LMFDB - Embedded newform 80.6.n.b.63.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(47,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("80.47");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.n (of order $4$, degree $2$, 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:	$12.8307055850$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{195})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 97x^{2} + 2401 $ x^4 - 97*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.2
Root			$-6.98212 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	80.63
Dual form			80.6.n.b.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13.9642 - 13.9642i) q^{3} +(-25.0000 + 50.0000i) q^{5} +(-125.678 - 125.678i) q^{7} -147.000i q^{9} +O(q^{10})$	\(q+(13.9642 - 13.9642i) q^{3} +(-25.0000 + 50.0000i) q^{5} +(-125.678 - 125.678i) q^{7} -147.000i q^{9} -418.927i q^{11} +(-695.000 - 695.000i) q^{13} +(349.106 + 1047.32i) q^{15} +(-95.0000 + 95.0000i) q^{17} +837.854 q^{19} -3510.00 q^{21} +(-2555.46 + 2555.46i) q^{23} +(-1875.00 - 2500.00i) q^{25} +(1340.57 + 1340.57i) q^{27} -2876.00i q^{29} -9635.33i q^{31} +(-5850.00 - 5850.00i) q^{33} +(9425.86 - 3141.95i) q^{35} +(-5155.00 + 5155.00i) q^{37} -19410.3 q^{39} +9218.00 q^{41} +(-1550.03 + 1550.03i) q^{43} +(7350.00 + 3675.00i) q^{45} +(12609.7 + 12609.7i) q^{47} +14783.0i q^{49} +2653.21i q^{51} +(11345.0 + 11345.0i) q^{53} +(20946.4 + 10473.2i) q^{55} +(11700.0 - 11700.0i) q^{57} -837.854 q^{59} +18678.0 q^{61} +(-18474.7 + 18474.7i) q^{63} +(52125.0 - 17375.0i) q^{65} +(-17385.5 - 17385.5i) q^{67} +71370.0i q^{69} -58230.9i q^{71} +(-24055.0 - 24055.0i) q^{73} +(-61093.6 - 8727.65i) q^{75} +(-52650.0 + 52650.0i) q^{77} +93839.7 q^{79} +73161.0 q^{81} +(35650.7 - 35650.7i) q^{83} +(-2375.00 - 7125.00i) q^{85} +(-40161.2 - 40161.2i) q^{87} -74296.0i q^{89} +174693. i q^{91} +(-134550. - 134550. i) q^{93} +(-20946.4 + 41892.7i) q^{95} +(-49255.0 + 49255.0i) q^{97} -61582.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 100 q^{5}+O(q^{10}) $ 4 * q - 100 * q^5	$ 4 q - 100 q^{5} - 2780 q^{13} - 380 q^{17} - 14040 q^{21} - 7500 q^{25} - 23400 q^{33} - 20620 q^{37} + 36872 q^{41} + 29400 q^{45} + 45380 q^{53} + 46800 q^{57} + 74712 q^{61} + 208500 q^{65} - 96220 q^{73} - 210600 q^{77} + 292644 q^{81} - 9500 q^{85} - 538200 q^{93} - 197020 q^{97}+O(q^{100}) $ 4 * q - 100 * q^5 - 2780 * q^13 - 380 * q^17 - 14040 * q^21 - 7500 * q^25 - 23400 * q^33 - 20620 * q^37 + 36872 * q^41 + 29400 * q^45 + 45380 * q^53 + 46800 * q^57 + 74712 * q^61 + 208500 * q^65 - 96220 * q^73 - 210600 * q^77 + 292644 * q^81 - 9500 * q^85 - 538200 * q^93 - 197020 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	13.9642	−	13.9642i	0.895806	−	0.895806i	−0.0992556	−	0.995062i	$-0.531646\pi$
$3$	13.9642	−	13.9642i	0.895806	−	0.895806i	0.995062	+	0.0992556i	$0.0316461\pi$
$4$		0			0
$5$	−25.0000	+	50.0000i	−0.447214	+	0.894427i
$5$	−25.0000	+	50.0000i	−0.447214	+	0.894427i
$6$		0			0
$7$	−125.678	−	125.678i	−0.969426	−	0.969426i	0.0301202	−	0.999546i	$-0.490411\pi$
$7$	−125.678	−	125.678i	−0.969426	−	0.969426i	−0.999546	+	0.0301202i	$0.990411\pi$
$8$		0			0
$9$		−	147.000i		−	0.604938i
$10$		0			0
$11$		−	418.927i		−	1.04390i	−0.852978	−	0.521948i	$-0.825206\pi$
$11$		−	418.927i		−	1.04390i	0.852978	−	0.521948i	$-0.174794\pi$
$12$		0			0
$13$	−695.000	−	695.000i	−1.14058	−	1.14058i	−0.988344	−	0.152238i	$-0.951352\pi$
$13$	−695.000	−	695.000i	−1.14058	−	1.14058i	−0.152238	−	0.988344i	$-0.548648\pi$
$14$		0			0
$15$	349.106	+	1047.32i	0.400617	+	1.20185i
$16$		0			0
$17$	−95.0000	+	95.0000i	−0.0797262	+	0.0797262i	−0.745845	−	0.666119i	$-0.767954\pi$
$17$	−95.0000	+	95.0000i	−0.0797262	+	0.0797262i	0.666119	+	0.745845i	$0.267954\pi$
$18$		0			0
$19$	837.854			0.532457			0.266229	−	0.963910i	$-0.414222\pi$
$19$	837.854			0.532457			0.266229	+	0.963910i	$0.414222\pi$
$20$		0			0
$21$	−3510.00			−1.73684
$22$		0			0
$23$	−2555.46	+	2555.46i	−1.00728	+	1.00728i	−0.00730341	+	0.999973i	$0.502325\pi$
$23$	−2555.46	+	2555.46i	−1.00728	+	1.00728i	−0.999973	+	0.00730341i	$0.997675\pi$
$24$		0			0
$25$	−1875.00	−	2500.00i	−0.600000	−	0.800000i
$26$		0			0
$27$	1340.57	+	1340.57i	0.353899	+	0.353899i
$28$		0			0
$29$		−	2876.00i		−	0.635029i	−0.948253	−	0.317515i	$-0.897152\pi$
$29$		−	2876.00i		−	0.635029i	0.948253	−	0.317515i	$-0.102848\pi$
$30$		0			0
$31$		−	9635.33i		−	1.80079i	−0.435077	−	0.900393i	$-0.643279\pi$
$31$		−	9635.33i		−	1.80079i	0.435077	−	0.900393i	$-0.356721\pi$
$32$		0			0
$33$	−5850.00	−	5850.00i	−0.935128	−	0.935128i
$34$		0			0
$35$	9425.86	−	3141.95i	1.30062	−	0.433541i
$36$		0			0
$37$	−5155.00	+	5155.00i	−0.619048	+	0.619048i	−0.945287	−	0.326239i	$-0.894219\pi$
$37$	−5155.00	+	5155.00i	−0.619048	+	0.619048i	0.326239	+	0.945287i	$0.394219\pi$
$38$		0			0
$39$	−19410.3			−2.04348
$40$		0			0
$41$	9218.00			0.856401			0.428200	−	0.903684i	$-0.359148\pi$
$41$	9218.00			0.856401			0.428200	+	0.903684i	$0.359148\pi$
$42$		0			0
$43$	−1550.03	+	1550.03i	−0.127841	+	0.127841i	−0.768132	−	0.640291i	$-0.778814\pi$
$43$	−1550.03	+	1550.03i	−0.127841	+	0.127841i	0.640291	+	0.768132i	$0.278814\pi$
$44$		0			0
$45$	7350.00	+	3675.00i	0.541073	+	0.270537i
$46$		0			0
$47$	12609.7	+	12609.7i	0.832646	+	0.832646i	0.987878	−	0.155232i	$-0.0496125\pi$
$47$	12609.7	+	12609.7i	0.832646	+	0.832646i	−0.155232	+	0.987878i	$0.549613\pi$
$48$		0			0
$49$			14783.0i			0.879574i
$50$		0			0
$51$			2653.21i			0.142839i
$52$		0			0
$53$	11345.0	+	11345.0i	0.554772	+	0.554772i	0.927814	−	0.373042i	$-0.121685\pi$
$53$	11345.0	+	11345.0i	0.554772	+	0.554772i	−0.373042	+	0.927814i	$0.621685\pi$
$54$		0			0
$55$	20946.4	+	10473.2i	0.933688	+	0.466844i
$56$		0			0
$57$	11700.0	−	11700.0i	0.476978	−	0.476978i
$58$		0			0
$59$	−837.854			−0.0313356			−0.0156678	−	0.999877i	$-0.504987\pi$
$59$	−837.854			−0.0313356			−0.0156678	+	0.999877i	$0.504987\pi$
$60$		0			0
$61$	18678.0			0.642696			0.321348	−	0.946961i	$-0.395864\pi$
$61$	18678.0			0.642696			0.321348	+	0.946961i	$0.395864\pi$
$62$		0			0
$63$	−18474.7	+	18474.7i	−0.586443	+	0.586443i
$64$		0			0
$65$	52125.0	−	17375.0i	1.53025	−	0.510084i
$66$		0			0
$67$	−17385.5	−	17385.5i	−0.473151	−	0.473151i	0.429782	−	0.902933i	$-0.358590\pi$
$67$	−17385.5	−	17385.5i	−0.473151	−	0.473151i	−0.902933	+	0.429782i	$0.858590\pi$
$68$		0			0
$69$			71370.0i			1.80465i
$70$		0			0
$71$		−	58230.9i		−	1.37091i	−0.728117	−	0.685453i	$-0.759604\pi$
