LMFDB - Embedded newform 380.2.d.b.379.8

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			379.8
Character	$\chi$	$=$	380.379
Dual form			380.2.d.b.379.5

$q$-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} +(0.196019 - 3.15620i) 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} +(1.71086 + 4.13194i) 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} +(-2.21562 - 0.137603i) 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} +(-5.02260 - 3.57400i) q^{38} +1.85596i q^{39} +(-4.73963 - 4.18759i) 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} +(5.91993 + 3.86709i) 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} +(2.90058 - 1.20100i) 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} +(0.232561 - 3.74458i) 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} +(8.60101 + 1.42216i) q^{76} -2.04078i q^{77} +(-1.15250 - 2.35815i) q^{78} -6.38375 q^{79} +(8.62250 + 2.37751i) 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} +(0.491461 - 7.91325i) 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	$-0.935046\pi$
$3$		−	0.701989i		−	0.405294i	0.979252	−	0.202647i	$-0.0649543\pi$
$4$	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	$-0.428019\pi$
$7$	1.18642			0.448425			0.224213	+	0.974540i	$0.428019\pi$
$8$	−0.581371	+	2.76803i	−0.205546	+	0.978648i
$9$	2.50721			0.835737
$10$	0.196019	−	3.15620i	0.0619866	−	0.998077i
$11$		−	1.72011i		−	0.518634i	−0.965792	−	0.259317i	$-0.916503\pi$
$11$		−	1.72011i		−	0.518634i	0.965792	−	0.259317i	$-0.0834974\pi$
$12$	−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
$20$	1.71086	+	4.13194i	0.382560	+	0.923931i
$21$		−	0.832855i		−	0.181744i
$22$	1.06815	+	2.18555i	0.227730	+	0.465962i
$23$	6.62976			1.38240			0.691200	−	0.722664i	$-0.257082\pi$
$23$	6.62976			1.38240			0.691200	+	0.722664i	$0.257082\pi$
$24$	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	$0.753414\pi$
$30$	−2.21562	−	0.137603i	−0.404514	−	0.0251228i
$31$	10.9809			1.97224			0.986118	−	0.166044i	$-0.0530995\pi$
$31$	10.9809			1.97224			0.986118	+	0.166044i	$0.0530995\pi$
$32$	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	$0.255977\pi$
$38$	−5.02260	−	3.57400i	−0.814774	−	0.579779i
$39$			1.85596i			0.297191i
$40$	−4.73963	−	4.18759i	−0.749401	−	0.662116i
$41$			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	$-0.750822\pi$
$43$	−9.29752			−1.41786			−0.708930	+	0.705279i	$0.750822\pi$
$44$	−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	$-0.403287\pi$
$47$	4.10213			0.598357			0.299178	+	0.954197i	$0.403287\pi$
$48$	−2.72234	+	0.688088i	−0.392936	+	0.0993169i
$49$	−5.59240			−0.798915
$50$	5.91993	+	3.86709i	0.837205	+	0.546890i
$51$	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	$-0.434546\pi$
$59$	3.13673			0.408367			0.204183	+	0.978933i	$0.434546\pi$
$60$	2.90058	−	1.20100i	0.374463	−	0.155049i
$61$	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	$-0.802743\pi$
$67$		−	9.50799i		−	1.16159i	0.814051	−	0.580793i	$-0.197257\pi$
$68$	7.29900	+	5.68367i	0.885133	+	0.689247i
$69$		−	4.65402i		−	0.560278i
$70$	0.232561	−	3.74458i	0.0277964	−	0.447563i
$71$	−9.11343			−1.08157			−0.540783	−	0.841162i	$-0.681872\pi$
$71$	−9.11343			−1.08157			−0.540783	+	0.841162i	$0.681872\pi$
$72$	−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
$76$	8.60101	+	1.42216i	0.986604	+	0.163133i
$77$		−	2.04078i		−	0.232569i
$78$	−1.15250	−	2.35815i	−0.130495	−	0.267008i
