LMFDB - Embedded newform 378.4.h.a.289.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,4,Mod(289,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("378.289");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	378.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$22.3027219822$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.9
Character	$\chi$	$=$	378.289
Dual form			378.4.h.a.361.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +4.38272 q^{5} +(-16.3832 - 8.63665i) q^{7} +8.00000 q^{8} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +4.38272 q^{5} +(-16.3832 - 8.63665i) q^{7} +8.00000 q^{8} +(-4.38272 - 7.59110i) q^{10} -7.77875 q^{11} +(6.22371 + 10.7798i) q^{13} +(1.42406 + 37.0131i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-2.65903 - 4.60557i) q^{17} +(-7.70538 + 13.3461i) q^{19} +(-8.76544 + 15.1822i) q^{20} +(7.77875 + 13.4732i) q^{22} +131.110 q^{23} -105.792 q^{25} +(12.4474 - 21.5596i) q^{26} +(62.6846 - 39.4797i) q^{28} +(-27.0158 + 46.7927i) q^{29} +(-131.597 + 227.932i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(-5.31806 + 9.21114i) q^{34} +(-71.8029 - 37.8520i) q^{35} +(-56.8818 + 98.5222i) q^{37} +30.8215 q^{38} +35.0618 q^{40} +(114.013 + 197.477i) q^{41} +(-186.945 + 323.798i) q^{43} +(15.5575 - 26.9464i) q^{44} +(-131.110 - 227.089i) q^{46} +(-252.017 - 436.507i) q^{47} +(193.817 + 282.991i) q^{49} +(105.792 + 183.237i) q^{50} -49.7897 q^{52} +(273.338 + 473.436i) q^{53} -34.0921 q^{55} +(-131.065 - 69.0932i) q^{56} +108.063 q^{58} +(-77.2483 + 133.798i) q^{59} +(349.156 + 604.756i) q^{61} +526.386 q^{62} +64.0000 q^{64} +(27.2768 + 47.2448i) q^{65} +(-1.58484 + 2.74503i) q^{67} +21.2722 q^{68} +(6.24127 + 162.218i) q^{70} +197.455 q^{71} +(125.660 + 217.649i) q^{73} +227.527 q^{74} +(-30.8215 - 53.3844i) q^{76} +(127.441 + 67.1823i) q^{77} +(344.790 + 597.193i) q^{79} +(-35.0618 - 60.7288i) q^{80} +(228.026 - 394.953i) q^{82} +(204.374 - 353.986i) q^{83} +(-11.6538 - 20.1849i) q^{85} +747.780 q^{86} -62.2300 q^{88} +(-583.456 + 1010.58i) q^{89} +(-8.86295 - 230.359i) q^{91} +(-262.220 + 454.179i) q^{92} +(-504.035 + 873.014i) q^{94} +(-33.7705 + 58.4923i) q^{95} +(350.852 - 607.693i) q^{97} +(296.339 - 618.692i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - 48 q^{4} + 20 q^{5} + 28 q^{7} + 192 q^{8}+O(q^{10}) $ 24 * q - 24 * q^2 - 48 * q^4 + 20 * q^5 + 28 * q^7 + 192 * q^8	$ 24 q - 24 q^{2} - 48 q^{4} + 20 q^{5} + 28 q^{7} + 192 q^{8} - 20 q^{10} - 8 q^{11} - 56 q^{13} - 46 q^{14} - 192 q^{16} - 92 q^{17} - 174 q^{19} - 40 q^{20} + 8 q^{22} + 10 q^{23} + 844 q^{25} - 112 q^{26} - 20 q^{28} + 152 q^{29} - 140 q^{31} - 384 q^{32} - 184 q^{34} + 331 q^{35} + 189 q^{37} + 696 q^{38} + 160 q^{40} - 465 q^{41} - 117 q^{43} + 16 q^{44} - 10 q^{46} + 273 q^{47} + 900 q^{49} - 844 q^{50} + 448 q^{52} + 78 q^{53} + 2144 q^{55} + 224 q^{56} - 608 q^{58} - 397 q^{59} - 1847 q^{61} + 560 q^{62} + 1536 q^{64} - 996 q^{65} - 628 q^{67} + 736 q^{68} + 134 q^{70} - 44 q^{71} - 838 q^{73} - 756 q^{74} - 696 q^{76} - 1147 q^{77} + 16 q^{79} - 160 q^{80} - 930 q^{82} - 947 q^{83} - 139 q^{85} + 468 q^{86} - 64 q^{88} - 207 q^{89} - 518 q^{91} - 20 q^{92} + 546 q^{94} + 2731 q^{95} - 2308 q^{97} - 462 q^{98}+O(q^{100}) $ 24 * q - 24 * q^2 - 48 * q^4 + 20 * q^5 + 28 * q^7 + 192 * q^8 - 20 * q^10 - 8 * q^11 - 56 * q^13 - 46 * q^14 - 192 * q^16 - 92 * q^17 - 174 * q^19 - 40 * q^20 + 8 * q^22 + 10 * q^23 + 844 * q^25 - 112 * q^26 - 20 * q^28 + 152 * q^29 - 140 * q^31 - 384 * q^32 - 184 * q^34 + 331 * q^35 + 189 * q^37 + 696 * q^38 + 160 * q^40 - 465 * q^41 - 117 * q^43 + 16 * q^44 - 10 * q^46 + 273 * q^47 + 900 * q^49 - 844 * q^50 + 448 * q^52 + 78 * q^53 + 2144 * q^55 + 224 * q^56 - 608 * q^58 - 397 * q^59 - 1847 * q^61 + 560 * q^62 + 1536 * q^64 - 996 * q^65 - 628 * q^67 + 736 * q^68 + 134 * q^70 - 44 * q^71 - 838 * q^73 - 756 * q^74 - 696 * q^76 - 1147 * q^77 + 16 * q^79 - 160 * q^80 - 930 * q^82 - 947 * q^83 - 139 * q^85 + 468 * q^86 - 64 * q^88 - 207 * q^89 - 518 * q^91 - 20 * q^92 + 546 * q^94 + 2731 * q^95 - 2308 * q^97 - 462 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	4.38272			0.392002			0.196001	−	0.980604i	$-0.437204\pi$
$5$	4.38272			0.392002			0.196001	+	0.980604i	$0.437204\pi$
$6$		0			0
$7$	−16.3832	−	8.63665i	−0.884608	−	0.466335i
$7$	−16.3832	−	8.63665i	−0.884608	−	0.466335i
$8$	8.00000			0.353553
$9$		0			0
$10$	−4.38272	−	7.59110i	−0.138594	−	0.240052i
$11$	−7.77875			−0.213217			−0.106608	−	0.994301i	$-0.533999\pi$
$11$	−7.77875			−0.213217			−0.106608	+	0.994301i	$0.533999\pi$
$12$		0			0
$13$	6.22371	+	10.7798i	0.132780	+	0.229983i	0.924747	−	0.380581i	$-0.124276\pi$
$13$	6.22371	+	10.7798i	0.132780	+	0.229983i	−0.791967	+	0.610564i	$0.790943\pi$
$14$	1.42406	+	37.0131i	0.0271855	+	0.706584i
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−2.65903	−	4.60557i	−0.0379358	−	0.0657068i	0.846434	−	0.532493i	$-0.178745\pi$
$17$	−2.65903	−	4.60557i	−0.0379358	−	0.0657068i	−0.884370	+	0.466787i	$0.845412\pi$
$18$		0			0
$19$	−7.70538	+	13.3461i	−0.0930387	+	0.161148i	−0.908788	−	0.417257i	$-0.862991\pi$
$19$	−7.70538	+	13.3461i	−0.0930387	+	0.161148i	0.815750	+	0.578405i	$0.196325\pi$
$20$	−8.76544	+	15.1822i	−0.0980006	+	0.169742i
$21$		0			0
$22$	7.77875	+	13.4732i	0.0753834	+	0.130568i
$23$	131.110			1.18862			0.594312	−	0.804235i	$-0.297424\pi$
$23$	131.110			1.18862			0.594312	+	0.804235i	$0.297424\pi$
$24$		0			0
$25$	−105.792			−0.846334
$26$	12.4474	−	21.5596i	0.0938900	−	0.162622i
$27$		0			0
$28$	62.6846	−	39.4797i	0.423081	−	0.266463i
$29$	−27.0158	+	46.7927i	−0.172990	+	0.299627i	−0.939464	−	0.342648i	$-0.888676\pi$
$29$	−27.0158	+	46.7927i	−0.172990	+	0.299627i	0.766474	+	0.642275i	$0.222009\pi$
$30$		0			0
$31$	−131.597	+	227.932i	−0.762433	+	1.32057i	0.179160	+	0.983820i	$0.442662\pi$
$31$	−131.597	+	227.932i	−0.762433	+	1.32057i	−0.941593	+	0.336753i	$0.890671\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−5.31806	+	9.21114i	−0.0268247	+	0.0464617i
$35$	−71.8029	−	37.8520i	−0.346769	−	0.182805i
$36$		0			0
$37$	−56.8818	+	98.5222i	−0.252738	+	0.437755i	−0.964279	−	0.264890i	$-0.914664\pi$
$37$	−56.8818	+	98.5222i	−0.252738	+	0.437755i	0.711541	+	0.702645i	$0.247998\pi$
$38$	30.8215			0.131577
$39$		0			0
$40$	35.0618			0.138594
$41$	114.013	+	197.477i	0.434290	+	0.752212i	0.997237	−	0.0742809i	$-0.0236661\pi$
$41$	114.013	+	197.477i	0.434290	+	0.752212i	−0.562948	+	0.826492i	$0.690333\pi$
$42$		0			0
$43$	−186.945	+	323.798i	−0.662996	+	1.14834i	0.316828	+	0.948483i	$0.397382\pi$
$43$	−186.945	+	323.798i	−0.662996	+	1.14834i	−0.979824	+	0.199860i	$0.935951\pi$
$44$	15.5575	−	26.9464i	0.0533041	−	0.0923255i
$45$		0			0
$46$	−131.110	−	227.089i	−0.420242	−	0.727881i
$47$	−252.017	−	436.507i	−0.782139	−	1.35470i	−0.930693	−	0.365800i	$-0.880795\pi$
$47$	−252.017	−	436.507i	−0.782139	−	1.35470i	0.148555	−	0.988904i	$-0.452538\pi$
$48$		0			0
$49$	193.817	+	282.991i	0.565063	+	0.825048i
$50$	105.792	+	183.237i	0.299224	+	0.518272i
$51$		0			0
$52$	−49.7897			−0.132780
$53$	273.338	+	473.436i	0.708413	+	1.22701i	0.965445	+	0.260605i	$0.0839221\pi$
$53$	273.338	+	473.436i	0.708413	+	1.22701i	−0.257032	+	0.966403i	$0.582745\pi$
$54$		0			0
$55$	−34.0921			−0.0835814
$56$	−131.065	−	69.0932i	−0.312756	−	0.164874i
$57$		0			0
$58$	108.063			0.244644
$59$	−77.2483	+	133.798i	−0.170455	+	0.295237i	−0.938579	−	0.345064i	$-0.887857\pi$
