LMFDB - Embedded newform 756.2.o.a.179.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(179,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 4]))

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

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

chi := DirichletCharacter("756.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.20
Character	$\chi$	$=$	756.179
Dual form			756.2.o.a.359.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.177841 + 1.40299i) q^{2} +(-1.93675 - 0.499017i) q^{4} +1.62292i q^{5} +(-1.09603 - 2.40805i) q^{7} +(1.04455 - 2.62848i) q^{8} +O(q^{10})$	\(q+(-0.177841 + 1.40299i) q^{2} +(-1.93675 - 0.499017i) q^{4} +1.62292i q^{5} +(-1.09603 - 2.40805i) q^{7} +(1.04455 - 2.62848i) q^{8} +(-2.27693 - 0.288621i) q^{10} +1.10792 q^{11} +(2.95905 - 5.12523i) q^{13} +(3.57338 - 1.10947i) q^{14} +(3.50196 + 1.93294i) q^{16} +(6.47792 + 3.74003i) q^{17} +(-3.12725 + 1.80552i) q^{19} +(0.809864 - 3.14318i) q^{20} +(-0.197034 + 1.55440i) q^{22} -0.527196 q^{23} +2.36614 q^{25} +(6.66439 + 5.06299i) q^{26} +(0.921081 + 5.21072i) q^{28} +(1.30418 - 0.752968i) q^{29} +(1.60482 - 0.926542i) q^{31} +(-3.33468 + 4.56945i) q^{32} +(-6.39925 + 8.42331i) q^{34} +(3.90807 - 1.77877i) q^{35} +(3.78593 + 6.55743i) q^{37} +(-1.97696 - 4.70858i) q^{38} +(4.26581 + 1.69521i) q^{40} +(-5.31155 - 3.06663i) q^{41} +(3.91977 - 2.26308i) q^{43} +(-2.14576 - 0.552871i) q^{44} +(0.0937571 - 0.739650i) q^{46} +(1.98329 - 3.43516i) q^{47} +(-4.59742 + 5.27861i) q^{49} +(-0.420796 + 3.31966i) q^{50} +(-8.28851 + 8.44965i) q^{52} +(-3.48372 - 2.01133i) q^{53} +1.79806i q^{55} +(-7.47438 + 0.365585i) q^{56} +(0.824468 + 1.96366i) q^{58} +(5.60375 + 9.70599i) q^{59} +(5.67256 - 9.82516i) q^{61} +(1.01452 + 2.41632i) q^{62} +(-5.81784 - 5.49115i) q^{64} +(8.31783 + 4.80230i) q^{65} +(11.8549 - 6.84441i) q^{67} +(-10.6797 - 10.4761i) q^{68} +(1.80058 + 5.79931i) q^{70} +8.08304 q^{71} +(-3.31356 + 5.73925i) q^{73} +(-9.87328 + 4.14543i) q^{74} +(6.95767 - 1.93628i) q^{76} +(-1.21432 - 2.66793i) q^{77} +(-1.60759 - 0.928144i) q^{79} +(-3.13700 + 5.68340i) q^{80} +(5.24705 - 6.90667i) q^{82} +(5.43313 + 9.41046i) q^{83} +(-6.06976 + 10.5131i) q^{85} +(2.47798 + 5.90185i) q^{86} +(1.15727 - 2.91215i) q^{88} +(-1.25062 + 0.722046i) q^{89} +(-15.5850 - 1.50812i) q^{91} +(1.02105 + 0.263080i) q^{92} +(4.46678 + 3.39344i) q^{94} +(-2.93021 - 5.07527i) q^{95} +(1.18819 + 2.05801i) q^{97} +(-6.58822 - 7.38887i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 3 q^{2} + q^{4}+O(q^{10}) $ 88 * q + 3 * q^2 + q^4	$ 88 q + 3 q^{2} + q^{4} + 2 q^{10} - 4 q^{13} + 3 q^{14} + q^{16} + 6 q^{20} - 6 q^{22} - 60 q^{25} + 6 q^{26} + 24 q^{29} - 27 q^{32} - 4 q^{34} - 4 q^{37} + 8 q^{40} + 12 q^{41} + 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} + 14 q^{52} + 66 q^{56} - 10 q^{58} + 2 q^{61} - 8 q^{64} - 18 q^{65} + 30 q^{70} - 4 q^{73} - 6 q^{76} + 30 q^{77} - 87 q^{80} - 4 q^{82} - 14 q^{85} - 18 q^{88} - 60 q^{89} - 24 q^{92} + 9 q^{94} - 4 q^{97} + 57 q^{98}+O(q^{100}) $ 88 * q + 3 * q^2 + q^4 + 2 * q^10 - 4 * q^13 + 3 * q^14 + q^16 + 6 * q^20 - 6 * q^22 - 60 * q^25 + 6 * q^26 + 24 * q^29 - 27 * q^32 - 4 * q^34 - 4 * q^37 + 8 * q^40 + 12 * q^41 + 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 + 14 * q^52 + 66 * q^56 - 10 * q^58 + 2 * q^61 - 8 * q^64 - 18 * q^65 + 30 * q^70 - 4 * q^73 - 6 * q^76 + 30 * q^77 - 87 * q^80 - 4 * q^82 - 14 * q^85 - 18 * q^88 - 60 * q^89 - 24 * q^92 + 9 * q^94 - 4 * q^97 + 57 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.177841	+	1.40299i	−0.125753	+	0.992062i
$2$	−0.177841	+	1.40299i	−0.125753	+	0.992062i
$3$		0			0
$3$		0			0
$4$	−1.93675	−	0.499017i	−0.968373	−	0.249509i
$5$			1.62292i			0.725791i	0.931830	+	0.362896i	$0.118212\pi$
$5$			1.62292i			0.725791i	−0.931830	+	0.362896i	$0.881788\pi$
$6$		0			0
$7$	−1.09603	−	2.40805i	−0.414262	−	0.910158i
$7$	−1.09603	−	2.40805i	−0.414262	−	0.910158i
$8$	1.04455	−	2.62848i	0.369303	−	0.929309i
$9$		0			0
$10$	−2.27693	−	0.288621i	−0.720030	−	0.0912701i
$11$	1.10792			0.334051			0.167025	−	0.985953i	$-0.446584\pi$
$11$	1.10792			0.334051			0.167025	+	0.985953i	$0.446584\pi$
$12$		0			0
$13$	2.95905	−	5.12523i	0.820694	−	1.42148i	−0.0844726	−	0.996426i	$-0.526921\pi$
$13$	2.95905	−	5.12523i	0.820694	−	1.42148i	0.905166	−	0.425058i	$-0.139746\pi$
$14$	3.57338	−	1.10947i	0.955027	−	0.296519i
$15$		0			0
$16$	3.50196	+	1.93294i	0.875491	+	0.483234i
$17$	6.47792	+	3.74003i	1.57113	+	0.907090i	0.996031	+	0.0890039i	$0.0283683\pi$
$17$	6.47792	+	3.74003i	1.57113	+	0.907090i	0.575095	+	0.818086i	$0.304965\pi$
$18$		0			0
$19$	−3.12725	+	1.80552i	−0.717440	+	0.414214i	−0.813810	−	0.581131i	$-0.802610\pi$
$19$	−3.12725	+	1.80552i	−0.717440	+	0.414214i	0.0963698	+	0.995346i	$0.469277\pi$
$20$	0.809864	−	3.14318i	0.181091	−	0.702836i
$21$		0			0
$22$	−0.197034	+	1.55440i	−0.0420077	+	0.331399i
$23$	−0.527196			−0.109928			−0.0549640	−	0.998488i	$-0.517504\pi$
$23$	−0.527196			−0.109928			−0.0549640	+	0.998488i	$0.517504\pi$
$24$		0			0
$25$	2.36614			0.473227
$26$	6.66439	+	5.06299i	1.30699	+	0.992934i
$27$		0			0
$28$	0.921081	+	5.21072i	0.174068	+	0.984734i
$29$	1.30418	−	0.752968i	0.242180	−	0.139823i	−0.373998	−	0.927429i	$-0.622013\pi$
$29$	1.30418	−	0.752968i	0.242180	−	0.139823i	0.616178	+	0.787607i	$0.288680\pi$
$30$		0			0
$31$	1.60482	−	0.926542i	0.288234	−	0.166412i	−0.348911	−	0.937156i	$-0.613449\pi$
$31$	1.60482	−	0.926542i	0.288234	−	0.166412i	0.637145	+	0.770744i	$0.280115\pi$
$32$	−3.33468	+	4.56945i	−0.589494	+	0.807773i
$33$		0			0
$34$	−6.39925	+	8.42331i	−1.09746	+	1.44459i
$35$	3.90807	−	1.77877i	0.660584	−	0.300668i
$36$		0			0
$37$	3.78593	+	6.55743i	0.622403	+	1.07803i	0.989037	+	0.147669i	$0.0471769\pi$
$37$	3.78593	+	6.55743i	0.622403	+	1.07803i	−0.366634	+	0.930365i	$0.619490\pi$
$38$	−1.97696	−	4.70858i	−0.320706	−	0.763833i
$39$		0			0
$40$	4.26581	+	1.69521i	0.674484	+	0.268037i
$41$	−5.31155	−	3.06663i	−0.829525	−	0.478926i	0.0241650	−	0.999708i	$-0.492307\pi$
$41$	−5.31155	−	3.06663i	−0.829525	−	0.478926i	−0.853690	+	0.520782i	$0.825641\pi$
$42$		0			0
$43$	3.91977	−	2.26308i	0.597759	−	0.345116i	−0.170400	−	0.985375i	$-0.554506\pi$
$43$	3.91977	−	2.26308i	0.597759	−	0.345116i	0.768160	+	0.640258i	$0.221173\pi$
$44$	−2.14576	−	0.552871i	−0.323485	−	0.0833485i
$45$		0			0
$46$	0.0937571	−	0.739650i	0.0138237	−	0.109055i
$47$	1.98329	−	3.43516i	0.289293	−	0.501070i	−0.684348	−	0.729155i	$-0.739913\pi$
$47$	1.98329	−	3.43516i	0.289293	−	0.501070i	0.973641	+	0.228085i	$0.0732466\pi$
$48$		0			0
$49$	−4.59742	+	5.27861i	−0.656774	+	0.754088i
$50$	−0.420796	+	3.31966i	−0.0595095	+	0.469471i
$51$		0			0
$52$	−8.28851	+	8.44965i	−1.14941	+	1.17176i
$53$	−3.48372	−	2.01133i	−0.478525	−	0.276277i	0.241276	−	0.970456i	$-0.422434\pi$
$53$	−3.48372	−	2.01133i	−0.478525	−	0.276277i	−0.719802	+	0.694180i	$0.755767\pi$
$54$		0			0
$55$			1.79806i			0.242451i
$56$	−7.47438	+	0.365585i	−0.998806	+	0.0488534i
$57$		0			0
$58$	0.824468	+	1.96366i	0.108258	+	0.257841i
$59$	5.60375	+	9.70599i	0.729547	+	1.26361i	0.957075	+	0.289841i	$0.0936023\pi$
$59$	5.60375	+	9.70599i	0.729547	+	1.26361i	−0.227528	+	0.973771i	$0.573064\pi$
$60$		0			0
$61$	5.67256	−	9.82516i	0.726297	−	1.25798i	−0.232141	−	0.972682i	$-0.574573\pi$
$61$	5.67256	−	9.82516i	0.726297	−	1.25798i	0.958438	−	0.285301i	$-0.0920935\pi$
$62$	1.01452	+	2.41632i	0.128845	+	0.306872i
$63$		0			0
$64$	−5.81784	−	5.49115i	−0.727230	−	0.686394i
$65$	8.31783	+	4.80230i	1.03170	+	0.595652i
$66$		0			0
$67$	11.8549	−	6.84441i	1.44830	−	0.836178i	0.449923	−	0.893067i	$-0.351451\pi$