$79$	−6.38375			−0.718228			−0.359114	−	0.933294i	$-0.616921\pi$
$79$	−6.38375			−0.718228			−0.359114	+	0.933294i	$0.616921\pi$
$80$	8.62250	+	2.37751i	0.964025	+	0.265813i
$81$	4.80774			0.534194
$82$	−4.59581	−	9.40357i	−0.507523	−	1.03845i
$83$	−10.7908			−1.18444			−0.592221	−	0.805775i	$-0.701749\pi$
$83$	−10.7908			−1.18444			−0.592221	+	0.805775i	$0.701749\pi$
$84$	−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	$-0.268695\pi$
$90$	0.491461	−	7.91325i	0.0518045	−	0.834130i
$91$	−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
$100$	−9.92315	−	1.23735i	−0.992315	−	0.123735i
$101$	−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	$0.281911\pi$
$103$			15.7171i			1.54865i	−0.632786	+	0.774327i	$0.718089\pi$
$104$	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	$-0.777790\pi$
$107$		−	13.2975i		−	1.28552i	0.766069	−	0.642758i	$-0.222210\pi$
$108$	−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	$0.973948\pi$
$110$	−5.42902	−	0.337175i	−0.517637	−	0.0321483i
$111$		−	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	$0.642337\pi$
$114$	−2.50891	+	3.52581i	−0.234981	+	0.330223i
$115$	−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
$120$	−2.93964	+	3.32717i	−0.268351	+	0.303727i
$121$	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	$-0.815934\pi$
$127$		−	12.3190i		−	1.09314i	0.837415	−	0.546568i	$-0.184066\pi$
$128$	11.3044	−	0.458637i	0.999178	−	0.0405381i
$129$			6.52676i			0.574649i
$130$	−0.518245	+	8.34452i	−0.0454531	+	0.731863i
$131$		−	14.7118i		−	1.28537i	−0.766128	−	0.642687i	$-0.777819\pi$
$131$		−	14.7118i		−	1.28537i	0.766128	−	0.642687i	$-0.222181\pi$
$132$	−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	$0.0143220\pi$
$139$			1.06058i			0.0899572i	−0.998988	+	0.0449786i	$0.985678\pi$
$140$	2.02980	+	4.90223i	0.171550	+	0.414314i
$141$		−	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	$0.555954\pi$
$150$	2.71466	−	4.15573i	0.221651	−	0.339314i
$151$	−4.16229			−0.338722			−0.169361	−	0.985554i	$-0.554170\pi$
$151$	−4.16229			−0.338722			−0.169361	+	0.985554i	$0.554170\pi$
$152$	−11.8115	+	3.53403i	−0.958036	+	0.286648i
$153$			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
$160$	−12.4320	+	2.33353i	−0.982836	+	0.184481i
$161$	7.86569			0.619903
$162$	−6.10865	+	2.98549i	−0.479941	+	0.234562i
$163$	−5.59539			−0.438265			−0.219132	−	0.975695i	$-0.570323\pi$
$163$	−5.59539			−0.438265			−0.219132	+	0.975695i	$0.570323\pi$
$164$	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	$0.0813217\pi$
$167$			6.53146i			0.505419i	−0.967542	+	0.252710i	$0.918678\pi$
$168$	2.30537	+	0.484198i	0.177863	+	0.0373567i
$169$	−6.01004			−0.462311
$170$	14.5989	+	0.906677i	1.11968	+	0.0695389i
$171$	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	$-0.764105\pi$
$179$	−19.7404			−1.47547			−0.737735	+	0.675091i	$0.764105\pi$
$180$	4.28949	+	10.3597i	0.319720	+	0.772163i
$181$			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
$190$	12.4962	−	5.81775i	0.906566	−	0.422064i
$191$		−	15.6844i		−	1.13489i	−0.823413	−	0.567443i	$-0.807933\pi$
$191$		−	15.6844i		−	1.13489i	0.823413	−	0.567443i	$-0.192067\pi$
$192$	−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	$-0.845691\pi$
$199$		−	13.1477i		−	0.932018i	0.884780	−	0.466009i	$-0.154309\pi$
$200$	13.3766	−	4.58987i	0.945868	−	0.324553i
$201$	−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
$210$	−2.62866	−	0.163255i	−0.181394	−	0.0112657i
