LMFDB - Embedded newform 225.4.k.e.124.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(49,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("225.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			124.13
Character	$\chi$	$=$	225.124
Dual form			225.4.k.e.49.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.412258 + 0.238017i) q^{2} +(-4.17746 + 3.09012i) q^{3} +(-3.88670 - 6.73195i) q^{4} +(-2.45769 + 0.279619i) q^{6} +(10.9820 + 6.34045i) q^{7} -7.50869i q^{8} +(7.90234 - 25.8177i) q^{9} +O(q^{10})$	\(q+(0.412258 + 0.238017i) q^{2} +(-4.17746 + 3.09012i) q^{3} +(-3.88670 - 6.73195i) q^{4} +(-2.45769 + 0.279619i) q^{6} +(10.9820 + 6.34045i) q^{7} -7.50869i q^{8} +(7.90234 - 25.8177i) q^{9} +(0.794994 - 1.37697i) q^{11} +(37.0390 + 16.1121i) q^{12} +(9.29622 - 5.36718i) q^{13} +(3.01828 + 5.22781i) q^{14} +(-29.3064 + 50.7601i) q^{16} +69.7787i q^{17} +(9.40287 - 8.76266i) q^{18} -98.5661 q^{19} +(-65.4695 + 7.44864i) q^{21} +(0.655486 - 0.378445i) q^{22} +(-27.3278 + 15.7777i) q^{23} +(23.2027 + 31.3672i) q^{24} +5.10993 q^{26} +(46.7680 + 132.272i) q^{27} -98.5736i q^{28} +(-150.627 + 260.893i) q^{29} +(58.6364 + 101.561i) q^{31} +(-76.1853 + 43.9856i) q^{32} +(0.933944 + 8.20886i) q^{33} +(-16.6086 + 28.7669i) q^{34} +(-204.517 + 47.1473i) q^{36} +169.562i q^{37} +(-40.6347 - 23.4605i) q^{38} +(-22.2494 + 51.1476i) q^{39} +(-70.9376 - 122.868i) q^{41} +(-28.7633 - 12.5121i) q^{42} +(-260.018 - 150.121i) q^{43} -12.3596 q^{44} -15.0215 q^{46} +(422.122 + 243.712i) q^{47} +(-34.4286 - 302.608i) q^{48} +(-91.0974 - 157.785i) q^{49} +(-215.625 - 291.498i) q^{51} +(-72.2632 - 41.7212i) q^{52} +459.166i q^{53} +(-12.2024 + 65.6616i) q^{54} +(47.6084 - 82.4602i) q^{56} +(411.756 - 304.581i) q^{57} +(-124.194 + 71.7037i) q^{58} +(-250.099 - 433.185i) q^{59} +(-290.915 + 503.880i) q^{61} +55.8259i q^{62} +(250.479 - 233.425i) q^{63} +427.024 q^{64} +(-1.56883 + 3.60647i) q^{66} +(-433.823 + 250.468i) q^{67} +(469.747 - 271.209i) q^{68} +(65.4059 - 150.357i) q^{69} +1066.69 q^{71} +(-193.857 - 59.3362i) q^{72} +435.288i q^{73} +(-40.3588 + 69.9034i) q^{74} +(383.096 + 663.542i) q^{76} +(17.4612 - 10.0812i) q^{77} +(-21.3465 + 15.7903i) q^{78} +(187.644 - 325.009i) q^{79} +(-604.106 - 408.040i) q^{81} -67.5375i q^{82} +(1119.97 + 646.617i) q^{83} +(304.604 + 411.787i) q^{84} +(-71.4630 - 123.778i) q^{86} +(-176.954 - 1555.33i) q^{87} +(-10.3392 - 5.96936i) q^{88} +403.296 q^{89} +136.121 q^{91} +(212.430 + 122.646i) q^{92} +(-558.787 - 243.074i) q^{93} +(116.016 + 200.945i) q^{94} +(182.340 - 419.170i) q^{96} +(-1369.59 - 790.735i) q^{97} -86.7311i q^{98} +(-29.2679 - 31.4062i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 96 q^{4} - 26 q^{6} + 122 q^{9}+O(q^{10}) $ 48 * q + 96 * q^4 - 26 * q^6 + 122 * q^9	$ 48 q + 96 q^{4} - 26 q^{6} + 122 q^{9} - 58 q^{11} - 138 q^{14} - 384 q^{16} + 300 q^{19} - 120 q^{21} - 684 q^{24} - 616 q^{26} + 212 q^{29} - 120 q^{31} - 216 q^{34} + 2606 q^{36} + 820 q^{39} + 706 q^{41} - 2284 q^{44} + 1080 q^{46} + 1332 q^{49} - 2738 q^{51} + 4256 q^{54} + 1140 q^{56} + 964 q^{59} - 804 q^{61} - 3900 q^{64} + 4082 q^{66} - 5712 q^{69} - 3776 q^{71} + 20 q^{74} + 924 q^{76} + 516 q^{79} + 6142 q^{81} + 5406 q^{84} - 3904 q^{86} + 2952 q^{89} - 2472 q^{91} + 126 q^{94} - 20848 q^{96} + 3394 q^{99}+O(q^{100}) $ 48 * q + 96 * q^4 - 26 * q^6 + 122 * q^9 - 58 * q^11 - 138 * q^14 - 384 * q^16 + 300 * q^19 - 120 * q^21 - 684 * q^24 - 616 * q^26 + 212 * q^29 - 120 * q^31 - 216 * q^34 + 2606 * q^36 + 820 * q^39 + 706 * q^41 - 2284 * q^44 + 1080 * q^46 + 1332 * q^49 - 2738 * q^51 + 4256 * q^54 + 1140 * q^56 + 964 * q^59 - 804 * q^61 - 3900 * q^64 + 4082 * q^66 - 5712 * q^69 - 3776 * q^71 + 20 * q^74 + 924 * q^76 + 516 * q^79 + 6142 * q^81 + 5406 * q^84 - 3904 * q^86 + 2952 * q^89 - 2472 * q^91 + 126 * q^94 - 20848 * q^96 + 3394 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.412258	+	0.238017i	0.145755	+	0.0841519i	0.571104	−	0.820878i	$-0.306515\pi$
$2$	0.412258	+	0.238017i	0.145755	+	0.0841519i	−0.425349	+	0.905030i	$0.639849\pi$
$3$	−4.17746	+	3.09012i	−0.803953	+	0.594694i
$3$	−4.17746	+	3.09012i	−0.803953	+	0.594694i
$4$	−3.88670	−	6.73195i	−0.485837	−	0.841494i
$5$		0			0
$5$		0			0
$6$	−2.45769	+	0.279619i	−0.167225	+	0.0190256i
$7$	10.9820	+	6.34045i	0.592971	+	0.342352i	0.766271	−	0.642517i	$-0.222110\pi$
$7$	10.9820	+	6.34045i	0.592971	+	0.342352i	−0.173300	+	0.984869i	$0.555443\pi$
$8$		−	7.50869i		−	0.331840i
$9$	7.90234	−	25.8177i	0.292679	−	0.956211i
$10$		0			0
$11$	0.794994	−	1.37697i	0.0217909	−	0.0377429i	−0.854924	−	0.518753i	$-0.826397\pi$
$11$	0.794994	−	1.37697i	0.0217909	−	0.0377429i	0.876715	+	0.481010i	$0.159730\pi$
$12$	37.0390	+	16.1121i	0.891021	+	0.387597i
$13$	9.29622	−	5.36718i	0.198331	−	0.114507i	−0.397546	−	0.917582i	$-0.630138\pi$
$13$	9.29622	−	5.36718i	0.198331	−	0.114507i	0.595877	+	0.803076i	$0.296805\pi$
$14$	3.01828	+	5.22781i	0.0576191	+	0.0997993i
$15$		0			0
$16$	−29.3064	+	50.7601i	−0.457912	+	0.793127i
$17$			69.7787i			0.995519i	0.867315	+	0.497760i	$0.165844\pi$
$17$			69.7787i			0.995519i	−0.867315	+	0.497760i	$0.834156\pi$
$18$	9.40287	−	8.76266i	0.123127	−	0.114743i
$19$	−98.5661			−1.19014			−0.595069	−	0.803675i	$-0.702875\pi$
$19$	−98.5661			−1.19014			−0.595069	+	0.803675i	$0.702875\pi$
$20$		0			0
$21$	−65.4695	+	7.44864i	−0.680315	+	0.0774013i
$22$	0.655486	−	0.378445i	0.00635227	−	0.00366749i
$23$	−27.3278	+	15.7777i	−0.247750	+	0.143038i	−0.618734	−	0.785601i	$-0.712354\pi$
$23$	−27.3278	+	15.7777i	−0.247750	+	0.143038i	0.370984	+	0.928639i	$0.379021\pi$
$24$	23.2027	+	31.3672i	0.197343	+	0.266784i
$25$		0			0
$26$	5.10993			0.0385438
$27$	46.7680	+	132.272i	0.333352	+	0.942802i
$28$		−	98.5736i		−	0.665309i
$29$	−150.627	+	260.893i	−0.964507	+	1.67058i	−0.253574	+	0.967316i	$0.581606\pi$
$29$	−150.627	+	260.893i	−0.964507	+	1.67058i	−0.710933	+	0.703260i	$0.751727\pi$
$30$		0			0
$31$	58.6364	+	101.561i	0.339723	+	0.588417i	0.984380	−	0.176054i	$-0.0563334\pi$
$31$	58.6364	+	101.561i	0.339723	+	0.588417i	−0.644658	+	0.764471i	$0.723000\pi$
$32$	−76.1853	+	43.9856i	−0.420868	+	0.242988i
$33$	0.933944	+	8.20886i	0.00492663	+	0.0433024i
$34$	−16.6086	+	28.7669i	−0.0837748	+	0.145102i
$35$		0			0
$36$	−204.517	+	47.1473i	−0.946840	+	0.218275i
$37$			169.562i			0.753402i	0.926335	+	0.376701i	$0.122941\pi$
$37$			169.562i			0.753402i	−0.926335	+	0.376701i	$0.877059\pi$
$38$	−40.6347	−	23.4605i	−0.173469	−	0.100152i
$39$	−22.2494	+	51.1476i	−0.0913526	+	0.210004i
$40$		0			0
$41$	−70.9376	−	122.868i	−0.270210	−	0.468017i	0.698706	−	0.715409i	$-0.253760\pi$
$41$	−70.9376	−	122.868i	−0.270210	−	0.468017i	−0.968915	+	0.247392i	$0.920426\pi$
$42$	−28.7633	−	12.5121i	−0.105673	−	0.0459682i
$43$	−260.018	−	150.121i	−0.922147	−	0.532402i	−0.0378277	−	0.999284i	$-0.512044\pi$
$43$	−260.018	−	150.121i	−0.922147	−	0.532402i	−0.884319	+	0.466882i	$0.845377\pi$
$44$	−12.3596			−0.0423472
$45$		0			0
$46$	−15.0215			−0.0481478
$47$	422.122	+	243.712i	1.31006	+	0.756364i	0.982106	−	0.188330i	$-0.0603075\pi$
$47$	422.122	+	243.712i	1.31006	+	0.756364i	0.327954	+	0.944694i	$0.393641\pi$
$48$	−34.4286	−	302.608i	−0.103528	−	0.909953i
$49$	−91.0974	−	157.785i	−0.265590	−	0.460016i
$50$		0			0
$51$	−215.625	−	291.498i	−0.592029	−	0.800350i
$52$	−72.2632	−	41.7212i	−0.192713	−	0.111263i
$53$			459.166i			1.19002i	0.803717	+	0.595012i	$0.202853\pi$
$53$			459.166i			1.19002i	−0.803717	+	0.595012i	$0.797147\pi$
$54$	−12.2024	+	65.6616i	−0.0307508	+	0.165471i
$55$		0			0
$56$	47.6084	−	82.4602i	0.113606	−	0.196772i
$57$	411.756	−	304.581i	0.956814	−	0.707767i
$58$	−124.194	+	71.7037i	−0.281164	+	0.162330i
$59$	−250.099	−	433.185i	−0.551867	−	0.955862i	−0.998140	−	0.0609650i	$-0.980582\pi$
$59$	−250.099	−	433.185i	−0.551867	−	0.955862i	0.446273	−	0.894897i	$-0.352751\pi$
$60$		0			0
$61$	−290.915	+	503.880i	−0.610621	+	1.05763i	0.380515	+	0.924775i	$0.375747\pi$
$61$	−290.915	+	503.880i	−0.610621	+	1.05763i	−0.991136	+	0.132852i	$0.957587\pi$
$62$			55.8259i			0.114353i
$63$	250.479	−	233.425i	0.500911	−	0.466806i
