LMFDB - Embedded newform 315.3.ca.b.37.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(37,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("315.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.ca (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:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.11
Character	$\chi$	$=$	315.37
Dual form			315.3.ca.b.298.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.84280 - 0.493776i) q^{2} +(-0.312015 + 0.180142i) q^{4} +(1.82066 + 4.65674i) q^{5} +(-6.63712 - 2.22456i) q^{7} +(-5.88211 + 5.88211i) q^{8} +O(q^{10})$	\(q+(1.84280 - 0.493776i) q^{2} +(-0.312015 + 0.180142i) q^{4} +(1.82066 + 4.65674i) q^{5} +(-6.63712 - 2.22456i) q^{7} +(-5.88211 + 5.88211i) q^{8} +(5.65448 + 7.68243i) q^{10} +(5.24180 + 9.07906i) q^{11} +(1.40565 - 1.40565i) q^{13} +(-13.3293 - 0.822171i) q^{14} +(-7.21453 + 12.4959i) q^{16} +(-6.55621 + 24.4681i) q^{17} +(-9.07193 - 5.23768i) q^{19} +(-1.40694 - 1.12499i) q^{20} +(14.1426 + 14.1426i) q^{22} +(7.89111 + 29.4500i) q^{23} +(-18.3704 + 16.9566i) q^{25} +(1.89626 - 3.28441i) q^{26} +(2.47161 - 0.501525i) q^{28} -55.6217i q^{29} +(8.12663 + 14.0757i) q^{31} +(1.48729 - 5.55064i) q^{32} +48.3271i q^{34} +(-1.72469 - 34.9575i) q^{35} +(14.8150 - 3.96966i) q^{37} +(-19.3040 - 5.17248i) q^{38} +(-38.1008 - 16.6822i) q^{40} +28.7305 q^{41} +(3.17014 - 3.17014i) q^{43} +(-3.27104 - 1.88853i) q^{44} +(29.0834 + 50.3740i) q^{46} +(1.71038 - 0.458294i) q^{47} +(39.1026 + 29.5294i) q^{49} +(-25.4802 + 40.3185i) q^{50} +(-0.185367 + 0.691801i) q^{52} +(56.9591 + 15.2621i) q^{53} +(-32.7353 + 40.9395i) q^{55} +(52.1254 - 25.9551i) q^{56} +(-27.4647 - 102.499i) q^{58} +(-57.7727 + 33.3551i) q^{59} +(6.16473 - 10.6776i) q^{61} +(21.9260 + 21.9260i) q^{62} -68.6793i q^{64} +(9.10496 + 3.98655i) q^{65} +(28.5890 - 106.696i) q^{67} +(-2.36209 - 8.81545i) q^{68} +(-20.4394 - 63.5679i) q^{70} -29.9403 q^{71} +(115.286 + 30.8909i) q^{73} +(25.3408 - 14.6305i) q^{74} +3.77410 q^{76} +(-14.5935 - 71.9195i) q^{77} +(-99.9248 - 57.6916i) q^{79} +(-71.3255 - 10.8454i) q^{80} +(52.9444 - 14.1864i) q^{82} +(-24.2475 + 24.2475i) q^{83} +(-125.878 + 14.0174i) q^{85} +(4.27659 - 7.40727i) q^{86} +(-84.2370 - 22.5712i) q^{88} +(-18.3646 - 10.6028i) q^{89} +(-12.4564 + 6.20252i) q^{91} +(-7.76732 - 7.76732i) q^{92} +(2.92558 - 1.68909i) q^{94} +(7.87366 - 51.7816i) q^{95} +(56.7300 + 56.7300i) q^{97} +(86.6391 + 35.1087i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8 - 16 * q^10 - 16 * q^11 + 80 * q^16 - 56 * q^17 - 96 * q^22 - 72 * q^23 - 4 * q^25 + 288 * q^26 - 380 * q^28 - 136 * q^31 + 48 * q^32 - 76 * q^35 - 28 * q^37 + 68 * q^38 + 164 * q^40 - 128 * q^41 + 344 * q^43 + 240 * q^46 - 412 * q^47 + 72 * q^50 + 388 * q^52 + 40 * q^53 - 8 * q^55 + 864 * q^56 + 56 * q^58 - 216 * q^61 + 912 * q^62 - 20 * q^65 - 368 * q^67 + 492 * q^68 + 416 * q^70 - 784 * q^71 - 316 * q^73 - 32 * q^76 - 844 * q^77 - 908 * q^80 + 556 * q^82 - 1408 * q^83 - 536 * q^85 - 1024 * q^86 + 372 * q^88 - 1064 * q^91 + 1704 * q^92 - 260 * q^95 + 352 * q^97 - 272 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.84280	−	0.493776i	0.921399	−	0.246888i	0.233216	−	0.972425i	$-0.425075\pi$
$2$	1.84280	−	0.493776i	0.921399	−	0.246888i	0.688183	+	0.725537i	$0.258409\pi$
$3$		0			0
$3$		0			0
$4$	−0.312015	+	0.180142i	−0.0780037	+	0.0450354i
$5$	1.82066	+	4.65674i	0.364131	+	0.931348i
$5$	1.82066	+	4.65674i	0.364131	+	0.931348i
$6$		0			0
$7$	−6.63712	−	2.22456i	−0.948160	−	0.317795i
$7$	−6.63712	−	2.22456i	−0.948160	−	0.317795i
$8$	−5.88211	+	5.88211i	−0.735264	+	0.735264i
$9$		0			0
$10$	5.65448	+	7.68243i	0.565448	+	0.768243i
$11$	5.24180	+	9.07906i	0.476527	+	0.825369i	0.999638	−	0.0268951i	$-0.00856202\pi$
$11$	5.24180	+	9.07906i	0.476527	+	0.825369i	−0.523111	+	0.852265i	$0.675229\pi$
$12$		0			0
$13$	1.40565	−	1.40565i	0.108127	−	0.108127i	−0.650973	−	0.759101i	$-0.725639\pi$
$13$	1.40565	−	1.40565i	0.108127	−	0.108127i	0.759101	+	0.650973i	$0.225639\pi$
$14$	−13.3293	−	0.822171i	−0.952093	−	0.0587265i
$15$		0			0
$16$	−7.21453	+	12.4959i	−0.450908	+	0.780996i
$17$	−6.55621	+	24.4681i	−0.385659	+	1.43930i	0.451465	+	0.892289i	$0.350901\pi$
$17$	−6.55621	+	24.4681i	−0.385659	+	1.43930i	−0.837125	+	0.547012i	$0.815765\pi$
$18$		0			0
$19$	−9.07193	−	5.23768i	−0.477470	−	0.275667i	0.241892	−	0.970303i	$-0.422232\pi$
$19$	−9.07193	−	5.23768i	−0.477470	−	0.275667i	−0.719362	+	0.694636i	$0.755566\pi$
$20$	−1.40694	−	1.12499i	−0.0703472	−	0.0562497i
$21$		0			0
$22$	14.1426	+	14.1426i	0.642845	+	0.642845i
$23$	7.89111	+	29.4500i	0.343092	+	1.28044i	0.894826	+	0.446416i	$0.147300\pi$
$23$	7.89111	+	29.4500i	0.343092	+	1.28044i	−0.551734	+	0.834020i	$0.686034\pi$
$24$		0			0
$25$	−18.3704	+	16.9566i	−0.734817	+	0.678265i
$26$	1.89626	−	3.28441i	0.0729329	−	0.126323i
$27$		0			0
$28$	2.47161	−	0.501525i	0.0882719	−	0.0179116i
$29$		−	55.6217i		−	1.91799i	−0.283425	−	0.958994i	$-0.591471\pi$
$29$		−	55.6217i		−	1.91799i	0.283425	−	0.958994i	$-0.408529\pi$
$30$		0			0
$31$	8.12663	+	14.0757i	0.262149	+	0.454056i	0.966813	−	0.255486i	$-0.0822354\pi$
$31$	8.12663	+	14.0757i	0.262149	+	0.454056i	−0.704664	+	0.709542i	$0.748902\pi$
$32$	1.48729	−	5.55064i	0.0464778	−	0.173457i
$33$		0			0
$34$			48.3271i			1.42138i
$35$	−1.72469	−	34.9575i	−0.0492768	−	0.998785i
$36$		0			0
$37$	14.8150	−	3.96966i	0.400404	−	0.107288i	−0.0529966	−	0.998595i	$-0.516877\pi$
$37$	14.8150	−	3.96966i	0.400404	−	0.107288i	0.453401	+	0.891307i	$0.350211\pi$
$38$	−19.3040	−	5.17248i	−0.507999	−	0.136118i
$39$		0			0
$40$	−38.1008	−	16.6822i	−0.952519	−	0.417054i
$41$	28.7305			0.700743			0.350371	−	0.936611i	$-0.386055\pi$
$41$	28.7305			0.700743			0.350371	+	0.936611i	$0.386055\pi$
$42$		0			0
$43$	3.17014	−	3.17014i	0.0737243	−	0.0737243i	−0.669283	−	0.743007i	$-0.733399\pi$
$43$	3.17014	−	3.17014i	0.0737243	−	0.0737243i	0.743007	+	0.669283i	$0.233399\pi$
$44$	−3.27104	−	1.88853i	−0.0743417	−	0.0429212i
$45$		0			0
$46$	29.0834	+	50.3740i	0.632249	+	1.09509i
$47$	1.71038	−	0.458294i	0.0363910	−	0.00975094i	−0.240578	−	0.970630i	$-0.577337\pi$
$47$	1.71038	−	0.458294i	0.0363910	−	0.00975094i	0.276969	+	0.960879i	$0.410670\pi$
$48$		0			0
$49$	39.1026	+	29.5294i	0.798013	+	0.602640i
$50$	−25.4802	+	40.3185i	−0.509604	+	0.806370i
$51$		0			0
$52$	−0.185367	+	0.691801i	−0.00356476	+	0.0133039i
$53$	56.9591	+	15.2621i	1.07470	+	0.287965i	0.752423	−	0.658680i	$-0.228885\pi$
$53$	56.9591	+	15.2621i	1.07470	+	0.287965i	0.322277	+	0.946645i	$0.395552\pi$
$54$		0			0
$55$	−32.7353	+	40.9395i	−0.595188	+	0.744355i
$56$	52.1254	−	25.9551i	0.930811	−	0.463485i
$57$		0			0
$58$	−27.4647	−	102.499i	−0.473528	−	1.76723i
$59$	−57.7727	+	33.3551i	−0.979198	+	0.565340i	−0.902028	−	0.431678i	$-0.857922\pi$
$59$	−57.7727	+	33.3551i	−0.979198	+	0.565340i	−0.0771698	+	0.997018i	$0.524588\pi$
$60$		0			0
$61$	6.16473	−	10.6776i	0.101061	−	0.175043i	−0.811061	−	0.584962i	$-0.801110\pi$
$61$	6.16473	−	10.6776i	0.101061	−	0.175043i	0.912122	+	0.409919i	$0.134443\pi$
$62$	21.9260	+	21.9260i	0.353645	+	0.353645i
$63$		0			0
$64$		−	68.6793i		−	1.07311i
$65$	9.10496	+	3.98655i	0.140076	+	0.0613315i
$66$		0			0
$67$	28.5890	−	106.696i	0.426702	−	1.59247i	−0.333476	−	0.942758i	$-0.608222\pi$
$67$	28.5890	−	106.696i	0.426702	−	1.59247i	0.760178	−	0.649715i	$-0.225112\pi$
$68$	−2.36209	−	8.81545i	−0.0347367	−	0.129639i
$69$		0			0
$70$	−20.4394	−	63.5679i	−0.291992	−	0.908113i
$71$	−29.9403			−0.421694			−0.210847	−	0.977519i	$-0.567622\pi$
$71$	−29.9403			−0.421694			−0.210847	+	0.977519i	$0.567622\pi$
$72$		0			0
