LMFDB - Embedded newform 380.2.d.b.379.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(379,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("380.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.d (of order $2$, degree $1$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.6
Character	$\chi$	$=$	380.379
Dual form			380.2.d.b.379.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27059 - 0.620975i) q^{2} +0.701989i q^{3} +(1.22878 + 1.57800i) q^{4} +(-1.10449 + 1.94425i) q^{5} +(0.435918 - 0.891938i) q^{6} -1.18642 q^{7} +(-0.581371 - 2.76803i) q^{8} +2.50721 q^{9} +O(q^{10})$	\(q+(-1.27059 - 0.620975i) q^{2} +0.701989i q^{3} +(1.22878 + 1.57800i) q^{4} +(-1.10449 + 1.94425i) q^{5} +(0.435918 - 0.891938i) q^{6} -1.18642 q^{7} +(-0.581371 - 2.76803i) q^{8} +2.50721 q^{9} +(2.61068 - 1.78448i) q^{10} +1.72011i q^{11} +(-1.10774 + 0.862590i) q^{12} -2.64385 q^{13} +(1.50745 + 0.736738i) q^{14} +(-1.36484 - 0.775339i) q^{15} +(-0.980197 + 3.87804i) q^{16} +4.62546i q^{17} +(-3.18563 - 1.55692i) q^{18} +(-2.08114 - 3.82999i) q^{19} +(-4.42521 + 0.646167i) q^{20} -0.832855i q^{21} +(1.06815 - 2.18555i) q^{22} -6.62976 q^{23} +(1.94313 - 0.408116i) q^{24} +(-2.56021 - 4.29480i) q^{25} +(3.35924 + 1.64177i) q^{26} +3.86600i q^{27} +(-1.45785 - 1.87218i) q^{28} +7.53366i q^{29} +(1.25268 + 1.83267i) q^{30} -10.9809 q^{31} +(3.65359 - 4.31871i) q^{32} -1.20750 q^{33} +(2.87229 - 5.87705i) q^{34} +(1.31039 - 2.30670i) q^{35} +(3.08081 + 3.95639i) q^{36} +8.43930 q^{37} +(0.265946 + 6.15867i) q^{38} -1.85596i q^{39} +(6.02386 + 1.92693i) q^{40} +7.40097i q^{41} +(-0.517182 + 1.05821i) q^{42} +9.29752 q^{43} +(-2.71435 + 2.11364i) q^{44} +(-2.76919 + 4.87464i) q^{45} +(8.42368 + 4.11691i) q^{46} -4.10213 q^{47} +(-2.72234 - 0.688088i) q^{48} -5.59240 q^{49} +(0.586003 + 7.04674i) q^{50} -3.24702 q^{51} +(-3.24871 - 4.17201i) q^{52} -1.98886 q^{53} +(2.40069 - 4.91209i) q^{54} +(-3.34433 - 1.89985i) q^{55} +(0.689751 + 3.28406i) q^{56} +(2.68861 - 1.46094i) q^{57} +(4.67822 - 9.57217i) q^{58} -3.13673 q^{59} +(-0.453602 - 3.10645i) q^{60} +3.75579 q^{61} +(13.9522 + 6.81889i) q^{62} -2.97461 q^{63} +(-7.32402 + 3.21851i) q^{64} +(2.92011 - 5.14031i) q^{65} +(1.53424 + 0.749828i) q^{66} +9.50799i q^{67} +(-7.29900 + 5.68367i) q^{68} -4.65402i q^{69} +(-3.09737 + 2.11714i) q^{70} +9.11343 q^{71} +(-1.45762 - 6.94004i) q^{72} -6.47318i q^{73} +(-10.7229 - 5.24059i) q^{74} +(3.01490 - 1.79724i) q^{75} +(3.48647 - 7.99028i) q^{76} -2.04078i q^{77} +(-1.15250 + 2.35815i) q^{78} +6.38375 q^{79} +(-6.45726 - 6.18900i) q^{80} +4.80774 q^{81} +(4.59581 - 9.40357i) q^{82} +10.7908 q^{83} +(1.31425 - 1.02340i) q^{84} +(-8.99304 - 5.10877i) q^{85} +(-11.8133 - 5.77353i) q^{86} -5.28855 q^{87} +(4.76133 - 1.00002i) q^{88} -14.1018i q^{89} +(6.54552 - 4.47406i) q^{90} +3.13673 q^{91} +(-8.14651 - 10.4618i) q^{92} -7.70851i q^{93} +(5.21211 + 2.54732i) q^{94} +(9.74506 + 0.183919i) q^{95} +(3.03169 + 2.56478i) q^{96} +3.39949 q^{97} +(7.10563 + 3.47274i) q^{98} +4.31269i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9}+O(q^{10}) $ 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9	$ 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9} - 8 q^{16} - 20 q^{20} - 40 q^{24} - 84 q^{25} - 24 q^{26} + 24 q^{30} + 24 q^{36} - 40 q^{44} - 12 q^{45} + 128 q^{49} - 120 q^{54} + 24 q^{61} + 72 q^{64} + 112 q^{66} + 32 q^{74} + 56 q^{76} + 96 q^{80} - 72 q^{81} + 44 q^{85} - 40 q^{96}+O(q^{100}) $ 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9 - 8 * q^16 - 20 * q^20 - 40 * q^24 - 84 * q^25 - 24 * q^26 + 24 * q^30 + 24 * q^36 - 40 * q^44 - 12 * q^45 + 128 * q^49 - 120 * q^54 + 24 * q^61 + 72 * q^64 + 112 * q^66 + 32 * q^74 + 56 * q^76 + 96 * q^80 - 72 * q^81 + 44 * q^85 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.27059	−	0.620975i	−0.898440	−	0.439096i
$2$	−1.27059	−	0.620975i	−0.898440	−	0.439096i
$3$			0.701989i			0.405294i	0.979252	+	0.202647i	$0.0649543\pi$
$3$			0.701989i			0.405294i	−0.979252	+	0.202647i	$0.935046\pi$
$4$	1.22878	+	1.57800i	0.614390	+	0.789002i
$5$	−1.10449	+	1.94425i	−0.493942	+	0.869495i
$5$	−1.10449	+	1.94425i	−0.493942	+	0.869495i
$6$	0.435918	−	0.891938i	0.177963	−	0.364132i
$7$	−1.18642			−0.448425			−0.224213	−	0.974540i	$-0.571981\pi$
$7$	−1.18642			−0.448425			−0.224213	+	0.974540i	$0.571981\pi$
$8$	−0.581371	−	2.76803i	−0.205546	−	0.978648i
$9$	2.50721			0.835737
$10$	2.61068	−	1.78448i	0.825569	−	0.564301i
$11$			1.72011i			0.518634i	0.965792	+	0.259317i	$0.0834974\pi$
$11$			1.72011i			0.518634i	−0.965792	+	0.259317i	$0.916503\pi$
$12$	−1.10774	+	0.862590i	−0.319778	+	0.249008i
$13$	−2.64385			−0.733273			−0.366636	−	0.930364i	$-0.619491\pi$
$13$	−2.64385			−0.733273			−0.366636	+	0.930364i	$0.619491\pi$
$14$	1.50745	+	0.736738i	0.402884	+	0.196902i
$15$	−1.36484	−	0.775339i	−0.352401	−	0.200192i
$16$	−0.980197	+	3.87804i	−0.245049	+	0.969511i
$17$			4.62546i			1.12184i	0.827870	+	0.560919i	$0.189552\pi$
$17$			4.62546i			1.12184i	−0.827870	+	0.560919i	$0.810448\pi$
$18$	−3.18563	−	1.55692i	−0.750860	−	0.366968i
$19$	−2.08114	−	3.82999i	−0.477447	−	0.878660i
$19$	−2.08114	−	3.82999i	−0.477447	−	0.878660i
$20$	−4.42521	+	0.646167i	−0.989507	+	0.144487i
$21$		−	0.832855i		−	0.181744i
$22$	1.06815	−	2.18555i	0.227730	−	0.465962i
$23$	−6.62976			−1.38240			−0.691200	−	0.722664i	$-0.742918\pi$
$23$	−6.62976			−1.38240			−0.691200	+	0.722664i	$0.742918\pi$
$24$	1.94313	−	0.408116i	0.396640	−	0.0833063i
$25$	−2.56021	−	4.29480i	−0.512042	−	0.858960i
$26$	3.35924	+	1.64177i	0.658802	+	0.321977i
$27$			3.86600i			0.744012i
$28$	−1.45785	−	1.87218i	−0.275508	−	0.353809i
$29$			7.53366i			1.39897i	0.714649	+	0.699483i	$0.246586\pi$
$29$			7.53366i			1.39897i	−0.714649	+	0.699483i	$0.753414\pi$
$30$	1.25268	+	1.83267i	0.228708	+	0.334598i
$31$	−10.9809			−1.97224			−0.986118	−	0.166044i	$-0.946901\pi$
$31$	−10.9809			−1.97224			−0.986118	+	0.166044i	$0.946901\pi$
$32$	3.65359	−	4.31871i	0.645870	−	0.763447i
$33$	−1.20750			−0.210199
$34$	2.87229	−	5.87705i	0.492594	−	1.00791i
$35$	1.31039	−	2.30670i	0.221496	−	0.389904i
$36$	3.08081	+	3.95639i	0.513469	+	0.659399i
$37$	8.43930			1.38741			0.693706	−	0.720258i	$-0.255977\pi$
$37$	8.43930			1.38741			0.693706	+	0.720258i	$0.255977\pi$
$38$	0.265946	+	6.15867i	0.0431422	+	0.999069i
$39$		−	1.85596i		−	0.297191i
$40$	6.02386	+	1.92693i	0.952456	+	0.304675i
$41$			7.40097i			1.15584i	0.816095	+	0.577918i	$0.196135\pi$
$41$			7.40097i			1.15584i	−0.816095	+	0.577918i	$0.803865\pi$
$42$	−0.517182	+	1.05821i	−0.0798029	+	0.163286i
$43$	9.29752			1.41786			0.708930	−	0.705279i	$-0.249178\pi$
$43$	9.29752			1.41786			0.708930	+	0.705279i	$0.249178\pi$
$44$	−2.71435	+	2.11364i	−0.409203	+	0.318644i
$45$	−2.76919	+	4.87464i	−0.412806	+	0.726669i
$46$	8.42368	+	4.11691i	1.24200	+	0.607005i
$47$	−4.10213			−0.598357			−0.299178	−	0.954197i	$-0.596713\pi$
$47$	−4.10213			−0.598357			−0.299178	+	0.954197i	$0.596713\pi$
$48$	−2.72234	−	0.688088i	−0.392936	−	0.0993169i
$49$	−5.59240			−0.798915
$50$	0.586003	+	7.04674i	0.0828734	+	0.996560i
$51$	−3.24702			−0.454674
$52$	−3.24871	−	4.17201i	−0.450516	−	0.578554i
$53$	−1.98886			−0.273190			−0.136595	−	0.990627i	$-0.543616\pi$
$53$	−1.98886			−0.273190			−0.136595	+	0.990627i	$0.543616\pi$
$54$	2.40069	−	4.91209i	0.326693	−	0.668451i
$55$	−3.34433	−	1.89985i	−0.450949	−	0.256175i
$56$	0.689751	+	3.28406i	0.0921719	+	0.438850i
$57$	2.68861	−	1.46094i	0.356115	−	0.193506i
$58$	4.67822	−	9.57217i	0.614280	−	1.25689i
$59$	−3.13673			−0.408367			−0.204183	−	0.978933i	$-0.565454\pi$
$59$	−3.13673			−0.408367			−0.204183	+	0.978933i	$0.565454\pi$
$60$	−0.453602	−	3.10645i	−0.0585598	−	0.401041i
$61$	3.75579			0.480880			0.240440	−	0.970664i	$-0.422708\pi$
$61$	3.75579			0.480880			0.240440	+	0.970664i	$0.422708\pi$
$62$	13.9522	+	6.81889i	1.77194	+	0.866000i
$63$	−2.97461			−0.374766
$64$	−7.32402	+	3.21851i	−0.915502	+	0.402313i
$65$	2.92011	−	5.14031i	0.362194	−	0.637577i
$66$	1.53424	+	0.749828i	0.188851	+	0.0922974i
$67$			9.50799i			1.16159i	0.814051	+	0.580793i	$0.197257\pi$
$67$			9.50799i			1.16159i	−0.814051	+	0.580793i	$0.802743\pi$