$71$		−	58230.9i		−	1.37091i	0.728117	−	0.685453i	$-0.240396\pi$
$72$		0			0
$73$	−24055.0	−	24055.0i	−0.528321	−	0.528321i	0.391750	−	0.920072i	$-0.371870\pi$
$73$	−24055.0	−	24055.0i	−0.528321	−	0.528321i	−0.920072	+	0.391750i	$0.871870\pi$
$74$		0			0
$75$	−61093.6	−	8727.65i	−1.25413	−	0.179161i
$76$		0			0
$77$	−52650.0	+	52650.0i	−1.01198	+	1.01198i
$78$		0			0
$79$	93839.7			1.69168			0.845841	−	0.533435i	$-0.179099\pi$
$79$	93839.7			1.69168			0.845841	+	0.533435i	$0.179099\pi$
$80$		0			0
$81$	73161.0			1.23899
$82$		0			0
$83$	35650.7	−	35650.7i	0.568032	−	0.568032i	−0.363545	−	0.931577i	$-0.618434\pi$
$83$	35650.7	−	35650.7i	0.568032	−	0.568032i	0.931577	+	0.363545i	$0.118434\pi$
$84$		0			0
$85$	−2375.00	−	7125.00i	−0.0356547	−	0.106964i
$86$		0			0
$87$	−40161.2	−	40161.2i	−0.568863	−	0.568863i
$88$		0			0
$89$		−	74296.0i		−	0.994238i	−0.867682	−	0.497119i	$-0.834391\pi$
$89$		−	74296.0i		−	0.994238i	0.867682	−	0.497119i	$-0.165609\pi$
$90$		0			0
$91$			174693.i			2.21142i
$92$		0			0
$93$	−134550.	−	134550.i	−1.61316	−	1.61316i
$94$		0			0
$95$	−20946.4	+	41892.7i	−0.238122	+	0.476244i
$96$		0			0
$97$	−49255.0	+	49255.0i	−0.531522	+	0.531522i	−0.921025	−	0.389503i	$-0.872647\pi$
$97$	−49255.0	+	49255.0i	−0.531522	+	0.531522i	0.389503	+	0.921025i	$0.372647\pi$
$98$		0			0
$99$	−61582.3			−0.631492
$100$		0			0
$101$	−100378.			−0.979118			−0.489559	−	0.871970i	$-0.662842\pi$
$101$	−100378.			−0.979118			−0.489559	+	0.871970i	$0.662842\pi$
$102$		0			0
$103$	55088.9	−	55088.9i	0.511648	−	0.511648i	−0.403383	−	0.915031i	$-0.632166\pi$
$103$	55088.9	−	55088.9i	0.511648	−	0.511648i	0.915031	+	0.403383i	$0.132166\pi$
$104$		0			0
$105$	87750.0	−	175500.i	0.776737	−	1.55347i
$106$		0			0
$107$	65394.5	+	65394.5i	0.552182	+	0.552182i	0.927070	−	0.374888i	$-0.122319\pi$
$107$	65394.5	+	65394.5i	0.552182	+	0.552182i	−0.374888	+	0.927070i	$0.622319\pi$
$108$		0			0
$109$			231276.i			1.86451i	0.361804	+	0.932254i	$0.382161\pi$
$109$			231276.i			1.86451i	−0.361804	+	0.932254i	$0.617839\pi$
$110$		0			0
$111$			143971.i			1.10909i
$112$		0			0
$113$	−181815.	−	181815.i	−1.33947	−	1.33947i	−0.896570	−	0.442902i	$-0.853949\pi$
$113$	−181815.	−	181815.i	−1.33947	−	1.33947i	−0.442902	−	0.896570i	$-0.646051\pi$
$114$		0			0
$115$	−63886.4	−	191659.i	−0.450468	−	1.35140i
$116$		0			0
$117$	−102165.	+	102165.i	−0.689982	+	0.689982i
$118$		0			0
$119$	23878.9			0.154577
$120$		0			0
$121$	−14449.0			−0.0897169
$122$		0			0
$123$	128722.	−	128722.i	0.767169	−	0.767169i
$124$		0			0
$125$	171875.	−	31250.0i	0.983870	−	0.178885i
$126$		0			0
$127$	−123123.	−	123123.i	−0.677375	−	0.677375i	0.282031	−	0.959405i	$-0.408992\pi$
$127$	−123123.	−	123123.i	−0.677375	−	0.677375i	−0.959405	+	0.282031i	$0.908992\pi$
$128$		0			0
$129$			43290.0i			0.229041i
$130$		0			0
$131$		−	166314.i		−	0.846741i	−0.905957	−	0.423371i	$-0.860847\pi$
$131$		−	166314.i		−	0.846741i	0.905957	−	0.423371i	$-0.139153\pi$
$132$		0			0
$133$	−105300.	−	105300.i	−0.516178	−	0.516178i
$134$		0			0
$135$	−100543.	+	33514.2i	−0.474805	+	0.158268i
$136$		0			0
$137$	38265.0	−	38265.0i	0.174181	−	0.174181i	−0.614633	−	0.788813i	$-0.710696\pi$
$137$	38265.0	−	38265.0i	0.174181	−	0.174181i	0.788813	+	0.614633i	$0.210696\pi$
$138$		0			0
$139$	−41054.9			−0.180230			−0.0901151	−	0.995931i	$-0.528723\pi$
$139$	−41054.9			−0.180230			−0.0901151	+	0.995931i	$0.528723\pi$
$140$		0			0
$141$	352170.			1.49178
$142$		0			0
$143$	−291154.	+	291154.i	−1.19065	+	1.19065i
$144$		0			0
$145$	143800.	+	71900.0i	0.567988	+	0.283994i
$146$		0			0
$147$	206433.	+	206433.i	0.787928	+	0.787928i
$148$		0			0
$149$			204196.i			0.753497i	0.926316	+	0.376749i	$0.122958\pi$
$149$			204196.i			0.753497i	−0.926316	+	0.376749i	$0.877042\pi$
$150$		0			0
$151$		−	219099.i		−	0.781984i	−0.920394	−	0.390992i	$-0.872132\pi$
$151$		−	219099.i		−	0.781984i	0.920394	−	0.390992i	$-0.127868\pi$
$152$		0			0
$153$	13965.0	+	13965.0i	0.0482295	+	0.0482295i
$154$		0			0
$155$	481766.	+	240883.i	1.61067	+	0.805336i
$156$		0			0
$157$	−305795.	+	305795.i	−0.990105	+	0.990105i	−0.999952	−	0.00984653i	$-0.996866\pi$
$157$	−305795.	+	305795.i	−0.990105	+	0.990105i	0.00984653	+	0.999952i	$0.496866\pi$
$158$		0			0
$159$	316849.			0.993937
$160$		0			0
$161$	642330.			1.95296
$162$		0			0
$163$	−188559.	+	188559.i	−0.555877	+	0.555877i	−0.928131	−	0.372254i	$-0.878585\pi$
$163$	−188559.	+	188559.i	−0.555877	+	0.555877i	0.372254	+	0.928131i	$0.378585\pi$
$164$		0			0
$165$	438750.	−	146250.i	1.25461	−	0.418202i
$166$		0			0
$167$	−157977.	−	157977.i	−0.438333	−	0.438333i	0.453118	−	0.891451i	$-0.350312\pi$
$167$	−157977.	−	157977.i	−0.438333	−	0.438333i	−0.891451	+	0.453118i	$0.850312\pi$
$168$		0			0
$169$			594757.i			1.60185i
$170$		0			0
$171$		−	123165.i		−	0.322104i
$172$		0			0
$173$	81465.0	+	81465.0i	0.206945	+	0.206945i	0.802968	−	0.596022i	$-0.203253\pi$
$173$	81465.0	+	81465.0i	0.206945	+	0.206945i	−0.596022	+	0.802968i	$0.703253\pi$
$174$		0			0
$175$	−78548.9	+	549842.i	−0.193885	+	1.35720i
$176$		0			0
$177$	−11700.0	+	11700.0i	−0.0280707	+	0.0280707i
$178$		0			0
$179$	−830314.			−1.93691			−0.968455	−	0.249187i	$-0.919837\pi$
$179$	−830314.			−1.93691			−0.968455	+	0.249187i	$0.919837\pi$
$180$		0			0
$181$	−444618.			−1.00877			−0.504383	−	0.863480i	$-0.668280\pi$
$181$	−444618.			−1.00877			−0.504383	+	0.863480i	$0.668280\pi$
$182$		0			0
$183$	260824.	−	260824.i	0.575731	−	0.575731i
$184$		0			0
$185$	−128875.	−	386625.i	−0.276847	−	0.830540i
$186$		0			0
$187$	39798.1	+	39798.1i	0.0832258	+	0.0832258i
$188$		0			0
$189$		−	336960.i		−	0.686158i
$190$		0			0
$191$		−	803921.i		−	1.59452i	−0.603636	−	0.797260i	$-0.706282\pi$
$191$		−	803921.i		−	1.59452i	0.603636	−	0.797260i	$-0.293718\pi$
$192$		0			0
$193$	69505.0	+	69505.0i	0.134314	+	0.134314i	0.771068	−	0.636753i	$-0.219723\pi$
$193$	69505.0	+	69505.0i	0.134314	+	0.134314i	−0.636753	+	0.771068i	$0.719723\pi$
$194$		0			0
$195$	485257.	−	970515.i	0.913872	−	1.82774i
$196$		0			0
$197$	627765.	−	627765.i	1.15248	−	1.15248i	0.166420	−	0.986055i	$-0.446779\pi$
$197$	627765.	−	627765.i	1.15248	−	1.15248i	0.986055	−	0.166420i	$-0.0532208\pi$
$198$		0			0
$199$	186004.			0.332958			0.166479	−	0.986045i	$-0.446760\pi$
$199$	186004.			0.332958			0.166479	+	0.986045i	$0.446760\pi$
$200$		0			0
$201$	−485550.			−0.847703
$202$		0			0
$203$	−361450.	+	361450.i	−0.615614	+	0.615614i
