LMFDB - Embedded newform 147.3.h.e.128.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,3,Mod(116,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("147.116");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	147.h (of order $6$, degree $2$, not 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:	$4.00545988610$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.39033114624.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 6x^{6} - 30x^{5} + 34x^{4} - 102x^{3} + 486x^{2} - 730x + 373 $ x^8 - 2x^7 + 6x^6 - 30x^5 + 34x^4 - 102x^3 + 486x^2 - 730*x + 373
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			128.2
Root			$-1.85391 - 1.90397i$ of defining polynomial
Character	$\chi$	$=$	147.128
Dual form			147.3.h.e.116.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13198 - 0.653548i) q^{2} +(2.97489 + 0.387321i) q^{3} +(-1.14575 - 1.98450i) q^{4} +(6.39086 + 3.68977i) q^{5} +(-3.11438 - 2.38267i) q^{6} +8.22359i q^{8} +(8.69997 + 2.30448i) q^{9} +O(q^{10})$	\(q+(-1.13198 - 0.653548i) q^{2} +(2.97489 + 0.387321i) q^{3} +(-1.14575 - 1.98450i) q^{4} +(6.39086 + 3.68977i) q^{5} +(-3.11438 - 2.38267i) q^{6} +8.22359i q^{8} +(8.69997 + 2.30448i) q^{9} +(-4.82288 - 8.35347i) q^{10} +(2.26395 - 1.30710i) q^{11} +(-2.63985 - 6.34745i) q^{12} -6.35425 q^{13} +(17.5830 + 13.4520i) q^{15} +(0.791503 - 1.37092i) q^{16} +(10.5178 - 6.07244i) q^{17} +(-8.34208 - 8.29445i) q^{18} +(5.11438 - 8.85836i) q^{19} -16.9102i q^{20} -3.41699 q^{22} +(3.72591 + 2.15115i) q^{23} +(-3.18517 + 24.4643i) q^{24} +(14.7288 + 25.5110i) q^{25} +(7.19287 + 4.15280i) q^{26} +(24.9889 + 10.2252i) q^{27} -17.3733i q^{29} +(-11.1121 - 26.7187i) q^{30} +(-19.6458 - 34.0274i) q^{31} +(26.6954 - 15.4126i) q^{32} +(7.24129 - 3.01159i) q^{33} -15.8745 q^{34} +(-5.39477 - 19.9054i) q^{36} +(-20.5203 + 35.5421i) q^{37} +(-11.5787 + 6.68498i) q^{38} +(-18.9032 - 2.46113i) q^{39} +(-30.3431 + 52.5559i) q^{40} +30.2802i q^{41} -55.8745 q^{43} +(-5.18786 - 2.99521i) q^{44} +(47.0973 + 46.8284i) q^{45} +(-2.81176 - 4.87011i) q^{46} +(-34.6193 - 19.9874i) q^{47} +(2.88562 - 3.77178i) q^{48} -38.5038i q^{50} +(33.6412 - 13.9911i) q^{51} +(7.28039 + 12.6100i) q^{52} +(-90.9340 + 52.5008i) q^{53} +(-21.6042 - 27.9062i) q^{54} +19.2915 q^{55} +(18.6458 - 24.3718i) q^{57} +(-11.3542 + 19.6661i) q^{58} +(-35.8223 + 20.6820i) q^{59} +(6.54968 - 50.3061i) q^{60} +(10.2399 - 17.7360i) q^{61} +51.3577i q^{62} -46.6235 q^{64} +(-40.6091 - 23.4457i) q^{65} +(-10.1652 - 1.32347i) q^{66} +(13.5830 + 23.5265i) q^{67} +(-24.1015 - 13.9150i) q^{68} +(10.2510 + 7.84257i) q^{69} +67.8049i q^{71} +(-18.9511 + 71.5450i) q^{72} +(-30.3948 - 52.6453i) q^{73} +(46.4569 - 26.8219i) q^{74} +(33.9355 + 81.5971i) q^{75} -23.4392 q^{76} +(19.7895 + 15.1401i) q^{78} +(31.6235 - 54.7735i) q^{79} +(10.1168 - 5.84092i) q^{80} +(70.3788 + 40.0977i) q^{81} +(19.7895 - 34.2765i) q^{82} -89.9435i q^{83} +89.6235 q^{85} +(63.2487 + 36.5166i) q^{86} +(6.72902 - 51.6836i) q^{87} +(10.7490 + 18.6178i) q^{88} +(54.7108 + 31.5873i) q^{89} +(-22.7085 - 83.7891i) q^{90} -9.85875i q^{92} +(-45.2645 - 108.837i) q^{93} +(26.1255 + 45.2507i) q^{94} +(65.3706 - 37.7417i) q^{95} +(85.3857 - 35.5112i) q^{96} +19.1660 q^{97} +(22.7085 - 6.15445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 12 q^{4} + 28 q^{6} + 20 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 + 12 * q^4 + 28 * q^6 + 20 * q^9	$ 8 q + 2 q^{3} + 12 q^{4} + 28 q^{6} + 20 q^{9} - 28 q^{10} + 22 q^{12} - 72 q^{13} + 56 q^{15} - 36 q^{16} - 56 q^{18} - 12 q^{19} - 112 q^{22} + 126 q^{24} + 12 q^{25} + 20 q^{27} + 28 q^{30} - 136 q^{31} - 28 q^{33} + 232 q^{36} - 16 q^{37} - 4 q^{39} - 84 q^{40} - 320 q^{43} + 140 q^{45} + 168 q^{46} + 76 q^{48} + 84 q^{51} - 164 q^{52} + 154 q^{54} + 112 q^{55} + 128 q^{57} - 112 q^{58} - 140 q^{60} + 156 q^{61} + 8 q^{64} + 28 q^{66} + 24 q^{67} + 336 q^{69} + 32 q^{73} - 146 q^{75} - 632 q^{76} - 392 q^{78} - 128 q^{79} + 68 q^{81} - 392 q^{82} + 336 q^{85} - 28 q^{87} - 168 q^{88} - 224 q^{90} + 96 q^{93} + 336 q^{94} + 98 q^{96} - 16 q^{97} + 224 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 12 * q^4 + 28 * q^6 + 20 * q^9 - 28 * q^10 + 22 * q^12 - 72 * q^13 + 56 * q^15 - 36 * q^16 - 56 * q^18 - 12 * q^19 - 112 * q^22 + 126 * q^24 + 12 * q^25 + 20 * q^27 + 28 * q^30 - 136 * q^31 - 28 * q^33 + 232 * q^36 - 16 * q^37 - 4 * q^39 - 84 * q^40 - 320 * q^43 + 140 * q^45 + 168 * q^46 + 76 * q^48 + 84 * q^51 - 164 * q^52 + 154 * q^54 + 112 * q^55 + 128 * q^57 - 112 * q^58 - 140 * q^60 + 156 * q^61 + 8 * q^64 + 28 * q^66 + 24 * q^67 + 336 * q^69 + 32 * q^73 - 146 * q^75 - 632 * q^76 - 392 * q^78 - 128 * q^79 + 68 * q^81 - 392 * q^82 + 336 * q^85 - 28 * q^87 - 168 * q^88 - 224 * q^90 + 96 * q^93 + 336 * q^94 + 98 * q^96 - 16 * q^97 + 224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.13198	−	0.653548i	−0.565989	−	0.326774i	0.189557	−	0.981870i	$-0.439295\pi$
$2$	−1.13198	−	0.653548i	−0.565989	−	0.326774i	−0.755546	+	0.655096i	$0.772628\pi$
$3$	2.97489	+	0.387321i	0.991631	+	0.129107i
$3$	2.97489	+	0.387321i	0.991631	+	0.129107i
$4$	−1.14575	−	1.98450i	−0.286438	−	0.496125i
$5$	6.39086	+	3.68977i	1.27817	+	0.737953i	0.976512	−	0.215462i	$-0.0691258\pi$
$5$	6.39086	+	3.68977i	1.27817	+	0.737953i	0.301660	+	0.953415i	$0.402459\pi$
$6$	−3.11438	−	2.38267i	−0.519063	−	0.397112i
$7$		0			0
$7$		0			0
$8$			8.22359i			1.02795i
$9$	8.69997	+	2.30448i	0.966663	+	0.256053i
$10$	−4.82288	−	8.35347i	−0.482288	−	0.835347i
$11$	2.26395	−	1.30710i	0.205814	−	0.118827i	−0.393550	−	0.919303i	$-0.628753\pi$
$11$	2.26395	−	1.30710i	0.205814	−	0.118827i	0.599365	+	0.800476i	$0.295420\pi$
$12$	−2.63985	−	6.34745i	−0.219987	−	0.528954i
$13$	−6.35425			−0.488788			−0.244394	−	0.969676i	$-0.578589\pi$
$13$	−6.35425			−0.488788			−0.244394	+	0.969676i	$0.578589\pi$
$14$		0			0
$15$	17.5830	+	13.4520i	1.17220	+	0.896798i
$16$	0.791503	−	1.37092i	0.0494689	−	0.0856827i
$17$	10.5178	−	6.07244i	0.618692	−	0.357202i	−0.157667	−	0.987492i	$-0.550397\pi$
$17$	10.5178	−	6.07244i	0.618692	−	0.357202i	0.776360	+	0.630290i	$0.217064\pi$
$18$	−8.34208	−	8.29445i	−0.463449	−	0.460803i
$19$	5.11438	−	8.85836i	0.269178	−	0.466230i	−0.699472	−	0.714660i	$-0.746581\pi$
$19$	5.11438	−	8.85836i	0.269178	−	0.466230i	0.968650	+	0.248430i	$0.0799147\pi$
$20$		−	16.9102i		−	0.845511i
$21$		0			0
$22$	−3.41699			−0.155318
$23$	3.72591	+	2.15115i	0.161996	+	0.0935284i	0.578806	−	0.815465i	$-0.303519\pi$
$23$	3.72591	+	2.15115i	0.161996	+	0.0935284i	−0.416810	+	0.908993i	$0.636852\pi$
$24$	−3.18517	+	24.4643i	−0.132715	+	1.01935i
$25$	14.7288	+	25.5110i	0.589150	+	1.02044i
$26$	7.19287	+	4.15280i	0.276649	+	0.159723i
$27$	24.9889	+	10.2252i	0.925514	+	0.378713i
$28$		0			0
$29$		−	17.3733i		−	0.599078i	−0.954084	−	0.299539i	$-0.903167\pi$
$29$		−	17.3733i		−	0.599078i	0.954084	−	0.299539i	$-0.0968328\pi$
$30$	−11.1121	−	26.7187i	−0.370402	−	0.890622i
$31$	−19.6458	−	34.0274i	−0.633734	−	1.09766i	−0.986782	−	0.162054i	$-0.948188\pi$
$31$	−19.6458	−	34.0274i	−0.633734	−	1.09766i	0.353048	−	0.935605i	$-0.385145\pi$
$32$	26.6954	−	15.4126i	0.834232	−	0.481644i
$33$	7.24129	−	3.01159i	0.219433	−	0.0912603i
$34$	−15.8745			−0.466897
$35$		0			0
$36$	−5.39477	−	19.9054i	−0.149855	−	0.552929i
$37$	−20.5203	+	35.5421i	−0.554602	+	0.960598i	0.443333	+	0.896357i	$0.353796\pi$
$37$	−20.5203	+	35.5421i	−0.554602	+	0.960598i	−0.997934	+	0.0642411i	$0.979537\pi$
$38$	−11.5787	+	6.68498i	−0.304703	+	0.175920i
$39$	−18.9032	−	2.46113i	−0.484698	−	0.0631060i
$40$	−30.3431	+	52.5559i	−0.758578	+	1.31390i
$41$			30.2802i			0.738541i	0.929322	+	0.369270i	$0.120392\pi$
$41$			30.2802i			0.738541i	−0.929322	+	0.369270i	$0.879608\pi$
$42$		0			0
$43$	−55.8745			−1.29941			−0.649704	−	0.760188i	$-0.725107\pi$
$43$	−55.8745			−1.29941			−0.649704	+	0.760188i	$0.725107\pi$
$44$	−5.18786	−	2.99521i	−0.117906	−	0.0680730i
$45$	47.0973	+	46.8284i	1.04661	+	1.04063i
$46$	−2.81176	−	4.87011i	−0.0611253	−	0.105872i
$47$	−34.6193	−	19.9874i	−0.736580	−	0.425265i	0.0842443	−	0.996445i	$-0.473152\pi$
$47$	−34.6193	−	19.9874i	−0.736580	−	0.425265i	−0.820825	+	0.571180i	$0.806486\pi$
$48$	2.88562	−	3.77178i	0.0601171	−	0.0785788i
$49$		0			0
$50$		−	38.5038i		−	0.770075i
$51$	33.6412	−	13.9911i	0.659632	−	0.274335i
$52$	7.28039	+	12.6100i	0.140007	+	0.242500i
$53$	−90.9340	+	52.5008i	−1.71574	+	0.990581i	−0.789404	+	0.613874i	$0.789610\pi$
$53$	−90.9340	+	52.5008i	−1.71574	+	0.990581i	−0.926332	+	0.376707i	$0.877056\pi$
$54$	−21.6042	−	27.9062i	−0.400077	−	0.516781i
$55$	19.2915			0.350755
$56$		0			0
