LMFDB - Embedded newform 945.2.i.d.631.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(316,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("945.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.142635249.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 3x^{6} + 3x^{5} - 11x^{4} + 6x^{3} + 12x^{2} - 24x + 16 $ x^8 - 3x^7 + 3x^6 + 3x^5 - 11x^4 + 6x^3 + 12x^2 - 24*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			631.4
Root			$0.818235 - 1.15347i$ of defining polynomial
Character	$\chi$	$=$	945.631
Dual form			945.2.i.d.316.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.875400 + 1.51624i) q^{2} +(-0.532651 + 0.922579i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{7} +1.63647 q^{8} +O(q^{10})$	\(q+(0.875400 + 1.51624i) q^{2} +(-0.532651 + 0.922579i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{7} +1.63647 q^{8} +1.75080 q^{10} +(-3.05503 - 5.29147i) q^{11} +(2.90805 - 5.03689i) q^{13} +(0.875400 - 1.51624i) q^{14} +(2.49787 + 4.32643i) q^{16} -4.73907 q^{17} +3.68123 q^{19} +(0.532651 + 0.922579i) q^{20} +(5.34875 - 9.26431i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{25} +10.1828 q^{26} +1.06530 q^{28} +(-0.839016 - 1.45322i) q^{29} +(3.47922 - 6.02618i) q^{31} +(-2.73680 + 4.74027i) q^{32} +(-4.14858 - 7.18556i) q^{34} -1.00000 q^{35} -4.49413 q^{37} +(3.22255 + 5.58163i) q^{38} +(0.818235 - 1.41722i) q^{40} +(-1.98736 + 3.44220i) q^{41} +(5.66350 + 9.80947i) q^{43} +6.50907 q^{44} -1.75080 q^{46} +(2.08768 + 3.61598i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(0.875400 - 1.51624i) q^{50} +(3.09795 + 5.36581i) q^{52} +8.30597 q^{53} -6.11007 q^{55} +(-0.818235 - 1.41722i) q^{56} +(1.46895 - 2.54430i) q^{58} +(0.418564 - 0.724974i) q^{59} +(4.62833 + 8.01651i) q^{61} +12.1828 q^{62} +0.408295 q^{64} +(-2.90805 - 5.03689i) q^{65} +(-2.25894 + 3.91259i) q^{67} +(2.52427 - 4.37217i) q^{68} +(-0.875400 - 1.51624i) q^{70} -10.3667 q^{71} +12.2346 q^{73} +(-3.93417 - 6.81418i) q^{74} +(-1.96081 + 3.39623i) q^{76} +(-3.05503 + 5.29147i) q^{77} +(-4.41643 - 7.64948i) q^{79} +4.99574 q^{80} -6.95892 q^{82} +(-3.17072 - 5.49185i) q^{83} +(-2.36954 + 4.10416i) q^{85} +(-9.91566 + 17.1744i) q^{86} +(-4.99947 - 8.65933i) q^{88} +9.66496 q^{89} -5.81610 q^{91} +(-0.532651 - 0.922579i) q^{92} +(-3.65512 + 6.33085i) q^{94} +(1.84062 - 3.18804i) q^{95} +(4.08677 + 7.07849i) q^{97} -1.75080 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) $ 8 * q - q^2 - q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8	$ 8 q - q^{2} - q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8} - 2 q^{10} - q^{11} + 12 q^{13} - q^{14} + q^{16} - 10 q^{17} - 18 q^{19} + q^{20} + 17 q^{22} - 4 q^{23} - 4 q^{25} + 2 q^{26} + 2 q^{28} - 15 q^{29} + 16 q^{31} - 2 q^{32} + 11 q^{34} - 8 q^{35} - 30 q^{37} + 24 q^{38} + 3 q^{40} - 2 q^{41} + 7 q^{43} - 6 q^{44} + 2 q^{46} - 10 q^{47} - 4 q^{49} - q^{50} + 15 q^{52} - 2 q^{55} - 3 q^{56} - 17 q^{58} - 13 q^{59} + 32 q^{61} + 18 q^{62} - 30 q^{64} - 12 q^{65} + 41 q^{68} + q^{70} - 26 q^{71} - 4 q^{73} + 13 q^{74} + 11 q^{76} - q^{77} + 2 q^{80} + 12 q^{82} + 17 q^{83} - 5 q^{85} - 15 q^{86} + 11 q^{88} + 34 q^{89} - 24 q^{91} - q^{92} - 15 q^{94} - 9 q^{95} + 4 q^{97} + 2 q^{98}+O(q^{100}) $ 8 * q - q^2 - q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8 - 2 * q^10 - q^11 + 12 * q^13 - q^14 + q^16 - 10 * q^17 - 18 * q^19 + q^20 + 17 * q^22 - 4 * q^23 - 4 * q^25 + 2 * q^26 + 2 * q^28 - 15 * q^29 + 16 * q^31 - 2 * q^32 + 11 * q^34 - 8 * q^35 - 30 * q^37 + 24 * q^38 + 3 * q^40 - 2 * q^41 + 7 * q^43 - 6 * q^44 + 2 * q^46 - 10 * q^47 - 4 * q^49 - q^50 + 15 * q^52 - 2 * q^55 - 3 * q^56 - 17 * q^58 - 13 * q^59 + 32 * q^61 + 18 * q^62 - 30 * q^64 - 12 * q^65 + 41 * q^68 + q^70 - 26 * q^71 - 4 * q^73 + 13 * q^74 + 11 * q^76 - q^77 + 2 * q^80 + 12 * q^82 + 17 * q^83 - 5 * q^85 - 15 * q^86 + 11 * q^88 + 34 * q^89 - 24 * q^91 - q^92 - 15 * q^94 - 9 * q^95 + 4 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.875400	+	1.51624i	0.619001	+	1.07214i	0.989668	+	0.143376i	$0.0457958\pi$
$2$	0.875400	+	1.51624i	0.619001	+	1.07214i	−0.370667	+	0.928766i	$0.620871\pi$
$3$		0			0
$3$		0			0
$4$	−0.532651	+	0.922579i	−0.266326	+	0.461289i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	1.63647			0.578579
$9$		0			0
$10$	1.75080			0.553652
$11$	−3.05503	−	5.29147i	−0.921127	−	1.59544i	−0.797674	−	0.603089i	$-0.793936\pi$
$11$	−3.05503	−	5.29147i	−0.921127	−	1.59544i	−0.123453	−	0.992350i	$-0.539397\pi$
$12$		0			0
$13$	2.90805	−	5.03689i	0.806548	−	1.39698i	−0.108693	−	0.994075i	$-0.534666\pi$
$13$	2.90805	−	5.03689i	0.806548	−	1.39698i	0.915241	−	0.402907i	$-0.132000\pi$
$14$	0.875400	−	1.51624i	0.233961	−	0.405232i
$15$		0			0
$16$	2.49787	+	4.32643i	0.624467	+	1.08161i
$17$	−4.73907			−1.14939			−0.574697	−	0.818367i	$-0.694880\pi$
$17$	−4.73907			−1.14939			−0.574697	+	0.818367i	$0.694880\pi$
$18$		0			0
$19$	3.68123			0.844533			0.422266	−	0.906472i	$-0.361235\pi$
$19$	3.68123			0.844533			0.422266	+	0.906472i	$0.361235\pi$
$20$	0.532651	+	0.922579i	0.119104	+	0.206295i
$21$		0			0
$22$	5.34875	−	9.26431i	1.14036	−	1.97516i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	−0.913434	−	0.406986i	$-0.866580\pi$
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	0.809177	+	0.587565i	$0.199913\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	10.1828			1.99702
$27$		0			0
$28$	1.06530			0.201323
$29$	−0.839016	−	1.45322i	−0.155801	−	0.269856i	0.777549	−	0.628822i	$-0.216463\pi$
$29$	−0.839016	−	1.45322i	−0.155801	−	0.269856i	−0.933351	+	0.358966i	$0.883129\pi$
$30$		0			0
$31$	3.47922	−	6.02618i	0.624886	−	1.08233i	−0.363677	−	0.931525i	$-0.618479\pi$
$31$	3.47922	−	6.02618i	0.624886	−	1.08233i	0.988563	−	0.150809i	$-0.0481879\pi$
$32$	−2.73680	+	4.74027i	−0.483802	+	0.837970i
$33$		0			0
$34$	−4.14858	−	7.18556i	−0.711476	−	1.23231i
$35$	−1.00000			−0.169031
$36$		0			0
$37$	−4.49413			−0.738831			−0.369416	−	0.929264i	$-0.620442\pi$
$37$	−4.49413			−0.738831			−0.369416	+	0.929264i	$0.620442\pi$
$38$	3.22255	+	5.58163i	0.522767	+	0.905459i
$39$		0			0
$40$	0.818235	−	1.41722i	0.129374	−	0.224083i
$41$	−1.98736	+	3.44220i	−0.310373	+	0.537581i	−0.978443	−	0.206517i	$-0.933787\pi$
$41$	−1.98736	+	3.44220i	−0.310373	+	0.537581i	0.668070	+	0.744098i	$0.267121\pi$
$42$		0			0
$43$	5.66350	+	9.80947i	0.863676	+	1.49593i	0.868356	+	0.495941i	$0.165177\pi$
$43$	5.66350	+	9.80947i	0.863676	+	1.49593i	−0.00468081	+	0.999989i	$0.501490\pi$
$44$	6.50907			0.981279
$45$		0			0
$46$	−1.75080			−0.258141
$47$	2.08768	+	3.61598i	0.304520	+	0.527444i	0.977154	−	0.212531i	$-0.0681706\pi$
$47$	2.08768	+	3.61598i	0.304520	+	0.527444i	−0.672634	+	0.739975i	$0.734837\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	0.875400	−	1.51624i	0.123800	−	0.214428i
$51$		0			0
$52$	3.09795	+	5.36581i	0.429609	+	0.744104i
$53$	8.30597			1.14091			0.570457	−	0.821328i	$-0.306766\pi$
$53$	8.30597			1.14091			0.570457	+	0.821328i	$0.306766\pi$
$54$		0			0
$55$	−6.11007			−0.823881
$56$	−0.818235	−	1.41722i	−0.109341	−	0.189385i
$57$		0			0
$58$	1.46895	−	2.54430i	0.192883	−	0.334082i
$59$	0.418564	−	0.724974i	0.0544924	−	0.0943836i	−0.837492	−	0.546449i	$-0.815979\pi$
