LMFDB - Embedded newform 350.4.e.e.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,4,Mod(51,350)]

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([0, 2]))

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

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

chi := DirichletCharacter("350.51");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	350.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$20.6506685020$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 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:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			51.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	350.51
Dual form			350.4.e.e.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-2.50000 - 4.33013i) q^{3} +(-2.00000 - 3.46410i) q^{4} -10.0000 q^{6} +(14.0000 + 12.1244i) q^{7} -8.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-2.50000 - 4.33013i) q^{3} +(-2.00000 - 3.46410i) q^{4} -10.0000 q^{6} +(14.0000 + 12.1244i) q^{7} -8.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(28.5000 + 49.3634i) q^{11} +(-10.0000 + 17.3205i) q^{12} +70.0000 q^{13} +(35.0000 - 12.1244i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(25.5000 + 44.1673i) q^{17} +(-2.00000 - 3.46410i) q^{18} +(-2.50000 + 4.33013i) q^{19} +(17.5000 - 90.9327i) q^{21} +114.000 q^{22} +(34.5000 - 59.7558i) q^{23} +(20.0000 + 34.6410i) q^{24} +(70.0000 - 121.244i) q^{26} -145.000 q^{27} +(14.0000 - 72.7461i) q^{28} +114.000 q^{29} +(-11.5000 - 19.9186i) q^{31} +(16.0000 + 27.7128i) q^{32} +(142.500 - 246.817i) q^{33} +102.000 q^{34} -8.00000 q^{36} +(-126.500 + 219.104i) q^{37} +(5.00000 + 8.66025i) q^{38} +(-175.000 - 303.109i) q^{39} -42.0000 q^{41} +(-140.000 - 121.244i) q^{42} +124.000 q^{43} +(114.000 - 197.454i) q^{44} +(-69.0000 - 119.512i) q^{46} +(100.500 - 174.071i) q^{47} +80.0000 q^{48} +(49.0000 + 339.482i) q^{49} +(127.500 - 220.836i) q^{51} +(-140.000 - 242.487i) q^{52} +(-196.500 - 340.348i) q^{53} +(-145.000 + 251.147i) q^{54} +(-112.000 - 96.9948i) q^{56} +25.0000 q^{57} +(114.000 - 197.454i) q^{58} +(-109.500 - 189.660i) q^{59} +(354.500 - 614.012i) q^{61} -46.0000 q^{62} +(35.0000 - 12.1244i) q^{63} +64.0000 q^{64} +(-285.000 - 493.634i) q^{66} +(209.500 + 362.865i) q^{67} +(102.000 - 176.669i) q^{68} -345.000 q^{69} -96.0000 q^{71} +(-8.00000 + 13.8564i) q^{72} +(-156.500 - 271.066i) q^{73} +(253.000 + 438.209i) q^{74} +20.0000 q^{76} +(-199.500 + 1036.63i) q^{77} -700.000 q^{78} +(-230.500 + 399.238i) q^{79} +(335.500 + 581.103i) q^{81} +(-42.0000 + 72.7461i) q^{82} +588.000 q^{83} +(-350.000 + 121.244i) q^{84} +(124.000 - 214.774i) q^{86} +(-285.000 - 493.634i) q^{87} +(-228.000 - 394.908i) q^{88} +(508.500 - 880.748i) q^{89} +(980.000 + 848.705i) q^{91} -276.000 q^{92} +(-57.5000 + 99.5929i) q^{93} +(-201.000 - 348.142i) q^{94} +(80.0000 - 138.564i) q^{96} +1834.00 q^{97} +(637.000 + 254.611i) q^{98} +114.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 5 q^{3} - 4 q^{4} - 20 q^{6} + 28 q^{7} - 16 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 5 * q^3 - 4 * q^4 - 20 * q^6 + 28 * q^7 - 16 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 5 q^{3} - 4 q^{4} - 20 q^{6} + 28 q^{7} - 16 q^{8} + 2 q^{9} + 57 q^{11} - 20 q^{12} + 140 q^{13} + 70 q^{14} - 16 q^{16} + 51 q^{17} - 4 q^{18} - 5 q^{19} + 35 q^{21} + 228 q^{22} + 69 q^{23} + 40 q^{24} + 140 q^{26} - 290 q^{27} + 28 q^{28} + 228 q^{29} - 23 q^{31} + 32 q^{32} + 285 q^{33} + 204 q^{34} - 16 q^{36} - 253 q^{37} + 10 q^{38} - 350 q^{39} - 84 q^{41} - 280 q^{42} + 248 q^{43} + 228 q^{44} - 138 q^{46} + 201 q^{47} + 160 q^{48} + 98 q^{49} + 255 q^{51} - 280 q^{52} - 393 q^{53} - 290 q^{54} - 224 q^{56} + 50 q^{57} + 228 q^{58} - 219 q^{59} + 709 q^{61} - 92 q^{62} + 70 q^{63} + 128 q^{64} - 570 q^{66} + 419 q^{67} + 204 q^{68} - 690 q^{69} - 192 q^{71} - 16 q^{72} - 313 q^{73} + 506 q^{74} + 40 q^{76} - 399 q^{77} - 1400 q^{78} - 461 q^{79} + 671 q^{81} - 84 q^{82} + 1176 q^{83} - 700 q^{84} + 248 q^{86} - 570 q^{87} - 456 q^{88} + 1017 q^{89} + 1960 q^{91} - 552 q^{92} - 115 q^{93} - 402 q^{94} + 160 q^{96} + 3668 q^{97} + 1274 q^{98} + 228 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 5 * q^3 - 4 * q^4 - 20 * q^6 + 28 * q^7 - 16 * q^8 + 2 * q^9 + 57 * q^11 - 20 * q^12 + 140 * q^13 + 70 * q^14 - 16 * q^16 + 51 * q^17 - 4 * q^18 - 5 * q^19 + 35 * q^21 + 228 * q^22 + 69 * q^23 + 40 * q^24 + 140 * q^26 - 290 * q^27 + 28 * q^28 + 228 * q^29 - 23 * q^31 + 32 * q^32 + 285 * q^33 + 204 * q^34 - 16 * q^36 - 253 * q^37 + 10 * q^38 - 350 * q^39 - 84 * q^41 - 280 * q^42 + 248 * q^43 + 228 * q^44 - 138 * q^46 + 201 * q^47 + 160 * q^48 + 98 * q^49 + 255 * q^51 - 280 * q^52 - 393 * q^53 - 290 * q^54 - 224 * q^56 + 50 * q^57 + 228 * q^58 - 219 * q^59 + 709 * q^61 - 92 * q^62 + 70 * q^63 + 128 * q^64 - 570 * q^66 + 419 * q^67 + 204 * q^68 - 690 * q^69 - 192 * q^71 - 16 * q^72 - 313 * q^73 + 506 * q^74 + 40 * q^76 - 399 * q^77 - 1400 * q^78 - 461 * q^79 + 671 * q^81 - 84 * q^82 + 1176 * q^83 - 700 * q^84 + 248 * q^86 - 570 * q^87 - 456 * q^88 + 1017 * q^89 + 1960 * q^91 - 552 * q^92 - 115 * q^93 - 402 * q^94 + 160 * q^96 + 3668 * q^97 + 1274 * q^98 + 228 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$	−2.50000	−	4.33013i	−0.481125	−	0.833333i	0.518640	−	0.854993i	$-0.326438\pi$
$3$	−2.50000	−	4.33013i	−0.481125	−	0.833333i	−0.999765	+	0.0216593i	$0.993105\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−10.0000			−0.680414
$7$	14.0000	+	12.1244i	0.755929	+	0.654654i
$7$	14.0000	+	12.1244i	0.755929	+	0.654654i
$8$	−8.00000			−0.353553
$9$	1.00000	−	1.73205i	0.0370370	−	0.0641500i
$10$		0			0
$11$	28.5000	+	49.3634i	0.781188	+	1.35306i	0.931250	+	0.364381i	$0.118720\pi$
$11$	28.5000	+	49.3634i	0.781188	+	1.35306i	−0.150061	+	0.988677i	$0.547947\pi$
$12$	−10.0000	+	17.3205i	−0.240563	+	0.416667i
$13$	70.0000			1.49342			0.746712	−	0.665148i	$-0.231631\pi$
$13$	70.0000			1.49342			0.746712	+	0.665148i	$0.231631\pi$
$14$	35.0000	−	12.1244i	0.668153	−	0.231455i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	25.5000	+	44.1673i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	25.5000	+	44.1673i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$	−2.00000	−	3.46410i	−0.0261891	−	0.0453609i
$19$	−2.50000	+	4.33013i	−0.0301863	+	0.0522842i	−0.880724	−	0.473630i	$-0.842943\pi$
$19$	−2.50000	+	4.33013i	−0.0301863	+	0.0522842i	0.850538	+	0.525914i	$0.176277\pi$
$20$		0			0
$21$	17.5000	−	90.9327i	0.181848	−	0.944911i
$22$	114.000			1.10477
$23$	34.5000	−	59.7558i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	34.5000	−	59.7558i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$	20.0000	+	34.6410i	0.170103	+	0.294628i
$25$		0			0
$26$	70.0000	−	121.244i	0.528005	−	0.914531i
$27$	−145.000			−1.03353
$28$	14.0000	−	72.7461i	0.0944911	−	0.490990i
$29$	114.000			0.729975			0.364987	−	0.931012i	$-0.381073\pi$
$29$	114.000			0.729975			0.364987	+	0.931012i	$0.381073\pi$
$30$		0			0
$31$	−11.5000	−	19.9186i	−0.0666278	−	0.115403i	0.830787	−	0.556590i	$-0.187891\pi$
$31$	−11.5000	−	19.9186i	−0.0666278	−	0.115403i	−0.897415	+	0.441188i	$0.854557\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	142.500	−	246.817i	0.751699	−	1.30198i
$34$	102.000			0.514496
$35$		0			0
$36$	−8.00000			−0.0370370
$37$	−126.500	+	219.104i	−0.562067	+	0.973528i	0.435249	+	0.900310i	$0.356660\pi$
$37$	−126.500	+	219.104i	−0.562067	+	0.973528i	−0.997316	+	0.0732182i	$0.976673\pi$
$38$	5.00000	+	8.66025i	0.0213449	+	0.0369705i
$39$	−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	$0.525489\pi$
$42$	−140.000	−	121.244i	−0.514344	−	0.445435i
$43$	124.000			0.439763			0.219882	−	0.975527i	$-0.429433\pi$
$43$	124.000			0.439763			0.219882	+	0.975527i	$0.429433\pi$
$44$	114.000	−	197.454i	0.390594	−	0.676529i
$45$		0			0
$46$	−69.0000	−	119.512i	−0.221163	−	0.383065i
$47$	100.500	−	174.071i	0.311903	−	0.540231i	−0.666871	−	0.745173i	$-0.732367\pi$
$47$	100.500	−	174.071i	0.311903	−	0.540231i	0.978774	+	0.204941i	$0.0657003\pi$
$48$	80.0000			0.240563
$49$	49.0000	+	339.482i	0.142857	+	0.989743i
$50$		0			0
$51$	127.500	−	220.836i	0.350070	−	0.606339i
