LMFDB - Embedded newform 124.6.f.a.97.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,6,Mod(33,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("124.33");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	124.f (of order $5$, degree $4$, 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:	$19.8875936568$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			97.4
Character	$\chi$	$=$	124.97
Dual form			124.6.f.a.101.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.50907 + 13.8775i) q^{3} +78.4326 q^{5} +(-14.7862 + 10.7428i) q^{7} +(24.3383 + 17.6828i) q^{9} +O(q^{10})$	\(q+(-4.50907 + 13.8775i) q^{3} +78.4326 q^{5} +(-14.7862 + 10.7428i) q^{7} +(24.3383 + 17.6828i) q^{9} +(497.817 - 361.685i) q^{11} +(79.1894 - 243.720i) q^{13} +(-353.658 + 1088.45i) q^{15} +(438.635 + 318.687i) q^{17} +(-849.929 - 2615.81i) q^{19} +(-82.4110 - 253.635i) q^{21} +(1680.92 + 1221.26i) q^{23} +3026.67 q^{25} +(-3223.72 + 2342.17i) q^{27} +(2583.40 + 7950.88i) q^{29} +(1027.33 + 5251.07i) q^{31} +(2774.59 + 8539.31i) q^{33} +(-1159.72 + 842.585i) q^{35} +14971.8 q^{37} +(3025.15 + 2197.90i) q^{39} +(1222.38 + 3762.11i) q^{41} +(-6504.72 - 20019.5i) q^{43} +(1908.91 + 1386.91i) q^{45} +(-1530.55 + 4710.55i) q^{47} +(-5090.43 + 15666.7i) q^{49} +(-6400.41 + 4650.17i) q^{51} +(-7988.15 - 5803.73i) q^{53} +(39045.1 - 28367.9i) q^{55} +40133.3 q^{57} +(-1766.19 + 5435.78i) q^{59} -39368.4 q^{61} -549.832 q^{63} +(6211.03 - 19115.6i) q^{65} -21185.3 q^{67} +(-24527.4 + 17820.2i) q^{69} +(62905.7 + 45703.7i) q^{71} +(15247.9 - 11078.3i) q^{73} +(-13647.5 + 42002.6i) q^{75} +(-3475.30 + 10695.9i) q^{77} +(-71525.4 - 51966.3i) q^{79} +(-15708.5 - 48345.6i) q^{81} +(-7914.74 - 24359.1i) q^{83} +(34403.3 + 24995.5i) q^{85} -121987. q^{87} +(-22593.8 + 16415.4i) q^{89} +(1447.32 + 4454.40i) q^{91} +(-77503.9 - 9420.75i) q^{93} +(-66662.2 - 205165. i) q^{95} +(1827.17 - 1327.52i) q^{97} +18511.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) $ 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9	$ 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9} - 509 q^{11} - 117 q^{13} + 89 q^{15} - 3504 q^{17} + 262 q^{19} + 352 q^{21} - 2448 q^{23} + 49618 q^{25} + 14324 q^{27} - 9888 q^{29} - 12771 q^{31} + 27699 q^{33} + 13840 q^{35} + 76096 q^{37} + 33520 q^{39} - 4843 q^{41} - 40778 q^{43} + 56692 q^{45} + 38922 q^{47} - 17126 q^{49} - 69292 q^{51} - 41728 q^{53} - 172096 q^{55} + 57066 q^{57} - 58198 q^{59} + 176328 q^{61} - 37444 q^{63} + 143863 q^{65} + 9812 q^{67} - 9250 q^{69} - 67356 q^{71} - 63512 q^{73} - 198012 q^{75} - 74257 q^{77} + 137651 q^{79} + 196077 q^{81} + 156427 q^{83} + 238828 q^{85} - 558144 q^{87} - 99292 q^{89} - 243609 q^{91} - 325925 q^{93} - 75077 q^{95} - 476340 q^{97} + 745812 q^{99}+O(q^{100}) $ 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9 - 509 * q^11 - 117 * q^13 + 89 * q^15 - 3504 * q^17 + 262 * q^19 + 352 * q^21 - 2448 * q^23 + 49618 * q^25 + 14324 * q^27 - 9888 * q^29 - 12771 * q^31 + 27699 * q^33 + 13840 * q^35 + 76096 * q^37 + 33520 * q^39 - 4843 * q^41 - 40778 * q^43 + 56692 * q^45 + 38922 * q^47 - 17126 * q^49 - 69292 * q^51 - 41728 * q^53 - 172096 * q^55 + 57066 * q^57 - 58198 * q^59 + 176328 * q^61 - 37444 * q^63 + 143863 * q^65 + 9812 * q^67 - 9250 * q^69 - 67356 * q^71 - 63512 * q^73 - 198012 * q^75 - 74257 * q^77 + 137651 * q^79 + 196077 * q^81 + 156427 * q^83 + 238828 * q^85 - 558144 * q^87 - 99292 * q^89 - 243609 * q^91 - 325925 * q^93 - 75077 * q^95 - 476340 * q^97 + 745812 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	−4.50907	+	13.8775i	−0.289257	+	0.890241i	0.695833	+	0.718203i	$0.255035\pi$
$3$	−4.50907	+	13.8775i	−0.289257	+	0.890241i	−0.985090	+	0.172038i	$0.944965\pi$
$4$		0			0
$5$	78.4326			1.40305			0.701523	−	0.712647i	$-0.252504\pi$
$5$	78.4326			1.40305			0.701523	+	0.712647i	$0.252504\pi$
$6$		0			0
$7$	−14.7862	+	10.7428i	−0.114054	+	0.0828651i	−0.643350	−	0.765572i	$-0.722456\pi$
$7$	−14.7862	+	10.7428i	−0.114054	+	0.0828651i	0.529296	+	0.848437i	$0.322456\pi$
$8$		0			0
$9$	24.3383	+	17.6828i	0.100157	+	0.0727686i
$10$		0			0
$11$	497.817	−	361.685i	1.24048	−	0.901258i	0.242846	−	0.970065i	$-0.421919\pi$
$11$	497.817	−	361.685i	1.24048	−	0.901258i	0.997630	+	0.0688067i	$0.0219192\pi$
$12$		0			0
$13$	79.1894	−	243.720i	0.129960	−	0.399975i	−0.864812	−	0.502095i	$-0.832563\pi$
$13$	79.1894	−	243.720i	0.129960	−	0.399975i	0.994772	+	0.102120i	$0.0325627\pi$
$14$		0			0
$15$	−353.658	+	1088.45i	−0.405840	+	1.24905i
$16$		0			0
$17$	438.635	+	318.687i	0.368113	+	0.267450i	0.756428	−	0.654077i	$-0.226943\pi$
$17$	438.635	+	318.687i	0.368113	+	0.267450i	−0.388315	+	0.921527i	$0.626943\pi$
$18$		0			0
$19$	−849.929	−	2615.81i	−0.540131	−	1.66235i	−0.732295	−	0.680988i	$-0.761551\pi$
$19$	−849.929	−	2615.81i	−0.540131	−	1.66235i	0.192164	−	0.981363i	$-0.438449\pi$
$20$		0			0
$21$	−82.4110	−	253.635i	−0.0407790	−	0.125505i
$22$		0			0
$23$	1680.92	+	1221.26i	0.662563	+	0.481380i	0.867528	−	0.497389i	$-0.165708\pi$
$23$	1680.92	+	1221.26i	0.662563	+	0.481380i	−0.204964	+	0.978769i	$0.565708\pi$
$24$		0			0
$25$	3026.67			0.968536
$26$		0			0
$27$	−3223.72	+	2342.17i	−0.851037	+	0.618315i
$28$		0			0
$29$	2583.40	+	7950.88i	0.570422	+	1.75558i	0.651263	+	0.758852i	$0.274240\pi$
$29$	2583.40	+	7950.88i	0.570422	+	1.75558i	−0.0808405	+	0.996727i	$0.525760\pi$
$30$		0			0
$31$	1027.33	+	5251.07i	0.192001	+	0.981395i
$31$	1027.33	+	5251.07i	0.192001	+	0.981395i
$32$		0			0
$33$	2774.59	+	8539.31i	0.443521	+	1.36502i
$34$		0			0
$35$	−1159.72	+	842.585i	−0.160023	+	0.116264i
$36$		0			0
$37$	14971.8			1.79792			0.898958	−	0.438034i	$-0.144325\pi$
$37$	14971.8			1.79792			0.898958	+	0.438034i	$0.144325\pi$
$38$		0			0
$39$	3025.15	+	2197.90i	0.318482	+	0.231391i
$40$		0			0
$41$	1222.38	+	3762.11i	0.113566	+	0.349520i	0.991645	−	0.128995i	$-0.0411752\pi$
$41$	1222.38	+	3762.11i	0.113566	+	0.349520i	−0.878079	+	0.478515i	$0.841175\pi$
$42$		0			0
$43$	−6504.72	−	20019.5i	−0.536485	−	1.65113i	−0.740418	−	0.672146i	$-0.765373\pi$
$43$	−6504.72	−	20019.5i	−0.536485	−	1.65113i	0.203933	−	0.978985i	$-0.434627\pi$
$44$		0			0
$45$	1908.91	+	1386.91i	0.140525	+	0.102098i
$46$		0			0
$47$	−1530.55	+	4710.55i	−0.101066	+	0.311048i	−0.988787	−	0.149333i	$-0.952287\pi$
$47$	−1530.55	+	4710.55i	−0.101066	+	0.311048i	0.887721	+	0.460381i	$0.152287\pi$
$48$		0			0
$49$	−5090.43	+	15666.7i	−0.302875	+	0.932154i
$50$		0			0
$51$	−6400.41	+	4650.17i	−0.344574	+	0.250348i
$52$		0			0
$53$	−7988.15	−	5803.73i	−0.390622	−	0.283803i	0.375088	−	0.926989i	$-0.377612\pi$
$53$	−7988.15	−	5803.73i	−0.390622	−	0.283803i	−0.765710	+	0.643186i	$0.777612\pi$
$54$		0			0
$55$	39045.1	−	28367.9i	1.74044	−	1.26451i
$56$		0			0
$57$	40133.3			1.63613
$58$		0			0
$59$	−1766.19	+	5435.78i	−0.0660553	+	0.203297i	−0.978636	−	0.205598i	$-0.934086\pi$
$59$	−1766.19	+	5435.78i	−0.0660553	+	0.203297i	0.912581	+	0.408896i	$0.134086\pi$
$60$		0			0