$59$	0.418564	−	0.724974i	0.0544924	−	0.0943836i	0.891985	+	0.452065i	$0.149313\pi$
$60$		0			0
$61$	4.62833	+	8.01651i	0.592597	+	1.02641i	0.993881	+	0.110455i	$0.0352308\pi$
$61$	4.62833	+	8.01651i	0.592597	+	1.02641i	−0.401284	+	0.915954i	$0.631436\pi$
$62$	12.1828			1.54722
$63$		0			0
$64$	0.408295			0.0510369
$65$	−2.90805	−	5.03689i	−0.360699	−	0.624750i
$66$		0			0
$67$	−2.25894	+	3.91259i	−0.275973	+	0.477999i	−0.970380	−	0.241583i	$-0.922333\pi$
$67$	−2.25894	+	3.91259i	−0.275973	+	0.477999i	0.694407	+	0.719582i	$0.255667\pi$
$68$	2.52427	−	4.37217i	0.306113	−	0.530203i
$69$		0			0
$70$	−0.875400	−	1.51624i	−0.104630	−	0.181225i
$71$	−10.3667			−1.23030			−0.615152	−	0.788408i	$-0.710906\pi$
$71$	−10.3667			−1.23030			−0.615152	+	0.788408i	$0.710906\pi$
$72$		0			0
$73$	12.2346			1.43195			0.715975	−	0.698126i	$-0.245983\pi$
$73$	12.2346			1.43195			0.715975	+	0.698126i	$0.245983\pi$
$74$	−3.93417	−	6.81418i	−0.457338	−	0.792132i
$75$		0			0
$76$	−1.96081	+	3.39623i	−0.224921	+	0.389574i
$77$	−3.05503	+	5.29147i	−0.348153	+	0.603019i
$78$		0			0
$79$	−4.41643	−	7.64948i	−0.496887	−	0.860634i	0.503106	−	0.864225i	$-0.332190\pi$
$79$	−4.41643	−	7.64948i	−0.496887	−	0.860634i	−0.999994	+	0.00359042i	$0.998857\pi$
$80$	4.99574			0.558540
$81$		0			0
$82$	−6.95892			−0.768485
$83$	−3.17072	−	5.49185i	−0.348032	−	0.602809i	0.637868	−	0.770146i	$-0.279817\pi$
$83$	−3.17072	−	5.49185i	−0.348032	−	0.602809i	−0.985900	+	0.167337i	$0.946483\pi$
$84$		0			0
$85$	−2.36954	+	4.10416i	−0.257012	+	0.445158i
$86$	−9.91566	+	17.1744i	−1.06923	+	1.85197i
$87$		0			0
$88$	−4.99947	−	8.65933i	−0.532945	−	0.923088i
$89$	9.66496			1.02448			0.512242	−	0.858841i	$-0.328815\pi$
$89$	9.66496			1.02448			0.512242	+	0.858841i	$0.328815\pi$
$90$		0			0
$91$	−5.81610			−0.609693
$92$	−0.532651	−	0.922579i	−0.0555327	−	0.0961855i
$93$		0			0
$94$	−3.65512	+	6.33085i	−0.376997	+	0.652977i
$95$	1.84062	−	3.18804i	0.188843	−	0.327086i
$96$		0			0
$97$	4.08677	+	7.07849i	0.414949	+	0.718712i	0.995423	−	0.0955664i	$-0.0304662\pi$
$97$	4.08677	+	7.07849i	0.414949	+	0.718712i	−0.580474	+	0.814278i	$0.697133\pi$
$98$	−1.75080			−0.176858
$99$		0			0
$100$	1.06530			0.106530
$101$	6.06599	+	10.5066i	0.603588	+	1.04545i	0.992273	+	0.124075i	$0.0395963\pi$
$101$	6.06599	+	10.5066i	0.603588	+	1.04545i	−0.388684	+	0.921371i	$0.627070\pi$
$102$		0			0
$103$	0.697899	−	1.20880i	0.0687661	−	0.119106i	−0.829592	−	0.558370i	$-0.811427\pi$
$103$	0.697899	−	1.20880i	0.0687661	−	0.119106i	0.898358	+	0.439263i	$0.144760\pi$
$104$	4.75894	−	8.24272i	0.466652	−	0.808265i
$105$		0			0
$106$	7.27105	+	12.5938i	0.706227	+	1.22322i
$107$	0.484840			0.0468713			0.0234356	−	0.999725i	$-0.492540\pi$
$107$	0.484840			0.0468713			0.0234356	+	0.999725i	$0.492540\pi$
$108$		0			0
$109$	−10.7345			−1.02818			−0.514091	−	0.857736i	$-0.671870\pi$
$109$	−10.7345			−1.02818			−0.514091	+	0.857736i	$0.671870\pi$
$110$	−5.34875	−	9.26431i	−0.509984	−	0.883318i
$111$		0			0
$112$	2.49787	−	4.32643i	0.236026	−	0.408810i
$113$	−0.559298	+	0.968732i	−0.0526143	+	0.0911306i	−0.891133	−	0.453742i	$-0.850089\pi$
$113$	−0.559298	+	0.968732i	−0.0526143	+	0.0911306i	0.838519	+	0.544873i	$0.183422\pi$
$114$		0			0
$115$	0.500000	+	0.866025i	0.0466252	+	0.0807573i
$116$	1.78761			0.165976
$117$		0			0
$118$	1.46564			0.134923
$119$	2.36954	+	4.10416i	0.217215	+	0.376227i
$120$		0			0
$121$	−13.1665	+	22.8050i	−1.19695	+	2.07318i
$122$	−8.10329	+	14.0353i	−0.733637	+	1.27070i
$123$		0			0
$124$	3.70642	+	6.41971i	0.332846	+	0.576507i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−11.7567			−1.04324			−0.521620	−	0.853178i	$-0.674672\pi$
$127$	−11.7567			−1.04324			−0.521620	+	0.853178i	$0.674672\pi$
$128$	5.83102	+	10.0996i	0.515394	+	0.892689i
$129$		0			0
$130$	5.09142	−	8.81859i	0.446547	−	0.773442i
$131$	−0.485084	+	0.840190i	−0.0423820	+	0.0734077i	−0.886438	−	0.462847i	$-0.846828\pi$
$131$	−0.485084	+	0.840190i	−0.0423820	+	0.0734077i	0.844056	+	0.536255i	$0.180161\pi$
$132$		0			0
$133$	−1.84062	−	3.18804i	−0.159602	−	0.276438i
$134$	−7.90990			−0.683311
$135$		0			0
$136$	−7.75534			−0.665015
$137$	5.38354	+	9.32456i	0.459947	+	0.796651i	0.998958	−	0.0456479i	$-0.0145352\pi$
$137$	5.38354	+	9.32456i	0.459947	+	0.796651i	−0.539011	+	0.842299i	$0.681202\pi$
$138$		0			0
$139$	5.41270	−	9.37507i	0.459099	−	0.795183i	−0.539814	−	0.841784i	$-0.681506\pi$
$139$	5.41270	−	9.37507i	0.459099	−	0.795183i	0.998914	+	0.0466010i	$0.0148389\pi$
$140$	0.532651	−	0.922579i	0.0450172	−	0.0779721i
$141$		0			0
$142$	−9.07504	−	15.7184i	−0.761560	−	1.31906i
$143$	−35.5368			−2.97173
$144$		0			0
$145$	−1.67803			−0.139353
$146$	10.7102	+	18.5505i	0.886378	+	1.53525i
$147$		0			0
$148$	2.39381	−	4.14619i	0.196770	−	0.340815i
$149$	−6.90752	+	11.9642i	−0.565886	+	0.980143i	0.431081	+	0.902313i	$0.358132\pi$
$149$	−6.90752	+	11.9642i	−0.565886	+	0.980143i	−0.996967	+	0.0778300i	$0.975201\pi$
$150$		0			0
$151$	−5.42006	−	9.38782i	−0.441078	−	0.763970i	0.556692	−	0.830719i	$-0.312071\pi$
$151$	−5.42006	−	9.38782i	−0.441078	−	0.763970i	−0.997770	+	0.0667494i	$0.978737\pi$
$152$	6.02423			0.488629
$153$		0			0
$154$	−10.6975			−0.862030
$155$	−3.47922	−	6.02618i	−0.279458	−	0.484035i
$156$		0			0
$157$	5.53503	−	9.58695i	0.441743	−	0.765122i	−0.556076	−	0.831132i	$-0.687694\pi$
$157$	5.53503	−	9.58695i	0.441743	−	0.765122i	0.997819	+	0.0660099i	$0.0210269\pi$
$158$	7.73229	−	13.3927i	0.615148	−	1.06547i
$159$		0			0
$160$	2.73680	+	4.74027i	0.216363	+	0.374752i
$161$	1.00000			0.0788110
$162$		0			0
$163$	11.2066			0.877767			0.438883	−	0.898544i	$-0.355374\pi$
$163$	11.2066			0.877767			0.438883	+	0.898544i	$0.355374\pi$
$164$	−2.11713	−	3.66698i	−0.165320	−	0.286343i
$165$		0			0
$166$	5.55130	−	9.61513i	0.430864	−	0.746279i
$167$	11.8200	−	20.4728i	0.914657	−	1.58423i	0.107255	−	0.994232i	$-0.465794\pi$
$167$	11.8200	−	20.4728i	0.914657	−	1.58423i	0.807403	−	0.590001i	$-0.200873\pi$
$168$		0			0
$169$	−10.4135	−	18.0368i	−0.801040	−	1.38744i
$170$	−8.29717			−0.636364
$171$		0			0
$172$	−12.0667			−0.920075
$173$	−1.54452	−	2.67519i	−0.117428	−	0.203391i	0.801320	−	0.598236i	$-0.204132\pi$
$173$	−1.54452	−	2.67519i	−0.117428	−	0.203391i	−0.918748	+	0.394845i	$0.870798\pi$
$174$		0			0
$175$	−0.500000	+	0.866025i	−0.0377964	+	0.0654654i
$176$	15.2621	−	26.4348i	1.15043	−	1.99260i
$177$		0			0
$178$	8.46071	+	14.6544i	0.634157	+	1.09839i
$179$	−22.9526			−1.71556			−0.857780	−	0.514017i	$-0.828157\pi$
$179$	−22.9526			−1.71556			−0.857780	+	0.514017i	$0.828157\pi$
$180$		0			0
$181$	−4.10028			−0.304772			−0.152386	−	0.988321i	$-0.548696\pi$
$181$	−4.10028			−0.304772			−0.152386	+	0.988321i	$0.548696\pi$
$182$	−5.09142	−	8.81859i	−0.377401	−	0.653678i
$183$		0			0
$184$	−0.818235	+	1.41722i	−0.0603211	+	0.104479i
$185$	−2.24707	+	3.89203i	−0.165208	+	0.286148i
$186$		0			0
$187$	14.4780	+	25.0767i	1.05874	+	1.83379i
$188$	−4.44803			−0.324406
$189$		0			0
$190$	6.44511			0.467577
$191$	−4.36740	−	7.56456i	−0.316014	−	0.547353i	0.663638	−	0.748054i	$-0.269011\pi$
$191$	−4.36740	−	7.56456i	−0.316014	−	0.547353i	−0.979653	+	0.200701i	$0.935678\pi$
$192$		0			0
$193$	8.09142	−	14.0147i	0.582433	−	1.00880i	−0.412757	−	0.910841i	$-0.635434\pi$