$68$	−7.29900	+	5.68367i	−0.885133	+	0.689247i
$69$		−	4.65402i		−	0.560278i
$70$	−3.09737	+	2.11714i	−0.370206	+	0.253047i
$71$	9.11343			1.08157			0.540783	−	0.841162i	$-0.318128\pi$
$71$	9.11343			1.08157			0.540783	+	0.841162i	$0.318128\pi$
$72$	−1.45762	−	6.94004i	−0.171782	−	0.817892i
$73$		−	6.47318i		−	0.757628i	−0.925473	−	0.378814i	$-0.876332\pi$
$73$		−	6.47318i		−	0.757628i	0.925473	−	0.378814i	$-0.123668\pi$
$74$	−10.7229	−	5.24059i	−1.24651	−	0.609207i
$75$	3.01490	−	1.79724i	0.348131	−	0.207527i
$76$	3.48647	−	7.99028i	0.399926	−	0.916547i
$77$		−	2.04078i		−	0.232569i
$78$	−1.15250	+	2.35815i	−0.130495	+	0.267008i
$79$	6.38375			0.718228			0.359114	−	0.933294i	$-0.383079\pi$
$79$	6.38375			0.718228			0.359114	+	0.933294i	$0.383079\pi$
$80$	−6.45726	−	6.18900i	−0.721944	−	0.691951i
$81$	4.80774			0.534194
$82$	4.59581	−	9.40357i	0.507523	−	1.03845i
$83$	10.7908			1.18444			0.592221	−	0.805775i	$-0.298251\pi$
$83$	10.7908			1.18444			0.592221	+	0.805775i	$0.298251\pi$
$84$	1.31425	−	1.02340i	0.143396	−	0.111662i
$85$	−8.99304	−	5.10877i	−0.975433	−	0.554124i
$86$	−11.8133	−	5.77353i	−1.27386	−	0.622576i
$87$	−5.28855			−0.566992
$88$	4.76133	−	1.00002i	0.507560	−	0.106603i
$89$		−	14.1018i		−	1.49479i	−0.664383	−	0.747393i	$-0.731305\pi$
$89$		−	14.1018i		−	1.49479i	0.664383	−	0.747393i	$-0.268695\pi$
$90$	6.54552	−	4.47406i	0.689959	−	0.471607i
$91$	3.13673			0.328818
$92$	−8.14651	−	10.4618i	−0.849333	−	1.09072i
$93$		−	7.70851i		−	0.799335i
$94$	5.21211	+	2.54732i	0.537588	+	0.262736i
$95$	9.74506	+	0.183919i	0.999822	+	0.0188697i
$96$	3.03169	+	2.56478i	0.309420	+	0.261767i
$97$	3.39949			0.345166			0.172583	−	0.984995i	$-0.444789\pi$
$97$	3.39949			0.345166			0.172583	+	0.984995i	$0.444789\pi$
$98$	7.10563	+	3.47274i	0.717777	+	0.350800i
$99$			4.31269i			0.433442i
$100$	3.63128	−	9.31739i	0.363128	−	0.931739i
$101$	−2.13821			−0.212760			−0.106380	−	0.994326i	$-0.533926\pi$
$101$	−2.13821			−0.212760			−0.106380	+	0.994326i	$0.533926\pi$
$102$	4.12562	+	2.01632i	0.408497	+	0.199645i
$103$		−	15.7171i		−	1.54865i	−0.632786	−	0.774327i	$-0.718089\pi$
$103$		−	15.7171i		−	1.54865i	0.632786	−	0.774327i	$-0.281911\pi$
$104$	1.53706	+	7.31827i	0.150721	+	0.717616i
$105$	1.61928	+	0.919879i	0.158025	+	0.0897710i
$106$	2.52701	+	1.23503i	0.245445	+	0.119957i
$107$			13.2975i			1.28552i	0.766069	+	0.642758i	$0.222210\pi$
$107$			13.2975i			1.28552i	−0.766069	+	0.642758i	$0.777790\pi$
$108$	−6.10057	+	4.75047i	−0.587028	+	0.457114i
$109$			1.70706i			0.163507i	0.996653	+	0.0817535i	$0.0260520\pi$
$109$			1.70706i			0.163507i	−0.996653	+	0.0817535i	$0.973948\pi$
$110$	3.06950	+	4.49067i	0.292666	+	0.428168i
$111$			5.92430i			0.562309i
$112$	1.16293	−	4.60100i	0.109886	−	0.434753i
$113$	−9.19317			−0.864821			−0.432410	−	0.901677i	$-0.642337\pi$
$113$	−9.19317			−0.864821			−0.432410	+	0.901677i	$0.642337\pi$
$114$	−4.32332	+	0.186691i	−0.404916	+	0.0174852i
$115$	7.32249	−	12.8899i	0.682826	−	1.20199i
$116$	−11.8882	+	9.25722i	−1.10379	+	0.859511i
$117$	−6.62870			−0.612823
$118$	3.98548	+	1.94783i	0.366893	+	0.179312i
$119$		−	5.48775i		−	0.503061i
$120$	−1.35268	+	4.22869i	−0.123483	+	0.386024i
$121$	8.04121			0.731019
$122$	−4.77206	−	2.33225i	−0.432042	−	0.211152i
$123$	−5.19540			−0.468453
$124$	−13.4932	−	17.3280i	−1.21172	−	1.55610i
$125$	11.1779	−	0.234124i	0.999781	−	0.0209407i
$126$	3.77950	+	1.84716i	0.336705	+	0.164558i
$127$			12.3190i			1.09314i	0.837415	+	0.546568i	$0.184066\pi$
$127$			12.3190i			1.09314i	−0.837415	+	0.546568i	$0.815934\pi$
$128$	11.3044	+	0.458637i	0.999178	+	0.0405381i
$129$			6.52676i			0.574649i
$130$	−6.90225	+	4.71789i	−0.605367	+	0.413787i
$131$			14.7118i			1.28537i	0.766128	+	0.642687i	$0.222181\pi$
$131$			14.7118i			1.28537i	−0.766128	+	0.642687i	$0.777819\pi$
$132$	−1.48375	−	1.90544i	−0.129144	−	0.165848i
$133$	2.46912	+	4.54399i	0.214100	+	0.394014i
$134$	5.90422	−	12.0807i	0.510047	−	1.04362i
$135$	−7.51647	−	4.26996i	−0.646915	−	0.367499i
$136$	12.8034	−	2.68911i	1.09788	−	0.230589i
$137$			3.46578i			0.296101i	0.988980	+	0.148051i	$0.0472999\pi$
$137$			3.46578i			0.296101i	−0.988980	+	0.148051i	$0.952700\pi$
$138$	−2.89003	+	5.91333i	−0.246015	+	0.503376i
$139$		−	1.06058i		−	0.0899572i	−0.998988	−	0.0449786i	$-0.985678\pi$
$139$		−	1.06058i		−	0.0899572i	0.998988	−	0.0449786i	$-0.0143220\pi$
$140$	5.25017	−	0.766627i	0.443720	−	0.0647918i
$141$		−	2.87965i		−	0.242510i
$142$	−11.5794	−	5.65921i	−0.971722	−	0.474910i
$143$		−	4.54773i		−	0.380300i
$144$	−2.45756	+	9.72307i	−0.204797	+	0.810256i
$145$	−14.6473	−	8.32085i	−1.21639	−	0.691009i
$146$	−4.01968	+	8.22473i	−0.332671	+	0.680683i
$147$		−	3.92581i		−	0.323795i
$148$	10.3701	+	13.3173i	0.852413	+	1.09467i
$149$	−4.26937			−0.349760			−0.174880	−	0.984590i	$-0.555954\pi$
$149$	−4.26937			−0.349760			−0.174880	+	0.984590i	$0.555954\pi$
$150$	−4.94674	+	0.411368i	−0.403899	+	0.0335880i
$151$	4.16229			0.338722			0.169361	−	0.985554i	$-0.445830\pi$
$151$	4.16229			0.338722			0.169361	+	0.985554i	$0.445830\pi$
$152$	−9.39163	+	7.98732i	−0.761762	+	0.647857i
$153$			11.5970i			0.937562i
$154$	−1.26727	+	2.59299i	−0.102120	+	0.208949i
$155$	12.1283	−	21.3497i	0.974171	−	1.71485i
$156$	2.92871	−	2.28056i	0.234484	−	0.182591i
$157$			8.17675i			0.652576i	0.945270	+	0.326288i	$0.105798\pi$
$157$			8.17675i			0.652576i	−0.945270	+	0.326288i	$0.894202\pi$
$158$	−8.11110	−	3.96415i	−0.645285	−	0.315371i
$159$		−	1.39616i		−	0.110722i
$160$	4.36130	+	11.8735i	0.344791	+	0.938679i
$161$	7.86569			0.619903
$162$	−6.10865	−	2.98549i	−0.479941	−	0.234562i
$163$	5.59539			0.438265			0.219132	−	0.975695i	$-0.429677\pi$
$163$	5.59539			0.438265			0.219132	+	0.975695i	$0.429677\pi$
$164$	−11.6788	+	9.09416i	−0.911958	+	0.710135i
$165$	1.33367	−	2.34768i	0.103826	−	0.182767i
$166$	−13.7106	−	6.70081i	−1.06415	−	0.520084i
$167$		−	6.53146i		−	0.505419i	−0.967542	−	0.252710i	$-0.918678\pi$
$167$		−	6.53146i		−	0.505419i	0.967542	−	0.252710i	$-0.0813217\pi$
$168$	−2.30537	+	0.484198i	−0.177863	+	0.0373567i
$169$	−6.01004			−0.462311
$170$	8.25403	+	12.0756i	0.633055	+	0.926155i
$171$	−5.21787	−	9.60260i	−0.399020	−	0.734329i
$172$	11.4246	+	14.6715i	0.871119	+	1.11869i
$173$	14.8750			1.13093			0.565463	−	0.824774i	$-0.308698\pi$
$173$	14.8750			1.13093			0.565463	+	0.824774i	$0.308698\pi$
$174$	6.71956	+	3.28406i	0.509409	+	0.248964i
$175$	3.03749	+	5.09545i	0.229613	+	0.385180i
$176$	−6.67068	−	1.68605i	−0.502821	−	0.127091i
$177$		−	2.20195i		−	0.165508i
$178$	−8.75685	+	17.9175i	−0.656354	+	1.34298i
$179$	19.7404			1.47547			0.737735	−	0.675091i	$-0.235895\pi$
$179$	19.7404			1.47547			0.737735	+	0.675091i	$0.235895\pi$
$180$	−11.0949	+	1.62008i	−0.826967	+	0.120753i
$181$			15.9415i			1.18492i	0.805598	+	0.592462i	$0.201844\pi$
$181$			15.9415i			1.18492i	−0.805598	+	0.592462i	$0.798156\pi$
$182$	−3.98548	−	1.94783i	−0.295423	−	0.144383i
$183$			2.63653i			0.194898i
$184$	3.85435	+	18.3514i	0.284146	+	1.35288i
$185$	−9.32112	+	16.4081i	−0.685302	+	1.20635i
$186$	−4.78679	+	9.79432i	−0.350984	+	0.718155i
$187$	−7.95632			−0.581824
$188$	−5.04061	−	6.47318i	−0.367625	−	0.472105i
$189$		−	4.58671i		−	0.333634i
$190$	−12.2677	−	6.28512i	−0.889995	−	0.455971i
$191$			15.6844i			1.13489i	0.823413	+	0.567443i	$0.192067\pi$
$191$			15.6844i			1.13489i	−0.823413	+	0.567443i	$0.807933\pi$
$192$	−2.25936	−	5.14138i	−0.163055	−	0.371047i
$193$	3.56232			0.256421			0.128211	−	0.991747i	$-0.459077\pi$
$193$	3.56232			0.256421			0.128211	+	0.991747i	$0.459077\pi$
$194$	−4.31935	−	2.11100i	−0.310111	−	0.151561i
$195$	3.60844	+	2.04988i	0.258406	+	0.146795i
$196$	−6.87184	−	8.82484i	−0.490845	−	0.630345i
$197$		−	2.70209i		−	0.192516i	−0.995356	−	0.0962581i	$-0.969313\pi$
$197$		−	2.70209i		−	0.192516i	0.995356	−	0.0962581i	$-0.0306874\pi$
$198$	2.67807	−	5.47965i	0.190322	−	0.389422i
$199$			13.1477i			0.932018i	0.884780	+	0.466009i	$0.154309\pi$
$199$			13.1477i			0.932018i	−0.884780	+	0.466009i	$0.845691\pi$
$200$	−10.3997	+	9.58362i	−0.735372	+	0.677664i
$201$	−6.67450			−0.470783
$202$	2.71678	+	1.32777i	0.191152	+	0.0934219i
