LMFDB - Embedded newform 925.2.o.d.174.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(174,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("925.174");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			174.2
Character	$\chi$	$=$	925.174
Dual form			925.2.o.d.824.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.18842 + 1.26349i) q^{2} +(-2.76175 - 1.59450i) q^{3} +(2.19280 - 3.79803i) q^{4} +8.05850 q^{6} +(2.85005 + 1.64548i) q^{7} +6.02833i q^{8} +(3.58484 + 6.20912i) q^{9} +O(q^{10})$	\(q+(-2.18842 + 1.26349i) q^{2} +(-2.76175 - 1.59450i) q^{3} +(2.19280 - 3.79803i) q^{4} +8.05850 q^{6} +(2.85005 + 1.64548i) q^{7} +6.02833i q^{8} +(3.58484 + 6.20912i) q^{9} +3.95612 q^{11} +(-12.1119 + 6.99281i) q^{12} +(4.56096 + 2.63327i) q^{13} -8.31616 q^{14} +(-3.23112 - 5.59646i) q^{16} +(2.02791 - 1.17081i) q^{17} +(-15.6903 - 9.05879i) q^{18} +(-2.43318 + 4.21440i) q^{19} +(-5.24742 - 9.08879i) q^{21} +(-8.65766 + 4.99850i) q^{22} -1.39184i q^{23} +(9.61215 - 16.6487i) q^{24} -13.3084 q^{26} -13.2971i q^{27} +(12.4992 - 7.21640i) q^{28} -3.38881 q^{29} +5.02590 q^{31} +(3.70074 + 2.13662i) q^{32} +(-10.9258 - 6.30802i) q^{33} +(-2.95861 + 5.12447i) q^{34} +31.4433 q^{36} +(2.93481 + 5.32793i) q^{37} -12.2972i q^{38} +(-8.39749 - 14.5449i) q^{39} +(-5.32661 + 9.22596i) q^{41} +(22.9671 + 13.2601i) q^{42} +7.67217i q^{43} +(8.67496 - 15.0255i) q^{44} +(1.75857 + 3.04594i) q^{46} -1.52419i q^{47} +20.6080i q^{48} +(1.91519 + 3.31721i) q^{49} -7.46743 q^{51} +(20.0025 - 11.5485i) q^{52} +(-2.89626 + 1.67216i) q^{53} +(16.8007 + 29.0996i) q^{54} +(-9.91948 + 17.1810i) q^{56} +(13.4397 - 7.75940i) q^{57} +(7.41614 - 4.28171i) q^{58} +(-1.74241 - 3.01793i) q^{59} +(0.659037 - 1.14149i) q^{61} +(-10.9988 + 6.35016i) q^{62} +23.5951i q^{63} +2.12610 q^{64} +31.8804 q^{66} +(-11.0920 - 6.40399i) q^{67} -10.2694i q^{68} +(-2.21929 + 3.84392i) q^{69} +(-3.64151 + 6.30728i) q^{71} +(-37.4306 + 21.6106i) q^{72} +8.70324i q^{73} +(-13.1544 - 7.95168i) q^{74} +(10.6709 + 18.4826i) q^{76} +(11.2751 + 6.50970i) q^{77} +(36.7545 + 21.2202i) q^{78} +(3.07393 - 5.32420i) q^{79} +(-10.4476 + 18.0958i) q^{81} -26.9204i q^{82} +(5.94990 - 3.43518i) q^{83} -46.0261 q^{84} +(-9.69368 - 16.7900i) q^{86} +(9.35904 + 5.40344i) q^{87} +23.8488i q^{88} +(-0.199381 - 0.345338i) q^{89} +(8.66599 + 15.0099i) q^{91} +(-5.28627 - 3.05203i) q^{92} +(-13.8803 - 8.01379i) q^{93} +(1.92579 + 3.33556i) q^{94} +(-6.81367 - 11.8016i) q^{96} +12.2002i q^{97} +(-8.38251 - 4.83964i) q^{98} +(14.1820 + 24.5640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 22 q^{4} + 20 q^{9}+O(q^{10}) $ 48 * q + 22 * q^4 + 20 * q^9	$ 48 q + 22 q^{4} + 20 q^{9} - 40 q^{14} - 26 q^{16} - 10 q^{19} - 12 q^{21} + 42 q^{24} - 40 q^{26} - 12 q^{29} + 76 q^{31} + 10 q^{34} - 4 q^{36} - 28 q^{39} - 26 q^{41} + 30 q^{44} - 26 q^{46} + 52 q^{49} - 92 q^{51} + 74 q^{54} + 14 q^{59} + 32 q^{61} - 40 q^{64} + 164 q^{66} - 42 q^{69} - 4 q^{71} - 96 q^{74} + 34 q^{76} + 42 q^{79} - 32 q^{81} - 152 q^{84} - 32 q^{86} - 58 q^{89} + 64 q^{91} + 26 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) $ 48 * q + 22 * q^4 + 20 * q^9 - 40 * q^14 - 26 * q^16 - 10 * q^19 - 12 * q^21 + 42 * q^24 - 40 * q^26 - 12 * q^29 + 76 * q^31 + 10 * q^34 - 4 * q^36 - 28 * q^39 - 26 * q^41 + 30 * q^44 - 26 * q^46 + 52 * q^49 - 92 * q^51 + 74 * q^54 + 14 * q^59 + 32 * q^61 - 40 * q^64 + 164 * q^66 - 42 * q^69 - 4 * q^71 - 96 * q^74 + 34 * q^76 + 42 * q^79 - 32 * q^81 - 152 * q^84 - 32 * q^86 - 58 * q^89 + 64 * q^91 + 26 * q^94 + 52 * q^96 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−2.18842	+	1.26349i	−1.54745	+	0.893420i	−0.549113	+	0.835748i	$0.685034\pi$
$2$	−2.18842	+	1.26349i	−1.54745	+	0.893420i	−0.998336	+	0.0576718i	$0.981632\pi$
$3$	−2.76175	−	1.59450i	−1.59450	−	0.920583i	−0.992522	−	0.122068i	$-0.961047\pi$
$3$	−2.76175	−	1.59450i	−1.59450	−	0.920583i	−0.601975	−	0.798515i	$-0.705619\pi$
$4$	2.19280	−	3.79803i	1.09640	−	1.89902i
$5$		0			0
$5$		0			0
$6$	8.05850			3.28987
$7$	2.85005	+	1.64548i	1.07722	+	0.621932i	0.930145	−	0.367193i	$-0.119681\pi$
$7$	2.85005	+	1.64548i	1.07722	+	0.621932i	0.147073	+	0.989126i	$0.453015\pi$
$8$			6.02833i			2.13134i
$9$	3.58484	+	6.20912i	1.19495	+	2.06971i
$10$		0			0
$11$	3.95612			1.19281			0.596407	−	0.802682i	$-0.296594\pi$
$11$	3.95612			1.19281			0.596407	+	0.802682i	$0.296594\pi$
$12$	−12.1119	+	6.99281i	−3.49641	+	2.01865i
$13$	4.56096	+	2.63327i	1.26498	+	0.730339i	0.974035	−	0.226400i	$-0.0726955\pi$
$13$	4.56096	+	2.63327i	1.26498	+	0.730339i	0.290949	+	0.956738i	$0.406029\pi$
$14$	−8.31616			−2.22259
$15$		0			0
$16$	−3.23112	−	5.59646i	−0.807780	−	1.39912i
$17$	2.02791	−	1.17081i	0.491840	−	0.283964i	−0.233498	−	0.972357i	$-0.575017\pi$
$17$	2.02791	−	1.17081i	0.491840	−	0.283964i	0.725337	+	0.688394i	$0.241684\pi$
$18$	−15.6903	−	9.05879i	−3.69824	−	2.13518i
$19$	−2.43318	+	4.21440i	−0.558210	+	0.966849i	0.439436	+	0.898274i	$0.355178\pi$
$19$	−2.43318	+	4.21440i	−0.558210	+	0.966849i	−0.997646	+	0.0685747i	$0.978155\pi$
$20$		0			0
$21$	−5.24742	−	9.08879i	−1.14508	−	1.98334i
$22$	−8.65766	+	4.99850i	−1.84582	+	1.06568i
$23$		−	1.39184i		−	0.290219i	−0.989416	−	0.145110i	$-0.953647\pi$
$23$		−	1.39184i		−	0.290219i	0.989416	−	0.145110i	$-0.0463535\pi$
$24$	9.61215	−	16.6487i	1.96207	−	3.39841i
$25$		0			0
$26$	−13.3084			−2.61000
$27$		−	13.2971i		−	2.55902i
$28$	12.4992	−	7.21640i	2.36212	−	1.36377i
$29$	−3.38881			−0.629286			−0.314643	−	0.949210i	$-0.601885\pi$
$29$	−3.38881			−0.629286			−0.314643	+	0.949210i	$0.601885\pi$
$30$		0			0
$31$	5.02590			0.902679			0.451339	−	0.892352i	$-0.350946\pi$
$31$	5.02590			0.902679			0.451339	+	0.892352i	$0.350946\pi$
$32$	3.70074	+	2.13662i	0.654204	+	0.377705i
$33$	−10.9258	−	6.30802i	−1.90194	−	1.09808i
$34$	−2.95861	+	5.12447i	−0.507398	+	0.878839i
$35$		0			0
$36$	31.4433			5.24055
$37$	2.93481	+	5.32793i	0.482480	+	0.875907i
$37$	2.93481	+	5.32793i	0.482480	+	0.875907i
$38$		−	12.2972i		−	1.99487i
$39$	−8.39749	−	14.5449i	−1.34468	−	2.32905i
$40$		0			0
$41$	−5.32661	+	9.22596i	−0.831877	+	1.44085i	0.0646717	+	0.997907i	$0.479400\pi$
$41$	−5.32661	+	9.22596i	−0.831877	+	1.44085i	−0.896548	+	0.442946i	$0.853933\pi$
$42$	22.9671	+	13.2601i	3.54391	+	2.04608i
$43$			7.67217i			1.16999i	0.811035	+	0.584997i	$0.198905\pi$
$43$			7.67217i			1.16999i	−0.811035	+	0.584997i	$0.801095\pi$
$44$	8.67496	−	15.0255i	1.30780	−	2.26518i
$45$		0			0
$46$	1.75857	+	3.04594i	0.259288	+	0.449099i
$47$		−	1.52419i		−	0.222325i	−0.993802	−	0.111163i	$-0.964543\pi$
$47$		−	1.52419i		−	0.222325i	0.993802	−	0.111163i	$-0.0354575\pi$
$48$			20.6080i			2.97451i
$49$	1.91519	+	3.31721i	0.273599	+	0.473888i
$50$		0			0
$51$	−7.46743			−1.04565
$52$	20.0025	−	11.5485i	2.77385	−	1.60148i
$53$	−2.89626	+	1.67216i	−0.397832	+	0.229689i	−0.685548	−	0.728027i	$-0.740437\pi$
$53$	−2.89626	+	1.67216i	−0.397832	+	0.229689i	0.287716	+	0.957716i	$0.407104\pi$
$54$	16.8007	+	29.0996i	2.28628	+	3.95996i
$55$		0			0
$56$	−9.91948	+	17.1810i	−1.32555	+	2.29591i
$57$	13.4397	−	7.75940i	1.78013	−	1.02776i
$58$	7.41614	−	4.28171i	0.973787	−	0.562216i
$59$	−1.74241	−	3.01793i	−0.226842	−	0.392902i	0.730029	−	0.683417i	$-0.239507\pi$
$59$	−1.74241	−	3.01793i	−0.226842	−	0.392902i	−0.956870	+	0.290515i	$0.906173\pi$
$60$		0			0
$61$	0.659037	−	1.14149i	0.0843811	−	0.146152i	−0.820746	−	0.571293i	$-0.806442\pi$
$61$	0.659037	−	1.14149i	0.0843811	−	0.146152i	0.905127	+	0.425141i	$0.139775\pi$
$62$	−10.9988	+	6.35016i	−1.39685	+	0.806471i
$63$			23.5951i			2.97270i
$64$	2.12610			0.265763
$65$		0			0
$66$	31.8804			3.92420
$67$	−11.0920	−	6.40399i	−1.35511	−	0.782371i	−0.366147	−	0.930557i	$-0.619323\pi$
