LMFDB - Embedded newform 147.3.h.c.116.3

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			116.3
Root			$1.03103 - 0.478705i$ of defining polynomial
Character	$\chi$	$=$	147.116
Dual form			147.3.h.c.128.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13198 - 0.653548i) q^{2} +(1.15202 + 2.76999i) q^{3} +(-1.14575 + 1.98450i) q^{4} +(6.39086 - 3.68977i) q^{5} +(3.11438 + 2.38267i) q^{6} +8.22359i q^{8} +(-6.34572 + 6.38215i) q^{9} +O(q^{10})$	\(q+(1.13198 - 0.653548i) q^{2} +(1.15202 + 2.76999i) q^{3} +(-1.14575 + 1.98450i) q^{4} +(6.39086 - 3.68977i) q^{5} +(3.11438 + 2.38267i) q^{6} +8.22359i q^{8} +(-6.34572 + 6.38215i) q^{9} +(4.82288 - 8.35347i) q^{10} +(-2.26395 - 1.30710i) q^{11} +(-6.81697 - 0.887547i) q^{12} +6.35425 q^{13} +(17.5830 + 13.4520i) q^{15} +(0.791503 + 1.37092i) q^{16} +(10.5178 + 6.07244i) q^{17} +(-3.01217 + 11.3717i) q^{18} +(-5.11438 - 8.85836i) q^{19} +16.9102i q^{20} -3.41699 q^{22} +(-3.72591 + 2.15115i) q^{23} +(-22.7793 + 9.47371i) q^{24} +(14.7288 - 25.5110i) q^{25} +(7.19287 - 4.15280i) q^{26} +(-24.9889 - 10.2252i) q^{27} -17.3733i q^{29} +(28.6951 + 3.73600i) q^{30} +(19.6458 - 34.0274i) q^{31} +(-26.6954 - 15.4126i) q^{32} +(1.01253 - 7.77693i) q^{33} +15.8745 q^{34} +(-5.39477 - 19.9054i) q^{36} +(-20.5203 - 35.5421i) q^{37} +(-11.5787 - 6.68498i) q^{38} +(7.32020 + 17.6012i) q^{39} +(30.3431 + 52.5559i) q^{40} -30.2802i q^{41} -55.8745 q^{43} +(5.18786 - 2.99521i) q^{44} +(-17.0060 + 64.2017i) q^{45} +(-2.81176 + 4.87011i) q^{46} +(-34.6193 + 19.9874i) q^{47} +(-2.88562 + 3.77178i) q^{48} -38.5038i q^{50} +(-4.70396 + 36.1297i) q^{51} +(-7.28039 + 12.6100i) q^{52} +(90.9340 + 52.5008i) q^{53} +(-34.9695 + 4.75668i) q^{54} -19.2915 q^{55} +(18.6458 - 24.3718i) q^{57} +(-11.3542 - 19.6661i) q^{58} +(-35.8223 - 20.6820i) q^{59} +(-46.8412 + 19.4809i) q^{60} +(-10.2399 - 17.7360i) q^{61} -51.3577i q^{62} -46.6235 q^{64} +(40.6091 - 23.4457i) q^{65} +(-3.93643 - 9.46505i) q^{66} +(13.5830 - 23.5265i) q^{67} +(-24.1015 + 13.9150i) q^{68} +(-10.2510 - 7.84257i) q^{69} +67.8049i q^{71} +(-52.4842 - 52.1846i) q^{72} +(30.3948 - 52.6453i) q^{73} +(-46.4569 - 26.8219i) q^{74} +(87.6329 + 11.4095i) q^{75} +23.4392 q^{76} +(19.7895 + 15.1401i) q^{78} +(31.6235 + 54.7735i) q^{79} +(10.1168 + 5.84092i) q^{80} +(-0.463763 - 80.9987i) q^{81} +(-19.7895 - 34.2765i) q^{82} +89.9435i q^{83} +89.6235 q^{85} +(-63.2487 + 36.5166i) q^{86} +(48.1238 - 20.0143i) q^{87} +(10.7490 - 18.6178i) q^{88} +(54.7108 - 31.5873i) q^{89} +(22.7085 + 83.7891i) q^{90} -9.85875i q^{92} +(116.888 + 15.2184i) q^{93} +(-26.1255 + 45.2507i) q^{94} +(-65.3706 - 37.7417i) q^{95} +(11.9393 - 91.7017i) 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	−0.189557	−	0.981870i	$-0.560705\pi$
$2$	1.13198	−	0.653548i	0.565989	−	0.326774i	0.755546	+	0.655096i	$0.227372\pi$
$3$	1.15202	+	2.76999i	0.384005	+	0.923331i
$3$	1.15202	+	2.76999i	0.384005	+	0.923331i
$4$	−1.14575	+	1.98450i	−0.286438	+	0.496125i
$5$	6.39086	−	3.68977i	1.27817	−	0.737953i	0.301660	−	0.953415i	$-0.402459\pi$
$5$	6.39086	−	3.68977i	1.27817	−	0.737953i	0.976512	+	0.215462i	$0.0691258\pi$
$6$	3.11438	+	2.38267i	0.519063	+	0.397112i
$7$		0			0
$7$		0			0
$8$			8.22359i			1.02795i
$9$	−6.34572	+	6.38215i	−0.705080	+	0.709128i
$10$	4.82288	−	8.35347i	0.482288	−	0.835347i
$11$	−2.26395	−	1.30710i	−0.205814	−	0.118827i	0.393550	−	0.919303i	$-0.371247\pi$
$11$	−2.26395	−	1.30710i	−0.205814	−	0.118827i	−0.599365	+	0.800476i	$0.704580\pi$
$12$	−6.81697	−	0.887547i	−0.568081	−	0.0739622i
$13$	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	0.776360	−	0.630290i	$-0.217064\pi$
$17$	10.5178	+	6.07244i	0.618692	+	0.357202i	−0.157667	+	0.987492i	$0.550397\pi$
$18$	−3.01217	+	11.3717i	−0.167343	+	0.631760i
$19$	−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	−0.578806	−	0.815465i	$-0.696481\pi$
$23$	−3.72591	+	2.15115i	−0.161996	+	0.0935284i	0.416810	+	0.908993i	$0.363148\pi$
$24$	−22.7793	+	9.47371i	−0.949137	+	0.394738i
$25$	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	$-0.0968328\pi$
$30$	28.6951	+	3.73600i	0.956502	+	0.124533i
$31$	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
$33$	1.01253	−	7.77693i	0.0306827	−	0.235665i
$34$	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
$39$	7.32020	+	17.6012i	0.187697	+	0.451313i
$40$	30.3431	+	52.5559i	0.758578	+	1.31390i
$41$		−	30.2802i		−	0.738541i	−0.929322	−	0.369270i	$-0.879608\pi$
$41$		−	30.2802i		−	0.738541i	0.929322	−	0.369270i	$-0.120392\pi$
$42$		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
$45$	−17.0060	+	64.2017i	−0.377910	+	1.42670i
$46$	−2.81176	+	4.87011i	−0.0611253	+	0.105872i
$47$	−34.6193	+	19.9874i	−0.736580	+	0.425265i	−0.820825	−	0.571180i	$-0.806486\pi$
$47$	−34.6193	+	19.9874i	−0.736580	+	0.425265i	0.0842443	+	0.996445i	$0.473152\pi$
$48$	−2.88562	+	3.77178i	−0.0601171	+	0.0785788i
$49$		0			0
$50$		−	38.5038i		−	0.770075i
