LMFDB - Embedded newform 144.3.m.c.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,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, 3, names="a")

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

chi := DirichletCharacter("144.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
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:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + \cdots + 65536 $ x^16 - 6x^14 - 4x^13 + 10x^12 + 56x^11 + 88x^10 - 128x^9 - 496x^8 - 512x^7 + 1408x^6 + 3584x^5 + 2560x^4 - 4096x^3 - 24576*x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.3
Root			$-1.25564 + 1.55672i$ of defining polynomial
Character	$\chi$	$=$	144.19
Dual form			144.3.m.c.91.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25564 - 1.55672i) q^{2} +(-0.846753 + 3.90935i) q^{4} +(-0.909023 + 0.909023i) q^{5} -0.654713 q^{7} +(7.14897 - 3.59057i) q^{8} +O(q^{10})$	\(q+(-1.25564 - 1.55672i) q^{2} +(-0.846753 + 3.90935i) q^{4} +(-0.909023 + 0.909023i) q^{5} -0.654713 q^{7} +(7.14897 - 3.59057i) q^{8} +(2.55650 + 0.273691i) q^{10} +(13.3760 + 13.3760i) q^{11} +(8.32795 + 8.32795i) q^{13} +(0.822082 + 1.01921i) q^{14} +(-14.5660 - 6.62050i) q^{16} +3.93529 q^{17} +(16.8974 - 16.8974i) q^{19} +(-2.78397 - 4.32340i) q^{20} +(4.02729 - 37.6181i) q^{22} +23.1787 q^{23} +23.3474i q^{25} +(2.50740 - 23.4212i) q^{26} +(0.554380 - 2.55950i) q^{28} +(-35.6105 - 35.6105i) q^{29} +45.5687i q^{31} +(7.98336 + 30.9882i) q^{32} +(-4.94130 - 6.12615i) q^{34} +(0.595149 - 0.595149i) q^{35} +(10.1527 - 10.1527i) q^{37} +(-47.5215 - 5.08752i) q^{38} +(-3.23467 + 9.76249i) q^{40} +28.4661i q^{41} +(22.7354 + 22.7354i) q^{43} +(-63.6176 + 40.9653i) q^{44} +(-29.1040 - 36.0827i) q^{46} -10.7746i q^{47} -48.5714 q^{49} +(36.3453 - 29.3158i) q^{50} +(-39.6086 + 25.5051i) q^{52} +(-41.5142 + 41.5142i) q^{53} -24.3182 q^{55} +(-4.68053 + 2.35079i) q^{56} +(-10.7217 + 100.149i) q^{58} +(21.0646 + 21.0646i) q^{59} +(-68.7531 - 68.7531i) q^{61} +(70.9377 - 57.2178i) q^{62} +(38.2157 - 51.3377i) q^{64} -15.1406 q^{65} +(67.8242 - 67.8242i) q^{67} +(-3.33222 + 15.3844i) q^{68} +(-1.67377 - 0.179189i) q^{70} -33.3094 q^{71} -18.6331i q^{73} +(-28.5531 - 3.05682i) q^{74} +(51.7499 + 80.3657i) q^{76} +(-8.75745 - 8.75745i) q^{77} +6.29222i q^{79} +(19.2590 - 7.22265i) q^{80} +(44.3137 - 35.7431i) q^{82} +(72.0774 - 72.0774i) q^{83} +(-3.57727 + 3.57727i) q^{85} +(6.84524 - 63.9400i) q^{86} +(143.652 + 47.5973i) q^{88} -10.6131i q^{89} +(-5.45242 - 5.45242i) q^{91} +(-19.6266 + 90.6135i) q^{92} +(-16.7730 + 13.5290i) q^{94} +30.7202i q^{95} +143.631 q^{97} +(60.9880 + 75.6120i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} + 12 q^{8}+O(q^{10}) $ 16 * q + 12 * q^4 + 12 * q^8	$ 16 q + 12 q^{4} + 12 q^{8} - 56 q^{10} - 32 q^{11} + 44 q^{14} + 32 q^{16} - 32 q^{19} - 80 q^{20} + 32 q^{22} + 128 q^{23} + 100 q^{26} - 120 q^{28} - 32 q^{29} - 160 q^{32} + 96 q^{34} - 96 q^{35} - 96 q^{37} - 168 q^{38} + 48 q^{40} + 160 q^{43} - 88 q^{44} + 136 q^{46} + 112 q^{49} + 236 q^{50} - 48 q^{52} + 160 q^{53} - 256 q^{55} + 224 q^{56} + 144 q^{58} + 128 q^{59} - 32 q^{61} + 276 q^{62} - 408 q^{64} + 32 q^{65} + 320 q^{67} + 448 q^{68} - 384 q^{70} - 512 q^{71} - 348 q^{74} + 72 q^{76} - 224 q^{77} - 552 q^{80} - 40 q^{82} + 160 q^{83} + 160 q^{85} - 528 q^{86} + 480 q^{88} - 480 q^{91} - 496 q^{92} + 312 q^{94} + 440 q^{98}+O(q^{100}) $ 16 * q + 12 * q^4 + 12 * q^8 - 56 * q^10 - 32 * q^11 + 44 * q^14 + 32 * q^16 - 32 * q^19 - 80 * q^20 + 32 * q^22 + 128 * q^23 + 100 * q^26 - 120 * q^28 - 32 * q^29 - 160 * q^32 + 96 * q^34 - 96 * q^35 - 96 * q^37 - 168 * q^38 + 48 * q^40 + 160 * q^43 - 88 * q^44 + 136 * q^46 + 112 * q^49 + 236 * q^50 - 48 * q^52 + 160 * q^53 - 256 * q^55 + 224 * q^56 + 144 * q^58 + 128 * q^59 - 32 * q^61 + 276 * q^62 - 408 * q^64 + 32 * q^65 + 320 * q^67 + 448 * q^68 - 384 * q^70 - 512 * q^71 - 348 * q^74 + 72 * q^76 - 224 * q^77 - 552 * q^80 - 40 * q^82 + 160 * q^83 + 160 * q^85 - 528 * q^86 + 480 * q^88 - 480 * q^91 - 496 * q^92 + 312 * q^94 + 440 * 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 $

$2$	−1.25564	−	1.55672i	−0.627818	−	0.778360i
$2$	−1.25564	−	1.55672i	−0.627818	−	0.778360i
$3$		0			0
$3$		0			0
$4$	−0.846753	+	3.90935i	−0.211688	+	0.977337i
$5$	−0.909023	+	0.909023i	−0.181805	+	0.181805i	−0.792142	−	0.610337i	$-0.791034\pi$
$5$	−0.909023	+	0.909023i	−0.181805	+	0.181805i	0.610337	+	0.792142i	$0.291034\pi$
$6$		0			0
$7$	−0.654713			−0.0935305			−0.0467652	−	0.998906i	$-0.514891\pi$
$7$	−0.654713			−0.0935305			−0.0467652	+	0.998906i	$0.514891\pi$
$8$	7.14897	−	3.59057i	0.893622	−	0.448821i
$9$		0			0
$10$	2.55650	+	0.273691i	0.255650	+	0.0273691i
$11$	13.3760	+	13.3760i	1.21600	+	1.21600i	0.969021	+	0.246980i	$0.0794382\pi$
$11$	13.3760	+	13.3760i	1.21600	+	1.21600i	0.246980	+	0.969021i	$0.420562\pi$
$12$		0			0
$13$	8.32795	+	8.32795i	0.640612	+	0.640612i	0.950706	−	0.310094i	$-0.100361\pi$
$13$	8.32795	+	8.32795i	0.640612	+	0.640612i	−0.310094	+	0.950706i	$0.600361\pi$
$14$	0.822082	+	1.01921i	0.0587202	+	0.0728004i
$15$		0			0
$16$	−14.5660	−	6.62050i	−0.910376	−	0.413781i
$17$	3.93529			0.231488			0.115744	−	0.993279i	$-0.463075\pi$
$17$	3.93529			0.231488			0.115744	+	0.993279i	$0.463075\pi$
$18$		0			0
$19$	16.8974	−	16.8974i	0.889336	−	0.889336i	−0.105123	−	0.994459i	$-0.533524\pi$
$19$	16.8974	−	16.8974i	0.889336	−	0.889336i	0.994459	+	0.105123i	$0.0335236\pi$
$20$	−2.78397	−	4.32340i	−0.139198	−	0.216170i
$21$		0			0
$22$	4.02729	−	37.6181i	0.183059	−	1.70991i
$23$	23.1787			1.00777			0.503884	−	0.863771i	$-0.331904\pi$
$23$	23.1787			1.00777			0.503884	+	0.863771i	$0.331904\pi$
$24$		0			0
$25$			23.3474i			0.933894i
$26$	2.50740	−	23.4212i	0.0964386	−	0.900814i
$27$		0			0
$28$	0.554380	−	2.55950i	0.0197993	−	0.0914108i
$29$	−35.6105	−	35.6105i	−1.22795	−	1.22795i	−0.964739	−	0.263209i	$-0.915219\pi$
$29$	−35.6105	−	35.6105i	−1.22795	−	1.22795i	−0.263209	−	0.964739i	$-0.584781\pi$
$30$		0			0
$31$			45.5687i			1.46996i	0.678089	+	0.734980i	$0.262808\pi$
$31$			45.5687i			1.46996i	−0.678089	+	0.734980i	$0.737192\pi$
$32$	7.98336	+	30.9882i	0.249480	+	0.968380i
$33$		0			0
$34$	−4.94130	−	6.12615i	−0.145332	−	0.180181i
$35$	0.595149	−	0.595149i	0.0170043	−	0.0170043i
$36$		0			0
$37$	10.1527	−	10.1527i	0.274398	−	0.274398i	−0.556470	−	0.830868i	$-0.687844\pi$
$37$	10.1527	−	10.1527i	0.274398	−	0.274398i	0.830868	+	0.556470i	$0.187844\pi$
$38$	−47.5215	−	5.08752i	−1.25057	−	0.133882i
$39$		0			0
$40$	−3.23467	+	9.76249i	−0.0808669	+	0.244062i
$41$			28.4661i			0.694295i	0.937811	+	0.347148i	$0.112850\pi$
$41$			28.4661i			0.694295i	−0.937811	+	0.347148i	$0.887150\pi$
$42$		0			0
$43$	22.7354	+	22.7354i	0.528730	+	0.528730i	0.920194	−	0.391464i	$-0.128031\pi$
$43$	22.7354	+	22.7354i	0.528730	+	0.528730i	−0.391464	+	0.920194i	$0.628031\pi$
$44$	−63.6176	+	40.9653i	−1.44586	+	0.931030i
$45$		0			0
$46$	−29.1040	−	36.0827i	−0.632696	−	0.784407i
$47$		−	10.7746i		−	0.229247i	−0.993409	−	0.114623i	$-0.963434\pi$
$47$		−	10.7746i		−	0.229247i	0.993409	−	0.114623i	$-0.0365661\pi$
$48$		0			0
$49$	−48.5714			−0.991252
$50$	36.3453	−	29.3158i	0.726906	−	0.586316i
$51$		0			0
$52$	−39.6086	+	25.5051i	−0.761703	+	0.490484i
$53$	−41.5142	+	41.5142i	−0.783287	+	0.783287i	−0.980384	−	0.197097i	$-0.936849\pi$
$53$	−41.5142	+	41.5142i	−0.783287	+	0.783287i	0.197097	+	0.980384i	$0.436849\pi$
$54$		0			0
$55$	−24.3182			−0.442149
$56$	−4.68053	+	2.35079i	−0.0835809	+	0.0419784i
$57$		0			0