$59$	−77.2483	+	133.798i	−0.170455	+	0.295237i	0.768124	+	0.640301i	$0.221191\pi$
$60$		0			0
$61$	349.156	+	604.756i	0.732867	+	1.26936i	0.955653	+	0.294495i	$0.0951515\pi$
$61$	349.156	+	604.756i	0.732867	+	1.26936i	−0.222786	+	0.974867i	$0.571515\pi$
$62$	526.386			1.07824
$63$		0			0
$64$	64.0000			0.125000
$65$	27.2768	+	47.2448i	0.0520503	+	0.0901537i
$66$		0			0
$67$	−1.58484	+	2.74503i	−0.00288984	+	0.00500535i	−0.867467	−	0.497495i	$-0.834253\pi$
$67$	−1.58484	+	2.74503i	−0.00288984	+	0.00500535i	0.864577	+	0.502501i	$0.167587\pi$
$68$	21.2722			0.0379358
$69$		0			0
$70$	6.24127	+	162.218i	0.0106568	+	0.276983i
$71$	197.455			0.330051			0.165025	−	0.986289i	$-0.447229\pi$
$71$	197.455			0.330051			0.165025	+	0.986289i	$0.447229\pi$
$72$		0			0
$73$	125.660	+	217.649i	0.201471	+	0.348957i	0.949002	−	0.315269i	$-0.102095\pi$
$73$	125.660	+	217.649i	0.201471	+	0.348957i	−0.747532	+	0.664226i	$0.768761\pi$
$74$	227.527			0.357426
$75$		0			0
$76$	−30.8215	−	53.3844i	−0.0465194	−	0.0805739i
$77$	127.441	+	67.1823i	0.188613	+	0.0994303i
$78$		0			0
$79$	344.790	+	597.193i	0.491036	+	0.850500i	0.999947	−	0.0103194i	$-0.00328484\pi$
$79$	344.790	+	597.193i	0.491036	+	0.850500i	−0.508910	+	0.860820i	$0.669952\pi$
$80$	−35.0618	−	60.7288i	−0.0490003	−	0.0848710i
$81$		0			0
$82$	228.026	−	394.953i	0.307089	−	0.531894i
$83$	204.374	−	353.986i	0.270277	−	0.468133i	−0.698656	−	0.715458i	$-0.746218\pi$
$83$	204.374	−	353.986i	0.270277	−	0.468133i	0.968933	+	0.247325i	$0.0795515\pi$
$84$		0			0
$85$	−11.6538	−	20.1849i	−0.0148709	−	0.0257572i
$86$	747.780			0.937618
$87$		0			0
$88$	−62.2300			−0.0753834
$89$	−583.456	+	1010.58i	−0.694901	+	1.20360i	0.275313	+	0.961355i	$0.411219\pi$
$89$	−583.456	+	1010.58i	−0.694901	+	1.20360i	−0.970214	+	0.242249i	$0.922115\pi$
$90$		0			0
$91$	−8.86295	−	230.359i	−0.0102098	−	0.265365i
$92$	−262.220	+	454.179i	−0.297156	+	0.514689i
$93$		0			0
$94$	−504.035	+	873.014i	−0.553056	+	0.957921i
$95$	−33.7705	+	58.4923i	−0.0364714	+	0.0631703i
$96$		0			0
$97$	350.852	−	607.693i	0.367254	−	0.636102i	−0.621881	−	0.783112i	$-0.713631\pi$
$97$	350.852	−	607.693i	0.367254	−	0.636102i	0.989135	+	0.147009i	$0.0469647\pi$
$98$	296.339	−	618.692i	0.305456	−	0.637728i
$99$		0			0
$100$	211.584	−	366.473i	0.211584	−	0.366473i
$101$	471.998			0.465006			0.232503	−	0.972596i	$-0.425308\pi$
$101$	471.998			0.465006			0.232503	+	0.972596i	$0.425308\pi$
$102$		0			0
$103$	319.603			0.305742			0.152871	−	0.988246i	$-0.451148\pi$
$103$	319.603			0.305742			0.152871	+	0.988246i	$0.451148\pi$
$104$	49.7897	+	86.2382i	0.0469450	+	0.0813111i
$105$		0			0
$106$	546.677	−	946.872i	0.500924	−	0.867626i
$107$	−212.446	+	367.968i	−0.191944	+	0.332456i	−0.945894	−	0.324475i	$-0.894812\pi$
$107$	−212.446	+	367.968i	−0.191944	+	0.332456i	0.753951	+	0.656931i	$0.228146\pi$
$108$		0			0
$109$	−677.179	−	1172.91i	−0.595064	−	1.03068i	−0.993538	−	0.113502i	$-0.963793\pi$
$109$	−677.179	−	1172.91i	−0.595064	−	1.03068i	0.398474	−	0.917180i	$-0.369540\pi$
$110$	34.0921	+	59.0492i	0.0295505	+	0.0511829i
$111$		0			0
$112$	11.3925	+	296.105i	0.00961152	+	0.249815i
$113$	537.748	+	931.408i	0.447674	+	0.775393i	0.998234	−	0.0594018i	$-0.0189193\pi$
$113$	537.748	+	931.408i	0.447674	+	0.775393i	−0.550561	+	0.834795i	$0.685586\pi$
$114$		0			0
$115$	574.619			0.465944
$116$	−108.063	−	187.171i	−0.0864948	−	0.149813i
$117$		0			0
$118$	308.993			0.241060
$119$	3.78662	+	98.4190i	0.00291697	+	0.0758156i
$120$		0			0
$121$	−1270.49			−0.954539
$122$	698.313	−	1209.51i	0.518215	−	0.897575i
$123$		0			0
$124$	−526.386	−	911.727i	−0.381217	−	0.660287i
$125$	−1011.50			−0.723768
$126$		0			0
$127$	−2324.68			−1.62426			−0.812132	−	0.583474i	$-0.801693\pi$
$127$	−2324.68			−1.62426			−0.812132	+	0.583474i	$0.801693\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	54.5536	−	94.4895i	0.0368051	−	0.0637483i
$131$	−2713.20			−1.80957			−0.904784	−	0.425871i	$-0.859968\pi$
$131$	−2713.20			−1.80957			−0.904784	+	0.425871i	$0.859968\pi$
$132$		0			0
$133$	241.504	−	152.103i	0.157452	−	0.0991654i
$134$	6.33937			0.00408685
$135$		0			0
$136$	−21.2722	−	36.8446i	−0.0134123	−	0.0232309i
$137$	379.001			0.236352			0.118176	−	0.992993i	$-0.462295\pi$
$137$	379.001			0.236352			0.118176	+	0.992993i	$0.462295\pi$
$138$		0			0
$139$	−320.799	−	555.640i	−0.195754	−	0.339056i	0.751393	−	0.659854i	$-0.229382\pi$
$139$	−320.799	−	555.640i	−0.195754	−	0.339056i	−0.947147	+	0.320799i	$0.896049\pi$
$140$	274.729	−	173.028i	0.165849	−	0.104454i
$141$		0			0
$142$	−197.455	−	342.002i	−0.116691	−	0.202114i
$143$	−48.4127	−	83.8532i	−0.0283110	−	0.0490361i
$144$		0			0
$145$	−118.403	+	205.079i	−0.0678124	+	0.117454i
$146$	251.319	−	435.298i	0.142461	−	0.246750i
$147$		0			0
$148$	−227.527	−	394.089i	−0.126369	−	0.218878i
$149$	584.615			0.321433			0.160717	−	0.987001i	$-0.448619\pi$
$149$	584.615			0.321433			0.160717	+	0.987001i	$0.448619\pi$
$150$		0			0
$151$	3232.00			1.74183			0.870916	−	0.491432i	$-0.163526\pi$
$151$	3232.00			1.74183			0.870916	+	0.491432i	$0.163526\pi$
$152$	−61.6430	+	106.769i	−0.0328942	+	0.0569743i
$153$		0			0
$154$	−11.0774	−	287.916i	−0.00579639	−	0.150655i
$155$	−576.751	+	998.962i	−0.298876	+	0.517668i
$156$		0			0
$157$	−1846.84	+	3198.83i	−0.938816	+	1.62608i	−0.171132	+	0.985248i	$0.554742\pi$
$157$	−1846.84	+	3198.83i	−0.938816	+	1.62608i	−0.767684	+	0.640829i	$0.778591\pi$
$158$	689.580	−	1194.39i	0.347215	−	0.601394i
$159$		0			0
$160$	−70.1235	+	121.458i	−0.0346485	+	0.0600129i
$161$	−2148.00	−	1132.35i	−1.05147	−	0.554297i
$162$		0			0
$163$	−225.060	+	389.815i	−0.108147	+	0.187317i	−0.915020	−	0.403409i	$-0.867825\pi$
$163$	−225.060	+	389.815i	−0.108147	+	0.187317i	0.806872	+	0.590726i	$0.201159\pi$
$164$	−912.106			−0.434290
$165$		0			0
$166$	−817.496			−0.382229
$167$	−1689.64	−	2926.54i	−0.782923	−	1.35606i	−0.930232	−	0.366972i	$-0.880394\pi$
$167$	−1689.64	−	2926.54i	−0.782923	−	1.35606i	0.147308	−	0.989091i	$-0.452939\pi$
$168$		0			0
$169$	1021.03	−	1768.48i	0.464739	−	0.804951i
$170$	−23.3076	+	40.3699i	−0.0105153	+	0.0182131i
$171$		0			0
$172$	−747.780	−	1295.19i	−0.331498	−	0.574171i
$173$	−227.401	−	393.871i	−0.0999365	−	0.173095i	0.811722	−	0.584044i	$-0.198531\pi$
$173$	−227.401	−	393.871i	−0.0999365	−	0.173095i	−0.911658	+	0.410949i	$0.865197\pi$
$174$		0			0
$175$	1733.20	+	913.686i	0.748674	+	0.394675i
$176$	62.2300	+	107.786i	0.0266521	+	0.0461627i
$177$		0			0
$178$	2333.82			0.982738
$179$	−576.208	−	998.022i	−0.240602	−	0.416735i	0.720284	−	0.693680i	$-0.244012\pi$
$179$	−576.208	−	998.022i	−0.240602	−	0.416735i	−0.960886	+	0.276944i	$0.910678\pi$
$180$		0			0
$181$	340.170			0.139694			0.0698471	−	0.997558i	$-0.477749\pi$
$181$	340.170			0.139694			0.0698471	+	0.997558i	$0.477749\pi$
$182$	−390.130	+	245.710i	−0.158892	+	0.100073i
$183$		0			0
$184$	1048.88			0.420242
$185$	−249.297	+	431.795i	−0.0990740	+	0.171601i
$186$		0			0
$187$	20.6839	+	35.8256i	0.00808854	+	0.0140098i
$188$	2016.14			0.782139
$189$		0			0
$190$	135.082			0.0515784
$191$	−2419.84	−	4191.28i	−0.916719	−	1.58780i	−0.804365	−	0.594136i	$-0.797494\pi$
$191$	−2419.84	−	4191.28i	−0.916719	−	1.58780i	−0.112354	−	0.993668i	$-0.535839\pi$
$192$		0			0
$193$	133.604	−	231.410i	0.0498293	−	0.0863069i	−0.840035	−	0.542532i	$-0.817466\pi$
$193$	133.604	−	231.410i	0.0498293	−	0.0863069i	0.889864	+	0.456225i	$0.150799\pi$
$194$	−1403.41			−0.519375