$73$	115.286	+	30.8909i	1.57926	+	0.423162i	0.938698	−	0.344741i	$-0.112033\pi$
$73$	115.286	+	30.8909i	1.57926	+	0.423162i	0.640566	+	0.767903i	$0.278700\pi$
$74$	25.3408	−	14.6305i	0.342444	−	0.197710i
$75$		0			0
$76$	3.77410			0.0496592
$77$	−14.5935	−	71.9195i	−0.189526	−	0.934020i
$78$		0			0
$79$	−99.9248	−	57.6916i	−1.26487	−	0.730274i	−0.290858	−	0.956766i	$-0.593941\pi$
$79$	−99.9248	−	57.6916i	−1.26487	−	0.730274i	−0.974013	+	0.226492i	$0.927274\pi$
$80$	−71.3255	−	10.8454i	−0.891568	−	0.135567i
$81$		0			0
$82$	52.9444	−	14.1864i	0.645663	−	0.173005i
$83$	−24.2475	+	24.2475i	−0.292139	+	0.292139i	−0.837925	−	0.545786i	$-0.816231\pi$
$83$	−24.2475	+	24.2475i	−0.292139	+	0.292139i	0.545786	+	0.837925i	$0.316231\pi$
$84$		0			0
$85$	−125.878	+	14.0174i	−1.48092	+	0.164911i
$86$	4.27659	−	7.40727i	0.0497278	−	0.0861311i
$87$		0			0
$88$	−84.2370	−	22.5712i	−0.957238	−	0.256491i
$89$	−18.3646	−	10.6028i	−0.206344	−	0.119133i	0.393267	−	0.919424i	$-0.371345\pi$
$89$	−18.3646	−	10.6028i	−0.206344	−	0.119133i	−0.599611	+	0.800292i	$0.704678\pi$
$90$		0			0
$91$	−12.4564	+	6.20252i	−0.136884	+	0.0681595i
$92$	−7.76732	−	7.76732i	−0.0844274	−	0.0844274i
$93$		0			0
$94$	2.92558	−	1.68909i	0.0311232	−	0.0179690i
$95$	7.87366	−	51.7816i	0.0828806	−	0.545070i
$96$		0			0
$97$	56.7300	+	56.7300i	0.584845	+	0.584845i	0.936231	−	0.351386i	$-0.114289\pi$
$97$	56.7300	+	56.7300i	0.584845	+	0.584845i	−0.351386	+	0.936231i	$0.614289\pi$
$98$	86.6391	+	35.1087i	0.884073	+	0.358252i
$99$		0			0
$100$	2.67725	−	8.60000i	0.0267725	−	0.0860000i
$101$	27.0096	+	46.7820i	0.267422	+	0.463188i	0.968195	−	0.250196i	$-0.0804950\pi$
$101$	27.0096	+	46.7820i	0.267422	+	0.463188i	−0.700774	+	0.713384i	$0.747162\pi$
$102$		0			0
$103$	40.5749	+	151.428i	0.393931	+	1.47017i	0.823593	+	0.567182i	$0.191966\pi$
$103$	40.5749	+	151.428i	0.393931	+	1.47017i	−0.429661	+	0.902990i	$0.641367\pi$
$104$			16.5364i			0.159004i
$105$		0			0
$106$	112.500			1.06132
$107$	80.1432	−	21.4743i	0.749001	−	0.200694i	0.135926	−	0.990719i	$-0.456599\pi$
$107$	80.1432	−	21.4743i	0.749001	−	0.200694i	0.613075	+	0.790025i	$0.289932\pi$
$108$		0			0
$109$	145.762	−	84.1557i	1.33727	−	0.772070i	0.350864	−	0.936426i	$-0.385888\pi$
$109$	145.762	−	84.1557i	1.33727	−	0.772070i	0.986401	+	0.164356i	$0.0525546\pi$
$110$	−40.1096	+	91.6072i	−0.364633	+	0.832793i
$111$		0			0
$112$	75.6817	−	66.8878i	0.675729	−	0.597212i
$113$	−105.863	+	105.863i	−0.936843	+	0.936843i	−0.998121	−	0.0612774i	$-0.980483\pi$
$113$	−105.863	+	105.863i	−0.936843	+	0.936843i	0.0612774	+	0.998121i	$0.480483\pi$
$114$		0			0
$115$	−122.774	+	90.3652i	−1.06760	+	0.785784i
$116$	10.0198	+	17.3548i	0.0863775	+	0.149610i
$117$		0			0
$118$	−89.9934	+	89.9934i	−0.762656	+	0.762656i
$119$	97.9452	−	147.813i	0.823069	−	1.24213i
$120$		0			0
$121$	5.54707	−	9.60780i	0.0458435	−	0.0794033i
$122$	6.08799	−	22.7207i	0.0499016	−	0.186235i
$123$		0			0
$124$	−5.07125	−	2.92789i	−0.0408972	−	0.0236120i
$125$	−112.409	−	54.6741i	−0.899270	−	0.437393i
$126$		0			0
$127$	−100.095	−	100.095i	−0.788153	−	0.788153i	0.193038	−	0.981191i	$-0.438166\pi$
$127$	−100.095	−	100.095i	−0.788153	−	0.788153i	−0.981191	+	0.193038i	$0.938166\pi$
$128$	−27.9631	−	104.360i	−0.218461	−	0.815309i
$129$		0			0
$130$	18.7471	+	2.85059i	0.144208	+	0.0219276i
$131$	−64.1225	+	111.063i	−0.489485	+	0.847813i	−0.999927	−	0.0120995i	$-0.996149\pi$
$131$	−64.1225	+	111.063i	−0.489485	+	0.847813i	0.510442	+	0.859912i	$0.329482\pi$
$132$		0			0
$133$	48.5599	+	54.9442i	0.365112	+	0.413114i
$134$		−	210.735i		−	1.57265i
$135$		0			0
$136$	−105.360	−	182.489i	−0.774705	−	1.34183i
$137$	−28.4034	+	106.003i	−0.207324	+	0.773745i	0.781404	+	0.624025i	$0.214504\pi$
$137$	−28.4034	+	106.003i	−0.207324	+	0.773745i	−0.988729	+	0.149719i	$0.952163\pi$
$138$		0			0
$139$		−	29.9231i		−	0.215274i	−0.994190	−	0.107637i	$-0.965672\pi$
$139$		−	29.9231i		−	0.215274i	0.994190	−	0.107637i	$-0.0343284\pi$
$140$	6.83543	+	10.5966i	0.0488245	+	0.0756897i
$141$		0			0
$142$	−55.1739	+	14.7838i	−0.388549	+	0.104111i
$143$	20.1302	+	5.39386i	0.140770	+	0.0377193i
$144$		0			0
$145$	259.016	−	101.268i	1.78631	−	0.698399i
$146$	227.702			1.55960
$147$		0			0
$148$	−3.90738	+	3.90738i	−0.0264012	+	0.0264012i
$149$	20.3618	+	11.7559i	0.136657	+	0.0788987i	0.566770	−	0.823876i	$-0.308193\pi$
$149$	20.3618	+	11.7559i	0.136657	+	0.0788987i	−0.430113	+	0.902775i	$0.641526\pi$
$150$		0			0
$151$	2.08556	+	3.61230i	0.0138117	+	0.0239225i	0.872849	−	0.487991i	$-0.162270\pi$
$151$	2.08556	+	3.61230i	0.0138117	+	0.0239225i	−0.859037	+	0.511914i	$0.828937\pi$
$152$	84.1708	−	22.5535i	0.553755	−	0.148378i
$153$		0			0
$154$	−62.4050	−	125.327i	−0.405227	−	0.813813i
$155$	−50.7512	+	63.4706i	−0.327427	+	0.409488i
$156$		0			0
$157$	−71.2889	+	266.054i	−0.454069	+	1.69461i	0.236741	+	0.971573i	$0.423921\pi$
$157$	−71.2889	+	266.054i	−0.454069	+	1.69461i	−0.690810	+	0.723036i	$0.742746\pi$
$158$	−212.628	−	56.9735i	−1.34575	−	0.360592i
$159$		0			0
$160$	28.5557	−	3.17988i	0.178473	−	0.0198743i
$161$	13.1392	−	213.018i	0.0816102	−	1.32309i
$162$		0			0
$163$	−10.2997	−	38.4390i	−0.0631884	−	0.235822i	0.927108	−	0.374795i	$-0.122287\pi$
$163$	−10.2997	−	38.4390i	−0.0631884	−	0.235822i	−0.990296	+	0.138972i	$0.955620\pi$
$164$	−8.96432	+	5.17555i	−0.0546605	+	0.0315583i
$165$		0			0
$166$	−32.7104	+	56.6561i	−0.197051	+	0.341302i
$167$	193.699	+	193.699i	1.15987	+	1.15987i	0.984503	+	0.175370i	$0.0561120\pi$
$167$	193.699	+	193.699i	1.15987	+	1.15987i	0.175370	+	0.984503i	$0.443888\pi$
$168$		0			0
$169$			165.048i			0.976617i
$170$	−225.046	+	87.9869i	−1.32380	+	0.517570i
$171$		0			0
$172$	−0.418056	+	1.56021i	−0.00243056	+	0.00907097i
$173$	−49.1239	−	183.333i	−0.283953	−	1.05973i	−0.949601	−	0.313461i	$-0.898511\pi$
$173$	−49.1239	−	183.333i	−0.283953	−	1.05973i	0.665648	−	0.746266i	$-0.268155\pi$
$174$		0			0
$175$	159.648	−	71.6769i	0.912273	−	0.409583i
$176$	−151.269			−0.859480
$177$		0			0
$178$	−39.0776	−	10.4708i	−0.219537	−	0.0588248i
$179$	22.1740	−	12.8022i	0.123877	−	0.0715205i	−0.436781	−	0.899568i	$-0.643882\pi$
$179$	22.1740	−	12.8022i	0.123877	−	0.0715205i	0.560658	+	0.828047i	$0.310548\pi$
$180$		0			0
$181$	223.291			1.23365			0.616826	−	0.787100i	$-0.288418\pi$
$181$	223.291			1.23365			0.616826	+	0.787100i	$0.288418\pi$
$182$	−19.8920	+	17.5807i	−0.109297	+	0.0965971i
$183$		0			0
$184$	−219.645	−	126.812i	−1.19372	−	0.689196i
$185$	45.4586	+	61.7620i	0.245722	+	0.333849i
$186$		0			0
$187$	−256.514	+	68.7327i	−1.37173	+	0.367554i
$188$	−0.451105	+	0.451105i	−0.00239949	+	0.00239949i
$189$		0			0
$190$	−11.0590	−	99.3109i	−0.0582051	−	0.522689i
$191$	79.1507	−	137.093i	0.414402	−	0.717765i	−0.580964	−	0.813930i	$-0.697324\pi$
$191$	79.1507	−	137.093i	0.414402	−	0.717765i	0.995365	+	0.0961645i	$0.0306575\pi$
$192$		0			0
$193$	34.5030	+	9.24505i	0.178772	+	0.0479018i	0.347095	−	0.937830i	$-0.387168\pi$
$193$	34.5030	+	9.24505i	0.178772	+	0.0479018i	−0.168322	+	0.985732i	$0.553835\pi$
$194$	132.554	+	76.5300i	0.683267	+	0.394484i
$195$		0			0
$196$	−17.5201	−	2.16958i	−0.0893881	−	0.0110693i
$197$	233.837	+	233.837i	1.18699	+	1.18699i	0.977896	+	0.209092i	$0.0670509\pi$
$197$	233.837	+	233.837i	1.18699	+	1.18699i	0.209092	+	0.977896i	$0.432949\pi$
$198$		0			0
$199$	−135.042	+	77.9668i	−0.678605	+	0.391793i	−0.799329	−	0.600893i	$-0.794812\pi$
$199$	−135.042	+	77.9668i	−0.678605	+	0.391793i	0.120724	+	0.992686i	$0.461478\pi$
$200$	8.31614	−	207.798i	0.0415807	−	1.03899i
$201$		0			0
$202$	72.8730	+	72.8730i	0.360757	+	0.360757i
