LMFDB - Embedded newform 350.4.j.b.249.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,4,Mod(149,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("350.149");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	350.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$20.6506685020$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	350.249
Dual form			350.4.j.b.149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 - 1.00000i) q^{2} +(-4.33013 - 2.50000i) q^{3} +(2.00000 - 3.46410i) q^{4} -10.0000 q^{6} +(-12.1244 - 14.0000i) q^{7} -8.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(1.73205 - 1.00000i) q^{2} +(-4.33013 - 2.50000i) q^{3} +(2.00000 - 3.46410i) q^{4} -10.0000 q^{6} +(-12.1244 - 14.0000i) q^{7} -8.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +(28.5000 - 49.3634i) q^{11} +(-17.3205 + 10.0000i) q^{12} +70.0000i q^{13} +(-35.0000 - 12.1244i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-44.1673 - 25.5000i) q^{17} +(-3.46410 - 2.00000i) q^{18} +(2.50000 + 4.33013i) q^{19} +(17.5000 + 90.9327i) q^{21} -114.000i q^{22} +(-59.7558 + 34.5000i) q^{23} +(-20.0000 + 34.6410i) q^{24} +(70.0000 + 121.244i) q^{26} +145.000i q^{27} +(-72.7461 + 14.0000i) q^{28} -114.000 q^{29} +(-11.5000 + 19.9186i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(-246.817 + 142.500i) q^{33} -102.000 q^{34} -8.00000 q^{36} +(-219.104 + 126.500i) q^{37} +(8.66025 + 5.00000i) q^{38} +(175.000 - 303.109i) q^{39} -42.0000 q^{41} +(121.244 + 140.000i) q^{42} +124.000i q^{43} +(-114.000 - 197.454i) q^{44} +(-69.0000 + 119.512i) q^{46} +(174.071 - 100.500i) q^{47} +80.0000i q^{48} +(-49.0000 + 339.482i) q^{49} +(127.500 + 220.836i) q^{51} +(242.487 + 140.000i) q^{52} +(-340.348 - 196.500i) q^{53} +(145.000 + 251.147i) q^{54} +(-112.000 + 96.9948i) q^{56} -25.0000i q^{57} +(-197.454 + 114.000i) q^{58} +(109.500 - 189.660i) q^{59} +(354.500 + 614.012i) q^{61} +46.0000i q^{62} +(-12.1244 + 35.0000i) q^{63} -64.0000 q^{64} +(-285.000 + 493.634i) q^{66} +(-362.865 - 209.500i) q^{67} +(-176.669 + 102.000i) q^{68} +345.000 q^{69} -96.0000 q^{71} +(-13.8564 + 8.00000i) q^{72} +(-271.066 - 156.500i) q^{73} +(-253.000 + 438.209i) q^{74} +20.0000 q^{76} +(-1036.63 + 199.500i) q^{77} -700.000i q^{78} +(230.500 + 399.238i) q^{79} +(335.500 - 581.103i) q^{81} +(-72.7461 + 42.0000i) q^{82} +588.000i q^{83} +(350.000 + 121.244i) q^{84} +(124.000 + 214.774i) q^{86} +(493.634 + 285.000i) q^{87} +(-394.908 - 228.000i) q^{88} +(-508.500 - 880.748i) q^{89} +(980.000 - 848.705i) q^{91} +276.000i q^{92} +(99.5929 - 57.5000i) q^{93} +(201.000 - 348.142i) q^{94} +(80.0000 + 138.564i) q^{96} -1834.00i q^{97} +(254.611 + 637.000i) q^{98} -114.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4} - 40 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q + 8 * q^4 - 40 * q^6 - 4 * q^9	$ 4 q + 8 q^{4} - 40 q^{6} - 4 q^{9} + 114 q^{11} - 140 q^{14} - 32 q^{16} + 10 q^{19} + 70 q^{21} - 80 q^{24} + 280 q^{26} - 456 q^{29} - 46 q^{31} - 408 q^{34} - 32 q^{36} + 700 q^{39} - 168 q^{41} - 456 q^{44} - 276 q^{46} - 196 q^{49} + 510 q^{51} + 580 q^{54} - 448 q^{56} + 438 q^{59} + 1418 q^{61} - 256 q^{64} - 1140 q^{66} + 1380 q^{69} - 384 q^{71} - 1012 q^{74} + 80 q^{76} + 922 q^{79} + 1342 q^{81} + 1400 q^{84} + 496 q^{86} - 2034 q^{89} + 3920 q^{91} + 804 q^{94} + 320 q^{96} - 456 q^{99}+O(q^{100}) $ 4 * q + 8 * q^4 - 40 * q^6 - 4 * q^9 + 114 * q^11 - 140 * q^14 - 32 * q^16 + 10 * q^19 + 70 * q^21 - 80 * q^24 + 280 * q^26 - 456 * q^29 - 46 * q^31 - 408 * q^34 - 32 * q^36 + 700 * q^39 - 168 * q^41 - 456 * q^44 - 276 * q^46 - 196 * q^49 + 510 * q^51 + 580 * q^54 - 448 * q^56 + 438 * q^59 + 1418 * q^61 - 256 * q^64 - 1140 * q^66 + 1380 * q^69 - 384 * q^71 - 1012 * q^74 + 80 * q^76 + 922 * q^79 + 1342 * q^81 + 1400 * q^84 + 496 * q^86 - 2034 * q^89 + 3920 * q^91 + 804 * q^94 + 320 * q^96 - 456 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	−4.33013	−	2.50000i	−0.833333	−	0.481125i	0.0216593	−	0.999765i	$-0.493105\pi$
$3$	−4.33013	−	2.50000i	−0.833333	−	0.481125i	−0.854993	+	0.518640i	$0.826438\pi$
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−10.0000			−0.680414
$7$	−12.1244	−	14.0000i	−0.654654	−	0.755929i
$7$	−12.1244	−	14.0000i	−0.654654	−	0.755929i
$8$		−	8.00000i		−	0.353553i
$9$	−1.00000	−	1.73205i	−0.0370370	−	0.0641500i
$10$		0			0
$11$	28.5000	−	49.3634i	0.781188	−	1.35306i	−0.150061	−	0.988677i	$-0.547947\pi$
$11$	28.5000	−	49.3634i	0.781188	−	1.35306i	0.931250	−	0.364381i	$-0.118720\pi$
$12$	−17.3205	+	10.0000i	−0.416667	+	0.240563i
$13$			70.0000i			1.49342i	0.665148	+	0.746712i	$0.268369\pi$
$13$			70.0000i			1.49342i	−0.665148	+	0.746712i	$0.731631\pi$
$14$	−35.0000	−	12.1244i	−0.668153	−	0.231455i
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−44.1673	−	25.5000i	−0.630126	−	0.363803i	0.150675	−	0.988583i	$-0.451855\pi$
$17$	−44.1673	−	25.5000i	−0.630126	−	0.363803i	−0.780801	+	0.624780i	$0.785189\pi$
$18$	−3.46410	−	2.00000i	−0.0453609	−	0.0261891i
$19$	2.50000	+	4.33013i	0.0301863	+	0.0522842i	0.880724	−	0.473630i	$-0.157057\pi$
$19$	2.50000	+	4.33013i	0.0301863	+	0.0522842i	−0.850538	+	0.525914i	$0.823723\pi$
$20$		0			0
$21$	17.5000	+	90.9327i	0.181848	+	0.944911i
$22$		−	114.000i		−	1.10477i
$23$	−59.7558	+	34.5000i	−0.541736	+	0.312772i	−0.745782	−	0.666190i	$-0.767924\pi$
$23$	−59.7558	+	34.5000i	−0.541736	+	0.312772i	0.204046	+	0.978961i	$0.434591\pi$
$24$	−20.0000	+	34.6410i	−0.170103	+	0.294628i
$25$		0			0
$26$	70.0000	+	121.244i	0.528005	+	0.914531i
$27$			145.000i			1.03353i
$28$	−72.7461	+	14.0000i	−0.490990	+	0.0944911i
$29$	−114.000			−0.729975			−0.364987	−	0.931012i	$-0.618927\pi$
$29$	−114.000			−0.729975			−0.364987	+	0.931012i	$0.618927\pi$
$30$		0			0
$31$	−11.5000	+	19.9186i	−0.0666278	+	0.115403i	−0.897415	−	0.441188i	$-0.854557\pi$
$31$	−11.5000	+	19.9186i	−0.0666278	+	0.115403i	0.830787	+	0.556590i	$0.187891\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	−246.817	+	142.500i	−1.30198	+	0.751699i
$34$	−102.000			−0.514496
$35$		0			0
$36$	−8.00000			−0.0370370
$37$	−219.104	+	126.500i	−0.973528	+	0.562067i	−0.900310	−	0.435249i	$-0.856660\pi$
$37$	−219.104	+	126.500i	−0.973528	+	0.562067i	−0.0732182	+	0.997316i	$0.523327\pi$
$38$	8.66025	+	5.00000i	0.0369705	+	0.0213449i
$39$	175.000	−	303.109i	0.718524	−	1.24452i
$40$		0			0
$41$	−42.0000			−0.159983			−0.0799914	−	0.996796i	$-0.525489\pi$
$41$	−42.0000			−0.159983			−0.0799914	+	0.996796i	$0.525489\pi$
$42$	121.244	+	140.000i	0.445435	+	0.514344i
$43$			124.000i			0.439763i	0.975527	+	0.219882i	$0.0705671\pi$
$43$			124.000i			0.439763i	−0.975527	+	0.219882i	$0.929433\pi$
$44$	−114.000	−	197.454i	−0.390594	−	0.676529i
$45$		0			0
$46$	−69.0000	+	119.512i	−0.221163	+	0.383065i
$47$	174.071	−	100.500i	0.540231	−	0.311903i	−0.204941	−	0.978774i	$-0.565700\pi$
$47$	174.071	−	100.500i	0.540231	−	0.311903i	0.745173	+	0.666871i	$0.232367\pi$
$48$			80.0000i			0.240563i
$49$	−49.0000	+	339.482i	−0.142857	+	0.989743i
$50$		0			0
$51$	127.500	+	220.836i	0.350070	+	0.606339i
$52$	242.487	+	140.000i	0.646671	+	0.373356i
$53$	−340.348	−	196.500i	−0.882083	−	0.509271i	−0.0107383	−	0.999942i	$-0.503418\pi$
$53$	−340.348	−	196.500i	−0.882083	−	0.509271i	−0.871345	+	0.490672i	$0.836751\pi$
$54$	145.000	+	251.147i	0.365407	+	0.632904i
$55$		0			0
$56$	−112.000	+	96.9948i	−0.267261	+	0.231455i
$57$		−	25.0000i		−	0.0580935i
$58$	−197.454	+	114.000i	−0.447016	+	0.258085i
$59$	109.500	−	189.660i	0.241622	−	0.418501i	−0.719555	−	0.694436i	$-0.755654\pi$
$59$	109.500	−	189.660i	0.241622	−	0.418501i	0.961176	+	0.275935i	$0.0889873\pi$
$60$		0			0
$61$	354.500	+	614.012i	0.744083	+	1.28879i	0.950622	+	0.310351i	$0.100447\pi$
$61$	354.500	+	614.012i	0.744083	+	1.28879i	−0.206539	+	0.978438i	$0.566220\pi$
$62$			46.0000i			0.0942259i
$63$	−12.1244	+	35.0000i	−0.0242464	+	0.0699934i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	−285.000	+	493.634i	−0.531531	+	0.920639i
$67$	−362.865	−	209.500i	−0.661656	−	0.382007i	0.131251	−	0.991349i	$-0.458100\pi$
