LMFDB - Embedded newform 912.2.ci.c.319.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(79,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))

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

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

chi := DirichletCharacter("912.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.ci (of order $18$, degree $6$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	12.0.101559956668416.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 8x^{6} + 64 $ x^12 - 8*x^6 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			319.2
Root			$1.39273 + 0.245576i$ of defining polynomial
Character	$\chi$	$=$	912.319
Dual form			912.2.ci.c.223.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{3} +(2.83242 - 2.37668i) q^{5} +(-2.26308 - 1.30659i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{3} +(2.83242 - 2.37668i) q^{5} +(-2.26308 - 1.30659i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(0.444674 - 0.256733i) q^{11} +(5.82321 + 1.02679i) q^{13} +(-2.83242 - 2.37668i) q^{15} +(-3.47955 - 1.26645i) q^{17} +(2.31951 - 3.69051i) q^{19} +(-0.893759 + 2.45558i) q^{21} +(1.12502 - 1.34074i) q^{23} +(1.50574 - 8.53950i) q^{25} +(0.500000 + 0.866025i) q^{27} +(-1.62264 - 4.45817i) q^{29} +(-4.54552 + 7.87307i) q^{31} +(-0.330049 - 0.393337i) q^{33} +(-9.51533 + 1.67781i) q^{35} +3.53752i q^{37} -5.91304i q^{39} +(1.13532 - 0.200187i) q^{41} +(-2.50015 - 2.97956i) q^{43} +(-1.84873 + 3.20210i) q^{45} +(-1.56336 - 4.29530i) q^{47} +(-0.0856544 - 0.148358i) q^{49} +(-0.642995 + 3.64660i) q^{51} +(-4.15387 + 4.95039i) q^{53} +(0.649332 - 1.78402i) q^{55} +(-4.03722 - 1.64342i) q^{57} +(3.14813 + 1.14582i) q^{59} +(-4.68357 - 3.92998i) q^{61} +(2.57348 + 0.453773i) q^{63} +(18.9341 - 10.9316i) q^{65} +(-3.30490 + 1.20289i) q^{67} +(-1.51573 - 0.875108i) q^{69} +(1.45471 - 1.22064i) q^{71} +(2.32869 + 13.2067i) q^{73} -8.67123 q^{75} -1.34178 q^{77} +(-1.21938 - 6.91542i) q^{79} +(0.766044 - 0.642788i) q^{81} +(12.6467 + 7.30158i) q^{83} +(-12.8655 + 4.68266i) q^{85} +(-4.10867 + 2.37214i) q^{87} +(15.6179 + 2.75386i) q^{89} +(-11.8368 - 9.93224i) q^{91} +(8.54278 + 3.10932i) q^{93} +(-2.20133 - 15.9658i) q^{95} +(-0.687600 + 1.88917i) q^{97} +(-0.330049 + 0.393337i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{5} - 18 q^{7}+O(q^{10}) $ 12 * q + 6 * q^5 - 18 * q^7	$ 12 q + 6 q^{5} - 18 q^{7} + 18 q^{13} - 6 q^{15} + 6 q^{17} - 12 q^{19} - 6 q^{21} + 18 q^{23} - 30 q^{25} + 6 q^{27} - 6 q^{29} - 18 q^{31} + 6 q^{33} - 36 q^{35} + 6 q^{41} + 6 q^{43} - 6 q^{47} + 12 q^{49} - 6 q^{51} - 36 q^{53} + 42 q^{55} + 6 q^{59} - 6 q^{61} - 6 q^{63} + 72 q^{65} - 6 q^{67} - 54 q^{71} - 12 q^{73} - 12 q^{75} - 36 q^{77} + 6 q^{79} - 18 q^{83} - 36 q^{85} + 36 q^{87} + 24 q^{89} - 12 q^{91} - 18 q^{93} - 24 q^{95} + 24 q^{97} + 6 q^{99}+O(q^{100}) $ 12 * q + 6 * q^5 - 18 * q^7 + 18 * q^13 - 6 * q^15 + 6 * q^17 - 12 * q^19 - 6 * q^21 + 18 * q^23 - 30 * q^25 + 6 * q^27 - 6 * q^29 - 18 * q^31 + 6 * q^33 - 36 * q^35 + 6 * q^41 + 6 * q^43 - 6 * q^47 + 12 * q^49 - 6 * q^51 - 36 * q^53 + 42 * q^55 + 6 * q^59 - 6 * q^61 - 6 * q^63 + 72 * q^65 - 6 * q^67 - 54 * q^71 - 12 * q^73 - 12 * q^75 - 36 * q^77 + 6 * q^79 - 18 * q^83 - 36 * q^85 + 36 * q^87 + 24 * q^89 - 12 * q^91 - 18 * q^93 - 24 * q^95 + 24 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$4$		0			0
$5$	2.83242	−	2.37668i	1.26670	−	1.06289i	0.271762	−	0.962364i	$-0.412394\pi$
$5$	2.83242	−	2.37668i	1.26670	−	1.06289i	0.994935	−	0.100521i	$-0.0320509\pi$
$6$		0			0
$7$	−2.26308	−	1.30659i	−0.855363	−	0.493844i	0.00709389	−	0.999975i	$-0.497742\pi$
$7$	−2.26308	−	1.30659i	−0.855363	−	0.493844i	−0.862457	+	0.506131i	$0.831075\pi$
$8$		0			0
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$		0			0
$11$	0.444674	−	0.256733i	0.134074	−	0.0774078i	−0.431463	−	0.902131i	$-0.642002\pi$
$11$	0.444674	−	0.256733i	0.134074	−	0.0774078i	0.565537	+	0.824723i	$0.308669\pi$
$12$		0			0
$13$	5.82321	+	1.02679i	1.61507	+	0.284780i	0.906926	−	0.421290i	$-0.138423\pi$
$13$	5.82321	+	1.02679i	1.61507	+	0.284780i	0.708142	+	0.706070i	$0.249534\pi$
$14$		0			0
$15$	−2.83242	−	2.37668i	−0.731328	−	0.613657i
$16$		0			0
$17$	−3.47955	−	1.26645i	−0.843914	−	0.307160i	−0.116358	−	0.993207i	$-0.537122\pi$
$17$	−3.47955	−	1.26645i	−0.843914	−	0.307160i	−0.727557	+	0.686048i	$0.759344\pi$
$18$		0			0
$19$	2.31951	−	3.69051i	0.532133	−	0.846661i
$19$	2.31951	−	3.69051i	0.532133	−	0.846661i
$20$		0			0
$21$	−0.893759	+	2.45558i	−0.195034	+	0.535852i
$22$		0			0
$23$	1.12502	−	1.34074i	0.234582	−	0.279564i	−0.635892	−	0.771778i	$-0.719368\pi$
$23$	1.12502	−	1.34074i	0.234582	−	0.279564i	0.870474	+	0.492214i	$0.163812\pi$
$24$		0			0
$25$	1.50574	−	8.53950i	0.301149	−	1.70790i
$26$		0			0
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$		0			0
$29$	−1.62264	−	4.45817i	−0.301317	−	0.827861i	−0.994272	−	0.106880i	$-0.965914\pi$
$29$	−1.62264	−	4.45817i	−0.301317	−	0.827861i	0.692955	−	0.720981i	$-0.256308\pi$
$30$		0			0
$31$	−4.54552	+	7.87307i	−0.816400	+	1.41405i	0.0919191	+	0.995766i	$0.470700\pi$
$31$	−4.54552	+	7.87307i	−0.816400	+	1.41405i	−0.908319	+	0.418279i	$0.862633\pi$
$32$		0			0
$33$	−0.330049	−	0.393337i	−0.0574542	−	0.0684712i
$34$		0			0
$35$	−9.51533	+	1.67781i	−1.60839	+	0.283602i
$36$		0			0
$37$			3.53752i			0.581565i	0.956789	+	0.290782i	$0.0939156\pi$
$37$			3.53752i			0.581565i	−0.956789	+	0.290782i	$0.906084\pi$
$38$		0			0
$39$		−	5.91304i		−	0.946845i
$40$		0			0
$41$	1.13532	−	0.200187i	0.177307	−	0.0312639i	−0.0842899	−	0.996441i	$-0.526862\pi$
$41$	1.13532	−	0.200187i	0.177307	−	0.0312639i	0.261596	+	0.965177i	$0.415751\pi$
$42$		0			0
$43$	−2.50015	−	2.97956i	−0.381269	−	0.454379i	0.540945	−	0.841058i	$-0.318067\pi$
$43$	−2.50015	−	2.97956i	−0.381269	−	0.454379i	−0.922215	+	0.386679i	$0.873622\pi$
$44$		0			0
$45$	−1.84873	+	3.20210i	−0.275593	+	0.477340i
$46$		0			0
$47$	−1.56336	−	4.29530i	−0.228040	−	0.626534i	0.771918	−	0.635722i	$-0.219298\pi$
$47$	−1.56336	−	4.29530i	−0.228040	−	0.626534i	−0.999958	+	0.00918781i	$0.997075\pi$
$48$		0			0
$49$	−0.0856544	−	0.148358i	−0.0122363	−	0.0211940i
$50$		0			0
$51$	−0.642995	+	3.64660i	−0.0900372	+	0.510627i
$52$		0			0
$53$	−4.15387	+	4.95039i	−0.570578	+	0.679988i	−0.971749	−	0.236015i	$-0.924159\pi$
$53$	−4.15387	+	4.95039i	−0.570578	+	0.679988i	0.401172	+	0.916003i	$0.368603\pi$
$54$		0			0
$55$	0.649332	−	1.78402i	0.0875559	−	0.240558i
$56$		0			0
$57$	−4.03722	−	1.64342i	−0.534743	−	0.217677i
$58$		0			0
$59$	3.14813	+	1.14582i	0.409851	+	0.149174i	0.538714	−	0.842489i	$-0.318910\pi$
$59$	3.14813	+	1.14582i	0.409851	+	0.149174i	−0.128863	+	0.991662i	$0.541133\pi$
$60$		0			0
$61$	−4.68357	−	3.92998i	−0.599670	−	0.503183i	0.291670	−	0.956519i	$-0.405789\pi$
$61$	−4.68357	−	3.92998i	−0.599670	−	0.503183i	−0.891340	+	0.453336i	$0.850234\pi$
$62$		0			0