$57$	18.6458	−	24.3718i	0.327118	−	0.427575i
$58$	−11.3542	+	19.6661i	−0.195763	+	0.339071i
$59$	−35.8223	+	20.6820i	−0.607157	+	0.350542i	−0.771852	−	0.635802i	$-0.780669\pi$
$59$	−35.8223	+	20.6820i	−0.607157	+	0.350542i	0.164695	+	0.986345i	$0.447336\pi$
$60$	6.54968	−	50.3061i	0.109161	−	0.838435i
$61$	10.2399	−	17.7360i	0.167867	−	0.290754i	−0.769803	−	0.638282i	$-0.779646\pi$
$61$	10.2399	−	17.7360i	0.167867	−	0.290754i	0.937670	+	0.347528i	$0.112979\pi$
$62$			51.3577i			0.828350i
$63$		0			0
$64$	−46.6235			−0.728493
$65$	−40.6091	−	23.4457i	−0.624756	−	0.360703i
$66$	−10.1652	−	1.32347i	−0.154018	−	0.0200526i
$67$	13.5830	+	23.5265i	0.202731	+	0.351141i	0.949408	−	0.314047i	$-0.101685\pi$
$67$	13.5830	+	23.5265i	0.202731	+	0.351141i	−0.746676	+	0.665188i	$0.768351\pi$
$68$	−24.1015	−	13.9150i	−0.354434	−	0.204632i
$69$	10.2510	+	7.84257i	0.148565	+	0.113660i
$70$		0			0
$71$			67.8049i			0.954999i	0.878632	+	0.477499i	$0.158457\pi$
$71$			67.8049i			0.954999i	−0.878632	+	0.477499i	$0.841543\pi$
$72$	−18.9511	+	71.5450i	−0.263209	+	0.993680i
$73$	−30.3948	−	52.6453i	−0.416367	−	0.721168i	0.579204	−	0.815183i	$-0.303363\pi$
$73$	−30.3948	−	52.6453i	−0.416367	−	0.721168i	−0.995571	+	0.0940143i	$0.970030\pi$
$74$	46.4569	−	26.8219i	0.627797	−	0.362458i
$75$	33.9355	+	81.5971i	0.452474	+	1.08796i
$76$	−23.4392			−0.308411
$77$		0			0
$78$	19.7895	+	15.1401i	0.253712	+	0.194104i
$79$	31.6235	−	54.7735i	0.400298	−	0.693336i	−0.593464	−	0.804861i	$-0.702240\pi$
$79$	31.6235	−	54.7735i	0.400298	−	0.693336i	0.993762	+	0.111525i	$0.0355734\pi$
$80$	10.1168	−	5.84092i	0.126460	−	0.0730115i
$81$	70.3788	+	40.0977i	0.868874	+	0.495033i
$82$	19.7895	−	34.2765i	0.241336	−	0.418006i
$83$		−	89.9435i		−	1.08366i	−0.840489	−	0.541828i	$-0.817732\pi$
$83$		−	89.9435i		−	1.08366i	0.840489	−	0.541828i	$-0.182268\pi$
$84$		0			0
$85$	89.6235			1.05439
$86$	63.2487	+	36.5166i	0.735450	+	0.424612i
$87$	6.72902	−	51.6836i	0.0773451	−	0.594064i
$88$	10.7490	+	18.6178i	0.122148	+	0.211566i
$89$	54.7108	+	31.5873i	0.614728	+	0.354913i	0.774813	−	0.632190i	$-0.217844\pi$
$89$	54.7108	+	31.5873i	0.614728	+	0.354913i	−0.160086	+	0.987103i	$0.551177\pi$
$90$	−22.7085	−	83.7891i	−0.252317	−	0.930990i
$91$		0			0
$92$		−	9.85875i		−	0.107160i
$93$	−45.2645	−	108.837i	−0.486715	−	1.17029i
$94$	26.1255	+	45.2507i	0.277931	+	0.481390i
$95$	65.3706	−	37.7417i	0.688111	−	0.397281i
$96$	85.3857	−	35.5112i	0.889434	−	0.369908i
$97$	19.1660			0.197588			0.0987939	−	0.995108i	$-0.468502\pi$
$97$	19.1660			0.197588			0.0987939	+	0.995108i	$0.468502\pi$
$98$		0			0
$99$	22.7085	−	6.15445i	0.229379	−	0.0621662i
$100$	33.7510	−	58.4584i	0.337510	−	0.584584i
$101$	85.4872	−	49.3561i	0.846408	−	0.488674i	−0.0130291	−	0.999915i	$-0.504147\pi$
$101$	85.4872	−	49.3561i	0.846408	−	0.488674i	0.859437	+	0.511241i	$0.170814\pi$
$102$	−47.2249	−	6.14853i	−0.462990	−	0.0602797i
$103$	28.1255	−	48.7148i	0.273063	−	0.472959i	−0.696582	−	0.717478i	$-0.745297\pi$
$103$	28.1255	−	48.7148i	0.273063	−	0.472959i	0.969645	+	0.244519i	$0.0786299\pi$
$104$		−	52.2547i		−	0.502449i
$105$		0			0
$106$	137.247			1.29478
$107$	106.640	+	61.5684i	0.996632	+	0.575406i	0.907250	−	0.420591i	$-0.138177\pi$
$107$	106.640	+	61.5684i	0.996632	+	0.575406i	0.0893823	+	0.995997i	$0.471511\pi$
$108$	−8.33906	−	61.3060i	−0.0772135	−	0.567648i
$109$	−82.2693	−	142.495i	−0.754764	−	1.30729i	−0.945492	−	0.325647i	$-0.894418\pi$
$109$	−82.2693	−	142.495i	−0.754764	−	1.30729i	0.190728	−	0.981643i	$-0.438915\pi$
$110$	−21.8375	−	12.6079i	−0.198523	−	0.114617i
$111$	−74.8118	+	97.7861i	−0.673980	+	0.880956i
$112$		0			0
$113$			144.050i			1.27478i	0.770540	+	0.637391i	$0.219986\pi$
$113$			144.050i			1.27478i	−0.770540	+	0.637391i	$0.780014\pi$
$114$	−37.0347	+	15.4024i	−0.324866	+	0.135109i
$115$	15.8745	+	27.4955i	0.138039	+	0.239091i
$116$	−34.4772	+	19.9054i	−0.297217	+	0.171599i
$117$	−55.2817	−	14.6432i	−0.472494	−	0.125156i
$118$	54.0667			0.458192
$119$		0			0
$120$	−110.624	+	144.595i	−0.921863	+	1.20496i
$121$	−57.0830	+	98.8707i	−0.471760	+	0.817113i
$122$	−23.1826	+	13.3845i	−0.190021	+	0.109709i
$123$	−11.7281	+	90.0803i	−0.0953507	+	0.732360i
$124$	−45.0183	+	77.9740i	−0.363051	+	0.628822i
$125$			32.8944i			0.263155i
$126$		0			0
$127$	−36.5830			−0.288055			−0.144028	−	0.989574i	$-0.546005\pi$
$127$	−36.5830			−0.288055			−0.144028	+	0.989574i	$0.546005\pi$
$128$	−54.0049	−	31.1798i	−0.421914	−	0.243592i
$129$	−166.221	−	21.6414i	−1.28853	−	0.167762i
$130$	30.6458	+	53.0800i	0.235737	+	0.408308i
$131$	29.1725	+	16.8427i	0.222691	+	0.128570i	0.607195	−	0.794552i	$-0.292294\pi$
$131$	29.1725	+	16.8427i	0.222691	+	0.128570i	−0.384505	+	0.923123i	$0.625628\pi$
$132$	−14.2732	−	10.9198i	−0.108130	−	0.0827257i
$133$		0			0
$134$		−	35.5086i		−	0.264989i
$135$	121.972	+	157.551i	0.903495	+	1.16705i
$136$	49.9373	+	86.4939i	0.367186	+	0.635984i
$137$	−34.6193	+	19.9874i	−0.252695	+	0.145894i	−0.620998	−	0.783812i	$-0.713272\pi$
$137$	−34.6193	+	19.9874i	−0.252695	+	0.145894i	0.368302	+	0.929706i	$0.379939\pi$
$138$	−6.47839	−	15.5771i	−0.0469449	−	0.112878i
$139$	−194.642			−1.40030			−0.700150	−	0.713995i	$-0.746884\pi$
$139$	−194.642			−1.40030			−0.700150	+	0.713995i	$0.746884\pi$
$140$		0			0
$141$	−95.2470	−	72.8693i	−0.675511	−	0.516803i
$142$	44.3137	−	76.7536i	0.312069	−	0.540519i
$143$	−14.3857	+	8.30561i	−0.100600	+	0.0580812i
$144$	10.0453	−	10.1030i	0.0697590	−	0.0701596i
$145$	64.1033	−	111.030i	0.442091	−	0.765725i
$146$			79.4577i			0.544231i
$147$		0			0
$148$	94.0445			0.635436
$149$	−176.396	−	101.842i	−1.18387	−	0.683506i	−0.226961	−	0.973904i	$-0.572879\pi$
$149$	−176.396	−	101.842i	−1.18387	−	0.683506i	−0.956906	+	0.290398i	$0.906212\pi$
$150$	14.9133	−	114.545i	0.0994221	−	0.763630i
$151$	−82.8745	−	143.543i	−0.548838	−	0.950615i	−0.998355	−	0.0573430i	$-0.981737\pi$
$151$	−82.8745	−	143.543i	−0.548838	−	0.950615i	0.449517	−	0.893272i	$-0.351596\pi$
$152$	72.8476	+	42.0586i	0.479260	+	0.276701i
$153$	105.498	−	28.5921i	0.689530	−	0.186876i
$154$		0			0
$155$		−	289.953i		−	1.87066i
$156$	16.7743	+	40.3332i	0.107527	+	0.258546i
$157$	151.361	+	262.166i	0.964086	+	1.66985i	0.712052	+	0.702127i	$0.247766\pi$
$157$	151.361	+	262.166i	0.964086	+	1.66985i	0.252033	+	0.967719i	$0.418901\pi$
$158$	−71.5942	+	41.3350i	−0.453128	+	0.261614i
$159$	−290.854	+	120.964i	−1.82927	+	0.760777i
$160$	227.476			1.42172
$161$		0			0
$162$	−53.4615	−	91.3856i	−0.330009	−	0.564109i
$163$	72.5203	−	125.609i	0.444910	−	0.770606i	−0.553136	−	0.833091i	$-0.686569\pi$
$163$	72.5203	−	125.609i	0.444910	−	0.770606i	0.998046	+	0.0624848i	$0.0199025\pi$
$164$	60.0910	−	34.6936i	0.366409	−	0.211546i
$165$	57.3901	+	7.47200i	0.347819	+	0.0452848i
$166$	−58.7824	+	101.814i	−0.354111	+	0.613338i
$167$		−	19.6594i		−	0.117721i	−0.998266	−	0.0588604i	$-0.981253\pi$
$167$		−	19.6594i		−	0.117721i	0.998266	−	0.0588604i	$-0.0187467\pi$
$168$		0			0
$169$	−128.624			−0.761086
$170$	−101.452	−	58.5732i	−0.596775	−	0.344548i
$171$	64.9088	−	65.2815i	0.379584	−	0.381763i
$172$	64.0183	+	110.883i	0.372199	+	0.644668i
$173$	17.0507	+	9.84422i	0.0985589	+	0.0569030i	0.548469	−	0.836171i	$-0.315211\pi$
$173$	17.0507	+	9.84422i	0.0985589	+	0.0569030i	−0.449910	+	0.893074i	$0.648544\pi$
$174$	−41.3948	+	54.1069i	−0.237901	+	0.310959i
$175$		0			0
$176$		−	4.13828i		−	0.0235129i
$177$	−114.578	+	47.6520i	−0.647333	+	0.269220i
$178$	−41.2876	−	71.5122i	−0.231953	−	0.401754i
$179$	295.960	−	170.872i	1.65341	−	0.954594i	0.677748	−	0.735294i	$-0.262956\pi$
$179$	295.960	−	170.872i	1.65341	−	0.954594i	0.975658	−	0.219300i	$-0.0703772\pi$
$180$	38.9692	−	147.118i	0.216495	−	0.817324i
$181$	215.889			1.19276			0.596378	−	0.802704i	$-0.296606\pi$
$181$	215.889			1.19276			0.596378	+	0.802704i	$0.296606\pi$
$182$		0			0
$183$	37.3320	−	48.7965i	0.204000	−	0.266648i
$184$	−17.6902	+	30.6403i	−0.0961424	+	0.166524i
$185$	−262.284	+	151.430i	−1.41775	+	0.818540i
$186$	−19.8919	+	152.784i	−0.106946	+	0.821418i
$187$	15.8745	−	27.4955i	0.0848904	−	0.147035i
$188$			91.6026i			0.487248i
$189$		0			0
$190$	−98.6640			−0.519284
$191$	38.7210	+	22.3556i	0.202728	+	0.117045i	0.597927	−	0.801550i	$-0.295991\pi$
$191$	38.7210	+	22.3556i	0.202728	+	0.117045i	−0.395199	+	0.918595i	$0.629324\pi$
$192$	−138.700	−	18.0583i	−0.722396	−	0.0940534i
$193$	72.5608	+	125.679i	0.375963	+	0.651186i	0.990471	−	0.137724i	$-0.0439788\pi$
$193$	72.5608	+	125.679i	0.375963	+	0.651186i	−0.614508	+	0.788911i	$0.710645\pi$
$194$	−21.6955	−	12.5259i	−0.111832	−	0.0645665i
$195$	−111.727	−	85.4772i	−0.572958	−	0.438344i