$64$	427.024			0.834032
$65$		0			0
$66$	−1.56883	+	3.60647i	−0.00292589	+	0.00672614i
$67$	−433.823	+	250.468i	−0.791044	+	0.456709i	−0.840330	−	0.542075i	$-0.817639\pi$
$67$	−433.823	+	250.468i	−0.791044	+	0.456709i	0.0492862	+	0.998785i	$0.484305\pi$
$68$	469.747	−	271.209i	0.837724	−	0.483660i
$69$	65.4059	−	150.357i	0.114115	−	0.262331i
$70$		0			0
$71$	1066.69			1.78299			0.891495	−	0.453031i	$-0.149657\pi$
$71$	1066.69			1.78299			0.891495	+	0.453031i	$0.149657\pi$
$72$	−193.857	−	59.3362i	−0.317309	−	0.0971227i
$73$			435.288i			0.697899i	0.937141	+	0.348950i	$0.113462\pi$
$73$			435.288i			0.697899i	−0.937141	+	0.348950i	$0.886538\pi$
$74$	−40.3588	+	69.9034i	−0.0634002	+	0.109812i
$75$		0			0
$76$	383.096	+	663.542i	0.578213	+	1.00149i
$77$	17.4612	−	10.0812i	0.0258427	−	0.0149203i
$78$	−21.3465	+	15.7903i	−0.0309874	+	0.0229218i
$79$	187.644	−	325.009i	0.267236	−	0.462866i	−0.700911	−	0.713248i	$-0.747223\pi$
$79$	187.644	−	325.009i	0.267236	−	0.462866i	0.968147	+	0.250383i	$0.0805564\pi$
$80$		0			0
$81$	−604.106	−	408.040i	−0.828678	−	0.559726i
$82$		−	67.5375i		−	0.0909546i
$83$	1119.97	+	646.617i	1.48112	+	0.855126i	0.999771	−	0.0214014i	$-0.00681280\pi$
$83$	1119.97	+	646.617i	1.48112	+	0.855126i	0.481351	+	0.876528i	$0.340146\pi$
$84$	304.604	+	411.787i	0.395655	+	0.534877i
$85$		0			0
$86$	−71.4630	−	123.778i	−0.0896053	−	0.155201i
$87$	−176.954	−	1555.33i	−0.218062	−	1.91665i
$88$	−10.3392	−	5.96936i	−0.0125246	−	0.00723109i
$89$	403.296			0.480330			0.240165	−	0.970732i	$-0.422799\pi$
$89$	403.296			0.480330			0.240165	+	0.970732i	$0.422799\pi$
$90$		0			0
$91$	136.121			0.156806
$92$	212.430	+	122.646i	0.240732	+	0.138987i
$93$	−558.787	−	243.074i	−0.623049	−	0.271028i
$94$	116.016	+	200.945i	0.127299	+	0.220488i
$95$		0			0
$96$	182.340	−	419.170i	0.193854	−	0.445639i
$97$	−1369.59	−	790.735i	−1.43362	−	0.827700i	−0.436225	−	0.899838i	$-0.643685\pi$
$97$	−1369.59	−	790.735i	−1.43362	−	0.827700i	−0.997395	+	0.0721373i	$0.977018\pi$
$98$		−	86.7311i		−	0.0893996i
$99$	−29.2679	−	31.4062i	−0.0297124	−	0.0318832i
$100$		0			0
$101$	577.422	−	1000.12i	0.568867	−	0.985307i	−0.427811	−	0.903868i	$-0.640715\pi$
$101$	577.422	−	1000.12i	0.568867	−	0.985307i	0.996678	−	0.0814388i	$-0.0259515\pi$
$102$	−19.5114	−	171.495i	−0.0189404	−	0.166476i
$103$	−1256.80	+	725.615i	−1.20229	+	0.694145i	−0.961065	−	0.276323i	$-0.910884\pi$
$103$	−1256.80	+	725.615i	−1.20229	+	0.694145i	−0.241230	+	0.970468i	$0.577551\pi$
$104$	−40.3004	−	69.8024i	−0.0379979	−	0.0658143i
$105$		0			0
$106$	−109.290	+	189.295i	−0.100143	+	0.173452i
$107$		−	136.728i		−	0.123533i	−0.998091	−	0.0617664i	$-0.980327\pi$
$107$		−	136.728i		−	0.123533i	0.998091	−	0.0617664i	$-0.0196734\pi$
$108$	708.673	−	828.939i	0.631408	−	0.738562i
$109$	−40.1176			−0.0352529			−0.0176265	−	0.999845i	$-0.505611\pi$
$109$	−40.1176			−0.0352529			−0.0176265	+	0.999845i	$0.505611\pi$
$110$		0			0
$111$	−523.967	−	708.339i	−0.448043	−	0.605699i
$112$	−643.684	+	371.631i	−0.543057	+	0.313534i
$113$	−1713.40	+	989.231i	−1.42640	+	0.823531i	−0.996834	−	0.0795054i	$-0.974666\pi$
$113$	−1713.40	+	989.231i	−1.42640	+	0.823531i	−0.429564	+	0.903037i	$0.641333\pi$
$114$	242.245	−	27.5609i	0.199021	−	0.0226431i
$115$		0			0
$116$	2341.76			1.87437
$117$	−65.1062	−	282.420i	−0.0514450	−	0.223160i
$118$		−	238.112i		−	0.185763i
$119$	−442.428	+	766.309i	−0.340818	+	0.590314i
$120$		0			0
$121$	664.236	+	1150.49i	0.499050	+	0.864381i
$122$	−239.865	+	138.486i	−0.178003	+	0.102770i
$123$	676.014	+	294.069i	0.495562	+	0.215571i
$124$	455.804	−	789.475i	0.330100	−	0.571750i
$125$		0			0
$126$	158.821	−	36.6130i	0.112293	−	0.0258869i
$127$		−	1318.35i		−	0.921142i	−0.887623	−	0.460571i	$-0.847645\pi$
$127$		−	1318.35i		−	0.921142i	0.887623	−	0.460571i	$-0.152355\pi$
$128$	785.527	+	453.524i	0.542433	+	0.313174i
$129$	1550.11	−	176.360i	1.05798	−	0.120369i
$130$		0			0
$131$	−792.463	−	1372.59i	−0.528533	−	0.915446i	−0.999447	−	0.0332667i	$-0.989409\pi$
$131$	−792.463	−	1372.59i	−0.528533	−	0.915446i	0.470913	−	0.882179i	$-0.343924\pi$
$132$	51.6317	−	38.1926i	0.0340452	−	0.0251836i
$133$	−1082.45	−	624.953i	−0.705717	−	0.407446i
$134$	−238.463			−0.153732
$135$		0			0
$136$	523.947			0.330353
$137$	330.406	+	190.760i	0.206047	+	0.118961i	0.599473	−	0.800395i	$-0.295377\pi$
$137$	330.406	+	190.760i	0.206047	+	0.118961i	−0.393426	+	0.919356i	$0.628710\pi$
$138$	62.7517	−	46.4182i	0.0387086	−	0.0286332i
$139$	−1231.19	−	2132.49i	−0.751283	−	1.30126i	−0.947201	−	0.320641i	$-0.896102\pi$
$139$	−1231.19	−	2132.49i	−0.751283	−	1.30126i	0.195918	−	0.980620i	$-0.437231\pi$
$140$		0			0
$141$	−2516.50	+	286.309i	−1.50303	+	0.171004i
$142$	439.750	+	253.890i	0.259880	+	0.150042i
$143$		−	17.0675i		−	0.00998080i
$144$	1078.92	+	1157.75i	0.624375	+	0.669992i
$145$		0			0
$146$	−103.606	+	179.451i	−0.0587295	+	0.101723i
$147$	868.131	+	377.640i	0.487090	+	0.211886i
$148$	1141.48	−	659.037i	0.633983	−	0.366030i
$149$	192.172	+	332.852i	0.105660	+	0.183008i	0.914008	−	0.405697i	$-0.132971\pi$
$149$	192.172	+	332.852i	0.105660	+	0.183008i	−0.808348	+	0.588705i	$0.799638\pi$
$150$		0			0
$151$	−398.550	+	690.308i	−0.214792	+	0.372030i	−0.953208	−	0.302315i	$-0.902241\pi$
$151$	−398.550	+	690.308i	−0.214792	+	0.372030i	0.738417	+	0.674345i	$0.235574\pi$
$152$			740.102i			0.394935i
$153$	1801.53	+	551.415i	0.951926	+	0.291368i
$154$	9.59804			0.00502229
$155$		0			0
$156$	430.800	−	49.0133i	0.221100	−	0.0251551i
$157$	754.300	−	435.496i	0.383438	−	0.221378i	−0.295875	−	0.955227i	$-0.595611\pi$
$157$	754.300	−	435.496i	0.383438	−	0.221378i	0.679313	+	0.733849i	$0.262278\pi$
$158$	154.716	−	89.3252i	0.0779021	−	0.0449768i
$159$	−1418.88	−	1918.15i	−0.707700	−	0.956723i
$160$		0			0
$161$	−400.152			−0.195878
$162$	−151.927	−	312.006i	−0.0736822	−	0.151318i
$163$		−	31.2604i		−	0.0150215i	−0.999972	−	0.00751074i	$-0.997609\pi$
$163$		−	31.2604i		−	0.0150215i	0.999972	−	0.00751074i	$-0.00239076\pi$
$164$	−551.426	+	955.097i	−0.262556	+	0.454759i
$165$		0			0
$166$	307.813	+	533.147i	0.143921	+	0.249278i
$167$	32.2881	−	18.6415i	0.0149612	−	0.00863787i	−0.492501	−	0.870312i	$-0.663917\pi$
$167$	32.2881	−	18.6415i	0.0149612	−	0.00863787i	0.507462	+	0.861674i	$0.330584\pi$
$168$	55.9295	+	491.590i	0.0256849	+	0.225756i
$169$	−1040.89	+	1802.87i	−0.473776	+	0.820605i
$170$		0			0
$171$	−778.903	+	2544.75i	−0.348329	+	1.13802i
$172$			2333.90i			1.03464i
$173$	1022.93	+	590.590i	0.449550	+	0.259548i	0.707640	−	0.706573i	$-0.249760\pi$
$173$	1022.93	+	590.590i	0.449550	+	0.259548i	−0.258090	+	0.966121i	$0.583093\pi$
$174$	297.244	−	683.315i	0.129506	−	0.297712i
$175$		0			0
$176$	46.5967	+	80.7079i	0.0199566	+	0.0345658i
$177$	2383.37	+	1036.78i	1.01212	+	0.440276i
$178$	166.262	+	95.9916i	0.0700106	+	0.0404206i
$179$	429.484			0.179336			0.0896680	−	0.995972i	$-0.471419\pi$
$179$	429.484			0.179336			0.0896680	+	0.995972i	$0.471419\pi$
$180$		0			0
$181$	−1787.97			−0.734246			−0.367123	−	0.930172i	$-0.619657\pi$
$181$	−1787.97			−0.734246			−0.367123	+	0.930172i	$0.619657\pi$
$182$	56.1171	+	32.3992i	0.0228554	+	0.0131956i
$183$	−341.762	−	3003.90i	−0.138053	−	1.21341i
$184$	118.470	+	205.196i	0.0474659	+	0.0822134i
$185$		0			0
$186$	−172.509	−	233.211i	−0.0680051	−	0.0919346i
$187$	96.0832	+	55.4736i	0.0375738	+	0.0216932i
$188$		−	3788.94i		−	1.46988i
$189$	−325.056	+	1749.13i	−0.125102	+	0.673178i
$190$		0			0
$191$	−392.583	+	679.974i	−0.148724	+	0.257598i	−0.930756	−	0.365640i	$-0.880850\pi$
$191$	−392.583	+	679.974i	−0.148724	+	0.257598i	0.782032	+	0.623238i	$0.214183\pi$
$192$	−1783.88	+	1319.56i	−0.670522	+	0.495994i
$193$	−413.162	+	238.539i	−0.154093	+	0.0889659i	−0.575064	−	0.818108i	$-0.695023\pi$
$193$	−413.162	+	238.539i	−0.154093	+	0.0889659i	0.420971	+	0.907074i	$0.361690\pi$
$194$	−376.417	−	651.974i	−0.139305	−	0.241284i
$195$		0			0
$196$	−708.136	+	1226.53i	−0.258067	+	0.446985i
$197$			4628.37i			1.67390i	0.547281	+	0.836949i	$0.315663\pi$
$197$			4628.37i			1.67390i	−0.547281	+	0.836949i	$0.684337\pi$
$198$	−4.59070	−	19.9137i	−0.00164771	−	0.00714751i
