LMFDB - Embedded newform 605.2.e.c.362.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(362,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("605.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			362.15
Character	$\chi$	$=$	605.362
Dual form			605.2.e.c.483.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05784 - 1.05784i) q^{2} +(1.53861 - 1.53861i) q^{3} -0.238041i q^{4} +(-1.92587 - 1.13622i) q^{5} -3.25521i q^{6} +(1.66576 - 1.66576i) q^{7} +(1.86387 + 1.86387i) q^{8} -1.73467i q^{9} +O(q^{10})$	\(q+(1.05784 - 1.05784i) q^{2} +(1.53861 - 1.53861i) q^{3} -0.238041i q^{4} +(-1.92587 - 1.13622i) q^{5} -3.25521i q^{6} +(1.66576 - 1.66576i) q^{7} +(1.86387 + 1.86387i) q^{8} -1.73467i q^{9} +(-3.23920 + 0.835322i) q^{10} +(-0.366253 - 0.366253i) q^{12} +(-4.40803 - 4.40803i) q^{13} -3.52421i q^{14} +(-4.71139 + 1.21497i) q^{15} +4.41942 q^{16} +(3.57788 - 3.57788i) q^{17} +(-1.83500 - 1.83500i) q^{18} +0.201039 q^{19} +(-0.270468 + 0.458437i) q^{20} -5.12593i q^{21} +(-2.77807 + 2.77807i) q^{23} +5.73555 q^{24} +(2.41799 + 4.37645i) q^{25} -9.32596 q^{26} +(1.94685 + 1.94685i) q^{27} +(-0.396519 - 0.396519i) q^{28} +2.19713 q^{29} +(-3.69865 + 6.26913i) q^{30} -6.45739 q^{31} +(0.947293 - 0.947293i) q^{32} -7.56963i q^{34} +(-5.10073 + 1.31537i) q^{35} -0.412922 q^{36} +(6.07431 + 6.07431i) q^{37} +(0.212666 - 0.212666i) q^{38} -13.5645 q^{39} +(-1.47180 - 5.70734i) q^{40} -2.91702i q^{41} +(-5.42240 - 5.42240i) q^{42} +(2.16502 + 2.16502i) q^{43} +(-1.97098 + 3.34076i) q^{45} +5.87749i q^{46} +(6.27650 + 6.27650i) q^{47} +(6.79978 - 6.79978i) q^{48} +1.45048i q^{49} +(7.18741 + 2.07174i) q^{50} -11.0099i q^{51} +(-1.04929 + 1.04929i) q^{52} +(-5.53885 + 5.53885i) q^{53} +4.11891 q^{54} +6.20951 q^{56} +(0.309321 - 0.309321i) q^{57} +(2.32421 - 2.32421i) q^{58} -10.9768i q^{59} +(0.289212 + 1.12150i) q^{60} +3.92965i q^{61} +(-6.83087 + 6.83087i) q^{62} +(-2.88955 - 2.88955i) q^{63} +6.83467i q^{64} +(3.48080 + 13.4978i) q^{65} +(-0.637836 - 0.637836i) q^{67} +(-0.851681 - 0.851681i) q^{68} +8.54875i q^{69} +(-4.00429 + 6.78719i) q^{70} +1.45273 q^{71} +(3.23320 - 3.23320i) q^{72} +(6.80990 + 6.80990i) q^{73} +12.8513 q^{74} +(10.4540 + 3.01332i) q^{75} -0.0478554i q^{76} +(-14.3491 + 14.3491i) q^{78} +8.04884 q^{79} +(-8.51125 - 5.02145i) q^{80} +11.1949 q^{81} +(-3.08573 - 3.08573i) q^{82} +(-1.70913 - 1.70913i) q^{83} -1.22018 q^{84} +(-10.9558 + 2.82527i) q^{85} +4.58048 q^{86} +(3.38054 - 3.38054i) q^{87} -10.2196i q^{89} +(1.44901 + 5.61895i) q^{90} -14.6855 q^{91} +(0.661293 + 0.661293i) q^{92} +(-9.93544 + 9.93544i) q^{93} +13.2790 q^{94} +(-0.387176 - 0.228425i) q^{95} -2.91504i q^{96} +(-2.07047 - 2.07047i) q^{97} +(1.53437 + 1.53437i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{3} - 4 q^{5}+O(q^{10}) $ 40 * q + 8 * q^3 - 4 * q^5	$ 40 q + 8 q^{3} - 4 q^{5} - 32 q^{12} + 32 q^{15} - 24 q^{16} + 32 q^{20} - 24 q^{23} - 52 q^{25} - 8 q^{26} + 32 q^{27} + 16 q^{31} - 40 q^{36} + 36 q^{37} + 32 q^{38} + 32 q^{42} + 64 q^{45} + 32 q^{47} - 16 q^{48} - 68 q^{53} + 80 q^{56} + 132 q^{58} - 64 q^{60} - 88 q^{67} - 8 q^{70} - 16 q^{75} - 248 q^{78} - 164 q^{80} - 40 q^{81} + 100 q^{82} - 80 q^{86} - 96 q^{91} - 56 q^{92} + 24 q^{93} - 68 q^{97}+O(q^{100}) $ 40 * q + 8 * q^3 - 4 * q^5 - 32 * q^12 + 32 * q^15 - 24 * q^16 + 32 * q^20 - 24 * q^23 - 52 * q^25 - 8 * q^26 + 32 * q^27 + 16 * q^31 - 40 * q^36 + 36 * q^37 + 32 * q^38 + 32 * q^42 + 64 * q^45 + 32 * q^47 - 16 * q^48 - 68 * q^53 + 80 * q^56 + 132 * q^58 - 64 * q^60 - 88 * q^67 - 8 * q^70 - 16 * q^75 - 248 * q^78 - 164 * q^80 - 40 * q^81 + 100 * q^82 - 80 * q^86 - 96 * q^91 - 56 * q^92 + 24 * q^93 - 68 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	1.05784	−	1.05784i	0.748004	−	0.748004i	−0.226100	−	0.974104i	$-0.572598\pi$
$2$	1.05784	−	1.05784i	0.748004	−	0.748004i	0.974104	+	0.226100i	$0.0725976\pi$
$3$	1.53861	−	1.53861i	0.888320	−	0.888320i	−0.106042	−	0.994362i	$-0.533818\pi$
$3$	1.53861	−	1.53861i	0.888320	−	0.888320i	0.994362	+	0.106042i	$0.0338178\pi$
$4$		−	0.238041i		−	0.119020i
$5$	−1.92587	−	1.13622i	−0.861277	−	0.508135i
$5$	−1.92587	−	1.13622i	−0.861277	−	0.508135i
$6$		−	3.25521i		−	1.32893i
$7$	1.66576	−	1.66576i	0.629598	−	0.629598i	−0.318369	−	0.947967i	$-0.603135\pi$
$7$	1.66576	−	1.66576i	0.629598	−	0.629598i	0.947967	+	0.318369i	$0.103135\pi$
$8$	1.86387	+	1.86387i	0.658976	+	0.658976i
$9$		−	1.73467i		−	0.578224i
$10$	−3.23920	+	0.835322i	−1.02433	+	0.264152i
$11$		0			0
$11$		0			0
$12$	−0.366253	−	0.366253i	−0.105728	−	0.105728i
$13$	−4.40803	−	4.40803i	−1.22257	−	1.22257i	−0.966716	−	0.255852i	$-0.917644\pi$
$13$	−4.40803	−	4.40803i	−1.22257	−	1.22257i	−0.255852	−	0.966716i	$-0.582356\pi$
$14$		−	3.52421i		−	0.941884i
$15$	−4.71139	+	1.21497i	−1.21648	+	0.313703i
$16$	4.41942			1.10485
$17$	3.57788	−	3.57788i	0.867763	−	0.867763i	−0.124462	−	0.992224i	$-0.539720\pi$
$17$	3.57788	−	3.57788i	0.867763	−	0.867763i	0.992224	+	0.124462i	$0.0397204\pi$
$18$	−1.83500	−	1.83500i	−0.432514	−	0.432514i
$19$	0.201039			0.0461215			0.0230607	−	0.999734i	$-0.492659\pi$
$19$	0.201039			0.0461215			0.0230607	+	0.999734i	$0.492659\pi$
$20$	−0.270468	+	0.458437i	−0.0604784	+	0.102510i
$21$		−	5.12593i		−	1.11857i
$22$		0			0
$23$	−2.77807	+	2.77807i	−0.579267	+	0.579267i	−0.934701	−	0.355434i	$-0.884333\pi$
$23$	−2.77807	+	2.77807i	−0.579267	+	0.579267i	0.355434	+	0.934701i	$0.384333\pi$
$24$	5.73555			1.17076
$25$	2.41799	+	4.37645i	0.483598	+	0.875290i
$26$	−9.32596			−1.82897
$27$	1.94685	+	1.94685i	0.374672	+	0.374672i
$28$	−0.396519	−	0.396519i	−0.0749350	−	0.0749350i
$29$	2.19713			0.407997			0.203999	−	0.978971i	$-0.434606\pi$
$29$	2.19713			0.407997			0.203999	+	0.978971i	$0.434606\pi$
$30$	−3.69865	+	6.26913i	−0.675278	+	1.14458i
$31$	−6.45739			−1.15978			−0.579891	−	0.814694i	$-0.696905\pi$
$31$	−6.45739			−1.15978			−0.579891	+	0.814694i	$0.696905\pi$
$32$	0.947293	−	0.947293i	0.167459	−	0.167459i
$33$		0			0
$34$		−	7.56963i		−	1.29818i
$35$	−5.10073	+	1.31537i	−0.862180	+	0.222338i
$36$	−0.412922			−0.0688204
$37$	6.07431	+	6.07431i	0.998611	+	0.998611i	0.999999	−	0.00138797i	$-0.000441805\pi$
$37$	6.07431	+	6.07431i	0.998611	+	0.998611i	−0.00138797	+	0.999999i	$0.500442\pi$
$38$	0.212666	−	0.212666i	0.0344991	−	0.0344991i
$39$	−13.5645			−2.17206
$40$	−1.47180	−	5.70734i	−0.232713	−	0.902410i
$41$		−	2.91702i		−	0.455562i	−0.973712	−	0.227781i	$-0.926853\pi$
$41$		−	2.91702i		−	0.455562i	0.973712	−	0.227781i	$-0.0731470\pi$
$42$	−5.42240	−	5.42240i	−0.836695	−	0.836695i
$43$	2.16502	+	2.16502i	0.330163	+	0.330163i	0.852648	−	0.522486i	$-0.174995\pi$
$43$	2.16502	+	2.16502i	0.330163	+	0.330163i	−0.522486	+	0.852648i	$0.674995\pi$
$44$		0			0
$45$	−1.97098	+	3.34076i	−0.293816	+	0.498011i
$46$			5.87749i			0.866589i
$47$	6.27650	+	6.27650i	0.915522	+	0.915522i	0.996700	−	0.0811776i	$-0.0258681\pi$
$47$	6.27650	+	6.27650i	0.915522	+	0.915522i	−0.0811776	+	0.996700i	$0.525868\pi$
$48$	6.79978	−	6.79978i	0.981464	−	0.981464i
$49$			1.45048i			0.207212i
$50$	7.18741	+	2.07174i	1.01645	+	0.292988i
$51$		−	11.0099i		−	1.54170i
$52$	−1.04929	+	1.04929i	−0.145510	+	0.145510i
$53$	−5.53885	+	5.53885i	−0.760819	+	0.760819i	−0.976470	−	0.215651i	$-0.930813\pi$
$53$	−5.53885	+	5.53885i	−0.760819	+	0.760819i	0.215651	+	0.976470i	$0.430813\pi$
$54$	4.11891			0.560513
$55$		0			0
$56$	6.20951			0.829781
$57$	0.309321	−	0.309321i	0.0409706	−	0.0409706i
$58$	2.32421	−	2.32421i	0.305184	−	0.305184i
$59$		−	10.9768i		−	1.42906i	−0.699604	−	0.714531i	$-0.746640\pi$
$59$		−	10.9768i		−	1.42906i	0.699604	−	0.714531i	$-0.253360\pi$
$60$	0.289212	+	1.12150i	0.0373371	+	0.144785i
$61$			3.92965i			0.503140i	0.967839	+	0.251570i	$0.0809469\pi$
$61$			3.92965i			0.503140i	−0.967839	+	0.251570i	$0.919053\pi$
$62$	−6.83087	+	6.83087i	−0.867522	+	0.867522i
$63$	−2.88955	−	2.88955i	−0.364049	−	0.364049i
$64$			6.83467i			0.854334i
$65$	3.48080	+	13.4978i	0.431741	+	1.67420i
$66$		0			0
$67$	−0.637836	−	0.637836i	−0.0779241	−	0.0779241i	0.667071	−	0.744995i	$-0.267548\pi$
