LMFDB - Embedded newform 1224.2.j.a.35.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1224,2,Mod(35,1224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1224, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1224.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1224 = 2^{3} \cdot 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1224.j (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:	$9.77368920740$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			35.20
Character	$\chi$	$=$	1224.35
Dual form			1224.2.j.a.35.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.769703 + 1.18641i) q^{2} +(-0.815114 - 1.82636i) q^{4} +1.43325 q^{5} -0.898362i q^{7} +(2.79420 + 0.438699i) q^{8} +O(q^{10})$	\(q+(-0.769703 + 1.18641i) q^{2} +(-0.815114 - 1.82636i) q^{4} +1.43325 q^{5} -0.898362i q^{7} +(2.79420 + 0.438699i) q^{8} +(-1.10318 + 1.70042i) q^{10} +1.19132i q^{11} -1.91661i q^{13} +(1.06582 + 0.691472i) q^{14} +(-2.67118 + 2.97738i) q^{16} +1.00000i q^{17} +1.78911 q^{19} +(-1.16826 - 2.61763i) q^{20} +(-1.41339 - 0.916962i) q^{22} +5.45281 q^{23} -2.94579 q^{25} +(2.27388 + 1.47522i) q^{26} +(-1.64073 + 0.732267i) q^{28} +5.66999 q^{29} +3.20304i q^{31} +(-1.47637 - 5.46080i) q^{32} +(-1.18641 - 0.769703i) q^{34} -1.28758i q^{35} -3.14922i q^{37} +(-1.37708 + 2.12260i) q^{38} +(4.00479 + 0.628766i) q^{40} -11.4999i q^{41} -6.76090 q^{43} +(2.17578 - 0.971061i) q^{44} +(-4.19704 + 6.46924i) q^{46} +9.32757 q^{47} +6.19295 q^{49} +(2.26738 - 3.49490i) q^{50} +(-3.50042 + 1.56226i) q^{52} +4.18621 q^{53} +1.70746i q^{55} +(0.394110 - 2.51020i) q^{56} +(-4.36421 + 6.72690i) q^{58} +2.21212i q^{59} -12.2989i q^{61} +(-3.80010 - 2.46539i) q^{62} +(7.61509 + 2.45162i) q^{64} -2.74699i q^{65} +7.96604 q^{67} +(1.82636 - 0.815114i) q^{68} +(1.52759 + 0.991053i) q^{70} +6.29388 q^{71} +6.85144 q^{73} +(3.73625 + 2.42397i) q^{74} +(-1.45833 - 3.26755i) q^{76} +1.07024 q^{77} +2.45723i q^{79} +(-3.82847 + 4.26734i) q^{80} +(13.6436 + 8.85154i) q^{82} +10.4309i q^{83} +1.43325i q^{85} +(5.20389 - 8.02117i) q^{86} +(-0.522631 + 3.32878i) q^{88} +5.54979i q^{89} -1.72181 q^{91} +(-4.44466 - 9.95879i) q^{92} +(-7.17946 + 11.0663i) q^{94} +2.56424 q^{95} -4.18149 q^{97} +(-4.76673 + 7.34734i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q + 16 q^{10} + 24 q^{16} + 8 q^{22} + 64 q^{25} + 8 q^{28} + 24 q^{40} - 64 q^{43} - 32 q^{46} - 32 q^{49} + 56 q^{52} + 40 q^{58} + 72 q^{64} + 32 q^{67} + 40 q^{70} + 32 q^{73} - 40 q^{76} - 40 q^{82} - 80 q^{88} + 8 q^{94} - 64 q^{97}+O(q^{100}) $ 64 * q + 16 * q^10 + 24 * q^16 + 8 * q^22 + 64 * q^25 + 8 * q^28 + 24 * q^40 - 64 * q^43 - 32 * q^46 - 32 * q^49 + 56 * q^52 + 40 * q^58 + 72 * q^64 + 32 * q^67 + 40 * q^70 + 32 * q^73 - 40 * q^76 - 40 * q^82 - 80 * q^88 + 8 * q^94 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1224\mathbb{Z}\right)^\times$.

$n$	$137$	$613$	$649$	$919$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.769703	+	1.18641i	−0.544262	+	0.838915i
$2$	−0.769703	+	1.18641i	−0.544262	+	0.838915i
$3$		0			0
$3$		0			0
$4$	−0.815114	−	1.82636i	−0.407557	−	0.913180i
$5$	1.43325			0.640970			0.320485	−	0.947254i	$-0.396154\pi$
$5$	1.43325			0.640970			0.320485	+	0.947254i	$0.396154\pi$
$6$		0			0
$7$		−	0.898362i		−	0.339549i	−0.985483	−	0.169774i	$-0.945696\pi$
$7$		−	0.898362i		−	0.339549i	0.985483	−	0.169774i	$-0.0543039\pi$
$8$	2.79420	+	0.438699i	0.987898	+	0.155104i
$9$		0			0
$10$	−1.10318	+	1.70042i	−0.348856	+	0.537719i
$11$			1.19132i			0.359196i	0.983740	+	0.179598i	$0.0574797\pi$
$11$			1.19132i			0.359196i	−0.983740	+	0.179598i	$0.942520\pi$
$12$		0			0
$13$		−	1.91661i		−	0.531573i	−0.964032	−	0.265786i	$-0.914368\pi$
$13$		−	1.91661i		−	0.531573i	0.964032	−	0.265786i	$-0.0856316\pi$
$14$	1.06582	+	0.691472i	0.284853	+	0.184804i
$15$		0			0
$16$	−2.67118	+	2.97738i	−0.667794	+	0.744346i
$17$			1.00000i			0.242536i
$17$			1.00000i			0.242536i
$18$		0			0
$19$	1.78911			0.410449			0.205224	−	0.978715i	$-0.434208\pi$
$19$	1.78911			0.410449			0.205224	+	0.978715i	$0.434208\pi$
$20$	−1.16826	−	2.61763i	−0.261232	−	0.585321i
$21$		0			0
$22$	−1.41339	−	0.916962i	−0.301335	−	0.195497i
$23$	5.45281			1.13699			0.568495	−	0.822687i	$-0.307526\pi$
$23$	5.45281			1.13699			0.568495	+	0.822687i	$0.307526\pi$
$24$		0			0
$25$	−2.94579			−0.589158
$26$	2.27388	+	1.47522i	0.445944	+	0.289315i
$27$		0			0
$28$	−1.64073	+	0.732267i	−0.310069	+	0.138385i
$29$	5.66999			1.05289			0.526445	−	0.850209i	$-0.323525\pi$
$29$	5.66999			1.05289			0.526445	+	0.850209i	$0.323525\pi$
$30$		0			0
$31$			3.20304i			0.575282i	0.957738	+	0.287641i	$0.0928710\pi$
$31$			3.20304i			0.575282i	−0.957738	+	0.287641i	$0.907129\pi$
$32$	−1.47637	−	5.46080i	−0.260987	−	0.965342i
$33$		0			0
$34$	−1.18641	−	0.769703i	−0.203467	−	0.132003i
$35$		−	1.28758i		−	0.217641i
$36$		0			0
$37$		−	3.14922i		−	0.517729i	−0.965914	−	0.258864i	$-0.916652\pi$
$37$		−	3.14922i		−	0.517729i	0.965914	−	0.258864i	$-0.0833483\pi$
$38$	−1.37708	+	2.12260i	−0.223392	+	0.344332i
$39$		0			0
$40$	4.00479	+	0.628766i	0.633213	+	0.0994167i
$41$		−	11.4999i		−	1.79599i	−0.440007	−	0.897994i	$-0.645024\pi$
$41$		−	11.4999i		−	1.79599i	0.440007	−	0.897994i	$-0.354976\pi$
$42$		0			0
$43$	−6.76090			−1.03103			−0.515514	−	0.856881i	$-0.672399\pi$
$43$	−6.76090			−1.03103			−0.515514	+	0.856881i	$0.672399\pi$
$44$	2.17578	−	0.971061i	0.328011	−	0.146393i
$45$		0			0
$46$	−4.19704	+	6.46924i	−0.618820	+	0.953837i
$47$	9.32757			1.36057			0.680283	−	0.732950i	$-0.261857\pi$
$47$	9.32757			1.36057			0.680283	+	0.732950i	$0.261857\pi$
$48$		0			0
$49$	6.19295			0.884707
$50$	2.26738	−	3.49490i	0.320656	−	0.494253i
$51$		0			0
$52$	−3.50042	+	1.56226i	−0.485421	+	0.216646i
$53$	4.18621			0.575020			0.287510	−	0.957778i	$-0.407172\pi$
$53$	4.18621			0.575020			0.287510	+	0.957778i	$0.407172\pi$
$54$		0			0
$55$			1.70746i			0.230234i
$56$	0.394110	−	2.51020i	0.0526652	−	0.335440i
$57$		0			0
$58$	−4.36421	+	6.72690i	−0.573049	+	0.883286i
$59$			2.21212i			0.287993i	0.989578	+	0.143997i	$0.0459954\pi$
$59$			2.21212i			0.287993i	−0.989578	+	0.143997i	$0.954005\pi$
$60$		0			0
$61$		−	12.2989i		−	1.57471i	−0.616498	−	0.787356i	$-0.711449\pi$
$61$		−	12.2989i		−	1.57471i	0.616498	−	0.787356i	$-0.288551\pi$
$62$	−3.80010	−	2.46539i	−0.482613	−	0.313104i
$63$		0			0
$64$	7.61509	+	2.45162i	0.951886	+	0.306453i
$65$		−	2.74699i		−	0.340722i
$66$		0			0
$67$	7.96604			0.973207			0.486604	−	0.873623i	$-0.338236\pi$
$67$	7.96604			0.973207			0.486604	+	0.873623i	$0.338236\pi$