$52$	−140.000	−	242.487i	−0.373356	−	0.646671i
$53$	−196.500	−	340.348i	−0.509271	−	0.882083i	−0.999942	−	0.0107383i	$-0.996582\pi$
$53$	−196.500	−	340.348i	−0.509271	−	0.882083i	0.490672	−	0.871345i	$-0.336751\pi$
$54$	−145.000	+	251.147i	−0.365407	+	0.632904i
$55$		0			0
$56$	−112.000	−	96.9948i	−0.267261	−	0.231455i
$57$	25.0000			0.0580935
$58$	114.000	−	197.454i	0.258085	−	0.447016i
$59$	−109.500	−	189.660i	−0.241622	−	0.418501i	0.719555	−	0.694436i	$-0.244346\pi$
$59$	−109.500	−	189.660i	−0.241622	−	0.418501i	−0.961176	+	0.275935i	$0.911013\pi$
$60$		0			0
$61$	354.500	−	614.012i	0.744083	−	1.28879i	−0.206539	−	0.978438i	$-0.566220\pi$
$61$	354.500	−	614.012i	0.744083	−	1.28879i	0.950622	−	0.310351i	$-0.100447\pi$
$62$	−46.0000			−0.0942259
$63$	35.0000	−	12.1244i	0.0699934	−	0.0242464i
$64$	64.0000			0.125000
$65$		0			0
$66$	−285.000	−	493.634i	−0.531531	−	0.920639i
$67$	209.500	+	362.865i	0.382007	+	0.661656i	0.991349	−	0.131251i	$-0.0418995\pi$
$67$	209.500	+	362.865i	0.382007	+	0.661656i	−0.609342	+	0.792908i	$0.708566\pi$
$68$	102.000	−	176.669i	0.181902	−	0.315063i
$69$	−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	$0.525566\pi$
$72$	−8.00000	+	13.8564i	−0.0130946	+	0.0226805i
$73$	−156.500	−	271.066i	−0.250917	−	0.434601i	0.712862	−	0.701305i	$-0.247399\pi$
$73$	−156.500	−	271.066i	−0.250917	−	0.434601i	−0.963779	+	0.266704i	$0.914065\pi$
$74$	253.000	+	438.209i	0.397441	+	0.688388i
$75$		0			0
$76$	20.0000			0.0301863
$77$	−199.500	+	1036.63i	−0.295261	+	1.53422i
$78$	−700.000			−1.01615
$79$	−230.500	+	399.238i	−0.328269	+	0.568579i	−0.982169	−	0.188003i	$-0.939799\pi$
$79$	−230.500	+	399.238i	−0.328269	+	0.568579i	0.653899	+	0.756582i	$0.273132\pi$
$80$		0			0
$81$	335.500	+	581.103i	0.460219	+	0.797124i
$82$	−42.0000	+	72.7461i	−0.0565625	+	0.0979691i
$83$	588.000			0.777607			0.388804	−	0.921321i	$-0.372888\pi$
$83$	588.000			0.777607			0.388804	+	0.921321i	$0.372888\pi$
$84$	−350.000	+	121.244i	−0.454621	+	0.157485i
$85$		0			0
$86$	124.000	−	214.774i	0.155480	−	0.269299i
$87$	−285.000	−	493.634i	−0.351209	−	0.608312i
$88$	−228.000	−	394.908i	−0.276192	−	0.478378i
$89$	508.500	−	880.748i	0.605628	−	1.04898i	−0.386324	−	0.922363i	$-0.626255\pi$
$89$	508.500	−	880.748i	0.605628	−	1.04898i	0.991952	−	0.126615i	$-0.0404114\pi$
$90$		0			0
$91$	980.000	+	848.705i	1.12892	+	0.977675i
$92$	−276.000			−0.312772
$93$	−57.5000	+	99.5929i	−0.0641126	+	0.111046i
$94$	−201.000	−	348.142i	−0.220549	−	0.382001i
$95$		0			0
$96$	80.0000	−	138.564i	0.0850517	−	0.147314i
$97$	1834.00			1.91974			0.959868	−	0.280451i	$-0.0904839\pi$
$97$	1834.00			1.91974			0.959868	+	0.280451i	$0.0904839\pi$
$98$	637.000	+	254.611i	0.656599	+	0.262445i
$99$	114.000			0.115732
$100$		0			0
$101$	142.500	+	246.817i	0.140389	+	0.243161i	0.927643	−	0.373468i	$-0.121831\pi$
$101$	142.500	+	246.817i	0.140389	+	0.243161i	−0.787254	+	0.616629i	$0.788498\pi$
$102$	−255.000	−	441.673i	−0.247537	−	0.428746i
$103$	−249.500	+	432.147i	−0.238679	+	0.413405i	−0.960336	−	0.278847i	$-0.910048\pi$
$103$	−249.500	+	432.147i	−0.238679	+	0.413405i	0.721656	+	0.692252i	$0.243381\pi$
$104$	−560.000			−0.528005
$105$		0			0
$106$	−786.000			−0.720218
$107$	−553.500	+	958.690i	−0.500083	+	0.866169i	0.499917	+	0.866073i	$0.333364\pi$
$107$	−553.500	+	958.690i	−0.500083	+	0.866169i	−1.00000		9.56665e-5i	$0.999970\pi$
$108$	290.000	+	502.295i	0.258382	+	0.447531i
$109$	−461.500	−	799.341i	−0.405538	−	0.702413i	0.588846	−	0.808246i	$-0.299583\pi$
$109$	−461.500	−	799.341i	−0.405538	−	0.702413i	−0.994384	+	0.105832i	$0.966249\pi$
$110$		0			0
$111$	1265.00			1.08170
$112$	−280.000	+	96.9948i	−0.236228	+	0.0818317i
$113$	−1542.00			−1.28371			−0.641855	−	0.766826i	$-0.721835\pi$
$113$	−1542.00			−1.28371			−0.641855	+	0.766826i	$0.721835\pi$
$114$	25.0000	−	43.3013i	0.0205392	−	0.0355749i
$115$		0			0
$116$	−228.000	−	394.908i	−0.182494	−	0.316088i
$117$	70.0000	−	121.244i	0.0553120	−	0.0958032i
$118$	−438.000			−0.341705
$119$	−178.500	+	927.513i	−0.137505	+	0.714496i
$120$		0			0
$121$	−959.000	+	1661.04i	−0.720511	+	1.24796i
$122$	−709.000	−	1228.02i	−0.526146	−	0.911312i
$123$	105.000	+	181.865i	0.0769718	+	0.133319i
$124$	−46.0000	+	79.6743i	−0.0333139	+	0.0577013i
$125$		0			0
$126$	14.0000	−	72.7461i	0.00989856	−	0.0514344i
$127$	2056.00			1.43654			0.718270	−	0.695765i	$-0.244934\pi$
$127$	2056.00			1.43654			0.718270	+	0.695765i	$0.244934\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	−310.000	−	536.936i	−0.211581	−	0.366469i
$130$		0			0
$131$	−1024.50	+	1774.49i	−0.683290	+	1.18349i	0.290681	+	0.956820i	$0.406118\pi$
$131$	−1024.50	+	1774.49i	−0.683290	+	1.18349i	−0.973971	+	0.226673i	$0.927215\pi$
$132$	−1140.00			−0.751699
$133$	−87.5000	+	30.3109i	−0.0570467	+	0.0197616i
$134$	838.000			0.540240
$135$		0			0
$136$	−204.000	−	353.338i	−0.128624	−	0.222783i
$137$	−70.5000	−	122.110i	−0.0439651	−	0.0761498i	0.843205	−	0.537591i	$-0.180666\pi$
$137$	−70.5000	−	122.110i	−0.0439651	−	0.0761498i	−0.887171	+	0.461442i	$0.847332\pi$
$138$	−345.000	+	597.558i	−0.212814	+	0.368605i
$139$	1484.00			0.905548			0.452774	−	0.891625i	$-0.350434\pi$
$139$	1484.00			0.905548			0.452774	+	0.891625i	$0.350434\pi$
$140$		0			0
$141$	−1005.00			−0.600257
$142$	−96.0000	+	166.277i	−0.0567334	+	0.0982651i
$143$	1995.00	+	3455.44i	1.16665	+	2.02069i
$144$	16.0000	+	27.7128i	0.00925926	+	0.0160375i
$145$		0			0
$146$	−626.000			−0.354850
$147$	1347.50	−	1060.88i	0.756054	−	0.595238i
$148$	1012.00			0.562067
$149$	28.5000	−	49.3634i	0.0156699	−	0.0271410i	−0.858084	−	0.513509i	$-0.828345\pi$
$149$	28.5000	−	49.3634i	0.0156699	−	0.0271410i	0.873754	+	0.486368i	$0.161679\pi$
$150$		0			0
$151$	−419.500	−	726.595i	−0.226082	−	0.391586i	0.730561	−	0.682847i	$-0.239258\pi$
$151$	−419.500	−	726.595i	−0.226082	−	0.391586i	−0.956644	+	0.291261i	$0.905925\pi$
$152$	20.0000	−	34.6410i	0.0106725	−	0.0184852i
$153$	102.000			0.0538968
$154$	1596.00	+	1382.18i	0.835126	+	0.723240i
$155$		0			0
$156$	−700.000	+	1212.44i	−0.359262	+	0.622260i
$157$	−1416.50	−	2453.45i	−0.720057	−	1.24718i	−0.960976	−	0.276631i	$-0.910782\pi$
$157$	−1416.50	−	2453.45i	−0.720057	−	1.24718i	0.240919	−	0.970545i	$-0.422551\pi$
$158$	461.000	+	798.475i	0.232121	+	0.402046i
$159$	−982.500	+	1701.74i	−0.490046	+	0.848785i
$160$		0			0
$161$	1207.50	−	418.290i	0.591083	−	0.204757i
$162$	1342.00			0.650849
$163$	−1155.50	+	2001.38i	−0.555250	+	0.961721i	0.442634	+	0.896702i	$0.354044\pi$
$163$	−1155.50	+	2001.38i	−0.555250	+	0.961721i	−0.997884	+	0.0650188i	$0.979289\pi$
$164$	84.0000	+	145.492i	0.0399957	+	0.0692746i
$165$		0			0
$166$	588.000	−	1018.45i	0.274926	−	0.476185i
$167$	−1260.00			−0.583843			−0.291921	−	0.956442i	$-0.594295\pi$
$167$	−1260.00			−0.583843			−0.291921	+	0.956442i	$0.594295\pi$
$168$	−140.000	+	727.461i	−0.0642931	+	0.334077i
$169$	2703.00			1.23031
$170$		0			0
$171$	5.00000	+	8.66025i	0.00223602	+	0.00387290i
$172$	−248.000	−	429.549i	−0.109941	−	0.190423i
$173$	1633.50	−	2829.30i	0.717877	−	1.24340i	−0.243962	−	0.969785i	$-0.578447\pi$
$173$	1633.50	−	2829.30i	0.717877	−	1.24340i	0.961839	−	0.273615i	$-0.0882193\pi$
$174$	−1140.00			−0.496685
$175$		0			0
$176$	−912.000			−0.390594
$177$	−547.500	+	948.298i	−0.232501	+	0.402703i
$178$	−1017.00	−	1761.50i	−0.428244	−	0.741740i
$179$	−643.500	−	1114.57i	−0.268701	−	0.465403i	0.699826	−	0.714314i	$-0.253261\pi$
$179$	−643.500	−	1114.57i	−0.268701	−	0.465403i	−0.968527	+	0.248910i	$0.919928\pi$
$180$		0			0
$181$	−2674.00			−1.09810			−0.549052	−	0.835788i	$-0.685011\pi$
$181$	−2674.00			−1.09810			−0.549052	+	0.835788i	$0.685011\pi$
$182$	2450.00	−	848.705i	0.997836	−	0.345660i
$183$	−3545.00			−1.43199
$184$	−276.000	+	478.046i	−0.110581	+	0.191533i
$185$		0			0
$186$	115.000	+	199.186i	0.0453345	+	0.0785216i
$187$	−1453.50	+	2517.54i	−0.568398	+	0.984494i
$188$	−804.000			−0.311903
$189$	−2030.00	−	1758.03i	−0.781274	−	0.676603i
$190$		0			0
$191$	−2092.50	+	3624.32i	−0.792712	+	1.37302i	0.131570	+	0.991307i	$0.457998\pi$
$191$	−2092.50	+	3624.32i	−0.792712	+	1.37302i	−0.924282	+	0.381711i	$0.875335\pi$