$203$		−	8.93811i		−	0.627332i
$204$	−3.98988	−	5.12381i	−0.279347	−	0.358739i
$205$	−14.3893	−	8.17429i	−1.00499	−	0.570917i
$206$	−9.75993	+	19.9700i	−0.680007	+	1.39137i
$207$	−16.6222			−1.15532
$208$	2.59150	−	10.2530i	0.179688	−	0.710916i
$209$	6.58802	−	3.57981i	0.455703	−	0.247620i
$210$	−1.48621	−	2.17432i	−0.102558	−	0.150042i
$211$	6.41162			0.441394			0.220697	−	0.975342i	$-0.429167\pi$
$211$	6.41162			0.441394			0.220697	+	0.975342i	$0.429167\pi$
$212$	−2.44387	−	3.13842i	−0.167846	−	0.215548i
$213$			6.39753i			0.438351i
$214$	8.25740	−	16.8956i	0.564465	−	1.15496i
$215$	−10.2690	+	18.0767i	−0.700341	+	1.23282i
$216$	10.7012	−	2.24758i	0.728126	−	0.152929i
$217$	13.0280			0.884401
$218$	1.06004	−	2.16897i	0.0717952	−	0.146901i
$219$	4.54410			0.307062
$220$	−1.11148	−	7.61186i	−0.0749361	−	0.513192i
$221$		−	12.2290i		−	0.822614i
$222$	3.67884	−	7.52733i	0.246908	−	0.505202i
$223$		−	0.157095i		−	0.0105198i	−0.999986	−	0.00525991i	$-0.998326\pi$
$223$		−	0.157095i		−	0.0105198i	0.999986	−	0.00525991i	$-0.00167429\pi$
$224$	−4.33470	+	5.12381i	−0.289624	+	0.342349i
$225$	−6.41899	−	10.7680i	−0.427932	−	0.717865i
$226$	11.6807	+	5.70873i	0.776990	+	0.379739i
$227$			0.135219i			0.00897481i	0.999990	+	0.00448740i	$0.00142839\pi$
$227$			0.135219i			0.00897481i	−0.999990	+	0.00448740i	$0.998572\pi$
$228$	5.60909	+	2.44747i	0.371471	+	0.162087i
$229$	14.9570			0.988387			0.494193	−	0.869352i	$-0.335463\pi$
$229$	14.9570			0.988387			0.494193	+	0.869352i	$0.335463\pi$
$230$	−17.3082	+	11.8306i	−1.14127	+	0.780090i
$231$	1.43261			0.0942586
$232$	20.8534	−	4.37985i	1.36909	−	0.287551i
$233$			10.4373i			0.683772i	0.939741	+	0.341886i	$0.111066\pi$
$233$			10.4373i			0.683772i	−0.939741	+	0.341886i	$0.888934\pi$
$234$	8.42233	+	4.11625i	0.550585	+	0.269088i
$235$	4.53075	−	7.97556i	0.295554	−	0.520268i
$236$	−3.85435	−	4.94977i	−0.250897	−	0.322202i
$237$			4.48132i			0.291093i
$238$	−3.40775	+	6.97266i	−0.220892	+	0.451970i
$239$			6.72707i			0.435138i	0.976045	+	0.217569i	$0.0698127\pi$
$239$			6.72707i			0.435138i	−0.976045	+	0.217569i	$0.930187\pi$
$240$	4.34461	−	4.53293i	0.280443	−	0.292599i
$241$		−	13.0619i		−	0.841390i	−0.907202	−	0.420695i	$-0.861786\pi$
$241$		−	13.0619i		−	0.841390i	0.907202	−	0.420695i	$-0.138214\pi$
$242$	−10.2170	−	4.99339i	−0.656777	−	0.320987i
$243$			14.9730i			0.960518i
$244$	4.61505	+	5.92666i	0.295448	+	0.379416i
$245$	6.17675	−	10.8730i	0.394618	−	0.694652i
$246$	6.60120	+	3.22621i	0.420877	+	0.205696i
$247$	5.50224	+	10.1259i	0.350099	+	0.644298i
$248$	6.38400	+	30.3956i	0.405385	+	1.93012i
$249$			7.57502i			0.480047i
$250$	−14.3479	−	6.64371i	−0.907438	−	0.420185i
$251$		−	16.5588i		−	1.04518i	−0.852584	−	0.522591i	$-0.824966\pi$
$251$		−	16.5588i		−	1.04518i	0.852584	−	0.522591i	$-0.175034\pi$
$252$	−3.65514	−	4.69395i	−0.230252	−	0.295691i
$253$		−	11.4039i		−	0.716959i
$254$	7.64980	−	15.6524i	0.479991	−	0.982117i
$255$	3.58630	−	6.31302i	0.224583	−	0.395337i
$256$	−14.0784	−	7.60249i	−0.879902	−	0.475156i
$257$	−3.05273			−0.190424			−0.0952119	−	0.995457i	$-0.530353\pi$
$257$	−3.05273			−0.190424			−0.0952119	+	0.995457i	$0.530353\pi$
$258$	4.05295	−	8.29281i	0.252326	−	0.516288i
$259$	−10.0126			−0.622151
$260$	11.6996	−	1.70837i	0.725578	−	0.105949i
$261$			18.8885i			1.16917i
$262$	9.13565	−	18.6926i	0.564402	−	1.15483i
$263$	−8.31015			−0.512426			−0.256213	−	0.966620i	$-0.582475\pi$
$263$	−8.31015			−0.512426			−0.256213	+	0.966620i	$0.582475\pi$
$264$	0.702006	+	3.34240i	0.0432055	+	0.205711i
$265$	2.19667	−	3.86683i	0.134940	−	0.237538i
$266$	−0.315524	−	7.30679i	−0.0193460	−	0.448008i
$267$	9.89929			0.605827
$268$	−15.0036	+	11.6832i	−0.916494	+	0.713667i
$269$		−	2.87965i		−	0.175575i	−0.996139	−	0.0877876i	$-0.972020\pi$
$269$		−	2.87965i		−	0.175575i	0.996139	−	0.0877876i	$-0.0279797\pi$
$270$	6.89879	+	10.0929i	0.419847	+	0.614234i
$271$		−	9.36177i		−	0.568687i	−0.958722	−	0.284343i	$-0.908224\pi$
$271$		−	9.36177i		−	0.568687i	0.958722	−	0.284343i	$-0.0917756\pi$
$272$	−17.9377	−	4.53386i	−1.08763	−	0.274906i
$273$			2.20195i			0.133268i
$274$	2.15216	−	4.40357i	0.130017	−	0.266029i
$275$	7.38755	−	4.40385i	0.445486	−	0.265562i
$276$	7.34406	−	5.71876i	0.442060	−	0.344229i
$277$			3.82001i			0.229522i	0.993393	+	0.114761i	$0.0366102\pi$
$277$			3.82001i			0.229522i	−0.993393	+	0.114761i	$0.963390\pi$
$278$	−0.658593	+	1.34756i	−0.0394998	+	0.0808212i
$279$	−27.5316			−1.64827
$280$	−7.14685	−	2.28615i	−0.427106	−	0.136624i
$281$		−	26.2895i		−	1.56830i	−0.620573	−	0.784149i	$-0.713100\pi$
$281$		−	26.2895i		−	1.56830i	0.620573	−	0.784149i	$-0.286900\pi$
$282$	−1.78819	+	3.65884i	−0.106485	+	0.217881i
$283$	−15.1066			−0.897995			−0.448997	−	0.893533i	$-0.648219\pi$
$283$	−15.1066			−0.897995			−0.448997	+	0.893533i	$0.648219\pi$
$284$	11.1984	+	14.3810i	0.664503	+	0.853357i
$285$	−0.129109	+	6.84092i	−0.00764775	+	0.405221i
$286$	−2.82403	+	5.77828i	−0.166988	+	0.341677i
$287$		−	8.78067i		−	0.518307i
$288$	9.16033	−	10.8279i	0.539777	−	0.638041i
$289$	−4.39487			−0.258522
$290$	13.4437	+	19.6680i	0.789438	+	1.15494i
$291$			2.38641i			0.139894i
$292$	10.2147	−	7.95411i	0.597770	−	0.465479i
$293$	−16.8794			−0.986105			−0.493052	−	0.870000i	$-0.664119\pi$
$293$	−16.8794			−0.986105			−0.493052	+	0.870000i	$0.664119\pi$
$294$	−2.43783	+	4.98808i	−0.142177	+	0.290910i
$295$	3.46448	−	6.09858i	0.201710	−	0.355073i
$296$	−4.90637	−	23.3603i	−0.285177	−	1.35779i
$297$	−6.64997			−0.385870
$298$	5.42460	+	2.65117i	0.314239	+	0.153578i
$299$	17.5281			1.01368
$300$	6.54071	+	2.54912i	0.377628	+	0.147174i
$301$	−11.0308			−0.635804
$302$	−5.28855	−	2.58468i	−0.304322	−	0.148731i
$303$		−	1.50100i		−	0.0862302i
$304$	16.8928	−	4.31662i	0.968869	−	0.247575i
$305$	−4.14823	+	7.30220i	−0.237527	+	0.418123i
$306$	7.20145	−	14.7350i	0.411679	−	0.842344i
$307$			27.0057i			1.54129i	0.637262	+	0.770647i	$0.280067\pi$
$307$			27.0057i			1.54129i	−0.637262	+	0.770647i	$0.719933\pi$
$308$	3.22036	−	2.50767i	0.183497	−	0.142888i
$309$	11.0332			0.627659
$310$	−28.6677	+	19.5953i	−1.62822	+	1.11294i
$311$		−	9.15647i		−	0.519216i	−0.965714	−	0.259608i	$-0.916407\pi$
$311$		−	9.15647i		−	0.519216i	0.965714	−	0.259608i	$-0.0835934\pi$
$312$	−5.13735	+	1.07900i	−0.290845	+	0.0610863i
$313$		−	10.2932i		−	0.581805i	−0.956753	−	0.290903i	$-0.906044\pi$
$313$		−	10.2932i		−	0.581805i	0.956753	−	0.290903i	$-0.0939555\pi$
$314$	5.07756	−	10.3893i	0.286543	−	0.586301i
$315$	3.28542	−	5.78339i	0.185113	−	0.325857i
$316$	7.84422	+	10.0736i	0.441272	+	0.566683i
$317$	−19.0000			−1.06714			−0.533572	−	0.845754i	$-0.679151\pi$
$317$	−19.0000			−1.06714			−0.533572	+	0.845754i	$0.679151\pi$
$318$	−0.866977	+	1.77394i	−0.0486177	+	0.0994774i
$319$	−12.9588			−0.725551
$320$	1.83171	−	17.7945i	0.102396	−	0.994744i
$321$	−9.33469			−0.521012
$322$	−9.99404	−	4.88439i	−0.556946	−	0.272197i
$323$	17.7155	−	9.62625i	0.985715	−	0.535619i
$324$	5.90766	+	7.58664i	0.328203	+	0.421480i
$325$	6.76882	+	11.3548i	0.375466	+	0.629852i
$326$	−7.10943	−	3.47460i	−0.393755	−	0.192440i
$327$	−1.19834			−0.0662683
$328$	20.4861	−	4.30271i	1.13116	−	0.237577i
$329$	4.86685			0.268318
$330$	−3.15240	+	2.15476i	−0.173534	+	0.118616i
$331$	−0.915268			−0.0503077			−0.0251538	−	0.999684i	$-0.508008\pi$
$331$	−0.915268			−0.0503077			−0.0251538	+	0.999684i	$0.508008\pi$
$332$	13.2595	+	17.0279i	0.727710	+	0.934528i
$333$	21.1591			1.15951
$334$	−4.05587	+	8.29878i	−0.221927	+	0.454089i
$335$	−18.4859	−	10.5015i	−1.00999	−	0.573756i
$336$	3.22985	+	0.816362i	0.176203	+	0.0445362i
$337$	35.9416			1.95786			0.978932	−	0.204188i	$-0.0654554\pi$
$337$	35.9416			1.95786			0.978932	+	0.204188i	$0.0654554\pi$
$338$	7.63628	+	3.73209i	0.415359	+	0.202999i
$339$		−	6.45351i		−	0.350506i
$340$	−2.98882	−	20.4686i	−0.162091	−	1.11007i
$341$		−	18.8885i		−	1.02287i
$342$	0.666783	+	15.4411i	0.0360555	+	0.834959i
$343$	14.9399			0.806679
$344$	−5.40531	−	25.7359i	−0.291435	−	1.38758i
$345$	9.04857	+	5.14031i	0.487158	+	0.276745i
$346$	−18.9000	−	9.23700i	−1.01607	−	0.496584i
$347$	0.105896			0.00568479			0.00284239	−	0.999996i	$-0.499095\pi$
