LMFDB - Embedded newform 196.6.e.l.165.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,6,Mod(165,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("196.165");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	196.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$31.4352286833$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4 x^{7} - 1166 x^{6} + 3512 x^{5} + 513939 x^{4} - 1033736 x^{3} - 101466410 x^{2} + \cdots + 7574050372 $ x^8 - 4x^7 - 1166x^6 + 3512x^5 + 513939x^4 - 1033736x^3 - 101466410x^2 + 101983864*x + 7574050372
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.3
Root			$-17.3608 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	196.165
Dual form			196.6.e.l.177.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(9.65464 - 16.7223i) q^{3} +(24.9936 + 43.2902i) q^{5} +(-64.9240 - 112.452i) q^{9} +(175.576 - 304.107i) q^{11} -853.910 q^{13} +965.216 q^{15} +(1133.70 - 1963.63i) q^{17} +(100.814 + 174.615i) q^{19} +(534.608 + 925.968i) q^{23} +(313.140 - 542.375i) q^{25} +2184.88 q^{27} +6862.06 q^{29} +(2701.41 - 4678.98i) q^{31} +(-3390.24 - 5872.08i) q^{33} +(-4958.55 - 8588.46i) q^{37} +(-8244.19 + 14279.4i) q^{39} +9383.43 q^{41} -22378.6 q^{43} +(3245.37 - 5621.14i) q^{45} +(-3396.47 - 5882.86i) q^{47} +(-21891.0 - 37916.3i) q^{51} +(-1747.06 + 3026.00i) q^{53} +17553.1 q^{55} +3893.29 q^{57} +(13771.8 - 23853.4i) q^{59} +(-14450.9 - 25029.7i) q^{61} +(-21342.3 - 36965.9i) q^{65} +(-35229.8 + 61019.9i) q^{67} +20645.8 q^{69} +24149.9 q^{71} +(31115.3 - 53893.3i) q^{73} +(-6046.51 - 10472.9i) q^{75} +(39879.0 + 69072.4i) q^{79} +(36870.8 - 63862.1i) q^{81} -6356.40 q^{83} +113341. q^{85} +(66250.7 - 114750. i) q^{87} +(-30094.8 - 52125.7i) q^{89} +(-52162.2 - 90347.6i) q^{93} +(-5039.41 + 8728.52i) q^{95} +3180.12 q^{97} -45596.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 1480 q^{9} + 444 q^{11} - 7648 q^{15} - 3408 q^{23} - 11904 q^{25} + 41448 q^{29} - 13732 q^{37} - 25608 q^{39} - 57992 q^{43} - 181852 q^{51} - 528 q^{53} + 179080 q^{57} - 110220 q^{65} - 195384 q^{67}+ \cdots + 132824 q^{99}+O(q^{100}) $ 8 * q - 1480 * q^9 + 444 * q^11 - 7648 * q^15 - 3408 * q^23 - 11904 * q^25 + 41448 * q^29 - 13732 * q^37 - 25608 * q^39 - 57992 * q^43 - 181852 * q^51 - 528 * q^53 + 179080 * q^57 - 110220 * q^65 - 195384 * q^67 + 43344 * q^71 + 117304 * q^79 - 182456 * q^81 - 182600 * q^85 - 250152 * q^93 + 255552 * q^95 + 132824 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	9.65464	−	16.7223i	0.619345	−	1.07274i	−0.370260	−	0.928928i	$-0.620731\pi$
$3$	9.65464	−	16.7223i	0.619345	−	1.07274i	0.989605	−	0.143809i	$-0.0459352\pi$
$4$		0			0
$5$	24.9936	+	43.2902i	0.447099	+	0.774398i	0.998196	−	0.0600431i	$-0.0191238\pi$
$5$	24.9936	+	43.2902i	0.447099	+	0.774398i	−0.551097	+	0.834441i	$0.685790\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−64.9240	−	112.452i	−0.267177	−	0.462764i
$10$		0			0
$11$	175.576	−	304.107i	0.437505	−	0.757782i	−0.559991	−	0.828499i	$-0.689195\pi$
$11$	175.576	−	304.107i	0.437505	−	0.757782i	0.997496	+	0.0707170i	$0.0225287\pi$
$12$		0			0
$13$	−853.910			−1.40137			−0.700687	−	0.713469i	$-0.747123\pi$
$13$	−853.910			−1.40137			−0.700687	+	0.713469i	$0.747123\pi$
$14$		0			0
$15$	965.216			1.10763
$16$		0			0
$17$	1133.70	−	1963.63i	0.951430	−	1.64792i	0.209095	−	0.977895i	$-0.432948\pi$
$17$	1133.70	−	1963.63i	0.951430	−	1.64792i	0.742334	−	0.670030i	$-0.233719\pi$
$18$		0			0
$19$	100.814	+	174.615i	0.0640674	+	0.110968i	0.896280	−	0.443489i	$-0.146259\pi$
$19$	100.814	+	174.615i	0.0640674	+	0.110968i	−0.832213	+	0.554457i	$0.812926\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	534.608	+	925.968i	0.210725	+	0.364986i	0.951942	−	0.306280i	$-0.0990842\pi$
$23$	534.608	+	925.968i	0.210725	+	0.364986i	−0.741217	+	0.671266i	$0.765751\pi$
$24$		0			0
$25$	313.140	−	542.375i	0.100205	−	0.173560i
$26$		0			0
$27$	2184.88			0.576791
$28$		0			0
$29$	6862.06			1.51516			0.757582	−	0.652740i	$-0.226380\pi$
$29$	6862.06			1.51516			0.757582	+	0.652740i	$0.226380\pi$
$30$		0			0
$31$	2701.41	−	4678.98i	0.504877	−	0.874473i	−0.495107	−	0.868832i	$-0.664871\pi$
$31$	2701.41	−	4678.98i	0.504877	−	0.874473i	0.999984	−	0.00564122i	$-0.00179567\pi$
$32$		0			0
$33$	−3390.24	−	5872.08i	−0.541934	−	0.938657i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4958.55	−	8588.46i	−0.595457	−	1.03136i	−0.993482	−	0.113988i	$-0.963638\pi$
$37$	−4958.55	−	8588.46i	−0.595457	−	1.03136i	0.398025	−	0.917375i	$-0.369696\pi$
$38$		0			0
$39$	−8244.19	+	14279.4i	−0.867934	+	1.50331i
$40$		0			0
$41$	9383.43			0.871770			0.435885	−	0.900002i	$-0.356435\pi$
$41$	9383.43			0.871770			0.435885	+	0.900002i	$0.356435\pi$
$42$		0			0
$43$	−22378.6			−1.84570			−0.922851	−	0.385158i	$-0.874147\pi$
$43$	−22378.6			−1.84570			−0.922851	+	0.385158i	$0.874147\pi$
$44$		0			0
$45$	3245.37	−	5621.14i	0.238909	−	0.413803i
$46$		0			0
$47$	−3396.47	−	5882.86i	−0.224276	−	0.388458i	0.731826	−	0.681492i	$-0.238668\pi$
$47$	−3396.47	−	5882.86i	−0.224276	−	0.388458i	−0.956102	+	0.293034i	$0.905335\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−21891.0	−	37916.3i	−1.17853	−	2.04127i
$52$		0			0
$53$	−1747.06	+	3026.00i	−0.0854317	+	0.147972i	−0.905575	−	0.424186i	$-0.860560\pi$
$53$	−1747.06	+	3026.00i	−0.0854317	+	0.147972i	0.820143	+	0.572158i	$0.193894\pi$
$54$		0			0
$55$	17553.1			0.782433
$56$		0			0
$57$	3893.29			0.158719
$58$		0			0
$59$	13771.8	−	23853.4i	0.515062	−	0.892114i	−0.484785	−	0.874633i	$-0.661102\pi$
$59$	13771.8	−	23853.4i	0.515062	−	0.892114i	0.999847	−	0.0174808i	$-0.00556458\pi$
$60$		0			0
$61$	−14450.9	−	25029.7i	−0.497245	−	0.861254i	0.502750	−	0.864432i	$-0.332322\pi$
$61$	−14450.9	−	25029.7i	−0.497245	−	0.861254i	−0.999995	+	0.00317808i	$0.998988\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−21342.3	−	36965.9i	−0.626553	−	1.08522i
$66$		0			0
$67$	−35229.8	+	61019.9i	−0.958790	+	1.66067i	−0.233345	+	0.972394i	$0.574967\pi$
$67$	−35229.8	+	61019.9i	−0.958790	+	1.66067i	−0.725445	+	0.688280i	$0.758366\pi$
$68$		0			0
$69$	20645.8			0.522046
$70$		0			0
$71$	24149.9			0.568550			0.284275	−	0.958743i	$-0.408247\pi$
$71$	24149.9			0.568550			0.284275	+	0.958743i	$0.408247\pi$
$72$		0			0
$73$	31115.3	−	53893.3i	0.683387	−	1.18366i	−0.290554	−	0.956859i	$-0.593840\pi$
