LMFDB - Embedded newform 1050.3.q.c.199.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(199,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1050.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.11007531417600000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} + 48x^{8} - 7x^{4} + 1 $ x^16 - 7x^12 + 48x^8 - 7*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.7
Root			$0.418778 - 1.56290i$ of defining polynomial
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.c.649.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(2.55620 + 6.51658i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(2.55620 + 6.51658i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-5.79240 + 10.0327i) q^{11} +(-1.73205 - 3.00000i) q^{12} -7.86371 q^{13} +(7.73861 + 6.17364i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-13.8033 + 23.9080i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(-27.2149 + 15.7125i) q^{19} +(11.9886 + 1.80922i) q^{21} +16.3834i q^{22} +(-15.7263 + 9.07959i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-9.63104 + 5.56049i) q^{26} -5.19615 q^{27} +(13.8433 + 2.08911i) q^{28} +2.30331 q^{29} +(-4.55860 - 2.63191i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(10.0327 + 17.3772i) q^{33} +39.0416i q^{34} -6.00000 q^{36} +(1.72017 - 0.993142i) q^{37} +(-22.2208 + 38.4876i) q^{38} +(-6.81018 + 11.7956i) q^{39} -22.1905i q^{41} +(15.9623 - 6.26139i) q^{42} -49.8368i q^{43} +(11.5848 + 20.0655i) q^{44} +(-12.8405 + 22.2404i) q^{46} +(-38.3335 - 66.3956i) q^{47} -6.92820 q^{48} +(-35.9317 + 33.3154i) q^{49} +(23.9080 + 41.4099i) q^{51} +(-7.86371 + 13.6204i) q^{52} +(49.4461 + 28.5477i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(18.4317 - 7.23003i) q^{56} +54.4297i q^{57} +(2.82097 - 1.62869i) q^{58} +(60.9245 + 35.1748i) q^{59} +(-58.5590 + 33.8091i) q^{61} -7.44416 q^{62} +(13.0963 - 16.4161i) q^{63} -8.00000 q^{64} +(24.5751 + 14.1884i) q^{66} +(-85.0131 - 49.0823i) q^{67} +(27.6066 + 47.8160i) q^{68} +31.4526i q^{69} -34.2597 q^{71} +(-7.34847 + 4.24264i) q^{72} +(9.74573 - 16.8801i) q^{73} +(1.40452 - 2.43269i) q^{74} +62.8501i q^{76} +(-80.1856 - 12.1010i) q^{77} +19.2621i q^{78} +(45.2142 + 78.3134i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-15.6911 - 27.1777i) q^{82} +133.803 q^{83} +(15.1223 - 18.9557i) q^{84} +(-35.2400 - 61.0374i) q^{86} +(1.99472 - 3.45496i) q^{87} +(28.3768 + 16.3834i) q^{88} +(9.58232 - 5.53235i) q^{89} +(-20.1012 - 51.2445i) q^{91} +36.3184i q^{92} +(-7.89573 + 4.55860i) q^{93} +(-93.8975 - 54.2118i) q^{94} +(-8.48528 + 4.89898i) q^{96} +72.3112 q^{97} +(-20.4496 + 66.2104i) q^{98} +34.7544 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) $ 16 * q + 16 * q^4 - 24 * q^9	$ 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 80 q^{14} - 32 q^{16} - 216 q^{19} - 192 q^{26} - 144 q^{29} - 264 q^{31} - 96 q^{36} - 48 q^{39} + 16 q^{44} + 16 q^{46} - 312 q^{49} + 168 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 128 q^{64} - 144 q^{66} + 16 q^{71} + 32 q^{74} - 24 q^{79} - 72 q^{81} - 80 q^{86} - 984 q^{89} - 616 q^{91} - 960 q^{94} + 48 q^{99}+O(q^{100}) $ 16 * q + 16 * q^4 - 24 * q^9 - 8 * q^11 + 80 * q^14 - 32 * q^16 - 216 * q^19 - 192 * q^26 - 144 * q^29 - 264 * q^31 - 96 * q^36 - 48 * q^39 + 16 * q^44 + 16 * q^46 - 312 * q^49 + 168 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 128 * q^64 - 144 * q^66 + 16 * q^71 + 32 * q^74 - 24 * q^79 - 72 * q^81 - 80 * q^86 - 984 * q^89 - 616 * q^91 - 960 * q^94 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		−	2.44949i		−	0.408248i
$7$	2.55620	+	6.51658i	0.365172	+	0.930940i
$7$	2.55620	+	6.51658i	0.365172	+	0.930940i
$8$		−	2.82843i		−	0.353553i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	−5.79240	+	10.0327i	−0.526582	+	0.912066i	0.472939	+	0.881095i	$0.343193\pi$
$11$	−5.79240	+	10.0327i	−0.526582	+	0.912066i	−0.999520	+	0.0309707i	$0.990140\pi$
$12$	−1.73205	−	3.00000i	−0.144338	−	0.250000i
$13$	−7.86371			−0.604901			−0.302451	−	0.953165i	$-0.597805\pi$
$13$	−7.86371			−0.604901			−0.302451	+	0.953165i	$0.597805\pi$
$14$	7.73861	+	6.17364i	0.552758	+	0.440975i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−13.8033	+	23.9080i	−0.811959	+	1.40635i	0.0995321	+	0.995034i	$0.468265\pi$
$17$	−13.8033	+	23.9080i	−0.811959	+	1.40635i	−0.911491	+	0.411320i	$0.865068\pi$
$18$	−3.67423	−	2.12132i	−0.204124	−	0.117851i
$19$	−27.2149	+	15.7125i	−1.43236	+	0.826974i	−0.997301	−	0.0734266i	$-0.976607\pi$
$19$	−27.2149	+	15.7125i	−1.43236	+	0.826974i	−0.435061	+	0.900401i	$0.643273\pi$
$20$		0			0
$21$	11.9886	+	1.80922i	0.570886	+	0.0861535i
$22$			16.3834i			0.744699i
$23$	−15.7263	+	9.07959i	−0.683753	+	0.394765i	−0.801268	−	0.598306i	$-0.795841\pi$
$23$	−15.7263	+	9.07959i	−0.683753	+	0.394765i	0.117515	+	0.993071i	$0.462507\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$		0			0
$26$	−9.63104	+	5.56049i	−0.370425	+	0.213865i
$27$	−5.19615			−0.192450
$28$	13.8433	+	2.08911i	0.494402	+	0.0746112i
$29$	2.30331			0.0794244			0.0397122	−	0.999211i	$-0.487356\pi$
$29$	2.30331			0.0794244			0.0397122	+	0.999211i	$0.487356\pi$
$30$		0			0
$31$	−4.55860	−	2.63191i	−0.147052	−	0.0849003i	0.424669	−	0.905349i	$-0.360391\pi$
$31$	−4.55860	−	2.63191i	−0.147052	−	0.0849003i	−0.571721	+	0.820448i	$0.693724\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$	10.0327	+	17.3772i	0.304022	+	0.526582i
$34$			39.0416i			1.14828i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	1.72017	−	0.993142i	0.0464912	−	0.0268417i	−0.476574	−	0.879134i	$-0.658122\pi$
$37$	1.72017	−	0.993142i	0.0464912	−	0.0268417i	0.523065	+	0.852293i	$0.324788\pi$
$38$	−22.2208	+	38.4876i	−0.584759	+	1.01283i
$39$	−6.81018	+	11.7956i	−0.174620	+	0.302451i
$40$		0			0
$41$		−	22.1905i		−	0.541233i	−0.962687	−	0.270616i	$-0.912773\pi$
$41$		−	22.1905i		−	0.541233i	0.962687	−	0.270616i	$-0.0872275\pi$
$42$	15.9623	−	6.26139i	0.380055	−	0.149081i
$43$		−	49.8368i		−	1.15900i	−0.814974	−	0.579498i	$-0.803249\pi$
$43$		−	49.8368i		−	1.15900i	0.814974	−	0.579498i	$-0.196751\pi$
$44$	11.5848	+	20.0655i	0.263291	+	0.456033i
$45$		0			0
$46$	−12.8405	+	22.2404i	−0.279141	+	0.483486i
$47$	−38.3335	−	66.3956i	−0.815606	−	1.41267i	−0.908892	−	0.417032i	$-0.863070\pi$
$47$	−38.3335	−	66.3956i	−0.815606	−	1.41267i	0.0932854	−	0.995639i	$-0.470263\pi$
$48$	−6.92820			−0.144338
$49$	−35.9317	+	33.3154i	−0.733300	+	0.679906i
$50$		0			0
$51$	23.9080	+	41.4099i	0.468785	+	0.811959i
$52$	−7.86371	+	13.6204i	−0.151225	+	0.261930i
$53$	49.4461	+	28.5477i	0.932945	+	0.538636i	0.887742	−	0.460342i	$-0.152273\pi$
$53$	49.4461	+	28.5477i	0.932945	+	0.538636i	0.0452033	+	0.998978i	$0.485606\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$		0			0
$56$	18.4317	−	7.23003i	0.329137	−	0.129108i
$57$			54.4297i			0.954908i
$58$	2.82097	−	1.62869i	0.0486373	−	0.0280808i
$59$	60.9245	+	35.1748i	1.03262	+	0.596182i	0.917734	−	0.397196i	$-0.130017\pi$
$59$	60.9245	+	35.1748i	1.03262	+	0.596182i	0.114885	+	0.993379i	$0.463350\pi$
$60$		0			0
$61$	−58.5590	+	33.8091i	−0.959984	+	0.554247i	−0.896168	−	0.443715i	$-0.853660\pi$
$61$	−58.5590	+	33.8091i	−0.959984	+	0.554247i	−0.0638160	+	0.997962i	$0.520327\pi$
$62$	−7.44416			−0.120067
$63$	13.0963	−	16.4161i	0.207877	−	0.260573i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	24.5751	+	14.1884i	0.372349	+	0.214976i
$67$	−85.0131	−	49.0823i	−1.26885	−	0.732572i	−0.294081	−	0.955780i	$-0.595014\pi$
$67$	−85.0131	−	49.0823i	−1.26885	−	0.732572i	−0.974771	+	0.223208i	$0.928347\pi$
$68$	27.6066	+	47.8160i	0.405979	+	0.703177i
$69$			31.4526i			0.455835i
$70$		0			0
$71$	−34.2597			−0.482531			−0.241266	−	0.970459i	$-0.577563\pi$
$71$	−34.2597			−0.482531			−0.241266	+	0.970459i	$0.577563\pi$
$72$	−7.34847	+	4.24264i	−0.102062	+	0.0589256i
