LMFDB - Embedded newform 495.3.j.a.298.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,3,Mod(298,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 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("495.298");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	495.j (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:	$13.4877730858$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 212 x^{16} - 792 x^{15} + 1480 x^{14} + 148 x^{13} + \cdots + 38416 $ x^20 - 4x^19 + 8x^18 + 4x^17 + 212x^16 - 792x^15 + 1480x^14 + 148x^13 + 11654x^12 - 43032x^11 + 79360x^10 - 4948x^9 + 109988x^8 - 423032x^7 + 812488x^6 - 86868x^5 - 87295x^4 + 20876x^3 + 561800x^2 + 207760*x + 38416
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 5 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			298.1
Root			$-2.27868 - 2.27868i$ of defining polynomial
Character	$\chi$	$=$	495.298
Dual form			495.3.j.a.397.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.27868 + 2.27868i) q^{2} -6.38475i q^{4} +(-2.55248 - 4.29940i) q^{5} +(-3.30878 + 3.30878i) q^{7} +(5.43407 + 5.43407i) q^{8} +(15.6132 + 3.98068i) q^{10} -3.31662 q^{11} +(7.65935 + 7.65935i) q^{13} -15.0793i q^{14} +0.773991 q^{16} +(19.8139 - 19.8139i) q^{17} -17.4895i q^{19} +(-27.4506 + 16.2969i) q^{20} +(7.55752 - 7.55752i) q^{22} +(11.7334 + 11.7334i) q^{23} +(-11.9697 + 21.9483i) q^{25} -34.9064 q^{26} +(21.1258 + 21.1258i) q^{28} +14.2026i q^{29} -44.6924 q^{31} +(-23.5000 + 23.5000i) q^{32} +90.2989i q^{34} +(22.6714 + 5.78020i) q^{35} +(-2.84977 + 2.84977i) q^{37} +(39.8529 + 39.8529i) q^{38} +(9.49291 - 37.2336i) q^{40} -61.2271 q^{41} +(-10.2480 - 10.2480i) q^{43} +21.1758i q^{44} -53.4734 q^{46} +(-58.6916 + 58.6916i) q^{47} +27.1039i q^{49} +(-22.7379 - 77.2881i) q^{50} +(48.9030 - 48.9030i) q^{52} +(45.5877 + 45.5877i) q^{53} +(8.46561 + 14.2595i) q^{55} -35.9603 q^{56} +(-32.3632 - 32.3632i) q^{58} +3.71455i q^{59} -15.3228 q^{61} +(101.840 - 101.840i) q^{62} -104.002i q^{64} +(13.3803 - 52.4809i) q^{65} +(-23.6682 + 23.6682i) q^{67} +(-126.507 - 126.507i) q^{68} +(-64.8320 + 38.4896i) q^{70} -66.4871 q^{71} +(93.3093 + 93.3093i) q^{73} -12.9874i q^{74} -111.666 q^{76} +(10.9740 - 10.9740i) q^{77} -57.1583i q^{79} +(-1.97559 - 3.32770i) q^{80} +(139.517 - 139.517i) q^{82} +(-45.3490 - 45.3490i) q^{83} +(-135.762 - 34.6133i) q^{85} +46.7036 q^{86} +(-18.0228 - 18.0228i) q^{88} +114.906i q^{89} -50.6863 q^{91} +(74.9150 - 74.9150i) q^{92} -267.479i q^{94} +(-75.1944 + 44.6415i) q^{95} +(-31.9248 + 31.9248i) q^{97} +(-61.7610 - 61.7610i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} + 8 q^{5} - 12 q^{8} + 12 q^{10} + 4 q^{13} - 16 q^{16} - 24 q^{17} + 8 q^{20} + 86 q^{23} + 90 q^{25} - 96 q^{26} + 76 q^{28} - 40 q^{31} - 184 q^{32} + 60 q^{35} - 126 q^{37} - 184 q^{38}+ \cdots - 620 q^{98}+O(q^{100}) $ 20 * q + 4 * q^2 + 8 * q^5 - 12 * q^8 + 12 * q^10 + 4 * q^13 - 16 * q^16 - 24 * q^17 + 8 * q^20 + 86 * q^23 + 90 * q^25 - 96 * q^26 + 76 * q^28 - 40 * q^31 - 184 * q^32 + 60 * q^35 - 126 * q^37 - 184 * q^38 + 64 * q^40 + 56 * q^41 - 24 * q^43 + 168 * q^46 - 156 * q^47 + 352 * q^50 - 100 * q^52 + 52 * q^53 + 66 * q^55 - 216 * q^56 - 344 * q^58 - 120 * q^61 + 540 * q^62 + 56 * q^65 - 242 * q^67 - 204 * q^68 + 112 * q^70 + 204 * q^71 - 228 * q^73 - 504 * q^76 - 640 * q^80 + 256 * q^82 - 464 * q^83 - 532 * q^85 + 128 * q^86 - 264 * q^88 - 96 * q^91 + 168 * q^92 - 508 * q^95 + 290 * q^97 - 620 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−2.27868	+	2.27868i	−1.13934	+	1.13934i	−0.150770	+	0.988569i	$0.548175\pi$
$2$	−2.27868	+	2.27868i	−1.13934	+	1.13934i	−0.988569	+	0.150770i	$0.951825\pi$
$3$		0			0
$3$		0			0
$4$		−	6.38475i		−	1.59619i
$5$	−2.55248	−	4.29940i	−0.510496	−	0.859880i
$5$	−2.55248	−	4.29940i	−0.510496	−	0.859880i
$6$		0			0
$7$	−3.30878	+	3.30878i	−0.472684	+	0.472684i	−0.902782	−	0.430098i	$-0.858479\pi$
$7$	−3.30878	+	3.30878i	−0.472684	+	0.472684i	0.430098	+	0.902782i	$0.358479\pi$
$8$	5.43407	+	5.43407i	0.679259	+	0.679259i
$9$		0			0
$10$	15.6132	+	3.98068i	1.56132	+	0.398068i
$11$	−3.31662			−0.301511
$11$	−3.31662			−0.301511
$12$		0			0
$13$	7.65935	+	7.65935i	0.589180	+	0.589180i	0.937409	−	0.348229i	$-0.113217\pi$
$13$	7.65935	+	7.65935i	0.589180	+	0.589180i	−0.348229	+	0.937409i	$0.613217\pi$
$14$		−	15.0793i		−	1.07709i
$15$		0			0
$16$	0.773991			0.0483744
$17$	19.8139	−	19.8139i	1.16552	−	1.16552i	0.182274	−	0.983248i	$-0.441654\pi$
$17$	19.8139	−	19.8139i	1.16552	−	1.16552i	0.983248	−	0.182274i	$-0.0583458\pi$
$18$		0			0
$19$		−	17.4895i		−	0.920499i	−0.887789	−	0.460250i	$-0.847760\pi$
$19$		−	17.4895i		−	0.920499i	0.887789	−	0.460250i	$-0.152240\pi$
$20$	−27.4506	+	16.2969i	−1.37253	+	0.814846i
$21$		0			0
$22$	7.55752	−	7.55752i	0.343524	−	0.343524i
$23$	11.7334	+	11.7334i	0.510149	+	0.510149i	0.914572	−	0.404423i	$-0.132528\pi$
$23$	11.7334	+	11.7334i	0.510149	+	0.510149i	−0.404423	+	0.914572i	$0.632528\pi$
$24$		0			0
$25$	−11.9697	+	21.9483i	−0.478789	+	0.877930i
$26$	−34.9064			−1.34255
$27$		0			0
$28$	21.1258	+	21.1258i	0.754491	+	0.754491i
$29$			14.2026i			0.489745i	0.969555	+	0.244873i	$0.0787461\pi$
$29$			14.2026i			0.489745i	−0.969555	+	0.244873i	$0.921254\pi$
$30$		0			0
$31$	−44.6924			−1.44169			−0.720846	−	0.693096i	$-0.756246\pi$
$31$	−44.6924			−1.44169			−0.720846	+	0.693096i	$0.756246\pi$
$32$	−23.5000	+	23.5000i	−0.734374	+	0.734374i
$33$		0			0
$34$			90.2989i			2.65585i
$35$	22.6714	+	5.78020i	0.647754	+	0.165148i
$36$		0			0
$37$	−2.84977	+	2.84977i	−0.0770207	+	0.0770207i	−0.744568	−	0.667547i	$-0.767344\pi$
$37$	−2.84977	+	2.84977i	−0.0770207	+	0.0770207i	0.667547	+	0.744568i	$0.267344\pi$
$38$	39.8529	+	39.8529i	1.04876	+	1.04876i
$39$		0			0
$40$	9.49291	−	37.2336i	0.237323	−	0.930840i
$41$	−61.2271			−1.49334			−0.746672	−	0.665192i	$-0.768350\pi$
$41$	−61.2271			−1.49334			−0.746672	+	0.665192i	$0.768350\pi$
$42$		0			0
$43$	−10.2480	−	10.2480i	−0.238325	−	0.238325i	0.577832	−	0.816156i	$-0.303899\pi$
$43$	−10.2480	−	10.2480i	−0.238325	−	0.238325i	−0.816156	+	0.577832i	$0.803899\pi$
$44$			21.1758i			0.481268i
$45$		0			0
$46$	−53.4734			−1.16247
$47$	−58.6916	+	58.6916i	−1.24876	+	1.24876i	−0.292489	+	0.956269i	$0.594484\pi$
$47$	−58.6916	+	58.6916i	−1.24876	+	1.24876i	−0.956269	+	0.292489i	$0.905516\pi$
$48$		0			0
$49$			27.1039i			0.553141i
$50$	−22.7379	−	77.2881i	−0.454758	−	1.54576i
$51$		0			0
$52$	48.9030	−	48.9030i	0.940442	−	0.940442i
$53$	45.5877	+	45.5877i	0.860145	+	0.860145i	0.991355	−	0.131210i	$-0.0418861\pi$
$53$	45.5877	+	45.5877i	0.860145	+	0.860145i	−0.131210	+	0.991355i	$0.541886\pi$
$54$		0			0
$55$	8.46561	+	14.2595i	0.153920	+	0.259264i
$56$	−35.9603			−0.642149
$57$		0			0
$58$	−32.3632	−	32.3632i	−0.557986	−	0.557986i
$59$			3.71455i			0.0629584i	0.999504	+	0.0314792i	$0.0100218\pi$
$59$			3.71455i			0.0629584i	−0.999504	+	0.0314792i	$0.989978\pi$
$60$		0			0
$61$	−15.3228			−0.251193			−0.125596	−	0.992081i	$-0.540084\pi$