$195$		0			0
$196$	−1367.94	+	105.418i	−0.498522	+	0.0384176i
$197$	−3285.84			−1.18836			−0.594178	−	0.804334i	$-0.702522\pi$
$197$	−3285.84			−1.18836			−0.594178	+	0.804334i	$0.702522\pi$
$198$		0			0
$199$	−697.784	−	1208.60i	−0.248566	−	0.430529i	0.714562	−	0.699572i	$-0.246626\pi$
$199$	−697.784	−	1208.60i	−0.248566	−	0.430529i	−0.963128	+	0.269043i	$0.913293\pi$
$200$	−846.334			−0.299224
$201$		0			0
$202$	−471.998	−	817.525i	−0.164404	−	0.284757i
$203$	846.735	−	533.287i	0.292755	−	0.184381i
$204$		0			0
$205$	499.688	+	865.485i	0.170243	+	0.294869i
$206$	−319.603	−	553.569i	−0.108096	−	0.187228i
$207$		0			0
$208$	99.5793	−	172.476i	0.0331951	−	0.0574956i
$209$	59.9382	−	103.816i	0.0198374	−	0.0343594i
$210$		0			0
$211$	−1949.90	−	3377.33i	−0.636194	−	1.10192i	−0.986261	−	0.165195i	$-0.947175\pi$
$211$	−1949.90	−	3377.33i	−0.636194	−	1.10192i	0.350067	−	0.936725i	$-0.386159\pi$
$212$	−2186.71			−0.708413
$213$		0			0
$214$	849.786			0.271449
$215$	−819.327	+	1419.12i	−0.259896	+	0.450153i
$216$		0			0
$217$	4124.53	−	2597.69i	1.29028	−	0.812640i
$218$	−1354.36	+	2345.82i	−0.420774	+	0.728802i
$219$		0			0
$220$	68.1842	−	118.098i	0.0208954	−	0.0361918i
$221$	33.0980	−	57.3275i	0.0100743	−	0.0174492i
$222$		0			0
$223$	−840.676	+	1456.09i	−0.252448	+	0.437252i	−0.964199	−	0.265179i	$-0.914569\pi$
$223$	−840.676	+	1456.09i	−0.252448	+	0.437252i	0.711752	+	0.702431i	$0.247902\pi$
$224$	501.477	−	315.837i	0.149582	−	0.0942088i
$225$		0			0
$226$	1075.50	−	1862.82i	0.316553	−	0.548286i
$227$	5817.50			1.70097			0.850487	−	0.525997i	$-0.176308\pi$
$227$	5817.50			1.70097			0.850487	+	0.525997i	$0.176308\pi$
$228$		0			0
$229$	−4538.98			−1.30980			−0.654901	−	0.755715i	$-0.727290\pi$
$229$	−4538.98			−1.30980			−0.654901	+	0.755715i	$0.727290\pi$
$230$	−574.619	−	995.270i	−0.164736	−	0.285331i
$231$		0			0
$232$	−216.126	+	374.341i	−0.0611611	+	0.105934i
$233$	2571.91	−	4454.68i	0.723139	−	1.25251i	−0.236596	−	0.971608i	$-0.576032\pi$
$233$	2571.91	−	4454.68i	0.723139	−	1.25251i	0.959735	−	0.280906i	$-0.0906349\pi$
$234$		0			0
$235$	−1104.52	−	1913.09i	−0.306600	−	0.531047i
$236$	−308.993	−	535.192i	−0.0852277	−	0.147619i
$237$		0			0
$238$	166.680	−	104.978i	0.0453961	−	0.0285911i
$239$	381.366	+	660.546i	0.103216	+	0.178775i	0.913008	−	0.407942i	$-0.133753\pi$
$239$	381.366	+	660.546i	0.103216	+	0.178775i	−0.809792	+	0.586717i	$0.800420\pi$
$240$		0			0
$241$	1206.28			0.322420			0.161210	−	0.986920i	$-0.448460\pi$
$241$	1206.28			0.322420			0.161210	+	0.986920i	$0.448460\pi$
$242$	1270.49	+	2200.56i	0.337480	+	0.584533i
$243$		0			0
$244$	−2793.25			−0.732867
$245$	849.444	+	1240.27i	0.221506	+	0.323421i
$246$		0			0
$247$	−191.824			−0.0494149
$248$	−1052.77	+	1823.45i	−0.269561	+	0.466893i
$249$		0			0
$250$	1011.50	+	1751.96i	0.255890	+	0.443215i
$251$	605.465			0.152257			0.0761287	−	0.997098i	$-0.475744\pi$
$251$	605.465			0.152257			0.0761287	+	0.997098i	$0.475744\pi$
$252$		0			0
$253$	−1019.87			−0.253434
$254$	2324.68	+	4026.46i	0.574264	+	0.994655i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	4268.62			1.03607			0.518033	−	0.855361i	$-0.326664\pi$
$257$	4268.62			1.03607			0.518033	+	0.855361i	$0.326664\pi$
$258$		0			0
$259$	1782.81	−	1122.84i	0.427715	−	0.269381i
$260$	−218.214			−0.0520503
$261$		0			0
$262$	2713.20	+	4699.40i	0.639779	+	1.10813i
$263$	6440.23			1.50997			0.754984	−	0.655743i	$-0.227644\pi$
$263$	6440.23			1.50997			0.754984	+	0.655743i	$0.227644\pi$
$264$		0			0
$265$	1197.97	+	2074.94i	0.277700	+	0.480990i
$266$	−504.954	−	266.195i	−0.116394	−	0.0613588i
$267$		0			0
$268$	−6.33937	−	10.9801i	−0.00144492	−	0.00250268i
$269$	2865.79	+	4963.69i	0.649554	+	1.12506i	0.983230	+	0.182372i	$0.0583777\pi$
$269$	2865.79	+	4963.69i	0.649554	+	1.12506i	−0.333676	+	0.942688i	$0.608289\pi$
$270$		0			0
$271$	−2319.36	+	4017.25i	−0.519893	+	0.900482i	0.479839	+	0.877356i	$0.340695\pi$
$271$	−2319.36	+	4017.25i	−0.519893	+	0.900482i	−0.999733	+	0.0231253i	$0.992638\pi$
$272$	−42.5445	+	73.6891i	−0.00948396	+	0.0164267i
$273$		0			0
$274$	−379.001	−	656.448i	−0.0835630	−	0.144735i
$275$	822.928			0.180452
$276$		0			0
$277$	−1396.04			−0.302815			−0.151408	−	0.988471i	$-0.548381\pi$
$277$	−1396.04			−0.302815			−0.151408	+	0.988471i	$0.548381\pi$
$278$	−641.598	+	1111.28i	−0.138419	+	0.239749i
$279$		0			0
$280$	−574.423	−	302.816i	−0.122601	−	0.0646312i
$281$	−4244.01	+	7350.84i	−0.900984	+	1.56055i	−0.0747638	+	0.997201i	$0.523820\pi$
$281$	−4244.01	+	7350.84i	−0.900984	+	1.56055i	−0.826220	+	0.563348i	$0.809513\pi$
$282$		0			0
$283$	−2788.33	+	4829.52i	−0.585685	+	1.01444i	0.409105	+	0.912487i	$0.365841\pi$
$283$	−2788.33	+	4829.52i	−0.585685	+	1.01444i	−0.994790	+	0.101949i	$0.967492\pi$
$284$	−394.910	+	684.004i	−0.0825127	+	0.142916i
$285$		0			0
$286$	−96.8254	+	167.706i	−0.0200189	+	0.0346737i
$287$	−162.362	−	4219.99i	−0.0333934	−	0.867937i
$288$		0			0
$289$	2442.36	−	4230.29i	0.497122	−	0.861040i
$290$	473.610			0.0959012
$291$		0			0
$292$	−1005.28			−0.201471
$293$	2804.95	+	4858.32i	0.559273	+	0.968690i	0.997557	+	0.0698531i	$0.0222531\pi$
$293$	2804.95	+	4858.32i	0.559273	+	0.968690i	−0.438284	+	0.898837i	$0.644414\pi$
$294$		0			0
$295$	−338.558	+	586.399i	−0.0668190	+	0.115734i
$296$	−455.055	+	788.178i	−0.0893564	+	0.154770i
$297$		0			0
$298$	−584.615	−	1012.58i	−0.113644	−	0.196837i
$299$	815.991	+	1413.34i	0.157826	+	0.273363i
$300$		0			0
$301$	5859.28	−	3690.26i	1.12200	−	0.706655i
$302$	−3232.00	−	5597.99i	−0.615831	−	1.06665i
$303$		0			0
$304$	246.572			0.0465194
$305$	1530.25	+	2650.48i	0.287286	+	0.497593i
$306$		0			0
$307$	5007.55			0.930932			0.465466	−	0.885066i	$-0.345887\pi$
$307$	5007.55			0.930932			0.465466	+	0.885066i	$0.345887\pi$
$308$	−487.608	+	307.103i	−0.0902079	+	0.0568143i
$309$		0			0
$310$	2307.00			0.422674
$311$	−3153.44	+	5461.92i	−0.574969	+	0.995876i	0.421076	+	0.907025i	$0.361653\pi$
$311$	−3153.44	+	5461.92i	−0.574969	+	0.995876i	−0.996045	+	0.0888502i	$0.971681\pi$
$312$		0			0
$313$	−116.451	−	201.699i	−0.0210294	−	0.0364240i	0.855319	−	0.518101i	$-0.173361\pi$
$313$	−116.451	−	201.699i	−0.0210294	−	0.0364240i	−0.876349	+	0.481677i	$0.840028\pi$
$314$	7387.37			1.32769
$315$		0			0
$316$	−2758.32			−0.491036
$317$	−4181.33	−	7242.28i	−0.740842	−	1.28318i	−0.952112	−	0.305748i	$-0.901093\pi$
$317$	−4181.33	−	7242.28i	−0.740842	−	1.28318i	0.211270	−	0.977428i	$-0.432240\pi$
$318$		0			0
$319$	210.149	−	363.988i	0.0368842	−	0.0638854i
$320$	280.494			0.0490003
$321$		0			0
$322$	186.709	+	4852.80i	0.0323133	+	0.839863i
$323$	81.9553			0.0141180
$324$		0			0
$325$	−658.417	−	1140.41i	−0.112377	−	0.194642i
$326$	900.239			0.152944
$327$		0			0
$328$	912.106	+	1579.81i	0.153545	+	0.265947i
$329$	358.889	+	9327.96i	0.0601403	+	1.56312i
$330$		0			0
$331$	−2867.84	−	4967.25i	−0.476226	−	0.824848i	0.523403	−	0.852085i	$-0.324662\pi$
$331$	−2867.84	−	4967.25i	−0.476226	−	0.824848i	−0.999629	+	0.0272375i	$0.991329\pi$
$332$	817.496	+	1415.94i	0.135138	+	0.234066i
$333$		0			0
$334$	−3379.28	+	5853.08i	−0.553610	+	0.958881i
$335$	−6.94592	+	12.0307i	−0.00113282	+	0.00196211i
$336$		0			0
$337$	4280.89	+	7414.72i	0.691973	+	1.19853i	0.971190	+	0.238305i	$0.0765917\pi$
$337$	4280.89	+	7414.72i	0.691973	+	1.19853i	−0.279217	+	0.960228i	$0.590075\pi$
$338$	−4084.12			−0.657240
$339$		0			0
$340$	93.2302			0.0148709
$341$	1023.66	−	1773.03i	0.162563	−	0.281568i
