LMFDB - Embedded newform 147.3.h.c.116.2

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			116.2
Root			$-1.85391 + 1.90397i$ of defining polynomial
Character	$\chi$	$=$	147.116
Dual form			147.3.h.c.128.2

$q$-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 $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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	−0.755546	−	0.655096i	$-0.772628\pi$
$2$	−1.13198	+	0.653548i	−0.565989	+	0.326774i	0.189557	+	0.981870i	$0.439295\pi$
$3$	−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	$-0.930874\pi$
$5$	−6.39086	+	3.68977i	−1.27817	+	0.737953i	−0.301660	+	0.953415i	$0.597541\pi$
$6$	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	0.599365	−	0.800476i	$-0.295420\pi$
$11$	2.26395	+	1.30710i	0.205814	+	0.118827i	−0.393550	+	0.919303i	$0.628753\pi$
$12$	2.63985	−	6.34745i	0.219987	−	0.528954i
$13$	6.35425			0.488788			0.244394	−	0.969676i	$-0.421411\pi$
$13$	6.35425			0.488788			0.244394	+	0.969676i	$0.421411\pi$
$14$		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	$-0.449603\pi$
$17$	−10.5178	−	6.07244i	−0.618692	−	0.357202i	−0.776360	+	0.630290i	$0.782936\pi$
$18$	−8.34208	+	8.29445i	−0.463449	+	0.460803i
$19$	−5.11438	−	8.85836i	−0.269178	−	0.466230i	0.699472	−	0.714660i	$-0.253419\pi$
$19$	−5.11438	−	8.85836i	−0.269178	−	0.466230i	−0.968650	+	0.248430i	$0.920085\pi$
$20$		−	16.9102i		−	0.845511i
$21$		0			0
$22$	−3.41699			−0.155318
$23$	3.72591	−	2.15115i	0.161996	−	0.0935284i	−0.416810	−	0.908993i	$-0.636852\pi$
$23$	3.72591	−	2.15115i	0.161996	−	0.0935284i	0.578806	+	0.815465i	$0.303519\pi$
$24$	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	$0.0968328\pi$
$29$			17.3733i			0.599078i	−0.954084	+	0.299539i	$0.903167\pi$
$30$	−11.1121	+	26.7187i	−0.370402	+	0.890622i
$31$	19.6458	−	34.0274i	0.633734	−	1.09766i	−0.353048	−	0.935605i	$-0.614855\pi$
$31$	19.6458	−	34.0274i	0.633734	−	1.09766i	0.986782	−	0.162054i	$-0.0518119\pi$
$32$	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	−0.997934	−	0.0642411i	$-0.979537\pi$
$37$	−20.5203	−	35.5421i	−0.554602	−	0.960598i	0.443333	−	0.896357i	$-0.353796\pi$
$38$	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	$-0.526848\pi$
$47$	34.6193	−	19.9874i	0.736580	−	0.425265i	0.820825	+	0.571180i	$0.193514\pi$
$48$	−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	−0.926332	−	0.376707i	$-0.877056\pi$
$53$	−90.9340	−	52.5008i	−1.71574	−	0.990581i	−0.789404	−	0.613874i	$-0.789610\pi$
$54$	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	$-0.219331\pi$
$59$	35.8223	+	20.6820i	0.607157	+	0.350542i	−0.164695	+	0.986345i	$0.552664\pi$
$60$	6.54968	+	50.3061i	0.109161	+	0.838435i
$61$	−10.2399	−	17.7360i	−0.167867	−	0.290754i	0.769803	−	0.638282i	$-0.220354\pi$
$61$	−10.2399	−	17.7360i	−0.167867	−	0.290754i	−0.937670	+	0.347528i	$0.887021\pi$
$62$			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	−0.746676	−	0.665188i	$-0.768351\pi$
$67$	13.5830	−	23.5265i	0.202731	−	0.351141i	0.949408	+	0.314047i	$0.101685\pi$
$68$	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	$-0.841543\pi$
$71$		−	67.8049i		−	0.954999i	0.878632	−	0.477499i	$-0.158457\pi$
$72$	−18.9511	−	71.5450i	−0.263209	−	0.993680i
$73$	30.3948	−	52.6453i	0.416367	−	0.721168i	−0.579204	−	0.815183i	$-0.696637\pi$
$73$	30.3948	−	52.6453i	0.416367	−	0.721168i	0.995571	+	0.0940143i	$0.0299699\pi$
