LMFDB - Embedded newform 144.5.m.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,5,Mod(19,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("144.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	144.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.8852746841$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + \cdots + 2097152 $ x^14 - 4x^13 + 15x^12 - 34x^11 + 62x^10 - 312x^9 + 1432x^8 - 4960x^7 + 11456x^6 - 19968x^5 + 31744x^4 - 139264x^3 + 491520x^2 - 1048576*x + 2097152
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{21} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.3
Root			$1.03712 + 2.63142i$ of defining polynomial
Character	$\chi$	$=$	144.19
Dual form			144.5.m.a.91.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59430 - 3.66854i) q^{2} +(-10.9164 + 11.6975i) q^{4} +(14.6016 - 14.6016i) q^{5} -24.0210 q^{7} +(60.3169 + 21.3980i) q^{8} +O(q^{10})$	\(q+(-1.59430 - 3.66854i) q^{2} +(-10.9164 + 11.6975i) q^{4} +(14.6016 - 14.6016i) q^{5} -24.0210 q^{7} +(60.3169 + 21.3980i) q^{8} +(-76.8459 - 30.2872i) q^{10} +(-61.7287 - 61.7287i) q^{11} +(-37.5611 - 37.5611i) q^{13} +(38.2966 + 88.1219i) q^{14} +(-17.6638 - 255.390i) q^{16} -96.8718 q^{17} +(-156.751 + 156.751i) q^{19} +(11.4053 + 330.199i) q^{20} +(-128.040 + 324.868i) q^{22} -959.783 q^{23} +198.587i q^{25} +(-77.9109 + 197.678i) q^{26} +(262.223 - 280.986i) q^{28} +(350.180 + 350.180i) q^{29} +237.885i q^{31} +(-908.747 + 471.968i) q^{32} +(154.443 + 355.378i) q^{34} +(-350.744 + 350.744i) q^{35} +(-560.815 + 560.815i) q^{37} +(824.957 + 325.140i) q^{38} +(1193.17 - 568.278i) q^{40} +1802.95i q^{41} +(206.090 + 206.090i) q^{43} +(1395.93 - 48.2163i) q^{44} +(1530.18 + 3521.01i) q^{46} +1599.92i q^{47} -1823.99 q^{49} +(728.526 - 316.608i) q^{50} +(849.405 - 29.3390i) q^{52} +(2234.17 - 2234.17i) q^{53} -1802.67 q^{55} +(-1448.87 - 514.000i) q^{56} +(726.358 - 1842.94i) q^{58} +(-2353.11 - 2353.11i) q^{59} +(-4443.45 - 4443.45i) q^{61} +(872.690 - 379.260i) q^{62} +(3180.25 + 2581.32i) q^{64} -1096.90 q^{65} +(-3995.40 + 3995.40i) q^{67} +(1057.49 - 1133.16i) q^{68} +(1845.91 + 727.529i) q^{70} -4929.25 q^{71} -2651.57i q^{73} +(2951.48 + 1163.27i) q^{74} +(-122.438 - 3544.76i) q^{76} +(1482.78 + 1482.78i) q^{77} -8792.34i q^{79} +(-3987.02 - 3471.18i) q^{80} +(6614.21 - 2874.45i) q^{82} +(228.231 - 228.231i) q^{83} +(-1414.48 + 1414.48i) q^{85} +(427.480 - 1084.62i) q^{86} +(-2402.41 - 5044.15i) q^{88} -10596.7i q^{89} +(902.254 + 902.254i) q^{91} +(10477.4 - 11227.1i) q^{92} +(5869.38 - 2550.75i) q^{94} +4577.63i q^{95} +11048.3 q^{97} +(2907.99 + 6691.40i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} + 92 q^{8}+O(q^{10}) $ 14 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 + 92 * q^8	$ 14 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} + 92 q^{8} - 100 q^{10} - 94 q^{11} - 2 q^{13} - 44 q^{14} - 168 q^{16} + 4 q^{17} - 706 q^{19} - 1900 q^{20} + 900 q^{22} - 1148 q^{23} + 3416 q^{26} - 3784 q^{28} - 862 q^{29} - 3208 q^{32} + 7508 q^{34} - 1340 q^{35} - 1826 q^{37} - 3568 q^{38} - 5144 q^{40} + 1694 q^{43} + 14636 q^{44} - 5316 q^{46} + 682 q^{49} - 20070 q^{50} + 20452 q^{52} + 482 q^{53} - 11780 q^{55} + 6952 q^{56} - 20456 q^{58} + 2786 q^{59} - 3778 q^{61} + 11472 q^{62} + 15808 q^{64} + 2020 q^{65} + 7998 q^{67} - 18032 q^{68} + 15296 q^{70} - 19964 q^{71} + 23780 q^{74} - 23996 q^{76} + 9508 q^{77} - 1384 q^{80} + 16016 q^{82} + 17282 q^{83} + 9948 q^{85} + 4796 q^{86} + 7288 q^{88} - 28036 q^{91} + 14632 q^{92} + 432 q^{94} - 4 q^{97} + 12246 q^{98}+O(q^{100}) $ 14 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 + 92 * q^8 - 100 * q^10 - 94 * q^11 - 2 * q^13 - 44 * q^14 - 168 * q^16 + 4 * q^17 - 706 * q^19 - 1900 * q^20 + 900 * q^22 - 1148 * q^23 + 3416 * q^26 - 3784 * q^28 - 862 * q^29 - 3208 * q^32 + 7508 * q^34 - 1340 * q^35 - 1826 * q^37 - 3568 * q^38 - 5144 * q^40 + 1694 * q^43 + 14636 * q^44 - 5316 * q^46 + 682 * q^49 - 20070 * q^50 + 20452 * q^52 + 482 * q^53 - 11780 * q^55 + 6952 * q^56 - 20456 * q^58 + 2786 * q^59 - 3778 * q^61 + 11472 * q^62 + 15808 * q^64 + 2020 * q^65 + 7998 * q^67 - 18032 * q^68 + 15296 * q^70 - 19964 * q^71 + 23780 * q^74 - 23996 * q^76 + 9508 * q^77 - 1384 * q^80 + 16016 * q^82 + 17282 * q^83 + 9948 * q^85 + 4796 * q^86 + 7288 * q^88 - 28036 * q^91 + 14632 * q^92 + 432 * q^94 - 4 * q^97 + 12246 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.59430	−	3.66854i	−0.398575	−	0.917136i
$2$	−1.59430	−	3.66854i	−0.398575	−	0.917136i
$3$		0			0
$3$		0			0
$4$	−10.9164	+	11.6975i	−0.682276	+	0.731095i
$5$	14.6016	−	14.6016i	0.584063	−	0.584063i	−0.351954	−	0.936017i	$-0.614483\pi$
$5$	14.6016	−	14.6016i	0.584063	−	0.584063i	0.936017	+	0.351954i	$0.114483\pi$
$6$		0			0
$7$	−24.0210			−0.490224			−0.245112	−	0.969495i	$-0.578825\pi$
$7$	−24.0210			−0.490224			−0.245112	+	0.969495i	$0.578825\pi$
$8$	60.3169	+	21.3980i	0.942451	+	0.334344i
$9$		0			0
$10$	−76.8459	−	30.2872i	−0.768459	−	0.302872i
$11$	−61.7287	−	61.7287i	−0.510154	−	0.510154i	0.404419	−	0.914574i	$-0.367474\pi$
$11$	−61.7287	−	61.7287i	−0.510154	−	0.510154i	−0.914574	+	0.404419i	$0.867474\pi$
$12$		0			0
$13$	−37.5611	−	37.5611i	−0.222255	−	0.222255i	0.587192	−	0.809447i	$-0.300233\pi$
$13$	−37.5611	−	37.5611i	−0.222255	−	0.222255i	−0.809447	+	0.587192i	$0.800233\pi$
$14$	38.2966	+	88.1219i	0.195391	+	0.449602i
$15$		0			0
$16$	−17.6638	−	255.390i	−0.0689991	−	0.997617i
$17$	−96.8718			−0.335197			−0.167598	−	0.985855i	$-0.553601\pi$
$17$	−96.8718			−0.335197			−0.167598	+	0.985855i	$0.553601\pi$
$18$		0			0
$19$	−156.751	+	156.751i	−0.434214	+	0.434214i	−0.890059	−	0.455845i	$-0.849337\pi$
$19$	−156.751	+	156.751i	−0.434214	+	0.434214i	0.455845	+	0.890059i	$0.349337\pi$
$20$	11.4053	+	330.199i	0.0285133	+	0.825498i
$21$		0			0
$22$	−128.040	+	324.868i	−0.264546	+	0.671216i
$23$	−959.783			−1.81433			−0.907167	−	0.420770i	$-0.861760\pi$
$23$	−959.783			−1.81433			−0.907167	+	0.420770i	$0.861760\pi$
$24$		0			0
$25$			198.587i			0.317740i
$26$	−77.9109	+	197.678i	−0.115253	+	0.292424i
$27$		0			0
$28$	262.223	−	280.986i	0.334468	−	0.358400i
$29$	350.180	+	350.180i	0.416385	+	0.416385i	0.883956	−	0.467571i	$-0.154871\pi$
$29$	350.180	+	350.180i	0.416385	+	0.416385i	−0.467571	+	0.883956i	$0.654871\pi$
$30$		0			0
$31$			237.885i			0.247539i	0.992311	+	0.123769i	$0.0394983\pi$
$31$			237.885i			0.247539i	−0.992311	+	0.123769i	$0.960502\pi$
$32$	−908.747	+	471.968i	−0.887449	+	0.460907i
$33$		0			0
$34$	154.443	+	355.378i	0.133601	+	0.307421i
$35$	−350.744	+	350.744i	−0.286322	+	0.286322i
$36$		0			0
$37$	−560.815	+	560.815i	−0.409653	+	0.409653i	−0.881617	−	0.471965i	$-0.843545\pi$
$37$	−560.815	+	560.815i	−0.409653	+	0.409653i	0.471965	+	0.881617i	$0.343545\pi$
$38$	824.957	+	325.140i	0.571300	+	0.225166i
$39$		0			0
$40$	1193.17	−	568.278i	0.745729	−	0.355173i
$41$			1802.95i			1.07255i	0.844044	+	0.536274i	$0.180169\pi$
$41$			1802.95i			1.07255i	−0.844044	+	0.536274i	$0.819831\pi$
$42$		0			0
$43$	206.090	+	206.090i	0.111460	+	0.111460i	0.760637	−	0.649177i	$-0.224887\pi$
$43$	206.090	+	206.090i	0.111460	+	0.111460i	−0.649177	+	0.760637i	$0.724887\pi$
$44$	1395.93	−	48.2163i	0.721037	−	0.0249051i
$45$		0			0
$46$	1530.18	+	3521.01i	0.723149	+	1.66399i
$47$			1599.92i			0.724274i	0.932125	+	0.362137i	$0.117953\pi$
$47$			1599.92i			0.724274i	−0.932125	+	0.362137i	$0.882047\pi$
$48$		0			0
$49$	−1823.99			−0.759681
$50$	728.526	−	316.608i	0.291410	−	0.126643i
$51$		0			0
$52$	849.405	−	29.3390i	0.314129	−	0.0108502i