$63$	2.57348	+	0.453773i	0.324228	+	0.0571701i
$64$		0			0
$65$	18.9341	−	10.9316i	2.34849	−	1.35590i
$66$		0			0
$67$	−3.30490	+	1.20289i	−0.403758	+	0.146956i	−0.535913	−	0.844273i	$-0.680032\pi$
$67$	−3.30490	+	1.20289i	−0.403758	+	0.146956i	0.132155	+	0.991229i	$0.457810\pi$
$68$		0			0
$69$	−1.51573	−	0.875108i	−0.182473	−	0.105351i
$70$		0			0
$71$	1.45471	−	1.22064i	0.172642	−	0.144864i	−0.552373	−	0.833597i	$-0.686277\pi$
$71$	1.45471	−	1.22064i	0.172642	−	0.144864i	0.725015	+	0.688733i	$0.241833\pi$
$72$		0			0
$73$	2.32869	+	13.2067i	0.272553	+	1.54572i	0.746629	+	0.665241i	$0.231671\pi$
$73$	2.32869	+	13.2067i	0.272553	+	1.54572i	−0.474076	+	0.880484i	$0.657218\pi$
$74$		0			0
$75$	−8.67123			−1.00127
$76$		0			0
$77$	−1.34178			−0.152909
$78$		0			0
$79$	−1.21938	−	6.91542i	−0.137190	−	0.778046i	−0.973309	−	0.229497i	$-0.926292\pi$
$79$	−1.21938	−	6.91542i	−0.137190	−	0.778046i	0.836119	−	0.548548i	$-0.184819\pi$
$80$		0			0
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$		0			0
$83$	12.6467	+	7.30158i	1.38816	+	0.801452i	0.993107	−	0.117208i	$-0.0373943\pi$
$83$	12.6467	+	7.30158i	1.38816	+	0.801452i	0.395049	+	0.918660i	$0.370728\pi$
$84$		0			0
$85$	−12.8655	+	4.68266i	−1.39546	+	0.507906i
$86$		0			0
$87$	−4.10867	+	2.37214i	−0.440495	+	0.254320i
$88$		0			0
$89$	15.6179	+	2.75386i	1.65550	+	0.291909i	0.921829	−	0.387597i	$-0.126695\pi$
$89$	15.6179	+	2.75386i	1.65550	+	0.291909i	0.733670	+	0.679506i	$0.237806\pi$
$90$		0			0
$91$	−11.8368	−	9.93224i	−1.24083	−	1.04118i
$92$		0			0
$93$	8.54278	+	3.10932i	0.885845	+	0.322421i
$94$		0			0
$95$	−2.20133	−	15.9658i	−0.225852	−	1.63806i
$96$		0			0
$97$	−0.687600	+	1.88917i	−0.0698152	+	0.191816i	−0.969693	−	0.244326i	$-0.921433\pi$
$97$	−0.687600	+	1.88917i	−0.0698152	+	0.191816i	0.899878	+	0.436142i	$0.143655\pi$
$98$		0			0
$99$	−0.330049	+	0.393337i	−0.0331712	+	0.0395319i
$100$		0			0
$101$	2.98930	−	16.9532i	0.297447	−	1.68691i	−0.359641	−	0.933091i	$-0.617101\pi$
$101$	2.98930	−	16.9532i	0.297447	−	1.68691i	0.657088	−	0.753814i	$-0.271788\pi$
$102$		0			0
$103$	−4.79089	−	8.29806i	−0.472060	−	0.817633i	0.527429	−	0.849599i	$-0.323156\pi$
$103$	−4.79089	−	8.29806i	−0.472060	−	0.817633i	−0.999489	+	0.0319668i	$0.989823\pi$
$104$		0			0
$105$	3.30464	+	9.07943i	0.322500	+	0.886061i
$106$		0			0
$107$	6.37260	−	11.0377i	0.616063	−	1.06705i	−0.374134	−	0.927375i	$-0.622060\pi$
$107$	6.37260	−	11.0377i	0.616063	−	1.06705i	0.990197	−	0.139677i	$-0.0446065\pi$
$108$		0			0
$109$	−0.453958	−	0.541007i	−0.0434813	−	0.0518190i	0.743865	−	0.668329i	$-0.232990\pi$
$109$	−0.453958	−	0.541007i	−0.0434813	−	0.0518190i	−0.787347	+	0.616510i	$0.788546\pi$
$110$		0			0
$111$	3.48378	−	0.614284i	0.330666	−	0.0583053i
$112$		0			0
$113$		−	19.8061i		−	1.86320i	−0.363487	−	0.931599i	$-0.618414\pi$
$113$		−	19.8061i		−	1.86320i	0.363487	−	0.931599i	$-0.381586\pi$
$114$		0			0
$115$		−	6.47136i		−	0.603457i
$116$		0			0
$117$	−5.82321	+	1.02679i	−0.538356	+	0.0949267i
$118$		0			0
$119$	6.21975	+	7.41242i	0.570164	+	0.679495i
$120$		0			0
$121$	−5.36818	+	9.29795i	−0.488016	+	0.845269i
$122$		0			0
$123$	−0.394291	−	1.08331i	−0.0355520	−	0.0976784i
$124$		0			0
$125$	−6.78713	−	11.7556i	−0.607059	−	1.05146i
$126$		0			0
$127$	−3.34090	+	18.9472i	−0.296457	+	1.68129i	0.364765	+	0.931100i	$0.381149\pi$
$127$	−3.34090	+	18.9472i	−0.296457	+	1.68129i	−0.661222	+	0.750191i	$0.729962\pi$
$128$		0			0
$129$	−2.50015	+	2.97956i	−0.220126	+	0.262336i
$130$		0			0
$131$	−5.71051	+	15.6895i	−0.498930	+	1.37080i	0.393380	+	0.919376i	$0.371306\pi$
$131$	−5.71051	+	15.6895i	−0.498930	+	1.37080i	−0.892310	+	0.451423i	$0.850917\pi$
$132$		0			0
$133$	−10.0712	+	5.32126i	−0.873285	+	0.461412i
$134$		0			0
$135$	3.47448	+	1.26461i	0.299036	+	0.108840i
$136$		0			0
$137$	10.4476	+	8.76658i	0.892599	+	0.748979i	0.968730	−	0.248118i	$-0.0798122\pi$
$137$	10.4476	+	8.76658i	0.892599	+	0.748979i	−0.0761308	+	0.997098i	$0.524257\pi$
$138$		0			0
$139$	10.2188	+	1.80184i	0.866744	+	0.152830i	0.589303	−	0.807912i	$-0.299402\pi$
$139$	10.2188	+	1.80184i	0.866744	+	0.152830i	0.277441	+	0.960743i	$0.410514\pi$
$140$		0			0
$141$	−3.95857	+	2.28548i	−0.333372	+	0.192472i
$142$		0			0
$143$	2.85304	−	1.03842i	0.238583	−	0.0868372i
$144$		0			0
$145$	−15.1916	−	8.77090i	−1.26160	−	0.728384i
$146$		0			0
$147$	−0.131230	+	0.110115i	−0.0108237	+	0.00908214i
$148$		0			0
$149$	1.15024	+	6.52332i	0.0942311	+	0.534411i	0.994980	+	0.100071i	$0.0319071\pi$
$149$	1.15024	+	6.52332i	0.0942311	+	0.534411i	−0.900749	+	0.434340i	$0.856982\pi$
$150$		0			0
$151$	21.8927			1.78160			0.890801	−	0.454394i	$-0.150144\pi$
$151$	21.8927			1.78160			0.890801	+	0.454394i	$0.150144\pi$
$152$		0			0
$153$	3.70286			0.299358
$154$		0			0
$155$	5.83697	+	33.1031i	0.468837	+	2.65891i
$156$		0			0
$157$	−16.2914	+	13.6701i	−1.30019	+	1.09099i	−0.310080	+	0.950711i	$0.600356\pi$
$157$	−16.2914	+	13.6701i	−1.30019	+	1.09099i	−0.990112	+	0.140280i	$0.955200\pi$
$158$		0			0
$159$	5.59649	+	3.23114i	0.443831	+	0.256246i
$160$		0			0
$161$	−4.29780	+	1.56427i	−0.338714	+	0.123282i
$162$		0			0
$163$	15.5945	−	9.00347i	1.22145	−	0.705207i	0.256226	−	0.966617i	$-0.417521\pi$
$163$	15.5945	−	9.00347i	1.22145	−	0.705207i	0.965228	+	0.261410i	$0.0841876\pi$
$164$		0			0
$165$	−1.86968	−	0.329674i	−0.145554	−	0.0256651i
$166$		0			0
$167$	16.5975	+	13.9270i	1.28436	+	1.07770i	0.992628	+	0.121201i	$0.0386745\pi$
$167$	16.5975	+	13.9270i	1.28436	+	1.07770i	0.291727	+	0.956501i	$0.405770\pi$
$168$		0			0
$169$	20.6395	+	7.51216i	1.58765	+	0.577858i
$170$		0			0
$171$	−0.917401	+	4.26126i	−0.0701554	+	0.325867i
$172$		0			0
$173$	2.56151	−	7.03769i	0.194748	−	0.535065i	−0.803430	−	0.595399i	$-0.796994\pi$
$173$	2.56151	−	7.03769i	0.194748	−	0.535065i	0.998178	+	0.0603333i	$0.0192163\pi$
$174$		0			0
$175$	−14.5652	+	17.3582i	−1.10103	+	1.31215i
$176$		0			0
$177$	0.581750	−	3.29927i	0.0437270	−	0.247988i
$178$		0			0
$179$	7.66338	+	13.2734i	0.572788	+	0.992097i	0.996278	+	0.0861968i	$0.0274714\pi$
$179$	7.66338	+	13.2734i	0.572788	+	0.992097i	−0.423490	+	0.905901i	$0.639195\pi$
$180$		0			0
$181$	−1.59750	−	4.38910i	−0.118741	−	0.326239i	0.866056	−	0.499947i	$-0.166647\pi$
$181$	−1.59750	−	4.38910i	−0.118741	−	0.326239i	−0.984797	+	0.173708i	$0.944425\pi$
$182$		0			0
$183$	−3.05698	+	5.29485i	−0.225979	+	0.391407i
$184$		0			0
$185$	8.40757	+	10.0197i	0.618137	+	0.736666i
$186$		0			0
$187$	−1.87240	+	0.330155i	−0.136924	+	0.0241433i
$188$		0			0
$189$		−	2.61318i		−	0.190081i
$190$		0			0
$191$		−	9.59573i		−	0.694323i	−0.937805	−	0.347161i	$-0.887146\pi$
$191$		−	9.59573i		−	0.694323i	0.937805	−	0.347161i	$-0.112854\pi$
$192$		0			0
$193$	5.22146	−	0.920683i	0.375849	−	0.0662722i	0.0174670	−	0.999847i	$-0.494440\pi$
$193$	5.22146	−	0.920683i	0.375849	−	0.0662722i	0.358382	+	0.933575i	$0.383329\pi$
$194$		0			0
$195$	−14.0534	−	16.7482i	−1.00639	−	1.19937i