$61$	−39368.4			−1.35464			−0.677319	−	0.735689i	$-0.736858\pi$
$61$	−39368.4			−1.35464			−0.677319	+	0.735689i	$0.736858\pi$
$62$		0			0
$63$	−549.832			−0.0174533
$64$		0			0
$65$	6211.03	−	19115.6i	0.182339	−	0.561183i
$66$		0			0
$67$	−21185.3			−0.576563			−0.288281	−	0.957546i	$-0.593084\pi$
$67$	−21185.3			−0.576563			−0.288281	+	0.957546i	$0.593084\pi$
$68$		0			0
$69$	−24527.4	+	17820.2i	−0.620196	+	0.450599i
$70$		0			0
$71$	62905.7	+	45703.7i	1.48096	+	1.07598i	0.977245	+	0.212115i	$0.0680350\pi$
$71$	62905.7	+	45703.7i	1.48096	+	1.07598i	0.503718	+	0.863868i	$0.331965\pi$
$72$		0			0
$73$	15247.9	−	11078.3i	0.334891	−	0.243312i	−0.407612	−	0.913155i	$-0.633638\pi$
$73$	15247.9	−	11078.3i	0.334891	−	0.243312i	0.742503	+	0.669843i	$0.233638\pi$
$74$		0			0
$75$	−13647.5	+	42002.6i	−0.280156	+	0.862230i
$76$		0			0
$77$	−3475.30	+	10695.9i	−0.0667984	+	0.205584i
$78$		0			0
$79$	−71525.4	−	51966.3i	−1.28942	−	0.936815i	−0.289622	−	0.957141i	$-0.593530\pi$
$79$	−71525.4	−	51966.3i	−1.28942	−	0.936815i	−0.999793	+	0.0203261i	$0.993530\pi$
$80$		0			0
$81$	−15708.5	−	48345.6i	−0.266024	−	0.818738i
$82$		0			0
$83$	−7914.74	−	24359.1i	−0.126108	−	0.388119i	0.867994	−	0.496575i	$-0.165409\pi$
$83$	−7914.74	−	24359.1i	−0.126108	−	0.388119i	−0.994101	+	0.108456i	$0.965409\pi$
$84$		0			0
$85$	34403.3	+	24995.5i	0.516479	+	0.375244i
$86$		0			0
$87$	−121987.			−1.72789
$88$		0			0
$89$	−22593.8	+	16415.4i	−0.302353	+	0.219672i	−0.728608	−	0.684931i	$-0.759832\pi$
$89$	−22593.8	+	16415.4i	−0.302353	+	0.219672i	0.426255	+	0.904603i	$0.359832\pi$
$90$		0			0
$91$	1447.32	+	4454.40i	0.0183215	+	0.0563879i
$92$		0			0
$93$	−77503.9	−	9420.75i	−0.929215	−	0.112948i
$94$		0			0
$95$	−66662.2	−	205165.i	−0.757827	−	2.33235i
$96$		0			0
$97$	1827.17	−	1327.52i	0.0197174	−	0.0143255i	−0.577883	−	0.816120i	$-0.696121\pi$
$97$	1827.17	−	1327.52i	0.0197174	−	0.0143255i	0.597600	+	0.801794i	$0.296121\pi$
$98$		0			0
$99$	18511.6			0.189826
$100$		0			0
$101$	53462.3	+	38842.6i	0.521488	+	0.378883i	0.817164	−	0.576405i	$-0.195545\pi$
$101$	53462.3	+	38842.6i	0.521488	+	0.378883i	−0.295676	+	0.955288i	$0.595545\pi$
$102$		0			0
$103$	−43422.7	−	133641.i	−0.403296	−	1.24122i	−0.922310	−	0.386452i	$-0.873701\pi$
$103$	−43422.7	−	133641.i	−0.403296	−	1.24122i	0.519013	−	0.854766i	$-0.326299\pi$
$104$		0			0
$105$	−6463.71	−	19893.2i	−0.0572148	−	0.176089i
$106$		0			0
$107$	−8760.94	−	6365.20i	−0.0739761	−	0.0537468i	0.550183	−	0.835044i	$-0.314558\pi$
$107$	−8760.94	−	6365.20i	−0.0739761	−	0.0537468i	−0.624159	+	0.781298i	$0.714558\pi$
$108$		0			0
$109$	30188.1	−	92909.3i	0.243371	−	0.749019i	−0.752529	−	0.658559i	$-0.771166\pi$
$109$	30188.1	−	92909.3i	0.243371	−	0.749019i	0.995900	−	0.0904600i	$-0.0288337\pi$
$110$		0			0
$111$	−67508.8	+	207771.i	−0.520060	+	1.60058i
$112$		0			0
$113$	78718.0	−	57192.0i	0.579933	−	0.421346i	−0.258767	−	0.965940i	$-0.583316\pi$
$113$	78718.0	−	57192.0i	0.579933	−	0.421346i	0.838700	+	0.544594i	$0.183316\pi$
$114$		0			0
$115$	131839.	+	95786.6i	0.929606	+	0.675399i
$116$		0			0
$117$	6236.98	−	4531.43i	0.0421221	−	0.0306035i
$118$		0			0
$119$	−9909.32			−0.0641470
$120$		0			0
$121$	67238.2	−	206938.i	0.417496	−	1.28492i
$122$		0			0
$123$	−57720.4			−0.344006
$124$		0			0
$125$	−7712.00			−0.0441461
$126$		0			0
$127$	−50590.5	+	155701.i	−0.278330	+	0.856610i	0.709990	+	0.704212i	$0.248700\pi$
$127$	−50590.5	+	155701.i	−0.278330	+	0.856610i	−0.988319	+	0.152398i	$0.951300\pi$
$128$		0			0
$129$	307150.			1.62509
$130$		0			0
$131$	−87368.2	+	63476.7i	−0.444811	+	0.323174i	−0.787544	−	0.616259i	$-0.788647\pi$
$131$	−87368.2	+	63476.7i	−0.444811	+	0.323174i	0.342733	+	0.939433i	$0.388647\pi$
$132$		0			0
$133$	40668.3	+	29547.3i	0.199355	+	0.144840i
$134$		0			0
$135$	−252845.	+	183703.i	−1.19404	+	0.867523i
$136$		0			0
$137$	84741.6	−	260808.i	0.385740	−	1.18719i	−0.550201	−	0.835032i	$-0.685449\pi$
$137$	84741.6	−	260808.i	0.385740	−	1.18719i	0.935942	−	0.352155i	$-0.114551\pi$
$138$		0			0
$139$	52943.7	−	162944.i	0.232422	−	0.715321i	−0.765031	−	0.643993i	$-0.777276\pi$
$139$	52943.7	−	162944.i	0.232422	−	0.715321i	0.997453	−	0.0713276i	$-0.0227236\pi$
$140$		0			0
$141$	−58469.2	−	42480.4i	−0.247674	−	0.179945i
$142$		0			0
$143$	−48728.1	−	149970.i	−0.199269	−	0.613286i
$144$		0			0
$145$	202623.	+	623609.i	0.800328	+	2.46316i
$146$		0			0
$147$	−194462.	−	141285.i	−0.742233	−	0.539264i
$148$		0			0
$149$	59850.2			0.220851			0.110426	−	0.993884i	$-0.464779\pi$
$149$	59850.2			0.220851			0.110426	+	0.993884i	$0.464779\pi$
$150$		0			0
$151$	−150526.	+	109363.i	−0.537240	+	0.390328i	−0.823059	−	0.567956i	$-0.807734\pi$
$151$	−150526.	+	109363.i	−0.537240	+	0.390328i	0.285819	+	0.958284i	$0.407734\pi$
$152$		0			0
$153$	5040.34	+	15512.6i	0.0174073	+	0.0535741i
$154$		0			0
$155$	80575.8	+	411855.i	0.269386	+	1.37694i
$156$		0			0
$157$	31238.2	+	96141.2i	0.101143	+	0.311287i	0.988806	−	0.149208i	$-0.0476722\pi$
$157$	31238.2	+	96141.2i	0.101143	+	0.311287i	−0.887663	+	0.460494i	$0.847672\pi$
$158$		0			0
$159$	116560.	−	84686.0i	0.365644	−	0.265656i
$160$		0			0
$161$	−37974.1			−0.115458
$162$		0			0
$163$	221386.	+	160846.i	0.652651	+	0.474179i	0.864173	−	0.503194i	$-0.167842\pi$
$163$	221386.	+	160846.i	0.652651	+	0.474179i	−0.211522	+	0.977373i	$0.567842\pi$
$164$		0			0
$165$	217618.	+	669761.i	0.622280	+	1.91518i
$166$		0			0
$167$	−45055.0	−	138665.i	−0.125012	−	0.384747i	0.868891	−	0.495003i	$-0.164833\pi$
$167$	−45055.0	−	138665.i	−0.125012	−	0.384747i	−0.993903	+	0.110256i	$0.964833\pi$
$168$		0			0
$169$	247254.	+	179640.i	0.665927	+	0.483824i
$170$		0			0
$171$	25569.0	−	78693.4i	0.0668689	−	0.205801i
$172$		0			0
$173$	48128.4	−	148124.i	0.122260	−	0.376279i	−0.871132	−	0.491050i	$-0.836613\pi$
$173$	48128.4	−	148124.i	0.122260	−	0.376279i	0.993392	+	0.114771i	$0.0366133\pi$
$174$		0			0
$175$	−44752.9	+	32514.9i	−0.110465	+	0.0802578i
$176$		0			0
$177$	−67471.0	−	49020.6i	−0.161877	−	0.117610i
$178$		0			0
$179$	−287743.	+	209058.i	−0.671232	+	0.487679i	−0.870437	−	0.492279i	$-0.836164\pi$
$179$	−287743.	+	209058.i	−0.671232	+	0.487679i	0.199205	+	0.979958i	$0.436164\pi$
$180$		0			0
$181$	−145150.			−0.329322			−0.164661	−	0.986350i	$-0.552653\pi$
$181$	−145150.			−0.329322			−0.164661	+	0.986350i	$0.552653\pi$
$182$		0			0
$183$	177515.	−	546335.i	0.391838	−	1.20595i
$184$		0			0
$185$	1.17428e6			2.52256
$186$		0			0
$187$	333624.			0.697676
$188$		0			0
$189$	22505.1	−	69263.6i	0.0458275	−	0.141043i
$190$		0			0
$191$	−202543.			−0.401730			−0.200865	−	0.979619i	$-0.564375\pi$
$191$	−202543.			−0.401730			−0.200865	+	0.979619i	$0.564375\pi$
$192$		0			0
$193$	−573027.	+	416328.i	−1.10734	+	0.804531i	−0.982243	−	0.187613i	$-0.939925\pi$
$193$	−573027.	+	416328.i	−1.10734	+	0.804531i	−0.125099	+	0.992144i	$0.539925\pi$
$194$		0			0
$195$	237270.	+	172387.i	0.446845	+	0.324652i
$196$		0			0
$197$	787364.	−	572053.i	1.44547	−	1.05020i	0.458610	−	0.888638i	$-0.348348\pi$
