LMFDB - Embedded newform 600.2.m.c.299.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(299,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))

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

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

chi := DirichletCharacter("600.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.m (of order $2$, degree $1$, 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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} + 4x^{12} + 12x^{10} + 16x^{8} + 48x^{6} + 64x^{4} + 64x^{2} + 256 $ x^16 + x^14 + 4x^12 + 12x^10 + 16x^8 + 48x^6 + 64x^4 + 64x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			299.12
Root			$0.842022 + 1.13622i$ of defining polynomial
Character	$\chi$	$=$	600.299
Dual form			600.2.m.c.299.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.842022 + 1.13622i) q^{2} +(-0.218455 + 1.71822i) q^{3} +(-0.581998 + 1.91345i) q^{4} +(-2.13622 + 1.19857i) q^{6} +3.64426 q^{7} +(-2.66415 + 0.949886i) q^{8} +(-2.90455 - 0.750707i) q^{9} +O(q^{10})$	\(q+(0.842022 + 1.13622i) q^{2} +(-0.218455 + 1.71822i) q^{3} +(-0.581998 + 1.91345i) q^{4} +(-2.13622 + 1.19857i) q^{6} +3.64426 q^{7} +(-2.66415 + 0.949886i) q^{8} +(-2.90455 - 0.750707i) q^{9} +5.07403i q^{11} +(-3.16058 - 1.41800i) q^{12} +1.70594 q^{13} +(3.06855 + 4.14069i) q^{14} +(-3.32256 - 2.22724i) q^{16} -4.08117 q^{17} +(-1.59273 - 3.93233i) q^{18} +1.26422 q^{19} +(-0.796108 + 6.26164i) q^{21} +(-5.76522 + 4.27244i) q^{22} -4.70066i q^{23} +(-1.05011 - 4.78511i) q^{24} +(1.43644 + 1.93832i) q^{26} +(1.92439 - 4.82667i) q^{27} +(-2.12095 + 6.97311i) q^{28} -1.06377 q^{29} +4.86950i q^{31} +(-0.267024 - 5.65055i) q^{32} +(-8.71829 - 1.10845i) q^{33} +(-3.43644 - 4.63712i) q^{34} +(3.12688 - 5.12080i) q^{36} +7.56830 q^{37} +(1.06450 + 1.43644i) q^{38} +(-0.372671 + 2.93118i) q^{39} -1.50141i q^{41} +(-7.78495 + 4.36789i) q^{42} -3.43644i q^{43} +(-9.70888 - 2.95307i) q^{44} +(5.34099 - 3.95806i) q^{46} -10.9176i q^{47} +(4.55272 - 5.22233i) q^{48} +6.28066 q^{49} +(0.891553 - 7.01235i) q^{51} +(-0.992853 + 3.26422i) q^{52} +8.87288i q^{53} +(7.10454 - 1.87762i) q^{54} +(-9.70888 + 3.46163i) q^{56} +(-0.276176 + 2.17221i) q^{57} +(-0.895716 - 1.20868i) q^{58} +0.788328i q^{59} +0.627594i q^{61} +(-5.53283 + 4.10023i) q^{62} +(-10.5850 - 2.73578i) q^{63} +(6.19543 - 5.06128i) q^{64} +(-6.08155 - 10.8392i) q^{66} +4.18178i q^{67} +(2.37523 - 7.80911i) q^{68} +(8.07677 + 1.02688i) q^{69} +6.21689 q^{71} +(8.45127 - 0.758995i) q^{72} +4.21689i q^{73} +(6.37267 + 8.59926i) q^{74} +(-0.735776 + 2.41903i) q^{76} +18.4911i q^{77} +(-3.64426 + 2.04468i) q^{78} +0.992853i q^{79} +(7.87288 + 4.36094i) q^{81} +(1.70594 - 1.26422i) q^{82} +7.72544 q^{83} +(-11.5180 - 5.16757i) q^{84} +(3.90455 - 2.89356i) q^{86} +(0.232385 - 1.82779i) q^{87} +(-4.81975 - 13.5180i) q^{88} +11.5742i q^{89} +6.21689 q^{91} +(8.99447 + 2.73578i) q^{92} +(-8.36687 - 1.06377i) q^{93} +(12.4048 - 9.19282i) q^{94} +(9.76721 + 0.775585i) q^{96} -7.40133i q^{97} +(5.28845 + 7.13622i) q^{98} +(3.80911 - 14.7378i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{4} - 14 q^{6}+O(q^{10}) $ 16 * q - 2 * q^4 - 14 * q^6	$ 16 q - 2 q^{4} - 14 q^{6} - 12 q^{14} - 14 q^{16} + 8 q^{19} + 8 q^{21} - 18 q^{24} - 32 q^{26} - 38 q^{36} + 32 q^{39} - 60 q^{44} - 16 q^{46} + 32 q^{49} + 40 q^{51} + 30 q^{54} - 60 q^{56} - 50 q^{64} + 36 q^{66} + 40 q^{69} + 48 q^{71} + 64 q^{74} - 24 q^{76} + 16 q^{81} + 4 q^{84} + 16 q^{86} + 48 q^{91} + 80 q^{94} + 34 q^{96} - 32 q^{99}+O(q^{100}) $ 16 * q - 2 * q^4 - 14 * q^6 - 12 * q^14 - 14 * q^16 + 8 * q^19 + 8 * q^21 - 18 * q^24 - 32 * q^26 - 38 * q^36 + 32 * q^39 - 60 * q^44 - 16 * q^46 + 32 * q^49 + 40 * q^51 + 30 * q^54 - 60 * q^56 - 50 * q^64 + 36 * q^66 + 40 * q^69 + 48 * q^71 + 64 * q^74 - 24 * q^76 + 16 * q^81 + 4 * q^84 + 16 * q^86 + 48 * q^91 + 80 * q^94 + 34 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.842022	+	1.13622i	0.595399	+	0.803430i
$2$	0.842022	+	1.13622i	0.595399	+	0.803430i
$3$	−0.218455	+	1.71822i	−0.126125	+	0.992014i
$3$	−0.218455	+	1.71822i	−0.126125	+	0.992014i
$4$	−0.581998	+	1.91345i	−0.290999	+	0.956723i
$5$		0			0
$5$		0			0
$6$	−2.13622	+	1.19857i	−0.872109	+	0.489312i
$7$	3.64426			1.37740			0.688701	−	0.725045i	$-0.258181\pi$
$7$	3.64426			1.37740			0.688701	+	0.725045i	$0.258181\pi$
$8$	−2.66415	+	0.949886i	−0.941921	+	0.335835i
$9$	−2.90455	−	0.750707i	−0.968185	−	0.250236i
$10$		0			0
$11$			5.07403i			1.52988i	0.644103	+	0.764938i	$0.277231\pi$
$11$			5.07403i			1.52988i	−0.644103	+	0.764938i	$0.722769\pi$
$12$	−3.16058	−	1.41800i	−0.912381	−	0.409342i
$13$	1.70594			0.473142			0.236571	−	0.971614i	$-0.423976\pi$
$13$	1.70594			0.473142			0.236571	+	0.971614i	$0.423976\pi$
$14$	3.06855	+	4.14069i	0.820105	+	1.10665i
$15$		0			0
$16$	−3.32256	−	2.22724i	−0.830639	−	0.556811i
$17$	−4.08117			−0.989830			−0.494915	−	0.868941i	$-0.664801\pi$
$17$	−4.08117			−0.989830			−0.494915	+	0.868941i	$0.664801\pi$
$18$	−1.59273	−	3.93233i	−0.375410	−	0.926859i
$19$	1.26422			0.290033			0.145016	−	0.989429i	$-0.453676\pi$
$19$	1.26422			0.290033			0.145016	+	0.989429i	$0.453676\pi$
$20$		0			0
$21$	−0.796108	+	6.26164i	−0.173725	+	1.36640i
$22$	−5.76522	+	4.27244i	−1.22915	+	0.910888i
$23$		−	4.70066i		−	0.980156i	−0.871679	−	0.490078i	$-0.836968\pi$
$23$		−	4.70066i		−	0.980156i	0.871679	−	0.490078i	$-0.163032\pi$
$24$	−1.05011	−	4.78511i	−0.214354	−	0.976756i
$25$		0			0
$26$	1.43644	+	1.93832i	0.281709	+	0.380137i
$27$	1.92439	−	4.82667i	0.370350	−	0.928892i
$28$	−2.12095	+	6.97311i	−0.400823	+	1.31779i
$29$	−1.06377			−0.197537			−0.0987683	−	0.995110i	$-0.531490\pi$
$29$	−1.06377			−0.197537			−0.0987683	+	0.995110i	$0.531490\pi$
$30$		0			0
$31$			4.86950i			0.874588i	0.899318	+	0.437294i	$0.144063\pi$
$31$			4.86950i			0.874588i	−0.899318	+	0.437294i	$0.855937\pi$
$32$	−0.267024	−	5.65055i	−0.0472036	−	0.998885i
$33$	−8.71829	−	1.10845i	−1.51766	−	0.192956i
$34$	−3.43644	−	4.63712i	−0.589344	−	0.795259i
$35$		0			0
$36$	3.12688	−	5.12080i	0.521147	−	0.853467i
$37$	7.56830			1.24422			0.622110	−	0.782930i	$-0.286276\pi$
$37$	7.56830			1.24422			0.622110	+	0.782930i	$0.286276\pi$
$38$	1.06450	+	1.43644i	0.172685	+	0.233021i
$39$	−0.372671	+	2.93118i	−0.0596751	+	0.469364i
$40$		0			0
$41$		−	1.50141i		−	0.234482i	−0.993104	−	0.117241i	$-0.962595\pi$
$41$		−	1.50141i		−	0.234482i	0.993104	−	0.117241i	$-0.0374049\pi$
$42$	−7.78495	+	4.36789i	−1.20124	+	0.673980i
$43$		−	3.43644i		−	0.524052i	−0.965061	−	0.262026i	$-0.915609\pi$
$43$		−	3.43644i		−	0.524052i	0.965061	−	0.262026i	$-0.0843906\pi$
$44$	−9.70888	−	2.95307i	−1.46367	−	0.445193i
$45$		0			0
$46$	5.34099	−	3.95806i	0.787486	−	0.583584i
$47$		−	10.9176i		−	1.59249i	−0.604975	−	0.796245i	$-0.706817\pi$
$47$		−	10.9176i		−	1.59249i	0.604975	−	0.796245i	$-0.293183\pi$
$48$	4.55272	−	5.22233i	0.657129	−	0.753778i
$49$	6.28066			0.897237
$50$		0			0
$51$	0.891553	−	7.01235i	0.124842	−	0.981926i
$52$	−0.992853	+	3.26422i	−0.137684	+	0.452666i
$53$			8.87288i			1.21878i	0.792869	+	0.609392i	$0.208586\pi$
$53$			8.87288i			1.21878i	−0.792869	+	0.609392i	$0.791414\pi$
$54$	7.10454	−	1.87762i	0.966806	−	0.255512i
$55$		0			0
$56$	−9.70888	+	3.46163i	−1.29740	+	0.462580i
$57$	−0.276176	+	2.17221i	−0.0365804	+	0.287717i
$58$	−0.895716	−	1.20868i	−0.117613	−	0.158707i
$59$			0.788328i			0.102632i	0.998682	+	0.0513158i	$0.0163415\pi$
$59$			0.788328i			0.102632i	−0.998682	+	0.0513158i	$0.983658\pi$
$60$		0			0
$61$			0.627594i			0.0803552i	0.999193	+	0.0401776i	$0.0127924\pi$
$61$			0.627594i			0.0803552i	−0.999193	+	0.0401776i	$0.987208\pi$
$62$	−5.53283	+	4.10023i	−0.702670	+	0.520730i
$63$	−10.5850	−	2.73578i	−1.33358	−	0.344675i