$51$	−4.70396	+	36.1297i	−0.0922346	+	0.708425i
$52$	−7.28039	+	12.6100i	−0.140007	+	0.242500i
$53$	90.9340	+	52.5008i	1.71574	+	0.990581i	0.926332	+	0.376707i	$0.122944\pi$
$53$	90.9340	+	52.5008i	1.71574	+	0.990581i	0.789404	+	0.613874i	$0.210390\pi$
$54$	−34.9695	+	4.75668i	−0.647584	+	0.0880867i
$55$	−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	0.164695	−	0.986345i	$-0.447336\pi$
$59$	−35.8223	−	20.6820i	−0.607157	−	0.350542i	−0.771852	+	0.635802i	$0.780669\pi$
$60$	−46.8412	+	19.4809i	−0.780686	+	0.324681i
$61$	−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
$66$	−3.93643	−	9.46505i	−0.0596429	−	0.143410i
$67$	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	$0.158457\pi$
$71$			67.8049i			0.954999i	−0.878632	+	0.477499i	$0.841543\pi$
$72$	−52.4842	−	52.1846i	−0.728948	−	0.724786i
$73$	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
$75$	87.6329	+	11.4095i	1.16844	+	0.152127i
$76$	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
$81$	−0.463763	−	80.9987i	−0.00572547	−	0.999984i
$82$	−19.7895	−	34.2765i	−0.241336	−	0.418006i
$83$			89.9435i			1.08366i	0.840489	+	0.541828i	$0.182268\pi$
$83$			89.9435i			1.08366i	−0.840489	+	0.541828i	$0.817732\pi$
$84$		0			0
$85$	89.6235			1.05439
$86$	−63.2487	+	36.5166i	−0.735450	+	0.424612i
$87$	48.1238	−	20.0143i	0.553147	−	0.230049i
$88$	10.7490	−	18.6178i	0.122148	−	0.211566i
$89$	54.7108	−	31.5873i	0.614728	−	0.354913i	−0.160086	−	0.987103i	$-0.551177\pi$
$89$	54.7108	−	31.5873i	0.614728	−	0.354913i	0.774813	+	0.632190i	$0.217844\pi$
$90$	22.7085	+	83.7891i	0.252317	+	0.930990i
$91$		0			0
$92$		−	9.85875i		−	0.107160i
$93$	116.888	+	15.2184i	1.25686	+	0.163639i
$94$	−26.1255	+	45.2507i	−0.277931	+	0.481390i
$95$	−65.3706	−	37.7417i	−0.688111	−	0.397281i
$96$	11.9393	−	91.7017i	0.124367	−	0.955226i
$97$	−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	0.859437	−	0.511241i	$-0.170814\pi$
$101$	85.4872	+	49.3561i	0.846408	+	0.488674i	−0.0130291	+	0.999915i	$0.504147\pi$
$102$	18.2877	+	43.9723i	0.179291	+	0.431101i
$103$	−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	−0.907250	−	0.420591i	$-0.861823\pi$
$107$	−106.640	+	61.5684i	−0.996632	+	0.575406i	−0.0893823	+	0.995997i	$0.528489\pi$
$108$	48.9230	−	37.8748i	0.452991	−	0.350693i
$109$	−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	$0.219986\pi$
$113$			144.050i			1.27478i	−0.770540	+	0.637391i	$0.780014\pi$
$114$	5.17846	−	39.7742i	0.0454251	−	0.348896i
$115$	−15.8745	+	27.4955i	−0.138039	+	0.239091i
$116$	34.4772	+	19.9054i	0.297217	+	0.171599i
$117$	−40.3223	+	40.5538i	−0.344635	+	0.346614i
$118$	−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
$123$	83.8759	−	34.8833i	0.681918	−	0.283604i
$124$	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
$129$	−64.3683	−	154.772i	−0.498979	−	1.19978i
$130$	30.6458	−	53.0800i	0.235737	−	0.408308i
$131$	29.1725	−	16.8427i	0.222691	−	0.128570i	−0.384505	−	0.923123i	$-0.625628\pi$
$131$	29.1725	−	16.8427i	0.222691	−	0.128570i	0.607195	+	0.794552i	$0.292294\pi$
$132$	14.2732	+	10.9198i	0.108130	+	0.0827257i
$133$		0			0
$134$		−	35.5086i		−	0.264989i
$135$	−197.429	+	26.8550i	−1.46244	+	0.198926i
$136$	−49.9373	+	86.4939i	−0.367186	+	0.635984i
$137$	34.6193	+	19.9874i	0.252695	+	0.145894i	0.620998	−	0.783812i	$-0.286728\pi$
$137$	34.6193	+	19.9874i	0.252695	+	0.145894i	−0.368302	+	0.929706i	$0.620061\pi$
$138$	−16.7294	−	2.17811i	−0.121227	−	0.0157834i
$139$	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
$144$	−13.7721	−	3.64800i	−0.0956395	−	0.0253333i
$145$	−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	$-0.427121\pi$
$149$	176.396	−	101.842i	1.18387	−	0.683506i	0.956906	+	0.290398i	$0.0937878\pi$
$150$	106.655	−	44.3570i	0.711034	−	0.295713i
$151$	−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
$156$	−43.3167	−	5.63969i	−0.277671	−	0.0361519i
$157$	−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
$159$	−40.6693	+	312.368i	−0.255782	+	1.96458i
$160$	−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
$165$	−22.2241	−	53.4373i	−0.134692	−	0.323863i
$166$	58.7824	+	101.814i	0.354111	+	0.613338i
$167$			19.6594i			0.117721i	0.998266	+	0.0588604i	$0.0187467\pi$
$167$			19.6594i			0.117721i	−0.998266	+	0.0588604i	$0.981253\pi$
$168$		0			0
$169$	−128.624			−0.761086
$170$	101.452	−	58.5732i	0.596775	−	0.344548i
$171$	88.9898	+	23.5719i	0.520408	+	0.137847i
$172$	64.0183	−	110.883i	0.372199	−	0.644668i
$173$	17.0507	−	9.84422i	0.0985589	−	0.0569030i	−0.449910	−	0.893074i	$-0.648544\pi$
$173$	17.0507	−	9.84422i	0.0985589	−	0.0569030i	0.548469	+	0.836171i	$0.315211\pi$
$174$	41.3948	−	54.1069i	0.237901	−	0.310959i
$175$		0			0
$176$		−	4.13828i		−	0.0235129i
$177$	16.0211	−	123.053i	0.0905149	−	0.695217i
$178$	41.2876	−	71.5122i	0.231953	−	0.401754i
$179$	−295.960	−	170.872i	−1.65341	−	0.954594i	−0.975658	−	0.219300i	$-0.929623\pi$
$179$	−295.960	−	170.872i	−1.65341	−	0.954594i	−0.677748	−	0.735294i	$-0.737044\pi$