$61$	−15.3228			−0.251193			−0.125596	+	0.992081i	$0.540084\pi$
$62$	101.840	−	101.840i	1.64258	−	1.64258i
$63$		0			0
$64$		−	104.002i		−	1.62503i
$65$	13.3803	−	52.4809i	0.205851	−	0.807399i
$66$		0			0
$67$	−23.6682	+	23.6682i	−0.353257	+	0.353257i	−0.861320	−	0.508063i	$-0.830362\pi$
$67$	−23.6682	+	23.6682i	−0.353257	+	0.353257i	0.508063	+	0.861320i	$0.330362\pi$
$68$	−126.507	−	126.507i	−1.86039	−	1.86039i
$69$		0			0
$70$	−64.8320	+	38.4896i	−0.926172	+	0.549851i
$71$	−66.4871			−0.936438			−0.468219	−	0.883613i	$-0.655104\pi$
$71$	−66.4871			−0.936438			−0.468219	+	0.883613i	$0.655104\pi$
$72$		0			0
$73$	93.3093	+	93.3093i	1.27821	+	1.27821i	0.941669	+	0.336541i	$0.109257\pi$
$73$	93.3093	+	93.3093i	1.27821	+	1.27821i	0.336541	+	0.941669i	$0.390743\pi$
$74$		−	12.9874i		−	0.175505i
$75$		0			0
$76$	−111.666			−1.46929
$77$	10.9740	−	10.9740i	0.142519	−	0.142519i
$78$		0			0
$79$		−	57.1583i		−	0.723523i	−0.932271	−	0.361762i	$-0.882175\pi$
$79$		−	57.1583i		−	0.723523i	0.932271	−	0.361762i	$-0.117825\pi$
$80$	−1.97559	−	3.32770i	−0.0246949	−	0.0415962i
$81$		0			0
$82$	139.517	−	139.517i	1.70143	−	1.70143i
$83$	−45.3490	−	45.3490i	−0.546373	−	0.546373i	0.379017	−	0.925390i	$-0.376262\pi$
$83$	−45.3490	−	45.3490i	−0.546373	−	0.546373i	−0.925390	+	0.379017i	$0.876262\pi$
$84$		0			0
$85$	−135.762	−	34.6133i	−1.59720	−	0.407216i
$86$	46.7036			0.543065
$87$		0			0
$88$	−18.0228	−	18.0228i	−0.204804	−	0.204804i
$89$			114.906i			1.29107i	0.763729	+	0.645537i	$0.223366\pi$
$89$			114.906i			1.29107i	−0.763729	+	0.645537i	$0.776634\pi$
$90$		0			0
$91$	−50.6863			−0.556992
$92$	74.9150	−	74.9150i	0.814294	−	0.814294i
$93$		0			0
$94$		−	267.479i		−	2.84552i
$95$	−75.1944	+	44.6415i	−0.791519	+	0.469911i
$96$		0			0
$97$	−31.9248	+	31.9248i	−0.329121	+	0.329121i	−0.852252	−	0.523131i	$-0.824764\pi$
$97$	−31.9248	+	31.9248i	−0.329121	+	0.329121i	0.523131	+	0.852252i	$0.324764\pi$
$98$	−61.7610	−	61.7610i	−0.630215	−	0.630215i
$99$		0			0
$100$	140.134	+	76.4236i	1.40134	+	0.764236i
$101$	−109.388			−1.08305			−0.541523	−	0.840686i	$-0.682152\pi$
$101$	−109.388			−1.08305			−0.541523	+	0.840686i	$0.682152\pi$
$102$		0			0
$103$	−28.7421	−	28.7421i	−0.279050	−	0.279050i	0.553680	−	0.832730i	$-0.313223\pi$
$103$	−28.7421	−	28.7421i	−0.279050	−	0.279050i	−0.832730	+	0.553680i	$0.813223\pi$
$104$			83.2429i			0.800412i
$105$		0			0
$106$	−207.759			−1.95999
$107$	53.4385	−	53.4385i	0.499425	−	0.499425i	−0.411834	−	0.911259i	$-0.635112\pi$
$107$	53.4385	−	53.4385i	0.499425	−	0.499425i	0.911259	+	0.411834i	$0.135112\pi$
$108$		0			0
$109$			97.4174i			0.893738i	0.894600	+	0.446869i	$0.147461\pi$
$109$			97.4174i			0.893738i	−0.894600	+	0.446869i	$0.852539\pi$
$110$	−51.7832	−	13.2024i	−0.470757	−	0.120022i
$111$		0			0
$112$	−2.56097	+	2.56097i	−0.0228658	+	0.0228658i
$113$	109.416	+	109.416i	0.968280	+	0.968280i	0.999512	−	0.0312321i	$-0.00994311\pi$
$113$	109.416	+	109.416i	0.968280	+	0.968280i	−0.0312321	+	0.999512i	$0.509943\pi$
$114$		0			0
$115$	20.4974	−	80.3961i	0.178238	−	0.699096i
$116$	90.6801			0.781725
$117$		0			0
$118$	−8.46425	−	8.46425i	−0.0717310	−	0.0717310i
$119$			131.120i			1.10185i
$120$		0			0
$121$	11.0000			0.0909091
$122$	34.9156	−	34.9156i	0.286194	−	0.286194i
$123$		0			0
$124$			285.350i			2.30121i
$125$	124.917	−	4.55981i	0.999334	−	0.0364785i
$126$		0			0
$127$	−3.94652	+	3.94652i	−0.0310749	+	0.0310749i	−0.722474	−	0.691399i	$-0.756995\pi$
$127$	−3.94652	+	3.94652i	−0.0310749	+	0.0310749i	0.691399	+	0.722474i	$0.256995\pi$
$128$	142.987	+	142.987i	1.11708	+	1.11708i
$129$		0			0
$130$	89.0977	+	150.077i	0.685367	+	1.15443i
$131$	165.435			1.26286			0.631430	−	0.775433i	$-0.282468\pi$
$131$	165.435			1.26286			0.631430	+	0.775433i	$0.282468\pi$
$132$		0			0
$133$	57.8690	+	57.8690i	0.435105	+	0.435105i
$134$		−	107.864i		−	0.804958i
$135$		0			0
$136$	215.340			1.58338
$137$	−47.3215	+	47.3215i	−0.345412	+	0.345412i	−0.858397	−	0.512985i	$-0.828540\pi$
$137$	−47.3215	+	47.3215i	−0.345412	+	0.345412i	0.512985	+	0.858397i	$0.328540\pi$
$138$		0			0
$139$			157.241i			1.13123i	0.824670	+	0.565614i	$0.191361\pi$
$139$			157.241i			1.13123i	−0.824670	+	0.565614i	$0.808639\pi$
$140$	36.9051	−	144.751i	0.263608	−	1.03394i
$141$		0			0
$142$	151.503	−	151.503i	1.06692	−	1.06692i
$143$	−25.4032	−	25.4032i	−0.177645	−	0.177645i
$144$		0			0
$145$	61.0627	−	36.2518i	0.421122	−	0.250013i
$146$	−425.244			−2.91263
$147$		0			0
$148$	18.1950	+	18.1950i	0.122939	+	0.122939i
$149$			91.9814i			0.617325i	0.951172	+	0.308663i	$0.0998814\pi$
$149$			91.9814i			0.617325i	−0.951172	+	0.308663i	$0.900119\pi$
$150$		0			0
$151$	178.745			1.18374			0.591870	−	0.806034i	$-0.298390\pi$
$151$	178.745			1.18374			0.591870	+	0.806034i	$0.298390\pi$
$152$	95.0391	−	95.0391i	0.625257	−	0.625257i
$153$		0			0
$154$			50.0124i			0.324756i
$155$	114.076	+	192.151i	0.735977	+	1.23968i
$156$		0			0
$157$	−85.3500	+	85.3500i	−0.543631	+	0.543631i	−0.924591	−	0.380961i	$-0.875593\pi$
$157$	−85.3500	+	85.3500i	−0.543631	+	0.543631i	0.380961	+	0.924591i	$0.375593\pi$
$158$	130.245	+	130.245i	0.824338	+	0.824338i
$159$		0			0
$160$	161.019	+	41.0527i	1.00637	+	0.256579i
$161$	−77.6468			−0.482278
$162$		0			0
$163$	34.8150	+	34.8150i	0.213589	+	0.213589i	0.805790	−	0.592201i	$-0.201741\pi$
$163$	34.8150	+	34.8150i	0.213589	+	0.213589i	−0.592201	+	0.805790i	$0.701741\pi$
$164$			390.920i			2.38366i
$165$		0			0
$166$	206.671			1.24501
$167$	8.73842	−	8.73842i	0.0523259	−	0.0523259i	−0.680460	−	0.732786i	$-0.738220\pi$
$167$	8.73842	−	8.73842i	0.0523259	−	0.0523259i	0.732786	+	0.680460i	$0.238220\pi$
$168$		0			0
$169$		−	51.6688i		−	0.305733i
$170$	388.231	−	230.486i	2.28371	−	1.35580i
$171$		0			0
$172$	−65.4306	+	65.4306i	−0.380411	+	0.380411i
$173$	−40.7527	−	40.7527i	−0.235565	−	0.235565i	0.579446	−	0.815011i	$-0.303269\pi$
$173$	−40.7527	−	40.7527i	−0.235565	−	0.235565i	−0.815011	+	0.579446i	$0.803269\pi$
$174$		0			0
$175$	−33.0168	−	112.227i	−0.188668	−	0.641299i
$176$	−2.56704			−0.0145854
$177$		0			0
$178$	−261.833	−	261.833i	−1.47097	−	1.47097i
$179$		−	299.550i		−	1.67346i	−0.547613	−	0.836732i	$-0.684463\pi$
$179$		−	299.550i		−	1.67346i	0.547613	−	0.836732i	$-0.315537\pi$
$180$		0			0
$181$	−204.042			−1.12730			−0.563651	−	0.826013i	$-0.690604\pi$
$181$	−204.042			−1.12730			−0.563651	+	0.826013i	$0.690604\pi$
$182$	115.498	−	115.498i	0.634602	−	0.634602i
$183$		0			0
$184$			127.521i			0.693047i
$185$	19.5263	+	4.97833i	0.105547	+	0.0269099i
$186$		0			0
$187$	−65.7152	+	65.7152i	−0.351418	+	0.351418i
$188$	374.731	+	374.731i	1.99325	+	1.99325i
$189$		0			0
$190$	69.6200	−	273.067i	0.366421	−	1.43720i
$191$	−68.1555			−0.356835			−0.178418	−	0.983955i	$-0.557098\pi$
$191$	−68.1555			−0.356835			−0.178418	+	0.983955i	$0.557098\pi$
$192$		0			0
$193$	56.3440	+	56.3440i	0.291938	+	0.291938i	0.837845	−	0.545908i	$-0.183815\pi$
$193$	56.3440	+	56.3440i	0.291938	+	0.291938i	−0.545908	+	0.837845i	$0.683815\pi$
