LMFDB - Embedded newform 320.6.l.a.81.10

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			81.10
Character	$\chi$	$=$	320.81
Dual form			320.6.l.a.241.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.2463 - 10.2463i) q^{3} +(-17.6777 + 17.6777i) q^{5} +107.195i q^{7} -33.0270i q^{9} +O(q^{10})$	\(q+(-10.2463 - 10.2463i) q^{3} +(-17.6777 + 17.6777i) q^{5} +107.195i q^{7} -33.0270i q^{9} +(-221.799 + 221.799i) q^{11} +(-803.282 - 803.282i) q^{13} +362.261 q^{15} +364.972 q^{17} +(-654.936 - 654.936i) q^{19} +(1098.35 - 1098.35i) q^{21} +3201.73i q^{23} -625.000i q^{25} +(-2828.25 + 2828.25i) q^{27} +(4482.55 + 4482.55i) q^{29} -5318.06 q^{31} +4545.24 q^{33} +(-1894.95 - 1894.95i) q^{35} +(-4842.58 + 4842.58i) q^{37} +16461.3i q^{39} -12004.8i q^{41} +(-196.241 + 196.241i) q^{43} +(583.841 + 583.841i) q^{45} +27915.6 q^{47} +5316.27 q^{49} +(-3739.61 - 3739.61i) q^{51} +(13547.2 - 13547.2i) q^{53} -7841.79i q^{55} +13421.3i q^{57} +(19135.0 - 19135.0i) q^{59} +(-27659.4 - 27659.4i) q^{61} +3540.33 q^{63} +28400.3 q^{65} +(10436.6 + 10436.6i) q^{67} +(32805.9 - 32805.9i) q^{69} +43847.1i q^{71} -32503.6i q^{73} +(-6403.93 + 6403.93i) q^{75} +(-23775.8 - 23775.8i) q^{77} +54063.2 q^{79} +49932.6 q^{81} +(-41170.0 - 41170.0i) q^{83} +(-6451.85 + 6451.85i) q^{85} -91859.0i q^{87} -21030.0i q^{89} +(86107.7 - 86107.7i) q^{91} +(54490.4 + 54490.4i) q^{93} +23155.5 q^{95} +76104.2 q^{97} +(7325.38 + 7325.38i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−10.2463	−	10.2463i	−0.657300	−	0.657300i	0.297440	−	0.954740i	$-0.403867\pi$
$3$	−10.2463	−	10.2463i	−0.657300	−	0.657300i	−0.954740	+	0.297440i	$0.903867\pi$
$4$		0			0
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$6$		0			0
$7$			107.195i			0.826854i	0.910537	+	0.413427i	$0.135668\pi$
$7$			107.195i			0.826854i	−0.910537	+	0.413427i	$0.864332\pi$
$8$		0			0
$9$		−	33.0270i		−	0.135914i
$10$		0			0
$11$	−221.799	+	221.799i	−0.552686	+	0.552686i	−0.927215	−	0.374529i	$-0.877804\pi$
$11$	−221.799	+	221.799i	−0.552686	+	0.552686i	0.374529	+	0.927215i	$0.377804\pi$
$12$		0			0
$13$	−803.282	−	803.282i	−1.31829	−	1.31829i	−0.915132	−	0.403154i	$-0.867914\pi$
$13$	−803.282	−	803.282i	−1.31829	−	1.31829i	−0.403154	−	0.915132i	$-0.632086\pi$
$14$		0			0
$15$	362.261			0.415713
$16$		0			0
$17$	364.972			0.306293			0.153146	−	0.988204i	$-0.451059\pi$
$17$	364.972			0.306293			0.153146	+	0.988204i	$0.451059\pi$
$18$		0			0
$19$	−654.936	−	654.936i	−0.416212	−	0.416212i	0.467684	−	0.883896i	$-0.345089\pi$
$19$	−654.936	−	654.936i	−0.416212	−	0.416212i	−0.883896	+	0.467684i	$0.845089\pi$
$20$		0			0
$21$	1098.35	−	1098.35i	0.543491	−	0.543491i
$22$		0			0
$23$			3201.73i			1.26202i	0.775776	+	0.631009i	$0.217359\pi$
$23$			3201.73i			1.26202i	−0.775776	+	0.631009i	$0.782641\pi$
$24$		0			0
$25$		−	625.000i		−	0.200000i
$26$		0			0
$27$	−2828.25	+	2828.25i	−0.746636	+	0.746636i
$28$		0			0
$29$	4482.55	+	4482.55i	0.989760	+	0.989760i	0.999948	−	0.0101878i	$-0.00324294\pi$
$29$	4482.55	+	4482.55i	0.989760	+	0.989760i	−0.0101878	+	0.999948i	$0.503243\pi$
$30$		0			0
$31$	−5318.06			−0.993914			−0.496957	−	0.867775i	$-0.665549\pi$
$31$	−5318.06			−0.993914			−0.496957	+	0.867775i	$0.665549\pi$
$32$		0			0
$33$	4545.24			0.726561
$34$		0			0
$35$	−1894.95	−	1894.95i	−0.261474	−	0.261474i
$36$		0			0
$37$	−4842.58	+	4842.58i	−0.581531	+	0.581531i	−0.935324	−	0.353793i	$-0.884892\pi$
$37$	−4842.58	+	4842.58i	−0.581531	+	0.581531i	0.353793	+	0.935324i	$0.384892\pi$
$38$		0			0
$39$			16461.3i			1.73302i
$40$		0			0
$41$		−	12004.8i		−	1.11530i	−0.830075	−	0.557652i	$-0.811702\pi$
$41$		−	12004.8i		−	1.11530i	0.830075	−	0.557652i	$-0.188298\pi$
$42$		0			0
$43$	−196.241	+	196.241i	−0.0161852	+	0.0161852i	−0.715153	−	0.698968i	$-0.753643\pi$
$43$	−196.241	+	196.241i	−0.0161852	+	0.0161852i	0.698968	+	0.715153i	$0.253643\pi$
$44$		0			0
$45$	583.841	+	583.841i	0.0429797	+	0.0429797i
$46$		0			0
$47$	27915.6			1.84333			0.921664	−	0.387990i	$-0.126830\pi$
$47$	27915.6			1.84333			0.921664	+	0.387990i	$0.126830\pi$
$48$		0			0
$49$	5316.27			0.316313
$50$		0			0
$51$	−3739.61	−	3739.61i	−0.201326	−	0.201326i
$52$		0			0
$53$	13547.2	−	13547.2i	0.662459	−	0.662459i	−0.293500	−	0.955959i	$-0.594820\pi$
$53$	13547.2	−	13547.2i	0.662459	−	0.662459i	0.955959	+	0.293500i	$0.0948200\pi$
$54$		0			0
$55$		−	7841.79i		−	0.349550i
$56$		0			0
$57$			13421.3i			0.547153i
$58$		0			0
$59$	19135.0	−	19135.0i	0.715646	−	0.715646i	−0.252064	−	0.967711i	$-0.581109\pi$
$59$	19135.0	−	19135.0i	0.715646	−	0.715646i	0.967711	+	0.252064i	$0.0811094\pi$
$60$		0			0
$61$	−27659.4	−	27659.4i	−0.951738	−	0.951738i	0.0471497	−	0.998888i	$-0.484986\pi$
$61$	−27659.4	−	27659.4i	−0.951738	−	0.951738i	−0.998888	+	0.0471497i	$0.984986\pi$
$62$		0			0
$63$	3540.33			0.112381
$64$		0			0
$65$	28400.3			0.833757
$66$		0			0
$67$	10436.6	+	10436.6i	0.284036	+	0.284036i	0.834716	−	0.550680i	$-0.185632\pi$
$67$	10436.6	+	10436.6i	0.284036	+	0.284036i	−0.550680	+	0.834716i	$0.685632\pi$
$68$		0			0
$69$	32805.9	−	32805.9i	0.829524	−	0.829524i
$70$		0			0
$71$			43847.1i			1.03227i	0.856506	+	0.516137i	$0.172630\pi$
$71$			43847.1i			1.03227i	−0.856506	+	0.516137i	$0.827370\pi$
$72$		0			0
$73$		−	32503.6i		−	0.713878i	−0.934128	−	0.356939i	$-0.883820\pi$
$73$		−	32503.6i		−	0.713878i	0.934128	−	0.356939i	$-0.116180\pi$
$74$		0			0
$75$	−6403.93	+	6403.93i	−0.131460	+	0.131460i
$76$		0			0
$77$	−23775.8	−	23775.8i	−0.456991	−	0.456991i
$78$		0			0
$79$	54063.2			0.974618			0.487309	−	0.873230i	$-0.337979\pi$
$79$	54063.2			0.974618			0.487309	+	0.873230i	$0.337979\pi$
$80$		0			0
$81$	49932.6			0.845614
$82$		0			0
$83$	−41170.0	−	41170.0i	−0.655973	−	0.655973i	0.298452	−	0.954425i	$-0.403530\pi$
$83$	−41170.0	−	41170.0i	−0.655973	−	0.655973i	−0.954425	+	0.298452i	$0.903530\pi$
$84$		0			0
$85$	−6451.85	+	6451.85i	−0.0968583	+	0.0968583i
$86$		0			0
$87$		−	91859.0i		−	1.30114i
$88$		0			0
$89$		−	21030.0i		−	0.281426i	−0.990050	−	0.140713i	$-0.955061\pi$
