LMFDB - Embedded newform 350.4.e.e.151.1

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			151.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	350.151
Dual form			350.4.e.e.51.1

$q$-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 $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$	−2.50000	+	4.33013i	−0.481125	+	0.833333i	−0.999765	−	0.0216593i	$-0.993105\pi$
$3$	−2.50000	+	4.33013i	−0.481125	+	0.833333i	0.518640	+	0.854993i	$0.326438\pi$
$4$	−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	−0.150061	−	0.988677i	$-0.547947\pi$
$11$	28.5000	−	49.3634i	0.781188	−	1.35306i	0.931250	−	0.364381i	$-0.118720\pi$
$12$	−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	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	25.5000	−	44.1673i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	−2.00000	+	3.46410i	−0.0261891	+	0.0453609i
$19$	−2.50000	−	4.33013i	−0.0301863	−	0.0522842i	0.850538	−	0.525914i	$-0.176277\pi$
$19$	−2.50000	−	4.33013i	−0.0301863	−	0.0522842i	−0.880724	+	0.473630i	$0.842943\pi$
$20$		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	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	34.5000	+	59.7558i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$	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	−0.897415	−	0.441188i	$-0.854557\pi$
$31$	−11.5000	+	19.9186i	−0.0666278	+	0.115403i	0.830787	+	0.556590i	$0.187891\pi$
$32$	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	−0.997316	−	0.0732182i	$-0.976673\pi$
$37$	−126.500	−	219.104i	−0.562067	−	0.973528i	0.435249	−	0.900310i	$-0.356660\pi$
$38$	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	0.978774	−	0.204941i	$-0.0657003\pi$
$47$	100.500	+	174.071i	0.311903	+	0.540231i	−0.666871	+	0.745173i	$0.732367\pi$
$48$	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	0.490672	+	0.871345i	$0.336751\pi$
$53$	−196.500	+	340.348i	−0.509271	+	0.882083i	−0.999942	+	0.0107383i	$0.996582\pi$
$54$	−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	−0.961176	−	0.275935i	$-0.911013\pi$
$59$	−109.500	+	189.660i	−0.241622	+	0.418501i	0.719555	+	0.694436i	$0.244346\pi$
$60$		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	$0.566220\pi$
$62$	−46.0000			−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	−0.609342	−	0.792908i	$-0.708566\pi$
$67$	209.500	−	362.865i	0.382007	−	0.661656i	0.991349	+	0.131251i	$0.0418995\pi$
$68$	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	−0.963779	−	0.266704i	$-0.914065\pi$
$73$	−156.500	+	271.066i	−0.250917	+	0.434601i	0.712862	+	0.701305i	$0.247399\pi$
$74$	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	0.653899	−	0.756582i	$-0.273132\pi$
$79$	−230.500	−	399.238i	−0.328269	−	0.568579i	−0.982169	+	0.188003i	$0.939799\pi$
$80$		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	0.991952	+	0.126615i	$0.0404114\pi$
$89$	508.500	+	880.748i	0.605628	+	1.04898i	−0.386324	+	0.922363i	$0.626255\pi$
$90$		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	−0.787254	−	0.616629i	$-0.788498\pi$
$101$	142.500	−	246.817i	0.140389	−	0.243161i	0.927643	+	0.373468i	$0.121831\pi$
$102$	−255.000	+	441.673i	−0.247537	+	0.428746i