$211$	−6.41162			−0.441394			−0.220697	−	0.975342i	$-0.570833\pi$
$211$	−6.41162			−0.441394			−0.220697	+	0.975342i	$0.570833\pi$
$212$	−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
$220$	7.10742	−	2.94287i	0.479182	−	0.198409i
$221$		−	12.2290i		−	0.822614i
$222$	3.67884	+	7.52733i	0.246908	+	0.505202i
$223$			0.157095i			0.0105198i	0.999986	+	0.00525991i	$0.00167429\pi$
$223$			0.157095i			0.0105198i	−0.999986	+	0.00525991i	$0.998326\pi$
$224$	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	$-0.998572\pi$
$227$		−	0.135219i		−	0.00897481i	0.999990	−	0.00448740i	$-0.00142839\pi$
$228$	0.998343	−	6.03782i	0.0661169	−	0.399864i
$229$	14.9570			0.988387			0.494193	−	0.869352i	$-0.335463\pi$
$229$	14.9570			0.988387			0.494193	+	0.869352i	$0.335463\pi$
$230$	1.29956	−	20.9248i	0.0856902	−	1.37974i
$231$	−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	$-0.930187\pi$
$239$		−	6.72707i		−	0.435138i	0.976045	−	0.217569i	$-0.0698127\pi$
$240$	1.66898	−	6.05290i	0.107732	−	0.390713i
$241$		−	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
$250$	−14.0571	+	7.23866i	−0.889048	+	0.457813i
$251$			16.5588i			1.04518i	0.852584	+	0.522591i	$0.175034\pi$
$251$			16.5588i			1.04518i	−0.852584	+	0.522591i	$0.824966\pi$
$252$	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
$260$	−4.52326	−	10.9242i	−0.280521	−	0.677493i
$261$			18.8885i			1.16917i
$262$	9.13565	+	18.6926i	0.564402	+	1.15483i
$263$	8.31015			0.512426			0.256213	−	0.966620i	$-0.417525\pi$
$263$	8.31015			0.512426			0.256213	+	0.966620i	$0.417525\pi$
$264$	0.702006	−	3.34240i	0.0432055	−	0.205711i
$265$	2.19667	−	3.86683i	0.134940	−	0.237538i
$266$	−5.95893	−	4.24027i	−0.365365	−	0.259988i
$267$	−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	$-0.0279797\pi$
$270$	−12.2019	−	0.757809i	−0.742582	−	0.0461188i
$271$			9.36177i			0.568687i	0.958722	+	0.284343i	$0.0917756\pi$
$271$			9.36177i			0.568687i	−0.958722	+	0.284343i	$0.908224\pi$
$272$	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
$280$	−5.62320	−	4.96825i	−0.336051	−	0.296910i
$281$		−	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	$-0.351781\pi$
$283$	15.1066			0.897995			0.448997	+	0.893533i	$0.351781\pi$
$284$	−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
$290$	23.7777	+	1.47674i	1.39628	+	0.0867171i
$291$		−	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
$300$	−0.868604	+	6.96594i	−0.0501489	+	0.402179i
$301$	−11.0308			−0.635804
$302$	5.28855	−	2.58468i	0.304322	−	0.148731i
$303$			1.50100i			0.0862302i
$304$	12.8129	−	11.8249i	0.734872	−	0.678205i
$305$	−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	$-0.719933\pi$
$307$		−	27.0057i		−	1.54129i	0.637262	−	0.770647i	$-0.280067\pi$
$308$	−3.22036	−	2.50767i	−0.183497	−	0.142888i
$309$	11.0332			0.627659
$310$	2.15247	−	34.6580i	0.122252	−	1.96844i
$311$			9.15647i			0.519216i	0.965714	+	0.259608i	$0.0835934\pi$
$311$			9.15647i			0.519216i	−0.965714	+	0.259608i	$0.916407\pi$
$312$	−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
$320$	14.3469	−	10.6849i	0.802015	−	0.597304i
$321$	−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
$330$	−0.236693	+	3.81111i	−0.0130295	+	0.209795i
$331$	0.915268			0.0503077			0.0251538	−	0.999684i	$-0.491992\pi$
$331$	0.915268			0.0503077			0.0251538	+	0.999684i	$0.491992\pi$
$332$	−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
$340$	−19.1121	+	7.91351i	−1.03650	+	0.429170i
$341$		−	18.8885i		−	1.02287i
