LMFDB - Embedded newform 1216.2.k.b.305.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(305,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1216.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.k (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 304)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			305.30
Character	$\chi$	$=$	1216.305
Dual form			1216.2.k.b.913.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.89015 - 1.89015i) q^{3} +(-1.06645 - 1.06645i) q^{5} -4.02959i q^{7} -4.14533i q^{9} +O(q^{10})$	\(q+(1.89015 - 1.89015i) q^{3} +(-1.06645 - 1.06645i) q^{5} -4.02959i q^{7} -4.14533i q^{9} +(-0.552303 - 0.552303i) q^{11} +(-4.37311 + 4.37311i) q^{13} -4.03151 q^{15} +0.608142 q^{17} +(0.707107 - 0.707107i) q^{19} +(-7.61653 - 7.61653i) q^{21} -0.900783i q^{23} -2.72536i q^{25} +(-2.16485 - 2.16485i) q^{27} +(6.34029 - 6.34029i) q^{29} -7.50604 q^{31} -2.08787 q^{33} +(-4.29737 + 4.29737i) q^{35} +(4.12547 + 4.12547i) q^{37} +16.5317i q^{39} +3.15335i q^{41} +(4.34630 + 4.34630i) q^{43} +(-4.42080 + 4.42080i) q^{45} -12.4949 q^{47} -9.23758 q^{49} +(1.14948 - 1.14948i) q^{51} +(0.257543 + 0.257543i) q^{53} +1.17801i q^{55} -2.67308i q^{57} +(3.92257 + 3.92257i) q^{59} +(4.73541 - 4.73541i) q^{61} -16.7040 q^{63} +9.32743 q^{65} +(9.32201 - 9.32201i) q^{67} +(-1.70262 - 1.70262i) q^{69} -0.270319i q^{71} -12.3210i q^{73} +(-5.15133 - 5.15133i) q^{75} +(-2.22555 + 2.22555i) q^{77} +1.74353 q^{79} +4.25220 q^{81} +(2.77691 - 2.77691i) q^{83} +(-0.648554 - 0.648554i) q^{85} -23.9682i q^{87} +10.4507i q^{89} +(17.6218 + 17.6218i) q^{91} +(-14.1875 + 14.1875i) q^{93} -1.50819 q^{95} -3.49540 q^{97} +(-2.28948 + 2.28948i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 4 q^{3} + 8 q^{5}+O(q^{10}) $ 68 * q - 4 * q^3 + 8 * q^5	$ 68 q - 4 q^{3} + 8 q^{5} - 4 q^{11} + 16 q^{15} + 4 q^{17} + 16 q^{21} - 28 q^{27} - 32 q^{31} - 16 q^{33} + 24 q^{35} - 24 q^{37} + 16 q^{43} + 24 q^{47} - 56 q^{49} + 52 q^{51} + 32 q^{53} - 28 q^{59} - 24 q^{63} - 16 q^{65} - 28 q^{67} - 8 q^{69} - 44 q^{75} - 12 q^{77} - 8 q^{79} - 76 q^{81} - 40 q^{83} - 8 q^{85} + 4 q^{91} - 84 q^{93} - 32 q^{95} - 16 q^{97} + 24 q^{99}+O(q^{100}) $ 68 * q - 4 * q^3 + 8 * q^5 - 4 * q^11 + 16 * q^15 + 4 * q^17 + 16 * q^21 - 28 * q^27 - 32 * q^31 - 16 * q^33 + 24 * q^35 - 24 * q^37 + 16 * q^43 + 24 * q^47 - 56 * q^49 + 52 * q^51 + 32 * q^53 - 28 * q^59 - 24 * q^63 - 16 * q^65 - 28 * q^67 - 8 * q^69 - 44 * q^75 - 12 * q^77 - 8 * q^79 - 76 * q^81 - 40 * q^83 - 8 * q^85 + 4 * q^91 - 84 * q^93 - 32 * q^95 - 16 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.89015	−	1.89015i	1.09128	−	1.09128i	0.0958864	−	0.995392i	$-0.469431\pi$
$3$	1.89015	−	1.89015i	1.09128	−	1.09128i	0.995392	−	0.0958864i	$-0.0305685\pi$
$4$		0			0
$5$	−1.06645	−	1.06645i	−0.476932	−	0.476932i	0.427217	−	0.904149i	$-0.359494\pi$
$5$	−1.06645	−	1.06645i	−0.476932	−	0.476932i	−0.904149	+	0.427217i	$0.859494\pi$
$6$		0			0
$7$		−	4.02959i		−	1.52304i	−0.648141	−	0.761521i	$-0.724453\pi$
$7$		−	4.02959i		−	1.52304i	0.648141	−	0.761521i	$-0.275547\pi$
$8$		0			0
$9$		−	4.14533i		−	1.38178i
$10$		0			0
$11$	−0.552303	−	0.552303i	−0.166526	−	0.166526i	0.618925	−	0.785450i	$-0.287569\pi$
$11$	−0.552303	−	0.552303i	−0.166526	−	0.166526i	−0.785450	+	0.618925i	$0.787569\pi$
$12$		0			0
$13$	−4.37311	+	4.37311i	−1.21288	+	1.21288i	−0.242807	+	0.970075i	$0.578068\pi$
$13$	−4.37311	+	4.37311i	−1.21288	+	1.21288i	−0.970075	+	0.242807i	$0.921932\pi$
$14$		0			0
$15$	−4.03151			−1.04093
$16$		0			0
$17$	0.608142			0.147496			0.0737480	−	0.997277i	$-0.476504\pi$
$17$	0.608142			0.147496			0.0737480	+	0.997277i	$0.476504\pi$
$18$		0			0
$19$	0.707107	−	0.707107i	0.162221	−	0.162221i
$19$	0.707107	−	0.707107i	0.162221	−	0.162221i
$20$		0			0
$21$	−7.61653	−	7.61653i	−1.66206	−	1.66206i
$22$		0			0
$23$		−	0.900783i		−	0.187826i	−0.995580	−	0.0939132i	$-0.970062\pi$
$23$		−	0.900783i		−	0.187826i	0.995580	−	0.0939132i	$-0.0299376\pi$
$24$		0			0
$25$		−	2.72536i		−	0.545071i
$26$		0			0
$27$	−2.16485	−	2.16485i	−0.416626	−	0.416626i
$28$		0			0
$29$	6.34029	−	6.34029i	1.17736	−	1.17736i	0.196949	−	0.980414i	$-0.436897\pi$
$29$	6.34029	−	6.34029i	1.17736	−	1.17736i	0.980414	−	0.196949i	$-0.0631033\pi$
$30$		0			0
$31$	−7.50604			−1.34813			−0.674063	−	0.738674i	$-0.735452\pi$
$31$	−7.50604			−1.34813			−0.674063	+	0.738674i	$0.735452\pi$
$32$		0			0
$33$	−2.08787			−0.363452
$34$		0			0
$35$	−4.29737	+	4.29737i	−0.726387	+	0.726387i
$36$		0			0
$37$	4.12547	+	4.12547i	0.678223	+	0.678223i	0.959598	−	0.281375i	$-0.0907905\pi$
$37$	4.12547	+	4.12547i	0.678223	+	0.678223i	−0.281375	+	0.959598i	$0.590790\pi$
$38$		0			0
$39$			16.5317i			2.64718i
$40$		0			0
$41$			3.15335i			0.492471i	0.969210	+	0.246236i	$0.0791937\pi$
$41$			3.15335i			0.492471i	−0.969210	+	0.246236i	$0.920806\pi$
$42$		0			0
$43$	4.34630	+	4.34630i	0.662805	+	0.662805i	0.956040	−	0.293235i	$-0.0947319\pi$
$43$	4.34630	+	4.34630i	0.662805	+	0.662805i	−0.293235	+	0.956040i	$0.594732\pi$
$44$		0			0
$45$	−4.42080	+	4.42080i	−0.659015	+	0.659015i
$46$		0			0
$47$	−12.4949			−1.82258			−0.911288	−	0.411770i	$-0.864911\pi$
$47$	−12.4949			−1.82258			−0.911288	+	0.411770i	$0.864911\pi$
$48$		0			0
$49$	−9.23758			−1.31965
$50$		0			0
$51$	1.14948	−	1.14948i	0.160959	−	0.160959i
$52$		0			0
$53$	0.257543	+	0.257543i	0.0353763	+	0.0353763i	0.724574	−	0.689197i	$-0.242037\pi$
$53$	0.257543	+	0.257543i	0.0353763	+	0.0353763i	−0.689197	+	0.724574i	$0.742037\pi$
$54$		0			0
$55$			1.17801i			0.158843i
$56$		0			0
$57$		−	2.67308i		−	0.354058i
$58$		0			0
$59$	3.92257	+	3.92257i	0.510675	+	0.510675i	0.914733	−	0.404059i	$-0.132401\pi$
$59$	3.92257	+	3.92257i	0.510675	+	0.510675i	−0.404059	+	0.914733i	$0.632401\pi$
$60$		0			0
$61$	4.73541	−	4.73541i	0.606307	−	0.606307i	−0.335672	−	0.941979i	$-0.608963\pi$
$61$	4.73541	−	4.73541i	0.606307	−	0.606307i	0.941979	+	0.335672i	$0.108963\pi$
$62$		0			0
$63$	−16.7040			−2.10451
$64$		0			0
$65$	9.32743			1.15692
$66$		0			0
$67$	9.32201	−	9.32201i	1.13886	−	1.13886i	0.150211	−	0.988654i	$-0.452005\pi$
$67$	9.32201	−	9.32201i	1.13886	−	1.13886i	0.988654	−	0.150211i	$-0.0479953\pi$
