LMFDB - Embedded newform 324.3.j.a.199.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(19,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

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

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

chi := DirichletCharacter("324.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.j (of order $18$, degree $6$, 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			199.13
Character	$\chi$	$=$	324.199
Dual form			324.3.j.a.127.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.670237 + 1.88435i) q^{2} +(-3.10156 - 2.52593i) q^{4} +(-3.98424 + 1.45015i) q^{5} +(-2.54522 + 0.448791i) q^{7} +(6.83852 - 4.15147i) q^{8} +O(q^{10})$	\(q+(-0.670237 + 1.88435i) q^{2} +(-3.10156 - 2.52593i) q^{4} +(-3.98424 + 1.45015i) q^{5} +(-2.54522 + 0.448791i) q^{7} +(6.83852 - 4.15147i) q^{8} +(-0.0621969 - 8.47966i) q^{10} +(0.818869 - 2.24982i) q^{11} +(-3.62870 - 3.04484i) q^{13} +(0.860220 - 5.09688i) q^{14} +(3.23940 + 15.6686i) q^{16} +(8.77670 - 15.2017i) q^{17} +(13.3776 - 7.72359i) q^{19} +(16.0204 + 5.56618i) q^{20} +(3.69062 + 3.05095i) q^{22} +(13.3426 + 2.35266i) q^{23} +(-5.37983 + 4.51422i) q^{25} +(8.16965 - 4.79699i) q^{26} +(9.02777 + 5.03708i) q^{28} +(33.3419 - 27.9772i) q^{29} +(46.8128 + 8.25437i) q^{31} +(-31.6964 - 4.39754i) q^{32} +(22.7629 + 26.7271i) q^{34} +(9.48996 - 5.47903i) q^{35} +(23.0118 - 39.8576i) q^{37} +(5.58776 + 30.3848i) q^{38} +(-21.2261 + 26.4573i) q^{40} +(-59.1080 - 49.5975i) q^{41} +(-11.2366 + 30.8724i) q^{43} +(-8.22266 + 4.90957i) q^{44} +(-13.3760 + 23.5654i) q^{46} +(36.6059 - 6.45461i) q^{47} +(-39.7682 + 14.4744i) q^{49} +(-4.90061 - 13.1631i) q^{50} +(3.56361 + 18.6096i) q^{52} +35.4346 q^{53} +10.1513i q^{55} +(-15.5424 + 13.6355i) q^{56} +(30.3719 + 81.5793i) q^{58} +(31.4856 + 86.5061i) q^{59} +(-17.4186 - 98.7856i) q^{61} +(-46.9298 + 82.6795i) q^{62} +(29.5306 - 56.7798i) q^{64} +(18.8731 + 6.86925i) q^{65} +(18.1558 - 21.6372i) q^{67} +(-65.6199 + 24.9797i) q^{68} +(3.96390 + 21.5547i) q^{70} +(40.2696 + 23.2497i) q^{71} +(-18.0611 - 31.2827i) q^{73} +(59.6823 + 70.0763i) q^{74} +(-61.0008 - 9.83574i) q^{76} +(-1.07450 + 6.09379i) q^{77} +(-58.8468 - 70.1309i) q^{79} +(-35.6284 - 57.7301i) q^{80} +(133.076 - 78.1382i) q^{82} +(-50.7354 - 60.4641i) q^{83} +(-12.9238 + 73.2948i) q^{85} +(-50.6433 - 41.8656i) q^{86} +(-3.74022 - 18.7850i) q^{88} +(31.6951 + 54.8975i) q^{89} +(10.6023 + 6.12126i) q^{91} +(-35.4403 - 40.9994i) q^{92} +(-12.3719 + 73.3046i) q^{94} +(-42.0995 + 50.1722i) q^{95} +(-74.9366 - 27.2747i) q^{97} +(-0.620810 - 84.6386i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.670237	+	1.88435i	−0.335119	+	0.942176i
$2$	−0.670237	+	1.88435i	−0.335119	+	0.942176i
$3$		0			0
$3$		0			0
$4$	−3.10156	−	2.52593i	−0.775391	−	0.631481i
$5$	−3.98424	+	1.45015i	−0.796849	+	0.290029i	−0.708180	−	0.706032i	$-0.750484\pi$
$5$	−3.98424	+	1.45015i	−0.796849	+	0.290029i	−0.0886688	+	0.996061i	$0.528261\pi$
$6$		0			0
$7$	−2.54522	+	0.448791i	−0.363603	+	0.0641129i	−0.352465	−	0.935825i	$-0.614656\pi$
$7$	−2.54522	+	0.448791i	−0.363603	+	0.0641129i	−0.0111376	+	0.999938i	$0.503545\pi$
$8$	6.83852	−	4.15147i	0.854815	−	0.518934i
$9$		0			0
$10$	−0.0621969	−	8.47966i	−0.00621969	−	0.847966i
$11$	0.818869	−	2.24982i	0.0744426	−	0.204529i	−0.896890	−	0.442253i	$-0.854179\pi$
$11$	0.818869	−	2.24982i	0.0744426	−	0.204529i	0.971333	+	0.237724i	$0.0764014\pi$
$12$		0			0
$13$	−3.62870	−	3.04484i	−0.279131	−	0.234219i	0.492464	−	0.870333i	$-0.336096\pi$
$13$	−3.62870	−	3.04484i	−0.279131	−	0.234219i	−0.771595	+	0.636114i	$0.780541\pi$
$14$	0.860220	−	5.09688i	0.0614443	−	0.364063i
$15$		0			0
$16$	3.23940	+	15.6686i	0.202462	+	0.979290i
$17$	8.77670	−	15.2017i	0.516277	−	0.894218i	−0.483545	−	0.875320i	$-0.660651\pi$
$17$	8.77670	−	15.2017i	0.516277	−	0.894218i	0.999821	−	0.0188979i	$-0.00601573\pi$
$18$		0			0
$19$	13.3776	−	7.72359i	0.704086	−	0.406504i	−0.104781	−	0.994495i	$-0.533414\pi$
$19$	13.3776	−	7.72359i	0.704086	−	0.406504i	0.808868	+	0.587991i	$0.200081\pi$
$20$	16.0204	+	5.56618i	0.801018	+	0.278309i
$21$		0			0
$22$	3.69062	+	3.05095i	0.167756	+	0.138680i
$23$	13.3426	+	2.35266i	0.580114	+	0.102290i	0.456002	−	0.889979i	$-0.349281\pi$
$23$	13.3426	+	2.35266i	0.580114	+	0.102290i	0.124112	+	0.992268i	$0.460392\pi$
$24$		0			0
$25$	−5.37983	+	4.51422i	−0.215193	+	0.180569i
$26$	8.16965	−	4.79699i	0.314217	−	0.184499i
$27$		0			0
$28$	9.02777	+	5.03708i	0.322420	+	0.179896i
$29$	33.3419	−	27.9772i	1.14972	−	0.964731i	0.150009	−	0.988685i	$-0.452070\pi$
$29$	33.3419	−	27.9772i	1.14972	−	0.964731i	0.999713	+	0.0239532i	$0.00762528\pi$
$30$		0			0
$31$	46.8128	+	8.25437i	1.51009	+	0.266270i	0.866530	−	0.499124i	$-0.166345\pi$
$31$	46.8128	+	8.25437i	1.51009	+	0.266270i	0.643562	+	0.765394i	$0.277456\pi$
$32$	−31.6964	−	4.39754i	−0.990512	−	0.137423i
$33$		0			0
$34$	22.7629	+	26.7271i	0.669496	+	0.786092i
$35$	9.48996	−	5.47903i	0.271142	−	0.156544i
$36$		0			0
$37$	23.0118	−	39.8576i	0.621940	−	1.07723i	−0.367184	−	0.930148i	$-0.619678\pi$
$37$	23.0118	−	39.8576i	0.621940	−	1.07723i	0.989124	−	0.147083i	$-0.0469885\pi$
$38$	5.58776	+	30.3848i	0.147046	+	0.799601i
$39$		0			0
$40$	−21.2261	+	26.4573i	−0.530652	+	0.661433i
$41$	−59.1080	−	49.5975i	−1.44166	−	1.20970i	−0.938396	−	0.345563i	$-0.887688\pi$
$41$	−59.1080	−	49.5975i	−1.44166	−	1.20970i	−0.503264	−	0.864133i	$-0.667868\pi$
$42$		0			0
$43$	−11.2366	+	30.8724i	−0.261317	+	0.717963i	0.737762	+	0.675061i	$0.235883\pi$
$43$	−11.2366	+	30.8724i	−0.261317	+	0.717963i	−0.999079	+	0.0429024i	$0.986340\pi$
$44$	−8.22266	+	4.90957i	−0.186879	+	0.111581i
$45$		0			0
$46$	−13.3760	+	23.5654i	−0.290782	+	0.512290i
$47$	36.6059	−	6.45461i	0.778850	−	0.137332i	0.229930	−	0.973207i	$-0.426150\pi$
$47$	36.6059	−	6.45461i	0.778850	−	0.137332i	0.548920	+	0.835875i	$0.315039\pi$