$204$		0			0
$205$	−230450.	+	460900.i	−0.382994	+	0.765988i
$206$		0			0
$207$	375652.	+	375652.i	0.609340	+	0.609340i
$208$		0			0
$209$		−	351000.i		−	0.555829i
$210$		0			0
$211$			396724.i			0.613455i	0.951797	+	0.306727i	$0.0992340\pi$
$211$			396724.i			0.613455i	−0.951797	+	0.306727i	$0.900766\pi$
$212$		0			0
$213$	−813150.	−	813150.i	−1.22807	−	1.22807i
$214$		0			0
$215$	−38750.8	−	116252.i	−0.0571721	−	0.171516i
$216$		0			0
$217$	−1.21095e6	+	1.21095e6i	−1.74573	+	1.74573i
$218$		0			0
$219$	−671820.			−0.946547
$220$		0			0
$221$	132050.			0.181869
$222$		0			0
$223$	17888.2	−	17888.2i	0.0240882	−	0.0240882i	−0.694960	−	0.719048i	$-0.744578\pi$
$223$	17888.2	−	17888.2i	0.0240882	−	0.0240882i	0.719048	+	0.694960i	$0.244578\pi$
$224$		0			0
$225$	−367500.	+	275625.i	−0.483951	+	0.362963i
$226$		0			0
$227$	293961.	+	293961.i	0.378639	+	0.378639i	0.870611	−	0.491972i	$-0.163724\pi$
$227$	293961.	+	293961.i	0.378639	+	0.378639i	−0.491972	+	0.870611i	$0.663724\pi$
$228$		0			0
$229$		−	413396.i		−	0.520928i	−0.965484	−	0.260464i	$-0.916124\pi$
$229$		−	413396.i		−	0.520928i	0.965484	−	0.260464i	$-0.0838755\pi$
$230$		0			0
$231$			1.47043e6i			1.81307i
$232$		0			0
$233$	−183695.	−	183695.i	−0.221670	−	0.221670i	0.587531	−	0.809202i	$-0.300100\pi$
$233$	−183695.	−	183695.i	−0.221670	−	0.221670i	−0.809202	+	0.587531i	$0.800100\pi$
$234$		0			0
$235$	−945728.	+	315243.i	−1.11711	+	0.372371i
$236$		0			0
$237$	1.31040e6	−	1.31040e6i	1.51542	−	1.51542i
$238$		0			0
$239$	1.09591e6			1.24103			0.620514	−	0.784195i	$-0.286924\pi$
$239$	1.09591e6			1.24103			0.620514	+	0.784195i	$0.286924\pi$
$240$		0			0
$241$	−1.05842e6			−1.17386			−0.586930	−	0.809638i	$-0.699664\pi$
$241$	−1.05842e6			−1.17386			−0.586930	+	0.809638i	$0.699664\pi$
$242$		0			0
$243$	695880.	−	695880.i	0.755995	−	0.755995i
$244$		0			0
$245$	−739150.	−	369575.i	−0.786715	−	0.393357i
$246$		0			0
$247$	−582309.	−	582309.i	−0.607311	−	0.607311i
$248$		0			0
$249$		−	995670.i		−	1.01769i
$250$		0			0
$251$			348129.i			0.348783i	0.984676	+	0.174391i	$0.0557958\pi$
$251$			348129.i			0.348783i	−0.984676	+	0.174391i	$0.944204\pi$
$252$		0			0
$253$	1.07055e6	+	1.07055e6i	1.05149	+	1.05149i
$254$		0			0
$255$	−132660.	−	66330.1i	−0.127759	−	0.0638793i
$256$		0			0
$257$	−160215.	+	160215.i	−0.151311	+	0.151311i	−0.778703	−	0.627392i	$-0.784122\pi$
$257$	−160215.	+	160215.i	−0.151311	+	0.151311i	0.627392	+	0.778703i	$0.284122\pi$
$258$		0			0
$259$	1.29574e6			1.20024
$260$		0			0
$261$	−422772.			−0.384154
$262$		0			0
$263$	218973.	−	218973.i	0.195210	−	0.195210i	−0.602733	−	0.797943i	$-0.705922\pi$
$263$	218973.	−	218973.i	0.195210	−	0.195210i	0.797943	+	0.602733i	$0.205922\pi$
$264$		0			0
$265$	−850875.	+	283625.i	−0.744305	+	0.248102i
$266$		0			0
$267$	−1.03749e6	−	1.03749e6i	−0.890645	−	0.890645i
$268$		0			0
$269$		−	507364.i		−	0.427503i	−0.976888	−	0.213751i	$-0.931432\pi$
$269$		−	507364.i		−	0.427503i	0.976888	−	0.213751i	$-0.0685682\pi$
$270$		0			0
$271$		−	1.29658e6i		−	1.07245i	−0.844076	−	0.536224i	$-0.819850\pi$
$271$		−	1.29658e6i		−	1.07245i	0.844076	−	0.536224i	$-0.180150\pi$
$272$		0			0
$273$	2.43945e6	+	2.43945e6i	1.98100	+	1.98100i
$274$		0			0
$275$	−1.04732e6	+	785489.i	−0.835116	+	0.626337i
$276$		0			0
$277$	682405.	−	682405.i	0.534371	−	0.534371i	−0.387499	−	0.921870i	$-0.626661\pi$
$277$	682405.	−	682405.i	0.534371	−	0.534371i	0.921870	+	0.387499i	$0.126661\pi$
$278$		0			0
$279$	−1.41639e6			−1.08936
$280$		0			0
$281$	729778.			0.551347			0.275673	−	0.961251i	$-0.411099\pi$
$281$	729778.			0.551347			0.275673	+	0.961251i	$0.411099\pi$
$282$		0			0
$283$	973377.	−	973377.i	0.722462	−	0.722462i	−0.246644	−	0.969106i	$-0.579328\pi$
$283$	973377.	−	973377.i	0.722462	−	0.722462i	0.969106	+	0.246644i	$0.0793278\pi$
$284$		0			0
$285$	292500.	+	877500.i	0.213311	+	0.639934i
$286$		0			0
$287$	−1.15850e6	−	1.15850e6i	−0.830217	−	0.830217i
$288$		0			0
$289$			1.40181e6i			0.987287i
$290$		0			0
$291$			1.37562e6i			0.952281i
$292$		0			0
$293$	622785.	+	622785.i	0.423808	+	0.423808i	0.886513	−	0.462705i	$-0.153121\pi$
$293$	622785.	+	622785.i	0.423808	+	0.423808i	−0.462705	+	0.886513i	$0.653121\pi$
$294$		0			0
$295$	20946.4	−	41892.7i	0.0140137	−	0.0280274i
$296$		0			0
$297$	561600.	−	561600.i	0.369433	−	0.369433i
$298$		0			0
$299$	3.55208e6			2.29776
$300$		0			0
$301$	389610.			0.247864
$302$		0			0
$303$	−1.40170e6	+	1.40170e6i	−0.877100	+	0.877100i
$304$		0			0
$305$	−466950.	+	933900.i	−0.287423	+	0.574845i
$306$		0			0
$307$	1.30844e6	+	1.30844e6i	0.792330	+	0.792330i	0.981873	−	0.189542i	$-0.0607004\pi$
$307$	1.30844e6	+	1.30844e6i	0.792330	+	0.792330i	−0.189542	+	0.981873i	$0.560700\pi$
$308$		0			0
$309$		−	1.53855e6i		−	0.916675i
$310$		0			0
$311$			1.48677e6i			0.871653i	0.900031	+	0.435826i	$0.143544\pi$
$311$			1.48677e6i			0.871653i	−0.900031	+	0.435826i	$0.856456\pi$
$312$		0			0
$313$	653225.	+	653225.i	0.376879	+	0.376879i	0.869975	−	0.493096i	$-0.164135\pi$
$313$	653225.	+	653225.i	0.376879	+	0.376879i	−0.493096	+	0.869975i	$0.664135\pi$
$314$		0			0
$315$	−461867.	−	1.38560e6i	−0.262265	−	0.786796i
$316$		0			0
$317$	1.08553e6	−	1.08553e6i	0.606725	−	0.606725i	−0.335364	−	0.942089i	$-0.608859\pi$
$317$	1.08553e6	−	1.08553e6i	0.606725	−	0.606725i	0.942089	+	0.335364i	$0.108859\pi$
$318$		0			0
$319$	−1.20483e6			−0.662904
$320$		0			0
$321$	1.82637e6			0.989296
$322$		0			0
$323$	−79596.2	+	79596.2i	−0.0424508	+	0.0424508i
$324$		0			0
$325$	−434375.	+	3.04063e6i	−0.228116	+	1.59681i
$326$		0			0
$327$	3.22959e6	+	3.22959e6i	1.67024	+	1.67024i
$328$		0			0
$329$		−	3.16953e6i		−	1.61438i
$330$		0			0
$331$		−	1.37785e6i		−	0.691246i	−0.938374	−	0.345623i	$-0.887668\pi$
$331$		−	1.37785e6i		−	0.691246i	0.938374	−	0.345623i	$-0.112332\pi$
$332$		0			0
$333$	757785.	+	757785.i	0.374486	+	0.374486i
$334$		0			0
$335$	1.30391e6	−	434637.i	0.634799	−	0.211600i
$336$		0			0
$337$	731425.	−	731425.i	0.350829	−	0.350829i	−0.509589	−	0.860418i	$-0.670203\pi$
$337$	731425.	−	731425.i	0.350829	−	0.350829i	0.860418	+	0.509589i	$0.170203\pi$
$338$		0			0
$339$	−5.07782e6			−2.39982
$340$		0			0
$341$	−4.03650e6			−1.87983
$342$		0			0
$343$	−254373.	+	254373.i	−0.116744	+	0.116744i
$344$		0			0
$345$	−3.56850e6	−	1.78425e6i	−1.61413	−	0.807064i
$346$		0			0
$347$	−1.68438e6	−	1.68438e6i	−0.750960	−	0.750960i	0.223699	−	0.974658i	$-0.428187\pi$
