.904630i	$-0.640147\pi$
$293$	2.46724	−	1.42446i	0.144138	−	0.0832180i	0.570335	+	0.821412i	$0.306814\pi$
$294$		0			0
$295$	−14.2120	−	11.9253i	−0.827457	−	0.694319i
$296$		0			0
$297$	−0.186673	−	0.107776i	−0.0108319	−	0.00625379i
$298$		0			0
$299$	−3.40647	−	19.3191i	−0.197001	−	1.11725i
$300$		0			0
$301$	12.5606	+	4.57169i	0.723983	+	0.263508i
$302$		0			0
$303$	−14.3992			−0.827213
$304$		0			0
$305$	−9.30334			−0.532708
$306$		0			0
$307$	7.06899	+	2.57290i	0.403449	+	0.146843i	0.535771	−	0.844363i	$-0.320021\pi$
$307$	7.06899	+	2.57290i	0.403449	+	0.146843i	−0.132322	+	0.991207i	$0.542243\pi$
$308$		0			0
$309$	3.29374	+	18.6797i	0.187374	+	1.06265i
$310$		0			0
$311$	3.63676	+	2.09968i	0.206222	+	0.119062i	0.599554	−	0.800334i	$-0.295345\pi$
$311$	3.63676	+	2.09968i	0.206222	+	0.119062i	−0.393333	+	0.919396i	$0.628678\pi$
$312$		0			0
$313$	−17.3461	−	14.5551i	−0.980461	−	0.822705i	0.00369775	−	0.999993i	$-0.498823\pi$
$313$	−17.3461	−	14.5551i	−0.980461	−	0.822705i	−0.984159	+	0.177289i	$0.943267\pi$
$314$		0			0
$315$	−3.84251	+	2.21847i	−0.216501	+	0.124997i
$316$		0			0
$317$	9.48585	+	26.0622i	0.532778	+	1.46380i	0.855751	+	0.517388i	$0.173096\pi$
$317$	9.48585	+	26.0622i	0.532778	+	1.46380i	−0.322973	+	0.946408i	$0.604682\pi$
$318$		0			0
$319$	−0.293516	+	1.66461i	−0.0164337	+	0.0932003i
$320$		0			0
$321$	12.2847	−	10.3081i	0.685665	−	0.575341i
$322$		0			0
$323$	1.52855	−	2.99487i	0.0850506	−	0.166639i
$324$		0			0
$325$	−11.6242	−	13.8532i	−0.644795	−	0.768437i
$326$		0			0
$327$	−9.74537	−	1.71837i	−0.538920	−	0.0950262i
$328$		0			0
$329$	0.145084	−	0.0528061i	0.00799872	−	0.00291129i
$330$		0			0
$331$	14.0036	+	24.2550i	0.769709	+	1.33317i	0.937721	+	0.347390i	$0.112932\pi$
$331$	14.0036	+	24.2550i	0.769709	+	1.33317i	−0.168012	+	0.985785i	$0.553735\pi$
$332$		0			0
$333$	−4.55457	+	5.42793i	−0.249589	+	0.297449i
$334$		0			0
$335$	−0.887654	+	1.53746i	−0.0484977	+	0.0840005i
$336$		0			0
$337$	32.1526	−	5.66938i	1.75147	−	0.308831i	0.796300	−	0.604902i	$-0.206788\pi$
$337$	32.1526	−	5.66938i	1.75147	−	0.308831i	0.955166	+	0.296071i	$0.0956766\pi$
$338$		0			0
$339$	−3.13146	+	8.60361i	−0.170078	+	0.467284i
$340$		0			0
$341$			0.954418i			0.0516846i
$342$		0			0
$343$		−	16.0449i		−	0.866341i
$344$		0			0
$345$	−8.28331	+	22.7582i	−0.445959	+	1.22526i
$346$		0			0
$347$	22.6446	−	3.99285i	1.21562	−	0.214347i	0.471183	−	0.882036i	$-0.343827\pi$
$347$	22.6446	−	3.99285i	1.21562	−	0.214347i	0.744441	+	0.667688i	$0.232716\pi$
$348$		0			0
$349$	−17.6390	+	30.5517i	−0.944196	+	1.63540i	−0.186843	+	0.982390i	$0.559825\pi$
$349$	−17.6390	+	30.5517i	−0.944196	+	1.63540i	−0.757353	+	0.653005i	$0.773508\pi$
$350$		0			0
$351$	1.77061	−	2.11014i	0.0945084	−	0.112631i
$352$		0			0
$353$	−11.8255	−	20.4823i	−0.629405	−	1.09016i	−0.987671	−	0.156542i	$-0.949965\pi$
$353$	−11.8255	−	20.4823i	−0.629405	−	1.09016i	0.358266	−	0.933620i	$-0.383368\pi$
$354$		0			0
$355$	−50.5883	+	18.4126i	−2.68495	+	0.977241i
$356$		0			0
$357$	−0.991137	−	0.174764i	−0.0524565	−	0.00924950i
$358$		0			0
$359$	19.0511	+	22.7042i	1.00548	+	1.19828i	0.980079	+	0.198606i	$0.0636413\pi$
$359$	19.0511	+	22.7042i	1.00548	+	1.19828i	0.0253993	+	0.999677i	$0.491914\pi$
$360$		0			0
$361$	13.2172	−	13.6494i	0.695642	−	0.718388i
$362$		0			0
$363$	8.39090	−	7.04080i	0.440408	−	0.369546i
$364$		0			0
$365$	−3.36679	+	19.0940i	−0.176226	+	0.999425i
$366$		0			0
$367$	2.94070	+	8.07949i	0.153503	+	0.421746i	0.992478	−	0.122424i	$-0.0390668\pi$
$367$	2.94070	+	8.07949i	0.153503	+	0.421746i	−0.838975	+	0.544170i	$0.816845\pi$
$368$		0			0
$369$	0.00233995	−	0.00135097i	0.000121813	−	7.03288e-5i
$370$		0			0
$371$	2.61935	+	2.19789i	0.135990	+	0.114109i
$372$		0			0
$373$	−11.1200	−	6.42015i	−0.575773	−	0.332423i	0.183679	−	0.982986i	$-0.441199\pi$
$373$	−11.1200	−	6.42015i	−0.575773	−	0.332423i	−0.759452	+	0.650564i	$0.774533\pi$
$374$		0			0
$375$	0.924229	+	5.24156i	0.0477270	+	0.270673i
$376$		0			0
$377$	−20.2979	−	7.38784i	−1.04540	−	0.380493i
$378$		0			0
$379$	17.3921			0.893370			0.446685	−	0.894691i	$-0.352604\pi$
$379$	17.3921			0.893370			0.446685	+	0.894691i	$0.352604\pi$
$380$		0			0
$381$	−8.45037			−0.432926
$382$		0			0
$383$	−9.35760	−	3.40589i	−0.478151	−	0.174033i	0.0916902	−	0.995788i	$-0.470773\pi$
$383$	−9.35760	−	3.40589i	−0.478151	−	0.174033i	−0.569841	+	0.821755i	$0.692995\pi$
$384$		0			0
$385$	0.166076	+	0.941861i	0.00846399	+	0.0480017i
$386$		0			0
$387$	8.87251	+	5.12255i	0.451015	+	0.260394i
$388$		0			0