$68$		0			0
$69$	−1.70262	−	1.70262i	−0.204971	−	0.204971i
$70$		0			0
$71$		−	0.270319i		−	0.0320809i	−0.999871	−	0.0160405i	$-0.994894\pi$
$71$		−	0.270319i		−	0.0320809i	0.999871	−	0.0160405i	$-0.00510605\pi$
$72$		0			0
$73$		−	12.3210i		−	1.44206i	−0.692903	−	0.721031i	$-0.743669\pi$
$73$		−	12.3210i		−	1.44206i	0.692903	−	0.721031i	$-0.256331\pi$
$74$		0			0
$75$	−5.15133	−	5.15133i	−0.594825	−	0.594825i
$76$		0			0
$77$	−2.22555	+	2.22555i	−0.253625	+	0.253625i
$78$		0			0
$79$	1.74353			0.196162			0.0980810	−	0.995178i	$-0.468730\pi$
$79$	1.74353			0.196162			0.0980810	+	0.995178i	$0.468730\pi$
$80$		0			0
$81$	4.25220			0.472467
$82$		0			0
$83$	2.77691	−	2.77691i	0.304805	−	0.304805i	−0.538085	−	0.842890i	$-0.680852\pi$
$83$	2.77691	−	2.77691i	0.304805	−	0.304805i	0.842890	+	0.538085i	$0.180852\pi$
$84$		0			0
$85$	−0.648554	−	0.648554i	−0.0703456	−	0.0703456i
$86$		0			0
$87$		−	23.9682i		−	2.56966i
$88$		0			0
$89$			10.4507i			1.10778i	0.832591	+	0.553888i	$0.186856\pi$
$89$			10.4507i			1.10778i	−0.832591	+	0.553888i	$0.813144\pi$
$90$		0			0
$91$	17.6218	+	17.6218i	1.84727	+	1.84727i
$92$		0			0
$93$	−14.1875	+	14.1875i	−1.47118	+	1.47118i
$94$		0			0
$95$	−1.50819			−0.154737
$96$		0			0
$97$	−3.49540			−0.354904			−0.177452	−	0.984129i	$-0.556785\pi$
$97$	−3.49540			−0.354904			−0.177452	+	0.984129i	$0.556785\pi$
$98$		0			0
$99$	−2.28948	+	2.28948i	−0.230102	+	0.230102i
$100$		0			0
$101$	−12.3075	−	12.3075i	−1.22464	−	1.22464i	−0.965965	−	0.258673i	$-0.916715\pi$
$101$	−12.3075	−	12.3075i	−1.22464	−	1.22464i	−0.258673	−	0.965965i	$-0.583285\pi$
$102$		0			0
$103$		−	5.57914i		−	0.549729i	−0.961483	−	0.274865i	$-0.911367\pi$
$103$		−	5.57914i		−	0.549729i	0.961483	−	0.274865i	$-0.0886330\pi$
$104$		0			0
$105$			16.2453i			1.58538i
$106$		0			0
$107$	−4.04485	−	4.04485i	−0.391031	−	0.391031i	0.484024	−	0.875055i	$-0.339175\pi$
$107$	−4.04485	−	4.04485i	−0.391031	−	0.391031i	−0.875055	+	0.484024i	$0.839175\pi$
$108$		0			0
$109$	3.65197	−	3.65197i	0.349796	−	0.349796i	−0.510238	−	0.860033i	$-0.670443\pi$
$109$	3.65197	−	3.65197i	0.349796	−	0.349796i	0.860033	+	0.510238i	$0.170443\pi$
$110$		0			0
$111$	15.5955			1.48026
$112$		0			0
$113$	−4.70937			−0.443020			−0.221510	−	0.975158i	$-0.571099\pi$
$113$	−4.70937			−0.443020			−0.221510	+	0.975158i	$0.571099\pi$
$114$		0			0
$115$	−0.960643	+	0.960643i	−0.0895804	+	0.0895804i
$116$		0			0
$117$	18.1280	+	18.1280i	1.67593	+	1.67593i
$118$		0			0
$119$		−	2.45056i		−	0.224643i
$120$		0			0
$121$		−	10.3899i		−	0.944538i
$122$		0			0
$123$	5.96031	+	5.96031i	0.537423	+	0.537423i
$124$		0			0
$125$	−8.23873	+	8.23873i	−0.736894	+	0.736894i
$126$		0			0
$127$	15.6940			1.39262			0.696311	−	0.717741i	$-0.254824\pi$
$127$	15.6940			1.39262			0.696311	+	0.717741i	$0.254824\pi$
$128$		0			0
$129$	16.4303			1.44661
$130$		0			0
$131$	−1.22078	+	1.22078i	−0.106660	+	0.106660i	−0.758423	−	0.651763i	$-0.774030\pi$
$131$	−1.22078	+	1.22078i	−0.106660	+	0.106660i	0.651763	+	0.758423i	$0.274030\pi$
$132$		0			0
$133$	−2.84935	−	2.84935i	−0.247070	−	0.247070i
$134$		0			0
$135$			4.61743i			0.397405i
$136$		0			0
$137$			0.501149i			0.0428160i	0.999771	+	0.0214080i	$0.00681491\pi$
$137$			0.501149i			0.0428160i	−0.999771	+	0.0214080i	$0.993185\pi$
$138$		0			0
$139$	−9.02230	−	9.02230i	−0.765261	−	0.765261i	0.212007	−	0.977268i	$-0.432000\pi$
$139$	−9.02230	−	9.02230i	−0.765261	−	0.765261i	−0.977268	+	0.212007i	$0.932000\pi$
$140$		0			0
$141$	−23.6173	+	23.6173i	−1.98894	+	1.98894i
$142$		0			0
$143$	4.83056			0.403952
$144$		0			0
$145$	−13.5232			−1.12304
$146$		0			0
$147$	−17.4604	+	17.4604i	−1.44011	+	1.44011i
$148$		0			0
$149$	15.6712	+	15.6712i	1.28383	+	1.28383i	0.938469	+	0.345363i	$0.112244\pi$
$149$	15.6712	+	15.6712i	1.28383	+	1.28383i	0.345363	+	0.938469i	$0.387756\pi$
$150$		0			0
$151$		−	12.8059i		−	1.04213i	−0.853516	−	0.521066i	$-0.825534\pi$
$151$		−	12.8059i		−	1.04213i	0.853516	−	0.521066i	$-0.174466\pi$
$152$		0			0
$153$		−	2.52095i		−	0.203807i
$154$		0			0
$155$	8.00484	+	8.00484i	0.642964	+	0.642964i
$156$		0			0
$157$	13.3219	−	13.3219i	1.06320	−	1.06320i	0.0653374	−	0.997863i	$-0.479188\pi$
$157$	13.3219	−	13.3219i	1.06320	−	1.06320i	0.997863	−	0.0653374i	$-0.0208124\pi$
$158$		0			0
$159$	0.973591			0.0772108
$160$		0			0
$161$	−3.62979			−0.286067
$162$		0			0
$163$	−2.50875	+	2.50875i	−0.196501	+	0.196501i	−0.798498	−	0.601997i	$-0.794372\pi$
$163$	−2.50875	+	2.50875i	−0.196501	+	0.196501i	0.601997	+	0.798498i	$0.294372\pi$
$164$		0			0
$165$	2.22662	+	2.22662i	0.173342	+	0.173342i
$166$		0			0
$167$			13.2280i			1.02361i	0.859101	+	0.511806i	$0.171023\pi$
$167$			13.2280i			1.02361i	−0.859101	+	0.511806i	$0.828977\pi$
$168$		0			0
$169$		−	25.2481i		−	1.94216i
$170$		0			0
$171$	−2.93119	−	2.93119i	−0.224154	−	0.224154i
$172$		0			0
$173$	2.64423	−	2.64423i	0.201037	−	0.201037i	−0.599407	−	0.800444i	$-0.704597\pi$
$173$	2.64423	−	2.64423i	0.201037	−	0.201037i	0.800444	+	0.599407i	$0.204597\pi$
$174$		0			0
$175$	−10.9821			−0.830166
$176$		0			0
$177$	14.8285			1.11458
$178$		0			0
$179$	5.58253	−	5.58253i	0.417258	−	0.417258i	−0.467000	−	0.884257i	$-0.654665\pi$
$179$	5.58253	−	5.58253i	0.417258	−	0.417258i	0.884257	+	0.467000i	$0.154665\pi$
$180$		0			0
$181$	12.3479	+	12.3479i	0.917815	+	0.917815i	0.996870	−	0.0790555i	$-0.0251904\pi$
$181$	12.3479	+	12.3479i	0.917815	+	0.917815i	−0.0790555	+	0.996870i	$0.525190\pi$
$182$		0			0
$183$		−	17.9013i		−	1.32330i
$184$		0			0
$185$		−	8.79924i		−	0.646933i
$186$		0			0
$187$	−0.335879	−	0.335879i	−0.0245619	−	0.0245619i
$188$		0			0
$189$	−8.72347	+	8.72347i	−0.634539	+	0.634539i
$190$		0			0
$191$	−2.01504			−0.145804			−0.0729018	−	0.997339i	$-0.523226\pi$
$191$	−2.01504			−0.145804			−0.0729018	+	0.997339i	$0.523226\pi$
$192$		0			0
$193$	2.51436			0.180987			0.0904937	−	0.995897i	$-0.471155\pi$
$193$	2.51436			0.180987			0.0904937	+	0.995897i	$0.471155\pi$
$194$		0			0
$195$	17.6302	−	17.6302i	1.26253	−	1.26253i
$196$		0			0
$197$	8.73121	+	8.73121i	0.622073	+	0.622073i	0.946061	−	0.323988i	$-0.105024\pi$
