LMFDB - Embedded newform 225.4.e.g.76.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(76,225)]

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, 0]))

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

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

chi := DirichletCharacter("225.76");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			76.16
Character	$\chi$	$=$	225.76
Dual form			225.4.e.g.151.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.52718 + 4.37720i) q^{2} +(-0.559681 + 5.16592i) q^{3} +(-8.77324 + 15.1957i) q^{4} +(-24.0267 + 10.6054i) q^{6} +(-10.5059 - 18.1967i) q^{7} -48.2513 q^{8} +(-26.3735 - 5.78253i) q^{9} +O(q^{10})$	\(q+(2.52718 + 4.37720i) q^{2} +(-0.559681 + 5.16592i) q^{3} +(-8.77324 + 15.1957i) q^{4} +(-24.0267 + 10.6054i) q^{6} +(-10.5059 - 18.1967i) q^{7} -48.2513 q^{8} +(-26.3735 - 5.78253i) q^{9} +(14.2815 + 24.7362i) q^{11} +(-73.5896 - 53.8266i) q^{12} +(5.03520 - 8.72122i) q^{13} +(53.1003 - 91.9724i) q^{14} +(-51.7535 - 89.6398i) q^{16} -82.7541 q^{17} +(-41.3392 - 130.056i) q^{18} +1.91981 q^{19} +(99.8826 - 44.0881i) q^{21} +(-72.1836 + 125.026i) q^{22} +(-85.2818 + 147.712i) q^{23} +(27.0053 - 249.262i) q^{24} +50.8993 q^{26} +(44.6329 - 133.007i) q^{27} +368.682 q^{28} +(128.214 + 222.074i) q^{29} +(-24.0262 + 41.6147i) q^{31} +(68.5756 - 118.776i) q^{32} +(-135.779 + 59.9326i) q^{33} +(-209.134 - 362.231i) q^{34} +(319.251 - 350.032i) q^{36} +161.834 q^{37} +(4.85169 + 8.40337i) q^{38} +(42.2350 + 30.8925i) q^{39} +(-139.674 + 241.922i) q^{41} +(445.403 + 325.787i) q^{42} +(-134.536 - 233.024i) q^{43} -501.179 q^{44} -862.088 q^{46} +(4.79420 + 8.30380i) q^{47} +(492.038 - 217.185i) q^{48} +(-49.2462 + 85.2969i) q^{49} +(46.3158 - 427.501i) q^{51} +(88.3500 + 153.027i) q^{52} +35.7716 q^{53} +(694.994 - 140.766i) q^{54} +(506.921 + 878.013i) q^{56} +(-1.07448 + 9.91757i) q^{57} +(-648.040 + 1122.44i) q^{58} +(281.385 - 487.374i) q^{59} +(39.6621 + 68.6968i) q^{61} -242.874 q^{62} +(171.854 + 540.661i) q^{63} -134.846 q^{64} +(-605.473 - 442.869i) q^{66} +(-233.376 + 404.219i) q^{67} +(726.021 - 1257.51i) q^{68} +(-715.340 - 523.231i) q^{69} +316.854 q^{71} +(1272.56 + 279.015i) q^{72} -633.515 q^{73} +(408.984 + 708.381i) q^{74} +(-16.8429 + 29.1728i) q^{76} +(300.078 - 519.751i) q^{77} +(-28.4874 + 262.942i) q^{78} +(395.658 + 685.299i) q^{79} +(662.125 + 305.011i) q^{81} -1411.92 q^{82} +(-114.039 - 197.521i) q^{83} +(-206.344 + 1904.58i) q^{84} +(679.994 - 1177.78i) q^{86} +(-1218.97 + 538.054i) q^{87} +(-689.099 - 1193.55i) q^{88} +53.9091 q^{89} -211.596 q^{91} +(-1496.39 - 2591.83i) q^{92} +(-201.531 - 147.409i) q^{93} +(-24.2316 + 41.9704i) q^{94} +(575.209 + 420.733i) q^{96} +(48.3470 + 83.7394i) q^{97} -497.815 q^{98} +(-233.614 - 734.964i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 54 q^{4} - 12 q^{6} + 18 q^{9}+O(q^{10}) $ 32 * q - 54 * q^4 - 12 * q^6 + 18 * q^9	$ 32 q - 54 q^{4} - 12 q^{6} + 18 q^{9} + 90 q^{11} + 102 q^{14} - 146 q^{16} + 8 q^{19} + 30 q^{21} - 462 q^{24} - 936 q^{26} + 516 q^{29} - 38 q^{31} - 212 q^{34} + 864 q^{36} - 330 q^{39} + 576 q^{41} - 3288 q^{44} - 580 q^{46} + 4 q^{49} + 1260 q^{51} + 3726 q^{54} + 2430 q^{56} + 2202 q^{59} - 20 q^{61} - 644 q^{64} - 5052 q^{66} - 1452 q^{69} - 5904 q^{71} + 4080 q^{74} + 396 q^{76} + 218 q^{79} + 198 q^{81} - 4662 q^{84} + 6108 q^{86} - 8148 q^{89} - 1884 q^{91} + 1078 q^{94} + 11874 q^{96} + 1602 q^{99}+O(q^{100}) $ 32 * q - 54 * q^4 - 12 * q^6 + 18 * q^9 + 90 * q^11 + 102 * q^14 - 146 * q^16 + 8 * q^19 + 30 * q^21 - 462 * q^24 - 936 * q^26 + 516 * q^29 - 38 * q^31 - 212 * q^34 + 864 * q^36 - 330 * q^39 + 576 * q^41 - 3288 * q^44 - 580 * q^46 + 4 * q^49 + 1260 * q^51 + 3726 * q^54 + 2430 * q^56 + 2202 * q^59 - 20 * q^61 - 644 * q^64 - 5052 * q^66 - 1452 * q^69 - 5904 * q^71 + 4080 * q^74 + 396 * q^76 + 218 * q^79 + 198 * q^81 - 4662 * q^84 + 6108 * q^86 - 8148 * q^89 - 1884 * q^91 + 1078 * q^94 + 11874 * q^96 + 1602 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	2.52718	+	4.37720i	0.893492	+	1.54757i	0.835660	+	0.549247i	$0.185085\pi$
$2$	2.52718	+	4.37720i	0.893492	+	1.54757i	0.0578315	+	0.998326i	$0.481581\pi$
$3$	−0.559681	+	5.16592i	−0.107711	+	0.994182i
$3$	−0.559681	+	5.16592i	−0.107711	+	0.994182i
$4$	−8.77324	+	15.1957i	−1.09665	+	1.89946i
$5$		0			0
$5$		0			0
$6$	−24.0267	+	10.6054i	−1.63481	+	0.721604i
$7$	−10.5059	−	18.1967i	−0.567263	−	0.982529i	−0.996835	−	0.0794959i	$-0.974669\pi$
$7$	−10.5059	−	18.1967i	−0.567263	−	0.982529i	0.429572	−	0.903033i	$-0.358664\pi$
$8$	−48.2513			−2.13243
$9$	−26.3735	−	5.78253i	−0.976797	−	0.214168i
$10$		0			0
$11$	14.2815	+	24.7362i	0.391457	+	0.678023i	0.992642	−	0.121087i	$-0.0386379\pi$
$11$	14.2815	+	24.7362i	0.391457	+	0.678023i	−0.601185	+	0.799110i	$0.705305\pi$
$12$	−73.5896	−	53.8266i	−1.77029	−	1.29487i
$13$	5.03520	−	8.72122i	0.107424	−	0.186064i	−0.807302	−	0.590139i	$-0.799073\pi$
$13$	5.03520	−	8.72122i	0.107424	−	0.186064i	0.914726	+	0.404075i	$0.132406\pi$
$14$	53.1003	−	91.9724i	1.01369	−	1.75576i
$15$		0			0
$16$	−51.7535	−	89.6398i	−0.808649	−	1.40062i
$17$	−82.7541			−1.18064			−0.590318	−	0.807171i	$-0.700998\pi$
$17$	−82.7541			−1.18064			−0.590318	+	0.807171i	$0.700998\pi$
$18$	−41.3392	−	130.056i	−0.541319	−	1.70302i
$19$	1.91981			0.0231807			0.0115904	−	0.999933i	$-0.496311\pi$
$19$	1.91981			0.0231807			0.0115904	+	0.999933i	$0.496311\pi$
$20$		0			0
$21$	99.8826	−	44.0881i	1.03791	−	0.458134i
$22$	−72.1836	+	125.026i	−0.699527	+	1.21162i
$23$	−85.2818	+	147.712i	−0.773151	+	1.33914i	0.162677	+	0.986679i	$0.447987\pi$
$23$	−85.2818	+	147.712i	−0.773151	+	1.33914i	−0.935828	+	0.352458i	$0.885346\pi$
$24$	27.0053	−	249.262i	0.229685	−	2.12002i
$25$		0			0
$26$	50.8993			0.383930
$27$	44.6329	−	133.007i	0.318133	−	0.948046i
$28$	368.682			2.48837
$29$	128.214	+	222.074i	0.820993	+	1.42200i	0.904944	+	0.425531i	$0.139913\pi$
$29$	128.214	+	222.074i	0.820993	+	1.42200i	−0.0839514	+	0.996470i	$0.526754\pi$
$30$		0			0
$31$	−24.0262	+	41.6147i	−0.139201	+	0.241104i	−0.927195	−	0.374580i	$-0.877787\pi$
$31$	−24.0262	+	41.6147i	−0.139201	+	0.241104i	0.787993	+	0.615684i	$0.211120\pi$
$32$	68.5756	−	118.776i	0.378830	−	0.656153i
$33$	−135.779	+	59.9326i	−0.716243	+	0.316149i
$34$	−209.134	−	362.231i	−1.05489	−	1.82712i
$35$		0			0
$36$	319.251	−	350.032i	1.47801	−	1.62052i
$37$	161.834			0.719065			0.359533	−	0.933132i	$-0.382936\pi$
$37$	161.834			0.719065			0.359533	+	0.933132i	$0.382936\pi$
$38$	4.85169	+	8.40337i	0.0207118	+	0.0358739i
$39$	42.2350	+	30.8925i	0.173411	+	0.126840i
$40$		0			0
$41$	−139.674	+	241.922i	−0.532034	+	0.921510i	0.467266	+	0.884117i	$0.345239\pi$
$41$	−139.674	+	241.922i	−0.532034	+	0.921510i	−0.999301	+	0.0373937i	$0.988094\pi$
$42$	445.403	+	325.787i	1.63636	+	1.19691i
$43$	−134.536	−	233.024i	−0.477130	−	0.826414i	0.522526	−	0.852623i	$-0.324990\pi$
$43$	−134.536	−	233.024i	−0.477130	−	0.826414i	−0.999656	+	0.0262093i	$0.991656\pi$
$44$	−501.179			−1.71717
$45$		0			0
$46$	−862.088			−2.76322
$47$	4.79420	+	8.30380i	0.0148789	+	0.0257709i	0.873369	−	0.487059i	$-0.161930\pi$
$47$	4.79420	+	8.30380i	0.0148789	+	0.0257709i	−0.858490	+	0.512830i	$0.828597\pi$
$48$	492.038	−	217.185i	1.47957	−	0.653083i
$49$	−49.2462	+	85.2969i	−0.143575	+	0.248679i
$50$		0			0
$51$	46.3158	−	427.501i	0.127167	−	1.17377i
$52$	88.3500	+	153.027i	0.235614	+	0.408096i
$53$	35.7716			0.0927095			0.0463547	−	0.998925i	$-0.485240\pi$
$53$	35.7716			0.0927095			0.0463547	+	0.998925i	$0.485240\pi$
$54$	694.994	−	140.766i	1.75142	−	0.354737i
$55$		0			0
$56$	506.921	+	878.013i	1.20965	+	2.09517i
$57$	−1.07448	+	9.91757i	−0.00249681	+	0.0230459i
$58$	−648.040	+	1122.44i	−1.46710	+	2.54109i
$59$	281.385	−	487.374i	0.620903	−	1.07544i	−0.368415	−	0.929661i	$-0.620100\pi$
$59$	281.385	−	487.374i	0.620903	−	1.07544i	0.989318	−	0.145774i	$-0.0465671\pi$
$60$		0			0
$61$	39.6621	+	68.6968i	0.0832494	+	0.144192i	0.904644	−	0.426168i	$-0.140137\pi$
$61$	39.6621	+	68.6968i	0.0832494	+	0.144192i	−0.821395	+	0.570360i	$0.806804\pi$
