LMFDB - Embedded newform 320.6.l.a.81.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,6,Mod(81,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("320.81");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	320.l (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$51.3228223402$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.11
Character	$\chi$	$=$	320.81
Dual form			320.6.l.a.241.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.88924 - 9.88924i) q^{3} +(-17.6777 + 17.6777i) q^{5} +122.335i q^{7} -47.4058i q^{9} +O(q^{10})$	\(q+(-9.88924 - 9.88924i) q^{3} +(-17.6777 + 17.6777i) q^{5} +122.335i q^{7} -47.4058i q^{9} +(301.232 - 301.232i) q^{11} +(-384.386 - 384.386i) q^{13} +349.637 q^{15} -1558.08 q^{17} +(2096.85 + 2096.85i) q^{19} +(1209.80 - 1209.80i) q^{21} -4768.93i q^{23} -625.000i q^{25} +(-2871.89 + 2871.89i) q^{27} +(-1907.21 - 1907.21i) q^{29} -1152.69 q^{31} -5957.91 q^{33} +(-2162.60 - 2162.60i) q^{35} +(-7429.66 + 7429.66i) q^{37} +7602.58i q^{39} +4115.54i q^{41} +(-8400.86 + 8400.86i) q^{43} +(838.025 + 838.025i) q^{45} +8941.71 q^{47} +1841.08 q^{49} +(15408.3 + 15408.3i) q^{51} +(24969.5 - 24969.5i) q^{53} +10650.2i q^{55} -41472.4i q^{57} +(-23257.6 + 23257.6i) q^{59} +(14305.9 + 14305.9i) q^{61} +5799.41 q^{63} +13590.1 q^{65} +(38864.6 + 38864.6i) q^{67} +(-47161.1 + 47161.1i) q^{69} -12843.7i q^{71} +28584.7i q^{73} +(-6180.78 + 6180.78i) q^{75} +(36851.3 + 36851.3i) q^{77} +50757.6 q^{79} +45282.1 q^{81} +(39493.3 + 39493.3i) q^{83} +(27543.3 - 27543.3i) q^{85} +37721.7i q^{87} +97259.4i q^{89} +(47024.0 - 47024.0i) q^{91} +(11399.2 + 11399.2i) q^{93} -74134.7 q^{95} -46757.9 q^{97} +(-14280.1 - 14280.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q+O(q^{10}) $ 80 * q	$ 80 q - 1208 q^{11} + 1800 q^{15} - 2360 q^{19} + 7464 q^{27} - 8144 q^{29} + 21296 q^{37} - 32072 q^{43} + 88360 q^{47} - 192080 q^{49} + 5920 q^{51} - 49456 q^{53} - 44984 q^{59} + 48080 q^{61} - 158760 q^{63} - 61160 q^{67} - 22320 q^{69} - 14896 q^{77} - 177680 q^{79} - 524880 q^{81} + 329240 q^{83} + 132400 q^{85} - 364832 q^{91} - 362352 q^{93} - 288800 q^{95} - 659000 q^{99}+O(q^{100}) $ 80 * q - 1208 * q^11 + 1800 * q^15 - 2360 * q^19 + 7464 * q^27 - 8144 * q^29 + 21296 * q^37 - 32072 * q^43 + 88360 * q^47 - 192080 * q^49 + 5920 * q^51 - 49456 * q^53 - 44984 * q^59 + 48080 * q^61 - 158760 * q^63 - 61160 * q^67 - 22320 * q^69 - 14896 * q^77 - 177680 * q^79 - 524880 * q^81 + 329240 * q^83 + 132400 * q^85 - 364832 * q^91 - 362352 * q^93 - 288800 * q^95 - 659000 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−9.88924	−	9.88924i	−0.634395	−	0.634395i	0.314772	−	0.949167i	$-0.398072\pi$
$3$	−9.88924	−	9.88924i	−0.634395	−	0.634395i	−0.949167	+	0.314772i	$0.898072\pi$
$4$		0			0
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$6$		0			0
$7$			122.335i			0.943641i	0.881695	+	0.471820i	$0.156403\pi$
$7$			122.335i			0.943641i	−0.881695	+	0.471820i	$0.843597\pi$
$8$		0			0
$9$		−	47.4058i		−	0.195086i
$10$		0			0
$11$	301.232	−	301.232i	0.750618	−	0.750618i	−0.223976	−	0.974595i	$-0.571904\pi$
$11$	301.232	−	301.232i	0.750618	−	0.750618i	0.974595	+	0.223976i	$0.0719039\pi$
$12$		0			0
$13$	−384.386	−	384.386i	−0.630826	−	0.630826i	0.317449	−	0.948275i	$-0.397174\pi$
$13$	−384.386	−	384.386i	−0.630826	−	0.630826i	−0.948275	+	0.317449i	$0.897174\pi$
$14$		0			0
$15$	349.637			0.401227
$16$		0			0
$17$	−1558.08			−1.30758			−0.653791	−	0.756676i	$-0.726822\pi$
$17$	−1558.08			−1.30758			−0.653791	+	0.756676i	$0.726822\pi$
$18$		0			0
$19$	2096.85	+	2096.85i	1.33255	+	1.33255i	0.903085	+	0.429462i	$0.141297\pi$
$19$	2096.85	+	2096.85i	1.33255	+	1.33255i	0.429462	+	0.903085i	$0.358703\pi$
$20$		0			0
$21$	1209.80	−	1209.80i	0.598641	−	0.598641i
$22$		0			0
$23$		−	4768.93i		−	1.87975i	−0.341513	−	0.939877i	$-0.610939\pi$
$23$		−	4768.93i		−	1.87975i	0.341513	−	0.939877i	$-0.389061\pi$
$24$		0			0
$25$		−	625.000i		−	0.200000i
$26$		0			0
$27$	−2871.89	+	2871.89i	−0.758157	+	0.758157i
$28$		0			0
$29$	−1907.21	−	1907.21i	−0.421117	−	0.421117i	0.464471	−	0.885588i	$-0.346244\pi$
$29$	−1907.21	−	1907.21i	−0.421117	−	0.421117i	−0.885588	+	0.464471i	$0.846244\pi$
$30$		0			0
$31$	−1152.69			−0.215431			−0.107715	−	0.994182i	$-0.534354\pi$
$31$	−1152.69			−0.215431			−0.107715	+	0.994182i	$0.534354\pi$
$32$		0			0
$33$	−5957.91			−0.952377
$34$		0			0
$35$	−2162.60	−	2162.60i	−0.298405	−	0.298405i
$36$		0			0
$37$	−7429.66	+	7429.66i	−0.892205	+	0.892205i	−0.994730	−	0.102525i	$-0.967308\pi$
$37$	−7429.66	+	7429.66i	−0.892205	+	0.892205i	0.102525	+	0.994730i	$0.467308\pi$
$38$		0			0
$39$			7602.58i			0.800386i
$40$		0			0
$41$			4115.54i			0.382356i	0.981555	+	0.191178i	$0.0612307\pi$
$41$			4115.54i			0.382356i	−0.981555	+	0.191178i	$0.938769\pi$
$42$		0			0
$43$	−8400.86	+	8400.86i	−0.692871	+	0.692871i	−0.962863	−	0.269992i	$-0.912979\pi$
$43$	−8400.86	+	8400.86i	−0.692871	+	0.692871i	0.269992	+	0.962863i	$0.412979\pi$
$44$		0			0
$45$	838.025	+	838.025i	0.0616915	+	0.0616915i
$46$		0			0
$47$	8941.71			0.590441			0.295220	−	0.955429i	$-0.404607\pi$
$47$	8941.71			0.590441			0.295220	+	0.955429i	$0.404607\pi$
$48$		0			0
$49$	1841.08			0.109543
$50$		0			0
$51$	15408.3	+	15408.3i	0.829523	+	0.829523i
$52$		0			0
$53$	24969.5	−	24969.5i	1.22101	−	1.22101i	0.253738	−	0.967273i	$-0.418340\pi$
$53$	24969.5	−	24969.5i	1.22101	−	1.22101i	0.967273	−	0.253738i	$-0.0816601\pi$
$54$		0			0
$55$			10650.2i			0.474733i
$56$		0			0
$57$		−	41472.4i		−	1.69072i
$58$		0			0
$59$	−23257.6	+	23257.6i	−0.869831	+	0.869831i	−0.992453	−	0.122622i	$-0.960870\pi$
$59$	−23257.6	+	23257.6i	−0.869831	+	0.869831i	0.122622	+	0.992453i	$0.460870\pi$
$60$		0			0
$61$	14305.9	+	14305.9i	0.492257	+	0.492257i	0.909017	−	0.416760i	$-0.136834\pi$
$61$	14305.9	+	14305.9i	0.492257	+	0.492257i	−0.416760	+	0.909017i	$0.636834\pi$
$62$		0			0
$63$	5799.41			0.184091
$64$		0			0
$65$	13590.1			0.398970
$66$		0			0
$67$	38864.6	+	38864.6i	1.05771	+	1.05771i	0.998229	+	0.0594820i	$0.0189449\pi$
$67$	38864.6	+	38864.6i	1.05771	+	1.05771i	0.0594820	+	0.998229i	$0.481055\pi$
$68$		0			0
$69$	−47161.1	+	47161.1i	−1.19251	+	1.19251i
$70$		0			0
$71$		−	12843.7i		−	0.302373i	−0.988505	−	0.151187i	$-0.951691\pi$
$71$		−	12843.7i		−	0.302373i	0.988505	−	0.151187i	$-0.0483094\pi$