$67$	−11.0920	−	6.40399i	−1.35511	−	0.782371i	−0.988960	+	0.148186i	$0.952657\pi$
$68$		−	10.2694i		−	1.24535i
$69$	−2.21929	+	3.84392i	−0.267171	+	0.462754i
$70$		0			0
$71$	−3.64151	+	6.30728i	−0.432168	+	0.748537i	−0.997060	−	0.0766282i	$-0.975585\pi$
$71$	−3.64151	+	6.30728i	−0.432168	+	0.748537i	0.564892	+	0.825165i	$0.308918\pi$
$72$	−37.4306	+	21.6106i	−4.41124	+	2.54683i
$73$			8.70324i			1.01864i	0.860578	+	0.509319i	$0.170103\pi$
$73$			8.70324i			1.01864i	−0.860578	+	0.509319i	$0.829897\pi$
$74$	−13.1544	−	7.95168i	−1.52917	−	0.924364i
$75$		0			0
$76$	10.6709	+	18.4826i	1.22404	+	2.12010i
$77$	11.2751	+	6.50970i	1.28492	+	0.741850i
$78$	36.7545	+	21.2202i	4.16163	+	2.40272i
$79$	3.07393	−	5.32420i	0.345844	−	0.599019i	−0.639663	−	0.768656i	$-0.720926\pi$
$79$	3.07393	−	5.32420i	0.345844	−	0.599019i	0.985507	+	0.169636i	$0.0542593\pi$
$80$		0			0
$81$	−10.4476	+	18.0958i	−1.16085	+	2.01065i
$82$		−	26.9204i		−	2.97286i
$83$	5.94990	−	3.43518i	0.653087	−	0.377060i	−0.136551	−	0.990633i	$-0.543602\pi$
$83$	5.94990	−	3.43518i	0.653087	−	0.377060i	0.789638	+	0.613573i	$0.210268\pi$
$84$	−46.0261			−5.02186
$85$		0			0
$86$	−9.69368	−	16.7900i	−1.04530	−	1.81051i
$87$	9.35904	+	5.40344i	1.00339	+	0.579310i
$88$			23.8488i			2.54229i
$89$	−0.199381	−	0.345338i	−0.0211343	−	0.0366057i	0.855265	−	0.518191i	$-0.173394\pi$
$89$	−0.199381	−	0.345338i	−0.0211343	−	0.0366057i	−0.876399	+	0.481585i	$0.840061\pi$
$90$		0			0
$91$	8.66599	+	15.0099i	0.908442	+	1.57347i
$92$	−5.28627	−	3.05203i	−0.551131	−	0.318196i
$93$	−13.8803	−	8.01379i	−1.43932	−	0.830991i
$94$	1.92579	+	3.33556i	0.198630	+	0.344037i
$95$		0			0
$96$	−6.81367	−	11.8016i	−0.695418	−	1.20450i
$97$			12.2002i			1.23874i	0.785100	+	0.619369i	$0.212612\pi$
$97$			12.2002i			1.23874i	−0.785100	+	0.619369i	$0.787388\pi$
$98$	−8.38251	−	4.83964i	−0.846761	−	0.488878i
$99$	14.1820	+	24.5640i	1.42535	+	2.46878i
$100$		0			0
$101$	−6.93451			−0.690010			−0.345005	−	0.938601i	$-0.612123\pi$
$101$	−6.93451			−0.690010			−0.345005	+	0.938601i	$0.612123\pi$
$102$	16.3419	−	9.43499i	1.61809	−	0.934203i
$103$		−	3.10601i		−	0.306044i	−0.988223	−	0.153022i	$-0.951099\pi$
$103$		−	3.10601i		−	0.306044i	0.988223	−	0.153022i	$-0.0489006\pi$
$104$	−15.8742	+	27.4950i	−1.55660	+	2.69611i
$105$		0			0
$106$	4.22550	−	7.31878i	0.410417	−	0.710863i
$107$	−14.0773	−	8.12752i	−1.36090	−	0.785717i	−0.371157	−	0.928570i	$-0.621039\pi$
$107$	−14.0773	−	8.12752i	−1.36090	−	0.785717i	−0.989744	+	0.142853i	$0.954372\pi$
$108$	−50.5028	−	29.1578i	−4.85963	−	2.80571i
$109$	1.70446	+	2.95221i	0.163257	+	0.282770i	0.936035	−	0.351907i	$-0.114467\pi$
$109$	1.70446	+	2.95221i	0.163257	+	0.282770i	−0.772778	+	0.634677i	$0.781133\pi$
$110$		0			0
$111$	0.390157	−	19.3940i	0.0370321	−	1.84079i
$112$		−	21.2669i		−	2.00954i
$113$	−7.27648	+	4.20108i	−0.684513	+	0.395204i	−0.801553	−	0.597923i	$-0.795993\pi$
$113$	−7.27648	+	4.20108i	−0.684513	+	0.395204i	0.117040	+	0.993127i	$0.462659\pi$
$114$	−19.6078	+	33.9617i	−1.83644	+	3.18081i
$115$		0			0
$116$	−7.43096	+	12.8708i	−0.689948	+	1.19502i
$117$			37.7595i			3.49086i
$118$	7.62624	+	4.40301i	0.702052	+	0.405330i
$119$	7.70618			0.706425
$120$		0			0
$121$	4.65087			0.422806
$122$			3.33074i			0.301551i
$123$	29.4215	−	16.9865i	2.65285	−	1.53162i
$124$	11.0208	−	19.0886i	0.989696	−	1.71420i
$125$		0			0
$126$	−29.8121	−	51.6360i	−2.65587	−	4.60010i
$127$	13.6727	−	7.89396i	1.21326	−	0.700475i	0.249791	−	0.968300i	$-0.419638\pi$
$127$	13.6727	−	7.89396i	1.21326	−	0.700475i	0.963468	+	0.267824i	$0.0863046\pi$
$128$	−12.0543	+	6.95955i	−1.06546	+	0.615143i
$129$	12.2332	−	21.1886i	1.07708	−	1.86555i
$130$		0			0
$131$	5.83322	+	10.1034i	0.509651	+	0.882741i	0.999938	+	0.0111797i	$0.00355868\pi$
$131$	5.83322	+	10.1034i	0.509651	+	0.882741i	−0.490287	+	0.871561i	$0.663108\pi$
$132$	−47.9161	+	27.6644i	−4.17056	+	2.40788i
$133$	−13.8694	+	8.00750i	−1.20263	+	0.694338i
$134$	32.3654			2.79594
$135$		0			0
$136$	7.05804	+	12.2249i	0.605222	+	1.04828i
$137$			1.47968i			0.126418i	0.998000	+	0.0632089i	$0.0201335\pi$
$137$			1.47968i			0.126418i	−0.998000	+	0.0632089i	$0.979867\pi$
$138$		−	11.2162i		−	0.954783i
$139$	−8.98874	−	15.5690i	−0.762415	−	1.32054i	−0.941603	−	0.336726i	$-0.890680\pi$
$139$	−8.98874	−	15.5690i	−0.762415	−	1.32054i	0.179188	−	0.983815i	$-0.442653\pi$
$140$		0			0
$141$	−2.43031	+	4.20942i	−0.204669	+	0.354497i
$142$		−	18.4040i		−	1.54443i
$143$	18.0437	+	10.4175i	1.50889	+	0.871159i
$144$	23.1661	−	40.1248i	1.93051	−	3.34374i
$145$		0			0
$146$	−10.9964	−	19.0464i	−0.910071	−	1.57629i
$147$		−	12.2151i		−	1.00748i
$148$	26.6711	+	0.536555i	2.19235	+	0.0441046i
$149$	2.24926			0.184267			0.0921334	−	0.995747i	$-0.470631\pi$
$149$	2.24926			0.184267			0.0921334	+	0.995747i	$0.470631\pi$
$150$		0			0
$151$	7.35344	−	12.7365i	0.598414	−	1.03648i	−0.394641	−	0.918835i	$-0.629131\pi$
$151$	7.35344	−	12.7365i	0.598414	−	1.03648i	0.993055	−	0.117649i	$-0.0375357\pi$
$152$	−25.4058	−	14.6680i	−2.06068	−	1.18973i
$153$	14.5394	+	8.39435i	1.17544	+	0.678643i
$154$	−32.8997			−2.65113
$155$		0			0
$156$	−73.6560			−5.89720
$157$	−3.12098	+	1.80190i	−0.249081	+	0.143807i	−0.619343	−	0.785120i	$-0.712601\pi$
$157$	−3.12098	+	1.80190i	−0.249081	+	0.143807i	0.370262	+	0.928927i	$0.379268\pi$
$158$			15.5355i			1.23594i
$159$	10.6650			0.845790
$160$		0			0
$161$	2.29025	−	3.96682i	0.180497	−	0.312629i
$162$		−	52.8018i		−	4.14850i
$163$	−2.77650	+	1.60301i	−0.217472	+	0.125558i	−0.604779	−	0.796393i	$-0.706739\pi$
$163$	−2.77650	+	1.60301i	−0.217472	+	0.125558i	0.387307	+	0.921951i	$0.373405\pi$
$164$	23.3603	+	40.4613i	1.82414	+	3.15950i
$165$		0			0
$166$	−8.68060	+	15.0352i	−0.673746	+	1.16696i
$167$	16.6044	+	9.58655i	1.28489	+	0.741829i	0.977737	−	0.209832i	$-0.0672917\pi$
$167$	16.6044	+	9.58655i	1.28489	+	0.741829i	0.307149	+	0.951662i	$0.400625\pi$
$168$	54.7902	−	31.6332i	4.22716	−	2.44055i
$169$	7.36827	+	12.7622i	0.566790	+	0.981708i
$170$		0			0
$171$	−34.8903			−2.66813
$172$	29.1392	+	16.8235i	2.22184	+	1.28278i
$173$	2.11405	−	1.22055i	0.160728	−	0.0927964i	−0.417479	−	0.908687i	$-0.637086\pi$
$173$	2.11405	−	1.22055i	0.160728	−	0.0927964i	0.578207	+	0.815890i	$0.303753\pi$
$174$	−27.3087			−2.07027
$175$		0			0
$176$	−12.7827	−	22.1403i	−0.963531	−	1.66889i
$177$			11.1130i			0.835307i
$178$	0.872659	+	0.503830i	0.0654085	+	0.0377636i
$179$	−7.26075			−0.542694			−0.271347	−	0.962482i	$-0.587469\pi$
$179$	−7.26075			−0.542694			−0.271347	+	0.962482i	$0.587469\pi$
$180$		0			0
$181$	−1.43380	+	2.48342i	−0.106574	+	0.184591i	−0.914380	−	0.404857i	$-0.867321\pi$
$181$	−1.43380	+	2.48342i	−0.106574	+	0.184591i	0.807806	+	0.589448i	$0.200655\pi$
$182$	−37.9297	−	21.8987i	−2.81154	−	1.62324i
$183$	−3.64019	+	2.10167i	−0.269091	+	0.155360i
$184$	8.39048			0.618555
$185$		0			0
$186$	40.5012			2.96970
$187$	8.02264	−	4.63187i	0.586673	−	0.338716i
$188$	−5.78891	−	3.34223i	−0.422200	−	0.243757i
$189$	21.8800	−	37.8974i	1.59154	−	2.75663i
$190$		0			0
$191$	13.5229			0.978481			0.489240	−	0.872149i	$-0.337274\pi$
$191$	13.5229			0.978481			0.489240	+	0.872149i	$0.337274\pi$
$192$	−5.87176	−	3.39006i	−0.423758	−	0.244657i
$193$			22.9305i			1.65058i	0.564712	+	0.825288i	$0.308987\pi$
$193$			22.9305i			1.65058i	−0.564712	+	0.825288i	$0.691013\pi$
$194$	−15.4147	−	26.6991i	−1.10671	−	1.91688i
$195$		0			0
$196$	16.7985			1.19989
$197$	16.8766	−	9.74370i	1.20241	−	0.694210i	0.241317	−	0.970446i	$-0.422421\pi$
$197$	16.8766	−	9.74370i	1.20241	−	0.694210i	0.961090	+	0.276236i	$0.0890872\pi$
$198$	−62.0726	−	35.8376i	−4.41131	−	2.54687i
$199$	7.46097			0.528894			0.264447	−	0.964400i	$-0.414811\pi$
