LMFDB - Embedded newform 350.4.j.h.149.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [350,4,Mod(149,350)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("350.149"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(350, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 4, names="a")

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

Newform invariants

comment:select newform

sage:traces = [12,0,0,24,0,24,0,0,112,0,52] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$20.6506685020$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 134x^{10} + 13467x^{8} - 530084x^{6} + 15364507x^{4} - 160351569x^{2} + 1275989841 $ x^12 - 134x^10 + 13467x^8 - 530084x^6 + 15364507x^4 - 160351569*x^2 + 1275989841
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.5
Root			$2.95806 + 1.70784i$ of defining polynomial
Character	$\chi$	$=$	350.149
Dual form			350.4.j.h.249.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 + 1.00000i) q^{2} +(3.82408 - 2.20784i) q^{3} +(2.00000 + 3.46410i) q^{4} +8.83134 q^{6} +(-18.4072 + 2.04309i) q^{7} +8.00000i q^{8} +(-3.75092 + 6.49679i) q^{9} +(18.5470 + 32.1243i) q^{11} +(15.2963 + 8.83134i) q^{12} +47.2663i q^{13} +(-33.9253 - 14.8685i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-32.7050 + 18.8822i) q^{17} +(-12.9936 + 7.50184i) q^{18} +(3.80388 - 6.58852i) q^{19} +(-65.8800 + 48.4531i) q^{21} +74.1880i q^{22} +(128.613 + 74.2546i) q^{23} +(17.6627 + 30.5927i) q^{24} +(-47.2663 + 81.8677i) q^{26} +152.349i q^{27} +(-43.8919 - 59.6783i) q^{28} +84.5885 q^{29} +(64.9551 + 112.505i) q^{31} +(-27.7128 + 16.0000i) q^{32} +(141.851 + 81.8974i) q^{33} -75.5290 q^{34} -30.0074 q^{36} +(-128.269 - 74.0562i) q^{37} +(13.1770 - 7.60777i) q^{38} +(104.356 + 180.750i) q^{39} +6.16453 q^{41} +(-162.560 + 18.0432i) q^{42} -523.347i q^{43} +(-74.1880 + 128.497i) q^{44} +(148.509 + 257.226i) q^{46} +(-367.149 - 211.974i) q^{47} +70.6507i q^{48} +(334.652 - 75.2151i) q^{49} +(-83.3778 + 144.415i) q^{51} +(-163.735 + 94.5327i) q^{52} +(298.608 - 172.401i) q^{53} +(-152.349 + 263.876i) q^{54} +(-16.3447 - 147.258i) q^{56} -33.5934i q^{57} +(146.512 + 84.5885i) q^{58} +(330.093 + 571.737i) q^{59} +(-5.95832 + 10.3201i) q^{61} +259.820i q^{62} +(55.7706 - 127.251i) q^{63} -64.0000 q^{64} +(163.795 + 283.701i) q^{66} +(-624.046 + 360.293i) q^{67} +(-130.820 - 75.5290i) q^{68} +655.768 q^{69} +161.471 q^{71} +(-51.9743 - 30.0074i) q^{72} +(-526.488 + 303.968i) q^{73} +(-148.112 - 256.538i) q^{74} +30.4311 q^{76} +(-407.031 - 553.427i) q^{77} +417.425i q^{78} +(107.781 - 186.682i) q^{79} +(235.086 + 407.181i) q^{81} +(10.6773 + 6.16453i) q^{82} -390.531i q^{83} +(-299.606 - 131.309i) q^{84} +(523.347 - 906.464i) q^{86} +(323.473 - 186.757i) q^{87} +(-256.995 + 148.376i) q^{88} +(-756.595 + 1310.46i) q^{89} +(-96.5692 - 870.042i) q^{91} +594.037i q^{92} +(496.787 + 286.820i) q^{93} +(-423.948 - 734.299i) q^{94} +(-70.6507 + 122.371i) q^{96} -853.143i q^{97} +(654.849 + 204.375i) q^{98} -278.273 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 24 q^{4} + 24 q^{6} + 112 q^{9} + 52 q^{11} + 16 q^{14} - 96 q^{16} - 36 q^{19} + 370 q^{21} + 48 q^{24} + 320 q^{26} + 1616 q^{29} + 1230 q^{31} + 240 q^{34} + 896 q^{36} - 180 q^{39} - 404 q^{41}+ \cdots + 228 q^{99}+O(q^{100}) $ 12 * q + 24 * q^4 + 24 * q^6 + 112 * q^9 + 52 * q^11 + 16 * q^14 - 96 * q^16 - 36 * q^19 + 370 * q^21 + 48 * q^24 + 320 * q^26 + 1616 * q^29 + 1230 * q^31 + 240 * q^34 + 896 * q^36 - 180 * q^39 - 404 * q^41 - 208 * q^44 + 212 * q^46 + 432 * q^49 + 678 * q^51 - 1296 * q^54 + 896 * q^56 - 182 * q^59 + 1294 * q^61 - 768 * q^64 - 1256 * q^66 + 6192 * q^69 + 2132 * q^71 + 1704 * q^74 - 288 * q^76 + 2842 * q^79 + 2786 * q^81 + 608 * q^84 + 996 * q^86 - 388 * q^89 - 7710 * q^91 - 1608 * q^94 - 192 * q^96 + 228 * q^99

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 $

$2$	1.73205	+	1.00000i	0.612372	+	0.353553i
$2$	1.73205	+	1.00000i	0.612372	+	0.353553i
$3$	3.82408	−	2.20784i	0.735945	−	0.424898i	−0.0846479	−	0.996411i	$-0.526977\pi$
$3$	3.82408	−	2.20784i	0.735945	−	0.424898i	0.820593	+	0.571513i	$0.193643\pi$
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	8.83134			0.600897
$7$	−18.4072	+	2.04309i	−0.993897	+	0.110316i
$7$	−18.4072	+	2.04309i	−0.993897	+	0.110316i
$8$			8.00000i			0.353553i
$9$	−3.75092	+	6.49679i	−0.138923	+	0.240622i
$10$		0			0
$11$	18.5470	+	32.1243i	0.508375	+	0.880532i	0.999953	+	0.00969816i	$0.00308707\pi$
$11$	18.5470	+	32.1243i	0.508375	+	0.880532i	−0.491578	+	0.870834i	$0.663580\pi$
$12$	15.2963	+	8.83134i	0.367973	+	0.212449i
$13$			47.2663i			1.00841i	0.863584	+	0.504205i	$0.168214\pi$
$13$			47.2663i			1.00841i	−0.863584	+	0.504205i	$0.831786\pi$
$14$	−33.9253	−	14.8685i	−0.647638	−	0.283841i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−32.7050	+	18.8822i	−0.466596	+	0.269389i	−0.714814	−	0.699315i	$-0.753488\pi$
$17$	−32.7050	+	18.8822i	−0.466596	+	0.269389i	0.248218	+	0.968704i	$0.420155\pi$
$18$	−12.9936	+	7.50184i	−0.170145	+	0.0982334i
$19$	3.80388	−	6.58852i	0.0459300	−	0.0795532i	−0.842146	−	0.539249i	$-0.818708\pi$
$19$	3.80388	−	6.58852i	0.0459300	−	0.0795532i	0.888076	+	0.459696i	$0.152042\pi$
$20$		0			0
$21$	−65.8800	+	48.4531i	−0.684580	+	0.503492i
$22$			74.1880i			0.718951i
$23$	128.613	+	74.2546i	1.16598	+	0.673181i	0.952731	−	0.303816i	$-0.0982609\pi$
$23$	128.613	+	74.2546i	1.16598	+	0.673181i	0.213253	+	0.976997i	$0.431594\pi$
$24$	17.6627	+	30.5927i	0.150224	+	0.260196i
$25$		0			0
$26$	−47.2663	+	81.8677i	−0.356527	+	0.617522i
$27$			152.349i			1.08591i
$28$	−43.8919	−	59.6783i	−0.296242	−	0.402791i
$29$	84.5885			0.541644			0.270822	−	0.962629i	$-0.412704\pi$
$29$	84.5885			0.541644			0.270822	+	0.962629i	$0.412704\pi$
$30$		0			0
$31$	64.9551	+	112.505i	0.376331	+	0.651825i	0.990525	−	0.137330i	$-0.0438521\pi$
$31$	64.9551	+	112.505i	0.376331	+	0.651825i	−0.614194	+	0.789155i	$0.710519\pi$
$32$	−27.7128	+	16.0000i	−0.153093	+	0.0883883i
$33$	141.851	+	81.8974i	0.748273	+	0.432016i
$34$	−75.5290			−0.380974
$35$		0			0
$36$	−30.0074			−0.138923
$37$	−128.269	−	74.0562i	−0.569927	−	0.329048i	0.187193	−	0.982323i	$-0.440061\pi$
$37$	−128.269	−	74.0562i	−0.569927	−	0.329048i	−0.757120	+	0.653275i	$0.773394\pi$
$38$	13.1770	−	7.60777i	0.0562526	−	0.0324774i
$39$	104.356	+	180.750i	0.428471	+	0.742134i
$40$		0			0
$41$	6.16453			0.0234814			0.0117407	−	0.999931i	$-0.496263\pi$
$41$	6.16453			0.0234814			0.0117407	+	0.999931i	$0.496263\pi$
$42$	−162.560	+	18.0432i	−0.597229	+	0.0662887i
$43$		−	523.347i		−	1.85604i	−0.372532	−	0.928020i	$-0.621510\pi$
$43$		−	523.347i		−	1.85604i	0.372532	−	0.928020i	$-0.378490\pi$
$44$	−74.1880	+	128.497i	−0.254188	+	0.440266i
$45$		0			0
$46$	148.509	+	257.226i	0.476011	+	0.824475i
$47$	−367.149	−	211.974i	−1.13945	−	0.657863i	−0.193157	−	0.981168i	$-0.561873\pi$
$47$	−367.149	−	211.974i	−1.13945	−	0.657863i	−0.946295	+	0.323305i	$0.895206\pi$
$48$			70.6507i			0.212449i
$49$	334.652	−	75.2151i	0.975661	−	0.219286i
$50$		0			0
$51$	−83.3778	+	144.415i	−0.228926	+	0.396511i
$52$	−163.735	+	94.5327i	−0.436654	+	0.252102i
$53$	298.608	−	172.401i	0.773905	−	0.446814i	−0.0603608	−	0.998177i	$-0.519225\pi$
$53$	298.608	−	172.401i	0.773905	−	0.446814i	0.834266	+	0.551362i	$0.185892\pi$
$54$	−152.349	+	263.876i	−0.383927	+	0.664981i
$55$		0			0
$56$	−16.3447	−	147.258i	−0.0390027	−	0.351395i
$57$		−	33.5934i		−	0.0780624i
$58$	146.512	+	84.5885i	0.331688	+	0.191500i
$59$	330.093	+	571.737i	0.728379	+	1.26159i	0.957568	+	0.288208i	$0.0930595\pi$
$59$	330.093	+	571.737i	0.728379	+	1.26159i	−0.229188	+	0.973382i	$0.573607\pi$
$60$		0			0
$61$	−5.95832	+	10.3201i	−0.0125063	+	0.0216616i	−0.872211	−	0.489130i	$-0.837314\pi$
$61$	−5.95832	+	10.3201i	−0.0125063	+	0.0216616i	0.859705	+	0.510792i	$0.170648\pi$
$62$			259.820i			0.532213i