$192$	−160.000	−	277.128i	−0.0601407	−	0.104167i
$193$	−42.5000	−	73.6122i	−0.0158509	−	0.0274545i	0.857991	−	0.513664i	$-0.171712\pi$
$193$	−42.5000	−	73.6122i	−0.0158509	−	0.0274545i	−0.873842	+	0.486210i	$0.838379\pi$
$194$	1834.00	−	3176.58i	0.678730	−	1.17559i
$195$		0			0
$196$	1078.00	−	848.705i	0.392857	−	0.309295i
$197$	390.000			0.141047			0.0705237	−	0.997510i	$-0.477533\pi$
$197$	390.000			0.141047			0.0705237	+	0.997510i	$0.477533\pi$
$198$	114.000	−	197.454i	0.0409173	−	0.0708709i
$199$	1416.50	+	2453.45i	0.504588	+	0.873972i	0.999986	+	0.00530596i	$0.00168895\pi$
$199$	1416.50	+	2453.45i	0.504588	+	0.873972i	−0.495398	+	0.868666i	$0.664978\pi$
$200$		0			0
$201$	1047.50	−	1814.32i	0.367587	−	0.636679i
$202$	570.000			0.198540
$203$	1596.00	+	1382.18i	0.551809	+	0.477881i
$204$	−1020.00			−0.350070
$205$		0			0
$206$	499.000	+	864.293i	0.168772	+	0.292321i
$207$	−69.0000	−	119.512i	−0.0231683	−	0.0401286i
$208$	−560.000	+	969.948i	−0.186678	+	0.323336i
$209$	−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	$0.506439\pi$
$212$	−786.000	+	1361.39i	−0.254635	+	0.441041i
$213$	240.000	+	415.692i	0.0772044	+	0.133722i
$214$	1107.00	+	1917.38i	0.353612	+	0.612474i
$215$		0			0
$216$	1160.00			0.365407
$217$	80.5000	−	418.290i	0.0251829	−	0.130854i
$218$	−1846.00			−0.573518
$219$	−782.500	+	1355.33i	−0.241445	+	0.418195i
$220$		0			0
$221$	1785.00	+	3091.71i	0.543313	+	0.941045i
$222$	1265.00	−	2191.04i	0.382438	−	0.662402i
$223$	−56.0000			−0.0168163			−0.00840816	−	0.999965i	$-0.502676\pi$
$223$	−56.0000			−0.0168163			−0.00840816	+	0.999965i	$0.502676\pi$
$224$	−112.000	+	581.969i	−0.0334077	+	0.173591i
$225$		0			0
$226$	−1542.00	+	2670.82i	−0.453860	+	0.786108i
$227$	−1528.50	−	2647.44i	−0.446917	−	0.774083i	0.551267	−	0.834329i	$-0.314145\pi$
$227$	−1528.50	−	2647.44i	−0.446917	−	0.774083i	−0.998184	+	0.0602465i	$0.980811\pi$
$228$	−50.0000	−	86.6025i	−0.0145234	−	0.0251552i
$229$	480.500	−	832.250i	0.138656	−	0.240160i	−0.788332	−	0.615250i	$-0.789055\pi$
$229$	480.500	−	832.250i	0.138656	−	0.240160i	0.926988	+	0.375090i	$0.122388\pi$
$230$		0			0
$231$	4987.50	−	1727.72i	1.42058	−	0.492102i
$232$	−912.000			−0.258085
$233$	−1414.50	+	2449.99i	−0.397712	+	0.688858i	−0.993443	−	0.114326i	$-0.963529\pi$
$233$	−1414.50	+	2449.99i	−0.397712	+	0.688858i	0.595731	+	0.803184i	$0.296862\pi$
$234$	−140.000	−	242.487i	−0.0391115	−	0.0677431i
$235$		0			0
$236$	−438.000	+	758.638i	−0.120811	+	0.209251i
$237$	2305.00			0.631755
$238$	1428.00	+	1236.68i	0.388922	+	0.336817i
$239$	−3540.00			−0.958090			−0.479045	−	0.877790i	$-0.659017\pi$
$239$	−3540.00			−0.958090			−0.479045	+	0.877790i	$0.659017\pi$
$240$		0			0
$241$	−2615.50	−	4530.18i	−0.699084	−	1.21085i	−0.968785	−	0.247904i	$-0.920258\pi$
$241$	−2615.50	−	4530.18i	−0.699084	−	1.21085i	0.269701	−	0.962944i	$-0.413075\pi$
$242$	1918.00	+	3322.07i	0.509478	+	0.882442i
$243$	−280.000	+	484.974i	−0.0739177	+	0.128029i
$244$	−2836.00			−0.744083
$245$		0			0
$246$	420.000			0.108855
$247$	−175.000	+	303.109i	−0.0450809	+	0.0780824i
$248$	92.0000	+	159.349i	0.0235565	+	0.0408010i
$249$	−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	$0.281532\pi$
$252$	−112.000	−	96.9948i	−0.0279974	−	0.0242464i
$253$	3933.00			0.977334
$254$	2056.00	−	3561.10i	0.507893	−	0.879697i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−718.500	+	1244.48i	−0.174392	+	0.302056i	−0.939951	−	0.341310i	$-0.889129\pi$
$257$	−718.500	+	1244.48i	−0.174392	+	0.302056i	0.765559	+	0.643366i	$0.222463\pi$
$258$	−1240.00			−0.299221
$259$	−4427.50	+	1533.73i	−1.06221	+	0.367959i
$260$		0			0
$261$	114.000	−	197.454i	0.0270361	−	0.0468279i
$262$	2049.00	+	3548.97i	0.483159	+	0.836856i
$263$	−1162.50	−	2013.51i	−0.272558	−	0.472085i	0.696958	−	0.717112i	$-0.254536\pi$
$263$	−1162.50	−	2013.51i	−0.272558	−	0.472085i	−0.969516	+	0.245027i	$0.921203\pi$
$264$	−1140.00	+	1974.54i	−0.265766	+	0.460320i
$265$		0			0
$266$	−35.0000	+	181.865i	−0.00806762	+	0.0419206i
$267$	−5085.00			−1.16553
$268$	838.000	−	1451.46i	0.191004	−	0.330828i
$269$	1192.50	+	2065.47i	0.270290	+	0.468156i	0.968936	−	0.247311i	$-0.0795471\pi$
$269$	1192.50	+	2065.47i	0.270290	+	0.468156i	−0.698646	+	0.715467i	$0.746214\pi$
$270$		0			0
$271$	165.500	−	286.654i	0.0370975	−	0.0642547i	−0.846881	−	0.531783i	$-0.821522\pi$
$271$	165.500	−	286.654i	0.0370975	−	0.0642547i	0.883978	+	0.467528i	$0.154855\pi$
$272$	−816.000			−0.181902
$273$	1225.00	−	6365.29i	0.271576	−	1.41115i
$274$	−282.000			−0.0621761
$275$		0			0
$276$	690.000	+	1195.12i	0.150482	+	0.260643i
$277$	2435.50	+	4218.41i	0.528285	+	0.915017i	0.999456	+	0.0329750i	$0.0104982\pi$
$277$	2435.50	+	4218.41i	0.528285	+	0.915017i	−0.471171	+	0.882042i	$0.656169\pi$
$278$	1484.00	−	2570.36i	0.320160	−	0.554533i
$279$	−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	$0.767930\pi$
$282$	−1005.00	+	1740.71i	−0.212223	+	0.367581i
$283$	−2676.50	−	4635.83i	−0.562196	−	0.973752i	−0.997305	−	0.0733738i	$-0.976623\pi$
$283$	−2676.50	−	4635.83i	−0.562196	−	0.973752i	0.435109	−	0.900378i	$-0.356710\pi$
$284$	192.000	+	332.554i	0.0401166	+	0.0694839i
$285$		0			0
$286$	7980.00			1.64989
$287$	−588.000	−	509.223i	−0.120936	−	0.104733i
$288$	64.0000			0.0130946
$289$	1156.00	−	2002.25i	0.235294	−	0.407541i
$290$		0			0
$291$	−4585.00	−	7941.45i	−0.923634	−	1.59978i
$292$	−626.000	+	1084.26i	−0.125458	+	0.217300i
$293$	−4158.00			−0.829054			−0.414527	−	0.910037i	$-0.636053\pi$
$293$	−4158.00			−0.829054			−0.414527	+	0.910037i	$0.636053\pi$
$294$	−490.000	−	3394.82i	−0.0972020	−	0.673435i
$295$		0			0
$296$	1012.00	−	1752.84i	0.198721	−	0.344194i
$297$	−4132.50	−	7157.70i	−0.807380	−	1.39842i
$298$	−57.0000	−	98.7269i	−0.0110803	−	0.0191916i
$299$	2415.00	−	4182.90i	0.467101	−	0.809042i
$300$		0			0
$301$	1736.00	+	1503.42i	0.332430	+	0.287893i
$302$	−1678.00			−0.319729
$303$	712.500	−	1234.09i	0.135089	−	0.233982i
$304$	−40.0000	−	69.2820i	−0.00754657	−	0.0130710i
$305$		0			0
$306$	102.000	−	176.669i	0.0190554	−	0.0330049i
$307$	9604.00			1.78544			0.892719	−	0.450615i	$-0.148795\pi$
$307$	9604.00			1.78544			0.892719	+	0.450615i	$0.148795\pi$
$308$	3990.00	−	1382.18i	0.738154	−	0.255704i
$309$	2495.00			0.459338
$310$		0			0
$311$	−5065.50	−	8773.70i	−0.923595	−	1.59971i	−0.793805	−	0.608173i	$-0.791903\pi$
$311$	−5065.50	−	8773.70i	−0.923595	−	1.59971i	−0.129791	−	0.991541i	$-0.541430\pi$
$312$	1400.00	+	2424.87i	0.254037	+	0.440004i
$313$	5399.50	−	9352.21i	0.975073	−	1.68888i	0.295378	−	0.955380i	$-0.404554\pi$
$313$	5399.50	−	9352.21i	0.975073	−	1.68888i	0.679695	−	0.733495i	$-0.262112\pi$
$314$	−5666.00			−1.01831
$315$		0			0
$316$	1844.00			0.328269
$317$	265.500	−	459.859i	0.0470409	−	0.0814772i	−0.841546	−	0.540185i	$-0.818354\pi$
$317$	265.500	−	459.859i	0.0470409	−	0.0814772i	0.888587	+	0.458708i	$0.151688\pi$
$318$	1965.00	+	3403.48i	0.346515	+	0.600181i
$319$	3249.00	+	5627.43i	0.570248	+	0.987698i
$320$		0			0
$321$	5535.00			0.962410
$322$	483.000	−	2509.74i	0.0835917	−	0.434355i
$323$	−255.000			−0.0439275
$324$	1342.00	−	2324.41i	0.230110	−	0.398562i
$325$		0			0
$326$	2311.00	+	4002.77i	0.392621	+	0.680040i
$327$	−2307.50	+	3996.71i	−0.390229	+	0.675897i
$328$	336.000			0.0565625
$329$	3517.50	−	1218.50i	0.589441	−	0.204188i
$330$		0			0
$331$	3507.50	−	6075.17i	0.582446	−	1.00883i	−0.412743	−	0.910848i	$-0.635429\pi$
$331$	3507.50	−	6075.17i	0.582446	−	1.00883i	0.995189	−	0.0979784i	$-0.0312376\pi$
$332$	−1176.00	−	2036.89i	−0.194402	−	0.336714i
$333$	253.000	+	438.209i	0.0416346	+	0.0721132i
$334$	−1260.00	+	2182.38i	−0.206420	+	0.357529i
$335$		0			0
$336$	1120.00	+	969.948i	0.181848	+	0.157485i
$337$	−8990.00			−1.45316			−0.726582	−	0.687079i	$-0.758892\pi$
$337$	−8990.00			−1.45316			−0.726582	+	0.687079i	$0.758892\pi$
$338$	2703.00	−	4681.73i	0.434982	−	0.753410i
$339$	3855.00	+	6677.06i	0.617625	+	1.06976i
$340$		0			0
$341$	655.500	−	1135.36i	0.104098	−	0.180303i
$342$	20.0000			0.00316221
$343$	−3430.00	+	5346.84i	−0.539949	+	0.841698i
$344$	−992.000			−0.155480
$345$		0			0
$346$	−3267.00	−	5658.61i	−0.507616	−	0.879216i