$199$	7.46097			0.528894			0.264447	+	0.964400i	$0.414811\pi$
$200$		0			0
$201$	20.4223	+	35.3724i	1.44048	+	2.49498i
$202$	15.1756	−	8.76166i	1.06775	−	0.616469i
$203$	−9.65827	−	5.57621i	−0.677878	−	0.391373i
$204$	−16.3745	+	28.3615i	−1.14645	+	1.98571i
$205$		0			0
$206$	3.92440	+	6.79726i	0.273426	+	0.473588i
$207$	8.64212	−	4.98953i	0.600669	−	0.346796i
$208$		−	34.0337i		−	2.35981i
$209$	−9.62596	+	16.6726i	−0.665841	+	1.15327i
$210$		0			0
$211$	−10.8872			−0.749503			−0.374751	−	0.927125i	$-0.622272\pi$
$211$	−10.8872			−0.749503			−0.374751	+	0.927125i	$0.622272\pi$
$212$			14.6668i			1.00732i
$213$	20.1139	−	11.6128i	1.37818	−	0.795693i
$214$	41.0760			2.80790
$215$		0			0
$216$	80.1592			5.45414
$217$	14.3241	+	8.27001i	0.972382	+	0.561405i
$218$	−7.46015	−	4.30712i	−0.505265	−	0.291715i
$219$	13.8773	−	24.0362i	0.937740	−	1.62421i
$220$		0			0
$221$	12.3323			0.829559
$222$	23.6502	+	42.9352i	1.58730	+	2.88162i
$223$			21.2934i			1.42591i	0.701210	+	0.712955i	$0.252644\pi$
$223$			21.2934i			1.42591i	−0.701210	+	0.712955i	$0.747356\pi$
$224$	7.03153	+	12.1790i	0.469814	+	0.813741i
$225$		0			0
$226$	10.6160	−	18.3875i	0.706166	−	1.22312i
$227$	6.61892	+	3.82143i	0.439313	+	0.253637i	0.703306	−	0.710887i	$-0.251706\pi$
$227$	6.61892	+	3.82143i	0.439313	+	0.253637i	−0.263993	+	0.964525i	$0.585040\pi$
$228$		−	68.0592i		−	4.50733i
$229$	0.824768	−	1.42854i	0.0545022	−	0.0944006i	−0.837487	−	0.546457i	$-0.815976\pi$
$229$	0.824768	−	1.42854i	0.0545022	−	0.0944006i	0.891989	+	0.452057i	$0.149309\pi$
$230$		0			0
$231$	−20.7594	−	35.9563i	−1.36587	−	2.36575i
$232$		−	20.4288i		−	1.34122i
$233$		−	15.6103i		−	1.02266i	−0.859383	−	0.511332i	$-0.829152\pi$
$233$		−	15.6103i		−	1.02266i	0.859383	−	0.511332i	$-0.170848\pi$
$234$	−47.7086	−	82.6337i	−3.11881	−	5.40193i
$235$		0			0
$236$	−15.2830			−0.994836
$237$	−16.9788	+	9.80274i	−1.10289	+	0.636756i
$238$	−16.8644	+	9.73666i	−1.09316	+	0.631134i
$239$	−3.08125	−	5.33687i	−0.199309	−	0.345214i	0.748995	−	0.662575i	$-0.230536\pi$
$239$	−3.08125	−	5.33687i	−0.199309	−	0.345214i	−0.948305	+	0.317361i	$0.897203\pi$
$240$		0			0
$241$	1.63082	−	2.82466i	0.105050	−	0.181952i	−0.808708	−	0.588210i	$-0.799833\pi$
$241$	1.63082	−	2.82466i	0.105050	−	0.181952i	0.913759	+	0.406257i	$0.133166\pi$
$242$	−10.1781	+	5.87631i	−0.654270	+	0.377743i
$243$	23.1606	−	13.3718i	1.48576	−	0.857802i
$244$	−2.89027	−	5.00609i	−0.185031	−	0.320482i
$245$		0			0
$246$	−42.9245	+	74.3474i	−2.73677	+	4.74022i
$247$	−22.1953	+	12.8145i	−1.41225	+	0.815365i
$248$			30.2978i			1.92391i
$249$	−21.9095			−1.38846
$250$		0			0
$251$	21.8269			1.37770			0.688850	−	0.724904i	$-0.258116\pi$
$251$	21.8269			1.37770			0.688850	+	0.724904i	$0.258116\pi$
$252$	89.6150	+	51.7392i	5.64521	+	3.25927i
$253$		−	5.50629i		−	0.346178i
$254$	−19.9478	+	34.5506i	−1.25164	+	2.16790i
$255$		0			0
$256$	15.4605	−	26.7783i	0.966280	−	1.67365i
$257$	−8.35378	+	4.82306i	−0.521094	+	0.300854i	−0.737382	−	0.675476i	$-0.763938\pi$
$257$	−8.35378	+	4.82306i	−0.521094	+	0.300854i	0.216288	+	0.976330i	$0.430605\pi$
$258$			61.8262i			3.84913i
$259$	−0.402632	+	20.0141i	−0.0250183	+	1.24361i
$260$		0			0
$261$	−12.1483	−	21.0415i	−0.751963	−	1.30244i
$262$	−25.5311	−	14.7404i	−1.57732	−	0.910664i
$263$	−26.9679	−	15.5699i	−1.66291	−	0.960084i	−0.971313	−	0.237803i	$-0.923573\pi$
$263$	−26.9679	−	15.5699i	−1.66291	−	0.960084i	−0.691600	−	0.722280i	$-0.743094\pi$
$264$	38.0268	−	65.8643i	2.34039	−	4.05367i
$265$		0			0
$266$	20.2347	−	35.0476i	1.24067	−	2.14890i
$267$			1.27165i			0.0778236i
$268$	−48.6451	+	28.0853i	−2.97147	+	1.71558i
$269$	5.78435			0.352678			0.176339	−	0.984330i	$-0.443575\pi$
$269$	5.78435			0.352678			0.176339	+	0.984330i	$0.443575\pi$
$270$		0			0
$271$	3.75250	+	6.49952i	0.227948	+	0.394818i	0.957200	−	0.289428i	$-0.0934650\pi$
$271$	3.75250	+	6.49952i	0.227948	+	0.394818i	−0.729252	+	0.684245i	$0.760132\pi$
$272$	−13.1048	−	7.56607i	−0.794596	−	0.458760i
$273$		−	55.2716i		−	3.34519i
$274$	−1.86956	−	3.23817i	−0.112944	−	0.195625i
$275$		0			0
$276$	9.73289	+	16.8579i	0.585851	+	1.01472i
$277$	−16.5067	−	9.53018i	−0.991794	−	0.572613i	−0.0859843	−	0.996296i	$-0.527403\pi$
$277$	−16.5067	−	9.53018i	−0.991794	−	0.572613i	−0.905810	+	0.423684i	$0.860737\pi$
$278$	39.3423	+	22.7143i	2.35960	+	1.36231i
$279$	18.0171	+	31.2065i	1.07865	+	1.86828i
$280$		0			0
$281$	0.440285	+	0.762595i	0.0262652	+	0.0454926i	0.878859	−	0.477081i	$-0.158305\pi$
$281$	0.440285	+	0.762595i	0.0262652	+	0.0454926i	−0.852594	+	0.522574i	$0.824972\pi$
$282$		−	12.2826i		−	0.731421i
$283$	−24.6798	−	14.2489i	−1.46706	−	0.847010i	−0.467743	−	0.883865i	$-0.654933\pi$
$283$	−24.6798	−	14.2489i	−1.46706	−	0.847010i	−0.999321	+	0.0368550i	$0.988266\pi$
$284$	15.9702	+	27.6612i	0.947656	+	1.64139i
$285$		0			0
$286$	−52.6497			−3.11324
$287$	−30.3622	+	17.5296i	−1.79222	+	1.03474i
$288$			30.6378i			1.80535i
$289$	−5.75840	+	9.97384i	−0.338729	+	0.586696i
$290$		0			0
$291$	19.4531	−	33.6938i	1.14036	−	1.97516i
$292$	33.0552	+	19.0844i	1.93441	+	1.11683i
$293$	−13.7555	−	7.94175i	−0.803606	−	0.463962i	0.0411247	−	0.999154i	$-0.486906\pi$
$293$	−13.7555	−	7.94175i	−0.803606	−	0.463962i	−0.844730	+	0.535192i	$0.820239\pi$
$294$	15.4336	+	26.7318i	0.900105	+	1.55903i
$295$		0			0
$296$	−32.1185	+	17.6920i	−1.86685	+	1.02833i
$297$		−	52.6048i		−	3.05244i
$298$	−4.92234	+	2.84191i	−0.285143	+	0.164628i
$299$	3.66510	−	6.34814i	0.211958	−	0.367123i
$300$		0			0
$301$	−12.6244	+	21.8661i	−0.727657	+	1.26034i
$302$			37.1639i			2.13854i
$303$	19.1514	+	11.0571i	1.10022	+	0.635211i
$304$	31.4476			1.80364
$305$		0			0
$306$	−42.4246			−2.42525
$307$		−	32.4664i		−	1.85296i	−0.376349	−	0.926478i	$-0.622821\pi$
$307$		−	32.4664i		−	1.85296i	0.376349	−	0.926478i	$-0.377179\pi$
$308$	49.4482	−	28.5489i	2.81757	−	1.62672i
$309$	−4.95252	+	8.57802i	−0.281739	+	0.487986i
$310$		0			0
$311$	11.5351	+	19.9793i	0.654093	+	1.13292i	0.982120	+	0.188254i	$0.0602829\pi$
$311$	11.5351	+	19.9793i	0.654093	+	1.13292i	−0.328027	+	0.944668i	$0.606384\pi$
$312$	87.6814	−	50.6229i	4.96398	−	2.86595i
$313$	22.5919	−	13.0434i	1.27697	−	0.737258i	0.300678	−	0.953726i	$-0.402787\pi$
$313$	22.5919	−	13.0434i	1.27697	−	0.737258i	0.976290	+	0.216468i	$0.0694537\pi$
$314$	4.55334	−	7.88662i	0.256960	−	0.445068i
$315$		0			0
$316$	−13.4810	−	23.3498i	−0.758365	−	1.31353i
$317$	−11.6837	+	6.74556i	−0.656220	+	0.378869i	−0.790835	−	0.612029i	$-0.790353\pi$
$317$	−11.6837	+	6.74556i	−0.656220	+	0.378869i	0.134615	+	0.990898i	$0.457020\pi$
$318$	−23.3395	+	13.4751i	−1.30882	+	0.755646i
$319$	−13.4065			−0.750621
$320$		0			0
$321$	25.9186	+	44.8923i	1.44663	+	2.50565i
$322$			11.5748i			0.645037i
$323$			11.3952i			0.634046i
$324$	45.8191	+	79.3609i	2.54550	+	4.40894i
$325$		0			0
$326$	4.05077	−	7.01615i	0.224352	−	0.388588i
$327$		−	10.8710i		−	0.601168i
$328$	−55.6171	−	32.1106i	−3.07094	−	1.77301i
$329$	2.50801	−	4.34401i	0.138271	−	0.239493i
$330$		0			0
$331$	−7.27021	−	12.5924i	−0.399607	−	0.692140i	0.594070	−	0.804413i	$-0.297520\pi$
$331$	−7.27021	−	12.5924i	−0.399607	−	0.692140i	−0.993677	+	0.112273i	$0.964187\pi$
$332$		−	30.1306i		−	1.65363i
$333$	−22.5610	+	37.3224i	−1.23633	+	2.04525i
$334$	−48.4499			−2.65106
$335$		0			0
$336$	−33.9101	+	58.7340i	−1.84995	+	3.20420i
$337$	−7.92779	−	4.57711i	−0.431854	−	0.249331i	0.268282	−	0.963340i	$-0.413544\pi$
$337$	−7.92779	−	4.57711i	−0.431854	−	0.249331i	−0.700136	+	0.714009i	$0.746877\pi$
$338$	−32.2498	−	18.6194i	−1.75416	−	1.01276i
$339$	26.7944			1.45527
$340$		0			0
$341$	19.8831			1.07673
$342$	76.3547	−	44.0834i	4.12879	−	2.38376i
$343$		−	10.4311i		−	0.563224i
$344$	−46.2504			−2.49365
$345$		0			0
