LMFDB - Embedded newform 225.3.j.e.101.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,3,Mod(101,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(225, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("225.101"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	225.j (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.13080594811$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 3 x^{18} - 19 x^{16} - 66 x^{14} + 109 x^{12} + 813 x^{10} + 981 x^{8} - 5346 x^{6} + \cdots + 59049 $ x^20 + 3x^18 - 19x^16 - 66x^14 + 109x^12 + 813x^10 + 981x^8 - 5346x^6 - 13851x^4 + 19683*x^2 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{10} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.10
Root			$0.961330 - 1.44078i$ of defining polynomial
Character	$\chi$	$=$	225.101
Dual form			225.3.j.e.176.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.19328 + 1.84364i) q^{2} +(2.49550 - 1.66507i) q^{3} +(4.79800 + 8.31039i) q^{4} +(11.0386 - 0.716233i) q^{6} +(-1.28370 + 2.22343i) q^{7} +20.6340i q^{8} +(3.45506 - 8.31039i) q^{9} +(-8.51311 - 4.91505i) q^{11} +(25.8108 + 12.7496i) q^{12} +(-6.03166 - 10.4471i) q^{13} +(-8.19840 + 4.73335i) q^{14} +(-18.8497 + 32.6486i) q^{16} +4.28451i q^{17} +(26.3543 - 20.1675i) q^{18} -7.16698 q^{19} +(0.498702 + 7.68602i) q^{21} +(-18.1231 - 31.3902i) q^{22} +(-0.442140 + 0.255270i) q^{23} +(34.3572 + 51.4923i) q^{24} -44.4808i q^{26} +(-5.21528 - 26.4915i) q^{27} -24.6367 q^{28} +(26.4589 + 15.2761i) q^{29} +(9.61361 + 16.6513i) q^{31} +(-48.9060 + 28.2359i) q^{32} +(-29.4284 + 1.90944i) q^{33} +(-7.89910 + 13.6816i) q^{34} +(85.6399 - 11.1604i) q^{36} -1.31851 q^{37} +(-22.8862 - 13.2133i) q^{38} +(-32.4473 - 16.0277i) q^{39} +(-29.9735 + 17.3052i) q^{41} +(-12.5778 + 25.4630i) q^{42} +(25.9734 - 44.9872i) q^{43} -94.3297i q^{44} -1.88250 q^{46} +(-44.1078 - 25.4656i) q^{47} +(7.32289 + 112.861i) q^{48} +(21.2042 + 36.7268i) q^{49} +(7.13403 + 10.6920i) q^{51} +(57.8799 - 100.251i) q^{52} -86.6349i q^{53} +(32.1870 - 94.2098i) q^{54} +(-45.8783 - 26.4879i) q^{56} +(-17.8852 + 11.9336i) q^{57} +(56.3270 + 97.5613i) q^{58} +(-91.7656 + 52.9809i) q^{59} +(-15.6600 + 27.1239i) q^{61} +70.8961i q^{62} +(14.0423 + 18.3501i) q^{63} -57.4297 q^{64} +(-97.4933 - 48.1580i) q^{66} +(39.0271 + 67.5968i) q^{67} +(-35.6060 + 20.5571i) q^{68} +(-0.678318 + 1.37322i) q^{69} +72.6762i q^{71} +(171.477 + 71.2919i) q^{72} -30.3097 q^{73} +(-4.21037 - 2.43086i) q^{74} +(-34.3872 - 59.5604i) q^{76} +(21.8565 - 12.6189i) q^{77} +(-74.0638 - 111.002i) q^{78} +(57.6398 - 99.8350i) q^{79} +(-57.1251 - 57.4258i) q^{81} -127.618 q^{82} +(51.9734 + 30.0069i) q^{83} +(-61.4810 + 41.0220i) q^{84} +(165.880 - 95.7710i) q^{86} +(91.4640 - 5.93457i) q^{87} +(101.417 - 175.660i) q^{88} +71.2992i q^{89} +30.9713 q^{91} +(-4.24278 - 2.44957i) q^{92} +(51.7163 + 25.5459i) q^{93} +(-93.8989 - 162.638i) q^{94} +(-75.0302 + 151.895i) q^{96} +(63.9819 - 110.820i) q^{97} +156.372i q^{98} +(-70.2593 + 53.7655i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 18 q^{4} + 12 q^{6} + 18 q^{9} - 24 q^{11} - 30 q^{14} - 26 q^{16} + 8 q^{19} - 96 q^{21} + 102 q^{24} + 114 q^{29} + 28 q^{31} + 4 q^{34} + 432 q^{36} - 240 q^{39} + 102 q^{41} + 116 q^{46} + 40 q^{49}+ \cdots + 468 q^{99}+O(q^{100}) $ 20 * q + 18 * q^4 + 12 * q^6 + 18 * q^9 - 24 * q^11 - 30 * q^14 - 26 * q^16 + 8 * q^19 - 96 * q^21 + 102 * q^24 + 114 * q^29 + 28 * q^31 + 4 * q^34 + 432 * q^36 - 240 * q^39 + 102 * q^41 + 116 * q^46 + 40 * q^49 - 156 * q^51 + 270 * q^54 - 618 * q^56 - 120 * q^59 - 50 * q^61 - 140 * q^64 - 768 * q^66 - 162 * q^69 - 504 * q^74 - 96 * q^76 + 128 * q^79 + 846 * q^81 - 450 * q^84 + 1488 * q^86 - 288 * q^91 - 218 * q^94 - 474 * q^96 + 468 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	3.19328	+	1.84364i	1.59664	+	0.921819i	0.992129	+	0.125221i	$0.0399639\pi$
$2$	3.19328	+	1.84364i	1.59664	+	0.921819i	0.604509	+	0.796599i	$0.293369\pi$
$3$	2.49550	−	1.66507i	0.831834	−	0.555024i
$3$	2.49550	−	1.66507i	0.831834	−	0.555024i
$4$	4.79800	+	8.31039i	1.19950	+	2.07760i
$5$		0			0
$5$		0			0
$6$	11.0386	−	0.716233i	1.83977	−	0.119372i
$7$	−1.28370	+	2.22343i	−0.183385	+	0.317633i	−0.943031	−	0.332704i	$-0.892039\pi$
$7$	−1.28370	+	2.22343i	−0.183385	+	0.317633i	0.759646	+	0.650337i	$0.225372\pi$
$8$			20.6340i			2.57925i
$9$	3.45506	−	8.31039i	0.383896	−	0.923376i
$10$		0			0
$11$	−8.51311	−	4.91505i	−0.773919	−	0.446823i	0.0603516	−	0.998177i	$-0.480778\pi$
$11$	−8.51311	−	4.91505i	−0.773919	−	0.446823i	−0.834271	+	0.551355i	$0.814111\pi$
$12$	25.8108	+	12.7496i	2.15090	+	1.06246i
$13$	−6.03166	−	10.4471i	−0.463974	−	0.803626i	0.535181	−	0.844738i	$-0.320243\pi$
$13$	−6.03166	−	10.4471i	−0.463974	−	0.803626i	−0.999155	+	0.0411114i	$0.986910\pi$
$14$	−8.19840	+	4.73335i	−0.585600	+	0.338096i
$15$		0			0
$16$	−18.8497	+	32.6486i	−1.17810	+	2.04054i
$17$			4.28451i			0.252030i	0.992028	+	0.126015i	$0.0402188\pi$
$17$			4.28451i			0.252030i	−0.992028	+	0.126015i	$0.959781\pi$
$18$	26.3543	−	20.1675i	1.46413	−	1.12041i
$19$	−7.16698			−0.377210			−0.188605	−	0.982053i	$-0.560397\pi$
$19$	−7.16698			−0.377210			−0.188605	+	0.982053i	$0.560397\pi$
$20$		0			0
$21$	0.498702	+	7.68602i	0.0237477	+	0.366001i
$22$	−18.1231	−	31.3902i	−0.823779	−	1.42683i
$23$	−0.442140	+	0.255270i	−0.0192235	+	0.0110987i	−0.509581	−	0.860423i	$-0.670200\pi$
$23$	−0.442140	+	0.255270i	−0.0192235	+	0.0110987i	0.490357	+	0.871521i	$0.336866\pi$
$24$	34.3572	+	51.4923i	1.43155	+	2.14551i
$25$		0			0
$26$		−	44.4808i		−	1.71080i
$27$	−5.21528	−	26.4915i	−0.193159	−	0.981168i
$28$	−24.6367			−0.879884
$29$	26.4589	+	15.2761i	0.912376	+	0.526760i	0.881195	−	0.472753i	$-0.156740\pi$
$29$	26.4589	+	15.2761i	0.912376	+	0.526760i	0.0311810	+	0.999514i	$0.490073\pi$
$30$		0			0
$31$	9.61361	+	16.6513i	0.310116	+	0.537137i	0.978387	−	0.206781i	$-0.0662986\pi$
$31$	9.61361	+	16.6513i	0.310116	+	0.537137i	−0.668271	+	0.743918i	$0.732965\pi$
$32$	−48.9060	+	28.2359i	−1.52831	+	0.882372i
$33$	−29.4284	+	1.90944i	−0.891770	+	0.0578618i
$34$	−7.89910	+	13.6816i	−0.232326	+	0.402401i
$35$		0			0
$36$	85.6399	−	11.1604i	2.37889	−	0.310010i
$37$	−1.31851			−0.0356355			−0.0178177	−	0.999841i	$-0.505672\pi$
$37$	−1.31851			−0.0356355			−0.0178177	+	0.999841i	$0.505672\pi$
$38$	−22.8862	−	13.2133i	−0.602267	−	0.347719i
$39$	−32.4473	−	16.0277i	−0.831981	−	0.410967i
$40$		0			0
$41$	−29.9735	+	17.3052i	−0.731061	+	0.422078i	−0.818810	−	0.574064i	$-0.805366\pi$
$41$	−29.9735	+	17.3052i	−0.731061	+	0.422078i	0.0877493	+	0.996143i	$0.472033\pi$
$42$	−12.5778	+	25.4630i	−0.299470	+	0.606262i
$43$	25.9734	−	44.9872i	0.604032	−	1.04621i	−0.388172	−	0.921587i	$-0.626893\pi$
$43$	25.9734	−	44.9872i	0.604032	−	1.04621i	0.992204	−	0.124627i	$-0.0397733\pi$
$44$		−	94.3297i		−	2.14386i
$45$		0			0
$46$	−1.88250			−0.0409239
$47$	−44.1078	−	25.4656i	−0.938463	−	0.541822i	−0.0489851	−	0.998800i	$-0.515599\pi$
$47$	−44.1078	−	25.4656i	−0.938463	−	0.541822i	−0.889478	+	0.456977i	$0.848932\pi$
$48$	7.32289	+	112.861i	0.152560	+	2.35126i
$49$	21.2042	+	36.7268i	0.432740	+	0.749527i
$50$		0			0
$51$	7.13403	+	10.6920i	0.139883	+	0.209647i
$52$	57.8799	−	100.251i	1.11307	−	1.92790i
$53$		−	86.6349i		−	1.63462i	−0.576197	−	0.817311i	$-0.695464\pi$
$53$		−	86.6349i		−	1.63462i	0.576197	−	0.817311i	$-0.304536\pi$
$54$	32.1870	−	94.2098i	0.596055	−	1.74463i
$55$		0			0
$56$	−45.8783	−	26.4879i	−0.819255	−	0.472997i
$57$	−17.8852	+	11.9336i	−0.313776	+	0.209361i
$58$	56.3270	+	97.5613i	0.971156	+	1.68209i
$59$	−91.7656	+	52.9809i	−1.55535	+	0.897982i	−0.557658	+	0.830071i	$0.688300\pi$
$59$	−91.7656	+	52.9809i	−1.55535	+	0.897982i	−0.997691	+	0.0679111i	$0.978367\pi$
$60$		0			0
$61$	−15.6600	+	27.1239i	−0.256721	+	0.444655i	−0.965362	−	0.260915i	$-0.915976\pi$
$61$	−15.6600	+	27.1239i	−0.256721	+	0.444655i	0.708640	+	0.705570i	$0.249309\pi$
$62$			70.8961i			1.14348i
$63$	14.0423	+	18.3501i	0.222894	+	0.291272i
$64$	−57.4297			−0.897339
$65$		0			0
$66$	−97.4933	−	48.1580i	−1.47717	−	0.729666i