$347$	−4354.50	−	7542.22i	−0.673665	−	1.16682i	−0.976857	−	0.213893i	$-0.931386\pi$
$347$	−4354.50	−	7542.22i	−0.673665	−	1.16682i	0.303192	−	0.952929i	$-0.401948\pi$
$348$	−1140.00	+	1974.54i	−0.175605	+	0.304156i
$349$	6482.00			0.994193			0.497097	−	0.867695i	$-0.334399\pi$
$349$	6482.00			0.994193			0.497097	+	0.867695i	$0.334399\pi$
$350$		0			0
$351$	−10150.0			−1.54350
$352$	−912.000	+	1579.63i	−0.138096	+	0.239189i
$353$	−1066.50	−	1847.23i	−0.160805	−	0.278522i	0.774353	−	0.632754i	$-0.218076\pi$
$353$	−1066.50	−	1847.23i	−0.160805	−	0.278522i	−0.935158	+	0.354232i	$0.884742\pi$
$354$	1095.00	+	1896.60i	0.164403	+	0.284754i
$355$		0			0
$356$	−4068.00			−0.605628
$357$	4462.50	−	1545.86i	0.661570	−	0.229175i
$358$	−2574.00			−0.380000
$359$	−1924.50	+	3333.33i	−0.282928	+	0.490046i	−0.972105	−	0.234548i	$-0.924639\pi$
$359$	−1924.50	+	3333.33i	−0.282928	+	0.490046i	0.689176	+	0.724594i	$0.257972\pi$
$360$		0			0
$361$	3417.00	+	5918.42i	0.498178	+	0.862869i
$362$	−2674.00	+	4631.50i	−0.388238	+	0.672449i
$363$	9590.00			1.38662
$364$	980.000	−	5092.23i	0.141115	−	0.733256i
$365$		0			0
$366$	−3545.00	+	6140.12i	−0.506284	+	0.876910i
$367$	3245.50	+	5621.37i	0.461618	+	0.799545i	0.999042	−	0.0437668i	$-0.0139358\pi$
$367$	3245.50	+	5621.37i	0.461618	+	0.799545i	−0.537424	+	0.843312i	$0.680603\pi$
$368$	552.000	+	956.092i	0.0781929	+	0.135434i
$369$	−42.0000	+	72.7461i	−0.00592529	+	0.0102629i
$370$		0			0
$371$	1375.50	−	7147.31i	0.192486	−	1.00019i
$372$	460.000			0.0641126
$373$	461.500	−	799.341i	0.0640632	−	0.110961i	−0.832215	−	0.554453i	$-0.812927\pi$
$373$	461.500	−	799.341i	0.0640632	−	0.110961i	0.896278	+	0.443493i	$0.146261\pi$
$374$	2907.00	+	5035.07i	0.401918	+	0.696143i
$375$		0			0
$376$	−804.000	+	1392.57i	−0.110274	+	0.191001i
$377$	7980.00			1.09016
$378$	−5075.00	+	1758.03i	−0.690555	+	0.239215i
$379$	6344.00			0.859814			0.429907	−	0.902873i	$-0.358546\pi$
$379$	6344.00			0.859814			0.429907	+	0.902873i	$0.358546\pi$
$380$		0			0
$381$	−5140.00	−	8902.74i	−0.691155	−	1.19712i
$382$	4185.00	+	7248.63i	0.560532	+	0.970870i
$383$	−2503.50	+	4336.19i	−0.334002	+	0.578509i	−0.983293	−	0.182032i	$-0.941733\pi$
$383$	−2503.50	+	4336.19i	−0.334002	+	0.578509i	0.649290	+	0.760541i	$0.275066\pi$
$384$	−640.000			−0.0850517
$385$		0			0
$386$	−170.000			−0.0224165
$387$	124.000	−	214.774i	0.0162875	−	0.0282108i
$388$	−3668.00	−	6353.16i	−0.479934	−	0.831270i
$389$	−6145.50	−	10644.3i	−0.801001	−	1.38737i	−0.918958	−	0.394355i	$-0.870968\pi$
$389$	−6145.50	−	10644.3i	−0.801001	−	1.38737i	0.117958	−	0.993019i	$-0.462365\pi$
$390$		0			0
$391$	3519.00			0.455150
$392$	−392.000	−	2715.86i	−0.0505076	−	0.349927i
$393$	10245.0			1.31499
$394$	390.000	−	675.500i	0.0498678	−	0.0863736i
$395$		0			0
$396$	−228.000	−	394.908i	−0.0289329	−	0.0501133i
$397$	443.500	−	768.165i	0.0560671	−	0.0971110i	−0.836630	−	0.547769i	$-0.815477\pi$
$397$	443.500	−	768.165i	0.0560671	−	0.0971110i	0.892697	+	0.450658i	$0.148811\pi$
$398$	5666.00			0.713595
$399$	350.000	+	303.109i	0.0439146	+	0.0380311i
$400$		0			0
$401$	−5977.50	+	10353.3i	−0.744394	+	1.28933i	0.206083	+	0.978535i	$0.433928\pi$
$401$	−5977.50	+	10353.3i	−0.744394	+	1.28933i	−0.950477	+	0.310794i	$0.899405\pi$
$402$	−2095.00	−	3628.65i	−0.259923	−	0.450200i
$403$	−805.000	−	1394.30i	−0.0995035	−	0.172345i
$404$	570.000	−	987.269i	0.0701945	−	0.121580i
$405$		0			0
$406$	3990.00	−	1382.18i	0.487735	−	0.168956i
$407$	−14421.0			−1.75632
$408$	−1020.00	+	1766.69i	−0.123768	+	0.214373i
$409$	1710.50	+	2962.67i	0.206794	+	0.358178i	0.950703	−	0.310103i	$-0.100364\pi$
$409$	1710.50	+	2962.67i	0.206794	+	0.358178i	−0.743909	+	0.668281i	$0.767030\pi$
$410$		0			0
$411$	−352.500	+	610.548i	−0.0423055	+	0.0732752i
$412$	1996.00			0.238679
$413$	766.500	−	3982.85i	0.0913245	−	0.474536i
$414$	−276.000			−0.0327649
$415$		0			0
$416$	1120.00	+	1939.90i	0.132001	+	0.228633i
$417$	−3710.00	−	6425.91i	−0.435682	−	0.754624i
$418$	−285.000	+	493.634i	−0.0333488	+	0.0577618i
$419$	−5460.00			−0.636607			−0.318304	−	0.947989i	$-0.603113\pi$
$419$	−5460.00			−0.636607			−0.318304	+	0.947989i	$0.603113\pi$
$420$		0			0
$421$	7730.00			0.894863			0.447431	−	0.894318i	$-0.352339\pi$
$421$	7730.00			0.894863			0.447431	+	0.894318i	$0.352339\pi$
$422$	−124.000	+	214.774i	−0.0143039	+	0.0247750i
$423$	−201.000	−	348.142i	−0.0231039	−	0.0400171i
$424$	1572.00	+	2722.78i	0.180054	+	0.311863i
$425$		0			0
$426$	960.000			0.109183
$427$	12407.5	−	4298.08i	1.40619	−	0.487117i
$428$	4428.00			0.500083
$429$	9975.00	−	17277.2i	1.12260	−	1.94441i
$430$		0			0
$431$	5656.50	+	9797.35i	0.632167	+	1.09495i	0.987108	+	0.160057i	$0.0511677\pi$
$431$	5656.50	+	9797.35i	0.632167	+	1.09495i	−0.354941	+	0.934889i	$0.615499\pi$
$432$	1160.00	−	2009.18i	0.129191	−	0.223765i
$433$	−4214.00			−0.467695			−0.233847	−	0.972273i	$-0.575132\pi$
$433$	−4214.00			−0.467695			−0.233847	+	0.972273i	$0.575132\pi$
$434$	−644.000	−	557.720i	−0.0712281	−	0.0616853i
$435$		0			0
$436$	−1846.00	+	3197.37i	−0.202769	+	0.351207i
$437$	172.500	+	298.779i	0.0188828	+	0.0327060i
$438$	1565.00	+	2710.66i	0.170727	+	0.295708i
$439$	−8276.50	+	14335.3i	−0.899808	+	1.55851i	−0.0720696	+	0.997400i	$0.522960\pi$
$439$	−8276.50	+	14335.3i	−0.899808	+	1.55851i	−0.827739	+	0.561114i	$0.810373\pi$
$440$		0			0
$441$	637.000	+	254.611i	0.0687831	+	0.0274929i
$442$	7140.00			0.768360
$443$	−8197.50	+	14198.5i	−0.879176	+	1.52278i	−0.0269294	+	0.999637i	$0.508573\pi$
$443$	−8197.50	+	14198.5i	−0.879176	+	1.52278i	−0.852247	+	0.523140i	$0.824760\pi$
$444$	−2530.00	−	4382.09i	−0.270425	−	0.468389i
$445$		0			0
$446$	−56.0000	+	96.9948i	−0.00594546	+	0.0102978i
$447$	−285.000			−0.0301567
$448$	896.000	+	775.959i	0.0944911	+	0.0818317i
$449$	−15090.0			−1.58606			−0.793030	−	0.609182i	$-0.791498\pi$
$449$	−15090.0			−1.58606			−0.793030	+	0.609182i	$0.791498\pi$
$450$		0			0
$451$	−1197.00	−	2073.26i	−0.124977	−	0.216466i
$452$	3084.00	+	5341.64i	0.320927	+	0.555862i
$453$	−2097.50	+	3632.98i	−0.217548	+	0.376804i
$454$	−6114.00			−0.632036
$455$		0			0
$456$	−200.000			−0.0205392
$457$	−7392.50	+	12804.2i	−0.756688	+	1.31062i	0.187842	+	0.982199i	$0.439851\pi$
$457$	−7392.50	+	12804.2i	−0.756688	+	1.31062i	−0.944531	+	0.328423i	$0.893483\pi$
$458$	−961.000	−	1664.50i	−0.0980449	−	0.169819i
$459$	−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	$0.453234\pi$
$462$	1995.00	−	10366.3i	0.200900	−	1.04391i
$463$	−464.000			−0.0465743			−0.0232872	−	0.999729i	$-0.507413\pi$
$463$	−464.000			−0.0465743			−0.0232872	+	0.999729i	$0.507413\pi$
$464$	−912.000	+	1579.63i	−0.0912468	+	0.158044i
$465$		0			0
$466$	2829.00	+	4899.97i	0.281225	+	0.487096i
$467$	2116.50	−	3665.89i	0.209721	−	0.363248i	−0.741905	−	0.670505i	$-0.766078\pi$
$467$	2116.50	−	3665.89i	0.209721	−	0.363248i	0.951627	+	0.307256i	$0.0994109\pi$
$468$	−560.000			−0.0553120
$469$	−1466.50	+	7620.16i	−0.144385	+	0.750248i
$470$		0			0
$471$	−7082.50	+	12267.2i	−0.692876	+	1.20010i
$472$	876.000	+	1517.28i	0.0854262	+	0.147963i
$473$	3534.00	+	6121.07i	0.343538	+	0.595025i
$474$	2305.00	−	3992.38i	0.223359	−	0.386869i
$475$		0			0
$476$	3570.00	−	1236.68i	0.343762	−	0.119083i
$477$	−786.000			−0.0754475
$478$	−3540.00	+	6131.46i	−0.338736	+	0.586708i
$479$	−1369.50	−	2372.04i	−0.130635	−	0.226266i	0.793287	−	0.608848i	$-0.208368\pi$
$479$	−1369.50	−	2372.04i	−0.130635	−	0.226266i	−0.923921	+	0.382582i	$0.875035\pi$
$480$		0			0
$481$	−8855.00	+	15337.3i	−0.839404	+	1.45389i
$482$	−10462.0			−0.988654
$483$	−4830.00	−	4182.90i	−0.455016	−	0.394055i
$484$	7672.00			0.720511
$485$		0			0
$486$	560.000	+	969.948i	0.0522677	+	0.0905304i
$487$	8525.50	+	14766.6i	0.793280	+	1.37400i	0.923926	+	0.382572i	$0.124962\pi$
$487$	8525.50	+	14766.6i	0.793280	+	1.37400i	−0.130646	+	0.991429i	$0.541705\pi$
$488$	−2836.00	+	4912.10i	−0.263073	+	0.455656i
$489$	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	$0.563259\pi$
$492$	420.000	−	727.461i	0.0384859	−	0.0666595i
$493$	2907.00	+	5035.07i	0.265567	+	0.459976i
$494$	350.000	+	606.218i	0.0318770	+	0.0552126i
$495$		0			0
$496$	368.000			0.0333139
$497$	−1344.00	−	1163.94i	−0.121301	−	0.105050i