$73$	31115.3	−	53893.3i	0.683387	−	1.18366i	0.973941	−	0.226802i	$-0.0728271\pi$
$74$		0			0
$75$	−6046.51	−	10472.9i	−0.124123	−	0.214987i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	39879.0	+	69072.4i	0.718913	+	1.24519i	0.961431	+	0.275046i	$0.0886932\pi$
$79$	39879.0	+	69072.4i	0.718913	+	1.24519i	−0.242518	+	0.970147i	$0.577973\pi$
$80$		0			0
$81$	36870.8	−	63862.1i	0.624410	−	1.08151i
$82$		0			0
$83$	−6356.40			−0.101278			−0.0506391	−	0.998717i	$-0.516126\pi$
$83$	−6356.40			−0.101278			−0.0506391	+	0.998717i	$0.516126\pi$
$84$		0			0
$85$	113341.			1.70153
$86$		0			0
$87$	66250.7	−	114750.i	0.938410	−	1.62537i
$88$		0			0
$89$	−30094.8	−	52125.7i	−0.402732	−	0.697552i	0.591323	−	0.806435i	$-0.298606\pi$
$89$	−30094.8	−	52125.7i	−0.402732	−	0.697552i	−0.994055	+	0.108883i	$0.965273\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−52162.2	−	90347.6i	−0.625387	−	1.08320i
$94$		0			0
$95$	−5039.41	+	8728.52i	−0.0572890	+	0.0992274i
$96$		0			0
$97$	3180.12			0.0343174			0.0171587	−	0.999853i	$-0.494538\pi$
$97$	3180.12			0.0343174			0.0171587	+	0.999853i	$0.494538\pi$
$98$		0			0
$99$	−45596.4			−0.467565
$100$		0			0
$101$	−57609.6	+	99782.7i	−0.561941	+	0.973311i	0.435386	+	0.900244i	$0.356612\pi$
$101$	−57609.6	+	99782.7i	−0.561941	+	0.973311i	−0.997327	+	0.0730671i	$0.976721\pi$
$102$		0			0
$103$	61032.7	+	105712.i	0.566852	+	0.981816i	0.996875	+	0.0789984i	$0.0251722\pi$
$103$	61032.7	+	105712.i	0.566852	+	0.981816i	−0.430023	+	0.902818i	$0.641494\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	27065.5	+	46878.8i	0.228537	+	0.395837i	0.957375	−	0.288849i	$-0.0932726\pi$
$107$	27065.5	+	46878.8i	0.228537	+	0.395837i	−0.728838	+	0.684686i	$0.759939\pi$
$108$		0			0
$109$	−19919.2	+	34501.1i	−0.160586	+	0.278142i	−0.935079	−	0.354440i	$-0.884672\pi$
$109$	−19919.2	+	34501.1i	−0.160586	+	0.278142i	0.774493	+	0.632582i	$0.218005\pi$
$110$		0			0
$111$	−191492.			−1.47517
$112$		0			0
$113$	−68432.6			−0.504159			−0.252079	−	0.967707i	$-0.581114\pi$
$113$	−68432.6			−0.504159			−0.252079	+	0.967707i	$0.581114\pi$
$114$		0			0
$115$	−26723.6	+	46286.6i	−0.188430	+	0.326370i
$116$		0			0
$117$	55439.3	+	96023.6i	0.374415	+	0.648505i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	18871.6	+	32686.6i	0.117178	+	0.202958i
$122$		0			0
$123$	90593.6	−	156913.i	0.539927	−	0.935180i
$124$		0			0
$125$	187516.			1.07340
$126$		0			0
$127$	−256765.			−1.41262			−0.706312	−	0.707901i	$-0.749642\pi$
$127$	−256765.			−1.41262			−0.706312	+	0.707901i	$0.749642\pi$
$128$		0			0
$129$	−216057.	+	374222.i	−1.14313	+	1.97995i
$130$		0			0
$131$	−111262.	−	192711.i	−0.566457	−	0.981133i	−0.996912	−	0.0785210i	$-0.974980\pi$
$131$	−111262.	−	192711.i	−0.566457	−	0.981133i	0.430455	−	0.902612i	$-0.358353\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	54608.1	+	94584.0i	0.257883	+	0.446666i
$136$		0			0
$137$	−44204.5	+	76564.4i	−0.201217	+	0.348518i	−0.948921	−	0.315514i	$-0.897823\pi$
$137$	−44204.5	+	76564.4i	−0.201217	+	0.348518i	0.747704	+	0.664033i	$0.231156\pi$
$138$		0			0
$139$	105621.			0.463674			0.231837	−	0.972755i	$-0.425526\pi$
$139$	105621.			0.463674			0.231837	+	0.972755i	$0.425526\pi$
$140$		0			0
$141$	−131167.			−0.555618
$142$		0			0
$143$	−149926.	+	259680.i	−0.613109	+	1.06194i
$144$		0			0
$145$	171508.	+	297060.i	0.677429	+	1.17334i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	224606.	+	389029.i	0.828811	+	1.43554i	0.898971	+	0.438008i	$0.144316\pi$
$149$	224606.	+	389029.i	0.828811	+	1.43554i	−0.0701597	+	0.997536i	$0.522351\pi$
$150$		0			0
$151$	−6412.37	+	11106.6i	−0.0228863	+	0.0396403i	−0.877242	−	0.480049i	$-0.840619\pi$
$151$	−6412.37	+	11106.6i	−0.0228863	+	0.0396403i	0.854355	+	0.519689i	$0.173952\pi$
$152$		0			0
$153$	−294418.			−1.01680
$154$		0			0
$155$	270072.			0.902921
$156$		0			0
$157$	−77714.5	+	134605.i	−0.251624	+	0.435826i	−0.963973	−	0.265999i	$-0.914298\pi$
$157$	−77714.5	+	134605.i	−0.251624	+	0.435826i	0.712349	+	0.701826i	$0.247631\pi$
$158$		0			0
$159$	33734.5	+	58429.9i	0.105823	+	0.183292i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	237031.	+	410551.i	0.698774	+	1.21031i	0.968892	+	0.247485i	$0.0796042\pi$
$163$	237031.	+	410551.i	0.698774	+	1.21031i	−0.270117	+	0.962827i	$0.587062\pi$
$164$		0			0
$165$	169469.	−	293529.i	0.484596	−	0.839345i
$166$		0			0
$167$	−308200.			−0.855147			−0.427574	−	0.903981i	$-0.640632\pi$
$167$	−308200.			−0.855147			−0.427574	+	0.903981i	$0.640632\pi$
$168$		0			0
$169$	357870.			0.963847
$170$		0			0
$171$	13090.5	−	22673.4i	0.0342347	−	0.0592962i
$172$		0			0
$173$	237470.	+	411311.i	0.603245	+	1.04485i	0.992326	+	0.123648i	$0.0394594\pi$
$173$	237470.	+	411311.i	0.603245	+	1.04485i	−0.389081	+	0.921204i	$0.627207\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−265923.	−	460592.i	−0.638003	−	1.10505i
$178$		0			0
$179$	309853.	−	536681.i	0.722808	−	1.25194i	−0.237062	−	0.971495i	$-0.576184\pi$
$179$	309853.	−	536681.i	0.722808	−	1.25194i	0.959870	−	0.280446i	$-0.0904823\pi$
$180$		0			0
$181$	108568.			0.246324			0.123162	−	0.992387i	$-0.460697\pi$
$181$	108568.			0.246324			0.123162	+	0.992387i	$0.460697\pi$
$182$		0			0
$183$	−558073.			−1.23187
$184$		0			0
$185$	247864.	−	429313.i	0.532457	−	0.922242i
$186$		0			0
$187$	−398102.	−	689533.i	−0.832512	−	1.44195i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	122158.	+	211585.i	0.242293	+	0.419663i	0.961367	−	0.275270i	$-0.0887673\pi$
$191$	122158.	+	211585.i	0.242293	+	0.419663i	−0.719074	+	0.694933i	$0.755434\pi$
$192$		0			0
$193$	−32459.2	+	56221.0i	−0.0627255	+	0.108644i	−0.895683	−	0.444693i	$-0.853313\pi$
$193$	−32459.2	+	56221.0i	−0.0627255	+	0.108644i	0.832957	+	0.553337i	$0.186646\pi$
$194$		0			0
$195$	−824208.			−1.55221
$196$		0			0
$197$	876652.			1.60939			0.804696	−	0.593687i	$-0.202328\pi$
$197$	876652.			1.60939			0.804696	+	0.593687i	$0.202328\pi$
$198$		0			0
$199$	41282.9	−	71504.2i	0.0738989	−	0.127997i	−0.826708	−	0.562631i	$-0.809789\pi$
$199$	41282.9	−	71504.2i	0.0738989	−	0.127997i	0.900607	+	0.434635i	$0.143122\pi$
$200$		0			0
$201$	680263.	+	1.17825e6i	1.18764	+	2.05706i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	234526.	+	406210.i	0.389768	+	0.675097i
