LMFDB - Embedded newform 441.3.l.b.391.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,3,Mod(97,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("441.97");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.l (of order $6$, 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:	$12.0163796583$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			391.12
Character	$\chi$	$=$	441.391
Dual form			441.3.l.b.97.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41697 + 2.45427i) q^{2} +(2.70216 - 1.30320i) q^{3} +(-2.01561 + 3.49114i) q^{4} +(2.07720 + 1.19927i) q^{5} +(7.02729 + 4.78521i) q^{6} -0.0884848 q^{8} +(5.60332 - 7.04292i) q^{9} +O(q^{10})$	\(q+(1.41697 + 2.45427i) q^{2} +(2.70216 - 1.30320i) q^{3} +(-2.01561 + 3.49114i) q^{4} +(2.07720 + 1.19927i) q^{5} +(7.02729 + 4.78521i) q^{6} -0.0884848 q^{8} +(5.60332 - 7.04292i) q^{9} +6.79734i q^{10} +(-5.69528 - 9.86452i) q^{11} +(-0.896835 + 12.0604i) q^{12} +(13.4628 + 7.77278i) q^{13} +(7.17583 + 0.533610i) q^{15} +(7.93707 + 13.7474i) q^{16} +12.1021i q^{17} +(25.2249 + 3.77242i) q^{18} +16.0014i q^{19} +(-8.37367 + 4.83454i) q^{20} +(16.1401 - 27.9555i) q^{22} +(8.02831 - 13.9054i) q^{23} +(-0.239100 + 0.115314i) q^{24} +(-9.62349 - 16.6684i) q^{25} +44.0552i q^{26} +(5.96270 - 26.3334i) q^{27} +(16.2339 + 28.1180i) q^{29} +(8.85832 + 18.3675i) q^{30} +(-36.7194 - 21.1999i) q^{31} +(-22.6701 + 39.2658i) q^{32} +(-28.2450 - 19.2334i) q^{33} +(-29.7018 + 17.1483i) q^{34} +(13.2937 + 33.7578i) q^{36} +7.22811 q^{37} +(-39.2718 + 22.6736i) q^{38} +(46.5083 + 3.45845i) q^{39} +(-0.183801 - 0.106117i) q^{40} +(7.55990 + 4.36471i) q^{41} +(-22.2113 - 38.4711i) q^{43} +45.9179 q^{44} +(20.0856 - 7.90966i) q^{45} +45.5035 q^{46} +(-22.8382 + 13.1856i) q^{47} +(39.3629 + 26.8040i) q^{48} +(27.2724 - 47.2372i) q^{50} +(15.7715 + 32.7018i) q^{51} +(-54.2717 + 31.3338i) q^{52} -68.1249 q^{53} +(73.0780 - 22.6795i) q^{54} -27.3208i q^{55} +(20.8531 + 43.2384i) q^{57} +(-46.0060 + 79.6847i) q^{58} +(82.4104 + 47.5797i) q^{59} +(-16.3266 + 23.9763i) q^{60} +(-42.8184 + 24.7212i) q^{61} -120.159i q^{62} -64.9952 q^{64} +(18.6434 + 32.2913i) q^{65} +(7.18145 - 96.5740i) q^{66} +(40.9350 - 70.9015i) q^{67} +(-42.2502 - 24.3931i) q^{68} +(3.57215 - 48.0372i) q^{69} -112.881 q^{71} +(-0.495809 + 0.623192i) q^{72} +67.9029i q^{73} +(10.2420 + 17.7397i) q^{74} +(-47.7265 - 32.4992i) q^{75} +(-55.8633 - 32.2527i) q^{76} +(57.4129 + 119.044i) q^{78} +(-68.4439 - 118.548i) q^{79} +38.0748i q^{80} +(-18.2056 - 78.9275i) q^{81} +24.7387i q^{82} +(-18.8674 + 10.8931i) q^{83} +(-14.5137 + 25.1385i) q^{85} +(62.9455 - 109.025i) q^{86} +(80.5101 + 54.8232i) q^{87} +(0.503946 + 0.872861i) q^{88} -108.432i q^{89} +(47.8732 + 38.0877i) q^{90} +(32.3639 + 56.0559i) q^{92} +(-126.849 - 9.43279i) q^{93} +(-64.7220 - 37.3673i) q^{94} +(-19.1901 + 33.2382i) q^{95} +(-10.0870 + 135.646i) q^{96} +(-96.5982 + 55.7710i) q^{97} +(-101.388 - 15.1626i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{2} - 23 q^{4} + 3 q^{5} - 12 q^{6} - 16 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q + q^2 - 23 * q^4 + 3 * q^5 - 12 * q^6 - 16 * q^8 + 6 * q^9	$ 28 q + q^{2} - 23 q^{4} + 3 q^{5} - 12 q^{6} - 16 q^{8} + 6 q^{9} + 7 q^{11} + 27 q^{12} - 15 q^{13} - 18 q^{15} - 27 q^{16} + 9 q^{18} - 108 q^{20} - 10 q^{22} + 34 q^{23} + 120 q^{24} + 31 q^{25} + 81 q^{27} + 70 q^{29} + 33 q^{30} + 45 q^{31} + 153 q^{32} - 111 q^{33} - 12 q^{34} - 174 q^{36} - 18 q^{37} - 87 q^{38} - 9 q^{39} + 102 q^{40} + 234 q^{41} + 30 q^{43} - 102 q^{44} + 3 q^{45} + 44 q^{46} - 111 q^{47} - 147 q^{48} + 241 q^{50} - 6 q^{51} + 219 q^{52} - 296 q^{53} + 207 q^{54} + 189 q^{57} + 17 q^{58} + 42 q^{59} - 489 q^{60} + 120 q^{61} - 48 q^{64} + 114 q^{65} - 705 q^{66} - 34 q^{67} + 18 q^{68} - 78 q^{69} - 350 q^{71} + 177 q^{72} + 359 q^{74} + 387 q^{75} - 72 q^{76} - 375 q^{78} - 82 q^{79} + 438 q^{81} - 738 q^{83} + 3 q^{85} + 17 q^{86} + 564 q^{87} + 25 q^{88} + 543 q^{90} + 288 q^{92} - 30 q^{93} - 3 q^{94} + 507 q^{95} - 813 q^{96} + 57 q^{97} - 162 q^{99}+O(q^{100}) $ 28 * q + q^2 - 23 * q^4 + 3 * q^5 - 12 * q^6 - 16 * q^8 + 6 * q^9 + 7 * q^11 + 27 * q^12 - 15 * q^13 - 18 * q^15 - 27 * q^16 + 9 * q^18 - 108 * q^20 - 10 * q^22 + 34 * q^23 + 120 * q^24 + 31 * q^25 + 81 * q^27 + 70 * q^29 + 33 * q^30 + 45 * q^31 + 153 * q^32 - 111 * q^33 - 12 * q^34 - 174 * q^36 - 18 * q^37 - 87 * q^38 - 9 * q^39 + 102 * q^40 + 234 * q^41 + 30 * q^43 - 102 * q^44 + 3 * q^45 + 44 * q^46 - 111 * q^47 - 147 * q^48 + 241 * q^50 - 6 * q^51 + 219 * q^52 - 296 * q^53 + 207 * q^54 + 189 * q^57 + 17 * q^58 + 42 * q^59 - 489 * q^60 + 120 * q^61 - 48 * q^64 + 114 * q^65 - 705 * q^66 - 34 * q^67 + 18 * q^68 - 78 * q^69 - 350 * q^71 + 177 * q^72 + 359 * q^74 + 387 * q^75 - 72 * q^76 - 375 * q^78 - 82 * q^79 + 438 * q^81 - 738 * q^83 + 3 * q^85 + 17 * q^86 + 564 * q^87 + 25 * q^88 + 543 * q^90 + 288 * q^92 - 30 * q^93 - 3 * q^94 + 507 * q^95 - 813 * q^96 + 57 * q^97 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.41697	+	2.45427i	0.708485	+	1.22713i	0.965419	+	0.260704i	$0.0839545\pi$
$2$	1.41697	+	2.45427i	0.708485	+	1.22713i	−0.256934	+	0.966429i	$0.582712\pi$
$3$	2.70216	−	1.30320i	0.900720	−	0.434401i
$3$	2.70216	−	1.30320i	0.900720	−	0.434401i
$4$	−2.01561	+	3.49114i	−0.503903	+	0.872785i
$5$	2.07720	+	1.19927i	0.415440	+	0.239855i	0.693125	−	0.720818i	$-0.256234\pi$
$5$	2.07720	+	1.19927i	0.415440	+	0.239855i	−0.277684	+	0.960672i	$0.589567\pi$
$6$	7.02729	+	4.78521i	1.17121	+	0.797535i
$7$		0			0
$7$		0			0
$8$	−0.0884848			−0.0110606
$9$	5.60332	−	7.04292i	0.622591	−	0.782547i
$10$			6.79734i			0.679734i
$11$	−5.69528	−	9.86452i	−0.517753	−	0.896775i	−0.999787	−	0.0206223i	$-0.993435\pi$
$11$	−5.69528	−	9.86452i	−0.517753	−	0.896775i	0.482034	−	0.876152i	$-0.339898\pi$
$12$	−0.896835	+	12.0604i	−0.0747362	+	1.00503i
$13$	13.4628	+	7.77278i	1.03560	+	0.597906i	0.918585	−	0.395224i	$-0.129333\pi$
$13$	13.4628	+	7.77278i	1.03560	+	0.597906i	0.117019	+	0.993130i	$0.462666\pi$
$14$		0			0
$15$	7.17583	+	0.533610i	0.478388	+	0.0355740i
$16$	7.93707	+	13.7474i	0.496067	+	0.859213i
$17$			12.1021i			0.711888i	0.934507	+	0.355944i	$0.115841\pi$
$17$			12.1021i			0.711888i	−0.934507	+	0.355944i	$0.884159\pi$
$18$	25.2249	+	3.77242i	1.40139	+	0.209579i
$19$			16.0014i			0.842181i	0.907019	+	0.421090i	$0.138352\pi$
$19$			16.0014i			0.842181i	−0.907019	+	0.421090i	$0.861648\pi$
$20$	−8.37367	+	4.83454i	−0.418683	+	0.241727i
$21$		0			0
$22$	16.1401	−	27.9555i	0.733641	−	1.27070i
$23$	8.02831	−	13.9054i	0.349057	−	0.604584i	−0.637025	−	0.770843i	$-0.719835\pi$
$23$	8.02831	−	13.9054i	0.349057	−	0.604584i	0.986082	+	0.166259i	$0.0531686\pi$
$24$	−0.239100	+	0.115314i	−0.00996250	+	0.00480474i
$25$	−9.62349	−	16.6684i	−0.384939	−	0.666735i
$26$			44.0552i			1.69443i
$27$	5.96270	−	26.3334i	0.220841	−	0.975310i
$28$		0			0
$29$	16.2339	+	28.1180i	0.559791	+	0.969586i	0.997513	+	0.0704760i	$0.0224518\pi$
$29$	16.2339	+	28.1180i	0.559791	+	0.969586i	−0.437723	+	0.899110i	$0.644215\pi$
$30$	8.85832	+	18.3675i	0.295277	+	0.612250i
$31$	−36.7194	−	21.1999i	−1.18450	−	0.683869i	−0.227445	−	0.973791i	$-0.573037\pi$
$31$	−36.7194	−	21.1999i	−1.18450	−	0.683869i	−0.957050	+	0.289922i	$0.906371\pi$
$32$	−22.6701	+	39.2658i	−0.708442	+	1.22706i
$33$	−28.2450	−	19.2334i	−0.855910	−	0.582830i
$34$	−29.7018	+	17.1483i	−0.873581	+	0.504362i
$35$		0			0
$36$	13.2937	+	33.7578i	0.369270	+	0.937716i
$37$	7.22811			0.195354			0.0976772	−	0.995218i	$-0.468859\pi$
$37$	7.22811			0.195354			0.0976772	+	0.995218i	$0.468859\pi$
$38$	−39.2718	+	22.6736i	−1.03347	+	0.596673i
$39$	46.5083	+	3.45845i	1.19252	+	0.0886783i
$40$	−0.183801	−	0.106117i	−0.00459502	−	0.00265294i
$41$	7.55990	+	4.36471i	0.184388	+	0.106456i	0.589353	−	0.807876i	$-0.299383\pi$
$41$	7.55990	+	4.36471i	0.184388	+	0.106456i	−0.404965	+	0.914332i	$0.632716\pi$
$42$		0			0
$43$	−22.2113	−	38.4711i	−0.516542	−	0.894676i	−0.999816	−	0.0192072i	$-0.993886\pi$
$43$	−22.2113	−	38.4711i	−0.516542	−	0.894676i	0.483274	−	0.875469i	$-0.339448\pi$
$44$	45.9179			1.04359
$45$	20.0856	−	7.90966i	0.446347	−	0.175770i
$46$	45.5035			0.989207
$47$	−22.8382	+	13.1856i	−0.485919	+	0.280545i	−0.722880	−	0.690974i	$-0.757182\pi$
$47$	−22.8382	+	13.1856i	−0.485919	+	0.280545i	0.236961	+	0.971519i	$0.423849\pi$
$48$	39.3629	+	26.8040i	0.820060	+	0.558418i
$49$		0			0
$50$	27.2724	−	47.2372i	0.545448	−	0.944744i
$51$	15.7715	+	32.7018i	0.309245	+	0.641212i
$52$	−54.2717	+	31.3338i	−1.04369	+	0.602573i
$53$	−68.1249			−1.28538			−0.642688	−	0.766128i	$-0.722181\pi$
