LMFDB - Embedded newform 630.2.ce.c.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(53,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 8]))

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

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

chi := DirichletCharacter("630.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.ce (of order $12$, degree $4$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.1
Character	$\chi$	$=$	630.107
Dual form			630.2.ce.c.53.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-2.16447 - 0.561299i) q^{5} +(2.06214 + 1.65758i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-2.16447 - 0.561299i) q^{5} +(2.06214 + 1.65758i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.0180339 + 2.23600i) q^{10} +(-0.565444 + 0.326459i) q^{11} +(0.771886 - 0.771886i) q^{13} +(1.06738 - 2.42089i) q^{14} +(0.500000 - 0.866025i) q^{16} +(2.06936 + 0.554483i) q^{17} +(4.34372 + 2.50785i) q^{19} +(2.15514 - 0.596138i) q^{20} +(0.461683 + 0.461683i) q^{22} +(-0.905652 + 0.242669i) q^{23} +(4.36989 + 2.42983i) q^{25} +(-0.945363 - 0.545806i) q^{26} +(-2.61466 - 0.404442i) q^{28} +9.79270 q^{29} +(-0.897620 - 1.55472i) q^{31} +(-0.965926 - 0.258819i) q^{32} -2.14236i q^{34} +(-3.53304 - 4.74527i) q^{35} +(6.26479 - 1.67864i) q^{37} +(1.29816 - 4.84479i) q^{38} +(-1.13362 - 1.92741i) q^{40} -7.90000i q^{41} +(-0.0657249 + 0.0657249i) q^{43} +(0.326459 - 0.565444i) q^{44} +(0.468800 + 0.811985i) q^{46} +(0.854209 + 3.18795i) q^{47} +(1.50482 + 6.83634i) q^{49} +(1.21603 - 4.84987i) q^{50} +(-0.282530 + 1.05442i) q^{52} +(1.91300 - 7.13943i) q^{53} +(1.40713 - 0.389229i) q^{55} +(0.286062 + 2.63024i) q^{56} +(-2.53454 - 9.45902i) q^{58} +(3.39154 + 5.87431i) q^{59} +(-4.33834 + 7.51422i) q^{61} +(-1.26943 + 1.26943i) q^{62} +1.00000i q^{64} +(-2.10399 + 1.23747i) q^{65} +(1.66489 - 6.21344i) q^{67} +(-2.06936 + 0.554483i) q^{68} +(-3.66916 + 4.64082i) q^{70} +7.68577i q^{71} +(-9.62903 - 2.58009i) q^{73} +(-3.24289 - 5.61685i) q^{74} -5.01569 q^{76} +(-1.70716 - 0.264067i) q^{77} +(10.3402 + 5.96992i) q^{79} +(-1.56834 + 1.59384i) q^{80} +(-7.63081 + 2.04467i) q^{82} +(0.838447 + 0.838447i) q^{83} +(-4.16784 - 2.36169i) q^{85} +(0.0804962 + 0.0464745i) q^{86} +(-0.630670 - 0.168988i) q^{88} +(-8.65123 + 14.9844i) q^{89} +(2.87120 - 0.312269i) q^{91} +(0.662983 - 0.662983i) q^{92} +(2.85824 - 1.65021i) q^{94} +(-7.99421 - 7.86629i) q^{95} +(-8.59970 - 8.59970i) q^{97} +(6.21392 - 3.22292i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 12 q^{7}+O(q^{10}) $ 32 * q - 12 * q^7	$ 32 q - 12 q^{7} + 8 q^{13} + 16 q^{16} + 32 q^{22} - 16 q^{25} - 56 q^{31} + 20 q^{37} + 4 q^{40} + 24 q^{46} + 4 q^{52} + 12 q^{58} - 48 q^{61} + 8 q^{67} + 24 q^{70} + 48 q^{73} - 36 q^{82} - 136 q^{85} - 16 q^{88} - 40 q^{97}+O(q^{100}) $ 32 * q - 12 * q^7 + 8 * q^13 + 16 * q^16 + 32 * q^22 - 16 * q^25 - 56 * q^31 + 20 * q^37 + 4 * q^40 + 24 * q^46 + 4 * q^52 + 12 * q^58 - 48 * q^61 + 8 * q^67 + 24 * q^70 + 48 * q^73 - 36 * q^82 - 136 * q^85 - 16 * q^88 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−2.16447	−	0.561299i	−0.967982	−	0.251020i
$5$	−2.16447	−	0.561299i	−0.967982	−	0.251020i
$6$		0			0
$7$	2.06214	+	1.65758i	0.779415	+	0.626508i
$7$	2.06214	+	1.65758i	0.779415	+	0.626508i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	0.0180339	+	2.23600i	0.00570281	+	0.707084i
$11$	−0.565444	+	0.326459i	−0.170488	+	0.0984311i	−0.582816	−	0.812604i	$-0.698049\pi$
$11$	−0.565444	+	0.326459i	−0.170488	+	0.0984311i	0.412328	+	0.911035i	$0.364716\pi$
$12$		0			0
$13$	0.771886	−	0.771886i	0.214083	−	0.214083i	−0.591917	−	0.805999i	$-0.701629\pi$
$13$	0.771886	−	0.771886i	0.214083	−	0.214083i	0.805999	+	0.591917i	$0.201629\pi$
$14$	1.06738	−	2.42089i	0.285270	−	0.647009i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.06936	+	0.554483i	0.501894	+	0.134482i	0.500879	−	0.865517i	$-0.333010\pi$
$17$	2.06936	+	0.554483i	0.501894	+	0.134482i	0.00101492	+	0.999999i	$0.499677\pi$
$18$		0			0
$19$	4.34372	+	2.50785i	0.996517	+	0.575339i	0.907216	−	0.420665i	$-0.138203\pi$
$19$	4.34372	+	2.50785i	0.996517	+	0.575339i	0.0893010	+	0.996005i	$0.471537\pi$
$20$	2.15514	−	0.596138i	0.481904	−	0.133300i
$21$		0			0
$22$	0.461683	+	0.461683i	0.0984311	+	0.0984311i
$23$	−0.905652	+	0.242669i	−0.188841	+	0.0505999i	−0.352000	−	0.936000i	$-0.614498\pi$
$23$	−0.905652	+	0.242669i	−0.188841	+	0.0505999i	0.163159	+	0.986600i	$0.447832\pi$
$24$		0			0
$25$	4.36989	+	2.42983i	0.873977	+	0.485966i
$26$	−0.945363	−	0.545806i	−0.185401	−	0.107041i
$27$		0			0
$28$	−2.61466	−	0.404442i	−0.494124	−	0.0764323i
$29$	9.79270			1.81846			0.909229	−	0.416296i	$-0.136672\pi$
$29$	9.79270			1.81846			0.909229	+	0.416296i	$0.136672\pi$
$30$		0			0
$31$	−0.897620	−	1.55472i	−0.161217	−	0.279237i	0.774088	−	0.633078i	$-0.218209\pi$
$31$	−0.897620	−	1.55472i	−0.161217	−	0.279237i	−0.935306	+	0.353841i	$0.884875\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$		0			0
$34$		−	2.14236i		−	0.367412i
$35$	−3.53304	−	4.74527i	−0.597193	−	0.802098i
$36$		0			0
$37$	6.26479	−	1.67864i	1.02992	−	0.275967i	0.295993	−	0.955190i	$-0.404350\pi$
$37$	6.26479	−	1.67864i	1.02992	−	0.275967i	0.733932	+	0.679223i	$0.237683\pi$
$38$	1.29816	−	4.84479i	0.210589	−	0.785928i
$39$		0			0
$40$	−1.13362	−	1.92741i	−0.179240	−	0.304751i
$41$		−	7.90000i		−	1.23377i	−0.787052	−	0.616886i	$-0.788394\pi$
$41$		−	7.90000i		−	1.23377i	0.787052	−	0.616886i	$-0.211606\pi$
$42$		0			0
$43$	−0.0657249	+	0.0657249i	−0.0100230	+	0.0100230i	−0.712100	−	0.702078i	$-0.752256\pi$
$43$	−0.0657249	+	0.0657249i	−0.0100230	+	0.0100230i	0.702078	+	0.712100i	$0.252256\pi$
$44$	0.326459	−	0.565444i	0.0492155	−	0.0852438i
$45$		0			0
$46$	0.468800	+	0.811985i	0.0691208	+	0.119721i
$47$	0.854209	+	3.18795i	0.124599	+	0.465011i	0.999825	−	0.0187039i	$-0.00595399\pi$
$47$	0.854209	+	3.18795i	0.124599	+	0.465011i	−0.875226	+	0.483714i	$0.839287\pi$
$48$		0			0
$49$	1.50482	+	6.83634i	0.214975	+	0.976620i
$50$	1.21603	−	4.84987i	0.171972	−	0.685876i
$51$		0			0
$52$	−0.282530	+	1.05442i	−0.0391798	+	0.146221i
$53$	1.91300	−	7.13943i	0.262771	−	0.980676i	−0.700829	−	0.713329i	$-0.747186\pi$
$53$	1.91300	−	7.13943i	0.262771	−	0.980676i	0.963600	−	0.267347i	$-0.0861469\pi$
$54$		0			0
$55$	1.40713	−	0.389229i	0.189737	−	0.0524836i
$56$	0.286062	+	2.63024i	0.0382267	+	0.351481i
$57$		0			0
$58$	−2.53454	−	9.45902i	−0.332801	−	1.24203i
$59$	3.39154	+	5.87431i	0.441540	+	0.764771i	0.997804	−	0.0662354i	$-0.0210988\pi$
$59$	3.39154	+	5.87431i	0.441540	+	0.764771i	−0.556264	+	0.831006i	$0.687765\pi$
$60$		0			0
$61$	−4.33834	+	7.51422i	−0.555467	+	0.962098i	0.442400	+	0.896818i	$0.354127\pi$
$61$	−4.33834	+	7.51422i	−0.555467	+	0.962098i	−0.997867	+	0.0652798i	$0.979206\pi$
$62$	−1.26943	+	1.26943i	−0.161217	+	0.161217i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−2.10399	+	1.23747i	−0.260967	+	0.153489i
$66$		0			0
$67$	1.66489	−	6.21344i	0.203398	−	0.759093i	−0.786534	−	0.617548i	$-0.788126\pi$
$67$	1.66489	−	6.21344i	0.203398	−	0.759093i	0.989932	−	0.141545i	$-0.0452070\pi$
$68$	−2.06936	+	0.554483i	−0.250947	+	0.0672410i
$69$		0			0
$70$	−3.66916	+	4.64082i	−0.438549	+	0.554684i
$71$			7.68577i			0.912134i	0.889946	+	0.456067i	$0.150742\pi$
$71$			7.68577i			0.912134i	−0.889946	+	0.456067i	$0.849258\pi$
$72$		0			0
$73$	−9.62903	−	2.58009i	−1.12699	−	0.301977i	−0.353283	−	0.935517i	$-0.614935\pi$
$73$	−9.62903	−	2.58009i	−1.12699	−	0.301977i	−0.773710	+	0.633540i	$0.781601\pi$
$74$	−3.24289	−	5.61685i	−0.376979	−	0.652946i
