LMFDB - Embedded newform 840.2.bg.j.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [840,2,Mod(121,840)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(840, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))

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

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

chi := DirichletCharacter("840.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.bg (of order $3$, degree $2$, 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:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.29428272.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 6x^{4} - 4x^{3} - 42x^{2} + 343 $ x^6 - 6x^4 - 4x^3 - 42*x^2 + 343
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.3
Root			$2.63435 + 0.245357i$ of defining polynomial
Character	$\chi$	$=$	840.121
Dual form			840.2.bg.j.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.63435 - 0.245357i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.63435 - 0.245357i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.92497 + 3.33415i) q^{11} +0.209380 q^{13} -1.00000 q^{15} +(3.66401 + 6.34625i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-1.52966 - 2.15874i) q^{21} +(3.13435 - 5.42885i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +3.20938 q^{29} +(-5.23904 - 9.07428i) q^{31} +(1.92497 - 3.33415i) q^{33} +(1.10469 - 2.40409i) q^{35} +(-3.95463 + 6.84962i) q^{37} +(-0.104690 - 0.181328i) q^{39} +2.26870 q^{41} +2.84994 q^{43} +(0.500000 + 0.866025i) q^{45} +(2.73904 - 4.74416i) q^{47} +(6.87960 - 1.29271i) q^{49} +(3.66401 - 6.34625i) q^{51} +(4.52966 + 7.84560i) q^{53} +3.84994 q^{55} +1.00000 q^{57} +(-4.39531 - 7.61290i) q^{59} +(-1.10469 + 2.40409i) q^{63} +(0.104690 - 0.181328i) q^{65} +(-1.42497 - 2.46812i) q^{67} -6.26870 q^{69} +13.4467 q^{71} +(-5.63435 - 9.75898i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(5.88910 + 8.31100i) q^{77} +(-0.179720 + 0.311284i) q^{79} +(-0.500000 - 0.866025i) q^{81} +3.20938 q^{83} +7.32802 q^{85} +(-1.60469 - 2.77940i) q^{87} +(-3.45463 + 5.98359i) q^{89} +(0.551580 - 0.0513728i) q^{91} +(-5.23904 + 9.07428i) q^{93} +(0.500000 + 0.866025i) q^{95} +8.00000 q^{97} -3.84994 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} + 3 q^{5} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 + 3 * q^5 - 3 * q^9	$ 6 q - 3 q^{3} + 3 q^{5} - 3 q^{9} + 3 q^{11} - 6 q^{13} - 6 q^{15} - 6 q^{17} - 3 q^{19} + 3 q^{21} + 3 q^{23} - 3 q^{25} + 6 q^{27} + 12 q^{29} - 12 q^{31} + 3 q^{33} + 3 q^{35} - 3 q^{37} + 3 q^{39} - 18 q^{41} + 3 q^{45} - 3 q^{47} + 12 q^{49} - 6 q^{51} + 15 q^{53} + 6 q^{55} + 6 q^{57} - 30 q^{59} - 3 q^{63} - 3 q^{65} - 6 q^{69} - 24 q^{71} - 18 q^{73} - 3 q^{75} + 33 q^{77} - 6 q^{79} - 3 q^{81} + 12 q^{83} - 12 q^{85} - 6 q^{87} + 30 q^{91} - 12 q^{93} + 3 q^{95} + 48 q^{97} - 6 q^{99}+O(q^{100}) $ 6 * q - 3 * q^3 + 3 * q^5 - 3 * q^9 + 3 * q^11 - 6 * q^13 - 6 * q^15 - 6 * q^17 - 3 * q^19 + 3 * q^21 + 3 * q^23 - 3 * q^25 + 6 * q^27 + 12 * q^29 - 12 * q^31 + 3 * q^33 + 3 * q^35 - 3 * q^37 + 3 * q^39 - 18 * q^41 + 3 * q^45 - 3 * q^47 + 12 * q^49 - 6 * q^51 + 15 * q^53 + 6 * q^55 + 6 * q^57 - 30 * q^59 - 3 * q^63 - 3 * q^65 - 6 * q^69 - 24 * q^71 - 18 * q^73 - 3 * q^75 + 33 * q^77 - 6 * q^79 - 3 * q^81 + 12 * q^83 - 12 * q^85 - 6 * q^87 + 30 * q^91 - 12 * q^93 + 3 * q^95 + 48 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$	$1$

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
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	2.63435	−	0.245357i	0.995691	−	0.0927361i
$7$	2.63435	−	0.245357i	0.995691	−	0.0927361i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	1.92497	+	3.33415i	0.580400	+	1.00528i	0.995432	+	0.0954758i	$0.0304372\pi$
$11$	1.92497	+	3.33415i	0.580400	+	1.00528i	−0.415031	+	0.909807i	$0.636229\pi$
$12$		0			0
$13$	0.209380			0.0580715			0.0290358	−	0.999578i	$-0.490756\pi$
$13$	0.209380			0.0580715			0.0290358	+	0.999578i	$0.490756\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	3.66401	+	6.34625i	0.888653	+	1.53919i	0.841469	+	0.540306i	$0.181691\pi$
$17$	3.66401	+	6.34625i	0.888653	+	1.53919i	0.0471843	+	0.998886i	$0.484975\pi$
$18$		0			0
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$		0			0
$21$	−1.52966	−	2.15874i	−0.333799	−	0.471075i
$22$		0			0
$23$	3.13435	−	5.42885i	0.653557	−	1.13199i	−0.328696	−	0.944436i	$-0.606609\pi$
$23$	3.13435	−	5.42885i	0.653557	−	1.13199i	0.982253	−	0.187559i	$-0.0600574\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	3.20938			0.595967			0.297983	−	0.954571i	$-0.403686\pi$
$29$	3.20938			0.595967			0.297983	+	0.954571i	$0.403686\pi$
$30$		0			0
$31$	−5.23904	−	9.07428i	−0.940959	−	1.62979i	−0.763646	−	0.645635i	$-0.776593\pi$
$31$	−5.23904	−	9.07428i	−0.940959	−	1.62979i	−0.177313	−	0.984154i	$-0.556741\pi$
$32$		0			0
$33$	1.92497	−	3.33415i	0.335094	−	0.580400i
$34$		0			0
$35$	1.10469	−	2.40409i	0.186727	−	0.406366i
$36$		0			0
$37$	−3.95463	+	6.84962i	−0.650137	+	1.12607i	0.332952	+	0.942944i	$0.391955\pi$
$37$	−3.95463	+	6.84962i	−0.650137	+	1.12607i	−0.983089	+	0.183127i	$0.941378\pi$
$38$		0			0
$39$	−0.104690	−	0.181328i	−0.0167638	−	0.0290358i
$40$		0			0
$41$	2.26870			0.354311			0.177156	−	0.984183i	$-0.443310\pi$
$41$	2.26870			0.354311			0.177156	+	0.984183i	$0.443310\pi$
$42$		0			0
$43$	2.84994			0.434612			0.217306	−	0.976104i	$-0.430273\pi$
$43$	2.84994			0.434612			0.217306	+	0.976104i	$0.430273\pi$
$44$		0			0
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$		0			0
$47$	2.73904	−	4.74416i	0.399530	−	0.692006i	−0.594138	−	0.804363i	$-0.702507\pi$
$47$	2.73904	−	4.74416i	0.399530	−	0.692006i	0.993668	+	0.112357i	$0.0358400\pi$
$48$		0			0
$49$	6.87960	−	1.29271i	0.982800	−	0.184673i
$50$		0			0
$51$	3.66401	−	6.34625i	0.513064	−	0.888653i
$52$		0			0
$53$	4.52966	+	7.84560i	0.622197	+	1.07768i	0.989076	+	0.147408i	$0.0470929\pi$
$53$	4.52966	+	7.84560i	0.622197	+	1.07768i	−0.366879	+	0.930269i	$0.619574\pi$
$54$		0			0
$55$	3.84994			0.519126
$56$		0			0
$57$	1.00000			0.132453
$58$		0			0
$59$	−4.39531	−	7.61290i	−0.572221	−	0.991115i	−0.996338	−	0.0855077i	$-0.972749\pi$
$59$	−4.39531	−	7.61290i	−0.572221	−	0.991115i	0.424117	−	0.905607i	$-0.360585\pi$
$60$		0			0
$61$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$61$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$62$		0			0
$63$	−1.10469	+	2.40409i	−0.139178	+	0.302887i
$64$		0			0
$65$	0.104690	−	0.181328i	0.0129852	−	0.0224910i
$66$		0			0
$67$	−1.42497	−	2.46812i	−0.174088	−	0.301529i	0.765757	−	0.643130i	$-0.222364\pi$
