LMFDB - Embedded newform 912.2.cc.c.545.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(257,912)]

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([0, 0, 9, 17]))

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

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

chi := DirichletCharacter("912.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.cc (of order $18$, degree $6$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 $ x^18 - x^15 - 18x^14 + 36x^13 + 10x^12 + 18x^11 + 90x^10 - 567x^9 + 270x^8 + 162x^7 + 270x^6 + 2916x^5 - 4374x^4 - 729x^3 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			545.2
Root			$-1.73189 + 0.0237018i$ of defining polynomial
Character	$\chi$	$=$	912.545
Dual form			912.2.cc.c.497.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.324081 - 1.70146i) q^{3} +(2.22841 - 0.392929i) q^{5} +(1.16829 - 2.02354i) q^{7} +(-2.78994 - 1.10282i) q^{9} +O(q^{10})$	\(q+(0.324081 - 1.70146i) q^{3} +(2.22841 - 0.392929i) q^{5} +(1.16829 - 2.02354i) q^{7} +(-2.78994 - 1.10282i) q^{9} +(-2.52163 + 1.45586i) q^{11} +(-0.451929 - 1.24167i) q^{13} +(0.0536321 - 3.91889i) q^{15} +(-3.72112 - 4.43466i) q^{17} +(1.79800 - 3.97079i) q^{19} +(-3.06435 - 2.64359i) q^{21} +(8.06194 + 1.42154i) q^{23} +(0.112953 - 0.0411116i) q^{25} +(-2.78058 + 4.38958i) q^{27} +(1.64718 + 1.38215i) q^{29} +(-5.27928 - 3.04799i) q^{31} +(1.65988 + 4.76227i) q^{33} +(1.80832 - 4.96833i) q^{35} -2.98954i q^{37} +(-2.25911 + 0.366540i) q^{39} +(8.52555 + 3.10304i) q^{41} +(0.0666074 + 0.377749i) q^{43} +(-6.65047 - 1.36129i) q^{45} +(-6.57494 + 7.83571i) q^{47} +(0.770194 + 1.33401i) q^{49} +(-8.75134 + 4.89415i) q^{51} +(-0.494197 + 2.80273i) q^{53} +(-5.04717 + 4.23508i) q^{55} +(-6.17345 - 4.34609i) q^{57} +(2.53779 - 2.12946i) q^{59} +(1.01879 - 5.77787i) q^{61} +(-5.49107 + 4.35714i) q^{63} +(-1.49497 - 2.58936i) q^{65} +(10.4361 - 12.4373i) q^{67} +(5.03141 - 13.2564i) q^{69} +(-2.29622 - 13.0225i) q^{71} +(5.84733 + 2.12826i) q^{73} +(-0.0333438 - 0.205509i) q^{75} +6.80348i q^{77} +(-1.77569 + 4.87866i) q^{79} +(6.56756 + 6.15363i) q^{81} +(1.62533 + 0.938386i) q^{83} +(-10.0347 - 8.42009i) q^{85} +(2.88550 - 2.35469i) q^{87} +(-5.82289 + 2.11936i) q^{89} +(-3.04054 - 0.536130i) q^{91} +(-6.89696 + 7.99469i) q^{93} +(2.44644 - 9.55504i) q^{95} +(6.13336 + 7.30946i) q^{97} +(8.64076 - 1.28086i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{3} - 3 q^{9}+O(q^{10}) $ 18 * q - 3 * q^3 - 3 * q^9	$ 18 q - 3 q^{3} - 3 q^{9} - 12 q^{13} - 18 q^{15} + 6 q^{17} + 6 q^{19} - 18 q^{25} + 6 q^{27} - 6 q^{29} - 24 q^{33} + 24 q^{35} - 6 q^{39} + 3 q^{41} + 6 q^{43} - 54 q^{45} - 30 q^{47} + 21 q^{49} - 42 q^{51} - 60 q^{53} - 30 q^{55} + 12 q^{57} - 3 q^{59} + 54 q^{61} + 18 q^{63} + 24 q^{65} + 15 q^{67} + 30 q^{69} - 36 q^{71} - 42 q^{73} + 6 q^{79} - 3 q^{81} - 36 q^{83} - 60 q^{89} + 18 q^{91} - 66 q^{93} - 6 q^{95} + 9 q^{97} + 102 q^{99}+O(q^{100}) $ 18 * q - 3 * q^3 - 3 * q^9 - 12 * q^13 - 18 * q^15 + 6 * q^17 + 6 * q^19 - 18 * q^25 + 6 * q^27 - 6 * q^29 - 24 * q^33 + 24 * q^35 - 6 * q^39 + 3 * q^41 + 6 * q^43 - 54 * q^45 - 30 * q^47 + 21 * q^49 - 42 * q^51 - 60 * q^53 - 30 * q^55 + 12 * q^57 - 3 * q^59 + 54 * q^61 + 18 * q^63 + 24 * q^65 + 15 * q^67 + 30 * q^69 - 36 * q^71 - 42 * q^73 + 6 * q^79 - 3 * q^81 - 36 * q^83 - 60 * q^89 + 18 * q^91 - 66 * q^93 - 6 * q^95 + 9 * q^97 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$-1$	$1$

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
$3$	0.324081	−	1.70146i	0.187108	−	0.982339i
$3$	0.324081	−	1.70146i	0.187108	−	0.982339i
$4$		0			0
$5$	2.22841	−	0.392929i	0.996575	−	0.175723i	0.348508	−	0.937306i	$-0.386689\pi$
$5$	2.22841	−	0.392929i	0.996575	−	0.175723i	0.648067	+	0.761583i	$0.275577\pi$
$6$		0			0
$7$	1.16829	−	2.02354i	0.441572	−	0.764826i	−0.556234	−	0.831026i	$-0.687754\pi$
$7$	1.16829	−	2.02354i	0.441572	−	0.764826i	0.997806	+	0.0661999i	$0.0210875\pi$
$8$		0			0
$9$	−2.78994	−	1.10282i	−0.929981	−	0.367608i
$10$		0			0
$11$	−2.52163	+	1.45586i	−0.760299	+	0.438959i	−0.829403	−	0.558650i	$-0.811319\pi$
$11$	−2.52163	+	1.45586i	−0.760299	+	0.438959i	0.0691039	+	0.997609i	$0.477986\pi$
$12$		0			0
$13$	−0.451929	−	1.24167i	−0.125343	−	0.344376i	0.861111	−	0.508417i	$-0.169769\pi$
$13$	−0.451929	−	1.24167i	−0.125343	−	0.344376i	−0.986453	+	0.164041i	$0.947547\pi$
$14$		0			0
$15$	0.0536321	−	3.91889i	0.0138478	−	1.01185i
$16$		0			0
$17$	−3.72112	−	4.43466i	−0.902504	−	1.07556i	−0.996793	−	0.0800172i	$-0.974502\pi$
$17$	−3.72112	−	4.43466i	−0.902504	−	1.07556i	0.0942898	−	0.995545i	$-0.469942\pi$
$18$		0			0
$19$	1.79800	−	3.97079i	0.412489	−	0.910962i
$19$	1.79800	−	3.97079i	0.412489	−	0.910962i
$20$		0			0
$21$	−3.06435	−	2.64359i	−0.668697	−	0.576879i
$22$		0			0
$23$	8.06194	+	1.42154i	1.68103	+	0.296411i	0.931007	−	0.365001i	$-0.118931\pi$
$23$	8.06194	+	1.42154i	1.68103	+	0.296411i	0.750023	+	0.661412i	$0.230042\pi$
$24$		0			0
$25$	0.112953	−	0.0411116i	0.0225906	−	0.00822231i
$26$		0			0
$27$	−2.78058	+	4.38958i	−0.535123	+	0.844774i
$28$		0			0
$29$	1.64718	+	1.38215i	0.305875	+	0.256659i	0.782784	−	0.622293i	$-0.213799\pi$
$29$	1.64718	+	1.38215i	0.305875	+	0.256659i	−0.476910	+	0.878952i	$0.658243\pi$
$30$		0			0
$31$	−5.27928	−	3.04799i	−0.948186	−	0.547436i	−0.0556692	−	0.998449i	$-0.517729\pi$
$31$	−5.27928	−	3.04799i	−0.948186	−	0.547436i	−0.892517	+	0.451014i	$0.851063\pi$
$32$		0			0
$33$	1.65988	+	4.76227i	0.288948	+	0.829005i
$34$		0			0
$35$	1.80832	−	4.96833i	0.305662	−	0.839801i
$36$		0			0
$37$		−	2.98954i		−	0.491477i	−0.969336	−	0.245738i	$-0.920970\pi$
$37$		−	2.98954i		−	0.491477i	0.969336	−	0.245738i	$-0.0790304\pi$
$38$		0			0
$39$	−2.25911	+	0.366540i	−0.361747	+	0.0586934i
$40$		0			0
$41$	8.52555	+	3.10304i	1.33147	+	0.484614i	0.907115	−	0.420883i	$-0.138280\pi$
$41$	8.52555	+	3.10304i	1.33147	+	0.484614i	0.424352	+	0.905497i	$0.360502\pi$
$42$		0			0
$43$	0.0666074	+	0.377749i	0.0101575	+	0.0576062i	0.989465	−	0.144771i	$-0.0462445\pi$
$43$	0.0666074	+	0.377749i	0.0101575	+	0.0576062i	−0.979308	+	0.202377i	$0.935133\pi$
$44$		0			0
$45$	−6.65047	−	1.36129i	−0.991393	−	0.202929i
$46$		0			0
$47$	−6.57494	+	7.83571i	−0.959054	+	1.14296i	0.0306076	+	0.999531i	$0.490256\pi$
$47$	−6.57494	+	7.83571i	−0.959054	+	1.14296i	−0.989661	+	0.143424i	$0.954189\pi$
$48$		0			0
$49$	0.770194	+	1.33401i	0.110028	+	0.190574i
$50$		0			0
$51$	−8.75134	+	4.89415i	−1.22543	+	0.685318i
$52$		0			0
$53$	−0.494197	+	2.80273i	−0.0678832	+	0.384985i	0.931870	+	0.362791i	$0.118176\pi$
$53$	−0.494197	+	2.80273i	−0.0678832	+	0.384985i	−0.999754	+	0.0221937i	$0.992935\pi$
$54$		0			0
$55$	−5.04717	+	4.23508i	−0.680560	+	0.571058i
$56$		0			0
$57$	−6.17345	−	4.34609i	−0.817694	−	0.575653i
$58$		0			0
$59$	2.53779	−	2.12946i	0.330392	−	0.277232i	−0.462468	−	0.886636i	$-0.653036\pi$
$59$	2.53779	−	2.12946i	0.330392	−	0.277232i	0.792860	+	0.609404i	$0.208591\pi$
$60$		0			0
$61$	1.01879	−	5.77787i	0.130443	−	0.739780i	−0.847482	−	0.530824i	$-0.821882\pi$