$203$	−123.734	+	369.168i	−0.609527	+	1.81856i
$204$		0			0
$205$	52.3082	+	133.790i	0.255162	+	0.652635i
$206$	149.543	+	259.016i	0.725936	+	1.25736i
$207$		0			0
$208$	7.42382	+	27.7061i	0.0356914	+	0.133202i
$209$		−	109.820i		−	0.525452i
$210$		0			0
$211$	71.3128			0.337975			0.168988	−	0.985618i	$-0.445950\pi$
$211$	71.3128			0.337975			0.168988	+	0.985618i	$0.445950\pi$
$212$	−20.5214	+	5.49870i	−0.0967991	+	0.0259372i
$213$		0			0
$214$	137.084	−	79.1455i	0.640580	−	0.369839i
$215$	20.5343	+	8.99079i	0.0955082	+	0.0418176i
$216$		0			0
$217$	−22.6250	−	111.500i	−0.104263	−	0.513827i
$218$	227.056	−	227.056i	1.04154	−	1.04154i
$219$		0			0
$220$	2.83898	−	18.6707i	0.0129044	−	0.0848670i
$221$	25.1779	+	43.6094i	0.113927	+	0.197328i
$222$		0			0
$223$	−65.3363	+	65.3363i	−0.292988	+	0.292988i	−0.838259	−	0.545272i	$-0.816427\pi$
$223$	−65.3363	+	65.3363i	−0.292988	+	0.292988i	0.545272	+	0.838259i	$0.316427\pi$
$224$	−22.2191	+	33.5317i	−0.0991922	+	0.149695i
$225$		0			0
$226$	−142.812	+	247.357i	−0.631911	+	1.09450i
$227$	−21.7660	+	81.2317i	−0.0958853	+	0.357849i	−0.997152	−	0.0754156i	$-0.975972\pi$
$227$	−21.7660	+	81.2317i	−0.0958853	+	0.357849i	0.901267	+	0.433264i	$0.142638\pi$
$228$		0			0
$229$	148.580	+	85.7827i	0.648821	+	0.374597i	0.788004	−	0.615670i	$-0.211114\pi$
$229$	148.580	+	85.7827i	0.648821	+	0.374597i	−0.139183	+	0.990267i	$0.544448\pi$
$230$	−181.628	+	227.148i	−0.789685	+	0.987598i
$231$		0			0
$232$	327.173	+	327.173i	1.41023	+	1.41023i
$233$	−51.2177	−	191.147i	−0.219818	−	0.820373i	−0.984415	−	0.175863i	$-0.943728\pi$
$233$	−51.2177	−	191.147i	−0.219818	−	0.820373i	0.764596	−	0.644510i	$-0.222938\pi$
$234$		0			0
$235$	5.24816	+	7.13038i	0.0223326	+	0.0303421i
$236$	12.0173	−	20.8145i	0.0509207	−	0.0881972i
$237$		0			0
$238$	107.507	−	320.752i	0.451708	−	1.34770i
$239$		−	88.3669i		−	0.369736i	−0.982763	−	0.184868i	$-0.940814\pi$
$239$		−	88.3669i		−	0.369736i	0.982763	−	0.184868i	$-0.0591857\pi$
$240$		0			0
$241$	−107.657	−	186.468i	−0.446711	−	0.773727i	0.551458	−	0.834203i	$-0.314072\pi$
$241$	−107.657	−	186.468i	−0.446711	−	0.773727i	−0.998170	+	0.0604755i	$0.980738\pi$
$242$	5.47802	−	20.4442i	0.0226364	−	0.0844804i
$243$		0			0
$244$			4.44210i			0.0182053i
$245$	−66.3182	+	235.854i	−0.270686	+	0.962668i
$246$		0			0
$247$	−20.1143	+	5.38962i	−0.0814346	+	0.0218203i
$248$	−130.597	−	34.9933i	−0.526600	−	0.141102i
$249$		0			0
$250$	−234.143	−	45.2485i	−0.936574	−	0.180994i
$251$	−202.957			−0.808594			−0.404297	−	0.914628i	$-0.632484\pi$
$251$	−202.957			−0.808594			−0.404297	+	0.914628i	$0.632484\pi$
$252$		0			0
$253$	−226.015	+	226.015i	−0.893340	+	0.893340i
$254$	−233.880	−	135.031i	−0.920789	−	0.531618i
$255$		0			0
$256$	34.2982	+	59.4062i	0.133977	+	0.232055i
$257$	−65.6771	+	17.5981i	−0.255553	+	0.0684752i	−0.384321	−	0.923200i	$-0.625564\pi$
$257$	−65.6771	+	17.5981i	−0.255553	+	0.0684752i	0.128768	+	0.991675i	$0.458898\pi$
$258$		0			0
$259$	−107.159	−	6.60975i	−0.413743	−	0.0255203i
$260$	−3.55903	+	0.396323i	−0.0136886	+	0.00152432i
$261$		0			0
$262$	−63.3243	+	236.330i	−0.241696	+	0.902021i
$263$	445.592	+	119.396i	1.69427	+	0.453977i	0.971485	−	0.237099i	$-0.0761967\pi$
$263$	445.592	+	119.396i	1.69427	+	0.453977i	0.722781	+	0.691077i	$0.242863\pi$
$264$		0			0
$265$	32.6310	+	293.031i	0.123136	+	1.10578i
$266$	116.616	+	77.2733i	0.438407	+	0.290501i
$267$		0			0
$268$	10.3002	+	38.4407i	0.0384334	+	0.143435i
$269$	37.2279	−	21.4935i	0.138394	−	0.0799016i	−0.429205	−	0.903207i	$-0.641206\pi$
$269$	37.2279	−	21.4935i	0.138394	−	0.0799016i	0.567598	+	0.823306i	$0.307873\pi$
$270$		0			0
$271$	84.6401	−	146.601i	0.312325	−	0.540963i	−0.666540	−	0.745469i	$-0.732226\pi$
$271$	84.6401	−	146.601i	0.312325	−	0.540963i	0.978865	+	0.204506i	$0.0655589\pi$
$272$	−258.452	−	258.452i	−0.950191	−	0.950191i
$273$		0			0
$274$			209.367i			0.764113i
$275$	−250.244	−	77.9030i	−0.909980	−	0.283284i
$276$		0			0
$277$	−59.9500	+	223.736i	−0.216426	+	0.807712i	0.769234	+	0.638967i	$0.220638\pi$
$277$	−59.9500	+	223.736i	−0.216426	+	0.807712i	−0.985660	+	0.168745i	$0.946029\pi$
$278$	−14.7753	−	55.1422i	−0.0531486	−	0.198353i
$279$		0			0
$280$	215.769	+	195.479i	0.770603	+	0.698140i
$281$	86.0504			0.306229			0.153115	−	0.988208i	$-0.451070\pi$
$281$	86.0504			0.306229			0.153115	+	0.988208i	$0.451070\pi$
$282$		0			0
$283$	65.1101	+	17.4462i	0.230071	+	0.0616474i	0.372013	−	0.928228i	$-0.378668\pi$
$283$	65.1101	+	17.4462i	0.230071	+	0.0616474i	−0.141941	+	0.989875i	$0.545334\pi$
$284$	9.34181	−	5.39350i	0.0328937	−	0.0189912i
$285$		0			0
$286$	39.7592			0.139018
$287$	−190.687	−	63.9127i	−0.664416	−	0.222692i
$288$		0			0
$289$	−305.423	−	176.336i	−1.05683	−	0.610159i
$290$	427.310	−	314.512i	1.47348	−	1.08452i
$291$		0			0
$292$	−41.5357	+	11.1295i	−0.142246	+	0.0381146i
$293$	−360.421	+	360.421i	−1.23011	+	1.23011i	−0.266183	+	0.963923i	$0.585762\pi$
$293$	−360.421	+	360.421i	−1.23011	+	1.23011i	−0.963923	+	0.266183i	$0.914238\pi$
$294$		0			0
$295$	−260.510	−	208.304i	−0.883084	−	0.706116i
$296$	−63.7933	+	110.493i	−0.215518	+	0.373288i
$297$		0			0
$298$	43.3275	+	11.6096i	0.145394	+	0.0389583i
$299$	52.4887	+	30.3043i	0.175547	+	0.101352i
$300$		0			0
$301$	−28.0928	+	13.9884i	−0.0933316	+	0.0464732i
$302$	5.62693	+	5.62693i	0.0186322	+	0.0186322i
$303$		0			0
$304$	130.899	−	75.5748i	0.430590	−	0.248601i
$305$	60.9467	+	9.26726i	0.199825	+	0.0303845i
$306$		0			0
$307$	22.4453	+	22.4453i	0.0731116	+	0.0731116i	0.742717	−	0.669605i	$-0.233537\pi$
$307$	22.4453	+	22.4453i	0.0731116	+	0.0731116i	−0.669605	+	0.742717i	$0.733537\pi$
$308$	17.5091	+	19.8110i	0.0568477	+	0.0643216i
$309$		0			0
$310$	−62.1839	+	142.023i	−0.200593	+	0.458140i
$311$	−186.522	−	323.065i	−0.599749	−	1.03880i	−0.992858	−	0.119304i	$-0.961934\pi$
$311$	−186.522	−	323.065i	−0.599749	−	1.03880i	0.393109	−	0.919492i	$-0.371400\pi$
$312$		0			0
$313$	−32.1578	−	120.014i	−0.102741	−	0.383433i	0.895339	−	0.445386i	$-0.146934\pi$
$313$	−32.1578	−	120.014i	−0.102741	−	0.383433i	−0.998079	+	0.0619535i	$0.980267\pi$
$314$			525.484i			1.67351i
$315$		0			0
$316$	41.5707			0.131553
$317$	−325.028	+	87.0910i	−1.02532	+	0.274735i	−0.732019	−	0.681284i	$-0.761422\pi$
$317$	−325.028	+	87.0910i	−1.02532	+	0.274735i	−0.293306	+	0.956019i	$0.594755\pi$
$318$		0			0
$319$	504.993	−	291.558i	1.58305	−	0.913974i
$320$	319.822	−	125.041i	0.999443	−	0.390754i
$321$		0			0
$322$	−80.9700	−	399.036i	−0.251460	−	1.23924i
$323$	187.634	−	187.634i	0.580909	−	0.580909i
$324$		0			0
$325$	−1.98731	+	49.6576i	−0.00611481	+	0.152793i
$326$	−37.9606	−	65.7496i	−0.116443	−	0.201686i
$327$		0			0
$328$	−168.996	+	168.996i	−0.515231	+	0.515231i
$329$	−12.3715	−	0.763091i	−0.0376033	−	0.00231942i
$330$		0			0
$331$	41.0476	−	71.0966i	0.124011	−	0.214793i	−0.797335	−	0.603537i	$-0.793758\pi$
$331$	41.0476	−	71.0966i	0.124011	−	0.214793i	0.921346	+	0.388744i	$0.127091\pi$
$332$	3.19759	−	11.9336i	0.00963130	−	0.0359445i
$333$		0			0
$334$	452.591	+	261.304i	1.35506	+	0.782346i
$335$	548.905	−	61.1244i	1.63852	−	0.182461i
$336$		0			0
$337$	55.2295	+	55.2295i	0.163886	+	0.163886i	0.784286	−	0.620400i	$-0.213030\pi$
$337$	55.2295	+	55.2295i	0.163886	+	0.163886i	−0.620400	+	0.784286i	$0.713030\pi$
$338$	81.4969	+	304.151i	0.241115	+	0.899854i
$339$		0			0
$340$	36.7507	−	27.0496i	0.108090	−	0.0795575i
$341$	−85.1963	+	147.564i	−0.249843	+	0.432740i
$342$		0			0
$343$	−193.839	−	282.976i	−0.565128	−	0.825004i
$344$			37.2943i			0.108414i
$345$		0			0
$346$	−181.051	−	313.589i	−0.523268	−	0.906326i