$58$	−10.7217	+	100.149i	−0.184857	+	1.72671i
$59$	21.0646	+	21.0646i	0.357027	+	0.357027i	0.862716	−	0.505689i	$-0.168762\pi$
$59$	21.0646	+	21.0646i	0.357027	+	0.357027i	−0.505689	+	0.862716i	$0.668762\pi$
$60$		0			0
$61$	−68.7531	−	68.7531i	−1.12710	−	1.12710i	−0.990647	−	0.136453i	$-0.956430\pi$
$61$	−68.7531	−	68.7531i	−1.12710	−	1.12710i	−0.136453	−	0.990647i	$-0.543570\pi$
$62$	70.9377	−	57.2178i	1.14416	−	0.922867i
$63$		0			0
$64$	38.2157	−	51.3377i	0.597120	−	0.802152i
$65$	−15.1406			−0.232932
$66$		0			0
$67$	67.8242	−	67.8242i	1.01230	−	1.01230i	0.0123779	−	0.999923i	$-0.496060\pi$
$67$	67.8242	−	67.8242i	1.01230	−	1.01230i	0.999923	−	0.0123779i	$-0.00394012\pi$
$68$	−3.33222	+	15.3844i	−0.0490033	+	0.226242i
$69$		0			0
$70$	−1.67377	−	0.179189i	−0.0239110	−	0.00255985i
$71$	−33.3094			−0.469147			−0.234573	−	0.972098i	$-0.575369\pi$
$71$	−33.3094			−0.469147			−0.234573	+	0.972098i	$0.575369\pi$
$72$		0			0
$73$		−	18.6331i		−	0.255248i	−0.991823	−	0.127624i	$-0.959265\pi$
$73$		−	18.6331i		−	0.255248i	0.991823	−	0.127624i	$-0.0407351\pi$
$74$	−28.5531	−	3.05682i	−0.385853	−	0.0413083i
$75$		0			0
$76$	51.7499	+	80.3657i	0.680920	+	1.05744i
$77$	−8.75745	−	8.75745i	−0.113733	−	0.113733i
$78$		0			0
$79$			6.29222i			0.0796483i	0.999207	+	0.0398242i	$0.0126798\pi$
$79$			6.29222i			0.0796483i	−0.999207	+	0.0398242i	$0.987320\pi$
$80$	19.2590	−	7.22265i	0.240738	−	0.0902832i
$81$		0			0
$82$	44.3137	−	35.7431i	0.540411	−	0.435891i
$83$	72.0774	−	72.0774i	0.868402	−	0.868402i	−0.123894	−	0.992296i	$-0.539538\pi$
$83$	72.0774	−	72.0774i	0.868402	−	0.868402i	0.992296	+	0.123894i	$0.0395382\pi$
$84$		0			0
$85$	−3.57727	+	3.57727i	−0.0420855	+	0.0420855i
$86$	6.84524	−	63.9400i	0.0795958	−	0.743489i
$87$		0			0
$88$	143.652	+	47.5973i	1.63241	+	0.540878i
$89$		−	10.6131i		−	0.119248i	−0.998221	−	0.0596240i	$-0.981010\pi$
$89$		−	10.6131i		−	0.119248i	0.998221	−	0.0596240i	$-0.0189902\pi$
$90$		0			0
$91$	−5.45242	−	5.45242i	−0.0599167	−	0.0599167i
$92$	−19.6266	+	90.6135i	−0.213333	+	0.984930i
$93$		0			0
$94$	−16.7730	+	13.5290i	−0.178436	+	0.143925i
$95$			30.7202i			0.323371i
$96$		0			0
$97$	143.631			1.48073			0.740366	−	0.672204i	$-0.234652\pi$
$97$	143.631			1.48073			0.740366	+	0.672204i	$0.234652\pi$
$98$	60.9880	+	75.6120i	0.622326	+	0.771551i
$99$		0			0
$100$	−91.2730	−	19.7694i	−0.912730	−	0.197694i
$101$	90.3100	−	90.3100i	0.894159	−	0.894159i	−0.100753	−	0.994912i	$-0.532125\pi$
$101$	90.3100	−	90.3100i	0.894159	−	0.894159i	0.994912	+	0.100753i	$0.0321251\pi$
$102$		0			0
$103$	−95.1656			−0.923938			−0.461969	−	0.886896i	$-0.652857\pi$
$103$	−95.1656			−0.923938			−0.461969	+	0.886896i	$0.652857\pi$
$104$	89.4384	+	29.6343i	0.859984	+	0.284945i
$105$		0			0
$106$	116.753	+	12.4992i	1.10144	+	0.117917i
$107$	−27.2524	−	27.2524i	−0.254695	−	0.254695i	0.568197	−	0.822892i	$-0.307641\pi$
$107$	−27.2524	−	27.2524i	−0.254695	−	0.254695i	−0.822892	+	0.568197i	$0.807641\pi$
$108$		0			0
$109$	−132.413	−	132.413i	−1.21480	−	1.21480i	−0.969430	−	0.245366i	$-0.921092\pi$
$109$	−132.413	−	132.413i	−1.21480	−	1.21480i	−0.245366	−	0.969430i	$-0.578908\pi$
$110$	30.5348	+	37.8566i	0.277589	+	0.344151i
$111$		0			0
$112$	9.53657	+	4.33453i	0.0851479	+	0.0387012i
$113$	−37.9551			−0.335886			−0.167943	−	0.985797i	$-0.553712\pi$
$113$	−37.9551			−0.335886			−0.167943	+	0.985797i	$0.553712\pi$
$114$		0			0
$115$	−21.0699	+	21.0699i	−0.183217	+	0.183217i
$116$	169.367	−	109.061i	1.46006	−	0.940177i
$117$		0			0
$118$	6.34219	−	59.2411i	0.0537474	−	0.502044i
$119$	−2.57649			−0.0216512
$120$		0			0
$121$			236.835i			1.95731i
$122$	−20.7004	+	193.358i	−0.169675	+	1.58490i
$123$		0			0
$124$	−178.144	−	38.5854i	−1.43665	−	0.311173i
$125$	−43.9488	−	43.9488i	−0.351591	−	0.351591i
$126$		0			0
$127$		−	96.5399i		−	0.760157i	−0.924954	−	0.380078i	$-0.875897\pi$
$127$		−	96.5399i		−	0.760157i	0.924954	−	0.380078i	$-0.124103\pi$
$128$	−127.903	+	4.97043i	−0.999246	+	0.0388315i
$129$		0			0
$130$	19.0111	+	23.5697i	0.146239	+	0.181305i
$131$	54.5082	−	54.5082i	0.416093	−	0.416093i	−0.467762	−	0.883855i	$-0.654939\pi$
$131$	54.5082	−	54.5082i	0.416093	−	0.416093i	0.883855	+	0.467762i	$0.154939\pi$
$132$		0			0
$133$	−11.0629	+	11.0629i	−0.0831801	+	0.0831801i
$134$	−190.746	−	20.4207i	−1.42348	−	0.152393i
$135$		0			0
$136$	28.1333	−	14.1299i	0.206863	−	0.103897i
$137$			25.9333i			0.189294i	0.995511	+	0.0946471i	$0.0301723\pi$
$137$			25.9333i			0.189294i	−0.995511	+	0.0946471i	$0.969828\pi$
$138$		0			0
$139$	3.64066	+	3.64066i	0.0261918	+	0.0261918i	0.720081	−	0.693890i	$-0.244104\pi$
$139$	3.64066	+	3.64066i	0.0261918	+	0.0261918i	−0.693890	+	0.720081i	$0.744104\pi$
$140$	1.82270	+	2.83059i	0.0130193	+	0.0202185i
$141$		0			0
$142$	41.8245	+	51.8534i	0.294539	+	0.365165i
$143$			222.789i			1.55797i
$144$		0			0
$145$	64.7415			0.446493
$146$	−29.0066	+	23.3964i	−0.198675	+	0.160250i
$147$		0			0
$148$	31.0937	+	48.2874i	0.210093	+	0.326266i
$149$	18.9718	−	18.9718i	0.127328	−	0.127328i	−0.640571	−	0.767899i	$-0.721302\pi$
$149$	18.9718	−	18.9718i	0.127328	−	0.127328i	0.767899	+	0.640571i	$0.221302\pi$
$150$		0			0
$151$	−103.209			−0.683503			−0.341751	−	0.939790i	$-0.611020\pi$
$151$	−103.209			−0.683503			−0.341751	+	0.939790i	$0.611020\pi$
$152$	60.1278	−	181.470i	0.395578	−	1.19388i
$153$		0			0
$154$	−2.63672	+	24.6291i	−0.0171216	+	0.159929i
$155$	−41.4230	−	41.4230i	−0.267245	−	0.267245i
$156$		0			0
$157$	88.2067	+	88.2067i	0.561826	+	0.561826i	0.929826	−	0.368000i	$-0.119957\pi$
$157$	88.2067	+	88.2067i	0.561826	+	0.561826i	−0.368000	+	0.929826i	$0.619957\pi$
$158$	9.79522	−	7.90074i	0.0619951	−	0.0500047i
$159$		0			0
$160$	−35.4260	−	20.9119i	−0.221412	−	0.130699i
$161$	−15.1754			−0.0942571
$162$		0			0
$163$	18.8038	−	18.8038i	0.115361	−	0.115361i	−0.647070	−	0.762431i	$-0.724006\pi$
$163$	18.8038	−	18.8038i	0.115361	−	0.115361i	0.762431	+	0.647070i	$0.224006\pi$
$164$	−111.284	−	24.1037i	−0.678561	−	0.146974i
$165$		0			0
$166$	−202.707	−	21.7013i	−1.22113	−	0.130731i
$167$	−267.105			−1.59943			−0.799715	−	0.600380i	$-0.795016\pi$
$167$	−267.105			−1.59943			−0.799715	+	0.600380i	$0.795016\pi$
$168$		0			0
$169$		−	30.2905i		−	0.179234i
$170$	10.0606	+	1.07706i	0.0591798	+	0.00633562i
$171$		0			0
$172$	−108.132	+	69.6293i	−0.628673	+	0.404822i
$173$	153.520	+	153.520i	0.887396	+	0.887396i	0.994272	−	0.106876i	$-0.0340849\pi$
$173$	153.520	+	153.520i	0.887396	+	0.887396i	−0.106876	+	0.994272i	$0.534085\pi$
$174$		0			0
$175$		−	15.2858i		−	0.0873476i
$176$	−106.279	−	283.391i	−0.603859	−	1.61018i
$177$		0			0
$178$	−16.5216	+	13.3262i	−0.0928179	+	0.0748661i
$179$	−123.581	+	123.581i	−0.690399	+	0.690399i	−0.962320	−	0.271921i	$-0.912341\pi$
$179$	−123.581	+	123.581i	−0.690399	+	0.690399i	0.271921	+	0.962320i	$0.412341\pi$
$180$		0			0
$181$	122.965	−	122.965i	0.679364	−	0.679364i	−0.280493	−	0.959856i	$-0.590498\pi$
$181$	122.965	−	122.965i	0.679364	−	0.679364i	0.959856	+	0.280493i	$0.0904978\pi$
$182$	−1.64163	+	15.3341i	−0.00901995	+	0.0842536i
$183$		0			0
$184$	165.704	−	83.2246i	0.900564	−	0.452307i
$185$			18.4581i			0.0997737i
$186$		0			0
$187$	52.6385	+	52.6385i	0.281489	+	0.281489i
$188$	42.1217	+	9.12342i	0.224051	+	0.0485288i
$189$		0			0
$190$	47.8228	−	38.5734i	0.251699	−	0.203018i
$191$		−	193.992i		−	1.01566i	−0.861456	−	0.507832i	$-0.830447\pi$
$191$		−	193.992i		−	1.01566i	0.861456	−	0.507832i	$-0.169553\pi$
$192$		0			0
$193$	141.555			0.733444			0.366722	−	0.930331i	$-0.380480\pi$