$347$	0.105896			0.00568479			0.00284239	+	0.999996i	$0.499095\pi$
$348$	−6.49847	−	8.34535i	−0.348354	−	0.447358i
$349$	−16.2260			−0.868558			−0.434279	−	0.900778i	$-0.642997\pi$
$349$	−16.2260			−0.868558			−0.434279	+	0.900778i	$0.642997\pi$
$350$	−0.695247	−	8.36041i	−0.0371625	−	0.446883i
$351$		−	10.2211i		−	0.545564i
$352$	7.42868	+	6.28460i	0.395950	+	0.334970i
$353$		−	13.2151i		−	0.703367i	−0.936119	−	0.351683i	$-0.885609\pi$
$353$		−	13.2151i		−	0.703367i	0.936119	−	0.351683i	$-0.114391\pi$
$354$	−1.36735	+	2.79776i	−0.0726740	+	0.148699i
$355$	−10.0657	+	17.7188i	−0.534231	+	0.940415i
$356$	22.2527	−	17.3280i	1.17939	−	0.918381i
$357$	3.85234			0.203887
$358$	−25.0819	−	12.2583i	−1.32562	−	0.647872i
$359$			5.71624i			0.301692i	0.988557	+	0.150846i	$0.0481997\pi$
$359$			5.71624i			0.301692i	−0.988557	+	0.150846i	$0.951800\pi$
$360$	15.1031	+	4.83123i	0.796003	+	0.254628i
$361$	−10.3377	+	15.9415i	−0.544088	+	0.839028i
$362$	9.89929	−	20.2551i	0.520295	−	1.06458i
$363$			5.64484i			0.296277i
$364$	3.85435	+	4.94977i	0.202023	+	0.259438i
$365$	12.5855	+	7.14955i	0.658753	+	0.374225i
$366$	1.63722	−	3.34994i	0.0855787	−	0.175104i
$367$	−30.6312			−1.59893			−0.799467	−	0.600710i	$-0.794885\pi$
$367$	−30.6312			−1.59893			−0.799467	+	0.600710i	$0.794885\pi$
$368$	6.49847	−	25.7105i	0.338756	−	1.34025i
$369$			18.5558i			0.965976i
$370$	22.0323	−	15.0597i	1.14541	−	0.782919i
$371$	2.35962			0.122506
$372$	12.1641	−	9.47206i	0.630677	−	0.491103i
$373$	3.34176			0.173030			0.0865150	−	0.996251i	$-0.472427\pi$
$373$	3.34176			0.173030			0.0865150	+	0.996251i	$0.472427\pi$
$374$	10.1092	+	4.94067i	0.522734	+	0.255476i
$375$	0.164352	+	7.84675i	0.00848712	+	0.405205i
$376$	2.38486	+	11.3548i	0.122990	+	0.585580i
$377$		−	19.9179i		−	1.02582i
$378$	−2.84823	+	5.82781i	−0.146497	+	0.299750i
$379$	−18.4712			−0.948804			−0.474402	−	0.880308i	$-0.657336\pi$
$379$	−18.4712			−0.948804			−0.474402	+	0.880308i	$0.657336\pi$
$380$	11.6843	+	15.6037i	0.599393	+	0.800455i
$381$	−8.64781			−0.443041
$382$	9.73964	−	19.9284i	0.498323	−	1.01963i
$383$			5.94860i			0.303959i	0.988384	+	0.151980i	$0.0485648\pi$
$383$			5.94860i			0.303959i	−0.988384	+	0.151980i	$0.951435\pi$
$384$	−0.321958	+	7.93557i	−0.0164298	+	0.404960i
$385$	3.96779	+	2.25402i	0.202217	+	0.114876i
$386$	−4.52623	−	2.21211i	−0.230379	−	0.112593i
$387$	23.3109			1.18496
$388$	4.17723	+	5.36442i	0.212067	+	0.272337i
$389$	−31.9734			−1.62111			−0.810557	−	0.585660i	$-0.800835\pi$
$389$	−31.9734			−1.62111			−0.810557	+	0.585660i	$0.800835\pi$
$390$	−3.31191	−	4.84530i	−0.167705	−	0.245351i
$391$		−	30.6657i		−	1.55083i
$392$	3.25126	+	15.4800i	0.164213	+	0.781856i
$393$	−10.3275			−0.520954
$394$	−1.67793	+	3.43325i	−0.0845330	+	0.172964i
$395$	−7.05078	+	12.4116i	−0.354763	+	0.624495i
$396$	−6.80545	+	5.29935i	−0.341986	+	0.266302i
$397$		−	17.6776i		−	0.887212i	−0.896222	−	0.443606i	$-0.853699\pi$
$397$		−	17.6776i		−	0.887212i	0.896222	−	0.443606i	$-0.146301\pi$
$398$	8.16441	−	16.7053i	0.409245	−	0.837363i
$399$	−3.18983	+	1.73329i	−0.159691	+	0.0867732i
$400$	19.1649	−	5.71885i	0.958247	−	0.285942i
$401$			26.2151i			1.30912i	0.756010	+	0.654560i	$0.227146\pi$
$401$			26.2151i			1.30912i	−0.756010	+	0.654560i	$0.772854\pi$
$402$	8.48053	+	4.14470i	0.422971	+	0.206719i
$403$	29.0320			1.44619
$404$	−2.62739	−	3.37410i	−0.130718	−	0.167868i
$405$	−5.31010	+	9.34745i	−0.263861	+	0.464479i
$406$	−5.55034	+	11.3566i	−0.275459	+	0.563620i
$407$			14.5166i			0.719560i
$408$	1.88772	+	8.98786i	0.0934562	+	0.444966i
$409$			28.4449i			1.40651i	0.710938	+	0.703255i	$0.248271\pi$
$409$			28.4449i			1.40651i	−0.710938	+	0.703255i	$0.751729\pi$
$410$	13.2069	+	19.3215i	0.652240	+	0.954223i
$411$	−2.43294			−0.120008
$412$	24.8017	−	19.3129i	1.22189	−	0.951478i
$413$	3.72148			0.183122
$414$	21.1199	+	10.3220i	1.03799	+	0.507297i
$415$	−11.9183	+	20.9800i	−0.585047	+	1.02987i
$416$	−9.65956	+	11.4180i	−0.473599	+	0.559815i
$417$	0.744515			0.0364591
$418$	−10.5936	+	0.457458i	−0.518151	+	0.0223750i
$419$		−	27.0191i		−	1.31997i	−0.751279	−	0.659985i	$-0.770563\pi$
$419$		−	27.0191i		−	1.31997i	0.751279	−	0.659985i	$-0.229437\pi$
$420$	0.538164	+	3.68556i	0.0262597	+	0.179837i
$421$		−	13.9691i		−	0.680811i	−0.940279	−	0.340406i	$-0.889436\pi$
$421$		−	13.9691i		−	0.680811i	0.940279	−	0.340406i	$-0.110564\pi$
$422$	−8.14651	−	3.98145i	−0.396566	−	0.193814i
$423$	−10.2849			−0.500069
$424$	1.15626	+	5.50522i	0.0561531	+	0.267357i
$425$	19.8654	−	11.8421i	0.963615	−	0.574428i
$426$	3.97270	−	8.12861i	0.192478	−	0.393833i
$427$	−4.45596			−0.215639
$428$	−20.9835	+	16.3397i	−1.01428	+	0.789809i
$429$	3.19246			0.154133
$430$	24.2728	−	16.5912i	1.17054	−	0.800100i
$431$	−1.73199			−0.0834270			−0.0417135	−	0.999130i	$-0.513282\pi$
$431$	−1.73199			−0.0834270			−0.0417135	+	0.999130i	$0.513282\pi$
$432$	−14.9925	−	3.78944i	−0.721328	−	0.182320i
$433$	−11.6977			−0.562155			−0.281078	−	0.959685i	$-0.590692\pi$
$433$	−11.6977			−0.562155			−0.281078	+	0.959685i	$0.590692\pi$
$434$	−16.5533	−	8.09009i	−0.794582	−	0.388337i
$435$	5.84114	−	10.2823i	0.280061	−	0.492996i
$436$	−2.69375	+	2.09760i	−0.129007	+	0.100457i
$437$	13.7975	+	25.3919i	0.660023	+	1.21466i
$438$	−5.77367	−	2.82177i	−0.275877	−	0.134829i
$439$	28.7806			1.37362			0.686810	−	0.726837i	$-0.259010\pi$
$439$	28.7806			1.37362			0.686810	+	0.726837i	$0.259010\pi$
$440$	−3.31454	+	10.3617i	−0.158015	+	0.493976i
$441$	−14.0213			−0.667683
$442$	−7.59392	+	15.5380i	−0.361206	+	0.739069i
$443$	−30.7613			−1.46151			−0.730756	−	0.682638i	$-0.760833\pi$
$443$	−30.7613			−1.46151			−0.730756	+	0.682638i	$0.760833\pi$
$444$	−9.34857	+	7.27966i	−0.443663	+	0.345477i
$445$	27.4174	+	15.5753i	1.29971	+	0.738338i
$446$	−0.0975518	+	0.199602i	−0.00461921	+	0.00945144i
$447$		−	2.99705i		−	0.141756i
$448$	8.68937	−	3.81851i	0.410534	−	0.180408i
$449$		−	27.7447i		−	1.30936i	−0.755908	−	0.654678i	$-0.772804\pi$
$449$		−	27.7447i		−	1.30936i	0.755908	−	0.654678i	$-0.227196\pi$
$450$	1.46923	+	17.6677i	0.0692604	+	0.832862i
$451$	−12.7305			−0.599456
$452$	−11.2964	−	14.5069i	−0.531338	−	0.682346i
$453$			2.92188i			0.137282i
$454$	0.0839677	−	0.171808i	0.00394080	−	0.00806333i
$455$	−3.46448	+	6.09858i	−0.162417	+	0.285906i
$456$	−5.60701	−	6.59282i	−0.262572	−	0.308737i
$457$			32.5891i			1.52445i	0.647311	+	0.762226i	$0.275894\pi$
$457$			32.5891i			1.52445i	−0.647311	+	0.762226i	$0.724106\pi$
$458$	−19.0042	−	9.28793i	−0.888007	−	0.433996i
$459$	−17.8820			−0.834662
$460$	29.3380	−	4.28393i	1.36789	−	0.199739i
$461$	8.64842			0.402797			0.201398	−	0.979509i	$-0.435451\pi$
$461$	8.64842			0.402797			0.201398	+	0.979509i	$0.435451\pi$
$462$	−1.82025	−	0.889613i	−0.0846857	−	0.0413885i
$463$	−18.6070			−0.864739			−0.432370	−	0.901697i	$-0.642322\pi$
$463$	−18.6070			−0.864739			−0.432370	+	0.901697i	$0.642322\pi$
$464$	−29.2159	−	7.38447i	−1.35631	−	0.342816i
$465$	14.9873	+	8.51396i	0.695017	+	0.394825i
$466$	6.48131	−	13.2615i	0.300241	−	0.614328i
$467$	16.9119			0.782591			0.391295	−	0.920265i	$-0.372027\pi$
$467$	16.9119			0.782591			0.391295	+	0.920265i	$0.372027\pi$
$468$	−8.14521	−	10.4601i	−0.376513	−	0.483519i
$469$		−	11.2805i		−	0.520884i
$470$	−10.7093	+	7.32015i	−0.493985	+	0.337653i
$471$	−5.73999			−0.264485
$472$	1.82360	+	8.68256i	0.0839380	+	0.399647i
$473$			15.9928i			0.735350i
$474$	2.78279	−	5.69391i	0.127818	−	0.261530i
$475$	−11.1209	+	18.7437i	−0.510262	+	0.860019i
$476$	8.65969	−	6.74324i	0.396916	−	0.309076i
$477$	−4.98648			−0.228315
$478$	4.17734	−	8.54733i	0.191067	−	0.390946i
$479$			31.4108i			1.43520i	0.696458	+	0.717598i	$0.254758\pi$
$479$			31.4108i			1.43520i	−0.696458	+	0.717598i	$0.745242\pi$
$480$	−8.33504	+	3.06158i	−0.380441	+	0.139742i
$481$	−22.3123			−1.01735
$482$	−8.11110	+	16.5963i	−0.369451	+	0.755939i
$483$			5.52163i			0.251243i
$484$	9.88088	+	12.6891i	0.449131	+	0.576775i
$485$	−3.75470	+	6.60946i	−0.170492	+	0.300120i
$486$	9.29785	−	19.0245i	0.421759	−	0.862968i
$487$			19.4993i			0.883599i	0.897114	+	0.441800i	$0.145660\pi$
$487$			19.4993i			0.883599i	−0.897114	+	0.441800i	$0.854340\pi$
