LMFDB - Embedded newform 400.3.i.b.357.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,3,Mod(93,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("400.93");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.i (of order $4$, degree $2$, 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:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			357.22
Character	$\chi$	$=$	400.357
Dual form			400.3.i.b.93.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99771 - 0.0957584i) q^{2} -4.94472i q^{3} +(3.98166 - 0.382594i) q^{4} +(-0.473499 - 9.87810i) q^{6} +(-3.22480 + 3.22480i) q^{7} +(7.91755 - 1.14559i) q^{8} -15.4503 q^{9} +O(q^{10})$	\(q+(1.99771 - 0.0957584i) q^{2} -4.94472i q^{3} +(3.98166 - 0.382594i) q^{4} +(-0.473499 - 9.87810i) q^{6} +(-3.22480 + 3.22480i) q^{7} +(7.91755 - 1.14559i) q^{8} -15.4503 q^{9} +(-7.67097 - 7.67097i) q^{11} +(-1.89182 - 19.6882i) q^{12} -22.2152i q^{13} +(-6.13341 + 6.75101i) q^{14} +(15.7072 - 3.04672i) q^{16} +(3.76038 + 3.76038i) q^{17} +(-30.8651 + 1.47949i) q^{18} +(-0.809445 - 0.809445i) q^{19} +(15.9458 + 15.9458i) q^{21} +(-16.0589 - 14.5898i) q^{22} +(-12.2839 - 12.2839i) q^{23} +(-5.66462 - 39.1501i) q^{24} +(-2.12729 - 44.3794i) q^{26} +31.8948i q^{27} +(-11.6063 + 14.0739i) q^{28} +(27.1574 + 27.1574i) q^{29} +25.5557 q^{31} +(31.0867 - 7.59056i) q^{32} +(-37.9308 + 37.9308i) q^{33} +(7.87223 + 7.15205i) q^{34} +(-61.5178 + 5.91119i) q^{36} -8.62466i q^{37} +(-1.69454 - 1.53952i) q^{38} -109.848 q^{39} +73.4504i q^{41} +(33.3819 + 30.3280i) q^{42} +17.5521 q^{43} +(-33.4781 - 27.6083i) q^{44} +(-25.7160 - 23.3634i) q^{46} +(-17.4590 - 17.4590i) q^{47} +(-15.0652 - 77.6680i) q^{48} +28.2013i q^{49} +(18.5940 - 18.5940i) q^{51} +(-8.49939 - 88.4532i) q^{52} +29.3309 q^{53} +(3.05420 + 63.7165i) q^{54} +(-21.8382 + 29.2268i) q^{56} +(-4.00248 + 4.00248i) q^{57} +(56.8532 + 51.6520i) q^{58} +(72.6508 - 72.6508i) q^{59} +(19.7110 - 19.7110i) q^{61} +(51.0529 - 2.44718i) q^{62} +(49.8241 - 49.8241i) q^{63} +(61.3753 - 18.1405i) q^{64} +(-72.1424 + 79.4068i) q^{66} -14.0319 q^{67} +(16.4113 + 13.5339i) q^{68} +(-60.7406 + 60.7406i) q^{69} -91.3292i q^{71} +(-122.328 + 17.6997i) q^{72} +(42.7665 + 42.7665i) q^{73} +(-0.825884 - 17.2295i) q^{74} +(-3.53262 - 2.91325i) q^{76} +49.4747 q^{77} +(-219.444 + 10.5188i) q^{78} +46.7110i q^{79} +18.6585 q^{81} +(7.03350 + 146.732i) q^{82} +82.9430i q^{83} +(69.5913 + 57.3898i) q^{84} +(35.0639 - 1.68076i) q^{86} +(134.286 - 134.286i) q^{87} +(-69.5231 - 51.9475i) q^{88} +131.145 q^{89} +(71.6395 + 71.6395i) q^{91} +(-53.6102 - 44.2106i) q^{92} -126.366i q^{93} +(-36.5499 - 33.2062i) q^{94} +(-37.5332 - 153.715i) q^{96} +(30.5363 + 30.5363i) q^{97} +(2.70051 + 56.3379i) q^{98} +(118.519 + 118.519i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} + 4 q^{4} - 4 q^{6} + 8 q^{8} - 108 q^{9}+O(q^{10}) $ 44 * q + 2 * q^2 + 4 * q^4 - 4 * q^6 + 8 * q^8 - 108 * q^9	$ 44 q + 2 q^{2} + 4 q^{4} - 4 q^{6} + 8 q^{8} - 108 q^{9} - 4 q^{11} + 8 q^{12} + 24 q^{16} + 4 q^{17} - 22 q^{18} + 32 q^{19} - 4 q^{21} - 92 q^{22} + 36 q^{24} - 52 q^{26} - 36 q^{28} - 8 q^{31} + 132 q^{32} + 4 q^{33} - 88 q^{34} - 116 q^{36} + 216 q^{38} + 72 q^{39} - 16 q^{42} - 124 q^{43} - 168 q^{44} + 108 q^{46} + 4 q^{47} - 340 q^{48} - 100 q^{51} - 48 q^{52} + 4 q^{53} + 228 q^{54} - 172 q^{56} - 36 q^{57} - 16 q^{58} + 64 q^{59} - 36 q^{61} + 356 q^{62} + 200 q^{63} - 176 q^{64} + 276 q^{66} + 292 q^{67} + 72 q^{68} - 60 q^{69} - 448 q^{72} - 48 q^{73} + 284 q^{74} + 252 q^{76} - 192 q^{77} - 620 q^{78} + 100 q^{81} + 240 q^{82} + 288 q^{84} + 20 q^{86} - 36 q^{87} + 624 q^{88} + 188 q^{91} + 412 q^{92} - 340 q^{94} - 24 q^{96} + 4 q^{97} + 78 q^{98} - 92 q^{99}+O(q^{100}) $ 44 * q + 2 * q^2 + 4 * q^4 - 4 * q^6 + 8 * q^8 - 108 * q^9 - 4 * q^11 + 8 * q^12 + 24 * q^16 + 4 * q^17 - 22 * q^18 + 32 * q^19 - 4 * q^21 - 92 * q^22 + 36 * q^24 - 52 * q^26 - 36 * q^28 - 8 * q^31 + 132 * q^32 + 4 * q^33 - 88 * q^34 - 116 * q^36 + 216 * q^38 + 72 * q^39 - 16 * q^42 - 124 * q^43 - 168 * q^44 + 108 * q^46 + 4 * q^47 - 340 * q^48 - 100 * q^51 - 48 * q^52 + 4 * q^53 + 228 * q^54 - 172 * q^56 - 36 * q^57 - 16 * q^58 + 64 * q^59 - 36 * q^61 + 356 * q^62 + 200 * q^63 - 176 * q^64 + 276 * q^66 + 292 * q^67 + 72 * q^68 - 60 * q^69 - 448 * q^72 - 48 * q^73 + 284 * q^74 + 252 * q^76 - 192 * q^77 - 620 * q^78 + 100 * q^81 + 240 * q^82 + 288 * q^84 + 20 * q^86 - 36 * q^87 + 624 * q^88 + 188 * q^91 + 412 * q^92 - 340 * q^94 - 24 * q^96 + 4 * q^97 + 78 * q^98 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	1.99771	−	0.0957584i	0.998853	−	0.0478792i
$2$	1.99771	−	0.0957584i	0.998853	−	0.0478792i
$3$		−	4.94472i		−	1.64824i	−0.566415	−	0.824120i	$-0.691670\pi$
$3$		−	4.94472i		−	1.64824i	0.566415	−	0.824120i	$-0.308330\pi$
$4$	3.98166	−	0.382594i	0.995415	−	0.0956486i
$5$		0			0
$5$		0			0
$6$	−0.473499	−	9.87810i	−0.0789165	−	1.64635i
$7$	−3.22480	+	3.22480i	−0.460686	+	0.460686i	−0.898880	−	0.438194i	$-0.855618\pi$
$7$	−3.22480	+	3.22480i	−0.460686	+	0.460686i	0.438194	+	0.898880i	$0.355618\pi$
$8$	7.91755	−	1.14559i	0.989694	−	0.143199i
$9$	−15.4503			−1.71670
$10$		0			0
$11$	−7.67097	−	7.67097i	−0.697361	−	0.697361i	0.266480	−	0.963841i	$-0.414139\pi$
$11$	−7.67097	−	7.67097i	−0.697361	−	0.697361i	−0.963841	+	0.266480i	$0.914139\pi$
$12$	−1.89182	−	19.6882i	−0.157652	−	1.64068i
$13$		−	22.2152i		−	1.70886i	−0.519568	−	0.854429i	$-0.673907\pi$
$13$		−	22.2152i		−	1.70886i	0.519568	−	0.854429i	$-0.326093\pi$
$14$	−6.13341	+	6.75101i	−0.438101	+	0.482215i
$15$		0			0
$16$	15.7072	−	3.04672i	0.981703	−	0.190420i
$17$	3.76038	+	3.76038i	0.221199	+	0.221199i	0.809003	−	0.587804i	$-0.200007\pi$
$17$	3.76038	+	3.76038i	0.221199	+	0.221199i	−0.587804	+	0.809003i	$0.700007\pi$
$18$	−30.8651	+	1.47949i	−1.71473	+	0.0821941i
$19$	−0.809445	−	0.809445i	−0.0426024	−	0.0426024i	0.685485	−	0.728087i	$-0.259590\pi$
$19$	−0.809445	−	0.809445i	−0.0426024	−	0.0426024i	−0.728087	+	0.685485i	$0.759590\pi$
$20$		0			0
$21$	15.9458	+	15.9458i	0.759322	+	0.759322i
$22$	−16.0589	−	14.5898i	−0.729950	−	0.663172i
$23$	−12.2839	−	12.2839i	−0.534083	−	0.534083i	0.387701	−	0.921785i	$-0.373269\pi$
$23$	−12.2839	−	12.2839i	−0.534083	−	0.534083i	−0.921785	+	0.387701i	$0.873269\pi$
$24$	−5.66462	−	39.1501i	−0.236026	−	1.63125i
$25$		0			0
$26$	−2.12729	−	44.3794i	−0.0818188	−	1.70690i
$27$			31.8948i			1.18129i
$28$	−11.6063	+	14.0739i	−0.414510	+	0.502638i
$29$	27.1574	+	27.1574i	0.936464	+	0.936464i	0.998099	−	0.0616350i	$-0.0196315\pi$
$29$	27.1574	+	27.1574i	0.936464	+	0.936464i	−0.0616350	+	0.998099i	$0.519631\pi$
$30$		0			0
$31$	25.5557			0.824379			0.412189	−	0.911098i	$-0.364764\pi$
$31$	25.5557			0.824379			0.412189	+	0.911098i	$0.364764\pi$
$32$	31.0867	−	7.59056i	0.971460	−	0.237205i
$33$	−37.9308	+	37.9308i	−1.14942	+	1.14942i
$34$	7.87223	+	7.15205i	0.231536	+	0.210354i
$35$		0			0
$36$	−61.5178	+	5.91119i	−1.70883	+	0.164200i
$37$		−	8.62466i		−	0.233099i	−0.993185	−	0.116550i	$-0.962817\pi$
$37$		−	8.62466i		−	0.233099i	0.993185	−	0.116550i	$-0.0371834\pi$
$38$	−1.69454	−	1.53952i	−0.0445933	−	0.0405137i
$39$	−109.848			−2.81661
$40$		0			0
$41$			73.4504i			1.79147i	0.444585	+	0.895737i	$0.353351\pi$
$41$			73.4504i			1.79147i	−0.444585	+	0.895737i	$0.646649\pi$
$42$	33.3819	+	30.3280i	0.794807	+	0.722095i
$43$	17.5521			0.408188			0.204094	−	0.978951i	$-0.434575\pi$
$43$	17.5521			0.408188			0.204094	+	0.978951i	$0.434575\pi$
$44$	−33.4781	−	27.6083i	−0.760865	−	0.627462i
$45$		0			0
$46$	−25.7160	−	23.3634i	−0.559042	−	0.507899i
$47$	−17.4590	−	17.4590i	−0.371469	−	0.371469i	0.496543	−	0.868012i	$-0.334602\pi$
$47$	−17.4590	−	17.4590i	−0.371469	−	0.371469i	−0.868012	+	0.496543i	$0.834602\pi$
$48$	−15.0652	−	77.6680i	−0.313858	−	1.61808i
$49$			28.2013i			0.575536i
$50$		0			0
$51$	18.5940	−	18.5940i	0.364589	−	0.364589i
$52$	−8.49939	−	88.4532i	−0.163450	−	1.70102i
$53$	29.3309			0.553413			0.276707	−	0.960954i	$-0.410757\pi$
$53$	29.3309			0.553413			0.276707	+	0.960954i	$0.410757\pi$
$54$	3.05420	+	63.7165i	0.0565592	+	1.17993i
$55$		0			0
$56$	−21.8382	+	29.2268i	−0.389969	+	0.521908i