$67$	−0.637836	−	0.637836i	−0.0779241	−	0.0779241i	−0.744995	+	0.667071i	$0.767548\pi$
$68$	−0.851681	−	0.851681i	−0.103281	−	0.103281i
$69$			8.54875i			1.02915i
$70$	−4.00429	+	6.78719i	−0.478604	+	0.811224i
$71$	1.45273			0.172408			0.0862039	−	0.996278i	$-0.472526\pi$
$71$	1.45273			0.172408			0.0862039	+	0.996278i	$0.472526\pi$
$72$	3.23320	−	3.23320i	0.381036	−	0.381036i
$73$	6.80990	+	6.80990i	0.797039	+	0.797039i	0.982627	−	0.185589i	$-0.0594193\pi$
$73$	6.80990	+	6.80990i	0.797039	+	0.797039i	−0.185589	+	0.982627i	$0.559419\pi$
$74$	12.8513			1.49393
$75$	10.4540	+	3.01332i	1.20713	+	0.347948i
$76$		−	0.0478554i		−	0.00548940i
$77$		0			0
$78$	−14.3491	+	14.3491i	−1.62471	+	1.62471i
$79$	8.04884			0.905566			0.452783	−	0.891621i	$-0.350431\pi$
$79$	8.04884			0.905566			0.452783	+	0.891621i	$0.350431\pi$
$80$	−8.51125	−	5.02145i	−0.951586	−	0.561415i
$81$	11.1949			1.24388
$82$	−3.08573	−	3.08573i	−0.340762	−	0.340762i
$83$	−1.70913	−	1.70913i	−0.187601	−	0.187601i	0.607057	−	0.794658i	$-0.292350\pi$
$83$	−1.70913	−	1.70913i	−0.187601	−	0.187601i	−0.794658	+	0.607057i	$0.792350\pi$
$84$	−1.22018			−0.133133
$85$	−10.9558	+	2.82527i	−1.18832	+	0.306444i
$86$	4.58048			0.493926
$87$	3.38054	−	3.38054i	0.362432	−	0.362432i
$88$		0			0
$89$		−	10.2196i		−	1.08327i	−0.840613	−	0.541636i	$-0.817805\pi$
$89$		−	10.2196i		−	1.08327i	0.840613	−	0.541636i	$-0.182195\pi$
$90$	1.44901	+	5.61895i	0.152739	+	0.592290i
$91$	−14.6855			−1.53945
$92$	0.661293	+	0.661293i	0.0689446	+	0.0689446i
$93$	−9.93544	+	9.93544i	−1.03026	+	1.03026i
$94$	13.2790			1.36963
$95$	−0.387176	−	0.228425i	−0.0397234	−	0.0234359i
$96$		−	2.91504i		−	0.297515i
$97$	−2.07047	−	2.07047i	−0.210225	−	0.210225i	0.594138	−	0.804363i	$-0.297493\pi$
$97$	−2.07047	−	2.07047i	−0.210225	−	0.210225i	−0.804363	+	0.594138i	$0.797493\pi$
$98$	1.53437	+	1.53437i	0.154995	+	0.154995i
$99$		0			0
$100$	1.04177	−	0.575580i	0.104177	−	0.0575580i
$101$			2.48257i			0.247025i	0.992343	+	0.123513i	$0.0394160\pi$
$101$			2.48257i			0.247025i	−0.992343	+	0.123513i	$0.960584\pi$
$102$	−11.6467	−	11.6467i	−1.15320	−	1.15320i
$103$	−9.06035	+	9.06035i	−0.892743	+	0.892743i	−0.994781	−	0.102038i	$-0.967464\pi$
$103$	−9.06035	+	9.06035i	−0.892743	+	0.892743i	0.102038	+	0.994781i	$0.467464\pi$
$104$		−	16.4320i		−	1.61129i
$105$	−5.82420	+	9.87190i	−0.568384	+	0.963399i
$106$			11.7184i			1.13819i
$107$	8.80917	−	8.80917i	0.851614	−	0.851614i	−0.138718	−	0.990332i	$-0.544298\pi$
$107$	8.80917	−	8.80917i	0.851614	−	0.851614i	0.990332	+	0.138718i	$0.0442981\pi$
$108$	0.463431	−	0.463431i	0.0445936	−	0.0445936i
$109$	−11.1595			−1.06889			−0.534445	−	0.845203i	$-0.679479\pi$
$109$	−11.1595			−1.06889			−0.534445	+	0.845203i	$0.679479\pi$
$110$		0			0
$111$	18.6921			1.77417
$112$	7.36169	−	7.36169i	0.695615	−	0.695615i
$113$	−0.108862	+	0.108862i	−0.0102409	+	0.0102409i	−0.712209	−	0.701968i	$-0.752305\pi$
$113$	−0.108862	+	0.108862i	−0.0102409	+	0.0102409i	0.701968	+	0.712209i	$0.252305\pi$
$114$		−	0.654424i		−	0.0612924i
$115$	8.50672	−	2.19370i	0.793256	−	0.204564i
$116$		−	0.523007i		−	0.0485600i
$117$	−7.64648	+	7.64648i	−0.706918	+	0.706918i
$118$	−11.6117	−	11.6117i	−1.06894	−	1.06894i
$119$		−	11.9198i		−	1.09268i
$120$	−11.0459	−	6.51687i	−1.00835	−	0.594906i
$121$		0			0
$122$	4.15693	+	4.15693i	0.376351	+	0.376351i
$123$	−4.48817	−	4.48817i	−0.404684	−	0.404684i
$124$			1.53712i			0.138038i
$125$	0.315886	−	11.1759i	0.0282537	−	0.999601i
$126$	−6.11334			−0.544620
$127$	−2.49710	+	2.49710i	−0.221582	+	0.221582i	−0.809164	−	0.587582i	$-0.800080\pi$
$127$	−2.49710	+	2.49710i	−0.221582	+	0.221582i	0.587582	+	0.809164i	$0.300080\pi$
$128$	9.12456	+	9.12456i	0.806505	+	0.806505i
$129$	6.66227			0.586580
$130$	17.9606	+	10.5964i	1.57525	+	0.929364i
$131$		−	6.36315i		−	0.555951i	−0.960588	−	0.277976i	$-0.910337\pi$
$131$		−	6.36315i		−	0.555951i	0.960588	−	0.277976i	$-0.0896634\pi$
$132$		0			0
$133$	0.334883	−	0.334883i	0.0290380	−	0.0290380i
$134$	−1.34945			−0.116575
$135$	−1.53733	−	5.96146i	−0.132313	−	0.513081i
$136$	13.3374			1.14367
$137$	−8.01187	−	8.01187i	−0.684500	−	0.684500i	0.276511	−	0.961011i	$-0.410822\pi$
$137$	−8.01187	−	8.01187i	−0.684500	−	0.684500i	−0.961011	+	0.276511i	$0.910822\pi$
$138$	9.04319	+	9.04319i	0.769808	+	0.769808i
$139$	−9.18304			−0.778895			−0.389447	−	0.921049i	$-0.627334\pi$
$139$	−9.18304			−0.778895			−0.389447	+	0.921049i	$0.627334\pi$
$140$	0.313112	+	1.21418i	0.0264628	+	0.102617i
$141$	19.3142			1.62655
$142$	1.53676	−	1.53676i	0.128962	−	0.128962i
$143$		0			0
$144$		−	7.66624i		−	0.638853i
$145$	−4.23140	−	2.49644i	−0.351399	−	0.207318i
$146$	14.4075			1.19238
$147$	2.23173	+	2.23173i	0.184070	+	0.184070i
$148$	1.44593	−	1.44593i	0.118855	−	0.118855i
$149$	−9.41125			−0.771000			−0.385500	−	0.922708i	$-0.625971\pi$
$149$	−9.41125			−0.771000			−0.385500	+	0.922708i	$0.625971\pi$
$150$	14.2463	−	7.87106i	1.16320	−	0.642669i
$151$			12.8847i			1.04854i	0.851552	+	0.524270i	$0.175662\pi$
$151$			12.8847i			1.04854i	−0.851552	+	0.524270i	$0.824338\pi$
$152$	0.374710	+	0.374710i	0.0303930	+	0.0303930i
$153$	−6.20644	−	6.20644i	−0.501761	−	0.501761i
$154$		0			0
$155$	12.4361	+	7.33705i	0.998894	+	0.589326i
$156$			3.22891i			0.258520i
$157$	12.9704	+	12.9704i	1.03515	+	1.03515i	0.999359	+	0.0357947i	$0.0113962\pi$
$157$	12.9704	+	12.9704i	1.03515	+	1.03515i	0.0357947	+	0.999359i	$0.488604\pi$
$158$	8.51437	−	8.51437i	0.677367	−	0.677367i
$159$			17.0443i			1.35170i
$160$	−2.90071	+	0.748031i	−0.229321	+	0.0591370i
$161$			9.25520i			0.729412i
$162$	11.8424	−	11.8424i	0.930428	−	0.930428i
$163$	5.52751	−	5.52751i	0.432948	−	0.432948i	−0.456682	−	0.889630i	$-0.650962\pi$
$163$	5.52751	−	5.52751i	0.432948	−	0.432948i	0.889630	+	0.456682i	$0.150962\pi$
$164$	−0.694369			−0.0542211
$165$		0			0
$166$	−3.61596			−0.280653
$167$	−15.8787	+	15.8787i	−1.22873	+	1.22873i	−0.264284	+	0.964445i	$0.585136\pi$
$167$	−15.8787	+	15.8787i	−1.22873	+	1.22873i	−0.964445	+	0.264284i	$0.914864\pi$
$168$	9.55405	−	9.55405i	0.737111	−	0.737111i
$169$			25.8615i			1.98934i
$170$	−8.60079	+	14.5782i	−0.659651	+	1.11809i
$171$		−	0.348736i		−	0.0266685i
$172$	0.515363	−	0.515363i	0.0392961	−	0.0392961i
$173$	−11.3160	−	11.3160i	−0.860340	−	0.860340i	0.131038	−	0.991377i	$-0.458169\pi$
$173$	−11.3160	−	11.3160i	−0.860340	−	0.860340i	−0.991377	+	0.131038i	$0.958169\pi$
$174$		−	7.15213i		−	0.542202i
$175$	11.3179	+	3.26233i	0.855554	+	0.246609i
$176$		0			0
$177$	−16.8891	−	16.8891i	−1.26946	−	1.26946i
$178$	−10.8106	−	10.8106i	−0.810292	−	0.810292i
$179$		−	6.76827i		−	0.505884i	−0.967481	−	0.252942i	$-0.918602\pi$
$179$		−	6.76827i		−	0.505884i	0.967481	−	0.252942i	$-0.0813983\pi$
$180$	0.795237	+	0.469172i	0.0592735	+	0.0349700i
$181$	3.98790			0.296418			0.148209	−	0.988956i	$-0.452649\pi$
$181$	3.98790			0.296418			0.148209	+	0.988956i	$0.452649\pi$
$182$	−15.5348	+	15.5348i	−1.15152	+	1.15152i
$183$	6.04621	+	6.04621i	0.446949	+	0.446949i
$184$	−10.3559			−0.763447
$185$	−4.79659	−	18.6002i	−0.352652	−	1.36751i
$186$			21.0202i			1.54127i
$187$		0			0
$188$	1.49406	−	1.49406i	0.108966	−	0.108966i
$189$	6.48599			0.471786
$190$	−0.651206	+	0.167932i	−0.0472434	+	0.0121831i
$191$	−12.4146			−0.898293			−0.449146	−	0.893458i	$-0.648272\pi$
$191$	−12.4146			−0.898293			−0.449146	+	0.893458i	$0.648272\pi$
$192$	10.5159	+	10.5159i	0.758922	+	0.758922i
$193$	3.92002	+	3.92002i	0.282169	+	0.282169i	0.833974	−	0.551804i	$-0.186060\pi$
$193$	3.92002	+	3.92002i	0.282169	+	0.282169i	−0.551804	+	0.833974i	$0.686060\pi$
$194$	−4.38045			−0.314498
$195$	26.1236	+	15.4123i	1.87075	+	1.10370i
$196$	0.345274			0.0246624
$197$	6.68003	−	6.68003i	0.475933	−	0.475933i	−0.427895	−	0.903828i	$-0.640745\pi$
$197$	6.68003	−	6.68003i	0.475933	−	0.475933i	0.903828	+	0.427895i	$0.140745\pi$
$198$		0			0
$199$		−	3.42575i		−	0.242845i	−0.992601	−	0.121423i	$-0.961254\pi$
$199$		−	3.42575i		−	0.242845i	0.992601	−	0.121423i	$-0.0387456\pi$
$200$	−3.65031	+	12.6639i	−0.258116	+	0.895475i
$201$	−1.96277			−0.138443
$202$	2.62616	+	2.62616i	0.184776	+	0.184776i