$72$		0			0
$73$			28584.7i			0.627807i	0.949455	+	0.313904i	$0.101637\pi$
$73$			28584.7i			0.627807i	−0.949455	+	0.313904i	$0.898363\pi$
$74$		0			0
$75$	−6180.78	+	6180.78i	−0.126879	+	0.126879i
$76$		0			0
$77$	36851.3	+	36851.3i	0.708314	+	0.708314i
$78$		0			0
$79$	50757.6			0.915025			0.457513	−	0.889203i	$-0.348740\pi$
$79$	50757.6			0.915025			0.457513	+	0.889203i	$0.348740\pi$
$80$		0			0
$81$	45282.1			0.766856
$82$		0			0
$83$	39493.3	+	39493.3i	0.629257	+	0.629257i	0.947881	−	0.318624i	$-0.103221\pi$
$83$	39493.3	+	39493.3i	0.629257	+	0.629257i	−0.318624	+	0.947881i	$0.603221\pi$
$84$		0			0
$85$	27543.3	−	27543.3i	0.413493	−	0.413493i
$86$		0			0
$87$			37721.7i			0.534309i
$88$		0			0
$89$			97259.4i			1.30154i	0.759276	+	0.650768i	$0.225553\pi$
$89$			97259.4i			1.30154i	−0.759276	+	0.650768i	$0.774447\pi$
$90$		0			0
$91$	47024.0	−	47024.0i	0.595273	−	0.595273i
$92$		0			0
$93$	11399.2	+	11399.2i	0.136668	+	0.136668i
$94$		0			0
$95$	−74134.7			−0.842777
$96$		0			0
$97$	−46757.9			−0.504575			−0.252287	−	0.967652i	$-0.581183\pi$
$97$	−46757.9			−0.504575			−0.252287	+	0.967652i	$0.581183\pi$
$98$		0			0
$99$	−14280.1	−	14280.1i	−0.146435	−	0.146435i
$100$		0			0
$101$	−62869.3	+	62869.3i	−0.613247	+	0.613247i	−0.943791	−	0.330544i	$-0.892768\pi$
$101$	−62869.3	+	62869.3i	−0.613247	+	0.613247i	0.330544	+	0.943791i	$0.392768\pi$
$102$		0			0
$103$			8850.12i			0.0821971i	0.999155	+	0.0410985i	$0.0130858\pi$
$103$			8850.12i			0.0821971i	−0.999155	+	0.0410985i	$0.986914\pi$
$104$		0			0
$105$			42773.0i			0.378614i
$106$		0			0
$107$	−119180.	+	119180.i	−1.00634	+	1.00634i	−0.00636140	+	0.999980i	$0.502025\pi$
$107$	−119180.	+	119180.i	−1.00634	+	1.00634i	−0.999980	+	0.00636140i	$0.997975\pi$
$108$		0			0
$109$	118189.	+	118189.i	0.952819	+	0.952819i	0.998936	−	0.0461173i	$-0.0146848\pi$
$109$	118189.	+	118189.i	0.952819	+	0.952819i	−0.0461173	+	0.998936i	$0.514685\pi$
$110$		0			0
$111$	146947.			1.13202
$112$		0			0
$113$	72392.2			0.533329			0.266665	−	0.963789i	$-0.414078\pi$
$113$	72392.2			0.533329			0.266665	+	0.963789i	$0.414078\pi$
$114$		0			0
$115$	84303.5	+	84303.5i	0.594430	+	0.594430i
$116$		0			0
$117$	−18222.2	+	18222.2i	−0.123065	+	0.123065i
$118$		0			0
$119$		−	190609.i		−	1.23389i
$120$		0			0
$121$		−	20430.2i		−	0.126855i
$122$		0			0
$123$	40699.6	−	40699.6i	0.242565	−	0.242565i
$124$		0			0
$125$	11048.5	+	11048.5i	0.0632456	+	0.0632456i
$126$		0			0
$127$	−122901.			−0.676153			−0.338076	−	0.941119i	$-0.609776\pi$
$127$	−122901.			−0.676153			−0.338076	+	0.941119i	$0.609776\pi$
$128$		0			0
$129$	166156.			0.879108
$130$		0			0
$131$	75109.1	+	75109.1i	0.382397	+	0.382397i	0.871965	−	0.489568i	$-0.162846\pi$
$131$	75109.1	+	75109.1i	0.382397	+	0.382397i	−0.489568	+	0.871965i	$0.662846\pi$
$132$		0			0
$133$	−256518.	+	256518.i	−1.25745	+	1.25745i
$134$		0			0
$135$		−	101537.i		−	0.479500i
$136$		0			0
$137$			73685.1i			0.335412i	0.985837	+	0.167706i	$0.0536359\pi$
$137$			73685.1i			0.335412i	−0.985837	+	0.167706i	$0.946364\pi$
$138$		0			0
$139$	−18908.2	+	18908.2i	−0.0830067	+	0.0830067i	−0.747391	−	0.664384i	$-0.768694\pi$
$139$	−18908.2	+	18908.2i	−0.0830067	+	0.0830067i	0.664384	+	0.747391i	$0.268694\pi$
$140$		0			0
$141$	−88426.8	−	88426.8i	−0.374573	−	0.374573i
$142$		0			0
$143$	−231579.			−0.947019
$144$		0			0
$145$	67430.0			0.266338
$146$		0			0
$147$	−18206.9	−	18206.9i	−0.0694932	−	0.0694932i
$148$		0			0
$149$	−147704.	+	147704.i	−0.545039	+	0.545039i	−0.925002	−	0.379963i	$-0.875937\pi$
$149$	−147704.	+	147704.i	−0.545039	+	0.545039i	0.379963	+	0.925002i	$0.375937\pi$
$150$		0			0
$151$			86096.9i			0.307288i	0.988126	+	0.153644i	$0.0491008\pi$
$151$			86096.9i			0.307288i	−0.988126	+	0.153644i	$0.950899\pi$
$152$		0			0
$153$			73862.3i			0.255090i
$154$		0			0
$155$	20376.8	−	20376.8i	0.0681251	−	0.0681251i
$156$		0			0
$157$	−141259.	−	141259.i	−0.457370	−	0.457370i	0.440421	−	0.897791i	$-0.354829\pi$
$157$	−141259.	−	141259.i	−0.457370	−	0.457370i	−0.897791	+	0.440421i	$0.854829\pi$
$158$		0			0
$159$	−493858.			−1.54921
$160$		0			0
$161$	583408.			1.77381
$162$		0			0
$163$	283813.	+	283813.i	0.836687	+	0.836687i	0.988421	−	0.151734i	$-0.0484858\pi$
$163$	283813.	+	283813.i	0.836687	+	0.836687i	−0.151734	+	0.988421i	$0.548486\pi$
$164$		0			0
$165$	105322.	−	105322.i	0.301168	−	0.301168i
$166$		0			0
$167$		−	15467.8i		−	0.0429178i	−0.999770	−	0.0214589i	$-0.993169\pi$
$167$		−	15467.8i		−	0.0429178i	0.999770	−	0.0214589i	$-0.00683110\pi$
$168$		0			0
$169$		−	75787.0i		−	0.204117i
$170$		0			0
$171$	99402.7	−	99402.7i	0.259961	−	0.259961i
$172$		0			0
$173$	−433381.	−	433381.i	−1.10092	−	1.10092i	−0.994300	−	0.106617i	$-0.965998\pi$
$173$	−433381.	−	433381.i	−1.10092	−	1.10092i	−0.106617	−	0.994300i	$-0.534002\pi$
$174$		0			0
$175$	76459.5			0.188728
$176$		0			0
$177$	460000.			1.10363
$178$		0			0
$179$	−197142.	−	197142.i	−0.459883	−	0.459883i	0.438734	−	0.898617i	$-0.355427\pi$
$179$	−197142.	−	197142.i	−0.459883	−	0.459883i	−0.898617	+	0.438734i	$0.855427\pi$
$180$		0			0
$181$	−86411.6	+	86411.6i	−0.196054	+	0.196054i	−0.798306	−	0.602252i	$-0.794270\pi$
$181$	−86411.6	+	86411.6i	−0.196054	+	0.196054i	0.602252	+	0.798306i	$0.294270\pi$
$182$		0			0
$183$		−	282950.i		−	0.624570i
$184$		0			0
$185$		−	262678.i		−	0.564280i
$186$		0			0
$187$	−469344.	+	469344.i	−0.981494	+	0.981494i
$188$		0			0
$189$	−351334.	−	351334.i	−0.715427	−	0.715427i
$190$		0			0
$191$	697785.			1.38401			0.692003	−	0.721895i	$-0.256729\pi$
$191$	697785.			1.38401			0.692003	+	0.721895i	$0.256729\pi$
$192$		0			0
$193$	−573139.			−1.10756			−0.553779	−	0.832663i	$-0.686815\pi$
$193$	−573139.			−1.10756			−0.553779	+	0.832663i	$0.686815\pi$
$194$		0			0
$195$	−134396.	−	134396.i	−0.253104	−	0.253104i
$196$		0			0
$197$	−259965.	+	259965.i	−0.477254	+	0.477254i	−0.904252	−	0.426999i	$-0.859571\pi$
$197$	−259965.	+	259965.i	−0.477254	+	0.477254i	0.426999	+	0.904252i	$0.359571\pi$
$198$		0			0
$199$			80858.1i			0.144741i	0.997378	+	0.0723704i	$0.0230564\pi$
$199$			80858.1i			0.144741i	−0.997378	+	0.0723704i	$0.976944\pi$
$200$		0			0
$201$		−	768683.i		−	1.34201i
$202$		0			0
$203$	233319.	−	233319.i	0.397383	−	0.397383i
$204$		0			0