$48$		0			0
$49$	−39.7682	+	14.4744i	−0.811596	+	0.295397i
$50$	−4.90061	−	13.1631i	−0.0980121	−	0.263262i
$51$		0			0
$52$	3.56361	+	18.6096i	0.0685309	+	0.357877i
$53$	35.4346			0.668578			0.334289	−	0.942471i	$-0.391504\pi$
$53$	35.4346			0.668578			0.334289	+	0.942471i	$0.391504\pi$
$54$		0			0
$55$			10.1513i			0.184570i
$56$	−15.5424	+	13.6355i	−0.277542	+	0.243490i
$57$		0			0
$58$	30.3719	+	81.5793i	0.523653	+	1.40654i
$59$	31.4856	+	86.5061i	0.533655	+	1.46620i	0.854691	+	0.519138i	$0.173747\pi$
$59$	31.4856	+	86.5061i	0.533655	+	1.46620i	−0.321036	+	0.947067i	$0.604031\pi$
$60$		0			0
$61$	−17.4186	−	98.7856i	−0.285550	−	1.61944i	−0.703314	−	0.710880i	$-0.748297\pi$
$61$	−17.4186	−	98.7856i	−0.285550	−	1.61944i	0.417764	−	0.908556i	$-0.362814\pi$
$62$	−46.9298	+	82.6795i	−0.756933	+	1.33354i
$63$		0			0
$64$	29.5306	−	56.7798i	0.461416	−	0.887184i
$65$	18.8731	+	6.86925i	0.290356	+	0.105681i
$66$		0			0
$67$	18.1558	−	21.6372i	0.270982	−	0.322943i	−0.613342	−	0.789817i	$-0.710175\pi$
$67$	18.1558	−	21.6372i	0.270982	−	0.322943i	0.884324	+	0.466874i	$0.154620\pi$
$68$	−65.6199	+	24.9797i	−0.964998	+	0.367349i
$69$		0			0
$70$	3.96390	+	21.5547i	0.0566271	+	0.307924i
$71$	40.2696	+	23.2497i	0.567177	+	0.327460i	0.756021	−	0.654547i	$-0.227141\pi$
$71$	40.2696	+	23.2497i	0.567177	+	0.327460i	−0.188844	+	0.982007i	$0.560474\pi$
$72$		0			0
$73$	−18.0611	−	31.2827i	−0.247412	−	0.428531i	0.715395	−	0.698720i	$-0.246247\pi$
$73$	−18.0611	−	31.2827i	−0.247412	−	0.428531i	−0.962807	+	0.270190i	$0.912914\pi$
$74$	59.6823	+	70.0763i	0.806518	+	0.946977i
$75$		0			0
$76$	−61.0008	−	9.83574i	−0.802642	−	0.129418i
$77$	−1.07450	+	6.09379i	−0.0139545	+	0.0791402i
$78$		0			0
$79$	−58.8468	−	70.1309i	−0.744896	−	0.887733i	0.251897	−	0.967754i	$-0.418946\pi$
$79$	−58.8468	−	70.1309i	−0.744896	−	0.887733i	−0.996793	+	0.0800214i	$0.974501\pi$
$80$	−35.6284	−	57.7301i	−0.445355	−	0.721626i
$81$		0			0
$82$	133.076	−	78.1382i	1.62287	−	0.952905i
$83$	−50.7354	−	60.4641i	−0.611270	−	0.728483i	0.368273	−	0.929718i	$-0.379949\pi$
$83$	−50.7354	−	60.4641i	−0.611270	−	0.728483i	−0.979543	+	0.201234i	$0.935505\pi$
$84$		0			0
$85$	−12.9238	+	73.2948i	−0.152045	+	0.862292i
$86$	−50.6433	−	41.8656i	−0.588876	−	0.486810i
$87$		0			0
$88$	−3.74022	−	18.7850i	−0.0425025	−	0.213466i
$89$	31.6951	+	54.8975i	0.356124	+	0.616826i	0.987310	−	0.158806i	$-0.0507646\pi$
$89$	31.6951	+	54.8975i	0.356124	+	0.616826i	−0.631185	+	0.775632i	$0.717431\pi$
$90$		0			0
$91$	10.6023	+	6.12126i	0.116509	+	0.0672666i
$92$	−35.4403	−	40.9994i	−0.385221	−	0.445646i
$93$		0			0
$94$	−12.3719	+	73.3046i	−0.131616	+	0.779836i
$95$	−42.0995	+	50.1722i	−0.443152	+	0.528128i
$96$		0			0
$97$	−74.9366	−	27.2747i	−0.772543	−	0.281183i	−0.0744832	−	0.997222i	$-0.523731\pi$
$97$	−74.9366	−	27.2747i	−0.772543	−	0.281183i	−0.698060	+	0.716040i	$0.745953\pi$
$98$	−0.620810	−	84.6386i	−0.00633479	−	0.863660i
$99$		0			0
$100$	28.0885	−	0.412070i	0.280885	−	0.00412070i
$101$	3.91355	+	22.1949i	0.0387480	+	0.219751i	0.998033	−	0.0626885i	$-0.0199675\pi$
$101$	3.91355	+	22.1949i	0.0387480	+	0.219751i	−0.959285	+	0.282440i	$0.908856\pi$
$102$		0			0
$103$	−63.0772	−	173.303i	−0.612400	−	1.68255i	−0.724858	−	0.688898i	$-0.758095\pi$
$103$	−63.0772	−	173.303i	−0.612400	−	1.68255i	0.112458	−	0.993656i	$-0.464127\pi$
$104$	−37.4555	−	5.75777i	−0.360149	−	0.0553632i
$105$		0			0
$106$	−23.7496	+	66.7713i	−0.224053	+	0.629918i
$107$		−	203.126i		−	1.89837i	−0.314712	−	0.949187i	$-0.601908\pi$
$107$		−	203.126i		−	1.89837i	0.314712	−	0.949187i	$-0.398092\pi$
$108$		0			0
$109$	−13.8141			−0.126735			−0.0633673	−	0.997990i	$-0.520184\pi$
$109$	−13.8141			−0.126735			−0.0633673	+	0.997990i	$0.520184\pi$
$110$	−19.1287	−	6.80380i	−0.173897	−	0.0618527i
$111$		0			0
$112$	−15.2769	−	38.4263i	−0.136401	−	0.343092i
$113$	−25.8778	+	9.41875i	−0.229007	+	0.0833518i	−0.453975	−	0.891014i	$-0.649994\pi$
$113$	−25.8778	+	9.41875i	−0.229007	+	0.0833518i	0.224968	+	0.974366i	$0.427772\pi$
$114$		0			0
$115$	−56.5720	+	9.97517i	−0.491930	+	0.0867406i
$116$	−174.081	+	2.55384i	−1.50069	+	0.0220159i
$117$		0			0
$118$	−184.111	+	1.35042i	−1.56026	+	0.0114442i
$119$	−15.5162	+	42.6305i	−0.130389	+	0.358240i
$120$		0			0
$121$	88.3002	+	74.0927i	0.729754	+	0.612336i
$122$	197.821	+	33.3871i	1.62149	+	0.273665i
$123$		0			0
$124$	−124.343	−	143.847i	−1.00277	−	1.16006i
$125$	67.8876	−	117.585i	0.543101	−	0.940678i
$126$		0			0
$127$	−17.4875	+	10.0964i	−0.137697	+	0.0794993i	−0.567266	−	0.823535i	$-0.691999\pi$
$127$	−17.4875	+	10.0964i	−0.137697	+	0.0794993i	0.429569	+	0.903034i	$0.358665\pi$
$128$	87.2005	+	93.7020i	0.681254	+	0.732047i
$129$		0			0
$130$	−25.5935	+	30.9596i	−0.196873	+	0.238150i
$131$	−104.468	−	18.4206i	−0.797469	−	0.140615i	−0.239956	−	0.970784i	$-0.577133\pi$
$131$	−104.468	−	18.4206i	−0.797469	−	0.140615i	−0.557513	+	0.830168i	$0.688244\pi$
$132$		0			0
$133$	−30.5827	+	25.6620i	−0.229945	+	0.192947i
$134$	28.6034	+	48.7139i	0.213458	+	0.363537i
$135$		0			0
$136$	−3.08973	−	140.393i	−0.0227186	−	1.03230i
$137$	−68.1869	+	57.2156i	−0.497714	+	0.417632i	−0.856781	−	0.515680i	$-0.827539\pi$
$137$	−68.1869	+	57.2156i	−0.497714	+	0.417632i	0.359067	+	0.933312i	$0.383095\pi$
$138$		0			0
$139$	194.732	+	34.3365i	1.40095	+	0.247025i	0.822534	−	0.568716i	$-0.192560\pi$
$139$	194.732	+	34.3365i	1.40095	+	0.247025i	0.578417	+	0.815741i	$0.303671\pi$
$140$	−43.2733	−	6.97737i	−0.309095	−	0.0498383i
$141$		0			0
$142$	−70.8007	+	60.2993i	−0.498596	+	0.424643i
$143$	−9.82180	+	5.67062i	−0.0686839	+	0.0396547i
$144$		0			0
$145$	−92.2714	+	159.819i	−0.636354	+	1.10220i
$146$	71.0529	−	13.0666i	0.486664	−	0.0894973i
$147$		0			0
$148$	−172.050	+	65.4947i	−1.16250	+	0.442532i
$149$	−70.9348	−	59.5214i	−0.476072	−	0.399472i	0.372931	−	0.927859i	$-0.378353\pi$