$73$	9.74573	−	16.8801i	0.133503	−	0.231234i	−0.791521	−	0.611141i	$-0.790711\pi$
$73$	9.74573	−	16.8801i	0.133503	−	0.231234i	0.925025	+	0.379907i	$0.124044\pi$
$74$	1.40452	−	2.43269i	0.0189799	−	0.0328742i
$75$		0			0
$76$			62.8501i			0.826974i
$77$	−80.1856	−	12.1010i	−1.04137	−	0.157155i
$78$			19.2621i			0.246950i
$79$	45.2142	+	78.3134i	0.572332	+	0.991308i	0.996326	+	0.0856432i	$0.0272945\pi$
$79$	45.2142	+	78.3134i	0.572332	+	0.991308i	−0.423994	+	0.905665i	$0.639372\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−15.6911	−	27.1777i	−0.191355	−	0.331436i
$83$	133.803			1.61209			0.806045	−	0.591854i	$-0.201604\pi$
$83$	133.803			1.61209			0.806045	+	0.591854i	$0.201604\pi$
$84$	15.1223	−	18.9557i	0.180027	−	0.225663i
$85$		0			0
$86$	−35.2400	−	61.0374i	−0.409767	−	0.709737i
$87$	1.99472	−	3.45496i	0.0229279	−	0.0397122i
$88$	28.3768	+	16.3834i	0.322464	+	0.186175i
$89$	9.58232	−	5.53235i	0.107666	−	0.0621613i	−0.445200	−	0.895431i	$-0.646867\pi$
$89$	9.58232	−	5.53235i	0.107666	−	0.0621613i	0.552866	+	0.833270i	$0.313534\pi$
$90$		0			0
$91$	−20.1012	−	51.2445i	−0.220893	−	0.563127i
$92$			36.3184i			0.394765i
$93$	−7.89573	+	4.55860i	−0.0849003	+	0.0490172i
$94$	−93.8975	−	54.2118i	−0.998910	−	0.576721i
$95$		0			0
$96$	−8.48528	+	4.89898i	−0.0883883	+	0.0510310i
$97$	72.3112			0.745476			0.372738	−	0.927937i	$-0.378419\pi$
$97$	72.3112			0.745476			0.372738	+	0.927937i	$0.378419\pi$
$98$	−20.4496	+	66.2104i	−0.208669	+	0.675616i
$99$	34.7544			0.351054
$100$		0			0
$101$	43.8670	+	25.3266i	0.434327	+	0.250759i	0.701188	−	0.712976i	$-0.252653\pi$
$101$	43.8670	+	25.3266i	0.434327	+	0.250759i	−0.266861	+	0.963735i	$0.585987\pi$
$102$	58.5625	+	33.8110i	0.574142	+	0.331481i
$103$	98.9823	+	171.442i	0.960993	+	1.66449i	0.720015	+	0.693958i	$0.244135\pi$
$103$	98.9823	+	171.442i	0.960993	+	1.66449i	0.240978	+	0.970531i	$0.422532\pi$
$104$			22.2419i			0.213865i
$105$		0			0
$106$	80.7451			0.761746
$107$	128.116	−	73.9679i	1.19735	−	0.691289i	0.237384	−	0.971416i	$-0.423710\pi$
$107$	128.116	−	73.9679i	1.19735	−	0.691289i	0.959963	+	0.280127i	$0.0903767\pi$
$108$	−5.19615	+	9.00000i	−0.0481125	+	0.0833333i
$109$	−27.1610	+	47.0442i	−0.249183	+	0.431598i	−0.963299	−	0.268429i	$-0.913495\pi$
$109$	−27.1610	+	47.0442i	−0.249183	+	0.431598i	0.714116	+	0.700027i	$0.246829\pi$
$110$		0			0
$111$		−	3.44035i		−	0.0309941i
$112$	17.4617	−	21.8881i	0.155908	−	0.195429i
$113$		−	47.7883i		−	0.422906i	−0.977388	−	0.211453i	$-0.932181\pi$
$113$		−	47.7883i		−	0.422906i	0.977388	−	0.211453i	$-0.0678195\pi$
$114$	38.4876	+	66.6625i	0.337611	+	0.584759i
$115$		0			0
$116$	2.30331	−	3.98945i	0.0198561	−	0.0343918i
$117$	11.7956	+	20.4305i	0.100817	+	0.174620i
$118$	99.4892			0.843129
$119$	−191.083	−	28.8367i	−1.60574	−	0.242325i
$120$		0			0
$121$	−6.60372	−	11.4380i	−0.0545762	−	0.0945288i
$122$	−47.8132	+	82.8150i	−0.391912	+	0.678811i
$123$	−33.2858	−	19.2176i	−0.270616	−	0.156240i
$124$	−9.11720	+	5.26382i	−0.0735258	+	0.0424501i
$125$		0			0
$126$	4.43168	−	29.3660i	0.0351720	−	0.233063i
$127$		−	101.973i		−	0.802940i	−0.915872	−	0.401470i	$-0.868499\pi$
$127$		−	101.973i		−	0.802940i	0.915872	−	0.401470i	$-0.131501\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$	−74.7552	−	43.1600i	−0.579498	−	0.334573i
$130$		0			0
$131$	−64.6037	+	37.2990i	−0.493158	+	0.284725i	−0.725884	−	0.687817i	$-0.758569\pi$
$131$	−64.6037	+	37.2990i	−0.493158	+	0.284725i	0.232726	+	0.972542i	$0.425236\pi$
$132$	40.1309			0.304022
$133$	−171.959	−	137.184i	−1.29292	−	1.03146i
$134$	−138.826			−1.03601
$135$		0			0
$136$	67.6221	+	39.0416i	0.497221	+	0.287071i
$137$	213.821	+	123.449i	1.56074	+	0.901091i	0.997183	+	0.0750109i	$0.0238992\pi$
$137$	213.821	+	123.449i	1.56074	+	0.901091i	0.563553	+	0.826080i	$0.309434\pi$
$138$	22.2404	+	38.5215i	0.161162	+	0.279141i
$139$			155.917i			1.12170i	0.827916	+	0.560852i	$0.189526\pi$
$139$			155.917i			1.12170i	−0.827916	+	0.560852i	$0.810474\pi$
$140$		0			0
$141$	−132.791			−0.941781
$142$	−41.9594	+	24.2253i	−0.295489	+	0.170601i
$143$	45.5498	−	78.8945i	0.318530	−	0.551710i
$144$	−6.00000	+	10.3923i	−0.0416667	+	0.0721688i
$145$		0			0
$146$		−	27.5651i		−	0.188802i
$147$	18.8553	+	82.7495i	0.128268	+	0.562922i
$148$		−	3.97257i		−	0.0268417i
$149$	81.5452	+	141.240i	0.547283	+	0.947922i	0.998459	+	0.0554872i	$0.0176712\pi$
$149$	81.5452	+	141.240i	0.547283	+	0.947922i	−0.451176	+	0.892435i	$0.648995\pi$
$150$		0			0
$151$	37.5149	−	64.9778i	0.248443	−	0.430316i	−0.714651	−	0.699481i	$-0.753414\pi$
$151$	37.5149	−	64.9778i	0.248443	−	0.430316i	0.963094	+	0.269165i	$0.0867477\pi$
$152$	44.4417	+	76.9753i	0.292380	+	0.506416i
$153$	82.8198			0.541306
$154$	−106.764	+	41.8792i	−0.693270	+	0.271943i
$155$		0			0
$156$	13.6204	+	23.5911i	0.0873100	+	0.151225i
$157$	112.365	−	194.622i	0.715702	−	1.23963i	−0.246986	−	0.969019i	$-0.579440\pi$
$157$	112.365	−	194.622i	0.715702	−	1.23963i	0.962688	−	0.270614i	$-0.0872266\pi$
$158$	110.752	+	63.9426i	0.700961	+	0.404700i
$159$	85.6431	−	49.4461i	0.538636	−	0.310982i
$160$		0			0
$161$	−99.3675	−	79.2726i	−0.617190	−	0.492376i
$162$			12.7279i			0.0785674i
$163$	199.288	−	115.059i	1.22262	−	0.705882i	0.257147	−	0.966372i	$-0.417218\pi$
$163$	199.288	−	115.059i	1.22262	−	0.705882i	0.965476	+	0.260491i	$0.0838843\pi$
$164$	−38.4351	−	22.1905i	−0.234361	−	0.135308i
$165$		0			0
$166$	163.875	−	94.6133i	0.987199	−	0.569960i
$167$	−277.788			−1.66340			−0.831702	−	0.555223i	$-0.812633\pi$
$167$	−277.788			−1.66340			−0.831702	+	0.555223i	$0.812633\pi$
$168$	5.11726	−	33.9089i	0.0304599	−	0.201839i
$169$	−107.162			−0.634095
$170$		0			0
$171$	81.6446	+	47.1375i	0.477454	+	0.275658i
$172$	−86.3199	−	49.8368i	−0.501860	−	0.289749i
$173$	−63.0327	−	109.176i	−0.364351	−	0.631074i	0.624321	−	0.781168i	$-0.285376\pi$
$173$	−63.0327	−	109.176i	−0.364351	−	0.631074i	−0.988672	+	0.150094i	$0.952042\pi$
$174$		−	5.64193i		−	0.0324249i
$175$		0			0
$176$	46.3392			0.263291
$177$	105.524	−	60.9245i	0.596182	−	0.344206i
$178$	7.82393	−	13.5514i	0.0439547	−	0.0761317i
$179$	38.5535	−	66.7766i	0.215382	−	0.373053i	−0.738008	−	0.674792i	$-0.764234\pi$
$179$	38.5535	−	66.7766i	0.215382	−	0.373053i	0.953391	+	0.301738i	$0.0975668\pi$
$180$		0			0
$181$			212.012i			1.17134i	0.810551	+	0.585668i	$0.199168\pi$
$181$			212.012i			1.17134i	−0.810551	+	0.585668i	$0.800832\pi$
$182$	−60.8542	−	48.5478i	−0.334364	−	0.266746i
$183$			117.118i			0.639989i
$184$	25.6810	+	44.4807i	0.139570	+	0.241743i
$185$		0			0
$186$	−6.44683	+	11.1662i	−0.0346604	+	0.0600336i
$187$	−159.908	−	276.969i	−0.855125	−	1.48112i
$188$	−153.334			−0.815606
$189$	−13.2824	−	33.8612i	−0.0702773	−	0.179160i
$190$		0			0
$191$	−82.8480	−	143.497i	−0.433759	−	0.751293i	0.563434	−	0.826161i	$-0.309480\pi$
$191$	−82.8480	−	143.497i	−0.433759	−	0.751293i	−0.997193	+	0.0748682i	$0.976146\pi$
$192$	−6.92820	+	12.0000i	−0.0360844	+	0.0625000i
$193$	−91.1920	−	52.6497i	−0.472497	−	0.272796i	0.244787	−	0.969577i	$-0.421282\pi$
$193$	−91.1920	−	52.6497i	−0.472497	−	0.272796i	−0.717285	+	0.696780i	$0.754615\pi$
$194$	88.5627	−	51.1317i	0.456509	−	0.263566i
$195$		0			0
$196$	21.7723	+	95.5509i	0.111083	+	0.487504i
$197$			244.736i			1.24231i	0.783687	+	0.621156i	$0.213337\pi$
$197$			244.736i			1.24231i	−0.783687	+	0.621156i	$0.786663\pi$
$198$	42.5653	−	24.5751i	0.214976	−	0.124116i
$199$	−84.8416	−	48.9833i	−0.426340	−	0.246147i	0.271446	−	0.962454i	$-0.412498\pi$
$199$	−84.8416	−	48.9833i	−0.426340	−	0.246147i	−0.697786	+	0.716306i	$0.745831\pi$
$200$		0			0
$201$	−147.247	+	85.0131i	−0.732572	+	0.422951i
$202$	71.6346			0.354627
$203$	5.88772	+	15.0097i	0.0290035	+	0.0739394i
$204$	95.6321			0.468785
$205$		0			0
$206$	242.456	+	139.982i	1.17697	+	0.679525i
$207$	47.1790	+	27.2388i	0.227918	+	0.131588i