$64$	6.19543	−	5.06128i	0.774429	−	0.632661i
$65$		0			0
$66$	−6.08155	−	10.8392i	−0.748587	−	1.33422i
$67$			4.18178i			0.510886i	0.966824	+	0.255443i	$0.0822213\pi$
$67$			4.18178i			0.510886i	−0.966824	+	0.255443i	$0.917779\pi$
$68$	2.37523	−	7.80911i	0.288040	−	0.946994i
$69$	8.07677	+	1.02688i	0.972329	+	0.123622i
$70$		0			0
$71$	6.21689			0.737810			0.368905	−	0.929467i	$-0.379733\pi$
$71$	6.21689			0.737810			0.368905	+	0.929467i	$0.379733\pi$
$72$	8.45127	−	0.758995i	0.995991	−	0.0894485i
$73$			4.21689i			0.493550i	0.969073	+	0.246775i	$0.0793709\pi$
$73$			4.21689i			0.493550i	−0.969073	+	0.246775i	$0.920629\pi$
$74$	6.37267	+	8.59926i	0.740808	+	0.999644i
$75$		0			0
$76$	−0.735776	+	2.41903i	−0.0843993	+	0.277481i
$77$			18.4911i			2.10726i
$78$	−3.64426	+	2.04468i	−0.412632	+	0.231514i
$79$			0.992853i			0.111705i	0.998439	+	0.0558524i	$0.0177876\pi$
$79$			0.992853i			0.111705i	−0.998439	+	0.0558524i	$0.982212\pi$
$80$		0			0
$81$	7.87288	+	4.36094i	0.874764	+	0.484549i
$82$	1.70594	−	1.26422i	0.188389	−	0.139610i
$83$	7.72544			0.847977			0.423989	−	0.905668i	$-0.360630\pi$
$83$	7.72544			0.847977			0.423989	+	0.905668i	$0.360630\pi$
$84$	−11.5180	−	5.16757i	−1.25672	−	0.563829i
$85$		0			0
$86$	3.90455	−	2.89356i	0.421039	−	0.312020i
$87$	0.232385	−	1.82779i	0.0249143	−	0.195959i
$88$	−4.81975	−	13.5180i	−0.513787	−	1.44102i
$89$			11.5742i			1.22687i	0.789747	+	0.613433i	$0.210212\pi$
$89$			11.5742i			1.22687i	−0.789747	+	0.613433i	$0.789788\pi$
$90$		0			0
$91$	6.21689			0.651708
$92$	8.99447	+	2.73578i	0.937738	+	0.285224i
$93$	−8.36687	−	1.06377i	−0.867604	−	0.110308i
$94$	12.4048	−	9.19282i	1.27945	−	0.948167i
$95$		0			0
$96$	9.76721	+	0.775585i	0.996862	+	0.0791578i
$97$		−	7.40133i		−	0.751491i	−0.926723	−	0.375745i	$-0.877387\pi$
$97$		−	7.40133i		−	0.751491i	0.926723	−	0.375745i	$-0.122613\pi$
$98$	5.28845	+	7.13622i	0.534215	+	0.720867i
$99$	3.80911	−	14.7378i	0.382830	−	1.48120i
$100$		0			0
$101$	−10.1535			−1.01031			−0.505157	−	0.863027i	$-0.668566\pi$
$101$	−10.1535			−1.01031			−0.505157	+	0.863027i	$0.668566\pi$
$102$	8.71829	−	4.89155i	0.863239	−	0.484336i
$103$	15.5400			1.53120			0.765599	−	0.643318i	$-0.222443\pi$
$103$	15.5400			1.53120			0.765599	+	0.643318i	$0.222443\pi$
$104$	−4.54489	+	1.62045i	−0.445663	+	0.158898i
$105$		0			0
$106$	−10.0816	+	7.47116i	−0.979207	+	0.725663i
$107$	14.8707			1.43760			0.718801	−	0.695216i	$-0.244691\pi$
$107$	14.8707			1.43760			0.718801	+	0.695216i	$0.244691\pi$
$108$	8.11558	+	6.49134i	0.780922	+	0.624629i
$109$			10.5376i			1.00932i	0.863319	+	0.504659i	$0.168382\pi$
$109$			10.5376i			1.00932i	−0.863319	+	0.504659i	$0.831618\pi$
$110$		0			0
$111$	−1.65333	+	13.0040i	−0.156927	+	1.23428i
$112$	−12.1083	−	8.11667i	−1.14412	−	0.766953i
$113$	9.94353			0.935409			0.467704	−	0.883885i	$-0.345081\pi$
$113$	9.94353			0.935409			0.467704	+	0.883885i	$0.345081\pi$
$114$	−2.70066	+	1.51526i	−0.252940	+	0.141917i
$115$		0			0
$116$	0.619110	−	2.03546i	0.0574830	−	0.188988i
$117$	−4.95499	−	1.28066i	−0.458089	−	0.118397i
$118$	−0.895716	+	0.663790i	−0.0824573	+	0.0611068i
$119$	−14.8729			−1.36339
$120$		0			0
$121$	−14.7458			−1.34052
$122$	−0.713086	+	0.528448i	−0.0645598	+	0.0478435i
$123$	2.57976	+	0.327992i	0.232609	+	0.0295740i
$124$	−9.31753	−	2.83404i	−0.836739	−	0.254504i
$125$		0			0
$126$	−5.80433	−	14.3304i	−0.517090	−	1.27666i
$127$	−5.62997			−0.499579			−0.249790	−	0.968300i	$-0.580361\pi$
$127$	−5.62997			−0.499579			−0.249790	+	0.968300i	$0.580361\pi$
$128$	10.9674	+	2.77767i	0.969393	+	0.245514i
$129$	5.90455	+	0.750707i	0.519867	+	0.0660961i
$130$		0			0
$131$			1.66215i			0.145223i	0.997360	+	0.0726113i	$0.0231333\pi$
$131$			1.66215i			0.145223i	−0.997360	+	0.0726113i	$0.976867\pi$
$132$	7.19498	−	16.0369i	0.626243	−	1.39583i
$133$	4.60717			0.399492
$134$	−4.75143	+	3.52115i	−0.410461	+	0.304181i
$135$		0			0
$136$	10.8729	−	3.87665i	0.932342	−	0.332420i
$137$	−13.3554			−1.14103			−0.570515	−	0.821287i	$-0.693256\pi$
$137$	−13.3554			−1.14103			−0.570515	+	0.821287i	$0.693256\pi$
$138$	5.63405	+	10.0417i	0.479602	+	0.854803i
$139$	−14.3540			−1.21749			−0.608745	−	0.793366i	$-0.708327\pi$
$139$	−14.3540			−1.21749			−0.608745	+	0.793366i	$0.708327\pi$
$140$		0			0
$141$	18.7588	+	2.38500i	1.57977	+	0.200853i
$142$	5.23476	+	7.06377i	0.439291	+	0.592778i
$143$			8.65598i			0.723850i
$144$	7.97854	+	8.96342i	0.664878	+	0.746952i
$145$		0			0
$146$	−4.79132	+	3.55072i	−0.396533	+	0.293859i
$147$	−1.37204	+	10.7916i	−0.113164	+	0.890072i
$148$	−4.40473	+	14.4815i	−0.362067	+	1.19037i
$149$	18.2742			1.49708			0.748540	−	0.663089i	$-0.230755\pi$
$149$	18.2742			1.49708			0.748540	+	0.663089i	$0.230755\pi$
$150$		0			0
$151$		−	16.7652i		−	1.36433i	−0.731197	−	0.682166i	$-0.761038\pi$
$151$		−	16.7652i		−	1.36433i	0.731197	−	0.682166i	$-0.238962\pi$
$152$	−3.36809	+	1.20087i	−0.273188	+	0.0974033i
$153$	11.8540	+	3.06377i	0.958339	+	0.247691i
$154$	−21.0100	+	15.5699i	−1.69303	+	1.25466i
$155$		0			0
$156$	−5.39176	−	2.41903i	−0.431686	−	0.193677i
$157$	6.31311			0.503841			0.251920	−	0.967748i	$-0.418938\pi$
$157$	6.31311			0.503841			0.251920	+	0.967748i	$0.418938\pi$
$158$	−1.12810	+	0.836004i	−0.0897469	+	0.0665089i
$159$	−15.2455	−	1.93832i	−1.20905	−	0.153719i
$160$		0			0
$161$		−	17.1305i		−	1.35007i
$162$	1.67414	+	12.6173i	0.131533	+	0.991312i
$163$		−	2.69110i		−	0.210783i	−0.994431	−	0.105391i	$-0.966390\pi$
$163$		−	2.69110i		−	0.210783i	0.994431	−	0.105391i	$-0.0336096\pi$
$164$	2.87288	+	0.873820i	0.224334	+	0.0682339i
$165$		0			0
$166$	6.50499	+	8.77781i	0.504885	+	0.681290i
$167$		−	16.6633i		−	1.28945i	−0.764416	−	0.644723i	$-0.776973\pi$
$167$		−	16.6633i		−	1.28945i	0.764416	−	0.644723i	$-0.223027\pi$
$168$	−3.82689	−	17.4382i	−0.295251	−	1.34539i
$169$	−10.0898			−0.776136
$170$		0			0
$171$	−3.67201	−	0.949062i	−0.280805	−	0.0725766i
$172$	6.57544	+	2.00000i	0.501373	+	0.152499i
$173$		−	11.7458i		−	0.893013i	−0.894780	−	0.446507i	$-0.852668\pi$
$173$		−	11.7458i		−	0.893013i	0.894780	−	0.446507i	$-0.147332\pi$
$174$	2.27244	−	1.27499i	0.172273	−	0.0966571i
$175$		0			0
$176$	11.3011	−	16.8587i	0.851852	−	1.27078i
$177$	−1.35452	−	0.172214i	−0.101812	−	0.0129444i
$178$	−13.1509	+	9.74575i	−0.985700	+	0.730475i
$179$		−	0.466861i		−	0.0348948i	−0.999848	−	0.0174474i	$-0.994446\pi$
$179$		−	0.466861i		−	0.0348948i	0.999848	−	0.0174474i	$-0.00555396\pi$
$180$		0			0
$181$		−	16.5628i		−	1.23110i	−0.788098	−	0.615550i	$-0.788934\pi$
$181$		−	16.5628i		−	1.23110i	0.788098	−	0.615550i	$-0.211066\pi$
$182$	5.23476	+	7.06377i	0.388026	+	0.523601i
$183$	−1.07834	−	0.137101i	−0.0797135	−	0.0101348i
$184$	4.46509	+	12.5233i	0.329171	+	0.923229i
$185$		0			0
$186$	−5.83642	−	10.4023i	−0.427947	−	0.762736i
$187$		−	20.7080i		−	1.51432i
$188$	20.8902	+	6.35399i	1.52357	+	0.463413i
$189$	7.01300	−	17.5896i	0.510121	−	1.27946i
$190$		0			0
$191$	6.49110			0.469679			0.234840	−	0.972034i	$-0.424544\pi$
$191$	6.49110			0.469679			0.234840	+	0.972034i	$0.424544\pi$
$192$	7.34297	+	11.7508i	0.529933	+	0.848039i
$193$		−	11.4013i		−	0.820685i	−0.911931	−	0.410343i	$-0.865409\pi$
$193$		−	11.4013i		−	0.820685i	0.911931	−	0.410343i	$-0.134591\pi$
$194$	8.40954	−	6.23208i	0.603770	−	0.447437i
$195$		0			0
$196$	−3.65533	+	12.0177i	−0.261095	+	0.858408i
$197$			3.56091i			0.253704i	0.991922	+	0.126852i	$0.0404874\pi$
$197$			3.56091i			0.253704i	−0.991922	+	0.126852i	$0.959513\pi$
$198$	19.9527	−	8.08155i	1.41798	−	0.574331i
$199$			4.40473i			0.312243i	0.987738	+	0.156122i	$0.0498992\pi$
$199$			4.40473i			0.312243i	−0.987738	+	0.156122i	$0.950101\pi$
$200$		0			0
$201$	−7.18522	−	0.913531i	−0.506806	−	0.0644355i