$180$	−107.924	−	107.307i	−0.599576	−	0.596153i
$181$	−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
$186$	142.261	−	59.1649i	0.764841	−	0.318091i
$187$	−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	$-0.704009\pi$
$191$	−38.7210	+	22.3556i	−0.202728	+	0.117045i	0.395199	+	0.918595i	$0.370676\pi$
$192$	−53.7111	−	129.147i	−0.279745	−	0.672640i
$193$	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	$-0.928745\pi$
$197$		−	87.4643i		−	0.443981i	0.975049	−	0.221991i	$-0.0712554\pi$
$198$	21.6833	−	21.8078i	0.109512	−	0.110140i
$199$	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
$201$	80.8159	+	10.5220i	0.402069	+	0.0523481i
$202$	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
$207$	9.91456	−	37.4299i	0.0478964	−	0.180821i
$208$	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
$213$	−187.819	+	78.1124i	−0.881780	+	0.366725i
$214$	−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
$219$	180.842	+	23.5451i	0.825764	+	0.107512i
$220$	22.1033	−	38.2840i	0.100469	−	0.174018i
$221$	66.8325	+	38.5858i	0.302410	+	0.174596i
$222$	20.7774	−	159.585i	0.0935918	−	0.718850i
$223$	−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	0.999966	−	0.00829388i	$-0.00264005\pi$
$227$	338.858	+	195.640i	1.49277	+	0.861849i	0.492800	+	0.870143i	$0.335973\pi$
$228$	27.0024	+	64.9265i	0.118431	+	0.284765i
$229$	−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	−0.701224	−	0.712941i	$-0.747363\pi$
$233$	−101.218	+	58.4383i	−0.434412	+	0.250808i	0.266812	+	0.963748i	$0.414030\pi$
$234$	−19.1401	+	72.2585i	−0.0817951	+	0.308797i
$235$	−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	$0.959964\pi$
$240$	−4.52462	+	34.7522i	−0.0188526	+	0.144801i
$241$	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
$243$	223.831	−	94.5964i	0.921117	−	0.389286i
$244$	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
$249$	−249.143	+	103.616i	−1.00057	+	0.416130i
$250$	−21.4980	−	37.2357i	−0.0859921	−	0.148943i
$251$			268.248i			1.06872i	0.845257	+	0.534359i	$0.179447\pi$
$251$			268.248i			1.06872i	−0.845257	+	0.534359i	$0.820553\pi$
$252$		0			0
$253$	11.2470			0.0444547
$254$	−41.4111	+	23.9087i	−0.163036	+	0.0941289i
$255$	103.248	+	248.256i	0.404893	+	0.973555i
$256$	134.002	−	232.098i	0.523445	−	0.906634i
$257$	202.762	−	117.064i	0.788956	−	0.455504i	−0.0506392	−	0.998717i	$-0.516126\pi$
$257$	202.762	−	117.064i	0.788956	−	0.455504i	0.839595	+	0.543213i	$0.182793\pi$
$258$	−174.014	−	133.131i	−0.674474	−	0.516010i
$259$		0			0
$260$			107.452i			0.413276i
$261$	110.879	+	110.246i	0.424823	+	0.422398i
$262$	22.0151	−	38.1312i	0.0840269	−	0.145539i
$263$	216.629	+	125.071i	0.823686	+	0.475555i	0.851686	−	0.524053i	$-0.175580\pi$
$263$	216.629	+	125.071i	0.823686	+	0.475555i	−0.0279999	+	0.999608i	$0.508914\pi$
$264$	63.9543	+	8.32663i	0.242251	+	0.0315403i
$265$	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	−0.161425	−	0.986885i	$-0.551609\pi$
$269$	−295.041	−	170.342i	−1.09681	−	0.633241i	−0.935380	+	0.353644i	$0.884942\pi$
$270$	−205.934	+	159.429i	−0.762720	+	0.590477i
$271$	−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
$276$	27.3087	−	11.3574i	0.0989444	−	0.0411501i
$277$	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	$0.137626\pi$
$281$			235.489i			0.838039i	−0.907977	+	0.419019i	$0.862374\pi$
$282$	−155.441	−	20.2379i	−0.551209	−	0.0717656i
$283$	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
$285$	29.2363	−	224.555i	0.102584	−	0.787913i
$286$	−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
$291$	−22.0796	−	53.0897i	−0.0758748	−	0.182439i
$292$	69.6497	+	120.637i	0.238526	+	0.413140i
$293$		−	531.625i		−	1.81442i	−0.420677	−	0.907211i	$-0.638207\pi$
$293$		−	531.625i		−	1.81442i	0.420677	−	0.907211i	$-0.361793\pi$
$294$		0			0
$295$	−305.247			−1.03474
$296$	292.284	−	168.750i	0.987446	−	0.570102i
$297$	43.2084	+	55.8123i	0.145483	+	0.187920i
$298$	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
$303$	−38.2333	+	293.658i	−0.126182	+	0.969168i
$304$	8.09609	−	14.0228i	0.0266319	−	0.0461277i
$305$	−130.883	−	75.5655i	−0.429125	−	0.247756i
$306$	−100.735	+	101.314i	−0.329200	+	0.331090i
$307$	−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	0.439291	−	0.898345i	$-0.355230\pi$
$311$	−37.0253	−	21.3766i	−0.119052	−	0.0687349i	−0.558344	+	0.829610i	$0.688563\pi$
$312$	−144.745	+	60.1983i	−0.463927	+	0.192943i
$313$	−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	−0.294963	−	0.955509i	$-0.595307\pi$
$317$	122.061	−	70.4721i	0.385051	−	0.222309i	0.680014	+	0.733199i	$0.261974\pi$
$318$	158.111	+	380.173i	0.497204	+	1.19551i
$319$	−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
$324$	161.273	+	91.8840i	0.497757	+	0.283593i
$325$	93.5902	−	162.103i	0.287970	−	0.498778i
$326$	164.183	+	94.7909i	0.503628	+	0.290770i
$327$	−489.484	−	63.7292i	−1.49689	−	0.194891i
$328$	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
