LMFDB - Embedded newform 225.4.e.g.76.15

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			76.15
Character	$\chi$	$=$	225.76
Dual form			225.4.e.g.151.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.51186 + 4.35066i) q^{2} +(4.79730 - 1.99648i) q^{3} +(-8.61884 + 14.9283i) q^{4} +(20.7361 + 15.8565i) q^{6} +(2.69099 + 4.66092i) q^{7} -46.4074 q^{8} +(19.0281 - 19.1554i) q^{9} +O(q^{10})$	\(q+(2.51186 + 4.35066i) q^{2} +(4.79730 - 1.99648i) q^{3} +(-8.61884 + 14.9283i) q^{4} +(20.7361 + 15.8565i) q^{6} +(2.69099 + 4.66092i) q^{7} -46.4074 q^{8} +(19.0281 - 19.1554i) q^{9} +(19.5509 + 33.8631i) q^{11} +(-11.5431 + 88.8227i) q^{12} +(-43.3135 + 75.0212i) q^{13} +(-13.5187 + 23.4151i) q^{14} +(-47.6180 - 82.4768i) q^{16} +15.4194 q^{17} +(131.135 + 34.6693i) q^{18} -26.8412 q^{19} +(22.2149 + 16.9873i) q^{21} +(-98.2180 + 170.119i) q^{22} +(55.5692 - 96.2486i) q^{23} +(-222.630 + 92.6515i) q^{24} -435.189 q^{26} +(53.0401 - 129.884i) q^{27} -92.7727 q^{28} +(-24.6174 - 42.6385i) q^{29} +(89.9383 - 155.778i) q^{31} +(53.5894 - 92.8196i) q^{32} +(161.398 + 123.419i) q^{33} +(38.7312 + 67.0844i) q^{34} +(121.957 + 449.154i) q^{36} +293.496 q^{37} +(-67.4211 - 116.777i) q^{38} +(-58.0094 + 446.374i) q^{39} +(-13.8016 + 23.9051i) q^{41} +(-18.1055 + 139.319i) q^{42} +(-30.2515 - 52.3971i) q^{43} -674.023 q^{44} +558.327 q^{46} +(-48.1175 - 83.3420i) q^{47} +(-393.101 - 300.597i) q^{48} +(157.017 - 271.962i) q^{49} +(73.9713 - 30.7845i) q^{51} +(-746.625 - 1293.19i) q^{52} +251.203 q^{53} +(698.309 - 95.4892i) q^{54} +(-124.882 - 216.301i) q^{56} +(-128.765 + 53.5879i) q^{57} +(123.671 - 214.204i) q^{58} +(38.4231 - 66.5508i) q^{59} +(-245.045 - 424.431i) q^{61} +903.648 q^{62} +(140.486 + 37.1417i) q^{63} -223.452 q^{64} +(-131.542 + 1012.20i) q^{66} +(119.360 - 206.738i) q^{67} +(-132.897 + 230.184i) q^{68} +(74.4232 - 572.676i) q^{69} -640.447 q^{71} +(-883.046 + 888.954i) q^{72} +769.257 q^{73} +(737.219 + 1276.90i) q^{74} +(231.340 - 400.692i) q^{76} +(-105.222 + 182.250i) q^{77} +(-2087.73 + 868.847i) q^{78} +(-331.176 - 573.613i) q^{79} +(-4.86094 - 728.984i) q^{81} -138.670 q^{82} +(651.071 + 1127.69i) q^{83} +(-445.058 + 185.219i) q^{84} +(151.975 - 263.228i) q^{86} +(-203.224 - 155.402i) q^{87} +(-907.306 - 1571.50i) q^{88} -995.544 q^{89} -466.224 q^{91} +(957.883 + 1659.10i) q^{92} +(120.453 - 926.872i) q^{93} +(241.729 - 418.686i) q^{94} +(71.7718 - 552.274i) q^{96} +(407.423 + 705.677i) q^{97} +1577.62 q^{98} +(1020.68 + 269.846i) 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 $

$2$	2.51186	+	4.35066i	0.888075	+	1.53819i	0.842148	+	0.539246i	$0.181291\pi$
$2$	2.51186	+	4.35066i	0.888075	+	1.53819i	0.0459269	+	0.998945i	$0.485376\pi$
$3$	4.79730	−	1.99648i	0.923240	−	0.384223i
$3$	4.79730	−	1.99648i	0.923240	−	0.384223i
$4$	−8.61884	+	14.9283i	−1.07735	+	1.86603i
$5$		0			0
$5$		0			0
$6$	20.7361	+	15.8565i	1.41092	+	1.07890i
$7$	2.69099	+	4.66092i	0.145300	+	0.251666i	0.929485	−	0.368861i	$-0.120252\pi$
$7$	2.69099	+	4.66092i	0.145300	+	0.251666i	−0.784185	+	0.620527i	$0.786919\pi$
$8$	−46.4074			−2.05094
$9$	19.0281	−	19.1554i	0.704745	−	0.709460i
$10$		0			0
$11$	19.5509	+	33.8631i	0.535892	+	0.928192i	0.999120	+	0.0419529i	$0.0133580\pi$
$11$	19.5509	+	33.8631i	0.535892	+	0.928192i	−0.463227	+	0.886239i	$0.653309\pi$
$12$	−11.5431	+	88.8227i	−0.277684	+	2.13674i
$13$	−43.3135	+	75.0212i	−0.924078	+	1.60055i	−0.131040	+	0.991377i	$0.541832\pi$
$13$	−43.3135	+	75.0212i	−0.924078	+	1.60055i	−0.793037	+	0.609173i	$0.791502\pi$
$14$	−13.5187	+	23.4151i	−0.258074	+	0.446997i
$15$		0			0
$16$	−47.6180	−	82.4768i	−0.744031	−	1.28870i
$17$	15.4194			0.219985			0.109993	−	0.993932i	$-0.464917\pi$
$17$	15.4194			0.219985			0.109993	+	0.993932i	$0.464917\pi$
$18$	131.135	+	34.6693i	1.71715	+	0.453979i
$19$	−26.8412			−0.324094			−0.162047	−	0.986783i	$-0.551810\pi$
$19$	−26.8412			−0.324094			−0.162047	+	0.986783i	$0.551810\pi$
$20$		0			0
$21$	22.2149	+	16.9873i	0.230842	+	0.176521i
$22$	−98.2180	+	170.119i	−0.951825	+	1.64861i
$23$	55.5692	−	96.2486i	0.503781	−	0.872575i	−0.496209	−	0.868203i	$-0.665275\pi$
$23$	55.5692	−	96.2486i	0.503781	−	0.872575i	0.999990	−	0.00437188i	$-0.00139162\pi$
$24$	−222.630	+	92.6515i	−1.89351	+	0.788017i
$25$		0			0
$26$	−435.189			−3.28260
$27$	53.0401	−	129.884i	0.378058	−	0.925782i
$28$	−92.7727			−0.626157
$29$	−24.6174	−	42.6385i	−0.157632	−	0.273027i	0.776382	−	0.630262i	$-0.217053\pi$
$29$	−24.6174	−	42.6385i	−0.157632	−	0.273027i	−0.934014	+	0.357236i	$0.883719\pi$
$30$		0			0
$31$	89.9383	−	155.778i	0.521077	−	0.902532i	−0.478622	−	0.878021i	$-0.658864\pi$
$31$	89.9383	−	155.778i	0.521077	−	0.902532i	0.999700	−	0.0245112i	$-0.00780295\pi$
$32$	53.5894	−	92.8196i	0.296043	−	0.512761i
$33$	161.398	+	123.419i	0.851390	+	0.651043i
$34$	38.7312	+	67.0844i	0.195363	+	0.338379i
$35$		0			0
$36$	121.957	+	449.154i	0.564616	+	2.07942i
$37$	293.496			1.30407			0.652033	−	0.758191i	$-0.273916\pi$
$37$	293.496			1.30407			0.652033	+	0.758191i	$0.273916\pi$
$38$	−67.4211	−	116.777i	−0.287820	−	0.498518i
$39$	−58.0094	+	446.374i	−0.238178	+	1.83274i
$40$		0			0
$41$	−13.8016	+	23.9051i	−0.0525719	+	0.0910571i	−0.891114	−	0.453780i	$-0.850075\pi$
$41$	−13.8016	+	23.9051i	−0.0525719	+	0.0910571i	0.838542	+	0.544837i	$0.183409\pi$
$42$	−18.1055	+	139.319i	−0.0665177	+	0.511844i
$43$	−30.2515	−	52.3971i	−0.107286	−	0.185825i	0.807384	−	0.590027i	$-0.200883\pi$
$43$	−30.2515	−	52.3971i	−0.107286	−	0.185825i	−0.914670	+	0.404201i	$0.867549\pi$
$44$	−674.023			−2.30938
$45$		0			0
$46$	558.327			1.78958
$47$	−48.1175	−	83.3420i	−0.149333	−	0.258653i	0.781648	−	0.623720i	$-0.214379\pi$
$47$	−48.1175	−	83.3420i	−0.149333	−	0.258653i	−0.930981	+	0.365067i	$0.881046\pi$
$48$	−393.101	−	300.597i	−1.18207	−	0.903906i
$49$	157.017	−	271.962i	0.457776	−	0.792891i
$50$		0			0
$51$	73.9713	−	30.7845i	0.203099	−	0.0845233i
$52$	−746.625	−	1293.19i	−1.99112	−	3.44872i
$53$	251.203			0.651046			0.325523	−	0.945534i	$-0.394460\pi$
$53$	251.203			0.651046			0.325523	+	0.945534i	$0.394460\pi$
$54$	698.309	−	95.4892i	1.75977	−	0.240638i
$55$		0			0
$56$	−124.882	−	216.301i	−0.298000	−	0.516152i
$57$	−128.765	+	53.5879i	−0.299217	+	0.124524i
$58$	123.671	−	214.204i	0.279978	−	0.484937i
$59$	38.4231	−	66.5508i	0.0847841	−	0.146850i	−0.820515	−	0.571625i	$-0.806313\pi$
$59$	38.4231	−	66.5508i	0.0847841	−	0.146850i	0.905299	+	0.424774i	$0.139647\pi$
$60$		0			0
$61$	−245.045	−	424.431i	−0.514342	−	0.890866i	−0.999862	−	0.0166406i	$-0.994703\pi$
$61$	−245.045	−	424.431i	−0.514342	−	0.890866i	0.485520	−	0.874226i	$-0.338630\pi$
$62$	903.648			1.85102
$63$	140.486	+	37.1417i	0.280946	+	0.0742763i
$64$	−223.452			−0.436430
$65$		0			0
$66$	−131.542	+	1012.20i	−0.245330	+	1.88778i
$67$	119.360	−	206.738i	0.217645	−	0.376972i	−0.736443	−	0.676500i	$-0.763496\pi$
$67$	119.360	−	206.738i	0.217645	−	0.376972i	0.954087	+	0.299528i	$0.0968292\pi$
$68$	−132.897	+	230.184i	−0.237002	+	0.410499i
$69$	74.4232	−	572.676i	0.129848	−	0.999161i
$70$		0			0
$71$	−640.447			−1.07052			−0.535261	−	0.844687i	$-0.679787\pi$
$71$	−640.447			−1.07052			−0.535261	+	0.844687i	$0.679787\pi$
$72$	−883.046	+	888.954i	−1.44539	+	1.45506i
$73$	769.257			1.23335			0.616676	−	0.787217i	$-0.288479\pi$
$73$	769.257			1.23335			0.616676	+	0.787217i	$0.288479\pi$
$74$	737.219	+	1276.90i	1.15811	+	2.00590i
$75$		0			0
$76$	231.340	−	400.692i	0.349164	−	0.604770i
$77$	−105.222	+	182.250i	−0.155730	+	0.269732i
$78$	−2087.73	+	868.847i	−3.03063	+	1.26125i
$79$	−331.176	−	573.613i	−0.471648	−	0.816918i	0.527826	−	0.849353i	$-0.323007\pi$
$79$	−331.176	−	573.613i	−0.471648	−	0.816918i	−0.999474	+	0.0324343i	$0.989674\pi$
$80$		0			0