$149$	−70.9348	−	59.5214i	−0.476072	−	0.399472i	−0.849004	+	0.528387i	$0.822797\pi$
$150$		0			0
$151$	−25.3592	+	69.6739i	−0.167942	+	0.461416i	−0.994902	−	0.100844i	$-0.967846\pi$
$151$	−25.3592	+	69.6739i	−0.167942	+	0.461416i	0.826960	+	0.562260i	$0.190068\pi$
$152$	59.4190	−	108.355i	0.390915	−	0.712860i
$153$		0			0
$154$	−10.7627	−	6.10902i	−0.0698875	−	0.0396690i
$155$	−198.484	+	34.9981i	−1.28054	+	0.225794i
$156$		0			0
$157$	210.559	−	76.6373i	1.34114	−	0.488135i	0.430969	−	0.902367i	$-0.358172\pi$
$157$	210.559	−	76.6373i	1.34114	−	0.488135i	0.910172	+	0.414231i	$0.135949\pi$
$158$	171.593	−	63.8837i	1.08603	−	0.404327i
$159$		0			0
$160$	132.663	−	28.4435i	0.829145	−	0.177772i
$161$	−35.0157			−0.217489
$162$		0			0
$163$			164.898i			1.01164i	0.862638	+	0.505822i	$0.168811\pi$
$163$			164.898i			1.01164i	−0.862638	+	0.505822i	$0.831189\pi$
$164$	58.0477	+	303.132i	0.353949	+	1.84837i
$165$		0			0
$166$	147.940	−	55.0781i	0.891208	−	0.331796i
$167$	41.2270	+	113.270i	0.246868	+	0.678264i	0.999797	+	0.0201622i	$0.00641826\pi$
$167$	41.2270	+	113.270i	0.246868	+	0.678264i	−0.752929	+	0.658102i	$0.771360\pi$
$168$		0			0
$169$	−25.4501	−	144.335i	−0.150592	−	0.854052i
$170$	−129.451	−	73.4780i	−0.761477	−	0.432223i
$171$		0			0
$172$	112.833	−	67.3699i	0.656004	−	0.391685i
$173$	2.93090	+	1.06676i	0.0169416	+	0.00616625i	0.350477	−	0.936571i	$-0.386019\pi$
$173$	2.93090	+	1.06676i	0.0169416	+	0.00616625i	−0.333535	+	0.942738i	$0.608242\pi$
$174$		0			0
$175$	11.6669	−	13.9041i	0.0666680	−	0.0794519i
$176$	37.9043	+	5.54249i	0.215366	+	0.0314914i
$177$		0			0
$178$	−124.689	+	22.9303i	−0.700502	+	0.128822i
$179$	204.401	+	118.011i	1.14190	+	0.659278i	0.946901	−	0.321525i	$-0.104195\pi$
$179$	204.401	+	118.011i	1.14190	+	0.659278i	0.195002	+	0.980803i	$0.437529\pi$
$180$		0			0
$181$	65.9812	+	114.283i	0.364537	+	0.631397i	0.988702	−	0.149896i	$-0.0478939\pi$
$181$	65.9812	+	114.283i	0.364537	+	0.631397i	−0.624165	+	0.781293i	$0.714561\pi$
$182$	−18.6407	+	15.8758i	−0.102421	+	0.0872299i
$183$		0			0
$184$	101.011	−	39.3027i	0.548972	−	0.213602i
$185$	−33.8852	+	192.173i	−0.183163	+	1.03877i
$186$		0			0
$187$	−27.0142	−	32.1942i	−0.144461	−	0.172162i
$188$	−129.840	−	72.4445i	−0.690636	−	0.385343i
$189$		0			0
$190$	−66.3254	−	112.957i	−0.349081	−	0.594513i
$191$	−50.3735	−	60.0328i	−0.263736	−	0.314308i	0.617883	−	0.786270i	$-0.287990\pi$
$191$	−50.3735	−	60.0328i	−0.263736	−	0.314308i	−0.881619	+	0.471962i	$0.843546\pi$
$192$		0			0
$193$	−4.46923	+	25.3463i	−0.0231567	+	0.131328i	−0.994195	−	0.107598i	$-0.965684\pi$
$193$	−4.46923	+	25.3463i	−0.0231567	+	0.131328i	0.971038	+	0.238926i	$0.0767952\pi$
$194$	101.620	−	122.926i	0.523817	−	0.633642i
$195$		0			0
$196$	159.905	+	55.5581i	0.815842	+	0.283460i
$197$	71.9902	+	124.691i	0.365432	+	0.632947i	0.988845	−	0.148945i	$-0.0475878\pi$
$197$	71.9902	+	124.691i	0.365432	+	0.632947i	−0.623413	+	0.781893i	$0.714255\pi$
$198$		0			0
$199$	201.908	+	116.571i	1.01461	+	0.585786i	0.912539	−	0.408990i	$-0.134119\pi$
$199$	201.908	+	116.571i	1.01461	+	0.585786i	0.102073	+	0.994777i	$0.467452\pi$
$200$	−18.0495	+	53.2047i	−0.0902473	+	0.266024i
$201$		0			0
$202$	−44.4459	−	7.50131i	−0.220029	−	0.0371352i
$203$	−72.3066	+	86.1716i	−0.356190	+	0.424491i
$204$		0			0
$205$	307.425	+	111.893i	1.49963	+	0.545821i
$206$	368.841	−	2.70538i	1.79049	−	0.0131329i
$207$		0			0
$208$	35.9537	−	66.7203i	0.172855	−	0.320771i
$209$	−6.42217	−	36.4219i	−0.0307281	−	0.174268i
$210$		0			0
$211$	7.12646	+	19.5798i	0.0337747	+	0.0927953i	0.955434	−	0.295205i	$-0.0953881\pi$
$211$	7.12646	+	19.5798i	0.0337747	+	0.0927953i	−0.921659	+	0.388001i	$0.873166\pi$
$212$	−109.903	−	89.5053i	−0.518409	−	0.422195i
$213$		0			0
$214$	382.761	+	136.143i	1.78860	+	0.636181i
$215$		−	139.298i		−	0.647898i
$216$		0			0
$217$	−122.853			−0.566145
$218$	9.25871	−	26.0306i	0.0424711	−	0.119406i
$219$		0			0
$220$	25.6415	−	31.4850i	0.116552	−	0.143114i
$221$	−78.1349	+	28.4388i	−0.353551	+	0.128682i
$222$		0			0
$223$	−264.230	+	46.5908i	−1.18489	+	0.208928i	−0.731155	−	0.682211i	$-0.761019\pi$
$223$	−264.230	+	46.5908i	−1.18489	+	0.208928i	−0.453732	+	0.891138i	$0.649908\pi$
$224$	82.6478	−	3.03234i	0.368963	−	0.0135372i
$225$		0			0
$226$	−0.403971	−	55.0757i	−0.00178748	−	0.243698i
$227$	93.7660	−	257.620i	0.413066	−	1.13489i	−0.542485	−	0.840065i	$-0.682517\pi$
$227$	93.7660	−	257.620i	0.413066	−	1.13489i	0.955551	−	0.294824i	$-0.0952612\pi$
$228$		0			0
$229$	150.793	+	126.530i	0.658483	+	0.552533i	0.909632	−	0.415415i	$-0.136364\pi$
$229$	150.793	+	126.530i	0.658483	+	0.552533i	−0.251148	+	0.967949i	$0.580808\pi$
$230$	19.1199	−	113.287i	0.0831301	−	0.492553i
$231$		0			0
$232$	111.863	−	329.741i	0.482168	−	1.42130i
$233$	−137.473	+	238.110i	−0.590012	+	1.02193i	0.404219	+	0.914662i	$0.367544\pi$
$233$	−137.473	+	238.110i	−0.590012	+	1.02193i	−0.994230	+	0.107268i	$0.965790\pi$
$234$		0			0
$235$	−136.487	+	78.8007i	−0.580795	+	0.335322i
$236$	120.853	−	347.835i	0.512090	−	1.47388i
$237$		0			0
$238$	−69.9314	−	57.8106i	−0.293829	−	0.242902i
$239$	245.841	+	43.3484i	1.02862	+	0.181374i	0.662398	−	0.749152i	$-0.269539\pi$
$239$	245.841	+	43.3484i	1.02862	+	0.181374i	0.366225	+	0.930526i	$0.380650\pi$
$240$		0			0
$241$	−14.5817	+	12.2355i	−0.0605051	+	0.0507698i	−0.672539	−	0.740062i	$-0.734796\pi$
$241$	−14.5817	+	12.2355i	−0.0605051	+	0.0507698i	0.612034	+	0.790832i	$0.290352\pi$
$242$	−198.799	+	116.729i	−0.821483	+	0.482351i
$243$		0			0
$244$	−195.500	+	350.388i	−0.801230	+	1.43602i
$245$	137.456	−	115.339i	0.561046	−	0.470773i
$246$		0			0
$247$	−72.0606	−	12.7062i	−0.291743	−	0.0514422i
$248$	354.398	−	137.894i	1.42902	−	0.556026i
$249$		0			0
$250$	176.070	+	206.734i	0.704281	+	0.826935i
$251$	5.39896	−	3.11709i	0.0215098	−	0.0124187i	−0.489207	−	0.872168i	$-0.662714\pi$