$202$	−8.54950	−	11.5367i	−0.601541	−	0.811717i
$203$	−3.87665			−0.272087
$204$	12.8989	+	5.78711i	0.903102	+	0.405179i
$205$		0			0
$206$	13.0850	+	17.6568i	0.911674	+	1.23021i
$207$	−3.52882	+	13.6533i	−0.245270	+	0.948972i
$208$	−5.66808	−	3.79954i	−0.393011	−	0.263451i
$209$			6.41471i			0.443715i
$210$		0			0
$211$	−16.1371			−1.11092			−0.555462	−	0.831542i	$-0.687459\pi$
$211$	−16.1371			−1.11092			−0.555462	+	0.831542i	$0.687459\pi$
$212$	−16.9778	−	5.16400i	−1.16604	−	0.354665i
$213$	−1.35811	+	10.6820i	−0.0930563	+	0.731918i
$214$	12.5214	+	16.8964i	0.855947	+	1.15501i
$215$		0			0
$216$	−0.542102	+	14.6869i	−0.0368853	+	0.999320i
$217$			17.7458i			1.20466i
$218$	−11.9730	+	8.87288i	−0.810916	+	0.600947i
$219$	−7.24555	−	0.921202i	−0.489609	−	0.0622490i
$220$		0			0
$221$	−6.96224			−0.468331
$222$	−16.1676	+	9.07109i	−1.08510	+	0.608812i
$223$	−6.09474			−0.408134			−0.204067	−	0.978957i	$-0.565416\pi$
$223$	−6.09474			−0.408134			−0.204067	+	0.978957i	$0.565416\pi$
$224$	−0.973105	−	20.5921i	−0.0650183	−	1.37587i
$225$		0			0
$226$	8.37267	+	11.2981i	0.556942	+	0.751535i
$227$	20.4673			1.35846			0.679230	−	0.733925i	$-0.262314\pi$
$227$	20.4673			1.35846			0.679230	+	0.733925i	$0.262314\pi$
$228$	−3.99568	−	1.79267i	−0.264621	−	0.118723i
$229$		−	26.4728i		−	1.74937i	−0.484693	−	0.874684i	$-0.661069\pi$
$229$		−	26.4728i		−	1.74937i	0.484693	−	0.874684i	$-0.338931\pi$
$230$		0			0
$231$	−31.7718	−	4.03947i	−2.09043	−	0.265778i
$232$	2.83404	−	1.01046i	0.186064	−	0.0663398i
$233$	−24.3773			−1.59701			−0.798504	−	0.601989i	$-0.794375\pi$
$233$	−24.3773			−1.59701			−0.798504	+	0.601989i	$0.794375\pi$
$234$	−2.71710	−	6.70832i	−0.177622	−	0.438536i
$235$		0			0
$236$	−1.50842	−	0.458805i	−0.0981901	−	0.0298657i
$237$	−1.70594	−	0.216894i	−0.110813	−	0.0140888i
$238$	−12.5233	−	16.8989i	−0.811764	−	1.09539i
$239$	5.47155			0.353925			0.176963	−	0.984218i	$-0.443373\pi$
$239$	5.47155			0.353925			0.176963	+	0.984218i	$0.443373\pi$
$240$		0			0
$241$	24.6446			1.58750			0.793750	−	0.608244i	$-0.208126\pi$
$241$	24.6446			1.58750			0.793750	+	0.608244i	$0.208126\pi$
$242$	−12.4162	−	16.7544i	−0.798147	−	1.07702i
$243$	−9.21292	+	12.5747i	−0.591009	+	0.806665i
$244$	−1.20087	−	0.365259i	−0.0768777	−	0.0233833i
$245$		0			0
$246$	1.79954	+	3.20735i	0.114735	+	0.204493i
$247$	2.15669			0.137227
$248$	−4.62547	−	12.9731i	−0.293718	−	0.823793i
$249$	−1.68766	+	13.2740i	−0.106951	+	0.841205i
$250$		0			0
$251$		−	1.74973i		−	0.110442i	−0.998474	−	0.0552210i	$-0.982414\pi$
$251$		−	1.74973i		−	0.110442i	0.998474	−	0.0552210i	$-0.0175863\pi$
$252$	11.3952	−	18.6616i	0.717829	−	1.17557i
$253$	23.8513			1.49952
$254$	−4.74056	−	6.39689i	−0.297449	−	0.401377i
$255$		0			0
$256$	6.07877	+	14.8003i	0.379923	+	0.925018i
$257$	−5.27646			−0.329137			−0.164568	−	0.986366i	$-0.552623\pi$
$257$	−5.27646			−0.329137			−0.164568	+	0.986366i	$0.552623\pi$
$258$	4.11880	+	7.34099i	0.256425	+	0.457030i
$259$	27.5809			1.71379
$260$		0			0
$261$	3.08977	+	0.798578i	0.191252	+	0.0494307i
$262$	−1.88857	+	1.39957i	−0.116676	+	0.0864655i
$263$			1.79043i			0.110403i	0.998475	+	0.0552014i	$0.0175801\pi$
$263$			1.79043i			0.110403i	−0.998475	+	0.0552014i	$0.982420\pi$
$264$	24.2798	−	5.32831i	1.49432	−	0.327935i
$265$		0			0
$266$	3.87934	+	5.23476i	0.237857	+	0.320964i
$267$	−19.8871	−	2.52845i	−1.21707	−	0.154739i
$268$	−8.00161	−	2.43379i	−0.488776	−	0.148667i
$269$	−18.7080			−1.14065			−0.570323	−	0.821420i	$-0.693182\pi$
$269$	−18.7080			−1.14065			−0.570323	+	0.821420i	$0.693182\pi$
$270$		0			0
$271$		−	24.8441i		−	1.50917i	−0.656200	−	0.754587i	$-0.727837\pi$
$271$		−	24.8441i		−	1.50917i	0.656200	−	0.754587i	$-0.272163\pi$
$272$	13.5599	+	9.08977i	0.822192	+	0.551148i
$273$	−1.35811	+	10.6820i	−0.0821967	+	0.646503i
$274$	−11.2455	−	15.1747i	−0.679368	−	0.916737i
$275$		0			0
$276$	−6.66555	+	14.8568i	−0.401219	+	0.894276i
$277$	−29.2030			−1.75464			−0.877319	−	0.479908i	$-0.840670\pi$
$277$	−29.2030			−1.75464			−0.877319	+	0.479908i	$0.840670\pi$
$278$	−12.0864	−	16.3093i	−0.724893	−	0.978168i
$279$	3.65557	−	14.1437i	0.218853	−	0.846763i
$280$		0			0
$281$			22.9856i			1.37121i	0.727975	+	0.685604i	$0.240462\pi$
$281$			22.9856i			1.37121i	−0.727975	+	0.685604i	$0.759538\pi$
$282$	13.0854	+	23.3223i	0.779224	+	1.38882i
$283$			2.03511i			0.120975i	0.998169	+	0.0604875i	$0.0192655\pi$
$283$			2.03511i			0.120975i	−0.998169	+	0.0604875i	$0.980734\pi$
$284$	−3.61822	+	11.8957i	−0.214702	+	0.705880i
$285$		0			0
$286$	−9.83511	+	7.28853i	−0.581562	+	0.430980i
$287$		−	5.47155i		−	0.322975i
$288$	−3.46632	+	16.6128i	−0.204255	+	0.978918i
$289$	−0.344017			−0.0202363
$290$		0			0
$291$	12.7171	+	1.61686i	0.745490	+	0.0947818i
$292$	−8.06880	−	2.45422i	−0.472191	−	0.143623i
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$	−13.4169	+	7.52778i	−0.782488	+	0.439029i
$295$		0			0
$296$	−20.1631	+	7.18902i	−1.17196	+	0.417853i
$297$	24.4906	+	9.76443i	1.42109	+	0.566590i
$298$	15.3873	+	20.7635i	0.891361	+	1.20280i
$299$		−	8.01905i		−	0.463753i
$300$		0			0
$301$		−	12.5233i		−	0.721830i
$302$	19.0490	−	14.1167i	1.09615	−	0.812323i
$303$	2.21809	−	17.4460i	0.127426	−	1.00225i
$304$	−4.20046	−	2.81574i	−0.240913	−	0.161494i
$305$		0			0
$306$	6.50021	+	16.0485i	0.371592	+	0.917433i
$307$			19.0547i			1.08751i	0.839245	+	0.543753i	$0.182997\pi$
$307$			19.0547i			1.08751i	−0.839245	+	0.543753i	$0.817003\pi$
$308$	−35.3817	−	10.7618i	−2.01606	−	0.613209i
$309$	−3.39478	+	26.7011i	−0.193122	+	1.51897i
$310$		0			0
$311$	26.0902			1.47944			0.739719	−	0.672916i	$-0.234958\pi$
$311$	26.0902			1.47944			0.739719	+	0.672916i	$0.234958\pi$
$312$	−1.79143	−	8.16310i	−0.101420	−	0.462145i
$313$		−	20.1795i		−	1.14062i	−0.821431	−	0.570308i	$-0.806824\pi$
$313$		−	20.1795i		−	1.14062i	0.821431	−	0.570308i	$-0.193176\pi$
$314$	5.31577	+	7.17309i	0.299987	+	0.404801i
$315$		0			0
$316$	−1.89977	−	0.577838i	−0.106871	−	0.0325060i
$317$			7.81598i			0.438989i	0.975614	+	0.219495i	$0.0704408\pi$
$317$			7.81598i			0.438989i	−0.975614	+	0.219495i	$0.929559\pi$
$318$	−10.6347	−	18.9544i	−0.596366	−	1.06291i
$319$		−	5.39759i		−	0.302207i
$320$		0			0
$321$	−3.24857	+	25.5511i	−0.181318	+	1.42612i
$322$	19.4640	−	14.4242i	1.08469	−	0.803830i
$323$	−5.15952			−0.287083
$324$	−12.9264	+	12.5263i	−0.718135	+	0.695904i
$325$		0			0
$326$	3.05768	−	2.26596i	0.169349	−	0.125500i
$327$	−18.1059	−	2.30199i	−1.00126	−	0.127300i
$328$	1.42617	+	4.00000i	0.0787472	+	0.220863i
$329$		−	39.7865i		−	2.19350i
$330$		0			0
$331$	−10.0424			−0.551982			−0.275991	−	0.961160i	$-0.589006\pi$
$331$	−10.0424			−0.551982			−0.275991	+	0.961160i	$0.589006\pi$
$332$	−4.49619	+	14.7822i	−0.246760	+	0.811279i
$333$	−21.9825	−	5.68157i	−1.20464	−	0.311348i
$334$	18.9332	−	14.0309i	1.03598	−	0.767735i
$335$		0			0
$336$	16.5913	−	19.0315i	0.905131	−	1.03826i
$337$		−	17.8733i		−	0.973620i	−0.873508	−	0.486810i	$-0.838160\pi$
$337$		−	17.8733i		−	0.973620i	0.873508	−	0.486810i	$-0.161840\pi$
$338$	−8.49581	−	11.4642i	−0.462111	−	0.623571i
$339$	−2.17221	+	17.0852i	−0.117978	+	0.927939i
$340$		0			0
$341$	−24.7080			−1.33801
$342$	−2.01357	−	4.97135i	−0.108881	−	0.268820i
$343$	−2.62146			−0.141546
$344$	3.26422	+	9.15520i	0.175995	+	0.493615i
$345$		0			0
$346$	13.3458	−	9.89018i	0.717473	−	0.531700i
$347$	−34.9886			−1.87829			−0.939143	−	0.343525i	$-0.888379\pi$
$347$	−34.9886			−1.87829			−0.939143	+	0.343525i	$0.888379\pi$
$348$	3.36212	+	1.50842i	0.180229	+	0.0808600i
$349$			8.24993i			0.441609i	0.975318	+	0.220804i	$0.0708682\pi$
$349$			8.24993i			0.441609i	−0.975318	+	0.220804i	$0.929132\pi$
$350$		0			0
$351$	3.28290	−	8.23400i	0.175228	−	0.439498i