$347$	24.0575	−	89.7837i	0.0693299	−	0.258743i	−0.922558	−	0.385858i	$-0.873905\pi$
$347$	24.0575	−	89.7837i	0.0693299	−	0.258743i	0.991888	+	0.127116i	$0.0405720\pi$
$348$		0			0
$349$		−	372.327i		−	1.06684i	−0.845851	−	0.533419i	$-0.820907\pi$
$349$		−	372.327i		−	1.06684i	0.845851	−	0.533419i	$-0.179093\pi$
$350$	258.806	−	210.916i	0.739446	−	0.602618i
$351$		0			0
$352$	58.1907	−	15.5921i	0.165314	−	0.0442959i
$353$	110.010	+	29.4770i	0.311642	+	0.0835042i	0.411250	−	0.911523i	$-0.365092\pi$
$353$	110.010	+	29.4770i	0.311642	+	0.0835042i	−0.0996082	+	0.995027i	$0.531759\pi$
$354$		0			0
$355$	−54.5110	−	139.424i	−0.153552	−	0.392744i
$356$	7.64003			0.0214608
$357$		0			0
$358$	34.5408	−	34.5408i	0.0964827	−	0.0964827i
$359$	85.1134	+	49.1402i	0.237085	+	0.136881i	0.613836	−	0.789434i	$-0.289626\pi$
$359$	85.1134	+	49.1402i	0.237085	+	0.136881i	−0.376751	+	0.926314i	$0.622959\pi$
$360$		0			0
$361$	−125.633	−	217.603i	−0.348015	−	0.602780i
$362$	411.480	−	110.256i	1.13669	−	0.304574i
$363$		0			0
$364$	2.76926	−	4.17920i	0.00760786	−	0.0114813i
$365$	66.0458	+	593.099i	0.180947	+	1.62493i
$366$		0			0
$367$	156.895	−	585.540i	0.427507	−	1.59548i	−0.330881	−	0.943673i	$-0.607346\pi$
$367$	156.895	−	585.540i	0.427507	−	1.59548i	0.758387	−	0.651804i	$-0.225988\pi$
$368$	−424.936	−	113.861i	−1.15472	−	0.309406i
$369$		0			0
$370$	114.268	+	91.3685i	0.308831	+	0.246942i
$371$	−344.093	−	228.006i	−0.927473	−	0.614571i
$372$		0			0
$373$	−131.534	−	490.890i	−0.352637	−	1.31606i	−0.883432	−	0.468560i	$-0.844773\pi$
$373$	−131.534	−	490.890i	−0.352637	−	1.31606i	0.530795	−	0.847501i	$-0.321894\pi$
$374$	−438.764	+	253.321i	−1.17317	+	0.677328i
$375$		0			0
$376$	−7.36489	+	12.7564i	−0.0195875	+	0.0339265i
$377$	−78.1848	−	78.1848i	−0.207387	−	0.207387i
$378$		0			0
$379$		−	329.156i		−	0.868486i	−0.900796	−	0.434243i	$-0.857016\pi$
$379$		−	329.156i		−	0.868486i	0.900796	−	0.434243i	$-0.142984\pi$
$380$	6.87133	+	17.5750i	0.0180825	+	0.0462500i
$381$		0			0
$382$	78.1655	−	291.718i	0.204622	−	0.763659i
$383$	−16.9976	−	63.4359i	−0.0443801	−	0.165629i	0.940179	−	0.340680i	$-0.110657\pi$
$383$	−16.9976	−	63.4359i	−0.0443801	−	0.165629i	−0.984559	+	0.175052i	$0.943991\pi$
$384$		0			0
$385$	308.341	−	198.899i	0.800885	−	0.516620i
$386$	68.1470			0.176547
$387$		0			0
$388$	−27.9200	−	7.48115i	−0.0719588	−	0.0192813i
$389$	203.539	−	117.513i	0.523236	−	0.302091i	−0.215021	−	0.976609i	$-0.568982\pi$
$389$	203.539	−	117.513i	0.523236	−	0.302091i	0.738258	+	0.674519i	$0.235649\pi$
$390$		0			0
$391$	−772.322			−1.97525
$392$	−403.701	+	56.3110i	−1.02985	+	0.143651i
$393$		0			0
$394$	546.377	+	315.451i	1.38674	+	0.800636i
$395$	86.7262	−	570.360i	0.219560	−	1.44395i
$396$		0			0
$397$	167.401	−	44.8551i	0.421666	−	0.112985i	−0.0417456	−	0.999128i	$-0.513292\pi$
$397$	167.401	−	44.8551i	0.421666	−	0.112985i	0.463411	+	0.886143i	$0.346625\pi$
$398$	−210.358	+	210.358i	−0.528537	+	0.528537i
$399$		0			0
$400$	−79.3549	−	351.890i	−0.198387	−	0.879725i
$401$	255.698	−	442.881i	0.637650	−	1.10444i	−0.348297	−	0.937384i	$-0.613240\pi$
$401$	255.698	−	442.881i	0.637650	−	1.10444i	0.985947	−	0.167058i	$-0.0534267\pi$
$402$		0			0
$403$	31.2088	+	8.36237i	0.0774412	+	0.0207503i
$404$	−16.8548	−	9.73111i	−0.0417197	−	0.0240869i
$405$		0			0
$406$	−45.7305	+	741.398i	−0.112637	+	1.82610i
$407$	113.698	+	113.698i	0.279356	+	0.279356i
$408$		0			0
$409$	−603.075	+	348.185i	−1.47451	+	0.851309i	−0.999588	−	0.0287182i	$-0.990857\pi$
$409$	−603.075	+	348.185i	−1.47451	+	0.851309i	−0.474923	+	0.880027i	$0.657524\pi$
$410$	162.456	+	220.720i	0.396234	+	0.538341i
$411$		0			0
$412$	−39.9384	−	39.9384i	−0.0969379	−	0.0969379i
$413$	457.644	−	92.8625i	1.10810	−	0.224849i
$414$		0			0
$415$	−157.061	−	68.7680i	−0.378460	−	0.165706i
$416$	−5.71166	−	9.89288i	−0.0137299	−	0.0237810i
$417$		0			0
$418$	−54.2262	−	202.375i	−0.129728	−	0.484151i
$419$		−	751.985i		−	1.79471i	−0.441305	−	0.897357i	$-0.645484\pi$
$419$		−	751.985i		−	1.79471i	0.441305	−	0.897357i	$-0.354516\pi$
$420$		0			0
$421$	666.816			1.58389			0.791943	−	0.610596i	$-0.209070\pi$
$421$	666.816			1.58389			0.791943	+	0.610596i	$0.209070\pi$
$422$	131.415	−	35.2125i	0.311410	−	0.0834420i
$423$		0			0
$424$	−424.814	+	245.266i	−1.00192	+	0.578458i
$425$	−294.456	−	560.661i	−0.692838	−	1.31920i
$426$		0			0
$427$	−64.6691	+	57.1548i	−0.151450	+	0.133852i
$428$	−21.1374	+	21.1374i	−0.0493865	+	0.0493865i
$429$		0			0
$430$	42.2799	+	6.42888i	0.0983254	+	0.0149509i
$431$	−131.194	−	227.235i	−0.304395	−	0.527228i	0.672731	−	0.739887i	$-0.265121\pi$
$431$	−131.194	−	227.235i	−0.304395	−	0.527228i	−0.977127	+	0.212659i	$0.931788\pi$
$432$		0			0
$433$	375.850	−	375.850i	0.868014	−	0.868014i	−0.124239	−	0.992252i	$-0.539649\pi$
$433$	375.850	−	375.850i	0.868014	−	0.868014i	0.992252	+	0.124239i	$0.0396488\pi$
$434$	−96.7496	−	194.301i	−0.222925	−	0.447698i
$435$		0			0
$436$	−30.3199	+	52.5156i	−0.0695410	+	0.120449i
$437$	82.6623	−	308.500i	0.189158	−	0.705949i
$438$		0			0
$439$	597.304	+	344.854i	1.36060	+	0.785544i	0.989704	−	0.143129i	$-0.0457165\pi$
$439$	597.304	+	344.854i	1.36060	+	0.785544i	0.370898	+	0.928673i	$0.379050\pi$
$440$	−48.2582	−	433.364i	−0.109678	−	0.984918i
$441$		0			0
$442$	67.9311	+	67.9311i	0.153690	+	0.153690i
$443$	−17.6494	−	65.8683i	−0.0398405	−	0.148687i	0.943140	−	0.332395i	$-0.107857\pi$
$443$	−17.6494	−	65.8683i	−0.0398405	−	0.148687i	−0.982981	+	0.183708i	$0.941190\pi$
$444$		0			0
$445$	15.9389	−	104.823i	0.0358177	−	0.235558i
$446$	−88.1401	+	152.663i	−0.197623	+	0.342294i
$447$		0			0
$448$	−152.782	+	455.833i	−0.341030	+	1.01748i
$449$			255.244i			0.568472i	0.958754	+	0.284236i	$0.0917398\pi$
$449$			255.244i			0.568472i	−0.958754	+	0.284236i	$0.908260\pi$
$450$		0			0
$451$	150.599	+	260.846i	0.333923	+	0.578372i
$452$	13.9605	−	52.1013i	0.0308861	−	0.115268i
$453$		0			0
$454$			160.441i			0.353394i
$455$	−51.5624	−	46.7138i	−0.113324	−	0.102668i
$456$		0			0
$457$	8.92672	−	2.39191i	0.0195333	−	0.00523394i	−0.249039	−	0.968493i	$-0.580115\pi$
$457$	8.92672	−	2.39191i	0.0195333	−	0.00523394i	0.268572	+	0.963259i	$0.413448\pi$
$458$	316.160	+	84.7149i	0.690306	+	0.184967i
$459$		0			0
$460$	22.0288	−	50.3120i	0.0478886	−	0.109374i
$461$	410.809			0.891127			0.445563	−	0.895250i	$-0.353003\pi$
$461$	410.809			0.891127			0.445563	+	0.895250i	$0.353003\pi$
$462$		0			0
$463$	−321.399	+	321.399i	−0.694166	+	0.694166i	−0.963146	−	0.268980i	$-0.913314\pi$
$463$	−321.399	+	321.399i	−0.694166	+	0.694166i	0.268980	+	0.963146i	$0.413314\pi$
$464$	695.045	+	401.284i	1.49794	+	0.864837i
$465$		0			0
$466$	−188.768	−	326.955i	−0.405081	−	0.701620i
$467$	−465.574	+	124.750i	−0.996946	+	0.267131i	−0.720166	−	0.693802i	$-0.755934\pi$
$467$	−465.574	+	124.750i	−0.996946	+	0.267131i	−0.276781	+	0.960933i	$0.589268\pi$
$468$		0			0
$469$	−427.100	+	644.554i	−0.910661	+	1.37431i
$470$	13.1921	+	10.5484i	0.0280683	+	0.0224435i
$471$		0			0
$472$	143.627	−	536.024i	0.304295	−	1.13564i
$473$	45.3992	+	12.1647i	0.0959814	+	0.0257181i
$474$		0			0
$475$	255.469	−	57.6109i	0.537829	−	0.121286i
$476$	−3.93305	+	63.7638i	−0.00826270	+	0.133958i
$477$		0			0
$478$	−43.6334	−	162.842i	−0.0912833	−	0.340674i
$479$	−679.727	+	392.441i	−1.41905	+	0.819291i	−0.996216	−	0.0869137i	$-0.972300\pi$
$479$	−679.727	+	392.441i	−1.41905	+	0.819291i	−0.422838	+	0.906205i	$0.638966\pi$
$480$		0			0
$481$	15.2447	−	26.4046i	0.0316938	−	0.0548953i
$482$	−290.464	−	290.464i	−0.602623	−	0.602623i
$483$		0			0
$484$			3.99703i			0.00825833i
$485$	−160.891	+	367.462i	−0.331734	+	0.757655i