$206$		0			0
$207$	69417.8	−	120235.i	0.112602	−	0.195032i
$208$		0			0
$209$	70802.1			0.112119
$210$		0			0
$211$	−271448.			−0.419740			−0.209870	−	0.977729i	$-0.567304\pi$
$211$	−271448.			−0.419740			−0.209870	+	0.977729i	$0.567304\pi$
$212$		0			0
$213$	233158.	−	403842.i	0.352129	−	0.609905i
$214$		0			0
$215$	−559321.	−	968773.i	−0.825211	−	1.42931i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−600813.	−	1.04064e6i	−0.846505	−	1.46619i
$220$		0			0
$221$	−968080.	+	1.67676e6i	−1.33331	+	2.30936i
$222$		0			0
$223$	1.33163e6			1.79316			0.896582	−	0.442878i	$-0.146043\pi$
$223$	1.33163e6			1.79316			0.896582	+	0.442878i	$0.146043\pi$
$224$		0			0
$225$	−81321.3			−0.107090
$226$		0			0
$227$	−275746.	+	477607.i	−0.355177	+	0.615185i	−0.987148	−	0.159807i	$-0.948913\pi$
$227$	−275746.	+	477607.i	−0.355177	+	0.615185i	0.631971	+	0.774992i	$0.282246\pi$
$228$		0			0
$229$	−379756.	−	657756.i	−0.478537	−	0.828850i	0.521160	−	0.853459i	$-0.325499\pi$
$229$	−379756.	−	657756.i	−0.478537	−	0.828850i	−0.999697	+	0.0246085i	$0.992166\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−403097.	−	698185.i	−0.486430	−	0.842521i	0.513448	−	0.858120i	$-0.328368\pi$
$233$	−403097.	−	698185.i	−0.486430	−	0.842521i	−0.999878	+	0.0155992i	$0.995034\pi$
$234$		0			0
$235$	169780.	−	294068.i	0.200547	−	0.347358i
$236$		0			0
$237$	1.54007e6			1.78102
$238$		0			0
$239$	−798850.			−0.904629			−0.452315	−	0.891858i	$-0.649402\pi$
$239$	−798850.			−0.904629			−0.452315	+	0.891858i	$0.649402\pi$
$240$		0			0
$241$	−36843.9	+	63815.6i	−0.0408624	+	0.0707757i	−0.885733	−	0.464195i	$-0.846344\pi$
$241$	−36843.9	+	63815.6i	−0.0408624	+	0.0707757i	0.844871	+	0.534970i	$0.179677\pi$
$242$		0			0
$243$	−446485.	−	773334.i	−0.485055	−	0.840140i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−86086.2	−	149106.i	−0.0897824	−	0.155508i
$248$		0			0
$249$	−61368.7	+	106294.i	−0.0627262	+	0.108645i
$250$		0			0
$251$	−25091.9			−0.0251391			−0.0125696	−	0.999921i	$-0.504001\pi$
$251$	−25091.9			−0.0251391			−0.0125696	+	0.999921i	$0.504001\pi$
$252$		0			0
$253$	375457.			0.368773
$254$		0			0
$255$	1.09427e6	−	1.89533e6i	1.05384	−	1.82530i
$256$		0			0
$257$	181765.	+	314826.i	0.171663	+	0.297329i	0.939001	−	0.343913i	$-0.111753\pi$
$257$	181765.	+	314826.i	0.171663	+	0.297329i	−0.767338	+	0.641243i	$0.778419\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−445513.	−	771650.i	−0.404817	−	0.701163i
$262$		0			0
$263$	−1.05325e6	+	1.82428e6i	−0.938946	+	1.62630i	−0.171505	+	0.985183i	$0.554863\pi$
$263$	−1.05325e6	+	1.82428e6i	−0.938946	+	1.62630i	−0.767441	+	0.641119i	$0.778470\pi$
$264$		0			0
$265$	−174662.			−0.152786
$266$		0			0
$267$	−1.16222e6			−0.997720
$268$		0			0
$269$	−368099.	+	637566.i	−0.310159	+	0.537211i	−0.978397	−	0.206737i	$-0.933716\pi$
$269$	−368099.	+	637566.i	−0.310159	+	0.537211i	0.668238	+	0.743948i	$0.267049\pi$
$270$		0			0
$271$	−282812.	−	489844.i	−0.233924	−	0.405168i	0.725036	−	0.688711i	$-0.241823\pi$
$271$	−282812.	−	489844.i	−0.233924	−	0.405168i	−0.958959	+	0.283544i	$0.908490\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−109960.	−	190456.i	−0.0876804	−	0.151867i
$276$		0			0
$277$	256114.	−	443603.i	0.200555	−	0.347372i	−0.748152	−	0.663527i	$-0.769059\pi$
$277$	256114.	−	443603.i	0.200555	−	0.347372i	0.948708	+	0.316155i	$0.102392\pi$
$278$		0			0
$279$	−701545.			−0.539566
$280$		0			0
$281$	541721.			0.409270			0.204635	−	0.978838i	$-0.434399\pi$
$281$	541721.			0.409270			0.204635	+	0.978838i	$0.434399\pi$
$282$		0			0
$283$	829595.	−	1.43690e6i	0.615744	−	1.06650i	−0.374510	−	0.927223i	$-0.622189\pi$
$283$	829595.	−	1.43690e6i	0.615744	−	1.06650i	0.990253	−	0.139277i	$-0.0444778\pi$
$284$		0			0
$285$	97307.4	+	168541.i	0.0709633	+	0.122912i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−1.86063e6	−	3.22271e6i	−1.31044	−	2.26974i
$290$		0			0
$291$	30702.9	−	53179.0i	0.0212543	−	0.0368136i
$292$		0			0
$293$	130633.			0.0888962			0.0444481	−	0.999012i	$-0.485847\pi$
$293$	130633.			0.0888962			0.0444481	+	0.999012i	$0.485847\pi$
$294$		0			0
$295$	1.37682e6			0.921136
$296$		0			0
$297$	383613.	−	664437.i	0.252349	−	0.437082i
$298$		0			0
$299$	−456507.	−	790694.i	−0.295304	−	0.511482i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	1.11240e6	+	1.92673e6i	0.696071	+	1.20563i
$304$		0			0
$305$	722360.	−	1.25116e6i	0.444636	−	0.770132i
$306$		0			0
$307$	−789634.			−0.478167			−0.239084	−	0.970999i	$-0.576847\pi$
$307$	−789634.			−0.478167			−0.239084	+	0.970999i	$0.576847\pi$
$308$		0			0
$309$	2.35699e6			1.40431
$310$		0			0
$311$	967984.	−	1.67660e6i	0.567502	−	0.982942i	−0.429310	−	0.903157i	$-0.641243\pi$
$311$	967984.	−	1.67660e6i	0.567502	−	0.982942i	0.996812	−	0.0797851i	$-0.0254234\pi$
$312$		0			0
$313$	914168.	+	1.58338e6i	0.527430	+	0.913536i	0.999489	+	0.0319688i	$0.0101777\pi$
$313$	914168.	+	1.58338e6i	0.527430	+	0.913536i	−0.472059	+	0.881567i	$0.656489\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	841575.	+	1.45765e6i	0.470376	+	0.814715i	0.999426	−	0.0338759i	$-0.0107851\pi$
$317$	841575.	+	1.45765e6i	0.470376	+	0.814715i	−0.529050	+	0.848590i	$0.677452\pi$
$318$		0			0
$319$	1.20481e6	−	2.08680e6i	0.662893	−	1.14816i
$320$		0			0
$321$	1.04523e6			0.566173
$322$		0			0
$323$	457173.			0.243823
$324$		0			0
$325$	−267394.	+	463139.i	−0.140424	+	0.243222i
$326$		0			0
$327$	384626.	+	666192.i	0.198916	+	0.344532i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.49080e6	+	2.58215e6i	0.747912	+	1.29542i	0.948822	+	0.315811i	$0.102277\pi$
$331$	1.49080e6	+	2.58215e6i	0.747912	+	1.29542i	−0.200910	+	0.979610i	$0.564390\pi$
$332$		0			0
$333$	−643858.	+	1.11519e6i	−0.318185	+	0.551112i
$334$		0			0
$335$	−3.52208e6			−1.71470
$336$		0			0
$337$	−1.45801e6			−0.699335			−0.349668	−	0.936874i	$-0.613705\pi$
$337$	−1.45801e6			−0.699335			−0.349668	+	0.936874i	$0.613705\pi$
$338$		0			0
$339$	−660692.	+	1.14435e6i	−0.312248	+	0.540830i
$340$		0			0
$341$	−948605.	−	1.64303e6i	−0.441773	−	0.765174i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	516012.	+	893760.i	0.233406	+	0.404271i
$346$		0			0
$347$	−1.67340e6	+	2.89842e6i	−0.746065	+	1.29222i	0.203631	+	0.979048i	$0.434726\pi$
$347$	−1.67340e6	+	2.89842e6i	−0.746065	+	1.29222i	−0.949696	+	0.313174i	$0.898608\pi$
