LMFDB - Embedded newform 144.3.m.c.91.3

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			91.3
Root			$-1.25564 - 1.55672i$ of defining polynomial
Character	$\chi$	$=$	144.91
Dual form			144.3.m.c.19.3

$q$-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 $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

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

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	0.610337	−	0.792142i	$-0.291034\pi$
$5$	−0.909023	−	0.909023i	−0.181805	−	0.181805i	−0.792142	+	0.610337i	$0.791034\pi$
$6$		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	0.246980	−	0.969021i	$-0.420562\pi$
$11$	13.3760	−	13.3760i	1.21600	−	1.21600i	0.969021	−	0.246980i	$-0.0794382\pi$
$12$		0			0
$13$	8.32795	−	8.32795i	0.640612	−	0.640612i	−0.310094	−	0.950706i	$-0.600361\pi$
$13$	8.32795	−	8.32795i	0.640612	−	0.640612i	0.950706	+	0.310094i	$0.100361\pi$
$14$	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	0.994459	−	0.105123i	$-0.0335236\pi$
$19$	16.8974	+	16.8974i	0.889336	+	0.889336i	−0.105123	+	0.994459i	$0.533524\pi$
$20$	−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	−0.263209	+	0.964739i	$0.584781\pi$
$29$	−35.6105	+	35.6105i	−1.22795	+	1.22795i	−0.964739	+	0.263209i	$0.915219\pi$
$30$		0			0
$31$		−	45.5687i		−	1.46996i	−0.678089	−	0.734980i	$-0.737192\pi$
$31$		−	45.5687i		−	1.46996i	0.678089	−	0.734980i	$-0.262808\pi$
$32$	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	0.830868	−	0.556470i	$-0.187844\pi$
$37$	10.1527	+	10.1527i	0.274398	+	0.274398i	−0.556470	+	0.830868i	$0.687844\pi$
$38$	−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	$-0.887150\pi$
$41$		−	28.4661i		−	0.694295i	0.937811	−	0.347148i	$-0.112850\pi$
$42$		0			0
$43$	22.7354	−	22.7354i	0.528730	−	0.528730i	−0.391464	−	0.920194i	$-0.628031\pi$
$43$	22.7354	−	22.7354i	0.528730	−	0.528730i	0.920194	+	0.391464i	$0.128031\pi$
$44$	−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	$0.0365661\pi$
$47$			10.7746i			0.229247i	−0.993409	+	0.114623i	$0.963434\pi$
$48$		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	0.197097	−	0.980384i	$-0.436849\pi$
$53$	−41.5142	−	41.5142i	−0.783287	−	0.783287i	−0.980384	+	0.197097i	$0.936849\pi$
$54$		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	−0.505689	−	0.862716i	$-0.668762\pi$
$59$	21.0646	−	21.0646i	0.357027	−	0.357027i	0.862716	+	0.505689i	$0.168762\pi$
$60$		0			0
$61$	−68.7531	+	68.7531i	−1.12710	+	1.12710i	−0.136453	+	0.990647i	$0.543570\pi$
$61$	−68.7531	+	68.7531i	−1.12710	+	1.12710i	−0.990647	+	0.136453i	$0.956430\pi$
$62$	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	0.999923	+	0.0123779i	$0.00394012\pi$
$67$	67.8242	+	67.8242i	1.01230	+	1.01230i	0.0123779	+	0.999923i	$0.496060\pi$
$68$	−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	$0.0407351\pi$
$73$			18.6331i			0.255248i	−0.991823	+	0.127624i	$0.959265\pi$
$74$	−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	$-0.987320\pi$
$79$		−	6.29222i		−	0.0796483i	0.999207	−	0.0398242i	$-0.0126798\pi$
$80$	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	0.992296	−	0.123894i	$-0.0395382\pi$
$83$	72.0774	+	72.0774i	0.868402	+	0.868402i	−0.123894	+	0.992296i	$0.539538\pi$
$84$		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	$0.0189902\pi$
$89$			10.6131i			0.119248i	−0.998221	+	0.0596240i	$0.981010\pi$
$90$		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	0.994912	−	0.100753i	$-0.0321251\pi$
$101$	90.3100	+	90.3100i	0.894159	+	0.894159i	−0.100753	+	0.994912i	$0.532125\pi$
$102$		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	−0.822892	−	0.568197i	$-0.807641\pi$