$346$	−3.08429	+	5.34214i	−0.165812	+	0.287195i
$347$			17.6591i			0.947992i	0.880527	+	0.473996i	$0.157189\pi$
$347$			17.6591i			0.947992i	−0.880527	+	0.473996i	$0.842811\pi$
$348$	41.0449	−	23.6973i	2.20024	−	1.27031i
$349$	0.654317	+	1.13331i	0.0350248	+	0.0606647i	0.883006	−	0.469361i	$-0.155516\pi$
$349$	0.654317	+	1.13331i	0.0350248	+	0.0606647i	−0.847982	+	0.530026i	$0.822182\pi$
$350$		0			0
$351$	35.0149	−	60.6475i	1.86895	−	3.23712i
$352$	14.6406	+	8.45273i	0.780344	+	0.450532i
$353$	2.27191	−	1.31169i	0.120921	−	0.0698140i	−0.438319	−	0.898819i	$-0.644426\pi$
$353$	2.27191	−	1.31169i	0.120921	−	0.0698140i	0.559241	+	0.829005i	$0.311093\pi$
$354$	−14.0412	−	24.3200i	−0.746280	−	1.29259i
$355$		0			0
$356$	−1.74881			−0.0926865
$357$	−21.2825	−	12.2875i	−1.12639	−	0.650323i
$358$	15.8896	−	9.17386i	0.839791	−	0.484854i
$359$	13.8068			0.728696			0.364348	−	0.931263i	$-0.381292\pi$
$359$	13.8068			0.728696			0.364348	+	0.931263i	$0.381292\pi$
$360$		0			0
$361$	−2.34076	−	4.05431i	−0.123198	−	0.213385i
$362$		−	7.24636i		−	0.380860i
$363$	−12.8445	−	7.41579i	−0.674163	−	0.389228i
$364$	76.0110			3.98406
$365$		0			0
$366$	5.31085	−	9.19867i	0.277603	−	0.480822i
$367$	16.4400	+	9.49165i	0.858162	+	0.495460i	0.863396	−	0.504526i	$-0.168333\pi$
$367$	16.4400	+	9.49165i	0.858162	+	0.495460i	−0.00523415	+	0.999986i	$0.501666\pi$
$368$	−7.78939	+	4.49721i	−0.406050	+	0.234433i
$369$	−76.3802			−3.97619
$370$		0			0
$371$	−11.0060			−0.571403
$372$	−60.8733	+	35.1452i	−3.15613	+	1.82219i
$373$	−1.88023	−	1.08555i	−0.0973546	−	0.0562077i	0.450532	−	0.892760i	$-0.351234\pi$
$373$	−1.88023	−	1.08555i	−0.0973546	−	0.0562077i	−0.547887	+	0.836552i	$0.684568\pi$
$374$	−11.7046	+	20.2730i	−0.605231	+	1.04829i
$375$		0			0
$376$	9.18829			0.473850
$377$	−15.4562	−	8.92366i	−0.796036	−	0.459592i
$378$			110.581i			5.68765i
$379$	−0.494841	−	0.857090i	−0.0254183	−	0.0440258i	0.853036	−	0.521851i	$-0.174758\pi$
$379$	−0.494841	−	0.857090i	−0.0254183	−	0.0440258i	−0.878455	+	0.477826i	$0.841425\pi$
$380$		0			0
$381$	−50.3476			−2.57938
$382$	−29.5938	+	17.0860i	−1.51415	+	0.874194i
$383$	26.9279	+	15.5468i	1.37595	+	0.794406i	0.991669	−	0.128809i	$-0.0411155\pi$
$383$	26.9279	+	15.5468i	1.37595	+	0.794406i	0.384283	+	0.923215i	$0.374449\pi$
$384$	44.3879			2.26516
$385$		0			0
$386$	−28.9724	−	50.1817i	−1.47466	−	2.55418i
$387$	−47.6375	+	27.5035i	−2.42155	+	1.39808i
$388$	46.3366	+	26.7525i	2.35239	+	1.35815i
$389$	−6.21022	+	10.7564i	−0.314871	+	0.545372i	−0.979410	−	0.201881i	$-0.935294\pi$
$389$	−6.21022	+	10.7564i	−0.314871	+	0.545372i	0.664539	+	0.747253i	$0.268628\pi$
$390$		0			0
$391$	−1.62959	−	2.82253i	−0.0824117	−	0.142741i
$392$	−19.9973	+	11.5454i	−1.01001	+	0.583132i
$393$		−	37.2042i		−	1.87670i
$394$	−24.6221	+	42.6467i	−1.24044	+	2.14851i
$395$		0			0
$396$	124.393			6.25100
$397$		−	16.4105i		−	0.823621i	−0.911270	−	0.411810i	$-0.864897\pi$
$397$		−	16.4105i		−	0.823621i	0.911270	−	0.411810i	$-0.135103\pi$
$398$	−16.3278	+	9.42684i	−0.818437	+	0.472525i
$399$	51.0717			2.55678
$400$		0			0
$401$	−11.1247			−0.555541			−0.277770	−	0.960647i	$-0.589595\pi$
$401$	−11.1247			−0.555541			−0.277770	+	0.960647i	$0.589595\pi$
$402$	−89.3851	−	51.6065i	−4.45812	−	2.57390i
$403$	22.9230	+	13.2346i	1.14187	+	0.659261i
$404$	−15.2060	+	26.3375i	−0.756526	+	1.31034i
$405$		0			0
$406$	28.1818			1.39864
$407$	11.6105	+	21.0779i	0.575509	+	1.04479i
$408$		−	45.0161i		−	2.22863i
$409$	1.44084	+	2.49562i	0.0712452	+	0.123400i	0.899447	−	0.437029i	$-0.143969\pi$
$409$	1.44084	+	2.49562i	0.0712452	+	0.123400i	−0.828202	+	0.560430i	$0.810636\pi$
$410$		0			0
$411$	2.35935	−	4.08651i	0.116378	−	0.201573i
$412$	−11.7967	−	6.81085i	−0.581183	−	0.335546i
$413$		−	11.4684i		−	0.564321i
$414$	−12.6084	+	21.8384i	−0.619670	+	1.07330i
$415$		0			0
$416$	11.2526	+	19.4901i	0.551705	+	0.955582i
$417$			57.3301i			2.80746i
$418$		−	48.6491i		−	2.37950i
$419$	−8.67351	−	15.0230i	−0.423729	−	0.733920i	0.572572	−	0.819854i	$-0.305946\pi$
$419$	−8.67351	−	15.0230i	−0.423729	−	0.733920i	−0.996301	+	0.0859347i	$0.972612\pi$
$420$		0			0
$421$	9.78275			0.476782			0.238391	−	0.971169i	$-0.423380\pi$
$421$	9.78275			0.476782			0.238391	+	0.971169i	$0.423380\pi$
$422$	23.8257	−	13.7558i	1.15982	−	0.669621i
$423$	9.46386	−	5.46396i	0.460148	−	0.265667i
$424$	−10.0803	−	17.4596i	−0.489544	−	0.847915i
$425$		0			0
$426$	−29.3451	+	50.8272i	−1.42178	+	2.46259i
$427$	3.75658	−	2.16886i	0.181794	−	0.104959i
$428$	−61.7372	+	35.6440i	−2.98418	+	1.72292i
$429$	−33.2215	−	57.5413i	−1.60395	−	2.77812i
$430$		0			0
$431$	15.5866	−	26.9968i	0.750779	−	1.30039i	−0.196666	−	0.980470i	$-0.563012\pi$
$431$	15.5866	−	26.9968i	0.750779	−	1.30039i	0.947445	−	0.319917i	$-0.103655\pi$
$432$	−74.4166	+	42.9644i	−3.58037	+	2.06713i
$433$		−	5.35722i		−	0.257452i	−0.991680	−	0.128726i	$-0.958911\pi$
$433$		−	5.35722i		−	0.257452i	0.991680	−	0.128726i	$-0.0410887\pi$
$434$	−41.7962			−2.00628
$435$		0			0
$436$	14.9501			0.715981
$437$	5.86577	+	3.38661i	0.280598	+	0.162003i
$438$			70.1351i			3.35118i
$439$	−10.1150	+	17.5196i	−0.482760	+	0.836165i	−0.999804	−	0.0197936i	$-0.993699\pi$
$439$	−10.1150	+	17.5196i	−0.482760	+	0.836165i	0.517044	+	0.855959i	$0.327032\pi$
$440$		0			0
$441$	−13.7313	+	23.7834i	−0.653873	+	1.13254i
$442$	−26.9882	+	15.5817i	−1.28370	+	0.741144i
$443$			18.5787i			0.882703i	0.897334	+	0.441351i	$0.145501\pi$
$443$			18.5787i			0.882703i	−0.897334	+	0.441351i	$0.854499\pi$
$444$	−72.8034	−	44.0088i	−3.45510	−	2.08857i
$445$		0			0
$446$	−26.9039	−	46.5989i	−1.27394	−	2.20652i
$447$	−6.21190	−	3.58644i	−0.293813	−	0.169633i
$448$	6.05950	+	3.49845i	0.286284	+	0.165286i
$449$	−11.1689	+	19.3452i	−0.527095	+	0.912955i	0.472406	+	0.881381i	$0.343385\pi$
$449$	−11.1689	+	19.3452i	−0.527095	+	0.912955i	−0.999501	+	0.0315744i	$0.989948\pi$
$450$		0			0
$451$	−21.0727	+	36.4990i	−0.992274	+	1.71867i
$452$			36.8484i			1.73320i
$453$	−40.6167	+	23.4501i	−1.90834	+	1.10178i
$454$	−19.3133			−0.906419
$455$		0			0
$456$	46.7762	+	81.0188i	2.19050	+	3.79405i
$457$	20.9238	+	12.0804i	0.978774	+	0.565095i	0.901900	−	0.431946i	$-0.142173\pi$
$457$	20.9238	+	12.0804i	0.978774	+	0.565095i	0.0768740	+	0.997041i	$0.475506\pi$
$458$			4.16833i			0.194773i
$459$	−15.5684	−	26.9652i	−0.726670	−	1.25863i
$460$		0			0
$461$	12.1756	+	21.0887i	0.567074	+	0.982201i	0.996853	+	0.0792671i	$0.0252580\pi$
$461$	12.1756	+	21.0887i	0.567074	+	0.982201i	−0.429779	+	0.902934i	$0.641409\pi$
$462$	90.8607	+	52.4584i	4.22722	+	2.44059i
$463$	20.7166	+	11.9607i	0.962782	+	0.555862i	0.897028	−	0.441974i	$-0.145721\pi$
$463$	20.7166	+	11.9607i	0.962782	+	0.555862i	0.0657538	+	0.997836i	$0.479055\pi$
$464$	10.9496	+	18.9653i	0.508324	+	0.880443i
$465$		0			0
$466$	19.7234	+	34.1619i	0.913669	+	1.58252i
$467$			32.3520i			1.49707i	0.663093	+	0.748537i	$0.269243\pi$
$467$			32.3520i			1.49707i	−0.663093	+	0.748537i	$0.730757\pi$
$468$	143.412	+	82.7988i	6.62921	+	3.82738i
$469$	−21.0752	−	36.5034i	−0.973164	−	1.68557i
$470$		0			0
$471$	11.4925			0.529545
$472$	18.1931	−	10.5038i	0.837405	−	0.483476i
$473$			30.3520i			1.39559i
$474$	24.7713	−	42.9051i	1.13778	−	1.97069i
$475$		0			0
$476$	16.8981	−	29.2684i	0.774523	−	1.34151i
$477$	−20.7653	−	11.9888i	−0.950777	−	0.548931i
$478$	13.4861	+	7.78622i	0.616842	+	0.356134i
$479$	−1.10970	−	1.92206i	−0.0507036	−	0.0878212i	0.839560	−	0.543267i	$-0.182813\pi$
$479$	−1.10970	−	1.92206i	−0.0507036	−	0.0878212i	−0.890263	+	0.455446i	$0.849480\pi$
$480$		0			0
$481$	−0.644336	+	32.0287i	−0.0293792	+	1.46038i
$482$			8.24207i			0.375416i
$483$	−12.6502	+	7.30358i	−0.575603	+	0.332324i
$484$	10.1984	−	17.6641i	0.463564	−	0.802916i