$67$	11.8549	−	6.84441i	1.44830	−	0.836178i	0.998381	+	0.0568892i	$0.0181182\pi$
$68$	−10.6797	−	10.4761i	−1.29511	−	1.27041i
$69$		0			0
$70$	1.80058	+	5.79931i	0.215211	+	0.693150i
$71$	8.08304			0.959280			0.479640	−	0.877465i	$-0.340767\pi$
$71$	8.08304			0.959280			0.479640	+	0.877465i	$0.340767\pi$
$72$		0			0
$73$	−3.31356	+	5.73925i	−0.387822	+	0.671728i	−0.992156	−	0.125003i	$-0.960106\pi$
$73$	−3.31356	+	5.73925i	−0.387822	+	0.671728i	0.604334	+	0.796731i	$0.293439\pi$
$74$	−9.87328	+	4.14543i	−1.14775	+	0.481897i
$75$		0			0
$76$	6.95767	−	1.93628i	0.798099	−	0.222106i
$77$	−1.21432	−	2.66793i	−0.138384	−	0.304039i
$78$		0			0
$79$	−1.60759	−	0.928144i	−0.180868	−	0.104424i	0.406832	−	0.913503i	$-0.366633\pi$
$79$	−1.60759	−	0.928144i	−0.180868	−	0.104424i	−0.587701	+	0.809078i	$0.699967\pi$
$80$	−3.13700	+	5.68340i	−0.350727	+	0.635424i
$81$		0			0
$82$	5.24705	−	6.90667i	0.579439	−	0.762714i
$83$	5.43313	+	9.41046i	0.596363	+	1.03293i	0.993353	+	0.115109i	$0.0367216\pi$
$83$	5.43313	+	9.41046i	0.596363	+	1.03293i	−0.396990	+	0.917823i	$0.629945\pi$
$84$		0			0
$85$	−6.06976	+	10.5131i	−0.658358	+	1.14031i
$86$	2.47798	+	5.90185i	0.267207	+	0.636413i
$87$		0			0
$88$	1.15727	−	2.91215i	0.123366	−	0.310436i
$89$	−1.25062	+	0.722046i	−0.132566	+	0.0765368i	−0.564816	−	0.825217i	$-0.691053\pi$
$89$	−1.25062	+	0.722046i	−0.132566	+	0.0765368i	0.432251	+	0.901754i	$0.357720\pi$
$90$		0			0
$91$	−15.5850	−	1.50812i	−1.63376	−	0.158094i
$92$	1.02105	+	0.263080i	0.106451	+	0.0274280i
$93$		0			0
$94$	4.46678	+	3.39344i	0.460713	+	0.350007i
$95$	−2.93021	−	5.07527i	−0.300633	−	0.520712i
$96$		0			0
$97$	1.18819	+	2.05801i	0.120643	+	0.208960i	0.920021	−	0.391868i	$-0.128171\pi$
$97$	1.18819	+	2.05801i	0.120643	+	0.208960i	−0.799378	+	0.600828i	$0.794838\pi$
$98$	−6.58822	−	7.38887i	−0.665510	−	0.746389i
$99$		0			0
$100$	−4.58260	−	1.18074i	−0.458260	−	0.118074i
$101$			0.222224i			0.0221121i	0.999939	+	0.0110561i	$0.00351932\pi$
$101$			0.222224i			0.0221121i	−0.999939	+	0.0110561i	$0.996481\pi$
$102$		0			0
$103$		−	5.22154i		−	0.514494i	−0.966346	−	0.257247i	$-0.917185\pi$
$103$		−	5.22154i		−	0.514494i	0.966346	−	0.257247i	$-0.0828154\pi$
$104$	−10.3807	−	13.1314i	−1.01791	−	1.28764i
$105$		0			0
$106$	3.44141	−	4.52991i	0.334259	−	0.439984i
$107$	−5.33662	−	9.24330i	−0.515910	−	0.893583i	−0.999829	−	0.0184703i	$-0.994120\pi$
$107$	−5.33662	−	9.24330i	−0.515910	−	0.893583i	0.483919	−	0.875113i	$-0.339213\pi$
$108$		0			0
$109$	4.53911	−	7.86197i	0.434768	−	0.753040i	−0.562509	−	0.826791i	$-0.690164\pi$
$109$	4.53911	−	7.86197i	0.434768	−	0.753040i	0.997277	+	0.0737515i	$0.0234972\pi$
$110$	−2.52266	−	0.319769i	−0.240526	−	0.0304888i
$111$		0			0
$112$	0.816340	−	10.5515i	0.0771369	−	0.997021i
$113$	−6.44412	−	3.72051i	−0.606212	−	0.349997i	0.165270	−	0.986248i	$-0.447151\pi$
$113$	−6.44412	−	3.72051i	−0.606212	−	0.349997i	−0.771481	+	0.636252i	$0.780484\pi$
$114$		0			0
$115$		−	0.855597i		−	0.0797848i
$116$	−2.90161	+	0.807500i	−0.269407	+	0.0749745i
$117$		0			0
$118$	−14.6140	+	6.13587i	−1.34532	+	0.564853i
$119$	1.90616	−	19.6984i	0.174737	−	1.80575i
$120$		0			0
$121$	−9.77251			−0.888410
$122$	12.7758	+	9.70584i	1.15666	+	0.878726i
$123$		0			0
$124$	−3.57048	+	0.993644i	−0.320639	+	0.0892319i
$125$			11.9546i			1.06926i
$126$		0			0
$127$		−	3.49748i		−	0.310351i	−0.987887	−	0.155175i	$-0.950406\pi$
$127$		−	3.49748i		−	0.310351i	0.987887	−	0.155175i	$-0.0495943\pi$
$128$	8.73866	−	7.18581i	0.772396	−	0.635142i
$129$		0			0
$130$	−8.21682	+	10.8158i	−0.720663	+	0.948605i
$131$	−2.16145			−0.188847			−0.0944235	−	0.995532i	$-0.530101\pi$
$131$	−2.16145			−0.188847			−0.0944235	+	0.995532i	$0.530101\pi$
$132$		0			0
$133$	7.77535	+	5.55166i	0.674208	+	0.481390i
$134$	7.49434	+	17.8495i	0.647413	+	1.54196i
$135$		0			0
$136$	16.5971	−	13.1205i	1.42319	−	1.12507i
$137$		−	10.7408i		−	0.917649i	−0.888527	−	0.458825i	$-0.848271\pi$
$137$		−	10.7408i		−	0.917649i	0.888527	−	0.458825i	$-0.151729\pi$
$138$		0			0
$139$	−7.57783	−	4.37506i	−0.642743	−	0.371088i	0.142927	−	0.989733i	$-0.454348\pi$
$139$	−7.57783	−	4.37506i	−0.642743	−	0.371088i	−0.785670	+	0.618645i	$0.787682\pi$
$140$	−8.45657	+	1.49484i	−0.714711	+	0.126337i
$141$		0			0
$142$	−1.43750	+	11.3404i	−0.120632	+	0.951665i
$143$	3.27840	−	5.67835i	0.274153	−	0.474847i
$144$		0			0
$145$	1.22201	+	2.11658i	0.101482	+	0.175772i
$146$	−7.46281	−	5.66955i	−0.617626	−	0.469215i
$147$		0			0
$148$	−4.06012	−	14.5893i	−0.333740	−	1.19923i
$149$			7.82979i			0.641441i	0.947174	+	0.320721i	$0.103925\pi$
$149$			7.82979i			0.641441i	−0.947174	+	0.320721i	$0.896075\pi$
$150$		0			0
$151$			5.66702i			0.461176i	0.973052	+	0.230588i	$0.0740649\pi$
$151$			5.66702i			0.461176i	−0.973052	+	0.230588i	$0.925935\pi$
$152$	1.47921	+	10.1059i	0.119980	+	0.819694i
$153$		0			0
$154$	3.95902	−	1.22921i	0.319027	−	0.0990523i
$155$	1.50370	+	2.60449i	0.120780	+	0.209198i
$156$		0			0
$157$	4.73343	+	8.19854i	0.377769	+	0.654315i	0.990737	−	0.135793i	$-0.0433581\pi$
$157$	4.73343	+	8.19854i	0.377769	+	0.654315i	−0.612969	+	0.790107i	$0.710025\pi$
$158$	1.58807	−	2.09037i	0.126340	−	0.166301i
$159$		0			0
$160$	−7.41585	−	5.41191i	−0.586275	−	0.427849i
$161$	0.577825	+	1.26952i	0.0455390	+	0.100052i
$162$		0			0
$163$	16.0226	−	9.25068i	1.25499	−	0.724569i	0.282894	−	0.959151i	$-0.408706\pi$
$163$	16.0226	−	9.25068i	1.25499	−	0.724569i	0.972096	+	0.234582i	$0.0753723\pi$
$164$	8.75682	+	8.58983i	0.683793	+	0.670753i
$165$		0			0
$166$	−14.1690	+	5.94905i	−1.09973	+	0.461735i
$167$	−10.6528	+	18.4512i	−0.824340	+	1.42780i	0.0780821	+	0.996947i	$0.475120\pi$
$167$	−10.6528	+	18.4512i	−0.824340	+	1.42780i	−0.902422	+	0.430852i	$0.858213\pi$
$168$		0			0
$169$	−11.0120	−	19.0733i	−0.847077	−	1.46718i
$170$	−13.6703	−	10.3855i	−1.04847	−	0.796529i
$171$		0			0
$172$	−8.72091	+	2.42698i	−0.664963	+	0.185055i
$173$	−0.219720	−	0.126856i	−0.0167050	−	0.00964466i	0.491624	−	0.870807i	$-0.336403\pi$
$173$	−0.219720	−	0.126856i	−0.0167050	−	0.00964466i	−0.508329	+	0.861163i	$0.669737\pi$
$174$		0			0
$175$	−2.59337	−	5.69778i	−0.196040	−	0.430711i
$176$	3.87990	+	2.14154i	0.292458	+	0.161425i
$177$		0			0
$178$	−0.790610	−	1.88301i	−0.0592587	−	0.141138i
$179$	−1.26089	+	2.18392i	−0.0942430	+	0.163234i	−0.909292	−	0.416158i	$-0.863376\pi$
$179$	−1.26089	+	2.18392i	−0.0942430	+	0.163234i	0.815049	+	0.579391i	$0.196710\pi$
$180$		0			0
$181$	4.61261			0.342853			0.171426	−	0.985197i	$-0.445162\pi$
$181$	4.61261			0.342853			0.171426	+	0.985197i	$0.445162\pi$
$182$	4.88753	−	21.5974i	0.362288	−	1.60091i
$183$		0			0
$184$	−0.550682	+	1.38573i	−0.0405968	+	0.102157i
$185$	−10.6422	+	6.14426i	−0.782428	+	0.451735i
$186$		0			0
$187$	7.17702	+	4.14365i	0.524836	+	0.303014i
$188$	−5.55533	+	5.66334i	−0.405164	+	0.413041i
$189$		0			0
$190$	7.64165	−	3.20845i	0.554383	−	0.232766i
$191$	3.40037	−	5.88961i	0.246042	−	0.426158i	−0.716382	−	0.697708i	$-0.754203\pi$
$191$	3.40037	−	5.88961i	0.246042	−	0.426158i	0.962424	+	0.271551i	$0.0875365\pi$
$192$		0			0
$193$	−11.4231	−	19.7853i	−0.822250	−	1.42418i	−0.904003	−	0.427526i	$-0.859385\pi$
$193$	−11.4231	−	19.7853i	−0.822250	−	1.42418i	0.0817532	−	0.996653i	$-0.473948\pi$
$194$	−3.09868	+	1.30102i	−0.222472	+	0.0934080i
$195$		0			0
$196$	11.5381	−	7.92914i	0.824153	−	0.566367i
$197$		−	9.16890i		−	0.653257i	−0.945153	−	0.326628i	$-0.894087\pi$
$197$		−	9.16890i		−	0.653257i	0.945153	−	0.326628i	$-0.105913\pi$
$198$		0			0
$199$	11.2145	+	6.47470i	0.794975	+	0.458979i	0.841711	−	0.539928i	$-0.181549\pi$
$199$	11.2145	+	6.47470i	0.794975	+	0.458979i	−0.0467358	+	0.998907i	$0.514882\pi$