$197$	787364.	−	572053.i	1.44547	−	1.05020i	0.986863	−	0.161560i	$-0.0516525\pi$
$198$		0			0
$199$	−176323.	+	542667.i	−0.315629	+	0.971406i	0.659866	+	0.751383i	$0.270613\pi$
$199$	−176323.	+	542667.i	−0.315629	+	0.971406i	−0.975495	+	0.220022i	$0.929387\pi$
$200$		0			0
$201$	95525.7	−	293998.i	0.166775	−	0.513280i
$202$		0			0
$203$	−123613.	−	89810.3i	−0.210535	−	0.152963i
$204$		0			0
$205$	95874.7	+	295072.i	0.159338	+	0.490392i
$206$		0			0
$207$	19315.4	+	59446.7i	0.0313312	+	0.0964276i
$208$		0			0
$209$	−1.36921e6	−	994790.i	−2.16823	−	1.57531i
$210$		0			0
$211$	36597.7			0.0565910			0.0282955	−	0.999600i	$-0.490992\pi$
$211$	36597.7			0.0565910			0.0282955	+	0.999600i	$0.490992\pi$
$212$		0			0
$213$	−917898.	+	666892.i	−1.38626	+	1.00718i
$214$		0			0
$215$	−510182.	−	1.57018e6i	−0.752713	−	2.31661i
$216$		0			0
$217$	−71601.4	−	66606.9i	−0.103222	−	0.0960219i
$218$		0			0
$219$	84984.4	+	261555.i	0.119737	+	0.368513i
$220$		0			0
$221$	112406.	−	81667.5i	0.154813	−	0.112478i
$222$		0			0
$223$	843619.			1.13602			0.568008	−	0.823023i	$-0.307714\pi$
$223$	843619.			1.13602			0.568008	+	0.823023i	$0.307714\pi$
$224$		0			0
$225$	73663.9	+	53520.0i	0.0970060	+	0.0704790i
$226$		0			0
$227$	−441771.	−	1.35963e6i	−0.569027	−	1.75128i	−0.655673	−	0.755045i	$-0.727615\pi$
$227$	−441771.	−	1.35963e6i	−0.569027	−	1.75128i	0.0866458	−	0.996239i	$-0.472385\pi$
$228$		0			0
$229$	−280853.	−	864378.i	−0.353908	−	1.08922i	−0.956640	−	0.291274i	$-0.905921\pi$
$229$	−280853.	−	864378.i	−0.353908	−	1.08922i	0.602731	−	0.797944i	$-0.294079\pi$
$230$		0			0
$231$	−132762.	−	96457.0i	−0.163698	−	0.118933i
$232$		0			0
$233$	−375525.	+	1.15575e6i	−0.453157	+	1.39467i	0.420128	+	0.907465i	$0.361985\pi$
$233$	−375525.	+	1.15575e6i	−0.453157	+	1.39467i	−0.873285	+	0.487210i	$0.838015\pi$
$234$		0			0
$235$	−120045.	+	369461.i	−0.141799	+	0.436414i
$236$		0			0
$237$	1.04367e6	−	758274.i	1.20696	−	0.876910i
$238$		0			0
$239$	−468685.	−	340519.i	−0.530745	−	0.385609i	0.289891	−	0.957060i	$-0.406381\pi$
$239$	−468685.	−	340519.i	−0.530745	−	0.385609i	−0.820636	+	0.571451i	$0.806381\pi$
$240$		0			0
$241$	−834546.	+	606333.i	−0.925567	+	0.672464i	−0.944903	−	0.327349i	$-0.893845\pi$
$241$	−834546.	+	606333.i	−0.925567	+	0.672464i	0.0193366	+	0.999813i	$0.493845\pi$
$242$		0			0
$243$	−226546.			−0.246116
$244$		0			0
$245$	−399255.	+	1.22878e6i	−0.424948	+	1.30785i
$246$		0			0
$247$	−704831.			−0.735094
$248$		0			0
$249$	373731.			0.381997
$250$		0			0
$251$	−476020.	+	1.46504e6i	−0.476915	+	1.46779i	0.366443	+	0.930440i	$0.380575\pi$
$251$	−476020.	+	1.46504e6i	−0.476915	+	1.46779i	−0.843358	+	0.537352i	$0.819425\pi$
$252$		0			0
$253$	1.27850e6			1.25574
$254$		0			0
$255$	−502001.	+	364725.i	−0.483453	+	0.351249i
$256$		0			0
$257$	651728.	+	473508.i	0.615508	+	0.447193i	0.851350	−	0.524599i	$-0.175785\pi$
$257$	651728.	+	473508.i	0.615508	+	0.447193i	−0.235842	+	0.971792i	$0.575785\pi$
$258$		0			0
$259$	−221376.	+	160839.i	−0.205060	+	0.148985i
$260$		0			0
$261$	−77718.3	+	239192.i	−0.0706191	+	0.217343i
$262$		0			0
$263$	227377.	−	699796.i	0.202702	−	0.623852i	−0.797098	−	0.603850i	$-0.793633\pi$
$263$	227377.	−	699796.i	0.202702	−	0.623852i	0.999800	−	0.0200024i	$-0.00636739\pi$
$264$		0			0
$265$	−626532.	−	455202.i	−0.548060	−	0.398189i
$266$		0			0
$267$	−125927.	−	387563.i	−0.108104	−	0.332709i
$268$		0			0
$269$	−367400.	−	1.13074e6i	−0.309570	−	0.952759i	−0.977932	−	0.208923i	$-0.933004\pi$
$269$	−367400.	−	1.13074e6i	−0.309570	−	0.952759i	0.668362	−	0.743836i	$-0.266996\pi$
$270$		0			0
$271$	−1.33379e6	−	969055.i	−1.10323	−	0.801540i	−0.121642	−	0.992574i	$-0.538816\pi$
$271$	−1.33379e6	−	969055.i	−1.10323	−	0.801540i	−0.981583	+	0.191034i	$0.938816\pi$
$272$		0			0
$273$	−68342.0			−0.0554985
$274$		0			0
$275$	1.50673e6	−	1.09470e6i	1.20144	−	0.872901i
$276$		0			0
$277$	−506268.	−	1.55813e6i	−0.396444	−	1.22013i	−0.927832	−	0.372999i	$-0.878329\pi$
$277$	−506268.	−	1.55813e6i	−0.396444	−	1.22013i	0.531388	−	0.847128i	$-0.321671\pi$
$278$		0			0
$279$	−67850.2	+	145968.i	−0.0521844	+	0.112266i
$280$		0			0
$281$	131554.	+	404881.i	0.0993889	+	0.305888i	0.988373	−	0.152051i	$-0.0485879\pi$
$281$	131554.	+	404881.i	0.0993889	+	0.305888i	−0.888984	+	0.457939i	$0.848588\pi$
$282$		0			0
$283$	−764703.	+	555589.i	−0.567579	+	0.412370i	−0.834225	−	0.551424i	$-0.814085\pi$
$283$	−764703.	+	555589.i	−0.567579	+	0.412370i	0.266646	+	0.963795i	$0.414085\pi$
$284$		0			0
$285$	3.14776e6			2.29556
$286$		0			0
$287$	−58489.9	−	42495.4i	−0.0419156	−	0.0304535i
$288$		0			0
$289$	−347921.	−	1.07079e6i	−0.245039	−	0.754153i
$290$		0			0
$291$	10183.8	+	31342.4i	0.00704979	+	0.0216970i
$292$		0			0
$293$	−2.11679e6	−	1.53794e6i	−1.44049	−	1.04658i	−0.987940	−	0.154835i	$-0.950515\pi$
$293$	−2.11679e6	−	1.53794e6i	−1.44049	−	1.04658i	−0.452548	−	0.891740i	$-0.649485\pi$
$294$		0			0
$295$	−138527.	+	426342.i	−0.0926786	+	0.285235i
$296$		0			0
$297$	−757696.	+	2.33195e6i	−0.498430	+	1.53401i
$298$		0			0
$299$	430756.	−	312963.i	0.278647	−	0.202449i
$300$		0			0
$301$	311245.	+	226133.i	0.198010	+	0.143862i
$302$		0			0
$303$	−780103.	+	566778.i	−0.488141	+	0.354655i
$304$		0			0
$305$	−3.08777e6			−1.90062
$306$		0			0
$307$	66234.3	−	203848.i	0.0401086	−	0.123441i	−0.928997	−	0.370086i	$-0.879328\pi$
$307$	66234.3	−	203848.i	0.0401086	−	0.123441i	0.969106	+	0.246645i	$0.0793281\pi$
$308$		0			0
$309$	2.05040e6			1.22164
$310$		0			0
$311$	2.48425e6			1.45644			0.728222	−	0.685341i	$-0.240347\pi$
$311$	2.48425e6			1.45644			0.728222	+	0.685341i	$0.240347\pi$
$312$		0			0
$313$	876008.	−	2.69607e6i	0.505414	−	1.55550i	−0.294660	−	0.955602i	$-0.595206\pi$
$313$	876008.	−	2.69607e6i	0.505414	−	1.55550i	0.800074	−	0.599901i	$-0.204794\pi$
$314$		0			0
$315$	−43124.8			−0.0244878
$316$		0			0
$317$	−477949.	+	347250.i	−0.267136	+	0.194086i	−0.713287	−	0.700872i	$-0.752794\pi$
$317$	−477949.	+	347250.i	−0.267136	+	0.194086i	0.446151	+	0.894958i	$0.352794\pi$
$318$		0			0
$319$	4.16178e6	+	3.02371e6i	2.28983	+	1.66366i
$320$		0			0
$321$	127837.	−	92878.7i	0.0692457	−	0.0503099i
$322$		0			0
$323$	460817.	−	1.41825e6i	0.245766	−	0.756390i
$324$		0			0
$325$	239681.	−	737661.i	0.125871	−	0.387390i
$326$		0			0
$327$	1.15323e6	+	837869.i	0.596411	+	0.433318i
$328$		0			0
$329$	−27973.4	−	86093.4i	−0.0142481	−	0.0438511i
$330$		0			0
$331$	641224.	+	1.97348e6i	0.321692	+	0.990065i	0.972912	+	0.231176i	$0.0742574\pi$
$331$	641224.	+	1.97348e6i	0.321692	+	0.990065i	−0.651220	+	0.758889i	$0.725743\pi$
$332$		0			0
$333$	364387.	+	264743.i	0.180075	+	0.130832i
$334$		0			0
$335$	−1.66161e6			−0.808944
$336$		0			0
$337$	−2.66393e6	+	1.93546e6i	−1.27775	+	0.928343i	−0.999483	−	0.0321591i	$-0.989762\pi$
$337$	−2.66393e6	+	1.93546e6i	−1.27775	+	0.928343i	−0.278272	+	0.960502i	$0.589762\pi$
$338$		0			0
$339$	438736.	+	1.35029e6i	0.207350	+	0.638158i
$340$		0			0
$341$	2.41066e6	+	2.24251e6i	1.12266	+	1.04435i