$62$	−242.874			−0.497501
$63$	171.854	+	540.661i	0.343675	+	1.08122i
$64$	−134.846			−0.263372
$65$		0			0
$66$	−605.473	−	442.869i	−1.12922	−	0.825961i
$67$	−233.376	+	404.219i	−0.425544	+	0.737063i	−0.996471	−	0.0839374i	$-0.973250\pi$
$67$	−233.376	+	404.219i	−0.425544	+	0.737063i	0.570927	+	0.821001i	$0.306584\pi$
$68$	726.021	−	1257.51i	1.29475	−	2.24257i
$69$	−715.340	−	523.231i	−1.24807	−	0.912892i
$70$		0			0
$71$	316.854			0.529628			0.264814	−	0.964299i	$-0.414689\pi$
$71$	316.854			0.529628			0.264814	+	0.964299i	$0.414689\pi$
$72$	1272.56	+	279.015i	2.08295	+	0.456697i
$73$	−633.515			−1.01572			−0.507859	−	0.861440i	$-0.669563\pi$
$73$	−633.515			−1.01572			−0.507859	+	0.861440i	$0.669563\pi$
$74$	408.984	+	708.381i	0.642479	+	1.11281i
$75$		0			0
$76$	−16.8429	+	29.1728i	−0.0254213	+	0.0440309i
$77$	300.078	−	519.751i	0.444118	−	0.769235i
$78$	−28.4874	+	262.942i	−0.0413533	+	0.381696i
$79$	395.658	+	685.299i	0.563481	+	0.975977i	0.997189	+	0.0749238i	$0.0238714\pi$
$79$	395.658	+	685.299i	0.563481	+	0.975977i	−0.433709	+	0.901053i	$0.642795\pi$
$80$		0			0
$81$	662.125	+	305.011i	0.908264	+	0.418397i
$82$	−1411.92			−1.90147
$83$	−114.039	−	197.521i	−0.150812	−	0.261214i	0.780714	−	0.624888i	$-0.214855\pi$
$83$	−114.039	−	197.521i	−0.150812	−	0.261214i	−0.931526	+	0.363674i	$0.881522\pi$
$84$	−206.344	+	1904.58i	−0.268024	+	2.47389i
$85$		0			0
$86$	679.994	−	1177.78i	0.852624	−	1.47679i
$87$	−1218.97	+	538.054i	−1.50216	+	0.663052i
$88$	−689.099	−	1193.55i	−0.834752	−	1.44583i
$89$	53.9091			0.0642062			0.0321031	−	0.999485i	$-0.489780\pi$
$89$	53.9091			0.0642062			0.0321031	+	0.999485i	$0.489780\pi$
$90$		0			0
$91$	−211.596			−0.243751
$92$	−1496.39	−	2591.83i	−1.69576	−	2.93714i
$93$	−201.531	−	147.409i	−0.224708	−	0.164361i
$94$	−24.2316	+	41.9704i	−0.0265883	+	0.0460522i
$95$		0			0
$96$	575.209	+	420.733i	0.611532	+	0.447301i
$97$	48.3470	+	83.7394i	0.0506071	+	0.0876541i	0.890219	−	0.455532i	$-0.150551\pi$
$97$	48.3470	+	83.7394i	0.0506071	+	0.0876541i	−0.839612	+	0.543186i	$0.817218\pi$
$98$	−497.815			−0.513132
$99$	−233.614	−	734.964i	−0.237163	−	0.746128i
$100$		0			0
$101$	541.711	+	938.271i	0.533686	+	0.924371i	0.999226	+	0.0393438i	$0.0125267\pi$
$101$	541.711	+	938.271i	0.533686	+	0.924371i	−0.465540	+	0.885027i	$0.654140\pi$
$102$	1988.31	−	877.637i	1.93011	−	0.851951i
$103$	−215.161	+	372.670i	−0.205830	+	0.356507i	−0.950397	−	0.311040i	$-0.899323\pi$
$103$	−215.161	+	372.670i	−0.205830	+	0.356507i	0.744567	+	0.667548i	$0.232656\pi$
$104$	−242.955	+	420.810i	−0.229074	+	0.396767i
$105$		0			0
$106$	90.4010	+	156.579i	0.0828351	+	0.143475i
$107$	12.9348			0.0116865			0.00584323	−	0.999983i	$-0.498140\pi$
$107$	12.9348			0.0116865			0.00584323	+	0.999983i	$0.498140\pi$
$108$	1629.56	+	1845.13i	1.45189	+	1.64396i
$109$	−20.1087			−0.0176703			−0.00883517	−	0.999961i	$-0.502812\pi$
$109$	−20.1087			−0.0176703			−0.00883517	+	0.999961i	$0.502812\pi$
$110$		0			0
$111$	−90.5756	+	836.024i	−0.0774510	+	0.714882i
$112$	−1087.43	+	1883.49i	−0.917434	+	1.58904i
$113$	−565.320	+	979.163i	−0.470627	+	0.815150i	−0.999436	−	0.0335912i	$-0.989306\pi$
$113$	−565.320	+	979.163i	−0.470627	+	0.815150i	0.528809	+	0.848741i	$0.322639\pi$
$114$	−46.1266	+	20.3602i	−0.0378960	+	0.0167273i
$115$		0			0
$116$	−4499.42			−3.60138
$117$	−183.227	+	200.893i	−0.144780	+	0.158740i
$118$	2844.44			2.21909
$119$	869.403	+	1505.85i	0.669731	+	1.16001i
$120$		0			0
$121$	257.579	−	446.140i	0.193523	−	0.335192i
$122$	−200.466	+	347.218i	−0.148765	+	0.257669i
$123$	−1171.58	−	856.944i	−0.858843	−	0.628195i
$124$	−421.576	−	730.191i	−0.305312	−	0.528815i
$125$		0			0
$126$	−1932.28	+	2118.58i	−1.36620	+	1.49792i
$127$	−277.149			−0.193646			−0.0968228	−	0.995302i	$-0.530868\pi$
$127$	−277.149			−0.193646			−0.0968228	+	0.995302i	$0.530868\pi$
$128$	−889.385	−	1540.46i	−0.614151	−	1.06374i
$129$	1279.08	−	564.586i	0.872998	−	0.385341i
$130$		0			0
$131$	251.299	−	435.263i	0.167604	−	0.290299i	−0.769973	−	0.638077i	$-0.779730\pi$
$131$	251.299	−	435.263i	0.167604	−	0.290299i	0.937577	+	0.347778i	$0.113064\pi$
$132$	280.500	−	2589.05i	0.184958	−	1.70718i
$133$	−20.1692	−	34.9341i	−0.0131496	−	0.0227757i
$134$	−2359.13			−1.52088
$135$		0			0
$136$	3992.99			2.51762
$137$	1110.56	+	1923.55i	0.692566	+	1.19956i	0.970994	+	0.239103i	$0.0768533\pi$
$137$	1110.56	+	1923.55i	0.692566	+	1.19956i	−0.278428	+	0.960457i	$0.589813\pi$
$138$	482.494	−	4453.48i	0.297628	−	2.74714i
$139$	−1316.39	+	2280.06i	−0.803273	+	1.39131i	0.114177	+	0.993460i	$0.463577\pi$
$139$	−1316.39	+	2280.06i	−0.803273	+	1.39131i	−0.917451	+	0.397850i	$0.869756\pi$
$140$		0			0
$141$	−45.5800	+	20.1190i	−0.0272236	+	0.0120165i
$142$	800.745	+	1386.93i	0.473218	+	0.819638i
$143$	287.640			0.168208
$144$	846.578	+	2663.38i	0.489918	+	1.54131i
$145$		0			0
$146$	−1601.00	−	2773.02i	−0.907535	−	1.57190i
$147$	−413.075	−	302.141i	−0.231768	−	0.169525i
$148$	−1419.81	+	2459.19i	−0.788567	+	1.36584i
$149$	1282.86	−	2221.97i	0.705340	−	1.22169i	−0.261228	−	0.965277i	$-0.584128\pi$
$149$	1282.86	−	2221.97i	0.705340	−	1.22169i	0.966569	−	0.256408i	$-0.0825392\pi$
$150$		0			0
$151$	752.244	+	1302.93i	0.405409	+	0.702189i	0.994369	−	0.105973i	$-0.0337957\pi$
$151$	752.244	+	1302.93i	0.405409	+	0.702189i	−0.588960	+	0.808162i	$0.700462\pi$
$152$	−92.6331			−0.0494312
$153$	2182.52	+	478.528i	1.15324	+	0.252854i
$154$	3033.40			1.58726
$155$		0			0
$156$	−839.972	+	370.763i	−0.431100	+	0.190287i
$157$	599.094	−	1037.66i	0.304541	−	0.527481i	−0.672618	−	0.739990i	$-0.734830\pi$
$157$	599.094	−	1037.66i	0.304541	−	0.527481i	0.977159	+	0.212509i	$0.0681636\pi$
$158$	−1999.79	+	3463.74i	−1.00693	+	1.74405i
$159$	−20.0206	+	184.793i	−0.00998579	+	0.0921701i
$160$		0			0
$161$	3583.83			1.75432
$162$	338.210	+	3669.07i	0.164026	+	1.77944i
$163$	2204.91			1.05952			0.529760	−	0.848148i	$-0.322282\pi$
$163$	2204.91			1.05952			0.529760	+	0.848148i	$0.322282\pi$
$164$	−2450.79	−	4244.88i	−1.16692	−	2.02116i
$165$		0			0
$166$	576.392	−	998.341i	0.269498	−	0.466785i
$167$	566.057	−	980.439i	0.262292	−	0.454303i	−0.704558	−	0.709646i	$-0.748855\pi$
$167$	566.057	−	980.439i	0.262292	−	0.454303i	0.966851	+	0.255343i	$0.0821883\pi$
$168$	−4819.46	+	2127.31i	−2.21327	+	0.976937i
$169$	1047.79	+	1814.83i	0.476920	+	0.826050i
$170$		0			0
$171$	−50.6320	−	11.1013i	−0.0226429	−	0.00496457i
$172$	4721.28			2.09299
$173$	926.998	+	1605.61i	0.407389	+	0.705619i	0.994596	−	0.103818i	$-0.0331059\pi$
$173$	926.998	+	1605.61i	0.407389	+	0.705619i	−0.587207	+	0.809437i	$0.699773\pi$
$174$	−5435.73	−	3975.93i	−2.36829	−	1.73227i
$175$		0			0
$176$	1478.23	−	2560.38i	0.633102	−	1.09657i
$177$	2360.25	+	1726.39i	1.00230	+	0.733126i
$178$	136.238	+	235.971i	0.0573677	+	0.0993638i
$179$	3205.81			1.33862			0.669312	−	0.742981i	$-0.266589\pi$
$179$	3205.81			1.33862			0.669312	+	0.742981i	$0.266589\pi$
$180$		0			0
$181$	2278.79			0.935806			0.467903	−	0.883780i	$-0.345010\pi$
$181$	2278.79			0.935806			0.467903	+	0.883780i	$0.345010\pi$
$182$	−534.741	−	926.199i	−0.217789	−	0.377222i
$183$	−377.080	+	166.443i	−0.152320	+	0.0672341i
$184$	4114.95	−	7127.31i	1.64869	−	2.85561i
$185$		0			0
$186$	135.932	−	1254.67i	0.0535861	−	0.494607i
$187$	−1181.85	−	2047.02i	−0.462168	−	0.800498i
$188$	−168.243			−0.0652679
$189$	−2889.20	+	585.185i	−1.11195	+	0.225216i
$190$		0			0
$191$	−1694.33	−	2934.66i	−0.641870	−	1.11175i	−0.985015	−	0.172469i	$-0.944826\pi$
$191$	−1694.33	−	2934.66i	−0.641870	−	1.11175i	0.343145	−	0.939282i	$-0.388508\pi$
$192$	75.4709	−	696.606i	0.0283679	−	0.261840i
$193$	1389.11	−	2406.01i	0.518085	−	0.897349i	−0.481695	−	0.876339i	$-0.659979\pi$
$193$	1389.11	−	2406.01i	0.518085	−	0.897349i	0.999779	−	0.0210098i	$-0.00668813\pi$
$194$	−244.363	+	423.249i	−0.0904341	+	0.156636i
$195$		0			0
$196$	−864.097	−	1496.66i	−0.314904	−	0.545430i
$197$	−2941.71			−1.06390			−0.531950	−	0.846776i	$-0.678541\pi$
$197$	−2941.71			−1.06390			−0.531950	+	0.846776i	$0.678541\pi$
$198$	2626.70	−	2879.96i	0.942785	−	1.03369i