$333$	357.051	+	94.5768i	1.07223	+	0.284015i
$334$	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
$339$	−399.019	+	165.948i	−1.17705	+	0.489523i
$340$	−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
$345$	−94.4499	−	12.2971i	−0.273768	−	0.0356436i
$346$	12.8673	−	22.2869i	0.0371888	−	0.0644129i
$347$	111.401	+	64.3176i	0.321041	+	0.185353i	0.651857	−	0.758342i	$-0.273990\pi$
$347$	111.401	+	64.3176i	0.321041	+	0.185353i	−0.330815	+	0.943696i	$0.607324\pi$
$348$	−15.4196	+	118.433i	−0.0443091	+	0.340325i
$349$	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	0.764317	−	0.644841i	$-0.223076\pi$
$353$	207.574	+	119.843i	0.588027	+	0.339498i	−0.176290	+	0.984338i	$0.556410\pi$
$354$	−62.2857	−	149.764i	−0.175948	−	0.423063i
$355$	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	$-0.747425\pi$
$359$	−156.071	+	90.1075i	−0.434738	+	0.250996i	0.266625	+	0.963800i	$0.414091\pi$
$360$	−527.968	−	139.850i	−1.46658	−	0.388472i
$361$	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
$366$	10.3682	−	79.6348i	0.0283284	−	0.217581i
$367$	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
$369$	193.253	+	192.149i	0.523720	+	0.520730i
$370$	−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
$375$	91.1171	−	37.8948i	0.242979	−	0.101053i
$376$	−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
$381$	−42.1442	−	101.335i	−0.110615	−	0.265970i
$382$	−29.2209	+	50.6121i	−0.0764945	+	0.132492i
$383$	515.797	−	297.796i	1.34673	−	0.777534i	0.358944	−	0.933359i	$-0.383137\pi$
$383$	515.797	−	297.796i	1.34673	−	0.777534i	0.987785	+	0.155825i	$0.0498037\pi$
$384$	148.582	+	113.674i	0.386933	+	0.296025i
$385$		0			0
$386$		−	189.688i		−	0.491419i
$387$	354.564	−	356.600i	0.916185	−	0.921446i
$388$	21.9595	−	38.0349i	0.0565966	−	0.0980282i
$389$	−318.132	−	183.673i	−0.817819	−	0.472168i	0.0318449	−	0.999493i	$-0.489862\pi$
$389$	−318.132	−	183.673i	−0.817819	−	0.472168i	−0.849664	+	0.527325i	$0.823195\pi$
$390$	182.336	+	23.7395i	0.467527	+	0.0608704i
$391$	−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
$396$	−13.8048	+	52.1165i	−0.0348606	+	0.131607i
$397$	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	−0.219435	−	0.975627i	$-0.570421\pi$
$401$	206.822	−	119.409i	0.515765	−	0.297777i	0.735200	+	0.677850i	$0.237088\pi$
$402$	98.3584	−	40.9064i	0.244673	−	0.101757i
$403$	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
$408$	−297.116	−	38.6835i	−0.728225	−	0.0948124i
$409$	−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
$411$	−15.4831	+	118.921i	−0.0376718	+	0.289345i
$412$	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
$417$	224.231	+	539.156i	0.537723	+	1.29294i
$418$	17.4758	+	30.2690i	0.0418081	+	0.0724138i
$419$		−	11.5178i		−	0.0274888i	−0.999906	−	0.0137444i	$-0.995625\pi$
$419$		−	11.5178i		−	0.0274888i	0.999906	−	0.0137444i	$-0.00437512\pi$
$420$		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
$423$	92.1211	−	347.780i	0.217780	−	0.822175i
$424$	−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
$429$	6.43387	−	49.4166i	0.0149974	−	0.115190i
$430$	−269.476	+	466.746i	−0.626688	+	1.08546i
$431$	601.025	+	347.002i	1.39449	+	0.805109i	0.993808	−	0.111108i	$-0.0354399\pi$
$431$	601.025	+	347.002i	1.39449	+	0.805109i	0.400682	+	0.916217i	$0.368773\pi$
$432$	−5.76075	−	42.3511i	−0.0133351	−	0.0980350i
$433$	−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
$438$	220.097	−	91.5366i	0.502505	−	0.208988i
$439$	−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	−0.741923	−	0.670485i	$-0.766086\pi$
$443$	−235.777	+	136.126i	−0.532228	+	0.307282i	0.209695	+	0.977767i	$0.432753\pi$
$444$	108.341	+	260.502i	0.244011	+	0.586717i
$445$	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	$0.800902\pi$
$450$	245.737	+	244.334i	0.546082	+	0.542964i
$451$	−39.5791	+	68.5530i	−0.0877585	+	0.152002i
$452$	−285.868	−	165.046i	−0.632451	−	0.365146i
$453$	−493.085	−	64.1980i	−1.08849	−	0.141718i
$454$	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
$459$	−200.735	−	259.290i	−0.437332	−	0.564902i
$460$	−36.3765	−	63.0059i	−0.0790793	−	0.136969i
$461$			687.879i			1.49214i	0.665865	+	0.746072i	$0.268063\pi$
$461$			687.879i			1.49214i	−0.665865	+	0.746072i	$0.731937\pi$
$462$		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
$465$	803.168	−	334.031i	1.72724	−	0.718345i
$466$	−76.3844	+	132.302i	−0.163915	+	0.283909i
$467$	141.468	−	81.6763i	0.302928	−	0.174896i	−0.340829	−	0.940125i	$-0.610708\pi$
$467$	141.468	−	81.6763i	0.302928	−	0.174896i	0.643758	+	0.765229i	$0.277374\pi$
$468$	−34.2797	−	126.484i	−0.0732472	−	0.270265i
$469$		0			0
$470$			385.588i			0.820400i
$471$	−900.568	−	117.251i	−1.91203	−	0.248940i
$472$	170.080	−	294.588i	0.360340	−	0.624127i
$473$	126.497	+	73.0333i	0.267436	+	0.154404i
$474$	−32.0198	+	245.934i	−0.0675523	+	0.518848i
$475$	−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	−0.291672	−	0.956518i	$-0.594212\pi$