$488$	−2.18351	−	10.3962i	−0.0988428	−	0.470612i
$489$			3.92790i			0.177626i
$490$	−14.6000	+	9.97951i	−0.659559	+	0.450828i
$491$			10.3678i			0.467893i	0.972249	+	0.233947i	$0.0751641\pi$
$491$			10.3678i			0.467893i	−0.972249	+	0.233947i	$0.924836\pi$
$492$	−6.38400	−	8.19836i	−0.287813	−	0.369611i
$493$	−34.8467			−1.56941
$494$	−0.703122	−	16.2826i	−0.0316350	−	0.732590i
$495$	−8.38494	−	4.76332i	−0.376875	−	0.214095i
$496$	10.7635	−	42.5846i	0.483295	−	1.91210i
$497$	−10.8124			−0.485001
$498$	4.70389	−	9.62471i	0.210787	−	0.431294i
$499$		−	25.0012i		−	1.11921i	−0.828760	−	0.559604i	$-0.810953\pi$
$499$		−	25.0012i		−	1.11921i	0.828760	−	0.559604i	$-0.189047\pi$
$500$	14.1046	+	17.3511i	0.630778	+	0.775964i
$501$	4.58501			0.204843
$502$	−10.2826	+	21.0394i	−0.458934	+	0.939033i
$503$	17.0206			0.758909			0.379454	−	0.925210i	$-0.376112\pi$
$503$	17.0206			0.758909			0.379454	+	0.925210i	$0.376112\pi$
$504$	1.72935	+	8.23382i	0.0770315	+	0.366764i
$505$	2.36163	−	4.15721i	0.105091	−	0.184993i
$506$	−7.08156	+	14.4897i	−0.314814	+	0.644145i
$507$		−	4.21899i		−	0.187372i
$508$	−19.4395	+	15.1374i	−0.862487	+	0.671612i
$509$		−	33.2834i		−	1.47526i	−0.675205	−	0.737630i	$-0.735945\pi$
$509$		−	33.2834i		−	1.47526i	0.675205	−	0.737630i	$-0.264055\pi$
$510$	−8.47693	+	5.79424i	−0.375365	+	0.256573i
$511$			7.67992i			0.339740i
$512$	13.1669	+	18.4020i	0.581901	+	0.813260i
$513$	14.8068	−	8.04571i	0.653734	−	0.355227i
$514$	3.87875	+	1.89567i	0.171084	+	0.0836142i
$515$	30.5580	+	17.3594i	1.34655	+	0.764946i
$516$	−10.2993	+	8.01996i	−0.453400	+	0.353059i
$517$		−	7.05613i		−	0.310328i
$518$	12.7218	+	6.21756i	0.558966	+	0.273184i
$519$			10.4421i			0.458357i
$520$	−15.9262	−	5.09452i	−0.698410	−	0.223410i
$521$			24.6478i			1.07984i	0.841717	+	0.539920i	$0.181545\pi$
$521$			24.6478i			1.07984i	−0.841717	+	0.539920i	$0.818455\pi$
$522$	11.7293	−	23.9995i	0.513376	−	1.05043i
$523$		−	19.1156i		−	0.835866i	−0.908478	−	0.417933i	$-0.862755\pi$
$523$		−	19.1156i		−	0.835866i	0.908478	−	0.417933i	$-0.137245\pi$
$524$	−23.2153	+	18.0776i	−1.01416	+	0.789722i
$525$	−3.57695	+	2.13228i	−0.156111	+	0.0930605i
$526$	10.5588	+	5.16039i	0.460384	+	0.225004i
$527$		−	50.7919i		−	2.21253i
$528$	1.18359	−	4.68274i	0.0515091	−	0.203790i
$529$	20.9537			0.911029
$530$	−5.19226	+	3.54907i	−0.225538	+	0.154162i
$531$	−7.86443			−0.341287
$532$	−4.13643	+	9.47984i	−0.179337	+	0.411003i
$533$		−	19.5671i		−	0.847544i
$534$	−12.5779	−	6.14721i	−0.544299	−	0.266016i
$535$	−25.8536	−	14.6869i	−1.11775	−	0.634971i
$536$	26.3184	−	5.52767i	1.13678	−	0.238759i
$537$			13.8576i			0.597998i
$538$	−1.78819	+	3.65884i	−0.0770943	+	0.157744i
$539$		−	9.61957i		−	0.414344i
$540$	−2.49808	−	17.1079i	−0.107500	−	0.736205i
$541$	13.6698			0.587713			0.293856	−	0.955850i	$-0.405061\pi$
$541$	13.6698			0.587713			0.293856	+	0.955850i	$0.405061\pi$
$542$	−5.81342	+	11.8949i	−0.249708	+	0.510931i
$543$	−11.1908			−0.480242
$544$	19.9760	+	16.8995i	0.856465	+	0.724562i
$545$	−3.31895	−	1.88543i	−0.142168	−	0.0807630i
$546$	1.36735	−	2.79776i	0.0585173	−	0.119733i
$547$		−	25.5816i		−	1.09379i	−0.837200	−	0.546896i	$-0.815809\pi$
$547$		−	25.5816i		−	1.09379i	0.837200	−	0.546896i	$-0.184191\pi$
$548$	−5.46901	+	4.25868i	−0.233625	+	0.181922i
$549$	9.41657			0.401889
$550$	−12.1212	+	1.00799i	−0.516850	+	0.0429810i
$551$	28.8539	−	15.6786i	1.22922	−	0.667933i
$552$	−12.8825	+	2.70571i	−0.548314	+	0.115163i
$553$	−7.57382			−0.322072
$554$	2.37213	−	4.85365i	0.100782	−	0.206212i
$555$	−11.5183	−	6.54332i	−0.488925	−	0.277748i
$556$	1.67360	−	1.30322i	0.0709764	−	0.0552688i
$557$		−	36.7162i		−	1.55571i	−0.628442	−	0.777857i	$-0.716307\pi$
$557$		−	36.7162i		−	1.55571i	0.628442	−	0.777857i	$-0.283693\pi$
$558$	34.9812	+	17.0964i	1.48087	+	0.723749i
$559$	−24.5813			−1.03968
$560$	7.66104	+	7.34277i	0.323738	+	0.310289i
$561$		−	5.58525i		−	0.235809i
$562$	−16.3251	+	33.4030i	−0.688632	+	1.40902i
$563$		−	0.293515i		−	0.0123702i	−0.999981	−	0.00618509i	$-0.998031\pi$
$563$		−	0.293515i		−	0.0123702i	0.999981	−	0.00618509i	$-0.00196879\pi$
$564$	4.54410	−	3.53846i	0.191341	−	0.148996i
$565$	10.1538	−	17.8738i	0.427172	−	0.751957i
$566$	19.1943	+	9.38082i	0.806795	+	0.394305i
$567$	−5.70401			−0.239546
$568$	−5.29828	−	25.2263i	−0.222311	−	1.05847i
$569$		−	8.44922i		−	0.354210i	−0.984192	−	0.177105i	$-0.943327\pi$
$569$		−	8.44922i		−	0.354210i	0.984192	−	0.177105i	$-0.0566732\pi$
$570$	4.41209	−	8.61181i	0.184802	−	0.360709i
$571$			24.5184i			1.02606i	0.858370	+	0.513032i	$0.171478\pi$
$571$			24.5184i			1.02606i	−0.858370	+	0.513032i	$0.828522\pi$
$572$	7.17634	−	5.58816i	0.300058	−	0.233653i
$573$	−11.0103			−0.459962
$574$	−5.45258	+	11.1566i	−0.227586	+	0.465668i
$575$	16.9736	+	28.4735i	0.707846	+	1.18743i
$576$	−18.3629	+	8.06948i	−0.765119	+	0.336228i
$577$			17.9579i			0.747599i	0.927510	+	0.373799i	$0.121945\pi$
$577$			17.9579i			0.747599i	−0.927510	+	0.373799i	$0.878055\pi$
$578$	5.58406	+	2.72910i	0.232266	+	0.113516i
$579$			2.50071i			0.103926i
$580$	−4.86801	−	33.3380i	−0.202133	−	1.38429i
$581$	−12.8024			−0.531134
$582$	1.48190	−	3.03214i	0.0614267	−	0.125686i
$583$		−	3.42106i		−	0.141686i
$584$	−17.9180	+	3.76332i	−0.741451	+	0.155727i
$585$	7.32132	−	12.8878i	0.302699	−	0.532847i
$586$	21.4467	+	10.4817i	0.885956	+	0.432994i
$587$	−4.71144			−0.194462			−0.0972310	−	0.995262i	$-0.530999\pi$
$587$	−4.71144			−0.194462			−0.0972310	+	0.995262i	$0.530999\pi$
$588$	6.19494	−	4.82395i	0.255475	−	0.198936i
$589$	22.8529	+	42.0569i	0.941639	+	1.73293i
$590$	−8.18898	+	5.59741i	−0.337135	+	0.230442i
$591$	1.89684			0.0780256
$592$	−8.27218	+	32.7280i	−0.339984	+	1.34511i
$593$		−	7.62570i		−	0.313150i	−0.987666	−	0.156575i	$-0.949955\pi$
$593$		−	7.62570i		−	0.313150i	0.987666	−	0.156575i	$-0.0500453\pi$
$594$	8.44936	+	4.12946i	0.346681	+	0.169434i
$595$	10.6695	+	6.06115i	0.437409	+	0.248483i
$596$	−5.24612	−	6.73709i	−0.214889	−	0.275962i
$597$	−9.22956			−0.377741
$598$	−22.2710	−	10.8845i	−0.910727	−	0.445101i
$599$	−1.28533			−0.0525171			−0.0262585	−	0.999655i	$-0.508359\pi$
$599$	−1.28533			−0.0525171			−0.0262585	+	0.999655i	$0.508359\pi$
$600$	−6.72759	−	7.30049i	−0.274653	−	0.298041i
$601$		−	35.4629i		−	1.44656i	−0.690554	−	0.723280i	$-0.742633\pi$
$601$		−	35.4629i		−	1.44656i	0.690554	−	0.723280i	$-0.257367\pi$
$602$	14.0156	+	6.84984i	0.571232	+	0.279179i
$603$			23.8385i			0.970780i
$604$	5.11454	+	6.56811i	0.208108	+	0.267253i
$605$	−8.88142	+	15.6341i	−0.361081	+	0.635617i
$606$	−0.932083	+	1.90715i	−0.0378633	+	0.0774727i
$607$		−	15.3707i		−	0.623877i	−0.950102	−	0.311939i	$-0.899022\pi$
$607$		−	15.3707i		−	0.623877i	0.950102	−	0.311939i	$-0.100978\pi$
$608$	−24.1443	−	5.00536i	−0.979180	−	0.202994i
$609$	6.27445			0.254254
$610$	9.80517	−	6.70213i	0.397000	−	0.271361i
$611$	10.8454			0.438759
$612$	−18.3001	+	14.2502i	−0.739739	+	0.576029i
$613$			2.12630i			0.0858804i	0.999078	+	0.0429402i	$0.0136725\pi$
$613$			2.12630i			0.0858804i	−0.999078	+	0.0429402i	$0.986328\pi$
$614$	16.7698	−	34.3130i	0.676775	−	1.38476i
$615$	5.73826	−	10.1011i	0.231389	−	0.407318i
$616$	−5.64895	+	1.18645i	−0.227603	+	0.0478035i
$617$		−	16.3926i		−	0.659940i	−0.943991	−	0.329970i	$-0.892961\pi$
$617$		−	16.3926i		−	0.659940i	0.943991	−	0.329970i	$-0.107039\pi$
$618$	−14.0187	−	6.85137i	−0.563914	−	0.275602i
$619$			43.4349i			1.74580i	0.487902	+	0.872898i	$0.337762\pi$
$619$			43.4349i			1.74580i	−0.487902	+	0.872898i	$0.662238\pi$
$620$	48.5930	−	7.09553i	1.95154	−	0.284963i
$621$		−	25.6306i		−	1.02852i
$622$	−5.68594	+	11.6341i	−0.227985	+	0.466485i
$623$			16.7307i			0.670300i
$624$	7.19747	+	1.81920i	0.288130	+	0.0728264i
$625$	−11.8907	+	21.9912i	−0.475626	+	0.879647i
$626$	−6.39181	+	13.0784i	−0.255468	+	0.522717i
$627$	2.51299	+	4.62472i	0.100359	+	0.184694i
$628$	−12.9030	+	10.0474i	−0.514884	+	0.400936i
$629$			39.0357i			1.55645i
$630$	−7.76575	+	5.30813i	−0.309395	+	0.211481i
$631$		−	46.6693i		−	1.85788i	−0.370235	−	0.928938i	$-0.620723\pi$
$631$		−	46.6693i		−	1.85788i	0.370235	−	0.928938i	$-0.379277\pi$