$53$	2234.17	−	2234.17i	0.795360	−	0.795360i	−0.187000	−	0.982360i	$-0.559876\pi$
$53$	2234.17	−	2234.17i	0.795360	−	0.795360i	0.982360	+	0.187000i	$0.0598765\pi$
$54$		0			0
$55$	−1802.67			−0.595925
$56$	−1448.87	−	514.000i	−0.462012	−	0.163903i
$57$		0			0
$58$	726.358	−	1842.94i	0.215921	−	0.547842i
$59$	−2353.11	−	2353.11i	−0.675988	−	0.675988i	0.283102	−	0.959090i	$-0.408636\pi$
$59$	−2353.11	−	2353.11i	−0.675988	−	0.675988i	−0.959090	+	0.283102i	$0.908636\pi$
$60$		0			0
$61$	−4443.45	−	4443.45i	−1.19415	−	1.19415i	−0.975890	−	0.218264i	$-0.929961\pi$
$61$	−4443.45	−	4443.45i	−1.19415	−	1.19415i	−0.218264	−	0.975890i	$-0.570039\pi$
$62$	872.690	−	379.260i	0.227027	−	0.0986627i
$63$		0			0
$64$	3180.25	+	2581.32i	0.776429	+	0.630205i
$65$	−1096.90			−0.259622
$66$		0			0
$67$	−3995.40	+	3995.40i	−0.890042	+	0.890042i	−0.994527	−	0.104485i	$-0.966681\pi$
$67$	−3995.40	+	3995.40i	−0.890042	+	0.890042i	0.104485	+	0.994527i	$0.466681\pi$
$68$	1057.49	−	1133.16i	0.228697	−	0.245060i
$69$		0			0
$70$	1845.91	+	727.529i	0.376717	+	0.148475i
$71$	−4929.25			−0.977832			−0.488916	−	0.872331i	$-0.662608\pi$
$71$	−4929.25			−0.977832			−0.488916	+	0.872331i	$0.662608\pi$
$72$		0			0
$73$		−	2651.57i		−	0.497574i	−0.968558	−	0.248787i	$-0.919968\pi$
$73$		−	2651.57i		−	0.497574i	0.968558	−	0.248787i	$-0.0800319\pi$
$74$	2951.48	+	1163.27i	0.538984	+	0.212430i
$75$		0			0
$76$	−122.438	−	3544.76i	−0.0211978	−	0.613705i
$77$	1482.78	+	1482.78i	0.250090	+	0.250090i
$78$		0			0
$79$		−	8792.34i		−	1.40880i	−0.709801	−	0.704402i	$-0.751215\pi$
$79$		−	8792.34i		−	1.40880i	0.709801	−	0.704402i	$-0.248785\pi$
$80$	−3987.02	−	3471.18i	−0.622971	−	0.542372i
$81$		0			0
$82$	6614.21	−	2874.45i	0.983672	−	0.427491i
$83$	228.231	−	228.231i	0.0331298	−	0.0331298i	−0.690348	−	0.723478i	$-0.742542\pi$
$83$	228.231	−	228.231i	0.0331298	−	0.0331298i	0.723478	+	0.690348i	$0.242542\pi$
$84$		0			0
$85$	−1414.48	+	1414.48i	−0.195776	+	0.195776i
$86$	427.480	−	1084.62i	0.0577988	−	0.146649i
$87$		0			0
$88$	−2402.41	−	5044.15i	−0.310229	−	0.651362i
$89$		−	10596.7i		−	1.33780i	−0.743353	−	0.668899i	$-0.766766\pi$
$89$		−	10596.7i		−	1.33780i	0.743353	−	0.668899i	$-0.233234\pi$
$90$		0			0
$91$	902.254	+	902.254i	0.108955	+	0.108955i
$92$	10477.4	−	11227.1i	1.23788	−	1.32645i
$93$		0			0
$94$	5869.38	−	2550.75i	0.664258	−	0.288677i
$95$			4577.63i			0.507217i
$96$		0			0
$97$	11048.3			1.17422			0.587111	−	0.809506i	$-0.300265\pi$
$97$	11048.3			1.17422			0.587111	+	0.809506i	$0.300265\pi$
$98$	2907.99	+	6691.40i	0.302790	+	0.696730i
$99$		0			0
$100$	−2322.98	−	2167.86i	−0.232298	−	0.216786i
$101$	7543.12	−	7543.12i	0.739449	−	0.739449i	−0.233022	−	0.972471i	$-0.574861\pi$
$101$	7543.12	−	7543.12i	0.739449	−	0.739449i	0.972471	+	0.233022i	$0.0748615\pi$
$102$		0			0
$103$	−6124.81			−0.577322			−0.288661	−	0.957431i	$-0.593210\pi$
$103$	−6124.81			−0.577322			−0.288661	+	0.957431i	$0.593210\pi$
$104$	−1461.84	−	3069.30i	−0.135155	−	0.283774i
$105$		0			0
$106$	−11758.1	−	4634.20i	−1.04646	−	0.412442i
$107$	−4636.79	−	4636.79i	−0.404995	−	0.404995i	0.474994	−	0.879989i	$-0.342450\pi$
$107$	−4636.79	−	4636.79i	−0.404995	−	0.404995i	−0.879989	+	0.474994i	$0.842450\pi$
$108$		0			0
$109$	15235.6	+	15235.6i	1.28235	+	1.28235i	0.939327	+	0.343022i	$0.111451\pi$
$109$	15235.6	+	15235.6i	1.28235	+	1.28235i	0.343022	+	0.939327i	$0.388549\pi$
$110$	2874.00	+	6613.18i	0.237521	+	0.546544i
$111$		0			0
$112$	424.301	+	6134.71i	0.0338250	+	0.489055i
$113$	−2902.13			−0.227279			−0.113639	−	0.993522i	$-0.536251\pi$
$113$	−2902.13			−0.227279			−0.113639	+	0.993522i	$0.536251\pi$
$114$		0			0
$115$	−14014.4	+	14014.4i	−1.05969	+	1.05969i
$116$	−7918.94	+	273.526i	−0.588506	+	0.0203274i
$117$		0			0
$118$	−4880.93	+	12384.1i	−0.350541	+	0.889404i
$119$	2326.95			0.164321
$120$		0			0
$121$		−	7020.14i		−	0.479485i
$122$	−9216.79	+	23385.2i	−0.619241	+	1.57116i
$123$		0			0
$124$	−2782.66	−	2596.85i	−0.180974	−	0.168890i
$125$	12025.7	+	12025.7i	0.769644	+	0.769644i
$126$		0			0
$127$		−	3992.46i		−	0.247533i	−0.992311	−	0.123766i	$-0.960503\pi$
$127$		−	3992.46i		−	0.247533i	0.992311	−	0.123766i	$-0.0394974\pi$
$128$	4399.41	−	15782.3i	0.268518	−	0.963275i
$129$		0			0
$130$	1748.79	+	4024.04i	0.103479	+	0.238109i
$131$	−16640.1	+	16640.1i	−0.969645	+	0.969645i	−0.999553	−	0.0299081i	$-0.990479\pi$
$131$	−16640.1	+	16640.1i	−0.969645	+	0.969645i	0.0299081	+	0.999553i	$0.490479\pi$
$132$		0			0
$133$	3765.31	−	3765.31i	0.212862	−	0.212862i
$134$	21027.2	+	8287.43i	1.17104	+	0.461541i
$135$		0			0
$136$	−5843.01	−	2072.86i	−0.315906	−	0.112071i
$137$		−	10746.6i		−	0.572573i	−0.958144	−	0.286286i	$-0.907579\pi$
$137$		−	10746.6i		−	0.572573i	0.958144	−	0.286286i	$-0.0924209\pi$
$138$		0			0
$139$	−7583.76	−	7583.76i	−0.392514	−	0.392514i	0.483069	−	0.875582i	$-0.339522\pi$
$139$	−7583.76	−	7583.76i	−0.392514	−	0.392514i	−0.875582	+	0.483069i	$0.839522\pi$
$140$	−273.967	−	7931.70i	−0.0139779	−	0.404679i
$141$		0			0
$142$	7858.70	+	18083.2i	0.389739	+	0.896805i
$143$			4637.20i			0.226769i
$144$		0			0
$145$	10226.4			0.486390
$146$	−9727.41	+	4227.40i	−0.456343	+	0.198321i
$147$		0			0
$148$	−438.053	−	12682.2i	−0.0199988	−	0.578991i
$149$	−3385.37	+	3385.37i	−0.152487	+	0.152487i	−0.779228	−	0.626741i	$-0.784389\pi$
$149$	−3385.37	+	3385.37i	−0.152487	+	0.152487i	0.626741	+	0.779228i	$0.284389\pi$
$150$		0			0
$151$	21697.8			0.951617			0.475809	−	0.879549i	$-0.342155\pi$
$151$	21697.8			0.951617			0.475809	+	0.879549i	$0.342155\pi$
$152$	−12808.9	+	6100.58i	−0.554402	+	0.264049i
$153$		0			0
$154$	3075.65	−	7803.65i	0.129687	−	0.329046i
$155$	3473.49	+	3473.49i	0.144578	+	0.144578i
$156$		0			0
$157$	14212.7	+	14212.7i	0.576603	+	0.576603i	0.933966	−	0.357363i	$-0.116324\pi$
$157$	14212.7	+	14212.7i	0.576603	+	0.576603i	−0.357363	+	0.933966i	$0.616324\pi$
$158$	−32255.1	+	14017.6i	−1.29206	+	0.561514i
$159$		0			0
$160$	−6377.67	+	20160.6i	−0.249128	+	0.787525i
$161$	23054.9			0.889430
$162$		0			0
$163$	−7450.28	+	7450.28i	−0.280412	+	0.280412i	−0.833273	−	0.552861i	$-0.813536\pi$
$163$	−7450.28	+	7450.28i	−0.280412	+	0.280412i	0.552861	+	0.833273i	$0.313536\pi$
$164$	−21090.1	−	19681.8i	−0.784134	−	0.731773i
$165$		0			0
$166$	−1201.14	−	473.407i	−0.0435892	−	0.0171798i
$167$	3997.25			0.143327			0.0716635	−	0.997429i	$-0.477169\pi$
$167$	3997.25			0.143327			0.0716635	+	0.997429i	$0.477169\pi$
$168$		0			0
$169$		−	25739.3i		−	0.901205i
$170$	7444.20	+	2933.98i	0.257585	+	0.101522i
$171$		0			0
$172$	−4660.50	+	160.977i	−0.157534	+	0.00544134i
$173$	16996.8	+	16996.8i	0.567903	+	0.567903i	0.931540	−	0.363638i	$-0.118465\pi$
$173$	16996.8	+	16996.8i	0.567903	+	0.567903i	−0.363638	+	0.931540i	$0.618465\pi$
$174$		0			0
$175$		−	4770.26i		−	0.155764i
$176$	−14674.5	+	16855.2i	−0.473738	+	0.544139i
$177$		0			0
$178$	−38874.4	+	16894.3i	−1.22694	+	0.533213i
$179$	−24121.3	+	24121.3i	−0.752826	+	0.752826i	−0.975006	−	0.222180i	$-0.928683\pi$
$179$	−24121.3	+	24121.3i	−0.752826	+	0.752826i	0.222180	+	0.975006i	$0.428683\pi$
$180$		0			0
$181$	13837.8	−	13837.8i	0.422386	−	0.422386i	−0.463638	−	0.886025i	$-0.653456\pi$
$181$	13837.8	−	13837.8i	0.422386	−	0.422386i	0.886025	+	0.463638i	$0.153456\pi$
$182$	1871.50	−	4748.42i	0.0564997	−	0.143353i
$183$		0			0
$184$	−57891.1	−	20537.4i	−1.70992	−	0.606611i
$185$			16377.6i			0.478526i
$186$		0			0
$187$	5979.77	+	5979.77i	0.171002	+	0.171002i
$188$	−18715.1	−	17465.4i	−0.529513	−	0.494155i
$189$		0			0
$190$	16793.2	−	7298.12i	0.465187	−	0.202164i