$196$		0			0
$197$		−	87.4643i		−	0.443981i	−0.975049	−	0.221991i	$-0.928745\pi$
$197$		−	87.4643i		−	0.443981i	0.975049	−	0.221991i	$-0.0712554\pi$
$198$	−29.7277	−	7.87438i	−0.150140	−	0.0397696i
$199$	−32.7085	−	56.6528i	−0.164364	−	0.284687i	0.772065	−	0.635544i	$-0.219224\pi$
$199$	−32.7085	−	56.6528i	−0.164364	−	0.284687i	−0.936429	+	0.350856i	$0.885891\pi$
$200$	−209.792	+	121.123i	−1.04896	+	0.605616i
$201$	31.2957	+	75.2496i	0.155700	+	0.374376i
$202$	−129.026			−0.638743
$203$		0			0
$204$	−66.3098	−	50.7307i	−0.325048	−	0.248680i
$205$	−111.727	+	193.516i	−0.545009	+	0.943983i
$206$	−63.6748	+	36.7627i	−0.309101	+	0.178460i
$207$	27.4580	+	27.3012i	0.132647	+	0.131890i
$208$	−5.02940	+	8.71118i	−0.0241798	+	0.0418807i
$209$		−	26.7399i		−	0.127942i
$210$		0			0
$211$	40.5830			0.192337			0.0961683	−	0.995365i	$-0.469341\pi$
$211$	40.5830			0.192337			0.0961683	+	0.995365i	$0.469341\pi$
$212$	208.376	+	120.306i	0.982904	+	0.567480i
$213$	−26.2623	+	201.712i	−0.123297	+	0.947006i
$214$	−80.4758	−	139.388i	−0.376055	−	0.651347i
$215$	−357.086	−	206.164i	−1.66087	−	0.958902i
$216$	−84.0882	+	205.498i	−0.389297	+	0.951381i
$217$		0			0
$218$			215.068i			0.986548i
$219$	−70.0305	−	168.387i	−0.319774	−	0.768888i
$220$	−22.1033	−	38.2840i	−0.100469	−	0.174018i
$221$	−66.8325	+	38.5858i	−0.302410	+	0.174596i
$222$	148.593	−	61.7986i	0.669338	−	0.278372i
$223$	100.959			0.452733			0.226367	−	0.974042i	$-0.427315\pi$
$223$	100.959			0.452733			0.226367	+	0.974042i	$0.427315\pi$
$224$		0			0
$225$	69.3503	+	255.886i	0.308224	+	1.13727i
$226$	94.1438	−	163.062i	0.416565	−	0.721512i
$227$	338.858	−	195.640i	1.49277	−	0.861849i	0.492800	−	0.870143i	$-0.335973\pi$
$227$	338.858	−	195.640i	1.49277	−	0.861849i	0.999966	+	0.00829388i	$0.00264005\pi$
$228$	−69.7292	−	9.07850i	−0.305830	−	0.0398180i
$229$	3.40588	−	5.89916i	0.0148728	−	0.0257605i	−0.858493	−	0.512825i	$-0.828599\pi$
$229$	3.40588	−	5.89916i	0.0148728	−	0.0257605i	0.873366	+	0.487064i	$0.161932\pi$
$230$		−	41.4990i		−	0.180430i
$231$		0			0
$232$	142.871			0.615821
$233$	101.218	+	58.4383i	0.434412	+	0.250808i	0.701224	−	0.712941i	$-0.252637\pi$
$233$	101.218	+	58.4383i	0.434412	+	0.250808i	−0.266812	+	0.963748i	$0.585970\pi$
$234$	53.0077	+	52.7050i	0.226528	+	0.225235i
$235$	−147.498	−	255.474i	−0.627651	−	1.08712i
$236$	82.0868	+	47.3929i	0.347826	+	0.200817i
$237$	115.292	−	150.697i	0.486462	−	0.635852i
$238$		0			0
$239$			59.9623i			0.250888i	0.992101	+	0.125444i	$0.0400356\pi$
$239$			59.9623i			0.250888i	−0.992101	+	0.125444i	$0.959964\pi$
$240$	32.3586	−	13.4577i	0.134828	−	0.0560736i
$241$	−67.3765	−	116.699i	−0.279570	−	0.484230i	0.691708	−	0.722178i	$-0.256859\pi$
$241$	−67.3765	−	116.699i	−0.279570	−	0.484230i	−0.971278	+	0.237947i	$0.923525\pi$
$242$	129.233	−	74.6129i	0.534022	−	0.308318i
$243$	193.839	+	146.546i	0.797690	+	0.603068i
$244$	−46.9294			−0.192334
$245$		0			0
$246$	72.1477	−	94.3039i	0.293283	−	0.383349i
$247$	−32.4980	+	56.2882i	−0.131571	+	0.227888i
$248$	279.828	−	161.559i	1.12834	−	0.651446i
$249$	34.8370	−	267.572i	0.139908	−	1.07459i
$250$	21.4980	−	37.2357i	0.0859921	−	0.148943i
$251$		−	268.248i		−	1.06872i	−0.845257	−	0.534359i	$-0.820553\pi$
$251$		−	268.248i		−	1.06872i	0.845257	−	0.534359i	$-0.179447\pi$
$252$		0			0
$253$	11.2470			0.0444547
$254$	41.4111	+	23.9087i	0.163036	+	0.0941289i
$255$	266.620	+	34.7131i	1.04557	+	0.136130i
$256$	134.002	+	232.098i	0.523445	+	0.906634i
$257$	202.762	+	117.064i	0.788956	+	0.455504i	0.839595	−	0.543213i	$-0.182793\pi$
$257$	202.762	+	117.064i	0.788956	+	0.455504i	−0.0506392	+	0.998717i	$0.516126\pi$
$258$	174.014	+	133.131i	0.674474	+	0.516010i
$259$		0			0
$260$			107.452i			0.413276i
$261$	40.0362	−	151.147i	0.153396	−	0.579106i
$262$	−22.0151	−	38.1312i	−0.0840269	−	0.145539i
$263$	−216.629	+	125.071i	−0.823686	+	0.475555i	−0.851686	−	0.524053i	$-0.824420\pi$
$263$	−216.629	+	125.071i	−0.823686	+	0.475555i	0.0279999	+	0.999608i	$0.491086\pi$
$264$	24.7661	+	59.5494i	0.0938109	+	0.225566i
$265$	−774.863			−2.92401
$266$		0			0
$267$	150.524	+	115.159i	0.563761	+	0.431308i
$268$	31.1255	−	53.9109i	0.116140	−	0.201160i
$269$	−295.041	+	170.342i	−1.09681	+	0.633241i	−0.935380	−	0.353644i	$-0.884942\pi$
$269$	−295.041	+	170.342i	−1.09681	+	0.633241i	−0.161425	+	0.986885i	$0.551609\pi$
$270$	−35.1021	−	258.059i	−0.130008	−	0.955774i
$271$	10.6497	−	18.4458i	0.0392977	−	0.0680657i	−0.845708	−	0.533647i	$-0.820821\pi$
$271$	10.6497	−	18.4458i	0.0392977	−	0.0680657i	0.885005	+	0.465581i	$0.154155\pi$
$272$		−	19.2254i		−	0.0706816i
$273$		0			0
$274$	52.2510			0.190697
$275$	66.6905	+	38.5038i	0.242511	+	0.140014i
$276$	3.81850	−	29.3287i	0.0138351	−	0.106263i
$277$	113.458	+	196.514i	0.409594	+	0.709437i	0.994844	−	0.101415i	$-0.0323371\pi$
$277$	113.458	+	196.514i	0.409594	+	0.709437i	−0.585250	+	0.810853i	$0.699004\pi$
$278$	220.330	+	127.208i	0.792555	+	0.457582i
$279$	−92.5020	−	341.311i	−0.331548	−	1.22334i
$280$		0			0
$281$			235.489i			0.838039i	0.907977	+	0.419019i	$0.137626\pi$
$281$			235.489i			0.838039i	−0.907977	+	0.419019i	$0.862374\pi$
$282$	60.1940	+	144.735i	0.213454	+	0.513244i
$283$	−184.317	−	319.246i	−0.651297	−	1.12808i	−0.982808	−	0.184628i	$-0.940892\pi$
$283$	−184.317	−	319.246i	−0.651297	−	1.12808i	0.331512	−	0.943451i	$-0.392441\pi$
$284$	134.559	−	77.6876i	0.473799	−	0.273548i
$285$	209.089	−	86.9582i	0.733644	−	0.305116i
$286$	21.7124			0.0759176
$287$		0			0
$288$	267.767	−	72.5703i	0.929748	−	0.251980i
$289$	−70.7510	+	122.544i	−0.244813	+	0.424029i
$290$	−145.127	+	83.7891i	−0.500438	+	0.288928i
$291$	57.0168	+	7.42339i	0.195934	+	0.0255099i
$292$	−69.6497	+	120.637i	−0.238526	+	0.413140i
$293$			531.625i			1.81442i	0.420677	+	0.907211i	$0.361793\pi$
$293$			531.625i			1.81442i	−0.420677	+	0.907211i	$0.638207\pi$
$294$		0			0
$295$	−305.247			−1.03474
$296$	−292.284	−	168.750i	−0.987446	−	0.570102i
$297$	69.9391	−	9.51336i	0.235485	−	0.0320315i
$298$	133.118	+	230.566i	0.446703	+	0.773713i
$299$	−23.6753	−	13.6690i	−0.0791817	−	0.0457156i
$300$	123.048	−	160.835i	0.410159	−	0.536117i
$301$		0			0
$302$			216.650i			0.717383i
$303$	273.432	−	113.718i	0.902416	−	0.375307i
$304$	−8.09609	−	14.0228i	−0.0266319	−	0.0461277i
$305$	130.883	−	75.5655i	0.429125	−	0.247756i
$306$	−138.108	−	36.5824i	−0.451332	−	0.119550i
$307$	567.763			1.84939			0.924696	−	0.380706i	$-0.124319\pi$
$307$	567.763			1.84939			0.924696	+	0.380706i	$0.124319\pi$
$308$		0			0
$309$	102.539	−	134.028i	0.331840	−	0.433746i
$310$	−189.498	+	328.220i	−0.611284	+	1.05877i
$311$	−37.0253	+	21.3766i	−0.119052	+	0.0687349i	−0.558344	−	0.829610i	$-0.688563\pi$
$311$	−37.0253	+	21.3766i	−0.119052	+	0.0687349i	0.439291	+	0.898345i	$0.355230\pi$
$312$	20.2393	−	155.452i	0.0648697	−	0.498244i
$313$	79.0588	−	136.934i	0.252584	−	0.437488i	−0.711652	−	0.702532i	$-0.752053\pi$
$313$	79.0588	−	136.934i	0.252584	−	0.437488i	0.964237	+	0.265043i	$0.0853862\pi$
$314$		−	395.688i		−	1.26015i
$315$		0			0
$316$	−144.931			−0.458642
$317$	−122.061	−	70.4721i	−0.385051	−	0.222309i	0.294963	−	0.955509i	$-0.404693\pi$
$317$	−122.061	−	70.4721i	−0.385051	−	0.222309i	−0.680014	+	0.733199i	$0.738026\pi$
$318$	408.295	+	53.1586i	1.28395	+	0.167166i
$319$	−22.7085	−	39.3323i	−0.0711865	−	0.123299i
$320$	−297.965	−	172.030i	−0.931139	−	0.537594i
$321$	293.395	+	224.463i	0.914002	+	0.699262i
$322$		0			0
$323$		−	124.227i		−	0.384604i
$324$	−1.06272	−	185.609i	−0.00327998	−	0.572866i
$325$	−93.5902	−	162.103i	−0.287970	−	0.498778i
$326$	−164.183	+	94.7909i	−0.503628	+	0.290770i
$327$	−189.551	−	455.771i	−0.579667	−	1.39379i
$328$	−249.012			−0.759182
$329$		0			0
$330$	−60.0810	−	45.9653i	−0.182064	−	0.139289i
$331$	129.184	−	223.754i	0.390285	−	0.675993i	−0.602202	−	0.798344i	$-0.705710\pi$
$331$	129.184	−	223.754i	0.390285	−	0.675993i	0.992487	+	0.122350i	$0.0390432\pi$
$332$	−178.493	+	103.053i	−0.537629	+	0.310400i
$333$	−260.431	+	261.927i	−0.782077	+	0.786567i
$334$	−12.8483	+	22.2540i	−0.0384681	+	0.0666287i
$335$			200.472i			0.598425i
$336$		0			0
$337$	328.959			0.976141			0.488070	−	0.872804i	$-0.337701\pi$
$337$	328.959			0.976141			0.488070	+	0.872804i	$0.337701\pi$
$338$	145.599	+	84.0616i	0.430766	+	0.248703i
$339$	−55.7937	+	428.534i	−0.164583	+	1.26411i
$340$	−102.686	−	177.858i	−0.302018	−	0.523111i
$341$	−88.9542	−	51.3577i	−0.260863	−	0.150609i
$342$	−116.140	+	31.4762i	−0.339590	+	0.0920357i
$343$		0			0
$344$		−	459.489i		−	1.33572i
$345$	36.5754	+	87.9445i	0.106016	+	0.254912i
$346$	−12.8673	−	22.2869i	−0.0371888	−	0.0644129i
