LMFDB - Embedded newform 48.3.l.a.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,3,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, 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("48.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$N$	$=$	$48 = 2^{4} \cdot 3$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	48.l (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:	$1.30790526893$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$2^{9}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.8
Root			$-1.96679 + 0.362960i$ of defining polynomial
Character	$\chi$	$=$	48.19
Dual form			48.3.l.a.43.8

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.96679 + 0.362960i) q^{2} +(-1.22474 + 1.22474i) q^{3} +(3.73652 + 1.42773i) q^{4} +(1.69930 - 1.69930i) q^{5} +(-2.85335 + 1.96428i) q^{6} -5.74280 q^{7} +(6.83074 + 4.16426i) q^{8} -3.00000i q^{9} +(3.95895 - 2.72539i) q^{10} +(-5.59560 - 5.59560i) q^{11} +(-6.32489 + 2.82768i) q^{12} +(-13.5782 - 13.5782i) q^{13} +(-11.2949 - 2.08441i) q^{14} +4.16243i q^{15} +(11.9232 + 10.6695i) q^{16} +19.7023 q^{17} +(1.08888 - 5.90037i) q^{18} +(-21.6943 + 21.6943i) q^{19} +(8.77563 - 3.92333i) q^{20} +(7.03347 - 7.03347i) q^{21} +(-8.97439 - 13.0363i) q^{22} +24.9257 q^{23} +(-13.4661 + 3.26576i) q^{24} +19.2247i q^{25} +(-21.7771 - 31.6337i) q^{26} +(3.67423 + 3.67423i) q^{27} +(-21.4581 - 8.19918i) q^{28} +(1.50581 + 1.50581i) q^{29} +(-1.51080 + 8.18662i) q^{30} -2.20037i q^{31} +(19.5777 + 25.3123i) q^{32} +13.7064 q^{33} +(38.7504 + 7.15116i) q^{34} +(-9.75877 + 9.75877i) q^{35} +(4.28320 - 11.2096i) q^{36} +(27.6956 - 27.6956i) q^{37} +(-50.5423 + 34.7940i) q^{38} +33.2596 q^{39} +(18.6838 - 4.53116i) q^{40} +51.3127i q^{41} +(16.3862 - 11.2805i) q^{42} +(21.4400 + 21.4400i) q^{43} +(-12.9191 - 28.8971i) q^{44} +(-5.09791 - 5.09791i) q^{45} +(49.0236 + 9.04703i) q^{46} -76.5216i q^{47} +(-27.6702 + 1.53542i) q^{48} -16.0202 q^{49} +(-6.97781 + 37.8110i) q^{50} +(-24.1303 + 24.1303i) q^{51} +(-31.3491 - 70.1211i) q^{52} +(-56.5145 + 56.5145i) q^{53} +(5.89284 + 8.56005i) q^{54} -19.0173 q^{55} +(-39.2276 - 23.9145i) q^{56} -53.1400i q^{57} +(2.41506 + 3.50816i) q^{58} +(-48.0041 - 48.0041i) q^{59} +(-5.94283 + 15.5530i) q^{60} +(-51.5587 - 51.5587i) q^{61} +(0.798646 - 4.32766i) q^{62} +17.2284i q^{63} +(29.3180 + 56.8899i) q^{64} -46.1469 q^{65} +(26.9575 + 4.97486i) q^{66} +(63.4445 - 63.4445i) q^{67} +(73.6182 + 28.1297i) q^{68} +(-30.5276 + 30.5276i) q^{69} +(-22.7355 + 15.6514i) q^{70} +43.4856 q^{71} +(12.4928 - 20.4922i) q^{72} +73.9992i q^{73} +(64.5239 - 44.4190i) q^{74} +(-23.5454 - 23.5454i) q^{75} +(-112.035 + 50.0876i) q^{76} +(32.1344 + 32.1344i) q^{77} +(65.4146 + 12.0719i) q^{78} -4.12659i q^{79} +(38.3918 - 2.13036i) q^{80} -9.00000 q^{81} +(-18.6245 + 100.921i) q^{82} +(38.4428 - 38.4428i) q^{83} +(36.3226 - 16.2388i) q^{84} +(33.4803 - 33.4803i) q^{85} +(34.3862 + 49.9499i) q^{86} -3.68846 q^{87} +(-14.9206 - 61.5236i) q^{88} -52.9839i q^{89} +(-8.17618 - 11.8769i) q^{90} +(77.9767 + 77.9767i) q^{91} +(93.1353 + 35.5872i) q^{92} +(2.69489 + 2.69489i) q^{93} +(27.7743 - 150.502i) q^{94} +73.7305i q^{95} +(-54.9788 - 7.02335i) q^{96} +23.1008 q^{97} +(-31.5084 - 5.81471i) q^{98} +(-16.7868 + 16.7868i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q + 12 q^{4} - 12 q^{8} - 56 q^{10} + 32 q^{11} - 24 q^{12} - 44 q^{14} + 32 q^{16} + 12 q^{18} - 32 q^{19} + 80 q^{20} + 32 q^{22} - 128 q^{23} + 36 q^{24} - 100 q^{26} - 120 q^{28} + 32 q^{29} + 72 q^{30}+ \cdots + 96 q^{99}+O(q^{100})$ 16 * q + 12 * q^4 - 12 * q^8 - 56 * q^10 + 32 * q^11 - 24 * q^12 - 44 * q^14 + 32 * q^16 + 12 * q^18 - 32 * q^19 + 80 * q^20 + 32 * q^22 - 128 * q^23 + 36 * q^24 - 100 * q^26 - 120 * q^28 + 32 * q^29 + 72 * q^30 + 160 * q^32 + 96 * q^34 + 96 * q^35 + 12 * q^36 - 96 * q^37 + 168 * q^38 + 48 * q^40 - 60 * q^42 + 160 * q^43 + 88 * q^44 + 136 * q^46 - 144 * q^48 + 112 * q^49 - 236 * q^50 - 96 * q^51 - 48 * q^52 - 160 * q^53 - 36 * q^54 - 256 * q^55 - 224 * q^56 + 144 * q^58 - 128 * q^59 - 72 * q^60 - 32 * q^61 - 276 * q^62 - 408 * q^64 - 32 * q^65 + 72 * q^66 + 320 * q^67 - 448 * q^68 + 96 * q^69 - 384 * q^70 + 512 * q^71 + 60 * q^72 + 348 * q^74 + 192 * q^75 + 72 * q^76 + 224 * q^77 + 396 * q^78 + 552 * q^80 - 144 * q^81 - 40 * q^82 - 160 * q^83 + 72 * q^84 + 160 * q^85 + 528 * q^86 + 480 * q^88 - 24 * q^90 - 480 * q^91 + 496 * q^92 + 312 * q^94 - 480 * q^96 - 440 * q^98 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$ .

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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

)

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

$2$	1.96679	+	0.362960i	0.983395	+	0.181480i
$2$	1.96679	+	0.362960i	0.983395	+	0.181480i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$	3.73652	+	1.42773i	0.934130	+	0.356933i
$5$	1.69930	−	1.69930i	0.339861	−	0.339861i	−0.516454	−	0.856315i	$-0.672748\pi$
$5$	1.69930	−	1.69930i	0.339861	−	0.339861i	0.856315	+	0.516454i	$0.172748\pi$
$6$	−2.85335	+	1.96428i	−0.475558	+	0.327380i
$7$	−5.74280			−0.820400			−0.410200	−	0.911996i	$-0.634541\pi$
$7$	−5.74280			−0.820400			−0.410200	+	0.911996i	$0.634541\pi$
$8$	6.83074	+	4.16426i	0.853842	+	0.520532i
$9$		−	3.00000i		−	0.333333i
$10$	3.95895	−	2.72539i	0.395895	−	0.272539i
$11$	−5.59560	−	5.59560i	−0.508691	−	0.508691i	0.405434	−	0.914125i	$-0.367121\pi$
$11$	−5.59560	−	5.59560i	−0.508691	−	0.508691i	−0.914125	+	0.405434i	$0.867121\pi$
$12$	−6.32489	+	2.82768i	−0.527074	+	0.235640i
$13$	−13.5782	−	13.5782i	−1.04447	−	1.04447i	−0.998964	−	0.0455110i	$-0.985508\pi$
$13$	−13.5782	−	13.5782i	−1.04447	−	1.04447i	−0.0455110	−	0.998964i	$-0.514492\pi$
$14$	−11.2949	−	2.08441i	−0.806777	−	0.148886i
$15$			4.16243i			0.277495i
$16$	11.9232	+	10.6695i	0.745198	+	0.666844i
$17$	19.7023			1.15896			0.579481	−	0.814986i	$-0.303255\pi$
$17$	19.7023			1.15896			0.579481	+	0.814986i	$0.303255\pi$
$18$	1.08888	−	5.90037i	0.0604933	−	0.327798i
$19$	−21.6943	+	21.6943i	−1.14181	+	1.14181i	−0.153687	+	0.988120i	$0.549115\pi$
$19$	−21.6943	+	21.6943i	−1.14181	+	1.14181i	−0.988120	+	0.153687i	$0.950885\pi$
$20$	8.77563	−	3.92333i	0.438782	−	0.196167i
$21$	7.03347	−	7.03347i	0.334927	−	0.334927i
$22$	−8.97439	−	13.0363i	−0.407927	−	0.592561i
$23$	24.9257			1.08373			0.541863	−	0.840467i	$-0.317719\pi$
$23$	24.9257			1.08373			0.541863	+	0.840467i	$0.317719\pi$
$24$	−13.4661	+	3.26576i	−0.561086	+	0.136073i
$25$			19.2247i			0.768989i
$26$	−21.7771	−	31.6337i	−0.837580	−	1.21668i
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	−21.4581	−	8.19918i	−0.766360	−	0.292828i
$29$	1.50581	+	1.50581i	0.0519245	+	0.0519245i	0.732592	−	0.680668i	$-0.238310\pi$
$29$	1.50581	+	1.50581i	0.0519245	+	0.0519245i	−0.680668	+	0.732592i	$0.738310\pi$
$30$	−1.51080	+	8.18662i	−0.0503598	+	0.272887i
$31$		−	2.20037i		−	0.0709796i	−0.999370	−	0.0354898i	$-0.988701\pi$
$31$		−	2.20037i		−	0.0709796i	0.999370	−	0.0354898i	$-0.0112991\pi$
$32$	19.5777	+	25.3123i	0.611805	+	0.791009i
$33$	13.7064			0.415344
$34$	38.7504	+	7.15116i	1.13972	+	0.210328i
$35$	−9.75877	+	9.75877i	−0.278822	+	0.278822i
$36$	4.28320	−	11.2096i	0.118978	−	0.311377i
$37$	27.6956	−	27.6956i	0.748530	−	0.748530i	−0.225673	−	0.974203i	$-0.572458\pi$
$37$	27.6956	−	27.6956i	0.748530	−	0.748530i	0.974203	+	0.225673i	$0.0724580\pi$
$38$	−50.5423	+	34.7940i	−1.33006	+	0.915631i
$39$	33.2596			0.852810
$40$	18.6838	−	4.53116i	0.467096	−	0.113279i
$41$			51.3127i			1.25153i	0.780012	+	0.625764i	$0.215213\pi$
$41$			51.3127i			1.25153i	−0.780012	+	0.625764i	$0.784787\pi$
$42$	16.3862	−	11.2805i	0.390148	−	0.268583i
$43$	21.4400	+	21.4400i	0.498606	+	0.498606i	0.911004	−	0.412398i	$-0.135309\pi$
$43$	21.4400	+	21.4400i	0.498606	+	0.498606i	−0.412398	+	0.911004i	$0.635309\pi$
$44$	−12.9191	−	28.8971i	−0.293615	−	0.656752i
$45$	−5.09791	−	5.09791i	−0.113287	−	0.113287i
$46$	49.0236	+	9.04703i	1.06573	+	0.196675i
$47$		−	76.5216i		−	1.62812i	−0.580781	−	0.814060i	$-0.697253\pi$
$47$		−	76.5216i		−	1.62812i	0.580781	−	0.814060i	$-0.302747\pi$
$48$	−27.6702	+	1.53542i	−0.576463	+	0.0319879i
$49$	−16.0202			−0.326944
$50$	−6.97781	+	37.8110i	−0.139556	+	0.756220i
$51$	−24.1303	+	24.1303i	−0.473144	+	0.473144i
$52$	−31.3491	−	70.1211i	−0.602868	−	1.34848i
$53$	−56.5145	+	56.5145i	−1.06631	+	1.06631i	−0.0686712	+	0.997639i	$0.521876\pi$