$486$		0			0
$487$	−93.7930	+	350.040i	−0.192593	+	0.718769i	0.800283	+	0.599622i	$0.204682\pi$
$487$	−93.7930	+	350.040i	−0.192593	+	0.718769i	−0.992877	+	0.119146i	$0.961984\pi$
$488$	26.5454	+	99.0686i	0.0543962	+	0.203009i
$489$		0			0
$490$	−5.75213	+	467.377i	−0.0117390	+	0.953830i
$491$	−672.749			−1.37016			−0.685080	−	0.728468i	$-0.740233\pi$
$491$	−672.749			−1.37016			−0.685080	+	0.728468i	$0.740233\pi$
$492$		0			0
$493$	1360.96	+	364.667i	2.76056	+	0.739690i
$494$	−34.4054	+	19.8640i	−0.0696465	+	0.0402104i
$495$		0			0
$496$	−234.519			−0.472821
$497$	198.717	+	66.6041i	0.399834	+	0.134012i
$498$		0			0
$499$	−266.252	−	153.721i	−0.533571	−	0.308057i	0.208899	−	0.977937i	$-0.433012\pi$
$499$	−266.252	−	153.721i	−0.533571	−	0.308057i	−0.742469	+	0.669880i	$0.766345\pi$
$500$	44.9223	−	3.19039i	0.0898446	−	0.00638079i
$501$		0			0
$502$	−374.009	+	100.215i	−0.745037	+	0.199632i
$503$	573.532	−	573.532i	1.14022	−	1.14022i	0.151813	−	0.988409i	$-0.451489\pi$
$503$	573.532	−	573.532i	1.14022	−	1.14022i	0.988409	−	0.151813i	$-0.0485112\pi$
$504$		0			0
$505$	−168.676	+	210.950i	−0.334012	+	0.417724i
$506$	−304.899	+	528.101i	−0.602567	+	1.04368i
$507$		0			0
$508$	49.2626	+	13.1999i	0.0969736	+	0.0259840i
$509$	132.234	+	76.3454i	0.259792	+	0.149991i	0.624240	−	0.781233i	$-0.285409\pi$
$509$	132.234	+	76.3454i	0.259792	+	0.149991i	−0.364448	+	0.931224i	$0.618742\pi$
$510$		0			0
$511$	−696.450	−	461.488i	−1.36291	−	0.903107i
$512$	398.124	+	398.124i	0.777586	+	0.777586i
$513$		0			0
$514$	−112.340	+	64.8596i	−0.218560	+	0.126186i
$515$	−631.286	+	464.645i	−1.22580	+	0.902222i
$516$		0			0
$517$	13.1263	+	13.1263i	0.0253894	+	0.0253894i
$518$	−200.737	+	40.7323i	−0.387523	+	0.0786338i
$519$		0			0
$520$	−77.0058	+	30.1071i	−0.148088	+	0.0578983i
$521$	−145.704	−	252.366i	−0.279662	−	0.484389i	0.691639	−	0.722244i	$-0.256889\pi$
$521$	−145.704	−	252.366i	−0.279662	−	0.484389i	−0.971301	+	0.237855i	$0.923556\pi$
$522$		0			0
$523$	−149.003	−	556.086i	−0.284900	−	1.06326i	−0.948912	−	0.315540i	$-0.897814\pi$
$523$	−149.003	−	556.086i	−0.284900	−	1.06326i	0.664012	−	0.747722i	$-0.268852\pi$
$524$		−	46.2046i		−	0.0881766i
$525$		0			0
$526$	880.091			1.67318
$527$	−397.686	+	106.560i	−0.754623	+	0.202201i
$528$		0			0
$529$	−346.907	+	200.287i	−0.655779	+	0.378614i
$530$	204.824	+	523.884i	0.386460	+	0.988460i
$531$		0			0
$532$	−25.0491	−	8.39573i	−0.0470849	−	0.0157814i
$533$	40.3850	−	40.3850i	0.0757693	−	0.0757693i
$534$		0			0
$535$	245.913	+	334.108i	0.459651	+	0.624502i
$536$	459.432	+	795.760i	0.857150	+	1.48463i
$537$		0			0
$538$	57.9905	−	57.9905i	0.107789	−	0.107789i
$539$	−63.1309	+	509.802i	−0.117126	+	0.945830i
$540$		0			0
$541$	−138.214	+	239.393i	−0.255478	+	0.442501i	−0.965025	−	0.262157i	$-0.915566\pi$
$541$	−138.214	+	239.393i	−0.255478	+	0.442501i	0.709547	+	0.704658i	$0.248900\pi$
$542$	83.5865	−	311.949i	0.154219	−	0.575552i
$543$		0			0
$544$	126.063	+	72.7823i	0.231733	+	0.133791i
$545$	657.273	+	525.557i	1.20601	+	0.964324i
$546$		0			0
$547$	−582.880	−	582.880i	−1.06559	−	1.06559i	−0.997692	−	0.0679024i	$-0.978369\pi$
$547$	−582.880	−	582.880i	−1.06559	−	1.06559i	−0.0679024	−	0.997692i	$-0.521631\pi$
$548$	−10.2333	−	38.1911i	−0.0186739	−	0.0696918i
$549$		0			0
$550$	−499.616	−	19.9948i	−0.908394	−	0.0363542i
$551$	−291.329	+	504.596i	−0.528727	+	0.915782i
$552$		0			0
$553$	534.874	+	605.195i	0.967223	+	1.09439i
$554$			441.902i			0.797658i
$555$		0			0
$556$	5.39040	+	9.33644i	0.00969496	+	0.0167922i
$557$	188.562	−	703.723i	0.338532	−	1.26342i	−0.561458	−	0.827505i	$-0.689759\pi$
$557$	188.562	−	703.723i	0.338532	−	1.26342i	0.899989	−	0.435912i	$-0.143574\pi$
$558$		0			0
$559$		−	8.91224i		−	0.0159432i
$560$	449.269	+	230.650i	0.802266	+	0.411875i
$561$		0			0
$562$	158.574	−	42.4896i	0.282159	−	0.0756043i
$563$	475.416	+	127.387i	0.844434	+	0.226265i	0.655001	−	0.755628i	$-0.272668\pi$
$563$	475.416	+	127.387i	0.844434	+	0.226265i	0.189433	+	0.981894i	$0.439335\pi$
$564$		0			0
$565$	−685.718	−	300.237i	−1.21366	−	0.531393i
$566$	128.599			0.227207
$567$		0			0
$568$	176.112	−	176.112i	0.310057	−	0.310057i
$569$	742.450	+	428.654i	1.30483	+	0.753346i	0.981229	−	0.192847i	$-0.0617719\pi$
$569$	742.450	+	428.654i	1.30483	+	0.753346i	0.323604	+	0.946192i	$0.395105\pi$
$570$		0			0
$571$	454.669	+	787.510i	0.796268	+	1.37918i	0.922031	+	0.387117i	$0.126529\pi$
$571$	454.669	+	787.510i	0.796268	+	1.37918i	−0.125762	+	0.992060i	$0.540138\pi$
$572$	−7.25256	+	1.94332i	−0.0126793	+	0.00339741i
$573$		0			0
$574$	−382.957	−	23.6213i	−0.667172	−	0.0411522i
$575$	−644.336	−	407.203i	−1.12058	−	0.708179i
$576$		0			0
$577$	−68.1343	+	254.281i	−0.118084	+	0.440695i	−0.999499	−	0.0316475i	$-0.989925\pi$
$577$	−68.1343	+	254.281i	−0.118084	+	0.440695i	0.881415	+	0.472342i	$0.156591\pi$
$578$	−649.903	−	174.141i	−1.12440	−	0.301282i
$579$		0			0
$580$	−62.5741	+	78.2566i	−0.107886	+	0.134925i
$581$	214.874	−	106.993i	0.369834	−	0.184154i
$582$		0			0
$583$	160.002	+	597.136i	0.274446	+	1.02425i
$584$	−859.830	+	496.423i	−1.47231	+	0.850040i
$585$		0			0
$586$	−486.215	+	842.150i	−0.829719	+	1.43712i
$587$	−507.344	−	507.344i	−0.864300	−	0.864300i	0.127534	−	0.991834i	$-0.459294\pi$
$587$	−507.344	−	507.344i	−0.864300	−	0.864300i	−0.991834	+	0.127534i	$0.959294\pi$
$588$		0			0
$589$		−	170.259i		−	0.289064i
$590$	−582.922	−	255.229i	−0.988004	−	0.432591i
$591$		0			0
$592$	−57.2784	+	213.766i	−0.0967541	+	0.361091i
$593$	−47.3392	−	176.672i	−0.0798301	−	0.297930i	0.914455	−	0.404688i	$-0.132620\pi$
$593$	−47.3392	−	176.672i	−0.0798301	−	0.297930i	−0.994285	+	0.106758i	$0.965953\pi$
$594$		0			0
$595$	866.651	+	186.989i	1.45656	+	0.314267i
$596$	−8.47092			−0.0142129
$597$		0			0
$598$	111.690	+	29.9271i	0.186772	+	0.0500453i
$599$	−218.188	+	125.971i	−0.364254	+	0.210302i	−0.670945	−	0.741507i	$-0.734111\pi$
$599$	−218.188	+	125.971i	−0.364254	+	0.210302i	0.306691	+	0.951809i	$0.400778\pi$
$600$		0			0
$601$	754.595			1.25557			0.627783	−	0.778388i	$-0.283963\pi$
$601$	754.595			1.25557			0.627783	+	0.778388i	$0.283963\pi$
$602$	−44.8622	+	39.6494i	−0.0745219	+	0.0658628i
$603$		0			0
$604$	−1.30145	−	0.751393i	−0.00215472	−	0.00124403i
$605$	54.8403	+	8.33875i	0.0906452	+	0.0137831i
$606$		0			0
$607$	−727.749	+	195.000i	−1.19893	+	0.321251i	−0.802408	−	0.596775i	$-0.796448\pi$
$607$	−727.749	+	195.000i	−1.19893	+	0.321251i	−0.396518	+	0.918027i	$0.629782\pi$
$608$	−42.5651	+	42.5651i	−0.0700083	+	0.0700083i
$609$		0			0
$610$	116.888	−	13.0164i	0.191620	−	0.0213383i
$611$	1.75999	−	3.04840i	0.00288051	−	0.00498919i
$612$		0			0
$613$	−225.113	−	60.3190i	−0.367232	−	0.0983996i	0.0704836	−	0.997513i	$-0.477546\pi$
$613$	−225.113	−	60.3190i	−0.367232	−	0.0983996i	−0.437716	+	0.899113i	$0.644212\pi$
$614$	52.4450	+	30.2792i	0.0854154	+	0.0493146i
$615$		0			0
$616$	508.879	+	337.198i	0.826103	+	0.547400i
$617$	−383.218	−	383.218i	−0.621098	−	0.621098i	0.324714	−	0.945812i	$-0.394732\pi$
$617$	−383.218	−	383.218i	−0.621098	−	0.621098i	−0.945812	+	0.324714i	$0.894732\pi$
$618$		0			0
$619$	262.181	−	151.370i	0.423556	−	0.244540i	−0.273042	−	0.962002i	$-0.588030\pi$
$619$	262.181	−	151.370i	0.423556	−	0.244540i	0.696597	+	0.717462i	$0.254696\pi$
$620$	4.40141	−	28.9462i	0.00709905	−	0.0466874i
$621$		0			0
$622$	−503.244	−	503.244i	−0.809074	−	0.809074i
$623$	98.3013	+	111.225i	0.157787	+	0.178532i
$624$		0			0
$625$	49.9454	−	623.001i	0.0799126	−	0.996802i
$626$	−118.521	−	205.284i	−0.189330	−	0.327929i
$627$		0			0