$53$	−68.1249			−1.28538			−0.642688	+	0.766128i	$0.722181\pi$
$54$	73.0780	−	22.6795i	1.35330	−	0.419992i
$55$		−	27.3208i		−	0.496742i
$56$		0			0
$57$	20.8531	+	43.2384i	0.365844	+	0.758568i
$58$	−46.0060	+	79.6847i	−0.793207	+	1.37387i
$59$	82.4104	+	47.5797i	1.39679	+	0.806435i	0.994055	−	0.108883i	$-0.0347274\pi$
$59$	82.4104	+	47.5797i	1.39679	+	0.806435i	0.402732	+	0.915318i	$0.368061\pi$
$60$	−16.3266	+	23.9763i	−0.272110	+	0.399605i
$61$	−42.8184	+	24.7212i	−0.701941	+	0.405266i	−0.808070	−	0.589087i	$-0.799488\pi$
$61$	−42.8184	+	24.7212i	−0.701941	+	0.405266i	0.106129	+	0.994352i	$0.466154\pi$
$62$		−	120.159i		−	1.93804i
$63$		0			0
$64$	−64.9952			−1.01555
$65$	18.6434	+	32.2913i	0.286821	+	0.496789i
$66$	7.18145	−	96.5740i	0.108810	−	1.46324i
$67$	40.9350	−	70.9015i	0.610971	−	1.05823i	−0.380107	−	0.924943i	$-0.624113\pi$
$67$	40.9350	−	70.9015i	0.610971	−	1.05823i	0.991077	−	0.133289i	$-0.0425539\pi$
$68$	−42.2502	−	24.3931i	−0.621326	−	0.358723i
$69$	3.57215	−	48.0372i	0.0517703	−	0.696192i
$70$		0			0
$71$	−112.881			−1.58987			−0.794936	−	0.606694i	$-0.792496\pi$
$71$	−112.881			−1.58987			−0.794936	+	0.606694i	$0.792496\pi$
$72$	−0.495809	+	0.623192i	−0.00688624	+	0.00865544i
$73$			67.9029i			0.930176i	0.885264	+	0.465088i	$0.153977\pi$
$73$			67.9029i			0.930176i	−0.885264	+	0.465088i	$0.846023\pi$
$74$	10.2420	+	17.7397i	0.138406	+	0.239726i
$75$	−47.7265	−	32.4992i	−0.636353	−	0.433323i
$76$	−55.8633	−	32.2527i	−0.735043	−	0.424377i
$77$		0			0
$78$	57.4129	+	119.044i	0.736063	+	1.52621i
$79$	−68.4439	−	118.548i	−0.866379	−	1.50061i	−0.865671	−	0.500613i	$-0.833108\pi$
$79$	−68.4439	−	118.548i	−0.866379	−	1.50061i	−0.000707812	−	1.00000i	$-0.500225\pi$
$80$			38.0748i			0.475936i
$81$	−18.2056	−	78.9275i	−0.224760	−	0.974414i
$82$			24.7387i			0.301691i
$83$	−18.8674	+	10.8931i	−0.227318	+	0.131242i	−0.609334	−	0.792913i	$-0.708563\pi$
$83$	−18.8674	+	10.8931i	−0.227318	+	0.131242i	0.382016	+	0.924156i	$0.375230\pi$
$84$		0			0
$85$	−14.5137	+	25.1385i	−0.170750	+	0.295747i
$86$	62.9455	−	109.025i	0.731924	−	1.26773i
$87$	80.5101	+	54.8232i	0.925404	+	0.630151i
$88$	0.503946	+	0.872861i	0.00572666	+	0.00991887i
$89$		−	108.432i		−	1.21834i	−0.793040	−	0.609169i	$-0.791503\pi$
$89$		−	108.432i		−	1.21834i	0.793040	−	0.609169i	$-0.208497\pi$
$90$	47.8732	+	38.0877i	0.531924	+	0.423197i
$91$		0			0
$92$	32.3639	+	56.0559i	0.351782	+	0.609304i
$93$	−126.849	−	9.43279i	−1.36397	−	0.101428i
$94$	−64.7220	−	37.3673i	−0.688532	−	0.397524i
$95$	−19.1901	+	33.2382i	−0.202001	+	0.349876i
$96$	−10.0870	+	135.646i	−0.105072	+	1.41298i
$97$	−96.5982	+	55.7710i	−0.995857	+	0.574959i	−0.907020	−	0.421088i	$-0.861649\pi$
$97$	−96.5982	+	55.7710i	−0.995857	+	0.574959i	−0.0888375	+	0.996046i	$0.528315\pi$
$98$		0			0
$99$	−101.388	−	15.1626i	−1.02412	−	0.153158i
$100$	77.5888			0.775888
$101$	66.5650	−	38.4313i	0.659059	−	0.380508i	−0.132859	−	0.991135i	$-0.542416\pi$
$101$	66.5650	−	38.4313i	0.659059	−	0.380508i	0.791919	+	0.610627i	$0.209082\pi$
$102$	−57.9111	+	85.0449i	−0.567756	+	0.833774i
$103$	−130.580	−	75.3905i	−1.26777	−	0.731946i	−0.293203	−	0.956050i	$-0.594721\pi$
$103$	−130.580	−	75.3905i	−1.26777	−	0.731946i	−0.974565	+	0.224104i	$0.928054\pi$
$104$	−1.19126	−	0.687773i	−0.0114544	−	0.00661320i
$105$		0			0
$106$	−96.5310	−	167.197i	−0.910669	−	1.57733i
$107$	76.6044			0.715929			0.357964	−	0.933735i	$-0.383471\pi$
$107$	76.6044			0.715929			0.357964	+	0.933735i	$0.383471\pi$
$108$	79.9150	+	73.8945i	0.739954	+	0.684208i
$109$	−25.1970			−0.231165			−0.115582	−	0.993298i	$-0.536873\pi$
$109$	−25.1970			−0.231165			−0.115582	+	0.993298i	$0.536873\pi$
$110$	67.0525	−	38.7128i	0.609568	−	0.351934i
$111$	19.5315	−	9.41970i	0.175960	−	0.0848622i
$112$		0			0
$113$	37.0748	−	64.2154i	0.328095	−	0.568277i	−0.654039	−	0.756461i	$-0.726927\pi$
$113$	37.0748	−	64.2154i	0.328095	−	0.568277i	0.982134	+	0.188184i	$0.0602600\pi$
$114$	−76.5702	+	112.447i	−0.671669	+	0.986374i
$115$	33.3528	−	19.2563i	0.290025	−	0.167446i
$116$	−130.885			−1.12832
$117$	130.180	−	51.2644i	1.11265	−	0.438157i
$118$			269.676i			2.28539i
$119$		0			0
$120$	−0.634952	−	0.0472164i	−0.00529127	−	0.000393470i
$121$	−4.37253	+	7.57345i	−0.0361366	+	0.0625905i
$122$	−121.345	−	70.0585i	−0.994629	−	0.574250i
$123$	26.1162	+	1.94205i	0.212327	+	0.0157891i
$124$	148.024	−	85.4617i	1.19374	−	0.689207i
$125$		−	106.128i		−	0.849027i
$126$		0			0
$127$	52.2864			0.411704			0.205852	−	0.978583i	$-0.434003\pi$
$127$	52.2864			0.411704			0.205852	+	0.978583i	$0.434003\pi$
$128$	−1.41571	−	2.45209i	−0.0110603	−	0.0191569i
$129$	−110.154	−	75.0092i	−0.853908	−	0.581466i
$130$	−52.8342	+	91.5116i	−0.406417	+	0.703935i
$131$	161.548	+	93.2696i	1.23319	+	0.711982i	0.967693	−	0.252131i	$-0.0811313\pi$
$131$	161.548	+	93.2696i	1.23319	+	0.711982i	0.265495	+	0.964112i	$0.414465\pi$
$132$	124.078	−	59.8404i	0.939981	−	0.453336i
$133$		0			0
$134$	232.015			1.73145
$135$	43.9666	−	47.5488i	0.325679	−	0.352213i
$136$		−	1.07085i		−	0.00787392i
$137$	76.6871	+	132.826i	0.559760	+	0.969533i	0.997516	+	0.0704389i	$0.0224400\pi$
$137$	76.6871	+	132.826i	0.559760	+	0.969533i	−0.437756	+	0.899094i	$0.644227\pi$
$138$	122.958	−	59.3003i	0.890998	−	0.429713i
$139$	79.0232	+	45.6241i	0.568513	+	0.328231i	0.756555	−	0.653930i	$-0.226881\pi$
$139$	79.0232	+	45.6241i	0.568513	+	0.328231i	−0.188043	+	0.982161i	$0.560214\pi$
$140$		0			0
$141$	−44.5288	+	65.3924i	−0.315807	+	0.463776i
$142$	−159.949	−	277.040i	−1.12640	−	1.95098i
$143$		−	177.073i		−	1.23827i
$144$	141.296	+	21.1310i	0.981221	+	0.146743i
$145$			77.8757i			0.537074i
$146$	−166.652	+	96.2164i	−1.14145	+	0.659016i
$147$		0			0
$148$	−14.5691	+	25.2344i	−0.0984396	+	0.170502i
$149$	−56.2062	+	97.3519i	−0.377223	+	0.653369i	−0.990657	−	0.136377i	$-0.956454\pi$
$149$	−56.2062	+	97.3519i	−0.377223	+	0.653369i	0.613434	+	0.789746i	$0.289787\pi$
$150$	12.1347	−	163.184i	0.0808980	−	1.08789i
$151$	−14.0984	−	24.4192i	−0.0933671	−	0.161717i	0.815559	−	0.578674i	$-0.196430\pi$
$151$	−14.0984	−	24.4192i	−0.0933671	−	0.161717i	−0.908926	+	0.416958i	$0.863096\pi$
$152$		−	1.41588i		−	0.00931503i
$153$	85.2342	+	67.8120i	0.557086	+	0.443216i
$154$		0			0
$155$	−50.8490	−	88.0731i	−0.328058	−	0.568214i
$156$	−105.817	+	155.396i	−0.678311	+	0.996128i
$157$	−8.87726	−	5.12529i	−0.0565431	−	0.0326452i	0.471462	−	0.881886i	$-0.343726\pi$
$157$	−8.87726	−	5.12529i	−0.0565431	−	0.0326452i	−0.528005	+	0.849241i	$0.677060\pi$
$158$	193.966	−	335.959i	1.22763	−	2.12632i
$159$	−184.084	+	88.7806i	−1.15776	+	0.558368i
$160$	−94.1810	+	54.3754i	−0.588631	+	0.339846i
$161$		0			0
$162$	167.912	−	156.519i	1.03650	−	0.966168i
$163$	−177.682			−1.09007			−0.545037	−	0.838412i	$-0.683485\pi$
$163$	−177.682			−1.09007			−0.545037	+	0.838412i	$0.683485\pi$
$164$	−30.4757	+	17.5951i	−0.185827	+	0.107287i
$165$	−35.6046	−	73.8252i	−0.215785	−	0.447425i
$166$	−53.4692	−	30.8705i	−0.322104	−	0.185967i
$167$	−53.9725	−	31.1611i	−0.323189	−	0.186593i	0.329624	−	0.944112i	$-0.393078\pi$
$167$	−53.9725	−	31.1611i	−0.323189	−	0.186593i	−0.652813	+	0.757519i	$0.726411\pi$
$168$		0			0
$169$	36.3322	+	62.9292i	0.214983	+	0.372362i
$170$	−82.2621			−0.483895
$171$	112.697	+	89.6612i	0.659046	+	0.524334i
$172$	179.077			1.04115
$173$	76.2216	−	44.0066i	0.440587	−	0.254373i	−0.263259	−	0.964725i	$-0.584797\pi$
$173$	76.2216	−	44.0066i	0.440587	−	0.254373i	0.703847	+	0.710352i	$0.251464\pi$
$174$	−20.4701	+	275.276i	−0.117644	+	1.58205i
$175$		0			0
$176$	90.4077	−	156.591i	0.513680	−	0.889720i
$177$	284.692	+	21.1703i	1.60843	+	0.119606i
$178$	266.121	−	153.645i	1.49506	−	0.863175i
$179$	12.9521			0.0723579			0.0361789	−	0.999345i	$-0.488481\pi$
$179$	12.9521			0.0723579			0.0361789	+	0.999345i	$0.488481\pi$
$180$	−12.8711	+	86.0646i	−0.0715059	+	0.478137i
$181$		−	225.852i		−	1.24780i	−0.781503	−	0.623901i	$-0.785547\pi$
$181$		−	225.852i		−	1.24780i	0.781503	−	0.623901i	$-0.214453\pi$
$182$		0			0
$183$	−83.4853	+	122.602i	−0.456204	+	0.669955i
$184$	−0.710384	+	1.23042i	−0.00386078	+	0.00668707i
$185$	15.0143	+	8.66848i	0.0811581	+	0.0468567i
$186$	−156.591	−	324.688i	−0.841889	−	1.74563i
$187$	119.381	−	68.9249i	0.638404	−	0.368582i
$188$		−	106.308i		−	0.565470i
$189$		0			0
$190$	−108.767			−0.572459
$191$	−51.9453	−	89.9718i	−0.271965	−	0.471057i	0.697400	−	0.716682i	$-0.254340\pi$
$191$	−51.9453	−	89.9718i	−0.271965	−	0.471057i	−0.969365	+	0.245625i	$0.921007\pi$
$192$	−175.627	+	84.7020i	−0.914726	+	0.441156i
$193$	−81.1711	+	140.592i	−0.420575	+	0.728458i	−0.995996	−	0.0893998i	$-0.971505\pi$