$200$	2.47154	−	6.21935i	0.174764	−	0.439774i
$201$		0			0
$202$	−0.311777	−	0.0395205i	−0.0219366	−	0.00278065i
$203$	−3.24261	−	2.31525i	−0.227587	−	0.162499i
$204$		0			0
$205$	4.97688	−	8.62021i	0.347601	−	0.602062i
$206$	7.32575	+	0.928604i	0.510410	+	0.0646989i
$207$		0			0
$208$	20.2693	−	12.2287i	1.40542	−	0.847908i
$209$	−3.46474	+	2.00037i	−0.239661	+	0.138368i
$210$		0			0
$211$	−5.76767	−	3.32997i	−0.397063	−	0.229244i	0.288153	−	0.957584i	$-0.406959\pi$
$211$	−5.76767	−	3.32997i	−0.397063	−	0.229244i	−0.685216	+	0.728340i	$0.740292\pi$
$212$	5.74339	+	5.63386i	0.394457	+	0.386935i
$213$		0			0
$214$	13.9173	−	5.84337i	0.951367	−	0.399445i
$215$	3.67279	+	6.36147i	0.250482	+	0.433848i
$216$		0			0
$217$	−3.99010	−	2.84896i	−0.270865	−	0.193400i
$218$	10.2230	+	7.76649i	0.692389	+	0.526013i
$219$		0			0
$220$	0.897265	−	3.48239i	0.0604936	−	0.234783i
$221$	38.3370	−	22.1339i	2.57883	−	1.48889i
$222$		0			0
$223$	0.151537	−	0.0874902i	0.0101477	−	0.00585878i	−0.494918	−	0.868940i	$-0.664802\pi$
$223$	0.151537	−	0.0874902i	0.0101477	−	0.00585878i	0.505065	+	0.863081i	$0.331468\pi$
$224$	14.6584	+	3.02180i	0.979406	+	0.201902i
$225$		0			0
$226$	6.36586	−	8.37936i	0.423451	−	0.557387i
$227$	−18.9352			−1.25678			−0.628388	−	0.777900i	$-0.716285\pi$
$227$	−18.9352			−1.25678			−0.628388	+	0.777900i	$0.716285\pi$
$228$		0			0
$229$	0.801763			0.0529820			0.0264910	−	0.999649i	$-0.491567\pi$
$229$	0.801763			0.0529820			0.0264910	+	0.999649i	$0.491567\pi$
$230$	1.20039	+	0.152160i	0.0791514	+	0.0100331i
$231$		0			0
$232$	−0.616887	−	4.21452i	−0.0405006	−	0.276697i
$233$	−7.35469	+	4.24623i	−0.481822	+	0.278180i	−0.721175	−	0.692753i	$-0.756398\pi$
$233$	−7.35469	+	4.24623i	−0.481822	+	0.278180i	0.239354	+	0.970932i	$0.423064\pi$
$234$		0			0
$235$	5.57499	+	3.21872i	0.363672	+	0.209966i
$236$	−6.00959	−	21.5944i	−0.391191	−	1.40568i
$237$		0			0
$238$	27.2976	+	6.17749i	1.76944	+	0.400427i
$239$	13.4726	−	23.3353i	0.871473	−	1.50944i	0.0109999	−	0.999939i	$-0.496499\pi$
$239$	13.4726	−	23.3353i	0.871473	−	1.50944i	0.860473	−	0.509496i	$-0.170168\pi$
$240$		0			0
$241$	−13.7367			−0.884856			−0.442428	−	0.896804i	$-0.645883\pi$
$241$	−13.7367			−0.884856			−0.442428	+	0.896804i	$0.645883\pi$
$242$	1.73795	−	13.7107i	0.111720	−	0.881358i
$243$		0			0
$244$	−15.8892	+	16.1981i	−1.01720	+	1.03698i
$245$	−8.56676	−	7.46123i	−0.547310	−	0.476681i
$246$		0			0
$247$			21.3705i			1.35977i
$248$	−0.759092	−	5.18605i	−0.0482024	−	0.329315i
$249$		0			0
$250$	−16.7722	−	2.12602i	−1.06077	−	0.134462i
$251$	−3.97381			−0.250825			−0.125412	−	0.992105i	$-0.540025\pi$
$251$	−3.97381			−0.250825			−0.125412	+	0.992105i	$0.540025\pi$
$252$		0			0
$253$	−0.584092			−0.0367215
$254$	4.90692	+	0.621995i	0.307887	+	0.0390274i
$255$		0			0
$256$	8.52750	+	13.5382i	0.532969	+	0.846135i
$257$			25.2173i			1.57301i	0.617584	+	0.786505i	$0.288112\pi$
$257$			25.2173i			1.57301i	−0.617584	+	0.786505i	$0.711888\pi$
$258$		0			0
$259$	11.6411	−	16.3039i	0.723343	−	1.01307i
$260$	−13.7131	−	13.4516i	−0.850450	−	0.834231i
$261$		0			0
$262$	0.384395	−	3.03249i	0.0237480	−	0.187348i
$263$	−29.6801			−1.83015			−0.915076	−	0.403282i	$-0.867869\pi$
$263$	−29.6801			−1.83015			−0.915076	+	0.403282i	$0.867869\pi$
$264$		0			0
$265$	3.26422	−	5.65379i	0.200519	−	0.347309i
$266$	−9.17169	+	9.92140i	−0.562352	+	0.608320i
$267$		0			0
$268$	−26.3753	+	7.34010i	−1.61113	+	0.448368i
$269$	−14.8466	−	8.57168i	−0.905213	−	0.522625i	−0.0263250	−	0.999653i	$-0.508380\pi$
$269$	−14.8466	−	8.57168i	−0.905213	−	0.522625i	−0.878888	+	0.477029i	$0.841714\pi$
$270$		0			0
$271$	−20.1315	+	11.6229i	−1.22290	+	0.706043i	−0.965536	−	0.260270i	$-0.916188\pi$
$271$	−20.1315	+	11.6229i	−1.22290	+	0.706043i	−0.257367	+	0.966314i	$0.582855\pi$
$272$	15.4562	+	25.6189i	0.937170	+	1.55337i
$273$		0			0
$274$	15.0692	+	1.91016i	0.910365	+	0.115397i
$275$	2.62149			0.158082
$276$		0			0
$277$	11.5064			0.691351			0.345676	−	0.938354i	$-0.387650\pi$
$277$	11.5064			0.691351			0.345676	+	0.938354i	$0.387650\pi$
$278$	7.48580	−	9.85353i	0.448969	−	0.590975i
$279$		0			0
$280$	−0.593315	−	12.1303i	−0.0354573	−	0.724925i
$281$	−14.9836	+	8.65081i	−0.893849	+	0.516064i	−0.875199	−	0.483762i	$-0.839270\pi$
$281$	−14.9836	+	8.65081i	−0.893849	+	0.516064i	−0.0186493	+	0.999826i	$0.505937\pi$
$282$		0			0
$283$	−17.7061	+	10.2226i	−1.05252	+	0.607673i	−0.923354	−	0.383950i	$-0.874563\pi$
$283$	−17.7061	+	10.2226i	−1.05252	+	0.607673i	−0.129166	+	0.991623i	$0.541230\pi$
$284$	−15.6548	−	4.03357i	−0.928941	−	0.239349i
$285$		0			0
$286$	7.38361	+	5.60939i	0.436602	+	0.331690i
$287$	−1.56295	+	16.1516i	−0.0922578	+	0.953400i
$288$		0			0
$289$	19.4756	+	33.7328i	1.14563	+	1.98428i
$290$	−3.18685	+	1.33804i	−0.187138	+	0.0785727i
$291$		0			0
$292$	9.28150	−	9.46194i	0.543159	−	0.553718i
$293$	−2.79032	−	1.61099i	−0.163012	−	0.0941152i	0.416274	−	0.909239i	$-0.363336\pi$
$293$	−2.79032	−	1.61099i	−0.163012	−	0.0941152i	−0.579287	+	0.815124i	$0.696669\pi$
$294$		0			0
$295$	−15.7520	+	9.09444i	−0.917118	+	0.529499i
$296$	21.1907	−	3.10171i	1.23168	−	0.180284i
$297$		0			0
$298$	−10.9851	−	1.39246i	−0.636349	−	0.0806629i
$299$	−1.56000	+	2.70200i	−0.0902173	+	0.156261i
$300$		0			0
$301$	−9.74581	−	6.95859i	−0.561739	−	0.401086i
$302$	−7.95076	−	1.00783i	−0.457515	−	0.0579940i
$303$		0			0
$304$	−14.4415	+	0.278080i	−0.828275	+	0.0159490i
$305$	15.9454	+	9.20610i	0.913033	+	0.527140i
$306$		0			0
$307$			12.1542i			0.693674i	0.937925	+	0.346837i	$0.112744\pi$
$307$			12.1542i			0.693674i	−0.937925	+	0.346837i	$0.887256\pi$
$308$	1.02048	+	5.77306i	0.0581475	+	0.328951i
$309$		0			0
$310$	−3.92148	+	1.64649i	−0.222725	+	0.0935143i
$311$	−1.68227	−	2.91378i	−0.0953928	−	0.165225i	0.814380	−	0.580332i	$-0.197077\pi$
$311$	−1.68227	−	2.91378i	−0.0953928	−	0.165225i	−0.909772	+	0.415107i	$0.863744\pi$
$312$		0			0
$313$	−4.10763	+	7.11462i	−0.232177	+	0.402142i	−0.958448	−	0.285266i	$-0.907918\pi$
$313$	−4.10763	+	7.11462i	−0.232177	+	0.402142i	0.726272	+	0.687408i	$0.241251\pi$
$314$	−12.3442	+	5.18290i	−0.696626	+	0.292488i
$315$		0			0
$316$	2.65034	+	2.59980i	0.149093	+	0.146250i
$317$	1.88173	+	1.08642i	0.105689	+	0.0610194i	0.551913	−	0.833902i	$-0.313898\pi$
$317$	1.88173	+	1.08642i	0.105689	+	0.0610194i	−0.446224	+	0.894921i	$0.647232\pi$
$318$		0			0
$319$	1.44493	−	0.834229i	0.0809004	−	0.0467078i
$320$	8.91169	−	9.44188i	0.498178	−	0.527817i
$321$		0			0
$322$	−1.88388	+	0.584910i	−0.104984	+	0.0325957i
$323$	−27.0108			−1.50292
$324$		0			0
$325$	7.00152	−	12.1270i	0.388375	−	0.672685i
$326$	10.1291	+	24.1247i	0.560999	+	1.33614i
$327$		0			0
$328$	−13.6087	+	10.7581i	−0.751417	+	0.594016i
$329$	−10.4458	−	1.01081i	−0.575895	−	0.0557278i
$330$		0			0
$331$	17.7312	+	10.2371i	0.974595	+	0.562683i	0.900634	−	0.434579i	$-0.143103\pi$
$331$	17.7312	+	10.2371i	0.974595	+	0.562683i	0.0739608	+	0.997261i	$0.476436\pi$
$332$	−5.82661	−	20.9369i	−0.319777	−	1.14906i
$333$		0			0
$334$	−23.9923	−	18.2272i	−1.31280	−	0.997346i
$335$	11.1079	+	19.2395i	0.606891	+	1.05117i
$336$		0			0
$337$	−10.5933	+	18.3482i	−0.577055	+	0.999489i	0.418760	+	0.908097i	$0.362465\pi$
$337$	−10.5933	+	18.3482i	−0.577055	+	0.999489i	−0.995815	+	0.0913920i	$0.970868\pi$
$338$	28.7180	−	12.0577i	1.56205	−	0.655851i
$339$		0			0
$340$	17.0018	−	17.3324i	0.922053	−	0.939979i
$341$	1.77801	−	1.02653i	0.0962846	−	0.0555900i
$342$		0			0
$343$	17.7501	+	5.28527i	0.958415	+	0.285378i
$344$	−1.85408	−	12.6669i	−0.0999654	−	0.682956i
$345$		0			0
$346$	0.217052	−	0.285705i	0.0116688	−	0.0153596i