$74$	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	0.993762	−	0.111525i	$-0.0355734\pi$
$79$	31.6235	+	54.7735i	0.400298	+	0.693336i	−0.593464	+	0.804861i	$0.702240\pi$
$80$	−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	$-0.782156\pi$
$89$	−54.7108	+	31.5873i	−0.614728	+	0.354913i	0.160086	+	0.987103i	$0.448823\pi$
$90$	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	$-0.531498\pi$
$97$	−19.1660			−0.197588			−0.0987939	+	0.995108i	$0.531498\pi$
$98$		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	$-0.495853\pi$
$101$	−85.4872	−	49.3561i	−0.846408	−	0.488674i	−0.859437	+	0.511241i	$0.829186\pi$
$102$	−47.2249	+	6.14853i	−0.462990	+	0.0602797i
$103$	−28.1255	−	48.7148i	−0.273063	−	0.472959i	0.696582	−	0.717478i	$-0.254703\pi$
$103$	−28.1255	−	48.7148i	−0.273063	−	0.472959i	−0.969645	+	0.244519i	$0.921370\pi$
$104$		−	52.2547i		−	0.502449i
$105$		0			0
$106$	137.247			1.29478
$107$	106.640	−	61.5684i	0.996632	−	0.575406i	0.0893823	−	0.995997i	$-0.471511\pi$
$107$	106.640	−	61.5684i	0.996632	−	0.575406i	0.907250	+	0.420591i	$0.138177\pi$
$108$	8.33906	−	61.3060i	0.0772135	−	0.567648i
$109$	−82.2693	+	142.495i	−0.754764	+	1.30729i	0.190728	+	0.981643i	$0.438915\pi$
$109$	−82.2693	+	142.495i	−0.754764	+	1.30729i	−0.945492	+	0.325647i	$0.894418\pi$
$110$	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	$-0.780014\pi$
$113$		−	144.050i		−	1.27478i	0.770540	−	0.637391i	$-0.219986\pi$
$114$	−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	$-0.707706\pi$
$131$	−29.1725	+	16.8427i	−0.222691	+	0.128570i	0.384505	+	0.923123i	$0.374372\pi$
$132$	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	0.368302	−	0.929706i	$-0.379939\pi$
$137$	−34.6193	−	19.9874i	−0.252695	−	0.145894i	−0.620998	+	0.783812i	$0.713272\pi$
$138$	6.47839	−	15.5771i	0.0469449	−	0.112878i
$139$	194.642			1.40030			0.700150	−	0.713995i	$-0.253116\pi$
$139$	194.642			1.40030			0.700150	+	0.713995i	$0.253116\pi$
$140$		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	−0.956906	−	0.290398i	$-0.906212\pi$
$149$	−176.396	+	101.842i	−1.18387	+	0.683506i	−0.226961	+	0.973904i	$0.572879\pi$
$150$	−14.9133	−	114.545i	−0.0994221	−	0.763630i
$151$	−82.8745	+	143.543i	−0.548838	+	0.950615i	0.449517	+	0.893272i	$0.351596\pi$
$151$	−82.8745	+	143.543i	−0.548838	+	0.950615i	−0.998355	+	0.0573430i	$0.981737\pi$
$152$	−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	−0.252033	+	0.967719i	$0.581099\pi$
$157$	−151.361	+	262.166i	−0.964086	+	1.66985i	−0.712052	+	0.702127i	$0.752234\pi$
$158$	−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	0.998046	−	0.0624848i	$-0.0199025\pi$
$163$	72.5203	+	125.609i	0.444910	+	0.770606i	−0.553136	+	0.833091i	$0.686569\pi$
$164$	−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	$-0.684789\pi$
$173$	−17.0507	+	9.84422i	−0.0985589	+	0.0569030i	0.449910	+	0.893074i	$0.351456\pi$
$174$	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	0.975658	+	0.219300i	$0.0703772\pi$
$179$	295.960	+	170.872i	1.65341	+	0.954594i	0.677748	+	0.735294i	$0.262956\pi$
$180$	−38.9692	−	147.118i	−0.216495	−	0.817324i
$181$	−215.889			−1.19276			−0.596378	−	0.802704i	$-0.703394\pi$
$181$	−215.889			−1.19276			−0.596378	+	0.802704i	$0.703394\pi$
$182$		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	−0.395199	−	0.918595i	$-0.629324\pi$
$191$	38.7210	−	22.3556i	0.202728	−	0.117045i	0.597927	+	0.801550i	$0.295991\pi$
$192$	138.700	−	18.0583i	0.722396	−	0.0940534i