$479$	−606.355	−	350.079i	−1.26588	−	0.730855i	−0.974205	+	0.225664i	$0.927545\pi$
$480$	−262.056	−	630.106i	−0.545950	−	1.31272i
$481$	−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
$486$	191.549	−	253.366i	0.394134	−	0.521328i
$487$	−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	$0.272404\pi$
$491$			741.494i			1.51017i	−0.655627	+	0.755085i	$0.727596\pi$
$492$	−26.8751	+	206.419i	−0.0546241	+	0.419551i
$493$	105.498	−	182.728i	0.213992	−	0.370645i
$494$	−73.5741	−	42.4780i	−0.148935	−	0.0859879i
$495$	122.418	−	123.121i	0.247310	−	0.248730i
$496$	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
$501$	−54.4564	+	22.6479i	−0.108695	+	0.0452055i
$502$	175.313	+	303.651i	0.349229	+	0.604883i
$503$		−	465.808i		−	0.926059i	−0.886343	−	0.463029i	$-0.846762\pi$
$503$		−	465.808i		−	0.926059i	0.886343	−	0.463029i	$-0.153238\pi$
$504$		0			0
$505$	728.450			1.44247
$506$	12.7314	−	7.35048i	0.0251609	−	0.0145266i
$507$	−148.176	−	356.286i	−0.292261	−	0.702734i
$508$	41.9150	−	72.5990i	0.0825099	−	0.142911i
$509$	−649.955	+	375.252i	−1.27692	+	0.737233i	−0.976282	−	0.216504i	$-0.930535\pi$
$509$	−649.955	+	375.252i	−1.27692	+	0.737233i	−0.300643	+	0.953737i	$0.597201\pi$
$510$	279.122	+	213.543i	0.547297	+	0.418713i
$511$		0			0
$512$		−	100.868i		−	0.197009i
$513$	37.2237	+	273.656i	0.0725608	+	0.533443i
$514$	153.014	−	265.029i	0.297693	−	0.515620i
$515$	−359.492	−	207.553i	−0.698043	−	0.403016i
$516$	380.895	+	49.5912i	0.738169	+	0.0961070i
$517$	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	0.962400	−	0.271635i	$-0.0875645\pi$
$521$	629.554	+	363.473i	1.20836	+	0.697645i	0.245957	+	0.969281i	$0.420898\pi$
$522$	197.563	+	52.3312i	0.378473	+	0.100251i
$523$	−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
$528$	11.4630	−	4.76736i	0.0217102	−	0.00902910i
$529$	−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
$534$	245.652	+	31.9831i	0.460023	+	0.0598934i
$535$	−454.346	+	786.951i	−0.849246	+	1.47094i
$536$	193.472	+	111.701i	0.360955	+	0.208398i
$537$	132.365	−	1016.65i	0.246489	−	1.89321i
$538$	−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
$543$	−248.708	−	598.011i	−0.458025	−	1.10131i
$544$	−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
$549$	178.173	+	47.1951i	0.324541	+	0.0859655i
$550$	−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
$555$	117.304	−	900.975i	0.211358	−	1.62338i
$556$	−223.011	+	386.267i	−0.401099	+	0.694724i
$557$	436.375	+	251.941i	0.783438	+	0.452318i	0.837647	−	0.546211i	$-0.183930\pi$
$557$	436.375	+	251.941i	0.783438	+	0.452318i	−0.0542092	+	0.998530i	$0.517264\pi$
$558$	327.773	+	325.902i	0.587407	+	0.584053i
$559$	−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	0.581293	−	0.813694i	$-0.302547\pi$
$563$	94.1672	+	54.3675i	0.167260	+	0.0965674i	−0.414033	+	0.910262i	$0.635880\pi$
$564$	253.738	−	105.528i	0.449891	−	0.187106i
$565$	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	$-0.791478\pi$
$569$	−376.610	+	217.436i	−0.661880	+	0.382136i	0.131113	+	0.991367i	$0.458145\pi$
$570$	−113.663	−	273.299i	−0.199408	−	0.479471i
$571$	−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
$576$	295.860	−	297.558i	0.513645	−	0.516595i
$577$	−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
$579$	431.721	+	56.2086i	0.745632	+	0.0970787i
$580$	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
$585$	−108.060	+	407.953i	−0.184718	+	0.697356i
$586$	−347.442	−	601.788i	−0.592905	−	1.02694i
$587$		−	736.236i		−	1.25424i	−0.778925	−	0.627118i	$-0.784235\pi$
$587$		−	736.236i		−	1.25424i	0.778925	−	0.627118i	$-0.215765\pi$
$588$		0			0
$589$	−401.903			−0.682348
$590$	−345.533	+	199.493i	−0.585649	+	0.338124i
$591$	242.275	−	100.760i	0.409942	−	0.170491i
$592$	32.4837	−	56.2634i	0.0548711	−	0.0950395i
$593$	−721.299	+	416.442i	−1.21636	+	0.702263i	−0.964137	−	0.265407i	$-0.914494\pi$
$593$	−721.299	+	416.442i	−1.21636	+	0.702263i	−0.252219	+	0.967670i	$0.581160\pi$
$594$	85.3869	+	34.9396i	0.143749	+	0.0588209i
$595$		0			0
$596$			466.744i			0.783127i
$597$	194.608	+	25.3374i	0.325977	+	0.0424411i
$598$	−17.8666	+	30.9459i	−0.0298773	+	0.0517490i
$599$	−60.0407	−	34.6645i	−0.100235	−	0.0578706i	0.449045	−	0.893509i	$-0.351764\pi$
$599$	−60.0407	−	34.6645i	−0.100235	−	0.0578706i	−0.549279	+	0.835639i	$0.685098\pi$
$600$	−93.8271	+	720.657i	−0.156379	+	1.20110i
$601$	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
$606$	148.640	+	357.402i	0.245281	+	0.589771i
$607$	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
$612$	64.1336	−	242.120i	0.104793	−	0.395621i
$613$	−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	$-0.709780\pi$
$617$		−	975.575i		−	1.58116i	0.612360	−	0.790579i	$-0.290220\pi$
$618$	28.4779	−	218.730i	0.0460808	−	0.353932i
$619$	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
$621$	115.102	−	15.6566i	0.185350	−	0.0252120i