$347$	10.2182	+	17.6984i	0.548539	+	0.950098i	0.998375	+	0.0569867i	$0.0181493\pi$
$347$	10.2182	+	17.6984i	0.548539	+	0.950098i	−0.449836	+	0.893111i	$0.648517\pi$
$348$		0			0
$349$	−12.7924	−	22.1570i	−0.684760	−	1.18604i	−0.973512	−	0.228635i	$-0.926574\pi$
$349$	−12.7924	−	22.1570i	−0.684760	−	1.18604i	0.288752	−	0.957404i	$-0.406760\pi$
$350$	8.45511	−	2.62516i	0.451945	−	0.140321i
$351$		0			0
$352$	−3.69456	+	5.06259i	−0.196921	+	0.269837i
$353$			22.0460i			1.17339i	0.809809	+	0.586694i	$0.199571\pi$
$353$			22.0460i			1.17339i	−0.809809	+	0.586694i	$0.800429\pi$
$354$		0			0
$355$			13.1181i			0.696237i
$356$	2.78245	−	0.774338i	0.147469	−	0.0410399i
$357$		0			0
$358$	−2.83977	−	2.15740i	−0.150087	−	0.114022i
$359$	11.3160	+	19.5999i	0.597236	+	1.03444i	0.993227	+	0.116189i	$0.0370679\pi$
$359$	11.3160	+	19.5999i	0.597236	+	1.03444i	−0.395991	+	0.918254i	$0.629599\pi$
$360$		0			0
$361$	−2.98021	+	5.16188i	−0.156853	+	0.271678i
$362$	−0.820311	+	6.47143i	−0.0431146	+	0.340131i
$363$		0			0
$364$	29.4317	+	10.6980i	1.54264	+	0.560730i
$365$	−9.31433	−	5.37763i	−0.487534	−	0.281478i
$366$		0			0
$367$			28.1813i			1.47105i	0.677496	+	0.735526i	$0.263065\pi$
$367$			28.1813i			1.47105i	−0.677496	+	0.735526i	$0.736935\pi$
$368$	−1.84622	−	1.01904i	−0.0962410	−	0.0531210i
$369$		0			0
$370$	−6.72770	−	16.0235i	−0.349756	−	0.833023i
$371$	−1.02510	+	10.5934i	−0.0532205	+	0.549984i
$372$		0			0
$373$	−13.8193			−0.715536			−0.357768	−	0.933810i	$-0.616462\pi$
$373$	−13.8193			−0.715536			−0.357768	+	0.933810i	$0.616462\pi$
$374$	−7.08986	+	9.33235i	−0.366608	+	0.482564i
$375$		0			0
$376$	−6.95762	−	8.80123i	−0.358812	−	0.453889i
$377$		−	8.91229i		−	0.459006i
$378$		0			0
$379$		−	5.31463i		−	0.272994i	−0.990640	−	0.136497i	$-0.956416\pi$
$379$		−	5.31463i		−	0.272994i	0.990640	−	0.136497i	$-0.0435844\pi$
$380$	3.14242	+	11.2917i	0.161203	+	0.579253i
$381$		0			0
$382$	7.65833	+	5.81809i	0.391834	+	0.297679i
$383$	−29.4870			−1.50672			−0.753358	−	0.657611i	$-0.771567\pi$
$383$	−29.4870			−1.50672			−0.753358	+	0.657611i	$0.771567\pi$
$384$		0			0
$385$	4.32983	−	1.97074i	0.220669	−	0.100438i
$386$	29.7900	−	12.5078i	1.51627	−	0.636628i
$387$		0			0
$388$	−1.27425	−	4.57878i	−0.0646901	−	0.232452i
$389$		−	28.7891i		−	1.45967i	−0.683626	−	0.729833i	$-0.739598\pi$
$389$		−	28.7891i		−	1.45967i	0.683626	−	0.729833i	$-0.260402\pi$
$390$		0			0
$391$	−3.41514	−	1.97173i	−0.172711	−	0.0997147i
$392$	9.07252	+	17.5980i	0.458232	+	0.888833i
$393$		0			0
$394$	12.8638	+	1.63061i	0.648071	+	0.0821487i
$395$	1.50630	−	2.60899i	0.0757903	−	0.131273i
$396$		0			0
$397$	12.1214	+	20.9948i	0.608354	+	1.05370i	0.991512	+	0.130017i	$0.0415031\pi$
$397$	12.1214	+	20.9948i	0.608354	+	1.05370i	−0.383158	+	0.923683i	$0.625164\pi$
$398$	−11.0783	+	14.5823i	−0.555306	+	0.730947i
$399$		0			0
$400$	8.28612	+	4.57359i	0.414306	+	0.228680i
$401$		−	6.74572i		−	0.336865i	−0.985713	−	0.168433i	$-0.946129\pi$
$401$		−	6.74572i		−	0.336865i	0.985713	−	0.168433i	$-0.0538706\pi$
$402$		0			0
$403$		−	10.9667i		−	0.546293i
$404$	0.110894	−	0.430391i	0.00551716	−	0.0214128i
$405$		0			0
$406$	3.82494	−	4.13759i	0.189828	−	0.205345i
$407$	4.19451	+	7.26510i	0.207914	+	0.360118i
$408$		0			0
$409$	0.232345	+	0.402434i	0.0114887	+	0.0198991i	0.871713	−	0.490017i	$-0.163010\pi$
$409$	0.232345	+	0.402434i	0.0114887	+	0.0198991i	−0.860224	+	0.509917i	$0.829676\pi$
$410$	11.2090	+	8.51553i	0.553571	+	0.420552i
$411$		0			0
$412$	−2.60564	+	10.1128i	−0.128371	+	0.498222i
$413$	17.2306	−	24.1322i	0.847863	−	1.18747i
$414$		0			0
$415$	−15.2724	+	8.81753i	−0.749693	+	0.432835i
$416$	13.5520	+	30.6123i	0.664442	+	1.50089i
$417$		0			0
$418$	−2.19032	−	5.21673i	−0.107132	−	0.255159i
$419$	12.9399	−	22.4126i	0.632156	−	1.09493i	−0.354954	−	0.934884i	$-0.615503\pi$
$419$	12.9399	−	22.4126i	0.632156	−	1.09493i	0.987110	−	0.160043i	$-0.0511633\pi$
$420$		0			0
$421$	11.7655	+	20.3784i	0.573413	+	0.993180i	0.996212	+	0.0869569i	$0.0277143\pi$
$421$	11.7655	+	20.3784i	0.573413	+	0.993180i	−0.422799	+	0.906223i	$0.638952\pi$
$422$	5.69763	−	7.49977i	0.277356	−	0.365083i
$423$		0			0
$424$	−8.92564	+	7.05597i	−0.433467	+	0.342668i
$425$	15.3276	+	8.84942i	0.743500	+	0.429260i
$426$		0			0
$427$	−29.8768	−	2.89110i	−1.44584	−	0.139910i
$428$	5.72311	+	20.5650i	0.276637	+	0.994045i
$429$		0			0
$430$	−9.57823	+	4.02155i	−0.461903	+	0.193937i
$431$	2.24774	−	3.89320i	0.108270	−	0.187529i	−0.806800	−	0.590825i	$-0.798802\pi$
$431$	2.24774	−	3.89320i	0.108270	−	0.187529i	0.915069	+	0.403296i	$0.132136\pi$
$432$		0			0
$433$	−8.15969			−0.392130			−0.196065	−	0.980591i	$-0.562816\pi$
$433$	−8.15969			−0.392130			−0.196065	+	0.980591i	$0.562816\pi$
$434$	4.70666	−	5.09139i	0.225927	−	0.244395i
$435$		0			0
$436$	−12.7144	+	12.9615i	−0.608907	+	0.620745i
$437$	1.64867	−	0.951862i	0.0788668	−	0.0455338i
$438$		0			0
$439$	−2.27227	−	1.31190i	−0.108450	−	0.0626135i	0.444794	−	0.895633i	$-0.353277\pi$
$439$	−2.27227	−	1.31190i	−0.108450	−	0.0626135i	−0.553244	+	0.833019i	$0.686610\pi$
$440$	4.72618	+	1.87816i	0.225312	+	0.0895379i
$441$		0			0
$442$	24.2357	+	57.7227i	1.15277	+	2.74559i
$443$	−2.57125	+	4.45353i	−0.122164	+	0.211594i	−0.920621	−	0.390458i	$-0.872317\pi$
$443$	−2.57125	+	4.45353i	−0.122164	+	0.211594i	0.798457	+	0.602052i	$0.205650\pi$
$444$		0			0
$445$	−1.17182	−	2.02966i	−0.0555497	−	0.0962149i
$446$	0.0957980	+	0.228164i	0.00453617	+	0.0108039i
$447$		0			0
$448$	−6.84641	+	20.0281i	−0.323462	+	0.946241i
$449$		−	11.1570i		−	0.526530i	−0.964724	−	0.263265i	$-0.915201\pi$
$449$		−	11.1570i		−	0.526530i	0.964724	−	0.263265i	$-0.0847993\pi$
$450$		0			0
$451$	−5.88477	−	3.39758i	−0.277103	−	0.159986i
$452$	10.6240	+	10.4214i	0.499712	+	0.490182i
$453$		0			0
$454$	3.36746	−	26.5659i	0.158043	−	1.24680i
$455$	2.44756	−	25.2932i	0.114743	−	1.18577i
$456$		0			0
$457$	−7.46245	+	12.9253i	−0.349079	+	0.604622i	−0.986086	−	0.166236i	$-0.946839\pi$
$457$	−7.46245	+	12.9253i	−0.349079	+	0.604622i	0.637007	+	0.770858i	$0.280172\pi$
$458$	−0.142586	+	1.12486i	−0.00666262	+	0.0525614i
$459$		0			0
$460$	−0.426957	+	1.65707i	−0.0199070	+	0.0772614i
$461$	27.5276	−	15.8931i	1.28209	−	0.740215i	0.304860	−	0.952397i	$-0.401390\pi$
$461$	27.5276	−	15.8931i	1.28209	−	0.740215i	0.977230	+	0.212183i	$0.0680571\pi$
$462$		0			0
$463$	19.3736	+	11.1854i	0.900368	+	0.519828i	0.877320	−	0.479907i	$-0.159329\pi$
$463$	19.3736	+	11.1854i	0.900368	+	0.519828i	0.0230485	+	0.999734i	$0.492663\pi$
$464$	6.02263	−	0.115970i	0.279594	−	0.00538377i
$465$		0			0
$466$	−4.64944	−	11.0737i	−0.215381	−	0.512979i
$467$	9.10952	+	15.7782i	0.421538	+	0.730126i	0.996090	−	0.0883422i	$-0.0281569\pi$
$467$	9.10952	+	15.7782i	0.421538	+	0.730126i	−0.574552	+	0.818468i	$0.694824\pi$
$468$		0			0
$469$	−29.4750	−	21.0454i	−1.36103	−	0.971787i
$470$	−5.50728	+	7.24921i	−0.254032	+	0.334381i
$471$		0			0
$472$	31.3654	−	4.59101i	1.44371	−	0.211318i
$473$	4.34279	−	2.50731i	0.199682	−	0.115286i
$474$		0			0
$475$	−7.39949	+	4.27210i	−0.339512	+	0.196017i
$476$	−13.5216	+	37.1995i	−0.619760	+	1.70504i
$477$		0			0
$478$	30.3431	+	23.0519i	1.38786	+	1.05437i
$479$	8.40407			0.383992			0.191996	−	0.981396i	$-0.438504\pi$
$479$	8.40407			0.383992			0.191996	+	0.981396i	$0.438504\pi$
$480$		0			0
$481$	44.8111			2.04321
$482$	2.44294	−	19.2723i	0.111273	−	0.877831i
$483$		0			0
$484$	18.9269	+	4.87665i	0.860312	+	0.221666i
$485$	−3.33999	+	1.92834i	−0.151661	+	0.0875615i
$486$		0			0
$487$	−11.0939	−	6.40506i	−0.502712	−	0.290241i	0.227121	−	0.973867i	$-0.427069\pi$
$487$	−11.0939	−	6.40506i	−0.502712	−	0.290241i	−0.729833	+	0.683625i	$0.760402\pi$