$67$	39.0271	+	67.5968i	0.582493	+	1.00891i	0.995183	+	0.0980363i	$0.0312561\pi$
$67$	39.0271	+	67.5968i	0.582493	+	1.00891i	−0.412689	+	0.910872i	$0.635411\pi$
$68$	−35.6060	+	20.5571i	−0.523617	+	0.302311i
$69$	−0.678318	+	1.37322i	−0.00983070	+	0.0199017i
$70$		0			0
$71$			72.6762i			1.02361i	0.859102	+	0.511804i	$0.171023\pi$
$71$			72.6762i			1.02361i	−0.859102	+	0.511804i	$0.828977\pi$
$72$	171.477	+	71.2919i	2.38162	+	0.990165i
$73$	−30.3097			−0.415201			−0.207601	−	0.978214i	$-0.566565\pi$
$73$	−30.3097			−0.415201			−0.207601	+	0.978214i	$0.566565\pi$
$74$	−4.21037	−	2.43086i	−0.0568969	−	0.0328494i
$75$		0			0
$76$	−34.3872	−	59.5604i	−0.452463	−	0.783690i
$77$	21.8565	−	12.6189i	0.283851	−	0.163881i
$78$	−74.0638	−	111.002i	−0.949535	−	1.42310i
$79$	57.6398	−	99.8350i	0.729617	−	1.26373i	−0.227428	−	0.973795i	$-0.573031\pi$
$79$	57.6398	−	99.8350i	0.729617	−	1.26373i	0.957045	−	0.289940i	$-0.0936352\pi$
$80$		0			0
$81$	−57.1251	−	57.4258i	−0.705248	−	0.708961i
$82$	−127.618			−1.55632
$83$	51.9734	+	30.0069i	0.626186	+	0.361529i	0.779274	−	0.626684i	$-0.215588\pi$
$83$	51.9734	+	30.0069i	0.626186	+	0.361529i	−0.153087	+	0.988213i	$0.548922\pi$
$84$	−61.4810	+	41.0220i	−0.731917	+	0.488357i
$85$		0			0
$86$	165.880	−	95.7710i	1.92884	−	1.11362i
$87$	91.4640	−	5.93457i	1.05131	−	0.0682135i
$88$	101.417	−	175.660i	1.15247	−	1.99613i
$89$			71.2992i			0.801115i	0.916272	+	0.400558i	$0.131184\pi$
$89$			71.2992i			0.801115i	−0.916272	+	0.400558i	$0.868816\pi$
$90$		0			0
$91$	30.9713			0.340344
$92$	−4.24278	−	2.44957i	−0.0461171	−	0.0266257i
$93$	51.7163	+	25.5459i	0.556090	+	0.274687i
$94$	−93.8989	−	162.638i	−0.998924	−	1.73019i
$95$		0			0
$96$	−75.0302	+	151.895i	−0.781565	+	1.58224i
$97$	63.9819	−	110.820i	0.659607	−	1.14247i	−0.321111	−	0.947042i	$-0.604056\pi$
$97$	63.9819	−	110.820i	0.659607	−	1.14247i	0.980717	−	0.195431i	$-0.0626106\pi$
$98$			156.372i			1.59563i
$99$	−70.2593	+	53.7655i	−0.709690	+	0.543085i
$100$		0			0
$101$	74.5445	+	43.0383i	0.738065	+	0.426122i	0.821365	−	0.570403i	$-0.193213\pi$
$101$	74.5445	+	43.0383i	0.738065	+	0.426122i	−0.0833005	+	0.996524i	$0.526546\pi$
$102$	3.06871	+	47.2951i	0.0300854	+	0.463678i
$103$	20.4416	+	35.4060i	0.198463	+	0.343747i	0.948030	−	0.318181i	$-0.103072\pi$
$103$	20.4416	+	35.4060i	0.198463	+	0.343747i	−0.749568	+	0.661928i	$0.769739\pi$
$104$	215.567	−	124.457i	2.07276	−	1.19671i
$105$		0			0
$106$	159.723	−	276.649i	1.50683	−	2.60990i
$107$			1.66026i			0.0155165i	0.999970	+	0.00775823i	$0.00246955\pi$
$107$			1.66026i			0.0155165i	−0.999970	+	0.00775823i	$0.997530\pi$
$108$	195.132	−	170.447i	1.80678	−	1.57822i
$109$	148.641			1.36368			0.681839	−	0.731502i	$-0.261180\pi$
$109$	148.641			1.36368			0.681839	+	0.731502i	$0.261180\pi$
$110$		0			0
$111$	−3.29035	+	2.19542i	−0.0296428	+	0.0197785i
$112$	−48.3946	−	83.8218i	−0.432094	−	0.748409i
$113$	−113.845	+	65.7284i	−1.00748	+	0.581667i	−0.910452	−	0.413615i	$-0.864266\pi$
$113$	−113.845	+	65.7284i	−1.00748	+	0.581667i	−0.0970249	+	0.995282i	$0.530933\pi$
$114$	−79.1136	+	5.13323i	−0.693979	+	0.0450283i
$115$		0			0
$116$			293.178i			2.52740i
$117$	−107.660	+	14.0299i	−0.920167	+	0.119914i
$118$	−390.711			−3.31111
$119$	−9.52631	−	5.50002i	−0.0800531	−	0.0462187i
$120$		0			0
$121$	−12.1846	−	21.1044i	−0.100699	−	0.174416i
$122$	−100.013	+	57.7428i	−0.819782	+	0.473301i
$123$	−45.9845	+	93.0932i	−0.373858	+	0.756856i
$124$	−92.2523	+	159.786i	−0.743970	+	1.28859i
$125$		0			0
$126$	11.0100	+	84.4859i	0.0873806	+	0.670523i
$127$	−101.150			−0.796460			−0.398230	−	0.917286i	$-0.630375\pi$
$127$	−101.150			−0.796460			−0.398230	+	0.917286i	$0.630375\pi$
$128$	12.2351	+	7.06394i	0.0955867	+	0.0551870i
$129$	−10.0904	−	155.513i	−0.0782198	−	1.20553i
$130$		0			0
$131$	−74.3023	+	42.8985i	−0.567193	+	0.327469i	−0.756028	−	0.654540i	$-0.772862\pi$
$131$	−74.3023	+	42.8985i	−0.567193	+	0.327469i	0.188834	+	0.982009i	$0.439529\pi$
$132$	−157.066	−	235.400i	−1.18989	−	1.78333i
$133$	9.20024	−	15.9353i	0.0691747	−	0.119814i
$134$			287.807i			2.14781i
$135$		0			0
$136$	−88.4068			−0.650050
$137$	60.3847	+	34.8631i	0.440764	+	0.254475i	0.703922	−	0.710278i	$-0.251431\pi$
$137$	60.3847	+	34.8631i	0.440764	+	0.254475i	−0.263158	+	0.964753i	$0.584764\pi$
$138$	−4.69778	+	3.13450i	−0.0340419	+	0.0227138i
$139$	69.4587	+	120.306i	0.499703	+	0.865511i	1.00000		0.000342926i	$-0.000109157\pi$
$139$	69.4587	+	120.306i	0.499703	+	0.865511i	−0.500297	+	0.865854i	$0.666776\pi$
$140$		0			0
$141$	−152.473	+	9.89312i	−1.08137	+	0.0701639i
$142$	−133.989	+	232.075i	−0.943582	+	1.63433i
$143$			118.584i			0.829256i
$144$	206.196	+	269.451i	1.43191	+	1.87119i
$145$		0			0
$146$	−96.7872	−	55.8801i	−0.662926	−	0.382740i
$147$	114.068	+	56.3453i	0.775973	+	0.383301i
$148$	−6.32622	−	10.9573i	−0.0427448	−	0.0740361i
$149$	−41.3586	+	23.8784i	−0.277574	+	0.160258i	−0.632325	−	0.774703i	$-0.717899\pi$
$149$	−41.3586	+	23.8784i	−0.277574	+	0.160258i	0.354750	+	0.934961i	$0.384566\pi$
$150$		0			0
$151$	−27.7457	+	48.0569i	−0.183746	+	0.318258i	−0.943153	−	0.332358i	$-0.892156\pi$
$151$	−27.7457	+	48.0569i	−0.183746	+	0.318258i	0.759407	+	0.650616i	$0.225489\pi$
$152$		−	147.884i		−	0.972920i
$153$	35.6060	+	14.8033i	0.232719	+	0.0967534i
$154$	93.0585			0.604276
$155$		0			0
$156$	−22.4857	−	346.550i	−0.144139	−	2.22148i
$157$	5.53607	+	9.58875i	0.0352616	+	0.0610749i	0.883118	−	0.469152i	$-0.155440\pi$
$157$	5.53607	+	9.58875i	0.0352616	+	0.0610749i	−0.847856	+	0.530226i	$0.822107\pi$
$158$	368.119	−	212.534i	2.32987	−	1.34515i
$159$	−144.254	−	216.198i	−0.907255	−	1.35973i
$160$		0			0
$161$		−	1.31076i		−	0.00814134i
$162$	−76.5436	−	288.694i	−0.472491	−	1.78206i
$163$	216.230			1.32656			0.663282	−	0.748370i	$-0.269163\pi$
$163$	216.230			1.32656			0.663282	+	0.748370i	$0.269163\pi$
$164$	−287.626	−	166.061i	−1.75382	−	1.01257i
$165$		0			0
$166$	110.644	+	191.640i	0.666528	+	1.15446i
$167$	−53.6475	+	30.9734i	−0.321242	+	0.185469i	−0.651946	−	0.758265i	$-0.726047\pi$
$167$	−53.6475	+	30.9734i	−0.321242	+	0.185469i	0.330704	+	0.943735i	$0.392714\pi$
$168$	−158.594	+	10.2902i	−0.944010	+	0.0612514i
$169$	11.7382	−	20.3311i	0.0694567	−	0.120302i
$170$		0			0
$171$	−24.7624	+	59.5604i	−0.144809	+	0.348307i
$172$	498.481			2.89815
$173$	−288.794	−	166.735i	−1.66933	−	0.963788i	−0.968000	−	0.250951i	$-0.919257\pi$
$173$	−288.794	−	166.735i	−1.66933	−	0.963788i	−0.701330	−	0.712837i	$-0.747410\pi$
$174$	303.011	+	149.676i	1.74144	+	0.860206i
$175$		0			0
$176$	320.939	−	185.294i	1.82352	−	1.05281i
$177$	−140.784	+	285.010i	−0.795391	+	1.61023i
$178$	−131.450	+	227.678i	−0.738483	+	1.27909i
$179$			193.521i			1.08112i	0.841304	+	0.540562i	$0.181788\pi$
$179$			193.521i			1.08112i	−0.841304	+	0.540562i	$0.818212\pi$
$180$		0			0
$181$	243.865			1.34732			0.673661	−	0.739041i	$-0.264721\pi$
$181$	243.865			1.34732			0.673661	+	0.739041i	$0.264721\pi$
$182$	98.8999	+	57.0999i	0.543406	+	0.313736i
$183$	6.08374	+	93.7629i	0.0332445	+	0.512365i
$184$	−5.26724	−	9.12313i	−0.0286263	−	0.0495822i
$185$		0			0
$186$	118.047	+	176.921i	0.634662	+	0.951190i
$187$	21.0586	−	36.4746i	0.112613	−	0.195051i
$188$		−	488.737i		−	2.59966i
$189$	65.5969	+	22.4113i	0.347073	+	0.118578i
$190$		0			0
$191$	−122.599	−	70.7825i	−0.641879	−	0.370589i	0.143459	−	0.989656i	$-0.454177\pi$
$191$	−122.599	−	70.7825i	−0.641879	−	0.370589i	−0.785338	+	0.619067i	$0.787511\pi$
$192$	−143.316	+	95.6247i	−0.746438	+	0.498045i
$193$	110.711	+	191.757i	0.573633	+	0.993561i	0.996189	+	0.0872244i	$0.0277997\pi$
$193$	110.711	+	191.757i	0.573633	+	0.993561i	−0.422556	+	0.906337i	$0.638867\pi$
$194$	408.623	−	235.919i	2.10631	−	1.21608i
$195$		0			0
$196$	−203.476	+	352.431i	−1.03814	+	1.79812i
$197$		−	28.4424i		−	0.144378i	−0.997391	−	0.0721889i	$-0.977002\pi$
$197$		−	28.4424i		−	0.144378i	0.997391	−	0.0721889i	$-0.0229984\pi$
$198$	−323.481	+	42.1552i	−1.63374	+	0.212905i
$199$	−153.875			−0.773244			−0.386622	−	0.922238i	$-0.626358\pi$
$199$	−153.875			−0.773244			−0.386622	+	0.922238i	$0.626358\pi$