$193$	8.09142	−	14.0147i	0.582433	−	1.00880i	0.995190	−	0.0979624i	$-0.0312325\pi$
$194$	−7.15512	+	12.3930i	−0.513708	+	0.889768i
$195$		0			0
$196$	−0.532651	−	0.922579i	−0.0380465	−	0.0658985i
$197$	0.418652			0.0298278			0.0149139	−	0.999889i	$-0.495253\pi$
$197$	0.418652			0.0298278			0.0149139	+	0.999889i	$0.495253\pi$
$198$		0			0
$199$	−7.48667			−0.530716			−0.265358	−	0.964150i	$-0.585490\pi$
$199$	−7.48667			−0.530716			−0.265358	+	0.964150i	$0.585490\pi$
$200$	−0.818235	−	1.41722i	−0.0578579	−	0.100213i
$201$		0			0
$202$	−10.6203	+	18.3950i	−0.747244	+	1.29426i
$203$	−0.839016	+	1.45322i	−0.0588874	+	0.101996i
$204$		0			0
$205$	1.98736	+	3.44220i	0.138803	+	0.240414i
$206$	2.44376			0.170265
$207$		0			0
$208$	29.0557			2.01465
$209$	−11.2463	−	19.4791i	−0.777922	−	1.34740i
$210$		0			0
$211$	−3.12969	+	5.42078i	−0.215457	+	0.373182i	−0.953414	−	0.301666i	$-0.902457\pi$
$211$	−3.12969	+	5.42078i	−0.215457	+	0.373182i	0.737957	+	0.674848i	$0.235791\pi$
$212$	−4.42419	+	7.66291i	−0.303854	+	0.526291i
$213$		0			0
$214$	0.424429	+	0.735133i	0.0290134	+	0.0502526i
$215$	11.3270			0.772495
$216$		0			0
$217$	−6.95844			−0.472369
$218$	−9.39701	−	16.2761i	−0.636446	−	1.10236i
$219$		0			0
$220$	3.25453	−	5.63702i	0.219421	−	0.380048i
$221$	−13.7815	+	23.8702i	−0.927041	+	1.60568i
$222$		0			0
$223$	11.6207	+	20.1277i	0.778181	+	1.34785i	0.932989	+	0.359904i	$0.117191\pi$
$223$	11.6207	+	20.1277i	0.778181	+	1.34785i	−0.154808	+	0.987945i	$0.549476\pi$
$224$	5.47360			0.365720
$225$		0			0
$226$	−1.95844			−0.130273
$227$	9.88422	+	17.1200i	0.656039	+	1.13629i	0.981632	+	0.190783i	$0.0611026\pi$
$227$	9.88422	+	17.1200i	0.656039	+	1.13629i	−0.325593	+	0.945510i	$0.605564\pi$
$228$		0			0
$229$	0.00517872	−	0.00896980i	0.000342219	−	0.000592741i	−0.865854	−	0.500296i	$-0.833224\pi$
$229$	0.00517872	−	0.00896980i	0.000342219	−	0.000592741i	0.866196	+	0.499704i	$0.166558\pi$
$230$	−0.875400	+	1.51624i	−0.0577222	+	0.0999777i
$231$		0			0
$232$	−1.37302	−	2.37815i	−0.0901435	−	0.156133i
$233$	6.48609			0.424918			0.212459	−	0.977170i	$-0.431853\pi$
$233$	6.48609			0.424918			0.212459	+	0.977170i	$0.431853\pi$
$234$		0			0
$235$	4.17537			0.272371
$236$	0.445897	+	0.772316i	0.0290254	+	0.0502735i
$237$		0			0
$238$	−4.14858	+	7.18556i	−0.268913	+	0.465770i
$239$	7.89928	−	13.6820i	0.510962	−	0.885012i	−0.488957	−	0.872308i	$-0.662623\pi$
$239$	7.89928	−	13.6820i	0.510962	−	0.885012i	0.999919	−	0.0127043i	$-0.00404400\pi$
$240$		0			0
$241$	3.20899	+	5.55814i	0.206709	+	0.358031i	0.950676	−	0.310186i	$-0.100391\pi$
$241$	3.20899	+	5.55814i	0.206709	+	0.358031i	−0.743967	+	0.668217i	$0.767058\pi$
$242$	−46.1037			−2.96366
$243$		0			0
$244$	−9.86115			−0.631295
$245$	0.500000	+	0.866025i	0.0319438	+	0.0553283i
$246$		0			0
$247$	10.7052	−	18.5420i	0.681157	−	1.17980i
$248$	5.69363	−	9.86166i	0.361546	−	0.626216i
$249$		0			0
$250$	−0.875400	−	1.51624i	−0.0553652	−	0.0958953i
$251$	−4.15861			−0.262489			−0.131245	−	0.991350i	$-0.541897\pi$
$251$	−4.15861			−0.262489			−0.131245	+	0.991350i	$0.541897\pi$
$252$		0			0
$253$	6.11007			0.384137
$254$	−10.2918	−	17.8260i	−0.645767	−	1.11850i
$255$		0			0
$256$	−9.80066	+	16.9752i	−0.612541	+	1.06095i
$257$	5.87404	−	10.1741i	0.366413	−	0.634645i	−0.622589	−	0.782549i	$-0.713919\pi$
$257$	5.87404	−	10.1741i	0.366413	−	0.634645i	0.989002	+	0.147903i	$0.0472525\pi$
$258$		0			0
$259$	2.24707	+	3.89203i	0.139626	+	0.241839i
$260$	6.19591			0.384254
$261$		0			0
$262$	−1.69857			−0.104938
$263$	−6.19926	−	10.7374i	−0.382263	−	0.662098i	0.609123	−	0.793076i	$-0.291522\pi$
$263$	−6.19926	−	10.7374i	−0.382263	−	0.662098i	−0.991385	+	0.130978i	$0.958188\pi$
$264$		0			0
$265$	4.15299	−	7.19318i	0.255116	−	0.441874i
$266$	3.22255	−	5.58163i	0.197587	−	0.342231i
$267$		0			0
$268$	−2.40645	−	4.16809i	−0.146997	−	0.254607i
$269$	18.8491			1.14925			0.574626	−	0.818416i	$-0.305148\pi$
$269$	18.8491			1.14925			0.574626	+	0.818416i	$0.305148\pi$
$270$		0			0
$271$	−21.0866			−1.28092			−0.640461	−	0.767991i	$-0.721257\pi$
$271$	−21.0866			−1.28092			−0.640461	+	0.767991i	$0.721257\pi$
$272$	−11.8376	−	20.5033i	−0.717758	−	1.24319i
$273$		0			0
$274$	−9.42550	+	16.3254i	−0.569415	+	0.986256i
$275$	−3.05503	+	5.29147i	−0.184225	+	0.319088i
$276$		0			0
$277$	9.24867	+	16.0192i	0.555699	+	0.962498i	0.997849	+	0.0655572i	$0.0208825\pi$
$277$	9.24867	+	16.0192i	0.555699	+	0.962498i	−0.442150	+	0.896941i	$0.645784\pi$
$278$	18.9531			1.13673
$279$		0			0
$280$	−1.63647			−0.0977978
$281$	8.81421	+	15.2667i	0.525812	+	0.910733i	0.999548	+	0.0300661i	$0.00957177\pi$
$281$	8.81421	+	15.2667i	0.525812	+	0.910733i	−0.473736	+	0.880667i	$0.657095\pi$
$282$		0			0
$283$	1.89594	−	3.28386i	0.112702	−	0.195205i	−0.804157	−	0.594417i	$-0.797383\pi$
$283$	1.89594	−	3.28386i	0.112702	−	0.195205i	0.916859	+	0.399212i	$0.130716\pi$
$284$	5.52185	−	9.56413i	0.327662	−	0.567526i
$285$		0			0
$286$	−31.1089	−	53.8822i	−1.83951	−	3.18612i
$287$	3.97471			0.234620
$288$		0			0
$289$	5.45878			0.321105
$290$	−1.46895	−	2.54430i	−0.0862597	−	0.149406i
$291$		0			0
$292$	−6.51676	+	11.2874i	−0.381365	+	0.660543i
$293$	−4.03730	+	6.99281i	−0.235861	+	0.408524i	−0.959523	−	0.281631i	$-0.909125\pi$
$293$	−4.03730	+	6.99281i	−0.235861	+	0.408524i	0.723661	+	0.690155i	$0.242458\pi$
$294$		0			0
$295$	−0.418564	−	0.724974i	−0.0243697	−	0.0422096i
$296$	−7.35451			−0.427472
$297$		0			0
$298$	−24.1874			−1.40114
$299$	2.90805	+	5.03689i	0.168177	+	0.291291i
$300$		0			0
$301$	5.66350	−	9.80947i	0.326439	−	0.565408i
$302$	9.48944	−	16.4362i	0.546056	−	0.945797i
$303$		0			0
$304$	9.19524	+	15.9266i	0.527383	+	0.913454i
$305$	9.25667			0.530035
$306$		0			0
$307$	−1.03255			−0.0589305			−0.0294653	−	0.999566i	$-0.509380\pi$
$307$	−1.03255			−0.0589305			−0.0294653	+	0.999566i	$0.509380\pi$
$308$	−3.25453	−	5.63702i	−0.185444	−	0.321199i
$309$		0			0
$310$	6.09142	−	10.5506i	0.345969	−	0.599236i
$311$	4.14471	−	7.17885i	0.235025	−	0.407075i	−0.724255	−	0.689532i	$-0.757816\pi$
$311$	4.14471	−	7.17885i	0.235025	−	0.407075i	0.959280	+	0.282457i	$0.0911495\pi$
$312$		0			0
$313$	−10.0346	−	17.3805i	−0.567191	−	0.982404i	−0.996842	−	0.0794088i	$-0.974697\pi$
$313$	−10.0346	−	17.3805i	−0.567191	−	0.982404i	0.429651	−	0.902995i	$-0.358637\pi$
$314$	19.3815			1.09376
$315$		0			0
$316$	9.40967			0.529335
$317$	10.3821	+	17.9823i	0.583116	+	1.00999i	0.995107	+	0.0987992i	$0.0315002\pi$
$317$	10.3821	+	17.9823i	0.583116	+	1.00999i	−0.411991	+	0.911188i	$0.635167\pi$
$318$		0			0
$319$	−5.12644	+	8.87926i	−0.287026	+	0.497143i
$320$	0.204148	−	0.353594i	0.0114122	−	0.0197665i
$321$		0			0
$322$	0.875400	+	1.51624i	0.0487841	+	0.0844966i
$323$	−17.4456			−0.970701
$324$		0			0
$325$	−5.81610			−0.322619
$326$	9.81024	+	16.9918i	0.543339	+	0.941090i
$327$		0			0
$328$	−3.25225	+	5.63306i	−0.179575	+	0.311033i
$329$	2.08768	−	3.61598i	0.115098	−	0.199355i
$330$		0			0
$331$	5.58158	+	9.66757i	0.306791	+	0.531378i	0.977659	−	0.210200i	$-0.0674114\pi$
$331$	5.58158	+	9.66757i	0.306791	+	0.531378i	−0.670867	+	0.741577i	$0.734078\pi$
$332$	6.75555			0.370759
$333$		0			0
$334$	41.3888			2.26470
$335$	2.25894	+	3.91259i	0.123419	+	0.213768i
$336$		0			0