$208$	15.7274	+	27.2407i	0.0756126	+	0.130965i
$209$		−	364.052i		−	1.74188i
$210$		0			0
$211$	−388.914			−1.84319			−0.921597	−	0.388149i	$-0.873114\pi$
$211$	−388.914			−1.84319			−0.921597	+	0.388149i	$0.873114\pi$
$212$	98.8922	−	57.0954i	0.466473	−	0.269318i
$213$	−29.6698	+	51.3896i	−0.139295	+	0.241266i
$214$	104.606	−	181.184i	0.488815	−	0.846652i
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	5.49835	−	36.4342i	0.0253380	−	0.167899i
$218$			76.8228i			0.352398i
$219$	−16.8801	−	29.2372i	−0.0770781	−	0.133503i
$220$		0			0
$221$	108.545	−	188.006i	0.491155	−	0.850705i
$222$	−2.43269	−	4.21355i	−0.0109581	−	0.0189799i
$223$	−251.913			−1.12965			−0.564827	−	0.825210i	$-0.691057\pi$
$223$	−251.913			−1.12965			−0.564827	+	0.825210i	$0.691057\pi$
$224$	5.90890	−	39.1546i	0.0263790	−	0.174797i
$225$		0			0
$226$	−33.7915	−	58.5285i	−0.149520	−	0.258976i
$227$	−133.911	+	231.941i	−0.589916	+	1.02176i	0.404327	+	0.914615i	$0.367506\pi$
$227$	−133.911	+	231.941i	−0.589916	+	1.02176i	−0.994243	+	0.107150i	$0.965827\pi$
$228$	94.2751	+	54.4297i	0.413487	+	0.238727i
$229$	−299.237	+	172.765i	−1.30671	+	0.754431i	−0.981546	−	0.191226i	$-0.938754\pi$
$229$	−299.237	+	172.765i	−1.30671	+	0.754431i	−0.325167	+	0.945657i	$0.605420\pi$
$230$		0			0
$231$	−87.5942	+	109.799i	−0.379196	+	0.475319i
$232$		−	6.51474i		−	0.0280808i
$233$	249.471	−	144.032i	1.07069	−	0.618164i	0.142321	−	0.989821i	$-0.454543\pi$
$233$	249.471	−	144.032i	1.07069	−	0.618164i	0.928370	+	0.371656i	$0.121210\pi$
$234$	28.8931	+	16.6815i	0.123475	+	0.0712883i
$235$		0			0
$236$	121.849	−	70.3495i	0.516309	−	0.298091i
$237$	156.627			0.660872
$238$	−254.418	+	99.7983i	−1.06898	+	0.419320i
$239$	188.810			0.789999			0.395000	−	0.918681i	$-0.370745\pi$
$239$	188.810			0.789999			0.395000	+	0.918681i	$0.370745\pi$
$240$		0			0
$241$	84.7389	+	48.9240i	0.351614	+	0.203004i	0.665396	−	0.746491i	$-0.268263\pi$
$241$	84.7389	+	48.9240i	0.351614	+	0.203004i	−0.313782	+	0.949495i	$0.601596\pi$
$242$	−16.1758	−	9.33908i	−0.0668420	−	0.0385912i
$243$	7.79423	+	13.5000i	0.0320750	+	0.0555556i
$244$			135.236i			0.554247i
$245$		0			0
$246$	−54.3555			−0.220957
$247$	214.010	−	123.559i	0.866437	−	0.500238i
$248$	−7.44416	+	12.8937i	−0.0300168	+	0.0519906i
$249$	115.877	−	200.705i	0.465370	−	0.806045i
$250$		0			0
$251$			241.345i			0.961533i	0.876849	+	0.480767i	$0.159642\pi$
$251$			241.345i			0.961533i	−0.876849	+	0.480767i	$0.840358\pi$
$252$	−15.3372	−	39.0995i	−0.0608619	−	0.155157i
$253$		−	210.370i		−	0.831504i
$254$	−72.1061	−	124.891i	−0.283882	−	0.491698i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−6.28197	−	10.8807i	−0.0244435	−	0.0423373i	0.853545	−	0.521019i	$-0.174448\pi$
$257$	−6.28197	−	10.8807i	−0.0244435	−	0.0423373i	−0.877988	+	0.478682i	$0.841115\pi$
$258$	−122.075			−0.473158
$259$	10.8690	+	8.67098i	0.0419653	+	0.0334787i
$260$		0			0
$261$	−3.45496	−	5.98417i	−0.0132374	−	0.0229279i
$262$	−52.7487	+	91.3635i	−0.201331	+	0.348716i
$263$	−184.014	−	106.240i	−0.699672	−	0.403956i	0.107554	−	0.994199i	$-0.465698\pi$
$263$	−184.014	−	106.240i	−0.699672	−	0.403956i	−0.807225	+	0.590244i	$0.799032\pi$
$264$	49.1501	−	28.3768i	0.186175	−	0.107488i
$265$		0			0
$266$	−307.609	−	46.4219i	−1.15642	−	0.174518i
$267$		−	19.1646i		−	0.0717777i
$268$	−170.026	+	98.1647i	−0.634426	+	0.366286i
$269$	289.769	+	167.298i	1.07721	+	0.621927i	0.930142	−	0.367200i	$-0.119683\pi$
$269$	289.769	+	167.298i	1.07721	+	0.621927i	0.147067	+	0.989127i	$0.453017\pi$
$270$		0			0
$271$	−157.920	+	91.1752i	−0.582731	+	0.336440i	−0.762218	−	0.647321i	$-0.775889\pi$
$271$	−157.920	+	91.1752i	−0.582731	+	0.336440i	0.179487	+	0.983760i	$0.442556\pi$
$272$	110.426			0.405979
$273$	−94.2750	−	14.2272i	−0.345330	−	0.0521144i
$274$	349.168			1.27434
$275$		0			0
$276$	54.4776	+	31.4526i	0.197382	+	0.113959i
$277$	−144.420	−	83.3807i	−0.521370	−	0.301013i	0.216125	−	0.976366i	$-0.430658\pi$
$277$	−144.420	−	83.3807i	−0.521370	−	0.301013i	−0.737495	+	0.675353i	$0.763991\pi$
$278$	110.250	+	190.958i	0.396582	+	0.686900i
$279$			15.7915i			0.0566002i
$280$		0			0
$281$	38.3085			0.136329			0.0681647	−	0.997674i	$-0.478286\pi$
$281$	38.3085			0.136329			0.0681647	+	0.997674i	$0.478286\pi$
$282$	−162.635	+	93.8975i	−0.576721	+	0.332970i
$283$	−192.748	+	333.849i	−0.681088	+	1.17968i	0.293561	+	0.955940i	$0.405160\pi$
$283$	−192.748	+	333.849i	−0.681088	+	1.17968i	−0.974649	+	0.223739i	$0.928174\pi$
$284$	−34.2597	+	59.3396i	−0.120633	+	0.208942i
$285$		0			0
$286$		−	128.834i		−	0.450469i
$287$	144.606	−	56.7235i	0.503855	−	0.197643i
$288$			16.9706i			0.0589256i
$289$	−236.562	−	409.738i	−0.818555	−	1.41778i
$290$		0			0
$291$	62.6233	−	108.467i	0.215200	−	0.372738i
$292$	−19.4915	−	33.7602i	−0.0667516	−	0.115617i
$293$	−90.9844			−0.310527			−0.155264	−	0.987873i	$-0.549623\pi$
$293$	−90.9844			−0.310527			−0.155264	+	0.987873i	$0.549623\pi$
$294$	81.6057	+	88.0143i	0.277570	+	0.299368i
$295$		0			0
$296$	−2.80903	−	4.86538i	−0.00948997	−	0.0164371i
$297$	30.0982	−	52.1316i	0.101341	−	0.175527i
$298$	199.744	+	115.322i	0.670282	+	0.386988i
$299$	123.667	−	71.3993i	0.413603	−	0.238794i
$300$		0			0
$301$	324.766	−	127.393i	1.07896	−	0.423232i
$302$		−	106.108i		−	0.351352i
$303$	75.9799	−	43.8670i	0.250759	−	0.144776i
$304$	108.859	+	62.8501i	0.358090	+	0.206744i
$305$		0			0
$306$	101.433	−	58.5625i	0.331481	−	0.191381i
$307$	−508.077			−1.65497			−0.827487	−	0.561485i	$-0.810230\pi$
$307$	−508.077			−1.65497			−0.827487	+	0.561485i	$0.810230\pi$
$308$	−101.145	+	126.785i	−0.328393	+	0.411638i
$309$	342.885			1.10966
$310$		0			0
$311$	90.3447	+	52.1605i	0.290497	+	0.167719i	0.638166	−	0.769899i	$-0.279693\pi$
$311$	90.3447	+	52.1605i	0.290497	+	0.167719i	−0.347669	+	0.937617i	$0.613027\pi$
$312$	33.3629	+	19.2621i	0.106932	+	0.0617375i
$313$	−132.934	−	230.249i	−0.424710	−	0.735619i	0.571683	−	0.820474i	$-0.306291\pi$
$313$	−132.934	−	230.249i	−0.424710	−	0.735619i	−0.996393	+	0.0848550i	$0.972957\pi$
$314$		−	317.817i		−	1.01216i
$315$		0			0
$316$	180.857			0.572332
$317$	−9.28575	+	5.36113i	−0.0292926	+	0.0169121i	−0.514575	−	0.857446i	$-0.672050\pi$
$317$	−9.28575	+	5.36113i	−0.0292926	+	0.0169121i	0.485282	+	0.874358i	$0.338717\pi$
$318$	69.9273	−	121.118i	0.219897	−	0.380873i
$319$	−13.3417	+	23.1085i	−0.0418234	+	0.0724403i
$320$		0			0
$321$		−	256.232i		−	0.798231i
$322$	−177.754	−	26.8252i	−0.552031	−	0.0833081i
$323$		−	867.538i		−	2.68588i
$324$	9.00000	+	15.5885i	0.0277778	+	0.0481125i
$325$		0			0
$326$	162.718	−	281.835i	0.499134	−	0.864525i
$327$	47.0442	+	81.4829i	0.143866	+	0.249183i
$328$	−62.7643			−0.191355
$329$	334.684	−	419.524i	1.01728	−	1.27515i
$330$		0			0
$331$	176.460	+	305.638i	0.533113	+	0.923379i	0.999252	+	0.0386675i	$0.0123113\pi$
$331$	176.460	+	305.638i	0.533113	+	0.923379i	−0.466139	+	0.884711i	$0.654355\pi$
$332$	133.803	−	231.754i	0.403022	−	0.698055i
$333$	−5.16052	−	2.97943i	−0.0154971	−	0.00894723i
$334$	−340.220	+	196.426i	−1.01862	+	0.588102i
$335$		0			0
$336$	−17.7099	−	45.1482i	−0.0527080	−	0.134370i
$337$			220.634i			0.654699i	0.944903	+	0.327349i	$0.106155\pi$
$337$			220.634i			0.654699i	−0.944903	+	0.327349i	$0.893845\pi$
$338$	−131.246	+	75.7750i	−0.388302	+	0.224186i
$339$	−71.6825	−	41.3859i	−0.211453	−	0.122082i
$340$		0			0
$341$	52.8104	−	30.4901i	0.154869	−	0.0894138i
$342$	133.325			0.389839
$343$	−308.951	−	148.991i	−0.900732	−	0.434376i
$344$	−140.960			−0.409767
$345$		0			0
$346$	−154.398	−	89.1417i	−0.446237	−	0.257635i
$347$	221.710	+	128.004i	0.638933	+	0.368888i	0.784204	−	0.620504i	$-0.213072\pi$
$347$	221.710	+	128.004i	0.638933	+	0.368888i	−0.145270	+	0.989392i	$0.546405\pi$
$348$	−3.98945	−	6.90993i	−0.0114639	−	0.0198561i