$488$	−19.9000	−	25.1731i	−0.900831	−	1.13953i
$489$		0			0
$490$	11.9915	−	10.6921i	0.541722	−	0.483022i
$491$	−4.56732	+	7.91082i	−0.206120	+	0.357010i	−0.950489	−	0.310758i	$-0.899417\pi$
$491$	−4.56732	+	7.91082i	−0.206120	+	0.357010i	0.744369	+	0.667769i	$0.232750\pi$
$492$		0			0
$493$	11.2645			0.507327
$494$	−29.9825	−	3.80055i	−1.34898	−	0.170995i
$495$		0			0
$496$	7.41096	−	0.142703i	0.332762	−	0.00640757i
$497$	−8.85929	−	19.4644i	−0.397393	−	0.873096i
$498$		0			0
$499$		−	24.7530i		−	1.10810i	−0.832484	−	0.554049i	$-0.813082\pi$
$499$		−	24.7530i		−	1.10810i	0.832484	−	0.554049i	$-0.186918\pi$
$500$	5.96557	−	23.1531i	0.266788	−	1.03544i
$501$		0			0
$502$	0.706706	−	5.57520i	0.0315418	−	0.248834i
$503$	−18.3846			−0.819728			−0.409864	−	0.912147i	$-0.634424\pi$
$503$	−18.3846			−0.819728			−0.409864	+	0.912147i	$0.634424\pi$
$504$		0			0
$505$	−0.360651			−0.0160488
$506$	0.103875	−	0.819473i	0.00461782	−	0.0364300i
$507$		0			0
$508$	−1.74530	+	6.77372i	−0.0774352	+	0.300535i
$509$			9.12210i			0.404330i	0.979351	+	0.202165i	$0.0647977\pi$
$509$			9.12210i			0.404330i	−0.979351	+	0.202165i	$0.935202\pi$
$510$		0			0
$511$	17.4522	+	1.68880i	0.772039	+	0.0747080i
$512$	−20.5104	+	9.55633i	−0.906440	+	0.422334i
$513$		0			0
$514$	−35.3795	−	4.48466i	−1.56052	−	0.197810i
$515$	8.47414			0.373415
$516$		0			0
$517$	2.19733	−	3.80588i	0.0966384	−	0.167383i
$518$	20.8039	+	19.2318i	0.914069	+	0.844997i
$519$		0			0
$520$	21.3111	−	16.8470i	0.934555	−	0.738792i
$521$	−2.72234	−	1.57174i	−0.119268	−	0.0688592i	0.439179	−	0.898399i	$-0.355269\pi$
$521$	−2.72234	−	1.57174i	−0.119268	−	0.0688592i	−0.558447	+	0.829540i	$0.688603\pi$
$522$		0			0
$523$	−15.0477	+	8.68779i	−0.657990	+	0.379891i	−0.791511	−	0.611155i	$-0.790705\pi$
$523$	−15.0477	+	8.68779i	−0.657990	+	0.379891i	0.133521	+	0.991046i	$0.457372\pi$
$524$	4.18618	+	1.07860i	0.182874	+	0.0471189i
$525$		0			0
$526$	5.27833	−	41.6408i	0.230146	−	1.81562i
$527$	13.8612			0.603802
$528$		0			0
$529$	−22.7221			−0.987916
$530$	7.35168	+	5.58513i	0.319337	+	0.242602i
$531$		0			0
$532$	−12.2885	−	14.6322i	−0.532774	−	0.634386i
$533$	−31.4343	+	18.1486i	−1.36157	+	0.786104i
$534$		0			0
$535$	15.0011	−	8.66090i	0.648555	−	0.374443i
$536$	−5.60745	−	38.3096i	−0.242205	−	1.65472i
$537$		0			0
$538$	14.6663	−	19.3052i	0.632309	−	0.832305i
$539$	−5.09357	+	5.84828i	−0.219396	+	0.251903i
$540$		0			0
$541$	−1.74253	−	3.01815i	−0.0749173	−	0.129761i	0.826133	−	0.563475i	$-0.190536\pi$
$541$	−1.74253	−	3.01815i	−0.0749173	−	0.129761i	−0.901050	+	0.433715i	$0.857203\pi$
$542$	−12.7266	−	30.3113i	−0.546655	−	1.30198i
$543$		0			0
$544$	−38.6917	+	17.1288i	−1.65889	+	0.734390i
$545$	12.7593	+	7.36660i	0.546550	+	0.315551i
$546$		0			0
$547$	−34.7908	+	20.0865i	−1.48755	+	0.858837i	−0.999899	−	0.0142029i	$-0.995479\pi$
$547$	−34.7908	+	20.0865i	−1.48755	+	0.858837i	−0.487649	+	0.873040i	$0.662146\pi$
$548$	−5.35985	+	20.8022i	−0.228961	+	0.888626i
$549$		0			0
$550$	−0.466208	+	3.67792i	−0.0198792	+	0.156827i
$551$	−2.71899	+	4.70944i	−0.115833	+	0.200629i
$552$		0			0
$553$	−0.473041	+	4.88844i	−0.0201158	+	0.207878i
$554$	−2.04631	+	16.1433i	−0.0869392	+	0.685863i
$555$		0			0
$556$	12.4931	+	12.2548i	0.529825	+	0.519721i
$557$	−30.1155	−	17.3872i	−1.27603	−	0.736718i	−0.299917	−	0.953965i	$-0.596959\pi$
$557$	−30.1155	−	17.3872i	−1.27603	−	0.736718i	−0.976117	+	0.217247i	$0.930292\pi$
$558$		0			0
$559$		−	26.7863i		−	1.13294i
$560$	17.1242	+	1.32485i	0.723629	+	0.0559852i
$561$		0			0
$562$	−9.47226	−	22.5603i	−0.399563	−	0.951649i
$563$	−14.5025	−	25.1191i	−0.611207	−	1.05864i	−0.991037	−	0.133586i	$-0.957351\pi$
$563$	−14.5025	−	25.1191i	−0.611207	−	1.05864i	0.379830	−	0.925056i	$-0.375983\pi$
$564$		0			0
$565$	6.03809	−	10.4583i	0.254024	−	0.439983i
$566$	−11.1934	−	26.6595i	−0.470492	−	1.12058i
$567$		0			0
$568$	8.44312	−	21.2461i	0.354265	−	0.891468i
$569$	30.3977	+	17.5501i	1.27434	+	0.735740i	0.975802	−	0.218658i	$-0.0701679\pi$
$569$	30.3977	+	17.5501i	1.27434	+	0.735740i	0.298538	+	0.954398i	$0.403501\pi$
$570$		0			0
$571$	7.63663	−	4.40901i	0.319583	−	0.184511i	−0.331624	−	0.943412i	$-0.607596\pi$
$571$	7.63663	−	4.40901i	0.319583	−	0.184511i	0.651207	+	0.758900i	$0.274263\pi$
$572$	−9.18301	+	9.36154i	−0.383961	+	0.391425i
$573$		0			0
$574$	−22.3825	−	5.06521i	−0.934229	−	0.211418i
$575$	−1.24742			−0.0520209
$576$		0			0
$577$	−6.92780	+	11.9993i	−0.288408	+	0.499537i	−0.973430	−	0.228985i	$-0.926459\pi$
$577$	−6.92780	+	11.9993i	−0.288408	+	0.499537i	0.685022	+	0.728522i	$0.259793\pi$
$578$	−50.7902	+	21.3250i	−2.11260	+	0.887003i
$579$		0			0
$580$	−1.31051	−	4.70907i	−0.0544158	−	0.195534i
$581$	16.7060	−	23.3974i	0.693080	−	0.970689i
$582$		0			0
$583$	−3.85968	−	2.22839i	−0.159852	−	0.0922904i
$584$	11.6243	+	14.7045i	0.481019	+	0.608478i
$585$		0			0
$586$	2.75644	−	3.62829i	0.113867	−	0.149883i
$587$	0.719382	+	1.24601i	0.0296921	+	0.0514282i	0.880490	−	0.474065i	$-0.157214\pi$
$587$	0.719382	+	1.24601i	0.0296921	+	0.0514282i	−0.850798	+	0.525494i	$0.823881\pi$
$588$		0			0
$589$	−3.34578	+	5.79505i	−0.137860	+	0.238781i
$590$	−9.95802	−	23.7173i	−0.409965	−	0.976424i
$591$		0			0
$592$	0.583098	+	30.2818i	0.0239652	+	1.24458i
$593$	0.152182	−	0.0878622i	0.00624935	−	0.00360807i	−0.496872	−	0.867824i	$-0.665518\pi$
$593$	0.152182	−	0.0878622i	0.00624935	−	0.00360807i	0.503121	+	0.864216i	$0.332185\pi$
$594$		0			0
$595$	31.9688	+	3.09354i	1.31059	+	0.126823i
$596$	3.90720	−	15.1643i	0.160045	−	0.621154i
$597$		0			0
$598$	−3.51344	−	2.66919i	−0.143675	−	0.109151i
$599$	16.9514	+	29.3607i	0.692616	+	1.19965i	0.970978	+	0.239170i	$0.0768752\pi$
$599$	16.9514	+	29.3607i	0.692616	+	1.19965i	−0.278362	+	0.960476i	$0.589791\pi$
$600$		0			0
$601$	3.53802	+	6.12803i	0.144319	+	0.249968i	0.929119	−	0.369782i	$-0.120568\pi$
$601$	3.53802	+	6.12803i	0.144319	+	0.249968i	−0.784800	+	0.619749i	$0.787234\pi$
$602$	11.4960	−	12.4357i	0.468543	−	0.506842i
$603$		0			0
$604$	2.82794	−	10.9756i	0.115067	−	0.446590i
$605$		−	15.8600i		−	0.644800i
$606$		0			0
$607$		−	20.4569i		−	0.830319i	−0.909749	−	0.415159i	$-0.863726\pi$
$607$		−	20.4569i		−	0.830319i	0.909749	−	0.415159i	$-0.136274\pi$
$608$	2.17814	−	20.3106i	0.0883353	−	0.823705i
$609$		0			0
$610$	−15.7518	+	20.7340i	−0.637771	+	0.839496i
$611$	−11.7373	−	20.3296i	−0.474841	−	0.822450i
$612$		0			0
$613$	23.2883	−	40.3365i	0.940604	−	1.62917i	0.176283	−	0.984340i	$-0.443593\pi$
$613$	23.2883	−	40.3365i	0.940604	−	1.62917i	0.764322	−	0.644835i	$-0.223074\pi$
$614$	−17.0521	−	2.16151i	−0.688168	−	0.0872313i
$615$		0			0
$616$	−8.28102	+	0.405039i	−0.333652	+	0.0163195i
$617$	17.0288	+	9.83161i	0.685555	+	0.395806i	0.801945	−	0.597398i	$-0.203799\pi$
$617$	17.0288	+	9.83161i	0.685555	+	0.395806i	−0.116389	+	0.993204i	$0.537132\pi$
$618$		0			0
$619$		−	30.6549i		−	1.23212i	−0.787698	−	0.616062i	$-0.788727\pi$
$619$		−	30.6549i		−	1.23212i	0.787698	−	0.616062i	$-0.211273\pi$
$620$	−1.61260	−	5.79460i	−0.0647637	−	0.232717i
$621$		0			0
$622$	4.38717	−	1.84201i	0.175909	−	0.0738580i
$623$	3.10945	+	2.22017i	0.124577	+	0.0889493i
$624$		0			0
$625$	−7.57072			−0.302829
$626$	−9.25121	−	7.02822i	−0.369753	−	0.280904i
$627$		0			0
$628$	−5.07623	−	18.2405i	−0.202564	−	0.727877i
$629$			56.6380i			2.25830i
$630$		0			0
$631$		−	33.9202i		−	1.35034i	−0.737661	−	0.675172i	$-0.764070\pi$
$631$		−	33.9202i		−	1.35034i	0.737661	−	0.675172i	$-0.235930\pi$
$632$	−4.11882	+	3.25604i	−0.163838	+	0.129518i
$633$		0			0
$634$	−1.85888	+	2.44684i	−0.0738256	+	0.0971763i
$635$	5.67612			0.225250
$636$		0			0