$57$	−4.00248	+	4.00248i	−0.0702190	+	0.0702190i
$58$	56.8532	+	51.6520i	0.980227	+	0.890553i
$59$	72.6508	−	72.6508i	1.23137	−	1.23137i	0.267931	−	0.963438i	$-0.413660\pi$
$59$	72.6508	−	72.6508i	1.23137	−	1.23137i	0.963438	−	0.267931i	$-0.0863398\pi$
$60$		0			0
$61$	19.7110	−	19.7110i	0.323132	−	0.323132i	−0.526835	−	0.849967i	$-0.676622\pi$
$61$	19.7110	−	19.7110i	0.323132	−	0.323132i	0.849967	+	0.526835i	$0.176622\pi$
$62$	51.0529	−	2.44718i	0.823433	−	0.0394706i
$63$	49.8241	−	49.8241i	0.790859	−	0.790859i
$64$	61.3753	−	18.1405i	0.958988	−	0.283446i
$65$		0			0
$66$	−72.1424	+	79.4068i	−1.09307	+	1.20313i
$67$	−14.0319			−0.209431			−0.104716	−	0.994502i	$-0.533393\pi$
$67$	−14.0319			−0.209431			−0.104716	+	0.994502i	$0.533393\pi$
$68$	16.4113	+	13.5339i	0.241342	+	0.199027i
$69$	−60.7406	+	60.7406i	−0.880298	+	0.880298i
$70$		0			0
$71$		−	91.3292i		−	1.28633i	−0.765729	−	0.643163i	$-0.777622\pi$
$71$		−	91.3292i		−	1.28633i	0.765729	−	0.643163i	$-0.222378\pi$
$72$	−122.328	+	17.6997i	−1.69900	+	0.245829i
$73$	42.7665	+	42.7665i	0.585843	+	0.585843i	0.936503	−	0.350660i	$-0.114043\pi$
$73$	42.7665	+	42.7665i	0.585843	+	0.585843i	−0.350660	+	0.936503i	$0.614043\pi$
$74$	−0.825884	−	17.2295i	−0.0111606	−	0.232832i
$75$		0			0
$76$	−3.53262	−	2.91325i	−0.0464819	−	0.0383322i
$77$	49.4747			0.642529
$78$	−219.444	+	10.5188i	−2.81338	+	0.134857i
$79$			46.7110i			0.591278i	0.955300	+	0.295639i	$0.0955326\pi$
$79$			46.7110i			0.591278i	−0.955300	+	0.295639i	$0.904467\pi$
$80$		0			0
$81$	18.6585			0.230352
$82$	7.03350	+	146.732i	0.0857744	+	1.78942i
$83$			82.9430i			0.999313i	0.866224	+	0.499656i	$0.166540\pi$
$83$			82.9430i			0.999313i	−0.866224	+	0.499656i	$0.833460\pi$
$84$	69.5913	+	57.3898i	0.828468	+	0.683212i
$85$		0			0
$86$	35.0639	−	1.68076i	0.407720	−	0.0195437i
$87$	134.286	−	134.286i	1.54352	−	1.54352i
$88$	−69.5231	−	51.9475i	−0.790035	−	0.590313i
$89$	131.145			1.47354			0.736768	−	0.676146i	$-0.236351\pi$
$89$	131.145			1.47354			0.736768	+	0.676146i	$0.236351\pi$
$90$		0			0
$91$	71.6395	+	71.6395i	0.787247	+	0.787247i
$92$	−53.6102	−	44.2106i	−0.582719	−	0.480550i
$93$		−	126.366i		−	1.35877i
$94$	−36.5499	−	33.2062i	−0.388828	−	0.353257i
$95$		0			0
$96$	−37.5332	−	153.715i	−0.390971	−	1.60120i
$97$	30.5363	+	30.5363i	0.314807	+	0.314807i	0.846769	−	0.531962i	$-0.178545\pi$
$97$	30.5363	+	30.5363i	0.314807	+	0.314807i	−0.531962	+	0.846769i	$0.678545\pi$
$98$	2.70051	+	56.3379i	0.0275562	+	0.574876i
$99$	118.519	+	118.519i	1.19716	+	1.19716i
$100$		0			0
$101$	22.0905	+	22.0905i	0.218718	+	0.218718i	0.807958	−	0.589240i	$-0.200573\pi$
$101$	22.0905	+	22.0905i	0.218718	+	0.218718i	−0.589240	+	0.807958i	$0.700573\pi$
$102$	35.3649	−	38.9260i	0.346715	−	0.381627i
$103$	−5.06551	−	5.06551i	−0.0491797	−	0.0491797i	0.682089	−	0.731269i	$-0.261072\pi$
$103$	−5.06551	−	5.06551i	−0.0491797	−	0.0491797i	−0.731269	+	0.682089i	$0.761072\pi$
$104$	−25.4494	−	175.890i	−0.244706	−	1.69125i
$105$		0			0
$106$	58.5945	−	2.80868i	0.552779	−	0.0264970i
$107$		−	54.6933i		−	0.511153i	−0.966789	−	0.255576i	$-0.917735\pi$
$107$		−	54.6933i		−	0.511153i	0.966789	−	0.255576i	$-0.0822652\pi$
$108$	12.2028	+	126.994i	0.112989	+	1.17587i
$109$	−81.8934	−	81.8934i	−0.751316	−	0.751316i	0.223409	−	0.974725i	$-0.428281\pi$
$109$	−81.8934	−	81.8934i	−0.751316	−	0.751316i	−0.974725	+	0.223409i	$0.928281\pi$
$110$		0			0
$111$	−42.6466			−0.384203
$112$	−40.8277	+	60.4778i	−0.364533	+	0.539981i
$113$	19.1764	−	19.1764i	0.169703	−	0.169703i	−0.617146	−	0.786849i	$-0.711711\pi$
$113$	19.1764	−	19.1764i	0.169703	−	0.169703i	0.786849	+	0.617146i	$0.211711\pi$
$114$	−7.61251	+	8.37905i	−0.0667764	+	0.0735005i
$115$		0			0
$116$	118.522	+	97.7415i	1.02174	+	0.842599i
$117$			343.230i			2.93359i
$118$	138.178	−	152.092i	1.17100	−	1.28891i
$119$	−24.2530			−0.203807
$120$		0			0
$121$		−	3.31247i		−	0.0273758i
$122$	37.4894	−	41.2644i	0.307290	−	0.338233i
$123$	363.192			2.95278
$124$	101.754	−	9.77749i	0.820599	−	0.0788507i
$125$		0			0
$126$	94.7628	−	104.305i	0.752086	−	0.827817i
$127$	−100.021	−	100.021i	−0.787565	−	0.787565i	0.193529	−	0.981094i	$-0.438007\pi$
$127$	−100.021	−	100.021i	−0.787565	−	0.787565i	−0.981094	+	0.193529i	$0.938007\pi$
$128$	120.873	−	42.1166i	0.944317	−	0.329036i
$129$		−	86.7901i		−	0.672792i
$130$		0			0
$131$	−48.8021	+	48.8021i	−0.372535	+	0.372535i	−0.868400	−	0.495865i	$-0.834851\pi$
$131$	−48.8021	+	48.8021i	−0.372535	+	0.372535i	0.495865	+	0.868400i	$0.334851\pi$
$132$	−136.515	+	165.540i	−1.03421	+	1.25409i
$133$	5.22060			0.0392526
$134$	−28.0316	+	1.34367i	−0.209191	+	0.0100274i
$135$		0			0
$136$	34.0809	+	25.4652i	0.250595	+	0.187244i
$137$	−116.195	+	116.195i	−0.848135	+	0.848135i	−0.989900	−	0.141765i	$-0.954722\pi$
$137$	−116.195	+	116.195i	−0.848135	+	0.848135i	0.141765	+	0.989900i	$0.454722\pi$
$138$	−115.525	+	127.158i	−0.837141	+	0.921437i
$139$	−25.5977	+	25.5977i	−0.184156	+	0.184156i	−0.793164	−	0.609008i	$-0.791568\pi$
$139$	−25.5977	+	25.5977i	−0.184156	+	0.184156i	0.609008	+	0.793164i	$0.291568\pi$
$140$		0			0
$141$	−86.3301	+	86.3301i	−0.612270	+	0.612270i
$142$	−8.74554	−	182.449i	−0.0615883	−	1.28485i
$143$	−170.412	+	170.412i	−1.19169	+	1.19169i
$144$	−242.681	+	47.0727i	−1.68529	+	0.326894i
$145$		0			0
$146$	89.5303	+	81.3397i	0.613221	+	0.557122i
$147$	139.448			0.948623
$148$	−3.29975	−	34.3405i	−0.0222956	−	0.232030i
$149$	−11.6294	+	11.6294i	−0.0780497	+	0.0780497i	−0.745054	−	0.667004i	$-0.767576\pi$
$149$	−11.6294	+	11.6294i	−0.0780497	+	0.0780497i	0.667004	+	0.745054i	$0.267576\pi$
$150$		0			0
$151$		−	84.9872i		−	0.562829i	−0.959586	−	0.281414i	$-0.909196\pi$
$151$		−	84.9872i		−	0.562829i	0.959586	−	0.281414i	$-0.0908036\pi$
$152$	−7.33611	−	5.48153i	−0.0482639	−	0.0360627i
$153$	−58.0989	−	58.0989i	−0.379732	−	0.379732i
$154$	98.8360	−	4.73762i	0.641792	−	0.0307638i
$155$		0			0
$156$	−437.376	+	42.0271i	−2.80370	+	0.269405i
$157$	−128.249			−0.816874			−0.408437	−	0.912787i	$-0.633926\pi$
$157$	−128.249			−0.816874			−0.408437	+	0.912787i	$0.633926\pi$
$158$	4.47297	+	93.3148i	0.0283099	+	0.590600i
$159$		−	145.033i		−	0.912158i
$160$		0			0
$161$	79.2265			0.492090
$162$	37.2743	−	1.78671i	0.230088	−	0.0110291i
$163$			82.0115i			0.503138i	0.967839	+	0.251569i	$0.0809466\pi$
$163$			82.0115i			0.503138i	−0.967839	+	0.251569i	$0.919053\pi$
$164$	28.1017	+	292.455i	0.171352	+	1.78326i
$165$		0			0
$166$	7.94249	+	165.696i	0.0478463	+	0.998167i
$167$	−131.169	+	131.169i	−0.785444	+	0.785444i	−0.980744	−	0.195299i	$-0.937432\pi$
$167$	−131.169	+	131.169i	−0.785444	+	0.785444i	0.195299	+	0.980744i	$0.437432\pi$
$168$	144.519	+	107.984i	0.860230	+	0.642762i
$169$	−324.513			−1.92020
$170$		0			0
$171$	12.5061	+	12.5061i	0.0731354	+	0.0731354i
$172$	69.8864	−	6.71533i	0.406316	−	0.0390426i
$173$			58.5238i			0.338288i	0.985591	+	0.169144i	$0.0541003\pi$
$173$			58.5238i			0.338288i	−0.985591	+	0.169144i	$0.945900\pi$
$174$	255.405	−	281.123i	1.46784	−	1.61565i
$175$		0			0
$176$	−143.861	−	97.1185i	−0.817393	−	0.551809i
$177$	−359.238	−	359.238i	−2.02959	−	2.02959i
$178$	261.988	−	12.5582i	1.47185	−	0.0705517i
$179$	114.264	+	114.264i	0.638347	+	0.638347i	0.950147	−	0.311801i	$-0.100932\pi$
$179$	114.264	+	114.264i	0.638347	+	0.638347i	−0.311801	+	0.950147i	$0.600932\pi$
$180$		0			0
$181$	74.0068	+	74.0068i	0.408878	+	0.408878i	0.881347	−	0.472470i	$-0.156637\pi$
$181$	74.0068	+	74.0068i	0.408878	+	0.408878i	−0.472470	+	0.881347i	$0.656637\pi$
$182$	149.975	+	136.255i	0.824037	+	0.748652i
$183$	−97.4656	−	97.4656i	−0.532599	−	0.532599i
$184$	−111.331	−	83.1863i	−0.605059	−	0.452099i
$185$		0			0
$186$	−12.1006	−	252.442i	−0.0650571	−	1.35722i
$187$		−	57.6915i		−	0.308511i
$188$	−76.1957	−	62.8362i	−0.405296	−	0.334235i
$189$	−102.855	−	102.855i	−0.544204	−	0.544204i
$190$		0			0
$191$	92.5178			0.484387			0.242193	−	0.970228i	$-0.422133\pi$
$191$	92.5178			0.484387			0.242193	+	0.970228i	$0.422133\pi$
$192$	−89.6998	−	303.484i	−0.467187	−	1.58064i
$193$	−52.8692	+	52.8692i	−0.273934	+	0.273934i	−0.830682	−	0.556748i	$-0.812049\pi$
$193$	−52.8692	+	52.8692i	−0.273934	+	0.273934i	0.556748	+	0.830682i	$0.312049\pi$