$389$	−10.2651	−	8.61348i	−0.520464	−	0.436721i	0.344330	−	0.938849i	$-0.388106\pi$
$389$	−10.2651	−	8.61348i	−0.520464	−	0.436721i	−0.864793	+	0.502128i	$0.832551\pi$
$390$		0			0
$391$	−4.75753	+	2.74676i	−0.240599	+	0.138910i
$392$		0			0
$393$	−2.05115	−	5.63548i	−0.103467	−	0.284273i
$394$		0			0
$395$	5.31170	−	30.1241i	0.267260	−	1.51571i
$396$		0			0
$397$	−26.7932	+	22.4821i	−1.34471	+	1.12835i	−0.364322	+	0.931273i	$0.618699\pi$
$397$	−26.7932	+	22.4821i	−1.34471	+	1.12835i	−0.980389	+	0.197073i	$0.936856\pi$
$398$		0			0
$399$	−5.06542	−	2.58533i	−0.253588	−	0.129428i
$400$		0			0
$401$	4.40525	+	5.24997i	0.219988	+	0.262171i	0.864739	−	0.502221i	$-0.167484\pi$
$401$	4.40525	+	5.24997i	0.219988	+	0.262171i	−0.644752	+	0.764392i	$0.723039\pi$
$402$		0			0
$403$	−12.0114	−	2.11794i	−0.598332	−	0.105502i
$404$		0			0
$405$	−3.19566	+	1.16312i	−0.158793	+	0.0577961i
$406$		0			0
$407$	0.763663	+	1.32270i	0.0378534	+	0.0655639i
$408$		0			0
$409$	−20.2519	+	24.1353i	−1.00139	+	1.19341i	−0.0203173	+	0.999794i	$0.506468\pi$
$409$	−20.2519	+	24.1353i	−1.00139	+	1.19341i	−0.981076	+	0.193621i	$0.937977\pi$
$410$		0			0
$411$	−4.82651	+	8.35976i	−0.238074	+	0.412356i
$412$		0			0
$413$	−7.00954	+	1.23597i	−0.344917	+	0.0608181i
$414$		0			0
$415$	9.77200	−	26.8483i	0.479688	−	1.31793i
$416$		0			0
$417$		−	5.45438i		−	0.267102i
$418$		0			0
$419$		−	28.1163i		−	1.37357i	−0.726860	−	0.686785i	$-0.759021\pi$
$419$		−	28.1163i		−	1.37357i	0.726860	−	0.686785i	$-0.240979\pi$
$420$		0			0
$421$	4.86278	−	13.3604i	0.236997	−	0.651145i	−0.762992	−	0.646408i	$-0.776270\pi$
$421$	4.86278	−	13.3604i	0.236997	−	0.651145i	0.999989	−	0.00473611i	$-0.00150756\pi$
$422$		0			0
$423$	0.116540	−	0.0205491i	0.00566636	−	0.000999132i
$424$		0			0
$425$	−2.53211	+	4.38574i	−0.122825	+	0.212740i
$426$		0			0
$427$	−2.29426	+	2.73419i	−0.111027	+	0.132317i
$428$		0			0
$429$	−0.296878	−	0.514208i	−0.0143334	−	0.0248262i
$430$		0			0
$431$	2.47187	−	0.899687i	0.119066	−	0.0433364i	−0.281800	−	0.959473i	$-0.590932\pi$
$431$	2.47187	−	0.899687i	0.119066	−	0.0433364i	0.400866	+	0.916137i	$0.368709\pi$
$432$		0			0
$433$	14.7012	+	2.59222i	0.706494	+	0.124574i	0.515340	−	0.856986i	$-0.327666\pi$
$433$	14.7012	+	2.59222i	0.706494	+	0.124574i	0.191155	+	0.981560i	$0.438777\pi$
$434$		0			0
$435$	17.1416	+	20.4286i	0.821877	+	0.979475i
$436$		0			0
$437$	−30.2515	+	6.96232i	−1.44713	+	0.333053i
$438$		0			0
$439$	14.9554	−	12.5491i	0.713784	−	0.598936i	−0.211874	−	0.977297i	$-0.567957\pi$
$439$	14.9554	−	12.5491i	0.713784	−	0.598936i	0.925658	+	0.378361i	$0.123512\pi$
$440$		0			0
$441$	0.919947	−	5.21728i	0.0438070	−	0.248442i
$442$		0			0
$443$	−8.16273	−	22.4269i	−0.387823	−	1.06554i	−0.967979	−	0.251030i	$-0.919231\pi$
$443$	−8.16273	−	22.4269i	−0.387823	−	1.06554i	0.580156	−	0.814505i	$-0.302991\pi$
$444$		0			0
$445$	−18.9807	+	10.9585i	−0.899772	+	0.519484i
$446$		0			0
$447$	−7.89361	−	6.62352i	−0.373355	−	0.313282i
$448$		0			0
$449$	25.5351	+	14.7427i	1.20508	+	0.695752i	0.961680	−	0.274175i	$-0.0884047\pi$
$449$	25.5351	+	14.7427i	1.20508	+	0.695752i	0.243397	+	0.969927i	$0.421738\pi$
$450$		0			0
$451$	−0.000101134	0	0.000573561i	−4.76222e−6	0	2.70079e-5i
$452$		0			0
$453$	7.48032	+	2.72261i	0.351456	+	0.127919i
$454$		0			0
$455$	−12.2219			−0.572973
$456$		0			0
$457$	7.83881			0.366684			0.183342	−	0.983049i	$-0.441308\pi$
$457$	7.83881			0.366684			0.183342	+	0.983049i	$0.441308\pi$
$458$		0			0
$459$	−0.724867	−	0.263830i	−0.0338339	−	0.0123145i
$460$		0			0
$461$	3.71734	+	21.0821i	0.173134	+	0.981891i	0.940276	+	0.340414i	$0.110567\pi$
$461$	3.71734	+	21.0821i	0.173134	+	0.981891i	−0.767142	+	0.641477i	$0.778322\pi$
$462$		0			0
$463$	−22.3120	−	12.8819i	−1.03693	−	0.598671i	−0.117967	−	0.993018i	$-0.537638\pi$
$463$	−22.3120	−	12.8819i	−1.03693	−	0.598671i	−0.918962	+	0.394347i	$0.870971\pi$
$464$		0			0
$465$	11.5349	+	9.67896i	0.534920	+	0.448851i
$466$		0			0
$467$	−27.8628	+	16.0866i	−1.28934	+	0.744399i	−0.978536	−	0.206077i	$-0.933930\pi$
$467$	−27.8628	+	16.0866i	−1.28934	+	0.744399i	−0.310800	+	0.950475i	$0.600597\pi$
$468$		0			0
$469$	0.232949	+	0.640022i	0.0107566	+	0.0295535i
$470$		0			0
$471$	−3.61141	+	20.4813i	−0.166405	+	0.943730i
$472$		0			0
$473$	1.69169	−	1.41950i	0.0777841	−	0.0652686i
$474$		0			0
$475$	−20.9421	+	19.5021i	−0.960891	+	0.894817i
$476$		0			0
$477$	1.68460	+	2.00763i	0.0771325	+	0.0919230i
$478$		0			0
$479$	31.3003	+	5.51908i	1.43015	+	0.252173i	0.834471	−	0.551052i	$-0.185774\pi$
$479$	31.3003	+	5.51908i	1.43015	+	0.252173i	0.595675	+	0.803226i	$0.296885\pi$