$352$	28.6710	−	1.35489i	1.52817	−	0.0722157i
$353$	0.935042			0.0497673			0.0248836	−	0.999690i	$-0.492078\pi$
$353$	0.935042			0.0497673			0.0248836	+	0.999690i	$0.492078\pi$
$354$	−0.944863	−	1.68404i	−0.0502189	−	0.0895059i
$355$		0			0
$356$	−22.1467	−	6.73618i	−1.17377	−	0.357017i
$357$	3.24906	−	25.5549i	0.171958	−	1.35251i
$358$	0.530457	−	0.393107i	0.0280355	−	0.0207763i
$359$	32.5813			1.71957			0.859787	−	0.510653i	$-0.170596\pi$
$359$	32.5813			1.71957			0.859787	+	0.510653i	$0.170596\pi$
$360$		0			0
$361$	−17.4017			−0.915881
$362$	18.8190	−	13.9462i	0.989103	−	0.732997i
$363$	3.22128	−	25.3364i	0.169074	−	1.32982i
$364$	−3.61822	+	11.8957i	−0.189646	+	0.623504i
$365$		0			0
$366$	−0.752213	−	1.34068i	−0.0393188	−	0.0700785i
$367$	0.791919			0.0413378			0.0206689	−	0.999786i	$-0.493420\pi$
$367$	0.791919			0.0413378			0.0206689	+	0.999786i	$0.493420\pi$
$368$	−10.4695	+	15.6182i	−0.545762	+	0.814156i
$369$	−1.12712	+	4.36094i	−0.0586757	+	0.227022i
$370$		0			0
$371$			32.3351i			1.67876i
$372$	6.90496	−	15.3905i	0.358006	−	0.797958i
$373$	−18.7335			−0.969982			−0.484991	−	0.874519i	$-0.661177\pi$
$373$	−18.7335			−0.969982			−0.484991	+	0.874519i	$0.661177\pi$
$374$	23.5289	−	17.4366i	1.21665	−	0.901624i
$375$		0			0
$376$	10.3704	+	29.0861i	0.534814	+	1.50000i
$377$	−1.81472			−0.0934630
$378$	25.8908	−	6.84255i	1.33168	−	0.351943i
$379$	−8.88244			−0.456260			−0.228130	−	0.973631i	$-0.573261\pi$
$379$	−8.88244			−0.456260			−0.228130	+	0.973631i	$0.573261\pi$
$380$		0			0
$381$	1.22990	−	9.67352i	0.0630095	−	0.495590i
$382$	5.46565	+	7.37532i	0.279647	+	0.377354i
$383$		−	3.48418i		−	0.178033i	−0.996030	−	0.0890167i	$-0.971628\pi$
$383$		−	3.48418i		−	0.178033i	0.996030	−	0.0890167i	$-0.0283724\pi$
$384$	−7.16854	+	18.2377i	−0.365818	+	0.930686i
$385$		0			0
$386$	12.9544	−	9.60017i	0.659363	−	0.488636i
$387$	−2.57976	+	9.98132i	−0.131137	+	0.507379i
$388$	14.1620	+	4.30756i	0.718969	+	0.218683i
$389$	−24.8027			−1.25754			−0.628772	−	0.777590i	$-0.716442\pi$
$389$	−24.8027			−1.25754			−0.628772	+	0.777590i	$0.716442\pi$
$390$		0			0
$391$			19.1842i			0.970188i
$392$	−16.7326	+	5.96591i	−0.845126	+	0.301324i
$393$	−2.85594	−	0.363105i	−0.144063	−	0.0183162i
$394$	−4.04598	+	2.99837i	−0.203834	+	0.151055i
$395$		0			0
$396$	25.9831	+	15.8659i	1.30570	+	0.797291i
$397$	−15.5873			−0.782306			−0.391153	−	0.920326i	$-0.627924\pi$
$397$	−15.5873			−0.782306			−0.391153	+	0.920326i	$0.627924\pi$
$398$	−5.00475	+	3.70888i	−0.250865	+	0.185909i
$399$	−1.00646	+	7.91612i	−0.0503860	+	0.396302i
$400$		0			0
$401$		−	26.3852i		−	1.31761i	−0.752313	−	0.658806i	$-0.771062\pi$
$401$		−	26.3852i		−	1.31761i	0.752313	−	0.658806i	$-0.228938\pi$
$402$	−5.01214	−	8.93321i	−0.249983	−	0.445548i
$403$			8.30708i			0.413805i
$404$	5.90934	−	19.4283i	0.294001	−	0.966592i
$405$		0			0
$406$	−3.26422	−	4.40473i	−0.162001	−	0.218603i
$407$			38.4017i			1.90350i
$408$	4.28570	+	19.5289i	0.212174	+	0.966823i
$409$	0.497143			0.0245821			0.0122911	−	0.999924i	$-0.496088\pi$
$409$	0.497143			0.0245821			0.0122911	+	0.999924i	$0.496088\pi$
$410$		0			0
$411$	2.91756	−	22.9475i	0.143912	−	1.13192i
$412$	−9.04422	+	29.7349i	−0.445577	+	1.46493i
$413$			2.87288i			0.141365i
$414$	−18.4846	+	7.48688i	−0.908466	+	0.367960i
$415$		0			0
$416$	−0.455526	−	9.63949i	−0.0223340	−	0.472615i
$417$	3.13570	−	24.6633i	0.153556	−	1.20777i
$418$	−7.28853	+	5.40133i	−0.356494	+	0.264187i
$419$			11.0240i			0.538556i	0.963063	+	0.269278i	$0.0867850\pi$
$419$			11.0240i			0.538556i	−0.963063	+	0.269278i	$0.913215\pi$
$420$		0			0
$421$			11.0971i			0.540840i	0.962742	+	0.270420i	$0.0871626\pi$
$421$			11.0971i			0.540840i	−0.962742	+	0.270420i	$0.912837\pi$
$422$	−13.5878	−	18.3353i	−0.661443	−	0.892549i
$423$	−8.19589	+	31.7106i	−0.398498	+	1.54182i
$424$	−8.42822	−	23.6387i	−0.409311	−	1.14800i
$425$		0			0
$426$	−13.2807	+	7.45135i	−0.643450	+	0.361019i
$427$			2.28712i			0.110681i
$428$	−8.65470	+	28.4542i	−0.418340	+	1.37539i
$429$	−14.8729	−	1.89094i	−0.718069	−	0.0912956i
$430$		0			0
$431$	−6.84000			−0.329471			−0.164736	−	0.986338i	$-0.552677\pi$
$431$	−6.84000			−0.329471			−0.164736	+	0.986338i	$0.552677\pi$
$432$	−17.1441	+	11.7508i	−0.824845	+	0.565360i
$433$			38.6378i			1.85681i	0.371567	+	0.928406i	$0.378821\pi$
$433$			38.6378i			1.85681i	−0.371567	+	0.928406i	$0.621179\pi$
$434$	−20.1631	+	14.9423i	−0.967860	+	0.717254i
$435$		0			0
$436$	−20.1631	−	6.13285i	−0.965638	−	0.293710i
$437$		−	5.94269i		−	0.284277i
$438$	−5.05422	−	9.00822i	−0.241500	−	0.430429i
$439$			4.07908i			0.194684i	0.995251	+	0.0973420i	$0.0310341\pi$
$439$			4.07908i			0.194684i	−0.995251	+	0.0973420i	$0.968966\pi$
$440$		0			0
$441$	−18.2425	−	4.71494i	−0.868692	−	0.224521i
$442$	−5.86236	−	7.91064i	−0.278844	−	0.376271i
$443$	−12.7140			−0.604059			−0.302030	−	0.953299i	$-0.597664\pi$
$443$	−12.7140			−0.604059			−0.302030	+	0.953299i	$0.597664\pi$
$444$	−23.9202	−	10.7319i	−1.13520	−	0.509311i
$445$		0			0
$446$	−5.13191	−	6.92498i	−0.243003	−	0.327907i
$447$	−3.99209	+	31.3991i	−0.188819	+	1.48513i
$448$	22.5778	−	18.4447i	1.06670	−	0.871428i
$449$		−	31.2985i		−	1.47707i	−0.674217	−	0.738533i	$-0.735519\pi$
$449$		−	31.2985i		−	1.47707i	0.674217	−	0.738533i	$-0.264481\pi$
$450$		0			0
$451$	7.61822			0.358728
$452$	−5.78711	+	19.0264i	−0.272203	+	0.894927i
$453$	28.8063	+	3.66244i	1.35344	+	0.172077i
$454$	17.2339	+	23.2554i	0.808827	+	1.09143i
$455$		0			0
$456$	−1.32758	−	6.04945i	−0.0621696	−	0.283291i
$457$			29.1097i			1.36170i	0.732425	+	0.680848i	$0.238388\pi$
$457$			29.1097i			1.36170i	−0.732425	+	0.680848i	$0.761612\pi$
$458$	30.0789	−	22.2906i	1.40549	−	1.04157i
$459$	−7.85379	+	19.6985i	−0.366583	+	0.919446i
$460$		0			0
$461$	−0.00687071			−0.000320001			−0.000160001	−	1.00000i	$-0.500051\pi$
$461$	−0.00687071			−0.000320001			−0.000160001		1.00000i	$0.500051\pi$
$462$	−22.1628	−	39.5011i	−1.03111	−	1.83776i
$463$	17.9904			0.836086			0.418043	−	0.908427i	$-0.362716\pi$
$463$	17.9904			0.836086			0.418043	+	0.908427i	$0.362716\pi$
$464$	3.53443	+	2.36927i	0.164082	+	0.109991i
$465$		0			0
$466$	−20.5262	−	27.6980i	−0.950858	−	1.28308i
$467$	3.99927			0.185064			0.0925321	−	0.995710i	$-0.470504\pi$
$467$	3.99927			0.185064			0.0925321	+	0.995710i	$0.470504\pi$
$468$	5.33427	−	8.73578i	0.246577	−	0.403811i
$469$			15.2395i			0.703695i
$470$		0			0
$471$	−1.37913	+	10.8473i	−0.0635470	+	0.499817i
$472$	−0.748822	−	2.10023i	−0.0344673	−	0.0966708i
$473$	17.4366			0.801735
$474$	−1.19000	−	2.12095i	−0.0546585	−	0.0974186i
$475$		0			0
$476$	8.65598	−	28.4585i	0.396746	−	1.30439i
$477$	6.66093	−	25.7718i	0.304983	−	1.18001i
$478$	4.60717	+	6.21689i	0.210727	+	0.284354i
$479$	34.1467			1.56020			0.780101	−	0.625654i	$-0.215168\pi$
$479$	34.1467			1.56020			0.780101	+	0.625654i	$0.215168\pi$
$480$		0			0
$481$	12.9111			0.588693
$482$	20.7513	+	28.0018i	0.945197	+	1.27545i
$483$	29.4339	+	3.74223i	1.33929	+	0.170278i
$484$	8.58200	−	28.2152i	0.390091	−	1.28251i
$485$		0			0
$486$	−22.0451	+	0.120220i	−0.999985	+	0.00545330i
$487$	0.851820			0.0385997			0.0192998	−	0.999814i	$-0.493856\pi$
$487$	0.851820			0.0385997			0.0192998	+	0.999814i	$0.493856\pi$
$488$	−0.596143	−	1.67201i	−0.0269861	−	0.0756883i
$489$	4.62389	+	0.587884i	0.209100	+	0.0265850i
$490$		0			0
$491$		−	6.09115i		−	0.274890i	−0.990509	−	0.137445i	$-0.956111\pi$
$491$		−	6.09115i		−	0.274890i	0.990509	−	0.137445i	$-0.0438890\pi$
$492$	−2.12901	+	4.74534i	−0.0959831	+	0.213937i
$493$	4.34142			0.195528
$494$	1.81598	+	2.45048i	0.0817048	+	0.110252i
$495$		0			0
$496$	10.8456	−	16.1792i	0.486980	−	0.726468i
$497$	22.6560			1.01626
$498$	−16.5032	+	9.25944i	−0.739528	+	0.414925i
