LMFDB - Embedded newform 315.3.ca.b.298.11

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			298.11
Character	$\chi$	$=$	315.298
Dual form			315.3.ca.b.37.11

$q$-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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.84280	+	0.493776i	0.921399	+	0.246888i	0.688183	−	0.725537i	$-0.258409\pi$
$2$	1.84280	+	0.493776i	0.921399	+	0.246888i	0.233216	+	0.972425i	$0.425075\pi$
$3$		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	−0.523111	−	0.852265i	$-0.675229\pi$
$11$	5.24180	−	9.07906i	0.476527	−	0.825369i	0.999638	+	0.0268951i	$0.00856202\pi$
$12$		0			0
$13$	1.40565	+	1.40565i	0.108127	+	0.108127i	0.759101	−	0.650973i	$-0.225639\pi$
$13$	1.40565	+	1.40565i	0.108127	+	0.108127i	−0.650973	+	0.759101i	$0.725639\pi$
$14$	−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	−0.837125	−	0.547012i	$-0.815765\pi$
$17$	−6.55621	−	24.4681i	−0.385659	−	1.43930i	0.451465	−	0.892289i	$-0.350901\pi$
$18$		0			0
$19$	−9.07193	+	5.23768i	−0.477470	+	0.275667i	−0.719362	−	0.694636i	$-0.755566\pi$
$19$	−9.07193	+	5.23768i	−0.477470	+	0.275667i	0.241892	+	0.970303i	$0.422232\pi$
$20$	−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	−0.551734	−	0.834020i	$-0.686034\pi$
$23$	7.89111	−	29.4500i	0.343092	−	1.28044i	0.894826	−	0.446416i	$-0.147300\pi$
$24$		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	$0.408529\pi$
$29$			55.6217i			1.91799i	−0.283425	+	0.958994i	$0.591471\pi$
$30$		0			0
$31$	8.12663	−	14.0757i	0.262149	−	0.454056i	−0.704664	−	0.709542i	$-0.748902\pi$
$31$	8.12663	−	14.0757i	0.262149	−	0.454056i	0.966813	+	0.255486i	$0.0822354\pi$
$32$	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	0.453401	−	0.891307i	$-0.350211\pi$
$37$	14.8150	+	3.96966i	0.400404	+	0.107288i	−0.0529966	+	0.998595i	$0.516877\pi$
$38$	−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	0.743007	−	0.669283i	$-0.233399\pi$
$43$	3.17014	+	3.17014i	0.0737243	+	0.0737243i	−0.669283	+	0.743007i	$0.733399\pi$
$44$	−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	0.276969	−	0.960879i	$-0.410670\pi$
$47$	1.71038	+	0.458294i	0.0363910	+	0.00975094i	−0.240578	+	0.970630i	$0.577337\pi$
$48$		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	0.322277	−	0.946645i	$-0.395552\pi$
$53$	56.9591	−	15.2621i	1.07470	−	0.287965i	0.752423	+	0.658680i	$0.228885\pi$
$54$		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	−0.0771698	−	0.997018i	$-0.524588\pi$
$59$	−57.7727	−	33.3551i	−0.979198	−	0.565340i	−0.902028	+	0.431678i	$0.857922\pi$
$60$		0			0
$61$	6.16473	+	10.6776i	0.101061	+	0.175043i	0.912122	−	0.409919i	$-0.134443\pi$
$61$	6.16473	+	10.6776i	0.101061	+	0.175043i	−0.811061	+	0.584962i	$0.801110\pi$
$62$	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	0.760178	+	0.649715i	$0.225112\pi$
$67$	28.5890	+	106.696i	0.426702	+	1.59247i	−0.333476	+	0.942758i	$0.608222\pi$
$68$	−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	0.640566	−	0.767903i	$-0.278700\pi$
$73$	115.286	−	30.8909i	1.57926	−	0.423162i	0.938698	+	0.344741i	$0.112033\pi$
$74$	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	−0.974013	−	0.226492i	$-0.927274\pi$
$79$	−99.9248	+	57.6916i	−1.26487	+	0.730274i	−0.290858	+	0.956766i	$0.593941\pi$
$80$	−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	0.545786	−	0.837925i	$-0.316231\pi$
$83$	−24.2475	−	24.2475i	−0.292139	−	0.292139i	−0.837925	+	0.545786i	$0.816231\pi$
$84$		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	−0.599611	−	0.800292i	$-0.704678\pi$