$63$	55.7706	−	127.251i	0.111531	−	0.254479i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	163.795	+	283.701i	0.305481	+	0.529109i
$67$	−624.046	+	360.293i	−1.13790	+	0.656967i	−0.945910	−	0.324430i	$-0.894828\pi$
$67$	−624.046	+	360.293i	−1.13790	+	0.656967i	−0.191991	+	0.981397i	$0.561494\pi$
$68$	−130.820	−	75.5290i	−0.233298	−	0.134695i
$69$	655.768			1.14413
$70$		0			0
$71$	161.471			0.269902			0.134951	−	0.990852i	$-0.456912\pi$
$71$	161.471			0.269902			0.134951	+	0.990852i	$0.456912\pi$
$72$	−51.9743	−	30.0074i	−0.0850726	−	0.0491167i
$73$	−526.488	+	303.968i	−0.844120	+	0.487353i	−0.858662	−	0.512542i	$-0.828704\pi$
$73$	−526.488	+	303.968i	−0.844120	+	0.487353i	0.0145428	+	0.999894i	$0.495371\pi$
$74$	−148.112	−	256.538i	−0.232672	−	0.403000i
$75$		0			0
$76$	30.4311			0.0459300
$77$	−407.031	−	553.427i	−0.602409	−	0.819076i
$78$			417.425i			0.605950i
$79$	107.781	−	186.682i	0.153498	−	0.265866i	−0.779013	−	0.627007i	$-0.784280\pi$
$79$	107.781	−	186.682i	0.153498	−	0.265866i	0.932511	+	0.361142i	$0.117613\pi$
$80$		0			0
$81$	235.086	+	407.181i	0.322478	+	0.558548i
$82$	10.6773	+	6.16453i	0.0143794	+	0.00830193i
$83$		−	390.531i		−	0.516462i	−0.966083	−	0.258231i	$-0.916861\pi$
$83$		−	390.531i		−	0.516462i	0.966083	−	0.258231i	$-0.0831395\pi$
$84$	−299.606	−	131.309i	−0.389163	−	0.170559i
$85$		0			0
$86$	523.347	−	906.464i	0.656209	−	1.13659i
$87$	323.473	−	186.757i	0.398620	−	0.230144i
$88$	−256.995	+	148.376i	−0.311315	+	0.179738i
$89$	−756.595	+	1310.46i	−0.901111	+	1.56077i	−0.0750572	+	0.997179i	$0.523914\pi$
$89$	−756.595	+	1310.46i	−0.901111	+	1.56077i	−0.826054	+	0.563591i	$0.809419\pi$
$90$		0			0
$91$	−96.5692	−	870.042i	−0.111244	−	1.00225i
$92$			594.037i			0.673181i
$93$	496.787	+	286.820i	0.553919	+	0.319805i
$94$	−423.948	−	734.299i	−0.465179	−	0.805714i
$95$		0			0
$96$	−70.6507	+	122.371i	−0.0751121	+	0.130098i
$97$		−	853.143i		−	0.893026i	−0.894777	−	0.446513i	$-0.852666\pi$
$97$		−	853.143i		−	0.893026i	0.894777	−	0.446513i	$-0.147334\pi$
$98$	654.849	+	204.375i	0.674997	+	0.210663i
$99$	−278.273			−0.282500
$100$		0			0
$101$	134.794	+	233.469i	0.132797	+	0.230011i	0.924754	−	0.380566i	$-0.124271\pi$
$101$	134.794	+	233.469i	0.132797	+	0.230011i	−0.791957	+	0.610577i	$0.790938\pi$
$102$	−288.829	+	166.756i	−0.280376	+	0.161875i
$103$	−838.254	−	483.966i	−0.801899	−	0.462977i	0.0422358	−	0.999108i	$-0.486552\pi$
$103$	−838.254	−	483.966i	−0.801899	−	0.462977i	−0.844135	+	0.536131i	$0.819885\pi$
$104$	−378.131			−0.356527
$105$		0			0
$106$	689.606			0.631891
$107$	879.072	+	507.532i	0.794234	+	0.458551i	0.841451	−	0.540333i	$-0.181702\pi$
$107$	879.072	+	507.532i	0.794234	+	0.458551i	−0.0472169	+	0.998885i	$0.515035\pi$
$108$	−527.752	+	304.698i	−0.470212	+	0.271477i
$109$	−34.4801	−	59.7213i	−0.0302991	−	0.0524795i	0.850478	−	0.526010i	$-0.176313\pi$
$109$	−34.4801	−	59.7213i	−0.0302991	−	0.0524795i	−0.880777	+	0.473531i	$0.842979\pi$
$110$		0			0
$111$	−654.016			−0.559247
$112$	118.948	−	271.403i	0.100353	−	0.228974i
$113$		−	1755.43i		−	1.46139i	−0.682705	−	0.730694i	$-0.739197\pi$
$113$		−	1755.43i		−	1.46139i	0.682705	−	0.730694i	$-0.260803\pi$
$114$	33.5934	−	58.1855i	0.0275992	−	0.0478032i
$115$		0			0
$116$	169.177	+	293.023i	0.135411	+	0.234539i
$117$	−307.079	−	177.292i	−0.242645	−	0.140091i
$118$			1320.37i			1.03008i
$119$	563.430	−	414.389i	0.434030	−	0.319218i
$120$		0			0
$121$	−22.4819	+	38.9397i	−0.0168910	+	0.0292560i
$122$	−20.6402	+	11.9166i	−0.0153170	+	0.00884329i
$123$	23.5737	−	13.6103i	0.0172810	−	0.00997721i
$124$	−259.820	+	450.022i	−0.188166	+	0.325913i
$125$		0			0
$126$	223.849	−	164.635i	0.158270	−	0.116404i
$127$			1852.45i			1.29432i	0.762356	+	0.647158i	$0.224042\pi$
$127$			1852.45i			1.29432i	−0.762356	+	0.647158i	$0.775958\pi$
$128$	−110.851	−	64.0000i	−0.0765466	−	0.0441942i
$129$	−1155.46	−	2001.32i	−0.788628	−	1.36594i
$130$		0			0
$131$	−216.970	+	375.803i	−0.144708	+	0.250642i	−0.929264	−	0.369416i	$-0.879558\pi$
$131$	−216.970	+	375.803i	−0.144708	+	0.250642i	0.784556	+	0.620058i	$0.212891\pi$
$132$			655.179i			0.432016i
$133$	−56.5580	+	129.048i	−0.0368737	+	0.0841345i
$134$	−1441.17			−0.929092
$135$		0			0
$136$	−151.058	−	261.640i	−0.0952435	−	0.164967i
$137$	2211.96	−	1277.07i	1.37942	−	0.796407i	0.387329	−	0.921942i	$-0.373398\pi$
$137$	2211.96	−	1277.07i	1.37942	−	0.796407i	0.992089	+	0.125534i	$0.0400645\pi$
$138$	1135.82	+	655.768i	0.700636	+	0.404512i
$139$	2743.94			1.67437			0.837187	−	0.546917i	$-0.184199\pi$
$139$	2743.94			1.67437			0.837187	+	0.546917i	$0.184199\pi$
$140$		0			0
$141$	−1872.01			−1.11810
$142$	279.675	+	161.471i	0.165280	+	0.0954247i
$143$	−1518.40	+	876.648i	−0.887937	+	0.512650i
$144$	−60.0147	−	103.949i	−0.0347308	−	0.0601554i
$145$		0			0
$146$	−1215.87			−0.689221
$147$	1113.67	−	1026.48i	0.624859	−	0.575939i
$148$		−	592.450i		−	0.329048i
$149$	413.244	−	715.759i	0.227210	−	0.393539i	−0.729770	−	0.683692i	$-0.760373\pi$
$149$	413.244	−	715.759i	0.227210	−	0.393539i	0.956980	+	0.290153i	$0.0937064\pi$
$150$		0			0
$151$	−830.302	−	1438.13i	−0.447477	−	0.775053i	0.550744	−	0.834674i	$-0.314344\pi$
$151$	−830.302	−	1438.13i	−0.447477	−	0.775053i	−0.998221	+	0.0596212i	$0.981011\pi$
$152$	52.7082	+	30.4311i	0.0281263	+	0.0162387i
$153$		−	283.303i		−	0.149697i
$154$	−151.572	−	1365.59i	−0.0793120	−	0.714563i
$155$		0			0
$156$	−417.425	+	723.002i	−0.214236	+	0.371067i
$157$	3170.37	−	1830.41i	1.61161	−	0.930464i	0.622613	−	0.782530i	$-0.286071\pi$
$157$	3170.37	−	1830.41i	1.61161	−	0.930464i	0.988997	−	0.147934i	$-0.0472622\pi$
$158$	373.364	−	215.562i	0.187995	−	0.108539i
$159$	761.268	−	1318.56i	0.379701	−	0.657662i
$160$		0			0
$161$	−2519.11	−	1104.05i	−1.23313	−	0.540445i
$162$			940.345i			0.456052i
$163$	1900.27	+	1097.12i	0.913131	+	0.527196i	0.881437	−	0.472301i	$-0.156577\pi$
$163$	1900.27	+	1097.12i	0.913131	+	0.527196i	0.0316935	+	0.999498i	$0.489910\pi$
$164$	12.3291	+	21.3546i	0.00587035	+	0.0101677i
$165$		0			0
$166$	390.531	−	676.419i	0.182597	−	0.316267i
$167$		−	2021.98i		−	0.936918i	−0.883485	−	0.468459i	$-0.844809\pi$
$167$		−	2021.98i		−	0.936918i	0.883485	−	0.468459i	$-0.155191\pi$
$168$	−387.624	−	527.040i	−0.178011	−	0.242036i
$169$	−37.1059			−0.0168893
$170$		0			0
$171$	28.5361	+	49.4261i	0.0127615	+	0.0221035i
$172$	1812.93	−	1046.69i	0.803688	−	0.464010i
$173$	132.011	+	76.2166i	0.0580151	+	0.0334950i	0.528727	−	0.848792i	$-0.322670\pi$
$173$	132.011	+	76.2166i	0.0580151	+	0.0334950i	−0.470712	+	0.882287i	$0.656003\pi$
$174$	747.030			0.325472
$175$		0			0
$176$	−593.504			−0.254188
$177$	2524.60	+	1457.58i	1.07209	+	0.618974i
$178$	−2620.92	+	1513.19i	−1.10363	+	0.637182i
$179$	2136.82	+	3701.09i	0.892255	+	1.54543i	0.837165	+	0.546950i	$0.184211\pi$
$179$	2136.82	+	3701.09i	0.892255	+	1.54543i	0.0550903	+	0.998481i	$0.482455\pi$
$180$		0			0
$181$	2607.33			1.07072			0.535362	−	0.844623i	$-0.320175\pi$
$181$	2607.33			1.07072			0.535362	+	0.844623i	$0.320175\pi$
$182$	702.779	−	1603.53i	0.286228	−	0.653084i
$183$			52.6200i			0.0212556i
$184$	−594.037	+	1028.90i	−0.238005	+	0.412237i
$185$		0			0
$186$	573.641	+	993.575i	0.226136	+	0.391680i
$187$	−1213.16	−	700.418i	−0.474412	−	0.273902i
$188$		−	1695.79i		−	0.657863i
$189$	−311.262	−	2804.32i	−0.119793	−	1.07928i
$190$		0			0
$191$	1754.48	−	3038.84i	0.664657	−	1.15122i	−0.314721	−	0.949184i	$-0.601911\pi$
$191$	1754.48	−	3038.84i	0.664657	−	1.15122i	0.979378	−	0.202036i	$-0.0647557\pi$
$192$	−244.741	+	141.301i	−0.0919932	+	0.0531123i
$193$	−56.9105	+	32.8573i	−0.0212254	+	0.0122545i	−0.510575	−	0.859833i	$-0.670567\pi$
$193$	−56.9105	+	32.8573i	−0.0212254	+	0.0122545i	0.489350	+	0.872088i	$0.337234\pi$
$194$	853.143	−	1477.69i	0.315732	−	0.546865i
$195$		0			0
$196$	929.856	+	1008.84i	0.338869	+	0.367652i
$197$			504.468i			0.182446i	0.995830	+	0.0912230i	$0.0290776\pi$