$499$	−13.1375			−0.588116			−0.294058	−	0.955788i	$-0.595006\pi$
$499$	−13.1375			−0.588116			−0.294058	+	0.955788i	$0.595006\pi$
$500$		0			0
$501$	28.6312	+	3.64018i	1.27915	+	0.162631i
$502$	1.98808	−	1.47331i	0.0887324	−	0.0657571i
$503$		−	27.6064i		−	1.23091i	−0.788172	−	0.615455i	$-0.788972\pi$
$503$		−	27.6064i		−	1.23091i	0.788172	−	0.615455i	$-0.211028\pi$
$504$	30.7987	−	2.76598i	1.37188	−	0.123207i
$505$		0			0
$506$	20.0833	+	27.1003i	0.892812	+	1.20476i
$507$	2.20416	−	17.3364i	0.0978902	−	0.769938i
$508$	3.27663	−	10.7726i	0.145377	−	0.477959i
$509$	−5.46468			−0.242218			−0.121109	−	0.992639i	$-0.538645\pi$
$509$	−5.46468			−0.242218			−0.121109	+	0.992639i	$0.538645\pi$
$510$		0			0
$511$			15.3675i			0.679817i
$512$	−11.6979	+	19.3690i	−0.516981	+	0.855997i
$513$	2.43287	−	6.10199i	0.107414	−	0.269409i
$514$	−4.44290	−	5.99523i	−0.195968	−	0.264438i
$515$		0			0
$516$	−4.87288	+	10.8611i	−0.214516	+	0.478135i
$517$	55.3960			2.43631
$518$	23.2237	+	31.3380i	1.02039	+	1.37691i
$519$	20.1818	+	2.56592i	0.885882	+	0.112631i
$520$		0			0
$521$		−	39.1312i		−	1.71437i	−0.515010	−	0.857184i	$-0.672212\pi$
$521$		−	39.1312i		−	1.71437i	0.515010	−	0.857184i	$-0.327788\pi$
$522$	1.69429	+	4.18308i	0.0741572	+	0.183089i
$523$			14.3467i			0.627336i	0.949533	+	0.313668i	$0.101558\pi$
$523$			14.3467i			0.627336i	−0.949533	+	0.313668i	$0.898442\pi$
$524$	−3.18043	−	0.967367i	−0.138938	−	0.0422596i
$525$		0			0
$526$	−2.03433	+	1.50758i	−0.0887009	+	0.0657338i
$527$		−	19.8733i		−	0.865694i
$528$	26.4982	+	23.1006i	1.15319	+	1.00533i
$529$	0.903770			0.0392944
$530$		0			0
$531$	0.591804	−	2.28974i	0.0256821	−	0.0993664i
$532$	−2.68136	+	8.81557i	−0.116252	+	0.382203i
$533$		−	2.56132i		−	0.110943i
$534$	−13.8725	−	24.7251i	−0.600320	−	1.06996i
$535$		0			0
$536$	−3.97221	−	11.1409i	−0.171574	−	0.481214i
$537$	0.802169	+	0.101988i	0.0346161	+	0.00440111i
$538$	−15.7525	−	21.2564i	−0.679140	−	0.916429i
$539$			31.8682i			1.37266i
$540$		0			0
$541$			29.8846i			1.28484i	0.766352	+	0.642420i	$0.222070\pi$
$541$			29.8846i			1.28484i	−0.766352	+	0.642420i	$0.777930\pi$
$542$	28.2284	−	20.9193i	1.21252	−	0.898562i
$543$	28.4585	+	3.61822i	1.22127	+	0.155273i
$544$	1.08977	+	23.0609i	0.0467235	+	0.988727i
$545$		0			0
$546$	−13.2807	+	7.45135i	−0.568360	+	0.318888i
$547$		−	2.78046i		−	0.118884i	−0.998232	−	0.0594418i	$-0.981068\pi$
$547$		−	2.78046i		−	0.118884i	0.998232	−	0.0594418i	$-0.0189321\pi$
$548$	7.77282	−	25.5549i	0.332038	−	1.09165i
$549$	0.471140	−	1.82288i	0.0201078	−	0.0777987i
$550$		0			0
$551$	−1.34484			−0.0572921
$552$	−22.4932	+	4.93623i	−0.957373	+	0.210100i
$553$			3.61822i			0.153862i
$554$	−24.5896	−	33.1811i	−1.04471	−	1.40973i
$555$		0			0
$556$	8.35399	−	27.4656i	0.354288	−	1.16480i
$557$		−	39.3640i		−	1.66791i	−0.551836	−	0.833953i	$-0.686073\pi$
$557$		−	39.3640i		−	1.66791i	0.551836	−	0.833953i	$-0.313927\pi$
$558$	19.1485	−	7.75580i	0.810620	−	0.328329i
$559$		−	5.86236i		−	0.247951i
$560$		0			0
$561$	35.5809	+	4.52376i	1.50223	+	0.190994i
$562$	−26.1168	+	19.3544i	−1.10167	+	0.816416i
$563$	−16.1259			−0.679624			−0.339812	−	0.940493i	$-0.610363\pi$
$563$	−16.1259			−0.679624			−0.339812	+	0.940493i	$0.610363\pi$
$564$	−15.4811	+	34.5058i	−0.651873	+	1.45296i
$565$		0			0
$566$	−2.31234	+	1.71361i	−0.0971949	+	0.0720284i
$567$	28.6908	+	15.8924i	1.20490	+	0.667419i
$568$	−16.5628	+	5.90534i	−0.694958	+	0.247783i
$569$			8.55906i			0.358814i	0.983775	+	0.179407i	$0.0574180\pi$
$569$			8.55906i			0.358814i	−0.983775	+	0.179407i	$0.942582\pi$
$570$		0			0
$571$	34.6984			1.45208			0.726042	−	0.687650i	$-0.241358\pi$
$571$	34.6984			1.45208			0.726042	+	0.687650i	$0.241358\pi$
$572$	−16.5628	−	5.03776i	−0.692524	−	0.210639i
$573$	−1.41801	+	11.1531i	−0.0592383	+	0.465929i
$574$	6.21689	−	4.60717i	0.259488	−	0.192299i
$575$		0			0
$576$	−21.7945	+	10.0498i	−0.908105	+	0.418742i
$577$		−	32.8684i		−	1.36833i	−0.729328	−	0.684165i	$-0.760167\pi$
$577$		−	32.8684i		−	1.36833i	0.729328	−	0.684165i	$-0.239833\pi$
$578$	−0.289670	−	0.390879i	−0.0120487	−	0.0162584i
$579$	19.5900	+	2.49068i	0.814132	+	0.103509i
$580$		0			0
$581$	28.1535			1.16801
$582$	8.87097	+	15.8109i	0.367714	+	0.655382i
$583$	−45.0212			−1.86459
$584$	−4.00557	−	11.2345i	−0.165752	−	0.464885i
$585$		0			0
$586$	6.81733	−	5.05213i	0.281621	−	0.208702i
$587$	15.4302			0.636872			0.318436	−	0.947944i	$-0.396842\pi$
$587$	15.4302			0.636872			0.318436	+	0.947944i	$0.396842\pi$
$588$	−19.8505	−	8.90599i	−0.818622	−	0.367277i
$589$			6.15614i			0.253659i
$590$		0			0
$591$	−6.11843	−	0.777899i	−0.251678	−	0.0319985i
$592$	−25.1461	−	16.8564i	−1.03350	−	0.692795i
$593$	14.0511			0.577008			0.288504	−	0.957479i	$-0.406842\pi$
$593$	14.0511			0.577008			0.288504	+	0.957479i	$0.406842\pi$
$594$	9.52710	+	36.0486i	0.390902	+	1.47909i
$595$		0			0
$596$	−10.6355	+	34.9667i	−0.435649	+	1.43229i
$597$	−7.56830	−	0.962236i	−0.309750	−	0.0393817i
$598$	9.11141	−	6.75221i	0.372593	−	0.276119i
$599$	−30.0200			−1.22658			−0.613291	−	0.789857i	$-0.710155\pi$
$599$	−30.0200			−1.22658			−0.613291	+	0.789857i	$0.710155\pi$
$600$		0			0
$601$	−29.3006			−1.19520			−0.597599	−	0.801795i	$-0.703878\pi$
$601$	−29.3006			−1.19520			−0.597599	+	0.801795i	$0.703878\pi$
$602$	14.2292	−	10.5449i	0.579940	−	0.429777i
$603$	3.13929	−	12.1462i	0.127842	−	0.494632i
$604$	32.0793	+	9.75731i	1.30529	+	0.397019i
$605$		0			0
$606$	21.6902	−	12.1697i	0.881104	−	0.494359i
$607$	38.9265			1.57998			0.789989	−	0.613122i	$-0.210086\pi$
$607$	38.9265			1.57998			0.789989	+	0.613122i	$0.210086\pi$
$608$	−0.337578	−	7.14356i	−0.0136906	−	0.289710i
$609$	0.846874	−	6.66093i	0.0343171	−	0.269915i
$610$		0			0
$611$		−	18.6247i		−	0.753474i
$612$	−12.7614	+	20.8989i	−0.515847	+	0.844787i
$613$	−28.9092			−1.16763			−0.583816	−	0.811886i	$-0.698441\pi$
$613$	−28.9092			−1.16763			−0.583816	+	0.811886i	$0.698441\pi$
$614$	−21.6503	+	16.0444i	−0.873735	+	0.647501i
$615$		0			0
$616$	−17.5644	−	49.2631i	−0.707691	−	1.98487i
$617$	26.5340			1.06822			0.534109	−	0.845416i	$-0.320647\pi$
$617$	26.5340			1.06822			0.534109	+	0.845416i	$0.320647\pi$
$618$	−33.1968	+	18.6257i	−1.33537	+	0.749234i
$619$	17.9531			0.721595			0.360798	−	0.932644i	$-0.382505\pi$
$619$	17.9531			0.721595			0.360798	+	0.932644i	$0.382505\pi$
$620$		0			0
$621$	−22.6885	−	9.04593i	−0.910459	−	0.363001i
$622$	21.9685	+	29.6442i	0.880857	+	1.18863i
$623$			42.1795i			1.68989i
$624$	7.76667	−	8.90898i	0.310916	−	0.356644i
$625$		0			0
$626$	22.9284	−	16.9916i	0.916404	−	0.679122i
$627$	−11.0219	−	1.40133i	−0.440171	−	0.0559635i
$628$	−3.67421	+	12.0798i	−0.146617	+	0.482036i
$629$	−30.8875			−1.23157
$630$		0			0
$631$			33.8875i			1.34904i	0.738257	+	0.674520i	$0.235649\pi$
$631$			33.8875i			1.34904i	−0.738257	+	0.674520i	$0.764351\pi$
$632$	−0.943097	−	2.64511i	−0.0375144	−	0.105217i
$633$	3.52523	−	27.7271i	0.140115	−	1.10205i
$634$	−8.88068	+	6.58123i	−0.352697	+	0.261374i
$635$		0			0
$636$	12.5818	−	28.0434i	0.498899	−	1.11199i
$637$	10.7144			0.424521
$638$	6.13285	−	4.54489i	0.242802	−	0.179934i
$639$	−18.0573	−	4.66707i	−0.714336	−	0.184626i
$640$		0			0
$641$			16.1456i			0.637711i	0.947803	+	0.318856i	$0.103298\pi$
$641$			16.1456i			0.637711i	−0.947803	+	0.318856i	$0.896702\pi$
$642$	−31.7670	+	17.8235i	−1.25374	+	0.703436i
$643$		−	41.9604i		−	1.65476i	−0.561645	−	0.827378i	$-0.689831\pi$
$643$		−	41.9604i		−	1.65476i	0.561645	−	0.827378i	$-0.310169\pi$
$644$	32.7782	+	9.96989i	1.29164	+	0.392869i
$645$		0			0
$646$	−4.34443	−	5.86236i	−0.170929	−	0.230651i
$647$			9.10158i			0.357820i	0.983865	+	0.178910i	$0.0572571\pi$
$647$			9.10158i			0.357820i	−0.983865	+	0.178910i	$0.942743\pi$