$194$	63.9266	+	58.0784i	0.329519	+	0.299373i
$195$		0			0
$196$	10.7897	+	112.288i	0.0550493	+	0.572898i
$197$			99.4134i			0.504637i	0.967644	+	0.252318i	$0.0811930\pi$
$197$			99.4134i			0.504637i	−0.967644	+	0.252318i	$0.918807\pi$
$198$	248.114	+	225.416i	1.25310	+	1.13847i
$199$	265.168			1.33250			0.666252	−	0.745727i	$-0.267898\pi$
$199$	265.168			1.33250			0.666252	+	0.745727i	$0.267898\pi$
$200$		0			0
$201$			69.3838i			0.345193i
$202$	46.2457	+	42.0150i	0.228939	+	0.207995i
$203$	−175.155			−0.862832
$204$	66.9212	−	81.1491i	0.328045	−	0.397790i
$205$		0			0
$206$	−10.6045	−	9.63433i	−0.0514779	−	0.0467686i
$207$	189.790	+	189.790i	0.916860	+	0.916860i
$208$	−67.6834	−	348.939i	−0.325401	−	1.67759i
$209$			12.4185i			0.0594184i
$210$		0			0
$211$	−226.573	+	226.573i	−1.07380	+	1.07380i	−0.0767547	+	0.997050i	$0.524456\pi$
$211$	−226.573	+	226.573i	−1.07380	+	1.07380i	−0.997050	+	0.0767547i	$0.975544\pi$
$212$	116.786	−	11.2218i	0.550876	−	0.0529332i
$213$	−451.597			−2.12017
$214$	−5.23735	−	109.261i	−0.0244736	−	0.510566i
$215$		0			0
$216$	36.5384	+	252.529i	0.169159	+	1.16912i
$217$	−82.4122	+	82.4122i	−0.379780	+	0.379780i
$218$	−171.441	−	155.757i	−0.786427	−	0.714482i
$219$	211.469	−	211.469i	0.965610	−	0.965610i
$220$		0			0
$221$	83.5374	−	83.5374i	0.377997	−	0.377997i
$222$	−85.1953	+	4.08377i	−0.383763	+	0.0183954i
$223$	238.888	−	238.888i	1.07125	−	1.07125i	0.0739871	−	0.997259i	$-0.476428\pi$
$223$	238.888	−	238.888i	1.07125	−	1.07125i	0.997259	−	0.0739871i	$-0.0235724\pi$
$224$	−75.7705	+	124.727i	−0.338261	+	0.556815i
$225$		0			0
$226$	36.4725	−	40.1451i	0.161383	−	0.177633i
$227$	442.991			1.95150			0.975751	−	0.218884i	$-0.0702416\pi$
$227$	442.991			1.95150			0.975751	+	0.218884i	$0.0702416\pi$
$228$	−14.4052	+	17.4678i	−0.0631807	+	0.0766134i
$229$	−218.763	+	218.763i	−0.955297	+	0.955297i	−0.999043	−	0.0437454i	$-0.986071\pi$
$229$	−218.763	+	218.763i	−0.955297	+	0.955297i	0.0437454	+	0.999043i	$0.486071\pi$
$230$		0			0
$231$		−	244.639i		−	1.05904i
$232$	246.132	+	183.909i	1.06091	+	0.792712i
$233$	−181.998	−	181.998i	−0.781108	−	0.781108i	0.198910	−	0.980018i	$-0.436260\pi$
$233$	−181.998	−	181.998i	−0.781108	−	0.781108i	−0.980018	+	0.198910i	$0.936260\pi$
$234$	32.8672	+	685.673i	0.140458	+	2.93023i
$235$		0			0
$236$	261.475	−	317.066i	1.10794	−	1.34350i
$237$	230.973			0.974569
$238$	−48.4503	+	2.32243i	−0.203573	+	0.00975810i
$239$		−	41.3149i		−	0.172866i	−0.996258	−	0.0864328i	$-0.972453\pi$
$239$		−	41.3149i		−	0.172866i	0.996258	−	0.0864328i	$-0.0275468\pi$
$240$		0			0
$241$	223.654			0.928023			0.464012	−	0.885829i	$-0.346410\pi$
$241$	223.654			0.928023			0.464012	+	0.885829i	$0.346410\pi$
$242$	−0.317197	−	6.61734i	−0.00131073	−	0.0273444i
$243$			194.792i			0.801614i
$244$	70.9414	−	86.0240i	0.290743	−	0.352557i
$245$		0			0
$246$	725.551	−	34.7787i	2.94939	−	0.141377i
$247$	−17.9819	+	17.9819i	−0.0728014	+	0.0728014i
$248$	202.339	−	29.2764i	0.815883	−	0.118050i
$249$	410.130			1.64711
$250$		0			0
$251$	−329.376	−	329.376i	−1.31226	−	1.31226i	−0.919749	−	0.392507i	$-0.871608\pi$
$251$	−329.376	−	329.376i	−1.31226	−	1.31226i	−0.392507	−	0.919749i	$-0.628392\pi$
$252$	179.320	−	217.445i	0.711588	−	0.862877i
$253$			188.459i			0.744898i
$254$	−209.390	−	190.234i	−0.824370	−	0.748954i
$255$		0			0
$256$	237.435	−	95.7112i	0.927480	−	0.373872i
$257$	102.275	+	102.275i	0.397958	+	0.397958i	0.877512	−	0.479555i	$-0.159202\pi$
$257$	102.275	+	102.275i	0.397958	+	0.397958i	−0.479555	+	0.877512i	$0.659202\pi$
$258$	−8.31089	−	173.381i	−0.0322127	−	0.672020i
$259$	27.8128	+	27.8128i	0.107386	+	0.107386i
$260$		0			0
$261$	−419.590	−	419.590i	−1.60762	−	1.60762i
$262$	−92.8191	+	102.165i	−0.354271	+	0.389945i
$263$	149.290	+	149.290i	0.567642	+	0.567642i	0.931467	−	0.363826i	$-0.118530\pi$
$263$	149.290	+	149.290i	0.567642	+	0.567642i	−0.363826	+	0.931467i	$0.618530\pi$
$264$	−256.866	+	343.772i	−0.972977	+	1.30217i
$265$		0			0
$266$	10.4292	−	0.499917i	0.0392076	−	0.00187939i
$267$		−	648.474i		−	2.42874i
$268$	−55.8702	+	5.36852i	−0.208471	+	0.0200318i
$269$	169.168	+	169.168i	0.628876	+	0.628876i	0.947785	−	0.318909i	$-0.103316\pi$
$269$	169.168	+	169.168i	0.628876	+	0.628876i	−0.318909	+	0.947785i	$0.603316\pi$
$270$		0			0
$271$	−389.998			−1.43911			−0.719554	−	0.694437i	$-0.755654\pi$
$271$	−389.998			−1.43911			−0.719554	+	0.694437i	$0.755654\pi$
$272$	70.5221	+	47.6084i	0.259272	+	0.175031i
$273$	354.237	−	354.237i	1.29757	−	1.29757i
$274$	−220.996	+	243.249i	−0.806554	+	0.887770i
$275$		0			0
$276$	−218.609	+	265.087i	−0.792063	+	0.960461i
$277$		−	290.668i		−	1.04934i	−0.851305	−	0.524671i	$-0.824188\pi$
$277$		−	290.668i		−	1.04934i	0.851305	−	0.524671i	$-0.175812\pi$
$278$	−48.6854	+	53.5878i	−0.175127	+	0.192762i
$279$	−394.843			−1.41521
$280$		0			0
$281$			235.390i			0.837688i	0.908058	+	0.418844i	$0.137565\pi$
$281$			235.390i			0.837688i	−0.908058	+	0.418844i	$0.862435\pi$
$282$	−164.195	+	180.729i	−0.582253	+	0.640883i
$283$	−468.675			−1.65609			−0.828047	−	0.560659i	$-0.810548\pi$
$283$	−468.675			−1.65609			−0.828047	+	0.560659i	$0.810548\pi$
$284$	−34.9420	−	363.642i	−0.123035	−	1.28043i
$285$		0			0
$286$	−324.114	+	356.751i	−1.13327	+	1.24738i
$287$	−236.863	−	236.863i	−0.825307	−	0.825307i
$288$	−480.298	+	117.276i	−1.66770	+	0.407209i
$289$		−	260.719i		−	0.902142i
$290$		0			0
$291$	150.993	−	150.993i	0.518878	−	0.518878i
$292$	186.644	+	153.920i	0.639192	+	0.527122i
$293$	−179.844			−0.613801			−0.306901	−	0.951742i	$-0.599292\pi$
$293$	−179.844			−0.613801			−0.306901	+	0.951742i	$0.599292\pi$
$294$	278.575	−	13.3533i	0.947535	−	0.0454193i
$295$		0			0
$296$	−9.88032	−	68.2862i	−0.0333795	−	0.230697i
$297$	244.664	−	244.664i	0.823785	−	0.823785i
$298$	−22.1185	+	24.3457i	−0.0742232	+	0.0816971i
$299$	−272.889	+	272.889i	−0.912673	+	0.912673i
$300$		0			0
$301$	−56.6020	+	56.6020i	−0.188047	+	0.188047i
$302$	−8.13824	−	169.779i	−0.0269478	−	0.562183i
$303$	109.231	−	109.231i	0.360500	−	0.360500i
$304$	−15.1803	−	10.2480i	−0.0499352	−	0.0337105i
$305$		0			0
$306$	−121.628	−	110.501i	−0.397477	−	0.361115i
$307$	−110.106			−0.358653			−0.179326	−	0.983790i	$-0.557392\pi$
$307$	−110.106			−0.358653			−0.179326	+	0.983790i	$0.557392\pi$
$308$	196.992	−	18.9288i	0.639583	−	0.0614570i
$309$	−25.0475	+	25.0475i	−0.0810599	+	0.0810599i
$310$		0			0
$311$			53.7610i			0.172865i	0.996258	+	0.0864325i	$0.0275467\pi$
$311$			53.7610i			0.172865i	−0.996258	+	0.0864325i	$0.972453\pi$
$312$	−869.725	+	125.840i	−2.78758	+	0.403335i
$313$	165.965	+	165.965i	0.530241	+	0.530241i	0.920644	−	0.390403i	$-0.127664\pi$
$313$	165.965	+	165.965i	0.530241	+	0.530241i	−0.390403	+	0.920644i	$0.627664\pi$
$314$	−256.204	+	12.2809i	−0.815937	+	0.0391113i
$315$		0			0
$316$	17.8714	+	185.987i	0.0565549	+	0.588567i
$317$	40.4315			0.127544			0.0637721	−	0.997964i	$-0.479687\pi$
$317$	40.4315			0.127544			0.0637721	+	0.997964i	$0.479687\pi$
$318$	−13.8882	−	289.734i	−0.0436734	−	0.911112i
$319$		−	416.648i		−	1.30611i
$320$		0			0
$321$	−270.443			−0.842503
$322$	158.271	−	7.58660i	0.491525	−	0.0235609i
$323$		−	6.08764i		−	0.0188472i
$324$	74.2920	−	7.13865i	0.229296	−	0.0220329i
$325$		0			0
$326$	7.85330	+	163.835i	0.0240899	+	0.502561i
$327$	−404.940	+	404.940i	−1.23835	+	1.23835i
$328$	84.1440	+	581.548i	0.256537	+	1.77301i
$329$	112.604			0.342261
$330$		0			0
$331$	−107.944	−	107.944i	−0.326116	−	0.326116i	0.524992	−	0.851107i	$-0.324068\pi$
$331$	−107.944	−	107.944i	−0.326116	−	0.326116i	−0.851107	+	0.524992i	$0.824068\pi$
$332$	31.7335	+	330.251i	0.0955829	+	0.994731i
$333$			133.253i			0.400160i
$334$	−249.477	+	274.598i	−0.746937	+	0.822150i
$335$		0			0
$336$	299.046	+	201.882i	0.890018	+	0.600838i
$337$	119.972	+	119.972i	0.356000	+	0.356000i	0.862336	−	0.506336i	$-0.169001\pi$
$337$	119.972	+	119.972i	0.356000	+	0.356000i	−0.506336	+	0.862336i	$0.669001\pi$
$338$	−648.282	+	31.0749i	−1.91799	+	0.0919375i
$339$	−94.8219	−	94.8219i	−0.279711	−	0.279711i
$340$		0			0
$341$	−196.037	−	196.037i	−0.574889	−	0.574889i
$342$	26.1812	+	23.7860i	0.0765532	+	0.0695498i
$343$	−248.959	−	248.959i	−0.725828	−	0.725828i