$197$			504.468i			0.182446i	−0.995830	+	0.0912230i	$0.970922\pi$
$198$	−481.983	−	278.273i	−0.172995	−	0.0998789i
$199$	−2474.42	−	4285.81i	−0.881441	−	1.52670i	−0.849740	−	0.527203i	$-0.823241\pi$
$199$	−2474.42	−	4285.81i	−0.881441	−	1.52670i	−0.0317011	−	0.999497i	$-0.510092\pi$
$200$		0			0
$201$	−1590.94	+	2755.58i	−0.558288	+	0.966984i
$202$			539.174i			0.187803i
$203$	−1557.04	+	172.821i	−0.538338	+	0.0597522i
$204$	−667.022			−0.228926
$205$		0			0
$206$	−967.932	−	1676.51i	−0.327374	−	0.567028i
$207$	−964.833	+	557.046i	−0.323964	+	0.187041i
$208$	−654.941	−	378.131i	−0.218327	−	0.126051i
$209$	282.202			0.0933988
$210$		0			0
$211$	3941.91			1.28613			0.643063	−	0.765813i	$-0.277663\pi$
$211$	3941.91			1.28613			0.643063	+	0.765813i	$0.277663\pi$
$212$	1194.43	+	689.606i	0.386953	+	0.223407i
$213$	617.477	−	356.501i	0.198633	−	0.114681i
$214$	1015.06	+	1758.14i	0.324245	+	0.561608i
$215$		0			0
$216$	−1218.79			−0.383927
$217$	−1425.50	−	1938.20i	−0.445941	−	0.606331i
$218$		−	137.921i		−	0.0428493i
$219$	−1342.22	+	2324.80i	−0.414151	+	0.717330i
$220$		0			0
$221$	−892.494	−	1545.85i	−0.271655	−	0.470520i
$222$	−1132.79	−	654.016i	−0.342468	−	0.197724i
$223$			938.296i			0.281762i	0.990027	+	0.140881i	$0.0449935\pi$
$223$			938.296i			0.281762i	−0.990027	+	0.140881i	$0.955006\pi$
$224$	477.427	−	351.135i	0.142408	−	0.104738i
$225$		0			0
$226$	1755.43	−	3040.49i	0.516679	−	0.894914i
$227$	−5179.15	+	2990.18i	−1.51433	+	0.874297i	−0.514469	+	0.857509i	$0.672011\pi$
$227$	−5179.15	+	2990.18i	−1.51433	+	0.874297i	−0.999859	+	0.0167883i	$0.994656\pi$
$228$	116.371	−	67.1868i	0.0338020	−	0.0195156i
$229$	−2189.24	+	3791.88i	−0.631743	+	1.09421i	0.355452	+	0.934694i	$0.384327\pi$
$229$	−2189.24	+	3791.88i	−0.631743	+	1.09421i	−0.987195	+	0.159517i	$0.949006\pi$
$230$		0			0
$231$	−2778.40	−	1217.69i	−0.791364	−	0.346832i
$232$			676.708i			0.191500i
$233$	2666.46	+	1539.48i	0.749724	+	0.432853i	0.825594	−	0.564265i	$-0.190840\pi$
$233$	2666.46	+	1539.48i	0.749724	+	0.432853i	−0.0758704	+	0.997118i	$0.524174\pi$
$234$	−354.585	−	614.159i	−0.0990595	−	0.171576i
$235$		0			0
$236$	−1320.37	+	2286.95i	−0.364190	+	0.630795i
$237$		−	951.851i		−	0.260883i
$238$	1390.28	−	154.312i	0.378649	−	0.0420276i
$239$	−2572.87			−0.696339			−0.348169	−	0.937432i	$-0.613197\pi$
$239$	−2572.87			−0.696339			−0.348169	+	0.937432i	$0.613197\pi$
$240$		0			0
$241$	1956.11	+	3388.08i	0.522838	+	0.905583i	0.999647	+	0.0265754i	$0.00846021\pi$
$241$	1956.11	+	3388.08i	0.522838	+	0.905583i	−0.476808	+	0.879007i	$0.658206\pi$
$242$	−77.8795	+	44.9637i	−0.0206871	+	0.0119437i
$243$	−1764.35	−	1018.65i	−0.465773	−	0.268914i
$244$	−47.6665			−0.0125063
$245$		0			0
$246$	54.4411			0.0141099
$247$	311.415	+	179.796i	0.0802222	+	0.0463163i
$248$	−900.044	+	519.641i	−0.230455	+	0.133053i
$249$	−862.228	−	1493.42i	−0.219444	−	0.380087i
$250$		0			0
$251$	1658.26			0.417005			0.208503	−	0.978022i	$-0.433141\pi$
$251$	1658.26			0.417005			0.208503	+	0.978022i	$0.433141\pi$
$252$	552.352	−	61.3076i	0.138075	−	0.0153255i
$253$			5508.80i			1.36891i
$254$	−1852.45	+	3208.53i	−0.457610	+	0.792603i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−223.746	−	129.180i	−0.0543070	−	0.0313541i	0.472601	−	0.881277i	$-0.343315\pi$
$257$	−223.746	−	129.180i	−0.0543070	−	0.0313541i	−0.526908	+	0.849923i	$0.676649\pi$
$258$		−	4621.86i		−	1.11529i
$259$	2512.38	+	1101.10i	0.602748	+	0.264167i
$260$		0			0
$261$	−317.285	+	549.553i	−0.0752469	+	0.130331i
$262$	−751.606	+	433.940i	−0.177230	+	0.102324i
$263$	4038.31	−	2331.52i	0.946817	−	0.546645i	0.0547265	−	0.998501i	$-0.482571\pi$
$263$	4038.31	−	2331.52i	0.946817	−	0.546645i	0.892091	+	0.451856i	$0.149238\pi$
$264$	−655.179	+	1134.80i	−0.152741	+	0.264554i
$265$		0			0
$266$	−227.009	+	166.960i	−0.0523265	+	0.0384848i
$267$			6681.75i			1.53152i
$268$	−2496.18	−	1441.17i	−0.568950	−	0.328484i
$269$	−2060.73	−	3569.29i	−0.467082	−	0.809010i	0.532211	−	0.846612i	$-0.321361\pi$
$269$	−2060.73	−	3569.29i	−0.467082	−	0.809010i	−0.999293	+	0.0376018i	$0.988028\pi$
$270$		0			0
$271$	1244.28	−	2155.16i	0.278911	−	0.483088i	−0.692203	−	0.721703i	$-0.743360\pi$
$271$	1244.28	−	2155.16i	0.278911	−	0.483088i	0.971114	+	0.238614i	$0.0766932\pi$
$272$		−	604.232i		−	0.134695i
$273$	−2290.20	−	3113.90i	−0.507726	−	0.690337i
$274$	5108.30			1.12629
$275$		0			0
$276$	1311.54	+	2271.65i	0.286033	+	0.495424i
$277$	−5502.62	+	3176.94i	−1.19358	+	0.689111i	−0.959116	−	0.283015i	$-0.908665\pi$
$277$	−5502.62	+	3176.94i	−1.19358	+	0.689111i	−0.234460	+	0.972126i	$0.575332\pi$
$278$	4752.64	+	2743.94i	1.02534	+	0.591981i
$279$	−974.566			−0.209124
$280$		0			0
$281$	7495.75			1.59131			0.795656	−	0.605748i	$-0.207126\pi$
$281$	7495.75			1.59131			0.795656	+	0.605748i	$0.207126\pi$
$282$	−3242.42	−	1872.01i	−0.684693	−	0.395308i
$283$	−7528.91	+	4346.82i	−1.58144	+	0.913044i	−0.586789	+	0.809740i	$0.699608\pi$
$283$	−7528.91	+	4346.82i	−1.58144	+	0.913044i	−0.994650	+	0.103304i	$0.967059\pi$
$284$	322.941	+	559.350i	0.0674755	+	0.116871i
$285$		0			0
$286$	−3506.59			−0.724997
$287$	−113.472	+	12.5947i	−0.0233381	+	0.00259038i
$288$		−	240.059i		−	0.0491167i
$289$	−1743.42	+	3019.70i	−0.354859	+	0.614634i
$290$		0			0
$291$	−1883.60	−	3262.49i	−0.379445	−	0.657218i
$292$	−2105.95	−	1215.87i	−0.422060	−	0.243676i
$293$		−	8086.06i		−	1.61226i	−0.591737	−	0.806131i	$-0.701558\pi$
$293$		−	8086.06i		−	1.61226i	0.591737	−	0.806131i	$-0.298442\pi$
$294$	2955.42	−	664.250i	0.586271	−	0.131768i
$295$		0			0
$296$	592.450	−	1026.15i	0.116336	−	0.201500i
$297$	−4894.10	+	2825.61i	−0.956178	+	0.552049i
$298$	1431.52	−	826.488i	0.278274	−	0.160662i
$299$	−3509.74	+	6079.05i	−0.678842	+	1.17579i
$300$		0			0
$301$	1069.24	+	9633.37i	0.204751	+	1.84471i
$302$		−	3321.21i		−	0.632828i
$303$	1030.92	+	595.204i	0.195462	+	0.112850i
$304$	60.8621	+	105.416i	0.0114825	+	0.0198883i
$305$		0			0
$306$	283.303	−	490.696i	0.0529260	−	0.0916706i
$307$		−	6235.13i		−	1.15915i	−0.814920	−	0.579573i	$-0.803219\pi$
$307$		−	6235.13i		−	1.15915i	0.814920	−	0.579573i	$-0.196781\pi$
$308$	1103.06	−	2516.85i	0.204068	−	0.465620i
$309$	−4274.07			−0.786872
$310$		0			0
$311$	−1288.41	−	2231.59i	−0.234917	−	0.406888i	0.724332	−	0.689452i	$-0.242148\pi$
$311$	−1288.41	−	2231.59i	−0.234917	−	0.406888i	−0.959248	+	0.282564i	$0.908815\pi$
$312$	−1446.00	+	834.850i	−0.262384	+	0.151487i
$313$	6834.07	+	3945.65i	1.23414	+	0.712529i	0.967889	−	0.251376i	$-0.0808831\pi$
$313$	6834.07	+	3945.65i	1.23414	+	0.712529i	0.266247	+	0.963905i	$0.414216\pi$
$314$	7321.65			1.31587
$315$		0			0
$316$	862.248			0.153498
$317$	5596.26	+	3231.00i	0.991538	+	0.572464i	0.905734	−	0.423848i	$-0.139321\pi$
$317$	5596.26	+	3231.00i	0.991538	+	0.572464i	0.0858040	+	0.996312i	$0.472654\pi$
$318$	2637.11	−	1522.54i	0.465037	−	0.268489i
$319$	1568.86	+	2717.35i	0.275359	+	0.476935i
$320$		0			0
$321$	4482.19			0.779351
$322$	−3259.18	−	4431.39i	−0.564058	−	0.766931i
$323$			287.303i			0.0494922i
$324$	−940.345	+	1628.73i	−0.161239	+	0.279274i
$325$		0			0
$326$	2194.24	+	3800.53i	0.372784	+	0.645681i
$327$	−263.710	−	152.253i	−0.0445969	−	0.0257480i
$328$			49.3162i			0.00830193i
$329$	7191.28	+	3151.73i	1.20507	+	0.528148i
$330$		0			0
$331$	−2638.51	+	4570.04i	−0.438144	+	0.758888i	−0.997546	−	0.0700081i	$-0.977697\pi$
$331$	−2638.51	+	4570.04i	−0.438144	+	0.758888i	0.559402	+	0.828896i	$0.311031\pi$
$332$	1352.84	−	781.061i	0.223634	−	0.129115i
$333$	962.255	−	555.558i	0.158352	−	0.0914246i
$334$	2021.98	−	3502.17i	0.331251	−	0.573743i
$335$		0			0
$336$	−144.346	−	1300.48i	−0.0234366	−	0.211152i
$337$			1009.76i			0.163220i	0.996664	+	0.0816101i	$0.0260062\pi$
$337$			1009.76i			0.163220i	−0.996664	+	0.0816101i	$0.973994\pi$
$338$	−64.2692	−	37.1059i	−0.0103426	−	0.00597128i
$339$	−3875.70	−	6712.91i	−0.620941	−	1.07550i
$340$		0			0