$81$	−4.86094	−	728.984i	−0.00666796	−	0.999978i
$82$	−138.670			−0.186751
$83$	651.071	+	1127.69i	0.861016	+	1.49132i	0.870949	+	0.491373i	$0.163505\pi$
$83$	651.071	+	1127.69i	0.861016	+	1.49132i	−0.00993336	+	0.999951i	$0.503162\pi$
$84$	−445.058	+	185.219i	−0.578093	+	0.240584i
$85$		0			0
$86$	151.975	−	263.228i	0.190557	−	0.330054i
$87$	−203.224	−	155.402i	−0.250436	−	0.191503i
$88$	−907.306	−	1571.50i	−1.09908	−	1.90366i
$89$	−995.544			−1.18570			−0.592851	−	0.805312i	$-0.701998\pi$
$89$	−995.544			−1.18570			−0.592851	+	0.805312i	$0.701998\pi$
$90$		0			0
$91$	−466.224			−0.537073
$92$	957.883	+	1659.10i	1.08550	+	1.88015i
$93$	120.453	−	926.872i	0.134306	−	1.03346i
$94$	241.729	−	418.686i	0.265238	−	0.459406i
$95$		0			0
$96$	71.7718	−	552.274i	0.0763040	−	0.587148i
$97$	407.423	+	705.677i	0.426470	+	0.738667i	0.996556	−	0.0829175i	$-0.0264238\pi$
$97$	407.423	+	705.677i	0.426470	+	0.738667i	−0.570087	+	0.821584i	$0.693090\pi$
$98$	1577.62			1.62616
$99$	1020.68	+	269.846i	1.03618	+	0.273945i
$100$		0			0
$101$	326.302	+	565.172i	0.321468	+	0.556799i	0.980791	−	0.195061i	$-0.0624904\pi$
$101$	326.302	+	565.172i	0.321468	+	0.556799i	−0.659323	+	0.751860i	$0.729157\pi$
$102$	319.738	+	244.498i	0.310380	+	0.237342i
$103$	−76.9776	+	133.329i	−0.0736391	+	0.127547i	−0.900494	−	0.434869i	$-0.856795\pi$
$103$	−76.9776	+	133.329i	−0.0736391	+	0.127547i	0.826855	+	0.562416i	$0.190128\pi$
$104$	2010.07	−	3481.54i	1.89523	−	3.28263i
$105$		0			0
$106$	630.987	+	1092.90i	0.578178	+	1.00143i
$107$	348.878			0.315209			0.157604	−	0.987502i	$-0.449623\pi$
$107$	348.878			0.315209			0.157604	+	0.987502i	$0.449623\pi$
$108$	1481.79	+	1911.24i	1.32024	+	1.70286i
$109$	1125.26			0.988815			0.494407	−	0.869230i	$-0.335385\pi$
$109$	1125.26			0.988815			0.494407	+	0.869230i	$0.335385\pi$
$110$		0			0
$111$	1407.99	−	585.959i	1.20397	−	0.501052i
$112$	256.279	−	443.888i	0.216215	−	0.374495i
$113$	−176.038	+	304.907i	−0.146551	+	0.253834i	−0.929951	−	0.367685i	$-0.880151\pi$
$113$	−176.038	+	304.907i	−0.146551	+	0.253834i	0.783400	+	0.621518i	$0.213484\pi$
$114$	−556.582	−	425.608i	−0.457269	−	0.349665i
$115$		0			0
$116$	848.692			0.679303
$117$	612.889	+	2257.20i	0.484287	+	1.78358i
$118$	386.053			0.301179
$119$	41.4933	+	71.8685i	0.0319637	+	0.0553628i
$120$		0			0
$121$	−98.9741	+	171.428i	−0.0743607	+	0.128797i
$122$	1231.04	−	2132.22i	0.913549	−	1.58231i
$123$	−18.4843	+	142.234i	−0.0135502	+	0.104267i
$124$	1550.33	+	2685.24i	1.12277	+	1.94469i
$125$		0			0
$126$	191.291	+	704.503i	0.135250	+	0.498112i
$127$	−1502.08			−1.04951			−0.524757	−	0.851252i	$-0.675844\pi$
$127$	−1502.08			−1.04951			−0.524757	+	0.851252i	$0.675844\pi$
$128$	−989.995	−	1714.72i	−0.683625	−	1.18407i
$129$	−249.735	−	190.968i	−0.170449	−	0.130340i
$130$		0			0
$131$	787.356	−	1363.74i	0.525127	−	0.909546i	−0.474445	−	0.880285i	$-0.657351\pi$
$131$	787.356	−	1363.74i	0.525127	−	0.909546i	0.999572	−	0.0292609i	$-0.00931535\pi$
$132$	−3233.49	+	1345.68i	−2.13212	+	0.887318i
$133$	−72.2292	−	125.105i	−0.0470907	−	0.0815635i
$134$	1199.26			0.773140
$135$		0			0
$136$	−715.573			−0.451175
$137$	−446.149	−	772.753i	−0.278227	−	0.481903i	0.692717	−	0.721209i	$-0.256413\pi$
$137$	−446.149	−	772.753i	−0.278227	−	0.481903i	−0.970944	+	0.239306i	$0.923080\pi$
$138$	2678.46	−	1114.69i	1.65221	−	0.687599i
$139$	−326.353	+	565.260i	−0.199143	+	0.344926i	−0.948251	−	0.317522i	$-0.897149\pi$
$139$	−326.353	+	565.260i	−0.199143	+	0.344926i	0.749108	+	0.662448i	$0.230483\pi$
$140$		0			0
$141$	−397.225	−	303.751i	−0.237251	−	0.181421i
$142$	−1608.71	−	2786.37i	−0.950704	−	1.64667i
$143$	−3387.27			−1.98082
$144$	−2485.96	−	657.235i	−1.43863	−	0.380345i
$145$		0			0
$146$	1932.26	+	3346.78i	1.09531	+	1.89713i
$147$	210.292	−	1618.16i	0.117990	−	0.907917i
$148$	−2529.59	+	4381.38i	−1.40494	+	2.43343i
$149$	−1718.93	+	2977.27i	−0.945101	+	1.63696i	−0.189551	+	0.981871i	$0.560703\pi$
$149$	−1718.93	+	2977.27i	−0.945101	+	1.63696i	−0.755550	+	0.655092i	$0.772630\pi$
$150$		0			0
$151$	−835.459	−	1447.06i	−0.450256	−	0.779867i	0.548145	−	0.836383i	$-0.315334\pi$
$151$	−835.459	−	1447.06i	−0.450256	−	0.779867i	−0.998402	+	0.0565162i	$0.982001\pi$
$152$	1245.63			0.664696
$153$	293.402	−	295.365i	0.155033	−	0.156071i
$154$	−1057.21			−0.553199
$155$		0			0
$156$	−6163.61	−	4713.20i	−3.16336	−	2.41896i
$157$	333.052	−	576.864i	0.169302	−	0.293240i	−0.768872	−	0.639402i	$-0.779182\pi$
$157$	333.052	−	576.864i	0.169302	−	0.293240i	0.938175	+	0.346162i	$0.112515\pi$
$158$	1663.73	−	2881.67i	0.837718	−	1.45097i
$159$	1205.10	−	501.523i	0.601072	−	0.250147i
$160$		0			0
$161$	598.143			0.292797
$162$	3159.35	−	1852.25i	1.53224	−	0.898312i
$163$	889.255			0.427312			0.213656	−	0.976909i	$-0.431463\pi$
$163$	889.255			0.427312			0.213656	+	0.976909i	$0.431463\pi$
$164$	−237.907	−	412.067i	−0.113277	−	0.196202i
$165$		0			0
$166$	−3270.79	+	5665.18i	−1.52929	+	2.64881i
$167$	−201.931	+	349.755i	−0.0935683	+	0.162065i	−0.909010	−	0.416774i	$-0.863161\pi$
$167$	−201.931	+	349.755i	−0.0935683	+	0.162065i	0.815442	+	0.578839i	$0.196494\pi$
$168$	−1030.94	−	788.338i	−0.473443	−	0.362033i
$169$	−2653.62	−	4596.21i	−1.20784	−	2.09204i
$170$		0			0
$171$	−510.737	+	514.154i	−0.228404	+	0.229932i
$172$	1042.93			0.462342
$173$	−118.031	−	204.435i	−0.0518712	−	0.0898435i	0.838924	−	0.544249i	$-0.183185\pi$
$173$	−118.031	−	204.435i	−0.0518712	−	0.0898435i	−0.890795	+	0.454405i	$0.849852\pi$
$174$	165.631	−	1274.50i	0.0721634	−	0.555287i
$175$		0			0
$176$	1861.95	−	3224.99i	0.797441	−	1.38121i
$177$	51.4597	−	395.975i	0.0218528	−	0.168154i
$178$	−2500.66	−	4331.28i	−1.05299	−	1.82384i
$179$	2404.31			1.00395			0.501973	−	0.864883i	$-0.332608\pi$
$179$	2404.31			1.00395			0.501973	+	0.864883i	$0.332608\pi$
$180$		0			0
$181$	−1218.41			−0.500354			−0.250177	−	0.968200i	$-0.580489\pi$
$181$	−1218.41			−0.500354			−0.250177	+	0.968200i	$0.580489\pi$
$182$	−1171.09	−	2028.38i	−0.476961	−	0.826120i
$183$	−2022.93	−	1546.89i	−0.817153	−	0.624862i
$184$	−2578.82	+	4466.65i	−1.03322	+	1.78960i
$185$		0			0
$186$	4335.07	−	1804.12i	1.70894	−	0.711205i
$187$	301.462	+	522.148i	0.117888	+	0.204188i
$188$	1658.87			0.643539
$189$	748.108	−	102.299i	0.287920	−	0.0393712i
$190$		0			0
$191$	−87.9715	−	152.371i	−0.0333267	−	0.0577235i	0.848881	−	0.528584i	$-0.177277\pi$
$191$	−87.9715	−	152.371i	−0.0333267	−	0.0577235i	−0.882208	+	0.470861i	$0.843944\pi$
$192$	−1071.97	+	446.118i	−0.402930	+	0.167686i
$193$	−1107.63	+	1918.47i	−0.413103	+	0.715516i	−0.995227	−	0.0975842i	$-0.968888\pi$
$193$	−1107.63	+	1918.47i	−0.413103	+	0.715516i	0.582124	+	0.813100i	$0.302222\pi$
$194$	−2046.78	+	3545.12i	−0.757474	+	1.31198i
$195$		0			0
$196$	2706.61	+	4687.99i	0.986374	+	1.70845i
$197$	−1054.08			−0.381218			−0.190609	−	0.981666i	$-0.561046\pi$
$197$	−1054.08			−0.381218			−0.190609	+	0.981666i	$0.561046\pi$
$198$	1389.79	+	5118.44i	0.498829	+	1.83713i
$199$	−3484.04			−1.24109			−0.620546	−	0.784170i	$-0.713089\pi$
$199$	−3484.04			−1.24109			−0.620546	+	0.784170i	$0.713089\pi$
$200$		0			0
$201$	159.858	−	1230.09i	0.0560972	−	0.431660i
$202$	−1639.25	+	2839.26i	−0.570975	+	0.988958i
$203$	132.490	−	229.479i	0.0458078	−	0.0793414i
$204$	−177.988	+	1369.59i	−0.0610864	+	0.470051i
$205$		0			0
$206$	−773.426			−0.261588
$207$	−786.307	−	2895.88i	−0.264020	−	0.972356i
$208$	8250.01			2.75017
$209$	−524.768	−	908.926i	−0.173679	−	0.300822i
$210$		0			0
$211$	2098.45	−	3634.62i	0.684660	−	1.18587i	−0.288884	−	0.957364i	$-0.593284\pi$
$211$	2098.45	−	3634.62i	0.684660	−	1.18587i	0.973544	−	0.228501i	$-0.0733825\pi$
$212$	−2165.08	+	3750.03i	−0.701408	+	1.21487i
$213$	−3072.41	+	1278.64i	−0.988349	+	0.411319i
$214$	876.331	+	1517.85i	0.279929	+	0.484851i