$342$		0			0
$343$	−187959.	−	578479.i	−0.0862637	−	0.265492i
$344$		0			0
$345$	−1.92375e6	+	1.39768e6i	−0.870163	+	0.632210i
$346$		0			0
$347$	976884.			0.435531			0.217766	−	0.976001i	$-0.430123\pi$
$347$	976884.			0.435531			0.217766	+	0.976001i	$0.430123\pi$
$348$		0			0
$349$	377012.	+	273915.i	0.165688	+	0.120380i	0.667540	−	0.744574i	$-0.267348\pi$
$349$	377012.	+	273915.i	0.165688	+	0.120380i	−0.501851	+	0.864954i	$0.667348\pi$
$350$		0			0
$351$	315549.	+	971161.i	0.136710	+	0.420749i
$352$		0			0
$353$	−711952.	−	2.19116e6i	−0.304098	−	0.935918i	−0.980012	−	0.198937i	$-0.936251\pi$
$353$	−711952.	−	2.19116e6i	−0.304098	−	0.935918i	0.675914	−	0.736980i	$-0.263749\pi$
$354$		0			0
$355$	4.93386e6	+	3.58466e6i	2.07786	+	1.50965i
$356$		0			0
$357$	44681.8	−	137516.i	0.0185550	−	0.0571063i
$358$		0			0
$359$	55449.9	−	170657.i	0.0227073	−	0.0698858i	−0.939061	−	0.343751i	$-0.888302\pi$
$359$	55449.9	−	170657.i	0.0227073	−	0.0698858i	0.961768	+	0.273865i	$0.0883023\pi$
$360$		0			0
$361$	−4.11689e6	+	2.99110e6i	−1.66265	+	1.20799i
$362$		0			0
$363$	2.56859e6	+	1.86619e6i	1.02313	+	0.743344i
$364$		0			0
$365$	1.19593e6	−	868896.i	0.469867	−	0.341378i
$366$		0			0
$367$	−550937.			−0.213519			−0.106759	−	0.994285i	$-0.534047\pi$
$367$	−550937.			−0.213519			−0.106759	+	0.994285i	$0.534047\pi$
$368$		0			0
$369$	−36773.8	+	113178.i	−0.0140596	+	0.0432710i
$370$		0			0
$371$	180462.			0.0680694
$372$		0			0
$373$	520482.			0.193702			0.0968509	−	0.995299i	$-0.469123\pi$
$373$	520482.			0.193702			0.0968509	+	0.995299i	$0.469123\pi$
$374$		0			0
$375$	34773.9	−	107023.i	0.0127696	−	0.0393006i
$376$		0			0
$377$	2.14237e6			0.776320
$378$		0			0
$379$	306340.	−	222569.i	0.109548	−	0.0795915i	−0.531662	−	0.846956i	$-0.678432\pi$
$379$	306340.	−	222569.i	0.109548	−	0.0795915i	0.641211	+	0.767365i	$0.278432\pi$
$380$		0			0
$381$	−1.93263e6	−	1.40414e6i	−0.682081	−	0.495561i
$382$		0			0
$383$	−1.58738e6	+	1.15330e6i	−0.552948	+	0.401740i	−0.828871	−	0.559440i	$-0.811016\pi$
$383$	−1.58738e6	+	1.15330e6i	−0.552948	+	0.401740i	0.275923	+	0.961180i	$0.411016\pi$
$384$		0			0
$385$	−272577.	+	838906.i	−0.0937212	+	0.288444i
$386$		0			0
$387$	195686.	−	602261.i	0.0664176	−	0.204412i
$388$		0			0
$389$	−3.33829e6	−	2.42541e6i	−1.11854	−	0.812665i	−0.134551	−	0.990907i	$-0.542959\pi$
$389$	−3.33829e6	−	2.42541e6i	−1.11854	−	0.812665i	−0.983987	+	0.178242i	$0.942959\pi$
$390$		0			0
$391$	348111.	+	1.07137e6i	0.115153	+	0.354405i
$392$		0			0
$393$	−486948.	−	1.49867e6i	−0.159038	−	0.489469i
$394$		0			0
$395$	−5.60993e6	−	4.07585e6i	−1.80911	−	1.31439i
$396$		0			0
$397$	883247.			0.281259			0.140629	−	0.990062i	$-0.455087\pi$
$397$	883247.			0.281259			0.140629	+	0.990062i	$0.455087\pi$
$398$		0			0
$399$	−593418.	+	431143.i	−0.186607	+	0.135578i
$400$		0			0
$401$	183320.	+	564199.i	0.0569309	+	0.175215i	0.975478	−	0.220096i	$-0.0706369\pi$
$401$	183320.	+	564199.i	0.0569309	+	0.175215i	−0.918547	+	0.395311i	$0.870637\pi$
$402$		0			0
$403$	1.36114e6	+	165450.i	0.417486	+	0.0507462i
$404$		0			0
$405$	−1.23205e6	−	3.79188e6i	−0.373244	−	1.14873i
$406$		0			0
$407$	7.45322e6	−	5.41508e6i	2.23027	−	1.62039i
$408$		0			0
$409$	−5.33469e6			−1.57689			−0.788444	−	0.615107i	$-0.789113\pi$
$409$	−5.33469e6			−1.57689			−0.788444	+	0.615107i	$0.789113\pi$
$410$		0			0
$411$	3.23725e6	+	2.35200e6i	0.945304	+	0.686804i
$412$		0			0
$413$	−32280.2	−	99348.2i	−0.00931238	−	0.0286606i
$414$		0			0
$415$	−620774.	−	1.91054e6i	−0.176935	−	0.544549i
$416$		0			0
$417$	2.02252e6	+	1.46945e6i	0.569578	+	0.413823i
$418$		0			0
$419$	1.77728e6	−	5.46990e6i	0.494562	−	1.52210i	−0.323077	−	0.946373i	$-0.604717\pi$
$419$	1.77728e6	−	5.46990e6i	0.494562	−	1.52210i	0.817639	−	0.575731i	$-0.195283\pi$
$420$		0			0
$421$	−2.14445e6	+	6.59992e6i	−0.589671	+	1.81482i	−0.0100286	+	0.999950i	$0.503192\pi$
$421$	−2.14445e6	+	6.59992e6i	−0.589671	+	1.81482i	−0.579642	+	0.814871i	$0.696808\pi$
$422$		0			0
$423$	−120547.	+	87582.2i	−0.0327570	+	0.0237993i
$424$		0			0
$425$	1.32760e6	+	964561.i	0.356530	+	0.259034i
$426$		0			0
$427$	582108.	−	422927.i	0.154502	−	0.112252i
$428$		0			0
$429$	2.30092e6			0.603613
$430$		0			0
$431$	−660391.	+	2.03247e6i	−0.171241	+	0.527026i	−0.999442	−	0.0334056i	$-0.989365\pi$
$431$	−660391.	+	2.03247e6i	−0.171241	+	0.527026i	0.828201	+	0.560432i	$0.189365\pi$
$432$		0			0
$433$	2.01357e6			0.516116			0.258058	−	0.966129i	$-0.416917\pi$
$433$	2.01357e6			0.516116			0.258058	+	0.966129i	$0.416917\pi$
$434$		0			0
$435$	−9.56776e6			−2.42430
$436$		0			0
$437$	1.76592e6	−	5.43496e6i	0.442353	−	1.36142i
$438$		0			0
$439$	3.31928e6			0.822020			0.411010	−	0.911631i	$-0.365176\pi$
$439$	3.31928e6			0.822020			0.411010	+	0.911631i	$0.365176\pi$
$440$		0			0
$441$	−400923.	+	291288.i	−0.0981668	+	0.0713223i
$442$		0			0
$443$	−3.17255e6	−	2.30499e6i	−0.768067	−	0.558034i	0.133307	−	0.991075i	$-0.457440\pi$
$443$	−3.17255e6	−	2.30499e6i	−0.768067	−	0.558034i	−0.901374	+	0.433041i	$0.857440\pi$
$444$		0			0
$445$	−1.77209e6	+	1.28750e6i	−0.424215	+	0.308210i
$446$		0			0
$447$	−269869.	+	830571.i	−0.0638828	+	0.196611i
$448$		0			0
$449$	−184428.	+	567612.i	−0.0431729	+	0.132873i	−0.970320	−	0.241826i	$-0.922254\pi$
$449$	−184428.	+	567612.i	−0.0431729	+	0.132873i	0.927147	+	0.374698i	$0.122254\pi$
$450$		0			0
$451$	1.96922e6	+	1.43072e6i	0.455883	+	0.331218i
$452$		0			0
$453$	−838957.	−	2.58205e6i	−0.192085	−	0.591178i
$454$		0			0
$455$	113517.	+	349370.i	0.0257059	+	0.0791148i
$456$		0			0
$457$	4.20718e6	+	3.05670e6i	0.942325	+	0.684639i	0.948979	−	0.315339i	$-0.102118\pi$
$457$	4.20718e6	+	3.05670e6i	0.942325	+	0.684639i	−0.00665416	+	0.999978i	$0.502118\pi$
$458$		0			0
$459$	−2.16046e6			−0.478646
$460$		0			0
$461$	2.26430e6	−	1.64511e6i	0.496229	−	0.360532i	−0.311346	−	0.950297i	$-0.600780\pi$
$461$	2.26430e6	−	1.64511e6i	0.496229	−	0.360532i	0.807575	+	0.589765i	$0.200780\pi$
$462$		0			0
$463$	−12322.6	−	37925.1i	−0.00267147	−	0.00822194i	0.949712	−	0.313125i	$-0.101376\pi$
$463$	−12322.6	−	37925.1i	−0.00267147	−	0.00822194i	−0.952383	+	0.304903i	$0.901376\pi$
$464$		0			0
$465$	−6.07884e6	−	738894.i	−1.30373	−	0.158471i
$466$		0			0
$467$	206146.	+	634451.i	0.0437403	+	0.134619i	0.970542	−	0.240933i	$-0.0774533\pi$
$467$	206146.	+	634451.i	0.0437403	+	0.134619i	−0.926801	+	0.375552i	$0.877453\pi$
$468$		0			0
$469$	313249.	−	227589.i	0.0657593	−	0.0477770i
$470$		0			0
$471$	−1.47505e6			−0.306376
$472$		0			0
$473$	−1.04789e7	−	7.61338e6i	−2.15359	−	1.56468i
$474$		0			0
$475$	−2.57246e6	−	7.91721e6i	−0.523136	−	1.61005i
$476$		0			0
$477$	−91791.6	−	282505.i	−0.0184717	−	0.0568500i
$478$		0			0
$479$	5.52310e6	+	4.01277e6i	1.09988	+	0.799108i	0.981040	−	0.193806i	$-0.0620832\pi$
$479$	5.52310e6	+	4.01277e6i	1.09988	+	0.799108i	0.118838	+	0.992914i	$0.462083\pi$
$480$		0			0
$481$	1.18561e6	−	3.64892e6i	0.233657	−	0.719121i
$482$		0			0
$483$	171228.	−	526985.i	0.0333969	−	0.102785i