$194$		−	145.493i		−	0.749962i
$195$		0			0
$196$	173.051			0.882916
$197$	−61.2935	+	61.2935i	−0.311134	+	0.311134i	−0.845349	−	0.534215i	$-0.820607\pi$
$197$	−61.2935	+	61.2935i	−0.311134	+	0.311134i	0.534215	+	0.845349i	$0.320607\pi$
$198$		0			0
$199$			291.772i			1.46619i	0.680125	+	0.733096i	$0.261925\pi$
$199$			291.772i			1.46619i	−0.680125	+	0.733096i	$0.738075\pi$
$200$	−184.313	+	54.2241i	−0.921563	+	0.271120i
$201$		0			0
$202$	249.259	−	249.259i	1.23396	−	1.23396i
$203$	−46.9934	−	46.9934i	−0.231494	−	0.231494i
$204$		0			0
$205$	156.281	+	263.240i	0.762346	+	1.28410i
$206$	130.988			0.635864
$207$		0			0
$208$	5.92826	+	5.92826i	0.0285013	+	0.0285013i
$209$			58.0061i			0.277541i
$210$		0			0
$211$	−93.8771			−0.444915			−0.222458	−	0.974942i	$-0.571408\pi$
$211$	−93.8771			−0.444915			−0.222458	+	0.974942i	$0.571408\pi$
$212$	291.066	−	291.066i	1.37295	−	1.37295i
$213$		0			0
$214$			243.538i			1.13803i
$215$	−17.9024	+	70.2178i	−0.0832670	+	0.326594i
$216$		0			0
$217$	147.878	−	147.878i	0.681464	−	0.681464i
$218$	−221.983	−	221.983i	−1.01827	−	1.01827i
$219$		0			0
$220$	91.0433	−	54.0508i	0.413833	−	0.245685i
$221$	303.523			1.37341
$222$		0			0
$223$	−158.088	−	158.088i	−0.708915	−	0.708915i	0.257392	−	0.966307i	$-0.417137\pi$
$223$	−158.088	−	158.088i	−0.708915	−	0.708915i	−0.966307	+	0.257392i	$0.917137\pi$
$224$		−	155.513i		−	0.694253i
$225$		0			0
$226$	−498.646			−2.20640
$227$	−158.917	+	158.917i	−0.700076	+	0.700076i	−0.964427	−	0.264351i	$-0.914842\pi$
$227$	−158.917	+	158.917i	−0.700076	+	0.700076i	0.264351	+	0.964427i	$0.414842\pi$
$228$		0			0
$229$			43.6426i			0.190579i	0.995450	+	0.0952895i	$0.0303777\pi$
$229$			43.6426i			0.190579i	−0.995450	+	0.0952895i	$0.969622\pi$
$230$	136.490	+	229.904i	0.593434	+	0.999582i
$231$		0			0
$232$	−77.1780	+	77.1780i	−0.332664	+	0.332664i
$233$	−231.736	−	231.736i	−0.994574	−	0.994574i	0.00541090	−	0.999985i	$-0.498278\pi$
$233$	−231.736	−	231.736i	−0.994574	−	0.994574i	−0.999985	+	0.00541090i	$0.998278\pi$
$234$		0			0
$235$	402.148	+	102.530i	1.71127	+	0.436297i
$236$	23.7164			0.100493
$237$		0			0
$238$	−298.780	−	298.780i	−1.25538	−	1.25538i
$239$		−	203.850i		−	0.852930i	−0.904504	−	0.426465i	$-0.859759\pi$
$239$		−	203.850i		−	0.852930i	0.904504	−	0.426465i	$-0.140241\pi$
$240$		0			0
$241$	96.8670			0.401938			0.200969	−	0.979598i	$-0.435591\pi$
$241$	96.8670			0.401938			0.200969	+	0.979598i	$0.435591\pi$
$242$	−25.0655	+	25.0655i	−0.103576	+	0.103576i
$243$		0			0
$244$			97.8320i			0.400951i
$245$	116.531	−	69.1821i	0.475635	−	0.282376i
$246$		0			0
$247$	133.958	−	133.958i	0.542340	−	0.542340i
$248$	−242.862	−	242.862i	−0.979282	−	0.979282i
$249$		0			0
$250$	−274.255	+	295.036i	−1.09702	+	1.18014i
$251$	165.654			0.659978			0.329989	−	0.943985i	$-0.392955\pi$
$251$	165.654			0.659978			0.329989	+	0.943985i	$0.392955\pi$
$252$		0			0
$253$	−38.9154	−	38.9154i	−0.153816	−	0.153816i
$254$		−	17.9857i		−	0.0708098i
$255$		0			0
$256$	−235.634			−0.920445
$257$	−168.525	+	168.525i	−0.655740	+	0.655740i	−0.954369	−	0.298629i	$-0.903471\pi$
$257$	−168.525	+	168.525i	−0.655740	+	0.655740i	0.298629	+	0.954369i	$0.403471\pi$
$258$		0			0
$259$		−	18.8585i		−	0.0728128i
$260$	−335.077	−	85.4298i	−1.28876	−	0.328576i
$261$		0			0
$262$	−376.972	+	376.972i	−1.43883	+	1.43883i
$263$	50.7899	+	50.7899i	0.193117	+	0.193117i	0.797042	−	0.603924i	$-0.206397\pi$
$263$	50.7899	+	50.7899i	0.193117	+	0.193117i	−0.603924	+	0.797042i	$0.706397\pi$
$264$		0			0
$265$	79.6382	−	312.361i	0.300522	−	1.17872i
$266$	−263.729			−0.991464
$267$		0			0
$268$	151.115	+	151.115i	0.563864	+	0.563864i
$269$			256.648i			0.954081i	0.878881	+	0.477041i	$0.158291\pi$
$269$			256.648i			0.954081i	−0.878881	+	0.477041i	$0.841709\pi$
$270$		0			0
$271$	−215.163			−0.793958			−0.396979	−	0.917828i	$-0.629941\pi$
$271$	−215.163			−0.793958			−0.396979	+	0.917828i	$0.629941\pi$
$272$	15.3358	−	15.3358i	0.0563815	−	0.0563815i
$273$		0			0
$274$		−	215.661i		−	0.787083i
$275$	39.6991	−	72.7941i	0.144360	−	0.264706i
$276$		0			0
$277$	73.9418	−	73.9418i	0.266938	−	0.266938i	−0.560927	−	0.827865i	$-0.689555\pi$
$277$	73.9418	−	73.9418i	0.266938	−	0.266938i	0.827865	+	0.560927i	$0.189555\pi$
$278$	−358.301	−	358.301i	−1.28885	−	1.28885i
$279$		0			0
$280$	91.7880	+	154.608i	0.327814	+	0.552171i
$281$	−190.836			−0.679133			−0.339566	−	0.940582i	$-0.610280\pi$
$281$	−190.836			−0.679133			−0.339566	+	0.940582i	$0.610280\pi$
$282$		0			0
$283$	−87.1090	−	87.1090i	−0.307806	−	0.307806i	0.536252	−	0.844058i	$-0.319840\pi$
$283$	−87.1090	−	87.1090i	−0.307806	−	0.307806i	−0.844058	+	0.536252i	$0.819840\pi$
$284$			424.503i			1.49473i
$285$		0			0
$286$	115.771			0.404795
$287$	202.587	−	202.587i	0.705879	−	0.705879i
$288$		0			0
$289$		−	496.179i		−	1.71688i
$290$	−56.5360	+	221.749i	−0.194952	+	0.764650i
$291$		0			0
$292$	595.756	−	595.756i	2.04026	−	2.04026i
$293$	317.484	+	317.484i	1.08356	+	1.08356i	0.996174	+	0.0873871i	$0.0278517\pi$
$293$	317.484	+	317.484i	1.08356	+	1.08356i	0.0873871	+	0.996174i	$0.472148\pi$
$294$		0			0
$295$	15.9703	−	9.48129i	0.0541367	−	0.0321400i
$296$	−30.9717			−0.104634
$297$		0			0
$298$	−209.596	−	209.596i	−0.703343	−	0.703343i
$299$			179.741i			0.601140i
$300$		0			0
$301$	67.8166			0.225304
$302$	−407.302	+	407.302i	−1.34868	+	1.34868i
$303$		0			0
$304$		−	13.5367i		−	0.0445286i
$305$	39.1110	+	65.8787i	0.128233	+	0.215996i
$306$		0			0
$307$	−263.140	+	263.140i	−0.857132	+	0.857132i	−0.990999	−	0.133867i	$-0.957261\pi$
$307$	−263.140	+	263.140i	−0.857132	+	0.857132i	0.133867	+	0.990999i	$0.457261\pi$
$308$	−70.0662	−	70.0662i	−0.227488	−	0.227488i
$309$		0			0
$310$	−697.793	−	177.906i	−2.25095	−	0.573891i
$311$	−301.613			−0.969816			−0.484908	−	0.874565i	$-0.661147\pi$
$311$	−301.613			−0.969816			−0.484908	+	0.874565i	$0.661147\pi$
$312$		0			0
$313$	98.0189	+	98.0189i	0.313159	+	0.313159i	0.846132	−	0.532973i	$-0.178925\pi$
$313$	98.0189	+	98.0189i	0.313159	+	0.313159i	−0.532973	+	0.846132i	$0.678925\pi$
$314$		−	388.971i		−	1.23876i
$315$		0			0
$316$	−364.941			−1.15488
$317$	−232.617	+	232.617i	−0.733806	+	0.733806i	−0.971372	−	0.237565i	$-0.923651\pi$
$317$	−232.617	+	232.617i	−0.733806	+	0.733806i	0.237565	+	0.971372i	$0.423651\pi$
$318$		0			0
$319$		−	47.1047i		−	0.147664i
$320$	−447.145	+	265.462i	−1.39733	+	0.829569i
$321$		0			0
$322$	176.932	−	176.932i	0.549479	−	0.549479i
$323$	−346.535	−	346.535i	−1.07286	−	1.07286i
$324$		0			0
$325$	−259.789	+	76.4291i	−0.799352	+	0.235166i
$326$	−158.664			−0.486701
$327$		0			0
$328$	−332.713	−	332.713i	−1.01437	−	1.01437i
$329$		−	388.396i		−	1.18053i
$330$		0			0
$331$	124.210			0.375256			0.187628	−	0.982240i	$-0.439920\pi$
$331$	124.210			0.375256			0.187628	+	0.982240i	$0.439920\pi$
$332$	−289.542	+	289.542i	−0.872113	+	0.872113i
$333$		0			0
$334$			39.8241i			0.119234i
$335$	162.172	+	41.3466i	0.484095	+	0.123423i
