LMFDB - Embedded newform 196.6.e.b.177.1

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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	196.177
Dual form			196.6.e.b.165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.50000 - 16.4545i) q^{3} +(9.50000 - 16.4545i) q^{5} +(-59.0000 + 102.191i) q^{9} +O(q^{10})$	\(q+(-9.50000 - 16.4545i) q^{3} +(9.50000 - 16.4545i) q^{5} +(-59.0000 + 102.191i) q^{9} +(279.500 + 484.108i) q^{11} -282.000 q^{13} -361.000 q^{15} +(629.500 + 1090.33i) q^{17} +(-978.500 + 1694.81i) q^{19} +(1488.50 - 2578.16i) q^{23} +(1382.00 + 2393.69i) q^{25} -2375.00 q^{27} -62.0000 q^{29} +(1018.50 + 1764.09i) q^{31} +(5310.50 - 9198.06i) q^{33} +(-3011.50 + 5216.07i) q^{37} +(2679.00 + 4640.16i) q^{39} +2178.00 q^{41} +23180.0 q^{43} +(1121.00 + 1941.63i) q^{45} +(13117.5 - 22720.2i) q^{47} +(11960.5 - 20716.2i) q^{51} +(-15133.5 - 26212.0i) q^{53} +10621.0 q^{55} +37183.0 q^{57} +(22482.5 + 38940.8i) q^{59} +(13819.5 - 23936.1i) q^{61} +(-2679.00 + 4640.16i) q^{65} +(29333.5 + 50807.1i) q^{67} -56563.0 q^{69} -9520.00 q^{71} +(-3392.50 - 5875.98i) q^{73} +(26258.0 - 45480.2i) q^{75} +(8464.50 - 14660.9i) q^{79} +(36899.5 + 63911.8i) q^{81} +59572.0 q^{83} +23921.0 q^{85} +(589.000 + 1020.18i) q^{87} +(-25936.5 + 44923.3i) q^{89} +(19351.5 - 33517.8i) q^{93} +(18591.5 + 32201.4i) q^{95} -134110. q^{97} -65962.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 19 q^{3} + 19 q^{5} - 118 q^{9}+O(q^{10}) $ 2 * q - 19 * q^3 + 19 * q^5 - 118 * q^9	$ 2 q - 19 q^{3} + 19 q^{5} - 118 q^{9} + 559 q^{11} - 564 q^{13} - 722 q^{15} + 1259 q^{17} - 1957 q^{19} + 2977 q^{23} + 2764 q^{25} - 4750 q^{27} - 124 q^{29} + 2037 q^{31} + 10621 q^{33} - 6023 q^{37} + 5358 q^{39} + 4356 q^{41} + 46360 q^{43} + 2242 q^{45} + 26235 q^{47} + 23921 q^{51} - 30267 q^{53} + 21242 q^{55} + 74366 q^{57} + 44965 q^{59} + 27639 q^{61} - 5358 q^{65} + 58667 q^{67} - 113126 q^{69} - 19040 q^{71} - 6785 q^{73} + 52516 q^{75} + 16929 q^{79} + 73799 q^{81} + 119144 q^{83} + 47842 q^{85} + 1178 q^{87} - 51873 q^{89} + 38703 q^{93} + 37183 q^{95} - 268220 q^{97} - 131924 q^{99}+O(q^{100}) $ 2 * q - 19 * q^3 + 19 * q^5 - 118 * q^9 + 559 * q^11 - 564 * q^13 - 722 * q^15 + 1259 * q^17 - 1957 * q^19 + 2977 * q^23 + 2764 * q^25 - 4750 * q^27 - 124 * q^29 + 2037 * q^31 + 10621 * q^33 - 6023 * q^37 + 5358 * q^39 + 4356 * q^41 + 46360 * q^43 + 2242 * q^45 + 26235 * q^47 + 23921 * q^51 - 30267 * q^53 + 21242 * q^55 + 74366 * q^57 + 44965 * q^59 + 27639 * q^61 - 5358 * q^65 + 58667 * q^67 - 113126 * q^69 - 19040 * q^71 - 6785 * q^73 + 52516 * q^75 + 16929 * q^79 + 73799 * q^81 + 119144 * q^83 + 47842 * q^85 + 1178 * q^87 - 51873 * q^89 + 38703 * q^93 + 37183 * q^95 - 268220 * q^97 - 131924 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−9.50000	−	16.4545i	−0.609425	−	1.05556i	−0.991335	−	0.131356i	$-0.958067\pi$
$3$	−9.50000	−	16.4545i	−0.609425	−	1.05556i	0.381910	−	0.924200i	$-0.375266\pi$
$4$		0			0
$5$	9.50000	−	16.4545i	0.169941	−	0.294347i	−0.768458	−	0.639900i	$-0.778976\pi$
$5$	9.50000	−	16.4545i	0.169941	−	0.294347i	0.938399	+	0.345554i	$0.112309\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−59.0000	+	102.191i	−0.242798	+	0.420539i
$10$		0			0
$11$	279.500	+	484.108i	0.696466	+	1.20631i	0.969684	+	0.244363i	$0.0785788\pi$
$11$	279.500	+	484.108i	0.696466	+	1.20631i	−0.273218	+	0.961952i	$0.588088\pi$
$12$		0			0
$13$	−282.000			−0.462797			−0.231399	−	0.972859i	$-0.574330\pi$
$13$	−282.000			−0.462797			−0.231399	+	0.972859i	$0.574330\pi$
$14$		0			0
$15$	−361.000			−0.414266
$16$		0			0
$17$	629.500	+	1090.33i	0.528291	+	0.915027i	0.999456	+	0.0329821i	$0.0105004\pi$
$17$	629.500	+	1090.33i	0.528291	+	0.915027i	−0.471165	+	0.882045i	$0.656166\pi$
$18$		0			0
$19$	−978.500	+	1694.81i	−0.621837	+	1.07705i	0.367306	+	0.930100i	$0.380280\pi$
$19$	−978.500	+	1694.81i	−0.621837	+	1.07705i	−0.989143	+	0.146954i	$0.953053\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1488.50	−	2578.16i	0.586718	−	1.01623i	−0.407941	−	0.913008i	$-0.633753\pi$
$23$	1488.50	−	2578.16i	0.586718	−	1.01623i	0.994659	−	0.103217i	$-0.0329135\pi$
$24$		0			0
$25$	1382.00	+	2393.69i	0.442240	+	0.765982i
$26$		0			0
$27$	−2375.00			−0.626981
$28$		0			0
$29$	−62.0000			−0.0136898			−0.00684489	−	0.999977i	$-0.502179\pi$
$29$	−62.0000			−0.0136898			−0.00684489	+	0.999977i	$0.502179\pi$
$30$		0			0
$31$	1018.50	+	1764.09i	0.190352	+	0.329699i	0.945367	−	0.326009i	$-0.105704\pi$
$31$	1018.50	+	1764.09i	0.190352	+	0.329699i	−0.755015	+	0.655707i	$0.772370\pi$
$32$		0			0
$33$	5310.50	−	9198.06i	0.848888	−	1.47032i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3011.50	+	5216.07i	−0.361642	+	0.626382i	−0.988231	−	0.152968i	$-0.951117\pi$
$37$	−3011.50	+	5216.07i	−0.361642	+	0.626382i	0.626589	+	0.779350i	$0.284450\pi$
$38$		0			0
$39$	2679.00	+	4640.16i	0.282040	+	0.488508i
$40$		0			0
$41$	2178.00			0.202348			0.101174	−	0.994869i	$-0.467740\pi$
$41$	2178.00			0.202348			0.101174	+	0.994869i	$0.467740\pi$
$42$		0			0
$43$	23180.0			1.91180			0.955900	−	0.293694i	$-0.0948845\pi$
$43$	23180.0			1.91180			0.955900	+	0.293694i	$0.0948845\pi$
$44$		0			0
$45$	1121.00	+	1941.63i	0.0825229	+	0.142934i
$46$		0			0
$47$	13117.5	−	22720.2i	0.866177	−	1.50026i	0.000302396	−	1.00000i	$-0.499904\pi$
$47$	13117.5	−	22720.2i	0.866177	−	1.50026i	0.865874	−	0.500262i	$-0.166763\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	11960.5	−	20716.2i	0.643908	−	1.11528i
$52$		0			0
$53$	−15133.5	−	26212.0i	−0.740031	−	1.28177i	−0.952481	−	0.304599i	$-0.901478\pi$
$53$	−15133.5	−	26212.0i	−0.740031	−	1.28177i	0.212450	−	0.977172i	$-0.431856\pi$
$54$		0			0
$55$	10621.0			0.473433
$56$		0			0
$57$	37183.0			1.51585
$58$		0			0
$59$	22482.5	+	38940.8i	0.840842	+	1.45638i	0.889183	+	0.457551i	$0.151273\pi$
$59$	22482.5	+	38940.8i	0.840842	+	1.45638i	−0.0483412	+	0.998831i	$0.515393\pi$
$60$		0			0
$61$	13819.5	−	23936.1i	0.475519	−	0.823623i	−0.524088	−	0.851664i	$-0.675594\pi$
$61$	13819.5	−	23936.1i	0.475519	−	0.823623i	0.999607	+	0.0280414i	$0.00892701\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2679.00	+	4640.16i	−0.0786483	+	0.136223i
$66$		0			0
$67$	29333.5	+	50807.1i	0.798320	+	1.38273i	0.920710	+	0.390248i	$0.127611\pi$
$67$	29333.5	+	50807.1i	0.798320	+	1.38273i	−0.122390	+	0.992482i	$0.539056\pi$
$68$		0			0
$69$	−56563.0			−1.43024
$70$		0			0
$71$	−9520.00			−0.224125			−0.112063	−	0.993701i	$-0.535746\pi$