$103$	−249.500	−	432.147i	−0.238679	−	0.413405i	0.721656	−	0.692252i	$-0.243381\pi$
$103$	−249.500	−	432.147i	−0.238679	−	0.413405i	−0.960336	+	0.278847i	$0.910048\pi$
$104$	−560.000			−0.528005
$105$		0			0
$106$	−786.000			−0.720218
$107$	−553.500	−	958.690i	−0.500083	−	0.866169i	−1.00000		9.56665e-5i	$-0.999970\pi$
$107$	−553.500	−	958.690i	−0.500083	−	0.866169i	0.499917	−	0.866073i	$-0.333364\pi$
$108$	290.000	−	502.295i	0.258382	−	0.447531i
$109$	−461.500	+	799.341i	−0.405538	+	0.702413i	−0.994384	−	0.105832i	$-0.966249\pi$
$109$	−461.500	+	799.341i	−0.405538	+	0.702413i	0.588846	+	0.808246i	$0.299583\pi$
$110$		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	−0.973971	−	0.226673i	$-0.927215\pi$
$131$	−1024.50	−	1774.49i	−0.683290	−	1.18349i	0.290681	−	0.956820i	$-0.406118\pi$
$132$	−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	−0.887171	−	0.461442i	$-0.847332\pi$
$137$	−70.5000	+	122.110i	−0.0439651	+	0.0761498i	0.843205	+	0.537591i	$0.180666\pi$
$138$	−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	0.873754	−	0.486368i	$-0.161679\pi$
$149$	28.5000	+	49.3634i	0.0156699	+	0.0271410i	−0.858084	+	0.513509i	$0.828345\pi$
$150$		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	$0.239258\pi$
$152$	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	0.240919	+	0.970545i	$0.422551\pi$
$157$	−1416.50	+	2453.45i	−0.720057	+	1.24718i	−0.960976	+	0.276631i	$0.910782\pi$
$158$	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	−0.997884	−	0.0650188i	$-0.979289\pi$
$163$	−1155.50	−	2001.38i	−0.555250	−	0.961721i	0.442634	−	0.896702i	$-0.354044\pi$
$164$	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	0.961839	+	0.273615i	$0.0882193\pi$
$173$	1633.50	+	2829.30i	0.717877	+	1.24340i	−0.243962	+	0.969785i	$0.578447\pi$
$174$	−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	−0.968527	−	0.248910i	$-0.919928\pi$
$179$	−643.500	+	1114.57i	−0.268701	+	0.465403i	0.699826	+	0.714314i	$0.253261\pi$
$180$		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	−0.924282	−	0.381711i	$-0.875335\pi$
$191$	−2092.50	−	3624.32i	−0.792712	−	1.37302i	0.131570	−	0.991307i	$-0.457998\pi$
$192$	−160.000	+	277.128i	−0.0601407	+	0.104167i
$193$	−42.5000	+	73.6122i	−0.0158509	+	0.0274545i	−0.873842	−	0.486210i	$-0.838379\pi$
$193$	−42.5000	+	73.6122i	−0.0158509	+	0.0274545i	0.857991	+	0.513664i	$0.171712\pi$
$194$	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	−0.495398	−	0.868666i	$-0.664978\pi$
$199$	1416.50	−	2453.45i	0.504588	−	0.873972i	0.999986	−	0.00530596i	$-0.00168895\pi$
$200$		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	−0.998184	−	0.0602465i	$-0.980811\pi$
$227$	−1528.50	+	2647.44i	−0.446917	+	0.774083i	0.551267	+	0.834329i	$0.314145\pi$
$228$	−50.0000	+	86.6025i	−0.0145234	+	0.0251552i
$229$	480.500	+	832.250i	0.138656	+	0.240160i	0.926988	−	0.375090i	$-0.122388\pi$
$229$	480.500	+	832.250i	0.138656	+	0.240160i	−0.788332	+	0.615250i	$0.789055\pi$
$230$		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	0.595731	−	0.803184i	$-0.296862\pi$
$233$	−1414.50	−	2449.99i	−0.397712	−	0.688858i	−0.993443	+	0.114326i	$0.963529\pi$