$191$		−	11717.4i		−	0.321193i	−0.987020	−	0.160596i	$-0.948658\pi$
$191$		−	11717.4i		−	0.321193i	0.987020	−	0.160596i	$-0.0513417\pi$
$192$		0			0
$193$	−68633.2			−1.84255			−0.921276	−	0.388910i	$-0.872852\pi$
$193$	−68633.2			−1.84255			−0.921276	+	0.388910i	$0.872852\pi$
$194$	−17614.2	−	40531.0i	−0.468016	−	1.07692i
$195$		0			0
$196$	19911.5	−	21336.2i	0.518312	−	0.555399i
$197$	22885.3	−	22885.3i	0.589689	−	0.589689i	−0.347858	−	0.937547i	$-0.613091\pi$
$197$	22885.3	−	22885.3i	0.589689	−	0.589689i	0.937547	+	0.347858i	$0.113091\pi$
$198$		0			0
$199$	59936.9			1.51352			0.756761	−	0.653692i	$-0.226781\pi$
$199$	59936.9			1.51352			0.756761	+	0.653692i	$0.226781\pi$
$200$	−4249.37	+	11978.2i	−0.106234	+	0.299454i
$201$		0			0
$202$	−39698.3	−	15646.3i	−0.972901	−	0.383449i
$203$	−8411.65	−	8411.65i	−0.204122	−	0.204122i
$204$		0			0
$205$	26326.0	+	26326.0i	0.626436	+	0.626436i
$206$	9764.78	+	22469.1i	0.230106	+	0.529483i
$207$		0			0
$208$	−8929.26	+	10256.2i	−0.206390	+	0.237061i
$209$	19352.1			0.443032
$210$		0			0
$211$	−12558.8	+	12558.8i	−0.282086	+	0.282086i	−0.833941	−	0.551854i	$-0.813920\pi$
$211$	−12558.8	+	12558.8i	−0.282086	+	0.282086i	0.551854	+	0.833941i	$0.313920\pi$
$212$	1745.11	+	50523.3i	0.0388285	+	1.12414i
$213$		0			0
$214$	−9617.83	+	24402.7i	−0.210015	+	0.532856i
$215$	6018.47			0.130199
$216$		0			0
$217$		−	5714.22i		−	0.121349i
$218$	31602.3	−	80182.5i	0.664976	−	1.68720i
$219$		0			0
$220$	19678.7	−	21086.8i	0.406585	−	0.435678i
$221$	3638.61	+	3638.61i	0.0744992	+	0.0744992i
$222$		0			0
$223$			22761.5i			0.457711i	0.973460	+	0.228856i	$0.0734983\pi$
$223$			22761.5i			0.457711i	−0.973460	+	0.228856i	$0.926502\pi$
$224$	21829.0	−	11337.1i	0.435048	−	0.225947i
$225$		0			0
$226$	4626.86	+	10646.6i	0.0905877	+	0.208446i
$227$	−6480.30	+	6480.30i	−0.125760	+	0.125760i	−0.767186	−	0.641425i	$-0.778343\pi$
$227$	−6480.30	+	6480.30i	−0.125760	+	0.125760i	0.641425	+	0.767186i	$0.278343\pi$
$228$		0			0
$229$	36068.6	−	36068.6i	0.687795	−	0.687795i	−0.273949	−	0.961744i	$-0.588330\pi$
$229$	36068.6	−	36068.6i	0.687795	−	0.687795i	0.961744	+	0.273949i	$0.0883301\pi$
$230$	73755.4	+	29069.2i	1.39424	+	0.549512i
$231$		0			0
$232$	13628.6	+	28614.9i	0.253207	+	0.531638i
$233$		−	68226.4i		−	1.25673i	−0.777920	−	0.628363i	$-0.783725\pi$
$233$		−	68226.4i		−	1.25673i	0.777920	−	0.628363i	$-0.216275\pi$
$234$		0			0
$235$	23361.4	+	23361.4i	0.423022	+	0.423022i
$236$	53213.1	−	1838.02i	0.955421	−	0.0330009i
$237$		0			0
$238$	−3709.86	−	8536.53i	−0.0654944	−	0.150705i
$239$		−	100556.i		−	1.76040i	−0.474599	−	0.880202i	$-0.657407\pi$
$239$		−	100556.i		−	1.76040i	0.474599	−	0.880202i	$-0.342593\pi$
$240$		0			0
$241$	−35563.1			−0.612302			−0.306151	−	0.951983i	$-0.599041\pi$
$241$	−35563.1			−0.612302			−0.306151	+	0.951983i	$0.599041\pi$
$242$	−25753.7	+	11192.2i	−0.439753	+	0.191111i
$243$		0			0
$244$	100484.	−	3470.78i	1.68778	−	0.0582972i
$245$	−26633.2	+	26633.2i	−0.443702	+	0.443702i
$246$		0			0
$247$	11775.5			0.193013
$248$	−5090.25	+	14348.5i	−0.0827630	+	0.233293i
$249$		0			0
$250$	24944.2	−	63289.3i	0.399107	−	1.01263i
$251$	29206.3	+	29206.3i	0.463585	+	0.463585i	0.899829	−	0.436244i	$-0.143691\pi$
$251$	29206.3	+	29206.3i	0.463585	+	0.463585i	−0.436244	+	0.899829i	$0.643691\pi$
$252$		0			0
$253$	59246.1	+	59246.1i	0.925591	+	0.925591i
$254$	−14646.5	+	6365.18i	−0.227021	+	0.0986604i
$255$		0			0
$256$	−64912.0	+	9022.29i	−0.990478	+	0.137669i
$257$	−2932.77			−0.0444029			−0.0222015	−	0.999754i	$-0.507068\pi$
$257$	−2932.77			−0.0444029			−0.0222015	+	0.999754i	$0.507068\pi$
$258$		0			0
$259$	13471.3	−	13471.3i	0.200821	−	0.200821i
$260$	11974.3	−	12831.1i	0.177134	−	0.189808i
$261$		0			0
$262$	87574.1	+	34515.5i	1.27577	+	0.502820i
$263$	−23253.5			−0.336184			−0.168092	−	0.985771i	$-0.553761\pi$
$263$	−23253.5			−0.336184			−0.168092	+	0.985771i	$0.553761\pi$
$264$		0			0
$265$		−	65244.7i		−	0.929081i
$266$	−19816.3	−	7810.18i	−0.280065	−	0.110382i
$267$		0			0
$268$	−3120.81	−	90351.7i	−0.0434508	−	1.25796i
$269$	−56836.3	−	56836.3i	−0.785455	−	0.785455i	0.195290	−	0.980745i	$-0.437435\pi$
$269$	−56836.3	−	56836.3i	−0.785455	−	0.785455i	−0.980745	+	0.195290i	$0.937435\pi$
$270$		0			0
$271$		−	91679.6i		−	1.24834i	−0.781287	−	0.624172i	$-0.785436\pi$
$271$		−	91679.6i		−	1.24834i	0.781287	−	0.624172i	$-0.214564\pi$
$272$	1711.12	+	24740.1i	0.0231283	+	0.334398i
$273$		0			0
$274$	−39424.4	+	17133.3i	−0.525127	+	0.228213i
$275$	12258.5	−	12258.5i	0.162096	−	0.162096i
$276$		0			0
$277$	−75831.0	+	75831.0i	−0.988297	+	0.988297i	−0.999932	−	0.0116353i	$-0.996296\pi$
$277$	−75831.0	+	75831.0i	−0.988297	+	0.988297i	0.0116353	+	0.999932i	$0.496296\pi$
$278$	−15730.6	+	39912.1i	−0.203542	+	0.516435i
$279$		0			0
$280$	−28661.0	+	13650.6i	−0.365574	+	0.174114i
$281$			77682.2i			0.983805i	0.870650	+	0.491903i	$0.163698\pi$
$281$			77682.2i			0.983805i	−0.870650	+	0.491903i	$0.836302\pi$
$282$		0			0
$283$	−43834.7	−	43834.7i	−0.547325	−	0.547325i	0.378341	−	0.925666i	$-0.376495\pi$
$283$	−43834.7	−	43834.7i	−0.547325	−	0.547325i	−0.925666	+	0.378341i	$0.876495\pi$
$284$	53809.7	−	57660.0i	0.667151	−	0.714888i
$285$		0			0
$286$	17011.8	−	7393.08i	0.207978	−	0.0903844i
$287$		−	43308.7i		−	0.525788i
$288$		0			0
$289$	−74136.9			−0.887643
$290$	−16303.9	−	37515.8i	−0.193863	−	0.446086i
$291$		0			0
$292$	31016.8	+	28945.7i	0.363774	+	0.339483i
$293$	−61916.9	+	61916.9i	−0.721231	+	0.721231i	−0.968856	−	0.247625i	$-0.920350\pi$
$293$	−61916.9	+	61916.9i	−0.721231	+	0.721231i	0.247625	+	0.968856i	$0.420350\pi$
$294$		0			0
$295$	−68718.4			−0.789639
$296$	−45826.9	+	21826.3i	−0.523042	+	0.249113i
$297$		0			0
$298$	17816.7	+	7022.09i	0.200629	+	0.0790740i
$299$	36050.5	+	36050.5i	0.403245	+	0.403245i
$300$		0			0
$301$	−4950.47	−	4950.47i	−0.0546404	−	0.0546404i
$302$	−34592.8	−	79599.4i	−0.379291	−	0.872762i
$303$		0			0
$304$	42801.5	+	37263.9i	0.463139	+	0.403219i
$305$	−129763.			−1.39492
$306$		0			0
$307$	−99698.5	+	99698.5i	−1.05782	+	1.05782i	−0.0595972	+	0.998223i	$0.518982\pi$
$307$	−99698.5	+	99698.5i	−1.05782	+	1.05782i	−0.998223	+	0.0595972i	$0.981018\pi$
$308$	−33531.5	+	1158.20i	−0.353470	+	0.0122091i
$309$		0			0
$310$	7204.87	−	18280.5i	0.0749726	−	0.190223i
$311$	127678.			1.32006			0.660031	−	0.751238i	$-0.270543\pi$
$311$	127678.			1.32006			0.660031	+	0.751238i	$0.270543\pi$
$312$		0			0
$313$		−	24132.5i		−	0.246328i	−0.992386	−	0.123164i	$-0.960696\pi$
$313$		−	24132.5i		−	0.246328i	0.992386	−	0.123164i	$-0.0393042\pi$
$314$	29480.6	−	74799.2i	0.299004	−	0.758643i
$315$		0			0
$316$	102849.	+	95980.9i	1.02997	+	0.961193i
$317$	63739.0	+	63739.0i	0.634289	+	0.634289i	0.949141	−	0.314852i	$-0.101955\pi$
$317$	63739.0	+	63739.0i	0.634289	+	0.634289i	−0.314852	+	0.949141i	$0.601955\pi$
$318$		0			0
$319$		−	43232.3i		−	0.424841i
$320$	84128.1	−	8745.36i	0.821563	−	0.0854039i
$321$		0			0
$322$	−36756.5	−	84578.0i	−0.354505	−	0.815728i
$323$	15184.8	−	15184.8i	0.145547	−	0.145547i
$324$		0			0
$325$	7459.16	−	7459.16i	0.0706193	−	0.0706193i
$326$	39209.6	+	15453.7i	0.368942	+	0.145411i
$327$		0			0
$328$	−38579.6	+	108748.i	−0.358599	+	1.01082i
$329$		−	38431.6i		−	0.355056i
$330$		0			0
$331$	−111266.	−	111266.i	−1.01556	−	1.01556i	−0.999877	−	0.0156868i	$-0.995007\pi$
$331$	−111266.	−	111266.i	−1.01556	−	1.01556i	−0.0156868	−	0.999877i	$-0.504993\pi$
$332$	178.271	+	5161.20i	0.00161736	+	0.0468247i
$333$		0			0
$334$	−6372.81	−	14664.1i	−0.0571266	−	0.131450i
$335$			116678.i			1.03968i
$336$		0			0