$347$	−111.401	+	64.3176i	−0.321041	+	0.185353i	−0.651857	−	0.758342i	$-0.726010\pi$
$347$	−111.401	+	64.3176i	−0.321041	+	0.185353i	0.330815	+	0.943696i	$0.392676\pi$
$348$	−110.276	+	45.8628i	−0.316884	+	0.131790i
$349$	−73.4837			−0.210555			−0.105277	−	0.994443i	$-0.533573\pi$
$349$	−73.4837			−0.210555			−0.105277	+	0.994443i	$0.533573\pi$
$350$		0			0
$351$	−158.786	−	64.9737i	−0.452381	−	0.185110i
$352$	40.2915	−	69.7869i	0.114464	−	0.198258i
$353$	207.574	−	119.843i	0.588027	−	0.339498i	−0.176290	−	0.984338i	$-0.556410\pi$
$353$	207.574	−	119.843i	0.588027	−	0.339498i	0.764317	+	0.644841i	$0.223076\pi$
$354$	160.843	+	20.9412i	0.454357	+	0.0591558i
$355$	−250.184	+	433.332i	−0.704745	+	1.22065i
$356$		−	144.765i		−	0.406642i
$357$		0			0
$358$	−446.693			−1.24775
$359$	156.071	+	90.1075i	0.434738	+	0.250996i	0.701363	−	0.712804i	$-0.252575\pi$
$359$	156.071	+	90.1075i	0.434738	+	0.250996i	−0.266625	+	0.963800i	$0.585909\pi$
$360$	−385.098	+	387.309i	−1.06972	+	1.07586i
$361$	128.186	+	222.025i	0.355087	+	0.615028i
$362$	−244.381	−	141.094i	−0.675087	−	0.389761i
$363$	−208.110	+	272.020i	−0.573307	+	0.749367i
$364$		0			0
$365$		−	448.598i		−	1.22904i
$366$	−74.1498	+	30.8383i	−0.202595	+	0.0842576i
$367$	−114.893	−	199.000i	−0.313059	−	0.542235i	0.665964	−	0.745984i	$-0.268021\pi$
$367$	−114.893	−	199.000i	−0.313059	−	0.542235i	−0.979023	+	0.203749i	$0.934687\pi$
$368$	5.89813	−	3.40529i	0.0160275	−	0.00925350i
$369$	−69.7799	+	263.436i	−0.189105	+	0.713920i
$370$	395.867			1.06991
$371$		0			0
$372$	−164.125	+	214.528i	−0.441198	+	0.576687i
$373$	−220.875	+	382.566i	−0.592157	+	1.02565i	0.401785	+	0.915734i	$0.368390\pi$
$373$	−220.875	+	382.566i	−0.592157	+	1.02565i	−0.993941	+	0.109912i	$0.964943\pi$
$374$	−35.9392	+	20.7495i	−0.0960940	+	0.0554799i
$375$	−12.7407	+	97.8572i	−0.0339751	+	0.260953i
$376$	164.369	−	284.695i	0.437151	−	0.757167i
$377$			110.394i			0.292822i
$378$		0			0
$379$	−421.203			−1.11135			−0.555676	−	0.831399i	$-0.687541\pi$
$379$	−421.203			−1.11135			−0.555676	+	0.831399i	$0.687541\pi$
$380$	−149.797	−	86.4853i	−0.394202	−	0.227593i
$381$	−108.830	−	14.1694i	−0.285644	−	0.0371899i
$382$	−29.2209	−	50.6121i	−0.0764945	−	0.132492i
$383$	515.797	+	297.796i	1.34673	+	0.777534i	0.987785	−	0.155825i	$-0.0498037\pi$
$383$	515.797	+	297.796i	1.34673	+	0.777534i	0.358944	+	0.933359i	$0.383137\pi$
$384$	−148.582	−	113.674i	−0.386933	−	0.296025i
$385$		0			0
$386$		−	189.688i		−	0.491419i
$387$	−486.106	−	128.761i	−1.25609	−	0.332717i
$388$	−21.9595	−	38.0349i	−0.0565966	−	0.0980282i
$389$	318.132	−	183.673i	0.817819	−	0.472168i	−0.0318449	−	0.999493i	$-0.510138\pi$
$389$	318.132	−	183.673i	0.817819	−	0.472168i	0.849664	+	0.527325i	$0.176805\pi$
$390$	70.6088	+	169.777i	0.181048	+	0.435326i
$391$	52.2510			0.133634
$392$		0			0
$393$	80.2614	+	61.4044i	0.204227	+	0.156245i
$394$	−57.1621	+	99.0076i	−0.145081	+	0.251288i
$395$	404.203	−	233.367i	1.02330	−	0.590802i
$396$	−38.2318	−	38.0135i	−0.0965450	−	0.0959938i
$397$	−204.173	+	353.638i	−0.514290	+	0.890777i	0.485572	+	0.874196i	$0.338611\pi$
$397$	−204.173	+	353.638i	−0.514290	+	0.890777i	−0.999863	+	0.0165802i	$0.994722\pi$
$398$			85.5062i			0.214840i
$399$		0			0
$400$	46.6314			0.116578
$401$	−206.822	−	119.409i	−0.515765	−	0.297777i	0.219435	−	0.975627i	$-0.429579\pi$
$401$	−206.822	−	119.409i	−0.515765	−	0.297777i	−0.735200	+	0.677850i	$0.762912\pi$
$402$	13.7532	−	105.634i	0.0342119	−	0.262771i
$403$	124.834	+	216.219i	0.309762	+	0.536523i
$404$	−195.894	−	113.100i	−0.484887	−	0.279949i
$405$	301.830	+	515.940i	0.745259	+	1.27393i
$406$		0			0
$407$			107.288i			0.263606i
$408$	115.057	+	276.652i	0.282003	+	0.678068i
$409$	324.682	+	562.366i	0.793844	+	1.37498i	0.923570	+	0.383429i	$0.125257\pi$
$409$	324.682	+	562.366i	0.793844	+	1.37498i	−0.129726	+	0.991550i	$0.541410\pi$
$410$	252.944	−	146.038i	0.616938	−	0.356189i
$411$	−110.730	+	46.0517i	−0.269416	+	0.112048i
$412$	−128.899			−0.312862
$413$		0			0
$414$	−13.2392	−	48.8495i	−0.0319787	−	0.117994i
$415$	331.871	−	574.817i	0.799688	−	1.38510i
$416$	−169.629	+	97.9356i	−0.407763	+	0.235422i
$417$	−579.038	−	75.3888i	−1.38858	−	0.180789i
$418$	−17.4758	+	30.2690i	−0.0418081	+	0.0724138i
$419$			11.5178i			0.0274888i	0.999906	+	0.0137444i	$0.00437512\pi$
$419$			11.5178i			0.0274888i	−0.999906	+	0.0137444i	$0.995625\pi$
$420$		0			0
$421$	−83.9921			−0.199506			−0.0997531	−	0.995012i	$-0.531805\pi$
$421$	−83.9921			−0.199506			−0.0997531	+	0.995012i	$0.531805\pi$
$422$	−45.9390	−	26.5229i	−0.108860	−	0.0628505i
$423$	−255.126	−	253.669i	−0.603135	−	0.599691i
$424$	−431.745	−	747.804i	−1.01827	−	1.76369i
$425$	309.827	+	178.879i	0.729006	+	0.420892i
$426$	161.557	−	211.170i	0.379241	−	0.495705i
$427$		0			0
$428$		−	282.168i		−	0.659272i
$429$	−46.0129	+	19.1364i	−0.107256	+	0.0446070i
$430$	269.476	+	466.746i	0.626688	+	1.08546i
$431$	−601.025	+	347.002i	−1.39449	+	0.805109i	−0.993808	−	0.111108i	$-0.964560\pi$
$431$	−601.025	+	347.002i	−1.39449	+	0.805109i	−0.400682	+	0.916217i	$0.631227\pi$
$432$	33.7968	−	26.1645i	0.0782333	−	0.0605660i
$433$	116.834			0.269824			0.134912	−	0.990858i	$-0.456925\pi$
$433$	116.834			0.269824			0.134912	+	0.990858i	$0.456925\pi$
$434$		0			0
$435$	233.705	−	305.474i	0.537252	−	0.702239i
$436$	−188.520	+	326.527i	−0.432386	+	0.748914i
$437$	38.1114	−	22.0036i	0.0872114	−	0.0503515i
$438$	−30.7756	+	236.378i	−0.0702640	+	0.539676i
$439$	264.037	−	457.325i	0.601450	−	1.04174i	−0.391152	−	0.920326i	$-0.627923\pi$
$439$	264.037	−	457.325i	0.601450	−	1.04174i	0.992602	−	0.121416i	$-0.0387435\pi$
$440$			158.645i			0.360558i
$441$		0			0
$442$	100.871			0.228214
$443$	235.777	+	136.126i	0.532228	+	0.307282i	0.741923	−	0.670485i	$-0.233914\pi$
$443$	235.777	+	136.126i	0.532228	+	0.307282i	−0.209695	+	0.977767i	$0.567247\pi$
$444$	279.772	+	36.4254i	0.630117	+	0.0820391i
$445$	233.099	+	403.740i	0.523819	+	0.907281i
$446$	−114.284	−	65.9818i	−0.256242	−	0.147941i
$447$	−485.314	−	371.292i	−1.08571	−	0.830631i
$448$		0			0
$449$			525.770i			1.17098i	0.810680	+	0.585490i	$0.199098\pi$
$449$			525.770i			1.17098i	−0.810680	+	0.585490i	$0.800902\pi$
$450$	88.7310	−	334.981i	0.197180	−	0.744403i
$451$	39.5791	+	68.5530i	0.0877585	+	0.152002i
$452$	285.868	−	165.046i	0.632451	−	0.365146i
$453$	−190.946	−	459.124i	−0.421513	−	1.01352i
$454$	−511.439			−1.12652
$455$		0			0
$456$	200.423	+	153.335i	0.439525	+	0.336261i
$457$	256.893	−	444.951i	0.562129	−	0.973635i	−0.435182	−	0.900343i	$-0.643316\pi$
$457$	256.893	−	444.951i	0.562129	−	0.973635i	0.997310	−	0.0732928i	$-0.0233508\pi$
$458$	−7.71076	+	4.45181i	−0.0168357	+	0.00972011i
$459$	324.920	−	44.1967i	0.707886	−	0.0962891i
$460$	36.3765	−	63.0059i	0.0790793	−	0.136969i
$461$		−	687.879i		−	1.49214i	−0.665865	−	0.746072i	$-0.731937\pi$
$461$		−	687.879i		−	1.49214i	0.665865	−	0.746072i	$-0.268063\pi$
$462$		0			0
$463$	781.061			1.68696			0.843479	−	0.537162i	$-0.180504\pi$
$463$	781.061			1.68696			0.843479	+	0.537162i	$0.180504\pi$
$464$	−23.8174	−	13.7510i	−0.0513306	−	0.0296357i
$465$	112.305	−	862.579i	0.241516	−	1.85501i
$466$	−76.3844	−	132.302i	−0.163915	−	0.283909i
$467$	141.468	+	81.6763i	0.302928	+	0.174896i	0.643758	−	0.765229i	$-0.277374\pi$
$467$	141.468	+	81.6763i	0.302928	+	0.174896i	−0.340829	+	0.940125i	$0.610708\pi$
$468$	34.2797	+	126.484i	0.0732472	+	0.270265i
$469$		0			0
$470$			385.588i			0.820400i
$471$	348.742	+	838.540i	0.740428	+	1.78034i
$472$	−170.080	−	294.588i	−0.360340	−	0.624127i
$473$	−126.497	+	73.0333i	−0.267436	+	0.154404i
$474$	−228.995	+	95.2371i	−0.483112	+	0.200922i
$475$	301.314			0.634345
$476$		0			0
$477$	−912.110	+	247.200i	−1.91218	+	0.518239i
$478$	39.1882	−	67.8760i	0.0819838	−	0.142000i
$479$	−606.355	+	350.079i	−1.26588	+	0.730855i	−0.974205	−	0.225664i	$-0.927545\pi$
$479$	−606.355	+	350.079i	−1.26588	+	0.730855i	−0.291672	+	0.956518i	$0.594212\pi$
$480$	676.716	+	88.1061i	1.40982	+	0.183554i
$481$	130.391	−	225.844i	0.271083	−	0.469529i
$482$			176.135i			0.365425i
$483$		0			0
$484$	261.612			0.540520
$485$	122.487	+	70.7181i	0.252551	+	0.145811i
$486$	−123.647	−	292.569i	−0.254417	−	0.601994i
$487$	−43.2954	−	74.9899i	−0.0889023	−	0.153983i	0.818145	−	0.575012i	$-0.195003\pi$
$487$	−43.2954	−	74.9899i	−0.0889023	−	0.153983i	−0.907047	+	0.421028i	$0.861669\pi$
$488$	145.853	+	84.2085i	0.298880	+	0.172558i
$489$	264.391	−	345.584i	0.540677	−	0.706716i
$490$		0			0
$491$			741.494i			1.51017i	0.655627	+	0.755085i	$0.272404\pi$
$491$			741.494i			1.51017i	−0.655627	+	0.755085i	$0.727596\pi$