$53$	−56.5145	+	56.5145i	−1.06631	+	1.06631i	−0.997639	+	0.0686712i	$0.978124\pi$
$54$	5.89284	+	8.56005i	0.109127	+	0.158519i
$55$	−19.0173			−0.345768
$56$	−39.2276	−	23.9145i	−0.700492	−	0.427044i
$57$		−	53.1400i		−	0.932281i
$58$	2.41506	+	3.50816i	0.0416390	+	0.0604855i
$59$	−48.0041	−	48.0041i	−0.813628	−	0.813628i	0.171547	−	0.985176i	$-0.445123\pi$
$59$	−48.0041	−	48.0041i	−0.813628	−	0.813628i	−0.985176	+	0.171547i	$0.945123\pi$
$60$	−5.94283	+	15.5530i	−0.0990472	+	0.259217i
$61$	−51.5587	−	51.5587i	−0.845224	−	0.845224i	0.144308	−	0.989533i	$-0.453904\pi$
$61$	−51.5587	−	51.5587i	−0.845224	−	0.845224i	−0.989533	+	0.144308i	$0.953904\pi$
$62$	0.798646	−	4.32766i	0.0128814	−	0.0698010i
$63$			17.2284i			0.273467i
$64$	29.3180	+	56.8899i	0.458093	+	0.888904i
$65$	−46.1469			−0.709952
$66$	26.9575	+	4.97486i	0.408447	+	0.0753767i
$67$	63.4445	−	63.4445i	0.946934	−	0.946934i	−0.0517277	−	0.998661i	$-0.516473\pi$
$67$	63.4445	−	63.4445i	0.946934	−	0.946934i	0.998661	+	0.0517277i	$0.0164728\pi$
$68$	73.6182	+	28.1297i	1.08262	+	0.413672i
$69$	−30.5276	+	30.5276i	−0.442429	+	0.442429i
$70$	−22.7355	+	15.6514i	−0.324793	+	0.223591i
$71$	43.4856			0.612473			0.306237	−	0.951955i	$-0.400930\pi$
$71$	43.4856			0.612473			0.306237	+	0.951955i	$0.400930\pi$
$72$	12.4928	−	20.4922i	0.173511	−	0.284614i
$73$			73.9992i			1.01369i	0.862038	+	0.506844i	$0.169188\pi$
$73$			73.9992i			1.01369i	−0.862038	+	0.506844i	$0.830812\pi$
$74$	64.5239	−	44.4190i	0.871944	−	0.600257i
$75$	−23.5454	−	23.5454i	−0.313939	−	0.313939i
$76$	−112.035	+	50.0876i	−1.47414	+	0.659047i
$77$	32.1344	+	32.1344i	0.417330	+	0.417330i
$78$	65.4146	+	12.0719i	0.838649	+	0.154768i
$79$		−	4.12659i		−	0.0522354i	−0.999659	−	0.0261177i	$-0.991686\pi$
$79$		−	4.12659i		−	0.0522354i	0.999659	−	0.0261177i	$-0.00831446\pi$
$80$	38.3918	−	2.13036i	0.479898	−	0.0266295i
$81$	−9.00000			−0.111111
$82$	−18.6245	+	100.921i	−0.227127	+	1.23075i
$83$	38.4428	−	38.4428i	0.463166	−	0.463166i	−0.436526	−	0.899692i	$-0.643791\pi$
$83$	38.4428	−	38.4428i	0.463166	−	0.463166i	0.899692	+	0.436526i	$0.143791\pi$
$84$	36.3226	−	16.2388i	0.432412	−	0.193319i
$85$	33.4803	−	33.4803i	0.393886	−	0.393886i
$86$	34.3862	+	49.9499i	0.399839	+	0.580813i
$87$	−3.68846			−0.0423961
$88$	−14.9206	−	61.5236i	−0.169552	−	0.699132i
$89$		−	52.9839i		−	0.595325i	−0.954671	−	0.297662i	$-0.903793\pi$
$89$		−	52.9839i		−	0.595325i	0.954671	−	0.297662i	$-0.0962070\pi$
$90$	−8.17618	−	11.8769i	−0.0908465	−	0.131965i
$91$	77.9767	+	77.9767i	0.856887	+	0.856887i
$92$	93.1353	+	35.5872i	1.01234	+	0.386817i
$93$	2.69489	+	2.69489i	0.0289773	+	0.0289773i
$94$	27.7743	−	150.502i	0.295471	−	1.60108i
$95$			73.7305i			0.776111i
$96$	−54.9788	−	7.02335i	−0.572696	−	0.0731599i
$97$	23.1008			0.238153			0.119077	−	0.992885i	$-0.462007\pi$
$97$	23.1008			0.238153			0.119077	+	0.992885i	$0.462007\pi$
$98$	−31.5084	−	5.81471i	−0.321515	−	0.0593337i
$99$	−16.7868	+	16.7868i	−0.169564	+	0.169564i
$100$	−27.4478	+	71.8336i	−0.274478	+	0.718336i
$101$	16.1216	−	16.1216i	0.159619	−	0.159619i	−0.622779	−	0.782398i	$-0.713996\pi$
$101$	16.1216	−	16.1216i	0.159619	−	0.159619i	0.782398	+	0.622779i	$0.213996\pi$
$102$	−56.2177	+	38.7010i	−0.551153	+	0.379421i
$103$	−98.8380			−0.959592			−0.479796	−	0.877380i	$-0.659289\pi$
$103$	−98.8380			−0.959592			−0.479796	+	0.877380i	$0.659289\pi$
$104$	−36.2060	−	149.292i	−0.348134	−	1.43550i
$105$		−	23.9040i		−	0.227657i
$106$	−131.665	+	90.6395i	−1.24212	+	0.855090i
$107$	15.6655	+	15.6655i	0.146406	+	0.146406i	0.776511	−	0.630104i	$-0.216988\pi$
$107$	15.6655	+	15.6655i	0.146406	+	0.146406i	−0.630104	+	0.776511i	$0.716988\pi$
$108$	8.48303	+	18.9747i	0.0785466	+	0.175691i
$109$	84.6938	+	84.6938i	0.777008	+	0.777008i	0.979321	−	0.202313i	$-0.0648459\pi$
$109$	84.6938	+	84.6938i	0.777008	+	0.777008i	−0.202313	+	0.979321i	$0.564846\pi$
$110$	−37.4029	−	6.90250i	−0.340027	−	0.0627500i
$111$			67.8401i			0.611172i
$112$	−68.4724	−	61.2728i	−0.611360	−	0.547079i
$113$	63.8537			0.565077			0.282538	−	0.959256i	$-0.408824\pi$
$113$	63.8537			0.565077			0.282538	+	0.959256i	$0.408824\pi$
$114$	19.2877	−	104.515i	0.169190	−	0.916800i
$115$	42.3563	−	42.3563i	0.368316	−	0.368316i
$116$	3.47659	+	7.77638i	0.0299706	+	0.0670377i
$117$	−40.7345	+	40.7345i	−0.348158	+	0.348158i
$118$	−76.9903	−	111.837i	−0.652461	−	0.947775i
$119$	−113.147			−0.950812
$120$	−17.3334	+	28.4325i	−0.144445	+	0.236937i
$121$		−	58.3785i		−	0.482467i
$122$	−82.6913	−	120.119i	−0.677798	−	0.984580i
$123$	−62.8449	−	62.8449i	−0.510934	−	0.510934i
$124$	3.14154	−	8.22172i	0.0253350	−	0.0663042i
$125$	75.1513	+	75.1513i	0.601210	+	0.601210i
$126$	−6.25322	+	33.8846i	−0.0496288	+	0.268926i
$127$			36.8901i			0.290473i	0.989397	+	0.145237i	$0.0463944\pi$
$127$			36.8901i			0.290473i	−0.989397	+	0.145237i	$0.953606\pi$
$128$	37.0135	+	122.532i	0.289168	+	0.957278i
$129$	−52.5172			−0.407110
$130$	−90.7612	−	16.7495i	−0.698163	−	0.128842i
$131$	−40.4136	+	40.4136i	−0.308500	+	0.308500i	−0.844328	−	0.535827i	$-0.820000\pi$
$131$	−40.4136	+	40.4136i	−0.308500	+	0.308500i	0.535827	+	0.844328i	$0.320000\pi$
$132$	51.2141	+	19.5690i	0.387986	+	0.148250i
$133$	124.586	−	124.586i	0.936738	−	0.936738i
$134$	147.810	−	101.754i	1.10306	−	0.759360i
$135$	12.4873			0.0924984
$136$	134.582	+	82.0456i	0.989570	+	0.603276i
$137$		−	253.499i		−	1.85036i	−0.379531	−	0.925179i	$-0.623915\pi$
$137$		−	253.499i		−	1.85036i	0.379531	−	0.925179i	$-0.376085\pi$
$138$	−71.1217	+	48.9611i	−0.515375	+	0.354790i
$139$	67.8065	+	67.8065i	0.487816	+	0.487816i	0.907617	−	0.419800i	$-0.137900\pi$
$139$	67.8065	+	67.8065i	0.487816	+	0.487816i	−0.419800	+	0.907617i	$0.637900\pi$
$140$	−50.3967	+	22.5309i	−0.359977	+	0.160935i
$141$	93.7194	+	93.7194i	0.664677	+	0.664677i
$142$	85.5270	+	15.7835i	0.602303	+	0.111152i
$143$			151.956i			1.06263i
$144$	32.0085	−	35.7695i	0.222281	−	0.248399i
$145$	5.11766			0.0352942
$146$	−26.8588	+	145.541i	−0.183964	+	0.996856i
$147$	19.6207	−	19.6207i	0.133474	−	0.133474i
$148$	143.027	−	63.9433i	0.966400	−	0.432049i
$149$	−43.9337	+	43.9337i	−0.294857	+	0.294857i	−0.838996	−	0.544138i	$-0.816857\pi$
$149$	−43.9337	+	43.9337i	−0.294857	+	0.294857i	0.544138	+	0.838996i	$0.316857\pi$
$150$	−37.7628	−	54.8549i	−0.251752	−	0.365699i
$151$	−223.084			−1.47738			−0.738688	−	0.674047i	$-0.764554\pi$
$151$	−223.084			−1.47738			−0.738688	+	0.674047i	$0.764554\pi$
$152$	−238.529	+	57.8475i	−1.56927	+	0.380576i
$153$		−	59.1070i		−	0.386320i
$154$	51.5381	+	74.8651i	0.334663	+	0.486137i
$155$	−3.73909	−	3.73909i	−0.0241232	−	0.0241232i
$156$	124.275	+	47.4858i	0.796636	+	0.304396i
$157$	−78.8526	−	78.8526i	−0.502246	−	0.502246i	0.409889	−	0.912135i	$-0.365567\pi$
$157$	−78.8526	−	78.8526i	−0.502246	−	0.502246i	−0.912135	+	0.409889i	$0.865567\pi$
$158$	1.49779	−	8.11614i	0.00947968	−	0.0513680i
$159$		−	138.432i		−	0.870639i
$160$	76.2818	+	9.74473i	0.476761	+	0.0609045i
$161$	−143.143			−0.889089
$162$	−17.7011	−	3.26664i	−0.109266	−	0.0201644i
$163$	52.2425	−	52.2425i	0.320506	−	0.320506i	−0.528455	−	0.848961i	$-0.677228\pi$
$163$	52.2425	−	52.2425i	0.320506	−	0.320506i	0.848961	+	0.528455i	$0.177228\pi$
$164$	−73.2607	+	191.731i	−0.446712	+	1.16909i
$165$	23.2913	−	23.2913i	0.141159	−	0.141159i
$166$	89.5620	−	61.6556i	0.539530	−	0.371419i
$167$	96.5201			0.577965			0.288982	−	0.957334i	$-0.406683\pi$
$167$	96.5201			0.577965			0.288982	+	0.957334i	$0.406683\pi$
$168$	77.3329	−	18.7546i	0.460315	−	0.111635i
$169$			199.734i			1.18186i
$170$	78.0006	−	53.6966i	0.458827	−	0.315863i
$171$	65.0830	+	65.0830i	0.380602	+	0.380602i
$172$	49.5005	+	110.722i	0.287794	+	0.643731i
$173$	−46.3076	−	46.3076i	−0.267674	−	0.267674i	0.560488	−	0.828162i	$-0.310614\pi$
$173$	−46.3076	−	46.3076i	−0.267674	−	0.267674i	−0.828162	+	0.560488i	$0.810614\pi$
$174$	−7.25443	−	1.33877i	−0.0416921	−	0.00769405i
$175$		−	110.404i		−	0.630879i
$176$	−7.01501	−	126.419i	−0.0398580	−	0.718293i
$177$	117.585			0.664325
$178$	19.2310	−	104.208i	0.108040	−	0.585439i
$179$	−93.5440	+	93.5440i	−0.522592	+	0.522592i	−0.918353	−	0.395761i	$-0.870481\pi$
$179$	−93.5440	+	93.5440i	−0.522592	+	0.522592i	0.395761	+	0.918353i	$0.370481\pi$
$180$	−11.7700	−	26.3269i	−0.0653889	−	0.146261i
$181$	−115.810	+	115.810i	−0.639836	+	0.639836i	−0.950515	−	0.310679i	$-0.899444\pi$
$181$	−115.810	+	115.810i	−0.639836	+	0.639836i	0.310679	+	0.950515i	$0.399444\pi$