$234$	−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	0.269701	+	0.962944i	$0.413075\pi$
$241$	−2615.50	+	4530.18i	−0.699084	+	1.21085i	−0.968785	+	0.247904i	$0.920258\pi$
$242$	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	0.765559	−	0.643366i	$-0.222463\pi$
$257$	−718.500	−	1244.48i	−0.174392	−	0.302056i	−0.939951	+	0.341310i	$0.889129\pi$
$258$	−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	−0.969516	−	0.245027i	$-0.921203\pi$
$263$	−1162.50	+	2013.51i	−0.272558	+	0.472085i	0.696958	+	0.717112i	$0.254536\pi$
$264$	−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	−0.698646	−	0.715467i	$-0.746214\pi$
$269$	1192.50	−	2065.47i	0.270290	−	0.468156i	0.968936	+	0.247311i	$0.0795471\pi$
$270$		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	$0.821522\pi$
$272$	−816.000			−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	−0.471171	−	0.882042i	$-0.656169\pi$
$277$	2435.50	−	4218.41i	0.528285	−	0.915017i	0.999456	−	0.0329750i	$-0.0104982\pi$
$278$	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	0.435109	+	0.900378i	$0.356710\pi$
$283$	−2676.50	+	4635.83i	−0.562196	+	0.973752i	−0.997305	+	0.0733738i	$0.976623\pi$
$284$	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	−0.129791	+	0.991541i	$0.541430\pi$
$311$	−5065.50	+	8773.70i	−0.923595	+	1.59971i	−0.793805	+	0.608173i	$0.791903\pi$
$312$	1400.00	−	2424.87i	0.254037	−	0.440004i
$313$	5399.50	+	9352.21i	0.975073	+	1.68888i	0.679695	+	0.733495i	$0.262112\pi$
$313$	5399.50	+	9352.21i	0.975073	+	1.68888i	0.295378	+	0.955380i	$0.404554\pi$
$314$	−5666.00			−1.01831
$315$		0			0
$316$	1844.00			0.328269
$317$	265.500	+	459.859i	0.0470409	+	0.0814772i	0.888587	−	0.458708i	$-0.151688\pi$
$317$	265.500	+	459.859i	0.0470409	+	0.0814772i	−0.841546	+	0.540185i	$0.818354\pi$
$318$	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	0.995189	+	0.0979784i	$0.0312376\pi$
$331$	3507.50	+	6075.17i	0.582446	+	1.00883i	−0.412743	+	0.910848i	$0.635429\pi$
$332$	−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	0.303192	+	0.952929i	$0.401948\pi$
$347$	−4354.50	+	7542.22i	−0.673665	+	1.16682i	−0.976857	+	0.213893i	$0.931386\pi$
$348$	−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	−0.935158	−	0.354232i	$-0.884742\pi$
$353$	−1066.50	+	1847.23i	−0.160805	+	0.278522i	0.774353	+	0.632754i	$0.218076\pi$
$354$	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	0.689176	−	0.724594i	$-0.257972\pi$
$359$	−1924.50	−	3333.33i	−0.282928	−	0.490046i	−0.972105	+	0.234548i	$0.924639\pi$
$360$		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	−0.537424	−	0.843312i	$-0.680603\pi$
$367$	3245.50	−	5621.37i	0.461618	−	0.799545i	0.999042	+	0.0437668i	$0.0139358\pi$
$368$	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	0.896278	−	0.443493i	$-0.146261\pi$
$373$	461.500	+	799.341i	0.0640632	+	0.110961i	−0.832215	+	0.554453i	$0.812927\pi$
$374$	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	0.649290	−	0.760541i	$-0.275066\pi$
$383$	−2503.50	−	4336.19i	−0.334002	−	0.578509i	−0.983293	+	0.182032i	$0.941733\pi$
$384$	−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	0.117958	+	0.993019i	$0.462365\pi$
$389$	−6145.50	+	10644.3i	−0.801001	+	1.38737i	−0.918958	+	0.394355i	$0.870968\pi$
