LMFDB - Embedded newform 1764.2.b.j.1567.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1567,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1764.1567");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.b (of order $2$, degree $1$, 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1567.8
Root			$1.40376 - 0.171630i$ of defining polynomial
Character	$\chi$	$=$	1764.1567
Dual form			1764.2.b.j.1567.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40376 + 0.171630i) q^{2} +(1.94109 + 0.481855i) q^{4} -0.963711i q^{5} +(2.64212 + 1.00956i) q^{8} +O(q^{10})$	\(q+(1.40376 + 0.171630i) q^{2} +(1.94109 + 0.481855i) q^{4} -0.963711i q^{5} +(2.64212 + 1.00956i) q^{8} +(0.165402 - 1.35282i) q^{10} -5.48322i q^{11} -3.75117i q^{13} +(3.53563 + 1.87065i) q^{16} -0.686521i q^{17} -4.88217 q^{19} +(0.464369 - 1.87065i) q^{20} +(0.941086 - 7.69713i) q^{22} -1.24090i q^{23} +4.07126 q^{25} +(0.643814 - 5.26574i) q^{26} +2.48011 q^{29} -4.82802 q^{31} +(4.64212 + 3.23276i) q^{32} +(0.117828 - 0.963711i) q^{34} -2.73287 q^{37} +(-6.85340 - 0.837928i) q^{38} +(0.972923 - 2.54624i) q^{40} -9.42976i q^{41} +5.97437i q^{43} +(2.64212 - 10.6434i) q^{44} +(0.212976 - 1.74193i) q^{46} +3.61504 q^{47} +(5.71508 + 0.698752i) q^{50} +(1.80752 - 7.28134i) q^{52} +4.09515 q^{53} -5.28424 q^{55} +(3.48148 + 0.425661i) q^{58} +12.6863 q^{59} +10.4121i q^{61} +(-6.77738 - 0.828634i) q^{62} +(5.96158 + 5.33475i) q^{64} -3.61504 q^{65} +9.43847i q^{67} +(0.330804 - 1.33260i) q^{68} -10.1163i q^{71} +6.66089i q^{73} +(-3.83629 - 0.469043i) q^{74} +(-9.47672 - 2.35250i) q^{76} -1.41442i q^{79} +(1.80276 - 3.40733i) q^{80} +(1.61843 - 13.2371i) q^{82} +0.543780 q^{83} -0.661608 q^{85} +(-1.02538 + 8.38658i) q^{86} +(5.53563 - 14.4873i) q^{88} -0.554380i q^{89} +(0.597935 - 2.40870i) q^{92} +(5.07465 + 0.620450i) q^{94} +4.70500i q^{95} -10.8747i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{4} - 4 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^4 - 4 * q^8	$ 8 q + 2 q^{2} + 2 q^{4} - 4 q^{8} + 8 q^{10} + 10 q^{16} - 12 q^{19} + 22 q^{20} - 6 q^{22} - 4 q^{25} - 6 q^{26} + 16 q^{29} + 12 q^{31} + 12 q^{32} + 28 q^{34} - 12 q^{37} - 2 q^{38} - 4 q^{40} - 4 q^{44} - 12 q^{46} - 8 q^{47} - 2 q^{50} - 4 q^{52} - 8 q^{53} + 8 q^{55} - 14 q^{58} + 28 q^{59} - 48 q^{62} + 2 q^{64} + 8 q^{65} + 16 q^{68} - 38 q^{74} - 44 q^{76} + 6 q^{80} + 4 q^{82} + 4 q^{83} - 32 q^{85} - 6 q^{86} + 26 q^{88} + 28 q^{92} + 32 q^{94}+O(q^{100}) $ 8 * q + 2 * q^2 + 2 * q^4 - 4 * q^8 + 8 * q^10 + 10 * q^16 - 12 * q^19 + 22 * q^20 - 6 * q^22 - 4 * q^25 - 6 * q^26 + 16 * q^29 + 12 * q^31 + 12 * q^32 + 28 * q^34 - 12 * q^37 - 2 * q^38 - 4 * q^40 - 4 * q^44 - 12 * q^46 - 8 * q^47 - 2 * q^50 - 4 * q^52 - 8 * q^53 + 8 * q^55 - 14 * q^58 + 28 * q^59 - 48 * q^62 + 2 * q^64 + 8 * q^65 + 16 * q^68 - 38 * q^74 - 44 * q^76 + 6 * q^80 + 4 * q^82 + 4 * q^83 - 32 * q^85 - 6 * q^86 + 26 * q^88 + 28 * q^92 + 32 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	1.40376	+	0.171630i	0.992608	+	0.121361i
$2$	1.40376	+	0.171630i	0.992608	+	0.121361i
$3$		0			0
$3$		0			0
$4$	1.94109	+	0.481855i	0.970543	+	0.240928i
$5$		−	0.963711i		−	0.430985i	−0.976506	−	0.215492i	$-0.930864\pi$
$5$		−	0.963711i		−	0.430985i	0.976506	−	0.215492i	$-0.0691356\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	2.64212	+	1.00956i	0.934130	+	0.356933i
$9$		0			0
$10$	0.165402	−	1.35282i	0.0523047	−	0.427799i
$11$		−	5.48322i		−	1.65325i	−0.562751	−	0.826626i	$-0.690257\pi$
$11$		−	5.48322i		−	1.65325i	0.562751	−	0.826626i	$-0.309743\pi$
$12$		0			0
$13$		−	3.75117i		−	1.04039i	−0.854048	−	0.520193i	$-0.825860\pi$
$13$		−	3.75117i		−	1.04039i	0.854048	−	0.520193i	$-0.174140\pi$
$14$		0			0
$15$		0			0
$16$	3.53563	+	1.87065i	0.883908	+	0.467661i
$17$		−	0.686521i		−	0.166506i	−0.996528	−	0.0832529i	$-0.973469\pi$
$17$		−	0.686521i		−	0.166506i	0.996528	−	0.0832529i	$-0.0265309\pi$
$18$		0			0
$19$	−4.88217			−1.12005			−0.560024	−	0.828477i	$-0.689208\pi$
$19$	−4.88217			−1.12005			−0.560024	+	0.828477i	$0.689208\pi$
$20$	0.464369	−	1.87065i	0.103836	−	0.418289i
$21$		0			0
$22$	0.941086	−	7.69713i	0.200640	−	1.64103i
$23$		−	1.24090i		−	0.258746i	−0.991596	−	0.129373i	$-0.958704\pi$
$23$		−	1.24090i		−	0.258746i	0.991596	−	0.129373i	$-0.0412964\pi$
$24$		0			0
$25$	4.07126			0.814252
$26$	0.643814	−	5.26574i	0.126262	−	1.03270i
$27$		0			0
$28$		0			0
$29$	2.48011			0.460544			0.230272	−	0.973126i	$-0.426038\pi$
$29$	2.48011			0.460544			0.230272	+	0.973126i	$0.426038\pi$
$30$		0			0
$31$	−4.82802			−0.867138			−0.433569	−	0.901120i	$-0.642746\pi$
$31$	−4.82802			−0.867138			−0.433569	+	0.901120i	$0.642746\pi$
$32$	4.64212	+	3.23276i	0.820618	+	0.571477i
$33$		0			0
$34$	0.117828	−	0.963711i	0.0202073	−	0.165275i
$35$		0			0
$36$		0			0
$37$	−2.73287			−0.449281			−0.224640	−	0.974442i	$-0.572121\pi$
$37$	−2.73287			−0.449281			−0.224640	+	0.974442i	$0.572121\pi$
$38$	−6.85340	−	0.837928i	−1.11177	−	0.135930i
$39$		0			0
$40$	0.972923	−	2.54624i	0.153833	−	0.402596i
$41$		−	9.42976i		−	1.47268i	−0.676611	−	0.736340i	$-0.736552\pi$
$41$		−	9.42976i		−	1.47268i	0.676611	−	0.736340i	$-0.263448\pi$
$42$		0			0
$43$			5.97437i			0.911083i	0.890215	+	0.455541i	$0.150554\pi$
$43$			5.97437i			0.911083i	−0.890215	+	0.455541i	$0.849446\pi$
$44$	2.64212	−	10.6434i	0.398314	−	1.60455i
$45$		0			0
$46$	0.212976	−	1.74193i	0.0314016	−	0.256833i
$47$	3.61504			0.527308			0.263654	−	0.964617i	$-0.415072\pi$
$47$	3.61504			0.527308			0.263654	+	0.964617i	$0.415072\pi$
$48$		0			0
$49$		0			0
$50$	5.71508	+	0.698752i	0.808234	+	0.0988184i
$51$		0			0
$52$	1.80752	−	7.28134i	0.250658	−	1.00974i
$53$	4.09515			0.562512			0.281256	−	0.959633i	$-0.409249\pi$
$53$	4.09515			0.562512			0.281256	+	0.959633i	$0.409249\pi$
$54$		0			0
$55$	−5.28424			−0.712526
$56$		0			0
$57$		0			0
$58$	3.48148	+	0.425661i	0.457140	+	0.0558921i
$59$	12.6863			1.65162			0.825808	−	0.563951i	$-0.190719\pi$
$59$	12.6863			1.65162			0.825808	+	0.563951i	$0.190719\pi$
$60$		0			0
$61$			10.4121i			1.33313i	0.745448	+	0.666564i	$0.232236\pi$
$61$			10.4121i			1.33313i	−0.745448	+	0.666564i	$0.767764\pi$
$62$	−6.77738	−	0.828634i	−0.860728	−	0.105237i
$63$		0			0
$64$	5.96158	+	5.33475i	0.745198	+	0.666843i
$65$	−3.61504			−0.448391
$66$		0			0
$67$			9.43847i			1.15309i	0.817064	+	0.576546i	$0.195600\pi$
$67$			9.43847i			1.15309i	−0.817064	+	0.576546i	$0.804400\pi$