$61$	1.01879	−	5.77787i	0.130443	−	0.739780i	0.977925	−	0.208956i	$-0.0670064\pi$
$62$		0			0
$63$	−5.49107	+	4.35714i	−0.691810	+	0.548948i
$64$		0			0
$65$	−1.49497	−	2.58936i	−0.185428	−	0.321171i
$66$		0			0
$67$	10.4361	−	12.4373i	1.27497	−	1.51945i	0.539305	−	0.842111i	$-0.318687\pi$
$67$	10.4361	−	12.4373i	1.27497	−	1.51945i	0.735668	−	0.677342i	$-0.236868\pi$
$68$		0			0
$69$	5.03141	−	13.2564i	0.605711	−	1.59588i
$70$		0			0
$71$	−2.29622	−	13.0225i	−0.272511	−	1.54549i	−0.746758	−	0.665095i	$-0.768391\pi$
$71$	−2.29622	−	13.0225i	−0.272511	−	1.54549i	0.474247	−	0.880392i	$-0.342720\pi$
$72$		0			0
$73$	5.84733	+	2.12826i	0.684379	+	0.249093i	0.660726	−	0.750627i	$-0.270248\pi$
$73$	5.84733	+	2.12826i	0.684379	+	0.249093i	0.0236522	+	0.999720i	$0.492471\pi$
$74$		0			0
$75$	−0.0333438	−	0.205509i	−0.00385021	−	0.0237301i
$76$		0			0
$77$			6.80348i			0.775329i
$78$		0			0
$79$	−1.77569	+	4.87866i	−0.199781	+	0.548893i	−0.998612	−	0.0526618i	$-0.983229\pi$
$79$	−1.77569	+	4.87866i	−0.199781	+	0.548893i	0.798832	+	0.601554i	$0.205452\pi$
$80$		0			0
$81$	6.56756	+	6.15363i	0.729729	+	0.683736i
$82$		0			0
$83$	1.62533	+	0.938386i	0.178403	+	0.103001i	0.586542	−	0.809919i	$-0.300489\pi$
$83$	1.62533	+	0.938386i	0.178403	+	0.103001i	−0.408139	+	0.912920i	$0.633822\pi$
$84$		0			0
$85$	−10.0347	−	8.42009i	−1.08841	−	0.913288i
$86$		0			0
$87$	2.88550	−	2.35469i	0.309358	−	0.252450i
$88$		0			0
$89$	−5.82289	+	2.11936i	−0.617225	+	0.224651i	−0.631661	−	0.775244i	$-0.717627\pi$
$89$	−5.82289	+	2.11936i	−0.617225	+	0.224651i	0.0144367	+	0.999896i	$0.495405\pi$
$90$		0			0
$91$	−3.04054	−	0.536130i	−0.318735	−	0.0562017i
$92$		0			0
$93$	−6.89696	+	7.99469i	−0.715181	+	0.829011i
$94$		0			0
$95$	2.44644	−	9.55504i	0.251000	−	0.980326i
$96$		0			0
$97$	6.13336	+	7.30946i	0.622748	+	0.742163i	0.981540	−	0.191255i	$-0.0612557\pi$
$97$	6.13336	+	7.30946i	0.622748	+	0.742163i	−0.358792	+	0.933418i	$0.616811\pi$
$98$		0			0
$99$	8.64076	−	1.28086i	0.868429	−	0.128732i
$100$		0			0
$101$	−4.28105	−	11.7621i	−0.425980	−	1.17037i	−0.948232	−	0.317580i	$-0.897130\pi$
$101$	−4.28105	−	11.7621i	−0.425980	−	1.17037i	0.522251	−	0.852792i	$-0.325092\pi$
$102$		0			0
$103$	−7.59279	+	4.38370i	−0.748140	+	0.431939i	−0.825021	−	0.565102i	$-0.808837\pi$
$103$	−7.59279	+	4.38370i	−0.748140	+	0.431939i	0.0768818	+	0.997040i	$0.475504\pi$
$104$		0			0
$105$	−7.86738	−	4.68693i	−0.767777	−	0.457398i
$106$		0			0
$107$	−4.04583	+	7.00758i	−0.391125	+	0.677449i	−0.992598	−	0.121444i	$-0.961247\pi$
$107$	−4.04583	+	7.00758i	−0.391125	+	0.677449i	0.601473	+	0.798893i	$0.294581\pi$
$108$		0			0
$109$	7.26213	−	1.28051i	0.695586	−	0.122651i	0.185334	−	0.982676i	$-0.440663\pi$
$109$	7.26213	−	1.28051i	0.695586	−	0.122651i	0.510252	+	0.860025i	$0.329552\pi$
$110$		0			0
$111$	−5.08658	−	0.968852i	−0.482797	−	0.0919594i
$112$		0			0
$113$	−14.8779			−1.39960			−0.699799	−	0.714340i	$-0.746727\pi$
$113$	−14.8779			−1.39960			−0.699799	+	0.714340i	$0.746727\pi$
$114$		0			0
$115$	18.5239			1.72736
$116$		0			0
$117$	−0.108480	+	3.96257i	−0.0100290	+	0.366340i
$118$		0			0
$119$	−13.3210	+	2.34886i	−1.22114	+	0.215320i
$120$		0			0
$121$	−1.26093	+	2.18399i	−0.114630	+	0.198545i
$122$		0			0
$123$	8.04268	−	13.5002i	0.725184	−	1.21728i
$124$		0			0
$125$	−9.56260	+	5.52097i	−0.855305	+	0.493811i
$126$		0			0
$127$	2.54056	+	6.98012i	0.225438	+	0.619386i	0.999913	−	0.0132192i	$-0.00420794\pi$
$127$	2.54056	+	6.98012i	0.225438	+	0.619386i	−0.774475	+	0.632605i	$0.781986\pi$
$128$		0			0
$129$	0.664312	+	0.00909146i	0.0584894	+	0.000800458i
$130$		0			0
$131$	11.4406	+	13.6344i	0.999574	+	1.19125i	0.981510	+	0.191409i	$0.0613057\pi$
$131$	11.4406	+	13.6344i	0.999574	+	1.19125i	0.0180637	+	0.999837i	$0.494250\pi$
$132$		0			0
$133$	−5.93447	−	8.27736i	−0.514584	−	0.717738i
$134$		0			0
$135$	−4.47148	+	10.8743i	−0.384843	+	0.935915i
$136$		0			0
$137$	16.1747	+	2.85204i	1.38190	+	0.243666i	0.814685	−	0.579904i	$-0.196910\pi$
$137$	16.1747	+	2.85204i	1.38190	+	0.243666i	0.567215	+	0.823570i	$0.308021\pi$
$138$		0			0
$139$	18.1680	−	6.61260i	1.54099	−	0.560873i	0.574705	−	0.818360i	$-0.305117\pi$
$139$	18.1680	−	6.61260i	1.54099	−	0.560873i	0.966282	+	0.257487i	$0.0828944\pi$
$140$		0			0
$141$	11.2013	+	13.7264i	0.943323	+	1.15597i
$142$		0			0
$143$	2.94729	+	2.47307i	0.246465	+	0.206809i
$144$		0			0
$145$	4.21369	+	2.43277i	0.349928	+	0.202031i
$146$		0			0
$147$	2.51938	−	0.878126i	0.207795	−	0.0724266i
$148$		0			0
$149$	−2.20295	+	6.05256i	−0.180473	+	0.495845i	−0.996634	−	0.0819794i	$-0.973876\pi$
$149$	−2.20295	+	6.05256i	−0.180473	+	0.495845i	0.816161	+	0.577824i	$0.196098\pi$
$150$		0			0
$151$		−	3.02833i		−	0.246442i	−0.992379	−	0.123221i	$-0.960678\pi$
$151$		−	3.02833i		−	0.246442i	0.992379	−	0.123221i	$-0.0393223\pi$
$152$		0			0
$153$	5.49107	+	16.4762i	0.443926	+	1.33202i
$154$		0			0
$155$	−12.9620	−	4.71780i	−1.04114	−	0.378942i
$156$		0			0
$157$	3.32082	+	18.8333i	0.265030	+	1.50306i	0.768949	+	0.639311i	$0.220780\pi$
$157$	3.32082	+	18.8333i	0.265030	+	1.50306i	−0.503918	+	0.863751i	$0.668109\pi$
$158$		0			0
$159$	4.60858	+	1.74917i	0.365484	+	0.138718i
$160$		0			0
$161$	12.2952	−	14.6529i	0.968999	−	1.15481i
$162$		0			0
$163$	3.09435	+	5.35958i	0.242368	+	0.419794i	0.961388	−	0.275195i	$-0.0887424\pi$
$163$	3.09435	+	5.35958i	0.242368	+	0.419794i	−0.719020	+	0.694989i	$0.755409\pi$
$164$		0			0
$165$	5.57013	+	9.96007i	0.433634	+	0.775391i
$166$		0			0
$167$	−0.758731	+	4.30298i	−0.0587124	+	0.332975i	−0.999989	−	0.00466148i	$-0.998516\pi$
$167$	−0.758731	+	4.30298i	−0.0587124	+	0.332975i	0.941277	+	0.337636i	$0.109627\pi$
$168$		0			0
$169$	8.62108	−	7.23395i	0.663160	−	0.556458i
$170$		0			0
$171$	−9.39540	+	9.09541i	−0.718484	+	0.695543i
$172$		0			0
$173$	11.4117	−	9.57556i	0.867616	−	0.728016i	−0.0959786	−	0.995383i	$-0.530598\pi$
$173$	11.4117	−	9.57556i	0.867616	−	0.728016i	0.963595	+	0.267367i	$0.0861536\pi$
$174$		0			0
$175$	0.0487712	−	0.276595i	0.00368676	−	0.0209086i
$176$		0			0
$177$	−2.80074	−	5.00807i	−0.210517	−	0.376429i
$178$		0			0
$179$	−1.68012	−	2.91005i	−0.125578	−	0.217507i	0.796381	−	0.604796i	$-0.206745\pi$
$179$	−1.68012	−	2.91005i	−0.125578	−	0.217507i	−0.921959	+	0.387288i	$0.873412\pi$
$180$		0			0
$181$	12.7706	−	15.2194i	0.949231	−	1.13125i	−0.0420013	−	0.999118i	$-0.513373\pi$
$181$	12.7706	−	15.2194i	0.949231	−	1.13125i	0.991232	−	0.132132i	$-0.0421822\pi$
$182$		0			0
$183$	−9.50065	−	3.60593i	−0.702308	−	0.266558i
$184$		0			0
$185$	−1.17467	−	6.66191i	−0.0863638	−	0.489794i
$186$		0			0
$187$	15.8395	+	5.76511i	1.15830	+	0.421587i
$188$		0			0
$189$	5.63396	+	10.7549i	0.409810	+	0.782305i
$190$		0			0
$191$			10.2346i			0.740548i	0.928923	+	0.370274i	$0.120736\pi$
$191$			10.2346i			0.740548i	−0.928923	+	0.370274i	$0.879264\pi$
$192$		0			0
$193$	−0.784644	+	2.15579i	−0.0564799	+	0.155177i	−0.964724	−	0.263264i	$-0.915201\pi$
$193$	−0.784644	+	2.15579i	−0.0564799	+	0.155177i	0.908244	+	0.418441i	$0.137423\pi$