$199$	−4929.28			−1.75592			−0.877959	−	0.478737i	$-0.841095\pi$
$199$	−4929.28			−1.75592			−0.877959	+	0.478737i	$0.841095\pi$
$200$		0			0
$201$	−1957.55	−	1431.84i	−0.686940	−	0.502457i
$202$	−2738.00	+	4742.35i	−0.953687	+	1.65183i
$203$	2694.00	−	4666.15i	0.931438	−	1.61330i
$204$	6089.84	+	4454.37i	2.09007	+	1.52877i
$205$		0			0
$206$	−2175.00			−0.735628
$207$	3103.33	−	3402.55i	1.04201	−	1.14248i
$208$	−1042.36			−0.347474
$209$	27.4177	+	47.4888i	0.00907425	+	0.0157171i
$210$		0			0
$211$	−2709.25	+	4692.57i	−0.883947	+	1.53104i	−0.0370311	+	0.999314i	$0.511790\pi$
$211$	−2709.25	+	4692.57i	−0.883947	+	1.53104i	−0.846916	+	0.531727i	$0.821543\pi$
$212$	−313.832	+	543.574i	−0.101670	+	0.176098i
$213$	−177.337	+	1636.84i	−0.0570466	+	0.526547i
$214$	32.6884	+	56.6180i	0.0104417	+	0.0180856i
$215$		0			0
$216$	−2153.59	+	6417.76i	−0.678395	+	2.02164i
$217$	1009.67			0.315855
$218$	−50.8183	−	88.0199i	−0.0157883	−	0.0273461i
$219$	354.566	−	3272.69i	0.109403	−	1.00981i
$220$		0			0
$221$	−416.683	+	721.716i	−0.126829	+	0.219674i
$222$	−3888.34	+	1716.31i	−1.17553	+	0.518880i
$223$	−2042.18	−	3537.15i	−0.613248	−	1.06218i	−0.990689	−	0.136143i	$-0.956529\pi$
$223$	−2042.18	−	3537.15i	−0.613248	−	1.06218i	0.377442	−	0.926033i	$-0.376804\pi$
$224$	−2881.78			−0.859586
$225$		0			0
$226$	−5714.65			−1.68201
$227$	110.915	+	192.110i	0.0324302	+	0.0561708i	0.881785	−	0.471652i	$-0.156342\pi$
$227$	110.915	+	192.110i	0.0324302	+	0.0561708i	−0.849355	+	0.527822i	$0.823009\pi$
$228$	−141.278	−	103.337i	−0.0410366	−	0.0300160i
$229$	799.037	−	1383.97i	0.230576	−	0.399369i	−0.727402	−	0.686212i	$-0.759272\pi$
$229$	799.037	−	1383.97i	0.230576	−	0.399369i	0.957978	+	0.286843i	$0.0926057\pi$
$230$		0			0
$231$	2517.04	+	1841.08i	0.716924	+	0.524389i
$232$	−6186.50	−	10715.3i	−1.75071	−	3.03231i
$233$	6620.40			1.86144			0.930722	−	0.365727i	$-0.119180\pi$
$233$	6620.40			1.86144			0.930722	+	0.365727i	$0.119180\pi$
$234$	−1342.39	−	294.327i	−0.375022	−	0.0822255i
$235$		0			0
$236$	4937.32	+	8551.69i	1.36183	+	2.35876i
$237$	−3761.64	+	1660.39i	−1.03099	+	0.455079i
$238$	−4394.27	+	7611.09i	−1.19680	+	2.07292i
$239$	−1778.60	+	3080.62i	−0.481372	+	0.833761i	−0.999771	−	0.0213776i	$-0.993195\pi$
$239$	−1778.60	+	3080.62i	−0.481372	+	0.833761i	0.518399	+	0.855139i	$0.326528\pi$
$240$		0			0
$241$	−1483.67	−	2569.79i	−0.396563	−	0.686867i	0.596736	−	0.802437i	$-0.296464\pi$
$241$	−1483.67	−	2569.79i	−0.396563	−	0.686867i	−0.993299	+	0.115570i	$0.963131\pi$
$242$	2603.79			0.691645
$243$	−1946.24	+	3249.78i	−0.513793	+	0.857914i
$244$	−1391.86			−0.365183
$245$		0			0
$246$	790.226	−	7293.88i	0.204809	−	1.89041i
$247$	9.66661	−	16.7431i	0.00249017	−	0.00431310i
$248$	1159.30	−	2007.96i	0.296836	−	0.514136i
$249$	1084.20	−	478.567i	0.275938	−	0.121799i
$250$		0			0
$251$	−903.562			−0.227220			−0.113610	−	0.993525i	$-0.536241\pi$
$251$	−903.562			−0.227220			−0.113610	+	0.993525i	$0.536241\pi$
$252$	−9723.43	−	2131.91i	−2.43063	−	0.532928i
$253$	−4871.79			−1.21062
$254$	−700.404	−	1213.14i	−0.173021	−	0.299681i
$255$		0			0
$256$	3955.88	−	6851.79i	0.965791	−	1.67280i
$257$	742.247	−	1285.61i	0.180156	−	0.312039i	−0.761778	−	0.647839i	$-0.775673\pi$
$257$	742.247	−	1285.61i	0.180156	−	0.312039i	0.941934	+	0.335799i	$0.109006\pi$
$258$	5703.76	+	4171.98i	1.37636	+	1.00673i
$259$	−1700.21	−	2944.85i	−0.407899	−	0.706502i
$260$		0			0
$261$	−2097.31	−	6598.26i	−0.497396	−	1.56484i
$262$	2540.31			0.599011
$263$	−1358.33	−	2352.69i	−0.318472	−	0.551609i	0.661698	−	0.749771i	$-0.269836\pi$
$263$	−1358.33	−	2352.69i	−0.318472	−	0.551609i	−0.980169	+	0.198162i	$0.936503\pi$
$264$	6551.49	−	2891.82i	1.52733	−	0.674164i
$265$		0			0
$266$	101.942	−	176.569i	0.0234981	−	0.0406998i
$267$	−30.1719	+	278.490i	−0.00691569	+	0.0638327i
$268$	−4094.93	−	7092.62i	−0.933349	−	1.61661i
$269$	7492.51			1.69824			0.849120	−	0.528201i	$-0.177133\pi$
$269$	7492.51			1.69824			0.849120	+	0.528201i	$0.177133\pi$
$270$		0			0
$271$	2013.02			0.451226			0.225613	−	0.974217i	$-0.427561\pi$
$271$	2013.02			0.451226			0.225613	+	0.974217i	$0.427561\pi$
$272$	4282.82	+	7418.06i	0.954720	+	1.65362i
$273$	118.426	−	1093.09i	0.0262545	−	0.242333i
$274$	−5613.16	+	9722.28i	−1.23760	+	2.14359i
$275$		0			0
$276$	14226.7	−	6279.66i	3.10271	−	1.36953i
$277$	1785.48	+	3092.55i	0.387290	+	0.670806i	0.992084	−	0.125576i	$-0.0400779\pi$
$277$	1785.48	+	3092.55i	0.387290	+	0.670806i	−0.604794	+	0.796382i	$0.706745\pi$
$278$	−13307.0			−2.87087
$279$	874.295	−	958.593i	0.187608	−	0.205697i
$280$		0			0
$281$	3380.70	+	5855.54i	0.717707	+	1.24310i	0.961906	+	0.273379i	$0.0881415\pi$
$281$	3380.70	+	5855.54i	0.717707	+	1.24310i	−0.244200	+	0.969725i	$0.578525\pi$
$282$	−203.254	−	148.669i	−0.0429205	−	0.0313939i
$283$	2006.14	−	3474.74i	0.421388	−	0.729866i	−0.574687	−	0.818373i	$-0.694876\pi$
$283$	2006.14	−	3474.74i	0.421388	−	0.729866i	0.996076	+	0.0885075i	$0.0282097\pi$
$284$	−2779.83	+	4814.81i	−0.580819	+	1.00601i
$285$		0			0
$286$	726.917	+	1259.06i	0.150292	+	0.260313i
$287$	5869.58			1.20721
$288$	−2495.41	+	2736.01i	−0.510567	+	0.559795i
$289$	1935.23			0.393901
$290$		0			0
$291$	−459.650	+	202.889i	−0.0925951	+	0.0408714i
$292$	5557.98	−	9626.71i	1.11389	−	1.92932i
$293$	1223.02	−	2118.34i	0.243856	−	0.422371i	−0.717953	−	0.696091i	$-0.754921\pi$
$293$	1223.02	−	2118.34i	0.243856	−	0.422371i	0.961809	+	0.273720i	$0.0882542\pi$
$294$	278.617	−	2571.67i	0.0552697	−	0.510147i
$295$		0			0
$296$	−7808.72			−1.53335
$297$	3927.52	−	795.489i	0.767332	−	0.155417i
$298$	12968.0			2.52086
$299$	858.821	+	1487.52i	0.166110	+	0.287711i
$300$		0			0
$301$	−2826.84	+	4896.23i	−0.541317	+	0.937588i
$302$	−3802.11	+	6585.45i	−0.724459	+	1.25480i
$303$	−5150.22	+	2273.30i	−0.976476	+	0.431016i
$304$	−99.3568	−	172.091i	−0.0187451	−	0.0324674i
$305$		0			0
$306$	3420.99	+	10762.6i	0.639101	+	2.01065i
$307$	−5539.06			−1.02974			−0.514871	−	0.857268i	$-0.672160\pi$
$307$	−5539.06			−1.02974			−0.514871	+	0.857268i	$0.672160\pi$
$308$	5265.32	+	9119.79i	0.974088	+	1.68717i
$309$	−1804.76	−	1320.08i	−0.332263	−	0.243032i
$310$		0			0
$311$	1762.60	−	3052.92i	0.321376	−	0.556640i	−0.659396	−	0.751796i	$-0.729188\pi$
$311$	1762.60	−	3052.92i	0.321376	−	0.556640i	0.980772	+	0.195156i	$0.0625213\pi$
$312$	−2037.89	−	1490.60i	−0.369785	−	0.270477i
$313$	3455.30	+	5984.75i	0.623977	+	1.08076i	0.988738	+	0.149659i	$0.0478175\pi$
$313$	3455.30	+	5984.75i	0.623977	+	1.08076i	−0.364761	+	0.931101i	$0.618849\pi$
$314$	6056.07			1.08842
$315$		0			0
$316$	−13884.8			−2.47177
$317$	−2104.83	−	3645.67i	−0.372930	−	0.645934i	0.617085	−	0.786897i	$-0.288314\pi$
$317$	−2104.83	−	3645.67i	−0.372930	−	0.645934i	−0.990015	+	0.140963i	$0.954980\pi$
$318$	−859.472	+	379.370i	−0.151562	+	0.0668995i
$319$	−3662.17	+	6343.07i	−0.642766	+	1.11330i
$320$		0			0
$321$	−7.23933	+	66.8200i	−0.00125875	+	0.0116185i
$322$	9056.98	+	15687.1i	1.56747	+	2.71494i
$323$	−158.872			−0.0273680
$324$	−10443.8	+	7385.51i	−1.79078	+	1.26638i
$325$		0			0
$326$	5572.19	+	9651.32i	0.946672	+	1.63968i
$327$	11.2545	−	103.880i	0.00190328	−	0.0175675i
$328$	6739.44	−	11673.1i	1.13452	−	1.96505i
$329$	100.734	−	174.477i	0.0168805	−	0.0292378i
$330$		0			0
$331$	848.119	+	1468.99i	0.140836	+	0.243936i	0.927812	−	0.373049i	$-0.121688\pi$
$331$	848.119	+	1468.99i	0.140836	+	0.243936i	−0.786975	+	0.616984i	$0.788354\pi$
$332$	4001.96			0.661554
$333$	−4268.14	−	935.813i	−0.702381	−	0.154001i
$334$	5722.10			0.937423
$335$		0			0
$336$	−9121.33	−	6671.74i	−1.48098	−	1.08325i
$337$	3602.61	−	6239.90i	0.582334	−	1.00863i	−0.412868	−	0.910791i	$-0.635473\pi$
$337$	3602.61	−	6239.90i	0.582334	−	1.00863i	0.995202	−	0.0978413i	$-0.0311938\pi$
$338$	−5295.92	+	9172.80i	−0.852248	+	1.47614i
$339$	−4741.88	−	3468.42i	−0.759716	−	0.555689i
$340$		0			0
$341$	−1372.52			−0.217965
$342$	−79.3633	−	249.682i	−0.0125482	−	0.0394773i
$343$	−5137.53			−0.808747
$344$	6491.55	+	11243.7i	1.01744	+	1.76227i
$345$		0			0
$346$	−4685.37	+	8115.30i	−0.727998	+	1.26093i
$347$	−3248.32	+	5626.26i	−0.502533	+	0.870413i	0.497463	+	0.867485i	$0.334265\pi$