$200$		0			0
$201$	209.946	+	103.705i	1.04451	+	0.515946i
$202$	158.694	+	274.866i	0.785615	+	1.36072i
$203$	−67.9304	+	39.2197i	−0.334633	+	0.193200i
$204$	−54.6257	+	110.587i	−0.267773	+	0.542093i
$205$		0			0
$206$			150.748i			0.731786i
$207$	0.593767	+	4.55632i	0.00286844	+	0.0220112i
$208$	454.779			2.18644
$209$	61.0133	+	35.2261i	0.291930	+	0.168546i
$210$		0			0
$211$	−90.0891	−	156.039i	−0.426962	−	0.739521i	0.569639	−	0.821895i	$-0.307083\pi$
$211$	−90.0891	−	156.039i	−0.426962	−	0.739521i	−0.996601	+	0.0823744i	$0.973750\pi$
$212$	719.970	−	415.675i	3.39608	−	1.96073i
$213$	121.011	+	181.364i	0.568127	+	0.851472i
$214$	−3.06092	+	5.30167i	−0.0143034	+	0.0247742i
$215$		0			0
$216$	546.627	−	107.612i	2.53068	−	0.498205i
$217$	−49.3638			−0.227483
$218$	474.651	+	274.040i	2.17730	+	1.25706i
$219$	−75.6379	+	50.4679i	−0.345379	+	0.230447i
$220$		0			0
$221$	44.7609	−	25.8427i	0.202538	−	0.116935i
$222$	−14.5545	+	0.944361i	−0.0655610	+	0.00425388i
$223$	107.701	−	186.544i	0.482966	−	0.836521i	−0.516843	−	0.856080i	$-0.672893\pi$
$223$	107.701	−	186.544i	0.482966	−	0.836521i	0.999809	+	0.0195592i	$0.00622628\pi$
$224$		−	144.985i		−	0.647256i
$225$		0			0
$226$	−484.717			−2.14477
$227$	−43.6615	−	25.2080i	−0.192341	−	0.111048i	0.400737	−	0.916193i	$-0.368754\pi$
$227$	−43.6615	−	25.2080i	−0.192341	−	0.111048i	−0.593078	+	0.805145i	$0.702088\pi$
$228$	−184.986	−	91.3759i	−0.811341	−	0.400772i
$229$	−3.08352	−	5.34081i	−0.0134652	−	0.0233223i	0.859214	−	0.511616i	$-0.170953\pi$
$229$	−3.08352	−	5.34081i	−0.0134652	−	0.0233223i	−0.872679	+	0.488294i	$0.837620\pi$
$230$		0			0
$231$	33.5317	−	67.8831i	0.145159	−	0.293866i
$232$	−315.207	+	545.954i	−1.35865	+	2.35325i
$233$		−	52.5336i		−	0.225466i	−0.993625	−	0.112733i	$-0.964040\pi$
$233$		−	52.5336i		−	0.225466i	0.993625	−	0.112733i	$-0.0359605\pi$
$234$	−369.653	−	153.684i	−1.57971	−	0.656769i
$235$		0			0
$236$	−880.584	−	508.405i	−3.73129	−	2.15426i
$237$	−22.3924	−	345.113i	−0.0944827	−	1.45617i
$238$	−20.2801	−	35.1262i	−0.0852105	−	0.147589i
$239$	−84.5102	+	48.7920i	−0.353599	+	0.204151i	−0.666269	−	0.745711i	$-0.732110\pi$
$239$	−84.5102	+	48.7920i	−0.353599	+	0.204151i	0.312670	+	0.949862i	$0.398777\pi$
$240$		0			0
$241$	71.3647	−	123.607i	0.296119	−	0.512893i	−0.679126	−	0.734022i	$-0.737641\pi$
$241$	71.3647	−	123.607i	0.296119	−	0.512893i	0.975245	+	0.221129i	$0.0709742\pi$
$242$		−	89.8560i		−	0.371306i
$243$	−238.174	−	48.1889i	−0.980140	−	0.198308i
$244$	−300.547			−1.23175
$245$		0			0
$246$	−318.471	+	212.494i	−1.29460	+	0.863795i
$247$	43.2288	+	74.8745i	0.175015	+	0.303136i
$248$	−343.583	+	198.367i	−1.38541	+	0.799869i
$249$	179.663	−	11.6573i	0.721540	−	0.0468166i
$250$		0			0
$251$		−	254.631i		−	1.01447i	−0.861809	−	0.507233i	$-0.830668\pi$
$251$		−	254.631i		−	1.01447i	0.861809	−	0.507233i	$-0.169332\pi$
$252$	−85.1215	+	204.741i	−0.337784	+	0.812464i
$253$	5.01865			0.0198366
$254$	−323.001	−	186.485i	−1.27166	−	0.734192i
$255$		0			0
$256$	140.906	+	244.057i	0.550415	+	0.953346i
$257$	−123.613	+	71.3682i	−0.480986	+	0.277697i	−0.720827	−	0.693115i	$-0.756238\pi$
$257$	−123.613	+	71.3682i	−0.480986	+	0.277697i	0.239841	+	0.970812i	$0.422905\pi$
$258$	254.489	−	515.199i	0.986390	−	1.99690i
$259$	1.69257	−	2.93162i	0.00653502	−	0.0113190i
$260$		0			0
$261$	218.367	−	167.104i	0.836656	−	0.640245i
$262$	−316.357			−1.20747
$263$	−218.644	−	126.234i	−0.831347	−	0.479979i	0.0229665	−	0.999736i	$-0.492689\pi$
$263$	−218.644	−	126.234i	−0.831347	−	0.479979i	−0.854314	+	0.519758i	$0.826022\pi$
$264$	−39.3995	−	607.227i	−0.149240	−	2.30010i
$265$		0			0
$266$	58.7578	−	33.9238i	0.220894	−	0.127533i
$267$	118.718	+	177.927i	0.444638	+	0.666395i
$268$	−374.504	+	648.660i	−1.39740	+	2.42037i
$269$		−	388.672i		−	1.44488i	−0.691435	−	0.722439i	$-0.743021\pi$
$269$		−	388.672i		−	1.44488i	0.691435	−	0.722439i	$-0.256979\pi$
$270$		0			0
$271$	−163.253			−0.602410			−0.301205	−	0.953559i	$-0.597389\pi$
$271$	−163.253			−0.602410			−0.301205	+	0.953559i	$0.597389\pi$
$272$	−139.883	−	80.7617i	−0.514277	−	0.296918i
$273$	77.2889	−	51.5695i	0.283110	−	0.188899i
$274$	128.550	+	222.655i	0.469160	+	0.812610i
$275$		0			0
$276$	−14.6666	+	0.951630i	−0.0531397	+	0.00344793i
$277$	241.912	−	419.003i	0.873328	−	1.51265i	0.0147939	−	0.999891i	$-0.495291\pi$
$277$	241.912	−	419.003i	0.873328	−	1.51265i	0.858534	−	0.512757i	$-0.171376\pi$
$278$			512.227i			1.84254i
$279$	171.594	−	22.3616i	0.615032	−	0.0801493i
$280$		0			0
$281$	231.798	+	133.829i	0.824906	+	0.476260i	0.852105	−	0.523371i	$-0.175326\pi$
$281$	231.798	+	133.829i	0.824906	+	0.476260i	−0.0271995	+	0.999630i	$0.508659\pi$
$282$	−505.128	−	249.514i	−1.79124	−	0.884802i
$283$	−245.898	−	425.908i	−0.868898	−	1.50498i	−0.863124	−	0.504993i	$-0.831495\pi$
$283$	−245.898	−	425.908i	−0.868898	−	1.50498i	−0.00577475	−	0.999983i	$-0.501838\pi$
$284$	−603.967	+	348.701i	−2.12664	+	1.22782i
$285$		0			0
$286$	−218.625	+	378.670i	−0.764424	+	1.32402i
$287$		−	88.8586i		−	0.309612i
$288$	65.6779	+	503.985i	0.228048	+	1.74995i
$289$	270.643			0.936481
$290$		0			0
$291$	−24.8562	−	383.086i	−0.0854166	−	1.31645i
$292$	−145.426	−	251.885i	−0.498034	−	0.862621i
$293$	278.986	−	161.073i	0.952172	−	0.549737i	0.0584171	−	0.998292i	$-0.481395\pi$
$293$	278.986	−	161.073i	0.952172	−	0.549737i	0.893755	+	0.448555i	$0.148061\pi$
$294$	260.370	+	390.226i	0.885614	+	1.32730i
$295$		0			0
$296$		−	27.2062i		−	0.0919129i
$297$	−85.8088	+	251.159i	−0.288919	+	0.845652i
$298$	−176.092			−0.590914
$299$	5.33367	+	3.07940i	0.0178384	+	0.0102990i
$300$		0			0
$301$	66.6839	+	115.500i	0.221541	+	0.383720i
$302$	−177.199	+	102.306i	−0.586752	+	0.338762i
$303$	257.688	−	16.7199i	0.850455	−	0.0551812i
$304$	135.095	−	233.992i	0.444392	−	0.769710i
$305$		0			0
$306$	86.4078	+	112.915i	0.282378	+	0.369005i
$307$	−426.031			−1.38772			−0.693861	−	0.720109i	$-0.744092\pi$
$307$	−426.031			−1.38772			−0.693861	+	0.720109i	$0.744092\pi$
$308$	209.735	+	121.091i	0.680959	+	0.393152i
$309$	109.966	+	54.3188i	0.355876	+	0.175789i
$310$		0			0
$311$	−1.01150	+	0.583987i	−0.00325240	+	0.00187777i	−0.501625	−	0.865085i	$-0.667264\pi$
$311$	−1.01150	+	0.583987i	−0.00325240	+	0.00187777i	0.498373	+	0.866963i	$0.333931\pi$
$312$	330.716	−	669.518i	1.05999	−	2.14589i
$313$	130.475	−	225.989i	0.416852	−	0.722009i	−0.578769	−	0.815492i	$-0.696467\pi$
$313$	130.475	−	225.989i	0.416852	−	0.722009i	0.995621	+	0.0934824i	$0.0297999\pi$
$314$			40.8260i			0.130019i
$315$		0			0
$316$	1106.22			3.50071
$317$	−113.480	−	65.5178i	−0.357981	−	0.206681i	0.310213	−	0.950667i	$-0.399599\pi$
$317$	−113.480	−	65.5178i	−0.357981	−	0.206681i	−0.668195	+	0.743986i	$0.732933\pi$
$318$	−62.0508	−	956.330i	−0.195128	−	3.00733i
$319$	−150.165	−	260.094i	−0.470737	−	0.815340i
$320$		0			0
$321$	2.76446	+	4.14318i	0.00861201	+	0.0129071i
$322$	2.41656	−	4.18560i	0.00750484	−	0.0129988i
$323$		−	30.7071i		−	0.0950683i
$324$	203.145	−	750.261i	0.626989	−	2.31562i
$325$		0			0
$326$	690.482	+	398.650i	2.11804	+	1.22285i
$327$	370.934	−	247.498i	1.13435	−	0.756874i
$328$	−357.076	−	618.474i	−1.08865	−	1.88559i
$329$	113.242	−	65.3803i	0.344201	−	0.198724i
$330$		0			0
$331$	−96.7419	+	167.562i	−0.292272	+	0.506229i	−0.974347	−	0.225053i	$-0.927745\pi$
$331$	−96.7419	+	167.562i	−0.292272	+	0.506229i	0.682075	+	0.731282i	$0.261078\pi$
$332$			575.893i			1.73462i
$333$	−4.55554	+	10.9573i	−0.0136803	+	0.0329049i
$334$	−228.415			−0.683877
$335$		0			0
$336$	−260.338	−	128.597i	−0.774816	−	0.382729i
$337$	231.798	+	401.485i	0.687827	+	1.19135i	0.972539	+	0.232738i	$0.0747686\pi$
$337$	231.798	+	401.485i	0.687827	+	1.19135i	−0.284712	+	0.958613i	$0.591898\pi$
$338$	74.9664	−	43.2819i	0.221794	−	0.128053i
$339$	−174.658	+	353.585i	−0.515214	+	1.04302i
$340$		0			0
$341$		−	189.005i		−	0.554268i
$342$	−188.881	+	144.540i	−0.552284	+	0.422631i
$343$	−234.682			−0.684203
$344$	928.267	+	535.935i	2.69845	+	1.55795i
$345$		0			0
$346$	−614.799	−	1064.86i	−1.77688	−	3.07764i