$193$	72.5608	−	125.679i	0.375963	−	0.651186i	−0.614508	−	0.788911i	$-0.710645\pi$
$193$	72.5608	−	125.679i	0.375963	−	0.651186i	0.990471	+	0.137724i	$0.0439788\pi$
$194$	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	$0.0712554\pi$
$197$			87.4643i			0.443981i	−0.975049	+	0.221991i	$0.928745\pi$
$198$	−29.7277	+	7.87438i	−0.150140	+	0.0397696i
$199$	32.7085	−	56.6528i	0.164364	−	0.284687i	−0.772065	−	0.635544i	$-0.780776\pi$
$199$	32.7085	−	56.6528i	0.164364	−	0.284687i	0.936429	+	0.350856i	$0.114109\pi$
$200$	−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	$-0.572685\pi$
$223$	−100.959			−0.452733			−0.226367	+	0.974042i	$0.572685\pi$
$224$		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	$-0.664027\pi$
$227$	−338.858	−	195.640i	−1.49277	−	0.861849i	−0.999966	+	0.00829388i	$0.997360\pi$
$228$	−69.7292	+	9.07850i	−0.305830	+	0.0398180i
$229$	−3.40588	−	5.89916i	−0.0148728	−	0.0257605i	0.858493	−	0.512825i	$-0.171401\pi$
$229$	−3.40588	−	5.89916i	−0.0148728	−	0.0257605i	−0.873366	+	0.487064i	$0.838068\pi$
$230$		−	41.4990i		−	0.180430i
$231$		0			0
$232$	142.871			0.615821
$233$	101.218	−	58.4383i	0.434412	−	0.250808i	−0.266812	−	0.963748i	$-0.585970\pi$
$233$	101.218	−	58.4383i	0.434412	−	0.250808i	0.701224	+	0.712941i	$0.252637\pi$
$234$	−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	$-0.959964\pi$
$239$		−	59.9623i		−	0.250888i	0.992101	−	0.125444i	$-0.0400356\pi$
$240$	32.3586	+	13.4577i	0.134828	+	0.0560736i
$241$	67.3765	−	116.699i	0.279570	−	0.484230i	−0.691708	−	0.722178i	$-0.743141\pi$
$241$	67.3765	−	116.699i	0.279570	−	0.484230i	0.971278	+	0.237947i	$0.0764746\pi$
$242$	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	$-0.817207\pi$
$257$	−202.762	+	117.064i	−0.788956	+	0.455504i	0.0506392	+	0.998717i	$0.483874\pi$
$258$	−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	0.0279999	−	0.999608i	$-0.491086\pi$
$263$	−216.629	−	125.071i	−0.823686	−	0.475555i	−0.851686	+	0.524053i	$0.824420\pi$
$264$	−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	$-0.115058\pi$
$269$	295.041	+	170.342i	1.09681	+	0.633241i	0.161425	+	0.986885i	$0.448391\pi$
$270$	−35.1021	+	258.059i	−0.130008	+	0.955774i
$271$	−10.6497	−	18.4458i	−0.0392977	−	0.0680657i	0.845708	−	0.533647i	$-0.179179\pi$
$271$	−10.6497	−	18.4458i	−0.0392977	−	0.0680657i	−0.885005	+	0.465581i	$0.845845\pi$
$272$		−	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	−0.585250	−	0.810853i	$-0.699004\pi$
$277$	113.458	−	196.514i	0.409594	−	0.709437i	0.994844	+	0.101415i	$0.0323371\pi$
$278$	−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	$-0.862374\pi$
$281$		−	235.489i		−	0.838039i	0.907977	−	0.419019i	$-0.137626\pi$
$282$	60.1940	−	144.735i	0.213454	−	0.513244i
$283$	184.317	−	319.246i	0.651297	−	1.12808i	−0.331512	−	0.943451i	$-0.607559\pi$
$283$	184.317	−	319.246i	0.651297	−	1.12808i	0.982808	−	0.184628i	$-0.0591080\pi$
$284$	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	$-0.875681\pi$
$307$	−567.763			−1.84939			−0.924696	+	0.380706i	$0.875681\pi$
$308$		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	$-0.311437\pi$
$311$	37.0253	+	21.3766i	0.119052	+	0.0687349i	−0.439291	+	0.898345i	$0.644770\pi$
$312$	20.2393	+	155.452i	0.0648697	+	0.498244i
$313$	−79.0588	−	136.934i	−0.252584	−	0.437488i	0.711652	−	0.702532i	$-0.247947\pi$
$313$	−79.0588	−	136.934i	−0.252584	−	0.437488i	−0.964237	+	0.265043i	$0.914614\pi$