$349$		−	407.250i		−	1.16691i	−0.812147	−	0.583453i	$-0.801701\pi$
$349$		−	407.250i		−	1.16691i	0.812147	−	0.583453i	$-0.198299\pi$
$350$		0			0
$351$	40.8611			0.116413
$352$	56.7537	−	32.7667i	0.161232	−	0.0930873i
$353$	−291.619	+	505.099i	−0.826116	+	1.43087i	0.0749482	+	0.997187i	$0.476121\pi$
$353$	−291.619	+	505.099i	−0.826116	+	1.43087i	−0.901064	+	0.433687i	$0.857212\pi$
$354$	86.1602	−	149.234i	0.243390	−	0.421565i
$355$		0			0
$356$		−	22.1294i		−	0.0621613i
$357$	−208.737	+	261.651i	−0.584698	+	0.732915i
$358$		−	109.046i		−	0.304597i
$359$	345.764	+	598.881i	0.963131	+	1.66819i	0.714554	+	0.699580i	$0.246630\pi$
$359$	345.764	+	598.881i	0.963131	+	1.66819i	0.248577	+	0.968612i	$0.420037\pi$
$360$		0			0
$361$	313.266	−	542.593i	0.867773	−	1.50303i
$362$	149.915	+	259.660i	0.414130	+	0.717294i
$363$	−22.8760			−0.0630192
$364$	−108.859	−	16.4282i	−0.299064	−	0.0451324i
$365$		0			0
$366$	82.8150	+	143.440i	0.226270	+	0.391912i
$367$	−114.863	+	198.949i	−0.312980	+	0.542096i	−0.979006	−	0.203832i	$-0.934660\pi$
$367$	−114.863	+	198.949i	−0.312980	+	0.542096i	0.666026	+	0.745928i	$0.267994\pi$
$368$	62.9053	+	36.3184i	0.170938	+	0.0986912i
$369$	−57.6527	+	33.2858i	−0.156240	+	0.0902054i
$370$		0			0
$371$	−59.6394	+	395.193i	−0.160753	+	1.06521i
$372$			18.2344i			0.0490172i
$373$	350.401	−	202.304i	0.939414	−	0.542371i	0.0496372	−	0.998767i	$-0.484193\pi$
$373$	350.401	−	202.304i	0.939414	−	0.542371i	0.889776	+	0.456397i	$0.150860\pi$
$374$	−391.694	−	226.145i	−1.04731	−	0.604665i
$375$		0			0
$376$	−187.795	+	108.424i	−0.499455	+	0.288360i
$377$	−18.1126			−0.0480439
$378$	−40.2110	−	32.0792i	−0.106378	−	0.0848656i
$379$	−265.866			−0.701493			−0.350746	−	0.936471i	$-0.614072\pi$
$379$	−265.866			−0.701493			−0.350746	+	0.936471i	$0.614072\pi$
$380$		0			0
$381$	−152.960	−	88.3115i	−0.401470	−	0.231789i
$382$	−202.935	−	117.165i	−0.531244	−	0.306714i
$383$	−153.202	−	265.353i	−0.400005	−	0.692829i	0.593721	−	0.804671i	$-0.297658\pi$
$383$	−153.202	−	265.353i	−0.400005	−	0.692829i	−0.993726	+	0.111842i	$0.964325\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−148.916			−0.385792
$387$	−129.480	+	74.7552i	−0.334573	+	0.193166i
$388$	72.3112	−	125.247i	0.186369	−	0.322801i
$389$	53.1772	−	92.1056i	0.136702	−	0.236775i	−0.789544	−	0.613694i	$-0.789683\pi$
$389$	53.1772	−	92.1056i	0.136702	−	0.236775i	0.926246	+	0.376918i	$0.123016\pi$
$390$		0			0
$391$		−	501.314i		−	1.28213i
$392$	94.2301	+	101.630i	0.240383	+	0.259261i
$393$			129.207i			0.328772i
$394$	173.054	+	299.739i	0.439224	+	0.760758i
$395$		0			0
$396$	34.7544	−	60.1964i	0.0877636	−	0.152011i
$397$	−108.913	−	188.643i	−0.274341	−	0.475172i	0.695628	−	0.718402i	$-0.255126\pi$
$397$	−108.913	−	188.643i	−0.274341	−	0.475172i	−0.969969	+	0.243230i	$0.921793\pi$
$398$	−138.546			−0.348105
$399$	−354.696	+	139.133i	−0.888962	+	0.348705i
$400$		0			0
$401$	−30.9907	−	53.6775i	−0.0772836	−	0.133859i	0.824793	−	0.565434i	$-0.191291\pi$
$401$	−30.9907	−	53.6775i	−0.0772836	−	0.133859i	−0.902077	+	0.431575i	$0.857958\pi$
$402$	−120.227	+	208.239i	−0.299071	+	0.518007i
$403$	35.8475	+	20.6966i	0.0889517	+	0.0513563i
$404$	87.7341	−	50.6533i	0.217164	−	0.125379i
$405$		0			0
$406$	17.8244	+	14.2198i	0.0439025	+	0.0350242i
$407$			23.0107i			0.0565373i
$408$	117.125	−	67.6221i	0.287071	−	0.165740i
$409$	376.167	+	217.180i	0.919724	+	0.531003i	0.883547	−	0.468342i	$-0.155149\pi$
$409$	376.167	+	217.180i	0.919724	+	0.531003i	0.0361772	+	0.999345i	$0.488482\pi$
$410$		0			0
$411$	370.348	−	213.821i	0.901091	−	0.520245i
$412$	395.929			0.960993
$413$	−73.4840	+	486.933i	−0.177927	+	1.17901i
$414$	77.0429			0.186094
$415$		0			0
$416$	38.5242	+	22.2419i	0.0926062	+	0.0534662i
$417$	233.875	+	135.028i	0.560852	+	0.323808i
$418$	−257.424	−	445.871i	−0.615847	−	1.06668i
$419$			457.221i			1.09122i	0.838040	+	0.545609i	$0.183702\pi$
$419$			457.221i			1.09122i	−0.838040	+	0.545609i	$0.816298\pi$
$420$		0			0
$421$	−653.149			−1.55142			−0.775712	−	0.631088i	$-0.782609\pi$
$421$	−653.149			−1.55142			−0.775712	+	0.631088i	$0.782609\pi$
$422$	−476.320	+	275.004i	−1.12872	+	0.651667i
$423$	−115.000	+	199.187i	−0.271869	+	0.470891i
$424$	80.7451	−	139.855i	0.190437	−	0.329846i
$425$		0			0
$426$			83.9188i			0.196993i
$427$	−370.008	−	295.182i	−0.866530	−	0.691293i
$428$		−	295.872i		−	0.691289i
$429$	−78.8945	−	136.649i	−0.183903	−	0.318530i
$430$		0			0
$431$	235.128	−	407.253i	0.545540	−	0.944904i	−0.453032	−	0.891494i	$-0.649658\pi$
$431$	235.128	−	407.253i	0.545540	−	0.944904i	0.998573	−	0.0534095i	$-0.0170089\pi$
$432$	10.3923	+	18.0000i	0.0240563	+	0.0416667i
$433$	−32.0299			−0.0739719			−0.0369860	−	0.999316i	$-0.511776\pi$
$433$	−32.0299			−0.0739719			−0.0369860	+	0.999316i	$0.511776\pi$
$434$	−19.0288	−	48.5105i	−0.0438451	−	0.111775i
$435$		0			0
$436$	54.3219	+	94.0883i	0.124592	+	0.215799i
$437$	285.326	−	494.200i	0.652921	−	1.13089i
$438$	−41.3476	−	23.8721i	−0.0944010	−	0.0545024i
$439$	−331.028	+	191.119i	−0.754051	+	0.435352i	−0.827156	−	0.561973i	$-0.810043\pi$
$439$	−331.028	+	191.119i	−0.754051	+	0.435352i	0.0731046	+	0.997324i	$0.476709\pi$
$440$		0			0
$441$	140.453	+	43.3802i	0.318488	+	0.0983677i
$442$		−	307.012i		−	0.694598i
$443$	−107.163	+	61.8708i	−0.241904	+	0.139663i	−0.616051	−	0.787706i	$-0.711269\pi$
$443$	−107.163	+	61.8708i	−0.241904	+	0.139663i	0.374148	+	0.927369i	$0.377935\pi$
$444$	−5.95885	−	3.44035i	−0.0134208	−	0.00774853i
$445$		0			0
$446$	−308.529	+	178.129i	−0.691769	+	0.399393i
$447$	282.481			0.631948
$448$	−20.4496	−	52.1327i	−0.0456464	−	0.116368i
$449$	266.985			0.594622			0.297311	−	0.954781i	$-0.403910\pi$
$449$	266.985			0.594622			0.297311	+	0.954781i	$0.403910\pi$
$450$		0			0
$451$	222.632	+	128.536i	0.493640	+	0.285003i
$452$	−82.7718	−	47.7883i	−0.183124	−	0.105726i
$453$	−64.9778	−	112.545i	−0.143439	−	0.248443i
$454$			378.757i			0.834267i
$455$		0			0
$456$	153.951			0.337611
$457$	−389.140	+	224.670i	−0.851509	+	0.491619i	−0.861160	−	0.508334i	$-0.830261\pi$
$457$	−389.140	+	224.670i	−0.851509	+	0.491619i	0.00965069	+	0.999953i	$0.496928\pi$
$458$	−244.326	+	423.185i	−0.533463	+	0.923985i
$459$	71.7241	−	124.230i	0.156262	−	0.270653i
$460$		0			0
$461$			105.528i			0.228912i	0.993428	+	0.114456i	$0.0365125\pi$
$461$			105.528i			0.228912i	−0.993428	+	0.114456i	$0.963487\pi$
$462$	−29.6412	+	196.414i	−0.0641584	+	0.425138i
$463$		−	588.555i		−	1.27118i	−0.772028	−	0.635588i	$-0.780758\pi$
$463$		−	588.555i		−	1.27118i	0.772028	−	0.635588i	$-0.219242\pi$
$464$	−4.60662	−	7.97889i	−0.00992805	−	0.0171959i
$465$		0			0
$466$	203.692	−	352.805i	0.437108	−	0.757093i
$467$	182.829	+	316.668i	0.391496	+	0.678091i	0.992647	−	0.121044i	$-0.0386244\pi$
$467$	182.829	+	316.668i	0.391496	+	0.678091i	−0.601151	+	0.799135i	$0.705291\pi$
$468$	47.1823			0.100817
$469$	102.539	−	679.459i	0.218632	−	1.44874i
$470$		0			0
$471$	−194.622	−	337.096i	−0.413211	−	0.715702i
$472$	99.4892	−	172.320i	0.210782	−	0.365086i
$473$	499.999	+	288.675i	1.05708	+	0.610306i
$474$	191.828	−	110.752i	0.404700	−	0.233654i
$475$		0			0
$476$	−241.029	+	302.128i	−0.506364	+	0.634723i
$477$		−	171.286i		−	0.359091i
$478$	231.244	−	133.509i	0.483774	−	0.279307i
$479$	421.907	+	243.588i	0.880808	+	0.508535i	0.870925	−	0.491416i	$-0.163521\pi$
$479$	421.907	+	243.588i	0.880808	+	0.508535i	0.00988318	+	0.999951i	$0.496854\pi$
$480$		0			0
$481$	−13.5270	+	7.80979i	−0.0281226	+	0.0162366i
$482$	138.378			0.287091
$483$	−204.964	+	80.3992i	−0.424355	+	0.166458i
$484$	−26.4149			−0.0545762
$485$		0			0
$486$	19.0919	+	11.0227i	0.0392837	+	0.0226805i
$487$	169.545	+	97.8870i	0.348142	+	0.201000i	0.663867	−	0.747851i	$-0.268914\pi$
$487$	169.545	+	97.8870i	0.348142	+	0.201000i	−0.315725	+	0.948851i	$0.602248\pi$
$488$	95.6265	+	165.630i	0.195956	+	0.339406i