$480$		0			0
$481$	−18.3410	+	6.67557i	−0.836276	+	0.304380i
$482$		0			0
$483$	4.64577	+	8.04671i	0.211390	+	0.366138i
$484$		0			0
$485$	−4.73079	+	5.63794i	−0.214814	+	0.256006i
$486$		0			0
$487$	1.50709	−	2.61036i	0.0682928	−	0.118287i	−0.829857	−	0.557976i	$-0.811578\pi$
$487$	1.50709	−	2.61036i	0.0682928	−	0.118287i	0.898150	+	0.439689i	$0.144911\pi$
$488$		0			0
$489$	−9.00356	+	1.58757i	−0.407155	+	0.0717924i
$490$		0			0
$491$	−0.163137	+	0.448217i	−0.00736229	+	0.0202277i	−0.943319	−	0.331886i	$-0.892315\pi$
$491$	−0.163137	+	0.448217i	−0.00736229	+	0.0202277i	0.935957	+	0.352114i	$0.114537\pi$
$492$		0			0
$493$			6.04898i			0.272432i
$494$		0			0
$495$			0.733037i			0.0329476i
$496$		0			0
$497$	−7.06401	+	19.4082i	−0.316864	+	0.870577i
$498$		0			0
$499$	−15.1072	+	2.66382i	−0.676293	+	0.119249i	−0.501238	−	0.865310i	$-0.667122\pi$
$499$	−15.1072	+	2.66382i	−0.676293	+	0.119249i	−0.175056	+	0.984559i	$0.556011\pi$
$500$		0			0
$501$	4.36719	−	7.56420i	0.195112	−	0.337944i
$502$		0			0
$503$	22.8023	−	27.1748i	1.01671	−	1.21166i	0.0395328	−	0.999218i	$-0.487413\pi$
$503$	22.8023	−	27.1748i	1.01671	−	1.21166i	0.977173	−	0.212445i	$-0.0681425\pi$
$504$		0			0
$505$	24.4840	+	42.4076i	1.08952	+	1.88711i
$506$		0			0
$507$	−5.08586	+	1.85110i	−0.225871	+	0.0822102i
$508$		0			0
$509$	12.5341	+	2.21010i	0.555563	+	0.0979608i	0.444379	−	0.895839i	$-0.353424\pi$
$509$	12.5341	+	2.21010i	0.555563	+	0.0979608i	0.111185	+	0.993800i	$0.464536\pi$
$510$		0			0
$511$	4.78132	+	5.69816i	0.211513	+	0.252072i
$512$		0			0
$513$	−3.47938	−	2.62563i	−0.153618	−	0.115925i
$514$		0			0
$515$	49.4137	−	41.4630i	2.17743	−	1.82708i
$516$		0			0
$517$	0.00442940	−	0.0251204i	0.000194805	−	0.00110479i
$518$		0			0
$519$	2.26199	+	6.21476i	0.0992902	+	0.272798i
$520$		0			0
$521$	17.0232	−	9.82836i	0.745801	−	0.430588i	−0.0783739	−	0.996924i	$-0.524973\pi$
$521$	17.0232	−	9.82836i	0.745801	−	0.430588i	0.824175	+	0.566336i	$0.191639\pi$
$522$		0			0
$523$	−8.25200	−	6.92425i	−0.360835	−	0.302776i	0.444289	−	0.895884i	$-0.353456\pi$
$523$	−8.25200	−	6.92425i	−0.360835	−	0.302776i	−0.805123	+	0.593107i	$0.797901\pi$
$524$		0			0
$525$	7.41788	+	4.28272i	0.323743	+	0.186913i
$526$		0			0
$527$	0.593102	+	3.36365i	0.0258359	+	0.146523i
$528$		0			0
$529$	26.0458	+	9.47989i	1.13243	+	0.412169i
$530$		0			0
$531$	−5.45542			−0.236745
$532$		0			0
$533$	0.00744274			0.000322381
$534$		0			0
$535$	−51.2473	−	18.6525i	−2.21561	−	0.806417i
$536$		0			0
$537$	−0.325364	−	1.84523i	−0.0140405	−	0.0796276i
$538$		0			0
$539$	−0.988952	−	0.570971i	−0.0425972	−	0.0245935i
$540$		0			0
$541$	6.28525	+	5.27395i	0.270224	+	0.226745i	0.767822	−	0.640663i	$-0.221340\pi$
$541$	6.28525	+	5.27395i	0.270224	+	0.226745i	−0.497599	+	0.867407i	$0.665785\pi$
$542$		0			0
$543$	−9.32437	+	5.38343i	−0.400147	+	0.231025i
$544$		0			0
$545$	11.5099	+	31.6233i	0.493031	+	1.35459i
$546$		0			0
$547$	5.51446	−	31.2740i	0.235781	−	1.33718i	−0.605181	−	0.796088i	$-0.706899\pi$
$547$	5.51446	−	31.2740i	0.235781	−	1.33718i	0.840963	−	0.541093i	$-0.181989\pi$
$548$		0			0
$549$	−2.09565	+	1.75846i	−0.0894402	+	0.0750492i
$550$		0			0
$551$	−10.0160	+	32.6807i	−0.426694	+	1.39225i
$552$		0			0
$553$	−7.54338	−	8.98985i	−0.320777	−	0.382287i
$554$		0			0
$555$	23.7304	+	4.18432i	1.00730	+	0.177614i
$556$		0			0
$557$	26.5542	−	9.66494i	1.12514	−	0.409517i	0.288613	−	0.957446i	$-0.406806\pi$
$557$	26.5542	−	9.66494i	1.12514	−	0.409517i	0.836525	+	0.547929i	$0.184584\pi$
$558$		0			0
$559$	14.1105	+	24.4401i	0.596810	+	1.03371i
$560$		0			0
$561$	−0.106879	+	0.127373i	−0.00451243	+	0.00537770i
$562$		0			0
$563$	17.9978	−	31.1731i	0.758516	−	1.31379i	−0.185092	−	0.982721i	$-0.559258\pi$
$563$	17.9978	−	31.1731i	0.758516	−	1.31379i	0.943608	−	0.331066i	$-0.107408\pi$
$564$		0			0
$565$	30.6634	−	5.40679i	1.29002	−	0.227465i
$566$		0			0
$567$	−0.446233	+	1.22601i	−0.0187400	+	0.0514878i
$568$		0			0
$569$			42.1546i			1.76721i	0.468231	+	0.883606i	$0.344892\pi$
$569$			42.1546i			1.76721i	−0.468231	+	0.883606i	$0.655108\pi$
$570$		0			0
$571$			12.5659i			0.525867i	0.964814	+	0.262933i	$0.0846899\pi$
$571$			12.5659i			0.525867i	−0.964814	+	0.262933i	$0.915310\pi$
$572$		0			0
$573$	−9.00840	+	24.7504i	−0.376332	+	1.03396i
$574$		0			0
$575$	46.0436	−	8.11873i	1.92015	−	0.338574i
$576$		0			0
$577$	0.947071	−	1.64038i	0.0394271	−	0.0682897i	−0.845638	−	0.533756i	$-0.820780\pi$
$577$	0.947071	−	1.64038i	0.0394271	−	0.0682897i	0.885066	+	0.465466i	$0.154113\pi$
$578$		0			0