$628$	−25.6842	−	95.8547i	−0.0408984	−	0.152635i
$629$			388.520i			0.617679i
$630$		0			0
$631$	−616.232			−0.976596			−0.488298	−	0.872677i	$-0.662382\pi$
$631$	−616.232			−0.976596			−0.488298	+	0.872677i	$0.662382\pi$
$632$	927.118	−	248.421i	1.46696	−	0.393071i
$633$		0			0
$634$	−555.957	+	320.982i	−0.876904	+	0.506281i
$635$	283.879	−	648.358i	0.447054	−	1.02104i
$636$		0			0
$637$	96.4728	−	13.4567i	0.151449	−	0.0211251i
$638$	786.635	−	786.635i	1.23297	−	1.23297i
$639$		0			0
$640$	435.064	−	320.219i	0.679788	−	0.500343i
$641$	315.011	+	545.614i	0.491436	+	0.851192i	0.999951	−	0.00986074i	$-0.00313882\pi$
$641$	315.011	+	545.614i	0.491436	+	0.851192i	−0.508515	+	0.861053i	$0.669805\pi$
$642$		0			0
$643$	−129.985	+	129.985i	−0.202154	+	0.202154i	−0.800922	−	0.598768i	$-0.795657\pi$
$643$	−129.985	+	129.985i	−0.202154	+	0.202154i	0.598768	+	0.800922i	$0.295657\pi$
$644$	34.2737	+	68.8315i	0.0532200	+	0.106881i
$645$		0			0
$646$	253.122	−	438.420i	0.391829	−	0.678668i
$647$	−243.586	+	909.075i	−0.376485	+	1.40506i	0.474678	+	0.880160i	$0.342565\pi$
$647$	−243.586	+	909.075i	−0.376485	+	1.40506i	−0.851163	+	0.524902i	$0.824102\pi$
$648$		0			0
$649$	−605.665	−	349.681i	−0.933229	−	0.538800i
$650$	20.8575	+	92.4901i	0.0320885	+	0.142292i
$651$		0			0
$652$	10.1381	+	10.1381i	0.0155493	+	0.0155493i
$653$	−79.6499	−	297.258i	−0.121975	−	0.455218i	0.877738	−	0.479140i	$-0.159051\pi$
$653$	−79.6499	−	297.258i	−0.121975	−	0.455218i	−0.999714	+	0.0239217i	$0.992385\pi$
$654$		0			0
$655$	−633.939	−	96.3936i	−0.967845	−	0.147166i
$656$	−207.277	+	359.014i	−0.315971	+	0.547277i
$657$		0			0
$658$	−23.1749	+	4.70252i	−0.0352202	+	0.00714668i
$659$		−	6.50016i		−	0.00986367i	−0.999988	−	0.00493183i	$-0.998430\pi$
$659$		−	6.50016i		−	0.00986367i	0.999988	−	0.00493183i	$-0.00156986\pi$
$660$		0			0
$661$	−268.548	−	465.138i	−0.406275	−	0.703688i	0.588194	−	0.808720i	$-0.299839\pi$
$661$	−268.548	−	465.138i	−0.406275	−	0.703688i	−0.994469	+	0.105031i	$0.966506\pi$
$662$	40.5367	−	151.285i	0.0612336	−	0.228527i
$663$		0			0
$664$		−	285.253i		−	0.429598i
$665$	−167.450	+	326.165i	−0.251804	+	0.490474i
$666$		0			0
$667$	1638.06	−	438.917i	2.45586	−	0.658046i
$668$	−95.3300	−	25.5436i	−0.142710	−	0.0382389i
$669$		0			0
$670$	981.338	−	383.676i	1.46468	−	0.572651i
$671$	129.257			0.192633
$672$		0			0
$673$	−502.493	+	502.493i	−0.746646	+	0.746646i	−0.973848	−	0.227202i	$-0.927042\pi$
$673$	−502.493	+	502.493i	−0.746646	+	0.746646i	0.227202	+	0.973848i	$0.427042\pi$
$674$	129.048	+	74.5058i	0.191466	+	0.110543i
$675$		0			0
$676$	−29.7321	−	51.4975i	−0.0439824	−	0.0761797i
$677$	79.0768	−	21.1886i	0.116805	−	0.0312977i	−0.199943	−	0.979807i	$-0.564076\pi$
$677$	79.0768	−	21.1886i	0.116805	−	0.0312977i	0.316748	+	0.948510i	$0.397409\pi$
$678$		0			0
$679$	−250.324	−	502.723i	−0.368666	−	0.740387i
$680$	657.978	−	822.882i	0.967614	−	1.21012i
$681$		0			0
$682$	−84.1358	+	313.999i	−0.123366	+	0.460409i
$683$	−670.938	−	179.777i	−0.982340	−	0.263217i	−0.268310	−	0.963333i	$-0.586465\pi$
$683$	−670.938	−	179.777i	−0.982340	−	0.263217i	−0.714030	+	0.700115i	$0.753132\pi$
$684$		0			0
$685$	−545.341	+	60.7276i	−0.796118	+	0.0886534i
$686$	−496.932	−	425.755i	−0.724391	−	0.620634i
$687$		0			0
$688$	16.7428	+	62.4850i	0.0243355	+	0.0908213i
$689$	101.518	−	58.6114i	0.147341	−	0.0850674i
$690$		0			0
$691$	57.5433	−	99.6680i	0.0832755	−	0.144237i	−0.821380	−	0.570382i	$-0.806795\pi$
$691$	57.5433	−	99.6680i	0.0832755	−	0.144237i	0.904655	+	0.426145i	$0.140129\pi$
$692$	48.3532	+	48.3532i	0.0698746	+	0.0698746i
$693$		0			0
$694$		−	177.332i		−	0.255522i
$695$	139.344	−	54.4796i	0.200495	−	0.0783879i
$696$		0			0
$697$	−188.363	+	702.980i	−0.270248	+	1.00858i
$698$	−183.846	−	686.123i	−0.263390	−	0.982984i
$699$		0			0
$700$	−36.9004	+	51.1235i	−0.0527149	+	0.0730335i
$701$	−809.046			−1.15413			−0.577066	−	0.816698i	$-0.695802\pi$
$701$	−809.046			−1.15413			−0.577066	+	0.816698i	$0.695802\pi$
$702$		0			0
$703$	−155.192	−	41.5836i	−0.220757	−	0.0591516i
$704$	623.544	−	360.003i	0.885716	−	0.511368i
$705$		0			0
$706$	217.280			0.307763
$707$	−75.1963	−	370.582i	−0.106360	−	0.524161i
$708$		0			0
$709$	1134.05	+	654.745i	1.59951	+	0.923477i	0.991582	+	0.129483i	$0.0413319\pi$
$709$	1134.05	+	654.745i	1.59951	+	0.923477i	0.607927	+	0.793993i	$0.292001\pi$
$710$	−169.297	−	230.014i	−0.238446	−	0.323964i
$711$		0			0
$712$	170.390	−	45.6557i	0.239311	−	0.0641232i
$713$	−350.403	+	350.403i	−0.491448	+	0.491448i
$714$		0			0
$715$	11.5323	+	103.561i	0.0161291	+	0.144841i
$716$	−4.61241	+	7.98893i	−0.00644191	+	0.0111577i
$717$		0			0
$718$	181.111	+	48.5285i	0.252244	+	0.0675885i
$719$	968.813	+	559.345i	1.34745	+	0.777948i	0.987887	−	0.155174i	$-0.0495939\pi$
$719$	968.813	+	559.345i	1.34745	+	0.777948i	0.359559	+	0.933123i	$0.382927\pi$
$720$		0			0
$721$	67.5600	−	1095.30i	0.0937032	−	1.51915i
$722$	−338.964	−	338.964i	−0.469480	−	0.469480i
$723$		0			0
$724$	−69.6700	+	40.2240i	−0.0962293	+	0.0555580i
$725$	943.156	+	1021.79i	1.30091	+	1.40937i
$726$		0			0
$727$	−28.5376	−	28.5376i	−0.0392540	−	0.0392540i	0.687207	−	0.726461i	$-0.258836\pi$
$727$	−28.5376	−	28.5376i	−0.0392540	−	0.0392540i	−0.726461	+	0.687207i	$0.758836\pi$
$728$	36.7863	−	109.754i	0.0505307	−	0.150761i
$729$		0			0
$730$	414.567	+	1060.35i	0.567901	+	1.45253i
$731$	56.7833	+	98.3516i	0.0776789	+	0.134544i
$732$		0			0
$733$	167.588	+	625.448i	0.228633	+	0.853272i	0.980916	+	0.194431i	$0.0622861\pi$
$733$	167.588	+	625.448i	0.228633	+	0.853272i	−0.752283	+	0.658841i	$0.771047\pi$
$734$		−	1156.50i		−	1.57562i
$735$		0			0
$736$	175.203			0.238047
$737$	1118.55	−	299.716i	1.51771	−	0.406670i
$738$		0			0
$739$	838.233	−	483.954i	1.13428	−	0.654877i	0.189272	−	0.981925i	$-0.439387\pi$
$739$	838.233	−	483.954i	1.13428	−	0.654877i	0.945008	+	0.327048i	$0.106054\pi$
$740$	−25.3097	−	11.0817i	−0.0342022	−	0.0149752i
$741$		0			0
$742$	−746.677	−	250.264i	−1.00630	−	0.337283i
$743$	243.308	−	243.308i	0.327467	−	0.327467i	−0.524155	−	0.851623i	$-0.675619\pi$
$743$	243.308	−	243.308i	0.327467	−	0.327467i	0.851623	+	0.524155i	$0.175619\pi$
$744$		0			0
$745$	−17.6723	+	116.223i	−0.0237212	+	0.156004i
$746$	−484.780	−	839.663i	−0.649839	−	1.12555i
$747$		0			0
$748$	67.6544	−	67.6544i	0.0904471	−	0.0904471i
$749$	−579.690	−	35.7562i	−0.773952	−	0.0477385i
$750$		0			0
$751$	75.0735	−	130.031i	0.0999647	−	0.173144i	−0.811705	−	0.584067i	$-0.801460\pi$
$751$	75.0735	−	130.031i	0.0999647	−	0.173144i	0.911670	+	0.410923i	$0.134794\pi$
$752$	−6.61275	+	24.6791i	−0.00879356	+	0.0328180i
$753$		0			0
$754$	−182.684	−	105.473i	−0.242287	−	0.139884i
$755$	−13.0244	+	16.2886i	−0.0172509	+	0.0215744i
$756$		0			0
$757$	405.586	+	405.586i	0.535780	+	0.535780i	0.922287	−	0.386507i	$-0.126318\pi$
$757$	405.586	+	405.586i	0.535780	+	0.535780i	−0.386507	+	0.922287i	$0.626318\pi$
$758$	−162.529	−	606.568i	−0.214419	−	0.800222i
$759$		0			0
$760$	258.272	+	350.899i	0.339831	+	0.461709i
$761$	529.787	−	917.617i	0.696172	−	1.20580i	−0.273612	−	0.961840i	$-0.588219\pi$
$761$	529.787	−	917.617i	0.696172	−	1.20580i	0.969784	−	0.243965i	$-0.0784481\pi$
$762$		0			0
$763$	−1154.65	+	234.294i	−1.51330	+	0.307070i
$764$			57.0334i			0.0746511i
$765$		0			0
$766$	−62.6462	−	108.506i	−0.0817836	−	0.141653i
$767$	−34.3227	+	128.094i	−0.0447492	+	0.167006i
$768$		0			0
$769$		−	370.215i		−	0.481424i	−0.970597	−	0.240712i	$-0.922619\pi$
$769$		−	370.215i		−	0.481424i	0.970597	−	0.240712i	$-0.0773810\pi$
$770$	469.998	−	518.781i	0.610387	−	0.673742i
$771$		0			0
$772$	−12.4309	+	3.33084i	−0.0161022	+	0.00431456i