$314$		−	395.688i		−	1.26015i
$315$		0			0
$316$	−144.931			−0.458642
$317$	−122.061	+	70.4721i	−0.385051	+	0.222309i	−0.680014	−	0.733199i	$-0.738026\pi$
$317$	−122.061	+	70.4721i	−0.385051	+	0.222309i	0.294963	+	0.955509i	$0.404693\pi$
$318$	−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	0.992487	−	0.122350i	$-0.0390432\pi$
$331$	129.184	+	223.754i	0.390285	+	0.675993i	−0.602202	+	0.798344i	$0.705710\pi$
$332$	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	0.330815	−	0.943696i	$-0.392676\pi$
$347$	−111.401	−	64.3176i	−0.321041	−	0.185353i	−0.651857	+	0.758342i	$0.726010\pi$
$348$	110.276	+	45.8628i	0.316884	+	0.131790i
$349$	73.4837			0.210555			0.105277	−	0.994443i	$-0.466427\pi$
$349$	73.4837			0.210555			0.105277	+	0.994443i	$0.466427\pi$
$350$		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	$-0.443590\pi$
$353$	−207.574	−	119.843i	−0.588027	−	0.339498i	−0.764317	+	0.644841i	$0.776924\pi$
$354$	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	−0.266625	−	0.963800i	$-0.585909\pi$
$359$	156.071	−	90.1075i	0.434738	−	0.250996i	0.701363	+	0.712804i	$0.252575\pi$
$360$	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	$-0.731979\pi$
$367$	114.893	−	199.000i	0.313059	−	0.542235i	0.979023	+	0.203749i	$0.0653128\pi$
$368$	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	−0.993941	−	0.109912i	$-0.964943\pi$
$373$	−220.875	−	382.566i	−0.592157	−	1.02565i	0.401785	−	0.915734i	$-0.368390\pi$
$374$	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	$-0.950196\pi$
$383$	−515.797	+	297.796i	−1.34673	+	0.777534i	−0.358944	+	0.933359i	$0.616863\pi$
$384$	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	0.849664	−	0.527325i	$-0.176805\pi$
$389$	318.132	+	183.673i	0.817819	+	0.472168i	−0.0318449	+	0.999493i	$0.510138\pi$
$390$	−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	0.999863	+	0.0165802i	$0.00527788\pi$
$397$	204.173	+	353.638i	0.514290	+	0.890777i	−0.485572	+	0.874196i	$0.661389\pi$
$398$			85.5062i			0.214840i
$399$		0			0
$400$	46.6314			0.116578
$401$	−206.822	+	119.409i	−0.515765	+	0.297777i	−0.735200	−	0.677850i	$-0.762912\pi$
$401$	−206.822	+	119.409i	−0.515765	+	0.297777i	0.219435	+	0.975627i	$0.429579\pi$
$402$	−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	0.129726	+	0.991550i	$0.458590\pi$
$409$	−324.682	+	562.366i	−0.793844	+	1.37498i	−0.923570	+	0.383429i	$0.874743\pi$
$410$	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	−0.400682	−	0.916217i	$-0.631227\pi$
$431$	−601.025	−	347.002i	−1.39449	−	0.805109i	−0.993808	+	0.111108i	$0.964560\pi$
$432$	−33.7968	−	26.1645i	−0.0782333	−	0.0605660i
$433$	−116.834			−0.269824			−0.134912	−	0.990858i	$-0.543075\pi$
$433$	−116.834			−0.269824			−0.134912	+	0.990858i	$0.543075\pi$
$434$		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	−0.992602	−	0.121416i	$-0.961257\pi$
$439$	−264.037	−	457.325i	−0.601450	−	1.04174i	0.391152	−	0.920326i	$-0.372077\pi$
$440$			158.645i			0.360558i
$441$		0			0
$442$	100.871			0.228214
$443$	235.777	−	136.126i	0.532228	−	0.307282i	−0.209695	−	0.977767i	$-0.567247\pi$
$443$	235.777	−	136.126i	0.532228	−	0.307282i	0.741923	+	0.670485i	$0.233914\pi$
$444$	−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	$-0.800902\pi$
$449$		−	525.770i		−	1.17098i	0.810680	−	0.585490i	$-0.199098\pi$
$450$	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	0.997310	+	0.0732928i	$0.0233508\pi$