$342$	−12.5927	−	8.96077i	−0.680937	−	0.484543i
$343$	−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	$-0.500905\pi$
$347$	−0.105896			−0.00568479			−0.00284239	+	0.999996i	$0.500905\pi$
$348$	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	$0.642997\pi$
$350$	7.02354	+	4.58800i	0.375424	+	0.245239i
$351$			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	$-0.951800\pi$
$359$		−	5.71624i		−	0.301692i	0.988557	−	0.150846i	$-0.0481997\pi$
$360$	−11.8833	−	10.4992i	−0.626302	−	0.553355i
$361$	−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	$-0.205115\pi$
$367$	30.6312			1.59893			0.799467	+	0.600710i	$0.205115\pi$
$368$	−6.49847	−	25.7105i	−0.338756	−	1.34025i
$369$			18.5558i			0.965976i
$370$	1.65426	−	26.6361i	0.0860010	−	1.38474i
$371$	−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	$-0.342664\pi$
$379$	18.4712			0.948804			0.474402	+	0.880308i	$0.342664\pi$
$380$	−12.2648	+	15.1518i	−0.629169	+	0.777268i
$381$	−8.64781			−0.443041
$382$	9.73964	+	19.9284i	0.498323	+	1.01963i
$383$		−	5.94860i		−	0.303959i	−0.988384	−	0.151980i	$-0.951435\pi$
$383$		−	5.94860i		−	0.303959i	0.988384	−	0.151980i	$-0.0485648\pi$
$384$	−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	$0.800835\pi$
$390$	5.85776	+	0.363802i	0.296619	+	0.0184218i
$391$			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
$400$	−14.1459	+	14.1384i	−0.707296	+	0.706918i
$401$			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	$0.751729\pi$
$410$	23.3589	+	1.45073i	1.15361	+	0.0716464i
$411$	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
$418$	−6.14768	+	8.63945i	−0.300693	+	0.422569i
$419$			27.0191i			1.31997i	0.751279	+	0.659985i	$0.229437\pi$
$419$			27.0191i			1.31997i	−0.751279	+	0.659985i	$0.770563\pi$
$420$	3.44131	−	1.42490i	0.167919	−	0.0695279i
$421$		−	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
$430$	−1.82249	+	29.3448i	−0.0878882	+	1.41513i
$431$	1.73199			0.0834270			0.0417135	−	0.999130i	$-0.486718\pi$
$431$	1.73199			0.0834270			0.0417135	+	0.999130i	$0.486718\pi$
$432$	−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	$-0.740990\pi$
$439$	−28.7806			−1.37362			−0.686810	+	0.726837i	$0.740990\pi$
$440$	−7.20314	+	8.15270i	−0.343396	+	0.388665i
$441$	−14.0213			−0.667683
$442$	7.59392	+	15.5380i	0.361206	+	0.739069i
$443$	30.7613			1.46151			0.730756	−	0.682638i	$-0.239167\pi$
$443$	30.7613			1.46151			0.730756	+	0.682638i	$0.239167\pi$
$444$	−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	$-0.227196\pi$
$450$	14.8425	+	9.69562i	0.699683	+	0.457056i
$451$	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
$456$	2.48085	+	8.29152i	0.116177	+	0.388286i
$457$			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
$460$	11.3426	+	27.3938i	0.528851	+	1.27724i
$461$	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	$-0.357678\pi$
$463$	18.6070			0.864739			0.432370	+	0.901697i	$0.357678\pi$
$464$	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	$-0.627973\pi$
$467$	−16.9119			−0.782591			−0.391295	+	0.920265i	$0.627973\pi$
$468$	−8.14521	+	10.4601i	−0.376513	+	0.483519i
$469$		−	11.2805i		−	0.520884i
$470$	0.804094	−	12.9471i	0.0370901	−	0.597206i
$471$	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	$-0.745242\pi$
$479$		−	31.4108i		−	1.43520i	0.696458	−	0.717598i	$-0.254758\pi$
$480$	1.63811	+	8.72713i	0.0747691	+	0.398337i
$481$	−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	$-0.854340\pi$