$75$		0			0
$76$	−5.01569			−0.575339
$77$	−1.70716	−	0.264067i	−0.194548	−	0.0300933i
$78$		0			0
$79$	10.3402	+	5.96992i	1.16336	+	0.671668i	0.952108	−	0.305763i	$-0.0989114\pi$
$79$	10.3402	+	5.96992i	1.16336	+	0.671668i	0.211256	+	0.977431i	$0.432245\pi$
$80$	−1.56834	+	1.59384i	−0.175345	+	0.178197i
$81$		0			0
$82$	−7.63081	+	2.04467i	−0.842682	+	0.225796i
$83$	0.838447	+	0.838447i	0.0920315	+	0.0920315i	0.751624	−	0.659592i	$-0.229271\pi$
$83$	0.838447	+	0.838447i	0.0920315	+	0.0920315i	−0.659592	+	0.751624i	$0.729271\pi$
$84$		0			0
$85$	−4.16784	−	2.36169i	−0.452066	−	0.256162i
$86$	0.0804962	+	0.0464745i	0.00868013	+	0.00501148i
$87$		0			0
$88$	−0.630670	−	0.168988i	−0.0672297	−	0.0180141i
$89$	−8.65123	+	14.9844i	−0.917028	+	1.58834i	−0.113124	+	0.993581i	$0.536086\pi$
$89$	−8.65123	+	14.9844i	−0.917028	+	1.58834i	−0.803904	+	0.594759i	$0.797247\pi$
$90$		0			0
$91$	2.87120	−	0.312269i	0.300984	−	0.0327347i
$92$	0.662983	−	0.662983i	0.0691208	−	0.0691208i
$93$		0			0
$94$	2.85824	−	1.65021i	0.294805	−	0.170206i
$95$	−7.99421	−	7.86629i	−0.820188	−	0.807064i
$96$		0			0
$97$	−8.59970	−	8.59970i	−0.873168	−	0.873168i	0.119649	−	0.992816i	$-0.461823\pi$
$97$	−8.59970	−	8.59970i	−0.873168	−	0.873168i	−0.992816	+	0.119649i	$0.961823\pi$
$98$	6.21392	−	3.22292i	0.627700	−	0.325564i
$99$		0			0
$100$	−4.99935	+	0.0806473i	−0.499935	+	0.00806473i
$101$	1.56938	−	0.906083i	0.156159	−	0.0901586i	−0.419884	−	0.907578i	$-0.637929\pi$
$101$	1.56938	−	0.906083i	0.156159	−	0.0901586i	0.576043	+	0.817419i	$0.304596\pi$
$102$		0			0
$103$	−5.15322	−	19.2321i	−0.507762	−	1.89499i	−0.441662	−	0.897181i	$-0.645611\pi$
$103$	−5.15322	−	19.2321i	−0.507762	−	1.89499i	−0.0660998	−	0.997813i	$-0.521056\pi$
$104$	1.09161			0.107041
$105$		0			0
$106$	−7.39128			−0.717905
$107$	4.67547	+	17.4491i	0.451995	+	1.68687i	0.696775	+	0.717289i	$0.254617\pi$
$107$	4.67547	+	17.4491i	0.451995	+	1.68687i	−0.244781	+	0.969579i	$0.578716\pi$
$108$		0			0
$109$	9.74887	−	5.62851i	0.933773	−	0.539114i	0.0457698	−	0.998952i	$-0.485426\pi$
$109$	9.74887	−	5.62851i	0.933773	−	0.539114i	0.888003	+	0.459838i	$0.152093\pi$
$110$	−0.740158	−	1.25844i	−0.0705713	−	0.119988i
$111$		0			0
$112$	2.46658	−	0.957071i	0.233070	−	0.0904347i
$113$	4.19672	+	4.19672i	0.394794	+	0.394794i	0.876392	−	0.481598i	$-0.159944\pi$
$113$	4.19672	+	4.19672i	0.394794	+	0.394794i	−0.481598	+	0.876392i	$0.659944\pi$
$114$		0			0
$115$	2.09647	−	0.0169086i	0.195497	−	0.00157673i
$116$	−8.48072	+	4.89635i	−0.787415	+	0.454615i
$117$		0			0
$118$	4.79636	−	4.79636i	0.441540	−	0.441540i
$119$	3.34820	+	4.57356i	0.306929	+	0.419258i
$120$		0			0
$121$	−5.28685	+	9.15709i	−0.480623	+	0.832463i
$122$	8.38103	+	2.24569i	0.758783	+	0.203315i
$123$		0			0
$124$	1.55472	+	0.897620i	0.139618	+	0.0806087i
$125$	−8.09464	−	7.71212i	−0.724007	−	0.689793i
$126$		0			0
$127$	0.928820	+	0.928820i	0.0824195	+	0.0824195i	0.747115	−	0.664695i	$-0.231439\pi$
$127$	0.928820	+	0.928820i	0.0824195	+	0.0824195i	−0.664695	+	0.747115i	$0.731439\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$		0			0
$130$	1.73985	+	1.71201i	0.152595	+	0.150154i
$131$	5.19621	+	3.00003i	0.453995	+	0.262114i	0.709516	−	0.704689i	$-0.248914\pi$
$131$	5.19621	+	3.00003i	0.453995	+	0.262114i	−0.255521	+	0.966804i	$0.582247\pi$
$132$		0			0
$133$	4.80037	+	12.3716i	0.416245	+	1.07275i
$134$	−6.43263			−0.555694
$135$		0			0
$136$	1.07118	+	1.85534i	0.0918529	+	0.159094i
$137$	−11.1872	−	2.99759i	−0.955784	−	0.256102i	−0.252969	−	0.967474i	$-0.581407\pi$
$137$	−11.1872	−	2.99759i	−0.955784	−	0.256102i	−0.702815	+	0.711373i	$0.748074\pi$
$138$		0			0
$139$		−	10.4380i		−	0.885339i	−0.896685	−	0.442669i	$-0.854032\pi$
$139$		−	10.4380i		−	0.885339i	0.896685	−	0.442669i	$-0.145968\pi$
$140$	5.43234	+	2.34301i	0.459117	+	0.198020i
$141$		0			0
$142$	7.42389	−	1.98922i	0.622999	−	0.166932i
$143$	−0.184469	+	0.688447i	−0.0154261	+	0.0575708i
$144$		0			0
$145$	−21.1960	−	5.49663i	−1.76023	−	0.456470i
$146$			9.96871i			0.825016i
$147$		0			0
$148$	−4.58614	+	4.58614i	−0.376979	+	0.376979i
$149$	−2.48624	+	4.30630i	−0.203681	+	0.352786i	−0.949712	−	0.313126i	$-0.898624\pi$
$149$	−2.48624	+	4.30630i	−0.203681	+	0.352786i	0.746031	+	0.665912i	$0.231957\pi$
$150$		0			0
$151$	11.1035	+	19.2318i	0.903590	+	1.56506i	0.822799	+	0.568332i	$0.192411\pi$
$151$	11.1035	+	19.2318i	0.903590	+	1.56506i	0.0807906	+	0.996731i	$0.474255\pi$
$152$	1.29816	+	4.84479i	0.105294	+	0.392964i
$153$		0			0
$154$	0.186775	+	1.71733i	0.0150508	+	0.138387i
$155$	1.07021	+	3.86899i	0.0859613	+	0.310765i
$156$		0			0
$157$	2.35366	−	8.78399i	0.187843	−	0.701039i	−0.806161	−	0.591696i	$-0.798459\pi$
$157$	2.35366	−	8.78399i	0.187843	−	0.701039i	0.994004	−	0.109343i	$-0.0348746\pi$
$158$	3.09026	−	11.5330i	0.245848	−	0.917516i
$159$		0			0
$160$	1.94545	+	1.10238i	0.153801	+	0.0871508i
$161$	−2.26982	−	1.00078i	−0.178887	−	0.0788724i
$162$		0			0
$163$	−3.88909	−	14.5143i	−0.304617	−	1.13685i	−0.933275	−	0.359164i	$-0.883062\pi$
$163$	−3.88909	−	14.5143i	−0.304617	−	1.13685i	0.628658	−	0.777682i	$-0.283605\pi$
$164$	3.95000	+	6.84160i	0.308443	+	0.534239i
$165$		0			0
$166$	0.592872	−	1.02688i	0.0460158	−	0.0797016i
$167$	−16.2008	+	16.2008i	−1.25365	+	1.25365i	−0.299584	+	0.954070i	$0.596848\pi$
$167$	−16.2008	+	16.2008i	−1.25365	+	1.25365i	−0.954070	+	0.299584i	$0.903152\pi$
$168$		0			0
$169$			11.8084i			0.908337i
$170$	−1.20250	+	4.63708i	−0.0922278	+	0.355648i
$171$		0			0
$172$	0.0240570	−	0.0897819i	0.00183433	−	0.00684581i
$173$	1.87299	−	0.501865i	0.142400	−	0.0381561i	−0.186915	−	0.982376i	$-0.559849\pi$
$173$	1.87299	−	0.501865i	0.142400	−	0.0381561i	0.329315	+	0.944220i	$0.393182\pi$
$174$		0			0
$175$	4.98366	+	12.2541i	0.376729	+	0.926323i
$176$			0.652918i			0.0492155i
$177$		0			0
$178$	16.7129	+	4.47821i	1.25268	+	0.335656i
$179$	−10.9132	−	18.9023i	−0.815694	−	1.41282i	−0.908829	−	0.417170i	$-0.863022\pi$
$179$	−10.9132	−	18.9023i	−0.815694	−	1.41282i	0.0931349	−	0.995653i	$-0.470311\pi$
$180$		0			0
$181$	−10.6095			−0.788598			−0.394299	−	0.918982i	$-0.629013\pi$
$181$	−10.6095			−0.788598			−0.394299	+	0.918982i	$0.629013\pi$
$182$	−1.04475	−	2.69255i	−0.0774420	−	0.199585i
$183$		0			0
$184$	−0.811985	−	0.468800i	−0.0598603	−	0.0345604i
$185$	−14.5022	+	0.116964i	−1.06622	+	0.00859935i
$186$		0			0
$187$	−1.35112	+	0.362032i	−0.0988039	+	0.0264744i
$188$	−2.33374	−	2.33374i	−0.170206	−	0.170206i
$189$		0			0
$190$	−5.52920	+	9.75776i	−0.401130	+	0.707902i
$191$	−0.576196	−	0.332667i	−0.0416921	−	0.0240709i	0.479009	−	0.877810i	$-0.340996\pi$
$191$	−0.576196	−	0.332667i	−0.0416921	−	0.0240709i	−0.520701	+	0.853739i	$0.674329\pi$
$192$		0			0
$193$	−20.1993	−	5.41238i	−1.45398	−	0.389592i	−0.556572	−	0.830800i	$-0.687884\pi$
$193$	−20.1993	−	5.41238i	−1.45398	−	0.389592i	−0.897405	+	0.441208i	$0.854550\pi$
$194$	−6.08091	+	10.5324i	−0.436584	+	0.756185i
$195$		0			0
$196$	−4.72139	−	5.16803i	−0.337242	−	0.369145i
$197$	5.67368	−	5.67368i	0.404233	−	0.404233i	−0.475489	−	0.879722i	$-0.657729\pi$
$197$	5.67368	−	5.67368i	0.404233	−	0.404233i	0.879722	+	0.475489i	$0.157729\pi$
$198$		0			0
$199$	−12.6522	+	7.30475i	−0.896890	+	0.517820i	−0.876190	−	0.481966i	$-0.839923\pi$
$199$	−12.6522	+	7.30475i	−0.896890	+	0.517820i	−0.0207004	+	0.999786i	$0.506590\pi$
$200$	1.37183	+	4.80813i	0.0970028	+	0.339986i
$201$		0			0
$202$	−1.28139	−	1.28139i	−0.0901586	−	0.0901586i
$203$	20.1939	+	16.2322i	1.41733	+	1.13928i
$204$		0			0
$205$	−4.43426	+	17.0993i	−0.309702	+	1.19427i