$390$		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	0.892697	−	0.450658i	$-0.148811\pi$
$397$	443.500	+	768.165i	0.0560671	+	0.0971110i	−0.836630	+	0.547769i	$0.815477\pi$
$398$	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	−0.950477	−	0.310794i	$-0.899405\pi$
$401$	−5977.50	−	10353.3i	−0.744394	−	1.28933i	0.206083	−	0.978535i	$-0.433928\pi$
$402$	−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	−0.743909	−	0.668281i	$-0.767030\pi$
$409$	1710.50	−	2962.67i	0.206794	−	0.358178i	0.950703	+	0.310103i	$0.100364\pi$
$410$		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	−0.354941	−	0.934889i	$-0.615499\pi$
$431$	5656.50	−	9797.35i	0.632167	−	1.09495i	0.987108	−	0.160057i	$-0.0511677\pi$
$432$	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	−0.827739	−	0.561114i	$-0.810373\pi$
$439$	−8276.50	−	14335.3i	−0.899808	−	1.55851i	−0.0720696	−	0.997400i	$-0.522960\pi$
$440$		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	−0.852247	−	0.523140i	$-0.824760\pi$
$443$	−8197.50	−	14198.5i	−0.879176	−	1.52278i	−0.0269294	−	0.999637i	$-0.508573\pi$
$444$	−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	−0.944531	−	0.328423i	$-0.893483\pi$
$457$	−7392.50	−	12804.2i	−0.756688	−	1.31062i	0.187842	−	0.982199i	$-0.439851\pi$
$458$	−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	0.951627	−	0.307256i	$-0.0994109\pi$
$467$	2116.50	+	3665.89i	0.209721	+	0.363248i	−0.741905	+	0.670505i	$0.766078\pi$
$468$	−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	−0.923921	−	0.382582i	$-0.875035\pi$
$479$	−1369.50	+	2372.04i	−0.130635	+	0.226266i	0.793287	+	0.608848i	$0.208368\pi$
$480$		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	−0.130646	−	0.991429i	$-0.541705\pi$
$487$	8525.50	−	14766.6i	0.793280	−	1.37400i	0.923926	−	0.382572i	$-0.124962\pi$
$488$	−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	0.779611	−	0.626264i	$-0.215417\pi$
$499$	−1700.50	−	2945.35i	−0.152555	−	0.264233i	−0.932166	+	0.362031i	$0.882083\pi$
$500$		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	0.823209	−	0.567738i	$-0.192181\pi$
$509$	−919.500	−	1592.62i	−0.0800710	−	0.138687i	−0.903280	+	0.429051i	$0.858848\pi$
$510$		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	−0.872325	−	0.488927i	$-0.837389\pi$
$521$	−151.500	+	262.406i	−0.0127396	+	0.0220656i	0.859585	+	0.510992i	$0.170722\pi$
$522$	−228.000	+	394.908i	−0.0191174	+	0.0331123i
$523$	−10833.5	−	18764.2i	−0.905767	−	1.56883i	−0.819885	−	0.572528i	$-0.805963\pi$
$523$	−10833.5	−	18764.2i	−0.905767	−	1.56883i	−0.0858815	−	0.996305i	$-0.527371\pi$
$524$	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	0.748376	−	0.663275i	$-0.230834\pi$
$541$	−2519.50	−	4363.90i	−0.200225	−	0.346800i	−0.948601	+	0.316475i	$0.897501\pi$
$542$	−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	0.0453775	+	0.998970i	$0.485551\pi$
$557$	−11074.5	+	19181.6i	−0.842445	+	1.45916i	−0.887822	+	0.460187i	$0.847782\pi$
$558$	−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	−0.978902	−	0.204332i	$-0.934498\pi$
$563$	−4174.50	+	7230.45i	−0.312494	+	0.541256i	0.666408	+	0.745588i	$0.267831\pi$