$579$	−10.8434	+	12.9227i	−0.450637	+	0.537048i
$580$		0			0
$581$	−5.48071	−	9.49287i	−0.227378	−	0.393831i
$582$		0			0
$583$	0.530844	−	0.193211i	0.0219853	−	0.00800199i
$584$		0			0
$585$	−9.22533	−	1.62668i	−0.381421	−	0.0672547i
$586$		0			0
$587$	10.0124	+	11.9323i	0.413257	+	0.492500i	0.932014	−	0.362421i	$-0.118050\pi$
$587$	10.0124	+	11.9323i	0.413257	+	0.492500i	−0.518758	+	0.854921i	$0.673605\pi$
$588$		0			0
$589$	−2.36522	+	19.1548i	−0.0974572	+	0.789260i
$590$		0			0
$591$	−7.08152	+	5.94210i	−0.291295	+	0.244425i
$592$		0			0
$593$	2.30026	−	13.0454i	0.0944605	−	0.535712i	−0.900451	−	0.434958i	$-0.856763\pi$
$593$	2.30026	−	13.0454i	0.0944605	−	0.535712i	0.994911	−	0.100754i	$-0.0321256\pi$
$594$		0			0
$595$	1.17060	+	3.21619i	0.0479899	+	0.131851i
$596$		0			0
$597$	−5.03933	+	2.90946i	−0.206246	+	0.119076i
$598$		0			0
$599$	−23.0029	−	19.3017i	−0.939872	−	0.788646i	0.0376910	−	0.999289i	$-0.488000\pi$
$599$	−23.0029	−	19.3017i	−0.939872	−	0.788646i	−0.977563	+	0.210643i	$0.932444\pi$
$600$		0			0
$601$	−35.9891	−	20.7783i	−1.46803	−	0.847566i	−0.468668	−	0.883374i	$-0.655266\pi$
$601$	−35.9891	−	20.7783i	−1.46803	−	0.847566i	−0.999359	+	0.0358083i	$0.988599\pi$
$602$		0			0
$603$	0.0906504	+	0.514104i	0.00369157	+	0.0209359i
$604$		0			0
$605$	−35.0037	−	12.7403i	−1.42310	−	0.517968i
$606$		0			0
$607$	−33.3517			−1.35370			−0.676852	−	0.736119i	$-0.736656\pi$
$607$	−33.3517			−1.35370			−0.676852	+	0.736119i	$0.736656\pi$
$608$		0			0
$609$	10.2310			0.414582
$610$		0			0
$611$	0.306313	+	0.111489i	0.0123921	+	0.00451035i
$612$		0			0
$613$	−7.12446	−	40.4048i	−0.287754	−	1.63193i	−0.695279	−	0.718740i	$-0.744719\pi$
$613$	−7.12446	−	40.4048i	−0.287754	−	1.63193i	0.407525	−	0.913194i	$-0.366392\pi$
$614$		0			0
$615$	−0.00795758	−	0.00459431i	−0.000320881	−	0.000185261i
$616$		0			0
$617$	−1.06090	−	0.890198i	−0.0427101	−	0.0358380i	0.621183	−	0.783666i	$-0.286652\pi$
$617$	−1.06090	−	0.890198i	−0.0427101	−	0.0358380i	−0.663893	+	0.747828i	$0.731097\pi$
$618$		0			0
$619$	−35.5313	+	20.5140i	−1.42812	+	0.824527i	−0.996973	−	0.0777536i	$-0.975225\pi$
$619$	−35.5313	+	20.5140i	−1.42812	+	0.824527i	−0.431150	+	0.902280i	$0.641892\pi$
$620$		0			0
$621$	2.43573	+	6.69213i	0.0977427	+	0.268546i
$622$		0			0
$623$	−1.46012	+	8.28074i	−0.0584984	+	0.331761i
$624$		0			0
$625$	−11.2801	+	9.46516i	−0.451205	+	0.378606i
$626$		0			0
$627$	−0.788338	+	0.511186i	−0.0314832	+	0.0204148i
$628$		0			0
$629$	3.51334	+	4.18703i	0.140086	+	0.166948i
$630$		0			0
$631$	36.6270	+	6.45832i	1.45810	+	0.257102i	0.845789	−	0.533518i	$-0.179130\pi$
$631$	36.6270	+	6.45832i	1.45810	+	0.257102i	0.612308	+	0.790620i	$0.290241\pi$
$632$		0			0
$633$	−8.85168	+	3.22175i	−0.351823	+	0.128053i
$634$		0			0
$635$	14.3688	+	24.8875i	0.570208	+	0.987629i
$636$		0			0
$637$	9.38030	−	11.1790i	0.371661	−	0.442928i
$638$		0			0
$639$	−7.91516	+	13.7095i	−0.313119	+	0.542338i
$640$		0			0
$641$	−6.79418	+	1.19800i	−0.268354	+	0.0473180i	−0.306206	−	0.951965i	$-0.599060\pi$
$641$	−6.79418	+	1.19800i	−0.268354	+	0.0473180i	0.0378519	+	0.999283i	$0.487948\pi$
$642$		0			0
$643$	−8.74204	+	24.0186i	−0.344752	+	0.947199i	0.639243	+	0.769005i	$0.279248\pi$
$643$	−8.74204	+	24.0186i	−0.344752	+	0.947199i	−0.983995	+	0.178194i	$0.942974\pi$
$644$		0			0
$645$		−	34.8410i		−	1.37186i
$646$		0			0
$647$		−	0.293356i		−	0.0115330i	−0.999983	−	0.00576650i	$-0.998164\pi$
$647$		−	0.293356i		−	0.0115330i	0.999983	−	0.00576650i	$-0.00183554\pi$
$648$		0			0
$649$	−0.402190	+	1.10501i	−0.0157873	+	0.0433754i
$650$		0			0
$651$	5.68916	−	1.00315i	0.222976	−	0.0393166i
$652$		0			0
$653$	10.7229	−	18.5725i	0.419618	−	0.726799i	−0.576283	−	0.817250i	$-0.695497\pi$
$653$	10.7229	−	18.5725i	0.419618	−	0.726799i	0.995901	+	0.0904509i	$0.0288308\pi$
$654$		0			0
$655$	−13.1095	+	15.6233i	−0.512232	+	0.610454i
$656$		0			0
$657$	2.85063	+	4.93744i	0.111214	+	0.192628i
$658$		0			0
$659$	−17.7956	+	6.47706i	−0.693217	+	0.252310i	−0.664512	−	0.747278i	$-0.731361\pi$
$659$	−17.7956	+	6.47706i	−0.693217	+	0.252310i	−0.0287049	+	0.999588i	$0.509138\pi$
$660$		0			0
$661$	−11.6130	−	2.04768i	−0.451693	−	0.0796456i	−0.0568262	−	0.998384i	$-0.518098\pi$
$661$	−11.6130	−	2.04768i	−0.451693	−	0.0796456i	−0.394867	+	0.918738i	$0.629209\pi$
$662$		0			0
$663$	−1.36583	−	1.62773i	−0.0530444	−	0.0632159i
$664$		0			0
$665$	0.998970	+	19.3144i	0.0387384	+	0.748979i
$666$		0			0
$667$	42.7801	−	35.8968i	1.65645	−	1.38993i
$668$		0			0
$669$	4.29828	−	24.3768i	0.166181	−	0.942460i
$670$		0			0