$344$	138.969	−	20.1075i	0.403981	−	0.0584519i
$345$		0			0
$346$	5.60415	+	116.913i	0.0161970	+	0.337900i
$347$			165.996i			0.478375i	0.970973	+	0.239188i	$0.0768811\pi$
$347$			165.996i			0.478375i	−0.970973	+	0.239188i	$0.923119\pi$
$348$	483.304	−	586.058i	1.38881	−	1.68408i
$349$	201.279	+	201.279i	0.576730	+	0.576730i	0.934001	−	0.357271i	$-0.116293\pi$
$349$	201.279	+	201.279i	0.576730	+	0.576730i	−0.357271	+	0.934001i	$0.616293\pi$
$350$		0			0
$351$	708.548			2.01866
$352$	−296.692	−	180.238i	−0.842875	−	0.512040i
$353$	5.16188	−	5.16188i	0.0146229	−	0.0146229i	−0.699758	−	0.714380i	$-0.746709\pi$
$353$	5.16188	−	5.16188i	0.0146229	−	0.0146229i	0.714380	+	0.699758i	$0.246709\pi$
$354$	−752.052	−	683.252i	−2.12444	−	1.93009i
$355$		0			0
$356$	522.173	−	50.1752i	1.46678	−	0.140942i
$357$			119.924i			0.335922i
$358$	239.208	+	217.324i	0.668178	+	0.607051i
$359$	−81.8547			−0.228008			−0.114004	−	0.993480i	$-0.536368\pi$
$359$	−81.8547			−0.228008			−0.114004	+	0.993480i	$0.536368\pi$
$360$		0			0
$361$		−	359.690i		−	0.996370i
$362$	154.931	+	140.757i	0.427985	+	0.388832i
$363$	−16.3792			−0.0451218
$364$	312.653	+	257.835i	0.858937	+	0.708339i
$365$		0			0
$366$	−204.041	−	185.375i	−0.557489	−	0.506488i
$367$	−120.769	−	120.769i	−0.329071	−	0.329071i	0.523162	−	0.852233i	$-0.324752\pi$
$367$	−120.769	−	120.769i	−0.329071	−	0.329071i	−0.852233	+	0.523162i	$0.824752\pi$
$368$	−230.372	−	155.521i	−0.626011	−	0.422611i
$369$		−	1134.83i		−	3.07542i
$370$		0			0
$371$	−94.5864	+	94.5864i	−0.254950	+	0.254950i
$372$	−48.3469	−	503.147i	−0.129965	−	1.35254i
$373$	320.574			0.859447			0.429724	−	0.902960i	$-0.358611\pi$
$373$	320.574			0.859447			0.429724	+	0.902960i	$0.358611\pi$
$374$	−5.52445	−	115.251i	−0.0147713	−	0.308157i
$375$		0			0
$376$	−158.234	−	118.232i	−0.420834	−	0.314447i
$377$	603.307	−	603.307i	1.60028	−	1.60028i
$378$	−215.322	−	195.624i	−0.569636	−	0.517524i
$379$	3.16506	−	3.16506i	0.00835109	−	0.00835109i	−0.702919	−	0.711270i	$-0.748120\pi$
$379$	3.16506	−	3.16506i	0.00835109	−	0.00835109i	0.711270	+	0.702919i	$0.248120\pi$
$380$		0			0
$381$	−494.575	+	494.575i	−1.29810	+	1.29810i
$382$	184.823	−	8.85936i	0.483831	−	0.0231921i
$383$	−401.423	+	401.423i	−1.04810	+	1.04810i	−0.0493197	+	0.998783i	$0.515705\pi$
$383$	−401.423	+	401.423i	−1.04810	+	1.04810i	−0.998783	+	0.0493197i	$0.984295\pi$
$384$	−208.255	−	597.681i	−0.542331	−	1.55646i
$385$		0			0
$386$	−100.554	+	110.680i	−0.260504	+	0.286735i
$387$	−271.184			−0.700735
$388$	133.268	+	109.902i	0.343474	+	0.283253i
$389$	−179.440	+	179.440i	−0.461286	+	0.461286i	−0.899077	−	0.437791i	$-0.855761\pi$
$389$	−179.440	+	179.440i	−0.461286	+	0.461286i	0.437791	+	0.899077i	$0.355761\pi$
$390$		0			0
$391$		−	92.3844i		−	0.236277i
$392$	32.3071	+	223.285i	0.0824160	+	0.569605i
$393$	241.313	+	241.313i	0.614028	+	0.614028i
$394$	9.51967	+	198.599i	0.0241616	+	0.504058i
$395$		0			0
$396$	517.245	+	426.556i	1.30618	+	1.07716i
$397$	−321.234			−0.809154			−0.404577	−	0.914504i	$-0.632581\pi$
$397$	−321.234			−0.809154			−0.404577	+	0.914504i	$0.632581\pi$
$398$	529.728	−	25.3921i	1.33097	−	0.0637992i
$399$		−	25.8144i		−	0.0646978i
$400$		0			0
$401$	649.404			1.61946			0.809730	−	0.586802i	$-0.199613\pi$
$401$	649.404			1.61946			0.809730	+	0.586802i	$0.199613\pi$
$402$	6.64408	+	138.608i	0.0165276	+	0.344797i
$403$		−	567.725i		−	1.40875i
$404$	96.4086	+	79.5052i	0.238635	+	0.196795i
$405$		0			0
$406$	−349.908	+	16.7726i	−0.861842	+	0.0413117i
$407$	−66.1595	+	66.1595i	−0.162554	+	0.162554i
$408$	125.918	−	168.520i	0.308623	−	0.413040i
$409$	−20.3455			−0.0497444			−0.0248722	−	0.999691i	$-0.507918\pi$
$409$	−20.3455			−0.0497444			−0.0248722	+	0.999691i	$0.507918\pi$
$410$		0			0
$411$	574.550	+	574.550i	1.39793	+	1.39793i
$412$	−22.1072	−	18.2311i	−0.0536582	−	0.0442502i
$413$			468.569i			1.13455i
$414$	397.319	+	360.971i	0.959707	+	0.871910i
$415$		0			0
$416$	−168.625	−	690.596i	−0.405350	−	1.66009i
$417$	126.573	+	126.573i	0.303533	+	0.303533i
$418$	1.18917	+	24.8084i	0.00284491	+	0.0593503i
$419$	204.233	+	204.233i	0.487430	+	0.487430i	0.907494	−	0.420064i	$-0.137992\pi$
$419$	204.233	+	204.233i	0.487430	+	0.487430i	−0.420064	+	0.907494i	$0.637992\pi$
$420$		0			0
$421$	−74.3563	−	74.3563i	−0.176618	−	0.176618i	0.613262	−	0.789880i	$-0.289857\pi$
$421$	−74.3563	−	74.3563i	−0.176618	−	0.176618i	−0.789880	+	0.613262i	$0.789857\pi$
$422$	−430.930	+	474.322i	−1.02116	+	1.12399i
$423$	269.747	+	269.747i	0.637699	+	0.637699i
$424$	232.229	−	33.6012i	0.547710	−	0.0792480i
$425$		0			0
$426$	−902.159	+	43.2442i	−2.11774	+	0.101512i
$427$			127.128i			0.297725i
$428$	−20.9254	−	217.770i	−0.0488910	−	0.508809i
$429$	842.639	+	842.639i	1.96419	+	1.96419i
$430$		0			0
$431$	30.9498			0.0718092			0.0359046	−	0.999355i	$-0.488569\pi$
$431$	30.9498			0.0718092			0.0359046	+	0.999355i	$0.488569\pi$
$432$	97.1747	+	500.980i	0.224941	+	1.15968i
$433$	68.9194	−	68.9194i	0.159167	−	0.159167i	−0.623030	−	0.782198i	$-0.714099\pi$
$433$	68.9194	−	68.9194i	0.159167	−	0.159167i	0.782198	+	0.623030i	$0.214099\pi$
$434$	−156.744	+	172.527i	−0.361161	+	0.397528i
$435$		0			0
$436$	−357.404	−	294.740i	−0.819733	−	0.676009i
$437$			19.8863i			0.0455064i
$438$	402.202	−	442.702i	0.918270	−	1.01074i
$439$	−755.005			−1.71983			−0.859914	−	0.510439i	$-0.829483\pi$
$439$	−755.005			−1.71983			−0.859914	+	0.510439i	$0.829483\pi$
$440$		0			0
$441$		−	435.718i		−	0.988022i
$442$	158.884	−	174.883i	0.359466	−	0.395662i
$443$	109.778			0.247806			0.123903	−	0.992294i	$-0.460459\pi$
$443$	109.778			0.247806			0.123903	+	0.992294i	$0.460459\pi$
$444$	−169.804	+	16.3163i	−0.382442	+	0.0367485i
$445$		0			0
$446$	454.352	−	500.103i	1.01873	−	1.12131i
$447$	57.5042	+	57.5042i	0.128645	+	0.128645i
$448$	−139.424	+	256.423i	−0.311213	+	0.572372i
$449$			491.218i			1.09403i	0.837124	+	0.547013i	$0.184235\pi$
$449$			491.218i			1.09403i	−0.837124	+	0.547013i	$0.815765\pi$
$450$		0			0
$451$	563.436	−	563.436i	1.24930	−	1.24930i
$452$	69.0171	−	83.6907i	0.152693	−	0.185156i
$453$	−420.238			−0.927678
$454$	884.966	−	42.4201i	1.94926	−	0.0934364i
$455$		0			0
$456$	−27.1046	+	36.2750i	−0.0594400	+	0.0795505i
$457$	−468.944	+	468.944i	−1.02614	+	1.02614i	−0.0264867	+	0.999649i	$0.508432\pi$
$457$	−468.944	+	468.944i	−1.02614	+	1.02614i	−0.999649	+	0.0264867i	$0.991568\pi$
$458$	−416.076	+	457.973i	−0.908463	+	0.999941i
$459$	−119.937	+	119.937i	−0.261300	+	0.261300i
$460$		0			0
$461$	−78.6933	+	78.6933i	−0.170701	+	0.170701i	−0.787287	−	0.616586i	$-0.788515\pi$
$461$	−78.6933	+	78.6933i	−0.170701	+	0.170701i	0.616586	+	0.787287i	$0.288515\pi$
$462$	−23.4262	−	488.716i	−0.0507061	−	1.05783i
$463$	382.322	−	382.322i	0.825749	−	0.825749i	−0.161176	−	0.986926i	$-0.551529\pi$
$463$	382.322	−	382.322i	0.825749	−	0.825749i	0.986926	+	0.161176i	$0.0515288\pi$
$464$	509.310	+	343.827i	1.09765	+	0.741007i
$465$		0			0
$466$	−381.007	−	346.151i	−0.817611	−	0.742813i
$467$	374.594			0.802129			0.401065	−	0.916050i	$-0.368640\pi$
$467$	374.594			0.802129			0.401065	+	0.916050i	$0.368640\pi$
$468$	131.318	+	1366.63i	0.280594	+	2.92014i
$469$	45.2501	−	45.2501i	0.0964820	−	0.0964820i
$470$		0			0
$471$			634.157i			1.34640i
$472$	491.988	−	658.444i	1.04235	−	1.39501i
$473$	−134.641	−	134.641i	−0.284654	−	0.284654i
$474$	461.416	−	22.1176i	0.973451	−	0.0466616i
$475$		0			0
$476$	−96.5671	+	9.27906i	−0.202872	+	0.0194938i
$477$	−453.171			−0.950043
$478$	−3.95625	−	82.5350i	−0.00827667	−	0.172667i
$479$			450.432i			0.940359i	0.882571	+	0.470179i	$0.155811\pi$
$479$			450.432i			0.940359i	−0.882571	+	0.470179i	$0.844189\pi$
$480$		0			0
$481$	−191.598			−0.398333
$482$	446.794	−	21.4167i	0.926959	−	0.0444330i
$483$		−	391.753i		−	0.811082i
$484$	−1.26733	−	13.1891i	−0.00261845	−	0.0272502i
$485$		0			0
$486$	18.6530	+	389.137i	0.0383806	+	0.800694i
$487$	−292.281	+	292.281i	−0.600166	+	0.600166i	−0.940357	−	0.340190i	$-0.889508\pi$
$487$	−292.281	+	292.281i	−0.600166	+	0.600166i	0.340190	+	0.940357i	$0.389508\pi$
$488$	133.482	−	178.644i	0.273530	−	0.366074i
$489$	405.524			0.829293
$490$		0			0