$215$		0			0
$216$	−2461.45	+	6027.56i	−0.775374	+	1.89872i
$217$	968.091			0.302849
$218$	2826.50	+	4895.65i	0.878142	+	1.52099i
$219$	3690.35	−	1535.81i	1.13868	−	0.473882i
$220$		0			0
$221$	−667.867	+	1156.78i	−0.203283	+	0.352097i
$222$	6085.97	+	4653.83i	1.83993	+	1.40696i
$223$	−1517.28	−	2628.00i	−0.455625	−	0.789166i	0.543098	−	0.839669i	$-0.317251\pi$
$223$	−1517.28	−	2628.00i	−0.455625	−	0.789166i	−0.998724	+	0.0505026i	$0.983918\pi$
$224$	576.834			0.172059
$225$		0			0
$226$	−1768.73			−0.520593
$227$	1618.08	+	2802.60i	0.473109	+	0.819450i	0.999526	−	0.0307770i	$-0.00979819\pi$
$227$	1618.08	+	2802.60i	0.473109	+	0.819450i	−0.526417	+	0.850227i	$0.676465\pi$
$228$	309.831	−	2384.10i	0.0899958	−	0.692505i
$229$	1487.28	−	2576.04i	0.429180	−	0.743361i	−0.567621	−	0.823290i	$-0.692136\pi$
$229$	1487.28	−	2576.04i	0.429180	−	0.743361i	0.996801	+	0.0799288i	$0.0254693\pi$
$230$		0			0
$231$	−140.923	+	1084.38i	−0.0401388	+	0.308862i
$232$	1142.43	+	1978.74i	0.323293	+	0.559961i
$233$	2927.42			0.823097			0.411549	−	0.911388i	$-0.364988\pi$
$233$	2927.42			0.823097			0.411549	+	0.911388i	$0.364988\pi$
$234$	−8280.84	+	8336.24i	−2.31340	+	2.32888i
$235$		0			0
$236$	662.325	+	1147.18i	0.182685	+	0.316420i
$237$	−2733.96	−	2090.61i	−0.749323	−	0.572994i
$238$	−208.450	+	361.047i	−0.0567724	+	0.0983327i
$239$	−1439.35	+	2493.02i	−0.389555	+	0.674729i	−0.992390	−	0.123137i	$-0.960705\pi$
$239$	−1439.35	+	2493.02i	−0.389555	+	0.674729i	0.602835	+	0.797866i	$0.294038\pi$
$240$		0			0
$241$	558.792	+	967.856i	0.149357	+	0.258693i	0.930990	−	0.365045i	$-0.118946\pi$
$241$	558.792	+	967.856i	0.149357	+	0.258693i	−0.781633	+	0.623738i	$0.785613\pi$
$242$	−994.435			−0.264152
$243$	−1478.72	−	3487.45i	−0.390371	−	0.920658i
$244$	8448.03			2.21651
$245$		0			0
$246$	−665.243	+	276.853i	−0.172416	+	0.0717540i
$247$	1162.59	−	2013.66i	0.299488	−	0.518729i
$248$	−4173.80	+	7229.24i	−1.06870	+	1.85104i
$249$	5374.79	+	4110.00i	1.36793	+	1.04603i
$250$		0			0
$251$	−4612.00			−1.15979			−0.579894	−	0.814692i	$-0.696906\pi$
$251$	−4612.00			−1.15979			−0.579894	+	0.814692i	$0.696906\pi$
$252$	−1765.29	+	1777.10i	−0.441281	+	0.444233i
$253$	4345.71			1.07989
$254$	−3773.02	−	6535.06i	−0.932048	−	1.61435i
$255$		0			0
$256$	4079.64	−	7066.14i	0.996006	−	1.72513i
$257$	−1893.86	+	3280.26i	−0.459672	+	0.796176i	−0.998943	−	0.0459562i	$-0.985367\pi$
$257$	−1893.86	+	3280.26i	−0.459672	+	0.796176i	0.539271	+	0.842132i	$0.318700\pi$
$258$	203.538	−	1566.20i	0.0491153	−	0.377935i
$259$	789.793	+	1367.96i	0.189480	+	0.328189i
$260$		0			0
$261$	−1285.18	−	339.775i	−0.304792	−	0.0805807i
$262$	7910.89			1.86541
$263$	−2494.78	−	4321.08i	−0.584923	−	1.01312i	−0.994885	−	0.101013i	$-0.967791\pi$
$263$	−2494.78	−	4321.08i	−0.584923	−	1.01312i	0.409962	−	0.912102i	$-0.365542\pi$
$264$	−7490.08	−	5727.53i	−1.74615	−	1.33525i
$265$		0			0
$266$	362.859	−	628.490i	0.0836402	−	0.144869i
$267$	−4775.92	+	1987.59i	−1.09469	+	0.455574i
$268$	2057.50	+	3563.69i	0.468961	+	0.812265i
$269$	−5845.57			−1.32495			−0.662473	−	0.749086i	$-0.730493\pi$
$269$	−5845.57			−1.32495			−0.662473	+	0.749086i	$0.730493\pi$
$270$		0			0
$271$	2766.09			0.620030			0.310015	−	0.950732i	$-0.399666\pi$
$271$	2766.09			0.620030			0.310015	+	0.950732i	$0.399666\pi$
$272$	−734.239	−	1271.74i	−0.163676	−	0.283495i
$273$	−2236.62	+	930.808i	−0.495847	+	0.206356i
$274$	2241.32	−	3882.09i	0.494173	−	0.855933i
$275$		0			0
$276$	7907.62	+	6046.81i	1.72457	+	1.31875i
$277$	946.900	+	1640.08i	0.205393	+	0.355750i	0.950258	−	0.311465i	$-0.100820\pi$
$277$	946.900	+	1640.08i	0.205393	+	0.355750i	−0.744865	+	0.667215i	$0.767486\pi$
$278$	−3279.01			−0.707417
$279$	−1272.63	−	4686.96i	−0.273084	−	1.00574i
$280$		0			0
$281$	−2242.19	−	3883.58i	−0.476006	−	0.824467i	0.523616	−	0.851954i	$-0.324583\pi$
$281$	−2242.19	−	3883.58i	−0.476006	−	0.824467i	−0.999622	+	0.0274877i	$0.991249\pi$
$282$	323.745	−	2491.17i	0.0683642	−	0.526053i
$283$	2898.82	−	5020.91i	0.608894	−	1.05464i	−0.382529	−	0.923944i	$-0.624947\pi$
$283$	2898.82	−	5020.91i	0.608894	−	1.05464i	0.991423	−	0.130692i	$-0.0417200\pi$
$284$	5519.91	−	9560.76i	1.15333	−	1.99763i
$285$		0			0
$286$	−8508.34	−	14736.9i	−1.75912	−	3.04689i
$287$	−148.560			−0.0305547
$288$	−758.293	−	2792.71i	−0.155149	−	0.571396i
$289$	−4675.24			−0.951607
$290$		0			0
$291$	3363.40	+	2571.93i	0.677547	+	0.518108i
$292$	−6630.10	+	11483.7i	−1.32876	+	2.30148i
$293$	−3955.13	+	6850.49i	−0.788605	+	1.36590i	0.138217	+	0.990402i	$0.455863\pi$
$293$	−3955.13	+	6850.49i	−0.788605	+	1.36590i	−0.926822	+	0.375502i	$0.877470\pi$
$294$	7568.30	−	3149.68i	1.50133	−	0.624807i
$295$		0			0
$296$	−13620.4			−2.67456
$297$	5435.25	−	743.235i	1.06190	−	0.145208i
$298$	−17270.8			−3.35728
$299$	4813.79	+	8337.74i	0.931066	+	1.61265i
$300$		0			0
$301$	162.813	−	282.000i	0.0311773	−	0.0540007i
$302$	4197.11	−	7269.60i	0.799723	−	1.38516i
$303$	2693.72	+	2059.84i	0.510727	+	0.390544i
$304$	1278.12	+	2213.77i	0.241136	+	0.417660i
$305$		0			0
$306$	2022.01	+	534.578i	0.377748	+	0.0998686i
$307$	−4426.37			−0.822887			−0.411443	−	0.911435i	$-0.634975\pi$
$307$	−4426.37			−0.822887			−0.411443	+	0.911435i	$0.634975\pi$
$308$	−1813.79	−	3141.57i	−0.335552	−	0.581194i
$309$	−103.095	+	793.304i	−0.0189802	+	0.146050i
$310$		0			0
$311$	−4848.62	+	8398.06i	−0.884052	+	1.53122i	−0.0372549	+	0.999306i	$0.511861\pi$
$311$	−4848.62	+	8398.06i	−0.884052	+	1.53122i	−0.846797	+	0.531917i	$0.821472\pi$
$312$	2692.07	−	20715.1i	0.488488	−	3.75884i
$313$	2261.55	+	3917.11i	0.408403	+	0.707375i	0.994711	−	0.102713i	$-0.0327524\pi$
$313$	2261.55	+	3917.11i	0.408403	+	0.707375i	−0.586308	+	0.810088i	$0.699419\pi$
$314$	3346.32			0.601413
$315$		0			0
$316$	11417.4			2.03253
$317$	−2661.10	−	4609.17i	−0.471491	−	0.816646i	0.527977	−	0.849258i	$-0.322951\pi$
$317$	−2661.10	−	4609.17i	−0.471491	−	0.816646i	−0.999468	+	0.0326127i	$0.989617\pi$
$318$	5208.99	+	3983.22i	0.918571	+	0.702415i
$319$	962.583	−	1667.24i	0.168948	−	0.292626i
$320$		0			0
$321$	1673.67	−	696.528i	0.291013	−	0.121110i
$322$	1502.45	+	2602.32i	0.260026	+	0.450378i
$323$	−413.874			−0.0712958
$324$	10924.4	+	6210.43i	1.87318	+	1.06489i
$325$		0			0
$326$	2233.68	+	3868.85i	0.379485	+	0.657287i
$327$	5398.23	−	2246.57i	0.912914	−	0.379925i
$328$	640.496	−	1109.37i	0.107822	−	0.186752i
$329$	258.967	−	448.544i	0.0433961	−	0.0751643i
$330$		0			0
$331$	3916.56	+	6783.67i	0.650373	+	1.12648i	0.983032	+	0.183432i	$0.0587207\pi$
$331$	3916.56	+	6783.67i	0.650373	+	1.12648i	−0.332660	+	0.943047i	$0.607946\pi$
$332$	−22445.9			−3.71048
$333$	5584.68	−	5622.04i	0.919034	−	0.925183i
$334$	−2028.89			−0.332383
$335$		0			0
$336$	343.232	−	2641.12i	0.0557286	−	0.428824i
$337$	4964.04	−	8597.97i	0.802399	−	1.38980i	−0.115633	−	0.993292i	$-0.536890\pi$
$337$	4964.04	−	8597.97i	0.802399	−	1.38980i	0.918033	−	0.396505i	$-0.129777\pi$
$338$	13331.0	−	23090.0i	2.14530	−	3.71578i
$339$	−235.766	+	1814.19i	−0.0377730	+	0.290658i
$340$		0			0
$341$	7033.49			1.11696
$342$	−3519.81	−	930.563i	−0.556519	−	0.147132i
$343$	3536.14			0.556658
$344$	1403.89	+	2431.62i	0.220037	+	0.381116i
$345$		0			0
$346$	592.952	−	1027.02i	0.0921310	−	0.159576i
$347$	2020.17	−	3499.03i	0.312531	−	0.541320i	−0.666379	−	0.745614i	$-0.732157\pi$
$347$	2020.17	−	3499.03i	0.312531	−	0.541320i	0.978910	+	0.204294i	$0.0654898\pi$
$348$	4071.43	−	1694.40i	0.627160	−	0.261004i
$349$	−2399.86	−	4156.68i	−0.368085	−	0.637541i	0.621181	−	0.783667i	$-0.286653\pi$
$349$	−2399.86	−	4156.68i	−0.368085	−	0.637541i	−0.989266	+	0.146125i	$0.953320\pi$
$350$		0			0
$351$	7446.67	+	9604.85i	1.13240	+	1.46060i
$352$	4190.88			0.634588
$353$	1594.74	+	2762.17i	0.240451	+	0.416474i	0.960843	−	0.277094i	$-0.0893712\pi$