$199$	−2533.85			−0.902611			−0.451305	−	0.892370i	$-0.649042\pi$
$199$	−2533.85			−0.902611			−0.451305	+	0.892370i	$0.649042\pi$
$200$		0			0
$201$	1038.30	−	2386.88i	0.364359	−	0.837601i
$202$	476.094	−	274.873i	0.165831	−	0.0957425i
$203$	−3308.36	+	1910.08i	−1.14385	+	0.660402i
$204$	−1124.28	+	2584.54i	−0.385861	+	0.887029i
$205$		0			0
$206$	−690.836			−0.233654
$207$	191.391	+	830.222i	0.0642636	+	0.278765i
$208$			629.170i			0.209736i
$209$	−78.3594	+	135.722i	−0.0259341	+	0.0449192i
$210$		0			0
$211$	−1382.70	−	2394.90i	−0.451131	−	0.781382i	0.547325	−	0.836920i	$-0.315646\pi$
$211$	−1382.70	−	2394.90i	−0.451131	−	0.781382i	−0.998457	+	0.0555378i	$0.982313\pi$
$212$	3091.08	−	1784.64i	1.00140	−	0.578158i
$213$	−4456.03	+	3296.18i	−1.43344	+	1.06033i
$214$	32.5437	−	56.3673i	0.0103955	−	0.0180056i
$215$		0			0
$216$	993.185	−	351.166i	0.312860	−	0.110620i
$217$			1487.12i			0.465219i
$218$	−16.5388	−	9.54869i	−0.00513830	−	0.00296660i
$219$	−1345.09	−	1818.40i	−0.415036	−	0.561078i
$220$		0			0
$221$	374.515	+	648.679i	0.113994	+	0.197443i
$222$	−47.4128	−	416.732i	−0.0143339	−	0.125988i
$223$	−406.502	−	234.694i	−0.122069	−	0.0704767i	0.437722	−	0.899110i	$-0.355785\pi$
$223$	−406.502	−	234.694i	−0.122069	−	0.0704767i	−0.559791	+	0.828634i	$0.689119\pi$
$224$	−1115.55			−0.332750
$225$		0			0
$226$	−941.817			−0.277207
$227$	−3713.50	−	2143.99i	−1.08579	−	0.626879i	−0.153335	−	0.988174i	$-0.549001\pi$
$227$	−3713.50	−	2143.99i	−1.08579	−	0.626879i	−0.932452	+	0.361295i	$0.882335\pi$
$228$	−3650.79	−	1588.11i	−1.06044	−	0.461294i
$229$	2052.30	+	3554.69i	0.592227	+	1.02577i	0.993932	+	0.109998i	$0.0350843\pi$
$229$	2052.30	+	3554.69i	0.592227	+	1.02577i	−0.401705	+	0.915769i	$0.631582\pi$
$230$		0			0
$231$	−41.7913	+	96.0711i	−0.0119033	+	0.0273637i
$232$	1958.97	+	1131.01i	0.554364	+	0.320062i
$233$		−	4272.57i		−	1.20131i	−0.799508	−	0.600656i	$-0.794906\pi$
$233$		−	4272.57i		−	1.20131i	0.799508	−	0.600656i	$-0.205094\pi$
$234$	40.3804	−	131.927i	0.0112810	−	0.0368560i
$235$		0			0
$236$	−1944.12	+	3367.31i	−0.536235	+	0.928786i
$237$	220.441	+	1937.56i	0.0604185	+	0.531045i
$238$	−364.790	+	210.611i	−0.0993521	+	0.0573610i
$239$	−780.619	−	1352.07i	−0.211272	−	0.365934i	0.740841	−	0.671681i	$-0.234427\pi$
$239$	−780.619	−	1352.07i	−0.211272	−	0.365934i	−0.952113	+	0.305747i	$0.901094\pi$
$240$		0			0
$241$	2410.77	−	4175.58i	0.644362	−	1.11607i	−0.340086	−	0.940394i	$-0.610456\pi$
$241$	2410.77	−	4175.58i	0.644362	−	1.11607i	0.984448	−	0.175674i	$-0.0562105\pi$
$242$			632.399i			0.167984i
$243$	3784.52	−	162.187i	0.999083	−	0.0428161i
$244$	4522.80			1.18665
$245$		0			0
$246$	208.699	+	282.135i	0.0540901	+	0.0731232i
$247$	−916.292	+	529.021i	−0.236042	+	0.136279i
$248$	762.591	−	440.282i	0.195260	−	0.112734i
$249$	−6676.77	+	759.634i	−1.69929	+	0.193333i
$250$		0			0
$251$	−3487.72			−0.877063			−0.438532	−	0.898716i	$-0.644501\pi$
$251$	−3487.72			−0.877063			−0.438532	+	0.898716i	$0.644501\pi$
$252$	−2544.94	−	778.962i	−0.636176	−	0.194722i
$253$			50.1728i			0.0124677i
$254$	313.791	−	543.503i	0.0775158	−	0.134261i
$255$		0			0
$256$	−1492.20	−	2584.57i	−0.364308	−	0.631000i
$257$	4262.35	−	2460.87i	1.03454	−	0.597295i	0.116261	−	0.993219i	$-0.462909\pi$
$257$	4262.35	−	2460.87i	1.03454	−	0.597295i	0.918283	+	0.395924i	$0.129576\pi$
$258$	681.021	+	296.247i	0.164335	+	0.0714865i
$259$	−1075.10	+	1862.13i	−0.257929	+	0.446745i
$260$		0			0
$261$	5545.36	+	5950.51i	1.31513	+	1.41121i
$262$		−	754.480i		−	0.177908i
$263$	4777.99	+	2758.58i	1.12024	+	0.646772i	0.941463	−	0.337117i	$-0.109452\pi$
$263$	4777.99	+	2758.58i	1.12024	+	0.646772i	0.178780	+	0.983889i	$0.442785\pi$
$264$	61.6377	−	7.01269i	0.0143695	−	0.00163485i
$265$		0			0
$266$	−297.500	−	515.284i	−0.0685747	−	0.118775i
$267$	−1684.75	+	1246.23i	−0.386162	+	0.285649i
$268$	3372.28	+	1946.98i	0.768636	+	0.443772i
$269$	7844.13			1.77794			0.888969	−	0.457968i	$-0.151423\pi$
$269$	7844.13			1.77794			0.888969	+	0.457968i	$0.151423\pi$
$270$		0			0
$271$	4301.35			0.964164			0.482082	−	0.876126i	$-0.339881\pi$
$271$	4301.35			0.964164			0.482082	+	0.876126i	$0.339881\pi$
$272$	−3541.98	−	2044.96i	−0.789573	−	0.455860i
$273$	−568.641	+	420.631i	−0.126065	+	0.0932517i
$274$	90.8083	+	157.285i	0.0200216	+	0.0346785i
$275$		0			0
$276$	−1266.41	+	144.083i	−0.276192	+	0.0314231i
$277$	1603.74	+	925.922i	0.347869	+	0.200842i	0.663746	−	0.747958i	$-0.268966\pi$
$277$	1603.74	+	925.922i	0.347869	+	0.200842i	−0.315877	+	0.948800i	$0.602299\pi$
$278$		−	1172.18i		−	0.252888i
$279$	3085.44	−	711.285i	0.662081	−	0.152629i
$280$		0			0
$281$	−3470.93	+	6011.82i	−0.736862	+	1.27628i	0.217040	+	0.976163i	$0.430360\pi$
$281$	−3470.93	+	6011.82i	−0.736862	+	1.27628i	−0.953902	+	0.300119i	$0.902974\pi$
$282$	−1105.59	−	480.937i	−0.233465	−	0.101558i
$283$	5570.64	−	3216.21i	1.17011	−	0.675562i	0.216402	−	0.976304i	$-0.430568\pi$
$283$	5570.64	−	3216.21i	1.17011	−	0.675562i	0.953705	+	0.300743i	$0.0972346\pi$
$284$	−4145.88	−	7180.87i	−0.866242	−	1.50038i
$285$		0			0
$286$	4.06236	−	7.03621i	0.000839903	−	0.00145476i
$287$		−	1799.10i		−	0.370027i
$288$	533.564	+	2314.52i	0.109169	+	0.473556i
$289$	43.9287			0.00894133
$290$		0			0
$291$	8164.88	−	928.941i	1.64479	−	0.187132i
$292$	2930.34	−	1691.83i	0.587278	−	0.339065i
$293$	−6617.98	+	3820.89i	−1.31955	+	0.761840i	−0.983655	−	0.180062i	$-0.942370\pi$
$293$	−6617.98	+	3820.89i	−1.31955	+	0.761840i	−0.335890	+	0.941901i	$0.609037\pi$
$294$	268.009	+	362.316i	0.0531654	+	0.0718731i
$295$		0			0
$296$	1273.19			0.250009
$297$	219.314	+	40.7569i	0.0428481	+	0.00796281i
$298$			182.961i			0.0355660i
$299$	−169.364	+	293.347i	−0.0327577	+	0.0567380i
$300$		0			0
$301$	−1903.67	−	3297.26i	−0.364538	−	0.631398i
$302$	−328.611	+	189.724i	−0.0626140	+	0.0361502i
$303$	678.344	+	5962.28i	0.128613	+	1.13044i
$304$	2888.61	−	5003.23i	0.544978	−	0.943930i
$305$		0			0
$306$	611.448	+	656.120i	0.114229	+	0.122575i
$307$		−	4517.66i		−	0.839857i	−0.907557	−	0.419929i	$-0.862055\pi$
$307$		−	4517.66i		−	0.839857i	0.907557	−	0.419929i	$-0.137945\pi$
$308$	−135.733	−	78.3654i	−0.0251107	−	0.0144977i
$309$	3008.00	−	6914.89i	0.553784	−	1.27306i
$310$		0			0
$311$	−1966.54	−	3406.15i	−0.358560	−	0.621044i	0.629160	−	0.777275i	$-0.283399\pi$
$311$	−1966.54	−	3406.15i	−0.358560	−	0.621044i	−0.987721	+	0.156231i	$0.950066\pi$
$312$	384.051	+	167.064i	0.0696879	+	0.0303145i
$313$	2742.00	+	1583.09i	0.495165	+	0.285884i	0.726715	−	0.686939i	$-0.241046\pi$
$313$	2742.00	+	1583.09i	0.495165	+	0.285884i	−0.231549	+	0.972823i	$0.574380\pi$
$314$	414.622			0.0745175
$315$		0			0
$316$	−2917.26			−0.519332
$317$	−6791.13	−	3920.86i	−1.20324	−	0.694692i	−0.241967	−	0.970284i	$-0.577793\pi$
$317$	−6791.13	−	3920.86i	−1.20324	−	0.694692i	−0.961275	+	0.275592i	$0.911126\pi$
$318$	−128.391	−	1128.49i	−0.0226410	−	0.199002i
$319$	239.495	+	414.817i	0.0420349	+	0.0728066i
$320$		0			0
$321$	422.506	+	571.176i	0.0734641	+	0.0993145i
$322$	−164.966	−	95.2431i	−0.0285503	−	0.0164835i
$323$		−	6877.82i		−	1.18480i
$324$	−398.932	+	5652.74i	−0.0684040	+	0.969263i
$325$		0			0
$326$	7.44051	−	12.8873i	0.00126409	−	0.00218946i
$327$	167.590	−	123.968i	0.0283417	−	0.0209647i
$328$	−922.574	+	532.648i	−0.155307	+	0.0896664i
$329$	3090.49	+	5352.89i	0.517885	+	0.897004i
$330$		0			0
$331$	5426.53	−	9399.03i	0.901115	−	1.56078i	0.0750663	−	0.997179i	$-0.476083\pi$
$331$	5426.53	−	9399.03i	0.901115	−	1.56078i	0.826049	−	0.563599i	$-0.190584\pi$
$332$		−	10052.8i		−	1.66181i
$333$	4377.70	+	1339.94i	0.720411	+	0.220505i
$334$	17.7480			0.00290757
$335$		0			0
$336$	1540.58	−	3541.53i	0.250135	−	0.575019i
$337$	5644.13	−	3258.64i	0.912331	−	0.526735i	0.0311507	−	0.999515i	$-0.490083\pi$
$337$	5644.13	−	3258.64i	0.912331	−	0.526735i	0.881180	+	0.472780i	$0.156749\pi$
$338$	−858.229	+	495.499i	−0.138111	+	0.0797384i
$339$	4100.81	−	9427.08i	0.657008	−	1.51035i
$340$		0			0
$341$	186.462			0.0296114
$342$	−926.804	+	863.701i	−0.146537	+	0.136560i
$343$		−	6659.94i		−	1.04841i
$344$	−1127.21	+	1952.39i	−0.176672	+	0.306005i
$345$		0			0