$203$	3.65990	−	3.65990i	0.256875	−	0.256875i
$204$	−2.62082			−0.183494
$205$	−3.31439	+	5.61781i	−0.231487	+	0.392365i
$206$			19.1688i			1.33555i
$207$	4.81903	+	4.81903i	0.334946	+	0.334946i
$208$	−19.4809	−	19.4809i	−1.35076	−	1.35076i
$209$		0			0
$210$	4.28180	+	16.6039i	0.295472	+	1.14578i
$211$			7.53611i			0.518807i	0.965769	+	0.259404i	$0.0835260\pi$
$211$			7.53611i			0.518807i	−0.965769	+	0.259404i	$0.916474\pi$
$212$	1.31847	+	1.31847i	0.0905530	+	0.0905530i
$213$	2.23520	−	2.23520i	0.153153	−	0.153153i
$214$		−	18.6373i		−	1.27402i
$215$	−1.70961	−	6.62951i	−0.116594	−	0.452129i
$216$			7.25735i			0.493800i
$217$	−10.7565	+	10.7565i	−0.730197	+	0.730197i
$218$	−11.8050	+	11.8050i	−0.799534	+	0.799534i
$219$	20.9556			1.41605
$220$		0			0
$221$	−31.5428			−2.12180
$222$	19.7732	−	19.7732i	1.32709	−	1.32709i
$223$	−13.9370	+	13.9370i	−0.933291	+	0.933291i	−0.997910	−	0.0646192i	$-0.979417\pi$
$223$	−13.9370	+	13.9370i	−0.933291	+	0.933291i	0.0646192	+	0.997910i	$0.479417\pi$
$224$		−	3.15593i		−	0.210864i
$225$	7.59170	−	4.19441i	0.506114	−	0.279628i
$226$			0.230316i			0.0153204i
$227$	3.86247	−	3.86247i	0.256361	−	0.256361i	−0.567211	−	0.823572i	$-0.691978\pi$
$227$	3.86247	−	3.86247i	0.256361	−	0.256361i	0.823572	+	0.567211i	$0.191978\pi$
$228$	−0.0736311	−	0.0736311i	−0.00487634	−	0.00487634i
$229$		−	0.421164i		−	0.0278313i	−0.999903	−	0.0139156i	$-0.995570\pi$
$229$		−	0.421164i		−	0.0278313i	0.999903	−	0.0139156i	$-0.00442963\pi$
$230$	6.67815	−	11.3193i	0.440344	−	0.746373i
$231$		0			0
$232$	4.09516	+	4.09516i	0.268861	+	0.268861i
$233$	−4.52723	−	4.52723i	−0.296589	−	0.296589i	0.543087	−	0.839676i	$-0.317255\pi$
$233$	−4.52723	−	4.52723i	−0.296589	−	0.296589i	−0.839676	+	0.543087i	$0.817255\pi$
$234$			16.1775i			1.05755i
$235$	−4.95625	−	19.2193i	−0.323310	−	1.25373i
$236$	−2.61293			−0.170087
$237$	12.3841	−	12.3841i	0.804432	−	0.804432i
$238$	−12.6092	−	12.6092i	−0.817332	−	0.817332i
$239$	−13.3450			−0.863214			−0.431607	−	0.902062i	$-0.642053\pi$
$239$	−13.3450			−0.863214			−0.431607	+	0.902062i	$0.642053\pi$
$240$	−20.8216	+	5.36945i	−1.34403	+	0.346597i
$241$			11.1671i			0.719337i	0.933080	+	0.359668i	$0.117110\pi$
$241$			11.1671i			0.719337i	−0.933080	+	0.359668i	$0.882890\pi$
$242$		0			0
$243$	11.3841	−	11.3841i	0.730292	−	0.730292i
$244$	0.935416			0.0598839
$245$	1.64807	−	2.79345i	0.105291	−	0.178467i
$246$	−9.49551			−0.605411
$247$	−0.886186	−	0.886186i	−0.0563866	−	0.0563866i
$248$	−12.0357	−	12.0357i	−0.764269	−	0.764269i
$249$	−5.25938			−0.333299
$250$	−11.4881	−	12.1564i	−0.726572	−	0.768839i
$251$	1.49555			0.0943986			0.0471993	−	0.998885i	$-0.484970\pi$
$251$	1.49555			0.0943986			0.0471993	+	0.998885i	$0.484970\pi$
$252$	−0.687830	+	0.687830i	−0.0433292	+	0.0433292i
$253$		0			0
$254$			5.28306i			0.331489i
$255$	−12.5098	+	21.2038i	−0.783392	+	1.32783i
$256$	5.63526			0.352204
$257$	−0.843193	−	0.843193i	−0.0525969	−	0.0525969i	0.680319	−	0.732916i	$-0.261841\pi$
$257$	−0.843193	−	0.843193i	−0.0525969	−	0.0525969i	−0.732916	+	0.680319i	$0.761841\pi$
$258$	7.04760	−	7.04760i	0.438764	−	0.438764i
$259$	20.2367			1.25745
$260$	3.21303	−	0.828573i	0.199264	−	0.0513859i
$261$		−	3.81130i		−	0.235914i
$262$	−6.73118	−	6.73118i	−0.415854	−	0.415854i
$263$	2.28570	+	2.28570i	0.140942	+	0.140942i	0.774058	−	0.633115i	$-0.218224\pi$
$263$	2.28570	+	2.28570i	0.140942	+	0.140942i	−0.633115	+	0.774058i	$0.718224\pi$
$264$		0			0
$265$	16.9605	−	4.37376i	1.04188	−	0.268678i
$266$		−	0.708503i		−	0.0434411i
$267$	−15.7240	−	15.7240i	−0.962291	−	0.962291i
$268$	−0.151831	+	0.151831i	−0.00927455	+	0.00927455i
$269$			12.0339i			0.733717i	0.930277	+	0.366858i	$0.119567\pi$
$269$			12.0339i			0.733717i	−0.930277	+	0.366858i	$0.880433\pi$
$270$	−7.93251	−	4.68001i	−0.482757	−	0.284816i
$271$		−	32.8228i		−	1.99384i	−0.0783956	−	0.996922i	$-0.524980\pi$
$271$		−	32.8228i		−	1.99384i	0.0783956	−	0.996922i	$-0.475020\pi$
$272$	15.8121	−	15.8121i	0.958751	−	0.958751i
$273$	−22.5953	+	22.5953i	−1.36753	+	1.36753i
$274$	−16.9505			−1.02402
$275$		0			0
$276$	2.03495			0.122490
$277$	13.4492	−	13.4492i	0.808085	−	0.808085i	−0.176259	−	0.984344i	$-0.556400\pi$
$277$	13.4492	−	13.4492i	0.808085	−	0.808085i	0.984344	+	0.176259i	$0.0563996\pi$
$278$	−9.71416	+	9.71416i	−0.582617	+	0.582617i
$279$			11.2015i			0.670613i
$280$	−11.9587	−	7.05540i	−0.714672	−	0.421641i
$281$		−	8.92482i		−	0.532410i	−0.963916	−	0.266205i	$-0.914230\pi$
$281$		−	8.92482i		−	0.532410i	0.963916	−	0.266205i	$-0.0857698\pi$
$282$	20.4313	−	20.4313i	1.21667	−	1.21667i
$283$	−6.72870	−	6.72870i	−0.399980	−	0.399980i	0.478246	−	0.878226i	$-0.341273\pi$
$283$	−6.72870	−	6.72870i	−0.399980	−	0.399980i	−0.878226	+	0.478246i	$0.841273\pi$
$284$		−	0.345810i		−	0.0205201i
$285$	−0.947173	+	0.244256i	−0.0561057	+	0.0144685i
$286$		0			0
$287$	−4.85906	−	4.85906i	−0.286821	−	0.286821i
$288$	−1.64324	−	1.64324i	−0.0968290	−	0.0968290i
$289$		−	8.60241i		−	0.506024i
$290$	−7.11696	+	1.83531i	−0.417923	+	0.107773i
$291$	−6.37132			−0.373494
$292$	1.62103	−	1.62103i	0.0948638	−	0.0948638i
$293$	−20.1376	−	20.1376i	−1.17645	−	1.17645i	−0.980642	−	0.195808i	$-0.937267\pi$
$293$	−20.1376	−	20.1376i	−1.17645	−	1.17645i	−0.195808	−	0.980642i	$-0.562733\pi$
$294$	4.72162			0.275370
$295$	−12.4721	+	21.1400i	−0.726156	+	1.23082i
$296$			22.6434i			1.31612i
$297$		0			0
$298$	−9.95557	+	9.95557i	−0.576711	+	0.576711i
$299$	24.4916			1.41639
$300$	0.717293	−	2.48848i	0.0414129	−	0.143673i
$301$	7.21281			0.415740
$302$	13.6299	+	13.6299i	0.784312	+	0.784312i
$303$	3.81973	+	3.81973i	0.219438	+	0.219438i
$304$	0.888475			0.0509575
$305$	4.46496	−	7.56801i	0.255663	−	0.433343i
$306$	−13.1308			−0.750638
$307$	−16.3606	+	16.3606i	−0.933747	+	0.933747i	−0.997938	−	0.0641908i	$-0.979553\pi$
$307$	−16.3606	+	16.3606i	−0.933747	+	0.933747i	0.0641908	+	0.997938i	$0.479553\pi$
$308$		0			0
$309$			27.8808i			1.58608i
$310$	20.9168	−	5.39400i	1.18800	−	0.306359i
$311$	7.40894			0.420122			0.210061	−	0.977688i	$-0.432634\pi$
$311$	7.40894			0.420122			0.210061	+	0.977688i	$0.432634\pi$
$312$	−25.2825	−	25.2825i	−1.43134	−	1.43134i
$313$	11.8942	−	11.8942i	0.672299	−	0.672299i	−0.285946	−	0.958246i	$-0.592308\pi$
$313$	11.8942	−	11.8942i	0.672299	−	0.672299i	0.958246	+	0.285946i	$0.0923079\pi$
$314$	27.4412			1.54860
$315$	2.28173	+	8.84808i	0.128561	+	0.498533i
$316$		−	1.91595i		−	0.107781i
$317$	−3.37040	−	3.37040i	−0.189301	−	0.189301i	0.606093	−	0.795394i	$-0.292736\pi$
$317$	−3.37040	−	3.37040i	−0.189301	−	0.189301i	−0.795394	+	0.606093i	$0.792736\pi$
$318$	18.0301	+	18.0301i	1.01108	+	1.01108i
$319$		0			0
$320$	7.76572	−	13.1627i	0.434117	−	0.735819i
$321$		−	27.1078i		−	1.51301i
$322$	9.79049	+	9.79049i	0.545603	+	0.545603i
$323$	0.719292	−	0.719292i	0.0400225	−	0.0400225i
$324$		−	2.66485i		−	0.148047i
$325$	8.63296	−	29.9501i	0.478871	−	1.66133i
$326$		−	11.6944i		−	0.647694i
$327$	−17.1702	+	17.1702i	−0.949516	+	0.949516i
$328$	5.43693	−	5.43693i	0.300204	−	0.300204i
$329$	20.9103			1.15282
$330$		0			0
$331$	0.635018			0.0349037			0.0174519	−	0.999848i	$-0.494445\pi$
$331$	0.635018			0.0349037			0.0174519	+	0.999848i	$0.494445\pi$
$332$	−0.406842	+	0.406842i	−0.0223283	+	0.0223283i
$333$	10.5369	−	10.5369i	0.577421	−	0.577421i
$334$			33.5941i			1.83819i
$335$	0.503668	+	1.95312i	0.0275183	+	0.106710i
$336$		−	22.6536i		−	1.23586i
$337$	−1.61144	+	1.61144i	−0.0877809	+	0.0877809i	−0.749634	−	0.661853i	$-0.769770\pi$
$337$	−1.61144	+	1.61144i	−0.0877809	+	0.0877809i	0.661853	+	0.749634i	$0.269770\pi$
$338$	27.3572	+	27.3572i	1.48804	+	1.48804i
$339$			0.334993i			0.0181943i
$340$	0.672530	+	2.60793i	0.0364731	+	0.141435i
$341$		0			0
$342$	−0.368906	−	0.368906i	−0.0199482	−	0.0199482i
$343$	14.0765	+	14.0765i	0.760059	+	0.760059i
$344$			8.07062i			0.435139i
$345$	9.71330	−	16.4638i	0.522947	−	0.886383i
$346$	−23.9410			−1.28708
$347$	−13.1056	+	13.1056i	−0.703544	+	0.703544i	−0.965170	−	0.261625i	$-0.915742\pi$
$347$	−13.1056	+	13.1056i	−0.703544	+	0.703544i	0.261625	+	0.965170i	$0.415742\pi$