$341$	−2409.44	+	4173.28i	−0.382635	+	0.662744i
$342$			114.145i			0.0180475i
$343$	−6006.34	+	2068.22i	−0.945515	+	0.325579i
$344$	4186.78			0.656209
$345$		0			0
$346$	152.433	+	264.022i	0.0236846	+	0.0410229i
$347$	−7418.45	+	4283.05i	−1.14768	+	0.662611i	−0.948320	−	0.317316i	$-0.897218\pi$
$347$	−7418.45	+	4283.05i	−1.14768	+	0.662611i	−0.199356	+	0.979927i	$0.563885\pi$
$348$	1293.89	+	747.030i	0.199310	+	0.115072i
$349$	10372.3			1.59087			0.795437	−	0.606036i	$-0.207241\pi$
$349$	10372.3			1.59087			0.795437	+	0.606036i	$0.207241\pi$
$350$		0			0
$351$	−7200.97			−1.09504
$352$	−1027.98	−	593.504i	−0.155658	−	0.0898689i
$353$	3873.74	−	2236.51i	0.584075	−	0.337216i	−0.178676	−	0.983908i	$-0.557181\pi$
$353$	3873.74	−	2236.51i	0.584075	−	0.337216i	0.762751	+	0.646692i	$0.223848\pi$
$354$	2915.16	+	5049.21i	0.437681	+	0.758086i
$355$		0			0
$356$	−6052.76			−0.901111
$357$	1239.70	−	2828.62i	0.183787	−	0.419346i
$358$			8547.30i			1.26184i
$359$	−5431.59	+	9407.79i	−0.798519	+	1.38308i	0.122061	+	0.992523i	$0.461050\pi$
$359$	−5431.59	+	9407.79i	−0.798519	+	1.38308i	−0.920580	+	0.390553i	$0.872284\pi$
$360$		0			0
$361$	3400.56	+	5889.94i	0.495781	+	0.858718i
$362$	4516.02	+	2607.33i	0.655682	+	0.378558i
$363$			198.545i			0.0287078i
$364$	2820.77	−	2074.61i	0.406178	−	0.298734i
$365$		0			0
$366$	−52.6200	+	91.1404i	−0.00751500	+	0.0130164i
$367$	−10039.3	+	5796.21i	−1.42793	+	0.824414i	−0.996957	−	0.0779523i	$-0.975162\pi$
$367$	−10039.3	+	5796.21i	−1.42793	+	0.824414i	−0.430970	+	0.902366i	$0.641828\pi$
$368$	−2057.80	+	1188.07i	−0.291496	+	0.168295i
$369$	−23.1227	+	40.0496i	−0.00326211	+	0.00565014i
$370$		0			0
$371$	−5144.31	+	3783.51i	−0.719891	+	0.529462i
$372$			2294.56i			0.319805i
$373$	8712.20	+	5029.99i	1.20939	+	0.698239i	0.962625	−	0.270838i	$-0.0873006\pi$
$373$	8712.20	+	5029.99i	1.20939	+	0.698239i	0.246760	+	0.969077i	$0.420634\pi$
$374$	−1400.84	−	2426.32i	−0.193678	−	0.335460i
$375$		0			0
$376$	1695.79	−	2937.20i	0.232590	−	0.402857i
$377$			3998.19i			0.546199i
$378$	2265.20	−	5168.48i	0.308225	−	0.703275i
$379$	3791.02			0.513804			0.256902	−	0.966438i	$-0.417298\pi$
$379$	3791.02			0.513804			0.256902	+	0.966438i	$0.417298\pi$
$380$		0			0
$381$	4089.90	+	7083.91i	0.549952	+	0.952545i
$382$	6077.69	−	3508.95i	0.814035	−	0.469983i
$383$	920.728	+	531.582i	0.122838	+	0.0709206i	0.560160	−	0.828384i	$-0.310740\pi$
$383$	920.728	+	531.582i	0.122838	+	0.0709206i	−0.437322	+	0.899305i	$0.644073\pi$
$384$	−565.206			−0.0751121
$385$		0			0
$386$	−131.429			−0.0173305
$387$	3400.07	+	1963.03i	0.446603	+	0.257847i
$388$	2955.37	−	1706.29i	0.386692	−	0.223257i
$389$	−3283.82	−	5687.75i	−0.428011	−	0.741338i	0.568685	−	0.822555i	$-0.307452\pi$
$389$	−3283.82	−	5687.75i	−0.428011	−	0.741338i	−0.996696	+	0.0812179i	$0.974119\pi$
$390$		0			0
$391$	−5608.37			−0.725390
$392$	601.721	+	2677.21i	0.0775293	+	0.344948i
$393$			1916.14i			0.245945i
$394$	−504.468	+	873.765i	−0.0645044	+	0.111725i
$395$		0			0
$396$	−556.547	−	963.967i	−0.0706250	−	0.122326i
$397$	4576.10	+	2642.01i	0.578509	+	0.334002i	0.760540	−	0.649291i	$-0.224934\pi$
$397$	4576.10	+	2642.01i	0.578509	+	0.334002i	−0.182032	+	0.983293i	$0.558267\pi$
$398$		−	9897.66i		−	1.24655i
$399$	68.6342	+	618.361i	0.00861155	+	0.0775859i
$400$		0			0
$401$	−456.959	+	791.475i	−0.0569063	+	0.0985646i	−0.893075	−	0.449907i	$-0.851457\pi$
$401$	−456.959	+	791.475i	−0.0569063	+	0.0985646i	0.836169	+	0.548472i	$0.184790\pi$
$402$	−5511.16	+	3181.87i	−0.683761	+	0.394769i
$403$	−5317.72	+	3070.19i	−0.657307	+	0.379496i
$404$	−539.174	+	933.877i	−0.0663983	+	0.115005i
$405$		0			0
$406$	−2869.69	−	1257.70i	−0.350789	−	0.153741i
$407$		−	5494.08i		−	0.669119i
$408$	−1155.32	−	667.022i	−0.140188	−	0.0809376i
$409$	−6003.44	−	10398.3i	−0.725797	−	1.25712i	−0.958645	−	0.284604i	$-0.908138\pi$
$409$	−6003.44	−	10398.3i	−0.725797	−	1.25712i	0.232849	−	0.972513i	$-0.425195\pi$
$410$		0			0
$411$	5639.14	−	9767.28i	0.676784	−	1.17222i
$412$		−	3871.73i		−	0.462977i
$413$	−7244.19	−	9849.68i	−0.863108	−	1.17354i
$414$	−2228.19			−0.264515
$415$		0			0
$416$	−756.261	−	1309.88i	−0.0891316	−	0.154381i
$417$	10493.1	−	6058.17i	1.23225	−	0.711439i
$418$	488.789	+	282.202i	0.0571949	+	0.0330215i
$419$	−2545.07			−0.296742			−0.148371	−	0.988932i	$-0.547403\pi$
$419$	−2545.07			−0.296742			−0.148371	+	0.988932i	$0.547403\pi$
$420$		0			0
$421$	7564.36			0.875688			0.437844	−	0.899051i	$-0.355742\pi$
$421$	7564.36			0.875688			0.437844	+	0.899051i	$0.355742\pi$
$422$	6827.60	+	3941.91i	0.787588	+	0.454714i
$423$	2754.30	−	1590.19i	0.316592	−	0.182785i
$424$	1379.21	+	2388.86i	0.157973	+	0.273617i
$425$		0			0
$426$	1426.00			0.162183
$427$	88.5912	−	202.138i	0.0100403	−	0.0229090i
$428$			4060.26i			0.458551i
$429$	−3870.99	+	6704.75i	−0.435648	+	0.754565i
$430$		0			0
$431$	−8082.76	−	13999.7i	−0.903324	−	1.56460i	−0.823151	−	0.567823i	$-0.807786\pi$
$431$	−8082.76	−	13999.7i	−0.903324	−	1.56460i	−0.0801735	−	0.996781i	$-0.525547\pi$
$432$	−2111.01	−	1218.79i	−0.235106	−	0.135739i
$433$			14107.6i			1.56574i	0.622183	+	0.782872i	$0.286246\pi$
$433$			14107.6i			1.56574i	−0.622183	+	0.782872i	$0.713754\pi$
$434$	−530.835	−	4782.57i	−0.0587118	−	0.528965i
$435$		0			0
$436$	137.921	−	238.885i	0.0151495	−	0.0262398i
$437$	978.456	−	564.912i	0.107107	−	0.0618384i
$438$	−4649.59	+	2684.44i	−0.507229	+	0.292849i
$439$	2052.48	−	3555.00i	0.223142	−	0.386494i	−0.732618	−	0.680640i	$-0.761702\pi$
$439$	2052.48	−	3555.00i	0.223142	−	0.386494i	0.955760	+	0.294146i	$0.0950352\pi$
$440$		0			0
$441$	−766.596	+	2456.29i	−0.0827768	+	0.265229i
$442$		−	3569.98i		−	0.384178i
$443$	−1670.81	−	964.645i	−0.179194	−	0.103457i	0.407720	−	0.913107i	$-0.366324\pi$
$443$	−1670.81	−	964.645i	−0.179194	−	0.103457i	−0.586914	+	0.809649i	$0.699657\pi$
$444$	−1308.03	−	2265.58i	−0.139812	−	0.242161i
$445$		0			0
$446$	−938.296	+	1625.18i	−0.0996180	+	0.172543i
$447$		−	3649.50i		−	0.386164i
$448$	1178.06	−	130.757i	0.124237	−	0.0137895i
$449$	−18750.0			−1.97075			−0.985375	−	0.170398i	$-0.945495\pi$
$449$	−18750.0			−1.97075			−0.985375	+	0.170398i	$0.945495\pi$
$450$		0			0
$451$	114.333	+	198.031i	0.0119374	+	0.0206761i
$452$	6080.98	−	3510.86i	0.632800	−	0.365347i
$453$	−6350.29	−	3666.34i	−0.658637	−	0.380264i
$454$	−11960.7			−1.23644
$455$		0			0
$456$	268.747			0.0275992
$457$	5751.54	+	3320.65i	0.588722	+	0.339899i	0.764592	−	0.644515i	$-0.222941\pi$
$457$	5751.54	+	3320.65i	0.588722	+	0.339899i	−0.175870	+	0.984413i	$0.556274\pi$
$458$	−7583.76	+	4378.48i	−0.773724	+	0.446710i
$459$	−2876.69	−	4982.57i	−0.292532	−	0.506681i
$460$		0			0
$461$	2904.35			0.293425			0.146712	−	0.989179i	$-0.453131\pi$
$461$	2904.35			0.293425			0.146712	+	0.989179i	$0.453131\pi$
$462$	−3594.63	−	4887.50i	−0.361986	−	0.492180i
$463$			6750.67i			0.677603i	0.940858	+	0.338801i	$0.110022\pi$
$463$			6750.67i			0.677603i	−0.940858	+	0.338801i	$0.889978\pi$
$464$	−676.708	+	1172.09i	−0.0677055	+	0.117269i
$465$		0			0
$466$	3078.96	+	5332.92i	0.306073	+	0.530135i
$467$	2274.14	+	1312.98i	0.225342	+	0.130101i	0.608421	−	0.793614i	$-0.291803\pi$
$467$	2274.14	+	1312.98i	0.225342	+	0.130101i	−0.383079	+	0.923715i	$0.625136\pi$
$468$		−	1418.34i		−	0.140091i
$469$	10750.8	−	7906.97i	1.05848	−	0.778486i
$470$		0			0
$471$	8082.50	−	13999.3i	0.790705	−	1.36954i
$472$	−4573.90	+	2640.74i	−0.446040	+	0.257521i
$473$	16812.2	−	9706.51i	1.63430	−	0.943564i
$474$	951.851	−	1648.65i	0.0922362	−	0.159758i
$475$		0			0
$476$	2562.35	+	1123.00i	0.246733	+	0.108136i
$477$			2586.66i			0.248291i
$478$	−4456.34	−	2572.87i	−0.426419	−	0.246193i
$479$	−4809.51	−	8330.31i	−0.458773	−	0.794617i	0.540124	−	0.841586i	$-0.318377\pi$
$479$	−4809.51	−	8330.31i	−0.458773	−	0.794617i	−0.998896	+	0.0469682i	$0.985044\pi$
$480$		0			0
$481$	3500.37	−	6062.81i	0.331815	−	0.574720i