$353$	1594.74	+	2762.17i	0.240451	+	0.416474i	−0.720391	+	0.693568i	$0.756038\pi$
$354$	1852.01	−	770.748i	0.278060	−	0.115720i
$355$		0			0
$356$	8580.43	−	14861.7i	1.27742	−	2.21256i
$357$	342.540	+	261.934i	0.0507819	+	0.0388320i
$358$	6039.27	+	10460.3i	0.891579	+	1.54426i
$359$	−1159.83			−0.170511			−0.0852554	−	0.996359i	$-0.527171\pi$
$359$	−1159.83			−0.170511			−0.0852554	+	0.996359i	$0.527171\pi$
$360$		0			0
$361$	−6138.55			−0.894963
$362$	−3060.48	−	5300.91i	−0.444352	−	0.769640i
$363$	−132.555	+	1019.99i	−0.0191662	+	0.147481i
$364$	4018.31	−	6959.92i	0.578618	−	1.00220i
$365$		0			0
$366$	1648.72	−	12686.6i	0.235464	−	1.81186i
$367$	5937.58	+	10284.2i	0.844520	+	1.46275i	0.886037	+	0.463614i	$0.153448\pi$
$367$	5937.58	+	10284.2i	0.844520	+	1.46275i	−0.0415170	+	0.999138i	$0.513219\pi$
$368$	−10584.4			−1.49932
$369$	195.293	+	719.244i	0.0275516	+	0.101470i
$370$		0			0
$371$	675.985	+	1170.84i	0.0945968	+	0.163846i
$372$	12798.4	+	9786.72i	1.78378	+	1.36403i
$373$	−1321.63	+	2289.13i	−0.183462	+	0.317766i	−0.943057	−	0.332631i	$-0.892064\pi$
$373$	−1321.63	+	2289.13i	−0.183462	+	0.317766i	0.759595	+	0.650396i	$0.225397\pi$
$374$	−1514.46	+	2623.12i	−0.209387	+	0.362669i
$375$		0			0
$376$	2233.01	+	3867.69i	0.306273	+	0.530480i
$377$	4265.06			0.582657
$378$	2324.21	+	2997.80i	0.316255	+	0.407911i
$379$	10452.7			1.41667			0.708335	−	0.705876i	$-0.249447\pi$
$379$	10452.7			1.41667			0.708335	+	0.705876i	$0.249447\pi$
$380$		0			0
$381$	−7205.94	+	2998.88i	−0.968954	+	0.403248i
$382$	441.943	−	765.468i	0.0591932	−	0.102526i
$383$	−5439.92	+	9422.23i	−0.725763	+	1.25706i	0.232896	+	0.972502i	$0.425180\pi$
$383$	−5439.92	+	9422.23i	−0.725763	+	1.25706i	−0.958659	+	0.284557i	$0.908154\pi$
$384$	−8172.71	−	6249.52i	−1.08610	−	0.830520i
$385$		0			0
$386$	−11128.8			−1.46747
$387$	−1579.32	−	417.539i	−0.207445	−	0.0548442i
$388$	−14046.1			−1.83784
$389$	−838.831	−	1452.90i	−0.109333	−	0.189370i	0.806167	−	0.591687i	$-0.201538\pi$
$389$	−838.831	−	1452.90i	−0.109333	−	0.189370i	−0.915500	+	0.402318i	$0.868205\pi$
$390$		0			0
$391$	856.841	−	1484.09i	0.110824	−	0.191953i
$392$	−7286.76	+	12621.0i	−0.938870	+	1.62617i
$393$	1054.50	−	8114.21i	0.135350	−	1.04150i
$394$	−2647.69	−	4585.93i	−0.338550	−	0.586385i
$395$		0			0
$396$	−12825.4	+	12911.2i	−1.62753	+	1.63842i
$397$	−13147.5			−1.66210			−0.831049	−	0.556199i	$-0.812259\pi$
$397$	−13147.5			−1.66210			−0.831049	+	0.556199i	$0.812259\pi$
$398$	−8751.41	−	15157.9i	−1.10218	−	1.90904i
$399$	−596.274	−	455.960i	−0.0748146	−	0.0572094i
$400$		0			0
$401$	3260.95	−	5648.14i	0.406095	−	0.703378i	−0.588353	−	0.808604i	$-0.700223\pi$
$401$	3260.95	−	5648.14i	0.406095	−	0.703378i	0.994448	+	0.105226i	$0.0335568\pi$
$402$	5753.23	−	2394.31i	0.713794	−	0.297058i
$403$	7791.09	+	13494.6i	0.963032	+	1.66802i
$404$	−11249.4			−1.38534
$405$		0			0
$406$	1331.18			0.162723
$407$	5738.10	+	9938.69i	0.698838	+	1.21042i
$408$	−3432.82	+	1428.63i	−0.416543	+	0.173352i
$409$	−2821.34	+	4886.70i	−0.341091	+	0.590786i	−0.984636	−	0.174622i	$-0.944130\pi$
$409$	−2821.34	+	4886.70i	−0.341091	+	0.590786i	0.643545	+	0.765408i	$0.277463\pi$
$410$		0			0
$411$	−3683.10	−	2816.40i	−0.442029	−	0.338011i
$412$	−1326.91	−	2298.28i	−0.158671	−	0.274826i
$413$	413.584			0.0492764
$414$	10623.9	−	10695.0i	1.26120	−	1.26964i
$415$		0			0
$416$	4642.30	+	8040.69i	0.547133	+	0.947662i
$417$	−437.082	+	3363.28i	−0.0513285	+	0.394965i
$418$	2636.29	−	4566.18i	0.308481	−	0.534304i
$419$	4810.87	−	8332.66i	0.560922	−	0.971545i	−0.436495	−	0.899707i	$-0.643780\pi$
$419$	4810.87	−	8332.66i	0.560922	−	0.971545i	0.997416	−	0.0718380i	$-0.0228865\pi$
$420$		0			0
$421$	−5015.14	−	8686.47i	−0.580577	−	1.00559i	−0.995411	−	0.0956916i	$-0.969494\pi$
$421$	−5015.14	−	8686.47i	−0.580577	−	1.00559i	0.414834	−	0.909897i	$-0.363840\pi$
$422$	21084.0			2.43212
$423$	−2512.04	−	664.130i	−0.288746	−	0.0763383i
$424$	−11657.7			−1.33525
$425$		0			0
$426$	−13280.4	−	10155.3i	−1.51042	−	1.15499i
$427$	1318.83	−	2284.28i	0.149467	−	0.258885i
$428$	−3006.92	+	5208.14i	−0.339591	+	0.588189i
$429$	−16249.7	+	6762.62i	−1.82878	+	0.761078i
$430$		0			0
$431$	3867.23			0.432200			0.216100	−	0.976371i	$-0.430666\pi$
$431$	3867.23			0.432200			0.216100	+	0.976371i	$0.430666\pi$
$432$	−13238.0	+	1810.22i	−1.47434	+	0.201607i
$433$	2345.27			0.260292			0.130146	−	0.991495i	$-0.458455\pi$
$433$	2345.27			0.260292			0.130146	+	0.991495i	$0.458455\pi$
$434$	2431.70	+	4211.83i	0.268953	+	0.465840i
$435$		0			0
$436$	−9698.47	+	16798.2i	−1.06530	+	1.84516i
$437$	−1491.54	+	2583.42i	−0.163273	+	0.282796i
$438$	15951.4	+	12197.8i	1.74016	+	1.33067i
$439$	7058.94	+	12226.4i	0.767437	+	1.32924i	0.938949	+	0.344057i	$0.111801\pi$
$439$	7058.94	+	12226.4i	0.767437	+	1.32924i	−0.171512	+	0.985182i	$0.554865\pi$
$440$		0			0
$441$	−2221.80	−	8182.65i	−0.239909	−	0.883560i
$442$	−6710.34			−0.722123
$443$	8898.31	+	15412.3i	0.954337	+	1.65296i	0.735877	+	0.677115i	$0.236770\pi$
$443$	8898.31	+	15412.3i	0.954337	+	1.65296i	0.218460	+	0.975846i	$0.429897\pi$
$444$	−3387.86	+	26069.1i	−0.362119	+	2.78645i
$445$		0			0
$446$	7622.37	−	13202.3i	0.809259	−	1.40168i
$447$	−2302.14	+	17714.7i	−0.243596	+	1.87444i
$448$	−601.307	−	1041.49i	−0.0634131	−	0.109835i
$449$	−11518.0			−1.21062			−0.605310	−	0.795990i	$-0.706951\pi$
$449$	−11518.0			−1.21062			−0.605310	+	0.795990i	$0.706951\pi$
$450$		0			0
$451$	−1079.33			−0.112691
$452$	−3034.49	−	5255.88i	−0.315775	−	0.546938i
$453$	−6896.97	−	5273.99i	−0.715338	−	0.547006i
$454$	−8128.77	+	14079.4i	−0.840313	+	1.45547i
$455$		0			0
$456$	5975.65	−	2486.87i	0.613674	−	0.255392i
$457$	4928.86	+	8537.03i	0.504512	+	0.873841i	0.999986	+	0.00521822i	$0.00166102\pi$
$457$	4928.86	+	8537.03i	0.504512	+	0.873841i	−0.495474	+	0.868623i	$0.665006\pi$
$458$	14943.3			1.52458
$459$	817.845	−	2002.72i	0.0831672	−	0.203658i
$460$		0			0
$461$	8040.79	+	13927.1i	0.812358	+	1.40704i	0.911210	+	0.411943i	$0.135150\pi$
$461$	8040.79	+	13927.1i	0.812358	+	1.40704i	−0.0988520	+	0.995102i	$0.531517\pi$
$462$	−5071.77	+	2110.71i	−0.510736	+	0.212552i
$463$	9447.88	−	16364.2i	0.948338	−	1.64257i	0.199411	−	0.979916i	$-0.436097\pi$
$463$	9447.88	−	16364.2i	0.948338	−	1.64257i	0.748927	−	0.662653i	$-0.230569\pi$
$464$	−2344.46	+	4060.72i	−0.234566	+	0.406281i
$465$		0			0
$466$	7353.25	+	12736.2i	0.730972	+	1.26608i
$467$	−10368.7			−1.02742			−0.513712	−	0.857963i	$-0.671730\pi$
$467$	−10368.7			−1.02742			−0.513712	+	0.857963i	$0.671730\pi$
$468$	−38978.5	−	10305.1i	−3.84996	−	1.01785i
$469$	1284.79			0.126495
$470$		0			0
$471$	446.054	−	3432.32i	0.0436371	−	0.335781i
$472$	−1783.12	+	3088.45i	−0.173887	+	0.301181i
$473$	1182.89	−	2048.82i	0.114988	−	0.199165i
$474$	2228.22	−	17145.8i	0.215919	−	1.66146i
$475$		0			0
$476$	−1430.50			−0.137745
$477$	4779.93	−	4811.91i	0.458822	−	0.461892i
$478$	−14461.7			−1.38382
$479$	4777.01	+	8274.02i	0.455672	+	0.789248i	0.998727	−	0.0504500i	$-0.0160655\pi$
$479$	4777.01	+	8274.02i	0.455672	+	0.789248i	−0.543054	+	0.839698i	$0.682732\pi$
$480$		0			0
$481$	−12712.3	+	22018.4i	−1.20506	+	2.08722i
$482$	−2807.21	+	4862.23i	−0.265280	+	0.459478i
$483$	2869.47	−	1194.18i	0.270322	−	0.112499i
$484$	−1706.08	−	2955.02i	−0.160226	−	0.277519i
$485$		0			0
$486$	11458.4	−	15193.4i	1.06947	−	1.41808i
$487$	17514.2			1.62966			0.814831	−	0.579699i	$-0.196830\pi$
$487$	17514.2			1.62966			0.814831	+	0.579699i	$0.196830\pi$
$488$	11371.9	+	19696.8i	1.05488	+	1.82711i
$489$	4266.02	−	1775.38i	0.394511	−	0.164183i
$490$		0			0
$491$	1933.27	−	3348.52i	0.177693	−	0.307773i	−0.763397	−	0.645929i	$-0.776470\pi$
$491$	1933.27	−	3348.52i	0.177693	−	0.307773i	0.941090	+	0.338157i	$0.109803\pi$