$671$	0.201682	+	0.554118i	0.00778586	+	0.0213915i
$672$		0			0
$673$	9.60710	−	5.54666i	0.370326	−	0.213808i	−0.303275	−	0.952903i	$-0.598080\pi$
$673$	9.60710	−	5.54666i	0.370326	−	0.213808i	0.673601	+	0.739095i	$0.264747\pi$
$674$		0			0
$675$	5.02914	+	4.21995i	0.193572	+	0.162426i
$676$		0			0
$677$	−27.8550	−	16.0821i	−1.07055	−	0.618084i	−0.142221	−	0.989835i	$-0.545424\pi$
$677$	−27.8550	−	16.0821i	−1.07055	−	0.618084i	−0.928333	+	0.371751i	$0.878758\pi$
$678$		0			0
$679$	0.490311	+	2.78069i	0.0188164	+	0.106713i
$680$		0			0
$681$	3.35464	+	1.22099i	0.128550	+	0.0467884i
$682$		0			0
$683$	−27.0811			−1.03623			−0.518114	−	0.855312i	$-0.673366\pi$
$683$	−27.0811			−1.03623			−0.518114	+	0.855312i	$0.673366\pi$
$684$		0			0
$685$	32.8275			1.25427
$686$		0			0
$687$	−18.3634	−	6.68375i	−0.700609	−	0.255001i
$688$		0			0
$689$	1.25359	+	7.10947i	0.0477580	+	0.270849i
$690$		0			0
$691$	26.7121	+	15.4223i	1.01618	+	0.586691i	0.912995	−	0.407972i	$-0.133764\pi$
$691$	26.7121	+	15.4223i	1.01618	+	0.586691i	0.103183	+	0.994662i	$0.467097\pi$
$692$		0			0
$693$	0.215434	+	0.180771i	0.00818368	+	0.00686692i
$694$		0			0
$695$	−16.0639	+	9.27448i	−0.609337	+	0.351801i
$696$		0			0
$697$	−0.000712854	−	0.00195855i	−2.70013e−5	−	7.41853e-5i
$698$		0			0
$699$	2.10353	−	11.9297i	0.0795627	−	0.451222i
$700$		0			0
$701$	−22.6771	+	19.0284i	−0.856504	+	0.718692i	−0.961212	−	0.275811i	$-0.911054\pi$
$701$	−22.6771	+	19.0284i	−0.856504	+	0.718692i	0.104708	+	0.994503i	$0.466609\pi$
$702$		0			0
$703$	12.0485	+	28.4386i	0.454419	+	1.07258i
$704$		0			0
$705$	−0.258681	−	0.308284i	−0.00974249	−	0.0116106i
$706$		0			0
$707$	18.5012	+	3.26226i	0.695809	+	0.122690i
$708$		0			0
$709$	−41.4568	+	15.0890i	−1.55694	+	0.566681i	−0.970033	−	0.242971i	$-0.921878\pi$
$709$	−41.4568	+	15.0890i	−1.55694	+	0.566681i	−0.586910	+	0.809652i	$0.699656\pi$
$710$		0			0
$711$	−4.49737	−	7.78967i	−0.168665	−	0.292136i
$712$		0			0
$713$	20.2690	−	24.1557i	0.759080	−	0.904637i
$714$		0			0
$715$	−1.00961	+	1.74869i	−0.0377571	+	0.0653973i
$716$		0			0
$717$	1.01410	−	0.178813i	0.0378723	−	0.00667791i
$718$		0			0
$719$	17.8813	−	49.1285i	0.666860	−	1.83218i	0.124149	−	0.992264i	$-0.460380\pi$
$719$	17.8813	−	49.1285i	0.666860	−	1.83218i	0.542711	−	0.839920i	$-0.317398\pi$
$720$		0			0
$721$		−	24.7473i		−	0.921639i
$722$		0			0
$723$			12.9256i			0.480709i
$724$		0			0
$725$	17.6076	−	48.3766i	0.653931	−	1.79666i
$726$		0			0
$727$	−3.55478	+	0.626803i	−0.131839	+	0.0232468i	−0.239178	−	0.970976i	$-0.576878\pi$
$727$	−3.55478	+	0.626803i	−0.131839	+	0.0232468i	0.107339	+	0.994222i	$0.465767\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	5.07991	−	6.05400i	0.187887	−	0.223915i
$732$		0			0
$733$	−19.3945	−	33.5923i	−0.716353	−	1.24076i	−0.962435	−	0.271511i	$-0.912477\pi$
$733$	−19.3945	−	33.5923i	−0.716353	−	1.24076i	0.246082	−	0.969249i	$-0.420857\pi$
$734$		0			0
$735$	−16.9298	+	6.16196i	−0.624466	+	0.227287i
$736$		0			0
$737$	0.110816	+	0.0195398i	0.00408196	+	0.000719760i
$738$		0			0
$739$	26.7779	+	31.9127i	0.985041	+	1.17393i	0.984759	+	0.173927i	$0.0556455\pi$
$739$	26.7779	+	31.9127i	0.985041	+	1.17393i	0.000282682		1.00000i	$0.499910\pi$
$740$		0			0
$741$	−4.68393	−	11.0557i	−0.172068	−	0.406140i
$742$		0			0
$743$	22.3321	−	18.7388i	0.819285	−	0.687461i	−0.133520	−	0.991046i	$-0.542628\pi$
$743$	22.3321	−	18.7388i	0.819285	−	0.687461i	0.952804	+	0.303585i	$0.0981835\pi$
$744$		0			0
$745$	−6.08507	+	34.5102i	−0.222940	+	1.26435i
$746$		0			0
$747$	−2.87349	−	7.89484i	−0.105135	−	0.288857i
$748$		0			0
$749$	−18.1197	+	10.4614i	−0.662079	+	0.382252i
$750$		0			0
$751$	−29.4635	−	24.7228i	−1.07514	−	0.902149i	−0.0796311	−	0.996824i	$-0.525374\pi$
$751$	−29.4635	−	24.7228i	−1.07514	−	0.902149i	−0.995508	+	0.0946754i	$0.969819\pi$
$752$		0			0
$753$	20.8893	+	12.0605i	0.761250	+	0.439508i
$754$		0			0
$755$	−4.70087	−	26.6600i	−0.171082	−	0.970256i
$756$		0			0
$757$	−29.4028	−	10.7017i	−1.06866	−	0.388961i	−0.252986	−	0.967470i	$-0.581413\pi$
$757$	−29.4028	−	10.7017i	−1.06866	−	0.388961i	−0.815676	+	0.578509i	$0.803635\pi$
$758$		0			0
$759$	1.53508			0.0557197
$760$		0			0
$761$	−47.9898			−1.73963			−0.869815	−	0.493379i	$-0.835762\pi$
$761$	−47.9898			−1.73963			−0.869815	+	0.493379i	$0.835762\pi$
$762$		0			0
$763$	12.1323	+	4.41579i	0.439218	+	0.159862i
$764$		0			0
$765$	0.455530	+	2.58344i	0.0164697	+	0.0934044i
$766$		0			0
$767$	−13.0141	−	7.51371i	−0.469913	−	0.271304i
$768$		0			0
$769$	27.1621	+	22.7917i	0.979491	+	0.821890i	0.984013	−	0.178099i	$-0.0569948\pi$