$89$		−	21030.0i		−	0.281426i	0.990050	−	0.140713i	$-0.0449395\pi$
$90$		0			0
$91$	86107.7	−	86107.7i	1.09003	−	1.09003i
$92$		0			0
$93$	54490.4	+	54490.4i	0.653300	+	0.653300i
$94$		0			0
$95$	23155.5			0.263236
$96$		0			0
$97$	76104.2			0.821258			0.410629	−	0.911803i	$-0.365309\pi$
$97$	76104.2			0.821258			0.410629	+	0.911803i	$0.365309\pi$
$98$		0			0
$99$	7325.38	+	7325.38i	0.0751177	+	0.0751177i
$100$		0			0
$101$	71459.7	−	71459.7i	0.697040	−	0.697040i	−0.266731	−	0.963771i	$-0.585943\pi$
$101$	71459.7	−	71459.7i	0.697040	−	0.697040i	0.963771	+	0.266731i	$0.0859434\pi$
$102$		0			0
$103$			11027.6i			0.102420i	0.998688	+	0.0512102i	$0.0163078\pi$
$103$			11027.6i			0.102420i	−0.998688	+	0.0512102i	$0.983692\pi$
$104$		0			0
$105$			38832.5i			0.343734i
$106$		0			0
$107$	52499.5	−	52499.5i	0.443298	−	0.443298i	−0.449821	−	0.893119i	$-0.648512\pi$
$107$	52499.5	−	52499.5i	0.443298	−	0.443298i	0.893119	+	0.449821i	$0.148512\pi$
$108$		0			0
$109$	77971.0	+	77971.0i	0.628589	+	0.628589i	0.947713	−	0.319124i	$-0.103389\pi$
$109$	77971.0	+	77971.0i	0.628589	+	0.628589i	−0.319124	+	0.947713i	$0.603389\pi$
$110$		0			0
$111$	99237.0			0.764480
$112$		0			0
$113$	−22081.2			−0.162677			−0.0813387	−	0.996687i	$-0.525920\pi$
$113$	−22081.2			−0.162677			−0.0813387	+	0.996687i	$0.525920\pi$
$114$		0			0
$115$	−56599.2	−	56599.2i	−0.399085	−	0.399085i
$116$		0			0
$117$	−26530.0	+	26530.0i	−0.179173	+	0.179173i
$118$		0			0
$119$			39123.1i			0.253259i
$120$		0			0
$121$			62661.0i			0.389076i
$122$		0			0
$123$	−123004.	+	123004.i	−0.733090	+	0.733090i
$124$		0			0
$125$	11048.5	+	11048.5i	0.0632456	+	0.0632456i
$126$		0			0
$127$	248802.			1.36881			0.684406	−	0.729101i	$-0.260062\pi$
$127$	248802.			1.36881			0.684406	+	0.729101i	$0.260062\pi$
$128$		0			0
$129$	4021.48			0.0212771
$130$		0			0
$131$	−85096.4	−	85096.4i	−0.433244	−	0.433244i	0.456486	−	0.889730i	$-0.349108\pi$
$131$	−85096.4	−	85096.4i	−0.433244	−	0.433244i	−0.889730	+	0.456486i	$0.849108\pi$
$132$		0			0
$133$	70205.8	−	70205.8i	0.344147	−	0.344147i
$134$		0			0
$135$		−	99993.9i		−	0.472214i
$136$		0			0
$137$			329996.i			1.50213i	0.660229	+	0.751064i	$0.270459\pi$
$137$			329996.i			1.50213i	−0.660229	+	0.751064i	$0.729541\pi$
$138$		0			0
$139$	−59892.9	+	59892.9i	−0.262929	+	0.262929i	−0.826243	−	0.563314i	$-0.809526\pi$
$139$	−59892.9	+	59892.9i	−0.262929	+	0.262929i	0.563314	+	0.826243i	$0.309526\pi$
$140$		0			0
$141$	−286031.	−	286031.i	−1.21162	−	1.21162i
$142$		0			0
$143$	356335.			1.45720
$144$		0			0
$145$	−158482.			−0.625979
$146$		0			0
$147$	−54472.0	−	54472.0i	−0.207912	−	0.207912i
$148$		0			0
$149$	270127.	−	270127.i	0.996788	−	0.996788i	−0.00320643	−	0.999995i	$-0.501021\pi$
$149$	270127.	−	270127.i	0.996788	−	0.996788i	0.999995	+	0.00320643i	$0.00102064\pi$
$150$		0			0
$151$		−	350356.i		−	1.25045i	−0.780444	−	0.625226i	$-0.785007\pi$
$151$		−	350356.i		−	1.25045i	0.780444	−	0.625226i	$-0.214993\pi$
$152$		0			0
$153$		−	12053.9i		−	0.0416294i
$154$		0			0
$155$	94010.9	−	94010.9i	0.314303	−	0.314303i
$156$		0			0
$157$	380068.	+	380068.i	1.23059	+	1.23059i	0.963739	+	0.266848i	$0.0859823\pi$
$157$	380068.	+	380068.i	1.23059	+	1.23059i	0.266848	+	0.963739i	$0.414018\pi$
$158$		0			0
$159$	−277617.			−0.870869
$160$		0			0
$161$	−343209.			−1.04350
$162$		0			0
$163$	300170.	+	300170.i	0.884909	+	0.884909i	0.994029	−	0.109120i	$-0.0348032\pi$
$163$	300170.	+	300170.i	0.884909	+	0.884909i	−0.109120	+	0.994029i	$0.534803\pi$
$164$		0			0
$165$	−80349.3	+	80349.3i	−0.229759	+	0.229759i
$166$		0			0
$167$			570089.i			1.58180i	0.611946	+	0.790900i	$0.290387\pi$
$167$			570089.i			1.58180i	−0.611946	+	0.790900i	$0.709613\pi$
$168$		0			0
$169$			919231.i			2.47576i
$170$		0			0
$171$	−21630.6	+	21630.6i	−0.0565690	+	0.0565690i
$172$		0			0
$173$	−235681.	−	235681.i	−0.598701	−	0.598701i	0.341266	−	0.939967i	$-0.389144\pi$
$173$	−235681.	−	235681.i	−0.598701	−	0.598701i	−0.939967	+	0.341266i	$0.889144\pi$
$174$		0			0
$175$	66996.8			0.165371
$176$		0			0
$177$	−392126.			−0.940788
$178$		0			0
$179$	−203552.	−	203552.i	−0.474836	−	0.474836i	0.428640	−	0.903476i	$-0.358993\pi$
$179$	−203552.	−	203552.i	−0.474836	−	0.474836i	−0.903476	+	0.428640i	$0.858993\pi$
$180$		0			0
$181$	530787.	−	530787.i	1.20427	−	1.20427i	0.231416	−	0.972855i	$-0.425664\pi$
$181$	530787.	−	530787.i	1.20427	−	1.20427i	0.972855	−	0.231416i	$-0.0743357\pi$
$182$		0			0
$183$			566812.i			1.25115i
$184$		0			0
$185$		−	171211.i		−	0.367792i
$186$		0			0
$187$	−80950.5	+	80950.5i	−0.169284	+	0.169284i
$188$		0			0
$189$	−303174.	−	303174.i	−0.617359	−	0.617359i
$190$		0			0
$191$	−129113.			−0.256087			−0.128044	−	0.991769i	$-0.540870\pi$
$191$	−129113.			−0.256087			−0.128044	+	0.991769i	$0.540870\pi$
$192$		0			0
$193$	−421524.			−0.814571			−0.407285	−	0.913301i	$-0.633525\pi$
$193$	−421524.			−0.814571			−0.407285	+	0.913301i	$0.633525\pi$
$194$		0			0
$195$	−290998.	−	290998.i	−0.548029	−	0.548029i
$196$		0			0
$197$	269272.	−	269272.i	0.494341	−	0.494341i	−0.415330	−	0.909671i	$-0.636334\pi$
$197$	269272.	−	269272.i	0.494341	−	0.494341i	0.909671	+	0.415330i	$0.136334\pi$
$198$		0			0
$199$		−	689798.i		−	1.23478i	−0.786658	−	0.617389i	$-0.788190\pi$
$199$		−	689798.i		−	1.23478i	0.786658	−	0.617389i	$-0.211810\pi$
$200$		0			0
$201$		−	213874.i		−	0.373394i
$202$		0			0
$203$	−480506.	+	480506.i	−0.818387	+	0.818387i
$204$		0			0
$205$	212216.	+	212216.i	0.352690	+	0.352690i
$206$		0			0
$207$	105744.			0.171526
$208$		0			0
$209$	290529.			0.460070
$210$		0			0
$211$	−257425.	−	257425.i	−0.398057	−	0.398057i	0.479490	−	0.877547i	$-0.340822\pi$
$211$	−257425.	−	257425.i	−0.398057	−	0.398057i	−0.877547	+	0.479490i	$0.840822\pi$
$212$		0			0
$213$	449270.	−	449270.i	0.678513	−	0.678513i
$214$		0			0
$215$		−	6938.16i		−	0.0102364i
$216$		0			0
$217$		−	570069.i		−	0.821822i
$218$		0			0
$219$	−333041.	+	333041.i	−0.469232	+	0.469232i
$220$		0			0
$221$	−293175.	−	293175.i	−0.403782	−	0.403782i
$222$		0			0
$223$	188545.			0.253895			0.126947	−	0.991909i	$-0.459482\pi$