$194$		0			0
$195$	−4.89019	+	1.70447i	−0.350194	+	0.122060i
$196$		0			0
$197$	5.46822	+	3.15708i	0.389595	+	0.224933i	0.681984	−	0.731367i	$-0.261117\pi$
$197$	5.46822	+	3.15708i	0.389595	+	0.224933i	−0.292390	+	0.956299i	$0.594450\pi$
$198$		0			0
$199$	7.96251	+	6.68134i	0.564447	+	0.473628i	0.879798	−	0.475348i	$-0.157678\pi$
$199$	7.96251	+	6.68134i	0.564447	+	0.473628i	−0.315351	+	0.948975i	$0.602122\pi$
$200$		0			0
$201$	−17.7794	−	21.7873i	−1.25406	−	1.53676i
$202$		0			0
$203$	4.72123	−	1.71839i	0.331365	−	0.120607i
$204$		0			0
$205$	20.2177	+	3.56492i	1.41206	+	0.248985i
$206$		0			0
$207$	−20.9246	−	12.8569i	−1.45436	−	0.893616i
$208$		0			0
$209$	1.24704	+	12.6305i	0.0862598	+	0.873670i
$210$		0			0
$211$	3.58388	+	4.27111i	0.246725	+	0.294035i	0.875167	−	0.483821i	$-0.160752\pi$
$211$	3.58388	+	4.27111i	0.246725	+	0.294035i	−0.628442	+	0.777856i	$0.716307\pi$
$212$		0			0
$213$	−22.9015	−	0.313418i	−1.56918	−	0.0214751i
$214$		0			0
$215$	0.296857	+	0.815608i	0.0202455	+	0.0556240i
$216$		0			0
$217$	−12.3355	+	7.12188i	−0.837386	+	0.483465i
$218$		0			0
$219$	5.51615	−	9.25929i	0.372747	−	0.625685i
$220$		0			0
$221$	−3.82468	+	6.62453i	−0.257276	+	0.445614i
$222$		0			0
$223$	−5.10735	+	0.900564i	−0.342014	+	0.0603062i	−0.342017	−	0.939694i	$-0.611110\pi$
$223$	−5.10735	+	0.900564i	−0.342014	+	0.0603062i	3.40741e−6		1.00000i	$0.499999\pi$
$224$		0			0
$225$	−0.360471	−	0.00986833i	−0.0240314	−	0.000657889i
$226$		0			0
$227$	17.0369			1.13078			0.565391	−	0.824823i	$-0.308725\pi$
$227$	17.0369			1.13078			0.565391	+	0.824823i	$0.308725\pi$
$228$		0			0
$229$	24.5203			1.62035			0.810173	−	0.586191i	$-0.199373\pi$
$229$	24.5203			1.62035			0.810173	+	0.586191i	$0.199373\pi$
$230$		0			0
$231$	11.5759	+	2.20488i	0.761636	+	0.145070i
$232$		0			0
$233$	−22.4936	+	3.96623i	−1.47360	+	0.259836i	−0.852019	−	0.523510i	$-0.824622\pi$
$233$	−22.4936	+	3.96623i	−1.47360	+	0.259836i	−0.621585	+	0.783346i	$0.713511\pi$
$234$		0			0
$235$	−11.5728	+	20.0447i	−0.754925	+	1.30757i
$236$		0			0
$237$	7.72539	+	4.60235i	0.501818	+	0.298955i
$238$		0			0
$239$	−2.62883	+	1.51775i	−0.170045	+	0.0981753i	−0.582607	−	0.812754i	$-0.697967\pi$
$239$	−2.62883	+	1.51775i	−0.170045	+	0.0981753i	0.412562	+	0.910929i	$0.364634\pi$
$240$		0			0
$241$	−1.35157	−	3.71341i	−0.0870624	−	0.239202i	0.888519	−	0.458840i	$-0.151735\pi$
$241$	−1.35157	−	3.71341i	−0.0870624	−	0.239202i	−0.975582	+	0.219638i	$0.929512\pi$
$242$		0			0
$243$	12.5986	−	9.18018i	0.808199	−	0.588909i
$244$		0			0
$245$	2.24048	+	2.67010i	0.143139	+	0.170586i
$246$		0			0
$247$	−5.74296	−	0.437996i	−0.365416	−	0.0278690i
$248$		0			0
$249$	2.12337	−	2.46133i	0.134563	−	0.155980i
$250$		0			0
$251$	−7.14276	−	1.25946i	−0.450847	−	0.0794965i	−0.0563857	−	0.998409i	$-0.517958\pi$
$251$	−7.14276	−	1.25946i	−0.450847	−	0.0794965i	−0.394461	+	0.918913i	$0.629069\pi$
$252$		0			0
$253$	−22.3988	+	8.15248i	−1.40820	+	0.512542i
$254$		0			0
$255$	−17.5785	+	14.3448i	−1.10081	+	0.898308i
$256$		0			0
$257$	7.10091	+	5.95837i	0.442942	+	0.371673i	0.836809	−	0.547495i	$-0.184418\pi$
$257$	7.10091	+	5.95837i	0.442942	+	0.371673i	−0.393867	+	0.919168i	$0.628863\pi$
$258$		0			0
$259$	−6.04944	−	3.49265i	−0.375894	−	0.217023i
$260$		0			0
$261$	−3.07128	−	5.67268i	−0.190108	−	0.351130i
$262$		0			0
$263$	−1.21399	+	3.33541i	−0.0748578	+	0.205670i	−0.971478	−	0.237131i	$-0.923793\pi$
$263$	−1.21399	+	3.33541i	−0.0748578	+	0.205670i	0.896620	+	0.442801i	$0.146015\pi$
$264$		0			0
$265$			6.43982i			0.395595i
$266$		0			0
$267$	1.71892	+	10.5943i	0.105196	+	0.648358i
$268$		0			0
$269$	−4.70855	−	1.71377i	−0.287086	−	0.104491i	0.194463	−	0.980910i	$-0.437703\pi$
$269$	−4.70855	−	1.71377i	−0.287086	−	0.104491i	−0.481549	+	0.876419i	$0.659926\pi$
$270$		0			0
$271$	1.60600	+	9.10806i	0.0975574	+	0.553275i	0.993934	+	0.109981i	$0.0350791\pi$
$271$	1.60600	+	9.10806i	0.0975574	+	0.553275i	−0.896376	+	0.443294i	$0.853810\pi$
$272$		0			0
$273$	−1.89759	+	4.99962i	−0.114847	+	0.302591i
$274$		0			0
$275$	−0.224973	+	0.268112i	−0.0135664	+	0.0161678i
$276$		0			0
$277$	3.80040	+	6.58248i	0.228344	+	0.395503i	0.957317	−	0.289039i	$-0.0933356\pi$
$277$	3.80040	+	6.58248i	0.228344	+	0.395503i	−0.728974	+	0.684542i	$0.760002\pi$
$278$		0			0
$279$	11.3675	+	14.3258i	0.680554	+	0.857665i
$280$		0			0
$281$	2.50185	−	14.1887i	0.149248	−	0.846425i	−0.814610	−	0.580009i	$-0.803049\pi$
$281$	2.50185	−	14.1887i	0.149248	−	0.846425i	0.963858	−	0.266417i	$-0.0858397\pi$
$282$		0			0
$283$	−7.59307	+	6.37134i	−0.451361	+	0.378737i	−0.839941	−	0.542678i	$-0.817410\pi$
$283$	−7.59307	+	6.37134i	−0.451361	+	0.378737i	0.388579	+	0.921415i	$0.372966\pi$
$284$		0			0
$285$	−15.4647	−	7.25913i	−0.916049	−	0.429994i
$286$		0			0
$287$	16.2394	−	13.6265i	0.958584	−	0.804348i
$288$		0			0
$289$	−2.86743	+	16.2620i	−0.168673	+	0.956589i
$290$		0			0
$291$	14.4245	−	8.06682i	0.845577	−	0.472886i
$292$		0			0
$293$	−4.11218	−	7.12251i	−0.240236	−	0.416102i	0.720545	−	0.693408i	$-0.243892\pi$
$293$	−4.11218	−	7.12251i	−0.240236	−	0.416102i	−0.960782	+	0.277306i	$0.910558\pi$
$294$		0			0
$295$	4.81851	−	5.74247i	0.280544	−	0.334340i
$296$		0			0
$297$	0.620963	−	15.1170i	0.0360319	−	0.877178i
$298$		0			0
$299$	−1.87835	−	10.6527i	−0.108628	−	0.616059i
$300$		0			0
$301$	0.842207	+	0.306538i	0.0485440	+	0.0176686i
$302$		0			0
$303$	−21.4001	+	3.47217i	−1.22941	+	0.199471i
$304$		0			0
$305$		−	13.2758i		−	0.760168i
$306$		0			0
$307$	3.47152	−	9.53794i	0.198130	−	0.544359i	−0.800346	−	0.599538i	$-0.795351\pi$
$307$	3.47152	−	9.53794i	0.198130	−	0.544359i	0.998476	+	0.0551795i	$0.0175731\pi$
$308$		0			0
$309$	4.99801	+	14.3395i	0.284327	+	0.815746i
$310$		0			0
$311$	−9.98316	−	5.76378i	−0.566093	−	0.326834i	0.189494	−	0.981882i	$-0.439315\pi$
$311$	−9.98316	−	5.76378i	−0.566093	−	0.326834i	−0.755587	+	0.655048i	$0.772648\pi$
$312$		0			0
$313$	2.29638	+	1.92690i	0.129799	+	0.108915i	0.705376	−	0.708833i	$-0.250778\pi$
$313$	2.29638	+	1.92690i	0.129799	+	0.108915i	−0.575577	+	0.817748i	$0.695222\pi$
$314$		0			0
$315$	−10.5243	+	11.8671i	−0.592977	+	0.668635i
$316$		0			0
$317$	−15.4509	+	5.62366i	−0.867808	+	0.315856i	−0.737279	−	0.675588i	$-0.763890\pi$
$317$	−15.4509	+	5.62366i	−0.867808	+	0.315856i	−0.130529	+	0.991445i	$0.541667\pi$
$318$		0			0
$319$	−6.16581	−	1.08720i	−0.345219	−	0.0608714i
$320$		0			0
$321$	10.6120	+	9.15485i	0.592302	+	0.510974i
$322$		0			0
$323$	−24.2997	+	6.80228i	−1.35207	+	0.378489i
$324$		0			0
$325$	−0.102094	−	0.121670i	−0.00566313	−	0.00674906i
$326$		0			0
$327$	0.174781	−	12.7712i	0.00966540	−	0.706250i
$328$		0			0
$329$	8.17442	+	22.4590i	0.450670	+	1.23821i
$330$		0			0
$331$	−1.51206	+	0.872986i	−0.0831101	+	0.0479837i	−0.540979	−	0.841036i	$-0.681946\pi$
$331$	−1.51206	+	0.872986i	−0.0831101	+	0.0479837i	0.457869	+	0.889020i	$0.348613\pi$
$332$		0			0
$333$	−3.29693	+	8.34064i	−0.180671	+	0.457064i
$334$		0			0
$335$	18.3689	−	31.8160i	1.00360	−	1.73829i
$336$		0			0