$346$	281.142	+	486.952i	0.0436829	+	0.0756609i
$347$	−5142.93	+	2969.27i	−0.795640	+	0.459363i	−0.841944	−	0.539564i	$-0.818589\pi$
$347$	−5142.93	+	2969.27i	−0.795640	+	0.459363i	0.0463041	+	0.998927i	$0.485256\pi$
$348$	−9782.62	+	7236.33i	−1.50691	+	1.11468i
$349$	−3648.27	+	6318.99i	−0.559563	+	0.969192i	0.437970	+	0.898990i	$0.355698\pi$
$349$	−3648.27	+	6318.99i	−0.559563	+	0.969192i	−0.997533	+	0.0702022i	$0.977636\pi$
$350$		0			0
$351$	1144.69	+	978.613i	0.174071	+	0.148816i
$352$			139.873i			0.0211797i
$353$	−1083.15	−	625.356i	−0.163315	−	0.0942900i	0.416115	−	0.909312i	$-0.363391\pi$
$353$	−1083.15	−	625.356i	−0.163315	−	0.0942900i	−0.579430	+	0.815022i	$0.696725\pi$
$354$	735.795	+	994.704i	0.110472	+	0.149344i
$355$		0			0
$356$	−1567.49	−	2714.97i	−0.233362	−	0.404195i
$357$	−519.757	−	4568.38i	−0.0770545	−	0.677267i
$358$	177.058	+	102.225i	0.0261392	+	0.0150915i
$359$	10928.3			1.60661			0.803303	−	0.595570i	$-0.203074\pi$
$359$	10928.3			1.60661			0.803303	+	0.595570i	$0.203074\pi$
$360$		0			0
$361$	2856.27			0.416427
$362$	−737.104	−	425.567i	−0.107020	−	0.0617882i
$363$	−6329.97	−	2753.56i	−0.915254	−	0.398139i
$364$	−529.062	−	916.362i	−0.0761823	−	0.131952i
$365$		0			0
$366$	574.087	−	1319.73i	0.0819891	−	0.188479i
$367$	−5569.68	−	3215.66i	−0.792194	−	0.457373i	0.0485405	−	0.998821i	$-0.484543\pi$
$367$	−5569.68	−	3215.66i	−0.792194	−	0.457373i	−0.840734	+	0.541448i	$0.817876\pi$
$368$		−	1849.55i		−	0.261996i
$369$	−3732.73	+	860.504i	−0.526607	+	0.121398i
$370$		0			0
$371$	−2911.32	+	5042.55i	−0.407407	+	0.705650i
$372$	535.470	+	4706.49i	0.0746312	+	0.655968i
$373$	4253.66	−	2455.85i	0.590472	−	0.340909i	−0.174812	−	0.984602i	$-0.555932\pi$
$373$	4253.66	−	2455.85i	0.590472	−	0.340909i	0.765284	+	0.643693i	$0.222598\pi$
$374$	26.4074	+	45.7389i	0.00365105	+	0.00632381i
$375$		0			0
$376$	1829.96	−	3169.58i	0.250992	−	0.434731i
$377$			3233.76i			0.441770i
$378$	−550.331	+	643.726i	−0.0748836	+	0.0875918i
$379$	−4805.81			−0.651340			−0.325670	−	0.945483i	$-0.605590\pi$
$379$	−4805.81			−0.651340			−0.325670	+	0.945483i	$0.605590\pi$
$380$		0			0
$381$	4073.87	+	5507.37i	0.547797	+	0.740554i
$382$	−323.691	+	186.883i	−0.0433547	+	0.0250308i
$383$	−3665.15	+	2116.08i	−0.488983	+	0.282314i	−0.724152	−	0.689640i	$-0.757769\pi$
$383$	−3665.15	+	2116.08i	−0.488983	+	0.282314i	0.235170	+	0.971954i	$0.424435\pi$
$384$	−4682.95	+	532.792i	−0.622333	+	0.0708045i
$385$		0			0
$386$	−227.106			−0.0299466
$387$	−5930.53	+	5526.75i	−0.778982	+	0.725944i
$388$			12293.4i			1.60851i
$389$	−1758.54	+	3045.89i	−0.229208	+	0.396999i	−0.957573	−	0.288189i	$-0.906947\pi$
$389$	−1758.54	+	3045.89i	−0.229208	+	0.396999i	0.728366	+	0.685188i	$0.240280\pi$
$390$		0			0
$391$	−1100.95	−	1906.90i	−0.142398	−	0.246640i
$392$	−1184.76	+	684.022i	−0.152652	+	0.0881335i
$393$	7551.94	+	3285.12i	0.969325	+	0.421660i
$394$	−1101.63	+	1908.09i	−0.140862	+	0.243980i
$395$		0			0
$396$	−97.6697	+	319.096i	−0.0123942	+	0.0404929i
$397$		−	3925.05i		−	0.496203i	−0.968734	−	0.248101i	$-0.920193\pi$
$397$		−	3925.05i		−	0.496203i	0.968734	−	0.248101i	$-0.0798066\pi$
$398$	−1044.60	−	603.100i	−0.131560	−	0.0759564i
$399$	6453.07	−	734.184i	0.809669	−	0.0921182i
$400$		0			0
$401$	−403.676	−	699.188i	−0.0502709	−	0.0870718i	0.839795	−	0.542904i	$-0.182675\pi$
$401$	−403.676	−	699.188i	−0.0502709	−	0.0870718i	−0.890066	+	0.455832i	$0.849342\pi$
$402$	996.169	−	736.879i	0.123593	−	0.0914233i
$403$	1090.19	+	629.424i	0.134755	+	0.0778011i
$404$	−8977.05			−1.10551
$405$		0			0
$406$	−1818.53			−0.222296
$407$	233.482	+	134.801i	0.0284356	+	0.0164173i
$408$	−2188.77	+	1619.06i	−0.265588	+	0.196459i
$409$	404.224	+	700.137i	0.0488694	+	0.0846444i	0.889425	−	0.457080i	$-0.151105\pi$
$409$	404.224	+	700.137i	0.0488694	+	0.0846444i	−0.840556	+	0.541725i	$0.817772\pi$
$410$		0			0
$411$	−1969.73	+	224.101i	−0.236398	+	0.0268956i
$412$	9769.61	+	5640.49i	1.16824	+	0.674482i
$413$		−	6342.97i		−	0.755732i
$414$	−118.705	+	387.821i	−0.0140919	+	0.0460395i
$415$		0			0
$416$	−472.157	+	817.800i	−0.0556476	+	0.0963844i
$417$	11732.9	+	5103.85i	1.37785	+	0.599369i
$418$	−64.6086	+	37.3018i	−0.00756008	+	0.00436481i
$419$	880.089	+	1524.36i	0.102614	+	0.177732i	0.912761	−	0.408495i	$-0.133946\pi$
$419$	880.089	+	1524.36i	0.102614	+	0.177732i	−0.810147	+	0.586227i	$0.800613\pi$
$420$		0			0
$421$	−7287.86	+	12622.9i	−0.843678	+	1.46129i	0.0430868	+	0.999071i	$0.486281\pi$
$421$	−7287.86	+	12622.9i	−0.843678	+	1.46129i	−0.886765	+	0.462221i	$0.847053\pi$
$422$		−	1316.42i		−	0.151854i
$423$	9627.84	−	8972.32i	1.10667	−	1.03132i
$424$	3447.73			0.394898
$425$		0			0
$426$	−2621.59	+	298.265i	−0.298160	+	0.0339225i
$427$	−6389.65	+	3689.07i	−0.724161	+	0.418095i
$428$	−920.447	+	531.421i	−0.103952	+	0.0600168i
$429$	52.7405	+	71.2987i	0.00593552	+	0.00802409i
$430$		0			0
$431$	5715.34			0.638743			0.319371	−	0.947630i	$-0.396528\pi$
$431$	5715.34			0.638743			0.319371	+	0.947630i	$0.396528\pi$
$432$	−8084.72	−	1502.45i	−0.900408	−	0.167330i
$433$		−	12751.4i		−	1.41523i	−0.706599	−	0.707614i	$-0.749772\pi$
$433$		−	12751.4i		−	1.41523i	0.706599	−	0.707614i	$-0.250228\pi$
$434$	−353.962	+	613.079i	−0.0391491	+	0.0678082i
$435$		0			0
$436$	155.925	+	270.070i	0.0171272	+	0.0296651i
$437$	2693.60	−	1555.15i	0.294856	−	0.170235i
$438$	−121.715	−	1069.81i	−0.0132780	−	0.116706i
$439$	2420.51	−	4192.44i	0.263154	−	0.455796i	−0.703924	−	0.710275i	$-0.748571\pi$
$439$	2420.51	−	4192.44i	0.263154	−	0.455796i	0.967078	+	0.254479i	$0.0819039\pi$
$440$		0			0
$441$	−4793.54	+	1105.05i	−0.517605	+	0.119323i
$442$			356.564i			0.0383711i
$443$	7747.43	+	4472.98i	0.830907	+	0.479724i	0.854163	−	0.520005i	$-0.174070\pi$
$443$	7747.43	+	4472.98i	0.830907	+	0.479724i	−0.0232564	+	0.999730i	$0.507403\pi$
$444$	−2732.01	+	6280.42i	−0.292016	+	0.671297i
$445$		0			0
$446$	−111.723	−	193.509i	−0.0118615	−	0.0205447i
$447$	−1831.34	−	796.640i	−0.193780	−	0.0842948i
$448$	4689.57	+	2707.53i	0.494557	+	0.285533i
$449$	2743.57			0.288367			0.144184	−	0.989551i	$-0.453944\pi$
$449$	2743.57			0.288367			0.144184	+	0.989551i	$0.453944\pi$
$450$		0			0
$451$	−225.580			−0.0235524
$452$	13318.9	+	7689.68i	1.38599	+	0.800204i
$453$	−468.209	−	4115.30i	−0.0485615	−	0.426829i
$454$	−1020.61	−	1767.76i	−0.105506	−	0.182742i
$455$		0			0
$456$	−2287.00	−	3091.75i	−0.234865	−	0.317509i
$457$	4860.74	+	2806.35i	0.497540	+	0.287255i	0.727697	−	0.685899i	$-0.240591\pi$
$457$	4860.74	+	2806.35i	0.497540	+	0.287255i	−0.230157	+	0.973153i	$0.573924\pi$
$458$			1953.93i			0.199348i
$459$	−9229.74	+	3263.41i	−0.938578	+	0.331858i
$460$		0			0
$461$	−6273.50	+	10866.0i	−0.633809	+	1.09779i	0.352957	+	0.935640i	$0.385176\pi$
$461$	−6273.50	+	10866.0i	−0.633809	+	1.09779i	−0.986766	+	0.162150i	$0.948157\pi$
$462$	−40.0954	+	29.6591i	−0.00403768	+	0.00298672i
$463$	−9285.74	+	5361.12i	−0.932062	+	0.538126i	−0.887463	−	0.460879i	$-0.847534\pi$
$463$	−9285.74	+	5361.12i	−0.932062	+	0.538126i	−0.0445990	+	0.999005i	$0.514201\pi$
$464$	−8828.65	−	15291.7i	−0.883319	−	1.52995i
$465$		0			0
$466$	1016.95	−	1761.40i	0.101093	−	0.175098i
$467$			12798.4i			1.26818i	0.773260	+	0.634089i	$0.218625\pi$
$467$			12798.4i			1.26818i	−0.773260	+	0.634089i	$0.781375\pi$
$468$	−1648.19	+	1535.97i	−0.162794	+	0.151710i
$469$	−6352.31			−0.625421
$470$		0			0
$471$	−1805.33	+	4150.14i	−0.176614	+	0.406005i
$472$	−3252.65	+	1877.92i	−0.317193	+	0.183132i
$473$	−413.425	+	238.691i	−0.0401888	+	0.0232030i
$474$	−370.293	+	851.242i	−0.0358822	+	0.0824870i
$475$		0			0
$476$	6878.34			0.662328
$477$	11854.6	+	3628.49i	1.13791	+	0.348296i
$478$		−	743.203i		−	0.0711158i
$479$	1207.38	−	2091.25i	0.115171	−	0.199481i	−0.802677	−	0.596413i	$-0.796592\pi$
$479$	1207.38	−	2091.25i	0.115171	−	0.199481i	0.917848	+	0.396932i	$0.129925\pi$
$480$		0			0
$481$	910.070	+	1576.29i	0.0862695	+	0.149423i
$482$	1987.72	−	1147.61i	0.187839	−	0.108449i
$483$	1671.62	−	1236.52i	0.157477	−	0.116487i
$484$	5163.37	−	8943.21i	0.484914	−	0.839896i
$485$		0			0
$486$	1598.80	+	833.919i	0.149225	+	0.0778340i