$223$	188545.			0.253895			0.126947	+	0.991909i	$0.459482\pi$
$224$		0			0
$225$	−20641.9			−0.0271828
$226$		0			0
$227$	−891273.	−	891273.i	−1.14801	−	1.14801i	−0.986943	−	0.161068i	$-0.948506\pi$
$227$	−891273.	−	891273.i	−1.14801	−	1.14801i	−0.161068	−	0.986943i	$-0.551494\pi$
$228$		0			0
$229$	−305125.	+	305125.i	−0.384493	+	0.384493i	−0.872718	−	0.488225i	$-0.837645\pi$
$229$	−305125.	+	305125.i	−0.384493	+	0.384493i	0.488225	+	0.872718i	$0.337645\pi$
$230$		0			0
$231$			487227.i			0.600760i
$232$		0			0
$233$			688626.i			0.830986i	0.909596	+	0.415493i	$0.136391\pi$
$233$			688626.i			0.830986i	−0.909596	+	0.415493i	$0.863609\pi$
$234$		0			0
$235$	−493483.	+	493483.i	−0.582911	+	0.582911i
$236$		0			0
$237$	−553948.	−	553948.i	−0.640616	−	0.640616i
$238$		0			0
$239$	137710.			0.155945			0.0779723	−	0.996956i	$-0.475155\pi$
$239$	137710.			0.155945			0.0779723	+	0.996956i	$0.475155\pi$
$240$		0			0
$241$	322174.			0.357312			0.178656	−	0.983912i	$-0.442825\pi$
$241$	322174.			0.357312			0.178656	+	0.983912i	$0.442825\pi$
$242$		0			0
$243$	175641.	+	175641.i	0.190814	+	0.190814i
$244$		0			0
$245$	−93979.2	+	93979.2i	−0.100027	+	0.100027i
$246$		0			0
$247$			1.05220e6i			1.09737i
$248$		0			0
$249$			843680.i			0.862341i
$250$		0			0
$251$	−598775.	+	598775.i	−0.599901	+	0.599901i	−0.940286	−	0.340385i	$-0.889442\pi$
$251$	−598775.	+	598775.i	−0.599901	+	0.599901i	0.340385	+	0.940286i	$0.389442\pi$
$252$		0			0
$253$	−710142.	−	710142.i	−0.697500	−	0.697500i
$254$		0			0
$255$	132215.			0.127330
$256$		0			0
$257$	956071.			0.902937			0.451469	−	0.892287i	$-0.350900\pi$
$257$	956071.			0.902937			0.451469	+	0.892287i	$0.350900\pi$
$258$		0			0
$259$	−519100.	−	519100.i	−0.480841	−	0.480841i
$260$		0			0
$261$	148045.	−	148045.i	0.134522	−	0.134522i
$262$		0			0
$263$			1.08736e6i			0.969356i	0.874693	+	0.484678i	$0.161063\pi$
$263$			1.08736e6i			0.969356i	−0.874693	+	0.484678i	$0.838937\pi$
$264$		0			0
$265$			478965.i			0.418976i
$266$		0			0
$267$	−215479.	+	215479.i	−0.184981	+	0.184981i
$268$		0			0
$269$	835027.	+	835027.i	0.703590	+	0.703590i	0.965179	−	0.261589i	$-0.0842465\pi$
$269$	835027.	+	835027.i	0.703590	+	0.703590i	−0.261589	+	0.965179i	$0.584246\pi$
$270$		0			0
$271$	516488.			0.427206			0.213603	−	0.976921i	$-0.431480\pi$
$271$	516488.			0.427206			0.213603	+	0.976921i	$0.431480\pi$
$272$		0			0
$273$	−1.76457e6			−1.43295
$274$		0			0
$275$	138625.	+	138625.i	0.110537	+	0.110537i
$276$		0			0
$277$	−1.28085e6	+	1.28085e6i	−1.00300	+	1.00300i	−0.00300220	+	0.999995i	$0.500956\pi$
$277$	−1.28085e6	+	1.28085e6i	−1.00300	+	1.00300i	−0.999995	+	0.00300220i	$0.999044\pi$
$278$		0			0
$279$			175640.i			0.135087i
$280$		0			0
$281$			1597.64i			0.00120702i	1.00000		0.000603508i	$0.000192103\pi$
$281$			1597.64i			0.00120702i	−1.00000		0.000603508i	$0.999808\pi$
$282$		0			0
$283$	−329511.	+	329511.i	−0.244570	+	0.244570i	−0.818738	−	0.574168i	$-0.805326\pi$
$283$	−329511.	+	329511.i	−0.244570	+	0.244570i	0.574168	+	0.818738i	$0.305326\pi$
$284$		0			0
$285$	−237258.	−	237258.i	−0.173025	−	0.173025i
$286$		0			0
$287$	1.28685e6			0.922194
$288$		0			0
$289$	−1.28665e6			−0.906185
$290$		0			0
$291$	−779786.	−	779786.i	−0.539813	−	0.539813i
$292$		0			0
$293$	−1.96984e6	+	1.96984e6i	−1.34048	+	1.34048i	−0.444905	+	0.895578i	$0.646763\pi$
$293$	−1.96984e6	+	1.96984e6i	−1.34048	+	1.34048i	−0.895578	+	0.444905i	$0.853237\pi$
$294$		0			0
$295$			676524.i			0.452614i
$296$		0			0
$297$		−	1.25461e6i		−	0.825311i
$298$		0			0
$299$	2.57189e6	−	2.57189e6i	1.66370	−	1.66370i
$300$		0			0
$301$	−21036.0	−	21036.0i	−0.0133828	−	0.0133828i
$302$		0			0
$303$	−1.46439e6			−0.916329
$304$		0			0
$305$	977906.			0.601932
$306$		0			0
$307$	−52781.8	−	52781.8i	−0.0319623	−	0.0319623i	0.690945	−	0.722907i	$-0.257195\pi$
$307$	−52781.8	−	52781.8i	−0.0319623	−	0.0319623i	−0.722907	+	0.690945i	$0.757195\pi$
$308$		0			0
$309$	112992.	−	112992.i	0.0673209	−	0.0673209i
$310$		0			0
$311$		−	1.68699e6i		−	0.989034i	−0.869168	−	0.494517i	$-0.835345\pi$
$311$		−	1.68699e6i		−	0.989034i	0.869168	−	0.494517i	$-0.164655\pi$
$312$		0			0
$313$			1.81610e6i			1.04780i	0.851780	+	0.523900i	$0.175524\pi$
$313$			1.81610e6i			1.04780i	−0.851780	+	0.523900i	$0.824476\pi$
$314$		0			0
$315$	−62584.8	+	62584.8i	−0.0355379	+	0.0355379i
$316$		0			0
$317$	−559123.	−	559123.i	−0.312507	−	0.312507i	0.533373	−	0.845880i	$-0.320924\pi$
$317$	−559123.	−	559123.i	−0.312507	−	0.312507i	−0.845880	+	0.533373i	$0.820924\pi$
$318$		0			0
$319$	−1.98845e6			−1.09405
$320$		0			0
$321$	−1.07585e6			−0.582759
$322$		0			0
$323$	−239033.	−	239033.i	−0.127483	−	0.127483i
$324$		0			0
$325$	−502051.	+	502051.i	−0.263657	+	0.263657i
$326$		0			0
$327$		−	1.59783e6i		−	0.826343i
$328$		0			0
$329$			2.99241e6i			1.52416i
$330$		0			0
$331$	578758.	−	578758.i	0.290353	−	0.290353i	−0.546866	−	0.837220i	$-0.684179\pi$
$331$	578758.	−	578758.i	0.290353	−	0.290353i	0.837220	+	0.546866i	$0.184179\pi$
$332$		0			0
$333$	159936.	+	159936.i	0.0790381	+	0.0790381i
$334$		0			0
$335$	−368991.			−0.179640
$336$		0			0
$337$	302009.			0.144859			0.0724294	−	0.997374i	$-0.476925\pi$
$337$	302009.			0.144859			0.0724294	+	0.997374i	$0.476925\pi$
$338$		0			0
$339$	226251.	+	226251.i	0.106928	+	0.106928i
$340$		0			0
$341$	1.17954e6	−	1.17954e6i	0.549323	−	0.549323i
$342$		0			0
$343$			2.37150e6i			1.08840i
$344$		0			0
$345$			1.15986e6i			0.524637i
$346$		0			0
$347$	−1.50429e6	+	1.50429e6i	−0.670668	+	0.670668i	−0.957870	−	0.287202i	$-0.907275\pi$
$347$	−1.50429e6	+	1.50429e6i	−0.670668	+	0.670668i	0.287202	+	0.957870i	$0.407275\pi$
$348$		0			0
$349$	1.83398e6	+	1.83398e6i	0.805991	+	0.805991i	0.984024	−	0.178033i	$-0.0569734\pi$
$349$	1.83398e6	+	1.83398e6i	0.805991	+	0.805991i	−0.178033	+	0.984024i	$0.556973\pi$
$350$		0			0
$351$	4.54377e6			1.96856
$352$		0			0
$353$	1.77583e6			0.758518			0.379259	−	0.925291i	$-0.376179\pi$
$353$	1.77583e6			0.758518			0.379259	+	0.925291i	$0.376179\pi$