$489$		−	398.575i		−	0.815082i
$490$		0			0
$491$	−349.221			−0.711244			−0.355622	−	0.934630i	$-0.615731\pi$
$491$	−349.221			−0.711244			−0.355622	+	0.934630i	$0.615731\pi$
$492$	−66.5716	+	38.4351i	−0.135308	+	0.0781202i
$493$	−31.7933	+	55.0675i	−0.0644894	+	0.111699i
$494$	174.738	−	302.656i	0.353722	−	0.612664i
$495$		0			0
$496$			21.0553i			0.0424501i
$497$	−87.5747	−	223.256i	−0.176207	−	0.449208i
$498$		−	327.750i		−	0.658133i
$499$	−167.719	−	290.498i	−0.336111	−	0.582161i	0.647587	−	0.761992i	$-0.275778\pi$
$499$	−167.719	−	290.498i	−0.336111	−	0.582161i	−0.983698	+	0.179831i	$0.942445\pi$
$500$		0			0
$501$	−240.572	+	416.683i	−0.480183	+	0.831702i
$502$	170.657	+	295.586i	0.339953	+	0.588817i
$503$	523.663			1.04108			0.520540	−	0.853837i	$-0.325731\pi$
$503$	523.663			1.04108			0.520540	+	0.853837i	$0.325731\pi$
$504$	−46.4317	−	37.0419i	−0.0921263	−	0.0734958i
$505$		0			0
$506$	−148.754	−	257.650i	−0.293981	−	0.509190i
$507$	−92.8050	+	160.743i	−0.183047	+	0.317047i
$508$	−176.623	−	101.973i	−0.347683	−	0.200735i
$509$	417.731	−	241.177i	0.820690	−	0.473825i	−0.0299645	−	0.999551i	$-0.509539\pi$
$509$	417.731	−	241.177i	0.820690	−	0.473825i	0.850654	+	0.525726i	$0.176206\pi$
$510$		0			0
$511$	134.913	+	20.3599i	0.264017	+	0.0398433i
$512$			22.6274i			0.0441942i
$513$	141.413	−	81.6446i	0.275658	−	0.159151i
$514$	−15.3876	−	8.88405i	−0.0299370	−	0.0172841i
$515$		0			0
$516$	−149.510	+	86.3199i	−0.289749	+	0.167287i
$517$	888.171			1.71793
$518$	19.4431	+	2.93419i	0.0375349	+	0.00566446i
$519$	−218.352			−0.420716
$520$		0			0
$521$	−61.7509	−	35.6519i	−0.118524	−	0.0684298i	0.439566	−	0.898210i	$-0.355132\pi$
$521$	−61.7509	−	35.6519i	−0.118524	−	0.0684298i	−0.558090	+	0.829780i	$0.688466\pi$
$522$	−8.46290	−	4.88606i	−0.0162124	−	0.00936026i
$523$	301.064	+	521.458i	0.575648	+	0.997052i	0.995971	+	0.0896773i	$0.0285836\pi$
$523$	301.064	+	521.458i	0.575648	+	0.997052i	−0.420323	+	0.907375i	$0.638083\pi$
$524$			149.196i			0.284725i
$525$		0			0
$526$	−300.493			−0.571279
$527$	125.847	−	72.6581i	0.238800	−	0.137871i
$528$	40.1309	−	69.5088i	0.0760055	−	0.131645i
$529$	−99.6220	+	172.550i	−0.188321	+	0.326182i
$530$		0			0
$531$		−	211.049i		−	0.397455i
$532$	−409.568	+	160.657i	−0.769864	+	0.301987i
$533$			174.500i			0.327392i
$534$	−13.5514	−	23.4718i	−0.0253772	−	0.0439547i
$535$		0			0
$536$	−138.826	+	240.453i	−0.259003	+	0.448607i
$537$	−66.7766	−	115.660i	−0.124351	−	0.215382i
$538$	473.191			0.879537
$539$	−126.114	−	553.469i	−0.233977	−	1.02684i
$540$		0			0
$541$	301.657	+	522.485i	0.557591	+	0.965776i	0.997697	+	0.0678303i	$0.0216077\pi$
$541$	301.657	+	522.485i	0.557591	+	0.965776i	−0.440106	+	0.897946i	$0.645059\pi$
$542$	−128.941	+	223.333i	−0.237899	+	0.412053i
$543$	318.018	+	183.608i	0.585668	+	0.338136i
$544$	135.244	−	78.0833i	0.248611	−	0.143535i
$545$		0			0
$546$	−125.523	+	49.2378i	−0.229896	+	0.0901791i
$547$		−	879.935i		−	1.60866i	−0.594185	−	0.804328i	$-0.702525\pi$
$547$		−	879.935i		−	1.60866i	0.594185	−	0.804328i	$-0.297475\pi$
$548$	427.642	−	246.899i	0.780368	−	0.450546i
$549$	175.677	+	101.427i	0.319995	+	0.184749i
$550$		0			0
$551$	−62.6842	+	36.1908i	−0.113765	+	0.0656820i
$552$	88.9615			0.161162
$553$	−394.759	+	494.827i	−0.713849	+	0.894805i
$554$	−235.836			−0.425697
$555$		0			0
$556$	270.056	+	155.917i	0.485712	+	0.280426i
$557$	764.533	+	441.404i	1.37259	+	0.792466i	0.991254	−	0.131970i	$-0.0421302\pi$
$557$	764.533	+	441.404i	1.37259	+	0.792466i	0.381338	+	0.924436i	$0.375464\pi$
$558$	11.1662	+	19.3405i	0.0200112	+	0.0346604i
$559$			391.903i			0.701078i
$560$		0			0
$561$	−553.939			−0.987414
$562$	46.9182	−	27.0882i	0.0834843	−	0.0481997i
$563$	−260.578	+	451.334i	−0.462838	+	0.801659i	−0.999101	−	0.0423920i	$-0.986502\pi$
$563$	−260.578	+	451.334i	−0.462838	+	0.801659i	0.536263	+	0.844051i	$0.319835\pi$
$564$	−132.791	+	230.001i	−0.235445	+	0.407803i
$565$		0			0
$566$			545.174i			0.963204i
$567$	−62.2946	−	9.40101i	−0.109867	−	0.0165803i
$568$			96.9011i			0.170601i
$569$	122.400	+	212.004i	0.215115	+	0.372590i	0.953308	−	0.301999i	$-0.0976541\pi$
$569$	122.400	+	212.004i	0.215115	+	0.372590i	−0.738193	+	0.674589i	$0.764321\pi$
$570$		0			0
$571$	208.126	−	360.486i	0.364495	−	0.631323i	−0.624200	−	0.781264i	$-0.714575\pi$
$571$	208.126	−	360.486i	0.364495	−	0.631323i	0.988695	+	0.149941i	$0.0479084\pi$
$572$	−91.0995	−	157.789i	−0.159265	−	0.275855i
$573$	−286.994			−0.500862
$574$	136.996	−	171.724i	0.238670	−	0.299171i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−386.784	+	669.929i	−0.670336	+	1.16106i	0.307473	+	0.951557i	$0.400517\pi$
$577$	−386.784	+	669.929i	−0.670336	+	1.16106i	−0.977809	+	0.209499i	$0.932817\pi$
$578$	−579.457	−	334.550i	−1.00252	−	0.578806i
$579$	−157.949	+	91.1920i	−0.272796	+	0.157499i
$580$		0			0
$581$	342.028	+	871.941i	0.588689	+	1.50076i
$582$		−	177.125i		−	0.304339i
$583$	−572.823	+	330.719i	−0.982543	+	0.567272i
$584$	−47.7441	−	27.5651i	−0.0817537	−	0.0472005i
$585$		0			0
$586$	−111.433	+	64.3357i	−0.190158	+	0.109788i
$587$	−633.860			−1.07983			−0.539915	−	0.841720i	$-0.681544\pi$
$587$	−633.860			−1.07983			−0.539915	+	0.841720i	$0.681544\pi$
$588$	162.182	+	50.0911i	0.275819	+	0.0851889i
$589$	165.416			0.280841
$590$		0			0
$591$	367.103	+	211.947i	0.621156	+	0.358625i
$592$	−6.88069	−	3.97257i	−0.0116228	−	0.00671042i
$593$	−46.4206	−	80.4028i	−0.0782809	−	0.135587i	0.824227	−	0.566259i	$-0.191610\pi$
$593$	−46.4206	−	80.4028i	−0.0782809	−	0.135587i	−0.902508	+	0.430672i	$0.858276\pi$
$594$		−	85.1305i		−	0.143317i
$595$		0			0
$596$	326.181			0.547283
$597$	−146.950	+	84.8416i	−0.246147	+	0.142113i
$598$	100.974	−	174.892i	0.168853	−	0.292461i
$599$	−307.680	+	532.918i	−0.513657	+	0.889679i	0.486218	+	0.873838i	$0.338376\pi$
$599$	−307.680	+	532.918i	−0.513657	+	0.889679i	−0.999875	+	0.0158418i	$0.994957\pi$
$600$		0			0
$601$		−	821.399i		−	1.36672i	−0.730081	−	0.683360i	$-0.760518\pi$
$601$		−	821.399i		−	1.36672i	0.730081	−	0.683360i	$-0.239482\pi$
$602$	307.675	−	385.668i	0.511088	−	0.640644i
$603$			294.494i			0.488381i
$604$	−75.0299	−	129.956i	−0.124222	−	0.215158i
$605$		0			0
$606$	62.0374	−	107.452i	0.102372	−	0.177313i
$607$	−502.282	−	869.979i	−0.827483	−	1.43324i	−0.900006	−	0.435876i	$-0.856438\pi$
$607$	−502.282	−	869.979i	−0.827483	−	1.43324i	0.0725231	−	0.997367i	$-0.476895\pi$
$608$	177.767			0.292380
$609$	27.6135	+	4.16720i	0.0453423	+	0.00684270i
$610$		0			0
$611$	301.444	+	522.116i	0.493361	+	0.854527i
$612$	82.8198	−	143.448i	0.135326	−	0.234392i
$613$	964.532	+	556.873i	1.57346	+	0.908438i	0.995740	+	0.0922038i	$0.0293911\pi$
$613$	964.532	+	556.873i	1.57346	+	0.908438i	0.577721	+	0.816234i	$0.303942\pi$
$614$	−622.264	+	359.265i	−1.01346	+	0.585121i
$615$		0			0
$616$	−34.2267	+	226.799i	−0.0555628	+	0.368180i
$617$		−	463.256i		−	0.750820i	−0.926859	−	0.375410i	$-0.877502\pi$
$617$		−	463.256i		−	0.750820i	0.926859	−	0.375410i	$-0.122498\pi$
$618$	419.946	−	242.456i	0.679525	−	0.392324i
$619$	−486.109	−	280.655i	−0.785314	−	0.453401i	0.0529963	−	0.998595i	$-0.483123\pi$
$619$	−486.109	−	280.655i	−0.785314	−	0.453401i	−0.838310	+	0.545193i	$0.816456\pi$
$620$		0			0
$621$	81.7163	−	47.1790i	0.131588	−	0.0759725i
$622$	147.532			0.237190
$623$	60.5464	+	48.3021i	0.0971852	+	0.0775315i
$624$	54.4814			0.0873100
$625$		0			0
$626$	−325.621	−	187.997i	−0.520161	−	0.300315i
$627$	−546.079	−	315.279i	−0.870939	−	0.502837i
$628$	−224.731	−	389.245i	−0.357851	−	0.619816i
$629$			54.8346i			0.0871774i
$630$		0			0
$631$	244.533			0.387533			0.193767	−	0.981048i	$-0.437930\pi$
$631$	244.533			0.387533			0.193767	+	0.981048i	$0.437930\pi$
$632$	221.504	−	127.885i	0.350480	−	0.202350i
$633$	−336.809	+	583.371i	−0.532084	+	0.921597i