$193$	−81.1711	+	140.592i	−0.420575	+	0.728458i	0.575420	+	0.817858i	$0.304838\pi$
$194$	−273.754	−	158.052i	−1.41110	−	0.814699i
$195$	92.4594	+	62.9600i	0.474151	+	0.322872i
$196$		0			0
$197$	301.595			1.53094			0.765470	−	0.643472i	$-0.222507\pi$
$197$	301.595			1.53094			0.765470	+	0.643472i	$0.222507\pi$
$198$	−106.450	−	270.317i	−0.537627	−	1.36524i
$199$			57.8010i			0.290457i	0.989398	+	0.145229i	$0.0463917\pi$
$199$			57.8010i			0.290457i	−0.989398	+	0.145229i	$0.953608\pi$
$200$	0.851533	+	1.47490i	0.00425766	+	0.00737449i
$201$	18.2138	−	244.934i	0.0906160	−	1.21858i
$202$	188.641	+	108.912i	0.933868	+	0.539169i
$203$		0			0
$204$	−145.956	−	10.8536i	−0.715470	−	0.0532039i
$205$	10.4690	+	18.1328i	0.0510681	+	0.0884526i
$206$		−	427.304i		−	2.07429i
$207$	−52.9497	−	134.459i	−0.255796	−	0.649562i
$208$			246.772i			1.18640i
$209$	157.846	−	91.1327i	0.755246	−	0.436042i
$210$		0			0
$211$	−21.2197	+	36.7535i	−0.100567	+	0.174187i	−0.911918	−	0.410371i	$-0.865399\pi$
$211$	−21.2197	+	36.7535i	−0.100567	+	0.174187i	0.811351	+	0.584559i	$0.198732\pi$
$212$	137.313	−	237.834i	0.647704	−	1.12186i
$213$	−305.022	+	147.107i	−1.43203	+	0.690642i
$214$	108.546	+	188.007i	0.507225	+	0.878540i
$215$		−	106.550i		−	0.495580i
$216$	−0.527609	+	2.33010i	−0.00244263	+	0.0107875i
$217$		0			0
$218$	−35.7034	−	61.8400i	−0.163777	−	0.283670i
$219$	88.4912	+	183.484i	0.404070	+	0.837828i
$220$	95.3808	+	55.0681i	0.433549	+	0.250310i
$221$	−94.0670	+	162.929i	−0.425642	+	0.737234i
$222$	50.7940	+	34.5881i	0.228802	+	0.155802i
$223$	−166.212	+	95.9625i	−0.745345	+	0.430325i	−0.824009	−	0.566576i	$-0.808268\pi$
$223$	−166.212	+	95.9625i	−0.745345	+	0.430325i	0.0786645	+	0.996901i	$0.474934\pi$
$224$		0			0
$225$	−171.318	−	25.6208i	−0.761411	−	0.113870i
$226$	210.135			0.929802
$227$	−194.664	+	112.390i	−0.857552	+	0.495108i	−0.863192	−	0.504876i	$-0.831538\pi$
$227$	−194.664	+	112.390i	−0.857552	+	0.495108i	0.00563942	+	0.999984i	$0.498205\pi$
$228$	−192.983	−	14.3506i	−0.846417	−	0.0629414i
$229$	138.693	+	80.0742i	0.605644	+	0.349669i	0.771259	−	0.636522i	$-0.219627\pi$
$229$	138.693	+	80.0742i	0.605644	+	0.349669i	−0.165614	+	0.986191i	$0.552961\pi$
$230$	94.5200	+	54.5712i	0.410957	+	0.237266i
$231$		0			0
$232$	−1.43646	−	2.48802i	−0.00619162	−	0.0107242i
$233$	−246.598			−1.05836			−0.529180	−	0.848510i	$-0.677500\pi$
$233$	−246.598			−1.05836			−0.529180	+	0.848510i	$0.677500\pi$
$234$	310.277	+	246.855i	1.32597	+	1.05494i
$235$	−63.2527			−0.269160
$236$	−332.215	+	191.804i	−1.40769	+	0.812730i
$237$	−339.439	−	231.140i	−1.43223	−	0.975275i
$238$		0			0
$239$	−110.141	+	190.769i	−0.460839	+	0.798197i	−0.999003	−	0.0446434i	$-0.985785\pi$
$239$	−110.141	+	190.769i	−0.460839	+	0.798197i	0.538164	+	0.842840i	$0.319118\pi$
$240$	49.6193	+	102.884i	0.206747	+	0.428684i
$241$	228.282	−	131.799i	0.947230	−	0.546883i	0.0550106	−	0.998486i	$-0.482481\pi$
$241$	228.282	−	131.799i	0.947230	−	0.546883i	0.892219	+	0.451602i	$0.149147\pi$
$242$	−24.7830			−0.102409
$243$	−152.053	−	189.549i	−0.625732	−	0.780038i
$244$		−	199.313i		−	0.816858i
$245$		0			0
$246$	32.2395	+	66.8478i	0.131055	+	0.271739i
$247$	−124.376	+	215.425i	−0.503545	+	0.872165i
$248$	3.24911	+	1.87587i	0.0131012	+	0.00756400i
$249$	−36.7868	+	54.0230i	−0.147738	+	0.216960i
$250$	260.467	−	150.381i	1.04187	−	0.601523i
$251$		−	23.0003i		−	0.0916348i	−0.998950	−	0.0458174i	$-0.985411\pi$
$251$		−	23.0003i		−	0.0916348i	0.998950	−	0.0458174i	$-0.0145892\pi$
$252$		0			0
$253$	−182.894			−0.722901
$254$	74.0883	+	128.325i	0.291686	+	0.505215i
$255$	−6.45780	+	86.8426i	−0.0253247	+	0.340559i
$256$	−125.978	+	218.201i	−0.492103	+	0.852347i
$257$	15.4300	+	8.90852i	0.0600389	+	0.0346635i	0.529719	−	0.848173i	$-0.322297\pi$
$257$	15.4300	+	8.90852i	0.0600389	+	0.0346635i	−0.469680	+	0.882837i	$0.655631\pi$
$258$	28.0072	−	376.633i	0.108555	−	1.45982i
$259$		0			0
$260$	−150.311			−0.578120
$261$	288.997	+	43.2198i	1.10727	+	0.165593i
$262$			528.641i			2.01771i
$263$	181.504	+	314.375i	0.690130	+	1.19534i	0.971795	+	0.235828i	$0.0757801\pi$
$263$	181.504	+	314.375i	0.690130	+	1.19534i	−0.281665	+	0.959513i	$0.590887\pi$
$264$	2.49926	+	1.70186i	0.00946688	+	0.00644645i
$265$	−141.509	−	81.7004i	−0.533997	−	0.308303i
$266$		0			0
$267$	−141.309	−	293.001i	−0.529248	−	1.09738i
$268$	165.018	+	285.820i	0.615740	+	1.06649i
$269$			196.159i			0.729215i	0.931161	+	0.364607i	$0.118797\pi$
$269$			196.159i			0.729215i	−0.931161	+	0.364607i	$0.881203\pi$
$270$	178.997	+	40.5305i	0.662951	+	0.150113i
$271$			95.2916i			0.351629i	0.984423	+	0.175815i	$0.0562560\pi$
$271$			95.2916i			0.351629i	−0.984423	+	0.175815i	$0.943744\pi$
$272$	−166.372	+	96.0552i	−0.611663	+	0.353144i
$273$		0			0
$274$	−217.327	+	376.421i	−0.793163	+	1.37380i
$275$	−109.617	+	189.862i	−0.398607	+	0.690408i
$276$	160.505	+	109.295i	0.581539	+	0.395997i
$277$	107.725	+	186.586i	0.388901	+	0.673596i	0.992302	−	0.123842i	$-0.0395216\pi$
$277$	107.725	+	186.586i	0.388901	+	0.673596i	−0.603401	+	0.797438i	$0.706188\pi$
$278$			258.592i			0.930187i
$279$	−355.060	+	139.822i	−1.27262	+	0.501153i
$280$		0			0
$281$	101.916	+	176.523i	0.362689	+	0.628196i	0.988402	−	0.151857i	$-0.0485254\pi$
$281$	101.916	+	176.523i	0.362689	+	0.628196i	−0.625713	+	0.780053i	$0.715192\pi$
$282$	−223.586	−	16.6264i	−0.792860	−	0.0589587i
$283$	−104.320	−	60.2294i	−0.368624	−	0.212825i	0.304233	−	0.952598i	$-0.401600\pi$
$283$	−104.320	−	60.2294i	−0.368624	−	0.212825i	−0.672857	+	0.739773i	$0.734933\pi$
$284$	227.524	−	394.083i	0.801141	−	1.38762i
$285$	−8.53852	+	114.823i	−0.0299597	+	0.402889i
$286$	434.583	−	250.907i	1.51952	−	0.877297i
$287$		0			0
$288$	149.518	+	379.683i	0.519161	+	1.31834i
$289$	142.539			0.493215
$290$	−191.128	+	110.348i	−0.659061	+	0.380509i
$291$	−188.343	+	276.589i	−0.647226	+	0.950478i
$292$	−237.059	−	136.866i	−0.811844	−	0.468719i
$293$	−151.688	−	87.5769i	−0.517705	−	0.298897i	0.218290	−	0.975884i	$-0.429952\pi$
$293$	−151.688	−	87.5769i	−0.517705	−	0.298897i	−0.735995	+	0.676987i	$0.763285\pi$
$294$		0			0
$295$	114.122	+	197.665i	0.386854	+	0.670051i
$296$	−0.639578			−0.00216074
$297$	−293.725	+	91.1568i	−0.988974	+	0.306925i
$298$	−318.570			−1.06903
$299$	216.168	−	124.805i	0.722969	−	0.417406i
$300$	209.657	−	101.114i	0.698858	−	0.337047i
$301$		0			0
$302$	39.9541	−	69.2026i	0.132298	−	0.229148i
$303$	129.785	−	190.595i	0.428335	−	0.629027i
$304$	−219.978	+	127.004i	−0.723612	+	0.417778i
$305$	−118.590			−0.388819
$306$	−45.6542	+	305.275i	−0.149197	+	0.997630i
$307$			18.3665i			0.0598259i	0.999553	+	0.0299129i	$0.00952300\pi$
$307$			18.3665i			0.0598259i	−0.999553	+	0.0299129i	$0.990477\pi$
$308$		0			0
$309$	−451.097	−	33.5446i	−1.45986	−	0.108558i
$310$	144.103	−	249.594i	0.464849	−	0.805142i
$311$	353.193	+	203.916i	1.13567	+	0.655679i	0.945355	−	0.326044i	$-0.105716\pi$
$311$	353.193	+	203.916i	1.13567	+	0.655679i	0.190315	+	0.981723i	$0.439049\pi$
$312$	−4.11528	−	0.306021i	−0.0131900	−	0.000980836i
$313$	−348.791	+	201.374i	−1.11435	+	0.643369i	−0.939952	−	0.341307i	$-0.889130\pi$
$313$	−348.791	+	201.374i	−1.11435	+	0.643369i	−0.174396	+	0.984676i	$0.555797\pi$
$314$		−	29.0495i		−	0.0925145i
$315$		0			0
$316$	551.826			1.74628
$317$	148.273	+	256.817i	0.467739	+	0.810149i	0.999320	−	0.0368589i	$-0.0117352\pi$
$317$	148.273	+	256.817i	0.467739	+	0.810149i	−0.531581	+	0.847007i	$0.678402\pi$
$318$	−478.733	−	325.992i	−1.50545	−	1.02513i
$319$	184.914	−	320.280i	0.579667	−	1.00401i
$320$	−135.008	−	77.9470i	−0.421901	−	0.243584i
$321$	206.997	−	99.8311i	0.644851	−	0.311000i
$322$		0			0
$323$	−193.651			−0.599539
$324$	312.243	+	95.5291i	0.963712	+	0.294843i
$325$		−	299.205i		−	0.920631i
$326$	−251.770	−	436.079i	−0.772302	−	1.33767i
$327$	−68.0862	+	32.8368i	−0.208215	+	0.100418i
$328$	−0.668937	−	0.386211i	−0.00203944	−	0.00117747i
$329$		0			0
$330$	130.736	−	191.991i	0.396169	−	0.581791i
$331$	−266.479	−	461.556i	−0.805074	−	1.39443i	−0.916241	−	0.400627i	$-0.868792\pi$
$331$	−266.479	−	461.556i	−0.805074	−	1.39443i	0.111167	−	0.993802i	$-0.464541\pi$
$332$		−	87.8252i		−	0.264534i
$333$	40.5014	−	50.9070i	0.121626	−	0.152874i
$334$		−	176.617i		−	0.528794i
$335$	170.061	−	98.1846i	0.507644	−	0.293088i
$336$		0			0
$337$	149.044	−	258.152i	0.442267	−	0.766029i	−0.555590	−	0.831456i	$-0.687508\pi$
$337$	149.044	−	258.152i	0.442267	−	0.766029i	0.997857	+	0.0654274i	$0.0208411\pi$
$338$	−102.963	+	178.338i	−0.304625	+	0.527626i
$339$	16.4962	−	221.836i	0.0486614	−	0.654384i