$337$	−14.3139	+	2.52392i	−0.779727	+	0.137487i	−0.549325	−	0.835609i	$-0.685115\pi$
$337$	−14.3139	+	2.52392i	−0.779727	+	0.137487i	−0.230402	+	0.973096i	$0.574004\pi$
$338$		0			0
$339$	−4.82166	+	25.3142i	−0.261876	+	1.37488i
$340$		0			0
$341$	17.7498			0.961207
$342$		0			0
$343$	19.9553			1.07749
$344$		0			0
$345$	6.00323	−	31.5176i	0.323203	−	1.69685i
$346$		0			0
$347$	5.30901	−	0.936123i	0.285003	−	0.0502537i	−0.0293192	−	0.999570i	$-0.509334\pi$
$347$	5.30901	−	0.936123i	0.285003	−	0.0502537i	0.314322	+	0.949316i	$0.398223\pi$
$348$		0			0
$349$	−1.57657	+	2.73070i	−0.0843920	+	0.146171i	−0.905132	−	0.425131i	$-0.860228\pi$
$349$	−1.57657	+	2.73070i	−0.0843920	+	0.146171i	0.820740	+	0.571302i	$0.193561\pi$
$350$		0			0
$351$	6.70701	+	1.46877i	0.357994	+	0.0783971i
$352$		0			0
$353$	19.6094	−	11.3215i	1.04370	−	0.602582i	0.122822	−	0.992429i	$-0.460805\pi$
$353$	19.6094	−	11.3215i	1.04370	−	0.602582i	0.920880	+	0.389847i	$0.127472\pi$
$354$		0			0
$355$	−10.2338	−	28.1172i	−0.543155	−	1.49231i
$356$		0			0
$357$	−0.320603	+	23.4265i	−0.0169681	+	1.23986i
$358$		0			0
$359$	10.4708	+	12.4786i	0.552628	+	0.658596i	0.967969	−	0.251069i	$-0.0807822\pi$
$359$	10.4708	+	12.4786i	0.552628	+	0.658596i	−0.415341	+	0.909666i	$0.636338\pi$
$360$		0			0
$361$	−12.5344	−	14.2790i	−0.659705	−	0.751525i
$362$		0			0
$363$	3.30734	+	2.85321i	0.173590	+	0.149755i
$364$		0			0
$365$	13.8665	+	2.44504i	0.725806	+	0.127979i
$366$		0			0
$367$	−13.5022	+	4.91441i	−0.704811	+	0.256530i	−0.669464	−	0.742845i	$-0.733476\pi$
$367$	−13.5022	+	4.91441i	−0.704811	+	0.256530i	−0.0353474	+	0.999375i	$0.511254\pi$
$368$		0			0
$369$	−20.3637	−	18.0595i	−1.06009	−	0.940139i
$370$		0			0
$371$	5.09407	+	4.27443i	0.264471	+	0.221918i
$372$		0			0
$373$	−31.7907	−	18.3543i	−1.64606	−	0.950352i	−0.978617	−	0.205689i	$-0.934056\pi$
$373$	−31.7907	−	18.3543i	−1.64606	−	0.950352i	−0.667441	−	0.744663i	$-0.732610\pi$
$374$		0			0
$375$	6.29466	+	18.0596i	0.325055	+	0.932596i
$376$		0			0
$377$	0.971760	−	2.66989i	0.0500482	−	0.137506i
$378$		0			0
$379$		−	26.0481i		−	1.33800i	−0.743263	−	0.669000i	$-0.766723\pi$
$379$		−	26.0481i		−	1.33800i	0.743263	−	0.669000i	$-0.233277\pi$
$380$		0			0
$381$	12.6998	−	2.06053i	0.650628	−	0.105564i
$382$		0			0
$383$	−2.22943	−	0.811445i	−0.113918	−	0.0414629i	0.284432	−	0.958696i	$-0.408195\pi$
$383$	−2.22943	−	0.811445i	−0.113918	−	0.0414629i	−0.398350	+	0.917233i	$0.630417\pi$
$384$		0			0
$385$	2.67328	+	15.1609i	0.136243	+	0.772673i
$386$		0			0
$387$	0.230760	−	1.12735i	0.0117302	−	0.0573067i
$388$		0			0
$389$	−15.0557	+	17.9426i	−0.763353	+	0.909728i	−0.998055	−	0.0623389i	$-0.980144\pi$
$389$	−15.0557	+	17.9426i	−0.763353	+	0.909728i	0.234702	+	0.972067i	$0.424588\pi$
$390$		0			0
$391$	−23.6954	−	41.0416i	−1.19833	−	2.07556i
$392$		0			0
$393$	26.9062	−	15.0472i	1.35724	−	0.759029i
$394$		0			0
$395$	−2.03999	+	11.5694i	−0.102643	+	0.582119i
$396$		0			0
$397$	5.26511	−	4.41795i	0.264248	−	0.221731i	−0.501031	−	0.865430i	$-0.667046\pi$
$397$	5.26511	−	4.41795i	0.264248	−	0.221731i	0.765279	+	0.643699i	$0.222601\pi$
$398$		0			0
$399$	−16.0069	+	7.41473i	−0.801345	+	0.371201i
$400$		0			0
$401$	−23.7988	+	19.9695i	−1.18845	+	0.997231i	−0.188569	+	0.982060i	$0.560385\pi$
$401$	−23.7988	+	19.9695i	−1.18845	+	0.997231i	−0.999885	+	0.0151712i	$0.995171\pi$
$402$		0			0
$403$	−1.39873	+	7.93257i	−0.0696755	+	0.395150i
$404$		0			0
$405$	17.0532	+	11.1322i	0.847378	+	0.553164i
$406$		0			0
$407$	4.35235	+	7.53850i	0.215738	+	0.373670i
$408$		0			0
$409$	−5.64702	+	6.72985i	−0.279227	+	0.332770i	−0.887370	−	0.461057i	$-0.847470\pi$
$409$	−5.64702	+	6.72985i	−0.279227	+	0.332770i	0.608143	+	0.793827i	$0.291915\pi$
$410$		0			0
$411$	10.0946	−	26.5964i	0.497928	−	1.31190i
$412$		0			0
$413$	−1.34417	−	7.62314i	−0.0661420	−	0.375110i
$414$		0			0
$415$	3.99063	+	1.45247i	0.195892	+	0.0712989i
$416$		0			0
$417$	−5.36319	−	33.0551i	−0.262637	−	1.61872i
$418$		0			0
$419$			0.268652i			0.0131245i	0.999978	+	0.00656225i	$0.00208885\pi$
$419$			0.268652i			0.0131245i	−0.999978	+	0.00656225i	$0.997911\pi$
$420$		0			0
$421$	6.44528	−	17.7083i	0.314124	−	0.863048i	−0.677689	−	0.735348i	$-0.737019\pi$
$421$	6.44528	−	17.7083i	0.314124	−	0.863048i	0.991813	−	0.127699i	$-0.0407592\pi$
$422$		0			0
$423$	26.9851	−	14.6102i	1.31206	−	0.710372i
$424$		0			0
$425$	−0.602627	−	0.347927i	−0.0292317	−	0.0168769i
$426$		0			0
$427$	−10.5015	−	8.81180i	−0.508203	−	0.426433i
$428$		0			0
$429$	5.16300	−	4.21323i	0.249272	−	0.203417i
$430$		0			0
$431$	−8.09752	+	2.94726i	−0.390044	+	0.141964i	−0.529595	−	0.848250i	$-0.677656\pi$
$431$	−8.09752	+	2.94726i	−0.390044	+	0.141964i	0.139551	+	0.990215i	$0.455434\pi$
$432$		0			0
$433$	8.52374	+	1.50296i	0.409625	+	0.0722279i	0.374664	−	0.927161i	$-0.377758\pi$
$433$	8.52374	+	1.50296i	0.409625	+	0.0722279i	0.0349610	+	0.999389i	$0.488869\pi$
$434$		0			0
$435$	5.50485	−	6.38102i	0.263937	−	0.305946i
$436$		0			0
$437$	20.1400	−	29.4564i	0.963426	−	1.40909i
$438$		0			0
$439$	16.0959	+	19.1824i	0.768216	+	0.915524i	0.998338	−	0.0576380i	$-0.0183569\pi$
$439$	16.0959	+	19.1824i	0.768216	+	0.915524i	−0.230122	+	0.973162i	$0.573912\pi$
$440$		0			0
$441$	−0.677615	−	4.57121i	−0.0322674	−	0.217677i
$442$		0			0
$443$	2.20842	+	6.06757i	0.104925	+	0.288279i	0.981035	−	0.193833i	$-0.0620920\pi$
$443$	2.20842	+	6.06757i	0.104925	+	0.288279i	−0.876110	+	0.482112i	$0.839870\pi$
$444$		0			0
$445$	−12.1430	+	7.01078i	−0.575634	+	0.332343i
$446$		0			0
$447$	9.58426	+	5.70975i	0.453320	+	0.270062i
$448$		0			0
$449$	−11.3528	+	19.6637i	−0.535774	+	0.927988i	0.463351	+	0.886175i	$0.346647\pi$
$449$	−11.3528	+	19.6637i	−0.535774	+	0.927988i	−0.999125	+	0.0418133i	$0.986687\pi$
$450$		0			0
$451$	−26.0159	+	4.58730i	−1.22504	+	0.216007i
$452$		0			0
$453$	−5.15258	−	0.981423i	−0.242089	−	0.0461113i
$454$		0			0
$455$	−6.98624			−0.327520
$456$		0			0
$457$	9.08970			0.425198			0.212599	−	0.977140i	$-0.431807\pi$
$457$	9.08970			0.425198			0.212599	+	0.977140i	$0.431807\pi$
$458$		0			0
$459$	29.8131	−	4.00323i	1.39156	−	0.186855i
$460$		0			0
$461$	−19.6634	+	3.46719i	−0.915818	+	0.161483i	−0.611644	−	0.791133i	$-0.709491\pi$
$461$	−19.6634	+	3.46719i	−0.915818	+	0.161483i	−0.304174	+	0.952617i	$0.598380\pi$
$462$		0			0
$463$	−0.304139	+	0.526785i	−0.0141346	+	0.0244818i	−0.873006	−	0.487709i	$-0.837833\pi$
$463$	−0.304139	+	0.526785i	−0.0141346	+	0.0244818i	0.858872	+	0.512191i	$0.171166\pi$
$464$		0			0
$465$	−12.2279	+	20.5255i	−0.567055	+	0.951845i
$466$		0			0
$467$	13.6575	−	7.88518i	0.631995	−	0.364883i	−0.149529	−	0.988757i	$-0.547776\pi$
$467$	13.6575	−	7.88518i	0.631995	−	0.364883i	0.781524	+	0.623875i	$0.214442\pi$
$468$		0			0
$469$	−12.9749	−	35.6482i	−0.599124	−	1.64608i
$470$		0			0
$471$	33.1204	+	0.453270i	1.52611	+	0.0208856i
$472$		0			0
$473$	−0.717910	−	0.855572i	−0.0330095	−	0.0393392i
$474$		0			0
$475$	0.0398441	−	0.522432i	0.00182817	−	0.0239708i
$476$		0			0
$477$	4.46970	−	7.27445i	0.204653	−	0.333074i