$487$			16386.9i			1.52477i	0.647125	+	0.762384i	$0.275971\pi$
$487$			16386.9i			1.52477i	−0.647125	+	0.762384i	$0.724029\pi$
$488$	3783.48	+	2184.39i	0.350963	+	0.202629i
$489$	96.5982	+	130.589i	0.00893317	+	0.0120766i
$490$		0			0
$491$	−7935.54	−	13744.8i	−0.729381	−	1.26332i	−0.957145	−	0.289609i	$-0.906475\pi$
$491$	−7935.54	−	13744.8i	−0.729381	−	1.26332i	0.227764	−	0.973716i	$-0.426858\pi$
$492$	−647.805	−	5693.85i	−0.0593604	−	0.521745i
$493$	−18204.8	−	10510.6i	−1.66309	−	0.960186i
$494$	−503.665			−0.0458724
$495$		0			0
$496$	−6873.68			−0.622252
$497$	11714.3	+	6763.26i	1.05726	+	0.610410i
$498$	−2933.36	−	1276.02i	−0.263950	−	0.114819i
$499$	5730.39	+	9925.33i	0.514083	+	0.890419i	0.999867	+	0.0163392i	$0.00520117\pi$
$499$	5730.39	+	9925.33i	0.514083	+	0.890419i	−0.485783	+	0.874079i	$0.661466\pi$
$500$		0			0
$501$	−77.2776	+	177.648i	−0.00689123	+	0.0158418i
$502$	−1437.84	−	830.138i	−0.127837	−	0.0738065i
$503$			1038.52i			0.0920585i	0.998940	+	0.0460293i	$0.0146568\pi$
$503$			1038.52i			0.0920585i	−0.998940	+	0.0460293i	$0.985343\pi$
$504$	−1752.71	−	1880.77i	−0.154905	−	0.166222i
$505$		0			0
$506$	−11.9420	+	20.6841i	−0.00104918	+	0.00181724i
$507$	−1222.81	−	10747.9i	−0.107115	−	0.941479i
$508$	−8875.10	+	5124.04i	−0.775135	+	0.447525i
$509$	−2514.44	−	4355.14i	−0.218960	−	0.379249i	0.735530	−	0.677492i	$-0.236933\pi$
$509$	−2514.44	−	4355.14i	−0.218960	−	0.379249i	−0.954490	+	0.298242i	$0.903600\pi$
$510$		0			0
$511$	−2759.92	+	4780.33i	−0.238927	+	0.413834i
$512$		−	8677.07i		−	0.748976i
$513$	−4609.74	−	13037.5i	−0.396735	−	1.12206i
$514$	2342.92			0.201054
$515$		0			0
$516$	−7212.04	−	9749.79i	−0.615295	−	0.831803i
$517$	671.169	−	387.499i	0.0570947	−	0.0329636i
$518$	−886.438	+	511.785i	−0.0751889	+	0.0434104i
$519$	−6098.25	+	693.815i	−0.515768	+	0.0586803i
$520$		0			0
$521$	7057.78			0.593487			0.296744	−	0.954957i	$-0.404099\pi$
$521$	7057.78			0.593487			0.296744	+	0.954957i	$0.404099\pi$
$522$	869.797	+	3773.04i	0.0729310	+	0.316363i
$523$			14453.5i			1.20843i	0.796821	+	0.604215i	$0.206513\pi$
$523$			14453.5i			1.20843i	−0.796821	+	0.604215i	$0.793487\pi$
$524$	−6160.13	+	10669.7i	−0.513562	+	0.889515i
$525$		0			0
$526$	1313.18	+	2274.49i	0.108854	+	0.188541i
$527$	−7086.81	+	4091.57i	−0.585781	+	0.338201i
$528$	−444.053	−	193.165i	−0.0366002	−	0.0159212i
$529$	−5585.63	+	9674.59i	−0.459080	+	0.795150i
$530$		0			0
$531$	−13160.2	+	3033.81i	−1.07553	+	0.247940i
$532$			9716.01i			0.791809i
$533$	−1318.90	−	761.469i	−0.107182	−	0.0618816i
$534$	−991.180	+	112.769i	−0.0803231	+	0.00913858i
$535$		0			0
$536$	1880.68	+	3257.44i	0.151554	+	0.262500i
$537$	−1794.15	+	1327.16i	−0.144178	+	0.106650i
$538$	3233.81	+	1867.04i	0.259144	+	0.149617i
$539$	−289.687			−0.0231498
$540$		0			0
$541$	4101.59			0.325954			0.162977	−	0.986630i	$-0.447890\pi$
$541$	4101.59			0.325954			0.162977	+	0.986630i	$0.447890\pi$
$542$	1773.27	+	1023.80i	0.140532	+	0.0811362i
$543$	7469.16	−	5525.03i	0.590299	−	0.436651i
$544$	−3069.26	−	5316.11i	−0.241900	−	0.418982i
$545$		0			0
$546$	−334.544	+	38.0620i	−0.0262219	+	0.00298334i
$547$	−14567.4	−	8410.52i	−1.13868	−	0.657418i	−0.192578	−	0.981282i	$-0.561685\pi$
$547$	−14567.4	−	8410.52i	−1.13868	−	0.657418i	−0.946104	+	0.323863i	$0.895018\pi$
$548$		−	2965.70i		−	0.231183i
$549$	10710.1	+	11492.6i	0.832598	+	0.893428i
$550$		0			0
$551$	14846.7	−	25715.2i	1.14790	−	1.98821i
$552$	−1128.98	−	491.112i	−0.0870521	−	0.0378680i
$553$	4121.41	−	2379.50i	0.316926	−	0.182977i
$554$	440.771	+	763.438i	0.0338025	+	0.0585476i
$555$		0			0
$556$	−9570.54	+	16576.7i	−0.730002	+	1.26440i
$557$			12248.8i			0.931771i	0.884845	+	0.465885i	$0.154264\pi$
$557$			12248.8i			0.931771i	−0.884845	+	0.465885i	$0.845736\pi$
$558$	1441.30	+	441.156i	0.109346	+	0.0334688i
$559$	−3222.91			−0.243854
$560$		0			0
$561$	−572.804	+	65.1694i	−0.0431084	+	0.00490455i
$562$	−2861.84	+	1652.28i	−0.214803	+	0.124017i
$563$	7660.62	−	4422.86i	0.573457	−	0.331086i	−0.185072	−	0.982725i	$-0.559252\pi$
$563$	7660.62	−	4422.86i	0.573457	−	0.331086i	0.758529	+	0.651639i	$0.225918\pi$
$564$	11708.3	+	15828.1i	0.874127	+	1.18171i
$565$		0			0
$566$	3062.06			0.227399
$567$	−4047.12	−	8311.39i	−0.299759	−	0.615601i
$568$		−	8009.40i		−	0.591667i
$569$	−4049.35	+	7013.68i	−0.298344	+	0.516747i	−0.975757	−	0.218856i	$-0.929768\pi$
$569$	−4049.35	+	7013.68i	−0.298344	+	0.516747i	0.677413	+	0.735603i	$0.263101\pi$
$570$		0			0
$571$	8189.02	+	14183.8i	0.600175	+	1.03953i	0.992794	+	0.119832i	$0.0382356\pi$
$571$	8189.02	+	14183.8i	0.600175	+	1.03953i	−0.392619	+	0.919701i	$0.628431\pi$
$572$	−114.897	+	66.3361i	−0.00839879	+	0.00484904i
$573$	−461.200	−	4053.69i	−0.0336246	−	0.295542i
$574$	428.218	−	741.696i	0.0311385	−	0.0539334i
$575$		0			0
$576$	3374.49	−	11024.8i	0.244104	−	0.797510i
$577$		−	24920.9i		−	1.79804i	−0.437907	−	0.899020i	$-0.644280\pi$
$577$		−	24920.9i		−	1.79804i	0.437907	−	0.899020i	$-0.355720\pi$
$578$	18.1100	+	10.4558i	0.00130325	+	0.000752430i
$579$	988.853	−	2273.21i	0.0709764	−	0.163163i
$580$		0			0
$581$	8199.69	+	14202.3i	0.585509	+	1.01413i
$582$	3587.15	+	1560.42i	0.255484	+	0.111137i
$583$	632.257	+	365.034i	0.0449150	+	0.0259317i
$584$	3268.44			0.231591
$585$		0			0
$586$	−3637.76			−0.256441
$587$	−7243.86	−	4182.25i	−0.509346	−	0.294071i	0.223219	−	0.974768i	$-0.428344\pi$
$587$	−7243.86	−	4182.25i	−0.509346	−	0.294071i	−0.732565	+	0.680697i	$0.761677\pi$
$588$	−831.905	−	7311.99i	−0.0583456	−	0.512826i
$589$	−5779.56	−	10010.5i	−0.404317	−	0.700297i
$590$		0			0
$591$	−14302.2	−	19334.8i	−0.995456	−	1.34573i
$592$	−8607.00	−	4969.25i	−0.597543	−	0.344992i
$593$			27169.7i			1.88150i	0.339105	+	0.940749i	$0.389876\pi$
$593$			27169.7i			1.88150i	−0.339105	+	0.940749i	$0.610124\pi$
$594$	80.7132	+	69.0030i	0.00557526	+	0.00476637i
$595$		0			0
$596$	1493.83	−	2587.39i	0.102667	−	0.177825i
$597$	10585.0	−	7829.88i	0.725656	−	0.536777i
$598$	−139.643	+	80.6231i	−0.00954923	+	0.00551325i
$599$	10666.2	+	18474.4i	0.727560	+	1.26017i	0.957911	+	0.287064i	$0.0926792\pi$
$599$	10666.2	+	18474.4i	0.727560	+	1.26017i	−0.230351	+	0.973108i	$0.573987\pi$
$600$		0			0
$601$	−292.016	+	505.786i	−0.0198196	+	0.0343285i	−0.875765	−	0.482738i	$-0.839643\pi$
$601$	−292.016	+	505.786i	−0.0198196	+	0.0343285i	0.855946	+	0.517066i	$0.172976\pi$
$602$		−	1812.43i		−	0.122706i
$603$	3038.28	+	13179.6i	0.205188	+	0.890074i
$604$	6196.17			0.417415
$605$		0			0
$606$	−1139.47	+	2619.46i	−0.0763827	+	0.175591i
$607$	−9760.32	+	5635.12i	−0.652651	+	0.376808i	−0.789471	−	0.613788i	$-0.789645\pi$
$607$	−9760.32	+	5635.12i	−0.652651	+	0.376808i	0.136820	+	0.990596i	$0.456312\pi$
$608$	7509.29	−	4335.49i	0.500891	−	0.289190i
$609$	7918.17	−	18202.5i	0.526864	−	1.21117i
$610$		0			0
$611$	5232.19			0.346435
$612$	−3289.88	−	14271.0i	−0.217297	−	0.942598i
$613$			4271.02i			0.281411i	0.990051	+	0.140706i	$0.0449371\pi$
$613$			4271.02i			0.281411i	−0.990051	+	0.140706i	$0.955063\pi$
$614$	1075.28	−	1862.44i	0.0706756	−	0.122414i
$615$		0			0
$616$	−75.6968	−	131.111i	−0.00495115	−	0.00857565i
$617$	6232.06	−	3598.08i	0.406634	−	0.234770i	−0.282708	−	0.959206i	$-0.591233\pi$
$617$	6232.06	−	3598.08i	0.406634	−	0.234770i	0.689342	+	0.724436i	$0.257900\pi$
$618$	2885.94	−	2134.76i	0.187847	−	0.138953i
$619$	5128.24	−	8882.36i	0.332991	−	0.576757i	−0.650106	−	0.759843i	$-0.725276\pi$
$619$	5128.24	−	8882.36i	0.332991	−	0.576757i	0.983097	+	0.183087i	$0.0586089\pi$
$620$		0			0
$621$	−3365.01	−	2876.80i	−0.217445	−	0.185897i
$622$		−	1872.28i		−	0.120694i
$623$	4428.99	+	2557.08i	0.284822	+	0.164442i
$624$	−1944.21	−	2628.33i	−0.124729	−	0.168618i
$625$		0			0
$626$	753.607	+	1305.29i	0.0481153	+	0.0833382i
$627$	−92.0552	−	809.115i	−0.00586337	−	0.0515358i
$628$	−5863.47	−	3385.28i	−0.372576	−	0.215107i
$629$	−11831.8			−0.750026
$630$		0			0
$631$	15187.7			0.958183			0.479091	−	0.877765i	$-0.340966\pi$
$631$	15187.7			0.958183			0.479091	+	0.877765i	$0.340966\pi$
$632$	−2440.39	−	1408.96i	−0.153597	−	0.0886795i
$633$	13176.7	+	5731.90i	0.827371	+	0.359909i