$89$	−18.3646	+	10.6028i	−0.206344	+	0.119133i	0.393267	+	0.919424i	$0.371345\pi$
$90$		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	−0.351386	−	0.936231i	$-0.614289\pi$
$97$	56.7300	−	56.7300i	0.584845	−	0.584845i	0.936231	+	0.351386i	$0.114289\pi$
$98$	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	−0.700774	−	0.713384i	$-0.747162\pi$
$101$	27.0096	−	46.7820i	0.267422	−	0.463188i	0.968195	+	0.250196i	$0.0804950\pi$
$102$		0			0
$103$	40.5749	−	151.428i	0.393931	−	1.47017i	−0.429661	−	0.902990i	$-0.641367\pi$
$103$	40.5749	−	151.428i	0.393931	−	1.47017i	0.823593	−	0.567182i	$-0.191966\pi$
$104$		−	16.5364i		−	0.159004i
$105$		0			0
$106$	112.500			1.06132
$107$	80.1432	+	21.4743i	0.749001	+	0.200694i	0.613075	−	0.790025i	$-0.289932\pi$
$107$	80.1432	+	21.4743i	0.749001	+	0.200694i	0.135926	+	0.990719i	$0.456599\pi$
$108$		0			0
$109$	145.762	+	84.1557i	1.33727	+	0.772070i	0.986401	−	0.164356i	$-0.0525546\pi$
$109$	145.762	+	84.1557i	1.33727	+	0.772070i	0.350864	+	0.936426i	$0.385888\pi$
$110$	−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	0.0612774	−	0.998121i	$-0.480483\pi$
$113$	−105.863	−	105.863i	−0.936843	−	0.936843i	−0.998121	+	0.0612774i	$0.980483\pi$
$114$		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	−0.981191	−	0.193038i	$-0.938166\pi$
$127$	−100.095	+	100.095i	−0.788153	+	0.788153i	0.193038	+	0.981191i	$0.438166\pi$
$128$	−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	0.510442	−	0.859912i	$-0.329482\pi$
$131$	−64.1225	−	111.063i	−0.489485	−	0.847813i	−0.999927	+	0.0120995i	$0.996149\pi$
$132$		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	−0.988729	−	0.149719i	$-0.952163\pi$
$137$	−28.4034	−	106.003i	−0.207324	−	0.773745i	0.781404	−	0.624025i	$-0.214504\pi$
$138$		0			0
$139$			29.9231i			0.215274i	0.994190	+	0.107637i	$0.0343284\pi$
$139$			29.9231i			0.215274i	−0.994190	+	0.107637i	$0.965672\pi$
$140$	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	−0.430113	−	0.902775i	$-0.641526\pi$
$149$	20.3618	−	11.7559i	0.136657	−	0.0788987i	0.566770	+	0.823876i	$0.308193\pi$
$150$		0			0
$151$	2.08556	−	3.61230i	0.0138117	−	0.0239225i	−0.859037	−	0.511914i	$-0.828937\pi$
$151$	2.08556	−	3.61230i	0.0138117	−	0.0239225i	0.872849	+	0.487991i	$0.162270\pi$
$152$	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	−0.690810	−	0.723036i	$-0.742746\pi$
$157$	−71.2889	−	266.054i	−0.454069	−	1.69461i	0.236741	−	0.971573i	$-0.423921\pi$
$158$	−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	−0.990296	−	0.138972i	$-0.955620\pi$
$163$	−10.2997	+	38.4390i	−0.0631884	+	0.235822i	0.927108	+	0.374795i	$0.122287\pi$
$164$	−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	0.175370	−	0.984503i	$-0.443888\pi$
$167$	193.699	−	193.699i	1.15987	−	1.15987i	0.984503	−	0.175370i	$-0.0561120\pi$
$168$		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	0.665648	+	0.746266i	$0.268155\pi$
$173$	−49.1239	+	183.333i	−0.283953	+	1.05973i	−0.949601	+	0.313461i	$0.898511\pi$
$174$		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	0.560658	−	0.828047i	$-0.310548\pi$
$179$	22.1740	+	12.8022i	0.123877	+	0.0715205i	−0.436781	+	0.899568i	$0.643882\pi$
$180$		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	0.995365	−	0.0961645i	$-0.0306575\pi$
$191$	79.1507	+	137.093i	0.414402	+	0.717765i	−0.580964	+	0.813930i	$0.697324\pi$
$192$		0			0
$193$	34.5030	−	9.24505i	0.178772	−	0.0479018i	−0.168322	−	0.985732i	$-0.553835\pi$