$71$	−9520.00			−0.224125			−0.112063	+	0.993701i	$0.535746\pi$
$72$		0			0
$73$	−3392.50	−	5875.98i	−0.0745097	−	0.129055i	0.826363	−	0.563137i	$-0.190406\pi$
$73$	−3392.50	−	5875.98i	−0.0745097	−	0.129055i	−0.900873	+	0.434083i	$0.857073\pi$
$74$		0			0
$75$	26258.0	−	45480.2i	0.539024	−	0.933618i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	8464.50	−	14660.9i	0.152593	−	0.264298i	−0.779587	−	0.626294i	$-0.784571\pi$
$79$	8464.50	−	14660.9i	0.152593	−	0.264298i	0.932180	+	0.361995i	$0.117904\pi$
$80$		0			0
$81$	36899.5	+	63911.8i	0.624896	+	1.08235i
$82$		0			0
$83$	59572.0			0.949176			0.474588	−	0.880208i	$-0.342597\pi$
$83$	59572.0			0.949176			0.474588	+	0.880208i	$0.342597\pi$
$84$		0			0
$85$	23921.0			0.359114
$86$		0			0
$87$	589.000	+	1020.18i	0.00834290	+	0.0144503i
$88$		0			0
$89$	−25936.5	+	44923.3i	−0.347085	+	0.601170i	−0.985730	−	0.168332i	$-0.946162\pi$
$89$	−25936.5	+	44923.3i	−0.347085	+	0.601170i	0.638645	+	0.769502i	$0.279495\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	19351.5	−	33517.8i	0.232010	−	0.401854i
$94$		0			0
$95$	18591.5	+	32201.4i	0.211352	+	0.366072i
$96$		0			0
$97$	−134110.			−1.44721			−0.723605	−	0.690214i	$-0.757516\pi$
$97$	−134110.			−1.44721			−0.723605	+	0.690214i	$0.757516\pi$
$98$		0			0
$99$	−65962.0			−0.676403
$100$		0			0
$101$	61023.5	+	105696.i	0.595242	+	1.03099i	0.993513	+	0.113722i	$0.0362772\pi$
$101$	61023.5	+	105696.i	0.595242	+	1.03099i	−0.398270	+	0.917268i	$0.630389\pi$
$102$		0			0
$103$	−40308.5	+	69816.4i	−0.374372	+	0.648432i	−0.990233	−	0.139423i	$-0.955475\pi$
$103$	−40308.5	+	69816.4i	−0.374372	+	0.648432i	0.615861	+	0.787855i	$0.288808\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−733.500	+	1270.46i	−0.00619356	+	0.0107276i	−0.869106	−	0.494627i	$-0.835305\pi$
$107$	−733.500	+	1270.46i	−0.00619356	+	0.0107276i	0.862912	+	0.505354i	$0.168638\pi$
$108$		0			0
$109$	−100263.	−	173661.i	−0.808308	−	1.40003i	−0.914035	−	0.405635i	$-0.867051\pi$
$109$	−100263.	−	173661.i	−0.808308	−	1.40003i	0.105728	−	0.994395i	$-0.466283\pi$
$110$		0			0
$111$	114437.			0.881574
$112$		0			0
$113$	−722.000			−0.00531914			−0.00265957	−	0.999996i	$-0.500847\pi$
$113$	−722.000			−0.00531914			−0.00265957	+	0.999996i	$0.500847\pi$
$114$		0			0
$115$	−28281.5	−	48985.0i	−0.199415	−	0.345397i
$116$		0			0
$117$	16638.0	−	28817.9i	0.112366	−	0.194624i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−75715.0	+	131142.i	−0.470131	+	0.814290i
$122$		0			0
$123$	−20691.0	−	35837.9i	−0.123316	−	0.213589i
$124$		0			0
$125$	111891.			0.640501
$126$		0			0
$127$	147288.			0.810323			0.405161	−	0.914245i	$-0.367215\pi$
$127$	147288.			0.810323			0.405161	+	0.914245i	$0.367215\pi$
$128$		0			0
$129$	−220210.	−	381415.i	−1.16510	−	2.01801i
$130$		0			0
$131$	−26996.5	+	46759.3i	−0.137445	+	0.238062i	−0.926529	−	0.376224i	$-0.877222\pi$
$131$	−26996.5	+	46759.3i	−0.137445	+	0.238062i	0.789084	+	0.614286i	$0.210556\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−22562.5	+	39079.4i	−0.106550	+	0.184550i
$136$		0			0
$137$	−61281.5	−	106143.i	−0.278951	−	0.483157i	0.692173	−	0.721731i	$-0.256653\pi$
$137$	−61281.5	−	106143.i	−0.278951	−	0.483157i	−0.971124	+	0.238574i	$0.923320\pi$
$138$		0			0
$139$	128108.			0.562392			0.281196	−	0.959650i	$-0.409269\pi$
$139$	128108.			0.562392			0.281196	+	0.959650i	$0.409269\pi$
$140$		0			0
$141$	−498465.			−2.11148
$142$		0			0
$143$	−78819.0	−	136519.i	−0.322323	−	0.558279i
$144$		0			0
$145$	−589.000	+	1020.18i	−0.00232646	+	0.00402954i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−65977.5	+	114276.i	−0.243461	+	0.421688i	−0.961698	−	0.274111i	$-0.911616\pi$
$149$	−65977.5	+	114276.i	−0.243461	+	0.421688i	0.718236	+	0.695799i	$0.244950\pi$
$150$		0			0
$151$	−70062.5	−	121352.i	−0.250059	−	0.433116i	0.713482	−	0.700673i	$-0.247117\pi$
$151$	−70062.5	−	121352.i	−0.250059	−	0.433116i	−0.963542	+	0.267557i	$0.913783\pi$
$152$		0			0
$153$	−148562.			−0.513073
$154$		0			0
$155$	38703.0			0.129394
$156$		0			0
$157$	161670.	+	280020.i	0.523455	+	0.906650i	0.999627	+	0.0272981i	$0.00869034\pi$
$157$	161670.	+	280020.i	0.523455	+	0.906650i	−0.476173	+	0.879352i	$0.657976\pi$
$158$		0			0
$159$	−287536.	+	498028.i	−0.901987	+	1.56229i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−61079.5	+	105793.i	−0.180064	+	0.311880i	−0.941902	−	0.335888i	$-0.890964\pi$
$163$	−61079.5	+	105793.i	−0.180064	+	0.311880i	0.761838	+	0.647767i	$0.224297\pi$
$164$		0			0
$165$	−100900.	−	174763.i	−0.288522	−	0.499735i
$166$		0			0
$167$	−185404.			−0.514432			−0.257216	−	0.966354i	$-0.582805\pi$
$167$	−185404.			−0.514432			−0.257216	+	0.966354i	$0.582805\pi$
$168$		0			0
$169$	−291769.			−0.785819
$170$		0			0
$171$	−115463.	−	199988.i	−0.301962	−	0.523014i
$172$		0			0
$173$	−179312.	+	310578.i	−0.455507	+	0.788962i	−0.998717	−	0.0506352i	$-0.983875\pi$
$173$	−179312.	+	310578.i	−0.455507	+	0.788962i	0.543210	+	0.839597i	$0.317209\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	427168.	−	739876.i	1.02486	−	1.77511i
$178$		0			0
$179$	230276.	+	398849.i	0.537174	+	0.930413i	0.999055	+	0.0434709i	$0.0138416\pi$
$179$	230276.	+	398849.i	0.537174	+	0.930413i	−0.461880	+	0.886942i	$0.652825\pi$
$180$		0			0
$181$	332538.			0.754475			0.377237	−	0.926117i	$-0.376874\pi$
$181$	332538.			0.754475			0.377237	+	0.926117i	$0.376874\pi$
$182$		0			0
$183$	−525141.			−1.15917
$184$		0			0
$185$	57218.5	+	99105.3i	0.122916	+	0.212896i
$186$		0			0
$187$	−351890.	+	609492.i	−0.735874	+	1.27457i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−493934.	+	855518.i	−0.979682	+	1.69686i	−0.316153	+	0.948708i	$0.602391\pi$
$191$	−493934.	+	855518.i	−0.979682	+	1.69686i	−0.663529	+	0.748150i	$0.730942\pi$
$192$		0			0
$193$	172206.	+	298270.i	0.332779	+	0.576391i	0.983056	−	0.183307i	$-0.0586803\pi$
$193$	172206.	+	298270.i	0.332779	+	0.576391i	−0.650276	+	0.759698i	$0.725347\pi$
$194$		0			0
$195$	101802.			0.191721
$196$		0			0
$197$	582362.			1.06912			0.534561	−	0.845130i	$-0.320477\pi$
$197$	582362.			1.06912			0.534561	+	0.845130i	$0.320477\pi$
$198$		0			0
$199$	−75477.5	−	130731.i	−0.135109	−	0.234016i	0.790530	−	0.612423i	$-0.209805\pi$
$199$	−75477.5	−	130731.i	−0.135109	−	0.234016i	−0.925639	+	0.378407i	$0.876472\pi$
$200$		0			0
$201$	557336.	−	965335.i	0.973032	−	1.68534i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	20691.0	−	35837.9i	0.0343872	−	0.0595604i