$492$	192.202	−	79.9351i	0.390654	−	0.162470i
$493$	−105.498	−	182.728i	−0.213992	−	0.370645i
$494$	73.5741	−	42.4780i	0.148935	−	0.0859879i
$495$	167.835	+	44.4568i	0.339061	+	0.0898117i
$496$	−62.1987			−0.125401
$497$		0			0
$498$	−214.306	+	280.118i	−0.430333	+	0.562486i
$499$	−189.907	+	328.929i	−0.380575	+	0.659176i	−0.991145	−	0.132787i	$-0.957607\pi$
$499$	−189.907	+	328.929i	−0.380575	+	0.659176i	0.610569	+	0.791963i	$0.290941\pi$
$500$	65.2789	−	37.6888i	0.130558	−	0.0753775i
$501$	7.61449	−	58.4846i	0.0151986	−	0.116736i
$502$	−175.313	+	303.651i	−0.349229	+	0.604883i
$503$			465.808i			0.926059i	0.886343	+	0.463029i	$0.153238\pi$
$503$			465.808i			0.926059i	−0.886343	+	0.463029i	$0.846762\pi$
$504$		0			0
$505$	728.450			1.44247
$506$	−12.7314	−	7.35048i	−0.0251609	−	0.0145266i
$507$	−382.641	−	49.8186i	−0.754716	−	0.0982615i
$508$	41.9150	+	72.5990i	0.0825099	+	0.142911i
$509$	−649.955	−	375.252i	−1.27692	−	0.737233i	−0.300643	−	0.953737i	$-0.597201\pi$
$509$	−649.955	−	375.252i	−1.27692	−	0.737233i	−0.976282	+	0.216504i	$0.930535\pi$
$510$	−279.122	−	213.543i	−0.547297	−	0.418713i
$511$		0			0
$512$		−	100.868i		−	0.197009i
$513$	218.382	−	169.065i	0.425695	−	0.329561i
$514$	−153.014	−	265.029i	−0.297693	−	0.515620i
$515$	359.492	−	207.553i	0.698043	−	0.403016i
$516$	147.500	+	354.660i	0.285853	+	0.687326i
$517$	−104.502			−0.202131
$518$		0			0
$519$	46.9111	+	35.8896i	0.0903875	+	0.0691514i
$520$	192.808	−	333.953i	0.370784	−	0.642217i
$521$	629.554	−	363.473i	1.20836	−	0.697645i	0.245957	−	0.969281i	$-0.420898\pi$
$521$	629.554	−	363.473i	1.20836	−	0.697645i	0.962400	+	0.271635i	$0.0875645\pi$
$522$	−144.102	+	144.929i	−0.276057	+	0.277642i
$523$	312.354	−	541.012i	0.597234	−	1.03444i	−0.395993	−	0.918253i	$-0.629600\pi$
$523$	312.354	−	541.012i	0.597234	−	1.03444i	0.993227	−	0.116187i	$-0.0370671\pi$
$524$		−	77.1903i		−	0.147310i
$525$		0			0
$526$	326.959			0.621596
$527$	−413.259	−	238.595i	−0.784173	−	0.452742i
$528$	1.60284	−	12.3109i	0.00303568	−	0.0233161i
$529$	−255.245	−	442.097i	−0.482505	−	0.835723i
$530$	877.127	+	506.410i	1.65496	+	0.955490i
$531$	−359.314	+	97.3812i	−0.676674	+	0.183392i
$532$		0			0
$533$		−	192.408i		−	0.360990i
$534$	−95.1279	−	228.732i	−0.178142	−	0.428338i
$535$	454.346	+	786.951i	0.849246	+	1.47094i
$536$	−193.472	+	111.701i	−0.360955	+	0.208398i
$537$	946.630	−	393.695i	1.76281	−	0.733139i
$538$	445.306			0.827706
$539$		0			0
$540$	172.911	−	422.568i	0.320206	−	0.782533i
$541$	145.878	−	252.669i	0.269646	−	0.467040i	−0.699124	−	0.715000i	$-0.746427\pi$
$541$	145.878	−	252.669i	0.269646	−	0.467040i	0.968770	+	0.247960i	$0.0797600\pi$
$542$	−24.1104	+	13.9202i	−0.0444842	+	0.0256829i
$543$	642.246	+	83.6182i	1.18277	+	0.153993i
$544$	187.184	−	324.213i	0.344089	−	0.595979i
$545$		−	1214.22i		−	2.22792i
$546$		0			0
$547$	204.952			0.374683			0.187342	−	0.982295i	$-0.440013\pi$
$547$	204.952			0.374683			0.187342	+	0.982295i	$0.440013\pi$
$548$	79.3302	+	45.8013i	0.144763	+	0.0835790i
$549$	129.959	−	130.705i	0.236719	−	0.238078i
$550$	−50.3281	−	87.1708i	−0.0915056	−	0.158492i
$551$	−153.899	−	88.8534i	−0.279308	−	0.161258i
$552$	−64.4941	+	84.2999i	−0.116837	+	0.152717i
$553$		0			0
$554$		−	296.599i		−	0.535378i
$555$	−838.920	+	348.900i	−1.51157	+	0.628648i
$556$	223.011	+	386.267i	0.401099	+	0.694724i
$557$	−436.375	+	251.941i	−0.783438	+	0.452318i	−0.837647	−	0.546211i	$-0.816070\pi$
$557$	−436.375	+	251.941i	−0.783438	+	0.452318i	0.0542092	+	0.998530i	$0.482736\pi$
$558$	−118.353	+	446.810i	−0.212101	+	0.800736i
$559$	355.041			0.635135
$560$		0			0
$561$	57.8745	−	75.6475i	0.103163	−	0.134844i
$562$	153.903	−	266.568i	0.273849	−	0.474321i
$563$	94.1672	−	54.3675i	0.167260	−	0.0965674i	−0.414033	−	0.910262i	$-0.635880\pi$
$563$	94.1672	−	54.3675i	0.167260	−	0.0965674i	0.581293	+	0.813694i	$0.302547\pi$
$564$	−35.4796	+	272.508i	−0.0629071	+	0.483170i
$565$	−531.512	+	920.606i	−0.940730	+	1.62939i
$566$			481.840i			0.851307i
$567$		0			0
$568$	−557.600			−0.981690
$569$	376.610	+	217.436i	0.661880	+	0.382136i	0.792993	−	0.609231i	$-0.208522\pi$
$569$	376.610	+	217.436i	0.661880	+	0.382136i	−0.131113	+	0.991367i	$0.541855\pi$
$570$	−293.515	−	38.2146i	−0.514938	−	0.0670432i
$571$	−59.5608	−	103.162i	−0.104310	−	0.180670i	0.809146	−	0.587607i	$-0.199930\pi$
$571$	−59.5608	−	103.162i	−0.104310	−	0.180670i	−0.913456	+	0.406938i	$0.866597\pi$
$572$	32.9649	+	19.0323i	0.0576310	+	0.0332733i
$573$	106.532	+	81.5029i	0.185920	+	0.142239i
$574$		0			0
$575$			126.735i			0.220409i
$576$	−405.623	−	107.443i	−0.704207	−	0.186533i
$577$	327.708	+	567.608i	0.567952	+	0.983722i	0.996768	+	0.0803304i	$0.0255975\pi$
$577$	327.708	+	567.608i	0.567952	+	0.983722i	−0.428816	+	0.903392i	$0.641069\pi$
$578$	160.177	−	92.4783i	0.277123	−	0.159997i
$579$	167.182	+	401.986i	0.288743	+	0.694276i
$580$	−293.786			−0.506527
$581$		0			0
$582$	−59.6902	−	45.6663i	−0.102560	−	0.0784645i
$583$	−137.247	+	237.719i	−0.235415	+	0.407751i
$584$	432.933	−	249.954i	0.741324	−	0.428004i
$585$	−299.268	−	297.559i	−0.511569	−	0.508649i
$586$	347.442	−	601.788i	0.592905	−	1.02694i
$587$			736.236i			1.25424i	0.778925	+	0.627118i	$0.215765\pi$
$587$			736.236i			1.25424i	−0.778925	+	0.627118i	$0.784235\pi$
$588$		0			0
$589$	−401.903			−0.682348
$590$	345.533	+	199.493i	0.585649	+	0.338124i
$591$	33.8767	−	260.197i	0.0573210	−	0.440265i
$592$	32.4837	+	56.2634i	0.0548711	+	0.0950395i
$593$	−721.299	−	416.442i	−1.21636	−	0.702263i	−0.252219	−	0.967670i	$-0.581160\pi$
$593$	−721.299	−	416.442i	−1.21636	−	0.702263i	−0.964137	+	0.265407i	$0.914494\pi$
$594$	−85.3869	−	34.9396i	−0.143749	−	0.0588209i
$595$		0			0
$596$			466.744i			0.783127i
$597$	−75.3614	−	181.205i	−0.126234	−	0.303525i
$598$	17.8666	+	30.9459i	0.0298773	+	0.0517490i
$599$	60.0407	−	34.6645i	0.100235	−	0.0578706i	−0.449045	−	0.893509i	$-0.648236\pi$
$599$	60.0407	−	34.6645i	0.100235	−	0.0578706i	0.549279	+	0.835639i	$0.314902\pi$
$600$	−671.021	+	279.072i	−1.11837	+	0.465120i
$601$	−161.720			−0.269085			−0.134543	−	0.990908i	$-0.542957\pi$
$601$	−161.720			−0.269085			−0.134543	+	0.990908i	$0.542957\pi$
$602$		0			0
$603$	63.9555	+	235.981i	0.106062	+	0.391345i
$604$	−189.907	+	328.929i	−0.314416	+	0.544584i
$605$	−729.619	+	421.246i	−1.20598	+	0.696274i
$606$	−383.839	−	49.9745i	−0.633398	−	0.0824662i
$607$	−464.804	+	805.064i	−0.765740	+	1.32630i	0.174115	+	0.984725i	$0.444293\pi$
$607$	−464.804	+	805.064i	−0.765740	+	1.32630i	−0.939855	+	0.341574i	$0.889040\pi$
$608$		−	315.304i		−	0.518592i
$609$		0			0
$610$	−197.542			−0.323840
$611$	219.979	+	127.005i	0.360032	+	0.207864i
$612$	−177.615	−	176.601i	−0.290221	−	0.288564i
$613$	−148.970	−	258.023i	−0.243018	−	0.420919i	0.718555	−	0.695470i	$-0.244804\pi$
$613$	−148.970	−	258.023i	−0.243018	−	0.420919i	−0.961572	+	0.274551i	$0.911471\pi$
$614$	−642.695	−	371.060i	−1.04674	−	0.604333i
$615$	−407.328	+	532.417i	−0.662322	+	0.865718i
$616$		0			0
$617$		−	975.575i		−	1.58116i	−0.612360	−	0.790579i	$-0.709780\pi$
$617$		−	975.575i		−	1.58116i	0.612360	−	0.790579i	$-0.290220\pi$
$618$	−203.665	+	84.7024i	−0.329555	+	0.137059i
$619$	−178.517	−	309.201i	−0.288396	−	0.499516i	0.685031	−	0.728514i	$-0.259789\pi$
$619$	−178.517	−	309.201i	−0.288396	−	0.499516i	−0.973427	+	0.228998i	$0.926455\pi$
$620$	−575.411	+	332.214i	−0.928083	+	0.535829i
$621$	71.1102	+	91.8532i	0.114509	+	0.147912i
$622$	55.8824			0.0898431
$623$		0			0
$624$	−18.3360	+	23.9668i	−0.0293845	+	0.0384084i
$625$	246.846	−	427.550i	0.394954	−	0.684081i
$626$	−178.986	+	103.337i	−0.285919	+	0.165076i
$627$	10.3569	−	79.5484i	0.0165182	−	0.126871i
$628$	346.845	−	600.753i	0.552301	−	0.956614i
$629$			498.432i			0.792420i
$630$		0			0
$631$	−813.223			−1.28879			−0.644393	−	0.764695i	$-0.722890\pi$
$631$	−813.223			−1.28879			−0.644393	+	0.764695i	$0.722890\pi$
$632$	450.435	+	260.059i	0.712714	+	0.411486i
$633$	120.730	+	15.7186i	0.190727	+	0.0248320i
$634$	92.1137	+	159.546i	0.145290	+	0.251649i
$635$	−233.797	−	134.983i	−0.368184	−	0.212571i
$636$	573.298	+	438.605i	0.901412	+	0.689630i
$637$		0			0
$638$			59.3643i			0.0930475i
$639$	−156.255	+	589.900i	−0.244530	+	0.923162i
$640$	−230.092	−	398.531i	−0.359519	−	0.622705i
$641$	560.082	−	323.363i	0.873762	−	0.504467i	0.00516570	−	0.999987i	$-0.498356\pi$
$641$	560.082	−	323.363i	0.873762	−	0.504467i	0.868597	+	0.495520i	$0.165022\pi$
$642$	−185.419	−	445.835i	−0.288814	−	0.694447i
$643$	144.561			0.224822			0.112411	−	0.993662i	$-0.464143\pi$
$643$	144.561			0.224822			0.112411	+	0.993662i	$0.464143\pi$
$644$		0			0