$354$		0			0
$355$	−775114.	−	775114.i	−0.326433	−	0.326433i
$356$		0			0
$357$	400866.	−	400866.i	0.166467	−	0.166467i
$358$		0			0
$359$		−	3.49681e6i		−	1.43198i	−0.698112	−	0.715989i	$-0.745976\pi$
$359$		−	3.49681e6i		−	1.43198i	0.698112	−	0.715989i	$-0.254024\pi$
$360$		0			0
$361$		−	1.61822e6i		−	0.653535i
$362$		0			0
$363$	642043.	−	642043.i	0.255739	−	0.255739i
$364$		0			0
$365$	574588.	+	574588.i	0.225748	+	0.225748i
$366$		0			0
$367$	2.62089e6			1.01574			0.507871	−	0.861433i	$-0.330433\pi$
$367$	2.62089e6			1.01574			0.507871	+	0.861433i	$0.330433\pi$
$368$		0			0
$369$	−396482.			−0.151585
$370$		0			0
$371$	1.45219e6	+	1.45219e6i	0.547757	+	0.547757i
$372$		0			0
$373$	2.79160e6	−	2.79160e6i	1.03892	−	1.03892i	0.0397054	−	0.999211i	$-0.487358\pi$
$373$	2.79160e6	−	2.79160e6i	1.03892	−	1.03892i	0.999211	−	0.0397054i	$-0.0126419\pi$
$374$		0			0
$375$		−	226413.i		−	0.0831426i
$376$		0			0
$377$		−	7.20150e6i		−	2.60957i
$378$		0			0
$379$	461750.	−	461750.i	0.165124	−	0.165124i	−0.619708	−	0.784832i	$-0.712749\pi$
$379$	461750.	−	461750.i	0.165124	−	0.165124i	0.784832	+	0.619708i	$0.212749\pi$
$380$		0			0
$381$	−2.54929e6	−	2.54929e6i	−0.899720	−	0.899720i
$382$		0			0
$383$	−4.80889e6			−1.67513			−0.837563	−	0.546341i	$-0.816020\pi$
$383$	−4.80889e6			−1.67513			−0.837563	+	0.546341i	$0.816020\pi$
$384$		0			0
$385$	840600.			0.289026
$386$		0			0
$387$	6481.25	+	6481.25i	0.00219979	+	0.00219979i
$388$		0			0
$389$	2.78429e6	−	2.78429e6i	0.932910	−	0.932910i	−0.0649768	−	0.997887i	$-0.520697\pi$
$389$	2.78429e6	−	2.78429e6i	0.932910	−	0.932910i	0.997887	+	0.0649768i	$0.0206974\pi$
$390$		0			0
$391$			1.16854e6i			0.386547i
$392$		0			0
$393$			1.74384e6i			0.569543i
$394$		0			0
$395$	−955712.	+	955712.i	−0.308201	+	0.308201i
$396$		0			0
$397$	3.23710e6	+	3.23710e6i	1.03081	+	1.03081i	0.999510	+	0.0313023i	$0.00996545\pi$
$397$	3.23710e6	+	3.23710e6i	1.03081	+	1.03081i	0.0313023	+	0.999510i	$0.490035\pi$
$398$		0			0
$399$	−1.43870e6			−0.452415
$400$		0			0
$401$	3.35378e6			1.04154			0.520768	−	0.853698i	$-0.325646\pi$
$401$	3.35378e6			1.04154			0.520768	+	0.853698i	$0.325646\pi$
$402$		0			0
$403$	4.27190e6	+	4.27190e6i	1.31026	+	1.31026i
$404$		0			0
$405$	−882693.	+	882693.i	−0.267407	+	0.267407i
$406$		0			0
$407$		−	2.14816e6i		−	0.642808i
$408$		0			0
$409$		−	4.64018e6i		−	1.37160i	−0.727791	−	0.685799i	$-0.759453\pi$
$409$		−	4.64018e6i		−	1.37160i	0.727791	−	0.685799i	$-0.240547\pi$
$410$		0			0
$411$	3.38123e6	−	3.38123e6i	0.987349	−	0.987349i
$412$		0			0
$413$	2.05117e6	+	2.05117e6i	0.591735	+	0.591735i
$414$		0			0
$415$	1.45558e6			0.414873
$416$		0			0
$417$	1.22736e6			0.345646
$418$		0			0
$419$	2.47570e6	+	2.47570e6i	0.688910	+	0.688910i	0.961991	−	0.273081i	$-0.0880427\pi$
$419$	2.47570e6	+	2.47570e6i	0.688910	+	0.688910i	−0.273081	+	0.961991i	$0.588043\pi$
$420$		0			0
$421$	−1.28841e6	+	1.28841e6i	−0.354281	+	0.354281i	−0.861700	−	0.507419i	$-0.830600\pi$
$421$	−1.28841e6	+	1.28841e6i	−0.354281	+	0.354281i	0.507419	+	0.861700i	$0.330600\pi$
$422$		0			0
$423$		−	921970.i		−	0.250534i
$424$		0			0
$425$		−	228107.i		−	0.0612586i
$426$		0			0
$427$	2.96494e6	−	2.96494e6i	0.786948	−	0.786948i
$428$		0			0
$429$	−3.65111e6	−	3.65111e6i	−0.957816	−	0.957816i
$430$		0			0
$431$	−1.61577e6			−0.418974			−0.209487	−	0.977811i	$-0.567179\pi$
$431$	−1.61577e6			−0.418974			−0.209487	+	0.977811i	$0.567179\pi$
$432$		0			0
$433$	−1.88619e6			−0.483466			−0.241733	−	0.970343i	$-0.577716\pi$
$433$	−1.88619e6			−0.483466			−0.241733	+	0.970343i	$0.577716\pi$
$434$		0			0
$435$	1.62385e6	+	1.62385e6i	0.411456	+	0.411456i
$436$		0			0
$437$	2.09693e6	−	2.09693e6i	0.525267	−	0.525267i
$438$		0			0
$439$		−	1.61358e6i		−	0.399604i	−0.979836	−	0.199802i	$-0.935970\pi$
$439$		−	1.61358e6i		−	0.399604i	0.979836	−	0.199802i	$-0.0640299\pi$
$440$		0			0
$441$		−	175581.i		−	0.0429912i
$442$		0			0
$443$	−577577.	+	577577.i	−0.139830	+	0.139830i	−0.773557	−	0.633727i	$-0.781524\pi$
$443$	−577577.	+	577577.i	−0.139830	+	0.139830i	0.633727	+	0.773557i	$0.281524\pi$
$444$		0			0
$445$	371761.	+	371761.i	0.0889947	+	0.0889947i
$446$		0			0
$447$	−5.53561e6			−1.31038
$448$		0			0
$449$	2.64466e6			0.619091			0.309545	−	0.950885i	$-0.399823\pi$
$449$	2.64466e6			0.619091			0.309545	+	0.950885i	$0.399823\pi$
$450$		0			0
$451$	2.66265e6	+	2.66265e6i	0.616414	+	0.616414i
$452$		0			0
$453$	−3.58985e6	+	3.58985e6i	−0.821922	+	0.821922i
$454$		0			0
$455$			3.04437e6i			0.689396i
$456$		0			0
$457$		−	6.80608e6i		−	1.52443i	−0.647325	−	0.762214i	$-0.724113\pi$
$457$		−	6.80608e6i		−	1.52443i	0.647325	−	0.762214i	$-0.275887\pi$
$458$		0			0
$459$	−1.03223e6	+	1.03223e6i	−0.228689	+	0.228689i
$460$		0			0
$461$	4.81633e6	+	4.81633e6i	1.05551	+	1.05551i	0.998366	+	0.0571485i	$0.0182009\pi$
$461$	4.81633e6	+	4.81633e6i	1.05551	+	1.05551i	0.0571485	+	0.998366i	$0.481799\pi$
$462$		0			0
$463$	4.09641e6			0.888078			0.444039	−	0.896007i	$-0.353545\pi$
$463$	4.09641e6			0.888078			0.444039	+	0.896007i	$0.353545\pi$
$464$		0			0
$465$	−1.92653e6			−0.413183
$466$		0			0
$467$	−4.72907e6	−	4.72907e6i	−1.00342	−	1.00342i	−0.999994	−	0.00342756i	$-0.998909\pi$
$467$	−4.72907e6	−	4.72907e6i	−1.00342	−	1.00342i	−0.00342756	−	0.999994i	$-0.501091\pi$
$468$		0			0
$469$	−1.11875e6	+	1.11875e6i	−0.234856	+	0.234856i
$470$		0			0
$471$		−	7.78858e6i		−	1.61773i
$472$		0			0
$473$		−	87052.1i		−	0.0178907i
$474$		0			0
$475$	−409335.	+	409335.i	−0.0832425	+	0.0832425i
$476$		0			0
$477$	−447423.	−	447423.i	−0.0900373	−	0.0900373i
$478$		0			0
$479$	−3.50516e6			−0.698023			−0.349011	−	0.937118i	$-0.613483\pi$
$479$	−3.50516e6			−0.698023			−0.349011	+	0.937118i	$0.613483\pi$
$480$		0			0
$481$	7.77992e6			1.53325
$482$		0			0
$483$	3.51662e6	+	3.51662e6i	0.685895	+	0.685895i
$484$		0			0
$485$	−1.34535e6	+	1.34535e6i	−0.259705	+	0.259705i
$486$		0			0
$487$		−	1.64836e6i		−	0.314942i	−0.987524	−	0.157471i	$-0.949666\pi$
$487$		−	1.64836e6i		−	0.314942i	0.987524	−	0.157471i	$-0.0503341\pi$