$632$	−3.71132	−	17.6704i	−0.147629	−	0.702892i
$633$			4.50088i			0.178894i
$634$	24.1411	+	11.7985i	0.958766	+	0.468578i
$635$	−23.9512	−	13.6062i	−0.950476	−	0.539946i
$636$	2.20314	−	1.71557i	0.0873602	−	0.0680267i
$637$	14.7855			0.585822
$638$	16.4652	+	8.04707i	0.651865	+	0.318586i
$639$	22.8493			0.903904
$640$	−13.3773	+	21.4720i	−0.528784	+	0.848756i
$641$		−	3.84520i		−	0.151876i	−0.997113	−	0.0759381i	$-0.975805\pi$
$641$		−	3.84520i		−	0.151876i	0.997113	−	0.0759381i	$-0.0241952\pi$
$642$	11.8605	+	5.79661i	0.468098	+	0.228774i
$643$	−4.94936			−0.195184			−0.0975919	−	0.995227i	$-0.531114\pi$
$643$	−4.94936			−0.195184			−0.0975919	+	0.995227i	$0.531114\pi$
$644$	9.66521	+	12.4121i	0.380862	+	0.489105i
$645$	−12.6896	−	7.20873i	−0.499654	−	0.283844i
$646$	−28.4867	+	1.23012i	−1.12079	+	0.0483985i
$647$	5.93211			0.233215			0.116608	−	0.993178i	$-0.462798\pi$
$647$	5.93211			0.233215			0.116608	+	0.993178i	$0.462798\pi$
$648$	−2.79508	−	13.3080i	−0.109801	−	0.522787i
$649$		−	5.39553i		−	0.211793i
$650$	−1.54931	−	18.6306i	−0.0607688	−	0.730750i
$651$			9.14554i			0.358442i
$652$	6.87551	+	8.82955i	0.269266	+	0.345792i
$653$			24.4578i			0.957109i	0.878058	+	0.478555i	$0.158839\pi$
$653$			24.4578i			0.957109i	−0.878058	+	0.478555i	$0.841161\pi$
$654$	1.52259	+	0.744138i	0.0595381	+	0.0290981i
$655$	−28.6034	−	16.2490i	−1.11763	−	0.634901i
$656$	−28.7013	−	7.25441i	−1.12060	−	0.283237i
$657$		−	16.2296i		−	0.633178i
$658$	−6.18376	−	3.02219i	−0.241068	−	0.117817i
$659$	43.0449			1.67679			0.838395	−	0.545063i	$-0.183494\pi$
$659$	43.0449			1.67679			0.838395	+	0.545063i	$0.183494\pi$
$660$	5.34345	−	0.780248i	0.207993	−	0.0303711i
$661$			10.9394i			0.425494i	0.977107	+	0.212747i	$0.0682411\pi$
$661$			10.9394i			0.425494i	−0.977107	+	0.212747i	$0.931759\pi$
$662$	1.16293	+	0.568358i	0.0451985	+	0.0220899i
$663$	8.58465			0.333400
$664$	−6.27345	−	29.8693i	−0.243457	−	1.15915i
$665$	−11.5618	−	0.218205i	−0.448346	−	0.00846164i
$666$	−26.8845	−	13.1393i	−1.04175	−	0.509137i
$667$		−	49.9463i		−	1.93393i
$668$	10.3067	−	8.02572i	0.398777	−	0.310525i
$669$	0.110279			0.00426362
$670$	16.9668	+	24.8223i	0.655484	+	0.958969i
$671$			6.46040i			0.249401i
$672$	−3.59686	−	3.04291i	−0.138752	−	0.117383i
$673$	−27.0370			−1.04220			−0.521099	−	0.853496i	$-0.674478\pi$
$673$	−27.0370			−1.04220			−0.521099	+	0.853496i	$0.674478\pi$
$674$	−45.6669	−	22.3188i	−1.75902	−	0.859689i
$675$	16.6037	−	9.89777i	0.639077	−	0.380966i
$676$	−7.38503	−	9.48388i	−0.284039	−	0.364765i
$677$	−46.8713			−1.80141			−0.900705	−	0.434432i	$-0.856949\pi$
$677$	−46.8713			−1.80141			−0.900705	+	0.434432i	$0.856949\pi$
$678$	−4.00746	+	8.19974i	−0.153906	+	0.314909i
$679$	−4.03324			−0.154781
$680$	−8.91294	+	27.8631i	−0.341796	+	1.06850i
$681$	−0.0949223			−0.00363743
$682$	−11.7293	+	23.9995i	−0.449137	+	0.918987i
$683$			24.4592i			0.935906i	0.883753	+	0.467953i	$0.155008\pi$
$683$			24.4592i			0.935906i	−0.883753	+	0.467953i	$0.844992\pi$
$684$	8.74133	−	20.0333i	0.334233	−	0.765993i
$685$	−6.73833	−	3.82791i	−0.257458	−	0.146257i
$686$	−18.9824	−	9.27731i	−0.724753	−	0.354209i
$687$			10.4997i			0.400587i
$688$	−9.11341	+	36.0562i	−0.347445	+	1.37463i
$689$	5.25824			0.200323
$690$	−8.30498	−	12.1501i	−0.316165	−	0.462548i
$691$			30.6383i			1.16554i	0.812638	+	0.582768i	$0.198031\pi$
$691$			30.6383i			1.16554i	−0.812638	+	0.582768i	$0.801969\pi$
$692$	18.2781	+	23.4728i	0.694830	+	0.892303i
$693$		−	5.11667i		−	0.194366i
$694$	−0.134550	−	0.0657587i	−0.00510744	−	0.00249617i
$695$	2.06203	+	1.17140i	0.0782173	+	0.0444337i
$696$	3.07461	+	14.6389i	0.116543	+	0.554885i
$697$	−34.2329			−1.29666
$698$	20.6166	+	10.0759i	0.780348	+	0.381380i
$699$	−7.32688			−0.277128
$700$	−4.30823	+	11.0544i	−0.162836	+	0.417816i
$701$	0.610212			0.0230474			0.0115237	−	0.999934i	$-0.496332\pi$
$701$	0.610212			0.0230474			0.0115237	+	0.999934i	$0.496332\pi$
$702$	−6.34707	+	12.9868i	−0.239555	+	0.490157i
$703$	−17.5634	−	32.3225i	−0.662417	−	1.21906i
$704$	−5.53620	−	12.5981i	−0.208653	−	0.474810i
$705$	5.59875	+	3.18054i	0.210861	+	0.119786i
$706$	−8.20622	+	16.7909i	−0.308845	+	0.631933i
$707$	2.53682			0.0954069
$708$	3.47468	−	2.70571i	0.130587	−	0.101687i
$709$	21.9791			0.825444			0.412722	−	0.910857i	$-0.364578\pi$
$709$	21.9791			0.825444			0.412722	+	0.910857i	$0.364578\pi$
$710$	23.7922	−	16.2627i	0.892907	−	0.610329i
$711$	16.0054			0.600249
$712$	−39.0342	+	8.19836i	−1.46287	+	0.307247i
$713$	72.8010			2.72642
$714$	−4.89473	−	2.39221i	−0.183181	−	0.0895260i
$715$	8.84192	+	5.02292i	0.330669	+	0.187846i
$716$	24.2567	+	31.1505i	0.906514	+	1.16415i
$717$	−4.72233			−0.176359
$718$	3.54964	−	7.26298i	0.132472	−	0.271052i
$719$		−	4.73226i		−	0.176483i	−0.996099	−	0.0882417i	$-0.971875\pi$
$719$		−	4.73226i		−	0.176483i	0.996099	−	0.0882417i	$-0.0281248\pi$
$720$	−16.1897	−	15.5171i	−0.603355	−	0.578289i
$721$			18.6471i			0.694456i
$722$	23.0342	−	13.8357i	0.857244	−	0.514910i
$723$	9.16930			0.341010
$724$	−25.1558	+	19.5886i	−0.934908	+	0.728006i
$725$	32.3556	−	19.2878i	1.20166	−	0.716329i
$726$	3.50530	−	7.17226i	0.130094	−	0.266187i
$727$	42.9864			1.59428			0.797139	−	0.603795i	$-0.206346\pi$
$727$	42.9864			1.59428			0.797139	+	0.603795i	$0.206346\pi$
$728$	−1.82360	−	8.68256i	−0.0675871	−	0.321797i
$729$	3.91236			0.144902
$730$	−11.5512	−	16.8994i	−0.427530	−	0.625474i
$731$			43.0053i			1.59061i
$732$	−4.16045	+	3.23971i	−0.153775	+	0.119743i
$733$			33.6704i			1.24364i	0.783159	+	0.621822i	$0.213607\pi$
$733$			33.6704i			1.24364i	−0.783159	+	0.621822i	$0.786393\pi$
$734$	38.9195	+	19.0212i	1.43655	+	0.702085i
$735$	7.63274	+	4.33601i	0.281538	+	0.159936i
$736$	−24.2224	+	28.6320i	−0.892850	+	1.05539i
$737$	−16.3548			−0.602438
$738$	11.5227	−	23.5767i	0.424156	−	0.867872i
$739$		−	12.2734i		−	0.451484i	−0.974187	−	0.225742i	$-0.927519\pi$
$739$		−	12.2734i		−	0.451484i	0.974187	−	0.225742i	$-0.0724806\pi$
$740$	−37.3457	+	5.45320i	−1.37285	+	0.200464i
$741$	−7.10829	+	3.86251i	−0.261130	+	0.141893i
$742$	−2.99811	−	1.46527i	−0.110064	−	0.0537916i
$743$		−	4.12811i		−	0.151446i	−0.997129	−	0.0757229i	$-0.975874\pi$
$743$		−	4.12811i		−	0.151446i	0.997129	−	0.0757229i	$-0.0241264\pi$
$744$	−21.3374	+	4.48150i	−0.782267	+	0.164300i
$745$	4.71547	−	8.30072i	0.172761	−	0.304115i
$746$	−4.24600	−	2.07515i	−0.155457	−	0.0759767i
$747$	27.0548			0.989883
$748$	−9.77657	−	12.5551i	−0.357467	−	0.459060i
$749$		−	15.7764i		−	0.576458i
$750$	4.66381	−	10.0720i	0.170298	−	0.367779i
$751$	41.3777			1.50989			0.754947	−	0.655786i	$-0.227662\pi$
$751$	41.3777			1.50989			0.754947	+	0.655786i	$0.227662\pi$
$752$	4.02089	−	15.9082i	0.146627	−	0.580113i
$753$	11.6241			0.423605
$754$	−12.3685	+	25.3074i	−0.450435	+	0.921642i
$755$	−4.59720	+	8.09253i	−0.167309	+	0.294517i
$756$	7.23785	−	5.63606i	0.263238	−	0.204982i
$757$			18.2143i			0.662011i	0.943629	+	0.331005i	$0.107388\pi$
$757$			18.2143i			0.662011i	−0.943629	+	0.331005i	$0.892612\pi$
$758$	23.4693	+	11.4702i	0.852443	+	0.416615i
$759$	8.00544			0.290579
$760$	−5.15640	−	27.0816i	−0.187042	−	0.982352i
$761$	47.2371			1.71234			0.856172	−	0.516691i	$-0.172836\pi$
$761$	47.2371			1.71234			0.856172	+	0.516691i	$0.172836\pi$
$762$	10.9878	+	5.37008i	0.398046	+	0.194537i
$763$		−	2.02530i		−	0.0733207i
$764$	−24.7501	+	19.2727i	−0.895428	+	0.697263i
$765$	−22.5475	−	12.8088i	−0.815205	−	0.463102i
$766$	3.69393	−	7.55821i	0.133467	−	0.273089i
$767$	8.29304			0.299444
$768$	5.33687	−	9.88290i	0.192578	−	0.356619i
$769$	3.39246			0.122335			0.0611676	−	0.998128i	$-0.480518\pi$
$769$	3.39246			0.122335			0.0611676	+	0.998128i	$0.480518\pi$
$770$	−3.64173	−	5.32783i	−0.131239	−	0.192001i
$771$		−	2.14298i		−	0.0771775i
$772$	4.37730	+	5.62135i	0.157543	+	0.202317i
$773$	28.9244			1.04034			0.520169	−	0.854063i	$-0.325869\pi$
$773$	28.9244			1.04034			0.520169	+	0.854063i	$0.325869\pi$
$774$	−29.6185	−	14.4755i	−1.06461	−	0.520310i
$775$	28.1135	+	47.1610i	1.00987	+	1.69407i
$776$	−1.97637	−	9.40991i	−0.0709474	−	0.337796i
$777$		−	7.02872i		−	0.252154i
$778$	40.6249	+	19.8547i	1.45647	+	0.711824i