$337$	−89183.5			−0.785280			−0.392640	−	0.919692i	$-0.628438\pi$
$337$	−89183.5			−0.785280			−0.392640	+	0.919692i	$0.628438\pi$
$338$	−94425.8	+	41036.2i	−0.826528	+	0.359198i
$339$		0			0
$340$	−1104.85	−	31987.0i	−0.00955755	−	0.276704i
$341$	14684.3	−	14684.3i	0.126283	−	0.126283i
$342$		0			0
$343$	101488.			0.862637
$344$	8020.78	+	16840.6i	0.0677797	+	0.142312i
$345$		0			0
$346$	35255.4	−	89451.3i	0.294492	−	0.747196i
$347$	17075.7	+	17075.7i	0.141814	+	0.141814i	0.774450	−	0.632635i	$-0.218027\pi$
$347$	17075.7	+	17075.7i	0.141814	+	0.141814i	−0.632635	+	0.774450i	$0.718027\pi$
$348$		0			0
$349$	−25961.7	−	25961.7i	−0.213149	−	0.213149i	0.592455	−	0.805604i	$-0.298159\pi$
$349$	−25961.7	−	25961.7i	−0.213149	−	0.213149i	−0.805604	+	0.592455i	$0.798159\pi$
$350$	−17499.9	+	7605.22i	−0.142856	+	0.0620835i
$351$		0			0
$352$	85229.8	+	26961.8i	0.687869	+	0.217602i
$353$	−221897.			−1.78075			−0.890374	−	0.455230i	$-0.849557\pi$
$353$	−221897.			−1.78075			−0.890374	+	0.455230i	$0.849557\pi$
$354$		0			0
$355$	−71974.9	+	71974.9i	−0.571116	+	0.571116i
$356$	123955.	+	115678.i	0.978057	+	0.912747i
$357$		0			0
$358$	126947.	+	50033.4i	0.990501	+	0.390386i
$359$	106831.			0.828908			0.414454	−	0.910070i	$-0.363973\pi$
$359$	106831.			0.828908			0.414454	+	0.910070i	$0.363973\pi$
$360$		0			0
$361$			81179.1i			0.622917i
$362$	−72826.1	−	28702.9i	−0.555738	−	0.219033i
$363$		0			0
$364$	−20403.5	+	704.752i	−0.153993	+	0.00531904i
$365$	−38717.2	−	38717.2i	−0.290615	−	0.290615i
$366$		0			0
$367$		−	79074.9i		−	0.587093i	−0.955945	−	0.293546i	$-0.905164\pi$
$367$		−	79074.9i		−	0.587093i	0.955945	−	0.293546i	$-0.0948355\pi$
$368$	16953.4	+	245119.i	0.125187	+	1.81001i
$369$		0			0
$370$	60081.8	−	26110.7i	0.438874	−	0.190729i
$371$	−53666.8	+	53666.8i	−0.389904	+	0.389904i
$372$		0			0
$373$	−86341.4	+	86341.4i	−0.620585	+	0.620585i	−0.945681	−	0.325096i	$-0.894603\pi$
$373$	−86341.4	+	86341.4i	−0.620585	+	0.620585i	0.325096	+	0.945681i	$0.394603\pi$
$374$	12403.5	−	31470.6i	0.0886749	−	0.224989i
$375$		0			0
$376$	−34235.1	+	96502.3i	−0.242156	+	0.682593i
$377$		−	26306.3i		−	0.185087i
$378$		0			0
$379$	168223.	+	168223.i	1.17114	+	1.17114i	0.981939	+	0.189199i	$0.0605890\pi$
$379$	168223.	+	168223.i	1.17114	+	1.17114i	0.189199	+	0.981939i	$0.439411\pi$
$380$	−53546.9	−	49971.3i	−0.370824	−	0.346062i
$381$		0			0
$382$	−42985.9	+	18681.1i	−0.294577	+	0.128019i
$383$			22177.8i			0.151189i	0.997139	+	0.0755946i	$0.0240855\pi$
$383$			22177.8i			0.151189i	−0.997139	+	0.0755946i	$0.975915\pi$
$384$		0			0
$385$	43301.9			0.292137
$386$	109422.	+	251784.i	0.734395	+	1.68987i
$387$		0			0
$388$	−120607.	+	129237.i	−0.801144	+	0.858468i
$389$	−163109.	+	163109.i	−1.07790	+	1.07790i	−0.0812004	+	0.996698i	$0.525875\pi$
$389$	−163109.	+	163109.i	−1.07790	+	1.07790i	−0.996698	+	0.0812004i	$0.974125\pi$
$390$		0			0
$391$	92975.9			0.608159
$392$	−110018.	−	39029.8i	−0.715962	−	0.253994i
$393$		0			0
$394$	−120442.	−	47469.6i	−0.775861	−	0.305790i
$395$	−128382.	−	128382.i	−0.822831	−	0.822831i
$396$		0			0
$397$	110463.	+	110463.i	0.700868	+	0.700868i	0.964597	−	0.263729i	$-0.0849525\pi$
$397$	110463.	+	110463.i	0.700868	+	0.700868i	−0.263729	+	0.964597i	$0.584953\pi$
$398$	−95557.5	−	219881.i	−0.603252	−	1.38810i
$399$		0			0
$400$	50717.2	−	3507.80i	0.316982	−	0.0219237i
$401$	−43913.8			−0.273094			−0.136547	−	0.990634i	$-0.543601\pi$
$401$	−43913.8			−0.273094			−0.136547	+	0.990634i	$0.543601\pi$
$402$		0			0
$403$	8935.22	−	8935.22i	0.0550168	−	0.0550168i
$404$	5891.94	+	170580.i	0.0360990	+	1.04512i
$405$		0			0
$406$	−17447.8	+	44269.2i	−0.105850	+	0.268565i
$407$	69236.7			0.417972
$408$		0			0
$409$		−	188666.i		−	1.12784i	−0.825830	−	0.563919i	$-0.809293\pi$
$409$		−	188666.i		−	1.12784i	0.825830	−	0.563919i	$-0.190707\pi$
$410$	54606.5	−	138549.i	0.324845	−	0.824208i
$411$		0			0
$412$	66861.0	−	71645.0i	0.393893	−	0.422077i
$413$	56524.0	+	56524.0i	0.331385	+	0.331385i
$414$		0			0
$415$		−	6665.07i		−	0.0386998i
$416$	51861.2	+	16405.9i	0.299679	+	0.0948012i
$417$		0			0
$418$	−30853.0	−	70994.0i	−0.176582	−	0.406321i
$419$	88556.3	−	88556.3i	0.504419	−	0.504419i	−0.408389	−	0.912808i	$-0.633909\pi$
$419$	88556.3	−	88556.3i	0.504419	−	0.504419i	0.912808	+	0.408389i	$0.133909\pi$
$420$		0			0
$421$	−42983.4	+	42983.4i	−0.242514	+	0.242514i	−0.817889	−	0.575375i	$-0.804856\pi$
$421$	−42983.4	+	42983.4i	−0.242514	+	0.242514i	0.575375	+	0.817889i	$0.304856\pi$
$422$	66094.8	+	26049.9i	0.371144	+	0.146279i
$423$		0			0
$424$	182565.	−	86951.2i	1.01551	−	0.483664i
$425$		−	19237.5i		−	0.106505i
$426$		0			0
$427$	106736.	+	106736.i	0.585403	+	0.585403i
$428$	104856.	−	3621.80i	0.572408	−	0.0197714i
$429$		0			0
$430$	−9595.25	−	22079.0i	−0.0518942	−	0.119411i
$431$		−	163696.i		−	0.881219i	−0.897699	−	0.440609i	$-0.854762\pi$
$431$		−	163696.i		−	0.881219i	0.897699	−	0.440609i	$-0.145238\pi$
$432$		0			0
$433$	49710.2			0.265137			0.132568	−	0.991174i	$-0.457678\pi$
$433$	49710.2			0.265137			0.132568	+	0.991174i	$0.457678\pi$
$434$	−20962.9	+	9110.18i	−0.111294	+	0.0483668i
$435$		0			0
$436$	−344537.	+	11900.5i	−1.81244	+	0.0626028i
$437$	150447.	−	150447.i	0.787809	−	0.787809i
$438$		0			0
$439$	182166.			0.945233			0.472617	−	0.881268i	$-0.343310\pi$
$439$	182166.			0.945233			0.472617	+	0.881268i	$0.343310\pi$
$440$	−108732.	−	38573.6i	−0.561630	−	0.199244i
$441$		0			0
$442$	7547.37	−	19149.5i	0.0386324	−	0.0980194i
$443$	3141.28	+	3141.28i	0.0160066	+	0.0160066i	0.715065	−	0.699058i	$-0.246397\pi$
$443$	3141.28	+	3141.28i	0.0160066	+	0.0160066i	−0.699058	+	0.715065i	$0.746397\pi$
$444$		0			0
$445$	−154729.	−	154729.i	−0.781359	−	0.781359i
$446$	83501.6	−	36288.7i	0.419783	−	0.182432i
$447$		0			0
$448$	−76392.7	−	62005.8i	−0.380624	−	0.308941i
$449$	108328.			0.537341			0.268670	−	0.963232i	$-0.413416\pi$
$449$	108328.			0.537341			0.268670	+	0.963232i	$0.413416\pi$
$450$		0			0
$451$	111294.	−	111294.i	0.547165	−	0.547165i
$452$	31680.8	−	33947.7i	0.155067	−	0.166162i
$453$		0			0
$454$	34104.8	+	13441.7i	0.165464	+	0.0652143i
$455$	26348.7			0.127273
$456$		0			0
$457$			220908.i			1.05774i	0.848703	+	0.528870i	$0.177384\pi$
$457$			220908.i			1.05774i	−0.848703	+	0.528870i	$0.822616\pi$
$458$	−189824.	−	74815.1i	−0.904939	−	0.356663i
$459$		0			0
$460$	−10946.6	−	316920.i	−0.0517326	−	1.49773i
$461$	137539.	+	137539.i	0.647176	+	0.647176i	0.952310	−	0.305133i	$-0.0987010\pi$
$461$	137539.	+	137539.i	0.647176	+	0.647176i	−0.305133	+	0.952310i	$0.598701\pi$
$462$		0			0
$463$		−	53332.6i		−	0.248789i	−0.992233	−	0.124394i	$-0.960301\pi$
$463$		−	53332.6i		−	0.248789i	0.992233	−	0.124394i	$-0.0396988\pi$
$464$	83246.8	−	95617.8i	0.386662	−	0.444123i
$465$		0			0
$466$	−250291.	+	108773.i	−1.15259	+	0.500899i
$467$	207164.	−	207164.i	0.949908	−	0.949908i	−0.0488961	−	0.998804i	$-0.515570\pi$
$467$	207164.	−	207164.i	0.949908	−	0.949908i	0.998804	+	0.0488961i	$0.0155703\pi$
$468$		0			0
$469$	95973.3	−	95973.3i	0.436320	−	0.436320i
$470$	48457.2	−	122947.i	0.219363	−	0.556575i
$471$		0			0
$472$	−91580.5	−	192284.i	−0.411073	−	0.863097i
$473$		−	25443.3i		−	0.113724i
$474$		0			0
$475$	−31128.8	−	31128.8i	−0.137967	−	0.137967i
$476$	−25402.0	+	27219.6i	−0.112113	+	0.120134i
$477$		0			0
$478$	−368894.	+	160316.i	−1.61453	+	0.701653i
$479$			269434.i			1.17430i	0.809477	+	0.587152i	$0.199751\pi$
$479$			269434.i			1.17430i	−0.809477	+	0.587152i	$0.800249\pi$
$480$		0			0
$481$	42129.6			0.182095
$482$	56698.2	+	130465.i	0.244048	+	0.561564i