$182$	125.061	+	181.666i	0.687150	+	0.998166i
$183$	126.292			0.690123
$184$	170.261	+	103.797i	0.925331	+	0.564114i
$185$		−	94.1266i		−	0.508792i
$186$	4.32214	+	6.27842i	0.0232373	+	0.0337549i
$187$	−110.246	−	110.246i	−0.589553	−	0.589553i
$188$	109.252	−	285.925i	0.581130	−	1.52088i
$189$	−21.1004	−	21.1004i	−0.111642	−	0.111642i
$190$	−26.7612	+	145.012i	−0.140849	+	0.763223i
$191$			35.2964i			0.184798i	0.995722	+	0.0923991i	$0.0294535\pi$
$191$			35.2964i			0.184798i	−0.995722	+	0.0923991i	$0.970546\pi$
$192$	−105.583	−	33.7686i	−0.549909	−	0.175878i
$193$	−364.339			−1.88777			−0.943884	−	0.330277i	$-0.892858\pi$
$193$	−364.339			−1.88777			−0.943884	+	0.330277i	$0.892858\pi$
$194$	45.4345	+	8.38468i	0.234198	+	0.0432200i
$195$	56.5182	−	56.5182i	0.289837	−	0.289837i
$196$	−59.8599	−	22.8726i	−0.305408	−	0.116697i
$197$	130.582	−	130.582i	0.662851	−	0.662851i	−0.293200	−	0.956051i	$-0.594720\pi$
$197$	130.582	−	130.582i	0.662851	−	0.662851i	0.956051	+	0.293200i	$0.0947203\pi$
$198$	−39.1090	+	26.9232i	−0.197520	+	0.135976i
$199$	−12.7493			−0.0640670			−0.0320335	−	0.999487i	$-0.510198\pi$
$199$	−12.7493			−0.0640670			−0.0320335	+	0.999487i	$0.510198\pi$
$200$	−80.0567	+	131.319i	−0.400283	+	0.656595i
$201$			155.407i			0.773168i
$202$	37.5592	−	25.8562i	0.185937	−	0.128001i
$203$	−8.64756	−	8.64756i	−0.0425988	−	0.0425988i
$204$	−124.615	+	55.7119i	−0.610859	+	0.273097i
$205$	87.1958	+	87.1958i	0.425346	+	0.425346i
$206$	−194.394	−	35.8743i	−0.943658	−	0.174147i
$207$		−	74.7771i		−	0.361242i
$208$	−17.0225	−	306.767i	−0.0818388	−	1.47484i
$209$	242.786			1.16165
$210$	8.67620	−	47.0141i	0.0413152	−	0.223877i
$211$	8.59499	−	8.59499i	0.0407345	−	0.0407345i	−0.686446	−	0.727181i	$-0.740830\pi$
$211$	8.59499	−	8.59499i	0.0407345	−	0.0407345i	0.727181	+	0.686446i	$0.240830\pi$
$212$	−291.855	+	130.480i	−1.37667	+	0.615471i
$213$	−53.2588	+	53.2588i	−0.250041	+	0.250041i
$214$	25.1247	+	36.4966i	0.117405	+	0.170545i
$215$	72.8663			0.338913
$216$	9.79728	+	40.3982i	0.0453578	+	0.187029i
$217$			12.6363i			0.0582317i
$218$	135.834	+	197.315i	0.623094	+	0.905117i
$219$	−90.6302	−	90.6302i	−0.413837	−	0.413837i
$220$	−71.0583	−	27.1515i	−0.322992	−	0.123416i
$221$	−267.522	−	267.522i	−1.21051	−	1.21051i
$222$	−24.6233	+	133.427i	−0.110916	+	0.601024i
$223$		−	50.5909i		−	0.226865i	−0.993546	−	0.113433i	$-0.963815\pi$
$223$		−	50.5909i		−	0.226865i	0.993546	−	0.113433i	$-0.0361846\pi$
$224$	−112.431	−	145.363i	−0.501925	−	0.648944i
$225$	57.6742			0.256330
$226$	125.587	+	23.1763i	0.555693	+	0.102550i
$227$	31.7175	−	31.7175i	0.139725	−	0.139725i	−0.633785	−	0.773509i	$-0.718499\pi$
$227$	31.7175	−	31.7175i	0.139725	−	0.139725i	0.773509	+	0.633785i	$0.218499\pi$
$228$	75.8697	−	198.559i	0.332762	−	0.870872i
$229$	−169.826	+	169.826i	−0.741599	+	0.741599i	−0.972886	−	0.231287i	$-0.925706\pi$
$229$	−169.826	+	169.826i	−0.741599	+	0.741599i	0.231287	+	0.972886i	$0.425706\pi$
$230$	98.6796	−	67.9323i	0.429042	−	0.295358i
$231$	−78.7129			−0.340749
$232$	4.01521	+	16.5564i	0.0173070	+	0.0713636i
$233$			363.082i			1.55829i	0.626844	+	0.779145i	$0.284346\pi$
$233$			363.082i			1.55829i	−0.626844	+	0.779145i	$0.715654\pi$
$234$	−94.9012	+	65.3312i	−0.405561	+	0.279193i
$235$	−130.033	−	130.033i	−0.553334	−	0.553334i
$236$	−110.831	−	247.905i	−0.469624	−	1.05045i
$237$	5.05402	+	5.05402i	0.0213250	+	0.0213250i
$238$	−222.536	−	41.0677i	−0.935024	−	0.172553i
$239$		−	27.6282i		−	0.115599i	−0.998328	−	0.0577996i	$-0.981592\pi$
$239$		−	27.6282i		−	0.115599i	0.998328	−	0.0577996i	$-0.0184084\pi$
$240$	−44.4110	+	49.6293i	−0.185046	+	0.206789i
$241$	368.121			1.52747			0.763737	−	0.645527i	$-0.223362\pi$
$241$	368.121			1.52747			0.763737	+	0.645527i	$0.223362\pi$
$242$	21.1891	−	114.818i	0.0875581	−	0.474456i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$	−119.038	−	266.262i	−0.487861	−	1.09124i
$245$	−27.2233	+	27.2233i	−0.111115	+	0.111115i
$246$	−100.793	−	146.413i	−0.409726	−	0.595175i
$247$	589.139			2.38518
$248$	9.16290	−	15.0301i	0.0369472	−	0.0606054i
$249$			94.1651i			0.378173i
$250$	120.530	+	175.084i	0.482119	+	0.700334i
$251$	329.839	+	329.839i	1.31410	+	1.31410i	0.918365	+	0.395734i	$0.129510\pi$
$251$	329.839	+	329.839i	1.31410	+	1.31410i	0.395734	+	0.918365i	$0.370490\pi$
$252$	−24.5975	+	64.3743i	−0.0976093	+	0.255453i
$253$	−139.474	−	139.474i	−0.551281	−	0.551281i
$254$	−13.3896	+	72.5551i	−0.0527151	+	0.285650i
$255$			82.0096i			0.321606i
$256$	28.3236	+	254.428i	0.110639	+	0.993861i
$257$	23.6762			0.0921252			0.0460626	−	0.998939i	$-0.485333\pi$
$257$	23.6762			0.0921252			0.0460626	+	0.998939i	$0.485333\pi$
$258$	−103.290	−	19.0616i	−0.400350	−	0.0738823i
$259$	−159.050	+	159.050i	−0.614094	+	0.614094i
$260$	−172.429	−	65.8854i	−0.663188	−	0.253405i
$261$	4.51743	−	4.51743i	0.0173082	−	0.0173082i
$262$	−94.1535	+	64.8164i	−0.359364	+	0.247391i
$263$	243.854			0.927202			0.463601	−	0.886044i	$-0.346557\pi$
$263$	243.854			0.927202			0.463601	+	0.886044i	$0.346557\pi$
$264$	93.6246	+	57.0768i	0.354639	+	0.216200i
$265$			192.071i			0.724794i
$266$	290.255	−	199.815i	1.09118	−	0.751184i
$267$	64.8918	+	64.8918i	0.243040	+	0.243040i
$268$	327.644	−	146.480i	1.22255	−	0.546567i
$269$	234.293	+	234.293i	0.870976	+	0.870976i	0.992579	−	0.121603i	$-0.0388035\pi$
$269$	234.293	+	234.293i	0.870976	+	0.870976i	−0.121603	+	0.992579i	$0.538803\pi$
$270$	24.5599	+	4.53239i	0.0909624	+	0.0167866i
$271$		−	30.9533i		−	0.114219i	−0.998368	−	0.0571094i	$-0.981812\pi$
$271$		−	30.9533i		−	0.114219i	0.998368	−	0.0571094i	$-0.0181884\pi$
$272$	234.914	+	210.214i	0.863655	+	0.772846i
$273$	−191.003			−0.699646
$274$	92.0100	−	498.579i	0.335803	−	1.81963i
$275$	107.574	−	107.574i	0.391178	−	0.391178i
$276$	−157.652	+	70.4818i	−0.571204	+	0.255369i
$277$	−41.4479	+	41.4479i	−0.149631	+	0.149631i	−0.777953	−	0.628322i	$-0.783742\pi$
$277$	−41.4479	+	41.4479i	−0.149631	+	0.149631i	0.628322	+	0.777953i	$0.283742\pi$
$278$	108.750	+	157.972i	0.391187	+	0.568245i
$279$	−6.60110			−0.0236599
$280$	−107.298	+	26.0216i	−0.383206	+	0.0929342i
$281$		−	93.3971i		−	0.332374i	−0.986094	−	0.166187i	$-0.946854\pi$
$281$		−	93.3971i		−	0.332374i	0.986094	−	0.166187i	$-0.0531455\pi$
$282$	150.310	+	218.343i	0.533014	+	0.774265i
$283$	40.0982	+	40.0982i	0.141690	+	0.141690i	0.774394	−	0.632704i	$-0.218055\pi$
$283$	40.0982	+	40.0982i	0.141690	+	0.141690i	−0.632704	+	0.774394i	$0.718055\pi$
$284$	162.485	+	62.0858i	0.572130	+	0.218612i
$285$	−90.3011	−	90.3011i	−0.316846	−	0.316846i
$286$	−55.1540	+	298.866i	−0.192846	+	1.04498i
$287$		−	294.678i		−	1.02675i
$288$	75.9369	−	58.7332i	0.263670	−	0.203935i
$289$	99.1824			0.343192
$290$	10.0654	+	1.85750i	0.0347081	+	0.00640519i
$291$	−28.2926	+	28.2926i	−0.0972256	+	0.0972256i
$292$	−105.651	+	276.500i	−0.361819	+	0.946917i
$293$	141.326	−	141.326i	0.482340	−	0.482340i	−0.423538	−	0.905878i	$-0.639212\pi$
$293$	141.326	−	141.326i	0.482340	−	0.482340i	0.905878	+	0.423538i	$0.139212\pi$
$294$	45.7113	−	31.4683i	0.155481	−	0.107035i
$295$	−163.147			−0.553041
$296$	304.513	−	73.8499i	1.02876	−	0.249493i
$297$		−	41.1191i		−	0.138448i
$298$	−102.355	+	70.4622i	−0.343472	+	0.236450i
$299$	−338.445	−	338.445i	−1.13192	−	1.13192i
$300$	−54.3613	−	121.594i	−0.181204	−	0.405314i
$301$	−123.126	−	123.126i	−0.409056	−	0.409056i
$302$	−438.759	−	80.9705i	−1.45284	−	0.268114i
$303$			39.4896i			0.130329i
$304$	−490.133	+	27.1974i	−1.61228	+	0.0894652i
$305$	−175.228			−0.574517
$306$	21.4535	−	116.251i	0.0701095	−	0.379905i
$307$	−285.548	+	285.548i	−0.930125	+	0.930125i	−0.997713	−	0.0675885i	$-0.978470\pi$
$307$	−285.548	+	285.548i	−0.930125	+	0.930125i	0.0675885	+	0.997713i	$0.478470\pi$
$308$	74.1916	+	165.950i	0.240882	+	0.538799i
$309$	121.051	−	121.051i	0.391752	−	0.391752i
$310$	−5.99687	−	8.71115i	−0.0193447	−	0.0281005i
$311$	−365.454			−1.17509			−0.587547	−	0.809190i	$-0.699906\pi$
$311$	−365.454			−1.17509			−0.587547	+	0.809190i	$0.699906\pi$
$312$	227.188	+	138.501i	0.728165	+	0.443915i
$313$		−	461.508i		−	1.47447i	−0.675638	−	0.737234i	$-0.736132\pi$
$313$		−	461.508i		−	1.47447i	0.675638	−	0.737234i	$-0.263868\pi$
$314$	−126.466	−	183.707i	−0.402758	−	0.585054i
$315$	29.2763	+	29.2763i	0.0929406	+	0.0929406i
$316$	5.89167	−	15.4191i	0.0186445	−	0.0487946i
$317$	−319.216	−	319.216i	−1.00699	−	1.00699i	−0.999975	−	0.00701388i	$-0.997767\pi$