$487$		−	19.4993i		−	0.883599i	0.897114	−	0.441800i	$-0.145660\pi$
$488$	−2.18351	+	10.3962i	−0.0988428	+	0.470612i
$489$			3.92790i			0.177626i
$490$	−1.09622	+	17.6507i	−0.0495220	+	0.797378i
$491$		−	10.3678i		−	0.467893i	−0.972249	−	0.233947i	$-0.924836\pi$
$491$		−	10.3678i		−	0.467893i	0.972249	−	0.233947i	$-0.0751641\pi$
$492$	6.38400	−	8.19836i	0.287813	−	0.369611i
$493$	−34.8467			−1.56941
$494$	13.2790	+	9.44912i	0.597451	+	0.425136i
$495$	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	$0.189047\pi$
$499$			25.0012i			1.11921i	−0.828760	+	0.559604i	$0.810953\pi$
$500$	13.3657	−	17.9264i	0.597733	−	0.801695i
$501$	4.58501			0.204843
$502$	−10.2826	−	21.0394i	−0.458934	−	0.939033i
$503$	−17.0206			−0.758909			−0.379454	−	0.925210i	$-0.623888\pi$
$503$	−17.0206			−0.758909			−0.379454	+	0.925210i	$0.623888\pi$
$504$	−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	$-0.264055\pi$
$510$	0.636477	−	10.2482i	0.0281837	−	0.453800i
$511$		−	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
$520$	12.5309	+	11.0714i	0.549515	+	0.485512i
$521$			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	$0.137245\pi$
$523$			19.1156i			0.835866i	−0.908478	+	0.417933i	$0.862755\pi$
$524$	−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
$530$	−0.389853	+	6.27722i	−0.0169341	+	0.272665i
$531$	7.86443			0.341287
$532$	10.2044	+	1.68729i	0.442418	+	0.0731531i
$533$		−	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
$540$	15.9741	−	6.61419i	0.687416	−	0.284629i
$541$	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	$0.184191\pi$
$547$			25.5816i			1.09379i	−0.837200	+	0.546896i	$0.815809\pi$
$548$	5.46901	+	4.25868i	0.233625	+	0.181922i
$549$	9.41657			0.401889
$550$	6.65184	−	10.1830i	0.283636	−	0.434203i
$551$	−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
$560$	10.2299	+	2.82073i	0.432293	+	0.119197i
$561$		−	5.58525i		−	0.235809i
$562$	16.3251	+	33.4030i	0.688632	+	1.40902i
$563$			0.293515i			0.0123702i	0.999981	+	0.00618509i	$0.00196879\pi$
$563$			0.293515i			0.0123702i	−0.999981	+	0.00618509i	$0.998031\pi$
$564$	−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	$-0.0566732\pi$
$570$	−4.08400	−	8.77216i	−0.171060	−	0.367425i
$571$		−	24.5184i		−	1.02606i	−0.858370	−	0.513032i	$-0.828522\pi$
$571$		−	24.5184i		−	1.02606i	0.858370	−	0.513032i	$-0.171478\pi$
$572$	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
$580$	−31.1287	+	12.8890i	−1.29255	+	0.535188i
$581$	−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	$-0.469001\pi$
$587$	4.71144			0.194462			0.0972310	+	0.995262i	$0.469001\pi$
$588$	6.19494	+	4.82395i	0.255475	+	0.198936i
$589$	22.8529	+	42.0569i	0.941639	+	1.73293i
$590$	0.614857	−	9.90012i	0.0253133	−	0.407582i
$591$	−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	$-0.491641\pi$
$599$	1.28533			0.0525171			0.0262585	+	0.999655i	$0.491641\pi$
$600$	−3.22204	−	9.39022i	−0.131539	−	0.383354i
$601$		−	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	$0.100978\pi$
$607$			15.3707i			0.623877i	−0.950102	+	0.311939i	$0.899022\pi$
$608$	−8.93697	+	22.9811i	−0.362442	+	0.932006i
$609$	6.27445			0.254254
$610$	0.736206	−	11.8540i	0.0298081	−	0.479956i
$611$	−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	$-0.662238\pi$
$619$		−	43.4349i		−	1.74580i	0.487902	−	0.872898i	$-0.337762\pi$
$620$	18.7869	+	45.3727i	0.754499	+	1.82221i
$621$		−	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