$196$		0			0
$197$	−10.6784	+	18.4955i	−0.760802	+	1.31775i	0.181636	+	0.983366i	$0.441861\pi$
$197$	−10.6784	+	18.4955i	−0.760802	+	1.31775i	−0.942438	+	0.334381i	$0.891473\pi$
$198$		0			0
$199$	4.34600	+	11.9405i	0.308080	+	0.846443i	0.993031	+	0.117854i	$0.0376014\pi$
$199$	4.34600	+	11.9405i	0.308080	+	0.846443i	−0.684951	+	0.728589i	$0.740176\pi$
$200$		0			0
$201$	1.75850	+	3.04581i	0.124035	+	0.214835i
$202$		0			0
$203$	−2.15283	+	12.2093i	−0.151099	+	0.856924i
$204$		0			0
$205$	2.73991	−	3.26530i	0.191364	−	0.228058i
$206$		0			0
$207$	−0.598609	+	1.64467i	−0.0416062	+	0.114312i
$208$		0			0
$209$	0.0839529	−	2.23657i	0.00580715	−	0.154707i
$210$		0			0
$211$	8.50815	+	3.09671i	0.585725	+	0.213186i	0.617848	−	0.786297i	$-0.288005\pi$
$211$	8.50815	+	3.09671i	0.585725	+	0.213186i	−0.0321232	+	0.999484i	$0.510227\pi$
$212$		0			0
$213$	−1.45471	−	1.22064i	−0.0996749	−	0.0836372i
$214$		0			0
$215$	−14.1630	−	2.49731i	−0.965906	−	0.170315i
$216$		0			0
$217$	20.5737	−	11.8782i	1.39664	−	0.806348i
$218$		0			0
$219$	12.6017	−	4.58663i	0.851541	−	0.309936i
$220$		0			0
$221$	−18.9618	−	10.9476i	−1.27551	−	0.736414i
$222$		0			0
$223$	−16.7005	+	14.0134i	−1.11835	+	0.938406i	−0.998520	−	0.0543890i	$-0.982679\pi$
$223$	−16.7005	+	14.0134i	−1.11835	+	0.938406i	−0.119828	+	0.992795i	$0.538234\pi$
$224$		0			0
$225$	1.50574	+	8.53950i	0.100383	+	0.569300i
$226$		0			0
$227$	5.06688			0.336301			0.168150	−	0.985761i	$-0.446221\pi$
$227$	5.06688			0.336301			0.168150	+	0.985761i	$0.446221\pi$
$228$		0			0
$229$	−12.9763			−0.857497			−0.428748	−	0.903424i	$-0.641045\pi$
$229$	−12.9763			−0.857497			−0.428748	+	0.903424i	$0.641045\pi$
$230$		0			0
$231$	0.232997	+	1.32139i	0.0153301	+	0.0869411i
$232$		0			0
$233$	−13.0084	+	10.9153i	−0.852206	+	0.715086i	−0.960274	−	0.279058i	$-0.909978\pi$
$233$	−13.0084	+	10.9153i	−0.852206	+	0.715086i	0.108068	+	0.994143i	$0.465534\pi$
$234$		0			0
$235$	−14.6367	−	8.45049i	−0.954792	−	0.551249i
$236$		0			0
$237$	−6.59862	+	2.40170i	−0.428626	+	0.156007i
$238$		0			0
$239$	20.2836	−	11.7107i	1.31204	−	0.757504i	0.329603	−	0.944120i	$-0.393085\pi$
$239$	20.2836	−	11.7107i	1.31204	−	0.757504i	0.982433	+	0.186616i	$0.0597519\pi$
$240$		0			0
$241$	2.86697	+	0.505524i	0.184678	+	0.0325637i	0.265222	−	0.964187i	$-0.414555\pi$
$241$	2.86697	+	0.505524i	0.184678	+	0.0325637i	−0.0805443	+	0.996751i	$0.525666\pi$
$242$		0			0
$243$	−0.766044	−	0.642788i	−0.0491418	−	0.0412348i
$244$		0			0
$245$	−0.595209	−	0.216638i	−0.0380265	−	0.0138405i
$246$		0			0
$247$	17.2964	−	19.1090i	1.10054	−	1.21587i
$248$		0			0
$249$	4.99457	−	13.7225i	0.316518	−	0.869627i
$250$		0			0
$251$	15.5655	−	18.5503i	0.982489	−	1.17088i	−0.00280173	−	0.999996i	$-0.500892\pi$
$251$	15.5655	−	18.5503i	0.982489	−	1.17088i	0.985290	−	0.170888i	$-0.0546637\pi$
$252$		0			0
$253$	0.156053	−	0.885022i	0.00981099	−	0.0556409i
$254$		0			0
$255$	6.84559	+	11.8569i	0.428687	+	0.742509i
$256$		0			0
$257$	−1.67654	−	4.60625i	−0.104580	−	0.287330i	0.876356	−	0.481664i	$-0.159968\pi$
$257$	−1.67654	−	4.60625i	−0.104580	−	0.287330i	−0.980935	+	0.194334i	$0.937745\pi$
$258$		0			0
$259$	4.62208	−	8.00568i	0.287202	−	0.497449i
$260$		0			0
$261$	3.04956	+	3.63433i	0.188763	+	0.224959i
$262$		0			0
$263$	−11.2107	+	1.97674i	−0.691279	+	0.121891i	−0.508241	−	0.861215i	$-0.669704\pi$
$263$	−11.2107	+	1.97674i	−0.691279	+	0.121891i	−0.183038	+	0.983106i	$0.558593\pi$
$264$		0			0
$265$			23.8940i			1.46780i
$266$		0			0
$267$		−	15.8589i		−	0.970547i
$268$		0			0
$269$	−0.210829	+	0.0371748i	−0.0128545	+	0.00226659i	−0.180072	−	0.983653i	$-0.557633\pi$
$269$	−0.210829	+	0.0371748i	−0.0128545	+	0.00226659i	0.167217	+	0.985920i	$0.446522\pi$
$270$		0			0
$271$	9.77463	+	11.6490i	0.593767	+	0.707623i	0.976325	−	0.216308i	$-0.0694015\pi$
$271$	9.77463	+	11.6490i	0.593767	+	0.707623i	−0.382559	+	0.923931i	$0.624957\pi$
$272$		0			0
$273$	−7.72591	+	13.3817i	−0.467593	+	0.809896i
$274$		0			0
$275$	−1.52280	−	4.18387i	−0.0918285	−	0.252297i
$276$		0			0
$277$	9.67566	+	16.7587i	0.581354	+	1.00693i	0.995319	+	0.0966421i	$0.0308102\pi$
$277$	9.67566	+	16.7587i	0.581354	+	1.00693i	−0.413965	+	0.910293i	$0.635856\pi$
$278$		0			0
$279$	1.57864	−	8.95293i	0.0945109	−	0.535998i
$280$		0			0
$281$	17.3397	−	20.6646i	1.03440	−	1.23275i	0.0623295	−	0.998056i	$-0.480147\pi$
$281$	17.3397	−	20.6646i	1.03440	−	1.23275i	0.972070	−	0.234693i	$-0.0754085\pi$
$282$		0			0
$283$	−6.05860	+	16.6459i	−0.360146	+	0.989493i	0.618831	+	0.785524i	$0.287607\pi$
$283$	−6.05860	+	16.6459i	−0.360146	+	0.989493i	−0.978977	+	0.203969i	$0.934616\pi$
$284$		0			0
$285$	−15.3410	+	4.94033i	−0.908723	+	0.292640i
$286$		0			0
$287$	−2.83087	−	1.03035i	−0.167101	−	0.0608198i
$288$		0			0
$289$	−2.51940	−	2.11403i	−0.148200	−	0.124355i
$290$		0			0
$291$	1.97986	+	0.349104i	0.116062	+	0.0204648i
$292$		0			0
$293$	−16.1263	+	9.31053i	−0.942109	+	0.543927i	−0.890621	−	0.454746i	$-0.849730\pi$
$293$	−16.1263	+	9.31053i	−0.942109	+	0.543927i	−0.0514885	+	0.998674i	$0.516397\pi$
$294$		0			0
$295$	11.6401	−	4.23664i	0.677712	−	0.246667i
$296$		0			0
$297$	0.444674	+	0.256733i	0.0258026	+	0.0148971i
$298$		0			0
$299$	7.92787	−	6.65227i	0.458481	−	0.384711i
$300$		0			0
$301$	1.76497	+	10.0097i	0.101731	+	0.576947i
$302$		0			0
$303$	−17.2147			−0.988960
$304$		0			0
$305$	−22.6062			−1.29443
$306$		0			0
$307$	−1.22507	−	6.94774i	−0.0699187	−	0.396528i	−0.999603	−	0.0281715i	$-0.991032\pi$
$307$	−1.22507	−	6.94774i	−0.0699187	−	0.396528i	0.929684	−	0.368357i	$-0.120080\pi$
$308$		0			0
$309$	−7.34007	+	6.15905i	−0.417562	+	0.350376i
$310$		0			0
$311$	−27.2984	−	15.7607i	−1.54795	−	0.893710i	−0.998298	−	0.0583164i	$-0.981427\pi$
$311$	−27.2984	−	15.7607i	−1.54795	−	0.893710i	−0.549653	−	0.835393i	$-0.685240\pi$
$312$		0			0
$313$	14.9455	−	5.43973i	0.844772	−	0.307472i	0.116865	−	0.993148i	$-0.462716\pi$
$313$	14.9455	−	5.43973i	0.844772	−	0.307472i	0.727907	+	0.685676i	$0.240493\pi$
$314$		0			0
$315$	8.36764	−	4.83106i	0.471463	−	0.272199i
$316$		0			0
$317$	28.9154	+	5.09856i	1.62405	+	0.286364i	0.910272	−	0.414010i	$-0.135872\pi$
$317$	28.9154	+	5.09856i	1.62405	+	0.286364i	0.713777	+	0.700373i	$0.246983\pi$
$318$		0			0
$319$	−1.86610	−	1.56585i	−0.104482	−	0.0876705i
$320$		0			0
$321$	−11.9766	−	4.35912i	−0.668467	−	0.243302i
$322$		0			0
$323$	−12.7447	+	9.90375i	−0.709135	+	0.551060i
$324$		0			0
$325$	17.5365	−	48.1812i	0.972752	−	2.67261i
$326$		0			0
$327$	−0.453958	+	0.541007i	−0.0251040	+	0.0299177i
$328$		0			0
$329$	−2.07418	+	11.7633i	−0.114353	+	0.648530i
$330$		0			0
$331$	−3.90090	−	6.75656i	−0.214413	−	0.371374i	0.738678	−	0.674059i	$-0.235451\pi$
$331$	−3.90090	−	6.75656i	−0.214413	−	0.371374i	−0.953091	+	0.302684i	$0.902117\pi$
$332$		0			0
$333$	−1.20990	−	3.32418i	−0.0663023	−	0.182164i
$334$		0			0
$335$	−6.50199	+	11.2618i	−0.355242	+	0.615297i
$336$		0			0