$193$	141.555			0.733444			0.366722	+	0.930331i	$0.380480\pi$
$194$	−180.348	−	223.593i	−0.929631	−	1.15254i
$195$		0			0
$196$	41.1279	−	189.882i	0.209836	−	0.968788i
$197$	−28.9507	+	28.9507i	−0.146958	+	0.146958i	−0.776758	−	0.629800i	$-0.783137\pi$
$197$	−28.9507	+	28.9507i	−0.146958	+	0.146958i	0.629800	+	0.776758i	$0.283137\pi$
$198$		0			0
$199$	−27.6253			−0.138821			−0.0694104	−	0.997588i	$-0.522112\pi$
$199$	−27.6253			−0.138821			−0.0694104	+	0.997588i	$0.522112\pi$
$200$	83.8302	+	166.910i	0.419151	+	0.834548i
$201$		0			0
$202$	−253.984	−	27.1908i	−1.25735	−	0.134608i
$203$	23.3147	+	23.3147i	0.114851	+	0.114851i
$204$		0			0
$205$	−25.8763	−	25.8763i	−0.126226	−	0.126226i
$206$	119.493	+	148.146i	0.580065	+	0.719156i
$207$		0			0
$208$	−66.1699	−	176.440i	−0.318124	−	0.848271i
$209$	452.039			2.16287
$210$		0			0
$211$	7.35041	−	7.35041i	0.0348361	−	0.0348361i	−0.689474	−	0.724310i	$-0.742158\pi$
$211$	7.35041	−	7.35041i	0.0348361	−	0.0348361i	0.724310	+	0.689474i	$0.242158\pi$
$212$	−127.141	−	197.446i	−0.599723	−	0.931348i
$213$		0			0
$214$	−8.20523	+	76.6435i	−0.0383422	+	0.358147i
$215$	−41.3340			−0.192251
$216$		0			0
$217$		−	29.8345i		−	0.137486i
$218$	−39.8673	+	372.392i	−0.182877	+	1.70822i
$219$		0			0
$220$	20.5915	−	95.0683i	0.0935977	−	0.432129i
$221$	32.7729	+	32.7729i	0.148294	+	0.148294i
$222$		0			0
$223$			386.106i			1.73142i	0.500549	+	0.865708i	$0.333131\pi$
$223$			386.106i			1.73142i	−0.500549	+	0.865708i	$0.666869\pi$
$224$	−5.22681	−	20.2884i	−0.0233340	−	0.0905730i
$225$		0			0
$226$	47.6579	+	59.0855i	0.210875	+	0.261440i
$227$	49.7286	−	49.7286i	0.219069	−	0.219069i	−0.589037	−	0.808106i	$-0.700493\pi$
$227$	49.7286	−	49.7286i	0.219069	−	0.219069i	0.808106	+	0.589037i	$0.200493\pi$
$228$		0			0
$229$	−191.870	+	191.870i	−0.837861	+	0.837861i	−0.988577	−	0.150716i	$-0.951842\pi$
$229$	−191.870	+	191.870i	−0.837861	+	0.837861i	0.150716	+	0.988577i	$0.451842\pi$
$230$	59.2562	+	6.34380i	0.257636	+	0.0275817i
$231$		0			0
$232$	−382.440	−	126.717i	−1.64845	−	0.546193i
$233$			298.610i			1.28159i	0.767712	+	0.640795i	$0.221395\pi$
$233$			298.610i			1.28159i	−0.767712	+	0.640795i	$0.778605\pi$
$234$		0			0
$235$	9.79435	+	9.79435i	0.0416781	+	0.0416781i
$236$	−100.185	+	64.5123i	−0.424514	+	0.273357i
$237$		0			0
$238$	3.23514	+	4.01087i	0.0135930	+	0.0168524i
$239$		−	247.352i		−	1.03495i	−0.855700	−	0.517473i	$-0.826873\pi$
$239$		−	247.352i		−	1.03495i	0.855700	−	0.517473i	$-0.173127\pi$
$240$		0			0
$241$	−220.337			−0.914260			−0.457130	−	0.889400i	$-0.651123\pi$
$241$	−220.337			−0.914260			−0.457130	+	0.889400i	$0.651123\pi$
$242$	368.686	−	297.379i	1.52350	−	1.22884i
$243$		0			0
$244$	326.997	−	210.563i	1.34015	−	0.862963i
$245$	44.1525	−	44.1525i	0.180214	−	0.180214i
$246$		0			0
$247$	281.441			1.13944
$248$	163.618	+	325.770i	0.659748	+	1.31359i
$249$		0			0
$250$	−13.2322	+	123.600i	−0.0529290	+	0.494399i
$251$	−162.716	−	162.716i	−0.648272	−	0.648272i	0.304303	−	0.952575i	$-0.401576\pi$
$251$	−162.716	−	162.716i	−0.648272	−	0.648272i	−0.952575	+	0.304303i	$0.901576\pi$
$252$		0			0
$253$	310.038	+	310.038i	1.22545	+	1.22545i
$254$	−150.286	+	121.219i	−0.591675	+	0.477240i
$255$		0			0
$256$	168.338	+	192.869i	0.657570	+	0.753394i
$257$	−101.165			−0.393637			−0.196819	−	0.980440i	$-0.563061\pi$
$257$	−101.165			−0.393637			−0.196819	+	0.980440i	$0.563061\pi$
$258$		0			0
$259$	−6.64713	+	6.64713i	−0.0256646	+	0.0256646i
$260$	12.8203	−	59.1899i	0.0493090	−	0.227653i
$261$		0			0
$262$	−153.296	−	16.4115i	−0.585101	−	0.0626393i
$263$	323.635			1.23055			0.615276	−	0.788312i	$-0.289045\pi$
$263$	323.635			1.23055			0.615276	+	0.788312i	$0.289045\pi$
$264$		0			0
$265$		−	75.4747i		−	0.284810i
$266$	31.1130	+	3.33087i	0.116966	+	0.0125220i
$267$		0			0
$268$	207.718	+	322.579i	0.775068	+	1.20365i
$269$	−1.51275	−	1.51275i	−0.00562361	−	0.00562361i	0.704289	−	0.709913i	$-0.251266\pi$
$269$	−1.51275	−	1.51275i	−0.00562361	−	0.00562361i	−0.709913	+	0.704289i	$0.751266\pi$
$270$		0			0
$271$			166.098i			0.612909i	0.951885	+	0.306454i	$0.0991427\pi$
$271$			166.098i			0.612909i	−0.951885	+	0.306454i	$0.900857\pi$
$272$	−57.3216	−	26.0536i	−0.210741	−	0.0957854i
$273$		0			0
$274$	40.3709	−	32.5628i	0.147339	−	0.118842i
$275$	−312.294	+	312.294i	−1.13562	+	1.13562i
$276$		0			0
$277$	317.830	−	317.830i	1.14740	−	1.14740i	0.160338	−	0.987062i	$-0.448741\pi$
$277$	317.830	−	317.830i	1.14740	−	1.14740i	0.987062	−	0.160338i	$-0.0512586\pi$
$278$	1.09614	−	10.2388i	0.00394296	−	0.0368304i
$279$		0			0
$280$	2.11778	−	6.39163i	0.00756352	−	0.0228272i
$281$		−	402.790i		−	1.43342i	−0.697374	−	0.716708i	$-0.745648\pi$
$281$		−	402.790i		−	1.43342i	0.697374	−	0.716708i	$-0.254352\pi$
$282$		0			0
$283$	−192.406	−	192.406i	−0.679881	−	0.679881i	0.280092	−	0.959973i	$-0.409635\pi$
$283$	−192.406	−	192.406i	−0.679881	−	0.679881i	−0.959973	+	0.280092i	$0.909635\pi$
$284$	28.2048	−	130.218i	0.0993128	−	0.458515i
$285$		0			0
$286$	346.821	−	279.743i	1.21266	−	0.978121i
$287$		−	18.6371i		−	0.0649378i
$288$		0			0
$289$	−273.513			−0.946413
$290$	−81.2918	−	100.784i	−0.280317	−	0.347532i
$291$		0			0
$292$	72.8434	+	15.7777i	0.249464	+	0.0540331i
$293$	75.3645	−	75.3645i	0.257217	−	0.257217i	−0.566704	−	0.823921i	$-0.691782\pi$
$293$	75.3645	−	75.3645i	0.257217	−	0.257217i	0.823921	+	0.566704i	$0.191782\pi$
$294$		0			0
$295$	−38.2964			−0.129818
$296$	36.1276	−	109.036i	0.122053	−	0.368364i
$297$		0			0
$298$	−53.3556	−	5.71210i	−0.179046	−	0.0191681i
$299$	193.031	+	193.031i	0.645588	+	0.645588i
$300$		0			0
$301$	−14.8852	−	14.8852i	−0.0494524	−	0.0494524i
$302$	129.593	+	160.667i	0.429116	+	0.532011i
$303$		0			0
$304$	−357.997	+	134.258i	−1.17762	+	0.441640i
$305$	124.996			0.409824
$306$		0			0
$307$	−111.544	+	111.544i	−0.363337	+	0.363337i	−0.865040	−	0.501703i	$-0.832707\pi$
$307$	−111.544	+	111.544i	−0.363337	+	0.363337i	0.501703	+	0.865040i	$0.332707\pi$
$308$	41.6513	−	26.8205i	0.135232	−	0.0870797i
$309$		0			0
$310$	−12.4718	+	116.496i	−0.0402315	+	0.375794i
$311$	224.484			0.721813			0.360906	−	0.932602i	$-0.382467\pi$
$311$	224.484			0.721813			0.360906	+	0.932602i	$0.382467\pi$
$312$		0			0
$313$		−	488.339i		−	1.56019i	−0.625661	−	0.780095i	$-0.715171\pi$
$313$		−	488.339i		−	1.56019i	0.625661	−	0.780095i	$-0.284829\pi$
$314$	26.5575	−	248.069i	0.0845781	−	0.790027i
$315$		0			0
$316$	−24.5985	−	5.32795i	−0.0778433	−	0.0168606i
$317$	−257.361	−	257.361i	−0.811863	−	0.811863i	0.173050	−	0.984913i	$-0.444638\pi$
$317$	−257.361	−	257.361i	−0.811863	−	0.811863i	−0.984913	+	0.173050i	$0.944638\pi$
$318$		0			0
$319$		−	952.652i		−	2.98637i
$320$	11.9282	+	81.4061i	0.0372757	+	0.254394i
$321$		0			0
$322$	19.0548	+	23.6238i	0.0591763	+	0.0733659i
$323$	66.4962	−	66.4962i	0.205871	−	0.205871i
$324$		0			0
$325$	−194.436	+	194.436i	−0.598263	+	0.598263i
$326$	−52.8829	−	5.66150i	−0.162218	−	0.0173666i
$327$		0			0
$328$	102.209	+	203.503i	0.311614	+	0.620437i
$329$			7.05427i			0.0214416i
$330$		0			0
$331$	−123.553	−	123.553i	−0.373271	−	0.373271i	0.495396	−	0.868667i	$-0.335023\pi$
$331$	−123.553	−	123.553i	−0.373271	−	0.373271i	−0.868667	+	0.495396i	$0.835023\pi$
$332$	220.744	+	342.807i	0.664891	+	1.03255i
$333$		0			0
$334$	335.387	+	415.807i	1.00415	+	1.24493i
$335$			123.307i			0.368082i
$336$		0			0
$337$	−246.234			−0.730665			−0.365333	−	0.930877i	$-0.619045\pi$
$337$	−246.234			−0.730665			−0.365333	+	0.930877i	$0.619045\pi$