$342$		0			0
$343$	−731.236	−	6310.22i	−0.115111	−	0.993353i
$344$	−1495.56	+	2590.38i	−0.234405	+	0.406001i
$345$		0			0
$346$	−454.803	+	787.742i	−0.0706658	+	0.122397i
$347$	1761.49	−	3051.00i	0.272513	−	0.472006i	−0.696992	−	0.717079i	$-0.745479\pi$
$347$	1761.49	−	3051.00i	0.272513	−	0.472006i	0.969505	+	0.245073i	$0.0788120\pi$
$348$		0			0
$349$	−4151.37	+	7190.38i	−0.636727	+	1.10284i	0.349420	+	0.936966i	$0.386379\pi$
$349$	−4151.37	+	7190.38i	−0.636727	+	1.10284i	−0.986146	+	0.165877i	$0.946955\pi$
$350$	−150.654	−	3915.68i	−0.0230080	−	0.598006i
$351$		0			0
$352$	124.460	−	215.571i	0.0188459	−	0.0326420i
$353$	1011.39			0.152496			0.0762480	−	0.997089i	$-0.475706\pi$
$353$	1011.39			0.152496			0.0762480	+	0.997089i	$0.475706\pi$
$354$		0			0
$355$	865.390			0.129381
$356$	−2333.82	−	4042.30i	−0.347451	−	0.601802i
$357$		0			0
$358$	−1152.42	+	1996.04i	−0.170132	+	0.294676i
$359$	5031.82	−	8715.36i	0.739747	−	1.28128i	−0.212862	−	0.977082i	$-0.568279\pi$
$359$	5031.82	−	8715.36i	0.739747	−	1.28128i	0.952609	−	0.304197i	$-0.0983881\pi$
$360$		0			0
$361$	3310.75	+	5734.39i	0.482688	+	0.836039i
$362$	−340.170	−	589.192i	−0.0493893	−	0.0855448i
$363$		0			0
$364$	815.713	+	430.016i	0.117459	+	0.0619202i
$365$	550.731	+	953.894i	0.0789769	+	0.136792i
$366$		0			0
$367$	−6431.31			−0.914746			−0.457373	−	0.889275i	$-0.651210\pi$
$367$	−6431.31			−0.914746			−0.457373	+	0.889275i	$0.651210\pi$
$368$	−1048.88	−	1816.72i	−0.148578	−	0.257345i
$369$		0			0
$370$	997.189			0.140112
$371$	−389.251	−	10117.1i	−0.0544714	−	1.41578i
$372$		0			0
$373$	11246.7			1.56121			0.780604	−	0.625026i	$-0.214912\pi$
$373$	11246.7			1.56121			0.780604	+	0.625026i	$0.214912\pi$
$374$	41.3678	−	71.6512i	0.00571947	−	0.00990640i
$375$		0			0
$376$	−2016.14	−	3492.06i	−0.276528	−	0.478960i
$377$	−672.553			−0.0918786
$378$		0			0
$379$	−12129.1			−1.64387			−0.821937	−	0.569579i	$-0.807106\pi$
$379$	−12129.1			−1.64387			−0.821937	+	0.569579i	$0.807106\pi$
$380$	−135.082	−	233.969i	−0.0182357	−	0.0315852i
$381$		0			0
$382$	−4839.68	+	8382.57i	−0.648218	+	1.12275i
$383$	6360.23			0.848544			0.424272	−	0.905535i	$-0.360530\pi$
$383$	6360.23			0.848544			0.424272	+	0.905535i	$0.360530\pi$
$384$		0			0
$385$	558.537	+	294.441i	0.0739368	+	0.0389769i
$386$	−534.417			−0.0704693
$387$		0			0
$388$	1403.41	+	2430.77i	0.183627	+	0.318051i
$389$	−1184.01			−0.154323			−0.0771615	−	0.997019i	$-0.524586\pi$
$389$	−1184.01			−0.154323			−0.0771615	+	0.997019i	$0.524586\pi$
$390$		0			0
$391$	−348.626	−	603.837i	−0.0450914	−	0.0781007i
$392$	1550.53	+	2263.93i	0.199780	+	0.291698i
$393$		0			0
$394$	3285.84	+	5691.23i	0.420147	+	0.727716i
$395$	1511.12	+	2617.33i	0.192488	+	0.333398i
$396$		0			0
$397$	−2701.50	+	4679.14i	−0.341522	+	0.591534i	−0.984716	−	0.174170i	$-0.944276\pi$
$397$	−2701.50	+	4679.14i	−0.341522	+	0.591534i	0.643193	+	0.765704i	$0.277609\pi$
$398$	−1395.57	+	2417.20i	−0.175763	+	0.304430i
$399$		0			0
$400$	846.334	+	1465.89i	0.105792	+	0.183237i
$401$	596.609			0.0742974			0.0371487	−	0.999310i	$-0.488172\pi$
$401$	596.609			0.0742974			0.0371487	+	0.999310i	$0.488172\pi$
$402$		0			0
$403$	−3276.07			−0.404945
$404$	−943.997	+	1635.05i	−0.116251	+	0.201353i
$405$		0			0
$406$	−1770.41	−	933.302i	−0.216414	−	0.114086i
$407$	442.470	−	766.380i	0.0538880	−	0.0933367i
$408$		0			0
$409$	−1217.12	+	2108.12i	−0.147146	+	0.254865i	−0.930172	−	0.367125i	$-0.880342\pi$
$409$	−1217.12	+	2108.12i	−0.147146	+	0.254865i	0.783025	+	0.621990i	$0.213675\pi$
$410$	999.376	−	1730.97i	0.120380	−	0.208504i
$411$		0			0
$412$	−639.207	+	1107.14i	−0.0764356	+	0.132390i
$413$	2421.14	−	1524.87i	0.288466	−	0.181680i
$414$		0			0
$415$	895.714	−	1551.42i	0.105949	−	0.183509i
$416$	−398.317			−0.0469450
$417$		0			0
$418$	−239.753			−0.0280543
$419$	3250.11	+	5629.36i	0.378946	+	0.656354i	0.990909	−	0.134532i	$-0.0429532\pi$
$419$	3250.11	+	5629.36i	0.378946	+	0.656354i	−0.611963	+	0.790886i	$0.709620\pi$
$420$		0			0
$421$	−102.420	+	177.397i	−0.0118566	+	0.0205363i	−0.871893	−	0.489697i	$-0.837108\pi$
$421$	−102.420	+	177.397i	−0.0118566	+	0.0205363i	0.860036	+	0.510233i	$0.170441\pi$
$422$	−3899.81	+	6754.66i	−0.449857	+	0.779175i
$423$		0			0
$424$	2186.71	+	3787.49i	0.250462	+	0.433813i
$425$	281.303	+	487.232i	0.0321064	+	0.0556099i
$426$		0			0
$427$	−497.220	−	12923.4i	−0.0563517	−	1.46465i
$428$	−849.786	−	1471.87i	−0.0959718	−	0.166228i
$429$		0			0
$430$	3277.31			0.367549
$431$	−1956.57	−	3388.88i	−0.218665	−	0.378739i	0.735735	−	0.677269i	$-0.236837\pi$
$431$	−1956.57	−	3388.88i	−0.218665	−	0.378739i	−0.954400	+	0.298530i	$0.903504\pi$
$432$		0			0
$433$	17098.5			1.89770			0.948848	−	0.315734i	$-0.102251\pi$
$433$	17098.5			1.89770			0.948848	+	0.315734i	$0.102251\pi$
$434$	−8623.87	−	4546.21i	−0.953823	−	0.502823i
$435$		0			0
$436$	5417.43			0.595064
$437$	−1010.25	+	1749.81i	−0.110588	+	0.191544i
$438$		0			0
$439$	−4325.63	−	7492.20i	−0.470275	−	0.814541i	0.529147	−	0.848530i	$-0.322512\pi$
$439$	−4325.63	−	7492.20i	−0.470275	−	0.814541i	−0.999422	+	0.0339895i	$0.989179\pi$
$440$	−272.737			−0.0295505
$441$		0			0
$442$	−132.392			−0.0142472
$443$	104.496	+	180.992i	0.0112071	+	0.0194113i	0.871575	−	0.490263i	$-0.163099\pi$
$443$	104.496	+	180.992i	0.0112071	+	0.0194113i	−0.860367	+	0.509674i	$0.829766\pi$
$444$		0			0
$445$	−2557.12	+	4429.07i	−0.272403	+	0.471816i
$446$	3362.70			0.357015
$447$		0			0
$448$	−1048.52	−	552.745i	−0.110576	−	0.0582919i
$449$	−14209.3			−1.49349			−0.746747	−	0.665108i	$-0.768386\pi$
$449$	−14209.3			−1.49349			−0.746747	+	0.665108i	$0.768386\pi$
$450$		0			0
$451$	−886.880	−	1536.12i	−0.0925977	−	0.160384i
$452$	−4301.99			−0.447674
$453$		0			0
$454$	−5817.50	−	10076.2i	−0.601385	−	1.04163i
$455$	−38.8438	−	1009.60i	−0.00400226	−	0.104024i
$456$		0			0
$457$	−3994.01	−	6917.84i	−0.408823	−	0.708102i	0.585935	−	0.810358i	$-0.300727\pi$
$457$	−3994.01	−	6917.84i	−0.408823	−	0.708102i	−0.994758	+	0.102256i	$0.967394\pi$
$458$	4538.98	+	7861.75i	0.463085	+	0.802086i
$459$		0			0
$460$	−1149.24	+	1990.54i	−0.116486	+	0.201760i
$461$	−508.300	+	880.402i	−0.0513534	+	0.0889467i	−0.890559	−	0.454867i	$-0.849687\pi$
$461$	−508.300	+	880.402i	−0.0513534	+	0.0889467i	0.839206	+	0.543814i	$0.183020\pi$
$462$		0			0
$463$	−8711.25	−	15088.3i	−0.874398	−	1.51450i	−0.857403	−	0.514646i	$-0.827923\pi$
$463$	−8711.25	−	15088.3i	−0.874398	−	1.51450i	−0.0169956	−	0.999856i	$-0.505410\pi$
$464$	864.504			0.0864948
$465$		0			0
$466$	−10287.6			−1.02267
$467$	−7634.38	+	13223.1i	−0.756482	+	1.31027i	0.188152	+	0.982140i	$0.439750\pi$
$467$	−7634.38	+	13223.1i	−0.756482	+	1.31027i	−0.944634	+	0.328126i	$0.893583\pi$
$468$		0			0
$469$	49.6726	−	31.2845i	0.00489055	−	0.00308014i
$470$	−2209.04	+	3826.18i	−0.216799	+	0.375507i
$471$		0			0
$472$	−617.986	+	1070.38i	−0.0602651	+	0.104382i
$473$	1454.20	−	2518.74i	0.141362	−	0.244846i
$474$		0			0
$475$	815.166	−	1411.91i	0.0787418	−	0.136385i
$476$	−348.507	−	183.721i	−0.0335583	−	0.0176908i
$477$		0			0
$478$	762.733	−	1321.09i	0.0729845	−	0.126413i
$479$	11292.3			1.07716			0.538581	−	0.842574i	$-0.318961\pi$
$479$	11292.3			1.07716			0.538581	+	0.842574i	$0.318961\pi$
$480$		0			0
$481$	−1416.06			−0.134235
$482$	−1206.28	−	2089.33i	−0.113993	−	0.197441i
$483$		0			0
$484$	2540.98	−	4401.11i	0.238635	−	0.413327i
$485$	1537.69	−	2663.35i	0.143964	−	0.249354i