$347$	−3248.32	+	5626.26i	−0.502533	+	0.870413i	−0.999996	+	0.00292757i	$0.999068\pi$
$348$	2518.24	−	23243.6i	0.387907	−	3.58043i
$349$	3232.25	+	5598.43i	0.495755	+	0.858673i	0.999988	−	0.00489459i	$-0.00155800\pi$
$349$	3232.25	+	5598.43i	0.495755	+	0.858673i	−0.504233	+	0.863568i	$0.668225\pi$
$350$		0			0
$351$	−935.249	−	1058.97i	−0.142222	−	0.161036i
$352$	3917.44			0.593183
$353$	5924.50	+	10261.5i	0.893284	+	1.54721i	0.835914	+	0.548860i	$0.184938\pi$
$353$	5924.50	+	10261.5i	0.893284	+	1.54721i	0.0573694	+	0.998353i	$0.481729\pi$
$354$	−1591.98	+	14694.2i	−0.239019	+	2.20618i
$355$		0			0
$356$	−472.957	+	819.186i	−0.0704121	+	0.121957i
$357$	−8265.69	+	3648.47i	−1.22540	+	0.540890i
$358$	8101.66	+	14032.5i	1.19605	+	2.07162i
$359$	−11702.9			−1.72048			−0.860242	−	0.509886i	$-0.829688\pi$
$359$	−11702.9			−1.72048			−0.860242	+	0.509886i	$0.829688\pi$
$360$		0			0
$361$	−6855.31			−0.999463
$362$	5758.90	+	9974.70i	0.836135	+	1.44823i
$363$	2160.57	+	1580.33i	0.312397	+	0.228501i
$364$	1856.39	−	3215.35i	0.267311	−	0.462995i
$365$		0			0
$366$	−1681.50	−	1229.92i	−0.240146	−	0.175654i
$367$	−1290.26	−	2234.79i	−0.183517	−	0.317861i	0.759559	−	0.650439i	$-0.225415\pi$
$367$	−1290.26	−	2234.79i	−0.183517	−	0.317861i	−0.943076	+	0.332578i	$0.892082\pi$
$368$	17654.5			2.50083
$369$	5082.62	−	5572.67i	0.717047	−	0.786184i
$370$		0			0
$371$	−375.811	−	650.924i	−0.0525907	−	0.0910897i
$372$	4008.06	−	1769.16i	0.558624	−	0.246576i
$373$	2249.78	−	3896.74i	0.312304	−	0.540926i	−0.666557	−	0.745454i	$-0.732233\pi$
$373$	2249.78	−	3896.74i	0.312304	−	0.540926i	0.978861	+	0.204528i	$0.0655660\pi$
$374$	5973.48	−	10346.4i	0.825886	−	1.43048i
$375$		0			0
$376$	−231.326	−	400.669i	−0.0317281	−	0.0549546i
$377$	2582.34			0.352777
$378$	−9862.98	−	11167.7i	−1.34205	−	1.51959i
$379$	−5888.24			−0.798044			−0.399022	−	0.916941i	$-0.630650\pi$
$379$	−5888.24			−0.798044			−0.399022	+	0.916941i	$0.630650\pi$
$380$		0			0
$381$	155.115	−	1431.73i	0.0208577	−	0.192519i
$382$	8563.72	−	14832.8i	1.14701	−	1.98668i
$383$	−4010.08	+	6945.66i	−0.535001	+	0.926650i	0.464162	+	0.885750i	$0.346356\pi$
$383$	−4010.08	+	6945.66i	−0.535001	+	0.926650i	−0.999163	+	0.0408993i	$0.986978\pi$
$384$	8455.67	−	3732.33i	1.12370	−	0.496002i
$385$		0			0
$386$	14042.1			1.85162
$387$	2200.73	+	6923.62i	0.289068	+	0.909425i
$388$	−1696.64			−0.221994
$389$	83.6900	+	144.955i	0.0109081	+	0.0188934i	0.871428	−	0.490524i	$-0.163194\pi$
$389$	83.6900	+	144.955i	0.0109081	+	0.0188934i	−0.860520	+	0.509417i	$0.829861\pi$
$390$		0			0
$391$	7057.41	−	12223.8i	0.912810	−	1.58103i
$392$	2376.19	−	4115.68i	0.306163	−	0.530289i
$393$	2107.89	+	1541.80i	0.270557	+	0.197897i
$394$	−7434.22	−	12876.5i	−0.950586	−	1.64646i
$395$		0			0
$396$	13217.9	+	2898.08i	1.67733	+	0.367763i
$397$	−5893.09			−0.745002			−0.372501	−	0.928032i	$-0.621500\pi$
$397$	−5893.09			−0.745002			−0.372501	+	0.928032i	$0.621500\pi$
$398$	−12457.2	−	21576.4i	−1.56890	−	2.71741i
$399$	191.755	−	84.6407i	0.0240596	−	0.0106199i
$400$		0			0
$401$	1316.43	−	2280.12i	0.163938	−	0.283950i	−0.772339	−	0.635210i	$-0.780913\pi$
$401$	1316.43	−	2280.12i	0.163938	−	0.283950i	0.936278	+	0.351260i	$0.114247\pi$
$402$	1320.36	−	12187.1i	0.163815	−	1.51203i
$403$	241.954	+	419.076i	0.0299071	+	0.0518007i
$404$	−19010.2			−2.34108
$405$		0			0
$406$	27232.9			3.32893
$407$	2311.23	+	4003.17i	0.281483	+	0.487543i
$408$	−2234.80	+	20627.5i	−0.271174	+	2.50297i
$409$	6845.15	−	11856.2i	0.827558	−	1.43337i	−0.0723910	−	0.997376i	$-0.523063\pi$
$409$	6845.15	−	11856.2i	0.827558	−	1.43337i	0.899949	−	0.435996i	$-0.143604\pi$
$410$		0			0
$411$	−10558.5	+	4660.50i	−1.26718	+	0.559332i
$412$	−3775.32	−	6539.04i	−0.451448	−	0.781931i
$413$	−11824.8			−1.40886
$414$	22736.3	+	4985.05i	2.69910	+	0.591792i
$415$		0			0
$416$	−690.584	−	1196.13i	−0.0813910	−	0.140973i
$417$	−11041.9	−	8076.49i	−1.29670	−	0.948459i
$418$	−138.578	+	240.025i	−0.0162155	+	0.0280861i
$419$	−129.486	+	224.277i	−0.0150974	+	0.0261495i	−0.873475	−	0.486868i	$-0.838139\pi$
$419$	−129.486	+	224.277i	−0.0150974	+	0.0261495i	0.858378	+	0.513018i	$0.171473\pi$
$420$		0			0
$421$	−6821.55	−	11815.3i	−0.789696	−	1.36779i	−0.926153	−	0.377147i	$-0.876905\pi$
$421$	−6821.55	−	11815.3i	−0.789696	−	1.36779i	0.136457	−	0.990646i	$-0.456428\pi$
$422$	−27387.1			−3.15920
$423$	−78.4230	−	246.723i	−0.00901432	−	0.0283596i
$424$	−1726.02			−0.197696
$425$		0			0
$426$	−7612.94	+	3360.35i	−0.865840	+	0.382182i
$427$	833.369	−	1443.44i	0.0944486	−	0.163590i
$428$	−113.480	+	196.553i	−0.0128160	+	0.0221980i
$429$	−160.987	+	1485.93i	−0.0181177	+	0.167229i
$430$		0			0
$431$	−13258.5			−1.48176			−0.740881	−	0.671636i	$-0.765592\pi$
$431$	−13258.5			−1.48176			−0.740881	+	0.671636i	$0.765592\pi$
$432$	−14232.6	+	2882.71i	−1.58511	+	0.321052i
$433$	−14980.2			−1.66259			−0.831295	−	0.555832i	$-0.812400\pi$
$433$	−14980.2			−1.66259			−0.831295	+	0.555832i	$0.812400\pi$
$434$	2551.60	+	4419.50i	0.282214	+	0.488809i
$435$		0			0
$436$	176.419	−	305.566i	0.0193783	−	0.0335641i
$437$	−163.724	+	283.579i	−0.0179222	+	0.0310422i
$438$	15221.3	−	6718.66i	1.66050	−	0.732945i
$439$	3681.30	+	6376.19i	0.400225	+	0.693210i	0.993753	−	0.111604i	$-0.0355987\pi$
$439$	3681.30	+	6376.19i	0.400225	+	0.693210i	−0.593528	+	0.804813i	$0.702265\pi$
$440$		0			0
$441$	1792.03	−	1964.81i	0.193503	−	0.212160i
$442$	−4212.13			−0.453282
$443$	−793.903	−	1375.08i	−0.0851456	−	0.147476i	0.820308	−	0.571922i	$-0.193802\pi$
$443$	−793.903	−	1375.08i	−0.0851456	−	0.147476i	−0.905453	+	0.424446i	$0.860469\pi$
$444$	−11909.3	−	8711.00i	−1.27295	−	0.931094i
$445$		0			0
$446$	10321.9	−	17878.0i	1.09586	−	1.89809i
$447$	10760.6	+	7870.73i	1.13861	+	0.832825i
$448$	1416.68	+	2453.76i	0.149401	+	0.258770i
$449$	−7331.63			−0.770604			−0.385302	−	0.922791i	$-0.625903\pi$
$449$	−7331.63			−0.770604			−0.385302	+	0.922791i	$0.625903\pi$
$450$		0			0
$451$	−7978.99			−0.833074
$452$	−9919.38	−	17180.9i	−1.03223	−	1.78788i
$453$	−7151.83	+	3156.81i	−0.741771	+	0.327417i
$454$	−560.601	+	970.990i	−0.0579523	+	0.100376i
$455$		0			0
$456$	51.8450	−	478.535i	0.00532426	−	0.0491436i
$457$	3148.41	+	5453.21i	0.322268	+	0.558185i	0.980956	−	0.194232i	$-0.0622214\pi$
$457$	3148.41	+	5453.21i	0.322268	+	0.558185i	−0.658687	+	0.752417i	$0.728888\pi$
$458$	8077.23			0.824070
$459$	−3693.55	+	11006.9i	−0.375600	+	1.11930i
$460$		0			0
$461$	−3167.73	−	5486.67i	−0.320034	−	0.554316i	0.660461	−	0.750861i	$-0.270361\pi$
$461$	−3167.73	−	5486.67i	−0.320034	−	0.554316i	−0.980495	+	0.196545i	$0.937028\pi$
$462$	−1697.74	+	15670.3i	−0.170965	+	1.57803i
$463$	−1147.86	+	1988.15i	−0.115217	+	0.199562i	−0.917867	−	0.396889i	$-0.870090\pi$
$463$	−1147.86	+	1988.15i	−0.115217	+	0.199562i	0.802649	+	0.596451i	$0.203423\pi$
$464$	13271.1	−	22986.2i	1.32779	−	2.29980i
$465$		0			0
$466$	16730.9	+	28978.8i	1.66319	+	2.88072i
$467$	6182.82			0.612648			0.306324	−	0.951927i	$-0.400901\pi$
$467$	6182.82			0.612648			0.306324	+	0.951927i	$0.400901\pi$
$468$	−1445.22	−	4546.74i	−0.142746	−	0.449088i
$469$	9807.26			0.965581
$470$		0			0
$471$	5025.18	+	3675.63i	0.491609	+	0.359585i
$472$	−13577.2	+	23516.4i	−1.32403	+	2.29328i
$473$	3842.75	−	6655.84i	0.373552	−	0.647011i
$474$	−16774.2	−	12269.4i	−1.62545	−	1.18893i
$475$		0			0
$476$	−30509.9			−2.93786
$477$	−943.422	−	206.850i	−0.0905583	−	0.0198554i
$478$	−17979.3			−1.72041
$479$	−1949.18	−	3376.08i	−0.185930	−	0.322040i	0.757960	−	0.652302i	$-0.226196\pi$
$479$	−1949.18	−	3376.08i	−0.185930	−	0.322040i	−0.943889	+	0.330262i	$0.892863\pi$
$480$		0			0
$481$	814.869	−	1411.39i	0.0772449	−	0.133792i
$482$	7499.00	−	12988.6i	0.708652	−	1.22742i
$483$	−2005.80	+	18513.8i	−0.188959	+	1.74411i
$484$	4519.61	+	7828.19i	0.424456	+	0.735180i
$485$		0			0
$486$	−19143.4	−	306.339i	−1.78675	−	0.0285923i
$487$	−14776.3			−1.37490			−0.687450	−	0.726232i	$-0.741270\pi$
$487$	−14776.3			−1.37490			−0.687450	+	0.726232i	$0.741270\pi$
$488$	−1913.75	−	3314.71i	−0.177523	−	0.307479i