$485$		0			0
$486$	−33.7902	+	58.5263i	−1.53275	+	2.65481i
$487$		−	33.1214i		−	1.50087i	−0.660942	−	0.750437i	$-0.729843\pi$
$487$		−	33.1214i		−	1.50087i	0.660942	−	0.750437i	$-0.270157\pi$
$488$	6.88125	+	3.97289i	0.311500	+	0.179844i
$489$	10.2240			0.462346
$490$		0			0
$491$	−23.9078			−1.07894			−0.539472	−	0.842003i	$-0.681376\pi$
$491$	−23.9078			−1.07894			−0.539472	+	0.842003i	$0.681376\pi$
$492$		−	148.992i		−	6.71708i
$493$	−6.87218	+	3.96766i	−0.309508	+	0.178694i
$494$	32.3818	−	56.0870i	1.45693	−	2.52347i
$495$		0			0
$496$	−16.2393	−	28.1273i	−0.729166	−	1.26295i
$497$	−20.7570	+	11.9841i	−0.931078	+	0.537558i
$498$	47.9473	−	27.6824i	2.14857	−	1.24048i
$499$	7.22843	−	12.5200i	0.323589	−	0.560472i	−0.657637	−	0.753335i	$-0.728444\pi$
$499$	7.22843	−	12.5200i	0.323589	−	0.560472i	0.981226	+	0.192863i	$0.0617772\pi$
$500$		0			0
$501$	−30.5714	−	52.9513i	−1.36583	−	2.36569i
$502$	−47.7664	+	27.5780i	−2.13192	+	1.23086i
$503$	18.0714	−	10.4336i	0.805766	−	0.465209i	−0.0397175	−	0.999211i	$-0.512646\pi$
$503$	18.0714	−	10.4336i	0.805766	−	0.465209i	0.845483	+	0.534002i	$0.179312\pi$
$504$	−142.239			−6.33583
$505$		0			0
$506$	6.95713	+	12.0501i	0.309282	+	0.535692i
$507$		−	46.9947i		−	2.08711i
$508$		−	69.2394i		−	3.07200i
$509$	4.07507	+	7.05823i	0.180624	+	0.312851i	0.942093	−	0.335351i	$-0.108855\pi$
$509$	4.07507	+	7.05823i	0.180624	+	0.312851i	−0.761469	+	0.648201i	$0.775521\pi$
$510$		0			0
$511$	−14.3210	+	24.8047i	−0.633523	+	1.09729i
$512$			50.2983i			2.22289i
$513$	56.0392	+	32.3542i	2.47419	+	1.42847i
$514$	12.1877	−	21.1098i	0.537578	−	0.931112i
$515$		0			0
$516$	−53.6501	−	92.9246i	−2.36181	−	4.09078i
$517$		−	6.02986i		−	0.265193i
$518$	−24.4064	−	44.3079i	−1.07235	−	1.94678i
$519$	−7.78463			−0.341707
$520$		0			0
$521$	14.6465	−	25.3684i	0.641673	−	1.11141i	−0.343386	−	0.939194i	$-0.611574\pi$
$521$	14.6465	−	25.3684i	0.641673	−	1.11141i	0.985059	−	0.172216i	$-0.0550926\pi$
$522$	53.1714	+	30.6985i	2.32725	+	1.34364i
$523$	11.8340	+	6.83238i	0.517466	+	0.298759i	0.735897	−	0.677093i	$-0.236761\pi$
$523$	11.8340	+	6.83238i	0.517466	+	0.298759i	−0.218431	+	0.975852i	$0.570094\pi$
$524$	51.1642			2.23512
$525$		0			0
$526$	78.6896			3.43103
$527$	10.1921	−	5.88439i	0.443973	−	0.256328i
$528$			81.5278i			3.54804i
$529$	21.0628			0.915773
$530$		0			0
$531$	12.4925	−	21.6376i	0.542128	−	0.938993i
$532$			70.2352i			3.04508i
$533$	−48.5890	+	28.0528i	−2.10462	+	1.21510i
$534$	−1.60671	−	2.78290i	−0.0695291	−	0.120428i
$535$		0			0
$536$	38.6053	−	66.8664i	1.66750	−	2.88819i
$537$	20.0524	+	11.5772i	0.865324	+	0.499595i
$538$	−12.6586	+	7.30845i	−0.545751	+	0.315089i
$539$	7.57673	+	13.1233i	0.326353	+	0.565260i
$540$		0			0
$541$	12.8675			0.553219			0.276609	−	0.960982i	$-0.410789\pi$
$541$	12.8675			0.553219			0.276609	+	0.960982i	$0.410789\pi$
$542$	−16.4241	−	9.48246i	−0.705476	−	0.407307i
$543$	7.91960	−	4.57238i	0.339863	−	0.196220i
$544$	10.0063			0.429018
$545$		0			0
$546$	69.8349	+	120.958i	2.98866	+	5.17650i
$547$		−	23.8649i		−	1.02039i	−0.860059	−	0.510194i	$-0.829574\pi$
$547$		−	23.8649i		−	1.02039i	0.860059	−	0.510194i	$-0.170426\pi$
$548$	5.61989	+	3.24464i	0.240070	+	0.138604i
$549$	9.45017			0.403323
$550$		0			0
$551$	8.24559	−	14.2818i	0.351274	−	0.608424i
$552$	−23.1724	−	13.3786i	−0.986283	−	0.569431i
$553$	17.5217	−	10.1162i	0.745099	−	0.430183i
$554$	48.1650			2.04633
$555$		0			0
$556$	−78.8419			−3.34364
$557$	27.8909	−	16.1028i	1.18178	−	0.682299i	0.225352	−	0.974277i	$-0.427647\pi$
$557$	27.8909	−	16.1028i	1.18178	−	0.682299i	0.956425	+	0.291978i	$0.0943135\pi$
$558$	−78.8579	−	45.5286i	−3.33832	−	1.92738i
$559$	−20.2029	+	34.9925i	−0.854493	+	1.48002i
$560$		0			0
$561$	−29.5420			−1.24726
$562$	−1.92706	−	1.11259i	−0.0812880	−	0.0469317i
$563$		−	7.68161i		−	0.323741i	−0.986812	−	0.161871i	$-0.948247\pi$
$563$		−	7.68161i		−	0.323741i	0.986812	−	0.161871i	$-0.0517528\pi$
$564$	10.6583	+	18.4608i	0.448797	+	0.777340i
$565$		0			0
$566$	72.0132			3.02694
$567$	−59.5526	+	34.3827i	−2.50097	+	1.44394i
$568$	−38.0224	−	21.9522i	−1.59538	−	0.921095i
$569$	27.5418			1.15461			0.577305	−	0.816528i	$-0.304104\pi$
$569$	27.5418			1.15461			0.577305	+	0.816528i	$0.304104\pi$
$570$		0			0
$571$	−8.40493	−	14.5578i	−0.351735	−	0.609224i	0.634818	−	0.772662i	$-0.281075\pi$
$571$	−8.40493	−	14.5578i	−0.351735	−	0.609224i	−0.986554	+	0.163438i	$0.947742\pi$
$572$	79.1324	−	45.6871i	3.30869	−	1.91027i
$573$	−37.3468	−	21.5622i	−1.56018	−	0.900773i
$574$	44.2969	−	76.7245i	1.84892	−	3.20242i
$575$		0			0
$576$	7.62173	+	13.2012i	0.317572	+	0.550051i
$577$	−8.14720	+	4.70379i	−0.339173	+	0.195821i	−0.659906	−	0.751348i	$-0.729404\pi$
$577$	−8.14720	+	4.70379i	−0.339173	+	0.195821i	0.320734	+	0.947169i	$0.396071\pi$
$578$		−	29.1026i		−	1.21051i
$579$	36.5627	−	63.3284i	1.51949	−	2.63184i
$580$		0			0
$581$	22.6100			0.938023
$582$			98.3150i			4.07529i
$583$	−11.4580	+	6.61526i	−0.474540	+	0.273976i
$584$	−52.4660			−2.17106
$585$		0			0
$586$	40.1372			1.65805
$587$	21.7905	+	12.5808i	0.899390	+	0.519263i	0.877002	−	0.480486i	$-0.159540\pi$
$587$	21.7905	+	12.5808i	0.899390	+	0.519263i	0.0223879	+	0.999749i	$0.492873\pi$
$588$	−46.3933	−	26.7852i	−1.91323	−	1.10460i
$589$	−12.2289	+	21.1811i	−0.503885	+	0.872754i
$590$		0			0
$591$	−62.1452			−2.55631
$592$	20.3349	−	33.6398i	0.835757	−	1.38259i
$593$			21.1331i			0.867832i	0.900953	+	0.433916i	$0.142869\pi$
$593$			21.1331i			0.867832i	−0.900953	+	0.433916i	$0.857131\pi$
$594$	66.4655	+	115.122i	2.72711	+	4.72349i
$595$		0			0
$596$	4.93218	−	8.54278i	0.202030	−	0.349926i
$597$	−20.6053	−	11.8965i	−0.843320	−	0.486891i
$598$			18.5232i			0.757471i
$599$	12.9166	−	22.3722i	0.527758	−	0.914104i	−0.471718	−	0.881749i	$-0.656366\pi$
$599$	12.9166	−	22.3722i	0.527758	−	0.914104i	0.999476	−	0.0323544i	$-0.0103005\pi$
$600$		0			0
$601$	−10.6619	−	18.4670i	−0.434909	−	0.753284i	0.562379	−	0.826879i	$-0.309886\pi$
$601$	−10.6619	−	18.4670i	−0.434909	−	0.753284i	−0.997288	+	0.0735952i	$0.976553\pi$
$602$		−	63.8030i		−	2.60041i
$603$		−	91.8290i		−	3.73957i
$604$	−32.2492	−	55.8572i	−1.31220	−	2.27280i
$605$		0			0
$606$	−55.8818			−2.27004
$607$	39.8850	−	23.0276i	1.61888	−	0.934661i	0.631671	−	0.775237i	$-0.282369\pi$
$607$	39.8850	−	23.0276i	1.61888	−	0.934661i	0.987210	−	0.159425i	$-0.0509639\pi$
$608$	−18.0091	+	10.3976i	−0.730367	+	0.421678i
$609$	17.7825	+	30.8002i	0.720583	+	1.24809i
$610$		0			0
$611$	4.01360	−	6.95176i	0.162373	−	0.281238i
$612$	63.7641	−	36.8142i	2.57751	−	1.48813i
$613$	30.7442	−	17.7502i	1.24175	−	0.716923i	0.272298	−	0.962213i	$-0.412216\pi$
$613$	30.7442	−	17.7502i	1.24175	−	0.716923i	0.969450	+	0.245290i	$0.0788831\pi$
$614$	41.0209	+	71.0502i	1.65547	+	2.86735i
$615$		0			0
$616$	−39.2426	+	67.9702i	−1.58113	+	2.73860i
$617$	26.4056	−	15.2453i	1.06305	−	0.613752i	0.136776	−	0.990602i	$-0.456326\pi$
$617$	26.4056	−	15.2453i	1.06305	−	0.613752i	0.926274	+	0.376850i	$0.122993\pi$
$618$		−	25.0298i		−	1.00685i
$619$	6.95720			0.279633			0.139817	−	0.990177i	$-0.455349\pi$
$619$	6.95720			0.279633			0.139817	+	0.990177i	$0.455349\pi$
$620$		0			0
$621$	−18.5074			−0.742678
$622$	−50.4872	−	29.1488i	−2.02435	−	1.16876i
$623$		−	1.31231i		−	0.0525764i
$624$	−54.2666	+	93.9925i	−2.17240	+	3.76271i
$625$		0			0
$626$	−32.9604	+	57.0890i	−1.31736	+	2.28174i
$627$	53.1690	−	30.6971i	2.12336	−	1.22592i
$628$			15.8048i			0.630679i
$629$	12.1895	+	7.36844i	0.486029	+	0.293799i
$630$		0			0
$631$	−10.9367	−	18.9429i	−0.435384	−	0.754107i	0.561943	−	0.827176i	$-0.310054\pi$
$631$	−10.9367	−	18.9429i	−0.435384	−	0.754107i	−0.997327	+	0.0730691i	$0.976721\pi$