$317$	−319.216	−	319.216i	−1.00699	−	1.00699i	−0.00701388	−	0.999975i	$-0.502233\pi$
$318$	50.2451	−	272.266i	0.158004	−	0.856182i
$319$		−	16.8518i		−	0.0528270i
$320$	146.493	+	46.8531i	0.457792	+	0.146416i
$321$	−38.3724			−0.119540
$322$	−281.533	−	51.9553i	−0.874325	−	0.161352i
$323$	−427.429	+	427.429i	−1.32331	+	1.32331i
$324$	−33.6287	−	12.8496i	−0.103792	−	0.0396592i
$325$	261.037	−	261.037i	0.803190	−	0.803190i
$326$	121.712	−	83.7881i	0.373350	−	0.257019i
$327$	−207.457			−0.634424
$328$	−213.679	+	350.503i	−0.651461	+	1.06861i
$329$			439.448i			1.33571i
$330$	54.2629	−	37.3552i	0.164433	−	0.113198i
$331$	−85.7864	−	85.7864i	−0.259173	−	0.259173i	0.565544	−	0.824718i	$-0.308666\pi$
$331$	−85.7864	−	85.7864i	−0.259173	−	0.259173i	−0.824718	+	0.565544i	$0.808666\pi$
$332$	198.528	−	88.7562i	0.597976	−	0.267338i
$333$	−83.0869	−	83.0869i	−0.249510	−	0.249510i
$334$	189.835	+	35.0329i	0.568367	+	0.104889i
$335$		−	215.623i		−	0.643651i
$336$	158.905	−	8.81761i	0.472931	−	0.0262429i
$337$	258.256			0.766339			0.383170	−	0.923678i	$-0.374832\pi$
$337$	258.256			0.766339			0.383170	+	0.923678i	$0.374832\pi$
$338$	−72.4953	+	392.834i	−0.214483	+	1.16223i
$339$	−78.2045	+	78.2045i	−0.230692	+	0.230692i
$340$	172.901	−	77.2989i	0.508531	−	0.227350i
$341$	−12.3124	+	12.3124i	−0.0361067	+	0.0361067i
$342$	104.382	+	151.627i	0.305210	+	0.443354i
$343$	373.398			1.08862
$344$	57.1695	+	235.733i	0.166190	+	0.685271i
$345$			103.751i			0.300729i
$346$	−74.2695	−	107.885i	−0.214652	−	0.311807i
$347$	27.7237	+	27.7237i	0.0798953	+	0.0798953i	0.745925	−	0.666030i	$-0.232008\pi$
$347$	27.7237	+	27.7237i	0.0798953	+	0.0798953i	−0.666030	+	0.745925i	$0.732008\pi$
$348$	−13.7820	−	5.26614i	−0.0396035	−	0.0151326i
$349$	321.089	+	321.089i	0.920027	+	0.920027i	0.997031	−	0.0770037i	$-0.0245353\pi$
$349$	321.089	+	321.089i	0.920027	+	0.920027i	−0.0770037	+	0.997031i	$0.524535\pi$
$350$	40.0722	−	217.141i	0.114492	−	0.620403i
$351$		−	99.7788i		−	0.284270i
$352$	32.0882	−	251.187i	0.0911596	−	0.713599i
$353$	−241.363			−0.683748			−0.341874	−	0.939746i	$-0.611062\pi$
$353$	−241.363			−0.683748			−0.341874	+	0.939746i	$0.611062\pi$
$354$	231.266	+	42.6788i	0.653293	+	0.120562i
$355$	73.8953	−	73.8953i	0.208156	−	0.208156i
$356$	75.6468	−	197.975i	0.212491	−	0.556111i
$357$	138.576	−	138.576i	0.388167	−	0.388167i
$358$	−217.934	+	150.029i	−0.608754	+	0.419074i
$359$	−363.821			−1.01343			−0.506714	−	0.862114i	$-0.669140\pi$
$359$	−363.821			−1.01343			−0.506714	+	0.862114i	$0.669140\pi$
$360$	−13.5935	−	56.0515i	−0.0377597	−	0.155699i
$361$		−	580.287i		−	1.60744i
$362$	−269.809	+	185.740i	−0.745329	+	0.513094i
$363$	71.4988	+	71.4988i	0.196966	+	0.196966i
$364$	180.032	+	402.692i	0.494593	+	1.10630i
$365$	125.747	+	125.747i	0.344513	+	0.344513i
$366$	248.391	+	45.8391i	0.678663	+	0.125244i
$367$			411.402i			1.12099i	0.828159	+	0.560493i	$0.189388\pi$
$367$			411.402i			1.12099i	−0.828159	+	0.560493i	$0.810612\pi$
$368$	297.193	+	265.945i	0.807590	+	0.722676i
$369$	153.938			0.417176
$370$	34.1642	−	185.127i	0.0923356	−	0.500344i
$371$	324.551	−	324.551i	0.874801	−	0.874801i
$372$	6.22193	+	13.9171i	0.0167256	+	0.0374115i
$373$	−225.677	+	225.677i	−0.605033	+	0.605033i	−0.941644	−	0.336611i	$-0.890719\pi$
$373$	−225.677	+	225.677i	−0.605033	+	0.605033i	0.336611	+	0.941644i	$0.390719\pi$
$374$	−176.816	−	256.847i	−0.472771	−	0.686756i
$375$	−184.082			−0.490886
$376$	318.656	−	522.699i	0.847488	−	1.39016i
$377$		−	40.8923i		−	0.108468i
$378$	−33.8414	−	49.1586i	−0.0895276	−	0.130049i
$379$	−157.180	−	157.180i	−0.414724	−	0.414724i	0.468656	−	0.883381i	$-0.344738\pi$
$379$	−157.180	−	157.180i	−0.414724	−	0.414724i	−0.883381	+	0.468656i	$0.844738\pi$
$380$	−105.267	+	275.496i	−0.277019	+	0.724988i
$381$	−45.1810	−	45.1810i	−0.118585	−	0.118585i
$382$	−12.8112	+	69.4207i	−0.0335372	+	0.181729i
$383$			703.356i			1.83644i	0.396072	+	0.918219i	$0.370373\pi$
$383$			703.356i			1.83644i	−0.396072	+	0.918219i	$0.629627\pi$
$384$	−195.402	−	104.738i	−0.508860	−	0.272755i
$385$	109.212			0.283668
$386$	−716.578	−	132.241i	−1.85642	−	0.342592i
$387$	64.3201	−	64.3201i	0.166202	−	0.166202i
$388$	86.3168	+	32.9818i	0.222466	+	0.0850047i
$389$	10.7401	−	10.7401i	0.0276095	−	0.0276095i	−0.693167	−	0.720777i	$-0.743785\pi$
$389$	10.7401	−	10.7401i	0.0276095	−	0.0276095i	0.720777	+	0.693167i	$0.243785\pi$
$390$	131.673	−	90.6455i	0.337623	−	0.232424i
$391$	491.095			1.25600
$392$	−109.430	−	66.7124i	−0.279158	−	0.170185i
$393$		−	98.9926i		−	0.251890i
$394$	304.222	−	209.431i	0.772138	−	0.531550i
$395$	−7.01234	−	7.01234i	−0.0177528	−	0.0177528i
$396$	−86.6913	+	38.7572i	−0.218917	+	0.0978716i
$397$	365.020	+	365.020i	0.919446	+	0.919446i	0.996989	−	0.0775433i	$-0.0247076\pi$
$397$	365.020	+	365.020i	0.919446	+	0.919446i	−0.0775433	+	0.996989i	$0.524708\pi$
$398$	−25.0753	−	4.62750i	−0.0630032	−	0.0116269i
$399$			305.173i			0.764844i
$400$	−205.118	+	229.220i	−0.512796	+	0.573049i
$401$	341.735			0.852207			0.426104	−	0.904674i	$-0.359886\pi$
$401$	341.735			0.852207			0.426104	+	0.904674i	$0.359886\pi$
$402$	−56.4065	+	305.652i	−0.140315	+	0.760329i
$403$	−29.8770	+	29.8770i	−0.0741364	+	0.0741364i
$404$	83.2558	−	37.2213i	0.206079	−	0.0921318i
$405$	−15.2937	+	15.2937i	−0.0377623	+	0.0377623i
$406$	−13.8692	−	20.1467i	−0.0341606	−	0.0496223i
$407$	−309.947			−0.761541
$408$	−265.313	+	64.3431i	−0.650277	+	0.157704i
$409$		−	368.259i		−	0.900389i	−0.892931	−	0.450194i	$-0.851355\pi$
$409$		−	368.259i		−	0.900389i	0.892931	−	0.450194i	$-0.148645\pi$
$410$	139.847	+	203.144i	0.341091	+	0.495474i
$411$	310.472	+	310.472i	0.755405	+	0.755405i
$412$	−369.310	−	141.114i	−0.896384	−	0.342510i
$413$	275.678	+	275.678i	0.667501	+	0.667501i
$414$	27.1411	−	147.071i	0.0655582	−	0.355243i
$415$		−	130.652i		−	0.314824i
$416$	77.8646	−	609.525i	0.187174	−	1.46520i
$417$	−166.091			−0.398300
$418$	477.508	+	88.1215i	1.14236	+	0.210817i
$419$	407.140	−	407.140i	0.971694	−	0.971694i	−0.0279165	−	0.999610i	$-0.508887\pi$
$419$	407.140	−	407.140i	0.971694	−	0.971694i	0.999610	+	0.0279165i	$0.00888725\pi$
$420$	34.1285	−	89.3178i	0.0812583	−	0.212661i
$421$	57.5576	−	57.5576i	0.136716	−	0.136716i	−0.635437	−	0.772153i	$-0.719180\pi$
$421$	57.5576	−	57.5576i	0.136716	−	0.136716i	0.772153	+	0.635437i	$0.219180\pi$
$422$	20.0242	−	13.7849i	0.0474506	−	0.0326656i
$423$	−229.565			−0.542706
$424$	−621.376	+	150.695i	−1.46551	+	0.355412i
$425$			378.772i			0.891229i
$426$	−124.080	+	85.4180i	−0.291267	+	0.200512i
$427$	296.091	+	296.091i	0.693422	+	0.693422i
$428$	36.1683	+	80.9005i	0.0845053	+	0.189020i
$429$	−186.107	−	186.107i	−0.433817	−	0.433817i
$430$	143.313	+	26.4476i	0.333285	+	0.0615060i
$431$		−	796.565i		−	1.84818i	−0.382177	−	0.924089i	$-0.624826\pi$
$431$		−	796.565i		−	1.84818i	0.382177	−	0.924089i	$-0.375174\pi$
$432$	4.60626	+	83.0107i	0.0106626	+	0.192154i
$433$	−335.804			−0.775529			−0.387764	−	0.921758i	$-0.626753\pi$
$433$	−335.804			−0.775529			−0.387764	+	0.921758i	$0.626753\pi$
$434$	−4.58646	+	24.8529i	−0.0105679	+	0.0572647i
$435$	−6.26782	+	6.26782i	−0.0144088	+	0.0144088i
$436$	195.540	+	437.380i	0.448487	+	1.00317i
$437$	−540.746	+	540.746i	−1.23741	+	1.23741i
$438$	−145.355	−	211.146i	−0.331862	−	0.482068i
$439$	−285.630			−0.650638			−0.325319	−	0.945604i	$-0.605472\pi$
$439$	−285.630			−0.650638			−0.325319	+	0.945604i	$0.605472\pi$
$440$	−129.902	−	79.1927i	−0.295232	−	0.179983i
$441$			48.0607i			0.108981i
$442$	−429.059	−	623.259i	−0.970722	−	1.41009i
$443$	111.596	+	111.596i	0.251909	+	0.251909i	0.821753	−	0.569844i	$-0.192996\pi$
$443$	111.596	+	111.596i	0.251909	+	0.251909i	−0.569844	+	0.821753i	$0.692996\pi$
$444$	−96.8575	+	253.486i	−0.218148	+	0.570914i
$445$	−90.0358	−	90.0358i	−0.202328	−	0.202328i
$446$	18.3625	−	99.5017i	0.0411715	−	0.223098i
$447$		−	107.615i		−	0.240750i
$448$	−168.367	−	326.707i	−0.375820	−	0.729257i
$449$	−99.6741			−0.221991			−0.110996	−	0.993821i	$-0.535404\pi$
$449$	−99.6741			−0.221991			−0.110996	+	0.993821i	$0.535404\pi$
$450$	113.433	+	20.9334i	0.252073	+	0.0465187i
$451$	287.125	−	287.125i	0.636641	−	0.636641i
$452$	238.591	+	91.1659i	0.527855	+	0.201695i
$453$	273.221	−	273.221i	0.603137	−	0.603137i
$454$	73.8939	−	50.8695i	0.162762	−	0.112047i
$455$	265.012			0.582445
$456$	221.289	−	362.986i	0.485282	−	0.796021i