$769$	27.1621	+	22.7917i	0.979491	+	0.821890i	−0.00452164	+	0.999990i	$0.501439\pi$
$770$		0			0
$771$	−23.3274	+	13.4681i	−0.840115	+	0.485041i
$772$		0			0
$773$	−6.21760	−	17.0827i	−0.223632	−	0.614423i	0.776240	−	0.630437i	$-0.217124\pi$
$773$	−6.21760	−	17.0827i	−0.223632	−	0.614423i	−0.999872	+	0.0160146i	$0.994902\pi$
$774$		0			0
$775$	5.04774	−	28.6271i	0.181320	−	1.02832i
$776$		0			0
$777$	7.08180	−	5.94233i	0.254058	−	0.213180i
$778$		0			0
$779$	−0.000608338	−	0.0117618i	−2.17960e−5	−	0.000421409i
$780$		0			0
$781$	2.19336	+	2.61394i	0.0784844	+	0.0935341i
$782$		0			0
$783$	7.72256	+	1.36169i	0.275982	+	0.0486630i
$784$		0			0
$785$	66.4610	−	24.1898i	2.37209	−	0.863372i
$786$		0			0
$787$	23.0520	+	39.9273i	0.821716	+	1.42325i	0.904403	+	0.426679i	$0.140316\pi$
$787$	23.0520	+	39.9273i	0.821716	+	1.42325i	−0.0826872	+	0.996576i	$0.526350\pi$
$788$		0			0
$789$	−4.18156	+	4.98339i	−0.148868	+	0.177413i
$790$		0			0
$791$	5.97276	−	10.3451i	0.212367	−	0.367830i
$792$		0			0
$793$	−7.42117	+	1.30855i	−0.263534	+	0.0464681i
$794$		0			0
$795$	3.04828	−	8.37509i	0.108111	−	0.297034i
$796$		0			0
$797$		−	19.1118i		−	0.676975i	−0.940971	−	0.338487i	$-0.890085\pi$
$797$		−	19.1118i		−	0.676975i	0.940971	−	0.338487i	$-0.109915\pi$
$798$		0			0
$799$		−	0.0912841i		−	0.00322940i
$800$		0			0
$801$	−2.20424	+	6.05611i	−0.0778831	+	0.213982i
$802$		0			0
$803$	1.21025	−	0.213399i	0.0427087	−	0.00753070i
$804$		0			0
$805$	15.7991	−	27.3648i	0.556845	−	0.964483i
$806$		0			0
$807$	1.46470	−	1.74556i	0.0515598	−	0.0614466i
$808$		0			0
$809$	−1.96972	−	3.41166i	−0.0692518	−	0.119948i	0.829320	−	0.558773i	$-0.188728\pi$
$809$	−1.96972	−	3.41166i	−0.0692518	−	0.119948i	−0.898572	+	0.438826i	$0.855395\pi$
$810$		0			0
$811$	−31.2894	+	11.3884i	−1.09872	+	0.399902i	−0.826844	−	0.562431i	$-0.809866\pi$
$811$	−31.2894	+	11.3884i	−1.09872	+	0.399902i	−0.271876	+	0.962332i	$0.587644\pi$
$812$		0			0
$813$	−24.1929	−	4.26585i	−0.848481	−	0.149610i
$814$		0			0
$815$	19.9850	+	23.8172i	0.700045	+	0.834281i
$816$		0			0
$817$	37.4694	−	24.2965i	1.31089	−	0.850026i
$818$		0			0
$819$	−2.75309	+	2.31011i	−0.0962007	+	0.0807219i
$820$		0			0
$821$	6.18540	−	35.0792i	0.215872	−	1.22427i	−0.663515	−	0.748163i	$-0.730936\pi$
$821$	6.18540	−	35.0792i	0.215872	−	1.22427i	0.879387	−	0.476108i	$-0.157953\pi$
$822$		0			0
$823$	10.3737	+	28.5016i	0.361605	+	0.993503i	0.978462	+	0.206427i	$0.0661836\pi$
$823$	10.3737	+	28.5016i	0.361605	+	0.993503i	−0.616857	+	0.787076i	$0.711594\pi$
$824$		0			0
$825$	1.22552	−	0.707557i	0.0426673	−	0.0246340i
$826$		0			0
$827$	−38.4816	−	32.2899i	−1.33814	−	1.12283i	−0.982100	−	0.188359i	$-0.939683\pi$
$827$	−38.4816	−	32.2899i	−1.33814	−	1.12283i	−0.356037	−	0.934472i	$-0.615872\pi$
$828$		0			0
$829$	12.9526	+	7.47817i	0.449861	+	0.259728i	0.707772	−	0.706441i	$-0.249701\pi$
$829$	12.9526	+	7.47817i	0.449861	+	0.259728i	−0.257910	+	0.966169i	$0.583034\pi$
$830$		0			0
$831$	−2.25839	−	12.8080i	−0.0783428	−	0.444304i
$832$		0			0
$833$	−3.84018	−	1.39771i	−0.133054	−	0.0484278i
$834$		0			0
$835$	−29.7034			−1.02793
$836$		0			0
$837$	4.42779			0.153047
$838$		0			0
$839$	−14.7696	−	5.37571i	−0.509905	−	0.185590i	0.0742389	−	0.997240i	$-0.476347\pi$
$839$	−14.7696	−	5.37571i	−0.509905	−	0.185590i	−0.584144	+	0.811650i	$0.698569\pi$
$840$		0			0
$841$	−5.64219	−	31.9985i	−0.194558	−	1.10339i
$842$		0			0
$843$	−5.48690	−	3.16786i	−0.188979	−	0.109107i
$844$		0			0
$845$	14.0996	+	11.8310i	0.485041	+	0.406997i
$846$		0			0
$847$	−12.3764	+	7.14552i	−0.425258	+	0.245523i
$848$		0			0
$849$	−6.82494	−	18.7514i	−0.234231	−	0.643545i
$850$		0			0
$851$	8.76251	−	49.6947i	0.300375	−	1.70351i
$852$		0			0
$853$	22.4491	−	18.8371i	0.768644	−	0.644969i	−0.171717	−	0.985146i	$-0.554932\pi$
$853$	22.4491	−	18.8371i	0.768644	−	0.644969i	0.940361	+	0.340177i	$0.110487\pi$
$854$		0			0
$855$	−1.81660	+	14.7118i	−0.0621264	+	0.503132i
$856$		0			0
$857$	−1.22924	−	1.46495i	−0.0419901	−	0.0500419i	0.744641	−	0.667466i	$-0.232621\pi$
$857$	−1.22924	−	1.46495i	−0.0419901	−	0.0500419i	−0.786631	+	0.617424i	$0.788176\pi$
$858$		0			0
$859$	26.4811	+	4.66934i	0.903524	+	0.159316i	0.606062	−	0.795418i	$-0.292748\pi$
$859$	26.4811	+	4.66934i	0.903524	+	0.159316i	0.297463	+	0.954733i	$0.403860\pi$
$860$		0			0
$861$	−0.00331262	+	0.00120570i	−0.000112894	+	4.10900e-5i
$862$		0			0
$863$	9.53560	+	16.5161i	0.324596	+	0.562216i	0.981430	−	0.191818i	$-0.0614384\pi$
$863$	9.53560	+	16.5161i	0.324596	+	0.562216i	−0.656835	+	0.754035i	$0.728105\pi$