$482$			7824.44i			0.739405i
$483$	−12070.9	+	1339.79i	−1.13715	+	0.126216i
$484$	−179.855			−0.0168910
$485$		0			0
$486$	−2037.29	−	3528.69i	−0.190151	−	0.329351i
$487$	9895.69	−	5713.28i	0.920773	−	0.531608i	0.0368913	−	0.999319i	$-0.488254\pi$
$487$	9895.69	−	5713.28i	0.920773	−	0.531608i	0.883882	+	0.467711i	$0.154921\pi$
$488$	−82.5609	−	47.6665i	−0.00765852	−	0.00442165i
$489$	9689.03			0.896019
$490$		0			0
$491$	−7139.55			−0.656219			−0.328110	−	0.944640i	$-0.606412\pi$
$491$	−7139.55			−0.656219			−0.328110	+	0.944640i	$0.606412\pi$
$492$	94.2947	+	54.4411i	0.00864052	+	0.00498860i
$493$	−2766.47	+	1597.22i	−0.252729	+	0.145913i
$494$	359.591	+	622.830i	0.0327506	+	0.0567256i
$495$		0			0
$496$	−2078.56			−0.188166
$497$	−2972.22	+	329.898i	−0.268255	+	0.0297746i
$498$		−	3448.91i		−	0.310340i
$499$	−2830.47	+	4902.51i	−0.253926	+	0.439813i	−0.964603	−	0.263705i	$-0.915055\pi$
$499$	−2830.47	+	4902.51i	−0.253926	+	0.439813i	0.710677	+	0.703518i	$0.248389\pi$
$500$		0			0
$501$	−4464.20	−	7732.21i	−0.398095	−	0.689521i
$502$	2872.19	+	1658.26i	0.255362	+	0.147434i
$503$			4802.55i			0.425716i	0.977083	+	0.212858i	$0.0682771\pi$
$503$			4802.55i			0.425716i	−0.977083	+	0.212858i	$0.931723\pi$
$504$	1018.01	+	446.164i	0.0899718	+	0.0394320i
$505$		0			0
$506$	−5508.80	+	9541.52i	−0.483984	+	0.838285i
$507$	−141.896	+	81.9236i	−0.0124296	+	0.00717624i
$508$	−6417.06	+	3704.89i	−0.560455	+	0.323579i
$509$	5361.57	−	9286.52i	0.466891	−	0.808679i	−0.532394	−	0.846497i	$-0.678707\pi$
$509$	5361.57	−	9286.52i	0.466891	−	0.808679i	0.999285	+	0.0378179i	$0.0120407\pi$
$510$		0			0
$511$	9070.14	−	6670.86i	0.785205	−	0.577498i
$512$		−	512.000i		−	0.0441942i
$513$	1003.75	+	579.517i	0.0863875	+	0.0498759i
$514$	−258.360	−	447.492i	−0.0221707	−	0.0384008i
$515$		0			0
$516$	4621.86	−	8005.29i	0.394314	−	0.682972i
$517$		−	15725.9i		−	1.33777i
$518$	3250.47	+	4419.55i	0.275709	+	0.374872i
$519$	673.095			0.0569279
$520$		0			0
$521$	−2943.23	−	5097.82i	−0.247496	−	0.428675i	0.715335	−	0.698782i	$-0.246274\pi$
$521$	−2943.23	−	5097.82i	−0.247496	−	0.428675i	−0.962830	+	0.270107i	$0.912941\pi$
$522$	−1099.11	+	634.569i	−0.0921582	+	0.0532076i
$523$	−8914.47	−	5146.77i	−0.745320	−	0.430311i	0.0786803	−	0.996900i	$-0.474929\pi$
$523$	−8914.47	−	5146.77i	−0.745320	−	0.430311i	−0.824000	+	0.566589i	$0.808263\pi$
$524$	−1735.76			−0.144708
$525$		0			0
$526$	9326.08			0.773073
$527$	−4248.71	−	2452.99i	−0.351189	−	0.202759i
$528$	−2269.61	+	1310.36i	−0.187068	+	0.108004i
$529$	4943.99	+	8563.25i	0.406345	+	0.703809i
$530$		0			0
$531$	−4952.61			−0.404755
$532$	−560.152	+	62.1733i	−0.0456497	+	0.00506683i
$533$			291.375i			0.0236789i
$534$	−6681.75	+	11573.1i	−0.541475	+	0.937862i
$535$		0			0
$536$	−2882.34	−	4992.37i	−0.232273	−	0.402309i
$537$	16342.8	+	9435.51i	1.31330	+	0.758235i
$538$		−	8242.93i		−	0.660554i
$539$	8623.01	+	9355.45i	0.689090	+	0.747621i
$540$		0			0
$541$	−893.487	+	1547.56i	−0.0710056	+	0.122985i	−0.899342	−	0.437245i	$-0.855954\pi$
$541$	−893.487	+	1547.56i	−0.0710056	+	0.122985i	0.828337	+	0.560231i	$0.189287\pi$
$542$	4310.33	−	2488.57i	0.341595	−	0.197220i
$543$	9970.63	−	5756.55i	0.787994	−	0.454949i
$544$	604.232	−	1046.56i	0.0476217	−	0.0824833i
$545$		0			0
$546$	−852.836	−	7683.64i	−0.0668461	−	0.602252i
$547$		−	20022.3i		−	1.56507i	−0.622607	−	0.782535i	$-0.713926\pi$
$547$		−	20022.3i		−	1.56507i	0.622607	−	0.782535i	$-0.286074\pi$
$548$	8847.83	+	5108.30i	0.689709	+	0.398204i
$549$	−44.6984	−	77.4199i	−0.00347483	−	0.00601858i
$550$		0			0
$551$	321.765	−	557.313i	0.0248777	−	0.0430895i
$552$			5246.14i			0.404512i
$553$	−1602.54	+	3656.51i	−0.123231	+	0.281176i
$554$	−12707.8			−0.974550
$555$		0			0
$556$	5487.88	+	9505.29i	0.418594	+	0.725025i
$557$	9295.77	−	5366.91i	0.707135	−	0.408265i	−0.102864	−	0.994695i	$-0.532801\pi$
$557$	9295.77	−	5366.91i	0.707135	−	0.408265i	0.809999	+	0.586431i	$0.199467\pi$
$558$	−1688.00	−	974.566i	−0.128062	−	0.0739366i
$559$	24736.7			1.87165
$560$		0			0
$561$	−6185.63			−0.465521
$562$	12983.0	+	7495.75i	0.974476	+	0.562614i
$563$	−14533.4	+	8390.87i	−1.08794	+	0.628122i	−0.933027	−	0.359806i	$-0.882843\pi$
$563$	−14533.4	+	8390.87i	−1.08794	+	0.628122i	−0.154913	+	0.987928i	$0.549510\pi$
$564$	−3744.03	−	6484.85i	−0.279525	−	0.484151i
$565$		0			0
$566$	−17387.3			−1.29124
$567$	−5159.19	−	7014.78i	−0.382126	−	0.519564i
$568$			1291.76i			0.0954247i
$569$	7996.61	−	13850.5i	0.589166	−	1.02047i	−0.405176	−	0.914239i	$-0.632790\pi$
$569$	7996.61	−	13850.5i	0.589166	−	1.02047i	0.994342	−	0.106226i	$-0.0338768\pi$
$570$		0			0
$571$	−455.006	−	788.094i	−0.0333475	−	0.0577596i	0.848870	−	0.528602i	$-0.177283\pi$
$571$	−455.006	−	788.094i	−0.0333475	−	0.0577596i	−0.882217	+	0.470842i	$0.843950\pi$
$572$	−6073.60	−	3506.59i	−0.443968	−	0.256325i
$573$		−	15494.4i		−	1.12965i
$574$	−209.134	−	91.6573i	−0.0152074	−	0.00666498i
$575$		0			0
$576$	240.059	−	415.794i	0.0173654	−	0.0300777i
$577$	7551.24	−	4359.71i	0.544822	−	0.314553i	−0.202209	−	0.979342i	$-0.564812\pi$
$577$	7551.24	−	4359.71i	0.544822	−	0.314553i	0.747031	+	0.664789i	$0.231479\pi$
$578$	−6039.39	+	3486.84i	−0.434612	+	0.250923i
$579$	−145.087	+	251.298i	−0.0104138	+	0.0180373i
$580$		0			0
$581$	797.888	+	7188.58i	0.0569741	+	0.513309i
$582$		−	7534.40i		−	0.536616i
$583$	11076.6	+	6395.06i	0.786869	+	0.454299i
$584$	−2431.74	−	4211.90i	−0.172305	−	0.298441i
$585$		0			0
$586$	8086.06	−	14005.5i	0.570021	−	0.987305i
$587$		−	10075.6i		−	0.708460i	−0.935158	−	0.354230i	$-0.884743\pi$
$587$		−	10075.6i		−	0.708460i	0.935158	−	0.354230i	$-0.115257\pi$
$588$	5783.19	+	1804.91i	0.405604	+	0.126587i
$589$	988.326			0.0691397
$590$		0			0
$591$	1113.78	+	1929.13i	0.0775210	+	0.134270i
$592$	2052.31	−	1184.90i	0.142482	−	0.0822619i
$593$	−18087.4	−	10442.8i	−1.25255	−	0.723159i	−0.280933	−	0.959727i	$-0.590644\pi$
$593$	−18087.4	−	10442.8i	−1.25255	−	0.723159i	−0.971615	+	0.236568i	$0.923977\pi$
$594$	−11302.4			−0.780716
$595$		0			0
$596$	3305.95			0.227210
$597$	−18924.7	−	10926.2i	−1.29738	−	0.749045i
$598$	−12158.1	+	7019.49i	−0.831408	+	0.480014i
$599$	−5579.76	−	9664.44i	−0.380606	−	0.659229i	0.610543	−	0.791983i	$-0.290951\pi$
$599$	−5579.76	−	9664.44i	−0.380606	−	0.659229i	−0.991149	+	0.132754i	$0.957618\pi$
$600$		0			0
$601$	−5881.15			−0.399163			−0.199582	−	0.979881i	$-0.563958\pi$
$601$	−5881.15			−0.399163			−0.199582	+	0.979881i	$0.563958\pi$
$602$	−7781.38	+	17754.7i	−0.526820	+	1.20204i
$603$		−	5405.72i		−	0.365071i
$604$	3321.21	−	5752.50i	0.223739	−	0.387527i
$605$		0			0
$606$	1190.41	+	2061.85i	0.0797971	+	0.138213i
$607$	7204.74	+	4159.66i	0.481765	+	0.278147i	0.721152	−	0.692777i	$-0.243613\pi$
$607$	7204.74	+	4159.66i	0.481765	+	0.278147i	−0.239387	+	0.970924i	$0.576946\pi$
$608$			243.449i			0.0162387i
$609$	−5572.68	+	4098.57i	−0.370799	+	0.272713i
$610$		0			0
$611$	10019.2	−	17353.8i	0.663395	−	1.14903i
$612$	981.391	−	566.607i	0.0648209	−	0.0374244i
$613$	14227.9	−	8214.50i	0.937456	−	0.541241i	0.0482942	−	0.998833i	$-0.484621\pi$
$613$	14227.9	−	8214.50i	0.937456	−	0.541241i	0.889162	+	0.457593i	$0.151288\pi$
$614$	6235.13	−	10799.6i	0.409820	−	0.709829i
$615$		0			0
$616$	4427.41	−	3256.25i	0.289587	−	0.212984i
$617$			7721.15i			0.503796i	0.967754	+	0.251898i	$0.0810547\pi$
$617$			7721.15i			0.503796i	−0.967754	+	0.251898i	$0.918945\pi$
$618$	−7402.91	−	4274.07i	−0.481859	−	0.278201i
$619$	3950.16	+	6841.87i	0.256495	+	0.444262i	0.965300	−	0.261142i	$-0.0840990\pi$
$619$	3950.16	+	6841.87i	0.256495	+	0.444262i	−0.708806	+	0.705404i	$0.750766\pi$
$620$		0			0
$621$	−11312.6	+	19594.0i	−0.731013	+	1.26615i
$622$		−	5153.64i		−	0.332222i
$623$	11249.4	−	25667.7i	0.723433	−	1.65065i
$624$	−3339.40			−0.214236
$625$		0			0
$626$	7891.31	+	13668.1i	0.503834	+	0.872666i
$627$	1079.17	−	623.057i	0.0687364	−	0.0396850i