$634$	−7.58178	+	13.1320i	−0.0119587	+	0.0207130i
$635$		0			0
$636$		−	197.784i		−	0.310982i
$637$	282.556	−	261.983i	0.443574	−	0.411276i
$638$			37.7360i			0.0591473i
$639$	51.3896	+	89.0094i	0.0804219	+	0.139295i
$640$		0			0
$641$	−325.885	+	564.449i	−0.508400	+	0.880575i	0.491553	+	0.870848i	$0.336430\pi$
$641$	−325.885	+	564.449i	−0.508400	+	0.880575i	−0.999953	+	0.00972698i	$0.996904\pi$
$642$	−181.184	−	313.819i	−0.282217	−	0.488815i
$643$	76.4894			0.118957			0.0594786	−	0.998230i	$-0.481056\pi$
$643$	76.4894			0.118957			0.0594786	+	0.998230i	$0.481056\pi$
$644$	−236.672	+	92.8371i	−0.367503	+	0.144157i
$645$		0			0
$646$	−613.442	−	1062.51i	−0.949601	−	1.64476i
$647$	−81.9453	+	141.933i	−0.126654	+	0.219372i	−0.922378	−	0.386288i	$-0.873757\pi$
$647$	−81.9453	+	141.933i	−0.126654	+	0.219372i	0.795724	+	0.605659i	$0.207091\pi$
$648$	22.0454	+	12.7279i	0.0340207	+	0.0196419i
$649$	−705.797	+	407.492i	−1.08752	+	0.627877i
$650$		0			0
$651$	−49.8895	−	39.8004i	−0.0766352	−	0.0611374i
$652$		−	460.235i		−	0.705882i
$653$	965.499	−	557.431i	1.47856	−	0.853647i	0.478854	−	0.877895i	$-0.341052\pi$
$653$	965.499	−	557.431i	1.47856	−	0.853647i	0.999706	+	0.0242480i	$0.00771913\pi$
$654$	115.234	+	66.5305i	0.176199	+	0.101729i
$655$		0			0
$656$	−76.8703	+	44.3811i	−0.117180	+	0.0676541i
$657$	−58.4744			−0.0890021
$658$	113.254	−	750.467i	0.172119	−	1.14053i
$659$	−1164.66			−1.76732			−0.883660	−	0.468130i	$-0.844928\pi$
$659$	−1164.66			−1.76732			−0.883660	+	0.468130i	$0.844928\pi$
$660$		0			0
$661$	542.087	+	312.974i	0.820101	+	0.473485i	0.850451	−	0.526054i	$-0.176329\pi$
$661$	542.087	+	312.974i	0.820101	+	0.473485i	−0.0303505	+	0.999539i	$0.509662\pi$
$662$	432.238	+	249.553i	0.652928	+	0.376968i
$663$	−188.006	−	325.636i	−0.283568	−	0.491155i
$664$		−	378.453i		−	0.569960i
$665$		0			0
$666$	−8.42709			−0.0126533
$667$	−36.2226	+	20.9131i	−0.0543067	+	0.0313540i
$668$	−277.788	+	481.144i	−0.415851	+	0.720275i
$669$	−218.163	+	377.869i	−0.326103	+	0.564827i
$670$		0			0
$671$		−	783.342i		−	1.16743i
$672$	−53.6147	−	42.7723i	−0.0797838	−	0.0636492i
$673$			38.0207i			0.0564943i	0.999601	+	0.0282471i	$0.00899254\pi$
$673$			38.0207i			0.0564943i	−0.999601	+	0.0282471i	$0.991007\pi$
$674$	156.011	+	270.220i	0.231471	+	0.400920i
$675$		0			0
$676$	−107.162	+	185.610i	−0.158524	+	0.274571i
$677$	390.857	+	676.984i	0.577336	+	0.999976i	0.995783	+	0.0917347i	$0.0292412\pi$
$677$	390.857	+	676.984i	0.577336	+	0.999976i	−0.418447	+	0.908241i	$0.637426\pi$
$678$	−117.057			−0.172651
$679$	184.842	+	471.222i	0.272227	+	0.693994i
$680$		0			0
$681$	231.941	+	401.733i	0.340588	+	0.589916i
$682$	43.1195	−	74.6852i	0.0632251	−	0.109509i
$683$	−116.427	−	67.2190i	−0.170464	−	0.0984172i	0.412341	−	0.911030i	$-0.364711\pi$
$683$	−116.427	−	67.2190i	−0.170464	−	0.0984172i	−0.582804	+	0.812612i	$0.698045\pi$
$684$	163.289	−	94.2751i	0.238727	−	0.137829i
$685$		0			0
$686$	−483.739	+	35.9855i	−0.705158	+	0.0524570i
$687$			598.474i			0.871142i
$688$	−172.640	+	99.6736i	−0.250930	+	0.144874i
$689$	−388.830	−	224.491i	−0.564340	−	0.325822i
$690$		0			0
$691$	−393.253	+	227.045i	−0.569107	+	0.328574i	−0.756792	−	0.653655i	$-0.773235\pi$
$691$	−393.253	+	227.045i	−0.569107	+	0.328574i	0.187686	+	0.982229i	$0.439901\pi$
$692$	−252.131			−0.364351
$693$	88.8392	+	226.480i	0.128195	+	0.326811i
$694$	362.051			0.521687
$695$		0			0
$696$	−9.77211	−	5.64193i	−0.0140404	−	0.00810622i
$697$	530.532	+	306.303i	0.761165	+	0.439459i
$698$	−287.969	−	498.778i	−0.412564	−	0.714581i
$699$		−	498.942i		−	0.713794i
$700$		0			0
$701$	982.015			1.40088			0.700439	−	0.713713i	$-0.252988\pi$
$701$	982.015			1.40088			0.700439	+	0.713713i	$0.252988\pi$
$702$	50.0444	−	28.8931i	0.0712883	−	0.0411583i
$703$	−31.2095	+	54.0565i	−0.0443948	+	0.0768940i
$704$	46.3392	−	80.2618i	0.0658227	−	0.114008i
$705$		0			0
$706$			824.822i			1.16830i
$707$	−52.9102	+	350.603i	−0.0748376	+	0.495903i
$708$		−	243.698i		−	0.344206i
$709$	−166.536	−	288.449i	−0.234889	−	0.406839i	0.724352	−	0.689431i	$-0.242139\pi$
$709$	−166.536	−	288.449i	−0.234889	−	0.406839i	−0.959240	+	0.282591i	$0.908806\pi$
$710$		0			0
$711$	135.643	−	234.940i	0.190777	−	0.330436i
$712$	−15.6479	−	27.1029i	−0.0219773	−	0.0380658i
$713$	95.5866			0.134063
$714$	−70.6351	+	468.055i	−0.0989287	+	0.655539i
$715$		0			0
$716$	−77.1069	−	133.553i	−0.107691	−	0.186527i
$717$	163.514	−	283.215i	0.228053	−	0.395000i
$718$	846.946	+	488.984i	1.17959	+	0.681037i
$719$	−1055.73	+	609.523i	−1.46832	+	0.847737i	−0.999370	−	0.0354852i	$-0.988702\pi$
$719$	−1055.73	+	609.523i	−1.46832	+	0.847737i	−0.468954	+	0.883223i	$0.655369\pi$
$720$		0			0
$721$	−864.200	+	1083.27i	−1.19861	+	1.50245i
$722$		−	886.051i		−	1.22722i
$723$	146.772	−	84.7389i	0.203004	−	0.117205i
$724$	367.215	+	212.012i	0.507203	+	0.292834i
$725$		0			0
$726$	−28.0172	+	16.1758i	−0.0385912	+	0.0222807i
$727$	215.108			0.295885			0.147942	−	0.988996i	$-0.452735\pi$
$727$	215.108			0.295885			0.147942	+	0.988996i	$0.452735\pi$
$728$	−144.941	+	56.8549i	−0.199095	+	0.0780974i
$729$	27.0000			0.0370370
$730$		0			0
$731$	1191.50	+	687.913i	1.62996	+	0.941057i
$732$	202.854	+	117.118i	0.277124	+	0.159997i
$733$	374.728	+	649.047i	0.511225	+	0.885467i	0.999915	+	0.0130099i	$0.00414129\pi$
$733$	374.728	+	649.047i	0.511225	+	0.885467i	−0.488691	+	0.872457i	$0.662525\pi$
$734$			324.883i			0.442620i
$735$		0			0
$736$	102.724			0.139570
$737$	984.859	−	568.609i	1.33631	−	0.771518i
$738$	−47.0732	+	81.5332i	−0.0637849	+	0.110479i
$739$	−467.102	+	809.045i	−0.632073	+	1.09478i	0.355054	+	0.934846i	$0.384462\pi$
$739$	−467.102	+	809.045i	−0.632073	+	1.09478i	−0.987127	+	0.159937i	$0.948871\pi$
$740$		0			0
$741$		−	428.020i		−	0.577625i
$742$	206.401	+	526.182i	0.278168	+	0.709140i
$743$		−	1232.47i		−	1.65878i	−0.558671	−	0.829389i	$-0.688689\pi$
$743$		−	1232.47i		−	1.65878i	0.558671	−	0.829389i	$-0.311311\pi$
$744$	12.8937	+	22.3325i	0.0173302	+	0.0300168i
$745$		0			0
$746$	286.101	−	495.542i	0.383514	−	0.664266i
$747$	−200.705	−	347.632i	−0.268682	−	0.465370i
$748$	−639.634			−0.855125
$749$	809.508	+	645.803i	1.08079	+	0.862220i
$750$		0			0
$751$	−393.353	−	681.307i	−0.523772	−	0.907200i	−0.999617	−	0.0276709i	$-0.991191\pi$
$751$	−393.353	−	681.307i	−0.523772	−	0.907200i	0.475845	−	0.879529i	$-0.342142\pi$
$752$	−153.334	+	265.582i	−0.203902	+	0.353168i
$753$	362.017	+	209.011i	0.480767	+	0.277571i
$754$	−22.1833	+	12.8075i	−0.0294208	+	0.0169861i
$755$		0			0
$756$	−71.9316	−	10.8553i	−0.0951477	−	0.0143589i
$757$			1303.18i			1.72151i	0.509023	+	0.860753i	$0.330007\pi$
$757$			1303.18i			1.72151i	−0.509023	+	0.860753i	$0.669993\pi$
$758$	−325.618	+	187.995i	−0.429575	+	0.248015i
$759$	−315.556	−	182.186i	−0.415752	−	0.240034i
$760$		0			0
$761$	601.784	−	347.440i	0.790780	−	0.456557i	−0.0494571	−	0.998776i	$-0.515749\pi$
$761$	601.784	−	347.440i	0.790780	−	0.456557i	0.840237	+	0.542219i	$0.182416\pi$
$762$	−249.783			−0.327799
$763$	−375.996	−	56.7423i	−0.492786	−	0.0743674i
$764$	−331.392			−0.433759
$765$		0			0
$766$	−375.266	−	216.660i	−0.489904	−	0.282846i
$767$	−479.093	−	276.604i	−0.624632	−	0.360631i
$768$	13.8564	+	24.0000i	0.0180422	+	0.0312500i
$769$			263.988i			0.343287i	0.985159	+	0.171644i	$0.0549077\pi$
$769$			263.988i			0.343287i	−0.985159	+	0.171644i	$0.945092\pi$
$770$		0			0
$771$	−21.7614			−0.0282249
$772$	−182.384	+	105.299i	−0.236249	+	0.136398i
$773$	−78.6802	+	136.278i	−0.101786	+	0.176298i	−0.912420	−	0.409254i	$-0.865789\pi$
$773$	−78.6802	+	136.278i	−0.101786	+	0.176298i	0.810635	+	0.585552i	$0.199122\pi$
$774$	−105.720	+	183.112i	−0.136589	+	0.236579i
$775$		0			0
$776$		−	204.527i		−	0.263566i
$777$	22.4193	−	8.79422i	0.0288537	−	0.0113182i
$778$		−	150.408i		−	0.193326i
$779$	348.669	+	603.913i	0.447586	+	0.775241i