$478$		0			0
$479$	−9.47350	−	1.67043i	−0.432855	−	0.0763241i	−0.0470248	−	0.998894i	$-0.514974\pi$
$479$	−9.47350	−	1.67043i	−0.432855	−	0.0763241i	−0.385831	+	0.922570i	$0.626085\pi$
$480$		0			0
$481$	−3.71200	+	1.35106i	−0.169253	+	0.0616030i
$482$		0			0
$483$	−20.9467	−	25.6686i	−0.953106	−	1.16796i
$484$		0			0
$485$	16.5397	+	13.8785i	0.751031	+	0.630190i
$486$		0			0
$487$	−28.7513	−	16.5996i	−1.30285	−	0.752198i	−0.321954	−	0.946755i	$-0.604340\pi$
$487$	−28.7513	−	16.5996i	−1.30285	−	0.752198i	−0.980891	+	0.194557i	$0.937673\pi$
$488$		0			0
$489$	10.1219	−	3.52798i	0.457730	−	0.159541i
$490$		0			0
$491$	3.75074	−	10.3051i	0.169268	−	0.465061i	−0.825834	−	0.563914i	$-0.809295\pi$
$491$	3.75074	−	10.3051i	0.169268	−	0.465061i	0.995102	+	0.0988527i	$0.0315173\pi$
$492$		0			0
$493$		−	12.4478i		−	0.560623i
$494$		0			0
$495$	18.7519	−	6.24949i	0.842833	−	0.280894i
$496$		0			0
$497$	−29.0342	−	10.5676i	−1.30236	−	0.474021i
$498$		0			0
$499$	5.30316	+	30.0757i	0.237402	+	1.34637i	0.837496	+	0.546444i	$0.184019\pi$
$499$	5.30316	+	30.0757i	0.237402	+	1.34637i	−0.600094	+	0.799930i	$0.704870\pi$
$500$		0			0
$501$	7.07546	+	2.68547i	0.316108	+	0.119978i
$502$		0			0
$503$	−10.7776	+	12.8442i	−0.480550	+	0.572697i	−0.950788	−	0.309843i	$-0.899724\pi$
$503$	−10.7776	+	12.8442i	−0.480550	+	0.572697i	0.470238	+	0.882540i	$0.344168\pi$
$504$		0			0
$505$	−14.1616	−	24.5286i	−0.630182	−	1.09151i
$506$		0			0
$507$	−9.51436	−	17.0128i	−0.422547	−	0.755566i
$508$		0			0
$509$	7.27364	−	41.2508i	0.322398	−	1.82841i	−0.204962	−	0.978770i	$-0.565707\pi$
$509$	7.27364	−	41.2508i	0.322398	−	1.82841i	0.527360	−	0.849642i	$-0.323182\pi$
$510$		0			0
$511$	11.1380	−	9.34588i	0.492716	−	0.413438i
$512$		0			0
$513$	12.4306	+	18.9336i	0.548825	+	0.835937i
$514$		0			0
$515$	−15.1974	+	12.7521i	−0.669676	+	0.561925i
$516$		0			0
$517$	5.17184	−	29.3310i	0.227457	−	1.28997i
$518$		0			0
$519$	−12.5941	−	22.5198i	−0.552821	−	0.988511i
$520$		0			0
$521$	5.82256	+	10.0850i	0.255091	+	0.441831i	0.964920	−	0.262543i	$-0.0845612\pi$
$521$	5.82256	+	10.0850i	0.255091	+	0.441831i	−0.709829	+	0.704374i	$0.751228\pi$
$522$		0			0
$523$	−1.24233	+	1.48055i	−0.0543231	+	0.0647398i	−0.792522	−	0.609844i	$-0.791232\pi$
$523$	−1.24233	+	1.48055i	−0.0543231	+	0.0647398i	0.738199	+	0.674583i	$0.235677\pi$
$524$		0			0
$525$	−0.454810	−	0.172622i	−0.0198495	−	0.00753382i
$526$		0			0
$527$	6.12802	+	34.7537i	0.266941	+	1.51390i
$528$		0			0
$529$	41.3611	+	15.0542i	1.79831	+	0.654531i
$530$		0			0
$531$	−9.42870	+	3.14233i	−0.409171	+	0.136366i
$532$		0			0
$533$		−	11.9882i		−	0.519268i
$534$		0			0
$535$	−6.26229	+	17.2055i	−0.270742	+	0.743858i
$536$		0			0
$537$	−5.49583	+	1.91557i	−0.237163	+	0.0826627i
$538$		0			0
$539$	−3.88428	−	2.24259i	−0.167308	−	0.0965953i
$540$		0			0
$541$	−7.95720	−	6.67688i	−0.342107	−	0.287062i	0.455505	−	0.890233i	$-0.349459\pi$
$541$	−7.95720	−	6.67688i	−0.342107	−	0.287062i	−0.797611	+	0.603172i	$0.793903\pi$
$542$		0			0
$543$	−21.7565	−	26.6610i	−0.933662	−	1.14413i
$544$		0			0
$545$	15.6798	−	5.70700i	0.671651	−	0.244461i
$546$		0			0
$547$	−24.0156	−	4.23461i	−1.02683	−	0.181059i	−0.365235	−	0.930915i	$-0.619011\pi$
$547$	−24.0156	−	4.23461i	−1.02683	−	0.181059i	−0.661600	+	0.749857i	$0.730122\pi$
$548$		0			0
$549$	−9.21434	+	14.9964i	−0.393258	+	0.640029i
$550$		0			0
$551$	8.44988	−	4.05552i	0.359977	−	0.172771i
$552$		0			0
$553$	7.79765	+	9.29287i	0.331590	+	0.395173i
$554$		0			0
$555$	−11.7157	−	0.160335i	−0.497303	−	0.00680585i
$556$		0			0
$557$	−6.96784	−	19.1440i	−0.295237	−	0.811156i	−0.995279	−	0.0970547i	$-0.969058\pi$
$557$	−6.96784	−	19.1440i	−0.295237	−	0.811156i	0.700042	−	0.714101i	$-0.253164\pi$
$558$		0			0
$559$	0.438936	−	0.253420i	0.0185650	−	0.0107185i
$560$		0			0
$561$	14.9424	−	25.0820i	0.630869	−	1.05896i
$562$		0			0
$563$	−0.391026	+	0.677277i	−0.0164798	+	0.0285438i	−0.874148	−	0.485660i	$-0.838579\pi$
$563$	−0.391026	+	0.677277i	−0.0164798	+	0.0285438i	0.857668	+	0.514204i	$0.171913\pi$
$564$		0			0
$565$	−33.1541	+	5.84597i	−1.39481	+	0.245942i
$566$		0			0
$567$	20.1249	−	6.10050i	0.845167	−	0.256197i
$568$		0			0
$569$	12.5732			0.527098			0.263549	−	0.964646i	$-0.415107\pi$
$569$	12.5732			0.527098			0.263549	+	0.964646i	$0.415107\pi$
$570$		0			0
$571$	2.14694			0.0898468			0.0449234	−	0.998990i	$-0.485696\pi$
$571$	2.14694			0.0898468			0.0449234	+	0.998990i	$0.485696\pi$
$572$		0			0
$573$	17.4137	+	3.31683i	0.727469	+	0.138563i
$574$		0			0
$575$	0.969062	−	0.170872i	0.0404127	−	0.00712585i
$576$		0			0
$577$	−19.9348	+	34.5282i	−0.829898	+	1.43743i	0.0682191	+	0.997670i	$0.478268\pi$
$577$	−19.9348	+	34.5282i	−0.829898	+	1.43743i	−0.898117	+	0.439756i	$0.855065\pi$
$578$		0			0
$579$	3.41371	+	2.03369i	0.141869	+	0.0845174i
$580$		0			0
$581$	3.79772	−	2.19262i	0.157556	−	0.0909650i
$582$		0			0
$583$	−2.83421	−	7.78693i	−0.117381	−	0.322502i
$584$		0			0
$585$	1.31527	+	8.87286i	0.0543798	+	0.366848i
$586$		0			0
$587$	−28.9490	−	34.5001i	−1.19485	−	1.42397i	−0.880095	−	0.474797i	$-0.842521\pi$
$587$	−28.9490	−	34.5001i	−1.19485	−	1.42397i	−0.314757	−	0.949172i	$-0.601923\pi$
$588$		0			0
$589$	−21.5951	+	15.4826i	−0.889810	+	0.637951i
$590$		0			0
$591$	7.14380	−	8.28082i	0.293856	−	0.340627i
$592$		0			0
$593$	29.2417	+	5.15610i	1.20081	+	0.211736i	0.738050	−	0.674746i	$-0.235747\pi$
$593$	29.2417	+	5.15610i	1.20081	+	0.211736i	0.462763	+	0.886482i	$0.346858\pi$
$594$		0			0
$595$	−28.7618	+	10.4684i	−1.17912	+	0.429164i
$596$		0			0
$597$	13.9485	−	11.3826i	0.570876	−	0.465859i
$598$		0			0
$599$	−23.2268	−	19.4896i	−0.949023	−	0.796325i	0.0301101	−	0.999547i	$-0.490414\pi$
$599$	−23.2268	−	19.4896i	−0.949023	−	0.796325i	−0.979133	+	0.203222i	$0.934859\pi$
$600$		0			0
$601$	19.5471	+	11.2855i	0.797343	+	0.460346i	0.842541	−	0.538632i	$-0.181059\pi$
$601$	19.5471	+	11.2855i	0.797343	+	0.460346i	−0.0451983	+	0.998978i	$0.514392\pi$
$602$		0			0
$603$	−42.8322	+	23.1901i	−1.74426	+	0.944373i
$604$		0			0
$605$	−1.95171	+	5.36229i	−0.0793484	+	0.218008i
$606$		0			0
$607$		−	22.1708i		−	0.899886i	−0.893057	−	0.449943i	$-0.851444\pi$
$607$		−	22.1708i		−	0.899886i	0.893057	−	0.449943i	$-0.148556\pi$
$608$		0			0
$609$	−1.39371	−	8.58989i	−0.0564759	−	0.348080i
$610$		0			0
$611$	12.7007	+	4.62269i	0.513817	+	0.187014i
$612$		0			0
$613$	−4.39349	−	24.9167i	−0.177451	−	1.00638i	−0.935276	−	0.353919i	$-0.884849\pi$
$613$	−4.39349	−	24.9167i	−0.177451	−	1.00638i	0.757825	−	0.652458i	$-0.226262\pi$
$614$		0			0
$615$	12.6177	−	33.2443i	0.508797	−	1.34054i
$616$		0			0
$617$	−3.45217	+	4.11414i	−0.138979	+	0.165629i	−0.831045	−	0.556206i	$-0.812257\pi$
$617$	−3.45217	+	4.11414i	−0.138979	+	0.165629i	0.692065	+	0.721835i	$0.256701\pi$
$618$		0			0
$619$	10.8898	+	18.8617i	0.437699	+	0.758117i	0.997512	−	0.0705023i	$-0.0224602\pi$
$619$	10.8898	+	18.8617i	0.437699	+	0.758117i	−0.559813	+	0.828619i	$0.689127\pi$
$620$		0			0
$621$	−28.6568	+	31.4358i	−1.14996	+	1.26148i