$489$	−1234.04	+	11390.4i	−0.114121	+	1.05336i
$490$		0			0
$491$	−1818.62	+	3149.94i	−0.167155	+	0.289521i	−0.937418	−	0.348205i	$-0.886791\pi$
$491$	−1818.62	+	3149.94i	−0.167155	+	0.289521i	0.770263	+	0.637726i	$0.220125\pi$
$492$	23300.4	−	10284.8i	2.13509	−	0.942427i
$493$	−10610.2	−	18377.5i	−0.969293	−	1.67886i
$494$	97.7169			0.00889978
$495$		0			0
$496$	4973.77			0.450260
$497$	−3328.82	−	5765.68i	−0.300439	−	0.520375i
$498$	4834.76	+	3536.35i	0.435041	+	0.318208i
$499$	1628.87	−	2821.29i	0.146129	−	0.253103i	−0.783665	−	0.621184i	$-0.786652\pi$
$499$	1628.87	−	2821.29i	0.146129	−	0.253103i	0.929794	+	0.368081i	$0.119985\pi$
$500$		0			0
$501$	4748.06	+	3472.94i	0.423409	+	0.309699i
$502$	−2283.46	−	3955.07i	−0.203019	−	0.351640i
$503$	20857.4			1.84888			0.924440	−	0.381327i	$-0.124533\pi$
$503$	20857.4			1.84888			0.924440	+	0.381327i	$0.124533\pi$
$504$	−8292.15	−	26087.6i	−0.732861	−	2.30562i
$505$		0			0
$506$	−12311.9	−	21324.8i	−1.08168	−	1.87352i
$507$	−9961.71	+	4397.09i	−0.872614	+	0.385171i
$508$	2431.49	−	4211.47i	0.212362	−	0.367822i
$509$	9953.74	−	17240.4i	0.866781	−	1.50131i	0.00151390	−	0.999999i	$-0.499518\pi$
$509$	9953.74	−	17240.4i	0.866781	−	1.50131i	0.865267	−	0.501311i	$-0.167149\pi$
$510$		0			0
$511$	6655.62	+	11527.9i	0.576179	+	0.997971i
$512$	25758.7			2.22340
$513$	85.6865	−	255.348i	0.00737456	−	0.0219764i
$514$	7503.15			0.643871
$515$		0			0
$516$	−2642.41	+	24389.8i	−0.225437	+	2.08081i
$517$	−136.937	+	237.181i	−0.0116489	+	0.0201764i
$518$	8593.46	−	14884.3i	0.728909	−	1.26251i
$519$	−8813.26	+	3890.17i	−0.745394	+	0.329016i
$520$		0			0
$521$	−4264.69			−0.358617			−0.179308	−	0.983793i	$-0.557386\pi$
$521$	−4264.69			−0.358617			−0.179308	+	0.983793i	$0.557386\pi$
$522$	23581.6	−	25855.3i	1.97728	−	2.16792i
$523$	3687.86			0.308334			0.154167	−	0.988045i	$-0.450731\pi$
$523$	3687.86			0.308334			0.154167	+	0.988045i	$0.450731\pi$
$524$	4409.42	+	7637.34i	0.367607	+	0.636715i
$525$		0			0
$526$	6865.46	−	11891.3i	0.569103	−	0.985716i
$527$	1988.27	−	3443.78i	0.164346	−	0.284656i
$528$	12399.4	+	9069.43i	1.02199	+	0.747531i
$529$	−8462.46	−	14657.4i	−0.695525	−	1.20469i
$530$		0			0
$531$	−10239.4	+	11226.6i	−0.836819	+	0.917504i
$532$	707.798			0.0576822
$533$	1406.57	+	2436.25i	0.114307	+	0.197985i
$534$	−1295.26	+	571.726i	−0.104965	+	0.0463314i
$535$		0			0
$536$	11260.7	−	19504.1i	0.907440	−	1.57173i
$537$	−1794.23	+	16561.0i	−0.144184	+	1.33084i
$538$	18934.9	+	32796.2i	1.51736	+	2.62815i
$539$	−2813.23			−0.224813
$540$		0			0
$541$	21551.0			1.71266			0.856331	−	0.516428i	$-0.172739\pi$
$541$	21551.0			1.71266			0.856331	+	0.516428i	$0.172739\pi$
$542$	5087.26	+	8811.39i	0.403167	+	0.698305i
$543$	−1275.39	+	11772.0i	−0.100796	+	0.930362i
$544$	−5674.91	+	9829.23i	−0.447261	+	0.774678i
$545$		0			0
$546$	5083.96	−	2244.06i	0.398486	−	0.175891i
$547$	9953.52	+	17240.0i	0.778029	+	1.34759i	0.933076	+	0.359678i	$0.117114\pi$
$547$	9953.52	+	17240.0i	0.778029	+	1.34759i	−0.155048	+	0.987907i	$0.549553\pi$
$548$	−38972.8			−3.03802
$549$	−648.788	−	2041.12i	−0.0504364	−	0.158676i
$550$		0			0
$551$	246.146	+	426.338i	0.0190312	+	0.0329630i
$552$	34516.1	+	25246.5i	2.66142	+	1.94667i
$553$	8313.45	−	14399.3i	0.639283	−	1.10727i
$554$	−9024.46	+	15630.8i	−0.692081	+	1.19872i
$555$		0			0
$556$	−23098.1	−	40007.0i	−1.76183	−	3.05157i
$557$	1747.00			0.132896			0.0664479	−	0.997790i	$-0.478833\pi$
$557$	1747.00			0.132896			0.0664479	+	0.997790i	$0.478833\pi$
$558$	6405.45	+	1404.43i	0.485957	+	0.106549i
$559$	−2709.67			−0.205021
$560$		0			0
$561$	11236.2	−	4959.66i	0.845622	−	0.373257i
$562$	−17087.2	+	29596.0i	−1.28253	+	2.22141i
$563$	1061.02	−	1837.74i	0.0794257	−	0.137569i	−0.823577	−	0.567205i	$-0.808025\pi$
$563$	1061.02	−	1837.74i	0.0794257	−	0.137569i	0.903002	+	0.429636i	$0.141358\pi$
$564$	94.1622	−	869.129i	0.00703004	−	0.0648882i
$565$		0			0
$566$	20279.5			1.50603
$567$	−1405.99	−	15252.9i	−0.104138	−	1.12974i
$568$	−15288.6			−1.12939
$569$	−5376.54	−	9312.43i	−0.396127	−	0.686112i	0.597118	−	0.802154i	$-0.296313\pi$
$569$	−5376.54	−	9312.43i	−0.396127	−	0.686112i	−0.993244	+	0.116042i	$0.962979\pi$
$570$		0			0
$571$	−362.873	+	628.514i	−0.0265950	+	0.0460639i	−0.879017	−	0.476791i	$-0.841800\pi$
$571$	−362.873	+	628.514i	−0.0265950	+	0.0460639i	0.852422	+	0.522855i	$0.175133\pi$
$572$	−2523.54	+	4370.89i	−0.184466	+	0.319504i
$573$	16108.5	−	7110.29i	1.17442	−	0.518388i
$574$	14833.5	+	25692.3i	1.07864	+	1.86825i
$575$		0			0
$576$	3556.37	+	779.753i	0.257261	+	0.0564058i
$577$	23839.3			1.72001			0.860003	−	0.510290i	$-0.170462\pi$
$577$	23839.3			1.72001			0.860003	+	0.510290i	$0.170462\pi$
$578$	4890.68	+	8470.91i	0.351947	+	0.609590i
$579$	11651.8	+	8522.63i	0.836325	+	0.611725i
$580$		0			0
$581$	−2396.15	+	4150.26i	−0.171100	+	0.296354i
$582$	−2049.70	−	1499.24i	−0.145985	−	0.106779i
$583$	510.870	+	884.853i	0.0362917	+	0.0628592i
$584$	30567.9			2.16594
$585$		0			0
$586$	12363.2			0.871534
$587$	−3888.84	−	6735.67i	−0.273440	−	0.473613i	0.696300	−	0.717751i	$-0.254828\pi$
$587$	−3888.84	−	6735.67i	−0.273440	−	0.473613i	−0.969740	+	0.244138i	$0.921495\pi$
$588$	8215.25	−	3626.21i	0.576175	−	0.254324i
$589$	−46.1257	+	79.8921i	−0.00322679	+	0.00558896i
$590$		0			0
$591$	1646.42	−	15196.7i	0.114593	−	1.05771i
$592$	−8375.51	−	14506.8i	−0.581472	−	1.00714i
$593$	6677.79			0.462435			0.231217	−	0.972902i	$-0.425729\pi$
$593$	6677.79			0.462435			0.231217	+	0.972902i	$0.425729\pi$
$594$	13407.5	+	15181.2i	0.926125	+	1.04864i
$595$		0			0
$596$	22509.6	+	38987.8i	1.54703	+	2.67953i
$597$	2758.82	−	25464.3i	0.189131	−	1.74570i
$598$	−4340.79	+	7518.46i	−0.296836	+	0.514135i
$599$	−6473.45	+	11212.3i	−0.441566	+	0.764815i	−0.997806	−	0.0662068i	$-0.978910\pi$
$599$	−6473.45	+	11212.3i	−0.441566	+	0.764815i	0.556240	+	0.831022i	$0.312244\pi$
$600$		0			0
$601$	2183.05	+	3781.15i	0.148167	+	0.256633i	0.930550	−	0.366165i	$-0.119329\pi$
$601$	2183.05	+	3781.15i	0.148167	+	0.256633i	−0.782383	+	0.622797i	$0.785996\pi$
$602$	−28575.7			−1.93465
$603$	8492.36	−	9311.17i	0.573525	−	0.628823i
$604$	−26398.5			−1.77838
$605$		0			0
$606$	−22966.2	−	16798.5i	−1.53950	−	1.12606i
$607$	12088.7	−	20938.3i	0.808347	−	1.40010i	−0.105660	−	0.994402i	$-0.533696\pi$
$607$	12088.7	−	20938.3i	0.808347	−	1.40010i	0.914008	−	0.405697i	$-0.132971\pi$
$608$	131.652	−	228.028i	0.00878156	−	0.0152101i
$609$	22597.2	+	16528.6i	1.50359	+	1.09979i
$610$		0			0
$611$	96.5591			0.00639339
$612$	−26419.3	+	28966.6i	−1.74499	+	1.91324i
$613$	7772.63			0.512127			0.256063	−	0.966660i	$-0.417574\pi$
$613$	7772.63			0.512127			0.256063	+	0.966660i	$0.417574\pi$
$614$	−13998.2	−	24245.5i	−0.920066	−	1.59360i
$615$		0			0
$616$	−14479.2	+	25078.6i	−0.947048	+	1.64034i
$617$	−313.130	+	542.357i	−0.0204313	+	0.0353881i	−0.876060	−	0.482202i	$-0.839837\pi$
$617$	−313.130	+	542.357i	−0.0204313	+	0.0353881i	0.855629	+	0.517590i	$0.173171\pi$
$618$	1217.30	−	11235.9i	0.0792349	−	0.731348i
$619$	−11417.5	−	19775.8i	−0.741373	−	1.28410i	−0.951870	−	0.306501i	$-0.900842\pi$
$619$	−11417.5	−	19775.8i	−0.741373	−	1.28410i	0.210497	−	0.977594i	$-0.432492\pi$
$620$		0			0
$621$	15840.4	+	17935.9i	1.02360	+	1.15901i
$622$	17817.6			1.14859
$623$	−566.361	−	980.967i	−0.0364218	−	0.0630844i
$624$	583.387	−	5384.74i	0.0374266	−	0.345452i
$625$		0			0
$626$	−17464.3	+	30249.0i	−1.11504	+	1.93130i
$627$	−260.668	+	115.059i	−0.0166030	+	0.00732857i
$628$	10512.0	+	18207.3i	0.667953	+	1.15693i
$629$	−13392.5			−0.848954
$630$		0			0
$631$	−26862.1			−1.69471			−0.847355	−	0.531027i	$-0.821806\pi$
$631$	−26862.1			−1.69471			−0.847355	+	0.531027i	$0.821806\pi$
$632$	−19091.0	−	33066.6i	−1.20158	−	2.08120i
$633$	−22725.1	−	16622.1i	−1.42692	−	1.04371i
$634$	10638.5	−	18426.5i	0.666420	−	1.15427i
$635$		0			0
$636$	−2632.41	−	1925.46i	−0.164123	−	0.120046i
$637$	495.929	+	858.973i	0.0308468	+	0.0534282i
$638$	−37019.8			−2.29723
$639$	−8356.54	−	1832.22i	−0.517339	−	0.113429i
$640$		0			0
$641$	−4304.99	−	7456.46i	−0.265268	−	0.459458i	0.702366	−	0.711816i	$-0.252127\pi$