$251$	5.39896	−	3.11709i	0.0215098	−	0.0124187i	0.510716	+	0.859749i	$0.329380\pi$
$252$		0			0
$253$	16.2189	−	28.0920i	0.0641065	−	0.111036i
$254$	−7.30442	−	39.7196i	−0.0287575	−	0.156376i
$255$		0			0
$256$	−235.013	+	101.514i	−0.918018	+	0.396539i
$257$	149.042	+	125.061i	0.579930	+	0.486619i	0.884924	−	0.465735i	$-0.154210\pi$
$257$	149.042	+	125.061i	0.579930	+	0.486619i	−0.304994	+	0.952354i	$0.598655\pi$
$258$		0			0
$259$	−40.6823	+	111.774i	−0.157074	+	0.431558i
$260$	−41.1849	−	68.9775i	−0.158404	−	0.265298i
$261$		0			0
$262$	104.730	−	184.509i	0.399731	−	0.704233i
$263$	−194.704	+	34.3316i	−0.740320	+	0.130538i	−0.531075	−	0.847325i	$-0.678212\pi$
$263$	−194.704	+	34.3316i	−0.740320	+	0.130538i	−0.209245	+	0.977863i	$0.567101\pi$
$264$		0			0
$265$	−141.180	+	51.3854i	−0.532756	+	0.193907i
$266$	−27.8585	−	74.8282i	−0.104731	−	0.281309i
$267$		0			0
$268$	−110.965	+	21.2490i	−0.414049	+	0.0792875i
$269$	−253.937			−0.944004			−0.472002	−	0.881597i	$-0.656469\pi$
$269$	−253.937			−0.944004			−0.472002	+	0.881597i	$0.656469\pi$
$270$		0			0
$271$			205.121i			0.756905i	0.925621	+	0.378452i	$0.123544\pi$
$271$			205.121i			0.756905i	−0.925621	+	0.378452i	$0.876456\pi$
$272$	266.621	+	88.2747i	0.980225	+	0.324539i
$273$		0			0
$274$	−62.1129	−	166.836i	−0.226689	−	0.608891i
$275$	5.75081	+	15.8002i	0.0209120	+	0.0574554i
$276$		0			0
$277$	−27.2346	−	154.455i	−0.0983197	−	0.557599i	−0.993679	−	0.112255i	$-0.964193\pi$
$277$	−27.2346	−	154.455i	−0.0983197	−	0.557599i	0.895360	−	0.445344i	$-0.146919\pi$
$278$	−195.219	+	343.930i	−0.702226	+	1.23716i
$279$		0			0
$280$	42.1512	−	76.8657i	0.150540	−	0.274520i
$281$	−19.5697	−	7.12277i	−0.0696429	−	0.0253479i	0.306964	−	0.951721i	$-0.400687\pi$
$281$	−19.5697	−	7.12277i	−0.0696429	−	0.0253479i	−0.376607	+	0.926373i	$0.622909\pi$
$282$		0			0
$283$	−10.4696	+	12.4772i	−0.0369951	+	0.0440890i	−0.784225	−	0.620477i	$-0.786939\pi$
$283$	−10.4696	+	12.4772i	−0.0369951	+	0.0440890i	0.747230	+	0.664566i	$0.231384\pi$
$284$	−66.1718	−	173.828i	−0.232999	−	0.612071i
$285$		0			0
$286$	−4.10250	−	22.3084i	−0.0143444	−	0.0780013i
$287$	172.702	+	99.7094i	0.601748	+	0.347419i
$288$		0			0
$289$	−9.56108	−	16.5603i	−0.0330833	−	0.0573020i
$290$	−239.311	−	280.988i	−0.825210	−	0.968925i
$291$		0			0
$292$	−23.0002	+	142.646i	−0.0787679	+	0.488515i
$293$	31.7417	−	180.016i	0.108333	−	0.614389i	−0.881503	−	0.472178i	$-0.843468\pi$
$293$	31.7417	−	180.016i	0.108333	−	0.614389i	0.989836	−	0.142211i	$-0.0454210\pi$
$294$		0			0
$295$	−250.893	−	299.003i	−0.850485	−	1.01357i
$296$	−8.10100	−	368.099i	−0.0273682	−	1.24358i
$297$		0			0
$298$	159.702	−	93.7727i	0.535914	−	0.314673i
$299$	−41.2529	−	49.1633i	−0.137970	−	0.164426i
$300$		0			0
$301$	14.7445	−	83.6199i	0.0489849	−	0.277807i
$302$	−114.293	−	94.4837i	−0.378455	−	0.312860i
$303$		0			0
$304$	164.354	+	184.590i	0.540637	+	0.607203i
$305$	212.653	+	368.326i	0.697224	+	1.20763i
$306$		0			0
$307$	−66.6563	−	38.4840i	−0.217121	−	0.125355i	0.387495	−	0.921872i	$-0.373340\pi$
$307$	−66.6563	−	38.4840i	−0.217121	−	0.125355i	−0.604617	+	0.796517i	$0.706674\pi$
$308$	18.7251	−	16.1862i	0.0607958	−	0.0525525i
$309$		0			0
$310$	67.0826	−	397.470i	0.216396	−	1.28216i
$311$	103.312	−	123.123i	0.332194	−	0.395893i	−0.573931	−	0.818904i	$-0.694582\pi$
$311$	103.312	−	123.123i	0.332194	−	0.395893i	0.906125	+	0.423011i	$0.139027\pi$
$312$		0			0
$313$	342.269	+	124.576i	1.09351	+	0.398006i	0.824921	−	0.565248i	$-0.191220\pi$
$313$	342.269	+	124.576i	1.09351	+	0.398006i	0.268591	+	0.963254i	$0.413442\pi$
$314$	3.28698	+	448.133i	0.0104681	+	1.42717i
$315$		0			0
$316$	5.37170	+	366.158i	0.0169991	+	1.15873i
$317$	−80.0708	−	454.104i	−0.252589	−	1.43251i	−0.802186	−	0.597075i	$-0.796330\pi$
$317$	−80.0708	−	454.104i	−0.252589	−	1.43251i	0.549596	−	0.835430i	$-0.314782\pi$
$318$		0			0
$319$	−35.6411	−	97.9232i	−0.111728	−	0.306969i
$320$	−35.3182	+	269.048i	−0.110370	+	0.840776i
$321$		0			0
$322$	23.4689	−	65.9820i	0.0728846	−	0.204913i
$323$		−	271.150i		−	0.839475i
$324$		0			0
$325$	33.2669			0.102360
$326$	−310.726	−	110.521i	−0.953146	−	0.339021i
$327$		0			0
$328$	−610.114	−	93.7884i	−1.86010	−	0.285940i
$329$	−90.2733	+	32.8568i	−0.274387	+	0.0998687i
$330$		0			0
$331$	560.929	−	98.9068i	1.69465	−	0.298812i	0.758828	−	0.651291i	$-0.225772\pi$
$331$	560.929	−	98.9068i	1.69465	−	0.298812i	0.935820	+	0.352479i	$0.114661\pi$
$332$	4.63127	+	315.687i	0.0139496	+	0.950865i
$333$		0			0
$334$	−241.073	+	1.76823i	−0.721774	+	0.00529409i
$335$	−40.9599	+	112.536i	−0.122268	+	0.335930i
$336$		0			0
$337$	−313.100	−	262.722i	−0.929079	−	0.779590i	0.0465731	−	0.998915i	$-0.485170\pi$
$337$	−313.100	−	262.722i	−0.929079	−	0.779590i	−0.975652	+	0.219325i	$0.929614\pi$
$338$	289.035	+	48.7816i	0.855134	+	0.144324i
$339$		0			0
$340$	225.221	−	194.684i	0.662416	−	0.572599i
$341$	56.9045	−	98.5614i	0.166875	−	0.289036i
$342$		0			0
$343$	204.396	−	118.008i	0.595906	−	0.344047i
$344$	51.3239	+	257.770i	0.149197	+	0.749332i
$345$		0			0
$346$	−3.97456	+	4.80787i	−0.0114872	+	0.0138956i
$347$	−67.6194	−	11.9231i	−0.194868	−	0.0343606i	0.0753620	−	0.997156i	$-0.475989\pi$
$347$	−67.6194	−	11.9231i	−0.194868	−	0.0343606i	−0.270230	+	0.962796i	$0.587100\pi$
$348$		0			0
$349$	−301.507	+	252.994i	−0.863916	+	0.724912i	−0.962808	−	0.270186i	$-0.912915\pi$
$349$	−301.507	+	252.994i	−0.863916	+	0.724912i	0.0988917	+	0.995098i	$0.468470\pi$
$350$	18.3806	+	31.3036i	0.0525159	+	0.0894388i
$351$		0			0
$352$	−35.8489	+	67.7103i	−0.101843	+	0.192359i
$353$	64.2850	−	53.9415i	0.182110	−	0.152809i	−0.547175	−	0.837018i	$-0.684297\pi$
$353$	64.2850	−	53.9415i	0.182110	−	0.152809i	0.729286	+	0.684209i	$0.239852\pi$
$354$		0			0
$355$	−194.159	−	34.2355i	−0.546927	−	0.0964381i
$356$	40.3627	−	250.327i	0.113378	−	0.703167i