$491$	434.376	+	434.376i	0.884677	+	0.884677i	0.994006	−	0.109329i	$-0.0348702\pi$
$491$	434.376	+	434.376i	0.884677	+	0.884677i	−0.109329	+	0.994006i	$0.534870\pi$
$492$	1446.11	−	138.955i	2.93924	−	0.282429i
$493$			204.245i			0.414289i
$494$	−34.2007	+	37.6446i	−0.0692322	+	0.0762036i
$495$		0			0
$496$	401.410	−	77.8613i	0.809295	−	0.156978i
$497$	294.519	+	294.519i	0.592593	+	0.592593i
$498$	819.319	−	39.2734i	1.64522	−	0.0788622i
$499$	−36.0616	−	36.0616i	−0.0722676	−	0.0722676i	0.670049	−	0.742317i	$-0.266273\pi$
$499$	−36.0616	−	36.0616i	−0.0722676	−	0.0722676i	−0.742317	+	0.670049i	$0.766273\pi$
$500$		0			0
$501$	648.595	+	648.595i	1.29460	+	1.29460i
$502$	−689.538	−	626.456i	−1.37358	−	1.24792i
$503$	196.896	+	196.896i	0.391444	+	0.391444i	0.875202	−	0.483758i	$-0.160729\pi$
$503$	196.896	+	196.896i	0.391444	+	0.391444i	−0.483758	+	0.875202i	$0.660729\pi$
$504$	337.407	−	451.563i	0.669458	−	0.895958i
$505$		0			0
$506$	18.0466	+	376.486i	0.0356651	+	0.744043i
$507$			1604.63i			3.16494i
$508$	−436.516	−	359.981i	−0.859284	−	0.708625i
$509$	−459.143	−	459.143i	−0.902049	−	0.902049i	0.0935638	−	0.995613i	$-0.470174\pi$
$509$	−459.143	−	459.143i	−0.902049	−	0.902049i	−0.995613	+	0.0935638i	$0.970174\pi$
$510$		0			0
$511$	−275.827			−0.539780
$512$	465.160	−	213.939i	0.908516	−	0.417850i
$513$	25.8171	−	25.8171i	0.0503257	−	0.0503257i
$514$	214.109	+	194.522i	0.416555	+	0.378447i
$515$		0			0
$516$	−33.2054	−	345.569i	−0.0643516	−	0.669707i
$517$			267.855i			0.518096i
$518$	58.2252	+	52.8986i	0.112404	+	0.102121i
$519$	289.384			0.557580
$520$		0			0
$521$			726.368i			1.39418i	0.716984	+	0.697090i	$0.245522\pi$
$521$			726.368i			1.39418i	−0.716984	+	0.697090i	$0.754478\pi$
$522$	−878.397	−	798.038i	−1.68275	−	1.52881i
$523$	−542.697			−1.03766			−0.518831	−	0.854877i	$-0.673633\pi$
$523$	−542.697			−1.03766			−0.518831	+	0.854877i	$0.673633\pi$
$524$	−175.642	+	212.985i	−0.335195	+	0.406460i
$525$		0			0
$526$	312.533	+	283.941i	0.594169	+	0.539812i
$527$	96.0993	+	96.0993i	0.182352	+	0.182352i
$528$	−480.224	+	711.353i	−0.909515	+	1.34726i
$529$		−	227.211i		−	0.429510i
$530$		0			0
$531$	−1122.47	+	1122.47i	−2.11389	+	2.11389i
$532$	20.7867	−	1.99737i	0.0390727	−	0.00375446i
$533$	1631.71			3.06137
$534$	−62.0968	−	1295.46i	−0.116286	−	2.42596i
$535$		0			0
$536$	−111.098	+	16.0748i	−0.207273	+	0.0299902i
$537$	565.004	−	565.004i	1.05215	−	1.05215i
$538$	354.147	+	321.748i	0.658265	+	0.598045i
$539$	216.331	−	216.331i	0.401357	−	0.401357i
$540$		0			0
$541$	727.376	−	727.376i	1.34450	−	1.34450i	0.452983	−	0.891519i	$-0.350360\pi$
$541$	727.376	−	727.376i	1.34450	−	1.34450i	0.891519	−	0.452983i	$-0.149640\pi$
$542$	−779.102	+	37.3456i	−1.43746	+	0.0689033i
$543$	365.943	−	365.943i	0.673929	−	0.673929i
$544$	145.441	+	88.3545i	0.267355	+	0.162416i
$545$		0			0
$546$	673.741	−	741.584i	1.23396	−	1.35821i
$547$	−511.401			−0.934920			−0.467460	−	0.884014i	$-0.654831\pi$
$547$	−511.401			−0.934920			−0.467460	+	0.884014i	$0.654831\pi$
$548$	−418.192	+	507.102i	−0.763124	+	0.925369i
$549$	−304.541	+	304.541i	−0.554720	+	0.554720i
$550$		0			0
$551$		−	43.9649i		−	0.0797911i
$552$	−411.333	+	550.500i	−0.745168	+	0.997283i
$553$	−150.634	−	150.634i	−0.272394	−	0.272394i
$554$	−27.8339	−	580.669i	−0.0502417	−	1.04814i
$555$		0			0
$556$	−92.1277	+	111.715i	−0.165697	+	0.200926i
$557$	804.398			1.44416			0.722081	−	0.691809i	$-0.243186\pi$
$557$	804.398			1.44416			0.722081	+	0.691809i	$0.243186\pi$
$558$	−788.781	+	37.8096i	−1.41359	+	0.0677591i
$559$		−	389.922i		−	0.697535i
$560$		0			0
$561$	−285.269			−0.508500
$562$	22.5406	+	470.241i	0.0401079	+	0.836728i
$563$			695.151i			1.23473i	0.786678	+	0.617363i	$0.211799\pi$
$563$			695.151i			1.23473i	−0.786678	+	0.617363i	$0.788201\pi$
$564$	−310.708	+	376.766i	−0.550900	+	0.668026i
$565$		0			0
$566$	−936.274	+	44.8795i	−1.65419	+	0.0792925i
$567$	−60.1701	+	60.1701i	−0.106120	+	0.106120i
$568$	−104.626	−	723.103i	−0.184200	−	1.27307i
$569$	−277.088			−0.486974			−0.243487	−	0.969904i	$-0.578291\pi$
$569$	−277.088			−0.486974			−0.243487	+	0.969904i	$0.578291\pi$
$570$		0			0
$571$	−569.098	−	569.098i	−0.996669	−	0.996669i	0.00332578	−	0.999994i	$-0.498941\pi$
$571$	−569.098	−	569.098i	−0.996669	−	0.996669i	−0.999994	+	0.00332578i	$0.998941\pi$
$572$	−613.323	+	743.720i	−1.07224	+	1.30021i
$573$		−	457.475i		−	0.798386i
$574$	−495.865	−	450.501i	−0.863876	−	0.784846i
$575$		0			0
$576$	−948.265	+	280.276i	−1.64629	+	0.486590i
$577$	−687.894	−	687.894i	−1.19219	−	1.19219i	−0.976451	−	0.215740i	$-0.930784\pi$
$577$	−687.894	−	687.894i	−1.19219	−	1.19219i	−0.215740	−	0.976451i	$-0.569216\pi$
$578$	−24.9660	−	520.840i	−0.0431939	−	0.901107i
$579$	261.424	+	261.424i	0.451509	+	0.451509i
$580$		0			0
$581$	−267.475	−	267.475i	−0.460370	−	0.460370i
$582$	287.182	−	316.099i	0.493439	−	0.543126i
$583$	−224.996	−	224.996i	−0.385929	−	0.385929i
$584$	387.599	+	289.613i	0.663697	+	0.495913i
$585$		0			0
$586$	−359.275	+	17.2216i	−0.613097	+	0.0293883i
$587$		−	78.2483i		−	0.133302i	−0.997776	−	0.0666510i	$-0.978769\pi$
$587$		−	78.2483i		−	0.133302i	0.997776	−	0.0666510i	$-0.0212314\pi$
$588$	555.233	−	53.3518i	0.944273	−	0.0907344i
$589$	−20.6860	−	20.6860i	−0.0351205	−	0.0351205i
$590$		0			0
$591$	491.572			0.831763
$592$	−26.2770	−	135.470i	−0.0443868	−	0.228834i
$593$	296.118	−	296.118i	0.499355	−	0.499355i	−0.411882	−	0.911237i	$-0.635128\pi$
$593$	296.118	−	296.118i	0.499355	−	0.499355i	0.911237	+	0.411882i	$0.135128\pi$
$594$	465.339	−	512.196i	0.783398	−	0.862283i
$595$		0			0
$596$	−41.8550	+	50.7537i	−0.0702265	+	0.0851572i
$597$		−	1311.18i		−	2.19629i
$598$	−519.021	+	571.284i	−0.867928	+	0.955324i
$599$	−48.2788			−0.0805990			−0.0402995	−	0.999188i	$-0.512831\pi$
$599$	−48.2788			−0.0805990			−0.0402995	+	0.999188i	$0.512831\pi$
$600$		0			0
$601$			592.230i			0.985408i	0.870197	+	0.492704i	$0.163992\pi$
$601$			592.230i			0.985408i	−0.870197	+	0.492704i	$0.836008\pi$
$602$	−107.654	+	118.494i	−0.178827	+	0.196834i
$603$	216.796			0.359530
$604$	−32.5156	−	338.390i	−0.0538338	−	0.560248i
$605$		0			0
$606$	207.752	−	228.672i	0.342826	−	0.377347i
$607$	289.382	+	289.382i	0.476741	+	0.476741i	0.904088	−	0.427346i	$-0.140552\pi$
$607$	289.382	+	289.382i	0.476741	+	0.476741i	−0.427346	+	0.904088i	$0.640552\pi$
$608$	−31.3071	−	19.0188i	−0.0514920	−	0.0312810i
$609$			866.092i			1.42215i
$610$		0			0
$611$	−387.855	+	387.855i	−0.634787	+	0.634787i
$612$	−253.559	−	209.102i	−0.414311	−	0.341670i
$613$	−719.493			−1.17373			−0.586863	−	0.809687i	$-0.699637\pi$
$613$	−719.493			−1.17373			−0.586863	+	0.809687i	$0.699637\pi$
$614$	−219.960	+	10.5436i	−0.358241	+	0.0171720i
$615$		0			0
$616$	391.719	−	56.6777i	0.635907	−	0.0920093i
$617$	−370.007	+	370.007i	−0.599687	+	0.599687i	−0.940229	−	0.340542i	$-0.889389\pi$
$617$	−370.007	+	370.007i	−0.599687	+	0.599687i	0.340542	+	0.940229i	$0.389389\pi$
$618$	−47.6391	+	52.4361i	−0.0770859	+	0.0848481i
$619$	524.739	−	524.739i	0.847721	−	0.847721i	−0.142127	−	0.989848i	$-0.545394\pi$
$619$	524.739	−	524.739i	0.847721	−	0.847721i	0.989848	+	0.142127i	$0.0453942\pi$
$620$		0			0
$621$	391.793	−	391.793i	0.630907	−	0.630907i
$622$	5.14807	+	107.399i	0.00827665	+	0.172667i
$623$	−422.916	+	422.916i	−0.678837	+	0.678837i
$624$	−1725.41	+	334.676i	−2.76507	+	0.536339i
$625$		0			0
$626$	347.443	+	315.658i	0.555020	+	0.504245i
$627$	61.4058			0.0979359
$628$	−510.645	+	49.0674i	−0.813129	+	0.0781328i
$629$	32.4320	−	32.4320i	0.0515612	−	0.0515612i
$630$		0			0
$631$			481.853i			0.763634i	0.924238	+	0.381817i	$0.124702\pi$
$631$			481.853i			0.763634i	−0.924238	+	0.381817i	$0.875298\pi$
$632$	53.5116	+	369.837i	0.0846702	+	0.585184i
$633$	1120.34	+	1120.34i	1.76989	+	1.76989i
$634$	80.7703	−	3.87166i	0.127398	−	0.00610672i
$635$		0			0
$636$	−55.4889	−	577.473i	−0.0872467	−	0.907976i
$637$	626.496			0.983510
$638$	−39.8975	−	832.340i	−0.0625353	−	1.30461i
$639$			1411.06i			2.20823i
$640$		0			0
$641$	602.798			0.940403			0.470202	−	0.882559i	$-0.344181\pi$
$641$	602.798			0.940403			0.470202	+	0.882559i	$0.344181\pi$
$642$	−540.266	+	25.8972i	−0.841536	+	0.0403384i