$336$		0			0
$337$	248.427	−	248.427i	0.737171	−	0.737171i	−0.234858	−	0.972030i	$-0.575463\pi$
$337$	248.427	−	248.427i	0.737171	−	0.737171i	0.972030	+	0.234858i	$0.0754626\pi$
$338$	117.737	+	117.737i	0.348333	+	0.348333i
$339$		0			0
$340$	−220.997	+	866.808i	−0.649992	+	2.54943i
$341$	148.228			0.434686
$342$		0			0
$343$	−251.811	−	251.811i	−0.734144	−	0.734144i
$344$		−	111.376i		−	0.323768i
$345$		0			0
$346$	185.724			0.536776
$347$	−194.711	+	194.711i	−0.561127	+	0.561127i	−0.929628	−	0.368501i	$-0.879871\pi$
$347$	−194.711	+	194.711i	−0.561127	+	0.561127i	0.368501	+	0.929628i	$0.379871\pi$
$348$		0			0
$349$		−	23.5545i		−	0.0674914i	−0.999430	−	0.0337457i	$-0.989256\pi$
$349$		−	23.5545i		−	0.0674914i	0.999430	−	0.0337457i	$-0.0107436\pi$
$350$	330.965	+	180.495i	0.945613	+	0.515700i
$351$		0			0
$352$	77.9406	−	77.9406i	0.221422	−	0.221422i
$353$	60.4688	+	60.4688i	0.171300	+	0.171300i	0.787550	−	0.616251i	$-0.211349\pi$
$353$	60.4688	+	60.4688i	0.171300	+	0.171300i	−0.616251	+	0.787550i	$0.711349\pi$
$354$		0			0
$355$	169.707	+	285.855i	0.478047	+	0.805224i
$356$	733.643			2.06080
$357$		0			0
$358$	682.578	+	682.578i	1.90664	+	1.90664i
$359$		−	502.684i		−	1.40024i	−0.714028	−	0.700118i	$-0.753131\pi$
$359$		−	502.684i		−	1.40024i	0.714028	−	0.700118i	$-0.246869\pi$
$360$		0			0
$361$	55.1177			0.152681
$362$	464.945	−	464.945i	1.28438	−	1.28438i
$363$		0			0
$364$			323.619i			0.889063i
$365$	163.004	−	639.344i	0.446587	−	1.75163i
$366$		0			0
$367$	−402.334	+	402.334i	−1.09628	+	1.09628i	−0.101437	+	0.994842i	$0.532344\pi$
$367$	−402.334	+	402.334i	−1.09628	+	1.09628i	−0.994842	+	0.101437i	$0.967656\pi$
$368$	9.08157	+	9.08157i	0.0246782	+	0.0246782i
$369$		0			0
$370$	−55.8381	+	33.1500i	−0.150914	+	0.0895947i
$371$	−301.680			−0.813153
$372$		0			0
$373$	−129.594	−	129.594i	−0.347437	−	0.347437i	0.511717	−	0.859154i	$-0.329010\pi$
$373$	−129.594	−	129.594i	−0.347437	−	0.347437i	−0.859154	+	0.511717i	$0.829010\pi$
$374$		−	299.487i		−	0.800769i
$375$		0			0
$376$	−637.869			−1.69646
$377$	−108.783	+	108.783i	−0.288548	+	0.288548i
$378$		0			0
$379$		−	308.983i		−	0.815260i	−0.913147	−	0.407630i	$-0.866355\pi$
$379$		−	308.983i		−	0.815260i	0.913147	−	0.407630i	$-0.133645\pi$
$380$	285.025	+	480.097i	0.750066	+	1.26341i
$381$		0			0
$382$	155.305	−	155.305i	0.406556	−	0.406556i
$383$	137.024	+	137.024i	0.357765	+	0.357765i	0.862989	−	0.505223i	$-0.168590\pi$
$383$	137.024	+	137.024i	0.357765	+	0.357765i	−0.505223	+	0.862989i	$0.668590\pi$
$384$		0			0
$385$	−75.1925	−	19.1707i	−0.195305	−	0.0497941i
$386$	−256.780			−0.665232
$387$		0			0
$388$	203.832	+	203.832i	0.525339	+	0.525339i
$389$			219.114i			0.563275i	0.959521	+	0.281637i	$0.0908775\pi$
$389$			219.114i			0.563275i	−0.959521	+	0.281637i	$0.909122\pi$
$390$		0			0
$391$	464.970			1.18918
$392$	−147.284	+	147.284i	−0.375726	+	0.375726i
$393$		0			0
$394$		−	279.336i		−	0.708975i
$395$	−245.747	+	145.895i	−0.622143	+	0.369355i
$396$		0			0
$397$	447.147	−	447.147i	1.12631	−	1.12631i	0.135542	−	0.990772i	$-0.456722\pi$
$397$	447.147	−	447.147i	1.12631	−	1.12631i	0.990772	−	0.135542i	$-0.0432777\pi$
$398$	−664.855	−	664.855i	−1.67049	−	1.67049i
$399$		0			0
$400$	−9.26445	+	16.9878i	−0.0231611	+	0.0424694i
$401$	697.196			1.73864			0.869321	−	0.494247i	$-0.164556\pi$
$401$	697.196			1.73864			0.869321	+	0.494247i	$0.164556\pi$
$402$		0			0
$403$	−342.315	−	342.315i	−0.849416	−	0.849416i
$404$			698.412i			1.72874i
$405$		0			0
$406$	214.166			0.527501
$407$	9.45161	−	9.45161i	0.0232226	−	0.0232226i
$408$		0			0
$409$			37.7115i			0.0922043i	0.998937	+	0.0461021i	$0.0146800\pi$
$409$			37.7115i			0.0922043i	−0.998937	+	0.0461021i	$0.985320\pi$
$410$	−955.953	−	243.725i	−2.33159	−	0.594452i
$411$		0			0
$412$	−183.511	+	183.511i	−0.445415	+	0.445415i
$413$	−12.2906	−	12.2906i	−0.0297594	−	0.0297594i
$414$		0			0
$415$	−79.2212	+	310.726i	−0.190894	+	0.748736i
$416$	−359.989			−0.865357
$417$		0			0
$418$	−132.177	−	132.177i	−0.316213	−	0.316213i
$419$		−	486.001i		−	1.15991i	−0.814650	−	0.579953i	$-0.803071\pi$
$419$		−	486.001i		−	1.15991i	0.814650	−	0.579953i	$-0.196929\pi$
$420$		0			0
$421$	−388.904			−0.923762			−0.461881	−	0.886942i	$-0.652825\pi$
$421$	−388.904			−0.923762			−0.461881	+	0.886942i	$0.652825\pi$
$422$	213.916	−	213.916i	0.506909	−	0.506909i
$423$		0			0
$424$			495.453i			1.16852i
$425$	197.714	+	672.046i	0.465208	+	1.58129i
$426$		0			0
$427$	50.6997	−	50.6997i	0.118735	−	0.118735i
$428$	−341.191	−	341.191i	−0.797175	−	0.797175i
$429$		0			0
$430$	−119.210	−	200.797i	−0.277232	−	0.466971i
$431$	−504.929			−1.17153			−0.585764	−	0.810482i	$-0.699205\pi$
$431$	−504.929			−1.17153			−0.585764	+	0.810482i	$0.699205\pi$
$432$		0			0
$433$	150.370	+	150.370i	0.347274	+	0.347274i	0.859093	−	0.511819i	$-0.171028\pi$
$433$	150.370	+	150.370i	0.347274	+	0.347274i	−0.511819	+	0.859093i	$0.671028\pi$
$434$			673.931i			1.55284i
$435$		0			0
$436$	621.985			1.42657
$437$	205.212	−	205.212i	0.469592	−	0.469592i
$438$		0			0
$439$			210.919i			0.480454i	0.970717	+	0.240227i	$0.0772219\pi$
$439$			210.919i			0.480454i	−0.970717	+	0.240227i	$0.922778\pi$
$440$	−31.4844	+	123.490i	−0.0715555	+	0.280659i
$441$		0			0
$442$	−691.630	+	691.630i	−1.56477	+	1.56477i
$443$	442.849	+	442.849i	0.999660	+	0.999660i	1.00000		0.000339697i	$-0.000108129\pi$
$443$	442.849	+	442.849i	0.999660	+	0.999660i	−0.000339697		1.00000i	$0.500108\pi$
$444$		0			0
$445$	494.026	−	293.294i	1.11017	−	0.659088i
$446$	720.463			1.61539
$447$		0			0
$448$	344.119	+	344.119i	0.768123	+	0.768123i
$449$		−	641.685i		−	1.42914i	−0.699563	−	0.714571i	$-0.746622\pi$
$449$		−	641.685i		−	1.42914i	0.699563	−	0.714571i	$-0.253378\pi$
$450$		0			0
$451$	203.067			0.450260
$452$	698.591	−	698.591i	1.54556	−	1.54556i
$453$		0			0
$454$		−	724.243i		−	1.59525i
$455$	129.376	+	217.921i	0.284342	+	0.478946i
$456$		0			0
$457$	−103.709	+	103.709i	−0.226934	+	0.226934i	−0.811411	−	0.584477i	$-0.801300\pi$
$457$	−103.709	+	103.709i	−0.226934	+	0.226934i	0.584477	+	0.811411i	$0.301300\pi$
$458$	−99.4474	−	99.4474i	−0.217134	−	0.217134i
$459$		0			0
$460$	−513.309	−	130.871i	−1.11589	−	0.284502i
$461$	800.040			1.73544			0.867722	−	0.497050i	$-0.165583\pi$
$461$	800.040			1.73544			0.867722	+	0.497050i	$0.165583\pi$
$462$		0			0
$463$	252.447	+	252.447i	0.545242	+	0.545242i	0.925061	−	0.379819i	$-0.124014\pi$
$463$	252.447	+	252.447i	0.545242	+	0.545242i	−0.379819	+	0.925061i	$0.624014\pi$
$464$			10.9927i			0.0236911i
$465$		0			0
$466$	1056.10			2.26631
$467$	−80.1036	+	80.1036i	−0.171528	+	0.171528i	−0.787650	−	0.616122i	$-0.788703\pi$
$467$	−80.1036	+	80.1036i	−0.171528	+	0.171528i	0.616122	+	0.787650i	$0.288703\pi$
$468$		0			0
$469$		−	156.626i		−	0.333957i
$470$	−1150.00	+	682.733i	−2.44680	+	1.45262i
$471$		0			0
$472$	−20.1851	+	20.1851i	−0.0427651	+	0.0427651i
$473$	33.9886	+	33.9886i	0.0718576	+	0.0718576i
$474$		0			0