$630$	0.583080	−	9.38846i	0.0232304	−	0.374045i
$631$			46.6693i			1.85788i	0.370235	+	0.928938i	$0.379277\pi$
$631$			46.6693i			1.85788i	−0.370235	+	0.928938i	$0.620723\pi$
$632$	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
$640$	−11.5939	+	22.4851i	−0.458289	+	0.888803i
$641$		−	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	$-0.468886\pi$
$643$	4.94936			0.195184			0.0975919	+	0.995227i	$0.468886\pi$
$644$	9.66521	−	12.4121i	0.380862	−	0.489105i
$645$	−12.6896	−	7.20873i	−0.499654	−	0.283844i
$646$	16.5314	−	23.2318i	0.650418	−	0.914045i
$647$	−5.93211			−0.233215			−0.116608	−	0.993178i	$-0.537202\pi$
$647$	−5.93211			−0.233215			−0.116608	+	0.993178i	$0.537202\pi$
$648$	−2.79508	+	13.3080i	−0.109801	+	0.522787i
$649$		−	5.39553i		−	0.211793i
$650$	−15.6514	−	10.2240i	−0.613899	−	0.401019i
$651$		−	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	$-0.816506\pi$
$659$	−43.0449			−1.67679			−0.838395	+	0.545063i	$0.816506\pi$
$660$	−2.06587	−	4.98933i	−0.0804137	−	0.194209i
$661$			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
$670$	−30.0091	−	1.86374i	−1.15935	−	0.0720027i
$671$		−	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
$680$	19.3695	−	21.9230i	0.742788	−	0.840707i
$681$	−0.0949223			−0.00363743
$682$	11.7293	+	23.9995i	0.449137	+	0.918987i
$683$		−	24.4592i		−	0.935906i	−0.883753	−	0.467953i	$-0.844992\pi$
$683$		−	24.4592i		−	0.935906i	0.883753	−	0.467953i	$-0.155008\pi$
$684$	21.5646	+	3.56566i	0.824542	+	0.136337i
$685$	−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
$690$	−14.6890	−	0.912274i	−0.559200	−	0.0347297i
$691$		−	30.6383i		−	1.16554i	−0.812638	−	0.582768i	$-0.801969\pi$
$691$		−	30.6383i		−	1.16554i	0.812638	−	0.582768i	$-0.198031\pi$
$692$	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
$700$	−11.7730	−	1.46802i	−0.444979	−	0.0554858i
$701$	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	$0.364578\pi$
$710$	−1.78640	+	28.7638i	−0.0670425	+	1.07949i
$711$	−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	$0.0281248\pi$
$719$			4.73226i			0.176483i	−0.996099	+	0.0882417i	$0.971875\pi$
$720$	21.6184	+	5.96091i	0.805671	+	0.222150i
$721$			18.6471i			0.694456i
$722$	3.23562	−	26.6745i	0.120417	−	0.992723i
$723$	−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	$-0.793654\pi$
$727$	−42.9864			−1.59428			−0.797139	+	0.603795i	$0.793654\pi$
$728$	1.82360	−	8.68256i	0.0675871	−	0.321797i
$729$	3.91236			0.144902
$730$	−20.4306	−	1.26886i	−0.756171	−	0.0469628i
$731$		−	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	$0.0724806\pi$
$739$			12.2734i			0.451484i	−0.974187	+	0.225742i	$0.927519\pi$
$740$	14.4385	+	34.8707i	0.530769	+	1.28187i
$741$	−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	$0.0241264\pi$
$743$			4.12811i			0.151446i	−0.997129	+	0.0757229i	$0.975874\pi$
$744$	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
$750$	5.08146	+	9.86792i	0.185549	+	0.360326i
$751$	−41.3777			−1.50989			−0.754947	−	0.655786i	$-0.772338\pi$
$751$	−41.3777			−1.50989			−0.754947	+	0.655786i	$0.772338\pi$
$752$	−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
$760$	6.17459	−	26.8677i	0.223976	−	0.974595i
$761$	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	$0.480518\pi$
$770$	−6.44111	−	0.400032i	−0.232121	−	0.0144161i
$771$			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
$780$	−7.66870	+	3.17528i	−0.274584	+	0.113693i
$781$			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	$-0.955043\pi$