$637$	13.4501	+	39.1825i	0.532913	+	1.55247i
$638$	0.913445	+	2.17557i	0.0361636	+	0.0861318i
$639$		0			0
$640$	11.6620	+	14.1821i	0.460980	+	0.560598i
$641$			41.0892i			1.62292i	0.584405	+	0.811462i	$0.301328\pi$
$641$			41.0892i			1.62292i	−0.584405	+	0.811462i	$0.698672\pi$
$642$		0			0
$643$	43.0434	+	24.8511i	1.69747	+	0.980033i	0.948151	+	0.317820i	$0.102951\pi$
$643$	43.0434	+	24.8511i	1.69747	+	0.980033i	0.749316	+	0.662213i	$0.230383\pi$
$644$	−0.485591	−	2.74707i	−0.0191349	−	0.108250i
$645$		0			0
$646$	4.80362	−	37.8957i	0.188996	−	1.49099i
$647$	8.17906	−	14.1666i	0.321552	−	0.556945i	−0.659256	−	0.751918i	$-0.729129\pi$
$647$	8.17906	−	14.1666i	0.321552	−	0.556945i	0.980808	+	0.194974i	$0.0624621\pi$
$648$		0			0
$649$	6.20851	+	10.7535i	0.243705	+	0.422110i
$650$	15.7689	+	11.9797i	0.618505	+	0.469883i
$651$		0			0
$652$	−35.6480	+	9.92063i	−1.39608	+	0.388522i
$653$		−	3.16554i		−	0.123877i	−0.998080	−	0.0619387i	$-0.980272\pi$
$653$		−	3.16554i		−	0.123877i	0.998080	−	0.0619387i	$-0.0197283\pi$
$654$		0			0
$655$		−	3.50786i		−	0.137063i
$656$	−12.6733	−	21.0061i	−0.494808	−	0.820151i
$657$		0			0
$658$	3.27585	−	14.4756i	0.127706	−	0.564316i
$659$	−12.9324	−	22.3996i	−0.503776	−	0.872565i	−0.999990	−	0.00436530i	$-0.998610\pi$
$659$	−12.9324	−	22.3996i	−0.503776	−	0.872565i	0.496215	−	0.868200i	$-0.334723\pi$
$660$		0			0
$661$	6.74063	+	11.6751i	0.262180	+	0.454109i	0.966821	−	0.255455i	$-0.0822253\pi$
$661$	6.74063	+	11.6751i	0.262180	+	0.454109i	−0.704641	+	0.709564i	$0.748892\pi$
$662$	−17.5159	+	23.0561i	−0.680773	+	0.896099i
$663$		0			0
$664$	30.4104	−	4.45122i	1.18015	−	0.172741i
$665$	−9.00990	+	12.6188i	−0.349389	+	0.489334i
$666$		0			0
$667$	−0.687559	+	0.396962i	−0.0266224	+	0.0153704i
$668$	29.8393	−	30.4194i	1.15452	−	1.17696i
$669$		0			0
$670$	−28.9682	+	12.1627i	−1.11914	+	0.469886i
$671$	6.28474	−	10.8855i	0.242620	−	0.420230i
$672$		0			0
$673$	−7.87176	−	13.6343i	−0.303434	−	0.525563i	0.673477	−	0.739208i	$-0.264800\pi$
$673$	−7.87176	−	13.6343i	−0.303434	−	0.525563i	−0.976911	+	0.213644i	$0.931467\pi$
$674$	−23.8583	−	18.1254i	−0.918989	−	0.698163i
$675$		0			0
$676$	11.8095	+	42.4354i	0.454212	+	1.63213i
$677$	−21.7832	−	12.5765i	−0.837197	−	0.483356i	0.0191135	−	0.999817i	$-0.493916\pi$
$677$	−21.7832	−	12.5765i	−0.837197	−	0.483356i	−0.856310	+	0.516461i	$0.827249\pi$
$678$		0			0
$679$	3.65350	−	5.11689i	0.140208	−	0.196368i
$680$	21.2934	+	26.9357i	0.816566	+	1.03294i
$681$		0			0
$682$	1.12401	+	2.67708i	0.0430406	+	0.102511i
$683$	14.5432	−	25.1896i	0.556480	−	0.963852i	−0.441307	−	0.897356i	$-0.645485\pi$
$683$	14.5432	−	25.1896i	0.556480	−	0.963852i	0.997787	−	0.0664956i	$-0.0211818\pi$
$684$		0			0
$685$	17.4315			0.666022
$686$	−10.5719	+	23.9632i	−0.403636	+	0.914920i
$687$		0			0
$688$	18.1013	−	0.348553i	0.690105	−	0.0132885i
$689$	−20.6170	+	11.9032i	−0.785446	+	0.453477i
$690$		0			0
$691$	31.9946	+	18.4721i	1.21713	+	0.702711i	0.964303	−	0.264801i	$-0.0853061\pi$
$691$	31.9946	+	18.4721i	1.21713	+	0.702711i	0.252828	+	0.967511i	$0.418639\pi$
$692$	0.362239	+	0.355331i	0.0137703	+	0.0135077i
$693$		0			0
$694$	−26.6478	+	11.1884i	−1.01154	+	0.424708i
$695$	7.10037	−	12.2982i	0.269332	−	0.466497i
$696$		0			0
$697$	−22.9385	−	39.7307i	−0.868859	−	1.50491i
$698$	33.3610	−	14.0071i	1.26273	−	0.530177i
$699$		0			0
$700$	2.17940	+	12.3293i	0.0823737	+	0.466003i
$701$			2.75255i			0.103962i	0.998648	+	0.0519812i	$0.0165536\pi$
$701$			2.75255i			0.103962i	−0.998648	+	0.0519812i	$0.983446\pi$
$702$		0			0
$703$	−23.6791	−	13.6711i	−0.893074	−	0.515616i
$704$	−6.44571	−	6.08375i	−0.242932	−	0.229290i
$705$		0			0
$706$	−30.9302	−	3.92067i	−1.16407	−	0.147556i
$707$	0.535126	−	0.243565i	0.0201255	−	0.00916021i
$708$		0			0
$709$	21.7068	−	37.5972i	0.815215	−	1.41199i	−0.0939581	−	0.995576i	$-0.529952\pi$
$709$	21.7068	−	37.5972i	0.815215	−	1.41199i	0.909173	−	0.416418i	$-0.136715\pi$
$710$	−18.4045	−	2.33294i	−0.690710	−	0.0875536i
$711$		0			0
$712$	0.591554	+	4.04145i	0.0221694	+	0.151460i
$713$	−0.846054	+	0.488470i	−0.0316850	+	0.0182933i
$714$		0			0
$715$	9.21549	+	5.32057i	0.344640	+	0.198978i
$716$	3.53183	−	3.60049i	0.131991	−	0.134557i
$717$		0			0
$718$	−29.5109	+	12.3906i	−1.10134	+	0.462411i
$719$	−22.6916	−	39.3031i	−0.846255	−	1.46576i	−0.884527	−	0.466489i	$-0.845519\pi$
$719$	−22.6916	−	39.3031i	−0.846255	−	1.46576i	0.0382718	−	0.999267i	$-0.487815\pi$
$720$		0			0
$721$	−12.5737	+	5.72299i	−0.468270	+	0.213135i
$722$	−6.71205	−	5.09919i	−0.249797	−	0.189772i
$723$		0			0
$724$	−8.93345	−	2.30177i	−0.332009	−	0.0855446i
$725$	3.08587	−	1.78163i	0.114606	−	0.0661679i
$726$		0			0
$727$	−2.94179	+	1.69844i	−0.109105	+	0.0629917i	−0.553559	−	0.832810i	$-0.686731\pi$
$727$	−2.94179	+	1.69844i	−0.109105	+	0.0629917i	0.444455	+	0.895801i	$0.353397\pi$
$728$	−20.2434	+	39.3897i	−0.750270	+	1.45988i
$729$		0			0
$730$	9.20122	−	12.1115i	0.340552	−	0.448268i
$731$	33.8559			1.25221
$732$		0			0
$733$	14.5421			0.537125			0.268563	−	0.963262i	$-0.413451\pi$
$733$	14.5421			0.537125			0.268563	+	0.963262i	$0.413451\pi$
$734$	−39.5380	−	5.01179i	−1.45937	−	0.184989i
$735$		0			0
$736$	1.75803	−	2.40900i	0.0648019	−	0.0887969i
$737$	13.1343	−	7.58306i	0.483806	−	0.279326i
$738$		0			0
$739$	1.89468	+	1.09390i	0.0696970	+	0.0402396i	0.534444	−	0.845204i	$-0.320521\pi$
$739$	1.89468	+	1.09390i	0.0696970	+	0.0402396i	−0.464747	+	0.885444i	$0.653855\pi$
$740$	23.6773	−	6.58924i	0.870393	−	0.242225i
$741$		0			0
$742$	−14.6802	−	3.32215i	−0.538926	−	0.121960i
$743$	−18.6078	+	32.2296i	−0.682654	+	1.18239i	0.291514	+	0.956567i	$0.405841\pi$
$743$	−18.6078	+	32.2296i	−0.682654	+	1.18239i	−0.974168	+	0.225825i	$0.927492\pi$
$744$		0			0
$745$	−12.7071			−0.465553
$746$	2.45764	−	19.3883i	0.0899805	−	0.709856i
$747$		0			0
$748$	−11.8323	−	11.6067i	−0.432632	−	0.424381i
$749$	−16.4092	+	22.9818i	−0.599579	+	0.839737i
$750$		0			0
$751$		−	7.94782i		−	0.290020i	−0.989430	−	0.145010i	$-0.953679\pi$
$751$		−	7.94782i		−	0.290020i	0.989430	−	0.145010i	$-0.0463214\pi$
$752$	13.5854	−	8.19623i	0.495407	−	0.298886i
$753$		0			0
$754$	12.5038	+	1.58497i	0.455363	+	0.0577212i
$755$	−9.19711			−0.334717
$756$		0			0
$757$	−26.6849			−0.969879			−0.484940	−	0.874548i	$-0.661158\pi$
$757$	−26.6849			−0.969879			−0.484940	+	0.874548i	$0.661158\pi$
$758$	7.45635	+	0.945158i	0.270827	+	0.0343297i
$759$		0			0
$760$	−16.4010	+	2.40064i	−0.594927	+	0.0870805i
$761$			19.0997i			0.692363i	0.938167	+	0.346182i	$0.112522\pi$
$761$			19.0997i			0.692363i	−0.938167	+	0.346182i	$0.887478\pi$
$762$		0			0
$763$	−23.9070	−	2.31342i	−0.865493	−	0.0837513i
$764$	−9.52467	+	9.70984i	−0.344590	+	0.351290i
$765$		0			0
$766$	5.24400	−	41.3699i	0.189473	−	1.49475i
$767$	66.3272			2.39494
$768$		0			0
$769$	7.07033	−	12.2462i	0.254963	−	0.441608i	−0.709923	−	0.704280i	$-0.751270\pi$
$769$	7.07033	−	12.2462i	0.254963	−	0.441608i	0.964885	+	0.262671i	$0.0846035\pi$
$770$	1.99490	+	6.42517i	0.0718913	+	0.231547i
$771$		0			0
$772$	12.2503	+	44.0194i	0.440900	+	1.58429i
$773$	1.43134	+	0.826385i	0.0514817	+	0.0297230i	0.525520	−	0.850781i	$-0.323871\pi$
$773$	1.43134	+	0.826385i	0.0514817	+	0.0297230i	−0.474038	+	0.880504i	$0.657204\pi$
$774$		0			0
$775$	3.79722	−	2.19232i	0.136400	−	0.0787506i
$776$	6.65058	−	0.973457i	0.238742	−	0.0349451i
$777$		0			0
$778$	40.3907	+	5.11988i	1.44808	+	0.183557i
$779$	22.1474			0.793512
$780$		0			0
$781$	8.95536			0.320448
$782$	3.37366	−	4.44074i	0.120642	−	0.158800i
$783$		0			0
$784$	−26.3032	+	9.59899i	−0.939401	+	0.342821i
$785$	−13.3056	+	7.68197i	−0.474896	+	0.274181i
$786$		0			0