$475$	383.864	+	209.344i	0.808134	+	0.440725i
$476$	837.166			1.75875
$477$		0			0
$478$	464.509	+	464.509i	0.971776	+	0.971776i
$479$		−	411.116i		−	0.858280i	−0.903238	−	0.429140i	$-0.858817\pi$
$479$		−	411.116i		−	0.858280i	0.903238	−	0.429140i	$-0.141183\pi$
$480$		0			0
$481$	−43.6547			−0.0907582
$482$	−220.729	+	220.729i	−0.457944	+	0.457944i
$483$		0			0
$484$		−	70.2322i		−	0.145108i
$485$	218.745	+	55.7702i	0.451020	+	0.114990i
$486$		0			0
$487$	−212.163	+	212.163i	−0.435652	+	0.435652i	−0.890546	−	0.454894i	$-0.849677\pi$
$487$	−212.163	+	212.163i	−0.435652	+	0.435652i	0.454894	+	0.890546i	$0.349677\pi$
$488$	−83.2650	−	83.2650i	−0.170625	−	0.170625i
$489$		0			0
$490$	−107.892	+	423.179i	−0.220187	+	0.863631i
$491$	−113.699			−0.231566			−0.115783	−	0.993275i	$-0.536938\pi$
$491$	−113.699			−0.231566			−0.115783	+	0.993275i	$0.536938\pi$
$492$		0			0
$493$	281.409	+	281.409i	0.570809	+	0.570809i
$494$			610.495i			1.23582i
$495$		0			0
$496$	−34.5915			−0.0697410
$497$	219.991	−	219.991i	0.442639	−	0.442639i
$498$		0			0
$499$		−	343.023i		−	0.687421i	−0.939076	−	0.343711i	$-0.888316\pi$
$499$		−	343.023i		−	0.687421i	0.939076	−	0.343711i	$-0.111684\pi$
$500$	−29.1133	−	797.562i	−0.0582265	−	1.59512i
$501$		0			0
$502$	−377.473	+	377.473i	−0.751939	+	0.751939i
$503$	625.342	+	625.342i	1.24323	+	1.24323i	0.958655	+	0.284571i	$0.0918510\pi$
$503$	625.342	+	625.342i	1.24323	+	1.24323i	0.284571	+	0.958655i	$0.408149\pi$
$504$		0			0
$505$	279.209	+	470.301i	0.552890	+	0.931290i
$506$	177.351			0.350497
$507$		0			0
$508$	25.1975	+	25.1975i	0.0496014	+	0.0496014i
$509$			106.269i			0.208780i	0.994536	+	0.104390i	$0.0332890\pi$
$509$			106.269i			0.208780i	−0.994536	+	0.104390i	$0.966711\pi$
$510$		0			0
$511$	−617.481			−1.20838
$512$	−35.0124	+	35.0124i	−0.0683837	+	0.0683837i
$513$		0			0
$514$		−	768.029i		−	1.49422i
$515$	−50.2103	+	196.937i	−0.0974957	+	0.382403i
$516$		0			0
$517$	194.658	−	194.658i	0.376515	−	0.376515i
$518$	42.9725	+	42.9725i	0.0829585	+	0.0829585i
$519$		0			0
$520$	357.895	−	212.476i	0.688259	−	0.408607i
$521$	−483.272			−0.927586			−0.463793	−	0.885944i	$-0.653512\pi$
$521$	−483.272			−0.927586			−0.463793	+	0.885944i	$0.653512\pi$
$522$		0			0
$523$	−224.917	−	224.917i	−0.430052	−	0.430052i	0.458594	−	0.888646i	$-0.348353\pi$
$523$	−224.917	−	224.917i	−0.430052	−	0.430052i	−0.888646	+	0.458594i	$0.848353\pi$
$524$		−	1056.26i		−	2.01576i
$525$		0			0
$526$	−231.468			−0.440052
$527$	−885.530	+	885.530i	−1.68032	+	1.68032i
$528$		0			0
$529$		−	253.653i		−	0.479495i
$530$	530.301	+	893.241i	1.00057	+	1.68536i
$531$		0			0
$532$	369.479	−	369.479i	0.694509	−	0.694509i
$533$	−468.960	−	468.960i	−0.879849	−	0.879849i
$534$		0			0
$535$	−366.154	−	93.3530i	−0.684400	−	0.174492i
$536$	−257.229			−0.479906
$537$		0			0
$538$	−584.818	−	584.818i	−1.08702	−	1.08702i
$539$		−	89.8934i		−	0.166778i
$540$		0			0
$541$	507.591			0.938246			0.469123	−	0.883133i	$-0.344570\pi$
$541$	507.591			0.938246			0.469123	+	0.883133i	$0.344570\pi$
$542$	490.286	−	490.286i	0.904587	−	0.904587i
$543$		0			0
$544$			931.251i			1.71186i
$545$	418.837	−	248.656i	0.768507	−	0.456249i
$546$		0			0
$547$	−224.439	+	224.439i	−0.410309	+	0.410309i	−0.881846	−	0.471537i	$-0.843699\pi$
$547$	−224.439	+	224.439i	−0.410309	+	0.410309i	0.471537	+	0.881846i	$0.343699\pi$
$548$	302.136	+	302.136i	0.551342	+	0.551342i
$549$		0			0
$550$	75.4130	+	256.336i	0.137115	+	0.466065i
$551$	248.396			0.450810
$552$		0			0
$553$	189.125	+	189.125i	0.341997	+	0.341997i
$554$			336.979i			0.608265i
$555$		0			0
$556$	1003.94			1.80565
$557$	−40.3442	+	40.3442i	−0.0724312	+	0.0724312i	−0.742394	−	0.669963i	$-0.766310\pi$
$557$	−40.3442	+	40.3442i	−0.0724312	+	0.0724312i	0.669963	+	0.742394i	$0.266310\pi$
$558$		0			0
$559$		−	156.985i		−	0.280832i
$560$	17.5475	+	4.47382i	0.0313347	+	0.00798896i
$561$		0			0
$562$	434.854	−	434.854i	0.773762	−	0.773762i
$563$	75.8838	+	75.8838i	0.134785	+	0.134785i	0.771280	−	0.636496i	$-0.219617\pi$
$563$	75.8838	+	75.8838i	0.134785	+	0.134785i	−0.636496	+	0.771280i	$0.719617\pi$
$564$		0			0
$565$	191.141	−	749.703i	0.338302	−	1.32691i
$566$	396.987			0.701390
$567$		0			0
$568$	−361.295	−	361.295i	−0.636084	−	0.636084i
$569$		−	940.148i		−	1.65228i	−0.563464	−	0.826141i	$-0.690532\pi$
$569$		−	940.148i		−	1.65228i	0.563464	−	0.826141i	$-0.309468\pi$
$570$		0			0
$571$	−77.9393			−0.136496			−0.0682481	−	0.997668i	$-0.521741\pi$
$571$	−77.9393			−0.136496			−0.0682481	+	0.997668i	$0.521741\pi$
$572$	−162.193	+	162.193i	−0.283554	+	0.283554i
$573$		0			0
$574$			923.263i			1.60847i
$575$	−397.974	+	117.083i	−0.692129	+	0.203622i
$576$		0			0
$577$	−500.861	+	500.861i	−0.868043	+	0.868043i	−0.992256	−	0.124213i	$-0.960359\pi$
$577$	−500.861	+	500.861i	−0.868043	+	0.868043i	0.124213	+	0.992256i	$0.460359\pi$
$578$	1130.63	+	1130.63i	1.95611	+	1.95611i
$579$		0			0
$580$	−231.459	−	389.870i	−0.399067	−	0.672190i
$581$	300.100			0.516523
$582$		0			0
$583$	−151.197	−	151.197i	−0.259343	−	0.259343i
$584$			1014.10i			1.73647i
$585$		0			0
$586$	−1446.89			−2.46909
$587$	101.416	−	101.416i	0.172771	−	0.172771i	−0.615425	−	0.788196i	$-0.711016\pi$
$587$	101.416	−	101.416i	0.172771	−	0.172771i	0.788196	+	0.615425i	$0.211016\pi$
$588$		0			0
$589$			781.648i			1.32708i
$590$	−14.7864	+	57.9960i	−0.0250617	+	0.0982984i
$591$		0			0
$592$	−2.20569	+	2.20569i	−0.00372583	+	0.00372583i
$593$	−597.297	−	597.297i	−1.00725	−	1.00725i	−0.999974	−	0.00727231i	$-0.997685\pi$
$593$	−597.297	−	597.297i	−1.00725	−	1.00725i	−0.00727231	−	0.999974i	$-0.502315\pi$
$594$		0			0
$595$	563.736	−	334.680i	0.947456	−	0.562487i
$596$	587.278			0.985366
$597$		0			0
$598$	−409.572	−	409.572i	−0.684902	−	0.684902i
$599$			347.771i			0.580585i	0.956938	+	0.290293i	$0.0937527\pi$
$599$			347.771i			0.580585i	−0.956938	+	0.290293i	$0.906247\pi$
$600$		0			0
$601$	−192.174			−0.319757			−0.159878	−	0.987137i	$-0.551110\pi$
$601$	−192.174			−0.319757			−0.159878	+	0.987137i	$0.551110\pi$
$602$	−154.532	+	154.532i	−0.256698	+	0.256698i
$603$		0			0
$604$		−	1141.24i		−	1.88947i
$605$	−28.0773	−	47.2934i	−0.0464087	−	0.0781709i
$606$		0			0
$607$	−74.3868	+	74.3868i	−0.122548	+	0.122548i	−0.765721	−	0.643173i	$-0.777618\pi$
$607$	−74.3868	+	74.3868i	−0.122548	+	0.122548i	0.643173	+	0.765721i	$0.277618\pi$
$608$	411.002	+	411.002i	0.675991	+	0.675991i
$609$		0			0
$610$	−239.238	−	60.9950i	−0.392193	−	0.0999918i
$611$	−899.079			−1.47149
$612$		0			0
$613$	599.202	+	599.202i	0.977491	+	0.977491i	0.999752	−	0.0222612i	$-0.00708655\pi$
$613$	599.202	+	599.202i	0.977491	+	0.977491i	−0.0222612	+	0.999752i	$0.507087\pi$
$614$		−	1199.22i		−	1.95313i
$615$		0			0
$616$	119.267			0.193615
$617$	95.9908	−	95.9908i	0.155577	−	0.155577i	−0.625027	−	0.780603i	$-0.714912\pi$
$617$	95.9908	−	95.9908i	0.155577	−	0.155577i	0.780603	+	0.625027i	$0.214912\pi$
$618$		0			0
$619$			349.611i			0.564800i	0.959297	+	0.282400i	$0.0911305\pi$