$348$		0			0
$349$	3.49755e6			1.53709			0.768546	−	0.639794i	$-0.220980\pi$
$349$	3.49755e6			1.53709			0.768546	+	0.639794i	$0.220980\pi$
$350$		0			0
$351$	−1.86569e6			−0.808300
$352$		0			0
$353$	−1.50300e6	+	2.60327e6i	−0.641981	+	1.11194i	0.343009	+	0.939332i	$0.388554\pi$
$353$	−1.50300e6	+	2.60327e6i	−0.641981	+	1.11194i	−0.984990	+	0.172611i	$0.944780\pi$
$354$		0			0
$355$	603592.	+	1.04545e6i	0.254198	+	0.440284i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−616235.	−	1.06735e6i	−0.252354	−	0.437090i	0.711819	−	0.702362i	$-0.247871\pi$
$359$	−616235.	−	1.06735e6i	−0.252354	−	0.437090i	−0.964173	+	0.265273i	$0.914538\pi$
$360$		0			0
$361$	1.21772e6	−	2.10916e6i	0.491791	−	0.851807i
$362$		0			0
$363$	728795.			0.290294
$364$		0			0
$365$	3.11073e6			1.22217
$366$		0			0
$367$	−1.08024e6	+	1.87103e6i	−0.418653	+	0.725128i	−0.995804	−	0.0915094i	$-0.970831\pi$
$367$	−1.08024e6	+	1.87103e6i	−0.418653	+	0.725128i	0.577152	+	0.816637i	$0.304164\pi$
$368$		0			0
$369$	−609210.	−	1.05518e6i	−0.232917	−	0.403424i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	667602.	+	1.15632e6i	0.248454	+	0.430335i	0.963097	−	0.269154i	$-0.0867442\pi$
$373$	667602.	+	1.15632e6i	0.248454	+	0.430335i	−0.714643	+	0.699489i	$0.753411\pi$
$374$		0			0
$375$	1.81040e6	−	3.13570e6i	0.664808	−	1.15148i
$376$		0			0
$377$	−5.85959e6			−2.12331
$378$		0			0
$379$	−3.68471e6			−1.31767			−0.658834	−	0.752289i	$-0.728950\pi$
$379$	−3.68471e6			−1.31767			−0.658834	+	0.752289i	$0.728950\pi$
$380$		0			0
$381$	−2.47897e6	+	4.29371e6i	−0.874902	+	1.51537i
$382$		0			0
$383$	2.00557e6	+	3.47375e6i	0.698620	+	1.21005i	0.968945	+	0.247276i	$0.0795355\pi$
$383$	2.00557e6	+	3.47375e6i	0.698620	+	1.21005i	−0.270325	+	0.962769i	$0.587131\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.45291e6	+	2.51651e6i	0.493129	+	0.854124i
$388$		0			0
$389$	903585.	−	1.56505e6i	0.302757	−	0.524391i	−0.674002	−	0.738729i	$-0.735426\pi$
$389$	903585.	−	1.56505e6i	0.302757	−	0.524391i	0.976760	+	0.214338i	$0.0687595\pi$
$390$		0			0
$391$	2.42435e6			0.801960
$392$		0			0
$393$	−4.29676e6			−1.40333
$394$		0			0
$395$	−1.99344e6	+	3.45273e6i	−0.642850	+	1.11345i
$396$		0			0
$397$	1.64164e6	+	2.84341e6i	0.522759	+	0.905446i	0.999649	+	0.0264828i	$0.00843073\pi$
$397$	1.64164e6	+	2.84341e6i	0.522759	+	0.905446i	−0.476890	+	0.878963i	$0.658236\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.54549e6	−	2.67686e6i	−0.479959	−	0.831313i	0.519777	−	0.854302i	$-0.326015\pi$
$401$	−1.54549e6	−	2.67686e6i	−0.479959	−	0.831313i	−0.999736	+	0.0229888i	$0.992682\pi$
$402$		0			0
$403$	−2.30676e6	+	3.99543e6i	−0.707522	+	1.22546i
$404$		0			0
$405$	3.68613e6			1.11669
$406$		0			0
$407$	−3.48241e6			−1.04206
$408$		0			0
$409$	−208424.	+	361000.i	−0.0616082	+	0.106709i	−0.895184	−	0.445696i	$-0.852956\pi$
$409$	−208424.	+	361000.i	−0.0616082	+	0.106709i	0.833576	+	0.552404i	$0.186290\pi$
$410$		0			0
$411$	853557.	+	1.47840e6i	0.249246	+	0.431706i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−158869.	−	275170.i	−0.0452814	−	0.0784297i
$416$		0			0
$417$	1.01973e6	−	1.76622e6i	0.287174	−	0.497400i
$418$		0			0
$419$	−4.70440e6			−1.30909			−0.654544	−	0.756024i	$-0.727139\pi$
$419$	−4.70440e6			−1.30909			−0.654544	+	0.756024i	$0.727139\pi$
$420$		0			0
$421$	−2.75525e6			−0.757626			−0.378813	−	0.925473i	$-0.623668\pi$
$421$	−2.75525e6			−0.757626			−0.378813	+	0.925473i	$0.623668\pi$
$422$		0			0
$423$	−441025.	+	763877.i	−0.119843	+	0.207574i
$424$		0			0
$425$	−710016.	−	1.22978e6i	−0.190676	−	0.330260i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	2.89497e6	+	5.01423e6i	0.759452	+	1.31541i
$430$		0			0
$431$	124955.	−	216428.i	0.0324011	−	0.0561203i	−0.849370	−	0.527798i	$-0.823018\pi$
$431$	124955.	−	216428.i	0.0324011	−	0.0561203i	0.881771	+	0.471677i	$0.156351\pi$
$432$		0			0
$433$	−7.61708e6			−1.95240			−0.976199	−	0.216875i	$-0.930414\pi$
$433$	−7.61708e6			−1.95240			−0.976199	+	0.216875i	$0.930414\pi$
$434$		0			0
$435$	6.62338e6			1.67825
$436$		0			0
$437$	−107792.	+	186701.i	−0.0270012	+	0.0467675i
$438$		0			0
$439$	−1.65424e6	−	2.86522e6i	−0.409672	−	0.709573i	0.585181	−	0.810903i	$-0.301024\pi$
$439$	−1.65424e6	−	2.86522e6i	−0.409672	−	0.709573i	−0.994853	+	0.101330i	$0.967690\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−695387.	−	1.20444e6i	−0.168351	−	0.291593i	0.769489	−	0.638660i	$-0.220511\pi$
$443$	−695387.	−	1.20444e6i	−0.168351	−	0.291593i	−0.937840	+	0.347067i	$0.887178\pi$
$444$		0			0
$445$	1.50435e6	−	2.60562e6i	0.360122	−	0.623750i
$446$		0			0
$447$	8.67396e6			2.05328
$448$		0			0
$449$	7.39368e6			1.73079			0.865396	−	0.501089i	$-0.167067\pi$
$449$	7.39368e6			1.73079			0.865396	+	0.501089i	$0.167067\pi$
$450$		0			0
$451$	1.64751e6	−	2.85356e6i	0.381404	−	0.660612i
$452$		0			0
$453$	123818.	+	214459.i	0.0283491	+	0.0491021i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.77267e6	+	3.07035e6i	0.397042	+	0.687697i	0.993360	−	0.115051i	$-0.0367033\pi$
$457$	1.77267e6	+	3.07035e6i	0.397042	+	0.687697i	−0.596317	+	0.802749i	$0.703370\pi$
$458$		0			0
$459$	2.47701e6	−	4.29030e6i	0.548777	−	0.950509i
$460$		0			0
$461$	−4.59122e6			−1.00618			−0.503090	−	0.864234i	$-0.667804\pi$
$461$	−4.59122e6			−1.00618			−0.503090	+	0.864234i	$0.667804\pi$
$462$		0			0
$463$	−183800.			−0.0398468			−0.0199234	−	0.999802i	$-0.506342\pi$
$463$	−183800.			−0.0398468			−0.0199234	+	0.999802i	$0.506342\pi$
$464$		0			0
$465$	2.60744e6	−	4.51622e6i	0.559220	−	0.968597i
$466$		0			0
$467$	−1.29180e6	−	2.23747e6i	−0.274097	−	0.474750i	0.695810	−	0.718226i	$-0.255046\pi$
$467$	−1.29180e6	−	2.23747e6i	−0.274097	−	0.474750i	−0.969907	+	0.243476i	$0.921712\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	1.50061e6	+	2.59913e6i	0.311685	+	0.539854i
$472$		0			0
$473$	−3.92914e6	+	6.80547e6i	−0.807504	+	1.39864i
$474$		0			0
$475$	126276.			0.0256795
$476$		0			0
$477$	453705.			0.0913015
$478$		0			0
$479$	−3.65373e6	+	6.32844e6i	−0.727608	+	1.26025i	0.230284	+	0.973123i	$0.426035\pi$
$479$	−3.65373e6	+	6.32844e6i	−0.727608	+	1.26025i	−0.957892	+	0.287130i	$0.907299\pi$
$480$		0			0
$481$	4.23416e6	+	7.33378e6i	0.834458	+	1.44532i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	79482.7	+	137668.i	0.0153433	+	0.0265753i