$193$	34.5030	−	9.24505i	0.178772	−	0.0479018i	0.347095	+	0.937830i	$0.387168\pi$
$194$	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	0.209092	−	0.977896i	$-0.432949\pi$
$197$	233.837	−	233.837i	1.18699	−	1.18699i	0.977896	−	0.209092i	$-0.0670509\pi$
$198$		0			0
$199$	−135.042	−	77.9668i	−0.678605	−	0.391793i	0.120724	−	0.992686i	$-0.461478\pi$
$199$	−135.042	−	77.9668i	−0.678605	−	0.391793i	−0.799329	+	0.600893i	$0.794812\pi$
$200$	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	0.545272	−	0.838259i	$-0.316427\pi$
$223$	−65.3363	−	65.3363i	−0.292988	−	0.292988i	−0.838259	+	0.545272i	$0.816427\pi$
$224$	−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	0.901267	−	0.433264i	$-0.142638\pi$
$227$	−21.7660	−	81.2317i	−0.0958853	−	0.357849i	−0.997152	+	0.0754156i	$0.975972\pi$
$228$		0			0
$229$	148.580	−	85.7827i	0.648821	−	0.374597i	−0.139183	−	0.990267i	$-0.544448\pi$
$229$	148.580	−	85.7827i	0.648821	−	0.374597i	0.788004	+	0.615670i	$0.211114\pi$
$230$	−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	0.764596	+	0.644510i	$0.222938\pi$
$233$	−51.2177	+	191.147i	−0.219818	+	0.820373i	−0.984415	+	0.175863i	$0.943728\pi$
$234$		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	$0.0591857\pi$
$239$			88.3669i			0.369736i	−0.982763	+	0.184868i	$0.940814\pi$
$240$		0			0
$241$	−107.657	+	186.468i	−0.446711	+	0.773727i	−0.998170	−	0.0604755i	$-0.980738\pi$
$241$	−107.657	+	186.468i	−0.446711	+	0.773727i	0.551458	+	0.834203i	$0.314072\pi$
$242$	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	0.128768	−	0.991675i	$-0.458898\pi$
$257$	−65.6771	−	17.5981i	−0.255553	−	0.0684752i	−0.384321	+	0.923200i	$0.625564\pi$
$258$		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	0.722781	−	0.691077i	$-0.242863\pi$
$263$	445.592	−	119.396i	1.69427	−	0.453977i	0.971485	+	0.237099i	$0.0761967\pi$
$264$		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	0.567598	−	0.823306i	$-0.307873\pi$
$269$	37.2279	+	21.4935i	0.138394	+	0.0799016i	−0.429205	+	0.903207i	$0.641206\pi$
$270$		0			0
$271$	84.6401	+	146.601i	0.312325	+	0.540963i	0.978865	−	0.204506i	$-0.0655589\pi$
$271$	84.6401	+	146.601i	0.312325	+	0.540963i	−0.666540	+	0.745469i	$0.732226\pi$
$272$	−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	−0.985660	−	0.168745i	$-0.946029\pi$
$277$	−59.9500	−	223.736i	−0.216426	−	0.807712i	0.769234	−	0.638967i	$-0.220638\pi$
$278$	−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	−0.141941	−	0.989875i	$-0.545334\pi$
$283$	65.1101	−	17.4462i	0.230071	−	0.0616474i	0.372013	+	0.928228i	$0.378668\pi$
$284$	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	−0.963923	−	0.266183i	$-0.914238\pi$
$293$	−360.421	−	360.421i	−1.23011	−	1.23011i	−0.266183	−	0.963923i	$-0.585762\pi$
$294$		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	−0.669605	−	0.742717i	$-0.733537\pi$
$307$	22.4453	−	22.4453i	0.0731116	−	0.0731116i	0.742717	+	0.669605i	$0.233537\pi$
$308$	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	0.393109	+	0.919492i	$0.371400\pi$
$311$	−186.522	+	323.065i	−0.599749	+	1.03880i	−0.992858	+	0.119304i	$0.961934\pi$
$312$		0			0
$313$	−32.1578	+	120.014i	−0.102741	+	0.383433i	−0.998079	−	0.0619535i	$-0.980267\pi$
$313$	−32.1578	+	120.014i	−0.102741	+	0.383433i	0.895339	+	0.445386i	$0.146934\pi$
$314$		−	525.484i		−	1.67351i
$315$		0			0
$316$	41.5707			0.131553
$317$	−325.028	−	87.0910i	−1.02532	−	0.274735i	−0.293306	−	0.956019i	$-0.594755\pi$