$337$	−3.03624	+	5.25893i	−0.165395	+	0.286472i	−0.936795	−	0.349878i	$-0.886223\pi$
$337$	−3.03624	+	5.25893i	−0.165395	+	0.286472i	0.771401	+	0.636350i	$0.219556\pi$
$338$	18.2320	−	31.5788i	0.991690	−	1.71766i
$339$		0			0
$340$	−2.52427	−	4.37217i	−0.136898	−	0.237114i
$341$	−42.5165			−2.30240
$342$		0			0
$343$	1.00000			0.0539949
$344$	9.26814	+	16.0529i	0.499705	+	0.865514i
$345$		0			0
$346$	2.70415	−	4.68372i	0.145376	−	0.251798i
$347$	9.75254	−	16.8919i	0.523544	−	0.906804i	−0.476081	−	0.879402i	$-0.657943\pi$
$347$	9.75254	−	16.8919i	0.523544	−	0.906804i	0.999624	−	0.0274029i	$-0.00872369\pi$
$348$		0			0
$349$	6.29410	+	10.9017i	0.336916	+	0.583555i	0.983851	−	0.178990i	$-0.0572830\pi$
$349$	6.29410	+	10.9017i	0.336916	+	0.583555i	−0.646935	+	0.762545i	$0.723950\pi$
$350$	−1.75080			−0.0935842
$351$		0			0
$352$	33.4440			1.78257
$353$	8.20857	+	14.2177i	0.436898	+	0.756729i	0.997448	−	0.0713908i	$-0.0227438\pi$
$353$	8.20857	+	14.2177i	0.436898	+	0.756729i	−0.560550	+	0.828120i	$0.689410\pi$
$354$		0			0
$355$	−5.18337	+	8.97785i	−0.275105	+	0.476495i
$356$	−5.14805	+	8.91669i	−0.272846	+	0.472583i
$357$		0			0
$358$	−20.0927	−	34.8016i	−1.06193	−	1.83932i
$359$	13.2324			0.698381			0.349191	−	0.937052i	$-0.386457\pi$
$359$	13.2324			0.698381			0.349191	+	0.937052i	$0.386457\pi$
$360$		0			0
$361$	−5.44852			−0.286764
$362$	−3.58939	−	6.21701i	−0.188654	−	0.326759i
$363$		0			0
$364$	3.09795	−	5.36581i	0.162377	−	0.281245i
$365$	6.11729	−	10.5955i	0.320194	−	0.554591i
$366$		0			0
$367$	10.1362	+	17.5564i	0.529104	+	0.916436i	0.999424	+	0.0339395i	$0.0108053\pi$
$367$	10.1362	+	17.5564i	0.529104	+	0.916436i	−0.470320	+	0.882496i	$0.655861\pi$
$368$	−4.99574			−0.260421
$369$		0			0
$370$	−7.86833			−0.409055
$371$	−4.15299	−	7.19318i	−0.215612	−	0.373451i
$372$		0			0
$373$	−15.1254	+	26.1979i	−0.783162	+	1.35648i	0.146929	+	0.989147i	$0.453061\pi$
$373$	−15.1254	+	26.1979i	−0.783162	+	1.35648i	−0.930091	+	0.367329i	$0.880272\pi$
$374$	−25.3481	+	43.9042i	−1.31072	+	2.27023i
$375$		0			0
$376$	3.41643	+	5.91743i	0.176189	+	0.305168i
$377$	−9.75961			−0.502645
$378$		0			0
$379$	−0.698602			−0.0358848			−0.0179424	−	0.999839i	$-0.505712\pi$
$379$	−0.698602			−0.0358848			−0.0179424	+	0.999839i	$0.505712\pi$
$380$	1.96081	+	3.39623i	0.100588	+	0.174223i
$381$		0			0
$382$	7.64645	−	13.2440i	0.391226	−	0.677624i
$383$	3.04757	−	5.27854i	0.155723	−	0.269721i	−0.777599	−	0.628761i	$-0.783562\pi$
$383$	3.04757	−	5.27854i	0.155723	−	0.269721i	0.933322	+	0.359040i	$0.116896\pi$
$384$		0			0
$385$	3.05503	+	5.29147i	0.155699	+	0.269678i
$386$	28.3329			1.44211
$387$		0			0
$388$	−8.70729			−0.442046
$389$	6.77943	+	11.7423i	0.343731	+	0.595359i	0.985122	−	0.171855i	$-0.0549759\pi$
$389$	6.77943	+	11.7423i	0.343731	+	0.595359i	−0.641392	+	0.767214i	$0.721643\pi$
$390$		0			0
$391$	2.36954	−	4.10416i	0.119833	−	0.207556i
$392$	−0.818235	+	1.41722i	−0.0413271	+	0.0715806i
$393$		0			0
$394$	0.366488	+	0.634777i	0.0184634	+	0.0319796i
$395$	−8.83286			−0.444430
$396$		0			0
$397$	−16.4109			−0.823639			−0.411819	−	0.911265i	$-0.635107\pi$
$397$	−16.4109			−0.823639			−0.411819	+	0.911265i	$0.635107\pi$
$398$	−6.55383	−	11.3516i	−0.328514	−	0.569003i
$399$		0			0
$400$	2.49787	−	4.32643i	0.124893	−	0.216322i
$401$	−1.75042	+	3.03181i	−0.0874117	+	0.151401i	−0.906416	−	0.422385i	$-0.861193\pi$
$401$	−1.75042	+	3.03181i	−0.0874117	+	0.151401i	0.819005	+	0.573787i	$0.194526\pi$
$402$		0			0
$403$	−20.2355	−	35.0489i	−1.00800	−	1.74591i
$404$	−12.9242			−0.643004
$405$		0			0
$406$	−2.93790			−0.145806
$407$	13.7297	+	23.7806i	0.680558	+	1.17876i
$408$		0			0
$409$	−3.37859	+	5.85188i	−0.167060	+	0.289357i	−0.937385	−	0.348295i	$-0.886761\pi$
$409$	−3.37859	+	5.85188i	−0.167060	+	0.289357i	0.770325	+	0.637652i	$0.220094\pi$
$410$	−3.47946	+	6.02661i	−0.171838	+	0.297633i
$411$		0			0
$412$	0.743474	+	1.28773i	0.0366283	+	0.0634421i
$413$	−0.837128			−0.0411924
$414$		0			0
$415$	−6.34144			−0.311289
$416$	15.9175	+	27.5699i	0.780420	+	1.35173i
$417$		0			0
$418$	19.6900	−	34.1041i	0.963070	−	1.66809i
$419$	−15.1142	+	26.1785i	−0.738376	+	1.27890i	0.214850	+	0.976647i	$0.431074\pi$
$419$	−15.1142	+	26.1785i	−0.738376	+	1.27890i	−0.953226	+	0.302258i	$0.902260\pi$
$420$		0			0
$421$	0.650611	+	1.12689i	0.0317088	+	0.0549213i	0.881444	−	0.472288i	$-0.156572\pi$
$421$	0.650611	+	1.12689i	0.0317088	+	0.0549213i	−0.849736	+	0.527209i	$0.823238\pi$
$422$	−10.9589			−0.533472
$423$		0			0
$424$	13.5925			0.660109
$425$	2.36954	+	4.10416i	0.114939	+	0.199081i
$426$		0			0
$427$	4.62833	−	8.01651i	0.223981	−	0.387946i
$428$	−0.258251	+	0.447303i	−0.0124830	+	0.0216212i
$429$		0			0
$430$	9.91566	+	17.1744i	0.478175	+	0.828224i
$431$	6.84759			0.329837			0.164918	−	0.986307i	$-0.447264\pi$
$431$	6.84759			0.329837			0.164918	+	0.986307i	$0.447264\pi$
$432$		0			0
$433$	−5.73858			−0.275779			−0.137889	−	0.990448i	$-0.544032\pi$
$433$	−5.73858			−0.275779			−0.137889	+	0.990448i	$0.544032\pi$
$434$	−6.09142	−	10.5506i	−0.292397	−	0.506447i
$435$		0			0
$436$	5.71776	−	9.90345i	0.273831	−	0.474289i
$437$	−1.84062	+	3.18804i	−0.0880487	+	0.152505i
$438$		0			0
$439$	−6.16981	−	10.6864i	−0.294469	−	0.510035i	0.680392	−	0.732848i	$-0.261809\pi$
$439$	−6.16981	−	10.6864i	−0.294469	−	0.510035i	−0.974861	+	0.222813i	$0.928476\pi$
$440$	−9.99894			−0.476681
$441$		0			0
$442$	−48.2572			−2.29536
$443$	5.16965	+	8.95410i	0.245618	+	0.425422i	0.962305	−	0.271972i	$-0.0876759\pi$
$443$	5.16965	+	8.95410i	0.245618	+	0.425422i	−0.716687	+	0.697394i	$0.754343\pi$
$444$		0			0
$445$	4.83248	−	8.37010i	0.229082	−	0.396781i
$446$	−20.3456	+	35.2395i	−0.963390	+	1.66864i
$447$		0			0
$448$	−0.204148	−	0.353594i	−0.00964506	−	0.0167057i
$449$	−24.4414			−1.15346			−0.576731	−	0.816934i	$-0.695672\pi$
$449$	−24.4414			−1.15346			−0.576731	+	0.816934i	$0.695672\pi$
$450$		0			0
$451$	24.2857			1.14357
$452$	−0.595821	−	1.03199i	−0.0280251	−	0.0485408i
$453$		0			0
$454$	−17.3053	+	29.9737i	−0.812178	+	1.40673i
$455$	−2.90805	+	5.03689i	−0.136332	+	0.236133i
$456$		0			0
$457$	19.9778	+	34.6025i	0.934520	+	1.61864i	0.775487	+	0.631364i	$0.217504\pi$
$457$	19.9778	+	34.6025i	0.934520	+	1.61864i	0.159033	+	0.987273i	$0.449162\pi$
$458$	0.0181338			0.000847337
$459$		0			0
$460$	−1.06530			−0.0496700
$461$	−7.58273	−	13.1337i	−0.353163	−	0.611696i	0.633639	−	0.773629i	$-0.281561\pi$
$461$	−7.58273	−	13.1337i	−0.353163	−	0.611696i	−0.986802	+	0.161933i	$0.948227\pi$
$462$		0			0
$463$	−5.21428	+	9.03139i	−0.242328	+	0.419724i	−0.961377	−	0.275235i	$-0.911244\pi$
$463$	−5.21428	+	9.03139i	−0.242328	+	0.419724i	0.719049	+	0.694959i	$0.244578\pi$
$464$	4.19150	−	7.25990i	0.194586	−	0.337032i
$465$		0			0
$466$	5.67793	+	9.83446i	0.263025	+	0.455573i
$467$	27.5899			1.27671			0.638353	−	0.769744i	$-0.279616\pi$
$467$	27.5899			1.27671			0.638353	+	0.769744i	$0.279616\pi$
$468$		0			0
$469$	4.51787			0.208616
$470$	3.65512	+	6.33085i	0.168598	+	0.292020i
$471$		0			0
$472$	0.684967	−	1.18640i	0.0315282	−	0.0546084i
$473$	34.6044	−	59.9365i	1.59111	−	2.75588i
$474$		0			0
$475$	−1.84062	−	3.18804i	−0.0844533	−	0.146277i
$476$	−5.04854			−0.231400
$477$		0			0
$478$	27.6601			1.26514