$628$	12681.5	+	7321.65i	0.805805	+	0.465232i
$629$	5593.39			0.354568
$630$		0			0
$631$	−14817.0			−0.934794			−0.467397	−	0.884047i	$-0.654808\pi$
$631$	−14817.0			−0.934794			−0.467397	+	0.884047i	$0.654808\pi$
$632$	1493.46	+	862.248i	0.0939977	+	0.0542696i
$633$	15074.2	−	8703.10i	0.946518	−	0.546473i
$634$	6462.01	+	11192.5i	0.404794	+	0.701123i
$635$		0			0
$636$	6090.15			0.379701
$637$	3555.14	+	15817.8i	0.221130	+	0.983865i
$638$			6275.45i			0.389416i
$639$	−605.664	+	1049.04i	−0.0374956	+	0.0649443i
$640$		0			0
$641$	6770.92	+	11727.6i	0.417216	+	0.722639i	0.995658	−	0.0930841i	$-0.0296725\pi$
$641$	6770.92	+	11727.6i	0.417216	+	0.722639i	−0.578442	+	0.815723i	$0.696339\pi$
$642$	7763.38	+	4482.19i	0.477253	+	0.275542i
$643$			24926.1i			1.52876i	0.644767	+	0.764379i	$0.276954\pi$
$643$			24926.1i			1.52876i	−0.644767	+	0.764379i	$0.723046\pi$
$644$	−1213.67	−	10934.6i	−0.0742628	−	0.669072i
$645$		0			0
$646$	−287.303	+	497.624i	−0.0174981	+	0.0303077i
$647$	−23761.5	+	13718.7i	−1.44384	+	0.833599i	−0.998103	−	0.0615667i	$-0.980390\pi$
$647$	−23761.5	+	13718.7i	−1.44384	+	0.833599i	−0.445733	+	0.895166i	$0.647057\pi$
$648$	−3257.45	+	1880.69i	−0.197476	+	0.114013i
$649$	−12244.4	+	21208.0i	−0.740580	+	1.28272i
$650$		0			0
$651$	−9730.47	−	4264.59i	−0.585818	−	0.256747i
$652$			8776.95i			0.527196i
$653$	521.045	+	300.825i	0.0312252	+	0.0180279i	0.515531	−	0.856871i	$-0.327595\pi$
$653$	521.045	+	300.825i	0.0312252	+	0.0180279i	−0.484306	+	0.874899i	$0.660928\pi$
$654$	−304.506	−	527.420i	−0.0182066	−	0.0315348i
$655$		0			0
$656$	−49.3162	+	85.4182i	−0.00293518	+	0.00508387i
$657$		−	4560.64i		−	0.270818i
$658$	9303.93	+	12650.2i	0.551224	+	0.749480i
$659$	−137.545			−0.00813047			−0.00406523	−	0.999992i	$-0.501294\pi$
$659$	−137.545			−0.00813047			−0.00406523	+	0.999992i	$0.501294\pi$
$660$		0			0
$661$	3251.91	+	5632.47i	0.191354	+	0.331434i	0.945699	−	0.325044i	$-0.105379\pi$
$661$	3251.91	+	5632.47i	0.191354	+	0.331434i	−0.754346	+	0.656478i	$0.772046\pi$
$662$	−9140.08	+	5277.03i	−0.536615	+	0.309815i
$663$	−6825.95	−	3940.96i	−0.399846	−	0.230851i
$664$	3124.25			0.182597
$665$		0			0
$666$	2222.23			0.129294
$667$	10879.2	+	6281.08i	0.631548	+	0.364624i
$668$	7004.34	−	4043.96i	0.405697	−	0.234230i
$669$	2071.60	+	3588.12i	0.119720	+	0.207362i
$670$		0			0
$671$	−442.036			−0.0254316
$672$	1050.47	−	2396.85i	0.0603017	−	0.137590i
$673$		−	5426.84i		−	0.310831i	−0.987849	−	0.155416i	$-0.950328\pi$
$673$		−	5426.84i		−	0.310831i	0.987849	−	0.155416i	$-0.0496717\pi$
$674$	−1009.76	+	1748.96i	−0.0577070	+	0.0999515i
$675$		0			0
$676$	−74.2117	−	128.538i	−0.00422233	−	0.00731329i
$677$	−2603.30	−	1503.02i	−0.147789	−	0.0853259i	0.424282	−	0.905530i	$-0.360526\pi$
$677$	−2603.30	−	1503.02i	−0.147789	−	0.0853259i	−0.572071	+	0.820204i	$0.693860\pi$
$678$		−	15502.8i		−	0.878143i
$679$	1743.04	+	15704.0i	0.0985153	+	0.887575i
$680$		0			0
$681$	−13203.7	+	22869.4i	−0.742975	+	1.28687i
$682$	−8346.55	+	4818.88i	−0.468631	+	0.270564i
$683$	−12982.1	+	7495.20i	−0.727298	+	0.419906i	−0.817433	−	0.576024i	$-0.804604\pi$
$683$	−12982.1	+	7495.20i	−0.727298	+	0.419906i	0.0901347	+	0.995930i	$0.471270\pi$
$684$	−114.145	+	197.704i	−0.00638074	+	0.0110518i
$685$		0			0
$686$	−12471.5	−	2424.07i	−0.694117	−	0.134915i
$687$			19333.9i			1.07371i
$688$	7251.71	+	4186.78i	0.401844	+	0.232005i
$689$	8148.78	+	14114.1i	0.450572	+	0.780413i
$690$		0			0
$691$	−11923.5	+	20652.1i	−0.656427	+	1.13697i	0.325107	+	0.945677i	$0.394600\pi$
$691$	−11923.5	+	20652.1i	−0.656427	+	1.13697i	−0.981534	+	0.191288i	$0.938734\pi$
$692$			609.733i			0.0334950i
$693$	5122.24	−	568.536i	0.280776	−	0.0311644i
$694$	−17132.2			−0.937073
$695$		0			0
$696$	1494.06	+	2587.79i	0.0813681	+	0.140934i
$697$	−201.611	+	116.400i	−0.0109563	+	0.00632564i
$698$	17965.3	+	10372.3i	0.974208	+	0.562459i
$699$	13595.7			0.735674
$700$		0			0
$701$	−6891.65			−0.371318			−0.185659	−	0.982614i	$-0.559442\pi$
$701$	−6891.65			−0.371318			−0.185659	+	0.982614i	$0.559442\pi$
$702$	−12472.4	−	7200.97i	−0.670573	−	0.387155i
$703$	−975.842	+	563.403i	−0.0523536	+	0.0302264i
$704$	−1187.01	−	2055.96i	−0.0635469	−	0.110066i
$705$		0			0
$706$	8946.02			0.476895
$707$	−2958.17	−	4022.13i	−0.157360	−	0.213957i
$708$			11660.6i			0.618974i
$709$	9356.79	−	16206.4i	0.495630	−	0.858456i	−0.504357	−	0.863495i	$-0.668271\pi$
$709$	9356.79	−	16206.4i	0.495630	−	0.858456i	0.999987	+	0.00503882i	$0.00160391\pi$
$710$		0			0
$711$	808.556	+	1400.46i	0.0426487	+	0.0738697i
$712$	−10483.7	−	6052.76i	−0.551816	−	0.318591i
$713$			19292.9i			1.01336i
$714$	4975.85	−	3659.61i	0.260807	−	0.191817i
$715$		0			0
$716$	−8547.30	+	14804.3i	−0.446128	+	0.772716i
$717$	−9838.86	+	5680.47i	−0.512467	+	0.295873i
$718$	−18815.6	+	10863.2i	−0.977982	+	0.564638i
$719$	−524.836	+	909.043i	−0.0272227	+	0.0471510i	−0.879316	−	0.476239i	$-0.842000\pi$
$719$	−524.836	+	909.043i	−0.0272227	+	0.0471510i	0.852093	+	0.523390i	$0.175333\pi$
$720$		0			0
$721$	16418.7	+	7195.84i	0.848078	+	0.371688i
$722$			13602.2i			0.701140i
$723$	14960.6	+	8637.53i	0.769561	+	0.444306i
$724$	5214.65	+	9032.04i	0.267681	+	0.463637i
$725$		0			0
$726$	−198.545	+	343.890i	−0.0101497	+	0.0175798i
$727$			28893.5i			1.47401i	0.675890	+	0.737003i	$0.263760\pi$
$727$			28893.5i			1.47401i	−0.675890	+	0.737003i	$0.736240\pi$
$728$	6960.33	−	772.553i	0.354350	−	0.0393307i
$729$	−21690.7			−1.10200
$730$		0			0
$731$	9881.97	+	17116.1i	0.499997	+	0.866020i
$732$	−182.281	+	105.240i	−0.00920395	+	0.00531391i
$733$	8035.71	+	4639.42i	0.404919	+	0.233780i	0.688604	−	0.725137i	$-0.258224\pi$
$733$	8035.71	+	4639.42i	0.404919	+	0.233780i	−0.283685	+	0.958917i	$0.591557\pi$
$734$	−23184.9			−1.16590
$735$		0			0
$736$	−4752.29			−0.238005
$737$	−23148.3	−	13364.7i	−1.15696	−	0.667972i
$738$	−80.0993	+	46.2453i	−0.00399525	+	0.00230666i
$739$	−414.012	−	717.090i	−0.0206085	−	0.0356950i	0.855537	−	0.517741i	$-0.173227\pi$
$739$	−414.012	−	717.090i	−0.0206085	−	0.0356950i	−0.876146	+	0.482046i	$0.839894\pi$
$740$		0			0
$741$	1587.84			0.0787188
$742$	−12693.7	+	1408.92i	−0.628034	+	0.0697078i
$743$		−	36020.2i		−	1.77854i	−0.457385	−	0.889269i	$-0.651214\pi$
$743$		−	36020.2i		−	1.77854i	0.457385	−	0.889269i	$-0.348786\pi$
$744$	−2294.56	+	3974.30i	−0.113068	+	0.195840i
$745$		0			0
$746$	10060.0	+	17424.4i	0.493729	+	0.855165i
$747$	2537.19	+	1464.85i	0.124272	+	0.0717484i
$748$		−	5603.34i		−	0.273902i
$749$	−17218.2	−	7546.24i	−0.839972	−	0.368136i
$750$		0			0
$751$	8475.57	−	14680.1i	0.411822	−	0.713296i	−0.583267	−	0.812280i	$-0.698226\pi$
$751$	8475.57	−	14680.1i	0.411822	−	0.713296i	0.995089	+	0.0989842i	$0.0315593\pi$
$752$	5874.39	−	3391.58i	0.284863	−	0.164466i
$753$	6341.32	−	3661.16i	0.306893	−	0.177185i
$754$	−3998.19	+	6925.06i	−0.193111	+	0.334477i
$755$		0			0
$756$	9091.92	−	6686.88i	0.437394	−	0.321692i
$757$		−	18313.3i		−	0.879273i	−0.898176	−	0.439636i	$-0.855107\pi$
$757$		−	18313.3i		−	0.879273i	0.898176	−	0.439636i	$-0.144893\pi$
$758$	6566.24	+	3791.02i	0.314639	+	0.181657i
$759$	12162.5	+	21066.1i	0.581649	+	1.00745i
$760$		0			0
$761$	14615.6	−	25314.9i	0.696207	−	1.20587i	−0.273565	−	0.961853i	$-0.588203\pi$
$761$	14615.6	−	25314.9i	0.696207	−	1.20587i	0.969772	−	0.244012i	$-0.0784638\pi$
$762$			16359.6i			0.777750i
$763$	756.699	+	1028.86i	0.0359035	+	0.0488167i
$764$	14035.8			0.664657
$765$		0			0
$766$	1063.16	+	1841.46i	0.0501484	+	0.0868597i
$767$	−27023.9	+	15602.3i	−1.27220	+	0.734505i
$768$	−978.965	−	565.206i	−0.0459966	−	0.0265561i
$769$	15569.7			0.730116			0.365058	−	0.930985i	$-0.381049\pi$
$769$	15569.7			0.730116			0.365058	+	0.930985i	$0.381049\pi$
$770$		0			0
$771$	−1140.83			−0.0532893
$772$	−227.642	−	131.429i	−0.0106127	−	0.00612726i
$773$	−17125.8	+	9887.58i	−0.796859	+	0.460067i	−0.842372	−	0.538897i	$-0.818841\pi$