$645$	−982.442	−	751.622i	−1.52317	−	1.16531i
$646$	−81.1882	+	140.622i	−0.125678	+	0.217681i
$647$	−620.640	+	358.327i	−0.959259	+	0.553828i	−0.895945	−	0.444166i	$-0.853500\pi$
$647$	−620.640	+	358.327i	−0.959259	+	0.553828i	−0.0633138	+	0.997994i	$0.520167\pi$
$648$	−329.747	+	578.766i	−0.508869	+	0.893158i
$649$	−54.0667	+	93.6462i	−0.0833077	+	0.144293i
$650$			244.663i			0.376404i
$651$		0			0
$652$	−332.361			−0.509756
$653$	−328.223	−	189.500i	−0.502639	−	0.290199i	0.227164	−	0.973857i	$-0.427055\pi$
$653$	−328.223	−	189.500i	−0.502639	−	0.290199i	−0.729803	+	0.683658i	$0.760388\pi$
$654$	−83.3001	+	639.803i	−0.127370	+	0.978292i
$655$	124.292	+	215.279i	0.189758	+	0.328671i
$656$	41.5118	+	23.9668i	0.0632802	+	0.0365348i
$657$	−143.114	−	528.056i	−0.217829	−	0.803738i
$658$		0			0
$659$		−	710.721i		−	1.07848i	−0.842151	−	0.539242i	$-0.818711\pi$
$659$		−	710.721i		−	1.07848i	0.842151	−	0.539242i	$-0.181289\pi$
$660$	−50.9266	−	122.452i	−0.0771616	−	0.185533i
$661$	−45.7523	−	79.2452i	−0.0692167	−	0.119887i	0.829340	−	0.558744i	$-0.188717\pi$
$661$	−45.7523	−	79.2452i	−0.0692167	−	0.119887i	−0.898557	+	0.438857i	$0.855383\pi$
$662$	−292.467	+	168.856i	−0.441794	+	0.255070i
$663$	−213.765	+	88.9029i	−0.322420	+	0.134092i
$664$	739.659			1.11394
$665$		0			0
$666$	465.984	−	126.291i	0.699676	−	0.189626i
$667$	37.3725	−	64.7311i	0.0560308	−	0.0970482i
$668$	−39.0140	+	22.5248i	−0.0584043	+	0.0337197i
$669$	300.344	+	39.1037i	0.448944	+	0.0584510i
$670$	131.018	−	226.930i	0.195550	−	0.338702i
$671$		−	53.5379i		−	0.0797883i
$672$		0			0
$673$	645.806			0.959594			0.479797	−	0.877380i	$-0.340710\pi$
$673$	645.806			0.959594			0.479797	+	0.877380i	$0.340710\pi$
$674$	−372.375	−	214.991i	−0.552485	−	0.318977i
$675$	107.200	+	788.095i	0.158814	+	1.16755i
$676$	147.371	+	255.253i	0.218004	+	0.377594i
$677$	290.613	+	167.786i	0.429266	+	0.247837i	0.699034	−	0.715088i	$-0.253614\pi$
$677$	290.613	+	167.786i	0.429266	+	0.247837i	−0.269768	+	0.962925i	$0.586947\pi$
$678$	343.225	−	448.627i	0.506231	−	0.661692i
$679$		0			0
$680$			737.027i			1.08386i
$681$	1083.84	−	450.760i	1.59154	−	0.661909i
$682$	67.1294	+	116.272i	0.0984302	+	0.170486i
$683$	−98.1521	+	56.6681i	−0.143707	+	0.0829694i	−0.570130	−	0.821555i	$-0.693107\pi$
$683$	−98.1521	+	56.6681i	−0.143707	+	0.0829694i	0.426422	+	0.904524i	$0.359774\pi$
$684$	−203.920	−	54.0151i	−0.298129	−	0.0789694i
$685$	−294.996			−0.430651
$686$		0			0
$687$	12.4170	−	16.2302i	0.0180742	−	0.0236247i
$688$	−44.2248	+	76.5996i	−0.0642803	+	0.111337i
$689$	577.818	−	333.603i	0.838632	−	0.484184i
$690$	16.0734	−	123.455i	0.0232948	−	0.178920i
$691$	−282.833	+	489.882i	−0.409310	+	0.708946i	−0.994813	−	0.101725i	$-0.967564\pi$
$691$	−282.833	+	489.882i	−0.409310	+	0.708946i	0.585502	+	0.810671i	$0.300897\pi$
$692$		−	45.1161i		−	0.0651967i
$693$		0			0
$694$	168.138			0.242274
$695$	−1243.93	−	718.183i	−1.78983	−	1.03336i
$696$	425.025	+	55.3367i	0.610667	+	0.0795068i
$697$	183.875	+	318.480i	0.263808	+	0.456930i
$698$	83.1819	+	48.0251i	0.119172	+	0.0688038i
$699$	278.478	+	213.051i	0.398395	+	0.304794i
$700$		0			0
$701$		−	872.955i		−	1.24530i	−0.782501	−	0.622650i	$-0.786056\pi$
$701$		−	872.955i		−	1.24530i	0.782501	−	0.622650i	$-0.213944\pi$
$702$	137.278	+	177.323i	0.195553	+	0.252596i
$703$	209.897	+	363.552i	0.298573	+	0.517143i
$704$	−105.554	+	60.9414i	−0.149934	+	0.0865645i
$705$	−339.840	−	817.137i	−0.482043	−	1.15906i
$706$	−313.292			−0.443756
$707$		0			0
$708$	225.843	+	172.783i	0.318988	+	0.244043i
$709$	−546.018	+	945.731i	−0.770125	+	1.33389i	0.167370	+	0.985894i	$0.446473\pi$
$709$	−546.018	+	945.731i	−0.770125	+	1.33389i	−0.937494	+	0.348001i	$0.886861\pi$
$710$	566.406	−	327.015i	0.797755	−	0.460584i
$711$	401.348	−	403.652i	0.564484	−	0.567725i
$712$	−259.761	+	449.919i	−0.364833	+	0.631909i
$713$		−	169.044i		−	0.237088i
$714$		0			0
$715$	−122.583			−0.171445
$716$	−678.192	−	391.554i	−0.947196	−	0.546864i
$717$	−23.2247	+	178.381i	−0.0323914	+	0.248789i
$718$	−117.779	−	203.999i	−0.164038	−	0.284122i
$719$	780.955	+	450.885i	1.08617	+	0.627099i	0.932554	−	0.361031i	$-0.117575\pi$
$719$	780.955	+	450.885i	1.08617	+	0.627099i	0.153614	+	0.988131i	$0.450909\pi$
$720$	101.476	−	27.5020i	0.140939	−	0.0381972i
$721$		0			0
$722$		−	335.103i		−	0.464132i
$723$	−155.238	−	373.265i	−0.214713	−	0.516272i
$724$	−247.355	−	428.431i	−0.341650	−	0.591756i
$725$	443.208	−	255.886i	0.611322	−	0.352947i
$726$	413.354	−	171.911i	0.569359	−	0.236791i
$727$	297.506			0.409224			0.204612	−	0.978843i	$-0.434407\pi$
$727$	297.506			0.409224			0.204612	+	0.978843i	$0.434407\pi$
$728$		0			0
$729$	519.889	+	511.035i	0.713153	+	0.701008i
$730$	−293.180	+	507.803i	−0.401617	+	0.695621i
$731$	−587.675	+	339.295i	−0.803933	+	0.464151i
$732$	−139.610	−	18.1767i	−0.190724	−	0.0248316i
$733$	−228.483	+	395.744i	−0.311709	+	0.539896i	−0.978733	−	0.205140i	$-0.934235\pi$
$733$	−228.483	+	395.744i	−0.311709	+	0.539896i	0.667023	+	0.745037i	$0.267568\pi$
$734$			300.352i			0.409198i
$735$		0			0
$736$	132.620			0.180190
$737$	61.5026	+	35.5086i	0.0834500	+	0.0481799i
$738$	251.158	−	252.600i	0.340322	−	0.342276i
$739$	166.099	+	287.692i	0.224762	+	0.389300i	0.956248	−	0.292557i	$-0.0945061\pi$
$739$	166.099	+	287.692i	0.224762	+	0.389300i	−0.731486	+	0.681857i	$0.761173\pi$
$740$	601.025	+	347.002i	0.812196	+	0.468922i
$741$	−118.480	+	154.864i	−0.159892	+	0.208994i
$742$		0			0
$743$			64.5346i			0.0868568i	0.999057	+	0.0434284i	$0.0138280\pi$
$743$			64.5346i			0.0868568i	−0.999057	+	0.0434284i	$0.986172\pi$
$744$	895.032	−	372.236i	1.20300	−	0.500318i
$745$	−751.549	−	1301.72i	−1.00879	−	1.74728i
$746$	500.050	−	288.704i	0.670308	−	0.387003i
$747$	207.273	−	782.505i	0.277473	−	1.04753i
$748$	−72.7530			−0.0972633
$749$		0			0
$750$	78.3765	−	102.446i	0.104502	−	0.136594i
$751$	305.834	−	529.720i	0.407236	−	0.705353i	−0.587343	−	0.809338i	$-0.699826\pi$
$751$	305.834	−	529.720i	0.407236	−	0.705353i	0.994579	+	0.103985i	$0.0331594\pi$
$752$	−54.8025	+	31.6402i	−0.0728757	+	0.0420748i
$753$	103.898	−	798.010i	0.137979	−	1.05977i
$754$	72.1477	−	124.964i	0.0956866	−	0.165734i
$755$		−	1223.15i		−	1.62007i
$756$		0			0
$757$	−207.357			−0.273919			−0.136960	−	0.990577i	$-0.543733\pi$
$757$	−207.357			−0.273919			−0.136960	+	0.990577i	$0.543733\pi$
$758$	476.792	+	275.276i	0.629013	+	0.363161i
$759$	33.4588	+	4.35622i	0.0440827	+	0.00573941i
$760$	310.373	+	537.581i	0.408385	+	0.707343i
$761$	292.518	+	168.885i	0.384386	+	0.221925i	0.679725	−	0.733467i	$-0.262099\pi$
$761$	292.518	+	168.885i	0.384386	+	0.221925i	−0.295339	+	0.955393i	$0.595433\pi$
$762$	113.933	+	87.1653i	0.149519	+	0.114390i
$763$		0			0
$764$		−	102.456i		−	0.134104i
$765$	779.722	+	206.535i	1.01924	+	0.269981i
$766$	−389.247	−	674.196i	−0.508155	−	0.880151i
$767$	227.624	−	131.419i	0.296771	−	0.171341i
$768$	308.745	+	742.369i	0.402012	+	0.966626i
$769$	−1042.22			−1.35529			−0.677646	−	0.735388i	$-0.737000\pi$
$769$	−1042.22			−1.35529			−0.677646	+	0.735388i	$0.737000\pi$
$770$		0			0
$771$	557.852	+	426.788i	0.723544	+	0.553551i
$772$	166.273	−	287.994i	0.215380	−	0.373049i
$773$	−252.401	+	145.724i	−0.326522	+	0.188517i	−0.654296	−	0.756239i	$-0.727035\pi$
$773$	−252.401	+	145.724i	−0.326522	+	0.188517i	0.327774	+	0.944756i	$0.393702\pi$
$774$	466.110	+	463.449i	0.602209	+	0.598771i
$775$	578.715	−	1002.36i	0.746729	−	1.29337i
$776$			157.613i			0.203110i
$777$		0			0
$778$	−480.157			−0.617168
$779$	268.233	+	154.864i	0.344330	+	0.198799i
$780$	−41.6183	+	319.657i	−0.0533568	+	0.409817i
$781$	88.6275	+	153.507i	0.113479	+	0.196552i
$782$	−59.1469	−	34.1485i	−0.0756355	−	0.0436682i
$783$	177.646	−	434.138i	0.226878	−	0.554455i
$784$		0			0
$785$			2233.95i			2.84580i
$786$	−50.7234	−	121.963i	−0.0645336	−	0.155169i
$787$	−146.944	−	254.515i	−0.186715	−	0.323399i	0.757438	−	0.652907i	$-0.226451\pi$
$787$	−146.944	−	254.515i	−0.186715	−	0.323399i	−0.944153	+	0.329507i	$0.893117\pi$
$788$	−173.573	+	100.212i	−0.220270	+	0.127173i
$789$	−692.892	+	288.168i	−0.878190	+	0.365232i
$790$	−610.065			−0.772235
$791$		0			0
$792$	50.6117	+	186.745i	0.0639037	+	0.235790i
$793$	−65.0667	+	112.699i	−0.0820513	+	0.142117i
$794$	462.239	−	266.874i	0.582165	−	0.336113i
$795$	−2305.13	−	300.120i	−2.89954	−	0.377510i
$796$	−74.9516	+	129.820i	−0.0941603	+	0.163090i
$797$			568.764i			0.713631i	0.934175	+	0.356816i	$0.116138\pi$
$797$			568.764i			0.713631i	−0.934175	+	0.356816i	$0.883862\pi$
$798$		0			0
$799$	−485.490			−0.607622
$800$	786.381	+	454.017i	0.982976	+	0.567522i