$641$	−4304.99	−	7456.46i	−0.265268	−	0.459458i	−0.967634	+	0.252358i	$0.918794\pi$
$642$	−310.779	+	137.178i	−0.0191051	+	0.00843299i
$643$	8586.71	−	14872.6i	0.526636	−	0.912160i	−0.472882	−	0.881125i	$-0.656786\pi$
$643$	8586.71	−	14872.6i	0.526636	−	0.912160i	0.999518	−	0.0310345i	$-0.00988017\pi$
$644$	−31441.8	+	54458.8i	−1.92388	+	3.33227i
$645$		0			0
$646$	−401.497	−	695.413i	−0.0244531	−	0.0423540i
$647$	1258.94			0.0764978			0.0382489	−	0.999268i	$-0.487822\pi$
$647$	1258.94			0.0764978			0.0382489	+	0.999268i	$0.487822\pi$
$648$	−31948.4	−	14717.2i	−1.93681	−	0.892200i
$649$	16074.4			0.972226
$650$		0			0
$651$	−565.090	+	5215.85i	−0.0340209	+	0.314017i
$652$	−19344.2	+	33505.1i	−1.16193	+	2.01252i
$653$	1270.21	−	2200.06i	0.0761209	−	0.131845i	−0.825452	−	0.564472i	$-0.809080\pi$
$653$	1270.21	−	2200.06i	0.0761209	−	0.131845i	0.901573	+	0.432627i	$0.142413\pi$
$654$	483.146	−	213.260i	0.0288876	−	0.0127510i
$655$		0			0
$656$	28914.5			1.72092
$657$	16708.0	+	3663.32i	0.992149	+	0.217534i
$658$	1018.29			0.0603302
$659$	13099.9	+	22689.7i	0.774356	+	1.34122i	0.935156	+	0.354237i	$0.115259\pi$
$659$	13099.9	+	22689.7i	0.774356	+	1.34122i	−0.160800	+	0.986987i	$0.551407\pi$
$660$		0			0
$661$	2721.89	−	4714.44i	0.160165	−	0.277414i	−0.774763	−	0.632252i	$-0.782131\pi$
$661$	2721.89	−	4714.44i	0.160165	−	0.277414i	0.934928	+	0.354838i	$0.115464\pi$
$662$	−4286.69	+	7424.77i	−0.251672	+	0.435909i
$663$	−3495.12	−	2556.48i	−0.204735	−	0.149752i
$664$	5502.52	+	9530.64i	0.321595	+	0.557019i
$665$		0			0
$666$	−6690.11	−	21047.5i	−0.389244	−	1.22458i
$667$	−43737.3			−2.53901
$668$	9932.30	+	17203.3i	0.575288	+	0.996428i
$669$	19415.6	−	8570.05i	1.12205	−	0.495272i
$670$		0			0
$671$	−1132.87	+	1962.18i	−0.0651771	+	0.112890i
$672$	1612.88	−	14887.1i	0.0925865	−	0.854585i
$673$	8410.41	+	14567.3i	0.481720	+	0.834364i	0.999780	−	0.0209808i	$-0.00667888\pi$
$673$	8410.41	+	14567.3i	0.481720	+	0.834364i	−0.518060	+	0.855344i	$0.673346\pi$
$674$	36417.7			2.08124
$675$		0			0
$676$	−36770.2			−2.09207
$677$	11599.7	+	20091.4i	0.658515	+	1.14058i	0.981000	+	0.194007i	$0.0621483\pi$
$677$	11599.7	+	20091.4i	0.658515	+	1.14058i	−0.322485	+	0.946574i	$0.604518\pi$
$678$	3198.38	−	29521.5i	0.181170	−	1.67222i
$679$	1015.85	−	1759.51i	0.0574151	−	0.0994459i
$680$		0			0
$681$	−1054.50	+	465.456i	−0.0593371	+	0.0261914i
$682$	−3468.60	−	6007.79i	−0.194750	−	0.337317i
$683$	24902.4			1.39512			0.697558	−	0.716528i	$-0.254270\pi$
$683$	24902.4			1.39512			0.697558	+	0.716528i	$0.254270\pi$
$684$	612.900	−	671.994i	0.0342614	−	0.0375648i
$685$		0			0
$686$	−12983.4	−	22488.0i	−0.722609	−	1.25160i
$687$	6702.29	+	4902.35i	0.372210	+	0.272251i
$688$	−13925.5	+	24119.6i	−0.771662	+	1.33656i
$689$	180.117	−	311.972i	0.00995923	−	0.0172499i
$690$		0			0
$691$	−4233.73	−	7333.03i	−0.233080	−	0.403707i	0.725633	−	0.688082i	$-0.241547\pi$
$691$	−4233.73	−	7333.03i	−0.233080	−	0.403707i	−0.958713	+	0.284375i	$0.908214\pi$
$692$	−32531.1			−1.78706
$693$	−10919.6	+	11972.4i	−0.598558	+	0.656270i
$694$	−32836.3			−1.79604
$695$		0			0
$696$	58817.0	−	25961.8i	3.20324	−	1.41391i
$697$	11558.6	−	20020.1i	0.628139	−	1.08797i
$698$	−16336.9	+	28296.4i	−0.885906	+	1.53443i
$699$	−3705.31	+	34200.5i	−0.200497	+	1.85062i
$700$		0			0
$701$	5972.30			0.321784			0.160892	−	0.986972i	$-0.448563\pi$
$701$	5972.30			0.321784			0.160892	+	0.986972i	$0.448563\pi$
$702$	2271.78	−	6769.98i	0.122141	−	0.363983i
$703$	310.691			0.0166685
$704$	−1925.80	−	3335.59i	−0.103099	−	0.178572i
$705$		0			0
$706$	−29944.5	+	51865.4i	−1.59628	+	2.76484i
$707$	11382.3	−	19714.7i	0.605480	−	1.04872i
$708$	−46940.7	+	20719.6i	−2.49172	+	1.09985i
$709$	3774.89	+	6538.30i	0.199956	+	0.346334i	0.948514	−	0.316735i	$-0.102587\pi$
$709$	3774.89	+	6538.30i	0.199956	+	0.346334i	−0.748558	+	0.663070i	$0.769253\pi$
$710$		0			0
$711$	−6472.12	−	20361.7i	−0.341383	−	1.07401i
$712$	−2601.18			−0.136915
$713$	−4098.00	−	7097.94i	−0.215247	−	0.372819i
$714$	−36858.9	−	26960.2i	−1.93195	−	1.41311i
$715$		0			0
$716$	−28125.4	+	48714.6i	−1.46801	+	2.54267i
$717$	−14918.8	−	10912.3i	−0.777062	−	0.568377i
$718$	−29575.2	−	51225.8i	−1.53724	−	2.66257i
$719$	−31449.7			−1.63126			−0.815631	−	0.578573i	$-0.803610\pi$
$719$	−31449.7			−1.63126			−0.815631	+	0.578573i	$0.803610\pi$
$720$		0			0
$721$	9041.81			0.467038
$722$	−17324.6	−	30007.1i	−0.893012	−	1.54674i
$723$	14105.7	−	6226.27i	0.725585	−	0.320273i
$724$	−19992.3	+	34627.8i	−1.02626	+	1.77753i
$725$		0			0
$726$	−1457.29	+	13451.0i	−0.0744975	+	0.687622i
$727$	3981.01	+	6895.32i	0.203092	+	0.351765i	0.949523	−	0.313697i	$-0.101568\pi$
$727$	3981.01	+	6895.32i	0.203092	+	0.351765i	−0.746431	+	0.665462i	$0.768234\pi$
$728$	10209.8			0.519780
$729$	−15698.8	−	11873.0i	−0.797582	−	0.603210i
$730$		0			0
$731$	11133.4	+	19283.7i	0.563317	+	0.975694i
$732$	778.998	−	7190.25i	0.0393341	−	0.363059i
$733$	−5501.61	+	9529.06i	−0.277226	+	0.480169i	−0.970694	−	0.240318i	$-0.922748\pi$
$733$	−5501.61	+	9529.06i	−0.277226	+	0.480169i	0.693469	+	0.720487i	$0.256082\pi$
$734$	6521.41	−	11295.4i	0.327942	−	0.568012i
$735$		0			0
$736$	11696.5	+	20258.9i	0.585786	+	1.01461i
$737$	−13331.8			−0.666328
$738$	37237.4	+	8164.49i	1.85735	+	0.407234i
$739$	24719.1			1.23046			0.615228	−	0.788349i	$-0.289064\pi$
$739$	24719.1			1.23046			0.615228	+	0.788349i	$0.289064\pi$
$740$		0			0
$741$	81.0831	+	59.3077i	0.00401979	+	0.00294025i
$742$	1899.48	−	3290.00i	0.0939786	−	0.162776i
$743$	−6663.39	+	11541.3i	−0.329012	+	0.569866i	−0.982316	−	0.187230i	$-0.940049\pi$
$743$	−6663.39	+	11541.3i	−0.329012	+	0.569866i	0.653304	+	0.757096i	$0.273382\pi$
$744$	9724.13	+	7112.65i	0.479172	+	0.350487i
$745$		0			0
$746$	22742.4			1.11616
$747$	1865.43	+	5868.76i	0.0913689	+	0.287452i
$748$	41474.6			2.02735
$749$	−135.891	−	235.370i	−0.00662929	−	0.0114823i
$750$		0			0
$751$	11900.5	−	20612.2i	0.578234	−	1.00153i	−0.417448	−	0.908701i	$-0.637075\pi$
$751$	11900.5	−	20612.2i	0.578234	−	1.00153i	0.995682	−	0.0928298i	$-0.0295913\pi$
$752$	496.234	−	859.503i	0.0240636	−	0.0416793i
$753$	505.706	−	4667.73i	0.0244740	−	0.225898i
$754$	6526.02	+	11303.4i	0.315204	+	0.545949i
$755$		0			0
$756$	16455.3	−	49037.3i	0.791633	−	2.35909i
$757$	−20867.5			−1.00191			−0.500953	−	0.865474i	$-0.667017\pi$
$757$	−20867.5			−1.00191			−0.500953	+	0.865474i	$0.667017\pi$
$758$	−14880.6	−	25774.0i	−0.713046	−	1.23503i
$759$	2726.65	−	25167.3i	0.130397	−	1.20358i
$760$		0			0
$761$	7743.76	−	13412.6i	0.368871	−	0.638904i	−0.620518	−	0.784192i	$-0.713078\pi$
$761$	7743.76	−	13412.6i	0.368871	−	0.638904i	0.989389	+	0.145288i	$0.0464110\pi$
$762$	6658.97	−	2939.27i	0.316573	−	0.139735i
$763$	211.260	+	365.912i	0.0100237	+	0.0173616i
$764$	59458.9			2.81564
$765$		0			0
$766$	−40536.7			−1.91208
$767$	−2833.66	−	4908.05i	−0.133400	−	0.231055i
$768$	33181.8	+	24270.6i	1.55904	+	1.14035i
$769$	9233.99	−	15993.7i	0.433012	−	0.749999i	−0.564119	−	0.825693i	$-0.690784\pi$
$769$	9233.99	−	15993.7i	0.433012	−	0.749999i	0.997131	+	0.0756946i	$0.0241174\pi$
$770$		0			0
$771$	6225.94	+	4553.92i	0.290819	+	0.212718i
$772$	24374.0	+	42217.0i	1.13632	+	1.96816i
$773$	−15379.9			−0.715621			−0.357810	−	0.933794i	$-0.616477\pi$
$773$	−15379.9			−0.715621			−0.357810	+	0.933794i	$0.616477\pi$
$774$	−24744.4	+	27130.2i	−1.14912	+	1.25992i
$775$		0			0
$776$	−2332.80	−	4040.53i	−0.107916	−	0.186916i
$777$	16164.4	−	7134.98i	0.746327	−	0.329428i
$778$	−422.999	+	732.655i	−0.0194926	+	0.0337622i
$779$	−268.147	+	464.444i	−0.0123329	+	0.0213613i
$780$		0			0
$781$	4525.13	+	7837.76i	0.207327	+	0.359100i
$782$	71341.3			3.26235
$783$	35259.9	−	7141.63i	1.60931	−	0.325953i
$784$	10194.7			0.464407
$785$		0			0
$786$	−1421.76	+	13123.0i	−0.0645198	+	0.595526i
$787$	19125.9	−	33127.1i	0.866284	−	1.50045i	0.000517066	−	1.00000i	$-0.499835\pi$
$787$	19125.9	−	33127.1i	0.866284	−	1.50045i	0.865767	−	0.500448i	$-0.166831\pi$
$788$	25808.3	−	44701.4i	1.16673	−	2.02084i
$789$	12914.0	−	5700.26i	0.582703	−	0.257205i
$790$		0			0