$197$	8.73121	+	8.73121i	0.622073	+	0.622073i	−0.323988	+	0.946061i	$0.605024\pi$
$198$		0			0
$199$		−	3.61211i		−	0.256056i	−0.991771	−	0.128028i	$-0.959135\pi$
$199$		−	3.61211i		−	0.256056i	0.991771	−	0.128028i	$-0.0408647\pi$
$200$		0			0
$201$		−	35.2400i		−	2.48564i
$202$		0			0
$203$	−25.5488	−	25.5488i	−1.79317	−	1.79317i
$204$		0			0
$205$	3.36290	−	3.36290i	0.234875	−	0.234875i
$206$		0			0
$207$	−3.73405			−0.259534
$208$		0			0
$209$	−0.781075			−0.0540281
$210$		0			0
$211$	−3.51585	+	3.51585i	−0.242041	+	0.242041i	−0.817694	−	0.575653i	$-0.804748\pi$
$211$	−3.51585	+	3.51585i	−0.242041	+	0.242041i	0.575653	+	0.817694i	$0.304748\pi$
$212$		0			0
$213$	−0.510943	−	0.510943i	−0.0350092	−	0.0350092i
$214$		0			0
$215$		−	9.27026i		−	0.632226i
$216$		0			0
$217$			30.2463i			2.05325i
$218$		0			0
$219$	−23.2885	−	23.2885i	−1.57369	−	1.57369i
$220$		0			0
$221$	−2.65947	+	2.65947i	−0.178895	+	0.178895i
$222$		0			0
$223$	25.9333			1.73663			0.868313	−	0.496017i	$-0.165205\pi$
$223$	25.9333			1.73663			0.868313	+	0.496017i	$0.165205\pi$
$224$		0			0
$225$	−11.2975			−0.753168
$226$		0			0
$227$	−15.5390	+	15.5390i	−1.03136	+	1.03136i	−0.0318692	+	0.999492i	$0.510146\pi$
$227$	−15.5390	+	15.5390i	−1.03136	+	1.03136i	−0.999492	+	0.0318692i	$0.989854\pi$
$228$		0			0
$229$	−7.93339	−	7.93339i	−0.524253	−	0.524253i	0.394600	−	0.918853i	$-0.370883\pi$
$229$	−7.93339	−	7.93339i	−0.524253	−	0.524253i	−0.918853	+	0.394600i	$0.870883\pi$
$230$		0			0
$231$			8.41326i			0.553552i
$232$		0			0
$233$		−	13.0596i		−	0.855564i	−0.903882	−	0.427782i	$-0.859295\pi$
$233$		−	13.0596i		−	0.855564i	0.903882	−	0.427782i	$-0.140705\pi$
$234$		0			0
$235$	13.3253	+	13.3253i	0.869245	+	0.869245i
$236$		0			0
$237$	3.29553	−	3.29553i	0.214067	−	0.214067i
$238$		0			0
$239$	−3.88146			−0.251071			−0.125535	−	0.992089i	$-0.540065\pi$
$239$	−3.88146			−0.251071			−0.125535	+	0.992089i	$0.540065\pi$
$240$		0			0
$241$	−21.7242			−1.39938			−0.699689	−	0.714448i	$-0.746678\pi$
$241$	−21.7242			−1.39938			−0.699689	+	0.714448i	$0.746678\pi$
$242$		0			0
$243$	14.5319	−	14.5319i	0.932220	−	0.932220i
$244$		0			0
$245$	9.85145	+	9.85145i	0.629386	+	0.629386i
$246$		0			0
$247$			6.18451i			0.393511i
$248$		0			0
$249$		−	10.4975i		−	0.665255i
$250$		0			0
$251$	20.9875	+	20.9875i	1.32472	+	1.32472i	0.909909	+	0.414807i	$0.136151\pi$
$251$	20.9875	+	20.9875i	1.32472	+	1.32472i	0.414807	+	0.909909i	$0.363849\pi$
$252$		0			0
$253$	−0.497505	+	0.497505i	−0.0312779	+	0.0312779i
$254$		0			0
$255$	−2.45173			−0.153533
$256$		0			0
$257$	3.05424			0.190518			0.0952590	−	0.995453i	$-0.469632\pi$
$257$	3.05424			0.190518			0.0952590	+	0.995453i	$0.469632\pi$
$258$		0			0
$259$	16.6239	−	16.6239i	1.03296	−	1.03296i
$260$		0			0
$261$	−26.2826	−	26.2826i	−1.62685	−	1.62685i
$262$		0			0
$263$			19.3970i			1.19607i	0.801469	+	0.598036i	$0.204052\pi$
$263$			19.3970i			1.19607i	−0.801469	+	0.598036i	$0.795948\pi$
$264$		0			0
$265$		−	0.549315i		−	0.0337442i
$266$		0			0
$267$	19.7535	+	19.7535i	1.20889	+	1.20889i
$268$		0			0
$269$	12.1781	−	12.1781i	0.742514	−	0.742514i	−0.230547	−	0.973061i	$-0.574052\pi$
$269$	12.1781	−	12.1781i	0.742514	−	0.742514i	0.973061	+	0.230547i	$0.0740516\pi$
$270$		0			0
$271$	18.7432			1.13857			0.569285	−	0.822140i	$-0.307220\pi$
$271$	18.7432			1.13857			0.569285	+	0.822140i	$0.307220\pi$
$272$		0			0
$273$	66.6158			4.03177
$274$		0			0
$275$	−1.50522	+	1.50522i	−0.0907684	+	0.0907684i
$276$		0			0
$277$	4.84631	+	4.84631i	0.291187	+	0.291187i	0.837549	−	0.546362i	$-0.183988\pi$
$277$	4.84631	+	4.84631i	0.291187	+	0.291187i	−0.546362	+	0.837549i	$0.683988\pi$
$278$		0			0
$279$			31.1151i			1.86281i
$280$		0			0
$281$			7.27330i			0.433889i	0.976184	+	0.216944i	$0.0696090\pi$
$281$			7.27330i			0.433889i	−0.976184	+	0.216944i	$0.930391\pi$
$282$		0			0
$283$	4.02007	+	4.02007i	0.238968	+	0.238968i	0.816423	−	0.577455i	$-0.195954\pi$
$283$	4.02007	+	4.02007i	0.238968	+	0.238968i	−0.577455	+	0.816423i	$0.695954\pi$
$284$		0			0
$285$	−2.85071	+	2.85071i	−0.168861	+	0.168861i
$286$		0			0
$287$	12.7067			0.750054
$288$		0			0
$289$	−16.6302			−0.978245
$290$		0			0
$291$	−6.60683	+	6.60683i	−0.387299	+	0.387299i
$292$		0			0
$293$	13.2722	+	13.2722i	0.775370	+	0.775370i	0.979040	−	0.203670i	$-0.0652869\pi$
$293$	13.2722	+	13.2722i	0.775370	+	0.775370i	−0.203670	+	0.979040i	$0.565287\pi$
$294$		0			0
$295$		−	8.36646i		−	0.487114i
$296$		0			0
$297$			2.39131i			0.138758i
$298$		0			0
$299$	3.93922	+	3.93922i	0.227811	+	0.227811i
$300$		0			0
$301$	17.5138	−	17.5138i	1.00948	−	1.00948i
$302$		0			0
$303$	−46.5259			−2.67284
$304$		0			0
$305$	−10.1002			−0.578335
$306$		0			0
$307$	−14.4957	+	14.4957i	−0.827315	+	0.827315i	−0.987145	−	0.159830i	$-0.948906\pi$
$307$	−14.4957	+	14.4957i	−0.827315	+	0.827315i	0.159830	+	0.987145i	$0.448906\pi$
$308$		0			0
$309$	−10.5454	−	10.5454i	−0.599908	−	0.599908i
$310$		0			0
$311$		−	5.20251i		−	0.295007i	−0.989062	−	0.147504i	$-0.952876\pi$
$311$		−	5.20251i		−	0.295007i	0.989062	−	0.147504i	$-0.0471238\pi$
$312$		0			0
$313$		−	25.8149i		−	1.45914i	−0.683904	−	0.729572i	$-0.739719\pi$
$313$		−	25.8149i		−	1.45914i	0.683904	−	0.729572i	$-0.260281\pi$
$314$		0			0
$315$	17.8140	+	17.8140i	1.00371	+	1.00371i
$316$		0			0
$317$	13.8188	−	13.8188i	0.776142	−	0.776142i	−0.203030	−	0.979172i	$-0.565079\pi$
$317$	13.8188	−	13.8188i	0.776142	−	0.776142i	0.979172	+	0.203030i	$0.0650790\pi$
$318$		0			0
$319$	−7.00353			−0.392122
$320$		0			0
$321$	−15.2908			−0.853447
$322$		0			0
$323$	0.430021	−	0.430021i	0.0239270	−	0.0239270i
$324$		0			0
$325$	11.9183	+	11.9183i	0.661107	+	0.661107i
$326$		0			0
$327$		−	13.8056i		−	0.763449i
$328$		0			0
$329$			50.3495i			2.77586i
$330$		0			0
$331$	12.6291	+	12.6291i	0.694160	+	0.694160i	0.963144	−	0.268985i	$-0.0866882\pi$
$331$	12.6291	+	12.6291i	0.694160	+	0.694160i	−0.268985	+	0.963144i	$0.586688\pi$
$332$		0			0
$333$	17.1014	−	17.1014i	0.937154	−	0.937154i
$334$		0			0
$335$	−19.8830			−1.08632
$336$		0			0
$337$	−11.1511			−0.607438			−0.303719	−	0.952762i	$-0.598228\pi$
$337$	−11.1511			−0.607438			−0.303719	+	0.952762i	$0.598228\pi$