$206$		0			0
$207$	175643.	+	304223.i	0.284908	+	0.493476i
$208$		0			0
$209$	−1.09396e6			−1.73236
$210$		0			0
$211$	272156.			0.420835			0.210417	−	0.977612i	$-0.432518\pi$
$211$	272156.			0.420835			0.210417	+	0.977612i	$0.432518\pi$
$212$		0			0
$213$	90440.0	+	156647.i	0.136588	+	0.236577i
$214$		0			0
$215$	220210.	−	381415.i	0.324893	−	0.562732i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−64457.5	+	111644.i	−0.0908162	+	0.157298i
$220$		0			0
$221$	−177519.	−	307472.i	−0.244492	−	0.423472i
$222$		0			0
$223$	939112.			1.26461			0.632303	−	0.774721i	$-0.282110\pi$
$223$	939112.			1.26461			0.632303	+	0.774721i	$0.282110\pi$
$224$		0			0
$225$	−326152.			−0.429501
$226$		0			0
$227$	240856.	+	417176.i	0.310237	+	0.537346i	0.978414	−	0.206656i	$-0.0662582\pi$
$227$	240856.	+	417176.i	0.310237	+	0.537346i	−0.668176	+	0.744003i	$0.732925\pi$
$228$		0			0
$229$	261573.	−	453059.i	0.329614	−	0.570907i	−0.652822	−	0.757512i	$-0.726415\pi$
$229$	261573.	−	453059.i	0.329614	−	0.570907i	0.982435	+	0.186604i	$0.0597482\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	613014.	−	1.06177e6i	0.739743	−	1.28127i	−0.212868	−	0.977081i	$-0.568280\pi$
$233$	613014.	−	1.06177e6i	0.739743	−	1.28127i	0.952611	−	0.304192i	$-0.0983863\pi$
$234$		0			0
$235$	−249233.	−	431683.i	−0.294398	−	0.509912i
$236$		0			0
$237$	−321651.			−0.371975
$238$		0			0
$239$	1.32568e6			1.50121			0.750607	−	0.660749i	$-0.229761\pi$
$239$	1.32568e6			1.50121			0.750607	+	0.660749i	$0.229761\pi$
$240$		0			0
$241$	135936.	+	235447.i	0.150761	+	0.261126i	0.931508	−	0.363722i	$-0.118494\pi$
$241$	135936.	+	235447.i	0.150761	+	0.261126i	−0.780746	+	0.624848i	$0.785161\pi$
$242$		0			0
$243$	412528.	−	714519.i	0.448165	−	0.776244i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	275937.	−	477937.i	0.287785	−	0.498458i
$248$		0			0
$249$	−565934.	−	980226.i	−0.578452	−	1.00191i
$250$		0			0
$251$	781368.			0.782837			0.391418	−	0.920213i	$-0.371985\pi$
$251$	781368.			0.782837			0.391418	+	0.920213i	$0.371985\pi$
$252$		0			0
$253$	1.66414e6			1.63452
$254$		0			0
$255$	−227250.	−	393608.i	−0.218853	−	0.379064i
$256$		0			0
$257$	501686.	−	868945.i	0.473804	−	0.820653i	−0.525746	−	0.850641i	$-0.676214\pi$
$257$	501686.	−	868945.i	0.473804	−	0.820653i	0.999550	+	0.0299888i	$0.00954718\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	3658.00	−	6335.84i	0.00332386	−	0.00575709i
$262$		0			0
$263$	554792.	+	960927.i	0.494584	+	0.856645i	0.999981	−	0.00624213i	$-0.00198694\pi$
$263$	554792.	+	960927.i	0.494584	+	0.856645i	−0.505396	+	0.862887i	$0.668654\pi$
$264$		0			0
$265$	−575073.			−0.503047
$266$		0			0
$267$	985587.			0.846090
$268$		0			0
$269$	862078.	+	1.49316e6i	0.726383	+	1.25813i	0.958402	+	0.285421i	$0.0921334\pi$
$269$	862078.	+	1.49316e6i	0.726383	+	1.25813i	−0.232019	+	0.972711i	$0.574533\pi$
$270$		0			0
$271$	415700.	−	720013.i	0.343840	−	0.595548i	−0.641302	−	0.767288i	$-0.721606\pi$
$271$	415700.	−	720013.i	0.343840	−	0.595548i	0.985142	+	0.171740i	$0.0549389\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−772538.	+	1.33808e6i	−0.616011	+	1.06696i
$276$		0			0
$277$	348379.	+	603409.i	0.272805	+	0.472512i	0.969579	−	0.244779i	$-0.0787154\pi$
$277$	348379.	+	603409.i	0.272805	+	0.472512i	−0.696774	+	0.717291i	$0.745382\pi$
$278$		0			0
$279$	−240366.			−0.184868
$280$		0			0
$281$	−2.26355e6			−1.71011			−0.855054	−	0.518539i	$-0.826476\pi$
$281$	−2.26355e6			−1.71011			−0.855054	+	0.518539i	$0.826476\pi$
$282$		0			0
$283$	211992.	+	367182.i	0.157346	+	0.272530i	0.933911	−	0.357507i	$-0.116373\pi$
$283$	211992.	+	367182.i	0.157346	+	0.272530i	−0.776565	+	0.630037i	$0.783040\pi$
$284$		0			0
$285$	353238.	−	611827.i	0.257606	−	0.446187i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−82612.0	+	143088.i	−0.0581833	+	0.100776i
$290$		0			0
$291$	1.27404e6	+	2.20671e6i	0.881967	+	1.52761i
$292$		0			0
$293$	−1.03724e6			−0.705845			−0.352923	−	0.935653i	$-0.614812\pi$
$293$	−1.03724e6			−0.705845			−0.352923	+	0.935653i	$0.614812\pi$
$294$		0			0
$295$	854335.			0.571575
$296$		0			0
$297$	−663812.	−	1.14976e6i	−0.436671	−	0.756336i
$298$		0			0
$299$	−419757.	+	727040.i	−0.271531	+	0.470306i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	1.15945e6	−	2.00822e6i	0.725511	−	1.25662i
$304$		0			0
$305$	−262570.	−	454785.i	−0.161620	−	0.279935i
$306$		0			0
$307$	152684.			0.0924587			0.0462293	−	0.998931i	$-0.485280\pi$
$307$	152684.			0.0924587			0.0462293	+	0.998931i	$0.485280\pi$
$308$		0			0
$309$	1.53172e6			0.912608
$310$		0			0
$311$	833172.	+	1.44310e6i	0.488466	+	0.846047i	0.999912	−	0.0132680i	$-0.00422346\pi$
$311$	833172.	+	1.44310e6i	0.488466	+	0.846047i	−0.511446	+	0.859315i	$0.670890\pi$
$312$		0			0
$313$	32235.5	−	55833.5i	0.0185983	−	0.0322132i	−0.856576	−	0.516020i	$-0.827413\pi$
$313$	32235.5	−	55833.5i	0.0185983	−	0.0322132i	0.875175	+	0.483807i	$0.160746\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−644672.	+	1.11660e6i	−0.360322	+	0.624095i	−0.988014	−	0.154366i	$-0.950666\pi$
$317$	−644672.	+	1.11660e6i	−0.360322	+	0.624095i	0.627692	+	0.778462i	$0.284000\pi$
$318$		0			0
$319$	−17329.0	−	30014.7i	−0.00953448	−	0.0165142i
$320$		0			0
$321$	27873.0			0.0150981
$322$		0			0
$323$	−2.46386e6			−1.31405
$324$		0			0
$325$	−389724.	−	675022.i	−0.204667	−	0.354494i
$326$		0			0
$327$	−1.90501e6	+	3.29957e6i	−0.985206	+	1.70643i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.32119e6	−	2.28837e6i	0.662819	−	1.14804i	−0.317053	−	0.948408i	$-0.602693\pi$
$331$	1.32119e6	−	2.28837e6i	0.662819	−	1.14804i	0.979872	−	0.199628i	$-0.0639734\pi$
$332$		0			0
$333$	−355357.	−	615496.i	−0.175612	−	0.304169i
$334$		0			0
$335$	1.11467e6			0.542670
$336$		0			0
$337$	−3.00561e6			−1.44164			−0.720822	−	0.693120i	$-0.756235\pi$
$337$	−3.00561e6			−1.44164			−0.720822	+	0.693120i	$0.756235\pi$
$338$		0			0
$339$	6859.00	+	11880.1i	0.00324162	+	0.00561464i
$340$		0			0
$341$	−569342.	+	986128.i	−0.265147	+	0.459248i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−537348.	+	930715.i	−0.243057	+	0.420987i
$346$		0			0
$347$	92653.5	+	160481.i	0.0413084	+	0.0715482i	0.885940	−	0.463799i	$-0.153514\pi$
$347$	92653.5	+	160481.i	0.0413084	+	0.0715482i	−0.844632	+	0.535347i	$0.820181\pi$
$348$		0			0
$349$	−2.82147e6			−1.23997			−0.619987	−	0.784612i	$-0.712862\pi$
$349$	−2.82147e6			−1.23997			−0.619987	+	0.784612i	$0.712862\pi$