$67$	−1.42497	−	2.46812i	−0.174088	−	0.301529i	−0.939845	+	0.341601i	$0.889031\pi$
$68$		0			0
$69$	−6.26870			−0.754663
$70$		0			0
$71$	13.4467			1.59583			0.797913	−	0.602773i	$-0.205938\pi$
$71$	13.4467			1.59583			0.797913	+	0.602773i	$0.205938\pi$
$72$		0			0
$73$	−5.63435	−	9.75898i	−0.659451	−	1.14220i	−0.980758	−	0.195227i	$-0.937456\pi$
$73$	−5.63435	−	9.75898i	−0.659451	−	1.14220i	0.321307	−	0.946975i	$-0.395878\pi$
$74$		0			0
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$		0			0
$77$	5.88910	+	8.31100i	0.671125	+	0.947127i
$78$		0			0
$79$	−0.179720	+	0.311284i	−0.0202201	+	0.0350222i	−0.875958	−	0.482387i	$-0.839770\pi$
$79$	−0.179720	+	0.311284i	−0.0202201	+	0.0350222i	0.855738	+	0.517409i	$0.173103\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	3.20938			0.352275			0.176138	−	0.984366i	$-0.443640\pi$
$83$	3.20938			0.352275			0.176138	+	0.984366i	$0.443640\pi$
$84$		0			0
$85$	7.32802			0.794835
$86$		0			0
$87$	−1.60469	−	2.77940i	−0.172041	−	0.297983i
$88$		0			0
$89$	−3.45463	+	5.98359i	−0.366190	+	0.634260i	−0.988966	−	0.148140i	$-0.952671\pi$
$89$	−3.45463	+	5.98359i	−0.366190	+	0.634260i	0.622776	+	0.782400i	$0.286005\pi$
$90$		0			0
$91$	0.551580	−	0.0513728i	0.0578213	−	0.00538533i
$92$		0			0
$93$	−5.23904	+	9.07428i	−0.543263	+	0.940959i
$94$		0			0
$95$	0.500000	+	0.866025i	0.0512989	+	0.0888523i
$96$		0			0
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$		0			0
$99$	−3.84994			−0.386934
$100$		0			0
$101$	−7.66401	−	13.2745i	−0.762598	−	1.32086i	−0.941507	−	0.336992i	$-0.890590\pi$
$101$	−7.66401	−	13.2745i	−0.762598	−	1.32086i	0.178910	−	0.983865i	$-0.442743\pi$
$102$		0			0
$103$	−2.21559	+	3.83751i	−0.218309	+	0.378122i	−0.954291	−	0.298879i	$-0.903387\pi$
$103$	−2.21559	+	3.83751i	−0.218309	+	0.378122i	0.735982	+	0.677001i	$0.236721\pi$
$104$		0			0
$105$	−2.63435	+	0.245357i	−0.257086	+	0.0239444i
$106$		0			0
$107$	−8.72333	+	15.1093i	−0.843316	+	1.46067i	0.0437593	+	0.999042i	$0.486067\pi$
$107$	−8.72333	+	15.1093i	−0.843316	+	1.46067i	−0.887076	+	0.461624i	$0.847267\pi$
$108$		0			0
$109$	−2.82028	−	4.88487i	−0.270134	−	0.467886i	0.698762	−	0.715354i	$-0.253735\pi$
$109$	−2.82028	−	4.88487i	−0.270134	−	0.467886i	−0.968896	+	0.247469i	$0.920401\pi$
$110$		0			0
$111$	7.90926			0.750714
$112$		0			0
$113$	−10.2373			−0.963042			−0.481521	−	0.876434i	$-0.659916\pi$
$113$	−10.2373			−0.963042			−0.481521	+	0.876434i	$0.659916\pi$
$114$		0			0
$115$	−3.13435	−	5.42885i	−0.292280	−	0.506243i
$116$		0			0
$117$	−0.104690	+	0.181328i	−0.00967859	+	0.0167638i
$118$		0			0
$119$	11.2094	+	15.8193i	1.02756	+	1.45015i
$120$		0			0
$121$	−1.91102	+	3.30998i	−0.173729	+	0.300908i
$122$		0			0
$123$	−1.13435	−	1.96475i	−0.102281	−	0.177156i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−20.4467			−1.81435			−0.907174	−	0.420756i	$-0.861765\pi$
$127$	−20.4467			−1.81435			−0.907174	+	0.420756i	$0.861765\pi$
$128$		0			0
$129$	−1.42497	−	2.46812i	−0.125462	−	0.217306i
$130$		0			0
$131$	1.52966	−	2.64945i	0.133647	−	0.231483i	−0.791433	−	0.611256i	$-0.790664\pi$
$131$	1.52966	−	2.64945i	0.133647	−	0.231483i	0.925080	+	0.379773i	$0.123998\pi$
$132$		0			0
$133$	−1.10469	+	2.40409i	−0.0957888	+	0.208461i
$134$		0			0
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$		0			0
$137$	5.02345	+	8.70087i	0.429182	+	0.743366i	0.996801	−	0.0799262i	$-0.0254685\pi$
$137$	5.02345	+	8.70087i	0.429182	+	0.743366i	−0.567619	+	0.823292i	$0.692135\pi$
$138$		0			0
$139$	−6.17796			−0.524008			−0.262004	−	0.965067i	$-0.584383\pi$
$139$	−6.17796			−0.524008			−0.262004	+	0.965067i	$0.584383\pi$
$140$		0			0
$141$	−5.47808			−0.461338
$142$		0			0
$143$	0.403050	+	0.698103i	0.0337047	+	0.0583783i
$144$		0			0
$145$	1.60469	−	2.77940i	0.133262	−	0.230817i
$146$		0			0
$147$	−4.55932	−	5.31155i	−0.376046	−	0.438090i
$148$		0			0
$149$	−6.41876	+	11.1176i	−0.525845	+	0.910791i	0.473701	+	0.880686i	$0.342918\pi$
$149$	−6.41876	+	11.1176i	−0.525845	+	0.910791i	−0.999547	+	0.0301053i	$0.990416\pi$
$150$		0			0
$151$	−11.1186	−	19.2580i	−0.904822	−	1.56720i	−0.821156	−	0.570704i	$-0.806670\pi$
$151$	−11.1186	−	19.2580i	−0.904822	−	1.56720i	−0.0836663	−	0.996494i	$-0.526663\pi$
$152$		0			0
$153$	−7.32802			−0.592435
$154$		0			0
$155$	−10.4781			−0.841620
$156$		0			0
$157$	9.00774	+	15.6019i	0.718896	+	1.24516i	0.961438	+	0.275023i	$0.0886856\pi$
$157$	9.00774	+	15.6019i	0.718896	+	1.24516i	−0.242542	+	0.970141i	$0.577981\pi$
$158$		0			0
$159$	4.52966	−	7.84560i	0.359225	−	0.622197i
$160$		0			0
$161$	6.92497	−	15.0705i	0.545764	−	1.18772i
$162$		0			0
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	−0.979076	−	0.203497i	$-0.934769\pi$
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	0.665771	+	0.746156i	$0.268103\pi$
$164$		0			0
$165$	−1.92497	−	3.33415i	−0.149859	−	0.259563i
$166$		0			0
$167$	15.9686			1.23569			0.617843	−	0.786302i	$-0.288007\pi$
$167$	15.9686			1.23569			0.617843	+	0.786302i	$0.288007\pi$
$168$		0			0
$169$	−12.9562			−0.996628
$170$		0			0
$171$	−0.500000	−	0.866025i	−0.0382360	−	0.0662266i
$172$		0			0
$173$	−8.00774	+	13.8698i	−0.608817	+	1.05450i	0.382618	+	0.923906i	$0.375022\pi$
$173$	−8.00774	+	13.8698i	−0.608817	+	1.05450i	−0.991436	+	0.130596i	$0.958311\pi$
$174$		0			0
$175$	−1.52966	−	2.15874i	−0.115631	−	0.163185i
$176$		0			0
$177$	−4.39531	+	7.61290i	−0.330372	+	0.572221i
$178$		0			0
$179$	9.79836	+	16.9713i	0.732364	+	1.26849i	0.955870	+	0.293789i	$0.0949163\pi$
$179$	9.79836	+	16.9713i	0.732364	+	1.26849i	−0.223507	+	0.974702i	$0.571750\pi$
$180$		0			0
$181$	−2.89684			−0.215320			−0.107660	−	0.994188i	$-0.534336\pi$
$181$	−2.89684			−0.215320			−0.107660	+	0.994188i	$0.534336\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.95463	+	6.84962i	0.290750	+	0.503594i
$186$		0			0
$187$	−14.1062	+	24.4327i	−1.03155	+	1.78670i
$188$		0			0
$189$	2.63435	−	0.245357i	0.191621	−	0.0178471i
$190$		0			0
$191$	5.41876	−	9.38557i	0.392088	−	0.679116i	−0.600637	−	0.799522i	$-0.705086\pi$
$191$	5.41876	−	9.38557i	0.392088	−	0.679116i	0.992725	+	0.120406i	$0.0384196\pi$
$192$		0			0
$193$	3.21559	+	5.56957i	0.231463	+	0.400906i	0.958239	−	0.285969i	$-0.0923154\pi$
$193$	3.21559	+	5.56957i	0.231463	+	0.400906i	−0.726776	+	0.686875i	$0.758982\pi$
$194$		0			0
$195$	−0.209380			−0.0149940
$196$		0			0
$197$	−5.43118			−0.386956			−0.193478	−	0.981105i	$-0.561977\pi$
$197$	−5.43118			−0.386956			−0.193478	+	0.981105i	$0.561977\pi$
$198$		0			0