$340$	−58.5081	−	101.339i	−0.172083	−	0.298056i
$341$			482.959i			1.41630i
$342$	−60.3642	+	403.635i	−0.176503	+	1.18022i
$343$		0			0
$344$	1.96536	+	3.40411i	0.00571326	+	0.00989566i
$345$	65.0298	−	95.4990i	0.188492	−	0.276809i
$346$	216.008	+	124.712i	0.624300	+	0.360439i
$347$	90.4019	−	156.581i	0.260524	−	0.451241i	−0.705857	−	0.708354i	$-0.749438\pi$
$347$	90.4019	−	156.581i	0.260524	−	0.451241i	0.966381	+	0.257113i	$0.0827712\pi$
$348$	−353.673	+	170.570i	−1.01630	+	0.490144i
$349$	−151.888	+	87.6925i	−0.435209	+	0.251268i	−0.701563	−	0.712607i	$-0.747514\pi$
$349$	−151.888	+	87.6925i	−0.435209	+	0.251268i	0.266354	+	0.963875i	$0.414181\pi$
$350$		0			0
$351$	284.958	−	308.175i	0.811847	−	0.877992i
$352$	516.452			1.46719
$353$	−34.0434	+	19.6549i	−0.0964401	+	0.0556797i	−0.547444	−	0.836842i	$-0.684399\pi$
$353$	−34.0434	+	19.6549i	−0.0964401	+	0.0556797i	0.451004	+	0.892522i	$0.351066\pi$
$354$	351.443	+	728.707i	0.992776	+	2.05849i
$355$	−234.476	−	135.375i	−0.660497	−	0.381338i
$356$	378.552	+	218.557i	1.06335	+	0.613924i
$357$		0			0
$358$	18.3527	+	31.7878i	0.0512645	+	0.0887927i
$359$	247.647			0.689824			0.344912	−	0.938635i	$-0.387909\pi$
$359$	247.647			0.689824			0.344912	+	0.938635i	$0.387909\pi$
$360$	−1.77727	+	0.699885i	−0.00493687	+	0.00194413i
$361$	104.954			0.290732
$362$	554.302	−	320.026i	1.53122	−	0.884050i
$363$	−1.94553	+	26.1630i	−0.00535959	+	0.0720742i
$364$		0			0
$365$	−81.4341	+	141.048i	−0.223107	+	0.386433i
$366$	−419.193	−	31.1721i	−1.14534	−	0.0851697i
$367$	−343.635	+	198.398i	−0.936334	+	0.540593i	−0.888809	−	0.458277i	$-0.848467\pi$
$367$	−343.635	+	198.398i	−0.936334	+	0.540593i	−0.0475248	+	0.998870i	$0.515133\pi$
$368$	254.885			0.692622
$369$	73.1009	−	28.7869i	0.198105	−	0.0780134i
$370$			49.1319i			0.132789i
$371$		0			0
$372$	288.610	−	423.836i	0.775834	−	1.13935i
$373$	−186.570	+	323.149i	−0.500189	+	0.866352i	0.499811	+	0.866134i	$0.333403\pi$
$373$	−186.570	+	323.149i	−0.500189	+	0.866352i	−1.00000		0.000217836i	$0.999931\pi$
$374$	338.320	+	195.329i	0.904599	+	0.522271i
$375$	−138.307	−	286.776i	−0.368818	−	0.764736i
$376$	2.02083	−	1.16673i	0.00537455	−	0.00310300i
$377$			504.731i			1.33881i
$378$		0			0
$379$	548.285			1.44666			0.723331	−	0.690502i	$-0.242610\pi$
$379$	548.285			1.44666			0.723331	+	0.690502i	$0.242610\pi$
$380$	−77.3595	−	133.991i	−0.203578	−	0.352607i
$381$	141.286	−	68.1398i	0.370830	−	0.178845i
$382$	147.210	−	254.975i	0.385366	−	0.667474i
$383$	−4.04111	−	2.33314i	−0.0105512	−	0.00609174i	0.494715	−	0.869055i	$-0.335272\pi$
$383$	−4.04111	−	2.33314i	−0.0105512	−	0.00609174i	−0.505266	+	0.862963i	$0.668606\pi$
$384$	−7.02105	−	4.78097i	−0.0182840	−	0.0124504i
$385$		0			0
$386$	−460.068			−1.19189
$387$	−395.406	−	59.1335i	−1.02172	−	0.152800i
$388$		−	449.651i		−	1.15889i
$389$	336.313	+	582.511i	0.864558	+	1.49746i	0.867486	+	0.497462i	$0.165735\pi$
$389$	336.313	+	582.511i	0.864558	+	1.49746i	−0.00292782	+	0.999996i	$0.500932\pi$
$390$	−23.5083	+	316.132i	−0.0602777	+	0.810596i
$391$	168.285	+	97.1594i	0.430397	+	0.248490i
$392$		0			0
$393$	558.077	+	41.4998i	1.42004	+	0.105597i
$394$	427.351	+	740.194i	1.08465	+	1.87867i
$395$		−	328.332i		−	0.831220i
$396$	257.293	−	323.396i	0.649730	−	0.816658i
$397$		−	106.271i		−	0.267684i	−0.991003	−	0.133842i	$-0.957268\pi$
$397$		−	106.271i		−	0.267684i	0.991003	−	0.133842i	$-0.0427315\pi$
$398$	−141.859	+	81.9023i	−0.356429	+	0.205785i
$399$		0			0
$400$	152.765	−	264.596i	0.381911	−	0.661490i
$401$	149.197	−	258.416i	0.372061	−	0.644429i	−0.617821	−	0.786319i	$-0.711985\pi$
$401$	149.197	−	258.416i	0.372061	−	0.644429i	0.989882	+	0.141890i	$0.0453178\pi$
$402$	626.941	−	302.363i	1.55955	−	0.752146i
$403$	−329.565	−	570.823i	−0.817779	−	1.41643i
$404$			309.850i			0.766957i
$405$	56.8391	−	185.782i	0.140343	−	0.458721i
$406$		0			0
$407$	−41.1662	−	71.3019i	−0.101145	−	0.175189i
$408$	−1.39554	−	2.89361i	−0.00342044	−	0.00709219i
$409$	−570.795	−	329.549i	−1.39559	−	0.805743i	−0.401661	−	0.915789i	$-0.631567\pi$
$409$	−570.795	−	329.549i	−1.39559	−	0.805743i	−0.993927	+	0.110046i	$0.964900\pi$
$410$	−29.6684	+	51.3872i	−0.0723620	+	0.125335i
$411$	380.320	+	258.978i	0.925353	+	0.630117i
$412$	526.398	−	303.916i	1.27766	−	0.737660i
$413$		0			0
$414$	254.971	−	320.478i	0.615872	−	0.774101i
$415$	−52.2553			−0.125916
$416$	−610.409	+	352.420i	−1.46733	+	0.847164i
$417$	272.991	+	20.3002i	0.654654	+	0.0486815i
$418$	447.328	+	258.265i	1.07016	+	0.617858i
$419$	485.296	+	280.186i	1.15822	+	0.668701i	0.950878	−	0.309566i	$-0.100184\pi$
$419$	485.296	+	280.186i	1.15822	+	0.668701i	0.207346	+	0.978268i	$0.433517\pi$
$420$		0			0
$421$	57.9969	+	100.454i	0.137760	+	0.238607i	0.926648	−	0.375929i	$-0.122676\pi$
$421$	57.9969	+	100.454i	0.137760	+	0.238607i	−0.788889	+	0.614536i	$0.789343\pi$
$422$	−120.271			−0.285001
$423$	−35.1043	+	234.731i	−0.0829889	+	0.554919i
$424$	6.02802			0.0142170
$425$	201.722	−	116.464i	0.474641	−	0.274034i
$426$	−793.246	−	540.159i	−1.86208	−	1.26798i
$427$		0			0
$428$	−154.405	+	267.437i	−0.360759	+	0.624852i
$429$	−230.762	−	478.479i	−0.537906	−	1.11533i
$430$	261.501	−	150.978i	0.608142	−	0.351111i
$431$	−322.507			−0.748277			−0.374138	−	0.927373i	$-0.622061\pi$
$431$	−322.507			−0.748277			−0.374138	+	0.927373i	$0.622061\pi$
$432$	409.342	−	127.038i	0.947550	−	0.294069i
$433$			117.316i			0.270937i	0.990782	+	0.135468i	$0.0432539\pi$
$433$			117.316i			0.270937i	−0.990782	+	0.135468i	$0.956746\pi$
$434$		0			0
$435$	101.488	+	210.432i	0.233305	+	0.483753i
$436$	50.7873	−	87.9662i	0.116485	−	0.201757i
$437$	222.507	+	128.464i	0.509169	+	0.293969i
$438$	−324.930	+	477.173i	−0.741849	+	1.08944i
$439$	−187.788	+	108.419i	−0.427763	+	0.246969i	−0.698393	−	0.715714i	$-0.746101\pi$
$439$	−187.788	+	108.419i	−0.427763	+	0.246969i	0.270630	+	0.962683i	$0.412768\pi$
$440$			2.41748i			0.00549427i
$441$		0			0
$442$	−533.160			−1.20625
$443$	74.8709	+	129.680i	0.169009	+	0.292732i	0.938072	−	0.346441i	$-0.112610\pi$
$443$	74.8709	+	129.680i	0.169009	+	0.292732i	−0.769063	+	0.639173i	$0.779277\pi$
$444$	−6.48242	+	87.1737i	−0.0146001	+	0.196337i
$445$	130.040	−	225.235i	0.292224	−	0.506147i
$446$	−471.035	−	271.952i	−1.05613	−	0.609758i
$447$	−25.0086	+	336.308i	−0.0559477	+	0.752368i
$448$		0			0
$449$	−263.767			−0.587455			−0.293727	−	0.955889i	$-0.594896\pi$
$449$	−263.767			−0.587455			−0.293727	+	0.955889i	$0.594896\pi$
$450$	−179.872	−	456.763i	−0.399715	−	1.01503i
$451$		−	99.4331i		−	0.220473i
$452$	149.457	+	258.866i	0.330656	+	0.572713i
$453$	−69.9194	−	47.6114i	−0.154347	−	0.105102i
$454$	−551.668	−	318.505i	−1.21513	−	0.701554i
$455$		0			0
$456$	−1.84518	−	3.82594i	−0.00404646	−	0.00839023i
$457$	109.396	+	189.480i	0.239379	+	0.414617i	0.960536	−	0.278154i	$-0.0897227\pi$
$457$	109.396	+	189.480i	0.239379	+	0.414617i	−0.721157	+	0.692772i	$0.756389\pi$
$458$			453.851i			0.990941i
$459$	318.689	+	72.1613i	0.694312	+	0.157214i
$460$			155.253i			0.337506i
$461$	−334.892	+	193.350i	−0.726446	+	0.419414i	−0.817121	−	0.576467i	$-0.804431\pi$
$461$	−334.892	+	193.350i	−0.726446	+	0.419414i	0.0906743	+	0.995881i	$0.471098\pi$
$462$		0			0
$463$	241.881	−	418.950i	0.522421	−	0.904860i	−0.477238	−	0.878774i	$-0.658362\pi$
$463$	241.881	−	418.950i	0.522421	−	0.904860i	0.999660	−	0.0260863i	$-0.00830447\pi$
$464$	−257.700	+	446.349i	−0.555387	+	0.961959i
$465$	−252.179	−	171.721i	−0.542321	−	0.369292i
$466$	−349.422	−	605.216i	−0.749832	−	1.29875i
$467$			115.519i			0.247363i	0.992322	+	0.123682i	$0.0394702\pi$
$467$			115.519i			0.247363i	−0.992322	+	0.123682i	$0.960530\pi$
$468$	−83.4205	+	557.805i	−0.178249	+	1.19189i
$469$		0			0
$470$	−89.6272	−	155.239i	−0.190696	−	0.330295i
$471$	−30.6671	−	2.28047i	−0.0651106	−	0.00484176i
$472$	−7.29207	−	4.21008i	−0.0154493	−	0.00891966i
$473$	−252.999	+	438.208i	−0.534882	+	0.926443i
$474$	86.3041	−	1160.59i	0.182076	−	2.44851i
$475$	266.718	−	153.990i	0.561511	−	0.324189i
$476$		0			0
$477$	−381.726	+	479.798i	−0.800264	+	1.00587i
$478$	−624.264			−1.30599
$479$	394.602	−	227.823i	0.823803	−	0.475623i	−0.0279230	−	0.999610i	$-0.508889\pi$
$479$	394.602	−	227.823i	0.823803	−	0.475623i	0.851726	+	0.523987i	$0.175556\pi$
$480$	−183.630	+	269.668i	−0.382562	+	0.561808i
$481$	97.3110	+	56.1825i	0.202310	+	0.116804i
$482$	646.939	+	373.510i	1.34220	+	0.774918i
$483$		0			0
$484$	−17.6267	−	30.5303i	−0.0364187	−	0.0630790i
$485$	−267.539			−0.551626
$486$	249.749	−	641.764i	0.513888	−	1.32050i
$487$	324.669			0.666671			0.333335	−	0.942808i	$-0.391826\pi$