$68$	1.82636	−	0.815114i	0.221479	−	0.0988471i
$69$		0			0
$70$	1.52759	+	0.991053i	0.182582	+	0.118454i
$71$	6.29388			0.746946			0.373473	−	0.927641i	$-0.378167\pi$
$71$	6.29388			0.746946			0.373473	+	0.927641i	$0.378167\pi$
$72$		0			0
$73$	6.85144			0.801901			0.400950	−	0.916100i	$-0.368680\pi$
$73$	6.85144			0.801901			0.400950	+	0.916100i	$0.368680\pi$
$74$	3.73625	+	2.42397i	0.434331	+	0.281780i
$75$		0			0
$76$	−1.45833	−	3.26755i	−0.167281	−	0.374814i
$77$	1.07024			0.121965
$78$		0			0
$79$			2.45723i			0.276460i	0.990400	+	0.138230i	$0.0441414\pi$
$79$			2.45723i			0.276460i	−0.990400	+	0.138230i	$0.955859\pi$
$80$	−3.82847	+	4.26734i	−0.428036	+	0.477103i
$81$		0			0
$82$	13.6436	+	8.85154i	1.50668	+	0.977489i
$83$			10.4309i			1.14494i	0.819925	+	0.572472i	$0.194015\pi$
$83$			10.4309i			1.14494i	−0.819925	+	0.572472i	$0.805985\pi$
$84$		0			0
$85$			1.43325i			0.155458i
$86$	5.20389	−	8.02117i	0.561149	−	0.864945i
$87$		0			0
$88$	−0.522631	+	3.32878i	−0.0557126	+	0.354849i
$89$			5.54979i			0.588277i	0.955763	+	0.294138i	$0.0950326\pi$
$89$			5.54979i			0.588277i	−0.955763	+	0.294138i	$0.904967\pi$
$90$		0			0
$91$	−1.72181			−0.180495
$92$	−4.44466	−	9.95879i	−0.463388	−	1.03828i
$93$		0			0
$94$	−7.17946	+	11.0663i	−0.740505	+	1.14140i
$95$	2.56424			0.263085
$96$		0			0
$97$	−4.18149			−0.424566			−0.212283	−	0.977208i	$-0.568090\pi$
$97$	−4.18149			−0.424566			−0.212283	+	0.977208i	$0.568090\pi$
$98$	−4.76673	+	7.34734i	−0.481512	+	0.742194i
$99$		0			0
$100$	2.40115	+	5.38007i	0.240115	+	0.538007i
$101$	2.24612			0.223498			0.111749	−	0.993736i	$-0.464355\pi$
$101$	2.24612			0.223498			0.111749	+	0.993736i	$0.464355\pi$
$102$		0			0
$103$		−	4.75340i		−	0.468366i	−0.972193	−	0.234183i	$-0.924758\pi$
$103$		−	4.75340i		−	0.468366i	0.972193	−	0.234183i	$-0.0752415\pi$
$104$	0.840816	−	5.35540i	0.0824488	−	0.525140i
$105$		0			0
$106$	−3.22214	+	4.96654i	−0.312962	+	0.482393i
$107$			9.93616i			0.960565i	0.877114	+	0.480282i	$0.159466\pi$
$107$			9.93616i			0.960565i	−0.877114	+	0.480282i	$0.840534\pi$
$108$		0			0
$109$			2.49633i			0.239105i	0.992828	+	0.119553i	$0.0381460\pi$
$109$			2.49633i			0.239105i	−0.992828	+	0.119553i	$0.961854\pi$
$110$	−2.02574	−	1.31424i	−0.193147	−	0.125308i
$111$		0			0
$112$	2.67477	+	2.39968i	0.252742	+	0.226749i
$113$			2.42048i			0.227700i	0.993498	+	0.113850i	$0.0363183\pi$
$113$			2.42048i			0.227700i	−0.993498	+	0.113850i	$0.963682\pi$
$114$		0			0
$115$	7.81525			0.728776
$116$	−4.62169	−	10.3554i	−0.429113	−	0.961478i
$117$		0			0
$118$	−2.62447	−	1.70267i	−0.241602	−	0.156744i
$119$	0.898362			0.0823527
$120$		0			0
$121$	9.58076			0.870978
$122$	14.5915	+	9.46650i	1.32105	+	0.857057i
$123$		0			0
$124$	5.84989	−	2.61084i	0.525336	−	0.234460i
$125$	−11.3883			−1.01860
$126$		0			0
$127$		−	9.70269i		−	0.860974i	−0.902597	−	0.430487i	$-0.858342\pi$
$127$		−	9.70269i		−	0.860974i	0.902597	−	0.430487i	$-0.141658\pi$
$128$	−8.76998	+	7.14755i	−0.775164	+	0.631760i
$129$		0			0
$130$	3.25904	+	2.11437i	0.285837	+	0.185442i
$131$			6.23151i			0.544450i	0.962234	+	0.272225i	$0.0877595\pi$
$131$			6.23151i			0.544450i	−0.962234	+	0.272225i	$0.912241\pi$
$132$		0			0
$133$		−	1.60726i		−	0.139367i
$134$	−6.13149	+	9.45095i	−0.529680	+	0.816438i
$135$		0			0
$136$	−0.438699	+	2.79420i	−0.0376181	+	0.239601i
$137$		−	1.84950i		−	0.158013i	−0.996874	−	0.0790067i	$-0.974825\pi$
$137$		−	1.84950i		−	0.158013i	0.996874	−	0.0790067i	$-0.0251749\pi$
$138$		0			0
$139$	−6.55465			−0.555958			−0.277979	−	0.960587i	$-0.589665\pi$
$139$	−6.55465			−0.555958			−0.277979	+	0.960587i	$0.589665\pi$
$140$	−2.35158	+	1.04952i	−0.198745	+	0.0887009i
$141$		0			0
$142$	−4.84442	+	7.46709i	−0.406535	+	0.626625i
$143$	2.28330			0.190939
$144$		0			0
$145$	8.12652			0.674871
$146$	−5.27358	+	8.12859i	−0.436444	+	0.672727i
$147$		0			0
$148$	−5.75161	+	2.56698i	−0.472780	+	0.211004i
$149$	−6.31241			−0.517133			−0.258566	−	0.965993i	$-0.583250\pi$
$149$	−6.31241			−0.517133			−0.258566	+	0.965993i	$0.583250\pi$
$150$		0			0
$151$			0.980846i			0.0798201i	0.999203	+	0.0399100i	$0.0127071\pi$
$151$			0.980846i			0.0798201i	−0.999203	+	0.0399100i	$0.987293\pi$
$152$	4.99912	+	0.784879i	0.405482	+	0.0636621i
$153$		0			0
$154$	−0.823764	+	1.26973i	−0.0663808	+	0.102318i
$155$			4.59076i			0.368739i
$156$		0			0
$157$		−	7.80070i		−	0.622564i	−0.950318	−	0.311282i	$-0.899242\pi$
$157$		−	7.80070i		−	0.622564i	0.950318	−	0.311282i	$-0.100758\pi$
$158$	−2.91527	−	1.89134i	−0.231927	−	0.150467i
$159$		0			0
$160$	−2.11601	−	7.82670i	−0.167285	−	0.618755i
$161$		−	4.89859i		−	0.386063i
$162$		0			0
$163$	−17.6406			−1.38172			−0.690861	−	0.722988i	$-0.742768\pi$
$163$	−17.6406			−1.38172			−0.690861	+	0.722988i	$0.742768\pi$
$164$	−21.0030	+	9.37376i	−1.64006	+	0.731968i
$165$		0			0
$166$	−12.3753	−	8.02872i	−0.960510	−	0.623149i
$167$	15.8796			1.22880			0.614399	−	0.788996i	$-0.289399\pi$
$167$	15.8796			1.22880			0.614399	+	0.788996i	$0.289399\pi$
$168$		0			0
$169$	9.32660			0.717430
$170$	−1.70042	−	1.10318i	−0.130416	−	0.0846099i
$171$		0			0
$172$	5.51090	+	12.3478i	0.420203	+	0.941513i
$173$	−4.01440			−0.305209			−0.152605	−	0.988287i	$-0.548766\pi$
$173$	−4.01440			−0.305209			−0.152605	+	0.988287i	$0.548766\pi$
$174$		0			0
$175$			2.64638i			0.200048i
$176$	−3.54701	−	3.18223i	−0.267366	−	0.239869i
$177$		0			0
$178$	−6.58430	−	4.27169i	−0.493514	−	0.320177i
$179$			20.1652i			1.50722i	0.657324	+	0.753608i	$0.271688\pi$
$179$			20.1652i			1.50722i	−0.657324	+	0.753608i	$0.728312\pi$
$180$		0			0
$181$			6.28918i			0.467471i	0.972300	+	0.233735i	$0.0750950\pi$
$181$			6.28918i			0.467471i	−0.972300	+	0.233735i	$0.924905\pi$
$182$	1.32528	−	2.04277i	0.0982366	−	0.151420i
$183$		0			0
$184$	15.2362	+	2.39214i	1.12323	+	0.176351i
$185$		−	4.51363i		−	0.331849i
$186$		0			0
$187$	−1.19132			−0.0871179
$188$	−7.60303	−	17.0355i	−0.554508	−	1.24244i
$189$		0			0
$190$	−1.97370	+	3.04223i	−0.143187	+	0.220706i
$191$	−8.34317			−0.603690			−0.301845	−	0.953357i	$-0.597603\pi$
$191$	−8.34317			−0.603690			−0.301845	+	0.953357i	$0.597603\pi$
$192$		0			0
$193$	13.7643			0.990776			0.495388	−	0.868672i	$-0.335026\pi$
$193$	13.7643			0.990776			0.495388	+	0.868672i	$0.335026\pi$
$194$	3.21851	−	4.96094i	0.231075	−	0.356175i
$195$		0			0
$196$	−5.04796	−	11.3105i	−0.360568	−	0.807896i
$197$	−7.31477			−0.521156			−0.260578	−	0.965453i	$-0.583913\pi$
$197$	−7.31477			−0.521156			−0.260578	+	0.965453i	$0.583913\pi$
$198$		0			0
$199$			3.37737i			0.239415i	0.992809	+	0.119708i	$0.0381957\pi$