$199$	4.47808	+	7.75626i	0.317443	+	0.549827i	0.979954	−	0.199225i	$-0.0638426\pi$
$199$	4.47808	+	7.75626i	0.317443	+	0.549827i	−0.662511	+	0.749052i	$0.730509\pi$
$200$		0			0
$201$	−1.42497	+	2.46812i	−0.100510	+	0.174088i
$202$		0			0
$203$	8.45463	−	0.787443i	0.593399	−	0.0552676i
$204$		0			0
$205$	1.13435	−	1.96475i	0.0792264	−	0.137224i
$206$		0			0
$207$	3.13435	+	5.42885i	0.217852	+	0.377331i
$208$		0			0
$209$	−3.84994			−0.266306
$210$		0			0
$211$	−15.5967			−1.07372			−0.536861	−	0.843671i	$-0.680390\pi$
$211$	−15.5967			−1.07372			−0.536861	+	0.843671i	$0.680390\pi$
$212$		0			0
$213$	−6.72333	−	11.6451i	−0.460675	−	0.797913i
$214$		0			0
$215$	1.42497	−	2.46812i	0.0971822	−	0.168324i
$216$		0			0
$217$	−16.0279	−	22.6194i	−1.08804	−	1.53551i
$218$		0			0
$219$	−5.63435	+	9.75898i	−0.380734	+	0.659451i
$220$		0			0
$221$	0.767170	+	1.32878i	0.0516055	+	0.0893833i
$222$		0			0
$223$	18.4188			1.23341			0.616706	−	0.787194i	$-0.288467\pi$
$223$	18.4188			1.23341			0.616706	+	0.787194i	$0.288467\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−9.72333	−	16.8413i	−0.645360	−	1.11780i	−0.984218	−	0.176959i	$-0.943374\pi$
$227$	−9.72333	−	16.8413i	−0.645360	−	1.11780i	0.338858	−	0.940837i	$-0.389959\pi$
$228$		0			0
$229$	11.2390	−	19.4666i	0.742697	−	1.28639i	−0.208567	−	0.978008i	$-0.566880\pi$
$229$	11.2390	−	19.4666i	0.742697	−	1.28639i	0.951263	−	0.308380i	$-0.0997869\pi$
$230$		0			0
$231$	4.25299	−	9.25561i	0.279826	−	0.608975i
$232$		0			0
$233$	−4.20938	+	7.29086i	−0.275766	+	0.477640i	−0.970328	−	0.241792i	$-0.922265\pi$
$233$	−4.20938	+	7.29086i	−0.275766	+	0.477640i	0.694562	+	0.719433i	$0.255598\pi$
$234$		0			0
$235$	−2.73904	−	4.74416i	−0.178675	−	0.309475i
$236$		0			0
$237$	0.359440			0.0233481
$238$		0			0
$239$	−5.16248			−0.333933			−0.166967	−	0.985963i	$-0.553397\pi$
$239$	−5.16248			−0.333933			−0.166967	+	0.985963i	$0.553397\pi$
$240$		0			0
$241$	−10.5297	−	18.2379i	−0.678275	−	1.17481i	−0.975500	−	0.219999i	$-0.929394\pi$
$241$	−10.5297	−	18.2379i	−0.678275	−	1.17481i	0.297225	−	0.954807i	$-0.403939\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	2.32028	−	6.60426i	0.148237	−	0.421931i
$246$		0			0
$247$	−0.104690	+	0.181328i	−0.00666126	+	0.0115376i
$248$		0			0
$249$	−1.60469	−	2.77940i	−0.101693	−	0.176138i
$250$		0			0
$251$	−15.6685			−0.988984			−0.494492	−	0.869182i	$-0.664646\pi$
$251$	−15.6685			−0.988984			−0.494492	+	0.869182i	$0.664646\pi$
$252$		0			0
$253$	24.1341			1.51730
$254$		0			0
$255$	−3.66401	−	6.34625i	−0.229449	−	0.397418i
$256$		0			0
$257$	−12.5140	+	21.6748i	−0.780599	+	1.35204i	0.150995	+	0.988535i	$0.451752\pi$
$257$	−12.5140	+	21.6748i	−0.780599	+	1.35204i	−0.931593	+	0.363502i	$0.881581\pi$
$258$		0			0
$259$	−8.73728	+	19.0146i	−0.542908	+	1.18151i
$260$		0			0
$261$	−1.60469	+	2.77940i	−0.0993278	+	0.172041i
$262$		0			0
$263$	3.20938	+	5.55881i	0.197899	+	0.342771i	0.947847	−	0.318726i	$-0.103255\pi$
$263$	3.20938	+	5.55881i	0.197899	+	0.342771i	−0.749948	+	0.661497i	$0.769922\pi$
$264$		0			0
$265$	9.05932			0.556510
$266$		0			0
$267$	6.90926			0.422840
$268$		0			0
$269$	−7.26870	−	12.5898i	−0.443180	−	0.767611i	0.554743	−	0.832022i	$-0.312817\pi$
$269$	−7.26870	−	12.5898i	−0.443180	−	0.767611i	−0.997923	+	0.0644107i	$0.979483\pi$
$270$		0			0
$271$	−5.94068	+	10.2896i	−0.360871	+	0.625046i	−0.988104	−	0.153785i	$-0.950854\pi$
$271$	−5.94068	+	10.2896i	−0.360871	+	0.625046i	0.627234	+	0.778831i	$0.284187\pi$
$272$		0			0
$273$	−0.320280	−	0.451996i	−0.0193842	−	0.0273560i
$274$		0			0
$275$	1.92497	−	3.33415i	0.116080	−	0.201057i
$276$		0			0
$277$	11.2749	+	19.5287i	0.677444	+	1.17337i	0.975748	+	0.218896i	$0.0702456\pi$
$277$	11.2749	+	19.5287i	0.677444	+	1.17337i	−0.298304	+	0.954471i	$0.596421\pi$
$278$		0			0
$279$	10.4781			0.627306
$280$		0			0
$281$	18.8778			1.12616			0.563079	−	0.826403i	$-0.309617\pi$
$281$	18.8778			1.12616			0.563079	+	0.826403i	$0.309617\pi$
$282$		0			0
$283$	−7.57503	−	13.1203i	−0.450289	−	0.779923i	0.548115	−	0.836403i	$-0.315346\pi$
$283$	−7.57503	−	13.1203i	−0.450289	−	0.779923i	−0.998404	+	0.0564800i	$0.982012\pi$
$284$		0			0
$285$	0.500000	−	0.866025i	0.0296174	−	0.0512989i
$286$		0			0
$287$	5.97655	−	0.556641i	0.352785	−	0.0328575i
$288$		0			0
$289$	−18.3499	+	31.7830i	−1.07941	+	1.86959i
$290$		0			0
$291$	−4.00000	−	6.92820i	−0.234484	−	0.406138i
$292$		0			0
$293$	−13.3594			−0.780467			−0.390233	−	0.920716i	$-0.627606\pi$
$293$	−13.3594			−0.780467			−0.390233	+	0.920716i	$0.627606\pi$
$294$		0			0
$295$	−8.79062			−0.511810
$296$		0			0
$297$	1.92497	+	3.33415i	0.111698	+	0.193467i
$298$		0			0
$299$	0.656270	−	1.13669i	0.0379531	−	0.0657367i
$300$		0			0
$301$	7.50774	−	0.699252i	0.432739	−	0.0403042i
$302$		0			0
$303$	−7.66401	+	13.2745i	−0.440286	+	0.762598i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−16.0434			−0.915644			−0.457822	−	0.889044i	$-0.651370\pi$
$307$	−16.0434			−0.915644			−0.457822	+	0.889044i	$0.651370\pi$
$308$		0			0
$309$	4.43118			0.252081
$310$		0			0
$311$	0.0358703	+	0.0621292i	0.00203402	+	0.00352302i	0.867041	−	0.498237i	$-0.166019\pi$
$311$	0.0358703	+	0.0621292i	0.00203402	+	0.00352302i	−0.865007	+	0.501760i	$0.832686\pi$
$312$		0			0
$313$	16.8123	−	29.1198i	0.950288	−	1.64595i	0.205488	−	0.978660i	$-0.434122\pi$
$313$	16.8123	−	29.1198i	0.950288	−	1.64595i	0.744800	−	0.667287i	$-0.232545\pi$
$314$		0			0
$315$	1.52966	+	2.15874i	0.0861866	+	0.121631i
$316$		0			0
$317$	6.60469	−	11.4397i	0.370956	−	0.642515i	−0.618757	−	0.785583i	$-0.712363\pi$
$317$	6.60469	−	11.4397i	0.370956	−	0.642515i	0.989713	+	0.143068i	$0.0456966\pi$
$318$		0			0
$319$	6.17796	+	10.7005i	0.345899	+	0.599115i
$320$		0			0
$321$	17.4467			0.973778
$322$		0			0
$323$	−7.32802			−0.407742
$324$		0			0
$325$	−0.104690	−	0.181328i	−0.00580715	−	0.0100583i
$326$		0			0
$327$	−2.82028	+	4.88487i	−0.155962	+	0.270134i
$328$		0			0
$329$	6.05158	−	13.1698i	0.333634	−	0.726075i
$330$		0			0
$331$	−11.1875	+	19.3772i	−0.614918	+	1.06507i	0.375480	+	0.926830i	$0.377478\pi$
$331$	−11.1875	+	19.3772i	−0.614918	+	1.06507i	−0.990399	+	0.138240i	$0.955856\pi$
$332$		0			0
$333$	−3.95463	−	6.84962i	−0.216712	−	0.375357i
$334$		0			0
$335$	−2.84994			−0.155709
$336$		0			0
$337$	3.92474			0.213794			0.106897	−	0.994270i	$-0.465908\pi$
$337$	3.92474			0.213794			0.106897	+	0.994270i	$0.465908\pi$
$338$		0			0
$339$	5.11864	+	8.86575i	0.278006	+	0.481521i
$340$		0			0
$341$	20.1700	−	34.9354i	1.09227	−	1.89186i
$342$		0			0