$632$	32.0960	+	18.5306i	1.27671	+	0.737110i
$633$	30.0676	+	17.3595i	1.19508	+	0.689979i
$634$	17.0459	−	29.5243i	0.676977	−	1.17256i
$635$		0			0
$636$	23.3862	−	40.5061i	0.927323	−	1.60617i
$637$			20.1729i			0.799280i
$638$	29.3391	−	16.9390i	1.16155	−	0.670620i
$639$	−52.2169			−2.06567
$640$		0			0
$641$	22.4003	+	38.7985i	0.884760	+	1.53245i	0.845988	+	0.533202i	$0.179011\pi$
$641$	22.4003	+	38.7985i	0.884760	+	1.53245i	0.0387721	+	0.999248i	$0.487655\pi$
$642$	−113.442	−	65.4956i	−4.47719	−	2.58490i
$643$			25.8107i			1.01787i	0.860804	+	0.508937i	$0.169962\pi$
$643$			25.8107i			1.01787i	−0.860804	+	0.508937i	$0.830038\pi$
$644$	−10.0441	−	17.3969i	−0.395792	−	0.685532i
$645$		0			0
$646$	−14.3977	−	24.9375i	−0.566469	−	0.981154i
$647$	15.2038	+	8.77792i	0.597723	+	0.345096i	0.768145	−	0.640276i	$-0.221180\pi$
$647$	15.2038	+	8.77792i	0.597723	+	0.345096i	−0.170422	+	0.985371i	$0.554513\pi$
$648$	−109.088	−	62.9818i	−4.28537	−	2.47416i
$649$	−6.89316	−	11.9393i	−0.270580	−	0.468659i
$650$		0			0
$651$	−26.3730	−	45.6794i	−1.03364	−	1.79032i
$652$			14.0603i			0.550645i
$653$	−4.88681	−	2.82140i	−0.191236	−	0.110410i	0.401325	−	0.915936i	$-0.368550\pi$
$653$	−4.88681	−	2.82140i	−0.191236	−	0.110410i	−0.592561	+	0.805526i	$0.701883\pi$
$654$	13.7354	+	23.7904i	0.537096	+	0.930277i
$655$		0			0
$656$	68.8436			2.68789
$657$	−54.0395	+	31.1997i	−2.10828	+	1.21722i
$658$			12.6754i			0.494137i
$659$	−6.60681	+	11.4433i	−0.257365	+	0.445769i	−0.965535	−	0.260273i	$-0.916188\pi$
$659$	−6.60681	+	11.4433i	−0.257365	+	0.445769i	0.708170	+	0.706042i	$0.249521\pi$
$660$		0			0
$661$	−17.6692	+	30.6039i	−0.687251	+	1.19035i	0.285473	+	0.958387i	$0.407849\pi$
$661$	−17.6692	+	30.6039i	−0.687251	+	1.19035i	−0.972724	+	0.231967i	$0.925484\pi$
$662$	31.8206	+	18.3716i	1.23674	+	0.714034i
$663$	−34.0587	−	19.6638i	−1.32273	−	0.763678i
$664$	20.7084	+	35.8680i	0.803641	+	1.39195i
$665$		0			0
$666$	2.21660	−	110.183i	0.0858914	−	4.26949i
$667$			4.71669i			0.182631i
$668$	72.8201	−	42.0427i	2.81749	−	1.62668i
$669$	33.9522	−	58.8070i	1.31267	−	2.27361i
$670$		0			0
$671$	2.60723	−	4.51585i	0.100651	−	0.174333i
$672$		−	44.8470i		−	1.73001i
$673$	6.88877	+	3.97723i	0.265543	+	0.153311i	0.626860	−	0.779132i	$-0.284340\pi$
$673$	6.88877	+	3.97723i	0.265543	+	0.153311i	−0.361318	+	0.932443i	$0.617673\pi$
$674$	23.1325			0.891029
$675$		0			0
$676$	64.6284			2.48571
$677$		−	1.18876i		−	0.0456878i	−0.999739	−	0.0228439i	$-0.992728\pi$
$677$		−	1.18876i		−	0.0456878i	0.999739	−	0.0228439i	$-0.00727207\pi$
$678$	−58.6375	+	33.8544i	−2.25196	+	1.30017i
$679$	−20.0751	+	34.7711i	−0.770411	+	1.33439i
$680$		0			0
$681$	−12.1865	−	21.1077i	−0.466989	−	0.808848i
$682$	−43.5126	+	25.1220i	−1.66618	+	0.961970i
$683$	14.7598	−	8.52157i	0.564768	−	0.326069i	−0.190289	−	0.981728i	$-0.560943\pi$
$683$	14.7598	−	8.52157i	0.564768	−	0.326069i	0.755057	+	0.655659i	$0.227609\pi$
$684$	−76.5073	+	132.514i	−2.92533	+	5.06682i
$685$		0			0
$686$	13.1795	+	22.8276i	0.503195	+	0.871560i
$687$	−4.55560	+	2.63018i	−0.173807	+	0.100348i
$688$	42.9370	−	24.7897i	1.63696	−	0.945098i
$689$	−17.6130			−0.671002
$690$		0			0
$691$	25.5042	+	44.1745i	0.970224	+	1.68048i	0.694873	+	0.719133i	$0.255461\pi$
$691$	25.5042	+	44.1745i	0.970224	+	1.68048i	0.275351	+	0.961344i	$0.411206\pi$
$692$		−	10.7056i		−	0.406967i
$693$			93.3450i			3.54588i
$694$	−22.3121	−	38.6456i	−0.846955	−	1.46697i
$695$		0			0
$696$	−32.5737	+	56.4193i	−1.23470	+	2.13857i
$697$			24.9458i			0.944891i
$698$	−2.86384	−	1.65344i	−0.108398	−	0.0625837i
$699$	−24.8906	+	43.1117i	−0.941448	+	1.63064i
$700$		0			0
$701$	−15.8614	−	27.4728i	−0.599077	−	1.03763i	−0.992958	−	0.118470i	$-0.962201\pi$
$701$	−15.8614	−	27.4728i	−0.599077	−	1.03763i	0.393881	−	0.919162i	$-0.371132\pi$
$702$			176.963i			6.67905i
$703$	−29.5950	−	0.595376i	−1.11619	−	0.0224550i
$704$	8.41111			0.317006
$705$		0			0
$706$	−3.31459	+	5.74105i	−0.124746	+	0.216067i
$707$	−19.7637	−	11.4106i	−0.743291	−	0.429139i
$708$	42.2077	+	24.3686i	1.58626	+	0.915829i
$709$	−26.0768			−0.979335			−0.489667	−	0.871909i	$-0.662882\pi$
$709$	−26.0768			−0.979335			−0.489667	+	0.871909i	$0.662882\pi$
$710$		0			0
$711$	44.0782			1.65306
$712$	2.08181	−	1.20193i	0.0780191	−	0.0450443i
$713$		−	6.99527i		−	0.261975i
$714$	62.1003			2.32404
$715$		0			0
$716$	−15.9213	+	27.5766i	−0.595009	+	1.03059i
$717$			19.6521i			0.733923i
$718$	−30.2152	+	17.4447i	−1.12762	+	0.651032i
$719$	7.49339	+	12.9789i	0.279456	+	0.484033i	0.971250	−	0.238063i	$-0.0765124\pi$
$719$	7.49339	+	12.9789i	0.279456	+	0.484033i	−0.691793	+	0.722096i	$0.743179\pi$
$720$		0			0
$721$	5.11087	−	8.85228i	0.190339	−	0.329676i
$722$	10.2451	+	5.91503i	0.381284	+	0.220135i
$723$	−9.00782	+	5.20067i	−0.335005	+	0.193415i
$724$	6.28807	+	10.8913i	0.233694	+	0.404770i
$725$		0			0
$726$	37.4790			1.39098
$727$	7.40937	+	4.27780i	0.274798	+	0.158655i	0.631066	−	0.775729i	$-0.282618\pi$
$727$	7.40937	+	4.27780i	0.274798	+	0.158655i	−0.356268	+	0.934384i	$0.615951\pi$
$728$	−90.4848	+	52.2414i	−3.35359	+	1.93620i
$729$	−22.5994			−0.837016
$730$		0			0
$731$	8.98267	+	15.5584i	0.332236	+	0.575450i
$732$			18.4341i			0.681344i
$733$	7.19360	+	4.15323i	0.265702	+	0.153403i	0.626933	−	0.779073i	$-0.284310\pi$
$733$	7.19360	+	4.15323i	0.265702	+	0.153403i	−0.361231	+	0.932476i	$0.617643\pi$
$734$	−47.9703			−1.77062
$735$		0			0
$736$	2.97384	−	5.15084i	0.109617	−	0.189863i
$737$	−43.8814	−	25.3349i	−1.61639	−	0.933224i
$738$	167.152	−	96.5053i	6.15295	−	3.55241i
$739$	9.63201			0.354319			0.177160	−	0.984182i	$-0.443309\pi$
$739$	9.63201			0.354319			0.177160	+	0.984182i	$0.443309\pi$
$740$		0			0
$741$	81.7305			3.00245
$742$	24.0858	−	13.9059i	0.884217	−	0.510503i
$743$	−41.3080	−	23.8492i	−1.51544	−	0.874943i	−0.999836	−	0.0181186i	$-0.994232\pi$
$743$	−41.3080	−	23.8492i	−1.51544	−	0.874943i	−0.515609	−	0.856824i	$-0.672434\pi$
$744$	48.3097	−	83.6749i	1.77112	−	3.06767i
$745$		0			0
$746$	5.48632			0.200868
$747$	42.6589	+	24.6291i	1.56081	+	0.901133i
$748$		−	40.6270i		−	1.48547i
$749$	−26.7473	−	46.3277i	−0.977325	−	1.69278i
$750$		0			0
$751$	−19.8275			−0.723516			−0.361758	−	0.932272i	$-0.617823\pi$
$751$	−19.8275			−0.723516			−0.361758	+	0.932272i	$0.617823\pi$
$752$	−8.53005	+	4.92482i	−0.311059	+	0.179590i
$753$	−60.2803	−	34.8029i	−2.19674	−	1.26829i
$754$	45.0997			1.64243
$755$		0			0
$756$	−95.9570	−	166.202i	−3.48992	−	6.04472i
$757$	−0.467883	+	0.270133i	−0.0170055	+	0.00981813i	−0.508479	−	0.861075i	$-0.669792\pi$
$757$	−0.467883	+	0.270133i	−0.0170055	+	0.00981813i	0.491473	+	0.870893i	$0.336459\pi$
$758$	2.16584	+	1.25045i	0.0786670	+	0.0454184i
$759$	−8.77976	+	15.2070i	−0.318685	+	0.551979i
$760$		0			0
$761$	7.62909	+	13.2140i	0.276554	+	0.479006i	0.970526	−	0.240996i	$-0.0774741\pi$
$761$	7.62909	+	13.2140i	0.276554	+	0.479006i	−0.693972	+	0.720002i	$0.744141\pi$
$762$	110.182	−	63.6135i	3.99146	−	2.30447i
$763$			11.2186i			0.406140i
$764$	29.6529	−	51.3603i	1.07280	−	1.85815i
$765$		0			0
$766$	−78.5729			−2.83895
$767$		−	18.3529i		−	0.662686i
$768$	−85.3960	+	49.3034i	−3.08146	+	1.77908i
$769$	18.7357			0.675628			0.337814	−	0.941213i	$-0.390312\pi$
$769$	18.7357			0.675628			0.337814	+	0.941213i	$0.390312\pi$
$770$		0			0
$771$	30.7614			1.10784
$772$	87.0909	+	50.2820i	3.13447	+	1.80969i
$773$	−8.27644	−	4.77841i	−0.297683	−	0.171867i	0.343719	−	0.939073i	$-0.388313\pi$
$773$	−8.27644	−	4.77841i	−0.297683	−	0.171867i	−0.641401	+	0.767205i	$0.721647\pi$
$774$	69.5006	−	120.379i	2.49815	−	4.32692i
$775$		0			0
$776$	−73.5466			−2.64017
$777$	33.0243	−	54.6318i	1.18474	−	1.95990i
$778$		−	31.3861i		−	1.12525i
$779$	−25.9212	−	44.8969i	−0.928724	−	1.60860i