$498$	−5880.00			−0.529095
$499$	−1700.50	+	2945.35i	−0.152555	+	0.264233i	−0.932166	−	0.362031i	$-0.882083\pi$
$499$	−1700.50	+	2945.35i	−0.152555	+	0.264233i	0.779611	+	0.626264i	$0.215417\pi$
$500$		0			0
$501$	3150.00	+	5455.96i	0.280901	+	0.486536i
$502$	5040.00	−	8729.54i	0.448100	−	0.776132i
$503$	−16800.0			−1.48921			−0.744607	−	0.667503i	$-0.767363\pi$
$503$	−16800.0			−1.48921			−0.744607	+	0.667503i	$0.767363\pi$
$504$	−280.000	+	96.9948i	−0.0247464	+	0.00857241i
$505$		0			0
$506$	3933.00	−	6812.16i	0.345540	−	0.598493i
$507$	−6757.50	−	11704.3i	−0.591935	−	1.02526i
$508$	−4112.00	−	7122.19i	−0.359135	−	0.622040i
$509$	−919.500	+	1592.62i	−0.0800710	+	0.138687i	−0.903280	−	0.429051i	$-0.858848\pi$
$509$	−919.500	+	1592.62i	−0.0800710	+	0.138687i	0.823209	+	0.567738i	$0.192181\pi$
$510$		0			0
$511$	1095.50	−	5692.38i	0.0948377	−	0.492791i
$512$	−512.000			−0.0441942
$513$	362.500	−	627.868i	0.0311984	−	0.0540372i
$514$	1437.00	+	2488.96i	0.123314	+	0.213586i
$515$		0			0
$516$	−1240.00	+	2147.74i	−0.105791	+	0.183235i
$517$	11457.0			0.974620
$518$	−1771.00	+	9202.39i	−0.150219	+	0.780559i
$519$	−16335.0			−1.38155
$520$		0			0
$521$	−151.500	−	262.406i	−0.0127396	−	0.0220656i	0.859585	−	0.510992i	$-0.170722\pi$
$521$	−151.500	−	262.406i	−0.0127396	−	0.0220656i	−0.872325	+	0.488927i	$0.837389\pi$
$522$	−228.000	−	394.908i	−0.0191174	−	0.0331123i
$523$	−10833.5	+	18764.2i	−0.905767	+	1.56883i	−0.0858815	+	0.996305i	$0.527371\pi$
$523$	−10833.5	+	18764.2i	−0.905767	+	1.56883i	−0.819885	+	0.572528i	$0.805963\pi$
$524$	8196.00			0.683290
$525$		0			0
$526$	−4650.00			−0.385456
$527$	586.500	−	1015.85i	0.0484788	−	0.0839678i
$528$	2280.00	+	3949.08i	0.187925	+	0.325495i
$529$	3703.00	+	6413.78i	0.304348	+	0.527146i
$530$		0			0
$531$	−438.000			−0.0357958
$532$	280.000	+	242.487i	0.0228187	+	0.0197616i
$533$	−2940.00			−0.238922
$534$	−5085.00	+	8807.48i	−0.412078	+	0.713739i
$535$		0			0
$536$	−1676.00	−	2902.92i	−0.135060	−	0.233931i
$537$	−3217.50	+	5572.87i	−0.258557	+	0.447835i
$538$	4770.00			0.382248
$539$	−15361.5	+	12094.0i	−1.22758	+	0.966470i
$540$		0			0
$541$	−2519.50	+	4363.90i	−0.200225	+	0.346800i	−0.948601	−	0.316475i	$-0.897501\pi$
$541$	−2519.50	+	4363.90i	−0.200225	+	0.346800i	0.748376	+	0.663275i	$0.230834\pi$
$542$	−331.000	−	573.309i	−0.0262319	−	0.0454349i
$543$	6685.00	+	11578.8i	0.528326	+	0.915087i
$544$	−816.000	+	1413.35i	−0.0643120	+	0.111392i
$545$		0			0
$546$	−9800.00	−	8487.05i	−0.768134	−	0.665224i
$547$	2392.00			0.186974			0.0934868	−	0.995621i	$-0.470199\pi$
$547$	2392.00			0.186974			0.0934868	+	0.995621i	$0.470199\pi$
$548$	−282.000	+	488.438i	−0.0219826	+	0.0380749i
$549$	−709.000	−	1228.02i	−0.0551173	−	0.0954659i
$550$		0			0
$551$	−285.000	+	493.634i	−0.0220352	+	0.0381661i
$552$	2760.00			0.212814
$553$	−8067.50	+	2794.66i	−0.620371	+	0.214903i
$554$	9742.00			0.747108
$555$		0			0
$556$	−2968.00	−	5140.73i	−0.226387	−	0.392114i
$557$	−11074.5	−	19181.6i	−0.842445	−	1.45916i	−0.887822	−	0.460187i	$-0.847782\pi$
$557$	−11074.5	−	19181.6i	−0.842445	−	1.45916i	0.0453775	−	0.998970i	$-0.485551\pi$
$558$	−46.0000	+	79.6743i	−0.00348985	+	0.00604459i
$559$	8680.00			0.656753
$560$		0			0
$561$	14535.0			1.09388
$562$	−7026.00	+	12169.4i	−0.527356	+	0.913407i
$563$	−4174.50	−	7230.45i	−0.312494	−	0.541256i	0.666408	−	0.745588i	$-0.267831\pi$
$563$	−4174.50	−	7230.45i	−0.312494	−	0.541256i	−0.978902	+	0.204332i	$0.934498\pi$
$564$	2010.00	+	3481.42i	0.150064	+	0.259919i
$565$		0			0
$566$	−10706.0			−0.795065
$567$	−2348.50	+	12203.2i	−0.173947	+	0.903853i
$568$	768.000			0.0567334
$569$	7672.50	−	13289.2i	0.565286	−	0.979105i	−0.431737	−	0.902000i	$-0.642099\pi$
$569$	7672.50	−	13289.2i	0.565286	−	0.979105i	0.997023	−	0.0771050i	$-0.0245677\pi$
$570$		0			0
$571$	5796.50	+	10039.8i	0.424827	+	0.735821i	0.996404	−	0.0847268i	$-0.0270017\pi$
$571$	5796.50	+	10039.8i	0.424827	+	0.735821i	−0.571578	+	0.820548i	$0.693668\pi$
$572$	7980.00	−	13821.8i	0.583323	−	1.01034i
$573$	20925.0			1.52557
$574$	−1470.00	+	509.223i	−0.106893	+	0.0370288i
$575$		0			0
$576$	64.0000	−	110.851i	0.00462963	−	0.00801875i
$577$	−7296.50	−	12637.9i	−0.526442	−	0.911825i	−0.999525	−	0.0308071i	$-0.990192\pi$
$577$	−7296.50	−	12637.9i	−0.526442	−	0.911825i	0.473083	−	0.881018i	$-0.343141\pi$
$578$	−2312.00	−	4004.50i	−0.166378	−	0.288175i
$579$	−212.500	+	368.061i	−0.0152525	+	0.0264181i
$580$		0			0
$581$	8232.00	+	7129.12i	0.587816	+	0.509063i
$582$	−18340.0			−1.30622
$583$	11200.5	−	19399.8i	0.795673	−	1.37815i
$584$	1252.00	+	2168.53i	0.0887125	+	0.153655i
$585$		0			0
$586$	−4158.00	+	7201.87i	−0.293115	+	0.507690i
$587$	15372.0			1.08087			0.540435	−	0.841386i	$-0.318260\pi$
$587$	15372.0			1.08087			0.540435	+	0.841386i	$0.318260\pi$
$588$	−6370.00	−	2546.11i	−0.446759	−	0.178571i
$589$	115.000			0.00804498
$590$		0			0
$591$	−975.000	−	1688.75i	−0.0678615	−	0.117540i
$592$	−2024.00	−	3505.67i	−0.140517	−	0.243382i
$593$	−7186.50	+	12447.4i	−0.497663	+	0.861978i	−0.999996	−	0.00269639i	$-0.999142\pi$
$593$	−7186.50	+	12447.4i	−0.497663	+	0.861978i	0.502333	+	0.864674i	$0.332475\pi$
$594$	−16530.0			−1.14181
$595$		0			0
$596$	−228.000			−0.0156699
$597$	7082.50	−	12267.2i	0.485540	−	0.840980i
$598$	−4830.00	−	8365.81i	−0.330290	−	0.572079i
$599$	−1273.50	−	2205.77i	−0.0868678	−	0.150459i	0.819318	−	0.573340i	$-0.194352\pi$
$599$	−1273.50	−	2205.77i	−0.0868678	−	0.150459i	−0.906186	+	0.422880i	$0.861019\pi$
$600$		0			0
$601$	−7042.00			−0.477952			−0.238976	−	0.971025i	$-0.576812\pi$
$601$	−7042.00			−0.477952			−0.238976	+	0.971025i	$0.576812\pi$
$602$	4340.00	−	1503.42i	0.293829	−	0.101785i
$603$	838.000			0.0565937
$604$	−1678.00	+	2906.38i	−0.113041	+	0.195793i
$605$		0			0
$606$	−1425.00	−	2468.17i	−0.0955226	−	0.165450i
$607$	−11295.5	+	19564.4i	−0.755305	+	1.30823i	0.189917	+	0.981800i	$0.439178\pi$
$607$	−11295.5	+	19564.4i	−0.755305	+	1.30823i	−0.945223	+	0.326427i	$0.894155\pi$
$608$	−160.000			−0.0106725
$609$	1995.00	−	10366.3i	0.132745	−	0.689761i
$610$		0			0
$611$	7035.00	−	12185.0i	0.465803	−	0.806794i
$612$	−204.000	−	353.338i	−0.0134742	−	0.0233380i
$613$	−4242.50	−	7348.23i	−0.279532	−	0.484163i	0.691737	−	0.722150i	$-0.256846\pi$
$613$	−4242.50	−	7348.23i	−0.279532	−	0.484163i	−0.971268	+	0.237987i	$0.923513\pi$
$614$	9604.00	−	16634.6i	0.631247	−	1.09335i
$615$		0			0
$616$	1596.00	−	8293.06i	0.104391	−	0.542430i
$617$	18282.0			1.19288			0.596439	−	0.802658i	$-0.296582\pi$
$617$	18282.0			1.19288			0.596439	+	0.802658i	$0.296582\pi$
$618$	2495.00	−	4321.47i	0.162401	−	0.281286i
$619$	−1145.50	−	1984.06i	−0.0743805	−	0.128831i	0.826436	−	0.563030i	$-0.190365\pi$
$619$	−1145.50	−	1984.06i	−0.0743805	−	0.128831i	−0.900817	+	0.434200i	$0.857031\pi$
$620$		0			0
$621$	−5002.50	+	8664.58i	−0.323258	+	0.559900i
$622$	−20262.0			−1.30616
$623$	17797.5	−	6165.23i	1.14453	−	0.396477i
$624$	5600.00			0.359262
$625$		0			0
$626$	−10799.0	−	18704.4i	−0.689481	−	1.19422i
$627$	712.500	+	1234.09i	0.0453820	+	0.0786039i
$628$	−5666.00	+	9813.80i	−0.360029	+	0.623588i
$629$	−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	$0.570130\pi$
$632$	1844.00	−	3193.90i	0.116061	−	0.201023i
$633$	310.000	+	536.936i	0.0194651	+	0.0337145i
$634$	−531.000	−	919.719i	−0.0332629	−	0.0576131i
$635$		0			0
$636$	7860.00			0.490046
$637$	3430.00	+	23763.7i	0.213346	+	1.47811i
$638$	12996.0			0.806452
$639$	−96.0000	+	166.277i	−0.00594319	+	0.0102939i
$640$		0			0
$641$	−12487.5	−	21629.0i	−0.769464	−	1.33275i	−0.937854	−	0.347031i	$-0.887190\pi$
$641$	−12487.5	−	21629.0i	−0.769464	−	1.33275i	0.168390	−	0.985721i	$-0.446143\pi$
$642$	5535.00	−	9586.90i	0.340263	−	0.589353i
$643$	−9548.00			−0.585593			−0.292797	−	0.956175i	$-0.594586\pi$
$643$	−9548.00			−0.585593			−0.292797	+	0.956175i	$0.594586\pi$
$644$	−3864.00	−	3346.32i	−0.236433	−	0.204757i
$645$		0			0
$646$	−255.000	+	441.673i	−0.0155307	+	0.0269000i
$647$	5065.50	+	8773.70i	0.307798	+	0.533122i	0.977880	−	0.209165i	$-0.0670745\pi$
$647$	5065.50	+	8773.70i	0.307798	+	0.533122i	−0.670082	+	0.742287i	$0.733741\pi$