$487$	324.669			0.666671			0.333335	+	0.942808i	$0.391826\pi$
$488$	3.78878	−	2.18745i	0.00776389	−	0.00448248i
$489$	−480.126	+	231.556i	−0.981852	+	0.473530i
$490$		0			0
$491$	−155.221	+	268.850i	−0.316132	+	0.547557i	−0.979678	−	0.200579i	$-0.935718\pi$
$491$	−155.221	+	268.850i	−0.316132	+	0.547557i	0.663545	+	0.748136i	$0.269051\pi$
$492$	−59.4200	+	87.2608i	−0.120772	+	0.177359i
$493$	−340.287	+	196.465i	−0.690237	+	0.398509i
$494$	−704.946			−1.42702
$495$	−192.418	−	153.087i	−0.388724	−	0.309267i
$496$		−	673.061i		−	1.35698i
$497$		0			0
$498$	−184.713	−	13.7356i	−0.370909	−	0.0275816i
$499$	387.110	−	670.494i	0.775771	−	1.34368i	−0.158589	−	0.987345i	$-0.550694\pi$
$499$	387.110	−	670.494i	0.775771	−	1.34368i	0.934360	−	0.356331i	$-0.115972\pi$
$500$	370.509	+	213.914i	0.741019	+	0.427827i
$501$	−186.452	−	13.8649i	−0.372159	−	0.0276745i
$502$	56.4489	−	32.5908i	0.112448	−	0.0649219i
$503$		−	106.472i		−	0.211674i	−0.994384	−	0.105837i	$-0.966248\pi$
$503$		−	106.472i		−	0.211674i	0.994384	−	0.105837i	$-0.0337521\pi$
$504$		0			0
$505$	184.359			0.365067
$506$	−259.155	−	448.870i	−0.512165	−	0.887096i
$507$	180.185	+	122.696i	0.355394	+	0.242005i
$508$	−105.389	+	182.539i	−0.207459	+	0.359329i
$509$	293.258	+	169.313i	0.576146	+	0.332638i	0.759600	−	0.650390i	$-0.225395\pi$
$509$	293.258	+	169.313i	0.576146	+	0.332638i	−0.183454	+	0.983028i	$0.558728\pi$
$510$	−222.285	+	107.204i	−0.435853	+	0.210204i
$511$		0			0
$512$	−725.356			−1.41671
$513$	421.372	+	95.4118i	0.821387	+	0.185988i
$514$			50.4924i			0.0982343i
$515$	−180.828	−	313.202i	−0.351121	−	0.608160i
$516$	483.895	−	233.374i	0.937782	−	0.452276i
$517$	260.140	+	150.192i	0.503172	+	0.290506i
$518$		0			0
$519$	148.613	−	218.245i	0.286346	−	0.420511i
$520$	−1.64966	−	2.85729i	−0.00317241	−	0.00549478i
$521$		−	97.1593i		−	0.186486i	−0.995643	−	0.0932431i	$-0.970277\pi$
$521$		−	97.1593i		−	0.186486i	0.995643	−	0.0932431i	$-0.0297234\pi$
$522$	303.427	+	770.516i	0.581278	+	1.47608i
$523$		−	593.254i		−	1.13433i	−0.823605	−	0.567164i	$-0.808041\pi$
$523$		−	593.254i		−	1.13433i	0.823605	−	0.567164i	$-0.191959\pi$
$524$	−651.235	+	375.990i	−1.24281	+	0.717539i
$525$		0			0
$526$	−514.372	+	890.919i	−0.977894	+	1.69376i
$527$	256.564	−	444.382i	0.486838	−	0.843229i
$528$	40.2264	−	540.953i	0.0761863	−	1.02453i
$529$	135.592	+	234.853i	0.256319	+	0.443957i
$530$		−	463.068i		−	0.873713i
$531$	796.872	−	313.806i	1.50070	−	0.590972i
$532$		0			0
$533$	67.8519	+	117.523i	0.127302	+	0.220493i
$534$	518.871	−	761.984i	0.971668	−	1.42694i
$535$	159.123	+	91.8696i	0.297426	+	0.171719i
$536$	−3.62213	+	6.27371i	−0.00675770	+	0.0117047i
$537$	34.9985	−	16.8792i	0.0651742	−	0.0314323i
$538$	−481.426	+	277.951i	−0.894843	+	0.516638i
$539$		0			0
$540$	77.3800	+	249.334i	0.143296	+	0.461729i
$541$	−578.154			−1.06868			−0.534338	−	0.845271i	$-0.679439\pi$
$541$	−578.154			−1.06868			−0.534338	+	0.845271i	$0.679439\pi$
$542$	−233.871	+	135.025i	−0.431496	+	0.249124i
$543$	−294.332	−	610.289i	−0.542047	−	1.12392i
$544$	−475.199	−	274.356i	−0.873528	−	0.504332i
$545$	−52.3392	−	30.2181i	−0.0960352	−	0.0554460i
$546$		0			0
$547$	110.283	+	191.016i	0.201615	+	0.349207i	0.949049	−	0.315129i	$-0.102048\pi$
$547$	110.283	+	191.016i	0.201615	+	0.349207i	−0.747434	+	0.664336i	$0.768714\pi$
$548$	−618.286			−1.12826
$549$	−65.8156	+	440.088i	−0.119883	+	0.801617i
$550$	−621.296			−1.12963
$551$	−449.928	+	259.766i	−0.816566	+	0.471445i
$552$	−0.316081	+	4.25057i	−0.000572611	+	0.00770030i
$553$		0			0
$554$	−305.288	+	528.774i	−0.551061	+	0.954465i
$555$	51.8677	+	3.85699i	0.0934553	+	0.00694954i
$556$	−318.560	+	183.921i	−0.572950	+	0.330793i
$557$	−359.594			−0.645590			−0.322795	−	0.946469i	$-0.604622\pi$
$557$	−359.594			−0.645590			−0.322795	+	0.946469i	$0.604622\pi$
$558$	−846.269	−	673.288i	−1.51661	−	1.20661i
$559$		−	690.574i		−	1.23537i
$560$		0			0
$561$	232.764	−	341.824i	0.414910	−	0.609313i
$562$	−288.823	+	500.256i	−0.513920	+	0.890135i
$563$	854.592	+	493.399i	1.51792	+	0.876374i	0.999778	+	0.0210827i	$0.00671133\pi$
$563$	854.592	+	493.399i	1.51792	+	0.876374i	0.518147	+	0.855292i	$0.326622\pi$
$564$	−138.541	−	287.262i	−0.245641	−	0.509330i
$565$	154.024	−	88.9255i	0.272608	−	0.157390i
$566$		−	341.373i		−	0.603133i
$567$		0			0
$568$	9.98825			0.0175849
$569$	−41.8937	−	72.5620i	−0.0736269	−	0.127525i	0.826861	−	0.562406i	$-0.190124\pi$
$569$	−41.8937	−	72.5620i	−0.0736269	−	0.127525i	−0.900488	+	0.434880i	$0.856791\pi$
$570$	−293.906	+	141.746i	−0.515625	+	0.248677i
$571$	175.350	−	303.715i	0.307093	−	0.531901i	−0.670632	−	0.741790i	$-0.733977\pi$
$571$	175.350	−	303.715i	0.307093	−	0.531901i	0.977725	+	0.209889i	$0.0673103\pi$
$572$	618.186	+	356.910i	1.08074	+	0.623968i
$573$	−257.616	−	175.423i	−0.449592	−	0.306148i
$574$		0			0
$575$	−309.041			−0.537463
$576$	−364.189	+	457.756i	−0.632273	+	0.794716i
$577$		−	753.475i		−	1.30585i	−0.757423	−	0.652925i	$-0.773542\pi$
$577$		−	753.475i		−	1.30585i	0.757423	−	0.652925i	$-0.226458\pi$
$578$	201.974	+	349.829i	0.349436	+	0.605240i
$579$	−36.1166	+	485.685i	−0.0623775	+	0.838835i
$580$	−271.875	−	156.967i	−0.468750	−	0.270633i
$581$		0			0
$582$	−945.699	−	70.3242i	−1.62491	−	0.120832i
$583$	387.991	+	672.019i	0.665507	+	1.15269i
$584$		−	6.00837i		−	0.0102883i
$585$	331.890	+	49.6345i	0.567333	+	0.0848453i
$586$		−	496.375i		−	0.847057i
$587$	112.348	−	64.8642i	0.191394	−	0.110501i	−0.401241	−	0.915972i	$-0.631421\pi$
$587$	112.348	−	64.8642i	0.191394	−	0.110501i	0.592635	+	0.805471i	$0.298088\pi$
$588$		0			0
$589$	339.229	−	587.562i	0.575941	−	0.997559i
$590$	−323.415	+	560.172i	−0.548161	+	0.949443i
$591$	814.958	−	393.040i	1.37895	−	0.665042i
$592$	57.3700	+	99.3678i	0.0969088	+	0.167851i
$593$		−	503.348i		−	0.848815i	−0.905471	−	0.424408i	$-0.860482\pi$
$593$		−	503.348i		−	0.848815i	0.905471	−	0.424408i	$-0.139518\pi$
$594$	−639.923	−	591.713i	−1.07731	−	0.996151i
$595$		0			0
$596$	−226.580	−	392.447i	−0.380167	−	0.658469i
$597$	75.3264	+	156.187i	0.126175	+	0.261620i
$598$	612.607	+	353.689i	1.02443	+	0.591453i
$599$	141.278	−	244.701i	0.235857	−	0.408516i	−0.723664	−	0.690152i	$-0.757544\pi$
$599$	141.278	−	244.701i	0.235857	−	0.408516i	0.959521	+	0.281636i	$0.0908770\pi$
$600$	4.22307	+	2.87569i	0.00703845	+	0.00479281i
$601$	159.905	−	92.3214i	0.266065	−	0.153613i	−0.361033	−	0.932553i	$-0.617576\pi$
$601$	159.905	−	92.3214i	0.266065	−	0.153613i	0.627098	+	0.778940i	$0.284242\pi$
$602$		0			0
$603$	−269.982	−	685.586i	−0.447731	−	1.13696i
$604$	113.668			0.188192
$605$	−18.1653	+	10.4877i	−0.0300252	+	0.0173351i
$606$	651.673	+	48.4598i	1.07537	+	0.0799667i
$607$	905.567	+	522.829i	1.49187	+	0.861333i	0.999957	−	0.00930928i	$-0.00296328\pi$
$607$	905.567	+	522.829i	1.49187	+	0.861333i	0.491916	+	0.870643i	$0.336297\pi$
$608$	−628.310	−	362.755i	−1.03340	−	0.596636i
$609$		0			0
$610$	−168.038	−	291.051i	−0.275473	−	0.477133i
$611$	−409.956			−0.670959
$612$	−408.540	+	160.882i	−0.667549	+	0.262879i
$613$	105.329			0.171826			0.0859131	−	0.996303i	$-0.472619\pi$
$613$	105.329			0.171826			0.0859131	+	0.996303i	$0.472619\pi$
$614$	−45.0764	+	26.0248i	−0.0734143	+	0.0423857i
$615$	51.9195	+	35.3545i	0.0844220	+	0.0574869i
$616$		0			0
$617$	269.908	−	467.495i	0.437452	−	0.757690i	−0.560040	−	0.828466i	$-0.689214\pi$
$617$	269.908	−	467.495i	0.437452	−	0.757690i	0.997492	+	0.0707759i	$0.0225475\pi$
$618$	−556.864	−	1154.64i	−0.901075	−	1.86836i
$619$	968.123	−	558.946i	1.56401	−	0.902982i	0.567166	−	0.823603i	$-0.308040\pi$
$619$	968.123	−	558.946i	1.56401	−	0.902982i	0.996845	−	0.0793787i	$-0.0252936\pi$
$620$	409.968			0.661238
$621$	−318.307	−	294.326i	−0.512571	−	0.473956i
$622$			1155.77i			1.85816i
$623$		0			0
$624$	321.594	+	666.818i	0.515376	+	1.06862i
$625$	−113.310	+	196.259i	−0.181296	+	0.314014i
$626$	−988.452	−	570.683i	−1.57900	−	0.911635i
$627$	307.762	−	451.961i	0.490848	−	0.720831i
$628$	35.7862	−	20.6612i	0.0569845	−	0.0329000i
$629$			87.4754i			0.139071i
$630$		0			0
$631$	−710.879			−1.12659			−0.563296	−	0.826255i	$-0.690467\pi$
$631$	−710.879			−1.12659			−0.563296	+	0.826255i	$0.690467\pi$
$632$	6.05625	+	10.4897i	0.00958268	+	0.0165977i
$633$	−9.44156	+	126.967i	−0.0149156	+	0.200580i
$634$	−420.198	+	727.805i	−0.662773	+	1.14796i
$635$	108.609	+	62.7057i	0.171038	+	0.0987491i
$636$	61.0968	−	821.611i	0.0960641	−	1.29184i
$637$		0			0
$638$	1048.07			1.64274
$639$	−632.508	+	795.011i	−0.989840	+	1.24415i
$640$		−	6.79131i		−	0.0106114i
$641$	−535.389	−	927.321i	−0.835240	−	1.44668i	−0.893835	−	0.448397i	$-0.851995\pi$