$338$	−47.1538	+	38.0339i	−0.139508	+	0.112526i
$339$		0			0
$340$	−10.9557	−	17.0139i	−0.0322228	−	0.0500408i
$341$	−609.528	+	609.528i	−1.78747	+	1.78747i
$342$		0			0
$343$	63.8813			0.186243
$344$	244.168	+	80.9018i	0.709790	+	0.235180i
$345$		0			0
$346$	46.2221	−	431.752i	0.133590	−	1.24784i
$347$	123.212	+	123.212i	0.355076	+	0.355076i	0.861994	−	0.506918i	$-0.169215\pi$
$347$	123.212	+	123.212i	0.355076	+	0.355076i	−0.506918	+	0.861994i	$0.669215\pi$
$348$		0			0
$349$	115.371	+	115.371i	0.330575	+	0.330575i	0.852805	−	0.522230i	$-0.174900\pi$
$349$	115.371	+	115.371i	0.330575	+	0.330575i	−0.522230	+	0.852805i	$0.674900\pi$
$350$	−23.7957	+	19.1934i	−0.0679878	+	0.0548384i
$351$		0			0
$352$	−307.712	+	521.283i	−0.874183	+	1.48092i
$353$	−650.544			−1.84290			−0.921451	−	0.388495i	$-0.872995\pi$
$353$	−650.544			−1.84290			−0.921451	+	0.388495i	$0.872995\pi$
$354$		0			0
$355$	30.2790	−	30.2790i	0.0852930	−	0.0852930i
$356$	41.4902	+	8.98665i	0.116546	+	0.0252434i
$357$		0			0
$358$	347.555	+	37.2083i	0.970824	+	0.103934i
$359$	−94.4878			−0.263197			−0.131599	−	0.991303i	$-0.542011\pi$
$359$	−94.4878			−0.263197			−0.131599	+	0.991303i	$0.542011\pi$
$360$		0			0
$361$		−	210.044i		−	0.581838i
$362$	−345.821	−	37.0226i	−0.955306	−	0.102272i
$363$		0			0
$364$	25.9323	−	16.6986i	0.0712425	−	0.0458752i
$365$	16.9379	+	16.9379i	0.0464053	+	0.0464053i
$366$		0			0
$367$			131.379i			0.357982i	0.983851	+	0.178991i	$0.0572832\pi$
$367$			131.379i			0.357982i	−0.983851	+	0.178991i	$0.942717\pi$
$368$	−337.621	−	153.455i	−0.917449	−	0.416996i
$369$		0			0
$370$	28.7341	−	23.1767i	0.0776598	−	0.0626398i
$371$	27.1799	−	27.1799i	0.0732612	−	0.0732612i
$372$		0			0
$373$	−275.796	+	275.796i	−0.739400	+	0.739400i	−0.972462	−	0.233062i	$-0.925126\pi$
$373$	−275.796	+	275.796i	−0.739400	+	0.739400i	0.233062	+	0.972462i	$0.425126\pi$
$374$	15.8486	−	148.038i	0.0423758	−	0.395824i
$375$		0			0
$376$	−38.6869	−	77.0273i	−0.102891	−	0.204860i
$377$		−	593.125i		−	1.57328i
$378$		0			0
$379$	−13.0427	−	13.0427i	−0.0344135	−	0.0344135i	0.689691	−	0.724104i	$-0.257747\pi$
$379$	−13.0427	−	13.0427i	−0.0344135	−	0.0344135i	−0.724104	+	0.689691i	$0.757747\pi$
$380$	−120.096	−	26.0124i	−0.316042	−	0.0684538i
$381$		0			0
$382$	−301.991	+	243.583i	−0.790553	+	0.637653i
$383$		−	121.974i		−	0.318470i	−0.987241	−	0.159235i	$-0.949097\pi$
$383$		−	121.974i		−	0.318470i	0.987241	−	0.159235i	$-0.0509027\pi$
$384$		0			0
$385$	15.9214			0.0413544
$386$	−177.741	−	220.361i	−0.460470	−	0.570883i
$387$		0			0
$388$	−121.620	+	561.504i	−0.313454	+	1.44717i
$389$	233.267	−	233.267i	0.599659	−	0.599659i	−0.340563	−	0.940222i	$-0.610618\pi$
$389$	233.267	−	233.267i	0.599659	−	0.599659i	0.940222	+	0.340563i	$0.110618\pi$
$390$		0			0
$391$	91.2149			0.233286
$392$	−347.235	+	174.399i	−0.885804	+	0.444894i
$393$		0			0
$394$	81.4198	+	8.71657i	0.206649	+	0.0221233i
$395$	−5.71977	−	5.71977i	−0.0144804	−	0.0144804i
$396$		0			0
$397$	−83.7693	−	83.7693i	−0.211006	−	0.211006i	0.593689	−	0.804695i	$-0.297671\pi$
$397$	−83.7693	−	83.7693i	−0.211006	−	0.211006i	−0.804695	+	0.593689i	$0.797671\pi$
$398$	34.6874	+	43.0049i	0.0871542	+	0.108053i
$399$		0			0
$400$	154.571	−	340.078i	0.386428	−	0.850195i
$401$	−589.134			−1.46916			−0.734581	−	0.678521i	$-0.762621\pi$
$401$	−589.134			−1.46916			−0.734581	+	0.678521i	$0.762621\pi$
$402$		0			0
$403$	−379.494	+	379.494i	−0.941673	+	0.941673i
$404$	276.583	+	429.524i	0.684612	+	1.06318i
$405$		0			0
$406$	7.01965	−	65.5691i	0.0172898	−	0.161500i
$407$	271.606			0.667337
$408$		0			0
$409$			449.285i			1.09850i	0.835659	+	0.549248i	$0.185086\pi$
$409$			449.285i			1.09850i	−0.835659	+	0.549248i	$0.814914\pi$
$410$	−7.79092	+	72.7735i	−0.0190023	+	0.177496i
$411$		0			0
$412$	80.5818	−	372.036i	0.195587	−	0.902999i
$413$	−13.7913	−	13.7913i	−0.0333929	−	0.0333929i
$414$		0			0
$415$			131.040i			0.315759i
$416$	−191.583	+	324.553i	−0.460536	+	0.780175i
$417$		0			0
$418$	−567.597	−	703.698i	−1.35789	−	1.68349i
$419$	218.639	−	218.639i	0.521811	−	0.521811i	−0.396307	−	0.918118i	$-0.629708\pi$
$419$	218.639	−	218.639i	0.521811	−	0.521811i	0.918118	+	0.396307i	$0.129708\pi$
$420$		0			0
$421$	−61.2101	+	61.2101i	−0.145392	+	0.145392i	−0.776056	−	0.630664i	$-0.782783\pi$
$421$	−61.2101	+	61.2101i	−0.145392	+	0.145392i	0.630664	+	0.776056i	$0.282783\pi$
$422$	−20.6720	−	2.21308i	−0.0489857	−	0.00524427i
$423$		0			0
$424$	−147.725	+	445.844i	−0.348407	+	1.05152i
$425$			91.8787i			0.216185i
$426$		0			0
$427$	45.0136	+	45.0136i	0.105418	+	0.105418i
$428$	129.615	−	83.4631i	0.302839	−	0.195007i
$429$		0			0
$430$	51.9004	+	64.3454i	0.120699	+	0.149640i
$431$			501.119i			1.16269i	0.813657	+	0.581345i	$0.197473\pi$
$431$			501.119i			1.16269i	−0.813657	+	0.581345i	$0.802527\pi$
$432$		0			0
$433$	75.5505			0.174482			0.0872408	−	0.996187i	$-0.472195\pi$
$433$	75.5505			0.174482			0.0872408	+	0.996187i	$0.472195\pi$
$434$	−46.4439	+	37.4612i	−0.107014	+	0.0863162i
$435$		0			0
$436$	629.769	−	405.527i	1.44442	−	0.930108i
$437$	391.659	−	391.659i	0.896245	−	0.896245i
$438$		0			0
$439$	717.251			1.63383			0.816915	−	0.576758i	$-0.195682\pi$
$439$	717.251			1.63383			0.816915	+	0.576758i	$0.195682\pi$
$440$	−173.850	+	87.3160i	−0.395114	+	0.198446i
$441$		0			0
$442$	9.86737	−	92.1692i	0.0223244	−	0.208528i
$443$	−299.093	−	299.093i	−0.675153	−	0.675153i	0.283746	−	0.958899i	$-0.408423\pi$
$443$	−299.093	−	299.093i	−0.675153	−	0.675153i	−0.958899	+	0.283746i	$0.908423\pi$
$444$		0			0
$445$	9.64753	+	9.64753i	0.0216798	+	0.0216798i
$446$	601.059	−	484.809i	1.34767	−	1.08702i
$447$		0			0
$448$	−25.0203	+	33.6115i	−0.0558489	+	0.0750257i
$449$	44.5560			0.0992339			0.0496170	−	0.998768i	$-0.484200\pi$
$449$	44.5560			0.0992339			0.0496170	+	0.998768i	$0.484200\pi$
$450$		0			0
$451$	−380.763	+	380.763i	−0.844263	+	0.844263i
$452$	32.1386	−	148.380i	0.0711031	−	0.328274i
$453$		0			0
$454$	−139.855	−	14.9725i	−0.308050	−	0.0329790i
$455$	9.91275			0.0217863
$456$		0			0
$457$		−	641.227i		−	1.40312i	−0.712609	−	0.701562i	$-0.752486\pi$
$457$		−	641.227i		−	1.40312i	0.712609	−	0.701562i	$-0.247514\pi$
$458$	539.607	+	57.7689i	1.17818	+	0.126133i
$459$		0			0
$460$	−64.5287	−	100.211i	−0.140280	−	0.217850i
$461$	393.690	+	393.690i	0.853991	+	0.853991i	0.990622	−	0.136631i	$-0.0436273\pi$
$461$	393.690	+	393.690i	0.853991	+	0.853991i	−0.136631	+	0.990622i	$0.543627\pi$
$462$		0			0
$463$		−	395.861i		−	0.854991i	−0.904018	−	0.427495i	$-0.859396\pi$
$463$		−	395.861i		−	0.854991i	0.904018	−	0.427495i	$-0.140604\pi$
$464$	282.944	+	754.462i	0.609792	+	1.62600i
$465$		0			0
$466$	464.853	−	374.946i	0.997538	−	0.804606i
$467$	83.1457	−	83.1457i	0.178042	−	0.178042i	−0.612460	−	0.790502i	$-0.709820\pi$
$467$	83.1457	−	83.1457i	0.178042	−	0.178042i	0.790502	+	0.612460i	$0.209820\pi$
$468$		0			0
$469$	−44.4054	+	44.4054i	−0.0946810	+	0.0946810i
$470$	2.94891	−	27.5452i	0.00627428	−	0.0586068i
$471$		0			0
$472$	226.224	+	74.9564i	0.479288	+	0.158806i
$473$			608.217i			1.28587i
$474$		0			0
$475$	394.509	+	394.509i	0.830546	+	0.830546i
$476$	2.18165	−	10.0724i	0.00458330	−	0.0211605i
$477$		0			0
$478$	−385.058	+	310.584i	−0.805560	+	0.649758i
$479$		−	430.043i		−	0.897793i	−0.893584	−	0.448896i	$-0.851817\pi$
$479$		−	430.043i		−	0.897793i	0.893584	−	0.448896i	$-0.148183\pi$
$480$		0			0
$481$	169.103			0.351565
$482$	276.663	+	343.003i	0.573989	+	0.711624i
$483$		0			0
$484$	−925.871	−	200.541i	−1.91296	−	0.414340i