$864$		0			0
$865$	14.4571	−	17.2293i	0.491555	−	0.585812i
$866$		0			0
$867$	8.20248	−	14.2071i	0.278571	−	0.482499i
$868$		0			0
$869$	−1.90938	+	0.336675i	−0.0647712	+	0.0114209i
$870$		0			0
$871$	−0.491821	+	1.35127i	−0.0166647	+	0.0457860i
$872$		0			0
$873$			2.16417i			0.0732462i
$874$		0			0
$875$		−	6.94415i		−	0.234755i
$876$		0			0
$877$	−7.89354	+	21.6873i	−0.266546	+	0.732329i	0.732144	+	0.681150i	$0.238520\pi$
$877$	−7.89354	+	21.6873i	−0.266546	+	0.732329i	−0.998690	+	0.0511785i	$0.983702\pi$
$878$		0			0
$879$	−2.80564	+	0.494711i	−0.0946320	+	0.0166862i
$880$		0			0
$881$	12.2975	−	21.3000i	0.414315	−	0.717614i	−0.581042	−	0.813874i	$-0.697355\pi$
$881$	12.2975	−	21.3000i	0.414315	−	0.717614i	0.995356	+	0.0962599i	$0.0306880\pi$
$882$		0			0
$883$	16.8234	−	20.0494i	0.566153	−	0.674715i	−0.404684	−	0.914457i	$-0.632618\pi$
$883$	16.8234	−	20.0494i	0.566153	−	0.674715i	0.970837	+	0.239742i	$0.0770629\pi$
$884$		0			0
$885$	9.27625	+	16.0669i	0.311818	+	0.540084i
$886$		0			0
$887$	−11.1800	+	4.06917i	−0.375386	+	0.136629i	−0.522821	−	0.852442i	$-0.675120\pi$
$887$	−11.1800	+	4.06917i	−0.375386	+	0.136629i	0.147435	+	0.989072i	$0.452898\pi$
$888$		0			0
$889$	10.8577	+	1.91450i	0.364155	+	0.0642103i
$890$		0			0
$891$	0.138554	+	0.165122i	0.00464173	+	0.00553180i
$892$		0			0
$893$	0.151149	−	0.493179i	0.00505801	−	0.0165036i
$894$		0			0
$895$	−4.88121	+	4.09582i	−0.163161	+	0.136908i
$896$		0			0
$897$	−3.40647	+	19.3191i	−0.113739	+	0.645045i
$898$		0			0
$899$	−11.8754	−	32.6274i	−0.396067	−	1.08818i
$900$		0			0
$901$	1.75078	−	1.01082i	0.0583270	−	0.0336751i
$902$		0			0
$903$	−10.2395	−	8.59197i	−0.340750	−	0.285923i
$904$		0			0
$905$	31.7098	+	18.3077i	1.05407	+	0.608568i
$906$		0			0
$907$	−3.60881	−	20.4666i	−0.119829	−	0.679581i	−0.984246	−	0.176806i	$-0.943423\pi$
$907$	−3.60881	−	20.4666i	−0.119829	−	0.679581i	0.864417	−	0.502775i	$-0.167688\pi$
$908$		0			0
$909$	13.5308	+	4.92482i	0.448789	+	0.163346i
$910$		0			0
$911$	5.44063			0.180256			0.0901281	−	0.995930i	$-0.471272\pi$
$911$	5.44063			0.180256			0.0901281	+	0.995930i	$0.471272\pi$
$912$		0			0
$913$	−1.81096			−0.0599340
$914$		0			0
$915$	8.74228	+	3.18193i	0.289011	+	0.105191i
$916$		0			0
$917$	1.35871	+	7.70560i	0.0448684	+	0.254461i
$918$		0			0
$919$	13.0481	+	7.53332i	0.430417	+	0.248501i	0.699524	−	0.714609i	$-0.253395\pi$
$919$	13.0481	+	7.53332i	0.430417	+	0.248501i	−0.269107	+	0.963110i	$0.586729\pi$
$920$		0			0
$921$	−5.76269	−	4.83547i	−0.189887	−	0.159334i
$922$		0			0
$923$	−37.7639	+	21.8030i	−1.24301	+	0.717654i
$924$		0			0
$925$	−15.9100	−	43.7125i	−0.523119	−	1.43726i
$926$		0			0
$927$	3.29374	−	18.6797i	0.108181	−	0.613523i
$928$		0			0
$929$	9.20687	−	7.72548i	0.302068	−	0.253465i	−0.479137	−	0.877740i	$-0.659050\pi$
$929$	9.20687	−	7.72548i	0.302068	−	0.253465i	0.781204	+	0.624275i	$0.214606\pi$
$930$		0			0
$931$	−18.4329	−	13.9100i	−0.604114	−	0.455881i
$932$		0			0
$933$	−2.69930	−	3.21690i	−0.0883712	−	0.105317i
$934$		0			0
$935$	0.556865	+	0.0981903i	0.0182114	+	0.00321117i
$936$		0			0
$937$	−6.28488	+	2.28751i	−0.205318	+	0.0747296i	−0.442632	−	0.896703i	$-0.645955\pi$
$937$	−6.28488	+	2.28751i	−0.205318	+	0.0747296i	0.237314	+	0.971433i	$0.423733\pi$
$938$		0			0
$939$	11.3219	+	19.6101i	0.369476	+	0.639951i
$940$		0			0
$941$	−16.8500	+	20.0810i	−0.549294	+	0.654623i	−0.967244	−	0.253847i	$-0.918304\pi$
$941$	−16.8500	+	20.0810i	−0.549294	+	0.654623i	0.417951	+	0.908470i	$0.362748\pi$
$942$		0			0
$943$	−0.00962109	+	0.0166642i	−0.000313306	+	0.000542662i
$944$		0			0
$945$	4.36954	−	0.770467i	0.142141	−	0.0250633i
$946$		0			0
$947$	−13.1565	+	36.1471i	−0.427528	+	1.17462i	0.519781	+	0.854300i	$0.326014\pi$
$947$	−13.1565	+	36.1471i	−0.427528	+	1.17462i	−0.947308	+	0.320323i	$0.896209\pi$
$948$		0			0
$949$			15.7046i			0.509794i
$950$		0			0
$951$		−	27.7348i		−	0.899361i
$952$		0			0
$953$	17.5629	−	48.2538i	0.568919	−	1.56309i	−0.237275	−	0.971442i	$-0.576254\pi$
$953$	17.5629	−	48.2538i	0.568919	−	1.56309i	0.806194	−	0.591651i	$-0.201523\pi$
$954$		0			0
$955$	88.2108	−	15.5539i	2.85444	−	0.503314i
$956$		0			0
$957$	0.845145	−	1.46383i	0.0273197	−	0.0473190i
$958$		0			0
$959$	8.09543	−	9.64776i	0.261415	−	0.311543i
$960$		0			0
$961$	5.69735	+	9.86809i	0.183785	+	0.318326i
$962$		0			0
$963$	−15.0694	+	5.48482i	−0.485605	+	0.176746i
$964$		0			0
$965$	56.4968	+	9.96191i	1.81870	+	0.320685i
$966$		0			0
$967$	13.9284	+	16.5992i	0.447906	+	0.533794i	0.941999	−	0.335615i	$-0.108944\pi$