$486$		0			0
$487$	2.54228e6	−	4.40336e6i	0.485737	−	0.841321i	−0.514129	−	0.857713i	$-0.671885\pi$
$487$	2.54228e6	−	4.40336e6i	0.485737	−	0.841321i	0.999866	+	0.0163923i	$0.00521806\pi$
$488$		0			0
$489$	9.15381e6			1.73113
$490$		0			0
$491$	5.83908e6			1.09305			0.546526	−	0.837442i	$-0.315950\pi$
$491$	5.83908e6			1.09305			0.546526	+	0.837442i	$0.315950\pi$
$492$		0			0
$493$	7.77954e6	−	1.34746e7i	1.44157	−	2.49688i
$494$		0			0
$495$	−1.13962e6	−	1.97388e6i	−0.209048	−	0.362082i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−4.39100e6	−	7.60544e6i	−0.789428	−	1.36733i	−0.926318	−	0.376743i	$-0.877044\pi$
$499$	−4.39100e6	−	7.60544e6i	−0.789428	−	1.36733i	0.136890	−	0.990586i	$-0.456289\pi$
$500$		0			0
$501$	−2.97555e6	+	5.15381e6i	−0.529631	+	0.917348i
$502$		0			0
$503$	−2.64568e6			−0.466248			−0.233124	−	0.972447i	$-0.574895\pi$
$503$	−2.64568e6			−0.466248			−0.233124	+	0.972447i	$0.574895\pi$
$504$		0			0
$505$	−5.75948e6			−1.00497
$506$		0			0
$507$	3.45510e6	−	5.98441e6i	0.596954	−	1.03396i
$508$		0			0
$509$	−5.58601e6	−	9.67525e6i	−0.955668	−	1.65527i	−0.732831	−	0.680410i	$-0.761802\pi$
$509$	−5.58601e6	−	9.67525e6i	−0.955668	−	1.65527i	−0.222837	−	0.974856i	$-0.571532\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	220267.	+	381514.i	0.0369535	+	0.0640054i
$514$		0			0
$515$	−3.05085e6	+	5.28424e6i	−0.506878	+	0.877938i
$516$		0			0
$517$	−2.38535e6			−0.392488
$518$		0			0
$519$	9.17076e6			1.49447
$520$		0			0
$521$	1.08803e6	−	1.88453e6i	0.175610	−	0.304165i	−0.764762	−	0.644312i	$-0.777144\pi$
$521$	1.08803e6	−	1.88453e6i	0.175610	−	0.304165i	0.940372	+	0.340148i	$0.110477\pi$
$522$		0			0
$523$	3.63489e6	+	6.29582e6i	0.581082	+	1.00646i	0.995352	+	0.0963088i	$0.0307036\pi$
$523$	3.63489e6	+	6.29582e6i	0.581082	+	1.00646i	−0.414270	+	0.910154i	$0.635963\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.12519e6	−	1.06091e7i	−0.960711	−	1.66400i
$528$		0			0
$529$	2.64656e6	−	4.58398e6i	0.411190	−	0.712202i
$530$		0			0
$531$	−3.57647e6			−0.550451
$532$		0			0
$533$	−8.01261e6			−1.22168
$534$		0			0
$535$	−1.35293e6	+	2.34334e6i	−0.204357	+	0.353957i
$536$		0			0
$537$	−5.98303e6	−	1.03629e7i	−0.895336	−	1.55077i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−1.83471e6	−	3.17782e6i	−0.269510	−	0.466805i	0.699225	−	0.714901i	$-0.253528\pi$
$541$	−1.83471e6	−	3.17782e6i	−0.269510	−	0.466805i	−0.968735	+	0.248096i	$0.920195\pi$
$542$		0			0
$543$	1.04819e6	−	1.81551e6i	0.152559	−	0.264241i
$544$		0			0
$545$	−1.99141e6			−0.287191
$546$		0			0
$547$	−2.30515e6			−0.329406			−0.164703	−	0.986343i	$-0.552667\pi$
$547$	−2.30515e6			−0.329406			−0.164703	+	0.986343i	$0.552667\pi$
$548$		0			0
$549$	−1.87642e6	+	3.25006e6i	−0.265705	+	0.460214i
$550$		0			0
$551$	691793.	+	1.19822e6i	0.0970727	+	0.168135i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−4.78608e6	−	8.28973e6i	−0.659549	−	1.14237i
$556$		0			0
$557$	−5.68748e6	+	9.85101e6i	−0.776752	+	1.34537i	0.157053	+	0.987590i	$0.449801\pi$
$557$	−5.68748e6	+	9.85101e6i	−0.776752	+	1.34537i	−0.933805	+	0.357783i	$0.883533\pi$
$558$		0			0
$559$	1.91093e7			2.58652
$560$		0			0
$561$	−1.53741e7			−2.06245
$562$		0			0
$563$	−1.74187e6	+	3.01701e6i	−0.231604	+	0.401150i	−0.958280	−	0.285830i	$-0.907731\pi$
$563$	−1.74187e6	+	3.01701e6i	−0.231604	+	0.401150i	0.726676	+	0.686980i	$0.241064\pi$
$564$		0			0
$565$	−1.71038e6	−	2.96246e6i	−0.225409	−	0.390420i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.48015e6	−	4.29574e6i	−0.321142	−	0.556234i	0.659582	−	0.751632i	$-0.270733\pi$
$569$	−2.48015e6	−	4.29574e6i	−0.321142	−	0.556234i	−0.980724	+	0.195399i	$0.937400\pi$
$570$		0			0
$571$	−5.42961e6	+	9.40436e6i	−0.696912	+	1.20709i	0.272619	+	0.962122i	$0.412110\pi$
$571$	−5.42961e6	+	9.40436e6i	−0.696912	+	1.20709i	−0.969532	+	0.244966i	$0.921223\pi$
$572$		0			0
$573$	4.71758e6			0.600251
$574$		0			0
$575$	669629.			0.0844627
$576$		0			0
$577$	2.92290e6	−	5.06261e6i	0.365489	−	0.633045i	−0.623366	−	0.781930i	$-0.714235\pi$
$577$	2.92290e6	−	5.06261e6i	0.365489	−	0.633045i	0.988854	+	0.148885i	$0.0475685\pi$
$578$		0			0
$579$	626763.	+	1.08559e6i	0.0776975	+	0.134576i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	613485.	+	1.06259e6i	0.0747537	+	0.129477i
$584$		0			0
$585$	−2.77125e6	+	4.79995e6i	−0.334801	+	0.579892i
$586$		0			0
$587$	−4.30716e6			−0.515936			−0.257968	−	0.966153i	$-0.583053\pi$
$587$	−4.30716e6			−0.515936			−0.257968	+	0.966153i	$0.583053\pi$
$588$		0			0
$589$	1.08936e6			0.129385
$590$		0			0
$591$	8.46376e6	−	1.46597e7i	0.996769	−	1.72645i
$592$		0			0
$593$	991555.	+	1.71742e6i	0.115792	+	0.200558i	0.918096	−	0.396358i	$-0.129726\pi$
$593$	991555.	+	1.71742e6i	0.115792	+	0.200558i	−0.802304	+	0.596916i	$0.796393\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−797144.	−	1.38069e6i	−0.0915379	−	0.158548i
$598$		0			0
$599$	2.58046e6	−	4.46949e6i	0.293853	−	0.508969i	−0.680864	−	0.732410i	$-0.738396\pi$
$599$	2.58046e6	−	4.46949e6i	0.293853	−	0.508969i	0.974717	+	0.223441i	$0.0717290\pi$
$600$		0			0
$601$	9.35142e6			1.05607			0.528033	−	0.849224i	$-0.322930\pi$
$601$	9.35142e6			1.05607			0.528033	+	0.849224i	$0.322930\pi$
$602$		0			0
$603$	9.14905e6			1.02467
$604$		0			0
$605$	−943340.	+	1.63391e6i	−0.104780	+	0.181485i
$606$		0			0
$607$	−2.49850e6	−	4.32753e6i	−0.275237	−	0.476725i	0.694958	−	0.719051i	$-0.255423\pi$
$607$	−2.49850e6	−	4.32753e6i	−0.275237	−	0.476725i	−0.970195	+	0.242325i	$0.922090\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.90028e6	+	5.02343e6i	0.314295	+	0.544374i
$612$		0			0
$613$	1.81619e6	−	3.14574e6i	0.195214	−	0.338121i	−0.751757	−	0.659441i	$-0.770793\pi$
$613$	1.81619e6	−	3.14574e6i	0.195214	−	0.338121i	0.946971	+	0.321320i	$0.104127\pi$
$614$		0			0
$615$	9.05704e6			0.965603
$616$		0			0
$617$	8.56763e6			0.906041			0.453021	−	0.891500i	$-0.350346\pi$
$617$	8.56763e6			0.906041			0.453021	+	0.891500i	$0.350346\pi$
$618$		0			0
$619$	−8.51560e6	+	1.47494e7i	−0.893282	+	1.54721i	−0.0573647	+	0.998353i	$0.518270\pi$
$619$	−8.51560e6	+	1.47494e7i	−0.893282	+	1.54721i	−0.835917	+	0.548856i	$0.815064\pi$
$620$		0			0
$621$	1.16806e6	+	2.02313e6i	0.121544	+	0.210521i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	3.70814e6	+	6.42268e6i	0.379713	+	0.657682i