$634$	−1866.47	−	3232.81i	−0.116919	−	0.202510i
$635$		0			0
$636$	−7398.14	+	17007.1i	−0.461250	+	1.06034i
$637$	−1693.72	−	977.872i	−0.105350	−	0.0608237i
$638$			228.016i			0.0141493i
$639$	8429.31	−	27539.3i	0.521844	−	1.70491i
$640$		0			0
$641$	14196.7	−	24589.4i	0.874783	−	1.51517i	0.0177891	−	0.999842i	$-0.494337\pi$
$641$	14196.7	−	24589.4i	0.874783	−	1.51517i	0.856994	−	0.515327i	$-0.172329\pi$
$642$	38.2317	+	336.036i	0.00235029	+	0.0206578i
$643$	−10122.1	+	5844.00i	−0.620804	+	0.358421i	−0.777182	−	0.629276i	$-0.783351\pi$
$643$	−10122.1	+	5844.00i	−0.620804	+	0.358421i	0.156378	+	0.987697i	$0.450018\pi$
$644$	1555.27	+	2693.80i	0.0951648	+	0.164830i
$645$		0			0
$646$	1637.04	−	2835.44i	0.0997036	−	0.172692i
$647$			12800.8i			0.777822i	0.921275	+	0.388911i	$0.127149\pi$
$647$			12800.8i			0.777822i	−0.921275	+	0.388911i	$0.872851\pi$
$648$	−3063.85	+	4536.04i	−0.185740	+	0.274989i
$649$	−795.310			−0.0481027
$650$		0			0
$651$	−4595.39	−	6212.40i	−0.276663	−	0.374014i
$652$	−210.443	+	121.500i	−0.0126405	+	0.00729799i
$653$	−5333.78	+	3079.46i	−0.319643	+	0.184546i	−0.651233	−	0.758877i	$-0.725748\pi$
$653$	−5333.78	+	3079.46i	−0.319643	+	0.184546i	0.331590	+	0.943423i	$0.392415\pi$
$654$	98.5968	−	11.2176i	0.00589517	−	0.000670709i
$655$		0			0
$656$	8315.69			0.494929
$657$	11238.1	+	3439.80i	0.667339	+	0.204261i
$658$			2942.36i			0.174324i
$659$	8289.10	−	14357.1i	0.489981	−	0.848672i	−0.509953	−	0.860202i	$-0.670337\pi$
$659$	8289.10	−	14357.1i	0.489981	−	0.848672i	0.999934	+	0.0115307i	$0.00367042\pi$
$660$		0			0
$661$	11469.8	+	19866.4i	0.674925	+	1.16900i	0.976491	+	0.215559i	$0.0691573\pi$
$661$	11469.8	+	19866.4i	0.674925	+	1.16900i	−0.301566	+	0.953445i	$0.597509\pi$
$662$	4474.27	−	2583.22i	0.262685	−	0.151661i
$663$	−3569.01	−	1552.53i	−0.209063	−	0.0909433i
$664$	4855.25	−	8409.53i	0.283765	−	0.491496i
$665$		0			0
$666$	1485.82	+	1594.37i	0.0864478	+	0.0927637i
$667$		−	9506.20i		−	0.551847i
$668$	−250.988	−	144.908i	−0.0145374	−	0.00839319i
$669$	2423.38	−	275.715i	0.140050	−	0.0159338i
$670$		0			0
$671$	462.552	+	801.163i	0.0266119	+	0.0460932i
$672$	4660.18	−	3447.19i	0.267515	−	0.197884i
$673$	−2046.62	−	1181.62i	−0.117223	−	0.0676790i	0.440242	−	0.897879i	$-0.354893\pi$
$673$	−2046.62	−	1181.62i	−0.117223	−	0.0676790i	−0.557465	+	0.830200i	$0.688226\pi$
$674$	3102.46			0.177303
$675$		0			0
$676$	16182.4			0.920712
$677$	−13551.7	−	7824.09i	−0.769328	−	0.444172i	0.0633068	−	0.997994i	$-0.479835\pi$
$677$	−13551.7	−	7824.09i	−0.769328	−	0.444172i	−0.832635	+	0.553822i	$0.813169\pi$
$678$	3934.40	−	2910.33i	0.222861	−	0.164853i
$679$	−10027.2	−	17367.7i	−0.566730	−	0.981605i
$680$		0			0
$681$	22138.2	−	2518.72i	1.24572	−	0.141729i
$682$	76.8706	+	44.3813i	0.00431602	+	0.00249186i
$683$			19626.7i			1.09955i	0.835311	+	0.549777i	$0.185287\pi$
$683$			19626.7i			1.09955i	−0.835311	+	0.549777i	$0.814713\pi$
$684$	20158.5	−	4647.12i	1.12687	−	0.259777i
$685$		0			0
$686$	1585.18	−	2745.62i	0.0882253	−	0.152811i
$687$	−19557.8	−	8507.72i	−1.08614	−	0.472474i
$688$	15240.3	−	8799.02i	0.844524	−	0.487586i
$689$	2464.42	+	4268.51i	0.136266	+	0.236019i
$690$		0			0
$691$	51.5955	−	89.3660i	0.00284050	−	0.00491989i	−0.864602	−	0.502458i	$-0.832429\pi$
$691$	51.5955	−	89.3660i	0.00284050	−	0.00491989i	0.867442	+	0.497538i	$0.165763\pi$
$692$		−	9181.78i		−	0.504391i
$693$	−122.290	−	530.473i	−0.00670332	−	0.0290779i
$694$	−2826.96			−0.154625
$695$		0			0
$696$	−11678.5	+	1328.69i	−0.636021	+	0.0723619i
$697$	8573.54	−	4949.93i	0.465920	−	0.268999i
$698$	−3008.06	+	1736.71i	−0.163119	+	0.0941766i
$699$	13202.8	+	17848.5i	0.714412	+	0.965797i
$700$		0			0
$701$	−17977.8			−0.968631			−0.484316	−	0.874893i	$-0.660931\pi$
$701$	−17977.8			−0.968631			−0.484316	+	0.874893i	$0.660931\pi$
$702$	238.981	+	675.898i	0.0128487	+	0.0363392i
$703$		−	16713.1i		−	0.896651i
$704$	339.482	−	588.000i	0.0181743	−	0.0314788i
$705$		0			0
$706$	−297.692	−	515.617i	−0.0158694	−	0.0274865i
$707$	12682.5	−	7322.22i	0.674644	−	0.389506i
$708$	−2283.92	−	20074.4i	−0.121236	−	1.06560i
$709$	5385.10	−	9327.26i	0.285249	−	0.494066i	−0.687421	−	0.726260i	$-0.741257\pi$
$709$	5385.10	−	9327.26i	0.285249	−	0.494066i	0.972670	+	0.232194i	$0.0745904\pi$
$710$		0			0
$711$	−6908.16	−	7412.87i	−0.364383	−	0.391005i
$712$		−	3028.23i		−	0.159393i
$713$	−3204.81	−	1850.30i	−0.168333	−	0.0971868i
$714$	873.080	−	2007.06i	0.0457622	−	0.105200i
$715$		0			0
$716$	−1669.27	−	2891.27i	−0.0871280	−	0.150910i
$717$	7439.06	+	3236.02i	0.387471	+	0.168551i
$718$	4505.27	+	2601.12i	0.234171	+	0.135199i
$719$	−24138.7			−1.25205			−0.626023	−	0.779804i	$-0.715319\pi$
$719$	−24138.7			−1.25205			−0.626023	+	0.779804i	$0.715319\pi$
$720$		0			0
$721$	−18402.9			−0.950568
$722$	1177.52	+	679.843i	0.0606964	+	0.0350431i
$723$	2832.13	+	24892.9i	0.145682	+	1.28046i
$724$	6949.28	+	12036.5i	0.356724	+	0.617864i
$725$		0			0
$726$	−1954.19	−	2641.82i	−0.0998991	−	0.135051i
$727$	−9345.20	−	5395.46i	−0.476746	−	0.275250i	0.242313	−	0.970198i	$-0.422094\pi$
$727$	−9345.20	−	5395.46i	−0.476746	−	0.275250i	−0.719059	+	0.694949i	$0.755427\pi$
$728$		−	1022.09i		−	0.0520347i
$729$	−15308.5	+	12372.1i	−0.777753	+	0.628570i
$730$		0			0
$731$	10475.3	−	18143.7i	0.530016	−	0.918015i
$732$	−18893.8	+	13976.0i	−0.954009	+	0.705692i
$733$	−18174.3	+	10492.9i	−0.915801	+	0.528738i	−0.882293	−	0.470700i	$-0.844001\pi$
$733$	−18174.3	+	10492.9i	−0.915801	+	0.528738i	−0.0335082	+	0.999438i	$0.510668\pi$
$734$	−1530.77	−	2651.36i	−0.0769776	−	0.133329i
$735$		0			0
$736$	1387.99	−	2404.06i	0.0695134	−	0.120401i
$737$			796.481i			0.0398084i
$738$	−1743.66	−	533.705i	−0.0869717	−	0.0266205i
$739$	−1773.47			−0.0882790			−0.0441395	−	0.999025i	$-0.514055\pi$
$739$	−1773.47			−0.0882790			−0.0441395	+	0.999025i	$0.514055\pi$
$740$		0			0
$741$	2193.03	−	5041.42i	0.108722	−	0.249934i
$742$	−2400.43	+	1385.89i	−0.118764	+	0.0685682i
$743$	−4573.28	+	2640.39i	−0.225811	+	0.130372i	−0.608638	−	0.793448i	$-0.708284\pi$
$743$	−4573.28	+	2640.39i	−0.225811	+	0.130372i	0.382827	+	0.923820i	$0.374950\pi$
$744$	−1825.17	+	4195.76i	−0.0899381	+	0.206753i
$745$		0			0
$746$	2338.14			0.114753
$747$	25544.6	−	23805.4i	1.25117	−	1.16599i
$748$		−	862.437i		−	0.0421575i
$749$	866.918	−	1501.55i	0.0422917	−	0.0732514i
$750$		0			0
$751$	−5514.51	−	9551.40i	−0.267946	−	0.464095i	0.700386	−	0.713765i	$-0.253011\pi$
$751$	−5514.51	−	9551.40i	−0.267946	−	0.464095i	−0.968331	+	0.249669i	$0.919678\pi$
$752$	−24741.7	+	14284.6i	−1.19978	+	0.692696i
$753$	14569.8	−	10777.5i	0.705117	−	0.521584i
$754$	−769.692	+	1333.15i	−0.0371758	+	0.0643904i
$755$		0			0
$756$	13038.5	−	4610.09i	0.627255	−	0.221782i
$757$			19897.2i			0.955318i	0.878545	+	0.477659i	$0.158514\pi$
$757$			19897.2i			0.955318i	−0.878545	+	0.477659i	$0.841486\pi$
$758$	−1981.24	−	1143.87i	−0.0949363	−	0.0548115i
$759$	−155.040	−	209.595i	−0.00741448	−	0.0100235i
$760$		0			0
$761$	12636.2	+	21886.5i	0.601920	+	1.04256i	0.992530	+	0.122000i	$0.0389307\pi$
$761$	12636.2	+	21886.5i	0.601920	+	1.04256i	−0.390610	+	0.920556i	$0.627736\pi$
$762$	368.636	+	3240.11i	0.0175253	+	0.154038i
$763$	−440.571	−	254.364i	−0.0209040	−	0.0120689i
$764$	6103.40			0.289023
$765$		0			0
$766$	−2014.65			−0.0950292
$767$	−4649.96	−	2684.65i	−0.218905	−	0.126385i
$768$	14220.3	+	6185.87i	0.668137	+	0.290642i
$769$	15167.1	+	26270.1i	0.711233	+	1.23189i	0.964395	+	0.264467i	$0.0851961\pi$
$769$	15167.1	+	26270.1i	0.711233	+	1.23189i	−0.253162	+	0.967424i	$0.581471\pi$
$770$		0			0
$771$	−10201.4	+	23451.3i	−0.476517	+	1.09543i
$772$	3211.67	+	1854.26i	0.149729	+	0.0864458i
$773$			6671.36i			0.310417i	0.987882	+	0.155208i	$0.0496049\pi$
$773$			6671.36i			0.310417i	−0.987882	+	0.155208i	$0.950395\pi$
$774$	−3760.37	+	866.877i	−0.174630	+	0.0402574i
$775$		0			0
$776$	−5937.38	+	10283.8i	−0.274664	+	0.475732i
$777$	−1263.01	−	11101.2i	−0.0583143	−	0.512551i
$778$	−1449.95	+	837.129i	−0.0668165	+	0.0385765i
$779$	6992.04	+	12110.6i	0.321586	+	0.557004i
$780$		0			0
$781$	848.008	−	1468.79i	0.0388529	−	0.0672952i