$107$	−27.2524	+	27.2524i	−0.254695	+	0.254695i	0.568197	+	0.822892i	$0.307641\pi$
$108$		0			0
$109$	−132.413	+	132.413i	−1.21480	+	1.21480i	−0.245366	+	0.969430i	$0.578908\pi$
$109$	−132.413	+	132.413i	−1.21480	+	1.21480i	−0.969430	+	0.245366i	$0.921092\pi$
$110$	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	$0.124103\pi$
$127$			96.5399i			0.760157i	−0.924954	+	0.380078i	$0.875897\pi$
$128$	−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	0.883855	−	0.467762i	$-0.154939\pi$
$131$	54.5082	+	54.5082i	0.416093	+	0.416093i	−0.467762	+	0.883855i	$0.654939\pi$
$132$		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	$-0.969828\pi$
$137$		−	25.9333i		−	0.189294i	0.995511	−	0.0946471i	$-0.0301723\pi$
$138$		0			0
$139$	3.64066	−	3.64066i	0.0261918	−	0.0261918i	−0.693890	−	0.720081i	$-0.744104\pi$
$139$	3.64066	−	3.64066i	0.0261918	−	0.0261918i	0.720081	+	0.693890i	$0.244104\pi$
$140$	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	0.767899	−	0.640571i	$-0.221302\pi$
$149$	18.9718	+	18.9718i	0.127328	+	0.127328i	−0.640571	+	0.767899i	$0.721302\pi$
$150$		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	−0.368000	−	0.929826i	$-0.619957\pi$
$157$	88.2067	−	88.2067i	0.561826	−	0.561826i	0.929826	+	0.368000i	$0.119957\pi$
$158$	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	0.762431	−	0.647070i	$-0.224006\pi$
$163$	18.8038	+	18.8038i	0.115361	+	0.115361i	−0.647070	+	0.762431i	$0.724006\pi$
$164$	−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	−0.106876	−	0.994272i	$-0.534085\pi$
$173$	153.520	−	153.520i	0.887396	−	0.887396i	0.994272	+	0.106876i	$0.0340849\pi$
$174$		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	0.271921	−	0.962320i	$-0.412341\pi$
$179$	−123.581	−	123.581i	−0.690399	−	0.690399i	−0.962320	+	0.271921i	$0.912341\pi$
$180$		0			0
$181$	122.965	+	122.965i	0.679364	+	0.679364i	0.959856	−	0.280493i	$-0.0904978\pi$
$181$	122.965	+	122.965i	0.679364	+	0.679364i	−0.280493	+	0.959856i	$0.590498\pi$
$182$	−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	$0.169553\pi$
$191$			193.992i			1.01566i	−0.861456	+	0.507832i	$0.830447\pi$
$192$		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	0.629800	−	0.776758i	$-0.283137\pi$
$197$	−28.9507	−	28.9507i	−0.146958	−	0.146958i	−0.776758	+	0.629800i	$0.783137\pi$
$198$		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	0.724310	−	0.689474i	$-0.242158\pi$
$211$	7.35041	+	7.35041i	0.0348361	+	0.0348361i	−0.689474	+	0.724310i	$0.742158\pi$
$212$	−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	$-0.666869\pi$
$223$		−	386.106i		−	1.73142i	0.500549	−	0.865708i	$-0.333131\pi$
$224$	−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	0.808106	−	0.589037i	$-0.200493\pi$
$227$	49.7286	+	49.7286i	0.219069	+	0.219069i	−0.589037	+	0.808106i	$0.700493\pi$
$228$		0			0
$229$	−191.870	−	191.870i	−0.837861	−	0.837861i	0.150716	−	0.988577i	$-0.451842\pi$
$229$	−191.870	−	191.870i	−0.837861	−	0.837861i	−0.988577	+	0.150716i	$0.951842\pi$
$230$	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	$-0.778605\pi$
$233$		−	298.610i		−	1.28159i	0.767712	−	0.640795i	$-0.221395\pi$
$234$		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	$0.173127\pi$
$239$			247.352i			1.03495i	−0.855700	+	0.517473i	$0.826873\pi$
$240$		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	−0.952575	−	0.304303i	$-0.901576\pi$
$251$	−162.716	+	162.716i	−0.648272	+	0.648272i	0.304303	+	0.952575i	$0.401576\pi$
$252$		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	−0.709913	−	0.704289i	$-0.751266\pi$
$269$	−1.51275	+	1.51275i	−0.00562361	+	0.00562361i	0.704289	+	0.709913i	$0.251266\pi$
$270$		0			0