$564$	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	0.997023	+	0.0771050i	$0.0245677\pi$
$569$	7672.50	+	13289.2i	0.565286	+	0.979105i	−0.431737	+	0.902000i	$0.642099\pi$
$570$		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	$0.0270017\pi$
$572$	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	0.473083	+	0.881018i	$0.343141\pi$
$577$	−7296.50	+	12637.9i	−0.526442	+	0.911825i	−0.999525	+	0.0308071i	$0.990192\pi$
$578$	−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	0.502333	−	0.864674i	$-0.332475\pi$
$593$	−7186.50	−	12447.4i	−0.497663	−	0.861978i	−0.999996	+	0.00269639i	$0.999142\pi$
$594$	−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	−0.906186	−	0.422880i	$-0.861019\pi$
$599$	−1273.50	+	2205.77i	−0.0868678	+	0.150459i	0.819318	+	0.573340i	$0.194352\pi$
$600$		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	−0.945223	−	0.326427i	$-0.894155\pi$
$607$	−11295.5	−	19564.4i	−0.755305	−	1.30823i	0.189917	−	0.981800i	$-0.439178\pi$
$608$	−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	−0.971268	−	0.237987i	$-0.923513\pi$
$613$	−4242.50	+	7348.23i	−0.279532	+	0.484163i	0.691737	+	0.722150i	$0.256846\pi$
$614$	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	−0.900817	−	0.434200i	$-0.857031\pi$
$619$	−1145.50	+	1984.06i	−0.0743805	+	0.128831i	0.826436	+	0.563030i	$0.190365\pi$
$620$		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	0.168390	+	0.985721i	$0.446143\pi$
$641$	−12487.5	+	21629.0i	−0.769464	+	1.33275i	−0.937854	+	0.347031i	$0.887190\pi$
$642$	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	−0.670082	−	0.742287i	$-0.733741\pi$
$647$	5065.50	−	8773.70i	0.307798	−	0.533122i	0.977880	+	0.209165i	$0.0670745\pi$
$648$	−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	1.00000		0.000957229i	$-0.000304695\pi$
$653$	8329.50	+	14427.1i	0.499171	+	0.864589i	−0.500829	+	0.865546i	$0.666971\pi$
$654$	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	−0.868822	−	0.495125i	$-0.835122\pi$
$661$	−95.5000	+	165.411i	−0.00561955	+	0.00973334i	0.863202	+	0.504859i	$0.168455\pi$
$662$	−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	0.800087	−	0.599885i	$-0.204787\pi$
$677$	−2104.50	−	3645.10i	−0.119472	−	0.206931i	−0.919559	+	0.392953i	$0.871453\pi$
$678$	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	−0.293979	−	0.955812i	$-0.594980\pi$
$683$	12151.5	−	21047.0i	0.680768	−	1.17912i	0.974747	−	0.223312i	$-0.0716869\pi$
$684$	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	0.581298	−	0.813691i	$-0.302545\pi$
$691$	−7520.50	−	13025.9i	−0.414028	−	0.717117i	−0.995326	+	0.0965734i	$0.969212\pi$
$692$	−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	0.924173	−	0.381975i	$-0.124756\pi$
$709$	2478.50	+	4292.89i	0.131286	+	0.227395i	−0.792886	+	0.609370i	$0.791423\pi$
$710$		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	−0.961956	−	0.273204i	$-0.911917\pi$
$719$	−13834.5	−	23962.1i	−0.717580	−	1.24288i	0.244376	−	0.969680i	$-0.421417\pi$
$720$		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	0.987769	−	0.155922i	$-0.0498349\pi$
$733$	7121.50	+	12334.8i	0.358852	+	0.621550i	−0.628917	+	0.777472i	$0.716502\pi$