$484$		0			0
$485$	143310.	−	104121.i	0.0276644	−	0.0200994i
$486$		0			0
$487$	−5.58479e6	−	4.05758e6i	−1.06705	−	0.775256i	−0.0916689	−	0.995790i	$-0.529220\pi$
$487$	−5.58479e6	−	4.05758e6i	−1.06705	−	0.775256i	−0.975379	+	0.220534i	$0.929220\pi$
$488$		0			0
$489$	−3.23039e6	+	2.34701e6i	−0.610917	+	0.443858i
$490$		0			0
$491$	−5.55882e6			−1.04059			−0.520294	−	0.853987i	$-0.674178\pi$
$491$	−5.55882e6			−1.04059			−0.520294	+	0.853987i	$0.674178\pi$
$492$		0			0
$493$	−1.40067e6	+	4.31083e6i	−0.259549	+	0.798811i
$494$		0			0
$495$	1.45191e6			0.266335
$496$		0			0
$497$	−1.42112e6			−0.258071
$498$		0			0
$499$	1.36349e6	−	4.19639e6i	0.245132	−	0.754439i	−0.750483	−	0.660890i	$-0.770179\pi$
$499$	1.36349e6	−	4.19639e6i	0.245132	−	0.754439i	0.995615	−	0.0935488i	$-0.0298211\pi$
$500$		0			0
$501$	2.12748e6			0.378678
$502$		0			0
$503$	−7.46780e6	+	5.42567e6i	−1.31605	+	0.956166i	−0.316078	+	0.948733i	$0.602366\pi$
$503$	−7.46780e6	+	5.42567e6i	−1.31605	+	0.956166i	−0.999972	+	0.00743317i	$0.997634\pi$
$504$		0			0
$505$	4.19319e6	+	3.04653e6i	0.731671	+	0.531590i
$506$		0			0
$507$	−3.60784e6	+	2.62125e6i	−0.623344	+	0.452886i
$508$		0			0
$509$	−1.91903e6	+	5.90616e6i	−0.328312	+	1.01044i	0.641612	+	0.767030i	$0.278266\pi$
$509$	−1.91903e6	+	5.90616e6i	−0.328312	+	1.01044i	−0.969923	+	0.243410i	$0.921734\pi$
$510$		0			0
$511$	−106447.	+	327610.i	−0.0180335	+	0.0555015i
$512$		0			0
$513$	8.86662e6	+	6.44198e6i	1.48753	+	1.08075i
$514$		0			0
$515$	−3.40576e6	−	1.04818e7i	−0.565843	−	1.74148i
$516$		0			0
$517$	941803.	+	2.89857e6i	0.154965	+	0.476933i
$518$		0			0
$519$	1.83857e6	+	1.33580e6i	0.299614	+	0.217683i
$520$		0			0
$521$	2.46340e6			0.397595			0.198798	−	0.980041i	$-0.436296\pi$
$521$	2.46340e6			0.397595			0.198798	+	0.980041i	$0.436296\pi$
$522$		0			0
$523$	4.05031e6	−	2.94272e6i	0.647491	−	0.470430i	−0.214924	−	0.976631i	$-0.568950\pi$
$523$	4.05031e6	−	2.94272e6i	0.647491	−	0.470430i	0.862416	+	0.506201i	$0.168950\pi$
$524$		0			0
$525$	−249431.	−	767670.i	−0.0394959	−	0.121556i
$526$		0			0
$527$	−1.22283e6	+	2.63070e6i	−0.191796	+	0.412615i
$528$		0			0
$529$	−654923.	−	2.01565e6i	−0.101754	−	0.313166i
$530$		0			0
$531$	−139106.	+	101066.i	−0.0214096	+	0.0155550i
$532$		0			0
$533$	1.01370e6			0.154558
$534$		0			0
$535$	−687144.	−	499239.i	−0.103792	−	0.0754092i
$536$		0			0
$537$	−1.60374e6	−	4.93581e6i	−0.239993	−	0.738623i
$538$		0			0
$539$	3.13232e6	+	9.64029e6i	0.464402	+	1.42928i
$540$		0			0
$541$	6.24723e6	+	4.53888e6i	0.917687	+	0.666739i	0.942947	−	0.332942i	$-0.108041\pi$
$541$	6.24723e6	+	4.53888e6i	0.917687	+	0.666739i	−0.0252603	+	0.999681i	$0.508041\pi$
$542$		0			0
$543$	654492.	−	2.01432e6i	0.0952587	−	0.293176i
$544$		0			0
$545$	2.36773e6	−	7.28712e6i	0.341461	−	1.05091i
$546$		0			0
$547$	−3.52772e6	+	2.56304e6i	−0.504110	+	0.366257i	−0.810585	−	0.585621i	$-0.800851\pi$
$547$	−3.52772e6	+	2.56304e6i	−0.504110	+	0.366257i	0.306475	+	0.951879i	$0.400851\pi$
$548$		0			0
$549$	−958158.	−	696143.i	−0.135677	−	0.0985752i
$550$		0			0
$551$	1.86023e7	−	1.35154e7i	2.61029	−	1.89648i
$552$		0			0
$553$	1.61585e6			0.224692
$554$		0			0
$555$	−5.29489e6	+	1.62960e7i	−0.729667	+	2.24568i
$556$		0			0
$557$	2.02487e6			0.276541			0.138271	−	0.990394i	$-0.455846\pi$
$557$	2.02487e6			0.276541			0.138271	+	0.990394i	$0.455846\pi$
$558$		0			0
$559$	−5.39425e6			−0.730132
$560$		0			0
$561$	−1.50434e6	+	4.62987e6i	−0.201808	+	0.621100i
$562$		0			0
$563$	8.29864e6			1.10341			0.551704	−	0.834040i	$-0.313978\pi$
$563$	8.29864e6			1.10341			0.551704	+	0.834040i	$0.313978\pi$
$564$		0			0
$565$	6.17406e6	−	4.48572e6i	0.813673	−	0.591168i
$566$		0			0
$567$	751635.	+	546095.i	0.0981859	+	0.0713363i
$568$		0			0
$569$	−1.42835e6	+	1.03776e6i	−0.184950	+	0.134374i	−0.676408	−	0.736528i	$-0.736464\pi$
$569$	−1.42835e6	+	1.03776e6i	−0.184950	+	0.134374i	0.491458	+	0.870901i	$0.336464\pi$
$570$		0			0
$571$	332338.	−	1.02283e6i	0.0426569	−	0.131284i	−0.927460	−	0.373922i	$-0.878013\pi$
$571$	332338.	−	1.02283e6i	0.0426569	−	0.131284i	0.970117	+	0.242638i	$0.0780127\pi$
$572$		0			0
$573$	913280.	−	2.81079e6i	0.116203	−	0.357636i
$574$		0			0
$575$	5.08760e6	+	3.69635e6i	0.641716	+	0.466234i
$576$		0			0
$577$	3.61832e6	+	1.11360e7i	0.452446	+	1.39249i	0.874107	+	0.485733i	$0.161447\pi$
$577$	3.61832e6	+	1.11360e7i	0.452446	+	1.39249i	−0.421661	+	0.906754i	$0.638553\pi$
$578$		0			0
$579$	−3.19377e6	−	9.82943e6i	−0.395920	−	1.21852i
$580$		0			0
$581$	378713.	+	275151.i	0.0465447	+	0.0338167i
$582$		0			0
$583$	−6.07576e6			−0.740337
$584$		0			0
$585$	489182.	−	355412.i	0.0590991	−	0.0429380i
$586$		0			0
$587$	1.87532e6	+	5.77163e6i	0.224636	+	0.691358i	0.998328	+	0.0577967i	$0.0184075\pi$
$587$	1.87532e6	+	5.77163e6i	0.224636	+	0.691358i	−0.773693	+	0.633561i	$0.781592\pi$
$588$		0			0
$589$	1.28627e7	−	7.15033e6i	1.52772	−	0.849254i
$590$		0			0
$591$	4.38838e6	+	1.35061e7i	0.516816	+	1.59060i
$592$		0			0
$593$	−8.72496e6	+	6.33905e6i	−1.01889	+	0.740266i	−0.966055	−	0.258337i	$-0.916825\pi$
$593$	−8.72496e6	+	6.33905e6i	−1.01889	+	0.740266i	−0.0528338	+	0.998603i	$0.516825\pi$
$594$		0			0
$595$	−777214.			−0.0900012
$596$		0			0
$597$	−6.73580e6	−	4.89384e6i	−0.773487	−	0.561972i
$598$		0			0
$599$	2.93597e6	+	9.03598e6i	0.334337	+	1.02898i	0.967048	+	0.254595i	$0.0819421\pi$
$599$	2.93597e6	+	9.03598e6i	0.334337	+	1.02898i	−0.632711	+	0.774388i	$0.718058\pi$
$600$		0			0
$601$	−1.03207e6	−	3.17639e6i	−0.116553	−	0.358714i	0.875715	−	0.482829i	$-0.160391\pi$
$601$	−1.03207e6	−	3.17639e6i	−0.116553	−	0.358714i	−0.992268	+	0.124115i	$0.960391\pi$
$602$		0			0
$603$	−515612.	−	374614.i	−0.0577470	−	0.0419557i
$604$		0			0
$605$	5.27367e6	−	1.62307e7i	0.585766	−	1.80280i
$606$		0			0
$607$	393975.	−	1.21253e6i	0.0434007	−	0.133574i	−0.927008	−	0.375041i	$-0.877629\pi$
$607$	393975.	−	1.21253e6i	0.0434007	−	0.133574i	0.970409	+	0.241467i	$0.0776286\pi$
$608$		0			0
$609$	1.80372e6	−	1.31048e6i	0.197073	−	0.143182i
$610$		0			0
$611$	1.02685e6	+	746051.i	0.111277	+	0.0808473i
$612$		0			0
$613$	−2.45531e6	+	1.78389e6i	−0.263910	+	0.191742i	−0.711869	−	0.702312i	$-0.752151\pi$
$613$	−2.45531e6	+	1.78389e6i	−0.263910	+	0.191742i	0.447959	+	0.894054i	$0.352151\pi$
$614$		0			0
$615$	−4.52716e6			−0.482656
$616$		0			0
$617$	−5.07840e6	+	1.56297e7i	−0.537049	+	1.65287i	0.202131	+	0.979358i	$0.435213\pi$
$617$	−5.07840e6	+	1.56297e7i	−0.537049	+	1.65287i	−0.739180	+	0.673508i	$0.764787\pi$
$618$		0			0
$619$	−5.53624e6			−0.580749			−0.290374	−	0.956913i	$-0.593780\pi$
$619$	−5.53624e6			−0.580749			−0.290374	+	0.956913i	$0.593780\pi$
$620$		0			0
$621$	−8.27922e6			−0.861511
$622$		0			0
$623$	157729.	−	485441.i	0.0162814	−	0.0501090i
$624$		0			0
$625$	−1.00632e7			−1.03047
$626$		0			0
$627$	1.99790e7	−	1.45156e7i	2.02958	−	1.47458i
$628$		0			0
$629$	6.56715e6	+	4.77132e6i	0.661836	+	0.480852i
$630$		0			0
$631$	2.78018e6	−	2.01992e6i	0.277971	−	0.201958i	−0.440061	−	0.897968i	$-0.645043\pi$