$343$	17.8061	−	5.09341i	0.961439	−	0.275018i
$344$		0			0
$345$	−3.13435	+	5.42885i	−0.168748	+	0.292280i
$346$		0			0
$347$	−9.17796	−	15.8967i	−0.492699	−	0.853379i	0.507266	−	0.861790i	$-0.330656\pi$
$347$	−9.17796	−	15.8967i	−0.492699	−	0.853379i	−0.999965	+	0.00841036i	$0.997323\pi$
$348$		0			0
$349$	12.9562			0.693527			0.346764	−	0.937953i	$-0.387281\pi$
$349$	12.9562			0.693527			0.346764	+	0.937953i	$0.387281\pi$
$350$		0			0
$351$	0.209380			0.0111759
$352$		0			0
$353$	−7.18593	−	12.4464i	−0.382468	−	0.662455i	0.608946	−	0.793212i	$-0.291593\pi$
$353$	−7.18593	−	12.4464i	−0.382468	−	0.662455i	−0.991414	+	0.130757i	$0.958259\pi$
$354$		0			0
$355$	6.72333	−	11.6451i	0.356837	−	0.618060i
$356$		0			0
$357$	8.09519	−	17.6172i	0.428443	−	0.932403i
$358$		0			0
$359$	10.0234	−	17.3611i	0.529017	−	0.916285i	−0.470410	−	0.882448i	$-0.655894\pi$
$359$	10.0234	−	17.3611i	0.529017	−	0.916285i	0.999427	−	0.0338371i	$-0.0107727\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$		0			0
$363$	3.82204			0.200605
$364$		0			0
$365$	−11.2687			−0.589831
$366$		0			0
$367$	1.77667	+	3.07728i	0.0927414	+	0.160633i	0.908664	−	0.417529i	$-0.137104\pi$
$367$	1.77667	+	3.07728i	0.0927414	+	0.160633i	−0.815922	+	0.578162i	$0.803770\pi$
$368$		0			0
$369$	−1.13435	+	1.96475i	−0.0590519	+	0.102281i
$370$		0			0
$371$	13.8577	+	19.5567i	0.719455	+	1.01533i
$372$		0			0
$373$	13.3218	−	23.0741i	0.689777	−	1.19473i	−0.282133	−	0.959375i	$-0.591042\pi$
$373$	13.3218	−	23.0741i	0.689777	−	1.19473i	0.971910	−	0.235354i	$-0.0756248\pi$
$374$		0			0
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$		0			0
$377$	0.671980			0.0346087
$378$		0			0
$379$	13.8375			0.710786			0.355393	−	0.934717i	$-0.384347\pi$
$379$	13.8375			0.710786			0.355393	+	0.934717i	$0.384347\pi$
$380$		0			0
$381$	10.2233	+	17.7073i	0.523757	+	0.907174i
$382$		0			0
$383$	−18.6483	+	32.2998i	−0.952884	+	1.65044i	−0.213745	+	0.976889i	$0.568566\pi$
$383$	−18.6483	+	32.2998i	−0.952884	+	1.65044i	−0.739139	+	0.673553i	$0.764767\pi$
$384$		0			0
$385$	10.1421	−	0.944608i	0.516889	−	0.0481417i
$386$		0			0
$387$	−1.42497	+	2.46812i	−0.0724353	+	0.125462i
$388$		0			0
$389$	−3.51395	−	6.08634i	−0.178164	−	0.308590i	0.763087	−	0.646295i	$-0.223683\pi$
$389$	−3.51395	−	6.08634i	−0.178164	−	0.308590i	−0.941252	+	0.337706i	$0.890349\pi$
$390$		0			0
$391$	45.9372			2.32314
$392$		0			0
$393$	−3.05932			−0.154322
$394$		0			0
$395$	0.179720	+	0.311284i	0.00904269	+	0.0156624i
$396$		0			0
$397$	0.725090	−	1.25589i	0.0363912	−	0.0630314i	−0.847256	−	0.531185i	$-0.821747\pi$
$397$	0.725090	−	1.25589i	0.0363912	−	0.0630314i	0.883647	+	0.468153i	$0.155080\pi$
$398$		0			0
$399$	2.63435	−	0.245357i	0.131882	−	0.0122832i
$400$		0			0
$401$	−0.110900	+	0.192085i	−0.00553809	+	0.00959226i	−0.868781	−	0.495196i	$-0.835096\pi$
$401$	−0.110900	+	0.192085i	−0.00553809	+	0.00959226i	0.863243	+	0.504788i	$0.168430\pi$
$402$		0			0
$403$	−1.09695	−	1.89997i	−0.0546430	−	0.0946444i
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−30.4502			−1.50936
$408$		0			0
$409$	−11.7171	−	20.2946i	−0.579374	−	1.00351i	−0.995551	−	0.0942221i	$-0.969964\pi$
$409$	−11.7171	−	20.2946i	−0.579374	−	1.00351i	0.416177	−	0.909284i	$-0.363370\pi$
$410$		0			0
$411$	5.02345	−	8.70087i	0.247789	−	0.429182i
$412$		0			0
$413$	−13.4467	−	18.9766i	−0.661667	−	0.933779i
$414$		0			0
$415$	1.60469	−	2.77940i	0.0787711	−	0.136436i
$416$		0			0
$417$	3.08898	+	5.35027i	0.151268	+	0.262004i
$418$		0			0
$419$	21.4152			1.04620			0.523101	−	0.852270i	$-0.324775\pi$
$419$	21.4152			1.04620			0.523101	+	0.852270i	$0.324775\pi$
$420$		0			0
$421$	−34.8340			−1.69771			−0.848853	−	0.528630i	$-0.822706\pi$
$421$	−34.8340			−1.69771			−0.848853	+	0.528630i	$0.822706\pi$
$422$		0			0
$423$	2.73904	+	4.74416i	0.133177	+	0.230669i
$424$		0			0
$425$	3.66401	−	6.34625i	0.177731	−	0.307838i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	0.403050	−	0.698103i	0.0194594	−	0.0337047i
$430$		0			0
$431$	5.26870	+	9.12566i	0.253784	+	0.439567i	0.964565	−	0.263847i	$-0.0849913\pi$
$431$	5.26870	+	9.12566i	0.253784	+	0.439567i	−0.710780	+	0.703414i	$0.751658\pi$
$432$		0			0
$433$	23.2059			1.11520			0.557601	−	0.830109i	$-0.311722\pi$
$433$	23.2059			1.11520			0.557601	+	0.830109i	$0.311722\pi$
$434$		0			0
$435$	−3.20938			−0.153878
$436$		0			0
$437$	3.13435	+	5.42885i	0.149936	+	0.259697i
$438$		0			0
$439$	−10.9686	+	18.9981i	−0.523502	+	0.906732i	0.476124	+	0.879378i	$0.342041\pi$
$439$	−10.9686	+	18.9981i	−0.523502	+	0.906732i	−0.999626	+	0.0273536i	$0.991292\pi$
$440$		0			0
$441$	−2.32028	+	6.60426i	−0.110490	+	0.314489i
$442$		0			0
$443$	−3.20938	+	5.55881i	−0.152482	+	0.264107i	−0.932139	−	0.362100i	$-0.882060\pi$
$443$	−3.20938	+	5.55881i	−0.152482	+	0.264107i	0.779657	+	0.626207i	$0.215393\pi$
$444$		0			0
$445$	3.45463	+	5.98359i	0.163765	+	0.283650i
$446$		0			0
$447$	12.8375			0.607194
$448$		0			0
$449$	10.7592			0.507758			0.253879	−	0.967236i	$-0.418293\pi$
$449$	10.7592			0.507758			0.253879	+	0.967236i	$0.418293\pi$
$450$		0			0
$451$	4.36718	+	7.56418i	0.205642	+	0.356183i
$452$		0			0
$453$	−11.1186	+	19.2580i	−0.522399	+	0.904822i
$454$		0			0
$455$	0.231300	−	0.503369i	0.0108435	−	0.0235983i
$456$		0			0
$457$	0.796830	−	1.38015i	0.0372741	−	0.0645607i	−0.846787	−	0.531933i	$-0.821466\pi$
$457$	0.796830	−	1.38015i	0.0372741	−	0.0645607i	0.884061	+	0.467372i	$0.154799\pi$
$458$		0			0
$459$	3.66401	+	6.34625i	0.171021	+	0.296218i
$460$		0			0
$461$	−31.2094			−1.45357			−0.726783	−	0.686867i	$-0.758985\pi$
$461$	−31.2094			−1.45357			−0.726783	+	0.686867i	$0.758985\pi$
$462$		0			0
$463$	40.9841			1.90469			0.952345	−	0.305022i	$-0.0986637\pi$
$463$	40.9841			1.90469			0.952345	+	0.305022i	$0.0986637\pi$
$464$		0			0
$465$	5.23904	+	9.07428i	0.242955	+	0.420810i
$466$		0			0
$467$	−11.6406	+	20.1620i	−0.538661	+	0.932988i	0.460316	+	0.887755i	$0.347736\pi$
$467$	−11.6406	+	20.1620i	−0.538661	+	0.932988i	−0.998976	+	0.0452327i	$0.985597\pi$
$468$		0			0
$469$	−4.35944	−	6.15227i	−0.201300	−	0.284085i
$470$		0			0
$471$	9.00774	−	15.6019i	0.415055	−	0.718896i
$472$		0			0
$473$	5.48605	+	9.50212i	0.252249	+	0.436908i
$474$		0			0
$475$	1.00000			0.0458831
$476$		0			0
$477$	−9.05932			−0.414798
$478$		0			0
$479$	−4.94068	−	8.55751i	−0.225745	−	0.391003i	0.730797	−	0.682594i	$-0.239148\pi$
$479$	−4.94068	−	8.55751i	−0.225745	−	0.391003i	−0.956543	+	0.291592i	$0.905815\pi$
$480$		0			0
$481$	−0.828020	+	1.43417i	−0.0377545	+	0.0653927i
$482$		0			0