$68$	0.330804	−	1.33260i	0.0401159	−	0.161601i
$69$		0			0
$70$		0			0
$71$		−	10.1163i		−	1.20058i	−0.799782	−	0.600291i	$-0.795052\pi$
$71$		−	10.1163i		−	1.20058i	0.799782	−	0.600291i	$-0.204948\pi$
$72$		0			0
$73$			6.66089i			0.779598i	0.920900	+	0.389799i	$0.127456\pi$
$73$			6.66089i			0.779598i	−0.920900	+	0.389799i	$0.872544\pi$
$74$	−3.83629	−	0.469043i	−0.445960	−	0.0545251i
$75$		0			0
$76$	−9.47672	−	2.35250i	−1.08705	−	0.269850i
$77$		0			0
$78$		0			0
$79$		−	1.41442i		−	0.159134i	−0.996830	−	0.0795671i	$-0.974646\pi$
$79$		−	1.41442i		−	0.159134i	0.996830	−	0.0795671i	$-0.0253538\pi$
$80$	1.80276	−	3.40733i	0.201555	−	0.380951i
$81$		0			0
$82$	1.61843	−	13.2371i	0.178726	−	1.46180i
$83$	0.543780			0.0596876			0.0298438	−	0.999555i	$-0.490499\pi$
$83$	0.543780			0.0596876			0.0298438	+	0.999555i	$0.490499\pi$
$84$		0			0
$85$	−0.661608			−0.0717614
$86$	−1.02538	+	8.38658i	−0.110570	+	0.904348i
$87$		0			0
$88$	5.53563	−	14.4873i	0.590100	−	1.54435i
$89$		−	0.554380i		−	0.0587641i	−0.999568	−	0.0293821i	$-0.990646\pi$
$89$		−	0.554380i		−	0.0587641i	0.999568	−	0.0293821i	$-0.00935395\pi$
$90$		0			0
$91$		0			0
$92$	0.597935	−	2.40870i	0.0623390	−	0.251124i
$93$		0			0
$94$	5.07465	+	0.620450i	0.523410	+	0.0639946i
$95$			4.70500i			0.482723i
$96$		0			0
$97$		−	10.8747i		−	1.10416i	−0.833790	−	0.552081i	$-0.813834\pi$
$97$		−	10.8747i		−	1.10416i	0.833790	−	0.552081i	$-0.186166\pi$
$98$		0			0
$99$		0			0
$100$	7.90267	+	1.96176i	0.790267	+	0.196176i
$101$			14.4305i			1.43589i	0.696099	+	0.717946i	$0.254918\pi$
$101$			14.4305i			1.43589i	−0.696099	+	0.717946i	$0.745082\pi$
$102$		0			0
$103$	15.0247			1.48043			0.740214	−	0.672372i	$-0.234724\pi$
$103$	15.0247			1.48043			0.740214	+	0.672372i	$0.234724\pi$
$104$	3.78702	−	9.91103i	0.371348	−	0.971857i
$105$		0			0
$106$	5.74861	+	0.702851i	0.558354	+	0.0682669i
$107$			12.1156i			1.17126i	0.810577	+	0.585632i	$0.199153\pi$
$107$			12.1156i			1.17126i	−0.810577	+	0.585632i	$0.800847\pi$
$108$		0			0
$109$	−6.07126			−0.581521			−0.290761	−	0.956796i	$-0.593908\pi$
$109$	−6.07126			−0.581521			−0.290761	+	0.956796i	$0.593908\pi$
$110$	−7.41780	−	0.906935i	−0.707260	−	0.0864729i
$111$		0			0
$112$		0			0
$113$	7.37939			0.694194			0.347097	−	0.937829i	$-0.387167\pi$
$113$	7.37939			0.694194			0.347097	+	0.937829i	$0.387167\pi$
$114$		0			0
$115$	−1.19587			−0.111515
$116$	4.81410	+	1.19505i	0.446978	+	0.110958i
$117$		0			0
$118$	17.8085	+	2.17735i	1.63941	+	0.200442i
$119$		0			0
$120$		0			0
$121$	−19.0657			−1.73324
$122$	−1.78702	+	14.6160i	−0.161790	+	1.32327i
$123$		0			0
$124$	−9.37160	−	2.32641i	−0.841594	−	0.208917i
$125$		−	8.74207i		−	0.781915i
$126$		0			0
$127$		−	11.6431i		−	1.03316i	−0.856240	−	0.516578i	$-0.827206\pi$
$127$		−	11.6431i		−	1.03316i	0.856240	−	0.516578i	$-0.172794\pi$
$128$	7.45303	+	8.51189i	0.658761	+	0.752352i
$129$		0			0
$130$	−5.07465	−	0.620450i	−0.445076	−	0.0544171i
$131$	−9.26156			−0.809186			−0.404593	−	0.914497i	$-0.632587\pi$
$131$	−9.26156			−0.809186			−0.404593	+	0.914497i	$0.632587\pi$
$132$		0			0
$133$		0			0
$134$	−1.61993	+	13.2494i	−0.139940	+	1.14457i
$135$		0			0
$136$	0.693083	−	1.81387i	0.0594314	−	0.155538i
$137$	−7.23008			−0.617708			−0.308854	−	0.951110i	$-0.599945\pi$
$137$	−7.23008			−0.617708			−0.308854	+	0.951110i	$0.599945\pi$
$138$		0			0
$139$	5.30812			0.450229			0.225115	−	0.974332i	$-0.427724\pi$
$139$	5.30812			0.450229			0.225115	+	0.974332i	$0.427724\pi$
$140$		0			0
$141$		0			0
$142$	1.73626	−	14.2008i	0.145704	−	1.19171i
$143$	−20.5685			−1.72002
$144$		0			0
$145$		−	2.39011i		−	0.198488i
$146$	−1.14321	+	9.35029i	−0.0946127	+	0.773836i
$147$		0			0
$148$	−5.30473	−	1.31685i	−0.436046	−	0.108244i
$149$	−4.66161			−0.381894			−0.190947	−	0.981600i	$-0.561156\pi$
$149$	−4.66161			−0.381894			−0.190947	+	0.981600i	$0.561156\pi$
$150$		0			0
$151$		−	12.2062i		−	0.993324i	−0.867944	−	0.496662i	$-0.834559\pi$
$151$		−	12.2062i		−	0.993324i	0.867944	−	0.496662i	$-0.165441\pi$
$152$	−12.8993	−	4.92884i	−1.04627	−	0.399782i
$153$		0			0
$154$		0			0
$155$			4.65281i			0.373723i
$156$		0			0
$157$			21.9329i			1.75043i	0.483731	+	0.875217i	$0.339281\pi$
$157$			21.9329i			1.75043i	−0.483731	+	0.875217i	$0.660719\pi$
$158$	0.242756	−	1.98550i	0.0193127	−	0.157958i
$159$		0			0
$160$	3.11545	−	4.47366i	0.246298	−	0.353674i
$161$		0			0
$162$		0			0
$163$		−	4.01848i		−	0.314752i	−0.987539	−	0.157376i	$-0.949697\pi$
$163$		−	4.01848i		−	0.314752i	0.987539	−	0.157376i	$-0.0503034\pi$
$164$	4.54378	−	18.3040i	0.354810	−	1.42930i
$165$		0			0
$166$	0.763337	+	0.0933291i	0.0592464	+	0.00724374i
$167$	−14.7178			−1.13890			−0.569448	−	0.822027i	$-0.692843\pi$
$167$	−14.7178			−1.13890			−0.569448	+	0.822027i	$0.692843\pi$
$168$		0			0
$169$	−1.07126			−0.0824047
$170$	−0.928739	−	0.113552i	−0.0712310	−	0.00870903i
$171$		0			0
$172$	−2.87878	+	11.5968i	−0.219505	+	0.884245i
$173$			11.6530i			0.885958i	0.896532	+	0.442979i	$0.146078\pi$
$173$			11.6530i			0.885958i	−0.896532	+	0.442979i	$0.853922\pi$
$174$		0			0
$175$		0			0
$176$	10.2572	−	19.3866i	0.773163	−	1.46132i
$177$		0			0
$178$	0.0951483	−	0.778216i	0.00713167	−	0.0583298i
$179$		−	2.59419i		−	0.193899i	−0.995289	−	0.0969494i	$-0.969091\pi$
$179$		−	2.59419i		−	0.193899i	0.995289	−	0.0969494i	$-0.0309085\pi$
$180$		0			0
$181$			9.53343i			0.708615i	0.935129	+	0.354307i	$0.115283\pi$
$181$			9.53343i			0.708615i	−0.935129	+	0.354307i	$0.884717\pi$
$182$		0			0
$183$		0			0
$184$	1.25276	−	3.27861i	0.0923548	−	0.241702i
$185$			2.63370i			0.193633i
$186$		0			0
$187$	−3.76434			−0.275276
$188$	7.01711	+	1.74193i	0.511775	+	0.127043i
$189$		0			0
$190$	−0.807521	+	6.60470i	−0.0585837	+	0.479155i
$191$		−	8.33274i		−	0.602936i	−0.953476	−	0.301468i	$-0.902523\pi$
$191$		−	8.33274i		−	0.602936i	0.953476	−	0.301468i	$-0.0974767\pi$
$192$		0			0
$193$	−12.3726			−0.890600			−0.445300	−	0.895382i	$-0.646903\pi$
$193$	−12.3726			−0.890600			−0.445300	+	0.895382i	$0.646903\pi$
$194$	1.86643	−	15.2655i	0.134002	−	1.09600i
$195$		0			0
$196$		0			0
$197$	−3.23686			−0.230617			−0.115308	−	0.993330i	$-0.536786\pi$
$197$	−3.23686			−0.230617			−0.115308	+	0.993330i	$0.536786\pi$
$198$		0			0
$199$	19.2301			1.36318			0.681592	−	0.731732i	$-0.261288\pi$
$199$	19.2301			1.36318			0.681592	+	0.731732i	$0.261288\pi$
$200$	10.7568	+	4.11018i	0.760618	+	0.290633i
$201$		0			0