$782$		−	1048.18i		−	0.0479321i
$783$	−41553.3	−	7722.18i	−1.89654	−	0.352450i
$784$	10678.9			0.486468
$785$		0			0
$786$	2331.43	+	3151.81i	0.105801	+	0.143030i
$787$	−18192.0	+	10503.1i	−0.823981	+	0.475726i	−0.851787	−	0.523888i	$-0.824481\pi$
$787$	−18192.0	+	10503.1i	−0.823981	+	0.475726i	0.0278064	+	0.999613i	$0.491148\pi$
$788$	31158.0	−	17989.1i	1.40858	−	0.813241i
$789$	−28484.2	+	3240.73i	−1.28525	+	0.146227i
$790$		0			0
$791$	−25088.7			−1.12775
$792$	−235.819	+	219.763i	−0.0105801	+	0.00985978i
$793$			6245.57i			0.279681i
$794$	934.230	−	1618.13i	0.0417564	−	0.0723242i
$795$		0			0
$796$	9848.29	+	17057.7i	0.438522	+	0.759542i
$797$	7909.00	−	4566.27i	0.351507	−	0.202943i	−0.313842	−	0.949475i	$-0.601616\pi$
$797$	7909.00	−	4566.27i	0.351507	−	0.202943i	0.665349	+	0.746533i	$0.268283\pi$
$798$	2835.08	+	1233.27i	0.125765	+	0.0547084i
$799$	−17005.9	+	29455.1i	−0.752975	+	1.30419i
$800$		0			0
$801$	3186.99	−	10412.2i	0.140583	−	0.459296i
$802$		−	384.328i		−	0.0169216i
$803$	599.379	+	346.051i	0.0263407	+	0.0152078i
$804$	−20104.0	+	2287.28i	−0.881856	+	0.100331i
$805$		0			0
$806$	299.628	+	518.970i	0.0130942	+	0.0226798i
$807$	−32768.5	+	24239.3i	−1.42938	+	1.05733i
$808$	−7509.61	−	4335.68i	−0.326964	−	0.188773i
$809$	−17687.6			−0.768681			−0.384341	−	0.923191i	$-0.625571\pi$
$809$	−17687.6			−0.768681			−0.384341	+	0.923191i	$0.625571\pi$
$810$		0			0
$811$	−7211.00			−0.312223			−0.156111	−	0.987739i	$-0.549896\pi$
$811$	−7211.00			−0.312223			−0.156111	+	0.987739i	$0.549896\pi$
$812$	25717.2	+	14847.8i	1.11145	+	0.641695i
$813$	−17968.7	+	13291.7i	−0.775142	+	0.573382i
$814$	64.1699	+	111.146i	0.00276309	+	0.00478581i
$815$		0			0
$816$	21115.6	−	2402.38i	0.905876	−	0.103064i
$817$	25628.9	+	14796.9i	1.09748	+	0.633631i
$818$			384.850i			0.0164498i
$819$	1075.68	−	3514.34i	0.0458940	−	0.149940i
$820$		0			0
$821$	−21037.2	+	36437.6i	−0.894281	+	1.54894i	−0.0595894	+	0.998223i	$0.518979\pi$
$821$	−21037.2	+	36437.6i	−0.894281	+	1.54894i	−0.834692	+	0.550717i	$0.814354\pi$
$822$	−865.376	−	376.442i	−0.0367195	−	0.0159731i
$823$	18078.5	−	10437.6i	0.765707	−	0.442081i	−0.0656341	−	0.997844i	$-0.520907\pi$
$823$	18078.5	−	10437.6i	0.765707	−	0.442081i	0.831341	+	0.555763i	$0.187574\pi$
$824$	5448.41	+	9436.93i	0.230345	+	0.398970i
$825$		0			0
$826$	1509.74	−	2614.94i	0.0635962	−	0.110152i
$827$		−	3128.34i		−	0.131540i	−0.997835	−	0.0657698i	$-0.979050\pi$
$827$		−	3128.34i		−	0.131540i	0.997835	−	0.0657698i	$-0.0209503\pi$
$828$	4845.14	−	4515.26i	0.203358	−	0.189512i
$829$	6854.35			0.287167			0.143583	−	0.989638i	$-0.454137\pi$
$829$	6854.35			0.287167			0.143583	+	0.989638i	$0.454137\pi$
$830$		0			0
$831$	−9560.78	+	1087.76i	−0.399109	+	0.0454078i
$832$	3969.71	−	2291.92i	0.165415	−	0.0955022i
$833$	11010.1	−	6356.66i	0.457954	−	0.264400i
$834$	3622.18	+	4896.74i	0.150391	+	0.203310i
$835$		0			0
$836$	1218.24			0.0503990
$837$	−10691.3	+	12505.7i	−0.441514	+	0.516442i
$838$			837.906i			0.0345405i
$839$	20793.2	−	36014.9i	0.855615	−	1.48197i	−0.0204588	−	0.999791i	$-0.506513\pi$
$839$	20793.2	−	36014.9i	0.855615	−	1.48197i	0.876074	−	0.482178i	$-0.160154\pi$
$840$		0			0
$841$	−33182.4	−	57473.6i	−1.36055	−	2.35654i
$842$	−6008.96	+	3469.27i	−0.245941	+	0.141994i
$843$	−4077.58	−	35839.7i	−0.166595	−	1.46428i
$844$	−10748.2	+	18616.5i	−0.438352	+	0.759249i
$845$		0			0
$846$	6104.73	−	1407.32i	0.248091	−	0.0571922i
$847$			16846.2i			0.683404i
$848$	−23307.3	−	13456.5i	−0.943840	−	0.544926i
$849$	−13332.7	+	30649.5i	−0.538958	+	1.23897i
$850$		0			0
$851$	−2675.31	−	4633.77i	−0.107765	−	0.186655i
$852$	39509.0	+	17186.6i	1.58868	+	0.691082i
$853$	15866.1	+	9160.28i	0.636863	+	0.367693i	0.783405	−	0.621512i	$-0.213481\pi$
$853$	15866.1	+	9160.28i	0.636863	+	0.367693i	−0.146542	+	0.989204i	$0.546814\pi$
$854$	−3512.25			−0.140734
$855$		0			0
$856$	−1026.65			−0.0409931
$857$	10720.5	+	6189.48i	0.427310	+	0.246708i	0.698200	−	0.715903i	$-0.253985\pi$
$857$	10720.5	+	6189.48i	0.427310	+	0.246708i	−0.270890	+	0.962610i	$0.587318\pi$
$858$	4.77239	+	41.9467i	0.000189891	+	0.00166904i
$859$	−14758.5	−	25562.5i	−0.586210	−	1.01534i	−0.994723	−	0.102593i	$-0.967286\pi$
$859$	−14758.5	−	25562.5i	−0.586210	−	1.01534i	0.408514	−	0.912752i	$-0.366047\pi$
$860$		0			0
$861$	5559.45	+	7515.69i	0.220053	+	0.297484i
$862$	2356.19	+	1360.35i	0.0931001	+	0.0537514i
$863$		−	41307.0i		−	1.62932i	−0.579937	−	0.814661i	$-0.696923\pi$
$863$		−	41307.0i		−	1.62932i	0.579937	−	0.814661i	$-0.303077\pi$
$864$	−9381.08	−	8020.03i	−0.369387	−	0.315795i
$865$		0			0
$866$	3035.06	−	5256.88i	0.119094	−	0.206277i
$867$	−183.511	+	135.745i	−0.00718840	+	0.00531735i
$868$	10011.3	−	5780.00i	0.391479	−	0.226021i
$869$	−298.352	−	516.760i	−0.0116466	−	0.0201725i
$870$		0			0
$871$	−2688.61	+	4656.81i	−0.104593	+	0.181160i
$872$			301.230i			0.0116983i
$873$	−31237.9	+	29111.1i	−1.21105	+	1.12859i
$874$	1480.61			0.0573025
$875$		0			0
$876$	−7013.42	+	16122.7i	−0.270504	+	0.621843i
$877$	33174.7	−	19153.4i	1.27734	−	0.737475i	0.300984	−	0.953629i	$-0.402685\pi$
$877$	33174.7	−	19153.4i	1.27734	−	0.737475i	0.976359	+	0.216155i	$0.0693515\pi$
$878$	1995.75	−	1152.25i	0.0767122	−	0.0442898i
$879$	15839.3	−	36412.0i	0.607790	−	1.39721i
$880$		0			0
$881$	−47903.1			−1.83189			−0.915946	−	0.401301i	$-0.868558\pi$
$881$	−47903.1			−1.83189			−0.915946	+	0.401301i	$0.868558\pi$
$882$	−2239.20	−	685.379i	−0.0854849	−	0.0261654i
$883$			39098.9i			1.49013i	0.666993	+	0.745064i	$0.267581\pi$
$883$			39098.9i			1.49013i	−0.666993	+	0.745064i	$0.732419\pi$
$884$	2911.25	−	5042.43i	0.110765	−	0.191850i
$885$		0			0
$886$	2129.30	+	3688.05i	0.0807394	+	0.139845i
$887$	24451.4	−	14117.0i	0.925590	−	0.534389i	0.0401756	−	0.999193i	$-0.487208\pi$
$887$	24451.4	−	14117.0i	0.925590	−	0.534389i	0.885414	+	0.464803i	$0.153875\pi$
$888$	−5318.70	+	3934.31i	−0.200995	+	0.148679i
$889$	8358.96	−	14478.1i	0.315355	−	0.546211i
$890$		0			0
$891$	−1042.12	+	507.446i	−0.0391833	+	0.0190798i
$892$			3648.74i			0.136961i
$893$	−41606.9	−	24021.8i	−1.55915	−	0.900177i
$894$	−565.371	−	764.313i	−0.0211508	−	0.0285933i
$895$		0			0
$896$	5751.09	+	9961.18i	0.214431	+	0.371406i
$897$	−198.965	−	1748.80i	−0.00740609	−	0.0650955i
$898$	1131.06	+	653.016i	0.0420311	+	0.0242666i
$899$	−35328.9			−1.31066
$900$		0			0
$901$	−32040.0			−1.18469
$902$	−92.9971	−	53.6919i	−0.00343289	−	0.00198198i
$903$	18141.4	+	7891.59i	0.668559	+	0.290826i
$904$	7427.83	+	12865.4i	0.273281	+	0.473336i
$905$		0			0
$906$	786.491	−	1808.01i	0.0288404	−	0.0662992i
$907$	16506.9	+	9530.28i	0.604304	+	0.348895i	0.770733	−	0.637159i	$-0.219890\pi$
$907$	16506.9	+	9530.28i	0.604304	+	0.348895i	−0.166429	+	0.986053i	$0.553224\pi$
$908$			33332.1i			1.21824i
$909$	−21257.9	−	22811.0i	−0.775665	−	0.832336i
$910$		0			0
$911$	727.041	−	1259.27i	0.0264412	−	0.0457975i	−0.852502	−	0.522724i	$-0.824916\pi$
$911$	727.041	−	1259.27i	0.0264412	−	0.0457975i	0.878943	+	0.476926i	$0.158249\pi$
$912$	3393.49	+	29826.9i	0.123212	+	1.08297i
$913$	1780.74	−	1028.11i	0.0645499	−	0.0372679i
$914$	1335.92	+	2313.88i	0.0483461	+	0.0837379i
$915$		0			0
$916$	15953.3	−	27632.0i	0.575451	−	0.996711i
$917$		−	20098.3i		−	0.723778i
$918$	−4581.79	−	851.470i	−0.164729	−	0.0306130i
$919$	6383.04			0.229115			0.114558	−	0.993417i	$-0.463455\pi$
$919$	6383.04			0.229115			0.114558	+	0.993417i	$0.463455\pi$
$920$		0			0
$921$	13960.1	+	18872.3i	0.499458	+	0.675205i
$922$	−5172.61	+	2986.41i	−0.184762	+	0.106673i
$923$	9916.14	−	5725.09i	0.353623	−	0.204164i
$924$	809.176	−	92.0622i	0.0288095	−	0.00327773i
$925$		0			0
$926$	−5104.16			−0.181137
$927$	8802.02	+	38181.8i	0.311862	+	1.35281i
$928$		−	26501.7i		−	0.937456i
$929$	14466.9	−	25057.5i	0.510920	−	0.884939i	−0.489000	−	0.872284i	$-0.662638\pi$
$929$	14466.9	−	25057.5i	0.510920	−	0.884939i	0.999920	−	0.0126553i	$-0.00402841\pi$
$930$		0			0
$931$	8979.11	+	15552.3i	0.316089	+	0.547482i
$932$	−28762.8	+	16606.2i	−1.01090	+	0.583641i
$933$	18740.5	+	8152.20i	0.657596	+	0.286057i
$934$	−3046.24	+	5276.25i	−0.106720	+	0.184844i
$935$		0			0