$483$	−16.5140	+	1.53807i	−0.751411	+	0.0699845i
$484$		0			0
$485$	4.00000	−	6.92820i	0.181631	−	0.314594i
$486$		0			0
$487$	−4.51571	−	7.82144i	−0.204626	−	0.354423i	0.745387	−	0.666632i	$-0.232265\pi$
$487$	−4.51571	−	7.82144i	−0.204626	−	0.354423i	−0.950014	+	0.312208i	$0.898931\pi$
$488$		0			0
$489$	8.00000			0.361773
$490$		0			0
$491$	−13.8185			−0.623621			−0.311811	−	0.950144i	$-0.600935\pi$
$491$	−13.8185			−0.623621			−0.311811	+	0.950144i	$0.600935\pi$
$492$		0			0
$493$	11.7592	+	20.3675i	0.529608	+	0.917308i
$494$		0			0
$495$	−1.92497	+	3.33415i	−0.0865210	+	0.149859i
$496$		0			0
$497$	35.4232	−	3.29923i	1.58895	−	0.147991i
$498$		0			0
$499$	−3.46084	+	5.99435i	−0.154928	+	0.268344i	−0.933033	−	0.359791i	$-0.882848\pi$
$499$	−3.46084	+	5.99435i	−0.154928	+	0.268344i	0.778104	+	0.628135i	$0.216181\pi$
$500$		0			0
$501$	−7.98429	−	13.8292i	−0.356712	−	0.617843i
$502$		0			0
$503$	9.46260			0.421916			0.210958	−	0.977495i	$-0.432342\pi$
$503$	9.46260			0.421916			0.210958	+	0.977495i	$0.432342\pi$
$504$		0			0
$505$	−15.3280			−0.682088
$506$		0			0
$507$	6.47808	+	11.2204i	0.287702	+	0.498314i
$508$		0			0
$509$	5.79062	−	10.0296i	0.256665	−	0.444556i	−0.708682	−	0.705528i	$-0.750710\pi$
$509$	5.79062	−	10.0296i	0.256665	−	0.444556i	0.965346	+	0.260972i	$0.0840431\pi$
$510$		0			0
$511$	−17.2373	−	24.3261i	−0.762532	−	1.07613i
$512$		0			0
$513$	−0.500000	+	0.866025i	−0.0220755	+	0.0382360i
$514$		0			0
$515$	2.21559	+	3.83751i	0.0976306	+	0.169101i
$516$		0			0
$517$	21.0903			0.927549
$518$		0			0
$519$	16.0155			0.703002
$520$		0			0
$521$	−14.9484	−	25.8914i	−0.654902	−	1.13432i	−0.981918	−	0.189305i	$-0.939376\pi$
$521$	−14.9484	−	25.8914i	−0.654902	−	1.13432i	0.327016	−	0.945019i	$-0.393957\pi$
$522$		0			0
$523$	−1.94689	+	3.37211i	−0.0851316	+	0.147452i	−0.905447	−	0.424459i	$-0.860464\pi$
$523$	−1.94689	+	3.37211i	−0.0851316	+	0.147452i	0.820316	+	0.571911i	$0.193798\pi$
$524$		0			0
$525$	−1.10469	+	2.40409i	−0.0482126	+	0.104923i
$526$		0			0
$527$	38.3918	−	66.4965i	1.67237	−	2.89663i
$528$		0			0
$529$	−8.14830	−	14.1133i	−0.354274	−	0.613620i
$530$		0			0
$531$	8.79062			0.381480
$532$		0			0
$533$	0.475020			0.0205754
$534$		0			0
$535$	8.72333	+	15.1093i	0.377142	+	0.653230i
$536$		0			0
$537$	9.79836	−	16.9713i	0.422830	−	0.732364i
$538$		0			0
$539$	17.5531	+	20.4492i	0.756066	+	0.880808i
$540$		0			0
$541$	0.820280	−	1.42077i	0.0352666	−	0.0610835i	−0.847853	−	0.530231i	$-0.822105\pi$
$541$	0.820280	−	1.42077i	0.0352666	−	0.0610835i	0.883120	+	0.469147i	$0.155439\pi$
$542$		0			0
$543$	1.44842	+	2.50874i	0.0621576	+	0.107660i
$544$		0			0
$545$	−5.64056			−0.241615
$546$		0			0
$547$	−17.8185			−0.761865			−0.380932	−	0.924603i	$-0.624397\pi$
$547$	−17.8185			−0.761865			−0.380932	+	0.924603i	$0.624397\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.60469	+	2.77940i	−0.0683621	+	0.118407i
$552$		0			0
$553$	−0.397069	+	0.864126i	−0.0168851	+	0.0367464i
$554$		0			0
$555$	3.95463	−	6.84962i	0.167865	−	0.290750i
$556$		0			0
$557$	18.8577	+	32.6625i	0.799026	+	1.38395i	0.920251	+	0.391328i	$0.127984\pi$
$557$	18.8577	+	32.6625i	0.799026	+	1.38395i	−0.121226	+	0.992625i	$0.538682\pi$
$558$		0			0
$559$	0.596720			0.0252386
$560$		0			0
$561$	28.2124			1.19113
$562$		0			0
$563$	−17.9562	−	31.1010i	−0.756762	−	1.31075i	−0.944494	−	0.328530i	$-0.893447\pi$
$563$	−17.9562	−	31.1010i	−0.756762	−	1.31075i	0.187732	−	0.982220i	$-0.439886\pi$
$564$		0			0
$565$	−5.11864	+	8.86575i	−0.215343	+	0.372985i
$566$		0			0
$567$	−1.52966	−	2.15874i	−0.0642397	−	0.0906584i
$568$		0			0
$569$	−8.86565	+	15.3558i	−0.371667	+	0.643747i	−0.989822	−	0.142310i	$-0.954547\pi$
$569$	−8.86565	+	15.3558i	−0.371667	+	0.643747i	0.618155	+	0.786056i	$0.287880\pi$
$570$		0			0
$571$	−3.82028	−	6.61692i	−0.159874	−	0.276909i	0.774949	−	0.632023i	$-0.217775\pi$
$571$	−3.82028	−	6.61692i	−0.159874	−	0.276909i	−0.934823	+	0.355114i	$0.884442\pi$
$572$		0			0
$573$	−10.8375			−0.452744
$574$		0			0
$575$	−6.26870			−0.261423
$576$		0			0
$577$	−1.75299	−	3.03627i	−0.0729779	−	0.126402i	0.827227	−	0.561868i	$-0.189917\pi$
$577$	−1.75299	−	3.03627i	−0.0729779	−	0.126402i	−0.900205	+	0.435466i	$0.856584\pi$
$578$		0			0
$579$	3.21559	−	5.56957i	0.133635	−	0.231463i
$580$		0			0
$581$	8.45463	−	0.787443i	0.350757	−	0.0326686i
$582$		0			0
$583$	−17.4389	+	30.2051i	−0.722246	+	1.25097i
$584$		0			0
$585$	0.104690	+	0.181328i	0.00432840	+	0.00749700i
$586$		0			0
$587$	6.19038			0.255504			0.127752	−	0.991806i	$-0.459224\pi$
$587$	6.19038			0.255504			0.127752	+	0.991806i	$0.459224\pi$
$588$		0			0
$589$	10.4781			0.431742
$590$		0			0
$591$	2.71559	+	4.70354i	0.111704	+	0.193478i
$592$		0			0
$593$	1.72333	−	2.98490i	0.0707687	−	0.122575i	−0.828470	−	0.560034i	$-0.810788\pi$
$593$	1.72333	−	2.98490i	0.0707687	−	0.122575i	0.899238	+	0.437459i	$0.144121\pi$
$594$		0			0
$595$	19.3046	−	1.79798i	0.791410	−	0.0737099i
$596$		0			0
$597$	4.47808	−	7.75626i	0.183276	−	0.317443i
$598$		0			0
$599$	−16.8061	−	29.1090i	−0.686679	−	1.18936i	−0.972906	−	0.231201i	$-0.925735\pi$
$599$	−16.8061	−	29.1090i	−0.686679	−	1.18936i	0.286227	−	0.958162i	$-0.407599\pi$
$600$		0			0
$601$	−22.9526			−0.936258			−0.468129	−	0.883660i	$-0.655072\pi$
$601$	−22.9526			−0.936258			−0.468129	+	0.883660i	$0.655072\pi$
$602$		0			0
$603$	2.84994			0.116059
$604$		0			0
$605$	1.91102	+	3.30998i	0.0776940	+	0.134570i
$606$		0			0
$607$	9.49203	−	16.4407i	0.385270	−	0.667307i	−0.606537	−	0.795055i	$-0.707442\pi$
$607$	9.49203	−	16.4407i	0.385270	−	0.667307i	0.991807	+	0.127749i	$0.0407751\pi$
$608$		0			0
$609$	−4.90926	−	6.92820i	−0.198933	−	0.280745i
$610$		0			0
$611$	0.573500	−	0.993331i	0.0232013	−	0.0401859i
$612$		0			0
$613$	6.79836	+	11.7751i	0.274583	+	0.475592i	0.970030	−	0.242986i	$-0.0781268\pi$
$613$	6.79836	+	11.7751i	0.274583	+	0.475592i	−0.695447	+	0.718578i	$0.744793\pi$
$614$		0			0
$615$	−2.26870			−0.0914828
$616$		0			0
$617$	−33.6999			−1.35671			−0.678353	−	0.734736i	$-0.737306\pi$
$617$	−33.6999			−1.35671			−0.678353	+	0.734736i	$0.737306\pi$
$618$		0			0
$619$	−7.82802	−	13.5585i	−0.314635	−	0.544963i	0.664725	−	0.747088i	$-0.268549\pi$
$619$	−7.82802	−	13.5585i	−0.314635	−	0.544963i	−0.979360	+	0.202125i	$0.935215\pi$
$620$		0			0
$621$	3.13435	−	5.42885i	0.125777	−	0.217852i
$622$		0			0
$623$	−7.63259	+	16.6105i	−0.305793	+	0.665486i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	1.92497	+	3.33415i	0.0768759	+	0.133153i
$628$		0			0
$629$	−57.9592			−2.31099