$486$		0			0
$487$	8249.11	+	14287.9i	0.767562	+	1.32946i	0.938881	+	0.344241i	$0.111864\pi$
$487$	8249.11	+	14287.9i	0.767562	+	1.32946i	−0.171319	+	0.985216i	$0.554803\pi$
$488$	2793.25	+	4838.05i	0.259108	+	0.448787i
$489$		0			0
$490$	1298.77	−	2711.55i	0.119740	−	0.249991i
$491$	−7174.59	−	12426.7i	−0.659439	−	1.14218i	−0.980761	−	0.195212i	$-0.937461\pi$
$491$	−7174.59	−	12426.7i	−0.659439	−	1.14218i	0.321322	−	0.946970i	$-0.395873\pi$
$492$		0			0
$493$	287.343			0.0262500
$494$	191.824	+	332.249i	0.0174708	+	0.0302603i
$495$		0			0
$496$	4211.09			0.381217
$497$	−3234.94	−	1705.35i	−0.291966	−	0.153914i
$498$		0			0
$499$	−1595.39			−0.143126			−0.0715628	−	0.997436i	$-0.522799\pi$
$499$	−1595.39			−0.143126			−0.0715628	+	0.997436i	$0.522799\pi$
$500$	2022.99	−	3503.92i	0.180942	−	0.313401i
$501$		0			0
$502$	−605.465	−	1048.70i	−0.0538311	−	0.0932382i
$503$	−14195.8			−1.25837			−0.629184	−	0.777257i	$-0.716611\pi$
$503$	−14195.8			−1.25837			−0.629184	+	0.777257i	$0.716611\pi$
$504$		0			0
$505$	2068.64			0.182283
$506$	1019.87	+	1766.47i	0.0896026	+	0.155196i
$507$		0			0
$508$	4649.35	−	8052.91i	0.406066	−	0.703327i
$509$	13356.8			1.16313			0.581564	−	0.813501i	$-0.302441\pi$
$509$	13356.8			1.16313			0.581564	+	0.813501i	$0.302441\pi$
$510$		0			0
$511$	−178.947	−	4651.06i	−0.0154915	−	0.402643i
$512$	512.000			0.0441942
$513$		0			0
$514$	−4268.62	−	7393.46i	−0.366305	−	0.634458i
$515$	1400.73			0.119852
$516$		0			0
$517$	1960.38	+	3395.48i	0.166765	+	0.288845i
$518$	−3727.62	−	1965.07i	−0.316182	−	0.166680i
$519$		0			0
$520$	218.214	+	377.958i	0.0184026	+	0.0318742i
$521$	−1802.26	−	3121.61i	−0.151552	−	0.262495i	0.780246	−	0.625472i	$-0.215094\pi$
$521$	−1802.26	−	3121.61i	−0.151552	−	0.262495i	−0.931798	+	0.362977i	$0.881760\pi$
$522$		0			0
$523$	−1312.27	+	2272.91i	−0.109716	+	0.190034i	−0.915655	−	0.401965i	$-0.868327\pi$
$523$	−1312.27	+	2272.91i	−0.109716	+	0.190034i	0.805939	+	0.591998i	$0.201661\pi$
$524$	5426.40	−	9398.80i	0.452392	−	0.783566i
$525$		0			0
$526$	−6440.23	−	11154.8i	−0.533855	−	0.924663i
$527$	1399.68			0.115694
$528$		0			0
$529$	5022.87			0.412827
$530$	2395.93	−	4149.88i	0.196363	−	0.340111i
$531$		0			0
$532$	43.8918	+	1140.80i	0.00357697	+	0.0929699i
$533$	−1419.17	+	2458.07i	−0.115330	+	0.199758i
$534$		0			0
$535$	−931.093	+	1612.70i	−0.0752424	+	0.130324i
$536$	−12.6787	+	21.9602i	−0.00102171	+	0.00176966i
$537$		0			0
$538$	5731.57	−	9927.37i	0.459304	−	0.795538i
$539$	−1507.65	−	2201.32i	−0.120481	−	0.175914i
$540$		0			0
$541$	−3260.57	+	5647.47i	−0.259118	+	0.448805i	−0.966006	−	0.258520i	$-0.916765\pi$
$541$	−3260.57	+	5647.47i	−0.259118	+	0.448805i	0.706888	+	0.707325i	$0.250098\pi$
$542$	9277.44			0.735240
$543$		0			0
$544$	170.178			0.0134123
$545$	−2967.89	−	5140.53i	−0.233267	−	0.404030i
$546$		0			0
$547$	482.353	−	835.459i	0.0377037	−	0.0653047i	−0.846558	−	0.532297i	$-0.821329\pi$
$547$	482.353	−	835.459i	0.0377037	−	0.0653047i	0.884261	+	0.466992i	$0.154662\pi$
$548$	−758.001	+	1312.90i	−0.0590880	+	0.102343i
$549$		0			0
$550$	−822.928	−	1425.35i	−0.0637996	−	0.110504i
$551$	−416.333	−	721.110i	−0.0321895	−	0.0557538i
$552$		0			0
$553$	−491.002	−	12761.8i	−0.0377568	−	0.981347i
$554$	1396.04	+	2418.01i	0.107061	+	0.185436i
$555$		0			0
$556$	2566.39			0.195754
$557$	6860.04	+	11881.9i	0.521848	+	0.903867i	0.999677	+	0.0254140i	$0.00809040\pi$
$557$	6860.04	+	11881.9i	0.521848	+	0.903867i	−0.477829	+	0.878453i	$0.658576\pi$
$558$		0			0
$559$	−4653.96			−0.352132
$560$	49.9301	+	1297.75i	0.00376774	+	0.0979282i
$561$		0			0
$562$	16976.0			1.27418
$563$	3511.08	−	6081.37i	0.262832	−	0.455238i	−0.704161	−	0.710040i	$-0.748677\pi$
$563$	3511.08	−	6081.37i	0.262832	−	0.455238i	0.966993	+	0.254802i	$0.0820102\pi$
$564$		0			0
$565$	2356.80	+	4082.10i	0.175489	+	0.303956i
$566$	11153.3			0.828284
$567$		0			0
$568$	1579.64			0.116691
$569$	−1629.47	−	2822.32i	−0.120054	−	0.207940i	0.799735	−	0.600354i	$-0.204974\pi$
$569$	−1629.47	−	2822.32i	−0.120054	−	0.207940i	−0.919789	+	0.392414i	$0.871640\pi$
$570$		0			0
$571$	13223.7	−	22904.1i	0.969168	−	1.67865i	0.271196	−	0.962524i	$-0.412581\pi$
$571$	13223.7	−	22904.1i	0.969168	−	1.67865i	0.697972	−	0.716125i	$-0.254086\pi$
$572$	387.301			0.0283110
$573$		0			0
$574$	−7146.87	+	4501.21i	−0.519694	+	0.327311i
$575$	−13870.4			−1.00597
$576$		0			0
$577$	10026.0	+	17365.5i	0.723375	+	1.25292i	0.959639	+	0.281234i	$0.0907437\pi$
$577$	10026.0	+	17365.5i	0.723375	+	1.25292i	−0.236264	+	0.971689i	$0.575923\pi$
$578$	−9769.44			−0.703036
$579$		0			0
$580$	−473.610	−	820.317i	−0.0339062	−	0.0587272i
$581$	−6405.55	+	4034.31i	−0.457396	+	0.288075i
$582$		0			0
$583$	−2126.23	−	3682.74i	−0.151045	−	0.261618i
$584$	1005.28	+	1741.19i	0.0712306	+	0.123375i
$585$		0			0
$586$	5609.90	−	9716.64i	0.395466	−	0.684967i
$587$	9435.36	−	16342.5i	0.663439	−	1.14911i	−0.316267	−	0.948670i	$-0.602429\pi$
$587$	9435.36	−	16342.5i	0.663439	−	1.14911i	0.979706	−	0.200440i	$-0.0642373\pi$
$588$		0			0
$589$	−2028.00	−	3512.60i	−0.141872	−	0.245729i
$590$	1354.23			0.0944963
$591$		0			0
$592$	1820.22			0.126369
$593$	−5829.09	+	10096.3i	−0.403663	+	0.699164i	−0.994165	−	0.107872i	$-0.965596\pi$
$593$	−5829.09	+	10096.3i	−0.403663	+	0.699164i	0.590502	+	0.807036i	$0.298930\pi$
$594$		0			0
$595$	16.5957	+	431.343i	0.00114346	+	0.0297199i
$596$	−1169.23	+	2025.17i	−0.0803583	+	0.139185i
$597$		0			0
$598$	1631.98	−	2826.68i	0.111600	−	0.193297i
$599$	−6054.85	+	10487.3i	−0.413013	+	0.715359i	−0.995218	−	0.0976832i	$-0.968857\pi$
$599$	−6054.85	+	10487.3i	−0.413013	+	0.715359i	0.582205	+	0.813042i	$0.302190\pi$
$600$		0			0
$601$	−9060.89	+	15693.9i	−0.614977	+	1.06517i	0.375411	+	0.926858i	$0.377501\pi$
$601$	−9060.89	+	15693.9i	−0.614977	+	1.06517i	−0.990389	+	0.138313i	$0.955832\pi$
$602$	−12251.0	−	6458.31i	−0.829425	−	0.437244i
$603$		0			0
$604$	−6464.01	+	11196.0i	−0.435458	+	0.754236i
$605$	−5568.21			−0.374182
$606$		0			0
$607$	7382.29			0.493638			0.246819	−	0.969062i	$-0.420615\pi$
$607$	7382.29			0.493638			0.246819	+	0.969062i	$0.420615\pi$
$608$	−246.572	−	427.076i	−0.0164471	−	0.0284872i
$609$		0			0
$610$	3060.51	−	5300.96i	0.203142	−	0.351852i
$611$	3136.97	−	5433.39i	0.207706	−	0.359757i
$612$		0			0
$613$	634.046	+	1098.20i	0.0417763	+	0.0723587i	0.886158	−	0.463384i	$-0.153365\pi$
$613$	634.046	+	1098.20i	0.0417763	+	0.0723587i	−0.844381	+	0.535743i	$0.820032\pi$
$614$	−5007.55	−	8673.33i	−0.329134	−	0.570077i
$615$		0			0
$616$	1019.52	+	537.459i	0.0666848	+	0.0351539i
$617$	−8335.18	−	14437.0i	−0.543860	−	0.941994i	−0.998678	−	0.0514091i	$-0.983629\pi$
$617$	−8335.18	−	14437.0i	−0.543860	−	0.941994i	0.454817	−	0.890585i	$-0.349705\pi$
$618$		0			0
$619$	18338.8			1.19079			0.595393	−	0.803434i	$-0.296996\pi$
$619$	18338.8			1.19079			0.595393	+	0.803434i	$0.296996\pi$
$620$	−2307.00	−	3995.85i	−0.149438	−	0.258834i
$621$		0			0
$622$	12613.8			0.813129
$623$	18286.8	−	11517.3i	1.17600	−	0.740661i
$624$		0			0
$625$	8790.87			0.562615
$626$	−232.902	+	403.398i	−0.0148700	+	0.0257556i
$627$		0			0
$628$	−7387.37	−	12795.3i	−0.469408	−	0.813038i
$629$	605.001			0.0383513
$630$		0			0
$631$	−20329.2			−1.28255			−0.641277	−	0.767309i	$-0.721595\pi$
$631$	−20329.2			−1.28255			−0.641277	+	0.767309i	$0.721595\pi$
$632$	2758.32	+	4777.55i	0.173608	+	0.300697i
$633$		0			0
$634$	−8362.66	+	14484.6i	−0.523854	+	0.907342i