$337$	−6.68614	−	7.96823i	−0.364217	−	0.434057i	0.552549	−	0.833480i	$-0.313655\pi$
$337$	−6.68614	−	7.96823i	−0.364217	−	0.434057i	−0.916767	+	0.399423i	$0.869211\pi$
$338$		0			0
$339$	−19.5052	+	3.43929i	−1.05938	+	0.186796i
$340$		0			0
$341$			4.66793i			0.252783i
$342$		0			0
$343$			18.7399i			1.01186i
$344$		0			0
$345$	−6.37304	+	1.12374i	−0.343113	+	0.0605001i
$346$		0			0
$347$	0.292246	+	0.348285i	0.0156886	+	0.0186969i	0.773832	−	0.633391i	$-0.218338\pi$
$347$	0.292246	+	0.348285i	0.0156886	+	0.0186969i	−0.758143	+	0.652088i	$0.773893\pi$
$348$		0			0
$349$	−7.84226	+	13.5832i	−0.419786	+	0.727091i	−0.995918	−	0.0902658i	$-0.971228\pi$
$349$	−7.84226	+	13.5832i	−0.419786	+	0.727091i	0.576131	+	0.817357i	$0.304562\pi$
$350$		0			0
$351$	2.02238	+	5.55644i	0.107947	+	0.296581i
$352$		0			0
$353$	−12.6892	−	21.9783i	−0.675378	−	1.16979i	−0.976358	−	0.216159i	$-0.930647\pi$
$353$	−12.6892	−	21.9783i	−0.675378	−	1.16979i	0.300980	−	0.953630i	$-0.402686\pi$
$354$		0			0
$355$	1.21926	−	6.91476i	0.0647115	−	0.366997i
$356$		0			0
$357$	6.21975	−	7.41242i	0.329184	−	0.392307i
$358$		0			0
$359$	5.19369	−	14.2695i	0.274113	−	0.753118i	−0.723888	−	0.689917i	$-0.757647\pi$
$359$	5.19369	−	14.2695i	0.274113	−	0.753118i	0.998001	−	0.0632008i	$-0.0201309\pi$
$360$		0			0
$361$	−8.23972	−	17.1204i	−0.433669	−	0.901072i
$362$		0			0
$363$	10.0889	+	3.67205i	0.529528	+	0.192733i
$364$		0			0
$365$	37.9839	+	31.8723i	1.98817	+	1.66827i
$366$		0			0
$367$	−24.6962	−	4.35461i	−1.28913	−	0.227309i	−0.513278	−	0.858222i	$-0.671569\pi$
$367$	−24.6962	−	4.35461i	−1.28913	−	0.227309i	−0.775853	+	0.630913i	$0.782680\pi$
$368$		0			0
$369$	−0.998380	+	0.576415i	−0.0519736	+	0.0300070i
$370$		0			0
$371$	15.8686	−	5.77571i	0.823859	−	0.299860i
$372$		0			0
$373$	6.46115	+	3.73035i	0.334546	+	0.193150i	0.657857	−	0.753142i	$-0.271463\pi$
$373$	6.46115	+	3.73035i	0.334546	+	0.193150i	−0.323312	+	0.946293i	$0.604796\pi$
$374$		0			0
$375$	−10.3985	+	8.72536i	−0.536975	+	0.450576i
$376$		0			0
$377$	−4.87138	−	27.6269i	−0.250889	−	1.42286i
$378$		0			0
$379$	13.1419			0.675052			0.337526	−	0.941316i	$-0.390410\pi$
$379$	13.1419			0.675052			0.337526	+	0.941316i	$0.390410\pi$
$380$		0			0
$381$	19.2395			0.985668
$382$		0			0
$383$	−1.49397	−	8.47274i	−0.0763385	−	0.432937i	−0.998892	−	0.0470671i	$-0.985013\pi$
$383$	−1.49397	−	8.47274i	−0.0763385	−	0.432937i	0.922553	−	0.385870i	$-0.126099\pi$
$384$		0			0
$385$	−3.80047	+	3.18898i	−0.193690	+	0.162525i
$386$		0			0
$387$	3.36844	+	1.94477i	0.171228	+	0.0988583i
$388$		0			0
$389$	−0.812381	+	0.295682i	−0.0411893	+	0.0149917i	−0.362533	−	0.931971i	$-0.618088\pi$
$389$	−0.812381	+	0.295682i	−0.0411893	+	0.0149917i	0.321343	+	0.946963i	$0.395866\pi$
$390$		0			0
$391$	−5.61254	+	3.24040i	−0.283838	+	0.163874i
$392$		0			0
$393$	16.4428	+	2.89930i	0.829428	+	0.146251i
$394$		0			0
$395$	−19.8895	−	16.6893i	−1.00075	−	0.839730i
$396$		0			0
$397$	−4.46370	−	1.62465i	−0.224027	−	0.0815390i	0.227568	−	0.973762i	$-0.426923\pi$
$397$	−4.46370	−	1.62465i	−0.224027	−	0.0815390i	−0.451595	+	0.892223i	$0.649145\pi$
$398$		0			0
$399$	6.98926	+	8.99418i	0.349901	+	0.450272i
$400$		0			0
$401$	−7.90088	+	21.7075i	−0.394551	+	1.08402i	0.570349	+	0.821403i	$0.306808\pi$
$401$	−7.90088	+	21.7075i	−0.394551	+	1.08402i	−0.964900	+	0.262618i	$0.915414\pi$
$402$		0			0
$403$	−34.5535	+	41.1793i	−1.72123	+	2.05129i
$404$		0			0
$405$	0.642058	−	3.64129i	0.0319041	−	0.180937i
$406$		0			0
$407$	0.908197	+	1.57304i	0.0450176	+	0.0779729i
$408$		0			0
$409$	0.530585	+	1.45777i	0.0262357	+	0.0720821i	0.952119	−	0.305727i	$-0.0988996\pi$
$409$	0.530585	+	1.45777i	0.0262357	+	0.0720821i	−0.925883	+	0.377810i	$0.876677\pi$
$410$		0			0
$411$	6.81919	−	11.8112i	0.336366	−	0.582603i
$412$		0			0
$413$	−5.62733	−	6.70640i	−0.276903	−	0.330000i
$414$		0			0
$415$	53.1743	−	9.37607i	2.61023	−	0.460253i
$416$		0			0
$417$		−	10.3764i		−	0.508135i
$418$		0			0
$419$		−	9.15254i		−	0.447131i	−0.974689	−	0.223566i	$-0.928230\pi$
$419$		−	9.15254i		−	0.447131i	0.974689	−	0.223566i	$-0.0717697\pi$
$420$		0			0
$421$	−16.4490	+	2.90039i	−0.801673	+	0.141357i	−0.559450	−	0.828864i	$-0.688988\pi$
$421$	−16.4490	+	2.90039i	−0.801673	+	0.141357i	−0.242223	+	0.970221i	$0.577877\pi$
$422$		0			0
$423$	2.93816	+	3.50156i	0.142858	+	0.170252i
$424$		0			0
$425$	−16.0542	+	27.8066i	−0.778742	+	1.34882i
$426$		0			0
$427$	5.46441	+	15.0134i	0.264442	+	0.726547i
$428$		0			0
$429$	−1.51807	−	2.62938i	−0.0732932	−	0.126947i
$430$		0			0
$431$	−4.72003	+	26.7686i	−0.227356	+	1.28940i	0.630774	+	0.775967i	$0.282738\pi$
$431$	−4.72003	+	26.7686i	−0.227356	+	1.28940i	−0.858130	+	0.513433i	$0.828374\pi$
$432$		0			0
$433$	10.5783	−	12.6068i	0.508362	−	0.605842i	−0.449426	−	0.893317i	$-0.648372\pi$
$433$	10.5783	−	12.6068i	0.508362	−	0.605842i	0.957788	+	0.287475i	$0.0928160\pi$
$434$		0			0
$435$	−5.99965	+	16.4839i	−0.287661	+	0.790343i
$436$		0			0
$437$	−2.33853	−	7.26176i	−0.111867	−	0.347377i
$438$		0			0
$439$	−4.00169	−	1.45650i	−0.190990	−	0.0695148i	0.244754	−	0.969585i	$-0.421293\pi$
$439$	−4.00169	−	1.45650i	−0.190990	−	0.0695148i	−0.435745	+	0.900070i	$0.643515\pi$
$440$		0			0
$441$	0.131230	+	0.110115i	0.00624905	+	0.00524358i
$442$		0			0
$443$	−0.384063	−	0.0677207i	−0.0182474	−	0.00321751i	0.164517	−	0.986374i	$-0.447393\pi$
$443$	−0.384063	−	0.0677207i	−0.0182474	−	0.00321751i	−0.182764	+	0.983157i	$0.558505\pi$
$444$		0			0
$445$	50.7816	−	29.3188i	2.40728	−	1.38984i
$446$		0			0
$447$	6.22448	−	2.26552i	0.294408	−	0.107156i
$448$		0			0
$449$	13.4622	+	7.77241i	0.635321	+	0.366803i	0.782810	−	0.622261i	$-0.213786\pi$
$449$	13.4622	+	7.77241i	0.635321	+	0.366803i	−0.147489	+	0.989064i	$0.547119\pi$
$450$		0			0
$451$	0.453451	−	0.380490i	0.0213522	−	0.0179166i
$452$		0			0
$453$	−3.80162	−	21.5601i	−0.178616	−	1.01298i
$454$		0			0
$455$	−57.1326			−2.67842
$456$		0			0
$457$	−19.8281			−0.927520			−0.463760	−	0.885961i	$-0.653500\pi$
$457$	−19.8281			−0.927520			−0.463760	+	0.885961i	$0.653500\pi$
$458$		0			0
$459$	−0.642995	−	3.64660i	−0.0300124	−	0.170209i
$460$		0			0
$461$	−3.64206	+	3.05605i	−0.169628	+	0.142334i	−0.723650	−	0.690168i	$-0.757537\pi$
$461$	−3.64206	+	3.05605i	−0.169628	+	0.142334i	0.554022	+	0.832502i	$0.313092\pi$
$462$		0			0
$463$	−20.5124	−	11.8428i	−0.953292	−	0.550383i	−0.0591900	−	0.998247i	$-0.518852\pi$
$463$	−20.5124	−	11.8428i	−0.953292	−	0.550383i	−0.894102	+	0.447863i	$0.852185\pi$
$464$		0			0
$465$	31.5866	−	11.4966i	1.46479	−	0.533142i
$466$		0			0
$467$	−2.25366	+	1.30115i	−0.104287	+	0.0602102i	−0.551236	−	0.834349i	$-0.685844\pi$
$467$	−2.25366	+	1.30115i	−0.104287	+	0.0602102i	0.446949	+	0.894559i	$0.352510\pi$
$468$		0			0
$469$	9.05092	+	1.59592i	0.417933	+	0.0736928i
$470$		0			0
$471$	16.2914	+	13.6701i	0.750666	+	0.629883i
$472$		0			0
$473$	−1.87670	−	0.683064i	−0.0862909	−	0.0314073i