$630$		0			0
$631$	5.28112			0.210238			0.105119	−	0.994460i	$-0.466478\pi$
$631$	5.28112			0.210238			0.105119	+	0.994460i	$0.466478\pi$
$632$		0			0
$633$	7.79836	+	13.5072i	0.309957	+	0.536861i
$634$		0			0
$635$	−10.2233	+	17.7073i	−0.405700	+	0.702694i
$636$		0			0
$637$	1.44045	−	0.270668i	0.0570727	−	0.0107242i
$638$		0			0
$639$	−6.72333	+	11.6451i	−0.265971	+	0.460675i
$640$		0			0
$641$	8.13435	+	14.0891i	0.321288	+	0.556486i	0.980754	−	0.195248i	$-0.0625511\pi$
$641$	8.13435	+	14.0891i	0.321288	+	0.556486i	−0.659466	+	0.751734i	$0.729218\pi$
$642$		0			0
$643$	39.7433			1.56732			0.783661	−	0.621189i	$-0.213350\pi$
$643$	39.7433			1.56732			0.783661	+	0.621189i	$0.213350\pi$
$644$		0			0
$645$	−2.84994			−0.112216
$646$		0			0
$647$	−2.13435	−	3.69680i	−0.0839100	−	0.145336i	0.821016	−	0.570905i	$-0.193407\pi$
$647$	−2.13435	−	3.69680i	−0.0839100	−	0.145336i	−0.904926	+	0.425569i	$0.860074\pi$
$648$		0			0
$649$	16.9217	−	29.3092i	0.664234	−	1.15049i
$650$		0			0
$651$	−11.5750	+	25.1903i	−0.453661	+	0.987285i
$652$		0			0
$653$	23.9843	−	41.5420i	0.938578	−	1.62566i	0.170452	−	0.985366i	$-0.445477\pi$
$653$	23.9843	−	41.5420i	0.938578	−	1.62566i	0.768126	−	0.640298i	$-0.221189\pi$
$654$		0			0
$655$	−1.52966	−	2.64945i	−0.0597688	−	0.103523i
$656$		0			0
$657$	11.2687			0.439634
$658$		0			0
$659$	−5.67504			−0.221068			−0.110534	−	0.993872i	$-0.535256\pi$
$659$	−5.67504			−0.221068			−0.110534	+	0.993872i	$0.535256\pi$
$660$		0			0
$661$	−0.610900	−	1.05811i	−0.0237613	−	0.0411557i	0.853900	−	0.520437i	$-0.174231\pi$
$661$	−0.610900	−	1.05811i	−0.0237613	−	0.0411557i	−0.877662	+	0.479281i	$0.840897\pi$
$662$		0			0
$663$	0.767170	−	1.32878i	0.0297944	−	0.0516055i
$664$		0			0
$665$	1.52966	+	2.15874i	0.0593177	+	0.0837122i
$666$		0			0
$667$	10.0593	−	17.4233i	0.389498	−	0.674631i
$668$		0			0
$669$	−9.20938	−	15.9511i	−0.356055	−	0.616706i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−15.0872			−0.581570			−0.290785	−	0.956788i	$-0.593916\pi$
$673$	−15.0872			−0.581570			−0.290785	+	0.956788i	$0.593916\pi$
$674$		0			0
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$		0			0
$677$	−7.28441	+	12.6170i	−0.279963	+	0.484909i	−0.971375	−	0.237551i	$-0.923655\pi$
$677$	−7.28441	+	12.6170i	−0.279963	+	0.484909i	0.691413	+	0.722460i	$0.256989\pi$
$678$		0			0
$679$	21.0748	−	1.96285i	0.808777	−	0.0753274i
$680$		0			0
$681$	−9.72333	+	16.8413i	−0.372599	+	0.645360i
$682$		0			0
$683$	−16.9920	−	29.4311i	−0.650182	−	1.12615i	−0.983078	−	0.183185i	$-0.941359\pi$
$683$	−16.9920	−	29.4311i	−0.650182	−	1.12615i	0.332897	−	0.942963i	$-0.391974\pi$
$684$		0			0
$685$	10.0469			0.383872
$686$		0			0
$687$	−22.4781			−0.857592
$688$		0			0
$689$	0.948420	+	1.64271i	0.0361319	+	0.0625823i
$690$		0			0
$691$	−23.6857	+	41.0248i	−0.901047	+	1.56066i	−0.0749086	+	0.997190i	$0.523866\pi$
$691$	−23.6857	+	41.0248i	−0.901047	+	1.56066i	−0.826138	+	0.563468i	$0.809467\pi$
$692$		0			0
$693$	−10.1421	+	0.944608i	−0.385266	+	0.0358827i
$694$		0			0
$695$	−3.08898	+	5.35027i	−0.117172	+	0.202947i
$696$		0			0
$697$	8.31254	+	14.3977i	0.314860	+	0.545353i
$698$		0			0
$699$	8.41876			0.318427
$700$		0			0
$701$	14.9093			0.563115			0.281557	−	0.959544i	$-0.409149\pi$
$701$	14.9093			0.563115			0.281557	+	0.959544i	$0.409149\pi$
$702$		0			0
$703$	−3.95463	−	6.84962i	−0.149152	−	0.258338i
$704$		0			0
$705$	−2.73904	+	4.74416i	−0.103158	+	0.178675i
$706$		0			0
$707$	−23.4467	−	33.0891i	−0.881802	−	1.24445i
$708$		0			0
$709$	−16.5374	+	28.6436i	−0.621075	+	1.07573i	0.368211	+	0.929742i	$0.379970\pi$
$709$	−16.5374	+	28.6436i	−0.621075	+	1.07573i	−0.989286	+	0.145991i	$0.953363\pi$
$710$		0			0
$711$	−0.179720	−	0.311284i	−0.00674002	−	0.0116741i
$712$		0			0
$713$	−65.6839			−2.45988
$714$		0			0
$715$	0.806100			0.0301464
$716$		0			0
$717$	2.58124	+	4.47084i	0.0963982	+	0.166967i
$718$		0			0
$719$	10.4467	−	18.0941i	0.389595	−	0.674798i	−0.602800	−	0.797892i	$-0.705948\pi$
$719$	10.4467	−	18.0941i	0.389595	−	0.674798i	0.992395	+	0.123094i	$0.0392818\pi$
$720$		0			0
$721$	−4.89508	+	10.6530i	−0.182302	+	0.396737i
$722$		0			0
$723$	−10.5297	+	18.2379i	−0.391602	+	0.678275i
$724$		0			0
$725$	−1.60469	−	2.77940i	−0.0595967	−	0.103224i
$726$		0			0
$727$	−40.9212			−1.51768			−0.758842	−	0.651275i	$-0.774235\pi$
$727$	−40.9212			−1.51768			−0.758842	+	0.651275i	$0.774235\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	10.4422	+	18.0864i	0.386219	+	0.668951i
$732$		0			0
$733$	10.4641	−	18.1244i	0.386501	−	0.669440i	−0.605475	−	0.795864i	$-0.707017\pi$
$733$	10.4641	−	18.1244i	0.386501	−	0.669440i	0.991976	+	0.126424i	$0.0403501\pi$
$734$		0			0
$735$	−6.87960	+	1.29271i	−0.253758	+	0.0476823i
$736$		0			0
$737$	5.48605	−	9.50212i	0.202081	−	0.350015i
$738$		0			0
$739$	−17.4093	−	30.1537i	−0.640410	−	1.10922i	−0.985341	−	0.170595i	$-0.945431\pi$
$739$	−17.4093	−	30.1537i	−0.640410	−	1.10922i	0.344931	−	0.938628i	$-0.387902\pi$
$740$		0			0
$741$	0.209380			0.00769176
$742$		0			0
$743$	−25.2497			−0.926322			−0.463161	−	0.886274i	$-0.653285\pi$
$743$	−25.2497			−0.926322			−0.463161	+	0.886274i	$0.653285\pi$
$744$		0			0
$745$	6.41876	+	11.1176i	0.235165	+	0.407318i
$746$		0			0
$747$	−1.60469	+	2.77940i	−0.0587125	+	0.101693i
$748$		0			0
$749$	−19.2732	+	41.9434i	−0.704226	+	1.53258i
$750$		0			0
$751$	−21.7295	+	37.6367i	−0.792922	+	1.37338i	0.131228	+	0.991352i	$0.458108\pi$
$751$	−21.7295	+	37.6367i	−0.792922	+	1.37338i	−0.924150	+	0.382029i	$0.875225\pi$
$752$		0			0
$753$	7.83423	+	13.5693i	0.285495	+	0.494492i
$754$		0			0
$755$	−22.2373			−0.809298
$756$		0			0
$757$	5.16248			0.187634			0.0938168	−	0.995589i	$-0.470093\pi$
$757$	5.16248			0.187634			0.0938168	+	0.995589i	$0.470093\pi$
$758$		0			0
$759$	−12.0671	−	20.9008i	−0.438007	−	0.758650i
$760$		0			0
$761$	−19.5810	+	33.9153i	−0.709811	+	1.22943i	0.255116	+	0.966910i	$0.417886\pi$
$761$	−19.5810	+	33.9153i	−0.709811	+	1.22943i	−0.964927	+	0.262518i	$0.915447\pi$
$762$		0			0
$763$	−8.62814	−	12.1765i	−0.312360	−	0.440818i
$764$		0			0
$765$	−3.66401	+	6.34625i	−0.132473	+	0.229449i
$766$		0			0
$767$	−0.920290	−	1.59399i	−0.0332297	−	0.0575556i
$768$		0			0
$769$	−28.6122			−1.03178			−0.515891	−	0.856654i	$-0.672539\pi$
$769$	−28.6122			−1.03178			−0.515891	+	0.856654i	$0.672539\pi$
$770$		0			0
$771$	25.0279			0.901358
$772$		0			0
$773$	−9.68417	−	16.7735i	−0.348315	−	0.603300i	0.637635	−	0.770339i	$-0.279913\pi$
$773$	−9.68417	−	16.7735i	−0.348315	−	0.603300i	−0.985950	+	0.167039i	$0.946580\pi$