$488$		0			0
$489$		−	6.15126e6i		−	1.16330i
$490$		0			0
$491$	−5.13183e6	+	5.13183e6i	−0.960658	+	0.960658i	−0.999255	−	0.0385967i	$-0.987711\pi$
$491$	−5.13183e6	+	5.13183e6i	−0.960658	+	0.960658i	0.0385967	+	0.999255i	$0.487711\pi$
$492$		0			0
$493$	1.63600e6	+	1.63600e6i	0.303156	+	0.303156i
$494$		0			0
$495$	−258991.			−0.0475086
$496$		0			0
$497$	−4.70018e6			−0.853539
$498$		0			0
$499$	3.30726e6	+	3.30726e6i	0.594589	+	0.594589i	0.938867	−	0.344279i	$-0.111877\pi$
$499$	3.30726e6	+	3.30726e6i	0.594589	+	0.594589i	−0.344279	+	0.938867i	$0.611877\pi$
$500$		0			0
$501$	5.84130e6	−	5.84130e6i	1.03972	−	1.03972i
$502$		0			0
$503$			359668.i			0.0633843i	0.999498	+	0.0316921i	$0.0100896\pi$
$503$			359668.i			0.0633843i	−0.999498	+	0.0316921i	$0.989910\pi$
$504$		0			0
$505$			2.52648e6i			0.440847i
$506$		0			0
$507$	9.41871e6	−	9.41871e6i	1.62731	−	1.62731i
$508$		0			0
$509$	−2.19114e6	−	2.19114e6i	−0.374866	−	0.374866i	0.494380	−	0.869246i	$-0.335395\pi$
$509$	−2.19114e6	−	2.19114e6i	−0.374866	−	0.374866i	−0.869246	+	0.494380i	$0.835395\pi$
$510$		0			0
$511$	3.48422e6			0.590273
$512$		0			0
$513$	3.70465e6			0.621518
$514$		0			0
$515$	−194942.	−	194942.i	−0.0323882	−	0.0323882i
$516$		0			0
$517$	−6.19167e6	+	6.19167e6i	−1.01878	+	1.01878i
$518$		0			0
$519$			4.82972e6i			0.787052i
$520$		0			0
$521$			4.25817e6i			0.687271i	0.939103	+	0.343636i	$0.111659\pi$
$521$			4.25817e6i			0.687271i	−0.939103	+	0.343636i	$0.888341\pi$
$522$		0			0
$523$	−7.40345e6	+	7.40345e6i	−1.18353	+	1.18353i	−0.204710	+	0.978823i	$0.565625\pi$
$523$	−7.40345e6	+	7.40345e6i	−1.18353	+	1.18353i	−0.978823	+	0.204710i	$0.934375\pi$
$524$		0			0
$525$	−686468.	−	686468.i	−0.108698	−	0.108698i
$526$		0			0
$527$	−1.94094e6			−0.304429
$528$		0			0
$529$	−3.81474e6			−0.592688
$530$		0			0
$531$	−631972.	−	631972.i	−0.0972662	−	0.0972662i
$532$		0			0
$533$	−9.64320e6	+	9.64320e6i	−1.47029	+	1.47029i
$534$		0			0
$535$			1.85614e6i			0.280366i
$536$		0			0
$537$			4.17131e6i			0.624219i
$538$		0			0
$539$	−1.17914e6	+	1.17914e6i	−0.174822	+	0.174822i
$540$		0			0
$541$	−5.76076e6	−	5.76076e6i	−0.846227	−	0.846227i	0.143433	−	0.989660i	$-0.454186\pi$
$541$	−5.76076e6	−	5.76076e6i	−0.846227	−	0.846227i	−0.989660	+	0.143433i	$0.954186\pi$
$542$		0			0
$543$	−1.08772e7			−1.58313
$544$		0			0
$545$	−2.75669e6			−0.397555
$546$		0			0
$547$	8.22698e6	+	8.22698e6i	1.17563	+	1.17563i	0.980845	+	0.194789i	$0.0624024\pi$
$547$	8.22698e6	+	8.22698e6i	1.17563	+	1.17563i	0.194789	+	0.980845i	$0.437598\pi$
$548$		0			0
$549$	−913507.	+	913507.i	−0.129354	+	0.129354i
$550$		0			0
$551$		−	5.87157e6i		−	0.823901i
$552$		0			0
$553$			5.79530e6i			0.805866i
$554$		0			0
$555$	−1.75428e6	+	1.75428e6i	−0.241750	+	0.241750i
$556$		0			0
$557$	7.73657e6	+	7.73657e6i	1.05660	+	1.05660i	0.998299	+	0.0583011i	$0.0185684\pi$
$557$	7.73657e6	+	7.73657e6i	1.05660	+	1.05660i	0.0583011	+	0.998299i	$0.481432\pi$
$558$		0			0
$559$	315273.			0.0426734
$560$		0			0
$561$	1.65888e6			0.222540
$562$		0			0
$563$	−2.50199e6	−	2.50199e6i	−0.332671	−	0.332671i	0.520929	−	0.853600i	$-0.325586\pi$
$563$	−2.50199e6	−	2.50199e6i	−0.332671	−	0.332671i	−0.853600	+	0.520929i	$0.825586\pi$
$564$		0			0
$565$	390345.	−	390345.i	0.0514431	−	0.0514431i
$566$		0			0
$567$			5.35252e6i			0.699199i
$568$		0			0
$569$		−	1.03796e7i		−	1.34400i	−0.740553	−	0.671998i	$-0.765436\pi$
$569$		−	1.03796e7i		−	1.34400i	0.740553	−	0.671998i	$-0.234564\pi$
$570$		0			0
$571$	5.45756e6	−	5.45756e6i	0.700501	−	0.700501i	−0.264017	−	0.964518i	$-0.585048\pi$
$571$	5.45756e6	−	5.45756e6i	0.700501	−	0.700501i	0.964518	+	0.264017i	$0.0850476\pi$
$572$		0			0
$573$	1.32293e6	+	1.32293e6i	0.168326	+	0.168326i
$574$		0			0
$575$	2.00108e6			0.252403
$576$		0			0
$577$	4.38574e6			0.548407			0.274203	−	0.961672i	$-0.411586\pi$
$577$	4.38574e6			0.548407			0.274203	+	0.961672i	$0.411586\pi$
$578$		0			0
$579$	4.31906e6	+	4.31906e6i	0.535417	+	0.535417i
$580$		0			0
$581$	4.41321e6	−	4.41321e6i	0.542393	−	0.542393i
$582$		0			0
$583$			6.00951e6i			0.732264i
$584$		0			0
$585$		−	937978.i		−	0.113319i
$586$		0			0
$587$	1.06219e7	−	1.06219e7i	1.27235	−	1.27235i	0.327498	−	0.944852i	$-0.393795\pi$
$587$	1.06219e7	−	1.06219e7i	1.27235	−	1.27235i	0.944852	−	0.327498i	$-0.106205\pi$
$588$		0			0
$589$	3.48299e6	+	3.48299e6i	0.413679	+	0.413679i
$590$		0			0
$591$	−5.51809e6			−0.649860
$592$		0			0
$593$	−6.12696e6			−0.715498			−0.357749	−	0.933818i	$-0.616456\pi$
$593$	−6.12696e6			−0.715498			−0.357749	+	0.933818i	$0.616456\pi$
$594$		0			0
$595$	−691605.	−	691605.i	−0.0800877	−	0.0800877i
$596$		0			0
$597$	−7.06787e6	+	7.06787e6i	−0.811620	+	0.811620i
$598$		0			0
$599$			9.90169e6i			1.12757i	0.825923	+	0.563784i	$0.190655\pi$
$599$			9.90169e6i			1.12757i	−0.825923	+	0.563784i	$0.809345\pi$
$600$		0			0
$601$		−	1.04602e7i		−	1.18128i	−0.806935	−	0.590640i	$-0.798875\pi$
$601$		−	1.04602e7i		−	1.18128i	0.806935	−	0.590640i	$-0.201125\pi$
$602$		0			0
$603$	344691.	−	344691.i	0.0386044	−	0.0386044i
$604$		0			0
$605$	−1.10770e6	−	1.10770e6i	−0.123037	−	0.123037i
$606$		0			0
$607$	−1.22247e7			−1.34668			−0.673342	−	0.739331i	$-0.735142\pi$
$607$	−1.22247e7			−1.34668			−0.673342	+	0.739331i	$0.735142\pi$
$608$		0			0
$609$	9.84681e6			1.07585
$610$		0			0
$611$	−2.24241e7	−	2.24241e7i	−2.43003	−	2.43003i
$612$		0			0
$613$	−6.55131e6	+	6.55131e6i	−0.704169	+	0.704169i	−0.965303	−	0.261134i	$-0.915904\pi$
$613$	−6.55131e6	+	6.55131e6i	−0.704169	+	0.704169i	0.261134	+	0.965303i	$0.415904\pi$
$614$		0			0
$615$		−	4.34886e6i		−	0.463647i
$616$		0			0
$617$			1.02198e6i			0.108076i	0.998539	+	0.0540382i	$0.0172093\pi$
$617$			1.02198e6i			0.108076i	−0.998539	+	0.0540382i	$0.982791\pi$
$618$		0			0
$619$	2.94048e6	−	2.94048e6i	0.308455	−	0.308455i	−0.535855	−	0.844310i	$-0.680011\pi$
$619$	2.94048e6	−	2.94048e6i	0.308455	−	0.308455i	0.844310	+	0.535855i	$0.180011\pi$
$620$		0			0
$621$	−9.05531e6	−	9.05531e6i	−0.942268	−	0.942268i
$622$		0			0
$623$	2.25431e6			0.232698