$347$	−1.68438e6	−	1.68438e6i	−0.750960	−	0.750960i	−0.974658	+	0.223699i	$0.928187\pi$
$348$		0			0
$349$			1.98680e6i			0.873155i	0.899667	+	0.436578i	$0.143810\pi$
$349$			1.98680e6i			0.873155i	−0.899667	+	0.436578i	$0.856190\pi$
$350$		0			0
$351$		−	1.86339e6i		−	0.807301i
$352$		0			0
$353$	1.98662e6	+	1.98662e6i	0.848553	+	0.848553i	0.989953	−	0.141399i	$-0.0451602\pi$
$353$	1.98662e6	+	1.98662e6i	0.848553	+	0.848553i	−0.141399	+	0.989953i	$0.545160\pi$
$354$		0			0
$355$	2.91154e6	+	1.45577e6i	1.22618	+	0.613088i
$356$		0			0
$357$	333450.	−	333450.i	0.138471	−	0.138471i
$358$		0			0
$359$	−1.34224e6			−0.549661			−0.274831	−	0.961493i	$-0.588622\pi$
$359$	−1.34224e6			−0.549661			−0.274831	+	0.961493i	$0.588622\pi$
$360$		0			0
$361$	−1.77410e6			−0.716490
$362$		0			0
$363$	−201769.	+	201769.i	−0.0803690	+	0.0803690i
$364$		0			0
$365$	1.80413e6	−	601375.i	0.708818	−	0.236273i
$366$		0			0
$367$	−882554.	−	882554.i	−0.342039	−	0.342039i	0.515094	−	0.857134i	$-0.327757\pi$
$367$	−882554.	−	882554.i	−0.342039	−	0.342039i	−0.857134	+	0.515094i	$0.827757\pi$
$368$		0			0
$369$		−	1.35505e6i		−	0.518070i
$370$		0			0
$371$		−	2.85164e6i		−	1.07562i
$372$		0			0
$373$	−2.80558e6	−	2.80558e6i	−1.04412	−	1.04412i	−0.998981	−	0.0451378i	$-0.985627\pi$
$373$	−2.80558e6	−	2.80558e6i	−1.04412	−	1.04412i	−0.0451378	−	0.998981i	$-0.514373\pi$
$374$		0			0
$375$	1.96372e6	−	2.83649e6i	0.721110	−	1.04160i
$376$		0			0
$377$	−1.99882e6	+	1.99882e6i	−0.724303	+	0.724303i
$378$		0			0
$379$	2.62667e6			0.939308			0.469654	−	0.882851i	$-0.344379\pi$
$379$	2.62667e6			0.939308			0.469654	+	0.882851i	$0.344379\pi$
$380$		0			0
$381$	−3.43863e6			−1.21359
$382$		0			0
$383$	2.16011e6	−	2.16011e6i	0.752454	−	0.752454i	−0.222483	−	0.974937i	$-0.571416\pi$
$383$	2.16011e6	−	2.16011e6i	0.752454	−	0.752454i	0.974937	+	0.222483i	$0.0714161\pi$
$384$		0			0
$385$	−1.31625e6	−	3.94875e6i	−0.452571	−	1.35771i
$386$		0			0
$387$	227855.	+	227855.i	0.0773357	+	0.0773357i
$388$		0			0
$389$		−	901324.i		−	0.302000i	−0.988534	−	0.151000i	$-0.951751\pi$
$389$		−	901324.i		−	0.302000i	0.988534	−	0.151000i	$-0.0482493\pi$
$390$		0			0
$391$		−	485537.i		−	0.160613i
$392$		0			0
$393$	−2.32245e6	−	2.32245e6i	−0.758516	−	0.758516i
$394$		0			0
$395$	−2.34599e6	+	4.69198e6i	−0.756543	+	1.51309i
$396$		0			0
$397$	658525.	−	658525.i	0.209699	−	0.209699i	−0.594441	−	0.804139i	$-0.702626\pi$
$397$	658525.	−	658525.i	0.209699	−	0.209699i	0.804139	+	0.594441i	$0.202626\pi$
$398$		0			0
$399$	−2.94087e6			−0.924791
$400$		0			0
$401$	3.90912e6			1.21400			0.606999	−	0.794702i	$-0.292373\pi$
$401$	3.90912e6			1.21400			0.606999	+	0.794702i	$0.292373\pi$
$402$		0			0
$403$	−6.69655e6	+	6.69655e6i	−2.05394	+	2.05394i
$404$		0			0
$405$	−1.82903e6	+	3.65805e6i	−0.554092	+	1.10818i
$406$		0			0
$407$	2.15957e6	+	2.15957e6i	0.646221	+	0.646221i
$408$		0			0
$409$		−	6.02390e6i		−	1.78061i	−0.455361	−	0.890307i	$-0.650490\pi$
$409$		−	6.02390e6i		−	1.78061i	0.455361	−	0.890307i	$-0.349510\pi$
$410$		0			0
$411$		−	1.06868e6i		−	0.312065i
$412$		0			0
$413$	105300.	+	105300.i	0.0303776	+	0.0303776i
$414$		0			0
$415$	891268.	+	2.67380e6i	0.254032	+	0.762095i
$416$		0			0
$417$	−573300.	+	573300.i	−0.161451	+	0.161451i
$418$		0			0
$419$	4.35768e6			1.21261			0.606304	−	0.795233i	$-0.292652\pi$
$419$	4.35768e6			1.21261			0.606304	+	0.795233i	$0.292652\pi$
$420$		0			0
$421$	−18482.0			−0.00508211			−0.00254105	−	0.999997i	$-0.500809\pi$
$421$	−18482.0			−0.00508211			−0.00254105	+	0.999997i	$0.500809\pi$
$422$		0			0
$423$	1.85363e6	−	1.85363e6i	0.503699	−	0.503699i
$424$		0			0
$425$	415625.	+	59375.0i	0.111617	+	0.0159452i
$426$		0			0
$427$	−2.34742e6	−	2.34742e6i	−0.623047	−	0.623047i
$428$		0			0
$429$			8.13150e6i			2.13318i
$430$		0			0
$431$			1.70629e6i			0.442446i	0.975223	+	0.221223i	$0.0710048\pi$
$431$			1.70629e6i			0.442446i	−0.975223	+	0.221223i	$0.928995\pi$
$432$		0			0
$433$	1.06674e6	+	1.06674e6i	0.273427	+	0.273427i	0.830478	−	0.557051i	$-0.188067\pi$
$433$	1.06674e6	+	1.06674e6i	0.273427	+	0.273427i	−0.557051	+	0.830478i	$0.688067\pi$
$434$		0			0
$435$	3.01209e6	−	1.00403e6i	0.763210	−	0.254403i
$436$		0			0
$437$	−2.14110e6	+	2.14110e6i	−0.536332	+	0.536332i
$438$		0			0
$439$	3.83570e6			0.949911			0.474956	−	0.880010i	$-0.342464\pi$
$439$	3.83570e6			0.949911			0.474956	+	0.880010i	$0.342464\pi$
$440$		0			0
$441$	2.17310e6			0.532088
$442$		0			0
$443$	−959720.	+	959720.i	−0.232346	+	0.232346i	−0.813671	−	0.581325i	$-0.802534\pi$
$443$	−959720.	+	959720.i	−0.232346	+	0.232346i	0.581325	+	0.813671i	$0.302534\pi$
$444$		0			0
$445$	3.71480e6	+	1.85740e6i	0.889274	+	0.444637i
$446$		0			0
$447$	2.85144e6	+	2.85144e6i	0.674987	+	0.674987i
$448$		0			0
$449$			2.34134e6i			0.548085i	0.961718	+	0.274042i	$0.0883609\pi$
$449$			2.34134e6i			0.548085i	−0.961718	+	0.274042i	$0.911639\pi$
$450$		0			0
$451$		−	3.86167e6i		−	0.893993i
$452$		0			0
$453$	−3.05955e6	−	3.05955e6i	−0.700506	−	0.700506i
$454$		0			0
$455$	−8.73463e6	−	4.36732e6i	−1.97795	−	0.988977i
$456$		0			0
$457$	1.63062e6	−	1.63062e6i	0.365228	−	0.365228i	−0.500506	−	0.865733i	$-0.666853\pi$
$457$	1.63062e6	−	1.63062e6i	0.365228	−	0.365228i	0.865733	+	0.500506i	$0.166853\pi$
$458$		0			0
$459$	−254708.			−0.0564300
$460$		0			0
$461$	2.39822e6			0.525578			0.262789	−	0.964853i	$-0.415358\pi$
$461$	2.39822e6			0.525578			0.262789	+	0.964853i	$0.415358\pi$
$462$		0			0
$463$	1.70332e6	−	1.70332e6i	0.369269	−	0.369269i	−0.497942	−	0.867211i	$-0.665911\pi$
$463$	1.70332e6	−	1.70332e6i	0.369269	−	0.369269i	0.867211	+	0.497942i	$0.165911\pi$
$464$		0			0
$465$	1.00912e7	−	3.36375e6i	2.16428	−	0.721425i
$466$		0			0
$467$	−3.78069e6	−	3.78069e6i	−0.802193	−	0.802193i	0.181245	−	0.983438i	$-0.441987\pi$
$467$	−3.78069e6	−	3.78069e6i	−0.802193	−	0.802193i	−0.983438	+	0.181245i	$0.941987\pi$
$468$		0			0
$469$			4.36995e6i			0.917370i
$470$		0			0
$471$			8.54039e6i			1.77388i
$472$		0			0
$473$	649350.	+	649350.i	0.133452	+	0.133452i
$474$		0			0
$475$	−1.57098e6	−	2.09464e6i	−0.319474	−	0.425966i
$476$		0			0
$477$	1.66772e6	−	1.66772e6i	0.335603	−	0.335603i
$478$		0			0
$479$	−3.68321e6			−0.733479			−0.366739	−	0.930324i	$-0.619526\pi$
$479$	−3.68321e6			−0.733479			−0.366739	+	0.930324i	$0.619526\pi$
$480$		0			0
$481$	7.16545e6			1.41215
$482$		0			0
$483$	8.96965e6	−	8.96965e6i	1.74947	−	1.74947i
$484$		0			0
$485$	−1.23138e6	−	3.69412e6i	−0.237704	−	0.713111i