$206$	−17.2430	+	9.95526i	−1.20138	+	0.693616i
$207$		0			0
$208$	−0.282530	−	1.05442i	−0.0195899	−	0.0731106i
$209$	−3.27484			−0.226525
$210$		0			0
$211$	21.8231			1.50237			0.751183	−	0.660093i	$-0.229483\pi$
$211$	21.8231			1.50237			0.751183	+	0.660093i	$0.229483\pi$
$212$	1.91300	+	7.13943i	0.131386	+	0.490338i
$213$		0			0
$214$	15.6444	−	9.03232i	1.06943	−	0.617436i
$215$	0.179151	−	0.105368i	0.0122180	−	0.00718607i
$216$		0			0
$217$	0.726070	−	4.69394i	0.0492888	−	0.318645i
$218$	−7.95992	−	7.95992i	−0.539114	−	0.539114i
$219$		0			0
$220$	−1.02399	+	1.04065i	−0.0690377	+	0.0701604i
$221$	2.02531	−	1.16931i	0.136237	−	0.0786565i
$222$		0			0
$223$	3.35691	−	3.35691i	0.224795	−	0.224795i	−0.585719	−	0.810514i	$-0.699188\pi$
$223$	3.35691	−	3.35691i	0.224795	−	0.224795i	0.810514	+	0.585719i	$0.199188\pi$
$224$	−1.56286	−	2.13482i	−0.104423	−	0.142639i
$225$		0			0
$226$	2.96753	−	5.13991i	0.197397	−	0.341901i
$227$	20.4660	+	5.48385i	1.35838	+	0.363976i	0.863220	−	0.504828i	$-0.168444\pi$
$227$	20.4660	+	5.48385i	1.35838	+	0.363976i	0.495157	+	0.868804i	$0.335111\pi$
$228$		0			0
$229$	−16.7965	−	9.69749i	−1.10995	−	0.640828i	−0.171131	−	0.985248i	$-0.554742\pi$
$229$	−16.7965	−	9.69749i	−1.10995	−	0.640828i	−0.938816	+	0.344420i	$0.888075\pi$
$230$	−0.558938	−	2.02066i	−0.0368553	−	0.133238i
$231$		0			0
$232$	6.92448	+	6.92448i	0.454615	+	0.454615i
$233$	−6.04437	+	1.61958i	−0.395980	+	0.106103i	−0.451314	−	0.892365i	$-0.649044\pi$
$233$	−6.04437	+	1.61958i	−0.395980	+	0.106103i	0.0553336	+	0.998468i	$0.482378\pi$
$234$		0			0
$235$	−0.0595192	−	7.37970i	−0.00388260	−	0.481399i
$236$	−5.87431	−	3.39154i	−0.382385	−	0.220770i
$237$		0			0
$238$	3.55114	−	4.41784i	0.230186	−	0.286366i
$239$	19.7847			1.27976			0.639882	−	0.768473i	$-0.278983\pi$
$239$	19.7847			1.27976			0.639882	+	0.768473i	$0.278983\pi$
$240$		0			0
$241$	−1.50878	−	2.61328i	−0.0971890	−	0.168336i	0.813331	−	0.581801i	$-0.197652\pi$
$241$	−1.50878	−	2.61328i	−0.0971890	−	0.168336i	−0.910520	+	0.413465i	$0.864318\pi$
$242$	10.2134	+	2.73667i	0.656543	+	0.175920i
$243$		0			0
$244$		−	8.67668i		−	0.555467i
$245$	0.580075	−	15.6417i	0.0370596	−	0.999313i
$246$		0			0
$247$	5.28863	−	1.41708i	0.336507	−	0.0901668i
$248$	0.464642	−	1.73407i	0.0295048	−	0.110113i
$249$		0			0
$250$	−5.35429	+	9.81487i	−0.338635	+	0.620747i
$251$		−	22.4148i		−	1.41481i	−0.706809	−	0.707404i	$-0.749866\pi$
$251$		−	22.4148i		−	1.41481i	0.706809	−	0.707404i	$-0.250134\pi$
$252$		0			0
$253$	0.432874	−	0.432874i	0.0272145	−	0.0272145i
$254$	0.656775	−	1.13757i	0.0412097	−	0.0713774i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.98775	−	11.1504i	−0.186371	−	0.695545i	−0.994333	−	0.106310i	$-0.966096\pi$
$257$	−2.98775	−	11.1504i	−0.186371	−	0.695545i	0.807962	−	0.589234i	$-0.200570\pi$
$258$		0			0
$259$	15.7014	+	6.92282i	0.975635	+	0.430163i
$260$	1.20337	−	2.12367i	0.0746299	−	0.131705i
$261$		0			0
$262$	1.55293	−	5.79562i	0.0959404	−	0.358055i
$263$	2.89442	−	10.8021i	0.178478	−	0.666088i	−0.817455	−	0.575992i	$-0.804616\pi$
$263$	2.89442	−	10.8021i	0.178478	−	0.666088i	0.995933	−	0.0900962i	$-0.0287174\pi$
$264$		0			0
$265$	−8.14800	+	14.3793i	−0.500528	+	0.883315i
$266$	10.7076	−	7.83881i	0.656526	−	0.480628i
$267$		0			0
$268$	1.66489	+	6.21344i	0.101699	+	0.379546i
$269$	2.72319	+	4.71670i	0.166036	+	0.287583i	0.937023	−	0.349269i	$-0.113570\pi$
$269$	2.72319	+	4.71670i	0.166036	+	0.287583i	−0.770987	+	0.636851i	$0.780237\pi$
$270$		0			0
$271$	10.6364	−	18.4227i	0.646113	−	1.11910i	−0.337930	−	0.941171i	$-0.609727\pi$
$271$	10.6364	−	18.4227i	0.646113	−	1.11910i	0.984043	−	0.177929i	$-0.0569398\pi$
$272$	1.51488	−	1.51488i	0.0918529	−	0.0918529i
$273$		0			0
$274$			11.5818i			0.699682i
$275$	−3.26417	+	0.0526561i	−0.196837	+	0.00317528i
$276$		0			0
$277$	4.65162	−	17.3601i	0.279489	−	1.04307i	−0.673284	−	0.739384i	$-0.735117\pi$
$277$	4.65162	−	17.3601i	0.279489	−	1.04307i	0.952773	−	0.303683i	$-0.0982164\pi$
$278$	−10.0823	+	2.70155i	−0.604698	+	0.162028i
$279$		0			0
$280$	0.857177	−	5.85365i	0.0512261	−	0.349823i
$281$		−	19.1920i		−	1.14490i	−0.819939	−	0.572450i	$-0.805993\pi$
$281$		−	19.1920i		−	1.14490i	0.819939	−	0.572450i	$-0.194007\pi$
$282$		0			0
$283$	−20.8629	−	5.59020i	−1.24017	−	0.332303i	−0.421640	−	0.906764i	$-0.638545\pi$
$283$	−20.8629	−	5.59020i	−1.24017	−	0.332303i	−0.818532	+	0.574460i	$0.805212\pi$
$284$	−3.84289	−	6.65608i	−0.228033	−	0.394965i
$285$		0			0
$286$	0.712733			0.0421448
$287$	13.0949	−	16.2909i	0.772969	−	0.961621i
$288$		0			0
$289$	−10.7476	−	6.20515i	−0.632214	−	0.365009i
$290$	0.176600	+	21.8964i	0.0103703	+	1.28580i
$291$		0			0
$292$	9.62903	−	2.58009i	0.563497	−	0.150988i
$293$	10.1225	+	10.1225i	0.591361	+	0.591361i	0.937999	−	0.346638i	$-0.112677\pi$
$293$	10.1225	+	10.1225i	0.591361	+	0.591361i	−0.346638	+	0.937999i	$0.612677\pi$
$294$		0			0
$295$	−4.04364	−	14.6185i	−0.235430	−	0.851120i
$296$	5.61685	+	3.24289i	0.326473	+	0.188489i
$297$		0			0
$298$	4.80305	+	1.28697i	0.278233	+	0.0745524i
$299$	−0.511747	+	0.886373i	−0.0295951	+	0.0512603i
$300$		0			0
$301$	−0.244478	+	0.0265892i	−0.0140915	+	0.00153258i
$302$	15.7027	−	15.7027i	0.903590	−	0.903590i
$303$		0			0
$304$	4.34372	−	2.50785i	0.249129	−	0.143835i
$305$	13.6079	−	13.8292i	0.779189	−	0.791860i
$306$		0			0
$307$	17.6475	+	17.6475i	1.00720	+	1.00720i	0.999974	+	0.00722381i	$0.00229943\pi$
$307$	17.6475	+	17.6475i	1.00720	+	1.00720i	0.00722381	+	0.999974i	$0.497701\pi$
$308$	1.61047	−	0.624889i	0.0917653	−	0.0356064i
$309$		0			0
$310$	3.46017	−	2.03511i	0.196524	−	0.115587i
$311$	6.02853	−	3.48057i	0.341847	−	0.197365i	−0.319242	−	0.947673i	$-0.603428\pi$
$311$	6.02853	−	3.48057i	0.341847	−	0.197365i	0.661088	+	0.750308i	$0.270095\pi$
$312$		0			0
$313$	1.20120	+	4.48293i	0.0678957	+	0.253390i	0.991529	−	0.129888i	$-0.0414617\pi$
$313$	1.20120	+	4.48293i	0.0678957	+	0.253390i	−0.923633	+	0.383278i	$0.874795\pi$
$314$	−9.09385			−0.513196
$315$		0			0
$316$	−11.9398			−0.671668
$317$	−7.48412	−	27.9311i	−0.420350	−	1.56877i	−0.773873	−	0.633341i	$-0.781683\pi$
$317$	−7.48412	−	27.9311i	−0.420350	−	1.56877i	0.353523	−	0.935426i	$-0.384984\pi$
$318$		0			0
$319$	−5.53722	+	3.19691i	−0.310025	+	0.178993i
$320$	0.561299	−	2.16447i	0.0313776	−	0.120998i
$321$		0			0
$322$	−0.379204	+	2.45150i	−0.0211322	+	0.136617i
$323$	7.59816	+	7.59816i	0.422773	+	0.422773i
$324$		0			0
$325$	5.24861	−	1.49750i	0.291140	−	0.0830664i
$326$	−13.0131	+	7.51314i	−0.720731	+	0.416115i
$327$		0			0
$328$	5.58614	−	5.58614i	0.308443	−	0.308443i
$329$	−3.52280	+	7.98992i	−0.194218	+	0.440499i
$330$		0			0
$331$	−5.41664	+	9.38189i	−0.297725	+	0.515675i	−0.975615	−	0.219488i	$-0.929561\pi$
$331$	−5.41664	+	9.38189i	−0.297725	+	0.515675i	0.677890	+	0.735163i	$0.262895\pi$
$332$	−1.14534	−	0.306893i	−0.0628587	−	0.0168429i
$333$		0			0
$334$	19.8418	+	11.4557i	1.08570	+	0.626827i
$335$	−7.09120	+	12.5143i	−0.387434	+	0.683731i
$336$		0			0
$337$	13.8548	+	13.8548i	0.754716	+	0.754716i	0.975356	−	0.220639i	$-0.0708143\pi$
$337$	13.8548	+	13.8548i	0.754716	+	0.754716i	−0.220639	+	0.975356i	$0.570814\pi$
$338$	11.4060	−	3.05623i	0.620406	−	0.166237i
$339$		0			0
$340$	4.79031	−	0.0386350i	0.259791	−	0.00209528i
$341$	1.01511	+	0.586072i	0.0549711	+	0.0317376i
$342$		0			0
$343$	−8.22865	+	16.5918i	−0.444305	+	0.895875i
$344$	−0.0929491			−0.00501148
$345$		0			0
$346$	−0.969529	−	1.67927i	−0.0521222	−	0.0902783i
$347$	−22.2650	−	5.96588i	−1.19525	−	0.320265i	−0.394289	−	0.918986i	$-0.629009\pi$