$317$	−325.028	−	87.0910i	−1.02532	−	0.274735i	−0.732019	+	0.681284i	$0.761422\pi$
$318$		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	0.921346	−	0.388744i	$-0.127091\pi$
$331$	41.0476	+	71.0966i	0.124011	+	0.214793i	−0.797335	+	0.603537i	$0.793758\pi$
$332$	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	−0.620400	−	0.784286i	$-0.713030\pi$
$337$	55.2295	−	55.2295i	0.163886	−	0.163886i	0.784286	+	0.620400i	$0.213030\pi$
$338$	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	0.991888	−	0.127116i	$-0.0405720\pi$
$347$	24.0575	+	89.7837i	0.0693299	+	0.258743i	−0.922558	+	0.385858i	$0.873905\pi$
$348$		0			0
$349$			372.327i			1.06684i	0.845851	+	0.533419i	$0.179093\pi$
$349$			372.327i			1.06684i	−0.845851	+	0.533419i	$0.820907\pi$
$350$	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	−0.0996082	−	0.995027i	$-0.531759\pi$
$353$	110.010	−	29.4770i	0.311642	−	0.0835042i	0.411250	+	0.911523i	$0.365092\pi$
$354$		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	−0.376751	−	0.926314i	$-0.622959\pi$
$359$	85.1134	−	49.1402i	0.237085	−	0.136881i	0.613836	+	0.789434i	$0.289626\pi$
$360$		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	0.758387	+	0.651804i	$0.225988\pi$
$367$	156.895	+	585.540i	0.427507	+	1.59548i	−0.330881	+	0.943673i	$0.607346\pi$
$368$	−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	0.530795	+	0.847501i	$0.321894\pi$
$373$	−131.534	+	490.890i	−0.352637	+	1.31606i	−0.883432	+	0.468560i	$0.844773\pi$
$374$	−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	$0.142984\pi$
$379$			329.156i			0.868486i	−0.900796	+	0.434243i	$0.857016\pi$
$380$	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	−0.984559	−	0.175052i	$-0.943991\pi$
$383$	−16.9976	+	63.4359i	−0.0443801	+	0.165629i	0.940179	+	0.340680i	$0.110657\pi$
$384$		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	0.738258	−	0.674519i	$-0.235649\pi$
$389$	203.539	+	117.513i	0.523236	+	0.302091i	−0.215021	+	0.976609i	$0.568982\pi$
$390$		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	0.463411	−	0.886143i	$-0.346625\pi$
$397$	167.401	+	44.8551i	0.421666	+	0.112985i	−0.0417456	+	0.999128i	$0.513292\pi$
$398$	−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	0.985947	+	0.167058i	$0.0534267\pi$
$401$	255.698	+	442.881i	0.637650	+	1.10444i	−0.348297	+	0.937384i	$0.613240\pi$
$402$		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	−0.474923	−	0.880027i	$-0.657524\pi$
$409$	−603.075	−	348.185i	−1.47451	−	0.851309i	−0.999588	+	0.0287182i	$0.990857\pi$
$410$	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	$0.354516\pi$
$419$			751.985i			1.79471i	−0.441305	+	0.897357i	$0.645484\pi$
$420$		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	−0.977127	−	0.212659i	$-0.931788\pi$
$431$	−131.194	+	227.235i	−0.304395	+	0.527228i	0.672731	+	0.739887i	$0.265121\pi$
$432$		0			0
$433$	375.850	+	375.850i	0.868014	+	0.868014i	0.992252	−	0.124239i	$-0.0396488\pi$
$433$	375.850	+	375.850i	0.868014	+	0.868014i	−0.124239	+	0.992252i	$0.539649\pi$
$434$	−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	0.370898	−	0.928673i	$-0.379050\pi$
$439$	597.304	−	344.854i	1.36060	−	0.785544i	0.989704	+	0.143129i	$0.0457165\pi$
$440$	−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	−0.982981	−	0.183708i	$-0.941190\pi$
$443$	−17.6494	+	65.8683i	−0.0398405	+	0.148687i	0.943140	+	0.332395i	$0.107857\pi$
$444$		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	$-0.908260\pi$