$202$	−2.47672	+	20.2570i	−0.174261	+	1.42528i
$203$		0			0
$204$		0			0
$205$	−9.08756			−0.634703
$206$	21.0911	+	2.57869i	1.46948	+	0.179666i
$207$		0			0
$208$	7.01711	−	13.2627i	0.486549	−	0.919606i
$209$			26.7700i			1.85172i
$210$		0			0
$211$			9.24637i			0.636546i	0.947999	+	0.318273i	$0.103103\pi$
$211$			9.24637i			0.636546i	−0.947999	+	0.318273i	$0.896897\pi$
$212$	7.94904	+	1.97327i	0.545942	+	0.135525i
$213$		0			0
$214$	−2.07941	+	17.0075i	−0.142146	+	1.16261i
$215$	5.75756			0.392663
$216$		0			0
$217$		0			0
$218$	−8.52260	−	1.04201i	−0.577223	−	0.0705740i
$219$		0			0
$220$	−10.2572	−	2.54624i	−0.691538	−	0.171667i
$221$	−2.57526			−0.173230
$222$		0			0
$223$	1.94585			0.130303			0.0651517	−	0.997875i	$-0.479247\pi$
$223$	1.94585			0.130303			0.0651517	+	0.997875i	$0.479247\pi$
$224$		0			0
$225$		0			0
$226$	10.3589	+	1.26653i	0.689063	+	0.0842480i
$227$	8.64531			0.573809			0.286905	−	0.957959i	$-0.407374\pi$
$227$	8.64531			0.573809			0.286905	+	0.957959i	$0.407374\pi$
$228$		0			0
$229$			16.7889i			1.10944i	0.832036	+	0.554721i	$0.187175\pi$
$229$			16.7889i			1.10944i	−0.832036	+	0.554721i	$0.812825\pi$
$230$	−1.67871	−	0.205247i	−0.110691	−	0.0135336i
$231$		0			0
$232$	6.55274	+	2.50381i	0.430208	+	0.164383i
$233$	1.04657			0.0685628			0.0342814	−	0.999412i	$-0.489086\pi$
$233$	1.04657			0.0685628			0.0342814	+	0.999412i	$0.489086\pi$
$234$		0			0
$235$		−	3.48385i		−	0.227262i
$236$	24.6252	+	6.11296i	1.60296	+	0.397920i
$237$		0			0
$238$		0			0
$239$			19.2479i			1.24505i	0.782602	+	0.622523i	$0.213892\pi$
$239$			19.2479i			1.24505i	−0.782602	+	0.622523i	$0.786108\pi$
$240$		0			0
$241$			2.75689i			0.177587i	0.996050	+	0.0887934i	$0.0283011\pi$
$241$			2.75689i			0.177587i	−0.996050	+	0.0887934i	$0.971699\pi$
$242$	−26.7637	−	3.27225i	−1.72043	−	0.210348i
$243$		0			0
$244$	−5.01711	+	20.2107i	−0.321187	+	1.29386i
$245$		0			0
$246$		0			0
$247$			18.3138i			1.16528i
$248$	−12.7562	−	4.87417i	−0.810019	−	0.309510i
$249$		0			0
$250$	1.50040	−	12.2718i	0.0948939	−	0.776135i
$251$	20.7493			1.30968			0.654841	−	0.755767i	$-0.272736\pi$
$251$	20.7493			1.30968			0.654841	+	0.755767i	$0.272736\pi$
$252$		0			0
$253$	−6.80413			−0.427772
$254$	1.99830	−	16.3441i	0.125385	−	1.02552i
$255$		0			0
$256$	9.00137	+	13.2278i	0.562586	+	0.826739i
$257$		−	7.45109i		−	0.464786i	−0.972622	−	0.232393i	$-0.925344\pi$
$257$		−	7.45109i		−	0.464786i	0.972622	−	0.232393i	$-0.0746555\pi$
$258$		0			0
$259$		0			0
$260$	−7.01711	−	1.74193i	−0.435182	−	0.108030i
$261$		0			0
$262$	−13.0010	−	1.58956i	−0.803205	−	0.0982036i
$263$			29.6797i			1.83013i	0.403305	+	0.915066i	$0.367861\pi$
$263$			29.6797i			1.83013i	−0.403305	+	0.915066i	$0.632139\pi$
$264$		0			0
$265$		−	3.94654i		−	0.242434i
$266$		0			0
$267$		0			0
$268$	−4.54798	+	18.3209i	−0.277812	+	1.11913i
$269$		−	4.31542i		−	0.263116i	−0.991308	−	0.131558i	$-0.958002\pi$
$269$		−	4.31542i		−	0.263116i	0.991308	−	0.131558i	$-0.0419980\pi$
$270$		0			0
$271$	−13.5828			−0.825099			−0.412550	−	0.910935i	$-0.635362\pi$
$271$	−13.5828			−0.825099			−0.412550	+	0.910935i	$0.635362\pi$
$272$	1.28424	−	2.42728i	0.0778683	−	0.147176i
$273$		0			0
$274$	−10.1493	−	1.24090i	−0.613142	−	0.0749656i
$275$		−	22.3236i		−	1.34616i
$276$		0			0
$277$	2.07126			0.124450			0.0622250	−	0.998062i	$-0.480180\pi$
$277$	2.07126			0.124450			0.0622250	+	0.998062i	$0.480180\pi$
$278$	7.45133	+	0.911035i	0.446901	+	0.0546402i
$279$		0			0
$280$		0			0
$281$	−23.7122			−1.41455			−0.707276	−	0.706938i	$-0.750076\pi$
$281$	−23.7122			−1.41455			−0.707276	+	0.706938i	$0.750076\pi$
$282$		0			0
$283$	12.2548			0.728471			0.364235	−	0.931307i	$-0.381330\pi$
$283$	12.2548			0.728471			0.364235	+	0.931307i	$0.381330\pi$
$284$	4.87458	−	19.6366i	0.289253	−	1.16522i
$285$		0			0
$286$	−28.8732	−	3.53017i	−1.70731	−	0.208743i
$287$		0			0
$288$		0			0
$289$	16.5287			0.972276
$290$	0.410214	−	3.35514i	0.0240886	−	0.197020i
$291$		0			0
$292$	−3.20959	+	12.9294i	−0.187827	+	0.756634i
$293$		−	10.7090i		−	0.625626i	−0.949815	−	0.312813i	$-0.898729\pi$
$293$		−	10.7090i		−	0.625626i	0.949815	−	0.312813i	$-0.101271\pi$
$294$		0			0
$295$		−	12.2259i		−	0.711821i
$296$	−7.22056	−	2.75899i	−0.419687	−	0.160363i
$297$		0			0
$298$	−6.54378	−	0.800073i	−0.379071	−	0.0463470i
$299$	−4.65483			−0.269196
$300$		0			0
$301$		0			0
$302$	2.09495	−	17.1345i	0.120551	−	0.985982i
$303$		0			0
$304$	−17.2616	−	9.13281i	−0.990018	−	0.523803i
$305$	10.0342			0.574557
$306$		0			0
$307$	4.22056			0.240880			0.120440	−	0.992721i	$-0.461569\pi$
$307$	4.22056			0.240880			0.120440	+	0.992721i	$0.461569\pi$
$308$		0			0
$309$		0			0
$310$	−0.798563	+	6.53143i	−0.0453554	+	0.370961i
$311$	−9.70139			−0.550116			−0.275058	−	0.961428i	$-0.588697\pi$
$311$	−9.70139			−0.550116			−0.275058	+	0.961428i	$0.588697\pi$
$312$		0			0
$313$			13.6634i			0.772299i	0.922436	+	0.386149i	$0.126195\pi$
$313$			13.6634i			0.772299i	−0.922436	+	0.386149i	$0.873805\pi$
$314$	−3.76434	+	30.7885i	−0.212434	+	1.73750i
$315$		0			0
$316$	0.681544	−	2.74550i	0.0383398	−	0.154447i
$317$	−20.0884			−1.12828			−0.564138	−	0.825681i	$-0.690791\pi$
$317$	−20.0884			−1.12828			−0.564138	+	0.825681i	$0.690791\pi$
$318$		0			0
$319$		−	13.5990i		−	0.761396i
$320$	5.14115	−	5.74524i	0.287399	−	0.321169i
$321$		0			0
$322$		0			0
$323$			3.35171i			0.186494i
$324$		0			0
$325$		−	15.2720i		−	0.847137i
$326$	0.689693	−	5.64098i	0.0381986	−	0.312425i
$327$		0			0
$328$	9.51989	−	24.9145i	0.525648	−	1.37568i
$329$		0			0
$330$		0			0
$331$			9.42104i			0.517827i	0.965900	+	0.258914i	$0.0833645\pi$
$331$			9.42104i			0.517827i	−0.965900	+	0.258914i	$0.916635\pi$
$332$	1.05552	+	0.262023i	0.0579294	+	0.0143804i
$333$		0			0
$334$	−20.6602	−	2.52602i	−1.13048	−	0.138217i
$335$	9.09596			0.496965
$336$		0			0
$337$	−13.4411			−0.732185			−0.366092	−	0.930578i	$-0.619305\pi$
$337$	−13.4411			−0.732185			−0.366092	+	0.930578i	$0.619305\pi$
$338$	−1.50379	−	0.183861i	−0.0817956	−	0.0100007i
$339$		0			0
$340$	−1.28424	−	0.318799i	−0.0696476	−	0.0172893i
$341$			26.4731i			1.43360i
$342$		0			0
$343$		0			0
$344$	−6.03148	+	15.7850i	−0.325195	+	0.851070i
$345$		0			0
$346$	−2.00000	+	16.3580i	−0.107521	+	0.879409i
$347$		−	22.6194i		−	1.21427i	−0.794598	−	0.607136i	$-0.792318\pi$
$347$		−	22.6194i		−	1.21427i	0.794598	−	0.607136i	$-0.207682\pi$
$348$		0			0
$349$			2.48180i			0.132848i	0.997791	+	0.0664239i	$0.0211590\pi$