$347$	−8.41662	+	4.85934i	−0.0242554	+	0.0140039i	−0.512079	−	0.858939i	$-0.671124\pi$
$347$	−8.41662	+	4.85934i	−0.0242554	+	0.0140039i	0.487823	+	0.872942i	$0.337791\pi$
$348$	488.163	+	731.627i	1.40277	+	2.10238i
$349$	−24.6679	+	42.7260i	−0.0706816	+	0.122424i	−0.899200	−	0.437537i	$-0.855851\pi$
$349$	−24.6679	+	42.7260i	−0.0706816	+	0.122424i	0.828519	+	0.559962i	$0.189184\pi$
$350$		0			0
$351$	−245.304	+	214.273i	−0.698871	+	0.610463i
$352$	555.123			1.57705
$353$	−82.5859	−	47.6810i	−0.233954	−	0.135074i	0.378441	−	0.925626i	$-0.376460\pi$
$353$	−82.5859	−	47.6810i	−0.233954	−	0.135074i	−0.612395	+	0.790552i	$0.709794\pi$
$354$	−975.019	+	650.562i	−2.75429	+	1.83774i
$355$		0			0
$356$	−592.524	+	342.094i	−1.66439	+	0.960938i
$357$	−32.9309	+	2.13670i	−0.0922433	+	0.00598514i
$358$	−356.783	+	617.966i	−0.996600	+	1.72616i
$359$		−	539.284i		−	1.50219i	−0.660197	−	0.751093i	$-0.729527\pi$
$359$		−	539.284i		−	1.50219i	0.660197	−	0.751093i	$-0.270473\pi$
$360$		0			0
$361$	−309.634			−0.857713
$362$	778.729	+	449.599i	2.15118	+	1.24199i
$363$	−65.5470	−	32.3777i	−0.180570	−	0.0891948i
$364$	148.600	+	257.383i	0.408243	+	0.707098i
$365$		0			0
$366$	−153.438	+	310.627i	−0.419229	+	0.848707i
$367$	151.544	−	262.482i	0.412927	−	0.715211i	−0.582281	−	0.812987i	$-0.697840\pi$
$367$	151.544	−	262.482i	0.412927	−	0.715211i	0.995208	+	0.0977766i	$0.0311731\pi$
$368$		−	19.2470i		−	0.0523016i
$369$	40.2526	+	308.882i	0.109086	+	0.837078i
$370$		0			0
$371$	192.627	+	111.213i	0.519209	+	0.299766i
$372$	35.8390	+	552.352i	0.0963413	+	1.48482i
$373$	65.3325	+	113.159i	0.175154	+	0.303376i	0.940215	−	0.340582i	$-0.110624\pi$
$373$	65.3325	+	113.159i	0.175154	+	0.303376i	−0.765060	+	0.643959i	$0.777291\pi$
$374$	134.492	−	77.6489i	0.359604	−	0.207617i
$375$		0			0
$376$	525.459	−	910.121i	1.39750	−	2.42054i
$377$		−	368.560i		−	0.977612i
$378$	168.151	+	192.502i	0.444843	+	0.509265i
$379$	−545.141			−1.43837			−0.719183	−	0.694821i	$-0.755484\pi$
$379$	−545.141			−1.43837			−0.719183	+	0.694821i	$0.755484\pi$
$380$		0			0
$381$	−252.421	+	168.423i	−0.662522	+	0.442054i
$382$	−260.995	−	452.056i	−0.683232	−	1.18339i
$383$	−1.07950	+	0.623248i	−0.00281853	+	0.00162728i	−0.501409	−	0.865211i	$-0.667185\pi$
$383$	−1.07950	+	0.623248i	−0.00281853	+	0.00162728i	0.498590	+	0.866838i	$0.333851\pi$
$384$	42.2947	−	2.74426i	0.110142	−	0.00714651i
$385$		0			0
$386$			816.445i			2.11514i
$387$	−284.121	−	371.282i	−0.734163	−	0.959386i
$388$	1227.94			3.16480
$389$	345.001	+	199.187i	0.886893	+	0.512048i	0.872925	−	0.487855i	$-0.162220\pi$
$389$	345.001	+	199.187i	0.886893	+	0.512048i	0.0139679	+	0.999902i	$0.495554\pi$
$390$		0			0
$391$	−1.09371	−	1.89435i	−0.00279720	−	0.00484490i
$392$	−757.822	+	437.529i	−1.93322	+	1.11615i
$393$	−113.993	+	230.772i	−0.290057	+	0.587206i
$394$	52.4376	−	90.8245i	0.133090	−	0.230519i
$395$		0			0
$396$	−783.916	−	325.915i	−1.97959	−	0.823018i
$397$	685.998			1.72795			0.863977	−	0.503531i	$-0.167966\pi$
$397$	685.998			1.72795			0.863977	+	0.503531i	$0.167966\pi$
$398$	−491.367	−	283.691i	−1.23459	−	0.712791i
$399$	−3.57419	−	55.0856i	−0.00895787	−	0.138059i
$400$		0			0
$401$	44.9212	−	25.9353i	0.112023	−	0.0646764i	−0.442942	−	0.896550i	$-0.646065\pi$
$401$	44.9212	−	25.9353i	0.112023	−	0.0646764i	0.554965	+	0.831874i	$0.312732\pi$
$402$	479.220	+	718.223i	1.19209	+	1.78663i
$403$	115.972	−	200.869i	0.287772	−	0.498435i
$404$			825.992i			2.04453i
$405$		0			0
$406$	−289.227			−0.712383
$407$	11.2246	+	6.48055i	0.0275790	+	0.0159227i
$408$	−220.619	+	147.204i	−0.540734	+	0.360794i
$409$	−135.648	−	234.950i	−0.331658	−	0.574449i	0.651179	−	0.758924i	$-0.274275\pi$
$409$	−135.648	−	234.950i	−0.331658	−	0.574449i	−0.982837	+	0.184475i	$0.940941\pi$
$410$		0			0
$411$	208.740	−	13.5439i	0.507883	−	0.0329536i
$412$	−196.158	+	339.756i	−0.476112	+	0.824650i
$413$		−	272.046i		−	0.658707i
$414$	−6.50415	+	15.6443i	−0.0157105	+	0.0377881i
$415$		0			0
$416$	589.969	+	340.619i	1.41819	+	0.818795i
$417$	373.653	+	184.570i	0.896050	+	0.442614i
$418$	129.888	+	224.973i	0.310738	+	0.538213i
$419$	−23.9467	+	13.8256i	−0.0571520	+	0.0329967i	−0.528304	−	0.849055i	$-0.677172\pi$
$419$	−23.9467	+	13.8256i	−0.0571520	+	0.0329967i	0.471152	+	0.882052i	$0.343838\pi$
$420$		0			0
$421$	218.613	−	378.649i	0.519271	−	0.899403i	−0.480478	−	0.877007i	$-0.659537\pi$
$421$	218.613	−	378.649i	0.519271	−	0.899403i	0.999749	−	0.0223967i	$-0.00712970\pi$
$422$		−	664.367i		−	1.57433i
$423$	−364.025	+	278.567i	−0.860578	+	0.658552i
$424$	1787.63			4.21610
$425$		0			0
$426$	52.0531	+	802.245i	0.122190	+	1.88320i
$427$	−40.2054	−	69.6378i	−0.0941579	−	0.163086i
$428$	−13.7974	+	7.96594i	−0.0322369	+	0.0186120i
$429$	197.450	+	295.926i	0.460257	+	0.689803i
$430$		0			0
$431$		−	54.3602i		−	0.126126i	−0.998010	−	0.0630629i	$-0.979913\pi$
$431$		−	54.3602i		−	0.126126i	0.998010	−	0.0630629i	$-0.0200869\pi$
$432$	963.217	+	329.085i	2.22967	+	0.761771i
$433$	526.426			1.21576			0.607882	−	0.794028i	$-0.292019\pi$
$433$	526.426			1.21576			0.607882	+	0.794028i	$0.292019\pi$
$434$	−157.632	−	91.0091i	−0.363208	−	0.209698i
$435$		0			0
$436$	713.180	+	1235.26i	1.63573	+	2.83317i
$437$	3.16881	−	1.82951i	0.00725128	−	0.00418653i
$438$	−334.577	+	21.7088i	−0.763875	+	0.0495635i
$439$	−208.124	+	360.481i	−0.474087	+	0.821142i	−0.999560	−	0.0296681i	$-0.990555\pi$
$439$	−208.124	+	360.481i	−0.474087	+	0.821142i	0.525473	+	0.850810i	$0.323888\pi$
$440$		0			0
$441$	378.476	−	49.3219i	0.858223	−	0.111841i
$442$	190.579			0.431173
$443$	369.935	+	213.582i	0.835069	+	0.482127i	0.855585	−	0.517662i	$-0.173198\pi$
$443$	369.935	+	213.582i	0.835069	+	0.482127i	−0.0205163	+	0.999790i	$0.506531\pi$
$444$	−34.0319	−	16.8104i	−0.0766484	−	0.0378614i
$445$		0			0
$446$	687.840	−	397.125i	1.54224	−	0.890414i
$447$	−63.4512	+	128.454i	−0.141949	+	0.287368i
$448$	73.7224	−	127.691i	0.164559	−	0.285024i
$449$		−	236.730i		−	0.527239i	−0.964627	−	0.263620i	$-0.915084\pi$
$449$		−	236.730i		−	0.527239i	0.964627	−	0.263620i	$-0.0849164\pi$
$450$		0			0
$451$	340.224			0.754376
$452$	−1092.46	−	630.730i	−2.41694	−	1.39542i
$453$	10.7789	+	166.125i	0.0237945	+	0.366721i
$454$	−92.9488	−	160.992i	−0.204733	−	0.354608i
$455$		0			0
$456$	−246.237	−	369.044i	−0.539994	−	0.809308i
$457$	−348.891	+	604.296i	−0.763437	+	1.32231i	0.177633	+	0.984097i	$0.443156\pi$
$457$	−348.891	+	604.296i	−0.763437	+	1.32231i	−0.941069	+	0.338214i	$0.890177\pi$
$458$		−	22.7396i		−	0.0496497i
$459$	113.503	−	22.3450i	0.247284	−	0.0486818i
$460$		0			0
$461$	−332.339	−	191.876i	−0.720910	−	0.416217i	0.0941777	−	0.995555i	$-0.469978\pi$
$461$	−332.339	−	191.876i	−0.720910	−	0.416217i	−0.815087	+	0.579338i	$0.803311\pi$
$462$	232.228	−	154.949i	0.502657	−	0.335388i
$463$	135.056	+	233.924i	0.291698	+	0.505235i	0.974211	−	0.225638i	$-0.0724466\pi$
$463$	135.056	+	233.924i	0.291698	+	0.505235i	−0.682514	+	0.730873i	$0.739113\pi$
$464$	−997.483	+	575.897i	−2.14975	+	1.24116i
$465$		0			0
$466$	96.8529	−	167.754i	0.207839	−	0.359987i
$467$			777.952i			1.66585i	0.553385	+	0.832926i	$0.313336\pi$
$467$			777.952i			1.66585i	−0.553385	+	0.832926i	$0.686664\pi$
$468$	−633.145	−	827.377i	−1.35287	−	1.76790i
$469$	−200.396			−0.427283
$470$		0			0
$471$	29.7812	+	14.7108i	0.0632298	+	0.0312331i
$472$	−1093.21	−	1893.50i	−2.31612	−	4.01164i
$473$	−442.228	+	255.321i	−0.934943	+	0.539790i
$474$	564.758	−	1143.32i	1.19147	−	2.41208i
$475$		0			0
$476$		−	105.556i		−	0.221757i
$477$	−719.970	−	299.329i	−1.50937	−	0.627525i
$478$	−359.819			−0.752760
$479$	−62.8429	−	36.2824i	−0.131196	−	0.0757460i	0.432966	−	0.901410i	$-0.357467\pi$
$479$	−62.8429	−	36.2824i	−0.131196	−	0.0757460i	−0.564162	+	0.825664i	$0.690800\pi$
$480$		0			0
$481$	7.95281	+	13.7747i	0.0165339	+	0.0286376i
$482$	455.774	−	263.141i	0.945590	−	0.545936i
$483$	−2.18250	−	3.27099i	−0.00451864	−	0.00677224i
$484$	116.924	−	202.518i	0.241578	−	0.418425i
$485$		0			0
$486$	−671.712	−	592.987i	−1.38212	−	1.22014i