$347$	−22.2650	−	5.96588i	−1.19525	−	0.320265i	−0.800958	+	0.598721i	$0.795676\pi$
$348$		0			0
$349$		−	12.6496i		−	0.677115i	−0.940946	−	0.338558i	$-0.890061\pi$
$349$		−	12.6496i		−	0.677115i	0.940946	−	0.338558i	$-0.109939\pi$
$350$	10.5467	−	7.98544i	0.563745	−	0.426840i
$351$		0			0
$352$	0.630670	−	0.168988i	0.0336148	−	0.00900707i
$353$	7.86188	−	29.3409i	0.418445	−	1.56166i	−0.359388	−	0.933188i	$-0.617014\pi$
$353$	7.86188	−	29.3409i	0.418445	−	1.56166i	0.777833	−	0.628471i	$-0.216319\pi$
$354$		0			0
$355$	4.31402	−	16.6357i	0.228964	−	0.882929i
$356$		−	17.3025i		−	0.917028i
$357$		0			0
$358$	−15.4337	+	15.4337i	−0.815694	+	0.815694i
$359$	4.14969	−	7.18748i	0.219012	−	0.379341i	−0.735494	−	0.677531i	$-0.763050\pi$
$359$	4.14969	−	7.18748i	0.219012	−	0.379341i	0.954506	+	0.298191i	$0.0963832\pi$
$360$		0			0
$361$	3.07858	+	5.33226i	0.162031	+	0.280645i
$362$	2.74594	+	10.2480i	0.144323	+	0.538622i
$363$		0			0
$364$	−2.33040	+	1.70603i	−0.122146	+	0.0894205i
$365$	19.3936	+	10.9893i	1.01511	+	0.575207i
$366$		0			0
$367$	−4.96408	+	18.5262i	−0.259123	+	0.967059i	0.706627	+	0.707586i	$0.250216\pi$
$367$	−4.96408	+	18.5262i	−0.259123	+	0.967059i	−0.965750	+	0.259474i	$0.916451\pi$
$368$	−0.242669	+	0.905652i	−0.0126500	+	0.0472104i
$369$		0			0
$370$	3.86642	+	13.9778i	0.201006	+	0.726669i
$371$	15.7791	−	11.5515i	0.819209	−	0.599725i
$372$		0			0
$373$	−0.431045	−	1.60868i	−0.0223187	−	0.0832944i	0.953868	−	0.300226i	$-0.0970619\pi$
$373$	−0.431045	−	1.60868i	−0.0223187	−	0.0832944i	−0.976187	+	0.216931i	$0.930395\pi$
$374$	0.699392	+	1.21138i	0.0361647	+	0.0626391i
$375$		0			0
$376$	−1.65021	+	2.85824i	−0.0851028	+	0.147402i
$377$	7.55885	−	7.55885i	0.389300	−	0.389300i
$378$		0			0
$379$		−	11.3712i		−	0.584098i	−0.956403	−	0.292049i	$-0.905663\pi$
$379$		−	11.3712i		−	0.584098i	0.956403	−	0.292049i	$-0.0943370\pi$
$380$	10.8563	+	2.81530i	0.556918	+	0.144422i
$381$		0			0
$382$	−0.172201	+	0.642663i	−0.00881058	+	0.0328815i
$383$	−18.9043	+	5.06539i	−0.965964	+	0.258829i	−0.707123	−	0.707091i	$-0.750007\pi$
$383$	−18.9043	+	5.06539i	−0.965964	+	0.258829i	−0.258841	+	0.965920i	$0.583341\pi$
$384$		0			0
$385$	3.54687	+	1.52979i	0.180765	+	0.0779654i
$386$			20.9118i			1.06438i
$387$		0			0
$388$	11.7474	+	3.14771i	0.596385	+	0.159801i
$389$	6.66518	+	11.5444i	0.337938	+	0.585326i	0.984045	−	0.177921i	$-0.0569372\pi$
$389$	6.66518	+	11.5444i	0.337938	+	0.585326i	−0.646107	+	0.763247i	$0.723604\pi$
$390$		0			0
$391$	−2.00868			−0.101583
$392$	−3.76995	+	5.89809i	−0.190411	+	0.297899i
$393$		0			0
$394$	−6.94881	−	4.01190i	−0.350076	−	0.202117i
$395$	−19.0302	−	18.7257i	−0.957512	−	0.942190i
$396$		0			0
$397$	−13.4065	+	3.59227i	−0.672854	+	0.180291i	−0.579040	−	0.815299i	$-0.696573\pi$
$397$	−13.4065	+	3.59227i	−0.672854	+	0.180291i	−0.0938140	+	0.995590i	$0.529906\pi$
$398$	10.3305	+	10.3305i	0.517820	+	0.517820i
$399$		0			0
$400$	4.28924	−	2.56952i	0.214462	−	0.128476i
$401$	−19.4231	−	11.2139i	−0.969941	−	0.559996i	−0.0707229	−	0.997496i	$-0.522531\pi$
$401$	−19.4231	−	11.2139i	−0.969941	−	0.559996i	−0.899218	+	0.437500i	$0.855864\pi$
$402$		0			0
$403$	−1.89293	−	0.507209i	−0.0942936	−	0.0252659i
$404$	−0.906083	+	1.56938i	−0.0450793	+	0.0780796i
$405$		0			0
$406$	10.4526	−	23.7070i	0.518752	−	1.17656i
$407$	−2.99437	+	2.99437i	−0.148426	+	0.148426i
$408$		0			0
$409$	−31.7438	+	18.3273i	−1.56963	+	0.906225i	−0.573417	+	0.819264i	$0.694382\pi$
$409$	−31.7438	+	18.3273i	−1.56963	+	0.906225i	−0.996212	+	0.0869614i	$0.972284\pi$
$410$	17.6644	−	0.142468i	0.872381	−	0.00703597i
$411$		0			0
$412$	14.0789	+	14.0789i	0.693616	+	0.693616i
$413$	−2.74336	+	17.7354i	−0.134992	+	0.872702i
$414$		0			0
$415$	−1.34418	−	2.28542i	−0.0659830	−	0.112187i
$416$	−0.945363	+	0.545806i	−0.0463503	+	0.0267603i
$417$		0			0
$418$	0.847590	+	3.16325i	0.0414570	+	0.154720i
$419$	−5.74367			−0.280597			−0.140298	−	0.990109i	$-0.544806\pi$
$419$	−5.74367			−0.280597			−0.140298	+	0.990109i	$0.544806\pi$
$420$		0			0
$421$	24.6051			1.19918			0.599589	−	0.800308i	$-0.295331\pi$
$421$	24.6051			1.19918			0.599589	+	0.800308i	$0.295331\pi$
$422$	−5.64824	−	21.0795i	−0.274952	−	1.02614i
$423$		0			0
$424$	6.40104	−	3.69564i	0.310862	−	0.179476i
$425$	7.69557	+	7.45123i	0.373290	+	0.361438i
$426$		0			0
$427$	−21.4017	+	8.30420i	−1.03570	+	0.401868i
$428$	−12.7736	−	12.7736i	−0.617436	−	0.617436i
$429$		0			0
$430$	−0.148146	−	0.145775i	−0.00714423	−	0.00702991i
$431$	2.17816	−	1.25756i	0.104918	−	0.0605745i	−0.446623	−	0.894722i	$-0.647373\pi$
$431$	2.17816	−	1.25756i	0.104918	−	0.0605745i	0.551541	+	0.834148i	$0.314040\pi$
$432$		0			0
$433$	−2.77846	+	2.77846i	−0.133524	+	0.133524i	−0.770710	−	0.637186i	$-0.780098\pi$
$433$	−2.77846	+	2.77846i	−0.133524	+	0.133524i	0.637186	+	0.770710i	$0.280098\pi$
$434$	−4.72191	+	0.513550i	−0.226659	+	0.0246512i
$435$		0			0
$436$	−5.62851	+	9.74887i	−0.269557	+	0.466886i
$437$	−4.54247	−	1.21715i	−0.217296	−	0.0582242i
$438$		0			0
$439$	24.2061	+	13.9754i	1.15529	+	0.667008i	0.950171	−	0.311729i	$-0.100908\pi$
$439$	24.2061	+	13.9754i	1.15529	+	0.667008i	0.205121	+	0.978737i	$0.434241\pi$
$440$	1.27022	+	0.719764i	0.0605552	+	0.0343134i
$441$		0			0
$442$	−1.65366	−	1.65366i	−0.0786565	−	0.0786565i
$443$	−22.6757	+	6.07594i	−1.07735	+	0.288676i	−0.753512	−	0.657434i	$-0.771642\pi$
$443$	−22.6757	+	6.07594i	−1.07735	+	0.288676i	−0.323843	+	0.946111i	$0.604975\pi$
$444$		0			0
$445$	27.1361	−	27.5773i	1.28637	−	1.30729i
$446$	−4.11136	−	2.37370i	−0.194679	−	0.112398i
$447$		0			0
$448$	−1.65758	+	2.06214i	−0.0783135	+	0.0974269i
$449$	6.06770			0.286353			0.143176	−	0.989697i	$-0.454268\pi$
$449$	6.06770			0.286353			0.143176	+	0.989697i	$0.454268\pi$
$450$		0			0
$451$	2.57903	+	4.46700i	0.121442	+	0.210343i
$452$	−5.73282	−	1.53610i	−0.269649	−	0.0722523i
$453$		0			0
$454$		−	21.1880i		−	0.994401i
$455$	−6.38992	−	0.935705i	−0.299564	−	0.0438665i
$456$		0			0
$457$	−5.40182	+	1.44741i	−0.252687	+	0.0677072i	−0.382939	−	0.923774i	$-0.625088\pi$
$457$	−5.40182	+	1.44741i	−0.252687	+	0.0677072i	0.130252	+	0.991481i	$0.458421\pi$
$458$	−5.01979	+	18.7341i	−0.234559	+	0.875387i
$459$		0			0
$460$	−1.80714	+	1.06288i	−0.0842584	+	0.0495569i
$461$		−	14.6330i		−	0.681528i	−0.940149	−	0.340764i	$-0.889314\pi$
$461$		−	14.6330i		−	0.681528i	0.940149	−	0.340764i	$-0.110686\pi$
$462$		0			0
$463$	19.8899	−	19.8899i	0.924361	−	0.924361i	−0.0729729	−	0.997334i	$-0.523249\pi$
$463$	19.8899	−	19.8899i	0.924361	−	0.924361i	0.997334	+	0.0729729i	$0.0232487\pi$
$464$	4.89635	−	8.48072i	0.227307	−	0.393708i
$465$		0			0
$466$	3.12880	+	5.41924i	0.144939	+	0.251041i
$467$	−1.17753	−	4.39462i	−0.0544898	−	0.203359i	0.933314	−	0.359060i	$-0.116903\pi$
$467$	−1.17753	−	4.39462i	−0.0544898	−	0.203359i	−0.987804	+	0.155702i	$0.950236\pi$
$468$		0			0
$469$	13.7325	−	10.0533i	0.634109	−	0.464217i
$470$	−7.11284	+	1.96750i	−0.328091	+	0.0907539i
$471$		0			0
$472$	−1.75559	+	6.55195i	−0.0808075	+	0.301578i
$473$	0.0157072	−	0.0586202i	0.000722220	−	0.00269536i
$474$		0			0
$475$	12.8879	+	21.5135i	0.591338	+	0.987107i
$476$	−5.18641	−	2.28672i	−0.237719	−	0.104812i
$477$		0			0
$478$	−5.12065	−	19.1105i	−0.234213	−	0.874095i
$479$	−2.21585	−	3.83796i	−0.101245	−	0.175361i	0.810953	−	0.585111i	$-0.198949\pi$
$479$	−2.21585	−	3.83796i	−0.101245	−	0.175361i	−0.912198	+	0.409750i	$0.865616\pi$
$480$		0			0
$481$	3.53998	−	6.13142i	0.161409	−	0.279569i
$482$	−2.13374	+	2.13374i	−0.0971890	+	0.0971890i
$483$		0			0
$484$		−	10.5737i		−	0.480623i
$485$	13.7868	+	23.4408i	0.626027	+	1.06439i
$486$		0			0