$779$	28.3456	−	15.4025i	1.01559	−	0.551851i
$780$	1.19926	+	8.21299i	0.0429403	+	0.294072i
$781$			15.6761i			0.560936i
$782$	−19.0426	+	38.9634i	−0.680962	+	1.39333i
$783$	−29.1252			−1.04085
$784$	5.48166	−	21.6876i	0.195773	−	0.774556i
$785$	−15.8976	−	9.03113i	−0.567411	−	0.322335i
$786$	13.1220	+	6.41313i	0.468046	+	0.228749i
$787$			7.89810i			0.281537i	0.990043	+	0.140768i	$0.0449573\pi$
$787$			7.89810i			0.281537i	−0.990043	+	0.140768i	$0.955043\pi$
$788$	4.26392	−	3.32028i	0.151896	−	0.118280i
$789$		−	5.83363i		−	0.207683i
$790$	16.6659	−	11.3916i	0.592946	−	0.405297i
$791$	10.9070			0.387808
$792$	11.9377	−	2.50727i	0.424187	−	0.0890921i
$793$	−9.92977			−0.352616
$794$	−10.9773	+	22.4609i	−0.389571	+	0.797107i
$795$	2.71447	+	1.54204i	0.0962725	+	0.0546905i
$796$	−20.7472	+	16.1557i	−0.735364	+	0.572623i
$797$	1.35212			0.0478945			0.0239472	−	0.999713i	$-0.492377\pi$
$797$	1.35212			0.0478945			0.0239472	+	0.999713i	$0.492377\pi$
$798$	5.12929	−	0.221495i	0.181575	−	0.00784083i
$799$		−	18.9742i		−	0.671260i
$800$	−27.9020	−	4.63465i	−0.986484	−	0.163860i
$801$		−	35.3561i		−	1.24925i
$802$	16.2789	−	33.3086i	0.574829	−	1.17617i
$803$	11.1346			0.392932
$804$	−8.20150	−	10.5324i	−0.289245	−	0.371449i
$805$	−8.68756	+	15.2929i	−0.306196	+	0.539002i
$806$	−36.8877	−	18.0281i	−1.29931	−	0.635014i
$807$	2.02148			0.0711595
$808$	1.24309	+	5.91863i	0.0437318	+	0.208217i
$809$	−39.6610			−1.39441			−0.697204	−	0.716873i	$-0.745573\pi$
$809$	−39.6610			−1.39441			−0.697204	+	0.716873i	$0.745573\pi$
$810$	12.5515	−	8.57931i	0.441014	−	0.301446i
$811$	−33.2165			−1.16639			−0.583195	−	0.812332i	$-0.698198\pi$
$811$	−33.2165			−1.16639			−0.583195	+	0.812332i	$0.698198\pi$
$812$	14.1044	−	10.9830i	0.494966	−	0.385427i
$813$	6.57186			0.230485
$814$	9.01442	−	18.4446i	0.315955	−	0.646481i
$815$	−6.18005	+	10.8788i	−0.216478	+	0.381069i
$816$	3.18272	−	12.5921i	0.111418	−	0.440811i
$817$	−19.3495	−	35.6094i	−0.676953	−	1.24582i
$818$	17.6636	−	36.1417i	0.617592	−	1.26367i
$819$	7.86443			0.274806
$820$	−4.78226	−	32.7508i	−0.167004	−	1.14371i
$821$	28.7126			1.00208			0.501038	−	0.865425i	$-0.332952\pi$
$821$	28.7126			1.00208			0.501038	+	0.865425i	$0.332952\pi$
$822$	3.09126	+	1.51079i	0.107820	+	0.0526950i
$823$	48.2280			1.68112			0.840561	−	0.541717i	$-0.182225\pi$
$823$	48.2280			1.68112			0.840561	+	0.541717i	$0.182225\pi$
$824$	−43.5055	+	9.13747i	−1.51559	+	0.318319i
$825$	3.09146	+	5.18598i	0.107631	+	0.180553i
$826$	−4.72846	−	2.31095i	−0.164524	−	0.0804081i
$827$		−	39.1821i		−	1.36249i	−0.732054	−	0.681247i	$-0.761438\pi$
$827$		−	39.1821i		−	1.36249i	0.732054	−	0.681247i	$-0.238562\pi$
$828$	−20.4250	−	26.2299i	−0.709819	−	0.911552i
$829$		−	36.4544i		−	1.26611i	−0.774106	−	0.633056i	$-0.781800\pi$
$829$		−	36.4544i		−	1.26611i	0.774106	−	0.633056i	$-0.218200\pi$
$830$	28.1713	−	19.2559i	0.977839	−	0.668383i
$831$	−2.68160			−0.0930238
$832$	19.3636	−	8.50926i	0.671313	−	0.295005i
$833$		−	25.8674i		−	0.896253i
$834$	−0.945971	−	0.462325i	−0.0327563	−	0.0160090i
$835$	12.6988	+	7.21392i	0.439459	+	0.249648i
$836$	13.7442	+	5.99713i	0.475353	+	0.207415i
$837$		−	42.4524i		−	1.46737i
$838$	−16.7782	+	34.3301i	−0.579593	+	1.18591i
$839$	−11.8061			−0.407593			−0.203796	−	0.979013i	$-0.565328\pi$
$839$	−11.8061			−0.407593			−0.203796	+	0.979013i	$0.565328\pi$
$840$	1.60486	−	5.01701i	0.0553728	−	0.173103i
$841$	−27.7561			−0.957107
$842$	−8.67445	+	17.7489i	−0.298941	+	0.611668i
$843$	18.4549			0.635621
$844$	7.87847	+	10.1176i	0.271188	+	0.348261i
$845$	6.63803	−	11.6850i	0.228355	−	0.401977i
$846$	13.0679	+	6.38666i	0.449282	+	0.219578i
$847$	−9.54027			−0.327807
$848$	1.94947	−	7.71287i	0.0669451	−	0.264861i
$849$		−	10.6047i		−	0.363951i
$850$	−32.5944	+	2.71053i	−1.11798	+	0.0929706i
$851$	−55.9505			−1.91796
$852$	−10.0953	+	7.86116i	−0.345860	+	0.269319i
$853$		−	27.9040i		−	0.955416i	−0.878519	−	0.477708i	$-0.841468\pi$
$853$		−	27.9040i		−	0.955416i	0.878519	−	0.477708i	$-0.158532\pi$
$854$	5.66168	+	2.76704i	0.193739	+	0.0946861i
$855$	24.4329	+	0.461123i	0.835588	+	0.0157701i
$856$	36.8079	−	7.73077i	1.25807	−	0.264232i
$857$	35.7067			1.21972			0.609858	−	0.792510i	$-0.291226\pi$
$857$	35.7067			1.21972			0.609858	+	0.792510i	$0.291226\pi$
$858$	−4.05629	−	1.98243i	−0.138479	−	0.0676792i
$859$			31.5568i			1.07670i	0.842720	+	0.538352i	$0.180953\pi$
$859$			31.5568i			1.07670i	−0.842720	+	0.538352i	$0.819047\pi$
$860$	−41.1435	+	6.00775i	−1.40298	+	0.204863i
$861$	6.16394			0.210066
$862$	2.20064	+	1.07552i	0.0749542	+	0.0366324i
$863$			42.2038i			1.43663i	0.695716	+	0.718317i	$0.255087\pi$
$863$			42.2038i			1.43663i	−0.695716	+	0.718317i	$0.744913\pi$
$864$	16.6961	+	14.1248i	0.568014	+	0.480535i
$865$	−16.4293	+	28.9207i	−0.558612	+	0.983334i
$866$	14.8629	+	7.26397i	0.505063	+	0.246840i
$867$		−	3.08515i		−	0.104777i
$868$	16.0086	+	20.5583i	0.543367	+	0.697794i
$869$			10.9808i			0.372497i
$870$	−13.8067	+	9.43730i	−0.468091	+	0.319954i
$871$		−	25.1377i		−	0.851759i
$872$	4.72521	−	0.992436i	0.160016	−	0.0336081i
$873$	8.52325			0.288468
$874$	−1.76316	−	40.8305i	−0.0596397	−	1.38111i
$875$	−13.2617	+	0.277770i	−0.448327	+	0.00939033i
$876$	5.58370	+	7.17061i	0.188656	+	0.242272i
$877$	3.33822			0.112724			0.0563618	−	0.998410i	$-0.482050\pi$
$877$	3.33822			0.112724			0.0563618	+	0.998410i	$0.482050\pi$
$878$	−36.5682	−	17.8720i	−1.23412	−	0.603151i
$879$		−	11.8491i		−	0.399662i
$880$	10.6458	−	11.1072i	0.358870	−	0.374425i
$881$	−12.4430			−0.419214			−0.209607	−	0.977786i	$-0.567218\pi$
$881$	−12.4430			−0.419214			−0.209607	+	0.977786i	$0.567218\pi$
$882$	17.8153	+	8.70690i	0.599873	+	0.293176i
$883$	−33.7017			−1.13415			−0.567076	−	0.823666i	$-0.691925\pi$
$883$	−33.7017			−1.13415			−0.567076	+	0.823666i	$0.691925\pi$
$884$	19.2975	−	15.0268i	0.649044	−	0.505406i
$885$	4.28113	+	2.43203i	0.143909	+	0.0817516i
$886$	39.0849	+	19.1020i	1.31308	+	0.641744i
$887$		−	25.7780i		−	0.865541i	−0.901504	−	0.432771i	$-0.857536\pi$
$887$		−	25.7780i		−	0.865541i	0.901504	−	0.432771i	$-0.142464\pi$
$888$	16.3987	−	3.44421i	0.550303	−	0.115580i
$889$		−	14.6156i		−	0.490190i
$890$	−25.1643	−	36.8152i	−0.843509	−	1.23405i
$891$			8.26987i			0.277051i
$892$	0.247896	−	0.193035i	0.00830017	−	0.00646328i
$893$	8.53712	+	15.7111i	0.285684	+	0.525752i
$894$	−1.86109	+	3.80801i	−0.0622443	+	0.127359i
$895$	−21.8031	+	38.3803i	−0.728797	+	1.28291i
$896$	−13.4118	−	0.544137i	−0.448057	−	0.0181783i
$897$			12.3045i			0.410836i
$898$	−17.2288	+	35.2521i	−0.574932	+	1.17638i
$899$		−	82.7268i		−	2.75909i
$900$	9.10439	−	23.3607i	0.303480	−	0.778689i
$901$		−	9.19937i		−	0.306476i
$902$	16.1752	+	7.90533i	0.538576	+	0.263219i
$903$		−	7.74349i		−	0.257687i
$904$	5.34464	+	25.4470i	0.177760	+	0.846355i
$905$	−30.9943	−	17.6072i	−1.03029	−	0.585285i
$906$	1.81441	−	3.71250i	0.0602799	−	0.123340i
$907$		−	13.6366i		−	0.452797i	−0.974035	−	0.226398i	$-0.927305\pi$
$907$		−	13.6366i		−	0.452797i	0.974035	−	0.226398i	$-0.0726951\pi$
$908$	−0.213376	+	0.166155i	−0.00708114	+	0.00551403i
$909$	−5.36094			−0.177811
$910$	8.18898	−	5.59741i	0.271462	−	0.185552i
$911$	−10.5097			−0.348202			−0.174101	−	0.984728i	$-0.555702\pi$
$911$	−10.5097			−0.348202			−0.174101	+	0.984728i	$0.555702\pi$
$912$	3.03022	+	11.8586i	0.100341	+	0.392676i
$913$			18.5614i			0.614292i
$914$	20.2370	−	41.4072i	0.669380	−	1.36963i
$915$	−5.12606	−	2.91201i	−0.169462	−	0.0962682i
$916$	18.3789	+	23.6022i	0.607255	+	0.779840i
$917$		−	17.4544i		−	0.576395i
$918$	22.7207	+	11.1043i	0.749894	+	0.366496i
$919$			45.2388i			1.49229i	0.665784	+	0.746145i	$0.268097\pi$
$919$			45.2388i			1.49229i	−0.665784	+	0.746145i	$0.731903\pi$
$920$	−39.9367	−	12.7751i	−1.31668	−	0.421182i
$921$	−18.9577			−0.624677
$922$	−10.9886	−	5.37045i	−0.361889	−	0.176866i
$923$	−24.0946			−0.793082
$924$	1.76036	+	2.26066i	0.0579116	+	0.0743702i
$925$	−21.6064	−	36.2451i	−0.710413	−	1.19173i
$926$	23.6418	+	11.5545i	0.776917	+	0.379703i
$927$		−	39.4061i		−	1.29427i
$928$	32.5357	+	27.5249i	1.06804	+	0.903550i
$929$	−18.6279			−0.611163			−0.305581	−	0.952166i	$-0.598851\pi$