$486$		0			0
$487$	−6.39999e6	−	6.39999e6i	−1.22280	−	1.22280i	−0.966631	−	0.256174i	$-0.917538\pi$
$487$	−6.39999e6	−	6.39999e6i	−1.22280	−	1.22280i	−0.256174	−	0.966631i	$-0.582462\pi$
$488$		0			0
$489$			5.26617e6i			0.995916i
$490$		0			0
$491$			5.75397e6i			1.07712i	0.842588	+	0.538559i	$0.181031\pi$
$491$			5.75397e6i			1.07712i	−0.842588	+	0.538559i	$0.818969\pi$
$492$		0			0
$493$	273220.	+	273220.i	0.0506285	+	0.0506285i
$494$		0			0
$495$	1.53956e6	−	3.07911e6i	0.282412	−	0.564824i
$496$		0			0
$497$	−7.31835e6	+	7.31835e6i	−1.32899	+	1.32899i
$498$		0			0
$499$	−3.52820e6			−0.634311			−0.317156	−	0.948374i	$-0.602728\pi$
$499$	−3.52820e6			−0.634311			−0.317156	+	0.948374i	$0.602728\pi$
$500$		0			0
$501$	−4.41207e6			−0.785323
$502$		0			0
$503$	407658.	−	407658.i	0.0718416	−	0.0718416i	−0.670273	−	0.742115i	$-0.733823\pi$
$503$	407658.	−	407658.i	0.0718416	−	0.0718416i	0.742115	+	0.670273i	$0.233823\pi$
$504$		0			0
$505$	2.50945e6	−	5.01890e6i	0.437875	−	0.875750i
$506$		0			0
$507$	8.30533e6	+	8.30533e6i	1.43495	+	1.43495i
$508$		0			0
$509$			7.05256e6i			1.20657i	0.797526	+	0.603285i	$0.206142\pi$
$509$			7.05256e6i			1.20657i	−0.797526	+	0.603285i	$0.793858\pi$
$510$		0			0
$511$			6.04638e6i			1.02434i
$512$		0			0
$513$	1.12320e6	+	1.12320e6i	0.188436	+	0.188436i
$514$		0			0
$515$	1.37722e6	+	4.13167e6i	0.228816	+	0.686448i
$516$		0			0
$517$	5.28255e6	−	5.28255e6i	0.869195	−	0.869195i
$518$		0			0
$519$	2.27519e6			0.370766
$520$		0			0
$521$	6.26348e6			1.01093			0.505466	−	0.862847i	$-0.331321\pi$
$521$	6.26348e6			1.01093			0.505466	+	0.862847i	$0.331321\pi$
$522$		0			0
$523$	1.57529e6	−	1.57529e6i	0.251830	−	0.251830i	−0.569891	−	0.821720i	$-0.693015\pi$
$523$	1.57529e6	−	1.57529e6i	0.251830	−	0.251830i	0.821720	+	0.569891i	$0.193015\pi$
$524$		0			0
$525$	6.58125e6	+	8.77500e6i	1.04210	+	1.38947i
$526$		0			0
$527$	915356.	+	915356.i	0.143570	+	0.143570i
$528$		0			0
$529$		−	6.62437e6i		−	1.02921i
$530$		0			0
$531$			123165.i			0.0189561i
$532$		0			0
$533$	−6.40651e6	−	6.40651e6i	−0.976795	−	0.976795i
$534$		0			0
$535$	−4.90459e6	+	1.63486e6i	−0.740830	+	0.246943i
$536$		0			0
$537$	−1.15947e7	+	1.15947e7i	−1.73510	+	1.73510i
$538$		0			0
$539$	6.19300e6			0.918183
$540$		0			0
$541$	4.32838e6			0.635817			0.317909	−	0.948121i	$-0.397019\pi$
$541$	4.32838e6			0.635817			0.317909	+	0.948121i	$0.397019\pi$
$542$		0			0
$543$	−6.20875e6	+	6.20875e6i	−0.903659	+	0.903659i
$544$		0			0
$545$	−1.15638e7	−	5.78190e6i	−1.66767	−	0.833833i
$546$		0			0
$547$	2.31554e6	+	2.31554e6i	0.330890	+	0.330890i	0.852924	−	0.522035i	$-0.174827\pi$
$547$	2.31554e6	+	2.31554e6i	0.330890	+	0.330890i	−0.522035	+	0.852924i	$0.674827\pi$
$548$		0			0
$549$		−	2.74567e6i		−	0.388792i
$550$		0			0
$551$		−	2.40967e6i		−	0.338126i
$552$		0			0
$553$	−1.17936e7	−	1.17936e7i	−1.63996	−	1.63996i
$554$		0			0
$555$	−7.19857e6	−	3.59928e6i	−0.992004	−	0.496002i
$556$		0			0
$557$	−2.07216e6	+	2.07216e6i	−0.282999	+	0.282999i	−0.834304	−	0.551305i	$-0.814130\pi$
$557$	−2.07216e6	+	2.07216e6i	−0.282999	+	0.282999i	0.551305	+	0.834304i	$0.314130\pi$
$558$		0			0
$559$	2.15454e6			0.291626
$560$		0			0
$561$	1.11150e6			0.149108
$562$		0			0
$563$	−4.08894e6	+	4.08894e6i	−0.543675	+	0.543675i	−0.924604	−	0.380929i	$-0.875604\pi$
$563$	−4.08894e6	+	4.08894e6i	−0.543675	+	0.543675i	0.380929	+	0.924604i	$0.375604\pi$
$564$		0			0
$565$	1.36361e7	−	4.54538e6i	1.79709	−	0.599030i
$566$		0			0
$567$	−9.19474e6	−	9.19474e6i	−1.20111	−	1.20111i
$568$		0			0
$569$			8.71458e6i			1.12841i	0.825636	+	0.564203i	$0.190817\pi$
$569$			8.71458e6i			1.12841i	−0.825636	+	0.564203i	$0.809183\pi$
$570$		0			0
$571$			1.40383e6i			0.180187i	0.995933	+	0.0900933i	$0.0287165\pi$
$571$			1.40383e6i			0.180187i	−0.995933	+	0.0900933i	$0.971283\pi$
$572$		0			0
$573$	−1.12261e7	−	1.12261e7i	−1.42838	−	1.42838i
$574$		0			0
$575$	1.11801e7	+	1.59716e6i	1.41019	+	0.201455i
$576$		0			0
$577$	520025.	−	520025.i	0.0650256	−	0.0650256i	−0.673846	−	0.738872i	$-0.735359\pi$
$577$	520025.	−	520025.i	0.0650256	−	0.0650256i	0.738872	+	0.673846i	$0.235359\pi$
$578$		0			0
$579$	1.94117e6			0.240640
$580$		0			0
$581$	−8.96103e6			−1.10133
$582$		0			0
$583$	4.75273e6	−	4.75273e6i	0.579124	−	0.579124i
$584$		0			0
$585$	−2.55412e6	−	7.66238e6i	−0.308569	−	0.925707i
$586$		0			0
$587$	−5.51706e6	−	5.51706e6i	−0.660865	−	0.660865i	0.294719	−	0.955584i	$-0.404774\pi$
$587$	−5.51706e6	−	5.51706e6i	−0.660865	−	0.660865i	−0.955584	+	0.294719i	$0.904774\pi$
$588$		0			0
$589$		−	8.07300e6i		−	0.958841i
$590$		0			0
$591$		−	1.75325e7i		−	2.06479i
$592$		0			0
$593$	4.30247e6	+	4.30247e6i	0.502436	+	0.502436i	0.912194	−	0.409758i	$-0.134387\pi$
$593$	4.30247e6	+	4.30247e6i	0.502436	+	0.502436i	−0.409758	+	0.912194i	$0.634387\pi$
$594$		0			0
$595$	−596971.	+	1.19394e6i	−0.0691291	+	0.138258i
$596$		0			0
$597$	2.59740e6	−	2.59740e6i	0.298265	−	0.298265i
$598$		0			0
$599$	2.73643e6			0.311615			0.155807	−	0.987787i	$-0.450202\pi$
$599$	2.73643e6			0.311615			0.155807	+	0.987787i	$0.450202\pi$
$600$		0			0
$601$	−1.17552e7			−1.32753			−0.663763	−	0.747943i	$-0.731042\pi$
$601$	−1.17552e7			−1.32753			−0.663763	+	0.747943i	$0.731042\pi$
$602$		0			0
$603$	−2.55567e6	+	2.55567e6i	−0.286227	+	0.286227i
$604$		0			0
$605$	361225.	−	722450.i	0.0401226	−	0.0802453i
$606$		0			0
$607$	1.17620e7	+	1.17620e7i	1.29572	+	1.29572i	0.931195	+	0.364521i	$0.118767\pi$
$607$	1.17620e7	+	1.17620e7i	1.29572	+	1.29572i	0.364521	+	0.931195i	$0.381233\pi$
$608$		0			0
$609$			1.00948e7i			1.10294i
$610$		0			0
$611$		−	1.75275e7i		−	1.89940i
$612$		0			0
$613$	65465.0	+	65465.0i	0.00703652	+	0.00703652i	0.710616	−	0.703580i	$-0.248416\pi$
$613$	65465.0	+	65465.0i	0.00703652	+	0.00703652i	−0.703580	+	0.710616i	$0.748416\pi$
$614$		0			0
$615$	3.21806e6	+	9.65418e6i	0.343089	+	1.02927i
$616$		0			0
$617$	−4.05174e6	+	4.05174e6i	−0.428478	+	0.428478i	−0.888110	−	0.459632i	$-0.847981\pi$
$617$	−4.05174e6	+	4.05174e6i	−0.428478	+	0.428478i	0.459632	+	0.888110i	$0.347981\pi$
$618$		0			0
$619$	−9.59595e6			−1.00661			−0.503305	−	0.864109i	$-0.667883\pi$
$619$	−9.59595e6			−1.00661			−0.503305	+	0.864109i	$0.667883\pi$
$620$		0			0
$621$	−6.85152e6			−0.712948
$622$		0			0
$623$	−9.33738e6	+	9.33738e6i	−0.963840	+	0.963840i
$624$		0			0
$625$	−2.73438e6	+	9.37500e6i	−0.280000	+	0.960000i
$626$		0			0