$457$	256.893	+	444.951i	0.562129	+	0.973635i	−0.435182	+	0.900343i	$0.643316\pi$
$458$	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	$-0.722626\pi$
$467$	−141.468	+	81.6763i	−0.302928	+	0.174896i	0.340829	+	0.940125i	$0.389292\pi$
$468$	−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	$-0.0724551\pi$
$479$	606.355	+	350.079i	1.26588	+	0.730855i	0.291672	+	0.956518i	$0.405788\pi$
$480$	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	−0.907047	−	0.421028i	$-0.861669\pi$
$487$	−43.2954	+	74.9899i	−0.0889023	+	0.153983i	0.818145	+	0.575012i	$0.195003\pi$
$488$	−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	$-0.727596\pi$
$491$		−	741.494i		−	1.51017i	0.655627	−	0.755085i	$-0.272404\pi$
$492$	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	0.610569	−	0.791963i	$-0.290941\pi$
$499$	−189.907	−	328.929i	−0.380575	−	0.659176i	−0.991145	+	0.132787i	$0.957607\pi$
$500$	−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	$-0.402799\pi$
$509$	649.955	−	375.252i	1.27692	−	0.737233i	0.976282	+	0.216504i	$0.0694654\pi$
$510$	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	$-0.579102\pi$
$521$	−629.554	−	363.473i	−1.20836	−	0.697645i	−0.962400	+	0.271635i	$0.912435\pi$
$522$	−144.102	−	144.929i	−0.276057	−	0.277642i
$523$	−312.354	−	541.012i	−0.597234	−	1.03444i	−0.993227	−	0.116187i	$-0.962933\pi$
$523$	−312.354	−	541.012i	−0.597234	−	1.03444i	0.395993	−	0.918253i	$-0.370400\pi$
$524$		−	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	0.968770	−	0.247960i	$-0.0797600\pi$
$541$	145.878	+	252.669i	0.269646	+	0.467040i	−0.699124	+	0.715000i	$0.746427\pi$
$542$	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	0.0542092	−	0.998530i	$-0.482736\pi$
$557$	−436.375	−	251.941i	−0.783438	−	0.452318i	−0.837647	+	0.546211i	$0.816070\pi$
$558$	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	$-0.364120\pi$
$563$	−94.1672	−	54.3675i	−0.167260	−	0.0965674i	−0.581293	+	0.813694i	$0.697453\pi$
$564$	−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	−0.131113	−	0.991367i	$-0.541855\pi$
$569$	376.610	−	217.436i	0.661880	−	0.382136i	0.792993	+	0.609231i	$0.208522\pi$
$570$	293.515	−	38.2146i	0.514938	−	0.0670432i
$571$	−59.5608	+	103.162i	−0.104310	+	0.180670i	−0.913456	−	0.406938i	$-0.866597\pi$
$571$	−59.5608	+	103.162i	−0.104310	+	0.180670i	0.809146	+	0.587607i	$0.199930\pi$
$572$	−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	0.428816	+	0.903392i	$0.358931\pi$
$577$	−327.708	+	567.608i	−0.567952	+	0.983722i	−0.996768	+	0.0803304i	$0.974402\pi$
$578$	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	$-0.418840\pi$
$593$	721.299	−	416.442i	1.21636	−	0.702263i	0.964137	+	0.265407i	$0.0855062\pi$
$594$	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	0.549279	−	0.835639i	$-0.314902\pi$
$599$	60.0407	+	34.6645i	0.100235	+	0.0578706i	−0.449045	+	0.893509i	$0.648236\pi$
$600$	671.021	+	279.072i	1.11837	+	0.465120i
$601$	161.720			0.269085			0.134543	−	0.990908i	$-0.457043\pi$
$601$	161.720			0.269085			0.134543	+	0.990908i	$0.457043\pi$
$602$		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	0.939855	+	0.341574i	$0.110960\pi$
$607$	464.804	+	805.064i	0.765740	+	1.32630i	−0.174115	+	0.984725i	$0.555707\pi$
$608$		−	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	−0.961572	−	0.274551i	$-0.911471\pi$
$613$	−148.970	+	258.023i	−0.243018	+	0.420919i	0.718555	+	0.695470i	$0.244804\pi$