$350$		0			0
$351$	669750.			0.290165
$352$		0			0
$353$	653762.	+	1.13235e6i	0.279243	+	0.483663i	0.971197	−	0.238279i	$-0.0765831\pi$
$353$	653762.	+	1.13235e6i	0.279243	+	0.483663i	−0.691954	+	0.721942i	$0.743250\pi$
$354$		0			0
$355$	−90440.0	+	156647.i	−0.0380881	+	0.0659706i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.44803e6	+	2.50805e6i	−0.592980	+	1.02707i	0.400848	+	0.916144i	$0.368715\pi$
$359$	−1.44803e6	+	2.50805e6i	−0.592980	+	1.02707i	−0.993829	+	0.110927i	$0.964618\pi$
$360$		0			0
$361$	−676875.	−	1.17238e6i	−0.273363	−	0.473479i
$362$		0			0
$363$	2.87717e6			1.14604
$364$		0			0
$365$	−128915.			−0.0506490
$366$		0			0
$367$	−2.35947e6	−	4.08672e6i	−0.914427	−	1.58383i	−0.807739	−	0.589541i	$-0.799309\pi$
$367$	−2.35947e6	−	4.08672e6i	−0.914427	−	1.58383i	−0.106688	−	0.994293i	$-0.534025\pi$
$368$		0			0
$369$	−128502.	+	222572.i	−0.0491297	+	0.0850951i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−219040.	+	379388.i	−0.0815174	+	0.141192i	−0.903902	−	0.427740i	$-0.859310\pi$
$373$	−219040.	+	379388.i	−0.0815174	+	0.141192i	0.822384	+	0.568932i	$0.192643\pi$
$374$		0			0
$375$	−1.06296e6	−	1.84111e6i	−0.390338	−	0.676085i
$376$		0			0
$377$	17484.0			0.00633560
$378$		0			0
$379$	−549632.			−0.196550			−0.0982752	−	0.995159i	$-0.531333\pi$
$379$	−549632.			−0.196550			−0.0982752	+	0.995159i	$0.531333\pi$
$380$		0			0
$381$	−1.39924e6	−	2.42355e6i	−0.493831	−	0.855341i
$382$		0			0
$383$	1.76500e6	−	3.05707e6i	0.614820	−	1.06490i	−0.375596	−	0.926784i	$-0.622562\pi$
$383$	1.76500e6	−	3.05707e6i	0.614820	−	1.06490i	0.990416	−	0.138116i	$-0.0441048\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.36762e6	+	2.36879e6i	−0.464182	+	0.803986i
$388$		0			0
$389$	−1.56698e6	−	2.71408e6i	−0.525035	−	0.909387i	−0.999575	−	0.0291533i	$-0.990719\pi$
$389$	−1.56698e6	−	2.71408e6i	−0.525035	−	0.909387i	0.474540	−	0.880234i	$-0.342614\pi$
$390$		0			0
$391$	3.74804e6			1.23983
$392$		0			0
$393$	1.02587e6			0.335050
$394$		0			0
$395$	−160826.	−	278558.i	−0.0518635	−	0.0898303i
$396$		0			0
$397$	−1.27695e6	+	2.21175e6i	−0.406630	+	0.704303i	−0.994510	−	0.104645i	$-0.966629\pi$
$397$	−1.27695e6	+	2.21175e6i	−0.406630	+	0.704303i	0.587880	+	0.808948i	$0.299963\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	351418.	−	608675.i	0.109135	−	0.189027i	−0.806285	−	0.591527i	$-0.798525\pi$
$401$	351418.	−	608675.i	0.109135	−	0.189027i	0.915420	+	0.402500i	$0.131859\pi$
$402$		0			0
$403$	−287217.	−	497474.i	−0.0880942	−	0.152584i
$404$		0			0
$405$	1.40218e6			0.424782
$406$		0			0
$407$	−3.36686e6			−1.00749
$408$		0			0
$409$	−2.73857e6	−	4.74335e6i	−0.809499	−	1.40209i	−0.913211	−	0.407486i	$-0.866406\pi$
$409$	−2.73857e6	−	4.74335e6i	−0.809499	−	1.40209i	0.103713	−	0.994607i	$-0.466928\pi$
$410$		0			0
$411$	−1.16435e6	+	2.01671e6i	−0.340000	+	0.588897i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	565934.	−	980226.i	0.161304	−	0.279387i
$416$		0			0
$417$	−1.21703e6	−	2.10795e6i	−0.342736	−	0.593636i
$418$		0			0
$419$	−5.80976e6			−1.61668			−0.808339	−	0.588718i	$-0.799633\pi$
$419$	−5.80976e6			−1.61668			−0.808339	+	0.588718i	$0.799633\pi$
$420$		0			0
$421$	1.69370e6			0.465726			0.232863	−	0.972510i	$-0.425191\pi$
$421$	1.69370e6			0.465726			0.232863	+	0.972510i	$0.425191\pi$
$422$		0			0
$423$	1.54786e6	+	2.68098e6i	0.420612	+	0.728522i
$424$		0			0
$425$	−1.73994e6	+	3.01366e6i	−0.467263	+	0.809323i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−1.49756e6	+	2.59385e6i	−0.392863	+	0.680459i
$430$		0			0
$431$	732338.	+	1.26845e6i	0.189897	+	0.328911i	0.945216	−	0.326446i	$-0.105851\pi$
$431$	732338.	+	1.26845e6i	0.189897	+	0.328911i	−0.755319	+	0.655358i	$0.772518\pi$
$432$		0			0
$433$	3.23418e6			0.828980			0.414490	−	0.910054i	$-0.363960\pi$
$433$	3.23418e6			0.828980			0.414490	+	0.910054i	$0.363960\pi$
$434$		0			0
$435$	22382.0			0.00567121
$436$		0			0
$437$	2.91299e6	+	5.04545e6i	0.729686	+	1.26385i
$438$		0			0
$439$	−1.27109e6	+	2.20159e6i	−0.314785	+	0.545223i	−0.979392	−	0.201970i	$-0.935266\pi$
$439$	−1.27109e6	+	2.20159e6i	−0.314785	+	0.545223i	0.664607	+	0.747193i	$0.268599\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−32969.5	+	57104.8i	−0.00798184	+	0.0138250i	−0.869989	−	0.493072i	$-0.835874\pi$
$443$	−32969.5	+	57104.8i	−0.00798184	+	0.0138250i	0.862007	+	0.506897i	$0.169207\pi$
$444$		0			0
$445$	492794.	+	853543.i	0.117968	+	0.204327i
$446$		0			0
$447$	2.50714e6			0.593486
$448$		0			0
$449$	−5.32399e6			−1.24630			−0.623149	−	0.782103i	$-0.714147\pi$
$449$	−5.32399e6			−1.24630			−0.623149	+	0.782103i	$0.714147\pi$
$450$		0			0
$451$	608751.	+	1.05439e6i	0.140928	+	0.244095i
$452$		0			0
$453$	−1.33119e6	+	2.30568e6i	−0.304785	+	0.527903i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	2.02912e6	−	3.51455e6i	0.454484	−	0.787189i	−0.544175	−	0.838972i	$-0.683157\pi$
$457$	2.02912e6	−	3.51455e6i	0.454484	−	0.787189i	0.998658	+	0.0517832i	$0.0164905\pi$
$458$		0			0
$459$	−1.49506e6	−	2.58952e6i	−0.331228	−	0.573705i
$460$		0			0
$461$	−3.73021e6			−0.817487			−0.408744	−	0.912649i	$-0.634033\pi$
$461$	−3.73021e6			−0.817487			−0.408744	+	0.912649i	$0.634033\pi$
$462$		0			0
$463$	−3.45186e6			−0.748342			−0.374171	−	0.927360i	$-0.622073\pi$
$463$	−3.45186e6			−0.748342			−0.374171	+	0.927360i	$0.622073\pi$
$464$		0			0
$465$	−367678.	−	636838.i	−0.0788562	−	0.136583i
$466$		0			0
$467$	1.96031e6	−	3.39536e6i	0.415942	−	0.720433i	−0.579585	−	0.814912i	$-0.696785\pi$
$467$	1.96031e6	−	3.39536e6i	0.415942	−	0.720433i	0.995527	+	0.0944791i	$0.0301186\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	3.07172e6	−	5.32038e6i	0.638013	−	1.10507i
$472$		0			0
$473$	6.47881e6	+	1.12216e7i	1.33150	+	2.30623i
$474$		0			0
$475$	−5.40915e6			−1.10001
$476$		0			0
$477$	3.57151e6			0.718713
$478$		0			0
$479$	−2.99337e6	−	5.18466e6i	−0.596103	−	1.03248i	−0.993390	−	0.114786i	$-0.963382\pi$
$479$	−2.99337e6	−	5.18466e6i	−0.596103	−	1.03248i	0.397287	−	0.917694i	$-0.369952\pi$
$480$		0			0
$481$	849243.	−	1.47093e6i	0.167367	−	0.289888i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.27404e6	+	2.20671e6i	−0.245941	+	0.425982i
$486$		0			0
$487$	−35936.5	−	62243.8i	−0.00686615	−	0.0118925i	0.862572	−	0.505934i	$-0.168852\pi$
$487$	−35936.5	−	62243.8i	−0.00686615	−	0.0118925i	−0.869438	+	0.494042i	$0.835519\pi$
$488$		0			0
$489$	2.32102e6			0.438942
$490$		0			0
$491$	1.01122e6			0.189295			0.0946477	−	0.995511i	$-0.469828\pi$