$474$		0			0
$475$	−28.0225	−	25.3644i	−1.28576	−	1.16380i
$476$		0			0
$477$	2.21023	−	6.07255i	0.101199	−	0.278043i
$478$		0			0
$479$	21.1054	−	25.1524i	0.964331	−	1.14924i	−0.0244245	−	0.999702i	$-0.507775\pi$
$479$	21.1054	−	25.1524i	0.964331	−	1.14924i	0.988755	−	0.149543i	$-0.0477802\pi$
$480$		0			0
$481$	−3.63229	+	20.5997i	−0.165618	+	0.939267i
$482$		0			0
$483$	2.28681	+	3.96087i	0.104054	+	0.180226i
$484$		0			0
$485$	2.54238	+	6.98512i	0.115443	+	0.317178i
$486$		0			0
$487$	11.6561	−	20.1889i	0.528186	−	0.914846i	−0.471274	−	0.881987i	$-0.656206\pi$
$487$	11.6561	−	20.1889i	0.528186	−	0.914846i	0.999460	−	0.0328586i	$-0.0104611\pi$
$488$		0			0
$489$	−11.5746	−	13.7941i	−0.523423	−	0.623792i
$490$		0			0
$491$	−6.45892	+	1.13888i	−0.291487	+	0.0513970i	−0.317480	−	0.948265i	$-0.602836\pi$
$491$	−6.45892	+	1.13888i	−0.291487	+	0.0513970i	0.0259926	+	0.999662i	$0.491725\pi$
$492$		0			0
$493$			17.5674i			0.791196i
$494$		0			0
$495$			1.89852i			0.0853321i
$496$		0			0
$497$	−4.88699	+	0.861709i	−0.219212	+	0.0386529i
$498$		0			0
$499$	−18.5828	−	22.1461i	−0.831878	−	0.991394i	−0.999984	−	0.00562503i	$-0.998209\pi$
$499$	−18.5828	−	22.1461i	−0.831878	−	0.991394i	0.168106	−	0.985769i	$-0.446235\pi$
$500$		0			0
$501$	10.8333	−	18.7638i	0.483995	−	0.838303i
$502$		0			0
$503$	−1.66432	−	4.57267i	−0.0742082	−	0.203885i	0.897043	−	0.441944i	$-0.145711\pi$
$503$	−1.66432	−	4.57267i	−0.0742082	−	0.203885i	−0.971251	+	0.238059i	$0.923489\pi$
$504$		0			0
$505$	−31.8254	−	55.1232i	−1.41621	−	2.45295i
$506$		0			0
$507$	3.81402	−	21.6304i	0.169387	−	0.960639i
$508$		0			0
$509$	16.8092	−	20.0325i	0.745057	−	0.887924i	−0.251749	−	0.967793i	$-0.581006\pi$
$509$	16.8092	−	20.0325i	0.745057	−	0.887924i	0.996805	+	0.0798688i	$0.0254501\pi$
$510$		0			0
$511$	11.9857	−	32.9304i	0.530215	−	1.45675i
$512$		0			0
$513$	4.35583	+	0.163503i	0.192315	+	0.00721882i
$514$		0			0
$515$	−33.2917	−	12.1172i	−1.46701	−	0.533947i
$516$		0			0
$517$	−1.79793	−	1.50864i	−0.0790729	−	0.0663501i
$518$		0			0
$519$	−7.37557	−	1.30051i	−0.323752	−	0.0570861i
$520$		0			0
$521$	14.7970	−	8.54304i	0.648268	−	0.374277i	−0.139525	−	0.990219i	$-0.544557\pi$
$521$	14.7970	−	8.54304i	0.648268	−	0.374277i	0.787792	+	0.615941i	$0.211224\pi$
$522$		0			0
$523$	−9.19500	+	3.34670i	−0.402069	+	0.146341i	−0.535136	−	0.844766i	$-0.679740\pi$
$523$	−9.19500	+	3.34670i	−0.402069	+	0.146341i	0.133067	+	0.991107i	$0.457517\pi$
$524$		0			0
$525$	19.6237	+	11.3297i	0.856447	+	0.494470i
$526$		0			0
$527$	25.7872	−	21.6380i	1.12331	−	0.942568i
$528$		0			0
$529$	3.46198	+	19.6339i	0.150521	+	0.853646i
$530$		0			0
$531$	−3.35017			−0.145385
$532$		0			0
$533$	6.81673			0.295265
$534$		0			0
$535$	−8.18316	−	46.4090i	−0.353789	−	2.00644i
$536$		0			0
$537$	11.7410	−	9.85185i	0.506660	−	0.425139i
$538$		0			0
$539$	−0.0761765	−	0.0439805i	−0.00328116	−	0.00189438i
$540$		0			0
$541$	6.11699	−	2.22640i	0.262990	−	0.0957205i	−0.207160	−	0.978307i	$-0.566422\pi$
$541$	6.11699	−	2.22640i	0.262990	−	0.0957205i	0.470150	+	0.882587i	$0.344200\pi$
$542$		0			0
$543$	−4.04502	+	2.33539i	−0.173588	+	0.100221i
$544$		0			0
$545$	−2.57160	−	0.453443i	−0.110155	−	0.0194234i
$546$		0			0
$547$	7.16229	+	6.00988i	0.306238	+	0.256964i	0.782935	−	0.622104i	$-0.213722\pi$
$547$	7.16229	+	6.00988i	0.306238	+	0.256964i	−0.476697	+	0.879067i	$0.658166\pi$
$548$		0			0
$549$	5.74525	+	2.09110i	0.245201	+	0.0892460i
$550$		0			0
$551$	−20.2166	−	4.35241i	−0.861258	−	0.185419i
$552$		0			0
$553$	−6.27607	+	17.2433i	−0.266885	+	0.733262i
$554$		0			0
$555$	8.40757	−	10.0197i	0.356881	−	0.425315i
$556$		0			0
$557$	−7.65933	+	43.4382i	−0.324536	+	1.84054i	0.188380	+	0.982096i	$0.439676\pi$
$557$	−7.65933	+	43.4382i	−0.324536	+	1.84054i	−0.512916	+	0.858439i	$0.671435\pi$
$558$		0			0
$559$	−11.4995	−	19.9178i	−0.486378	−	0.842431i
$560$		0			0
$561$	0.650279	+	1.78663i	0.0274548	+	0.0754315i
$562$		0			0
$563$	−6.72397	+	11.6463i	−0.283382	+	0.490831i	−0.972215	−	0.234088i	$-0.924790\pi$
$563$	−6.72397	+	11.6463i	−0.283382	+	0.490831i	0.688834	+	0.724919i	$0.258123\pi$
$564$		0			0
$565$	−47.0728	−	56.0991i	−1.98037	−	2.36011i
$566$		0			0
$567$	−2.57348	+	0.453773i	−0.108076	+	0.0190567i
$568$		0			0
$569$			20.0058i			0.838686i	0.907828	+	0.419343i	$0.137740\pi$
$569$			20.0058i			0.838686i	−0.907828	+	0.419343i	$0.862260\pi$
$570$		0			0
$571$			36.0510i			1.50869i	0.656480	+	0.754343i	$0.272045\pi$
$571$			36.0510i			1.50869i	−0.656480	+	0.754343i	$0.727955\pi$
$572$		0			0
$573$	−9.44995	+	1.66628i	−0.394777	+	0.0696099i
$574$		0			0
$575$	−9.75529	−	11.6259i	−0.406824	−	0.484833i
$576$		0			0
$577$	15.8742	−	27.4949i	0.660851	−	1.14463i	−0.319541	−	0.947572i	$-0.603529\pi$
$577$	15.8742	−	27.4949i	0.660851	−	1.14463i	0.980392	−	0.197055i	$-0.0631379\pi$
$578$		0			0
$579$	−1.81339	−	4.98225i	−0.0753620	−	0.207055i
$580$		0			0
$581$	−19.0803	−	33.0481i	−0.791585	−	1.37107i
$582$		0			0
$583$	−0.576191	+	3.26774i	−0.0238634	+	0.135336i
$584$		0			0
$585$	−14.0534	+	16.7482i	−0.581038	+	0.692454i
$586$		0			0
$587$	−14.9173	+	40.9851i	−0.615705	+	1.69164i	0.101555	+	0.994830i	$0.467618\pi$
$587$	−14.9173	+	40.9851i	−0.615705	+	1.69164i	−0.717260	+	0.696805i	$0.754604\pi$
$588$		0			0
$589$	18.5123	+	35.0370i	0.762784	+	1.44367i
$590$		0			0
$591$	20.0687	+	7.30443i	0.825518	+	0.300464i
$592$		0			0
$593$	4.86775	+	4.08453i	0.199895	+	0.167731i	0.737240	−	0.675631i	$-0.236129\pi$
$593$	4.86775	+	4.08453i	0.199895	+	0.167731i	−0.537346	+	0.843362i	$0.680573\pi$
$594$		0			0
$595$	35.2339	+	6.21269i	1.44445	+	0.254696i
$596$		0			0
$597$	11.0045	−	6.35343i	0.450383	−	0.260029i
$598$		0			0
$599$	13.2957	−	4.83925i	0.543248	−	0.197726i	−0.0557958	−	0.998442i	$-0.517770\pi$
$599$	13.2957	−	4.83925i	0.543248	−	0.197726i	0.599044	+	0.800716i	$0.295547\pi$
$600$		0			0
$601$	32.7028	+	18.8810i	1.33398	+	0.770171i	0.985906	−	0.167297i	$-0.0535040\pi$
$601$	32.7028	+	18.8810i	1.33398	+	0.770171i	0.348069	+	0.937469i	$0.386837\pi$
$602$		0			0
$603$	2.69418	−	2.26068i	0.109715	−	0.0920622i
$604$		0			0
$605$	6.89336	+	39.0942i	0.280255	+	1.58940i
$606$		0			0
$607$	−38.6875			−1.57028			−0.785139	−	0.619320i	$-0.787408\pi$
$607$	−38.6875			−1.57028			−0.785139	+	0.619320i	$0.787408\pi$
$608$		0			0
$609$	12.3976			0.502378
$610$		0			0
$611$	−4.69342	−	26.6177i	−0.189875	−	1.07684i
$612$		0			0
$613$	−8.08852	+	6.78708i	−0.326692	+	0.274127i	−0.791351	−	0.611363i	$-0.790622\pi$
$613$	−8.08852	+	6.78708i	−0.326692	+	0.274127i	0.464658	+	0.885490i	$0.346177\pi$
$614$		0			0
$615$	−3.69147	−	2.13127i	−0.148855	−	0.0859412i
$616$		0			0
$617$	9.63339	−	3.50627i	0.387826	−	0.141157i	−0.140746	−	0.990046i	$-0.544950\pi$
$617$	9.63339	−	3.50627i	0.387826	−	0.141157i	0.528572	+	0.848889i	$0.322728\pi$
$618$		0			0
$619$	28.6625	−	16.5483i	1.15204	−	0.665132i	0.202659	−	0.979249i	$-0.435042\pi$