$648$	−25.1170	−	4.13988i	−0.986687	−	0.162630i
$649$	−4.00000			−0.157014
$650$		0			0
$651$	−30.4911	−	3.87665i	−1.19504	−	0.151938i
$652$	5.14927	+	1.56621i	0.201661	+	0.0613376i
$653$			12.0573i			0.471839i	0.971773	+	0.235919i	$0.0758102\pi$
$653$			12.0573i			0.471839i	−0.971773	+	0.235919i	$0.924190\pi$
$654$	−12.6300	−	22.5106i	−0.493871	−	0.880235i
$655$		0			0
$656$	−3.34402	+	4.98854i	−0.130562	+	0.194770i
$657$	3.16565	−	12.2482i	0.123504	−	0.477848i
$658$	45.2062	−	33.5011i	1.76232	−	1.30601i
$659$		−	12.1916i		−	0.474916i	−0.971398	−	0.237458i	$-0.923686\pi$
$659$		−	12.1916i		−	0.474916i	0.971398	−	0.237458i	$-0.0763142\pi$
$660$		0			0
$661$			22.0284i			0.856806i	0.903588	+	0.428403i	$0.140924\pi$
$661$			22.0284i			0.856806i	−0.903588	+	0.428403i	$0.859076\pi$
$662$	−8.45596	−	11.4104i	−0.328650	−	0.443479i
$663$	1.52094	−	11.9626i	0.0590682	−	0.464591i
$664$	−20.5818	+	7.33828i	−0.798727	+	0.284781i
$665$		0			0
$666$	−12.0542	−	29.7610i	−0.467093	−	1.15322i
$667$			5.00041i			0.193617i
$668$	31.8844	+	9.69801i	1.23364	+	0.375227i
$669$	1.33143	−	10.4721i	0.0514759	−	0.404875i
$670$		0			0
$671$	−3.18443			−0.122934
$672$	35.5943	+	2.82644i	1.37308	+	0.109032i
$673$		−	25.3258i		−	0.976238i	−0.872777	−	0.488119i	$-0.837683\pi$
$673$		−	25.3258i		−	0.976238i	0.872777	−	0.488119i	$-0.162317\pi$
$674$	20.3080	−	15.0497i	0.782235	−	0.579693i
$675$		0			0
$676$	5.87223	−	19.3062i	0.225855	−	0.742548i
$677$			21.9435i			0.843358i	0.906745	+	0.421679i	$0.138559\pi$
$677$			21.9435i			0.843358i	−0.906745	+	0.421679i	$0.861441\pi$
$678$	−21.2416	+	11.9180i	−0.815778	+	0.457707i
$679$		−	26.9724i		−	1.03511i
$680$		0			0
$681$	−4.47118	+	35.1673i	−0.171336	+	1.34761i
$682$	−20.8047	−	28.0737i	−0.796652	−	1.07500i
$683$	16.0383			0.613687			0.306844	−	0.951760i	$-0.400727\pi$
$683$	16.0383			0.613687			0.306844	+	0.951760i	$0.400727\pi$
$684$	3.95308	−	6.47384i	0.151150	−	0.247533i
$685$		0			0
$686$	−2.20733	−	2.97856i	−0.0842762	−	0.113722i
$687$	45.4860	+	5.78311i	1.73540	+	0.220639i
$688$	−7.65379	+	11.4178i	−0.291798	+	0.435298i
$689$			15.1366i			0.576658i
$690$		0			0
$691$	−23.0993			−0.878740			−0.439370	−	0.898306i	$-0.644798\pi$
$691$	−23.0993			−0.878740			−0.439370	+	0.898306i	$0.644798\pi$
$692$	22.4749	+	6.83600i	0.854367	+	0.259866i
$693$	13.8814	−	53.7084i	0.527311	−	2.04021i
$694$	−29.4612	−	39.7548i	−1.11833	−	1.50907i
$695$		0			0
$696$	1.11708	+	5.09024i	0.0423427	+	0.192945i
$697$			6.12753i			0.232097i
$698$	−9.37375	+	6.94662i	−0.354802	+	0.262934i
$699$	5.32534	−	41.8855i	0.201423	−	1.58426i
$700$		0			0
$701$	0.254246			0.00960274			0.00480137	−	0.999988i	$-0.498472\pi$
$701$	0.254246			0.00960274			0.00480137	+	0.999988i	$0.498472\pi$
$702$	12.1199	−	3.20311i	0.457437	−	0.120894i
$703$	9.56802			0.360865
$704$	25.6811	+	31.4358i	0.967893	+	1.18478i
$705$		0			0
$706$	0.787326	+	1.06241i	0.0296314	+	0.0399845i
$707$	−37.0022			−1.39161
$708$	1.11785	−	2.49158i	0.0420114	−	0.0936391i
$709$		−	19.9746i		−	0.750163i	−0.926992	−	0.375082i	$-0.877615\pi$
$709$		−	19.9746i		−	0.750163i	0.926992	−	0.375082i	$-0.122385\pi$
$710$		0			0
$711$	0.745342	−	2.88380i	0.0279525	−	0.108151i
$712$	−10.9942	−	30.8355i	−0.412025	−	1.15561i
$713$	22.8899			0.857233
$714$	31.7718	−	17.8261i	1.18903	−	0.667125i
$715$		0			0
$716$	0.893313	+	0.271712i	0.0333847	+	0.0101543i
$717$	−1.19529	+	9.40133i	−0.0446389	+	0.351099i
$718$	27.4342	+	37.0195i	1.02383	+	1.38156i
$719$	33.7978			1.26044			0.630222	−	0.776415i	$-0.282964\pi$
$719$	33.7978			1.26044			0.630222	+	0.776415i	$0.282964\pi$
$720$		0			0
$721$	56.6317			2.10908
$722$	−14.6526	−	19.7722i	−0.545315	−	0.735846i
$723$	−5.38374	+	42.3449i	−0.200224	+	1.57482i
$724$	31.6920	+	9.63949i	1.17782	+	0.358249i
$725$		0			0
$726$	31.5002	−	17.6737i	1.16908	−	0.655934i
$727$	−27.0308			−1.00252			−0.501258	−	0.865298i	$-0.667129\pi$
$727$	−27.0308			−1.00252			−0.501258	+	0.865298i	$0.667129\pi$
$728$	−16.5628	+	5.90534i	−0.613857	+	0.218866i
$729$	−19.5934	−	18.5768i	−0.725682	−	0.688030i
$730$		0			0
$731$			14.0247i			0.518722i
$732$	0.889930	−	1.98356i	0.0328928	−	0.0733146i
$733$	−15.8811			−0.586583			−0.293291	−	0.956023i	$-0.594751\pi$
$733$	−15.8811			−0.586583			−0.293291	+	0.956023i	$0.594751\pi$
$734$	0.666813	+	0.899795i	0.0246125	+	0.0332121i
$735$		0			0
$736$	−26.5613	+	1.25519i	−0.979063	+	0.0462669i
$737$	−21.2185			−0.781592
$738$	−5.90406	+	2.39135i	−0.217331	+	0.0880267i
$739$	14.1753			0.521446			0.260723	−	0.965414i	$-0.416039\pi$
$739$	14.1753			0.521446			0.260723	+	0.965414i	$0.416039\pi$
$740$		0			0
$741$	−0.471140	+	3.70567i	−0.0173078	+	0.136131i
$742$	−36.7398	+	27.2269i	−1.34876	+	0.999530i
$743$			29.5744i			1.08498i	0.840063	+	0.542489i	$0.182518\pi$
$743$			29.5744i			1.08498i	−0.840063	+	0.542489i	$0.817482\pi$
$744$	23.3011	−	5.11353i	0.854260	−	0.187471i
$745$		0			0
$746$	−15.7740	−	21.2854i	−0.577527	−	0.779313i
$747$	−22.4390	−	5.79954i	−0.820999	−	0.212194i
$748$	39.6236	+	12.0520i	1.44878	+	0.440665i
$749$	54.1926			1.98016
$750$		0			0
$751$			7.58573i			0.276807i	0.990376	+	0.138404i	$0.0441971\pi$
$751$			7.58573i			0.276807i	−0.990376	+	0.138404i	$0.955803\pi$
$752$	−24.3161	+	36.2742i	−0.886716	+	1.32278i
$753$	3.00642	+	0.382237i	0.109560	+	0.0139295i
$754$	−1.52804	−	2.06193i	−0.0556478	−	0.0750909i
$755$		0			0
$756$	29.5753	+	23.6561i	1.07564	+	0.860366i
$757$	−31.1258			−1.13129			−0.565643	−	0.824650i	$-0.691372\pi$
$757$	−31.1258			−1.13129			−0.565643	+	0.824650i	$0.691372\pi$
$758$	−7.47921	−	10.0924i	−0.271657	−	0.366573i
$759$	−5.21043	+	40.9817i	−0.189127	+	1.48754i
$760$		0			0
$761$			8.24575i			0.298908i	0.988769	+	0.149454i	$0.0477516\pi$
$761$			8.24575i			0.298908i	−0.988769	+	0.149454i	$0.952248\pi$
$762$	12.0269	−	6.74789i	0.435687	−	0.244450i
$763$			38.4017i			1.39024i
$764$	−3.77780	+	12.4204i	−0.136676	+	0.449353i
$765$		0			0
$766$	3.95880	−	2.93376i	0.143037	−	0.106001i
$767$			1.34484i			0.0485594i
$768$	−26.7581	+	7.21146i	−0.965549	+	0.260221i
$769$	26.3262			0.949347			0.474674	−	0.880162i	$-0.342566\pi$
$769$	26.3262			0.949347			0.474674	+	0.880162i	$0.342566\pi$
$770$		0			0
$771$	1.15267	−	9.06612i	0.0415124	−	0.326508i
$772$	21.8158	+	6.63555i	0.785169	+	0.238819i
$773$		−	27.2417i		−	0.979817i	−0.871774	−	0.489909i	$-0.837030\pi$
$773$		−	27.2417i		−	0.979817i	0.871774	−	0.489909i	$-0.162970\pi$
$774$	−13.5132	+	5.47332i	−0.485722	+	0.196734i
$775$		0			0
$776$	7.03041	+	19.7183i	0.252377	+	0.707845i
$777$	−6.02518	+	47.3900i	−0.216152	+	1.70011i
$778$	−20.8844	−	28.1813i	−0.748741	−	1.01035i
$779$		−	1.89812i		−	0.0680074i
$780$		0			0
$781$			31.5447i			1.12876i
$782$	−21.7975	+	16.1535i	−0.779478	+	0.577649i
$783$	−2.04711	+	5.13445i	−0.0731577	+	0.183490i
$784$	−20.8679	−	13.9886i	−0.745281	−	0.499592i
$785$		0			0
$786$	−1.99219	−	3.55072i	−0.0710592	−	0.126650i
$787$		−	26.9324i		−	0.960037i	−0.877258	−	0.480019i	$-0.840630\pi$
$787$		−	26.9324i		−	0.960037i	0.877258	−	0.480019i	$-0.159370\pi$
$788$	−6.81361	−	2.07244i	−0.242725	−	0.0738277i
$789$	−3.07636	−	0.391129i	−0.109521	−	0.0139246i
$790$		0			0
$791$	36.2369			1.28843
$792$	3.85116	+	42.8820i	0.136845	+	1.52374i
$793$			1.07064i			0.0380195i
$794$	−13.1249	−	17.7107i	−0.465785	−	0.628528i
$795$		0			0
$796$	−8.42822	−	2.56354i	−0.298730	−	0.0908624i
$797$		−	13.1279i		−	0.465016i	−0.972595	−	0.232508i	$-0.925307\pi$
$797$		−	13.1279i		−	0.465016i	0.972595	−	0.232508i	$-0.0746931\pi$
$798$	−9.84193	+	5.52199i	−0.348400	+	0.195476i
$799$			44.5565i			1.57629i
$800$		0			0
$801$	8.68886	−	33.6180i	0.307006	−	1.18783i
$802$	29.9794	−	22.2169i	1.05861	−	0.784506i
$803$	−21.3966			−0.755071