$487$	3.22861	−	12.0493i	0.146302	−	0.546007i	−0.853392	−	0.521270i	$-0.825458\pi$
$487$	3.22861	−	12.0493i	0.146302	−	0.546007i	0.999694	−	0.0247373i	$-0.00787493\pi$
$488$	−8.38103	+	2.24569i	−0.379391	+	0.101658i
$489$		0			0
$490$	−15.2589	+	3.48807i	−0.689326	+	0.157575i
$491$			26.2419i			1.18428i	0.805836	+	0.592139i	$0.201716\pi$
$491$			26.2419i			1.18428i	−0.805836	+	0.592139i	$0.798284\pi$
$492$		0			0
$493$	20.2646	+	5.42989i	0.912673	+	0.244550i
$494$	−2.73759	−	4.74165i	−0.123170	−	0.213337i
$495$		0			0
$496$	−1.79524			−0.0806087
$497$	−12.7398	+	15.8491i	−0.571459	+	0.710930i
$498$		0			0
$499$	−8.84482	−	5.10656i	−0.395949	−	0.228601i	0.288786	−	0.957394i	$-0.406748\pi$
$499$	−8.84482	−	5.10656i	−0.395949	−	0.228601i	−0.684734	+	0.728793i	$0.740082\pi$
$500$	10.8662	+	2.63157i	0.485952	+	0.117687i
$501$		0			0
$502$	−21.6510	+	5.80137i	−0.966332	+	0.258928i
$503$	18.7420	+	18.7420i	0.835664	+	0.835664i	0.988285	−	0.152621i	$-0.0487714\pi$
$503$	18.7420	+	18.7420i	0.835664	+	0.835664i	−0.152621	+	0.988285i	$0.548771\pi$
$504$		0			0
$505$	−3.90547	+	1.08030i	−0.173791	+	0.0480727i
$506$	−0.530160	−	0.306088i	−0.0235685	−	0.0136073i
$507$		0			0
$508$	−1.26879	−	0.339972i	−0.0562935	−	0.0150838i
$509$	−14.8511	+	25.7228i	−0.658262	+	1.14014i	0.322804	+	0.946466i	$0.395375\pi$
$509$	−14.8511	+	25.7228i	−0.658262	+	1.14014i	−0.981065	+	0.193677i	$0.937959\pi$
$510$		0			0
$511$	−15.5797	−	21.2814i	−0.689204	−	0.941436i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	−9.99720	+	5.77189i	−0.440958	+	0.254587i
$515$	0.359064	+	44.5198i	0.0158222	+	1.96178i
$516$		0			0
$517$	−1.52374	−	1.52374i	−0.0670141	−	0.0670141i
$518$	2.62312	−	16.9581i	0.115253	−	0.745096i
$519$		0			0
$520$	−2.36276	−	0.612720i	−0.103614	−	0.0268696i
$521$	−7.25859	+	4.19075i	−0.318005	+	0.183600i	−0.650503	−	0.759504i	$-0.725442\pi$
$521$	−7.25859	+	4.19075i	−0.318005	+	0.183600i	0.332498	+	0.943104i	$0.392108\pi$
$522$		0			0
$523$	9.82073	+	36.6515i	0.429430	+	1.60266i	0.754054	+	0.656813i	$0.228096\pi$
$523$	9.82073	+	36.6515i	0.429430	+	1.60266i	−0.324623	+	0.945843i	$0.605238\pi$
$524$	−6.00007			−0.262114
$525$		0			0
$526$	−11.1832			−0.487610
$527$	−0.995431	−	3.71500i	−0.0433617	−	0.161828i
$528$		0			0
$529$	−19.1573	+	11.0605i	−0.832925	+	0.480889i
$530$	15.9982	+	4.14872i	0.694919	+	0.180209i
$531$		0			0
$532$	−10.3430	−	8.31393i	−0.448428	−	0.360455i
$533$	−6.09790	−	6.09790i	−0.264129	−	0.264129i
$534$		0			0
$535$	−0.325775	−	40.3924i	−0.0140845	−	1.74632i
$536$	5.57082	−	3.21631i	0.240623	−	0.138924i
$537$		0			0
$538$	3.85117	−	3.85117i	0.166036	−	0.166036i
$539$	−3.08268	−	3.37430i	−0.132780	−	0.145341i
$540$		0			0
$541$	−2.55510	+	4.42556i	−0.109852	+	0.190270i	−0.915710	−	0.401839i	$-0.868371\pi$
$541$	−2.55510	+	4.42556i	−0.109852	+	0.190270i	0.805858	+	0.592109i	$0.201704\pi$
$542$	−20.5479	−	5.50578i	−0.882607	−	0.236494i
$543$		0			0
$544$	−1.85534	−	1.07118i	−0.0795469	−	0.0459265i
$545$	−24.2604	+	6.71074i	−1.03920	+	0.287456i
$546$		0			0
$547$	−20.5460	−	20.5460i	−0.878484	−	0.878484i	0.114894	−	0.993378i	$-0.463347\pi$
$547$	−20.5460	−	20.5460i	−0.878484	−	0.878484i	−0.993378	+	0.114894i	$0.963347\pi$
$548$	11.1872	−	2.99759i	0.477892	−	0.128051i
$549$		0			0
$550$	0.895690	+	3.13931i	0.0381923	+	0.133861i
$551$	42.5367	+	24.5586i	1.81212	+	1.04623i
$552$		0			0
$553$	11.4273	+	29.4505i	0.485937	+	1.25236i
$554$	−17.9725			−0.763578
$555$		0			0
$556$	5.21899	+	9.03956i	0.221335	+	0.383363i
$557$	33.6396	+	9.01371i	1.42536	+	0.381923i	0.887381	−	0.461037i	$-0.152522\pi$
$557$	33.6396	+	9.01371i	1.42536	+	0.381923i	0.537976	+	0.842960i	$0.319189\pi$
$558$		0			0
$559$			0.101464i			0.00429148i
$560$	−5.87605	+	0.687067i	−0.248308	+	0.0290339i
$561$		0			0
$562$	−18.5381	+	4.96726i	−0.781982	+	0.209531i
$563$	2.03247	−	7.58528i	0.0856584	−	0.319681i	−0.909780	−	0.415091i	$-0.863750\pi$
$563$	2.03247	−	7.58528i	0.0856584	−	0.319681i	0.995438	+	0.0954101i	$0.0304162\pi$
$564$		0			0
$565$	−6.72807	−	11.4393i	−0.283052	−	0.481254i
$566$			21.5989i			0.907869i
$567$		0			0
$568$	−5.43466	+	5.43466i	−0.228033	+	0.228033i
$569$	10.0967	−	17.4880i	0.423277	−	0.733137i	−0.572981	−	0.819569i	$-0.694213\pi$
$569$	10.0967	−	17.4880i	0.423277	−	0.733137i	0.996258	+	0.0864319i	$0.0275465\pi$
$570$		0			0
$571$	11.0336	+	19.1107i	0.461741	+	0.799760i	0.999048	−	0.0436275i	$-0.0138915\pi$
$571$	11.0336	+	19.1107i	0.461741	+	0.799760i	−0.537306	+	0.843387i	$0.680558\pi$
$572$	−0.184469	−	0.688447i	−0.00771303	−	0.0287854i
$573$		0			0
$574$	−19.1250	−	8.43233i	−0.798262	−	0.351959i
$575$	−4.54724	−	1.14015i	−0.189633	−	0.0475474i
$576$		0			0
$577$	−6.61199	+	24.6763i	−0.275261	+	1.02729i	0.680406	+	0.732836i	$0.261804\pi$
$577$	−6.61199	+	24.6763i	−0.275261	+	1.02729i	−0.955666	+	0.294451i	$0.904863\pi$
$578$	−3.21202	+	11.9874i	−0.133602	+	0.498611i
$579$		0			0
$580$	21.1046	−	5.83779i	0.876321	−	0.242401i
$581$	0.339196	+	3.11879i	0.0140722	+	0.129389i
$582$		0			0
$583$	1.24903	+	4.66146i	0.0517297	+	0.193058i
$584$	−4.98435	−	8.63316i	−0.206254	−	0.357243i
$585$		0			0
$586$	7.15766	−	12.3974i	0.295680	−	0.512133i
$587$	−29.2059	+	29.2059i	−1.20546	+	1.20546i	−0.232975	+	0.972483i	$0.574846\pi$
$587$	−29.2059	+	29.2059i	−1.20546	+	1.20546i	−0.972483	+	0.232975i	$0.925154\pi$
$588$		0			0
$589$		−	9.00437i		−	0.371019i
$590$	−13.0738	+	7.68940i	−0.538239	+	0.316567i
$591$		0			0
$592$	1.67864	−	6.26479i	0.0689919	−	0.257481i
$593$	9.46544	−	2.53626i	0.388699	−	0.104152i	−0.0591765	−	0.998248i	$-0.518847\pi$
$593$	9.46544	−	2.53626i	0.388699	−	0.104152i	0.447875	+	0.894096i	$0.352181\pi$
$594$		0			0
$595$	−4.67996	−	11.7787i	−0.191860	−	0.482879i
$596$		−	4.97249i		−	0.203681i
$597$		0			0
$598$	0.988620	+	0.264900i	0.0404277	+	0.0108326i
$599$	−8.90006	−	15.4154i	−0.363647	−	0.629854i	0.624911	−	0.780696i	$-0.285135\pi$
$599$	−8.90006	−	15.4154i	−0.363647	−	0.629854i	−0.988558	+	0.150841i	$0.951802\pi$
$600$		0			0
$601$	−22.8923			−0.933798			−0.466899	−	0.884311i	$-0.654629\pi$
$601$	−22.8923			−0.933798			−0.466899	+	0.884311i	$0.654629\pi$
$602$	0.0889589	+	0.229266i	0.00362569	+	0.00934419i
$603$		0			0
$604$	−19.2318	−	11.1035i	−0.782532	−	0.451795i
$605$	16.5831	−	16.8528i	0.674199	−	0.685163i
$606$		0			0
$607$	11.6477	−	3.12100i	0.472767	−	0.126677i	−0.0145659	−	0.999894i	$-0.504637\pi$
$607$	11.6477	−	3.12100i	0.472767	−	0.126677i	0.487333	+	0.873216i	$0.337970\pi$
$608$	−3.54663	−	3.54663i	−0.143835	−	0.143835i
$609$		0			0
$610$	−16.8800	−	9.56500i	−0.683452	−	0.387275i
$611$	3.12009	+	1.80138i	0.126225	+	0.0728762i
$612$		0			0
$613$	5.80020	+	1.55416i	0.234268	+	0.0627719i	0.374043	−	0.927411i	$-0.377971\pi$
$613$	5.80020	+	1.55416i	0.234268	+	0.0627719i	−0.139775	+	0.990183i	$0.544638\pi$
$614$	12.4787	−	21.6137i	0.503599	−	0.872259i
$615$		0			0
$616$	−1.02042	−	1.39387i	−0.0411138	−	0.0561604i
$617$	−29.7410	+	29.7410i	−1.19733	+	1.19733i	−0.222361	+	0.974964i	$0.571376\pi$
$617$	−29.7410	+	29.7410i	−1.19733	+	1.19733i	−0.974964	+	0.222361i	$0.928624\pi$
$618$		0			0
$619$	1.14774	−	0.662650i	0.0461317	−	0.0266341i	−0.476757	−	0.879035i	$-0.658188\pi$
$619$	1.14774	−	0.662650i	0.0461317	−	0.0266341i	0.522888	+	0.852401i	$0.324854\pi$
$620$	−2.86132	−	2.81554i	−0.114914	−	0.113075i
$621$		0			0
$622$	−4.92227	−	4.92227i	−0.197365	−	0.197365i
$623$	−42.6779	+	16.5597i	−1.70985	+	0.663450i
$624$		0			0
$625$	13.1918	+	21.2362i	0.527673	+	0.849447i
$626$	4.01929	−	2.32054i	0.160643	−	0.0927473i
$627$		0			0
$628$	2.35366	+	8.78399i	0.0939214	+	0.350519i