$967$	13.9284	+	16.5992i	0.447906	+	0.533794i	−0.494093	+	0.869409i	$0.664500\pi$
$968$		0			0
$969$	−2.46067	+	2.29147i	−0.0790482	+	0.0736125i
$970$		0			0
$971$	7.59860	−	6.37598i	0.243851	−	0.204615i	−0.512668	−	0.858587i	$-0.671343\pi$
$971$	7.59860	−	6.37598i	0.243851	−	0.204615i	0.756519	+	0.653972i	$0.226898\pi$
$972$		0			0
$973$	−1.23573	+	7.00820i	−0.0396158	+	0.224672i
$974$		0			0
$975$	6.18511	+	16.9935i	0.198082	+	0.544226i
$976$		0			0
$977$	43.0607	−	24.8611i	1.37763	−	0.795377i	0.385758	−	0.922600i	$-0.373940\pi$
$977$	43.0607	−	24.8611i	1.37763	−	0.795377i	0.991874	+	0.127223i	$0.0406065\pi$
$978$		0			0
$979$	1.06418	+	0.892950i	0.0340112	+	0.0285388i
$980$		0			0
$981$	8.56994	+	4.94785i	0.273617	+	0.157973i
$982$		0			0
$983$	8.13919	+	46.1596i	0.259600	+	1.47226i	0.783984	+	0.620781i	$0.213184\pi$
$983$	8.13919	+	46.1596i	0.259600	+	1.47226i	−0.524384	+	0.851482i	$0.675704\pi$
$984$		0			0
$985$	29.5415	+	10.7522i	0.941271	+	0.342594i
$986$		0			0
$987$	−0.154395			−0.00491444
$988$		0			0
$989$	−72.9616			−2.32004
$990$		0			0
$991$	13.2965	+	4.83952i	0.422376	+	0.153732i	0.544459	−	0.838788i	$-0.316735\pi$
$991$	13.2965	+	4.83952i	0.422376	+	0.153732i	−0.122083	+	0.992520i	$0.538957\pi$
$992$		0			0
$993$	−4.86341	−	27.5818i	−0.154336	−	0.875281i
$994$		0			0
$995$	17.1375	+	9.89433i	0.543294	+	0.313671i
$996$		0			0
$997$	−35.6572	−	29.9199i	−1.12927	−	0.947574i	−0.130239	−	0.991483i	$-0.541574\pi$
$997$	−35.6572	−	29.9199i	−1.12927	−	0.947574i	−0.999036	+	0.0439091i	$0.986019\pi$
$998$		0			0
$999$	6.13636	−	3.54283i	0.194146	−	0.112090i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.f.127.3	yes	18
4.3	odd	2		912.2.ci.e.127.3	yes	18
19.3	odd	18		912.2.ci.e.79.3	✓	18
76.3	even	18	inner	912.2.ci.f.79.3	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.e.79.3	✓	18	19.3	odd	18
912.2.ci.e.127.3	yes	18	4.3	odd	2
912.2.ci.f.79.3	yes	18	76.3	even	18	inner
912.2.ci.f.127.3	yes	18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{3} +(0.590533 + 3.34908i) q^{5} +(1.12990 + 0.652348i) q^{7} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{3} +(0.590533 + 3.34908i) q^{5} +(1.12990 + 0.652348i) q^{7} +(0.766044 + 0.642788i) q^{9} +(0.186673 - 0.107776i) q^{11} +(0.942124 + 2.58846i) q^{13} +(0.590533 - 3.34908i) q^{15} +(0.590917 - 0.495838i) q^{17} +(4.01355 - 1.70041i) q^{19} +(-0.838643 - 0.999456i) q^{21} +(-7.01342 - 1.23665i) q^{23} +(-6.16915 + 2.24539i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(-5.04054 + 6.00708i) q^{29} +(-2.21389 + 3.83458i) q^{31} +(-0.212277 + 0.0374302i) q^{33} +(-1.51752 + 4.16936i) q^{35} +7.08565i q^{37} -2.75459i q^{39} +(0.000924119 - 0.00253900i) q^{41} +(10.0894 - 1.77904i) q^{43} +(-1.70037 + 2.94513i) q^{45} +(0.0760659 - 0.0906519i) q^{47} +(-2.64888 - 4.58800i) q^{49} +(-0.724867 + 0.263830i) q^{51} +(2.58096 + 0.455092i) q^{53} +(0.471187 + 0.561539i) q^{55} +(-4.35308 + 0.225148i) q^{57} +(-4.17909 + 3.50668i) q^{59} +(-0.475045 + 2.69412i) q^{61} +(0.446233 + 1.22601i) q^{63} +(-8.11262 + 4.68382i) q^{65} +(0.399902 + 0.335557i) q^{67} +(6.16750 + 3.56081i) q^{69} +(2.74891 + 15.5898i) q^{71} +(5.35744 + 1.94995i) q^{73} +6.56507 q^{75} +0.281230 q^{77} +(-8.45229 - 3.07638i) q^{79} +(0.173648 + 0.984808i) q^{81} +(-7.27592 - 4.20076i) q^{83} +(2.00956 + 1.68622i) q^{85} +(6.79110 - 3.92084i) q^{87} +(2.20424 + 6.05611i) q^{89} +(-0.624074 + 3.53930i) q^{91} +(3.39188 - 2.84613i) q^{93} +(8.06495 + 12.4376i) q^{95} +(1.39110 + 1.65785i) q^{97} +(0.212277 + 0.0374302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q+O(q^{10}) \) 18 * q	\( 18 q + 3 q^{13} + 12 q^{17} + 3 q^{19} + 15 q^{21} + 6 q^{23} + 24 q^{25} - 9 q^{27} + 12 q^{29} + 12 q^{31} + 6 q^{33} - 36 q^{35} + 12 q^{41} + 21 q^{43} - 6 q^{45} - 24 q^{47} - 3 q^{49} - 6 q^{51} + 6 q^{53} + 12 q^{55} + 54 q^{59} - 24 q^{61} + 12 q^{63} + 36 q^{65} - 21 q^{67} + 15 q^{73} + 18 q^{75} - 60 q^{79} + 54 q^{85} + 18 q^{87} + 36 q^{89} + 24 q^{91} + 24 q^{93} - 6 q^{95} - 6 q^{97} - 6 q^{99}+O(q^{100}) \) 18 * q + 3 * q^13 + 12 * q^17 + 3 * q^19 + 15 * q^21 + 6 * q^23 + 24 * q^25 - 9 * q^27 + 12 * q^29 + 12 * q^31 + 6 * q^33 - 36 * q^35 + 12 * q^41 + 21 * q^43 - 6 * q^45 - 24 * q^47 - 3 * q^49 - 6 * q^51 + 6 * q^53 + 12 * q^55 + 54 * q^59 - 24 * q^61 + 12 * q^63 + 36 * q^65 - 21 * q^67 + 15 * q^73 + 18 * q^75 - 60 * q^79 + 54 * q^85 + 18 * q^87 + 36 * q^89 + 24 * q^91 + 24 * q^93 - 6 * q^95 - 6 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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