$734$	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	−0.120244	+	0.992744i	$0.538368\pi$
$739$	−18479.5	+	32007.4i	−0.919864	+	1.59325i	−0.799620	+	0.600507i	$0.794966\pi$
$740$		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	0.997015	−	0.0772090i	$-0.0246009\pi$
$751$	8883.50	+	15386.7i	0.431643	+	0.747627i	−0.565372	+	0.824836i	$0.691268\pi$
$752$	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	0.987466	+	0.157834i	$0.0504510\pi$
$761$	13234.5	+	22922.8i	0.630421	+	1.09192i	−0.357045	+	0.934087i	$0.616216\pi$
$762$	−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	0.0726439	+	0.997358i	$0.476856\pi$
$773$	−17782.5	+	30800.2i	−0.827415	+	1.43313i	−0.900059	+	0.435767i	$0.856477\pi$
$774$	−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	−0.947038	−	0.321121i	$-0.895940\pi$
$787$	−4314.50	+	7472.93i	−0.195420	+	0.338477i	0.751618	+	0.659598i	$0.229274\pi$
$788$	−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	−0.634856	−	0.772631i	$-0.718940\pi$
$809$	8092.50	−	14016.6i	0.351690	−	0.609145i	0.986546	+	0.163486i	$0.0522738\pi$
$810$		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	0.986885	+	0.161426i	$0.0516094\pi$
$821$	14896.5	+	25801.5i	0.633242	+	1.09681i	−0.353643	+	0.935380i	$0.615057\pi$
$822$	705.000	−	1221.10i	0.0299145	−	0.0518134i
$823$	15161.5	−	26260.5i	0.642159	−	1.11225i	−0.342791	−	0.939412i	$-0.611372\pi$
$823$	15161.5	−	26260.5i	0.642159	−	1.11225i	0.984950	−	0.172840i	$-0.0552943\pi$
$824$	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	−0.805547	−	0.592532i	$-0.798129\pi$
$829$	2634.50	−	4563.09i	0.110374	−	0.191173i	0.915921	+	0.401358i	$0.131462\pi$
$830$		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	0.361430	+	0.932399i	$0.382289\pi$
$857$	−15724.5	+	27235.6i	−0.626766	+	1.08559i	−0.988196	+	0.153192i	$0.951045\pi$
$858$	−19950.0	+	34554.4i	−0.793802	+	1.37490i
$859$	12261.5	+	21237.5i	0.487028	+	0.843557i	0.999889	−	0.0149147i	$-0.00474766\pi$
$859$	12261.5	+	21237.5i	0.487028	+	0.843557i	−0.512861	+	0.858472i	$0.671414\pi$
$860$		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	0.774233	−	0.632901i	$-0.218136\pi$
$863$	−4081.50	−	7069.37i	−0.160992	−	0.278846i	−0.935225	+	0.354055i	$0.884803\pi$
$864$	−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	0.904996	−	0.425421i	$-0.139874\pi$
$877$	2183.50	+	3781.93i	0.0840725	+	0.145618i	−0.820923	+	0.571039i	$0.806541\pi$
$878$	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	0.993055	+	0.117654i	$0.0375374\pi$
$887$	15808.5	+	27381.1i	0.598419	+	1.03649i	−0.394636	+	0.918838i	$0.629129\pi$
$888$	−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	−0.962851	−	0.270034i	$-0.912965\pi$
$907$	−6762.50	+	11713.0i	−0.247569	+	0.428802i	0.715282	+	0.698836i	$0.246298\pi$
$908$	−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	0.933441	−	0.358730i	$-0.116790\pi$
$919$	4347.50	+	7530.09i	0.156051	+	0.270288i	−0.777390	+	0.629019i	$0.783457\pi$
$920$		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	0.641201	−	0.767373i	$-0.278437\pi$
$929$	−9739.50	−	16869.3i	−0.343964	−	0.595763i	−0.985165	+	0.171610i	$0.945103\pi$