$629$	13.8949			0.554025
$630$		0			0
$631$	−12.2808			−0.488892			−0.244446	−	0.969663i	$-0.578606\pi$
$631$	−12.2808			−0.488892			−0.244446	+	0.969663i	$0.578606\pi$
$632$	3.09026	+	11.5330i	0.122924	+	0.458758i
$633$		0			0
$634$	−25.0423	+	14.4582i	−0.994558	+	0.574209i
$635$	−1.48906	−	2.53175i	−0.0590916	−	0.100470i
$636$		0			0
$637$	6.43843	+	4.11532i	0.255100	+	0.163055i
$638$	4.52112	+	4.52112i	0.178993	+	0.178993i
$639$		0			0
$640$	−2.23600	+	0.0180339i	−0.0883855	+	0.000712851i
$641$	−0.0942649	+	0.0544239i	−0.00372324	+	0.00214961i	−0.501860	−	0.864949i	$-0.667351\pi$
$641$	−0.0942649	+	0.0544239i	−0.00372324	+	0.00214961i	0.498137	+	0.867098i	$0.334018\pi$
$642$		0			0
$643$	−4.92268	+	4.92268i	−0.194132	+	0.194132i	−0.797479	−	0.603347i	$-0.793833\pi$
$643$	−4.92268	+	4.92268i	−0.194132	+	0.194132i	0.603347	+	0.797479i	$0.293833\pi$
$644$	2.46611	−	0.268212i	0.0971785	−	0.0105690i
$645$		0			0
$646$	5.37271	−	9.30580i	0.211386	−	0.366132i
$647$	29.9054	+	8.01312i	1.17570	+	0.315028i	0.793220	−	0.608935i	$-0.208403\pi$
$647$	29.9054	+	8.01312i	1.17570	+	0.315028i	0.382481	+	0.923963i	$0.375070\pi$
$648$		0			0
$649$	−3.83545	−	2.21440i	−0.150554	−	0.0869226i
$650$	−2.80492	−	4.68218i	−0.110018	−	0.183650i
$651$		0			0
$652$	10.6252	+	10.6252i	0.416115	+	0.416115i
$653$	−31.1115	+	8.33630i	−1.21749	+	0.326224i	−0.809695	−	0.586851i	$-0.800368\pi$
$653$	−31.1115	+	8.33630i	−1.21749	+	0.326224i	−0.407791	+	0.913075i	$0.633701\pi$
$654$		0			0
$655$	−9.56314	−	9.41012i	−0.373663	−	0.367684i
$656$	−6.84160	−	3.95000i	−0.267120	−	0.154222i
$657$		0			0
$658$	8.62944	+	1.33482i	0.336411	+	0.0520368i
$659$	−10.4880			−0.408556			−0.204278	−	0.978913i	$-0.565485\pi$
$659$	−10.4880			−0.408556			−0.204278	+	0.978913i	$0.565485\pi$
$660$		0			0
$661$	−12.9829	−	22.4870i	−0.504975	−	0.874643i	−0.999983	−	0.00575465i	$-0.998168\pi$
$661$	−12.9829	−	22.4870i	−0.504975	−	0.874643i	0.495008	−	0.868888i	$-0.335165\pi$
$662$	10.4641	+	2.80386i	0.406700	+	0.108975i
$663$		0			0
$664$			1.18574i			0.0460158i
$665$	−3.44612	−	29.4724i	−0.133635	−	1.14289i
$666$		0			0
$667$	−8.86877	+	2.37638i	−0.343400	+	0.0920138i
$668$	5.92990	−	22.1307i	0.229435	−	0.856262i
$669$		0			0
$670$	13.9232	+	3.61063i	0.537902	+	0.139491i
$671$		−	5.66516i		−	0.218701i
$672$		0			0
$673$	−10.2926	+	10.2926i	−0.396752	+	0.396752i	−0.877086	−	0.480334i	$-0.840516\pi$
$673$	−10.2926	+	10.2926i	−0.396752	+	0.396752i	0.480334	+	0.877086i	$0.340516\pi$
$674$	9.79679	−	16.9685i	0.377358	−	0.653604i
$675$		0			0
$676$	−5.90419	−	10.2264i	−0.227084	−	0.393322i
$677$	−9.27935	−	34.6310i	−0.356634	−	1.33098i	−0.878415	−	0.477898i	$-0.841399\pi$
$677$	−9.27935	−	34.6310i	−0.356634	−	1.33098i	0.521781	−	0.853080i	$-0.325268\pi$
$678$		0			0
$679$	−3.47904	−	31.9885i	−0.133513	−	1.22761i
$680$	−1.27714	−	4.61708i	−0.0489761	−	0.177057i
$681$		0			0
$682$	0.303373	−	1.13220i	0.0116168	−	0.0433544i
$683$	−3.88960	+	14.5162i	−0.148831	+	0.555447i	0.850723	+	0.525614i	$0.176164\pi$
$683$	−3.88960	+	14.5162i	−0.148831	+	0.555447i	−0.999555	+	0.0298330i	$0.990502\pi$
$684$		0			0
$685$	22.5318	+	12.7675i	0.860895	+	0.487823i
$686$	18.1562	+	3.65398i	0.693208	+	0.139510i
$687$		0			0
$688$	0.0240570	+	0.0897819i	0.000917164	+	0.00342290i
$689$	−4.03420	−	6.98745i	−0.153691	−	0.266200i
$690$		0			0
$691$	9.47524	−	16.4116i	0.360455	−	0.624327i	−0.627581	−	0.778552i	$-0.715955\pi$
$691$	9.47524	−	16.4116i	0.360455	−	0.624327i	0.988036	+	0.154225i	$0.0492880\pi$
$692$	−1.37112	+	1.37112i	−0.0521222	+	0.0521222i
$693$		0			0
$694$			23.0504i			0.874981i
$695$	−5.85883	+	22.5927i	−0.222238	+	0.856992i
$696$		0			0
$697$	4.38042	−	16.3479i	0.165920	−	0.619223i
$698$	−12.2185	+	3.27395i	−0.462478	+	0.123921i
$699$		0			0
$700$	−10.4430	−	8.12054i	−0.394709	−	0.306928i
$701$			23.9293i			0.903798i	0.892069	+	0.451899i	$0.149253\pi$
$701$			23.9293i			0.903798i	−0.892069	+	0.451899i	$0.850747\pi$
$702$		0			0
$703$	31.4222	+	8.41956i	1.18511	+	0.317550i
$704$	−0.326459	−	0.565444i	−0.0123039	−	0.0213110i
$705$		0			0
$706$	−30.3760			−1.14321
$707$	4.73819	+	0.732915i	0.178198	+	0.0275641i
$708$		0			0
$709$	1.87883	+	1.08474i	0.0705608	+	0.0407383i	0.534865	−	0.844937i	$-0.320362\pi$
$709$	1.87883	+	1.08474i	0.0705608	+	0.0407383i	−0.464305	+	0.885676i	$0.653696\pi$
$710$	−17.1854	+	0.138604i	−0.644955	+	0.00520173i
$711$		0			0
$712$	−16.7129	+	4.47821i	−0.626342	+	0.167828i
$713$	1.19021	+	1.19021i	0.0445739	+	0.0445739i
$714$		0			0
$715$	0.785702	−	1.38658i	0.0293836	−	0.0518553i
$716$	18.9023	+	10.9132i	0.706412	+	0.407847i
$717$		0			0
$718$	−8.01659	−	2.14804i	−0.299176	−	0.0801641i
$719$	12.5298	−	21.7022i	0.467281	−	0.809354i	−0.532020	−	0.846732i	$-0.678567\pi$
$719$	12.5298	−	21.7022i	0.467281	−	0.809354i	0.999301	+	0.0373772i	$0.0119003\pi$
$720$		0			0
$721$	21.2522	−	48.2011i	0.791472	−	1.79510i
$722$	4.35377	−	4.35377i	0.162031	−	0.162031i
$723$		0			0
$724$	9.18809	−	5.30475i	0.341473	−	0.197149i
$725$	42.7930	+	23.7946i	1.58929	+	0.883710i
$726$		0			0
$727$	−10.6897	−	10.6897i	−0.396460	−	0.396460i	0.480523	−	0.876982i	$-0.340447\pi$
$727$	−10.6897	−	10.6897i	−0.396460	−	0.396460i	−0.876982	+	0.480523i	$0.840447\pi$
$728$	2.25105	+	1.80944i	0.0834296	+	0.0670623i
$729$		0			0
$730$	5.59542	−	21.5770i	0.207096	−	0.798601i
$731$	−0.172452	+	0.0995651i	−0.00637836	+	0.00368255i
$732$		0			0
$733$	7.00900	+	26.1579i	0.258883	+	0.966165i	0.965889	+	0.258957i	$0.0833789\pi$
$733$	7.00900	+	26.1579i	0.258883	+	0.966165i	−0.707006	+	0.707208i	$0.749954\pi$
$734$	19.1797			0.707937
$735$		0			0
$736$	0.937600			0.0345604
$737$	1.08703	+	4.05687i	0.0400414	+	0.149437i
$738$		0			0
$739$	−40.4463	+	23.3517i	−1.48784	+	0.859006i	−0.999904	−	0.0138727i	$-0.995584\pi$
$739$	−40.4463	+	23.3517i	−1.48784	+	0.859006i	−0.487938	+	0.872878i	$0.662251\pi$
$740$	12.5008	−	7.35239i	0.459538	−	0.270279i
$741$		0			0
$742$	−15.2418	−	12.2517i	−0.559545	−	0.449773i
$743$	−25.2408	−	25.2408i	−0.925997	−	0.925997i	0.0714474	−	0.997444i	$-0.477238\pi$
$743$	−25.2408	−	25.2408i	−0.925997	−	0.925997i	−0.997444	+	0.0714474i	$0.977238\pi$
$744$		0			0
$745$	7.79853	−	7.92535i	0.285716	−	0.290362i
$746$	−1.44230	+	0.832715i	−0.0528065	+	0.0304879i
$747$		0			0
$748$	0.989090	−	0.989090i	0.0361647	−	0.0361647i
$749$	−19.2819	+	43.7324i	−0.704545	+	1.59795i
$750$		0			0
$751$	−24.7674	+	42.8984i	−0.903775	+	1.56538i	−0.0812216	+	0.996696i	$0.525882\pi$
$751$	−24.7674	+	42.8984i	−0.903775	+	1.56538i	−0.822553	+	0.568688i	$0.807451\pi$
$752$	3.18795	+	0.854209i	0.116253	+	0.0311498i
$753$		0			0
$754$	−9.25766	−	5.34491i	−0.337144	−	0.194650i
$755$	−13.2384	−	47.8591i	−0.481796	−	1.74177i
$756$		0			0
$757$	−27.1533	−	27.1533i	−0.986902	−	0.986902i	0.0130130	−	0.999915i	$-0.495858\pi$
$757$	−27.1533	−	27.1533i	−0.986902	−	0.986902i	−0.999915	+	0.0130130i	$0.995858\pi$
$758$	−10.9837	+	2.94308i	−0.398946	+	0.106897i
$759$		0			0
$760$	−0.0904523	−	11.2151i	−0.00328105	−	0.406813i
$761$	6.77173	+	3.90966i	0.245475	+	0.141725i	0.617691	−	0.786421i	$-0.288068\pi$
$761$	6.77173	+	3.90966i	0.245475	+	0.141725i	−0.372216	+	0.928146i	$0.621402\pi$
$762$		0			0
$763$	29.4333	+	4.55281i	1.06556	+	0.164823i
$764$	0.665334			0.0240709
$765$		0			0
$766$	9.78557	+	16.9491i	0.353567	+	0.612396i
$767$	7.15218	+	1.91642i	0.258250	+	0.0691980i
$768$		0			0
$769$			2.94104i			0.106056i	0.998593	+	0.0530282i	$0.0168873\pi$
$769$			2.94104i			0.106056i	−0.998593	+	0.0530282i	$0.983113\pi$
$770$	0.559666	−	3.82195i	0.0201690	−	0.137734i