$338$		0			0
$339$	−8.90141	+	8.90141i	−0.483458	+	0.483458i
$340$		0			0
$341$	4.14561	+	4.14561i	0.224497	+	0.224497i
$342$		0			0
$343$			9.01654i			0.486847i
$344$		0			0
$345$			3.63152i			0.195514i
$346$		0			0
$347$	10.3939	+	10.3939i	0.557974	+	0.557974i	0.928730	−	0.370756i	$-0.120901\pi$
$347$	10.3939	+	10.3939i	0.557974	+	0.557974i	−0.370756	+	0.928730i	$0.620901\pi$
$348$		0			0
$349$	−10.9522	+	10.9522i	−0.586258	+	0.586258i	−0.936616	−	0.350358i	$-0.886060\pi$
$349$	−10.9522	+	10.9522i	−0.586258	+	0.586258i	0.350358	+	0.936616i	$0.386060\pi$
$350$		0			0
$351$	18.9343			1.01064
$352$		0			0
$353$	28.2593			1.50409			0.752045	−	0.659111i	$-0.229067\pi$
$353$	28.2593			1.50409			0.752045	+	0.659111i	$0.229067\pi$
$354$		0			0
$355$	−0.288282	+	0.288282i	−0.0153004	+	0.0153004i
$356$		0			0
$357$	−4.63193	−	4.63193i	−0.245148	−	0.245148i
$358$		0			0
$359$			6.64825i			0.350881i	0.984490	+	0.175441i	$0.0561350\pi$
$359$			6.64825i			0.350881i	−0.984490	+	0.175441i	$0.943865\pi$
$360$		0			0
$361$		−	1.00000i		−	0.0526316i
$362$		0			0
$363$	−19.6385	−	19.6385i	−1.03075	−	1.03075i
$364$		0			0
$365$	−13.1397	+	13.1397i	−0.687765	+	0.687765i
$366$		0			0
$367$	8.84035			0.461462			0.230731	−	0.973018i	$-0.425888\pi$
$367$	8.84035			0.461462			0.230731	+	0.973018i	$0.425888\pi$
$368$		0			0
$369$	13.0717			0.680486
$370$		0			0
$371$	1.03779	−	1.03779i	0.0538795	−	0.0538795i
$372$		0			0
$373$	−8.66241	−	8.66241i	−0.448522	−	0.448522i	0.446341	−	0.894863i	$-0.352727\pi$
$373$	−8.66241	−	8.66241i	−0.448522	−	0.448522i	−0.894863	+	0.446341i	$0.852727\pi$
$374$		0			0
$375$			31.1449i			1.60831i
$376$		0			0
$377$			55.4536i			2.85600i
$378$		0			0
$379$	−8.58240	−	8.58240i	−0.440848	−	0.440848i	0.451449	−	0.892297i	$-0.350907\pi$
$379$	−8.58240	−	8.58240i	−0.440848	−	0.440848i	−0.892297	+	0.451449i	$0.850907\pi$
$380$		0			0
$381$	29.6641	−	29.6641i	1.51974	−	1.51974i
$382$		0			0
$383$	29.4894			1.50684			0.753420	−	0.657540i	$-0.228403\pi$
$383$	29.4894			1.50684			0.753420	+	0.657540i	$0.228403\pi$
$384$		0			0
$385$	4.74690			0.241924
$386$		0			0
$387$	18.0169	−	18.0169i	0.915850	−	0.915850i
$388$		0			0
$389$	−9.54195	−	9.54195i	−0.483796	−	0.483796i	0.422546	−	0.906342i	$-0.361137\pi$
$389$	−9.54195	−	9.54195i	−0.483796	−	0.483796i	−0.906342	+	0.422546i	$0.861137\pi$
$390$		0			0
$391$		−	0.547804i		−	0.0277036i
$392$		0			0
$393$			4.61492i			0.232792i
$394$		0			0
$395$	−1.85939	−	1.85939i	−0.0935560	−	0.0935560i
$396$		0			0
$397$	−16.2249	+	16.2249i	−0.814306	+	0.814306i	−0.985276	−	0.170970i	$-0.945310\pi$
$397$	−16.2249	+	16.2249i	−0.814306	+	0.814306i	0.170970	+	0.985276i	$0.445310\pi$
$398$		0			0
$399$	−10.7714			−0.539244
$400$		0			0
$401$	10.8292			0.540783			0.270392	−	0.962750i	$-0.412847\pi$
$401$	10.8292			0.540783			0.270392	+	0.962750i	$0.412847\pi$
$402$		0			0
$403$	32.8247	−	32.8247i	1.63512	−	1.63512i
$404$		0			0
$405$	−4.53478	−	4.53478i	−0.225335	−	0.225335i
$406$		0			0
$407$		−	4.55702i		−	0.225883i
$408$		0			0
$409$			19.3955i			0.959048i	0.877529	+	0.479524i	$0.159191\pi$
$409$			19.3955i			0.959048i	−0.877529	+	0.479524i	$0.840809\pi$
$410$		0			0
$411$	0.947247	+	0.947247i	0.0467242	+	0.0467242i
$412$		0			0
$413$	15.8063	−	15.8063i	0.777779	−	0.777779i
$414$		0			0
$415$	−5.92288			−0.290743
$416$		0			0
$417$	−34.1070			−1.67023
$418$		0			0
$419$	−7.01113	+	7.01113i	−0.342516	+	0.342516i	−0.857313	−	0.514796i	$-0.827868\pi$
$419$	−7.01113	+	7.01113i	−0.342516	+	0.342516i	0.514796	+	0.857313i	$0.327868\pi$
$420$		0			0
$421$	4.19487	+	4.19487i	0.204445	+	0.204445i	0.801902	−	0.597456i	$-0.203822\pi$
$421$	4.19487	+	4.19487i	0.204445	+	0.204445i	−0.597456	+	0.801902i	$0.703822\pi$
$422$		0			0
$423$			51.7957i			2.51840i
$424$		0			0
$425$		−	1.65740i		−	0.0803959i
$426$		0			0
$427$	−19.0818	−	19.0818i	−0.923431	−	0.923431i
$428$		0			0
$429$	9.13049	−	9.13049i	0.440824	−	0.440824i
$430$		0			0
$431$	−1.34988			−0.0650215			−0.0325107	−	0.999471i	$-0.510350\pi$
$431$	−1.34988			−0.0650215			−0.0325107	+	0.999471i	$0.510350\pi$
$432$		0			0
$433$	29.1510			1.40091			0.700454	−	0.713698i	$-0.252981\pi$
$433$	29.1510			1.40091			0.700454	+	0.713698i	$0.252981\pi$
$434$		0			0
$435$	−25.5610	+	25.5610i	−1.22555	+	1.22555i
$436$		0			0
$437$	−0.636950	−	0.636950i	−0.0304695	−	0.0304695i
$438$		0			0
$439$		−	4.37163i		−	0.208646i	−0.994543	−	0.104323i	$-0.966732\pi$
$439$		−	4.37163i		−	0.208646i	0.994543	−	0.104323i	$-0.0332676\pi$
$440$		0			0
$441$			38.2929i			1.82347i
$442$		0			0
$443$	20.5023	+	20.5023i	0.974092	+	0.974092i	0.999673	−	0.0255807i	$-0.00814349\pi$
$443$	20.5023	+	20.5023i	0.974092	+	0.974092i	−0.0255807	+	0.999673i	$0.508143\pi$
$444$		0			0
$445$	11.1452	−	11.1452i	0.528334	−	0.528334i
$446$		0			0
$447$	59.2417			2.80204
$448$		0			0
$449$	−8.68234			−0.409745			−0.204873	−	0.978789i	$-0.565678\pi$
$449$	−8.68234			−0.409745			−0.204873	+	0.978789i	$0.565678\pi$
$450$		0			0
$451$	1.74161	−	1.74161i	0.0820091	−	0.0820091i
$452$		0			0
$453$	−24.2051	−	24.2051i	−1.13726	−	1.13726i
$454$		0			0
$455$		−	37.5857i		−	1.76204i
$456$		0			0
$457$			25.4118i			1.18871i	0.804202	+	0.594356i	$0.202593\pi$
$457$			25.4118i			1.18871i	−0.804202	+	0.594356i	$0.797407\pi$
$458$		0			0
$459$	−1.31654	−	1.31654i	−0.0614507	−	0.0614507i
$460$		0			0
$461$	−4.47785	+	4.47785i	−0.208554	+	0.208554i	−0.803653	−	0.595098i	$-0.797113\pi$
$461$	−4.47785	+	4.47785i	−0.208554	+	0.208554i	0.595098	+	0.803653i	$0.297113\pi$
$462$		0			0
$463$	14.9185			0.693320			0.346660	−	0.937991i	$-0.387316\pi$
$463$	14.9185			0.693320			0.346660	+	0.937991i	$0.387316\pi$
$464$		0			0
$465$	30.2607			1.40331
$466$		0			0
$467$	−21.1197	+	21.1197i	−0.977301	+	0.977301i	−0.999748	−	0.0224468i	$-0.992854\pi$
$467$	−21.1197	+	21.1197i	−0.977301	+	0.977301i	0.0224468	+	0.999748i	$0.492854\pi$
$468$		0			0
$469$	−37.5639	−	37.5639i	−1.73454	−	1.73454i
$470$		0			0
$471$		−	50.3606i		−	2.32050i
$472$		0			0
$473$		−	4.80095i		−	0.220748i
$474$		0			0
$475$	−1.92712	−	1.92712i	−0.0884223	−	0.0884223i
$476$		0			0
$477$	1.06760	−	1.06760i	0.0488822	−	0.0488822i
$478$		0			0