$357$		0			0
$358$	−359.371	+	306.068i	−1.00383	+	0.854937i
$359$	−516.172	+	298.012i	−1.43781	+	0.830117i	−0.997697	−	0.0678276i	$-0.978393\pi$
$359$	−516.172	+	298.012i	−1.43781	+	0.830117i	−0.440108	+	0.897945i	$0.645060\pi$
$360$		0			0
$361$	−61.1925	+	105.988i	−0.169508	+	0.293597i
$362$	−259.572	+	47.7352i	−0.717050	+	0.131865i
$363$		0			0
$364$	−17.4220	−	45.7662i	−0.0478626	−	0.125731i
$365$	117.324	+	98.4468i	0.321437	+	0.269717i
$366$		0			0
$367$	−54.1761	+	148.847i	−0.147619	+	0.405579i	−0.991360	−	0.131172i	$-0.958126\pi$
$367$	−54.1761	+	148.847i	−0.147619	+	0.405579i	0.843741	+	0.536751i	$0.180348\pi$
$368$	6.35901	+	216.682i	0.0172799	+	0.588810i
$369$		0			0
$370$	−339.410	−	192.653i	−0.917324	−	0.520684i
$371$	−90.1889	+	15.9027i	−0.243097	+	0.0428645i
$372$		0			0
$373$	13.0433	−	4.74739i	0.0349688	−	0.0127276i	−0.324477	−	0.945894i	$-0.605188\pi$
$373$	13.0433	−	4.74739i	0.0349688	−	0.0127276i	0.359445	+	0.933166i	$0.382966\pi$
$374$	78.7712	−	29.3264i	0.210618	−	0.0784129i
$375$		0			0
$376$	223.534	−	196.108i	0.594506	−	0.521565i
$377$	−206.174			−0.546881
$378$		0			0
$379$		−	388.683i		−	1.02555i	−0.858523	−	0.512774i	$-0.828618\pi$
$379$		−	388.683i		−	1.02555i	0.858523	−	0.512774i	$-0.171382\pi$
$380$	257.305	−	49.2721i	0.677119	−	0.129663i
$381$		0			0
$382$	146.885	−	54.6852i	0.384516	−	0.143155i
$383$	−97.1646	−	266.958i	−0.253694	−	0.697017i	−0.999523	−	0.0308805i	$-0.990169\pi$
$383$	−97.1646	−	266.958i	−0.253694	−	0.697017i	0.745829	−	0.666137i	$-0.232053\pi$
$384$		0			0
$385$	−4.55582	−	25.8373i	−0.0118333	−	0.0671100i
$386$	−44.7659	−	25.4096i	−0.115974	−	0.0658281i
$387$		0			0
$388$	163.527	+	273.879i	0.421461	+	0.705873i
$389$	23.9834	+	8.72924i	0.0616540	+	0.0224402i	0.372663	−	0.927967i	$-0.378445\pi$
$389$	23.9834	+	8.72924i	0.0616540	+	0.0224402i	−0.311009	+	0.950407i	$0.600667\pi$
$390$		0			0
$391$	152.869	−	182.182i	0.390969	−	0.465938i
$392$	−211.865	+	264.080i	−0.540473	+	0.673674i
$393$		0			0
$394$	−283.211	+	52.0825i	−0.718811	+	0.132189i
$395$	336.160	+	194.082i	0.851038	+	0.491347i
$396$		0			0
$397$	−211.963	−	367.130i	−0.533911	−	0.924761i	−0.999215	−	0.0396104i	$-0.987388\pi$
$397$	−211.963	−	367.130i	−0.533911	−	0.924761i	0.465304	−	0.885151i	$-0.345945\pi$
$398$	−354.988	+	302.335i	−0.891929	+	0.759635i
$399$		0			0
$400$	−88.1590	−	69.6713i	−0.220398	−	0.174178i
$401$	26.4342	−	149.916i	0.0659207	−	0.373855i	−0.933944	−	0.357419i	$-0.883657\pi$
$401$	26.4342	−	149.916i	0.0659207	−	0.373855i	0.999865	−	0.0164359i	$-0.00523196\pi$
$402$		0			0
$403$	−144.737	−	172.490i	−0.359148	−	0.428016i
$404$	43.9244	−	78.7241i	0.108724	−	0.194862i
$405$		0			0
$406$	−113.915	−	194.007i	−0.280579	−	0.477849i
$407$	−70.8289	−	84.4106i	−0.174027	−	0.207397i
$408$		0			0
$409$	57.5159	−	326.189i	0.140626	−	0.797528i	−0.830150	−	0.557540i	$-0.811745\pi$
$409$	57.5159	−	326.189i	0.140626	−	0.797528i	0.970776	−	0.239988i	$-0.0771435\pi$
$410$	−416.894	+	504.301i	−1.01681	+	1.23000i
$411$		0			0
$412$	−242.113	+	696.839i	−0.587653	+	1.69136i
$413$	−118.961	−	206.046i	−0.288041	−	0.498902i
$414$		0			0
$415$	289.824	+	167.330i	0.698372	+	0.403205i
$416$	101.627	+	112.468i	0.244296	+	0.270356i
$417$		0			0
$418$	72.9361	+	12.3097i	0.174488	+	0.0294491i
$419$	−255.170	+	304.100i	−0.608997	+	0.725775i	−0.979137	−	0.203201i	$-0.934865\pi$
$419$	−255.170	+	304.100i	−0.608997	+	0.725775i	0.370140	+	0.928976i	$0.379310\pi$
$420$		0			0
$421$	612.453	+	222.915i	1.45476	+	0.529488i	0.943916	−	0.330187i	$-0.107112\pi$
$421$	612.453	+	222.915i	1.45476	+	0.529488i	0.510841	+	0.859675i	$0.329334\pi$
$422$	−41.6717	+	0.305654i	−0.0987480	+	0.000724300i
$423$		0			0
$424$	242.320	−	147.106i	0.571510	−	0.346948i
$425$	21.4065	+	121.403i	0.0503683	+	0.285653i
$426$		0			0
$427$	88.6680	+	243.613i	0.207654	+	0.570523i
$428$	−513.081	+	630.009i	−1.19879	+	1.47198i
$429$		0			0
$430$	262.487	+	93.3628i	0.610434	+	0.217123i
$431$			248.329i			0.576170i	0.957605	+	0.288085i	$0.0930186\pi$
$431$			248.329i			0.576170i	−0.957605	+	0.288085i	$0.906981\pi$
$432$		0			0
$433$	−426.359			−0.984663			−0.492332	−	0.870408i	$-0.663855\pi$
$433$	−426.359			−0.984663			−0.492332	+	0.870408i	$0.663855\pi$
$434$	82.3409	−	231.499i	0.189726	−	0.533408i
$435$		0			0
$436$	42.8452	+	34.8933i	0.0982689	+	0.0800306i
$437$	196.664	−	71.5798i	0.450032	−	0.163798i
$438$		0			0
$439$	760.647	−	134.123i	1.73268	−	0.305518i	0.783768	−	0.621054i	$-0.213295\pi$
$439$	760.647	−	134.123i	1.73268	−	0.305518i	0.948914	+	0.315536i	$0.102184\pi$
$440$	42.1429	+	69.4200i	0.0957794	+	0.157773i
$441$		0			0
$442$	−1.21974	−	166.294i	−0.00275959	−	0.376231i
$443$	−245.427	+	674.306i	−0.554012	+	1.52213i	0.274173	+	0.961680i	$0.411596\pi$
$443$	−245.427	+	674.306i	−0.554012	+	1.52213i	−0.828185	+	0.560455i	$0.810626\pi$
$444$		0			0
$445$	−205.890	−	172.762i	−0.462675	−	0.388230i
$446$	89.3031	−	529.129i	0.200231	−	1.18639i
$447$		0			0
$448$	−49.6796	+	157.770i	−0.110892	+	0.352165i
$449$	101.434	−	175.689i	0.225911	−	0.391289i	−0.730682	−	0.682718i	$-0.760798\pi$
$449$	101.434	−	175.689i	0.225911	−	0.391289i	0.956592	+	0.291430i	$0.0941309\pi$
$450$		0			0
$451$	−159.987	+	92.3688i	−0.354739	+	0.204809i
$452$	104.053	+	36.1526i	0.230205	+	0.0799835i
$453$		0			0
$454$	422.601	+	349.355i	0.930840	+	0.769504i
$455$	−51.1190	−	9.01366i	−0.112350	−	0.0198102i
$456$		0			0
$457$	−619.478	+	519.804i	−1.35553	+	1.13743i	−0.378198	+	0.925725i	$0.623456\pi$
$457$	−619.478	+	519.804i	−1.35553	+	1.13743i	−0.977334	+	0.211702i	$0.932100\pi$
$458$	−339.494	+	199.341i	−0.741253	+	0.435243i
$459$		0			0
$460$	200.658	+	111.958i	0.436213	+	0.243387i
$461$	141.765	−	118.955i	0.307517	−	0.258037i	−0.475948	−	0.879473i	$-0.657895\pi$
$461$	141.765	−	118.955i	0.307517	−	0.258037i	0.783465	+	0.621436i	$0.213450\pi$
$462$		0			0