$479$	10.7444	+	18.6099i	0.490924	+	0.850306i	0.999945	−	0.0104482i	$-0.00332581\pi$
$479$	10.7444	+	18.6099i	0.490924	+	0.850306i	−0.509021	+	0.860754i	$0.669992\pi$
$480$		0			0
$481$	−13.0692	+	22.6365i	−0.595903	+	1.03213i
$482$	−5.61831	+	9.73119i	−0.255907	+	0.443244i
$483$		0			0
$484$	−14.0263	−	24.2942i	−0.637557	−	1.10428i
$485$	8.17354			0.371141
$486$		0			0
$487$	11.6178			0.526451			0.263225	−	0.964734i	$-0.415214\pi$
$487$	11.6178			0.526451			0.263225	+	0.964734i	$0.415214\pi$
$488$	7.57413	+	13.1188i	0.342865	+	0.593859i
$489$		0			0
$490$	−0.875400	+	1.51624i	−0.0395466	+	0.0684966i
$491$	17.3701	−	30.0860i	0.783903	−	1.35776i	−0.145749	−	0.989322i	$-0.546559\pi$
$491$	17.3701	−	30.0860i	0.783903	−	1.35776i	0.929652	−	0.368438i	$-0.120107\pi$
$492$		0			0
$493$	3.97616	+	6.88690i	0.179077	+	0.310171i
$494$	37.4854			1.68655
$495$		0			0
$496$	34.7625			1.56088
$497$	5.18337	+	8.97785i	0.232506	+	0.402712i
$498$		0			0
$499$	1.51854	−	2.63020i	0.0679794	−	0.117744i	−0.830032	−	0.557715i	$-0.811678\pi$
$499$	1.51854	−	2.63020i	0.0679794	−	0.117744i	0.898012	+	0.439971i	$0.145011\pi$
$500$	0.532651	−	0.922579i	0.0238209	−	0.0412590i
$501$		0			0
$502$	−3.64045	−	6.30544i	−0.162481	−	0.281425i
$503$	3.40995			0.152042			0.0760210	−	0.997106i	$-0.475778\pi$
$503$	3.40995			0.152042			0.0760210	+	0.997106i	$0.475778\pi$
$504$		0			0
$505$	12.1320			0.539866
$506$	5.34875	+	9.26431i	0.237781	+	0.411849i
$507$		0			0
$508$	6.26223	−	10.8465i	0.277841	−	0.481235i
$509$	−15.6708	+	27.1427i	−0.694597	+	1.20308i	0.275719	+	0.961238i	$0.411084\pi$
$509$	−15.6708	+	27.1427i	−0.694597	+	1.20308i	−0.970316	+	0.241839i	$0.922249\pi$
$510$		0			0
$511$	−6.11729	−	10.5955i	−0.270613	−	0.468715i
$512$	−10.9939			−0.485867
$513$		0			0
$514$	20.5686			0.907240
$515$	−0.697899	−	1.20880i	−0.0307531	−	0.0532660i
$516$		0			0
$517$	12.7559	−	22.0939i	0.561003	−	0.971686i
$518$	−3.93417	+	6.81418i	−0.172857	+	0.299398i
$519$		0			0
$520$	−4.75894	−	8.24272i	−0.208693	−	0.361467i
$521$	11.9819			0.524936			0.262468	−	0.964941i	$-0.415464\pi$
$521$	11.9819			0.524936			0.262468	+	0.964941i	$0.415464\pi$
$522$		0			0
$523$	−23.4259			−1.02434			−0.512172	−	0.858883i	$-0.671159\pi$
$523$	−23.4259			−1.02434			−0.512172	+	0.858883i	$0.671159\pi$
$524$	−0.516761	−	0.895056i	−0.0225748	−	0.0391007i
$525$		0			0
$526$	10.8537	−	18.7991i	0.473242	−	0.819679i
$527$	−16.4883	+	28.5585i	−0.718240	+	1.24403i
$528$		0			0
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$	14.5421			0.631669
$531$		0			0
$532$	3.92163			0.170024
$533$	11.5587	+	20.0202i	0.500661	+	0.867171i
$534$		0			0
$535$	0.242420	−	0.419884i	0.0104807	−	0.0181532i
$536$	−3.69668	+	6.40284i	−0.159672	+	0.276561i
$537$		0			0
$538$	16.5005	+	28.5798i	0.711389	+	1.23216i
$539$	6.11007			0.263179
$540$		0			0
$541$	7.62446			0.327801			0.163901	−	0.986477i	$-0.447592\pi$
$541$	7.62446			0.327801			0.163901	+	0.986477i	$0.447592\pi$
$542$	−18.4592	−	31.9724i	−0.792893	−	1.37333i
$543$		0			0
$544$	12.9699	−	22.4645i	0.556079	−	0.963157i
$545$	−5.36726	+	9.29637i	−0.229908	+	0.398213i
$546$		0			0
$547$	−20.6792	−	35.8175i	−0.884180	−	1.53145i	−0.846650	−	0.532150i	$-0.821384\pi$
$547$	−20.6792	−	35.8175i	−0.884180	−	1.53145i	−0.0375304	−	0.999295i	$-0.511949\pi$
$548$	−11.4702			−0.489982
$549$		0			0
$550$	−10.6975			−0.456143
$551$	−3.08861	−	5.34964i	−0.131579	−	0.227902i
$552$		0			0
$553$	−4.41643	+	7.64948i	−0.187806	+	0.325289i
$554$	−16.1926	+	28.0464i	−0.687956	+	1.19158i
$555$		0			0
$556$	5.76616	+	9.98728i	0.244540	+	0.423555i
$557$	10.2775			0.435472			0.217736	−	0.976008i	$-0.430133\pi$
$557$	10.2775			0.435472			0.217736	+	0.976008i	$0.430133\pi$
$558$		0			0
$559$	65.8790			2.78638
$560$	−2.49787	−	4.32643i	−0.105554	−	0.182825i
$561$		0			0
$562$	−15.4319	+	26.7289i	−0.650957	+	1.12749i
$563$	−4.49496	+	7.78550i	−0.189440	+	0.328120i	−0.945064	−	0.326886i	$-0.894001\pi$
$563$	−4.49496	+	7.78550i	−0.189440	+	0.328120i	0.755624	+	0.655006i	$0.227334\pi$
$564$		0			0
$565$	0.559298	+	0.968732i	0.0235298	+	0.0407549i
$566$	6.63882			0.279050
$567$		0			0
$568$	−16.9648			−0.711829
$569$	3.97112	+	6.87818i	0.166478	+	0.288348i	0.937179	−	0.348849i	$-0.113427\pi$
$569$	3.97112	+	6.87818i	0.166478	+	0.288348i	−0.770701	+	0.637197i	$0.780094\pi$
$570$		0			0
$571$	−19.5862	+	33.9243i	−0.819656	+	1.41969i	0.0862797	+	0.996271i	$0.472502\pi$
$571$	−19.5862	+	33.9243i	−0.819656	+	1.41969i	−0.905936	+	0.423415i	$0.860831\pi$
$572$	18.9287	−	32.7855i	0.791449	−	1.37083i
$573$		0			0
$574$	3.47946	+	6.02661i	0.145230	+	0.251546i
$575$	1.00000			0.0417029
$576$		0			0
$577$	5.80815			0.241796			0.120898	−	0.992665i	$-0.461423\pi$
$577$	5.80815			0.241796			0.120898	+	0.992665i	$0.461423\pi$
$578$	4.77862	+	8.27681i	0.198764	+	0.344270i
$579$		0			0
$580$	0.893806	−	1.54812i	0.0371133	−	0.0642821i
$581$	−3.17072	+	5.49185i	−0.131544	+	0.227840i
$582$		0			0
$583$	−25.3750	−	43.9508i	−1.05093	−	1.82026i
$584$	20.0215			0.828496
$585$		0			0
$586$	−14.1370			−0.583994
$587$	1.00014	+	1.73229i	0.0412802	+	0.0714993i	0.885927	−	0.463824i	$-0.153523\pi$
$587$	1.00014	+	1.73229i	0.0412802	+	0.0714993i	−0.844647	+	0.535323i	$0.820190\pi$
$588$		0			0
$589$	12.8078	−	22.1838i	0.527737	−	0.914067i
$590$	0.732822	−	1.26928i	0.0301698	−	0.0522556i
$591$		0			0
$592$	−11.2258	−	19.4436i	−0.461376	−	0.799126i
$593$	−18.6458			−0.765690			−0.382845	−	0.923813i	$-0.625056\pi$
$593$	−18.6458			−0.765690			−0.382845	+	0.923813i	$0.625056\pi$
$594$		0			0
$595$	4.73907			0.194283
$596$	−7.35860	−	12.7455i	−0.301420	−	0.522074i
$597$		0			0
$598$	−5.09142	+	8.81859i	−0.208204	+	0.360619i
$599$	14.0200	−	24.2833i	0.572840	−	0.992188i	−0.423432	−	0.905928i	$-0.639175\pi$
$599$	14.0200	−	24.2833i	0.572840	−	0.992188i	0.996273	−	0.0862606i	$-0.0274918\pi$
$600$		0			0
$601$	−14.9532	−	25.8996i	−0.609952	−	1.05647i	−0.991248	−	0.132015i	$-0.957855\pi$
$601$	−14.9532	−	25.8996i	−0.609952	−	1.05647i	0.381296	−	0.924453i	$-0.375478\pi$
$602$	19.8313			0.808264
$603$		0			0
$604$	11.5480			0.469882
$605$	13.1665	+	22.8050i	0.535293	+	0.927154i
$606$		0			0
$607$	−7.62634	+	13.2092i	−0.309544	+	0.536145i	−0.978263	−	0.207370i	$-0.933510\pi$
$607$	−7.62634	+	13.2092i	−0.309544	+	0.536145i	0.668719	+	0.743515i	$0.266843\pi$
$608$	−10.0748	+	17.4501i	−0.408587	+	0.707693i
$609$		0			0
$610$	8.10329	+	14.0353i	0.328093	+	0.568273i
$611$	24.2844			0.982441
$612$		0			0
$613$	21.4518			0.866431			0.433215	−	0.901290i	$-0.357379\pi$
$613$	21.4518			0.866431			0.433215	+	0.901290i	$0.357379\pi$
$614$	−0.903891	−	1.56559i	−0.0364781	−	0.0631819i
$615$		0			0
$616$	−4.99947	+	8.65933i	−0.201434	+	0.348894i
$617$	−15.8000	+	27.3664i	−0.636085	+	1.10173i	0.350199	+	0.936675i	$0.386114\pi$
$617$	−15.8000	+	27.3664i	−0.636085	+	1.10173i	−0.986284	+	0.165056i	$0.947220\pi$
$618$		0			0
$619$	−9.37249	−	16.2336i	−0.376712	−	0.652485i	0.613869	−	0.789408i	$-0.289612\pi$
$619$	−9.37249	−	16.2336i	−0.376712	−	0.652485i	−0.990582	+	0.136923i	$0.956279\pi$
$620$	7.41284			0.297707
$621$		0			0
$622$	14.5131			0.581923
$623$	−4.83248	−	8.37010i	−0.193609	−	0.335341i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	17.5686	−	30.4298i	0.702184	−	1.21622i
$627$		0			0