$492$	−1964.00	−	1501.83i	−0.179967	−	0.137618i
$493$	−379.584	−	657.459i	−0.0346767	−	0.0600618i
$494$	11681.0			1.06387
$495$		0			0
$496$	−17130.7			−1.55079
$497$	−1723.43	−	2985.08i	−0.155546	−	0.269414i
$498$	−4380.54	+	33707.6i	−0.394170	+	3.03308i
$499$	−2427.98	+	4205.39i	−0.217818	+	0.377272i	−0.954141	−	0.299358i	$-0.903227\pi$
$499$	−2427.98	+	4205.39i	−0.217818	+	0.377272i	0.736322	+	0.676631i	$0.236561\pi$
$500$		0			0
$501$	−270.445	+	2081.03i	−0.0241169	+	0.185576i
$502$	−11584.7	−	20065.2i	−1.02998	−	1.78398i
$503$	−5481.79			−0.485927			−0.242963	−	0.970035i	$-0.578119\pi$
$503$	−5481.79			−0.485927			−0.242963	+	0.970035i	$0.578119\pi$
$504$	−6519.61	−	1723.65i	−0.576203	−	0.152336i
$505$		0			0
$506$	10915.8	+	18906.7i	0.959023	+	1.66108i
$507$	−21906.5	−	16751.5i	−1.91894	−	1.46738i
$508$	12946.2	−	22423.5i	1.13070	−	1.95843i
$509$	10213.5	−	17690.4i	0.889405	−	1.54049i	0.0488251	−	0.998807i	$-0.484452\pi$
$509$	10213.5	−	17690.4i	0.889405	−	1.54049i	0.840580	−	0.541687i	$-0.182214\pi$
$510$		0			0
$511$	2070.06	+	3585.45i	0.179206	+	0.310393i
$512$	25150.0			2.17086
$513$	−1423.66	+	3486.23i	−0.122526	+	0.300040i
$514$	−19028.4			−1.63289
$515$		0			0
$516$	5003.25	−	2082.19i	0.426852	−	0.177642i
$517$	1881.48	−	3258.82i	0.160053	−	0.277220i
$518$	−3967.69	+	6872.25i	−0.336545	+	0.582914i
$519$	−974.380	−	745.091i	−0.0824095	−	0.0630170i
$520$		0			0
$521$	−5768.55			−0.485076			−0.242538	−	0.970142i	$-0.577980\pi$
$521$	−5768.55			−0.485076			−0.242538	+	0.970142i	$0.577980\pi$
$522$	−1749.94	−	6444.86i	−0.146730	−	0.540390i
$523$	−1753.72			−0.146625			−0.0733126	−	0.997309i	$-0.523357\pi$
$523$	−1753.72			−0.146625			−0.0733126	+	0.997309i	$0.523357\pi$
$524$	13572.2	+	23507.7i	1.13149	+	1.95981i
$525$		0			0
$526$	12533.1	−	21707.9i	1.03891	−	1.79945i
$527$	1386.79	−	2401.99i	0.114629	−	0.198544i
$528$	2493.69	−	19188.6i	0.205538	−	1.58158i
$529$	−92.3641	−	159.979i	−0.00759136	−	0.0131486i
$530$		0			0
$531$	−543.689	−	2002.35i	−0.0444333	−	0.163643i
$532$	2490.13			0.202934
$533$	−1195.59	−	2070.82i	−0.0971610	−	0.168288i
$534$	−20643.7	−	15785.9i	−1.67293	−	1.27926i
$535$		0			0
$536$	−5539.21	+	9594.19i	−0.446376	+	0.773145i
$537$	11534.2	−	4800.15i	0.926883	−	0.385739i
$538$	−14683.2	−	25432.1i	−1.17665	−	2.03802i
$539$	12279.3			0.981274
$540$		0			0
$541$	7146.18			0.567908			0.283954	−	0.958838i	$-0.408354\pi$
$541$	7146.18			0.567908			0.283954	+	0.958838i	$0.408354\pi$
$542$	6948.03	+	12034.3i	0.550633	+	0.953725i
$543$	−5845.10	+	2432.54i	−0.461947	+	0.192247i
$544$	826.315	−	1431.22i	0.0651250	−	0.112800i
$545$		0			0
$546$	−9667.69	−	7392.71i	−0.757764	−	0.579448i
$547$	−3703.95	−	6415.42i	−0.289523	−	0.501469i	0.684173	−	0.729320i	$-0.260163\pi$
$547$	−3703.95	−	6415.42i	−0.289523	−	0.501469i	−0.973696	+	0.227851i	$0.926830\pi$
$548$	15381.1			1.19900
$549$	−12792.9	−	3382.18i	−0.994514	−	0.262929i
$550$		0			0
$551$	660.759	+	1144.47i	0.0510876	+	0.0884863i
$552$	−3453.79	+	26576.4i	−0.266310	+	2.04922i
$553$	1782.38	−	3087.17i	0.137061	−	0.237396i
$554$	−4756.95	+	8239.29i	−0.364808	+	0.631866i
$555$		0			0
$556$	−5625.57	−	9743.77i	−0.429096	−	0.743216i
$557$	−11116.3			−0.845626			−0.422813	−	0.906217i	$-0.638957\pi$
$557$	−11116.3			−0.845626			−0.422813	+	0.906217i	$0.638957\pi$
$558$	17194.7	−	17309.8i	1.30450	−	1.31323i
$559$	5241.20			0.396564
$560$		0			0
$561$	2488.66	+	1903.04i	0.187293	+	0.143220i
$562$	11264.1	−	19510.0i	0.845458	−	1.46438i
$563$	5603.29	−	9705.19i	0.419450	−	0.726509i	−0.576434	−	0.817144i	$-0.695556\pi$
$563$	5603.29	−	9705.19i	0.419450	−	0.726509i	0.995884	+	0.0906344i	$0.0288895\pi$
$564$	7958.09	−	3311.90i	0.594142	−	0.247263i
$565$		0			0
$566$	29125.7			2.16298
$567$	3384.66	−	1984.34i	0.250692	−	0.146974i
$568$	29721.5			2.19557
$569$	−7936.88	−	13747.1i	−0.584765	−	1.01284i	−0.994905	−	0.100820i	$-0.967853\pi$
$569$	−7936.88	−	13747.1i	−0.584765	−	1.01284i	0.410140	−	0.912023i	$-0.365480\pi$
$570$		0			0
$571$	1194.23	−	2068.46i	0.0875250	−	0.151598i	−0.818939	−	0.573880i	$-0.805438\pi$
$571$	1194.23	−	2068.46i	0.0875250	−	0.151598i	0.906464	+	0.422282i	$0.138771\pi$
$572$	29194.3	−	50566.1i	2.13405	−	3.69628i
$573$	−726.231	−	555.336i	−0.0529472	−	0.0404878i
$574$	−373.160	−	646.332i	−0.0271348	−	0.0469989i
$575$		0			0
$576$	−4251.88	+	4280.32i	−0.307572	+	0.309630i
$577$	−10429.0			−0.752455			−0.376227	−	0.926527i	$-0.622779\pi$
$577$	−10429.0			−0.752455			−0.376227	+	0.926527i	$0.622779\pi$
$578$	−11743.5	−	20340.4i	−0.845098	−	1.46375i
$579$	−1483.44	+	11414.8i	−0.106476	+	0.819317i
$580$		0			0
$581$	−3504.05	+	6069.19i	−0.250211	+	0.433377i
$582$	−2741.23	+	21093.3i	−0.195236	+	1.50231i
$583$	4911.25	+	8506.54i	0.348891	+	0.604296i
$584$	−35699.2			−2.52953
$585$		0			0
$586$	−39738.9			−2.80136
$587$	1574.02	+	2726.29i	0.110676	+	0.191697i	0.916043	−	0.401080i	$-0.131365\pi$
$587$	1574.02	+	2726.29i	0.110676	+	0.191697i	−0.805367	+	0.592777i	$0.798032\pi$
$588$	22343.9	+	17086.0i	1.56709	+	1.19832i
$589$	−2414.05	+	4181.25i	−0.168878	+	0.292505i
$590$		0			0
$591$	−5056.72	+	2104.44i	−0.351955	+	0.146473i
$592$	−13975.7	−	24206.6i	−0.970265	−	1.68055i
$593$	−12123.4			−0.839542			−0.419771	−	0.907630i	$-0.637890\pi$
$593$	−12123.4			−0.839542			−0.419771	+	0.907630i	$0.637890\pi$
$594$	16886.1	+	21780.0i	1.16641	+	1.50445i
$595$		0			0
$596$	−29630.3	−	51321.2i	−2.03642	−	3.52718i
$597$	−16714.0	+	6955.83i	−1.14583	+	0.476856i
$598$	−24183.1	+	41886.4i	−1.65371	+	2.86432i
$599$	7921.39	−	13720.3i	0.540333	−	0.935884i	−0.458552	−	0.888668i	$-0.651632\pi$
$599$	7921.39	−	13720.3i	0.540333	−	0.935884i	0.998885	−	0.0472161i	$-0.0150349\pi$
$600$		0			0
$601$	12845.1	+	22248.3i	0.871815	+	1.51003i	0.860118	+	0.510096i	$0.170390\pi$
$601$	12845.1	+	22248.3i	0.871815	+	1.51003i	0.0116971	+	0.999932i	$0.496277\pi$
$602$	1635.85			0.110751
$603$	−1688.96	−	6220.24i	−0.114062	−	0.420079i
$604$	28802.8			1.94034
$605$		0			0
$606$	−2195.43	+	16893.5i	−0.147167	+	1.13243i
$607$	7261.64	−	12577.5i	0.485570	−	0.841031i	−0.514293	−	0.857615i	$-0.671946\pi$
$607$	7261.64	−	12577.5i	0.485570	−	0.841031i	0.999862	+	0.0165834i	$0.00527892\pi$
$608$	−1438.40	+	2491.39i	−0.0959456	+	0.166183i
$609$	177.443	−	1365.39i	0.0118068	−	0.0908516i
$610$		0			0
$611$	8336.56			0.551982
$612$	1880.50	+	6925.68i	0.124207	+	0.457441i
$613$	−26426.7			−1.74121			−0.870606	−	0.491981i	$-0.836273\pi$
$613$	−26426.7			−1.74121			−0.870606	+	0.491981i	$0.836273\pi$
$614$	−11118.4	−	19257.6i	−0.730785	−	1.26576i
$615$		0			0
$616$	4883.09	−	8457.77i	0.319392	−	0.553203i
$617$	−1878.89	+	3254.33i	−0.122595	+	0.212341i	−0.920790	−	0.390058i	$-0.872455\pi$
$617$	−1878.89	+	3254.33i	−0.122595	+	0.212341i	0.798195	+	0.602399i	$0.205788\pi$
$618$	−3710.36	+	1544.13i	−0.241509	+	0.100508i
$619$	11740.3	+	20334.7i	0.762327	+	1.32039i	0.941648	+	0.336599i	$0.109277\pi$
$619$	11740.3	+	20334.7i	0.762327	+	1.32039i	−0.179321	+	0.983791i	$0.557390\pi$
$620$		0			0
$621$	−9553.72	−	12322.6i	−0.617355	−	0.796276i
$622$	−48716.1			−3.14042
$623$	−2679.00	−	4640.16i	−0.172282	−	0.298401i
$624$	39577.8	−	16471.0i	2.53907	−	1.05668i
$625$		0			0
$626$	−11361.4	+	19678.5i	−0.725385	+	1.25640i
$627$	−4332.12	−	3312.70i	−0.275930	−	0.210999i
$628$	5741.05	+	9943.79i	0.364797	+	0.631848i
$629$	4525.52			0.286875
$630$		0			0
$631$	8654.12			0.545983			0.272991	−	0.962016i	$-0.411987\pi$
$631$	8654.12			0.545983			0.272991	+	0.962016i	$0.411987\pi$
$632$	15369.0	+	26619.9i	0.967320	+	1.67545i
$633$	2810.43	−	21625.9i	0.176469	−	1.35790i
$634$	13368.6	−	23155.1i	0.837438	−	1.45049i
$635$		0			0
$636$	−2899.67	+	22312.6i	−0.180785	+	1.39112i
$637$	13601.9	+	23559.2i	0.846041	+	1.46539i