$348$	−0.804707	−	0.804707i	−0.0431368	−	0.0431368i
$349$	13.9208			0.745165			0.372582	−	0.927999i	$-0.378472\pi$
$349$	13.9208			0.745165			0.372582	+	0.927999i	$0.378472\pi$
$350$	15.4235	−	8.52150i	0.824422	−	0.455493i
$351$		−	17.1636i		−	0.916124i
$352$		0			0
$353$	−17.8777	+	17.8777i	−0.951536	+	0.951536i	−0.998879	−	0.0473428i	$-0.984925\pi$
$353$	−17.8777	+	17.8777i	−0.951536	+	0.951536i	0.0473428	+	0.998879i	$0.484925\pi$
$354$	−35.7319			−1.89913
$355$	−2.79779	−	1.65063i	−0.148491	−	0.0876065i
$356$	−2.43267			−0.128931
$357$	−18.3399	−	18.3399i	−0.970653	−	0.970653i
$358$	−7.15973	−	7.15973i	−0.378404	−	0.378404i
$359$	1.44158			0.0760838			0.0380419	−	0.999276i	$-0.487888\pi$
$359$	1.44158			0.0760838			0.0380419	+	0.999276i	$0.487888\pi$
$360$	−9.90037	+	2.55310i	−0.521795	+	0.134560i
$361$	−18.9596			−0.997873
$362$	4.21855	−	4.21855i	0.221722	−	0.221722i
$363$		0			0
$364$			3.49574i			0.183226i
$365$	−5.37744	−	20.8526i	−0.281468	−	1.09147i
$366$	12.7918			0.668640
$367$	−10.6753	−	10.6753i	−0.557248	−	0.557248i	0.371275	−	0.928523i	$-0.378921\pi$
$367$	−10.6753	−	10.6753i	−0.557248	−	0.557248i	−0.928523	+	0.371275i	$0.878921\pi$
$368$	−12.2774	+	12.2774i	−0.640006	+	0.640006i
$369$	−5.06007			−0.263417
$370$	−24.7499	−	14.6019i	−1.28669	−	0.759118i
$371$			18.4528i			0.958021i
$372$	2.36504	+	2.36504i	0.122622	+	0.122622i
$373$	−16.3505	−	16.3505i	−0.846595	−	0.846595i	0.143111	−	0.989707i	$-0.454289\pi$
$373$	−16.3505	−	16.3505i	−0.846595	−	0.846595i	−0.989707	+	0.143111i	$0.954289\pi$
$374$		0			0
$375$	−16.7093	−	17.6814i	−0.862867	−	0.913063i
$376$			23.3971i			1.20661i
$377$	−9.68503	−	9.68503i	−0.498805	−	0.498805i
$378$	6.86112	−	6.86112i	0.352898	−	0.352898i
$379$			14.9740i			0.769162i	0.923091	+	0.384581i	$0.125654\pi$
$379$			14.9740i			0.769162i	−0.923091	+	0.384581i	$0.874346\pi$
$380$	−0.0543745	+	0.0921636i	−0.00278935	+	0.00472789i
$381$			7.68416i			0.393672i
$382$	−13.1327	+	13.1327i	−0.671927	+	0.671927i
$383$	7.23757	−	7.23757i	0.369823	−	0.369823i	−0.497590	−	0.867412i	$-0.665781\pi$
$383$	7.23757	−	7.23757i	0.369823	−	0.369823i	0.867412	+	0.497590i	$0.165781\pi$
$384$	28.0784			1.43287
$385$		0			0
$386$	8.29350			0.422128
$387$	3.75560	−	3.75560i	0.190908	−	0.190908i
$388$	−0.492857	+	0.492857i	−0.0250210	+	0.0250210i
$389$		−	14.6390i		−	0.742225i	−0.928588	−	0.371112i	$-0.878976\pi$
$389$		−	14.6390i		−	0.742225i	0.928588	−	0.371112i	$-0.121024\pi$
$390$	43.9383	−	11.3307i	2.22490	−	0.573755i
$391$			19.8792i			1.00533i
$392$	−2.70350	+	2.70350i	−0.136548	+	0.136548i
$393$	−9.79044	−	9.79044i	−0.493862	−	0.493862i
$394$		−	14.1328i		−	0.711999i
$395$	−15.5011	−	9.14529i	−0.779943	−	0.460150i
$396$		0			0
$397$	−14.9376	−	14.9376i	−0.749697	−	0.749697i	0.224725	−	0.974422i	$-0.427852\pi$
$397$	−14.9376	−	14.9376i	−0.749697	−	0.749697i	−0.974422	+	0.224725i	$0.927852\pi$
$398$	−3.62389	−	3.62389i	−0.181649	−	0.181649i
$399$		−	1.03051i		−	0.0515901i
$400$	10.6861	+	19.3414i	0.534305	+	0.967069i
$401$	27.9673			1.39662			0.698310	−	0.715796i	$-0.253936\pi$
$401$	27.9673			1.39662			0.698310	+	0.715796i	$0.253936\pi$
$402$	−2.07629	+	2.07629i	−0.103556	+	0.103556i
$403$	28.4644	+	28.4644i	1.41791	+	1.41791i
$404$	0.590954			0.0294011
$405$	−21.5600	−	12.7200i	−1.07133	−	0.632059i
$406$		−	7.74316i		−	0.384287i
$407$		0			0
$408$	20.5211	−	20.5211i	1.01594	−	1.01594i
$409$	−29.5127			−1.45931			−0.729654	−	0.683817i	$-0.760319\pi$
$409$	−29.5127			−1.45931			−0.729654	+	0.683817i	$0.760319\pi$
$410$	2.43665	+	9.44882i	0.120338	+	0.466644i
$411$	−24.6544			−1.21611
$412$	2.15673	+	2.15673i	0.106255	+	0.106255i
$413$	−18.2848	−	18.2848i	−0.899735	−	0.899735i
$414$	10.1955			0.501082
$415$	1.34961	+	5.23352i	0.0662499	+	0.256903i
$416$	−8.35139			−0.409461
$417$	−14.1292	+	14.1292i	−0.691908	+	0.691908i
$418$		0			0
$419$			24.6856i			1.20597i	0.797751	+	0.602986i	$0.206023\pi$
$419$			24.6856i			1.20597i	−0.797751	+	0.602986i	$0.793977\pi$
$420$	2.34991	+	1.38640i	0.114664	+	0.0676493i
$421$	−11.0011			−0.536160			−0.268080	−	0.963397i	$-0.586389\pi$
$421$	−11.0011			−0.536160			−0.268080	+	0.963397i	$0.586389\pi$
$422$	7.97198	+	7.97198i	0.388070	+	0.388070i
$423$	10.8877	−	10.8877i	0.529377	−	0.529377i
$424$	−20.6474			−1.00272
$425$	24.3097	+	7.00714i	1.17919	+	0.339896i
$426$		−	4.72895i		−	0.229119i
$427$	6.54585	+	6.54585i	0.316776	+	0.316776i
$428$	−2.09694	−	2.09694i	−0.101359	−	0.101359i
$429$		0			0
$430$	−8.82143	−	5.20445i	−0.425407	−	0.250981i
$431$		−	17.4183i		−	0.839008i	−0.907753	−	0.419504i	$-0.862204\pi$
$431$		−	17.4183i		−	0.839008i	0.907753	−	0.419504i	$-0.137796\pi$
$432$	8.60396	+	8.60396i	0.413958	+	0.413958i
$433$	−19.0746	+	19.0746i	−0.916668	+	0.916668i	−0.996785	−	0.0801174i	$-0.974470\pi$
$433$	−19.0746	+	19.0746i	−0.916668	+	0.916668i	0.0801174	+	0.996785i	$0.474470\pi$
$434$			22.7572i			1.09238i
$435$	−10.3516	+	2.66945i	−0.496319	+	0.127990i
$436$			2.65642i			0.127220i
$437$	−0.558500	+	0.558500i	−0.0267167	+	0.0267167i
$438$	22.1677	−	22.1677i	1.05921	−	1.05921i
$439$	−40.2775			−1.92234			−0.961169	−	0.275959i	$-0.911005\pi$
$439$	−40.2775			−1.92234			−0.961169	+	0.275959i	$0.911005\pi$
$440$		0			0
$441$	2.51611			0.119815
$442$	−33.3671	+	33.3671i	−1.58711	+	1.58711i
$443$	15.3250	−	15.3250i	0.728111	−	0.728111i	−0.242132	−	0.970243i	$-0.577847\pi$
$443$	15.3250	−	15.3250i	0.728111	−	0.728111i	0.970243	+	0.242132i	$0.0778467\pi$
$444$		−	4.44947i		−	0.211163i
$445$	−11.6117	+	19.6816i	−0.550448	+	0.932997i
$446$			29.4862i			1.39621i
$447$	−14.4803	+	14.4803i	−0.684894	+	0.684894i
$448$	11.3849	+	11.3849i	0.537887	+	0.537887i
$449$			23.9526i			1.13040i	0.824956	+	0.565198i	$0.191200\pi$
$449$			23.9526i			1.13040i	−0.824956	+	0.565198i	$0.808800\pi$
$450$	3.59378	−	12.4678i	0.169412	−	0.587738i
$451$		0			0
$452$	0.0259135	+	0.0259135i	0.00121887	+	0.00121887i
$453$	19.8246	+	19.8246i	0.931439	+	0.931439i
$454$		−	8.17174i		−	0.383519i
$455$	28.2823	+	16.6860i	1.32590	+	0.782250i
$456$	1.15307			0.0539973
$457$	6.59968	−	6.59968i	0.308720	−	0.308720i	−0.535693	−	0.844413i	$-0.679950\pi$
$457$	6.59968	−	6.59968i	0.308720	−	0.308720i	0.844413	+	0.535693i	$0.179950\pi$
$458$	−0.445523	−	0.445523i	−0.0208179	−	0.0208179i
$459$	13.9312			0.650253
$460$	−0.522191	−	2.02495i	−0.0243473	−	0.0944136i
$461$		−	39.9758i		−	1.86186i	−0.365198	−	0.930930i	$-0.618999\pi$
$461$		−	39.9758i		−	1.86186i	0.365198	−	0.930930i	$-0.381001\pi$
$462$		0			0
$463$	24.4793	−	24.4793i	1.13765	−	1.13765i	0.148778	−	0.988871i	$-0.452466\pi$
$463$	24.4793	−	24.4793i	1.13765	−	1.13765i	0.988871	−	0.148778i	$-0.0475341\pi$
$464$	9.71005			0.450778
$465$	30.4233	−	7.84553i	1.41085	−	0.363828i
$466$	−9.57815			−0.443699
$467$	−13.8781	−	13.8781i	−0.642203	−	0.642203i	0.308894	−	0.951097i	$-0.400041\pi$
$467$	−13.8781	−	13.8781i	−0.642203	−	0.642203i	−0.951097	+	0.308894i	$0.900041\pi$
$468$	1.82017	+	1.82017i	0.0841376	+	0.0841376i
$469$	−2.12496			−0.0981218
$470$	−25.5738	−	15.0880i	−1.17963	−	0.695956i
$471$	39.9130			1.83909
$472$	20.4593	−	20.4593i	0.941718	−	0.941718i
$473$		0			0
$474$		−	26.2007i		−	1.20344i
$475$	0.486110	+	0.879837i	0.0223042	+	0.0403697i
$476$	−2.83739			−0.130052
$477$	9.60808	+	9.60808i	0.439924	+	0.439924i
$478$	−14.1168	+	14.1168i	−0.645687	+	0.645687i
$479$	28.2011			1.28854			0.644270	−	0.764798i	$-0.277161\pi$
$479$	28.2011			1.28854			0.644270	+	0.764798i	$0.277161\pi$
$480$	−3.31214	+	5.61400i	−0.151178	+	0.256243i
$481$		−	53.5515i		−	2.44174i
$482$	11.8130	+	11.8130i	0.538067	+	0.538067i
$483$	14.2402	+	14.2402i	0.647951	+	0.647951i
$484$		0			0
$485$	1.63495	+	6.34000i	0.0742393	+	0.287884i
$486$		−	24.0851i		−	1.09252i
$487$	27.7543	+	27.7543i	1.25767	+	1.25767i	0.952205	+	0.305461i	$0.0988106\pi$
$487$	27.7543	+	27.7543i	1.25767	+	1.25767i	0.305461	+	0.952205i	$0.401189\pi$
$488$	−7.32434	+	7.32434i	−0.331557	+	0.331557i
$489$		−	17.0094i		−	0.769193i
$490$	−1.21162	−	4.69840i	−0.0547354	−	0.212252i
$491$		−	24.2459i		−	1.09420i	−0.837066	−	0.547102i	$-0.815731\pi$