$624$		0			0
$625$	−390625.			−0.0400000
$626$		0			0
$627$	−2.97684e6	−	2.97684e6i	−0.302404	−	0.302404i
$628$		0			0
$629$	−1.76741e6	+	1.76741e6i	−0.178119	+	0.178119i
$630$		0			0
$631$		−	1.12174e7i		−	1.12155i	−0.827967	−	0.560777i	$-0.810503\pi$
$631$		−	1.12174e7i		−	1.12155i	0.827967	−	0.560777i	$-0.189497\pi$
$632$		0			0
$633$			5.27531e6i			0.523285i
$634$		0			0
$635$	−4.39823e6	+	4.39823e6i	−0.432856	+	0.432856i
$636$		0			0
$637$	−4.27046e6	−	4.27046e6i	−0.416991	−	0.416991i
$638$		0			0
$639$	1.44814e6			0.140300
$640$		0			0
$641$	−2.58254e6			−0.248257			−0.124128	−	0.992266i	$-0.539613\pi$
$641$	−2.58254e6			−0.248257			−0.124128	+	0.992266i	$0.539613\pi$
$642$		0			0
$643$	−1.03616e7	−	1.03616e7i	−0.988322	−	0.988322i	0.0116102	−	0.999933i	$-0.496304\pi$
$643$	−1.03616e7	−	1.03616e7i	−0.988322	−	0.988322i	−0.999933	+	0.0116102i	$0.996304\pi$
$644$		0			0
$645$	−71090.4	+	71090.4i	−0.00672839	+	0.00672839i
$646$		0			0
$647$		−	1.27987e7i		−	1.20201i	−0.799247	−	0.601003i	$-0.794768\pi$
$647$		−	1.27987e7i		−	1.20201i	0.799247	−	0.601003i	$-0.205232\pi$
$648$		0			0
$649$			8.48826e6i			0.791056i
$650$		0			0
$651$	−5.84109e6	+	5.84109e6i	−0.540183	+	0.540183i
$652$		0			0
$653$	1.02668e7	+	1.02668e7i	0.942221	+	0.942221i	0.998420	−	0.0561986i	$-0.0178980\pi$
$653$	1.02668e7	+	1.02668e7i	0.942221	+	0.942221i	−0.0561986	+	0.998420i	$0.517898\pi$
$654$		0			0
$655$	3.00861e6			0.274008
$656$		0			0
$657$	−1.07350e6			−0.0970259
$658$		0			0
$659$	−1.28343e6	−	1.28343e6i	−0.115122	−	0.115122i	0.647199	−	0.762321i	$-0.275940\pi$
$659$	−1.28343e6	−	1.28343e6i	−0.115122	−	0.115122i	−0.762321	+	0.647199i	$0.775940\pi$
$660$		0			0
$661$	−5.96696e6	+	5.96696e6i	−0.531190	+	0.531190i	−0.920926	−	0.389737i	$-0.872566\pi$
$661$	−5.96696e6	+	5.96696e6i	−0.531190	+	0.531190i	0.389737	+	0.920926i	$0.372566\pi$
$662$		0			0
$663$			6.00792e6i			0.530811i
$664$		0			0
$665$			2.48215e6i			0.217658i
$666$		0			0
$667$	−1.43519e7	+	1.43519e7i	−1.24909	+	1.24909i
$668$		0			0
$669$	−1.93189e6	−	1.93189e6i	−0.166885	−	0.166885i
$670$		0			0
$671$	1.22697e7			1.05203
$672$		0			0
$673$	−1.19602e7			−1.01789			−0.508946	−	0.860798i	$-0.669965\pi$
$673$	−1.19602e7			−1.01789			−0.508946	+	0.860798i	$0.669965\pi$
$674$		0			0
$675$	1.76766e6	+	1.76766e6i	0.149327	+	0.149327i
$676$		0			0
$677$	7.18308e6	−	7.18308e6i	0.602337	−	0.602337i	−0.338595	−	0.940932i	$-0.609952\pi$
$677$	7.18308e6	−	7.18308e6i	0.602337	−	0.602337i	0.940932	+	0.338595i	$0.109952\pi$
$678$		0			0
$679$			8.15798e6i			0.679060i
$680$		0			0
$681$			1.82645e7i			1.50918i
$682$		0			0
$683$	41039.4	−	41039.4i	0.00336627	−	0.00336627i	−0.705422	−	0.708788i	$-0.749242\pi$
$683$	41039.4	−	41039.4i	0.00336627	−	0.00336627i	0.708788	+	0.705422i	$0.249242\pi$
$684$		0			0
$685$	−5.83356e6	−	5.83356e6i	−0.475015	−	0.475015i
$686$		0			0
$687$	6.25279e6			0.505454
$688$		0			0
$689$	−2.17644e7			−1.74662
$690$		0			0
$691$	1.21095e7	+	1.21095e7i	0.964789	+	0.964789i	0.999401	−	0.0346122i	$-0.0110196\pi$
$691$	1.21095e7	+	1.21095e7i	0.964789	+	0.964789i	−0.0346122	+	0.999401i	$0.511020\pi$
$692$		0			0
$693$	−785243.	+	785243.i	−0.0621113	+	0.0621113i
$694$		0			0
$695$		−	2.11753e6i		−	0.166291i
$696$		0			0
$697$		−	4.38139e6i		−	0.341610i
$698$		0			0
$699$	7.05586e6	−	7.05586e6i	0.546207	−	0.546207i
$700$		0			0
$701$	−1.18871e7	−	1.18871e7i	−0.913655	−	0.913655i	0.0829024	−	0.996558i	$-0.473581\pi$
$701$	−1.18871e7	−	1.18871e7i	−0.913655	−	0.913655i	−0.996558	+	0.0829024i	$0.973581\pi$
$702$		0			0
$703$	6.34317e6			0.484081
$704$		0			0
$705$	1.01127e7			0.766295
$706$		0			0
$707$	7.66011e6	+	7.66011e6i	0.576351	+	0.576351i
$708$		0			0
$709$	−7.00006e6	+	7.00006e6i	−0.522981	+	0.522981i	−0.918471	−	0.395489i	$-0.870575\pi$
$709$	−7.00006e6	+	7.00006e6i	−0.522981	+	0.522981i	0.395489	+	0.918471i	$0.370575\pi$
$710$		0			0
$711$		−	1.78555e6i		−	0.132464i
$712$		0			0
$713$		−	1.70270e7i		−	1.25434i
$714$		0			0
$715$	−6.29917e6	+	6.29917e6i	−0.460806	+	0.460806i
$716$		0			0
$717$	−1.41102e6	−	1.41102e6i	−0.102502	−	0.102502i
$718$		0			0
$719$	−1.18229e6			−0.0852909			−0.0426454	−	0.999090i	$-0.513579\pi$
$719$	−1.18229e6			−0.0852909			−0.0426454	+	0.999090i	$0.513579\pi$
$720$		0			0
$721$	−1.18210e6			−0.0846867
$722$		0			0
$723$	−3.30109e6	−	3.30109e6i	−0.234861	−	0.234861i
$724$		0			0
$725$	2.80159e6	−	2.80159e6i	0.197952	−	0.197952i
$726$		0			0
$727$			2.63581e7i			1.84960i	0.380451	+	0.924801i	$0.375769\pi$
$727$			2.63581e7i			1.84960i	−0.380451	+	0.924801i	$0.624231\pi$
$728$		0			0
$729$		−	1.57330e7i		−	1.09646i
$730$		0			0
$731$	−71622.3	+	71622.3i	−0.00495741	+	0.00495741i
$732$		0			0
$733$	9.55283e6	+	9.55283e6i	0.656708	+	0.656708i	0.954600	−	0.297892i	$-0.0962835\pi$
$733$	9.55283e6	+	9.55283e6i	0.656708	+	0.656708i	−0.297892	+	0.954600i	$0.596283\pi$
$734$		0			0
$735$	1.92588e6			0.131495
$736$		0			0
$737$	−4.62968e6			−0.313966
$738$		0			0
$739$	−5.06534e6	−	5.06534e6i	−0.341191	−	0.341191i	0.515624	−	0.856815i	$-0.327560\pi$
$739$	−5.06534e6	−	5.06534e6i	−0.341191	−	0.341191i	−0.856815	+	0.515624i	$0.827560\pi$
$740$		0			0
$741$	1.07811e7	−	1.07811e7i	0.721304	−	0.721304i
$742$		0			0
$743$		−	6.79201e6i		−	0.451364i	−0.974201	−	0.225682i	$-0.927539\pi$
$743$		−	6.79201e6i		−	0.451364i	0.974201	−	0.225682i	$-0.0724610\pi$
$744$		0			0
$745$			9.55045e6i			0.630424i
$746$		0			0
$747$	−1.35972e6	+	1.35972e6i	−0.0891557	+	0.0891557i
$748$		0			0
$749$	5.62767e6	+	5.62767e6i	0.366543	+	0.366543i
$750$		0			0
$751$	1.64280e7			1.06288			0.531440	−	0.847096i	$-0.321651\pi$
$751$	1.64280e7			1.06288			0.531440	+	0.847096i	$0.321651\pi$
$752$		0			0
$753$	1.22704e7			0.788629
$754$		0			0
$755$	6.19348e6	+	6.19348e6i	0.395428	+	0.395428i
$756$		0			0
$757$	1.46559e7	−	1.46559e7i	0.929551	−	0.929551i	−0.0681256	−	0.997677i	$-0.521702\pi$
$757$	1.46559e7	−	1.46559e7i	0.929551	−	0.929551i	0.997677	+	0.0681256i	$0.0217019\pi$
$758$		0			0
$759$			1.45526e7i			0.916933i
$760$		0			0