$349$			2.48180i			0.132848i	−0.997791	+	0.0664239i	$0.978841\pi$
$350$		0			0
$351$		0			0
$352$	17.7259	−	25.4538i	0.944795	−	1.35669i
$353$		−	9.11423i		−	0.485101i	−0.970139	−	0.242551i	$-0.922016\pi$
$353$		−	9.11423i		−	0.485101i	0.970139	−	0.242551i	$-0.0779841\pi$
$354$		0			0
$355$	−9.74917			−0.517432
$356$	0.267131	−	1.07610i	0.0141579	−	0.0570331i
$357$		0			0
$358$	0.445241	−	3.64162i	0.0235317	−	0.192466i
$359$			6.92820i			0.365657i	0.983145	+	0.182828i	$0.0585252\pi$
$359$			6.92820i			0.365657i	−0.983145	+	0.182828i	$0.941475\pi$
$360$		0			0
$361$	4.83561			0.254506
$362$	−1.63623	+	13.3827i	−0.0859981	+	0.703377i
$363$		0			0
$364$		0			0
$365$	6.41917			0.335995
$366$		0			0
$367$	3.83359			0.200112			0.100056	−	0.994982i	$-0.468098\pi$
$367$	3.83359			0.200112			0.100056	+	0.994982i	$0.468098\pi$
$368$	2.32129	−	4.38737i	0.121005	−	0.228707i
$369$		0			0
$370$	−0.452022	+	3.69708i	−0.0234995	+	0.192202i
$371$		0			0
$372$		0			0
$373$	−26.8300			−1.38921			−0.694603	−	0.719393i	$-0.744420\pi$
$373$	−26.8300			−1.38921			−0.694603	+	0.719393i	$0.744420\pi$
$374$	−5.28424	−	0.646075i	−0.273241	−	0.0334078i
$375$		0			0
$376$	9.55137	+	3.64960i	0.492574	+	0.188214i
$377$		−	9.30330i		−	0.479144i
$378$		0			0
$379$			6.93692i			0.356325i	0.984001	+	0.178163i	$0.0570153\pi$
$379$			6.93692i			0.356325i	−0.984001	+	0.178163i	$0.942985\pi$
$380$	−2.26713	+	9.13281i	−0.116301	+	0.468504i
$381$		0			0
$382$	1.43015	−	11.6972i	0.0731729	−	0.598479i
$383$	2.25761			0.115359			0.0576793	−	0.998335i	$-0.481630\pi$
$383$	2.25761			0.115359			0.0576793	+	0.998335i	$0.481630\pi$
$384$		0			0
$385$		0			0
$386$	−17.3682	−	2.12351i	−0.884017	−	0.108084i
$387$		0			0
$388$	5.24005	−	21.1088i	0.266023	−	1.07164i
$389$	−30.6095			−1.55196			−0.775981	−	0.630756i	$-0.782745\pi$
$389$	−30.6095			−1.55196			−0.775981	+	0.630756i	$0.782745\pi$
$390$		0			0
$391$	−0.851904			−0.0430827
$392$		0			0
$393$		0			0
$394$	−4.54378	−	0.555544i	−0.228912	−	0.0279879i
$395$	−1.36309			−0.0685844
$396$		0			0
$397$		−	13.8989i		−	0.697568i	−0.937203	−	0.348784i	$-0.886595\pi$
$397$		−	13.8989i		−	0.697568i	0.937203	−	0.348784i	$-0.113405\pi$
$398$	26.9944	+	3.30046i	1.35311	+	0.165437i
$399$		0			0
$400$	14.3945	+	7.61589i	0.719724	+	0.380794i
$401$	10.2766			0.513191			0.256596	−	0.966519i	$-0.417399\pi$
$401$	10.2766			0.513191			0.256596	+	0.966519i	$0.417399\pi$
$402$		0			0
$403$			18.1107i			0.902158i
$404$	−6.95343	+	28.0109i	−0.345946	+	1.39360i
$405$		0			0
$406$		0			0
$407$			14.9849i			0.742775i
$408$		0			0
$409$		−	12.1639i		−	0.601464i	−0.953709	−	0.300732i	$-0.902769\pi$
$409$		−	12.1639i		−	0.601464i	0.953709	−	0.300732i	$-0.0972310\pi$
$410$	−12.7568	−	1.55970i	−0.630011	−	0.0770281i
$411$		0			0
$412$	29.1642	+	7.23973i	1.43682	+	0.356676i
$413$		0			0
$414$		0			0
$415$		−	0.524047i		−	0.0257244i
$416$	12.1266	−	17.4134i	0.594557	−	0.853761i
$417$		0			0
$418$	−4.59454	+	37.5787i	−0.224727	+	1.83803i
$419$	−16.2245			−0.792619			−0.396310	−	0.918117i	$-0.629709\pi$
$419$	−16.2245			−0.792619			−0.396310	+	0.918117i	$0.629709\pi$
$420$		0			0
$421$	−9.58477			−0.467133			−0.233567	−	0.972341i	$-0.575040\pi$
$421$	−9.58477			−0.467133			−0.233567	+	0.972341i	$0.575040\pi$
$422$	−1.58696	+	12.9797i	−0.0772518	+	0.631841i
$423$		0			0
$424$	10.8199	+	4.13429i	0.525459	+	0.200779i
$425$		−	2.79501i		−	0.135578i
$426$		0			0
$427$		0			0
$428$	−5.83799	+	23.5175i	−0.282190	+	1.13676i
$429$		0			0
$430$	8.08224	+	0.988172i	0.389760	+	0.0476539i
$431$		−	0.151894i		−	0.00731648i	−0.999993	−	0.00365824i	$-0.998836\pi$
$431$		−	0.151894i		−	0.00731648i	0.999993	−	0.00365824i	$-0.00116446\pi$
$432$		0			0
$433$			9.46997i			0.455098i	0.973767	+	0.227549i	$0.0730711\pi$
$433$			9.46997i			0.455098i	−0.973767	+	0.227549i	$0.926929\pi$
$434$		0			0
$435$		0			0
$436$	−11.7848	−	2.92547i	−0.564392	−	0.140105i
$437$			6.05829i			0.289807i
$438$		0			0
$439$	33.4745			1.59765			0.798826	−	0.601562i	$-0.205455\pi$
$439$	33.4745			1.59765			0.798826	+	0.601562i	$0.205455\pi$
$440$	−13.9616	−	5.33475i	−0.665592	−	0.254324i
$441$		0			0
$442$	−3.61504	−	0.441992i	−0.171950	−	0.0210234i
$443$			26.1554i			1.24268i	0.783540	+	0.621341i	$0.213412\pi$
$443$			26.1554i			1.24268i	−0.783540	+	0.621341i	$0.786588\pi$
$444$		0			0
$445$	−0.534262			−0.0253264
$446$	2.73150	+	0.333966i	0.129340	+	0.0158137i
$447$		0			0
$448$		0			0
$449$	−10.2918			−0.485701			−0.242851	−	0.970064i	$-0.578082\pi$
$449$	−10.2918			−0.485701			−0.242851	+	0.970064i	$0.578082\pi$
$450$		0			0
$451$	−51.7054			−2.43471
$452$	14.3240	+	3.55580i	0.673745	+	0.167251i
$453$		0			0
$454$	12.1359	+	1.48380i	0.569568	+	0.0696380i
$455$		0			0
$456$		0			0
$457$	11.9315			0.558131			0.279065	−	0.960272i	$-0.409975\pi$
$457$	11.9315			0.558131			0.279065	+	0.960272i	$0.409975\pi$
$458$	−2.88148	+	23.5676i	−0.134643	+	1.10124i
$459$		0			0
$460$	−2.32129	−	0.576236i	−0.108231	−	0.0268672i
$461$			30.0093i			1.39767i	0.715281	+	0.698837i	$0.246299\pi$
$461$			30.0093i			1.39767i	−0.715281	+	0.698837i	$0.753701\pi$
$462$		0			0
$463$		−	13.2736i		−	0.616875i	−0.951245	−	0.308437i	$-0.900194\pi$
$463$		−	13.2736i		−	0.616875i	0.951245	−	0.308437i	$-0.0998060\pi$
$464$	8.76874	+	4.63940i	0.407079	+	0.215379i
$465$		0			0
$466$	1.46913	+	0.179622i	0.0680561	+	0.00832085i
$467$	29.6493			1.37200			0.686002	−	0.727600i	$-0.259364\pi$
$467$	29.6493			1.37200			0.686002	+	0.727600i	$0.259364\pi$
$468$		0			0
$469$		0			0
$470$	0.597935	−	4.89050i	0.0275807	−	0.225582i
$471$		0			0
$472$	33.5187	+	12.8076i	1.54282	+	0.589516i
$473$	32.7588			1.50625
$474$		0			0
$475$	−19.8766			−0.912001
$476$		0			0
$477$		0			0
$478$	−3.30353	+	27.0195i	−0.151100	+	1.23584i
$479$	−11.5355			−0.527069			−0.263535	−	0.964650i	$-0.584888\pi$
$479$	−11.5355			−0.527069			−0.263535	+	0.964650i	$0.584888\pi$
$480$		0			0
$481$			10.2515i			0.467426i
$482$	−0.473165	+	3.87001i	−0.0215521	+	0.176274i
$483$		0			0
$484$	−37.0081	−	9.18691i	−1.68219	−	0.417587i
$485$	−10.4801			−0.475877
$486$		0			0
$487$			9.75517i			0.442049i	0.975268	+	0.221024i	$0.0709400\pi$
$487$			9.75517i			0.442049i	−0.975268	+	0.221024i	$0.929060\pi$
$488$	−10.5116	+	27.5099i	−0.475837	+	1.24531i
$489$		0			0
$490$		0			0
$491$		−	40.4736i		−	1.82655i	−0.407346	−	0.913274i	$-0.633546\pi$
$491$		−	40.4736i		−	1.82655i	0.407346	−	0.913274i	$-0.366454\pi$