$628$	5.89648	+	10.2130i	0.235295	+	0.407543i
$629$	21.2980			0.849208
$630$		0			0
$631$	−34.9978			−1.39324			−0.696619	−	0.717441i	$-0.745313\pi$
$631$	−34.9978			−1.39324			−0.696619	+	0.717441i	$0.745313\pi$
$632$	−7.22736	−	12.5181i	−0.287489	−	0.497945i
$633$		0			0
$634$	−18.1770	+	31.4834i	−0.721900	+	1.25037i
$635$	−5.87836	+	10.1816i	−0.233276	+	0.404045i
$636$		0			0
$637$	2.90805	+	5.03689i	0.115221	+	0.199569i
$638$	−17.9508			−0.710677
$639$		0			0
$640$	11.6620			0.460983
$641$	−20.6415	−	35.7522i	−0.815291	−	1.41213i	−0.909119	−	0.416537i	$-0.863244\pi$
$641$	−20.6415	−	35.7522i	−0.815291	−	1.41213i	0.0938280	−	0.995588i	$-0.470090\pi$
$642$		0			0
$643$	−2.63091	+	4.55687i	−0.103753	+	0.179705i	−0.913228	−	0.407449i	$-0.866418\pi$
$643$	−2.63091	+	4.55687i	−0.103753	+	0.179705i	0.809475	+	0.587154i	$0.199752\pi$
$644$	−0.532651	+	0.922579i	−0.0209894	+	0.0363547i
$645$		0			0
$646$	−15.2719	−	26.4517i	−0.600865	−	1.04073i
$647$	4.79934			0.188682			0.0943408	−	0.995540i	$-0.469926\pi$
$647$	4.79934			0.188682			0.0943408	+	0.995540i	$0.469926\pi$
$648$		0			0
$649$	−5.11491			−0.200778
$650$	−5.09142	−	8.81859i	−0.199702	−	0.345894i
$651$		0			0
$652$	−5.96919	+	10.3389i	−0.233772	+	0.404904i
$653$	7.23824	−	12.5370i	0.283254	−	0.490611i	−0.688930	−	0.724828i	$-0.741919\pi$
$653$	7.23824	−	12.5370i	0.283254	−	0.490611i	0.972184	+	0.234217i	$0.0752526\pi$
$654$		0			0
$655$	0.485084	+	0.840190i	0.0189538	+	0.0328289i
$656$	−19.8566			−0.775270
$657$		0			0
$658$	7.31024			0.284983
$659$	−14.0086	−	24.2636i	−0.545696	−	0.945174i	−0.998563	−	0.0535955i	$-0.982932\pi$
$659$	−14.0086	−	24.2636i	−0.545696	−	0.945174i	0.452866	−	0.891578i	$-0.350401\pi$
$660$		0			0
$661$	24.2168	−	41.9448i	0.941926	−	1.63146i	0.180134	−	0.983642i	$-0.442347\pi$
$661$	24.2168	−	41.9448i	0.941926	−	1.63146i	0.761792	−	0.647822i	$-0.224320\pi$
$662$	−9.77222	+	16.9260i	−0.379808	+	0.657847i
$663$		0			0
$664$	−5.18879	−	8.98725i	−0.201364	−	0.348773i
$665$	−3.68123			−0.142752
$666$		0			0
$667$	1.67803			0.0649737
$668$	12.5918	+	21.8097i	0.487193	+	0.843843i
$669$		0			0
$670$	−3.95495	+	6.85017i	−0.152793	+	0.264645i
$671$	28.2794	−	48.9814i	1.09171	−	1.89091i
$672$		0			0
$673$	17.9700	+	31.1250i	0.692693	+	1.19978i	0.970952	+	0.239274i	$0.0769094\pi$
$673$	17.9700	+	31.1250i	0.692693	+	1.19978i	−0.278259	+	0.960506i	$0.589757\pi$
$674$	−10.6317			−0.409518
$675$		0			0
$676$	22.1871			0.853350
$677$	−14.2219	−	24.6331i	−0.546593	−	0.946727i	−0.998505	−	0.0546646i	$-0.982591\pi$
$677$	−14.2219	−	24.6331i	−0.546593	−	0.946727i	0.451911	−	0.892063i	$-0.350742\pi$
$678$		0			0
$679$	4.08677	−	7.07849i	0.156836	−	0.271648i
$680$	−3.87767	+	6.71632i	−0.148702	+	0.257559i
$681$		0			0
$682$	−37.2190	−	64.4651i	−1.42519	−	2.46850i
$683$	41.1926			1.57619			0.788096	−	0.615553i	$-0.211067\pi$
$683$	41.1926			1.57619			0.788096	+	0.615553i	$0.211067\pi$
$684$		0			0
$685$	10.7671			0.411389
$686$	0.875400	+	1.51624i	0.0334229	+	0.0578902i
$687$		0			0
$688$	−28.2933	+	49.0055i	−1.07867	+	1.86832i
$689$	24.1542	−	41.8363i	0.920202	−	1.59384i
$690$		0			0
$691$	3.28345	+	5.68710i	0.124908	+	0.216348i	0.921697	−	0.387910i	$-0.126803\pi$
$691$	3.28345	+	5.68710i	0.124908	+	0.216348i	−0.796789	+	0.604258i	$0.793470\pi$
$692$	3.29076			0.125096
$693$		0			0
$694$	34.1495			1.29630
$695$	−5.41270	−	9.37507i	−0.205315	−	0.355617i
$696$		0			0
$697$	9.41822	−	16.3128i	0.356740	−	0.617892i
$698$	−11.0197	+	19.0867i	−0.417103	+	0.722443i
$699$		0			0
$700$	−0.532651	−	0.922579i	−0.0201323	−	0.0348702i
$701$	2.61012			0.0985828			0.0492914	−	0.998784i	$-0.484304\pi$
$701$	2.61012			0.0985828			0.0492914	+	0.998784i	$0.484304\pi$
$702$		0			0
$703$	−16.5440			−0.623967
$704$	−1.24735	−	2.16048i	−0.0470115	−	0.0814262i
$705$		0			0
$706$	−14.3716	+	24.8923i	−0.540881	+	0.936833i
$707$	6.06599	−	10.5066i	0.228135	−	0.395141i
$708$		0			0
$709$	6.45282	+	11.1766i	0.242341	+	0.419746i	0.961381	−	0.275223i	$-0.0887515\pi$
$709$	6.45282	+	11.1766i	0.242341	+	0.419746i	−0.719040	+	0.694969i	$0.755418\pi$
$710$	−18.1501			−0.681160
$711$		0			0
$712$	15.8164			0.592745
$713$	3.47922	+	6.02618i	0.130298	+	0.225682i
$714$		0			0
$715$	−17.7684	+	30.7757i	−0.664500	+	1.15095i
$716$	12.2257	−	21.1756i	0.456897	−	0.791369i
$717$		0			0
$718$	11.5837	+	20.0635i	0.432299	+	0.748764i
$719$	−8.13828			−0.303507			−0.151753	−	0.988418i	$-0.548492\pi$
$719$	−8.13828			−0.303507			−0.151753	+	0.988418i	$0.548492\pi$
$720$		0			0
$721$	−1.39580			−0.0519823
$722$	−4.76963	−	8.26125i	−0.177507	−	0.307452i
$723$		0			0
$724$	2.18402	−	3.78283i	0.0811685	−	0.140588i
$725$	−0.839016	+	1.45322i	−0.0311603	+	0.0539712i
$726$		0			0
$727$	−14.2624	−	24.7031i	−0.528962	−	0.916189i	−0.999430	−	0.0337717i	$-0.989248\pi$
$727$	−14.2624	−	24.7031i	−0.528962	−	0.916189i	0.470468	−	0.882417i	$-0.344085\pi$
$728$	−9.51787			−0.352756
$729$		0			0
$730$	21.4203			0.792801
$731$	−26.8397	−	46.4878i	−0.992703	−	1.71941i
$732$		0			0
$733$	18.9040	−	32.7427i	0.698236	−	1.20938i	−0.270841	−	0.962624i	$-0.587302\pi$
$733$	18.9040	−	32.7427i	0.698236	−	1.20938i	0.969077	−	0.246757i	$-0.0793649\pi$
$734$	−17.7464	+	30.7377i	−0.655033	+	1.13455i
$735$		0			0
$736$	−2.73680	−	4.74027i	−0.100880	−	0.174729i
$737$	27.6045			1.01683
$738$		0			0
$739$	−39.0949			−1.43813			−0.719065	−	0.694943i	$-0.755430\pi$
$739$	−39.0949			−1.43813			−0.719065	+	0.694943i	$0.755430\pi$
$740$	−2.39381	−	4.14619i	−0.0879980	−	0.152417i
$741$		0			0
$742$	7.27105	−	12.5938i	0.266929	−	0.462334i
$743$	4.65459	−	8.06198i	0.170760	−	0.295765i	−0.767926	−	0.640539i	$-0.778711\pi$
$743$	4.65459	−	8.06198i	0.170760	−	0.295765i	0.938686	+	0.344774i	$0.112044\pi$
$744$		0			0
$745$	6.90752	+	11.9642i	0.253072	+	0.438333i
$746$	−52.9630			−1.93911
$747$		0			0
$748$	−30.8469			−1.12788
$749$	−0.242420	−	0.419884i	−0.00885783	−	0.0153422i
$750$		0			0
$751$	8.88756	−	15.3937i	0.324312	−	0.561725i	−0.657061	−	0.753837i	$-0.728201\pi$
$751$	8.88756	−	15.3937i	0.324312	−	0.561725i	0.981373	+	0.192113i	$0.0615340\pi$
$752$	−10.4295	+	18.0645i	−0.380325	+	0.658743i
$753$		0			0
$754$	−8.54356	−	14.7979i	−0.311138	−	0.538907i
$755$	−10.8401			−0.394512
$756$		0			0
$757$	−11.2184			−0.407739			−0.203870	−	0.978998i	$-0.565352\pi$
$757$	−11.2184			−0.407739			−0.203870	+	0.978998i	$0.565352\pi$
$758$	−0.611556	−	1.05925i	−0.0222127	−	0.0384736i
$759$		0			0
$760$	3.01211	−	5.21713i	0.109261	−	0.189245i
$761$	−21.0958	+	36.5391i	−0.764723	+	1.32454i	0.175669	+	0.984449i	$0.443791\pi$
$761$	−21.0958	+	36.5391i	−0.764723	+	1.32454i	−0.940393	+	0.340091i	$0.889542\pi$
$762$		0			0
$763$	5.36726	+	9.29637i	0.194308	+	0.336551i
$764$	9.30521			0.336651
$765$		0			0
$766$	10.6714			0.385572
$767$	−2.43441	−	4.21652i	−0.0879015	−	0.152250i
$768$		0			0
$769$	−1.72091	+	2.98070i	−0.0620575	+	0.107487i	−0.895385	−	0.445293i	$-0.853100\pi$
$769$	−1.72091	+	2.98070i	−0.0620575	+	0.107487i	0.833327	+	0.552780i	$0.186433\pi$
$770$	−5.34875	+	9.26431i	−0.192756	+	0.333863i
$771$		0			0
$772$	8.61980	+	14.9299i	0.310234	+	0.537340i
$773$	−20.9848			−0.754770			−0.377385	−	0.926056i	$-0.623177\pi$
$773$	−20.9848			−0.754770			−0.377385	+	0.926056i	$0.623177\pi$
$774$		0			0