$773$	1383.87	+	370.808i	1.79026	+	0.479700i	0.992391	−	0.123127i	$-0.0392923\pi$
$773$	1383.87	+	370.808i	1.79026	+	0.479700i	0.797872	+	0.602827i	$0.205959\pi$
$774$		0			0
$775$	−387.967	−	120.777i	−0.500602	−	0.155841i
$776$	−667.385			−0.860032
$777$		0			0
$778$	317.056	−	317.056i	0.407527	−	0.407527i
$779$	−260.641	−	150.481i	−0.334584	−	0.193172i
$780$		0			0
$781$	−156.941	−	271.830i	−0.200949	−	0.348054i
$782$	−1423.23	+	381.354i	−1.81999	+	0.487665i
$783$		0			0
$784$	−651.104	+	275.583i	−0.830490	+	0.351509i
$785$	−1368.73	+	152.418i	−1.74361	+	0.194163i
$786$		0			0
$787$	37.7320	−	140.818i	0.0479441	−	0.178930i	−0.937802	−	0.347171i	$-0.887142\pi$
$787$	37.7320	−	140.818i	0.0479441	−	0.178930i	0.985746	+	0.168242i	$0.0538089\pi$
$788$	−115.084	−	30.8367i	−0.146046	−	0.0391329i
$789$		0			0
$790$	−121.812	−	1093.88i	−0.154192	−	1.38466i
$791$	938.127	−	467.127i	1.18600	−	0.590553i
$792$		0			0
$793$	−6.34356	−	23.6745i	−0.00799945	−	0.0298543i
$794$	286.338	−	165.318i	0.360628	−	0.208209i
$795$		0			0
$796$	28.0902	−	48.6536i	0.0352891	−	0.0611226i
$797$	241.988	+	241.988i	0.303624	+	0.303624i	0.842430	−	0.538806i	$-0.181124\pi$
$797$	241.988	+	241.988i	0.303624	+	0.303624i	−0.538806	+	0.842430i	$0.681124\pi$
$798$		0			0
$799$			44.8544i			0.0561381i
$800$	66.7980	+	127.187i	0.0834975	+	0.158984i
$801$		0			0
$802$	252.515	−	942.398i	0.314856	−	1.17506i
$803$	323.847	+	1208.61i	0.403297	+	1.50512i
$804$		0			0
$805$	1015.89	−	326.645i	1.26197	−	0.405771i
$806$	61.6406			0.0764772
$807$		0			0
$808$	−434.050	−	116.303i	−0.537191	−	0.143940i
$809$	175.788	−	101.491i	0.217290	−	0.125453i	−0.387405	−	0.921910i	$-0.626628\pi$
$809$	175.788	−	101.491i	0.217290	−	0.125453i	0.604695	+	0.796457i	$0.293295\pi$
$810$		0			0
$811$	−276.530			−0.340974			−0.170487	−	0.985360i	$-0.554534\pi$
$811$	−276.530			−0.340974			−0.170487	+	0.985360i	$0.554534\pi$
$812$	−27.8957	−	137.475i	−0.0343543	−	0.169305i
$813$		0			0
$814$	265.663	+	153.381i	0.326368	+	0.188428i
$815$	160.248	−	117.947i	0.196624	−	0.144721i
$816$		0			0
$817$	−45.3635	+	12.1551i	−0.0555245	+	0.0148778i
$818$	−939.419	+	939.419i	−1.14843	+	1.14843i
$819$		0			0
$820$	−40.4221	−	32.3216i	−0.0492953	−	0.0394166i
$821$	−78.8816	+	136.627i	−0.0960799	+	0.166415i	−0.910059	−	0.414479i	$-0.863964\pi$
$821$	−78.8816	+	136.627i	−0.0960799	+	0.166415i	0.813979	+	0.580894i	$0.197297\pi$
$822$		0			0
$823$	−387.465	−	103.821i	−0.470795	−	0.126149i	0.0156180	−	0.999878i	$-0.495028\pi$
$823$	−387.465	−	103.821i	−0.470795	−	0.126149i	−0.486413	+	0.873729i	$0.661695\pi$
$824$	−1129.38	−	652.049i	−1.37061	−	0.791321i
$825$		0			0
$826$	797.492	−	397.100i	0.965487	−	0.480751i
$827$	330.030	+	330.030i	0.399069	+	0.399069i	0.877905	−	0.478835i	$-0.158941\pi$
$827$	330.030	+	330.030i	0.399069	+	0.399069i	−0.478835	+	0.877905i	$0.658941\pi$
$828$		0			0
$829$	175.549	−	101.353i	0.211760	−	0.122259i	−0.390369	−	0.920658i	$-0.627653\pi$
$829$	175.549	−	101.353i	0.211760	−	0.122259i	0.602129	+	0.798399i	$0.294319\pi$
$830$	−323.387	−	49.1726i	−0.389623	−	0.0592441i
$831$		0			0
$832$	−96.5393	−	96.5393i	−0.116033	−	0.116033i
$833$	−978.893	+	763.167i	−1.17514	+	0.916166i
$834$		0			0
$835$	−549.346	+	1254.66i	−0.657899	+	1.50259i
$836$	19.7831	+	34.2653i	0.0236640	+	0.0409872i
$837$		0			0
$838$	−371.312	−	1385.76i	−0.443093	−	1.65365i
$839$			717.236i			0.854870i	0.904046	+	0.427435i	$0.140583\pi$
$839$			717.236i			0.854870i	−0.904046	+	0.427435i	$0.859417\pi$
$840$		0			0
$841$	−2252.77			−2.67868
$842$	1228.81	−	329.258i	1.45939	−	0.391042i
$843$		0			0
$844$	−22.2506	+	12.8464i	−0.0263633	+	0.0152209i
$845$	−768.587	+	300.496i	−0.909570	+	0.355617i
$846$		0			0
$847$	−58.1897	+	51.4283i	−0.0687010	+	0.0607182i
$848$	−601.648	+	601.648i	−0.709490	+	0.709490i
$849$		0			0
$850$	−819.464	−	887.789i	−0.964075	−	1.04446i
$851$	233.813	+	404.976i	0.274751	+	0.475882i
$852$		0			0
$853$	959.961	−	959.961i	1.12539	−	1.12539i	0.134477	−	0.990917i	$-0.457065\pi$
$853$	959.961	−	959.961i	1.12539	−	1.12539i	0.990917	−	0.134477i	$-0.0429355\pi$
$854$	−90.9503	+	137.257i	−0.106499	+	0.160722i
$855$		0			0
$856$	−345.097	+	597.726i	−0.403151	+	0.698277i
$857$	−335.104	+	1250.62i	−0.391020	+	1.45930i	0.437436	+	0.899250i	$0.355887\pi$
$857$	−335.104	+	1250.62i	−0.391020	+	1.45930i	−0.828455	+	0.560055i	$0.810780\pi$
$858$		0			0
$859$	901.682	+	520.586i	1.04969	+	0.606038i	0.922562	−	0.385849i	$-0.126091\pi$
$859$	901.682	+	520.586i	1.04969	+	0.606038i	0.127126	+	0.991887i	$0.459425\pi$
$860$	−8.02661	+	0.893820i	−0.00933327	+	0.00103933i
$861$		0			0
$862$	−353.968	−	353.968i	−0.410636	−	0.410636i
$863$	−196.443	−	733.137i	−0.227629	−	0.849521i	−0.981334	−	0.192309i	$-0.938402\pi$
$863$	−196.443	−	733.137i	−0.227629	−	0.849521i	0.753706	−	0.657212i	$-0.228264\pi$
$864$		0			0
$865$	764.295	−	562.543i	0.883578	−	0.650338i
$866$	507.030	−	878.201i	0.585484	−	1.01409i
$867$		0			0
$868$	27.1452	+	30.7141i	0.0312733	+	0.0353849i
$869$		−	1209.63i		−	1.39198i
$870$		0			0
$871$	−109.791	−	190.163i	−0.126051	−	0.218328i
$872$	−362.375	+	1352.40i	−0.415568	+	1.55092i
$873$		0			0
$874$		−	609.319i		−	0.697161i
$875$	624.444	+	612.939i	0.713651	+	0.700502i
$876$		0			0
$877$	884.182	−	236.916i	1.00819	−	0.270143i	0.283316	−	0.959026i	$-0.408565\pi$
$877$	884.182	−	236.916i	1.00819	−	0.270143i	0.724872	+	0.688883i	$0.241899\pi$
$878$	1270.99	+	340.561i	1.44760	+	0.387883i
$879$		0			0
$880$	−275.408	−	704.418i	−0.312963	−	0.800475i
$881$	−679.564			−0.771355			−0.385677	−	0.922634i	$-0.626032\pi$
$881$	−679.564			−0.771355			−0.385677	+	0.922634i	$0.626032\pi$
$882$		0			0
$883$	1081.25	−	1081.25i	1.22452	−	1.22452i	0.258514	−	0.966008i	$-0.416767\pi$
$883$	1081.25	−	1081.25i	1.22452	−	1.22452i	0.966008	−	0.258514i	$-0.0832328\pi$
$884$	−15.7117	−	9.07118i	−0.0177735	−	0.0102615i
$885$		0			0
$886$	−65.0484	−	112.667i	−0.0734180	−	0.127164i
$887$	−551.111	+	147.670i	−0.621320	+	0.166482i	−0.555728	−	0.831364i	$-0.687560\pi$
$887$	−551.111	+	147.670i	−0.621320	+	0.166482i	−0.0655924	+	0.997846i	$0.520894\pi$
$888$		0			0
$889$	441.676	+	887.014i	0.496824	+	0.997766i
$890$	−22.3870	−	201.038i	−0.0251540	−	0.225885i
$891$		0			0
$892$	8.61609	−	32.1557i	0.00965929	−	0.0360490i
$893$	−17.9168	−	4.80080i	−0.0200636	−	0.00537603i
$894$		0			0
$895$	99.9876	+	79.9502i	0.111718	+	0.0893299i
$896$	−46.5604	+	754.852i	−0.0519647	+	0.842469i
$897$		0			0
$898$	126.033	+	470.362i	0.140349	+	0.523789i
$899$	782.916	−	452.017i	0.870874	−	0.502799i
$900$		0			0
$901$	−746.871	+	1293.62i	−0.828936	+	1.43576i
$902$	406.323	+	406.323i	0.450469	+	0.450469i
$903$		0			0
$904$		−	1245.40i		−	1.37766i
$905$	406.536	+	1039.81i	0.449211	+	1.14896i
$906$		0			0
$907$	−281.744	+	1051.48i	−0.310633	+	1.15930i	0.617354	+	0.786685i	$0.288204\pi$
$907$	−281.744	+	1051.48i	−0.310633	+	1.15930i	−0.927987	+	0.372612i	$0.878462\pi$
$908$	−7.84191	−	29.2664i	−0.00863647	−	0.0322317i
$909$		0			0
$910$	−118.085	−	60.6237i	−0.129764	−	0.0666195i
$911$	783.294			0.859818			0.429909	−	0.902872i	$-0.358546\pi$
$911$	783.294			0.859818			0.429909	+	0.902872i	$0.358546\pi$
$912$		0			0
$913$	−347.245	−	93.0441i	−0.380335	−	0.101910i
$914$	15.2691	−	8.81561i	0.0167058	−	0.00964508i
$915$		0			0
$916$	−61.8122			−0.0674806
$917$	672.656	−	594.497i	0.733540	−	0.648306i
$918$		0			0
$919$	815.004	+	470.543i	0.886838	+	0.512016i	0.872907	−	0.487887i	$-0.162232\pi$
$919$	815.004	+	470.543i	0.886838	+	0.512016i	0.0139309	+	0.999903i	$0.495566\pi$
$920$	190.633	−	1253.71i	0.207210	−	1.36273i