$614$	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	$0.290220\pi$
$617$			975.575i			1.58116i	−0.612360	+	0.790579i	$0.709780\pi$
$618$	−203.665	−	84.7024i	−0.329555	−	0.137059i
$619$	178.517	−	309.201i	0.288396	−	0.499516i	−0.685031	−	0.728514i	$-0.740211\pi$
$619$	178.517	−	309.201i	0.288396	−	0.499516i	0.973427	+	0.228998i	$0.0735448\pi$
$620$	−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	0.868597	−	0.495520i	$-0.165022\pi$
$641$	560.082	+	323.363i	0.873762	+	0.504467i	0.00516570	+	0.999987i	$0.498356\pi$
$642$	185.419	−	445.835i	0.288814	−	0.694447i
$643$	−144.561			−0.224822			−0.112411	−	0.993662i	$-0.535857\pi$
$643$	−144.561			−0.224822			−0.112411	+	0.993662i	$0.535857\pi$
$644$		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	$-0.146500\pi$
$647$	620.640	+	358.327i	0.959259	+	0.553828i	0.0633138	+	0.997994i	$0.479833\pi$
$648$	−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	−0.729803	−	0.683658i	$-0.760388\pi$
$653$	−328.223	+	189.500i	−0.502639	+	0.290199i	0.227164	+	0.973857i	$0.427055\pi$
$654$	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	$0.181289\pi$
$659$			710.721i			1.07848i	−0.842151	+	0.539242i	$0.818711\pi$
$660$	−50.9266	+	122.452i	−0.0771616	+	0.185533i
$661$	45.7523	−	79.2452i	0.0692167	−	0.119887i	−0.829340	−	0.558744i	$-0.811283\pi$
$661$	45.7523	−	79.2452i	0.0692167	−	0.119887i	0.898557	+	0.438857i	$0.144617\pi$
$662$	−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	$-0.746386\pi$
$677$	−290.613	+	167.786i	−0.429266	+	0.247837i	0.269768	+	0.962925i	$0.413053\pi$
$678$	−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	0.426422	−	0.904524i	$-0.359774\pi$
$683$	−98.1521	−	56.6681i	−0.143707	−	0.0829694i	−0.570130	+	0.821555i	$0.693107\pi$
$684$	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	$-0.0324361\pi$
$691$	282.833	+	489.882i	0.409310	+	0.708946i	−0.585502	+	0.810671i	$0.699103\pi$
$692$		−	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	$0.213944\pi$
$701$			872.955i			1.24530i	−0.782501	+	0.622650i	$0.786056\pi$
$702$	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	−0.937494	−	0.348001i	$-0.886861\pi$
$709$	−546.018	−	945.731i	−0.770125	−	1.33389i	0.167370	−	0.985894i	$-0.446473\pi$
$710$	−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	$-0.882425\pi$
$719$	−780.955	+	450.885i	−1.08617	+	0.627099i	−0.153614	+	0.988131i	$0.549091\pi$
$720$	−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	$-0.565593\pi$
$727$	−297.506			−0.409224			−0.204612	+	0.978843i	$0.565593\pi$
$728$		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	$-0.0657651\pi$
$733$	228.483	+	395.744i	0.311709	+	0.539896i	−0.667023	+	0.745037i	$0.732432\pi$
$734$			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	−0.731486	−	0.681857i	$-0.761173\pi$
$739$	166.099	−	287.692i	0.224762	−	0.389300i	0.956248	+	0.292557i	$0.0945061\pi$
$740$	−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	$-0.986172\pi$
$743$		−	64.5346i		−	0.0868568i	0.999057	−	0.0434284i	$-0.0138280\pi$
$744$	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	0.994579	−	0.103985i	$-0.0331594\pi$
$751$	305.834	+	529.720i	0.407236	+	0.705353i	−0.587343	+	0.809338i	$0.699826\pi$
$752$	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	$-0.737901\pi$
$761$	−292.518	+	168.885i	−0.384386	+	0.221925i	0.295339	+	0.955393i	$0.404567\pi$