$492$		0			0
$493$		−	1.70265i		−	0.0766833i
$494$	−3.14321	+	25.7083i	−0.141420	+	1.15667i
$495$		0			0
$496$	−17.0701	−	9.03151i	−0.766470	−	0.405527i
$497$		0			0
$498$		0			0
$499$		−	31.9652i		−	1.43096i	−0.698633	−	0.715480i	$-0.746208\pi$
$499$		−	31.9652i		−	1.43096i	0.698633	−	0.715480i	$-0.253792\pi$
$500$	4.21242	−	16.9691i	0.188385	−	0.758882i
$501$		0			0
$502$	29.1270	+	3.56120i	1.30000	+	0.158944i
$503$	−22.7110			−1.01263			−0.506317	−	0.862348i	$-0.668993\pi$
$503$	−22.7110			−1.01263			−0.506317	+	0.862348i	$0.668993\pi$
$504$		0			0
$505$	13.9069			0.618847
$506$	−9.55137	−	1.16779i	−0.424610	−	0.0519148i
$507$		0			0
$508$	5.61028	−	22.6002i	0.248916	−	1.00272i
$509$			2.29725i			0.101824i	0.998703	+	0.0509118i	$0.0162128\pi$
$509$			2.29725i			0.101824i	−0.998703	+	0.0509118i	$0.983787\pi$
$510$		0			0
$511$		0			0
$512$	10.3655	+	20.1136i	0.458093	+	0.888904i
$513$		0			0
$514$	1.27883	−	10.4595i	0.0564068	−	0.461350i
$515$		−	14.4795i		−	0.638041i
$516$		0			0
$517$		−	19.8221i		−	0.871773i
$518$		0			0
$519$		0			0
$520$	−9.55137	−	3.64960i	−0.418855	−	0.160045i
$521$		−	37.6100i		−	1.64772i	−0.566791	−	0.823862i	$-0.691815\pi$
$521$		−	37.6100i		−	1.64772i	0.566791	−	0.823862i	$-0.308185\pi$
$522$		0			0
$523$	35.6887			1.56056			0.780279	−	0.625431i	$-0.215077\pi$
$523$	35.6887			1.56056			0.780279	+	0.625431i	$0.215077\pi$
$524$	−17.9775	−	4.46273i	−0.785350	−	0.194955i
$525$		0			0
$526$	−5.09394	+	41.6632i	−0.222106	+	1.81660i
$527$			3.31454i			0.144383i
$528$		0			0
$529$	21.4602			0.933051
$530$	0.677345	−	5.53999i	0.0294220	−	0.240642i
$531$		0			0
$532$		0			0
$533$	−35.3726			−1.53216
$534$		0			0
$535$	11.6760			0.504796
$536$	−9.52869	+	24.9376i	−0.411577	+	1.07714i
$537$		0			0
$538$	0.740657	−	6.05782i	0.0319320	−	0.261171i
$539$		0			0
$540$		0			0
$541$	37.0203			1.59163			0.795814	−	0.605541i	$-0.207043\pi$
$541$	37.0203			1.59163			0.795814	+	0.605541i	$0.207043\pi$
$542$	−19.0671	−	2.33123i	−0.819000	−	0.100135i
$543$		0			0
$544$	2.21936	−	3.18691i	0.0951541	−	0.136638i
$545$			5.85094i			0.250627i
$546$		0			0
$547$			2.09106i			0.0894073i	0.999000	+	0.0447036i	$0.0142344\pi$
$547$			2.09106i			0.0894073i	−0.999000	+	0.0447036i	$0.985766\pi$
$548$	−14.0342	−	3.48385i	−0.599512	−	0.148823i
$549$		0			0
$550$	3.83141	−	31.3370i	0.163372	−	1.33621i
$551$	−12.1083			−0.515831
$552$		0			0
$553$		0			0
$554$	2.90755	+	0.355491i	0.123530	+	0.0151034i
$555$		0			0
$556$	10.3035	+	2.55775i	0.436967	+	0.108473i
$557$	16.7977			0.711743			0.355872	−	0.934535i	$-0.384184\pi$
$557$	16.7977			0.711743			0.355872	+	0.934535i	$0.384184\pi$
$558$		0			0
$559$	22.4109			0.947878
$560$		0			0
$561$		0			0
$562$	−33.2863	−	4.06973i	−1.40410	−	0.171671i
$563$	17.3957			0.733141			0.366570	−	0.930390i	$-0.380532\pi$
$563$	17.3957			0.733141			0.366570	+	0.930390i	$0.380532\pi$
$564$		0			0
$565$		−	7.11159i		−	0.299187i
$566$	17.2028	+	2.10329i	0.723086	+	0.0884079i
$567$		0			0
$568$	10.2130	−	26.7284i	0.428527	−	1.12150i
$569$	34.2850			1.43730			0.718652	−	0.695370i	$-0.244759\pi$
$569$	34.2850			1.43730			0.718652	+	0.695370i	$0.244759\pi$
$570$		0			0
$571$		−	5.93719i		−	0.248464i	−0.992253	−	0.124232i	$-0.960353\pi$
$571$		−	5.93719i		−	0.248464i	0.992253	−	0.124232i	$-0.0396467\pi$
$572$	−39.9252	−	9.91103i	−1.66936	−	0.414401i
$573$		0			0
$574$		0			0
$575$		−	5.05203i		−	0.210684i
$576$		0			0
$577$		−	39.0208i		−	1.62446i	−0.583338	−	0.812229i	$-0.698254\pi$
$577$		−	39.0208i		−	1.62446i	0.583338	−	0.812229i	$-0.301746\pi$
$578$	23.2023	+	2.83682i	0.965089	+	0.117996i
$579$		0			0
$580$	1.15169	−	4.63940i	0.0478211	−	0.192641i
$581$		0			0
$582$		0			0
$583$		−	22.4546i		−	0.929974i
$584$	−6.72456	+	17.5989i	−0.278264	+	0.728246i
$585$		0			0
$586$	1.83799	−	15.0329i	0.0759266	−	0.621002i
$587$	7.71931			0.318610			0.159305	−	0.987229i	$-0.449075\pi$
$587$	7.71931			0.318610			0.159305	+	0.987229i	$0.449075\pi$
$588$		0			0
$589$	23.5712			0.971235
$590$	2.09834	−	17.1623i	0.0863872	−	0.706560i
$591$		0			0
$592$	−9.66242	−	5.11223i	−0.397123	−	0.210111i
$593$		−	0.388414i		−	0.0159503i	−0.999968	−	0.00797513i	$-0.997461\pi$
$593$		−	0.388414i		−	0.0159503i	0.999968	−	0.00797513i	$-0.00253859\pi$
$594$		0			0
$595$		0			0
$596$	−9.04858	−	2.24622i	−0.370644	−	0.0920088i
$597$		0			0
$598$	−6.53426	−	0.798909i	−0.267206	−	0.0326698i
$599$			20.7846i			0.849236i	0.905373	+	0.424618i	$0.139592\pi$
$599$			20.7846i			0.849236i	−0.905373	+	0.424618i	$0.860408\pi$
$600$		0			0
$601$			26.4110i			1.07733i	0.842521	+	0.538664i	$0.181071\pi$
$601$			26.4110i			1.07733i	−0.842521	+	0.538664i	$0.818929\pi$
$602$		0			0
$603$		0			0
$604$	5.88161	−	23.6932i	0.239319	−	0.964064i
$605$			18.3738i			0.747002i
$606$		0			0
$607$	−40.7061			−1.65221			−0.826106	−	0.563515i	$-0.809449\pi$
$607$	−40.7061			−1.65221			−0.826106	+	0.563515i	$0.809449\pi$
$608$	−22.6636	−	15.7829i	−0.919131	−	0.640081i
$609$		0			0
$610$	14.0856	+	1.72217i	0.570310	+	0.0697288i
$611$		−	13.5606i		−	0.548604i
$612$		0			0
$613$	17.3384			0.700291			0.350146	−	0.936695i	$-0.386132\pi$
$613$	17.3384			0.700291			0.350146	+	0.936695i	$0.386132\pi$
$614$	5.92466	+	0.724376i	0.239100	+	0.0292335i
$615$		0			0
$616$		0			0
$617$	46.4753			1.87103			0.935513	−	0.353291i	$-0.114938\pi$
$617$	46.4753			1.87103			0.935513	+	0.353291i	$0.114938\pi$
$618$		0			0
$619$	−26.3821			−1.06039			−0.530194	−	0.847877i	$-0.677881\pi$
$619$	−26.3821			−1.06039			−0.530194	+	0.847877i	$0.677881\pi$
$620$	−2.24198	+	9.03151i	−0.0900402	+	0.362714i
$621$		0			0
$622$	−13.6184	−	1.66505i	−0.546049	−	0.0667625i
$623$		0			0
$624$		0			0
$625$	11.9315			0.477259
$626$	−2.34505	+	19.1801i	−0.0937269	+	0.766590i
$627$		0			0
$628$	−10.5685	+	42.5736i	−0.421728	+	1.69887i
$629$			1.87617i			0.0748079i
$630$		0			0
$631$			41.0696i			1.63495i	0.575961	+	0.817477i	$0.304628\pi$
$631$			41.0696i			1.63495i	−0.575961	+	0.817477i	$0.695372\pi$
$632$	1.42794	−	3.73705i	0.0568002	−	0.148652i
$633$		0			0
$634$	−28.1993	−	3.44777i	−1.11994	−	0.136928i
$635$	−11.2206			−0.445275
$636$		0			0
$637$		0			0
$638$	2.33399	−	19.0897i	0.0924037	−	0.755768i
$639$		0			0
$640$	8.20301	−	7.18257i	0.324252	−	0.283916i
$641$	−45.4478			−1.79508			−0.897540	−	0.440932i	$-0.854648\pi$
$641$	−45.4478			−1.79508			−0.897540	+	0.440932i	$0.854648\pi$
$642$		0			0
$643$	−30.5534			−1.20491			−0.602454	−	0.798154i	$-0.705810\pi$