$787$		−	7.89810i		−	0.281537i	0.990043	−	0.140768i	$-0.0449573\pi$
$788$	−4.26392	−	3.32028i	−0.151896	−	0.118280i
$789$		−	5.83363i		−	0.207683i
$790$	−1.25133	+	20.1484i	−0.0445205	+	0.716846i
$791$	−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	$0.492377\pi$
$798$	−2.97662	+	4.18310i	−0.105371	+	0.148080i
$799$			18.9742i			0.671260i
$800$	9.19405	−	26.7483i	0.325059	−	0.945694i
$801$		−	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	$0.745573\pi$
$810$	0.942408	−	15.1742i	0.0331128	−	0.533166i
$811$	33.2165			1.16639			0.583195	−	0.812332i	$-0.301802\pi$
$811$	33.2165			1.16639			0.583195	+	0.812332i	$0.301802\pi$
$812$	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
$820$	−30.5804	+	12.6620i	−1.06791	+	0.442177i
$821$	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	$-0.817775\pi$
$823$	−48.2280			−1.68112			−0.840561	+	0.541717i	$0.817775\pi$
$824$	−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	$0.238562\pi$
$827$			39.1821i			1.36249i	−0.732054	+	0.681247i	$0.761438\pi$
$828$	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	$-0.218200\pi$
$830$	−2.11520	+	34.0579i	−0.0734196	+	1.18217i
$831$	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
$836$	2.44628	−	14.7947i	0.0846065	−	0.511686i
$837$		−	42.4524i		−	1.46737i
$838$	−16.7782	−	34.3301i	−0.579593	−	1.18591i
$839$	11.8061			0.407593			0.203796	−	0.979013i	$-0.434672\pi$
$839$	11.8061			0.407593			0.203796	+	0.979013i	$0.434672\pi$
$840$	−3.48766	+	3.94743i	−0.120336	+	0.136199i
$841$	−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
$850$	−17.8871	+	27.3824i	−0.613522	+	0.939209i
$851$	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	$-0.819047\pi$
$859$		−	31.5568i		−	1.07670i	0.842720	−	0.538352i	$-0.180953\pi$
$860$	−15.9068	−	38.4168i	−0.542416	−	1.31000i
$861$	6.16394			0.210066
$862$	−2.20064	+	1.07552i	−0.0749542	+	0.0366324i
$863$		−	42.2038i		−	1.43663i	−0.695716	−	0.718317i	$-0.744913\pi$
$863$		−	42.2038i		−	1.43663i	0.695716	−	0.718317i	$-0.255087\pi$
$864$	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
$870$	1.03665	−	16.6917i	0.0351459	−	0.565902i
$871$			25.1377i			0.851759i
$872$	−4.72521	−	0.992436i	−0.160016	−	0.0336081i
$873$	8.52325			0.288468
$874$	−33.2986	−	23.6947i	−1.12634	−	0.801486i
$875$	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
$880$	4.08958	−	14.8317i	0.137860	−	0.499976i
$881$	−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	$-0.308075\pi$
$883$	33.7017			1.13415			0.567076	+	0.823666i	$0.308075\pi$
$884$	−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	$0.142464\pi$
$887$			25.7780i			0.865541i	−0.901504	+	0.432771i	$0.857536\pi$
$888$	16.3987	+	3.44421i	0.550303	+	0.115580i
$889$		−	14.6156i		−	0.490190i
$890$	−44.5080	−	2.76421i	−1.49191	−	0.0926566i
$891$		−	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
$900$	−24.8794	−	3.10229i	−0.829315	−	0.103410i
$901$		−	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	$0.0726951\pi$
$907$			13.6366i			0.452797i	−0.974035	+	0.226398i	$0.927305\pi$
$908$	−0.213376	−	0.166155i	−0.00708114	−	0.00551403i
$909$	−5.36094			−0.177811
$910$	−0.614857	+	9.90012i	−0.0203823	+	0.328186i
$911$	10.5097			0.348202			0.174101	−	0.984728i	$-0.444298\pi$
$911$	10.5097			0.348202			0.174101	+	0.984728i	$0.444298\pi$
$912$	−8.30096	−	8.99454i	−0.274872	−	0.297839i
$913$			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	$-0.731903\pi$