$626$		0			0
$627$	683569.	−	1.18398e6i	0.0694406	−	0.120275i
$628$		0			0
$629$	−2.24861e7			−2.26614
$630$		0			0
$631$	5.97254e6			0.597153			0.298576	−	0.954386i	$-0.403488\pi$
$631$	5.97254e6			0.597153			0.298576	+	0.954386i	$0.403488\pi$
$632$		0			0
$633$	−2.62073e6	+	4.53924e6i	−0.259964	+	0.450271i
$634$		0			0
$635$	−6.41748e6	−	1.11154e7i	−0.631583	−	1.09393i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−1.56791e6	−	2.71569e6i	−0.151903	−	0.263104i
$640$		0			0
$641$	−3.19514e6	+	5.53414e6i	−0.307146	+	0.531992i	−0.977737	−	0.209835i	$-0.932707\pi$
$641$	−3.19514e6	+	5.53414e6i	−0.307146	+	0.531992i	0.670591	+	0.741827i	$0.266041\pi$
$642$		0			0
$643$	4.19353e6			0.399993			0.199996	−	0.979797i	$-0.435907\pi$
$643$	4.19353e6			0.399993			0.199996	+	0.979797i	$0.435907\pi$
$644$		0			0
$645$	−2.16002e7			−2.04436
$646$		0			0
$647$	4.51885e6	−	7.82688e6i	0.424392	−	0.735069i	−0.571971	−	0.820274i	$-0.693821\pi$
$647$	4.51885e6	−	7.82688e6i	0.424392	−	0.735069i	0.996363	+	0.0852048i	$0.0271544\pi$
$648$		0			0
$649$	−4.83599e6	−	8.37617e6i	−0.450685	−	0.780610i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.38371e6	+	7.59281e6i	0.402308	+	0.696818i	0.994004	−	0.109343i	$-0.0348747\pi$
$653$	4.38371e6	+	7.59281e6i	0.402308	+	0.696818i	−0.591696	+	0.806161i	$0.701541\pi$
$654$		0			0
$655$	5.56166e6	−	9.63307e6i	0.506525	−	0.877327i
$656$		0			0
$657$	−8.08051e6			−0.730341
$658$		0			0
$659$	1.87668e7			1.68336			0.841680	−	0.539977i	$-0.181567\pi$
$659$	1.87668e7			1.68336			0.841680	+	0.539977i	$0.181567\pi$
$660$		0			0
$661$	3.50973e6	−	6.07902e6i	0.312442	−	0.541166i	−0.666448	−	0.745551i	$-0.732186\pi$
$661$	3.50973e6	−	6.07902e6i	0.312442	−	0.541166i	0.978890	+	0.204386i	$0.0655196\pi$
$662$		0			0
$663$	1.86929e7	+	3.23771e7i	1.65156	+	2.86058i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.66852e6	+	6.35406e6i	0.319283	+	0.553014i
$668$		0			0
$669$	1.28564e7	−	2.22679e7i	1.11059	−	1.92359i
$670$		0			0
$671$	−1.01489e7			−0.870190
$672$		0			0
$673$	1.21574e7			1.03468			0.517338	−	0.855781i	$-0.326923\pi$
$673$	1.21574e7			1.03468			0.517338	+	0.855781i	$0.326923\pi$
$674$		0			0
$675$	684175.	−	1.18503e6i	0.0577973	−	0.100108i
$676$		0			0
$677$	−445488.	−	771608.i	−0.0373564	−	0.0647031i	0.846743	−	0.532003i	$-0.178560\pi$
$677$	−445488.	−	771608.i	−0.0373564	−	0.0647031i	−0.884099	+	0.467299i	$0.845227\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	5.32446e6	+	9.22223e6i	0.439954	+	0.762023i
$682$		0			0
$683$	−9.85489e6	+	1.70692e7i	−0.808351	+	1.40011i	0.105654	+	0.994403i	$0.466307\pi$
$683$	−9.85489e6	+	1.70692e7i	−0.808351	+	1.40011i	−0.914005	+	0.405703i	$0.867027\pi$
$684$		0			0
$685$	−4.41932e6			−0.359856
$686$		0			0
$687$	−1.46656e7			−1.18552
$688$		0			0
$689$	1.49184e6	−	2.58394e6i	0.119722	−	0.207364i
$690$		0			0
$691$	6.87441e6	+	1.19068e7i	0.547697	+	0.948639i	0.998432	+	0.0559814i	$0.0178287\pi$
$691$	6.87441e6	+	1.19068e7i	0.547697	+	0.948639i	−0.450735	+	0.892658i	$0.648838\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.63984e6	+	4.57234e6i	0.207308	+	0.359068i
$696$		0			0
$697$	1.06380e7	−	1.84256e7i	0.829428	−	1.43661i
$698$		0			0
$699$	−1.55670e7			−1.20507
$700$		0			0
$701$	1.40261e7			1.07806			0.539031	−	0.842286i	$-0.318791\pi$
$701$	1.40261e7			1.07806			0.539031	+	0.842286i	$0.318791\pi$
$702$		0			0
$703$	999784.	−	1.73168e6i	0.0762988	−	0.132153i
$704$		0			0
$705$	−3.27833e6	−	5.67823e6i	−0.248416	−	0.430269i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−5.99965e6	−	1.03917e7i	−0.448239	−	0.776373i	0.550032	−	0.835143i	$-0.314615\pi$
$709$	−5.99965e6	−	1.03917e7i	−0.448239	−	0.776373i	−0.998272	+	0.0587701i	$0.981282\pi$
$710$		0			0
$711$	5.17820e6	−	8.96891e6i	0.384154	−	0.665374i
$712$		0			0
$713$	5.77678e6			0.425561
$714$		0			0
$715$	−1.49888e7			−1.09648
$716$		0			0
$717$	−7.71261e6	+	1.33586e7i	−0.560278	+	0.970430i
$718$		0			0
$719$	1.15673e7	+	2.00352e7i	0.834470	+	1.44534i	0.894461	+	0.447145i	$0.147559\pi$
$719$	1.15673e7	+	2.00352e7i	0.834470	+	1.44534i	−0.0599918	+	0.998199i	$0.519107\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	711430.	+	1.23223e6i	0.0506158	+	0.0876692i
$724$		0			0
$725$	2.14879e6	−	3.72181e6i	0.151827	−	0.262972i
$726$		0			0
$727$	−117783.			−0.00826505			−0.00413252	−	0.999991i	$-0.501315\pi$
$727$	−117783.			−0.00826505			−0.00413252	+	0.999991i	$0.501315\pi$
$728$		0			0
$729$	676615.			0.0471545
$730$		0			0
$731$	−2.53706e7	+	4.39433e7i	−1.75606	+	3.04158i
$732$		0			0
$733$	−5.48298e6	−	9.49681e6i	−0.376927	−	0.652856i	0.613687	−	0.789550i	$-0.289686\pi$
$733$	−5.48298e6	−	9.49681e6i	−0.376927	−	0.652856i	−0.990613	+	0.136693i	$0.956353\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.23710e7	+	2.14273e7i	0.838952	+	1.45311i
$738$		0			0
$739$	−2.33080e6	+	4.03707e6i	−0.156998	+	0.271929i	−0.933785	−	0.357835i	$-0.883515\pi$
$739$	−2.33080e6	+	4.03707e6i	−0.156998	+	0.271929i	0.776787	+	0.629764i	$0.216848\pi$
$740$		0			0
$741$	−3.32452e6			−0.222425
$742$		0			0
$743$	−1.32766e7			−0.882296			−0.441148	−	0.897434i	$-0.645429\pi$
$743$	−1.32766e7			−0.882296			−0.441148	+	0.897434i	$0.645429\pi$
$744$		0			0
$745$	−1.12274e7	+	1.94465e7i	−0.741122	+	1.28366i
$746$		0			0
$747$	412683.	+	714788.i	0.0270592	+	0.0468679i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	6.34018e6	+	1.09815e7i	0.410206	+	0.710497i	0.994912	−	0.100748i	$-0.0321235\pi$
$751$	6.34018e6	+	1.09815e7i	0.410206	+	0.710497i	−0.584706	+	0.811245i	$0.698790\pi$
$752$		0			0
$753$	−242253.	+	419595.i	−0.0155698	+	0.0269677i
$754$		0			0
$755$	−641073.			−0.0409298
$756$		0			0
$757$	−9.32262e6			−0.591287			−0.295643	−	0.955298i	$-0.595534\pi$
$757$	−9.32262e6			−0.591287			−0.295643	+	0.955298i	$0.595534\pi$
$758$		0			0
$759$	3.62491e6	−	6.27852e6i	0.228398	−	0.395597i
$760$		0			0
$761$	−9.49205e6	−	1.64407e7i	−0.594153	−	1.02910i	−0.993666	−	0.112375i	$-0.964154\pi$
$761$	−9.49205e6	−	1.64407e7i	−0.594153	−	1.02910i	0.399513	−	0.916728i	$-0.369179\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−7.35856e6	−	1.27454e7i	−0.454610	−	0.787408i
$766$		0			0
$767$	−1.17599e7	+	2.03687e7i	−0.721795	+	1.25019i