$762$	−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	$-0.263000\pi$
$769$	1042.22			1.35529			0.677646	+	0.735388i	$0.263000\pi$
$770$		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	$-0.272965\pi$
$773$	252.401	+	145.724i	0.326522	+	0.188517i	−0.327774	+	0.944756i	$0.606298\pi$
$774$	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	$-0.773549\pi$
$787$	146.944	−	254.515i	0.186715	−	0.323399i	0.944153	+	0.329507i	$0.106883\pi$
$788$	−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	0.595090	−	0.803659i	$-0.297116\pi$
$809$	159.086	+	91.8486i	0.196646	+	0.113534i	−0.398444	+	0.917193i	$0.630450\pi$
$810$	4.47335	−	781.293i	0.00552265	−	0.964559i
$811$	544.663			0.671594			0.335797	−	0.941934i	$-0.390994\pi$
$811$	544.663			0.671594			0.335797	+	0.941934i	$0.390994\pi$
$812$		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	0.282078	−	0.959391i	$-0.408976\pi$
$821$	1029.51	−	594.390i	1.25397	−	0.723983i	0.971897	+	0.235409i	$0.0756428\pi$
$822$	−155.441	+	20.2379i	−0.189101	+	0.0246203i
$823$	−632.575	+	1095.65i	−0.768621	+	1.33129i	0.169690	+	0.985498i	$0.445723\pi$
$823$	−632.575	+	1095.65i	−0.768621	+	1.33129i	−0.938311	+	0.345793i	$0.887610\pi$
$824$	−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	$-0.841290\pi$
$827$		−	790.941i		−	0.956398i	0.878252	−	0.478199i	$-0.158710\pi$
$828$	22.7192	+	85.7708i	0.0274387	+	0.103588i
$829$	49.5981	−	85.9064i	0.0598288	−	0.103626i	−0.834560	−	0.550918i	$-0.814278\pi$
$829$	49.5981	−	85.9064i	0.0598288	−	0.103626i	0.894388	+	0.447291i	$0.147611\pi$
$830$	−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	$-0.271524\pi$
$853$	1122.06			1.31543			0.657713	+	0.753268i	$0.271524\pi$
$854$		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	$-0.503116\pi$
$857$	−754.732	−	435.744i	−0.880667	−	0.508453i	−0.870878	+	0.491499i	$0.836449\pi$
$858$	64.5921	−	8.40968i	0.0752822	−	0.00980149i
$859$	−837.461	−	1450.52i	−0.974925	−	1.68862i	−0.680182	−	0.733044i	$-0.738099\pi$
$859$	−837.461	−	1450.52i	−0.974925	−	1.68862i	−0.294744	−	0.955576i	$-0.595234\pi$
$860$			944.850i			1.09866i
$861$		0			0
$862$	907.129			1.05235
$863$	−1143.80	+	660.372i	−1.32537	+	0.765205i	−0.984580	−	0.174934i	$-0.944029\pi$
$863$	−1143.80	+	660.372i	−1.32537	+	0.765205i	−0.340793	+	0.940138i	$0.610696\pi$
$864$	−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	0.947415	−	0.320007i	$-0.103685\pi$
$877$	172.395	+	298.596i	0.196573	+	0.340475i	−0.750842	+	0.660482i	$0.770352\pi$
$878$	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	$-0.714070\pi$
$887$	−227.949	+	131.607i	−0.256989	+	0.148373i	0.365971	+	0.930626i	$0.380737\pi$
$888$	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	−0.0718739	−	0.997414i	$-0.522898\pi$
$907$	750.859	−	1300.53i	0.827849	−	1.43388i	0.899723	−	0.436462i	$-0.143769\pi$
$908$	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	$0.160284\pi$
$911$			879.178i			0.965069i	−0.875877	+	0.482534i	$0.839716\pi$
$912$	−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	0.844322	−	0.535836i	$-0.180004\pi$
$919$	−38.4941	−	66.6737i	−0.0418869	−	0.0725503i	−0.886209	+	0.463286i	$0.846670\pi$
$920$	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	−0.519538	+	0.854447i	$0.673896\pi$
$929$	−1411.41	+	814.879i	−1.51928	+	0.877157i	−0.999742	+	0.0227099i	$0.992771\pi$
$930$	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	$-0.414432\pi$