$936$	−2120.60	+	488.862i	−0.0740536	+	0.0170715i
$937$			8282.43i			0.288768i	0.989522	+	0.144384i	$0.0461200\pi$
$937$			8282.43i			0.288768i	−0.989522	+	0.144384i	$0.953880\pi$
$938$	−2618.80	−	1511.96i	−0.0911585	−	0.0526304i
$939$	−16346.5	+	1859.79i	−0.568103	+	0.0646346i
$940$		0			0
$941$	18408.2	+	31883.9i	0.637715	+	1.10455i	0.985933	+	0.167141i	$0.0534534\pi$
$941$	18408.2	+	31883.9i	0.637715	+	1.10455i	−0.348219	+	0.937413i	$0.613213\pi$
$942$	−1732.07	+	1281.23i	−0.0599085	+	0.0443151i
$943$	3877.14	+	2238.47i	0.133889	+	0.0773007i
$944$	29318.0			1.01083
$945$		0			0
$946$	−227.250			−0.00781031
$947$	806.104	+	465.404i	0.0276609	+	0.0159700i	0.513767	−	0.857930i	$-0.328250\pi$
$947$	806.104	+	465.404i	0.0276609	+	0.0159700i	−0.486106	+	0.873900i	$0.661583\pi$
$948$	12186.7	−	9014.69i	0.417518	−	0.308843i
$949$	2336.27	+	4046.54i	0.0799141	+	0.138415i
$950$		0			0
$951$	40485.6	−	4606.15i	1.38048	−	0.157061i
$952$	5753.97	+	3322.06i	0.195890	+	0.113097i
$953$			11327.1i			0.385016i	0.981295	+	0.192508i	$0.0616621\pi$
$953$			11327.1i			0.385016i	−0.981295	+	0.192508i	$0.938338\pi$
$954$	4023.52	+	4317.48i	0.136547	+	0.146524i
$955$		0			0
$956$	−6068.05	+	10510.2i	−0.205287	+	0.355568i
$957$	−2282.31	−	992.815i	−0.0770917	−	0.0335352i
$958$	995.507	−	574.756i	0.0335734	−	0.0193836i
$959$	2419.00	+	4189.84i	0.0814533	+	0.141081i
$960$		0			0
$961$	8019.05	−	13889.4i	0.269177	−	0.466228i
$962$			866.451i			0.0290390i
$963$	−3530.00	−	1080.47i	−0.118123	−	0.0361555i
$964$	−37479.7			−1.25222
$965$		0			0
$966$	983.451	−	111.890i	0.0327557	−	0.00372670i
$967$	36215.3	−	20908.9i	1.20435	−	0.695330i	0.242829	−	0.970069i	$-0.421925\pi$
$967$	36215.3	−	20908.9i	1.20435	−	0.695330i	0.961519	+	0.274739i	$0.0885914\pi$
$968$	8638.67	−	4987.54i	0.286836	−	0.165605i
$969$	21253.3	+	28731.8i	0.704596	+	0.952527i
$970$		0			0
$971$	−40444.6			−1.33669			−0.668346	−	0.743850i	$-0.732997\pi$
$971$	−40444.6			−1.33669			−0.668346	+	0.743850i	$0.732997\pi$
$972$	−15801.1	−	24846.9i	−0.521421	−	0.819921i
$973$		−	31225.3i		−	1.02881i
$974$	−3900.37	+	6755.64i	−0.128312	+	0.222243i
$975$		0			0
$976$	−17051.3	−	29533.8i	−0.559221	−	0.968600i
$977$	−36843.1	+	21271.4i	−1.20646	+	0.696553i	−0.961985	−	0.273102i	$-0.911950\pi$
$977$	−36843.1	+	21271.4i	−1.20646	+	0.696553i	−0.244479	+	0.969655i	$0.578617\pi$
$978$	8.74098	+	76.8284i	0.000285793	+	0.00251197i
$979$	320.618	−	555.327i	0.0104668	−	0.0181290i
$980$		0			0
$981$	−317.023	+	1035.74i	−0.0103178	+	0.0337092i
$982$		−	7555.19i		−	0.245515i
$983$	−15490.6	−	8943.52i	−0.502619	−	0.290187i	0.227175	−	0.973854i	$-0.427051\pi$
$983$	−15490.6	−	8943.52i	−0.502619	−	0.290187i	−0.729794	+	0.683667i	$0.760384\pi$
$984$	2208.07	−	5075.98i	0.0715352	−	0.164447i
$985$		0			0
$986$	−5003.39	−	8666.13i	−0.161603	−	0.279904i
$987$	−29451.5	−	12811.5i	−0.949797	−	0.413165i
$988$	7122.70	+	4112.29i	0.229355	+	0.132418i
$989$	9474.29			0.304616
$990$		0			0
$991$	41046.0			1.31571			0.657856	−	0.753144i	$-0.271464\pi$
$991$	41046.0			1.31571			0.657856	+	0.753144i	$0.271464\pi$
$992$	−8934.46	−	5158.31i	−0.285957	−	0.165097i
$993$	6374.99	+	56032.7i	0.203730	+	1.79068i
$994$	3219.55	+	5576.42i	0.102734	+	0.177941i
$995$		0			0
$996$	31064.4	+	41995.3i	0.988266	+	1.33601i
$997$	−21504.2	−	12415.4i	−0.683093	−	0.394384i	0.117926	−	0.993022i	$-0.462375\pi$
$997$	−21504.2	−	12415.4i	−0.683093	−	0.394384i	−0.801019	+	0.598638i	$0.795709\pi$
$998$			5455.74i			0.173044i
$999$	−22428.3	+	7930.09i	−0.710309	+	0.251148i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.k.e.124.13		48
5.2	odd	4		225.4.e.f.151.6	yes	24
5.3	odd	4		225.4.e.e.151.7	yes	24
5.4	even	2	inner	225.4.k.e.124.12		48
9.4	even	3	inner	225.4.k.e.49.12		48
45.2	even	12		2025.4.a.bj.1.6		12
45.4	even	6	inner	225.4.k.e.49.13		48
45.7	odd	12		2025.4.a.bf.1.7		12
45.13	odd	12		225.4.e.e.76.7	✓	24
45.22	odd	12		225.4.e.f.76.6	yes	24
45.38	even	12		2025.4.a.be.1.7		12
45.43	odd	12		2025.4.a.bi.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.e.e.76.7	✓	24	45.13	odd	12
225.4.e.e.151.7	yes	24	5.3	odd	4
225.4.e.f.76.6	yes	24	45.22	odd	12
225.4.e.f.151.6	yes	24	5.2	odd	4
225.4.k.e.49.12		48	9.4	even	3	inner
225.4.k.e.49.13		48	45.4	even	6	inner
225.4.k.e.124.12		48	5.4	even	2	inner
225.4.k.e.124.13		48	1.1	even	1	trivial
2025.4.a.be.1.7		12	45.38	even	12
2025.4.a.bf.1.7		12	45.7	odd	12
2025.4.a.bi.1.6		12	45.43	odd	12
2025.4.a.bj.1.6		12	45.2	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.412258 + 0.238017i) q^{2} +(-4.17746 + 3.09012i) q^{3} +(-3.88670 - 6.73195i) q^{4} +(-2.45769 + 0.279619i) q^{6} +(10.9820 + 6.34045i) q^{7} -7.50869i q^{8} +(7.90234 - 25.8177i) q^{9} +O(q^{10})\)	\(q+(0.412258 + 0.238017i) q^{2} +(-4.17746 + 3.09012i) q^{3} +(-3.88670 - 6.73195i) q^{4} +(-2.45769 + 0.279619i) q^{6} +(10.9820 + 6.34045i) q^{7} -7.50869i q^{8} +(7.90234 - 25.8177i) q^{9} +(0.794994 - 1.37697i) q^{11} +(37.0390 + 16.1121i) q^{12} +(9.29622 - 5.36718i) q^{13} +(3.01828 + 5.22781i) q^{14} +(-29.3064 + 50.7601i) q^{16} +69.7787i q^{17} +(9.40287 - 8.76266i) q^{18} -98.5661 q^{19} +(-65.4695 + 7.44864i) q^{21} +(0.655486 - 0.378445i) q^{22} +(-27.3278 + 15.7777i) q^{23} +(23.2027 + 31.3672i) q^{24} +5.10993 q^{26} +(46.7680 + 132.272i) q^{27} -98.5736i q^{28} +(-150.627 + 260.893i) q^{29} +(58.6364 + 101.561i) q^{31} +(-76.1853 + 43.9856i) q^{32} +(0.933944 + 8.20886i) q^{33} +(-16.6086 + 28.7669i) q^{34} +(-204.517 + 47.1473i) q^{36} +169.562i q^{37} +(-40.6347 - 23.4605i) q^{38} +(-22.2494 + 51.1476i) q^{39} +(-70.9376 - 122.868i) q^{41} +(-28.7633 - 12.5121i) q^{42} +(-260.018 - 150.121i) q^{43} -12.3596 q^{44} -15.0215 q^{46} +(422.122 + 243.712i) q^{47} +(-34.4286 - 302.608i) q^{48} +(-91.0974 - 157.785i) q^{49} +(-215.625 - 291.498i) q^{51} +(-72.2632 - 41.7212i) q^{52} +459.166i q^{53} +(-12.2024 + 65.6616i) q^{54} +(47.6084 - 82.4602i) q^{56} +(411.756 - 304.581i) q^{57} +(-124.194 + 71.7037i) q^{58} +(-250.099 - 433.185i) q^{59} +(-290.915 + 503.880i) q^{61} +55.8259i q^{62} +(250.479 - 233.425i) q^{63} +427.024 q^{64} +(-1.56883 + 3.60647i) q^{66} +(-433.823 + 250.468i) q^{67} +(469.747 - 271.209i) q^{68} +(65.4059 - 150.357i) q^{69} +1066.69 q^{71} +(-193.857 - 59.3362i) q^{72} +435.288i q^{73} +(-40.3588 + 69.9034i) q^{74} +(383.096 + 663.542i) q^{76} +(17.4612 - 10.0812i) q^{77} +(-21.3465 + 15.7903i) q^{78} +(187.644 - 325.009i) q^{79} +(-604.106 - 408.040i) q^{81} -67.5375i q^{82} +(1119.97 + 646.617i) q^{83} +(304.604 + 411.787i) q^{84} +(-71.4630 - 123.778i) q^{86} +(-176.954 - 1555.33i) q^{87} +(-10.3392 - 5.96936i) q^{88} +403.296 q^{89} +136.121 q^{91} +(212.430 + 122.646i) q^{92} +(-558.787 - 243.074i) q^{93} +(116.016 + 200.945i) q^{94} +(182.340 - 419.170i) q^{96} +(-1369.59 - 790.735i) q^{97} -86.7311i q^{98} +(-29.2679 - 31.4062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 96 q^{4} - 26 q^{6} + 122 q^{9}+O(q^{10}) \) 48 * q + 96 * q^4 - 26 * q^6 + 122 * q^9	\( 48 q + 96 q^{4} - 26 q^{6} + 122 q^{9} - 58 q^{11} - 138 q^{14} - 384 q^{16} + 300 q^{19} - 120 q^{21} - 684 q^{24} - 616 q^{26} + 212 q^{29} - 120 q^{31} - 216 q^{34} + 2606 q^{36} + 820 q^{39} + 706 q^{41} - 2284 q^{44} + 1080 q^{46} + 1332 q^{49} - 2738 q^{51} + 4256 q^{54} + 1140 q^{56} + 964 q^{59} - 804 q^{61} - 3900 q^{64} + 4082 q^{66} - 5712 q^{69} - 3776 q^{71} + 20 q^{74} + 924 q^{76} + 516 q^{79} + 6142 q^{81} + 5406 q^{84} - 3904 q^{86} + 2952 q^{89} - 2472 q^{91} + 126 q^{94} - 20848 q^{96} + 3394 q^{99}+O(q^{100}) \) 48 * q + 96 * q^4 - 26 * q^6 + 122 * q^9 - 58 * q^11 - 138 * q^14 - 384 * q^16 + 300 * q^19 - 120 * q^21 - 684 * q^24 - 616 * q^26 + 212 * q^29 - 120 * q^31 - 216 * q^34 + 2606 * q^36 + 820 * q^39 + 706 * q^41 - 2284 * q^44 + 1080 * q^46 + 1332 * q^49 - 2738 * q^51 + 4256 * q^54 + 1140 * q^56 + 964 * q^59 - 804 * q^61 - 3900 * q^64 + 4082 * q^66 - 5712 * q^69 - 3776 * q^71 + 20 * q^74 + 924 * q^76 + 516 * q^79 + 6142 * q^81 + 5406 * q^84 - 3904 * q^86 + 2952 * q^89 - 2472 * q^91 + 126 * q^94 - 20848 * q^96 + 3394 * q^99

Introduction

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