$199$			3.37737i			0.239415i	−0.992809	+	0.119708i	$0.961804\pi$
$200$	−8.23112	−	1.29231i	−0.582028	−	0.0913805i
$201$		0			0
$202$	−1.72885	+	2.66481i	−0.121641	+	0.187496i
$203$		−	5.09370i		−	0.357508i
$204$		0			0
$205$		−	16.4823i		−	1.15117i
$206$	5.63946	+	3.65871i	0.392920	+	0.254914i
$207$		0			0
$208$	5.70649	+	5.11961i	0.395674	+	0.354981i
$209$			2.13140i			0.147432i
$210$		0			0
$211$	−10.6590			−0.733795			−0.366897	−	0.930261i	$-0.619580\pi$
$211$	−10.6590			−0.733795			−0.366897	+	0.930261i	$0.619580\pi$
$212$	−3.41224	−	7.64553i	−0.234354	−	0.525097i
$213$		0			0
$214$	−11.7883	−	7.64789i	−0.805832	−	0.522799i
$215$	−9.69007			−0.660858
$216$		0			0
$217$	2.87748			0.195336
$218$	−2.96166	−	1.92143i	−0.200589	−	0.130136i
$219$		0			0
$220$	3.11844	−	1.39178i	0.210245	−	0.0938335i
$221$	1.91661			0.128925
$222$		0			0
$223$		−	22.3187i		−	1.49457i	−0.664503	−	0.747285i	$-0.731357\pi$
$223$		−	22.3187i		−	1.49457i	0.664503	−	0.747285i	$-0.268643\pi$
$224$	−4.90577	+	1.32631i	−0.327781	+	0.0886180i
$225$		0			0
$226$	−2.87167	−	1.86305i	−0.191021	−	0.123928i
$227$			4.70361i			0.312190i	0.987742	+	0.156095i	$0.0498905\pi$
$227$			4.70361i			0.312190i	−0.987742	+	0.156095i	$0.950109\pi$
$228$		0			0
$229$		−	15.7001i		−	1.03749i	−0.854928	−	0.518747i	$-0.826399\pi$
$229$		−	15.7001i		−	1.03749i	0.854928	−	0.518747i	$-0.173601\pi$
$230$	−6.01542	+	9.27205i	−0.396645	+	0.611381i
$231$		0			0
$232$	15.8431	+	2.48742i	1.04015	+	0.163307i
$233$		−	20.5634i		−	1.34715i	−0.739118	−	0.673576i	$-0.764757\pi$
$233$		−	20.5634i		−	1.34715i	0.739118	−	0.673576i	$-0.235243\pi$
$234$		0			0
$235$	13.3688			0.872082
$236$	4.04012	−	1.80313i	0.262990	−	0.117374i
$237$		0			0
$238$	−0.691472	+	1.06582i	−0.0448215	+	0.0690869i
$239$	−10.2576			−0.663509			−0.331754	−	0.943366i	$-0.607641\pi$
$239$	−10.2576			−0.663509			−0.331754	+	0.943366i	$0.607641\pi$
$240$		0			0
$241$	−7.82949			−0.504342			−0.252171	−	0.967683i	$-0.581145\pi$
$241$	−7.82949			−0.504342			−0.252171	+	0.967683i	$0.581145\pi$
$242$	−7.37434	+	11.3667i	−0.474041	+	0.730677i
$243$		0			0
$244$	−22.4622	+	10.0250i	−1.43800	+	0.641785i
$245$	8.87605			0.567070
$246$		0			0
$247$		−	3.42902i		−	0.218183i
$248$	−1.40517	+	8.94992i	−0.0892283	+	0.568320i
$249$		0			0
$250$	8.76562	−	13.5112i	0.554387	−	0.854521i
$251$			4.59202i			0.289846i	0.989443	+	0.144923i	$0.0462934\pi$
$251$			4.59202i			0.289846i	−0.989443	+	0.144923i	$0.953707\pi$
$252$		0			0
$253$			6.49604i			0.408402i
$254$	11.5113	+	7.46819i	0.722284	+	0.468596i
$255$		0			0
$256$	−1.72962	−	15.9062i	−0.108101	−	0.994140i
$257$		−	18.4277i		−	1.14949i	−0.818332	−	0.574745i	$-0.805101\pi$
$257$		−	18.4277i		−	1.14949i	0.818332	−	0.574745i	$-0.194899\pi$
$258$		0			0
$259$	−2.82914			−0.175794
$260$	−5.01699	+	2.23911i	−0.311141	+	0.138864i
$261$		0			0
$262$	−7.39310	−	4.79641i	−0.456747	−	0.296323i
$263$	23.7626			1.46526			0.732632	−	0.680625i	$-0.238292\pi$
$263$	23.7626			1.46526			0.732632	+	0.680625i	$0.238292\pi$
$264$		0			0
$265$	5.99990			0.368571
$266$	1.90687	+	1.23712i	0.116917	+	0.0758524i
$267$		0			0
$268$	−6.49323	−	14.5489i	−0.396637	−	0.888713i
$269$	−6.26636			−0.382067			−0.191033	−	0.981584i	$-0.561184\pi$
$269$	−6.26636			−0.382067			−0.191033	+	0.981584i	$0.561184\pi$
$270$		0			0
$271$			18.3036i			1.11186i	0.831228	+	0.555932i	$0.187639\pi$
$271$			18.3036i			1.11186i	−0.831228	+	0.555932i	$0.812361\pi$
$272$	−2.97738	−	2.67118i	−0.180530	−	0.161964i
$273$		0			0
$274$	2.19426	+	1.42357i	0.132560	+	0.0860008i
$275$		−	3.50937i		−	0.211623i
$276$		0			0
$277$		−	2.82761i		−	0.169895i	−0.996385	−	0.0849473i	$-0.972928\pi$
$277$		−	2.82761i		−	0.169895i	0.996385	−	0.0849473i	$-0.0270722\pi$
$278$	5.04513	−	7.77647i	0.302587	−	0.466402i
$279$		0			0
$280$	0.564860	−	3.59775i	0.0337568	−	0.215007i
$281$			18.0191i			1.07493i	0.843287	+	0.537464i	$0.180618\pi$
$281$			18.0191i			1.07493i	−0.843287	+	0.537464i	$0.819382\pi$
$282$		0			0
$283$	−16.5755			−0.985308			−0.492654	−	0.870225i	$-0.663973\pi$
$283$	−16.5755			−0.985308			−0.492654	+	0.870225i	$0.663973\pi$
$284$	−5.13023	−	11.4949i	−0.304423	−	0.682096i
$285$		0			0
$286$	−1.75746	+	2.70892i	−0.103921	+	0.160182i
$287$	−10.3311			−0.609826
$288$		0			0
$289$	−1.00000			−0.0588235
$290$	−6.25501	+	9.64135i	−0.367307	+	0.566159i
$291$		0			0
$292$	−5.58471	−	12.5132i	−0.326820	−	0.732280i
$293$	−30.9345			−1.80722			−0.903608	−	0.428361i	$-0.859091\pi$
$293$	−30.9345			−1.80722			−0.903608	+	0.428361i	$0.859091\pi$
$294$		0			0
$295$			3.17052i			0.184595i
$296$	1.38156	−	8.79955i	0.0803016	−	0.511463i
$297$		0			0
$298$	4.85868	−	7.48907i	0.281456	−	0.433830i
$299$		−	10.4509i		−	0.604392i
$300$		0			0
$301$			6.07373i			0.350084i
$302$	−1.16368	−	0.754960i	−0.0669623	−	0.0434431i
$303$		0			0
$304$	−4.77902	+	5.32685i	−0.274096	+	0.305516i
$305$		−	17.6274i		−	1.00934i
$306$		0			0
$307$	−1.04461			−0.0596191			−0.0298095	−	0.999556i	$-0.509490\pi$
$307$	−1.04461			−0.0596191			−0.0298095	+	0.999556i	$0.509490\pi$
$308$	−0.872364	−	1.95463i	−0.0497075	−	0.111376i
$309$		0			0
$310$	−5.44650	−	3.53352i	−0.309340	−	0.200690i
$311$	20.9030			1.18530			0.592651	−	0.805460i	$-0.298081\pi$
$311$	20.9030			1.18530			0.592651	+	0.805460i	$0.298081\pi$
$312$		0			0
$313$	1.89294			0.106995			0.0534977	−	0.998568i	$-0.482963\pi$
$313$	1.89294			0.106995			0.0534977	+	0.998568i	$0.482963\pi$
$314$	9.25479	+	6.00422i	0.522278	+	0.338838i
$315$		0			0
$316$	4.48779	−	2.00293i	0.252458	−	0.112673i
$317$	−16.6067			−0.932723			−0.466362	−	0.884594i	$-0.654435\pi$
$317$	−16.6067			−0.932723			−0.466362	+	0.884594i	$0.654435\pi$
$318$		0			0
$319$			6.75477i			0.378194i
$320$	10.9143	+	3.51380i	0.610130	+	0.196427i
$321$		0			0
$322$	5.81172	+	3.77046i	0.323874	+	0.210120i
$323$			1.78911i			0.0995485i
$324$		0			0
$325$			5.64594i			0.313180i
$326$	13.5781	−	20.9290i	0.752019	−	1.15915i
$327$		0			0
$328$	5.04501	−	32.1331i	0.278564	−	1.77425i
$329$		−	8.37953i		−	0.461979i
$330$		0			0
$331$	−29.7699			−1.63630			−0.818150	−	0.575006i	$-0.805000\pi$
$331$	−29.7699			−1.63630			−0.818150	+	0.575006i	$0.805000\pi$
$332$	19.0506	−	8.50240i	1.04554	−	0.466630i
$333$		0			0
$334$	−12.2226	+	18.8396i	−0.668788	+	1.03086i
$335$	11.4173			0.623796
$336$		0			0
$337$	12.2555			0.667597			0.333799	−	0.942644i	$-0.391669\pi$
$337$	12.2555			0.667597			0.333799	+	0.942644i	$0.391669\pi$
$338$	−7.17871	+	11.0651i	−0.390470	+	0.601863i
$339$		0			0
$340$	2.61763	−	1.16826i	0.141961	−	0.0633580i
$341$	−3.81584			−0.206639