$641$	−535.389	−	927.321i	−0.835240	−	1.44668i	0.0585942	−	0.998282i	$-0.481338\pi$
$642$	538.321	+	366.568i	0.838506	+	0.570979i
$643$	664.371	+	383.575i	1.03324	+	0.596539i	0.917910	−	0.396788i	$-0.129875\pi$
$643$	664.371	+	383.575i	1.03324	+	0.596539i	0.115326	+	0.993328i	$0.463209\pi$
$644$		0			0
$645$	−138.856	−	287.914i	−0.215280	−	0.446378i
$646$	−274.398	−	475.271i	−0.424764	−	0.735713i
$647$			17.1084i			0.0264427i	0.999913	+	0.0132214i	$0.00420861\pi$
$647$			17.1084i			0.0264427i	−0.999913	+	0.0132214i	$0.995791\pi$
$648$	1.61092	+	6.98389i	0.00248598	+	0.0107776i
$649$		−	1083.92i		−	1.67014i
$650$	734.328	−	423.965i	1.12974	−	0.652253i
$651$		0			0
$652$	358.138	−	620.314i	0.549292	−	0.951402i
$653$	484.144	−	838.561i	0.741414	−	1.28417i	−0.210437	−	0.977607i	$-0.567489\pi$
$653$	484.144	−	838.561i	0.741414	−	1.28417i	0.951851	−	0.306560i	$-0.0991779\pi$
$654$	−177.066	−	120.573i	−0.270744	−	0.184362i
$655$	223.711	+	387.480i	0.341544	+	0.591572i
$656$			138.572i			0.211238i
$657$	478.235	+	380.482i	0.727907	+	0.579120i
$658$		0			0
$659$	470.849	+	815.535i	0.714490	+	1.23753i	0.963156	+	0.268944i	$0.0866747\pi$
$659$	470.849	+	815.535i	0.714490	+	1.23753i	−0.248665	+	0.968589i	$0.579992\pi$
$660$	329.499	+	24.5023i	0.499241	+	0.0371246i
$661$	4.75875	+	2.74747i	0.00719933	+	0.00415653i	0.503595	−	0.863940i	$-0.332010\pi$
$661$	4.75875	+	2.74747i	0.00719933	+	0.00415653i	−0.496396	+	0.868096i	$0.665344\pi$
$662$	755.187	−	1308.02i	1.14077	−	1.97586i
$663$	−41.8546	+	562.848i	−0.0631290	+	0.848941i
$664$	1.66948	−	0.963876i	0.00251428	−	0.00145162i
$665$		0			0
$666$	182.329	+	27.2675i	0.273767	+	0.0409422i
$667$	521.324			0.781595
$668$	217.575	−	125.617i	0.325712	−	0.188050i
$669$	−324.072	+	475.914i	−0.484413	+	0.711381i
$670$	481.942	+	278.249i	0.719316	+	0.415297i
$671$	487.726	+	281.589i	0.726864	+	0.419655i
$672$		0			0
$673$	329.366	+	570.479i	0.489400	+	0.847666i	0.999926	−	0.0121964i	$-0.00388233\pi$
$673$	329.366	+	570.479i	0.489400	+	0.847666i	−0.510525	+	0.859863i	$0.670549\pi$
$674$	844.764			1.25336
$675$	−496.316	+	154.030i	−0.735283	+	0.228193i
$676$	−292.926			−0.433323
$677$	−730.516	+	421.763i	−1.07905	+	0.622989i	−0.930639	−	0.365937i	$-0.880748\pi$
$677$	−730.516	+	421.763i	−1.07905	+	0.622989i	−0.148409	+	0.988926i	$0.547415\pi$
$678$	567.819	−	273.849i	0.837491	−	0.403907i
$679$		0			0
$680$	1.28424	−	2.22438i	0.00188860	−	0.00327114i
$681$	−379.548	+	557.382i	−0.557339	+	0.818475i
$682$	−1185.31	+	684.338i	−1.73799	+	1.00343i
$683$	580.828			0.850407			0.425203	−	0.905098i	$-0.360203\pi$
$683$	580.828			0.850407			0.425203	+	0.905098i	$0.360203\pi$
$684$	−540.173	+	212.719i	−0.789727	+	0.310992i
$685$			367.875i			0.537044i
$686$		0			0
$687$	479.122	+	35.6286i	0.697412	+	0.0518611i
$688$	352.585	−	610.695i	0.512478	−	0.887638i
$689$	−917.155	−	529.520i	−1.33114	−	0.768534i
$690$	326.525	+	24.2811i	0.473225	+	0.0351900i
$691$	−976.744	+	563.924i	−1.41352	+	0.816098i	−0.995718	−	0.0924390i	$-0.970534\pi$
$691$	−976.744	+	563.924i	−1.41352	+	0.816098i	−0.417805	+	0.908537i	$0.637200\pi$
$692$			354.801i			0.512718i
$693$		0			0
$694$	512.388			0.738311
$695$	109.432	+	189.541i	0.157455	+	0.272721i
$696$	−7.12392	−	4.85102i	−0.0102355	−	0.00696985i
$697$	−52.8222	+	91.4907i	−0.0757851	+	0.131264i
$698$	−430.441	−	248.515i	−0.616678	−	0.356039i
$699$	−666.346	+	321.367i	−0.953285	+	0.459752i
$700$		0			0
$701$	352.754			0.503216			0.251608	−	0.967829i	$-0.419041\pi$
$701$	352.754			0.503216			0.251608	+	0.967829i	$0.419041\pi$
$702$	1160.12	+	262.688i	1.65259	+	0.374200i
$703$			115.660i			0.164524i
$704$	370.166	+	641.147i	0.525804	+	0.910720i
$705$	−170.919	+	82.4311i	−0.242438	+	0.116924i
$706$	−96.4769	−	55.7009i	−0.136653	−	0.0788965i
$707$		0			0
$708$	−647.737	+	951.229i	−0.914883	+	1.34354i
$709$	396.038	+	685.959i	0.558587	+	0.967502i	0.997615	+	0.0690279i	$0.0219898\pi$
$709$	396.038	+	685.959i	0.558587	+	0.967502i	−0.439027	+	0.898474i	$0.644677\pi$
$710$		−	767.290i		−	1.08069i
$711$	−1218.44	−	182.219i	−1.71370	−	0.256286i
$712$			9.59460i			0.0134756i
$713$	−589.589	+	340.399i	−0.826913	+	0.477418i
$714$		0			0
$715$	212.359	−	367.816i	0.297005	−	0.514428i
$716$	−26.1063	+	45.2175i	−0.0364613	+	0.0631529i
$717$	−49.0064	+	659.024i	−0.0683493	+	0.919141i
$718$	350.908	+	607.791i	0.488730	+	0.846505i
$719$		−	546.494i		−	0.760075i	−0.924971	−	0.380037i	$-0.875911\pi$
$719$		−	546.494i		−	0.760075i	0.924971	−	0.380037i	$-0.124089\pi$
$720$	268.158	+	213.346i	0.372442	+	0.296313i
$721$		0			0
$722$	148.717	+	257.586i	0.205979	+	0.356767i
$723$	445.094	−	653.640i	0.615622	−	0.904066i
$724$	788.483	+	455.231i	1.08906	+	0.628772i
$725$	312.454	−	541.186i	0.430971	−	0.746464i
$726$	−66.9676	+	32.2973i	−0.0922418	+	0.0444866i
$727$	113.839	−	65.7248i	0.156587	−	0.0904055i	−0.419659	−	0.907682i	$-0.637850\pi$
$727$	113.839	−	65.7248i	0.156587	−	0.0904055i	0.576246	+	0.817276i	$0.304517\pi$
$728$		0			0
$729$	−657.892	−	314.036i	−0.902459	−	0.430777i
$730$	−461.559			−0.632272
$731$	465.581	−	268.803i	0.636910	−	0.367720i
$732$	−259.746	−	538.576i	−0.354844	−	0.735760i
$733$	1107.87	+	639.630i	1.51142	+	0.872620i	0.999911	+	0.0133434i	$0.00424746\pi$
$733$	1107.87	+	639.630i	1.51142	+	0.872620i	0.511511	+	0.859277i	$0.329086\pi$
$734$	−973.840	−	562.247i	−1.32676	−	0.766004i
$735$		0			0
$736$	364.006	+	630.477i	0.494573	+	0.856626i
$737$	−932.546			−1.26533
$738$	174.233	+	138.619i	0.236088	+	0.187830i
$739$	−19.8731			−0.0268919			−0.0134460	−	0.999910i	$-0.504280\pi$
$739$	−19.8731			−0.0268919			−0.0134460	+	0.999910i	$0.504280\pi$
$740$	−60.5258	+	34.9446i	−0.0817916	+	0.0472224i
$741$	−55.3402	+	744.199i	−0.0746831	+	1.00432i
$742$		0			0
$743$	729.663	−	1263.81i	0.982050	−	1.70096i	0.327677	−	0.944790i	$-0.393734\pi$
$743$	729.663	−	1263.81i	0.982050	−	1.70096i	0.654374	−	0.756171i	$-0.272932\pi$
$744$	11.2242	+	0.834659i	0.0150864	+	0.00112185i
$745$	−233.503	+	134.813i	−0.313427	+	0.180957i
$746$	−1057.46			−1.41751
$747$	−29.0009	+	193.920i	−0.0388232	+	0.259598i
$748$			555.703i			0.742919i
$749$		0			0
$750$	507.847	−	745.795i	0.677130	−	0.994393i
$751$	494.911	−	857.211i	0.659003	−	1.14143i	−0.321871	−	0.946784i	$-0.604312\pi$
$751$	494.911	−	857.211i	0.659003	−	1.14143i	0.980874	−	0.194643i	$-0.0623549\pi$
$752$	−362.536	−	209.310i	−0.482096	−	0.278338i
$753$	−29.9741	−	62.1505i	−0.0398062	−	0.0825372i
$754$	−1238.74	+	715.189i	−1.64290	+	0.948527i
$755$		−	67.6315i		−	0.0895781i
$756$		0			0
$757$	−499.688			−0.660089			−0.330045	−	0.943965i	$-0.607064\pi$
$757$	−499.688			−0.660089			−0.330045	+	0.943965i	$0.607064\pi$
$758$	776.903	+	1345.64i	1.02494	+	1.77525i
$759$	−494.209	+	238.348i	−0.651131	+	0.314029i
$760$	1.69803	−	2.94108i	0.00223425	−	0.00386984i
$761$	594.048	+	342.974i	0.780614	+	0.450688i	0.836648	−	0.547741i	$-0.184512\pi$
$761$	594.048	+	342.974i	0.780614	+	0.450688i	−0.0560336	+	0.998429i	$0.517845\pi$
$762$	367.431	+	250.201i	0.482193	+	0.328348i
$763$		0			0
$764$	418.806			0.548175
$765$	95.7236	+	243.078i	0.125129	+	0.317749i
$766$		−	13.2239i		−	0.0172636i
$767$	739.652	+	1281.12i	0.964345	+	1.67029i
$768$	−56.0534	+	753.789i	−0.0729861	+	0.981496i
$769$	−586.160	−	338.420i	−0.762237	−	0.440078i	0.0678613	−	0.997695i	$-0.478382\pi$
$769$	−586.160	−	338.420i	−0.762237	−	0.440078i	−0.830098	+	0.557617i	$0.811716\pi$
$770$		0			0
$771$	53.3039	+	3.96379i	0.0691361	+	0.00514111i
$772$	−327.219	−	566.759i	−0.423858	−	0.734144i
$773$			505.019i			0.653323i	0.945141	+	0.326661i	$0.105924\pi$
$773$			505.019i			0.653323i	−0.945141	+	0.326661i	$0.894076\pi$
$774$	−415.149	−	1054.22i	−0.536369	−	1.36204i
$775$			816.069i			1.05299i
$776$	8.54747	−	4.93489i	0.0110148	−	0.00635939i
$777$		0			0
$778$	−953.091	+	1650.80i	−1.22505	+	2.12185i
$779$	−69.8416	+	120.969i	−0.0896555	+	0.155288i
$780$	−406.165	+	195.886i	−0.520724	+	0.251136i
$781$	642.889	+	1113.52i	0.823161	+	1.42576i
$782$			550.688i			0.704205i
$783$	837.240	−	259.835i	1.06927	−	0.331845i
$784$		0			0
$785$	−12.2932	−	21.2925i	−0.0156602	−	0.0271242i
$786$	688.927	+	1428.47i	0.876497	+	1.81739i
$787$	−16.0382	−	9.25964i	−0.0203789	−	0.0117657i	0.489776	−	0.871848i	$-0.337079\pi$
$787$	−16.0382	−	9.25964i	−0.0203789	−	0.0117657i	−0.510155	+	0.860083i	$0.670412\pi$
$788$	−607.898	+	1052.91i	−0.771445	+	1.33618i
$789$	900.147	+	612.953i	1.14087	+	0.776873i
$790$	805.814	−	465.237i	1.02002	−	0.588907i
$791$		0			0
$792$	8.97126	+	1.34166i	0.0113274	+	0.00169402i
$793$	−768.610			−0.969243
$794$	260.817	−	150.583i	0.328484	−	0.189651i