$491$		−	24.2459i		−	1.09420i	0.837066	−	0.547102i	$-0.184269\pi$
$492$	−1.06837	+	1.06837i	−0.0481657	+	0.0481657i
$493$	7.86107	−	7.86107i	0.354045	−	0.354045i
$494$	−1.87488			−0.0843549
$495$		0			0
$496$	−28.5379			−1.28139
$497$	2.41991	−	2.41991i	0.108548	−	0.108548i
$498$	−5.56357	+	5.56357i	−0.249309	+	0.249309i
$499$		−	40.6308i		−	1.81888i	−0.415831	−	0.909442i	$-0.636509\pi$
$499$		−	40.6308i		−	1.81888i	0.415831	−	0.909442i	$-0.363491\pi$
$500$	−2.66031	−	0.0751938i	−0.118973	−	0.00336277i
$501$			48.8623i			2.18301i
$502$	1.58205	−	1.58205i	0.0706105	−	0.0706105i
$503$	−1.12936	−	1.12936i	−0.0503556	−	0.0503556i	0.681481	−	0.731836i	$-0.261336\pi$
$503$	−1.12936	−	1.12936i	−0.0503556	−	0.0503556i	−0.731836	+	0.681481i	$0.761336\pi$
$504$		−	10.7715i		−	0.479799i
$505$	2.82076	−	4.78113i	0.125522	−	0.212757i
$506$		0			0
$507$	39.7908	+	39.7908i	1.76717	+	1.76717i
$508$	0.594413	+	0.594413i	0.0263728	+	0.0263728i
$509$		−	12.2411i		−	0.542575i	−0.962498	−	0.271288i	$-0.912551\pi$
$509$		−	12.2411i		−	0.542575i	0.962498	−	0.271288i	$-0.0874495\pi$
$510$	9.19686	+	35.6635i	0.407244	+	1.57920i
$511$	22.6873			1.00363
$512$	−12.2879	+	12.2879i	−0.543055	+	0.543055i
$513$	0.391393	+	0.391393i	0.0172804	+	0.0172804i
$514$	−1.78392			−0.0786854
$515$	27.7437	−	7.15451i	1.22253	−	0.315265i
$516$		−	1.58589i		−	0.0698150i
$517$		0			0
$518$	21.4072	−	21.4072i	0.940576	−	0.940576i
$519$	−34.8219			−1.52851
$520$	−18.6704	+	31.6459i	−0.818751	+	1.38776i
$521$	2.16153			0.0946983			0.0473491	−	0.998878i	$-0.484923\pi$
$521$	2.16153			0.0946983			0.0473491	+	0.998878i	$0.484923\pi$
$522$	−4.03174	−	4.03174i	−0.176464	−	0.176464i
$523$	15.6370	+	15.6370i	0.683757	+	0.683757i	0.960845	−	0.277088i	$-0.0893694\pi$
$523$	15.6370	+	15.6370i	0.683757	+	0.683757i	−0.277088	+	0.960845i	$0.589369\pi$
$524$	−1.51469			−0.0661695
$525$	22.4334	−	12.3944i	0.979073	−	0.540938i
$526$	4.83580			0.210851
$527$	−23.1038	+	23.1038i	−1.00642	+	1.00642i
$528$		0			0
$529$			7.56467i			0.328899i
$530$	13.3147	−	22.5682i	0.578355	−	0.980299i
$531$	−19.0412			−0.826317
$532$	−0.0797157	−	0.0797157i	−0.00345612	−	0.00345612i
$533$	−12.8583	+	12.8583i	−0.556955	+	0.556955i
$534$	−33.2668			−1.43960
$535$	−26.9745	+	6.95616i	−1.16621	+	0.300741i
$536$		−	2.37768i		−	0.102700i
$537$	−10.4138	−	10.4138i	−0.449387	−	0.449387i
$538$	12.7299	+	12.7299i	0.548823	+	0.548823i
$539$		0			0
$540$	−1.41907	+	0.365948i	−0.0610671	+	0.0157479i
$541$		−	9.55174i		−	0.410661i	−0.978693	−	0.205331i	$-0.934173\pi$
$541$		−	9.55174i		−	0.410661i	0.978693	−	0.205331i	$-0.0658270\pi$
$542$	−34.7212	−	34.7212i	−1.49140	−	1.49140i
$543$	6.13584	−	6.13584i	0.263314	−	0.263314i
$544$		−	6.77860i		−	0.290630i
$545$	21.4919	+	12.6797i	0.920611	+	0.543140i
$546$			47.8042i			2.04583i
$547$	−13.5241	+	13.5241i	−0.578249	+	0.578249i	−0.934421	−	0.356172i	$-0.884082\pi$
$547$	−13.5241	+	13.5241i	−0.578249	+	0.578249i	0.356172	+	0.934421i	$0.384082\pi$
$548$	−1.90715	+	1.90715i	−0.0814694	+	0.0814694i
$549$	6.81665			0.290927
$550$		0			0
$551$	0.441709			0.0188174
$552$	−15.9337	+	15.9337i	−0.678185	+	0.678185i
$553$	13.4074	−	13.4074i	0.570143	−	0.570143i
$554$		−	28.4542i		−	1.20890i
$555$	−35.9986	−	21.2384i	−1.52805	−	0.901519i
$556$			2.18594i			0.0927044i
$557$	9.99502	−	9.99502i	0.423502	−	0.423502i	−0.462905	−	0.886408i	$-0.653193\pi$
$557$	9.99502	−	9.99502i	0.423502	−	0.423502i	0.886408	+	0.462905i	$0.153193\pi$
$558$	11.8493	+	11.8493i	0.501622	+	0.501622i
$559$		−	19.0870i		−	0.807292i
$560$	−22.5422	+	5.81317i	−0.952583	+	0.245651i
$561$		0			0
$562$	−9.44101	−	9.44101i	−0.398245	−	0.398245i
$563$	29.6872	+	29.6872i	1.25117	+	1.25117i	0.955198	+	0.295968i	$0.0956423\pi$
$563$	29.6872	+	29.6872i	1.25117	+	1.25117i	0.295968	+	0.955198i	$0.404358\pi$
$564$		−	4.59758i		−	0.193593i
$565$	0.333346	−	0.0859628i	0.0140240	−	0.00361648i
$566$	−14.2358			−0.598373
$567$	18.6481	−	18.6481i	0.783146	−	0.783146i
$568$	2.70770	+	2.70770i	0.113613	+	0.113613i
$569$	4.21191			0.176572			0.0882862	−	0.996095i	$-0.471861\pi$
$569$	4.21191			0.176572			0.0882862	+	0.996095i	$0.471861\pi$
$570$	−0.743572	+	1.26034i	−0.0311448	+	0.0527898i
$571$			25.3055i			1.05900i	0.848309	+	0.529502i	$0.177621\pi$
$571$			25.3055i			1.05900i	−0.848309	+	0.529502i	$0.822379\pi$
$572$		0			0
$573$	−19.1014	+	19.1014i	−0.797971	+	0.797971i
$574$	−10.2802			−0.429087
$575$	−18.8754	−	5.44074i	−0.787159	−	0.226895i
$576$	11.8559			0.493996
$577$	−1.24397	−	1.24397i	−0.0517873	−	0.0517873i	0.680739	−	0.732526i	$-0.261659\pi$
$577$	−1.24397	−	1.24397i	−0.0517873	−	0.0517873i	−0.732526	+	0.680739i	$0.761659\pi$
$578$	−9.09995	−	9.09995i	−0.378508	−	0.378508i
$579$	12.0628			0.501313
$580$	−0.594254	+	1.00725i	−0.0246750	+	0.0418236i
$581$	−5.69399			−0.236227
$582$	−6.73983	+	6.73983i	−0.279375	+	0.279375i
$583$		0			0
$584$			25.3855i			1.05046i
$585$	23.4143	−	6.03805i	0.968062	−	0.249643i
$586$	−42.6046			−1.75998
$587$	31.2614	+	31.2614i	1.29029	+	1.29029i	0.934604	+	0.355690i	$0.115754\pi$
$587$	31.2614	+	31.2614i	1.29029	+	1.29029i	0.355690	+	0.934604i	$0.384246\pi$
$588$	0.531243	−	0.531243i	0.0219081	−	0.0219081i
$589$	−1.29819			−0.0534909
$590$	9.16919	+	35.5562i	0.377490	+	1.46383i
$591$		−	20.5560i		−	0.845561i
$592$	26.8449	+	26.8449i	1.10332	+	1.10332i
$593$	12.3805	+	12.3805i	0.508407	+	0.508407i	0.914037	−	0.405630i	$-0.132948\pi$
$593$	12.3805	+	12.3805i	0.508407	+	0.508407i	−0.405630	+	0.914037i	$0.632948\pi$
$594$		0			0
$595$	−13.5435	+	22.9560i	−0.555231	+	0.941104i
$596$			2.24026i			0.0917647i
$597$	−5.27091	−	5.27091i	−0.215724	−	0.215724i
$598$	25.9082	−	25.9082i	1.05946	−	1.05946i
$599$		−	12.3007i		−	0.502593i	−0.967910	−	0.251296i	$-0.919143\pi$
$599$		−	12.3007i		−	0.502593i	0.967910	−	0.251296i	$-0.0808569\pi$
$600$	13.8685	+	25.1013i	0.566179	+	1.02476i
$601$			44.4894i			1.81476i	0.420311	+	0.907380i	$0.361921\pi$
$601$			44.4894i			1.81476i	−0.420311	+	0.907380i	$0.638079\pi$
$602$	7.62999	−	7.62999i	0.310975	−	0.310975i
$603$	−1.10644	+	1.10644i	−0.0450575	+	0.0450575i
$604$	3.06708			0.124798
$605$		0			0
$606$	8.08130			0.328280
$607$	3.60942	−	3.60942i	0.146502	−	0.146502i	−0.630051	−	0.776553i	$-0.716966\pi$
$607$	3.60942	−	3.60942i	0.146502	−	0.146502i	0.776553	+	0.630051i	$0.216966\pi$
$608$	0.190443	−	0.190443i	0.00772347	−	0.00772347i
$609$		−	11.2624i		−	0.456373i
$610$	−3.28252	−	12.7289i	−0.132905	−	0.515379i
$611$		−	55.3340i		−	2.23858i
$612$	−1.47739	+	1.47739i	−0.0597198	+	0.0597198i
$613$	23.6313	+	23.6313i	0.954458	+	0.954458i	0.999007	−	0.0445492i	$-0.0141852\pi$
$613$	23.6313	+	23.6313i	0.954458	+	0.954458i	−0.0445492	+	0.999007i	$0.514185\pi$
$614$			34.6136i			1.39689i
$615$	3.54409	+	13.7432i	0.142911	+	0.554180i
$616$		0			0
$617$	8.99619	+	8.99619i	0.362173	+	0.362173i	0.864612	−	0.502439i	$-0.167564\pi$
$617$	8.99619	+	8.99619i	0.362173	+	0.362173i	−0.502439	+	0.864612i	$0.667564\pi$
$618$	29.4933	+	29.4933i	1.18640	+	1.18640i
$619$		−	25.2518i		−	1.01496i	−0.861664	−	0.507479i	$-0.830578\pi$
$619$		−	25.2518i		−	1.01496i	0.861664	−	0.507479i	$-0.169422\pi$
$620$	1.74652	−	2.96031i	0.0701418	−	0.118889i
$621$	−10.8170			−0.434071
$622$	7.83745	−	7.83745i	0.314253	−	0.314253i
$623$	−17.0233	−	17.0233i	−0.682026	−	0.682026i
$624$	−59.9473			−2.39981
$625$	−13.3067	+	21.1644i	−0.532266	+	0.846577i
$626$		−	25.1642i		−	1.00577i
$627$		0			0
$628$	3.08749	−	3.08749i	0.123204	−	0.123204i
$629$	43.4663			1.73311
$630$	11.7735	+	6.94613i	0.469069	+	0.276740i
$631$	23.8568			0.949726			0.474863	−	0.880060i	$-0.342498\pi$
$631$	23.8568			0.949726			0.474863	+	0.880060i	$0.342498\pi$
$632$	15.0020	+	15.0020i	0.596746	+	0.596746i
$633$	11.5952	+	11.5952i	0.460867	+	0.460867i
$634$	−7.13067			−0.283195
$635$	7.64638	−	1.97184i	0.303437	−	0.0782501i
$636$	4.05724			0.160880
$637$	6.39377	−	6.39377i	0.253330	−	0.253330i
$638$		0			0
$639$		−	2.52002i		−	0.0996903i
$640$	−7.20521	−	27.9403i	−0.284811	−	1.10444i
$641$	−13.0841			−0.516790			−0.258395	−	0.966039i	$-0.583194\pi$
$641$	−13.0841			−0.516790			−0.258395	+	0.966039i	$0.583194\pi$