$342$		0			0
$343$		−	11.8520i		−	0.639950i
$344$	−18.8913	−	2.96600i	−1.01855	−	0.159916i
$345$		0			0
$346$	3.08990	−	4.76271i	0.166114	−	0.256045i
$347$		−	24.3411i		−	1.30670i	−0.757057	−	0.653349i	$-0.773364\pi$
$347$		−	24.3411i		−	1.30670i	0.757057	−	0.653349i	$-0.226636\pi$
$348$		0			0
$349$		−	17.7264i		−	0.948874i	−0.880290	−	0.474437i	$-0.842652\pi$
$349$		−	17.7264i		−	0.948874i	0.880290	−	0.474437i	$-0.157348\pi$
$350$	−3.13968	−	2.03693i	−0.167823	−	0.108878i
$351$		0			0
$352$	6.50556	−	1.75883i	0.346747	−	0.0937457i
$353$			13.3014i			0.707960i	0.935253	+	0.353980i	$0.115172\pi$
$353$			13.3014i			0.707960i	−0.935253	+	0.353980i	$0.884828\pi$
$354$		0			0
$355$	9.02072			0.478770
$356$	10.1359	−	4.52371i	0.537202	−	0.239756i
$357$		0			0
$358$	−23.9241	−	15.5212i	−1.26443	−	0.820321i
$359$	−3.30483			−0.174422			−0.0872112	−	0.996190i	$-0.527795\pi$
$359$	−3.30483			−0.174422			−0.0872112	+	0.996190i	$0.527795\pi$
$360$		0			0
$361$	−15.7991			−0.831532
$362$	−7.46151	−	4.84080i	−0.392168	−	0.254427i
$363$		0			0
$364$	1.40347	+	3.14465i	0.0735620	+	0.164824i
$365$	9.81985			0.513994
$366$		0			0
$367$		−	19.1746i		−	1.00090i	−0.865764	−	0.500452i	$-0.833167\pi$
$367$		−	19.1746i		−	1.00090i	0.865764	−	0.500452i	$-0.166833\pi$
$368$	−14.5654	+	16.2351i	−0.759275	+	0.846313i
$369$		0			0
$370$	5.35499	+	3.47415i	0.278393	+	0.180613i
$371$		−	3.76073i		−	0.195247i
$372$		0			0
$373$		−	32.5037i		−	1.68298i	−0.540275	−	0.841488i	$-0.681680\pi$
$373$		−	32.5037i		−	1.68298i	0.540275	−	0.841488i	$-0.318320\pi$
$374$	0.916962	−	1.41339i	0.0474150	−	0.0730845i
$375$		0			0
$376$	26.0631	+	4.09200i	1.34410	+	0.211029i
$377$		−	10.8672i		−	0.559688i
$378$		0			0
$379$	3.19923			0.164333			0.0821666	−	0.996619i	$-0.473816\pi$
$379$	3.19923			0.164333			0.0821666	+	0.996619i	$0.473816\pi$
$380$	−2.09015	−	4.68322i	−0.107222	−	0.240244i
$381$		0			0
$382$	6.42176	−	9.89837i	0.328566	−	0.506445i
$383$	−24.0955			−1.23122			−0.615612	−	0.788050i	$-0.711091\pi$
$383$	−24.0955			−1.23122			−0.615612	+	0.788050i	$0.711091\pi$
$384$		0			0
$385$	1.53392			0.0781757
$386$	−10.5944	+	16.3300i	−0.539242	+	0.831177i
$387$		0			0
$388$	3.40839	+	7.63691i	0.173035	+	0.387705i
$389$	−25.3512			−1.28536			−0.642679	−	0.766135i	$-0.722177\pi$
$389$	−25.3512			−1.28536			−0.642679	+	0.766135i	$0.722177\pi$
$390$		0			0
$391$			5.45281i			0.275760i
$392$	17.3043	+	2.71684i	0.874000	+	0.137221i
$393$		0			0
$394$	5.63020	−	8.67828i	0.283645	−	0.437205i
$395$			3.52184i			0.177203i
$396$		0			0
$397$			21.0902i			1.05849i	0.848470	+	0.529243i	$0.177524\pi$
$397$			21.0902i			1.05849i	−0.848470	+	0.529243i	$0.822476\pi$
$398$	−4.00693	−	2.59957i	−0.200849	−	0.130305i
$399$		0			0
$400$	7.86873	−	8.77074i	0.393436	−	0.438537i
$401$		−	7.37022i		−	0.368051i	−0.982921	−	0.184026i	$-0.941087\pi$
$401$		−	7.37022i		−	0.368051i	0.982921	−	0.184026i	$-0.0589130\pi$
$402$		0			0
$403$	6.13898			0.305804
$404$	−1.83085	−	4.10223i	−0.0910880	−	0.204094i
$405$		0			0
$406$	6.04319	+	3.92064i	0.299919	+	0.194578i
$407$	3.75173			0.185966
$408$		0			0
$409$	1.72601			0.0853456			0.0426728	−	0.999089i	$-0.486413\pi$
$409$	1.72601			0.0853456			0.0426728	+	0.999089i	$0.486413\pi$
$410$	19.5547	+	12.6865i	0.965737	+	0.626541i
$411$		0			0
$412$	−8.68141	+	3.87456i	−0.427703	+	0.190886i
$413$	1.98728			0.0977877
$414$		0			0
$415$			14.9502i			0.733874i
$416$	−10.4662	+	2.82963i	−0.513150	+	0.138734i
$417$		0			0
$418$	−2.52870	−	1.64054i	−0.123683	−	0.0802415i
$419$			25.3266i			1.23729i	0.785672	+	0.618643i	$0.212317\pi$
$419$			25.3266i			1.23729i	−0.785672	+	0.618643i	$0.787683\pi$
$420$		0			0
$421$			18.7025i			0.911504i	0.890107	+	0.455752i	$0.150630\pi$
$421$			18.7025i			0.911504i	−0.890107	+	0.455752i	$0.849370\pi$
$422$	8.20426	−	12.6459i	0.399377	−	0.615592i
$423$		0			0
$424$	11.6971	+	1.83649i	0.568062	+	0.0891877i
$425$		−	2.94579i		−	0.142892i
$426$		0			0
$427$	−11.0489			−0.534692
$428$	18.1470	−	8.09910i	0.877168	−	0.391485i
$429$		0			0
$430$	7.45848	−	11.4964i	0.359680	−	0.554403i
$431$	−26.7900			−1.29043			−0.645215	−	0.764001i	$-0.723232\pi$
$431$	−26.7900			−1.29043			−0.645215	+	0.764001i	$0.723232\pi$
$432$		0			0
$433$	−38.3109			−1.84110			−0.920552	−	0.390621i	$-0.872260\pi$
$433$	−38.3109			−1.84110			−0.920552	+	0.390621i	$0.872260\pi$
$434$	−2.21481	+	3.41386i	−0.106314	+	0.163871i
$435$		0			0
$436$	4.55920	−	2.03480i	0.218346	−	0.0974490i
$437$	9.75565			0.466676
$438$		0			0
$439$			39.3524i			1.87819i	0.343661	+	0.939094i	$0.388333\pi$
$439$			39.3524i			1.87819i	−0.343661	+	0.939094i	$0.611667\pi$
$440$	−0.749062	+	4.77098i	−0.0357101	+	0.227448i
$441$		0			0
$442$	−1.47522	+	2.27388i	−0.0701692	+	0.108157i
$443$			34.5154i			1.63988i	0.572452	+	0.819938i	$0.305992\pi$
$443$			34.5154i			1.63988i	−0.572452	+	0.819938i	$0.694008\pi$
$444$		0			0
$445$			7.95425i			0.377068i
$446$	26.4790	+	17.1788i	1.25382	+	0.813438i
$447$		0			0
$448$	2.20245	−	6.84110i	0.104056	−	0.323212i
$449$			20.1332i			0.950147i	0.879946	+	0.475073i	$0.157578\pi$
$449$			20.1332i			0.950147i	−0.879946	+	0.475073i	$0.842422\pi$
$450$		0			0
$451$	13.7001			0.645112
$452$	4.42067	−	1.97297i	0.207931	−	0.0928006i
$453$		0			0
$454$	−5.58039	−	3.62038i	−0.261901	−	0.169913i
$455$	−2.46779			−0.115692
$456$		0			0
$457$	−16.9534			−0.793049			−0.396524	−	0.918024i	$-0.629784\pi$
$457$	−16.9534			−0.793049			−0.396524	+	0.918024i	$0.629784\pi$
$458$	18.6267	+	12.0844i	0.870369	+	0.564668i
$459$		0			0
$460$	−6.37032	−	14.2735i	−0.297018	−	0.665503i
$461$	17.8048			0.829250			0.414625	−	0.909992i	$-0.363913\pi$
$461$	17.8048			0.829250			0.414625	+	0.909992i	$0.363913\pi$
$462$		0			0
$463$		−	1.16111i		−	0.0539613i	−0.999636	−	0.0269806i	$-0.991411\pi$
$463$		−	1.16111i		−	0.0539613i	0.999636	−	0.0269806i	$-0.00858925\pi$
$464$	−15.1455	+	16.8817i	−0.703114	+	0.783714i
$465$		0			0
$466$	24.3965	+	15.8277i	1.13015	+	0.733204i
$467$			11.6783i			0.540409i	0.962803	+	0.270205i	$0.0870913\pi$
$467$			11.6783i			0.540409i	−0.962803	+	0.270205i	$0.912909\pi$
$468$		0			0
$469$		−	7.15639i		−	0.330451i
$470$	−10.2900	+	15.8608i	−0.474641	+	0.731603i
$471$		0			0
$472$	−0.970454	+	6.18109i	−0.0446688	+	0.284508i
$473$		−	8.05439i		−	0.370341i
$474$		0			0
$475$	−5.27033			−0.241819
$476$	−0.732267	−	1.64073i	−0.0335634	−	0.0752028i
$477$		0			0
$478$	7.89531	−	12.1697i	0.361123	−	0.556628i
$479$	32.0414			1.46401			0.732004	−	0.681301i	$-0.238585\pi$
$479$	32.0414			1.46401			0.732004	+	0.681301i	$0.238585\pi$