$483$		0			0
$484$	82118.2	+	76634.8i	0.350549	+	0.327141i
$485$	161322.	−	161322.i	0.685821	−	0.685821i
$486$		0			0
$487$	−114893.			−0.484436			−0.242218	−	0.970222i	$-0.577875\pi$
$487$	−114893.			−0.484436			−0.242218	+	0.970222i	$0.577875\pi$
$488$	−172934.	−	363096.i	−0.726174	−	1.52469i
$489$		0			0
$490$	140166.	+	55243.7i	0.583783	+	0.230086i
$491$	−83485.8	−	83485.8i	−0.346298	−	0.346298i	0.512431	−	0.858728i	$-0.328745\pi$
$491$	−83485.8	−	83485.8i	−0.346298	−	0.346298i	−0.858728	+	0.512431i	$0.828745\pi$
$492$		0			0
$493$	−33922.5	−	33922.5i	−0.139571	−	0.139571i
$494$	−18773.7	−	43198.9i	−0.0769300	−	0.177019i
$495$		0			0
$496$	60753.3	−	4201.94i	0.246949	−	0.0170799i
$497$	118405.			0.479356
$498$		0			0
$499$	−8291.04	+	8291.04i	−0.0332972	+	0.0332972i	−0.723559	−	0.690262i	$-0.757495\pi$
$499$	−8291.04	+	8291.04i	−0.0332972	+	0.0332972i	0.690262	+	0.723559i	$0.257495\pi$
$500$	−271948.	+	9393.27i	−1.08779	+	0.0375731i
$501$		0			0
$502$	60581.0	−	153708.i	0.240397	−	0.609944i
$503$	−302384.			−1.19515			−0.597575	−	0.801813i	$-0.703869\pi$
$503$	−302384.			−1.19515			−0.597575	+	0.801813i	$0.703869\pi$
$504$		0			0
$505$		−	220283.i		−	0.863770i
$506$	122891.	−	311803.i	0.479975	−	1.21781i
$507$		0			0
$508$	46701.8	+	43583.3i	0.180970	+	0.168886i
$509$	41954.6	+	41954.6i	0.161936	+	0.161936i	0.783424	−	0.621488i	$-0.213471\pi$
$509$	41954.6	+	41954.6i	0.161936	+	0.161936i	−0.621488	+	0.783424i	$0.713471\pi$
$510$		0			0
$511$			63693.3i			0.243923i
$512$	136588.	+	223748.i	0.521041	+	0.853532i
$513$		0			0
$514$	4675.71	+	10759.0i	0.0176979	+	0.0407235i
$515$	−89431.9	+	89431.9i	−0.337193	+	0.337193i
$516$		0			0
$517$	98761.0	−	98761.0i	0.369492	−	0.369492i
$518$	−70897.4	−	27942.8i	−0.264223	−	0.104138i
$519$		0			0
$520$	−66161.8	−	23471.5i	−0.244681	−	0.0868030i
$521$		−	16852.7i		−	0.0620860i	−0.999518	−	0.0310430i	$-0.990117\pi$
$521$		−	16852.7i		−	0.0620860i	0.999518	−	0.0310430i	$-0.00988289\pi$
$522$		0			0
$523$	−92911.9	−	92911.9i	−0.339678	−	0.339678i	0.516568	−	0.856246i	$-0.327209\pi$
$523$	−92911.9	−	92911.9i	−0.339678	−	0.339678i	−0.856246	+	0.516568i	$0.827209\pi$
$524$	−12997.6	−	376297.i	−0.0473369	−	1.37047i
$525$		0			0
$526$	37073.1	+	85306.6i	0.133995	+	0.308327i
$527$		−	23044.3i		−	0.0829741i
$528$		0			0
$529$	641343.			2.29181
$530$	−239353.	+	104020.i	−0.852094	+	0.370309i
$531$		0			0
$532$	2941.09	+	85148.6i	0.0103917	+	0.300853i
$533$	67720.9	−	67720.9i	0.238379	−	0.238379i
$534$		0			0
$535$	−135409.			−0.473086
$536$	−326483.	+	155496.i	−1.13640	+	0.541241i
$537$		0			0
$538$	−117892.	+	299121.i	−0.407306	+	1.03343i
$539$	112593.	+	112593.i	0.387554	+	0.387554i
$540$		0			0
$541$	−40690.8	−	40690.8i	−0.139028	−	0.139028i	0.634168	−	0.773196i	$-0.281343\pi$
$541$	−40690.8	−	40690.8i	−0.139028	−	0.139028i	−0.773196	+	0.634168i	$0.781343\pi$
$542$	−336331.	+	146165.i	−1.14490	+	0.497559i
$543$		0			0
$544$	88032.0	−	45720.4i	0.297470	−	0.154494i
$545$	444928.			1.49795
$546$		0			0
$547$	222264.	−	222264.i	0.742839	−	0.742839i	−0.230284	−	0.973123i	$-0.573966\pi$
$547$	222264.	−	222264.i	0.742839	−	0.742839i	0.973123	+	0.230284i	$0.0739656\pi$
$548$	125709.	+	117315.i	0.418605	+	0.390653i
$549$		0			0
$550$	−64514.7	−	25427.2i	−0.213272	−	0.0840568i
$551$	−109782.			−0.361600
$552$		0			0
$553$			211201.i			0.690629i
$554$	399087.	+	157292.i	1.30031	+	0.512492i
$555$		0			0
$556$	171499.	−	5923.68i	0.554768	−	0.0191621i
$557$	−223795.	−	223795.i	−0.721341	−	0.721341i	0.247537	−	0.968878i	$-0.420379\pi$
$557$	−223795.	−	223795.i	−0.721341	−	0.721341i	−0.968878	+	0.247537i	$0.920379\pi$
$558$		0			0
$559$		−	15481.9i		−	0.0495451i
$560$	95772.0	+	83381.1i	0.305395	+	0.265883i
$561$		0			0
$562$	284981.	−	123849.i	0.902283	−	0.392120i
$563$	−201474.	+	201474.i	−0.635626	+	0.635626i	−0.949474	−	0.313847i	$-0.898382\pi$
$563$	−201474.	+	201474.i	−0.635626	+	0.635626i	0.313847	+	0.949474i	$0.398382\pi$
$564$		0			0
$565$	−42375.6	+	42375.6i	−0.132745	+	0.132745i
$566$	−90923.9	+	230695.i	−0.283821	+	0.720121i
$567$		0			0
$568$	−297317.	−	105476.i	−0.921559	−	0.326932i
$569$			473995.i			1.46403i	0.681289	+	0.732014i	$0.261420\pi$
$569$			473995.i			1.46403i	−0.681289	+	0.732014i	$0.738580\pi$
$570$		0			0
$571$	303262.	+	303262.i	0.930133	+	0.930133i	0.997714	−	0.0675806i	$-0.0215280\pi$
$571$	303262.	+	303262.i	0.930133	+	0.930133i	−0.0675806	+	0.997714i	$0.521528\pi$
$572$	−54243.7	−	50621.6i	−0.165790	−	0.154719i
$573$		0			0
$574$	−158880.	+	69047.0i	−0.482219	+	0.209566i
$575$		−	190601.i		−	0.576486i
$576$		0			0
$577$	−340809.			−1.02367			−0.511834	−	0.859084i	$-0.671034\pi$
$577$	−340809.			−1.02367			−0.511834	+	0.859084i	$0.671034\pi$
$578$	118196.	+	271974.i	0.353792	+	0.814089i
$579$		0			0
$580$	−111635.	+	119623.i	−0.331852	+	0.355597i
$581$	−5482.33	+	5482.33i	−0.0162410	+	0.0162410i
$582$		0			0
$583$	−275824.			−0.811512
$584$	56738.3	−	159935.i	0.166361	−	0.468939i
$585$		0			0
$586$	325859.	+	128431.i	0.948931	+	0.374002i
$587$	253433.	+	253433.i	0.735507	+	0.735507i	0.971705	−	0.236198i	$-0.0759014\pi$
$587$	253433.	+	253433.i	0.735507	+	0.735507i	−0.236198	+	0.971705i	$0.575901\pi$
$588$		0			0
$589$	−37288.7	−	37288.7i	−0.107485	−	0.107485i
$590$	109558.	+	252096.i	0.314730	+	0.724206i
$591$		0			0
$592$	153132.	+	133320.i	0.436942	+	0.380411i
$593$	−117236.			−0.333390			−0.166695	−	0.986009i	$-0.553309\pi$
$593$	−117236.			−0.333390			−0.166695	+	0.986009i	$0.553309\pi$
$594$		0			0
$595$	33977.2	−	33977.2i	0.0959741	−	0.0959741i
$596$	−2644.32	−	76556.6i	−0.00744425	−	0.215521i
$597$		0			0
$598$	74777.6	−	189728.i	0.209107	−	0.530554i
$599$	−277087.			−0.772257			−0.386129	−	0.922445i	$-0.626188\pi$
$599$	−277087.			−0.772257			−0.386129	+	0.922445i	$0.626188\pi$
$600$		0			0
$601$			323876.i			0.896665i	0.893867	+	0.448333i	$0.147982\pi$
$601$			323876.i			0.896665i	−0.893867	+	0.448333i	$0.852018\pi$
$602$	−10268.5	+	26053.5i	−0.0283343	+	0.0718909i
$603$		0			0
$604$	−236863.	+	253811.i	−0.649266	+	0.695723i
$605$	−102505.	−	102505.i	−0.280050	−	0.280050i
$606$		0			0
$607$			715467.i			1.94184i	0.239414	+	0.970918i	$0.423045\pi$
$607$			715467.i			1.94184i	−0.239414	+	0.970918i	$0.576955\pi$
$608$	68465.6	−	216429.i	0.185210	−	0.585475i
$609$		0			0
$610$	206881.	+	476040.i	0.555982	+	1.27933i
$611$	60094.8	−	60094.8i	0.160974	−	0.160974i
$612$		0			0
$613$	137200.	−	137200.i	0.365117	−	0.365117i	−0.500576	−	0.865693i	$-0.666878\pi$
$613$	137200.	−	137200.i	0.365117	−	0.365117i	0.865693	+	0.500576i	$0.166878\pi$
$614$	524697.	+	206799.i	1.39178	+	0.548544i
$615$		0			0
$616$	57708.2	+	121165.i	0.152082	+	0.319313i
$617$		−	106650.i		−	0.280149i	−0.990141	−	0.140074i	$-0.955266\pi$
$617$		−	106650.i		−	0.280149i	0.990141	−	0.140074i	$-0.0447342\pi$
$618$		0			0
$619$	−373667.	−	373667.i	−0.975221	−	0.975221i	0.0244790	−	0.999700i	$-0.492207\pi$
$619$	−373667.	−	373667.i	−0.975221	−	0.975221i	−0.999700	+	0.0244790i	$0.992207\pi$
$620$	−78549.3	+	2713.15i	−0.204343	+	0.00705814i
$621$		0			0
$622$	−203557.	−	468392.i	−0.526144	−	1.21068i
$623$			254543.i			0.655820i
$624$		0			0
$625$	227071.			0.581302
$626$	−88531.2	+	38474.5i	−0.225916	+	0.0981803i
$627$		0			0
$628$	−321405.	+	11101.5i	−0.814954	+	0.0281491i
$629$	54327.1	−	54327.1i	0.137314	−	0.137314i
$630$		0			0
$631$	−445762.			−1.11955			−0.559777	−	0.828644i	$-0.689113\pi$
$631$	−445762.			−1.11955			−0.559777	+	0.828644i	$0.689113\pi$
$632$	188138.	−	530327.i	0.471024	−	1.32773i
$633$		0			0