$271$		−	166.098i		−	0.612909i	−0.951885	−	0.306454i	$-0.900857\pi$
$271$		−	166.098i		−	0.612909i	0.951885	−	0.306454i	$-0.0991427\pi$
$272$	−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	0.987062	+	0.160338i	$0.0512586\pi$
$277$	317.830	+	317.830i	1.14740	+	1.14740i	0.160338	+	0.987062i	$0.448741\pi$
$278$	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	$0.254352\pi$
$281$			402.790i			1.43342i	−0.697374	+	0.716708i	$0.745648\pi$
$282$		0			0
$283$	−192.406	+	192.406i	−0.679881	+	0.679881i	−0.959973	−	0.280092i	$-0.909635\pi$
$283$	−192.406	+	192.406i	−0.679881	+	0.679881i	0.280092	+	0.959973i	$0.409635\pi$
$284$	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	0.823921	−	0.566704i	$-0.191782\pi$
$293$	75.3645	+	75.3645i	0.257217	+	0.257217i	−0.566704	+	0.823921i	$0.691782\pi$
$294$		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	0.501703	−	0.865040i	$-0.332707\pi$
$307$	−111.544	−	111.544i	−0.363337	−	0.363337i	−0.865040	+	0.501703i	$0.832707\pi$
$308$	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	$0.284829\pi$
$313$			488.339i			1.56019i	−0.625661	+	0.780095i	$0.715171\pi$
$314$	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	−0.984913	−	0.173050i	$-0.944638\pi$
$317$	−257.361	+	257.361i	−0.811863	+	0.811863i	0.173050	+	0.984913i	$0.444638\pi$
$318$		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	−0.868667	−	0.495396i	$-0.835023\pi$
$331$	−123.553	+	123.553i	−0.373271	+	0.373271i	0.495396	+	0.868667i	$0.335023\pi$
$332$	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	−0.506918	−	0.861994i	$-0.669215\pi$
$347$	123.212	−	123.212i	0.355076	−	0.355076i	0.861994	+	0.506918i	$0.169215\pi$
$348$		0			0
$349$	115.371	−	115.371i	0.330575	−	0.330575i	−0.522230	−	0.852805i	$-0.674900\pi$
$349$	115.371	−	115.371i	0.330575	−	0.330575i	0.852805	+	0.522230i	$0.174900\pi$
$350$	−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	$-0.942717\pi$
$367$		−	131.379i		−	0.357982i	0.983851	−	0.178991i	$-0.0572832\pi$
$368$	−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	0.233062	−	0.972462i	$-0.425126\pi$
$373$	−275.796	−	275.796i	−0.739400	−	0.739400i	−0.972462	+	0.233062i	$0.925126\pi$
$374$	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	−0.724104	−	0.689691i	$-0.757747\pi$
$379$	−13.0427	+	13.0427i	−0.0344135	+	0.0344135i	0.689691	+	0.724104i	$0.257747\pi$
$380$	−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	$0.0509027\pi$
$383$			121.974i			0.318470i	−0.987241	+	0.159235i	$0.949097\pi$
$384$		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	0.940222	−	0.340563i	$-0.110618\pi$
$389$	233.267	+	233.267i	0.599659	+	0.599659i	−0.340563	+	0.940222i	$0.610618\pi$
$390$		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	−0.804695	−	0.593689i	$-0.797671\pi$
$397$	−83.7693	+	83.7693i	−0.211006	+	0.211006i	0.593689	+	0.804695i	$0.297671\pi$
$398$	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	$-0.814914\pi$
$409$		−	449.285i		−	1.09850i	0.835659	−	0.549248i	$-0.185086\pi$
$410$	−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	0.918118	−	0.396307i	$-0.129708\pi$
$419$	218.639	+	218.639i	0.521811	+	0.521811i	−0.396307	+	0.918118i	$0.629708\pi$
$420$		0			0
$421$	−61.2101	−	61.2101i	−0.145392	−	0.145392i	0.630664	−	0.776056i	$-0.282783\pi$
$421$	−61.2101	−	61.2101i	−0.145392	−	0.145392i	−0.776056	+	0.630664i	$0.782783\pi$
$422$	−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	$-0.802527\pi$
$431$		−	501.119i		−	1.16269i	0.813657	−	0.581345i	$-0.197473\pi$
$432$		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	−0.958899	−	0.283746i	$-0.908423\pi$