$930$		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	−0.693621	−	0.720340i	$-0.743986\pi$
$941$	7996.50	−	13850.3i	0.277023	−	0.479818i	0.970643	+	0.240523i	$0.0773189\pi$
$942$	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	0.945408	+	0.325888i	$0.105663\pi$
$947$	22000.5	+	38106.0i	0.754932	+	1.30758i	−0.190477	+	0.981692i	$0.561003\pi$
$948$	−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	0.912580	−	0.408898i	$-0.134087\pi$
$971$	3091.50	+	5354.64i	0.102174	+	0.176971i	−0.810406	+	0.585869i	$0.800753\pi$
$972$	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	−0.833937	−	0.551860i	$-0.813918\pi$
$977$	1861.50	−	3224.21i	0.0609567	−	0.105580i	0.894893	+	0.446280i	$0.147252\pi$
$978$	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	0.205779	+	0.978599i	$0.434027\pi$
$983$	−22948.5	+	39748.0i	−0.744602	+	1.28969i	−0.950381	+	0.311089i	$0.899306\pi$
$984$	−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	−0.913185	−	0.407545i	$-0.866385\pi$
$991$	−3233.50	+	5600.59i	−0.103648	+	0.179524i	0.809537	+	0.587069i	$0.199718\pi$
$992$	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	−0.623000	−	0.782222i	$-0.714086\pi$
$997$	11519.5	−	19952.4i	0.365924	−	0.633799i	0.988924	+	0.148423i	$0.0474197\pi$
$998$	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.151.1		2
5.2	odd	4		350.4.j.b.249.1		4
5.3	odd	4		350.4.j.b.249.2		4
5.4	even	2		14.4.c.a.11.1	yes	2
7.2	even	3	inner	350.4.e.e.51.1		2
7.3	odd	6		2450.4.a.d.1.1		1
7.4	even	3		2450.4.a.q.1.1		1
15.14	odd	2		126.4.g.d.109.1		2
20.19	odd	2		112.4.i.a.81.1		2
35.2	odd	12		350.4.j.b.149.2		4
35.4	even	6		98.4.a.d.1.1		1
35.9	even	6		14.4.c.a.9.1	✓	2
35.19	odd	6		98.4.c.a.79.1		2
35.23	odd	12		350.4.j.b.149.1		4
35.24	odd	6		98.4.a.f.1.1		1
35.34	odd	2		98.4.c.a.67.1		2
40.19	odd	2		448.4.i.e.193.1		2
40.29	even	2		448.4.i.b.193.1		2
105.44	odd	6		126.4.g.d.37.1		2
105.59	even	6		882.4.a.c.1.1		1
105.74	odd	6		882.4.a.f.1.1		1
105.89	even	6		882.4.g.u.667.1		2
105.104	even	2		882.4.g.u.361.1		2
140.39	odd	6		784.4.a.p.1.1		1
140.59	even	6		784.4.a.c.1.1		1
140.79	odd	6		112.4.i.a.65.1		2
280.149	even	6		448.4.i.b.65.1		2
280.219	odd	6		448.4.i.e.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.4.c.a.9.1	✓	2	35.9	even	6
14.4.c.a.11.1	yes	2	5.4	even	2
98.4.a.d.1.1		1	35.4	even	6
98.4.a.f.1.1		1	35.24	odd	6
98.4.c.a.67.1		2	35.34	odd	2
98.4.c.a.79.1		2	35.19	odd	6
112.4.i.a.65.1		2	140.79	odd	6
112.4.i.a.81.1		2	20.19	odd	2
126.4.g.d.37.1		2	105.44	odd	6
126.4.g.d.109.1		2	15.14	odd	2
350.4.e.e.51.1		2	7.2	even	3	inner
350.4.e.e.151.1		2	1.1	even	1	trivial
350.4.j.b.149.1		4	35.23	odd	12
350.4.j.b.149.2		4	35.2	odd	12
350.4.j.b.249.1		4	5.2	odd	4
350.4.j.b.249.2		4	5.3	odd	4
448.4.i.b.65.1		2	280.149	even	6
448.4.i.b.193.1		2	40.29	even	2
448.4.i.e.65.1		2	280.219	odd	6
448.4.i.e.193.1		2	40.19	odd	2
784.4.a.c.1.1		1	140.59	even	6
784.4.a.p.1.1		1	140.39	odd	6
882.4.a.c.1.1		1	105.59	even	6
882.4.a.f.1.1		1	105.74	odd	6
882.4.g.u.361.1		2	105.104	even	2
882.4.g.u.667.1		2	105.89	even	6
2450.4.a.d.1.1		1	7.3	odd	6
2450.4.a.q.1.1		1	7.4	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

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