$619$	28.6625	−	16.5483i	1.15204	−	0.665132i	0.949384	+	0.314117i	$0.101708\pi$
$620$		0			0
$621$	1.72363	+	0.303922i	0.0691667	+	0.0121960i
$622$		0			0
$623$	−31.7464	−	26.6384i	−1.27189	−	1.06725i
$624$		0			0
$625$	−6.42198	−	2.33741i	−0.256879	−	0.0934964i
$626$		0			0
$627$	−2.21717	+	0.305698i	−0.0885452	+	0.0122084i
$628$		0			0
$629$	4.48010	−	12.3090i	0.178633	−	0.490791i
$630$		0			0
$631$	3.05481	−	3.64058i	0.121610	−	0.144929i	−0.701804	−	0.712370i	$-0.747622\pi$
$631$	3.05481	−	3.64058i	0.121610	−	0.144929i	0.823414	+	0.567441i	$0.192066\pi$
$632$		0			0
$633$	1.57224	−	8.91663i	0.0624910	−	0.354404i
$634$		0			0
$635$	35.5686	+	61.6066i	1.41150	+	2.44479i
$636$		0			0
$637$	−0.346451	−	0.951867i	−0.0137269	−	0.0377144i
$638$		0			0
$639$	−0.949493	+	1.64457i	−0.0375614	+	0.0650582i
$640$		0			0
$641$	−24.0755	−	28.6921i	−0.950927	−	1.13327i	−0.990972	−	0.134073i	$-0.957194\pi$
$641$	−24.0755	−	28.6921i	−0.950927	−	1.13327i	0.0400447	−	0.999198i	$-0.487250\pi$
$642$		0			0
$643$	0.966822	−	0.170477i	0.0381277	−	0.00672295i	−0.154552	−	0.987985i	$-0.549393\pi$
$643$	0.966822	−	0.170477i	0.0381277	−	0.00672295i	0.192680	+	0.981262i	$0.438282\pi$
$644$		0			0
$645$			14.3814i			0.566269i
$646$		0			0
$647$			25.1727i			0.989640i	0.868996	+	0.494820i	$0.164766\pi$
$647$			25.1727i			0.989640i	−0.868996	+	0.494820i	$0.835234\pi$
$648$		0			0
$649$	1.69406	−	0.298709i	0.0664977	−	0.0117253i
$650$		0			0
$651$	−15.2704	−	18.1985i	−0.598493	−	0.713257i
$652$		0			0
$653$	2.45329	−	4.24922i	0.0960045	−	0.166285i	−0.814023	−	0.580833i	$-0.802727\pi$
$653$	2.45329	−	4.24922i	0.0960045	−	0.166285i	0.910027	+	0.414548i	$0.136060\pi$
$654$		0			0
$655$	21.1144	+	58.0114i	0.825008	+	2.26669i
$656$		0			0
$657$	−6.70521	−	11.6138i	−0.261595	−	0.453096i
$658$		0			0
$659$	3.38519	−	19.1984i	0.131868	−	0.747862i	−0.845121	−	0.534575i	$-0.820472\pi$
$659$	3.38519	−	19.1984i	0.131868	−	0.747862i	0.976989	−	0.213288i	$-0.0684171\pi$
$660$		0			0
$661$	3.54367	−	4.22319i	0.137833	−	0.164263i	−0.692712	−	0.721214i	$-0.743584\pi$
$661$	3.54367	−	4.22319i	0.137833	−	0.164263i	0.830545	+	0.556951i	$0.188029\pi$
$662$		0			0
$663$	−7.48858	+	20.5747i	−0.290833	+	0.799056i
$664$		0			0
$665$	−15.8790	+	39.0081i	−0.615760	+	1.51267i
$666$		0			0
$667$	−7.80275	−	2.83997i	−0.302124	−	0.109964i
$668$		0			0
$669$	16.7005	+	14.0134i	0.645679	+	0.541789i
$670$		0			0
$671$	−3.09162	−	0.545136i	−0.119351	−	0.0210447i
$672$		0			0
$673$	−21.7157	+	12.5376i	−0.837079	+	0.483288i	−0.856270	−	0.516528i	$-0.827224\pi$
$673$	−21.7157	+	12.5376i	−0.837079	+	0.483288i	0.0191910	+	0.999816i	$0.493891\pi$
$674$		0			0
$675$	8.14829	−	2.96574i	0.313628	−	0.114151i
$676$		0			0
$677$	−27.1334	−	15.6655i	−1.04282	−	0.602074i	−0.122191	−	0.992507i	$-0.538992\pi$
$677$	−27.1334	−	15.6655i	−1.04282	−	0.602074i	−0.920631	+	0.390433i	$0.872325\pi$
$678$		0			0
$679$	4.02445	−	3.37692i	0.154444	−	0.129594i
$680$		0			0
$681$	−0.879854	−	4.98990i	−0.0337161	−	0.191213i
$682$		0			0
$683$	−0.746003			−0.0285450			−0.0142725	−	0.999898i	$-0.504543\pi$
$683$	−0.746003			−0.0285450			−0.0142725	+	0.999898i	$0.504543\pi$
$684$		0			0
$685$	50.4274			1.92673
$686$		0			0
$687$	2.25331	+	12.7791i	0.0859690	+	0.487555i
$688$		0			0
$689$	−29.2719	+	24.5620i	−1.11517	+	0.935738i
$690$		0			0
$691$	−17.2610	−	9.96565i	−0.656640	−	0.379111i	0.134356	−	0.990933i	$-0.457104\pi$
$691$	−17.2610	−	9.96565i	−0.656640	−	0.379111i	−0.790995	+	0.611822i	$0.790437\pi$
$692$		0			0
$693$	1.26086	−	0.458914i	0.0478960	−	0.0174327i
$694$		0			0
$695$	33.2263	−	19.1832i	1.26034	−	0.727660i
$696$		0			0
$697$	−4.20391	−	0.741263i	−0.159235	−	0.0280774i
$698$		0			0
$699$	13.0084	+	10.9153i	0.492022	+	0.412855i
$700$		0			0
$701$	−1.47415	−	0.536546i	−0.0556778	−	0.0202651i	0.314031	−	0.949413i	$-0.398320\pi$
$701$	−1.47415	−	0.536546i	−0.0556778	−	0.0202651i	−0.369709	+	0.929148i	$0.620543\pi$
$702$		0			0
$703$	13.0553	+	8.20533i	0.492388	+	0.309470i
$704$		0			0
$705$	−5.78048	+	15.8817i	−0.217705	+	0.598140i
$706$		0			0
$707$	−28.9159	+	34.4606i	−1.08749	+	1.29602i
$708$		0			0
$709$	1.40513	−	7.96888i	0.0527707	−	0.299278i	−0.946987	−	0.321271i	$-0.895890\pi$
$709$	1.40513	−	7.96888i	0.0527707	−	0.299278i	0.999758	+	0.0219930i	$0.00700116\pi$
$710$		0			0
$711$	3.51105	+	6.08132i	0.131675	+	0.228067i
$712$		0			0
$713$	5.44198	+	14.9517i	0.203804	+	0.559946i
$714$		0			0
$715$	5.61301	−	9.72202i	0.209915	−	0.363583i
$716$		0			0
$717$	−15.0550	−	17.9419i	−0.562240	−	0.670052i
$718$		0			0
$719$	−17.4462	+	3.07624i	−0.650635	+	0.114724i	−0.489218	−	0.872162i	$-0.662718\pi$
$719$	−17.4462	+	3.07624i	−0.650635	+	0.114724i	−0.161417	+	0.986886i	$0.551607\pi$
$720$		0			0
$721$			25.0389i			0.932497i
$722$		0			0
$723$		−	2.91120i		−	0.108269i
$724$		0			0
$725$	−40.5138	+	7.14367i	−1.50464	+	0.265309i
$726$		0			0
$727$	29.9914	+	35.7423i	1.11232	+	1.32561i	0.940235	+	0.340527i	$0.110606\pi$
$727$	29.9914	+	35.7423i	1.11232	+	1.32561i	0.172084	+	0.985082i	$0.444950\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	4.92592	+	13.5339i	0.182192	+	0.500568i
$732$		0			0
$733$	−11.2393	−	19.4671i	−0.415135	−	0.719034i	0.580308	−	0.814397i	$-0.302932\pi$
$733$	−11.2393	−	19.4671i	−0.415135	−	0.719034i	−0.995443	+	0.0953629i	$0.969599\pi$
$734$		0			0
$735$	−0.109990	+	0.623785i	−0.00405705	+	0.0230087i
$736$		0			0
$737$	−1.16078	+	1.38337i	−0.0427580	+	0.0509570i
$738$		0			0
$739$	−9.53594	+	26.1998i	−0.350785	+	0.963774i	0.631333	+	0.775511i	$0.282508\pi$
$739$	−9.53594	+	26.1998i	−0.350785	+	0.963774i	−0.982119	+	0.188263i	$0.939714\pi$
$740$		0			0
$741$	−21.8221	−	13.7154i	−0.801656	−	0.503847i
$742$		0			0
$743$	−19.8894	−	7.23913i	−0.729670	−	0.265578i	−0.0496447	−	0.998767i	$-0.515809\pi$
$743$	−19.8894	−	7.23913i	−0.729670	−	0.265578i	−0.680025	+	0.733189i	$0.738031\pi$
$744$		0			0
$745$	18.7618	+	15.7430i	0.687380	+	0.576780i
$746$		0			0
$747$	−14.3813	−	2.53581i	−0.526184	−	0.0927805i
$748$		0			0
$749$	−28.8434	+	16.6527i	−1.05391	+	0.608478i
$750$		0			0
$751$	−37.3104	+	13.5799i	−1.36147	+	0.495536i	−0.916510	−	0.400012i	$-0.869006\pi$
$751$	−37.3104	+	13.5799i	−1.36147	+	0.495536i	−0.444965	+	0.895548i	$0.646784\pi$
$752$		0			0
$753$	−20.9714	−	12.1078i	−0.764241	−	0.441234i
$754$		0			0
$755$	62.0093	−	52.0320i	2.25675	−	1.89364i
$756$		0			0
$757$	−7.21836	−	40.9374i	−0.262356	−	1.48789i	−0.776460	−	0.630166i	$-0.782987\pi$
$757$	−7.21836	−	40.9374i	−0.262356	−	1.48789i	0.514105	−	0.857728i	$-0.328124\pi$
$758$		0			0
$759$	−0.898675			−0.0326198
$760$		0			0
$761$	10.3359			0.374676			0.187338	−	0.982295i	$-0.440014\pi$
$761$	10.3359			0.374676			0.187338	+	0.982295i	$0.440014\pi$
$762$		0			0
$763$	0.320470	+	1.81748i	0.0116018	+	0.0657971i
$764$		0			0
$765$	10.4881	−	8.80052i	0.379196	−	0.318184i
$766$		0			0
$767$	17.1557	+	9.90484i	0.619456	+	0.357643i
$768$		0			0