$485$	−130.564	+	130.564i	−0.269204	+	0.269204i
$486$		0			0
$487$	573.790			1.17821			0.589107	−	0.808055i	$-0.299480\pi$
$487$	573.790			1.17821			0.589107	+	0.808055i	$0.299480\pi$
$488$	−738.376	−	244.652i	−1.51307	−	0.501335i
$489$		0			0
$490$	−124.172	−	13.2936i	−0.253413	−	0.0271297i
$491$	489.133	+	489.133i	0.996197	+	0.996197i	0.999993	−	0.00379588i	$-0.00120827\pi$
$491$	489.133	+	489.133i	0.996197	+	0.996197i	−0.00379588	+	0.999993i	$0.501208\pi$
$492$		0			0
$493$	−140.138	−	140.138i	−0.284255	−	0.284255i
$494$	−353.388	−	438.125i	−0.715360	−	0.886893i
$495$		0			0
$496$	301.688	−	663.755i	0.608242	−	1.33822i
$497$	21.8081			0.0438795
$498$		0			0
$499$	260.469	−	260.469i	0.521982	−	0.521982i	−0.396188	−	0.918170i	$-0.629667\pi$
$499$	260.469	−	260.469i	0.521982	−	0.521982i	0.918170	+	0.396188i	$0.129667\pi$
$500$	209.025	−	134.598i	0.418050	−	0.269195i
$501$		0			0
$502$	−48.9911	+	457.616i	−0.0975919	+	0.911586i
$503$	975.416			1.93920			0.969598	−	0.244701i	$-0.0786900\pi$
$503$	975.416			1.93920			0.969598	+	0.244701i	$0.0786900\pi$
$504$		0			0
$505$			164.188i			0.325124i
$506$	93.3472	−	871.938i	0.184481	−	1.72320i
$507$		0			0
$508$	377.408	+	81.7454i	0.742929	+	0.160916i
$509$	420.191	+	420.191i	0.825523	+	0.825523i	0.986894	−	0.161371i	$-0.0515916\pi$
$509$	420.191	+	420.191i	0.825523	+	0.825523i	−0.161371	+	0.986894i	$0.551592\pi$
$510$		0			0
$511$			12.1994i			0.0238735i
$512$	88.8714	−	504.228i	0.173577	−	0.984820i
$513$		0			0
$514$	127.026	+	157.485i	0.247133	+	0.306391i
$515$	86.5077	−	86.5077i	0.167976	−	0.167976i
$516$		0			0
$517$	144.121	−	144.121i	0.278764	−	0.278764i
$518$	18.6941	+	2.00134i	0.0360890	+	0.00386359i
$519$		0			0
$520$	−108.240	+	54.3633i	−0.208153	+	0.104545i
$521$		−	396.333i		−	0.760716i	−0.924839	−	0.380358i	$-0.875801\pi$
$521$		−	396.333i		−	0.760716i	0.924839	−	0.380358i	$-0.124199\pi$
$522$		0			0
$523$	564.600	+	564.600i	1.07954	+	1.07954i	0.996550	+	0.0829913i	$0.0264474\pi$
$523$	564.600	+	564.600i	1.07954	+	1.07954i	0.0829913	+	0.996550i	$0.473553\pi$
$524$	166.937	+	259.246i	0.318581	+	0.494745i
$525$		0			0
$526$	−406.368	−	503.809i	−0.772563	−	0.957812i
$527$			179.326i			0.340278i
$528$		0			0
$529$	8.25115			0.0155976
$530$	−117.493	+	94.7688i	−0.221685	+	0.178809i
$531$		0			0
$532$	−33.8813	−	52.6165i	−0.0636867	−	0.0989032i
$533$	−237.064	+	237.064i	−0.444773	+	0.444773i
$534$		0			0
$535$	49.5461			0.0926095
$536$	241.346	−	728.401i	0.450273	−	1.35896i
$537$		0			0
$538$	−0.455463	+	4.25439i	−0.000846586	+	0.00790779i
$539$	−649.691	−	649.691i	−1.20536	−	1.20536i
$540$		0			0
$541$	−29.5601	−	29.5601i	−0.0546398	−	0.0546398i	0.679259	−	0.733899i	$-0.262301\pi$
$541$	−29.5601	−	29.5601i	−0.0546398	−	0.0546398i	−0.733899	+	0.679259i	$0.762301\pi$
$542$	258.568	−	208.559i	0.477064	−	0.384795i
$543$		0			0
$544$	31.4169	+	121.948i	0.0577516	+	0.224168i
$545$	240.733			0.441711
$546$		0			0
$547$	−138.608	+	138.608i	−0.253397	+	0.253397i	−0.822362	−	0.568965i	$-0.807344\pi$
$547$	−138.608	+	138.608i	−0.253397	+	0.253397i	0.568965	+	0.822362i	$0.307344\pi$
$548$	−101.382	−	21.9591i	−0.185004	−	0.0400713i
$549$		0			0
$550$	878.283	+	94.0265i	1.59688	+	0.170957i
$551$	−1203.45			−2.18412
$552$		0			0
$553$		−	4.11960i		−	0.00744955i
$554$	−893.851	−	95.6932i	−1.61345	−	0.172731i
$555$		0			0
$556$	−17.3154	+	11.1499i	−0.0311428	+	0.0200538i
$557$	−60.4400	−	60.4400i	−0.108510	−	0.108510i	0.650767	−	0.759277i	$-0.274447\pi$
$557$	−60.4400	−	60.4400i	−0.108510	−	0.108510i	−0.759277	+	0.650767i	$0.774447\pi$
$558$		0			0
$559$			378.678i			0.677421i
$560$	−12.6091	+	4.72877i	−0.0225163	+	0.00844423i
$561$		0			0
$562$	−627.031	+	505.758i	−1.11571	+	0.899924i
$563$	−267.325	+	267.325i	−0.474822	+	0.474822i	−0.903471	−	0.428649i	$-0.858990\pi$
$563$	−267.325	+	267.325i	−0.474822	+	0.474822i	0.428649	+	0.903471i	$0.358990\pi$
$564$		0			0
$565$	34.5021	−	34.5021i	0.0610656	−	0.0610656i
$566$	−57.9303	+	541.115i	−0.102350	+	0.956034i
$567$		0			0
$568$	−238.128	+	119.600i	−0.419240	+	0.210563i
$569$			315.715i			0.554859i	0.960746	+	0.277429i	$0.0894825\pi$
$569$			315.715i			0.554859i	−0.960746	+	0.277429i	$0.910518\pi$
$570$		0			0
$571$	−670.572	−	670.572i	−1.17438	−	1.17438i	−0.981154	−	0.193228i	$-0.938104\pi$
$571$	−670.572	−	670.572i	−1.17438	−	1.17438i	−0.193228	−	0.981154i	$-0.561896\pi$
$572$	−870.962	−	188.648i	−1.52266	−	0.329803i
$573$		0			0
$574$	−29.0128	+	23.4015i	−0.0505449	+	0.0407691i
$575$			541.161i			0.941149i
$576$		0			0
$577$	413.628			0.716859			0.358430	−	0.933557i	$-0.383312\pi$
$577$	413.628			0.716859			0.358430	+	0.933557i	$0.383312\pi$
$578$	343.434	+	425.784i	0.594176	+	0.736650i
$579$		0			0
$580$	−54.8200	+	253.097i	−0.0945173	+	0.436374i
$581$	−47.1900	+	47.1900i	−0.0812220	+	0.0812220i
$582$		0			0
$583$	−1110.59			−1.90495
$584$	−66.9035	−	133.208i	−0.114561	−	0.228095i
$585$		0			0
$586$	−211.952	−	22.6910i	−0.361693	−	0.0387218i
$587$	420.085	+	420.085i	0.715647	+	0.715647i	0.967711	−	0.252064i	$-0.0811093\pi$
$587$	420.085	+	420.085i	0.715647	+	0.715647i	−0.252064	+	0.967711i	$0.581109\pi$
$588$		0			0
$589$	769.993	+	769.993i	1.30729	+	1.30729i
$590$	48.0863	+	59.6167i	0.0815023	+	0.101045i
$591$		0			0
$592$	−215.101	+	80.6687i	−0.363347	+	0.136265i
$593$	740.798			1.24924			0.624619	−	0.780930i	$-0.285254\pi$
$593$	740.798			1.24924			0.624619	+	0.780930i	$0.285254\pi$
$594$		0			0
$595$	2.34209	−	2.34209i	0.00393628	−	0.00393628i
$596$	58.1031	+	90.2320i	0.0974885	+	0.151396i
$597$		0			0
$598$	58.1183	−	542.872i	0.0971878	−	0.907812i
$599$	−435.161			−0.726479			−0.363240	−	0.931696i	$-0.618329\pi$
$599$	−435.161			−0.726479			−0.363240	+	0.931696i	$0.618329\pi$
$600$		0			0
$601$			380.001i			0.632280i	0.948712	+	0.316140i	$0.102387\pi$
$601$			380.001i			0.632280i	−0.948712	+	0.316140i	$0.897613\pi$
$602$	−4.48167	+	41.8624i	−0.00744463	+	0.0695388i
$603$		0			0
$604$	87.3924	−	403.480i	0.144689	−	0.668013i
$605$	−215.288	−	215.288i	−0.355849	−	0.355849i
$606$		0			0
$607$			181.813i			0.299527i	0.988722	+	0.149763i	$0.0478512\pi$
$607$			181.813i			0.299527i	−0.988722	+	0.149763i	$0.952149\pi$
$608$	658.517	+	388.721i	1.08309	+	0.639344i
$609$		0			0
$610$	−156.950	−	194.584i	−0.257295	−	0.318990i
$611$	89.7303	−	89.7303i	0.146858	−	0.146858i
$612$		0			0
$613$	55.1479	−	55.1479i	0.0899640	−	0.0899640i	−0.660693	−	0.750657i	$-0.729737\pi$
$613$	55.1479	−	55.1479i	0.0899640	−	0.0899640i	0.750657	+	0.660693i	$0.229737\pi$
$614$	313.703	+	33.5841i	0.510917	+	0.0546973i
$615$		0			0
$616$	−94.0510	−	31.1626i	−0.152680	−	0.0505886i
$617$		−	579.674i		−	0.939504i	−0.882798	−	0.469752i	$-0.844343\pi$
$617$		−	579.674i		−	0.939504i	0.882798	−	0.469752i	$-0.155657\pi$
$618$		0			0
$619$	91.1070	+	91.1070i	0.147184	+	0.147184i	0.776859	−	0.629675i	$-0.216812\pi$
$619$	91.1070	+	91.1070i	0.147184	+	0.147184i	−0.629675	+	0.776859i	$0.716812\pi$
$620$	197.012	−	126.862i	0.317761	−	0.204616i
$621$		0			0
$622$	−281.870	−	349.458i	−0.453167	−	0.561830i
$623$			6.94852i			0.0111533i
$624$		0			0
$625$	−503.783			−0.806053
$626$	−760.208	+	613.177i	−1.21439	+	0.979516i
$627$		0			0
$628$	−419.520	+	270.141i	−0.668025	+	0.430162i
$629$	39.9540	−	39.9540i	0.0635199	−	0.0635199i
$630$		0			0
$631$	−693.474			−1.09901			−0.549504	−	0.835491i	$-0.685183\pi$
$631$	−693.474			−1.09901			−0.549504	+	0.835491i	$0.685183\pi$
$632$	22.5926	+	44.9829i	0.0357478	+	0.0711755i
$633$		0			0
$634$	−77.4869	+	723.790i	−0.122219	+	1.14162i