$491$	1.01122e6			0.189295			0.0946477	+	0.995511i	$0.469828\pi$
$492$		0			0
$493$	−39029.0	−	67600.2i	−0.00723219	−	0.0125265i
$494$		0			0
$495$	−626639.	+	1.08537e6i	−0.114949	+	0.199097i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−3.90234e6	+	6.75906e6i	−0.701575	+	1.21516i	0.266338	+	0.963880i	$0.414186\pi$
$499$	−3.90234e6	+	6.75906e6i	−0.701575	+	1.21516i	−0.967913	+	0.251284i	$0.919147\pi$
$500$		0			0
$501$	1.76134e6	+	3.05073e6i	0.313508	+	0.543011i
$502$		0			0
$503$	−7.89298e6			−1.39098			−0.695490	−	0.718536i	$-0.744813\pi$
$503$	−7.89298e6			−1.39098			−0.695490	+	0.718536i	$0.744813\pi$
$504$		0			0
$505$	2.31889e6			0.404625
$506$		0			0
$507$	2.77181e6	+	4.80091e6i	0.478898	+	0.829475i
$508$		0			0
$509$	3.31325e6	−	5.73872e6i	0.566839	−	0.981794i	−0.430037	−	0.902811i	$-0.641500\pi$
$509$	3.31325e6	−	5.73872e6i	0.566839	−	0.981794i	0.996876	−	0.0789826i	$-0.0251672\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	2.32394e6	−	4.02518e6i	0.389880	−	0.675292i
$514$		0			0
$515$	765862.	+	1.32651e6i	0.127242	+	0.220390i
$516$		0			0
$517$	1.46654e7			2.41305
$518$		0			0
$519$	6.81387e6			1.11039
$520$		0			0
$521$	3.63931e6	+	6.30347e6i	0.587387	+	1.01738i	0.994573	+	0.104039i	$0.0331767\pi$
$521$	3.63931e6	+	6.30347e6i	0.587387	+	1.01738i	−0.407186	+	0.913345i	$0.633490\pi$
$522$		0			0
$523$	2.37639e6	−	4.11603e6i	0.379895	−	0.657997i	−0.611152	−	0.791513i	$-0.709294\pi$
$523$	2.37639e6	−	4.11603e6i	0.379895	−	0.657997i	0.991047	+	0.133516i	$0.0426268\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.28229e6	+	2.22099e6i	−0.201122	+	0.348354i
$528$		0			0
$529$	−1.21309e6	−	2.10114e6i	−0.188476	−	0.326449i
$530$		0			0
$531$	−5.30587e6			−0.816621
$532$		0			0
$533$	−614196.			−0.0936459
$534$		0			0
$535$	13936.5	+	24138.7i	0.00210508	+	0.00364611i
$536$		0			0
$537$	4.37523e6	−	7.57813e6i	0.654735	−	1.13403i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	4.62581e6	−	8.01213e6i	0.679508	−	1.17694i	−0.295622	−	0.955305i	$-0.595527\pi$
$541$	4.62581e6	−	8.01213e6i	0.679508	−	1.17694i	0.975129	−	0.221637i	$-0.0711399\pi$
$542$		0			0
$543$	−3.15911e6	−	5.47174e6i	−0.459796	−	0.796390i
$544$		0			0
$545$	−3.81001e6			−0.549459
$546$		0			0
$547$	4.66834e6			0.667104			0.333552	−	0.942732i	$-0.391753\pi$
$547$	4.66834e6			0.667104			0.333552	+	0.942732i	$0.391753\pi$
$548$		0			0
$549$	1.63070e6	+	2.82446e6i	0.230910	+	0.399949i
$550$		0			0
$551$	60667.0	−	105078.i	0.00851282	−	0.0147446i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	1.08715e6	−	1.88300e6i	0.149816	−	0.259489i
$556$		0			0
$557$	3.25047e6	+	5.62998e6i	0.443924	+	0.768899i	0.997977	−	0.0635829i	$-0.0202527\pi$
$557$	3.25047e6	+	5.62998e6i	0.443924	+	0.768899i	−0.554053	+	0.832482i	$0.686919\pi$
$558$		0			0
$559$	−6.53676e6			−0.884775
$560$		0			0
$561$	1.33718e7			1.79384
$562$		0			0
$563$	5.32109e6	+	9.21640e6i	0.707505	+	1.22544i	0.965780	+	0.259363i	$0.0835128\pi$
$563$	5.32109e6	+	9.21640e6i	0.707505	+	1.22544i	−0.258275	+	0.966072i	$0.583154\pi$
$564$		0			0
$565$	−6859.00	+	11880.1i	−0.000903940	+	0.00156567i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−4.85500e6	+	8.40911e6i	−0.628650	+	1.08885i	0.359173	+	0.933271i	$0.383059\pi$
$569$	−4.85500e6	+	8.40911e6i	−0.628650	+	1.08885i	−0.987823	+	0.155583i	$0.950275\pi$
$570$		0			0
$571$	−5.78466e6	−	1.00193e7i	−0.742485	−	1.28602i	−0.951360	−	0.308080i	$-0.900314\pi$
$571$	−5.78466e6	−	1.00193e7i	−0.742485	−	1.28602i	0.208875	−	0.977942i	$-0.433020\pi$
$572$		0			0
$573$	1.87695e7			2.38817
$574$		0			0
$575$	8.22843e6			1.03788
$576$		0			0
$577$	−2.86275e6	−	4.95843e6i	−0.357968	−	0.620019i	0.629653	−	0.776876i	$-0.283197\pi$
$577$	−2.86275e6	−	4.95843e6i	−0.357968	−	0.620019i	−0.987621	+	0.156857i	$0.949864\pi$
$578$		0			0
$579$	3.27192e6	−	5.66714e6i	0.405608	−	0.702534i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	8.45963e6	−	1.46525e7i	1.03081	−	1.78542i
$584$		0			0
$585$	−316122.	−	547539.i	−0.0381914	−	0.0661494i
$586$		0			0
$587$	−2.35929e6			−0.282609			−0.141305	−	0.989966i	$-0.545130\pi$
$587$	−2.35929e6			−0.282609			−0.141305	+	0.989966i	$0.545130\pi$
$588$		0			0
$589$	−3.98641e6			−0.473471
$590$		0			0
$591$	−5.53244e6	−	9.58247e6i	−0.651550	−	1.12852i
$592$		0			0
$593$	1.45512e6	−	2.52034e6i	0.169927	−	0.294322i	−0.768467	−	0.639889i	$-0.778980\pi$
$593$	1.45512e6	−	2.52034e6i	0.169927	−	0.294322i	0.938394	+	0.345567i	$0.112313\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.43407e6	+	2.48389e6i	−0.164678	+	0.285230i
$598$		0			0
$599$	−4.99733e6	−	8.65563e6i	−0.569077	−	0.985671i	−0.996658	−	0.0816933i	$-0.973967\pi$
$599$	−4.99733e6	−	8.65563e6i	−0.569077	−	0.985671i	0.427580	−	0.903977i	$-0.359366\pi$
$600$		0			0
$601$	−6.12412e6			−0.691604			−0.345802	−	0.938308i	$-0.612393\pi$
$601$	−6.12412e6			−0.691604			−0.345802	+	0.938308i	$0.612393\pi$
$602$		0			0
$603$	−6.92271e6			−0.775323
$604$		0			0
$605$	1.43858e6	+	2.49170e6i	0.159789	+	0.276763i
$606$		0			0
$607$	8.85235e6	−	1.53327e7i	0.975185	−	1.68907i	0.295862	−	0.955231i	$-0.404393\pi$
$607$	8.85235e6	−	1.53327e7i	0.975185	−	1.68907i	0.679323	−	0.733839i	$-0.262273\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3.69914e6	+	6.40709e6i	−0.400864	+	0.694317i
$612$		0			0
$613$	4.41608e6	+	7.64887e6i	0.474663	+	0.822140i	0.999579	−	0.0290136i	$-0.00923660\pi$
$613$	4.41608e6	+	7.64887e6i	0.474663	+	0.822140i	−0.524916	+	0.851154i	$0.675903\pi$
$614$		0			0
$615$	−786258.			−0.0838257
$616$		0			0
$617$	1.07392e6			0.113569			0.0567843	−	0.998386i	$-0.481915\pi$
$617$	1.07392e6			0.113569			0.0567843	+	0.998386i	$0.481915\pi$
$618$		0			0
$619$	−176106.	−	305024.i	−0.0184734	−	0.0319968i	0.856641	−	0.515913i	$-0.172547\pi$
$619$	−176106.	−	305024.i	−0.0184734	−	0.0319968i	−0.875114	+	0.483916i	$0.839214\pi$
$620$		0			0
$621$	−3.53519e6	+	6.12312e6i	−0.367861	+	0.637154i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−3.25579e6	+	5.63919e6i	−0.333392	+	0.577453i
$626$		0			0
$627$	1.03926e7	+	1.80006e7i	1.05574	+	1.82860i
$628$		0			0
$629$	−7.58296e6			−0.764209
$630$		0			0
$631$	775808.			0.0775677			0.0387838	−	0.999248i	$-0.487652\pi$
$631$	775808.			0.0775677			0.0387838	+	0.999248i	$0.487652\pi$
$632$		0			0
$633$	−2.58548e6	−	4.47819e6i	−0.256467	−	0.444215i
$634$		0			0
$635$	1.39924e6	−	2.42355e6i	0.137707	−	0.238516i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	561680.	−	972858.i	0.0544173	−	0.0942535i