$634$	132210.	−	335449.i	0.328917	−	0.834540i
$635$	−58296.2	−	58296.2i	−0.144575	−	0.144575i
$636$		0			0
$637$	68511.2	+	68511.2i	0.168843	+	0.168843i
$638$	−158599.	+	68925.2i	−0.389637	+	0.169331i
$639$		0			0
$640$	−166208.	−	294685.i	−0.405782	−	0.719445i
$641$	412550.			1.00406			0.502031	−	0.864850i	$-0.332586\pi$
$641$	412550.			1.00406			0.502031	+	0.864850i	$0.332586\pi$
$642$		0			0
$643$	−71290.0	+	71290.0i	−0.172428	+	0.172428i	−0.788045	−	0.615617i	$-0.788907\pi$
$643$	−71290.0	+	71290.0i	−0.172428	+	0.172428i	0.615617	+	0.788045i	$0.288907\pi$
$644$	−251677.	+	269685.i	−0.606837	+	0.650258i
$645$		0			0
$646$	−79915.1	−	31496.9i	−0.191498	−	0.0754750i
$647$	−138722.			−0.331388			−0.165694	−	0.986177i	$-0.552986\pi$
$647$	−138722.			−0.331388			−0.165694	+	0.986177i	$0.552986\pi$
$648$		0			0
$649$			290509.i			0.689716i
$650$	−39256.4	−	15472.1i	−0.0929146	−	0.0366204i
$651$		0			0
$652$	−5819.42	−	168480.i	−0.0136894	−	0.396327i
$653$	−467444.	−	467444.i	−1.09623	−	1.09623i	−0.994847	−	0.101387i	$-0.967672\pi$
$653$	−467444.	−	467444.i	−1.09623	−	1.09623i	−0.101387	−	0.994847i	$-0.532328\pi$
$654$		0			0
$655$			485943.i			1.13267i
$656$	460456.	−	31846.9i	1.06999	−	0.0740048i
$657$		0			0
$658$	−140988.	+	61271.6i	−0.325635	+	0.141517i
$659$	−180573.	+	180573.i	−0.415797	+	0.415797i	−0.883752	−	0.467955i	$-0.844991\pi$
$659$	−180573.	+	180573.i	−0.415797	+	0.415797i	0.467955	+	0.883752i	$0.344991\pi$
$660$		0			0
$661$	142726.	−	142726.i	0.326664	−	0.326664i	−0.524652	−	0.851317i	$-0.675805\pi$
$661$	142726.	−	142726.i	0.326664	−	0.326664i	0.851317	+	0.524652i	$0.175805\pi$
$662$	−230793.	+	585576.i	−0.526631	+	1.33619i
$663$		0			0
$664$	18649.9	−	8882.50i	0.0422999	−	0.0201465i
$665$		−	109959.i		−	0.248650i
$666$		0			0
$667$	−336097.	−	336097.i	−0.755462	−	0.755462i
$668$	−43635.6	+	46757.9i	−0.0977886	+	0.104786i
$669$		0			0
$670$	428039.	−	186020.i	0.953529	−	0.414391i
$671$			548576.i			1.21841i
$672$		0			0
$673$	−272445.			−0.601517			−0.300759	−	0.953700i	$-0.597240\pi$
$673$	−272445.			−0.601517			−0.300759	+	0.953700i	$0.597240\pi$
$674$	142185.	+	327173.i	0.312993	+	0.720208i
$675$		0			0
$676$	301086.	+	280981.i	0.658866	+	0.614871i
$677$	−285404.	+	285404.i	−0.622706	+	0.622706i	−0.946222	−	0.323517i	$-0.895135\pi$
$677$	−285404.	+	285404.i	−0.622706	+	0.622706i	0.323517	+	0.946222i	$0.395135\pi$
$678$		0			0
$679$	−265390.			−0.575632
$680$	−115584.	+	55050.1i	−0.249966	+	0.119053i
$681$		0			0
$682$	−77281.2	−	30458.8i	−0.166152	−	0.0654854i
$683$	−186551.	−	186551.i	−0.399904	−	0.399904i	0.478295	−	0.878199i	$-0.341255\pi$
$683$	−186551.	−	186551.i	−0.399904	−	0.399904i	−0.878199	+	0.478295i	$0.841255\pi$
$684$		0			0
$685$	−156918.	−	156918.i	−0.334419	−	0.334419i
$686$	−161803.	−	372315.i	−0.343826	−	0.791155i
$687$		0			0
$688$	48992.9	−	56273.5i	0.103504	−	0.118885i
$689$	−167836.			−0.353546
$690$		0			0
$691$	544261.	−	544261.i	1.13986	−	1.13986i	0.151383	−	0.988475i	$-0.451627\pi$
$691$	544261.	−	544261.i	1.13986	−	1.13986i	0.988475	−	0.151383i	$-0.0483727\pi$
$692$	−384364.	+	13276.2i	−0.802657	+	0.0277243i
$693$		0			0
$694$	35419.2	−	89866.9i	0.0735394	−	0.186587i
$695$	−221470.			−0.458506
$696$		0			0
$697$		−	174655.i		−	0.359514i
$698$	−53850.9	+	136632.i	−0.110531	+	0.280442i
$699$		0			0
$700$	55800.2	+	52074.1i	0.113878	+	0.106274i
$701$	69213.2	+	69213.2i	0.140849	+	0.140849i	0.774015	−	0.633167i	$-0.218245\pi$
$701$	69213.2	+	69213.2i	0.140849	+	0.140849i	−0.633167	+	0.774015i	$0.718245\pi$
$702$		0			0
$703$		−	175817.i		−	0.355754i
$704$	−36971.3	−	355654.i	−0.0745967	−	0.717600i
$705$		0			0
$706$	353771.	+	814040.i	0.709762	+	1.63319i
$707$	−181193.	+	181193.i	−0.362496	+	0.362496i
$708$		0			0
$709$	133745.	−	133745.i	0.266063	−	0.266063i	−0.561448	−	0.827512i	$-0.689756\pi$
$709$	133745.	−	133745.i	0.266063	−	0.266063i	0.827512	+	0.561448i	$0.189756\pi$
$710$	378792.	+	149293.i	0.751423	+	0.296158i
$711$		0			0
$712$	226748.	−	639160.i	0.447284	−	1.26081i
$713$		−	228318.i		−	0.449118i
$714$		0			0
$715$	67710.4	+	67710.4i	0.132447	+	0.132447i
$716$	−18841.2	−	545477.i	−0.0367520	−	1.06402i
$717$		0			0
$718$	−170320.	−	391912.i	−0.330382	−	0.760221i
$719$		−	762270.i		−	1.47452i	−0.675609	−	0.737261i	$-0.736119\pi$
$719$		−	762270.i		−	1.47452i	0.675609	−	0.737261i	$-0.263881\pi$
$720$		0			0
$721$	147124.			0.283017
$722$	297809.	−	129424.i	0.571299	−	0.248279i
$723$		0			0
$724$	10808.7	+	312927.i	0.0206204	+	0.596988i
$725$	−69541.2	+	69541.2i	−0.132302	+	0.132302i
$726$		0			0
$727$	−664888.			−1.25800			−0.628999	−	0.777406i	$-0.716535\pi$
$727$	−664888.			−1.25800			−0.628999	+	0.777406i	$0.716535\pi$
$728$	35114.7	+	73727.6i	0.0662562	+	0.139113i
$729$		0			0
$730$	−80308.8	+	203762.i	−0.150701	+	0.382365i
$731$	−19964.3	−	19964.3i	−0.0373610	−	0.0373610i
$732$		0			0
$733$	−616942.	−	616942.i	−1.14825	−	1.14825i	−0.986897	−	0.161352i	$-0.948414\pi$
$733$	−616942.	−	616942.i	−1.14825	−	1.14825i	−0.161352	−	0.986897i	$-0.551586\pi$
$734$	−290090.	+	126069.i	−0.538444	+	0.234001i
$735$		0			0
$736$	872201.	−	452987.i	1.61013	−	0.836239i
$737$	493261.			0.908117
$738$		0			0
$739$	−204895.	+	204895.i	−0.375182	+	0.375182i	−0.869360	−	0.494179i	$-0.835469\pi$
$739$	−204895.	+	204895.i	−0.375182	+	0.375182i	0.494179	+	0.869360i	$0.335469\pi$
$740$	−191577.	−	178784.i	−0.349848	−	0.326487i
$741$		0			0
$742$	282440.	+	111318.i	0.513001	+	0.202189i
$743$	−183598.			−0.332576			−0.166288	−	0.986077i	$-0.553178\pi$
$743$	−183598.			−0.332576			−0.166288	+	0.986077i	$0.553178\pi$
$744$		0			0
$745$			98863.7i			0.178125i
$746$	454401.	+	179093.i	0.816511	+	0.321811i
$747$		0			0
$748$	−135226.	+	4670.80i	−0.241689	+	0.00834811i
$749$	111380.	+	111380.i	0.198538	+	0.198538i
$750$		0			0
$751$			167996.i			0.297864i	0.988847	+	0.148932i	$0.0475836\pi$
$751$			167996.i			0.297864i	−0.988847	+	0.148932i	$0.952416\pi$
$752$	408604.	−	28260.6i	0.722548	−	0.0499742i
$753$		0			0
$754$	−96505.7	+	41940.1i	−0.169750	+	0.0737712i
$755$	316823.	−	316823.i	0.555805	−	0.555805i
$756$		0			0
$757$	−414105.	+	414105.i	−0.722634	+	0.722634i	−0.969141	−	0.246507i	$-0.920717\pi$
$757$	−414105.	+	414105.i	−0.722634	+	0.722634i	0.246507	+	0.969141i	$0.420717\pi$
$758$	348936.	−	885333.i	0.607306	−	1.54088i
$759$		0			0
$760$	−97952.1	+	276109.i	−0.169585	+	0.478027i
$761$		−	315375.i		−	0.544575i	−0.962216	−	0.272287i	$-0.912220\pi$
$761$		−	315375.i		−	0.544575i	0.962216	−	0.272287i	$-0.0877801\pi$
$762$		0			0
$763$	−365974.	−	365974.i	−0.628638	−	0.628638i
$764$	137065.	+	127912.i	0.234822	+	0.219142i
$765$		0			0
$766$	81360.2	−	35358.1i	0.138661	−	0.0602603i
$767$			176771.i			0.300483i
$768$		0			0
$769$	156016.			0.263825			0.131913	−	0.991261i	$-0.457888\pi$
$769$	156016.			0.263825			0.131913	+	0.991261i	$0.457888\pi$
$770$	−69036.3	−	158855.i	−0.116438	−	0.267929i
$771$		0			0
$772$	749229.	−	802838.i	1.25713	−	1.34708i
$773$	151026.	−	151026.i	0.252751	−	0.252751i	−0.569347	−	0.822098i	$-0.692804\pi$
$773$	151026.	−	151026.i	0.252751	−	0.252751i	0.822098	+	0.569347i	$0.192804\pi$
$774$		0			0
$775$	−47240.9			−0.0786529
$776$	666397.	+	236411.i	1.10665	+	0.392594i
$777$		0			0
$778$	858415.	+	338327.i	1.41820	+	0.558956i
$779$	−282615.	−	282615.i	−0.465715	−	0.465715i
$780$		0			0
$781$	304276.	+	304276.i	0.498845	+	0.498845i
$782$	−148232.	−	341086.i	−0.242397	−	0.557764i
$783$		0			0
$784$	32218.6	+	465829.i	0.0524172	+	0.757870i
$785$	415056.			0.673546
$786$		0			0