$643$	−30.5534			−1.20491			−0.602454	+	0.798154i	$0.705810\pi$
$644$		0			0
$645$		0			0
$646$	−0.575255	+	4.70500i	−0.0226331	+	0.185116i
$647$	36.1792			1.42235			0.711175	−	0.703015i	$-0.248164\pi$
$647$	36.1792			1.42235			0.711175	+	0.703015i	$0.248164\pi$
$648$		0			0
$649$		−	69.5618i		−	2.73054i
$650$	2.62113	−	21.4382i	0.102809	−	0.840876i
$651$		0			0
$652$	1.93633	−	7.80022i	0.0758324	−	0.305480i
$653$	8.23089			0.322100			0.161050	−	0.986946i	$-0.448512\pi$
$653$	8.23089			0.322100			0.161050	+	0.986946i	$0.448512\pi$
$654$		0			0
$655$			8.92546i			0.348747i
$656$	17.6397	−	33.3401i	0.688716	−	1.30171i
$657$		0			0
$658$		0			0
$659$		−	22.8837i		−	0.891422i	−0.895177	−	0.445711i	$-0.852951\pi$
$659$		−	22.8837i		−	0.891422i	0.895177	−	0.445711i	$-0.147049\pi$
$660$		0			0
$661$			20.4627i			0.795906i	0.917406	+	0.397953i	$0.130279\pi$
$661$			20.4627i			0.795906i	−0.917406	+	0.397953i	$0.869721\pi$
$662$	−1.61694	+	13.2249i	−0.0628440	+	0.514000i
$663$		0			0
$664$	1.43673	+	0.548978i	0.0557560	+	0.0213045i
$665$		0			0
$666$		0			0
$667$		−	3.07757i		−	0.119164i
$668$	−28.5685	−	7.09184i	−1.10535	−	0.274392i
$669$		0			0
$670$	12.7685	+	1.56114i	0.493292	+	0.0603121i
$671$	57.0916			2.20400
$672$		0			0
$673$	4.23008			0.163058			0.0815289	−	0.996671i	$-0.474020\pi$
$673$	4.23008			0.163058			0.0815289	+	0.996671i	$0.474020\pi$
$674$	−18.8681	−	2.30690i	−0.726773	−	0.0888586i
$675$		0			0
$676$	−2.07941	−	0.516193i	−0.0799773	−	0.0198536i
$677$		−	24.0134i		−	0.922908i	−0.887164	−	0.461454i	$-0.847328\pi$
$677$		−	24.0134i		−	0.922908i	0.887164	−	0.461454i	$-0.152672\pi$
$678$		0			0
$679$		0			0
$680$	−1.74805	−	0.667932i	−0.0670345	−	0.0256140i
$681$		0			0
$682$	−4.54358	+	37.1619i	−0.173983	+	1.42300i
$683$		−	8.19781i		−	0.313680i	−0.987624	−	0.156840i	$-0.949869\pi$
$683$		−	8.19781i		−	0.313680i	0.987624	−	0.156840i	$-0.0501307\pi$
$684$		0			0
$685$			6.96771i			0.266222i
$686$		0			0
$687$		0			0
$688$	−11.1759	+	21.1232i	−0.426078	+	0.805313i
$689$		−	15.3616i		−	0.585230i
$690$		0			0
$691$	−35.9849			−1.36893			−0.684465	−	0.729046i	$-0.739964\pi$
$691$	−35.9849			−1.36893			−0.684465	+	0.729046i	$0.739964\pi$
$692$	−5.61504	+	22.6194i	−0.213452	+	0.859860i
$693$		0			0
$694$	3.88217	−	31.7522i	0.147365	−	1.20530i
$695$		−	5.11550i		−	0.194042i
$696$		0			0
$697$	−6.47373			−0.245210
$698$	−0.425952	+	3.48385i	−0.0161225	+	0.131866i
$699$		0			0
$700$		0			0
$701$	12.9471			0.489003			0.244502	−	0.969649i	$-0.421376\pi$
$701$	12.9471			0.489003			0.244502	+	0.969649i	$0.421376\pi$
$702$		0			0
$703$	13.3423			0.503216
$704$	29.2516	−	32.6887i	1.10246	−	1.23200i
$705$		0			0
$706$	1.56428	−	12.7942i	0.0588723	−	0.481516i
$707$		0			0
$708$		0			0
$709$	13.3121			0.499945			0.249973	−	0.968253i	$-0.419578\pi$
$709$	13.3121			0.499945			0.249973	+	0.968253i	$0.419578\pi$
$710$	−13.6855	−	1.67325i	−0.513607	−	0.0627960i
$711$		0			0
$712$	0.559679	−	1.46474i	0.0209749	−	0.0548934i
$713$			5.99109i			0.224368i
$714$		0			0
$715$			19.8221i			0.741303i
$716$	1.25002	−	5.03555i	0.0467156	−	0.188187i
$717$		0			0
$718$	−1.18909	+	9.72554i	−0.0443764	+	0.362954i
$719$	−47.5040			−1.77160			−0.885800	−	0.464068i	$-0.846389\pi$
$719$	−47.5040			−1.77160			−0.885800	+	0.464068i	$0.846389\pi$
$720$		0			0
$721$		0			0
$722$	6.78803	+	0.829936i	0.252624	+	0.0308870i
$723$		0			0
$724$	−4.59374	+	18.5052i	−0.170725	+	0.687741i
$725$	10.0972			0.374999
$726$		0			0
$727$	24.3567			0.903340			0.451670	−	0.892185i	$-0.350828\pi$
$727$	24.3567			0.903340			0.451670	+	0.892185i	$0.350828\pi$
$728$		0			0
$729$		0			0
$730$	9.01098	+	1.10172i	0.333511	+	0.0407766i
$731$	4.10153			0.151701
$732$		0			0
$733$			3.87763i			0.143223i	0.997433	+	0.0716117i	$0.0228142\pi$
$733$			3.87763i			0.143223i	−0.997433	+	0.0716117i	$0.977186\pi$
$734$	5.38144	+	0.657960i	0.198633	+	0.0242857i
$735$		0			0
$736$	4.01153	−	5.76041i	0.147867	−	0.212331i
$737$	51.7532			1.90635
$738$		0			0
$739$			8.61981i			0.317085i	0.987352	+	0.158542i	$0.0506795\pi$
$739$			8.61981i			0.317085i	−0.987352	+	0.158542i	$0.949321\pi$
$740$	−1.26906	+	5.11223i	−0.0466516	+	0.187929i
$741$		0			0
$742$		0			0
$743$			6.12929i			0.224862i	0.993660	+	0.112431i	$0.0358637\pi$
$743$			6.12929i			0.224862i	−0.993660	+	0.112431i	$0.964136\pi$
$744$		0			0
$745$			4.49244i			0.164590i
$746$	−37.6629	−	4.60484i	−1.37894	−	0.168595i
$747$		0			0
$748$	−7.30692	−	1.81387i	−0.267167	−	0.0663216i
$749$		0			0
$750$		0			0
$751$			35.4662i			1.29418i	0.762414	+	0.647090i	$0.224014\pi$
$751$			35.4662i			1.29418i	−0.762414	+	0.647090i	$0.775986\pi$
$752$	12.7815	+	6.76246i	0.466092	+	0.246602i
$753$		0			0
$754$	1.59673	−	13.0596i	0.0581494	−	0.475603i
$755$	−11.7632			−0.428108
$756$		0			0
$757$	29.4204			1.06930			0.534651	−	0.845073i	$-0.320443\pi$
$757$	29.4204			1.06930			0.534651	+	0.845073i	$0.320443\pi$
$758$	−1.19058	+	9.73777i	−0.0432440	+	0.353692i
$759$		0			0
$760$	−4.74998	+	12.4312i	−0.172300	+	0.450926i
$761$		−	50.2950i		−	1.82319i	−0.411086	−	0.911597i	$-0.634850\pi$
$761$		−	50.2950i		−	1.82319i	0.411086	−	0.911597i	$-0.365150\pi$
$762$		0			0
$763$		0			0
$764$	4.01518	−	16.1746i	0.145264	−	0.585175i
$765$		0			0
$766$	3.16915	+	0.387475i	0.114506	+	0.0140000i
$767$		−	47.5885i		−	1.71832i
$768$		0			0
$769$			20.2817i			0.731377i	0.930737	+	0.365689i	$0.119167\pi$
$769$			20.2817i			0.731377i	−0.930737	+	0.365689i	$0.880833\pi$
$770$		0			0
$771$		0			0
$772$	−24.0163	−	5.96181i	−0.864365	−	0.214570i
$773$		−	21.7255i		−	0.781413i	−0.920515	−	0.390706i	$-0.872231\pi$
$773$		−	21.7255i		−	0.781413i	0.920515	−	0.390706i	$-0.127769\pi$
$774$		0			0
$775$	−19.6561			−0.706069
$776$	10.9787	−	28.7324i	0.394112	−	1.03143i
$777$		0			0
$778$	−42.9684	−	5.25351i	−1.54049	−	0.188347i
$779$			46.0377i			1.64947i
$780$		0			0
$781$	−55.4698			−1.98486
$782$	−1.19587	−	0.146213i	−0.0427642	−	0.00522855i
$783$		0			0
$784$		0			0
$785$	21.1369			0.754410
$786$		0			0
$787$	−0.598657			−0.0213398			−0.0106699	−	0.999943i	$-0.503396\pi$
$787$	−0.598657			−0.0213398			−0.0106699	+	0.999943i	$0.503396\pi$
$788$	−6.28303	−	1.55970i	−0.223824	−	0.0555620i
$789$		0			0
$790$	−1.91345	−	0.233947i	−0.0680774	−	0.00832346i
$791$		0			0
$792$		0			0
$793$	39.0574			1.38697
$794$	2.38548	−	19.5108i	0.0846575	−	0.692412i
$795$		0			0
$796$	37.3272	+	9.26612i	1.32303	+	0.328429i