$635$	−10188.4			−0.636716
$636$		0			0
$637$	−1844.33	+	3850.56i	−0.114717	+	0.239505i
$638$	−840.595			−0.0521622
$639$		0			0
$640$	−280.494	−	485.830i	−0.0173242	−	0.0300064i
$641$	−21862.8			−1.34716			−0.673580	−	0.739115i	$-0.735244\pi$
$641$	−21862.8			−1.34716			−0.673580	+	0.739115i	$0.735244\pi$
$642$		0			0
$643$	33.5166	+	58.0525i	0.00205563	+	0.00356045i	0.867051	−	0.498219i	$-0.166012\pi$
$643$	33.5166	+	58.0525i	0.00205563	+	0.00356045i	−0.864996	+	0.501779i	$0.832679\pi$
$644$	8218.58	−	5176.19i	0.502884	−	0.316724i
$645$		0			0
$646$	−81.9553	−	141.951i	−0.00499147	−	0.00864548i
$647$	−7474.78	−	12946.7i	−0.454195	−	0.786688i	0.544447	−	0.838795i	$-0.316740\pi$
$647$	−7474.78	−	12946.7i	−0.454195	−	0.786688i	−0.998641	+	0.0521072i	$0.983406\pi$
$648$		0			0
$649$	600.895	−	1040.78i	0.0363439	−	0.0629495i
$650$	−1316.83	+	2280.82i	−0.0794623	+	0.137633i
$651$		0			0
$652$	−900.239	−	1559.26i	−0.0540737	−	0.0936584i
$653$	−7291.18			−0.436946			−0.218473	−	0.975843i	$-0.570108\pi$
$653$	−7291.18			−0.436946			−0.218473	+	0.975843i	$0.570108\pi$
$654$		0			0
$655$	−11891.2			−0.709355
$656$	1824.21	−	3159.63i	0.108572	−	0.188053i
$657$		0			0
$658$	15797.6	−	9949.57i	0.935950	−	0.589475i
$659$	−7262.98	+	12579.9i	−0.429326	+	0.743614i	−0.996813	−	0.0797678i	$-0.974582\pi$
$659$	−7262.98	+	12579.9i	−0.429326	+	0.743614i	0.567488	+	0.823382i	$0.307915\pi$
$660$		0			0
$661$	−7132.82	+	12354.4i	−0.419719	+	0.726975i	−0.995911	−	0.0903393i	$-0.971205\pi$
$661$	−7132.82	+	12354.4i	−0.419719	+	0.726975i	0.576192	+	0.817315i	$0.304538\pi$
$662$	−5735.68	+	9934.50i	−0.336743	+	0.583256i
$663$		0			0
$664$	1634.99	−	2831.89i	0.0955572	−	0.165510i
$665$	1058.45	−	666.625i	0.0617214	−	0.0388731i
$666$		0			0
$667$	−3542.04	+	6134.99i	−0.205620	+	0.356144i
$668$	13517.1			0.782923
$669$		0			0
$670$	27.7837			0.00160206
$671$	−2716.00	−	4704.25i	−0.156259	−	0.270649i
$672$		0			0
$673$	3626.28	−	6280.91i	0.207701	−	0.359749i	−0.743289	−	0.668971i	$-0.766735\pi$
$673$	3626.28	−	6280.91i	0.207701	−	0.359749i	0.950990	+	0.309222i	$0.100068\pi$
$674$	8561.78	−	14829.4i	0.489299	−	0.847491i
$675$		0			0
$676$	4084.12	+	7073.91i	0.232369	+	0.402476i
$677$	3785.35	+	6556.42i	0.214894	+	0.372207i	0.953240	−	0.302215i	$-0.0977262\pi$
$677$	3785.35	+	6556.42i	0.214894	+	0.372207i	−0.738346	+	0.674422i	$0.764393\pi$
$678$		0			0
$679$	−10996.5	+	6925.76i	−0.621513	+	0.391438i
$680$	−93.2302	−	161.479i	−0.00525767	−	0.00910655i
$681$		0			0
$682$	−4094.63			−0.229899
$683$	10005.9	+	17330.7i	0.560564	+	0.970926i	0.997447	+	0.0714074i	$0.0227491\pi$
$683$	10005.9	+	17330.7i	0.560564	+	0.970926i	−0.436883	+	0.899518i	$0.643918\pi$
$684$		0			0
$685$	1661.05			0.0926505
$686$	−10198.4	+	7576.76i	−0.567604	+	0.421694i
$687$		0			0
$688$	5982.24			0.331498
$689$	−3402.36	+	5893.05i	−0.188127	+	0.325845i
$690$		0			0
$691$	9549.15	+	16539.6i	0.525712	+	0.910560i	0.999551	+	0.0299485i	$0.00953434\pi$
$691$	9549.15	+	16539.6i	0.525712	+	0.910560i	−0.473840	+	0.880611i	$0.657132\pi$
$692$	1819.21			0.0999365
$693$		0			0
$694$	−7045.97			−0.385391
$695$	−1405.97	−	2435.21i	−0.0767360	−	0.132911i
$696$		0			0
$697$	606.329	−	1050.19i	0.0329503	−	0.0570715i
$698$	16605.5			0.900468
$699$		0			0
$700$	−6631.51	+	4176.62i	−0.358068	+	0.225517i
$701$	26142.9			1.40857			0.704283	−	0.709919i	$-0.251268\pi$
$701$	26142.9			1.40857			0.704283	+	0.709919i	$0.251268\pi$
$702$		0			0
$703$	−876.592	−	1518.30i	−0.0470289	−	0.0814564i
$704$	−497.840			−0.0266521
$705$		0			0
$706$	−1011.39	−	1751.79i	−0.0539155	−	0.0933843i
$707$	−7732.83	−	4076.48i	−0.411348	−	0.216849i
$708$		0			0
$709$	−11844.7	−	20515.7i	−0.627417	−	1.08672i	−0.988068	−	0.154017i	$-0.950779\pi$
$709$	−11844.7	−	20515.7i	−0.627417	−	1.08672i	0.360652	−	0.932701i	$-0.382554\pi$
$710$	−865.390	−	1498.90i	−0.0457430	−	0.0792292i
$711$		0			0
$712$	−4667.65	+	8084.60i	−0.245685	+	0.425538i
$713$	−17253.6	+	29884.2i	−0.906247	+	1.56967i
$714$		0			0
$715$	−212.179	−	367.505i	−0.0110980	−	0.0192223i
$716$	4609.66			0.240602
$717$		0			0
$718$	−20127.3			−1.04616
$719$	−10583.5	+	18331.2i	−0.548956	+	0.950820i	0.449390	+	0.893336i	$0.351641\pi$
$719$	−10583.5	+	18331.2i	−0.548956	+	0.950820i	−0.998346	+	0.0574848i	$0.981692\pi$
$720$		0			0
$721$	−5236.12	−	2760.30i	−0.270462	−	0.142578i
$722$	6621.51	−	11468.8i	0.341312	−	0.591169i
$723$		0			0
$724$	−680.340	+	1178.38i	−0.0349235	+	0.0604893i
$725$	2858.04	−	4950.28i	0.146407	−	0.253584i
$726$		0			0
$727$	−10263.9	+	17777.6i	−0.523613	+	0.906924i	0.476009	+	0.879440i	$0.342083\pi$
$727$	−10263.9	+	17777.6i	−0.523613	+	0.906924i	−0.999622	+	0.0274840i	$0.991250\pi$
$728$	−70.9036	−	1842.87i	−0.00360970	−	0.0938206i
$729$		0			0
$730$	1101.46	−	1907.79i	0.0558451	−	0.0967266i
$731$	1988.37			0.100605
$732$		0			0
$733$	9810.42			0.494347			0.247173	−	0.968971i	$-0.420498\pi$
$733$	9810.42			0.494347			0.247173	+	0.968971i	$0.420498\pi$
$734$	6431.31	+	11139.4i	0.323411	+	0.560165i
$735$		0			0
$736$	−2097.76	+	3633.43i	−0.105061	+	0.181970i
$737$	12.3281	−	21.3529i	0.000616162	−	0.00106722i
$738$		0			0
$739$	4123.42	+	7141.98i	0.205254	+	0.355510i	0.950214	−	0.311599i	$-0.100865\pi$
$739$	4123.42	+	7141.98i	0.205254	+	0.355510i	−0.744960	+	0.667109i	$0.767531\pi$
$740$	−997.189	−	1727.18i	−0.0495370	−	0.0858006i
$741$		0			0
$742$	−17134.1	+	10791.3i	−0.847726	+	0.533910i
$743$	10307.9	+	17853.9i	0.508966	+	0.881555i	0.999946	+	0.0103842i	$0.00330544\pi$
$743$	10307.9	+	17853.9i	0.508966	+	0.881555i	−0.490980	+	0.871171i	$0.663361\pi$
$744$		0			0
$745$	2562.21			0.126003
$746$	−11246.7	−	19479.8i	−0.551970	−	0.956040i
$747$		0			0
$748$	−165.471			−0.00808854
$749$	6658.56	−	4193.66i	0.324831	−	0.204583i
$750$		0			0
$751$	−9510.05			−0.462086			−0.231043	−	0.972944i	$-0.574214\pi$
$751$	−9510.05			−0.462086			−0.231043	+	0.972944i	$0.574214\pi$
$752$	−4032.28	+	6984.11i	−0.195535	+	0.338676i
$753$		0			0
$754$	672.553	+	1164.90i	0.0324840	+	0.0562639i
$755$	14165.0			0.682803
$756$		0			0
$757$	−2569.81			−0.123383			−0.0616917	−	0.998095i	$-0.519650\pi$
$757$	−2569.81			−0.123383			−0.0616917	+	0.998095i	$0.519650\pi$
$758$	12129.1	+	21008.1i	0.581197	+	1.00666i
$759$		0			0
$760$	−270.164	+	467.938i	−0.0128946	+	0.0223341i
$761$	2804.25			0.133580			0.0667899	−	0.997767i	$-0.478724\pi$
$761$	2804.25			0.133580			0.0667899	+	0.997767i	$0.478724\pi$
$762$		0			0
$763$	964.345	+	25064.5i	0.0457558	+	1.18925i
$764$	19358.7			0.916719
$765$		0			0
$766$	−6360.23	−	11016.2i	−0.300006	−	0.519625i
$767$	−1923.08			−0.0905326
$768$		0			0
$769$	8325.95	+	14421.0i	0.390431	+	0.676246i	0.992506	−	0.122193i	$-0.0389927\pi$
$769$	8325.95	+	14421.0i	0.390431	+	0.676246i	−0.602076	+	0.798439i	$0.705659\pi$
$770$	−48.5493	−	1261.86i	−0.00227220	−	0.0590573i
$771$		0			0
$772$	534.417	+	925.638i	0.0249146	+	0.0431534i
$773$	−3795.60	−	6574.17i	−0.176608	−	0.305895i	0.764108	−	0.645088i	$-0.223179\pi$
$773$	−3795.60	−	6574.17i	−0.176608	−	0.305895i	−0.940717	+	0.339193i	$0.889846\pi$
$774$		0			0
$775$	13921.8	−	24113.3i	0.645273	−	1.11765i
$776$	2806.82	−	4861.55i	0.129844	−	0.224896i
$777$		0			0
$778$	1184.01	+	2050.76i	0.0545614	+	0.0945032i
$779$	−3514.06			−0.161623
$780$		0			0
$781$	−1535.95			−0.0703723
$782$	−697.251	+	1207.67i	−0.0318845	+	0.0552255i
$783$		0			0
$784$	2370.71	−	4949.53i	0.107995	−	0.225471i
$785$	−8094.20	+	14019.6i	−0.368018	+	0.637426i