$449$		−	255.244i		−	0.568472i	0.958754	−	0.284236i	$-0.0917398\pi$
$450$		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	0.268572	−	0.963259i	$-0.413448\pi$
$457$	8.92672	+	2.39191i	0.0195333	+	0.00523394i	−0.249039	+	0.968493i	$0.580115\pi$
$458$	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	0.268980	−	0.963146i	$-0.413314\pi$
$463$	−321.399	−	321.399i	−0.694166	−	0.694166i	−0.963146	+	0.268980i	$0.913314\pi$
$464$	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	−0.276781	−	0.960933i	$-0.589268\pi$
$467$	−465.574	−	124.750i	−0.996946	−	0.267131i	−0.720166	+	0.693802i	$0.755934\pi$
$468$		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	−0.422838	−	0.906205i	$-0.638966\pi$
$479$	−679.727	−	392.441i	−1.41905	−	0.819291i	−0.996216	+	0.0869137i	$0.972300\pi$
$480$		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	−0.992877	−	0.119146i	$-0.961984\pi$
$487$	−93.7930	−	350.040i	−0.192593	−	0.718769i	0.800283	−	0.599622i	$-0.204682\pi$
$488$	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	−0.742469	−	0.669880i	$-0.766345\pi$
$499$	−266.252	+	153.721i	−0.533571	+	0.308057i	0.208899	+	0.977937i	$0.433012\pi$
$500$	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	0.988409	+	0.151813i	$0.0485112\pi$
$503$	573.532	+	573.532i	1.14022	+	1.14022i	0.151813	+	0.988409i	$0.451489\pi$
$504$		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	−0.364448	−	0.931224i	$-0.618742\pi$
$509$	132.234	−	76.3454i	0.259792	−	0.149991i	0.624240	+	0.781233i	$0.285409\pi$
$510$		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	−0.971301	−	0.237855i	$-0.923556\pi$
$521$	−145.704	+	252.366i	−0.279662	+	0.484389i	0.691639	+	0.722244i	$0.256889\pi$
$522$		0			0
$523$	−149.003	+	556.086i	−0.284900	+	1.06326i	0.664012	+	0.747722i	$0.268852\pi$
$523$	−149.003	+	556.086i	−0.284900	+	1.06326i	−0.948912	+	0.315540i	$0.897814\pi$
$524$			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	0.709547	−	0.704658i	$-0.248900\pi$
$541$	−138.214	−	239.393i	−0.255478	−	0.442501i	−0.965025	+	0.262157i	$0.915566\pi$
$542$	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	−0.0679024	+	0.997692i	$0.521631\pi$
$547$	−582.880	+	582.880i	−1.06559	+	1.06559i	−0.997692	+	0.0679024i	$0.978369\pi$
$548$	−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	0.899989	+	0.435912i	$0.143574\pi$
$557$	188.562	+	703.723i	0.338532	+	1.26342i	−0.561458	+	0.827505i	$0.689759\pi$
$558$		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	0.189433	−	0.981894i	$-0.439335\pi$
$563$	475.416	−	127.387i	0.844434	−	0.226265i	0.655001	+	0.755628i	$0.272668\pi$
$564$		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	0.323604	−	0.946192i	$-0.395105\pi$
$569$	742.450	−	428.654i	1.30483	−	0.753346i	0.981229	+	0.192847i	$0.0617719\pi$
$570$		0			0
$571$	454.669	−	787.510i	0.796268	−	1.37918i	−0.125762	−	0.992060i	$-0.540138\pi$
$571$	454.669	−	787.510i	0.796268	−	1.37918i	0.922031	−	0.387117i	$-0.126529\pi$
$572$	−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	0.881415	−	0.472342i	$-0.156591\pi$
$577$	−68.1343	−	254.281i	−0.118084	−	0.440695i	−0.999499	+	0.0316475i	$0.989925\pi$
$578$	−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	−0.991834	−	0.127534i	$-0.959294\pi$
$587$	−507.344	+	507.344i	−0.864300	+	0.864300i	0.127534	+	0.991834i	$0.459294\pi$
$588$		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	−0.994285	−	0.106758i	$-0.965953\pi$
$593$	−47.3392	+	176.672i	−0.0798301	+	0.297930i	0.914455	+	0.404688i	$0.132620\pi$