$622$	−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
$627$	−74.0694	+	30.8048i	−0.118133	+	0.0491305i
$628$	−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
$633$	46.7523	+	112.415i	0.0738583	+	0.177590i
$634$	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
$639$	−432.741	−	430.271i	−0.677216	−	0.673350i
$640$	230.092	−	398.531i	0.359519	−	0.622705i
$641$	−560.082	−	323.363i	−0.873762	−	0.504467i	−0.00516570	−	0.999987i	$-0.501644\pi$
$641$	−560.082	−	323.363i	−0.873762	−	0.504467i	−0.868597	+	0.495520i	$0.834978\pi$
$642$	−478.814	−	62.3399i	−0.745816	−	0.0971027i
$643$	−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	−0.0633138	−	0.997994i	$-0.520167\pi$
$647$	−620.640	−	358.327i	−0.959259	−	0.553828i	−0.895945	+	0.444166i	$0.853500\pi$
$648$	666.100	−	3.81380i	1.02793	−	0.00588550i
$649$	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	$-0.572945\pi$
$653$	328.223	−	189.500i	0.502639	−	0.290199i	0.729803	+	0.683658i	$0.239612\pi$
$654$	−595.735	+	247.761i	−0.910910	+	0.378840i
$655$	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	$-0.181289\pi$
$660$	131.510	+	17.1221i	0.199257	+	0.0259426i
$661$	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
$663$	−29.8902	+	229.577i	−0.0450832	+	0.346270i
$664$	−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
$669$	−116.307	−	279.657i	−0.173852	−	0.418022i
$670$	−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
$675$	−628.911	+	486.885i	−0.931720	+	0.721311i
$676$	147.371	−	255.253i	0.218004	−	0.377594i
$677$	290.613	−	167.786i	0.429266	−	0.247837i	−0.269768	−	0.962925i	$-0.586947\pi$
$677$	290.613	−	167.786i	0.429266	−	0.247837i	0.699034	+	0.715088i	$0.253614\pi$
$678$	−343.225	+	448.627i	−0.506231	+	0.661692i
$679$		0			0
$680$			737.027i			1.08386i
$681$	−151.551	+	1164.01i	−0.222541	+	1.70927i
$682$	−67.1294	+	116.272i	−0.0984302	+	0.170486i
$683$	98.1521	+	56.6681i	0.143707	+	0.0829694i	0.570130	−	0.821555i	$-0.306893\pi$
$683$	98.1521	+	56.6681i	0.143707	+	0.0829694i	−0.426422	+	0.904524i	$0.640226\pi$
$684$	−148.739	+	149.593i	−0.217454	+	0.218703i
$685$	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
$690$	−114.952	+	47.8075i	−0.166597	+	0.0692862i
$691$	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
$696$	164.589	+	395.750i	0.236479	+	0.568607i
$697$	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	$-0.213944\pi$
$702$	−222.205	+	30.2251i	−0.316532	+	0.0430557i
$703$	−209.897	+	363.552i	−0.298573	+	0.517143i
$704$	105.554	+	60.9414i	0.149934	+	0.0865645i
$705$	−877.581	−	114.258i	−1.24480	−	0.162068i
$706$	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
$711$	−550.247	−	145.751i	−0.773906	−	0.204995i
$712$	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
$717$	−166.095	+	69.0776i	−0.231653	+	0.0963425i
$718$	−117.779	+	203.999i	−0.164038	+	0.284122i
$719$	780.955	−	450.885i	1.08617	−	0.627099i	0.153614	−	0.988131i	$-0.450909\pi$
$719$	780.955	−	450.885i	1.08617	−	0.627099i	0.932554	+	0.361031i	$0.117575\pi$
$720$	−101.476	+	27.5020i	−0.140939	+	0.0381972i
$721$		0			0
$722$		−	335.103i		−	0.464132i
$723$	400.875	+	52.1926i	0.554461	+	0.0721890i
$724$	247.355	−	428.431i	0.341650	−	0.591756i
$725$	−443.208	−	255.886i	−0.611322	−	0.352947i
$726$	57.7983	−	443.931i	0.0796119	−	0.611475i
$727$	−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
$732$	54.0634	+	129.994i	0.0738571	+	0.177587i
$733$	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
$738$	344.337	+	91.2090i	0.466581	+	0.123589i
$739$	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	$0.0138280\pi$
$743$			64.5346i			0.0868568i	−0.999057	+	0.0434284i	$0.986172\pi$
$744$	−125.150	+	961.239i	−0.168212	+	1.29199i
$745$	751.549	−	1301.72i	1.00879	−	1.74728i
$746$	−500.050	−	288.704i	−0.670308	−	0.387003i
$747$	−574.033	−	570.756i	−0.768452	−	0.764064i
$748$	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
$753$	−743.046	+	309.026i	−0.986781	+	0.410394i
$754$	−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
$759$	12.9568	+	31.1542i	0.0170709	+	0.0410464i
$760$	310.373	−	537.581i	0.408385	−	0.707343i
$761$	292.518	−	168.885i	0.384386	−	0.221925i	−0.295339	−	0.955393i	$-0.595433\pi$
$761$	292.518	−	168.885i	0.384386	−	0.221925i	0.679725	+	0.733467i	$0.262099\pi$
$762$	−113.933	−	87.1653i	−0.149519	−	0.114390i
$763$		0			0
$764$		−	102.456i		−	0.134104i
$765$	−568.725	+	571.991i	−0.743432	+	0.747701i
$766$	389.247	−	674.196i	0.508155	−	0.880151i
$767$	−227.624	−	131.419i	−0.296771	−	0.171341i
$768$	797.283	+	103.803i	1.03813	+	0.135161i
$769$	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	0.327774	−	0.944756i	$-0.393702\pi$
$773$	−252.401	−	145.724i	−0.326522	−	0.188517i	−0.654296	+	0.756239i	$0.727035\pi$
$774$	168.303	−	635.387i	0.217446	−	0.820914i
$775$	−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
$780$	−297.641	+	123.786i	−0.381590	+	0.158700i
$781$	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