$775$	−6.95844			−0.249954
$776$	6.68787	+	11.5837i	0.240081	+	0.415832i
$777$		0			0
$778$	−11.8694	+	20.5585i	−0.425540	+	0.737056i
$779$	−7.31592	+	12.6715i	−0.262120	+	0.454005i
$780$		0			0
$781$	31.6707	+	54.8553i	1.13327	+	1.96288i
$782$	8.29717			0.296706
$783$		0			0
$784$	−4.99574			−0.178419
$785$	−5.53503	−	9.58695i	−0.197554	−	0.342173i
$786$		0			0
$787$	13.3900	−	23.1922i	0.477303	−	0.826713i	−0.522359	−	0.852726i	$-0.674948\pi$
$787$	13.3900	−	23.1922i	0.477303	−	0.826713i	0.999662	+	0.0260129i	$0.00828109\pi$
$788$	−0.222996	+	0.386240i	−0.00794389	+	0.0137592i
$789$		0			0
$790$	−7.73229	−	13.3927i	−0.275103	−	0.476492i
$791$	1.11860			0.0397727
$792$		0			0
$793$	53.8377			1.91183
$794$	−14.3661	−	24.8828i	−0.509834	−	0.883058i
$795$		0			0
$796$	3.98778	−	6.90704i	0.141343	−	0.244814i
$797$	24.8167	−	42.9839i	0.879054	−	1.52257i	0.0266739	−	0.999644i	$-0.491508\pi$
$797$	24.8167	−	42.9839i	0.879054	−	1.52257i	0.852380	−	0.522922i	$-0.175158\pi$
$798$		0			0
$799$	−9.89368	−	17.1364i	−0.350013	−	0.606241i
$800$	5.47360			0.193521
$801$		0			0
$802$	−6.12926			−0.216432
$803$	−37.3770	−	64.7389i	−1.31901	−	2.28459i
$804$		0			0
$805$	0.500000	−	0.866025i	0.0176227	−	0.0305234i
$806$	35.4283	−	61.3636i	1.24791	−	2.16144i
$807$		0			0
$808$	9.92681	+	17.1937i	0.349224	+	0.604873i
$809$	55.4296			1.94880			0.974401	−	0.224818i	$-0.0721789\pi$
$809$	55.4296			1.94880			0.974401	+	0.224818i	$0.0721789\pi$
$810$		0			0
$811$	−51.0851			−1.79384			−0.896920	−	0.442193i	$-0.854200\pi$
$811$	−51.0851			−1.79384			−0.896920	+	0.442193i	$0.854200\pi$
$812$	−0.893806	−	1.54812i	−0.0313664	−	0.0543282i
$813$		0			0
$814$	−24.0380	+	41.6351i	−0.842532	+	1.45931i
$815$	5.60329	−	9.70518i	0.196275	−	0.339958i
$816$		0			0
$817$	20.8487	+	36.1109i	0.729402	+	1.26336i
$818$	−11.8305			−0.413642
$819$		0			0
$820$	−4.23427			−0.147867
$821$	2.55717	+	4.42914i	0.0892457	+	0.154578i	0.907192	−	0.420716i	$-0.138221\pi$
$821$	2.55717	+	4.42914i	0.0892457	+	0.154578i	−0.817947	+	0.575294i	$0.804888\pi$
$822$		0			0
$823$	18.6307	−	32.2693i	0.649425	−	1.12484i	−0.333835	−	0.942632i	$-0.608343\pi$
$823$	18.6307	−	32.2693i	0.649425	−	1.12484i	0.983260	−	0.182206i	$-0.0583238\pi$
$824$	1.14209	−	1.97816i	0.0397866	−	0.0689124i
$825$		0			0
$826$	−0.732822	−	1.26928i	−0.0254981	−	0.0441641i
$827$	−23.9366			−0.832356			−0.416178	−	0.909283i	$-0.636631\pi$
$827$	−23.9366			−0.832356			−0.416178	+	0.909283i	$0.636631\pi$
$828$		0			0
$829$	−11.3556			−0.394397			−0.197198	−	0.980364i	$-0.563184\pi$
$829$	−11.3556			−0.394397			−0.197198	+	0.980364i	$0.563184\pi$
$830$	−5.55130	−	9.61513i	−0.192688	−	0.333746i
$831$		0			0
$832$	1.18734	−	2.05654i	0.0411637	−	0.0712976i
$833$	2.36954	−	4.10416i	0.0820995	−	0.142201i
$834$		0			0
$835$	−11.8200	−	20.4728i	−0.409047	−	0.708490i
$836$	23.9614			0.828722
$837$		0			0
$838$	−52.9238			−1.82822
$839$	−18.9639	−	32.8465i	−0.654707	−	1.13399i	−0.981967	−	0.189051i	$-0.939459\pi$
$839$	−18.9639	−	32.8465i	−0.654707	−	1.13399i	0.327260	−	0.944934i	$-0.393875\pi$
$840$		0			0
$841$	13.0921	−	22.6762i	0.451452	−	0.781938i
$842$	−1.13909	+	1.97296i	−0.0392556	+	0.0679927i
$843$		0			0
$844$	−3.33407	−	5.77477i	−0.114763	−	0.198776i
$845$	−20.8270			−0.716472
$846$		0			0
$847$	26.3329			0.904810
$848$	20.7472	+	35.9352i	0.712463	+	1.23402i
$849$		0			0
$850$	−4.14858	+	7.18556i	−0.142295	+	0.246463i
$851$	2.24707	−	3.89203i	0.0770285	−	0.133417i
$852$		0			0
$853$	−19.5193	−	33.8085i	−0.668329	−	1.15758i	−0.978371	−	0.206857i	$-0.933677\pi$
$853$	−19.5193	−	33.8085i	−0.668329	−	1.15758i	0.310042	−	0.950723i	$-0.399657\pi$
$854$	16.2066			0.554578
$855$		0			0
$856$	0.793426			0.0271187
$857$	11.8587	+	20.5399i	0.405087	+	0.701631i	0.994332	−	0.106324i	$-0.0339080\pi$
$857$	11.8587	+	20.5399i	0.405087	+	0.701631i	−0.589245	+	0.807954i	$0.700575\pi$
$858$		0			0
$859$	−22.8542	+	39.5847i	−0.779777	+	1.35061i	0.152294	+	0.988335i	$0.451334\pi$
$859$	−22.8542	+	39.5847i	−0.779777	+	1.35061i	−0.932070	+	0.362278i	$0.881999\pi$
$860$	−6.03334	+	10.4500i	−0.205735	+	0.356344i
$861$		0			0
$862$	5.99438	+	10.3826i	0.204169	+	0.353632i
$863$	5.54957			0.188909			0.0944547	−	0.995529i	$-0.469889\pi$
$863$	5.54957			0.188909			0.0944547	+	0.995529i	$0.469889\pi$
$864$		0			0
$865$	−3.08904			−0.105031
$866$	−5.02356	−	8.70105i	−0.170707	−	0.295674i
$867$		0			0
$868$	3.70642	−	6.41971i	0.125804	−	0.217899i
$869$	−26.9847	+	46.7389i	−0.915393	+	1.58551i
$870$		0			0
$871$	13.1382	+	22.7560i	0.445171	+	0.771059i
$872$	−17.5667			−0.594884
$873$		0			0
$874$	−6.44511			−0.218009
$875$	0.500000	+	0.866025i	0.0169031	+	0.0292770i
$876$		0			0
$877$	−10.6589	+	18.4617i	−0.359924	+	0.623406i	−0.987948	−	0.154788i	$-0.950531\pi$
$877$	−10.6589	+	18.4617i	−0.359924	+	0.623406i	0.628024	+	0.778194i	$0.283864\pi$
$878$	10.8021	−	18.7098i	0.364553	−	0.631425i
$879$		0			0
$880$	−15.2621	−	26.4348i	−0.514487	−	0.891117i
$881$	−8.12987			−0.273902			−0.136951	−	0.990578i	$-0.543730\pi$
$881$	−8.12987			−0.273902			−0.136951	+	0.990578i	$0.543730\pi$
$882$		0			0
$883$	−4.24853			−0.142975			−0.0714873	−	0.997442i	$-0.522775\pi$
$883$	−4.24853			−0.142975			−0.0714873	+	0.997442i	$0.522775\pi$
$884$	−14.6814	−	25.4290i	−0.493789	−	0.855268i
$885$		0			0
$886$	−9.05103	+	15.6768i	−0.304075	+	0.526674i
$887$	−25.7749	+	44.6434i	−0.865435	+	1.49898i	0.00117920	+	0.999999i	$0.499625\pi$
$887$	−25.7749	+	44.6434i	−0.865435	+	1.49898i	−0.866614	+	0.498978i	$0.833709\pi$
$888$		0			0
$889$	5.87836	+	10.1816i	0.197154	+	0.341480i
$890$	16.9214			0.567207
$891$		0			0
$892$	−24.7592			−0.828998
$893$	7.68525	+	13.3113i	0.257177	+	0.445444i
$894$		0			0
$895$	−11.4763	+	19.8776i	−0.383611	+	0.664433i
$896$	5.83102	−	10.0996i	0.194801	−	0.337405i
$897$		0			0
$898$	−21.3960	−	37.0590i	−0.713995	−	1.23668i
$899$	−11.6765			−0.389432
$900$		0			0
$901$	−39.3626			−1.31136
$902$	21.2597	+	36.8230i	0.707872	+	1.22607i
$903$		0			0
$904$	−0.915274	+	1.58530i	−0.0304415	+	0.0527263i
$905$	−2.05014	+	3.55095i	−0.0681490	+	0.118038i
$906$		0			0
$907$	1.07275	+	1.85806i	0.0356202	+	0.0616959i	0.883286	−	0.468835i	$-0.155326\pi$
$907$	1.07275	+	1.85806i	0.0356202	+	0.0616959i	−0.847666	+	0.530531i	$0.821993\pi$
$908$	−21.0594			−0.698880
$909$		0			0
$910$	−10.1828			−0.337558
$911$	17.1698	+	29.7389i	0.568860	+	0.985295i	0.996679	+	0.0814303i	$0.0259488\pi$
$911$	17.1698	+	29.7389i	0.568860	+	0.985295i	−0.427819	+	0.903865i	$0.640718\pi$
$912$		0			0
$913$	−19.3733	+	33.5556i	−0.641163	+	1.11053i
$914$	−34.9771	+	60.5821i	−1.15694	+	2.00388i
$915$		0			0
$916$	0.00551690	+	0.00955555i	0.000182283	+	0.000315724i
$917$	0.970168			0.0320378
$918$		0			0
$919$	2.02313			0.0667370			0.0333685	−	0.999443i	$-0.489377\pi$
$919$	2.02313			0.0667370			0.0333685	+	0.999443i	$0.489377\pi$
$920$	0.818235	+	1.41722i	0.0269764	+	0.0467245i
$921$		0			0
$922$	13.2759	−	22.9945i	0.437217	−	0.757282i
$923$	−30.1470	+	52.2161i	−0.992300	+	1.71871i
$924$		0			0
$925$	2.24707	+	3.89203i	0.0738831	+	0.127969i
$926$	−18.2583			−0.600006
$927$		0			0
$928$	9.18487			0.301508
$929$	−5.84648	−	10.1264i	−0.191817	−	0.332237i	0.754036	−	0.656834i	$-0.228105\pi$
$929$	−5.84648	−	10.1264i	−0.191817	−	0.332237i	−0.945852	+	0.324597i	$0.894771\pi$