$769$	−5.83021	+	2.12202i	−0.210243	+	0.0765222i	−0.444995	−	0.895533i	$-0.646794\pi$
$769$	−5.83021	+	2.12202i	−0.210243	+	0.0765222i	0.234752	+	0.972055i	$0.424572\pi$
$770$		0			0
$771$	−4.24514	+	2.45093i	−0.152885	+	0.0882682i
$772$		0			0
$773$	−10.0991	−	1.78074i	−0.363238	−	0.0640487i	−0.0109495	−	0.999940i	$-0.503485\pi$
$773$	−10.0991	−	1.78074i	−0.363238	−	0.0640487i	−0.352289	+	0.935891i	$0.614597\pi$
$774$		0			0
$775$	60.3877	+	50.6713i	2.16919	+	1.82017i
$776$		0			0
$777$	−8.68667	−	3.16169i	−0.311633	−	0.113425i
$778$		0			0
$779$	1.89459	−	4.65423i	0.0678807	−	0.166755i
$780$		0			0
$781$	0.333491	−	0.916260i	0.0119333	−	0.0327863i
$782$		0			0
$783$	3.04956	−	3.63433i	0.108983	−	0.129880i
$784$		0			0
$785$	−13.6545	+	77.4388i	−0.487352	+	2.76391i
$786$		0			0
$787$	−14.3650	−	24.8809i	−0.512057	−	0.886909i	−0.999902	−	0.0139788i	$-0.995550\pi$
$787$	−14.3650	−	24.8809i	−0.512057	−	0.886909i	0.487845	−	0.872930i	$-0.337783\pi$
$788$		0			0
$789$	3.89342	+	10.6971i	0.138610	+	0.380827i
$790$		0			0
$791$	−25.8784	+	44.8227i	−0.920129	+	1.59371i
$792$		0			0
$793$	−23.2382	−	27.6942i	−0.825211	−	0.983448i
$794$		0			0
$795$	23.5310	−	4.14915i	0.834559	−	0.147155i
$796$		0			0
$797$			32.9912i			1.16861i	0.811534	+	0.584305i	$0.198633\pi$
$797$			32.9912i			1.16861i	−0.811534	+	0.584305i	$0.801367\pi$
$798$		0			0
$799$			16.9256i			0.598786i
$800$		0			0
$801$	−15.6179	+	2.75386i	−0.551833	+	0.0973030i
$802$		0			0
$803$	4.42609	+	5.27481i	0.156193	+	0.186144i
$804$		0			0
$805$	−8.45540	+	14.6452i	−0.298014	+	0.516175i
$806$		0			0
$807$	0.0732200	+	0.201170i	0.00257747	+	0.00708153i
$808$		0			0
$809$	−6.86994	−	11.8991i	−0.241534	−	0.418350i	0.719617	−	0.694371i	$-0.244317\pi$
$809$	−6.86994	−	11.8991i	−0.241534	−	0.418350i	−0.961152	+	0.276021i	$0.910984\pi$
$810$		0			0
$811$	−7.09275	+	40.2250i	−0.249060	+	1.41249i	0.561811	+	0.827266i	$0.310105\pi$
$811$	−7.09275	+	40.2250i	−0.249060	+	1.41249i	−0.810871	+	0.585225i	$0.801006\pi$
$812$		0			0
$813$	9.77463	−	11.6490i	0.342811	−	0.408547i
$814$		0			0
$815$	22.7717	−	62.5648i	0.797658	−	2.19155i
$816$		0			0
$817$	−16.7952	+	2.31569i	−0.587591	+	0.0810158i
$818$		0			0
$819$	14.5200	+	5.28484i	0.507369	+	0.184667i
$820$		0			0
$821$	8.06510	+	6.76743i	0.281474	+	0.236185i	0.772584	−	0.634913i	$-0.218964\pi$
$821$	8.06510	+	6.76743i	0.281474	+	0.236185i	−0.491110	+	0.871098i	$0.663409\pi$
$822$		0			0
$823$	−26.0326	−	4.59026i	−0.907441	−	0.160006i	−0.299600	−	0.954065i	$-0.596853\pi$
$823$	−26.0326	−	4.59026i	−0.907441	−	0.160006i	−0.607841	+	0.794059i	$0.707964\pi$
$824$		0			0
$825$	−3.85587	+	2.22619i	−0.134244	+	0.0775059i
$826$		0			0
$827$	−25.7871	+	9.38573i	−0.896705	+	0.326374i	−0.748932	−	0.662647i	$-0.769433\pi$
$827$	−25.7871	+	9.38573i	−0.896705	+	0.326374i	−0.147773	+	0.989021i	$0.547211\pi$
$828$		0			0
$829$	37.4611	+	21.6282i	1.30108	+	0.751178i	0.980589	−	0.196073i	$-0.0628191\pi$
$829$	37.4611	+	21.6282i	1.30108	+	0.751178i	0.320490	+	0.947252i	$0.396152\pi$
$830$		0			0
$831$	14.8240	−	12.4388i	0.514238	−	0.431497i
$832$		0			0
$833$	0.110151	+	0.624695i	0.00381649	+	0.0216444i
$834$		0			0
$835$	80.1112			2.77236
$836$		0			0
$837$	−9.09104			−0.314232
$838$		0			0
$839$	−7.26214	−	41.1857i	−0.250717	−	1.42189i	−0.806832	−	0.590781i	$-0.798820\pi$
$839$	−7.26214	−	41.1857i	−0.250717	−	1.42189i	0.556115	−	0.831105i	$-0.312291\pi$
$840$		0			0
$841$	4.97301	−	4.17285i	0.171483	−	0.143891i
$842$		0			0
$843$	−23.3617	−	13.4879i	−0.804620	−	0.464547i
$844$		0			0
$845$	76.3137	−	27.7759i	2.62527	−	0.955521i
$846$		0			0
$847$	24.2972	−	14.0280i	0.834862	−	0.482008i
$848$		0			0
$849$	17.4450	+	3.07603i	0.598712	+	0.105569i
$850$		0			0
$851$	4.74291	+	3.97977i	0.162585	+	0.136425i
$852$		0			0
$853$	33.4425	+	12.1721i	1.14505	+	0.416764i	0.843734	−	0.536761i	$-0.180352\pi$
$853$	33.4425	+	12.1721i	1.14505	+	0.416764i	0.301314	+	0.953525i	$0.402575\pi$
$854$		0			0
$855$	7.52921	+	14.2501i	0.257494	+	0.487342i
$856$		0			0
$857$	4.83901	−	13.2951i	0.165298	−	0.454151i	−0.829195	−	0.558960i	$-0.811201\pi$
$857$	4.83901	−	13.2951i	0.165298	−	0.454151i	0.994492	+	0.104808i	$0.0334229\pi$
$858$		0			0
$859$	20.3598	−	24.2639i	0.694669	−	0.827874i	−0.297243	−	0.954802i	$-0.596067\pi$
$859$	20.3598	−	24.2639i	0.694669	−	0.827874i	0.991912	+	0.126928i	$0.0405116\pi$
$860$		0			0
$861$	−0.523123	+	2.96678i	−0.0178280	+	0.101108i
$862$		0			0
$863$	7.85321	+	13.6022i	0.267327	+	0.463023i	0.968171	−	0.250291i	$-0.0805264\pi$
$863$	7.85321	+	13.6022i	0.267327	+	0.463023i	−0.700844	+	0.713315i	$0.747193\pi$
$864$		0			0
$865$	−9.47108	−	26.0216i	−0.322026	−	0.884760i
$866$		0			0
$867$	−1.64442	+	2.84822i	−0.0558475	+	0.0967307i
$868$		0			0
$869$	−2.31764	−	2.76205i	−0.0786205	−	0.0936963i
$870$		0			0
$871$	−20.4802	+	3.61122i	−0.693946	+	0.122361i
$872$		0			0
$873$		−	2.01041i		−	0.0680420i
$874$		0			0
$875$			35.4719i			1.19917i
$876$		0			0
$877$	−8.61187	+	1.51851i	−0.290802	+	0.0512763i	−0.317146	−	0.948377i	$-0.602725\pi$
$877$	−8.61187	+	1.51851i	−0.290802	+	0.0512763i	0.0263439	+	0.999653i	$0.491613\pi$
$878$		0			0
$879$	11.9694	+	14.2646i	0.403718	+	0.481132i
$880$		0			0
$881$	−21.5096	+	37.2558i	−0.724678	+	1.25518i	0.234428	+	0.972133i	$0.424678\pi$
$881$	−21.5096	+	37.2558i	−0.724678	+	1.25518i	−0.959106	+	0.283046i	$0.908655\pi$
$882$		0			0
$883$	5.06402	+	13.9133i	0.170418	+	0.468219i	0.995272	−	0.0971265i	$-0.0309651\pi$
$883$	5.06402	+	13.9133i	0.170418	+	0.468219i	−0.824854	+	0.565345i	$0.808743\pi$
$884$		0			0
$885$	−6.19356	−	10.7276i	−0.208194	−	0.360603i
$886$		0			0
$887$	5.79387	−	32.8587i	0.194539	−	1.10329i	−0.718535	−	0.695491i	$-0.755187\pi$
$887$	5.79387	−	32.8587i	0.194539	−	1.10329i	0.913074	−	0.407794i	$-0.133702\pi$
$888$		0			0
$889$	32.3169	−	38.5137i	1.08387	−	1.29171i
$890$		0			0
$891$	0.175615	−	0.482500i	0.00588334	−	0.0161643i
$892$		0			0
$893$	−19.4781	−	4.19341i	−0.651810	−	0.140327i
$894$		0			0
$895$	53.2525	+	19.3823i	1.78003	+	0.647879i
$896$		0			0
$897$	−7.92787	−	6.65227i	−0.264704	−	0.222113i
$898$		0			0
$899$	42.4752	+	7.48952i	1.41663	+	0.249790i
$900$		0			0
$901$	20.7230	−	11.9644i	0.690384	−	0.398593i
$902$		0			0
$903$	9.55110	−	3.47632i	0.317841	−	0.115685i
$904$		0			0
$905$	−14.9563	−	8.63502i	−0.497164	−	0.287038i
$906$		0			0
$907$	−7.96926	+	6.68700i	−0.264615	+	0.222038i	−0.765435	−	0.643513i	$-0.777476\pi$
$907$	−7.96926	+	6.68700i	−0.264615	+	0.222038i	0.500820	+	0.865551i	$0.333032\pi$
$908$		0			0
$909$	2.98930	+	16.9532i	0.0991490	+	0.562302i
$910$		0			0
$911$	−60.0492			−1.98952			−0.994760	−	0.102237i	$-0.967400\pi$
$911$	−60.0492			−1.98952			−0.994760	+	0.102237i	$0.967400\pi$
$912$		0			0
$913$	7.49821			0.248155
$914$		0			0
$915$	3.92552	+	22.2627i	0.129774	+	0.735983i
$916$		0			0
$917$	33.4231	−	28.0453i	1.10373	−	0.926137i
$918$		0			0