$643$			1220.05i			1.89744i	0.316118	+	0.948720i	$0.397621\pi$
$643$			1220.05i			1.89744i	−0.316118	+	0.948720i	$0.602379\pi$
$644$	315.453	−	30.3116i	0.489834	−	0.0470677i
$645$		0			0
$646$	−0.582943	−	12.1613i	−0.000902389	−	0.0188256i
$647$	674.538	−	674.538i	1.04256	−	1.04256i	0.0435096	−	0.999053i	$-0.486146\pi$
$647$	674.538	−	674.538i	1.04256	−	1.04256i	0.999053	−	0.0435096i	$-0.0138539\pi$
$648$	147.730	−	21.3750i	0.227978	−	0.0329861i
$649$	−1114.60			−1.71742
$650$		0			0
$651$	407.506	+	407.506i	0.625969	+	0.625969i
$652$	31.3772	+	326.542i	0.0481245	+	0.500831i
$653$		−	1069.12i		−	1.63724i	−0.574336	−	0.818620i	$-0.694740\pi$
$653$		−	1069.12i		−	1.63724i	0.574336	−	0.818620i	$-0.305260\pi$
$654$	−770.175	+	847.728i	−1.17764	+	1.29622i
$655$		0			0
$656$	223.783	+	1153.70i	0.341133	+	1.75869i
$657$	−660.755	−	660.755i	−1.00572	−	1.00572i
$658$	224.949	−	10.7828i	0.341869	−	0.0163872i
$659$	392.851	+	392.851i	0.596131	+	0.596131i	0.939281	−	0.343149i	$-0.111494\pi$
$659$	392.851	+	392.851i	0.596131	+	0.596131i	−0.343149	+	0.939281i	$0.611494\pi$
$660$		0			0
$661$	−251.961	−	251.961i	−0.381182	−	0.381182i	0.490346	−	0.871528i	$-0.336871\pi$
$661$	−251.961	−	251.961i	−0.381182	−	0.381182i	−0.871528	+	0.490346i	$0.836871\pi$
$662$	−225.978	−	205.305i	−0.341356	−	0.310128i
$663$	−413.069	−	413.069i	−0.623031	−	0.623031i
$664$	95.0185	+	656.705i	0.143100	+	0.989014i
$665$		0			0
$666$	12.7601	+	266.201i	0.0191594	+	0.399702i
$667$		−	667.200i		−	1.00030i
$668$	−472.087	+	572.456i	−0.706717	+	0.856970i
$669$	−1181.23	−	1181.23i	−1.76567	−	1.76567i
$670$		0			0
$671$	−302.406			−0.450679
$672$	616.738	+	374.664i	0.917765	+	0.557536i
$673$	54.2702	−	54.2702i	0.0806392	−	0.0806392i	−0.665637	−	0.746276i	$-0.731840\pi$
$673$	54.2702	−	54.2702i	0.0806392	−	0.0806392i	0.746276	+	0.665637i	$0.231840\pi$
$674$	251.157	+	228.180i	0.372637	+	0.338547i
$675$		0			0
$676$	−1292.10	+	124.157i	−1.91139	+	0.183664i
$677$			862.549i			1.27408i	0.770832	+	0.637038i	$0.219841\pi$
$677$			862.549i			1.27408i	−0.770832	+	0.637038i	$0.780159\pi$
$678$	−198.506	−	180.346i	−0.292782	−	0.265998i
$679$	−196.947			−0.290054
$680$		0			0
$681$		−	2190.47i		−	3.21654i
$682$	−410.397	−	372.853i	−0.601755	−	0.546705i
$683$	887.581			1.29953			0.649766	−	0.760134i	$-0.274867\pi$
$683$	887.581			1.29953			0.649766	+	0.760134i	$0.274867\pi$
$684$	54.5800	+	45.0105i	0.0797954	+	0.0658048i
$685$		0			0
$686$	−521.187	−	473.507i	−0.759748	−	0.690243i
$687$	1081.72	+	1081.72i	1.57456	+	1.57456i
$688$	275.695	−	53.4763i	0.400719	−	0.0777272i
$689$		−	651.591i		−	0.945705i
$690$		0			0
$691$	810.243	−	810.243i	1.17257	−	1.17257i	0.190969	−	0.981596i	$-0.438837\pi$
$691$	810.243	−	810.243i	1.17257	−	1.17257i	0.981596	−	0.190969i	$-0.0611631\pi$
$692$	22.3909	+	233.022i	0.0323568	+	0.336737i
$693$	−764.398			−1.10303
$694$	15.8955	+	331.612i	0.0229042	+	0.477826i
$695$		0			0
$696$	909.380	−	1217.05i	1.30658	−	1.74864i
$697$	−276.202	+	276.202i	−0.396272	+	0.396272i
$698$	421.370	+	382.821i	0.603682	+	0.548455i
$699$	−899.930	+	899.930i	−1.28745	+	1.28745i
$700$		0			0
$701$	768.186	−	768.186i	1.09584	−	1.09584i	0.100952	−	0.994891i	$-0.467811\pi$
$701$	768.186	−	768.186i	1.09584	−	1.09584i	0.994891	−	0.100952i	$-0.0321889\pi$
$702$	1415.47	−	67.8495i	2.01634	−	0.0966517i
$703$	−6.98119	+	6.98119i	−0.00993057	+	0.00993057i
$704$	−609.963	−	331.652i	−0.866425	−	0.471097i
$705$		0			0
$706$	9.81763	−	10.8062i	0.0139060	−	0.0153063i
$707$	−142.475			−0.201521
$708$	−1567.81	−	1292.92i	−2.21441	−	1.82616i
$709$	587.694	−	587.694i	0.828906	−	0.828906i	−0.158459	−	0.987365i	$-0.550653\pi$
$709$	587.694	−	587.694i	0.828906	−	0.828906i	0.987365	+	0.158459i	$0.0506527\pi$
$710$		0			0
$711$		−	721.697i		−	1.01505i
$712$	1038.34	−	150.238i	1.45835	−	0.211008i
$713$	−313.925	−	313.925i	−0.440287	−	0.440287i
$714$	11.4838	+	239.573i	0.0160837	+	0.335537i
$715$		0			0
$716$	498.677	+	411.244i	0.696477	+	0.574363i
$717$	−204.291			−0.284924
$718$	−163.522	+	7.83828i	−0.227746	+	0.0109168i
$719$		−	735.293i		−	1.02266i	−0.859384	−	0.511330i	$-0.829153\pi$
$719$		−	735.293i		−	1.02266i	0.859384	−	0.511330i	$-0.170847\pi$
$720$		0			0
$721$	32.6705			0.0453128
$722$	−34.4433	−	718.554i	−0.0477054	−	0.995227i
$723$		−	1105.90i		−	1.52961i
$724$	322.985	+	266.355i	0.446111	+	0.367894i
$725$		0			0
$726$	−32.7209	+	1.56845i	−0.0450701	+	0.00216040i
$727$	−282.639	+	282.639i	−0.388775	+	0.388775i	−0.874250	−	0.485475i	$-0.838647\pi$
$727$	−282.639	+	282.639i	−0.388775	+	0.388775i	0.485475	+	0.874250i	$0.338647\pi$
$728$	649.279	+	485.140i	0.891867	+	0.666401i
$729$	1131.12			1.55160
$730$		0			0
$731$	66.0025	+	66.0025i	0.0902907	+	0.0902907i
$732$	−425.365	−	350.785i	−0.581100	−	0.479215i
$733$		−	1241.78i		−	1.69410i	−0.531513	−	0.847050i	$-0.678376\pi$
$733$		−	1241.78i		−	1.69410i	0.531513	−	0.847050i	$-0.321624\pi$
$734$	−252.826	−	229.697i	−0.344450	−	0.312938i
$735$		0			0
$736$	−475.108	−	288.625i	−0.645528	−	0.392153i
$737$	107.638	+	107.638i	0.146049	+	0.146049i
$738$	−108.669	−	2267.06i	−0.147249	−	3.07189i
$739$	−682.480	−	682.480i	−0.923518	−	0.923518i	0.0737578	−	0.997276i	$-0.476501\pi$
$739$	−682.480	−	682.480i	−0.923518	−	0.923518i	−0.997276	+	0.0737578i	$0.976501\pi$
$740$		0			0
$741$	88.9157	+	88.9157i	0.119994	+	0.119994i
$742$	−179.898	+	198.013i	−0.242451	+	0.266864i
$743$	−603.646	−	603.646i	−0.812444	−	0.812444i	0.172556	−	0.985000i	$-0.444797\pi$
$743$	−603.646	−	603.646i	−0.812444	−	0.812444i	−0.985000	+	0.172556i	$0.944797\pi$
$744$	−144.764	−	1000.51i	−0.194575	−	1.34477i
$745$		0			0
$746$	640.412	−	30.6977i	0.858462	−	0.0411497i
$747$		−	1281.49i		−	1.71552i
$748$	−22.0725	−	229.708i	−0.0295086	−	0.307096i
$749$	176.375	+	176.375i	0.235481	+	0.235481i
$750$		0			0
$751$	849.499			1.13116			0.565578	−	0.824695i	$-0.308653\pi$
$751$	849.499			1.13116			0.565578	+	0.824695i	$0.308653\pi$
$752$	−327.426	−	221.040i	−0.435407	−	0.293937i
$753$	−1628.67	+	1628.67i	−2.16291	+	2.16291i
$754$	1147.46	−	1263.00i	1.52183	−	1.67507i
$755$		0			0
$756$	−448.883	−	370.180i	−0.593761	−	0.489656i
$757$		−	410.039i		−	0.541663i	−0.962627	−	0.270832i	$-0.912701\pi$
$757$		−	410.039i		−	0.541663i	0.962627	−	0.270832i	$-0.0872986\pi$
$758$	6.01978	−	6.62595i	0.00794167	−	0.00874135i
$759$	931.878			1.22777
$760$		0			0
$761$			582.295i			0.765171i	0.923920	+	0.382585i	$0.124966\pi$
$761$			582.295i			0.765171i	−0.923920	+	0.382585i	$0.875034\pi$
$762$	−940.656	+	1035.38i	−1.23446	+	1.35876i
$763$	528.180			0.692242
$764$	368.375	−	35.3968i	0.482166	−	0.0463309i
$765$		0			0
$766$	−763.486	+	840.366i	−0.996718	+	1.09708i
$767$	−1613.95	−	1613.95i	−2.10423	−	2.10423i
$768$	−473.265	−	1174.05i	−0.616231	−	1.52871i
$769$			1386.11i			1.80249i	0.433311	+	0.901245i	$0.357345\pi$
$769$			1386.11i			1.80249i	−0.433311	+	0.901245i	$0.642655\pi$
$770$		0			0
$771$	505.722	−	505.722i	0.655930	−	0.655930i
$772$	−190.280	+	230.735i	−0.246476	+	0.298879i
$773$	1124.50			1.45473			0.727363	−	0.686253i	$-0.240746\pi$
$773$	1124.50			1.45473			0.727363	+	0.686253i	$0.240746\pi$
$774$	−541.747	+	25.9682i	−0.699931	+	0.0335506i
$775$		0			0
$776$	276.755	+	206.791i	0.356642	+	0.266483i
$777$	137.527	−	137.527i	0.176997	−	0.176997i
$778$	−341.286	+	375.652i	−0.438671	+	0.482843i
$779$	59.4541	−	59.4541i	0.0763210	−	0.0763210i
$780$		0			0
$781$	−700.583	+	700.583i	−0.897033	+	0.897033i
$782$	−8.84659	−	184.557i	−0.0113128	−	0.236006i
$783$	−866.182	+	866.182i	−1.10623	+	1.10623i
$784$	85.9215	+	442.964i	0.109594	+	0.565006i
$785$		0			0
$786$	505.180	+	458.964i	0.642723	+	0.583924i
$787$	785.121			0.997612			0.498806	−	0.866714i	$-0.333772\pi$
$787$	785.121			0.997612			0.498806	+	0.866714i	$0.333772\pi$
$788$	38.0350	+	395.831i	0.0482678	+	0.502323i
$789$	738.196	−	738.196i	0.935610	−	0.935610i
$790$		0			0
$791$			123.680i			0.156359i
$792$	1074.15	+	802.603i	1.35625	+	1.01339i
$793$	−437.884	−	437.884i	−0.552186	−	0.552186i
$794$	−641.731	+	30.7609i	−0.808226	+	0.0387416i
$795$		0			0
$796$	1055.81	−	101.452i	1.32639	−	0.127452i
$797$	58.6173			0.0735474			0.0367737	−	0.999324i	$-0.488292\pi$