$642$	−28.6757	−	28.6757i	−1.13174	−	1.13174i
$643$	−3.58296	+	3.58296i	−0.141298	+	0.141298i	−0.774218	−	0.632919i	$-0.781856\pi$
$643$	−3.58296	+	3.58296i	−0.141298	+	0.141298i	0.632919	+	0.774218i	$0.281856\pi$
$644$	2.20311			0.0868148
$645$	−12.8307	−	7.56983i	−0.505208	−	0.298062i
$646$		−	1.52179i		−	0.0598740i
$647$	25.0924	+	25.0924i	0.986483	+	0.986483i	0.999910	−	0.0134265i	$-0.00427392\pi$
$647$	25.0924	+	25.0924i	0.986483	+	0.986483i	−0.0134265	+	0.999910i	$0.504274\pi$
$648$	20.8659	+	20.8659i	0.819688	+	0.819688i
$649$		0			0
$650$	−22.5501	−	40.8146i	−0.884487	−	1.60088i
$651$			33.1001i			1.29730i
$652$	−1.31577	−	1.31577i	−0.0515297	−	0.0515297i
$653$	−2.88489	+	2.88489i	−0.112894	+	0.112894i	−0.761297	−	0.648403i	$-0.775437\pi$
$653$	−2.88489	+	2.88489i	−0.112894	+	0.112894i	0.648403	+	0.761297i	$0.275437\pi$
$654$			36.3266i			1.42048i
$655$	−7.22997	+	12.2546i	−0.282498	+	0.478828i
$656$		−	12.8915i		−	0.503329i
$657$	11.8129	−	11.8129i	0.460867	−	0.460867i
$658$	22.1197	−	22.1197i	0.862316	−	0.862316i
$659$	13.9779			0.544503			0.272252	−	0.962226i	$-0.412232\pi$
$659$	13.9779			0.544503			0.272252	+	0.962226i	$0.412232\pi$
$660$		0			0
$661$	22.6375			0.880495			0.440247	−	0.897876i	$-0.354891\pi$
$661$	22.6375			0.880495			0.440247	+	0.897876i	$0.354891\pi$
$662$	0.671746	−	0.671746i	0.0261081	−	0.0261081i
$663$	−48.5322	+	48.5322i	−1.88483	+	1.88483i
$664$		−	6.37117i		−	0.247249i
$665$	−1.02544	+	0.264440i	−0.0397650	+	0.0102546i
$666$		−	22.2927i		−	0.863826i
$667$	−6.10379	+	6.10379i	−0.236340	+	0.236340i
$668$	3.77977	+	3.77977i	0.146244	+	0.146244i
$669$			42.8874i			1.65812i
$670$	2.59888	+	1.53328i	0.100403	+	0.0592359i
$671$		0			0
$672$	−4.85576	−	4.85576i	−0.187315	−	0.187315i
$673$	−22.9662	−	22.9662i	−0.885283	−	0.885283i	0.108783	−	0.994066i	$-0.465305\pi$
$673$	−22.9662	−	22.9662i	−0.885283	−	0.885283i	−0.994066	+	0.108783i	$0.965305\pi$
$674$			3.40929i			0.131321i
$675$	−3.81284	+	13.2278i	−0.146756	+	0.509138i
$676$	6.15608			0.236772
$677$	−14.0251	+	14.0251i	−0.539028	+	0.539028i	−0.923244	−	0.384215i	$-0.874472\pi$
$677$	−14.0251	+	14.0251i	−0.539028	+	0.539028i	0.384215	+	0.923244i	$0.374472\pi$
$678$	0.354368	+	0.354368i	0.0136094	+	0.0136094i
$679$	−6.89783			−0.264714
$680$	−25.6861	−	15.1542i	−0.985017	−	0.581139i
$681$		−	11.8857i		−	0.455461i
$682$		0			0
$683$	10.8713	−	10.8713i	0.415977	−	0.415977i	−0.467837	−	0.883815i	$-0.654967\pi$
$683$	10.8713	−	10.8713i	0.415977	−	0.415977i	0.883815	+	0.467837i	$0.154967\pi$
$684$	−0.0830135			−0.00317410
$685$	6.32658	+	24.5331i	0.241726	+	0.937363i
$686$	29.7813			1.13705
$687$	−0.648008	−	0.648008i	−0.0247231	−	0.0247231i
$688$	9.56813	+	9.56813i	0.364782	+	0.364782i
$689$	48.8308			1.86031
$690$	−7.14096	−	27.6912i	−0.271852	−	1.05418i
$691$	−30.5928			−1.16381			−0.581903	−	0.813259i	$-0.697691\pi$
$691$	−30.5928			−1.16381			−0.581903	+	0.813259i	$0.697691\pi$
$692$	−2.69367	+	2.69367i	−0.102398	+	0.102398i
$693$		0			0
$694$			27.7271i			1.05251i
$695$	17.6854	+	10.4340i	0.670845	+	0.395784i
$696$	12.6018			0.477669
$697$	−10.4367	−	10.4367i	−0.395319	−	0.395319i
$698$	14.7260	−	14.7260i	0.557386	−	0.557386i
$699$	−13.9313			−0.526931
$700$	0.776568	−	2.69412i	0.0293515	−	0.101828i
$701$		−	32.2169i		−	1.21682i	−0.793624	−	0.608409i	$-0.791808\pi$
$701$		−	32.2169i		−	1.21682i	0.793624	−	0.608409i	$-0.208192\pi$
$702$	−18.1563	−	18.1563i	−0.685265	−	0.685265i
$703$	1.22117	+	1.22117i	0.0460574	+	0.0460574i
$704$		0			0
$705$	−37.1968	−	21.9453i	−1.40091	−	0.826508i
$706$			37.8235i			1.42351i
$707$	4.13538	+	4.13538i	0.155527	+	0.155527i
$708$	−4.02030	+	4.02030i	−0.151092	+	0.151092i
$709$		−	40.0729i		−	1.50497i	−0.658610	−	0.752485i	$-0.728855\pi$
$709$		−	40.0729i		−	1.50497i	0.658610	−	0.752485i	$-0.271145\pi$
$710$	−4.70570	+	1.21350i	−0.176602	+	0.0455419i
$711$		−	13.9621i		−	0.523619i
$712$	19.0479	−	19.0479i	0.713850	−	0.713850i
$713$	17.9391	−	17.9391i	0.671824	−	0.671824i
$714$	−38.8014			−1.45210
$715$		0			0
$716$	−1.61112			−0.0602106
$717$	−20.5328	+	20.5328i	−0.766810	+	0.766810i
$718$	1.52496	−	1.52496i	0.0569110	−	0.0569110i
$719$			32.0865i			1.19662i	0.801263	+	0.598312i	$0.204162\pi$
$719$			32.0865i			1.19662i	−0.801263	+	0.598312i	$0.795838\pi$
$720$	−8.71056	+	14.7642i	−0.324624	+	0.550230i
$721$			30.1848i			1.12414i
$722$	−20.0562	+	20.0562i	−0.746413	+	0.746413i
$723$	17.1819	+	17.1819i	0.639001	+	0.639001i
$724$		−	0.949282i		−	0.0352798i
$725$	5.31264	+	9.61565i	0.197307	+	0.357116i
$726$		0			0
$727$	31.2393	+	31.2393i	1.15860	+	1.15860i	0.984777	+	0.173824i	$0.0556124\pi$
$727$	31.2393	+	31.2393i	1.15860	+	1.15860i	0.173824	+	0.984777i	$0.444388\pi$
$728$	−27.3717	−	27.3717i	−1.01446	−	1.01446i
$729$		−	1.44677i		−	0.0535840i
$730$	−27.7471	−	16.3702i	−1.02697	−	0.605888i
$731$	15.4924			0.573006
$732$	1.43925	−	1.43925i	0.0531960	−	0.0531960i
$733$	−36.7604	−	36.7604i	−1.35778	−	1.35778i	−0.876651	−	0.481126i	$-0.840228\pi$
$733$	−36.7604	−	36.7604i	−1.35778	−	1.35778i	−0.481126	−	0.876651i	$-0.659772\pi$
$734$	−22.5855			−0.833648
$735$	−1.76229	−	6.83378i	−0.0650030	−	0.252068i
$736$			5.26329i			0.194007i
$737$		0			0
$738$	−5.35273	+	5.35273i	−0.197037	+	0.197037i
$739$	25.9734			0.955447			0.477724	−	0.878510i	$-0.341462\pi$
$739$	25.9734			0.955447			0.477724	+	0.878510i	$0.341462\pi$
$740$	−4.42759	+	1.14178i	−0.162762	+	0.0419728i
$741$	−2.72700			−0.100179
$742$	19.5201	+	19.5201i	0.716604	+	0.716604i
$743$	30.1770	+	30.1770i	1.10709	+	1.10709i	0.993532	+	0.113555i	$0.0362240\pi$
$743$	30.1770	+	30.1770i	1.10709	+	1.10709i	0.113555	+	0.993532i	$0.463776\pi$
$744$	−37.0367			−1.35783
$745$	18.1249	+	10.6933i	0.664045	+	0.391772i
$746$	−34.5923			−1.26651
$747$	−2.96477	+	2.96477i	−0.108475	+	0.108475i
$748$		0			0
$749$		−	29.3479i		−	1.07235i
$750$	−36.3798	−	1.02828i	−1.32840	−	0.0375473i
$751$	48.0853			1.75466			0.877329	−	0.479889i	$-0.159323\pi$
$751$	48.0853			1.75466			0.877329	+	0.479889i	$0.159323\pi$
$752$	27.7385	+	27.7385i	1.01152	+	1.01152i
$753$	2.30108	−	2.30108i	0.0838561	−	0.0838561i
$754$	−20.4904			−0.746216
$755$	14.6399	−	24.8143i	0.532800	−	0.903084i
$756$		−	1.54393i		−	0.0561522i
$757$	−8.06170	−	8.06170i	−0.293007	−	0.293007i	0.545260	−	0.838267i	$-0.316431\pi$
$757$	−8.06170	−	8.06170i	−0.293007	−	0.293007i	−0.838267	+	0.545260i	$0.816431\pi$
$758$	15.8400	+	15.8400i	0.575336	+	0.575336i
$759$		0			0
$760$	−0.295890	−	1.14740i	−0.0107330	−	0.0416205i
$761$		−	10.0931i		−	0.365873i	−0.983125	−	0.182937i	$-0.941440\pi$
$761$		−	10.0931i		−	0.365873i	0.983125	−	0.182937i	$-0.0585603\pi$
$762$	8.12860	+	8.12860i	0.294468	+	0.294468i
$763$	−18.5891	+	18.5891i	−0.672971	+	0.672971i
$764$			2.95519i			0.106915i
$765$	4.90092	+	19.0047i	0.177193	+	0.687118i
$766$		−	15.3124i		−	0.553258i
$767$	−48.3862	+	48.3862i	−1.74712	+	1.74712i
$768$	8.67049	−	8.67049i	0.312869	−	0.312869i
$769$	31.7043			1.14328			0.571642	−	0.820503i	$-0.306306\pi$
$769$	31.7043			1.14328			0.571642	+	0.820503i	$0.306306\pi$
$770$		0			0
$771$	−2.59470			−0.0934458
$772$	0.933125	−	0.933125i	0.0335839	−	0.0335839i
$773$	−17.1009	+	17.1009i	−0.615077	+	0.615077i	−0.944264	−	0.329188i	$-0.893225\pi$
$773$	−17.1009	+	17.1009i	−0.615077	+	0.615077i	0.329188	+	0.944264i	$0.393225\pi$
$774$		−	7.94563i		−	0.285600i
$775$	−15.6139	−	28.2605i	−0.560868	−	1.01515i
$776$		−	7.71817i		−	0.277066i
$777$	31.1365	−	31.1365i	1.11702	−	1.11702i
$778$	−15.4856	−	15.4856i	−0.555187	−	0.555187i
$779$		−	0.586434i		−	0.0210112i
$780$	3.66876	−	6.21848i	0.131363	−	0.222657i
$781$		0			0
$782$	21.0289	+	21.0289i	0.751993	+	0.751993i
$783$	4.27750	+	4.27750i	0.152865	+	0.152865i
$784$			6.41028i			0.228939i
$785$	−10.2421	−	39.7168i	−0.365557	−	1.41755i
$786$	−20.7134			−0.738822
$787$	6.70534	−	6.70534i	0.239019	−	0.239019i	−0.577425	−	0.816444i	$-0.695942\pi$
$787$	6.70534	−	6.70534i	0.239019	−	0.239019i	0.816444	+	0.577425i	$0.195942\pi$
$788$	−1.59012	−	1.59012i	−0.0566457	−	0.0566457i
$789$	7.03362			0.250404
$790$	−26.0718	+	6.72338i	−0.927595	+	0.239207i