$479$	−27.6920			−1.26528			−0.632641	−	0.774446i	$-0.718029\pi$
$479$	−27.6920			−1.26528			−0.632641	+	0.774446i	$0.718029\pi$
$480$		0			0
$481$	−36.0822			−1.64521
$482$		0			0
$483$	−6.86084	+	6.86084i	−0.312179	+	0.312179i
$484$		0			0
$485$	3.72768	+	3.72768i	0.169265	+	0.169265i
$486$		0			0
$487$			35.2062i			1.59534i	0.603091	+	0.797672i	$0.293935\pi$
$487$			35.2062i			1.59534i	−0.603091	+	0.797672i	$0.706065\pi$
$488$		0			0
$489$			9.48384i			0.428874i
$490$		0			0
$491$	−21.0214	−	21.0214i	−0.948681	−	0.948681i	0.0500647	−	0.998746i	$-0.484057\pi$
$491$	−21.0214	−	21.0214i	−0.948681	−	0.948681i	−0.998746	+	0.0500647i	$0.984057\pi$
$492$		0			0
$493$	3.85580	−	3.85580i	0.173656	−	0.173656i
$494$		0			0
$495$	4.88325			0.219486
$496$		0			0
$497$	−1.08927			−0.0488605
$498$		0			0
$499$	0.953966	−	0.953966i	0.0427054	−	0.0427054i	−0.685432	−	0.728137i	$-0.740386\pi$
$499$	0.953966	−	0.953966i	0.0427054	−	0.0427054i	0.728137	+	0.685432i	$0.240386\pi$
$500$		0			0
$501$	25.0029	+	25.0029i	1.11705	+	1.11705i
$502$		0			0
$503$			4.28185i			0.190918i	0.995433	+	0.0954592i	$0.0304320\pi$
$503$			4.28185i			0.190918i	−0.995433	+	0.0954592i	$0.969568\pi$
$504$		0			0
$505$			26.2506i			1.16814i
$506$		0			0
$507$	−47.7228	−	47.7228i	−2.11944	−	2.11944i
$508$		0			0
$509$	−21.8211	+	21.8211i	−0.967202	+	0.967202i	−0.999479	−	0.0322767i	$-0.989724\pi$
$509$	−21.8211	+	21.8211i	−0.967202	+	0.967202i	0.0322767	+	0.999479i	$0.489724\pi$
$510$		0			0
$511$	−49.6485			−2.19632
$512$		0			0
$513$	−3.06157			−0.135171
$514$		0			0
$515$	−5.94989	+	5.94989i	−0.262184	+	0.262184i
$516$		0			0
$517$	6.90100	+	6.90100i	0.303506	+	0.303506i
$518$		0			0
$519$		−	9.99598i		−	0.438775i
$520$		0			0
$521$		−	32.0921i		−	1.40598i	−0.711199	−	0.702991i	$-0.751848\pi$
$521$		−	32.0921i		−	1.40598i	0.711199	−	0.702991i	$-0.248152\pi$
$522$		0			0
$523$	−23.2846	−	23.2846i	−1.01816	−	1.01816i	−0.999832	−	0.0183319i	$-0.994164\pi$
$523$	−23.2846	−	23.2846i	−1.01816	−	1.01816i	−0.0183319	−	0.999832i	$-0.505836\pi$
$524$		0			0
$525$	−20.7578	+	20.7578i	−0.905943	+	0.905943i
$526$		0			0
$527$	−4.56474			−0.198843
$528$		0			0
$529$	22.1886			0.964721
$530$		0			0
$531$	16.2603	−	16.2603i	0.705639	−	0.705639i
$532$		0			0
$533$	−13.7900	−	13.7900i	−0.597309	−	0.597309i
$534$		0			0
$535$			8.62729i			0.372990i
$536$		0			0
$537$		−	21.1036i		−	0.910689i
$538$		0			0
$539$	5.10195	+	5.10195i	0.219756	+	0.219756i
$540$		0			0
$541$	−12.1744	+	12.1744i	−0.523420	+	0.523420i	−0.918602	−	0.395183i	$-0.870681\pi$
$541$	−12.1744	+	12.1744i	−0.523420	+	0.523420i	0.395183	+	0.918602i	$0.370681\pi$
$542$		0			0
$543$	46.6789			2.00318
$544$		0			0
$545$	−7.78931			−0.333658
$546$		0			0
$547$	10.7020	−	10.7020i	0.457584	−	0.457584i	−0.440277	−	0.897862i	$-0.645120\pi$
$547$	10.7020	−	10.7020i	0.457584	−	0.457584i	0.897862	+	0.440277i	$0.145120\pi$
$548$		0			0
$549$	−19.6299	−	19.6299i	−0.837782	−	0.837782i
$550$		0			0
$551$		−	8.96653i		−	0.381987i
$552$		0			0
$553$		−	7.02569i		−	0.298763i
$554$		0			0
$555$	−16.6319	−	16.6319i	−0.705984	−	0.705984i
$556$		0			0
$557$	10.6604	−	10.6604i	0.451695	−	0.451695i	−0.444222	−	0.895917i	$-0.646520\pi$
$557$	10.6604	−	10.6604i	0.451695	−	0.451695i	0.895917	+	0.444222i	$0.146520\pi$
$558$		0			0
$559$	−38.0137			−1.60781
$560$		0			0
$561$	−1.26972			−0.0536077
$562$		0			0
$563$	−12.8332	+	12.8332i	−0.540854	+	0.540854i	−0.923779	−	0.382926i	$-0.874917\pi$
$563$	−12.8332	+	12.8332i	−0.540854	+	0.540854i	0.382926	+	0.923779i	$0.374917\pi$
$564$		0			0
$565$	5.02232	+	5.02232i	0.211291	+	0.211291i
$566$		0			0
$567$		−	17.1346i		−	0.719587i
$568$		0			0
$569$		−	15.4815i		−	0.649020i	−0.945882	−	0.324510i	$-0.894801\pi$
$569$		−	15.4815i		−	0.649020i	0.945882	−	0.324510i	$-0.105199\pi$
$570$		0			0
$571$	−17.8262	−	17.8262i	−0.746004	−	0.746004i	0.227722	−	0.973726i	$-0.426872\pi$
$571$	−17.8262	−	17.8262i	−0.746004	−	0.746004i	−0.973726	+	0.227722i	$0.926872\pi$
$572$		0			0
$573$	−3.80874	+	3.80874i	−0.159112	+	0.159112i
$574$		0			0
$575$	−2.45496			−0.102379
$576$		0			0
$577$	−5.29423			−0.220401			−0.110201	−	0.993909i	$-0.535149\pi$
$577$	−5.29423			−0.220401			−0.110201	+	0.993909i	$0.535149\pi$
$578$		0			0
$579$	4.75251	−	4.75251i	0.197508	−	0.197508i
$580$		0			0
$581$	−11.1898	−	11.1898i	−0.464231	−	0.464231i
$582$		0			0
$583$		−	0.284484i		−	0.0117821i
$584$		0			0
$585$		−	38.6653i		−	1.59861i
$586$		0			0
$587$	27.4763	+	27.4763i	1.13407	+	1.13407i	0.989494	+	0.144574i	$0.0461811\pi$
$587$	27.4763	+	27.4763i	1.13407	+	1.13407i	0.144574	+	0.989494i	$0.453819\pi$
$588$		0			0
$589$	−5.30757	+	5.30757i	−0.218695	+	0.218695i
$590$		0			0
$591$	33.0066			1.35771
$592$		0			0
$593$	−26.3502			−1.08207			−0.541036	−	0.841000i	$-0.681968\pi$
$593$	−26.3502			−1.08207			−0.541036	+	0.841000i	$0.681968\pi$
$594$		0			0
$595$	−2.61341	+	2.61341i	−0.107139	+	0.107139i
$596$		0			0
$597$	−6.82744	−	6.82744i	−0.279428	−	0.279428i
$598$		0			0
$599$			18.7420i			0.765776i	0.923795	+	0.382888i	$0.125070\pi$
$599$			18.7420i			0.765776i	−0.923795	+	0.382888i	$0.874930\pi$
$600$		0			0
$601$			6.35121i			0.259071i	0.991575	+	0.129536i	$0.0413486\pi$
$601$			6.35121i			0.259071i	−0.991575	+	0.129536i	$0.958651\pi$
$602$		0			0
$603$	−38.6429	−	38.6429i	−1.57366	−	1.57366i
$604$		0			0
$605$	−11.0804	+	11.0804i	−0.450481	+	0.450481i
$606$		0			0
$607$	−21.4722			−0.871531			−0.435765	−	0.900060i	$-0.643522\pi$
$607$	−21.4722			−0.871531			−0.435765	+	0.900060i	$0.643522\pi$
$608$		0			0
$609$	−96.5820			−3.91370
$610$		0			0
$611$	54.6418	−	54.6418i	2.21057	−	2.21057i
$612$		0			0
$613$	29.5806	+	29.5806i	1.19475	+	1.19475i	0.975717	+	0.219033i	$0.0702904\pi$
$613$	29.5806	+	29.5806i	1.19475	+	1.19475i	0.219033	+	0.975717i	$0.429710\pi$
$614$		0			0
$615$		−	12.7128i		−	0.512629i
$616$		0			0
$617$		−	17.8609i		−	0.719051i	−0.933135	−	0.359525i	$-0.882939\pi$
$617$		−	17.8609i		−	0.719051i	0.933135	−	0.359525i	$-0.117061\pi$
$618$		0			0
$619$	3.98730	+	3.98730i	0.160263	+	0.160263i	0.782683	−	0.622420i	$-0.213850\pi$
$619$	3.98730	+	3.98730i	0.160263	+	0.160263i	−0.622420	+	0.782683i	$0.713850\pi$