$648$	−2684.00	−	4648.82i	−0.162712	−	0.281826i
$649$	6241.50	−	10810.6i	0.377504	−	0.653857i
$650$		0			0
$651$	−2012.50	+	697.150i	−0.121161	+	0.0419716i
$652$	9244.00			0.555250
$653$	8329.50	−	14427.1i	0.499171	−	0.864589i	−0.500829	−	0.865546i	$-0.666971\pi$
$653$	8329.50	−	14427.1i	0.499171	−	0.864589i	1.00000		0.000957229i	$0.000304695\pi$
$654$	4615.00	+	7993.41i	0.275934	+	0.477932i
$655$		0			0
$656$	336.000	−	581.969i	0.0199979	−	0.0346373i
$657$	−626.000			−0.0371729
$658$	1407.00	−	7310.99i	0.0833595	−	0.433149i
$659$	29556.0			1.74710			0.873550	−	0.486735i	$-0.161812\pi$
$659$	29556.0			1.74710			0.873550	+	0.486735i	$0.161812\pi$
$660$		0			0
$661$	−95.5000	−	165.411i	−0.00561955	−	0.00973334i	0.863202	−	0.504859i	$-0.168455\pi$
$661$	−95.5000	−	165.411i	−0.00561955	−	0.00973334i	−0.868822	+	0.495125i	$0.835122\pi$
$662$	−7015.00	−	12150.3i	−0.411852	−	0.713348i
$663$	8925.00	−	15458.6i	0.522803	−	0.905521i
$664$	−4704.00			−0.274926
$665$		0			0
$666$	1012.00			0.0588802
$667$	3933.00	−	6812.16i	0.228315	−	0.395454i
$668$	2520.00	+	4364.77i	0.145961	+	0.252811i
$669$	140.000	+	242.487i	0.00809075	+	0.0140136i
$670$		0			0
$671$	40413.0			2.32508
$672$	2800.00	−	969.948i	0.160733	−	0.0556794i
$673$	−2606.00			−0.149263			−0.0746314	−	0.997211i	$-0.523778\pi$
$673$	−2606.00			−0.149263			−0.0746314	+	0.997211i	$0.523778\pi$
$674$	−8990.00	+	15571.1i	−0.513771	+	0.889878i
$675$		0			0
$676$	−5406.00	−	9363.47i	−0.307579	−	0.532742i
$677$	−2104.50	+	3645.10i	−0.119472	+	0.206931i	−0.919559	−	0.392953i	$-0.871453\pi$
$677$	−2104.50	+	3645.10i	−0.119472	+	0.206931i	0.800087	+	0.599885i	$0.204787\pi$
$678$	15420.0			0.873454
$679$	25676.0	+	22236.1i	1.45118	+	1.25676i
$680$		0			0
$681$	−7642.50	+	13237.2i	−0.430046	+	0.744861i
$682$	−1311.00	−	2270.72i	−0.0736082	−	0.127493i
$683$	12151.5	+	21047.0i	0.680768	+	1.17912i	0.974747	+	0.223312i	$0.0716869\pi$
$683$	12151.5	+	21047.0i	0.680768	+	1.17912i	−0.293979	+	0.955812i	$0.594980\pi$
$684$	20.0000	−	34.6410i	0.00111801	−	0.00193645i
$685$		0			0
$686$	5831.00	+	11287.8i	0.324532	+	0.628235i
$687$	−4805.00			−0.266845
$688$	−992.000	+	1718.19i	−0.0549704	+	0.0952116i
$689$	−13755.0	−	23824.4i	−0.760557	−	1.31732i
$690$		0			0
$691$	−7520.50	+	13025.9i	−0.414028	+	0.717117i	−0.995326	−	0.0965734i	$-0.969212\pi$
$691$	−7520.50	+	13025.9i	−0.414028	+	0.717117i	0.581298	+	0.813691i	$0.302545\pi$
$692$	−13068.0			−0.717877
$693$	1596.00	+	1382.18i	0.0874849	+	0.0757641i
$694$	−17418.0			−0.952706
$695$		0			0
$696$	2280.00	+	3949.08i	0.124171	+	0.215071i
$697$	−1071.00	−	1855.03i	−0.0582023	−	0.100809i
$698$	6482.00	−	11227.2i	0.351500	−	0.608817i
$699$	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	$0.267958\pi$
$702$	−10150.0	+	17580.3i	−0.545708	+	0.945194i
$703$	−632.500	−	1095.52i	−0.0339334	−	0.0587744i
$704$	1824.00	+	3159.26i	0.0976486	+	0.169132i
$705$		0			0
$706$	−4266.00			−0.227412
$707$	−997.500	+	5183.16i	−0.0530620	+	0.275718i
$708$	4380.00			0.232501
$709$	2478.50	−	4292.89i	0.131286	−	0.227395i	−0.792886	−	0.609370i	$-0.791423\pi$
$709$	2478.50	−	4292.89i	0.131286	−	0.227395i	0.924173	+	0.381975i	$0.124756\pi$
$710$		0			0
$711$	461.000	+	798.475i	0.0243162	+	0.0421170i
$712$	−4068.00	+	7045.98i	−0.214122	+	0.370870i
$713$	−1587.00			−0.0833571
$714$	1785.00	−	9275.13i	0.0935601	−	0.486153i
$715$		0			0
$716$	−2574.00	+	4458.30i	−0.134350	+	0.232702i
$717$	8850.00	+	15328.6i	0.460961	+	0.798409i
$718$	3849.00	+	6666.66i	0.200060	+	0.346515i
$719$	−13834.5	+	23962.1i	−0.717580	+	1.24288i	0.244376	+	0.969680i	$0.421417\pi$
$719$	−13834.5	+	23962.1i	−0.717580	+	1.24288i	−0.961956	+	0.273204i	$0.911917\pi$
$720$		0			0
$721$	−8732.50	+	3025.03i	−0.451061	+	0.156252i
$722$	13668.0			0.704529
$723$	−13077.5	+	22650.9i	−0.672694	+	1.16514i
$724$	5348.00	+	9263.01i	0.274526	+	0.475493i
$725$		0			0
$726$	9590.00	−	16610.4i	0.490246	−	0.849130i
$727$	13888.0			0.708497			0.354249	−	0.935151i	$-0.384737\pi$
$727$	13888.0			0.708497			0.354249	+	0.935151i	$0.384737\pi$
$728$	−7840.00	−	6789.64i	−0.399134	−	0.345660i
$729$	20917.0			1.06269
$730$		0			0
$731$	3162.00	+	5476.74i	0.159987	+	0.277106i
$732$	7090.00	+	12280.2i	0.357997	+	0.620069i
$733$	7121.50	−	12334.8i	0.358852	−	0.621550i	−0.628917	−	0.777472i	$-0.716502\pi$
$733$	7121.50	−	12334.8i	0.358852	−	0.621550i	0.987769	+	0.155922i	$0.0498349\pi$
$734$	12982.0			0.652826
$735$		0			0
$736$	2208.00			0.110581
$737$	−11941.5	+	20683.3i	−0.596840	+	1.03376i
$738$	84.0000	+	145.492i	0.00418981	+	0.00725697i
$739$	−18479.5	−	32007.4i	−0.919864	−	1.59325i	−0.799620	−	0.600507i	$-0.794966\pi$
$739$	−18479.5	−	32007.4i	−0.919864	−	1.59325i	−0.120244	−	0.992744i	$-0.538368\pi$
$740$		0			0
$741$	1750.00			0.0867582
$742$	−11004.0	−	9529.74i	−0.544433	−	0.471493i
$743$	12528.0			0.618584			0.309292	−	0.950967i	$-0.399908\pi$
$743$	12528.0			0.618584			0.309292	+	0.950967i	$0.399908\pi$
$744$	460.000	−	796.743i	0.0226672	−	0.0392608i
$745$		0			0
$746$	−923.000	−	1598.68i	−0.0452995	−	0.0784610i
$747$	588.000	−	1018.45i	0.0288003	−	0.0498835i
$748$	11628.0			0.568398
$749$	−19372.5	+	6710.83i	−0.945068	+	0.327381i
$750$		0			0
$751$	8883.50	−	15386.7i	0.431643	−	0.747627i	−0.565372	−	0.824836i	$-0.691268\pi$
$751$	8883.50	−	15386.7i	0.431643	−	0.747627i	0.997015	+	0.0772090i	$0.0246009\pi$
$752$	1608.00	+	2785.14i	0.0779757	+	0.135058i
$753$	−12600.0	−	21823.8i	−0.609787	−	1.05618i
$754$	7980.00	−	13821.8i	0.385430	−	0.667585i
$755$		0			0
$756$	−2030.00	+	10548.2i	−0.0976592	+	0.507452i
$757$	28726.0			1.37921			0.689606	−	0.724184i	$-0.257784\pi$
$757$	28726.0			1.37921			0.689606	+	0.724184i	$0.257784\pi$
$758$	6344.00	−	10988.1i	0.303990	−	0.526526i
$759$	−9832.50	−	17030.4i	−0.470220	−	0.814445i
$760$		0			0
$761$	13234.5	−	22922.8i	0.630421	−	1.09192i	−0.357045	−	0.934087i	$-0.616216\pi$
$761$	13234.5	−	22922.8i	0.630421	−	1.09192i	0.987466	−	0.157834i	$-0.0504510\pi$
$762$	−20560.0			−0.977441
$763$	3230.50	−	16786.2i	0.153279	−	0.796462i
$764$	16740.0			0.792712
$765$		0			0
$766$	5007.00	+	8672.38i	0.236175	+	0.409068i
$767$	−7665.00	−	13276.2i	−0.360844	−	0.625000i
$768$	−640.000	+	1108.51i	−0.0300703	+	0.0520833i
$769$	5054.00			0.236999			0.118499	−	0.992954i	$-0.462192\pi$
$769$	5054.00			0.236999			0.118499	+	0.992954i	$0.462192\pi$
$770$		0			0
$771$	7185.00			0.335618
$772$	−170.000	+	294.449i	−0.00792543	+	0.0137273i
$773$	−17782.5	−	30800.2i	−0.827415	−	1.43313i	−0.900059	−	0.435767i	$-0.856477\pi$
$773$	−17782.5	−	30800.2i	−0.827415	−	1.43313i	0.0726439	−	0.997358i	$-0.476856\pi$
$774$	−248.000	−	429.549i	−0.0115170	−	0.0199481i
$775$		0			0
$776$	−14672.0			−0.678730
$777$	17710.0	+	15337.3i	0.817687	+	0.708138i
$778$	−24582.0			−1.13279
$779$	105.000	−	181.865i	0.00482929	−	0.00836457i
$780$		0			0
$781$	−2736.00	−	4738.89i	−0.125354	−	0.217120i
$782$	3519.00	−	6095.09i	0.160920	−	0.278721i
$783$	−16530.0			−0.754450
$784$	−5096.00	−	2036.89i	−0.232143	−	0.0927884i
$785$		0			0
$786$	10245.0	−	17744.9i	0.464920	−	0.805265i
$787$	−4314.50	−	7472.93i	−0.195420	−	0.338477i	0.751618	−	0.659598i	$-0.229274\pi$
$787$	−4314.50	−	7472.93i	−0.195420	−	0.338477i	−0.947038	+	0.321121i	$0.895940\pi$
$788$	−780.000	−	1351.00i	−0.0352619	−	0.0610753i
$789$	−5812.50	+	10067.5i	−0.262269	+	0.454264i
$790$		0			0
$791$	−21588.0	−	18695.8i	−0.970393	−	0.840385i
$792$	−912.000			−0.0409173
$793$	24815.0	−	42980.8i	1.11123	−	1.92471i
$794$	−887.000	−	1536.33i	−0.0396454	−	0.0686679i
$795$		0			0
$796$	5666.00	−	9813.80i	0.252294	−	0.436986i
$797$	−20706.0			−0.920256			−0.460128	−	0.887853i	$-0.652197\pi$
$797$	−20706.0			−0.920256			−0.460128	+	0.887853i	$0.652197\pi$
$798$	875.000	−	303.109i	0.0388154	−	0.0134460i
$799$	10251.0			0.453885
$800$		0			0
$801$	−1017.00	−	1761.50i	−0.0448613	−	0.0777021i
$802$	11955.0	+	20706.7i	0.526366	+	0.911693i
$803$	8920.50	−	15450.8i	0.392027	−	0.679011i
$804$	−8380.00			−0.367587
$805$		0			0
$806$	−3220.00			−0.140719
$807$	5962.50	−	10327.4i	0.260087	−	0.450483i
$808$	−1140.00	−	1974.54i	−0.0496350	−	0.0859703i
$809$	8092.50	+	14016.6i	0.351690	+	0.609145i	0.986546	−	0.163486i	$-0.0522738\pi$