$773$	−17125.8	+	9887.58i	−0.796859	+	0.460067i	0.0455126	+	0.998964i	$0.485508\pi$
$774$	3926.07	+	6800.15i	0.182325	+	0.315796i
$775$		0			0
$776$	6825.14			0.315732
$777$	12038.6	−	1336.21i	0.555834	−	0.0616941i
$778$		−	13135.3i		−	0.605300i
$779$	23.4492	−	40.6151i	0.00107850	−	0.00186802i
$780$		0			0
$781$	2994.79	+	5187.13i	0.137211	+	0.237657i
$782$	−9713.99	−	5608.37i	−0.444209	−	0.256464i
$783$			12887.0i			0.588176i
$784$	−1635.00	+	5238.79i	−0.0744808	+	0.238647i
$785$		0			0
$786$	−1916.14	+	3318.84i	−0.0869546	+	0.150610i
$787$	2037.05	−	1176.09i	0.0922654	−	0.0532694i	−0.453157	−	0.891431i	$-0.649702\pi$
$787$	2037.05	−	1176.09i	0.0922654	−	0.0532694i	0.545423	+	0.838161i	$0.316369\pi$
$788$	−1747.53	+	1008.94i	−0.0790015	+	0.0456115i
$789$	10295.2	−	17831.9i	0.464537	−	0.804602i
$790$		0			0
$791$	3586.49	+	32312.6i	0.161215	+	1.45247i
$792$		−	2226.19i		−	0.0998789i
$793$	−487.794	−	281.628i	−0.0218437	−	0.0126115i
$794$	5284.03	+	9152.20i	0.236175	+	0.409067i
$795$		0			0
$796$	9897.66	−	17143.3i	0.440720	−	0.763350i
$797$		−	22204.6i		−	0.986858i	−0.869786	−	0.493429i	$-0.835743\pi$
$797$		−	22204.6i		−	0.986858i	0.869786	−	0.493429i	$-0.164257\pi$
$798$	−499.483	+	1139.67i	−0.0221573	+	0.0505561i
$799$	16010.2			0.708885
$800$		0			0
$801$	−5675.86	−	9830.87i	−0.250370	−	0.433654i
$802$	−1582.95	+	913.917i	−0.0696957	+	0.0402388i
$803$	−19529.5	−	11275.4i	−0.858259	−	0.495516i
$804$	−12727.5			−0.558288
$805$		0			0
$806$	−12280.8			−0.536689
$807$	−15760.8	−	9099.52i	−0.687494	−	0.396925i
$808$	−1867.75	+	1078.35i	−0.0813210	+	0.0469507i
$809$	2216.30	+	3838.75i	0.0963178	+	0.166827i	0.910158	−	0.414262i	$-0.135960\pi$
$809$	2216.30	+	3838.75i	0.0963178	+	0.166827i	−0.813840	+	0.581089i	$0.802627\pi$
$810$		0			0
$811$	38921.6			1.68523			0.842615	−	0.538517i	$-0.181015\pi$
$811$	38921.6			1.68523			0.842615	+	0.538517i	$0.181015\pi$
$812$	−3712.75	−	5048.10i	−0.160458	−	0.218169i
$813$		−	10988.7i		−	0.474035i
$814$	5494.08	−	9516.03i	0.236569	−	0.409750i
$815$		0			0
$816$	−1334.04	−	2310.63i	−0.0572315	−	0.0991279i
$817$	−3448.08	−	1990.75i	−0.147654	−	0.0852480i
$818$		−	24013.7i		−	1.02643i
$819$	6014.70	+	2636.07i	0.256619	+	0.112469i
$820$		0			0
$821$	18684.6	−	32362.7i	0.794272	−	1.37572i	−0.129028	−	0.991641i	$-0.541186\pi$
$821$	18684.6	−	32362.7i	0.794272	−	1.37572i	0.923300	−	0.384079i	$-0.125481\pi$
$822$	19534.6	−	11278.3i	0.828888	−	0.478559i
$823$	15334.3	−	8853.29i	0.649479	−	0.374977i	−0.138777	−	0.990324i	$-0.544317\pi$
$823$	15334.3	−	8853.29i	0.649479	−	0.374977i	0.788257	+	0.615346i	$0.210984\pi$
$824$	3871.73	−	6706.03i	0.163687	−	0.283514i
$825$		0			0
$826$	−2697.63	−	24304.3i	−0.113635	−	1.02380i
$827$			1336.91i			0.0562141i	0.999605	+	0.0281070i	$0.00894793\pi$
$827$			1336.91i			0.0562141i	−0.999605	+	0.0281070i	$0.991052\pi$
$828$	−3859.33	−	2228.19i	−0.161982	−	0.0935203i
$829$	9366.66	+	16223.5i	0.392422	+	0.679694i	0.992768	−	0.120045i	$-0.0383040\pi$
$829$	9366.66	+	16223.5i	0.392422	+	0.679694i	−0.600347	+	0.799740i	$0.704971\pi$
$830$		0			0
$831$	−14028.3	+	24297.8i	−0.585604	+	1.01430i
$832$		−	3025.05i		−	0.126051i
$833$	−9524.55	+	8778.88i	−0.396166	+	0.365150i
$834$	24232.7			1.00613
$835$		0			0
$836$	564.405	+	977.578i	0.0233497	+	0.0404429i
$837$	−17140.1	+	9895.83i	−0.707823	+	0.408662i
$838$	−4408.19	−	2545.07i	−0.181716	−	0.104914i
$839$	−33497.2			−1.37837			−0.689185	−	0.724585i	$-0.742031\pi$
$839$	−33497.2			−1.37837			−0.689185	+	0.724585i	$0.742031\pi$
$840$		0			0
$841$	−17233.8			−0.706622
$842$	13101.9	+	7564.36i	0.536247	+	0.309602i
$843$	28664.4	−	16549.4i	1.17112	−	0.676146i
$844$	7883.83	+	13655.2i	0.321531	+	0.556909i
$845$		0			0
$846$	6360.78			0.258497
$847$	334.272	−	762.705i	0.0135605	−	0.0309408i
$848$			5516.85i			0.223407i
$849$	−19194.1	+	33245.2i	−0.775901	+	1.34390i
$850$		0			0
$851$	−10998.0	−	19049.1i	−0.443017	−	0.767328i
$852$	2469.91	+	1426.00i	0.0993165	+	0.0573404i
$853$			32741.3i			1.31423i	0.753789	+	0.657117i	$0.228224\pi$
$853$			32741.3i			1.31423i	−0.753789	+	0.657117i	$0.771776\pi$
$854$	355.582	−	261.522i	0.0142480	−	0.0104790i
$855$		0			0
$856$	−4060.26	+	7032.57i	−0.162122	+	0.280804i
$857$	32692.6	−	18875.1i	1.30310	−	0.752346i	0.322166	−	0.946683i	$-0.395589\pi$
$857$	32692.6	−	18875.1i	1.30310	−	0.752346i	0.980935	+	0.194338i	$0.0622557\pi$
$858$	−13409.5	+	7741.98i	−0.533558	+	0.308050i
$859$	−7664.57	+	13275.4i	−0.304438	+	0.527301i	−0.977136	−	0.212615i	$-0.931802\pi$
$859$	−7664.57	+	13275.4i	−0.304438	+	0.527301i	0.672698	+	0.739917i	$0.265135\pi$
$860$		0			0
$861$	−406.119	+	298.690i	−0.0160749	+	0.0118227i
$862$		−	32331.0i		−	1.27749i
$863$	−16521.5	−	9538.67i	−0.651677	−	0.376246i	0.137422	−	0.990513i	$-0.456119\pi$
$863$	−16521.5	−	9538.67i	−0.651677	−	0.376246i	−0.789098	+	0.614267i	$0.789452\pi$
$864$	−2437.58	−	4222.01i	−0.0959817	−	0.166245i
$865$		0			0
$866$	−14107.6	+	24435.0i	−0.553574	+	0.958818i
$867$			15396.8i			0.603116i
$868$	3863.14	−	8814.49i	0.151064	−	0.344681i
$869$	7996.05			0.312138
$870$		0			0
$871$	−17029.7	−	29496.4i	−0.662492	−	1.14747i
$872$	477.771	−	275.841i	0.0185543	−	0.0107123i
$873$	5542.69	+	3200.07i	0.214881	+	0.124062i
$874$	2259.65			0.0874528
$875$		0			0
$876$	−10737.8			−0.414151
$877$	−23577.7	−	13612.6i	−0.907826	−	0.524134i	−0.0280952	−	0.999605i	$-0.508944\pi$
$877$	−23577.7	−	13612.6i	−0.907826	−	0.524134i	−0.879731	+	0.475471i	$0.842278\pi$
$878$	7110.00	−	4104.96i	0.273292	−	0.157785i
$879$	−17852.7	−	30921.8i	−0.685047	−	1.18654i
$880$		0			0
$881$	8754.14			0.334773			0.167386	−	0.985891i	$-0.446467\pi$
$881$	8754.14			0.334773			0.167386	+	0.985891i	$0.446467\pi$
$882$	−3784.07	+	3487.82i	−0.144463	+	0.133153i
$883$		−	32353.2i		−	1.23304i	−0.787340	−	0.616519i	$-0.788542\pi$
$883$		−	32353.2i		−	1.23304i	0.787340	−	0.616519i	$-0.211458\pi$
$884$	3569.98	−	6183.38i	0.135827	−	0.235260i
$885$		0			0
$886$	−1929.29	−	3341.63i	−0.0731555	−	0.126709i
$887$	−16978.2	−	9802.39i	−0.642698	−	0.371062i	0.142955	−	0.989729i	$-0.454340\pi$
$887$	−16978.2	−	9802.39i	−0.642698	−	0.371062i	−0.785653	+	0.618667i	$0.787673\pi$
$888$		−	5232.13i		−	0.197724i
$889$	−3784.71	−	34098.4i	−0.142784	−	1.28642i
$890$		0			0
$891$	−8720.29	+	15104.0i	−0.327879	+	0.567904i
$892$	−3250.35	+	1876.59i	−0.122007	+	0.0704405i
$893$	−2793.19	+	1612.65i	−0.104670	+	0.0604314i
$894$	3649.50	−	6321.12i	0.136530	−	0.236476i
$895$		0			0
$896$	2171.22	+	951.584i	0.0809547	+	0.0354801i
$897$			30995.7i			1.15375i
$898$	−32475.9	−	18750.0i	−1.20683	−	0.696766i
$899$	5494.45	+	9516.66i	0.203838	+	0.353057i
$900$		0			0
$901$	−6510.65	+	11276.8i	−0.240734	+	0.416963i
$902$			457.334i			0.0168820i
$903$	25357.8	+	34478.1i	0.934500	+	1.27061i
$904$	14043.4			0.516679
$905$		0			0
$906$	−7332.68	−	12700.6i	−0.268888	−	0.465727i
$907$	4806.82	−	2775.22i	0.175973	−	0.101598i	−0.409426	−	0.912343i	$-0.634271\pi$
$907$	4806.82	−	2775.22i	0.175973	−	0.101598i	0.585399	+	0.810745i	$0.300938\pi$
$908$	−20716.6	−	11960.7i	−0.757164	−	0.437149i
$909$	−2022.40			−0.0737941
$910$		0			0
$911$	22886.6			0.832347			0.416173	−	0.909285i	$-0.363371\pi$
$911$	22886.6			0.832347			0.416173	+	0.909285i	$0.363371\pi$
$912$	465.484	+	268.747i	0.0169010	+	0.00975780i
$913$	12545.5	−	7243.17i	0.454761	−	0.262556i
$914$	6641.31	+	11503.1i	0.240345	+	0.416289i
$915$		0			0
$916$	−17513.9			−0.631743
$917$	3226.01	−	7360.77i	0.116175	−	0.265075i
$918$		−	11506.7i		−	0.413703i
$919$	21732.9	−	37642.5i	0.780089	−	1.35115i	−0.151800	−	0.988411i	$-0.548507\pi$
$919$	21732.9	−	37642.5i	0.780089	−	1.35115i	0.931889	−	0.362743i	$-0.118160\pi$
$920$		0			0
$921$	−13766.2	−	23843.7i	−0.492519	−	0.853068i
$922$	5030.47	+	2904.35i	0.179685	+	0.103741i
$923$			7632.12i			0.272172i
$924$	−1338.59	−	12060.0i	−0.0476583	−	0.429379i
$925$		0			0