$787$	−5.44534	+	3.14387i	−0.194105	+	0.112067i	−0.593903	−	0.804537i	$-0.702414\pi$
$787$	−5.44534	+	3.14387i	−0.194105	+	0.112067i	0.399798	+	0.916603i	$0.369080\pi$
$788$	−4.57544	+	17.7578i	−0.162993	+	0.632596i
$789$		0			0
$790$	3.39250	+	2.57731i	0.120700	+	0.0916965i
$791$	−1.89621	+	19.5956i	−0.0674215	+	0.696739i
$792$		0			0
$793$	−33.5708	−	58.1463i	−1.19213	−	2.06484i
$794$	−31.6111	+	13.2724i	−1.12184	+	0.471019i
$795$		0			0
$796$	−18.4887	−	18.1361i	−0.655313	−	0.642816i
$797$	−3.45212	−	1.99308i	−0.122280	−	0.0705986i	0.437612	−	0.899164i	$-0.355824\pi$
$797$	−3.45212	−	1.99308i	−0.122280	−	0.0705986i	−0.559893	+	0.828565i	$0.689158\pi$
$798$		0			0
$799$	25.6952	−	14.8351i	0.909031	−	0.524829i
$800$	−7.89030	+	10.8119i	−0.278964	+	0.382260i
$801$		0			0
$802$	9.46416	+	1.19967i	0.334191	+	0.0423617i
$803$	−3.67116	+	6.35863i	−0.129552	+	0.224391i
$804$		0			0
$805$	−2.06032	+	0.937764i	−0.0726168	+	0.0330518i
$806$	15.3862	+	1.95034i	0.541956	+	0.0686977i
$807$		0			0
$808$	0.584112	+	0.232123i	0.0205490	+	0.00816607i
$809$	11.9903	+	6.92261i	0.421557	+	0.243386i	0.695743	−	0.718291i	$-0.255075\pi$
$809$	11.9903	+	6.92261i	0.421557	+	0.243386i	−0.274186	+	0.961677i	$0.588408\pi$
$810$		0			0
$811$			31.3223i			1.09988i	0.835206	+	0.549938i	$0.185349\pi$
$811$			31.3223i			1.09988i	−0.835206	+	0.549938i	$0.814651\pi$
$812$	5.12476	+	6.10217i	0.179844	+	0.214144i
$813$		0			0
$814$	−10.9388	+	4.59281i	−0.383405	+	0.160978i
$815$	15.0131	+	26.0034i	0.525886	+	0.910861i
$816$		0			0
$817$	−8.17206	+	14.1544i	−0.285904	+	0.495201i
$818$	−0.605930	+	0.254408i	−0.0211859	+	0.00889518i
$819$		0			0
$820$	−13.9406	+	14.2116i	−0.486826	+	0.496291i
$821$	−40.1722	−	23.1934i	−1.40202	−	0.809457i	−0.407421	−	0.913241i	$-0.633572\pi$
$821$	−40.1722	−	23.1934i	−1.40202	−	0.809457i	−0.994600	+	0.103784i	$0.966905\pi$
$822$		0			0
$823$	−3.32006	+	1.91684i	−0.115730	+	0.0668168i	−0.556748	−	0.830682i	$-0.687951\pi$
$823$	−3.32006	+	1.91684i	−0.115730	+	0.0668168i	0.441018	+	0.897498i	$0.354618\pi$
$824$	−13.7247	−	5.45415i	−0.478124	−	0.190004i
$825$		0			0
$826$	30.7929	+	28.4660i	1.07142	+	0.990459i
$827$	29.9172			1.04032			0.520162	−	0.854068i	$-0.325872\pi$
$827$	29.9172			1.04032			0.520162	+	0.854068i	$0.325872\pi$
$828$		0			0
$829$	−6.90778	+	11.9646i	−0.239917	+	0.415549i	−0.960690	−	0.277622i	$-0.910454\pi$
$829$	−6.90778	+	11.9646i	−0.239917	+	0.415549i	0.720773	+	0.693171i	$0.243787\pi$
$830$	−9.65482	−	22.9951i	−0.335124	−	0.798172i
$831$		0			0
$832$	−45.3587	+	13.5692i	−1.57253	+	0.470427i
$833$	−49.5239	+	17.0000i	−1.71590	+	0.589014i
$834$		0			0
$835$	−29.9448	−	17.2887i	−1.03628	−	0.598299i
$836$	7.70854	−	2.14524i	0.266605	−	0.0741947i
$837$		0			0
$838$	29.1433	+	22.1404i	1.00674	+	0.764828i
$839$	−14.7035	−	25.4672i	−0.507621	−	0.879225i	−0.999961	−	0.00882220i	$-0.997192\pi$
$839$	−14.7035	−	25.4672i	−0.507621	−	0.879225i	0.492340	−	0.870403i	$-0.336142\pi$
$840$		0			0
$841$	−13.3661	+	23.1507i	−0.460899	+	0.798301i
$842$	−30.6829	+	12.8827i	−1.05740	+	0.443966i
$843$		0			0
$844$	9.50880	+	9.32747i	0.327306	+	0.321065i
$845$	30.9545	−	17.8716i	1.06487	−	0.614801i
$846$		0			0
$847$	10.7110	+	23.5327i	0.368035	+	0.808593i
$848$	−8.31209	−	13.7774i	−0.285438	−	0.473118i
$849$		0			0
$850$	−15.1415	+	19.9307i	−0.519349	+	0.683617i
$851$	−1.99593	−	3.45705i	−0.0684196	−	0.118506i
$852$		0			0
$853$	3.70601	+	6.41901i	0.126892	+	0.219783i	0.922471	−	0.386067i	$-0.126167\pi$
$853$	3.70601	+	6.41901i	0.126892	+	0.219783i	−0.795579	+	0.605850i	$0.792833\pi$
$854$	9.36949	−	41.4026i	0.320617	−	1.41677i
$855$		0			0
$856$	−29.8702	+	4.37215i	−1.02094	+	0.149437i
$857$			23.0231i			0.786454i	0.919441	+	0.393227i	$0.128641\pi$
$857$			23.0231i			0.786454i	−0.919441	+	0.393227i	$0.871359\pi$
$858$		0			0
$859$		−	39.6857i		−	1.35406i	−0.735955	−	0.677030i	$-0.763267\pi$
$859$		−	39.6857i		−	1.35406i	0.735955	−	0.677030i	$-0.236733\pi$
$860$	−3.93879	−	14.1533i	−0.134311	−	0.482624i
$861$		0			0
$862$	5.06236	+	3.84592i	0.172425	+	0.130992i
$863$	1.00969	+	1.74883i	0.0343701	+	0.0595308i	0.882699	−	0.469939i	$-0.155724\pi$
$863$	1.00969	+	1.74883i	0.0343701	+	0.0595308i	−0.848329	+	0.529470i	$0.822391\pi$
$864$		0			0
$865$	0.205876	−	0.356588i	0.00700001	−	0.0121244i
$866$	1.45113	−	11.4479i	0.0493113	−	0.389017i
$867$		0			0
$868$	6.30612	+	7.50884i	0.214044	+	0.254867i
$869$	−1.78108	−	1.02831i	−0.0604192	−	0.0348830i
$870$		0			0
$871$		−	81.0120i		−	2.74499i
$872$	−15.9237	−	20.1432i	−0.539245	−	0.682133i
$873$		0			0
$874$	1.04225	+	2.48235i	0.0352546	+	0.0839667i
$875$	28.7874	−	13.1027i	0.973191	−	0.442952i
$876$		0			0
$877$	56.4662			1.90673			0.953363	−	0.301825i	$-0.0975958\pi$
$877$	56.4662			1.90673			0.953363	+	0.301825i	$0.0975958\pi$
$878$	2.24468	−	2.95466i	0.0757542	−	0.0997150i
$879$		0			0
$880$	−3.47555	+	6.29676i	−0.117161	+	0.212264i
$881$		−	37.0303i		−	1.24758i	−0.781591	−	0.623791i	$-0.785592\pi$
$881$		−	37.0303i		−	1.24758i	0.781591	−	0.623791i	$-0.214408\pi$
$882$		0			0
$883$		−	6.71801i		−	0.226079i	−0.993590	−	0.113040i	$-0.963941\pi$
$883$		−	6.71801i		−	0.226079i	0.993590	−	0.113040i	$-0.0360587\pi$
$884$	−85.2942	+	23.7369i	−2.86876	+	0.798358i
$885$		0			0
$886$	−5.79097	−	4.39944i	−0.194551	−	0.147802i
$887$	−43.4080			−1.45750			−0.728749	−	0.684781i	$-0.759898\pi$
$887$	−43.4080			−1.45750			−0.728749	+	0.684781i	$0.759898\pi$
$888$		0			0
$889$	−8.42210	+	3.83336i	−0.282468	+	0.128567i
$890$	3.05598	−	1.28310i	0.102437	−	0.0430095i
$891$		0			0
$892$	−0.337149	+	0.0938264i	−0.0112886	+	0.00314154i
$893$			14.3235i			0.479317i
$894$		0			0
$895$	−3.54432	−	2.04631i	−0.118474	−	0.0684007i
$896$	−26.8817	−	13.1672i	−0.898053	−	0.439887i
$897$		0			0
$898$	15.6531	+	1.98417i	0.522350	+	0.0662125i
$899$	1.39531	−	2.41675i	0.0465363	−	0.0806032i
$900$		0			0
$901$	−15.0448	−	26.0584i	−0.501216	−	0.868131i
$902$	5.81331	−	7.65203i	0.193562	−	0.254785i
$903$		0			0
$904$	−16.5105	+	13.0520i	−0.549131	+	0.434103i
$905$			7.48589i			0.248839i
$906$		0			0
$907$		−	13.9802i		−	0.464204i	−0.972692	−	0.232102i	$-0.925440\pi$
$907$		−	13.9802i		−	0.464204i	0.972692	−	0.232102i	$-0.0745602\pi$
$908$	36.6727	+	9.44901i	1.21703	+	0.313576i
$909$		0			0
$910$	35.0508	+	7.93207i	1.16192	+	0.262945i
$911$	−12.6875	−	21.9753i	−0.420354	−	0.728075i	0.575620	−	0.817717i	$-0.304761\pi$
$911$	−12.6875	−	21.9753i	−0.420354	−	0.728075i	−0.995974	+	0.0896426i	$0.971428\pi$
$912$		0			0
$913$	6.01947	+	10.4260i	0.199215	+	0.345051i
$914$	−16.8070	−	12.7684i	−0.555925	−	0.422340i
$915$		0			0
$916$	−1.55281	−	0.400093i	−0.0513063	−	0.0132195i
$917$	2.36903	+	5.20489i	0.0782322	+	0.171881i
$918$		0			0
$919$	44.5267	−	25.7075i	1.46880	−	0.848012i	0.469412	−	0.882979i	$-0.344466\pi$
$919$	44.5267	−	25.7075i	1.46880	−	0.848012i	0.999388	+	0.0349671i	$0.0111326\pi$
$920$	−2.24892	−	0.893711i	−0.0741447	−	0.0294648i
$921$		0			0
$922$	17.4023	+	41.4474i	0.573113	+	1.36500i
$923$	23.9181	−	41.4274i	0.787275	−	1.36360i
$924$		0			0
$925$	8.95803	+	15.5158i	0.294538	+	0.510155i
$926$	−19.1383	+	25.1917i	−0.628925	+	0.827851i
$927$		0			0
$928$	−0.908366	+	8.47030i	−0.0298186	+	0.278051i
$929$	−0.520910	−	0.300748i	−0.0170905	−	0.00986721i	0.491430	−	0.870917i	$-0.336474\pi$
$929$	−0.520910	−	0.300748i	−0.0170905	−	0.00986721i	−0.508521	+	0.861050i	$0.669808\pi$
$930$		0			0
$931$	4.84663	−	24.8083i	0.158842	−	0.813058i
$932$	16.3631	−	4.55375i	0.535991	−	0.149163i
$933$		0			0
$934$	−23.7566	+	9.97454i	−0.777340	+	0.326377i
$935$	−6.72481	+	11.6477i	−0.219925	+	0.380921i
$936$		0			0
$937$	−7.87037			−0.257114			−0.128557	−	0.991702i	$-0.541034\pi$