$638$	9671.48			0.600153
$639$	−12186.5	+	12268.0i	−0.754446	+	0.759493i
$640$		0			0
$641$	−9588.81	−	16608.3i	−0.590850	−	1.02338i	−0.994118	−	0.108301i	$-0.965459\pi$
$641$	−9588.81	−	16608.3i	−0.590850	−	1.02338i	0.403268	−	0.915082i	$-0.367874\pi$
$642$	7234.38	+	5532.00i	0.444732	+	0.340079i
$643$	−4917.78	+	8517.85i	−0.301615	+	0.522413i	−0.976502	−	0.215509i	$-0.930859\pi$
$643$	−4917.78	+	8517.85i	−0.301615	+	0.522413i	0.674887	+	0.737921i	$0.264192\pi$
$644$	−5155.30	+	8929.24i	−0.315446	+	0.546369i
$645$		0			0
$646$	−1039.59	−	1800.62i	−0.0633160	−	0.109667i
$647$	7621.18			0.463090			0.231545	−	0.972824i	$-0.425622\pi$
$647$	7621.18			0.463090			0.231545	+	0.972824i	$0.425622\pi$
$648$	225.584	+	33830.2i	0.0136756	+	2.05089i
$649$	3004.82			0.181741
$650$		0			0
$651$	4644.22	−	1932.77i	0.279603	−	0.116362i
$652$	−7664.34	+	13275.0i	−0.460366	+	0.797378i
$653$	2198.16	−	3807.33i	0.131731	−	0.228166i	−0.792613	−	0.609726i	$-0.791280\pi$
$653$	2198.16	−	3807.33i	0.131731	−	0.228166i	0.924344	+	0.381560i	$0.124613\pi$
$654$	23333.6	+	17842.8i	1.39513	+	1.06683i
$655$		0			0
$656$	2628.82			0.156460
$657$	14637.5	−	14735.4i	0.869199	−	0.875015i
$658$	2601.95			0.154156
$659$	−5410.13	−	9370.61i	−0.319801	−	0.553911i	0.660646	−	0.750698i	$-0.270283\pi$
$659$	−5410.13	−	9370.61i	−0.319801	−	0.553911i	−0.980446	+	0.196787i	$0.936949\pi$
$660$		0			0
$661$	14457.8	−	25041.6i	0.850744	−	1.47353i	−0.0297946	−	0.999556i	$-0.509485\pi$
$661$	14457.8	−	25041.6i	0.850744	−	1.47353i	0.880538	−	0.473975i	$-0.157181\pi$
$662$	−19675.6	+	34079.2i	−1.15516	+	2.00080i
$663$	−894.468	+	6882.80i	−0.0523956	+	0.403176i
$664$	−30214.5	−	52333.1i	−1.76589	−	3.05861i
$665$		0			0
$666$	38487.5	+	10175.3i	2.23928	+	0.592018i
$667$	−5471.87			−0.317649
$668$	−3480.82	−	6028.96i	−0.201612	−	0.349203i
$669$	−12525.6	−	9578.10i	−0.723868	−	0.553529i
$670$		0			0
$671$	9581.71	−	16596.0i	0.551264	−	0.954817i
$672$	2767.24	−	1151.64i	0.158852	−	0.0661092i
$673$	−2530.58	−	4383.09i	−0.144943	−	0.251049i	0.784409	−	0.620244i	$-0.212967\pi$
$673$	−2530.58	−	4383.09i	−0.144943	−	0.251049i	−0.929352	+	0.369196i	$0.879633\pi$
$674$	49875.8			2.85036
$675$		0			0
$676$	91484.6			5.20509
$677$	−6029.63	−	10443.6i	−0.342300	−	0.592882i	0.642559	−	0.766236i	$-0.277873\pi$
$677$	−6029.63	−	10443.6i	−0.342300	−	0.592882i	−0.984860	+	0.173354i	$0.944539\pi$
$678$	−8485.12	+	3531.23i	−0.480633	+	0.200024i
$679$	−2192.74	+	3797.94i	−0.123932	+	0.214656i
$680$		0			0
$681$	13357.8	+	10214.4i	0.751645	+	0.574769i
$682$	17667.1	+	30600.3i	0.991948	+	1.71810i
$683$	−6110.33			−0.342321			−0.171160	−	0.985243i	$-0.554752\pi$
$683$	−6110.33			−0.342321			−0.171160	+	0.985243i	$0.554752\pi$
$684$	−3273.47	−	12055.8i	−0.182989	−	0.673927i
$685$		0			0
$686$	8882.27	+	15384.6i	0.494354	+	0.856246i
$687$	1991.90	−	15327.4i	0.110620	−	0.851202i
$688$	−2881.03	+	4990.09i	−0.159649	+	0.276520i
$689$	−10880.5	+	18845.6i	−0.601617	+	1.04203i
$690$		0			0
$691$	−13604.9	−	23564.3i	−0.748991	−	1.29729i	−0.948307	−	0.317356i	$-0.897205\pi$
$691$	−13604.9	−	23564.3i	−0.748991	−	1.29729i	0.199315	−	0.979935i	$-0.436128\pi$
$692$	4069.15			0.223535
$693$	1488.90	+	5483.46i	0.0816143	+	0.300576i
$694$	20297.5			1.11020
$695$		0			0
$696$	9431.09	+	7211.79i	0.513627	+	0.392762i
$697$	−212.812	+	368.601i	−0.0115650	+	0.0200312i
$698$	12056.2	−	20882.0i	0.653774	−	1.13237i
$699$	14043.7	−	5844.54i	0.759916	−	0.316253i
$700$		0			0
$701$	−30424.7			−1.63927			−0.819633	−	0.572888i	$-0.805823\pi$
$701$	−30424.7			−1.63927			−0.819633	+	0.572888i	$0.805823\pi$
$702$	−23082.5	+	56524.0i	−1.24102	+	3.03897i
$703$	−7877.77			−0.422640
$704$	−4368.69	−	7566.79i	−0.233879	−	0.405091i
$705$		0			0
$706$	−8011.51	+	13876.3i	−0.427078	+	0.739721i
$707$	−1756.15	+	3041.74i	−0.0934183	+	0.161805i
$708$	5467.69	+	4181.05i	0.290238	+	0.221940i
$709$	−923.205	−	1599.04i	−0.0489022	−	0.0847012i	0.840538	−	0.541752i	$-0.182239\pi$
$709$	−923.205	−	1599.04i	−0.0489022	−	0.0847012i	−0.889440	+	0.457051i	$0.848906\pi$
$710$		0			0
$711$	−17289.5	−	4570.97i	−0.911963	−	0.241104i
$712$	46200.6			2.43180
$713$	−9995.59	−	17312.9i	−0.525018	−	0.909358i
$714$	−279.176	+	2148.22i	−0.0146329	+	0.112598i
$715$		0			0
$716$	−20722.3	+	35892.1i	−1.08161	+	1.87340i
$717$	−1927.70	+	14833.4i	−0.100406	+	0.772613i
$718$	−2913.32	−	5046.02i	−0.151426	−	0.262278i
$719$	13301.3			0.689923			0.344961	−	0.938617i	$-0.387892\pi$
$719$	13301.3			0.689923			0.344961	+	0.938617i	$0.387892\pi$
$720$		0			0
$721$	−828.583			−0.0427989
$722$	−15419.2	−	26706.8i	−0.794794	−	1.37662i
$723$	4613.00	+	3527.47i	0.237288	+	0.181450i
$724$	10501.3	−	18188.8i	0.539058	−	0.933676i
$725$		0			0
$726$	−4770.60	+	1985.37i	−0.243875	+	0.101493i
$727$	−12957.6	−	22443.2i	−0.661031	−	1.14494i	−0.980345	−	0.197290i	$-0.936786\pi$
$727$	−12957.6	−	22443.2i	−0.661031	−	1.14494i	0.319314	−	0.947649i	$-0.396548\pi$
$728$	21636.3			1.10150
$729$	−14056.5	−	13778.1i	−0.714144	−	0.699999i
$730$		0			0
$731$	−466.459	−	807.931i	−0.0236014	−	0.0408788i
$732$	40527.7	−	16866.3i	2.04638	−	0.851636i
$733$	11123.9	−	19267.1i	0.560532	−	0.970871i	−0.436918	−	0.899502i	$-0.643930\pi$
$733$	11123.9	−	19267.1i	0.560532	−	0.970871i	0.997450	−	0.0713691i	$-0.0227368\pi$
$734$	−29828.7	+	51664.8i	−1.49999	+	2.59807i
$735$		0			0
$736$	−5955.84	−	10315.8i	−0.298282	−	0.516639i
$737$	9334.41			0.466536
$738$	−2638.64	+	2656.29i	−0.131612	+	0.132492i
$739$	−23675.6			−1.17851			−0.589256	−	0.807947i	$-0.700579\pi$
$739$	−23675.6			−1.17851			−0.589256	+	0.807947i	$0.700579\pi$
$740$		0			0
$741$	1557.04	−	11981.2i	0.0771920	−	0.593981i
$742$	−3395.95	+	5881.96i	−0.168018	+	0.291016i
$743$	−16777.6	+	29059.6i	−0.828411	+	1.43485i	0.0708729	+	0.997485i	$0.477422\pi$
$743$	−16777.6	+	29059.6i	−0.828411	+	1.43485i	−0.899284	+	0.437365i	$0.855912\pi$
$744$	−5589.93	+	43013.7i	−0.275453	+	2.11957i
$745$		0			0
$746$	−13279.0			−0.651713
$747$	33990.0	+	8986.24i	1.66483	+	0.440147i
$748$	−10393.0			−0.508030
$749$	938.826	+	1626.09i	0.0457997	+	0.0793274i
$750$		0			0
$751$	−10944.9	+	18957.1i	−0.531804	+	0.921111i	0.467507	+	0.883989i	$0.345152\pi$
$751$	−10944.9	+	18957.1i	−0.531804	+	0.921111i	−0.999311	+	0.0371219i	$0.988181\pi$
$752$	−4582.52	+	7937.16i	−0.222217	+	0.384891i
$753$	−22125.1	+	9207.77i	−1.07076	+	0.445617i
$754$	10713.2	+	18555.8i	0.517444	+	0.896238i
$755$		0			0
$756$	−4920.67	+	12049.6i	−0.236724	+	0.579684i
$757$	−24362.3			−1.16970			−0.584851	−	0.811141i	$-0.698847\pi$
$757$	−24362.3			−1.16970			−0.584851	+	0.811141i	$0.698847\pi$
$758$	26255.6	+	45476.1i	1.25811	+	2.17911i
$759$	20847.6	−	8676.12i	0.996998	−	0.414919i
$760$		0			0
$761$	13842.7	−	23976.2i	0.659391	−	1.14210i	−0.321383	−	0.946949i	$-0.604148\pi$
$761$	13842.7	−	23976.2i	0.659391	−	1.14210i	0.980774	−	0.195149i	$-0.0625189\pi$
$762$	−31147.4	−	23817.9i	−1.48078	−	1.13232i
$763$	3028.07	+	5244.77i	0.143674	+	0.248851i
$764$	3032.85			0.143619
$765$		0			0
$766$	−54657.2			−2.57813
$767$	3328.48	+	5765.10i	0.156694	+	0.271402i
$768$	5463.82	−	42043.3i	0.256717	−	1.97540i
$769$	3498.05	−	6058.81i	0.164035	−	0.284117i	−0.772277	−	0.635286i	$-0.780882\pi$
$769$	3498.05	−	6058.81i	0.164035	−	0.284117i	0.936312	+	0.351169i	$0.114216\pi$
$770$		0			0
$771$	−2536.43	+	19517.5i	−0.118479	+	0.911679i
$772$	−19093.0	−	33070.0i	−0.890117	−	1.54173i
$773$	−19650.7			−0.914342			−0.457171	−	0.889379i	$-0.651137\pi$
$773$	−19650.7			−0.914342			−0.457171	+	0.889379i	$0.651137\pi$
$774$	−2150.45	−	7919.88i	−0.0998661	−	0.367796i
$775$		0			0
$776$	−18907.4	−	32748.7i	−0.874662	−	1.51496i
$777$	6519.98	+	4985.71i	0.301034	+	0.230195i
$778$	4214.04	−	7298.94i	0.194191	−	0.336349i