$487$	−729.487			−1.49792			−0.748959	−	0.662616i	$-0.769446\pi$
$487$	−729.487			−1.49792			−0.748959	+	0.662616i	$0.769446\pi$
$488$	−559.676	−	323.129i	−1.14688	−	0.662150i
$489$	539.602	−	360.039i	1.10348	−	0.736275i
$490$		0			0
$491$	3.30449	−	1.90785i	0.00673012	−	0.00388564i	−0.496631	−	0.867962i	$-0.665430\pi$
$491$	3.30449	−	1.90785i	0.00673012	−	0.00388564i	0.503361	+	0.864076i	$0.332096\pi$
$492$	−994.275	+	64.5128i	−2.02088	+	0.131124i
$493$	−65.4505	+	113.364i	−0.132760	+	0.229946i
$494$			318.793i			0.645330i
$495$		0			0
$496$	−724.853			−1.46140
$497$	−161.590	−	93.2942i	−0.325131	−	0.187715i
$498$	595.207	+	294.009i	1.19519	+	0.590380i
$499$	102.651	+	177.797i	0.205714	+	0.356307i	0.950360	−	0.311152i	$-0.100715\pi$
$499$	102.651	+	177.797i	0.205714	+	0.356307i	−0.744646	+	0.667460i	$0.767382\pi$
$500$		0			0
$501$	−82.3044	+	166.621i	−0.164280	+	0.332577i
$502$	469.448	−	813.107i	0.935155	−	1.61974i
$503$		−	224.016i		−	0.445360i	−0.974892	−	0.222680i	$-0.928519\pi$
$503$		−	224.016i		−	0.445360i	0.974892	−	0.222680i	$-0.0714806\pi$
$504$	−378.637	+	289.749i	−0.751263	+	0.574899i
$505$		0			0
$506$	16.0259	+	9.25257i	0.0316718	+	0.0182857i
$507$	−4.56015	−	70.2813i	−0.00899438	−	0.138622i
$508$	−485.320	−	840.599i	−0.955354	−	1.65472i
$509$	399.073	−	230.405i	0.784033	−	0.452662i	−0.0538245	−	0.998550i	$-0.517141\pi$
$509$	399.073	−	230.405i	0.784033	−	0.452662i	0.837858	+	0.545889i	$0.183808\pi$
$510$		0			0
$511$	38.9085	−	67.3915i	0.0761418	−	0.131882i
$512$			982.608i			1.91916i
$513$	37.3778	+	189.864i	0.0728613	+	0.370106i
$514$	−526.309			−1.02395
$515$		0			0
$516$	1243.96	−	830.007i	2.41078	−	1.60854i
$517$	250.330	+	433.584i	0.484197	+	0.838653i
$518$	10.8097	−	6.24097i	0.0208681	−	0.0120482i
$519$	−998.313	+	64.7748i	−1.92353	+	0.124807i
$520$		0			0
$521$		−	182.438i		−	0.350168i	−0.984554	−	0.175084i	$-0.943980\pi$
$521$		−	182.438i		−	0.350168i	0.984554	−	0.175084i	$-0.0560197\pi$
$522$	1005.39	−	131.019i	1.92603	−	0.250994i
$523$	−431.339			−0.824741			−0.412370	−	0.911016i	$-0.635299\pi$
$523$	−431.339			−0.824741			−0.412370	+	0.911016i	$0.635299\pi$
$524$	−713.006	−	411.654i	−1.36070	−	0.785599i
$525$		0			0
$526$	−465.461	−	806.202i	−0.884907	−	1.53270i
$527$	−71.3426	+	41.1896i	−0.135375	+	0.0781587i
$528$	492.375	−	996.788i	0.932529	−	1.88786i
$529$	−264.370	+	457.902i	−0.499754	+	0.865599i
$530$		0			0
$531$	123.236	+	945.660i	0.232083	+	1.78090i
$532$	176.571			0.331901
$533$	361.580	+	208.758i	0.678386	+	0.391666i
$534$	51.0669	+	787.045i	0.0956308	+	1.47387i
$535$		0			0
$536$	−1394.80	+	805.285i	−2.60223	+	1.50240i
$537$	322.227	+	482.932i	0.600050	+	0.899315i
$538$	716.571	−	1241.14i	1.33192	−	2.30695i
$539$		−	416.879i		−	0.773431i
$540$		0			0
$541$	−649.924			−1.20134			−0.600669	−	0.799498i	$-0.705099\pi$
$541$	−649.924			−1.20134			−0.600669	+	0.799498i	$0.705099\pi$
$542$	−521.312	−	300.980i	−0.961830	−	0.555313i
$543$	608.566	−	406.053i	1.12075	−	0.747796i
$544$	−120.977	−	209.539i	−0.222384	−	0.385181i
$545$		0			0
$546$	341.880	−	22.1827i	0.626154	−	0.0406276i
$547$	212.658	−	368.334i	0.388771	−	0.673371i	−0.603513	−	0.797353i	$-0.706233\pi$
$547$	212.658	−	368.334i	0.388771	−	0.673371i	0.992285	+	0.123982i	$0.0395663\pi$
$548$			669.094i			1.22097i
$549$	171.304	+	223.856i	0.312029	+	0.407752i
$550$		0			0
$551$	−189.631	−	109.483i	−0.344157	−	0.198699i
$552$	−28.3351	−	13.9964i	−0.0513317	−	0.0253559i
$553$	147.984	+	256.316i	0.267602	+	0.463501i
$554$	1544.98	−	891.995i	2.78878	−	1.61010i
$555$		0			0
$556$	−666.526	+	1154.46i	−1.19879	+	2.07636i
$557$		−	325.885i		−	0.585073i	−0.956254	−	0.292536i	$-0.905501\pi$
$557$		−	325.885i		−	0.585073i	0.956254	−	0.292536i	$-0.0944992\pi$
$558$	589.174	+	244.950i	1.05587	+	0.438979i
$559$	−626.650			−1.12102
$560$		0			0
$561$	−8.18103	−	126.086i	−0.0145829	−	0.224753i
$562$	493.464	+	854.705i	0.878050	+	1.52083i
$563$	−612.075	+	353.382i	−1.08717	+	0.627676i	−0.932821	−	0.360341i	$-0.882660\pi$
$563$	−612.075	+	353.382i	−1.08717	+	0.627676i	−0.154346	+	0.988017i	$0.549327\pi$
$564$	−813.783	−	1219.64i	−1.44288	−	2.16249i
$565$		0			0
$566$		−	1813.39i		−	3.20387i
$567$	201.014	−	53.2962i	0.354521	−	0.0939967i
$568$	−1499.60			−2.64015
$569$	485.178	+	280.118i	0.852686	+	0.492299i	0.861556	−	0.507662i	$-0.169490\pi$
$569$	485.178	+	280.118i	0.852686	+	0.492299i	−0.00887015	+	0.999961i	$0.502823\pi$
$570$		0			0
$571$	105.346	+	182.465i	0.184494	+	0.319553i	0.943406	−	0.331640i	$-0.107602\pi$
$571$	105.346	+	182.465i	0.184494	+	0.319553i	−0.758912	+	0.651193i	$0.774269\pi$
$572$	−985.475	+	568.965i	−1.72286	+	0.994693i
$573$	−423.804	+	27.4982i	−0.739623	+	0.0479899i
$574$	163.823	−	283.750i	0.285406	−	0.494338i
$575$		0			0
$576$	−198.423	+	477.263i	−0.344485	+	0.828582i
$577$	−502.258			−0.870464			−0.435232	−	0.900318i	$-0.643334\pi$
$577$	−502.258			−0.870464			−0.435232	+	0.900318i	$0.643334\pi$
$578$	864.237	+	498.968i	1.49522	+	0.863266i
$579$	595.570	+	294.189i	1.02862	+	0.508098i
$580$		0			0
$581$	−133.436	+	77.0395i	−0.229667	+	0.132598i
$582$	626.899	−	1269.12i	1.07715	−	2.18063i
$583$	−425.815	+	737.533i	−0.730386	+	1.26507i
$584$		−	625.411i		−	1.07091i
$585$		0			0
$586$	1187.84			2.02703
$587$	354.873	+	204.886i	0.604554	+	0.349040i	0.770831	−	0.637040i	$-0.219841\pi$
$587$	354.873	+	204.886i	0.604554	+	0.349040i	−0.166277	+	0.986079i	$0.553175\pi$
$588$	79.0482	+	1218.29i	0.134436	+	2.07193i
$589$	−68.9006	−	119.339i	−0.116979	−	0.202613i
$590$		0			0
$591$	−47.3587	−	70.9782i	−0.0801332	−	0.120098i
$592$	24.8535	−	43.0476i	0.0419823	−	0.0727155i
$593$			944.139i			1.59214i	0.605204	+	0.796070i	$0.293092\pi$
$593$			944.139i			1.59214i	−0.605204	+	0.796070i	$0.706908\pi$
$594$	−737.057	+	643.818i	−1.24084	+	1.08387i
$595$		0			0
$596$	−396.877	−	229.137i	−0.665902	−	0.384458i
$597$	−383.997	+	256.214i	−0.643210	+	0.429169i
$598$	11.3546	+	19.6667i	0.0189876	+	0.0328875i
$599$	−461.021	+	266.171i	−0.769652	+	0.444359i	−0.832750	−	0.553649i	$-0.813235\pi$
$599$	−461.021	+	266.171i	−0.769652	+	0.444359i	0.0630986	+	0.998007i	$0.479902\pi$
$600$		0			0
$601$	−257.783	+	446.493i	−0.428923	+	0.742917i	−0.996778	−	0.0802121i	$-0.974440\pi$
$601$	−257.783	+	446.493i	−0.428923	+	0.742917i	0.567855	+	0.823129i	$0.307774\pi$
$602$			491.764i			0.816883i
$603$	696.597	−	90.7785i	1.15522	−	0.150545i
$604$	−532.496			−0.881615
$605$		0			0
$606$	853.694	+	421.692i	1.40874	+	0.695862i
$607$	−85.5764	−	148.223i	−0.140983	−	0.244189i	0.786884	−	0.617101i	$-0.211693\pi$
$607$	−85.5764	−	148.223i	−0.140983	−	0.244189i	−0.927867	+	0.372912i	$0.878360\pi$
$608$	350.509	−	202.366i	0.576494	−	0.332839i
$609$	−104.217	+	210.982i	−0.171128	+	0.346440i
$610$		0			0
$611$			614.400i			1.00557i
$612$	47.8167	+	366.926i	0.0781319	+	0.599552i
$613$	−875.826			−1.42875			−0.714377	−	0.699761i	$-0.753290\pi$
$613$	−875.826			−1.42875			−0.714377	+	0.699761i	$0.753290\pi$
$614$	−1360.43	−	785.447i	−2.21569	−	1.27923i
$615$		0			0
$616$	260.378	+	450.988i	0.422692	+	0.732124i
$617$	980.122	−	565.874i	1.58853	−	0.917137i	0.594978	−	0.803742i	$-0.297161\pi$
$617$	980.122	−	565.874i	1.58853	−	0.917137i	0.993550	−	0.113396i	$-0.0361728\pi$
$618$	251.006	+	376.192i	0.406159	+	0.608725i
$619$	260.187	−	450.658i	0.420335	−	0.728042i	−0.575637	−	0.817705i	$-0.695246\pi$
$619$	260.187	−	450.658i	0.420335	−	0.728042i	0.995972	+	0.0896637i	$0.0285792\pi$
$620$		0			0
$621$	9.06836	+	10.3817i	0.0146028	+	0.0167176i
$622$	−4.30664			−0.00692386
$623$	−158.529	−	91.5266i	−0.254460	−	0.146913i
$624$	1134.90	−	757.241i	1.81875	−	1.21353i
$625$		0			0
$626$	833.284	−	481.097i	1.33112	−	0.768525i
$627$	210.913	−	13.6849i	0.336384	−	0.0218261i
$628$	−53.1242	+	92.0138i	−0.0845926	+	0.146519i
$629$		−	5.64918i		−	0.00898121i
$630$		0			0
$631$	−607.475			−0.962718			−0.481359	−	0.876523i	$-0.659857\pi$
$631$	−607.475			−0.962718			−0.481359	+	0.876523i	$0.659857\pi$
$632$	2060.00	+	1189.34i	3.25949	+	1.88187i
$633$	−484.633	−	239.390i	−0.765614	−	0.378184i