$67$	−362.865	−	209.500i	−0.661656	−	0.382007i	−0.792908	+	0.609342i	$0.791434\pi$
$68$	−176.669	+	102.000i	−0.315063	+	0.181902i
$69$	345.000			0.601929
$70$		0			0
$71$	−96.0000			−0.160466			−0.0802331	−	0.996776i	$-0.525566\pi$
$71$	−96.0000			−0.160466			−0.0802331	+	0.996776i	$0.525566\pi$
$72$	−13.8564	+	8.00000i	−0.0226805	+	0.0130946i
$73$	−271.066	−	156.500i	−0.434601	−	0.250917i	0.266704	−	0.963779i	$-0.414065\pi$
$73$	−271.066	−	156.500i	−0.434601	−	0.250917i	−0.701305	+	0.712862i	$0.747399\pi$
$74$	−253.000	+	438.209i	−0.397441	+	0.688388i
$75$		0			0
$76$	20.0000			0.0301863
$77$	−1036.63	+	199.500i	−1.53422	+	0.295261i
$78$		−	700.000i		−	1.01615i
$79$	230.500	+	399.238i	0.328269	+	0.568579i	0.982169	−	0.188003i	$-0.0602013\pi$
$79$	230.500	+	399.238i	0.328269	+	0.568579i	−0.653899	+	0.756582i	$0.726868\pi$
$80$		0			0
$81$	335.500	−	581.103i	0.460219	−	0.797124i
$82$	−72.7461	+	42.0000i	−0.0979691	+	0.0565625i
$83$			588.000i			0.777607i	0.921321	+	0.388804i	$0.127112\pi$
$83$			588.000i			0.777607i	−0.921321	+	0.388804i	$0.872888\pi$
$84$	350.000	+	121.244i	0.454621	+	0.157485i
$85$		0			0
$86$	124.000	+	214.774i	0.155480	+	0.269299i
$87$	493.634	+	285.000i	0.608312	+	0.351209i
$88$	−394.908	−	228.000i	−0.478378	−	0.276192i
$89$	−508.500	−	880.748i	−0.605628	−	1.04898i	−0.991952	−	0.126615i	$-0.959589\pi$
$89$	−508.500	−	880.748i	−0.605628	−	1.04898i	0.386324	−	0.922363i	$-0.373745\pi$
$90$		0			0
$91$	980.000	−	848.705i	1.12892	−	0.977675i
$92$			276.000i			0.312772i
$93$	99.5929	−	57.5000i	0.111046	−	0.0641126i
$94$	201.000	−	348.142i	0.220549	−	0.382001i
$95$		0			0
$96$	80.0000	+	138.564i	0.0850517	+	0.147314i
$97$		−	1834.00i		−	1.91974i	−0.280451	−	0.959868i	$-0.590484\pi$
$97$		−	1834.00i		−	1.91974i	0.280451	−	0.959868i	$-0.409516\pi$
$98$	254.611	+	637.000i	0.262445	+	0.656599i
$99$	−114.000			−0.115732
$100$		0			0
$101$	142.500	−	246.817i	0.140389	−	0.243161i	−0.787254	−	0.616629i	$-0.788498\pi$
$101$	142.500	−	246.817i	0.140389	−	0.243161i	0.927643	+	0.373468i	$0.121831\pi$
$102$	441.673	+	255.000i	0.428746	+	0.247537i
$103$	432.147	−	249.500i	0.413405	−	0.238679i	−0.278847	−	0.960336i	$-0.589952\pi$
$103$	432.147	−	249.500i	0.413405	−	0.238679i	0.692252	+	0.721656i	$0.256619\pi$
$104$	560.000			0.528005
$105$		0			0
$106$	−786.000			−0.720218
$107$	−958.690	+	553.500i	−0.866169	+	0.500083i	−0.866073	−	0.499917i	$-0.833364\pi$
$107$	−958.690	+	553.500i	−0.866169	+	0.500083i	−9.56665e−5		1.00000i	$0.500030\pi$
$108$	502.295	+	290.000i	0.447531	+	0.258382i
$109$	461.500	−	799.341i	0.405538	−	0.702413i	−0.588846	−	0.808246i	$-0.700417\pi$
$109$	461.500	−	799.341i	0.405538	−	0.702413i	0.994384	+	0.105832i	$0.0337507\pi$
$110$		0			0
$111$	1265.00			1.08170
$112$	−96.9948	+	280.000i	−0.0818317	+	0.236228i
$113$		−	1542.00i		−	1.28371i	−0.766826	−	0.641855i	$-0.778165\pi$
$113$		−	1542.00i		−	1.28371i	0.766826	−	0.641855i	$-0.221835\pi$
$114$	−25.0000	−	43.3013i	−0.0205392	−	0.0355749i
$115$		0			0
$116$	−228.000	+	394.908i	−0.182494	+	0.316088i
$117$	121.244	−	70.0000i	0.0958032	−	0.0553120i
$118$		−	438.000i		−	0.341705i
$119$	178.500	+	927.513i	0.137505	+	0.714496i
$120$		0			0
$121$	−959.000	−	1661.04i	−0.720511	−	1.24796i
$122$	1228.02	+	709.000i	0.911312	+	0.526146i
$123$	181.865	+	105.000i	0.133319	+	0.0769718i
$124$	46.0000	+	79.6743i	0.0333139	+	0.0577013i
$125$		0			0
$126$	14.0000	+	72.7461i	0.00989856	+	0.0514344i
$127$		−	2056.00i		−	1.43654i	−0.695765	−	0.718270i	$-0.744934\pi$
$127$		−	2056.00i		−	1.43654i	0.695765	−	0.718270i	$-0.255066\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	310.000	−	536.936i	0.211581	−	0.366469i
$130$		0			0
$131$	−1024.50	−	1774.49i	−0.683290	−	1.18349i	−0.973971	−	0.226673i	$-0.927215\pi$
$131$	−1024.50	−	1774.49i	−0.683290	−	1.18349i	0.290681	−	0.956820i	$-0.406118\pi$
$132$			1140.00i			0.751699i
$133$	30.3109	−	87.5000i	0.0197616	−	0.0570467i
$134$	−838.000			−0.540240
$135$		0			0
$136$	−204.000	+	353.338i	−0.128624	+	0.222783i
$137$	122.110	+	70.5000i	0.0761498	+	0.0439651i	0.537591	−	0.843205i	$-0.319334\pi$
$137$	122.110	+	70.5000i	0.0761498	+	0.0439651i	−0.461442	+	0.887171i	$0.652668\pi$
$138$	597.558	−	345.000i	0.368605	−	0.212814i
$139$	−1484.00			−0.905548			−0.452774	−	0.891625i	$-0.649566\pi$
$139$	−1484.00			−0.905548			−0.452774	+	0.891625i	$0.649566\pi$
$140$		0			0
$141$	−1005.00			−0.600257
$142$	−166.277	+	96.0000i	−0.0982651	+	0.0567334i
$143$	3455.44	+	1995.00i	2.02069	+	1.16665i
$144$	−16.0000	+	27.7128i	−0.00925926	+	0.0160375i
$145$		0			0
$146$	−626.000			−0.354850
$147$	1060.88	−	1347.50i	0.595238	−	0.756054i
$148$			1012.00i			0.562067i
$149$	−28.5000	−	49.3634i	−0.0156699	−	0.0271410i	0.858084	−	0.513509i	$-0.171655\pi$
$149$	−28.5000	−	49.3634i	−0.0156699	−	0.0271410i	−0.873754	+	0.486368i	$0.838321\pi$
$150$		0			0
$151$	−419.500	+	726.595i	−0.226082	+	0.391586i	−0.956644	−	0.291261i	$-0.905925\pi$
$151$	−419.500	+	726.595i	−0.226082	+	0.391586i	0.730561	+	0.682847i	$0.239258\pi$
$152$	34.6410	−	20.0000i	0.0184852	−	0.0106725i
$153$			102.000i			0.0538968i
$154$	−1596.00	+	1382.18i	−0.835126	+	0.723240i
$155$		0			0
$156$	−700.000	−	1212.44i	−0.359262	−	0.622260i
$157$	2453.45	+	1416.50i	1.24718	+	0.720057i	0.970545	−	0.240919i	$-0.0774488\pi$
$157$	2453.45	+	1416.50i	1.24718	+	0.720057i	0.276631	+	0.960976i	$0.410782\pi$
$158$	798.475	+	461.000i	0.402046	+	0.232121i
$159$	982.500	+	1701.74i	0.490046	+	0.848785i
$160$		0			0
$161$	1207.50	+	418.290i	0.591083	+	0.204757i
$162$		−	1342.00i		−	0.650849i
$163$	2001.38	−	1155.50i	0.961721	−	0.555250i	0.0650188	−	0.997884i	$-0.479289\pi$
$163$	2001.38	−	1155.50i	0.961721	−	0.555250i	0.896702	+	0.442634i	$0.145956\pi$
$164$	−84.0000	+	145.492i	−0.0399957	+	0.0692746i
$165$		0			0
$166$	588.000	+	1018.45i	0.274926	+	0.476185i
$167$			1260.00i			0.583843i	0.956442	+	0.291921i	$0.0942945\pi$
$167$			1260.00i			0.583843i	−0.956442	+	0.291921i	$0.905705\pi$
$168$	727.461	−	140.000i	0.334077	−	0.0642931i
$169$	−2703.00			−1.23031
$170$		0			0
$171$	5.00000	−	8.66025i	0.00223602	−	0.00387290i
$172$	429.549	+	248.000i	0.190423	+	0.109941i
$173$	−2829.30	+	1633.50i	−1.24340	+	0.717877i	−0.969785	−	0.243962i	$-0.921553\pi$
$173$	−2829.30	+	1633.50i	−1.24340	+	0.717877i	−0.273615	+	0.961839i	$0.588219\pi$
$174$	1140.00			0.496685
$175$		0			0
$176$	−912.000			−0.390594
$177$	−948.298	+	547.500i	−0.402703	+	0.232501i
$178$	−1761.50	−	1017.00i	−0.741740	−	0.428244i
$179$	643.500	−	1114.57i	0.268701	−	0.465403i	−0.699826	−	0.714314i	$-0.746739\pi$
$179$	643.500	−	1114.57i	0.268701	−	0.465403i	0.968527	+	0.248910i	$0.0800724\pi$
$180$		0			0
$181$	−2674.00			−1.09810			−0.549052	−	0.835788i	$-0.685011\pi$
$181$	−2674.00			−1.09810			−0.549052	+	0.835788i	$0.685011\pi$
$182$	848.705	−	2450.00i	0.345660	−	0.997836i
$183$		−	3545.00i		−	1.43199i
$184$	276.000	+	478.046i	0.110581	+	0.191533i
$185$		0			0
$186$	115.000	−	199.186i	0.0453345	−	0.0785216i
$187$	−2517.54	+	1453.50i	−0.984494	+	0.568398i
$188$		−	804.000i		−	0.311903i
$189$	2030.00	−	1758.03i	0.781274	−	0.676603i
$190$		0			0
$191$	−2092.50	−	3624.32i	−0.792712	−	1.37302i	−0.924282	−	0.381711i	$-0.875335\pi$
$191$	−2092.50	−	3624.32i	−0.792712	−	1.37302i	0.131570	−	0.991307i	$-0.457998\pi$
$192$	277.128	+	160.000i	0.104167	+	0.0601407i
$193$	−73.6122	−	42.5000i	−0.0274545	−	0.0158509i	0.486210	−	0.873842i	$-0.338379\pi$
$193$	−73.6122	−	42.5000i	−0.0274545	−	0.0158509i	−0.513664	+	0.857991i	$0.671712\pi$
$194$	−1834.00	−	3176.58i	−0.678730	−	1.17559i
$195$		0			0
$196$	1078.00	+	848.705i	0.392857	+	0.309295i
$197$		−	390.000i		−	0.141047i	−0.997510	−	0.0705237i	$-0.977533\pi$
$197$		−	390.000i		−	0.141047i	0.997510	−	0.0705237i	$-0.0224671\pi$
$198$	−197.454	+	114.000i	−0.0708709	+	0.0409173i
$199$	−1416.50	+	2453.45i	−0.504588	+	0.873972i	0.495398	+	0.868666i	$0.335022\pi$
$199$	−1416.50	+	2453.45i	−0.504588	+	0.873972i	−0.999986	+	0.00530596i	$0.998311\pi$
$200$		0			0
$201$	1047.50	+	1814.32i	0.367587	+	0.636679i
$202$		−	570.000i		−	0.198540i
$203$	1382.18	+	1596.00i	0.477881	+	0.551809i