$627$	−4.90145e6	−	4.90145e6i	−0.497915	−	0.497915i
$628$		0			0
$629$		−	979450.i		−	0.0987088i
$630$		0			0
$631$		−	5.59142e6i		−	0.559048i	−0.960139	−	0.279524i	$-0.909823\pi$
$631$		−	5.59142e6i		−	0.559048i	0.960139	−	0.279524i	$-0.0901766\pi$
$632$		0			0
$633$	5.53995e6	+	5.53995e6i	0.549537	+	0.549537i
$634$		0			0
$635$	9.23420e6	−	3.07807e6i	0.908793	−	0.302931i
$636$		0			0
$637$	1.02742e7	−	1.02742e7i	1.00323	−	1.00323i
$638$		0			0
$639$	−8.55994e6			−0.829313
$640$		0			0
$641$	1.09802e7			1.05552			0.527759	−	0.849394i	$-0.323032\pi$
$641$	1.09802e7			1.05552			0.527759	+	0.849394i	$0.323032\pi$
$642$		0			0
$643$	−1.04686e6	+	1.04686e6i	−0.0998527	+	0.0998527i	−0.755268	−	0.655416i	$-0.772493\pi$
$643$	−1.04686e6	+	1.04686e6i	−0.0998527	+	0.0998527i	0.655416	+	0.755268i	$0.272493\pi$
$644$		0			0
$645$	−2.16450e6	−	1.08225e6i	−0.204861	−	0.102430i
$646$		0			0
$647$	8.50443e6	+	8.50443e6i	0.798702	+	0.798702i	0.982891	−	0.184189i	$-0.0589659\pi$
$647$	8.50443e6	+	8.50443e6i	0.798702	+	0.798702i	−0.184189	+	0.982891i	$0.558966\pi$
$648$		0			0
$649$			351000.i			0.0327111i
$650$		0			0
$651$			3.38200e7i			3.12767i
$652$		0			0
$653$	−428015.	−	428015.i	−0.0392804	−	0.0392804i	0.687194	−	0.726474i	$-0.258842\pi$
$653$	−428015.	−	428015.i	−0.0392804	−	0.0392804i	−0.726474	+	0.687194i	$0.758842\pi$
$654$		0			0
$655$	8.31570e6	+	4.15785e6i	0.757349	+	0.378674i
$656$		0			0
$657$	−3.53608e6	+	3.53608e6i	−0.319602	+	0.319602i
$658$		0			0
$659$	−1.76243e7			−1.58088			−0.790438	−	0.612543i	$-0.790147\pi$
$659$	−1.76243e7			−1.58088			−0.790438	+	0.612543i	$0.790147\pi$
$660$		0			0
$661$	1.19379e7			1.06273			0.531367	−	0.847141i	$-0.321678\pi$
$661$	1.19379e7			1.06273			0.531367	+	0.847141i	$0.321678\pi$
$662$		0			0
$663$	1.84398e6	−	1.84398e6i	0.162919	−	0.162919i
$664$		0			0
$665$	7.89750e6	−	2.63250e6i	0.692525	−	0.230842i
$666$		0			0
$667$	7.34949e6	+	7.34949e6i	0.639650	+	0.639650i
$668$		0			0
$669$		−	499590.i		−	0.0431567i
$670$		0			0
$671$		−	7.82472e6i		−	0.670907i
$672$		0			0
$673$	2.24978e6	+	2.24978e6i	0.191471	+	0.191471i	0.796332	−	0.604860i	$-0.206771\pi$
$673$	2.24978e6	+	2.24978e6i	0.191471	+	0.191471i	−0.604860	+	0.796332i	$0.706771\pi$
$674$		0			0
$675$	837854.	−	5.86498e6i	0.0707798	−	0.495458i
$676$		0			0
$677$	−3.74008e6	+	3.74008e6i	−0.313624	+	0.313624i	−0.846312	−	0.532688i	$-0.821182\pi$
$677$	−3.74008e6	+	3.74008e6i	−0.313624	+	0.313624i	0.532688	+	0.846312i	$0.321182\pi$
$678$		0			0
$679$	1.23806e7			1.03054
$680$		0			0
$681$	8.20989e6			0.678375
$682$		0			0
$683$	1.13021e7	−	1.13021e7i	0.927060	−	0.927060i	−0.0704550	−	0.997515i	$-0.522445\pi$
$683$	1.13021e7	−	1.13021e7i	0.927060	−	0.927060i	0.997515	+	0.0704550i	$0.0224451\pi$
$684$		0			0
$685$	956625.	+	2.86988e6i	0.0778960	+	0.233688i
$686$		0			0
$687$	−5.77276e6	−	5.77276e6i	−0.466650	−	0.466650i
$688$		0			0
$689$		−	1.57696e7i		−	1.26553i
$690$		0			0
$691$		−	2.15706e6i		−	0.171857i	−0.996301	−	0.0859283i	$-0.972614\pi$
$691$		−	2.15706e6i		−	0.171857i	0.996301	−	0.0859283i	$-0.0273856\pi$
$692$		0			0
$693$	7.73955e6	+	7.73955e6i	0.612185	+	0.612185i
$694$		0			0
$695$	1.02637e6	−	2.05274e6i	0.0806014	−	0.161203i
$696$		0			0
$697$	−875710.	+	875710.i	−0.0682776	+	0.0682776i
$698$		0			0
$699$	−5.13032e6			−0.397147
$700$		0			0
$701$	1.74934e7			1.34456			0.672278	−	0.740298i	$-0.265316\pi$
$701$	1.74934e7			1.34456			0.672278	+	0.740298i	$0.265316\pi$
$702$		0			0
$703$	−4.31914e6	+	4.31914e6i	−0.329616	+	0.329616i
$704$		0			0
$705$	−8.80425e6	+	1.76085e7i	−0.667144	+	1.33429i
$706$		0			0
$707$	1.26153e7	+	1.26153e7i	0.949183	+	0.949183i
$708$		0			0
$709$			1.36270e7i			1.01809i	0.860741	+	0.509043i	$0.170001\pi$
$709$			1.36270e7i			1.01809i	−0.860741	+	0.509043i	$0.829999\pi$
$710$		0			0
$711$		−	1.37944e7i		−	1.02336i
$712$		0			0
$713$	2.46226e7	+	2.46226e7i	1.81389	+	1.81389i
$714$		0			0
$715$	−7.27886e6	−	2.18366e7i	−0.532474	−	1.59742i
$716$		0			0
$717$	1.53036e7	−	1.53036e7i	1.11172	−	1.11172i
$718$		0			0
$719$	−7.26252e6			−0.523920			−0.261960	−	0.965079i	$-0.584369\pi$
$719$	−7.26252e6			−0.523920			−0.261960	+	0.965079i	$0.584369\pi$
$720$		0			0
$721$	−1.38470e7			−0.992010
$722$		0			0
$723$	−1.47801e7	+	1.47801e7i	−1.05155	+	1.05155i
$724$		0			0
$725$	−7.19000e6	+	5.39250e6i	−0.508024	+	0.381018i
$726$		0			0
$727$	−1.70374e7	−	1.70374e7i	−1.19555	−	1.19555i	−0.975486	−	0.220062i	$-0.929374\pi$
$727$	−1.70374e7	−	1.70374e7i	−1.19555	−	1.19555i	−0.220062	−	0.975486i	$-0.570626\pi$
$728$		0			0
$729$		−	1.65675e6i		−	0.115462i
$730$		0			0
$731$		−	294506.i		−	0.0203845i
$732$		0			0
$733$	4.93802e6	+	4.93802e6i	0.339464	+	0.339464i	0.856165	−	0.516702i	$-0.172840\pi$
$733$	4.93802e6	+	4.93802e6i	0.339464	+	0.339464i	−0.516702	+	0.856165i	$0.672840\pi$
$734$		0			0
$735$	−1.54825e7	+	5.16083e6i	−1.05712	+	0.352372i
$736$		0			0
$737$	−7.28325e6	+	7.28325e6i	−0.493920	+	0.493920i
$738$		0			0
$739$	8.95247e6			0.603020			0.301510	−	0.953463i	$-0.402509\pi$
$739$	8.95247e6			0.603020			0.301510	+	0.953463i	$0.402509\pi$
$740$		0			0
$741$	−1.62630e7			−1.08807
$742$		0			0
$743$	318175.	−	318175.i	0.0211443	−	0.0211443i	−0.696456	−	0.717600i	$-0.745241\pi$
$743$	318175.	−	318175.i	0.0211443	−	0.0211443i	0.717600	+	0.696456i	$0.245241\pi$
$744$		0			0
$745$	−1.02098e7	−	5.10490e6i	−0.673948	−	0.336974i
$746$		0			0
$747$	−5.24065e6	−	5.24065e6i	−0.343624	−	0.343624i
$748$		0			0
$749$		−	1.64373e7i		−	1.07060i
$750$		0			0
$751$			4.49467e6i			0.290802i	0.989373	+	0.145401i	$0.0464473\pi$
$751$			4.49467e6i			0.290802i	−0.989373	+	0.145401i	$0.953553\pi$
$752$		0			0
$753$	4.86135e6	+	4.86135e6i	0.312442	+	0.312442i
$754$		0			0
$755$	1.09549e7	+	5.47747e6i	0.699428	+	0.349714i
$756$		0			0
$757$	1.86118e7	−	1.86118e7i	1.18045	−	1.18045i	0.200823	−	0.979627i	$-0.435638\pi$
$757$	1.86118e7	−	1.86118e7i	1.18045	−	1.18045i	0.979627	−	0.200823i	$-0.0643617\pi$
$758$		0			0
$759$	2.98988e7			1.88387
$760$		0			0
$761$	−9.57628e6			−0.599425			−0.299713	−	0.954030i	$-0.596891\pi$
$761$	−9.57628e6			−0.599425			−0.299713	+	0.954030i	$0.596891\pi$
$762$		0			0
$763$	2.90663e7	−	2.90663e7i	1.80750	−	1.80750i
$764$		0			0
$765$	−1.04738e6	+	349125.i	−0.0647066	+	0.0215689i
$766$		0			0
$767$	582309.	+	582309.i	0.0357409	+	0.0357409i
$768$		0			0
$769$		−	6.01858e6i		−	0.367010i	−0.983019	−	0.183505i	$-0.941256\pi$
$769$		−	6.01858e6i		−	0.367010i	0.983019	−	0.183505i	$-0.0587444\pi$