$926$	−6750.67	+	11692.5i	−0.239569	+	0.414945i
$927$	6288.45	−	3630.64i	0.222804	−	0.128636i
$928$	−2344.18	+	1353.42i	−0.0829220	+	0.0478750i
$929$	−22368.4	+	38743.2i	−0.789970	+	1.36827i	0.136014	+	0.990707i	$0.456571\pi$
$929$	−22368.4	+	38743.2i	−0.789970	+	1.36827i	−0.925984	+	0.377562i	$0.876763\pi$
$930$		0			0
$931$	777.420	−	2490.97i	0.0273672	−	0.0876887i
$932$			12315.9i			0.432853i
$933$	−9853.98	−	5689.20i	−0.345772	−	0.199631i
$934$	2625.96	+	4548.29i	0.0919956	+	0.159341i
$935$		0			0
$936$	1418.34	−	2456.63i	0.0495297	−	0.0857880i
$937$			7708.34i			0.268752i	0.990930	+	0.134376i	$0.0429030\pi$
$937$			7708.34i			0.268752i	−0.990930	+	0.134376i	$0.957097\pi$
$938$	26528.0	−	2944.44i	0.923421	−	0.102494i
$939$	34845.4			1.21101
$940$		0			0
$941$	−14053.3	−	24341.1i	−0.486849	−	0.843248i	0.513036	−	0.858367i	$-0.328521\pi$
$941$	−14053.3	−	24341.1i	−0.486849	−	0.843248i	−0.999886	+	0.0151190i	$0.995187\pi$
$942$	27998.6	−	16165.0i	0.968411	−	0.559113i
$943$	792.837	+	457.745i	0.0273789	+	0.0158072i
$944$	−10563.0			−0.364190
$945$		0			0
$946$	38826.1			1.33440
$947$	27260.6	+	15738.9i	0.935428	+	0.540070i	0.888524	−	0.458830i	$-0.151731\pi$
$947$	27260.6	+	15738.9i	0.935428	+	0.540070i	0.0469041	+	0.998899i	$0.485064\pi$
$948$	3297.31	−	1903.70i	0.112966	−	0.0652208i
$949$	−14367.4	−	24885.1i	−0.491451	−	0.851218i
$950$		0			0
$951$	28534.1			0.972957
$952$	3315.11	+	4507.44i	0.112861	+	0.153453i
$953$			40699.5i			1.38341i	0.722182	+	0.691703i	$0.243139\pi$
$953$			40699.5i			1.38341i	−0.722182	+	0.691703i	$0.756861\pi$
$954$	−2586.66	+	4480.22i	−0.0877842	+	0.152047i
$955$		0			0
$956$	−5145.74	−	8912.68i	−0.174085	−	0.301524i
$957$	11998.9	+	6927.58i	0.405298	+	0.233999i
$958$		−	19238.0i		−	0.648802i
$959$	−38106.8	+	28026.6i	−1.28314	+	0.943719i
$960$		0			0
$961$	6457.18	−	11184.2i	0.216749	−	0.375421i
$962$	12125.6	−	7000.73i	0.406388	−	0.234628i
$963$	−6594.66	+	3807.43i	−0.220675	+	0.127407i
$964$	−7824.44	+	13552.3i	−0.261419	+	0.452791i
$965$		0			0
$966$	−22247.1	−	9750.28i	−0.740984	−	0.324752i
$967$		−	7786.47i		−	0.258941i	−0.991583	−	0.129471i	$-0.958672\pi$
$967$		−	7786.47i		−	0.258941i	0.991583	−	0.129471i	$-0.0413278\pi$
$968$	−311.518	−	179.855i	−0.0103436	−	0.00597186i
$969$	634.319	+	1098.67i	0.0210292	+	0.0364236i
$970$		0			0
$971$	9385.53	−	16256.2i	0.310192	−	0.537268i	−0.668212	−	0.743971i	$-0.732940\pi$
$971$	9385.53	−	16256.2i	0.310192	−	0.537268i	0.978404	+	0.206703i	$0.0662735\pi$
$972$		−	8149.16i		−	0.268914i
$973$	−50508.3	+	5606.11i	−1.66415	+	0.184711i
$974$	22853.1			0.751808
$975$		0			0
$976$	−95.3331	−	165.122i	−0.00312658	−	0.00541539i
$977$	−25018.4	+	14444.4i	−0.819253	+	0.472996i	−0.850159	−	0.526526i	$-0.823494\pi$
$977$	−25018.4	+	14444.4i	−0.819253	+	0.472996i	0.0309059	+	0.999522i	$0.490161\pi$
$978$	16781.9	+	9689.03i	0.548697	+	0.316791i
$979$	−56130.2			−1.83241
$980$		0			0
$981$	517.329			0.0168369
$982$	−12366.1	−	7139.55i	−0.401850	−	0.232008i
$983$	−6332.49	+	3656.06i	−0.205468	+	0.118627i	−0.599203	−	0.800597i	$-0.704516\pi$
$983$	−6332.49	+	3656.06i	−0.205468	+	0.118627i	0.393736	+	0.919224i	$0.371183\pi$
$984$	108.882	+	188.589i	0.00352748	+	0.00610977i
$985$		0			0
$986$	−6388.88			−0.206352
$987$	34458.6	−	3824.68i	1.11127	−	0.123345i
$988$			1438.37i			0.0463163i
$989$	38860.9	−	67309.1i	1.24945	−	2.16411i
$990$		0			0
$991$	24476.6	+	42394.8i	0.784587	+	1.35895i	0.929245	+	0.369463i	$0.120459\pi$
$991$	24476.6	+	42394.8i	0.784587	+	1.35895i	−0.144658	+	0.989482i	$0.546208\pi$
$992$	−3600.18	−	2078.56i	−0.115228	−	0.0665266i
$993$			23301.6i			0.744667i
$994$	−5477.94	−	2400.82i	−0.174799	−	0.0766092i
$995$		0			0
$996$	3448.91	−	5973.69i	0.109722	−	0.190044i
$997$	33788.0	−	19507.5i	1.07330	−	0.619668i	0.144216	−	0.989546i	$-0.453934\pi$
$997$	33788.0	−	19507.5i	1.07330	−	0.619668i	0.929080	+	0.369879i	$0.120601\pi$
$998$	−9805.02	+	5660.93i	−0.310995	+	0.179553i
$999$	11282.4	−	19541.6i	0.357316	−	0.618889i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.4.j.h.149.5		12
5.2	odd	4		350.4.e.i.51.2	✓	6
5.3	odd	4		350.4.e.j.51.2	yes	6
5.4	even	2	inner	350.4.j.h.149.2		12
7.4	even	3	inner	350.4.j.h.249.2		12
35.2	odd	12		2450.4.a.ci.1.2		3
35.4	even	6	inner	350.4.j.h.249.5		12
35.12	even	12		2450.4.a.ch.1.2		3
35.18	odd	12		350.4.e.j.151.2	yes	6
35.23	odd	12		2450.4.a.cc.1.2		3
35.32	odd	12		350.4.e.i.151.2	yes	6
35.33	even	12		2450.4.a.cd.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.4.e.i.51.2	✓	6	5.2	odd	4
350.4.e.i.151.2	yes	6	35.32	odd	12
350.4.e.j.51.2	yes	6	5.3	odd	4
350.4.e.j.151.2	yes	6	35.18	odd	12
350.4.j.h.149.2		12	5.4	even	2	inner
350.4.j.h.149.5		12	1.1	even	1	trivial
350.4.j.h.249.2		12	7.4	even	3	inner
350.4.j.h.249.5		12	35.4	even	6	inner
2450.4.a.cc.1.2		3	35.23	odd	12
2450.4.a.cd.1.2		3	35.33	even	12
2450.4.a.ch.1.2		3	35.12	even	12
2450.4.a.ci.1.2		3	35.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.73205 + 1.00000i) q^{2} +(3.82408 - 2.20784i) q^{3} +(2.00000 + 3.46410i) q^{4} +8.83134 q^{6} +(-18.4072 + 2.04309i) q^{7} +8.00000i q^{8} +(-3.75092 + 6.49679i) q^{9} +(18.5470 + 32.1243i) q^{11} +(15.2963 + 8.83134i) q^{12} +47.2663i q^{13} +(-33.9253 - 14.8685i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-32.7050 + 18.8822i) q^{17} +(-12.9936 + 7.50184i) q^{18} +(3.80388 - 6.58852i) q^{19} +(-65.8800 + 48.4531i) q^{21} +74.1880i q^{22} +(128.613 + 74.2546i) q^{23} +(17.6627 + 30.5927i) q^{24} +(-47.2663 + 81.8677i) q^{26} +152.349i q^{27} +(-43.8919 - 59.6783i) q^{28} +84.5885 q^{29} +(64.9551 + 112.505i) q^{31} +(-27.7128 + 16.0000i) q^{32} +(141.851 + 81.8974i) q^{33} -75.5290 q^{34} -30.0074 q^{36} +(-128.269 - 74.0562i) q^{37} +(13.1770 - 7.60777i) q^{38} +(104.356 + 180.750i) q^{39} +6.16453 q^{41} +(-162.560 + 18.0432i) q^{42} -523.347i q^{43} +(-74.1880 + 128.497i) q^{44} +(148.509 + 257.226i) q^{46} +(-367.149 - 211.974i) q^{47} +70.6507i q^{48} +(334.652 - 75.2151i) q^{49} +(-83.3778 + 144.415i) q^{51} +(-163.735 + 94.5327i) q^{52} +(298.608 - 172.401i) q^{53} +(-152.349 + 263.876i) q^{54} +(-16.3447 - 147.258i) q^{56} -33.5934i q^{57} +(146.512 + 84.5885i) q^{58} +(330.093 + 571.737i) q^{59} +(-5.95832 + 10.3201i) q^{61} +259.820i q^{62} +(55.7706 - 127.251i) q^{63} -64.0000 q^{64} +(163.795 + 283.701i) q^{66} +(-624.046 + 360.293i) q^{67} +(-130.820 - 75.5290i) q^{68} +655.768 q^{69} +161.471 q^{71} +(-51.9743 - 30.0074i) q^{72} +(-526.488 + 303.968i) q^{73} +(-148.112 - 256.538i) q^{74} +30.4311 q^{76} +(-407.031 - 553.427i) q^{77} +417.425i q^{78} +(107.781 - 186.682i) q^{79} +(235.086 + 407.181i) q^{81} +(10.6773 + 6.16453i) q^{82} -390.531i q^{83} +(-299.606 - 131.309i) q^{84} +(523.347 - 906.464i) q^{86} +(323.473 - 186.757i) q^{87} +(-256.995 + 148.376i) q^{88} +(-756.595 + 1310.46i) q^{89} +(-96.5692 - 870.042i) q^{91} +594.037i q^{92} +(496.787 + 286.820i) q^{93} +(-423.948 - 734.299i) q^{94} +(-70.6507 + 122.371i) q^{96} -853.143i q^{97} +(654.849 + 204.375i) q^{98} -278.273 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 24 q^{4} + 24 q^{6} + 112 q^{9} + 52 q^{11} + 16 q^{14} - 96 q^{16} - 36 q^{19} + 370 q^{21} + 48 q^{24} + 320 q^{26} + 1616 q^{29} + 1230 q^{31} + 240 q^{34} + 896 q^{36} - 180 q^{39} - 404 q^{41}+ \cdots + 228 q^{99}+O(q^{100}) \) 12 * q + 24 * q^4 + 24 * q^6 + 112 * q^9 + 52 * q^11 + 16 * q^14 - 96 * q^16 - 36 * q^19 + 370 * q^21 + 48 * q^24 + 320 * q^26 + 1616 * q^29 + 1230 * q^31 + 240 * q^34 + 896 * q^36 - 180 * q^39 - 404 * q^41 - 208 * q^44 + 212 * q^46 + 432 * q^49 + 678 * q^51 - 1296 * q^54 + 896 * q^56 - 182 * q^59 + 1294 * q^61 - 768 * q^64 - 1256 * q^66 + 6192 * q^69 + 2132 * q^71 + 1704 * q^74 - 288 * q^76 + 2842 * q^79 + 2786 * q^81 + 608 * q^84 + 996 * q^86 - 388 * q^89 - 7710 * q^91 - 1608 * q^94 - 192 * q^96 + 228 * q^99

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