$463$	−501.788	−	88.4787i	−1.08377	−	0.191099i	−0.396891	−	0.917866i	$-0.629911\pi$
$463$	−501.788	−	88.4787i	−1.08377	−	0.191099i	−0.686884	+	0.726767i	$0.741022\pi$
$464$	546.373	+	431.794i	1.17753	+	0.930590i
$465$		0			0
$466$	−356.543	−	418.637i	−0.765114	−	0.898363i
$467$	358.476	−	206.966i	0.767615	−	0.443183i	−0.0644080	−	0.997924i	$-0.520516\pi$
$467$	358.476	−	206.966i	0.767615	−	0.443183i	0.832023	+	0.554741i	$0.187183\pi$
$468$		0			0
$469$	−36.4998	+	63.2195i	−0.0778248	+	0.134796i
$470$	−57.0097	−	310.004i	−0.121297	−	0.659584i
$471$		0			0
$472$	574.442	+	460.862i	1.21704	+	0.976402i
$473$	60.2562	+	50.5609i	0.127392	+	0.106894i
$474$		0			0
$475$	−37.1035	+	101.941i	−0.0781127	+	0.214613i
$476$	155.806	−	93.0284i	0.327324	−	0.195438i
$477$		0			0
$478$	−246.455	+	434.197i	−0.515597	+	0.908363i
$479$	676.603	−	119.303i	1.41253	−	0.249067i	0.585249	−	0.810853i	$-0.300997\pi$
$479$	676.603	−	119.303i	1.41253	−	0.249067i	0.827283	+	0.561786i	$0.189886\pi$
$480$		0			0
$481$	−204.863	+	74.5640i	−0.425911	+	0.155019i
$482$	−13.2828	−	35.6778i	−0.0275577	−	0.0740204i
$483$		0			0
$484$	−86.7162	−	452.843i	−0.179166	−	0.935626i
$485$	338.118			0.697151
$486$		0			0
$487$			15.2210i			0.0312545i	0.999878	+	0.0156273i	$0.00497452\pi$
$487$			15.2210i			0.0312545i	−0.999878	+	0.0156273i	$0.995025\pi$
$488$	−529.222	−	603.234i	−1.08447	−	1.23614i
$489$		0			0
$490$	125.212	+	336.321i	0.255534	+	0.686369i
$491$	−163.650	−	449.624i	−0.333299	−	0.915732i	−0.987248	−	0.159193i	$-0.949111\pi$
$491$	−163.650	−	449.624i	−0.333299	−	0.915732i	0.653948	−	0.756539i	$-0.273111\pi$
$492$		0			0
$493$	−132.669	−	752.402i	−0.269105	−	1.52617i
$494$	72.2407	−	127.271i	0.146236	−	0.257634i
$495$		0			0
$496$	22.3107	+	760.233i	0.0449813	+	1.53273i
$497$	−112.929	−	41.1028i	−0.227221	−	0.0827018i
$498$		0			0
$499$	321.114	−	382.689i	0.643516	−	0.766913i	−0.341405	−	0.939916i	$-0.610903\pi$
$499$	321.114	−	382.689i	0.643516	−	0.766913i	0.984921	+	0.173004i	$0.0553473\pi$
$500$	−507.568	+	193.218i	−1.01514	+	0.386435i
$501$		0			0
$502$	2.25511	+	12.2627i	0.00449225	+	0.0244277i
$503$	−385.032	−	222.299i	−0.765472	−	0.441946i	0.0657849	−	0.997834i	$-0.479045\pi$
$503$	−385.032	−	222.299i	−0.765472	−	0.441946i	−0.831257	+	0.555888i	$0.812378\pi$
$504$		0			0
$505$	−47.7783	−	82.7545i	−0.0946106	−	0.163870i
$506$	42.0647	+	49.3905i	0.0831319	+	0.0976097i
$507$		0			0
$508$	79.7414	+	12.8575i	0.156971	+	0.0253099i
$509$	115.845	−	656.990i	0.227594	−	1.29075i	−0.630071	−	0.776537i	$-0.716974\pi$
$509$	115.845	−	656.990i	0.227594	−	1.29075i	0.857665	−	0.514209i	$-0.171915\pi$
$510$		0			0
$511$	60.0088	+	71.5157i	0.117434	+	0.139953i
$512$	−33.7737	−	510.885i	−0.0659643	−	0.997822i
$513$		0			0
$514$	−335.553	+	197.027i	−0.652826	+	0.383321i
$515$	502.630	+	599.011i	0.975980	+	1.16313i
$516$		0			0
$517$	15.4537	−	87.6424i	0.0298911	−	0.169521i
$518$	−183.354	−	151.575i	−0.353965	−	0.292615i
$519$		0			0
$520$	157.582	−	31.3756i	0.303041	−	0.0603378i
$521$	−177.270	−	307.041i	−0.340250	−	0.589330i	0.644229	−	0.764833i	$-0.277178\pi$
$521$	−177.270	−	307.041i	−0.340250	−	0.589330i	−0.984479	+	0.175503i	$0.943845\pi$
$522$		0			0
$523$	−826.762	−	477.331i	−1.58081	−	0.912679i	−0.994742	−	0.102415i	$-0.967343\pi$
$523$	−826.762	−	477.331i	−1.58081	−	0.912679i	−0.586065	−	0.810264i	$-0.699324\pi$
$524$	277.486	+	321.012i	0.529554	+	0.612619i
$525$		0			0
$526$	65.8052	−	389.901i	0.125105	−	0.741257i
$527$	536.343	−	639.189i	1.01773	−	1.21288i
$528$		0			0
$529$	−324.607	−	118.147i	−0.613623	−	0.223341i
$530$	−2.20392	−	300.474i	−0.00415834	−	0.566931i
$531$		0			0
$532$	159.675	−	2.34250i	0.300140	−	0.00440319i
$533$	63.4688	+	359.949i	0.119078	+	0.675327i
$534$		0			0
$535$	294.563	+	809.304i	0.550584	+	1.51272i
$536$	34.3324	−	223.340i	0.0640529	−	0.416678i
$537$		0			0
$538$	170.198	−	478.507i	0.316353	−	0.889418i
$539$			101.324i			0.187985i
$540$		0			0
$541$	705.012			1.30316			0.651582	−	0.758578i	$-0.274105\pi$
$541$	705.012			1.30316			0.651582	+	0.758578i	$0.274105\pi$
$542$	−386.521	−	137.480i	−0.713137	−	0.253653i
$543$		0			0
$544$	−345.040	+	443.243i	−0.634265	+	0.814785i
$545$	55.0387	−	20.0324i	0.100988	−	0.0367568i
$546$		0			0
$547$	−43.3865	+	7.65021i	−0.0793172	+	0.0139858i	−0.213166	−	0.977016i	$-0.568377\pi$
$547$	−43.3865	+	7.65021i	−0.0793172	+	0.0139858i	0.133849	+	0.991002i	$0.457266\pi$
$548$	356.008	−	5.22280i	0.649650	−	0.00953066i
$549$		0			0
$550$	−33.6276	+	0.246653i	−0.0611411	+	0.000448459i
$551$	229.952	−	631.788i	0.417336	−	1.14662i
$552$		0			0
$553$	181.252	+	152.088i	0.327761	+	0.275024i
$554$	309.301	+	52.2019i	0.558305	+	0.0942273i
$555$		0			0
$556$	−517.243	−	598.376i	−0.930293	−	1.07622i
$557$	242.720	−	420.403i	0.435762	−	0.754762i	−0.561595	−	0.827412i	$-0.689812\pi$
$557$	242.720	−	420.403i	0.435762	−	0.754762i	0.997358	+	0.0726498i	$0.0231455\pi$
$558$		0			0
$559$	134.776	−	77.8131i	0.241102	−	0.139200i
$560$	116.591	+	130.946i	0.208198	+	0.233832i
$561$		0			0
$562$	26.5381	−	32.1022i	0.0472209	−	0.0571213i
$563$	269.918	+	47.5938i	0.479428	+	0.0845360i	0.408139	−	0.912920i	$-0.366178\pi$
$563$	269.918	+	47.5938i	0.479428	+	0.0845360i	0.0712885	+	0.997456i	$0.477289\pi$
$564$		0			0
$565$	89.4449	−	75.0532i	0.158310	−	0.132838i
$566$	−16.4943	−	28.0911i	−0.0291419	−	0.0496309i
$567$		0			0
$568$	371.904	−	8.18474i	0.654761	−	0.0144098i
$569$	−534.345	+	448.369i	−0.939095	+	0.787995i	−0.977428	−	0.211270i	$-0.932240\pi$
$569$	−534.345	+	448.369i	−0.939095	+	0.787995i	0.0383322	+	0.999265i	$0.487795\pi$
$570$		0			0
$571$	−145.993	−	25.7425i	−0.255679	−	0.0450831i	0.0443393	−	0.999017i	$-0.485882\pi$
$571$	−145.993	−	25.7425i	−0.255679	−	0.0450831i	−0.300018	+	0.953933i	$0.596993\pi$
$572$	44.7865	+	7.22135i	0.0782981	+	0.0126247i
$573$		0			0
$574$	−303.639	+	258.602i	−0.528987	+	0.450526i