$204$	1020.00			0.350070
$205$		0			0
$206$	499.000	−	864.293i	0.168772	−	0.292321i
$207$	119.512	+	69.0000i	0.0401286	+	0.0231683i
$208$	969.948	−	560.000i	0.323336	−	0.186678i
$209$	285.000			0.0943247
$210$		0			0
$211$	−124.000			−0.0404574			−0.0202287	−	0.999795i	$-0.506439\pi$
$211$	−124.000			−0.0404574			−0.0202287	+	0.999795i	$0.506439\pi$
$212$	−1361.39	+	786.000i	−0.441041	+	0.254635i
$213$	415.692	+	240.000i	0.133722	+	0.0772044i
$214$	−1107.00	+	1917.38i	−0.353612	+	0.612474i
$215$		0			0
$216$	1160.00			0.365407
$217$	418.290	−	80.5000i	0.130854	−	0.0251829i
$218$		−	1846.00i		−	0.573518i
$219$	782.500	+	1355.33i	0.241445	+	0.418195i
$220$		0			0
$221$	1785.00	−	3091.71i	0.543313	−	0.941045i
$222$	2191.04	−	1265.00i	0.662402	−	0.382438i
$223$		−	56.0000i		−	0.0168163i	−0.999965	−	0.00840816i	$-0.997324\pi$
$223$		−	56.0000i		−	0.0168163i	0.999965	−	0.00840816i	$-0.00267643\pi$
$224$	112.000	+	581.969i	0.0334077	+	0.173591i
$225$		0			0
$226$	−1542.00	−	2670.82i	−0.453860	−	0.786108i
$227$	2647.44	+	1528.50i	0.774083	+	0.446917i	0.834329	−	0.551267i	$-0.185855\pi$
$227$	2647.44	+	1528.50i	0.774083	+	0.446917i	−0.0602465	+	0.998184i	$0.519189\pi$
$228$	−86.6025	−	50.0000i	−0.0251552	−	0.0145234i
$229$	−480.500	−	832.250i	−0.138656	−	0.240160i	0.788332	−	0.615250i	$-0.210945\pi$
$229$	−480.500	−	832.250i	−0.138656	−	0.240160i	−0.926988	+	0.375090i	$0.877612\pi$
$230$		0			0
$231$	4987.50	+	1727.72i	1.42058	+	0.492102i
$232$			912.000i			0.258085i
$233$	2449.99	−	1414.50i	0.688858	−	0.397712i	−0.114326	−	0.993443i	$-0.536471\pi$
$233$	2449.99	−	1414.50i	0.688858	−	0.397712i	0.803184	+	0.595731i	$0.203138\pi$
$234$	140.000	−	242.487i	0.0391115	−	0.0677431i
$235$		0			0
$236$	−438.000	−	758.638i	−0.120811	−	0.209251i
$237$		−	2305.00i		−	0.631755i
$238$	1236.68	+	1428.00i	0.336817	+	0.388922i
$239$	3540.00			0.958090			0.479045	−	0.877790i	$-0.340983\pi$
$239$	3540.00			0.958090			0.479045	+	0.877790i	$0.340983\pi$
$240$		0			0
$241$	−2615.50	+	4530.18i	−0.699084	+	1.21085i	0.269701	+	0.962944i	$0.413075\pi$
$241$	−2615.50	+	4530.18i	−0.699084	+	1.21085i	−0.968785	+	0.247904i	$0.920258\pi$
$242$	−3322.07	−	1918.00i	−0.882442	−	0.509478i
$243$	484.974	−	280.000i	0.128029	−	0.0739177i
$244$	2836.00			0.744083
$245$		0			0
$246$	420.000			0.108855
$247$	−303.109	+	175.000i	−0.0780824	+	0.0450809i
$248$	159.349	+	92.0000i	0.0408010	+	0.0235565i
$249$	1470.00	−	2546.11i	0.374126	−	0.648006i
$250$		0			0
$251$	5040.00			1.26742			0.633709	−	0.773571i	$-0.281532\pi$
$251$	5040.00			1.26742			0.633709	+	0.773571i	$0.281532\pi$
$252$	96.9948	+	112.000i	0.0242464	+	0.0279974i
$253$			3933.00i			0.977334i
$254$	−2056.00	−	3561.10i	−0.507893	−	0.879697i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−1244.48	+	718.500i	−0.302056	+	0.174392i	−0.643366	−	0.765559i	$-0.722463\pi$
$257$	−1244.48	+	718.500i	−0.302056	+	0.174392i	0.341310	+	0.939951i	$0.389129\pi$
$258$		−	1240.00i		−	0.299221i
$259$	4427.50	+	1533.73i	1.06221	+	0.367959i
$260$		0			0
$261$	114.000	+	197.454i	0.0270361	+	0.0468279i
$262$	−3548.97	−	2049.00i	−0.836856	−	0.483159i
$263$	−2013.51	−	1162.50i	−0.472085	−	0.272558i	0.245027	−	0.969516i	$-0.421203\pi$
$263$	−2013.51	−	1162.50i	−0.472085	−	0.272558i	−0.717112	+	0.696958i	$0.754536\pi$
$264$	1140.00	+	1974.54i	0.265766	+	0.460320i
$265$		0			0
$266$	−35.0000	−	181.865i	−0.00806762	−	0.0419206i
$267$			5085.00i			1.16553i
$268$	−1451.46	+	838.000i	−0.330828	+	0.191004i
$269$	−1192.50	+	2065.47i	−0.270290	+	0.468156i	−0.968936	−	0.247311i	$-0.920453\pi$
$269$	−1192.50	+	2065.47i	−0.270290	+	0.468156i	0.698646	+	0.715467i	$0.253786\pi$
$270$		0			0
$271$	165.500	+	286.654i	0.0370975	+	0.0642547i	0.883978	−	0.467528i	$-0.154855\pi$
$271$	165.500	+	286.654i	0.0370975	+	0.0642547i	−0.846881	+	0.531783i	$0.821522\pi$
$272$			816.000i			0.181902i
$273$	−6365.29	+	1225.00i	−1.41115	+	0.271576i
$274$	282.000			0.0621761
$275$		0			0
$276$	690.000	−	1195.12i	0.150482	−	0.260643i
$277$	−4218.41	−	2435.50i	−0.915017	−	0.528285i	−0.0329750	−	0.999456i	$-0.510498\pi$
$277$	−4218.41	−	2435.50i	−0.915017	−	0.528285i	−0.882042	+	0.471171i	$0.843831\pi$
$278$	−2570.36	+	1484.00i	−0.554533	+	0.320160i
$279$	46.0000			0.00987078
$280$		0			0
$281$	−7026.00			−1.49159			−0.745794	−	0.666177i	$-0.767930\pi$
$281$	−7026.00			−1.49159			−0.745794	+	0.666177i	$0.767930\pi$
$282$	−1740.71	+	1005.00i	−0.367581	+	0.212223i
$283$	−4635.83	−	2676.50i	−0.973752	−	0.562196i	−0.0733738	−	0.997305i	$-0.523377\pi$
$283$	−4635.83	−	2676.50i	−0.973752	−	0.562196i	−0.900378	+	0.435109i	$0.856710\pi$
$284$	−192.000	+	332.554i	−0.0401166	+	0.0694839i
$285$		0			0
$286$	7980.00			1.64989
$287$	509.223	+	588.000i	0.104733	+	0.120936i
$288$			64.0000i			0.0130946i
$289$	−1156.00	−	2002.25i	−0.235294	−	0.407541i
$290$		0			0
$291$	−4585.00	+	7941.45i	−0.923634	+	1.59978i
$292$	−1084.26	+	626.000i	−0.217300	+	0.125458i
$293$		−	4158.00i		−	0.829054i	−0.910037	−	0.414527i	$-0.863947\pi$
$293$		−	4158.00i		−	0.829054i	0.910037	−	0.414527i	$-0.136053\pi$
$294$	490.000	−	3394.82i	0.0972020	−	0.673435i
$295$		0			0
$296$	1012.00	+	1752.84i	0.198721	+	0.344194i
$297$	7157.70	+	4132.50i	1.39842	+	0.807380i
$298$	−98.7269	−	57.0000i	−0.0191916	−	0.0110803i
$299$	−2415.00	−	4182.90i	−0.467101	−	0.809042i
$300$		0			0
$301$	1736.00	−	1503.42i	0.332430	−	0.287893i
$302$			1678.00i			0.319729i
$303$	−1234.09	+	712.500i	−0.233982	+	0.135089i
$304$	40.0000	−	69.2820i	0.00754657	−	0.0130710i
$305$		0			0
$306$	102.000	+	176.669i	0.0190554	+	0.0330049i
$307$		−	9604.00i		−	1.78544i	−0.450615	−	0.892719i	$-0.648795\pi$
$307$		−	9604.00i		−	1.78544i	0.450615	−	0.892719i	$-0.351205\pi$
$308$	−1382.18	+	3990.00i	−0.255704	+	0.738154i
$309$	−2495.00			−0.459338
$310$		0			0
$311$	−5065.50	+	8773.70i	−0.923595	+	1.59971i	−0.129791	+	0.991541i	$0.541430\pi$
$311$	−5065.50	+	8773.70i	−0.923595	+	1.59971i	−0.793805	+	0.608173i	$0.791903\pi$
$312$	−2424.87	−	1400.00i	−0.440004	−	0.254037i
$313$	−9352.21	+	5399.50i	−1.68888	+	0.975073i	−0.733495	+	0.679695i	$0.762112\pi$
$313$	−9352.21	+	5399.50i	−1.68888	+	0.975073i	−0.955380	+	0.295378i	$0.904554\pi$
$314$	5666.00			1.01831
$315$		0			0
$316$	1844.00			0.328269
$317$	459.859	−	265.500i	0.0814772	−	0.0470409i	−0.458708	−	0.888587i	$-0.651688\pi$
$317$	459.859	−	265.500i	0.0814772	−	0.0470409i	0.540185	+	0.841546i	$0.318354\pi$
$318$	3403.48	+	1965.00i	0.600181	+	0.346515i
$319$	−3249.00	+	5627.43i	−0.570248	+	0.987698i
$320$		0			0
$321$	5535.00			0.962410
$322$	2509.74	−	483.000i	0.434355	−	0.0835917i
$323$		−	255.000i		−	0.0439275i
$324$	−1342.00	−	2324.41i	−0.230110	−	0.398562i
$325$		0			0
$326$	2311.00	−	4002.77i	0.392621	−	0.680040i
$327$	−3996.71	+	2307.50i	−0.675897	+	0.390229i
$328$			336.000i			0.0565625i
$329$	−3517.50	−	1218.50i	−0.589441	−	0.204188i
$330$		0			0
$331$	3507.50	+	6075.17i	0.582446	+	1.00883i	0.995189	+	0.0979784i	$0.0312376\pi$
$331$	3507.50	+	6075.17i	0.582446	+	1.00883i	−0.412743	+	0.910848i	$0.635429\pi$
$332$	2036.89	+	1176.00i	0.336714	+	0.194402i
$333$	438.209	+	253.000i	0.0721132	+	0.0416346i
$334$	1260.00	+	2182.38i	0.206420	+	0.357529i
$335$		0			0
$336$	1120.00	−	969.948i	0.181848	−	0.157485i
$337$			8990.00i			1.45316i	0.687079	+	0.726582i	$0.258892\pi$
$337$			8990.00i			1.45316i	−0.687079	+	0.726582i	$0.741108\pi$
$338$	−4681.73	+	2703.00i	−0.753410	+	0.434982i
$339$	−3855.00	+	6677.06i	−0.617625	+	1.06976i
$340$		0			0
$341$	655.500	+	1135.36i	0.104098	+	0.180303i
$342$		−	20.0000i		−	0.00316221i
$343$	5346.84	−	3430.00i	0.841698	−	0.539949i
$344$	992.000			0.155480
$345$		0			0
$346$	−3267.00	+	5658.61i	−0.507616	+	0.879216i
$347$	7542.22	+	4354.50i	1.16682	+	0.673665i	0.952929	−	0.303192i	$-0.0980523\pi$
$347$	7542.22	+	4354.50i	1.16682	+	0.673665i	0.213893	+	0.976857i	$0.431386\pi$
$348$	1974.54	−	1140.00i	0.304156	−	0.175605i
$349$	−6482.00			−0.994193			−0.497097	−	0.867695i	$-0.665601\pi$
$349$	−6482.00			−0.994193			−0.497097	+	0.867695i	$0.665601\pi$
$350$		0			0
$351$	−10150.0			−1.54350