$787$	95574.5	−	95574.5i	0.154310	−	0.154310i	−0.625730	−	0.780040i	$-0.715199\pi$
$787$	95574.5	−	95574.5i	0.154310	−	0.154310i	0.780040	+	0.625730i	$0.215199\pi$
$788$	17875.7	+	517526.i	0.0287879	+	0.833450i
$789$		0			0
$790$	−266296.	+	675655.i	−0.426688	+	1.08261i
$791$	69711.8			0.111418
$792$		0			0
$793$			333802.i			0.530814i
$794$	229127.	−	581350.i	0.363442	−	0.922139i
$795$		0			0
$796$	−654297.	+	701113.i	−1.03264	+	1.10653i
$797$	497721.	+	497721.i	0.783555	+	0.783555i	0.980429	−	0.196874i	$-0.0630790\pi$
$797$	497721.	+	497721.i	0.783555	+	0.783555i	−0.196874	+	0.980429i	$0.563079\pi$
$798$		0			0
$799$		−	154987.i		−	0.242774i
$800$	−93726.9	−	180466.i	−0.146448	−	0.281978i
$801$		0			0
$802$	70011.8	+	161100.i	0.108849	+	0.250464i
$803$	−163678.	+	163678.i	−0.253840	+	0.253840i
$804$		0			0
$805$	336638.	−	336638.i	0.519484	−	0.519484i
$806$	−47024.6	−	18533.8i	−0.0723861	−	0.0285295i
$807$		0			0
$808$	616385.	−	293570.i	0.944125	−	0.449665i
$809$			363878.i			0.555979i	0.960584	+	0.277990i	$0.0896681\pi$
$809$			363878.i			0.555979i	−0.960584	+	0.277990i	$0.910332\pi$
$810$		0			0
$811$	−53046.1	−	53046.1i	−0.0806513	−	0.0806513i	0.665630	−	0.746282i	$-0.268163\pi$
$811$	−53046.1	−	53046.1i	−0.0806513	−	0.0806513i	−0.746282	+	0.665630i	$0.768163\pi$
$812$	190221.	−	6570.35i	0.288500	−	0.00996498i
$813$		0			0
$814$	−110384.	−	253998.i	−0.166593	−	0.383337i
$815$			217572.i			0.327557i
$816$		0			0
$817$	−64609.6			−0.0967950
$818$	−692129.	+	300790.i	−1.03438	+	0.449528i
$819$		0			0
$820$	−595334.	+	20563.2i	−0.885386	+	0.0305818i
$821$	540562.	−	540562.i	0.801972	−	0.801972i	−0.181432	−	0.983404i	$-0.558073\pi$
$821$	540562.	−	540562.i	0.801972	−	0.801972i	0.983404	+	0.181432i	$0.0580731\pi$
$822$		0			0
$823$	956590.			1.41230			0.706148	−	0.708064i	$-0.250431\pi$
$823$	956590.			1.41230			0.706148	+	0.708064i	$0.250431\pi$
$824$	−369429.	−	131059.i	−0.544098	−	0.193024i
$825$		0			0
$826$	117245.	−	297477.i	0.171843	−	0.436007i
$827$	83207.7	+	83207.7i	0.121661	+	0.121661i	0.765316	−	0.643655i	$-0.222583\pi$
$827$	83207.7	+	83207.7i	0.121661	+	0.121661i	−0.643655	+	0.765316i	$0.722583\pi$
$828$		0			0
$829$	−673529.	−	673529.i	−0.980048	−	0.980048i	0.0197565	−	0.999805i	$-0.493711\pi$
$829$	−673529.	−	673529.i	−0.980048	−	0.980048i	−0.999805	+	0.0197565i	$0.993711\pi$
$830$	−24451.1	+	10626.1i	−0.0354930	+	0.0154248i
$831$		0			0
$832$	−22496.6	−	216411.i	−0.0324990	−	0.312632i
$833$	176694.			0.254642
$834$		0			0
$835$	58366.2	−	58366.2i	0.0837121	−	0.0837121i
$836$	−211255.	+	226371.i	−0.302270	+	0.323898i
$837$		0			0
$838$	−466058.	−	183687.i	−0.663670	−	0.261572i
$839$	488503.			0.693975			0.346987	−	0.937870i	$-0.387205\pi$
$839$	488503.			0.693975			0.346987	+	0.937870i	$0.387205\pi$
$840$		0			0
$841$		−	462029.i		−	0.653247i
$842$	226215.	+	89158.1i	0.319078	+	0.125758i
$843$		0			0
$844$	−9809.66	−	284003.i	−0.0137711	−	0.398692i
$845$	−375835.	−	375835.i	−0.526361	−	0.526361i
$846$		0			0
$847$			168631.i			0.235055i
$848$	−610047.	−	531120.i	−0.848343	−	0.738585i
$849$		0			0
$850$	−70573.7	+	30670.4i	−0.0976798	+	0.0424503i
$851$	538260.	−	538260.i	0.743247	−	0.743247i
$852$		0			0
$853$	−462565.	+	462565.i	−0.635733	+	0.635733i	−0.949500	−	0.313767i	$-0.898409\pi$
$853$	−462565.	+	462565.i	−0.635733	+	0.635733i	0.313767	+	0.949500i	$0.398409\pi$
$854$	221396.	−	561734.i	0.303567	−	0.770221i
$855$		0			0
$856$	−180459.	−	378895.i	−0.246281	−	0.517096i
$857$			1.08100e6i			1.47185i	0.677064	+	0.735924i	$0.263252\pi$
$857$			1.08100e6i			1.47185i	−0.677064	+	0.735924i	$0.736748\pi$
$858$		0			0
$859$	911196.	+	911196.i	1.23488	+	1.23488i	0.962066	+	0.272816i	$0.0879549\pi$
$859$	911196.	+	911196.i	1.23488	+	1.23488i	0.272816	+	0.962066i	$0.412045\pi$
$860$	−65700.1	+	70401.1i	−0.0888320	+	0.0951881i
$861$		0			0
$862$	−600526.	+	260981.i	−0.808197	+	0.351232i
$863$			35108.9i			0.0471406i	0.999722	+	0.0235703i	$0.00750335\pi$
$863$			35108.9i			0.0471406i	−0.999722	+	0.0235703i	$0.992497\pi$
$864$		0			0
$865$	496359.			0.663382
$866$	−79253.0	−	182364.i	−0.105677	−	0.243166i
$867$		0			0
$868$	66842.2	+	62378.8i	0.0887179	+	0.0827937i
$869$	−542740.	+	542740.i	−0.718707	+	0.718707i
$870$		0			0
$871$	300143.			0.395633
$872$	592952.	+	1.24497e6i	0.779807	+	1.63730i
$873$		0			0
$874$	−791780.	−	312064.i	−1.03653	−	0.408527i
$875$	−288868.	−	288868.i	−0.377298	−	0.377298i
$876$		0			0
$877$	134545.	+	134545.i	0.174931	+	0.174931i	0.789142	−	0.614211i	$-0.210526\pi$
$877$	134545.	+	134545.i	0.174931	+	0.174931i	−0.614211	+	0.789142i	$0.710526\pi$
$878$	−290428.	−	668285.i	−0.376746	−	0.866907i
$879$		0			0
$880$	31842.0	+	460384.i	0.0411183	+	0.594505i
$881$	−1.27287e6			−1.63995			−0.819975	−	0.572399i	$-0.806013\pi$
$881$	−1.27287e6			−1.63995			−0.819975	+	0.572399i	$0.806013\pi$
$882$		0			0
$883$	484264.	−	484264.i	0.621098	−	0.621098i	−0.324714	−	0.945812i	$-0.605268\pi$
$883$	484264.	−	484264.i	0.621098	−	0.621098i	0.945812	+	0.324714i	$0.105268\pi$
$884$	−82283.4	+	2842.12i	−0.105295	+	0.00363696i
$885$		0			0
$886$	6515.77	−	16532.1i	0.00830039	−	0.0210600i
$887$	66348.3			0.0843301			0.0421650	−	0.999111i	$-0.486574\pi$
$887$	66348.3			0.0843301			0.0421650	+	0.999111i	$0.486574\pi$
$888$		0			0
$889$			95902.7i			0.121347i
$890$	−320945.	+	814312.i	−0.405182	+	1.02804i
$891$		0			0
$892$	−266253.	−	248474.i	−0.334630	−	0.312285i
$893$	−250790.	−	250790.i	−0.314490	−	0.314490i
$894$		0			0
$895$			704418.i			0.879396i
$896$	−105678.	+	379106.i	−0.131634	+	0.472220i
$897$		0			0
$898$	−172708.	−	397407.i	−0.214171	−	0.492814i
$899$	−83302.4	+	83302.4i	−0.103071	+	0.103071i
$900$		0			0
$901$	−216428.	+	216428.i	−0.266602	+	0.266602i
$902$	−585722.	−	230851.i	−0.719911	−	0.283738i
$903$		0			0
$904$	−175047.	−	62099.6i	−0.214199	−	0.0759893i
$905$		−	404107.i		−	0.493401i
$906$		0			0
$907$	846133.	+	846133.i	1.02855	+	1.02855i	0.999580	+	0.0289661i	$0.00922147\pi$
$907$	846133.	+	846133.i	1.02855	+	1.02855i	0.0289661	+	0.999580i	$0.490779\pi$
$908$	−5061.77	−	146545.i	−0.00613946	−	0.177746i
$909$		0			0
$910$	−42007.7	−	96661.3i	−0.0507278	−	0.116727i
$911$		−	133938.i		−	0.161386i	−0.996739	−	0.0806932i	$-0.974287\pi$
$911$		−	133938.i		−	0.161386i	0.996739	−	0.0806932i	$-0.0257134\pi$
$912$		0			0
$913$	−28176.8			−0.0338026
$914$	810410.	−	352194.i	0.970091	−	0.421589i
$915$		0			0
$916$	28173.2	+	815654.i	0.0335773	+	0.972109i
$917$	399711.	−	399711.i	0.475343	−	0.475343i
$918$		0			0
$919$	−469228.			−0.555589			−0.277794	−	0.960641i	$-0.589603\pi$
$919$	−469228.			−0.555589			−0.277794	+	0.960641i	$0.589603\pi$
$920$	−1.14518e6	+	545423.i	−1.35300	+	0.644404i
$921$		0			0
$922$	285288.	−	723844.i	0.335600	−	0.851497i
$923$	185148.	+	185148.i	0.217328	+	0.217328i
$924$		0			0
$925$	−111371.	−	111371.i	−0.130163	−	0.130163i
$926$	−195653.	+	85028.1i	−0.228173	+	0.0991609i
$927$		0			0
$928$	−483499.	−	152951.i	−0.561435	−	0.177606i
$929$	−728330.			−0.843911			−0.421955	−	0.906617i	$-0.638656\pi$
$929$	−728330.			−0.843911			−0.421955	+	0.906617i	$0.638656\pi$
$930$		0			0
$931$	285913.	−	285913.i	0.329864	−	0.329864i
$932$	798079.	+	744787.i	0.918785	+	0.857434i
$933$		0			0
$934$	−1.09027e6	−	429709.i	−1.24980	−	0.492585i
$935$	174628.			0.199752
$936$		0			0
$937$			572084.i			0.651599i	0.945439	+	0.325800i	$0.105634\pi$
$937$			572084.i			0.651599i	−0.945439	+	0.325800i	$0.894366\pi$
$938$	−505092.	−	199072.i	−0.574070	−	0.226258i
$939$		0			0
$940$	−528293.	+	18247.6i	−0.597887	+	0.0206514i
$941$	270062.	+	270062.i	0.304989	+	0.304989i	0.842962	−	0.537973i	$-0.180810\pi$