$929$	−18.6279			−0.611163			−0.305581	+	0.952166i	$0.598851\pi$
$930$	−13.7557	−	20.1244i	−0.451066	−	0.659906i
$931$	11.6386	+	21.4189i	0.381440	+	0.701975i
$932$	−16.4701	+	12.8252i	−0.539497	+	0.420103i
$933$	6.42774			0.210435
$934$	−21.4881	−	10.5019i	−0.703111	−	0.343632i
$935$	8.78766	−	15.4691i	0.287387	−	0.505893i
$936$	3.85373	+	18.3485i	0.125963	+	0.599738i
$937$			44.1593i			1.44262i	0.692611	+	0.721311i	$0.256460\pi$
$937$			44.1593i			1.44262i	−0.692611	+	0.721311i	$0.743540\pi$
$938$	−7.00490	+	14.3328i	−0.228718	+	0.467984i
$939$	7.22570			0.235802
$940$	18.1528	−	2.65066i	0.592078	−	0.0864550i
$941$			52.9600i			1.72645i	0.504822	+	0.863223i	$0.331558\pi$
$941$			52.9600i			1.72645i	−0.504822	+	0.863223i	$0.668442\pi$
$942$	7.29316	+	3.56439i	0.237624	+	0.116134i
$943$		−	49.0666i		−	1.59783i
$944$	3.07461	−	12.1644i	0.100070	−	0.395916i
$945$	8.91771	+	5.06597i	0.290093	+	0.164796i
$946$	9.93113	−	20.3202i	0.322889	−	0.660668i
$947$	3.69022			0.119916			0.0599580	−	0.998201i	$-0.480903\pi$
$947$	3.69022			0.119916			0.0599580	+	0.998201i	$0.480903\pi$
$948$	−7.07154	+	5.50656i	−0.229673	+	0.178845i
$949$			17.1141i			0.555548i
$950$	25.7694	−	16.9097i	0.836070	−	0.548623i
$951$		−	13.3378i		−	0.432507i
$952$	−15.1903	+	3.19042i	−0.492319	+	0.103402i
$953$	−29.8142			−0.965777			−0.482888	−	0.875682i	$-0.660412\pi$
$953$	−29.8142			−0.965777			−0.482888	+	0.875682i	$0.660412\pi$
$954$	6.33576	+	3.09648i	0.205128	+	0.100252i
$955$	−30.4945	−	17.3233i	−0.986777	−	0.560568i
$956$	−10.6154	+	8.26610i	−0.343325	+	0.267345i
$957$		−	9.09691i		−	0.294061i
$958$	19.5053	−	39.9101i	0.630188	−	1.28944i
$959$		−	4.11187i		−	0.132779i
$960$	12.4916	+	1.28584i	0.403163	+	0.0415004i
$961$	89.5812			2.88972
$962$	28.3497	+	13.8554i	0.914030	+	0.446715i
$963$			33.3396i			1.07435i
$964$	20.6117	−	16.0502i	0.663859	−	0.516942i
$965$	−3.93454	+	6.92603i	−0.126657	+	0.222957i
$966$	3.42879	−	7.01571i	0.110320	−	0.225727i
$967$	47.6952			1.53377			0.766886	−	0.641783i	$-0.221805\pi$
$967$	47.6952			1.53377			0.766886	+	0.641783i	$0.221805\pi$
$968$	−4.67492	−	22.2583i	−0.150258	−	0.715410i
$969$	6.75752	+	12.4361i	0.217083	+	0.399504i
$970$	8.87499	−	6.06632i	0.284959	−	0.194778i
$971$	13.1772			0.422876			0.211438	−	0.977391i	$-0.432185\pi$
$971$	13.1772			0.422876			0.211438	+	0.977391i	$0.432185\pi$
$972$	−23.6274	+	18.3985i	−0.757851	+	0.590133i
$973$			1.25830i			0.0403391i
$974$	12.1086	−	24.7756i	0.387984	−	0.793861i
$975$	−7.97096	+	4.75163i	−0.255275	+	0.152174i
$976$	−3.68142	+	14.5651i	−0.117839	+	0.466219i
$977$	9.59665			0.307024			0.153512	−	0.988147i	$-0.450942\pi$
$977$	9.59665			0.307024			0.153512	+	0.988147i	$0.450942\pi$
$978$	2.43913	−	4.99074i	0.0779947	−	0.159586i
$979$	24.2567			0.775246
$980$	24.7475	−	3.61363i	0.790531	−	0.115433i
$981$			4.27997i			0.136649i
$982$	6.43816	−	13.1732i	0.205450	−	0.420374i
$983$			39.4865i			1.25942i	0.776829	+	0.629711i	$0.216827\pi$
$983$			39.4865i			1.25942i	−0.776829	+	0.629711i	$0.783173\pi$
$984$	3.02045	+	14.3810i	0.0962885	+	0.458451i
$985$	5.25355	+	2.98443i	0.167392	+	0.0950920i
$986$	44.2757	+	21.6389i	1.41003	+	0.689123i
$987$			3.41648i			0.108748i
$988$	−9.21772	+	21.1251i	−0.293255	+	0.672079i
$989$	−61.6403			−1.96005
$990$	7.69590	+	11.2590i	0.244592	+	0.357836i
$991$	−32.4827			−1.03185			−0.515923	−	0.856635i	$-0.672551\pi$
$991$	−32.4827			−1.03185			−0.515923	+	0.856635i	$0.672551\pi$
$992$	−40.1199	+	47.4235i	−1.27381	+	1.50570i
$993$		−	0.642508i		−	0.0203894i
$994$	13.7381	+	6.71421i	0.435745	+	0.212962i
$995$	−25.5625	−	14.5215i	−0.810385	−	0.460363i
$996$	−11.9534	+	9.30803i	−0.378758	+	0.294936i
$997$		−	3.65978i		−	0.115906i	−0.998319	−	0.0579531i	$-0.981543\pi$
$997$		−	3.65978i		−	0.115906i	0.998319	−	0.0579531i	$-0.0184574\pi$
$998$	−15.5251	+	31.7662i	−0.491439	+	1.00554i
$999$			32.6264i			1.03225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.d.b.379.6	yes	40
4.3	odd	2	inner	380.2.d.b.379.8	yes	40
5.4	even	2	inner	380.2.d.b.379.35	yes	40
19.18	odd	2	inner	380.2.d.b.379.36	yes	40
20.19	odd	2	inner	380.2.d.b.379.33	yes	40
76.75	even	2	inner	380.2.d.b.379.34	yes	40
95.94	odd	2	inner	380.2.d.b.379.5	✓	40
380.379	even	2	inner	380.2.d.b.379.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.d.b.379.5	✓	40	95.94	odd	2	inner
380.2.d.b.379.6	yes	40	1.1	even	1	trivial
380.2.d.b.379.7	yes	40	380.379	even	2	inner
380.2.d.b.379.8	yes	40	4.3	odd	2	inner
380.2.d.b.379.33	yes	40	20.19	odd	2	inner
380.2.d.b.379.34	yes	40	76.75	even	2	inner
380.2.d.b.379.35	yes	40	5.4	even	2	inner
380.2.d.b.379.36	yes	40	19.18	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27059 - 0.620975i) q^{2} +0.701989i q^{3} +(1.22878 + 1.57800i) q^{4} +(-1.10449 + 1.94425i) q^{5} +(0.435918 - 0.891938i) q^{6} -1.18642 q^{7} +(-0.581371 - 2.76803i) q^{8} +2.50721 q^{9} +O(q^{10})\)	\(q+(-1.27059 - 0.620975i) q^{2} +0.701989i q^{3} +(1.22878 + 1.57800i) q^{4} +(-1.10449 + 1.94425i) q^{5} +(0.435918 - 0.891938i) q^{6} -1.18642 q^{7} +(-0.581371 - 2.76803i) q^{8} +2.50721 q^{9} +(2.61068 - 1.78448i) q^{10} +1.72011i q^{11} +(-1.10774 + 0.862590i) q^{12} -2.64385 q^{13} +(1.50745 + 0.736738i) q^{14} +(-1.36484 - 0.775339i) q^{15} +(-0.980197 + 3.87804i) q^{16} +4.62546i q^{17} +(-3.18563 - 1.55692i) q^{18} +(-2.08114 - 3.82999i) q^{19} +(-4.42521 + 0.646167i) q^{20} -0.832855i q^{21} +(1.06815 - 2.18555i) q^{22} -6.62976 q^{23} +(1.94313 - 0.408116i) q^{24} +(-2.56021 - 4.29480i) q^{25} +(3.35924 + 1.64177i) q^{26} +3.86600i q^{27} +(-1.45785 - 1.87218i) q^{28} +7.53366i q^{29} +(1.25268 + 1.83267i) q^{30} -10.9809 q^{31} +(3.65359 - 4.31871i) q^{32} -1.20750 q^{33} +(2.87229 - 5.87705i) q^{34} +(1.31039 - 2.30670i) q^{35} +(3.08081 + 3.95639i) q^{36} +8.43930 q^{37} +(0.265946 + 6.15867i) q^{38} -1.85596i q^{39} +(6.02386 + 1.92693i) q^{40} +7.40097i q^{41} +(-0.517182 + 1.05821i) q^{42} +9.29752 q^{43} +(-2.71435 + 2.11364i) q^{44} +(-2.76919 + 4.87464i) q^{45} +(8.42368 + 4.11691i) q^{46} -4.10213 q^{47} +(-2.72234 - 0.688088i) q^{48} -5.59240 q^{49} +(0.586003 + 7.04674i) q^{50} -3.24702 q^{51} +(-3.24871 - 4.17201i) q^{52} -1.98886 q^{53} +(2.40069 - 4.91209i) q^{54} +(-3.34433 - 1.89985i) q^{55} +(0.689751 + 3.28406i) q^{56} +(2.68861 - 1.46094i) q^{57} +(4.67822 - 9.57217i) q^{58} -3.13673 q^{59} +(-0.453602 - 3.10645i) q^{60} +3.75579 q^{61} +(13.9522 + 6.81889i) q^{62} -2.97461 q^{63} +(-7.32402 + 3.21851i) q^{64} +(2.92011 - 5.14031i) q^{65} +(1.53424 + 0.749828i) q^{66} +9.50799i q^{67} +(-7.29900 + 5.68367i) q^{68} -4.65402i q^{69} +(-3.09737 + 2.11714i) q^{70} +9.11343 q^{71} +(-1.45762 - 6.94004i) q^{72} -6.47318i q^{73} +(-10.7229 - 5.24059i) q^{74} +(3.01490 - 1.79724i) q^{75} +(3.48647 - 7.99028i) q^{76} -2.04078i q^{77} +(-1.15250 + 2.35815i) q^{78} +6.38375 q^{79} +(-6.45726 - 6.18900i) q^{80} +4.80774 q^{81} +(4.59581 - 9.40357i) q^{82} +10.7908 q^{83} +(1.31425 - 1.02340i) q^{84} +(-8.99304 - 5.10877i) q^{85} +(-11.8133 - 5.77353i) q^{86} -5.28855 q^{87} +(4.76133 - 1.00002i) q^{88} -14.1018i q^{89} +(6.54552 - 4.47406i) q^{90} +3.13673 q^{91} +(-8.14651 - 10.4618i) q^{92} -7.70851i q^{93} +(5.21211 + 2.54732i) q^{94} +(9.74506 + 0.183919i) q^{95} +(3.03169 + 2.56478i) q^{96} +3.39949 q^{97} +(7.10563 + 3.47274i) q^{98} +4.31269i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9}+O(q^{10}) \) 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9	\( 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9} - 8 q^{16} - 20 q^{20} - 40 q^{24} - 84 q^{25} - 24 q^{26} + 24 q^{30} + 24 q^{36} - 40 q^{44} - 12 q^{45} + 128 q^{49} - 120 q^{54} + 24 q^{61} + 72 q^{64} + 112 q^{66} + 32 q^{74} + 56 q^{76} + 96 q^{80} - 72 q^{81} + 44 q^{85} - 40 q^{96}+O(q^{100}) \) 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9 - 8 * q^16 - 20 * q^20 - 40 * q^24 - 84 * q^25 - 24 * q^26 + 24 * q^30 + 24 * q^36 - 40 * q^44 - 12 * q^45 + 128 * q^49 - 120 * q^54 + 24 * q^61 + 72 * q^64 + 112 * q^66 + 32 * q^74 + 56 * q^76 + 96 * q^80 - 72 * q^81 + 44 * q^85 - 40 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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