$352$	−1579.63	+	912.000i	−0.239189	+	0.138096i
$353$	−1847.23	−	1066.50i	−0.278522	−	0.160805i	0.354232	−	0.935158i	$-0.384742\pi$
$353$	−1847.23	−	1066.50i	−0.278522	−	0.160805i	−0.632754	+	0.774353i	$0.718076\pi$
$354$	−1095.00	+	1896.60i	−0.164403	+	0.284754i
$355$		0			0
$356$	−4068.00			−0.605628
$357$	1545.86	−	4462.50i	0.229175	−	0.661570i
$358$		−	2574.00i		−	0.380000i
$359$	1924.50	+	3333.33i	0.282928	+	0.490046i	0.972105	−	0.234548i	$-0.0753608\pi$
$359$	1924.50	+	3333.33i	0.282928	+	0.490046i	−0.689176	+	0.724594i	$0.742028\pi$
$360$		0			0
$361$	3417.00	−	5918.42i	0.498178	−	0.862869i
$362$	−4631.50	+	2674.00i	−0.672449	+	0.388238i
$363$			9590.00i			1.38662i
$364$	−980.000	−	5092.23i	−0.141115	−	0.733256i
$365$		0			0
$366$	−3545.00	−	6140.12i	−0.506284	−	0.876910i
$367$	−5621.37	−	3245.50i	−0.799545	−	0.461618i	0.0437668	−	0.999042i	$-0.486064\pi$
$367$	−5621.37	−	3245.50i	−0.799545	−	0.461618i	−0.843312	+	0.537424i	$0.819397\pi$
$368$	956.092	+	552.000i	0.135434	+	0.0781929i
$369$	42.0000	+	72.7461i	0.00592529	+	0.0102629i
$370$		0			0
$371$	1375.50	+	7147.31i	0.192486	+	1.00019i
$372$		−	460.000i		−	0.0641126i
$373$	−799.341	+	461.500i	−0.110961	+	0.0640632i	−0.554453	−	0.832215i	$-0.687073\pi$
$373$	−799.341	+	461.500i	−0.110961	+	0.0640632i	0.443493	+	0.896278i	$0.353739\pi$
$374$	−2907.00	+	5035.07i	−0.401918	+	0.696143i
$375$		0			0
$376$	−804.000	−	1392.57i	−0.110274	−	0.191001i
$377$		−	7980.00i		−	1.09016i
$378$	1758.03	−	5075.00i	0.239215	−	0.690555i
$379$	−6344.00			−0.859814			−0.429907	−	0.902873i	$-0.641454\pi$
$379$	−6344.00			−0.859814			−0.429907	+	0.902873i	$0.641454\pi$
$380$		0			0
$381$	−5140.00	+	8902.74i	−0.691155	+	1.19712i
$382$	−7248.63	−	4185.00i	−0.970870	−	0.560532i
$383$	4336.19	−	2503.50i	0.578509	−	0.334002i	−0.182032	−	0.983293i	$-0.558267\pi$
$383$	4336.19	−	2503.50i	0.578509	−	0.334002i	0.760541	+	0.649290i	$0.224934\pi$
$384$	640.000			0.0850517
$385$		0			0
$386$	−170.000			−0.0224165
$387$	214.774	−	124.000i	0.0282108	−	0.0162875i
$388$	−6353.16	−	3668.00i	−0.831270	−	0.479934i
$389$	6145.50	−	10644.3i	0.801001	−	1.38737i	−0.117958	−	0.993019i	$-0.537635\pi$
$389$	6145.50	−	10644.3i	0.801001	−	1.38737i	0.918958	−	0.394355i	$-0.129032\pi$
$390$		0			0
$391$	3519.00			0.455150
$392$	2715.86	+	392.000i	0.349927	+	0.0505076i
$393$			10245.0i			1.31499i
$394$	−390.000	−	675.500i	−0.0498678	−	0.0863736i
$395$		0			0
$396$	−228.000	+	394.908i	−0.0289329	+	0.0501133i
$397$	768.165	−	443.500i	0.0971110	−	0.0560671i	−0.450658	−	0.892697i	$-0.648811\pi$
$397$	768.165	−	443.500i	0.0971110	−	0.0560671i	0.547769	+	0.836630i	$0.315477\pi$
$398$			5666.00i			0.713595i
$399$	−350.000	+	303.109i	−0.0439146	+	0.0380311i
$400$		0			0
$401$	−5977.50	−	10353.3i	−0.744394	−	1.28933i	−0.950477	−	0.310794i	$-0.899405\pi$
$401$	−5977.50	−	10353.3i	−0.744394	−	1.28933i	0.206083	−	0.978535i	$-0.433928\pi$
$402$	3628.65	+	2095.00i	0.450200	+	0.259923i
$403$	−1394.30	−	805.000i	−0.172345	−	0.0995035i
$404$	−570.000	−	987.269i	−0.0701945	−	0.121580i
$405$		0			0
$406$	3990.00	+	1382.18i	0.487735	+	0.168956i
$407$			14421.0i			1.75632i
$408$	1766.69	−	1020.00i	0.214373	−	0.123768i
$409$	−1710.50	+	2962.67i	−0.206794	+	0.358178i	−0.950703	−	0.310103i	$-0.899636\pi$
$409$	−1710.50	+	2962.67i	−0.206794	+	0.358178i	0.743909	+	0.668281i	$0.232970\pi$
$410$		0			0
$411$	−352.500	−	610.548i	−0.0423055	−	0.0732752i
$412$		−	1996.00i		−	0.238679i
$413$	−3982.85	+	766.500i	−0.474536	+	0.0913245i
$414$	276.000			0.0327649
$415$		0			0
$416$	1120.00	−	1939.90i	0.132001	−	0.228633i
$417$	6425.91	+	3710.00i	0.754624	+	0.435682i
$418$	493.634	−	285.000i	0.0577618	−	0.0333488i
$419$	5460.00			0.636607			0.318304	−	0.947989i	$-0.396887\pi$
$419$	5460.00			0.636607			0.318304	+	0.947989i	$0.396887\pi$
$420$		0			0
$421$	7730.00			0.894863			0.447431	−	0.894318i	$-0.352339\pi$
$421$	7730.00			0.894863			0.447431	+	0.894318i	$0.352339\pi$
$422$	−214.774	+	124.000i	−0.0247750	+	0.0143039i
$423$	−348.142	−	201.000i	−0.0400171	−	0.0231039i
$424$	−1572.00	+	2722.78i	−0.180054	+	0.311863i
$425$		0			0
$426$	960.000			0.109183
$427$	4298.08	−	12407.5i	0.487117	−	1.40619i
$428$			4428.00i			0.500083i
$429$	−9975.00	−	17277.2i	−1.12260	−	1.94441i
$430$		0			0
$431$	5656.50	−	9797.35i	0.632167	−	1.09495i	−0.354941	−	0.934889i	$-0.615499\pi$
$431$	5656.50	−	9797.35i	0.632167	−	1.09495i	0.987108	−	0.160057i	$-0.0511677\pi$
$432$	2009.18	−	1160.00i	0.223765	−	0.129191i
$433$		−	4214.00i		−	0.467695i	−0.972273	−	0.233847i	$-0.924868\pi$
$433$		−	4214.00i		−	0.467695i	0.972273	−	0.233847i	$-0.0751316\pi$
$434$	644.000	−	557.720i	0.0712281	−	0.0616853i
$435$		0			0
$436$	−1846.00	−	3197.37i	−0.202769	−	0.351207i
$437$	−298.779	−	172.500i	−0.0327060	−	0.0188828i
$438$	2710.66	+	1565.00i	0.295708	+	0.170727i
$439$	8276.50	+	14335.3i	0.899808	+	1.55851i	0.827739	+	0.561114i	$0.189627\pi$
$439$	8276.50	+	14335.3i	0.899808	+	1.55851i	0.0720696	+	0.997400i	$0.477040\pi$
$440$		0			0
$441$	637.000	−	254.611i	0.0687831	−	0.0274929i
$442$		−	7140.00i		−	0.768360i
$443$	14198.5	−	8197.50i	1.52278	−	0.879176i	0.523140	−	0.852247i	$-0.324760\pi$
$443$	14198.5	−	8197.50i	1.52278	−	0.879176i	0.999637	−	0.0269294i	$-0.00857293\pi$
$444$	2530.00	−	4382.09i	0.270425	−	0.468389i
$445$		0			0
$446$	−56.0000	−	96.9948i	−0.00594546	−	0.0102978i
$447$			285.000i			0.0301567i
$448$	775.959	+	896.000i	0.0818317	+	0.0944911i
$449$	15090.0			1.58606			0.793030	−	0.609182i	$-0.208502\pi$
$449$	15090.0			1.58606			0.793030	+	0.609182i	$0.208502\pi$
$450$		0			0
$451$	−1197.00	+	2073.26i	−0.124977	+	0.216466i
$452$	−5341.64	−	3084.00i	−0.555862	−	0.320927i
$453$	3632.98	−	2097.50i	0.376804	−	0.217548i
$454$	6114.00			0.632036
$455$		0			0
$456$	−200.000			−0.0205392
$457$	−12804.2	+	7392.50i	−1.31062	+	0.756688i	−0.982199	−	0.187842i	$-0.939851\pi$
$457$	−12804.2	+	7392.50i	−1.31062	+	0.756688i	−0.328423	+	0.944531i	$0.606517\pi$
$458$	−1664.50	−	961.000i	−0.169819	−	0.0980449i
$459$	3697.50	−	6404.26i	0.376001	−	0.651253i
$460$		0			0
$461$	2898.00			0.292784			0.146392	−	0.989227i	$-0.453234\pi$
$461$	2898.00			0.292784			0.146392	+	0.989227i	$0.453234\pi$
$462$	10366.3	−	1995.00i	1.04391	−	0.200900i
$463$		−	464.000i		−	0.0465743i	−0.999729	−	0.0232872i	$-0.992587\pi$
$463$		−	464.000i		−	0.0465743i	0.999729	−	0.0232872i	$-0.00741320\pi$
$464$	912.000	+	1579.63i	0.0912468	+	0.158044i
$465$		0			0
$466$	2829.00	−	4899.97i	0.281225	−	0.487096i
$467$	3665.89	−	2116.50i	0.363248	−	0.209721i	−0.307256	−	0.951627i	$-0.599411\pi$
$467$	3665.89	−	2116.50i	0.363248	−	0.209721i	0.670505	+	0.741905i	$0.266078\pi$
$468$		−	560.000i		−	0.0553120i
$469$	1466.50	+	7620.16i	0.144385	+	0.750248i
$470$		0			0
$471$	−7082.50	−	12267.2i	−0.692876	−	1.20010i
$472$	−1517.28	−	876.000i	−0.147963	−	0.0854262i
$473$	6121.07	+	3534.00i	0.595025	+	0.343538i
$474$	−2305.00	−	3992.38i	−0.223359	−	0.386869i
$475$		0			0
$476$	3570.00	+	1236.68i	0.343762	+	0.119083i
$477$			786.000i			0.0754475i
$478$	6131.46	−	3540.00i	0.586708	−	0.338736i
$479$	1369.50	−	2372.04i	0.130635	−	0.226266i	−0.793287	−	0.608848i	$-0.791632\pi$
$479$	1369.50	−	2372.04i	0.130635	−	0.226266i	0.923921	+	0.382582i	$0.124965\pi$
$480$		0			0
$481$	−8855.00	−	15337.3i	−0.839404	−	1.45389i
$482$			10462.0i			0.988654i
$483$	−4182.90	−	4830.00i	−0.394055	−	0.455016i
$484$	−7672.00			−0.720511
$485$		0			0
$486$	560.000	−	969.948i	0.0522677	−	0.0905304i
$487$	−14766.6	−	8525.50i	−1.37400	−	0.793280i	−0.382572	−	0.923926i	$-0.624962\pi$
$487$	−14766.6	−	8525.50i	−1.37400	−	0.793280i	−0.991429	+	0.130646i	$0.958295\pi$
$488$	4912.10	−	2836.00i	0.455656	−	0.263073i
$489$	−11555.0			−1.06858
$490$		0			0
$491$	−4296.00			−0.394859			−0.197429	−	0.980317i	$-0.563259\pi$
$491$	−4296.00			−0.394859			−0.197429	+	0.980317i	$0.563259\pi$
$492$	727.461	−	420.000i	0.0666595	−	0.0384859i
$493$	5035.07	+	2907.00i	0.459976	+	0.265567i
$494$	−350.000	+	606.218i	−0.0318770	+	0.0552126i
$495$		0			0
$496$	368.000			0.0333139
$497$	1163.94	+	1344.00i	0.105050	+	0.121301i