$205$	−72753.2	−	72753.2i	−0.120912	−	0.120912i
$206$		0			0
$207$	−226075.			−0.366713
$208$		0			0
$209$	1.26327e6			2.00047
$210$		0			0
$211$	520212.	+	520212.i	0.804404	+	0.804404i	0.983780	−	0.179377i	$-0.0574082\pi$
$211$	520212.	+	520212.i	0.804404	+	0.804404i	−0.179377	+	0.983780i	$0.557408\pi$
$212$		0			0
$213$	−127014.	+	127014.i	−0.191824	+	0.191824i
$214$		0			0
$215$		−	297015.i		−	0.438210i
$216$		0			0
$217$		−	141014.i		−	0.203289i
$218$		0			0
$219$	282681.	−	282681.i	0.398278	−	0.398278i
$220$		0			0
$221$	598907.	+	598907.i	0.824856	+	0.824856i
$222$		0			0
$223$	126355.			0.170150			0.0850749	−	0.996375i	$-0.472887\pi$
$223$	126355.			0.170150			0.0850749	+	0.996375i	$0.472887\pi$
$224$		0			0
$225$	−29628.7			−0.0390172
$226$		0			0
$227$	918677.	+	918677.i	1.18331	+	1.18331i	0.978882	+	0.204427i	$0.0655332\pi$
$227$	918677.	+	918677.i	1.18331	+	1.18331i	0.204427	+	0.978882i	$0.434467\pi$
$228$		0			0
$229$	−347876.	+	347876.i	−0.438365	+	0.438365i	−0.891461	−	0.453097i	$-0.850319\pi$
$229$	−347876.	+	347876.i	−0.438365	+	0.438365i	0.453097	+	0.891461i	$0.350319\pi$
$230$		0			0
$231$		−	728862.i		−	0.898702i
$232$		0			0
$233$		−	728178.i		−	0.878714i	−0.898313	−	0.439357i	$-0.855206\pi$
$233$		−	728178.i		−	0.878714i	0.898313	−	0.439357i	$-0.144794\pi$
$234$		0			0
$235$	−158069.	+	158069.i	−0.186714	+	0.186714i
$236$		0			0
$237$	−501954.	−	501954.i	−0.580488	−	0.580488i
$238$		0			0
$239$	−203434.			−0.230372			−0.115186	−	0.993344i	$-0.536746\pi$
$239$	−203434.			−0.230372			−0.115186	+	0.993344i	$0.536746\pi$
$240$		0			0
$241$	−131370.			−0.145698			−0.0728490	−	0.997343i	$-0.523209\pi$
$241$	−131370.			−0.145698			−0.0728490	+	0.997343i	$0.523209\pi$
$242$		0			0
$243$	250065.	+	250065.i	0.271667	+	0.271667i
$244$		0			0
$245$	−32546.0	+	32546.0i	−0.0346404	+	0.0346404i
$246$		0			0
$247$		−	1.61200e6i		−	1.68121i
$248$		0			0
$249$		−	781117.i		−	0.798395i
$250$		0			0
$251$	−487551.	+	487551.i	−0.488467	+	0.488467i	−0.907822	−	0.419355i	$-0.862256\pi$
$251$	−487551.	+	487551.i	−0.488467	+	0.488467i	0.419355	+	0.907822i	$0.362256\pi$
$252$		0			0
$253$	−1.43655e6	−	1.43655e6i	−1.41098	−	1.41098i
$254$		0			0
$255$	−544765.			−0.524636
$256$		0			0
$257$	−1.90822e6			−1.80217			−0.901084	−	0.433645i	$-0.857227\pi$
$257$	−1.90822e6			−1.80217			−0.901084	+	0.433645i	$0.857227\pi$
$258$		0			0
$259$	−908910.	−	908910.i	−0.841921	−	0.841921i
$260$		0			0
$261$	−90412.8	+	90412.8i	−0.0821540	+	0.0821540i
$262$		0			0
$263$		−	484503.i		−	0.431924i	−0.976402	−	0.215962i	$-0.930711\pi$
$263$		−	484503.i		−	0.431924i	0.976402	−	0.215962i	$-0.0692887\pi$
$264$		0			0
$265$			882804.i			0.772235i
$266$		0			0
$267$	961821.	−	961821.i	0.825689	−	0.825689i
$268$		0			0
$269$	986492.	+	986492.i	0.831214	+	0.831214i	0.987683	−	0.156469i	$-0.0500110\pi$
$269$	986492.	+	986492.i	0.831214	+	0.831214i	−0.156469	+	0.987683i	$0.550011\pi$
$270$		0			0
$271$	−1.22694e6			−1.01484			−0.507422	−	0.861698i	$-0.669401\pi$
$271$	−1.22694e6			−1.01484			−0.507422	+	0.861698i	$0.669401\pi$
$272$		0			0
$273$	−930064.			−0.755277
$274$		0			0
$275$	−188270.	−	188270.i	−0.150124	−	0.150124i
$276$		0			0
$277$	1.69007e6	−	1.69007e6i	1.32344	−	1.32344i	0.412473	−	0.910970i	$-0.364665\pi$
$277$	1.69007e6	−	1.69007e6i	1.32344	−	1.32344i	0.910970	−	0.412473i	$-0.135335\pi$
$278$		0			0
$279$			54644.1i			0.0420275i
$280$		0			0
$281$		−	1.34620e6i		−	1.01705i	−0.861046	−	0.508527i	$-0.830190\pi$
$281$		−	1.34620e6i		−	1.01705i	0.861046	−	0.508527i	$-0.169810\pi$
$282$		0			0
$283$	−944602.	+	944602.i	−0.701104	+	0.701104i	−0.964648	−	0.263543i	$-0.915109\pi$
$283$	−944602.	+	944602.i	−0.701104	+	0.701104i	0.263543	+	0.964648i	$0.415109\pi$
$284$		0			0
$285$	733136.	+	733136.i	0.534653	+	0.534653i
$286$		0			0
$287$	−503476.			−0.360806
$288$		0			0
$289$	1.00777e6			0.709768
$290$		0			0
$291$	462400.	+	462400.i	0.320100	+	0.320100i
$292$		0			0
$293$	−838880.	+	838880.i	−0.570862	+	0.570862i	−0.932369	−	0.361508i	$-0.882262\pi$
$293$	−838880.	+	838880.i	−0.570862	+	0.570862i	0.361508	+	0.932369i	$0.382262\pi$
$294$		0			0
$295$		−	822281.i		−	0.550130i
$296$		0			0
$297$			1.73021e6i			1.13817i
$298$		0			0
$299$	−1.83311e6	+	1.83311e6i	−1.18580	+	1.18580i
$300$		0			0
$301$	−1.02772e6	−	1.02772e6i	−0.653821	−	0.653821i
$302$		0			0
$303$	1.24346e6			0.778082
$304$		0			0
$305$	−505791.			−0.311330
$306$		0			0
$307$	521897.	+	521897.i	0.316038	+	0.316038i	0.847243	−	0.531205i	$-0.178261\pi$
$307$	521897.	+	521897.i	0.316038	+	0.316038i	−0.531205	+	0.847243i	$0.678261\pi$
$308$		0			0
$309$	87521.0	−	87521.0i	0.0521454	−	0.0521454i
$310$		0			0
$311$		−	1.29428e6i		−	0.758798i	−0.925233	−	0.379399i	$-0.876131\pi$
$311$		−	1.29428e6i		−	0.758798i	0.925233	−	0.379399i	$-0.123869\pi$
$312$		0			0
$313$		−	2.45861e6i		−	1.41850i	−0.704957	−	0.709251i	$-0.749034\pi$
$313$		−	2.45861e6i		−	1.41850i	0.704957	−	0.709251i	$-0.250966\pi$
$314$		0			0
$315$	−102520.	+	102520.i	−0.0582146	+	0.0582146i
$316$		0			0
$317$	1.88035e6	+	1.88035e6i	1.05097	+	1.05097i	0.998629	+	0.0523414i	$0.0166684\pi$
$317$	1.88035e6	+	1.88035e6i	1.05097	+	1.05097i	0.0523414	+	0.998629i	$0.483332\pi$
$318$		0			0
$319$	−1.14902e6			−0.632197
$320$		0			0
$321$	2.35721e6			1.27684
$322$		0			0
$323$	−3.26706e6	−	3.26706e6i	−1.74241	−	1.74241i
$324$		0			0
$325$	−240242.	+	240242.i	−0.126165	+	0.126165i
$326$		0			0
$327$		−	2.33760e6i		−	1.20893i
$328$		0			0
$329$			1.09389e6i			0.557164i
$330$		0			0
$331$	2.05885e6	−	2.05885e6i	1.03289	−	1.03289i	0.0334519	−	0.999440i	$-0.489350\pi$
$331$	2.05885e6	−	2.05885e6i	1.03289	−	1.03289i	0.999440	−	0.0334519i	$-0.0106500\pi$
$332$		0			0
$333$	352209.	+	352209.i	0.174057	+	0.174057i
$334$		0			0
$335$	−1.37407e6			−0.668955
$336$		0			0
$337$	−256497.			−0.123029			−0.0615145	−	0.998106i	$-0.519593\pi$
$337$	−256497.			−0.123029			−0.0615145	+	0.998106i	$0.519593\pi$
$338$		0			0
$339$	−715904.	−	715904.i	−0.338342	−	0.338342i
$340$		0			0
$341$	−347226.	+	347226.i	−0.161706	+	0.161706i
$342$		0			0
$343$			2.28132e6i			1.04701i
$344$		0			0
$345$		−	1.66740e6i		−	0.754207i
$346$		0			0
$347$	297841.	−	297841.i	0.132789	−	0.132789i	−0.637589	−	0.770377i	$-0.720068\pi$
$347$	297841.	−	297841.i	0.132789	−	0.132789i	0.770377	+	0.637589i	$0.220068\pi$