$622$		0			0
$623$	−2.51422	+	14.2589i	−0.100730	+	0.571269i
$624$		0			0
$625$	−19.6004	+	16.4467i	−0.784018	+	0.657869i
$626$		0			0
$627$	21.8945	+	1.97151i	0.874380	+	0.0787345i
$628$		0			0
$629$	−13.2576	+	11.1244i	−0.528614	+	0.443560i
$630$		0			0
$631$	2.49759	−	14.1646i	0.0994276	−	0.563882i	−0.893873	−	0.448321i	$-0.852022\pi$
$631$	2.49759	−	14.1646i	0.0994276	−	0.563882i	0.993300	−	0.115561i	$-0.0368667\pi$
$632$		0			0
$633$	8.42859	−	4.71366i	0.335006	−	0.187351i
$634$		0			0
$635$	8.40409	+	14.5563i	0.333506	+	0.577650i
$636$		0			0
$637$	1.30833	−	1.55920i	0.0518378	−	0.0617779i
$638$		0			0
$639$	−7.95520	+	38.8644i	−0.314703	+	1.53745i
$640$		0			0
$641$	1.24354	+	7.05244i	0.0491167	+	0.278555i	0.999468	−	0.0326255i	$-0.0103869\pi$
$641$	1.24354	+	7.05244i	0.0491167	+	0.278555i	−0.950351	+	0.311180i	$0.899276\pi$
$642$		0			0
$643$	−9.97359	−	3.63009i	−0.393320	−	0.143157i	0.137786	−	0.990462i	$-0.456001\pi$
$643$	−9.97359	−	3.63009i	−0.393320	−	0.143157i	−0.531106	+	0.847305i	$0.678224\pi$
$644$		0			0
$645$	1.48393	−	0.240768i	0.0584297	−	0.00948022i
$646$		0			0
$647$		−	25.2527i		−	0.992786i	−0.868098	−	0.496393i	$-0.834658\pi$
$647$		−	25.2527i		−	0.992786i	0.868098	−	0.496393i	$-0.165342\pi$
$648$		0			0
$649$	−3.29916	+	9.06437i	−0.129503	+	0.355808i
$650$		0			0
$651$	8.11992	+	23.2964i	0.318245	+	0.913057i
$652$		0			0
$653$	4.44155	+	2.56433i	0.173811	+	0.100350i	0.584382	−	0.811479i	$-0.301337\pi$
$653$	4.44155	+	2.56433i	0.173811	+	0.100350i	−0.410570	+	0.911829i	$0.634670\pi$
$654$		0			0
$655$	30.8518	+	25.8877i	1.20548	+	1.01152i
$656$		0			0
$657$	−13.9666	−	12.3863i	−0.544890	−	0.483235i
$658$		0			0
$659$	39.0596	−	14.2165i	1.52154	−	0.553797i	0.560011	−	0.828485i	$-0.310797\pi$
$659$	39.0596	−	14.2165i	1.52154	−	0.553797i	0.961533	+	0.274688i	$0.0885747\pi$
$660$		0			0
$661$	−46.7645	−	8.24585i	−1.81893	−	0.320726i	−0.842851	−	0.538147i	$-0.819125\pi$
$661$	−46.7645	−	8.24585i	−1.81893	−	0.320726i	−0.976078	+	0.217421i	$0.930236\pi$
$662$		0			0
$663$	10.0319	+	8.65443i	0.389606	+	0.336110i
$664$		0			0
$665$	−16.4768	−	16.1135i	−0.638944	−	0.624856i
$666$		0			0
$667$	11.3147	+	13.4844i	0.438108	+	0.522116i
$668$		0			0
$669$	−0.122921	+	8.98182i	−0.00475240	+	0.347257i
$670$		0			0
$671$	5.84276	+	16.0529i	0.225557	+	0.619713i
$672$		0			0
$673$	−37.0622	+	21.3979i	−1.42864	+	0.824827i	−0.997014	−	0.0772240i	$-0.975394\pi$
$673$	−37.0622	+	21.3979i	−1.42864	+	0.824827i	−0.431629	+	0.902051i	$0.642061\pi$
$674$		0			0
$675$	−0.133613	+	0.610130i	−0.00514275	+	0.0234839i
$676$		0			0
$677$	−16.0186	+	27.7451i	−0.615646	+	1.06633i	0.374625	+	0.927176i	$0.377771\pi$
$677$	−16.0186	+	27.7451i	−0.615646	+	1.06633i	−0.990271	+	0.139153i	$0.955562\pi$
$678$		0			0
$679$	21.9565	−	3.87153i	0.842614	−	0.148576i
$680$		0			0
$681$	5.52135	−	28.9877i	0.211578	−	1.11081i
$682$		0			0
$683$	8.09665			0.309810			0.154905	−	0.987929i	$-0.450493\pi$
$683$	8.09665			0.309810			0.154905	+	0.987929i	$0.450493\pi$
$684$		0			0
$685$	37.1646			1.41998
$686$		0			0
$687$	7.94656	−	41.7203i	0.303180	−	1.59173i
$688$		0			0
$689$	3.70340	−	0.653009i	0.141088	−	0.0248777i
$690$		0			0
$691$	−14.6326	+	25.3445i	−0.556652	+	0.964149i	0.441121	+	0.897447i	$0.354581\pi$
$691$	−14.6326	+	25.3445i	−0.556652	+	0.964149i	−0.997773	+	0.0667014i	$0.978753\pi$
$692$		0			0
$693$	7.50304	−	18.9813i	0.285017	−	0.721041i
$694$		0			0
$695$	37.8874	−	21.8743i	1.43715	−	0.829740i
$696$		0			0
$697$	−17.9636	−	49.3547i	−0.680421	−	1.86944i
$698$		0			0
$699$	−0.541363	+	39.5574i	−0.0204762	+	1.49620i
$700$		0			0
$701$	−6.18601	−	7.37220i	−0.233642	−	0.278444i	0.636466	−	0.771305i	$-0.280396\pi$
$701$	−6.18601	−	7.37220i	−0.233642	−	0.278444i	−0.870108	+	0.492861i	$0.835951\pi$
$702$		0			0
$703$	−11.8708	−	5.37519i	−0.447717	−	0.202729i
$704$		0			0
$705$	30.3547	+	26.1867i	1.14322	+	0.986250i
$706$		0			0
$707$	−28.8025	−	5.07867i	−1.08323	−	0.191003i
$708$		0			0
$709$	2.54680	−	0.926959i	0.0956471	−	0.0348127i	−0.293753	−	0.955881i	$-0.594904\pi$
$709$	2.54680	−	0.926959i	0.0956471	−	0.0348127i	0.389400	+	0.921069i	$0.372682\pi$
$710$		0			0
$711$	10.3344	−	11.6529i	0.387569	−	0.437019i
$712$		0			0
$713$	−38.2284	−	32.0774i	−1.43166	−	1.20131i
$714$		0			0
$715$	7.53951	+	4.35294i	0.281962	+	0.162791i
$716$		0			0
$717$	1.73045	+	4.96472i	0.0646247	+	0.185411i
$718$		0			0
$719$	−3.02583	+	8.31341i	−0.112845	+	0.310038i	−0.983240	−	0.182315i	$-0.941641\pi$
$719$	−3.02583	+	8.31341i	−0.112845	+	0.310038i	0.870396	+	0.492353i	$0.163863\pi$
$720$		0			0
$721$			20.4857i			0.762929i
$722$		0			0
$723$	−6.75625	+	1.09620i	−0.251268	+	0.0407681i
$724$		0			0
$725$	0.242877	+	0.0884000i	0.00902023	+	0.00328309i
$726$		0			0
$727$	6.48485	+	36.7774i	0.240510	+	1.36400i	0.830693	+	0.556730i	$0.187944\pi$
$727$	6.48485	+	36.7774i	0.240510	+	1.36400i	−0.590183	+	0.807269i	$0.700945\pi$
$728$		0			0
$729$	−11.5368	−	24.4111i	−0.427288	−	0.904116i
$730$		0			0
$731$	1.42733	−	1.70103i	0.0527918	−	0.0629149i
$732$		0			0
$733$	17.5306	+	30.3638i	0.647506	+	1.12151i	0.983717	+	0.179726i	$0.0575211\pi$
$733$	17.5306	+	30.3638i	0.647506	+	1.12151i	−0.336211	+	0.941787i	$0.609146\pi$
$734$		0			0
$735$	5.26917	−	2.94676i	0.194356	−	0.108693i
$736$		0			0
$737$	−8.20902	+	46.5557i	−0.302383	+	1.71490i
$738$		0			0
$739$	−20.2995	+	17.0333i	−0.746731	+	0.626581i	−0.934636	−	0.355606i	$-0.884275\pi$
$739$	−20.2995	+	17.0333i	−0.746731	+	0.626581i	0.187905	+	0.982187i	$0.439830\pi$
$740$		0			0
$741$	−2.60642	+	9.62949i	−0.0957492	+	0.353748i
$742$		0			0
$743$	−24.2865	+	20.3788i	−0.890984	+	0.747624i	−0.968407	−	0.249374i	$-0.919775\pi$
$743$	−24.2865	+	20.3788i	−0.890984	+	0.747624i	0.0774234	+	0.996998i	$0.475331\pi$
$744$		0			0
$745$	−2.53085	+	14.3532i	−0.0927233	+	0.525860i
$746$		0			0
$747$	−3.49971	−	4.41050i	−0.128048	−	0.161372i
$748$		0			0
$749$	9.45341	+	16.3738i	0.345420	+	0.598285i
$750$		0			0
$751$	1.60959	−	1.91823i	0.0587347	−	0.0699973i	−0.735877	−	0.677115i	$-0.763230\pi$
$751$	1.60959	−	1.91823i	0.0587347	−	0.0699973i	0.794612	+	0.607118i	$0.207674\pi$
$752$		0			0
$753$	−4.45776	+	11.7450i	−0.162450	+	0.428010i
$754$		0			0
$755$	−1.18992	−	6.74835i	−0.0433055	−	0.245598i
$756$		0			0
$757$	−7.22987	−	2.63146i	−0.262774	−	0.0956419i	0.207273	−	0.978283i	$-0.433541\pi$
$757$	−7.22987	−	2.63146i	−0.262774	−	0.0956419i	−0.470048	+	0.882641i	$0.655763\pi$
$758$		0			0
$759$	6.61212	+	40.7527i	0.240005	+	1.47923i
$760$		0			0
$761$			26.1918i			0.949453i	0.880133	+	0.474727i	$0.157453\pi$
$761$			26.1918i			0.949453i	−0.880133	+	0.474727i	$0.842547\pi$
$762$		0			0
$763$	5.89312	−	16.1912i	0.213345	−	0.586161i
$764$		0			0
$765$	18.7103	+	34.5581i	0.676473	+	1.24945i
$766$		0			0
$767$	−3.79097	−	2.18872i	−0.136884	−	0.0790301i
$768$		0			0
$769$	35.3779	+	29.6856i	1.27576	+	1.07049i	0.993814	+	0.111061i	$0.0354249\pi$
$769$	35.3779	+	29.6856i	1.27576	+	1.07049i	0.281948	+	0.959430i	$0.409020\pi$
$770$		0			0