$770$		0			0
$771$			4.47456e6i			0.271091i
$772$		0			0
$773$	9.70370e6	+	9.70370e6i	0.584102	+	0.584102i	0.936028	−	0.351926i	$-0.114473\pi$
$773$	9.70370e6	+	9.70370e6i	0.584102	+	0.584102i	−0.351926	+	0.936028i	$0.614473\pi$
$774$		0			0
$775$	−2.40883e7	+	1.80662e7i	−1.44063	+	1.08047i
$776$		0			0
$777$	1.80940e7	−	1.80940e7i	1.07519	−	1.07519i
$778$		0			0
$779$	7.72334e6			0.455997
$780$		0			0
$781$	−2.43945e7			−1.43108
$782$		0			0
$783$	3.85547e6	−	3.85547e6i	0.224736	−	0.224736i
$784$		0			0
$785$	−7.64488e6	−	2.29346e7i	−0.442788	−	1.32837i
$786$		0			0
$787$	−1.56306e6	−	1.56306e6i	−0.0899578	−	0.0899578i	0.660696	−	0.750654i	$-0.270261\pi$
$787$	−1.56306e6	−	1.56306e6i	−0.0899578	−	0.0899578i	−0.750654	+	0.660696i	$0.770261\pi$
$788$		0			0
$789$		−	6.11559e6i		−	0.349740i
$790$		0			0
$791$			4.57003e7i			2.59704i
$792$		0			0
$793$	−1.29812e7	−	1.29812e7i	−0.733048	−	0.733048i
$794$		0			0
$795$	−7.92122e6	+	1.58424e7i	−0.444502	+	0.889005i
$796$		0			0
$797$	−1.96731e7	+	1.96731e7i	−1.09705	+	1.09705i	−0.102299	+	0.994754i	$0.532620\pi$
$797$	−1.96731e7	+	1.96731e7i	−1.09705	+	1.09705i	−0.994754	+	0.102299i	$0.967380\pi$
$798$		0			0
$799$	−2.39584e6			−0.132767
$800$		0			0
$801$	−1.09215e7			−0.601453
$802$		0			0
$803$	−1.00773e7	+	1.00773e7i	−0.551512	+	0.551512i
$804$		0			0
$805$	−1.60582e7	+	3.21165e7i	−0.873391	+	1.74678i
$806$		0			0
$807$	−7.08495e6	−	7.08495e6i	−0.382960	−	0.382960i
$808$		0			0
$809$		−	2.70507e7i		−	1.45314i	−0.687093	−	0.726569i	$-0.741114\pi$
$809$		−	2.70507e7i		−	1.45314i	0.687093	−	0.726569i	$-0.258886\pi$
$810$		0			0
$811$			1.56205e7i			0.833957i	0.908916	+	0.416979i	$0.136911\pi$
$811$			1.56205e7i			0.833957i	−0.908916	+	0.416979i	$0.863089\pi$
$812$		0			0
$813$	−1.81057e7	−	1.81057e7i	−0.960705	−	0.960705i
$814$		0			0
$815$	−4.71398e6	−	1.41419e7i	−0.248596	−	0.745787i
$816$		0			0
$817$	−1.29870e6	+	1.29870e6i	−0.0680697	+	0.0680697i
$818$		0			0
$819$	2.56798e7			1.33777
$820$		0			0
$821$	1.73448e6			0.0898071			0.0449036	−	0.998991i	$-0.485702\pi$
$821$	1.73448e6			0.0898071			0.0449036	+	0.998991i	$0.485702\pi$
$822$		0			0
$823$	−1.15442e7	+	1.15442e7i	−0.594105	+	0.594105i	−0.938738	−	0.344633i	$-0.888003\pi$
$823$	−1.15442e7	+	1.15442e7i	−0.594105	+	0.594105i	0.344633	+	0.938738i	$0.388003\pi$
$824$		0			0
$825$	−3.65625e6	+	2.55938e7i	−0.187026	+	1.30918i
$826$		0			0
$827$	−1.40364e7	−	1.40364e7i	−0.713659	−	0.713659i	0.253640	−	0.967299i	$-0.418372\pi$
$827$	−1.40364e7	−	1.40364e7i	−0.713659	−	0.713659i	−0.967299	+	0.253640i	$0.918372\pi$
$828$		0			0
$829$			8.17528e6i			0.413158i	0.978430	+	0.206579i	$0.0662330\pi$
$829$			8.17528e6i			0.413158i	−0.978430	+	0.206579i	$0.933767\pi$
$830$		0			0
$831$		−	1.90585e7i		−	0.957386i
$832$		0			0
$833$	−1.40439e6	−	1.40439e6i	−0.0701251	−	0.0701251i
$834$		0			0
$835$	1.18483e7	−	3.94944e6i	0.588085	−	0.196028i
$836$		0			0
$837$	1.29168e7	−	1.29168e7i	0.637296	−	0.637296i
$838$		0			0
$839$	−8.59806e6			−0.421692			−0.210846	−	0.977519i	$-0.567622\pi$
$839$	−8.59806e6			−0.421692			−0.210846	+	0.977519i	$0.567622\pi$
$840$		0			0
$841$	1.22398e7			0.596738
$842$		0			0
$843$	1.01908e7	−	1.01908e7i	0.493900	−	0.493900i
$844$		0			0
$845$	−2.97378e7	−	1.48689e7i	−1.43274	−	0.716371i
$846$		0			0
$847$	1.81592e6	+	1.81592e6i	0.0869739	+	0.0869739i
$848$		0			0
$849$		−	2.71850e7i		−	1.29437i
$850$		0			0
$851$		−	2.63468e7i		−	1.24711i
$852$		0			0
$853$	2.98181e7	+	2.98181e7i	1.40316	+	1.40316i	0.789813	+	0.613348i	$0.210178\pi$
$853$	2.98181e7	+	2.98181e7i	1.40316	+	1.40316i	0.613348	+	0.789813i	$0.289822\pi$
$854$		0			0
$855$	6.15823e6	+	3.07911e6i	0.288098	+	0.144049i
$856$		0			0
$857$	2.65803e6	−	2.65803e6i	0.123625	−	0.123625i	−0.642587	−	0.766212i	$-0.722139\pi$
$857$	2.65803e6	−	2.65803e6i	0.123625	−	0.123625i	0.766212	+	0.642587i	$0.222139\pi$
$858$		0			0
$859$	−3.94403e7			−1.82372			−0.911859	−	0.410504i	$-0.865353\pi$
$859$	−3.94403e7			−1.82372			−0.911859	+	0.410504i	$0.865353\pi$
$860$		0			0
$861$	−3.23552e7			−1.48743
$862$		0			0
$863$	3.00362e7	−	3.00362e7i	1.37283	−	1.37283i	0.516618	−	0.856216i	$-0.327191\pi$
$863$	3.00362e7	−	3.00362e7i	1.37283	−	1.37283i	0.856216	−	0.516618i	$-0.172809\pi$
$864$		0			0
$865$	−6.10988e6	+	2.03662e6i	−0.277646	+	0.0925488i
$866$		0			0
$867$	1.95752e7	+	1.95752e7i	0.884418	+	0.884418i
$868$		0			0
$869$		−	3.93120e7i		−	1.76594i
$870$		0			0
$871$			2.41658e7i			1.07933i
$872$		0			0
$873$	7.24048e6	+	7.24048e6i	0.321538	+	0.321538i
$874$		0			0
$875$	−2.55284e7	−	1.76735e7i	−1.12721	−	0.780373i
$876$		0			0
$877$	−2.78300e7	+	2.78300e7i	−1.22184	+	1.22184i	−0.254864	+	0.966977i	$0.582031\pi$
$877$	−2.78300e7	+	2.78300e7i	−1.22184	+	1.22184i	−0.966977	+	0.254864i	$0.917969\pi$
$878$		0			0
$879$	1.73934e7			0.759300
$880$		0			0
$881$	4.21278e6			0.182864			0.0914321	−	0.995811i	$-0.470856\pi$
$881$	4.21278e6			0.182864			0.0914321	+	0.995811i	$0.470856\pi$
$882$		0			0
$883$	−1.24366e7	+	1.24366e7i	−0.536787	+	0.536787i	−0.922584	−	0.385797i	$-0.873926\pi$
$883$	−1.24366e7	+	1.24366e7i	−0.536787	+	0.536787i	0.385797	+	0.922584i	$0.373926\pi$
$884$		0			0
$885$	−292500.	−	877500.i	−0.0125536	−	0.0376607i
$886$		0			0
$887$	−1.07191e6	−	1.07191e6i	−0.0457456	−	0.0457456i	0.683864	−	0.729610i	$-0.260298\pi$
$887$	−1.07191e6	−	1.07191e6i	−0.0457456	−	0.0457456i	−0.729610	+	0.683864i	$0.760298\pi$
$888$		0			0
$889$			3.09477e7i			1.31333i
$890$		0			0
$891$		−	3.06491e7i		−	1.29337i
$892$		0			0
$893$	1.05651e7	+	1.05651e7i	0.443348	+	0.443348i
$894$		0			0
$895$	2.07578e7	−	4.15157e7i	0.866213	−	1.73243i
$896$		0			0
$897$	4.96021e7	−	4.96021e7i	2.05835	−	2.05835i
$898$		0			0
$899$	−2.77112e7			−1.14355
$900$		0			0
$901$	−2.15555e6			−0.0884598
$902$		0			0
$903$	5.44061e6	−	5.44061e6i	0.222038	−	0.222038i
$904$		0			0
$905$	1.11154e7	−	2.22309e7i	0.451134	−	0.902268i
$906$		0			0
$907$	1.60054e7	+	1.60054e7i	0.646024	+	0.646024i	0.952030	−	0.306006i	$-0.0989927\pi$
$907$	1.60054e7	+	1.60054e7i	0.646024	+	0.646024i	−0.306006	+	0.952030i	$0.598993\pi$
$908$		0			0
$909$			1.47556e7i			0.592306i
$910$		0			0
$911$			1.50483e7i			0.600746i	0.953822	+	0.300373i	$0.0971112\pi$
$911$			1.50483e7i			0.600746i	−0.953822	+	0.300373i	$0.902889\pi$
$912$		0			0
$913$	−1.49350e7	−	1.49350e7i	−0.592966	−	0.592966i
$914$		0			0
$915$	6.52060e6	+	1.95618e7i	0.257475	+	0.772425i
$916$		0			0