$640$		0			0
$641$	5.92106e6	+	1.02556e7i	0.569187	+	0.985860i	0.996647	+	0.0818259i	$0.0260752\pi$
$641$	5.92106e6	+	1.02556e7i	0.569187	+	0.985860i	−0.427460	+	0.904034i	$0.640592\pi$
$642$		0			0
$643$	−307460.			−0.0293266			−0.0146633	−	0.999892i	$-0.504668\pi$
$643$	−307460.			−0.0293266			−0.0146633	+	0.999892i	$0.504668\pi$
$644$		0			0
$645$	−8.36798e6			−0.791993
$646$		0			0
$647$	6.53542e6	+	1.13197e7i	0.613780	+	1.06310i	0.990597	+	0.136811i	$0.0436852\pi$
$647$	6.53542e6	+	1.13197e7i	0.613780	+	1.06310i	−0.376817	+	0.926288i	$0.622981\pi$
$648$		0			0
$649$	−1.25677e7	+	2.17679e7i	−1.17124	+	2.02864i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−463832.	+	803380.i	−0.0425674	+	0.0737289i	−0.886524	−	0.462682i	$-0.846887\pi$
$653$	−463832.	+	803380.i	−0.0425674	+	0.0737289i	0.843957	+	0.536411i	$0.180220\pi$
$654$		0			0
$655$	512933.	+	888427.i	0.0467152	+	0.0809130i
$656$		0			0
$657$	800630.			0.0723633
$658$		0			0
$659$	−1.90355e7			−1.70746			−0.853731	−	0.520715i	$-0.825666\pi$
$659$	−1.90355e7			−1.70746			−0.853731	+	0.520715i	$0.825666\pi$
$660$		0			0
$661$	−1.08618e6	−	1.88132e6i	−0.0966939	−	0.167479i	0.813620	−	0.581396i	$-0.197493\pi$
$661$	−1.08618e6	−	1.88132e6i	−0.0966939	−	0.167479i	−0.910314	+	0.413918i	$0.864160\pi$
$662$		0			0
$663$	−3.37286e6	+	5.84197e6i	−0.297999	+	0.516149i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−92287.0	+	159846.i	−0.00803204	+	0.0139119i
$668$		0			0
$669$	−8.92156e6	−	1.54526e7i	−0.770683	−	1.33486i
$670$		0			0
$671$	1.54502e7			1.32473
$672$		0			0
$673$	1.32268e7			1.12569			0.562844	−	0.826563i	$-0.309707\pi$
$673$	1.32268e7			1.12569			0.562844	+	0.826563i	$0.309707\pi$
$674$		0			0
$675$	−3.28225e6	−	5.68502e6i	−0.277276	−	0.480256i
$676$		0			0
$677$	−7.98311e6	+	1.38271e7i	−0.669422	+	1.15947i	0.308643	+	0.951178i	$0.400125\pi$
$677$	−7.98311e6	+	1.38271e7i	−0.669422	+	1.15947i	−0.978066	+	0.208296i	$0.933208\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	4.57627e6	−	7.92634e6i	0.378133	−	0.654945i
$682$		0			0
$683$	−7.00145e6	−	1.21269e7i	−0.574297	−	0.994711i	−0.996118	−	0.0880320i	$-0.971942\pi$
$683$	−7.00145e6	−	1.21269e7i	−0.574297	−	0.994711i	0.421821	−	0.906679i	$-0.361391\pi$
$684$		0			0
$685$	−2.32870e6			−0.189621
$686$		0			0
$687$	−9.93979e6			−0.803499
$688$		0			0
$689$	4.26765e6	+	7.39178e6i	0.342484	+	0.593200i
$690$		0			0
$691$	−5.26230e6	+	9.11457e6i	−0.419257	+	0.726175i	−0.995865	−	0.0908464i	$-0.971043\pi$
$691$	−5.26230e6	+	9.11457e6i	−0.419257	+	0.726175i	0.576608	+	0.817021i	$0.304376\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.21703e6	−	2.10795e6i	0.0955736	−	0.165538i
$696$		0			0
$697$	1.37105e6	+	2.37473e6i	0.106899	+	0.185154i
$698$		0			0
$699$	−2.32946e7			−1.80327
$700$		0			0
$701$	−1.30811e7			−1.00542			−0.502710	−	0.864455i	$-0.667664\pi$
$701$	−1.30811e7			−1.00542			−0.502710	+	0.864455i	$0.667664\pi$
$702$		0			0
$703$	−5.89351e6	−	1.02079e7i	−0.449765	−	0.779015i
$704$		0			0
$705$	−4.73542e6	+	8.20198e6i	−0.358827	+	0.621507i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−244260.	+	423070.i	−0.0182489	+	0.0316080i	−0.875006	−	0.484113i	$-0.839142\pi$
$709$	−244260.	+	423070.i	−0.0182489	+	0.0316080i	0.856757	+	0.515721i	$0.172476\pi$
$710$		0			0
$711$	998811.	+	1.72999e6i	0.0740985	+	0.128342i
$712$		0			0
$713$	6.06415e6			0.446731
$714$		0			0
$715$	−2.99512e6			−0.219104
$716$		0			0
$717$	−1.25939e7	−	2.18133e7i	−0.914878	−	1.58461i
$718$		0			0
$719$	−4.20425e6	+	7.28198e6i	−0.303296	+	0.525324i	−0.976880	−	0.213786i	$-0.931420\pi$
$719$	−4.20425e6	+	7.28198e6i	−0.303296	+	0.525324i	0.673585	+	0.739110i	$0.264754\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	2.58277e6	−	4.47350e6i	0.183756	−	0.318274i
$724$		0			0
$725$	−85684.0	−	148409.i	−0.00605417	−	0.0104861i
$726$		0			0
$727$	2.44145e7			1.71322			0.856608	−	0.515968i	$-0.172568\pi$
$727$	2.44145e7			1.71322			0.856608	+	0.515968i	$0.172568\pi$
$728$		0			0
$729$	2.25709e6			0.157301
$730$		0			0
$731$	1.45918e7	+	2.52738e7i	1.00999	+	1.74935i
$732$		0			0
$733$	5.69578e6	−	9.86539e6i	0.391556	−	0.678194i	−0.601099	−	0.799174i	$-0.705270\pi$
$733$	5.69578e6	−	9.86539e6i	0.391556	−	0.678194i	0.992655	+	0.120980i	$0.0386037\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.63974e7	+	2.84012e7i	−1.11201	+	1.92605i
$738$		0			0
$739$	1.09482e6	+	1.89628e6i	0.0737445	+	0.127729i	0.900540	−	0.434774i	$-0.143172\pi$
$739$	1.09482e6	+	1.89628e6i	0.0737445	+	0.127729i	−0.826795	+	0.562503i	$0.809838\pi$
$740$		0			0
$741$	−1.04856e7			−0.701533
$742$		0			0
$743$	−7.06982e6			−0.469825			−0.234913	−	0.972016i	$-0.575480\pi$
$743$	−7.06982e6			−0.469825			−0.234913	+	0.972016i	$0.575480\pi$
$744$		0			0
$745$	1.25357e6	+	2.17125e6i	0.0827482	+	0.143324i
$746$		0			0
$747$	−3.51475e6	+	6.08772e6i	−0.230458	+	0.399166i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−3.27940e6	+	5.68008e6i	−0.212175	+	0.367498i	−0.952395	−	0.304867i	$-0.901388\pi$
$751$	−3.27940e6	+	5.68008e6i	−0.212175	+	0.367498i	0.740220	+	0.672365i	$0.234721\pi$
$752$		0			0
$753$	−7.42300e6	−	1.28570e7i	−0.477081	−	0.826328i
$754$		0			0
$755$	−2.66238e6			−0.169982
$756$		0			0
$757$	2.17588e6			0.138005			0.0690026	−	0.997616i	$-0.478018\pi$
$757$	2.17588e6			0.138005			0.0690026	+	0.997616i	$0.478018\pi$
$758$		0			0
$759$	−1.58094e7	−	2.73826e7i	−0.996116	−	1.72532i
$760$		0			0
$761$	7.93160e6	−	1.37379e7i	0.496477	−	0.859923i	−0.503515	−	0.863987i	$-0.667960\pi$
$761$	7.93160e6	−	1.37379e7i	0.496477	−	0.859923i	0.999992	+	0.00406339i	$0.00129342\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.41134e6	+	2.44451e6i	−0.0871922	+	0.151021i
$766$		0			0
$767$	−6.34006e6	−	1.09813e7i	−0.389139	−	0.674009i
$768$		0			0
$769$	1.86634e7			1.13809			0.569044	−	0.822307i	$-0.307313\pi$
$769$	1.86634e7			1.13809			0.569044	+	0.822307i	$0.307313\pi$
$770$		0			0
$771$	−1.90640e7			−1.15499
$772$		0			0
$773$	−1.13198e7	−	1.96066e7i	−0.681384	−	1.18019i	−0.974559	−	0.224133i	$-0.928045\pi$
$773$	−1.13198e7	−	1.96066e7i	−0.681384	−	1.18019i	0.293175	−	0.956059i	$-0.405288\pi$
$774$		0			0
$775$	−2.81513e6	+	4.87596e6i	−0.168362	+	0.291612i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.13117e6	+	3.69130e6i	−0.125827	+	0.217939i
$780$		0			0
$781$	−2.66084e6	−	4.60871e6i	−0.156096	−	0.270366i
$782$		0			0