$779$	370.451	−	641.639i	0.0170382	−	0.0295111i
$780$		0			0
$781$	−12521.3	−	21687.5i	−0.573684	−	0.993651i
$782$	8609.05			0.393681
$783$	−6843.75	+	935.840i	−0.312357	+	0.0427129i
$784$	−29907.4			−1.36240
$785$		0			0
$786$	37950.9	−	15794.0i	1.72222	−	0.716732i
$787$	656.480	−	1137.06i	0.0297344	−	0.0515016i	−0.850775	−	0.525530i	$-0.823867\pi$
$787$	656.480	−	1137.06i	0.0297344	−	0.0515016i	0.880510	+	0.474028i	$0.157201\pi$
$788$	9084.91	−	15735.5i	0.410706	−	0.711364i
$789$	−20595.2	−	15748.7i	−0.929287	−	0.710609i
$790$		0			0
$791$	−1894.86			−0.0851752
$792$	−47367.1	−	12522.9i	−2.12515	−	0.561844i
$793$	42455.1			1.90117
$794$	−33024.6	−	57200.2i	−1.47607	−	2.55662i
$795$		0			0
$796$	30028.4	−	52010.7i	1.33710	−	2.31592i
$797$	1195.82	−	2071.21i	0.0531468	−	0.0920529i	−0.838228	−	0.545320i	$-0.816408\pi$
$797$	1195.82	−	2071.21i	0.0531468	−	0.0920529i	0.891375	+	0.453267i	$0.149742\pi$
$798$	485.973	−	3739.49i	0.0215580	−	0.165885i
$799$	−741.942	−	1285.08i	−0.0328511	−	0.0568997i
$800$		0			0
$801$	−18943.3	+	19070.1i	−0.835618	+	0.841209i
$802$	32764.2			1.44257
$803$	15039.7	+	26049.4i	0.660944	+	1.14479i
$804$	16985.3	+	12988.3i	0.745055	+	0.569730i
$805$		0			0
$806$	−39140.2	+	67792.8i	−1.71049	+	2.96265i
$807$	−28042.9	+	11670.6i	−1.22324	+	0.509075i
$808$	−15142.8	−	26228.2i	−0.659311	−	1.14196i
$809$	−7059.58			−0.306801			−0.153400	−	0.988164i	$-0.549022\pi$
$809$	−7059.58			−0.306801			−0.153400	+	0.988164i	$0.549022\pi$
$810$		0			0
$811$	12699.2			0.549849			0.274925	−	0.961466i	$-0.411347\pi$
$811$	12699.2			0.549849			0.274925	+	0.961466i	$0.411347\pi$
$812$	2283.82	+	3955.69i	0.0987024	+	0.170958i
$813$	13269.8	−	5522.45i	0.572437	−	0.238230i
$814$	−28826.6	+	49929.1i	−1.24124	+	2.14989i
$815$		0			0
$816$	−6061.37	−	4635.02i	−0.260037	−	0.198846i
$817$	811.986	+	1406.40i	0.0347708	+	0.0602249i
$818$	−28347.1			−1.21166
$819$	−8871.38	+	8930.73i	−0.378499	+	0.381032i
$820$		0			0
$821$	−812.003	−	1406.43i	−0.0345178	−	0.0597865i	0.848250	−	0.529595i	$-0.177656\pi$
$821$	−812.003	−	1406.43i	−0.0345178	−	0.0597865i	−0.882768	+	0.469809i	$0.844323\pi$
$822$	3001.78	−	23098.3i	0.127371	−	0.980104i
$823$	10575.8	−	18317.9i	0.447935	−	0.775846i	−0.550317	−	0.834956i	$-0.685493\pi$
$823$	10575.8	−	18317.9i	0.447935	−	0.775846i	0.998251	+	0.0591102i	$0.0188263\pi$
$824$	3572.33	−	6187.46i	0.151029	−	0.261590i
$825$		0			0
$826$	1038.86	+	1799.36i	0.0437611	+	0.0757965i
$827$	18269.2			0.768178			0.384089	−	0.923296i	$-0.374516\pi$
$827$	18269.2			0.768178			0.384089	+	0.923296i	$0.374516\pi$
$828$	50007.5	+	13220.9i	2.09889	+	0.554903i
$829$	19893.4			0.833446			0.416723	−	0.909034i	$-0.363179\pi$
$829$	19893.4			0.833446			0.416723	+	0.909034i	$0.363179\pi$
$830$		0			0
$831$	7816.95	+	5977.48i	0.326314	+	0.249526i
$832$	9678.50	−	16763.7i	0.403295	−	0.698528i
$833$	2421.11	−	4193.48i	0.100704	−	0.174424i
$834$	−15730.4	+	6546.48i	−0.653116	+	0.271806i
$835$		0			0
$836$	18091.6			0.748457
$837$	−15462.6	−	19944.0i	−0.638550	−	0.823613i
$838$	48336.8			1.99256
$839$	5852.88	+	10137.5i	0.240839	+	0.417145i	0.960954	−	0.276710i	$-0.0892441\pi$
$839$	5852.88	+	10137.5i	0.240839	+	0.417145i	−0.720115	+	0.693855i	$0.755911\pi$
$840$		0			0
$841$	10982.5	−	19022.2i	0.450304	−	0.779950i
$842$	25194.6	−	43638.3i	1.03119	−	1.78608i
$843$	−18509.9	−	14154.2i	−0.756247	−	0.578288i
$844$	36172.4	+	62652.4i	1.47524	+	2.55519i
$845$		0			0
$846$	−3420.47	−	12597.2i	−0.139005	−	0.511940i
$847$	−1065.35			−0.0432183
$848$	−11961.8	−	20718.5i	−0.484399	−	0.839003i
$849$	3882.36	−	29874.2i	0.156940	−	1.20763i
$850$		0			0
$851$	16309.3	−	28248.6i	0.656964	−	1.13790i
$852$	7392.76	−	56886.2i	0.297267	−	2.28743i
$853$	529.139	+	916.495i	0.0212396	+	0.0367880i	0.876450	−	0.481493i	$-0.159905\pi$
$853$	529.139	+	916.495i	0.0212396	+	0.0367880i	−0.855210	+	0.518281i	$0.826572\pi$
$854$	13250.8			0.530953
$855$		0			0
$856$	−16190.5			−0.646473
$857$	−12017.7	−	20815.2i	−0.479015	−	0.829678i	0.520695	−	0.853742i	$-0.325673\pi$
$857$	−12017.7	−	20815.2i	−0.479015	−	0.829678i	−0.999710	+	0.0240642i	$0.992339\pi$
$858$	−70238.9	−	53710.4i	−2.79477	−	2.13711i
$859$	17547.1	−	30392.5i	0.696973	−	1.20719i	−0.272538	−	0.962145i	$-0.587863\pi$
$859$	17547.1	−	30392.5i	0.696973	−	1.20719i	0.969511	−	0.245047i	$-0.0788035\pi$
$860$		0			0
$861$	−712.684	+	296.596i	−0.0282093	+	0.0117398i
$862$	9713.93	+	16825.0i	0.383826	+	0.664805i
$863$	41958.9			1.65504			0.827518	−	0.561439i	$-0.189752\pi$
$863$	41958.9			1.65504			0.827518	+	0.561439i	$0.189752\pi$
$864$	−9213.36	−	11883.6i	−0.362783	−	0.467924i
$865$		0			0
$866$	5890.98	+	10203.5i	0.231159	+	0.400379i
$867$	−22428.5	+	9334.04i	−0.878562	+	0.365629i
$868$	−8343.81	+	14451.9i	−0.326276	+	0.565127i
$869$	12949.6	−	22429.3i	0.505505	−	0.875560i
$870$		0			0
$871$	10339.8	+	17909.1i	0.402241	+	0.696703i
$872$	−52220.6			−2.02800
$873$	21270.1	+	5623.36i	0.824607	+	0.218009i
$874$	−14986.1			−0.579993
$875$		0			0
$876$	−8879.63	+	68327.5i	−0.342483	+	2.63535i
$877$	−9805.55	+	16983.7i	−0.377548	+	0.653933i	−0.990705	−	0.136028i	$-0.956566\pi$
$877$	−9805.55	+	16983.7i	−0.377548	+	0.653933i	0.613157	+	0.789961i	$0.289899\pi$
$878$	−35462.1	+	61422.1i	−1.36308	+	2.36093i
$879$	−5297.07	+	40760.2i	−0.203260	+	1.56406i
$880$		0			0
$881$	10465.2			0.400204			0.200102	−	0.979775i	$-0.435873\pi$
$881$	10465.2			0.400204			0.200102	+	0.979775i	$0.435873\pi$
$882$	30019.1	−	30219.9i	1.14603	−	1.15369i
$883$	−10812.2			−0.412074			−0.206037	−	0.978544i	$-0.566057\pi$
$883$	−10812.2			−0.412074			−0.206037	+	0.978544i	$0.566057\pi$
$884$	−11512.5	−	19940.2i	−0.438016	−	0.758667i
$885$		0			0
$886$	−44702.5	+	77427.1i	−1.69505	+	2.93591i
$887$	−18000.3	+	31177.4i	−0.681387	+	1.18020i	0.293171	+	0.956060i	$0.405289\pi$
$887$	−18000.3	+	31177.4i	−0.681387	+	1.18020i	−0.974558	+	0.224137i	$0.928044\pi$
$888$	−65341.0	+	27192.8i	−2.46926	+	1.02763i
$889$	−4042.09	−	7001.10i	−0.152494	−	0.264127i
$890$		0			0
$891$	24590.6	−	14416.9i	0.924598	−	0.542069i
$892$	52308.7			1.96348
$893$	1291.53	+	2237.00i	0.0483980	+	0.0838278i
$894$	−82853.1	+	34480.8i	−3.09958	+	1.28994i
$895$		0			0
$896$	5328.13	−	9228.58i	0.198661	−	0.344091i
$897$	39739.3	+	30387.9i	1.47922	+	1.13113i
$898$	−28931.6	−	50110.9i	−1.07512	−	1.86216i
$899$	−8856.18			−0.328554
$900$		0			0
$901$	3873.40			0.143220
$902$	−2711.13	−	4695.81i	−0.100078	−	0.173341i
$903$	218.054	−	1677.89i	0.00803585	−	0.0618347i
$904$	8169.47	−	14149.9i	0.300567	−	0.520597i
$905$		0			0
$906$	5621.14	−	43253.9i	0.206126	−	1.58611i
$907$	2605.82	+	4513.41i	0.0953968	+	0.165232i	0.909774	−	0.415104i	$-0.136255\pi$
$907$	2605.82	+	4513.41i	0.0953968	+	0.165232i	−0.814377	+	0.580336i	$0.802921\pi$
$908$	−55783.9			−2.03883
$909$	17035.0	+	4503.70i	0.621580	+	0.164333i
$910$		0			0
$911$	8366.56	+	14491.3i	0.304277	+	0.527024i	0.977100	−	0.212780i	$-0.0682517\pi$
$911$	8366.56	+	14491.3i	0.304277	+	0.527024i	−0.672823	+	0.739804i	$0.734918\pi$
$912$	10551.3	+	8068.38i	0.383101	+	0.292950i
$913$	−25458.0	+	44094.6i	−0.922823	+	1.59838i
$914$	−24761.1	+	42887.6i	−0.896090	+	1.55207i
$915$		0			0
$916$	25637.2	+	44405.0i	0.924758	+	1.60173i
$917$	8475.05			0.305203
$918$	10767.5	−	1472.38i	0.387124	−	0.0529367i
$919$	16722.8			0.600255			0.300127	−	0.953899i	$-0.402971\pi$
$919$	16722.8			0.600255			0.300127	+	0.953899i	$0.402971\pi$
$920$		0			0
$921$	−21234.6	+	8837.16i	−0.759722	+	0.316172i
$922$	−40394.6	+	69965.5i	−1.44287	+	2.49912i
$923$	27740.0	−	48047.1i	0.989246	−	1.71342i
$924$	−14973.4	−	11449.9i	−0.533104	−	0.407655i
$925$		0			0
$926$	94926.8			3.36878
$927$	1089.24	+	4011.54i	0.0385925	+	0.142132i
$928$	−5276.93			−0.186663
$929$	17672.3	+	30609.2i	0.624120	+	1.08101i	0.988710	+	0.149840i	$0.0478759\pi$