$797$	58.6173			0.0735474			0.0367737	+	0.999324i	$0.488292\pi$
$798$	−2.47195	−	51.5696i	−0.00309768	−	0.0646236i
$799$		−	131.305i		−	0.164337i
$800$		0			0
$801$	−2026.22			−2.52961
$802$	1297.32	−	62.1859i	1.61760	−	0.0775385i
$803$		−	656.122i		−	0.817088i
$804$	26.5458	+	276.263i	0.0330172	+	0.343610i
$805$		0			0
$806$	−54.3644	−	1134.15i	−0.0674497	−	1.40713i
$807$	836.488	−	836.488i	1.03654	−	1.03654i
$808$	200.209	+	149.596i	0.247784	+	0.185144i
$809$	−361.896			−0.447337			−0.223669	−	0.974665i	$-0.571803\pi$
$809$	−361.896			−0.447337			−0.223669	+	0.974665i	$0.571803\pi$
$810$		0			0
$811$	88.5414	+	88.5414i	0.109176	+	0.109176i	0.759584	−	0.650409i	$-0.225402\pi$
$811$	88.5414	+	88.5414i	0.109176	+	0.109176i	−0.650409	+	0.759584i	$0.725402\pi$
$812$	−697.407	+	67.0133i	−0.858876	+	0.0825287i
$813$			1928.43i			2.37200i
$814$	−125.832	+	138.503i	−0.154585	+	0.170151i
$815$		0			0
$816$	235.410	−	348.712i	0.288493	−	0.427343i
$817$	−14.2074	−	14.2074i	−0.0173898	−	0.0173898i
$818$	−40.6443	+	1.94825i	−0.0496873	+	0.00238172i
$819$	−1106.85	−	1106.85i	−1.35147	−	1.35147i
$820$		0			0
$821$	−74.7330	−	74.7330i	−0.0910268	−	0.0910268i	0.660127	−	0.751154i	$-0.270502\pi$
$821$	−74.7330	−	74.7330i	−0.0910268	−	0.0910268i	−0.751154	+	0.660127i	$0.770502\pi$
$822$	1202.80	+	1092.76i	1.46326	+	1.32940i
$823$	−481.562	−	481.562i	−0.585131	−	0.585131i	0.351178	−	0.936309i	$-0.385781\pi$
$823$	−481.562	−	481.562i	−0.585131	−	0.585131i	−0.936309	+	0.351178i	$0.885781\pi$
$824$	−45.9094	−	34.3034i	−0.0557153	−	0.0416304i
$825$		0			0
$826$	44.8694	+	936.063i	0.0543213	+	1.13325i
$827$			1232.64i			1.49049i	0.666789	+	0.745246i	$0.267668\pi$
$827$			1232.64i			1.49049i	−0.666789	+	0.745246i	$0.732332\pi$
$828$	828.292	+	683.067i	1.00035	+	0.824960i
$829$	−503.806	−	503.806i	−0.607727	−	0.607727i	0.334624	−	0.942352i	$-0.391391\pi$
$829$	−503.806	−	503.806i	−0.607727	−	0.607727i	−0.942352	+	0.334624i	$0.891391\pi$
$830$		0			0
$831$	−1437.27			−1.72957
$832$	−402.994	−	1363.46i	−0.484368	−	1.63877i
$833$	−106.048	+	106.048i	−0.127308	+	0.127308i
$834$	264.977	+	240.736i	0.317718	+	0.288652i
$835$		0			0
$836$	4.75123	+	49.4461i	0.00568329	+	0.0591460i
$837$			815.096i			0.973830i
$838$	427.555	+	388.441i	0.510209	+	0.463534i
$839$	949.352			1.13153			0.565764	−	0.824567i	$-0.308581\pi$
$839$	949.352			1.13153			0.565764	+	0.824567i	$0.308581\pi$
$840$		0			0
$841$			634.054i			0.753929i
$842$	−155.662	−	141.422i	−0.184872	−	0.167959i
$843$	1163.94			1.38071
$844$	−815.450	+	988.821i	−0.966174	+	1.17159i
$845$		0			0
$846$	564.706	+	513.044i	0.667501	+	0.606436i
$847$	10.6821	+	10.6821i	0.0126116	+	0.0126116i
$848$	460.708	−	89.3631i	0.543287	−	0.105381i
$849$			2317.47i			2.72964i
$850$		0			0
$851$	−105.945	+	105.945i	−0.124494	+	0.124494i
$852$	−1798.11	+	172.779i	−2.11045	+	0.202792i
$853$	331.721			0.388887			0.194444	−	0.980914i	$-0.437710\pi$
$853$	331.721			0.388887			0.194444	+	0.980914i	$0.437710\pi$
$854$	12.1736	+	253.965i	0.0142548	+	0.297383i
$855$		0			0
$856$	−62.6561	−	433.037i	−0.0731964	−	0.505885i
$857$	−207.103	+	207.103i	−0.241660	+	0.241660i	−0.817537	−	0.575876i	$-0.804661\pi$
$857$	−207.103	+	207.103i	−0.241660	+	0.241660i	0.575876	+	0.817537i	$0.304661\pi$
$858$	1764.03	+	1602.65i	2.05598	+	1.86790i
$859$	−315.715	+	315.715i	−0.367538	+	0.367538i	−0.866579	−	0.499041i	$-0.833686\pi$
$859$	−315.715	+	315.715i	−0.367538	+	0.367538i	0.499041	+	0.866579i	$0.333686\pi$
$860$		0			0
$861$	−1171.22	+	1171.22i	−1.36030	+	1.36030i
$862$	61.8285	−	2.96370i	0.0717268	−	0.00343817i
$863$	−278.969	+	278.969i	−0.323255	+	0.323255i	−0.850014	−	0.526760i	$-0.823407\pi$
$863$	−278.969	+	278.969i	−0.323255	+	0.323255i	0.526760	+	0.850014i	$0.323407\pi$
$864$	242.099	+	991.505i	0.280208	+	1.14758i
$865$		0			0
$866$	131.081	−	144.280i	0.151364	−	0.166606i
$867$	−1289.18			−1.48695
$868$	−296.607	+	359.668i	−0.341713	+	0.414364i
$869$	358.318	−	358.318i	0.412334	−	0.412334i
$870$		0			0
$871$			311.720i			0.357888i
$872$	−742.212	−	554.579i	−0.851160	−	0.635985i
$873$	−471.794	−	471.794i	−0.540428	−	0.540428i
$874$	1.90428	+	39.7270i	0.00217881	+	0.0454543i
$875$		0			0
$876$	761.090	−	922.903i	0.868824	−	1.05354i
$877$	1338.50			1.52623			0.763114	−	0.646263i	$-0.223669\pi$
$877$	1338.50			1.52623			0.763114	+	0.646263i	$0.223669\pi$
$878$	−1508.28	+	72.2981i	−1.71786	+	0.0823440i
$879$			889.277i			1.01169i
$880$		0			0
$881$	−138.825			−0.157576			−0.0787881	−	0.996891i	$-0.525105\pi$
$881$	−138.825			−0.157576			−0.0787881	+	0.996891i	$0.525105\pi$
$882$	−41.7236	−	870.436i	−0.0473057	−	0.986889i
$883$			212.516i			0.240675i	0.992733	+	0.120337i	$0.0383976\pi$
$883$			212.516i			0.240675i	−0.992733	+	0.120337i	$0.961602\pi$
$884$	300.657	−	364.579i	0.340109	−	0.412419i
$885$		0			0
$886$	219.304	−	10.5122i	0.247522	−	0.0118648i
$887$	−368.959	+	368.959i	−0.415963	+	0.415963i	−0.883810	−	0.467847i	$-0.845030\pi$
$887$	−368.959	+	368.959i	−0.415963	+	0.415963i	0.467847	+	0.883810i	$0.345030\pi$
$888$	−337.656	+	48.8554i	−0.380244	+	0.0550174i
$889$	645.095			0.725641
$890$		0			0
$891$	−143.129	−	143.129i	−0.160639	−	0.160639i
$892$	859.773	−	1042.57i	0.963872	−	1.16880i
$893$			28.2643i			0.0316509i
$894$	120.383	+	109.370i	0.134657	+	0.122338i
$895$		0			0
$896$	−253.973	+	525.608i	−0.283452	+	0.586616i
$897$	1349.36	+	1349.36i	1.50430	+	1.50430i
$898$	47.0383	+	981.309i	0.0523811	+	1.09277i
$899$	694.029	+	694.029i	0.772001	+	0.772001i
$900$		0			0
$901$	110.295	+	110.295i	0.122414	+	0.122414i
$902$	1071.63	−	1179.53i	1.18806	−	1.30769i
$903$	279.881	+	279.881i	0.309946	+	0.309946i
$904$	129.862	−	173.798i	0.143652	−	0.192255i
$905$		0			0
$906$	−839.512	+	40.2413i	−0.926614	+	0.0444165i
$907$			783.206i			0.863513i	0.901990	+	0.431756i	$0.142106\pi$
$907$			783.206i			0.863513i	−0.901990	+	0.431756i	$0.857894\pi$
$908$	1763.84	−	169.486i	1.94255	−	0.186658i
$909$	−341.304	−	341.304i	−0.375472	−	0.375472i
$910$		0			0
$911$	−1463.16			−1.60610			−0.803052	−	0.595909i	$-0.796792\pi$
$911$	−1463.16			−1.60610			−0.803052	+	0.595909i	$0.796792\pi$
$912$	−50.6735	+	75.0624i	−0.0555630	+	0.0823052i
$913$	636.253	−	636.253i	0.696882	−	0.696882i
$914$	−891.907	+	981.718i	−0.975828	+	1.07409i
$915$		0			0
$916$	−787.343	+	954.738i	−0.859545	+	1.04229i
$917$		−	314.754i		−	0.343244i
$918$	−228.113	+	251.083i	−0.248489	+	0.273511i
$919$	−1217.73			−1.32506			−0.662529	−	0.749036i	$-0.730517\pi$
$919$	−1217.73			−1.32506			−0.662529	+	0.749036i	$0.730517\pi$
$920$		0			0
$921$			544.445i			0.591146i
$922$	−149.670	+	164.742i	−0.162332	+	0.178678i
$923$	−2028.89			−2.19815
$924$	−93.5974	−	974.069i	−0.101296	−	1.05419i
$925$		0			0
$926$	727.156	−	800.378i	0.785266	−	0.864339i
$927$	78.2635	+	78.2635i	0.0844266	+	0.0844266i
$928$	1050.38	+	638.095i	1.13187	+	0.687603i
$929$		−	169.265i		−	0.182201i	−0.995842	−	0.0911004i	$-0.970962\pi$
$929$		−	169.265i		−	0.182201i	0.995842	−	0.0911004i	$-0.0290384\pi$
$930$		0			0
$931$	22.8274	−	22.8274i	0.0245192	−	0.0245192i
$932$	−794.286	−	655.023i	−0.852238	−	0.702815i
$933$	265.833			0.284923
$934$	748.330	−	35.8706i	0.801209	−	0.0384053i
$935$		0			0
$936$	393.201	+	2717.54i	0.420086	+	2.90336i
$937$	−457.486	+	457.486i	−0.488245	+	0.488245i	−0.907752	−	0.419507i	$-0.862203\pi$
$937$	−457.486	+	457.486i	−0.488245	+	0.488245i	0.419507	+	0.907752i	$0.362203\pi$
$938$	86.0633	−	94.7294i	0.0917519	−	0.100991i
$939$	820.653	−	820.653i	0.873965	−	0.873965i
$940$		0			0
$941$	−206.539	+	206.539i	−0.219489	+	0.219489i	−0.808283	−	0.588794i	$-0.799603\pi$
$941$	−206.539	+	206.539i	−0.219489	+	0.219489i	0.588794	+	0.808283i	$0.299603\pi$
$942$	60.7258	+	1266.86i	0.0644648	+	1.34486i
$943$	902.259	−	902.259i	0.956797	−	0.956797i
$944$	919.796	−	1362.49i	0.974361	−	1.44332i
$945$		0			0
$946$	−281.867	−	256.081i	−0.297957	−	0.270699i
$947$	−952.719			−1.00604			−0.503019	−	0.864275i	$-0.667778\pi$
$947$	−952.719			−1.00604			−0.503019	+	0.864275i	$0.667778\pi$
$948$	919.655	−	88.3689i	0.970100	−	0.0932161i
$949$	950.065	−	950.065i	1.00112	−	1.00112i
$950$		0			0
$951$		−	199.923i		−	0.210224i
$952$	−192.024	+	27.7839i	−0.201706	+	0.0291848i