$780$		0			0
$781$	−14.4062	+	24.9524i	−0.515496	+	0.892865i
$782$	7.13245	+	4.11792i	0.255056	+	0.147257i
$783$			45.0612i			1.61036i
$784$	12.3764	−	21.4366i	0.442016	−	0.765594i
$785$		0			0
$786$	47.0070	+	81.4185i	1.67668	+	2.90410i
$787$		−	9.16265i		−	0.326613i	−0.986575	−	0.163307i	$-0.947784\pi$
$787$		−	9.16265i		−	0.326613i	0.986575	−	0.163307i	$-0.0522160\pi$
$788$		−	85.4638i		−	3.04452i
$789$	49.6524	+	86.0005i	1.76767	+	3.06170i
$790$		0			0
$791$	−27.6511			−0.983160
$792$	−148.080	+	85.4940i	−5.26179	+	3.03790i
$793$	6.01169	−	3.47085i	0.213481	−	0.123254i
$794$	20.7345	+	35.9132i	0.735839	+	1.27451i
$795$		0			0
$796$	16.3604	−	28.3370i	0.579879	−	1.00438i
$797$	25.6810	−	14.8269i	0.909668	−	0.525197i	0.0293436	−	0.999569i	$-0.490658\pi$
$797$	25.6810	−	14.8269i	0.909668	−	0.525197i	0.880324	+	0.474372i	$0.157325\pi$
$798$	−111.766	+	64.5284i	−3.95649	+	2.28428i
$799$	−1.78454	−	3.09091i	−0.0631323	−	0.109348i
$800$		0			0
$801$	1.42950	−	2.47596i	0.0505088	−	0.0874837i
$802$	24.3455	−	14.0559i	0.859671	−	0.496331i
$803$			34.4310i			1.21505i
$804$	179.127			6.31734
$805$		0			0
$806$	−66.8869			−2.35599
$807$	−15.9749	−	9.22312i	−0.562344	−	0.324669i
$808$		−	41.8035i		−	1.47064i
$809$	−12.0874	+	20.9361i	−0.424972	+	0.736073i	−0.996418	−	0.0845668i	$-0.973049\pi$
$809$	−12.0874	+	20.9361i	−0.424972	+	0.736073i	0.571446	+	0.820640i	$0.306383\pi$
$810$		0			0
$811$	23.9012	−	41.3981i	0.839285	−	1.45368i	−0.0512077	−	0.998688i	$-0.516307\pi$
$811$	23.9012	−	41.3981i	0.839285	−	1.45368i	0.890493	−	0.454997i	$-0.150360\pi$
$812$	−42.3573	+	24.4550i	−1.48645	+	0.858201i
$813$		−	23.9334i		−	0.839381i
$814$	−52.0403	−	31.4578i	−1.82401	−	1.10259i
$815$		0			0
$816$	24.1281	+	41.7912i	0.844654	+	1.46298i
$817$	−32.3336	−	18.6678i	−1.13121	−	0.653103i
$818$	−6.30635	−	3.64097i	−0.220496	−	0.127304i
$819$	−62.1324	+	107.616i	−2.17108	+	3.76042i
$820$		0			0
$821$	24.6636	−	42.7186i	0.860766	−	1.49089i	−0.0104240	−	0.999946i	$-0.503318\pi$
$821$	24.6636	−	42.7186i	0.860766	−	1.49089i	0.871190	−	0.490945i	$-0.163349\pi$
$822$			11.9240i			0.415898i
$823$	19.8372	−	11.4530i	0.691483	−	0.399228i	−0.112684	−	0.993631i	$-0.535945\pi$
$823$	19.8372	−	11.4530i	0.691483	−	0.399228i	0.804167	+	0.594403i	$0.202612\pi$
$824$	18.7240			0.652283
$825$		0			0
$826$	14.4901	+	25.0976i	0.504176	+	0.873258i
$827$	29.9270	+	17.2783i	1.04066	+	0.600827i	0.920021	−	0.391870i	$-0.128172\pi$
$827$	29.9270	+	17.2783i	1.04066	+	0.600827i	0.120641	+	0.992696i	$0.461505\pi$
$828$		−	43.7641i		−	1.52091i
$829$	−14.3873	−	24.9195i	−0.499690	−	0.865489i	0.500310	−	0.865847i	$-0.333220\pi$
$829$	−14.3873	−	24.9195i	−0.499690	−	0.865489i	−1.00000		0.000357485i	$0.999886\pi$
$830$		0			0
$831$	30.3917	+	52.6399i	1.05428	+	1.82606i
$832$	9.69708	+	5.59861i	0.336186	+	0.194097i
$833$	7.76767	+	4.48467i	0.269134	+	0.155384i
$834$	−72.4358	−	125.462i	−2.50824	−	4.34441i
$835$		0			0
$836$	42.2155	+	73.1194i	1.46005	+	2.52889i
$837$		−	66.8298i		−	2.30998i
$838$	37.9626	+	21.9177i	1.31140	+	0.757135i
$839$	−21.2799	−	36.8579i	−0.734664	−	1.27247i	−0.954871	−	0.297022i	$-0.904007\pi$
$839$	−21.2799	−	36.8579i	−0.734664	−	1.27247i	0.220207	−	0.975453i	$-0.429327\pi$
$840$		0			0
$841$	−17.5160			−0.604000
$842$	−21.4088	+	12.3604i	−0.737796	+	0.425967i
$843$		−	2.80813i		−	0.0967171i
$844$	−23.8733	+	41.3498i	−0.821753	+	1.42332i
$845$		0			0
$846$	−13.8073	+	23.9149i	−0.474704	+	0.822212i
$847$	13.2552	+	7.65290i	0.455454	+	0.262957i
$848$	18.7163	+	10.8059i	0.642722	+	0.371076i
$849$	45.4397	+	78.7038i	1.55949	+	2.70111i
$850$		0			0
$851$	7.41564	−	4.08480i	0.254205	−	0.140025i
$852$		−	101.858i		−	3.48959i
$853$	−40.6051	+	23.4434i	−1.39029	+	0.802686i	−0.993347	−	0.115156i	$-0.963263\pi$
$853$	−40.6051	+	23.4434i	−1.39029	+	0.802686i	−0.396946	+	0.917842i	$0.629930\pi$
$854$	−5.48066	+	9.49278i	−0.187544	+	0.324836i
$855$		0			0
$856$	48.9953	−	84.8624i	1.67463	−	2.90054i
$857$		−	50.9300i		−	1.73973i	−0.493286	−	0.869867i	$-0.664204\pi$
$857$		−	50.9300i		−	1.73973i	0.493286	−	0.869867i	$-0.335796\pi$
$858$	145.405	+	83.9498i	4.96405	+	2.86600i
$859$	−39.3751			−1.34346			−0.671730	−	0.740796i	$-0.734449\pi$
$859$	−39.3751			−1.34346			−0.671730	+	0.740796i	$0.734449\pi$
$860$		0			0
$861$	111.804			3.81026
$862$			78.7737i			2.68304i
$863$	−43.3369	+	25.0206i	−1.47520	+	0.851709i	−0.999609	−	0.0279549i	$-0.991101\pi$
$863$	−43.3369	+	25.0206i	−1.47520	+	0.851709i	−0.475595	+	0.879664i	$0.657767\pi$
$864$	28.4108	−	49.2090i	0.966556	−	1.67412i
$865$		0			0
$866$	6.76878	+	11.7239i	0.230013	+	0.398393i
$867$	31.8065	−	18.3635i	1.08021	−	0.623657i
$868$	62.8196	−	36.2689i	2.13224	−	1.23105i
$869$	12.1608	−	21.0632i	0.412528	−	0.714519i
$870$		0			0
$871$	−33.7269	−	58.4167i	−1.14279	−	1.97937i
$872$	−17.7969	+	10.2750i	−0.602678	+	0.347956i
$873$	−75.7523	+	43.7356i	−2.56383	+	1.48023i
$874$	−17.1157			−0.578948
$875$		0			0
$876$	−60.8601	−	105.413i	−2.05627	−	3.56157i
$877$			22.1624i			0.748371i	0.927354	+	0.374186i	$0.122078\pi$
$877$			22.1624i			0.748371i	−0.927354	+	0.374186i	$0.877922\pi$
$878$		−	51.1204i		−	1.72523i
$879$	25.3262	+	43.8662i	0.854231	+	1.47957i
$880$		0			0
$881$	−5.02013	+	8.69512i	−0.169132	+	0.292946i	−0.938115	−	0.346324i	$-0.887430\pi$
$881$	−5.02013	+	8.69512i	−0.169132	+	0.292946i	0.768983	+	0.639270i	$0.220763\pi$
$882$		−	69.3974i		−	2.33673i
$883$	−12.2437	−	7.06890i	−0.412033	−	0.237887i	0.279630	−	0.960108i	$-0.409788\pi$
$883$	−12.2437	−	7.06890i	−0.412033	−	0.237887i	−0.691663	+	0.722220i	$0.743122\pi$
$884$	27.0422	−	46.8384i	0.909527	−	1.57535i
$885$		0			0
$886$	−23.4740	−	40.6581i	−0.788624	−	1.36594i
$887$			1.07996i			0.0362614i	0.999836	+	0.0181307i	$0.00577150\pi$
$887$			1.07996i			0.0362614i	−0.999836	+	0.0181307i	$0.994229\pi$
$888$	116.913	+	2.35200i	3.92335	+	0.0789279i
$889$	51.9573			1.74259
$890$		0			0
$891$	−41.3321	+	71.5892i	−1.38468	+	2.39833i
$892$	80.8730	+	46.6921i	2.70783	+	1.56337i
$893$	6.42352	+	3.70862i	0.214955	+	0.124104i
$894$	18.1257			0.606214
$895$		0			0
$896$	−45.8071			−1.53031
$897$	−20.2442	+	11.6880i	−0.675934	+	0.390251i
$898$		−	56.4472i		−	1.88367i
$899$	−17.0318			−0.568043
$900$		0			0
$901$	−3.91557	+	6.78196i	−0.130447	+	0.225940i
$902$		−	106.500i		−	3.54607i
$903$	69.7308	−	40.2591i	2.32049	−	1.33974i
$904$	−25.3255	−	43.8650i	−0.842312	−	1.45893i
$905$		0			0
$906$	59.2577	−	102.637i	1.96870	−	3.40990i
$907$	−42.8975	−	24.7669i	−1.42439	−	0.822370i	−0.427717	−	0.903913i	$-0.640682\pi$
$907$	−42.8975	−	24.7669i	−1.42439	−	0.822370i	−0.996670	+	0.0815429i	$0.974015\pi$
$908$	29.0279	−	16.7593i	0.963324	−	0.556175i
$909$	−24.8591	−	43.0573i	−0.824525	−	1.42812i
$910$		0			0
$911$	−26.1259			−0.865588			−0.432794	−	0.901493i	$-0.642472\pi$
$911$	−26.1259			−0.865588			−0.432794	+	0.901493i	$0.642472\pi$
$912$	−86.8504	−	50.1431i	−2.87590	−	1.66040i
$913$	23.5385	−	13.5900i	0.779011	−	0.449762i
$914$	−61.0535			−2.01947
$915$		0			0
$916$	−3.61710	−	6.26499i	−0.119512	−	0.207001i
$917$			38.3937i			1.26787i
$918$	68.1404	+	39.3409i	2.24897	+	1.29844i
$919$	−36.0960			−1.19070			−0.595349	−	0.803467i	$-0.702986\pi$
$919$	−36.0960			−1.19070			−0.595349	+	0.803467i	$0.702986\pi$
$920$		0			0
$921$	−51.7676	+	89.6641i	−1.70580	+	2.95453i
$922$	−53.2907	−	30.7674i	−1.75504	−	1.01327i
$923$	−33.2176	+	19.1782i	−1.09337	+	0.631258i
$924$	−182.085			−5.99014
$925$		0			0
$926$	−60.4489			−1.98647
$927$	19.2856	−	11.1345i	0.633422	−	0.365706i
$928$	−12.5411	−	7.24060i	−0.411681	−	0.237684i
$929$	−6.34623	+	10.9920i	−0.208213	+	0.360635i	−0.951152	−	0.308724i	$-0.900098\pi$
$929$	−6.34623	+	10.9920i	−0.208213	+	0.360635i	0.742939	+	0.669359i	$0.233431\pi$