$443$	−299.093	+	299.093i	−0.675153	+	0.675153i	0.283746	+	0.958899i	$0.408423\pi$
$444$		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	$0.247514\pi$
$457$			641.227i			1.40312i	−0.712609	+	0.701562i	$0.752486\pi$
$458$	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	−0.136631	−	0.990622i	$-0.543627\pi$
$461$	393.690	−	393.690i	0.853991	−	0.853991i	0.990622	+	0.136631i	$0.0436273\pi$
$462$		0			0
$463$			395.861i			0.854991i	0.904018	+	0.427495i	$0.140604\pi$
$463$			395.861i			0.854991i	−0.904018	+	0.427495i	$0.859396\pi$
$464$	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	0.790502	−	0.612460i	$-0.209820\pi$
$467$	83.1457	+	83.1457i	0.178042	+	0.178042i	−0.612460	+	0.790502i	$0.709820\pi$
$468$		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	$0.148183\pi$
$479$			430.043i			0.897793i	−0.893584	+	0.448896i	$0.851817\pi$
$480$		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	−0.00379588	−	0.999993i	$-0.501208\pi$
$491$	489.133	−	489.133i	0.996197	−	0.996197i	0.999993	+	0.00379588i	$0.00120827\pi$
$492$		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	0.918170	−	0.396188i	$-0.129667\pi$
$499$	260.469	+	260.469i	0.521982	+	0.521982i	−0.396188	+	0.918170i	$0.629667\pi$
$500$	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	−0.161371	−	0.986894i	$-0.551592\pi$
$509$	420.191	−	420.191i	0.825523	−	0.825523i	0.986894	+	0.161371i	$0.0515916\pi$
$510$		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	$0.124199\pi$
$521$			396.333i			0.760716i	−0.924839	+	0.380358i	$0.875801\pi$
$522$		0			0
$523$	564.600	−	564.600i	1.07954	−	1.07954i	0.0829913	−	0.996550i	$-0.473553\pi$
$523$	564.600	−	564.600i	1.07954	−	1.07954i	0.996550	−	0.0829913i	$-0.0264474\pi$
$524$	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	−0.733899	−	0.679259i	$-0.762301\pi$
$541$	−29.5601	+	29.5601i	−0.0546398	+	0.0546398i	0.679259	+	0.733899i	$0.262301\pi$
$542$	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	0.568965	−	0.822362i	$-0.307344\pi$
$547$	−138.608	−	138.608i	−0.253397	−	0.253397i	−0.822362	+	0.568965i	$0.807344\pi$
$548$	−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	−0.759277	−	0.650767i	$-0.774447\pi$
$557$	−60.4400	+	60.4400i	−0.108510	+	0.108510i	0.650767	+	0.759277i	$0.274447\pi$
$558$		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	0.428649	−	0.903471i	$-0.358990\pi$
$563$	−267.325	−	267.325i	−0.474822	−	0.474822i	−0.903471	+	0.428649i	$0.858990\pi$
$564$		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	$-0.910518\pi$
$569$		−	315.715i		−	0.554859i	0.960746	−	0.277429i	$-0.0894825\pi$
$570$		0			0
$571$	−670.572	+	670.572i	−1.17438	+	1.17438i	−0.193228	+	0.981154i	$0.561896\pi$
$571$	−670.572	+	670.572i	−1.17438	+	1.17438i	−0.981154	+	0.193228i	$0.938104\pi$
$572$	−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	−0.252064	−	0.967711i	$-0.581109\pi$
$587$	420.085	−	420.085i	0.715647	−	0.715647i	0.967711	+	0.252064i	$0.0811093\pi$
$588$		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	$-0.897613\pi$
$601$		−	380.001i		−	0.632280i	0.948712	−	0.316140i	$-0.102387\pi$
$602$	−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	$-0.952149\pi$
$607$		−	181.813i		−	0.299527i	0.988722	−	0.149763i	$-0.0478512\pi$
$608$	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	0.750657	−	0.660693i	$-0.229737\pi$
$613$	55.1479	+	55.1479i	0.0899640	+	0.0899640i	−0.660693	+	0.750657i	$0.729737\pi$
$614$	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	$0.155657\pi$
$617$			579.674i			0.939504i	−0.882798	+	0.469752i	$0.844343\pi$
$618$		0			0
$619$	91.1070	−	91.1070i	0.147184	−	0.147184i	−0.629675	−	0.776859i	$-0.716812\pi$