$619$			349.611i			0.564800i	−0.959297	+	0.282400i	$0.908869\pi$
$620$	1226.83	−	728.349i	1.97876	−	1.17476i
$621$		0			0
$622$	687.279	−	687.279i	1.10495	−	1.10495i
$623$	−380.198	−	380.198i	−0.610270	−	0.610270i
$624$		0			0
$625$	−338.452	−	525.429i	−0.541523	−	0.840686i
$626$	−446.707			−0.713590
$627$		0			0
$628$	544.938	+	544.938i	0.867736	+	0.867736i
$629$			112.930i			0.179539i
$630$		0			0
$631$	249.068			0.394720			0.197360	−	0.980331i	$-0.436763\pi$
$631$	249.068			0.394720			0.197360	+	0.980331i	$0.436763\pi$
$632$	310.602	−	310.602i	0.491460	−	0.491460i
$633$		0			0
$634$		−	1060.12i		−	1.67211i
$635$	27.0411	+	6.89426i	0.0425843	+	0.0108571i
$636$		0			0
$637$	−207.598	+	207.598i	−0.325900	+	0.325900i
$638$	107.337	+	107.337i	0.168239	+	0.168239i
$639$		0			0
$640$	249.787	−	979.727i	0.390292	−	1.53082i
$641$	−1112.98			−1.73632			−0.868159	−	0.496287i	$-0.834696\pi$
$641$	−1112.98			−1.73632			−0.868159	+	0.496287i	$0.834696\pi$
$642$		0			0
$643$	−396.093	−	396.093i	−0.616008	−	0.616008i	0.328497	−	0.944505i	$-0.393458\pi$
$643$	−396.093	−	396.093i	−0.616008	−	0.616008i	−0.944505	+	0.328497i	$0.893458\pi$
$644$			495.755i			0.769806i
$645$		0			0
$646$	1579.28			2.44471
$647$	−190.770	+	190.770i	−0.294854	+	0.294854i	−0.838994	−	0.544140i	$-0.816856\pi$
$647$	−190.770	+	190.770i	−0.294854	+	0.294854i	0.544140	+	0.838994i	$0.316856\pi$
$648$		0			0
$649$		−	12.3198i		−	0.0189827i
$650$	417.819	−	766.134i	0.642799	−	1.17867i
$651$		0			0
$652$	222.285	−	222.285i	0.340928	−	0.340928i
$653$	−41.7823	−	41.7823i	−0.0639851	−	0.0639851i	0.674390	−	0.738375i	$-0.264407\pi$
$653$	−41.7823	−	41.7823i	−0.0639851	−	0.0639851i	−0.738375	+	0.674390i	$0.764407\pi$
$654$		0			0
$655$	−422.268	−	711.270i	−0.644684	−	1.08591i
$656$	−47.3892			−0.0722397
$657$		0			0
$658$	885.029	+	885.029i	1.34503	+	1.34503i
$659$		−	690.184i		−	1.04732i	−0.851927	−	0.523660i	$-0.824566\pi$
$659$		−	690.184i		−	1.04732i	0.851927	−	0.523660i	$-0.175434\pi$
$660$		0			0
$661$	−658.583			−0.996344			−0.498172	−	0.867078i	$-0.665995\pi$
$661$	−658.583			−0.996344			−0.498172	+	0.867078i	$0.665995\pi$
$662$	−283.034	+	283.034i	−0.427544	+	0.427544i
$663$		0			0
$664$		−	492.859i		−	0.742258i
$665$	101.093	−	396.511i	0.152019	−	0.596257i
$666$		0			0
$667$	−166.645	+	166.645i	−0.249843	+	0.249843i
$668$	−55.7926	−	55.7926i	−0.0835219	−	0.0835219i
$669$		0			0
$670$	−463.753	+	275.322i	−0.692168	+	0.410928i
$671$	50.8198			0.0757375
$672$		0			0
$673$	−901.911	−	901.911i	−1.34014	−	1.34014i	−0.895920	−	0.444216i	$-0.853482\pi$
$673$	−901.911	−	901.911i	−1.34014	−	1.34014i	−0.444216	−	0.895920i	$-0.646518\pi$
$674$			1132.17i			1.67978i
$675$		0			0
$676$	−329.893			−0.488007
$677$	485.397	−	485.397i	0.716982	−	0.716982i	−0.251004	−	0.967986i	$-0.580761\pi$
$677$	485.397	−	485.397i	0.716982	−	0.716982i	0.967986	+	0.251004i	$0.0807608\pi$
$678$		0			0
$679$		−	211.264i		−	0.311141i
$680$	−549.651	−	925.833i	−0.808310	−	1.36152i
$681$		0			0
$682$	−337.764	+	337.764i	−0.495255	+	0.495255i
$683$	−713.724	−	713.724i	−1.04498	−	1.04498i	−0.998939	−	0.0460448i	$-0.985338\pi$
$683$	−713.724	−	713.724i	−1.04498	−	1.04498i	−0.0460448	−	0.998939i	$-0.514662\pi$
$684$		0			0
$685$	324.241	+	82.6670i	0.473345	+	0.120682i
$686$	1147.59			1.67288
$687$		0			0
$688$	−7.93183	−	7.93183i	−0.0115288	−	0.0115288i
$689$			698.344i			1.01356i
$690$		0			0
$691$	−1319.75			−1.90991			−0.954954	−	0.296754i	$-0.904096\pi$
$691$	−1319.75			−1.90991			−0.954954	+	0.296754i	$0.904096\pi$
$692$	−260.195	+	260.195i	−0.376005	+	0.376005i
$693$		0			0
$694$		−	887.368i		−	1.27863i
$695$	676.041	−	401.353i	0.972721	−	0.577487i
$696$		0			0
$697$	−1213.15	+	1213.15i	−1.74053	+	1.74053i
$698$	53.6731	+	53.6731i	0.0768955	+	0.0768955i
$699$		0			0
$700$	−716.543	+	210.804i	−1.02363	+	0.301149i
$701$	1276.93			1.82159			0.910795	−	0.412859i	$-0.135470\pi$
$701$	1276.93			1.82159			0.910795	+	0.412859i	$0.135470\pi$
$702$		0			0
$703$	49.8410	+	49.8410i	0.0708975	+	0.0708975i
$704$			344.935i			0.489964i
$705$		0			0
$706$	−275.578			−0.390337
$707$	361.940	−	361.940i	0.511938	−	0.511938i
$708$		0			0
$709$			746.781i			1.05329i	0.850086	+	0.526644i	$0.176550\pi$
$709$			746.781i			1.05329i	−0.850086	+	0.526644i	$0.823450\pi$
$710$	−1038.08	−	264.664i	−1.46208	−	0.372766i
$711$		0			0
$712$	−624.405	+	624.405i	−0.876974	+	0.876974i
$713$	−524.396	−	524.396i	−0.735478	−	0.735478i
$714$		0			0
$715$	−44.3774	+	174.060i	−0.0620663	+	0.243440i
$716$	−1912.55			−2.67116
$717$		0			0
$718$	1145.46	+	1145.46i	1.59534	+	1.59534i
$719$			135.949i			0.189080i	0.995521	+	0.0945402i	$0.0301381\pi$
$719$			135.949i			0.189080i	−0.995521	+	0.0945402i	$0.969862\pi$
$720$		0			0
$721$	190.203			0.263804
$722$	−125.596	+	125.596i	−0.173955	+	0.173955i
$723$		0			0
$724$			1302.75i			1.79938i
$725$	−311.723	−	170.001i	−0.429962	−	0.234484i
$726$		0			0
$727$	192.127	−	192.127i	0.264273	−	0.264273i	−0.562514	−	0.826788i	$-0.690166\pi$
$727$	192.127	−	192.127i	0.264273	−	0.264273i	0.826788	+	0.562514i	$0.190166\pi$
$728$	−275.433	−	275.433i	−0.378342	−	0.378342i
$729$		0			0
$730$	1085.43	+	1828.29i	1.48688	+	2.50451i
$731$	−406.103			−0.555545
$732$		0			0
$733$	−288.677	−	288.677i	−0.393830	−	0.393830i	0.482220	−	0.876050i	$-0.339830\pi$
$733$	−288.677	−	288.677i	−0.393830	−	0.393830i	−0.876050	+	0.482220i	$0.839830\pi$
$734$		−	1833.58i		−	2.49807i
$735$		0			0
$736$	−551.471			−0.749281
$737$	78.4985	−	78.4985i	0.106511	−	0.106511i
$738$		0			0
$739$		−	135.495i		−	0.183349i	−0.995789	−	0.0916746i	$-0.970778\pi$
$739$		−	135.495i		−	0.183349i	0.995789	−	0.0916746i	$-0.0292220\pi$
$740$	31.7854	−	124.670i	0.0429532	−	0.168473i
$741$		0			0
$742$	687.431	−	687.431i	0.926457	−	0.926457i
$743$	350.021	+	350.021i	0.471091	+	0.471091i	0.902268	−	0.431177i	$-0.141901\pi$
$743$	350.021	+	350.021i	0.471091	+	0.471091i	−0.431177	+	0.902268i	$0.641901\pi$
$744$		0			0
$745$	395.465	−	234.781i	0.530826	−	0.315142i
$746$	590.605			0.791696
$747$		0			0
$748$	419.575	+	419.575i	0.560929	+	0.560929i
$749$			353.633i			0.472140i
$750$		0			0
$751$	1143.86			1.52311			0.761556	−	0.648099i	$-0.224436\pi$
$751$	1143.86			1.52311			0.761556	+	0.648099i	$0.224436\pi$
$752$	−45.4268	+	45.4268i	−0.0604080	+	0.0604080i
$753$		0			0
$754$		−	495.761i		−	0.657509i
$755$	−456.242	−	768.495i	−0.604294	−	1.01787i
$756$		0			0
$757$	−99.4207	+	99.4207i	−0.131335	+	0.131335i	−0.769719	−	0.638383i	$-0.779603\pi$
$757$	−99.4207	+	99.4207i	−0.131335	+	0.131335i	0.638383	+	0.769719i	$0.279603\pi$
$758$	704.074	+	704.074i	0.928857	+	0.928857i
$759$		0			0
$760$	−651.197	−	166.026i	−0.856838	−	0.218456i
$761$	782.950			1.02884			0.514421	−	0.857537i	$-0.328007\pi$
$761$	782.950			1.02884			0.514421	+	0.857537i	$0.328007\pi$
$762$		0			0
$763$	−322.333	−	322.333i	−0.422455	−	0.422455i
$764$			435.156i			0.569576i
$765$		0			0
$766$	−624.467			−0.815231
$767$	−28.4510	+	28.4510i	−0.0370939	+	0.0370939i