$480$		0			0
$481$	−6.03584			−0.275211
$482$	6.02639	−	9.28895i	0.274494	−	0.423100i
$483$		0			0
$484$	−7.80941	−	17.4979i	−0.354973	−	0.795360i
$485$	−5.99313			−0.272134
$486$		0			0
$487$			40.8488i			1.85104i	0.378703	+	0.925518i	$0.376370\pi$
$487$			40.8488i			1.85104i	−0.378703	+	0.925518i	$0.623630\pi$
$488$	5.39552	−	34.3656i	0.244244	−	1.55566i
$489$		0			0
$490$	−6.83193	+	10.5306i	−0.308635	+	0.475724i
$491$			3.40321i			0.153585i	0.997047	+	0.0767923i	$0.0244678\pi$
$491$			3.40321i			0.153585i	−0.997047	+	0.0767923i	$0.975532\pi$
$492$		0			0
$493$			5.66999i			0.255363i
$494$	4.06821	+	2.63933i	0.183037	+	0.118749i
$495$		0			0
$496$	−9.53666	−	8.55588i	−0.428209	−	0.384170i
$497$		−	5.65418i		−	0.253625i
$498$		0			0
$499$	8.10583			0.362867			0.181433	−	0.983403i	$-0.441926\pi$
$499$	8.10583			0.362867			0.181433	+	0.983403i	$0.441926\pi$
$500$	9.28278	+	20.7992i	0.415138	+	0.930167i
$501$		0			0
$502$	−5.44800	−	3.53449i	−0.243156	−	0.157752i
$503$	−33.9240			−1.51259			−0.756297	−	0.654228i	$-0.772994\pi$
$503$	−33.9240			−1.51259			−0.756297	+	0.654228i	$0.772994\pi$
$504$		0			0
$505$	3.21926			0.143255
$506$	−7.70693	−	5.00002i	−0.342615	−	0.222278i
$507$		0			0
$508$	−17.7206	+	7.90880i	−0.786224	+	0.350896i
$509$	−18.7951			−0.833080			−0.416540	−	0.909117i	$-0.636757\pi$
$509$	−18.7951			−0.833080			−0.416540	+	0.909117i	$0.636757\pi$
$510$		0			0
$511$		−	6.15507i		−	0.272284i
$512$	20.2025	+	10.1911i	0.892834	+	0.450385i
$513$		0			0
$514$	21.8628	+	14.1839i	0.964325	+	0.625624i
$515$		−	6.81282i		−	0.300209i
$516$		0			0
$517$			11.1121i			0.488710i
$518$	2.17760	−	3.35651i	0.0956782	−	0.147476i
$519$		0			0
$520$	1.20510	−	7.67563i	0.0528472	−	0.336599i
$521$			7.21342i			0.316026i	0.987437	+	0.158013i	$0.0505088\pi$
$521$			7.21342i			0.316026i	−0.987437	+	0.158013i	$0.949491\pi$
$522$		0			0
$523$	−26.8501			−1.17408			−0.587038	−	0.809560i	$-0.699706\pi$
$523$	−26.8501			−1.17408			−0.587038	+	0.809560i	$0.699706\pi$
$524$	11.3810	−	5.07939i	0.497180	−	0.221894i
$525$		0			0
$526$	−18.2901	+	28.1920i	−0.797488	+	1.22923i
$527$	−3.20304			−0.139526
$528$		0			0
$529$	6.73312			0.292744
$530$	−4.61814	+	7.11831i	−0.200599	+	0.309200i
$531$		0			0
$532$	−2.93544	+	1.31010i	−0.127268	+	0.0568002i
$533$	−22.0409			−0.954698
$534$		0			0
$535$			14.2410i			0.615693i
$536$	22.2587	+	3.49470i	0.961429	+	0.150948i
$537$		0			0
$538$	4.82324	−	7.43445i	0.207945	−	0.320522i
$539$			7.37778i			0.317783i
$540$		0			0
$541$			39.8126i			1.71168i	0.517243	+	0.855839i	$0.326958\pi$
$541$			39.8126i			1.71168i	−0.517243	+	0.855839i	$0.673042\pi$
$542$	−21.7155	−	14.0883i	−0.932760	−	0.605146i
$543$		0			0
$544$	5.46080	−	1.47637i	0.234130	−	0.0632988i
$545$			3.57787i			0.153259i
$546$		0			0
$547$	42.4596			1.81544			0.907720	−	0.419577i	$-0.137822\pi$
$547$	42.4596			1.81544			0.907720	+	0.419577i	$0.137822\pi$
$548$	−3.37785	+	1.50755i	−0.144295	+	0.0643995i
$549$		0			0
$550$	4.16354	+	2.70118i	0.177534	+	0.115179i
$551$	10.1442			0.432158
$552$		0			0
$553$	2.20748			0.0938718
$554$	3.35469	+	2.17642i	0.142527	+	0.0924673i
$555$		0			0
$556$	5.34279	+	11.9711i	0.226585	+	0.507690i
$557$	35.7128			1.51320			0.756600	−	0.653877i	$-0.226859\pi$
$557$	35.7128			1.51320			0.756600	+	0.653877i	$0.226859\pi$
$558$		0			0
$559$			12.9580i			0.548066i
$560$	3.83361	+	3.43935i	0.162000	+	0.145339i
$561$		0			0
$562$	−21.3779	−	13.8693i	−0.901774	−	0.585043i
$563$		−	11.6668i		−	0.491696i	−0.969308	−	0.245848i	$-0.920934\pi$
$563$		−	11.6668i		−	0.491696i	0.969308	−	0.245848i	$-0.0790665\pi$
$564$		0			0
$565$			3.46916i			0.145949i
$566$	12.7582	−	19.6652i	0.536266	−	0.826590i
$567$		0			0
$568$	17.5864	+	2.76112i	0.737907	+	0.115854i
$569$		−	14.0492i		−	0.588971i	−0.955656	−	0.294486i	$-0.904852\pi$
$569$		−	14.0492i		−	0.588971i	0.955656	−	0.294486i	$-0.0951483\pi$
$570$		0			0
$571$	−26.9501			−1.12783			−0.563913	−	0.825834i	$-0.690705\pi$
$571$	−26.9501			−1.12783			−0.563913	+	0.825834i	$0.690705\pi$
$572$	−1.86115	−	4.17012i	−0.0778185	−	0.174362i
$573$		0			0
$574$	7.95188	−	12.2569i	0.331905	−	0.511592i
$575$	−16.0628			−0.669866
$576$		0			0
$577$	20.5752			0.856557			0.428278	−	0.903647i	$-0.359120\pi$
$577$	20.5752			0.856557			0.428278	+	0.903647i	$0.359120\pi$
$578$	0.769703	−	1.18641i	0.0320154	−	0.0493479i
$579$		0			0
$580$	−6.62404	−	14.8420i	−0.275048	−	0.616278i
$581$	9.37075			0.388764
$582$		0			0
$583$			4.98711i			0.206545i
$584$	19.1443	+	3.00572i	0.792196	+	0.124378i
$585$		0			0
$586$	23.8104	−	36.7009i	0.983599	−	1.51610i
$587$		−	38.9668i		−	1.60833i	−0.594405	−	0.804165i	$-0.702613\pi$
$587$		−	38.9668i		−	1.60833i	0.594405	−	0.804165i	$-0.297387\pi$
$588$		0			0
$589$			5.73057i			0.236124i
$590$	−3.76152	−	2.44036i	−0.154859	−	0.100468i
$591$		0			0
$592$	9.37644	+	8.41213i	0.385369	+	0.345737i
$593$		−	13.3467i		−	0.548084i	−0.961718	−	0.274042i	$-0.911639\pi$
$593$		−	13.3467i		−	0.548084i	0.961718	−	0.274042i	$-0.0883608\pi$
$594$		0			0
$595$	1.28758			0.0527856
$596$	5.14533	+	11.5287i	0.210761	+	0.472235i
$597$		0			0
$598$	12.3990	+	8.04411i	0.507034	+	0.328948i
$599$	−33.0056			−1.34857			−0.674286	−	0.738471i	$-0.735548\pi$
$599$	−33.0056			−1.34857			−0.674286	+	0.738471i	$0.735548\pi$
$600$		0			0
$601$	7.10217			0.289704			0.144852	−	0.989453i	$-0.453729\pi$
$601$	7.10217			0.289704			0.144852	+	0.989453i	$0.453729\pi$
$602$	−7.20591	−	4.67497i	−0.293691	−	0.190538i
$603$		0			0
$604$	1.79138	−	0.799501i	0.0728901	−	0.0325312i
$605$	13.7316			0.558271
$606$		0			0
$607$			13.3292i			0.541017i	0.962718	+	0.270509i	$0.0871919\pi$
$607$			13.3292i			0.541017i	−0.962718	+	0.270509i	$0.912808\pi$
$608$	−2.64138	−	9.76995i	−0.107122	−	0.396224i
$609$		0			0
$610$	20.9133	+	13.5679i	0.846754	+	0.549348i
$611$		−	17.8773i		−	0.723240i
$612$		0			0
$613$			20.1456i			0.813672i	0.913501	+	0.406836i	$0.133368\pi$
$613$			20.1456i			0.813672i	−0.913501	+	0.406836i	$0.866632\pi$
$614$	0.804040	−	1.23933i	0.0324484	−	0.0500153i
$615$		0			0
$616$	2.99045	+	0.469511i	0.120489	+	0.0189171i
$617$			32.3006i			1.30037i	0.759774	+	0.650187i	$0.225310\pi$
$617$			32.3006i			1.30037i	−0.759774	+	0.650187i	$0.774690\pi$
$618$		0			0
$619$	−1.33393			−0.0536153			−0.0268077	−	0.999641i	$-0.508534\pi$
$619$	−1.33393			−0.0536153			−0.0268077	+	0.999641i	$0.508534\pi$
$620$	8.38437	−	3.74199i	0.336725	−	0.150282i
$621$		0			0
$622$	−16.0891	+	24.7994i	−0.645115	+	0.994367i
$623$	4.98572			0.199749
$624$		0			0
$625$	−1.59339			−0.0637355
$626$	−1.45700	+	2.24580i	−0.0582336	+	0.0897601i