$631$	2.78018e6	−	2.01992e6i	0.277971	−	0.201958i	0.718032	+	0.696010i	$0.245043\pi$
$632$		0			0
$633$	−165021.	+	507883.i	−0.0163693	+	0.0503796i
$634$		0			0
$635$	−3.96794e6	+	1.22121e7i	−0.390509	+	1.20186i
$636$		0			0
$637$	3.41518e6	+	2.48128e6i	0.333477	+	0.242285i
$638$		0			0
$639$	722847.	+	2.22469e6i	0.0700317	+	0.215535i
$640$		0			0
$641$	−3.57870e6	−	1.10141e7i	−0.344018	−	1.05878i	−0.962108	−	0.272670i	$-0.912093\pi$
$641$	−3.57870e6	−	1.10141e7i	−0.344018	−	1.05878i	0.618090	−	0.786107i	$-0.287907\pi$
$642$		0			0
$643$	−9.06507e6	−	6.58616e6i	−0.864656	−	0.628210i	0.0644913	−	0.997918i	$-0.479458\pi$
$643$	−9.06507e6	−	6.58616e6i	−0.864656	−	0.628210i	−0.929148	+	0.369709i	$0.879458\pi$
$644$		0			0
$645$	2.40906e7			2.28007
$646$		0			0
$647$	−8.18549e6	+	5.94711e6i	−0.768748	+	0.558528i	−0.901581	−	0.432610i	$-0.857593\pi$
$647$	−8.18549e6	+	5.94711e6i	−0.768748	+	0.558528i	0.132833	+	0.991138i	$0.457593\pi$
$648$		0			0
$649$	1.08680e6	+	3.34483e6i	0.101283	+	0.311718i
$650$		0			0
$651$	1.24719e6	−	693311.i	0.115340	−	0.0641174i
$652$		0			0
$653$	190452.	+	586151.i	0.0174784	+	0.0537931i	0.959415	−	0.281997i	$-0.0909968\pi$
$653$	190452.	+	586151.i	0.0174784	+	0.0537931i	−0.941937	+	0.335790i	$0.890997\pi$
$654$		0			0
$655$	−6.85252e6	+	4.97864e6i	−0.624089	+	0.453427i
$656$		0			0
$657$	567002.			0.0512473
$658$		0			0
$659$	2.80255e6	+	2.03617e6i	0.251385	+	0.182642i	0.706340	−	0.707872i	$-0.250345\pi$
$659$	2.80255e6	+	2.03617e6i	0.251385	+	0.182642i	−0.454955	+	0.890514i	$0.650345\pi$
$660$		0			0
$661$	1.50470e6	+	4.63100e6i	0.133951	+	0.412260i	0.995425	−	0.0955414i	$-0.0304582\pi$
$661$	1.50470e6	+	4.63100e6i	0.133951	+	0.412260i	−0.861474	+	0.507802i	$0.830458\pi$
$662$		0			0
$663$	626494.	+	1.92815e6i	0.0553520	+	0.170356i
$664$		0			0
$665$	3.18972e6	+	2.31747e6i	0.279704	+	0.203217i
$666$		0			0
$667$	−5.36761e6	+	1.65198e7i	−0.467161	+	1.43777i
$668$		0			0
$669$	−3.80393e6	+	1.17073e7i	−0.328600	+	1.01133i
$670$		0			0
$671$	−1.95983e7	+	1.42390e7i	−1.68040	+	1.22088i
$672$		0			0
$673$	−7.00359e6	−	5.08840e6i	−0.596050	−	0.433056i	0.248425	−	0.968651i	$-0.420087\pi$
$673$	−7.00359e6	−	5.08840e6i	−0.596050	−	0.433056i	−0.844475	+	0.535595i	$0.820087\pi$
$674$		0			0
$675$	−9.75716e6	+	7.08899e6i	−0.824260	+	0.598860i
$676$		0			0
$677$	2.50518e6			0.210072			0.105036	−	0.994468i	$-0.466504\pi$
$677$	2.50518e6			0.210072			0.105036	+	0.994468i	$0.466504\pi$
$678$		0			0
$679$	−12755.6	+	39257.8i	−0.00106176	+	0.00326777i
$680$		0			0
$681$	2.08602e7			1.72366
$682$		0			0
$683$	1.12662e7			0.924118			0.462059	−	0.886849i	$-0.347111\pi$
$683$	1.12662e7			0.924118			0.462059	+	0.886849i	$0.347111\pi$
$684$		0			0
$685$	6.64650e6	−	2.04558e7i	0.541211	−	1.66568i
$686$		0			0
$687$	1.32618e7			1.07204
$688$		0			0
$689$	−2.04706e6	+	1.48728e6i	−0.164279	+	0.119356i
$690$		0			0
$691$	−3.97349e6	−	2.88691e6i	−0.316575	−	0.230006i	0.418137	−	0.908384i	$-0.362683\pi$
$691$	−3.97349e6	−	2.88691e6i	−0.316575	−	0.230006i	−0.734713	+	0.678378i	$0.762683\pi$
$692$		0			0
$693$	−273716.	+	198866.i	−0.0216504	+	0.0157300i
$694$		0			0
$695$	4.15251e6	−	1.27801e7i	0.326098	−	1.00363i
$696$		0			0
$697$	−662755.	+	2.03975e6i	−0.0516739	+	0.159036i
$698$		0			0
$699$	−1.43456e7	−	1.04227e7i	−1.11052	−	0.806838i
$700$		0			0
$701$	154158.	+	474449.i	0.0118487	+	0.0364665i	0.956806	−	0.290727i	$-0.0938971\pi$
$701$	154158.	+	474449.i	0.0118487	+	0.0364665i	−0.944957	+	0.327193i	$0.893897\pi$
$702$		0			0
$703$	−1.27250e7	−	3.91634e7i	−0.971110	−	2.98877i
$704$		0			0
$705$	−4.58589e6	−	3.33185e6i	−0.347497	−	0.252471i
$706$		0			0
$707$	−1.20778e6			−0.0908740
$708$		0			0
$709$	1.48695e7	−	1.08033e7i	1.11091	−	0.807126i	0.128106	−	0.991760i	$-0.459110\pi$
$709$	1.48695e7	−	1.08033e7i	1.11091	−	0.807126i	0.982807	+	0.184635i	$0.0591102\pi$
$710$		0			0
$711$	−821896.	−	2.52954e6i	−0.0609738	−	0.187658i
$712$		0			0
$713$	−4.68607e6	+	1.00813e7i	−0.345211	+	0.742662i
$714$		0			0
$715$	−3.82187e6	−	1.17625e7i	−0.279583	−	0.860468i
$716$		0			0
$717$	6.83888e6	−	4.96874e6i	0.496806	−	0.360951i
$718$		0			0
$719$	−2.28901e7			−1.65129			−0.825647	−	0.564187i	$-0.809190\pi$
$719$	−2.28901e7			−1.65129			−0.825647	+	0.564187i	$0.809190\pi$
$720$		0			0
$721$	2.07774e6	+	1.50956e6i	0.148851	+	0.108147i
$722$		0			0
$723$	−4.65135e6	−	1.43154e7i	−0.330928	−	1.01849i
$724$		0			0
$725$	7.81911e6	+	2.40647e7i	0.552474	+	1.70034i
$726$		0			0
$727$	−1.17291e7	−	8.52172e6i	−0.823057	−	0.597986i	0.0945294	−	0.995522i	$-0.469865\pi$
$727$	−1.17291e7	−	8.52172e6i	−0.823057	−	0.597986i	−0.917587	+	0.397536i	$0.869865\pi$
$728$		0			0
$729$	4.83867e6	−	1.48919e7i	0.337215	−	1.03784i
$730$		0			0
$731$	3.52675e6	−	1.08542e7i	0.244107	−	0.751285i
$732$		0			0
$733$	−1.53100e7	+	1.11233e7i	−1.05248	+	0.764672i	−0.972683	−	0.232139i	$-0.925428\pi$
$733$	−1.53100e7	+	1.11233e7i	−1.05248	+	0.764672i	−0.0797983	+	0.996811i	$0.525428\pi$
$734$		0			0
$735$	−1.52521e7	−	1.10813e7i	−1.04139	−	0.756612i
$736$		0			0
$737$	−1.05464e7	+	7.66240e6i	−0.715212	+	0.519632i
$738$		0			0
$739$	7.99280e6			0.538379			0.269190	−	0.963087i	$-0.413244\pi$
$739$	7.99280e6			0.538379			0.269190	+	0.963087i	$0.413244\pi$
$740$		0			0
$741$	3.17813e6	−	9.78128e6i	0.212631	−	0.654411i
$742$		0			0
$743$	−7.26055e6			−0.482500			−0.241250	−	0.970463i	$-0.577557\pi$
$743$	−7.26055e6			−0.482500			−0.241250	+	0.970463i	$0.577557\pi$
$744$		0			0
$745$	4.69421e6			0.309864
$746$		0			0
$747$	238105.	−	732812.i	0.0156123	−	0.0480497i
$748$		0			0
$749$	197921.			0.0128910
$750$		0			0
$751$	2.29092e7	−	1.66445e7i	1.48221	−	1.07689i	0.505376	−	0.862899i	$-0.331354\pi$
$751$	2.29092e7	−	1.66445e7i	1.48221	−	1.07689i	0.976836	−	0.213991i	$-0.0686462\pi$
$752$		0			0
$753$	−1.81846e7	−	1.32119e7i	−1.16874	−	0.849138i
$754$		0			0
$755$	−1.18061e7	+	8.57765e6i	−0.753772	+	0.547647i
$756$		0			0
$757$	3.13489e6	−	9.64821e6i	0.198830	−	0.611937i	−0.801080	−	0.598557i	$-0.795741\pi$
$757$	3.13489e6	−	9.64821e6i	0.198830	−	0.611937i	0.999910	−	0.0133800i	$-0.00425911\pi$
$758$		0			0
$759$	−5.76486e6	+	1.77424e7i	−0.363232	+	1.11791i
$760$		0			0
$761$	8.11728e6	+	5.89755e6i	0.508100	+	0.369156i	0.812102	−	0.583515i	$-0.198323\pi$
$761$	8.11728e6	+	5.89755e6i	0.508100	+	0.369156i	−0.304003	+	0.952671i	$0.598323\pi$
$762$		0			0
$763$	551739.	+	1.69808e6i	0.0343101	+	0.105596i
$764$		0			0
$765$	395327.	+	1.21669e6i	0.0244232	+	0.0751669i
$766$		0			0
$767$	1.18494e6	+	860912.i	0.0727293	+	0.0528409i
$768$		0			0
$769$	−2.35703e7			−1.43730			−0.718652	−	0.695370i	$-0.755241\pi$
$769$	−2.35703e7			−1.43730			−0.718652	+	0.695370i	$0.755241\pi$
$770$		0			0
$771$	−9.50979e6	+	6.90927e6i	−0.576149	+	0.418597i
$772$		0			0
$773$	−9.32152e6	−	2.86887e7i	−0.561097	−	1.72688i	−0.679273	−	0.733886i	$-0.737705\pi$
$773$	−9.32152e6	−	2.86887e7i	−0.561097	−	1.72688i	0.118176	−	0.992993i	$-0.462295\pi$
$774$		0			0