$783$	147250.			0.00858323
$784$		0			0
$785$	6.14344e6			0.355826
$786$		0			0
$787$	−4.83027e6	−	8.36627e6i	−0.277993	−	0.481498i	0.692893	−	0.721041i	$-0.256336\pi$
$787$	−4.83027e6	−	8.36627e6i	−0.277993	−	0.481498i	−0.970886	+	0.239542i	$0.923003\pi$
$788$		0			0
$789$	1.05410e7	−	1.82576e7i	0.602824	−	1.04412i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−3.89710e6	+	6.74997e6i	−0.220069	+	0.381170i
$794$		0			0
$795$	5.46319e6	+	9.46253e6i	0.306569	+	0.530994i
$796$		0			0
$797$	−1.15546e7			−0.644330			−0.322165	−	0.946684i	$-0.604411\pi$
$797$	−1.15546e7			−0.644330			−0.322165	+	0.946684i	$0.604411\pi$
$798$		0			0
$799$	3.30299e7			1.83037
$800$		0			0
$801$	−3.06051e6	−	5.30095e6i	−0.168544	−	0.291926i
$802$		0			0
$803$	1.89641e6	−	3.28467e6i	0.103787	−	0.179764i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.63795e7	−	2.83701e7i	0.885352	−	1.53348i
$808$		0			0
$809$	−9.26536e6	−	1.60481e7i	−0.497727	−	0.862088i	0.502270	−	0.864711i	$-0.332498\pi$
$809$	−9.26536e6	−	1.60481e7i	−0.497727	−	0.862088i	−0.999997	+	0.00262295i	$0.999165\pi$
$810$		0			0
$811$	1.31357e7			0.701298			0.350649	−	0.936507i	$-0.385961\pi$
$811$	1.31357e7			0.701298			0.350649	+	0.936507i	$0.385961\pi$
$812$		0			0
$813$	−1.57966e7			−0.838179
$814$		0			0
$815$	1.16051e6	+	2.01006e6i	0.0612005	+	0.106002i
$816$		0			0
$817$	−2.26816e7	+	3.92857e7i	−1.18883	+	2.05911i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	2.10434e6	−	3.64482e6i	0.108958	−	0.188720i	−0.806391	−	0.591383i	$-0.798582\pi$
$821$	2.10434e6	−	3.64482e6i	0.108958	−	0.188720i	0.915348	+	0.402663i	$0.131915\pi$
$822$		0			0
$823$	−5.52186e6	−	9.56414e6i	−0.284175	−	0.492206i	0.688234	−	0.725489i	$-0.258386\pi$
$823$	−5.52186e6	−	9.56414e6i	−0.284175	−	0.492206i	−0.972409	+	0.233283i	$0.925053\pi$
$824$		0			0
$825$	2.93564e7			1.50165
$826$		0			0
$827$	1.74824e7			0.888867			0.444433	−	0.895812i	$-0.353405\pi$
$827$	1.74824e7			0.888867			0.444433	+	0.895812i	$0.353405\pi$
$828$		0			0
$829$	1.17709e7	+	2.03878e7i	0.594871	+	1.03035i	0.993565	+	0.113263i	$0.0361302\pi$
$829$	1.17709e7	+	2.03878e7i	0.594871	+	1.03035i	−0.398694	+	0.917084i	$0.630536\pi$
$830$		0			0
$831$	6.61919e6	−	1.14648e7i	0.332508	−	0.575921i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.76134e6	+	3.05073e6i	−0.0874232	+	0.151421i
$836$		0			0
$837$	−2.41894e6	−	4.18972e6i	−0.119347	−	0.206715i
$838$		0			0
$839$	−2.64326e7			−1.29639			−0.648195	−	0.761474i	$-0.724476\pi$
$839$	−2.64326e7			−1.29639			−0.648195	+	0.761474i	$0.724476\pi$
$840$		0			0
$841$	−2.05073e7			−0.999813
$842$		0			0
$843$	2.15037e7	+	3.72455e7i	1.04218	+	1.80511i
$844$		0			0
$845$	−2.77181e6	+	4.80091e6i	−0.133543	+	0.231303i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	4.02786e6	−	6.97645e6i	0.191781	−	0.332174i
$850$		0			0
$851$	8.96524e6	+	1.55282e7i	0.424363	+	0.735019i
$852$		0			0
$853$	−3.86472e7			−1.81863			−0.909317	−	0.416103i	$-0.863395\pi$
$853$	−3.86472e7			−1.81863			−0.909317	+	0.416103i	$0.863395\pi$
$854$		0			0
$855$	−4.38759e6			−0.205263
$856$		0			0
$857$	1.23354e7	+	2.13655e7i	0.573721	+	0.993714i	0.996179	+	0.0873313i	$0.0278339\pi$
$857$	1.23354e7	+	2.13655e7i	0.573721	+	0.993714i	−0.422459	+	0.906382i	$0.638833\pi$
$858$		0			0
$859$	1.37162e7	−	2.37571e7i	0.634235	−	1.09853i	−0.352441	−	0.935834i	$-0.614648\pi$
$859$	1.37162e7	−	2.37571e7i	0.634235	−	1.09853i	0.986677	−	0.162694i	$-0.0520183\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	3.05485e6	−	5.29115e6i	0.139625	−	0.241837i	−0.787730	−	0.616021i	$-0.788744\pi$
$863$	3.05485e6	−	5.29115e6i	0.139625	−	0.241837i	0.927355	+	0.374184i	$0.122077\pi$
$864$		0			0
$865$	3.40694e6	+	5.90099e6i	0.154819	+	0.268154i
$866$		0			0
$867$	3.13926e6			0.141834
$868$		0			0
$869$	9.46331e6			0.425103
$870$		0			0
$871$	−8.27205e6	−	1.43276e7i	−0.369460	−	0.639924i
$872$		0			0
$873$	7.91249e6	−	1.37048e7i	0.351380	−	0.608609i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	3.81306e6	−	6.60442e6i	0.167408	−	0.289958i	−0.770100	−	0.637923i	$-0.779794\pi$
$877$	3.81306e6	−	6.60442e6i	0.167408	−	0.289958i	0.937508	+	0.347965i	$0.113127\pi$
$878$		0			0
$879$	9.85376e6	+	1.70672e7i	0.430160	+	0.745059i
$880$		0			0
$881$	3.22357e6			0.139925			0.0699627	−	0.997550i	$-0.477712\pi$
$881$	3.22357e6			0.139925			0.0699627	+	0.997550i	$0.477712\pi$
$882$		0			0
$883$	7.31409e6			0.315688			0.157844	−	0.987464i	$-0.449546\pi$
$883$	7.31409e6			0.315688			0.157844	+	0.987464i	$0.449546\pi$
$884$		0			0
$885$	−8.11618e6	−	1.40576e7i	−0.348332	−	0.603329i
$886$		0			0
$887$	−2.16067e7	+	3.74239e7i	−0.922103	+	1.59713i	−0.125948	+	0.992037i	$0.540197\pi$
$887$	−2.16067e7	+	3.74239e7i	−0.922103	+	1.59713i	−0.796155	+	0.605093i	$0.793136\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−2.06268e7	+	3.57267e7i	−0.870438	+	1.50764i
$892$		0			0
$893$	2.56709e7	+	4.44634e7i	1.07724	+	1.86584i
$894$		0			0
$895$	8.75047e6			0.365152
$896$		0			0
$897$	1.59508e7			0.661912
$898$		0			0
$899$	−63147.0	−	109374.i	−0.00260587	−	0.00451351i
$900$		0			0
$901$	1.90531e7	−	3.30009e7i	0.781903	−	1.35430i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3.15911e6	−	5.47174e6i	0.128216	−	0.222077i
$906$		0			0
$907$	7.44889e6	+	1.29019e7i	0.300659	+	0.520756i	0.976285	−	0.216488i	$-0.0694602\pi$
$907$	7.44889e6	+	1.29019e7i	0.300659	+	0.520756i	−0.675627	+	0.737244i	$0.736127\pi$
$908$		0			0
$909$	−1.44015e7			−0.578095
$910$		0			0
$911$	1.65823e7			0.661987			0.330993	−	0.943633i	$-0.392616\pi$
$911$	1.65823e7			0.661987			0.330993	+	0.943633i	$0.392616\pi$
$912$		0			0
$913$	1.66504e7	+	2.88393e7i	0.661069	+	1.14501i
$914$		0			0
$915$	−4.98884e6	+	8.64092e6i	−0.196991	+	0.341199i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	9.71656e6	−	1.68296e7i	0.379510	−	0.657331i	−0.611481	−	0.791259i	$-0.709426\pi$
$919$	9.71656e6	−	1.68296e7i	0.379510	−	0.657331i	0.990991	+	0.133928i	$0.0427591\pi$
$920$		0			0
$921$	−1.45050e6	−	2.51234e6i	−0.0563466	−	0.0975953i
$922$		0			0
$923$	2.68464e6			0.103725
$924$		0			0
$925$	−1.66476e7			−0.639730
$926$		0			0
$927$	−4.75640e6	−	8.23833e6i	−0.181794	−	0.314876i
$928$		0			0
$929$	2.30583e7	−	3.99382e7i	0.876573	−	1.51827i	0.0214956	−	0.999769i	$-0.493157\pi$
$929$	2.30583e7	−	3.99382e7i	0.876573	−	1.51827i	0.855077	−	0.518500i	$-0.173509\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	1.58303e7	−	2.74188e7i	0.595367	−	1.03121i