$634$	−241.582	−	418.433i	−0.381044	−	0.659988i
$635$		0			0
$636$	1104.56	−	2236.12i	1.73673	−	3.51591i
$637$	255.794	−	443.047i	0.401560	−	0.695522i
$638$		−	1107.40i		−	1.73574i
$639$	603.967	+	251.101i	0.945176	+	0.392959i
$640$		0			0
$641$	161.252	+	93.0990i	0.251564	+	0.145240i	0.620480	−	0.784222i	$-0.286938\pi$
$641$	161.252	+	93.0990i	0.251564	+	0.145240i	−0.368916	+	0.929463i	$0.620271\pi$
$642$	1.18913	+	18.3270i	0.00185223	+	0.0285467i
$643$	398.761	+	690.674i	0.620157	+	1.07414i	0.989456	+	0.144833i	$0.0462645\pi$
$643$	398.761	+	690.674i	0.620157	+	1.07414i	−0.369299	+	0.929311i	$0.620402\pi$
$644$	10.8929	−	6.28901i	0.0169144	−	0.00976554i
$645$		0			0
$646$	56.6127	−	98.0561i	0.0876357	−	0.151790i
$647$			849.489i			1.31297i	0.754341	+	0.656483i	$0.227957\pi$
$647$			849.489i			1.31297i	−0.754341	+	0.656483i	$0.772043\pi$
$648$	1184.93	−	1178.72i	1.82859	−	1.81901i
$649$	1041.61			1.60495
$650$		0			0
$651$	−123.188	+	82.1944i	−0.189228	+	0.126259i
$652$	1037.47	+	1796.95i	1.59122	+	2.75607i
$653$	901.696	−	520.594i	1.38085	−	0.797235i	0.388591	−	0.921410i	$-0.372962\pi$
$653$	901.696	−	520.594i	1.38085	−	0.797235i	0.992260	+	0.124175i	$0.0396285\pi$
$654$	1640.79	−	106.461i	2.50885	−	0.162785i
$655$		0			0
$656$		−	1304.79i		−	1.98901i
$657$	−104.722	+	251.885i	−0.159394	+	0.383387i
$658$	482.151			0.732752
$659$	−556.318	−	321.190i	−0.844185	−	0.487390i	0.0144997	−	0.999895i	$-0.495384\pi$
$659$	−556.318	−	321.190i	−0.844185	−	0.487390i	−0.858685	+	0.512505i	$0.828718\pi$
$660$		0			0
$661$	394.759	+	683.742i	0.597214	+	1.03441i	0.993230	+	0.116162i	$0.0370591\pi$
$661$	394.759	+	683.742i	0.597214	+	1.03441i	−0.396016	+	0.918244i	$0.629608\pi$
$662$	−617.847	+	356.714i	−0.933304	+	0.538843i
$663$	68.6710	−	139.021i	0.103576	−	0.209684i
$664$	−619.163	+	1072.42i	−0.932474	+	1.61509i
$665$		0			0
$666$	−34.7485	+	26.5910i	−0.0521749	+	0.0399265i
$667$	−15.5980			−0.0233854
$668$	−514.802	−	297.221i	−0.770661	−	0.444941i
$669$	−41.8408	−	644.852i	−0.0625422	−	0.963904i
$670$		0			0
$671$	266.631	−	153.939i	0.397363	−	0.229418i
$672$	−241.411	−	361.811i	−0.359243	−	0.538410i
$673$	507.967	−	879.824i	0.754780	−	1.30732i	−0.190704	−	0.981648i	$-0.561077\pi$
$673$	507.967	−	879.824i	0.754780	−	1.30732i	0.945484	−	0.325669i	$-0.105590\pi$
$674$			1709.40i			2.53621i
$675$		0			0
$676$	225.279			0.333253
$677$	−643.996	−	371.811i	−0.951249	−	0.549204i	−0.0577802	−	0.998329i	$-0.518402\pi$
$677$	−643.996	−	371.811i	−0.951249	−	0.549204i	−0.893469	+	0.449126i	$0.851736\pi$
$678$	−1209.61	+	807.090i	−1.78409	+	1.19040i
$679$	164.267	+	284.518i	0.241924	+	0.419025i
$680$		0			0
$681$	−150.930	+	9.79301i	−0.221631	+	0.0143803i
$682$	348.458	−	603.546i	0.510935	−	0.884965i
$683$		−	152.482i		−	0.223254i	−0.993750	−	0.111627i	$-0.964394\pi$
$683$		−	152.482i		−	0.223254i	0.993750	−	0.111627i	$-0.0356061\pi$
$684$	−613.780	+	79.9861i	−0.897339	+	0.116939i
$685$		0			0
$686$	−749.403	−	432.668i	−1.09242	−	0.630711i
$687$	−16.5878	−	8.19373i	−0.0241452	−	0.0119268i
$688$	979.179	+	1695.99i	1.42322	+	2.46510i
$689$	−905.087	+	522.552i	−1.31362	+	0.758422i
$690$		0			0
$691$	−388.586	+	673.050i	−0.562353	+	0.974023i	0.434938	+	0.900460i	$0.356770\pi$
$691$	−388.586	+	673.050i	−0.562353	+	0.974023i	−0.997291	+	0.0735628i	$0.976563\pi$
$692$		−	3199.99i		−	4.62426i
$693$	−29.3520	−	225.235i	−0.0423550	−	0.325015i
$694$	−35.8355			−0.0516361
$695$		0			0
$696$	122.454	+	1887.27i	0.175940	+	2.71160i
$697$	−74.1444	−	128.422i	−0.106376	−	0.184249i
$698$	−157.543	+	90.9573i	−0.225706	+	0.130311i
$699$	−87.4722	−	131.098i	−0.125139	−	0.187550i
$700$		0			0
$701$			461.657i			0.658569i	0.944231	+	0.329284i	$0.106808\pi$
$701$			461.657i			0.658569i	−0.944231	+	0.329284i	$0.893192\pi$
$702$	−1178.36	+	231.980i	−1.67858	+	0.330456i
$703$	9.44975			0.0134420
$704$	488.906	+	282.270i	0.694468	+	0.400952i
$705$		0			0
$706$	−175.813	−	304.517i	−0.249027	−	0.431327i
$707$	−191.385	+	110.496i	−0.270701	+	0.156289i
$708$	−3044.03	+	197.510i	−4.29948	+	0.278969i
$709$	−179.227	+	310.431i	−0.252789	+	0.437843i	−0.964293	−	0.264839i	$-0.914681\pi$
$709$	−179.227	+	310.431i	−0.252789	+	0.437843i	0.711504	+	0.702682i	$0.248014\pi$
$710$		0			0
$711$	−630.519	−	823.945i	−0.886805	−	1.15885i
$712$	−1471.19			−2.06628
$713$	−8.50112	−	4.90812i	−0.0119230	−	0.00688376i
$714$	−109.097	−	53.8896i	−0.152796	−	0.0754756i
$715$		0			0
$716$	−1608.24	+	928.515i	−2.24614	+	1.29681i
$717$	−129.653	+	262.476i	−0.180827	+	0.366076i
$718$	994.245	−	1722.08i	1.38474	−	2.39845i
$719$			283.414i			0.394178i	0.980386	+	0.197089i	$0.0631488\pi$
$719$			283.414i			0.394178i	−0.980386	+	0.197089i	$0.936851\pi$
$720$		0			0
$721$	−104.964			−0.145580
$722$	−988.748	−	570.854i	−1.36946	−	0.790656i
$723$	−27.7244	−	427.290i	−0.0383463	−	0.590995i
$724$	1170.07	+	2026.61i	1.61611	+	2.79919i
$725$		0			0
$726$	−149.617	−	224.236i	−0.206084	−	0.308865i
$727$	−77.6796	+	134.545i	−0.106850	+	0.185069i	−0.914492	−	0.404603i	$-0.867410\pi$
$727$	−77.6796	+	134.545i	−0.106850	+	0.185069i	0.807643	+	0.589672i	$0.200743\pi$
$728$			639.063i			0.877833i
$729$	−674.602	+	276.322i	−0.925380	+	0.379042i
$730$		0			0
$731$	192.748	+	111.283i	0.263677	+	0.152234i
$732$	−750.016	+	500.433i	−1.02461	+	0.683652i
$733$	−52.4658	−	90.8735i	−0.0715768	−	0.123975i	0.828016	−	0.560705i	$-0.189470\pi$
$733$	−52.4658	−	90.8735i	−0.0715768	−	0.123975i	−0.899593	+	0.436730i	$0.856136\pi$
$734$	967.845	−	558.786i	1.31859	−	0.761288i
$735$		0			0
$736$	14.4155	−	24.9684i	0.0195863	−	0.0339245i
$737$		−	767.279i		−	1.04108i
$738$	−440.929	+	1060.56i	−0.597465	+	1.43707i
$739$	627.375			0.848951			0.424476	−	0.905439i	$-0.360458\pi$
$739$	627.375			0.848951			0.424476	+	0.905439i	$0.360458\pi$
$740$		0			0
$741$	232.549	+	114.870i	0.313831	+	0.155021i
$742$	410.073	+	710.268i	0.552659	+	0.957234i
$743$	334.797	−	193.295i	0.450602	−	0.260155i	−0.257483	−	0.966283i	$-0.582893\pi$
$743$	334.797	−	193.295i	0.450602	−	0.260155i	0.708084	+	0.706128i	$0.249560\pi$
$744$	−527.115	+	1067.12i	−0.708488	+	1.43430i
$745$		0			0
$746$			481.798i			0.645842i
$747$	428.940	−	328.244i	0.574217	−	0.439416i
$748$	404.157			0.540317
$749$	−3.69147	−	2.13127i	−0.00492853	−	0.00284549i
$750$		0			0
$751$	−452.601	−	783.928i	−0.602665	−	1.04385i	−0.992416	−	0.122926i	$-0.960772\pi$
$751$	−452.601	−	783.928i	−0.602665	−	1.04385i	0.389751	−	0.920920i	$-0.372561\pi$
$752$	1662.83	−	960.038i	2.21122	−	1.27665i
$753$	−423.979	−	635.433i	−0.563054	−	0.843868i
$754$	679.491	−	1176.91i	0.901182	−	1.56089i
$755$		0			0
$756$	128.488	+	652.665i	0.169957	+	0.863313i
$757$	332.222			0.438867			0.219433	−	0.975627i	$-0.429579\pi$
$757$	332.222			0.438867			0.219433	+	0.975627i	$0.429579\pi$
$758$	−1740.78	−	1005.04i	−2.29655	−	1.32591i
$759$	12.5240	−	8.35641i	0.0165007	−	0.0110098i
$760$		0			0
$761$	−396.726	+	229.050i	−0.521322	+	0.300986i	−0.737475	−	0.675374i	$-0.763982\pi$
$761$	−396.726	+	229.050i	−0.521322	+	0.300986i	0.216153	+	0.976359i	$0.430649\pi$
$762$	−1116.56	+	72.4472i	−1.46530	+	0.0950751i
$763$	−190.810	+	330.492i	−0.250079	+	0.433149i
$764$		−	1358.46i		−	1.77809i
$765$		0			0
$766$	−4.59618			−0.00600023
$767$	1107.00	+	639.126i	1.44328	+	0.833280i
$768$	758.004	+	374.425i	0.986984	+	0.487532i
$769$	−458.196	−	793.618i	−0.595833	−	1.03201i	−0.993429	−	0.114453i	$-0.963489\pi$
$769$	−458.196	−	793.618i	−0.595833	−	1.03201i	0.397595	−	0.917561i	$-0.369845\pi$
$770$		0			0
$771$	−189.644	+	383.925i	−0.245972	+	0.497957i
$772$	−1062.39	+	1840.11i	−1.37615	+	2.38356i
$773$		−	1186.06i		−	1.53436i	−0.641434	−	0.767178i	$-0.721660\pi$
$773$		−	1186.06i		−	1.53436i	0.641434	−	0.767178i	$-0.278340\pi$
$774$	−222.767	−	1709.42i	−0.287813	−	2.20856i
$775$		0			0
$776$	2286.66	+	1320.20i	2.94673	+	1.70129i
$777$	−0.657544	−	10.1341i	−0.000846261	−	0.0130426i
$778$	734.456	+	1272.12i	0.944031	+	1.63511i
$779$	214.820	−	124.026i	0.275763	−	0.159212i
$780$		0			0
$781$	357.207	−	618.701i	0.457371	−	0.792190i
$782$		−	8.06559i		−	0.0103141i