$761$			1.02339e7i			0.640590i	0.947318	+	0.320295i	$0.103782\pi$
$761$			1.02339e7i			0.640590i	−0.947318	+	0.320295i	$0.896218\pi$
$762$		0			0
$763$	−8.35809e6	+	8.35809e6i	−0.519751	+	0.519751i
$764$		0			0
$765$	213085.	+	213085.i	0.0131644	+	0.0131644i
$766$		0			0
$767$	−3.07416e7			−1.88685
$768$		0			0
$769$	−276535.			−0.0168630			−0.00843150	−	0.999964i	$-0.502684\pi$
$769$	−276535.			−0.0168630			−0.00843150	+	0.999964i	$0.502684\pi$
$770$		0			0
$771$	−9.79619e6	−	9.79619e6i	−0.593500	−	0.593500i
$772$		0			0
$773$	1.43785e6	−	1.43785e6i	0.0865495	−	0.0865495i	−0.662507	−	0.749056i	$-0.730507\pi$
$773$	1.43785e6	−	1.43785e6i	0.0865495	−	0.0865495i	0.749056	+	0.662507i	$0.230507\pi$
$774$		0			0
$775$			3.32379e6i			0.198783i
$776$		0			0
$777$			1.06377e7i			0.632114i
$778$		0			0
$779$	−7.86235e6	+	7.86235e6i	−0.464204	+	0.464204i
$780$		0			0
$781$	−9.72525e6	−	9.72525e6i	−0.570523	−	0.570523i
$782$		0			0
$783$	−2.53556e7			−1.47798
$784$		0			0
$785$	−1.34374e7			−0.778292
$786$		0			0
$787$	1.62966e7	+	1.62966e7i	0.937907	+	0.937907i	0.998182	−	0.0602747i	$-0.0191977\pi$
$787$	1.62966e7	+	1.62966e7i	0.937907	+	0.937907i	−0.0602747	+	0.998182i	$0.519198\pi$
$788$		0			0
$789$	1.11414e7	−	1.11414e7i	0.637158	−	0.637158i
$790$		0			0
$791$		−	2.36700e6i		−	0.134510i
$792$		0			0
$793$			4.44365e7i			2.50933i
$794$		0			0
$795$	4.90762e6	−	4.90762e6i	0.275393	−	0.275393i
$796$		0			0
$797$	5.31047e6	+	5.31047e6i	0.296133	+	0.296133i	0.839497	−	0.543364i	$-0.182850\pi$
$797$	5.31047e6	+	5.31047e6i	0.296133	+	0.296133i	−0.543364	+	0.839497i	$0.682850\pi$
$798$		0			0
$799$	1.01884e7			0.564598
$800$		0			0
$801$	−694558.			−0.0382496
$802$		0			0
$803$	7.20928e6	+	7.20928e6i	0.394551	+	0.394551i
$804$		0			0
$805$	6.06714e6	−	6.06714e6i	0.329985	−	0.329985i
$806$		0			0
$807$		−	1.71119e7i		−	0.924940i
$808$		0			0
$809$		−	1.89696e7i		−	1.01903i	−0.860462	−	0.509515i	$-0.829825\pi$
$809$		−	1.89696e7i		−	1.01903i	0.860462	−	0.509515i	$-0.170175\pi$
$810$		0			0
$811$	−1.42784e7	+	1.42784e7i	−0.762303	+	0.762303i	−0.976738	−	0.214436i	$-0.931209\pi$
$811$	−1.42784e7	+	1.42784e7i	−0.762303	+	0.762303i	0.214436	+	0.976738i	$0.431209\pi$
$812$		0			0
$813$	−5.29209e6	−	5.29209e6i	−0.280802	−	0.280802i
$814$		0			0
$815$	−1.06126e7			−0.559665
$816$		0			0
$817$	257050.			0.0134730
$818$		0			0
$819$	−2.84388e6	−	2.84388e6i	−0.148150	−	0.148150i
$820$		0			0
$821$	1.41311e7	−	1.41311e7i	0.731673	−	0.731673i	−0.239278	−	0.970951i	$-0.576911\pi$
$821$	1.41311e7	−	1.41311e7i	0.731673	−	0.731673i	0.970951	+	0.239278i	$0.0769109\pi$
$822$		0			0
$823$			2.98115e6i			0.153421i	0.997053	+	0.0767105i	$0.0244417\pi$
$823$			2.98115e6i			0.153421i	−0.997053	+	0.0767105i	$0.975558\pi$
$824$		0			0
$825$		−	2.84078e6i		−	0.145312i
$826$		0			0
$827$	1.64045e7	−	1.64045e7i	0.834065	−	0.834065i	−0.154005	−	0.988070i	$-0.549217\pi$
$827$	1.64045e7	−	1.64045e7i	0.834065	−	0.834065i	0.988070	+	0.154005i	$0.0492172\pi$
$828$		0			0
$829$	1.79457e7	+	1.79457e7i	0.906932	+	0.906932i	0.996023	−	0.0890916i	$-0.0283964\pi$
$829$	1.79457e7	+	1.79457e7i	0.906932	+	0.906932i	−0.0890916	+	0.996023i	$0.528396\pi$
$830$		0			0
$831$	2.62480e7			1.31854
$832$		0			0
$833$	1.94029e6			0.0968843
$834$		0			0
$835$	−1.00778e7	−	1.00778e7i	−0.500209	−	0.500209i
$836$		0			0
$837$	1.50408e7	−	1.50408e7i	0.742092	−	0.742092i
$838$		0			0
$839$		−	2.12568e7i		−	1.04254i	−0.853392	−	0.521270i	$-0.825459\pi$
$839$		−	2.12568e7i		−	1.04254i	0.853392	−	0.521270i	$-0.174541\pi$
$840$		0			0
$841$			1.96753e7i			0.959251i
$842$		0			0
$843$	16369.9	−	16369.9i	0.000793372	−	0.000793372i
$844$		0			0
$845$	−1.62499e7	−	1.62499e7i	−0.782903	−	0.782903i
$846$		0			0
$847$	−6.71694e6			−0.321709
$848$		0			0
$849$	6.75253e6			0.321512
$850$		0			0
$851$	−1.55047e7	−	1.55047e7i	−0.733902	−	0.733902i
$852$		0			0
$853$	2.63420e7	−	2.63420e7i	1.23959	−	1.23959i	0.279416	−	0.960170i	$-0.409859\pi$
$853$	2.63420e7	−	2.63420e7i	1.23959	−	1.23959i	0.960170	−	0.279416i	$-0.0901408\pi$
$854$		0			0
$855$		−	764757.i		−	0.0357774i
$856$		0			0
$857$		−	1.97050e7i		−	0.916485i	−0.888827	−	0.458243i	$-0.848479\pi$
$857$		−	1.97050e7i		−	0.916485i	0.888827	−	0.458243i	$-0.151521\pi$
$858$		0			0
$859$	−1.05690e7	+	1.05690e7i	−0.488708	+	0.488708i	−0.907898	−	0.419190i	$-0.862314\pi$
$859$	−1.05690e7	+	1.05690e7i	−0.488708	+	0.488708i	0.419190	+	0.907898i	$0.362314\pi$
$860$		0			0
$861$	−1.31854e7	−	1.31854e7i	−0.606158	−	0.606158i
$862$		0			0
$863$	3.83591e7			1.75324			0.876621	−	0.481182i	$-0.159792\pi$
$863$	3.83591e7			1.75324			0.876621	+	0.481182i	$0.159792\pi$
$864$		0			0
$865$	8.33260e6			0.378652
$866$		0			0
$867$	1.31834e7	+	1.31834e7i	0.595635	+	0.595635i
$868$		0			0
$869$	−1.19912e7	+	1.19912e7i	−0.538658	+	0.538658i
$870$		0			0
$871$		−	1.67671e7i		−	0.748881i
$872$		0			0
$873$		−	2.51350e6i		−	0.111620i
$874$		0			0
$875$	−1.18435e6	+	1.18435e6i	−0.0522948	+	0.0522948i
$876$		0			0
$877$	2.54322e7	+	2.54322e7i	1.11657	+	1.11657i	0.992241	+	0.124326i	$0.0396769\pi$
$877$	2.54322e7	+	2.54322e7i	1.11657	+	1.11657i	0.124326	+	0.992241i	$0.460323\pi$
$878$		0			0
$879$	4.03671e7			1.76220
$880$		0			0
$881$	2.54983e7			1.10681			0.553404	−	0.832913i	$-0.313329\pi$
$881$	2.54983e7			1.10681			0.553404	+	0.832913i	$0.313329\pi$
$882$		0			0
$883$	−7.56172e6	−	7.56172e6i	−0.326376	−	0.326376i	0.524830	−	0.851207i	$-0.324129\pi$
$883$	−7.56172e6	−	7.56172e6i	−0.326376	−	0.326376i	−0.851207	+	0.524830i	$0.824129\pi$
$884$		0			0
$885$	6.93187e6	−	6.93187e6i	0.297503	−	0.297503i
$886$		0			0
$887$			2.91011e7i			1.24194i	0.783834	+	0.620970i	$0.213261\pi$
$887$			2.91011e7i			1.24194i	−0.783834	+	0.620970i	$0.786739\pi$
$888$		0			0
$889$			2.66702e7i			1.13181i
$890$		0			0
$891$	−1.10750e7	+	1.10750e7i	−0.467359	+	0.467359i
$892$		0			0
$893$	−1.82829e7	−	1.82829e7i	−0.767216	−	0.767216i
$894$		0			0
$895$	7.19666e6			0.300313
$896$		0			0
$897$	−5.27047e7			−2.18710
$898$		0			0
$899$	−2.38385e7	−	2.38385e7i	−0.983737	−	0.983737i
$900$		0			0