$457$			32.1643i			0.0703813i	0.999381	+	0.0351907i	$0.0112039\pi$
$457$			32.1643i			0.0703813i	−0.999381	+	0.0351907i	$0.988796\pi$
$458$	−395.652	+	272.372i	−0.863870	+	0.594699i
$459$	72.3910	+	72.3910i	0.157715	+	0.157715i
$460$	218.739	−	97.7918i	0.475519	−	0.212591i
$461$	165.361	+	165.361i	0.358701	+	0.358701i	0.863334	−	0.504633i	$-0.168372\pi$
$461$	165.361	+	165.361i	0.358701	+	0.358701i	−0.504633	+	0.863334i	$0.668372\pi$
$462$	−154.812	−	28.5697i	−0.335090	−	0.0618391i
$463$			923.215i			1.99398i	0.0774991	+	0.996992i	$0.475307\pi$
$463$			923.215i			1.99398i	−0.0774991	+	0.996992i	$0.524693\pi$
$464$	1.88778	+	34.0202i	0.00406849	+	0.0733195i
$465$	9.15887			0.0196965
$466$	−131.784	+	714.105i	−0.282798	+	1.53241i
$467$	507.842	−	507.842i	1.08746	−	1.08746i	0.0916660	−	0.995790i	$-0.470781\pi$
$467$	507.842	−	507.842i	1.08746	−	1.08746i	0.995790	−	0.0916660i	$-0.0292192\pi$
$468$	−210.363	+	94.0474i	−0.449494	+	0.200956i
$469$	−364.349	+	364.349i	−0.776864	+	0.776864i
$470$	−208.551	−	302.945i	−0.443727	−	0.644565i
$471$	193.149			0.410082
$472$	−128.002	−	527.805i	−0.271191	−	1.11823i
$473$		−	239.940i		−	0.507272i
$474$	8.10579	+	11.7746i	0.0171008	+	0.0248409i
$475$	−417.068	−	417.068i	−0.878037	−	0.878037i
$476$	−422.775	−	161.543i	−0.888182	−	0.339376i
$477$	169.543	+	169.543i	0.355437	+	0.355437i
$478$	10.0279	−	54.3389i	0.0209789	−	0.113680i
$479$		−	52.3866i		−	0.109367i	−0.998504	−	0.0546833i	$-0.982585\pi$
$479$		−	52.3866i		−	0.109367i	0.998504	−	0.0546833i	$-0.0174149\pi$
$480$	−105.361	+	81.4910i	−0.219501	+	0.169773i
$481$	−752.112			−1.56364
$482$	724.017	+	133.613i	1.50211	+	0.277206i
$483$	175.314	−	175.314i	0.362969	−	0.362969i
$484$	83.3489	−	218.132i	0.172208	−	0.450687i
$485$	39.2554	−	39.2554i	0.0809389	−	0.0809389i
$486$	25.6801	−	17.6785i	0.0528398	−	0.0363756i
$487$	−715.733			−1.46968			−0.734839	−	0.678241i	$-0.762742\pi$
$487$	−715.733			−1.46968			−0.734839	+	0.678241i	$0.762742\pi$
$488$	−137.480	−	566.887i	−0.281722	−	1.16165i
$489$			127.968i			0.261692i
$490$	−63.4234	+	43.6614i	−0.129435	+	0.0891050i
$491$	−22.3258	−	22.3258i	−0.0454701	−	0.0454701i	0.684006	−	0.729476i	$-0.260236\pi$
$491$	−22.3258	−	22.3258i	−0.0454701	−	0.0454701i	−0.729476	+	0.684006i	$0.760236\pi$
$492$	−145.096	−	324.547i	−0.294910	−	0.659649i
$493$	29.6680	+	29.6680i	0.0601784	+	0.0601784i
$494$	1158.71	+	213.834i	2.34557	+	0.432862i
$495$			57.0518i			0.115256i
$496$	23.4768	−	26.2353i	0.0473323	−	0.0528938i
$497$	−249.729			−0.502473
$498$	−34.1782	+	185.203i	−0.0686309	+	0.371894i
$499$	84.0984	−	84.0984i	0.168534	−	0.168534i	−0.617801	−	0.786335i	$-0.711976\pi$
$499$	84.0984	−	84.0984i	0.168534	−	0.168534i	0.786335	+	0.617801i	$0.211976\pi$
$500$	173.508	+	388.100i	0.347017	+	0.776200i
$501$	−118.213	+	118.213i	−0.235953	+	0.235953i
$502$	529.005	+	768.442i	1.05380	+	1.53076i
$503$	327.870			0.651829			0.325914	−	0.945399i	$-0.394328\pi$
$503$	327.870			0.651829			0.325914	+	0.945399i	$0.394328\pi$
$504$	−71.7435	+	117.683i	−0.142348	+	0.233497i
$505$		−	54.7909i		−	0.108497i
$506$	−223.693	−	324.940i	−0.442081	−	0.642174i
$507$	−244.623	−	244.623i	−0.482490	−	0.482490i
$508$	−52.6692	+	137.841i	−0.103680	+	0.271340i
$509$	34.6224	+	34.6224i	0.0680205	+	0.0680205i	0.740299	−	0.672278i	$-0.234684\pi$
$509$	34.6224	+	34.6224i	0.0680205	+	0.0680205i	−0.672278	+	0.740299i	$0.734684\pi$
$510$	−29.7662	+	161.296i	−0.0583651	+	0.316266i
$511$		−	424.963i		−	0.831630i
$512$	−36.6407	+	510.687i	−0.0715639	+	0.997436i
$513$	−159.420			−0.310760
$514$	46.5661	+	8.59351i	0.0905954	+	0.0167189i
$515$	−167.956	+	167.956i	−0.326128	+	0.326128i
$516$	−196.231	−	74.9804i	−0.380294	−	0.145311i
$517$	−428.184	+	428.184i	−0.828210	+	0.828210i
$518$	−370.548	+	255.090i	−0.715343	+	0.492451i
$519$	113.430			0.218555
$520$	−315.217	−	192.167i	−0.606187	−	0.369553i
$521$		−	235.719i		−	0.452436i	−0.974077	−	0.226218i	$-0.927364\pi$
$521$		−	235.719i		−	0.452436i	0.974077	−	0.226218i	$-0.0726362\pi$
$522$	10.5245	−	7.24518i	0.0201618	−	0.0138797i
$523$	−185.851	−	185.851i	−0.355356	−	0.355356i	0.506742	−	0.862098i	$-0.330850\pi$
$523$	−185.851	−	185.851i	−0.355356	−	0.355356i	−0.862098	+	0.506742i	$0.830850\pi$
$524$	−208.706	+	93.3063i	−0.398294	+	0.178066i
$525$	135.216	+	135.216i	0.257555	+	0.257555i
$526$	479.610	+	88.5093i	0.911805	+	0.168269i
$527$		−	43.3524i		−	0.0822626i
$528$	163.423	+	146.240i	0.309514	+	0.276970i
$529$	92.2900			0.174461
$530$	−69.7139	+	377.762i	−0.131536	+	0.712759i
$531$	−144.012	+	144.012i	−0.271209	+	0.271209i
$532$	643.394	−	287.643i	1.20939	−	0.540683i
$533$	696.732	−	696.732i	1.30719	−	1.30719i
$534$	104.075	+	151.182i	0.194898	+	0.283111i
$535$	53.2408			0.0995155
$536$	697.572	−	169.174i	1.30144	−	0.315623i
$537$		−	229.135i		−	0.426695i
$538$	375.765	+	545.843i	0.698448	+	1.01458i
$539$	89.6428	+	89.6428i	0.166313	+	0.166313i
$540$	46.6590	+	17.8285i	0.0864055	+	0.0330157i
$541$	−315.952	−	315.952i	−0.584015	−	0.584015i	0.351989	−	0.936004i	$-0.385506\pi$
$541$	−315.952	−	315.952i	−0.584015	−	0.584015i	−0.936004	+	0.351989i	$0.885506\pi$
$542$	11.2348	−	60.8786i	0.0207284	−	0.112322i
$543$		−	283.676i		−	0.522424i
$544$	385.728	+	498.711i	0.709058	+	0.916749i
$545$	287.841			0.528149
$546$	−375.663	−	69.3266i	−0.688028	−	0.126972i
$547$	−550.957	+	550.957i	−1.00723	+	1.00723i	−0.00725954	+	0.999974i	$0.502311\pi$
$547$	−550.957	+	550.957i	−1.00723	+	1.00723i	−0.999974	+	0.00725954i	$0.997689\pi$
$548$	361.929	−	947.204i	0.660454	−	1.72847i
$549$	−154.676	+	154.676i	−0.281741	+	0.281741i
$550$	250.620	−	172.530i	0.455673	−	0.313691i
$551$	−65.3350			−0.118575
$552$	−335.651	+	81.4013i	−0.608063	+	0.147466i
$553$			23.6982i			0.0428539i
$554$	−96.5631	+	66.4753i	−0.174302	+	0.119992i
$555$	115.281	+	115.281i	0.207714	+	0.207714i
$556$	156.551	+	350.170i	0.281566	+	0.629802i
$557$	2.35545	+	2.35545i	0.00422882	+	0.00422882i	0.709218	−	0.704989i	$-0.249048\pi$
$557$	2.35545	+	2.35545i	0.00422882	+	0.00422882i	−0.704989	+	0.709218i	$0.749048\pi$
$558$	−12.9830	−	2.39594i	−0.0232670	−	0.00429379i
$559$		−	582.233i		−	1.04156i
$560$	−220.476	+	12.2342i	−0.393708	+	0.0218468i
$561$	270.048			0.481368
$562$	33.8994	−	183.692i	0.0603192	−	0.326855i
$563$	269.210	−	269.210i	0.478170	−	0.478170i	−0.426376	−	0.904546i	$-0.640210\pi$
$563$	269.210	−	269.210i	0.478170	−	0.478170i	0.904546	+	0.426376i	$0.140210\pi$
$564$	216.378	+	483.991i	0.383650	+	0.858140i
$565$	108.507	−	108.507i	0.192047	−	0.192047i
$566$	64.3106	+	93.4187i	0.113623	+	0.165051i
$567$	51.6852			0.0911556
$568$	297.039	+	181.085i	0.522956	+	0.318812i
$569$			342.558i			0.602035i	0.953619	+	0.301018i	$0.0973263\pi$
$569$			342.558i			0.602035i	−0.953619	+	0.301018i	$0.902674\pi$
$570$	−144.827	−	210.379i	−0.254083	−	0.369086i
$571$	153.948	+	153.948i	0.269610	+	0.269610i	0.828943	−	0.559333i	$-0.188943\pi$
$571$	153.948	+	153.948i	0.269610	+	0.269610i	−0.559333	+	0.828943i	$0.688943\pi$
$572$	−216.953	+	567.787i	−0.379288	+	0.992634i
$573$	−43.2291	−	43.2291i	−0.0754435	−	0.0754435i
$574$	106.957	−	579.570i	0.186335	−	1.00970i
$575$			479.190i			0.833373i
$576$	170.670	−	87.9539i	0.296301	−	0.152698i
$577$	563.693			0.976938			0.488469	−	0.872581i	$-0.337556\pi$
$577$	563.693			0.976938			0.488469	+	0.872581i	$0.337556\pi$
$578$	195.071	+	35.9992i	0.337493	+	0.0622824i
$579$	446.223	−	446.223i	0.770678	−	0.770678i
$580$	19.1222	+	7.30664i	0.0329693	+	0.0125977i
$581$	−220.769	+	220.769i	−0.379981	+	0.379981i
$582$	−65.9148	+	45.3766i	−0.113256	+	0.0779666i
$583$	632.465			1.08484
$584$	−308.152	+	505.469i	−0.527657	+	0.865530i
$585$			138.441i			0.236651i
$586$	329.253	−	226.662i	0.561866	−	0.386796i
$587$	176.603	+	176.603i	0.300857	+	0.300857i	0.841349	−	0.540492i	$-0.181762\pi$
$587$	176.603	+	176.603i	0.300857	+	0.300857i	−0.540492	+	0.841349i	$0.681762\pi$
$588$	101.326	−	45.3000i	0.172324	−	0.0770409i
$589$	47.7355	+	47.7355i	0.0810450	+	0.0810450i
$590$	−320.876	−	59.2159i	−0.543857	−	0.100366i
$591$			319.858i			0.541215i
$592$	625.718	−	34.7210i	1.05696	−	0.0586504i
$593$	−996.597			−1.68060			−0.840301	−	0.542120i	$-0.817622\pi$
$593$	−996.597			−1.68060			−0.840301	+	0.542120i	$0.817622\pi$
$594$	14.9246	−	80.8726i	0.0251256	−	0.136149i
$595$	−192.271	+	192.271i	−0.323144	+	0.323144i
$596$	−226.885	+	101.434i	−0.380679	+	0.170191i
$597$	15.6147	−	15.6147i	0.0261553	−	0.0261553i