$775$	3.10938e6	+	1.58933e7i	0.185960	+	0.950516i
$776$		0			0
$777$	−1.23384e6	−	3.79737e6i	−0.0733173	−	0.225647i
$778$		0			0
$779$	8.80203e6	−	6.39505e6i	0.519684	−	0.377572i
$780$		0			0
$781$	4.78459e7			2.80684
$782$		0			0
$783$	−2.69505e7	−	1.95807e7i	−1.57095	−	1.14136i
$784$		0			0
$785$	2.45009e6	+	7.54060e6i	0.141908	+	0.436749i
$786$		0			0
$787$	8.54975e6	+	2.63134e7i	0.492058	+	1.51440i	0.821492	+	0.570221i	$0.193142\pi$
$787$	8.54975e6	+	2.63134e7i	0.492058	+	1.51440i	−0.329434	+	0.944179i	$0.606858\pi$
$788$		0			0
$789$	8.68614e6	+	6.31085e6i	0.496746	+	0.360907i
$790$		0			0
$791$	−549537.	+	1.69130e6i	−0.0312288	+	0.0961125i
$792$		0			0
$793$	−3.11756e6	+	9.59487e6i	−0.176048	+	0.541821i
$794$		0			0
$795$	9.14213e6	−	6.64215e6i	0.513014	−	0.372727i
$796$		0			0
$797$	−1.93163e7	−	1.40341e7i	−1.07715	−	0.782598i	−0.0999691	−	0.994991i	$-0.531874\pi$
$797$	−1.93163e7	−	1.40341e7i	−1.07715	−	0.782598i	−0.977184	+	0.212393i	$0.931874\pi$
$798$		0			0
$799$	−2.17254e6	+	1.57845e6i	−0.120393	+	0.0874707i
$800$		0			0
$801$	−840162.			−0.0462681
$802$		0			0
$803$	3.58383e6	−	1.10299e7i	0.196137	−	0.603646i
$804$		0			0
$805$	−2.97841e6			−0.161992
$806$		0			0
$807$	1.73485e7			0.937730
$808$		0			0
$809$	−3.94482e6	+	1.21409e7i	−0.211912	+	0.652199i	0.787446	+	0.616383i	$0.211403\pi$
$809$	−3.94482e6	+	1.21409e7i	−0.211912	+	0.652199i	−0.999358	+	0.0358152i	$0.988597\pi$
$810$		0			0
$811$	6.74505e6			0.360108			0.180054	−	0.983657i	$-0.442373\pi$
$811$	6.74505e6			0.360108			0.180054	+	0.983657i	$0.442373\pi$
$812$		0			0
$813$	1.94622e7	−	1.41401e7i	1.03268	−	0.750285i
$814$		0			0
$815$	1.73639e7	+	1.26156e7i	0.915699	+	0.665294i
$816$		0			0
$817$	−4.68387e7	+	3.40303e7i	−2.45499	+	1.78365i
$818$		0			0
$819$	−43540.9	+	134005.i	−0.00226823	+	0.00698090i
$820$		0			0
$821$	−3.80453e6	+	1.17091e7i	−0.196989	+	0.606271i	0.802958	+	0.596035i	$0.203258\pi$
$821$	−3.80453e6	+	1.17091e7i	−0.196989	+	0.606271i	−0.999948	+	0.0102358i	$0.996742\pi$
$822$		0			0
$823$	−2.27364e7	−	1.65189e7i	−1.17010	−	0.850125i	−0.179076	−	0.983835i	$-0.557311\pi$
$823$	−2.27364e7	−	1.65189e7i	−1.17010	−	0.850125i	−0.991020	+	0.133711i	$0.957311\pi$
$824$		0			0
$825$	8.39778e6	+	2.58457e7i	0.429566	+	1.32207i
$826$		0			0
$827$	9.09042e6	+	2.79774e7i	0.462189	+	1.42247i	0.862483	+	0.506086i	$0.168908\pi$
$827$	9.09042e6	+	2.79774e7i	0.462189	+	1.42247i	−0.400294	+	0.916387i	$0.631092\pi$
$828$		0			0
$829$	1.01203e7	+	7.35283e6i	0.511454	+	0.371593i	0.813375	−	0.581740i	$-0.197628\pi$
$829$	1.01203e7	+	7.35283e6i	0.511454	+	0.371593i	−0.301921	+	0.953333i	$0.597628\pi$
$830$		0			0
$831$	2.39058e7			1.20088
$832$		0			0
$833$	−7.22562e6	+	5.24972e6i	−0.360797	+	0.262134i
$834$		0			0
$835$	−3.53378e6	−	1.08759e7i	−0.175397	−	0.539818i
$836$		0			0
$837$	−1.56107e7	−	1.45218e7i	−0.770211	−	0.716486i
$838$		0			0
$839$	4.72780e6	+	1.45507e7i	0.231875	+	0.713638i	0.997521	+	0.0703755i	$0.0224198\pi$
$839$	4.72780e6	+	1.45507e7i	0.231875	+	0.713638i	−0.765645	+	0.643263i	$0.777580\pi$
$840$		0			0
$841$	−3.99487e7	+	2.90245e7i	−1.94766	+	1.41506i
$842$		0			0
$843$	−6.21192e6			−0.301063
$844$		0			0
$845$	1.93928e7	+	1.40897e7i	0.934325	+	0.678827i
$846$		0			0
$847$	1.22889e6	+	3.78214e6i	0.0588580	+	0.181146i
$848$		0			0
$849$	−4.26208e6	−	1.31173e7i	−0.202933	−	0.624563i
$850$		0			0
$851$	2.51664e7	+	1.82844e7i	1.19123	+	0.865482i
$852$		0			0
$853$	9.29216e6	−	2.85983e7i	0.437265	−	1.34576i	−0.453484	−	0.891265i	$-0.649819\pi$
$853$	9.29216e6	−	2.85983e7i	0.437265	−	1.34576i	0.890748	−	0.454497i	$-0.150181\pi$
$854$		0			0
$855$	2.00545e6	−	6.17213e6i	0.0938201	−	0.288749i
$856$		0			0
$857$	2.55806e7	−	1.85854e7i	1.18976	−	0.864408i	0.196517	−	0.980500i	$-0.437037\pi$
$857$	2.55806e7	−	1.85854e7i	1.18976	−	0.864408i	0.993238	+	0.116092i	$0.0370368\pi$
$858$		0			0
$859$	−2.85548e6	−	2.07463e6i	−0.132037	−	0.0959306i	0.519806	−	0.854284i	$-0.326004\pi$
$859$	−2.85548e6	−	2.07463e6i	−0.132037	−	0.0959306i	−0.651843	+	0.758354i	$0.726004\pi$
$860$		0			0
$861$	853464.	−	620078.i	0.0392353	−	0.0285061i
$862$		0			0
$863$	3.43234e7			1.56879			0.784393	−	0.620264i	$-0.212975\pi$
$863$	3.43234e7			1.56879			0.784393	+	0.620264i	$0.212975\pi$
$864$		0			0
$865$	3.77483e6	−	1.16177e7i	0.171537	−	0.527936i
$866$		0			0
$867$	1.64287e7			0.742257
$868$		0			0
$869$	−5.44020e7			−2.44380
$870$		0			0
$871$	−1.67765e6	+	5.16327e6i	−0.0749299	+	0.230611i
$872$		0			0
$873$	67944.4			0.00301730
$874$		0			0
$875$	114031.	−	82848.4i	0.00503504	−	0.00365817i
$876$		0			0
$877$	3.23021e7	+	2.34688e7i	1.41818	+	1.03037i	0.992069	+	0.125697i	$0.0401166\pi$
$877$	3.23021e7	+	2.34688e7i	1.41818	+	1.03037i	0.426111	+	0.904671i	$0.359883\pi$
$878$		0			0
$879$	3.08875e7	−	2.24411e7i	1.34838	−	0.979652i
$880$		0			0
$881$	950556.	−	2.92551e6i	0.0412608	−	0.126988i	−0.928304	−	0.371821i	$-0.878733\pi$
$881$	950556.	−	2.92551e6i	0.0412608	−	0.126988i	0.969565	+	0.244834i	$0.0787334\pi$
$882$		0			0
$883$	−7.60267e6	+	2.33986e7i	−0.328144	+	1.00992i	0.641857	+	0.766824i	$0.278164\pi$
$883$	−7.60267e6	+	2.33986e7i	−0.328144	+	1.00992i	−0.970001	+	0.243100i	$0.921836\pi$
$884$		0			0
$885$	−5.29193e6	−	3.84481e6i	−0.227120	−	0.165013i
$886$		0			0
$887$	−3.24085e6	−	9.97431e6i	−0.138309	−	0.425671i	0.857781	−	0.514015i	$-0.171842\pi$
$887$	−3.24085e6	−	9.97431e6i	−0.138309	−	0.425671i	−0.996090	+	0.0883443i	$0.971842\pi$
$888$		0			0
$889$	−924628.	−	2.84571e6i	−0.0392385	−	0.120764i
$890$		0			0
$891$	−2.53059e7	−	1.83858e7i	−1.06789	−	0.775868i
$892$		0			0
$893$	1.36228e7			0.571659
$894$		0			0
$895$	−2.25685e7	+	1.63970e7i	−0.941769	+	0.684235i
$896$		0			0
$897$	2.40083e6	+	7.38899e6i	0.0996276	+	0.306622i
$898$		0			0
$899$	−3.90967e7	+	2.17338e7i	−1.61339	+	0.896883i
$900$		0			0
$901$	−1.65431e6	−	5.09144e6i	−0.0678898	−	0.208943i
$902$		0			0
$903$	−4.54158e6	+	3.29965e6i	−0.185348	+	0.134663i
$904$		0			0
$905$	−1.13845e7			−0.462054
$906$		0			0
$907$	−4.56220e6	−	3.31463e6i	−0.184143	−	0.133788i	0.491895	−	0.870655i	$-0.336304\pi$
$907$	−4.56220e6	−	3.31463e6i	−0.184143	−	0.133788i	−0.676038	+	0.736867i	$0.736304\pi$
$908$		0			0
$909$	614333.	+	1.89072e6i	0.0246601	+	0.0758959i
$910$		0			0
$911$	6.02746e6	+	1.85506e7i	0.240624	+	0.740564i	0.996325	+	0.0856479i	$0.0272960\pi$
$911$	6.02746e6	+	1.85506e7i	0.240624	+	0.740564i	−0.755702	+	0.654916i	$0.772704\pi$
$912$		0			0
$913$	−1.27504e7	−	9.26372e6i	−0.506229	−	0.367797i
$914$		0			0
$915$	1.39230e7	−	4.28504e7i	0.549767	−	1.69201i
$916$		0			0
$917$	609925.	−	1.87716e6i	0.0239526	−	0.0737186i
$918$		0			0
$919$	2.31046e7	−	1.67865e7i	0.902421	−	0.655647i	−0.0366655	−	0.999328i	$-0.511674\pi$
$919$	2.31046e7	−	1.67865e7i	0.902421	−	0.655647i	0.939087	+	0.343680i	$0.111674\pi$
$920$		0			0
$921$	2.53025e6	+	1.83833e6i	0.0982910	+	0.0714126i
$922$		0			0
$923$	1.61204e7	−	1.17121e7i	0.622832	−	0.452514i
$924$		0			0
$925$	4.53147e7			1.74135