$934$		0			0
$935$	6.68592e6	+	1.15804e7i	0.250111	+	0.433204i
$936$		0			0
$937$	−1.59157e7			−0.592210			−0.296105	−	0.955155i	$-0.595688\pi$
$937$	−1.59157e7			−0.592210			−0.296105	+	0.955155i	$0.595688\pi$
$938$		0			0
$939$	−1.22495e6			−0.0453371
$940$		0			0
$941$	−5.36507e6	−	9.29257e6i	−0.197516	−	0.342107i	0.750207	−	0.661203i	$-0.229954\pi$
$941$	−5.36507e6	−	9.29257e6i	−0.197516	−	0.342107i	−0.947722	+	0.319096i	$0.896621\pi$
$942$		0			0
$943$	3.24195e6	−	5.61523e6i	0.118721	−	0.205631i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.13816e7	+	1.97135e7i	−0.412410	+	0.714315i	−0.995153	−	0.0983417i	$-0.968646\pi$
$947$	−1.13816e7	+	1.97135e7i	−0.412410	+	0.714315i	0.582743	+	0.812657i	$0.301980\pi$
$948$		0			0
$949$	956685.	+	1.65703e6i	0.0344829	+	0.0597261i
$950$		0			0
$951$	2.44975e7			0.878356
$952$		0			0
$953$	2.69718e7			0.962005			0.481002	−	0.876719i	$-0.340273\pi$
$953$	2.69718e7			0.962005			0.481002	+	0.876719i	$0.340273\pi$
$954$		0			0
$955$	9.38474e6	+	1.62548e7i	0.332977	+	0.576732i
$956$		0			0
$957$	−329251.	+	570279.i	−0.0116211	+	0.0201283i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	1.22399e7	−	2.12001e7i	0.427532	−	0.740508i
$962$		0			0
$963$	−86553.0	−	149914.i	−0.00300757	−	0.00520927i
$964$		0			0
$965$	6.54385e6			0.226212
$966$		0			0
$967$	1.02880e7			0.353805			0.176902	−	0.984228i	$-0.443392\pi$
$967$	1.02880e7			0.353805			0.176902	+	0.984228i	$0.443392\pi$
$968$		0			0
$969$	2.34067e7	+	4.05416e7i	0.800812	+	1.38705i
$970$		0			0
$971$	1.42902e7	−	2.47513e7i	0.486395	−	0.842461i	−0.513482	−	0.858100i	$-0.671645\pi$
$971$	1.42902e7	−	2.47513e7i	0.486395	−	0.842461i	0.999878	+	0.0156388i	$0.00497817\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−7.40476e6	+	1.28254e7i	−0.249459	+	0.432076i
$976$		0			0
$977$	1.42149e6	+	2.46210e6i	0.0476441	+	0.0825219i	0.888864	−	0.458171i	$-0.151495\pi$
$977$	1.42149e6	+	2.46210e6i	0.0476441	+	0.0825219i	−0.841220	+	0.540693i	$0.818162\pi$
$978$		0			0
$979$	−2.89970e7			−0.966933
$980$		0			0
$981$	2.36622e7			0.785023
$982$		0			0
$983$	−2.65833e7	−	4.60436e7i	−0.877455	−	1.51980i	−0.854124	−	0.520069i	$-0.825906\pi$
$983$	−2.65833e7	−	4.60436e7i	−0.877455	−	1.51980i	−0.0233310	−	0.999728i	$-0.507427\pi$
$984$		0			0
$985$	5.53244e6	−	9.58247e6i	0.181688	−	0.314693i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.45034e7	−	5.97617e7i	1.12169	−	1.94282i
$990$		0			0
$991$	−2.70937e7	−	4.69276e7i	−0.876363	−	1.51790i	−0.855304	−	0.518126i	$-0.826630\pi$
$991$	−2.70937e7	−	4.69276e7i	−0.876363	−	1.51790i	−0.0210586	−	0.999778i	$-0.506704\pi$
$992$		0			0
$993$	−5.02052e7			−1.61575
$994$		0			0
$995$	−2.86814e6			−0.0918424
$996$		0			0
$997$	3.27587e6	+	5.67398e6i	0.104373	+	0.180780i	0.913482	−	0.406879i	$-0.133383\pi$
$997$	3.27587e6	+	5.67398e6i	0.104373	+	0.180780i	−0.809109	+	0.587659i	$0.800050\pi$
$998$		0			0
$999$	7.15231e6	−	1.23882e7i	0.226742	−	0.392729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.6.e.b.177.1		2
7.2	even	3		196.6.a.g.1.1		1
7.3	odd	6		28.6.e.a.25.1	yes	2
7.4	even	3	inner	196.6.e.b.165.1		2
7.5	odd	6		196.6.a.b.1.1		1
7.6	odd	2		28.6.e.a.9.1	✓	2
21.17	even	6		252.6.k.c.109.1		2
21.20	even	2		252.6.k.c.37.1		2
28.3	even	6		112.6.i.a.81.1		2
28.19	even	6		784.6.a.k.1.1		1
28.23	odd	6		784.6.a.a.1.1		1
28.27	even	2		112.6.i.a.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.6.e.a.9.1	✓	2	7.6	odd	2
28.6.e.a.25.1	yes	2	7.3	odd	6
112.6.i.a.65.1		2	28.27	even	2
112.6.i.a.81.1		2	28.3	even	6
196.6.a.b.1.1		1	7.5	odd	6
196.6.a.g.1.1		1	7.2	even	3
196.6.e.b.165.1		2	7.4	even	3	inner
196.6.e.b.177.1		2	1.1	even	1	trivial
252.6.k.c.37.1		2	21.20	even	2
252.6.k.c.109.1		2	21.17	even	6
784.6.a.a.1.1		1	28.23	odd	6
784.6.a.k.1.1		1	28.19	even	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)

\(f(q)\)	\(=\)	\(q+(-9.50000 - 16.4545i) q^{3} +(9.50000 - 16.4545i) q^{5} +(-59.0000 + 102.191i) q^{9} +O(q^{10})\)	\(q+(-9.50000 - 16.4545i) q^{3} +(9.50000 - 16.4545i) q^{5} +(-59.0000 + 102.191i) q^{9} +(279.500 + 484.108i) q^{11} -282.000 q^{13} -361.000 q^{15} +(629.500 + 1090.33i) q^{17} +(-978.500 + 1694.81i) q^{19} +(1488.50 - 2578.16i) q^{23} +(1382.00 + 2393.69i) q^{25} -2375.00 q^{27} -62.0000 q^{29} +(1018.50 + 1764.09i) q^{31} +(5310.50 - 9198.06i) q^{33} +(-3011.50 + 5216.07i) q^{37} +(2679.00 + 4640.16i) q^{39} +2178.00 q^{41} +23180.0 q^{43} +(1121.00 + 1941.63i) q^{45} +(13117.5 - 22720.2i) q^{47} +(11960.5 - 20716.2i) q^{51} +(-15133.5 - 26212.0i) q^{53} +10621.0 q^{55} +37183.0 q^{57} +(22482.5 + 38940.8i) q^{59} +(13819.5 - 23936.1i) q^{61} +(-2679.00 + 4640.16i) q^{65} +(29333.5 + 50807.1i) q^{67} -56563.0 q^{69} -9520.00 q^{71} +(-3392.50 - 5875.98i) q^{73} +(26258.0 - 45480.2i) q^{75} +(8464.50 - 14660.9i) q^{79} +(36899.5 + 63911.8i) q^{81} +59572.0 q^{83} +23921.0 q^{85} +(589.000 + 1020.18i) q^{87} +(-25936.5 + 44923.3i) q^{89} +(19351.5 - 33517.8i) q^{93} +(18591.5 + 32201.4i) q^{95} -134110. q^{97} -65962.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 19 q^{3} + 19 q^{5} - 118 q^{9}+O(q^{10}) \) 2 * q - 19 * q^3 + 19 * q^5 - 118 * q^9	\( 2 q - 19 q^{3} + 19 q^{5} - 118 q^{9} + 559 q^{11} - 564 q^{13} - 722 q^{15} + 1259 q^{17} - 1957 q^{19} + 2977 q^{23} + 2764 q^{25} - 4750 q^{27} - 124 q^{29} + 2037 q^{31} + 10621 q^{33} - 6023 q^{37} + 5358 q^{39} + 4356 q^{41} + 46360 q^{43} + 2242 q^{45} + 26235 q^{47} + 23921 q^{51} - 30267 q^{53} + 21242 q^{55} + 74366 q^{57} + 44965 q^{59} + 27639 q^{61} - 5358 q^{65} + 58667 q^{67} - 113126 q^{69} - 19040 q^{71} - 6785 q^{73} + 52516 q^{75} + 16929 q^{79} + 73799 q^{81} + 119144 q^{83} + 47842 q^{85} + 1178 q^{87} - 51873 q^{89} + 38703 q^{93} + 37183 q^{95} - 268220 q^{97} - 131924 q^{99}+O(q^{100}) \) 2 * q - 19 * q^3 + 19 * q^5 - 118 * q^9 + 559 * q^11 - 564 * q^13 - 722 * q^15 + 1259 * q^17 - 1957 * q^19 + 2977 * q^23 + 2764 * q^25 - 4750 * q^27 - 124 * q^29 + 2037 * q^31 + 10621 * q^33 - 6023 * q^37 + 5358 * q^39 + 4356 * q^41 + 46360 * q^43 + 2242 * q^45 + 26235 * q^47 + 23921 * q^51 - 30267 * q^53 + 21242 * q^55 + 74366 * q^57 + 44965 * q^59 + 27639 * q^61 - 5358 * q^65 + 58667 * q^67 - 113126 * q^69 - 19040 * q^71 - 6785 * q^73 + 52516 * q^75 + 16929 * q^79 + 73799 * q^81 + 119144 * q^83 + 47842 * q^85 + 1178 * q^87 - 51873 * q^89 + 38703 * q^93 + 37183 * q^95 - 268220 * q^97 - 131924 * q^99

Introduction

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