$619$	91.1070	−	91.1070i	0.147184	−	0.147184i	0.776859	+	0.629675i	$0.216812\pi$
$620$	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	0.844353	+	0.535787i	$0.179985\pi$
$643$	887.430	+	887.430i	1.38014	+	1.38014i	0.535787	+	0.844353i	$0.320015\pi$
$644$	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	−0.987028	−	0.160549i	$-0.948674\pi$
$653$	−539.691	+	539.691i	−0.826479	+	0.826479i	0.160549	+	0.987028i	$0.448674\pi$
$654$		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	0.0500862	−	0.998745i	$-0.484050\pi$
$659$	−625.166	−	625.166i	−0.948659	−	0.948659i	−0.998745	+	0.0500862i	$0.984050\pi$
$660$		0			0
$661$	−326.893	−	326.893i	−0.494544	−	0.494544i	0.415191	−	0.909734i	$-0.363715\pi$
$661$	−326.893	−	326.893i	−0.494544	−	0.494544i	−0.909734	+	0.415191i	$0.863715\pi$
$662$	−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	0.794025	−	0.607885i	$-0.207982\pi$
$677$	126.017	+	126.017i	0.186140	+	0.186140i	−0.607885	+	0.794025i	$0.707982\pi$
$678$		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	−0.996315	−	0.0857647i	$-0.972667\pi$
$683$	−621.906	+	621.906i	−0.910551	+	0.910551i	0.0857647	+	0.996315i	$0.472667\pi$
$684$		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	0.352176	−	0.935934i	$-0.385442\pi$
$691$	−403.376	−	403.376i	−0.583758	−	0.583758i	−0.935934	+	0.352176i	$0.885442\pi$
$692$	−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	−0.956697	−	0.291086i	$-0.905983\pi$
$701$	−466.593	+	466.593i	−0.665611	+	0.665611i	0.291086	+	0.956697i	$0.405983\pi$
$702$		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	0.984376	+	0.176081i	$0.0563422\pi$
$709$	822.764	+	822.764i	1.16046	+	1.16046i	0.176081	+	0.984376i	$0.443658\pi$
$710$	−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	$-0.835593\pi$
$719$		−	710.142i		−	0.987681i	0.869553	−	0.493840i	$-0.164407\pi$
$720$		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	−0.769662	−	0.638452i	$-0.779575\pi$
$733$	−96.1768	+	96.1768i	−0.131210	+	0.131210i	0.638452	+	0.769662i	$0.279575\pi$
$734$	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	0.974757	+	0.223268i	$0.0716726\pi$
$739$	885.341	+	885.341i	1.19803	+	1.19803i	0.223268	+	0.974757i	$0.428327\pi$
$740$	−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	$-0.723400\pi$
$751$		−	1147.02i		−	1.52732i	0.645618	−	0.763661i	$-0.276600\pi$
$752$	−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	0.963177	−	0.268869i	$-0.0866497\pi$
$757$	525.591	+	525.591i	0.694308	+	0.694308i	−0.268869	+	0.963177i	$0.586650\pi$
$758$	−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	$-0.826747\pi$
$761$		−	788.107i		−	1.03562i	0.855495	−	0.517810i	$-0.173253\pi$
$762$		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	0.505743	−	0.862684i	$-0.331218\pi$
$773$	−275.915	−	275.915i	−0.356941	−	0.356941i	−0.862684	+	0.505743i	$0.831218\pi$
$774$		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	0.843356	−	0.537354i	$-0.180576\pi$
$787$	240.824	+	240.824i	0.306002	+	0.306002i	−0.537354	+	0.843356i	$0.680576\pi$
$788$	−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	−0.136187	−	0.990683i	$-0.543485\pi$
$797$	681.033	−	681.033i	0.854496	−	0.854496i	0.990683	+	0.136187i	$0.0434848\pi$
$798$		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	$0.0887539\pi$
$809$			445.322i			0.550459i	−0.961379	+	0.275230i	$0.911246\pi$
$810$		0			0
$811$	223.787	−	223.787i	0.275939	−	0.275939i	−0.555546	−	0.831485i	$-0.687491\pi$
$811$	223.787	−	223.787i	0.275939	−	0.275939i	0.831485	+	0.555546i	$0.187491\pi$
$812$	−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	0.434664	−	0.900593i	$-0.356867\pi$