$801$	403.190	+	400.888i	0.503358	+	0.500484i
$802$	156.078	+	270.336i	0.194612	+	0.337077i
$803$	−137.625	−	79.4577i	−0.171388	−	0.0989511i
$804$	113.476	−	148.324i	0.141139	−	0.184482i
$805$		0			0
$806$		−	326.340i		−	0.404888i
$807$	−943.691	+	392.473i	−1.16938	+	0.486336i
$808$	405.884	+	703.012i	0.502332	+	0.870064i
$809$	159.086	−	91.8486i	0.196646	−	0.113534i	−0.398444	−	0.917193i	$-0.630450\pi$
$809$	159.086	−	91.8486i	0.196646	−	0.113534i	0.595090	+	0.803659i	$0.297116\pi$
$810$	−4.47335	−	781.293i	−0.00552265	−	0.964559i
$811$	−544.663			−0.671594			−0.335797	−	0.941934i	$-0.609006\pi$
$811$	−544.663			−0.671594			−0.335797	+	0.941934i	$0.609006\pi$
$812$		0			0
$813$	38.8261	−	50.7494i	0.0477566	−	0.0624224i
$814$	70.1176	−	121.447i	0.0861396	−	0.149198i
$815$	926.934	−	535.166i	1.13734	−	0.656645i
$816$	7.44640	−	57.1935i	0.00912549	−	0.0700901i
$817$	−285.763	+	494.957i	−0.349772	+	0.605822i
$818$		−	848.781i		−	1.03763i
$819$		0			0
$820$	512.044			0.624444
$821$	1029.51	+	594.390i	1.25397	+	0.723983i	0.971897	−	0.235409i	$-0.0756428\pi$
$821$	1029.51	+	594.390i	1.25397	+	0.723983i	0.282078	+	0.959391i	$0.408976\pi$
$822$	155.441	+	20.2379i	0.189101	+	0.0246203i
$823$	−632.575	−	1095.65i	−0.768621	−	1.33129i	−0.938311	−	0.345793i	$-0.887610\pi$
$823$	−632.575	−	1095.65i	−0.768621	−	1.33129i	0.169690	−	0.985498i	$-0.445723\pi$
$824$	400.610	+	231.293i	0.486178	+	0.280695i
$825$	183.484	+	140.375i	0.222404	+	0.170152i
$826$		0			0
$827$			790.941i			0.956398i	0.878252	+	0.478199i	$0.158710\pi$
$827$			790.941i			0.956398i	−0.878252	+	0.478199i	$0.841290\pi$
$828$	22.7192	−	85.7708i	0.0274387	−	0.103588i
$829$	−49.5981	−	85.9064i	−0.0598288	−	0.103626i	0.834560	−	0.550918i	$-0.185722\pi$
$829$	−49.5981	−	85.9064i	−0.0598288	−	0.103626i	−0.894388	+	0.447291i	$0.852389\pi$
$830$	−751.340	+	433.786i	−0.905229	+	0.522634i
$831$	261.410	+	628.553i	0.314573	+	0.756381i
$832$	296.257			0.356079
$833$		0			0
$834$	606.188	+	463.768i	0.726844	+	0.556076i
$835$	72.5385	−	125.640i	0.0868725	−	0.150468i
$836$	−53.0653	+	30.6373i	−0.0634753	+	0.0366475i
$837$	−142.987	−	1051.19i	−0.170832	−	1.25590i
$838$	7.52744	−	13.0379i	0.00898262	−	0.0155584i
$839$		−	243.824i		−	0.290612i	−0.989387	−	0.145306i	$-0.953583\pi$
$839$		−	243.824i		−	0.290612i	0.989387	−	0.145306i	$-0.0464167\pi$
$840$		0			0
$841$	539.170			0.641106
$842$	95.0772	+	54.8928i	0.112918	+	0.0651934i
$843$	−91.2098	+	700.554i	−0.108197	+	0.831025i
$844$	−46.4980	−	80.5370i	−0.0550925	−	0.0954229i
$845$	−822.015	−	474.591i	−0.972799	−	0.561646i
$846$	123.012	+	453.885i	0.145404	+	0.536507i
$847$		0			0
$848$			166.218i			0.196012i
$849$	−424.672	−	1021.11i	−0.500203	−	1.20272i
$850$	−233.812	−	404.974i	−0.275073	−	0.476440i
$851$	−152.913	+	88.2844i	−0.179686	+	0.103742i
$852$	430.388	−	178.995i	0.505150	−	0.210088i
$853$	−1122.06			−1.31543			−0.657713	−	0.753268i	$-0.728476\pi$
$853$	−1122.06			−1.31543			−0.657713	+	0.753268i	$0.728476\pi$
$854$		0			0
$855$	655.697	−	177.707i	0.766897	−	0.207844i
$856$	−506.314	+	876.961i	−0.591488	+	1.02449i
$857$	754.732	−	435.744i	0.880667	−	0.508453i	0.00978864	−	0.999952i	$-0.496884\pi$
$857$	754.732	−	435.744i	0.880667	−	0.508453i	0.870878	+	0.491499i	$0.163551\pi$
$858$	64.5921	+	8.40968i	0.0752822	+	0.00980149i
$859$	837.461	−	1450.52i	0.974925	−	1.68862i	0.294744	−	0.955576i	$-0.404766\pi$
$859$	837.461	−	1450.52i	0.974925	−	1.68862i	0.680182	−	0.733044i	$-0.261901\pi$
$860$			944.850i			1.09866i
$861$		0			0
$862$	907.129			1.05235
$863$	−1143.80	−	660.372i	−1.32537	−	0.765205i	−0.340793	−	0.940138i	$-0.610696\pi$
$863$	−1143.80	−	660.372i	−1.32537	−	0.765205i	−0.984580	+	0.174934i	$0.944029\pi$
$864$	824.687	−	112.177i	0.954499	−	0.129834i
$865$	72.6458	+	125.826i	0.0839835	+	0.145464i
$866$	−132.253	−	76.3566i	−0.152718	−	0.0881716i
$867$	−257.940	+	337.153i	−0.297509	+	0.388873i
$868$		0			0
$869$		−	165.340i		−	0.190264i
$870$	−464.190	+	193.053i	−0.533552	+	0.221900i
$871$	−86.3098	−	149.493i	−0.0990928	−	0.171634i
$872$	1171.82	−	676.549i	1.34383	−	0.775859i
$873$	166.744	+	44.1676i	0.191001	+	0.0505929i
$874$	−57.5217			−0.0658142
$875$		0			0
$876$	−253.925	+	331.905i	−0.289869	+	0.378887i
$877$	172.395	−	298.596i	0.196573	−	0.340475i	−0.750842	−	0.660482i	$-0.770352\pi$
$877$	172.395	−	298.596i	0.196573	−	0.340475i	0.947415	+	0.320007i	$0.103685\pi$
$878$	−597.767	+	345.121i	−0.680828	+	0.393076i
$879$	−205.910	+	1581.53i	−0.234254	+	1.79924i
$880$	15.2693	−	26.4472i	0.0173514	−	0.0300536i
$881$		−	518.737i		−	0.588805i	−0.955682	−	0.294403i	$-0.904879\pi$
$881$		−	518.737i		−	0.588805i	0.955682	−	0.294403i	$-0.0951206\pi$
$882$		0			0
$883$	−584.008			−0.661391			−0.330695	−	0.943738i	$-0.607283\pi$
$883$	−584.008			−0.661391			−0.330695	+	0.943738i	$0.607283\pi$
$884$	153.147	+	88.4194i	0.173243	+	0.100022i
$885$	−908.077	−	118.229i	−1.02608	−	0.133592i
$886$	−177.929	−	308.183i	−0.200823	−	0.347836i
$887$	227.949	+	131.607i	0.256989	+	0.148373i	0.622960	−	0.782254i	$-0.285930\pi$
$887$	227.949	+	131.607i	0.256989	+	0.148373i	−0.365971	+	0.930626i	$0.619263\pi$
$888$	−804.153	−	615.221i	−0.905577	−	0.692817i
$889$		0			0
$890$		−	609.366i		−	0.684681i
$891$	211.746	−	1.21237i	0.237650	−	0.00136068i
$892$	−115.674	−	200.354i	−0.129680	−	0.224612i
$893$	−354.112	+	204.447i	−0.396542	+	0.228944i
$894$	306.707	+	737.470i	0.343073	+	0.824910i
$895$	2521.92			2.81778
$896$		0			0
$897$	−65.1373	−	49.8336i	−0.0726168	−	0.0555559i
$898$	343.616	−	595.160i	0.382645	−	0.662761i
$899$	−591.167	+	341.311i	−0.657583	+	0.379656i
$900$	428.348	−	430.808i	0.475943	−	0.478675i
$901$	−637.616	+	1104.38i	−0.707676	+	1.22573i
$902$		−	103.467i		−	0.114709i
$903$		0			0
$904$	−1184.61			−1.31041
$905$	1379.72	+	796.580i	1.52455	+	0.880198i
$906$	−83.9129	+	644.510i	−0.0926191	+	0.711379i
$907$	750.859	+	1300.53i	0.827849	+	1.43388i	0.899723	+	0.436462i	$0.143769\pi$
$907$	750.859	+	1300.53i	0.827849	+	1.43388i	−0.0718739	+	0.997414i	$0.522898\pi$
$908$	−776.494	−	448.309i	−0.855169	−	0.493732i
$909$	857.476	−	232.393i	0.943318	−	0.255658i
$910$		0			0
$911$		−	879.178i		−	0.965069i	−0.875877	−	0.482534i	$-0.839716\pi$
$911$		−	879.178i		−	0.965069i	0.875877	−	0.482534i	$-0.160284\pi$
$912$	−18.6537	−	44.8522i	−0.0204536	−	0.0491800i
$913$	−117.565	−	203.628i	−0.128767	−	0.223032i
$914$	−581.594	+	335.783i	−0.636317	+	0.367378i
$915$	418.632	−	174.105i	0.457521	−	0.190279i
$916$	−15.6092			−0.0170406
$917$		0			0
$918$	−396.686	−	162.321i	−0.432120	−	0.176820i
$919$	−38.4941	+	66.6737i	−0.0418869	+	0.0725503i	−0.886209	−	0.463286i	$-0.846670\pi$
$919$	−38.4941	+	66.6737i	−0.0418869	+	0.0725503i	0.844322	+	0.535836i	$0.180004\pi$
$920$	−226.111	+	130.545i	−0.245773	+	0.141897i
$921$	1689.03	+	219.907i	1.83391	+	0.238769i
$922$	−449.561	+	778.663i	−0.487594	+	0.844537i
$923$		−	430.849i		−	0.466792i
$924$		0			0
$925$	−1208.95			−1.30697
$926$	−884.144	−	510.461i	−0.954799	−	0.551253i
$927$	356.953	−	359.002i	0.385062	−	0.387273i
$928$	−267.767	−	463.787i	−0.288542	−	0.499770i
$929$	1411.41	+	814.879i	1.51928	+	0.877157i	0.999742	+	0.0227099i	$0.00722941\pi$
$929$	1411.41	+	814.879i	1.51928	+	0.877157i	0.519538	+	0.854447i	$0.326104\pi$
$930$	−690.863	+	903.023i	−0.742863	+	0.970993i
$931$		0			0
$932$		−	267.823i		−	0.287364i
$933$	−118.426	+	49.2523i	−0.126930	+	0.0527892i
$934$	−106.759	−	184.912i	−0.114303	−	0.197978i
$935$	202.904	−	117.146i	0.217009	−	0.125290i
$936$	120.420	−	454.614i	0.128654	−	0.485699i
$937$	−497.720			−0.531185			−0.265592	−	0.964085i	$-0.585568\pi$
$937$	−497.720			−0.531185			−0.265592	+	0.964085i	$0.585568\pi$
$938$		0			0
$939$	288.229	−	376.742i	0.306953	−	0.401217i
$940$	−337.992	+	585.420i	−0.359566	+	0.622787i
$941$	206.888	−	119.447i	0.219860	−	0.126936i	−0.386025	−	0.922488i	$-0.626152\pi$
$941$	206.888	−	119.447i	0.219860	−	0.126936i	0.605886	+	0.795552i	$0.292819\pi$
$942$	153.258	−	1177.13i	0.162694	−	1.24960i
$943$	−65.1373	+	112.821i	−0.0690746	+	0.119641i
$944$			65.4794i			0.0693638i
$945$		0			0
$946$	190.923			0.201821
$947$	−578.427	−	333.955i	−0.610799	−	0.352645i	0.162479	−	0.986712i	$-0.448051\pi$
$947$	−578.427	−	333.955i	−0.610799	−	0.352645i	−0.773278	+	0.634067i	$0.781384\pi$
$948$	−431.153	−	56.1347i	−0.454803	−	0.0592138i
$949$	193.136	+	334.521i	0.203515	+	0.352499i
$950$	−341.080	−	196.923i	−0.359032	−	0.207287i
$951$	−335.824	−	256.924i	−0.353127	−	0.270162i
$952$		0			0
$953$			11.3247i			0.0118832i	0.999982	+	0.00594162i	$0.00189129\pi$
$953$			11.3247i			0.0118832i	−0.999982	+	0.00594162i	$0.998109\pi$