$620$		0			0
$621$	−1.95006	+	1.95006i	−0.0782534	+	0.0782534i
$622$		0			0
$623$	42.1122			1.68719
$624$		0			0
$625$	3.94565			0.157826
$626$		0			0
$627$	−1.47635	+	1.47635i	−0.0589597	+	0.0589597i
$628$		0			0
$629$	2.50887	+	2.50887i	0.100035	+	0.100035i
$630$		0			0
$631$		−	30.3473i		−	1.20811i	−0.796944	−	0.604053i	$-0.793552\pi$
$631$		−	30.3473i		−	1.20811i	0.796944	−	0.604053i	$-0.206448\pi$
$632$		0			0
$633$			13.2910i			0.528269i
$634$		0			0
$635$	−16.7370	−	16.7370i	−0.664186	−	0.664186i
$636$		0			0
$637$	40.3969	−	40.3969i	1.60059	−	1.60059i
$638$		0			0
$639$	−1.12056			−0.0443287
$640$		0			0
$641$	−26.6647			−1.05319			−0.526595	−	0.850116i	$-0.676532\pi$
$641$	−26.6647			−1.05319			−0.526595	+	0.850116i	$0.676532\pi$
$642$		0			0
$643$	17.4776	−	17.4776i	0.689250	−	0.689250i	−0.272816	−	0.962066i	$-0.587955\pi$
$643$	17.4776	−	17.4776i	0.689250	−	0.689250i	0.962066	+	0.272816i	$0.0879550\pi$
$644$		0			0
$645$	−17.5222	−	17.5222i	−0.689935	−	0.689935i
$646$		0			0
$647$		−	21.9528i		−	0.863055i	−0.902100	−	0.431528i	$-0.857975\pi$
$647$		−	21.9528i		−	0.863055i	0.902100	−	0.431528i	$-0.142025\pi$
$648$		0			0
$649$		−	4.33289i		−	0.170081i
$650$		0			0
$651$	57.1700	+	57.1700i	2.24067	+	2.24067i
$652$		0			0
$653$	−20.4948	+	20.4948i	−0.802024	+	0.802024i	−0.983412	−	0.181387i	$-0.941941\pi$
$653$	−20.4948	+	20.4948i	−0.802024	+	0.802024i	0.181387	+	0.983412i	$0.441941\pi$
$654$		0			0
$655$	2.60381			0.101739
$656$		0			0
$657$	−51.0746			−1.99261
$658$		0			0
$659$	−36.1034	+	36.1034i	−1.40639	+	1.40639i	−0.628905	+	0.777482i	$0.716496\pi$
$659$	−36.1034	+	36.1034i	−1.40639	+	1.40639i	−0.777482	+	0.628905i	$0.783504\pi$
$660$		0			0
$661$	−6.46495	−	6.46495i	−0.251457	−	0.251457i	0.570111	−	0.821568i	$-0.306900\pi$
$661$	−6.46495	−	6.46495i	−0.251457	−	0.251457i	−0.821568	+	0.570111i	$0.806900\pi$
$662$		0			0
$663$			10.0536i			0.390449i
$664$		0			0
$665$			6.07739i			0.235671i
$666$		0			0
$667$	−5.71123	−	5.71123i	−0.221140	−	0.221140i
$668$		0			0
$669$	49.0179	−	49.0179i	1.89514	−	1.89514i
$670$		0			0
$671$	−5.23077			−0.201932
$672$		0			0
$673$	4.15503			0.160165			0.0800823	−	0.996788i	$-0.474482\pi$
$673$	4.15503			0.160165			0.0800823	+	0.996788i	$0.474482\pi$
$674$		0			0
$675$	−5.90000	+	5.90000i	−0.227091	+	0.227091i
$676$		0			0
$677$	−2.06257	−	2.06257i	−0.0792710	−	0.0792710i	0.666360	−	0.745631i	$-0.267852\pi$
$677$	−2.06257	−	2.06257i	−0.0792710	−	0.0792710i	−0.745631	+	0.666360i	$0.767852\pi$
$678$		0			0
$679$			14.0850i			0.540534i
$680$		0			0
$681$			58.7422i			2.25100i
$682$		0			0
$683$	−10.6287	−	10.6287i	−0.406695	−	0.406695i	0.473890	−	0.880584i	$-0.342850\pi$
$683$	−10.6287	−	10.6287i	−0.406695	−	0.406695i	−0.880584	+	0.473890i	$0.842850\pi$
$684$		0			0
$685$	0.534452	−	0.534452i	0.0204204	−	0.0204204i
$686$		0			0
$687$	−29.9906			−1.14421
$688$		0			0
$689$	−2.25253			−0.0858145
$690$		0			0
$691$	−16.9758	+	16.9758i	−0.645790	+	0.645790i	−0.951973	−	0.306183i	$-0.900948\pi$
$691$	−16.9758	+	16.9758i	−0.645790	+	0.645790i	0.306183	+	0.951973i	$0.400948\pi$
$692$		0			0
$693$	9.22567	+	9.22567i	0.350454	+	0.350454i
$694$		0			0
$695$			19.2437i			0.729956i
$696$		0			0
$697$			1.91769i			0.0726375i
$698$		0			0
$699$	−24.6847	−	24.6847i	−0.933659	−	0.933659i
$700$		0			0
$701$	−8.20712	+	8.20712i	−0.309979	+	0.309979i	−0.844901	−	0.534922i	$-0.820341\pi$
$701$	−8.20712	+	8.20712i	−0.309979	+	0.309979i	0.534922	+	0.844901i	$0.320341\pi$
$702$		0			0
$703$	5.83429			0.220045
$704$		0			0
$705$	50.3735			1.89718
$706$		0			0
$707$	−49.5940	+	49.5940i	−1.86517	+	1.86517i
$708$		0			0
$709$	2.94396	+	2.94396i	0.110563	+	0.110563i	0.760224	−	0.649661i	$-0.225089\pi$
$709$	2.94396	+	2.94396i	0.110563	+	0.110563i	−0.649661	+	0.760224i	$0.725089\pi$
$710$		0			0
$711$		−	7.22750i		−	0.271052i
$712$		0			0
$713$			6.76132i			0.253213i
$714$		0			0
$715$	−5.15157	−	5.15157i	−0.192658	−	0.192658i
$716$		0			0
$717$	−7.33654	+	7.33654i	−0.273988	+	0.273988i
$718$		0			0
$719$	−11.3521			−0.423362			−0.211681	−	0.977339i	$-0.567894\pi$
$719$	−11.3521			−0.423362			−0.211681	+	0.977339i	$0.567894\pi$
$720$		0			0
$721$	−22.4816			−0.837260
$722$		0			0
$723$	−41.0620	+	41.0620i	−1.52711	+	1.52711i
$724$		0			0
$725$	−17.2796	−	17.2796i	−0.641747	−	0.641747i
$726$		0			0
$727$		−	7.72299i		−	0.286430i	−0.989692	−	0.143215i	$-0.954256\pi$
$727$		−	7.72299i		−	0.286430i	0.989692	−	0.143215i	$-0.0457440\pi$
$728$		0			0
$729$		−	42.1782i		−	1.56216i
$730$		0			0
$731$	2.64317	+	2.64317i	0.0977611	+	0.0977611i
$732$		0			0
$733$	25.6965	−	25.6965i	0.949122	−	0.949122i	−0.0496448	−	0.998767i	$-0.515809\pi$
$733$	25.6965	−	25.6965i	0.949122	−	0.949122i	0.998767	+	0.0496448i	$0.0158089\pi$
$734$		0			0
$735$	37.2414			1.37367
$736$		0			0
$737$	−10.2972			−0.379300
$738$		0			0
$739$	14.2617	−	14.2617i	0.524627	−	0.524627i	−0.394338	−	0.918965i	$-0.629026\pi$
$739$	14.2617	−	14.2617i	0.524627	−	0.524627i	0.918965	+	0.394338i	$0.129026\pi$
$740$		0			0
$741$	11.6896	+	11.6896i	0.429430	+	0.429430i
$742$		0			0
$743$		−	19.0364i		−	0.698379i	−0.937052	−	0.349190i	$-0.886457\pi$
$743$		−	19.0364i		−	0.698379i	0.937052	−	0.349190i	$-0.113543\pi$
$744$		0			0
$745$		−	33.4251i		−	1.22460i
$746$		0			0
$747$	−11.5112	−	11.5112i	−0.421173	−	0.421173i
$748$		0			0
$749$	−16.2991	+	16.2991i	−0.595556	+	0.595556i
$750$		0			0
$751$	30.0230			1.09556			0.547778	−	0.836624i	$-0.315474\pi$
$751$	30.0230			1.09556			0.547778	+	0.836624i	$0.315474\pi$
$752$		0			0
$753$	79.3389			2.89127
$754$		0			0
$755$	−13.6569	+	13.6569i	−0.497027	+	0.497027i
$756$		0			0
$757$	18.8213	+	18.8213i	0.684071	+	0.684071i	0.960915	−	0.276844i	$-0.0892884\pi$
$757$	18.8213	+	18.8213i	0.684071	+	0.684071i	−0.276844	+	0.960915i	$0.589288\pi$
$758$		0			0
$759$			1.88072i			0.0682658i
$760$		0			0
$761$			0.500291i			0.0181355i	0.999959	+	0.00906777i	$0.00288640\pi$
$761$			0.500291i			0.0181355i	−0.999959	+	0.00906777i	$0.997114\pi$
$762$		0			0
$763$	−14.7159	−	14.7159i	−0.532753	−	0.532753i
$764$		0			0
$765$	−2.68847	+	2.68847i	−0.0972020	+	0.0972020i
$766$		0			0