$498$		−	5880.00i		−	0.529095i
$499$	1700.50	+	2945.35i	0.152555	+	0.264233i	0.932166	−	0.362031i	$-0.117917\pi$
$499$	1700.50	+	2945.35i	0.152555	+	0.264233i	−0.779611	+	0.626264i	$0.784583\pi$
$500$		0			0
$501$	3150.00	−	5455.96i	0.280901	−	0.486536i
$502$	8729.54	−	5040.00i	0.776132	−	0.448100i
$503$		−	16800.0i		−	1.48921i	−0.667503	−	0.744607i	$-0.732637\pi$
$503$		−	16800.0i		−	1.48921i	0.667503	−	0.744607i	$-0.267363\pi$
$504$	280.000	+	96.9948i	0.0247464	+	0.00857241i
$505$		0			0
$506$	3933.00	+	6812.16i	0.345540	+	0.598493i
$507$	11704.3	+	6757.50i	1.02526	+	0.591935i
$508$	−7122.19	−	4112.00i	−0.622040	−	0.359135i
$509$	919.500	+	1592.62i	0.0800710	+	0.138687i	0.903280	−	0.429051i	$-0.141152\pi$
$509$	919.500	+	1592.62i	0.0800710	+	0.138687i	−0.823209	+	0.567738i	$0.807819\pi$
$510$		0			0
$511$	1095.50	+	5692.38i	0.0948377	+	0.492791i
$512$			512.000i			0.0441942i
$513$	−627.868	+	362.500i	−0.0540372	+	0.0311984i
$514$	−1437.00	+	2488.96i	−0.123314	+	0.213586i
$515$		0			0
$516$	−1240.00	−	2147.74i	−0.105791	−	0.183235i
$517$		−	11457.0i		−	0.974620i
$518$	9202.39	−	1771.00i	0.780559	−	0.150219i
$519$	16335.0			1.38155
$520$		0			0
$521$	−151.500	+	262.406i	−0.0127396	+	0.0220656i	−0.872325	−	0.488927i	$-0.837389\pi$
$521$	−151.500	+	262.406i	−0.0127396	+	0.0220656i	0.859585	+	0.510992i	$0.170722\pi$
$522$	394.908	+	228.000i	0.0331123	+	0.0191174i
$523$	18764.2	−	10833.5i	1.56883	−	0.905767i	0.572528	−	0.819885i	$-0.305963\pi$
$523$	18764.2	−	10833.5i	1.56883	−	0.905767i	0.996305	−	0.0858815i	$-0.0273706\pi$
$524$	−8196.00			−0.683290
$525$		0			0
$526$	−4650.00			−0.385456
$527$	1015.85	−	586.500i	0.0839678	−	0.0484788i
$528$	3949.08	+	2280.00i	0.325495	+	0.187925i
$529$	−3703.00	+	6413.78i	−0.304348	+	0.527146i
$530$		0			0
$531$	−438.000			−0.0357958
$532$	−242.487	−	280.000i	−0.0197616	−	0.0228187i
$533$		−	2940.00i		−	0.238922i
$534$	5085.00	+	8807.48i	0.412078	+	0.713739i
$535$		0			0
$536$	−1676.00	+	2902.92i	−0.135060	+	0.233931i
$537$	−5572.87	+	3217.50i	−0.447835	+	0.258557i
$538$			4770.00i			0.382248i
$539$	15361.5	+	12094.0i	1.22758	+	0.966470i
$540$		0			0
$541$	−2519.50	−	4363.90i	−0.200225	−	0.346800i	0.748376	−	0.663275i	$-0.230834\pi$
$541$	−2519.50	−	4363.90i	−0.200225	−	0.346800i	−0.948601	+	0.316475i	$0.897501\pi$
$542$	573.309	+	331.000i	0.0454349	+	0.0262319i
$543$	11578.8	+	6685.00i	0.915087	+	0.528326i
$544$	816.000	+	1413.35i	0.0643120	+	0.111392i
$545$		0			0
$546$	−9800.00	+	8487.05i	−0.768134	+	0.665224i
$547$		−	2392.00i		−	0.186974i	−0.995621	−	0.0934868i	$-0.970199\pi$
$547$		−	2392.00i		−	0.186974i	0.995621	−	0.0934868i	$-0.0298013\pi$
$548$	488.438	−	282.000i	0.0380749	−	0.0219826i
$549$	709.000	−	1228.02i	0.0551173	−	0.0954659i
$550$		0			0
$551$	−285.000	−	493.634i	−0.0220352	−	0.0381661i
$552$		−	2760.00i		−	0.212814i
$553$	2794.66	−	8067.50i	0.214903	−	0.620371i
$554$	−9742.00			−0.747108
$555$		0			0
$556$	−2968.00	+	5140.73i	−0.226387	+	0.392114i
$557$	19181.6	+	11074.5i	1.45916	+	0.842445i	0.998970	−	0.0453775i	$-0.0144491\pi$
$557$	19181.6	+	11074.5i	1.45916	+	0.842445i	0.460187	+	0.887822i	$0.347782\pi$
$558$	79.6743	−	46.0000i	0.00604459	−	0.00348985i
$559$	−8680.00			−0.656753
$560$		0			0
$561$	14535.0			1.09388
$562$	−12169.4	+	7026.00i	−0.913407	+	0.527356i
$563$	−7230.45	−	4174.50i	−0.541256	−	0.312494i	0.204332	−	0.978902i	$-0.434498\pi$
$563$	−7230.45	−	4174.50i	−0.541256	−	0.312494i	−0.745588	+	0.666408i	$0.767831\pi$
$564$	−2010.00	+	3481.42i	−0.150064	+	0.259919i
$565$		0			0
$566$	−10706.0			−0.795065
$567$	−12203.2	+	2348.50i	−0.903853	+	0.173947i
$568$			768.000i			0.0567334i
$569$	−7672.50	−	13289.2i	−0.565286	−	0.979105i	−0.997023	−	0.0771050i	$-0.975432\pi$
$569$	−7672.50	−	13289.2i	−0.565286	−	0.979105i	0.431737	−	0.902000i	$-0.357901\pi$
$570$		0			0
$571$	5796.50	−	10039.8i	0.424827	−	0.735821i	−0.571578	−	0.820548i	$-0.693668\pi$
$571$	5796.50	−	10039.8i	0.424827	−	0.735821i	0.996404	+	0.0847268i	$0.0270017\pi$
$572$	13821.8	−	7980.00i	1.01034	−	0.583323i
$573$			20925.0i			1.52557i
$574$	1470.00	+	509.223i	0.106893	+	0.0370288i
$575$		0			0
$576$	64.0000	+	110.851i	0.00462963	+	0.00801875i
$577$	12637.9	+	7296.50i	0.911825	+	0.526442i	0.881018	−	0.473083i	$-0.156859\pi$
$577$	12637.9	+	7296.50i	0.911825	+	0.526442i	0.0308071	+	0.999525i	$0.490192\pi$
$578$	−4004.50	−	2312.00i	−0.288175	−	0.166378i
$579$	212.500	+	368.061i	0.0152525	+	0.0264181i
$580$		0			0
$581$	8232.00	−	7129.12i	0.587816	−	0.509063i
$582$			18340.0i			1.30622i
$583$	−19399.8	+	11200.5i	−1.37815	+	0.795673i
$584$	−1252.00	+	2168.53i	−0.0887125	+	0.153655i
$585$		0			0
$586$	−4158.00	−	7201.87i	−0.293115	−	0.507690i
$587$		−	15372.0i		−	1.08087i	−0.841386	−	0.540435i	$-0.818260\pi$
$587$		−	15372.0i		−	1.08087i	0.841386	−	0.540435i	$-0.181740\pi$
$588$	−2546.11	−	6370.00i	−0.178571	−	0.446759i
$589$	−115.000			−0.00804498
$590$		0			0
$591$	−975.000	+	1688.75i	−0.0678615	+	0.117540i
$592$	3505.67	+	2024.00i	0.243382	+	0.140517i
$593$	12447.4	−	7186.50i	0.861978	−	0.497663i	−0.00269639	−	0.999996i	$-0.500858\pi$
$593$	12447.4	−	7186.50i	0.861978	−	0.497663i	0.864674	+	0.502333i	$0.167525\pi$
$594$	16530.0			1.14181
$595$		0			0
$596$	−228.000			−0.0156699
$597$	12267.2	−	7082.50i	0.840980	−	0.485540i
$598$	−8365.81	−	4830.00i	−0.572079	−	0.330290i
$599$	1273.50	−	2205.77i	0.0868678	−	0.150459i	−0.819318	−	0.573340i	$-0.805648\pi$
$599$	1273.50	−	2205.77i	0.0868678	−	0.150459i	0.906186	+	0.422880i	$0.138981\pi$
$600$		0			0
$601$	−7042.00			−0.477952			−0.238976	−	0.971025i	$-0.576812\pi$
$601$	−7042.00			−0.477952			−0.238976	+	0.971025i	$0.576812\pi$
$602$	1503.42	−	4340.00i	0.101785	−	0.293829i
$603$			838.000i			0.0565937i
$604$	1678.00	+	2906.38i	0.113041	+	0.195793i
$605$		0			0
$606$	−1425.00	+	2468.17i	−0.0955226	+	0.165450i
$607$	−19564.4	+	11295.5i	−1.30823	+	0.755305i	−0.981800	−	0.189917i	$-0.939178\pi$
$607$	−19564.4	+	11295.5i	−1.30823	+	0.755305i	−0.326427	+	0.945223i	$0.605845\pi$
$608$		−	160.000i		−	0.0106725i
$609$	−1995.00	−	10366.3i	−0.132745	−	0.689761i
$610$		0			0
$611$	7035.00	+	12185.0i	0.465803	+	0.806794i
$612$	353.338	+	204.000i	0.0233380	+	0.0134742i
$613$	−7348.23	−	4242.50i	−0.484163	−	0.279532i	0.237987	−	0.971268i	$-0.423513\pi$
$613$	−7348.23	−	4242.50i	−0.484163	−	0.279532i	−0.722150	+	0.691737i	$0.756846\pi$
$614$	−9604.00	−	16634.6i	−0.631247	−	1.09335i
$615$		0			0
$616$	1596.00	+	8293.06i	0.104391	+	0.542430i
$617$		−	18282.0i		−	1.19288i	−0.802658	−	0.596439i	$-0.796582\pi$
$617$		−	18282.0i		−	1.19288i	0.802658	−	0.596439i	$-0.203418\pi$
$618$	−4321.47	+	2495.00i	−0.281286	+	0.162401i
$619$	1145.50	−	1984.06i	0.0743805	−	0.128831i	−0.826436	−	0.563030i	$-0.809635\pi$
$619$	1145.50	−	1984.06i	0.0743805	−	0.128831i	0.900817	+	0.434200i	$0.142969\pi$
$620$		0			0
$621$	−5002.50	−	8664.58i	−0.323258	−	0.559900i
$622$			20262.0i			1.30616i
$623$	−6165.23	+	17797.5i	−0.396477	+	1.14453i
$624$	−5600.00			−0.359262
$625$		0			0
$626$	−10799.0	+	18704.4i	−0.689481	+	1.19422i
$627$	−1234.09	−	712.500i	−0.0786039	−	0.0453820i
$628$	9813.80	−	5666.00i	0.623588	−	0.360029i
$629$	12903.0			0.817927
$630$		0			0
$631$	−6928.00			−0.437083			−0.218541	−	0.975828i	$-0.570130\pi$
$631$	−6928.00			−0.437083			−0.218541	+	0.975828i	$0.570130\pi$
$632$	3193.90	−	1844.00i	0.201023	−	0.116061i
$633$	536.936	+	310.000i	0.0337145	+	0.0194651i
$634$	531.000	−	919.719i	0.0332629	−	0.0576131i
$635$		0			0
$636$	7860.00			0.490046
$637$	−23763.7	−	3430.00i	−1.47811	−	0.213346i
$638$			12996.0i			0.806452i
$639$	96.0000	+	166.277i	0.00594319	+	0.0102939i
$640$		0			0
$641$	−12487.5	+	21629.0i	−0.769464	+	1.33275i	0.168390	+	0.985721i	$0.446143\pi$
$641$	−12487.5	+	21629.0i	−0.769464	+	1.33275i	−0.937854	+	0.347031i	$0.887190\pi$
$642$	9586.90	−	5535.00i	0.589353	−	0.340263i
$643$		−	9548.00i		−	0.585593i	−0.956175	−	0.292797i	$-0.905414\pi$
$643$		−	9548.00i		−	0.585593i	0.956175	−	0.292797i	$-0.0945859\pi$
$644$	3864.00	−	3346.32i	0.236433	−	0.204757i
$645$		0			0