$795$	−488.852	−	36.3521i	−0.614909	−	0.0457259i
$796$	−201.791	−	116.504i	−0.253507	−	0.146362i
$797$	615.232	+	355.205i	0.771935	+	0.445677i	0.833565	−	0.552422i	$-0.186296\pi$
$797$	615.232	+	355.205i	0.771935	+	0.445677i	−0.0616293	+	0.998099i	$0.519630\pi$
$798$		0			0
$799$	−159.574	−	276.390i	−0.199717	−	0.345920i
$800$	872.664			1.09083
$801$	−763.679	−	607.580i	−0.953407	−	0.758527i
$802$	845.628			1.05440
$803$	669.829	−	386.726i	0.834159	−	0.481602i
$804$	818.387	+	557.279i	1.01789	+	0.693133i
$805$		0			0
$806$	933.967	−	1617.68i	1.15877	−	2.00705i
$807$	255.635	+	530.052i	0.316772	+	0.656818i
$808$	−5.88999	+	3.40059i	−0.00728960	+	0.00420865i
$809$	1131.54			1.39869			0.699344	−	0.714786i	$-0.253476\pi$
$809$	1131.54			1.39869			0.699344	+	0.714786i	$0.253476\pi$
$810$	536.497	−	123.749i	0.662342	−	0.152777i
$811$			199.736i			0.246283i	0.992389	+	0.123142i	$0.0392970\pi$
$811$			199.736i			0.246283i	−0.992389	+	0.123142i	$0.960703\pi$
$812$		0			0
$813$	124.184	+	257.493i	0.152748	+	0.316720i
$814$	116.662	−	202.065i	0.143320	−	0.248238i
$815$	−369.082	−	213.090i	−0.452861	−	0.261460i
$816$	−324.385	+	476.373i	−0.397531	+	0.583791i
$817$	615.592	−	355.412i	0.753479	−	0.435021i
$818$		−	1867.84i		−	2.28343i
$819$		0			0
$820$	−84.4055			−0.102934
$821$	−196.680	−	340.660i	−0.239562	−	0.414933i	0.721027	−	0.692907i	$-0.243670\pi$
$821$	−196.680	−	340.660i	−0.239562	−	0.414933i	−0.960589	+	0.277974i	$0.910337\pi$
$822$	−96.6983	+	1300.37i	−0.117638	+	1.58196i
$823$	424.378	−	735.045i	0.515648	−	0.893128i	−0.484187	−	0.874965i	$-0.660885\pi$
$823$	424.378	−	735.045i	0.515648	−	0.893128i	0.999835	−	0.0181639i	$-0.00578208\pi$
$824$	11.5544	+	6.67091i	0.0140223	+	0.00809577i
$825$	−48.7735	+	655.891i	−0.0591193	+	0.795019i
$826$		0			0
$827$	495.009			0.598559			0.299280	−	0.954165i	$-0.403254\pi$
$827$	495.009			0.598559			0.299280	+	0.954165i	$0.403254\pi$
$828$	576.143	+	86.1629i	0.695825	+	0.104061i
$829$			947.240i			1.14263i	0.820731	+	0.571315i	$0.193566\pi$
$829$			947.240i			1.14263i	−0.820731	+	0.571315i	$0.806434\pi$
$830$	−74.0442	−	128.248i	−0.0892099	−	0.154516i
$831$	534.251	+	363.797i	0.642901	+	0.437782i
$832$	−875.021	−	505.193i	−1.05171	−	0.607204i
$833$		0			0
$834$	336.998	+	698.757i	0.404074	+	0.837838i
$835$	−74.7412	−	129.456i	−0.0895105	−	0.155037i
$836$			734.752i			0.878891i
$837$	−777.212	+	840.536i	−0.928569	+	1.00422i
$838$			1588.06i			1.89506i
$839$	787.270	−	454.531i	0.938343	−	0.541753i	0.0489028	−	0.998804i	$-0.484428\pi$
$839$	787.270	−	454.531i	0.938343	−	0.541753i	0.889441	+	0.457051i	$0.151094\pi$
$840$		0			0
$841$	−106.581	+	184.604i	−0.126731	+	0.219505i
$842$	−164.360	+	284.680i	−0.195202	+	0.338099i
$843$	505.438	+	344.177i	0.599570	+	0.408276i
$844$	−85.5412	−	148.162i	−0.101352	−	0.175547i
$845$			174.289i			0.206259i
$846$	−625.833	+	246.451i	−0.739756	+	0.291314i
$847$		0			0
$848$	−540.712	−	936.540i	−0.637632	−	1.10441i
$849$	−360.382	−	26.7987i	−0.424478	−	0.0315651i
$850$	571.669	+	330.053i	0.672552	+	0.388298i
$851$	58.0295	−	100.510i	0.0681898	−	0.118108i
$852$	101.236	−	1361.39i	0.118821	−	1.59787i
$853$	−768.763	+	443.845i	−0.901246	+	0.520335i	−0.877604	−	0.479386i	$-0.840859\pi$
$853$	−768.763	+	443.845i	−0.901246	+	0.520335i	−0.0236417	+	0.999720i	$0.507526\pi$
$854$		0			0
$855$	126.566	+	321.399i	0.148030	+	0.375905i
$856$	−6.77833			−0.00791861
$857$	−151.668	+	87.5656i	−0.176976	+	0.102177i	−0.585871	−	0.810404i	$-0.699247\pi$
$857$	−151.668	+	87.5656i	−0.176976	+	0.102177i	0.408895	+	0.912581i	$0.365914\pi$
$858$	847.331	−	1244.34i	0.987565	−	1.45028i
$859$	−1192.54	−	688.515i	−1.38829	−	0.801531i	−0.395170	−	0.918608i	$-0.629314\pi$
$859$	−1192.54	−	688.515i	−1.38829	−	0.801531i	−0.993123	+	0.117077i	$0.962648\pi$
$860$	371.980	+	214.763i	0.432535	+	0.249724i
$861$		0			0
$862$	−456.983	−	791.518i	−0.530143	−	0.918235i
$863$	1522.75			1.76448			0.882241	−	0.470799i	$-0.156034\pi$
$863$	1522.75			1.76448			0.882241	+	0.470799i	$0.156034\pi$
$864$	898.827	+	831.112i	1.04031	+	0.961935i
$865$	211.104			0.244050
$866$	−287.924	+	166.233i	−0.332475	+	0.191955i
$867$	385.163	−	185.757i	0.444248	−	0.214253i
$868$		0			0
$869$	−779.616	+	1350.33i	−0.897141	+	1.55389i
$870$	−372.652	+	547.255i	−0.428335	+	0.629028i
$871$	1102.20	−	636.358i	1.26545	−	0.730606i
$872$	2.22955			0.00255682
$873$	−148.480	+	992.836i	−0.170080	+	1.13727i
$874$			728.121i			0.833091i
$875$		0			0
$876$	−818.934	−	60.8977i	−0.934856	−	0.0695179i
$877$	359.527	−	622.719i	0.409951	−	0.710056i	−0.584933	−	0.811082i	$-0.698879\pi$
$877$	359.527	−	622.719i	0.409951	−	0.710056i	0.994884	+	0.101026i	$0.0322124\pi$
$878$	−532.180	−	307.254i	−0.606128	−	0.349948i
$879$	−524.014	−	38.9668i	−0.596148	−	0.0443309i
$880$	375.590	−	216.847i	0.426807	−	0.246417i
$881$		−	1065.56i		−	1.20949i	−0.796418	−	0.604747i	$-0.793274\pi$
$881$		−	1065.56i		−	1.20949i	0.796418	−	0.604747i	$-0.206726\pi$
$882$		0			0
$883$	−378.403			−0.428543			−0.214271	−	0.976774i	$-0.568738\pi$
$883$	−378.403			−0.428543			−0.214271	+	0.976774i	$0.568738\pi$
$884$	−379.205	−	656.802i	−0.428965	−	0.742989i
$885$	565.974	+	385.398i	0.639518	+	0.435478i
$886$	−212.180	+	367.506i	−0.239481	+	0.414793i
$887$	−1522.62	−	879.087i	−1.71660	−	0.991079i	−0.924938	−	0.380118i	$-0.875883\pi$
$887$	−1522.62	−	879.087i	−1.71660	−	0.991079i	−0.791661	−	0.610960i	$-0.790783\pi$
$888$	−1.72824	+	0.833501i	−0.00194622	+	0.000938627i
$889$		0			0
$890$	737.050			0.828146
$891$	−674.897	+	629.104i	−0.757460	+	0.706065i
$892$		−	773.693i		−	0.867368i
$893$	−210.989	−	365.443i	−0.236270	−	0.409231i
$894$	−860.826	+	415.161i	−0.962893	+	0.464386i
$895$	26.9040	+	15.5331i	0.0300604	+	0.0173554i
$896$		0			0
$897$	421.474	−	618.952i	0.469871	−	0.690025i
$898$	−373.750	−	647.355i	−0.416203	−	0.720885i
$899$		−	1376.63i		−	1.53129i
$900$	434.755	−	546.452i	0.483061	−	0.607169i
$901$		−	824.454i		−	0.915044i
$902$	244.035	−	140.894i	0.270549	−	0.156202i
$903$		0			0
$904$	−3.28055	+	5.68209i	−0.00362893	+	0.00628549i
$905$	270.859	−	469.141i	0.299291	−	0.518388i
$906$	17.7774	−	239.065i	0.0196218	−	0.263868i
$907$	−371.175	−	642.893i	−0.409233	−	0.708813i	0.585571	−	0.810621i	$-0.300870\pi$
$907$	−371.175	−	642.893i	−0.409233	−	0.708813i	−0.994804	+	0.101808i	$0.967537\pi$
$908$		−	906.135i		−	0.997946i
$909$	102.316	−	684.155i	0.112559	−	0.752646i
$910$		0			0
$911$	394.703	+	683.645i	0.433263	+	0.750434i	0.997152	−	0.0754169i	$-0.0240288\pi$
$911$	394.703	+	683.645i	0.433263	+	0.750434i	−0.563889	+	0.825851i	$0.690695\pi$
$912$	−428.903	+	629.862i	−0.470288	+	0.690638i
$913$	214.911	+	124.079i	0.235390	+	0.135902i
$914$	−310.023	+	536.975i	−0.339193	+	0.587500i
$915$	−320.449	+	154.547i	−0.350217	+	0.168904i
$916$	−559.101	+	322.797i	−0.610372	+	0.352398i
$917$		0			0
$918$	274.470	+	884.398i	0.298987	+	0.963396i
$919$	−427.558			−0.465243			−0.232621	−	0.972567i	$-0.574730\pi$
$919$	−427.558			−0.465243			−0.232621	+	0.972567i	$0.574730\pi$
$920$	−2.95122	+	1.70389i	−0.00320785	+	0.00185205i
$921$	23.9353	+	49.6293i	0.0259884	+	0.0538863i
$922$	−949.064	−	547.942i	−1.02935	−	0.594297i
$923$	−1519.70	−	877.398i	−1.64648	−	0.950594i
$924$		0			0
$925$	−69.5596	−	120.481i	−0.0751996	−	0.130250i
$926$	1370.95			1.48051
$927$	−1262.65	+	497.229i	−1.36208	+	0.536385i
$928$	−1472.10			−1.58632
$929$	−978.107	+	564.711i	−1.05286	+	0.607869i	−0.923449	−	0.383722i	$-0.874642\pi$
$929$	−978.107	+	564.711i	−1.05286	+	0.607869i	−0.129412	+	0.991591i	$0.541309\pi$
$930$	64.1179	−	862.238i	0.0689440	−	0.927138i
$931$		0			0
$932$	497.045	−	860.908i	0.533310	−	0.923721i
$933$	1220.13	+	90.7313i	1.30775	+	0.0972469i
$934$	−283.514	+	163.687i	−0.303548	+	0.175253i
$935$	330.639			0.353625
$936$	−11.5189	+	4.53612i	−0.0123066	+	0.00484629i
$937$		−	736.130i		−	0.785625i	−0.919619	−	0.392812i	$-0.871502\pi$
$937$		−	736.130i		−	0.785625i	0.919619	−	0.392812i	$-0.128498\pi$
$938$		0			0
$939$	−680.056	+	998.691i	−0.724234	+	1.06357i
$940$	127.493	−	220.824i	0.135631	−	0.234919i
$941$	75.0157	+	43.3103i	0.0797191	+	0.0460259i	0.539330	−	0.842095i	$-0.318678\pi$
$941$	75.0157	+	43.3103i	0.0797191	+	0.0460259i	−0.459611	+	0.888121i	$0.652011\pi$
$942$	−37.8575	−	78.4965i	−0.0401884	−	0.0833296i
$943$	121.386	−	70.0825i	0.128724	−	0.0743187i
$944$			1510.57i			1.60018i
$945$		0			0
$946$	−1433.97			−1.51582
$947$	−293.684	−	508.676i	−0.310121	−	0.537145i	0.668268	−	0.743921i	$-0.267036\pi$
$947$	−293.684	−	508.676i	−0.310121	−	0.537145i	−0.978388	+	0.206776i	$0.933703\pi$
$948$	1491.12	−	719.141i	1.57291	−	0.758588i