$635$	87.7570	+	87.7570i	0.138200	+	0.138200i
$636$		0			0
$637$	−404.500	−	404.500i	−0.635007	−	0.635007i
$638$	−1483.01	+	1196.19i	−2.32447	+	1.87490i
$639$		0			0
$640$	111.749	−	120.785i	0.174608	−	0.188727i
$641$	218.329			0.340607			0.170304	−	0.985392i	$-0.445525\pi$
$641$	218.329			0.340607			0.170304	+	0.985392i	$0.445525\pi$
$642$		0			0
$643$	887.430	−	887.430i	1.38014	−	1.38014i	0.535787	−	0.844353i	$-0.320015\pi$
$643$	887.430	−	887.430i	1.38014	−	1.38014i	0.844353	−	0.535787i	$-0.179985\pi$
$644$	12.8498	−	59.3259i	0.0199531	−	0.0921210i
$645$		0			0
$646$	−187.011	−	20.0209i	−0.289491	−	0.0309921i
$647$	223.177			0.344941			0.172470	−	0.985015i	$-0.444825\pi$
$647$	223.177			0.344941			0.172470	+	0.985015i	$0.444825\pi$
$648$		0			0
$649$			563.520i			0.868290i
$650$	546.822	+	58.5413i	0.841265	+	0.0900635i
$651$		0			0
$652$	57.5884	+	89.4327i	0.0883258	+	0.137167i
$653$	−539.691	−	539.691i	−0.826479	−	0.826479i	0.160549	−	0.987028i	$-0.448674\pi$
$653$	−539.691	−	539.691i	−0.826479	−	0.826479i	−0.987028	+	0.160549i	$0.948674\pi$
$654$		0			0
$655$			99.0983i			0.151295i
$656$	188.460	−	414.638i	0.287286	−	0.632070i
$657$		0			0
$658$	10.9815	−	8.85760i	0.0166892	−	0.0134614i
$659$	−625.166	+	625.166i	−0.948659	+	0.948659i	−0.998745	−	0.0500862i	$-0.984050\pi$
$659$	−625.166	+	625.166i	−0.948659	+	0.948659i	0.0500862	+	0.998745i	$0.484050\pi$
$660$		0			0
$661$	−326.893	+	326.893i	−0.494544	+	0.494544i	−0.909734	−	0.415191i	$-0.863715\pi$
$661$	−326.893	+	326.893i	−0.494544	+	0.494544i	0.415191	+	0.909734i	$0.363715\pi$
$662$	−37.1996	+	347.474i	−0.0561928	+	0.524886i
$663$		0			0
$664$	256.481	−	774.078i	0.386266	−	1.16578i
$665$		−	20.1129i		−	0.0302450i
$666$		0			0
$667$	−825.404	−	825.404i	−1.23749	−	1.23749i
$668$	226.172	−	1044.21i	0.338581	−	1.56318i
$669$		0			0
$670$	191.955	−	154.829i	0.286500	−	0.231089i
$671$		−	1839.28i		−	2.74111i
$672$		0			0
$673$	422.147			0.627262			0.313631	−	0.949545i	$-0.398455\pi$
$673$	422.147			0.627262			0.313631	+	0.949545i	$0.398455\pi$
$674$	309.181	+	383.318i	0.458725	+	0.568720i
$675$		0			0
$676$	118.416	+	25.6486i	0.175172	+	0.0379417i
$677$	126.017	−	126.017i	0.186140	−	0.186140i	−0.607885	−	0.794025i	$-0.707982\pi$
$677$	126.017	−	126.017i	0.186140	−	0.186140i	0.794025	+	0.607885i	$0.207982\pi$
$678$		0			0
$679$	−94.0372			−0.138494
$680$	−12.7294	+	38.4183i	−0.0187197	+	0.0564974i
$681$		0			0
$682$	1714.21	+	183.518i	2.51350	+	0.269089i
$683$	−621.906	−	621.906i	−0.910551	−	0.910551i	0.0857647	−	0.996315i	$-0.472667\pi$
$683$	−621.906	−	621.906i	−0.910551	−	0.910551i	−0.996315	+	0.0857647i	$0.972667\pi$
$684$		0			0
$685$	−23.5740	−	23.5740i	−0.0344145	−	0.0344145i
$686$	−80.2117	−	99.4452i	−0.116927	−	0.144964i
$687$		0			0
$688$	−180.644	−	481.684i	−0.262564	−	0.700122i
$689$	−691.456			−1.00357
$690$		0			0
$691$	−403.376	+	403.376i	−0.583758	+	0.583758i	−0.935934	−	0.352176i	$-0.885442\pi$
$691$	−403.376	+	403.376i	−0.583758	+	0.583758i	0.352176	+	0.935934i	$0.385442\pi$
$692$	−730.154	+	470.168i	−1.05514	+	0.679434i
$693$		0			0
$694$	37.0969	−	346.515i	0.0534537	−	0.499301i
$695$	−6.61889			−0.00952359
$696$		0			0
$697$			112.022i			0.160721i
$698$	34.7361	−	324.463i	0.0497652	−	0.464847i
$699$		0			0
$700$	59.7576	+	12.9433i	0.0853680	+	0.0184904i
$701$	−466.593	−	466.593i	−0.665611	−	0.665611i	0.291086	−	0.956697i	$-0.405983\pi$
$701$	−466.593	−	466.593i	−0.665611	−	0.665611i	−0.956697	+	0.291086i	$0.905983\pi$
$702$		0			0
$703$		−	343.109i		−	0.488065i
$704$	1197.87	−	175.521i	1.70152	−	0.249319i
$705$		0			0
$706$	816.847	+	1012.72i	1.15701	+	1.43444i
$707$	−59.1272	+	59.1272i	−0.0836311	+	0.0836311i
$708$		0			0
$709$	822.764	−	822.764i	1.16046	−	1.16046i	0.176081	−	0.984376i	$-0.443658\pi$
$709$	822.764	−	822.764i	1.16046	−	1.16046i	0.984376	−	0.176081i	$-0.0563422\pi$
$710$	−85.1554	−	9.11650i	−0.119937	−	0.0128401i
$711$		0			0
$712$	−38.1069	−	75.8726i	−0.0535210	−	0.106563i
$713$			1056.22i			1.48138i
$714$		0			0
$715$	−202.521	−	202.521i	−0.283246	−	0.283246i
$716$	−378.480	−	587.766i	−0.528603	−	0.820902i
$717$		0			0
$718$	118.642	+	147.091i	0.165240	+	0.204862i
$719$			710.142i			0.987681i	0.869553	+	0.493840i	$0.164407\pi$
$719$			710.142i			0.987681i	−0.869553	+	0.493840i	$0.835593\pi$
$720$		0			0
$721$	62.3062			0.0864164
$722$	−326.979	+	263.738i	−0.452879	+	0.365289i
$723$		0			0
$724$	376.592	+	584.833i	0.520154	+	0.807781i
$725$	831.411	−	831.411i	1.14677	−	1.14677i
$726$		0			0
$727$	−214.095			−0.294490			−0.147245	−	0.989100i	$-0.547041\pi$
$727$	−214.095			−0.294490			−0.147245	+	0.989100i	$0.547041\pi$
$728$	−58.5565	−	19.4019i	−0.0804347	−	0.0266510i
$729$		0			0
$730$	5.09972	−	47.6355i	0.00698592	−	0.0652541i
$731$	89.4704	+	89.4704i	0.122395	+	0.122395i
$732$		0			0
$733$	−96.1768	−	96.1768i	−0.131210	−	0.131210i	0.638452	−	0.769662i	$-0.279575\pi$
$733$	−96.1768	−	96.1768i	−0.131210	−	0.131210i	−0.769662	+	0.638452i	$0.779575\pi$
$734$	204.521	−	164.965i	0.278638	−	0.224747i
$735$		0			0
$736$	185.044	+	718.265i	0.251418	+	0.975903i
$737$	1814.43			2.46192
$738$		0			0
$739$	885.341	−	885.341i	1.19803	−	1.19803i	0.223268	−	0.974757i	$-0.428327\pi$
$739$	885.341	−	885.341i	1.19803	−	1.19803i	0.974757	−	0.223268i	$-0.0716726\pi$
$740$	−72.1593	−	15.6295i	−0.0975125	−	0.0211209i
$741$		0			0
$742$	−76.4396	−	8.18341i	−0.103018	−	0.0110289i
$743$	−906.258			−1.21973			−0.609864	−	0.792506i	$-0.708776\pi$
$743$	−906.258			−1.21973			−0.609864	+	0.792506i	$0.708776\pi$
$744$		0			0
$745$			34.4917i			0.0462976i
$746$	775.637	+	83.0376i	1.03973	+	0.111310i
$747$		0			0
$748$	−250.354	+	161.211i	−0.334698	+	0.215522i
$749$	17.8425	+	17.8425i	0.0238218	+	0.0238218i
$750$		0			0
$751$			1147.02i			1.52732i	0.645618	+	0.763661i	$0.276600\pi$
$751$			1147.02i			1.52732i	−0.645618	+	0.763661i	$0.723400\pi$
$752$	−71.3333	+	156.943i	−0.0948581	+	0.208701i
$753$		0			0
$754$	−923.329	+	744.749i	−1.22457	+	0.987731i
$755$	93.8192	−	93.8192i	0.124264	−	0.124264i
$756$		0			0
$757$	525.591	−	525.591i	0.694308	−	0.694308i	−0.268869	−	0.963177i	$-0.586650\pi$
$757$	525.591	−	525.591i	0.694308	−	0.694308i	0.963177	+	0.268869i	$0.0866497\pi$
$758$	−3.92694	+	36.6808i	−0.00518066	+	0.0483915i
$759$		0			0
$760$	110.303	+	219.618i	0.145135	+	0.288971i
$761$			788.107i			1.03562i	0.855495	+	0.517810i	$0.173253\pi$
$761$			788.107i			1.03562i	−0.855495	+	0.517810i	$0.826747\pi$
$762$		0			0
$763$	86.6925	+	86.6925i	0.113621	+	0.113621i
$764$	758.382	+	164.263i	0.992647	+	0.215004i
$765$		0			0
$766$	−189.879	+	153.155i	−0.247884	+	0.199941i
$767$			350.850i			0.457431i
$768$		0			0
$769$	−768.187			−0.998943			−0.499471	−	0.866330i	$-0.666472\pi$
$769$	−768.187			−0.998943			−0.499471	+	0.866330i	$0.666472\pi$
$770$	−19.9915	−	24.7852i	−0.0259630	−	0.0321886i
$771$		0			0
$772$	−119.862	+	553.387i	−0.155261	+	0.716822i
$773$	−275.915	+	275.915i	−0.356941	+	0.356941i	−0.862684	−	0.505743i	$-0.831218\pi$
$773$	−275.915	+	275.915i	−0.356941	+	0.356941i	0.505743	+	0.862684i	$0.331218\pi$
$774$		0			0
$775$	−1063.91			−1.37279
$776$	1026.81	−	515.717i	1.32321	−	0.664583i
$777$		0			0
$778$	−656.031	−	70.2328i	−0.843227	−	0.0902735i
$779$	481.003	+	481.003i	0.617462	+	0.617462i
$780$		0			0
$781$	−445.547	−	445.547i	−0.570483	−	0.570483i
$782$	−114.533	−	141.996i	−0.146461	−	0.181581i
$783$		0			0
$784$	707.491	+	321.567i	0.902412	+	0.410162i
$785$	−160.364			−0.204285
$786$		0			0