$791$	23756.7			1.06788
$792$	11272.2	+	35463.0i	0.505732	+	1.59106i
$793$	798.826			0.0357720
$794$	−14892.9	−	25795.2i	−0.665653	−	1.15295i
$795$		0			0
$796$	43245.8	−	74903.9i	1.92564	−	3.33530i
$797$	−19490.8	+	33759.1i	−0.866249	+	1.50039i	−0.000448165		1.00000i	$0.500143\pi$
$797$	−19490.8	+	33759.1i	−0.866249	+	1.50039i	−0.865801	+	0.500388i	$0.833191\pi$
$798$	855.088	+	625.449i	0.0379321	+	0.0277452i
$799$	−396.740	−	687.174i	−0.0175665	−	0.0304261i
$800$		0			0
$801$	−1421.77	−	311.731i	−0.0627164	−	0.0137509i
$802$	13307.4			0.585911
$803$	−9047.53	−	15670.8i	−0.397609	−	0.688680i
$804$	38931.8	−	17184.5i	1.70773	−	0.753793i
$805$		0			0
$806$	−1222.92	+	2118.16i	−0.0534436	+	0.0925670i
$807$	−4193.41	+	38705.7i	−0.182918	+	1.68836i
$808$	−26138.2	−	45272.8i	−1.13804	−	1.97115i
$809$	−4490.50			−0.195152			−0.0975758	−	0.995228i	$-0.531109\pi$
$809$	−4490.50			−0.195152			−0.0975758	+	0.995228i	$0.531109\pi$
$810$		0			0
$811$	33791.9			1.46312			0.731562	−	0.681775i	$-0.238792\pi$
$811$	33791.9			1.46312			0.731562	+	0.681775i	$0.238792\pi$
$812$	47270.2	+	81874.5i	2.04293	+	3.53846i
$813$	−1126.65	+	10399.1i	−0.0486018	+	0.448601i
$814$	−11681.8	+	20233.5i	−0.503006	+	0.871231i
$815$		0			0
$816$	−40718.1	+	17973.0i	−1.74684	+	0.771053i
$817$	−258.284	−	447.361i	−0.0110602	−	0.0191569i
$818$	69195.7			2.95766
$819$	5580.54	+	1223.56i	0.238095	+	0.0522036i
$820$		0			0
$821$	−3382.78	−	5859.15i	−0.143800	−	0.249069i	0.785125	−	0.619338i	$-0.212599\pi$
$821$	−3382.78	−	5859.15i	−0.143800	−	0.249069i	−0.928925	+	0.370269i	$0.879266\pi$
$822$	−47083.0	−	34438.5i	−1.99782	−	1.46129i
$823$	−19674.0	+	34076.3i	−0.833282	+	1.44329i	0.0621398	+	0.998067i	$0.480208\pi$
$823$	−19674.0	+	34076.3i	−0.833282	+	1.44329i	−0.895422	+	0.445219i	$0.853126\pi$
$824$	10381.8	−	17981.8i	0.438916	−	0.760225i
$825$		0			0
$826$	−29883.3	−	51759.4i	−1.25881	−	2.18031i
$827$	632.071			0.0265771			0.0132885	−	0.999912i	$-0.495770\pi$
$827$	632.071			0.0265771			0.0132885	+	0.999912i	$0.495770\pi$
$828$	24477.8	+	77008.7i	1.02737	+	3.23217i
$829$	−19585.8			−0.820560			−0.410280	−	0.911959i	$-0.634569\pi$
$829$	−19585.8			−0.820560			−0.410280	+	0.911959i	$0.634569\pi$
$830$		0			0
$831$	−16975.2	+	7492.83i	−0.708618	+	0.312784i
$832$	−678.978	+	1176.02i	−0.0282925	+	0.0490040i
$833$	4075.32	−	7058.66i	0.169510	−	0.293599i
$834$	7447.69	−	68743.1i	0.309223	−	2.85417i
$835$		0			0
$836$	−962.167			−0.0398053
$837$	4462.69	+	5053.04i	0.184293	+	0.208672i
$838$	−1308.94			−0.0539577
$839$	−5836.32	−	10108.8i	−0.240157	−	0.415965i	0.720602	−	0.693349i	$-0.243866\pi$
$839$	−5836.32	−	10108.8i	−0.240157	−	0.415965i	−0.960759	+	0.277385i	$0.910532\pi$
$840$		0			0
$841$	−20683.3	+	35824.5i	−0.848057	+	1.46888i
$842$	34478.5	−	59718.5i	1.41117	−	2.44422i
$843$	−32141.4	+	14187.2i	−1.31318	+	0.579636i
$844$	−47537.9	−	82338.0i	−1.93877	−	3.35805i
$845$		0			0
$846$	881.767	−	966.786i	0.0358343	−	0.0392893i
$847$	−10824.4			−0.439114
$848$	−1851.31	−	3206.55i	−0.0749694	−	0.129851i
$849$	16827.4	+	12308.3i	0.680231	+	0.497551i
$850$		0			0
$851$	−13801.5	+	23904.9i	−0.555946	+	0.962927i
$852$	−23317.1	−	17055.2i	−0.937596	−	0.685798i
$853$	11050.5	+	19140.0i	0.443565	+	0.768276i	0.997951	−	0.0639830i	$-0.0203804\pi$
$853$	11050.5	+	19140.0i	0.443565	+	0.768276i	−0.554386	+	0.832259i	$0.687047\pi$
$854$	8424.28			0.337556
$855$		0			0
$856$	−624.118			−0.0249205
$857$	14948.9	+	25892.3i	0.595853	+	1.03205i	0.993426	+	0.114477i	$0.0365194\pi$
$857$	14948.9	+	25892.3i	0.595853	+	1.03205i	−0.397573	+	0.917571i	$0.630147\pi$
$858$	−6911.04	+	3050.53i	−0.274987	+	0.121379i
$859$	−7041.73	+	12196.6i	−0.279698	+	0.484452i	−0.971310	−	0.237818i	$-0.923568\pi$
$859$	−7041.73	+	12196.6i	−0.279698	+	0.484452i	0.691611	+	0.722270i	$0.256901\pi$
$860$		0			0
$861$	−3285.09	+	30321.8i	−0.130030	+	1.20019i
$862$	−33506.6	−	58035.1i	−1.32394	−	2.29313i
$863$	−11367.8			−0.448396			−0.224198	−	0.974544i	$-0.571976\pi$
$863$	−11367.8			−0.448396			−0.224198	+	0.974544i	$0.571976\pi$
$864$	−12737.4	−	14422.4i	−0.501545	−	0.567893i
$865$		0			0
$866$	−37857.5	−	65571.2i	−1.48551	−	2.57298i
$867$	−1083.11	+	9997.27i	−0.0424273	+	0.391609i
$868$	−8858.04	+	15342.6i	−0.346384	+	0.599955i
$869$	−11301.1	+	19574.2i	−0.441157	+	0.764106i
$870$		0			0
$871$	2350.19	+	4070.65i	0.0914272	+	0.158357i
$872$	970.272			0.0376807
$873$	−790.854	−	2488.07i	−0.0306602	−	0.0964587i
$874$	−1655.04			−0.0640534
$875$		0			0
$876$	46620.1	+	34100.0i	1.79811	+	1.31522i
$877$	−22410.4	+	38815.9i	−0.862879	+	1.49455i	0.00625950	+	0.999980i	$0.498008\pi$
$877$	−22410.4	+	38815.9i	−0.862879	+	1.49455i	−0.869138	+	0.494569i	$0.835326\pi$
$878$	−18606.6	+	32227.5i	−0.715195	+	1.23875i
$879$	10258.7	+	7503.64i	0.393648	+	0.287931i
$880$		0			0
$881$	11986.7			0.458391			0.229196	−	0.973380i	$-0.426390\pi$
$881$	11986.7			0.458391			0.229196	+	0.973380i	$0.426390\pi$
$882$	13129.1	+	2878.63i	0.501226	+	0.109896i
$883$	−14223.4			−0.542078			−0.271039	−	0.962568i	$-0.587367\pi$
$883$	−14223.4			−0.542078			−0.271039	+	0.962568i	$0.587367\pi$
$884$	−7311.32	−	12663.6i	−0.278175	−	0.481813i
$885$		0			0
$886$	4012.67	−	6950.14i	0.152154	−	0.263538i
$887$	11570.0	−	20039.8i	0.437973	−	0.758592i	−0.559560	−	0.828790i	$-0.689030\pi$
$887$	11570.0	−	20039.8i	0.437973	−	0.758592i	0.997533	+	0.0701980i	$0.0223631\pi$
$888$	4370.39	−	40339.2i	0.165158	−	1.52443i
$889$	2911.69	+	5043.19i	0.109848	+	0.190262i
$890$		0			0
$891$	1911.28	+	20734.5i	0.0718633	+	0.779608i
$892$	71666.0			2.69008
$893$	9.20394	+	15.9417i	0.000344903	+	0.000597389i
$894$	−7257.95	+	66991.8i	−0.271524	+	2.50620i
$895$		0			0
$896$	−18687.5	+	32367.7i	−0.696770	+	1.20684i
$897$	−8165.09	+	3604.07i	−0.303929	+	0.134154i
$898$	−18528.3	−	32092.0i	−0.688528	−	1.19257i
$899$	−12322.0			−0.457133
$900$		0			0
$901$	−2960.24			−0.109456
$902$	−20164.3	−	34925.6i	−0.744344	−	1.28924i
$903$	−23711.4	−	17343.6i	−0.873828	−	0.639156i
$904$	27277.4	−	47245.9i	1.00358	−	1.73825i
$905$		0			0
$906$	−31891.9	−	23327.1i	−1.16947	−	0.855400i
$907$	12262.9	+	21240.0i	0.448934	+	0.777576i	0.998317	−	0.0579945i	$-0.0184706\pi$
$907$	12262.9	+	21240.0i	0.448934	+	0.777576i	−0.549383	+	0.835571i	$0.685137\pi$
$908$	−3892.32			−0.142259
$909$	−8861.24	−	27878.0i	−0.323332	−	1.01722i
$910$		0			0
$911$	4226.93	+	7321.26i	0.153726	+	0.266261i	0.932594	−	0.360926i	$-0.117539\pi$
$911$	4226.93	+	7321.26i	0.153726	+	0.266261i	−0.778868	+	0.627187i	$0.784206\pi$
$912$	944.617	−	416.954i	0.0342976	−	0.0151389i
$913$	3257.28	−	5641.78i	0.118073	−	0.204508i
$914$	−15913.2	+	27562.5i	−0.575888	+	0.997467i
$915$		0			0
$916$	14020.3	+	24283.8i	0.505724	+	0.875940i
$917$	−10560.5			−0.380302
$918$	−57513.6	+	11648.9i	−2.06779	+	0.418815i
$919$	29199.7			1.04811			0.524053	−	0.851686i	$-0.324419\pi$
$919$	29199.7			1.04811			0.524053	+	0.851686i	$0.324419\pi$
$920$		0			0
$921$	3100.10	−	28614.3i	0.110914	−	1.02375i
$922$	16010.8	−	27731.5i	0.571896	−	0.990553i
$923$	1595.42	−	2763.35i	0.0568948	−	0.0985447i
$924$	−50059.0	+	22096.0i	−1.78227	+	0.786695i
$925$		0			0
$926$	−11603.4			−0.411783
$927$	7829.53	−	8584.44i	0.277406	−	0.304153i
$928$	35169.5			1.24407
$929$	25303.4	+	43826.7i	0.893624	+	1.54780i	0.835498	+	0.549493i	$0.185179\pi$
$929$	25303.4	+	43826.7i	0.893624	+	1.54780i	0.0581262	+	0.998309i	$0.481487\pi$
$930$		0			0
$931$	−94.5431	+	163.754i	−0.00332817	+	0.00576456i
$932$	−58082.3	+	100602.i	−2.04136	+	3.53574i
$933$	14784.6	+	10814.1i	0.518786	+	0.379462i
$934$	15625.1	+	27063.4i	0.547396	+	0.948118i
$935$		0			0
$936$	8840.92	−	9693.34i	0.308733	−	0.338501i
$937$	30351.9			1.05822			0.529110	−	0.848553i	$-0.322526\pi$
$937$	30351.9			1.05822			0.529110	+	0.848553i	$0.322526\pi$
$938$	24784.7	+	42928.3i	0.862738	+	1.49431i
$939$	−32850.6	+	14500.2i	−1.14168	+	0.503938i
$940$		0			0
$941$	11250.3	−	19486.0i	0.389743	−	0.675054i	−0.602672	−	0.797989i	$-0.705897\pi$
$941$	11250.3	−	19486.0i	0.389743	−	0.675054i	0.992415	+	0.122935i	$0.0392306\pi$
$942$	−3389.46	+	31285.2i	−0.117234	+	1.08209i