$804$	5.92977	−	13.2169i	0.209127	−	0.466123i
$805$		0			0
$806$	−9.43868	+	6.99474i	−0.332463	+	0.246379i
$807$	4.08685	−	32.1444i	0.143864	−	1.13154i
$808$	27.0506	−	9.64470i	0.951636	−	0.339299i
$809$			29.5632i			1.03939i	0.854353	+	0.519693i	$0.173954\pi$
$809$			29.5632i			1.03939i	−0.854353	+	0.519693i	$0.826046\pi$
$810$		0			0
$811$	29.2269			1.02629			0.513147	−	0.858301i	$-0.328480\pi$
$811$	29.2269			1.02629			0.513147	+	0.858301i	$0.328480\pi$
$812$	2.25620	−	7.41776i	0.0791772	−	0.260312i
$813$	42.6877	+	5.42733i	1.49712	+	0.190345i
$814$	−43.6329	+	32.3351i	−1.52933	+	1.13334i
$815$		0			0
$816$	−18.5805	+	21.3132i	−0.650446	+	0.746112i
$817$		−	4.34443i		−	0.151992i
$818$	0.418605	+	0.564865i	0.0146362	+	0.0197500i
$819$	−18.0573	−	4.66707i	−0.630973	−	0.163081i
$820$		0			0
$821$	−5.29201			−0.184692			−0.0923462	−	0.995727i	$-0.529437\pi$
$821$	−5.29201			−0.184692			−0.0923462	+	0.995727i	$0.529437\pi$
$822$	28.5301	−	16.0073i	0.995102	−	0.558320i
$823$	−16.0047			−0.557890			−0.278945	−	0.960307i	$-0.589985\pi$
$823$	−16.0047			−0.557890			−0.278945	+	0.960307i	$0.589985\pi$
$824$	−41.4008	+	14.7612i	−1.44227	+	0.514230i
$825$		0			0
$826$	−3.26422	+	2.41903i	−0.113577	+	0.0841687i
$827$	4.13539			0.143802			0.0719009	−	0.997412i	$-0.477093\pi$
$827$	4.13539			0.143802			0.0719009	+	0.997412i	$0.477093\pi$
$828$	−24.0712	−	14.6984i	−0.836531	−	0.510806i
$829$			22.5879i			0.784512i	0.919856	+	0.392256i	$0.128305\pi$
$829$			22.5879i			0.784512i	−0.919856	+	0.392256i	$0.871695\pi$
$830$		0			0
$831$	6.37954	−	50.1771i	0.221304	−	1.74063i
$832$	10.5690	−	8.63424i	0.366415	−	0.299339i
$833$	−25.6325			−0.888113
$834$	30.6633	−	17.2042i	1.06178	−	0.595733i
$835$		0			0
$836$	−12.2742	−	3.73335i	−0.424512	−	0.129120i
$837$	23.5035	+	9.37084i	0.812399	+	0.323904i
$838$	−12.5257	+	9.28242i	−0.432692	+	0.320656i
$839$	−32.0329			−1.10590			−0.552949	−	0.833215i	$-0.686498\pi$
$839$	−32.0329			−1.10590			−0.552949	+	0.833215i	$0.686498\pi$
$840$		0			0
$841$	−27.8684			−0.960979
$842$	−12.6088	+	9.34402i	−0.434527	+	0.322016i
$843$	−39.4944	−	5.02133i	−1.36026	−	0.172944i
$844$	9.39176	−	30.8775i	0.323278	−	1.06285i
$845$		0			0
$846$	−42.9314	+	17.3887i	−1.47601	+	0.597836i
$847$	−53.7374			−1.84644
$848$	19.7621	−	29.4806i	0.678632	−	1.01237i
$849$	−3.49677	−	0.444581i	−0.120009	−	0.0152580i
$850$		0			0
$851$		−	35.5760i		−	1.21953i
$852$	−19.6490	−	8.81557i	−0.673163	−	0.302016i
$853$	−10.3607			−0.354745			−0.177372	−	0.984144i	$-0.556760\pi$
$853$	−10.3607			−0.354745			−0.177372	+	0.984144i	$0.556760\pi$
$854$	−2.59867	+	1.92581i	−0.0889248	+	0.0658997i
$855$		0			0
$856$	−39.6177	+	14.1254i	−1.35411	+	0.482797i
$857$	18.1893			0.621334			0.310667	−	0.950519i	$-0.399448\pi$
$857$	18.1893			0.621334			0.310667	+	0.950519i	$0.399448\pi$
$858$	−10.3748	−	18.4911i	−0.354188	−	0.631276i
$859$	−27.2650			−0.930271			−0.465136	−	0.885239i	$-0.653994\pi$
$859$	−27.2650			−0.930271			−0.465136	+	0.885239i	$0.653994\pi$
$860$		0			0
$861$	9.40133	+	1.19529i	0.320396	+	0.0407353i
$862$	−5.75943	−	7.77176i	−0.196167	−	0.264707i
$863$		−	12.4082i		−	0.422381i	−0.977445	−	0.211191i	$-0.932266\pi$
$863$		−	12.4082i		−	0.422381i	0.977445	−	0.211191i	$-0.0677341\pi$
$864$	−27.7872	−	9.58505i	−0.945339	−	0.326090i
$865$		0			0
$866$	−43.9011	+	32.5338i	−1.49182	+	1.10555i
$867$	0.0751522	−	0.591096i	0.00255230	−	0.0200747i
$868$	−33.9556	−	10.3280i	−1.15253	−	0.350555i
$869$	−5.03776			−0.170894
$870$		0			0
$871$			7.13386i			0.241722i
$872$	−10.0095	−	28.0737i	−0.338964	−	0.950697i
$873$	−5.55623	+	21.4976i	−0.188050	+	0.727582i
$874$	6.75221	−	5.00388i	0.228397	−	0.169259i
$875$		0			0
$876$	5.97956	−	13.3278i	0.202031	−	0.450306i
$877$	−9.19349			−0.310442			−0.155221	−	0.987880i	$-0.549609\pi$
$877$	−9.19349			−0.310442			−0.155221	+	0.987880i	$0.549609\pi$
$878$	−4.63474	+	3.43468i	−0.156415	+	0.115915i
$879$	10.3093	+	1.31073i	0.347725	+	0.0442098i
$880$		0			0
$881$			38.4479i			1.29534i	0.761920	+	0.647671i	$0.224257\pi$
$881$			38.4479i			1.29534i	−0.761920	+	0.647671i	$0.775743\pi$
$882$	−10.0034	−	24.6976i	−0.336832	−	0.831612i
$883$		−	5.12406i		−	0.172438i	−0.996276	−	0.0862192i	$-0.972521\pi$
$883$		−	5.12406i		−	0.172438i	0.996276	−	0.0862192i	$-0.0274785\pi$
$884$	4.05201	−	13.3219i	0.136284	−	0.448063i
$885$		0			0
$886$	−10.7054	−	14.4459i	−0.359656	−	0.485319i
$887$			1.79043i			0.0601169i	0.999548	+	0.0300584i	$0.00956934\pi$
$887$			1.79043i			0.0601169i	−0.999548	+	0.0300584i	$0.990431\pi$
$888$	−7.94757	−	36.2151i	−0.266703	−	1.21530i
$889$	−20.5171			−0.688121
$890$		0			0
$891$	−22.1275	+	39.9472i	−0.741300	+	1.33828i
$892$	3.54713	−	11.6620i	0.118767	−	0.390471i
$893$		−	13.8022i		−	0.461874i
$894$	−39.0377	+	21.9028i	−1.30562	+	0.732540i
$895$		0			0
$896$	39.9682	+	10.1226i	1.33524	+	0.338171i
$897$	13.7785	+	1.75180i	0.460050	+	0.0584909i
$898$	35.5620	−	26.3540i	1.18672	−	0.879444i
$899$		−	5.18002i		−	0.172763i
$900$		0			0
$901$		−	36.2118i		−	1.20639i
$902$	6.41471	+	8.65598i	0.213586	+	0.288213i
$903$	21.5178	+	2.73578i	0.716066	+	0.0910409i
$904$	−26.4911	+	9.44522i	−0.881081	+	0.314143i
$905$		0			0
$906$	20.0942	+	35.8142i	0.667584	+	1.18985i
$907$			34.5506i			1.14724i	0.819123	+	0.573618i	$0.194460\pi$
$907$			34.5506i			1.14724i	−0.819123	+	0.573618i	$0.805540\pi$
$908$	−11.9119	+	39.1630i	−0.395311	+	1.29967i
$909$	29.4915	+	7.62234i	0.978172	+	0.252817i
$910$		0			0
$911$	−52.6515			−1.74442			−0.872211	−	0.489130i	$-0.837314\pi$
$911$	−52.6515			−1.74442			−0.872211	+	0.489130i	$0.837314\pi$
$912$	5.75566	−	6.60219i	0.190589	−	0.218620i
$913$			39.1991i			1.29730i
$914$	−33.0751	+	24.5110i	−1.09403	+	0.810753i
$915$		0			0
$916$	50.6542	+	15.4071i	1.67366	+	0.509064i
$917$			6.05731i			0.200030i
$918$	−28.9949	+	7.66290i	−0.956974	+	0.252913i
$919$			13.0595i			0.430794i	0.976527	+	0.215397i	$0.0691046\pi$
$919$			13.0595i			0.430794i	−0.976527	+	0.215397i	$0.930895\pi$
$920$		0			0
$921$	−32.7401	−	4.16259i	−1.07882	−	0.137162i
$922$	−0.00578529	−	0.00780665i	−0.000190528	−	0.000257098i
$923$	10.6056			0.349089
$924$	26.2204	−	58.4426i	0.862588	−	1.92262i
$925$		0			0
$926$	15.1483	+	20.4411i	0.497805	+	0.671737i
$927$	−45.1367	−	11.6660i	−1.48248	−	0.383160i
$928$	0.284051	+	6.01087i	0.00932444	+	0.197316i
$929$			20.9794i			0.688313i	0.938912	+	0.344156i	$0.111835\pi$
$929$			20.9794i			0.688313i	−0.938912	+	0.344156i	$0.888165\pi$
$930$		0			0
$931$	7.94016			0.260228
$932$	14.1875	−	46.6446i	0.464728	−	1.52790i
$933$	−5.69953	+	44.8287i	−0.186594	+	1.46762i
$934$	3.36748	+	4.54406i	0.110187	+	0.148686i
$935$		0			0
$936$	14.4174	−	1.29480i	0.471246	−	0.0423219i
$937$			5.78393i			0.188953i	0.995527	+	0.0944764i	$0.0301177\pi$
$937$			5.78393i			0.188953i	−0.995527	+	0.0944764i	$0.969882\pi$
$938$	−17.3155	+	12.8320i	−0.565370	+	0.418980i
$939$	34.6729	+	4.40832i	1.13151	+	0.143860i
$940$		0			0
$941$	−42.0131			−1.36959			−0.684794	−	0.728737i	$-0.740108\pi$
$941$	−42.0131			−1.36959			−0.684794	+	0.728737i	$0.740108\pi$
$942$	−13.4862	+	7.56667i	−0.439404	+	0.246535i
$943$	−7.05764			−0.229829
$944$	1.75580	−	2.61927i	0.0571464	−	0.0852498i
$945$		0			0
$946$	14.6820	+	19.8118i	0.477353	+	0.644138i
$947$	23.5854			0.766421			0.383211	−	0.923661i	$-0.374818\pi$
$947$	23.5854			0.766421			0.383211	+	0.923661i	$0.374818\pi$
$948$	1.40787	−	3.13799i	0.0457254	−	0.101917i
$949$			7.19377i			0.233520i
$950$		0			0
$951$	−13.4296	−	1.70744i	−0.435484	−	0.0553675i
$952$	39.6236	−	14.1275i	1.28421	−	0.457876i
$953$	−31.8648			−1.03220			−0.516102	−	0.856527i	$-0.672617\pi$
$953$	−31.8648			−1.03220			−0.516102	+	0.856527i	$0.672617\pi$
$954$	34.8911	−	14.1321i	1.12964	−	0.457543i