$809$	8092.50	+	14016.6i	0.351690	+	0.609145i	−0.634856	+	0.772631i	$0.718940\pi$
$810$		0			0
$811$	−11788.0			−0.510398			−0.255199	−	0.966889i	$-0.582141\pi$
$811$	−11788.0			−0.510398			−0.255199	+	0.966889i	$0.582141\pi$
$812$	1596.00	−	8293.06i	0.0689761	−	0.358411i
$813$	−1655.00			−0.0713941
$814$	−14421.0	+	24977.9i	−0.620953	+	1.07552i
$815$		0			0
$816$	2040.00	+	3533.38i	0.0875175	+	0.151585i
$817$	−310.000	+	536.936i	−0.0132748	+	0.0229927i
$818$	6842.00			0.292451
$819$	2450.00	−	848.705i	0.104530	−	0.0362102i
$820$		0			0
$821$	14896.5	−	25801.5i	0.633242	−	1.09681i	−0.353643	−	0.935380i	$-0.615057\pi$
$821$	14896.5	−	25801.5i	0.633242	−	1.09681i	0.986885	−	0.161426i	$-0.0516094\pi$
$822$	705.000	+	1221.10i	0.0299145	+	0.0518134i
$823$	15161.5	+	26260.5i	0.642159	+	1.11225i	0.984950	+	0.172840i	$0.0552943\pi$
$823$	15161.5	+	26260.5i	0.642159	+	1.11225i	−0.342791	+	0.939412i	$0.611372\pi$
$824$	1996.00	−	3457.17i	0.0843859	−	0.146161i
$825$		0			0
$826$	−6132.00	−	5310.47i	−0.258305	−	0.223698i
$827$	−21156.0			−0.889560			−0.444780	−	0.895640i	$-0.646718\pi$
$827$	−21156.0			−0.889560			−0.444780	+	0.895640i	$0.646718\pi$
$828$	−276.000	+	478.046i	−0.0115841	+	0.0200643i
$829$	2634.50	+	4563.09i	0.110374	+	0.191173i	0.915921	−	0.401358i	$-0.131462\pi$
$829$	2634.50	+	4563.09i	0.110374	+	0.191173i	−0.805547	+	0.592532i	$0.798129\pi$
$830$		0			0
$831$	12177.5	−	21092.0i	0.508343	−	0.880475i
$832$	4480.00			0.186678
$833$	−13744.5	+	10821.0i	−0.571691	+	0.450090i
$834$	−14840.0			−0.616148
$835$		0			0
$836$	570.000	+	987.269i	0.0235812	+	0.0408438i
$837$	1667.50	+	2888.19i	0.0688617	+	0.119272i
$838$	−5460.00	+	9457.00i	−0.225075	+	0.389841i
$839$	−39816.0			−1.63838			−0.819190	−	0.573522i	$-0.805577\pi$
$839$	−39816.0			−1.63838			−0.819190	+	0.573522i	$0.805577\pi$
$840$		0			0
$841$	−11393.0			−0.467137
$842$	7730.00	−	13388.8i	0.316382	−	0.547989i
$843$	17565.0	+	30423.5i	0.717640	+	1.24299i
$844$	248.000	+	429.549i	0.0101144	+	0.0175186i
$845$		0			0
$846$	−804.000			−0.0326739
$847$	−33565.0	+	11627.3i	−1.36164	+	0.471685i
$848$	6288.00			0.254635
$849$	−13382.5	+	23179.2i	−0.540973	+	0.936993i
$850$		0			0
$851$	8728.50	+	15118.2i	0.351597	+	0.608984i
$852$	960.000	−	1662.77i	0.0386022	−	0.0668609i
$853$	−14546.0			−0.583875			−0.291938	−	0.956437i	$-0.594300\pi$
$853$	−14546.0			−0.583875			−0.291938	+	0.956437i	$0.594300\pi$
$854$	4963.00	−	25788.5i	0.198865	−	1.03333i
$855$		0			0
$856$	4428.00	−	7669.52i	0.176806	−	0.306237i
$857$	−15724.5	−	27235.6i	−0.626766	−	1.08559i	−0.988196	−	0.153192i	$-0.951045\pi$
$857$	−15724.5	−	27235.6i	−0.626766	−	1.08559i	0.361430	−	0.932399i	$-0.382289\pi$
$858$	−19950.0	−	34554.4i	−0.793802	−	1.37490i
$859$	12261.5	−	21237.5i	0.487028	−	0.843557i	−0.512861	−	0.858472i	$-0.671414\pi$
$859$	12261.5	−	21237.5i	0.487028	−	0.843557i	0.999889	+	0.0149147i	$0.00474766\pi$
$860$		0			0
$861$	−735.000	+	3819.17i	−0.0290926	+	0.151170i
$862$	22626.0			0.894019
$863$	−4081.50	+	7069.37i	−0.160992	+	0.278846i	−0.935225	−	0.354055i	$-0.884803\pi$
$863$	−4081.50	+	7069.37i	−0.160992	+	0.278846i	0.774233	+	0.632901i	$0.218136\pi$
$864$	−2320.00	−	4018.36i	−0.0913519	−	0.158226i
$865$		0			0
$866$	−4214.00	+	7298.86i	−0.165355	+	0.286403i
$867$	−11560.0			−0.452824
$868$	−1610.00	+	557.720i	−0.0629573	+	0.0218091i
$869$	−26277.0			−1.02576
$870$		0			0
$871$	14665.0	+	25400.5i	0.570499	+	0.988133i
$872$	3692.00	+	6394.73i	0.143379	+	0.248341i
$873$	1834.00	−	3176.58i	0.0711014	−	0.123151i
$874$	690.000			0.0267043
$875$		0			0
$876$	6260.00			0.241445
$877$	2183.50	−	3781.93i	0.0840725	−	0.145618i	−0.820923	−	0.571039i	$-0.806541\pi$
$877$	2183.50	−	3781.93i	0.0840725	−	0.145618i	0.904996	+	0.425421i	$0.139874\pi$
$878$	16553.0	+	28670.6i	0.636260	+	1.10204i
$879$	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	$0.909295\pi$
$882$	1078.00	−	848.705i	0.0411544	−	0.0324007i
$883$	−12308.0			−0.469079			−0.234540	−	0.972107i	$-0.575358\pi$
$883$	−12308.0			−0.469079			−0.234540	+	0.972107i	$0.575358\pi$
$884$	7140.00	−	12366.8i	0.271656	−	0.470523i
$885$		0			0
$886$	16395.0	+	28397.0i	0.621671	+	1.07677i
$887$	15808.5	−	27381.1i	0.598419	−	1.03649i	−0.394636	−	0.918838i	$-0.629129\pi$
$887$	15808.5	−	27381.1i	0.598419	−	1.03649i	0.993055	−	0.117654i	$-0.0375374\pi$
$888$	−10120.0			−0.382438
$889$	28784.0	+	24927.7i	1.08592	+	0.940436i
$890$		0			0
$891$	−19123.5	+	33122.9i	−0.719036	+	1.24541i
$892$	112.000	+	193.990i	0.00420408	+	0.00728168i
$893$	502.500	+	870.356i	0.0188304	+	0.0326152i
$894$	−285.000	+	493.634i	−0.0106620	+	0.0184671i
$895$		0			0
$896$	2240.00	−	775.959i	0.0835191	−	0.0289319i
$897$	−24150.0			−0.898935
$898$	−15090.0	+	26136.6i	−0.560757	+	0.971260i
$899$	−1311.00	−	2270.72i	−0.0486366	−	0.0842411i
$900$		0			0
$901$	10021.5	−	17357.7i	0.370549	−	0.641810i
$902$	−4788.00			−0.176744
$903$	2170.00	−	11275.7i	0.0799702	−	0.415537i
$904$	12336.0			0.453860
$905$		0			0
$906$	4195.00	+	7265.95i	0.153830	+	0.266441i
$907$	−6762.50	−	11713.0i	−0.247569	−	0.428802i	0.715282	−	0.698836i	$-0.246298\pi$
$907$	−6762.50	−	11713.0i	−0.247569	−	0.428802i	−0.962851	+	0.270034i	$0.912965\pi$
$908$	−6114.00	+	10589.8i	−0.223458	+	0.387041i
$909$	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	$0.613821\pi$
$912$	−200.000	+	346.410i	−0.00726169	+	0.0125776i
$913$	16758.0	+	29025.7i	0.607458	+	1.05215i
$914$	14785.0	+	25608.4i	0.535059	+	0.926750i
$915$		0			0
$916$	−3844.00			−0.138656
$917$	−35857.5	+	12421.4i	−1.29130	+	0.447318i
$918$	−14790.0			−0.531746
$919$	4347.50	−	7530.09i	0.156051	−	0.270288i	−0.777390	−	0.629019i	$-0.783457\pi$
$919$	4347.50	−	7530.09i	0.156051	−	0.270288i	0.933441	+	0.358730i	$0.116790\pi$
$920$		0			0
$921$	−24010.0	−	41586.5i	−0.859019	−	1.48786i
$922$	2898.00	−	5019.48i	0.103515	−	0.179293i
$923$	−6720.00			−0.239644
$924$	−15960.0	−	13821.8i	−0.568231	−	0.492102i
$925$		0			0
$926$	−464.000	+	803.672i	−0.0164665	+	0.0285208i
$927$	499.000	+	864.293i	0.0176799	+	0.0306226i
$928$	1824.00	+	3159.26i	0.0645213	+	0.111754i
$929$	−9739.50	+	16869.3i	−0.343964	+	0.595763i	−0.985165	−	0.171610i	$-0.945103\pi$
$929$	−9739.50	+	16869.3i	−0.343964	+	0.595763i	0.641201	+	0.767373i	$0.278437\pi$
$930$		0			0
$931$	−1592.50	−	636.529i	−0.0560602	−	0.0224075i
$932$	11316.0			0.397712
$933$	−25327.5	+	43868.5i	−0.888730	+	1.53933i
$934$	−4233.00	−	7331.77i	−0.148295	−	0.256855i
$935$		0			0
$936$	−560.000	+	969.948i	−0.0195557	+	0.0338715i
$937$	12502.0			0.435883			0.217942	−	0.975962i	$-0.430066\pi$
$937$	12502.0			0.435883			0.217942	+	0.975962i	$0.430066\pi$
$938$	11732.0	+	10160.2i	0.408383	+	0.353670i
$939$	−53995.0			−1.87653
$940$		0			0
$941$	7996.50	+	13850.3i	0.277023	+	0.479818i	0.970643	−	0.240523i	$-0.0773189\pi$
$941$	7996.50	+	13850.3i	0.277023	+	0.479818i	−0.693621	+	0.720340i	$0.743986\pi$
$942$	14165.0	+	24534.5i	0.489937	+	0.848596i
$943$	−1449.00	+	2509.74i	−0.0500381	+	0.0866685i
$944$	3504.00			0.120811
$945$		0			0
$946$	14136.0			0.485836
$947$	22000.5	−	38106.0i	0.754932	−	1.30758i	−0.190477	−	0.981692i	$-0.561003\pi$
$947$	22000.5	−	38106.0i	0.754932	−	1.30758i	0.945408	−	0.325888i	$-0.105663\pi$
$948$	−4610.00	−	7984.75i	−0.157939	−	0.273558i
$949$	−10955.0	−	18974.6i	−0.374725	−	0.649043i
$950$		0			0
$951$	−2655.00			−0.0905303
$952$	1428.00	−	7420.11i	0.0486153	−	0.252612i
$953$	4002.00			0.136031			0.0680155	−	0.997684i	$-0.478333\pi$
$953$	4002.00			0.136031			0.0680155	+	0.997684i	$0.478333\pi$
$954$	−786.000	+	1361.39i	−0.0266747	+	0.0462020i
$955$		0			0
$956$	7080.00	+	12262.9i	0.239523	+	0.414865i
$957$	16245.0	−	28137.2i	0.548721	−	0.950413i
$958$	−5478.00			−0.184745
$959$	493.500	−	2564.30i	0.0166173	−	0.0863458i
$960$		0			0
$961$	14631.0	−	25341.6i	0.491121	−	0.850647i
$962$	17710.0	+	30674.6i	0.593548	+	1.02806i
$963$	1107.00	+	1917.38i	0.0370432	+	0.0641607i
$964$	−10462.0	+	18120.7i	−0.349542	+	0.605424i
$965$		0			0
$966$	−12075.0	+	4182.90i	−0.402181	+	0.139320i
$967$	−10544.0			−0.350643			−0.175322	−	0.984511i	$-0.556097\pi$
$967$	−10544.0			−0.350643			−0.175322	+	0.984511i	$0.556097\pi$