$787$	240.824	−	240.824i	0.306002	−	0.306002i	−0.537354	−	0.843356i	$-0.680576\pi$
$787$	240.824	−	240.824i	0.306002	−	0.306002i	0.843356	+	0.537354i	$0.180576\pi$
$788$	−88.6644	−	137.693i	−0.112518	−	0.174737i
$789$		0			0
$790$	−1.72213	+	16.0860i	−0.00217991	+	0.0203621i
$791$	24.8497			0.0314156
$792$		0			0
$793$		−	1145.14i		−	1.44407i
$794$	−25.2215	+	235.589i	−0.0317651	+	0.296712i
$795$		0			0
$796$	23.3918	−	107.997i	0.0293867	−	0.135675i
$797$	681.033	+	681.033i	0.854496	+	0.854496i	0.990683	−	0.136187i	$-0.0434848\pi$
$797$	681.033	+	681.033i	0.854496	+	0.854496i	−0.136187	+	0.990683i	$0.543485\pi$
$798$		0			0
$799$		−	42.4012i		−	0.0530678i
$800$	−723.492	+	186.390i	−0.904364	+	0.232988i
$801$		0			0
$802$	739.739	+	917.117i	0.922367	+	1.14354i
$803$	249.237	−	249.237i	0.310382	−	0.310382i
$804$		0			0
$805$	13.7948	−	13.7948i	0.0171364	−	0.0171364i
$806$	1067.27	+	114.259i	1.32416	+	0.141761i
$807$		0			0
$808$	321.360	−	969.888i	0.397723	−	1.20036i
$809$		−	445.322i		−	0.550459i	−0.961379	−	0.275230i	$-0.911246\pi$
$809$		−	445.322i		−	0.550459i	0.961379	−	0.275230i	$-0.0887539\pi$
$810$		0			0
$811$	223.787	+	223.787i	0.275939	+	0.275939i	0.831485	−	0.555546i	$-0.187491\pi$
$811$	223.787	+	223.787i	0.275939	+	0.275939i	−0.555546	+	0.831485i	$0.687491\pi$
$812$	−110.887	+	71.4034i	−0.136560	+	0.0879352i
$813$		0			0
$814$	−341.039	−	422.815i	−0.418966	−	0.519428i
$815$			34.1861i			0.0419462i
$816$		0			0
$817$	768.337			0.940437
$818$	699.411	−	564.139i	0.855026	−	0.689656i
$819$		0			0
$820$	123.070	−	79.2488i	0.150086	−	0.0966448i
$821$	−382.528	+	382.528i	−0.465929	+	0.465929i	−0.900593	−	0.434664i	$-0.856867\pi$
$821$	−382.528	+	382.528i	−0.465929	+	0.465929i	0.434664	+	0.900593i	$0.356867\pi$
$822$		0			0
$823$	−730.046			−0.887055			−0.443527	−	0.896261i	$-0.646273\pi$
$823$	−730.046			−0.887055			−0.443527	+	0.896261i	$0.646273\pi$
$824$	−680.337	+	341.698i	−0.825651	+	0.414683i
$825$		0			0
$826$	−4.15232	+	38.7860i	−0.00502702	+	0.0469564i
$827$	−252.094	−	252.094i	−0.304829	−	0.304829i	0.538071	−	0.842900i	$-0.319153\pi$
$827$	−252.094	−	252.094i	−0.304829	−	0.304829i	−0.842900	+	0.538071i	$0.819153\pi$
$828$		0			0
$829$	−870.285	−	870.285i	−1.04980	−	1.04980i	−0.998693	−	0.0511072i	$-0.983725\pi$
$829$	−870.285	−	870.285i	−1.04980	−	1.04980i	−0.0511072	−	0.998693i	$-0.516275\pi$
$830$	203.992	−	164.539i	0.245774	−	0.198239i
$831$		0			0
$832$	745.796	−	109.280i	0.896390	−	0.131346i
$833$	−191.143			−0.229463
$834$		0			0
$835$	242.804	−	242.804i	0.290784	−	0.290784i
$836$	−382.765	+	1767.18i	−0.457853	+	2.11385i
$837$		0			0
$838$	−614.890	−	65.8284i	−0.733759	−	0.0785542i
$839$	−550.145			−0.655715			−0.327858	−	0.944727i	$-0.606327\pi$
$839$	−550.145			−0.655715			−0.327858	+	0.944727i	$0.606327\pi$
$840$		0			0
$841$			1695.21i			2.01571i
$842$	172.145	+	18.4293i	0.204447	+	0.0218876i
$843$		0			0
$844$	22.5113	+	34.9593i	0.0266722	+	0.0414210i
$845$	27.5348	+	27.5348i	0.0325855	+	0.0325855i
$846$		0			0
$847$		−	155.059i		−	0.183069i
$848$	879.542	−	329.852i	1.03720	−	0.388976i
$849$		0			0
$850$	143.029	−	115.366i	0.168270	−	0.135725i
$851$	235.327	−	235.327i	0.276530	−	0.276530i
$852$		0			0
$853$	−676.266	+	676.266i	−0.792809	+	0.792809i	−0.981950	−	0.189141i	$-0.939430\pi$
$853$	−676.266	+	676.266i	−0.792809	+	0.792809i	0.189141	+	0.981950i	$0.439430\pi$
$854$	13.5528	−	126.594i	0.0158698	−	0.148237i
$855$		0			0
$856$	−292.678	−	96.9752i	−0.341914	−	0.113289i
$857$		−	291.272i		−	0.339874i	−0.985455	−	0.169937i	$-0.945644\pi$
$857$		−	291.272i		−	0.339874i	0.985455	−	0.169937i	$-0.0543563\pi$
$858$		0			0
$859$	988.357	+	988.357i	1.15059	+	1.15059i	0.986434	+	0.164156i	$0.0524899\pi$
$859$	988.357	+	988.357i	1.15059	+	1.15059i	0.164156	+	0.986434i	$0.447510\pi$
$860$	34.9996	−	161.589i	0.0406973	−	0.187894i
$861$		0			0
$862$	780.102	−	629.224i	0.904991	−	0.729958i
$863$		−	922.512i		−	1.06896i	−0.845181	−	0.534480i	$-0.820508\pi$
$863$		−	922.512i		−	1.06896i	0.845181	−	0.534480i	$-0.179492\pi$
$864$		0			0
$865$	−279.105			−0.322665
$866$	−94.8640	−	117.611i	−0.109543	−	0.135809i
$867$		0			0
$868$	116.633	+	25.2624i	0.134370	+	0.0291042i
$869$	−84.1648	+	84.1648i	−0.0968524	+	0.0968524i
$870$		0			0
$871$	1129.67			1.29698
$872$	−1422.05	−	471.179i	−1.63079	−	0.540343i
$873$		0			0
$874$	−1101.49	−	117.922i	−1.26028	−	0.134922i
$875$	28.7739	+	28.7739i	0.0328845	+	0.0328845i
$876$		0			0
$877$	−406.278	−	406.278i	−0.463259	−	0.463259i	0.436463	−	0.899722i	$-0.356231\pi$
$877$	−406.278	−	406.278i	−0.463259	−	0.463259i	−0.899722	+	0.436463i	$0.856231\pi$
$878$	−900.607	−	1116.56i	−1.02575	−	1.27171i
$879$		0			0
$880$	354.219	+	160.999i	0.402522	+	0.182953i
$881$	1009.42			1.14577			0.572884	−	0.819637i	$-0.305825\pi$
$881$	1009.42			1.14577			0.572884	+	0.819637i	$0.305825\pi$
$882$		0			0
$883$	56.3792	−	56.3792i	0.0638496	−	0.0638496i	−0.674461	−	0.738311i	$-0.735624\pi$
$883$	56.3792	−	56.3792i	0.0638496	−	0.0638496i	0.738311	+	0.674461i	$0.235624\pi$
$884$	−155.871	+	100.370i	−0.176325	+	0.113541i
$885$		0			0
$886$	−90.0518	+	841.156i	−0.101639	+	0.949386i
$887$	−21.0431			−0.0237239			−0.0118620	−	0.999930i	$-0.503776\pi$
$887$	−21.0431			−0.0237239			−0.0118620	+	0.999930i	$0.503776\pi$
$888$		0			0
$889$			63.2060i			0.0710978i
$890$	2.90471	−	27.1323i	0.00326371	−	0.0304857i
$891$		0			0
$892$	−1509.42	−	326.936i	−1.69218	−	0.366520i
$893$	−182.063	−	182.063i	−0.203877	−	0.203877i
$894$		0			0
$895$		−	224.677i		−	0.251035i
$896$	83.7401	−	3.25421i	0.0934599	−	0.00363193i
$897$		0			0
$898$	−55.9462	−	69.3613i	−0.0623009	−	0.0772397i
$899$	1622.72	−	1622.72i	1.80503	−	1.80503i
$900$		0			0
$901$	−163.371	+	163.371i	−0.181321	+	0.181321i
$902$	1070.84	+	114.641i	1.18718	+	0.127097i
$903$		0			0
$904$	−271.340	+	136.280i	−0.300155	+	0.150753i
$905$			223.556i			0.247023i
$906$		0			0
$907$	496.202	+	496.202i	0.547080	+	0.547080i	0.925595	−	0.378515i	$-0.123565\pi$
$907$	496.202	+	496.202i	0.547080	+	0.547080i	−0.378515	+	0.925595i	$0.623565\pi$
$908$	152.299	+	236.515i	0.167730	+	0.260479i
$909$		0			0
$910$	−12.4468	−	15.4314i	−0.0136778	−	0.0169575i
$911$			1532.15i			1.68183i	0.541163	+	0.840917i	$0.317984\pi$
$911$			1532.15i			1.68183i	−0.541163	+	0.840917i	$0.682016\pi$
$912$		0			0
$913$	1928.21			2.11195
$914$	−998.211	+	805.149i	−1.09213	+	0.880907i
$915$		0			0
$916$	−587.621	−	912.554i	−0.641508	−	0.996238i
$917$	−35.6872	+	35.6872i	−0.0389174	+	0.0389174i
$918$		0			0
$919$	727.639			0.791773			0.395886	−	0.918299i	$-0.370437\pi$
$919$	727.639			0.791773			0.395886	+	0.918299i	$0.370437\pi$
$920$	−74.9755	+	226.282i	−0.0814951	+	0.245958i
$921$		0			0
$922$	118.533	−	1107.20i	0.128561	−	1.20086i
$923$	−277.399	−	277.399i	−0.300541	−	0.300541i
$924$		0			0
$925$	237.040	+	237.040i	0.256259	+	0.256259i
$926$	−616.244	+	497.057i	−0.665490	+	0.536779i
$927$		0			0
$928$	819.212	−	1387.79i	0.882772	−	1.49547i
$929$	−1544.59			−1.66264			−0.831318	−	0.555797i	$-0.812413\pi$
$929$	−1544.59			−1.66264			−0.831318	+	0.555797i	$0.812413\pi$
$930$		0			0
$931$	−820.729	+	820.729i	−0.881556	+	0.881556i
$932$	−1167.37	−	252.849i	−1.25255	−	0.271297i
$933$		0			0
$934$	−233.835	−	25.0338i	−0.250359	−	0.0268027i
$935$	−95.6992			−0.102352
$936$		0			0
$937$			716.111i			0.764259i	0.924109	+	0.382130i	$0.124809\pi$
$937$			716.111i			0.764259i	−0.924109	+	0.382130i	$0.875191\pi$
$938$	124.884	+	13.3697i	0.133138	+	0.0142534i
$939$		0			0
$940$	−46.5829	+	29.9961i	−0.0495563	+	0.0319108i