$783$	266.695	−	780.605i	0.340607	−	0.996942i
$784$	−1598.77			−2.03925
$785$		0			0
$786$	−789.470	+	526.757i	−1.00441	+	0.670175i
$787$	−441.240	−	764.249i	−0.560660	−	0.971092i	−0.997439	−	0.0715229i	$-0.977214\pi$
$787$	−441.240	−	764.249i	−0.560660	−	0.971092i	0.436779	−	0.899569i	$-0.356119\pi$
$788$	236.368	−	136.467i	0.299959	−	0.173181i
$789$	−755.817	+	49.0406i	−0.957943	+	0.0621554i
$790$		0			0
$791$		−	337.501i		−	0.426677i
$792$	−1109.40	−	1449.73i	−1.40076	−	1.83047i
$793$	377.823			0.476448
$794$	2190.58	+	1264.73i	2.75892	+	1.59286i
$795$		0			0
$796$	−738.295	−	1278.76i	−0.927507	−	1.60649i
$797$	−124.537	+	71.9016i	−0.156258	+	0.0902153i	−0.576090	−	0.817386i	$-0.695422\pi$
$797$	−124.537	+	71.9016i	−0.156258	+	0.0902153i	0.419832	+	0.907602i	$0.362089\pi$
$798$	90.1446	−	182.493i	0.112963	−	0.228688i
$799$	109.108	−	188.980i	0.136556	−	0.236521i
$800$		0			0
$801$	592.524	+	246.343i	0.739731	+	0.307545i
$802$	191.261			0.238480
$803$	258.030	+	148.974i	0.321332	+	0.185521i
$804$	145.491	+	2242.31i	0.180958	+	2.78894i
$805$		0			0
$806$	740.661	−	427.621i	0.918934	−	0.530547i
$807$	−647.167	−	969.932i	−0.801942	−	1.20190i
$808$	−888.054	+	1538.15i	−1.09908	+	1.90366i
$809$			52.3078i			0.0646574i	0.999477	+	0.0323287i	$0.0102923\pi$
$809$			52.3078i			0.0646574i	−0.999477	+	0.0323287i	$0.989708\pi$
$810$		0			0
$811$	1518.65			1.87256			0.936281	−	0.351253i	$-0.114244\pi$
$811$	1518.65			1.87256			0.936281	+	0.351253i	$0.114244\pi$
$812$	−651.861	−	376.352i	−0.802785	−	0.463488i
$813$	−407.398	+	271.828i	−0.501105	+	0.334352i
$814$	23.8956	+	41.3883i	0.0293557	+	0.0508456i
$815$		0			0
$816$	−483.553	+	31.3750i	−0.592590	+	0.0384498i
$817$	−186.151	+	322.422i	−0.227847	+	0.394642i
$818$		−	1000.35i		−	1.22292i
$819$	107.008	−	257.383i	0.130657	−	0.314266i
$820$		0			0
$821$	950.059	+	548.517i	1.15720	+	0.668108i	0.950631	−	0.310324i	$-0.100438\pi$
$821$	950.059	+	548.517i	1.15720	+	0.668108i	0.206567	+	0.978432i	$0.433771\pi$
$822$	691.534	+	341.591i	0.841282	+	0.415561i
$823$	−478.550	−	828.873i	−0.581470	−	1.00714i	−0.995305	−	0.0967841i	$-0.969144\pi$
$823$	−478.550	−	828.873i	−0.581470	−	1.00714i	0.413835	−	0.910352i	$-0.364189\pi$
$824$	−730.568	+	421.793i	−0.886611	+	0.511885i
$825$		0			0
$826$	501.554	−	868.717i	0.607208	−	1.05172i
$827$		−	171.626i		−	0.207529i	−0.994602	−	0.103764i	$-0.966911\pi$
$827$		−	171.626i		−	0.207529i	0.994602	−	0.103764i	$-0.0330888\pi$
$828$	−35.0159	+	26.7957i	−0.0422898	+	0.0323620i
$829$	−203.896			−0.245954			−0.122977	−	0.992410i	$-0.539244\pi$
$829$	−203.896			−0.245954			−0.122977	+	0.992410i	$0.539244\pi$
$830$		0			0
$831$	−93.9800	−	1448.42i	−0.113093	−	1.74299i
$832$	346.397	+	599.976i	0.416342	+	0.721126i
$833$	−157.357	+	90.8499i	−0.188904	+	0.109063i
$834$	852.895	+	1278.26i	1.02266	+	1.53269i
$835$		0			0
$836$			676.059i			0.808683i
$837$	390.979	−	341.520i	0.467120	−	0.408029i
$838$	−101.958			−0.121668
$839$	1348.10	+	778.323i	1.60679	+	0.927680i	0.990083	+	0.140486i	$0.0448664\pi$
$839$	1348.10	+	778.323i	1.60679	+	0.927680i	0.616705	+	0.787194i	$0.288467\pi$
$840$		0			0
$841$	46.2156	+	80.0477i	0.0549531	+	0.0951816i
$842$	1396.18	−	806.087i	1.65817	−	0.957347i
$843$	801.289	−	51.9910i	0.950520	−	0.0616738i
$844$	864.495	−	1497.35i	1.02428	−	1.77411i
$845$		0			0
$846$	−1676.01	+	218.413i	−1.98110	+	0.258171i
$847$	62.5654			0.0738670
$848$	2828.51	+	1633.04i	3.33551	+	1.92576i
$849$	−1322.81	−	653.416i	−1.55808	−	0.769631i
$850$		0			0
$851$	0.582966	−	0.336576i	0.000685037	−	0.000395506i
$852$	−926.589	+	1875.83i	−1.08755	+	2.20168i
$853$	−281.964	+	488.377i	−0.330556	+	0.572540i	−0.982621	−	0.185623i	$-0.940570\pi$
$853$	−281.964	+	488.377i	−0.330556	+	0.572540i	0.652065	+	0.758163i	$0.273903\pi$
$854$		−	296.497i		−	0.347186i
$855$		0			0
$856$	−34.2579			−0.0400209
$857$	−826.107	−	476.953i	−0.963952	−	0.556538i	−0.0665649	−	0.997782i	$-0.521204\pi$
$857$	−826.107	−	476.953i	−0.963952	−	0.556538i	−0.897387	+	0.441244i	$0.854537\pi$
$858$	84.9334	+	1309.00i	0.0989900	+	1.52564i
$859$	422.728	+	732.186i	0.492116	+	0.852371i	0.999959	−	0.00907936i	$-0.00289009\pi$
$859$	422.728	+	732.186i	0.492116	+	0.852371i	−0.507842	+	0.861450i	$0.669557\pi$
$860$		0			0
$861$	−147.956	−	221.747i	−0.171842	−	0.257546i
$862$	100.221	−	173.587i	0.116265	−	0.201377i
$863$			1109.42i			1.28554i	0.766061	+	0.642768i	$0.222214\pi$
$863$			1109.42i			1.28554i	−0.766061	+	0.642768i	$0.777786\pi$
$864$	1003.07	+	1148.34i	1.16096	+	1.32909i
$865$		0			0
$866$	1681.02	+	970.538i	1.94113	+	1.12071i
$867$	675.390	−	450.640i	0.778997	−	0.519770i
$868$	−236.848	−	410.233i	−0.272866	−	0.472618i
$869$	−981.388	+	566.605i	−1.12933	+	0.652019i
$870$		0			0
$871$	470.796	−	815.442i	0.540523	−	0.936214i
$872$			3067.06i			3.51727i
$873$	−699.894	−	914.604i	−0.801712	−	1.04766i
$874$	13.4918			0.0154369
$875$		0			0
$876$	−782.318	−	386.435i	−0.893058	−	0.441136i
$877$	507.331	+	878.724i	0.578485	+	1.00197i	0.995653	+	0.0931364i	$0.0296893\pi$
$877$	507.331	+	878.724i	0.578485	+	1.00197i	−0.417168	+	0.908829i	$0.636977\pi$
$878$	−1329.19	+	767.411i	−1.51389	+	0.874044i
$879$	428.013	−	866.491i	0.486932	−	0.985769i
$880$		0			0
$881$		−	1226.86i		−	1.39257i	−0.717764	−	0.696287i	$-0.754834\pi$
$881$		−	1226.86i		−	1.39257i	0.717764	−	0.696287i	$-0.245166\pi$
$882$	1299.51	+	540.275i	1.47337	+	0.612556i
$883$	−659.407			−0.746780			−0.373390	−	0.927674i	$-0.621805\pi$
$883$	−659.407			−0.746780			−0.373390	+	0.927674i	$0.621805\pi$
$884$	429.526	+	247.987i	0.485889	+	0.280528i
$885$		0			0
$886$	787.537	+	1364.05i	0.888868	+	1.53956i
$887$	−668.543	+	385.984i	−0.753713	+	0.435156i	−0.827034	−	0.562152i	$-0.809974\pi$
$887$	−668.543	+	385.984i	−0.753713	+	0.435156i	0.0733209	+	0.997308i	$0.476640\pi$
$888$	−45.3003	−	67.8932i	−0.0510139	−	0.0764563i
$889$	129.846	−	224.901i	0.146059	−	0.252982i
$890$		0			0
$891$	204.061	+	769.645i	0.229025	+	0.863799i
$892$	2067.01			2.31727
$893$	316.120	+	182.512i	0.353998	+	0.204381i
$894$	−439.439	+	293.207i	−0.491543	+	0.327972i
$895$		0			0
$896$	−31.4123	+	18.1359i	−0.0350584	+	0.0202410i
$897$	18.4376	−	1.19631i	0.0205548	−	0.00133368i
$898$	436.445	−	755.945i	0.486019	−	0.841810i
$899$			587.432i			0.653428i
$900$		0			0
$901$	371.189			0.411974
$902$	1086.43	+	627.249i	1.20447	+	0.695398i
$903$	358.725	+	177.197i	0.397260	+	0.196231i
$904$	−1356.24	−	2349.08i	−1.50027	−	2.59854i
$905$		0			0
$906$	−271.854	+	550.355i	−0.300060	+	0.607455i
$907$	−60.7354	+	105.197i	−0.0669629	+	0.115983i	−0.897563	−	0.440886i	$-0.854664\pi$
$907$	−60.7354	+	105.197i	−0.0669629	+	0.115983i	0.830600	+	0.556869i	$0.187998\pi$
$908$		−	483.792i		−	0.532810i
$909$	615.221	−	470.794i	0.676811	−	0.517925i
$910$		0			0
$911$	−1000.46	−	577.616i	−1.09820	−	0.634046i	−0.162453	−	0.986716i	$-0.551940\pi$
$911$	−1000.46	−	577.616i	−1.09820	−	0.634046i	−0.935748	+	0.352670i	$0.885274\pi$
$912$	−52.4830	−	808.871i	−0.0575472	−	0.886920i
$913$	−294.971	−	510.904i	−0.323078	−	0.559588i
$914$	−2228.21	+	1286.46i	−2.43786	+	1.40750i
$915$		0			0
$916$	29.5895	−	51.2505i	0.0323029	−	0.0559503i
$917$		−	220.275i		−	0.240212i
$918$	403.643	+	137.905i	0.439699	+	0.150224i
$919$	994.576			1.08224			0.541119	−	0.840946i	$-0.318001\pi$
$919$	994.576			1.08224			0.541119	+	0.840946i	$0.318001\pi$
$920$		0			0
$921$	−1063.16	+	709.372i	−1.15436	+	0.770220i
$922$	−707.501	−	1225.43i	−0.767354	−	1.32910i
$923$	759.258	−	438.358i	0.822598	−	0.474927i
$924$	725.020	−	47.0424i	0.784654	−	0.0509117i
$925$		0			0
$926$			995.977i			1.07557i
$927$	364.864	−	47.5481i	0.393597	−	0.0512924i
$928$	−1725.33			−1.85919
$929$	−140.236	−	80.9655i	−0.150954	−	0.0871534i	0.422620	−	0.906307i	$-0.361110\pi$
$929$	−140.236	−	80.9655i	−0.150954	−	0.0871534i	−0.573575	+	0.819153i	$0.694444\pi$
$930$		0			0
$931$	−151.970	−	263.221i	−0.163234	−	0.282729i
$932$	436.574	−	252.056i	0.468427	−	0.270447i
$933$	−1.55181	+	3.14155i	−0.00166324	+	0.00336715i
$934$	−1434.26	+	2484.22i	−1.53561	+	2.65976i