$771$		0			0
$772$	20.1993	−	5.41238i	0.726988	−	0.194796i
$773$	−6.23578	+	23.2723i	−0.224286	+	0.837045i	0.758404	+	0.651785i	$0.225979\pi$
$773$	−6.23578	+	23.2723i	−0.224286	+	0.837045i	−0.982690	+	0.185260i	$0.940687\pi$
$774$		0			0
$775$	−0.144781	−	8.97503i	−0.00520070	−	0.322393i
$776$		−	12.1618i		−	0.436584i
$777$		0			0
$778$	9.42599	−	9.42599i	0.337938	−	0.337938i
$779$	19.8120	−	34.3154i	0.709838	−	1.22948i
$780$		0			0
$781$	−2.50909	−	4.34587i	−0.0897823	−	0.155508i
$782$	0.519884	+	1.94023i	0.0185910	+	0.0693825i
$783$		0			0
$784$	6.67285	+	2.11495i	0.238316	+	0.0755340i
$785$	−10.0249	+	17.6916i	−0.357803	+	0.631440i
$786$		0			0
$787$	5.67382	−	21.1750i	0.202250	−	0.754807i	−0.788020	−	0.615649i	$-0.788894\pi$
$787$	5.67382	−	21.1750i	0.202250	−	0.754807i	0.990270	−	0.139158i	$-0.0444395\pi$
$788$	−2.07671	+	7.75039i	−0.0739798	+	0.276096i
$789$		0			0
$790$	−13.1622	+	23.2283i	−0.468291	+	0.826426i
$791$	1.69779	+	15.6106i	0.0603666	+	0.555050i
$792$		0			0
$793$	2.45142	+	9.14883i	0.0870525	+	0.324884i
$794$	6.93973	+	12.0200i	0.246282	+	0.426572i
$795$		0			0
$796$	7.30475	−	12.6522i	0.258910	−	0.448445i
$797$	1.72825	−	1.72825i	0.0612178	−	0.0612178i	−0.675835	−	0.737053i	$-0.736217\pi$
$797$	1.72825	−	1.72825i	0.0612178	−	0.0612178i	0.737053	+	0.675835i	$0.236217\pi$
$798$		0			0
$799$			7.07067i			0.250142i
$800$	−3.59210	−	3.47805i	−0.127000	−	0.122968i
$801$		0			0
$802$	−5.80475	+	21.6636i	−0.204973	+	0.764969i
$803$	6.28697	−	1.68459i	0.221862	−	0.0594478i
$804$		0			0
$805$	4.35123	+	3.44021i	0.153361	+	0.121251i
$806$			1.95971i			0.0690277i
$807$		0			0
$808$	1.75042	+	0.469023i	0.0615795	+	0.0165002i
$809$	−0.419280	−	0.726214i	−0.0147411	−	0.0255323i	0.858561	−	0.512712i	$-0.171359\pi$
$809$	−0.419280	−	0.726214i	−0.0147411	−	0.0255323i	−0.873302	+	0.487180i	$0.838026\pi$
$810$		0			0
$811$	−25.2799			−0.887699			−0.443849	−	0.896101i	$-0.646387\pi$
$811$	−25.2799			−0.887699			−0.443849	+	0.896101i	$0.646387\pi$
$812$	−25.6045	−	3.96057i	−0.898543	−	0.138989i
$813$		0			0
$814$	3.66735	+	2.11734i	0.128540	+	0.0742128i
$815$	0.270982	+	33.5987i	0.00949209	+	1.17691i
$816$		0			0
$817$	−0.450318	+	0.120662i	−0.0157546	+	0.00422144i
$818$	25.9187	+	25.9187i	0.906225	+	0.906225i
$819$		0			0
$820$	−4.70949	−	17.0256i	−0.164462	−	0.594559i
$821$	7.48620	+	4.32216i	0.261270	+	0.150844i	0.624914	−	0.780694i	$-0.285134\pi$
$821$	7.48620	+	4.32216i	0.261270	+	0.150844i	−0.363644	+	0.931538i	$0.618467\pi$
$822$		0			0
$823$	−28.1292	−	7.53721i	−0.980524	−	0.262731i	−0.267259	−	0.963625i	$-0.586118\pi$
$823$	−28.1292	−	7.53721i	−0.980524	−	0.262731i	−0.713265	+	0.700894i	$0.752784\pi$
$824$	9.95526	−	17.2430i	0.346808	−	0.600689i
$825$		0			0
$826$	17.8411	−	1.94038i	0.620772	−	0.0675145i
$827$	17.2791	−	17.2791i	0.600853	−	0.600853i	−0.339686	−	0.940539i	$-0.610321\pi$
$827$	17.2791	−	17.2791i	0.600853	−	0.600853i	0.940539	+	0.339686i	$0.110321\pi$
$828$		0			0
$829$	0.217326	−	0.125473i	0.00754804	−	0.00435787i	−0.496221	−	0.868196i	$-0.665280\pi$
$829$	0.217326	−	0.125473i	0.00754804	−	0.00435787i	0.503769	+	0.863838i	$0.331946\pi$
$830$	−1.85964	+	1.88988i	−0.0645492	+	0.0655988i
$831$		0			0
$832$	0.771886	+	0.771886i	0.0267603	+	0.0267603i
$833$	−0.676611	+	14.9812i	−0.0234432	+	0.519069i
$834$		0			0
$835$	44.1596	−	25.9727i	1.52821	−	0.898822i
$836$	2.83609	−	1.63742i	0.0980882	−	0.0566313i
$837$		0			0
$838$	1.48657	+	5.54796i	0.0513527	+	0.191651i
$839$	35.4029			1.22224			0.611122	−	0.791537i	$-0.290719\pi$
$839$	35.4029			1.22224			0.611122	+	0.791537i	$0.290719\pi$
$840$		0			0
$841$	66.8969			2.30679
$842$	−6.36826	−	23.7667i	−0.219465	−	0.819054i
$843$		0			0
$844$	−18.8994	+	10.9116i	−0.650544	+	0.375592i
$845$	6.62803	−	25.5589i	0.228011	−	0.879254i
$846$		0			0
$847$	−26.0809	+	10.1198i	−0.896149	+	0.347720i
$848$	−5.22642	−	5.22642i	−0.179476	−	0.179476i
$849$		0			0
$850$	5.20557	−	9.36187i	0.178550	−	0.321109i
$851$	−5.26636	+	3.04054i	−0.180529	+	0.104228i
$852$		0			0
$853$	28.1055	−	28.1055i	0.962316	−	0.962316i	−0.0369997	−	0.999315i	$-0.511780\pi$
$853$	28.1055	−	28.1055i	0.962316	−	0.962316i	0.999315	+	0.0369997i	$0.0117800\pi$
$854$	13.5604	+	18.5232i	0.464028	+	0.633850i
$855$		0			0
$856$	−9.03232	+	15.6444i	−0.308718	+	0.534716i
$857$	−35.0632	−	9.39516i	−1.19774	−	0.320932i	−0.395797	−	0.918338i	$-0.629532\pi$
$857$	−35.0632	−	9.39516i	−1.19774	−	0.320932i	−0.801939	+	0.597406i	$0.796198\pi$
$858$		0			0
$859$	21.6216	+	12.4833i	0.737721	+	0.425924i	0.821240	−	0.570583i	$-0.193283\pi$
$859$	21.6216	+	12.4833i	0.737721	+	0.425924i	−0.0835190	+	0.996506i	$0.526616\pi$
$860$	−0.102465	+	0.180827i	−0.00349403	+	0.00616616i
$861$		0			0
$862$	−1.77846	−	1.77846i	−0.0605745	−	0.0605745i
$863$	−3.12652	+	0.837748i	−0.106428	+	0.0285173i	−0.311640	−	0.950200i	$-0.600878\pi$
$863$	−3.12652	+	0.837748i	−0.106428	+	0.0285173i	0.205212	+	0.978718i	$0.434212\pi$
$864$		0			0
$865$	−4.33572	+	0.0349687i	−0.147419	+	0.00118897i
$866$	3.40290	+	1.96467i	0.115635	+	0.0667621i
$867$		0			0
$868$	1.71817	+	4.42810i	0.0583186	+	0.150300i
$869$	−7.79573			−0.264452
$870$		0			0
$871$	−3.51097	−	6.08117i	−0.118965	−	0.206053i
$872$	10.8735	+	2.91353i	0.368222	+	0.0986647i
$873$		0			0
$874$			4.70271i			0.159072i
$875$	−3.90878	−	29.3210i	−0.132141	−	0.991231i
$876$		0			0
$877$	23.3401	−	6.25395i	0.788138	−	0.211181i	0.157769	−	0.987476i	$-0.449570\pi$
$877$	23.3401	−	6.25395i	0.788138	−	0.211181i	0.630370	+	0.776295i	$0.282903\pi$
$878$	7.23418	−	26.9983i	0.244142	−	0.911150i
$879$		0			0
$880$	0.366482	−	1.41322i	0.0123541	−	0.0476397i
$881$		−	18.8570i		−	0.635308i	−0.948207	−	0.317654i	$-0.897105\pi$
$881$		−	18.8570i		−	0.635308i	0.948207	−	0.317654i	$-0.102895\pi$
$882$		0			0
$883$	−6.13769	+	6.13769i	−0.206550	+	0.206550i	−0.802799	−	0.596250i	$-0.796657\pi$
$883$	−6.13769	+	6.13769i	−0.206550	+	0.206550i	0.596250	+	0.802799i	$0.296657\pi$
$884$	−1.16931	+	2.02531i	−0.0393282	+	0.0681185i
$885$		0			0
$886$	11.7378	+	20.3305i	0.394339	+	0.683016i
$887$	−6.04124	−	22.5462i	−0.202845	−	0.757028i	−0.990096	−	0.140395i	$-0.955163\pi$
$887$	−6.04124	−	22.5462i	−0.202845	−	0.757028i	0.787251	−	0.616633i	$-0.211504\pi$
$888$		0			0
$889$	0.375757	+	3.45495i	0.0126025	+	0.115875i
$890$	−33.6610	−	19.0739i	−1.12832	−	0.639358i
$891$		0			0
$892$	−1.22872	+	4.58563i	−0.0411404	+	0.153538i
$893$	−4.28445	+	15.9898i	−0.143374	+	0.535078i
$894$		0			0
$895$	13.0116	+	47.0391i	0.434929	+	1.57234i
$896$	2.42089	+	1.06738i	0.0808761	+	0.0356588i
$897$		0			0
$898$	−1.57044	−	5.86095i	−0.0524062	−	0.195582i
$899$	−8.79012	−	15.2249i	−0.293167	−	0.507780i
$900$		0			0
$901$	7.91739	−	13.7133i	0.263766	−	0.456857i
$902$	3.64729	−	3.64729i	0.121442	−	0.121442i
$903$		0			0
$904$			5.93505i			0.197397i
$905$	22.9640	+	5.95510i	0.763348	+	0.197954i
$906$		0			0
$907$	−15.1487	+	56.5358i	−0.503005	+	1.87724i	−0.0234563	+	0.999725i	$0.507467\pi$
$907$	−15.1487	+	56.5358i	−0.503005	+	1.87724i	−0.479549	+	0.877515i	$0.659200\pi$
$908$	−20.4660	+	5.48385i	−0.679189	+	0.181988i
$909$		0			0
$910$	0.750010	+	6.41436i	0.0248626	+	0.212634i
$911$		−	48.1428i		−	1.59504i	−0.603290	−	0.797522i	$-0.706144\pi$
$911$		−	48.1428i		−	1.59504i	0.603290	−	0.797522i	$-0.293856\pi$
$912$		0			0
$913$	−0.747813	−	0.200376i	−0.0247490	−	0.00663148i
$914$	2.79619	+	4.84314i	0.0924897	+	0.160197i
$915$		0			0
$916$	19.3950			0.640828
$917$	5.74249	+	14.7996i	0.189634	+	0.488727i
$918$		0			0
$919$	35.2708	+	20.3636i	1.16348	+	0.671733i	0.952134	−	0.305680i	$-0.0988837\pi$