$941$	−537.759	−	537.759i	−0.571476	−	0.571476i	0.361065	−	0.932541i	$-0.382413\pi$
$941$	−537.759	−	537.759i	−0.571476	−	0.571476i	−0.932541	+	0.361065i	$0.882413\pi$
$942$		0			0
$943$			659.807i			0.699689i
$944$	−167.369	−	446.285i	−0.177298	−	0.472760i
$945$		0			0
$946$	946.824	−	763.700i	1.00087	−	0.807294i
$947$	−734.420	+	734.420i	−0.775523	+	0.775523i	−0.979066	−	0.203543i	$-0.934754\pi$
$947$	−734.420	+	734.420i	−0.775523	+	0.775523i	0.203543	+	0.979066i	$0.434754\pi$
$948$		0			0
$949$	155.176	−	155.176i	0.163515	−	0.163515i
$950$	118.780	−	1109.50i	0.125032	−	1.16790i
$951$		0			0
$952$	−18.4193	+	9.25106i	−0.0193480	+	0.00971750i
$953$		−	138.512i		−	0.145343i	−0.997356	−	0.0726714i	$-0.976848\pi$
$953$		−	138.512i		−	0.145343i	0.997356	−	0.0726714i	$-0.0231524\pi$
$954$		0			0
$955$	176.343	+	176.343i	0.184652	+	0.184652i
$956$	966.986	+	209.446i	1.01149	+	0.219086i
$957$		0			0
$958$	−669.456	+	539.977i	−0.698806	+	0.563651i
$959$		−	16.9789i		−	0.0177048i
$960$		0			0
$961$	−1115.51			−1.16078
$962$	−212.332	−	263.246i	−0.220719	−	0.273644i
$963$		0			0
$964$	186.571	−	861.373i	0.193538	−	0.893541i
$965$	−128.676	+	128.676i	−0.133343	+	0.133343i
$966$		0			0
$967$	−701.820			−0.725770			−0.362885	−	0.931834i	$-0.618208\pi$
$967$	−701.820			−0.725770			−0.362885	+	0.931834i	$0.618208\pi$
$968$	850.372	+	1693.13i	0.878483	+	1.74910i
$969$		0			0
$970$	367.192	+	39.3106i	0.378549	+	0.0405264i
$971$	62.5684	+	62.5684i	0.0644371	+	0.0644371i	0.738591	−	0.674154i	$-0.235492\pi$
$971$	62.5684	+	62.5684i	0.0644371	+	0.0644371i	−0.674154	+	0.738591i	$0.735492\pi$
$972$		0			0
$973$	−2.38359	−	2.38359i	−0.00244973	−	0.00244973i
$974$	−720.472	−	893.230i	−0.739704	−	0.917074i
$975$		0			0
$976$	546.279	+	1456.64i	0.559712	+	1.49246i
$977$	−1740.21			−1.78117			−0.890587	−	0.454814i	$-0.849706\pi$
$977$	−1740.21			−1.78117			−0.890587	+	0.454814i	$0.849706\pi$
$978$		0			0
$979$	141.961	−	141.961i	0.145006	−	0.145006i
$980$	135.221	+	209.994i	0.137981	+	0.214279i
$981$		0			0
$982$	147.270	−	1375.62i	0.149969	−	1.40083i
$983$	1451.81			1.47692			0.738460	−	0.674298i	$-0.235554\pi$
$983$	1451.81			1.47692			0.738460	+	0.674298i	$0.235554\pi$
$984$		0			0
$985$		−	52.6337i		−	0.0534353i
$986$	−42.1931	+	394.117i	−0.0427922	+	0.399713i
$987$		0			0
$988$	−238.311	+	1100.25i	−0.241206	+	1.11362i
$989$	526.976	+	526.976i	0.532837	+	0.532837i
$990$		0			0
$991$		−	22.1684i		−	0.0223698i	−0.999937	−	0.0111849i	$-0.996440\pi$
$991$		−	22.1684i		−	0.0223698i	0.999937	−	0.0111849i	$-0.00356033\pi$
$992$	−1412.09	+	363.792i	−1.42348	+	0.366725i
$993$		0			0
$994$	−27.3831	−	33.9491i	−0.0275484	−	0.0341541i
$995$	25.1121	−	25.1121i	0.0252382	−	0.0252382i
$996$		0			0
$997$	13.5020	−	13.5020i	0.0135426	−	0.0135426i	−0.700303	−	0.713846i	$-0.746952\pi$
$997$	13.5020	−	13.5020i	0.0135426	−	0.0135426i	0.713846	+	0.700303i	$0.246952\pi$
$998$	−732.532	−	78.4228i	−0.734000	−	0.0785799i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.m.c.19.3		16
3.2	odd	2		48.3.l.a.19.6	✓	16
4.3	odd	2		576.3.m.c.559.5		16
8.3	odd	2		1152.3.m.c.991.4		16
8.5	even	2		1152.3.m.f.991.4		16
12.11	even	2		192.3.l.a.175.2		16
16.3	odd	4		1152.3.m.f.415.4		16
16.5	even	4		576.3.m.c.271.5		16
16.11	odd	4	inner	144.3.m.c.91.3		16
16.13	even	4		1152.3.m.c.415.4		16
24.5	odd	2		384.3.l.a.223.3		16
24.11	even	2		384.3.l.b.223.7		16
48.5	odd	4		192.3.l.a.79.2		16
48.11	even	4		48.3.l.a.43.6	yes	16
48.29	odd	4		384.3.l.b.31.7		16
48.35	even	4		384.3.l.a.31.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.l.a.19.6	✓	16	3.2	odd	2
48.3.l.a.43.6	yes	16	48.11	even	4
144.3.m.c.19.3		16	1.1	even	1	trivial
144.3.m.c.91.3		16	16.11	odd	4	inner
192.3.l.a.79.2		16	48.5	odd	4
192.3.l.a.175.2		16	12.11	even	2
384.3.l.a.31.3		16	48.35	even	4
384.3.l.a.223.3		16	24.5	odd	2
384.3.l.b.31.7		16	48.29	odd	4
384.3.l.b.223.7		16	24.11	even	2
576.3.m.c.271.5		16	16.5	even	4
576.3.m.c.559.5		16	4.3	odd	2
1152.3.m.c.415.4		16	16.13	even	4
1152.3.m.c.991.4		16	8.3	odd	2
1152.3.m.f.415.4		16	16.3	odd	4
1152.3.m.f.991.4		16	8.5	even	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25564 - 1.55672i) q^{2} +(-0.846753 + 3.90935i) q^{4} +(-0.909023 + 0.909023i) q^{5} -0.654713 q^{7} +(7.14897 - 3.59057i) q^{8} +O(q^{10})\)	\(q+(-1.25564 - 1.55672i) q^{2} +(-0.846753 + 3.90935i) q^{4} +(-0.909023 + 0.909023i) q^{5} -0.654713 q^{7} +(7.14897 - 3.59057i) q^{8} +(2.55650 + 0.273691i) q^{10} +(13.3760 + 13.3760i) q^{11} +(8.32795 + 8.32795i) q^{13} +(0.822082 + 1.01921i) q^{14} +(-14.5660 - 6.62050i) q^{16} +3.93529 q^{17} +(16.8974 - 16.8974i) q^{19} +(-2.78397 - 4.32340i) q^{20} +(4.02729 - 37.6181i) q^{22} +23.1787 q^{23} +23.3474i q^{25} +(2.50740 - 23.4212i) q^{26} +(0.554380 - 2.55950i) q^{28} +(-35.6105 - 35.6105i) q^{29} +45.5687i q^{31} +(7.98336 + 30.9882i) q^{32} +(-4.94130 - 6.12615i) q^{34} +(0.595149 - 0.595149i) q^{35} +(10.1527 - 10.1527i) q^{37} +(-47.5215 - 5.08752i) q^{38} +(-3.23467 + 9.76249i) q^{40} +28.4661i q^{41} +(22.7354 + 22.7354i) q^{43} +(-63.6176 + 40.9653i) q^{44} +(-29.1040 - 36.0827i) q^{46} -10.7746i q^{47} -48.5714 q^{49} +(36.3453 - 29.3158i) q^{50} +(-39.6086 + 25.5051i) q^{52} +(-41.5142 + 41.5142i) q^{53} -24.3182 q^{55} +(-4.68053 + 2.35079i) q^{56} +(-10.7217 + 100.149i) q^{58} +(21.0646 + 21.0646i) q^{59} +(-68.7531 - 68.7531i) q^{61} +(70.9377 - 57.2178i) q^{62} +(38.2157 - 51.3377i) q^{64} -15.1406 q^{65} +(67.8242 - 67.8242i) q^{67} +(-3.33222 + 15.3844i) q^{68} +(-1.67377 - 0.179189i) q^{70} -33.3094 q^{71} -18.6331i q^{73} +(-28.5531 - 3.05682i) q^{74} +(51.7499 + 80.3657i) q^{76} +(-8.75745 - 8.75745i) q^{77} +6.29222i q^{79} +(19.2590 - 7.22265i) q^{80} +(44.3137 - 35.7431i) q^{82} +(72.0774 - 72.0774i) q^{83} +(-3.57727 + 3.57727i) q^{85} +(6.84524 - 63.9400i) q^{86} +(143.652 + 47.5973i) q^{88} -10.6131i q^{89} +(-5.45242 - 5.45242i) q^{91} +(-19.6266 + 90.6135i) q^{92} +(-16.7730 + 13.5290i) q^{94} +30.7202i q^{95} +143.631 q^{97} +(60.9880 + 75.6120i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} + 12 q^{8}+O(q^{10}) \) 16 * q + 12 * q^4 + 12 * q^8	\( 16 q + 12 q^{4} + 12 q^{8} - 56 q^{10} - 32 q^{11} + 44 q^{14} + 32 q^{16} - 32 q^{19} - 80 q^{20} + 32 q^{22} + 128 q^{23} + 100 q^{26} - 120 q^{28} - 32 q^{29} - 160 q^{32} + 96 q^{34} - 96 q^{35} - 96 q^{37} - 168 q^{38} + 48 q^{40} + 160 q^{43} - 88 q^{44} + 136 q^{46} + 112 q^{49} + 236 q^{50} - 48 q^{52} + 160 q^{53} - 256 q^{55} + 224 q^{56} + 144 q^{58} + 128 q^{59} - 32 q^{61} + 276 q^{62} - 408 q^{64} + 32 q^{65} + 320 q^{67} + 448 q^{68} - 384 q^{70} - 512 q^{71} - 348 q^{74} + 72 q^{76} - 224 q^{77} - 552 q^{80} - 40 q^{82} + 160 q^{83} + 160 q^{85} - 528 q^{86} + 480 q^{88} - 480 q^{91} - 496 q^{92} + 312 q^{94} + 440 q^{98}+O(q^{100}) \) 16 * q + 12 * q^4 + 12 * q^8 - 56 * q^10 - 32 * q^11 + 44 * q^14 + 32 * q^16 - 32 * q^19 - 80 * q^20 + 32 * q^22 + 128 * q^23 + 100 * q^26 - 120 * q^28 - 32 * q^29 - 160 * q^32 + 96 * q^34 - 96 * q^35 - 96 * q^37 - 168 * q^38 + 48 * q^40 + 160 * q^43 - 88 * q^44 + 136 * q^46 + 112 * q^49 + 236 * q^50 - 48 * q^52 + 160 * q^53 - 256 * q^55 + 224 * q^56 + 144 * q^58 + 128 * q^59 - 32 * q^61 + 276 * q^62 - 408 * q^64 + 32 * q^65 + 320 * q^67 + 448 * q^68 - 384 * q^70 - 512 * q^71 - 348 * q^74 + 72 * q^76 - 224 * q^77 - 552 * q^80 - 40 * q^82 + 160 * q^83 + 160 * q^85 - 528 * q^86 + 480 * q^88 - 480 * q^91 - 496 * q^92 + 312 * q^94 + 440 * q^98

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