$774$		0			0
$775$	−5.23904	+	9.07428i	−0.188192	+	0.325958i
$776$		0			0
$777$	20.8358	−	1.94059i	0.747479	−	0.0696183i
$778$		0			0
$779$	−1.13435	+	1.96475i	−0.0406423	+	0.0703945i
$780$		0			0
$781$	25.8844	+	44.8331i	0.926217	+	1.60426i
$782$		0			0
$783$	3.20938			0.114694
$784$		0			0
$785$	18.0155			0.643000
$786$		0			0
$787$	23.9686	+	41.5148i	0.854388	+	1.47984i	0.877212	+	0.480103i	$0.159401\pi$
$787$	23.9686	+	41.5148i	0.854388	+	1.47984i	−0.0228243	+	0.999739i	$0.507266\pi$
$788$		0			0
$789$	3.20938	−	5.55881i	0.114257	−	0.197899i
$790$		0			0
$791$	−26.9686	+	2.51178i	−0.958892	+	0.0893088i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−4.52966	−	7.84560i	−0.160650	−	0.278255i
$796$		0			0
$797$	−3.53434			−0.125193			−0.0625964	−	0.998039i	$-0.519938\pi$
$797$	−3.53434			−0.125193			−0.0625964	+	0.998039i	$0.519938\pi$
$798$		0			0
$799$	40.1435			1.42017
$800$		0			0
$801$	−3.45463	−	5.98359i	−0.122063	−	0.211420i
$802$		0			0
$803$	21.6919	−	37.5715i	0.765491	−	1.32587i
$804$		0			0
$805$	−9.58898	−	13.5325i	−0.337967	−	0.476957i
$806$		0			0
$807$	−7.26870	+	12.5898i	−0.255870	+	0.443180i
$808$		0			0
$809$	−7.15780	−	12.3977i	−0.251655	−	0.435879i	0.712327	−	0.701848i	$-0.247641\pi$
$809$	−7.15780	−	12.3977i	−0.251655	−	0.435879i	−0.963982	+	0.265969i	$0.914308\pi$
$810$		0			0
$811$	−24.5777			−0.863041			−0.431520	−	0.902103i	$-0.642023\pi$
$811$	−24.5777			−0.863041			−0.431520	+	0.902103i	$0.642023\pi$
$812$		0			0
$813$	11.8814			0.416697
$814$		0			0
$815$	4.00000	+	6.92820i	0.140114	+	0.242684i
$816$		0			0
$817$	−1.42497	+	2.46812i	−0.0498534	+	0.0863486i
$818$		0			0
$819$	−0.231300	+	0.503369i	−0.00808227	+	0.0175891i
$820$		0			0
$821$	12.6047	−	21.8320i	0.439907	−	0.761941i	−0.557775	−	0.829992i	$-0.688345\pi$
$821$	12.6047	−	21.8320i	0.439907	−	0.761941i	0.997682	+	0.0680513i	$0.0216782\pi$
$822$		0			0
$823$	−9.15006	−	15.8484i	−0.318951	−	0.552439i	0.661318	−	0.750105i	$-0.269997\pi$
$823$	−9.15006	−	15.8484i	−0.318951	−	0.552439i	−0.980269	+	0.197666i	$0.936664\pi$
$824$		0			0
$825$	−3.84994			−0.134038
$826$		0			0
$827$	−8.41876			−0.292749			−0.146374	−	0.989229i	$-0.546760\pi$
$827$	−8.41876			−0.292749			−0.146374	+	0.989229i	$0.546760\pi$
$828$		0			0
$829$	23.2669	+	40.2995i	0.808094	+	1.39966i	0.914182	+	0.405304i	$0.132834\pi$
$829$	23.2669	+	40.2995i	0.808094	+	1.39966i	−0.106088	+	0.994357i	$0.533832\pi$
$830$		0			0
$831$	11.2749	−	19.5287i	0.391122	−	0.677444i
$832$		0			0
$833$	33.4108	+	38.9232i	1.15762	+	1.34861i
$834$		0			0
$835$	7.98429	−	13.8292i	0.276308	−	0.478579i
$836$		0			0
$837$	−5.23904	−	9.07428i	−0.181088	−	0.313653i
$838$		0			0
$839$	−22.6091			−0.780554			−0.390277	−	0.920697i	$-0.627621\pi$
$839$	−22.6091			−0.780554			−0.390277	+	0.920697i	$0.627621\pi$
$840$		0			0
$841$	−18.6999			−0.644823
$842$		0			0
$843$	−9.43892	−	16.3487i	−0.325094	−	0.563079i
$844$		0			0
$845$	−6.47808	+	11.2204i	−0.222853	+	0.385992i
$846$		0			0
$847$	−4.22217	+	9.18854i	−0.145075	+	0.315722i
$848$		0			0
$849$	−7.57503	+	13.1203i	−0.259974	+	0.450289i
$850$		0			0
$851$	24.7904	+	42.9382i	0.849804	+	1.47190i
$852$		0			0
$853$	−55.7278			−1.90808			−0.954041	−	0.299675i	$-0.903122\pi$
$853$	−55.7278			−1.90808			−0.954041	+	0.299675i	$0.903122\pi$
$854$		0			0
$855$	−1.00000			−0.0341993
$856$		0			0
$857$	−7.51395	−	13.0145i	−0.256672	−	0.444568i	0.708677	−	0.705534i	$-0.249293\pi$
$857$	−7.51395	−	13.0145i	−0.256672	−	0.444568i	−0.965348	+	0.260965i	$0.915959\pi$
$858$		0			0
$859$	13.6875	−	23.7074i	0.467010	−	0.808885i	−0.532280	−	0.846569i	$-0.678664\pi$
$859$	13.6875	−	23.7074i	0.467010	−	0.808885i	0.999290	+	0.0376834i	$0.0119978\pi$
$860$		0			0
$861$	−3.47034	−	4.89752i	−0.118269	−	0.166907i
$862$		0			0
$863$	−21.5451	+	37.3173i	−0.733405	+	1.27029i	0.222014	+	0.975043i	$0.428737\pi$
$863$	−21.5451	+	37.3173i	−0.733405	+	1.27029i	−0.955420	+	0.295252i	$0.904597\pi$
$864$		0			0
$865$	8.00774	+	13.8698i	0.272271	+	0.471588i
$866$		0			0
$867$	36.6999			1.24639
$868$		0			0
$869$	−1.38382			−0.0469429
$870$		0			0
$871$	−0.298360	−	0.516775i	−0.0101095	−	0.0175103i
$872$		0			0
$873$	−4.00000	+	6.92820i	−0.135379	+	0.234484i
$874$		0			0
$875$	−2.63435	+	0.245357i	−0.0890573	+	0.00829457i
$876$		0			0
$877$	7.14232	−	12.3709i	0.241179	−	0.417734i	−0.719871	−	0.694107i	$-0.755799\pi$
$877$	7.14232	−	12.3709i	0.241179	−	0.417734i	0.961050	+	0.276373i	$0.0891326\pi$
$878$		0			0
$879$	6.67972	+	11.5696i	0.225301	+	0.390233i
$880$		0			0
$881$	8.55288			0.288154			0.144077	−	0.989566i	$-0.453979\pi$
$881$	8.55288			0.288154			0.144077	+	0.989566i	$0.453979\pi$
$882$		0			0
$883$	34.4312			1.15870			0.579351	−	0.815078i	$-0.303306\pi$
$883$	34.4312			1.15870			0.579351	+	0.815078i	$0.303306\pi$
$884$		0			0
$885$	4.39531	+	7.61290i	0.147747	+	0.255905i
$886$		0			0
$887$	11.8420	−	20.5109i	0.397614	−	0.688688i	−0.595817	−	0.803121i	$-0.703171\pi$
$887$	11.8420	−	20.5109i	0.397614	−	0.688688i	0.993431	+	0.114432i	$0.0365048\pi$
$888$		0			0
$889$	−53.8637	+	5.01672i	−1.80653	+	0.168255i
$890$		0			0
$891$	1.92497	−	3.33415i	0.0644889	−	0.111698i
$892$		0			0
$893$	2.73904	+	4.74416i	0.0916585	+	0.158757i
$894$		0			0
$895$	19.5967			0.655046
$896$		0			0
$897$	−1.31254			−0.0438244
$898$		0			0
$899$	−16.8141	−	29.1228i	−0.560781	−	0.971301i
$900$		0			0
$901$	−33.1934	+	57.4927i	−1.10583	+	1.91536i
$902$		0			0
$903$	−4.35944	−	6.15227i	−0.145073	−	0.204735i
$904$		0			0
$905$	−1.44842	+	2.50874i	−0.0481471	+	0.0833932i
$906$		0			0
$907$	−25.3342	−	43.8802i	−0.841209	−	1.45702i	−0.888873	−	0.458154i	$-0.848511\pi$
$907$	−25.3342	−	43.8802i	−0.841209	−	1.45702i	0.0476636	−	0.998863i	$-0.484822\pi$
$908$		0			0
$909$	15.3280			0.508398
$910$		0			0
$911$	−11.1465			−0.369301			−0.184651	−	0.982804i	$-0.559115\pi$
$911$	−11.1465			−0.369301			−0.184651	+	0.982804i	$0.559115\pi$
$912$		0			0
$913$	6.17796	+	10.7005i	0.204461	+	0.354136i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.37960	−	7.35489i	0.111604	−	0.242880i
$918$		0			0
$919$	8.78886	−	15.2228i	0.289918	−	0.502152i	−0.683872	−	0.729602i	$-0.739705\pi$
$919$	8.78886	−	15.2228i	0.289918	−	0.502152i	0.973790	+	0.227450i	$0.0730387\pi$
$920$		0			0
$921$	8.02169	+	13.8940i	0.264324	+	0.457822i
$922$		0			0
$923$	2.81546			0.0926720
$924$		0			0
$925$	7.90926			0.260055
$926$		0			0
$927$	−2.21559	−	3.83751i	−0.0727695	−	0.126041i
$928$		0			0
$929$	14.7625	−	25.5694i	0.484342	−	0.838904i	−0.515497	−	0.856892i	$-0.672393\pi$