$348$		0			0
$349$	−1.06398e6	−	1.06398e6i	−0.467597	−	0.467597i	0.433538	−	0.901135i	$-0.357265\pi$
$349$	−1.06398e6	−	1.06398e6i	−0.467597	−	0.467597i	−0.901135	+	0.433538i	$0.857265\pi$
$350$		0			0
$351$	2.20783e6			0.956530
$352$		0			0
$353$	2.71943e6			1.16156			0.580780	−	0.814060i	$-0.302748\pi$
$353$	2.71943e6			1.16156			0.580780	+	0.814060i	$0.302748\pi$
$354$		0			0
$355$	227046.	+	227046.i	0.0956187	+	0.0956187i
$356$		0			0
$357$	−1.88497e6	+	1.88497e6i	−0.782771	+	0.782771i
$358$		0			0
$359$			1.93088e6i			0.790714i	0.918528	+	0.395357i	$0.129379\pi$
$359$			1.93088e6i			0.790714i	−0.918528	+	0.395357i	$0.870621\pi$
$360$		0			0
$361$			6.31742e6i			2.55136i
$362$		0			0
$363$	−202039.	+	202039.i	−0.0804764	+	0.0804764i
$364$		0			0
$365$	−505311.	−	505311.i	−0.198530	−	0.198530i
$366$		0			0
$367$	4.26731e6			1.65382			0.826911	−	0.562332i	$-0.190096\pi$
$367$	4.26731e6			1.65382			0.826911	+	0.562332i	$0.190096\pi$
$368$		0			0
$369$	195101.			0.0745922
$370$		0			0
$371$	3.05465e6	+	3.05465e6i	1.15220	+	1.15220i
$372$		0			0
$373$	−1.60230e6	+	1.60230e6i	−0.596311	+	0.596311i	−0.939329	−	0.343018i	$-0.888551\pi$
$373$	−1.60230e6	+	1.60230e6i	−0.596311	+	0.596311i	0.343018	+	0.939329i	$0.388551\pi$
$374$		0			0
$375$		−	218523.i		−	0.0802453i
$376$		0			0
$377$			1.46621e6i			0.531304i
$378$		0			0
$379$	1.32305e6	−	1.32305e6i	0.473127	−	0.473127i	−0.429798	−	0.902925i	$-0.641415\pi$
$379$	1.32305e6	−	1.32305e6i	0.473127	−	0.473127i	0.902925	+	0.429798i	$0.141415\pi$
$380$		0			0
$381$	1.21539e6	+	1.21539e6i	0.428948	+	0.428948i
$382$		0			0
$383$	−2.69607e6			−0.939149			−0.469574	−	0.882893i	$-0.655593\pi$
$383$	−2.69607e6			−0.939149			−0.469574	+	0.882893i	$0.655593\pi$
$384$		0			0
$385$	−1.30289e6			−0.447977
$386$		0			0
$387$	398250.	+	398250.i	0.135169	+	0.135169i
$388$		0			0
$389$	2.79493e6	−	2.79493e6i	0.936475	−	0.936475i	−0.0616242	−	0.998099i	$-0.519628\pi$
$389$	2.79493e6	−	2.79493e6i	0.936475	−	0.936475i	0.998099	+	0.0616242i	$0.0196280\pi$
$390$		0			0
$391$			7.43039e6i			2.45793i
$392$		0			0
$393$		−	1.48554e6i		−	0.485181i
$394$		0			0
$395$	−897276.	+	897276.i	−0.289356	+	0.289356i
$396$		0			0
$397$	2.49038e6	+	2.49038e6i	0.793030	+	0.793030i	0.981986	−	0.188956i	$-0.0605103\pi$
$397$	2.49038e6	+	2.49038e6i	0.793030	+	0.793030i	−0.188956	+	0.981986i	$0.560510\pi$
$398$		0			0
$399$	5.07354e6			1.59543
$400$		0			0
$401$	−4.48252e6			−1.39207			−0.696036	−	0.718007i	$-0.745054\pi$
$401$	−4.48252e6			−1.39207			−0.696036	+	0.718007i	$0.745054\pi$
$402$		0			0
$403$	443078.	+	443078.i	0.135899	+	0.135899i
$404$		0			0
$405$	−800481.	+	800481.i	−0.242501	+	0.242501i
$406$		0			0
$407$			4.47610e6i			1.33941i
$408$		0			0
$409$			2.36608e6i			0.699393i	0.936863	+	0.349696i	$0.113715\pi$
$409$			2.36608e6i			0.699393i	−0.936863	+	0.349696i	$0.886285\pi$
$410$		0			0
$411$	728690.	−	728690.i	0.212784	−	0.212784i
$412$		0			0
$413$	−2.84523e6	−	2.84523e6i	−0.820808	−	0.820808i
$414$		0			0
$415$	−1.39630e6			−0.397977
$416$		0			0
$417$	373975.			0.105318
$418$		0			0
$419$	1.04928e6	+	1.04928e6i	0.291983	+	0.291983i	0.837863	−	0.545880i	$-0.183805\pi$
$419$	1.04928e6	+	1.04928e6i	0.291983	+	0.291983i	−0.545880	+	0.837863i	$0.683805\pi$
$420$		0			0
$421$	−83315.8	+	83315.8i	−0.0229099	+	0.0229099i	−0.718469	−	0.695559i	$-0.755157\pi$
$421$	−83315.8	+	83315.8i	−0.0229099	+	0.0229099i	0.695559	+	0.718469i	$0.255157\pi$
$422$		0			0
$423$		−	423890.i		−	0.115187i
$424$		0			0
$425$			973803.i			0.261516i
$426$		0			0
$427$	−1.75012e6	+	1.75012e6i	−0.464513	+	0.464513i
$428$		0			0
$429$	2.29014e6	+	2.29014e6i	0.600784	+	0.600784i
$430$		0			0
$431$	−1.89615e6			−0.491676			−0.245838	−	0.969311i	$-0.579063\pi$
$431$	−1.89615e6			−0.491676			−0.245838	+	0.969311i	$0.579063\pi$
$432$		0			0
$433$	−6.49433e6			−1.66462			−0.832309	−	0.554312i	$-0.812982\pi$
$433$	−6.49433e6			−1.66462			−0.832309	+	0.554312i	$0.812982\pi$
$434$		0			0
$435$	−666831.	−	666831.i	−0.168963	−	0.168963i
$436$		0			0
$437$	9.99970e6	−	9.99970e6i	2.50486	−	2.50486i
$438$		0			0
$439$			2.58577e6i			0.640365i	0.947356	+	0.320183i	$0.103744\pi$
$439$			2.58577e6i			0.640365i	−0.947356	+	0.320183i	$0.896256\pi$
$440$		0			0
$441$		−	87278.0i		−	0.0213702i
$442$		0			0
$443$	562901.	−	562901.i	0.136277	−	0.136277i	−0.635678	−	0.771955i	$-0.719279\pi$
$443$	562901.	−	562901.i	0.136277	−	0.136277i	0.771955	+	0.635678i	$0.219279\pi$
$444$		0			0
$445$	−1.71932e6	−	1.71932e6i	−0.411582	−	0.411582i
$446$		0			0
$447$	2.92137e6			0.691540
$448$		0			0
$449$	6.62708e6			1.55134			0.775669	−	0.631141i	$-0.217413\pi$
$449$	6.62708e6			1.55134			0.775669	+	0.631141i	$0.217413\pi$
$450$		0			0
$451$	1.23973e6	+	1.23973e6i	0.287003	+	0.287003i
$452$		0			0
$453$	851433.	−	851433.i	0.194942	−	0.194942i
$454$		0			0
$455$			1.66255e6i			0.376484i
$456$		0			0
$457$			2.47813e6i			0.555052i	0.960718	+	0.277526i	$0.0895145\pi$
$457$			2.47813e6i			0.555052i	−0.960718	+	0.277526i	$0.910485\pi$
$458$		0			0
$459$	4.47465e6	−	4.47465e6i	0.991351	−	0.991351i
$460$		0			0
$461$	2.88325e6	+	2.88325e6i	0.631872	+	0.631872i	0.948537	−	0.316665i	$-0.102563\pi$
$461$	2.88325e6	+	2.88325e6i	0.631872	+	0.631872i	−0.316665	+	0.948537i	$0.602563\pi$
$462$		0			0
$463$	−4.18992e6			−0.908351			−0.454175	−	0.890912i	$-0.650066\pi$
$463$	−4.18992e6			−0.908351			−0.454175	+	0.890912i	$0.650066\pi$
$464$		0			0
$465$	−403023.			−0.0864365
$466$		0			0
$467$	1.38927e6	+	1.38927e6i	0.294777	+	0.294777i	0.838964	−	0.544187i	$-0.183162\pi$
$467$	1.38927e6	+	1.38927e6i	0.294777	+	0.294777i	−0.544187	+	0.838964i	$0.683162\pi$
$468$		0			0
$469$	−4.75451e6	+	4.75451e6i	−0.998099	+	0.998099i
$470$		0			0
$471$			2.79389e6i			0.580306i
$472$		0			0
$473$			5.06121e6i			1.04016i
$474$		0			0
$475$	1.31053e6	−	1.31053e6i	0.266509	−	0.266509i
$476$		0			0
$477$	−1.18370e6	−	1.18370e6i	−0.238202	−	0.238202i
$478$		0			0
$479$	3.01097e6			0.599609			0.299804	−	0.954001i	$-0.403079\pi$
$479$	3.01097e6			0.599609			0.299804	+	0.954001i	$0.403079\pi$
$480$		0			0
$481$	5.71172e6			1.12565
$482$		0			0
$483$	−5.76946e6	−	5.76946e6i	−1.12530	−	1.12530i
$484$		0			0
$485$	826570.	−	826570.i	0.159561	−	0.159561i
$486$		0			0