$791$			0.362675i			0.0128953i
$792$		0			0
$793$	17.3220	−	17.3220i	0.615123	−	0.615123i
$794$	−31.6031			−1.12155
$795$	19.3662	−	32.8252i	0.686847	−	1.16419i
$796$	−0.815469			−0.0289035
$797$	26.7675	+	26.7675i	0.948155	+	0.948155i	0.998721	−	0.0505655i	$-0.0161024\pi$
$797$	26.7675	+	26.7675i	0.948155	+	0.948155i	−0.0505655	+	0.998721i	$0.516102\pi$
$798$	−1.09011	−	1.09011i	−0.0385896	−	0.0385896i
$799$	44.9131			1.58891
$800$	6.43633	+	1.85524i	0.227559	+	0.0655926i
$801$	−17.7276			−0.626373
$802$	29.5848	−	29.5848i	1.04468	−	1.04468i
$803$		0			0
$804$			0.467219i			0.0164775i
$805$	10.5160	−	17.8243i	0.370640	−	0.628226i
$806$	60.2214			2.12121
$807$	18.5155	+	18.5155i	0.651775	+	0.651775i
$808$	−4.62719	+	4.62719i	−0.162784	+	0.162784i
$809$	−37.3798			−1.31420			−0.657102	−	0.753802i	$-0.728218\pi$
$809$	−37.3798			−1.31420			−0.657102	+	0.753802i	$0.728218\pi$
$810$	−36.2627	+	9.35137i	−1.27414	+	0.328574i
$811$			4.37634i			0.153674i	0.997044	+	0.0768370i	$0.0244821\pi$
$811$			4.37634i			0.153674i	−0.997044	+	0.0768370i	$0.975518\pi$
$812$	−0.871205	−	0.871205i	−0.0305733	−	0.0305733i
$813$	−50.5017	−	50.5017i	−1.77117	−	1.77117i
$814$		0			0
$815$	−16.9258	+	4.36480i	−0.592885	+	0.152892i
$816$		−	48.6576i		−	1.70336i
$817$	0.435253	+	0.435253i	0.0152276	+	0.0152276i
$818$	−31.2196	+	31.2196i	−1.09157	+	1.09157i
$819$			25.4744i			0.890148i
$820$	1.33727	+	0.788959i	0.0466994	+	0.0275517i
$821$			5.58492i			0.194915i	0.995240	+	0.0974576i	$0.0310710\pi$
$821$			5.58492i			0.194915i	−0.995240	+	0.0974576i	$0.968929\pi$
$822$	−26.0803	+	26.0803i	−0.909655	+	0.909655i
$823$	12.4511	−	12.4511i	0.434020	−	0.434020i	−0.455974	−	0.889993i	$-0.650709\pi$
$823$	12.4511	−	12.4511i	0.434020	−	0.434020i	0.889993	+	0.455974i	$0.150709\pi$
$824$	−33.7746			−1.17659
$825$		0			0
$826$	−38.6846			−1.34601
$827$	−15.5697	+	15.5697i	−0.541412	+	0.541412i	−0.923943	−	0.382531i	$-0.875053\pi$
$827$	−15.5697	+	15.5697i	−0.541412	+	0.541412i	0.382531	+	0.923943i	$0.375053\pi$
$828$	1.14713	−	1.14713i	0.0398654	−	0.0398654i
$829$		−	12.8841i		−	0.447484i	−0.974648	−	0.223742i	$-0.928173\pi$
$829$		−	12.8841i		−	0.447484i	0.974648	−	0.223742i	$-0.0718273\pi$
$830$	6.96388	+	4.10854i	0.241720	+	0.142609i
$831$		−	41.3863i		−	1.43568i
$832$	30.1274	−	30.1274i	1.04448	−	1.04448i
$833$	5.18964	+	5.18964i	0.179810	+	0.179810i
$834$			29.8927i			1.03510i
$835$	48.6221	−	12.5386i	1.68264	−	0.433916i
$836$		0			0
$837$	−12.5716	−	12.5716i	−0.434538	−	0.434538i
$838$	26.1134	+	26.1134i	0.902073	+	0.902073i
$839$			18.8163i			0.649610i	0.945781	+	0.324805i	$0.105299\pi$
$839$			18.8163i			0.649610i	−0.945781	+	0.324805i	$0.894701\pi$
$840$	−29.2554	+	7.54436i	−1.00941	+	0.260305i
$841$	−24.1726			−0.833538
$842$	−11.6374	+	11.6374i	−0.401050	+	0.401050i
$843$	−13.7319	−	13.7319i	−0.472950	−	0.472950i
$844$	1.79390			0.0617486
$845$	29.3844	−	49.8060i	1.01086	−	1.71338i
$846$		−	23.0348i		−	0.791952i
$847$		0			0
$848$	−24.4785	+	24.4785i	−0.840595	+	0.840595i
$849$	−20.7058			−0.710620
$850$	33.1281	−	18.3033i	1.13628	−	0.627797i
$851$	−33.7497			−1.15693
$852$	−0.532068	−	0.532068i	−0.0182284	−	0.0182284i
$853$	−33.2410	−	33.2410i	−1.13815	−	1.13815i	−0.988782	−	0.149368i	$-0.952276\pi$
$853$	−33.2410	−	33.2410i	−1.13815	−	1.13815i	−0.149368	−	0.988782i	$-0.547724\pi$
$854$	13.8489			0.473900
$855$	−0.396243	+	0.671623i	−0.0135512	+	0.0229690i
$856$	32.8382			1.12239
$857$	11.3933	−	11.3933i	0.389186	−	0.389186i	−0.485211	−	0.874397i	$-0.661257\pi$
$857$	11.3933	−	11.3933i	0.389186	−	0.389186i	0.874397	+	0.485211i	$0.161257\pi$
$858$		0			0
$859$		−	49.9871i		−	1.70554i	−0.522289	−	0.852769i	$-0.674922\pi$
$859$		−	49.9871i		−	1.70554i	0.522289	−	0.852769i	$-0.325078\pi$
$860$	−1.57809	+	0.406957i	−0.0538125	+	0.0138771i
$861$	−14.9524			−0.509577
$862$	−18.4257	−	18.4257i	−0.627582	−	0.627582i
$863$	39.2999	−	39.2999i	1.33778	−	1.33778i	0.439579	−	0.898204i	$-0.355128\pi$
$863$	39.2999	−	39.2999i	1.33778	−	1.33778i	0.898204	−	0.439579i	$-0.144872\pi$
$864$	3.68848			0.125485
$865$	8.93569	+	34.6507i	0.303823	+	1.17816i
$866$			40.3557i			1.37134i
$867$	−13.2358	−	13.2358i	−0.449511	−	0.449511i
$868$	2.56048	+	2.56048i	0.0869083	+	0.0869083i
$869$		0			0
$870$	−8.12642	+	13.7741i	−0.275512	+	0.466986i
$871$			5.62320i			0.190535i
$872$	−20.7999	−	20.7999i	−0.704373	−	0.704373i
$873$	−3.59159	+	3.59159i	−0.121557	+	0.121557i
$874$			1.18160i			0.0399684i
$875$	−18.0901	−	19.1425i	−0.611559	−	0.647136i
$876$		−	4.98829i		−	0.168539i
$877$	8.75692	−	8.75692i	0.295700	−	0.295700i	−0.543627	−	0.839327i	$-0.682949\pi$
$877$	8.75692	−	8.75692i	0.295700	−	0.295700i	0.839327	+	0.543627i	$0.182949\pi$
$878$	−42.6070	+	42.6070i	−1.43792	+	1.43792i
$879$	−61.9680			−2.09013
$880$		0			0
$881$	49.9355			1.68237			0.841185	−	0.540748i	$-0.181859\pi$
$881$	49.9355			1.68237			0.841185	+	0.540748i	$0.181859\pi$
$882$	2.66163	−	2.66163i	0.0896218	−	0.0896218i
$883$	23.9079	−	23.9079i	0.804566	−	0.804566i	−0.179239	−	0.983806i	$-0.557364\pi$
$883$	23.9079	−	23.9079i	0.804566	−	0.804566i	0.983806	+	0.179239i	$0.0573636\pi$
$884$			7.50847i			0.252537i
$885$	13.3365	+	51.7161i	0.448302	+	1.73842i
$886$		−	32.4227i		−	1.08926i
$887$	−39.9042	+	39.9042i	−1.33985	+	1.33985i	−0.443656	+	0.896197i	$0.646319\pi$
$887$	−39.9042	+	39.9042i	−1.33985	+	1.33985i	−0.896197	+	0.443656i	$0.853681\pi$
$888$	34.8395	+	34.8395i	1.16914	+	1.16914i
$889$			8.31916i			0.279016i
$890$	8.53663	+	33.1032i	0.286148	+	1.10962i
$891$		0			0
$892$	3.31758	+	3.31758i	0.111081	+	0.111081i
$893$	1.26182	+	1.26182i	0.0422252	+	0.0422252i
$894$			30.6356i			1.02461i
$895$	−7.69028	+	13.0348i	−0.257058	+	0.435707i
$896$	30.3987			1.01555
$897$	37.6832	−	37.6832i	1.25820	−	1.25820i
$898$	25.3380	+	25.3380i	0.845540	+	0.845540i
$899$	−14.1878			−0.473188
$900$	−0.998442	−	1.80713i	−0.0332814	−	0.0602378i
$901$			39.6346i			1.32042i
$902$		0			0
$903$	11.0977	−	11.0977i	0.369310	−	0.369310i
$904$	−0.405808			−0.0134970
$905$	−7.68019	−	4.53115i	−0.255298	−	0.150620i
$906$	41.9423			1.39344
$907$	23.3877	+	23.3877i	0.776575	+	0.776575i	0.979247	−	0.202672i	$-0.0649624\pi$
$907$	23.3877	+	23.3877i	0.776575	+	0.776575i	−0.202672	+	0.979247i	$0.564962\pi$
$908$	−0.919426	−	0.919426i	−0.0305122	−	0.0305122i
$909$	4.30645			0.142836
$910$	47.5692	−	12.2671i	1.57690	−	0.406650i
$911$	−24.0845			−0.797954			−0.398977	−	0.916961i	$-0.630635\pi$
$911$	−24.0845			−0.797954			−0.398977	+	0.916961i	$0.630635\pi$
$912$	1.36702	−	1.36702i	0.0452666	−	0.0452666i
$913$		0			0
$914$		−	13.9628i		−	0.461848i
$915$	−4.77440	−	18.5141i	−0.157837	−	0.612058i
$916$	−0.100254			−0.00331249
$917$	−10.5995	−	10.5995i	−0.350026	−	0.350026i
$918$	14.7370	−	14.7370i	0.486392	−	0.486392i
$919$	−17.8182			−0.587769			−0.293884	−	0.955841i	$-0.594948\pi$
$919$	−17.8182			−0.587769			−0.293884	+	0.955841i	$0.594948\pi$
$920$	19.9442	+	11.7666i	0.657540	+	0.387934i
$921$			50.3452i			1.65893i
$922$	−42.2879	−	42.2879i	−1.39268	−	1.39268i
$923$	−6.40370	−	6.40370i	−0.210780	−	0.210780i
$924$		0			0
$925$	−11.8963	+	41.2716i	−0.391149	+	1.35700i
$926$		−	51.7902i		−	1.70193i
$927$	15.7167	+	15.7167i	0.516205	+	0.516205i
$928$	2.08133	−	2.08133i	0.0683230	−	0.0683230i
$929$		−	23.9829i		−	0.786853i	−0.919356	−	0.393427i	$-0.871290\pi$
$929$		−	23.9829i		−	0.786853i	0.919356	−	0.393427i	$-0.128710\pi$
$930$	23.8836	−	40.4822i	0.783175	−	1.32746i
$931$			0.291603i			0.00955691i
$932$	−1.07767	+	1.07767i	−0.0353001	+	0.0353001i
$933$	11.3995	−	11.3995i	0.373203	−	0.373203i
$934$	−29.3616			−0.960741
$935$		0			0
$936$	−28.5040			−0.931684
$937$	21.4626	−	21.4626i	0.701153	−	0.701153i	−0.263505	−	0.964658i	$-0.584878\pi$
$937$	21.4626	−	21.4626i	0.701153	−	0.701153i	0.964658	+	0.263505i	$0.0848784\pi$
$938$	−2.24787	+	2.24787i	−0.0733955	+	0.0733955i
$939$		−	36.6012i		−	1.19443i
$940$	−4.57497	+	1.17979i	−0.149219	+	0.0384805i
$941$		−	4.47383i		−	0.145843i	−0.997338	−	0.0729213i	$-0.976768\pi$
$941$		−	4.47383i		−	0.145843i	0.997338	−	0.0729213i	$-0.0232322\pi$
$942$	42.2215	−	42.2215i	1.37565	−	1.37565i