$955$		0			0
$956$	−3.18443	+	10.4695i	−0.102992	+	0.338609i
$957$	9.27423	+	1.17913i	0.299793	+	0.0381159i
$958$	28.7522	+	38.7982i	0.928943	+	1.25351i
$959$	−48.6706			−1.57166
$960$		0			0
$961$	7.28794			0.235095
$962$	10.8714	+	14.6698i	0.350508	+	0.472974i
$963$	−43.1927	−	11.1635i	−1.39186	−	0.359739i
$964$	−14.3431	+	47.1562i	−0.461961	+	1.51880i
$965$		0			0
$966$	20.5320	+	36.5944i	0.660605	+	1.17741i
$967$	11.1038			0.357073			0.178537	−	0.983933i	$-0.442864\pi$
$967$	11.1038			0.357073			0.178537	+	0.983933i	$0.442864\pi$
$968$	39.2850	−	14.0068i	1.26267	−	0.450195i
$969$	1.12712	−	8.86519i	0.0362084	−	0.284791i
$970$		0			0
$971$			47.5500i			1.52595i	0.646427	+	0.762976i	$0.276263\pi$
$971$			47.5500i			1.52595i	−0.646427	+	0.762976i	$0.723737\pi$
$972$	−18.6990	−	24.9469i	−0.599772	−	0.800171i
$973$	−52.3097			−1.67697
$974$	0.717251	+	0.967856i	0.0229822	+	0.0310121i
$975$		0			0
$976$	1.39781	−	2.08522i	0.0447427	−	0.0667462i
$977$	−51.9896			−1.66329			−0.831647	−	0.555304i	$-0.812602\pi$
$977$	−51.9896			−1.66329			−0.831647	+	0.555304i	$0.812602\pi$
$978$	3.22545	+	5.74878i	0.103139	+	0.183826i
$979$	−58.7279			−1.87695
$980$		0			0
$981$	7.91064	−	30.6070i	0.252567	−	0.977206i
$982$	6.92090	−	5.12888i	0.220855	−	0.163669i
$983$		−	27.4842i		−	0.876609i	−0.898826	−	0.438305i	$-0.855579\pi$
$983$		−	27.4842i		−	0.876609i	0.898826	−	0.438305i	$-0.144421\pi$
$984$	−7.18443	+	1.57666i	−0.229031	+	0.0502620i
$985$		0			0
$986$	3.65557	+	4.93281i	0.116417	+	0.157093i
$987$	68.3619	+	8.69155i	2.17598	+	0.276655i
$988$	−1.25519	+	4.12671i	−0.0399329	+	0.131288i
$989$	−16.1535			−0.513653
$990$		0			0
$991$			24.4556i			0.776858i	0.921479	+	0.388429i	$0.126982\pi$
$991$			24.4556i			0.776858i	−0.921479	+	0.388429i	$0.873018\pi$
$992$	27.5154	−	1.30027i	0.873614	−	0.0412837i
$993$	2.19382	−	17.2551i	0.0696188	−	0.547575i
$994$	19.0769	+	25.7422i	0.605081	+	0.816494i
$995$		0			0
$996$	−24.4169	−	10.9547i	−0.773678	−	0.347113i
$997$	−39.1729			−1.24062			−0.620309	−	0.784358i	$-0.712993\pi$
$997$	−39.1729			−1.24062			−0.620309	+	0.784358i	$0.712993\pi$
$998$	−11.0621	−	14.9271i	−0.350164	−	0.472510i
$999$	14.5644	−	36.5296i	0.460797	−	1.15575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.m.c.299.12		16
3.2	odd	2		600.2.m.d.299.5		16
4.3	odd	2		2400.2.m.d.1199.9		16
5.2	odd	4		600.2.b.f.251.2		8
5.3	odd	4		120.2.b.a.11.7	✓	8
5.4	even	2	inner	600.2.m.c.299.5		16
8.3	odd	2		600.2.m.d.299.11		16
8.5	even	2		2400.2.m.c.1199.9		16
12.11	even	2		2400.2.m.c.1199.7		16
15.2	even	4		600.2.b.e.251.7		8
15.8	even	4		120.2.b.b.11.2	yes	8
15.14	odd	2		600.2.m.d.299.12		16
20.3	even	4		480.2.b.b.431.8		8
20.7	even	4		2400.2.b.f.2351.1		8
20.19	odd	2		2400.2.m.d.1199.8		16
24.5	odd	2		2400.2.m.d.1199.7		16
24.11	even	2	inner	600.2.m.c.299.6		16
40.3	even	4		120.2.b.b.11.1	yes	8
40.13	odd	4		480.2.b.a.431.8		8
40.19	odd	2		600.2.m.d.299.6		16
40.27	even	4		600.2.b.e.251.8		8
40.29	even	2		2400.2.m.c.1199.8		16
40.37	odd	4		2400.2.b.e.2351.1		8
60.23	odd	4		480.2.b.a.431.7		8
60.47	odd	4		2400.2.b.e.2351.2		8
60.59	even	2		2400.2.m.c.1199.10		16
120.29	odd	2		2400.2.m.d.1199.10		16
120.53	even	4		480.2.b.b.431.7		8
120.59	even	2	inner	600.2.m.c.299.11		16
120.77	even	4		2400.2.b.f.2351.2		8
120.83	odd	4		120.2.b.a.11.8	yes	8
120.107	odd	4		600.2.b.f.251.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.b.a.11.7	✓	8	5.3	odd	4
120.2.b.a.11.8	yes	8	120.83	odd	4
120.2.b.b.11.1	yes	8	40.3	even	4
120.2.b.b.11.2	yes	8	15.8	even	4
480.2.b.a.431.7		8	60.23	odd	4
480.2.b.a.431.8		8	40.13	odd	4
480.2.b.b.431.7		8	120.53	even	4
480.2.b.b.431.8		8	20.3	even	4
600.2.b.e.251.7		8	15.2	even	4
600.2.b.e.251.8		8	40.27	even	4
600.2.b.f.251.1		8	120.107	odd	4
600.2.b.f.251.2		8	5.2	odd	4
600.2.m.c.299.5		16	5.4	even	2	inner
600.2.m.c.299.6		16	24.11	even	2	inner
600.2.m.c.299.11		16	120.59	even	2	inner
600.2.m.c.299.12		16	1.1	even	1	trivial
600.2.m.d.299.5		16	3.2	odd	2
600.2.m.d.299.6		16	40.19	odd	2
600.2.m.d.299.11		16	8.3	odd	2
600.2.m.d.299.12		16	15.14	odd	2
2400.2.b.e.2351.1		8	40.37	odd	4
2400.2.b.e.2351.2		8	60.47	odd	4
2400.2.b.f.2351.1		8	20.7	even	4
2400.2.b.f.2351.2		8	120.77	even	4
2400.2.m.c.1199.7		16	12.11	even	2
2400.2.m.c.1199.8		16	40.29	even	2
2400.2.m.c.1199.9		16	8.5	even	2
2400.2.m.c.1199.10		16	60.59	even	2
2400.2.m.d.1199.7		16	24.5	odd	2
2400.2.m.d.1199.8		16	20.19	odd	2
2400.2.m.d.1199.9		16	4.3	odd	2
2400.2.m.d.1199.10		16	120.29	odd	2

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.m (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.842022 + 1.13622i) q^{2} +(-0.218455 + 1.71822i) q^{3} +(-0.581998 + 1.91345i) q^{4} +(-2.13622 + 1.19857i) q^{6} +3.64426 q^{7} +(-2.66415 + 0.949886i) q^{8} +(-2.90455 - 0.750707i) q^{9} +O(q^{10})\)	\(q+(0.842022 + 1.13622i) q^{2} +(-0.218455 + 1.71822i) q^{3} +(-0.581998 + 1.91345i) q^{4} +(-2.13622 + 1.19857i) q^{6} +3.64426 q^{7} +(-2.66415 + 0.949886i) q^{8} +(-2.90455 - 0.750707i) q^{9} +5.07403i q^{11} +(-3.16058 - 1.41800i) q^{12} +1.70594 q^{13} +(3.06855 + 4.14069i) q^{14} +(-3.32256 - 2.22724i) q^{16} -4.08117 q^{17} +(-1.59273 - 3.93233i) q^{18} +1.26422 q^{19} +(-0.796108 + 6.26164i) q^{21} +(-5.76522 + 4.27244i) q^{22} -4.70066i q^{23} +(-1.05011 - 4.78511i) q^{24} +(1.43644 + 1.93832i) q^{26} +(1.92439 - 4.82667i) q^{27} +(-2.12095 + 6.97311i) q^{28} -1.06377 q^{29} +4.86950i q^{31} +(-0.267024 - 5.65055i) q^{32} +(-8.71829 - 1.10845i) q^{33} +(-3.43644 - 4.63712i) q^{34} +(3.12688 - 5.12080i) q^{36} +7.56830 q^{37} +(1.06450 + 1.43644i) q^{38} +(-0.372671 + 2.93118i) q^{39} -1.50141i q^{41} +(-7.78495 + 4.36789i) q^{42} -3.43644i q^{43} +(-9.70888 - 2.95307i) q^{44} +(5.34099 - 3.95806i) q^{46} -10.9176i q^{47} +(4.55272 - 5.22233i) q^{48} +6.28066 q^{49} +(0.891553 - 7.01235i) q^{51} +(-0.992853 + 3.26422i) q^{52} +8.87288i q^{53} +(7.10454 - 1.87762i) q^{54} +(-9.70888 + 3.46163i) q^{56} +(-0.276176 + 2.17221i) q^{57} +(-0.895716 - 1.20868i) q^{58} +0.788328i q^{59} +0.627594i q^{61} +(-5.53283 + 4.10023i) q^{62} +(-10.5850 - 2.73578i) q^{63} +(6.19543 - 5.06128i) q^{64} +(-6.08155 - 10.8392i) q^{66} +4.18178i q^{67} +(2.37523 - 7.80911i) q^{68} +(8.07677 + 1.02688i) q^{69} +6.21689 q^{71} +(8.45127 - 0.758995i) q^{72} +4.21689i q^{73} +(6.37267 + 8.59926i) q^{74} +(-0.735776 + 2.41903i) q^{76} +18.4911i q^{77} +(-3.64426 + 2.04468i) q^{78} +0.992853i q^{79} +(7.87288 + 4.36094i) q^{81} +(1.70594 - 1.26422i) q^{82} +7.72544 q^{83} +(-11.5180 - 5.16757i) q^{84} +(3.90455 - 2.89356i) q^{86} +(0.232385 - 1.82779i) q^{87} +(-4.81975 - 13.5180i) q^{88} +11.5742i q^{89} +6.21689 q^{91} +(8.99447 + 2.73578i) q^{92} +(-8.36687 - 1.06377i) q^{93} +(12.4048 - 9.19282i) q^{94} +(9.76721 + 0.775585i) q^{96} -7.40133i q^{97} +(5.28845 + 7.13622i) q^{98} +(3.80911 - 14.7378i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4} - 14 q^{6}+O(q^{10}) \) 16 * q - 2 * q^4 - 14 * q^6	\( 16 q - 2 q^{4} - 14 q^{6} - 12 q^{14} - 14 q^{16} + 8 q^{19} + 8 q^{21} - 18 q^{24} - 32 q^{26} - 38 q^{36} + 32 q^{39} - 60 q^{44} - 16 q^{46} + 32 q^{49} + 40 q^{51} + 30 q^{54} - 60 q^{56} - 50 q^{64} + 36 q^{66} + 40 q^{69} + 48 q^{71} + 64 q^{74} - 24 q^{76} + 16 q^{81} + 4 q^{84} + 16 q^{86} + 48 q^{91} + 80 q^{94} + 34 q^{96} - 32 q^{99}+O(q^{100}) \) 16 * q - 2 * q^4 - 14 * q^6 - 12 * q^14 - 14 * q^16 + 8 * q^19 + 8 * q^21 - 18 * q^24 - 32 * q^26 - 38 * q^36 + 32 * q^39 - 60 * q^44 - 16 * q^46 + 32 * q^49 + 40 * q^51 + 30 * q^54 - 60 * q^56 - 50 * q^64 + 36 * q^66 + 40 * q^69 + 48 * q^71 + 64 * q^74 - 24 * q^76 + 16 * q^81 + 4 * q^84 + 16 * q^86 + 48 * q^91 + 80 * q^94 + 34 * q^96 - 32 * q^99

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