$646$	−255.000	−	441.673i	−0.0155307	−	0.0269000i
$647$	−8773.70	−	5065.50i	−0.533122	−	0.307798i	0.209165	−	0.977880i	$-0.432925\pi$
$647$	−8773.70	−	5065.50i	−0.533122	−	0.307798i	−0.742287	+	0.670082i	$0.766259\pi$
$648$	−4648.82	−	2684.00i	−0.281826	−	0.162712i
$649$	−6241.50	−	10810.6i	−0.377504	−	0.653857i
$650$		0			0
$651$	−2012.50	−	697.150i	−0.121161	−	0.0419716i
$652$		−	9244.00i		−	0.555250i
$653$	−14427.1	+	8329.50i	−0.864589	+	0.499171i	−0.865546	−	0.500829i	$-0.833029\pi$
$653$	−14427.1	+	8329.50i	−0.864589	+	0.499171i	0.000957229		1.00000i	$0.499695\pi$
$654$	−4615.00	+	7993.41i	−0.275934	+	0.477932i
$655$		0			0
$656$	336.000	+	581.969i	0.0199979	+	0.0346373i
$657$			626.000i			0.0371729i
$658$	−7310.99	+	1407.00i	−0.433149	+	0.0833595i
$659$	−29556.0			−1.74710			−0.873550	−	0.486735i	$-0.838188\pi$
$659$	−29556.0			−1.74710			−0.873550	+	0.486735i	$0.838188\pi$
$660$		0			0
$661$	−95.5000	+	165.411i	−0.00561955	+	0.00973334i	−0.868822	−	0.495125i	$-0.835122\pi$
$661$	−95.5000	+	165.411i	−0.00561955	+	0.00973334i	0.863202	+	0.504859i	$0.168455\pi$
$662$	12150.3	+	7015.00i	0.713348	+	0.411852i
$663$	−15458.6	+	8925.00i	−0.905521	+	0.522803i
$664$	4704.00			0.274926
$665$		0			0
$666$	1012.00			0.0588802
$667$	6812.16	−	3933.00i	0.395454	−	0.228315i
$668$	4364.77	+	2520.00i	0.252811	+	0.145961i
$669$	−140.000	+	242.487i	−0.00809075	+	0.0140136i
$670$		0			0
$671$	40413.0			2.32508
$672$	969.948	−	2800.00i	0.0556794	−	0.160733i
$673$		−	2606.00i		−	0.149263i	−0.997211	−	0.0746314i	$-0.976222\pi$
$673$		−	2606.00i		−	0.149263i	0.997211	−	0.0746314i	$-0.0237780\pi$
$674$	8990.00	+	15571.1i	0.513771	+	0.889878i
$675$		0			0
$676$	−5406.00	+	9363.47i	−0.307579	+	0.532742i
$677$	−3645.10	+	2104.50i	−0.206931	+	0.119472i	−0.599885	−	0.800087i	$-0.704787\pi$
$677$	−3645.10	+	2104.50i	−0.206931	+	0.119472i	0.392953	+	0.919559i	$0.371453\pi$
$678$			15420.0i			0.873454i
$679$	−25676.0	+	22236.1i	−1.45118	+	1.25676i
$680$		0			0
$681$	−7642.50	−	13237.2i	−0.430046	−	0.744861i
$682$	2270.72	+	1311.00i	0.127493	+	0.0736082i
$683$	21047.0	+	12151.5i	1.17912	+	0.680768i	0.955812	−	0.293979i	$-0.0949797\pi$
$683$	21047.0	+	12151.5i	1.17912	+	0.680768i	0.223312	+	0.974747i	$0.428313\pi$
$684$	−20.0000	−	34.6410i	−0.00111801	−	0.00193645i
$685$		0			0
$686$	5831.00	−	11287.8i	0.324532	−	0.628235i
$687$			4805.00i			0.266845i
$688$	1718.19	−	992.000i	0.0952116	−	0.0549704i
$689$	13755.0	−	23824.4i	0.760557	−	1.31732i
$690$		0			0
$691$	−7520.50	−	13025.9i	−0.414028	−	0.717117i	0.581298	−	0.813691i	$-0.302545\pi$
$691$	−7520.50	−	13025.9i	−0.414028	−	0.717117i	−0.995326	+	0.0965734i	$0.969212\pi$
$692$			13068.0i			0.717877i
$693$	1382.18	+	1596.00i	0.0757641	+	0.0874849i
$694$	17418.0			0.952706
$695$		0			0
$696$	2280.00	−	3949.08i	0.124171	−	0.215071i
$697$	1855.03	+	1071.00i	0.100809	+	0.0582023i
$698$	−11227.2	+	6482.00i	−0.608817	+	0.351500i
$699$	−14145.0			−0.765398
$700$		0			0
$701$	24726.0			1.33222			0.666111	−	0.745852i	$-0.267958\pi$
$701$	24726.0			1.33222			0.666111	+	0.745852i	$0.267958\pi$
$702$	−17580.3	+	10150.0i	−0.945194	+	0.545708i
$703$	−1095.52	−	632.500i	−0.0587744	−	0.0339334i
$704$	−1824.00	+	3159.26i	−0.0976486	+	0.169132i
$705$		0			0
$706$	−4266.00			−0.227412
$707$	−5183.16	+	997.500i	−0.275718	+	0.0530620i
$708$			4380.00i			0.232501i
$709$	−2478.50	−	4292.89i	−0.131286	−	0.227395i	0.792886	−	0.609370i	$-0.208577\pi$
$709$	−2478.50	−	4292.89i	−0.131286	−	0.227395i	−0.924173	+	0.381975i	$0.875244\pi$
$710$		0			0
$711$	461.000	−	798.475i	0.0243162	−	0.0421170i
$712$	−7045.98	+	4068.00i	−0.370870	+	0.214122i
$713$		−	1587.00i		−	0.0833571i
$714$	−1785.00	−	9275.13i	−0.0935601	−	0.486153i
$715$		0			0
$716$	−2574.00	−	4458.30i	−0.134350	−	0.232702i
$717$	−15328.6	−	8850.00i	−0.798409	−	0.460961i
$718$	6666.66	+	3849.00i	0.346515	+	0.200060i
$719$	13834.5	+	23962.1i	0.717580	+	1.24288i	0.961956	+	0.273204i	$0.0880834\pi$
$719$	13834.5	+	23962.1i	0.717580	+	1.24288i	−0.244376	+	0.969680i	$0.578583\pi$
$720$		0			0
$721$	−8732.50	−	3025.03i	−0.451061	−	0.156252i
$722$		−	13668.0i		−	0.704529i
$723$	22650.9	−	13077.5i	1.16514	−	0.672694i
$724$	−5348.00	+	9263.01i	−0.274526	+	0.475493i
$725$		0			0
$726$	9590.00	+	16610.4i	0.490246	+	0.849130i
$727$		−	13888.0i		−	0.708497i	−0.935151	−	0.354249i	$-0.884737\pi$
$727$		−	13888.0i		−	0.708497i	0.935151	−	0.354249i	$-0.115263\pi$
$728$	−6789.64	−	7840.00i	−0.345660	−	0.399134i
$729$	−20917.0			−1.06269
$730$		0			0
$731$	3162.00	−	5476.74i	0.159987	−	0.277106i
$732$	−12280.2	−	7090.00i	−0.620069	−	0.357997i
$733$	−12334.8	+	7121.50i	−0.621550	+	0.358852i	−0.777472	−	0.628917i	$-0.783498\pi$
$733$	−12334.8	+	7121.50i	−0.621550	+	0.358852i	0.155922	+	0.987769i	$0.450165\pi$
$734$	−12982.0			−0.652826
$735$		0			0
$736$	2208.00			0.110581
$737$	−20683.3	+	11941.5i	−1.03376	+	0.596840i
$738$	145.492	+	84.0000i	0.00725697	+	0.00418981i
$739$	18479.5	−	32007.4i	0.919864	−	1.59325i	0.120244	−	0.992744i	$-0.461632\pi$
$739$	18479.5	−	32007.4i	0.919864	−	1.59325i	0.799620	−	0.600507i	$-0.205034\pi$
$740$		0			0
$741$	1750.00			0.0867582
$742$	9529.74	+	11004.0i	0.471493	+	0.544433i
$743$			12528.0i			0.618584i	0.950967	+	0.309292i	$0.100092\pi$
$743$			12528.0i			0.618584i	−0.950967	+	0.309292i	$0.899908\pi$
$744$	−460.000	−	796.743i	−0.0226672	−	0.0392608i
$745$		0			0
$746$	−923.000	+	1598.68i	−0.0452995	+	0.0784610i
$747$	1018.45	−	588.000i	0.0498835	−	0.0288003i
$748$			11628.0i			0.568398i
$749$	19372.5	+	6710.83i	0.945068	+	0.327381i
$750$		0			0
$751$	8883.50	+	15386.7i	0.431643	+	0.747627i	0.997015	−	0.0772090i	$-0.0246009\pi$
$751$	8883.50	+	15386.7i	0.431643	+	0.747627i	−0.565372	+	0.824836i	$0.691268\pi$
$752$	−2785.14	−	1608.00i	−0.135058	−	0.0779757i
$753$	−21823.8	−	12600.0i	−1.05618	−	0.609787i
$754$	−7980.00	−	13821.8i	−0.385430	−	0.667585i
$755$		0			0
$756$	−2030.00	−	10548.2i	−0.0976592	−	0.507452i
$757$		−	28726.0i		−	1.37921i	−0.724184	−	0.689606i	$-0.757784\pi$
$757$		−	28726.0i		−	1.37921i	0.724184	−	0.689606i	$-0.242216\pi$
$758$	−10988.1	+	6344.00i	−0.526526	+	0.303990i
$759$	9832.50	−	17030.4i	0.470220	−	0.814445i
$760$		0			0
$761$	13234.5	+	22922.8i	0.630421	+	1.09192i	0.987466	+	0.157834i	$0.0504510\pi$
$761$	13234.5	+	22922.8i	0.630421	+	1.09192i	−0.357045	+	0.934087i	$0.616216\pi$
$762$			20560.0i			0.977441i
$763$	−16786.2	+	3230.50i	−0.796462	+	0.153279i
$764$	−16740.0			−0.792712
$765$		0			0
$766$	5007.00	−	8672.38i	0.236175	−	0.409068i
$767$	13276.2	+	7665.00i	0.625000	+	0.360844i
$768$	1108.51	−	640.000i	0.0520833	−	0.0300703i
$769$	−5054.00			−0.236999			−0.118499	−	0.992954i	$-0.537808\pi$
$769$	−5054.00			−0.236999			−0.118499	+	0.992954i	$0.537808\pi$
$770$		0			0
$771$	7185.00			0.335618
$772$	−294.449	+	170.000i	−0.0137273	+	0.00792543i
$773$	−30800.2	−	17782.5i	−1.43313	−	0.827415i	−0.435767	−	0.900059i	$-0.643523\pi$
$773$	−30800.2	−	17782.5i	−1.43313	−	0.827415i	−0.997358	+	0.0726439i	$0.976856\pi$
$774$	248.000	−	429.549i	0.0115170	−	0.0199481i
$775$		0			0
$776$	−14672.0			−0.678730
$777$	−15337.3	−	17710.0i	−0.708138	−	0.817687i
$778$		−	24582.0i		−	1.13279i
$779$	−105.000	−	181.865i	−0.00482929	−	0.00836457i
$780$		0			0
$781$	−2736.00	+	4738.89i	−0.125354	+	0.217120i
$782$	6095.09	−	3519.00i	0.278721	−	0.160920i
$783$		−	16530.0i		−	0.754450i
$784$	5096.00	−	2036.89i	0.232143	−	0.0927884i
$785$		0			0
$786$	10245.0	+	17744.9i	0.464920	+	0.805265i
$787$	7472.93	+	4314.50i	0.338477	+	0.195420i	0.659598	−	0.751618i	$-0.270726\pi$
$787$	7472.93	+	4314.50i	0.338477	+	0.195420i	−0.321121	+	0.947038i	$0.604060\pi$
$788$	−1351.00	−	780.000i	−0.0610753	−	0.0352619i
$789$	5812.50	+	10067.5i	0.262269	+	0.454264i
$790$		0			0
$791$	−21588.0	+	18695.8i	−0.970393	+	0.840385i
$792$			912.000i			0.0409173i
$793$	−42980.8	+	24815.0i	−1.92471	+	1.11123i
$794$	887.000	−	1536.33i	0.0396454	−	0.0686679i
$795$		0			0
$796$	5666.00	+	9813.80i	0.252294	+	0.436986i
$797$			20706.0i			0.920256i	0.887853	+	0.460128i	$0.152197\pi$
$797$			20706.0i			0.920256i	−0.887853	+	0.460128i	$0.847803\pi$