$627$		0			0
$628$	−14.2469	+	6.35846i	−0.568513	+	0.253730i
$629$	3.14922			0.125568
$630$		0			0
$631$			4.26894i			0.169944i	0.996383	+	0.0849719i	$0.0270801\pi$
$631$			4.26894i			0.169944i	−0.996383	+	0.0849719i	$0.972920\pi$
$632$	−1.07799	+	6.86600i	−0.0428800	+	0.273115i
$633$		0			0
$634$	12.7822	−	19.7022i	0.507646	−	0.782476i
$635$		−	13.9064i		−	0.551859i
$636$		0			0
$637$		−	11.8695i		−	0.470286i
$638$	−8.01389	−	5.19916i	−0.317273	−	0.205837i
$639$		0			0
$640$	−12.5696	+	10.2442i	−0.496857	+	0.404939i
$641$		−	12.6275i		−	0.498754i	−0.968406	−	0.249377i	$-0.919774\pi$
$641$		−	12.6275i		−	0.498754i	0.968406	−	0.249377i	$-0.0802259\pi$
$642$		0			0
$643$	−22.7663			−0.897815			−0.448908	−	0.893578i	$-0.648187\pi$
$643$	−22.7663			−0.897815			−0.448908	+	0.893578i	$0.648187\pi$
$644$	−8.94659	+	3.99291i	−0.352545	+	0.157343i
$645$		0			0
$646$	−2.12260	−	1.37708i	−0.0835127	−	0.0541805i
$647$	0.548502			0.0215639			0.0107819	−	0.999942i	$-0.496568\pi$
$647$	0.548502			0.0215639			0.0107819	+	0.999942i	$0.496568\pi$
$648$		0			0
$649$	−2.63534			−0.103446
$650$	−6.69837	−	4.34569i	−0.262732	−	0.170452i
$651$		0			0
$652$	14.3791	+	32.2182i	0.563131	+	1.26176i
$653$	−7.48180			−0.292785			−0.146393	−	0.989227i	$-0.546766\pi$
$653$	−7.48180			−0.292785			−0.146393	+	0.989227i	$0.546766\pi$
$654$		0			0
$655$			8.93133i			0.348976i
$656$	34.2397	+	30.7184i	1.33684	+	1.19935i
$657$		0			0
$658$	9.94152	+	6.44975i	0.387561	+	0.251437i
$659$			27.1441i			1.05739i	0.848813	+	0.528693i	$0.177318\pi$
$659$			27.1441i			1.05739i	−0.848813	+	0.528693i	$0.822682\pi$
$660$		0			0
$661$			43.7516i			1.70174i	0.525377	+	0.850870i	$0.323924\pi$
$661$			43.7516i			1.70174i	−0.525377	+	0.850870i	$0.676076\pi$
$662$	22.9139	−	35.3191i	0.890576	−	1.37272i
$663$		0			0
$664$	−4.57604	+	29.1461i	−0.177585	+	1.13109i
$665$		−	2.30361i		−	0.0893303i
$666$		0			0
$667$	30.9174			1.19712
$668$	−12.9437	−	29.0018i	−0.500805	−	1.12211i
$669$		0			0
$670$	−8.78797	+	13.5456i	−0.339509	+	0.523312i
$671$	14.6519			0.565631
$672$		0			0
$673$	3.52932			0.136045			0.0680226	−	0.997684i	$-0.478331\pi$
$673$	3.52932			0.136045			0.0680226	+	0.997684i	$0.478331\pi$
$674$	−9.43306	+	14.5399i	−0.363348	+	0.560057i
$675$		0			0
$676$	−7.60224	−	17.0337i	−0.292394	−	0.655143i
$677$	49.9662			1.92036			0.960178	−	0.279389i	$-0.0901319\pi$
$677$	49.9662			1.92036			0.960178	+	0.279389i	$0.0901319\pi$
$678$		0			0
$679$			3.75649i			0.144161i
$680$	−0.628766	+	4.00479i	−0.0241121	+	0.153577i
$681$		0			0
$682$	2.93706	−	4.52713i	0.112466	−	0.173353i
$683$		−	38.0174i		−	1.45470i	−0.686269	−	0.727348i	$-0.740753\pi$
$683$		−	38.0174i		−	1.45470i	0.686269	−	0.727348i	$-0.259247\pi$
$684$		0			0
$685$		−	2.65080i		−	0.101282i
$686$	14.0613	+	9.12255i	0.536864	+	0.348301i
$687$		0			0
$688$	18.0596	−	20.1298i	0.688515	−	0.767441i
$689$		−	8.02335i		−	0.305665i
$690$		0			0
$691$	18.3872			0.699483			0.349742	−	0.936846i	$-0.386269\pi$
$691$	18.3872			0.699483			0.349742	+	0.936846i	$0.386269\pi$
$692$	3.27220	+	7.33174i	0.124390	+	0.278711i
$693$		0			0
$694$	28.8784	+	18.7354i	1.09621	+	0.711186i
$695$	−9.39446			−0.356352
$696$		0			0
$697$	11.4999			0.435591
$698$	21.0307	+	13.6441i	0.796024	+	0.516436i
$699$		0			0
$700$	4.83325	−	2.15710i	0.182680	−	0.0815309i
$701$	−30.6255			−1.15671			−0.578355	−	0.815785i	$-0.696305\pi$
$701$	−30.6255			−1.15671			−0.578355	+	0.815785i	$0.696305\pi$
$702$		0			0
$703$		−	5.63429i		−	0.212501i
$704$	−2.92067	+	9.07200i	−0.110077	+	0.341914i
$705$		0			0
$706$	−15.7808	−	10.2381i	−0.593919	−	0.385316i
$707$		−	2.01783i		−	0.0758883i
$708$		0			0
$709$			47.3852i			1.77959i	0.456361	+	0.889795i	$0.349152\pi$
$709$			47.3852i			1.77959i	−0.456361	+	0.889795i	$0.650848\pi$
$710$	−6.94328	+	10.7022i	−0.260577	+	0.401647i
$711$		0			0
$712$	−2.43469	+	15.5072i	−0.0912438	+	0.581157i
$713$			17.4655i			0.654090i
$714$		0			0
$715$	3.27254			0.122386
$716$	36.8289	−	16.4369i	1.37636	−	0.614277i
$717$		0			0
$718$	2.54374	−	3.92087i	0.0949315	−	0.146326i
$719$	41.1042			1.53293			0.766464	−	0.642287i	$-0.222014\pi$
$719$	41.1042			1.53293			0.766464	+	0.642287i	$0.222014\pi$
$720$		0			0
$721$	−4.27027			−0.159033
$722$	12.1606	−	18.7441i	0.452571	−	0.697584i
$723$		0			0
$724$	11.4863	−	5.12640i	0.426885	−	0.190521i
$725$	−16.7026			−0.620318
$726$		0			0
$727$		−	22.3923i		−	0.830484i	−0.909711	−	0.415242i	$-0.863697\pi$
$727$		−	22.3923i		−	0.830484i	0.909711	−	0.415242i	$-0.136303\pi$
$728$	−4.81108	−	0.755357i	−0.178311	−	0.0279954i
$729$		0			0
$730$	−7.55837	+	11.6503i	−0.279748	+	0.431198i
$731$		−	6.76090i		−	0.250061i
$732$		0			0
$733$		−	31.2355i		−	1.15371i	−0.816847	−	0.576854i	$-0.804280\pi$
$733$		−	31.2355i		−	1.15371i	0.816847	−	0.576854i	$-0.195720\pi$
$734$	22.7488	+	14.7587i	0.839674	+	0.544755i
$735$		0			0
$736$	−8.05035	−	29.7767i	−0.296740	−	1.09758i
$737$			9.49010i			0.349572i
$738$		0			0
$739$	49.3194			1.81424			0.907121	−	0.420870i	$-0.138275\pi$
$739$	49.3194			1.81424			0.907121	+	0.420870i	$0.138275\pi$
$740$	−8.24351	+	3.67912i	−0.303037	+	0.135247i
$741$		0			0
$742$	4.46175	+	2.89465i	0.163796	+	0.106266i
$743$	−15.8453			−0.581308			−0.290654	−	0.956828i	$-0.593873\pi$
$743$	−15.8453			−0.581308			−0.290654	+	0.956828i	$0.593873\pi$
$744$		0			0
$745$	−9.04727			−0.331466
$746$	38.5625	+	25.0182i	1.41187	+	0.915981i
$747$		0			0
$748$	0.971061	+	2.17578i	0.0355055	+	0.0795543i
$749$	8.92626			0.326159
$750$		0			0
$751$		−	16.2582i		−	0.593271i	−0.954991	−	0.296635i	$-0.904135\pi$
$751$		−	16.2582i		−	0.593271i	0.954991	−	0.296635i	$-0.0958646\pi$
$752$	−24.9156	+	27.7717i	−0.908579	+	1.01273i
$753$		0			0
$754$	12.8929	+	8.36450i	0.469531	+	0.304617i
$755$			1.40580i			0.0511623i
$756$		0			0
$757$			4.39434i			0.159715i	0.996806	+	0.0798576i	$0.0254465\pi$
$757$			4.39434i			0.159715i	−0.996806	+	0.0798576i	$0.974553\pi$
$758$	−2.46246	+	3.79558i	−0.0894404	+	0.137862i
$759$		0			0
$760$	7.16499	+	1.12493i	0.259902	+	0.0408055i
$761$		−	2.30004i		−	0.0833764i	−0.999131	−	0.0416882i	$-0.986726\pi$
$761$		−	2.30004i		−	0.0833764i	0.999131	−	0.0416882i	$-0.0132736\pi$
$762$		0			0
$763$	2.24261			0.0811879
$764$	6.80063	+	15.2376i	0.246038	+	0.551278i
$765$		0			0
$766$	18.5464	−	28.5870i	0.670108	−	1.03289i
$767$	4.23977			0.153089
$768$		0			0
$769$	−9.25375			−0.333699			−0.166849	−	0.985982i	$-0.553359\pi$
$769$	−9.25375			−0.333699			−0.166849	+	0.985982i	$0.553359\pi$
$770$	−1.18066	+	1.81985i	−0.0425481	+	0.0655827i
$771$		0			0