$935$		0			0
$936$	−289.493	−	2221.45i	−0.309288	−	2.37334i
$937$	660.489			0.704898			0.352449	−	0.935831i	$-0.385349\pi$
$937$	660.489			0.704898			0.352449	+	0.935831i	$0.385349\pi$
$938$	−639.919	−	369.457i	−0.682216	−	0.393878i
$939$	−50.6880	−	781.206i	−0.0539808	−	0.831955i
$940$		0			0
$941$	−1378.06	+	795.624i	−1.46446	+	0.845509i	−0.999213	−	0.0396696i	$-0.987369\pi$
$941$	−1378.06	+	795.624i	−1.46446	+	0.845509i	−0.465252	+	0.885179i	$0.654036\pi$
$942$	67.9783	+	101.881i	0.0721638	+	0.108154i
$943$	8.83498	−	15.3026i	0.00936902	−	0.0162276i
$944$		−	3994.69i		−	4.23167i
$945$		0			0
$946$	−1882.88			−1.99035
$947$	1353.91	+	781.678i	1.42968	+	0.825426i	0.997095	−	0.0761680i	$-0.0242685\pi$
$947$	1353.91	+	781.678i	1.42968	+	0.825426i	0.432584	+	0.901594i	$0.357602\pi$
$948$	2760.58	−	1841.94i	2.91201	−	1.94298i
$949$	182.818	+	316.650i	0.192643	+	0.333667i
$950$		0			0
$951$	−392.282	+	25.4529i	−0.412494	+	0.0267644i
$952$	113.488	−	196.566i	0.119210	−	0.206477i
$953$			996.612i			1.04576i	0.852405	+	0.522881i	$0.175143\pi$
$953$			996.612i			1.04576i	−0.852405	+	0.522881i	$0.824857\pi$
$954$	−1747.21	−	2283.20i	−1.83145	−	2.39330i
$955$		0			0
$956$	−810.961	−	468.209i	−0.848285	−	0.489758i
$957$	−807.812	−	399.028i	−0.844109	−	0.416957i
$958$	−133.783	−	231.719i	−0.139648	−	0.241878i
$959$	−155.031	+	89.5074i	−0.161659	+	0.0933341i
$960$		0			0
$961$	295.657	−	512.093i	0.307656	−	0.532875i
$962$			58.6484i			0.0609651i
$963$	13.7974	+	5.73631i	0.0143275	+	0.00595670i
$964$	1369.63			1.42078
$965$		0			0
$966$	−0.938806	−	14.4689i	−0.000971849	−	0.0149782i
$967$	−325.000	−	562.916i	−0.336091	−	0.582126i	0.647603	−	0.761978i	$-0.275771\pi$
$967$	−325.000	−	562.916i	−0.336091	−	0.582126i	−0.983694	+	0.179852i	$0.942438\pi$
$968$	435.468	−	251.418i	0.449864	−	0.259729i
$969$	−51.1295	−	76.6295i	−0.0527652	−	0.0790810i
$970$		0			0
$971$			1717.75i			1.76905i	0.466495	+	0.884524i	$0.345517\pi$
$971$			1717.75i			1.76905i	−0.466495	+	0.884524i	$0.654483\pi$
$972$	−742.291	−	2210.53i	−0.763674	−	2.27421i
$973$	−356.656			−0.366553
$974$	−2329.45	−	1344.91i	−2.39163	−	1.38081i
$975$		0			0
$976$	−590.372	−	1022.55i	−0.604889	−	1.04770i
$977$	−244.324	+	141.061i	−0.250076	+	0.144381i	−0.619799	−	0.784761i	$-0.712786\pi$
$977$	−244.324	+	141.061i	−0.250076	+	0.144381i	0.369723	+	0.929142i	$0.379453\pi$
$978$	2386.88	−	154.871i	2.44057	−	0.158355i
$979$	350.439	−	606.979i	0.357956	−	0.619998i
$980$		0			0
$981$	513.564	−	1235.26i	0.523510	−	1.25919i
$982$	14.0695			0.0143274
$983$	333.017	+	192.267i	0.338776	+	0.195592i	0.659731	−	0.751502i	$-0.270670\pi$
$983$	333.017	+	192.267i	0.338776	+	0.195592i	−0.320955	+	0.947095i	$0.604004\pi$
$984$	−1920.89	−	948.846i	−1.95212	−	0.964274i
$985$		0			0
$986$	−418.003	+	241.334i	−0.423938	+	0.244761i
$987$	173.733	−	351.713i	0.176021	−	0.356346i
$988$	−414.824	+	718.496i	−0.419862	+	0.727223i
$989$			26.5208i			0.0268158i
$990$		0			0
$991$	399.250			0.402876			0.201438	−	0.979501i	$-0.435439\pi$
$991$	399.250			0.402876			0.201438	+	0.979501i	$0.435439\pi$
$992$	−940.326	−	542.898i	−0.947910	−	0.547276i
$993$	37.5832	+	579.234i	0.0378481	+	0.583317i
$994$	−344.002	−	595.828i	−0.346078	−	0.599425i
$995$		0			0
$996$	958.903	+	1437.14i	0.962754	+	1.44291i
$997$	−726.087	+	1257.62i	−0.728272	+	1.26140i	0.229341	+	0.973346i	$0.426343\pi$
$997$	−726.087	+	1257.62i	−0.728272	+	1.26140i	−0.957613	+	0.288058i	$0.906991\pi$
$998$			757.008i			0.758525i
$999$	6.87641	+	34.9294i	0.00688329	+	0.0349643i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.3.j.e.101.10		20
3.2	odd	2		675.3.j.e.251.1		20
5.2	odd	4		45.3.h.a.29.1	yes	20
5.3	odd	4		45.3.h.a.29.10	yes	20
5.4	even	2	inner	225.3.j.e.101.1		20
9.4	even	3		675.3.j.e.476.1		20
9.5	odd	6	inner	225.3.j.e.176.10		20
15.2	even	4		135.3.h.a.89.10		20
15.8	even	4		135.3.h.a.89.1		20
15.14	odd	2		675.3.j.e.251.10		20
45.2	even	12		405.3.d.a.404.2		20
45.4	even	6		675.3.j.e.476.10		20
45.7	odd	12		405.3.d.a.404.19		20
45.13	odd	12		135.3.h.a.44.10		20
45.14	odd	6	inner	225.3.j.e.176.1		20
45.22	odd	12		135.3.h.a.44.1		20
45.23	even	12		45.3.h.a.14.1	✓	20
45.32	even	12		45.3.h.a.14.10	yes	20
45.38	even	12		405.3.d.a.404.20		20
45.43	odd	12		405.3.d.a.404.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.h.a.14.1	✓	20	45.23	even	12
45.3.h.a.14.10	yes	20	45.32	even	12
45.3.h.a.29.1	yes	20	5.2	odd	4
45.3.h.a.29.10	yes	20	5.3	odd	4
135.3.h.a.44.1		20	45.22	odd	12
135.3.h.a.44.10		20	45.13	odd	12
135.3.h.a.89.1		20	15.8	even	4
135.3.h.a.89.10		20	15.2	even	4
225.3.j.e.101.1		20	5.4	even	2	inner
225.3.j.e.101.10		20	1.1	even	1	trivial
225.3.j.e.176.1		20	45.14	odd	6	inner
225.3.j.e.176.10		20	9.5	odd	6	inner
405.3.d.a.404.1		20	45.43	odd	12
405.3.d.a.404.2		20	45.2	even	12
405.3.d.a.404.19		20	45.7	odd	12
405.3.d.a.404.20		20	45.38	even	12
675.3.j.e.251.1		20	3.2	odd	2
675.3.j.e.251.10		20	15.14	odd	2
675.3.j.e.476.1		20	9.4	even	3
675.3.j.e.476.10		20	45.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	225.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.19328 + 1.84364i) q^{2} +(2.49550 - 1.66507i) q^{3} +(4.79800 + 8.31039i) q^{4} +(11.0386 - 0.716233i) q^{6} +(-1.28370 + 2.22343i) q^{7} +20.6340i q^{8} +(3.45506 - 8.31039i) q^{9} +(-8.51311 - 4.91505i) q^{11} +(25.8108 + 12.7496i) q^{12} +(-6.03166 - 10.4471i) q^{13} +(-8.19840 + 4.73335i) q^{14} +(-18.8497 + 32.6486i) q^{16} +4.28451i q^{17} +(26.3543 - 20.1675i) q^{18} -7.16698 q^{19} +(0.498702 + 7.68602i) q^{21} +(-18.1231 - 31.3902i) q^{22} +(-0.442140 + 0.255270i) q^{23} +(34.3572 + 51.4923i) q^{24} -44.4808i q^{26} +(-5.21528 - 26.4915i) q^{27} -24.6367 q^{28} +(26.4589 + 15.2761i) q^{29} +(9.61361 + 16.6513i) q^{31} +(-48.9060 + 28.2359i) q^{32} +(-29.4284 + 1.90944i) q^{33} +(-7.89910 + 13.6816i) q^{34} +(85.6399 - 11.1604i) q^{36} -1.31851 q^{37} +(-22.8862 - 13.2133i) q^{38} +(-32.4473 - 16.0277i) q^{39} +(-29.9735 + 17.3052i) q^{41} +(-12.5778 + 25.4630i) q^{42} +(25.9734 - 44.9872i) q^{43} -94.3297i q^{44} -1.88250 q^{46} +(-44.1078 - 25.4656i) q^{47} +(7.32289 + 112.861i) q^{48} +(21.2042 + 36.7268i) q^{49} +(7.13403 + 10.6920i) q^{51} +(57.8799 - 100.251i) q^{52} -86.6349i q^{53} +(32.1870 - 94.2098i) q^{54} +(-45.8783 - 26.4879i) q^{56} +(-17.8852 + 11.9336i) q^{57} +(56.3270 + 97.5613i) q^{58} +(-91.7656 + 52.9809i) q^{59} +(-15.6600 + 27.1239i) q^{61} +70.8961i q^{62} +(14.0423 + 18.3501i) q^{63} -57.4297 q^{64} +(-97.4933 - 48.1580i) q^{66} +(39.0271 + 67.5968i) q^{67} +(-35.6060 + 20.5571i) q^{68} +(-0.678318 + 1.37322i) q^{69} +72.6762i q^{71} +(171.477 + 71.2919i) q^{72} -30.3097 q^{73} +(-4.21037 - 2.43086i) q^{74} +(-34.3872 - 59.5604i) q^{76} +(21.8565 - 12.6189i) q^{77} +(-74.0638 - 111.002i) q^{78} +(57.6398 - 99.8350i) q^{79} +(-57.1251 - 57.4258i) q^{81} -127.618 q^{82} +(51.9734 + 30.0069i) q^{83} +(-61.4810 + 41.0220i) q^{84} +(165.880 - 95.7710i) q^{86} +(91.4640 - 5.93457i) q^{87} +(101.417 - 175.660i) q^{88} +71.2992i q^{89} +30.9713 q^{91} +(-4.24278 - 2.44957i) q^{92} +(51.7163 + 25.5459i) q^{93} +(-93.8989 - 162.638i) q^{94} +(-75.0302 + 151.895i) q^{96} +(63.9819 - 110.820i) q^{97} +156.372i q^{98} +(-70.2593 + 53.7655i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 18 q^{4} + 12 q^{6} + 18 q^{9} - 24 q^{11} - 30 q^{14} - 26 q^{16} + 8 q^{19} - 96 q^{21} + 102 q^{24} + 114 q^{29} + 28 q^{31} + 4 q^{34} + 432 q^{36} - 240 q^{39} + 102 q^{41} + 116 q^{46} + 40 q^{49}+ \cdots + 468 q^{99}+O(q^{100}) \) 20 * q + 18 * q^4 + 12 * q^6 + 18 * q^9 - 24 * q^11 - 30 * q^14 - 26 * q^16 + 8 * q^19 - 96 * q^21 + 102 * q^24 + 114 * q^29 + 28 * q^31 + 4 * q^34 + 432 * q^36 - 240 * q^39 + 102 * q^41 + 116 * q^46 + 40 * q^49 - 156 * q^51 + 270 * q^54 - 618 * q^56 - 120 * q^59 - 50 * q^61 - 140 * q^64 - 768 * q^66 - 162 * q^69 - 504 * q^74 - 96 * q^76 + 128 * q^79 + 846 * q^81 - 450 * q^84 + 1488 * q^86 - 288 * q^91 - 218 * q^94 - 474 * q^96 + 468 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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