$929$	17672.3	+	30609.2i	0.624120	+	1.08101i	−0.364590	+	0.931168i	$0.618791\pi$
$930$		0			0
$931$	−4214.52	+	7299.77i	−0.148362	+	0.256971i
$932$	−25230.9	+	43701.3i	−0.886767	+	1.53593i
$933$	−6493.71	+	49968.2i	−0.227861	+	1.75336i
$934$	−26044.7	−	45110.8i	−0.912430	−	1.58037i
$935$		0			0
$936$	−28442.6	−	104751.i	−0.993242	−	3.65800i
$937$	−2015.96			−0.0702867			−0.0351433	−	0.999382i	$-0.511189\pi$
$937$	−2015.96			−0.0702867			−0.0351433	+	0.999382i	$0.511189\pi$
$938$	3227.21	+	5589.68i	0.112337	+	0.194573i
$939$	18669.8	+	14276.4i	0.648844	+	0.496159i
$940$		0			0
$941$	−19940.2	+	34537.4i	−0.690787	+	1.19648i	0.280794	+	0.959768i	$0.409402\pi$
$941$	−19940.2	+	34537.4i	−0.690787	+	1.19648i	−0.971580	+	0.236710i	$0.923931\pi$
$942$	16053.3	−	6680.86i	0.555249	−	0.231077i
$943$	1533.89	+	2656.77i	0.0529694	+	0.0917458i
$944$	−7318.52			−0.252328
$945$		0			0
$946$	11885.0			0.408471
$947$	17505.1	+	30319.7i	0.600675	+	1.04040i	0.992719	+	0.120453i	$0.0384349\pi$
$947$	17505.1	+	30319.7i	0.600675	+	1.04040i	−0.392044	+	0.919947i	$0.628232\pi$
$948$	54772.7	−	22794.6i	1.87651	−	0.780944i
$949$	−33319.2	+	57710.6i	−1.13971	+	1.97404i
$950$		0			0
$951$	−21968.2	−	16798.7i	−0.749073	−	0.572803i
$952$	−1925.60	−	3335.23i	−0.0655556	−	0.113546i
$953$	49213.8			1.67281			0.836407	−	0.548109i	$-0.184652\pi$
$953$	49213.8			1.67281			0.836407	+	0.548109i	$0.184652\pi$
$954$	32941.5	+	8709.04i	1.11795	+	0.295561i
$955$		0			0
$956$	−24811.0	−	42973.9i	−0.839378	−	1.45384i
$957$	1289.18	−	9920.04i	0.0435457	−	0.335078i
$958$	−23998.3	+	41566.3i	−0.809342	+	1.40182i
$959$	2401.16	−	4158.94i	0.0808525	−	0.140041i
$960$		0			0
$961$	−1282.29	−	2220.98i	−0.0430427	−	0.0745522i
$962$	−127726.			−4.28073
$963$	6638.49	−	6682.91i	0.222142	−	0.223628i
$964$	−19264.5			−0.643640
$965$		0			0
$966$	12403.2	+	9484.49i	0.413112	+	0.315899i
$967$	−609.670	+	1055.98i	−0.0202747	+	0.0351169i	−0.875985	−	0.482339i	$-0.839787\pi$
$967$	−609.670	+	1055.98i	−0.0202747	+	0.0351169i	0.855710	+	0.517456i	$0.173121\pi$
$968$	4593.13	−	7955.54i	0.152509	−	0.264154i
$969$	−1985.48	+	826.291i	−0.0658232	+	0.0273935i
$970$		0			0
$971$	−1660.33			−0.0548740			−0.0274370	−	0.999624i	$-0.508735\pi$
$971$	−1660.33			−0.0548740			−0.0274370	+	0.999624i	$0.508735\pi$
$972$	64806.4	+	7982.99i	2.13855	+	0.263431i
$973$	−3512.85			−0.115742
$974$	43993.2	+	76198.5i	1.44726	+	2.50673i
$975$		0			0
$976$	−23337.1	+	40421.1i	−0.765373	+	1.32566i
$977$	23653.9	−	40969.7i	0.774569	−	1.34159i	−0.160467	−	0.987041i	$-0.551300\pi$
$977$	23653.9	−	40969.7i	0.774569	−	1.34159i	0.935036	−	0.354552i	$-0.115367\pi$
$978$	18439.7	+	14100.5i	0.602901	+	0.461027i
$979$	−19463.8	−	33712.2i	−0.635408	−	1.10056i
$980$		0			0
$981$	21411.7	−	21554.9i	0.696863	−	0.701525i
$982$	19424.4			0.631218
$983$	−20601.5	−	35682.9i	−0.668450	−	1.15779i	−0.978338	−	0.207016i	$-0.933625\pi$
$983$	−20601.5	−	35682.9i	−0.668450	−	1.15779i	0.309888	−	0.950773i	$-0.399709\pi$
$984$	857.810	−	6600.72i	0.0277906	−	0.213845i
$985$		0			0
$986$	1906.92	−	3302.89i	0.0615910	−	0.106679i
$987$	346.832	−	2668.82i	0.0111852	−	0.0860685i
$988$	20040.3	+	34710.8i	0.645310	+	1.11771i
$989$	−6724.20			−0.216195
$990$		0			0
$991$	−29805.3			−0.955395			−0.477698	−	0.878524i	$-0.658529\pi$
$991$	−29805.3			−0.955395			−0.477698	+	0.878524i	$0.658529\pi$
$992$	−9639.48	−	16696.1i	−0.308522	−	0.534376i
$993$	32332.4	+	24724.0i	1.03327	+	0.790122i
$994$	8658.04	−	14996.2i	0.276274	−	0.478520i
$995$		0			0
$996$	−107680.	+	44812.8i	−3.42566	+	1.42565i
$997$	19916.4	+	34496.2i	0.632657	+	1.09579i	0.987006	+	0.160680i	$0.0513688\pi$
$997$	19916.4	+	34496.2i	0.632657	+	1.09579i	−0.354350	+	0.935113i	$0.615298\pi$
$998$	−24395.0			−0.773756
$999$	15567.1	−	38120.3i	0.493013	−	1.20728i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.e.g.76.15		32
5.2	odd	4		45.4.j.a.4.2	✓	32
5.3	odd	4		45.4.j.a.4.15	yes	32
5.4	even	2	inner	225.4.e.g.76.2		32
9.4	even	3		2025.4.a.bk.1.2		16
9.5	odd	6		2025.4.a.bl.1.15		16
9.7	even	3	inner	225.4.e.g.151.15		32
15.2	even	4		135.4.j.a.64.15		32
15.8	even	4		135.4.j.a.64.2		32
45.2	even	12		135.4.j.a.19.2		32
45.4	even	6		2025.4.a.bk.1.15		16
45.7	odd	12		45.4.j.a.34.15	yes	32
45.13	odd	12		405.4.b.e.244.15		16
45.14	odd	6		2025.4.a.bl.1.2		16
45.22	odd	12		405.4.b.e.244.2		16
45.23	even	12		405.4.b.f.244.2		16
45.32	even	12		405.4.b.f.244.15		16
45.34	even	6	inner	225.4.e.g.151.2		32
45.38	even	12		135.4.j.a.19.15		32
45.43	odd	12		45.4.j.a.34.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.j.a.4.2	✓	32	5.2	odd	4
45.4.j.a.4.15	yes	32	5.3	odd	4
45.4.j.a.34.2	yes	32	45.43	odd	12
45.4.j.a.34.15	yes	32	45.7	odd	12
135.4.j.a.19.2		32	45.2	even	12
135.4.j.a.19.15		32	45.38	even	12
135.4.j.a.64.2		32	15.8	even	4
135.4.j.a.64.15		32	15.2	even	4
225.4.e.g.76.2		32	5.4	even	2	inner
225.4.e.g.76.15		32	1.1	even	1	trivial
225.4.e.g.151.2		32	45.34	even	6	inner
225.4.e.g.151.15		32	9.7	even	3	inner
405.4.b.e.244.2		16	45.22	odd	12
405.4.b.e.244.15		16	45.13	odd	12
405.4.b.f.244.2		16	45.23	even	12
405.4.b.f.244.15		16	45.32	even	12
2025.4.a.bk.1.2		16	9.4	even	3
2025.4.a.bk.1.15		16	45.4	even	6
2025.4.a.bl.1.2		16	45.14	odd	6
2025.4.a.bl.1.15		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)

\(f(q)\)	\(=\)	\(q+(2.51186 + 4.35066i) q^{2} +(4.79730 - 1.99648i) q^{3} +(-8.61884 + 14.9283i) q^{4} +(20.7361 + 15.8565i) q^{6} +(2.69099 + 4.66092i) q^{7} -46.4074 q^{8} +(19.0281 - 19.1554i) q^{9} +O(q^{10})\)	\(q+(2.51186 + 4.35066i) q^{2} +(4.79730 - 1.99648i) q^{3} +(-8.61884 + 14.9283i) q^{4} +(20.7361 + 15.8565i) q^{6} +(2.69099 + 4.66092i) q^{7} -46.4074 q^{8} +(19.0281 - 19.1554i) q^{9} +(19.5509 + 33.8631i) q^{11} +(-11.5431 + 88.8227i) q^{12} +(-43.3135 + 75.0212i) q^{13} +(-13.5187 + 23.4151i) q^{14} +(-47.6180 - 82.4768i) q^{16} +15.4194 q^{17} +(131.135 + 34.6693i) q^{18} -26.8412 q^{19} +(22.2149 + 16.9873i) q^{21} +(-98.2180 + 170.119i) q^{22} +(55.5692 - 96.2486i) q^{23} +(-222.630 + 92.6515i) q^{24} -435.189 q^{26} +(53.0401 - 129.884i) q^{27} -92.7727 q^{28} +(-24.6174 - 42.6385i) q^{29} +(89.9383 - 155.778i) q^{31} +(53.5894 - 92.8196i) q^{32} +(161.398 + 123.419i) q^{33} +(38.7312 + 67.0844i) q^{34} +(121.957 + 449.154i) q^{36} +293.496 q^{37} +(-67.4211 - 116.777i) q^{38} +(-58.0094 + 446.374i) q^{39} +(-13.8016 + 23.9051i) q^{41} +(-18.1055 + 139.319i) q^{42} +(-30.2515 - 52.3971i) q^{43} -674.023 q^{44} +558.327 q^{46} +(-48.1175 - 83.3420i) q^{47} +(-393.101 - 300.597i) q^{48} +(157.017 - 271.962i) q^{49} +(73.9713 - 30.7845i) q^{51} +(-746.625 - 1293.19i) q^{52} +251.203 q^{53} +(698.309 - 95.4892i) q^{54} +(-124.882 - 216.301i) q^{56} +(-128.765 + 53.5879i) q^{57} +(123.671 - 214.204i) q^{58} +(38.4231 - 66.5508i) q^{59} +(-245.045 - 424.431i) q^{61} +903.648 q^{62} +(140.486 + 37.1417i) q^{63} -223.452 q^{64} +(-131.542 + 1012.20i) q^{66} +(119.360 - 206.738i) q^{67} +(-132.897 + 230.184i) q^{68} +(74.4232 - 572.676i) q^{69} -640.447 q^{71} +(-883.046 + 888.954i) q^{72} +769.257 q^{73} +(737.219 + 1276.90i) q^{74} +(231.340 - 400.692i) q^{76} +(-105.222 + 182.250i) q^{77} +(-2087.73 + 868.847i) q^{78} +(-331.176 - 573.613i) q^{79} +(-4.86094 - 728.984i) q^{81} -138.670 q^{82} +(651.071 + 1127.69i) q^{83} +(-445.058 + 185.219i) q^{84} +(151.975 - 263.228i) q^{86} +(-203.224 - 155.402i) q^{87} +(-907.306 - 1571.50i) q^{88} -995.544 q^{89} -466.224 q^{91} +(957.883 + 1659.10i) q^{92} +(120.453 - 926.872i) q^{93} +(241.729 - 418.686i) q^{94} +(71.7718 - 552.274i) q^{96} +(407.423 + 705.677i) q^{97} +1577.62 q^{98} +(1020.68 + 269.846i) 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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