$919$	−18.5335	−	10.7003i	−0.611364	−	0.352971i	0.162135	−	0.986769i	$-0.448162\pi$
$919$	−18.5335	−	10.7003i	−0.611364	−	0.352971i	−0.773499	+	0.633798i	$0.781495\pi$
$920$		0			0
$921$	−6.62946	+	2.41292i	−0.218448	+	0.0795086i
$922$		0			0
$923$	9.72441	−	5.61439i	0.320083	−	0.184800i
$924$		0			0
$925$	30.2086	+	5.32660i	0.993254	+	0.175138i
$926$		0			0
$927$	7.34007	+	6.15905i	0.241080	+	0.202290i
$928$		0			0
$929$	−39.7335	−	14.4618i	−1.30361	−	0.474477i	−0.405442	−	0.914121i	$-0.632882\pi$
$929$	−39.7335	−	14.4618i	−1.30361	−	0.474477i	−0.898172	+	0.439644i	$0.855104\pi$
$930$		0			0
$931$	−0.746192	−	0.0280094i	−0.0244555	−	0.000917972i
$932$		0			0
$933$	−10.7810	+	29.6205i	−0.352954	+	0.969732i
$934$		0			0
$935$	−4.51876	+	5.38525i	−0.147779	+	0.176117i
$936$		0			0
$937$	−2.44374	+	13.8592i	−0.0798336	+	0.452759i	0.918519	+	0.395378i	$0.129386\pi$
$937$	−2.44374	+	13.8592i	−0.0798336	+	0.452759i	−0.998352	+	0.0573815i	$0.981725\pi$
$938$		0			0
$939$	−7.95235	−	13.7739i	−0.259515	−	0.449494i
$940$		0			0
$941$	2.98201	+	8.19300i	0.0972107	+	0.267084i	0.978761	−	0.205007i	$-0.0657216\pi$
$941$	2.98201	+	8.19300i	0.0972107	+	0.267084i	−0.881550	+	0.472091i	$0.843499\pi$
$942$		0			0
$943$	1.00885	−	1.74738i	0.0328527	−	0.0569025i
$944$		0			0
$945$	−6.21069	−	7.40162i	−0.202034	−	0.240775i
$946$		0			0
$947$	−25.9197	+	4.57033i	−0.842276	+	0.148516i	−0.578107	−	0.815961i	$-0.696209\pi$
$947$	−25.9197	+	4.57033i	−0.842276	+	0.148516i	−0.264168	+	0.964477i	$0.585097\pi$
$948$		0			0
$949$			79.2963i			2.57407i
$950$		0			0
$951$		−	29.3614i		−	0.952110i
$952$		0			0
$953$	25.0632	−	4.41932i	0.811876	−	0.143156i	0.247728	−	0.968830i	$-0.420316\pi$
$953$	25.0632	−	4.41932i	0.811876	−	0.143156i	0.564148	+	0.825674i	$0.309205\pi$
$954$		0			0
$955$	−22.8060	−	27.1791i	−0.737985	−	0.879497i
$956$		0			0
$957$	−1.21801	+	2.10966i	−0.0393727	+	0.0681956i
$958$		0			0
$959$	−12.1894	−	33.4902i	−0.393617	−	1.08145i
$960$		0			0
$961$	−25.8235	−	44.7276i	−0.833016	−	1.44283i
$962$		0			0
$963$	−2.21318	+	12.5516i	−0.0713188	+	0.404469i
$964$		0			0
$965$	12.6012	−	15.0175i	0.405647	−	0.483431i
$966$		0			0
$967$	−3.95865	+	10.8763i	−0.127301	+	0.349758i	−0.986927	−	0.161166i	$-0.948474\pi$
$967$	−3.95865	+	10.8763i	−0.127301	+	0.349758i	0.859626	+	0.510924i	$0.170697\pi$
$968$		0			0
$969$	11.9664	+	10.8313i	0.384416	+	0.347952i
$970$		0			0
$971$	−4.16795	−	1.51701i	−0.133756	−	0.0486832i	0.274275	−	0.961651i	$-0.411562\pi$
$971$	−4.16795	−	1.51701i	−0.133756	−	0.0486832i	−0.408031	+	0.912968i	$0.633784\pi$
$972$		0			0
$973$	−20.7716	−	17.4294i	−0.665906	−	0.558762i
$974$		0			0
$975$	−50.4944	−	8.90353i	−1.61712	−	0.285141i
$976$		0			0
$977$	25.8704	−	14.9363i	0.827667	−	0.477853i	−0.0253865	−	0.999678i	$-0.508082\pi$
$977$	25.8704	−	14.9363i	0.827667	−	0.477853i	0.853053	+	0.521824i	$0.174748\pi$
$978$		0			0
$979$	7.65190	−	2.78506i	0.244556	−	0.0890110i
$980$		0			0
$981$	0.611617	+	0.353117i	0.0195274	+	0.0112742i
$982$		0			0
$983$	17.4759	−	14.6640i	0.557394	−	0.467709i	−0.320042	−	0.947404i	$-0.603697\pi$
$983$	17.4759	−	14.6640i	0.557394	−	0.467709i	0.877436	+	0.479694i	$0.159252\pi$
$984$		0			0
$985$	13.7122	+	77.7660i	0.436908	+	2.47783i
$986$		0			0
$987$	11.9447			0.380205
$988$		0			0
$989$	−6.80754			−0.216467
$990$		0			0
$991$	6.03480	+	34.2250i	0.191702	+	1.08719i	0.917038	+	0.398800i	$0.130573\pi$
$991$	6.03480	+	34.2250i	0.191702	+	1.08719i	−0.725336	+	0.688395i	$0.758316\pi$
$992$		0			0
$993$	−5.97653	+	5.01490i	−0.189659	+	0.159143i
$994$		0			0
$995$	40.6886	+	23.4916i	1.28992	+	0.744733i
$996$		0			0
$997$	37.2789	−	13.5684i	1.18063	−	0.429716i	0.324208	−	0.945986i	$-0.394902\pi$
$997$	37.2789	−	13.5684i	1.18063	−	0.429716i	0.856426	+	0.516270i	$0.172680\pi$
$998$		0			0
$999$	−3.06358	+	1.76876i	−0.0969275	+	0.0559611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.c.319.2	yes	12
4.3	odd	2		912.2.ci.d.319.2	yes	12
19.14	odd	18		912.2.ci.d.223.2	yes	12
76.71	even	18	inner	912.2.ci.c.223.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.c.223.2	✓	12	76.71	even	18	inner
912.2.ci.c.319.2	yes	12	1.1	even	1	trivial
912.2.ci.d.223.2	yes	12	19.14	odd	18
912.2.ci.d.319.2	yes	12	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{3} +(2.83242 - 2.37668i) q^{5} +(-2.26308 - 1.30659i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{3} +(2.83242 - 2.37668i) q^{5} +(-2.26308 - 1.30659i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(0.444674 - 0.256733i) q^{11} +(5.82321 + 1.02679i) q^{13} +(-2.83242 - 2.37668i) q^{15} +(-3.47955 - 1.26645i) q^{17} +(2.31951 - 3.69051i) q^{19} +(-0.893759 + 2.45558i) q^{21} +(1.12502 - 1.34074i) q^{23} +(1.50574 - 8.53950i) q^{25} +(0.500000 + 0.866025i) q^{27} +(-1.62264 - 4.45817i) q^{29} +(-4.54552 + 7.87307i) q^{31} +(-0.330049 - 0.393337i) q^{33} +(-9.51533 + 1.67781i) q^{35} +3.53752i q^{37} -5.91304i q^{39} +(1.13532 - 0.200187i) q^{41} +(-2.50015 - 2.97956i) q^{43} +(-1.84873 + 3.20210i) q^{45} +(-1.56336 - 4.29530i) q^{47} +(-0.0856544 - 0.148358i) q^{49} +(-0.642995 + 3.64660i) q^{51} +(-4.15387 + 4.95039i) q^{53} +(0.649332 - 1.78402i) q^{55} +(-4.03722 - 1.64342i) q^{57} +(3.14813 + 1.14582i) q^{59} +(-4.68357 - 3.92998i) q^{61} +(2.57348 + 0.453773i) q^{63} +(18.9341 - 10.9316i) q^{65} +(-3.30490 + 1.20289i) q^{67} +(-1.51573 - 0.875108i) q^{69} +(1.45471 - 1.22064i) q^{71} +(2.32869 + 13.2067i) q^{73} -8.67123 q^{75} -1.34178 q^{77} +(-1.21938 - 6.91542i) q^{79} +(0.766044 - 0.642788i) q^{81} +(12.6467 + 7.30158i) q^{83} +(-12.8655 + 4.68266i) q^{85} +(-4.10867 + 2.37214i) q^{87} +(15.6179 + 2.75386i) q^{89} +(-11.8368 - 9.93224i) q^{91} +(8.54278 + 3.10932i) q^{93} +(-2.20133 - 15.9658i) q^{95} +(-0.687600 + 1.88917i) q^{97} +(-0.330049 + 0.393337i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{5} - 18 q^{7}+O(q^{10}) \) 12 * q + 6 * q^5 - 18 * q^7	\( 12 q + 6 q^{5} - 18 q^{7} + 18 q^{13} - 6 q^{15} + 6 q^{17} - 12 q^{19} - 6 q^{21} + 18 q^{23} - 30 q^{25} + 6 q^{27} - 6 q^{29} - 18 q^{31} + 6 q^{33} - 36 q^{35} + 6 q^{41} + 6 q^{43} - 6 q^{47} + 12 q^{49} - 6 q^{51} - 36 q^{53} + 42 q^{55} + 6 q^{59} - 6 q^{61} - 6 q^{63} + 72 q^{65} - 6 q^{67} - 54 q^{71} - 12 q^{73} - 12 q^{75} - 36 q^{77} + 6 q^{79} - 18 q^{83} - 36 q^{85} + 36 q^{87} + 24 q^{89} - 12 q^{91} - 18 q^{93} - 24 q^{95} + 24 q^{97} + 6 q^{99}+O(q^{100}) \) 12 * q + 6 * q^5 - 18 * q^7 + 18 * q^13 - 6 * q^15 + 6 * q^17 - 12 * q^19 - 6 * q^21 + 18 * q^23 - 30 * q^25 + 6 * q^27 - 6 * q^29 - 18 * q^31 + 6 * q^33 - 36 * q^35 + 6 * q^41 + 6 * q^43 - 6 * q^47 + 12 * q^49 - 6 * q^51 - 36 * q^53 + 42 * q^55 + 6 * q^59 - 6 * q^61 - 6 * q^63 + 72 * q^65 - 6 * q^67 - 54 * q^71 - 12 * q^73 - 12 * q^75 - 36 * q^77 + 6 * q^79 - 18 * q^83 - 36 * q^85 + 36 * q^87 + 24 * q^89 - 12 * q^91 - 18 * q^93 - 24 * q^95 + 24 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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