$798$	−303.109	+	875.000i	−0.0134460	+	0.0388154i
$799$	−10251.0			−0.453885
$800$		0			0
$801$	−1017.00	+	1761.50i	−0.0448613	+	0.0777021i
$802$	−20706.7	−	11955.0i	−0.911693	−	0.526366i
$803$	−15450.8	+	8920.50i	−0.679011	+	0.392027i
$804$	8380.00			0.367587
$805$		0			0
$806$	−3220.00			−0.140719
$807$	10327.4	−	5962.50i	0.450483	−	0.260087i
$808$	−1974.54	−	1140.00i	−0.0859703	−	0.0496350i
$809$	−8092.50	+	14016.6i	−0.351690	+	0.609145i	−0.986546	−	0.163486i	$-0.947726\pi$
$809$	−8092.50	+	14016.6i	−0.351690	+	0.609145i	0.634856	+	0.772631i	$0.281060\pi$
$810$		0			0
$811$	−11788.0			−0.510398			−0.255199	−	0.966889i	$-0.582141\pi$
$811$	−11788.0			−0.510398			−0.255199	+	0.966889i	$0.582141\pi$
$812$	8293.06	−	1596.00i	0.358411	−	0.0689761i
$813$		−	1655.00i		−	0.0713941i
$814$	14421.0	+	24977.9i	0.620953	+	1.07552i
$815$		0			0
$816$	2040.00	−	3533.38i	0.0875175	−	0.151585i
$817$	−536.936	+	310.000i	−0.0229927	+	0.0132748i
$818$			6842.00i			0.292451i
$819$	−2450.00	−	848.705i	−0.104530	−	0.0362102i
$820$		0			0
$821$	14896.5	+	25801.5i	0.633242	+	1.09681i	0.986885	+	0.161426i	$0.0516094\pi$
$821$	14896.5	+	25801.5i	0.633242	+	1.09681i	−0.353643	+	0.935380i	$0.615057\pi$
$822$	−1221.10	−	705.000i	−0.0518134	−	0.0299145i
$823$	26260.5	+	15161.5i	1.11225	+	0.642159i	0.939412	−	0.342791i	$-0.111372\pi$
$823$	26260.5	+	15161.5i	1.11225	+	0.642159i	0.172840	+	0.984950i	$0.444706\pi$
$824$	−1996.00	−	3457.17i	−0.0843859	−	0.146161i
$825$		0			0
$826$	−6132.00	+	5310.47i	−0.258305	+	0.223698i
$827$			21156.0i			0.889560i	0.895640	+	0.444780i	$0.146718\pi$
$827$			21156.0i			0.889560i	−0.895640	+	0.444780i	$0.853282\pi$
$828$	478.046	−	276.000i	0.0200643	−	0.0115841i
$829$	−2634.50	+	4563.09i	−0.110374	+	0.191173i	−0.915921	−	0.401358i	$-0.868538\pi$
$829$	−2634.50	+	4563.09i	−0.110374	+	0.191173i	0.805547	+	0.592532i	$0.201871\pi$
$830$		0			0
$831$	12177.5	+	21092.0i	0.508343	+	0.880475i
$832$		−	4480.00i		−	0.186678i
$833$	10821.0	−	13744.5i	0.450090	−	0.571691i
$834$	14840.0			0.616148
$835$		0			0
$836$	570.000	−	987.269i	0.0235812	−	0.0408438i
$837$	−2888.19	−	1667.50i	−0.119272	−	0.0688617i
$838$	9457.00	−	5460.00i	0.389841	−	0.225075i
$839$	39816.0			1.63838			0.819190	−	0.573522i	$-0.194423\pi$
$839$	39816.0			1.63838			0.819190	+	0.573522i	$0.194423\pi$
$840$		0			0
$841$	−11393.0			−0.467137
$842$	13388.8	−	7730.00i	0.547989	−	0.316382i
$843$	30423.5	+	17565.0i	1.24299	+	0.717640i
$844$	−248.000	+	429.549i	−0.0101144	+	0.0175186i
$845$		0			0
$846$	−804.000			−0.0326739
$847$	−11627.3	+	33565.0i	−0.471685	+	1.36164i
$848$			6288.00i			0.254635i
$849$	13382.5	+	23179.2i	0.540973	+	0.936993i
$850$		0			0
$851$	8728.50	−	15118.2i	0.351597	−	0.608984i
$852$	1662.77	−	960.000i	0.0668609	−	0.0386022i
$853$		−	14546.0i		−	0.583875i	−0.956437	−	0.291938i	$-0.905700\pi$
$853$		−	14546.0i		−	0.583875i	0.956437	−	0.291938i	$-0.0943000\pi$
$854$	−4963.00	−	25788.5i	−0.198865	−	1.03333i
$855$		0			0
$856$	4428.00	+	7669.52i	0.176806	+	0.306237i
$857$	27235.6	+	15724.5i	1.08559	+	0.626766i	0.932399	−	0.361430i	$-0.117711\pi$
$857$	27235.6	+	15724.5i	1.08559	+	0.626766i	0.153192	+	0.988196i	$0.451045\pi$
$858$	−34554.4	−	19950.0i	−1.37490	−	0.793802i
$859$	−12261.5	−	21237.5i	−0.487028	−	0.843557i	0.512861	−	0.858472i	$-0.328586\pi$
$859$	−12261.5	−	21237.5i	−0.487028	−	0.843557i	−0.999889	+	0.0149147i	$0.995252\pi$
$860$		0			0
$861$	−735.000	−	3819.17i	−0.0290926	−	0.151170i
$862$		−	22626.0i		−	0.894019i
$863$	7069.37	−	4081.50i	0.278846	−	0.160992i	−0.354055	−	0.935225i	$-0.615197\pi$
$863$	7069.37	−	4081.50i	0.278846	−	0.160992i	0.632901	+	0.774233i	$0.281864\pi$
$864$	2320.00	−	4018.36i	0.0913519	−	0.158226i
$865$		0			0
$866$	−4214.00	−	7298.86i	−0.165355	−	0.286403i
$867$			11560.0i			0.452824i
$868$	557.720	−	1610.00i	0.0218091	−	0.0629573i
$869$	26277.0			1.02576
$870$		0			0
$871$	14665.0	−	25400.5i	0.570499	−	0.988133i
$872$	−6394.73	−	3692.00i	−0.248341	−	0.143379i
$873$	−3176.58	+	1834.00i	−0.123151	+	0.0711014i
$874$	−690.000			−0.0267043
$875$		0			0
$876$	6260.00			0.241445
$877$	3781.93	−	2183.50i	0.145618	−	0.0840725i	−0.425421	−	0.904996i	$-0.639874\pi$
$877$	3781.93	−	2183.50i	0.145618	−	0.0840725i	0.571039	+	0.820923i	$0.306541\pi$
$878$	28670.6	+	16553.0i	1.10204	+	0.636260i
$879$	−10395.0	+	18004.7i	−0.398879	+	0.690879i
$880$		0			0
$881$	−50190.0			−1.91935			−0.959673	−	0.281118i	$-0.909295\pi$
$881$	−50190.0			−1.91935			−0.959673	+	0.281118i	$0.909295\pi$
$882$	848.705	−	1078.00i	0.0324007	−	0.0411544i
$883$		−	12308.0i		−	0.469079i	−0.972107	−	0.234540i	$-0.924642\pi$
$883$		−	12308.0i		−	0.469079i	0.972107	−	0.234540i	$-0.0753583\pi$
$884$	−7140.00	−	12366.8i	−0.271656	−	0.470523i
$885$		0			0
$886$	16395.0	−	28397.0i	0.621671	−	1.07677i
$887$	27381.1	−	15808.5i	1.03649	−	0.598419i	0.117654	−	0.993055i	$-0.462463\pi$
$887$	27381.1	−	15808.5i	1.03649	−	0.598419i	0.918838	+	0.394636i	$0.129129\pi$
$888$		−	10120.0i		−	0.382438i
$889$	−28784.0	+	24927.7i	−1.08592	+	0.940436i
$890$		0			0
$891$	−19123.5	−	33122.9i	−0.719036	−	1.24541i
$892$	−193.990	−	112.000i	−0.00728168	−	0.00420408i
$893$	870.356	+	502.500i	0.0326152	+	0.0188304i
$894$	285.000	+	493.634i	0.0106620	+	0.0184671i
$895$		0			0
$896$	2240.00	+	775.959i	0.0835191	+	0.0289319i
$897$			24150.0i			0.898935i
$898$	26136.6	−	15090.0i	0.971260	−	0.560757i
$899$	1311.00	−	2270.72i	0.0486366	−	0.0842411i
$900$		0			0
$901$	10021.5	+	17357.7i	0.370549	+	0.641810i
$902$			4788.00i			0.176744i
$903$	−11275.7	+	2170.00i	−0.415537	+	0.0799702i
$904$	−12336.0			−0.453860
$905$		0			0
$906$	4195.00	−	7265.95i	0.153830	−	0.266441i
$907$	11713.0	+	6762.50i	0.428802	+	0.247569i	0.698836	−	0.715282i	$-0.253702\pi$
$907$	11713.0	+	6762.50i	0.428802	+	0.247569i	−0.270034	+	0.962851i	$0.587035\pi$
$908$	10589.8	−	6114.00i	0.387041	−	0.223458i
$909$	−570.000			−0.0207984
$910$		0			0
$911$	−19248.0			−0.700016			−0.350008	−	0.936747i	$-0.613821\pi$
$911$	−19248.0			−0.700016			−0.350008	+	0.936747i	$0.613821\pi$
$912$	−346.410	+	200.000i	−0.0125776	+	0.00726169i
$913$	29025.7	+	16758.0i	1.05215	+	0.607458i
$914$	−14785.0	+	25608.4i	−0.535059	+	0.926750i
$915$		0			0
$916$	−3844.00			−0.138656
$917$	−12421.4	+	35857.5i	−0.447318	+	1.29130i
$918$		−	14790.0i		−	0.531746i
$919$	−4347.50	−	7530.09i	−0.156051	−	0.270288i	0.777390	−	0.629019i	$-0.216543\pi$
$919$	−4347.50	−	7530.09i	−0.156051	−	0.270288i	−0.933441	+	0.358730i	$0.883210\pi$
$920$		0			0
$921$	−24010.0	+	41586.5i	−0.859019	+	1.48786i
$922$	5019.48	−	2898.00i	0.179293	−	0.103515i
$923$		−	6720.00i		−	0.239644i
$924$	15960.0	−	13821.8i	0.568231	−	0.492102i
$925$		0			0
$926$	−464.000	−	803.672i	−0.0164665	−	0.0285208i
$927$	−864.293	−	499.000i	−0.0306226	−	0.0176799i
$928$	3159.26	+	1824.00i	0.111754	+	0.0645213i
$929$	9739.50	+	16869.3i	0.343964	+	0.595763i	0.985165	−	0.171610i	$-0.0548968\pi$
$929$	9739.50	+	16869.3i	0.343964	+	0.595763i	−0.641201	+	0.767373i	$0.721563\pi$
$930$		0			0
$931$	−1592.50	+	636.529i	−0.0560602	+	0.0224075i
$932$		−	11316.0i		−	0.397712i
$933$	43868.5	−	25327.5i	1.53933	−	0.888730i
$934$	4233.00	−	7331.77i	0.148295	−	0.256855i
$935$		0			0
$936$	−560.000	−	969.948i	−0.0195557	−	0.0338715i
$937$		−	12502.0i		−	0.435883i	−0.975962	−	0.217942i	$-0.930066\pi$
$937$		−	12502.0i		−	0.435883i	0.975962	−	0.217942i	$-0.0699342\pi$
$938$	10160.2	+	11732.0i	0.353670	+	0.408383i
$939$	53995.0			1.87653
$940$		0			0
$941$	7996.50	−	13850.3i	0.277023	−	0.479818i	−0.693621	−	0.720340i	$-0.743986\pi$
$941$	7996.50	−	13850.3i	0.277023	−	0.479818i	0.970643	+	0.240523i	$0.0773189\pi$
$942$	−24534.5	−	14165.0i	−0.848596	−	0.489937i
$943$	2509.74	−	1449.00i	0.0866685	−	0.0500381i
$944$	−3504.00			−0.120811
$945$		0			0
$946$	14136.0			0.485836
$947$	38106.0	−	22000.5i	1.30758	−	0.754932i	0.325888	−	0.945408i	$-0.394337\pi$
$947$	38106.0	−	22000.5i	1.30758	−	0.754932i	0.981692	+	0.190477i	$0.0610034\pi$
$948$	−7984.75	−	4610.00i	−0.273558	−	0.157939i
$949$	10955.0	−	18974.6i	0.374725	−	0.649043i