$954$	1194.04	+	316.282i	1.25162	+	0.331533i
$955$	164.974	+	285.743i	0.172747	+	0.299207i
$956$	118.995	−	68.7019i	0.124472	−	0.0718639i
$957$	−52.3211	−	125.805i	−0.0546720	−	0.131457i
$958$	915.174			0.955296
$959$		0			0
$960$	−819.782	−	627.178i	−0.853939	−	0.653311i
$961$	−291.411	+	504.739i	−0.303237	+	0.525222i
$962$	−295.199	+	170.433i	−0.306860	+	0.177165i
$963$	785.878	+	781.392i	0.816073	+	0.811414i
$964$	−154.393	+	267.417i	−0.160159	+	0.277404i
$965$			1070.93i			1.10977i
$966$		0			0
$967$	830.324			0.858660			0.429330	−	0.903148i	$-0.358750\pi$
$967$	830.324			0.858660			0.429330	+	0.903148i	$0.358750\pi$
$968$	−813.072	−	469.427i	−0.839950	−	0.484946i
$969$	48.1157	−	369.562i	0.0496550	−	0.381385i
$970$	−92.4353	−	160.103i	−0.0952941	−	0.165054i
$971$	−1054.45	−	608.788i	−1.08594	−	0.626970i	−0.153450	−	0.988156i	$-0.549038\pi$
$971$	−1054.45	−	608.788i	−1.08594	−	0.626970i	−0.932494	+	0.361187i	$0.882372\pi$
$972$	68.7286	−	552.577i	0.0707085	−	0.568495i
$973$		0			0
$974$			113.183i			0.116204i
$975$	−215.635	−	518.488i	−0.221164	−	0.531783i
$976$	−16.2098	−	28.0761i	−0.0166084	−	0.0287665i
$977$	−367.696	+	212.289i	−0.376352	+	0.217287i	−0.676230	−	0.736691i	$-0.736387\pi$
$977$	−367.696	+	212.289i	−0.376352	+	0.217287i	0.299878	+	0.953978i	$0.403054\pi$
$978$	−525.140	+	218.401i	−0.536953	+	0.223314i
$979$	165.150			0.168693
$980$		0			0
$981$	−387.365	−	1429.29i	−0.394867	−	1.45697i
$982$	484.601	−	839.354i	0.493484	−	0.854739i
$983$	−66.4478	+	38.3636i	−0.0675969	+	0.0390271i	−0.533418	−	0.845852i	$-0.679093\pi$
$983$	−66.4478	+	38.3636i	−0.0675969	+	0.0390271i	0.465821	+	0.884879i	$0.345759\pi$
$984$	−740.783	−	96.4475i	−0.752829	−	0.0980157i
$985$	322.723	−	558.972i	0.327637	−	0.567485i
$986$			275.792i			0.279708i
$987$		0			0
$988$	148.939			0.150748
$989$	−208.183	−	120.195i	−0.210499	−	0.121531i
$990$	−160.931	−	160.012i	−0.162557	−	0.161629i
$991$	−90.6353	−	156.985i	−0.0914585	−	0.158411i	0.816667	−	0.577110i	$-0.195820\pi$
$991$	−90.6353	−	156.985i	−0.0914585	−	0.158411i	−0.908125	+	0.418699i	$0.862486\pi$
$992$	−1048.90	−	605.585i	−1.05736	−	0.610469i
$993$	470.974	−	615.608i	0.474294	−	0.619947i
$994$		0			0
$995$		−	482.747i		−	0.485173i
$996$	−570.911	+	237.437i	−0.573204	+	0.238391i
$997$	592.216	+	1025.75i	0.593998	+	1.02884i	0.993687	+	0.112184i	$0.0357847\pi$
$997$	592.216	+	1025.75i	0.593998	+	1.02884i	−0.399689	+	0.916651i	$0.630882\pi$
$998$	429.941	−	248.227i	0.430803	−	0.248724i
$999$	−876.205	+	678.334i	−0.877082	+	0.679013i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.3.h.e.128.2		8
3.2	odd	2	inner	147.3.h.e.128.3		8
7.2	even	3		21.3.b.a.8.3	yes	4
7.3	odd	6		147.3.h.c.116.3		8
7.4	even	3	inner	147.3.h.e.116.3		8
7.5	odd	6		147.3.b.f.50.3		4
7.6	odd	2		147.3.h.c.128.2		8
21.2	odd	6		21.3.b.a.8.2	✓	4
21.5	even	6		147.3.b.f.50.2		4
21.11	odd	6	inner	147.3.h.e.116.2		8
21.17	even	6		147.3.h.c.116.2		8
21.20	even	2		147.3.h.c.128.3		8
28.23	odd	6		336.3.d.c.113.3		4
35.2	odd	12		525.3.f.a.449.4		8
35.9	even	6		525.3.c.a.176.2		4
35.23	odd	12		525.3.f.a.449.5		8
56.37	even	6		1344.3.d.f.449.3		4
56.51	odd	6		1344.3.d.b.449.2		4
63.2	odd	6		567.3.r.c.134.2		8
63.16	even	3		567.3.r.c.134.3		8
63.23	odd	6		567.3.r.c.512.3		8
63.58	even	3		567.3.r.c.512.2		8
84.23	even	6		336.3.d.c.113.4		4
105.2	even	12		525.3.f.a.449.6		8
105.23	even	12		525.3.f.a.449.3		8
105.44	odd	6		525.3.c.a.176.3		4
168.107	even	6		1344.3.d.b.449.1		4
168.149	odd	6		1344.3.d.f.449.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.b.a.8.2	✓	4	21.2	odd	6
21.3.b.a.8.3	yes	4	7.2	even	3
147.3.b.f.50.2		4	21.5	even	6
147.3.b.f.50.3		4	7.5	odd	6
147.3.h.c.116.2		8	21.17	even	6
147.3.h.c.116.3		8	7.3	odd	6
147.3.h.c.128.2		8	7.6	odd	2
147.3.h.c.128.3		8	21.20	even	2
147.3.h.e.116.2		8	21.11	odd	6	inner
147.3.h.e.116.3		8	7.4	even	3	inner
147.3.h.e.128.2		8	1.1	even	1	trivial
147.3.h.e.128.3		8	3.2	odd	2	inner
336.3.d.c.113.3		4	28.23	odd	6
336.3.d.c.113.4		4	84.23	even	6
525.3.c.a.176.2		4	35.9	even	6
525.3.c.a.176.3		4	105.44	odd	6
525.3.f.a.449.3		8	105.23	even	12
525.3.f.a.449.4		8	35.2	odd	12
525.3.f.a.449.5		8	35.23	odd	12
525.3.f.a.449.6		8	105.2	even	12
567.3.r.c.134.2		8	63.2	odd	6
567.3.r.c.134.3		8	63.16	even	3
567.3.r.c.512.2		8	63.58	even	3
567.3.r.c.512.3		8	63.23	odd	6
1344.3.d.b.449.1		4	168.107	even	6
1344.3.d.b.449.2		4	56.51	odd	6
1344.3.d.f.449.3		4	56.37	even	6
1344.3.d.f.449.4		4	168.149	odd	6

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	147.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.13198 - 0.653548i) q^{2} +(2.97489 + 0.387321i) q^{3} +(-1.14575 - 1.98450i) q^{4} +(6.39086 + 3.68977i) q^{5} +(-3.11438 - 2.38267i) q^{6} +8.22359i q^{8} +(8.69997 + 2.30448i) q^{9} +O(q^{10})\)	\(q+(-1.13198 - 0.653548i) q^{2} +(2.97489 + 0.387321i) q^{3} +(-1.14575 - 1.98450i) q^{4} +(6.39086 + 3.68977i) q^{5} +(-3.11438 - 2.38267i) q^{6} +8.22359i q^{8} +(8.69997 + 2.30448i) q^{9} +(-4.82288 - 8.35347i) q^{10} +(2.26395 - 1.30710i) q^{11} +(-2.63985 - 6.34745i) q^{12} -6.35425 q^{13} +(17.5830 + 13.4520i) q^{15} +(0.791503 - 1.37092i) q^{16} +(10.5178 - 6.07244i) q^{17} +(-8.34208 - 8.29445i) q^{18} +(5.11438 - 8.85836i) q^{19} -16.9102i q^{20} -3.41699 q^{22} +(3.72591 + 2.15115i) q^{23} +(-3.18517 + 24.4643i) q^{24} +(14.7288 + 25.5110i) q^{25} +(7.19287 + 4.15280i) q^{26} +(24.9889 + 10.2252i) q^{27} -17.3733i q^{29} +(-11.1121 - 26.7187i) q^{30} +(-19.6458 - 34.0274i) q^{31} +(26.6954 - 15.4126i) q^{32} +(7.24129 - 3.01159i) q^{33} -15.8745 q^{34} +(-5.39477 - 19.9054i) q^{36} +(-20.5203 + 35.5421i) q^{37} +(-11.5787 + 6.68498i) q^{38} +(-18.9032 - 2.46113i) q^{39} +(-30.3431 + 52.5559i) q^{40} +30.2802i q^{41} -55.8745 q^{43} +(-5.18786 - 2.99521i) q^{44} +(47.0973 + 46.8284i) q^{45} +(-2.81176 - 4.87011i) q^{46} +(-34.6193 - 19.9874i) q^{47} +(2.88562 - 3.77178i) q^{48} -38.5038i q^{50} +(33.6412 - 13.9911i) q^{51} +(7.28039 + 12.6100i) q^{52} +(-90.9340 + 52.5008i) q^{53} +(-21.6042 - 27.9062i) q^{54} +19.2915 q^{55} +(18.6458 - 24.3718i) q^{57} +(-11.3542 + 19.6661i) q^{58} +(-35.8223 + 20.6820i) q^{59} +(6.54968 - 50.3061i) q^{60} +(10.2399 - 17.7360i) q^{61} +51.3577i q^{62} -46.6235 q^{64} +(-40.6091 - 23.4457i) q^{65} +(-10.1652 - 1.32347i) q^{66} +(13.5830 + 23.5265i) q^{67} +(-24.1015 - 13.9150i) q^{68} +(10.2510 + 7.84257i) q^{69} +67.8049i q^{71} +(-18.9511 + 71.5450i) q^{72} +(-30.3948 - 52.6453i) q^{73} +(46.4569 - 26.8219i) q^{74} +(33.9355 + 81.5971i) q^{75} -23.4392 q^{76} +(19.7895 + 15.1401i) q^{78} +(31.6235 - 54.7735i) q^{79} +(10.1168 - 5.84092i) q^{80} +(70.3788 + 40.0977i) q^{81} +(19.7895 - 34.2765i) q^{82} -89.9435i q^{83} +89.6235 q^{85} +(63.2487 + 36.5166i) q^{86} +(6.72902 - 51.6836i) q^{87} +(10.7490 + 18.6178i) q^{88} +(54.7108 + 31.5873i) q^{89} +(-22.7085 - 83.7891i) q^{90} -9.85875i q^{92} +(-45.2645 - 108.837i) q^{93} +(26.1255 + 45.2507i) q^{94} +(65.3706 - 37.7417i) q^{95} +(85.3857 - 35.5112i) q^{96} +19.1660 q^{97} +(22.7085 - 6.15445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 12 q^{4} + 28 q^{6} + 20 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 12 * q^4 + 28 * q^6 + 20 * q^9	\( 8 q + 2 q^{3} + 12 q^{4} + 28 q^{6} + 20 q^{9} - 28 q^{10} + 22 q^{12} - 72 q^{13} + 56 q^{15} - 36 q^{16} - 56 q^{18} - 12 q^{19} - 112 q^{22} + 126 q^{24} + 12 q^{25} + 20 q^{27} + 28 q^{30} - 136 q^{31} - 28 q^{33} + 232 q^{36} - 16 q^{37} - 4 q^{39} - 84 q^{40} - 320 q^{43} + 140 q^{45} + 168 q^{46} + 76 q^{48} + 84 q^{51} - 164 q^{52} + 154 q^{54} + 112 q^{55} + 128 q^{57} - 112 q^{58} - 140 q^{60} + 156 q^{61} + 8 q^{64} + 28 q^{66} + 24 q^{67} + 336 q^{69} + 32 q^{73} - 146 q^{75} - 632 q^{76} - 392 q^{78} - 128 q^{79} + 68 q^{81} - 392 q^{82} + 336 q^{85} - 28 q^{87} - 168 q^{88} - 224 q^{90} + 96 q^{93} + 336 q^{94} + 98 q^{96} - 16 q^{97} + 224 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 12 * q^4 + 28 * q^6 + 20 * q^9 - 28 * q^10 + 22 * q^12 - 72 * q^13 + 56 * q^15 - 36 * q^16 - 56 * q^18 - 12 * q^19 - 112 * q^22 + 126 * q^24 + 12 * q^25 + 20 * q^27 + 28 * q^30 - 136 * q^31 - 28 * q^33 + 232 * q^36 - 16 * q^37 - 4 * q^39 - 84 * q^40 - 320 * q^43 + 140 * q^45 + 168 * q^46 + 76 * q^48 + 84 * q^51 - 164 * q^52 + 154 * q^54 + 112 * q^55 + 128 * q^57 - 112 * q^58 - 140 * q^60 + 156 * q^61 + 8 * q^64 + 28 * q^66 + 24 * q^67 + 336 * q^69 + 32 * q^73 - 146 * q^75 - 632 * q^76 - 392 * q^78 - 128 * q^79 + 68 * q^81 - 392 * q^82 + 336 * q^85 - 28 * q^87 - 168 * q^88 - 224 * q^90 + 96 * q^93 + 336 * q^94 + 98 * q^96 - 16 * q^97 + 224 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more