$594$		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	0.306691	−	0.951809i	$-0.400778\pi$
$599$	−218.188	−	125.971i	−0.364254	−	0.210302i	−0.670945	+	0.741507i	$0.734111\pi$
$600$		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	−0.396518	−	0.918027i	$-0.629782\pi$
$607$	−727.749	−	195.000i	−1.19893	−	0.321251i	−0.802408	+	0.596775i	$0.796448\pi$
$608$	−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	−0.437716	−	0.899113i	$-0.644212\pi$
$613$	−225.113	+	60.3190i	−0.367232	+	0.0983996i	0.0704836	+	0.997513i	$0.477546\pi$
$614$	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	−0.945812	−	0.324714i	$-0.894732\pi$
$617$	−383.218	+	383.218i	−0.621098	+	0.621098i	0.324714	+	0.945812i	$0.394732\pi$
$618$		0			0
$619$	262.181	+	151.370i	0.423556	+	0.244540i	0.696597	−	0.717462i	$-0.254696\pi$
$619$	262.181	+	151.370i	0.423556	+	0.244540i	−0.273042	+	0.962002i	$0.588030\pi$
$620$	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	−0.508515	−	0.861053i	$-0.669805\pi$
$641$	315.011	−	545.614i	0.491436	−	0.851192i	0.999951	+	0.00986074i	$0.00313882\pi$
$642$		0			0
$643$	−129.985	−	129.985i	−0.202154	−	0.202154i	0.598768	−	0.800922i	$-0.295657\pi$
$643$	−129.985	−	129.985i	−0.202154	−	0.202154i	−0.800922	+	0.598768i	$0.795657\pi$
$644$	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	−0.851163	−	0.524902i	$-0.824102\pi$
$647$	−243.586	−	909.075i	−0.376485	−	1.40506i	0.474678	−	0.880160i	$-0.342565\pi$
$648$		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	−0.999714	−	0.0239217i	$-0.992385\pi$
$653$	−79.6499	+	297.258i	−0.121975	+	0.455218i	0.877738	+	0.479140i	$0.159051\pi$
$654$		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	$0.00156986\pi$
$659$			6.50016i			0.00986367i	−0.999988	+	0.00493183i	$0.998430\pi$
$660$		0			0
$661$	−268.548	+	465.138i	−0.406275	+	0.703688i	−0.994469	−	0.105031i	$-0.966506\pi$
$661$	−268.548	+	465.138i	−0.406275	+	0.703688i	0.588194	+	0.808720i	$0.299839\pi$
$662$	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	0.227202	−	0.973848i	$-0.427042\pi$
$673$	−502.493	−	502.493i	−0.746646	−	0.746646i	−0.973848	+	0.227202i	$0.927042\pi$
$674$	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	0.316748	−	0.948510i	$-0.397409\pi$
$677$	79.0768	+	21.1886i	0.116805	+	0.0312977i	−0.199943	+	0.979807i	$0.564076\pi$
$678$		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	−0.714030	−	0.700115i	$-0.753132\pi$
$683$	−670.938	+	179.777i	−0.982340	+	0.263217i	−0.268310	+	0.963333i	$0.586465\pi$
$684$		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	0.904655	−	0.426145i	$-0.140129\pi$
$691$	57.5433	+	99.6680i	0.0832755	+	0.144237i	−0.821380	+	0.570382i	$0.806795\pi$
$692$	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	0.607927	−	0.793993i	$-0.292001\pi$
$709$	1134.05	−	654.745i	1.59951	−	0.923477i	0.991582	−	0.129483i	$-0.0413319\pi$
$710$	−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	0.359559	−	0.933123i	$-0.382927\pi$
$719$	968.813	−	559.345i	1.34745	−	0.777948i	0.987887	+	0.155174i	$0.0495939\pi$
$720$		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	−0.726461	−	0.687207i	$-0.758836\pi$
$727$	−28.5376	+	28.5376i	−0.0392540	+	0.0392540i	0.687207	+	0.726461i	$0.258836\pi$
$728$	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	−0.752283	−	0.658841i	$-0.771047\pi$
$733$	167.588	−	625.448i	0.228633	−	0.853272i	0.980916	−	0.194431i	$-0.0622861\pi$
$734$			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	0.945008	−	0.327048i	$-0.106054\pi$