$921$		0			0
$922$	757.038	−	202.848i	0.821083	−	0.220009i
$923$	−42.0857	+	42.0857i	−0.0455966	+	0.0455966i
$924$		0			0
$925$	−204.845	+	324.136i	−0.221454	+	0.350417i
$926$	−433.574	+	750.972i	−0.468223	+	0.810985i
$927$		0			0
$928$	−308.736	−	82.7255i	−0.332689	−	0.0891439i
$929$	−912.306	−	526.720i	−0.982030	−	0.566975i	−0.0791477	−	0.996863i	$-0.525220\pi$
$929$	−912.306	−	526.720i	−0.982030	−	0.566975i	−0.902882	+	0.429888i	$0.858553\pi$
$930$		0			0
$931$	−200.071	−	472.696i	−0.214899	−	0.507729i
$932$	50.4142	+	50.4142i	0.0540925	+	0.0540925i
$933$		0			0
$934$	−796.360	+	459.778i	−0.852633	+	0.492268i
$935$	−787.093	−	1069.38i	−0.841811	−	1.14372i
$936$		0			0
$937$	248.568	+	248.568i	0.265281	+	0.265281i	0.827195	−	0.561914i	$-0.189935\pi$
$937$	248.568	+	248.568i	0.265281	+	0.265281i	−0.561914	+	0.827195i	$0.689935\pi$
$938$	−468.794	+	1398.67i	−0.499780	+	1.49112i
$939$		0			0
$940$	−2.92198	−	1.27937i	−0.00310849	−	0.00136103i
$941$	102.084	+	176.814i	0.108484	+	0.187900i	0.915156	−	0.403099i	$-0.132067\pi$
$941$	102.084	+	176.814i	0.108484	+	0.187900i	−0.806672	+	0.590999i	$0.798734\pi$
$942$		0			0
$943$	226.715	+	846.113i	0.240419	+	0.897256i
$944$		−	962.564i		−	1.01967i
$945$		0			0
$946$	89.6682			0.0947866
$947$	−304.991	+	81.7222i	−0.322061	+	0.0862959i	−0.416227	−	0.909261i	$-0.636648\pi$
$947$	−304.991	+	81.7222i	−0.322061	+	0.0862959i	0.0941668	+	0.995556i	$0.469981\pi$
$948$		0			0
$949$	205.474	−	118.631i	0.216517	−	0.125006i
$950$	442.330	−	232.310i	0.465611	−	0.244536i
$951$		0			0
$952$	293.328	+	1445.58i	0.308118	+	1.51846i
$953$	210.461	−	210.461i	0.220841	−	0.220841i	−0.588012	−	0.808852i	$-0.700089\pi$
$953$	210.461	−	210.461i	0.220841	−	0.220841i	0.808852	+	0.588012i	$0.200089\pi$
$954$		0			0
$955$	782.513	+	118.985i	0.819385	+	0.124592i
$956$	15.9186	+	27.5718i	0.0166512	+	0.0288407i
$957$		0			0
$958$	−1058.82	+	1058.82i	−1.10524	+	1.10524i
$959$	424.327	−	640.369i	0.442468	−	0.667747i
$960$		0			0
$961$	348.416	−	603.474i	0.362555	−	0.627965i
$962$	15.0550	−	56.1859i	0.0156496	−	0.0584053i
$963$		0			0
$964$	67.1814	+	38.7872i	0.0696903	+	0.0402357i
$965$	19.7663	+	177.504i	0.0204832	+	0.183942i
$966$		0			0
$967$	269.098	+	269.098i	0.278282	+	0.278282i	0.832423	−	0.554141i	$-0.186953\pi$
$967$	269.098	+	269.098i	0.278282	+	0.278282i	−0.554141	+	0.832423i	$0.686953\pi$
$968$	23.8857	+	89.1427i	0.0246753	+	0.0920896i
$969$		0			0
$970$	−115.045	+	756.603i	−0.118603	+	0.780003i
$971$	−286.988	+	497.078i	−0.295559	+	0.511924i	−0.975115	−	0.221700i	$-0.928839\pi$
$971$	−286.988	+	497.078i	−0.295559	+	0.511924i	0.679556	+	0.733624i	$0.262173\pi$
$972$		0			0
$973$	−66.5658	+	198.603i	−0.0684130	+	0.204114i
$974$			691.366i			0.709821i
$975$		0			0
$976$	88.9512	+	154.068i	0.0911386	+	0.157857i
$977$	16.3397	−	60.9807i	0.0167244	−	0.0624163i	−0.957059	−	0.289892i	$-0.906381\pi$
$977$	16.3397	−	60.9807i	0.0167244	−	0.0624163i	0.973784	+	0.227476i	$0.0730473\pi$
$978$		0			0
$979$		−	222.311i		−	0.227080i
$980$	−21.7948	−	85.5364i	−0.0222396	−	0.0872821i
$981$		0			0
$982$	−1239.74	+	332.187i	−1.26246	+	0.338276i
$983$	143.285	+	38.3930i	0.145763	+	0.0390570i	0.330963	−	0.943644i	$-0.392627\pi$
$983$	143.285	+	38.3930i	0.145763	+	0.0390570i	−0.185200	+	0.982701i	$0.559293\pi$
$984$		0			0
$985$	−663.180	+	1514.65i	−0.673280	+	1.53772i
$986$	2688.03			2.72620
$987$		0			0
$988$	5.30507	−	5.30507i	0.00536951	−	0.00536951i
$989$	118.377	+	68.3449i	0.119693	+	0.0691050i
$990$		0			0
$991$	925.131	+	1602.37i	0.933533	+	1.61693i	0.777229	+	0.629217i	$0.216625\pi$
$991$	925.131	+	1602.37i	0.933533	+	1.61693i	0.156304	+	0.987709i	$0.450042\pi$
$992$	90.2159	−	24.1733i	0.0909435	−	0.0243682i
$993$		0			0
$994$	399.083	+	24.6160i	0.401492	+	0.0247646i
$995$	−608.937	−	486.907i	−0.611997	−	0.489354i
$996$		0			0
$997$	−245.790	+	917.302i	−0.246530	+	0.920062i	0.726078	+	0.687612i	$0.241341\pi$
$997$	−245.790	+	917.302i	−0.246530	+	0.920062i	−0.972608	+	0.232450i	$0.925326\pi$
$998$	−566.551	−	151.807i	−0.567687	−	0.152111i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.ca.b.37.11		64
3.2	odd	2		105.3.v.a.37.6	✓	64
5.3	odd	4	inner	315.3.ca.b.163.6		64
7.4	even	3	inner	315.3.ca.b.172.6		64
15.8	even	4		105.3.v.a.58.11	yes	64
21.11	odd	6		105.3.v.a.67.11	yes	64
35.18	odd	12	inner	315.3.ca.b.298.11		64
105.53	even	12		105.3.v.a.88.6	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.6	✓	64	3.2	odd	2
105.3.v.a.58.11	yes	64	15.8	even	4
105.3.v.a.67.11	yes	64	21.11	odd	6
105.3.v.a.88.6	yes	64	105.53	even	12
315.3.ca.b.37.11		64	1.1	even	1	trivial
315.3.ca.b.163.6		64	5.3	odd	4	inner
315.3.ca.b.172.6		64	7.4	even	3	inner
315.3.ca.b.298.11		64	35.18	odd	12	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.ca (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.84280 - 0.493776i) q^{2} +(-0.312015 + 0.180142i) q^{4} +(1.82066 + 4.65674i) q^{5} +(-6.63712 - 2.22456i) q^{7} +(-5.88211 + 5.88211i) q^{8} +O(q^{10})\)	\(q+(1.84280 - 0.493776i) q^{2} +(-0.312015 + 0.180142i) q^{4} +(1.82066 + 4.65674i) q^{5} +(-6.63712 - 2.22456i) q^{7} +(-5.88211 + 5.88211i) q^{8} +(5.65448 + 7.68243i) q^{10} +(5.24180 + 9.07906i) q^{11} +(1.40565 - 1.40565i) q^{13} +(-13.3293 - 0.822171i) q^{14} +(-7.21453 + 12.4959i) q^{16} +(-6.55621 + 24.4681i) q^{17} +(-9.07193 - 5.23768i) q^{19} +(-1.40694 - 1.12499i) q^{20} +(14.1426 + 14.1426i) q^{22} +(7.89111 + 29.4500i) q^{23} +(-18.3704 + 16.9566i) q^{25} +(1.89626 - 3.28441i) q^{26} +(2.47161 - 0.501525i) q^{28} -55.6217i q^{29} +(8.12663 + 14.0757i) q^{31} +(1.48729 - 5.55064i) q^{32} +48.3271i q^{34} +(-1.72469 - 34.9575i) q^{35} +(14.8150 - 3.96966i) q^{37} +(-19.3040 - 5.17248i) q^{38} +(-38.1008 - 16.6822i) q^{40} +28.7305 q^{41} +(3.17014 - 3.17014i) q^{43} +(-3.27104 - 1.88853i) q^{44} +(29.0834 + 50.3740i) q^{46} +(1.71038 - 0.458294i) q^{47} +(39.1026 + 29.5294i) q^{49} +(-25.4802 + 40.3185i) q^{50} +(-0.185367 + 0.691801i) q^{52} +(56.9591 + 15.2621i) q^{53} +(-32.7353 + 40.9395i) q^{55} +(52.1254 - 25.9551i) q^{56} +(-27.4647 - 102.499i) q^{58} +(-57.7727 + 33.3551i) q^{59} +(6.16473 - 10.6776i) q^{61} +(21.9260 + 21.9260i) q^{62} -68.6793i q^{64} +(9.10496 + 3.98655i) q^{65} +(28.5890 - 106.696i) q^{67} +(-2.36209 - 8.81545i) q^{68} +(-20.4394 - 63.5679i) q^{70} -29.9403 q^{71} +(115.286 + 30.8909i) q^{73} +(25.3408 - 14.6305i) q^{74} +3.77410 q^{76} +(-14.5935 - 71.9195i) q^{77} +(-99.9248 - 57.6916i) q^{79} +(-71.3255 - 10.8454i) q^{80} +(52.9444 - 14.1864i) q^{82} +(-24.2475 + 24.2475i) q^{83} +(-125.878 + 14.0174i) q^{85} +(4.27659 - 7.40727i) q^{86} +(-84.2370 - 22.5712i) q^{88} +(-18.3646 - 10.6028i) q^{89} +(-12.4564 + 6.20252i) q^{91} +(-7.76732 - 7.76732i) q^{92} +(2.92558 - 1.68909i) q^{94} +(7.87366 - 51.7816i) q^{95} +(56.7300 + 56.7300i) q^{97} +(86.6391 + 35.1087i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) \) 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8 - 16 * q^10 - 16 * q^11 + 80 * q^16 - 56 * q^17 - 96 * q^22 - 72 * q^23 - 4 * q^25 + 288 * q^26 - 380 * q^28 - 136 * q^31 + 48 * q^32 - 76 * q^35 - 28 * q^37 + 68 * q^38 + 164 * q^40 - 128 * q^41 + 344 * q^43 + 240 * q^46 - 412 * q^47 + 72 * q^50 + 388 * q^52 + 40 * q^53 - 8 * q^55 + 864 * q^56 + 56 * q^58 - 216 * q^61 + 912 * q^62 - 20 * q^65 - 368 * q^67 + 492 * q^68 + 416 * q^70 - 784 * q^71 - 316 * q^73 - 32 * q^76 - 844 * q^77 - 908 * q^80 + 556 * q^82 - 1408 * q^83 - 536 * q^85 - 1024 * q^86 + 372 * q^88 - 1064 * q^91 + 1704 * q^92 - 260 * q^95 + 352 * q^97 - 272 * q^98

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