$598$	−542.808	−	788.493i	−0.907707	−	1.31855i
$599$	−854.031			−1.42576			−0.712880	−	0.701286i	$-0.752610\pi$
$599$	−854.031			−1.42576			−0.712880	+	0.701286i	$0.752610\pi$
$600$	−62.7834	−	258.881i	−0.104639	−	0.431469i
$601$			345.733i			0.575263i	0.957741	+	0.287631i	$0.0928678\pi$
$601$			345.733i			0.575263i	−0.957741	+	0.287631i	$0.907132\pi$
$602$	−197.473	−	286.853i	−0.328028	−	0.476499i
$603$	−190.334	−	190.334i	−0.315645	−	0.315645i
$604$	−833.557	−	318.504i	−1.38006	−	0.527325i
$605$	−99.2029	−	99.2029i	−0.163972	−	0.163972i
$606$	−14.3331	+	77.6677i	−0.0236521	+	0.128165i
$607$		−	526.354i		−	0.867141i	−0.901120	−	0.433570i	$-0.857254\pi$
$607$		−	526.354i		−	0.867141i	0.901120	−	0.433570i	$-0.142746\pi$
$608$	−973.859	−	124.407i	−1.60174	−	0.204617i
$609$	21.1821			0.0347818
$610$	−344.636	−	63.6007i	−0.564977	−	0.104263i
$611$	−1039.02	+	1039.02i	−1.70053	+	1.70053i
$612$	84.3890	−	220.855i	0.137891	−	0.360874i
$613$	410.567	−	410.567i	0.669767	−	0.669767i	−0.287895	−	0.957662i	$-0.592955\pi$
$613$	410.567	−	410.567i	0.669767	−	0.669767i	0.957662	+	0.287895i	$0.0929554\pi$
$614$	−665.256	+	457.971i	−1.08348	+	0.745881i
$615$	−213.585			−0.347293
$616$	85.6859	+	353.318i	0.139100	+	0.573568i
$617$		−	514.755i		−	0.834287i	−0.908841	−	0.417144i	$-0.863031\pi$
$617$		−	514.755i		−	0.834287i	0.908841	−	0.417144i	$-0.136969\pi$
$618$	282.019	−	194.146i	0.456342	−	0.314152i
$619$	314.214	+	314.214i	0.507615	+	0.507615i	0.913794	−	0.406179i	$-0.133139\pi$
$619$	314.214	+	314.214i	0.507615	+	0.507615i	−0.406179	+	0.913794i	$0.633139\pi$
$620$	−8.63278	−	19.3096i	−0.0139238	−	0.0311446i
$621$	91.5828	+	91.5828i	0.147476	+	0.147476i
$622$	−718.772	−	132.645i	−1.15558	−	0.213256i
$623$			304.276i			0.488404i
$624$	396.560	+	354.863i	0.635512	+	0.568691i
$625$	−225.209			−0.360334
$626$	167.509	−	907.690i	0.267586	−	1.44998i
$627$	−297.350	+	297.350i	−0.474243	+	0.474243i
$628$	−182.054	−	407.215i	−0.289895	−	0.648431i
$629$	545.669	−	545.669i	0.867518	−	0.867518i
$630$	46.9542	+	68.2064i	0.0745304	+	0.108264i
$631$	−230.081			−0.364629			−0.182315	−	0.983240i	$-0.558359\pi$
$631$	−230.081			−0.364629			−0.182315	+	0.983240i	$0.558359\pi$
$632$	17.1842	−	28.1877i	0.0271902	−	0.0446008i
$633$			21.0533i			0.0332596i
$634$	−511.967	−	743.692i	−0.807519	−	1.17302i
$635$	62.6875	+	62.6875i	0.0987205	+	0.0987205i
$636$	197.643	−	517.252i	0.310760	−	0.813290i
$637$	217.526	+	217.526i	0.341484	+	0.341484i
$638$	6.11654	−	33.1440i	0.00958705	−	0.0519498i
$639$		−	130.457i		−	0.204158i
$640$	271.116	+	145.321i	0.423618	+	0.227065i
$641$	746.825			1.16509			0.582547	−	0.812797i	$-0.302056\pi$
$641$	746.825			1.16509			0.582547	+	0.812797i	$0.302056\pi$
$642$	−75.4705	−	13.9277i	−0.117555	−	0.0216942i
$643$	548.092	−	548.092i	0.852398	−	0.852398i	−0.138030	−	0.990428i	$-0.544077\pi$
$643$	548.092	−	548.092i	0.852398	−	0.852398i	0.990428	+	0.138030i	$0.0440772\pi$
$644$	−534.858	−	204.370i	−0.830524	−	0.317345i
$645$	−89.2426	+	89.2426i	−0.138361	+	0.138361i
$646$	−995.803	+	685.523i	−1.54149	+	1.06118i
$647$	1055.00			1.63060			0.815302	−	0.579036i	$-0.196571\pi$
$647$	1055.00			1.63060			0.815302	+	0.579036i	$0.196571\pi$
$648$	−61.4766	−	37.4783i	−0.0948714	−	0.0578369i
$649$			537.223i			0.827771i
$650$	608.150	−	418.658i	0.935616	−	0.644090i
$651$	−15.4762	−	15.4762i	−0.0237730	−	0.0237730i
$652$	269.794	−	120.617i	0.413794	−	0.184995i
$653$	−854.888	−	854.888i	−1.30917	−	1.30917i	−0.922015	−	0.387155i	$-0.873458\pi$
$653$	−854.888	−	854.888i	−1.30917	−	1.30917i	−0.387155	−	0.922015i	$-0.626542\pi$
$654$	−408.024	−	75.2985i	−0.623889	−	0.115135i
$655$			137.350i			0.209694i
$656$	−547.480	+	611.809i	−0.834574	+	0.932636i
$657$	221.998			0.337896
$658$	−159.502	+	864.302i	−0.242405	+	1.31353i
$659$	−768.766	+	768.766i	−1.16656	+	1.16656i	−0.183556	+	0.983009i	$0.558761\pi$
$659$	−768.766	+	768.766i	−1.16656	+	1.16656i	−0.983009	+	0.183556i	$0.941239\pi$
$660$	120.282	−	53.7746i	0.182246	−	0.0814767i
$661$	312.323	−	312.323i	0.472500	−	0.472500i	−0.430223	−	0.902723i	$-0.641565\pi$
$661$	312.323	−	312.323i	0.472500	−	0.472500i	0.902723	+	0.430223i	$0.141565\pi$
$662$	−137.587	−	199.861i	−0.207835	−	0.301904i
$663$	655.292			0.988374
$664$	422.678	−	102.507i	0.636563	−	0.154378i
$665$		−	423.420i		−	0.636721i
$666$	−133.257	−	193.572i	−0.200086	−	0.290648i
$667$	37.5333	+	37.5333i	0.0562719	+	0.0562719i
$668$	360.649	+	137.805i	0.539894	+	0.206295i
$669$	61.9610	+	61.9610i	0.0926173	+	0.0926173i
$670$	78.2626	−	424.085i	0.116810	−	0.632963i
$671$			577.004i			0.859916i
$672$	315.733	+	40.3337i	0.469840	+	0.0600204i
$673$	740.565			1.10039			0.550197	−	0.835035i	$-0.314553\pi$
$673$	740.565			1.10039			0.550197	+	0.835035i	$0.314553\pi$
$674$	507.936	+	93.7367i	0.753614	+	0.139075i
$675$	−70.6362	+	70.6362i	−0.104646	+	0.104646i
$676$	−285.166	+	746.308i	−0.421843	+	1.10401i
$677$	−547.118	+	547.118i	−0.808151	+	0.808151i	−0.984354	−	0.176203i	$-0.943619\pi$
$677$	−547.118	+	547.118i	−0.808151	+	0.808151i	0.176203	+	0.984354i	$0.443619\pi$
$678$	−182.197	+	125.427i	−0.268727	+	0.184995i
$679$	−132.664			−0.195381
$680$	368.115	−	89.2746i	0.541346	−	0.131286i
$681$			77.6918i			0.114085i
$682$	−28.6848	+	19.7470i	−0.0420598	+	0.0289545i
$683$	−407.623	−	407.623i	−0.596813	−	0.596813i	0.342650	−	0.939463i	$-0.388676\pi$
$683$	−407.623	−	407.623i	−0.596813	−	0.596813i	−0.939463	+	0.342650i	$0.888676\pi$
$684$	150.263	+	336.105i	0.219682	+	0.491381i
$685$	−430.772	−	430.772i	−0.628864	−	0.628864i
$686$	734.396	+	135.529i	1.07055	+	0.197564i
$687$		−	415.987i		−	0.605513i
$688$	26.8786	+	484.388i	0.0390678	+	0.704052i
$689$	1534.73			2.22747
$690$	−37.6576	+	204.057i	−0.0545763	+	0.295735i
$691$	17.6037	−	17.6037i	0.0254757	−	0.0254757i	−0.694254	−	0.719730i	$-0.744266\pi$
$691$	17.6037	−	17.6037i	0.0254757	−	0.0254757i	0.719730	+	0.694254i	$0.244266\pi$
$692$	−106.915	−	239.144i	−0.154501	−	0.345584i
$693$	96.4033	−	96.4033i	0.139110	−	0.139110i
$694$	44.4640	+	64.5892i	0.0640692	+	0.0930680i
$695$	230.448			0.331579
$696$	−25.1949	−	15.3597i	−0.0361996	−	0.0220685i
$697$			1010.98i			1.45047i
$698$	514.973	+	748.058i	0.737783	+	1.07172i
$699$	−444.682	−	444.682i	−0.636169	−	0.636169i
$700$	157.627	−	412.526i	0.225181	−	0.589323i
$701$	164.273	+	164.273i	0.234341	+	0.234341i	0.814502	−	0.580161i	$-0.197010\pi$
$701$	164.273	+	164.273i	0.234341	+	0.234341i	−0.580161	+	0.814502i	$0.697010\pi$
$702$	36.2157	−	196.244i	0.0515893	−	0.279550i
$703$			1201.68i			1.70935i
$704$	154.281	−	482.385i	0.219150	−	0.685205i
$705$	318.516			0.451795
$706$	−474.710	−	87.6051i	−0.672394	−	0.124087i
$707$	−92.5829	+	92.5829i	−0.130952	+	0.130952i
$708$	439.361	+	167.881i	0.620566	+	0.237119i
$709$	422.796	−	422.796i	0.596327	−	0.596327i	−0.343006	−	0.939333i	$-0.611445\pi$
$709$	422.796	−	422.796i	0.596327	−	0.596327i	0.939333	+	0.343006i	$0.111445\pi$
$710$	172.157	−	118.515i	0.242475	−	0.166923i
$711$	−12.3798			−0.0174118
$712$	220.638	−	361.919i	0.309886	−	0.508313i
$713$		−	54.8457i		−	0.0769224i
$714$	322.847	−	222.252i	0.452166	−	0.311277i
$715$	258.220	+	258.220i	0.361146	+	0.361146i
$716$	−483.085	+	215.973i	−0.674699	+	0.301639i
$717$	33.8375	+	33.8375i	0.0471932	+	0.0471932i
$718$	−715.559	−	132.052i	−0.996601	−	0.183917i
$719$		−	1029.00i		−	1.43115i	−0.698534	−	0.715577i	$-0.746164\pi$
$719$		−	1029.00i		−	1.43115i	0.698534	−	0.715577i	$-0.253836\pi$
$720$	−6.39107	−	115.175i	−0.00887649	−	0.159966i
$721$	567.607			0.787250
$722$	210.621	−	1141.30i	0.291719	−	1.58075i
$723$	−450.855	+	450.855i	−0.623589	+	0.623589i
$724$	−598.074	+	267.381i	−0.826068	+	0.369311i
$725$	−28.9488	+	28.9488i	−0.0399293	+	0.0399293i
$726$	114.672	+	166.574i	0.157950	+	0.229441i
$727$	−475.001			−0.653372			−0.326686	−	0.945133i	$-0.605932\pi$
$727$	−475.001			−0.653372			−0.326686	+	0.945133i	$0.605932\pi$
$728$	207.924	+	857.354i	0.285609	+	1.17768i
$729$			27.0000i			0.0370370i
$730$	201.677	+	292.960i	0.276270	+	0.401314i
$731$	422.419	+	422.419i	0.577865	+	0.577865i
$732$	471.894	+	180.312i	0.644664	+	0.246328i
$733$	−344.939	−	344.939i	−0.470586	−	0.470586i	0.431519	−	0.902104i	$-0.357978\pi$
$733$	−344.939	−	344.939i	−0.470586	−	0.470586i	−0.902104	+	0.431519i	$0.857978\pi$
$734$	−149.322	+	809.141i	−0.203437	+	1.10237i
$735$		−	66.6831i		−	0.0907253i
$736$	487.989	+	630.926i	0.663028	+	0.857237i