$487$			1.73420e6i			0.331341i	0.986181	+	0.165671i	$0.0529789\pi$
$487$			1.73420e6i			0.331341i	−0.986181	+	0.165671i	$0.947021\pi$
$488$		0			0
$489$		−	5.61339e6i		−	1.06158i
$490$		0			0
$491$	−2.65718e6	+	2.65718e6i	−0.497414	+	0.497414i	−0.910632	−	0.413218i	$-0.864405\pi$
$491$	−2.65718e6	+	2.65718e6i	−0.497414	+	0.497414i	0.413218	+	0.910632i	$0.364405\pi$
$492$		0			0
$493$	2.97159e6	+	2.97159e6i	0.550645	+	0.550645i
$494$		0			0
$495$	504879.			0.0926136
$496$		0			0
$497$	1.57123e6			0.285331
$498$		0			0
$499$	−7.30951e6	−	7.30951e6i	−1.31413	−	1.31413i	−0.918345	−	0.395781i	$-0.870474\pi$
$499$	−7.30951e6	−	7.30951e6i	−1.31413	−	1.31413i	−0.395781	−	0.918345i	$-0.629526\pi$
$500$		0			0
$501$	−152965.	+	152965.i	−0.0272268	+	0.0272268i
$502$		0			0
$503$			5.49766e6i			0.968853i	0.874832	+	0.484426i	$0.160972\pi$
$503$			5.49766e6i			0.968853i	−0.874832	+	0.484426i	$0.839028\pi$
$504$		0			0
$505$		−	2.22277e6i		−	0.387851i
$506$		0			0
$507$	−749476.	+	749476.i	−0.129491	+	0.129491i
$508$		0			0
$509$	−2.60875e6	−	2.60875e6i	−0.446311	−	0.446311i	0.447815	−	0.894126i	$-0.352202\pi$
$509$	−2.60875e6	−	2.60875e6i	−0.446311	−	0.446311i	−0.894126	+	0.447815i	$0.852202\pi$
$510$		0			0
$511$	−3.49692e6			−0.592424
$512$		0			0
$513$	−1.20438e7			−2.02056
$514$		0			0
$515$	−156450.	−	156450.i	−0.0259930	−	0.0259930i
$516$		0			0
$517$	2.69353e6	−	2.69353e6i	0.443195	−	0.443195i
$518$		0			0
$519$			8.57162e6i			1.39683i
$520$		0			0
$521$		−	9.50774e6i		−	1.53456i	−0.641314	−	0.767279i	$-0.721610\pi$
$521$		−	9.50774e6i		−	1.53456i	0.641314	−	0.767279i	$-0.278390\pi$
$522$		0			0
$523$	−2.12191e6	+	2.12191e6i	−0.339213	+	0.339213i	−0.856071	−	0.516858i	$-0.827102\pi$
$523$	−2.12191e6	+	2.12191e6i	−0.339213	+	0.339213i	0.516858	+	0.856071i	$0.327102\pi$
$524$		0			0
$525$	−756127.	−	756127.i	−0.119728	−	0.119728i
$526$		0			0
$527$	1.79598e6			0.281693
$528$		0			0
$529$	−1.63063e7			−2.53348
$530$		0			0
$531$	1.10255e6	+	1.10255e6i	0.169692	+	0.169692i
$532$		0			0
$533$	1.58196e6	−	1.58196e6i	0.241200	−	0.241200i
$534$		0			0
$535$		−	4.21366e6i		−	0.636466i
$536$		0			0
$537$			3.89918e6i			0.583495i
$538$		0			0
$539$	554592.	−	554592.i	0.0822246	−	0.0822246i
$540$		0			0
$541$	7.92767e6	+	7.92767e6i	1.16454	+	1.16454i	0.983471	+	0.181064i	$0.0579541\pi$
$541$	7.92767e6	+	7.92767e6i	1.16454	+	1.16454i	0.181064	+	0.983471i	$0.442046\pi$
$542$		0			0
$543$	1.70909e6			0.248751
$544$		0			0
$545$	−4.17861e6			−0.602615
$546$		0			0
$547$	−2.38242e6	−	2.38242e6i	−0.340447	−	0.340447i	0.516088	−	0.856535i	$-0.327388\pi$
$547$	−2.38242e6	−	2.38242e6i	−0.340447	−	0.340447i	−0.856535	+	0.516088i	$0.827388\pi$
$548$		0			0
$549$	678185.	−	678185.i	0.0960323	−	0.0960323i
$550$		0			0
$551$		−	7.99824e6i		−	1.12232i
$552$		0			0
$553$			6.20944e6i			0.863455i
$554$		0			0
$555$	−2.59769e6	+	2.59769e6i	−0.357976	+	0.357976i
$556$		0			0
$557$	−2.36995e6	−	2.36995e6i	−0.323669	−	0.323669i	0.526504	−	0.850173i	$-0.323503\pi$
$557$	−2.36995e6	−	2.36995e6i	−0.323669	−	0.323669i	−0.850173	+	0.526504i	$0.823503\pi$
$558$		0			0
$559$	6.45835e6			0.874162
$560$		0			0
$561$	9.28292e6			1.24531
$562$		0			0
$563$	−6.69440e6	−	6.69440e6i	−0.890104	−	0.890104i	0.104429	−	0.994532i	$-0.466699\pi$
$563$	−6.69440e6	−	6.69440e6i	−0.890104	−	0.890104i	−0.994532	+	0.104429i	$0.966699\pi$
$564$		0			0
$565$	−1.27973e6	+	1.27973e6i	−0.168654	+	0.168654i
$566$		0			0
$567$			5.53959e6i			0.723636i
$568$		0			0
$569$			6.90268e6i			0.893793i	0.894586	+	0.446897i	$0.147471\pi$
$569$			6.90268e6i			0.893793i	−0.894586	+	0.446897i	$0.852529\pi$
$570$		0			0
$571$	6.09499e6	−	6.09499e6i	0.782317	−	0.782317i	−0.197904	−	0.980221i	$-0.563414\pi$
$571$	6.09499e6	−	6.09499e6i	0.782317	−	0.782317i	0.980221	+	0.197904i	$0.0634135\pi$
$572$		0			0
$573$	−6.90056e6	−	6.90056e6i	−0.878006	−	0.878006i
$574$		0			0
$575$	−2.98058e6			−0.375951
$576$		0			0
$577$	−6.40682e6			−0.801130			−0.400565	−	0.916268i	$-0.631186\pi$
$577$	−6.40682e6			−0.801130			−0.400565	+	0.916268i	$0.631186\pi$
$578$		0			0
$579$	5.66791e6	+	5.66791e6i	0.702630	+	0.702630i
$580$		0			0
$581$	−4.83142e6	+	4.83142e6i	−0.593792	+	0.593792i
$582$		0			0
$583$		−	1.50432e7i		−	1.83303i
$584$		0			0
$585$		−	644251.i		−	0.0778333i
$586$		0			0
$587$	3.17862e6	−	3.17862e6i	0.380754	−	0.380754i	−0.490620	−	0.871374i	$-0.663230\pi$
$587$	3.17862e6	−	3.17862e6i	0.380754	−	0.380754i	0.871374	+	0.490620i	$0.163230\pi$
$588$		0			0
$589$	−2.41701e6	−	2.41701e6i	−0.287071	−	0.287071i
$590$		0			0
$591$	5.14171e6			0.605535
$592$		0			0
$593$	6.93794e6			0.810203			0.405102	−	0.914272i	$-0.367236\pi$
$593$	6.93794e6			0.810203			0.405102	+	0.914272i	$0.367236\pi$
$594$		0			0
$595$	3.36952e6	+	3.36952e6i	0.390189	+	0.390189i
$596$		0			0
$597$	799625.	−	799625.i	0.0918228	−	0.0918228i
$598$		0			0
$599$		−	1.29586e7i		−	1.47568i	−0.674978	−	0.737838i	$-0.735847\pi$
$599$		−	1.29586e7i		−	1.47568i	0.674978	−	0.737838i	$-0.264153\pi$
$600$		0			0
$601$		−	3.22149e6i		−	0.363806i	−0.983316	−	0.181903i	$-0.941774\pi$
$601$		−	3.22149e6i		−	0.363806i	0.983316	−	0.181903i	$-0.0582257\pi$
$602$		0			0
$603$	1.84241e6	−	1.84241e6i	0.206344	−	0.206344i
$604$		0			0
$605$	361158.	+	361158.i	0.0401152	+	0.0401152i
$606$		0			0
$607$	2.77321e6			0.305500			0.152750	−	0.988265i	$-0.451187\pi$
$607$	2.77321e6			0.305500			0.152750	+	0.988265i	$0.451187\pi$
$608$		0			0
$609$	−4.61469e6			−0.504196
$610$		0			0
$611$	−3.43707e6	−	3.43707e6i	−0.372465	−	0.372465i
$612$		0			0
$613$	3.18104e6	−	3.18104e6i	0.341915	−	0.341915i	−0.515172	−	0.857087i	$-0.672272\pi$
$613$	3.18104e6	−	3.18104e6i	0.341915	−	0.341915i	0.857087	+	0.515172i	$0.172272\pi$
$614$		0			0
$615$			1.43895e6i			0.153411i
$616$		0			0
$617$			2.69222e6i			0.284707i	0.989816	+	0.142353i	$0.0454669\pi$
$617$			2.69222e6i			0.284707i	−0.989816	+	0.142353i	$0.954533\pi$
$618$		0			0
$619$	−1.97397e6	+	1.97397e6i	−0.207069	+	0.207069i	−0.803020	−	0.595952i	$-0.796775\pi$
$619$	−1.97397e6	+	1.97397e6i	−0.207069	+	0.207069i	0.595952	+	0.803020i	$0.296775\pi$
$620$		0			0
$621$	1.36958e7	+	1.36958e7i	1.42515	+	1.42515i
$622$		0			0
$623$	−1.18983e7			−1.22818
$624$		0			0
$625$	−390625.			−0.0400000
$626$		0			0
$627$	−1.24928e7	−	1.24928e7i	−1.26909	−	1.26909i