$768$		0			0
$769$	9.22276e6			0.562400			0.281200	−	0.959649i	$-0.409268\pi$
$769$	9.22276e6			0.562400			0.281200	+	0.959649i	$0.409268\pi$
$770$		0			0
$771$	7.01949e6			0.425275
$772$		0			0
$773$	3.77508e6	−	6.53864e6i	0.227236	−	0.393585i	−0.729752	−	0.683712i	$-0.760364\pi$
$773$	3.77508e6	−	6.53864e6i	0.227236	−	0.393585i	0.956988	+	0.290127i	$0.0936977\pi$
$774$		0			0
$775$	−1.69184e6	−	2.93035e6i	−0.101182	−	0.175253i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	945982.	+	1.63849e6i	0.0558521	+	0.0967386i
$780$		0			0
$781$	4.24014e6	−	7.34413e6i	0.248744	−	0.430837i
$782$		0			0
$783$	1.49928e7			0.873934
$784$		0			0
$785$	−7.76946e6			−0.450004
$786$		0			0
$787$	2.83241e6	−	4.90589e6i	0.163012	−	0.282345i	−0.772935	−	0.634485i	$-0.781212\pi$
$787$	2.83241e6	−	4.90589e6i	0.163012	−	0.282345i	0.935948	+	0.352139i	$0.114546\pi$
$788$		0			0
$789$	2.03374e7	+	3.52255e7i	1.16306	+	2.01449i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	1.23398e7	+	2.13731e7i	0.696826	+	1.20694i
$794$		0			0
$795$	−1.68629e6	+	2.92075e6i	−0.0946271	+	0.163899i
$796$		0			0
$797$	2.25166e6			0.125561			0.0627807	−	0.998027i	$-0.480003\pi$
$797$	2.25166e6			0.125561			0.0627807	+	0.998027i	$0.480003\pi$
$798$		0			0
$799$	−1.54023e7			−0.853532
$800$		0			0
$801$	−3.90774e6	+	6.76841e6i	−0.215201	+	0.372740i
$802$		0			0
$803$	−1.09262e7	−	1.89247e7i	−0.597971	−	1.03572i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	7.10773e6	+	1.23109e7i	0.384191	+	0.665438i
$808$		0			0
$809$	−5.98181e6	+	1.03608e7i	−0.321338	+	0.556573i	−0.980764	−	0.195196i	$-0.937466\pi$
$809$	−5.98181e6	+	1.03608e7i	−0.321338	+	0.556573i	0.659427	+	0.751769i	$0.270799\pi$
$810$		0			0
$811$	958303.			0.0511624			0.0255812	−	0.999673i	$-0.491856\pi$
$811$	958303.			0.0511624			0.0255812	+	0.999673i	$0.491856\pi$
$812$		0			0
$813$	−1.09218e7			−0.579518
$814$		0			0
$815$	−1.18485e7	+	2.05223e7i	−0.624843	+	1.08226i
$816$		0			0
$817$	−2.25608e6	−	3.90764e6i	−0.118249	−	0.204814i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.28014e7	−	2.21727e7i	−0.662828	−	1.14805i	−0.979869	−	0.199640i	$-0.936023\pi$
$821$	−1.28014e7	−	2.21727e7i	−0.662828	−	1.14805i	0.317041	−	0.948412i	$-0.397311\pi$
$822$		0			0
$823$	5.79776e6	−	1.00420e7i	0.298374	−	0.516799i	−0.677390	−	0.735624i	$-0.736889\pi$
$823$	5.79776e6	−	1.00420e7i	0.298374	−	0.516799i	0.975764	+	0.218825i	$0.0702224\pi$
$824$		0			0
$825$	−4.24649e6			−0.217218
$826$		0			0
$827$	−4.22668e6			−0.214900			−0.107450	−	0.994211i	$-0.534269\pi$
$827$	−4.22668e6			−0.214900			−0.107450	+	0.994211i	$0.534269\pi$
$828$		0			0
$829$	−6.64999e6	+	1.15181e7i	−0.336074	+	0.582097i	−0.983691	−	0.179869i	$-0.942432\pi$
$829$	−6.64999e6	+	1.15181e7i	−0.336074	+	0.582097i	0.647617	+	0.761966i	$0.275766\pi$
$830$		0			0
$831$	−4.94538e6	−	8.56565e6i	−0.248426	−	0.430287i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−7.70302e6	−	1.33420e7i	−0.382335	−	0.662224i
$836$		0			0
$837$	5.90226e6	−	1.02230e7i	0.291209	−	0.504389i
$838$		0			0
$839$	3.03054e7			1.48633			0.743166	−	0.669107i	$-0.233323\pi$
$839$	3.03054e7			1.48633			0.743166	+	0.669107i	$0.233323\pi$
$840$		0			0
$841$	2.65768e7			1.29572
$842$		0			0
$843$	5.23012e6	−	9.05883e6i	0.253479	−	0.439039i
$844$		0			0
$845$	8.94445e6	+	1.54922e7i	0.430935	+	0.746402i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−1.60189e7	−	2.77455e7i	−0.762716	−	1.32106i
$850$		0			0
$851$	5.30177e6	−	9.18293e6i	0.250955	−	0.434668i
$852$		0			0
$853$	−1.04047e7			−0.489616			−0.244808	−	0.969572i	$-0.578725\pi$
$853$	−1.04047e7			−0.489616			−0.244808	+	0.969572i	$0.578725\pi$
$854$		0			0
$855$	1.30872e6			0.0612251
$856$		0			0
$857$	1.09750e7	−	1.90092e7i	0.510448	−	0.884122i	−0.489479	−	0.872015i	$-0.662813\pi$
$857$	1.09750e7	−	1.90092e7i	0.510448	−	0.884122i	0.999927	−	0.0121066i	$-0.00385374\pi$
$858$		0			0
$859$	−4.54468e6	−	7.87162e6i	−0.210146	−	0.363983i	0.741614	−	0.670827i	$-0.234061\pi$
$859$	−4.54468e6	−	7.87162e6i	−0.210146	−	0.363983i	−0.951760	+	0.306843i	$0.900727\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−912508.	−	1.58051e6i	−0.0417071	−	0.0722387i	0.844418	−	0.535684i	$-0.179946\pi$
$863$	−912508.	−	1.58051e6i	−0.0417071	−	0.0722387i	−0.886125	+	0.463446i	$0.846613\pi$
$864$		0			0
$865$	−1.18705e7	+	2.05603e7i	−0.539421	+	0.934304i
$866$		0			0
$867$	−7.18550e7			−3.24645
$868$		0			0
$869$	2.80072e7			1.25811
$870$		0			0
$871$	3.00831e7	−	5.21055e7i	1.34362	−	2.32722i
$872$		0			0
$873$	−206466.	−	357610.i	−0.00916882	−	0.0158809i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	7.49745e6	+	1.29860e7i	0.329166	+	0.570132i	0.982347	−	0.187070i	$-0.0598992\pi$
$877$	7.49745e6	+	1.29860e7i	0.329166	+	0.570132i	−0.653181	+	0.757202i	$0.726566\pi$
$878$		0			0
$879$	1.26121e6	−	2.18448e6i	0.0550574	−	0.0953622i
$880$		0			0
$881$	−1.71560e6			−0.0744692			−0.0372346	−	0.999307i	$-0.511855\pi$
$881$	−1.71560e6			−0.0744692			−0.0372346	+	0.999307i	$0.511855\pi$
$882$		0			0
$883$	3.86989e7			1.67031			0.835155	−	0.550015i	$-0.185378\pi$
$883$	3.86989e7			1.67031			0.835155	+	0.550015i	$0.185378\pi$
$884$		0			0
$885$	1.32927e7	−	2.30237e7i	0.570501	−	0.988137i
$886$		0			0
$887$	−2.91307e6	−	5.04559e6i	−0.124320	−	0.215329i	0.797147	−	0.603786i	$-0.206342\pi$
$887$	−2.91307e6	−	5.04559e6i	−0.124320	−	0.215329i	−0.921467	+	0.388457i	$0.873008\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1.29472e7	−	2.24253e7i	−0.546365	−	0.946333i
$892$		0			0
$893$	684824.	−	1.18615e6i	0.0287376	−	0.0497750i
$894$		0			0
$895$	3.09774e7			1.29267
$896$		0			0
$897$	−1.76297e7			−0.731581
$898$		0			0
$899$	1.85372e7	−	3.21074e7i	0.764972	−	1.32497i
$900$		0			0
$901$	3.96130e6	+	6.86118e6i	0.162565	+	0.281570i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.71351e6	+	4.69994e6i	0.110131	+	0.190753i
$906$		0			0
$907$	−4.91979e6	+	8.52132e6i	−0.198577	+	0.343945i	−0.948067	−	0.318070i	$-0.896965\pi$
$907$	−4.91979e6	+	8.52132e6i	−0.198577	+	0.343945i	0.749491	+	0.662015i	$0.230299\pi$
$908$		0			0
$909$	1.49610e7			0.600551
$910$		0			0
$911$	−2.53673e7			−1.01269			−0.506347	−	0.862330i	$-0.669004\pi$
$911$	−2.53673e7			−1.01269			−0.506347	+	0.862330i	$0.669004\pi$
$912$		0			0
$913$	−1.11603e6	+	1.93302e6i	−0.0443098	+	0.0767468i