$737$	−710.021			−0.963393
$738$	302.764	+	55.8734i	0.410249	+	0.0757092i
$739$	363.340	−	363.340i	0.491665	−	0.491665i	−0.417166	−	0.908831i	$-0.636976\pi$
$739$	363.340	−	363.340i	0.491665	−	0.491665i	0.908831	+	0.417166i	$0.136976\pi$
$740$	134.388	−	351.706i	0.181605	−	0.475278i
$741$	−721.544	+	721.544i	−0.973744	+	0.973744i
$742$	756.123	−	520.525i	1.01903	−	0.701516i
$743$	271.667			0.365636			0.182818	−	0.983147i	$-0.441478\pi$
$743$	271.667			0.365636			0.182818	+	0.983147i	$0.441478\pi$
$744$	7.18588	+	29.6303i	0.00965843	+	0.0398257i
$745$			149.314i			0.200421i
$746$	−525.771	+	361.948i	−0.704787	+	0.485185i
$747$	−115.328	−	115.328i	−0.154389	−	0.154389i
$748$	−254.536	−	569.340i	−0.340288	−	0.761150i
$749$	−89.9637	−	89.9637i	−0.120112	−	0.120112i
$750$	−362.051	−	66.8145i	−0.482735	−	0.0890860i
$751$		−	1105.27i		−	1.47173i	−0.677128	−	0.735866i	$-0.736776\pi$
$751$		−	1105.27i		−	1.47173i	0.677128	−	0.735866i	$-0.263224\pi$
$752$	816.447	−	912.380i	1.08570	−	1.21327i
$753$	−807.937			−1.07296
$754$	14.8423	−	80.4265i	0.0196847	−	0.106666i
$755$	−379.087	+	379.087i	−0.502102	+	0.502102i
$756$	−48.7163	−	108.968i	−0.0644396	−	0.144137i
$757$	554.565	−	554.565i	0.732583	−	0.732583i	−0.238548	−	0.971131i	$-0.576671\pi$
$757$	554.565	−	554.565i	0.732583	−	0.732583i	0.971131	+	0.238548i	$0.0766713\pi$
$758$	−252.091	−	366.191i	−0.332573	−	0.483102i
$759$	341.641			0.450119
$760$	−307.033	+	503.634i	−0.403990	+	0.662676i
$761$			188.496i			0.247695i	0.992301	+	0.123847i	$0.0395234\pi$
$761$			188.496i			0.247695i	−0.992301	+	0.123847i	$0.960477\pi$
$762$	−72.4626	−	105.260i	−0.0950952	−	0.138137i
$763$	−486.380	−	486.380i	−0.637457	−	0.637457i
$764$	−50.3939	+	131.886i	−0.0659605	+	0.172625i
$765$	−100.441	−	100.441i	−0.131295	−	0.131295i
$766$	−255.290	+	1383.35i	−0.333277	+	1.80594i
$767$			1303.62i			1.69963i
$768$	−346.299	−	276.921i	−0.450910	−	0.360574i
$769$	−593.354			−0.771592			−0.385796	−	0.922584i	$-0.626073\pi$
$769$	−593.354			−0.771592			−0.385796	+	0.922584i	$0.626073\pi$
$770$	214.798	+	39.6397i	0.278958	+	0.0514801i
$771$	−28.9973	+	28.9973i	−0.0376100	+	0.0376100i
$772$	−1361.36	−	520.179i	−1.76342	−	0.673807i
$773$	514.720	−	514.720i	0.665873	−	0.665873i	−0.290885	−	0.956758i	$-0.593950\pi$
$773$	514.720	−	514.720i	0.665873	−	0.665873i	0.956758	+	0.290885i	$0.0939498\pi$
$774$	149.850	−	103.159i	0.193604	−	0.133280i
$775$	42.3015			0.0545826
$776$	157.796	+	96.1978i	0.203345	+	0.123966i
$777$		−	389.592i		−	0.501406i
$778$	25.0218	−	17.2253i	0.0321616	−	0.0221405i
$779$	−1113.19	−	1113.19i	−1.42900	−	1.42900i
$780$	291.874	−	130.488i	0.374198	−	0.167293i
$781$	−243.328	−	243.328i	−0.311560	−	0.311560i
$782$	965.879	+	178.248i	1.23514	+	0.227938i
$783$			11.0654i			0.0141320i
$784$	−191.012	−	170.928i	−0.243638	−	0.218020i
$785$	−267.989			−0.341387
$786$	35.9304	−	194.698i	0.0457129	−	0.247707i
$787$	96.1835	−	96.1835i	0.122215	−	0.122215i	−0.643354	−	0.765569i	$-0.722458\pi$
$787$	96.1835	−	96.1835i	0.122215	−	0.122215i	0.765569	+	0.643354i	$0.222458\pi$
$788$	674.356	−	301.485i	0.855782	−	0.382595i
$789$	−298.659	+	298.659i	−0.378529	+	0.378529i
$790$	−11.2466	−	16.3370i	−0.0142362	−	0.0206797i
$791$	−366.699			−0.463589
$792$	−184.571	+	44.7617i	−0.233044	+	0.0565173i
$793$			1400.15i			1.76563i
$794$	585.430	+	850.405i	0.737317	+	1.07104i
$795$	−235.237	−	235.237i	−0.295896	−	0.295896i
$796$	−47.6382	−	18.2026i	−0.0598469	−	0.0228676i
$797$	−664.410	−	664.410i	−0.833639	−	0.833639i	0.154374	−	0.988013i	$-0.450664\pi$
$797$	−664.410	−	664.410i	−0.833639	−	0.833639i	−0.988013	+	0.154374i	$0.950664\pi$
$798$	−110.765	+	600.210i	−0.138804	+	0.752143i
$799$		−	1507.66i		−	1.88693i
$800$	−486.622	+	376.377i	−0.608277	+	0.470471i
$801$	−158.952			−0.198442
$802$	672.121	+	124.036i	0.838056	+	0.154659i
$803$	414.070	−	414.070i	0.515654	−	0.515654i
$804$	−221.879	+	580.680i	−0.275969	+	0.722239i
$805$	−243.244	+	243.244i	−0.302166	+	0.302166i
$806$	−69.6059	+	47.9176i	−0.0863596	+	0.0594511i
$807$	−573.897			−0.711149
$808$	177.256	−	42.9878i	0.219377	−	0.0532028i
$809$		−	1371.63i		−	1.69547i	−0.530422	−	0.847734i	$-0.677966\pi$
$809$		−	1371.63i		−	1.69547i	0.530422	−	0.847734i	$-0.322034\pi$
$810$	−35.6306	+	24.5285i	−0.0439884	+	0.0302822i
$811$	809.783	+	809.783i	0.998500	+	0.998500i	0.999999	−	0.00149916i	$-0.000477196\pi$
$811$	809.783	+	809.783i	0.998500	+	0.998500i	−0.00149916	+	0.999999i	$0.500477\pi$
$812$	−19.9654	−	44.6582i	−0.0245879	−	0.0549978i
$813$	37.9099	+	37.9099i	0.0466296	+	0.0466296i
$814$	−609.601	−	112.498i	−0.748895	−	0.138205i
$815$		−	177.552i		−	0.217855i
$816$	−545.169	+	30.2514i	−0.668099	+	0.0370728i
$817$	−930.255			−1.13862
$818$	133.663	−	724.288i	0.163403	−	0.885437i
$819$	233.930	−	233.930i	0.285629	−	0.285629i
$820$	201.317	+	450.301i	0.245508	+	0.549148i
$821$	−1144.74	+	1144.74i	−1.39432	+	1.39432i	−0.578980	+	0.815342i	$0.696549\pi$
$821$	−1144.74	+	1144.74i	−1.39432	+	1.39432i	−0.815342	+	0.578980i	$0.803451\pi$
$822$	497.943	+	723.321i	0.605771	+	0.879953i
$823$	439.361			0.533853			0.266926	−	0.963717i	$-0.413992\pi$
$823$	439.361			0.533853			0.266926	+	0.963717i	$0.413992\pi$
$824$	−675.137	−	411.587i	−0.819340	−	0.499498i
$825$			263.501i			0.319395i
$826$	442.140	+	642.260i	0.535279	+	0.777555i
$827$	911.996	+	911.996i	1.10278	+	1.10278i	0.994074	+	0.108701i	$0.0346693\pi$
$827$	911.996	+	911.996i	1.10278	+	1.10278i	0.108701	+	0.994074i	$0.465331\pi$
$828$	106.762	−	279.406i	0.128939	−	0.337447i
$829$	470.575	+	470.575i	0.567642	+	0.567642i	0.931467	−	0.363825i	$-0.118529\pi$
$829$	470.575	+	470.575i	0.567642	+	0.567642i	−0.363825	+	0.931467i	$0.618529\pi$
$830$	47.4214	−	256.965i	0.0571342	−	0.309596i
$831$		−	101.526i		−	0.122173i
$832$	374.376	−	1170.54i	0.449972	−	1.40690i
$833$	−315.636			−0.378915
$834$	−326.667	−	60.2845i	−0.391687	−	0.0722836i
$835$	164.017	−	164.017i	0.196428	−	0.196428i
$836$	907.173	+	346.633i	1.08514	+	0.414632i
$837$	8.08467	−	8.08467i	0.00965910	−	0.00965910i
$838$	948.533	−	652.983i	1.13190	−	0.779215i
$839$	1432.91			1.70787			0.853937	−	0.520376i	$-0.174208\pi$
$839$	1432.91			1.70787			0.853937	+	0.520376i	$0.174208\pi$
$840$	99.5423	−	163.282i	0.118503	−	0.194383i
$841$		−	836.465i		−	0.994608i
$842$	134.095	−	92.3126i	0.159258	−	0.109635i
$843$	114.388	+	114.388i	0.135691	+	0.135691i
$844$	44.3867	−	19.8440i	0.0525909	−	0.0235119i
$845$	339.408	+	339.408i	0.401666	+	0.401666i
$846$	−451.506	−	83.3229i	−0.533695	−	0.0984904i
$847$			335.256i			0.395816i
$848$	−1276.81	+	70.8502i	−1.50567	+	0.0835498i
$849$	−98.2201			−0.115689
$850$	−137.479	+	744.965i	−0.161740	+	0.876430i
$851$	690.332	−	690.332i	0.811201	−	0.811201i
$852$	−275.042	+	122.963i	−0.322819	+	0.144323i
$853$	211.443	−	211.443i	0.247881	−	0.247881i	−0.572219	−	0.820101i	$-0.693917\pi$
$853$	211.443	−	211.443i	0.247881	−	0.247881i	0.820101	+	0.572219i	$0.193917\pi$
$854$	474.880	+	689.818i	0.556065	+	0.807750i
$855$	221.192			0.258704
$856$	41.7717	+	172.242i	0.0487987	+	0.201217i
$857$			710.925i			0.829551i	0.909924	+	0.414775i	$0.136140\pi$
$857$			710.925i			0.829551i	−0.909924	+	0.414775i	$0.863860\pi$
$858$	−298.484	−	433.584i	−0.347884	−	0.505342i
$859$	348.557	+	348.557i	0.405771	+	0.405771i	0.880261	−	0.474490i	$-0.157368\pi$
$859$	348.557	+	348.557i	0.405771	+	0.405771i	−0.474490	+	0.880261i	$0.657368\pi$
$860$	272.266	+	104.034i	0.316589	+	0.120969i
$861$	360.906	+	360.906i	0.419171	+	0.419171i
$862$	289.121	−	1566.68i	0.335407	−	1.81749i
$863$		−	1493.19i		−	1.73023i	−0.501571	−	0.865116i	$-0.667245\pi$
$863$		−	1493.19i		−	1.73023i	0.501571	−	0.865116i	$-0.332755\pi$
$864$	−21.0700	+	164.937i	−0.0243866	+	0.190899i
$865$	−157.382			−0.181944
$866$	−660.456	−	121.883i	−0.762651	−	0.140743i
$867$	−121.473	+	121.473i	−0.140107	+	0.140107i
$868$	−18.0412	+	47.2157i	−0.0207848	+	0.0543960i
$869$	−23.0908	+	23.0908i	−0.0265717	+	0.0265717i
$870$	−14.6025	+	10.0525i	−0.0167844	+	0.0115546i
$871$	−1722.92			−1.97810
$872$	225.835	+	931.208i	0.258985	+	1.06790i
$873$		−	69.3025i		−	0.0793843i
$874$	−1259.80	+	867.264i	−1.44142	+	0.992293i
$875$	−431.579	−	431.579i	−0.493233	−	0.493233i
$876$	−209.246	−	468.037i	−0.238865	−	0.534289i
$877$	−332.929	−	332.929i	−0.379623	−	0.379623i	0.491343	−	0.870966i	$-0.336506\pi$
$877$	−332.929	−	332.929i	−0.379623	−	0.379623i	−0.870966	+	0.491343i	$0.836506\pi$