$771$	12.4392	−	10.1509i	0.447987	−	0.365577i
$772$		0			0
$773$	6.91607	−	2.51724i	0.248754	−	0.0905390i	−0.214634	−	0.976695i	$-0.568856\pi$
$773$	6.91607	−	2.51724i	0.248754	−	0.0905390i	0.463388	+	0.886156i	$0.346634\pi$
$774$		0			0
$775$	−0.721618	−	0.127241i	−0.0259213	−	0.00457062i
$776$		0			0
$777$	−7.90312	+	9.16100i	−0.283523	+	0.328649i
$778$		0			0
$779$	27.6505	−	28.2739i	0.990681	−	1.01302i
$780$		0			0
$781$	24.7492	+	29.4949i	0.885596	+	1.05541i
$782$		0			0
$783$	−10.6472	+	3.38726i	−0.380500	+	0.121051i
$784$		0			0
$785$	14.8003	+	40.6635i	0.528245	+	1.45134i
$786$		0			0
$787$	−15.0496	+	8.68891i	−0.536462	+	0.309726i	−0.743644	−	0.668576i	$-0.766904\pi$
$787$	−15.0496	+	8.68891i	−0.536462	+	0.309726i	0.207182	+	0.978302i	$0.433571\pi$
$788$		0			0
$789$	5.28164	+	3.14650i	0.188031	+	0.112018i
$790$		0			0
$791$	−17.3818	+	30.1061i	−0.618024	+	1.07045i
$792$		0			0
$793$	−7.63460	+	1.34619i	−0.271113	+	0.0478045i
$794$		0			0
$795$	10.9571	+	2.08702i	0.388609	+	0.0740191i
$796$		0			0
$797$	4.12081			0.145966			0.0729832	−	0.997333i	$-0.476748\pi$
$797$	4.12081			0.145966			0.0729832	+	0.997333i	$0.476748\pi$
$798$		0			0
$799$	59.2148			2.09487
$800$		0			0
$801$	18.5828	+	0.508726i	0.656591	+	0.0179749i
$802$		0			0
$803$	−17.8432	+	3.14625i	−0.629674	+	0.111029i
$804$		0			0
$805$	21.6413	−	37.4838i	0.762754	−	1.32113i
$806$		0			0
$807$	−4.44187	+	7.45602i	−0.156361	+	0.262464i
$808$		0			0
$809$	31.6692	−	18.2842i	1.11343	−	0.642839i	0.173714	−	0.984796i	$-0.444423\pi$
$809$	31.6692	−	18.2842i	1.11343	−	0.642839i	0.939716	+	0.341957i	$0.111090\pi$
$810$		0			0
$811$	−12.5283	−	34.4211i	−0.439927	−	1.20869i	−0.939540	−	0.342440i	$-0.888747\pi$
$811$	−12.5283	−	34.4211i	−0.439927	−	1.20869i	0.499613	−	0.866249i	$-0.333476\pi$
$812$		0			0
$813$	16.0175	+	0.219208i	0.561758	+	0.00768795i
$814$		0			0
$815$	9.00142	+	10.7275i	0.315306	+	0.375767i
$816$		0			0
$817$	1.61972	+	0.414709i	0.0566670	+	0.0145088i
$818$		0			0
$819$	7.89168	+	4.84895i	0.275758	+	0.169436i
$820$		0			0
$821$	−40.6182	−	7.16208i	−1.41758	−	0.249958i	−0.588235	−	0.808690i	$-0.700177\pi$
$821$	−40.6182	−	7.16208i	−1.41758	−	0.249958i	−0.829349	+	0.558732i	$0.811288\pi$
$822$		0			0
$823$	−40.6757	+	14.8047i	−1.41787	+	0.516061i	−0.933428	−	0.358765i	$-0.883198\pi$
$823$	−40.6757	+	14.8047i	−1.41787	+	0.516061i	−0.484438	+	0.874826i	$0.660976\pi$
$824$		0			0
$825$	0.383273	+	0.469673i	0.0133439	+	0.0163519i
$826$		0			0
$827$	17.4100	+	14.6087i	0.605405	+	0.507995i	0.893178	−	0.449704i	$-0.148470\pi$
$827$	17.4100	+	14.6087i	0.605405	+	0.507995i	−0.287773	+	0.957699i	$0.592915\pi$
$828$		0			0
$829$	−6.17465	−	3.56494i	−0.214455	−	0.123815i	0.388925	−	0.921269i	$-0.372846\pi$
$829$	−6.17465	−	3.56494i	−0.214455	−	0.123815i	−0.603380	+	0.797454i	$0.706180\pi$
$830$		0			0
$831$	12.4315	−	4.33298i	0.431243	−	0.150309i
$832$		0			0
$833$	3.04991	−	8.37957i	0.105673	−	0.290335i
$834$		0			0
$835$			9.88693i			0.342151i
$836$		0			0
$837$	28.0588	−	14.6986i	0.969855	−	0.508058i
$838$		0			0
$839$	1.63571	+	0.595349i	0.0564710	+	0.0205537i	0.370101	−	0.928991i	$-0.379323\pi$
$839$	1.63571	+	0.595349i	0.0564710	+	0.0205537i	−0.313630	+	0.949545i	$0.601545\pi$
$840$		0			0
$841$	−4.23292	−	24.0061i	−0.145963	−	0.827797i
$842$		0			0
$843$	−23.3307	−	8.85508i	−0.803551	−	0.304985i
$844$		0			0
$845$	16.3689	−	19.5077i	0.563107	−	0.671084i
$846$		0			0
$847$	2.94626	+	5.10308i	0.101235	+	0.175344i
$848$		0			0
$849$	8.37983	+	14.9842i	0.287595	+	0.514255i
$850$		0			0
$851$	4.24974	−	24.1015i	0.145679	−	0.826187i
$852$		0			0
$853$	−22.0984	+	18.5427i	−0.756634	+	0.634891i	−0.937248	−	0.348663i	$-0.886636\pi$
$853$	−22.0984	+	18.5427i	−0.756634	+	0.634891i	0.180614	+	0.983554i	$0.442191\pi$
$854$		0			0
$855$	−17.3629	+	23.9600i	−0.593800	+	0.819415i
$856$		0			0
$857$	9.31787	−	7.81862i	0.318292	−	0.267079i	−0.469617	−	0.882870i	$-0.655608\pi$
$857$	9.31787	−	7.81862i	0.318292	−	0.267079i	0.787909	+	0.615791i	$0.211164\pi$
$858$		0			0
$859$	−3.16859	+	17.9700i	−0.108111	+	0.613127i	0.881821	+	0.471584i	$0.156318\pi$
$859$	−3.16859	+	17.9700i	−0.108111	+	0.613127i	−0.989932	+	0.141543i	$0.954794\pi$
$860$		0			0
$861$	−17.9221	−	32.0469i	−0.610783	−	1.09216i
$862$		0			0
$863$	−22.3079	−	38.6385i	−0.759371	−	1.31527i	−0.943172	−	0.332306i	$-0.892173\pi$
$863$	−22.3079	−	38.6385i	−0.759371	−	1.31527i	0.183800	−	0.982964i	$-0.441160\pi$
$864$		0			0
$865$	21.6674	−	25.8223i	0.736715	−	0.877983i
$866$		0			0
$867$	26.7399	+	10.1490i	0.908135	+	0.344679i
$868$		0			0
$869$	−2.62504	−	14.8873i	−0.0890483	−	0.505018i
$870$		0			0
$871$	−20.1593	−	7.33738i	−0.683072	−	0.248618i
$872$		0			0
$873$	−9.05069	−	27.1570i	−0.306320	−	0.919124i
$874$		0			0
$875$			25.8004i			0.872212i
$876$		0			0
$877$	−1.46003	+	4.01139i	−0.0493016	+	0.135455i	−0.961900	−	0.273403i	$-0.911851\pi$
$877$	−1.46003	+	4.01139i	−0.0493016	+	0.135455i	0.912598	+	0.408858i	$0.134073\pi$
$878$		0			0
$879$	−13.4514	+	4.68845i	−0.453703	+	0.158138i
$880$		0			0
$881$	−9.81390	−	5.66606i	−0.330639	−	0.190894i	0.325486	−	0.945547i	$-0.394472\pi$
$881$	−9.81390	−	5.66606i	−0.330639	−	0.190894i	−0.656125	+	0.754653i	$0.727805\pi$
$882$		0			0
$883$	−30.0308	−	25.1988i	−1.01062	−	0.848008i	−0.0221970	−	0.999754i	$-0.507066\pi$
$883$	−30.0308	−	25.1988i	−1.01062	−	0.848008i	−0.988420	+	0.151746i	$0.951511\pi$
$884$		0			0
$885$	−8.20901	−	10.0595i	−0.275943	−	0.338147i
$886$		0			0
$887$	−38.4635	+	13.9996i	−1.29148	+	0.470059i	−0.894212	−	0.447644i	$-0.852263\pi$
$887$	−38.4635	+	13.9996i	−1.29148	+	0.470059i	−0.397266	+	0.917704i	$0.630041\pi$
$888$		0			0
$889$	17.0927	+	3.01390i	0.573269	+	0.101083i
$890$		0			0
$891$	−25.5198	−	5.95568i	−0.854945	−	0.199523i
$892$		0			0
$893$	19.2922	+	40.1963i	0.645590	+	1.34512i
$894$		0			0
$895$	−4.88744	−	5.82462i	−0.163369	−	0.194696i
$896$		0			0
$897$	−18.7338	−	0.256382i	−0.625505	−	0.00856036i
$898$		0			0
$899$	−4.48316	−	12.3174i	−0.149522	−	0.410807i
$900$		0			0
$901$	14.2681	−	8.23770i	0.475340	−	0.274438i
$902$		0			0
$903$	0.794506	−	1.33364i	0.0264395	−	0.0443808i
$904$		0			0
$905$	22.4780	−	38.9330i	0.747193	−	1.29418i
$906$		0			0
$907$	21.5815	−	3.80540i	0.716602	−	0.126356i	0.196554	−	0.980493i	$-0.437025\pi$
$907$	21.5815	−	3.80540i	0.716602	−	0.126356i	0.520049	+	0.854137i	$0.325914\pi$
$908$		0			0
$909$	−1.02761	+	37.5368i	−0.0340838	+	1.24502i
$910$		0			0
$911$	41.3461			1.36986			0.684928	−	0.728610i	$-0.259833\pi$
$911$	41.3461			1.36986			0.684928	+	0.728610i	$0.259833\pi$
$912$		0			0
$913$	−5.46465			−0.180853
$914$		0			0
$915$	−22.5882	−	4.30242i	−0.746743	−	0.142234i
$916$		0			0
$917$	40.9558	−	7.22161i	1.35248	−	0.238479i
$918$		0			0
$919$	15.0651	−	26.0936i	0.496953	−	0.860748i	−0.503041	−	0.864263i	$-0.667786\pi$
$919$	15.0651	−	26.0936i	0.496953	−	0.860748i	0.999994	+	0.00351494i	$0.00111884\pi$
$920$		0			0
$921$	−15.1034	−	8.99773i	−0.497673	−	0.296485i
$922$		0			0
$923$	−15.1319	+	8.73639i	−0.498071	+	0.287562i