$767$	−34.3076			−1.23878
$768$		0			0
$769$	−6.22678			−0.224543			−0.112272	−	0.993678i	$-0.535813\pi$
$769$	−6.22678			−0.224543			−0.112272	+	0.993678i	$0.535813\pi$
$770$		0			0
$771$	5.77297	−	5.77297i	0.207908	−	0.207908i
$772$		0			0
$773$	−22.7785	−	22.7785i	−0.819287	−	0.819287i	0.166718	−	0.986005i	$-0.446683\pi$
$773$	−22.7785	−	22.7785i	−0.819287	−	0.819287i	−0.986005	+	0.166718i	$0.946683\pi$
$774$		0			0
$775$			20.4566i			0.734824i
$776$		0			0
$777$		−	62.8435i		−	2.25450i
$778$		0			0
$779$	2.22976	+	2.22976i	0.0798893	+	0.0798893i
$780$		0			0
$781$	−0.149298	+	0.149298i	−0.00534229	+	0.00534229i
$782$		0			0
$783$	−27.4516			−0.981041
$784$		0			0
$785$	−28.4143			−1.01415
$786$		0			0
$787$	−15.6427	+	15.6427i	−0.557601	+	0.557601i	−0.928624	−	0.371023i	$-0.879007\pi$
$787$	−15.6427	+	15.6427i	−0.557601	+	0.557601i	0.371023	+	0.928624i	$0.379007\pi$
$788$		0			0
$789$	36.6633	+	36.6633i	1.30525	+	1.30525i
$790$		0			0
$791$			18.9768i			0.674738i
$792$		0			0
$793$			41.4169i			1.47076i
$794$		0			0
$795$	−1.03829	−	1.03829i	−0.0368243	−	0.0368243i
$796$		0			0
$797$	−31.3227	+	31.3227i	−1.10951	+	1.10951i	−0.116291	+	0.993215i	$0.537100\pi$
$797$	−31.3227	+	31.3227i	−1.10951	+	1.10951i	−0.993215	+	0.116291i	$0.962900\pi$
$798$		0			0
$799$	−7.59870			−0.268823
$800$		0			0
$801$	43.3218			1.53070
$802$		0			0
$803$	−6.80491	+	6.80491i	−0.240140	+	0.240140i
$804$		0			0
$805$	3.87100	+	3.87100i	0.136435	+	0.136435i
$806$		0			0
$807$		−	46.0370i		−	1.62058i
$808$		0			0
$809$			42.4127i			1.49115i	0.666421	+	0.745575i	$0.267825\pi$
$809$			42.4127i			1.49115i	−0.666421	+	0.745575i	$0.732175\pi$
$810$		0			0
$811$	14.3351	+	14.3351i	0.503374	+	0.503374i	0.912485	−	0.409111i	$-0.134161\pi$
$811$	14.3351	+	14.3351i	0.503374	+	0.503374i	−0.409111	+	0.912485i	$0.634161\pi$
$812$		0			0
$813$	35.4275	−	35.4275i	1.24250	−	1.24250i
$814$		0			0
$815$	5.35094			0.187435
$816$		0			0
$817$	6.14660			0.215042
$818$		0			0
$819$	73.0484	−	73.0484i	2.55252	−	2.55252i
$820$		0			0
$821$	0.414946	+	0.414946i	0.0144817	+	0.0144817i	0.714311	−	0.699829i	$-0.246740\pi$
$821$	0.414946	+	0.414946i	0.0144817	+	0.0144817i	−0.699829	+	0.714311i	$0.746740\pi$
$822$		0			0
$823$			24.2381i			0.844888i	0.906389	+	0.422444i	$0.138828\pi$
$823$			24.2381i			0.844888i	−0.906389	+	0.422444i	$0.861172\pi$
$824$		0			0
$825$			5.69020i			0.198107i
$826$		0			0
$827$	13.1438	+	13.1438i	0.457056	+	0.457056i	0.897688	−	0.440632i	$-0.145246\pi$
$827$	13.1438	+	13.1438i	0.457056	+	0.457056i	−0.440632	+	0.897688i	$0.645246\pi$
$828$		0			0
$829$	13.6134	−	13.6134i	0.472814	−	0.472814i	−0.430010	−	0.902824i	$-0.641490\pi$
$829$	13.6134	−	13.6134i	0.472814	−	0.472814i	0.902824	+	0.430010i	$0.141490\pi$
$830$		0			0
$831$	18.3205			0.635531
$832$		0			0
$833$	−5.61776			−0.194644
$834$		0			0
$835$	14.1070	−	14.1070i	0.488194	−	0.488194i
$836$		0			0
$837$	16.2495	+	16.2495i	0.561664	+	0.561664i
$838$		0			0
$839$		−	29.7619i		−	1.02750i	−0.857941	−	0.513748i	$-0.828257\pi$
$839$		−	29.7619i		−	1.02750i	0.857941	−	0.513748i	$-0.171743\pi$
$840$		0			0
$841$		−	51.3986i		−	1.77237i
$842$		0			0
$843$	13.7476	+	13.7476i	0.473493	+	0.473493i
$844$		0			0
$845$	−26.9259	+	26.9259i	−0.926281	+	0.926281i
$846$		0			0
$847$	−41.8671			−1.43857
$848$		0			0
$849$	15.1971			0.521562
$850$		0			0
$851$	3.71615	−	3.71615i	0.127388	−	0.127388i
$852$		0			0
$853$	−2.40701	−	2.40701i	−0.0824143	−	0.0824143i	0.664698	−	0.747112i	$-0.268560\pi$
$853$	−2.40701	−	2.40701i	−0.0824143	−	0.0824143i	−0.747112	+	0.664698i	$0.768560\pi$
$854$		0			0
$855$			6.25196i			0.213813i
$856$		0			0
$857$			42.4913i			1.45148i	0.687972	+	0.725738i	$0.258501\pi$
$857$			42.4913i			1.45148i	−0.687972	+	0.725738i	$0.741499\pi$
$858$		0			0
$859$	36.3033	+	36.3033i	1.23865	+	1.23865i	0.960552	+	0.278102i	$0.0897053\pi$
$859$	36.3033	+	36.3033i	1.23865	+	1.23865i	0.278102	+	0.960552i	$0.410295\pi$
$860$		0			0
$861$	24.0176	−	24.0176i	0.818518	−	0.818518i
$862$		0			0
$863$	40.3605			1.37389			0.686943	−	0.726711i	$-0.258952\pi$
$863$	40.3605			1.37389			0.686943	+	0.726711i	$0.258952\pi$
$864$		0			0
$865$	−5.63989			−0.191762
$866$		0			0
$867$	−31.4335	+	31.4335i	−1.06754	+	1.06754i
$868$		0			0
$869$	−0.962955	−	0.962955i	−0.0326660	−	0.0326660i
$870$		0			0
$871$			81.5323i			2.76262i
$872$		0			0
$873$			14.4896i			0.490399i
$874$		0			0
$875$	33.1987	+	33.1987i	1.12232	+	1.12232i
$876$		0			0
$877$	−12.7663	+	12.7663i	−0.431087	+	0.431087i	−0.888998	−	0.457911i	$-0.848598\pi$
$877$	−12.7663	+	12.7663i	−0.431087	+	0.431087i	0.457911	+	0.888998i	$0.348598\pi$
$878$		0			0
$879$	50.1729			1.69229
$880$		0			0
$881$	−53.9328			−1.81704			−0.908521	−	0.417839i	$-0.862788\pi$
$881$	−53.9328			−1.81704			−0.908521	+	0.417839i	$0.862788\pi$
$882$		0			0
$883$	34.7449	−	34.7449i	1.16926	−	1.16926i	0.186874	−	0.982384i	$-0.440164\pi$
$883$	34.7449	−	34.7449i	1.16926	−	1.16926i	0.982384	−	0.186874i	$-0.0598356\pi$
$884$		0			0
$885$	−15.8139	−	15.8139i	−0.531577	−	0.531577i
$886$		0			0
$887$			45.2215i			1.51839i	0.650864	+	0.759195i	$0.274407\pi$
$887$			45.2215i			1.51839i	−0.650864	+	0.759195i	$0.725593\pi$
$888$		0			0
$889$		−	63.2405i		−	2.12102i
$890$		0			0
$891$	−2.34851	−	2.34851i	−0.0786779	−	0.0786779i
$892$		0			0
$893$	−8.83526	+	8.83526i	−0.295661	+	0.295661i
$894$		0			0
$895$	−11.9070			−0.398007
$896$		0			0
$897$	14.8914			0.497211
$898$		0			0
$899$	−47.5905	+	47.5905i	−1.58723	+	1.58723i
$900$		0			0
$901$	0.156623	+	0.156623i	0.00521786	+	0.00521786i
$902$		0			0
$903$		−	66.2075i		−	2.20325i
$904$		0			0
$905$		−	26.3370i		−	0.875471i
$906$		0			0
$907$	−11.5383	−	11.5383i	−0.383123	−	0.383123i	0.489103	−	0.872226i	$-0.337324\pi$
$907$	−11.5383	−	11.5383i	−0.383123	−	0.383123i	−0.872226	+	0.489103i	$0.837324\pi$
$908$		0			0
$909$	−51.0185	+	51.0185i	−1.69218	+	1.69218i
$910$		0			0
$911$	−28.5045			−0.944395			−0.472198	−	0.881493i	$-0.656539\pi$
$911$	−28.5045			−0.944395			−0.472198	+	0.881493i	$0.656539\pi$
$912$		0			0
$913$	−3.06739			−0.101516
$914$		0			0
$915$	−19.0909	+	19.0909i	−0.631125	+	0.631125i
$916$		0			0