$919$	35.2708	+	20.3636i	1.16348	+	0.671733i	0.211341	+	0.977412i	$0.432217\pi$
$920$	1.49438	+	1.47047i	0.0492684	+	0.0484800i
$921$		0			0
$922$	−14.1344	+	3.78731i	−0.465493	+	0.124728i
$923$	5.93254	+	5.93254i	0.195272	+	0.195272i
$924$		0			0
$925$	31.4552	+	7.88689i	1.03424	+	0.259319i
$926$	−24.3600	−	14.0643i	−0.800520	−	0.462181i
$927$		0			0
$928$	−9.45902	−	2.53454i	−0.310508	−	0.0832002i
$929$	28.9809	−	50.1964i	0.950833	−	1.64689i	0.207206	−	0.978297i	$-0.433563\pi$
$929$	28.9809	−	50.1964i	0.950833	−	1.64689i	0.743628	−	0.668594i	$-0.233104\pi$
$930$		0			0
$931$	−10.6079	+	33.4690i	−0.347661	+	1.09690i
$932$	4.42479	−	4.42479i	0.144939	−	0.144939i
$933$		0			0
$934$	−3.94011	+	2.27482i	−0.128924	+	0.0744345i
$935$	3.12768	−	0.0252255i	0.102286	−	0.000824962i
$936$		0			0
$937$	37.3931	+	37.3931i	1.22158	+	1.22158i	0.967071	+	0.254508i	$0.0819135\pi$
$937$	37.3931	+	37.3931i	1.22158	+	1.22158i	0.254508	+	0.967071i	$0.418087\pi$
$938$	−13.2650	−	10.6626i	−0.433116	−	0.348147i
$939$		0			0
$940$	3.74140	+	6.36125i	0.122031	+	0.207481i
$941$	−40.6115	+	23.4471i	−1.32390	+	0.764353i	−0.984348	−	0.176235i	$-0.943608\pi$
$941$	−40.6115	+	23.4471i	−1.32390	+	0.764353i	−0.339550	+	0.940588i	$0.610275\pi$
$942$		0			0
$943$	1.91708	+	7.15465i	0.0624288	+	0.232987i
$944$	6.78307			0.220770
$945$		0			0
$946$	−0.0606881			−0.00197314
$947$	−1.07230	−	4.00187i	−0.0348450	−	0.130043i	0.946312	−	0.323254i	$-0.104777\pi$
$947$	−1.07230	−	4.00187i	−0.0348450	−	0.130043i	−0.981157	+	0.193210i	$0.938110\pi$
$948$		0			0
$949$	−9.42405	+	5.44098i	−0.305918	+	0.176622i
$950$	17.4448	−	18.0169i	0.565985	−	0.584544i
$951$		0			0
$952$	−0.866459	+	5.60153i	−0.0280821	+	0.181547i
$953$	−19.4496	−	19.4496i	−0.630036	−	0.630036i	0.318041	−	0.948077i	$-0.396975\pi$
$953$	−19.4496	−	19.4496i	−0.630036	−	0.630036i	−0.948077	+	0.318041i	$0.896975\pi$
$954$		0			0
$955$	1.06044	+	1.04347i	0.0343149	+	0.0337658i
$956$	−17.1340	+	9.89233i	−0.554154	+	0.319941i
$957$		0			0
$958$	−3.13368	+	3.13368i	−0.101245	+	0.101245i
$959$	−18.1007	−	24.7251i	−0.584502	−	0.798416i
$960$		0			0
$961$	13.8886	−	24.0557i	0.448018	−	0.775990i
$962$	−6.83872	−	1.83243i	−0.220489	−	0.0590799i
$963$		0			0
$964$	2.61328	+	1.50878i	0.0841682	+	0.0485945i
$965$	40.6829	+	23.0528i	1.30963	+	0.742096i
$966$		0			0
$967$	−4.31421	−	4.31421i	−0.138736	−	0.138736i	0.634328	−	0.773064i	$-0.281277\pi$
$967$	−4.31421	−	4.31421i	−0.138736	−	0.138736i	−0.773064	+	0.634328i	$0.781277\pi$
$968$	−10.2134	+	2.73667i	−0.328271	+	0.0879600i
$969$		0			0
$970$	19.0738	−	19.3840i	0.612423	−	0.622382i
$971$	26.3375	+	15.2060i	0.845211	+	0.487983i	0.859032	−	0.511921i	$-0.171066\pi$
$971$	26.3375	+	15.2060i	0.845211	+	0.487983i	−0.0138209	+	0.999904i	$0.504399\pi$
$972$		0			0
$973$	17.3019	−	21.5246i	0.554672	−	0.690046i
$974$	−12.4744			−0.399705
$975$		0			0
$976$	4.33834	+	7.51422i	0.138867	+	0.240524i
$977$	−2.22860	−	0.597152i	−0.0712993	−	0.0191046i	0.222993	−	0.974820i	$-0.428417\pi$
$977$	−2.22860	−	0.597152i	−0.0712993	−	0.0191046i	−0.294292	+	0.955715i	$0.595084\pi$
$978$		0			0
$979$		−	11.2971i		−	0.361056i
$980$	7.31850	+	13.8362i	0.233781	+	0.441980i
$981$		0			0
$982$	25.3477	−	6.79189i	0.808877	−	0.216738i
$983$	1.52430	−	5.68876i	0.0486175	−	0.181443i	−0.937347	−	0.348397i	$-0.886726\pi$
$983$	1.52430	−	5.68876i	0.0486175	−	0.181443i	0.985965	+	0.166953i	$0.0533929\pi$
$984$		0			0
$985$	−15.4652	+	9.09590i	−0.492761	+	0.289820i
$986$		−	20.9795i		−	0.668123i
$987$		0			0
$988$	−3.87154	+	3.87154i	−0.123170	+	0.123170i
$989$	0.0435745	−	0.0754733i	0.00138559	−	0.00239991i
$990$		0			0
$991$	27.1283	+	46.9876i	0.861759	+	1.49261i	0.870230	+	0.492646i	$0.163970\pi$
$991$	27.1283	+	46.9876i	0.861759	+	1.49261i	−0.00847044	+	0.999964i	$0.502696\pi$
$992$	0.464642	+	1.73407i	0.0147524	+	0.0550567i
$993$		0			0
$994$	18.6064	+	8.20367i	0.590159	+	0.260205i
$995$	31.4855	−	8.70927i	0.998157	−	0.276102i
$996$		0			0
$997$	−3.05872	+	11.4153i	−0.0968706	+	0.361526i	−0.997296	−	0.0734837i	$-0.976588\pi$
$997$	−3.05872	+	11.4153i	−0.0968706	+	0.361526i	0.900426	+	0.435009i	$0.143255\pi$
$998$	−2.64335	+	9.86512i	−0.0836738	+	0.312275i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.ce.c.107.1	yes	32
3.2	odd	2	inner	630.2.ce.c.107.8	yes	32
5.3	odd	4	inner	630.2.ce.c.233.1	yes	32
7.4	even	3	inner	630.2.ce.c.557.8	yes	32
15.8	even	4	inner	630.2.ce.c.233.8	yes	32
21.11	odd	6	inner	630.2.ce.c.557.1	yes	32
35.18	odd	12	inner	630.2.ce.c.53.8	yes	32
105.53	even	12	inner	630.2.ce.c.53.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ce.c.53.1	✓	32	105.53	even	12	inner
630.2.ce.c.53.8	yes	32	35.18	odd	12	inner
630.2.ce.c.107.1	yes	32	1.1	even	1	trivial
630.2.ce.c.107.8	yes	32	3.2	odd	2	inner
630.2.ce.c.233.1	yes	32	5.3	odd	4	inner
630.2.ce.c.233.8	yes	32	15.8	even	4	inner
630.2.ce.c.557.1	yes	32	21.11	odd	6	inner
630.2.ce.c.557.8	yes	32	7.4	even	3	inner

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-2.16447 - 0.561299i) q^{5} +(2.06214 + 1.65758i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-2.16447 - 0.561299i) q^{5} +(2.06214 + 1.65758i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.0180339 + 2.23600i) q^{10} +(-0.565444 + 0.326459i) q^{11} +(0.771886 - 0.771886i) q^{13} +(1.06738 - 2.42089i) q^{14} +(0.500000 - 0.866025i) q^{16} +(2.06936 + 0.554483i) q^{17} +(4.34372 + 2.50785i) q^{19} +(2.15514 - 0.596138i) q^{20} +(0.461683 + 0.461683i) q^{22} +(-0.905652 + 0.242669i) q^{23} +(4.36989 + 2.42983i) q^{25} +(-0.945363 - 0.545806i) q^{26} +(-2.61466 - 0.404442i) q^{28} +9.79270 q^{29} +(-0.897620 - 1.55472i) q^{31} +(-0.965926 - 0.258819i) q^{32} -2.14236i q^{34} +(-3.53304 - 4.74527i) q^{35} +(6.26479 - 1.67864i) q^{37} +(1.29816 - 4.84479i) q^{38} +(-1.13362 - 1.92741i) q^{40} -7.90000i q^{41} +(-0.0657249 + 0.0657249i) q^{43} +(0.326459 - 0.565444i) q^{44} +(0.468800 + 0.811985i) q^{46} +(0.854209 + 3.18795i) q^{47} +(1.50482 + 6.83634i) q^{49} +(1.21603 - 4.84987i) q^{50} +(-0.282530 + 1.05442i) q^{52} +(1.91300 - 7.13943i) q^{53} +(1.40713 - 0.389229i) q^{55} +(0.286062 + 2.63024i) q^{56} +(-2.53454 - 9.45902i) q^{58} +(3.39154 + 5.87431i) q^{59} +(-4.33834 + 7.51422i) q^{61} +(-1.26943 + 1.26943i) q^{62} +1.00000i q^{64} +(-2.10399 + 1.23747i) q^{65} +(1.66489 - 6.21344i) q^{67} +(-2.06936 + 0.554483i) q^{68} +(-3.66916 + 4.64082i) q^{70} +7.68577i q^{71} +(-9.62903 - 2.58009i) q^{73} +(-3.24289 - 5.61685i) q^{74} -5.01569 q^{76} +(-1.70716 - 0.264067i) q^{77} +(10.3402 + 5.96992i) q^{79} +(-1.56834 + 1.59384i) q^{80} +(-7.63081 + 2.04467i) q^{82} +(0.838447 + 0.838447i) q^{83} +(-4.16784 - 2.36169i) q^{85} +(0.0804962 + 0.0464745i) q^{86} +(-0.630670 - 0.168988i) q^{88} +(-8.65123 + 14.9844i) q^{89} +(2.87120 - 0.312269i) q^{91} +(0.662983 - 0.662983i) q^{92} +(2.85824 - 1.65021i) q^{94} +(-7.99421 - 7.86629i) q^{95} +(-8.59970 - 8.59970i) q^{97} +(6.21392 - 3.22292i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 12 q^{7}+O(q^{10}) \) 32 * q - 12 * q^7	\( 32 q - 12 q^{7} + 8 q^{13} + 16 q^{16} + 32 q^{22} - 16 q^{25} - 56 q^{31} + 20 q^{37} + 4 q^{40} + 24 q^{46} + 4 q^{52} + 12 q^{58} - 48 q^{61} + 8 q^{67} + 24 q^{70} + 48 q^{73} - 36 q^{82} - 136 q^{85} - 16 q^{88} - 40 q^{97}+O(q^{100}) \) 32 * q - 12 * q^7 + 8 * q^13 + 16 * q^16 + 32 * q^22 - 16 * q^25 - 56 * q^31 + 20 * q^37 + 4 * q^40 + 24 * q^46 + 4 * q^52 + 12 * q^58 - 48 * q^61 + 8 * q^67 + 24 * q^70 + 48 * q^73 - 36 * q^82 - 136 * q^85 - 16 * q^88 - 40 * q^97

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