$924$		0			0
$925$	−0.122905	−	0.337677i	−0.00404108	−	0.0111028i
$926$		0			0
$927$	26.0179	−	3.85677i	0.854539	−	0.126673i
$928$		0			0
$929$	−3.69874	−	4.40799i	−0.121352	−	0.144621i	0.701948	−	0.712228i	$-0.252314\pi$
$929$	−3.69874	−	4.40799i	−0.121352	−	0.144621i	−0.823300	+	0.567607i	$0.807869\pi$
$930$		0			0
$931$	6.68190	−	0.659722i	0.218991	−	0.0216215i
$932$		0			0
$933$	−13.0422	+	15.1180i	−0.426983	+	0.494942i
$934$		0			0
$935$	37.5622	+	6.62323i	1.22842	+	0.216603i
$936$		0			0
$937$	−19.6146	+	7.13914i	−0.640782	+	0.233226i	−0.641917	−	0.766774i	$-0.721861\pi$
$937$	−19.6146	+	7.13914i	−0.640782	+	0.233226i	0.00113542	+	0.999999i	$0.499639\pi$
$938$		0			0
$939$	4.02275	−	3.28274i	0.131278	−	0.107128i
$940$		0			0
$941$	13.7670	+	11.5519i	0.448792	+	0.376581i	0.838987	−	0.544151i	$-0.183148\pi$
$941$	13.7670	+	11.5519i	0.448792	+	0.376581i	−0.390196	+	0.920732i	$0.627593\pi$
$942$		0			0
$943$	64.3213	+	37.1359i	2.09459	+	1.20931i
$944$		0			0
$945$	16.7807	+	21.7526i	0.545875	+	0.707612i
$946$		0			0
$947$	−3.35631	+	9.22139i	−0.109065	+	0.299655i	−0.982204	−	0.187817i	$-0.939859\pi$
$947$	−3.35631	+	9.22139i	−0.109065	+	0.299655i	0.873139	+	0.487472i	$0.162081\pi$
$948$		0			0
$949$		−	8.22225i		−	0.266906i
$950$		0			0
$951$	4.56110	+	28.1116i	0.147904	+	0.911581i
$952$		0			0
$953$	−9.56813	−	3.48251i	−0.309942	−	0.112810i	0.182366	−	0.983231i	$-0.441624\pi$
$953$	−9.56813	−	3.48251i	−0.309942	−	0.112810i	−0.492308	+	0.870421i	$0.663847\pi$
$954$		0			0
$955$	4.02146	+	22.8068i	0.130131	+	0.738012i
$956$		0			0
$957$	−3.84805	+	10.1385i	−0.124390	+	0.327733i
$958$		0			0
$959$	24.6680	−	29.3982i	0.796571	−	0.949316i
$960$		0			0
$961$	3.08051	+	5.33561i	0.0993714	+	0.172116i
$962$		0			0
$963$	19.0158	−	15.0889i	0.612774	−	0.486234i
$964$		0			0
$965$	−0.901436	+	5.11230i	−0.0290183	+	0.164571i
$966$		0			0
$967$	−34.6570	+	29.0807i	−1.11449	+	0.935171i	−0.998313	−	0.0580574i	$-0.981509\pi$
$967$	−34.6570	+	29.0807i	−1.11449	+	0.935171i	−0.116180	+	0.993228i	$0.537065\pi$
$968$		0			0
$969$	3.69876	+	43.5494i	0.118821	+	1.39901i
$970$		0			0
$971$	−11.6835	+	9.80361i	−0.374941	+	0.314613i	−0.810712	−	0.585444i	$-0.800920\pi$
$971$	−11.6835	+	9.80361i	−0.374941	+	0.314613i	0.435772	+	0.900057i	$0.356476\pi$
$972$		0			0
$973$	7.84462	−	44.4890i	0.251487	−	1.42625i
$974$		0			0
$975$	−0.240104	+	0.134277i	−0.00768949	+	0.00430031i
$976$		0			0
$977$	−29.3626	−	50.8576i	−0.939394	−	1.62708i	−0.766605	−	0.642119i	$-0.778055\pi$
$977$	−29.3626	−	50.8576i	−0.939394	−	1.62708i	−0.172789	−	0.984959i	$-0.555278\pi$
$978$		0			0
$979$	11.5977	−	13.8216i	0.370663	−	0.441739i
$980$		0			0
$981$	−21.6731	−	4.43629i	−0.691969	−	0.141640i
$982$		0			0
$983$	−6.80396	−	38.5872i	−0.217013	−	1.23074i	−0.877380	−	0.479797i	$-0.840710\pi$
$983$	−6.80396	−	38.5872i	−0.217013	−	1.23074i	0.660367	−	0.750943i	$-0.270401\pi$
$984$		0			0
$985$	13.4259	+	4.88664i	0.427786	+	0.155701i
$986$		0			0
$987$	40.8624	−	6.62991i	1.30066	−	0.211033i
$988$		0			0
$989$			3.14008i			0.0998486i
$990$		0			0
$991$	13.8647	−	38.0930i	0.440428	−	1.21007i	−0.498784	−	0.866726i	$-0.666220\pi$
$991$	13.8647	−	38.0930i	0.440428	−	1.21007i	0.939212	−	0.343339i	$-0.111558\pi$
$992$		0			0
$993$	0.995324	+	2.85562i	0.0315856	+	0.0906205i
$994$		0			0
$995$	20.3690	+	11.7601i	0.645742	+	0.372819i
$996$		0			0
$997$	46.7056	+	39.1907i	1.47918	+	1.24118i	0.907052	+	0.421019i	$0.138327\pi$
$997$	46.7056	+	39.1907i	1.47918	+	1.24118i	0.572131	+	0.820162i	$0.306117\pi$
$998$		0			0
$999$	13.1228	+	8.31264i	0.415187	+	0.263000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.cc.c.545.2		18
3.2	odd	2		912.2.cc.d.545.2		18
4.3	odd	2		114.2.l.b.89.2	yes	18
12.11	even	2		114.2.l.a.89.2	yes	18
19.3	odd	18		912.2.cc.d.497.2		18
57.41	even	18	inner	912.2.cc.c.497.2		18
76.3	even	18		114.2.l.a.41.2	✓	18
228.155	odd	18		114.2.l.b.41.2	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.41.2	✓	18	76.3	even	18
114.2.l.a.89.2	yes	18	12.11	even	2
114.2.l.b.41.2	yes	18	228.155	odd	18
114.2.l.b.89.2	yes	18	4.3	odd	2
912.2.cc.c.497.2		18	57.41	even	18	inner
912.2.cc.c.545.2		18	1.1	even	1	trivial
912.2.cc.d.497.2		18	19.3	odd	18
912.2.cc.d.545.2		18	3.2	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.cc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.324081 - 1.70146i) q^{3} +(2.22841 - 0.392929i) q^{5} +(1.16829 - 2.02354i) q^{7} +(-2.78994 - 1.10282i) q^{9} +O(q^{10})\)	\(q+(0.324081 - 1.70146i) q^{3} +(2.22841 - 0.392929i) q^{5} +(1.16829 - 2.02354i) q^{7} +(-2.78994 - 1.10282i) q^{9} +(-2.52163 + 1.45586i) q^{11} +(-0.451929 - 1.24167i) q^{13} +(0.0536321 - 3.91889i) q^{15} +(-3.72112 - 4.43466i) q^{17} +(1.79800 - 3.97079i) q^{19} +(-3.06435 - 2.64359i) q^{21} +(8.06194 + 1.42154i) q^{23} +(0.112953 - 0.0411116i) q^{25} +(-2.78058 + 4.38958i) q^{27} +(1.64718 + 1.38215i) q^{29} +(-5.27928 - 3.04799i) q^{31} +(1.65988 + 4.76227i) q^{33} +(1.80832 - 4.96833i) q^{35} -2.98954i q^{37} +(-2.25911 + 0.366540i) q^{39} +(8.52555 + 3.10304i) q^{41} +(0.0666074 + 0.377749i) q^{43} +(-6.65047 - 1.36129i) q^{45} +(-6.57494 + 7.83571i) q^{47} +(0.770194 + 1.33401i) q^{49} +(-8.75134 + 4.89415i) q^{51} +(-0.494197 + 2.80273i) q^{53} +(-5.04717 + 4.23508i) q^{55} +(-6.17345 - 4.34609i) q^{57} +(2.53779 - 2.12946i) q^{59} +(1.01879 - 5.77787i) q^{61} +(-5.49107 + 4.35714i) q^{63} +(-1.49497 - 2.58936i) q^{65} +(10.4361 - 12.4373i) q^{67} +(5.03141 - 13.2564i) q^{69} +(-2.29622 - 13.0225i) q^{71} +(5.84733 + 2.12826i) q^{73} +(-0.0333438 - 0.205509i) q^{75} +6.80348i q^{77} +(-1.77569 + 4.87866i) q^{79} +(6.56756 + 6.15363i) q^{81} +(1.62533 + 0.938386i) q^{83} +(-10.0347 - 8.42009i) q^{85} +(2.88550 - 2.35469i) q^{87} +(-5.82289 + 2.11936i) q^{89} +(-3.04054 - 0.536130i) q^{91} +(-6.89696 + 7.99469i) q^{93} +(2.44644 - 9.55504i) q^{95} +(6.13336 + 7.30946i) q^{97} +(8.64076 - 1.28086i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{3} - 3 q^{9}+O(q^{10}) \) 18 * q - 3 * q^3 - 3 * q^9	\( 18 q - 3 q^{3} - 3 q^{9} - 12 q^{13} - 18 q^{15} + 6 q^{17} + 6 q^{19} - 18 q^{25} + 6 q^{27} - 6 q^{29} - 24 q^{33} + 24 q^{35} - 6 q^{39} + 3 q^{41} + 6 q^{43} - 54 q^{45} - 30 q^{47} + 21 q^{49} - 42 q^{51} - 60 q^{53} - 30 q^{55} + 12 q^{57} - 3 q^{59} + 54 q^{61} + 18 q^{63} + 24 q^{65} + 15 q^{67} + 30 q^{69} - 36 q^{71} - 42 q^{73} + 6 q^{79} - 3 q^{81} - 36 q^{83} - 60 q^{89} + 18 q^{91} - 66 q^{93} - 6 q^{95} + 9 q^{97} + 102 q^{99}+O(q^{100}) \) 18 * q - 3 * q^3 - 3 * q^9 - 12 * q^13 - 18 * q^15 + 6 * q^17 + 6 * q^19 - 18 * q^25 + 6 * q^27 - 6 * q^29 - 24 * q^33 + 24 * q^35 - 6 * q^39 + 3 * q^41 + 6 * q^43 - 54 * q^45 - 30 * q^47 + 21 * q^49 - 42 * q^51 - 60 * q^53 - 30 * q^55 + 12 * q^57 - 3 * q^59 + 54 * q^61 + 18 * q^63 + 24 * q^65 + 15 * q^67 + 30 * q^69 - 36 * q^71 - 42 * q^73 + 6 * q^79 - 3 * q^81 - 36 * q^83 - 60 * q^89 + 18 * q^91 - 66 * q^93 - 6 * q^95 + 9 * q^97 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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