$628$		0			0
$629$	1.15760e7	−	1.15760e7i	1.16663	−	1.16663i
$630$		0			0
$631$		−	7.74739e6i		−	0.774608i	−0.921952	−	0.387304i	$-0.873406\pi$
$631$		−	7.74739e6i		−	0.774608i	0.921952	−	0.387304i	$-0.126594\pi$
$632$		0			0
$633$		−	1.02890e7i		−	1.02062i
$634$		0			0
$635$	2.17260e6	−	2.17260e6i	0.213818	−	0.213818i
$636$		0			0
$637$	−707687.	−	707687.i	−0.0691023	−	0.0691023i
$638$		0			0
$639$	−608865.			−0.0589887
$640$		0			0
$641$	1.28304e7			1.23337			0.616687	−	0.787209i	$-0.288475\pi$
$641$	1.28304e7			1.23337			0.616687	+	0.787209i	$0.288475\pi$
$642$		0			0
$643$	−4.34386e6	−	4.34386e6i	−0.414332	−	0.414332i	0.468912	−	0.883245i	$-0.344646\pi$
$643$	−4.34386e6	−	4.34386e6i	−0.414332	−	0.414332i	−0.883245	+	0.468912i	$0.844646\pi$
$644$		0			0
$645$	−2.93725e6	+	2.93725e6i	−0.277998	+	0.277998i
$646$		0			0
$647$			4.82724e6i			0.453355i	0.973970	+	0.226678i	$0.0727863\pi$
$647$			4.82724e6i			0.453355i	−0.973970	+	0.226678i	$0.927214\pi$
$648$		0			0
$649$			1.40119e7i			1.30582i
$650$		0			0
$651$	−1.39453e6	+	1.39453e6i	−0.128966	+	0.128966i
$652$		0			0
$653$	4.17503e6	+	4.17503e6i	0.383157	+	0.383157i	0.872238	−	0.489081i	$-0.162668\pi$
$653$	4.17503e6	+	4.17503e6i	0.383157	+	0.383157i	−0.489081	+	0.872238i	$0.662668\pi$
$654$		0			0
$655$	−2.65551e6			−0.241849
$656$		0			0
$657$	1.35508e6			0.122476
$658$		0			0
$659$	1.12655e7	+	1.12655e7i	1.01051	+	1.01051i	0.999944	+	0.0105615i	$0.00336189\pi$
$659$	1.12655e7	+	1.12655e7i	1.01051	+	1.01051i	0.0105615	+	0.999944i	$0.496638\pi$
$660$		0			0
$661$	6.22807e6	−	6.22807e6i	0.554434	−	0.554434i	−0.373284	−	0.927717i	$-0.621768\pi$
$661$	6.22807e6	−	6.22807e6i	0.554434	−	0.554434i	0.927717	+	0.373284i	$0.121768\pi$
$662$		0			0
$663$		−	1.18455e7i		−	1.04657i
$664$		0			0
$665$		−	9.06929e6i		−	0.795278i
$666$		0			0
$667$	−9.09533e6	+	9.09533e6i	−0.791597	+	0.791597i
$668$		0			0
$669$	−1.24956e6	−	1.24956e6i	−0.107942	−	0.107942i
$670$		0			0
$671$	8.61880e6			0.738994
$672$		0			0
$673$	−5.79021e6			−0.492784			−0.246392	−	0.969170i	$-0.579245\pi$
$673$	−5.79021e6			−0.492784			−0.246392	+	0.969170i	$0.579245\pi$
$674$		0			0
$675$	1.79493e6	+	1.79493e6i	0.151631	+	0.151631i
$676$		0			0
$677$	−1.96617e6	+	1.96617e6i	−0.164873	+	0.164873i	−0.784721	−	0.619849i	$-0.787194\pi$
$677$	−1.96617e6	+	1.96617e6i	−0.164873	+	0.164873i	0.619849	+	0.784721i	$0.287194\pi$
$678$		0			0
$679$		−	5.72014e6i		−	0.476137i
$680$		0			0
$681$		−	1.81700e7i		−	1.50137i
$682$		0			0
$683$	554999.	−	554999.i	0.0455240	−	0.0455240i	−0.683978	−	0.729502i	$-0.739752\pi$
$683$	554999.	−	554999.i	0.0455240	−	0.0455240i	0.729502	+	0.683978i	$0.239752\pi$
$684$		0			0
$685$	−1.30258e6	−	1.30258e6i	−0.106067	−	0.106067i
$686$		0			0
$687$	6.88046e6			0.556193
$688$		0			0
$689$	−1.91959e7			−1.54049
$690$		0			0
$691$	1.32042e7	+	1.32042e7i	1.05200	+	1.05200i	0.998572	+	0.0534279i	$0.0170147\pi$
$691$	1.32042e7	+	1.32042e7i	1.05200	+	1.05200i	0.0534279	+	0.998572i	$0.482985\pi$
$692$		0			0
$693$	1.74697e6	−	1.74697e6i	0.138182	−	0.138182i
$694$		0			0
$695$		−	668506.i		−	0.0524980i
$696$		0			0
$697$		−	6.41236e6i		−	0.499961i
$698$		0			0
$699$	−7.20112e6	+	7.20112e6i	−0.557452	+	0.557452i
$700$		0			0
$701$	−1.03528e7	−	1.03528e7i	−0.795723	−	0.795723i	0.186695	−	0.982418i	$-0.440222\pi$
$701$	−1.03528e7	−	1.03528e7i	−0.795723	−	0.795723i	−0.982418	+	0.186695i	$0.940222\pi$
$702$		0			0
$703$	−3.11577e7			−2.37781
$704$		0			0
$705$	3.12636e6			0.236900
$706$		0			0
$707$	−7.69114e6	−	7.69114e6i	−0.578685	−	0.578685i
$708$		0			0
$709$	−2.20601e6	+	2.20601e6i	−0.164813	+	0.164813i	−0.784695	−	0.619882i	$-0.787181\pi$
$709$	−2.20601e6	+	2.20601e6i	−0.164813	+	0.164813i	0.619882	+	0.784695i	$0.287181\pi$
$710$		0			0
$711$		−	2.40621e6i		−	0.178508i
$712$		0			0
$713$			5.49708e6i			0.404957i
$714$		0			0
$715$	4.09377e6	−	4.09377e6i	0.299474	−	0.299474i
$716$		0			0
$717$	2.01181e6	+	2.01181e6i	0.146147	+	0.146147i
$718$		0			0
$719$	7.60007e6			0.548271			0.274136	−	0.961691i	$-0.411608\pi$
$719$	7.60007e6			0.548271			0.274136	+	0.961691i	$0.411608\pi$
$720$		0			0
$721$	−1.08268e6			−0.0775645
$722$		0			0
$723$	1.29915e6	+	1.29915e6i	0.0924301	+	0.0924301i
$724$		0			0
$725$	−1.19200e6	+	1.19200e6i	−0.0842235	+	0.0842235i
$726$		0			0
$727$			1.18770e7i			0.833432i	0.909037	+	0.416716i	$0.136819\pi$
$727$			1.18770e7i			0.833432i	−0.909037	+	0.416716i	$0.863181\pi$
$728$		0			0
$729$		−	1.59494e7i		−	1.11154i
$730$		0			0
$731$	1.30892e7	−	1.30892e7i	0.905985	−	0.905985i
$732$		0			0
$733$	−1.72162e7	−	1.72162e7i	−1.18352	−	1.18352i	−0.978825	−	0.204698i	$-0.934379\pi$
$733$	−1.72162e7	−	1.72162e7i	−1.18352	−	1.18352i	−0.204698	−	0.978825i	$-0.565621\pi$
$734$		0			0
$735$	643711.			0.0439514
$736$		0			0
$737$	2.34145e7			1.58787
$738$		0			0
$739$	−7.02153e6	−	7.02153e6i	−0.472956	−	0.472956i	0.429914	−	0.902870i	$-0.358544\pi$
$739$	−7.02153e6	−	7.02153e6i	−0.472956	−	0.472956i	−0.902870	+	0.429914i	$0.858544\pi$
$740$		0			0
$741$	−1.59414e7	+	1.59414e7i	−1.06655	+	1.06655i
$742$		0			0
$743$		−	3.78191e6i		−	0.251327i	−0.992073	−	0.125664i	$-0.959894\pi$
$743$		−	3.78191e6i		−	0.251327i	0.992073	−	0.125664i	$-0.0401060\pi$
$744$		0			0
$745$		−	5.22214e6i		−	0.344713i
$746$		0			0
$747$	1.87221e6	−	1.87221e6i	0.122759	−	0.122759i
$748$		0			0
$749$	−1.45800e7	−	1.45800e7i	−0.949624	−	0.949624i
$750$		0			0
$751$	−1.35554e7			−0.877027			−0.438514	−	0.898725i	$-0.644495\pi$
$751$	−1.35554e7			−0.877027			−0.438514	+	0.898725i	$0.644495\pi$
$752$		0			0
$753$	9.64301e6			0.619762
$754$		0			0
$755$	−1.52199e6	−	1.52199e6i	−0.0971729	−	0.0971729i
$756$		0			0
$757$	−1.42526e7	+	1.42526e7i	−0.903974	+	0.903974i	−0.995777	−	0.0918036i	$-0.970737\pi$
$757$	−1.42526e7	+	1.42526e7i	−0.903974	+	0.903974i	0.0918036	+	0.995777i	$0.470737\pi$
$758$		0			0
$759$			2.84128e7i			1.79023i
$760$		0			0
$761$			5.64585e6i			0.353401i	0.984265	+	0.176701i	$0.0565424\pi$
$761$			5.64585e6i			0.353401i	−0.984265	+	0.176701i	$0.943458\pi$
$762$		0			0
$763$	−1.44587e7	+	1.44587e7i	−0.899118	+	0.899118i
$764$		0			0
$765$	−1.30571e6	−	1.30571e6i	−0.0806667	−	0.0806667i
$766$		0			0
$767$	1.78798e7			1.09743
$768$		0			0
$769$	1.87425e7			1.14291			0.571455	−	0.820633i	$-0.306379\pi$