$772$	−11.2195	−	25.1386i	−0.403798	−	0.904757i
$773$	24.7137			0.888890			0.444445	−	0.895806i	$-0.353401\pi$
$773$	24.7137			0.888890			0.444445	+	0.895806i	$0.353401\pi$
$774$		0			0
$775$		−	9.43547i		−	0.338932i
$776$	−11.6839	−	1.83442i	−0.419428	−	0.0658517i
$777$		0			0
$778$	19.5129	−	30.0768i	0.699572	−	1.07831i
$779$		−	20.5746i		−	0.737162i
$780$		0			0
$781$			7.49802i			0.268300i
$782$	−6.46924	−	4.19704i	−0.231340	−	0.150086i
$783$		0			0
$784$	−16.5425	+	18.4388i	−0.590802	+	0.658528i
$785$		−	11.1804i		−	0.399045i
$786$		0			0
$787$	−43.4442			−1.54862			−0.774309	−	0.632807i	$-0.781903\pi$
$787$	−43.4442			−1.54862			−0.774309	+	0.632807i	$0.781903\pi$
$788$	5.96237	+	13.3594i	0.212401	+	0.475909i
$789$		0			0
$790$	−4.17832	−	2.71077i	−0.148658	−	0.0964448i
$791$	2.17447			0.0773151
$792$		0			0
$793$	−23.5722			−0.837075
$794$	−25.0215	−	16.2332i	−0.887979	−	0.576094i
$795$		0			0
$796$	6.16829	−	2.75294i	0.218629	−	0.0975754i
$797$	−15.4292			−0.546530			−0.273265	−	0.961939i	$-0.588104\pi$
$797$	−15.4292			−0.546530			−0.273265	+	0.961939i	$0.588104\pi$
$798$		0			0
$799$			9.32757i			0.329986i
$800$	4.34907	+	16.0864i	0.153763	+	0.568739i
$801$		0			0
$802$	8.74407	+	5.67288i	0.308764	+	0.200317i
$803$			8.16226i			0.288040i
$804$		0			0
$805$		−	7.02092i		−	0.247455i
$806$	−4.72519	+	7.28332i	−0.166438	+	0.256544i
$807$		0			0
$808$	6.27611	+	0.985372i	0.220793	+	0.0346653i
$809$			0.523613i			0.0184092i	0.999958	+	0.00920462i	$0.00292996\pi$
$809$			0.523613i			0.0184092i	−0.999958	+	0.00920462i	$0.997070\pi$
$810$		0			0
$811$	−2.61807			−0.0919330			−0.0459665	−	0.998943i	$-0.514637\pi$
$811$	−2.61807			−0.0919330			−0.0459665	+	0.998943i	$0.514637\pi$
$812$	−9.30293	+	4.15195i	−0.326469	+	0.145705i
$813$		0			0
$814$	−2.88772	+	4.45107i	−0.101214	+	0.156010i
$815$	−25.2835			−0.885642
$816$		0			0
$817$	−12.0960			−0.423184
$818$	−1.32851	+	2.04774i	−0.0464504	+	0.0715977i
$819$		0			0
$820$	−30.1026	+	13.4350i	−1.05123	+	0.469169i
$821$	48.1728			1.68124			0.840622	−	0.541622i	$-0.182190\pi$
$821$	48.1728			1.68124			0.840622	+	0.541622i	$0.182190\pi$
$822$		0			0
$823$			20.6068i			0.718309i	0.933278	+	0.359154i	$0.116935\pi$
$823$			20.6068i			0.718309i	−0.933278	+	0.359154i	$0.883065\pi$
$824$	2.08531	−	13.2819i	0.0726453	−	0.462698i
$825$		0			0
$826$	−1.52962	+	2.35772i	−0.0532222	+	0.0820356i
$827$		−	43.4162i		−	1.50973i	−0.655880	−	0.754865i	$-0.727702\pi$
$827$		−	43.4162i		−	1.50973i	0.655880	−	0.754865i	$-0.272298\pi$
$828$		0			0
$829$			30.0235i			1.04276i	0.853325	+	0.521380i	$0.174583\pi$
$829$			30.0235i			1.04276i	−0.853325	+	0.521380i	$0.825417\pi$
$830$	−17.7369	−	11.5072i	−0.615658	−	0.399420i
$831$		0			0
$832$	4.69881	−	14.5952i	0.162902	−	0.505997i
$833$			6.19295i			0.214573i
$834$		0			0
$835$	22.7594			0.787622
$836$	3.89269	−	1.73733i	0.134632	−	0.0600868i
$837$		0			0
$838$	−30.0476	−	19.4940i	−1.03798	−	0.673408i
$839$	9.42772			0.325481			0.162741	−	0.986669i	$-0.447967\pi$
$839$	9.42772			0.325481			0.162741	+	0.986669i	$0.447967\pi$
$840$		0			0
$841$	3.14876			0.108578
$842$	−22.1887	−	14.3954i	−0.764675	−	0.496097i
$843$		0			0
$844$	8.68829	+	19.4671i	0.299063	+	0.670087i
$845$	13.3674			0.459851
$846$		0			0
$847$		−	8.60699i		−	0.295740i
$848$	−11.1821	+	12.4640i	−0.383995	+	0.428014i
$849$		0			0
$850$	3.49490	+	2.26738i	0.119874	+	0.0777706i
$851$		−	17.1721i		−	0.588652i
$852$		0			0
$853$		−	52.5169i		−	1.79815i	−0.437799	−	0.899073i	$-0.644242\pi$
$853$		−	52.5169i		−	1.79815i	0.437799	−	0.899073i	$-0.355758\pi$
$854$	8.50434	−	13.1084i	0.291013	−	0.448561i
$855$		0			0
$856$	−4.35898	+	27.7636i	−0.148987	+	0.948940i
$857$			32.2199i			1.10061i	0.834963	+	0.550305i	$0.185489\pi$
$857$			32.2199i			1.10061i	−0.834963	+	0.550305i	$0.814511\pi$
$858$		0			0
$859$	−57.5287			−1.96285			−0.981427	−	0.191833i	$-0.938557\pi$
$859$	−57.5287			−1.96285			−0.981427	+	0.191833i	$0.938557\pi$
$860$	7.89852	+	17.6976i	0.269337	+	0.603482i
$861$		0			0
$862$	20.6204	−	31.7838i	0.702332	−	1.08256i
$863$	11.5947			0.394687			0.197343	−	0.980334i	$-0.436769\pi$
$863$	11.5947			0.394687			0.197343	+	0.980334i	$0.436769\pi$
$864$		0			0
$865$	−5.75365			−0.195630
$866$	29.4880	−	45.4522i	1.00204	−	1.54453i
$867$		0			0
$868$	−2.34548	−	5.25532i	−0.0796107	−	0.178377i
$869$	−2.92735			−0.0993035
$870$		0			0
$871$		−	15.2678i		−	0.517330i
$872$	−1.09514	+	6.97525i	−0.0370861	+	0.236212i
$873$		0			0
$874$	−7.50895	+	11.5742i	−0.253994	+	0.391502i
$875$			10.2308i			0.345865i
$876$		0			0
$877$		−	29.6562i		−	1.00142i	−0.865616	−	0.500709i	$-0.833073\pi$
$877$		−	29.6562i		−	1.00142i	0.865616	−	0.500709i	$-0.166927\pi$
$878$	−46.6879	−	30.2897i	−1.57564	−	1.02223i
$879$		0			0
$880$	−5.08376	−	4.56093i	−0.171374	−	0.153749i
$881$		−	1.76691i		−	0.0595289i	−0.999557	−	0.0297644i	$-0.990524\pi$
$881$		−	1.76691i		−	0.0595289i	0.999557	−	0.0297644i	$-0.00947571\pi$
$882$		0			0
$883$	32.2707			1.08600			0.542998	−	0.839734i	$-0.317289\pi$
$883$	32.2707			1.08600			0.542998	+	0.839734i	$0.317289\pi$
$884$	−1.56226	−	3.50042i	−0.0525444	−	0.117732i
$885$		0			0
$886$	−40.9493	−	26.5666i	−1.37572	−	0.892523i
$887$	10.2973			0.345751			0.172876	−	0.984944i	$-0.444694\pi$
$887$	10.2973			0.345751			0.172876	+	0.984944i	$0.444694\pi$
$888$		0			0
$889$	−8.71652			−0.292343
$890$	−9.43696	−	6.12241i	−0.316328	−	0.205224i
$891$		0			0
$892$	−40.7620	+	18.1923i	−1.36481	+	0.609123i
$893$	16.6880			0.558443
$894$		0			0
$895$			28.9018i			0.966081i
$896$	6.42109	+	7.87861i	0.214513	+	0.263206i
$897$		0			0
$898$	−23.8862	−	15.4966i	−0.797092	−	0.517129i
$899$			18.1612i			0.605709i
$900$		0			0
$901$			4.18621i			0.139463i
$902$	−10.5450	+	16.2539i	−0.351110	+	0.541194i
$903$		0			0
$904$	−1.06186	+	6.76330i	−0.0353170	+	0.224944i
$905$			9.01398i			0.299635i
$906$		0			0
$907$	25.1046			0.833585			0.416793	−	0.909002i	$-0.363154\pi$
$907$	25.1046			0.833585			0.416793	+	0.909002i	$0.363154\pi$
$908$	8.59049	−	3.83398i	0.285085	−	0.127235i
$909$		0			0
$910$	1.89947	−	2.92780i	0.0629667	−	0.0970556i
$911$	−31.0470			−1.02863			−0.514317	−	0.857600i	$-0.671954\pi$
$911$	−31.0470			−1.02863			−0.514317	+	0.857600i	$0.671954\pi$
$912$		0			0
$913$	−12.4266			−0.411259
$914$	13.0491	−	20.1137i	0.431627	−	0.665301i
$915$		0			0
$916$	−28.6741	+	12.7974i	−0.947418	+	0.422838i
$917$	5.59815			0.184867
$918$		0			0
$919$		−	51.5485i		−	1.70043i	−0.526437	−	0.850214i	$-0.676472\pi$
$919$		−	51.5485i		−	1.70043i	0.526437	−	0.850214i	$-0.323528\pi$