$930$		0			0
$931$	−1.84062	+	3.18804i	−0.0603238	+	0.104484i
$932$	−3.45482	+	5.98393i	−0.113167	+	0.196010i
$933$		0			0
$934$	24.1522	+	41.8328i	0.790283	+	1.36881i
$935$	28.9560			0.946964
$936$		0			0
$937$	13.5123			0.441427			0.220713	−	0.975339i	$-0.429161\pi$
$937$	13.5123			0.441427			0.220713	+	0.975339i	$0.429161\pi$
$938$	3.95495	+	6.85017i	0.129134	+	0.223666i
$939$		0			0
$940$	−2.22401	+	3.85211i	−0.0725394	+	0.125642i
$941$	−2.79192	+	4.83575i	−0.0910140	+	0.157641i	−0.907938	−	0.419104i	$-0.862344\pi$
$941$	−2.79192	+	4.83575i	−0.0910140	+	0.157641i	0.816924	+	0.576745i	$0.195677\pi$
$942$		0			0
$943$	−1.98736	−	3.44220i	−0.0647172	−	0.112093i
$944$	4.18207			0.136115
$945$		0			0
$946$	121.171			3.93960
$947$	−12.6053	−	21.8331i	−0.409618	−	0.709480i	0.585229	−	0.810868i	$-0.301005\pi$
$947$	−12.6053	−	21.8331i	−0.409618	−	0.709480i	−0.994847	+	0.101389i	$0.967671\pi$
$948$		0			0
$949$	35.5788	−	61.6243i	1.15494	−	2.00041i
$950$	3.22255	−	5.58163i	0.104553	−	0.181092i
$951$		0			0
$952$	3.87767	+	6.71632i	0.125676	+	0.217677i
$953$	−32.3742			−1.04870			−0.524351	−	0.851502i	$-0.675692\pi$
$953$	−32.3742			−1.04870			−0.524351	+	0.851502i	$0.675692\pi$
$954$		0			0
$955$	−8.73481			−0.282652
$956$	8.41512	+	14.5754i	0.272164	+	0.471403i
$957$		0			0
$958$	−18.8113	+	32.5821i	−0.607766	+	1.05268i
$959$	5.38354	−	9.32456i	0.173843	−	0.301106i
$960$		0			0
$961$	−8.70992	−	15.0860i	−0.280965	−	0.486646i
$962$	−45.7630			−1.47546
$963$		0			0
$964$	−6.83710			−0.220208
$965$	−8.09142	−	14.0147i	−0.260472	−	0.451151i
$966$		0			0
$967$	−13.7076	+	23.7423i	−0.440808	+	0.763502i	−0.997750	−	0.0670499i	$-0.978641\pi$
$967$	−13.7076	+	23.7423i	−0.440808	+	0.763502i	0.556942	+	0.830552i	$0.311975\pi$
$968$	−21.5465	+	37.3196i	−0.692531	+	1.19950i
$969$		0			0
$970$	7.15512	+	12.3930i	0.229737	+	0.397916i
$971$	−16.6145			−0.533185			−0.266592	−	0.963809i	$-0.585898\pi$
$971$	−16.6145			−0.533185			−0.266592	+	0.963809i	$0.585898\pi$
$972$		0			0
$973$	−10.8254			−0.347046
$974$	10.1702	+	17.6153i	0.325874	+	0.564430i
$975$		0			0
$976$	−23.1219	+	40.0484i	−0.740115	+	1.28192i
$977$	−30.5289	+	52.8776i	−0.976707	+	1.69171i	−0.302523	+	0.953142i	$0.597829\pi$
$977$	−30.5289	+	52.8776i	−0.976707	+	1.69171i	−0.674183	+	0.738564i	$0.735504\pi$
$978$		0			0
$979$	−29.5268	−	51.1419i	−0.943680	−	1.63450i
$980$	−1.06530			−0.0340298
$981$		0			0
$982$	60.8233			1.94095
$983$	3.51023	+	6.07990i	0.111959	+	0.193919i	0.916560	−	0.399897i	$-0.130954\pi$
$983$	3.51023	+	6.07990i	0.111959	+	0.193919i	−0.804601	+	0.593816i	$0.797621\pi$
$984$		0			0
$985$	0.209326	−	0.362564i	0.00666969	−	0.0115522i
$986$	−6.96146	+	12.0576i	−0.221698	+	0.383992i
$987$		0			0
$988$	11.4043	+	19.7528i	0.362819	+	0.628421i
$989$	−11.3270			−0.360178
$990$		0			0
$991$	60.0698			1.90818			0.954090	−	0.299522i	$-0.0968270\pi$
$991$	60.0698			1.90818			0.954090	+	0.299522i	$0.0968270\pi$
$992$	19.0438	+	32.9849i	0.604643	+	1.04727i
$993$		0			0
$994$	−9.07504	+	15.7184i	−0.287843	+	0.498558i
$995$	−3.74333	+	6.48365i	−0.118672	+	0.205545i
$996$		0			0
$997$	−7.44502	−	12.8951i	−0.235786	−	0.408393i	0.723715	−	0.690099i	$-0.242433\pi$
$997$	−7.44502	−	12.8951i	−0.235786	−	0.408393i	−0.959501	+	0.281706i	$0.909100\pi$
$998$	5.31734			0.168317
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.i.d.631.4		8
3.2	odd	2		315.2.i.c.211.1	yes	8
9.2	odd	6		315.2.i.c.106.1	✓	8
9.4	even	3		2835.2.a.p.1.1		4
9.5	odd	6		2835.2.a.m.1.4		4
9.7	even	3	inner	945.2.i.d.316.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.i.c.106.1	✓	8	9.2	odd	6
315.2.i.c.211.1	yes	8	3.2	odd	2
945.2.i.d.316.4		8	9.7	even	3	inner
945.2.i.d.631.4		8	1.1	even	1	trivial
2835.2.a.m.1.4		4	9.5	odd	6
2835.2.a.p.1.1		4	9.4	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.875400 + 1.51624i) q^{2} +(-0.532651 + 0.922579i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{7} +1.63647 q^{8} +O(q^{10})\)	\(q+(0.875400 + 1.51624i) q^{2} +(-0.532651 + 0.922579i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{7} +1.63647 q^{8} +1.75080 q^{10} +(-3.05503 - 5.29147i) q^{11} +(2.90805 - 5.03689i) q^{13} +(0.875400 - 1.51624i) q^{14} +(2.49787 + 4.32643i) q^{16} -4.73907 q^{17} +3.68123 q^{19} +(0.532651 + 0.922579i) q^{20} +(5.34875 - 9.26431i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{25} +10.1828 q^{26} +1.06530 q^{28} +(-0.839016 - 1.45322i) q^{29} +(3.47922 - 6.02618i) q^{31} +(-2.73680 + 4.74027i) q^{32} +(-4.14858 - 7.18556i) q^{34} -1.00000 q^{35} -4.49413 q^{37} +(3.22255 + 5.58163i) q^{38} +(0.818235 - 1.41722i) q^{40} +(-1.98736 + 3.44220i) q^{41} +(5.66350 + 9.80947i) q^{43} +6.50907 q^{44} -1.75080 q^{46} +(2.08768 + 3.61598i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(0.875400 - 1.51624i) q^{50} +(3.09795 + 5.36581i) q^{52} +8.30597 q^{53} -6.11007 q^{55} +(-0.818235 - 1.41722i) q^{56} +(1.46895 - 2.54430i) q^{58} +(0.418564 - 0.724974i) q^{59} +(4.62833 + 8.01651i) q^{61} +12.1828 q^{62} +0.408295 q^{64} +(-2.90805 - 5.03689i) q^{65} +(-2.25894 + 3.91259i) q^{67} +(2.52427 - 4.37217i) q^{68} +(-0.875400 - 1.51624i) q^{70} -10.3667 q^{71} +12.2346 q^{73} +(-3.93417 - 6.81418i) q^{74} +(-1.96081 + 3.39623i) q^{76} +(-3.05503 + 5.29147i) q^{77} +(-4.41643 - 7.64948i) q^{79} +4.99574 q^{80} -6.95892 q^{82} +(-3.17072 - 5.49185i) q^{83} +(-2.36954 + 4.10416i) q^{85} +(-9.91566 + 17.1744i) q^{86} +(-4.99947 - 8.65933i) q^{88} +9.66496 q^{89} -5.81610 q^{91} +(-0.532651 - 0.922579i) q^{92} +(-3.65512 + 6.33085i) q^{94} +(1.84062 - 3.18804i) q^{95} +(4.08677 + 7.07849i) q^{97} -1.75080 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) \) 8 * q - q^2 - q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8	\( 8 q - q^{2} - q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8} - 2 q^{10} - q^{11} + 12 q^{13} - q^{14} + q^{16} - 10 q^{17} - 18 q^{19} + q^{20} + 17 q^{22} - 4 q^{23} - 4 q^{25} + 2 q^{26} + 2 q^{28} - 15 q^{29} + 16 q^{31} - 2 q^{32} + 11 q^{34} - 8 q^{35} - 30 q^{37} + 24 q^{38} + 3 q^{40} - 2 q^{41} + 7 q^{43} - 6 q^{44} + 2 q^{46} - 10 q^{47} - 4 q^{49} - q^{50} + 15 q^{52} - 2 q^{55} - 3 q^{56} - 17 q^{58} - 13 q^{59} + 32 q^{61} + 18 q^{62} - 30 q^{64} - 12 q^{65} + 41 q^{68} + q^{70} - 26 q^{71} - 4 q^{73} + 13 q^{74} + 11 q^{76} - q^{77} + 2 q^{80} + 12 q^{82} + 17 q^{83} - 5 q^{85} - 15 q^{86} + 11 q^{88} + 34 q^{89} - 24 q^{91} - q^{92} - 15 q^{94} - 9 q^{95} + 4 q^{97} + 2 q^{98}+O(q^{100}) \) 8 * q - q^2 - q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8 - 2 * q^10 - q^11 + 12 * q^13 - q^14 + q^16 - 10 * q^17 - 18 * q^19 + q^20 + 17 * q^22 - 4 * q^23 - 4 * q^25 + 2 * q^26 + 2 * q^28 - 15 * q^29 + 16 * q^31 - 2 * q^32 + 11 * q^34 - 8 * q^35 - 30 * q^37 + 24 * q^38 + 3 * q^40 - 2 * q^41 + 7 * q^43 - 6 * q^44 + 2 * q^46 - 10 * q^47 - 4 * q^49 - q^50 + 15 * q^52 - 2 * q^55 - 3 * q^56 - 17 * q^58 - 13 * q^59 + 32 * q^61 + 18 * q^62 - 30 * q^64 - 12 * q^65 + 41 * q^68 + q^70 - 26 * q^71 - 4 * q^73 + 13 * q^74 + 11 * q^76 - q^77 + 2 * q^80 + 12 * q^82 + 17 * q^83 - 5 * q^85 - 15 * q^86 + 11 * q^88 + 34 * q^89 - 24 * q^91 - q^92 - 15 * q^94 - 9 * q^95 + 4 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more