$917$	−2.09020e7	+	2.09020e7i	−0.820853	+	0.820853i
$918$		0			0
$919$	−8.45060e6			−0.330064			−0.165032	−	0.986288i	$-0.552773\pi$
$919$	−8.45060e6			−0.330064			−0.165032	+	0.986288i	$0.552773\pi$
$920$		0			0
$921$	3.65426e7			1.41955
$922$		0			0
$923$	−4.04705e7	+	4.04705e7i	−1.56363	+	1.56363i
$924$		0			0
$925$	2.25531e7	+	3.22188e6i	0.866667	+	0.123810i
$926$		0			0
$927$	−8.09807e6	−	8.09807e6i	−0.309515	−	0.309515i
$928$		0			0
$929$			2.19539e7i			0.834588i	0.908771	+	0.417294i	$0.137022\pi$
$929$			2.19539e7i			0.834588i	−0.908771	+	0.417294i	$0.862978\pi$
$930$		0			0
$931$			1.23860e7i			0.468335i
$932$		0			0
$933$	2.07617e7	+	2.07617e7i	0.780832	+	0.780832i
$934$		0			0
$935$	−2.98486e6	+	994952.i	−0.111659	+	0.0372197i
$936$		0			0
$937$	4.59650e6	−	4.59650e6i	0.171033	−	0.171033i	−0.616400	−	0.787433i	$-0.711410\pi$
$937$	4.59650e6	−	4.59650e6i	0.171033	−	0.171033i	0.787433	+	0.616400i	$0.211410\pi$
$938$		0			0
$939$	1.82436e7			0.675221
$940$		0			0
$941$	3.48051e7			1.28135			0.640677	−	0.767811i	$-0.278654\pi$
$941$	3.48051e7			1.28135			0.640677	+	0.767811i	$0.278654\pi$
$942$		0			0
$943$	−2.35562e7	+	2.35562e7i	−0.862633	+	0.862633i
$944$		0			0
$945$	1.68480e7	+	8.42400e6i	0.613718	+	0.306859i
$946$		0			0
$947$	1.83175e7	+	1.83175e7i	0.663732	+	0.663732i	0.956258	−	0.292526i	$-0.0944958\pi$
$947$	1.83175e7	+	1.83175e7i	0.663732	+	0.663732i	−0.292526	+	0.956258i	$0.594496\pi$
$948$		0			0
$949$			3.34365e7i			1.20519i
$950$		0			0
$951$		−	3.03171e7i		−	1.08702i
$952$		0			0
$953$	1.99314e7	+	1.99314e7i	0.710895	+	0.710895i	0.966722	−	0.255828i	$-0.0823480\pi$
$953$	1.99314e7	+	1.99314e7i	0.710895	+	0.710895i	−0.255828	+	0.966722i	$0.582348\pi$
$954$		0			0
$955$	4.01961e7	+	2.00980e7i	1.42618	+	0.713091i
$956$		0			0
$957$	−1.68246e7	+	1.68246e7i	−0.593834	+	0.593834i
$958$		0			0
$959$	−9.61815e6			−0.337711
$960$		0			0
$961$	−6.42103e7			−2.24283
$962$		0			0
$963$	9.61300e6	−	9.61300e6i	0.334036	−	0.334036i
$964$		0			0
$965$	−5.21288e6	+	1.73762e6i	−0.180202	+	0.0600673i
$966$		0			0
$967$	3.06617e7	+	3.06617e7i	1.05446	+	1.05446i	0.998429	+	0.0560293i	$0.0178440\pi$
$967$	3.06617e7	+	3.06617e7i	1.05446	+	1.05446i	0.0560293	+	0.998429i	$0.482156\pi$
$968$		0			0
$969$			2.22300e6i			0.0760554i
$970$		0			0
$971$		−	7.93658e6i		−	0.270138i	−0.990836	−	0.135069i	$-0.956874\pi$
$971$		−	7.93658e6i		−	0.270138i	0.990836	−	0.135069i	$-0.0431256\pi$
$972$		0			0
$973$	5.15970e6	+	5.15970e6i	0.174720	+	0.174720i
$974$		0			0
$975$	3.63943e7	+	4.85257e7i	1.22609	+	1.63478i
$976$		0			0
$977$	1.81534e7	−	1.81534e7i	0.608445	−	0.608445i	−0.334095	−	0.942540i	$-0.608431\pi$
$977$	1.81534e7	−	1.81534e7i	0.608445	−	0.608445i	0.942540	+	0.334095i	$0.108431\pi$
$978$		0			0
$979$	−3.11246e7			−1.03788
$980$		0			0
$981$	3.39976e7			1.12791
$982$		0			0
$983$	2.49746e7	−	2.49746e7i	0.824354	−	0.824354i	−0.162375	−	0.986729i	$-0.551915\pi$
$983$	2.49746e7	−	2.49746e7i	0.824354	−	0.824354i	0.986729	+	0.162375i	$0.0519154\pi$
$984$		0			0
$985$	1.56941e7	+	4.70824e7i	0.515403	+	1.54621i
$986$		0			0
$987$	−4.42601e7	−	4.42601e7i	−1.44617	−	1.44617i
$988$		0			0
$989$		−	7.92207e6i		−	0.257542i
$990$		0			0
$991$		−	4.23716e7i		−	1.37054i	−0.728291	−	0.685268i	$-0.759685\pi$
$991$		−	4.23716e7i		−	1.37054i	0.728291	−	0.685268i	$-0.240315\pi$
$992$		0			0
$993$	−1.92406e7	−	1.92406e7i	−0.619222	−	0.619222i
$994$		0			0
$995$	−4.65009e6	+	9.30018e6i	−0.148903	+	0.297806i
$996$		0			0
$997$	8.55612e6	−	8.55612e6i	0.272608	−	0.272608i	−0.557541	−	0.830149i	$-0.688255\pi$
$997$	8.55612e6	−	8.55612e6i	0.272608	−	0.272608i	0.830149	+	0.557541i	$0.188255\pi$
$998$		0			0
$999$	−1.38212e7			−0.438161

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.n.b.63.2	yes	4
4.3	odd	2	inner	80.6.n.b.63.1	yes	4
5.2	odd	4	inner	80.6.n.b.47.1	✓	4
5.3	odd	4		400.6.n.d.207.2		4
5.4	even	2		400.6.n.d.143.1		4
20.3	even	4		400.6.n.d.207.1		4
20.7	even	4	inner	80.6.n.b.47.2	yes	4
20.19	odd	2		400.6.n.d.143.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.n.b.47.1	✓	4	5.2	odd	4	inner
80.6.n.b.47.2	yes	4	20.7	even	4	inner
80.6.n.b.63.1	yes	4	4.3	odd	2	inner
80.6.n.b.63.2	yes	4	1.1	even	1	trivial
400.6.n.d.143.1		4	5.4	even	2
400.6.n.d.143.2		4	20.19	odd	2
400.6.n.d.207.1		4	20.3	even	4
400.6.n.d.207.2		4	5.3	odd	4

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(13.9642 - 13.9642i) q^{3} +(-25.0000 + 50.0000i) q^{5} +(-125.678 - 125.678i) q^{7} -147.000i q^{9} +O(q^{10})\)	\(q+(13.9642 - 13.9642i) q^{3} +(-25.0000 + 50.0000i) q^{5} +(-125.678 - 125.678i) q^{7} -147.000i q^{9} -418.927i q^{11} +(-695.000 - 695.000i) q^{13} +(349.106 + 1047.32i) q^{15} +(-95.0000 + 95.0000i) q^{17} +837.854 q^{19} -3510.00 q^{21} +(-2555.46 + 2555.46i) q^{23} +(-1875.00 - 2500.00i) q^{25} +(1340.57 + 1340.57i) q^{27} -2876.00i q^{29} -9635.33i q^{31} +(-5850.00 - 5850.00i) q^{33} +(9425.86 - 3141.95i) q^{35} +(-5155.00 + 5155.00i) q^{37} -19410.3 q^{39} +9218.00 q^{41} +(-1550.03 + 1550.03i) q^{43} +(7350.00 + 3675.00i) q^{45} +(12609.7 + 12609.7i) q^{47} +14783.0i q^{49} +2653.21i q^{51} +(11345.0 + 11345.0i) q^{53} +(20946.4 + 10473.2i) q^{55} +(11700.0 - 11700.0i) q^{57} -837.854 q^{59} +18678.0 q^{61} +(-18474.7 + 18474.7i) q^{63} +(52125.0 - 17375.0i) q^{65} +(-17385.5 - 17385.5i) q^{67} +71370.0i q^{69} -58230.9i q^{71} +(-24055.0 - 24055.0i) q^{73} +(-61093.6 - 8727.65i) q^{75} +(-52650.0 + 52650.0i) q^{77} +93839.7 q^{79} +73161.0 q^{81} +(35650.7 - 35650.7i) q^{83} +(-2375.00 - 7125.00i) q^{85} +(-40161.2 - 40161.2i) q^{87} -74296.0i q^{89} +174693. i q^{91} +(-134550. - 134550. i) q^{93} +(-20946.4 + 41892.7i) q^{95} +(-49255.0 + 49255.0i) q^{97} -61582.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 100 q^{5}+O(q^{10}) \) 4 * q - 100 * q^5	\( 4 q - 100 q^{5} - 2780 q^{13} - 380 q^{17} - 14040 q^{21} - 7500 q^{25} - 23400 q^{33} - 20620 q^{37} + 36872 q^{41} + 29400 q^{45} + 45380 q^{53} + 46800 q^{57} + 74712 q^{61} + 208500 q^{65} - 96220 q^{73} - 210600 q^{77} + 292644 q^{81} - 9500 q^{85} - 538200 q^{93} - 197020 q^{97}+O(q^{100}) \) 4 * q - 100 * q^5 - 2780 * q^13 - 380 * q^17 - 14040 * q^21 - 7500 * q^25 - 23400 * q^33 - 20620 * q^37 + 36872 * q^41 + 29400 * q^45 + 45380 * q^53 + 46800 * q^57 + 74712 * q^61 + 208500 * q^65 - 96220 * q^73 - 210600 * q^77 + 292644 * q^81 - 9500 * q^85 - 538200 * q^93 - 197020 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more