$929$	14.7625	−	25.5694i	0.484342	−	0.838904i	0.999838	+	0.0179874i	$0.00572587\pi$
$930$		0			0
$931$	−2.32028	+	6.60426i	−0.0760441	+	0.216446i
$932$		0			0
$933$	0.0358703	−	0.0621292i	0.00117434	−	0.00203402i
$934$		0			0
$935$	14.1062	+	24.4327i	0.461323	+	0.799034i
$936$		0			0
$937$	−33.4811			−1.09378			−0.546891	−	0.837204i	$-0.684189\pi$
$937$	−33.4811			−1.09378			−0.546891	+	0.837204i	$0.684189\pi$
$938$		0			0
$939$	−33.6246			−1.09730
$940$		0			0
$941$	17.5733	+	30.4378i	0.572872	+	0.992244i	0.996269	+	0.0862996i	$0.0275042\pi$
$941$	17.5733	+	30.4378i	0.572872	+	0.992244i	−0.423397	+	0.905944i	$0.639162\pi$
$942$		0			0
$943$	7.11090	−	12.3164i	0.231563	−	0.401078i
$944$		0			0
$945$	1.10469	−	2.40409i	0.0359356	−	0.0782051i
$946$		0			0
$947$	24.8296	−	43.0060i	0.806852	−	1.39751i	−0.108182	−	0.994131i	$-0.534503\pi$
$947$	24.8296	−	43.0060i	0.806852	−	1.39751i	0.915034	−	0.403377i	$-0.132164\pi$
$948$		0			0
$949$	−1.17972	−	2.04333i	−0.0382953	−	0.0663295i
$950$		0			0
$951$	−13.2094			−0.428343
$952$		0			0
$953$	49.2183			1.59434			0.797168	−	0.603757i	$-0.206330\pi$
$953$	49.2183			1.59434			0.797168	+	0.603757i	$0.206330\pi$
$954$		0			0
$955$	−5.41876	−	9.38557i	−0.175347	−	0.303710i
$956$		0			0
$957$	6.17796	−	10.7005i	0.199705	−	0.345899i
$958$		0			0
$959$	15.3683	+	21.6886i	0.496270	+	0.700361i
$960$		0			0
$961$	−39.3951	+	68.2343i	−1.27081	+	2.20111i
$962$		0			0
$963$	−8.72333	−	15.1093i	−0.281105	−	0.486889i
$964$		0			0
$965$	6.43118			0.207027
$966$		0			0
$967$	−6.61266			−0.212649			−0.106324	−	0.994331i	$-0.533908\pi$
$967$	−6.61266			−0.212649			−0.106324	+	0.994331i	$0.533908\pi$
$968$		0			0
$969$	3.66401	+	6.34625i	0.117705	+	0.203871i
$970$		0			0
$971$	−18.5137	+	32.0667i	−0.594134	+	1.02907i	0.399535	+	0.916718i	$0.369172\pi$
$971$	−18.5137	+	32.0667i	−0.594134	+	1.02907i	−0.993669	+	0.112352i	$0.964162\pi$
$972$		0			0
$973$	−16.2749	+	1.51580i	−0.521750	+	0.0485944i
$974$		0			0
$975$	−0.104690	+	0.181328i	−0.00335276	+	0.00580715i
$976$		0			0
$977$	7.08277	+	12.2677i	0.226598	+	0.392479i	0.956798	−	0.290755i	$-0.0939063\pi$
$977$	7.08277	+	12.2677i	0.226598	+	0.392479i	−0.730200	+	0.683234i	$0.760573\pi$
$978$		0			0
$979$	−26.6002			−0.850147
$980$		0			0
$981$	5.64056			0.180089
$982$		0			0
$983$	0.865650	+	1.49935i	0.0276099	+	0.0478218i	0.879500	−	0.475898i	$-0.157877\pi$
$983$	0.865650	+	1.49935i	0.0276099	+	0.0478218i	−0.851890	+	0.523720i	$0.824544\pi$
$984$		0			0
$985$	−2.71559	+	4.70354i	−0.0865259	+	0.149867i
$986$		0			0
$987$	−14.4312	+	1.34408i	−0.459350	+	0.0427826i
$988$		0			0
$989$	8.93271	−	15.4719i	0.284044	−	0.491978i
$990$		0			0
$991$	−25.7171	−	44.5434i	−0.816931	−	1.41497i	−0.907933	−	0.419116i	$-0.862340\pi$
$991$	−25.7171	−	44.5434i	−0.816931	−	1.41497i	0.0910016	−	0.995851i	$-0.470993\pi$
$992$		0			0
$993$	22.3749			0.710047
$994$		0			0
$995$	8.95616			0.283929
$996$		0			0
$997$	10.3063	+	17.8511i	0.326405	+	0.565350i	0.981796	−	0.189940i	$-0.0608294\pi$
$997$	10.3063	+	17.8511i	0.326405	+	0.565350i	−0.655391	+	0.755290i	$0.727496\pi$
$998$		0			0
$999$	−3.95463	+	6.84962i	−0.125119	+	0.216712i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bg.j.121.3	✓	6
3.2	odd	2		2520.2.bi.n.1801.3		6
4.3	odd	2		1680.2.bg.v.961.1		6
7.2	even	3		5880.2.a.bv.1.2		3
7.4	even	3	inner	840.2.bg.j.361.3	yes	6
7.5	odd	6		5880.2.a.bu.1.2		3
21.11	odd	6		2520.2.bi.n.361.3		6
28.11	odd	6		1680.2.bg.v.1201.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bg.j.121.3	✓	6	1.1	even	1	trivial
840.2.bg.j.361.3	yes	6	7.4	even	3	inner
1680.2.bg.v.961.1		6	4.3	odd	2
1680.2.bg.v.1201.1		6	28.11	odd	6
2520.2.bi.n.361.3		6	21.11	odd	6
2520.2.bi.n.1801.3		6	3.2	odd	2
5880.2.a.bu.1.2		3	7.5	odd	6
5880.2.a.bv.1.2		3	7.2	even	3

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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bg (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.63435 - 0.245357i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.63435 - 0.245357i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.92497 + 3.33415i) q^{11} +0.209380 q^{13} -1.00000 q^{15} +(3.66401 + 6.34625i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-1.52966 - 2.15874i) q^{21} +(3.13435 - 5.42885i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +3.20938 q^{29} +(-5.23904 - 9.07428i) q^{31} +(1.92497 - 3.33415i) q^{33} +(1.10469 - 2.40409i) q^{35} +(-3.95463 + 6.84962i) q^{37} +(-0.104690 - 0.181328i) q^{39} +2.26870 q^{41} +2.84994 q^{43} +(0.500000 + 0.866025i) q^{45} +(2.73904 - 4.74416i) q^{47} +(6.87960 - 1.29271i) q^{49} +(3.66401 - 6.34625i) q^{51} +(4.52966 + 7.84560i) q^{53} +3.84994 q^{55} +1.00000 q^{57} +(-4.39531 - 7.61290i) q^{59} +(-1.10469 + 2.40409i) q^{63} +(0.104690 - 0.181328i) q^{65} +(-1.42497 - 2.46812i) q^{67} -6.26870 q^{69} +13.4467 q^{71} +(-5.63435 - 9.75898i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(5.88910 + 8.31100i) q^{77} +(-0.179720 + 0.311284i) q^{79} +(-0.500000 - 0.866025i) q^{81} +3.20938 q^{83} +7.32802 q^{85} +(-1.60469 - 2.77940i) q^{87} +(-3.45463 + 5.98359i) q^{89} +(0.551580 - 0.0513728i) q^{91} +(-5.23904 + 9.07428i) q^{93} +(0.500000 + 0.866025i) q^{95} +8.00000 q^{97} -3.84994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} + 3 q^{5} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 + 3 * q^5 - 3 * q^9	\( 6 q - 3 q^{3} + 3 q^{5} - 3 q^{9} + 3 q^{11} - 6 q^{13} - 6 q^{15} - 6 q^{17} - 3 q^{19} + 3 q^{21} + 3 q^{23} - 3 q^{25} + 6 q^{27} + 12 q^{29} - 12 q^{31} + 3 q^{33} + 3 q^{35} - 3 q^{37} + 3 q^{39} - 18 q^{41} + 3 q^{45} - 3 q^{47} + 12 q^{49} - 6 q^{51} + 15 q^{53} + 6 q^{55} + 6 q^{57} - 30 q^{59} - 3 q^{63} - 3 q^{65} - 6 q^{69} - 24 q^{71} - 18 q^{73} - 3 q^{75} + 33 q^{77} - 6 q^{79} - 3 q^{81} + 12 q^{83} - 12 q^{85} - 6 q^{87} + 30 q^{91} - 12 q^{93} + 3 q^{95} + 48 q^{97} - 6 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 + 3 * q^5 - 3 * q^9 + 3 * q^11 - 6 * q^13 - 6 * q^15 - 6 * q^17 - 3 * q^19 + 3 * q^21 + 3 * q^23 - 3 * q^25 + 6 * q^27 + 12 * q^29 - 12 * q^31 + 3 * q^33 + 3 * q^35 - 3 * q^37 + 3 * q^39 - 18 * q^41 + 3 * q^45 - 3 * q^47 + 12 * q^49 - 6 * q^51 + 15 * q^53 + 6 * q^55 + 6 * q^57 - 30 * q^59 - 3 * q^63 - 3 * q^65 - 6 * q^69 - 24 * q^71 - 18 * q^73 - 3 * q^75 + 33 * q^77 - 6 * q^79 - 3 * q^81 + 12 * q^83 - 12 * q^85 - 6 * q^87 + 30 * q^91 - 12 * q^93 + 3 * q^95 + 48 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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