$797$		−	36.1789i		−	1.28152i	−0.767741	−	0.640760i	$-0.778619\pi$
$797$		−	36.1789i		−	1.28152i	0.767741	−	0.640760i	$-0.221381\pi$
$798$		0			0
$799$		−	2.48180i		−	0.0877998i
$800$	18.8993	+	13.1614i	0.668190	+	0.465326i
$801$		0			0
$802$	14.4260	+	1.76378i	0.509398	+	0.0622814i
$803$	36.5231			1.28887
$804$		0			0
$805$		0			0
$806$	−3.10834	+	25.4231i	−0.109487	+	0.895490i
$807$		0			0
$808$	−14.5685	+	38.1272i	−0.512517	+	1.34131i
$809$	30.1206			1.05898			0.529491	−	0.848315i	$-0.322383\pi$
$809$	30.1206			1.05898			0.529491	+	0.848315i	$0.322383\pi$
$810$		0			0
$811$	21.5947			0.758292			0.379146	−	0.925337i	$-0.376218\pi$
$811$	21.5947			0.758292			0.379146	+	0.925337i	$0.376218\pi$
$812$		0			0
$813$		0			0
$814$	−2.57187	+	21.0352i	−0.0901438	+	0.737285i
$815$	−3.87265			−0.135653
$816$		0			0
$817$		−	29.1679i		−	1.02046i
$818$	2.08769	−	17.0751i	0.0729942	−	0.597018i
$819$		0			0
$820$	−17.6397	−	4.37889i	−0.616006	−	0.152917i
$821$	−50.2528			−1.75384			−0.876918	−	0.480640i	$-0.840405\pi$
$821$	−50.2528			−1.75384			−0.876918	+	0.480640i	$0.840405\pi$
$822$		0			0
$823$		−	3.31789i		−	0.115654i	−0.998327	−	0.0578272i	$-0.981583\pi$
$823$		−	3.31789i		−	0.115654i	0.998327	−	0.0578272i	$-0.0184172\pi$
$824$	39.6970	+	15.1683i	1.38291	+	0.528413i
$825$		0			0
$826$		0			0
$827$			29.3948i			1.02216i	0.859534	+	0.511078i	$0.170754\pi$
$827$			29.3948i			1.02216i	−0.859534	+	0.511078i	$0.829246\pi$
$828$		0			0
$829$		−	32.6757i		−	1.13487i	−0.823417	−	0.567437i	$-0.807935\pi$
$829$		−	32.6757i		−	1.13487i	0.823417	−	0.567437i	$-0.192065\pi$
$830$	0.0899422	−	0.735636i	0.00312194	−	0.0255343i
$831$		0			0
$832$	20.0115	−	22.3629i	0.693775	−	0.775294i
$833$		0			0
$834$		0			0
$835$			14.1837i			0.490847i
$836$	−12.8993	+	51.9629i	−0.446131	+	1.79717i
$837$		0			0
$838$	−22.7753	−	2.78462i	−0.786760	−	0.0961930i
$839$	−8.66161			−0.299032			−0.149516	−	0.988759i	$-0.547772\pi$
$839$	−8.66161			−0.299032			−0.149516	+	0.988759i	$0.547772\pi$
$840$		0			0
$841$	−22.8491			−0.787899
$842$	−13.4547	−	1.64504i	−0.463680	−	0.0566917i
$843$		0			0
$844$	−4.45541	+	17.9480i	−0.153362	+	0.617795i
$845$			1.03239i			0.0355152i
$846$		0			0
$847$		0			0
$848$	14.4789	+	7.66057i	0.497209	+	0.263065i
$849$		0			0
$850$	0.479708	−	3.92352i	0.0164538	−	0.134576i
$851$			3.39122i			0.116250i
$852$		0			0
$853$		−	7.17809i		−	0.245773i	−0.992421	−	0.122887i	$-0.960785\pi$
$853$		−	7.17809i		−	0.245773i	0.992421	−	0.122887i	$-0.0392151\pi$
$854$		0			0
$855$		0			0
$856$	−12.2315	+	32.0110i	−0.418062	+	1.09411i
$857$			45.6493i			1.55935i	0.626184	+	0.779675i	$0.284616\pi$
$857$			45.6493i			1.55935i	−0.626184	+	0.779675i	$0.715384\pi$
$858$		0			0
$859$	13.5589			0.462623			0.231311	−	0.972880i	$-0.425698\pi$
$859$	13.5589			0.462623			0.231311	+	0.972880i	$0.425698\pi$
$860$	11.1759	+	2.77431i	0.381096	+	0.0946033i
$861$		0			0
$862$	0.0260696	−	0.213223i	0.000887934	−	0.00726240i
$863$		−	41.6327i		−	1.41719i	−0.705614	−	0.708597i	$-0.749329\pi$
$863$		−	41.6327i		−	1.41719i	0.705614	−	0.708597i	$-0.250671\pi$
$864$		0			0
$865$	11.2301			0.381834
$866$	−1.62533	+	13.2936i	−0.0552311	+	0.451734i
$867$		0			0
$868$		0			0
$869$	−7.75555			−0.263089
$870$		0			0
$871$	35.4053			1.19966
$872$	−16.0410	−	6.12929i	−0.543217	−	0.207564i
$873$		0			0
$874$	−1.03979	+	8.50439i	−0.0351713	+	0.287665i
$875$		0			0
$876$		0			0
$877$	−19.6848			−0.664708			−0.332354	−	0.943155i	$-0.607843\pi$
$877$	−19.6848			−0.664708			−0.332354	+	0.943155i	$0.607843\pi$
$878$	46.9902	+	5.74524i	1.58584	+	0.193893i
$879$		0			0
$880$	−18.6831	−	9.88494i	−0.629808	−	0.333221i
$881$		−	7.24606i		−	0.244126i	−0.992522	−	0.122063i	$-0.961049\pi$
$881$		−	7.24606i		−	0.244126i	0.992522	−	0.122063i	$-0.0389510\pi$
$882$		0			0
$883$		−	35.4533i		−	1.19310i	−0.802577	−	0.596549i	$-0.796538\pi$
$883$		−	35.4533i		−	1.19310i	0.802577	−	0.596549i	$-0.203462\pi$
$884$	−4.99879	−	1.24090i	−0.168128	−	0.0417360i
$885$		0			0
$886$	−4.48906	+	36.7160i	−0.150813	+	1.23350i
$887$	17.9737			0.603497			0.301749	−	0.953388i	$-0.402430\pi$
$887$	17.9737			0.603497			0.301749	+	0.953388i	$0.402430\pi$
$888$		0			0
$889$		0			0
$890$	−0.749976	−	0.0916955i	−0.0251392	−	0.00307364i
$891$		0			0
$892$	3.77705	+	0.937616i	0.126465	+	0.0313937i
$893$	−17.6493			−0.590610
$894$		0			0
$895$	−2.50005			−0.0835674
$896$		0			0
$897$		0			0
$898$	−14.4473	−	1.76639i	−0.482111	−	0.0589451i
$899$	−11.9740			−0.399355
$900$		0			0
$901$		−	2.81141i		−	0.0936615i
$902$	−72.5820	−	8.87421i	−2.41672	−	0.295479i
$903$		0			0
$904$	19.4972	+	7.44992i	0.648468	+	0.247781i
$905$	9.18747			0.305402
$906$		0			0
$907$			8.78577i			0.291727i	0.989305	+	0.145863i	$0.0465960\pi$
$907$			8.78577i			0.291727i	−0.989305	+	0.145863i	$0.953404\pi$
$908$	16.7813	+	4.16579i	0.556907	+	0.138247i
$909$		0			0
$910$		0			0
$911$			21.5478i			0.713911i	0.934121	+	0.356955i	$0.116185\pi$
$911$			21.5478i			0.713911i	−0.934121	+	0.356955i	$0.883815\pi$
$912$		0			0
$913$		−	2.98166i		−	0.0986787i
$914$	16.7489	+	2.04780i	0.554005	+	0.0677353i
$915$		0			0
$916$	−8.08983	+	32.5887i	−0.267295	+	1.07676i
$917$		0			0
$918$		0			0
$919$		−	31.8627i		−	1.05105i	−0.850777	−	0.525527i	$-0.823868\pi$
$919$		−	31.8627i		−	1.05105i	0.850777	−	0.525527i	$-0.176132\pi$
$920$	−3.15963	−	1.20730i	−0.104170	−	0.0398035i
$921$		0			0
$922$	−5.15051	+	42.1259i	−0.169623	+	1.38734i
$923$	−37.9479			−1.24907
$924$		0			0
$925$	−11.1262			−0.365828
$926$	2.27814	−	18.6329i	0.0748645	−	0.612315i
$927$		0			0
$928$	11.5130	+	8.01759i	0.377931	+	0.263190i
$929$		−	51.0088i		−	1.67355i	−0.547550	−	0.836773i	$-0.684439\pi$
$929$		−	51.0088i		−	1.67355i	0.547550	−	0.836773i	$-0.315561\pi$
$930$		0			0
$931$		0			0
$932$	2.03148	+	0.504294i	0.0665432	+	0.0165187i
$933$		0			0
$934$	41.6204	+	5.08871i	1.36186	+	0.166508i
$935$			3.62774i			0.118640i
$936$		0			0
$937$			2.65742i			0.0868141i	0.999057	+	0.0434071i	$0.0138212\pi$
$937$			2.65742i			0.0868141i	−0.999057	+	0.0434071i	$0.986179\pi$
$938$		0			0
$939$		0			0
$940$	1.67871	−	6.76246i	0.0547536	−	0.220567i
$941$			30.3594i			0.989689i	0.868982	+	0.494844i	$0.164775\pi$
$941$			30.3594i			0.989689i	−0.868982	+	0.494844i	$0.835225\pi$
$942$		0			0
$943$	−11.7014			−0.381050
$944$	44.8541	+	23.7316i	1.45988	+	0.772397i
$945$		0			0
$946$	45.9855	+	5.62240i	1.49512	+	0.182800i
$947$		−	43.4750i		−	1.41275i	−0.707839	−	0.706374i	$-0.750330\pi$