$901$	4.94434e6	−	4.94434e6i	0.202907	−	0.202907i
$902$		0			0
$903$			431082.i			0.0175930i
$904$		0			0
$905$			1.87662e7i			0.761648i
$906$		0			0
$907$	2.12490e7	−	2.12490e7i	0.857671	−	0.857671i	−0.133393	−	0.991063i	$-0.542587\pi$
$907$	2.12490e7	−	2.12490e7i	0.857671	−	0.857671i	0.991063	+	0.133393i	$0.0425871\pi$
$908$		0			0
$909$	−2.36010e6	−	2.36010e6i	−0.0947374	−	0.0947374i
$910$		0			0
$911$	4.64368e7			1.85381			0.926907	−	0.375291i	$-0.122457\pi$
$911$	4.64368e7			1.85381			0.926907	+	0.375291i	$0.122457\pi$
$912$		0			0
$913$	1.82630e7			0.725094
$914$		0			0
$915$	−1.00199e7	−	1.00199e7i	−0.395650	−	0.395650i
$916$		0			0
$917$	9.12189e6	−	9.12189e6i	0.358230	−	0.358230i
$918$		0			0
$919$		−	1.87009e7i		−	0.730423i	−0.930925	−	0.365212i	$-0.880997\pi$
$919$		−	1.87009e7i		−	0.730423i	0.930925	−	0.365212i	$-0.119003\pi$
$920$		0			0
$921$			1.08163e6i			0.0420176i
$922$		0			0
$923$	3.52216e7	−	3.52216e7i	1.36083	−	1.36083i
$924$		0			0
$925$	3.02661e6	+	3.02661e6i	0.116306	+	0.116306i
$926$		0			0
$927$	364208.			0.0139203
$928$		0			0
$929$	1.06672e6			0.0405519			0.0202760	−	0.999794i	$-0.493546\pi$
$929$	1.06672e6			0.0405519			0.0202760	+	0.999794i	$0.493546\pi$
$930$		0			0
$931$	−3.48182e6	−	3.48182e6i	−0.131653	−	0.131653i
$932$		0			0
$933$	−1.72854e7	+	1.72854e7i	−0.650092	+	0.650092i
$934$		0			0
$935$		−	2.86203e6i		−	0.107065i
$936$		0			0
$937$		−	1.48071e7i		−	0.550960i	−0.961307	−	0.275480i	$-0.911163\pi$
$937$		−	1.48071e7i		−	0.550960i	0.961307	−	0.275480i	$-0.0888368\pi$
$938$		0			0
$939$	1.86083e7	−	1.86083e7i	0.688719	−	0.688719i
$940$		0			0
$941$	−513689.	−	513689.i	−0.0189115	−	0.0189115i	0.697588	−	0.716499i	$-0.254257\pi$
$941$	−513689.	−	513689.i	−0.0189115	−	0.0189115i	−0.716499	+	0.697588i	$0.754257\pi$
$942$		0			0
$943$	3.84360e7			1.40753
$944$		0			0
$945$	1.07188e7			0.390452
$946$		0			0
$947$	−5.85570e6	−	5.85570e6i	−0.212180	−	0.212180i	0.593013	−	0.805193i	$-0.297938\pi$
$947$	−5.85570e6	−	5.85570e6i	−0.212180	−	0.212180i	−0.805193	+	0.593013i	$0.797938\pi$
$948$		0			0
$949$	−2.61095e7	+	2.61095e7i	−0.941096	+	0.941096i
$950$		0			0
$951$			1.14579e7i			0.410821i
$952$		0			0
$953$		−	5.32492e7i		−	1.89924i	−0.313399	−	0.949621i	$-0.601468\pi$
$953$		−	5.32492e7i		−	1.89924i	0.313399	−	0.949621i	$-0.398532\pi$
$954$		0			0
$955$	2.28242e6	−	2.28242e6i	0.0809818	−	0.0809818i
$956$		0			0
$957$	2.03743e7	+	2.03743e7i	0.719121	+	0.719121i
$958$		0			0
$959$	−3.53738e7			−1.24204
$960$		0			0
$961$	−347397.			−0.0121344
$962$		0			0
$963$	−1.73390e6	−	1.73390e6i	−0.0602503	−	0.0602503i
$964$		0			0
$965$	7.45156e6	−	7.45156e6i	0.257590	−	0.257590i
$966$		0			0
$967$			1.67078e7i			0.574583i	0.957843	+	0.287292i	$0.0927549\pi$
$967$			1.67078e7i			0.574583i	−0.957843	+	0.287292i	$0.907245\pi$
$968$		0			0
$969$			4.89841e6i			0.167589i
$970$		0			0
$971$	−3.23173e7	+	3.23173e7i	−1.09999	+	1.09999i	−0.105574	+	0.994411i	$0.533668\pi$
$971$	−3.23173e7	+	3.23173e7i	−1.09999	+	1.09999i	−0.994411	+	0.105574i	$0.966332\pi$
$972$		0			0
$973$	−6.42021e6	−	6.42021e6i	−0.217404	−	0.217404i
$974$		0			0
$975$	1.02883e7			0.346604
$976$		0			0
$977$	−8.51625e6			−0.285438			−0.142719	−	0.989763i	$-0.545585\pi$
$977$	−8.51625e6			−0.285438			−0.142719	+	0.989763i	$0.545585\pi$
$978$		0			0
$979$	4.66444e6	+	4.66444e6i	0.155540	+	0.155540i
$980$		0			0
$981$	2.57515e6	−	2.57515e6i	0.0854339	−	0.0854339i
$982$		0			0
$983$			1.69108e7i			0.558187i	0.960264	+	0.279093i	$0.0900339\pi$
$983$			1.69108e7i			0.558187i	−0.960264	+	0.279093i	$0.909966\pi$
$984$		0			0
$985$			9.52022e6i			0.312648i
$986$		0			0
$987$	3.06611e7	−	3.06611e7i	1.00183	−	1.00183i
$988$		0			0
$989$	−628310.	−	628310.i	−0.0204260	−	0.0204260i
$990$		0			0
$991$	1.52457e7			0.493134			0.246567	−	0.969126i	$-0.420698\pi$
$991$	1.52457e7			0.493134			0.246567	+	0.969126i	$0.420698\pi$
$992$		0			0
$993$	−1.18602e7			−0.381699
$994$		0			0
$995$	1.21940e7	+	1.21940e7i	0.390471	+	0.390471i
$996$		0			0
$997$	−2.71880e7	+	2.71880e7i	−0.866241	+	0.866241i	−0.992054	−	0.125813i	$-0.959846\pi$
$997$	−2.71880e7	+	2.71880e7i	−0.866241	+	0.866241i	0.125813	+	0.992054i	$0.459846\pi$
$998$		0			0
$999$		−	2.73921e7i		−	0.868384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.6.l.a.81.10		80
4.3	odd	2		80.6.l.a.61.11	yes	80
16.5	even	4	inner	320.6.l.a.241.10		80
16.11	odd	4		80.6.l.a.21.11	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.11	✓	80	16.11	odd	4
80.6.l.a.61.11	yes	80	4.3	odd	2
320.6.l.a.81.10		80	1.1	even	1	trivial
320.6.l.a.241.10		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)

\(f(q)\)	\(=\)	\(q+(-10.2463 - 10.2463i) q^{3} +(-17.6777 + 17.6777i) q^{5} +107.195i q^{7} -33.0270i q^{9} +O(q^{10})\)	\(q+(-10.2463 - 10.2463i) q^{3} +(-17.6777 + 17.6777i) q^{5} +107.195i q^{7} -33.0270i q^{9} +(-221.799 + 221.799i) q^{11} +(-803.282 - 803.282i) q^{13} +362.261 q^{15} +364.972 q^{17} +(-654.936 - 654.936i) q^{19} +(1098.35 - 1098.35i) q^{21} +3201.73i q^{23} -625.000i q^{25} +(-2828.25 + 2828.25i) q^{27} +(4482.55 + 4482.55i) q^{29} -5318.06 q^{31} +4545.24 q^{33} +(-1894.95 - 1894.95i) q^{35} +(-4842.58 + 4842.58i) q^{37} +16461.3i q^{39} -12004.8i q^{41} +(-196.241 + 196.241i) q^{43} +(583.841 + 583.841i) q^{45} +27915.6 q^{47} +5316.27 q^{49} +(-3739.61 - 3739.61i) q^{51} +(13547.2 - 13547.2i) q^{53} -7841.79i q^{55} +13421.3i q^{57} +(19135.0 - 19135.0i) q^{59} +(-27659.4 - 27659.4i) q^{61} +3540.33 q^{63} +28400.3 q^{65} +(10436.6 + 10436.6i) q^{67} +(32805.9 - 32805.9i) q^{69} +43847.1i q^{71} -32503.6i q^{73} +(-6403.93 + 6403.93i) q^{75} +(-23775.8 - 23775.8i) q^{77} +54063.2 q^{79} +49932.6 q^{81} +(-41170.0 - 41170.0i) q^{83} +(-6451.85 + 6451.85i) q^{85} -91859.0i q^{87} -21030.0i q^{89} +(86107.7 - 86107.7i) q^{91} +(54490.4 + 54490.4i) q^{93} +23155.5 q^{95} +76104.2 q^{97} +(7325.38 + 7325.38i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 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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