$953$	−830.106	−	830.106i	−0.871045	−	0.871045i	0.121542	−	0.992586i	$-0.461216\pi$
$953$	−830.106	−	830.106i	−0.871045	−	0.871045i	−0.992586	+	0.121542i	$0.961216\pi$
$954$	−905.302	+	43.3949i	−0.948954	+	0.0454873i
$955$		0			0
$956$	−15.8068	−	164.502i	−0.0165344	−	0.172073i
$957$	−2060.21			−2.15278
$958$	43.1326	+	899.830i	0.0450236	+	0.939280i
$959$		−	749.409i		−	0.781448i
$960$		0			0
$961$	−307.904			−0.320400
$962$	−382.757	+	18.3471i	−0.397876	+	0.0190719i
$963$			845.027i			0.877494i
$964$	890.513	−	85.5686i	0.923768	−	0.0887641i
$965$		0			0
$966$	−37.5136	−	782.607i	−0.0388340	−	0.810152i
$967$	34.0691	−	34.0691i	0.0352318	−	0.0352318i	−0.689271	−	0.724503i	$-0.742069\pi$
$967$	34.0691	−	34.0691i	0.0352318	−	0.0352318i	0.724503	+	0.689271i	$0.242069\pi$
$968$	−3.79473	−	26.2266i	−0.00392017	−	0.0270936i
$969$	−30.1017			−0.0310647
$970$		0			0
$971$	−84.7430	−	84.7430i	−0.0872739	−	0.0872739i	0.662122	−	0.749396i	$-0.269656\pi$
$971$	−84.7430	−	84.7430i	−0.0872739	−	0.0872739i	−0.749396	+	0.662122i	$0.769656\pi$
$972$	74.5264	+	775.596i	0.0766732	+	0.797938i
$973$		−	165.095i		−	0.169676i
$974$	−555.903	+	611.880i	−0.570742	+	0.628213i
$975$		0			0
$976$	249.552	−	369.660i	0.255689	−	0.378750i
$977$	−28.0540	−	28.0540i	−0.0287145	−	0.0287145i	0.692604	−	0.721318i	$-0.256463\pi$
$977$	−28.0540	−	28.0540i	−0.0287145	−	0.0287145i	−0.721318	+	0.692604i	$0.756463\pi$
$978$	810.118	−	38.8324i	0.828342	−	0.0397059i
$979$	−1006.01	−	1006.01i	−1.02759	−	1.02759i
$980$		0			0
$981$	1265.28	+	1265.28i	1.28978	+	1.28978i
$982$	909.351	+	826.161i	0.926020	+	0.841304i
$983$	359.158	+	359.158i	0.365370	+	0.365370i	0.865785	−	0.500416i	$-0.166819\pi$
$983$	359.158	+	359.158i	0.365370	+	0.365370i	−0.500416	+	0.865785i	$0.666819\pi$
$984$	2875.59	−	416.069i	2.92235	−	0.422834i
$985$		0			0
$986$	19.5582	+	408.021i	0.0198359	+	0.413814i
$987$		−	556.795i		−	0.564129i
$988$	−64.7182	+	78.4778i	−0.0655043	+	0.0794310i
$989$	−215.608	−	215.608i	−0.218006	−	0.218006i
$990$		0			0
$991$	301.699			0.304439			0.152219	−	0.988347i	$-0.451358\pi$
$991$	301.699			0.304439			0.152219	+	0.988347i	$0.451358\pi$
$992$	794.444	−	193.982i	0.800851	−	0.195547i
$993$	−533.755	+	533.755i	−0.537517	+	0.537517i
$994$	616.564	+	560.159i	0.620286	+	0.563540i
$995$		0			0
$996$	1633.00	−	156.913i	1.63956	−	0.157544i
$997$		−	701.351i		−	0.703461i	−0.936101	−	0.351731i	$-0.885593\pi$
$997$		−	701.351i		−	0.703461i	0.936101	−	0.351731i	$-0.114407\pi$
$998$	−75.4936	−	68.5872i	−0.0756449	−	0.0687246i
$999$	275.082			0.275357

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.i.b.357.22		44
5.2	odd	4		80.3.t.a.53.12	yes	44
5.3	odd	4		400.3.t.b.293.11		44
5.4	even	2		80.3.i.a.37.1	yes	44
16.13	even	4		400.3.t.b.157.11		44
20.7	even	4		320.3.t.a.113.20		44
20.19	odd	2		320.3.i.a.177.3		44
40.19	odd	2		640.3.i.a.97.20		44
40.27	even	4		640.3.t.a.353.3		44
40.29	even	2		640.3.i.b.97.3		44
40.37	odd	4		640.3.t.b.353.20		44
80.13	odd	4	inner	400.3.i.b.93.22		44
80.19	odd	4		320.3.t.a.17.20		44
80.27	even	4		640.3.i.a.33.3		44
80.29	even	4		80.3.t.a.77.12	yes	44
80.37	odd	4		640.3.i.b.33.20		44
80.59	odd	4		640.3.t.a.417.3		44
80.67	even	4		320.3.i.a.273.20		44
80.69	even	4		640.3.t.b.417.20		44
80.77	odd	4		80.3.i.a.13.1	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.1	✓	44	80.77	odd	4
80.3.i.a.37.1	yes	44	5.4	even	2
80.3.t.a.53.12	yes	44	5.2	odd	4
80.3.t.a.77.12	yes	44	80.29	even	4
320.3.i.a.177.3		44	20.19	odd	2
320.3.i.a.273.20		44	80.67	even	4
320.3.t.a.17.20		44	80.19	odd	4
320.3.t.a.113.20		44	20.7	even	4
400.3.i.b.93.22		44	80.13	odd	4	inner
400.3.i.b.357.22		44	1.1	even	1	trivial
400.3.t.b.157.11		44	16.13	even	4
400.3.t.b.293.11		44	5.3	odd	4
640.3.i.a.33.3		44	80.27	even	4
640.3.i.a.97.20		44	40.19	odd	2
640.3.i.b.33.20		44	80.37	odd	4
640.3.i.b.97.3		44	40.29	even	2
640.3.t.a.353.3		44	40.27	even	4
640.3.t.a.417.3		44	80.59	odd	4
640.3.t.b.353.20		44	40.37	odd	4
640.3.t.b.417.20		44	80.69	even	4

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.99771 - 0.0957584i) q^{2} -4.94472i q^{3} +(3.98166 - 0.382594i) q^{4} +(-0.473499 - 9.87810i) q^{6} +(-3.22480 + 3.22480i) q^{7} +(7.91755 - 1.14559i) q^{8} -15.4503 q^{9} +O(q^{10})\)	\(q+(1.99771 - 0.0957584i) q^{2} -4.94472i q^{3} +(3.98166 - 0.382594i) q^{4} +(-0.473499 - 9.87810i) q^{6} +(-3.22480 + 3.22480i) q^{7} +(7.91755 - 1.14559i) q^{8} -15.4503 q^{9} +(-7.67097 - 7.67097i) q^{11} +(-1.89182 - 19.6882i) q^{12} -22.2152i q^{13} +(-6.13341 + 6.75101i) q^{14} +(15.7072 - 3.04672i) q^{16} +(3.76038 + 3.76038i) q^{17} +(-30.8651 + 1.47949i) q^{18} +(-0.809445 - 0.809445i) q^{19} +(15.9458 + 15.9458i) q^{21} +(-16.0589 - 14.5898i) q^{22} +(-12.2839 - 12.2839i) q^{23} +(-5.66462 - 39.1501i) q^{24} +(-2.12729 - 44.3794i) q^{26} +31.8948i q^{27} +(-11.6063 + 14.0739i) q^{28} +(27.1574 + 27.1574i) q^{29} +25.5557 q^{31} +(31.0867 - 7.59056i) q^{32} +(-37.9308 + 37.9308i) q^{33} +(7.87223 + 7.15205i) q^{34} +(-61.5178 + 5.91119i) q^{36} -8.62466i q^{37} +(-1.69454 - 1.53952i) q^{38} -109.848 q^{39} +73.4504i q^{41} +(33.3819 + 30.3280i) q^{42} +17.5521 q^{43} +(-33.4781 - 27.6083i) q^{44} +(-25.7160 - 23.3634i) q^{46} +(-17.4590 - 17.4590i) q^{47} +(-15.0652 - 77.6680i) q^{48} +28.2013i q^{49} +(18.5940 - 18.5940i) q^{51} +(-8.49939 - 88.4532i) q^{52} +29.3309 q^{53} +(3.05420 + 63.7165i) q^{54} +(-21.8382 + 29.2268i) q^{56} +(-4.00248 + 4.00248i) q^{57} +(56.8532 + 51.6520i) q^{58} +(72.6508 - 72.6508i) q^{59} +(19.7110 - 19.7110i) q^{61} +(51.0529 - 2.44718i) q^{62} +(49.8241 - 49.8241i) q^{63} +(61.3753 - 18.1405i) q^{64} +(-72.1424 + 79.4068i) q^{66} -14.0319 q^{67} +(16.4113 + 13.5339i) q^{68} +(-60.7406 + 60.7406i) q^{69} -91.3292i q^{71} +(-122.328 + 17.6997i) q^{72} +(42.7665 + 42.7665i) q^{73} +(-0.825884 - 17.2295i) q^{74} +(-3.53262 - 2.91325i) q^{76} +49.4747 q^{77} +(-219.444 + 10.5188i) q^{78} +46.7110i q^{79} +18.6585 q^{81} +(7.03350 + 146.732i) q^{82} +82.9430i q^{83} +(69.5913 + 57.3898i) q^{84} +(35.0639 - 1.68076i) q^{86} +(134.286 - 134.286i) q^{87} +(-69.5231 - 51.9475i) q^{88} +131.145 q^{89} +(71.6395 + 71.6395i) q^{91} +(-53.6102 - 44.2106i) q^{92} -126.366i q^{93} +(-36.5499 - 33.2062i) q^{94} +(-37.5332 - 153.715i) q^{96} +(30.5363 + 30.5363i) q^{97} +(2.70051 + 56.3379i) q^{98} +(118.519 + 118.519i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} + 4 q^{4} - 4 q^{6} + 8 q^{8} - 108 q^{9}+O(q^{10}) \) 44 * q + 2 * q^2 + 4 * q^4 - 4 * q^6 + 8 * q^8 - 108 * q^9	\( 44 q + 2 q^{2} + 4 q^{4} - 4 q^{6} + 8 q^{8} - 108 q^{9} - 4 q^{11} + 8 q^{12} + 24 q^{16} + 4 q^{17} - 22 q^{18} + 32 q^{19} - 4 q^{21} - 92 q^{22} + 36 q^{24} - 52 q^{26} - 36 q^{28} - 8 q^{31} + 132 q^{32} + 4 q^{33} - 88 q^{34} - 116 q^{36} + 216 q^{38} + 72 q^{39} - 16 q^{42} - 124 q^{43} - 168 q^{44} + 108 q^{46} + 4 q^{47} - 340 q^{48} - 100 q^{51} - 48 q^{52} + 4 q^{53} + 228 q^{54} - 172 q^{56} - 36 q^{57} - 16 q^{58} + 64 q^{59} - 36 q^{61} + 356 q^{62} + 200 q^{63} - 176 q^{64} + 276 q^{66} + 292 q^{67} + 72 q^{68} - 60 q^{69} - 448 q^{72} - 48 q^{73} + 284 q^{74} + 252 q^{76} - 192 q^{77} - 620 q^{78} + 100 q^{81} + 240 q^{82} + 288 q^{84} + 20 q^{86} - 36 q^{87} + 624 q^{88} + 188 q^{91} + 412 q^{92} - 340 q^{94} - 24 q^{96} + 4 q^{97} + 78 q^{98} - 92 q^{99}+O(q^{100}) \) 44 * q + 2 * q^2 + 4 * q^4 - 4 * q^6 + 8 * q^8 - 108 * q^9 - 4 * q^11 + 8 * q^12 + 24 * q^16 + 4 * q^17 - 22 * q^18 + 32 * q^19 - 4 * q^21 - 92 * q^22 + 36 * q^24 - 52 * q^26 - 36 * q^28 - 8 * q^31 + 132 * q^32 + 4 * q^33 - 88 * q^34 - 116 * q^36 + 216 * q^38 + 72 * q^39 - 16 * q^42 - 124 * q^43 - 168 * q^44 + 108 * q^46 + 4 * q^47 - 340 * q^48 - 100 * q^51 - 48 * q^52 + 4 * q^53 + 228 * q^54 - 172 * q^56 - 36 * q^57 - 16 * q^58 + 64 * q^59 - 36 * q^61 + 356 * q^62 + 200 * q^63 - 176 * q^64 + 276 * q^66 + 292 * q^67 + 72 * q^68 - 60 * q^69 - 448 * q^72 - 48 * q^73 + 284 * q^74 + 252 * q^76 - 192 * q^77 - 620 * q^78 + 100 * q^81 + 240 * q^82 + 288 * q^84 + 20 * q^86 - 36 * q^87 + 624 * q^88 + 188 * q^91 + 412 * q^92 - 340 * q^94 - 24 * q^96 + 4 * q^97 + 78 * q^98 - 92 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more