$941$	270062.	+	270062.i	0.304989	+	0.304989i	−0.537973	+	0.842962i	$0.680810\pi$
$942$		0			0
$943$		−	1.73044e6i		−	1.94596i
$944$	−559396.	+	642526.i	−0.627734	+	0.721019i
$945$		0			0
$946$	−93339.7	+	40564.2i	−0.104300	+	0.0453274i
$947$	803359.	−	803359.i	0.895797	−	0.895797i	−0.0992642	−	0.995061i	$-0.531649\pi$
$947$	803359.	−	803359.i	0.895797	−	0.895797i	0.995061	+	0.0992642i	$0.0316489\pi$
$948$		0			0
$949$	−99596.1	+	99596.1i	−0.110588	+	0.110588i
$950$	−64568.7	+	163826.i	−0.0715443	+	0.181525i
$951$		0			0
$952$	140355.	+	49792.1i	0.154865	+	0.0549398i
$953$		−	188445.i		−	0.207491i	−0.994604	−	0.103746i	$-0.966917\pi$
$953$		−	188445.i		−	0.207491i	0.994604	−	0.103746i	$-0.0330827\pi$
$954$		0			0
$955$	−171093.	−	171093.i	−0.187597	−	0.187597i
$956$	1.17626e6	+	1.09771e6i	1.28702	+	1.20108i
$957$		0			0
$958$	988429.	−	429558.i	1.07700	−	0.468048i
$959$			258144.i			0.280689i
$960$		0			0
$961$	866932.			0.938725
$962$	−67167.3	−	154554.i	−0.0725785	−	0.167006i
$963$		0			0
$964$	388221.	−	416000.i	0.417759	−	0.447650i
$965$	−1.00215e6	+	1.00215e6i	−1.07617	+	1.07617i
$966$		0			0
$967$	1.17554e6			1.25715			0.628573	−	0.777751i	$-0.283639\pi$
$967$	1.17554e6			1.25715			0.628573	+	0.777751i	$0.283639\pi$
$968$	150217.	−	423433.i	0.160313	−	0.451891i
$969$		0			0
$970$	−849013.	−	334621.i	−0.902341	−	0.355640i
$971$	784226.	+	784226.i	0.831769	+	0.831769i	0.987759	−	0.155989i	$-0.0498565\pi$
$971$	784226.	+	784226.i	0.831769	+	0.831769i	−0.155989	+	0.987759i	$0.549857\pi$
$972$		0			0
$973$	182169.	+	182169.i	0.192420	+	0.192420i
$974$	183174.	+	421491.i	0.193084	+	0.444293i
$975$		0			0
$976$	−1.05632e6	+	1.21330e6i	−1.10891	+	1.27370i
$977$	−710097.			−0.743924			−0.371962	−	0.928248i	$-0.621315\pi$
$977$	−710097.			−0.743924			−0.371962	+	0.928248i	$0.621315\pi$
$978$		0			0
$979$	−654120.	+	654120.i	−0.682483	+	0.682483i
$980$	−20803.2	−	602281.i	−0.0216610	−	0.627115i
$981$		0			0
$982$	−173170.	+	439373.i	−0.179576	+	0.455628i
$983$	−471799.			−0.488259			−0.244129	−	0.969743i	$-0.578502\pi$
$983$	−471799.			−0.488259			−0.244129	+	0.969743i	$0.578502\pi$
$984$		0			0
$985$		−	668322.i		−	0.688832i
$986$	−70363.6	+	178529.i	−0.0723759	+	0.183635i
$987$		0			0
$988$	−128546.	+	137744.i	−0.131688	+	0.141110i
$989$	−197801.	−	197801.i	−0.202226	−	0.202226i
$990$		0			0
$991$		−	1.06681e6i		−	1.08627i	−0.839644	−	0.543137i	$-0.817237\pi$
$991$		−	1.06681e6i		−	1.08627i	0.839644	−	0.543137i	$-0.182763\pi$
$992$	−112274.	−	216177.i	−0.114092	−	0.219678i
$993$		0			0
$994$	−188774.	−	434375.i	−0.191059	−	0.439635i
$995$	875175.	−	875175.i	0.883992	−	0.883992i
$996$		0			0
$997$	−303115.	+	303115.i	−0.304942	+	0.304942i	−0.842944	−	0.538002i	$-0.819179\pi$
$997$	−303115.	+	303115.i	−0.304942	+	0.304942i	0.538002	+	0.842944i	$0.319179\pi$
$998$	43634.4	+	17197.6i	0.0438095	+	0.0172666i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.5.m.a.19.3		14
3.2	odd	2		16.5.f.a.3.5	✓	14
4.3	odd	2		576.5.m.a.559.6		14
12.11	even	2		64.5.f.a.47.1		14
16.5	even	4		576.5.m.a.271.6		14
16.11	odd	4	inner	144.5.m.a.91.3		14
24.5	odd	2		128.5.f.b.95.1		14
24.11	even	2		128.5.f.a.95.7		14
48.5	odd	4		64.5.f.a.15.1		14
48.11	even	4		16.5.f.a.11.5	yes	14
48.29	odd	4		128.5.f.a.31.7		14
48.35	even	4		128.5.f.b.31.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.5.f.a.3.5	✓	14	3.2	odd	2
16.5.f.a.11.5	yes	14	48.11	even	4
64.5.f.a.15.1		14	48.5	odd	4
64.5.f.a.47.1		14	12.11	even	2
128.5.f.a.31.7		14	48.29	odd	4
128.5.f.a.95.7		14	24.11	even	2
128.5.f.b.31.1		14	48.35	even	4
128.5.f.b.95.1		14	24.5	odd	2
144.5.m.a.19.3		14	1.1	even	1	trivial
144.5.m.a.91.3		14	16.11	odd	4	inner
576.5.m.a.271.6		14	16.5	even	4
576.5.m.a.559.6		14	4.3	odd	2

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	144.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59430 - 3.66854i) q^{2} +(-10.9164 + 11.6975i) q^{4} +(14.6016 - 14.6016i) q^{5} -24.0210 q^{7} +(60.3169 + 21.3980i) q^{8} +O(q^{10})\)	\(q+(-1.59430 - 3.66854i) q^{2} +(-10.9164 + 11.6975i) q^{4} +(14.6016 - 14.6016i) q^{5} -24.0210 q^{7} +(60.3169 + 21.3980i) q^{8} +(-76.8459 - 30.2872i) q^{10} +(-61.7287 - 61.7287i) q^{11} +(-37.5611 - 37.5611i) q^{13} +(38.2966 + 88.1219i) q^{14} +(-17.6638 - 255.390i) q^{16} -96.8718 q^{17} +(-156.751 + 156.751i) q^{19} +(11.4053 + 330.199i) q^{20} +(-128.040 + 324.868i) q^{22} -959.783 q^{23} +198.587i q^{25} +(-77.9109 + 197.678i) q^{26} +(262.223 - 280.986i) q^{28} +(350.180 + 350.180i) q^{29} +237.885i q^{31} +(-908.747 + 471.968i) q^{32} +(154.443 + 355.378i) q^{34} +(-350.744 + 350.744i) q^{35} +(-560.815 + 560.815i) q^{37} +(824.957 + 325.140i) q^{38} +(1193.17 - 568.278i) q^{40} +1802.95i q^{41} +(206.090 + 206.090i) q^{43} +(1395.93 - 48.2163i) q^{44} +(1530.18 + 3521.01i) q^{46} +1599.92i q^{47} -1823.99 q^{49} +(728.526 - 316.608i) q^{50} +(849.405 - 29.3390i) q^{52} +(2234.17 - 2234.17i) q^{53} -1802.67 q^{55} +(-1448.87 - 514.000i) q^{56} +(726.358 - 1842.94i) q^{58} +(-2353.11 - 2353.11i) q^{59} +(-4443.45 - 4443.45i) q^{61} +(872.690 - 379.260i) q^{62} +(3180.25 + 2581.32i) q^{64} -1096.90 q^{65} +(-3995.40 + 3995.40i) q^{67} +(1057.49 - 1133.16i) q^{68} +(1845.91 + 727.529i) q^{70} -4929.25 q^{71} -2651.57i q^{73} +(2951.48 + 1163.27i) q^{74} +(-122.438 - 3544.76i) q^{76} +(1482.78 + 1482.78i) q^{77} -8792.34i q^{79} +(-3987.02 - 3471.18i) q^{80} +(6614.21 - 2874.45i) q^{82} +(228.231 - 228.231i) q^{83} +(-1414.48 + 1414.48i) q^{85} +(427.480 - 1084.62i) q^{86} +(-2402.41 - 5044.15i) q^{88} -10596.7i q^{89} +(902.254 + 902.254i) q^{91} +(10477.4 - 11227.1i) q^{92} +(5869.38 - 2550.75i) q^{94} +4577.63i q^{95} +11048.3 q^{97} +(2907.99 + 6691.40i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} + 92 q^{8}+O(q^{10}) \) 14 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 + 92 * q^8	\( 14 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} + 92 q^{8} - 100 q^{10} - 94 q^{11} - 2 q^{13} - 44 q^{14} - 168 q^{16} + 4 q^{17} - 706 q^{19} - 1900 q^{20} + 900 q^{22} - 1148 q^{23} + 3416 q^{26} - 3784 q^{28} - 862 q^{29} - 3208 q^{32} + 7508 q^{34} - 1340 q^{35} - 1826 q^{37} - 3568 q^{38} - 5144 q^{40} + 1694 q^{43} + 14636 q^{44} - 5316 q^{46} + 682 q^{49} - 20070 q^{50} + 20452 q^{52} + 482 q^{53} - 11780 q^{55} + 6952 q^{56} - 20456 q^{58} + 2786 q^{59} - 3778 q^{61} + 11472 q^{62} + 15808 q^{64} + 2020 q^{65} + 7998 q^{67} - 18032 q^{68} + 15296 q^{70} - 19964 q^{71} + 23780 q^{74} - 23996 q^{76} + 9508 q^{77} - 1384 q^{80} + 16016 q^{82} + 17282 q^{83} + 9948 q^{85} + 4796 q^{86} + 7288 q^{88} - 28036 q^{91} + 14632 q^{92} + 432 q^{94} - 4 q^{97} + 12246 q^{98}+O(q^{100}) \) 14 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 + 92 * q^8 - 100 * q^10 - 94 * q^11 - 2 * q^13 - 44 * q^14 - 168 * q^16 + 4 * q^17 - 706 * q^19 - 1900 * q^20 + 900 * q^22 - 1148 * q^23 + 3416 * q^26 - 3784 * q^28 - 862 * q^29 - 3208 * q^32 + 7508 * q^34 - 1340 * q^35 - 1826 * q^37 - 3568 * q^38 - 5144 * q^40 + 1694 * q^43 + 14636 * q^44 - 5316 * q^46 + 682 * q^49 - 20070 * q^50 + 20452 * q^52 + 482 * q^53 - 11780 * q^55 + 6952 * q^56 - 20456 * q^58 + 2786 * q^59 - 3778 * q^61 + 11472 * q^62 + 15808 * q^64 + 2020 * q^65 + 7998 * q^67 - 18032 * q^68 + 15296 * q^70 - 19964 * q^71 + 23780 * q^74 - 23996 * q^76 + 9508 * q^77 - 1384 * q^80 + 16016 * q^82 + 17282 * q^83 + 9948 * q^85 + 4796 * q^86 + 7288 * q^88 - 28036 * q^91 + 14632 * q^92 + 432 * q^94 - 4 * q^97 + 12246 * q^98

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