$786$	130.985	+	17.0538i	0.166647	+	0.0216969i
$787$	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
$789$	−96.8852	+	744.146i	−0.122795	+	0.943150i
$790$	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
$795$	892.655	+	2146.36i	1.12284	+	2.69983i
$796$	74.9516	+	129.820i	0.0941603	+	0.163090i
$797$		−	568.764i		−	0.713631i	−0.934175	−	0.356816i	$-0.883862\pi$
$797$		−	568.764i		−	0.713631i	0.934175	−	0.356816i	$-0.116138\pi$
$798$		0			0
$799$	−485.490			−0.607622
$800$	−786.381	+	454.017i	−0.982976	+	0.567522i
$801$	−145.584	+	549.616i	−0.181753	+	0.686163i
$802$	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
$807$	131.954	−	1013.50i	0.163512	−	1.25588i
$808$	−405.884	+	703.012i	−0.502332	+	0.870064i
$809$	−159.086	−	91.8486i	−0.196646	−	0.113534i	0.398444	−	0.917193i	$-0.369550\pi$
$809$	−159.086	−	91.8486i	−0.196646	−	0.113534i	−0.595090	+	0.803659i	$0.702884\pi$
$810$	−678.856	−	386.772i	−0.838094	−	0.477497i
$811$	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
$816$	−53.2542	+	22.1480i	−0.0652625	+	0.0271421i
$817$	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	$-0.924357\pi$
$821$	−1029.51	+	594.390i	−1.25397	+	0.723983i	−0.282078	+	0.959391i	$0.591024\pi$
$822$	60.1940	+	144.735i	0.0732287	+	0.176076i
$823$	−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	$0.158710\pi$
$827$			790.941i			0.956398i	−0.878252	+	0.478199i	$0.841290\pi$
$828$	62.9200	+	62.5608i	0.0759904	+	0.0755565i
$829$	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
$831$	675.048	+	87.8889i	0.812332	+	0.105763i
$832$	−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
$837$	−838.864	+	649.425i	−1.00223	+	0.775896i
$838$	−7.52744	−	13.0379i	−0.00898262	−	0.0155584i
$839$			243.824i			0.290612i	0.989387	+	0.145306i	$0.0464167\pi$
$839$			243.824i			0.290612i	−0.989387	+	0.145306i	$0.953583\pi$
$840$		0			0
$841$	539.170			0.641106
$842$	−95.0772	+	54.8928i	−0.112918	+	0.0651934i
$843$	−652.303	+	271.287i	−0.773787	+	0.321812i
$844$	−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
$849$	1096.65	+	142.780i	1.29169	+	0.168174i
$850$	233.812	−	404.974i	0.275073	−	0.476440i
$851$	152.913	+	88.2844i	0.179686	+	0.103742i
$852$	60.1800	−	462.224i	0.0706338	−	0.542517i
$853$	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	0.870878	−	0.491499i	$-0.163551\pi$
$857$	754.732	+	435.744i	0.880667	+	0.508453i	0.00978864	+	0.999952i	$0.496884\pi$
$858$	−25.0131	−	60.1433i	−0.0291528	−	0.0700971i
$859$	−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	0.340793	−	0.940138i	$-0.389304\pi$
$863$	1143.80	−	660.372i	1.32537	−	0.765205i	0.984580	+	0.174934i	$0.0559711\pi$
$864$	509.491	+	658.111i	0.589689	+	0.761703i
$865$	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
$870$	64.9065	−	498.527i	0.0746052	−	0.573019i
$871$	86.3098	−	149.493i	0.0990928	−	0.171634i
$872$	−1171.82	−	676.549i	−1.34383	−	0.775859i
$873$	121.622	−	122.320i	0.139315	−	0.140115i
$874$	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
$879$	1472.60	−	612.441i	1.67531	−	0.696748i
$880$	−15.2693	−	26.4472i	−0.0173514	−	0.0300536i
$881$			518.737i			0.588805i	0.955682	+	0.294403i	$0.0951206\pi$
$881$			518.737i			0.588805i	−0.955682	+	0.294403i	$0.904879\pi$
$882$		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
$885$	−351.650	−	845.532i	−0.397344	−	0.955403i
$886$	−177.929	+	308.183i	−0.200823	+	0.347836i
$887$	227.949	−	131.607i	0.256989	−	0.148373i	−0.365971	−	0.930626i	$-0.619263\pi$
$887$	227.949	−	131.607i	0.256989	−	0.148373i	0.622960	+	0.782254i	$0.285930\pi$
$888$	804.153	+	615.221i	0.905577	+	0.692817i
$889$		0			0
$890$		−	609.366i		−	0.684681i
$891$	−104.823	+	183.984i	−0.117646	+	0.206491i
$892$	115.674	−	200.354i	0.129680	−	0.224612i
$893$	354.112	+	204.447i	0.396542	+	0.228944i
$894$	792.021	+	103.118i	0.885930	+	0.115345i
$895$	−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
$900$	−587.265	−	155.557i	−0.652516	−	0.172841i
$901$	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
$906$	−600.118	+	249.584i	−0.662382	+	0.275479i
$907$	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	$-0.839716\pi$
$911$		−	879.178i		−	0.965069i	0.875877	−	0.482534i	$-0.160284\pi$
$912$	48.1700	+	6.27157i	0.0528180	+	0.00687672i
$913$	117.565	−	203.628i	0.128767	−	0.223032i
$914$	581.594	+	335.783i	0.636317	+	0.367378i
$915$	58.5362	−	449.598i	0.0639739	−	0.491364i
$916$	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
$921$	−654.073	−	1572.70i	−0.710177	−	1.70760i
$922$	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
$927$	489.382	+	129.629i	0.527920	+	0.139837i
$928$	−267.767	+	463.787i	−0.288542	+	0.499770i
$929$	1411.41	−	814.879i	1.51928	−	0.877157i	0.519538	−	0.854447i	$-0.326104\pi$
$929$	1411.41	−	814.879i	1.51928	−	0.877157i	0.999742	−	0.0227099i	$-0.00722941\pi$
$930$	690.863	−	903.023i	0.742863	−	0.970993i
$931$		0			0
$932$		−	267.823i		−	0.287364i