$786$		0			0
$787$	−17659.0	+	30586.3i	−0.799843	+	1.38537i	0.119875	+	0.992789i	$0.461751\pi$
$787$	−17659.0	+	30586.3i	−0.799843	+	1.38537i	−0.919718	+	0.392580i	$0.871583\pi$
$788$	6571.67	−	11382.5i	0.297089	−	0.514573i
$789$		0			0
$790$	3022.23	−	5234.66i	0.136109	−	0.235748i
$791$	−765.787	−	19903.8i	−0.0344226	−	0.894685i
$792$		0			0
$793$	−4346.09	+	7527.66i	−0.194621	+	0.337093i
$794$	10806.0			0.482986
$795$		0			0
$796$	5582.27			0.248566
$797$	12353.0	+	21396.1i	0.549017	+	0.950925i	0.998342	+	0.0575567i	$0.0183310\pi$
$797$	12353.0	+	21396.1i	0.549017	+	0.950925i	−0.449326	+	0.893368i	$0.648336\pi$
$798$		0			0
$799$	−1340.24	+	2321.37i	−0.0593422	+	0.102784i
$800$	1692.67	−	2931.79i	0.0748061	−	0.129568i
$801$		0			0
$802$	−596.609	−	1033.36i	−0.0262681	−	0.0454977i
$803$	−977.475	−	1693.04i	−0.0429568	−	0.0744034i
$804$		0			0
$805$	−9414.09	−	4962.78i	−0.412178	−	0.217286i
$806$	3276.07	+	5674.33i	0.143170	+	0.247977i
$807$		0			0
$808$	3775.99			0.164404
$809$	14599.2	+	25286.5i	0.634462	+	1.09892i	0.986629	+	0.162984i	$0.0521118\pi$
$809$	14599.2	+	25286.5i	0.634462	+	1.09892i	−0.352166	+	0.935937i	$0.614555\pi$
$810$		0			0
$811$	−7349.09			−0.318202			−0.159101	−	0.987262i	$-0.550860\pi$
$811$	−7349.09			−0.318202			−0.159101	+	0.987262i	$0.550860\pi$
$812$	153.888	+	3999.75i	0.00665077	+	0.172862i
$813$		0			0
$814$	−1769.88			−0.0762091
$815$	−986.374	+	1708.45i	−0.0423941	+	0.0734287i
$816$		0			0
$817$	−2880.96	−	4989.97i	−0.123369	−	0.213681i
$818$	4868.49			0.208096
$819$		0			0
$820$	−3997.50			−0.170243
$821$	−3761.27	−	6514.72i	−0.159890	−	0.276937i	0.774939	−	0.632036i	$-0.217780\pi$
$821$	−3761.27	−	6514.72i	−0.159890	−	0.276937i	−0.934829	+	0.355099i	$0.884447\pi$
$822$		0			0
$823$	−1373.31	+	2378.64i	−0.0581660	+	0.100746i	−0.893642	−	0.448780i	$-0.851859\pi$
$823$	−1373.31	+	2378.64i	−0.0581660	+	0.100746i	0.835476	+	0.549527i	$0.185192\pi$
$824$	2556.83			0.108096
$825$		0			0
$826$	−5062.29	−	2668.66i	−0.213244	−	0.112415i
$827$	24374.1			1.02487			0.512437	−	0.858725i	$-0.328743\pi$
$827$	24374.1			1.02487			0.512437	+	0.858725i	$0.328743\pi$
$828$		0			0
$829$	−19441.0	−	33672.8i	−0.814492	−	1.41074i	−0.909692	−	0.415283i	$-0.863683\pi$
$829$	−19441.0	−	33672.8i	−0.814492	−	1.41074i	0.0952004	−	0.995458i	$-0.469651\pi$
$830$	−3582.86			−0.149835
$831$		0			0
$832$	398.317	+	689.906i	0.0165976	+	0.0287478i
$833$	787.973	−	1645.12i	0.0327751	−	0.0684273i
$834$		0			0
$835$	−7405.22	−	12826.2i	−0.306908	−	0.531580i
$836$	239.753	+	415.264i	0.00991870	+	0.0171797i
$837$		0			0
$838$	6500.23	−	11258.7i	0.267955	−	0.464112i
$839$	−2299.01	+	3982.01i	−0.0946016	+	0.163855i	−0.909442	−	0.415830i	$-0.863491\pi$
$839$	−2299.01	+	3982.01i	−0.0946016	+	0.163855i	0.814841	+	0.579685i	$0.196824\pi$
$840$		0			0
$841$	10734.8	+	18593.2i	0.440149	+	0.762361i
$842$	409.680			0.0167678
$843$		0			0
$844$	15599.2			0.636194
$845$	4474.89	−	7750.74i	0.182179	−	0.315543i
$846$		0			0
$847$	20814.7	+	10972.8i	0.844393	+	0.445135i
$848$	4373.41	−	7574.97i	0.177103	−	0.306752i
$849$		0			0
$850$	562.607	−	974.463i	0.0227026	−	0.0393221i
$851$	−7457.78	+	12917.3i	−0.300411	+	0.520327i
$852$		0			0
$853$	−6521.43	+	11295.5i	−0.261770	+	0.453399i	−0.966712	−	0.255866i	$-0.917639\pi$
$853$	−6521.43	+	11295.5i	−0.261770	+	0.453399i	0.704943	+	0.709264i	$0.250973\pi$
$854$	−21886.7	+	13784.6i	−0.876988	+	0.552340i
$855$		0			0
$856$	−1699.57	+	2943.74i	−0.0678623	+	0.117541i
$857$	9103.78			0.362869			0.181435	−	0.983403i	$-0.441926\pi$
$857$	9103.78			0.362869			0.181435	+	0.983403i	$0.441926\pi$
$858$		0			0
$859$	30470.2			1.21028			0.605140	−	0.796119i	$-0.293117\pi$
$859$	30470.2			1.21028			0.605140	+	0.796119i	$0.293117\pi$
$860$	−3277.31	−	5676.47i	−0.129948	−	0.225077i
$861$		0			0
$862$	−3913.14	+	6777.76i	−0.154620	+	0.267809i
$863$	20595.8	−	35673.0i	0.812387	−	1.40709i	−0.0988027	−	0.995107i	$-0.531501\pi$
$863$	20595.8	−	35673.0i	0.812387	−	1.40709i	0.911189	−	0.411988i	$-0.135165\pi$
$864$		0			0
$865$	−996.637	−	1726.23i	−0.0391753	−	0.0678537i
$866$	−17098.5	−	29615.5i	−0.670937	−	1.16210i
$867$		0			0
$868$	749.606	+	19483.2i	0.0293126	+	0.761870i
$869$	−2682.03	−	4645.42i	−0.104697	−	0.181341i
$870$		0			0
$871$	−39.4544			−0.00153486
$872$	−5417.43	−	9383.27i	−0.210387	−	0.364401i
$873$		0			0
$874$	4041.01			0.156395
$875$	16571.5	+	8735.93i	0.640251	+	0.337518i
$876$		0			0
$877$	−1311.03			−0.0504792			−0.0252396	−	0.999681i	$-0.508035\pi$
$877$	−1311.03			−0.0504792			−0.0252396	+	0.999681i	$0.508035\pi$
$878$	−8651.25	+	14984.4i	−0.332535	+	0.575967i
$879$		0			0
$880$	272.737	+	472.394i	0.0104477	+	0.0180959i
$881$	−26582.1			−1.01654			−0.508271	−	0.861197i	$-0.669715\pi$
$881$	−26582.1			−1.01654			−0.508271	+	0.861197i	$0.669715\pi$
$882$		0			0
$883$	−5122.48			−0.195227			−0.0976133	−	0.995224i	$-0.531121\pi$
$883$	−5122.48			−0.195227			−0.0976133	+	0.995224i	$0.531121\pi$
$884$	132.392	+	229.310i	0.00503714	+	0.00872458i
$885$		0			0
$886$	208.992	−	361.985i	0.00792463	−	0.0137259i
$887$	−44833.4			−1.69713			−0.848567	−	0.529088i	$-0.822534\pi$
$887$	−44833.4			−1.69713			−0.848567	+	0.529088i	$0.822534\pi$
$888$		0			0
$889$	38085.6	+	20077.4i	1.43684	+	0.757451i
$890$	10228.5			0.385236
$891$		0			0
$892$	−3362.70	−	5824.37i	−0.126224	−	0.218626i
$893$	7767.56			0.291077
$894$		0			0
$895$	−2525.36	−	4374.05i	−0.0943167	−	0.163361i
$896$	91.1400	+	2368.84i	0.00339818	+	0.0883230i
$897$		0			0
$898$	14209.3	+	24611.3i	0.528030	+	0.914575i
$899$	−7110.36	−	12315.5i	−0.263786	−	0.456891i
$900$		0			0
$901$	1453.63	−	2517.76i	0.0537485	−	0.0930951i
$902$	−1773.76	+	3072.24i	−0.0654765	+	0.113409i
$903$		0			0
$904$	4301.99	+	7451.26i	0.158277	+	0.274143i
$905$	1490.87			0.0547605
$906$		0			0
$907$	27744.9			1.01572			0.507858	−	0.861441i	$-0.330437\pi$
$907$	27744.9			1.01572			0.507858	+	0.861441i	$0.330437\pi$
$908$	−11635.0	+	20152.4i	−0.425243	+	0.736543i
$909$		0			0
$910$	−1709.83	+	1076.88i	−0.0622862	+	0.0392288i
$911$	2364.30	−	4095.09i	0.0859855	−	0.148931i	−0.819825	−	0.572614i	$-0.805929\pi$
$911$	2364.30	−	4095.09i	0.0859855	−	0.148931i	0.905811	+	0.423683i	$0.139263\pi$
$912$		0			0
$913$	−1589.77	+	2753.57i	−0.0576275	+	0.0998137i
$914$	−7988.03	+	13835.7i	−0.289081	+	0.500704i
$915$		0			0
$916$	9077.97	−	15723.5i	0.327450	−	0.567161i
$917$	44450.8	+	23433.0i	1.60076	+	0.843865i
$918$		0			0
$919$	−7811.85	+	13530.5i	−0.280402	+	0.485670i	−0.971484	−	0.237106i	$-0.923801\pi$
$919$	−7811.85	+	13530.5i	−0.280402	+	0.485670i	0.691082	+	0.722776i	$0.257134\pi$
$920$	4596.95			0.164736
$921$		0			0
$922$	2033.20			0.0726246
$923$	1228.90	+	2128.52i	0.0438243	+	0.0759059i
$924$		0			0
$925$	6017.63	−	10422.8i	0.213901	−	0.370487i
$926$	−17422.5	+	30176.7i	−0.618293	+	1.07091i
$927$		0			0
$928$	−864.504	−	1497.36i	−0.0305805	−	0.0529670i
$929$	7492.81	+	12977.9i	0.264619	+	0.458334i	0.967464	−	0.253010i	$-0.0814204\pi$
$929$	7492.81	+	12977.9i	0.264619	+	0.458334i	−0.702845	+	0.711343i	$0.748087\pi$
$930$		0			0
$931$	−5270.26	+	406.143i	−0.185527	+	0.0142973i
$932$	10287.6	+	17818.7i	0.361570	+	0.626257i
$933$		0			0
$934$	30537.5			1.06983
$935$	90.6518	+	157.014i	0.00317073	+	0.00549186i
$936$		0			0
$937$	−19285.4			−0.672387			−0.336193	−	0.941793i	$-0.609140\pi$
$937$	−19285.4			−0.672387			−0.336193	+	0.941793i	$0.609140\pi$