$769$	1.87425e7			1.14291			0.571455	+	0.820633i	$0.306379\pi$
$770$		0			0
$771$	1.88708e7	+	1.88708e7i	1.14329	+	1.14329i
$772$		0			0
$773$	5.14466e6	−	5.14466e6i	0.309676	−	0.309676i	−0.535108	−	0.844784i	$-0.679729\pi$
$773$	5.14466e6	−	5.14466e6i	0.309676	−	0.309676i	0.844784	+	0.535108i	$0.179729\pi$
$774$		0			0
$775$			720430.i			0.0430861i
$776$		0			0
$777$			1.79769e7i			1.06822i
$778$		0			0
$779$	−8.62966e6	+	8.62966e6i	−0.509507	+	0.509507i
$780$		0			0
$781$	−3.86892e6	−	3.86892e6i	−0.226967	−	0.226967i
$782$		0			0
$783$	1.09546e7			0.638546
$784$		0			0
$785$	4.99426e6			0.289266
$786$		0			0
$787$	−3.76779e6	−	3.76779e6i	−0.216845	−	0.216845i	0.590322	−	0.807168i	$-0.299001\pi$
$787$	−3.76779e6	−	3.76779e6i	−0.216845	−	0.216845i	−0.807168	+	0.590322i	$0.799001\pi$
$788$		0			0
$789$	−4.79136e6	+	4.79136e6i	−0.274010	+	0.274010i
$790$		0			0
$791$			8.85612e6i			0.503271i
$792$		0			0
$793$		−	1.09980e7i		−	0.621057i
$794$		0			0
$795$	8.73026e6	−	8.73026e6i	0.489902	−	0.489902i
$796$		0			0
$797$	−1.12687e7	−	1.12687e7i	−0.628388	−	0.628388i	0.319274	−	0.947662i	$-0.396561\pi$
$797$	−1.12687e7	−	1.12687e7i	−0.628388	−	0.628388i	−0.947662	+	0.319274i	$0.896561\pi$
$798$		0			0
$799$	−1.39319e7			−0.772049
$800$		0			0
$801$	4.61066e6			0.253911
$802$		0			0
$803$	8.61062e6	+	8.61062e6i	0.471244	+	0.471244i
$804$		0			0
$805$	−1.03133e7	+	1.03133e7i	−0.560929	+	0.560929i
$806$		0			0
$807$		−	1.95113e7i		−	1.05464i
$808$		0			0
$809$			3.50449e6i			0.188258i	0.995560	+	0.0941291i	$0.0300066\pi$
$809$			3.50449e6i			0.188258i	−0.995560	+	0.0941291i	$0.969993\pi$
$810$		0			0
$811$	3.02322e6	−	3.02322e6i	0.161405	−	0.161405i	−0.621784	−	0.783189i	$-0.713592\pi$
$811$	3.02322e6	−	3.02322e6i	0.161405	−	0.161405i	0.783189	+	0.621784i	$0.213592\pi$
$812$		0			0
$813$	1.21335e7	+	1.21335e7i	0.643812	+	0.643812i
$814$		0			0
$815$	−1.00343e7			−0.529167
$816$		0			0
$817$	−3.52306e7			−1.84657
$818$		0			0
$819$	−2.22921e6	−	2.22921e6i	−0.116129	−	0.116129i
$820$		0			0
$821$	247372.	−	247372.i	0.0128083	−	0.0128083i	−0.700674	−	0.713482i	$-0.747117\pi$
$821$	247372.	−	247372.i	0.0128083	−	0.0128083i	0.713482	+	0.700674i	$0.247117\pi$
$822$		0			0
$823$			2.01832e7i			1.03870i	0.854562	+	0.519350i	$0.173826\pi$
$823$			2.01832e7i			1.03870i	−0.854562	+	0.519350i	$0.826174\pi$
$824$		0			0
$825$			3.72369e6i			0.190475i
$826$		0			0
$827$	1.59793e7	−	1.59793e7i	0.812445	−	0.812445i	−0.172555	−	0.985000i	$-0.555202\pi$
$827$	1.59793e7	−	1.59793e7i	0.812445	−	0.812445i	0.985000	+	0.172555i	$0.0552022\pi$
$828$		0			0
$829$	1.10547e7	+	1.10547e7i	0.558675	+	0.558675i	0.928930	−	0.370255i	$-0.120730\pi$
$829$	1.10547e7	+	1.10547e7i	0.558675	+	0.558675i	−0.370255	+	0.928930i	$0.620730\pi$
$830$		0			0
$831$	−3.34270e7			−1.67917
$832$		0			0
$833$	−2.86856e6			−0.143236
$834$		0			0
$835$	273435.	+	273435.i	0.0135718	+	0.0135718i
$836$		0			0
$837$	3.31040e6	−	3.31040e6i	0.163330	−	0.163330i
$838$		0			0
$839$		−	3.34841e7i		−	1.64223i	−0.570762	−	0.821116i	$-0.693352\pi$
$839$		−	3.34841e7i		−	1.64223i	0.570762	−	0.821116i	$-0.306648\pi$
$840$		0			0
$841$		−	1.32363e7i		−	0.645320i
$842$		0			0
$843$	−1.33129e7	+	1.33129e7i	−0.645215	+	0.645215i
$844$		0			0
$845$	1.33974e6	+	1.33974e6i	0.0645473	+	0.0645473i
$846$		0			0
$847$	2.49933e6			0.119706
$848$		0			0
$849$	1.86828e7			0.889554
$850$		0			0
$851$	3.54315e7	+	3.54315e7i	1.67713	+	1.67713i
$852$		0			0
$853$	−1.30905e7	+	1.30905e7i	−0.616004	+	0.616004i	−0.944504	−	0.328500i	$-0.893457\pi$
$853$	−1.30905e7	+	1.30905e7i	−0.616004	+	0.616004i	0.328500	+	0.944504i	$0.393457\pi$
$854$		0			0
$855$			3.51442e6i			0.164414i
$856$		0			0
$857$			3.48281e7i			1.61986i	0.586525	+	0.809931i	$0.300496\pi$
$857$			3.48281e7i			1.61986i	−0.586525	+	0.809931i	$0.699504\pi$
$858$		0			0
$859$	9.28672e6	−	9.28672e6i	0.429417	−	0.429417i	−0.459013	−	0.888430i	$-0.651797\pi$
$859$	9.28672e6	−	9.28672e6i	0.429417	−	0.429417i	0.888430	+	0.459013i	$0.151797\pi$
$860$		0			0
$861$	4.97900e6	+	4.97900e6i	0.228894	+	0.228894i
$862$		0			0
$863$	3.92643e7			1.79462			0.897308	−	0.441406i	$-0.145520\pi$
$863$	3.92643e7			1.79462			0.897308	+	0.441406i	$0.145520\pi$
$864$		0			0
$865$	1.53223e7			0.696281
$866$		0			0
$867$	−9.96607e6	−	9.96607e6i	−0.450273	−	0.450273i
$868$		0			0
$869$	1.52898e7	−	1.52898e7i	0.686835	−	0.686835i
$870$		0			0
$871$		−	2.98781e7i		−	1.33446i
$872$		0			0
$873$			2.21660e6i			0.0984354i
$874$		0			0
$875$	−1.35163e6	+	1.35163e6i	−0.0596811	+	0.0596811i
$876$		0			0
$877$	−1.40868e7	−	1.40868e7i	−0.618462	−	0.618462i	0.326675	−	0.945137i	$-0.394072\pi$
$877$	−1.40868e7	−	1.40868e7i	−0.618462	−	0.618462i	−0.945137	+	0.326675i	$0.894072\pi$
$878$		0			0
$879$	1.65918e7			0.724303
$880$		0			0
$881$	4.17564e7			1.81252			0.906261	−	0.422718i	$-0.138924\pi$
$881$	4.17564e7			1.81252			0.906261	+	0.422718i	$0.138924\pi$
$882$		0			0
$883$	1.75653e7	+	1.75653e7i	0.758148	+	0.758148i	0.975985	−	0.217837i	$-0.0699002\pi$
$883$	1.75653e7	+	1.75653e7i	0.758148	+	0.758148i	−0.217837	+	0.975985i	$0.569900\pi$
$884$		0			0
$885$	−8.13173e6	+	8.13173e6i	−0.349000	+	0.349000i
$886$		0			0
$887$			1.97380e7i			0.842353i	0.906979	+	0.421177i	$0.138383\pi$
$887$			1.97380e7i			0.842353i	−0.906979	+	0.421177i	$0.861617\pi$
$888$		0			0
$889$		−	1.50351e7i		−	0.638045i
$890$		0			0
$891$	1.36404e7	−	1.36404e7i	0.575616	−	0.575616i
$892$		0			0
$893$	1.87494e7	+	1.87494e7i	0.786790	+	0.786790i
$894$		0			0
$895$	6.97004e6			0.290856
$896$		0			0
$897$	3.62562e7			1.50453
$898$		0			0
$899$	2.19842e6	+	2.19842e6i	0.0907216	+	0.0907216i
$900$		0			0
$901$	−3.89045e7	+	3.89045e7i	−1.59657	+	1.59657i
$902$		0			0
$903$			2.03268e7i			0.829562i
$904$		0			0
$905$		−	3.05511e6i		−	0.123995i
$906$		0			0
$907$	−3.47142e7	+	3.47142e7i	−1.40116	+	1.40116i	−0.604738	+	0.796424i	$0.706722\pi$
$907$	−3.47142e7	+	3.47142e7i	−1.40116	+	1.40116i	−0.796424	+	0.604738i	$0.793278\pi$
$908$		0			0
$909$	2.98037e6	+	2.98037e6i	0.119636	+	0.119636i
$910$		0			0
$911$	−3.91881e7			−1.56444			−0.782220	−	0.623003i	$-0.785913\pi$
$911$	−3.91881e7			−1.56444			−0.782220	+	0.623003i	$0.785913\pi$
$912$		0			0
$913$	2.37933e7			0.944663
$914$		0			0
$915$	5.00189e6	+	5.00189e6i	0.197507	+	0.197507i
$916$		0			0