$575$	−82.4015	+	47.5745i	−0.143307	+	0.0827383i
$576$		0			0
$577$	398.974	−	691.043i	0.691462	−	1.19765i	−0.279896	−	0.960030i	$-0.590300\pi$
$577$	398.974	−	691.043i	0.691462	−	1.19765i	0.971359	−	0.237618i	$-0.0763666\pi$
$578$	37.6136	−	6.91713i	0.0650754	−	0.0119673i
$579$		0			0
$580$	689.876	−	262.617i	1.18944	−	0.452789i
$581$	156.268	+	131.125i	0.268965	+	0.225688i
$582$		0			0
$583$	29.0163	−	79.7217i	0.0497707	−	0.136744i
$584$	−253.380	−	138.947i	−0.433871	−	0.237924i
$585$		0			0
$586$	317.939	+	180.466i	0.542558	+	0.307962i
$587$	1075.96	−	189.721i	1.83298	−	0.323204i	0.852940	−	0.522009i	$-0.174817\pi$
$587$	1075.96	−	189.721i	1.83298	−	0.323204i	0.980039	+	0.198806i	$0.0637062\pi$
$588$		0			0
$589$	689.999	−	251.139i	1.17148	−	0.426382i
$590$	731.584	−	272.368i	1.23997	−	0.461641i
$591$		0			0
$592$	699.058	+	231.449i	1.18084	+	0.390961i
$593$	−175.815			−0.296484			−0.148242	−	0.988951i	$-0.547361\pi$
$593$	−175.815			−0.296484			−0.148242	+	0.988951i	$0.547361\pi$
$594$		0			0
$595$		−	192.351i		−	0.323279i
$596$	69.6623	+	363.785i	0.116883	+	0.610378i
$597$		0			0
$598$	120.290	−	44.7839i	0.201154	−	0.0748895i
$599$	134.650	+	369.949i	0.224792	+	0.617611i	0.999899	−	0.0142191i	$-0.00452625\pi$
$599$	134.650	+	369.949i	0.224792	+	0.617611i	−0.775107	+	0.631830i	$0.782304\pi$
$600$		0			0
$601$	−140.037	−	794.189i	−0.233007	−	1.32145i	−0.846771	−	0.531957i	$-0.821457\pi$
$601$	−140.037	−	794.189i	−0.233007	−	1.32145i	0.613765	−	0.789489i	$-0.289654\pi$
$602$	147.687	+	83.8289i	0.245327	+	0.139251i
$603$		0			0
$604$	254.644	−	152.042i	0.421596	−	0.251726i
$605$	−459.255	−	167.155i	−0.759099	−	0.276289i
$606$		0			0
$607$	−747.526	+	890.867i	−1.23151	+	1.46766i	−0.395934	+	0.918279i	$0.629579\pi$
$607$	−747.526	+	890.867i	−1.23151	+	1.46766i	−0.835575	+	0.549376i	$0.814865\pi$
$608$	−457.988	+	185.981i	−0.753269	+	0.305890i
$609$		0			0
$610$	−836.585	+	153.848i	−1.37145	+	0.252209i
$611$	−152.485	−	88.0375i	−0.249567	−	0.144088i
$612$		0			0
$613$	453.450	+	785.398i	0.739723	+	1.28124i	0.952620	+	0.304163i	$0.0983766\pi$
$613$	453.450	+	785.398i	0.739723	+	1.28124i	−0.212897	+	0.977075i	$0.568290\pi$
$614$	117.193	−	99.8105i	0.190868	−	0.162558i
$615$		0			0
$616$	17.9502	+	46.1333i	0.0291399	+	0.0748917i
$617$	−117.850	+	668.362i	−0.191005	+	1.08324i	0.726988	+	0.686650i	$0.240919\pi$
$617$	−117.850	+	668.362i	−0.191005	+	1.08324i	−0.917994	+	0.396595i	$0.870192\pi$
$618$		0			0
$619$	380.515	+	453.480i	0.614725	+	0.732601i	0.980154	−	0.198239i	$-0.0635221\pi$
$619$	380.515	+	453.480i	0.614725	+	0.732601i	−0.365429	+	0.930839i	$0.619078\pi$
$620$	704.013	+	392.807i	1.13550	+	0.633559i
$621$		0			0
$622$	162.763	+	277.198i	0.261677	+	0.445656i
$623$	−105.308	−	125.502i	−0.169034	−	0.201447i
$624$		0			0
$625$	−69.4779	+	394.029i	−0.111165	+	0.630446i
$626$	−464.146	+	561.461i	−0.741448	+	0.896902i
$627$		0			0
$628$	−846.643	−	294.161i	−1.34816	−	0.468410i
$629$	−403.935	−	699.636i	−0.642186	−	1.11230i
$630$		0			0
$631$	−57.7491	−	33.3415i	−0.0915200	−	0.0528391i	0.453542	−	0.891235i	$-0.350160\pi$
$631$	−57.7491	−	33.3415i	−0.0915200	−	0.0528391i	−0.545062	+	0.838396i	$0.683494\pi$
$632$	−693.571	−	235.291i	−1.09742	−	0.372295i
$633$		0			0
$634$	909.358	+	153.476i	1.43432	+	0.242076i
$635$	55.0332	−	65.5860i	0.0866664	−	0.103285i
$636$		0			0
$637$	188.379	+	68.5645i	0.295729	+	0.107637i
$638$	208.410	−	1.52865i	0.326661	−	0.00239600i
$639$		0			0
$640$	−483.310	−	246.878i	−0.755172	−	0.385747i
$641$	168.295	+	954.448i	0.262551	+	1.48900i	0.775920	+	0.630831i	$0.217286\pi$
$641$	168.295	+	954.448i	0.262551	+	1.48900i	−0.513370	+	0.858167i	$0.671603\pi$
$642$		0			0
$643$	−57.0470	−	156.735i	−0.0887201	−	0.243757i	0.887395	−	0.461009i	$-0.152513\pi$
$643$	−57.0470	−	156.735i	−0.0887201	−	0.243757i	−0.976115	+	0.217253i	$0.930290\pi$
$644$	108.604	+	88.4471i	0.168639	+	0.137340i
$645$		0			0
$646$	510.943	+	181.735i	0.790933	+	0.281324i
$647$			453.807i			0.701402i	0.936487	+	0.350701i	$0.114057\pi$
$647$			453.807i			0.701402i	−0.936487	+	0.350701i	$0.885943\pi$
$648$		0			0
$649$	220.406			0.339609
$650$	−22.2967	+	62.6865i	−0.0343026	+	0.0964408i
$651$		0			0
$652$	416.520	−	511.441i	0.638834	−	0.784419i
$653$	505.399	−	183.950i	0.773965	−	0.281700i	0.0753113	−	0.997160i	$-0.476005\pi$
$653$	505.399	−	183.950i	0.773965	−	0.281700i	0.698654	+	0.715460i	$0.253783\pi$
$654$		0			0
$655$	442.940	−	78.1023i	0.676245	−	0.119240i
$656$	585.651	−	1086.81i	0.892761	−	1.65672i
$657$		0			0
$658$	−1.40923	−	192.129i	−0.00214169	−	0.291989i
$659$	−54.5893	+	149.983i	−0.0828366	+	0.227592i	−0.974195	−	0.225707i	$-0.927531\pi$
$659$	−54.5893	+	149.983i	−0.0828366	+	0.227592i	0.891359	+	0.453299i	$0.149753\pi$
$660$		0			0
$661$	−159.965	−	134.227i	−0.242005	−	0.203066i	0.513716	−	0.857961i	$-0.328269\pi$
$661$	−159.965	−	134.227i	−0.242005	−	0.203066i	−0.755720	+	0.654894i	$0.772713\pi$
$662$	−189.580	+	1123.28i	−0.286375	+	1.69679i
$663$		0			0
$664$	−597.970	−	202.858i	−0.900557	−	0.305510i
$665$	84.6355	−	146.593i	0.127271	−	0.220441i
$666$		0			0
$667$	510.690	−	294.847i	0.765652	−	0.442049i
$668$	158.244	−	455.451i	0.236892	−	0.681813i
$669$		0			0
$670$	−184.605	−	152.609i	−0.275530	−	0.227775i
$671$	−236.514	−	41.7037i	−0.352479	−	0.0621516i
$672$		0			0
$673$	−894.100	+	750.239i	−1.32853	+	1.11477i	−0.344109	+	0.938930i	$0.611819\pi$
$673$	−894.100	+	750.239i	−1.32853	+	1.11477i	−0.984419	+	0.175838i	$0.943736\pi$
$674$	704.911	−	413.904i	1.04586	−	0.614101i
$675$		0			0
$676$	−285.644	+	511.949i	−0.422550	+	0.757321i
$677$	−88.3923	+	74.1700i	−0.130565	+	0.109557i	−0.705732	−	0.708479i	$-0.749382\pi$
$677$	−88.3923	+	74.1700i	−0.130565	+	0.109557i	0.575167	+	0.818036i	$0.304937\pi$
$678$		0			0
$679$	202.971	+	35.7892i	0.298926	+	0.0527087i