$780$		0			0
$781$	198.446	−	343.718i	0.254092	−	0.440100i
$782$	−354.482	−	613.981i	−0.453302	−	0.785142i
$783$	−11.9683			−0.0152852
$784$	187.271	+	57.8402i	0.238866	+	0.0737758i
$785$		0			0
$786$	91.3635	+	158.246i	0.116239	+	0.201331i
$787$	−491.129	+	850.660i	−0.624052	+	1.08089i	0.364671	+	0.931136i	$0.381181\pi$
$787$	−491.129	+	850.660i	−0.624052	+	1.08089i	−0.988723	+	0.149754i	$0.952152\pi$
$788$	423.894	+	244.736i	0.537937	+	0.310578i
$789$	−318.721	+	184.014i	−0.403956	+	0.233224i
$790$		0			0
$791$	311.417	−	122.157i	0.393700	−	0.154433i
$792$		−	98.3002i		−	0.124116i
$793$	460.492	−	265.865i	0.580695	−	0.335265i
$794$	−266.782	−	154.027i	−0.335998	−	0.193988i
$795$		0			0
$796$	−169.683	+	97.9667i	−0.213170	+	0.123074i
$797$	−946.927			−1.18811			−0.594057	−	0.804423i	$-0.702475\pi$
$797$	−946.927			−1.18811			−0.594057	+	0.804423i	$0.702475\pi$
$798$	−336.030	+	421.211i	−0.421090	+	0.527833i
$799$	2116.52			2.64896
$800$		0			0
$801$	−28.7470	−	16.5971i	−0.0358888	−	0.0207204i
$802$	−75.9114	−	43.8275i	−0.0946526	−	0.0546477i
$803$	112.902	+	195.553i	0.140601	+	0.243527i
$804$			340.052i			0.422951i
$805$		0			0
$806$	58.5388			0.0726287
$807$	501.895	−	289.769i	0.621927	−	0.359070i
$808$	71.6346	−	124.075i	0.0886567	−	0.153558i
$809$	214.568	−	371.642i	0.265226	−	0.459385i	−0.702397	−	0.711786i	$-0.747887\pi$
$809$	214.568	−	371.642i	0.265226	−	0.459385i	0.967623	+	0.252401i	$0.0812201\pi$
$810$		0			0
$811$			948.404i			1.16943i	0.811241	+	0.584713i	$0.198793\pi$
$811$			948.404i			1.16943i	−0.811241	+	0.584713i	$0.801207\pi$
$812$	31.8853	+	4.81187i	0.0392676	+	0.00592595i
$813$			315.840i			0.388487i
$814$	16.2710	+	28.1822i	0.0199890	+	0.0346219i
$815$		0			0
$816$	95.6321	−	165.640i	0.117196	−	0.202990i
$817$	783.062	+	1356.30i	0.958460	+	1.66010i
$818$	614.278			0.750952
$819$	−102.985	+	129.091i	−0.125745	+	0.157621i
$820$		0			0
$821$	201.884	+	349.673i	0.245900	+	0.425911i	0.962384	−	0.271692i	$-0.0875832\pi$
$821$	201.884	+	349.673i	0.245900	+	0.425911i	−0.716484	+	0.697603i	$0.754250\pi$
$822$	302.388	−	523.752i	0.367869	−	0.637168i
$823$	750.003	+	433.014i	0.911303	+	0.526141i	0.880850	−	0.473395i	$-0.156972\pi$
$823$	750.003	+	433.014i	0.911303	+	0.526141i	0.0304530	+	0.999536i	$0.490305\pi$
$824$	484.912	−	279.964i	0.588486	−	0.339762i
$825$		0			0
$826$	254.314	+	648.330i	0.307887	+	0.784903i
$827$		−	363.528i		−	0.439574i	−0.975548	−	0.219787i	$-0.929464\pi$
$827$		−	363.528i		−	0.439574i	0.975548	−	0.219787i	$-0.0705363\pi$
$828$	94.3579	−	54.4776i	0.113959	−	0.0657942i
$829$	−208.617	−	120.445i	−0.251649	−	0.145290i	0.368870	−	0.929481i	$-0.379745\pi$
$829$	−208.617	−	120.445i	−0.251649	−	0.145290i	−0.620519	+	0.784191i	$0.713078\pi$
$830$		0			0
$831$	−250.142	+	144.420i	−0.301013	+	0.173790i
$832$	62.9097			0.0756126
$833$	−300.529	−	1318.92i	−0.360779	−	1.58333i
$834$	381.917			0.457934
$835$		0			0
$836$	−630.557	−	364.052i	−0.754255	−	0.435469i
$837$	23.6872	+	13.6758i	0.0283001	+	0.0163391i
$838$	323.304	+	559.979i	0.385804	+	0.668232i
$839$		−	214.638i		−	0.255826i	−0.991785	−	0.127913i	$-0.959172\pi$
$839$		−	214.638i		−	0.255826i	0.991785	−	0.127913i	$-0.0408278\pi$
$840$		0			0
$841$	−835.695			−0.993692
$842$	−799.941	+	461.846i	−0.950049	+	0.548511i
$843$	33.1762	−	57.4628i	0.0393549	−	0.0681647i
$844$	−388.914	+	673.618i	−0.460798	+	0.798126i
$845$		0			0
$846$			325.271i			0.384481i
$847$	57.6561	−	72.2715i	0.0680710	−	0.0853264i
$848$		−	228.382i		−	0.269318i
$849$	333.849	+	578.244i	0.393226	+	0.681088i
$850$		0			0
$851$	−18.0347	+	31.2369i	−0.0211923	+	0.0367062i
$852$	59.3396	+	102.779i	0.0696474	+	0.120633i
$853$	1388.39			1.62765			0.813825	−	0.581110i	$-0.197382\pi$
$853$	1388.39			1.62765			0.813825	+	0.581110i	$0.197382\pi$
$854$	−661.891	−	99.8873i	−0.775048	−	0.116964i
$855$		0			0
$856$	−209.213	−	362.367i	−0.244407	−	0.423326i
$857$	−548.489	+	950.012i	−0.640011	+	1.10853i	0.345419	+	0.938449i	$0.387737\pi$
$857$	−548.489	+	950.012i	−0.640011	+	1.10853i	−0.985430	+	0.170083i	$0.945596\pi$
$858$	−193.251	−	111.574i	−0.225235	−	0.130039i
$859$	234.305	−	135.276i	0.272764	−	0.157481i	−0.357379	−	0.933959i	$-0.616330\pi$
$859$	234.305	−	135.276i	0.272764	−	0.157481i	0.630143	+	0.776479i	$0.282996\pi$
$860$		0			0
$861$	40.1477	−	266.034i	0.0466291	−	0.308982i
$862$		−	665.042i		−	0.771511i
$863$	−232.280	+	134.107i	−0.269154	+	0.155396i	−0.628503	−	0.777807i	$-0.716332\pi$
$863$	−232.280	+	134.107i	−0.269154	+	0.155396i	0.359349	+	0.933203i	$0.382999\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$		0			0
$866$	−39.2284	+	22.6485i	−0.0452984	+	0.0261530i
$867$	−819.476			−0.945186
$868$	−57.6075	−	45.9576i	−0.0663681	−	0.0529465i
$869$	−1047.60			−1.20552
$870$		0			0
$871$	668.519	+	385.970i	0.767530	+	0.443134i
$872$	133.061	+	76.8228i	0.152593	+	0.0880995i
$873$	−108.467	−	187.870i	−0.124246	−	0.215200i
$874$		−	807.025i		−	0.923370i
$875$		0			0
$876$	−67.5204			−0.0770781
$877$	439.430	−	253.705i	0.501061	−	0.289288i	−0.228091	−	0.973640i	$-0.573248\pi$
$877$	439.430	−	253.705i	0.501061	−	0.289288i	0.729152	+	0.684352i	$0.239915\pi$
$878$	−270.284	+	468.145i	−0.307840	+	0.533195i
$879$	−78.7948	+	136.477i	−0.0896414	+	0.155264i
$880$		0			0
$881$		−	833.545i		−	0.946135i	−0.881026	−	0.473067i	$-0.843147\pi$
$881$		−	833.545i		−	0.946135i	0.881026	−	0.473067i	$-0.156853\pi$
$882$	202.694	−	46.1859i	0.229812	−	0.0523650i
$883$			1350.99i			1.53000i	0.644028	+	0.765002i	$0.277262\pi$
$883$			1350.99i			1.53000i	−0.644028	+	0.765002i	$0.722738\pi$
$884$	−217.090	−	376.012i	−0.245577	−	0.425353i
$885$		0			0
$886$	−87.4985	+	151.552i	−0.0987568	+	0.171052i
$887$	187.065	+	324.005i	0.210896	+	0.365282i	0.951995	−	0.306113i	$-0.0990286\pi$
$887$	187.065	+	324.005i	0.210896	+	0.365282i	−0.741099	+	0.671395i	$0.765695\pi$
$888$	−9.73077			−0.0109581
$889$	664.518	−	260.664i	0.747489	−	0.293211i
$890$		0			0
$891$	−52.1316	−	90.2945i	−0.0585091	−	0.101341i
$892$	−251.913	+	436.326i	−0.282413	+	0.489154i
$893$	2086.48	+	1204.63i	2.33649	+	1.34897i
$894$	345.967	−	199.744i	0.386988	−	0.223427i
$895$		0			0
$896$	−61.9089	−	49.3891i	−0.0690948	−	0.0551218i
$897$		−	247.335i		−	0.275735i
$898$	326.989	−	188.787i	0.364130	−	0.210230i
$899$	−10.4999	−	6.06210i	−0.0116795	−	0.00674316i
$900$		0			0
$901$	−1365.04	+	788.105i	−1.51503	+	0.874701i
$902$	363.556			0.403055
$903$	90.1660	−	597.474i	0.0998516	−	0.661655i
$904$	−135.166			−0.149520
$905$		0			0
$906$	−159.162	−	91.8925i	−0.175676	−	0.101427i
$907$	309.618	+	178.758i	0.341365	+	0.197087i	0.660875	−	0.750496i	$-0.270185\pi$
$907$	309.618	+	178.758i	0.341365	+	0.197087i	−0.319510	+	0.947583i	$0.603518\pi$
$908$	267.822	+	463.881i	0.294958	+	0.510882i
$909$		−	151.960i		−	0.167173i
$910$		0			0
$911$	−1503.55			−1.65044			−0.825219	−	0.564813i	$-0.808948\pi$
$911$	−1503.55			−1.65044			−0.825219	+	0.564813i	$0.808948\pi$
$912$	188.550	−	108.859i	0.206744	−	0.119363i
$913$	−775.043	+	1342.41i	−0.848897	+	1.47033i
$914$	−317.731	+	550.327i	−0.347627	+	0.602108i
$915$		0			0
$916$			691.059i			0.754431i
$917$	−408.202	−	325.652i	−0.445149	−	0.355127i
$918$		−	202.866i		−	0.220987i
$919$	−312.499	−	541.265i	−0.340043	−	0.588971i	0.644398	−	0.764691i	$-0.277108\pi$
$919$	−312.499	−	541.265i	−0.340043	−	0.588971i	−0.984440	+	0.175719i	$0.943775\pi$
$920$		0			0
$921$	−440.007	+	762.115i	−0.477750	+	0.827487i
$922$	74.6199	+	129.245i	0.0809327	+	0.140179i
$923$	269.409			0.291884
$924$	102.583	+	261.516i	0.111020	+	0.283026i
$925$		0			0
$926$	−416.171	−	720.829i	−0.449429	−	0.778433i
$927$	296.947	−	514.327i	0.320331	−	0.554830i
$928$	−11.2839	−	6.51474i	−0.0121593	−	0.00702019i
$929$	942.883	−	544.374i	1.01494	−	0.585978i	0.102309	−	0.994753i	$-0.467377\pi$