$933$	16.5592	−	127.186i	0.0177483	−	0.136319i
$934$	106.759	−	184.912i	0.114303	−	0.197978i
$935$	−202.904	−	117.146i	−0.217009	−	0.125290i
$936$	−333.498	−	331.594i	−0.356301	−	0.354267i
$937$	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	0.605886	−	0.795552i	$-0.292819\pi$
$941$	206.888	+	119.447i	0.219860	+	0.126936i	−0.386025	+	0.922488i	$0.626152\pi$
$942$	−1096.05	+	455.839i	−1.16354	+	0.483905i
$943$	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	$-0.551949\pi$
$947$	578.427	−	333.955i	0.610799	−	0.352645i	0.773278	+	0.634067i	$0.218616\pi$
$948$	−166.963	−	401.457i	−0.176121	−	0.423478i
$949$	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	$0.998109\pi$
$954$	−870.931	+	875.932i	−0.912925	+	0.918167i
$955$	−164.974	+	285.743i	−0.172747	+	0.299207i
$956$	−118.995	−	68.7019i	−0.124472	−	0.0718639i
$957$	−135.111	−	17.5909i	−0.141181	−	0.0183813i
$958$	−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
$963$	283.766	−	1071.29i	0.294669	−	1.11245i
$964$	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
$969$	344.108	−	143.112i	0.355116	−	0.147690i
$970$	−92.4353	+	160.103i	−0.0952941	+	0.165054i
$971$	−1054.45	+	608.788i	−1.08594	+	0.626970i	−0.932494	−	0.361187i	$-0.882372\pi$
$971$	−1054.45	+	608.788i	−1.08594	+	0.626970i	−0.153450	+	0.988156i	$0.549038\pi$
$972$	−68.7286	+	552.577i	−0.0707085	+	0.568495i
$973$		0			0
$974$			113.183i			0.116204i
$975$	556.841	+	72.4988i	0.571119	+	0.0743578i
$976$	16.2098	−	28.0761i	0.0166084	−	0.0287665i
$977$	367.696	+	212.289i	0.376352	+	0.217287i	0.676230	−	0.736691i	$-0.263613\pi$
$977$	367.696	+	212.289i	0.376352	+	0.217287i	−0.299878	+	0.953978i	$0.596946\pi$
$978$	−73.4289	+	563.985i	−0.0750807	+	0.576672i
$979$	−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	0.465821	−	0.884879i	$-0.345759\pi$
$983$	−66.4478	−	38.3636i	−0.0675969	−	0.0390271i	−0.533418	+	0.845852i	$0.679093\pi$
$984$	286.866	+	689.761i	0.291530	+	0.700976i
$985$	−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
$990$	58.1092	−	219.377i	0.0586962	−	0.221593i
$991$	−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
$996$	79.8291	−	613.142i	0.0801497	−	0.615605i
$997$	−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
$999$	149.352	+	1097.98i	0.149501	+	1.09908i

Twists

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

\(f(q)\)	\(=\)	\(q+(1.13198 - 0.653548i) q^{2} +(1.15202 + 2.76999i) q^{3} +(-1.14575 + 1.98450i) q^{4} +(6.39086 - 3.68977i) q^{5} +(3.11438 + 2.38267i) q^{6} +8.22359i q^{8} +(-6.34572 + 6.38215i) q^{9} +O(q^{10})\)	\(q+(1.13198 - 0.653548i) q^{2} +(1.15202 + 2.76999i) q^{3} +(-1.14575 + 1.98450i) q^{4} +(6.39086 - 3.68977i) q^{5} +(3.11438 + 2.38267i) q^{6} +8.22359i q^{8} +(-6.34572 + 6.38215i) q^{9} +(4.82288 - 8.35347i) q^{10} +(-2.26395 - 1.30710i) q^{11} +(-6.81697 - 0.887547i) q^{12} +6.35425 q^{13} +(17.5830 + 13.4520i) q^{15} +(0.791503 + 1.37092i) q^{16} +(10.5178 + 6.07244i) q^{17} +(-3.01217 + 11.3717i) q^{18} +(-5.11438 - 8.85836i) q^{19} +16.9102i q^{20} -3.41699 q^{22} +(-3.72591 + 2.15115i) q^{23} +(-22.7793 + 9.47371i) q^{24} +(14.7288 - 25.5110i) q^{25} +(7.19287 - 4.15280i) q^{26} +(-24.9889 - 10.2252i) q^{27} -17.3733i q^{29} +(28.6951 + 3.73600i) q^{30} +(19.6458 - 34.0274i) q^{31} +(-26.6954 - 15.4126i) q^{32} +(1.01253 - 7.77693i) q^{33} +15.8745 q^{34} +(-5.39477 - 19.9054i) q^{36} +(-20.5203 - 35.5421i) q^{37} +(-11.5787 - 6.68498i) q^{38} +(7.32020 + 17.6012i) q^{39} +(30.3431 + 52.5559i) q^{40} -30.2802i q^{41} -55.8745 q^{43} +(5.18786 - 2.99521i) q^{44} +(-17.0060 + 64.2017i) q^{45} +(-2.81176 + 4.87011i) q^{46} +(-34.6193 + 19.9874i) q^{47} +(-2.88562 + 3.77178i) q^{48} -38.5038i q^{50} +(-4.70396 + 36.1297i) q^{51} +(-7.28039 + 12.6100i) q^{52} +(90.9340 + 52.5008i) q^{53} +(-34.9695 + 4.75668i) q^{54} -19.2915 q^{55} +(18.6458 - 24.3718i) q^{57} +(-11.3542 - 19.6661i) q^{58} +(-35.8223 - 20.6820i) q^{59} +(-46.8412 + 19.4809i) q^{60} +(-10.2399 - 17.7360i) q^{61} -51.3577i q^{62} -46.6235 q^{64} +(40.6091 - 23.4457i) q^{65} +(-3.93643 - 9.46505i) q^{66} +(13.5830 - 23.5265i) q^{67} +(-24.1015 + 13.9150i) q^{68} +(-10.2510 - 7.84257i) q^{69} +67.8049i q^{71} +(-52.4842 - 52.1846i) q^{72} +(30.3948 - 52.6453i) q^{73} +(-46.4569 - 26.8219i) q^{74} +(87.6329 + 11.4095i) q^{75} +23.4392 q^{76} +(19.7895 + 15.1401i) q^{78} +(31.6235 + 54.7735i) q^{79} +(10.1168 + 5.84092i) q^{80} +(-0.463763 - 80.9987i) q^{81} +(-19.7895 - 34.2765i) q^{82} +89.9435i q^{83} +89.6235 q^{85} +(-63.2487 + 36.5166i) q^{86} +(48.1238 - 20.0143i) q^{87} +(10.7490 - 18.6178i) q^{88} +(54.7108 - 31.5873i) q^{89} +(22.7085 + 83.7891i) q^{90} -9.85875i q^{92} +(116.888 + 15.2184i) q^{93} +(-26.1255 + 45.2507i) q^{94} +(-65.3706 - 37.7417i) q^{95} +(11.9393 - 91.7017i) 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

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Database

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