$930$		0			0
$931$	−18.6401			−0.610904
$932$	−59.2884	−	34.2302i	−1.94206	−	1.12125i
$933$		−	73.5704i		−	2.40859i
$934$	−40.8764	−	70.7999i	−1.33752	−	2.31664i
$935$		0			0
$936$	−227.626			−7.44020
$937$	−1.34475	+	0.776389i	−0.0439309	+	0.0253635i	−0.521805	−	0.853065i	$-0.674741\pi$
$937$	−1.34475	+	0.776389i	−0.0439309	+	0.0253635i	0.477874	+	0.878429i	$0.341408\pi$
$938$	92.2430	+	53.2565i	3.01184	+	1.73889i
$939$	−83.1908			−2.71483
$940$		0			0
$941$	14.7864	+	25.6108i	0.482023	+	0.834889i	0.999787	−	0.0206348i	$-0.00656872\pi$
$941$	14.7864	+	25.6108i	0.482023	+	0.834889i	−0.517764	+	0.855524i	$0.673235\pi$
$942$	−25.1504	+	14.5206i	−0.819444	+	0.473106i
$943$	12.8411	+	7.41380i	0.418163	+	0.241427i
$944$	−11.2598	+	19.5026i	−0.366477	+	0.634756i
$945$		0			0
$946$	−38.3494	−	66.4230i	−1.24684	−	2.15960i
$947$	12.6065	−	7.27836i	0.409656	−	0.236515i	−0.280986	−	0.959712i	$-0.590661\pi$
$947$	12.6065	−	7.27836i	0.409656	−	0.236515i	0.690642	+	0.723197i	$0.257328\pi$
$948$			85.9816i			2.79255i
$949$	−22.9180	+	39.6952i	−0.743950	+	1.28856i
$950$		0			0
$951$	43.0231			1.39512
$952$			46.4554i			1.50563i
$953$	44.5479	−	25.7197i	1.44305	−	0.833144i	0.444996	−	0.895532i	$-0.353205\pi$
$953$	44.5479	−	25.7197i	1.44305	−	0.833144i	0.998052	+	0.0623881i	$0.0198717\pi$
$954$	60.5910			1.96170
$955$		0			0
$956$	−27.0262			−0.874089
$957$	37.0254	+	21.3767i	1.19686	+	0.691009i
$958$	4.85700	+	2.80419i	0.156922	+	0.0905992i
$959$	−2.43479	+	4.21717i	−0.0786233	+	0.136180i
$960$		0			0
$961$	−5.74029			−0.185171
$962$	−39.0577	−	70.9064i	−1.25927	−	2.28611i
$963$		−	116.543i		−	3.75556i
$964$	−7.15211	−	12.3878i	−0.230354	−	0.398985i
$965$		0			0
$966$	18.4559	−	31.9666i	0.593810	−	1.02851i
$967$	−15.6312	−	9.02470i	−0.502667	−	0.290215i	0.227147	−	0.973860i	$-0.427060\pi$
$967$	−15.6312	−	9.02470i	−0.502667	−	0.290215i	−0.729814	+	0.683646i	$0.760393\pi$
$968$			28.0369i			0.901142i
$969$	18.1696	−	31.4707i	0.583692	−	1.01098i
$970$		0			0
$971$	−7.37261	−	12.7697i	−0.236598	−	0.409800i	0.723138	−	0.690704i	$-0.242699\pi$
$971$	−7.37261	−	12.7697i	−0.236598	−	0.409800i	−0.959736	+	0.280904i	$0.909366\pi$
$972$		−	117.287i		−	3.76197i
$973$		−	59.1631i		−	1.89668i
$974$	41.8484	+	72.4836i	1.34091	+	2.32252i
$975$		0			0
$976$	−8.51771			−0.272645
$977$	−25.3267	+	14.6224i	−0.810275	+	0.467812i	−0.847051	−	0.531511i	$-0.821624\pi$
$977$	−25.3267	+	14.6224i	−0.810275	+	0.467812i	0.0367767	+	0.999324i	$0.488291\pi$
$978$	−22.3744	+	12.9179i	−0.715456	+	0.413069i
$979$	−0.788774	−	1.36620i	−0.0252093	−	0.0436638i
$980$		0			0
$981$	−12.2204	+	21.1664i	−0.390168	+	0.675790i
$982$	52.3204	−	30.2072i	1.66961	−	0.963951i
$983$	46.1157	−	26.6249i	1.47086	−	0.849203i	0.471398	−	0.881920i	$-0.343749\pi$
$983$	46.1157	−	26.6249i	1.47086	−	0.849203i	0.999465	+	0.0327171i	$0.0104160\pi$
$984$	102.400	+	177.363i	3.26440	+	5.65411i
$985$		0			0
$986$	10.0262	−	17.3658i	0.319298	−	0.553041i
$987$	−13.8530	+	7.99804i	−0.440946	+	0.254580i
$988$			112.398i			3.57586i
$989$	10.6785			0.339555
$990$		0			0
$991$	9.92245			0.315197			0.157598	−	0.987503i	$-0.449625\pi$
$991$	9.92245			0.315197			0.157598	+	0.987503i	$0.449625\pi$
$992$	18.5996	+	10.7385i	0.590536	+	0.340946i
$993$			46.3693i			1.47149i
$994$	30.2834	−	52.4523i	0.960530	−	1.66369i
$995$		0			0
$996$	−48.0431	+	83.2131i	−1.52230	+	2.63671i
$997$	−41.8763	+	24.1773i	−1.32624	+	0.765703i	−0.984716	−	0.174170i	$-0.944276\pi$
$997$	−41.8763	+	24.1773i	−1.32624	+	0.765703i	−0.341522	+	0.939874i	$0.610942\pi$
$998$			36.5321i			1.15640i
$999$	70.8460	−	39.0244i	2.24147	−	1.23468i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.o.d.174.2		48
5.2	odd	4		925.2.e.d.26.2	✓	24
5.3	odd	4		925.2.e.e.26.11	yes	24
5.4	even	2	inner	925.2.o.d.174.23		48
37.10	even	3	inner	925.2.o.d.824.23		48
185.47	odd	12		925.2.e.d.676.2	yes	24
185.84	even	6	inner	925.2.o.d.824.2		48
185.158	odd	12		925.2.e.e.676.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.e.d.26.2	✓	24	5.2	odd	4
925.2.e.d.676.2	yes	24	185.47	odd	12
925.2.e.e.26.11	yes	24	5.3	odd	4
925.2.e.e.676.11	yes	24	185.158	odd	12
925.2.o.d.174.2		48	1.1	even	1	trivial
925.2.o.d.174.23		48	5.4	even	2	inner
925.2.o.d.824.2		48	185.84	even	6	inner
925.2.o.d.824.23		48	37.10	even	3	inner

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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.18842 + 1.26349i) q^{2} +(-2.76175 - 1.59450i) q^{3} +(2.19280 - 3.79803i) q^{4} +8.05850 q^{6} +(2.85005 + 1.64548i) q^{7} +6.02833i q^{8} +(3.58484 + 6.20912i) q^{9} +O(q^{10})\)	\(q+(-2.18842 + 1.26349i) q^{2} +(-2.76175 - 1.59450i) q^{3} +(2.19280 - 3.79803i) q^{4} +8.05850 q^{6} +(2.85005 + 1.64548i) q^{7} +6.02833i q^{8} +(3.58484 + 6.20912i) q^{9} +3.95612 q^{11} +(-12.1119 + 6.99281i) q^{12} +(4.56096 + 2.63327i) q^{13} -8.31616 q^{14} +(-3.23112 - 5.59646i) q^{16} +(2.02791 - 1.17081i) q^{17} +(-15.6903 - 9.05879i) q^{18} +(-2.43318 + 4.21440i) q^{19} +(-5.24742 - 9.08879i) q^{21} +(-8.65766 + 4.99850i) q^{22} -1.39184i q^{23} +(9.61215 - 16.6487i) q^{24} -13.3084 q^{26} -13.2971i q^{27} +(12.4992 - 7.21640i) q^{28} -3.38881 q^{29} +5.02590 q^{31} +(3.70074 + 2.13662i) q^{32} +(-10.9258 - 6.30802i) q^{33} +(-2.95861 + 5.12447i) q^{34} +31.4433 q^{36} +(2.93481 + 5.32793i) q^{37} -12.2972i q^{38} +(-8.39749 - 14.5449i) q^{39} +(-5.32661 + 9.22596i) q^{41} +(22.9671 + 13.2601i) q^{42} +7.67217i q^{43} +(8.67496 - 15.0255i) q^{44} +(1.75857 + 3.04594i) q^{46} -1.52419i q^{47} +20.6080i q^{48} +(1.91519 + 3.31721i) q^{49} -7.46743 q^{51} +(20.0025 - 11.5485i) q^{52} +(-2.89626 + 1.67216i) q^{53} +(16.8007 + 29.0996i) q^{54} +(-9.91948 + 17.1810i) q^{56} +(13.4397 - 7.75940i) q^{57} +(7.41614 - 4.28171i) q^{58} +(-1.74241 - 3.01793i) q^{59} +(0.659037 - 1.14149i) q^{61} +(-10.9988 + 6.35016i) q^{62} +23.5951i q^{63} +2.12610 q^{64} +31.8804 q^{66} +(-11.0920 - 6.40399i) q^{67} -10.2694i q^{68} +(-2.21929 + 3.84392i) q^{69} +(-3.64151 + 6.30728i) q^{71} +(-37.4306 + 21.6106i) q^{72} +8.70324i q^{73} +(-13.1544 - 7.95168i) q^{74} +(10.6709 + 18.4826i) q^{76} +(11.2751 + 6.50970i) q^{77} +(36.7545 + 21.2202i) q^{78} +(3.07393 - 5.32420i) q^{79} +(-10.4476 + 18.0958i) q^{81} -26.9204i q^{82} +(5.94990 - 3.43518i) q^{83} -46.0261 q^{84} +(-9.69368 - 16.7900i) q^{86} +(9.35904 + 5.40344i) q^{87} +23.8488i q^{88} +(-0.199381 - 0.345338i) q^{89} +(8.66599 + 15.0099i) q^{91} +(-5.28627 - 3.05203i) q^{92} +(-13.8803 - 8.01379i) q^{93} +(1.92579 + 3.33556i) q^{94} +(-6.81367 - 11.8016i) q^{96} +12.2002i q^{97} +(-8.38251 - 4.83964i) q^{98} +(14.1820 + 24.5640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 22 q^{4} + 20 q^{9}+O(q^{10}) \) 48 * q + 22 * q^4 + 20 * q^9	\( 48 q + 22 q^{4} + 20 q^{9} - 40 q^{14} - 26 q^{16} - 10 q^{19} - 12 q^{21} + 42 q^{24} - 40 q^{26} - 12 q^{29} + 76 q^{31} + 10 q^{34} - 4 q^{36} - 28 q^{39} - 26 q^{41} + 30 q^{44} - 26 q^{46} + 52 q^{49} - 92 q^{51} + 74 q^{54} + 14 q^{59} + 32 q^{61} - 40 q^{64} + 164 q^{66} - 42 q^{69} - 4 q^{71} - 96 q^{74} + 34 q^{76} + 42 q^{79} - 32 q^{81} - 152 q^{84} - 32 q^{86} - 58 q^{89} + 64 q^{91} + 26 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) \) 48 * q + 22 * q^4 + 20 * q^9 - 40 * q^14 - 26 * q^16 - 10 * q^19 - 12 * q^21 + 42 * q^24 - 40 * q^26 - 12 * q^29 + 76 * q^31 + 10 * q^34 - 4 * q^36 - 28 * q^39 - 26 * q^41 + 30 * q^44 - 26 * q^46 + 52 * q^49 - 92 * q^51 + 74 * q^54 + 14 * q^59 + 32 * q^61 - 40 * q^64 + 164 * q^66 - 42 * q^69 - 4 * q^71 - 96 * q^74 + 34 * q^76 + 42 * q^79 - 32 * q^81 - 152 * q^84 - 32 * q^86 - 58 * q^89 + 64 * q^91 + 26 * q^94 + 52 * q^96 + 30 * q^99

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