$768$		0			0
$769$		−	1060.55i		−	1.37913i	−0.724224	−	0.689565i	$-0.757802\pi$
$769$		−	1060.55i		−	1.37913i	0.724224	−	0.689565i	$-0.242198\pi$
$770$	215.023	−	127.656i	0.279251	−	0.165786i
$771$		0			0
$772$	359.742	−	359.742i	0.465987	−	0.465987i
$773$	599.585	+	599.585i	0.775660	+	0.775660i	0.979090	−	0.203429i	$-0.0652087\pi$
$773$	599.585	+	599.585i	0.775660	+	0.775660i	−0.203429	+	0.979090i	$0.565209\pi$
$774$		0			0
$775$	534.956	−	980.921i	0.690265	−	1.26570i
$776$	−346.963			−0.447117
$777$		0			0
$778$	−499.290	−	499.290i	−0.641761	−	0.641761i
$779$			1070.83i			1.37462i
$780$		0			0
$781$	220.513			0.282347
$782$	−1059.52	+	1059.52i	−1.35488	+	1.35488i
$783$		0			0
$784$			20.9782i			0.0267579i
$785$	584.808	+	149.100i	0.744979	+	0.189936i
$786$		0			0
$787$	−10.9757	+	10.9757i	−0.0139462	+	0.0139462i	−0.714046	−	0.700099i	$-0.753139\pi$
$787$	−10.9757	+	10.9757i	−0.0139462	+	0.0139462i	0.700099	+	0.714046i	$0.253139\pi$
$788$	391.343	+	391.343i	0.496628	+	0.496628i
$789$		0			0
$790$	227.529	−	892.426i	0.288011	−	1.12965i
$791$	−724.066			−0.915380
$792$		0			0
$793$	−117.362	−	117.362i	−0.147998	−	0.147998i
$794$			2037.81i			2.56651i
$795$		0			0
$796$	1862.89			2.34032
$797$	−291.068	+	291.068i	−0.365205	+	0.365205i	−0.865725	−	0.500520i	$-0.833142\pi$
$797$	−291.068	+	291.068i	−0.365205	+	0.365205i	0.500520	+	0.865725i	$0.333142\pi$
$798$		0			0
$799$			2325.82i			2.91091i
$800$	−234.495	−	797.071i	−0.293119	−	0.996339i
$801$		0			0
$802$	−1588.68	+	1588.68i	−1.98090	+	1.98090i
$803$	−309.472	−	309.472i	−0.385395	−	0.385395i
$804$		0			0
$805$	198.192	+	333.835i	0.246201	+	0.414702i
$806$	1560.05			1.93555
$807$		0			0
$808$	−594.420	−	594.420i	−0.735669	−	0.735669i
$809$			934.080i			1.15461i	0.816528	+	0.577305i	$0.195896\pi$
$809$			934.080i			1.15461i	−0.816528	+	0.577305i	$0.804104\pi$
$810$		0			0
$811$	247.443			0.305109			0.152554	−	0.988295i	$-0.451250\pi$
$811$	247.443			0.305109			0.152554	+	0.988295i	$0.451250\pi$
$812$	−300.041	+	300.041i	−0.369508	+	0.369508i
$813$		0			0
$814$			43.0743i			0.0529169i
$815$	60.8192	−	238.548i	0.0746248	−	0.292697i
$816$		0			0
$817$	−179.232	+	179.232i	−0.219378	+	0.219378i
$818$	−85.9325	−	85.9325i	−0.105052	−	0.105052i
$819$		0			0
$820$	1680.72	−	997.814i	2.04966	−	1.21685i
$821$	958.912			1.16798			0.583990	−	0.811761i	$-0.301491\pi$
$821$	958.912			1.16798			0.583990	+	0.811761i	$0.301491\pi$
$822$		0			0
$823$	−841.533	−	841.533i	−1.02252	−	1.02252i	−0.999741	−	0.0227782i	$-0.992749\pi$
$823$	−841.533	−	841.533i	−1.02252	−	1.02252i	−0.0227782	−	0.999741i	$-0.507251\pi$
$824$		−	312.373i		−	0.379094i
$825$		0			0
$826$	56.0128			0.0678121
$827$	−501.948	+	501.948i	−0.606951	+	0.606951i	−0.942148	−	0.335197i	$-0.891197\pi$
$827$	−501.948	+	501.948i	−0.606951	+	0.606951i	0.335197	+	0.942148i	$0.391197\pi$
$828$		0			0
$829$		−	219.411i		−	0.264670i	−0.991205	−	0.132335i	$-0.957753\pi$
$829$		−	219.411i		−	0.264670i	0.991205	−	0.132335i	$-0.0422474\pi$
$830$	−527.524	−	888.563i	−0.635571	−	1.07056i
$831$		0			0
$832$	796.585	−	796.585i	0.957434	−	0.957434i
$833$	537.033	+	537.033i	0.644697	+	0.644697i
$834$		0			0
$835$	−59.8746	−	15.2654i	−0.0717061	−	0.0182819i
$836$	370.354			0.443007
$837$		0			0
$838$	1107.44	+	1107.44i	1.32153	+	1.32153i
$839$			1101.77i			1.31320i	0.754241	+	0.656598i	$0.228005\pi$
$839$			1101.77i			1.31320i	−0.754241	+	0.656598i	$0.771995\pi$
$840$		0			0
$841$	639.286			0.760150
$842$	886.187	−	886.187i	1.05248	−	1.05248i
$843$		0			0
$844$			599.381i			0.710168i
$845$	−222.145	+	131.884i	−0.262894	+	0.156075i
$846$		0			0
$847$	−36.3966	+	36.3966i	−0.0429712	+	0.0429712i
$848$	35.2845	+	35.2845i	0.0416090	+	0.0416090i
$849$		0			0
$850$	−1981.90	−	1080.85i	−2.33165	−	1.27159i
$851$	−66.8751			−0.0785841
$852$		0			0
$853$	1045.69	+	1045.69i	1.22589	+	1.22589i	0.965504	+	0.260387i	$0.0838501\pi$
$853$	1045.69	+	1045.69i	1.22589	+	1.22589i	0.260387	+	0.965504i	$0.416150\pi$
$854$			231.057i			0.270558i
$855$		0			0
$856$	580.777			0.678478
$857$	1006.72	−	1006.72i	1.17471	−	1.17471i	0.193632	−	0.981074i	$-0.437973\pi$
$857$	1006.72	−	1006.72i	1.17471	−	1.17471i	0.981074	−	0.193632i	$-0.0620268\pi$
$858$		0			0
$859$			1366.58i			1.59090i	0.606021	+	0.795448i	$0.292765\pi$
$859$			1366.58i			1.59090i	−0.606021	+	0.795448i	$0.707235\pi$
$860$	448.323	+	114.302i	0.521305	+	0.132910i
$861$		0			0
$862$	1150.57	−	1150.57i	1.33477	−	1.33477i
$863$	−947.174	−	947.174i	−1.09754	−	1.09754i	−0.994698	−	0.102838i	$-0.967208\pi$
$863$	−947.174	−	947.174i	−1.09754	−	1.09754i	−0.102838	−	0.994698i	$-0.532792\pi$
$864$		0			0
$865$	−71.1918	+	279.232i	−0.0823027	+	0.322812i
$866$	−685.288			−0.791325
$867$		0			0
$868$	−944.161	−	944.161i	−1.08774	−	1.08774i
$869$			189.573i			0.218150i
$870$		0			0
$871$	−362.566			−0.416264
$872$	−529.373	+	529.373i	−0.607079	+	0.607079i
$873$		0			0
$874$			935.223i			1.07005i
$875$	−398.235	+	428.410i	−0.455126	+	0.489612i
$876$		0			0
$877$	−87.0484	+	87.0484i	−0.0992570	+	0.0992570i	−0.754992	−	0.655735i	$-0.772359\pi$
$877$	−87.0484	+	87.0484i	−0.0992570	+	0.0992570i	0.655735	+	0.754992i	$0.272359\pi$
$878$	−480.617	−	480.617i	−0.547400	−	0.547400i
$879$		0			0
$880$	6.55231	+	11.0367i	0.00744580	+	0.0125417i
$881$	−868.490			−0.985800			−0.492900	−	0.870086i	$-0.664063\pi$
$881$	−868.490			−0.985800			−0.492900	+	0.870086i	$0.664063\pi$
$882$		0			0
$883$	608.328	+	608.328i	0.688934	+	0.688934i	0.961996	−	0.273063i	$-0.0880366\pi$
$883$	608.328	+	608.328i	0.688934	+	0.688934i	−0.273063	+	0.961996i	$0.588037\pi$
$884$		−	1937.92i		−	2.19221i
$885$		0			0
$886$	−2018.22			−2.27790
$887$	−495.738	+	495.738i	−0.558892	+	0.558892i	−0.928992	−	0.370100i	$-0.879324\pi$
$887$	−495.738	+	495.738i	−0.558892	+	0.558892i	0.370100	+	0.928992i	$0.379324\pi$
$888$		0			0
$889$		−	26.1163i		−	0.0293772i
$890$	−457.402	+	1794.05i	−0.513935	+	2.01578i
$891$		0			0
$892$	−1009.35	+	1009.35i	−1.13156	+	1.13156i
$893$	1026.49	+	1026.49i	1.14948	+	1.14948i
$894$		0			0
$895$	−1287.89	+	764.595i	−1.43898	+	0.854296i
$896$	−946.224			−1.05605
$897$		0			0
$898$	1462.19	+	1462.19i	1.62828	+	1.62828i
$899$		−	634.749i		−	0.706061i
$900$		0			0
$901$	1806.54			2.00504
$902$	−462.725	+	462.725i	−0.512999	+	0.512999i
$903$		0			0
$904$			1189.14i			1.31543i
$905$	520.812	+	877.257i	0.575483	+	0.969345i
$906$		0			0
$907$	163.744	−	163.744i	0.180534	−	0.180534i	−0.611055	−	0.791588i	$-0.709254\pi$
$907$	163.744	−	163.744i	0.180534	−	0.180534i	0.791588	+	0.611055i	$0.209254\pi$
$908$	1014.65	+	1014.65i	1.11745	+	1.11745i
$909$		0			0
$910$	−791.376	−	201.766i	−0.869644	−	0.221720i
$911$	−1750.93			−1.92199			−0.960995	−	0.276566i	$-0.910804\pi$
$911$	−1750.93			−1.92199			−0.960995	+	0.276566i	$0.910804\pi$
$912$		0			0
$913$	150.405	+	150.405i	0.164738	+	0.164738i
$914$		−	472.638i		−	0.517109i
$915$		0			0
$916$	278.647			0.304200
$917$	−547.388	+	547.388i	−0.596933	+	0.596933i