$920$	21.8374	+	3.42854i	0.719956	+	0.113036i
$921$		0			0
$922$	−13.7044	+	21.1237i	−0.451330	+	0.695671i
$923$		−	12.0629i		−	0.397056i
$924$		0			0
$925$			9.27694i			0.305024i
$926$	1.37754	+	0.893709i	0.0452689	+	0.0293691i
$927$		0			0
$928$	−8.37099	−	30.9627i	−0.274791	−	1.01640i
$929$			44.0352i			1.44475i	0.691502	+	0.722375i	$0.256949\pi$
$929$			44.0352i			1.44475i	−0.691502	+	0.722375i	$0.743051\pi$
$930$		0			0
$931$	11.0798			0.363127
$932$	−37.5561	+	16.7615i	−1.23019	+	0.549042i
$933$		0			0
$934$	−13.8552	−	8.98885i	−0.453357	−	0.294124i
$935$	−1.70746			−0.0558399
$936$		0			0
$937$	−43.5078			−1.42134			−0.710669	−	0.703527i	$-0.751608\pi$
$937$	−43.5078			−1.42134			−0.710669	+	0.703527i	$0.751608\pi$
$938$	8.49037	+	5.50829i	0.277221	+	0.179852i
$939$		0			0
$940$	−10.8971	−	24.4162i	−0.355423	−	0.796367i
$941$	−42.6443			−1.39016			−0.695082	−	0.718930i	$-0.744632\pi$
$941$	−42.6443			−1.39016			−0.695082	+	0.718930i	$0.744632\pi$
$942$		0			0
$943$		−	62.7069i		−	2.04202i
$944$	−6.58632	−	5.90896i	−0.214366	−	0.192320i
$945$		0			0
$946$	9.55577	+	6.19949i	0.310685	+	0.201563i
$947$			14.3513i			0.466356i	0.972434	+	0.233178i	$0.0749125\pi$
$947$			14.3513i			0.466356i	−0.972434	+	0.233178i	$0.925088\pi$
$948$		0			0
$949$		−	13.1316i		−	0.426269i
$950$	4.05659	−	6.25274i	0.131613	−	0.202866i
$951$		0			0
$952$	2.51020	+	0.394110i	0.0813561	+	0.0127732i
$953$		−	1.68938i		−	0.0547243i	−0.999626	−	0.0273622i	$-0.991289\pi$
$953$		−	1.68938i		−	0.0547243i	0.999626	−	0.0273622i	$-0.00871073\pi$
$954$		0			0
$955$	−11.9579			−0.386947
$956$	8.36111	+	18.7341i	0.270418	+	0.605903i
$957$		0			0
$958$	−24.6623	+	38.0140i	−0.796804	+	1.22818i
$959$	−1.66152			−0.0536533
$960$		0			0
$961$	20.7406			0.669050
$962$	4.64580	−	7.16095i	0.149787	−	0.230878i
$963$		0			0
$964$	6.38193	+	14.2995i	0.205548	+	0.460555i
$965$	19.7277			0.635058
$966$		0			0
$967$		−	31.9902i		−	1.02874i	−0.857570	−	0.514368i	$-0.828027\pi$
$967$		−	31.9902i		−	1.02874i	0.857570	−	0.514368i	$-0.171973\pi$
$968$	26.7705	+	4.20307i	0.860438	+	0.135092i
$969$		0			0
$970$	4.61293	−	7.11028i	0.148112	−	0.228297i
$971$		−	11.9525i		−	0.383574i	−0.981437	−	0.191787i	$-0.938572\pi$
$971$		−	11.9525i		−	0.383574i	0.981437	−	0.191787i	$-0.0614282\pi$
$972$		0			0
$973$			5.88844i			0.188775i
$974$	−48.4633	−	31.4415i	−1.55286	−	1.00745i
$975$		0			0
$976$	36.6185	+	32.8526i	1.17213	+	1.05158i
$977$			32.9607i			1.05451i	0.849708	+	0.527253i	$0.176778\pi$
$977$			32.9607i			1.05451i	−0.849708	+	0.527253i	$0.823222\pi$
$978$		0			0
$979$	−6.61157			−0.211307
$980$	−7.23500	−	16.2109i	−0.231113	−	0.517837i
$981$		0			0
$982$	−4.03758	−	2.61946i	−0.128844	−	0.0835903i
$983$	14.3983			0.459234			0.229617	−	0.973281i	$-0.426253\pi$
$983$	14.3983			0.459234			0.229617	+	0.973281i	$0.426253\pi$
$984$		0			0
$985$	−10.4839			−0.334045
$986$	−6.72690	−	4.36421i	−0.214228	−	0.138985i
$987$		0			0
$988$	−6.26263	+	2.79504i	−0.199241	+	0.0889222i
$989$	−36.8659			−1.17227
$990$		0			0
$991$			37.2301i			1.18265i	0.806432	+	0.591326i	$0.201395\pi$
$991$			37.2301i			1.18265i	−0.806432	+	0.591326i	$0.798605\pi$
$992$	17.4911	−	4.72886i	0.555344	−	0.150141i
$993$		0			0
$994$	6.70815	+	4.35204i	0.212770	+	0.138038i
$995$			4.84062i			0.153458i
$996$		0			0
$997$			28.7273i			0.909802i	0.890542	+	0.454901i	$0.150325\pi$
$997$			28.7273i			0.909802i	−0.890542	+	0.454901i	$0.849675\pi$
$998$	−6.23909	+	9.61680i	−0.197495	+	0.304415i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1224.2.j.a.35.20	yes	64
3.2	odd	2	inner	1224.2.j.a.35.45	yes	64
4.3	odd	2		4896.2.j.a.1871.46		64
8.3	odd	2	inner	1224.2.j.a.35.46	yes	64
8.5	even	2		4896.2.j.a.1871.19		64
12.11	even	2		4896.2.j.a.1871.20		64
24.5	odd	2		4896.2.j.a.1871.45		64
24.11	even	2	inner	1224.2.j.a.35.19	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1224.2.j.a.35.19	✓	64	24.11	even	2	inner
1224.2.j.a.35.20	yes	64	1.1	even	1	trivial
1224.2.j.a.35.45	yes	64	3.2	odd	2	inner
1224.2.j.a.35.46	yes	64	8.3	odd	2	inner
4896.2.j.a.1871.19		64	8.5	even	2
4896.2.j.a.1871.20		64	12.11	even	2
4896.2.j.a.1871.45		64	24.5	odd	2
4896.2.j.a.1871.46		64	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1224.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.769703 + 1.18641i) q^{2} +(-0.815114 - 1.82636i) q^{4} +1.43325 q^{5} -0.898362i q^{7} +(2.79420 + 0.438699i) q^{8} +O(q^{10})\)	\(q+(-0.769703 + 1.18641i) q^{2} +(-0.815114 - 1.82636i) q^{4} +1.43325 q^{5} -0.898362i q^{7} +(2.79420 + 0.438699i) q^{8} +(-1.10318 + 1.70042i) q^{10} +1.19132i q^{11} -1.91661i q^{13} +(1.06582 + 0.691472i) q^{14} +(-2.67118 + 2.97738i) q^{16} +1.00000i q^{17} +1.78911 q^{19} +(-1.16826 - 2.61763i) q^{20} +(-1.41339 - 0.916962i) q^{22} +5.45281 q^{23} -2.94579 q^{25} +(2.27388 + 1.47522i) q^{26} +(-1.64073 + 0.732267i) q^{28} +5.66999 q^{29} +3.20304i q^{31} +(-1.47637 - 5.46080i) q^{32} +(-1.18641 - 0.769703i) q^{34} -1.28758i q^{35} -3.14922i q^{37} +(-1.37708 + 2.12260i) q^{38} +(4.00479 + 0.628766i) q^{40} -11.4999i q^{41} -6.76090 q^{43} +(2.17578 - 0.971061i) q^{44} +(-4.19704 + 6.46924i) q^{46} +9.32757 q^{47} +6.19295 q^{49} +(2.26738 - 3.49490i) q^{50} +(-3.50042 + 1.56226i) q^{52} +4.18621 q^{53} +1.70746i q^{55} +(0.394110 - 2.51020i) q^{56} +(-4.36421 + 6.72690i) q^{58} +2.21212i q^{59} -12.2989i q^{61} +(-3.80010 - 2.46539i) q^{62} +(7.61509 + 2.45162i) q^{64} -2.74699i q^{65} +7.96604 q^{67} +(1.82636 - 0.815114i) q^{68} +(1.52759 + 0.991053i) q^{70} +6.29388 q^{71} +6.85144 q^{73} +(3.73625 + 2.42397i) q^{74} +(-1.45833 - 3.26755i) q^{76} +1.07024 q^{77} +2.45723i q^{79} +(-3.82847 + 4.26734i) q^{80} +(13.6436 + 8.85154i) q^{82} +10.4309i q^{83} +1.43325i q^{85} +(5.20389 - 8.02117i) q^{86} +(-0.522631 + 3.32878i) q^{88} +5.54979i q^{89} -1.72181 q^{91} +(-4.44466 - 9.95879i) q^{92} +(-7.17946 + 11.0663i) q^{94} +2.56424 q^{95} -4.18149 q^{97} +(-4.76673 + 7.34734i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q + 16 q^{10} + 24 q^{16} + 8 q^{22} + 64 q^{25} + 8 q^{28} + 24 q^{40} - 64 q^{43} - 32 q^{46} - 32 q^{49} + 56 q^{52} + 40 q^{58} + 72 q^{64} + 32 q^{67} + 40 q^{70} + 32 q^{73} - 40 q^{76} - 40 q^{82} - 80 q^{88} + 8 q^{94} - 64 q^{97}+O(q^{100}) \) 64 * q + 16 * q^10 + 24 * q^16 + 8 * q^22 + 64 * q^25 + 8 * q^28 + 24 * q^40 - 64 * q^43 - 32 * q^46 - 32 * q^49 + 56 * q^52 + 40 * q^58 + 72 * q^64 + 32 * q^67 + 40 * q^70 + 32 * q^73 - 40 * q^76 - 40 * q^82 - 80 * q^88 + 8 * q^94 - 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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