$937$	−7.87037			−0.257114			−0.128557	+	0.991702i	$0.541034\pi$
$938$	34.7683	−	37.6104i	1.13523	−	1.22802i
$939$		0			0
$940$	−9.19113	−	9.01585i	−0.299782	−	0.294065i
$941$	25.2685	−	14.5888i	0.823731	−	0.475581i	−0.0279707	−	0.999609i	$-0.508905\pi$
$941$	25.2685	−	14.5888i	0.823731	−	0.475581i	0.851701	+	0.524028i	$0.175571\pi$
$942$		0			0
$943$	2.80023	+	1.61671i	0.0911881	+	0.0526475i
$944$	0.863074	+	44.8217i	0.0280907	+	1.45882i
$945$		0			0
$946$	2.74540	+	6.53878i	0.0892607	+	0.212594i
$947$	−26.2206	+	45.4154i	−0.852056	+	1.47580i	0.0272941	+	0.999627i	$0.491311\pi$
$947$	−26.2206	+	45.4154i	−0.852056	+	1.47580i	−0.879350	+	0.476176i	$0.842022\pi$
$948$		0			0
$949$	19.6100	+	33.9655i	0.636567	+	1.10257i
$950$	−4.67777	−	11.1411i	−0.151767	−	0.361467i
$951$		0			0
$952$	−49.7857	−	25.5862i	−1.61356	−	0.829252i
$953$			13.6937i			0.443583i	0.975094	+	0.221792i	$0.0711905\pi$
$953$			13.6937i			0.443583i	−0.975094	+	0.221792i	$0.928810\pi$
$954$		0			0
$955$	9.55836	+	5.51852i	0.309301	+	0.178575i
$956$	−37.7378	+	38.4715i	−1.22053	+	1.24426i
$957$		0			0
$958$	−1.49459	+	11.7908i	−0.0482879	+	0.380943i
$959$	−25.8644	+	11.7723i	−0.835205	+	0.380147i
$960$		0			0
$961$	−13.7830	+	23.8729i	−0.444614	+	0.770094i
$962$	−7.96925	+	62.8694i	−0.256939	+	2.02699i
$963$		0			0
$964$	26.6044	+	6.85483i	0.856870	+	0.220779i
$965$	32.1100	−	18.5387i	1.03366	−	0.596782i
$966$		0			0
$967$	4.97450	+	2.87203i	0.159969	+	0.0923583i	0.577848	−	0.816145i	$-0.303893\pi$
$967$	4.97450	+	2.87203i	0.159969	+	0.0923583i	−0.417878	+	0.908503i	$0.637226\pi$
$968$	−10.2079	+	25.6869i	−0.328093	+	0.825608i
$969$		0			0
$970$	−2.11145	−	5.02890i	−0.0677947	−	0.161468i
$971$	−4.17759	−	7.23580i	−0.134065	−	0.232208i	0.791175	−	0.611590i	$-0.209470\pi$
$971$	−4.17759	−	7.23580i	−0.134065	−	0.232208i	−0.925240	+	0.379382i	$0.876136\pi$
$972$		0			0
$973$	−2.22981	+	23.0430i	−0.0714844	+	0.738725i
$974$	10.9592	−	14.4255i	0.351154	−	0.462223i
$975$		0			0
$976$	38.8565	−	23.4427i	1.24377	−	0.750381i
$977$	38.2702	−	22.0953i	1.22437	−	0.706891i	0.258524	−	0.966005i	$-0.416764\pi$
$977$	38.2702	−	22.0953i	1.22437	−	0.706891i	0.965847	+	0.259114i	$0.0834305\pi$
$978$		0			0
$979$	−1.38559	+	0.799970i	−0.0442836	+	0.0255671i
$980$	12.8683	+	18.7255i	0.411064	+	0.598163i
$981$		0			0
$982$	−10.2865	−	7.81475i	−0.328256	−	0.249379i
$983$	−16.6293			−0.530392			−0.265196	−	0.964195i	$-0.585437\pi$
$983$	−16.6293			−0.530392			−0.265196	+	0.964195i	$0.585437\pi$
$984$		0			0
$985$	14.8804			0.474128
$986$	−2.00329	+	15.8039i	−0.0637977	+	0.503300i
$987$		0			0
$988$	10.6642	−	41.3892i	0.339275	−	1.31677i
$989$	−2.06649	+	1.19309i	−0.0657105	+	0.0379380i
$990$		0			0
$991$	−2.55015	−	1.47233i	−0.0810081	−	0.0467700i	0.458949	−	0.888463i	$-0.348226\pi$
$991$	−2.55015	−	1.47233i	−0.0810081	−	0.0467700i	−0.539957	+	0.841693i	$0.681559\pi$
$992$	−1.11776	+	10.4229i	−0.0354890	+	0.330926i
$993$		0			0
$994$	28.8838	−	8.96791i	0.916139	−	0.284445i
$995$	−10.5079	+	18.2002i	−0.333123	+	0.576986i
$996$		0			0
$997$	30.7962			0.975325			0.487663	−	0.873032i	$-0.337850\pi$
$997$	30.7962			0.975325			0.487663	+	0.873032i	$0.337850\pi$
$998$	34.7282	+	4.40211i	1.09930	+	0.139346i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.o.a.179.20		88
3.2	odd	2		252.2.o.a.95.25	yes	88
4.3	odd	2	inner	756.2.o.a.179.35		88
7.2	even	3		756.2.bb.a.611.40		88
9.2	odd	6		756.2.bb.a.683.5		88
9.7	even	3		252.2.bb.a.11.40	yes	88
12.11	even	2		252.2.o.a.95.10	✓	88
21.2	odd	6		252.2.bb.a.23.5	yes	88
28.23	odd	6		756.2.bb.a.611.5		88
36.7	odd	6		252.2.bb.a.11.5	yes	88
36.11	even	6		756.2.bb.a.683.40		88
63.2	odd	6	inner	756.2.o.a.359.35		88
63.16	even	3		252.2.o.a.191.10	yes	88
84.23	even	6		252.2.bb.a.23.40	yes	88
252.79	odd	6		252.2.o.a.191.25	yes	88
252.191	even	6	inner	756.2.o.a.359.20		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.10	✓	88	12.11	even	2
252.2.o.a.95.25	yes	88	3.2	odd	2
252.2.o.a.191.10	yes	88	63.16	even	3
252.2.o.a.191.25	yes	88	252.79	odd	6
252.2.bb.a.11.5	yes	88	36.7	odd	6
252.2.bb.a.11.40	yes	88	9.7	even	3
252.2.bb.a.23.5	yes	88	21.2	odd	6
252.2.bb.a.23.40	yes	88	84.23	even	6
756.2.o.a.179.20		88	1.1	even	1	trivial
756.2.o.a.179.35		88	4.3	odd	2	inner
756.2.o.a.359.20		88	252.191	even	6	inner
756.2.o.a.359.35		88	63.2	odd	6	inner
756.2.bb.a.611.5		88	28.23	odd	6
756.2.bb.a.611.40		88	7.2	even	3
756.2.bb.a.683.5		88	9.2	odd	6
756.2.bb.a.683.40		88	36.11	even	6

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.177841 + 1.40299i) q^{2} +(-1.93675 - 0.499017i) q^{4} +1.62292i q^{5} +(-1.09603 - 2.40805i) q^{7} +(1.04455 - 2.62848i) q^{8} +O(q^{10})\)	\(q+(-0.177841 + 1.40299i) q^{2} +(-1.93675 - 0.499017i) q^{4} +1.62292i q^{5} +(-1.09603 - 2.40805i) q^{7} +(1.04455 - 2.62848i) q^{8} +(-2.27693 - 0.288621i) q^{10} +1.10792 q^{11} +(2.95905 - 5.12523i) q^{13} +(3.57338 - 1.10947i) q^{14} +(3.50196 + 1.93294i) q^{16} +(6.47792 + 3.74003i) q^{17} +(-3.12725 + 1.80552i) q^{19} +(0.809864 - 3.14318i) q^{20} +(-0.197034 + 1.55440i) q^{22} -0.527196 q^{23} +2.36614 q^{25} +(6.66439 + 5.06299i) q^{26} +(0.921081 + 5.21072i) q^{28} +(1.30418 - 0.752968i) q^{29} +(1.60482 - 0.926542i) q^{31} +(-3.33468 + 4.56945i) q^{32} +(-6.39925 + 8.42331i) q^{34} +(3.90807 - 1.77877i) q^{35} +(3.78593 + 6.55743i) q^{37} +(-1.97696 - 4.70858i) q^{38} +(4.26581 + 1.69521i) q^{40} +(-5.31155 - 3.06663i) q^{41} +(3.91977 - 2.26308i) q^{43} +(-2.14576 - 0.552871i) q^{44} +(0.0937571 - 0.739650i) q^{46} +(1.98329 - 3.43516i) q^{47} +(-4.59742 + 5.27861i) q^{49} +(-0.420796 + 3.31966i) q^{50} +(-8.28851 + 8.44965i) q^{52} +(-3.48372 - 2.01133i) q^{53} +1.79806i q^{55} +(-7.47438 + 0.365585i) q^{56} +(0.824468 + 1.96366i) q^{58} +(5.60375 + 9.70599i) q^{59} +(5.67256 - 9.82516i) q^{61} +(1.01452 + 2.41632i) q^{62} +(-5.81784 - 5.49115i) q^{64} +(8.31783 + 4.80230i) q^{65} +(11.8549 - 6.84441i) q^{67} +(-10.6797 - 10.4761i) q^{68} +(1.80058 + 5.79931i) q^{70} +8.08304 q^{71} +(-3.31356 + 5.73925i) q^{73} +(-9.87328 + 4.14543i) q^{74} +(6.95767 - 1.93628i) q^{76} +(-1.21432 - 2.66793i) q^{77} +(-1.60759 - 0.928144i) q^{79} +(-3.13700 + 5.68340i) q^{80} +(5.24705 - 6.90667i) q^{82} +(5.43313 + 9.41046i) q^{83} +(-6.06976 + 10.5131i) q^{85} +(2.47798 + 5.90185i) q^{86} +(1.15727 - 2.91215i) q^{88} +(-1.25062 + 0.722046i) q^{89} +(-15.5850 - 1.50812i) q^{91} +(1.02105 + 0.263080i) q^{92} +(4.46678 + 3.39344i) q^{94} +(-2.93021 - 5.07527i) q^{95} +(1.18819 + 2.05801i) q^{97} +(-6.58822 - 7.38887i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 3 q^{2} + q^{4}+O(q^{10}) \) 88 * q + 3 * q^2 + q^4	\( 88 q + 3 q^{2} + q^{4} + 2 q^{10} - 4 q^{13} + 3 q^{14} + q^{16} + 6 q^{20} - 6 q^{22} - 60 q^{25} + 6 q^{26} + 24 q^{29} - 27 q^{32} - 4 q^{34} - 4 q^{37} + 8 q^{40} + 12 q^{41} + 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} + 14 q^{52} + 66 q^{56} - 10 q^{58} + 2 q^{61} - 8 q^{64} - 18 q^{65} + 30 q^{70} - 4 q^{73} - 6 q^{76} + 30 q^{77} - 87 q^{80} - 4 q^{82} - 14 q^{85} - 18 q^{88} - 60 q^{89} - 24 q^{92} + 9 q^{94} - 4 q^{97} + 57 q^{98}+O(q^{100}) \) 88 * q + 3 * q^2 + q^4 + 2 * q^10 - 4 * q^13 + 3 * q^14 + q^16 + 6 * q^20 - 6 * q^22 - 60 * q^25 + 6 * q^26 + 24 * q^29 - 27 * q^32 - 4 * q^34 - 4 * q^37 + 8 * q^40 + 12 * q^41 + 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 + 14 * q^52 + 66 * q^56 - 10 * q^58 + 2 * q^61 - 8 * q^64 - 18 * q^65 + 30 * q^70 - 4 * q^73 - 6 * q^76 + 30 * q^77 - 87 * q^80 - 4 * q^82 - 14 * q^85 - 18 * q^88 - 60 * q^89 - 24 * q^92 + 9 * q^94 - 4 * q^97 + 57 * q^98

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