$947$		−	43.4750i		−	1.41275i	0.707839	−	0.706374i	$-0.249670\pi$
$948$		0			0
$949$	24.9861			0.811084
$950$	−27.9020	−	3.41143i	−0.905260	−	0.110681i
$951$		0			0
$952$		0			0
$953$	53.8683			1.74497			0.872483	−	0.488645i	$-0.162509\pi$
$953$	53.8683			1.74497			0.872483	+	0.488645i	$0.162509\pi$
$954$		0			0
$955$	−8.03035			−0.259856
$956$	−9.27472	+	37.3619i	−0.299966	+	1.20837i
$957$		0			0
$958$	−16.1930	−	1.97984i	−0.523173	−	0.0639656i
$959$		0			0
$960$		0			0
$961$	−7.69025			−0.248073
$962$	−1.75946	+	14.3906i	−0.0567272	+	0.463971i
$963$		0			0
$964$	−1.32842	+	5.35136i	−0.0427856	+	0.172356i
$965$			11.9236i			0.383835i
$966$		0			0
$967$		−	44.9529i		−	1.44559i	−0.691064	−	0.722794i	$-0.742858\pi$
$967$		−	44.9529i		−	1.44559i	0.691064	−	0.722794i	$-0.257142\pi$
$968$	−50.3738	−	19.2479i	−1.61908	−	0.618652i
$969$		0			0
$970$	−14.7116	−	1.79870i	−0.472360	−	0.0577529i
$971$	1.28352			0.0411900			0.0205950	−	0.999788i	$-0.493444\pi$
$971$	1.28352			0.0411900			0.0205950	+	0.999788i	$0.493444\pi$
$972$		0			0
$973$		0			0
$974$	−1.67428	+	13.6939i	−0.0536474	+	0.438781i
$975$		0			0
$976$	−19.4773	+	36.8132i	−0.623452	+	1.17836i
$977$	−19.3536			−0.619176			−0.309588	−	0.950871i	$-0.600191\pi$
$977$	−19.3536			−0.619176			−0.309588	+	0.950871i	$0.600191\pi$
$978$		0			0
$979$	−3.03979			−0.0971520
$980$		0			0
$981$		0			0
$982$	6.94649	−	56.8152i	0.221671	−	1.81305i
$983$	−8.43273			−0.268962			−0.134481	−	0.990916i	$-0.542937\pi$
$983$	−8.43273			−0.268962			−0.134481	+	0.990916i	$0.542937\pi$
$984$		0			0
$985$			3.11940i			0.0993923i
$986$	0.292225	−	2.39011i	0.00930635	−	0.0761165i
$987$		0			0
$988$	−8.82463	+	35.5488i	−0.280749	+	1.13096i
$989$	7.41360			0.235739
$990$		0			0
$991$		−	24.4758i		−	0.777500i	−0.921343	−	0.388750i	$-0.872907\pi$
$991$		−	24.4758i		−	0.777500i	0.921343	−	0.388750i	$-0.127093\pi$
$992$	−22.4122	−	15.6078i	−0.711589	−	0.495549i
$993$		0			0
$994$		0			0
$995$		−	18.5322i		−	0.587511i
$996$		0			0
$997$			33.5179i			1.06152i	0.847522	+	0.530761i	$0.178094\pi$
$997$			33.5179i			1.06152i	−0.847522	+	0.530761i	$0.821906\pi$
$998$	5.48620	−	44.8715i	0.173663	−	1.42038i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.b.j.1567.8		8
3.2	odd	2		588.2.b.a.391.1		8
4.3	odd	2		1764.2.b.i.1567.7		8
7.2	even	3		252.2.bf.f.199.2		8
7.3	odd	6		252.2.bf.g.19.2		8
7.6	odd	2		1764.2.b.i.1567.8		8
12.11	even	2		588.2.b.b.391.2		8
21.2	odd	6		84.2.o.b.31.3	yes	8
21.5	even	6		588.2.o.b.31.3		8
21.11	odd	6		588.2.o.d.19.3		8
21.17	even	6		84.2.o.a.19.3	✓	8
21.20	even	2		588.2.b.b.391.1		8
28.3	even	6		252.2.bf.f.19.2		8
28.23	odd	6		252.2.bf.g.199.2		8
28.27	even	2	inner	1764.2.b.j.1567.7		8
84.11	even	6		588.2.o.b.19.3		8
84.23	even	6		84.2.o.a.31.3	yes	8
84.47	odd	6		588.2.o.d.31.3		8
84.59	odd	6		84.2.o.b.19.3	yes	8
84.83	odd	2		588.2.b.a.391.2		8
168.59	odd	6		1344.2.bl.i.1279.2		8
168.101	even	6		1344.2.bl.j.1279.2		8
168.107	even	6		1344.2.bl.j.703.2		8
168.149	odd	6		1344.2.bl.i.703.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.3	✓	8	21.17	even	6
84.2.o.a.31.3	yes	8	84.23	even	6
84.2.o.b.19.3	yes	8	84.59	odd	6
84.2.o.b.31.3	yes	8	21.2	odd	6
252.2.bf.f.19.2		8	28.3	even	6
252.2.bf.f.199.2		8	7.2	even	3
252.2.bf.g.19.2		8	7.3	odd	6
252.2.bf.g.199.2		8	28.23	odd	6
588.2.b.a.391.1		8	3.2	odd	2
588.2.b.a.391.2		8	84.83	odd	2
588.2.b.b.391.1		8	21.20	even	2
588.2.b.b.391.2		8	12.11	even	2
588.2.o.b.19.3		8	84.11	even	6
588.2.o.b.31.3		8	21.5	even	6
588.2.o.d.19.3		8	21.11	odd	6
588.2.o.d.31.3		8	84.47	odd	6
1344.2.bl.i.703.2		8	168.149	odd	6
1344.2.bl.i.1279.2		8	168.59	odd	6
1344.2.bl.j.703.2		8	168.107	even	6
1344.2.bl.j.1279.2		8	168.101	even	6
1764.2.b.i.1567.7		8	4.3	odd	2
1764.2.b.i.1567.8		8	7.6	odd	2
1764.2.b.j.1567.7		8	28.27	even	2	inner
1764.2.b.j.1567.8		8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40376 + 0.171630i) q^{2} +(1.94109 + 0.481855i) q^{4} -0.963711i q^{5} +(2.64212 + 1.00956i) q^{8} +O(q^{10})\)	\(q+(1.40376 + 0.171630i) q^{2} +(1.94109 + 0.481855i) q^{4} -0.963711i q^{5} +(2.64212 + 1.00956i) q^{8} +(0.165402 - 1.35282i) q^{10} -5.48322i q^{11} -3.75117i q^{13} +(3.53563 + 1.87065i) q^{16} -0.686521i q^{17} -4.88217 q^{19} +(0.464369 - 1.87065i) q^{20} +(0.941086 - 7.69713i) q^{22} -1.24090i q^{23} +4.07126 q^{25} +(0.643814 - 5.26574i) q^{26} +2.48011 q^{29} -4.82802 q^{31} +(4.64212 + 3.23276i) q^{32} +(0.117828 - 0.963711i) q^{34} -2.73287 q^{37} +(-6.85340 - 0.837928i) q^{38} +(0.972923 - 2.54624i) q^{40} -9.42976i q^{41} +5.97437i q^{43} +(2.64212 - 10.6434i) q^{44} +(0.212976 - 1.74193i) q^{46} +3.61504 q^{47} +(5.71508 + 0.698752i) q^{50} +(1.80752 - 7.28134i) q^{52} +4.09515 q^{53} -5.28424 q^{55} +(3.48148 + 0.425661i) q^{58} +12.6863 q^{59} +10.4121i q^{61} +(-6.77738 - 0.828634i) q^{62} +(5.96158 + 5.33475i) q^{64} -3.61504 q^{65} +9.43847i q^{67} +(0.330804 - 1.33260i) q^{68} -10.1163i q^{71} +6.66089i q^{73} +(-3.83629 - 0.469043i) q^{74} +(-9.47672 - 2.35250i) q^{76} -1.41442i q^{79} +(1.80276 - 3.40733i) q^{80} +(1.61843 - 13.2371i) q^{82} +0.543780 q^{83} -0.661608 q^{85} +(-1.02538 + 8.38658i) q^{86} +(5.53563 - 14.4873i) q^{88} -0.554380i q^{89} +(0.597935 - 2.40870i) q^{92} +(5.07465 + 0.620450i) q^{94} +4.70500i q^{95} -10.8747i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{4} - 4 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^4 - 4 * q^8	\( 8 q + 2 q^{2} + 2 q^{4} - 4 q^{8} + 8 q^{10} + 10 q^{16} - 12 q^{19} + 22 q^{20} - 6 q^{22} - 4 q^{25} - 6 q^{26} + 16 q^{29} + 12 q^{31} + 12 q^{32} + 28 q^{34} - 12 q^{37} - 2 q^{38} - 4 q^{40} - 4 q^{44} - 12 q^{46} - 8 q^{47} - 2 q^{50} - 4 q^{52} - 8 q^{53} + 8 q^{55} - 14 q^{58} + 28 q^{59} - 48 q^{62} + 2 q^{64} + 8 q^{65} + 16 q^{68} - 38 q^{74} - 44 q^{76} + 6 q^{80} + 4 q^{82} + 4 q^{83} - 32 q^{85} - 6 q^{86} + 26 q^{88} + 28 q^{92} + 32 q^{94}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^4 - 4 * q^8 + 8 * q^10 + 10 * q^16 - 12 * q^19 + 22 * q^20 - 6 * q^22 - 4 * q^25 - 6 * q^26 + 16 * q^29 + 12 * q^31 + 12 * q^32 + 28 * q^34 - 12 * q^37 - 2 * q^38 - 4 * q^40 - 4 * q^44 - 12 * q^46 - 8 * q^47 - 2 * q^50 - 4 * q^52 - 8 * q^53 + 8 * q^55 - 14 * q^58 + 28 * q^59 - 48 * q^62 + 2 * q^64 + 8 * q^65 + 16 * q^68 - 38 * q^74 - 44 * q^76 + 6 * q^80 + 4 * q^82 + 4 * q^83 - 32 * q^85 - 6 * q^86 + 26 * q^88 + 28 * q^92 + 32 * q^94

Introduction

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