$943$	−23823.3	−	41263.1i	−0.822686	−	1.42493i
$944$	−58250.8			−2.00837
$945$		0			0
$946$	38845.3			1.33506
$947$	−18314.7	−	31722.1i	−0.628457	−	1.08852i	−0.987861	−	0.155338i	$-0.950353\pi$
$947$	−18314.7	−	31722.1i	−0.628457	−	1.08852i	0.359404	−	0.933182i	$-0.382980\pi$
$948$	7771.05	−	71727.8i	0.266236	−	2.45739i
$949$	−3189.88	+	5525.03i	−0.109112	+	0.188988i
$950$		0			0
$951$	20011.3	−	8832.97i	0.682345	−	0.301187i
$952$	−41949.8	−	72659.1i	−1.42815	−	2.47363i
$953$	−29632.2			−1.00722			−0.503611	−	0.863931i	$-0.667995\pi$
$953$	−29632.2			−1.00722			−0.503611	+	0.863931i	$0.667995\pi$
$954$	−1478.77	−	4652.29i	−0.0501854	−	0.157886i
$955$		0			0
$956$	−31208.1	−	54054.1i	−1.05580	−	1.82870i
$957$	−30718.2	−	22468.6i	−1.03759	−	0.758941i
$958$	9851.85	−	17063.9i	0.332254	−	0.575480i
$959$	23334.8	−	40417.0i	0.785734	−	1.36093i
$960$		0			0
$961$	13741.0	+	23800.1i	0.461246	+	0.798901i
$962$	8237.27			0.276071
$963$	−341.135	−	74.7957i	−0.0114153	−	0.00250286i
$964$	52066.4			1.73957
$965$		0			0
$966$	−86107.6	+	38007.9i	−2.86798	+	1.26592i
$967$	−24857.4	+	43054.3i	−0.826639	+	1.43178i	0.0740216	+	0.997257i	$0.476417\pi$
$967$	−24857.4	+	43054.3i	−0.826639	+	1.43178i	−0.900660	+	0.434524i	$0.856917\pi$
$968$	−12428.5	+	21526.8i	−0.412674	+	0.714772i
$969$	88.9175	−	820.719i	0.00294782	−	0.0272088i
$970$		0			0
$971$	−22201.1			−0.733745			−0.366872	−	0.930271i	$-0.619571\pi$
$971$	−22201.1			−0.733745			−0.366872	+	0.930271i	$0.619571\pi$
$972$	−32307.7	−	58085.6i	−1.06612	−	1.91677i
$973$	55319.4			1.82267
$974$	−37342.2	−	64678.6i	−1.22846	−	2.12776i
$975$		0			0
$976$	4105.31	−	7110.61i	0.134639	−	0.233202i
$977$	−3953.68	+	6847.97i	−0.129467	+	0.224244i	−0.923470	−	0.383670i	$-0.874660\pi$
$977$	−3953.68	+	6847.97i	−0.129467	+	0.224244i	0.794003	+	0.607914i	$0.207993\pi$
$978$	−52976.6	+	23383.9i	−1.73211	+	0.764553i
$979$	769.901	+	1333.51i	0.0251340	+	0.0435333i
$980$		0			0
$981$	530.338	+	116.279i	0.0172603	+	0.00378442i
$982$	−18383.9			−0.597406
$983$	4092.42	+	7088.28i	0.132785	+	0.229991i	0.924749	−	0.380577i	$-0.124275\pi$
$983$	4092.42	+	7088.28i	0.132785	+	0.229991i	−0.791964	+	0.610568i	$0.790941\pi$
$984$	56530.2	+	41348.6i	1.83142	+	1.33958i
$985$		0			0
$986$	53627.9	−	92886.3i	1.73211	−	3.00010i
$987$	844.957	+	618.038i	0.0272495	+	0.0199315i
$988$	169.615	+	293.782i	0.00546171	+	0.00945996i
$989$	45894.0			1.47558
$990$		0			0
$991$	−4964.85			−0.159146			−0.0795729	−	0.996829i	$-0.525356\pi$
$991$	−4964.85			−0.159146			−0.0795729	+	0.996829i	$0.525356\pi$
$992$	3295.23	+	5707.50i	0.105467	+	0.182675i
$993$	−8063.34	+	3559.16i	−0.257686	+	0.113743i
$994$	16825.0	−	29141.8i	0.536879	−	0.929901i
$995$		0			0
$996$	−2239.82	+	20673.8i	−0.0712564	+	0.657706i
$997$	−3549.14	−	6147.30i	−0.112741	−	0.195273i	0.804134	−	0.594449i	$-0.202630\pi$
$997$	−3549.14	−	6147.30i	−0.112741	−	0.195273i	−0.916874	+	0.399176i	$0.869296\pi$
$998$	16465.8			0.522261
$999$	7223.14	−	21525.1i	0.228759	−	0.681707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.e.g.76.16		32
5.2	odd	4		45.4.j.a.4.1	✓	32
5.3	odd	4		45.4.j.a.4.16	yes	32
5.4	even	2	inner	225.4.e.g.76.1		32
9.4	even	3		2025.4.a.bk.1.1		16
9.5	odd	6		2025.4.a.bl.1.16		16
9.7	even	3	inner	225.4.e.g.151.16		32
15.2	even	4		135.4.j.a.64.16		32
15.8	even	4		135.4.j.a.64.1		32
45.2	even	12		135.4.j.a.19.1		32
45.4	even	6		2025.4.a.bk.1.16		16
45.7	odd	12		45.4.j.a.34.16	yes	32
45.13	odd	12		405.4.b.e.244.16		16
45.14	odd	6		2025.4.a.bl.1.1		16
45.22	odd	12		405.4.b.e.244.1		16
45.23	even	12		405.4.b.f.244.1		16
45.32	even	12		405.4.b.f.244.16		16
45.34	even	6	inner	225.4.e.g.151.1		32
45.38	even	12		135.4.j.a.19.16		32
45.43	odd	12		45.4.j.a.34.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.j.a.4.1	✓	32	5.2	odd	4
45.4.j.a.4.16	yes	32	5.3	odd	4
45.4.j.a.34.1	yes	32	45.43	odd	12
45.4.j.a.34.16	yes	32	45.7	odd	12
135.4.j.a.19.1		32	45.2	even	12
135.4.j.a.19.16		32	45.38	even	12
135.4.j.a.64.1		32	15.8	even	4
135.4.j.a.64.16		32	15.2	even	4
225.4.e.g.76.1		32	5.4	even	2	inner
225.4.e.g.76.16		32	1.1	even	1	trivial
225.4.e.g.151.1		32	45.34	even	6	inner
225.4.e.g.151.16		32	9.7	even	3	inner
405.4.b.e.244.1		16	45.22	odd	12
405.4.b.e.244.16		16	45.13	odd	12
405.4.b.f.244.1		16	45.23	even	12
405.4.b.f.244.16		16	45.32	even	12
2025.4.a.bk.1.1		16	9.4	even	3
2025.4.a.bk.1.16		16	45.4	even	6
2025.4.a.bl.1.1		16	45.14	odd	6
2025.4.a.bl.1.16		16	9.5	odd	6

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

\(f(q)\)	\(=\)	\(q+(2.52718 + 4.37720i) q^{2} +(-0.559681 + 5.16592i) q^{3} +(-8.77324 + 15.1957i) q^{4} +(-24.0267 + 10.6054i) q^{6} +(-10.5059 - 18.1967i) q^{7} -48.2513 q^{8} +(-26.3735 - 5.78253i) q^{9} +O(q^{10})\)	\(q+(2.52718 + 4.37720i) q^{2} +(-0.559681 + 5.16592i) q^{3} +(-8.77324 + 15.1957i) q^{4} +(-24.0267 + 10.6054i) q^{6} +(-10.5059 - 18.1967i) q^{7} -48.2513 q^{8} +(-26.3735 - 5.78253i) q^{9} +(14.2815 + 24.7362i) q^{11} +(-73.5896 - 53.8266i) q^{12} +(5.03520 - 8.72122i) q^{13} +(53.1003 - 91.9724i) q^{14} +(-51.7535 - 89.6398i) q^{16} -82.7541 q^{17} +(-41.3392 - 130.056i) q^{18} +1.91981 q^{19} +(99.8826 - 44.0881i) q^{21} +(-72.1836 + 125.026i) q^{22} +(-85.2818 + 147.712i) q^{23} +(27.0053 - 249.262i) q^{24} +50.8993 q^{26} +(44.6329 - 133.007i) q^{27} +368.682 q^{28} +(128.214 + 222.074i) q^{29} +(-24.0262 + 41.6147i) q^{31} +(68.5756 - 118.776i) q^{32} +(-135.779 + 59.9326i) q^{33} +(-209.134 - 362.231i) q^{34} +(319.251 - 350.032i) q^{36} +161.834 q^{37} +(4.85169 + 8.40337i) q^{38} +(42.2350 + 30.8925i) q^{39} +(-139.674 + 241.922i) q^{41} +(445.403 + 325.787i) q^{42} +(-134.536 - 233.024i) q^{43} -501.179 q^{44} -862.088 q^{46} +(4.79420 + 8.30380i) q^{47} +(492.038 - 217.185i) q^{48} +(-49.2462 + 85.2969i) q^{49} +(46.3158 - 427.501i) q^{51} +(88.3500 + 153.027i) q^{52} +35.7716 q^{53} +(694.994 - 140.766i) q^{54} +(506.921 + 878.013i) q^{56} +(-1.07448 + 9.91757i) q^{57} +(-648.040 + 1122.44i) q^{58} +(281.385 - 487.374i) q^{59} +(39.6621 + 68.6968i) q^{61} -242.874 q^{62} +(171.854 + 540.661i) q^{63} -134.846 q^{64} +(-605.473 - 442.869i) q^{66} +(-233.376 + 404.219i) q^{67} +(726.021 - 1257.51i) q^{68} +(-715.340 - 523.231i) q^{69} +316.854 q^{71} +(1272.56 + 279.015i) q^{72} -633.515 q^{73} +(408.984 + 708.381i) q^{74} +(-16.8429 + 29.1728i) q^{76} +(300.078 - 519.751i) q^{77} +(-28.4874 + 262.942i) q^{78} +(395.658 + 685.299i) q^{79} +(662.125 + 305.011i) q^{81} -1411.92 q^{82} +(-114.039 - 197.521i) q^{83} +(-206.344 + 1904.58i) q^{84} +(679.994 - 1177.78i) q^{86} +(-1218.97 + 538.054i) q^{87} +(-689.099 - 1193.55i) q^{88} +53.9091 q^{89} -211.596 q^{91} +(-1496.39 - 2591.83i) q^{92} +(-201.531 - 147.409i) q^{93} +(-24.2316 + 41.9704i) q^{94} +(575.209 + 420.733i) q^{96} +(48.3470 + 83.7394i) q^{97} -497.815 q^{98} +(-233.614 - 734.964i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 54 q^{4} - 12 q^{6} + 18 q^{9}+O(q^{10}) \) 32 * q - 54 * q^4 - 12 * q^6 + 18 * q^9	\( 32 q - 54 q^{4} - 12 q^{6} + 18 q^{9} + 90 q^{11} + 102 q^{14} - 146 q^{16} + 8 q^{19} + 30 q^{21} - 462 q^{24} - 936 q^{26} + 516 q^{29} - 38 q^{31} - 212 q^{34} + 864 q^{36} - 330 q^{39} + 576 q^{41} - 3288 q^{44} - 580 q^{46} + 4 q^{49} + 1260 q^{51} + 3726 q^{54} + 2430 q^{56} + 2202 q^{59} - 20 q^{61} - 644 q^{64} - 5052 q^{66} - 1452 q^{69} - 5904 q^{71} + 4080 q^{74} + 396 q^{76} + 218 q^{79} + 198 q^{81} - 4662 q^{84} + 6108 q^{86} - 8148 q^{89} - 1884 q^{91} + 1078 q^{94} + 11874 q^{96} + 1602 q^{99}+O(q^{100}) \) 32 * q - 54 * q^4 - 12 * q^6 + 18 * q^9 + 90 * q^11 + 102 * q^14 - 146 * q^16 + 8 * q^19 + 30 * q^21 - 462 * q^24 - 936 * q^26 + 516 * q^29 - 38 * q^31 - 212 * q^34 + 864 * q^36 - 330 * q^39 + 576 * q^41 - 3288 * q^44 - 580 * q^46 + 4 * q^49 + 1260 * q^51 + 3726 * q^54 + 2430 * q^56 + 2202 * q^59 - 20 * q^61 - 644 * q^64 - 5052 * q^66 - 1452 * q^69 - 5904 * q^71 + 4080 * q^74 + 396 * q^76 + 218 * q^79 + 198 * q^81 - 4662 * q^84 + 6108 * q^86 - 8148 * q^89 - 1884 * q^91 + 1078 * q^94 + 11874 * q^96 + 1602 * q^99

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