$914$		0			0
$915$	−1.39483e7	−	2.41591e7i	−0.550766	−	0.953955i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	2.92923e6	+	5.07358e6i	0.114410	+	0.198164i	0.917544	−	0.397635i	$-0.130169\pi$
$919$	2.92923e6	+	5.07358e6i	0.114410	+	0.198164i	−0.803134	+	0.595799i	$0.796835\pi$
$920$		0			0
$921$	−7.62362e6	+	1.32045e7i	−0.296150	+	0.512948i
$922$		0			0
$923$	−2.06218e7			−0.796751
$924$		0			0
$925$	−6.21089e6			−0.238671
$926$		0			0
$927$	7.92498e6	−	1.37265e7i	0.302900	−	0.524637i
$928$		0			0
$929$	−9264.30	−	16046.2i	−0.000352187	−	0.000610006i	0.865849	−	0.500305i	$-0.166779\pi$
$929$	−9264.30	−	16046.2i	−0.000352187	−	0.000610006i	−0.866201	+	0.499695i	$0.833445\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−1.86911e7	−	3.23739e7i	−0.702959	−	1.21756i
$934$		0			0
$935$	1.99000e7	−	3.44678e7i	0.744430	−	1.28939i
$936$		0			0
$937$	3.91119e7			1.45533			0.727663	−	0.685935i	$-0.240606\pi$
$937$	3.91119e7			1.45533			0.727663	+	0.685935i	$0.240606\pi$
$938$		0			0
$939$	3.53038e7			1.30665
$940$		0			0
$941$	4.45258e6	−	7.71210e6i	0.163922	−	0.283922i	−0.772350	−	0.635197i	$-0.780919\pi$
$941$	4.45258e6	−	7.71210e6i	0.163922	−	0.283922i	0.936272	+	0.351276i	$0.114252\pi$
$942$		0			0
$943$	5.01646e6	+	8.68876e6i	0.183704	+	0.318184i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.71918e6	+	6.44181e6i	0.134764	+	0.233417i	0.925507	−	0.378730i	$-0.123639\pi$
$947$	3.71918e6	+	6.44181e6i	0.134764	+	0.233417i	−0.790744	+	0.612148i	$0.790306\pi$
$948$		0			0
$949$	−2.65697e7	+	4.60200e7i	−0.957680	+	1.65875i
$950$		0			0
$951$	3.25004e7			1.16530
$952$		0			0
$953$	3.87886e7			1.38348			0.691739	−	0.722148i	$-0.256845\pi$
$953$	3.87886e7			1.38348			0.691739	+	0.722148i	$0.256845\pi$
$954$		0			0
$955$	−6.10636e6	+	1.05765e7i	−0.216658	+	0.375262i
$956$		0			0
$957$	−2.32641e7	−	4.02946e7i	−0.821119	−	1.42222i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−280639.	−	486080.i	−0.00980255	−	0.0169785i
$962$		0			0
$963$	3.51440e6	−	6.08711e6i	0.122119	−	0.211517i
$964$		0			0
$965$	−3.24509e6			−0.112178
$966$		0			0
$967$	−2.80184e7			−0.963557			−0.481779	−	0.876293i	$-0.660009\pi$
$967$	−2.80184e7			−0.963557			−0.481779	+	0.876293i	$0.660009\pi$
$968$		0			0
$969$	4.41384e6	−	7.64499e6i	0.151010	−	0.261558i
$970$		0			0
$971$	−2.22621e7	−	3.85591e7i	−0.757736	−	1.31244i	−0.944002	−	0.329939i	$-0.892972\pi$
$971$	−2.22621e7	−	3.85591e7i	−0.757736	−	1.31244i	0.186266	−	0.982499i	$-0.440361\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	5.16318e6	+	8.94289e6i	0.173942	+	0.301277i
$976$		0			0
$977$	−461021.	+	798513.i	−0.0154520	+	0.0267637i	−0.873648	−	0.486558i	$-0.838252\pi$
$977$	−461021.	+	798513.i	−0.0154520	+	0.0267637i	0.858196	+	0.513322i	$0.171585\pi$
$978$		0			0
$979$	−2.11357e7			−0.704790
$980$		0			0
$981$	5.17294e6			0.171619
$982$		0			0
$983$	2.06353e6	−	3.57414e6i	0.0681125	−	0.117974i	−0.829958	−	0.557826i	$-0.811636\pi$
$983$	2.06353e6	−	3.57414e6i	0.0681125	−	0.117974i	0.898070	+	0.439852i	$0.144969\pi$
$984$		0			0
$985$	2.19107e7	+	3.79504e7i	0.719558	+	1.24631i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.19638e7	−	2.07219e7i	−0.388935	−	0.673656i
$990$		0			0
$991$	−1.74696e6	+	3.02582e6i	−0.0565065	+	0.0978722i	−0.892895	−	0.450265i	$-0.851330\pi$
$991$	−1.74696e6	+	3.02582e6i	−0.0565065	+	0.0978722i	0.836388	+	0.548137i	$0.184663\pi$
$992$		0			0
$993$	5.75726e7			1.85286
$994$		0			0
$995$	4.12724e6			0.132161
$996$		0			0
$997$	5.80524e6	−	1.00550e7i	0.184962	−	0.320364i	−0.758602	−	0.651555i	$-0.774117\pi$
$997$	5.80524e6	−	1.00550e7i	0.184962	−	0.320364i	0.943564	+	0.331191i	$0.107450\pi$
$998$		0			0
$999$	−1.08339e7	−	1.87648e7i	−0.343455	−	0.594881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.6.e.l.165.3		8
7.2	even	3	inner	196.6.e.l.177.3		8
7.3	odd	6		196.6.a.k.1.3	yes	4
7.4	even	3		196.6.a.k.1.2	✓	4
7.5	odd	6	inner	196.6.e.l.177.2		8
7.6	odd	2	inner	196.6.e.l.165.2		8
28.3	even	6		784.6.a.bi.1.2		4
28.11	odd	6		784.6.a.bi.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.6.a.k.1.2	✓	4	7.4	even	3
196.6.a.k.1.3	yes	4	7.3	odd	6
196.6.e.l.165.2		8	7.6	odd	2	inner
196.6.e.l.165.3		8	1.1	even	1	trivial
196.6.e.l.177.2		8	7.5	odd	6	inner
196.6.e.l.177.3		8	7.2	even	3	inner
784.6.a.bi.1.2		4	28.3	even	6
784.6.a.bi.1.3		4	28.11	odd	6

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	196.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(9.65464 - 16.7223i) q^{3} +(24.9936 + 43.2902i) q^{5} +(-64.9240 - 112.452i) q^{9} +(175.576 - 304.107i) q^{11} -853.910 q^{13} +965.216 q^{15} +(1133.70 - 1963.63i) q^{17} +(100.814 + 174.615i) q^{19} +(534.608 + 925.968i) q^{23} +(313.140 - 542.375i) q^{25} +2184.88 q^{27} +6862.06 q^{29} +(2701.41 - 4678.98i) q^{31} +(-3390.24 - 5872.08i) q^{33} +(-4958.55 - 8588.46i) q^{37} +(-8244.19 + 14279.4i) q^{39} +9383.43 q^{41} -22378.6 q^{43} +(3245.37 - 5621.14i) q^{45} +(-3396.47 - 5882.86i) q^{47} +(-21891.0 - 37916.3i) q^{51} +(-1747.06 + 3026.00i) q^{53} +17553.1 q^{55} +3893.29 q^{57} +(13771.8 - 23853.4i) q^{59} +(-14450.9 - 25029.7i) q^{61} +(-21342.3 - 36965.9i) q^{65} +(-35229.8 + 61019.9i) q^{67} +20645.8 q^{69} +24149.9 q^{71} +(31115.3 - 53893.3i) q^{73} +(-6046.51 - 10472.9i) q^{75} +(39879.0 + 69072.4i) q^{79} +(36870.8 - 63862.1i) q^{81} -6356.40 q^{83} +113341. q^{85} +(66250.7 - 114750. i) q^{87} +(-30094.8 - 52125.7i) q^{89} +(-52162.2 - 90347.6i) q^{93} +(-5039.41 + 8728.52i) q^{95} +3180.12 q^{97} -45596.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 1480 q^{9} + 444 q^{11} - 7648 q^{15} - 3408 q^{23} - 11904 q^{25} + 41448 q^{29} - 13732 q^{37} - 25608 q^{39} - 57992 q^{43} - 181852 q^{51} - 528 q^{53} + 179080 q^{57} - 110220 q^{65} - 195384 q^{67}+ \cdots + 132824 q^{99}+O(q^{100}) \) 8 * q - 1480 * q^9 + 444 * q^11 - 7648 * q^15 - 3408 * q^23 - 11904 * q^25 + 41448 * q^29 - 13732 * q^37 - 25608 * q^39 - 57992 * q^43 - 181852 * q^51 - 528 * q^53 + 179080 * q^57 - 110220 * q^65 - 195384 * q^67 + 43344 * q^71 + 117304 * q^79 - 182456 * q^81 - 182600 * q^85 - 250152 * q^93 + 255552 * q^95 + 132824 * q^99

Introduction

L-functions

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Database

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