$917$	−9.18849e6	+	9.18849e6i	−0.360845	+	0.360845i
$918$		0			0
$919$			1.20777e7i			0.471732i	0.971786	+	0.235866i	$0.0757926\pi$
$919$			1.20777e7i			0.471732i	−0.971786	+	0.235866i	$0.924207\pi$
$920$		0			0
$921$		−	1.03223e7i		−	0.400985i
$922$		0			0
$923$	−4.93693e6	+	4.93693e6i	−0.190745	+	0.190745i
$924$		0			0
$925$	4.64354e6	+	4.64354e6i	0.178441	+	0.178441i
$926$		0			0
$927$	419548.			0.0160355
$928$		0			0
$929$	−2.07335e7			−0.788196			−0.394098	−	0.919068i	$-0.628943\pi$
$929$	−2.07335e7			−0.788196			−0.394098	+	0.919068i	$0.628943\pi$
$930$		0			0
$931$	3.86046e6	+	3.86046e6i	0.145971	+	0.145971i
$932$		0			0
$933$	−1.27994e7	+	1.27994e7i	−0.481377	+	0.481377i
$934$		0			0
$935$		−	1.65938e7i		−	0.620751i
$936$		0			0
$937$			2.96264e6i			0.110238i	0.998480	+	0.0551188i	$0.0175538\pi$
$937$			2.96264e6i			0.110238i	−0.998480	+	0.0551188i	$0.982446\pi$
$938$		0			0
$939$	−2.43138e7	+	2.43138e7i	−0.899890	+	0.899890i
$940$		0			0
$941$	−3.93651e6	−	3.93651e6i	−0.144923	−	0.144923i	0.630923	−	0.775846i	$-0.282676\pi$
$941$	−3.93651e6	−	3.93651e6i	−0.144923	−	0.144923i	−0.775846	+	0.630923i	$0.782676\pi$
$942$		0			0
$943$	1.96267e7			0.718735
$944$		0			0
$945$	1.24215e7			0.452476
$946$		0			0
$947$	−3.98729e6	−	3.98729e6i	−0.144478	−	0.144478i	0.631168	−	0.775646i	$-0.282576\pi$
$947$	−3.98729e6	−	3.98729e6i	−0.144478	−	0.144478i	−0.775646	+	0.631168i	$0.782576\pi$
$948$		0			0
$949$	1.09876e7	−	1.09876e7i	0.396037	−	0.396037i
$950$		0			0
$951$		−	3.71905e7i		−	1.33346i
$952$		0			0
$953$			2.98015e7i			1.06293i	0.847079	+	0.531467i	$0.178359\pi$
$953$			2.98015e7i			1.06293i	−0.847079	+	0.531467i	$0.821641\pi$
$954$		0			0
$955$	−1.23352e7	+	1.23352e7i	−0.437661	+	0.437661i
$956$		0			0
$957$	1.13630e7	+	1.13630e7i	0.401062	+	0.401062i
$958$		0			0
$959$	−9.01429e6			−0.316508
$960$		0			0
$961$	−2.73005e7			−0.953590
$962$		0			0
$963$	5.64985e6	+	5.64985e6i	0.196323	+	0.196323i
$964$		0			0
$965$	1.01318e7	−	1.01318e7i	0.350241	−	0.350241i
$966$		0			0
$967$			1.00777e7i			0.346574i	0.984871	+	0.173287i	$0.0554388\pi$
$967$			1.00777e7i			0.346574i	−0.984871	+	0.173287i	$0.944561\pi$
$968$		0			0
$969$			6.46175e7i			2.21076i
$970$		0			0
$971$	−1.87643e7	+	1.87643e7i	−0.638683	+	0.638683i	−0.950231	−	0.311548i	$-0.899153\pi$
$971$	−1.87643e7	+	1.87643e7i	−0.638683	+	0.638683i	0.311548	+	0.950231i	$0.399153\pi$
$972$		0			0
$973$	−2.31314e6	−	2.31314e6i	−0.0783285	−	0.0783285i
$974$		0			0
$975$	4.75161e6			0.160077
$976$		0			0
$977$	2.26099e6			0.0757812			0.0378906	−	0.999282i	$-0.487936\pi$
$977$	2.26099e6			0.0757812			0.0378906	+	0.999282i	$0.487936\pi$
$978$		0			0
$979$	2.92976e7	+	2.92976e7i	0.976957	+	0.976957i
$980$		0			0
$981$	5.60284e6	−	5.60284e6i	0.185881	−	0.185881i
$982$		0			0
$983$		−	3.91938e7i		−	1.29370i	−0.762618	−	0.646849i	$-0.776086\pi$
$983$		−	3.91938e7i		−	1.29370i	0.762618	−	0.646849i	$-0.223914\pi$
$984$		0			0
$985$		−	9.19115e6i		−	0.301842i
$986$		0			0
$987$	1.08177e7	−	1.08177e7i	0.353462	−	0.353462i
$988$		0			0
$989$	4.00631e7	+	4.00631e7i	1.30243	+	1.30243i
$990$		0			0
$991$	−5.81615e7			−1.88127			−0.940635	−	0.339420i	$-0.889769\pi$
$991$	−5.81615e7			−1.88127			−0.940635	+	0.339420i	$0.889769\pi$
$992$		0			0
$993$	−4.07210e7			−1.31052
$994$		0			0
$995$	−1.42938e6	−	1.42938e6i	−0.0457710	−	0.0457710i
$996$		0			0
$997$	4.33030e7	−	4.33030e7i	1.37969	−	1.37969i	0.534546	−	0.845139i	$-0.320483\pi$
$997$	4.33030e7	−	4.33030e7i	1.37969	−	1.37969i	0.845139	−	0.534546i	$-0.179517\pi$
$998$		0			0
$999$		−	4.26744e7i		−	1.35286i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.6.l.a.81.11		80
4.3	odd	2		80.6.l.a.61.20	yes	80
16.5	even	4	inner	320.6.l.a.241.11		80
16.11	odd	4		80.6.l.a.21.20	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.20	✓	80	16.11	odd	4
80.6.l.a.61.20	yes	80	4.3	odd	2
320.6.l.a.81.11		80	1.1	even	1	trivial
320.6.l.a.241.11		80	16.5	even	4	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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	320.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-9.88924 - 9.88924i) q^{3} +(-17.6777 + 17.6777i) q^{5} +122.335i q^{7} -47.4058i q^{9} +O(q^{10})\)	\(q+(-9.88924 - 9.88924i) q^{3} +(-17.6777 + 17.6777i) q^{5} +122.335i q^{7} -47.4058i q^{9} +(301.232 - 301.232i) q^{11} +(-384.386 - 384.386i) q^{13} +349.637 q^{15} -1558.08 q^{17} +(2096.85 + 2096.85i) q^{19} +(1209.80 - 1209.80i) q^{21} -4768.93i q^{23} -625.000i q^{25} +(-2871.89 + 2871.89i) q^{27} +(-1907.21 - 1907.21i) q^{29} -1152.69 q^{31} -5957.91 q^{33} +(-2162.60 - 2162.60i) q^{35} +(-7429.66 + 7429.66i) q^{37} +7602.58i q^{39} +4115.54i q^{41} +(-8400.86 + 8400.86i) q^{43} +(838.025 + 838.025i) q^{45} +8941.71 q^{47} +1841.08 q^{49} +(15408.3 + 15408.3i) q^{51} +(24969.5 - 24969.5i) q^{53} +10650.2i q^{55} -41472.4i q^{57} +(-23257.6 + 23257.6i) q^{59} +(14305.9 + 14305.9i) q^{61} +5799.41 q^{63} +13590.1 q^{65} +(38864.6 + 38864.6i) q^{67} +(-47161.1 + 47161.1i) q^{69} -12843.7i q^{71} +28584.7i q^{73} +(-6180.78 + 6180.78i) q^{75} +(36851.3 + 36851.3i) q^{77} +50757.6 q^{79} +45282.1 q^{81} +(39493.3 + 39493.3i) q^{83} +(27543.3 - 27543.3i) q^{85} +37721.7i q^{87} +97259.4i q^{89} +(47024.0 - 47024.0i) q^{91} +(11399.2 + 11399.2i) q^{93} -74134.7 q^{95} -46757.9 q^{97} +(-14280.1 - 14280.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 80 * q	\( 80 q - 1208 q^{11} + 1800 q^{15} - 2360 q^{19} + 7464 q^{27} - 8144 q^{29} + 21296 q^{37} - 32072 q^{43} + 88360 q^{47} - 192080 q^{49} + 5920 q^{51} - 49456 q^{53} - 44984 q^{59} + 48080 q^{61} - 158760 q^{63} - 61160 q^{67} - 22320 q^{69} - 14896 q^{77} - 177680 q^{79} - 524880 q^{81} + 329240 q^{83} + 132400 q^{85} - 364832 q^{91} - 362352 q^{93} - 288800 q^{95} - 659000 q^{99}+O(q^{100}) \) 80 * q - 1208 * q^11 + 1800 * q^15 - 2360 * q^19 + 7464 * q^27 - 8144 * q^29 + 21296 * q^37 - 32072 * q^43 + 88360 * q^47 - 192080 * q^49 + 5920 * q^51 - 49456 * q^53 - 44984 * q^59 + 48080 * q^61 - 158760 * q^63 - 61160 * q^67 - 22320 * q^69 - 14896 * q^77 - 177680 * q^79 - 524880 * q^81 + 329240 * q^83 + 132400 * q^85 - 364832 * q^91 - 362352 * q^93 - 288800 * q^95 - 659000 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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