$918$		0			0
$919$		−	1637.39i		−	1.78170i	−0.454293	−	0.890852i	$-0.650108\pi$
$919$		−	1637.39i		−	1.78170i	0.454293	−	0.890852i	$-0.349892\pi$
$920$	548.263	−	325.494i	0.595938	−	0.353797i
$921$		0			0
$922$	−1823.03	+	1823.03i	−1.97726	+	1.97726i
$923$	−509.247	−	509.247i	−0.551731	−	0.551731i
$924$		0			0
$925$	−28.4365	−	96.6583i	−0.0307422	−	0.104495i
$926$	−1150.49			−1.24243
$927$		0			0
$928$	−333.761	−	333.761i	−0.359656	−	0.359656i
$929$		−	1639.43i		−	1.76473i	−0.470568	−	0.882364i	$-0.655951\pi$
$929$		−	1639.43i		−	1.76473i	0.470568	−	0.882364i	$-0.344049\pi$
$930$		0			0
$931$	474.033			0.509166
$932$	−1479.57	+	1479.57i	−1.58753	+	1.58753i
$933$		0			0
$934$		−	365.061i		−	0.390857i
$935$	450.273	+	114.799i	0.481575	+	0.122780i
$936$		0			0
$937$	−141.600	+	141.600i	−0.151121	+	0.151121i	−0.778618	−	0.627498i	$-0.784079\pi$
$937$	−141.600	+	141.600i	−0.151121	+	0.151121i	0.627498	+	0.778618i	$0.284079\pi$
$938$	356.900	+	356.900i	0.380491	+	0.380491i
$939$		0			0
$940$	654.627	−	2567.61i	0.696412	−	2.73150i
$941$	−1074.74			−1.14212			−0.571062	−	0.820907i	$-0.693469\pi$
$941$	−1074.74			−1.14212			−0.571062	+	0.820907i	$0.693469\pi$
$942$		0			0
$943$	−718.405	−	718.405i	−0.761829	−	0.761829i
$944$			2.87502i			0.00304558i
$945$		0			0
$946$	−154.898			−0.163740
$947$	1127.43	−	1127.43i	1.19053	−	1.19053i	0.213609	−	0.976919i	$-0.431478\pi$
$947$	1127.43	−	1127.43i	1.19053	−	1.19053i	0.976919	−	0.213609i	$-0.0685217\pi$
$948$		0			0
$949$			1429.38i			1.50619i
$950$	−1351.73	+	397.674i	−1.42287	+	0.418604i
$951$		0			0
$952$	−712.514	+	712.514i	−0.748439	+	0.748439i
$953$	−99.4706	−	99.4706i	−0.104376	−	0.104376i	0.652990	−	0.757366i	$-0.273514\pi$
$953$	−99.4706	−	99.4706i	−0.104376	−	0.104376i	−0.757366	+	0.652990i	$0.773514\pi$
$954$		0			0
$955$	173.965	+	293.028i	0.182163	+	0.306836i
$956$	−1301.53			−1.36144
$957$		0			0
$958$	936.801	+	936.801i	0.977871	+	0.977871i
$959$		−	313.153i		−	0.326541i
$960$		0			0
$961$	1036.41			1.07847
$962$	99.4750	−	99.4750i	0.103404	−	0.103404i
$963$		0			0
$964$		−	618.472i		−	0.641568i
$965$	98.4287	−	386.062i	0.101999	−	0.400065i
$966$		0			0
$967$	1260.15	−	1260.15i	1.30315	−	1.30315i	0.376896	−	0.926256i	$-0.376992\pi$
$967$	1260.15	−	1260.15i	1.30315	−	1.30315i	0.926256	−	0.376896i	$-0.123008\pi$
$968$	59.7748	+	59.7748i	0.0617508	+	0.0617508i
$969$		0			0
$970$	−625.531	+	371.367i	−0.644878	+	0.382852i
$971$	−1148.23			−1.18252			−0.591261	−	0.806481i	$-0.701370\pi$
$971$	−1148.23			−1.18252			−0.591261	+	0.806481i	$0.701370\pi$
$972$		0			0
$973$	−520.275	−	520.275i	−0.534713	−	0.534713i
$974$		−	966.900i		−	0.992711i
$975$		0			0
$976$	−11.8597			−0.0121513
$977$	−145.709	+	145.709i	−0.149139	+	0.149139i	−0.777733	−	0.628594i	$-0.783631\pi$
$977$	−145.709	+	145.709i	−0.149139	+	0.149139i	0.628594	+	0.777733i	$0.283631\pi$
$978$		0			0
$979$		−	381.099i		−	0.389274i
$980$	−441.710	−	744.018i	−0.450725	−	0.759202i
$981$		0			0
$982$	259.083	−	259.083i	0.263832	−	0.263832i
$983$	562.675	+	562.675i	0.572406	+	0.572406i	0.932800	−	0.360394i	$-0.117358\pi$
$983$	562.675	+	562.675i	0.572406	+	0.572406i	−0.360394	+	0.932800i	$0.617358\pi$
$984$		0			0
$985$	419.975	+	107.075i	0.426371	+	0.108706i
$986$	−1282.48			−1.30069
$987$		0			0
$988$	−855.288	−	855.288i	−0.865676	−	0.865676i
$989$		−	240.487i		−	0.243162i
$990$		0			0
$991$	−1445.80			−1.45893			−0.729464	−	0.684019i	$-0.760231\pi$
$991$	−1445.80			−1.45893			−0.729464	+	0.684019i	$0.760231\pi$
$992$	1050.27	−	1050.27i	1.05874	−	1.05874i
$993$		0			0
$994$			1002.58i			1.00863i
$995$	1254.45	−	744.742i	1.26075	−	0.748484i
$996$		0			0
$997$	273.932	−	273.932i	0.274757	−	0.274757i	−0.556255	−	0.831012i	$-0.687762\pi$
$997$	273.932	−	273.932i	0.274757	−	0.274757i	0.831012	+	0.556255i	$0.187762\pi$
$998$	781.639	+	781.639i	0.783206	+	0.783206i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.3.j.a.298.1		20
3.2	odd	2		55.3.f.a.23.10	yes	20
5.2	odd	4	inner	495.3.j.a.397.1		20
15.2	even	4		55.3.f.a.12.10	✓	20
15.8	even	4		275.3.f.b.232.1		20
15.14	odd	2		275.3.f.b.243.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.f.a.12.10	✓	20	15.2	even	4
55.3.f.a.23.10	yes	20	3.2	odd	2
275.3.f.b.232.1		20	15.8	even	4
275.3.f.b.243.1		20	15.14	odd	2
495.3.j.a.298.1		20	1.1	even	1	trivial
495.3.j.a.397.1		20	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	495.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.27868 + 2.27868i) q^{2} -6.38475i q^{4} +(-2.55248 - 4.29940i) q^{5} +(-3.30878 + 3.30878i) q^{7} +(5.43407 + 5.43407i) q^{8} +(15.6132 + 3.98068i) q^{10} -3.31662 q^{11} +(7.65935 + 7.65935i) q^{13} -15.0793i q^{14} +0.773991 q^{16} +(19.8139 - 19.8139i) q^{17} -17.4895i q^{19} +(-27.4506 + 16.2969i) q^{20} +(7.55752 - 7.55752i) q^{22} +(11.7334 + 11.7334i) q^{23} +(-11.9697 + 21.9483i) q^{25} -34.9064 q^{26} +(21.1258 + 21.1258i) q^{28} +14.2026i q^{29} -44.6924 q^{31} +(-23.5000 + 23.5000i) q^{32} +90.2989i q^{34} +(22.6714 + 5.78020i) q^{35} +(-2.84977 + 2.84977i) q^{37} +(39.8529 + 39.8529i) q^{38} +(9.49291 - 37.2336i) q^{40} -61.2271 q^{41} +(-10.2480 - 10.2480i) q^{43} +21.1758i q^{44} -53.4734 q^{46} +(-58.6916 + 58.6916i) q^{47} +27.1039i q^{49} +(-22.7379 - 77.2881i) q^{50} +(48.9030 - 48.9030i) q^{52} +(45.5877 + 45.5877i) q^{53} +(8.46561 + 14.2595i) q^{55} -35.9603 q^{56} +(-32.3632 - 32.3632i) q^{58} +3.71455i q^{59} -15.3228 q^{61} +(101.840 - 101.840i) q^{62} -104.002i q^{64} +(13.3803 - 52.4809i) q^{65} +(-23.6682 + 23.6682i) q^{67} +(-126.507 - 126.507i) q^{68} +(-64.8320 + 38.4896i) q^{70} -66.4871 q^{71} +(93.3093 + 93.3093i) q^{73} -12.9874i q^{74} -111.666 q^{76} +(10.9740 - 10.9740i) q^{77} -57.1583i q^{79} +(-1.97559 - 3.32770i) q^{80} +(139.517 - 139.517i) q^{82} +(-45.3490 - 45.3490i) q^{83} +(-135.762 - 34.6133i) q^{85} +46.7036 q^{86} +(-18.0228 - 18.0228i) q^{88} +114.906i q^{89} -50.6863 q^{91} +(74.9150 - 74.9150i) q^{92} -267.479i q^{94} +(-75.1944 + 44.6415i) q^{95} +(-31.9248 + 31.9248i) q^{97} +(-61.7610 - 61.7610i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} + 8 q^{5} - 12 q^{8} + 12 q^{10} + 4 q^{13} - 16 q^{16} - 24 q^{17} + 8 q^{20} + 86 q^{23} + 90 q^{25} - 96 q^{26} + 76 q^{28} - 40 q^{31} - 184 q^{32} + 60 q^{35} - 126 q^{37} - 184 q^{38}+ \cdots - 620 q^{98}+O(q^{100}) \) 20 * q + 4 * q^2 + 8 * q^5 - 12 * q^8 + 12 * q^10 + 4 * q^13 - 16 * q^16 - 24 * q^17 + 8 * q^20 + 86 * q^23 + 90 * q^25 - 96 * q^26 + 76 * q^28 - 40 * q^31 - 184 * q^32 + 60 * q^35 - 126 * q^37 - 184 * q^38 + 64 * q^40 + 56 * q^41 - 24 * q^43 + 168 * q^46 - 156 * q^47 + 352 * q^50 - 100 * q^52 + 52 * q^53 + 66 * q^55 - 216 * q^56 - 344 * q^58 - 120 * q^61 + 540 * q^62 + 56 * q^65 - 242 * q^67 - 204 * q^68 + 112 * q^70 + 204 * q^71 - 228 * q^73 - 504 * q^76 - 640 * q^80 + 256 * q^82 - 464 * q^83 - 532 * q^85 + 128 * q^86 - 264 * q^88 - 96 * q^91 + 168 * q^92 - 508 * q^95 + 290 * q^97 - 620 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more