$943$	8.10368	+	8.10368i	0.263892	+	0.263892i
$944$		−	48.5112i		−	1.57891i
$945$	−12.4912	−	7.36954i	−0.406339	−	0.239731i
$946$		0			0
$947$	−34.1643	−	34.1643i	−1.11019	−	1.11019i	−0.993124	−	0.117067i	$-0.962651\pi$
$947$	−34.1643	−	34.1643i	−1.11019	−	1.11019i	−0.117067	−	0.993124i	$-0.537349\pi$
$948$	−2.94791	−	2.94791i	−0.0957438	−	0.0957438i
$949$		−	60.0365i		−	1.94887i
$950$	1.44495	+	0.416499i	0.0468804	+	0.0135130i
$951$	−10.3715			−0.336319
$952$	22.2169	−	22.2169i	0.720053	−	0.720053i
$953$	−31.2622	−	31.2622i	−1.01268	−	1.01268i	−0.999919	−	0.0127642i	$-0.995937\pi$
$953$	−31.2622	−	31.2622i	−1.01268	−	1.01268i	−0.0127642	−	0.999919i	$-0.504063\pi$
$954$	20.3276			0.658130
$955$	23.9091	+	14.1058i	0.773679	+	0.456454i
$956$			3.17664i			0.102740i
$957$		0			0
$958$	29.8322	−	29.8322i	0.963833	−	0.963833i
$959$	−26.6917			−0.861920
$960$	−8.30391	−	32.2008i	−0.268008	−	1.03928i
$961$	10.6979			0.345094
$962$	−56.6488	−	56.6488i	−1.82643	−	1.82643i
$963$	−15.2810	−	15.2810i	−0.492423	−	0.492423i
$964$	2.65823			0.0856157
$965$	−3.09545	−	12.0035i	−0.0996460	−	0.386406i
$966$	30.1276			0.969340
$967$	−18.6938	+	18.6938i	−0.601151	+	0.601151i	−0.940618	−	0.339467i	$-0.889753\pi$
$967$	−18.6938	+	18.6938i	−0.601151	+	0.601151i	0.339467	+	0.940618i	$0.389753\pi$
$968$		0			0
$969$		−	2.21343i		−	0.0711055i
$970$	8.43620	+	4.97717i	0.270870	+	0.159807i
$971$	33.1039			1.06236			0.531178	−	0.847260i	$-0.321750\pi$
$971$	33.1039			1.06236			0.531178	+	0.847260i	$0.321750\pi$
$972$	−2.70989	−	2.70989i	−0.0869196	−	0.0869196i
$973$	−15.2967	+	15.2967i	−0.490391	+	0.490391i
$974$	58.7190			1.88148
$975$	−32.7989	−	59.3645i	−1.05040	−	1.90118i
$976$			17.3668i			0.555896i
$977$	15.1069	+	15.1069i	0.483311	+	0.483311i	0.906187	−	0.422876i	$-0.138979\pi$
$977$	15.1069	+	15.1069i	0.483311	+	0.483311i	−0.422876	+	0.906187i	$0.638979\pi$
$978$	−17.9932	−	17.9932i	−0.575359	−	0.575359i
$979$		0			0
$980$	−0.664954	−	0.392308i	−0.0212412	−	0.0125318i
$981$			19.3581i			0.618057i
$982$	−25.6483	−	25.6483i	−0.818469	−	0.818469i
$983$	−29.6143	+	29.6143i	−0.944550	+	0.944550i	−0.998541	−	0.0539912i	$-0.982806\pi$
$983$	−29.6143	+	29.6143i	−0.944550	+	0.944550i	0.0539912	+	0.998541i	$0.482806\pi$
$984$		−	16.7307i		−	0.533355i
$985$	−20.4549	+	5.27489i	−0.651748	+	0.168072i
$986$		−	16.6315i		−	0.529654i
$987$	32.1729	−	32.1729i	1.02407	−	1.02407i
$988$	−0.210948	+	0.210948i	−0.00671116	+	0.00671116i
$989$	−12.0292			−0.382505
$990$		0			0
$991$	−5.00640			−0.159033			−0.0795167	−	0.996834i	$-0.525338\pi$
$991$	−5.00640			−0.159033			−0.0795167	+	0.996834i	$0.525338\pi$
$992$	−6.11704	+	6.11704i	−0.194216	+	0.194216i
$993$	0.977048	−	0.977048i	0.0310057	−	0.0310057i
$994$		−	5.11974i		−	0.162388i
$995$	−3.89242	+	6.59757i	−0.123398	+	0.209157i
$996$			1.25195i			0.0396694i
$997$	−9.87615	+	9.87615i	−0.312781	+	0.312781i	−0.845986	−	0.533205i	$-0.820987\pi$
$997$	−9.87615	+	9.87615i	−0.312781	+	0.312781i	0.533205	+	0.845986i	$0.320987\pi$
$998$	−42.9808	−	42.9808i	−1.36053	−	1.36053i
$999$			23.6516i			0.748304i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.e.c.362.15	yes	40
5.3	odd	4	inner	605.2.e.c.483.6	yes	40
11.2	odd	10		605.2.m.g.282.15		160
11.3	even	5		605.2.m.g.112.6		160
11.4	even	5		605.2.m.g.457.15		160
11.5	even	5		605.2.m.g.602.6		160
11.6	odd	10		605.2.m.g.602.15		160
11.7	odd	10		605.2.m.g.457.6		160
11.8	odd	10		605.2.m.g.112.15		160
11.9	even	5		605.2.m.g.282.6		160
11.10	odd	2	inner	605.2.e.c.362.6	✓	40
55.3	odd	20		605.2.m.g.233.6		160
55.8	even	20		605.2.m.g.233.15		160
55.13	even	20		605.2.m.g.403.6		160
55.18	even	20		605.2.m.g.578.6		160
55.28	even	20		605.2.m.g.118.6		160
55.38	odd	20		605.2.m.g.118.15		160
55.43	even	4	inner	605.2.e.c.483.15	yes	40
55.48	odd	20		605.2.m.g.578.15		160
55.53	odd	20		605.2.m.g.403.15		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.c.362.6	✓	40	11.10	odd	2	inner
605.2.e.c.362.15	yes	40	1.1	even	1	trivial
605.2.e.c.483.6	yes	40	5.3	odd	4	inner
605.2.e.c.483.15	yes	40	55.43	even	4	inner
605.2.m.g.112.6		160	11.3	even	5
605.2.m.g.112.15		160	11.8	odd	10
605.2.m.g.118.6		160	55.28	even	20
605.2.m.g.118.15		160	55.38	odd	20
605.2.m.g.233.6		160	55.3	odd	20
605.2.m.g.233.15		160	55.8	even	20
605.2.m.g.282.6		160	11.9	even	5
605.2.m.g.282.15		160	11.2	odd	10
605.2.m.g.403.6		160	55.13	even	20
605.2.m.g.403.15		160	55.53	odd	20
605.2.m.g.457.6		160	11.7	odd	10
605.2.m.g.457.15		160	11.4	even	5
605.2.m.g.578.6		160	55.18	even	20
605.2.m.g.578.15		160	55.48	odd	20
605.2.m.g.602.6		160	11.5	even	5
605.2.m.g.602.15		160	11.6	odd	10

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.05784 - 1.05784i) q^{2} +(1.53861 - 1.53861i) q^{3} -0.238041i q^{4} +(-1.92587 - 1.13622i) q^{5} -3.25521i q^{6} +(1.66576 - 1.66576i) q^{7} +(1.86387 + 1.86387i) q^{8} -1.73467i q^{9} +O(q^{10})\)	\(q+(1.05784 - 1.05784i) q^{2} +(1.53861 - 1.53861i) q^{3} -0.238041i q^{4} +(-1.92587 - 1.13622i) q^{5} -3.25521i q^{6} +(1.66576 - 1.66576i) q^{7} +(1.86387 + 1.86387i) q^{8} -1.73467i q^{9} +(-3.23920 + 0.835322i) q^{10} +(-0.366253 - 0.366253i) q^{12} +(-4.40803 - 4.40803i) q^{13} -3.52421i q^{14} +(-4.71139 + 1.21497i) q^{15} +4.41942 q^{16} +(3.57788 - 3.57788i) q^{17} +(-1.83500 - 1.83500i) q^{18} +0.201039 q^{19} +(-0.270468 + 0.458437i) q^{20} -5.12593i q^{21} +(-2.77807 + 2.77807i) q^{23} +5.73555 q^{24} +(2.41799 + 4.37645i) q^{25} -9.32596 q^{26} +(1.94685 + 1.94685i) q^{27} +(-0.396519 - 0.396519i) q^{28} +2.19713 q^{29} +(-3.69865 + 6.26913i) q^{30} -6.45739 q^{31} +(0.947293 - 0.947293i) q^{32} -7.56963i q^{34} +(-5.10073 + 1.31537i) q^{35} -0.412922 q^{36} +(6.07431 + 6.07431i) q^{37} +(0.212666 - 0.212666i) q^{38} -13.5645 q^{39} +(-1.47180 - 5.70734i) q^{40} -2.91702i q^{41} +(-5.42240 - 5.42240i) q^{42} +(2.16502 + 2.16502i) q^{43} +(-1.97098 + 3.34076i) q^{45} +5.87749i q^{46} +(6.27650 + 6.27650i) q^{47} +(6.79978 - 6.79978i) q^{48} +1.45048i q^{49} +(7.18741 + 2.07174i) q^{50} -11.0099i q^{51} +(-1.04929 + 1.04929i) q^{52} +(-5.53885 + 5.53885i) q^{53} +4.11891 q^{54} +6.20951 q^{56} +(0.309321 - 0.309321i) q^{57} +(2.32421 - 2.32421i) q^{58} -10.9768i q^{59} +(0.289212 + 1.12150i) q^{60} +3.92965i q^{61} +(-6.83087 + 6.83087i) q^{62} +(-2.88955 - 2.88955i) q^{63} +6.83467i q^{64} +(3.48080 + 13.4978i) q^{65} +(-0.637836 - 0.637836i) q^{67} +(-0.851681 - 0.851681i) q^{68} +8.54875i q^{69} +(-4.00429 + 6.78719i) q^{70} +1.45273 q^{71} +(3.23320 - 3.23320i) q^{72} +(6.80990 + 6.80990i) q^{73} +12.8513 q^{74} +(10.4540 + 3.01332i) q^{75} -0.0478554i q^{76} +(-14.3491 + 14.3491i) q^{78} +8.04884 q^{79} +(-8.51125 - 5.02145i) q^{80} +11.1949 q^{81} +(-3.08573 - 3.08573i) q^{82} +(-1.70913 - 1.70913i) q^{83} -1.22018 q^{84} +(-10.9558 + 2.82527i) q^{85} +4.58048 q^{86} +(3.38054 - 3.38054i) q^{87} -10.2196i q^{89} +(1.44901 + 5.61895i) q^{90} -14.6855 q^{91} +(0.661293 + 0.661293i) q^{92} +(-9.93544 + 9.93544i) q^{93} +13.2790 q^{94} +(-0.387176 - 0.228425i) q^{95} -2.91504i q^{96} +(-2.07047 - 2.07047i) q^{97} +(1.53437 + 1.53437i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{3} - 4 q^{5}+O(q^{10}) \) 40 * q + 8 * q^3 - 4 * q^5	\( 40 q + 8 q^{3} - 4 q^{5} - 32 q^{12} + 32 q^{15} - 24 q^{16} + 32 q^{20} - 24 q^{23} - 52 q^{25} - 8 q^{26} + 32 q^{27} + 16 q^{31} - 40 q^{36} + 36 q^{37} + 32 q^{38} + 32 q^{42} + 64 q^{45} + 32 q^{47} - 16 q^{48} - 68 q^{53} + 80 q^{56} + 132 q^{58} - 64 q^{60} - 88 q^{67} - 8 q^{70} - 16 q^{75} - 248 q^{78} - 164 q^{80} - 40 q^{81} + 100 q^{82} - 80 q^{86} - 96 q^{91} - 56 q^{92} + 24 q^{93} - 68 q^{97}+O(q^{100}) \) 40 * q + 8 * q^3 - 4 * q^5 - 32 * q^12 + 32 * q^15 - 24 * q^16 + 32 * q^20 - 24 * q^23 - 52 * q^25 - 8 * q^26 + 32 * q^27 + 16 * q^31 - 40 * q^36 + 36 * q^37 + 32 * q^38 + 32 * q^42 + 64 * q^45 + 32 * q^47 - 16 * q^48 - 68 * q^53 + 80 * q^56 + 132 * q^58 - 64 * q^60 - 88 * q^67 - 8 * q^70 - 16 * q^75 - 248 * q^78 - 164 * q^80 - 40 * q^81 + 100 * q^82 - 80 * q^86 - 96 * q^91 - 56 * q^92 + 24 * q^93 - 68 * q^97

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