$739$	838.233	+	483.954i	1.13428	+	0.654877i	0.189272	+	0.981925i	$0.439387\pi$
$740$	−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	0.851623	−	0.524155i	$-0.175619\pi$
$743$	243.308	+	243.308i	0.327467	+	0.327467i	−0.524155	+	0.851623i	$0.675619\pi$
$744$		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	0.911670	−	0.410923i	$-0.134794\pi$
$751$	75.0735	+	130.031i	0.0999647	+	0.173144i	−0.811705	+	0.584067i	$0.801460\pi$
$752$	−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	−0.386507	−	0.922287i	$-0.626318\pi$
$757$	405.586	−	405.586i	0.535780	−	0.535780i	0.922287	+	0.386507i	$0.126318\pi$
$758$	−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	0.969784	+	0.243965i	$0.0784481\pi$
$761$	529.787	+	917.617i	0.696172	+	1.20580i	−0.273612	+	0.961840i	$0.588219\pi$
$762$		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	$0.0773810\pi$
$769$			370.215i			0.481424i	−0.970597	+	0.240712i	$0.922619\pi$
$770$	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	0.797872	−	0.602827i	$-0.205959\pi$
$773$	1383.87	−	370.808i	1.79026	−	0.479700i	0.992391	+	0.123127i	$0.0392923\pi$
$774$		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	0.985746	−	0.168242i	$-0.0538089\pi$
$787$	37.7320	+	140.818i	0.0479441	+	0.178930i	−0.937802	+	0.347171i	$0.887142\pi$
$788$	−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	−0.538806	−	0.842430i	$-0.681124\pi$
$797$	241.988	−	241.988i	0.303624	−	0.303624i	0.842430	+	0.538806i	$0.181124\pi$
$798$		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	0.604695	−	0.796457i	$-0.293295\pi$
$809$	175.788	+	101.491i	0.217290	+	0.125453i	−0.387405	+	0.921910i	$0.626628\pi$
$810$		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	0.813979	−	0.580894i	$-0.197297\pi$
$821$	−78.8816	−	136.627i	−0.0960799	−	0.166415i	−0.910059	+	0.414479i	$0.863964\pi$
$822$		0			0
$823$	−387.465	+	103.821i	−0.470795	+	0.126149i	−0.486413	−	0.873729i	$-0.661695\pi$
$823$	−387.465	+	103.821i	−0.470795	+	0.126149i	0.0156180	+	0.999878i	$0.495028\pi$
$824$	−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	−0.478835	−	0.877905i	$-0.658941\pi$
$827$	330.030	−	330.030i	0.399069	−	0.399069i	0.877905	+	0.478835i	$0.158941\pi$
$828$		0			0
$829$	175.549	+	101.353i	0.211760	+	0.122259i	0.602129	−	0.798399i	$-0.294319\pi$
$829$	175.549	+	101.353i	0.211760	+	0.122259i	−0.390369	+	0.920658i	$0.627653\pi$
$830$	−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	$-0.859417\pi$
$839$		−	717.236i		−	0.854870i	0.904046	−	0.427435i	$-0.140583\pi$
$840$		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	0.990917	+	0.134477i	$0.0429355\pi$
$853$	959.961	+	959.961i	1.12539	+	1.12539i	0.134477	+	0.990917i	$0.457065\pi$
$854$	−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	−0.828455	−	0.560055i	$-0.810780\pi$
$857$	−335.104	−	1250.62i	−0.391020	−	1.45930i	0.437436	−	0.899250i	$-0.355887\pi$
$858$		0			0
$859$	901.682	−	520.586i	1.04969	−	0.606038i	0.127126	−	0.991887i	$-0.459425\pi$
$859$	901.682	−	520.586i	1.04969	−	0.606038i	0.922562	+	0.385849i	$0.126091\pi$
$860$	−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	0.753706	+	0.657212i	$0.228264\pi$
$863$	−196.443	+	733.137i	−0.227629	+	0.849521i	−0.981334	+	0.192309i	$0.938402\pi$
$864$		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	0.724872	−	0.688883i	$-0.241899\pi$
$877$	884.182	+	236.916i	1.00819	+	0.270143i	0.283316	+	0.959026i	$0.408565\pi$