$937$	497.720			0.531185			0.265592	+	0.964085i	$0.414432\pi$
$938$		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	$-0.373848\pi$
$941$	−206.888	−	119.447i	−0.219860	−	0.126936i	−0.605886	+	0.795552i	$0.707181\pi$
$942$	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	−0.773278	−	0.634067i	$-0.781384\pi$
$947$	−578.427	+	333.955i	−0.610799	+	0.352645i	0.162479	+	0.986712i	$0.448051\pi$
$948$	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	$-0.998109\pi$
$953$		−	11.3247i		−	0.0118832i	0.999982	−	0.00594162i	$-0.00189129\pi$
$954$	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	$-0.450962\pi$
$971$	1054.45	−	608.788i	1.08594	−	0.626970i	0.932494	+	0.361187i	$0.117628\pi$
$972$	−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	0.299878	−	0.953978i	$-0.403054\pi$
$977$	−367.696	−	212.289i	−0.376352	−	0.217287i	−0.676230	+	0.736691i	$0.736387\pi$
$978$	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	$-0.320907\pi$
$983$	66.4478	+	38.3636i	0.0675969	+	0.0390271i	−0.465821	+	0.884879i	$0.654241\pi$
$984$	−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	−0.908125	−	0.418699i	$-0.862486\pi$
$991$	−90.6353	+	156.985i	−0.0914585	+	0.158411i	0.816667	+	0.577110i	$0.195820\pi$
$992$	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	0.399689	+	0.916651i	$0.369118\pi$
$997$	−592.216	+	1025.75i	−0.593998	+	1.02884i	−0.993687	+	0.112184i	$0.964215\pi$
$998$	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.c.116.2		8
3.2	odd	2	inner	147.3.h.c.116.3		8
7.2	even	3	inner	147.3.h.c.128.3		8
7.3	odd	6		21.3.b.a.8.2	✓	4
7.4	even	3		147.3.b.f.50.2		4
7.5	odd	6		147.3.h.e.128.3		8
7.6	odd	2		147.3.h.e.116.2		8
21.2	odd	6	inner	147.3.h.c.128.2		8
21.5	even	6		147.3.h.e.128.2		8
21.11	odd	6		147.3.b.f.50.3		4
21.17	even	6		21.3.b.a.8.3	yes	4
21.20	even	2		147.3.h.e.116.3		8
28.3	even	6		336.3.d.c.113.4		4
35.3	even	12		525.3.f.a.449.3		8
35.17	even	12		525.3.f.a.449.6		8
35.24	odd	6		525.3.c.a.176.3		4
56.3	even	6		1344.3.d.b.449.1		4
56.45	odd	6		1344.3.d.f.449.4		4
63.31	odd	6		567.3.r.c.512.3		8
63.38	even	6		567.3.r.c.134.3		8
63.52	odd	6		567.3.r.c.134.2		8
63.59	even	6		567.3.r.c.512.2		8
84.59	odd	6		336.3.d.c.113.3		4
105.17	odd	12		525.3.f.a.449.4		8
105.38	odd	12		525.3.f.a.449.5		8
105.59	even	6		525.3.c.a.176.2		4
168.59	odd	6		1344.3.d.b.449.2		4
168.101	even	6		1344.3.d.f.449.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.b.a.8.2	✓	4	7.3	odd	6
21.3.b.a.8.3	yes	4	21.17	even	6
147.3.b.f.50.2		4	7.4	even	3
147.3.b.f.50.3		4	21.11	odd	6
147.3.h.c.116.2		8	1.1	even	1	trivial
147.3.h.c.116.3		8	3.2	odd	2	inner
147.3.h.c.128.2		8	21.2	odd	6	inner
147.3.h.c.128.3		8	7.2	even	3	inner
147.3.h.e.116.2		8	7.6	odd	2
147.3.h.e.116.3		8	21.20	even	2
147.3.h.e.128.2		8	21.5	even	6
147.3.h.e.128.3		8	7.5	odd	6
336.3.d.c.113.3		4	84.59	odd	6
336.3.d.c.113.4		4	28.3	even	6
525.3.c.a.176.2		4	105.59	even	6
525.3.c.a.176.3		4	35.24	odd	6
525.3.f.a.449.3		8	35.3	even	12
525.3.f.a.449.4		8	105.17	odd	12
525.3.f.a.449.5		8	105.38	odd	12
525.3.f.a.449.6		8	35.17	even	12
567.3.r.c.134.2		8	63.52	odd	6
567.3.r.c.134.3		8	63.38	even	6
567.3.r.c.512.2		8	63.59	even	6
567.3.r.c.512.3		8	63.31	odd	6
1344.3.d.b.449.1		4	56.3	even	6
1344.3.d.b.449.2		4	168.59	odd	6
1344.3.d.f.449.3		4	168.101	even	6
1344.3.d.f.449.4		4	56.45	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

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