$821$	−382.528	−	382.528i	−0.465929	−	0.465929i	−0.900593	+	0.434664i	$0.856867\pi$
$822$		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	−0.842900	−	0.538071i	$-0.819153\pi$
$827$	−252.094	+	252.094i	−0.304829	+	0.304829i	0.538071	+	0.842900i	$0.319153\pi$
$828$		0			0
$829$	−870.285	+	870.285i	−1.04980	+	1.04980i	−0.0511072	+	0.998693i	$0.516275\pi$
$829$	−870.285	+	870.285i	−1.04980	+	1.04980i	−0.998693	+	0.0511072i	$0.983725\pi$
$830$	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	0.189141	−	0.981950i	$-0.439430\pi$
$853$	−676.266	−	676.266i	−0.792809	−	0.792809i	−0.981950	+	0.189141i	$0.939430\pi$
$854$	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	$0.0543563\pi$
$857$			291.272i			0.339874i	−0.985455	+	0.169937i	$0.945644\pi$
$858$		0			0
$859$	988.357	−	988.357i	1.15059	−	1.15059i	0.164156	−	0.986434i	$-0.447510\pi$
$859$	988.357	−	988.357i	1.15059	−	1.15059i	0.986434	−	0.164156i	$-0.0524899\pi$
$860$	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	$0.179492\pi$
$863$			922.512i			1.06896i	−0.845181	+	0.534480i	$0.820508\pi$
$864$		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	−0.899722	−	0.436463i	$-0.856231\pi$
$877$	−406.278	+	406.278i	−0.463259	+	0.463259i	0.436463	+	0.899722i	$0.356231\pi$
$878$	−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	0.738311	−	0.674461i	$-0.235624\pi$
$883$	56.3792	+	56.3792i	0.0638496	+	0.0638496i	−0.674461	+	0.738311i	$0.735624\pi$
$884$	−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	−0.378515	−	0.925595i	$-0.623565\pi$
$907$	496.202	−	496.202i	0.547080	−	0.547080i	0.925595	+	0.378515i	$0.123565\pi$
$908$	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	$-0.682016\pi$
$911$		−	1532.15i		−	1.68183i	0.541163	−	0.840917i	$-0.317984\pi$
$912$		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	$-0.875191\pi$
$937$		−	716.111i		−	0.764259i	0.924109	−	0.382130i	$-0.124809\pi$
$938$	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	−0.932541	−	0.361065i	$-0.882413\pi$
$941$	−537.759	+	537.759i	−0.571476	+	0.571476i	0.361065	+	0.932541i	$0.382413\pi$
$942$		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	0.203543	−	0.979066i	$-0.434754\pi$
$947$	−734.420	−	734.420i	−0.775523	−	0.775523i	−0.979066	+	0.203543i	$0.934754\pi$
$948$		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	$0.0231524\pi$
$953$			138.512i			0.145343i	−0.997356	+	0.0726714i	$0.976848\pi$
$954$		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	−0.674154	−	0.738591i	$-0.735492\pi$
$971$	62.5684	−	62.5684i	0.0644371	−	0.0644371i	0.738591	+	0.674154i	$0.235492\pi$
$972$		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	$0.00356033\pi$
$991$			22.1684i			0.0223698i	−0.999937	+	0.0111849i	$0.996440\pi$
$992$	−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	0.713846	−	0.700303i	$-0.246952\pi$
$997$	13.5020	+	13.5020i	0.0135426	+	0.0135426i	−0.700303	+	0.713846i	$0.746952\pi$
$998$	−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.91.3		16
3.2	odd	2		48.3.l.a.43.6	yes	16
4.3	odd	2		576.3.m.c.271.5		16
8.3	odd	2		1152.3.m.c.415.4		16
8.5	even	2		1152.3.m.f.415.4		16
12.11	even	2		192.3.l.a.79.2		16
16.3	odd	4	inner	144.3.m.c.19.3		16
16.5	even	4		1152.3.m.c.991.4		16
16.11	odd	4		1152.3.m.f.991.4		16
16.13	even	4		576.3.m.c.559.5		16
24.5	odd	2		384.3.l.a.31.3		16
24.11	even	2		384.3.l.b.31.7		16
48.5	odd	4		384.3.l.b.223.7		16
48.11	even	4		384.3.l.a.223.3		16
48.29	odd	4		192.3.l.a.175.2		16
48.35	even	4		48.3.l.a.19.6	✓	16

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

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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