$878$	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	0.966008	+	0.258514i	$0.0832328\pi$
$883$	1081.25	+	1081.25i	1.22452	+	1.22452i	0.258514	+	0.966008i	$0.416767\pi$
$884$	−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	−0.0655924	−	0.997846i	$-0.520894\pi$
$887$	−551.111	−	147.670i	−0.621320	−	0.166482i	−0.555728	+	0.831364i	$0.687560\pi$
$888$		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	−0.927987	−	0.372612i	$-0.878462\pi$
$907$	−281.744	−	1051.48i	−0.310633	−	1.15930i	0.617354	−	0.786685i	$-0.288204\pi$
$908$	−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	0.0139309	−	0.999903i	$-0.495566\pi$
$919$	815.004	−	470.543i	0.886838	−	0.512016i	0.872907	+	0.487887i	$0.162232\pi$
$920$	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	−0.902882	−	0.429888i	$-0.858553\pi$
$929$	−912.306	+	526.720i	−0.982030	+	0.566975i	−0.0791477	+	0.996863i	$0.525220\pi$
$930$		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	−0.561914	−	0.827195i	$-0.689935\pi$
$937$	248.568	−	248.568i	0.265281	−	0.265281i	0.827195	+	0.561914i	$0.189935\pi$
$938$	−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	−0.806672	−	0.590999i	$-0.798734\pi$
$941$	102.084	−	176.814i	0.108484	−	0.187900i	0.915156	+	0.403099i	$0.132067\pi$
$942$		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	0.0941668	−	0.995556i	$-0.469981\pi$
$947$	−304.991	−	81.7222i	−0.322061	−	0.0862959i	−0.416227	+	0.909261i	$0.636648\pi$
$948$		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	0.808852	−	0.588012i	$-0.200089\pi$
$953$	210.461	+	210.461i	0.220841	+	0.220841i	−0.588012	+	0.808852i	$0.700089\pi$
$954$		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	−0.554141	−	0.832423i	$-0.686953\pi$
$967$	269.098	−	269.098i	0.278282	−	0.278282i	0.832423	+	0.554141i	$0.186953\pi$
$968$	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	0.679556	−	0.733624i	$-0.262173\pi$
$971$	−286.988	−	497.078i	−0.295559	−	0.511924i	−0.975115	+	0.221700i	$0.928839\pi$
$972$		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	0.973784	−	0.227476i	$-0.0730473\pi$
$977$	16.3397	+	60.9807i	0.0167244	+	0.0624163i	−0.957059	+	0.289892i	$0.906381\pi$
$978$		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	−0.185200	−	0.982701i	$-0.559293\pi$
$983$	143.285	−	38.3930i	0.145763	−	0.0390570i	0.330963	+	0.943644i	$0.392627\pi$
$984$		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	0.156304	−	0.987709i	$-0.450042\pi$
$991$	925.131	−	1602.37i	0.933533	−	1.61693i	0.777229	−	0.629217i	$-0.216625\pi$
$992$	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	−0.972608	−	0.232450i	$-0.925326\pi$
$997$	−245.790	−	917.302i	−0.246530	−	0.920062i	0.726078	−	0.687612i	$-0.241341\pi$
$998$	−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.298.11		64
3.2	odd	2		105.3.v.a.88.6	yes	64
5.2	odd	4	inner	315.3.ca.b.172.6		64
7.2	even	3	inner	315.3.ca.b.163.6		64
15.2	even	4		105.3.v.a.67.11	yes	64
21.2	odd	6		105.3.v.a.58.11	yes	64
35.2	odd	12	inner	315.3.ca.b.37.11		64
105.2	even	12		105.3.v.a.37.6	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.6	✓	64	105.2	even	12
105.3.v.a.58.11	yes	64	21.2	odd	6
105.3.v.a.67.11	yes	64	15.2	even	4
105.3.v.a.88.6	yes	64	3.2	odd	2
315.3.ca.b.37.11		64	35.2	odd	12	inner
315.3.ca.b.163.6		64	7.2	even	3	inner
315.3.ca.b.172.6		64	5.2	odd	4	inner
315.3.ca.b.298.11		64	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
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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