$919$		−	45.2388i		−	1.49229i	0.665784	−	0.746145i	$-0.268097\pi$
$920$	−31.4226	−	27.7627i	−1.03597	−	0.915309i
$921$	−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	$0.598851\pi$
$930$	−24.3296	−	1.51101i	−0.797798	−	0.0495480i
$931$	−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
$940$	7.01816	+	16.9498i	0.228907	+	0.552840i
$941$			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	$-0.519097\pi$
$947$	−3.69022			−0.119916			−0.0599580	+	0.998201i	$0.519097\pi$
$948$	7.07154	+	5.50656i	0.229673	+	0.178845i
$949$			17.1141i			0.555548i
$950$	−2.49070	+	30.7213i	−0.0808089	+	0.996730i
$951$			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
$960$	−7.50069	−	10.0713i	−0.242084	−	0.325051i
$961$	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	$-0.778195\pi$
$967$	−47.6952			−1.53377			−0.766886	+	0.641783i	$0.778195\pi$
$968$	−4.67492	+	22.2583i	−0.150258	+	0.715410i
$969$	6.75752	+	12.4361i	0.217083	+	0.399504i
$970$	0.666365	−	10.7295i	0.0213957	−	0.344503i
$971$	−13.1772			−0.422876			−0.211438	−	0.977391i	$-0.567815\pi$
$971$	−13.1772			−0.422876			−0.211438	+	0.977391i	$0.567815\pi$
$972$	−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
$980$	−9.56782	−	23.1075i	−0.305633	−	0.738142i
$981$			4.27997i			0.136649i
$982$	6.43816	+	13.1732i	0.205450	+	0.420374i
$983$		−	39.4865i		−	1.25942i	−0.776829	−	0.629711i	$-0.783173\pi$
$983$		−	39.4865i		−	1.25942i	0.776829	−	0.629711i	$-0.216827\pi$
$984$	−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
$988$	−22.7398	−	3.75999i	−0.723450	−	0.119621i
$989$	−61.6403			−1.96005
$990$	−13.6117	−	0.845368i	−0.432608	−	0.0268676i
$991$	32.4827			1.03185			0.515923	−	0.856635i	$-0.327449\pi$
$991$	32.4827			1.03185			0.515923	+	0.856635i	$0.327449\pi$
$992$	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.379.8	yes	40
4.3	odd	2	inner	380.2.d.b.379.6	yes	40
5.4	even	2	inner	380.2.d.b.379.33	yes	40
19.18	odd	2	inner	380.2.d.b.379.34	yes	40
20.19	odd	2	inner	380.2.d.b.379.35	yes	40
76.75	even	2	inner	380.2.d.b.379.36	yes	40
95.94	odd	2	inner	380.2.d.b.379.7	yes	40
380.379	even	2	inner	380.2.d.b.379.5	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.d.b.379.5	✓	40	380.379	even	2	inner
380.2.d.b.379.6	yes	40	4.3	odd	2	inner
380.2.d.b.379.7	yes	40	95.94	odd	2	inner
380.2.d.b.379.8	yes	40	1.1	even	1	trivial
380.2.d.b.379.33	yes	40	5.4	even	2	inner
380.2.d.b.379.34	yes	40	19.18	odd	2	inner
380.2.d.b.379.35	yes	40	20.19	odd	2	inner
380.2.d.b.379.36	yes	40	76.75	even	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} +(0.196019 - 3.15620i) 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} +(1.71086 + 4.13194i) 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} +(-2.21562 - 0.137603i) 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} +(-5.02260 - 3.57400i) q^{38} +1.85596i q^{39} +(-4.73963 - 4.18759i) 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} +(5.91993 + 3.86709i) 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} +(2.90058 - 1.20100i) 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} +(0.232561 - 3.74458i) 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} +(8.60101 + 1.42216i) q^{76} -2.04078i q^{77} +(-1.15250 - 2.35815i) q^{78} -6.38375 q^{79} +(8.62250 + 2.37751i) 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} +(0.491461 - 7.91325i) 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

Properties

Related objects

Downloads

Learn more