$926$		0			0
$927$	1.30632e6	−	4.02043e6i	0.0499286	−	0.153665i
$928$		0			0
$929$	2.54982e7			0.969328			0.484664	−	0.874700i	$-0.338942\pi$
$929$	2.54982e7			0.969328			0.484664	+	0.874700i	$0.338942\pi$
$930$		0			0
$931$	4.53077e7			1.71316
$932$		0			0
$933$	−1.12016e7	+	3.44751e7i	−0.421287	+	1.29659i
$934$		0			0
$935$	2.61670e7			0.978871
$936$		0			0
$937$	1.98302e7	−	1.44075e7i	0.737867	−	0.536091i	−0.154176	−	0.988043i	$-0.549272\pi$
$937$	1.98302e7	−	1.44075e7i	0.737867	−	0.536091i	0.892042	+	0.451952i	$0.149272\pi$
$938$		0			0
$939$	3.34648e7	+	2.43136e7i	1.23858	+	0.899880i
$940$		0			0
$941$	8.26957e6	−	6.00819e6i	0.304445	−	0.221192i	−0.425064	−	0.905163i	$-0.639749\pi$
$941$	8.26957e6	−	6.00819e6i	0.304445	−	0.221192i	0.729509	+	0.683971i	$0.239749\pi$
$942$		0			0
$943$	−2.53978e6	+	7.81665e6i	−0.0930074	+	0.286247i
$944$		0			0
$945$	1.76513e6	−	5.43252e6i	0.0642981	−	0.197889i
$946$		0			0
$947$	3.06562e7	+	2.22730e7i	1.11082	+	0.807057i	0.982792	−	0.184714i	$-0.0591358\pi$
$947$	3.06562e7	+	2.22730e7i	1.11082	+	0.807057i	0.128026	+	0.991771i	$0.459136\pi$
$948$		0			0
$949$	−1.49252e6	−	4.59350e6i	−0.0537965	−	0.165569i
$950$		0			0
$951$	−2.66385e6	−	8.19850e6i	−0.0955122	−	0.293956i
$952$		0			0
$953$	−3.36546e7	−	2.44515e7i	−1.20036	−	0.872113i	−0.206041	−	0.978543i	$-0.566058\pi$
$953$	−3.36546e7	−	2.44515e7i	−1.20036	−	0.872113i	−0.994320	+	0.106430i	$0.966058\pi$
$954$		0			0
$955$	−1.58860e7			−0.563645
$956$		0			0
$957$	−6.07272e7	+	4.41209e7i	−2.14340	+	1.55727i
$958$		0			0
$959$	1.54880e6	+	4.76671e6i	0.0543811	+	0.167368i
$960$		0			0
$961$	−2.65184e7	+	1.07891e7i	−0.926271	+	0.376858i
$962$		0			0
$963$	−100672.	−	309836.i	−0.00349818	−	0.0107663i
$964$		0			0
$965$	−4.49440e7	+	3.26537e7i	−1.55365	+	1.12879i
$966$		0			0
$967$	1.72092e6			0.0591825			0.0295913	−	0.999562i	$-0.490579\pi$
$967$	1.72092e6			0.0591825			0.0295913	+	0.999562i	$0.490579\pi$
$968$		0			0
$969$	1.76039e7	+	1.27900e7i	0.602280	+	0.437582i
$970$		0			0
$971$	1.71928e7	+	5.29141e7i	0.585193	+	1.80104i	0.598494	+	0.801128i	$0.295766\pi$
$971$	1.71928e7	+	5.29141e7i	0.585193	+	1.80104i	−0.0133004	+	0.999912i	$0.504234\pi$
$972$		0			0
$973$	967637.	+	2.97808e6i	0.0327665	+	0.100845i
$974$		0			0
$975$	9.15614e6	+	6.65233e6i	0.308461	+	0.224110i
$976$		0			0
$977$	7.93574e6	−	2.44237e7i	0.265981	−	0.818606i	−0.725485	−	0.688238i	$-0.758384\pi$
$977$	7.93574e6	−	2.44237e7i	0.265981	−	0.818606i	0.991466	−	0.130367i	$-0.0416157\pi$
$978$		0			0
$979$	−5.31039e6	+	1.63437e7i	−0.177080	+	0.544996i
$980$		0			0
$981$	2.37762e6	−	1.72744e6i	0.0788805	−	0.0573100i
$982$		0			0
$983$	−2.63481e7	−	1.91430e7i	−0.869692	−	0.631868i	0.0608124	−	0.998149i	$-0.480631\pi$
$983$	−2.63481e7	−	1.91430e7i	−0.869692	−	0.631868i	−0.930504	+	0.366281i	$0.880631\pi$
$984$		0			0
$985$	6.17550e7	−	4.48676e7i	2.02806	−	1.47347i
$986$		0			0
$987$	1.32089e6			0.0431594
$988$		0			0
$989$	1.35151e7	−	4.15951e7i	0.439367	−	1.35223i
$990$		0			0
$991$	3.08974e7			0.999396			0.499698	−	0.866200i	$-0.333444\pi$
$991$	3.08974e7			0.999396			0.499698	+	0.866200i	$0.333444\pi$
$992$		0			0
$993$	−3.02783e7			−0.974448
$994$		0			0
$995$	−1.38295e7	+	4.25628e7i	−0.442842	+	1.36293i
$996$		0			0
$997$	5.04151e6			0.160629			0.0803143	−	0.996770i	$-0.474408\pi$
$997$	5.04151e6			0.160629			0.0803143	+	0.996770i	$0.474408\pi$
$998$		0			0
$999$	−4.82649e7	+	3.50665e7i	−1.53009	+	1.11168i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.6.f.a.97.4	✓	56
31.8	even	5	inner	124.6.f.a.101.4	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.6.f.a.97.4	✓	56	1.1	even	1	trivial
124.6.f.a.101.4	yes	56	31.8	even	5	inner

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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	124.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.50907 + 13.8775i) q^{3} +78.4326 q^{5} +(-14.7862 + 10.7428i) q^{7} +(24.3383 + 17.6828i) q^{9} +O(q^{10})\)	\(q+(-4.50907 + 13.8775i) q^{3} +78.4326 q^{5} +(-14.7862 + 10.7428i) q^{7} +(24.3383 + 17.6828i) q^{9} +(497.817 - 361.685i) q^{11} +(79.1894 - 243.720i) q^{13} +(-353.658 + 1088.45i) q^{15} +(438.635 + 318.687i) q^{17} +(-849.929 - 2615.81i) q^{19} +(-82.4110 - 253.635i) q^{21} +(1680.92 + 1221.26i) q^{23} +3026.67 q^{25} +(-3223.72 + 2342.17i) q^{27} +(2583.40 + 7950.88i) q^{29} +(1027.33 + 5251.07i) q^{31} +(2774.59 + 8539.31i) q^{33} +(-1159.72 + 842.585i) q^{35} +14971.8 q^{37} +(3025.15 + 2197.90i) q^{39} +(1222.38 + 3762.11i) q^{41} +(-6504.72 - 20019.5i) q^{43} +(1908.91 + 1386.91i) q^{45} +(-1530.55 + 4710.55i) q^{47} +(-5090.43 + 15666.7i) q^{49} +(-6400.41 + 4650.17i) q^{51} +(-7988.15 - 5803.73i) q^{53} +(39045.1 - 28367.9i) q^{55} +40133.3 q^{57} +(-1766.19 + 5435.78i) q^{59} -39368.4 q^{61} -549.832 q^{63} +(6211.03 - 19115.6i) q^{65} -21185.3 q^{67} +(-24527.4 + 17820.2i) q^{69} +(62905.7 + 45703.7i) q^{71} +(15247.9 - 11078.3i) q^{73} +(-13647.5 + 42002.6i) q^{75} +(-3475.30 + 10695.9i) q^{77} +(-71525.4 - 51966.3i) q^{79} +(-15708.5 - 48345.6i) q^{81} +(-7914.74 - 24359.1i) q^{83} +(34403.3 + 24995.5i) q^{85} -121987. q^{87} +(-22593.8 + 16415.4i) q^{89} +(1447.32 + 4454.40i) q^{91} +(-77503.9 - 9420.75i) q^{93} +(-66662.2 - 205165. i) q^{95} +(1827.17 - 1327.52i) q^{97} +18511.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) \) 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9	\( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9} - 509 q^{11} - 117 q^{13} + 89 q^{15} - 3504 q^{17} + 262 q^{19} + 352 q^{21} - 2448 q^{23} + 49618 q^{25} + 14324 q^{27} - 9888 q^{29} - 12771 q^{31} + 27699 q^{33} + 13840 q^{35} + 76096 q^{37} + 33520 q^{39} - 4843 q^{41} - 40778 q^{43} + 56692 q^{45} + 38922 q^{47} - 17126 q^{49} - 69292 q^{51} - 41728 q^{53} - 172096 q^{55} + 57066 q^{57} - 58198 q^{59} + 176328 q^{61} - 37444 q^{63} + 143863 q^{65} + 9812 q^{67} - 9250 q^{69} - 67356 q^{71} - 63512 q^{73} - 198012 q^{75} - 74257 q^{77} + 137651 q^{79} + 196077 q^{81} + 156427 q^{83} + 238828 q^{85} - 558144 q^{87} - 99292 q^{89} - 243609 q^{91} - 325925 q^{93} - 75077 q^{95} - 476340 q^{97} + 745812 q^{99}+O(q^{100}) \) 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9 - 509 * q^11 - 117 * q^13 + 89 * q^15 - 3504 * q^17 + 262 * q^19 + 352 * q^21 - 2448 * q^23 + 49618 * q^25 + 14324 * q^27 - 9888 * q^29 - 12771 * q^31 + 27699 * q^33 + 13840 * q^35 + 76096 * q^37 + 33520 * q^39 - 4843 * q^41 - 40778 * q^43 + 56692 * q^45 + 38922 * q^47 - 17126 * q^49 - 69292 * q^51 - 41728 * q^53 - 172096 * q^55 + 57066 * q^57 - 58198 * q^59 + 176328 * q^61 - 37444 * q^63 + 143863 * q^65 + 9812 * q^67 - 9250 * q^69 - 67356 * q^71 - 63512 * q^73 - 198012 * q^75 - 74257 * q^77 + 137651 * q^79 + 196077 * q^81 + 156427 * q^83 + 238828 * q^85 - 558144 * q^87 - 99292 * q^89 - 243609 * q^91 - 325925 * q^93 - 75077 * q^95 - 476340 * q^97 + 745812 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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