$917$	4.91925	+	4.91925i	0.162448	+	0.162448i
$918$		0			0
$919$			5.64101i			0.186080i	0.995662	+	0.0930399i	$0.0296584\pi$
$919$			5.64101i			0.186080i	−0.995662	+	0.0930399i	$0.970342\pi$
$920$		0			0
$921$			54.7982i			1.80566i
$922$		0			0
$923$	1.18213	+	1.18213i	0.0389103	+	0.0389103i
$924$		0			0
$925$	11.2434	−	11.2434i	0.369680	−	0.369680i
$926$		0			0
$927$	−23.1274			−0.759604
$928$		0			0
$929$	14.2171			0.466448			0.233224	−	0.972423i	$-0.425072\pi$
$929$	14.2171			0.466448			0.233224	+	0.972423i	$0.425072\pi$
$930$		0			0
$931$	−6.53196	+	6.53196i	−0.214076	+	0.214076i
$932$		0			0
$933$	−9.83353	−	9.83353i	−0.321935	−	0.321935i
$934$		0			0
$935$			0.716397i			0.0234287i
$936$		0			0
$937$		−	19.4713i		−	0.636101i	−0.948074	−	0.318051i	$-0.896972\pi$
$937$		−	19.4713i		−	0.636101i	0.948074	−	0.318051i	$-0.103028\pi$
$938$		0			0
$939$	−48.7940	−	48.7940i	−1.59233	−	1.59233i
$940$		0			0
$941$	38.1234	−	38.1234i	1.24279	−	1.24279i	0.283947	−	0.958840i	$-0.408356\pi$
$941$	38.1234	−	38.1234i	1.24279	−	1.24279i	0.958840	−	0.283947i	$-0.0916441\pi$
$942$		0			0
$943$	2.84049			0.0924990
$944$		0			0
$945$	18.6063			0.605264
$946$		0			0
$947$	−8.23030	+	8.23030i	−0.267449	+	0.267449i	−0.828071	−	0.560623i	$-0.810562\pi$
$947$	−8.23030	+	8.23030i	−0.267449	+	0.267449i	0.560623	+	0.828071i	$0.310562\pi$
$948$		0			0
$949$	53.8810	+	53.8810i	1.74905	+	1.74905i
$950$		0			0
$951$		−	52.2393i		−	1.69397i
$952$		0			0
$953$		−	13.2093i		−	0.427890i	−0.976846	−	0.213945i	$-0.931369\pi$
$953$		−	13.2093i		−	0.427890i	0.976846	−	0.213945i	$-0.0686314\pi$
$954$		0			0
$955$	2.14895	+	2.14895i	0.0695384	+	0.0695384i
$956$		0			0
$957$	−13.2377	+	13.2377i	−0.427915	+	0.427915i
$958$		0			0
$959$	2.01942			0.0652106
$960$		0			0
$961$	25.3407			0.817441
$962$		0			0
$963$	−16.7673	+	16.7673i	−0.540318	+	0.540318i
$964$		0			0
$965$	−2.68144	−	2.68144i	−0.0863187	−	0.0863187i
$966$		0			0
$967$			9.64759i			0.310246i	0.987895	+	0.155123i	$0.0495773\pi$
$967$			9.64759i			0.310246i	−0.987895	+	0.155123i	$0.950423\pi$
$968$		0			0
$969$		−	1.62561i		−	0.0522221i
$970$		0			0
$971$	−1.09782	−	1.09782i	−0.0352307	−	0.0352307i	0.689272	−	0.724503i	$-0.257931\pi$
$971$	−1.09782	−	1.09782i	−0.0352307	−	0.0352307i	−0.724503	+	0.689272i	$0.757931\pi$
$972$		0			0
$973$	−36.3562	+	36.3562i	−1.16552	+	1.16552i
$974$		0			0
$975$	45.0547			1.44290
$976$		0			0
$977$	0.637383			0.0203917			0.0101958	−	0.999948i	$-0.496755\pi$
$977$	0.637383			0.0203917			0.0101958	+	0.999948i	$0.496755\pi$
$978$		0			0
$979$	5.77197	−	5.77197i	0.184473	−	0.184473i
$980$		0			0
$981$	−15.1386	−	15.1386i	−0.483340	−	0.483340i
$982$		0			0
$983$		−	17.4766i		−	0.557418i	−0.960376	−	0.278709i	$-0.910093\pi$
$983$		−	17.4766i		−	0.557418i	0.960376	−	0.278709i	$-0.0899065\pi$
$984$		0			0
$985$		−	18.6229i		−	0.593374i
$986$		0			0
$987$	95.1681	+	95.1681i	3.02923	+	3.02923i
$988$		0			0
$989$	3.91508	−	3.91508i	0.124492	−	0.124492i
$990$		0			0
$991$	13.2083			0.419576			0.209788	−	0.977747i	$-0.432723\pi$
$991$	13.2083			0.419576			0.209788	+	0.977747i	$0.432723\pi$
$992$		0			0
$993$	47.7419			1.51504
$994$		0			0
$995$	−3.85215	+	3.85215i	−0.122121	+	0.122121i
$996$		0			0
$997$	14.8543	+	14.8543i	0.470440	+	0.470440i	0.902057	−	0.431617i	$-0.142057\pi$
$997$	14.8543	+	14.8543i	0.470440	+	0.470440i	−0.431617	+	0.902057i	$0.642057\pi$
$998$		0			0
$999$		−	17.8621i		−	0.565131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.k.b.305.30		68
4.3	odd	2		304.2.k.b.229.34	yes	68
16.3	odd	4		304.2.k.b.77.34	✓	68
16.13	even	4	inner	1216.2.k.b.913.30		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.k.b.77.34	✓	68	16.3	odd	4
304.2.k.b.229.34	yes	68	4.3	odd	2
1216.2.k.b.305.30		68	1.1	even	1	trivial
1216.2.k.b.913.30		68	16.13	even	4	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:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.k (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.89015 - 1.89015i) q^{3} +(-1.06645 - 1.06645i) q^{5} -4.02959i q^{7} -4.14533i q^{9} +O(q^{10})\)	\(q+(1.89015 - 1.89015i) q^{3} +(-1.06645 - 1.06645i) q^{5} -4.02959i q^{7} -4.14533i q^{9} +(-0.552303 - 0.552303i) q^{11} +(-4.37311 + 4.37311i) q^{13} -4.03151 q^{15} +0.608142 q^{17} +(0.707107 - 0.707107i) q^{19} +(-7.61653 - 7.61653i) q^{21} -0.900783i q^{23} -2.72536i q^{25} +(-2.16485 - 2.16485i) q^{27} +(6.34029 - 6.34029i) q^{29} -7.50604 q^{31} -2.08787 q^{33} +(-4.29737 + 4.29737i) q^{35} +(4.12547 + 4.12547i) q^{37} +16.5317i q^{39} +3.15335i q^{41} +(4.34630 + 4.34630i) q^{43} +(-4.42080 + 4.42080i) q^{45} -12.4949 q^{47} -9.23758 q^{49} +(1.14948 - 1.14948i) q^{51} +(0.257543 + 0.257543i) q^{53} +1.17801i q^{55} -2.67308i q^{57} +(3.92257 + 3.92257i) q^{59} +(4.73541 - 4.73541i) q^{61} -16.7040 q^{63} +9.32743 q^{65} +(9.32201 - 9.32201i) q^{67} +(-1.70262 - 1.70262i) q^{69} -0.270319i q^{71} -12.3210i q^{73} +(-5.15133 - 5.15133i) q^{75} +(-2.22555 + 2.22555i) q^{77} +1.74353 q^{79} +4.25220 q^{81} +(2.77691 - 2.77691i) q^{83} +(-0.648554 - 0.648554i) q^{85} -23.9682i q^{87} +10.4507i q^{89} +(17.6218 + 17.6218i) q^{91} +(-14.1875 + 14.1875i) q^{93} -1.50819 q^{95} -3.49540 q^{97} +(-2.28948 + 2.28948i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 4 q^{3} + 8 q^{5}+O(q^{10}) \) 68 * q - 4 * q^3 + 8 * q^5	\( 68 q - 4 q^{3} + 8 q^{5} - 4 q^{11} + 16 q^{15} + 4 q^{17} + 16 q^{21} - 28 q^{27} - 32 q^{31} - 16 q^{33} + 24 q^{35} - 24 q^{37} + 16 q^{43} + 24 q^{47} - 56 q^{49} + 52 q^{51} + 32 q^{53} - 28 q^{59} - 24 q^{63} - 16 q^{65} - 28 q^{67} - 8 q^{69} - 44 q^{75} - 12 q^{77} - 8 q^{79} - 76 q^{81} - 40 q^{83} - 8 q^{85} + 4 q^{91} - 84 q^{93} - 32 q^{95} - 16 q^{97} + 24 q^{99}+O(q^{100}) \) 68 * q - 4 * q^3 + 8 * q^5 - 4 * q^11 + 16 * q^15 + 4 * q^17 + 16 * q^21 - 28 * q^27 - 32 * q^31 - 16 * q^33 + 24 * q^35 - 24 * q^37 + 16 * q^43 + 24 * q^47 - 56 * q^49 + 52 * q^51 + 32 * q^53 - 28 * q^59 - 24 * q^63 - 16 * q^65 - 28 * q^67 - 8 * q^69 - 44 * q^75 - 12 * q^77 - 8 * q^79 - 76 * q^81 - 40 * q^83 - 8 * q^85 + 4 * q^91 - 84 * q^93 - 32 * q^95 - 16 * q^97 + 24 * q^99

Introduction

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