$878$	−561.774	−	103.672i	−0.639834	−	0.118078i
$879$			346.176i			0.393829i
$880$	−226.746	−	202.905i	−0.257666	−	0.230573i
$881$	−637.491			−0.723599			−0.361799	−	0.932256i	$-0.617838\pi$
$881$	−637.491			−0.723599			−0.361799	+	0.932256i	$0.617838\pi$
$882$	−17.4441	+	94.5253i	−0.0197779	+	0.107172i
$883$	134.646	−	134.646i	0.152487	−	0.152487i	−0.626741	−	0.779228i	$-0.715612\pi$
$883$	134.646	−	134.646i	0.152487	−	0.152487i	0.779228	+	0.626741i	$0.215612\pi$
$884$	−617.651	−	1381.55i	−0.698700	−	1.56284i
$885$	199.814	−	199.814i	0.225778	−	0.225778i
$886$	178.980	+	259.990i	0.202010	+	0.293442i
$887$	3.90891			0.00440688			0.00220344	−	0.999998i	$-0.499299\pi$
$887$	3.90891			0.00440688			0.00220344	+	0.999998i	$0.499299\pi$
$888$	−282.504	+	463.398i	−0.318135	+	0.521845i
$889$		−	211.853i		−	0.238304i
$890$	−144.402	−	209.761i	−0.162249	−	0.235686i
$891$	50.3604	+	50.3604i	0.0565212	+	0.0565212i
$892$	72.2303	−	189.034i	0.0809756	−	0.211922i
$893$	1660.08	+	1660.08i	1.85900	+	1.85900i
$894$	39.0600	−	211.656i	0.0436913	−	0.236752i
$895$			317.919i			0.355217i
$896$	−212.561	−	703.675i	−0.237233	−	0.785351i
$897$	829.018			0.924212
$898$	−196.038	−	36.1777i	−0.218305	−	0.0402870i
$899$	3.31333	−	3.31333i	0.00368558	−	0.00368558i
$900$	215.501	+	82.3433i	0.239445	+	0.0914925i
$901$	−1113.47	+	1113.47i	−1.23581	+	1.23581i
$902$	668.930	−	460.500i	0.741607	−	0.510532i
$903$	301.596			0.333993
$904$	436.168	+	265.903i	0.482486	+	0.294140i
$905$			393.594i			0.434910i
$906$	636.536	−	438.200i	0.702578	−	0.483664i
$907$	697.707	+	697.707i	0.769247	+	0.769247i	0.977974	−	0.208727i	$-0.0669319\pi$
$907$	697.707	+	697.707i	0.769247	+	0.769247i	−0.208727	+	0.977974i	$0.566932\pi$
$908$	163.797	−	73.2290i	0.180393	−	0.0806487i
$909$	−48.3647	−	48.3647i	−0.0532065	−	0.0532065i
$910$	521.224	+	96.1889i	0.572773	+	0.105702i
$911$			796.856i			0.874705i	0.899290	+	0.437353i	$0.144084\pi$
$911$			796.856i			0.874705i	−0.899290	+	0.437353i	$0.855916\pi$
$912$	566.977	−	633.597i	0.621686	−	0.694734i
$913$	−430.221			−0.471216
$914$	−11.6743	+	63.2603i	−0.0127728	+	0.0692126i
$915$	214.609	−	214.609i	0.234546	−	0.234546i
$916$	−877.025	+	392.093i	−0.957451	+	0.428049i
$917$	232.087	−	232.087i	0.253094	−	0.253094i
$918$	116.103	+	168.653i	0.126474	+	0.183718i
$919$	420.532			0.457597			0.228798	−	0.973474i	$-0.426520\pi$
$919$	420.532			0.457597			0.228798	+	0.973474i	$0.426520\pi$
$920$	465.708	−	112.942i	0.506204	−	0.122763i
$921$		−	699.448i		−	0.759444i
$922$	265.211	+	385.250i	0.287647	+	0.417841i
$923$	−590.455	−	590.455i	−0.639713	−	0.639713i
$924$	−294.112	−	112.381i	−0.318304	−	0.121624i
$925$	532.441	+	532.441i	0.575612	+	0.575612i
$926$	−335.090	+	1815.77i	−0.361868	+	1.96087i
$927$			296.514i			0.319864i
$928$	−8.63512	+	67.5958i	−0.00930509	+	0.0728403i
$929$	1178.38			1.26843			0.634217	−	0.773155i	$-0.281323\pi$
$929$	1178.38			1.26843			0.634217	+	0.773155i	$0.281323\pi$
$930$	18.0136	+	3.32431i	0.0193694	+	0.00357452i
$931$	347.548	−	347.548i	0.373306	−	0.373306i
$932$	−518.383	+	1356.66i	−0.556205	+	1.45565i
$933$	447.588	−	447.588i	0.479730	−	0.479730i
$934$	1183.14	−	814.492i	1.26675	−	0.872047i
$935$	−374.684			−0.400732
$936$	−447.876	+	108.618i	−0.478500	+	0.116045i
$937$			405.962i			0.433257i	0.976254	+	0.216629i	$0.0695061\pi$
$937$			405.962i			0.433257i	−0.976254	+	0.216629i	$0.930494\pi$
$938$	−848.843	+	584.354i	−0.904950	+	0.622979i
$939$	565.230	+	565.230i	0.601949	+	0.601949i
$940$	−300.220	−	671.526i	−0.319383	−	0.714389i
$941$	429.859	+	429.859i	0.456810	+	0.456810i	0.897607	−	0.440797i	$-0.145304\pi$
$941$	429.859	+	429.859i	0.456810	+	0.456810i	−0.440797	+	0.897607i	$0.645304\pi$
$942$	379.883	+	70.1053i	0.403273	+	0.0744217i
$943$			1279.00i			1.35631i
$944$	−60.1810	−	1084.54i	−0.0637511	−	1.14888i
$945$	−71.7120			−0.0758857
$946$	87.0886	−	471.911i	0.0920598	−	0.498849i
$947$	661.681	−	661.681i	0.698713	−	0.698713i	−0.265420	−	0.964133i	$-0.585511\pi$
$947$	661.681	−	661.681i	0.698713	−	0.698713i	0.964133	+	0.265420i	$0.0855107\pi$
$948$	11.6687	+	26.1003i	0.0123087	+	0.0275319i
$949$	1004.77	−	1004.77i	1.05877	−	1.05877i
$950$	−668.905	−	971.663i	−0.704111	−	1.02280i
$951$	781.915			0.822203
$952$	−772.875	−	471.172i	−0.811844	−	0.494928i
$953$			31.1854i			0.0327234i	0.999866	+	0.0163617i	$0.00520833\pi$
$953$			31.1854i			0.0327234i	−0.999866	+	0.0163617i	$0.994792\pi$
$954$	271.919	+	394.994i	0.285030	+	0.414039i
$955$	59.9794	+	59.9794i	0.0628056	+	0.0628056i
$956$	39.4457	−	103.233i	0.0412612	−	0.107985i
$957$	20.6392	+	20.6392i	0.0215665	+	0.0215665i
$958$	19.0142	−	103.033i	0.0198478	−	0.107550i
$959$			1455.79i			1.51803i
$960$	−236.800	+	122.034i	−0.246667	+	0.127119i
$961$	956.158			0.994962
$962$	−1479.25	−	272.987i	−1.53768	−	0.283770i
$963$	46.9964	−	46.9964i	0.0488021	−	0.0488021i
$964$	1375.49	+	525.579i	1.42686	+	0.545206i
$965$	−619.123	+	619.123i	−0.641578	+	0.641578i
$966$	408.438	−	281.174i	0.422813	−	0.291070i
$967$	−1312.55			−1.35734			−0.678672	−	0.734442i	$-0.737444\pi$
$967$	−1312.55			−1.35734			−0.678672	+	0.734442i	$0.737444\pi$
$968$	243.103	−	398.768i	0.251140	−	0.411951i
$969$		−	1046.98i		−	1.08048i
$970$	91.4551	−	62.9589i	0.0942837	−	0.0649061i
$971$	318.758	+	318.758i	0.328278	+	0.328278i	0.851931	−	0.523653i	$-0.175431\pi$
$971$	318.758	+	318.758i	0.328278	+	0.328278i	−0.523653	+	0.851931i	$0.675431\pi$
$972$	56.9240	−	25.4491i	0.0585638	−	0.0261822i
$973$	−389.399	−	389.399i	−0.400205	−	0.400205i
$974$	−1407.70	−	259.783i	−1.44527	−	0.266717i
$975$			639.407i			0.655802i
$976$	−64.6373	−	1164.85i	−0.0662268	−	1.19349i
$977$	−531.045			−0.543546			−0.271773	−	0.962361i	$-0.587610\pi$
$977$	−531.045			−0.543546			−0.271773	+	0.962361i	$0.587610\pi$
$978$	−46.4471	+	251.685i	−0.0474919	+	0.257347i
$979$	−296.477	+	296.477i	−0.302836	+	0.302836i
$980$	−140.588	+	62.8527i	−0.143457	+	0.0641354i
$981$	254.082	−	254.082i	0.259003	−	0.259003i
$982$	−35.8068	−	52.0135i	−0.0364631	−	0.0529669i
$983$	−1796.17			−1.82723			−0.913614	−	0.406582i	$-0.866721\pi$
$983$	−1796.17			−1.82723			−0.913614	+	0.406582i	$0.866721\pi$
$984$	−167.575	−	690.980i	−0.170300	−	0.702215i
$985$		−	443.796i		−	0.450554i
$986$	47.5824	+	69.1189i	0.0482580	+	0.0701003i
$987$	−538.212	−	538.212i	−0.545301	−	0.545301i
$988$	2201.33	+	841.132i	2.22806	+	0.851348i
$989$	534.408	+	534.408i	0.540352	+	0.540352i
$990$	−20.7075	+	112.209i	−0.0209167	+	0.113342i
$991$		−	506.064i		−	0.510660i	−0.966854	−	0.255330i	$-0.917816\pi$
$991$		−	506.064i		−	0.510660i	0.966854	−	0.255330i	$-0.0821841\pi$
$992$	55.6964	−	43.0783i	0.0561455	−	0.0434257i
$993$	210.133			0.211614
$994$	−491.165	−	90.6417i	−0.494129	−	0.0911889i
$995$	−21.6650	+	21.6650i	−0.0217739	+	0.0217739i
$996$	−134.443	+	351.850i	−0.134983	+	0.353263i
$997$	−249.068	+	249.068i	−0.249817	+	0.249817i	−0.820896	−	0.571078i	$-0.806525\pi$
$997$	−249.068	+	249.068i	−0.249817	+	0.249817i	0.571078	+	0.820896i	$0.306525\pi$
$998$	195.928	−	134.879i	0.196321	−	0.135150i
$999$	203.520			0.203724

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.3.l.a.19.8	✓	16
3.2	odd	2		144.3.m.c.19.1		16
4.3	odd	2		192.3.l.a.175.7		16
8.3	odd	2		384.3.l.b.223.2		16
8.5	even	2		384.3.l.a.223.6		16
12.11	even	2		576.3.m.c.559.3		16
16.3	odd	4		384.3.l.a.31.6		16
16.5	even	4		192.3.l.a.79.7		16
16.11	odd	4	inner	48.3.l.a.43.8	yes	16
16.13	even	4		384.3.l.b.31.2		16
24.5	odd	2		1152.3.m.f.991.6		16
24.11	even	2		1152.3.m.c.991.6		16
48.5	odd	4		576.3.m.c.271.3		16
48.11	even	4		144.3.m.c.91.1		16
48.29	odd	4		1152.3.m.c.415.6		16
48.35	even	4		1152.3.m.f.415.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.l.a.19.8	✓	16	1.1	even	1	trivial
48.3.l.a.43.8	yes	16	16.11	odd	4	inner
144.3.m.c.19.1		16	3.2	odd	2
144.3.m.c.91.1		16	48.11	even	4
192.3.l.a.79.7		16	16.5	even	4
192.3.l.a.175.7		16	4.3	odd	2
384.3.l.a.31.6		16	16.3	odd	4
384.3.l.a.223.6		16	8.5	even	2
384.3.l.b.31.2		16	16.13	even	4
384.3.l.b.223.2		16	8.3	odd	2
576.3.m.c.271.3		16	48.5	odd	4
576.3.m.c.559.3		16	12.11	even	2
1152.3.m.c.415.6		16	48.29	odd	4
1152.3.m.c.991.6		16	24.11	even	2
1152.3.m.f.415.6		16	48.35	even	4
1152.3.m.f.991.6		16	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	48.3.l.a.19.8

Level	$48$
Weight	$3$
Character	48.19
Analytic conductor	$1.308$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$