$929$	942.883	−	544.374i	1.01494	−	0.585978i	0.912636	+	0.408774i	$0.134044\pi$
$930$		0			0
$931$	454.408	−	1471.25i	0.488086	−	1.58029i
$932$		−	576.129i		−	0.618164i
$933$	156.482	−	90.3447i	0.167719	−	0.0968325i
$934$	447.837	+	258.559i	0.479483	+	0.276829i
$935$		0			0
$936$	57.7863	−	33.3629i	0.0617375	−	0.0356441i
$937$	252.836			0.269835			0.134918	−	0.990857i	$-0.456923\pi$
$937$	252.836			0.269835			0.134918	+	0.990857i	$0.456923\pi$
$938$	−354.867	−	904.670i	−0.378323	−	0.964467i
$939$	−460.498			−0.490413
$940$		0			0
$941$	−332.262	−	191.832i	−0.353095	−	0.203859i	0.312953	−	0.949769i	$-0.398682\pi$
$941$	−332.262	−	191.832i	−0.353095	−	0.203859i	−0.666048	+	0.745909i	$0.732015\pi$
$942$	−476.726	−	275.238i	−0.506078	−	0.292184i
$943$	201.481	+	348.975i	0.213660	+	0.370069i
$944$		−	281.398i		−	0.298091i
$945$		0			0
$946$	816.495			0.863103
$947$	−244.032	+	140.892i	−0.257690	+	0.148777i	−0.623280	−	0.781999i	$-0.714200\pi$
$947$	−244.032	+	140.892i	−0.257690	+	0.148777i	0.365591	+	0.930776i	$0.380867\pi$
$948$	156.627	−	271.285i	0.165218	−	0.286166i
$949$	−76.6377	+	132.740i	−0.0807562	+	0.139874i
$950$		0			0
$951$			18.5715i			0.0195284i
$952$	−81.5624	+	540.463i	−0.0856748	+	0.567713i
$953$			332.322i			0.348711i	0.984683	+	0.174356i	$0.0557842\pi$
$953$			332.322i			0.348711i	−0.984683	+	0.174356i	$0.944216\pi$
$954$	−121.118	−	209.782i	−0.126958	−	0.219897i
$955$		0			0
$956$	188.810	−	327.028i	0.197500	−	0.342080i
$957$	23.1085	+	40.0250i	0.0241468	+	0.0418234i
$958$	688.971			0.719177
$959$	−257.900	+	1708.94i	−0.268926	+	1.78200i
$960$		0			0
$961$	−466.646	−	808.255i	−0.485584	−	0.841056i
$962$	−11.0447	+	19.1300i	−0.0114810	+	0.0198857i
$963$	−384.348	−	221.904i	−0.399116	−	0.230430i
$964$	169.478	−	97.8480i	0.175807	−	0.101502i
$965$		0			0
$966$	−194.177	+	243.400i	−0.201012	+	0.251967i
$967$			1155.53i			1.19496i	0.801882	+	0.597482i	$0.203832\pi$
$967$			1155.53i			1.19496i	−0.801882	+	0.597482i	$0.796168\pi$
$968$	−32.3515	+	18.6782i	−0.0334210	+	0.0192956i
$969$	−1301.31	−	751.310i	−1.34294	−	0.775346i
$970$		0			0
$971$	−1307.94	+	755.140i	−1.34700	+	0.777693i	−0.987824	−	0.155576i	$-0.950277\pi$
$971$	−1307.94	+	755.140i	−1.34700	+	0.777693i	−0.359179	+	0.933269i	$0.616943\pi$
$972$	31.1769			0.0320750
$973$	−1016.04	+	398.555i	−1.04424	+	0.409614i
$974$	276.866			0.284257
$975$		0			0
$976$	234.236	+	135.236i	0.239996	+	0.138562i
$977$	−694.220	−	400.808i	−0.710563	−	0.410244i	0.100706	−	0.994916i	$-0.467890\pi$
$977$	−694.220	−	400.808i	−0.710563	−	0.410244i	−0.811269	+	0.584672i	$0.801223\pi$
$978$	−281.835	−	488.153i	−0.288175	−	0.499134i
$979$			128.182i			0.130932i
$980$		0			0
$981$	162.966			0.166122
$982$	−427.707	+	246.937i	−0.435547	+	0.251463i
$983$	−547.395	+	948.116i	−0.556862	+	0.964513i	0.440894	+	0.897559i	$0.354661\pi$
$983$	−547.395	+	948.116i	−0.556862	+	0.964513i	−0.997756	+	0.0669540i	$0.978672\pi$
$984$	−54.3555	+	94.1465i	−0.0552393	+	0.0956773i
$985$		0			0
$986$			89.9249i			0.0912018i
$987$	−339.441	−	865.344i	−0.343912	−	0.876742i
$988$		−	494.235i		−	0.500238i
$989$	452.498	+	783.750i	0.457531	+	0.792467i
$990$		0			0
$991$	−21.9962	+	38.0986i	−0.0221960	+	0.0384446i	−0.876910	−	0.480655i	$-0.840399\pi$
$991$	−21.9962	+	38.0986i	−0.0221960	+	0.0384446i	0.854714	+	0.519099i	$0.173732\pi$
$992$	14.8883	+	25.7873i	0.0150084	+	0.0259953i
$993$	611.277			0.615586
$994$	−265.123	−	211.507i	−0.266723	−	0.212784i
$995$		0			0
$996$	−231.754	−	401.410i	−0.232685	−	0.403022i
$997$	−6.12803	+	10.6141i	−0.00614647	+	0.0106460i	−0.869082	−	0.494668i	$-0.835290\pi$
$997$	−6.12803	+	10.6141i	−0.00614647	+	0.0106460i	0.862936	+	0.505314i	$0.168623\pi$
$998$	−410.827	−	237.191i	−0.411650	−	0.237666i
$999$	−8.93828	+	5.16052i	−0.00894723	+	0.00516569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.q.c.199.7		16
5.2	odd	4		1050.3.p.b.451.3		8
5.3	odd	4		210.3.o.a.31.2	✓	8
5.4	even	2	inner	1050.3.q.c.199.2		16
7.5	odd	6	inner	1050.3.q.c.649.2		16
15.8	even	4		630.3.v.b.451.3		8
35.3	even	12		1470.3.f.a.391.7		8
35.12	even	12		1050.3.p.b.901.3		8
35.18	odd	12		1470.3.f.a.391.6		8
35.19	odd	6	inner	1050.3.q.c.649.7		16
35.33	even	12		210.3.o.a.61.2	yes	8
105.68	odd	12		630.3.v.b.271.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.a.31.2	✓	8	5.3	odd	4
210.3.o.a.61.2	yes	8	35.33	even	12
630.3.v.b.271.3		8	105.68	odd	12
630.3.v.b.451.3		8	15.8	even	4
1050.3.p.b.451.3		8	5.2	odd	4
1050.3.p.b.901.3		8	35.12	even	12
1050.3.q.c.199.2		16	5.4	even	2	inner
1050.3.q.c.199.7		16	1.1	even	1	trivial
1050.3.q.c.649.2		16	7.5	odd	6	inner
1050.3.q.c.649.7		16	35.19	odd	6	inner
1470.3.f.a.391.6		8	35.18	odd	12
1470.3.f.a.391.7		8	35.3	even	12

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(2.55620 + 6.51658i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(2.55620 + 6.51658i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-5.79240 + 10.0327i) q^{11} +(-1.73205 - 3.00000i) q^{12} -7.86371 q^{13} +(7.73861 + 6.17364i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-13.8033 + 23.9080i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(-27.2149 + 15.7125i) q^{19} +(11.9886 + 1.80922i) q^{21} +16.3834i q^{22} +(-15.7263 + 9.07959i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-9.63104 + 5.56049i) q^{26} -5.19615 q^{27} +(13.8433 + 2.08911i) q^{28} +2.30331 q^{29} +(-4.55860 - 2.63191i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(10.0327 + 17.3772i) q^{33} +39.0416i q^{34} -6.00000 q^{36} +(1.72017 - 0.993142i) q^{37} +(-22.2208 + 38.4876i) q^{38} +(-6.81018 + 11.7956i) q^{39} -22.1905i q^{41} +(15.9623 - 6.26139i) q^{42} -49.8368i q^{43} +(11.5848 + 20.0655i) q^{44} +(-12.8405 + 22.2404i) q^{46} +(-38.3335 - 66.3956i) q^{47} -6.92820 q^{48} +(-35.9317 + 33.3154i) q^{49} +(23.9080 + 41.4099i) q^{51} +(-7.86371 + 13.6204i) q^{52} +(49.4461 + 28.5477i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(18.4317 - 7.23003i) q^{56} +54.4297i q^{57} +(2.82097 - 1.62869i) q^{58} +(60.9245 + 35.1748i) q^{59} +(-58.5590 + 33.8091i) q^{61} -7.44416 q^{62} +(13.0963 - 16.4161i) q^{63} -8.00000 q^{64} +(24.5751 + 14.1884i) q^{66} +(-85.0131 - 49.0823i) q^{67} +(27.6066 + 47.8160i) q^{68} +31.4526i q^{69} -34.2597 q^{71} +(-7.34847 + 4.24264i) q^{72} +(9.74573 - 16.8801i) q^{73} +(1.40452 - 2.43269i) q^{74} +62.8501i q^{76} +(-80.1856 - 12.1010i) q^{77} +19.2621i q^{78} +(45.2142 + 78.3134i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-15.6911 - 27.1777i) q^{82} +133.803 q^{83} +(15.1223 - 18.9557i) q^{84} +(-35.2400 - 61.0374i) q^{86} +(1.99472 - 3.45496i) q^{87} +(28.3768 + 16.3834i) q^{88} +(9.58232 - 5.53235i) q^{89} +(-20.1012 - 51.2445i) q^{91} +36.3184i q^{92} +(-7.89573 + 4.55860i) q^{93} +(-93.8975 - 54.2118i) q^{94} +(-8.48528 + 4.89898i) q^{96} +72.3112 q^{97} +(-20.4496 + 66.2104i) q^{98} +34.7544 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 16 * q + 16 * q^4 - 24 * q^9	\( 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 80 q^{14} - 32 q^{16} - 216 q^{19} - 192 q^{26} - 144 q^{29} - 264 q^{31} - 96 q^{36} - 48 q^{39} + 16 q^{44} + 16 q^{46} - 312 q^{49} + 168 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 128 q^{64} - 144 q^{66} + 16 q^{71} + 32 q^{74} - 24 q^{79} - 72 q^{81} - 80 q^{86} - 984 q^{89} - 616 q^{91} - 960 q^{94} + 48 q^{99}+O(q^{100}) \) 16 * q + 16 * q^4 - 24 * q^9 - 8 * q^11 + 80 * q^14 - 32 * q^16 - 216 * q^19 - 192 * q^26 - 144 * q^29 - 264 * q^31 - 96 * q^36 - 48 * q^39 + 16 * q^44 + 16 * q^46 - 312 * q^49 + 168 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 128 * q^64 - 144 * q^66 + 16 * q^71 + 32 * q^74 - 24 * q^79 - 72 * q^81 - 80 * q^86 - 984 * q^89 - 616 * q^91 - 960 * q^94 + 48 * q^99

Introduction

L-functions

Modular forms

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