$938$	−103.859	−	54.7509i	−0.00361526	−	0.00190584i
$939$		0			0
$940$	8836.18			0.306600
$941$	12828.1	−	22218.9i	0.444404	−	0.769729i	−0.553607	−	0.832778i	$-0.686749\pi$
$941$	12828.1	−	22218.9i	0.444404	−	0.769729i	0.998010	+	0.0630486i	$0.0200823\pi$
$942$		0			0
$943$	14948.3	+	25891.2i	0.516207	+	0.894097i
$944$	2471.95			0.0852277
$945$		0			0
$946$	−5816.79			−0.199916
$947$	8970.70	+	15537.7i	0.307823	+	0.533165i	0.977886	−	0.209139i	$-0.0670662\pi$
$947$	8970.70	+	15537.7i	0.307823	+	0.533165i	−0.670063	+	0.742304i	$0.733733\pi$
$948$		0			0
$949$	−1564.14	+	2709.17i	−0.0535027	+	0.0926694i
$950$	−3260.66			−0.111358
$951$		0			0
$952$	30.2930	+	787.352i	0.00103130	+	0.0268048i
$953$	17724.2			0.602460			0.301230	−	0.953551i	$-0.402603\pi$
$953$	17724.2			0.602460			0.301230	+	0.953551i	$0.402603\pi$
$954$		0			0
$955$	−10605.5	−	18369.2i	−0.359356	−	0.622423i
$956$	−3050.93			−0.103216
$957$		0			0
$958$	−11292.3	−	19558.9i	−0.380834	−	0.659624i
$959$	−6209.23	−	3273.29i	−0.209079	−	0.110219i
$960$		0			0
$961$	−19739.8	−	34190.3i	−0.662609	−	1.14767i
$962$	1416.06	+	2452.69i	0.0474592	+	0.0822017i
$963$		0			0
$964$	−2412.55	+	4178.67i	−0.0806049	+	0.139612i
$965$	585.551	−	1014.20i	0.0195332	−	0.0338325i
$966$		0			0
$967$	11463.1	+	19854.7i	0.381209	+	0.660273i	0.991235	−	0.132108i	$-0.0421746\pi$
$967$	11463.1	+	19854.7i	0.381209	+	0.660273i	−0.610027	+	0.792381i	$0.708841\pi$
$968$	−10163.9			−0.337480
$969$		0			0
$970$	−6150.75			−0.203596
$971$	12903.8	−	22350.0i	0.426470	−	0.738668i	−0.570086	−	0.821585i	$-0.693090\pi$
$971$	12903.8	−	22350.0i	0.426470	−	0.738668i	0.996556	+	0.0829166i	$0.0264235\pi$
$972$		0			0
$973$	456.837	+	11873.8i	0.0150519	+	0.391218i
$974$	16498.2	−	28575.7i	0.542748	−	0.940068i
$975$		0			0
$976$	5586.50	−	9676.10i	0.183217	−	0.317341i
$977$	27400.1	−	47458.3i	0.897242	−	1.55407i	0.0662372	−	0.997804i	$-0.478901\pi$
$977$	27400.1	−	47458.3i	0.897242	−	1.55407i	0.831005	−	0.556265i	$-0.187766\pi$
$978$		0			0
$979$	4538.56	−	7861.01i	0.148164	−	0.256628i
$980$	−5995.32	+	462.018i	−0.195422	+	0.0150598i
$981$		0			0
$982$	−14349.2	+	24853.5i	−0.466294	+	0.807645i
$983$	−54913.9			−1.78177			−0.890885	−	0.454229i	$-0.849915\pi$
$983$	−54913.9			−1.78177			−0.890885	+	0.454229i	$0.849915\pi$
$984$		0			0
$985$	−14400.9			−0.465838
$986$	−287.343	−	497.692i	−0.00928078	−	0.0160748i
$987$		0			0
$988$	383.648	−	664.498i	0.0123537	−	0.0213973i
$989$	−24510.4	+	42453.2i	−0.788053	+	1.36495i
$990$		0			0
$991$	−20761.1	−	35959.3i	−0.665488	−	1.15266i	−0.979153	−	0.203125i	$-0.934890\pi$
$991$	−20761.1	−	35959.3i	−0.665488	−	1.15266i	0.313665	−	0.949534i	$-0.398443\pi$
$992$	−4211.09	−	7293.82i	−0.134780	−	0.233447i
$993$		0			0
$994$	281.188	+	7308.43i	0.00897258	+	0.233209i
$995$	−3058.19	−	5296.95i	−0.0974384	−	0.168768i
$996$		0			0
$997$	36737.6			1.16699			0.583496	−	0.812116i	$-0.301684\pi$
$997$	36737.6			1.16699			0.583496	+	0.812116i	$0.301684\pi$
$998$	1595.39	+	2763.30i	0.0506025	+	0.0876462i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.4.h.a.289.9		24
3.2	odd	2		126.4.h.b.79.5	yes	24
7.4	even	3		378.4.e.b.235.4		24
9.4	even	3		378.4.e.b.37.4		24
9.5	odd	6		126.4.e.a.121.12	yes	24
21.11	odd	6		126.4.e.a.25.12	✓	24
63.4	even	3	inner	378.4.h.a.361.9		24
63.32	odd	6		126.4.h.b.67.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.e.a.25.12	✓	24	21.11	odd	6
126.4.e.a.121.12	yes	24	9.5	odd	6
126.4.h.b.67.5	yes	24	63.32	odd	6
126.4.h.b.79.5	yes	24	3.2	odd	2
378.4.e.b.37.4		24	9.4	even	3
378.4.e.b.235.4		24	7.4	even	3
378.4.h.a.289.9		24	1.1	even	1	trivial
378.4.h.a.361.9		24	63.4	even	3	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	378.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +4.38272 q^{5} +(-16.3832 - 8.63665i) q^{7} +8.00000 q^{8} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +4.38272 q^{5} +(-16.3832 - 8.63665i) q^{7} +8.00000 q^{8} +(-4.38272 - 7.59110i) q^{10} -7.77875 q^{11} +(6.22371 + 10.7798i) q^{13} +(1.42406 + 37.0131i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-2.65903 - 4.60557i) q^{17} +(-7.70538 + 13.3461i) q^{19} +(-8.76544 + 15.1822i) q^{20} +(7.77875 + 13.4732i) q^{22} +131.110 q^{23} -105.792 q^{25} +(12.4474 - 21.5596i) q^{26} +(62.6846 - 39.4797i) q^{28} +(-27.0158 + 46.7927i) q^{29} +(-131.597 + 227.932i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(-5.31806 + 9.21114i) q^{34} +(-71.8029 - 37.8520i) q^{35} +(-56.8818 + 98.5222i) q^{37} +30.8215 q^{38} +35.0618 q^{40} +(114.013 + 197.477i) q^{41} +(-186.945 + 323.798i) q^{43} +(15.5575 - 26.9464i) q^{44} +(-131.110 - 227.089i) q^{46} +(-252.017 - 436.507i) q^{47} +(193.817 + 282.991i) q^{49} +(105.792 + 183.237i) q^{50} -49.7897 q^{52} +(273.338 + 473.436i) q^{53} -34.0921 q^{55} +(-131.065 - 69.0932i) q^{56} +108.063 q^{58} +(-77.2483 + 133.798i) q^{59} +(349.156 + 604.756i) q^{61} +526.386 q^{62} +64.0000 q^{64} +(27.2768 + 47.2448i) q^{65} +(-1.58484 + 2.74503i) q^{67} +21.2722 q^{68} +(6.24127 + 162.218i) q^{70} +197.455 q^{71} +(125.660 + 217.649i) q^{73} +227.527 q^{74} +(-30.8215 - 53.3844i) q^{76} +(127.441 + 67.1823i) q^{77} +(344.790 + 597.193i) q^{79} +(-35.0618 - 60.7288i) q^{80} +(228.026 - 394.953i) q^{82} +(204.374 - 353.986i) q^{83} +(-11.6538 - 20.1849i) q^{85} +747.780 q^{86} -62.2300 q^{88} +(-583.456 + 1010.58i) q^{89} +(-8.86295 - 230.359i) q^{91} +(-262.220 + 454.179i) q^{92} +(-504.035 + 873.014i) q^{94} +(-33.7705 + 58.4923i) q^{95} +(350.852 - 607.693i) q^{97} +(296.339 - 618.692i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - 48 q^{4} + 20 q^{5} + 28 q^{7} + 192 q^{8}+O(q^{10}) \) 24 * q - 24 * q^2 - 48 * q^4 + 20 * q^5 + 28 * q^7 + 192 * q^8	\( 24 q - 24 q^{2} - 48 q^{4} + 20 q^{5} + 28 q^{7} + 192 q^{8} - 20 q^{10} - 8 q^{11} - 56 q^{13} - 46 q^{14} - 192 q^{16} - 92 q^{17} - 174 q^{19} - 40 q^{20} + 8 q^{22} + 10 q^{23} + 844 q^{25} - 112 q^{26} - 20 q^{28} + 152 q^{29} - 140 q^{31} - 384 q^{32} - 184 q^{34} + 331 q^{35} + 189 q^{37} + 696 q^{38} + 160 q^{40} - 465 q^{41} - 117 q^{43} + 16 q^{44} - 10 q^{46} + 273 q^{47} + 900 q^{49} - 844 q^{50} + 448 q^{52} + 78 q^{53} + 2144 q^{55} + 224 q^{56} - 608 q^{58} - 397 q^{59} - 1847 q^{61} + 560 q^{62} + 1536 q^{64} - 996 q^{65} - 628 q^{67} + 736 q^{68} + 134 q^{70} - 44 q^{71} - 838 q^{73} - 756 q^{74} - 696 q^{76} - 1147 q^{77} + 16 q^{79} - 160 q^{80} - 930 q^{82} - 947 q^{83} - 139 q^{85} + 468 q^{86} - 64 q^{88} - 207 q^{89} - 518 q^{91} - 20 q^{92} + 546 q^{94} + 2731 q^{95} - 2308 q^{97} - 462 q^{98}+O(q^{100}) \) 24 * q - 24 * q^2 - 48 * q^4 + 20 * q^5 + 28 * q^7 + 192 * q^8 - 20 * q^10 - 8 * q^11 - 56 * q^13 - 46 * q^14 - 192 * q^16 - 92 * q^17 - 174 * q^19 - 40 * q^20 + 8 * q^22 + 10 * q^23 + 844 * q^25 - 112 * q^26 - 20 * q^28 + 152 * q^29 - 140 * q^31 - 384 * q^32 - 184 * q^34 + 331 * q^35 + 189 * q^37 + 696 * q^38 + 160 * q^40 - 465 * q^41 - 117 * q^43 + 16 * q^44 - 10 * q^46 + 273 * q^47 + 900 * q^49 - 844 * q^50 + 448 * q^52 + 78 * q^53 + 2144 * q^55 + 224 * q^56 - 608 * q^58 - 397 * q^59 - 1847 * q^61 + 560 * q^62 + 1536 * q^64 - 996 * q^65 - 628 * q^67 + 736 * q^68 + 134 * q^70 - 44 * q^71 - 838 * q^73 - 756 * q^74 - 696 * q^76 - 1147 * q^77 + 16 * q^79 - 160 * q^80 - 930 * q^82 - 947 * q^83 - 139 * q^85 + 468 * q^86 - 64 * q^88 - 207 * q^89 - 518 * q^91 - 20 * q^92 + 546 * q^94 + 2731 * q^95 - 2308 * q^97 - 462 * q^98

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