$950$		0			0
$951$	−2655.00			−0.0905303
$952$	7420.11	−	1428.00i	0.252612	−	0.0486153i
$953$			4002.00i			0.136031i	0.997684	+	0.0680155i	$0.0216667\pi$
$953$			4002.00i			0.136031i	−0.997684	+	0.0680155i	$0.978333\pi$
$954$	786.000	+	1361.39i	0.0266747	+	0.0462020i
$955$		0			0
$956$	7080.00	−	12262.9i	0.239523	−	0.414865i
$957$	28137.2	−	16245.0i	0.950413	−	0.548721i
$958$		−	5478.00i		−	0.184745i
$959$	−493.500	−	2564.30i	−0.0166173	−	0.0863458i
$960$		0			0
$961$	14631.0	+	25341.6i	0.491121	+	0.850647i
$962$	−30674.6	−	17710.0i	−1.02806	−	0.593548i
$963$	1917.38	+	1107.00i	0.0641607	+	0.0370432i
$964$	10462.0	+	18120.7i	0.349542	+	0.605424i
$965$		0			0
$966$	−12075.0	−	4182.90i	−0.402181	−	0.139320i
$967$			10544.0i			0.350643i	0.984511	+	0.175322i	$0.0560966\pi$
$967$			10544.0i			0.350643i	−0.984511	+	0.175322i	$0.943903\pi$
$968$	−13288.3	+	7672.00i	−0.441221	+	0.254739i
$969$	−637.500	+	1104.18i	−0.0211346	+	0.0366062i
$970$		0			0
$971$	3091.50	+	5354.64i	0.102174	+	0.176971i	0.912580	−	0.408898i	$-0.134087\pi$
$971$	3091.50	+	5354.64i	0.102174	+	0.176971i	−0.810406	+	0.585869i	$0.800753\pi$
$972$		−	2240.00i		−	0.0739177i
$973$	17992.5	+	20776.0i	0.592821	+	0.684530i
$974$	−34102.0			−1.12187
$975$		0			0
$976$	5672.00	−	9824.19i	0.186021	−	0.322197i
$977$	−3224.21	−	1861.50i	−0.105580	−	0.0609567i	0.446280	−	0.894893i	$-0.352748\pi$
$977$	−3224.21	−	1861.50i	−0.105580	−	0.0609567i	−0.551860	+	0.833937i	$0.686082\pi$
$978$	−20013.8	+	11555.0i	−0.654368	+	0.377800i
$979$	−57969.0			−1.89244
$980$		0			0
$981$	−1846.00			−0.0600798
$982$	−7440.89	+	4296.00i	−0.241801	+	0.139604i
$983$	−39748.0	−	22948.5i	−1.28969	−	0.744602i	−0.311089	−	0.950381i	$-0.600694\pi$
$983$	−39748.0	−	22948.5i	−1.28969	−	0.744602i	−0.978599	+	0.205779i	$0.934027\pi$
$984$	840.000	−	1454.92i	0.0272136	−	0.0471354i
$985$		0			0
$986$	11628.0			0.375569
$987$	12185.0	+	14070.0i	0.392961	+	0.453752i
$988$			1400.00i			0.0450809i
$989$	−4278.00	−	7409.71i	−0.137545	−	0.238236i
$990$		0			0
$991$	−3233.50	+	5600.59i	−0.103648	+	0.179524i	−0.913185	−	0.407545i	$-0.866385\pi$
$991$	−3233.50	+	5600.59i	−0.103648	+	0.179524i	0.809537	+	0.587069i	$0.199718\pi$
$992$	637.395	−	368.000i	0.0204005	−	0.0117782i
$993$		−	35075.0i		−	1.12092i
$994$	3360.00	+	1163.94i	0.107216	+	0.0371407i
$995$		0			0
$996$	−5880.00	−	10184.5i	−0.187063	−	0.324003i
$997$	−19952.4	−	11519.5i	−0.633799	−	0.365924i	0.148423	−	0.988924i	$-0.452580\pi$
$997$	−19952.4	−	11519.5i	−0.633799	−	0.365924i	−0.782222	+	0.623000i	$0.785914\pi$
$998$	5890.70	+	3401.00i	0.186841	+	0.107873i
$999$	−18342.5	−	31770.1i	−0.580912	−	1.00617i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.4.j.b.249.2		4
5.2	odd	4		350.4.e.e.151.1		2
5.3	odd	4		14.4.c.a.11.1	yes	2
5.4	even	2	inner	350.4.j.b.249.1		4
7.2	even	3	inner	350.4.j.b.149.1		4
15.8	even	4		126.4.g.d.109.1		2
20.3	even	4		112.4.i.a.81.1		2
35.2	odd	12		350.4.e.e.51.1		2
35.3	even	12		98.4.a.f.1.1		1
35.9	even	6	inner	350.4.j.b.149.2		4
35.13	even	4		98.4.c.a.67.1		2
35.17	even	12		2450.4.a.d.1.1		1
35.18	odd	12		98.4.a.d.1.1		1
35.23	odd	12		14.4.c.a.9.1	✓	2
35.32	odd	12		2450.4.a.q.1.1		1
35.33	even	12		98.4.c.a.79.1		2
40.3	even	4		448.4.i.e.193.1		2
40.13	odd	4		448.4.i.b.193.1		2
105.23	even	12		126.4.g.d.37.1		2
105.38	odd	12		882.4.a.c.1.1		1
105.53	even	12		882.4.a.f.1.1		1
105.68	odd	12		882.4.g.u.667.1		2
105.83	odd	4		882.4.g.u.361.1		2
140.3	odd	12		784.4.a.c.1.1		1
140.23	even	12		112.4.i.a.65.1		2
140.123	even	12		784.4.a.p.1.1		1
280.93	odd	12		448.4.i.b.65.1		2
280.163	even	12		448.4.i.e.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.4.c.a.9.1	✓	2	35.23	odd	12
14.4.c.a.11.1	yes	2	5.3	odd	4
98.4.a.d.1.1		1	35.18	odd	12
98.4.a.f.1.1		1	35.3	even	12
98.4.c.a.67.1		2	35.13	even	4
98.4.c.a.79.1		2	35.33	even	12
112.4.i.a.65.1		2	140.23	even	12
112.4.i.a.81.1		2	20.3	even	4
126.4.g.d.37.1		2	105.23	even	12
126.4.g.d.109.1		2	15.8	even	4
350.4.e.e.51.1		2	35.2	odd	12
350.4.e.e.151.1		2	5.2	odd	4
350.4.j.b.149.1		4	7.2	even	3	inner
350.4.j.b.149.2		4	35.9	even	6	inner
350.4.j.b.249.1		4	5.4	even	2	inner
350.4.j.b.249.2		4	1.1	even	1	trivial
448.4.i.b.65.1		2	280.93	odd	12
448.4.i.b.193.1		2	40.13	odd	4
448.4.i.e.65.1		2	280.163	even	12
448.4.i.e.193.1		2	40.3	even	4
784.4.a.c.1.1		1	140.3	odd	12
784.4.a.p.1.1		1	140.123	even	12
882.4.a.c.1.1		1	105.38	odd	12
882.4.a.f.1.1		1	105.53	even	12
882.4.g.u.361.1		2	105.83	odd	4
882.4.g.u.667.1		2	105.68	odd	12
2450.4.a.d.1.1		1	35.17	even	12
2450.4.a.q.1.1		1	35.32	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(-4.33013 - 2.50000i) q^{3} +(2.00000 - 3.46410i) q^{4} -10.0000 q^{6} +(-12.1244 - 14.0000i) q^{7} -8.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(1.73205 - 1.00000i) q^{2} +(-4.33013 - 2.50000i) q^{3} +(2.00000 - 3.46410i) q^{4} -10.0000 q^{6} +(-12.1244 - 14.0000i) q^{7} -8.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +(28.5000 - 49.3634i) q^{11} +(-17.3205 + 10.0000i) q^{12} +70.0000i q^{13} +(-35.0000 - 12.1244i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-44.1673 - 25.5000i) q^{17} +(-3.46410 - 2.00000i) q^{18} +(2.50000 + 4.33013i) q^{19} +(17.5000 + 90.9327i) q^{21} -114.000i q^{22} +(-59.7558 + 34.5000i) q^{23} +(-20.0000 + 34.6410i) q^{24} +(70.0000 + 121.244i) q^{26} +145.000i q^{27} +(-72.7461 + 14.0000i) q^{28} -114.000 q^{29} +(-11.5000 + 19.9186i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(-246.817 + 142.500i) q^{33} -102.000 q^{34} -8.00000 q^{36} +(-219.104 + 126.500i) q^{37} +(8.66025 + 5.00000i) q^{38} +(175.000 - 303.109i) q^{39} -42.0000 q^{41} +(121.244 + 140.000i) q^{42} +124.000i q^{43} +(-114.000 - 197.454i) q^{44} +(-69.0000 + 119.512i) q^{46} +(174.071 - 100.500i) q^{47} +80.0000i q^{48} +(-49.0000 + 339.482i) q^{49} +(127.500 + 220.836i) q^{51} +(242.487 + 140.000i) q^{52} +(-340.348 - 196.500i) q^{53} +(145.000 + 251.147i) q^{54} +(-112.000 + 96.9948i) q^{56} -25.0000i q^{57} +(-197.454 + 114.000i) q^{58} +(109.500 - 189.660i) q^{59} +(354.500 + 614.012i) q^{61} +46.0000i q^{62} +(-12.1244 + 35.0000i) q^{63} -64.0000 q^{64} +(-285.000 + 493.634i) q^{66} +(-362.865 - 209.500i) q^{67} +(-176.669 + 102.000i) q^{68} +345.000 q^{69} -96.0000 q^{71} +(-13.8564 + 8.00000i) q^{72} +(-271.066 - 156.500i) q^{73} +(-253.000 + 438.209i) q^{74} +20.0000 q^{76} +(-1036.63 + 199.500i) q^{77} -700.000i q^{78} +(230.500 + 399.238i) q^{79} +(335.500 - 581.103i) q^{81} +(-72.7461 + 42.0000i) q^{82} +588.000i q^{83} +(350.000 + 121.244i) q^{84} +(124.000 + 214.774i) q^{86} +(493.634 + 285.000i) q^{87} +(-394.908 - 228.000i) q^{88} +(-508.500 - 880.748i) q^{89} +(980.000 - 848.705i) q^{91} +276.000i q^{92} +(99.5929 - 57.5000i) q^{93} +(201.000 - 348.142i) q^{94} +(80.0000 + 138.564i) q^{96} -1834.00i q^{97} +(254.611 + 637.000i) q^{98} -114.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} - 40 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q + 8 * q^4 - 40 * q^6 - 4 * q^9	\( 4 q + 8 q^{4} - 40 q^{6} - 4 q^{9} + 114 q^{11} - 140 q^{14} - 32 q^{16} + 10 q^{19} + 70 q^{21} - 80 q^{24} + 280 q^{26} - 456 q^{29} - 46 q^{31} - 408 q^{34} - 32 q^{36} + 700 q^{39} - 168 q^{41} - 456 q^{44} - 276 q^{46} - 196 q^{49} + 510 q^{51} + 580 q^{54} - 448 q^{56} + 438 q^{59} + 1418 q^{61} - 256 q^{64} - 1140 q^{66} + 1380 q^{69} - 384 q^{71} - 1012 q^{74} + 80 q^{76} + 922 q^{79} + 1342 q^{81} + 1400 q^{84} + 496 q^{86} - 2034 q^{89} + 3920 q^{91} + 804 q^{94} + 320 q^{96} - 456 q^{99}+O(q^{100}) \) 4 * q + 8 * q^4 - 40 * q^6 - 4 * q^9 + 114 * q^11 - 140 * q^14 - 32 * q^16 + 10 * q^19 + 70 * q^21 - 80 * q^24 + 280 * q^26 - 456 * q^29 - 46 * q^31 - 408 * q^34 - 32 * q^36 + 700 * q^39 - 168 * q^41 - 456 * q^44 - 276 * q^46 - 196 * q^49 + 510 * q^51 + 580 * q^54 - 448 * q^56 + 438 * q^59 + 1418 * q^61 - 256 * q^64 - 1140 * q^66 + 1380 * q^69 - 384 * q^71 - 1012 * q^74 + 80 * q^76 + 922 * q^79 + 1342 * q^81 + 1400 * q^84 + 496 * q^86 - 2034 * q^89 + 3920 * q^91 + 804 * q^94 + 320 * q^96 - 456 * q^99

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