$968$	7672.00	−	13288.3i	0.254739	−	0.441221i
$969$	637.500	+	1104.18i	0.0211346	+	0.0366062i
$970$		0			0
$971$	3091.50	−	5354.64i	0.102174	−	0.176971i	−0.810406	−	0.585869i	$-0.800753\pi$
$971$	3091.50	−	5354.64i	0.102174	−	0.176971i	0.912580	+	0.408898i	$0.134087\pi$
$972$	2240.00			0.0739177
$973$	20776.0	+	17992.5i	0.684530	+	0.592821i
$974$	34102.0			1.12187
$975$		0			0
$976$	5672.00	+	9824.19i	0.186021	+	0.322197i
$977$	1861.50	+	3224.21i	0.0609567	+	0.105580i	0.894893	−	0.446280i	$-0.147252\pi$
$977$	1861.50	+	3224.21i	0.0609567	+	0.105580i	−0.833937	+	0.551860i	$0.813918\pi$
$978$	11555.0	−	20013.8i	0.377800	−	0.654368i
$979$	57969.0			1.89244
$980$		0			0
$981$	−1846.00			−0.0600798
$982$	−4296.00	+	7440.89i	−0.139604	+	0.241801i
$983$	−22948.5	−	39748.0i	−0.744602	−	1.28969i	−0.950381	−	0.311089i	$-0.899306\pi$
$983$	−22948.5	−	39748.0i	−0.744602	−	1.28969i	0.205779	−	0.978599i	$-0.434027\pi$
$984$	−840.000	−	1454.92i	−0.0272136	−	0.0471354i
$985$		0			0
$986$	11628.0			0.375569
$987$	−14070.0	−	12185.0i	−0.453752	−	0.392961i
$988$	1400.00			0.0450809
$989$	4278.00	−	7409.71i	0.137545	−	0.238236i
$990$		0			0
$991$	−3233.50	−	5600.59i	−0.103648	−	0.179524i	0.809537	−	0.587069i	$-0.199718\pi$
$991$	−3233.50	−	5600.59i	−0.103648	−	0.179524i	−0.913185	+	0.407545i	$0.866385\pi$
$992$	368.000	−	637.395i	0.0117782	−	0.0204005i
$993$	−35075.0			−1.12092
$994$	−3360.00	+	1163.94i	−0.107216	+	0.0371407i
$995$		0			0
$996$	−5880.00	+	10184.5i	−0.187063	+	0.324003i
$997$	11519.5	+	19952.4i	0.365924	+	0.633799i	0.988924	−	0.148423i	$-0.0474197\pi$
$997$	11519.5	+	19952.4i	0.365924	+	0.633799i	−0.623000	+	0.782222i	$0.714086\pi$
$998$	3401.00	+	5890.70i	0.107873	+	0.186841i
$999$	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.e.e.51.1		2
5.2	odd	4		350.4.j.b.149.2		4
5.3	odd	4		350.4.j.b.149.1		4
5.4	even	2		14.4.c.a.9.1	✓	2
7.2	even	3		2450.4.a.q.1.1		1
7.4	even	3	inner	350.4.e.e.151.1		2
7.5	odd	6		2450.4.a.d.1.1		1
15.14	odd	2		126.4.g.d.37.1		2
20.19	odd	2		112.4.i.a.65.1		2
35.4	even	6		14.4.c.a.11.1	yes	2
35.9	even	6		98.4.a.d.1.1		1
35.18	odd	12		350.4.j.b.249.2		4
35.19	odd	6		98.4.a.f.1.1		1
35.24	odd	6		98.4.c.a.67.1		2
35.32	odd	12		350.4.j.b.249.1		4
35.34	odd	2		98.4.c.a.79.1		2
40.19	odd	2		448.4.i.e.65.1		2
40.29	even	2		448.4.i.b.65.1		2
105.44	odd	6		882.4.a.f.1.1		1
105.59	even	6		882.4.g.u.361.1		2
105.74	odd	6		126.4.g.d.109.1		2
105.89	even	6		882.4.a.c.1.1		1
105.104	even	2		882.4.g.u.667.1		2
140.19	even	6		784.4.a.c.1.1		1
140.39	odd	6		112.4.i.a.81.1		2
140.79	odd	6		784.4.a.p.1.1		1
280.109	even	6		448.4.i.b.193.1		2
280.179	odd	6		448.4.i.e.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.4.c.a.9.1	✓	2	5.4	even	2
14.4.c.a.11.1	yes	2	35.4	even	6
98.4.a.d.1.1		1	35.9	even	6
98.4.a.f.1.1		1	35.19	odd	6
98.4.c.a.67.1		2	35.24	odd	6
98.4.c.a.79.1		2	35.34	odd	2
112.4.i.a.65.1		2	20.19	odd	2
112.4.i.a.81.1		2	140.39	odd	6
126.4.g.d.37.1		2	15.14	odd	2
126.4.g.d.109.1		2	105.74	odd	6
350.4.e.e.51.1		2	1.1	even	1	trivial
350.4.e.e.151.1		2	7.4	even	3	inner
350.4.j.b.149.1		4	5.3	odd	4
350.4.j.b.149.2		4	5.2	odd	4
350.4.j.b.249.1		4	35.32	odd	12
350.4.j.b.249.2		4	35.18	odd	12
448.4.i.b.65.1		2	40.29	even	2
448.4.i.b.193.1		2	280.109	even	6
448.4.i.e.65.1		2	40.19	odd	2
448.4.i.e.193.1		2	280.179	odd	6
784.4.a.c.1.1		1	140.19	even	6
784.4.a.p.1.1		1	140.79	odd	6
882.4.a.c.1.1		1	105.89	even	6
882.4.a.f.1.1		1	105.44	odd	6
882.4.g.u.361.1		2	105.59	even	6
882.4.g.u.667.1		2	105.104	even	2
2450.4.a.d.1.1		1	7.5	odd	6
2450.4.a.q.1.1		1	7.2	even	3

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.50000 - 4.33013i) q^{3} +(-2.00000 - 3.46410i) q^{4} -10.0000 q^{6} +(14.0000 + 12.1244i) q^{7} -8.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.50000 - 4.33013i) q^{3} +(-2.00000 - 3.46410i) q^{4} -10.0000 q^{6} +(14.0000 + 12.1244i) q^{7} -8.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(28.5000 + 49.3634i) q^{11} +(-10.0000 + 17.3205i) q^{12} +70.0000 q^{13} +(35.0000 - 12.1244i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(25.5000 + 44.1673i) q^{17} +(-2.00000 - 3.46410i) q^{18} +(-2.50000 + 4.33013i) q^{19} +(17.5000 - 90.9327i) q^{21} +114.000 q^{22} +(34.5000 - 59.7558i) q^{23} +(20.0000 + 34.6410i) q^{24} +(70.0000 - 121.244i) q^{26} -145.000 q^{27} +(14.0000 - 72.7461i) q^{28} +114.000 q^{29} +(-11.5000 - 19.9186i) q^{31} +(16.0000 + 27.7128i) q^{32} +(142.500 - 246.817i) q^{33} +102.000 q^{34} -8.00000 q^{36} +(-126.500 + 219.104i) q^{37} +(5.00000 + 8.66025i) q^{38} +(-175.000 - 303.109i) q^{39} -42.0000 q^{41} +(-140.000 - 121.244i) q^{42} +124.000 q^{43} +(114.000 - 197.454i) q^{44} +(-69.0000 - 119.512i) q^{46} +(100.500 - 174.071i) q^{47} +80.0000 q^{48} +(49.0000 + 339.482i) q^{49} +(127.500 - 220.836i) q^{51} +(-140.000 - 242.487i) q^{52} +(-196.500 - 340.348i) q^{53} +(-145.000 + 251.147i) q^{54} +(-112.000 - 96.9948i) q^{56} +25.0000 q^{57} +(114.000 - 197.454i) q^{58} +(-109.500 - 189.660i) q^{59} +(354.500 - 614.012i) q^{61} -46.0000 q^{62} +(35.0000 - 12.1244i) q^{63} +64.0000 q^{64} +(-285.000 - 493.634i) q^{66} +(209.500 + 362.865i) q^{67} +(102.000 - 176.669i) q^{68} -345.000 q^{69} -96.0000 q^{71} +(-8.00000 + 13.8564i) q^{72} +(-156.500 - 271.066i) q^{73} +(253.000 + 438.209i) q^{74} +20.0000 q^{76} +(-199.500 + 1036.63i) q^{77} -700.000 q^{78} +(-230.500 + 399.238i) q^{79} +(335.500 + 581.103i) q^{81} +(-42.0000 + 72.7461i) q^{82} +588.000 q^{83} +(-350.000 + 121.244i) q^{84} +(124.000 - 214.774i) q^{86} +(-285.000 - 493.634i) q^{87} +(-228.000 - 394.908i) q^{88} +(508.500 - 880.748i) q^{89} +(980.000 + 848.705i) q^{91} -276.000 q^{92} +(-57.5000 + 99.5929i) q^{93} +(-201.000 - 348.142i) q^{94} +(80.0000 - 138.564i) q^{96} +1834.00 q^{97} +(637.000 + 254.611i) q^{98} +114.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 5 q^{3} - 4 q^{4} - 20 q^{6} + 28 q^{7} - 16 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 5 * q^3 - 4 * q^4 - 20 * q^6 + 28 * q^7 - 16 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 5 q^{3} - 4 q^{4} - 20 q^{6} + 28 q^{7} - 16 q^{8} + 2 q^{9} + 57 q^{11} - 20 q^{12} + 140 q^{13} + 70 q^{14} - 16 q^{16} + 51 q^{17} - 4 q^{18} - 5 q^{19} + 35 q^{21} + 228 q^{22} + 69 q^{23} + 40 q^{24} + 140 q^{26} - 290 q^{27} + 28 q^{28} + 228 q^{29} - 23 q^{31} + 32 q^{32} + 285 q^{33} + 204 q^{34} - 16 q^{36} - 253 q^{37} + 10 q^{38} - 350 q^{39} - 84 q^{41} - 280 q^{42} + 248 q^{43} + 228 q^{44} - 138 q^{46} + 201 q^{47} + 160 q^{48} + 98 q^{49} + 255 q^{51} - 280 q^{52} - 393 q^{53} - 290 q^{54} - 224 q^{56} + 50 q^{57} + 228 q^{58} - 219 q^{59} + 709 q^{61} - 92 q^{62} + 70 q^{63} + 128 q^{64} - 570 q^{66} + 419 q^{67} + 204 q^{68} - 690 q^{69} - 192 q^{71} - 16 q^{72} - 313 q^{73} + 506 q^{74} + 40 q^{76} - 399 q^{77} - 1400 q^{78} - 461 q^{79} + 671 q^{81} - 84 q^{82} + 1176 q^{83} - 700 q^{84} + 248 q^{86} - 570 q^{87} - 456 q^{88} + 1017 q^{89} + 1960 q^{91} - 552 q^{92} - 115 q^{93} - 402 q^{94} + 160 q^{96} + 3668 q^{97} + 1274 q^{98} + 228 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 5 * q^3 - 4 * q^4 - 20 * q^6 + 28 * q^7 - 16 * q^8 + 2 * q^9 + 57 * q^11 - 20 * q^12 + 140 * q^13 + 70 * q^14 - 16 * q^16 + 51 * q^17 - 4 * q^18 - 5 * q^19 + 35 * q^21 + 228 * q^22 + 69 * q^23 + 40 * q^24 + 140 * q^26 - 290 * q^27 + 28 * q^28 + 228 * q^29 - 23 * q^31 + 32 * q^32 + 285 * q^33 + 204 * q^34 - 16 * q^36 - 253 * q^37 + 10 * q^38 - 350 * q^39 - 84 * q^41 - 280 * q^42 + 248 * q^43 + 228 * q^44 - 138 * q^46 + 201 * q^47 + 160 * q^48 + 98 * q^49 + 255 * q^51 - 280 * q^52 - 393 * q^53 - 290 * q^54 - 224 * q^56 + 50 * q^57 + 228 * q^58 - 219 * q^59 + 709 * q^61 - 92 * q^62 + 70 * q^63 + 128 * q^64 - 570 * q^66 + 419 * q^67 + 204 * q^68 - 690 * q^69 - 192 * q^71 - 16 * q^72 - 313 * q^73 + 506 * q^74 + 40 * q^76 - 399 * q^77 - 1400 * q^78 - 461 * q^79 + 671 * q^81 - 84 * q^82 + 1176 * q^83 - 700 * q^84 + 248 * q^86 - 570 * q^87 - 456 * q^88 + 1017 * q^89 + 1960 * q^91 - 552 * q^92 - 115 * q^93 - 402 * q^94 + 160 * q^96 + 3668 * q^97 + 1274 * q^98 + 228 * q^99

Introduction

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