$949$	−527.794	+	914.166i	−0.556158	+	0.963294i
$950$	755.862	+	436.397i	0.795645	+	0.459366i
$951$	735.343	+	500.730i	0.773232	+	0.526530i
$952$		0			0
$953$	−396.549			−0.416106			−0.208053	−	0.978118i	$-0.566713\pi$
$953$	−396.549			−0.416106			−0.208053	+	0.978118i	$0.566713\pi$
$954$	−1718.45	−	256.996i	−1.80131	−	0.269388i
$955$		−	249.186i		−	0.260928i
$956$	−444.001	−	769.033i	−0.464436	−	0.804427i
$957$	82.2763	−	1106.43i	0.0859732	−	1.15614i
$958$	1118.28	+	645.638i	1.16730	+	0.673944i
$959$		0			0
$960$	−466.394	−	34.6821i	−0.485828	−	0.0361272i
$961$	418.375	+	724.646i	0.435353	+	0.754054i
$962$			318.436i			0.331014i
$963$	429.239	−	539.519i	0.445731	−	0.560248i
$964$			1062.62i			1.10230i
$965$	−337.217	+	194.693i	−0.349448	+	0.201754i
$966$		0			0
$967$	−163.959	+	283.985i	−0.169554	+	0.293676i	−0.938263	−	0.345922i	$-0.887566\pi$
$967$	−163.959	+	283.985i	−0.169554	+	0.293676i	0.768709	+	0.639598i	$0.220899\pi$
$968$	0.386903	−	0.670135i	0.000399693	−	0.000692288i
$969$	−523.276	+	252.367i	−0.540016	+	0.260440i
$970$	−379.094	−	656.611i	−0.390819	−	0.676918i
$971$		−	1039.52i		−	1.07057i	−0.844673	−	0.535283i	$-0.820205\pi$
$971$		−	1039.52i		−	1.07057i	0.844673	−	0.535283i	$-0.179795\pi$
$972$	968.223	−	148.781i	0.996114	−	0.153067i
$973$		0			0
$974$	460.046	+	796.823i	0.472326	+	0.818093i
$975$	−389.925	−	808.499i	−0.399923	−	0.829230i
$976$	−679.705	−	392.428i	−0.696419	−	0.402078i
$977$	−743.417	+	1287.64i	−0.760918	+	1.31795i	0.181460	+	0.983398i	$0.441918\pi$
$977$	−743.417	+	1287.64i	−0.760918	+	1.31795i	−0.942378	+	0.334550i	$0.891416\pi$
$978$	−1248.62	−	850.247i	−1.27671	−	0.869373i
$979$	−1069.63	+	617.552i	−1.09258	+	0.630799i
$980$		0			0
$981$	−141.187	+	177.460i	−0.143921	+	0.180897i
$982$	−879.774			−0.895900
$983$	−958.645	+	553.474i	−0.975223	+	0.563045i	−0.900825	−	0.434183i	$-0.857037\pi$
$983$	−958.645	+	553.474i	−0.975223	+	0.563045i	−0.0743987	+	0.997229i	$0.523704\pi$
$984$	−2.31088	−	0.171842i	−0.00234846	−	0.000174637i
$985$	626.474	+	361.695i	0.636014	+	0.367203i
$986$	−964.353	−	556.769i	−0.978046	−	0.564675i
$987$		0			0
$988$	−501.386	−	868.425i	−0.507475	−	0.878973i
$989$	−713.277			−0.721210
$990$	103.066	−	689.166i	0.104107	−	0.696127i
$991$	1087.01			1.09688			0.548439	−	0.836191i	$-0.315222\pi$
$991$	1087.01			1.09688			0.548439	+	0.836191i	$0.315222\pi$
$992$	1664.87	−	961.211i	1.67829	−	0.968963i
$993$	−1321.57	−	899.920i	−1.33089	−	0.906264i
$994$		0			0
$995$	−69.3191	+	120.064i	−0.0696675	+	0.120668i
$996$	−114.454	−	237.318i	−0.114914	−	0.238271i
$997$	−716.543	+	413.696i	−0.718699	+	0.414941i	−0.814274	−	0.580481i	$-0.802864\pi$
$997$	−716.543	+	413.696i	−0.718699	+	0.414941i	0.0955746	+	0.995422i	$0.469531\pi$
$998$	2194.09			2.19849
$999$	43.0991	−	190.341i	0.0431422	−	0.190531i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.l.b.391.12		28
7.2	even	3		441.3.k.b.31.12		28
7.3	odd	6		441.3.t.a.166.3		28
7.4	even	3		63.3.t.a.40.3	yes	28
7.5	odd	6		63.3.k.a.31.12	✓	28
7.6	odd	2		441.3.l.a.391.12		28
9.7	even	3		441.3.l.a.97.12		28
21.5	even	6		189.3.k.a.10.3		28
21.11	odd	6		189.3.t.a.145.12		28
63.11	odd	6		189.3.k.a.19.3		28
63.16	even	3		441.3.t.a.178.3		28
63.25	even	3		63.3.k.a.61.12	yes	28
63.34	odd	6	inner	441.3.l.b.97.12		28
63.47	even	6		189.3.t.a.73.12		28
63.52	odd	6		441.3.k.b.313.12		28
63.61	odd	6		63.3.t.a.52.3	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.12	✓	28	7.5	odd	6
63.3.k.a.61.12	yes	28	63.25	even	3
63.3.t.a.40.3	yes	28	7.4	even	3
63.3.t.a.52.3	yes	28	63.61	odd	6
189.3.k.a.10.3		28	21.5	even	6
189.3.k.a.19.3		28	63.11	odd	6
189.3.t.a.73.12		28	63.47	even	6
189.3.t.a.145.12		28	21.11	odd	6
441.3.k.b.31.12		28	7.2	even	3
441.3.k.b.313.12		28	63.52	odd	6
441.3.l.a.97.12		28	9.7	even	3
441.3.l.a.391.12		28	7.6	odd	2
441.3.l.b.97.12		28	63.34	odd	6	inner
441.3.l.b.391.12		28	1.1	even	1	trivial
441.3.t.a.166.3		28	7.3	odd	6
441.3.t.a.178.3		28	63.16	even	3

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41697 + 2.45427i) q^{2} +(2.70216 - 1.30320i) q^{3} +(-2.01561 + 3.49114i) q^{4} +(2.07720 + 1.19927i) q^{5} +(7.02729 + 4.78521i) q^{6} -0.0884848 q^{8} +(5.60332 - 7.04292i) q^{9} +O(q^{10})\)	\(q+(1.41697 + 2.45427i) q^{2} +(2.70216 - 1.30320i) q^{3} +(-2.01561 + 3.49114i) q^{4} +(2.07720 + 1.19927i) q^{5} +(7.02729 + 4.78521i) q^{6} -0.0884848 q^{8} +(5.60332 - 7.04292i) q^{9} +6.79734i q^{10} +(-5.69528 - 9.86452i) q^{11} +(-0.896835 + 12.0604i) q^{12} +(13.4628 + 7.77278i) q^{13} +(7.17583 + 0.533610i) q^{15} +(7.93707 + 13.7474i) q^{16} +12.1021i q^{17} +(25.2249 + 3.77242i) q^{18} +16.0014i q^{19} +(-8.37367 + 4.83454i) q^{20} +(16.1401 - 27.9555i) q^{22} +(8.02831 - 13.9054i) q^{23} +(-0.239100 + 0.115314i) q^{24} +(-9.62349 - 16.6684i) q^{25} +44.0552i q^{26} +(5.96270 - 26.3334i) q^{27} +(16.2339 + 28.1180i) q^{29} +(8.85832 + 18.3675i) q^{30} +(-36.7194 - 21.1999i) q^{31} +(-22.6701 + 39.2658i) q^{32} +(-28.2450 - 19.2334i) q^{33} +(-29.7018 + 17.1483i) q^{34} +(13.2937 + 33.7578i) q^{36} +7.22811 q^{37} +(-39.2718 + 22.6736i) q^{38} +(46.5083 + 3.45845i) q^{39} +(-0.183801 - 0.106117i) q^{40} +(7.55990 + 4.36471i) q^{41} +(-22.2113 - 38.4711i) q^{43} +45.9179 q^{44} +(20.0856 - 7.90966i) q^{45} +45.5035 q^{46} +(-22.8382 + 13.1856i) q^{47} +(39.3629 + 26.8040i) q^{48} +(27.2724 - 47.2372i) q^{50} +(15.7715 + 32.7018i) q^{51} +(-54.2717 + 31.3338i) q^{52} -68.1249 q^{53} +(73.0780 - 22.6795i) q^{54} -27.3208i q^{55} +(20.8531 + 43.2384i) q^{57} +(-46.0060 + 79.6847i) q^{58} +(82.4104 + 47.5797i) q^{59} +(-16.3266 + 23.9763i) q^{60} +(-42.8184 + 24.7212i) q^{61} -120.159i q^{62} -64.9952 q^{64} +(18.6434 + 32.2913i) q^{65} +(7.18145 - 96.5740i) q^{66} +(40.9350 - 70.9015i) q^{67} +(-42.2502 - 24.3931i) q^{68} +(3.57215 - 48.0372i) q^{69} -112.881 q^{71} +(-0.495809 + 0.623192i) q^{72} +67.9029i q^{73} +(10.2420 + 17.7397i) q^{74} +(-47.7265 - 32.4992i) q^{75} +(-55.8633 - 32.2527i) q^{76} +(57.4129 + 119.044i) q^{78} +(-68.4439 - 118.548i) q^{79} +38.0748i q^{80} +(-18.2056 - 78.9275i) q^{81} +24.7387i q^{82} +(-18.8674 + 10.8931i) q^{83} +(-14.5137 + 25.1385i) q^{85} +(62.9455 - 109.025i) q^{86} +(80.5101 + 54.8232i) q^{87} +(0.503946 + 0.872861i) q^{88} -108.432i q^{89} +(47.8732 + 38.0877i) q^{90} +(32.3639 + 56.0559i) q^{92} +(-126.849 - 9.43279i) q^{93} +(-64.7220 - 37.3673i) q^{94} +(-19.1901 + 33.2382i) q^{95} +(-10.0870 + 135.646i) q^{96} +(-96.5982 + 55.7710i) q^{97} +(-101.388 - 15.1626i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} - 23 q^{4} + 3 q^{5} - 12 q^{6} - 16 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q + q^2 - 23 * q^4 + 3 * q^5 - 12 * q^6 - 16 * q^8 + 6 * q^9	\( 28 q + q^{2} - 23 q^{4} + 3 q^{5} - 12 q^{6} - 16 q^{8} + 6 q^{9} + 7 q^{11} + 27 q^{12} - 15 q^{13} - 18 q^{15} - 27 q^{16} + 9 q^{18} - 108 q^{20} - 10 q^{22} + 34 q^{23} + 120 q^{24} + 31 q^{25} + 81 q^{27} + 70 q^{29} + 33 q^{30} + 45 q^{31} + 153 q^{32} - 111 q^{33} - 12 q^{34} - 174 q^{36} - 18 q^{37} - 87 q^{38} - 9 q^{39} + 102 q^{40} + 234 q^{41} + 30 q^{43} - 102 q^{44} + 3 q^{45} + 44 q^{46} - 111 q^{47} - 147 q^{48} + 241 q^{50} - 6 q^{51} + 219 q^{52} - 296 q^{53} + 207 q^{54} + 189 q^{57} + 17 q^{58} + 42 q^{59} - 489 q^{60} + 120 q^{61} - 48 q^{64} + 114 q^{65} - 705 q^{66} - 34 q^{67} + 18 q^{68} - 78 q^{69} - 350 q^{71} + 177 q^{72} + 359 q^{74} + 387 q^{75} - 72 q^{76} - 375 q^{78} - 82 q^{79} + 438 q^{81} - 738 q^{83} + 3 q^{85} + 17 q^{86} + 564 q^{87} + 25 q^{88} + 543 q^{90} + 288 q^{92} - 30 q^{93} - 3 q^{94} + 507 q^{95} - 813 q^{96} + 57 q^{97} - 162 q^{99}+O(q^{100}) \) 28 * q + q^2 - 23 * q^4 + 3 * q^5 - 12 * q^6 - 16 * q^8 + 6 * q^9 + 7 * q^11 + 27 * q^12 - 15 * q^13 - 18 * q^15 - 27 * q^16 + 9 * q^18 - 108 * q^20 - 10 * q^22 + 34 * q^23 + 120 * q^24 + 31 * q^25 + 81 * q^27 + 70 * q^29 + 33 * q^30 + 45 * q^31 + 153 * q^32 - 111 * q^33 - 12 * q^34 - 174 * q^36 - 18 * q^37 - 87 * q^38 - 9 * q^39 + 102 * q^40 + 234 * q^41 + 30 * q^43 - 102 * q^44 + 3 * q^45 + 44 * q^46 - 111 * q^47 - 147 * q^48 + 241 * q^50 - 6 * q^51 + 219 * q^52 - 296 * q^53 + 207 * q^54 + 189 * q^57 + 17 * q^58 + 42 * q^59 - 489 * q^60 + 120 * q^61 - 48 * q^64 + 114 * q^65 - 705 * q^66 - 34 * q^67 + 18 * q^68 - 78 * q^69 - 350 * q^71 + 177 * q^72 + 359 * q^74 + 387 * q^75 - 72 * q^76 - 375 * q^78 - 82 * q^79 + 438 * q^81 - 738 * q^83 + 3 * q^85 + 17 * q^86 + 564 * q^87 + 25 * q^88 + 543 * q^90 + 288 * q^92 - 30 * q^93 - 3 * q^94 + 507 * q^95 - 813 * q^96 + 57 * q^97 - 162 * q^99

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