$680$	215.901	+	554.881i	0.317501	+	0.816001i
$681$		0			0
$682$	147.585	+	173.288i	0.216400	+	0.254087i
$683$	−1124.02	+	648.952i	−1.64571	+	0.950150i	−0.666956	+	0.745097i	$0.732403\pi$
$683$	−1124.02	+	648.952i	−1.64571	+	0.950150i	−0.978751	+	0.205053i	$0.934263\pi$
$684$		0			0
$685$	188.702	−	326.842i	0.275478	−	0.477141i
$686$	85.3749	+	464.247i	0.124453	+	0.676745i
$687$		0			0
$688$	−520.129	−	76.0549i	−0.756001	−	0.110545i
$689$	−128.582	−	107.893i	−0.186621	−	0.156593i
$690$		0			0
$691$	−399.004	+	1096.25i	−0.577430	+	1.58648i	0.215067	+	0.976599i	$0.431003\pi$
$691$	−399.004	+	1096.25i	−0.577430	+	1.58648i	−0.792497	+	0.609876i	$0.791219\pi$
$692$	−6.39583	−	10.7119i	−0.00924252	−	0.0154796i
$693$		0			0
$694$	67.7884	−	119.427i	0.0976778	−	0.172086i
$695$	−825.653	+	145.585i	−1.18799	+	0.209475i
$696$		0			0
$697$	−1272.74	+	463.240i	−1.82603	+	0.664619i
$698$	−274.649	−	737.711i	−0.393480	−	1.05689i
$699$		0			0
$700$	−71.3063	+	13.6546i	−0.101866	+	0.0195066i
$701$	188.390			0.268744			0.134372	−	0.990931i	$-0.457098\pi$
$701$	188.390			0.268744			0.134372	+	0.990931i	$0.457098\pi$
$702$		0			0
$703$		−	710.934i		−	1.01129i
$704$	−103.563	−	112.934i	−0.147106	−	0.160417i
$705$		0			0
$706$	58.5586	+	157.289i	0.0829442	+	0.222789i
$707$	−19.9217	−	54.7344i	−0.0281778	−	0.0774178i
$708$		0			0
$709$	79.4255	+	450.444i	0.112025	+	0.635323i	0.988180	+	0.153295i	$0.0489885\pi$
$709$	79.4255	+	450.444i	0.112025	+	0.635323i	−0.876156	+	0.482028i	$0.839900\pi$
$710$	194.644	−	342.918i	0.274147	−	0.482984i
$711$		0			0
$712$	444.652	+	243.836i	0.624512	+	0.342467i
$713$	605.186	+	220.270i	0.848789	+	0.308934i
$714$		0			0
$715$	30.9092	−	36.8362i	0.0432297	−	0.0515191i
$716$	−335.875	−	882.319i	−0.469100	−	1.23229i
$717$		0			0
$718$	−215.602	−	1172.39i	−0.300281	−	1.63285i
$719$	−905.273	−	522.660i	−1.25907	−	0.726926i	−0.286178	−	0.958176i	$-0.592385\pi$
$719$	−905.273	−	522.660i	−1.25907	−	0.726926i	−0.972894	+	0.231251i	$0.925718\pi$
$720$		0			0
$721$	238.322	+	412.786i	0.330544	+	0.572518i
$722$	−158.706	−	186.346i	−0.219815	−	0.258096i
$723$		0			0
$724$	84.0250	−	521.119i	0.116057	−	0.719778i
$725$	−53.0789	+	301.025i	−0.0732123	+	0.415207i
$726$		0			0
$727$	−29.5874	−	35.2609i	−0.0406979	−	0.0485019i	0.745312	−	0.666716i	$-0.232301\pi$
$727$	−29.5874	−	35.2609i	−0.0406979	−	0.0485019i	−0.786009	+	0.618214i	$0.787856\pi$
$728$	97.9165	−	2.15491i	0.134501	−	0.00296004i
$729$		0			0
$730$	−264.144	+	155.098i	−0.361841	+	0.212463i
$731$	370.693	+	441.774i	0.507103	+	0.604342i
$732$		0			0
$733$	−179.034	+	1015.35i	−0.244248	+	1.38520i	0.577983	+	0.816049i	$0.303840\pi$
$733$	−179.034	+	1015.35i	−0.244248	+	1.38520i	−0.822232	+	0.569153i	$0.807271\pi$
$734$	−244.170	−	201.850i	−0.332657	−	0.275000i
$735$		0			0
$736$	−412.567	−	133.246i	−0.560553	−	0.181040i
$737$	−33.8127	−	58.5653i	−0.0458788	−	0.0794645i
$738$		0			0
$739$	−477.275	−	275.555i	−0.645839	−	0.372875i	0.141021	−	0.990007i	$-0.454961\pi$
$739$	−477.275	−	275.555i	−0.645839	−	0.372875i	−0.786860	+	0.617131i	$0.788295\pi$
$740$	590.511	−	510.444i	0.797988	−	0.689790i
$741$		0			0
$742$	30.4816	−	180.606i	0.0410803	−	0.243404i
$743$	−309.908	+	369.334i	−0.417104	+	0.497085i	−0.933156	−	0.359473i	$-0.882957\pi$
$743$	−309.908	+	369.334i	−0.417104	+	0.497085i	0.516052	+	0.856557i	$0.327401\pi$
$744$		0			0
$745$	368.936	+	134.282i	0.495216	+	0.180244i
$746$	0.203616	+	27.7601i	0.000272943	+	0.0372120i
$747$		0			0
$748$	2.46593	+	168.088i	0.00329670	+	0.224717i
$749$	91.1611	+	517.000i	0.121710	+	0.690254i
$750$		0			0
$751$	289.824	+	796.286i	0.385918	+	1.06030i	0.968822	+	0.247760i	$0.0796943\pi$
$751$	289.824	+	796.286i	0.385918	+	1.06030i	−0.582903	+	0.812541i	$0.698083\pi$
$752$	219.716	+	552.656i	0.292176	+	0.734915i
$753$		0			0
$754$	138.186	−	388.505i	0.183270	−	0.515258i
$755$		−	314.372i		−	0.416387i
$756$		0			0
$757$	774.769			1.02347			0.511736	−	0.859143i	$-0.329002\pi$
$757$	774.769			1.02347			0.511736	+	0.859143i	$0.329002\pi$
$758$	732.416	+	260.510i	0.966247	+	0.343681i
$759$		0			0
$760$	−79.6097	+	517.878i	−0.104750	+	0.681418i
$761$	−496.314	+	180.644i	−0.652187	+	0.237377i	−0.646860	−	0.762609i	$-0.723918\pi$
$761$	−496.314	+	180.644i	−0.652187	+	0.237377i	−0.00532749	+	0.999986i	$0.501696\pi$
$762$		0			0
$763$	35.1598	−	6.19963i	0.0460810	−	0.00812533i
$764$	4.59824	+	313.435i	0.00601864	+	0.410256i
$765$		0			0
$766$	568.166	−	4.16740i	0.741731	−	0.00544047i
$767$	149.145	−	409.774i	0.194453	−	0.534255i
$768$		0			0
$769$	795.277	+	667.317i	1.03417	+	0.867772i	0.991341	−	0.131310i	$-0.0419185\pi$
$769$	795.277	+	667.317i	1.03417	+	0.867772i	0.0428291	+	0.999082i	$0.486363\pi$
$770$	51.7401	+	8.73238i	0.0671950	+	0.0113408i
$771$		0			0
$772$	77.8845	−	67.3242i	0.100887	−	0.0872075i
$773$	−176.398	+	305.531i	−0.228200	+	0.395253i	−0.957275	−	0.289181i	$-0.906617\pi$
$773$	−176.398	+	305.531i	−0.228200	+	0.395253i	0.729075	+	0.684434i	$0.239951\pi$
$774$		0			0
$775$	−289.107	+	166.916i	−0.373042	+	0.215376i
$776$	−625.686	+	124.579i	−0.806296	+	0.160539i
$777$		0			0
$778$	−32.5235	+	39.3425i	−0.0418040	+	0.0505687i
$779$	−1173.80	−	206.972i	−1.50680	−	0.265689i
$780$		0			0
$781$	85.2831	−	71.5610i	0.109197	−	0.0916275i
$782$	240.836	+	410.164i	0.307975	+	0.524506i
$783$		0			0
$784$	−355.620	−	576.225i	−0.453597	−	0.734981i
$785$	−727.784	+	610.683i	−0.927113	+	0.777940i
$786$		0			0
$787$	580.832	+	102.416i	0.738033	+	0.130135i	0.530013	−	0.847990i	$-0.322187\pi$
$787$	580.832	+	102.416i	0.738033	+	0.130135i	0.208020	+	0.978125i	$0.433298\pi$
$788$	91.6772	−	568.578i	0.116342	−	0.721545i
$789$		0			0
$790$	−591.026	+	503.363i	−0.748134	+	0.637168i
$791$	61.6376	−	35.5865i	0.0779236	−	0.0449892i
$792$		0			0
$793$	−237.580	+	411.500i	−0.299596	+	0.518916i
$794$	833.868	−	153.348i	1.05021	−	0.193134i
$795$		0			0
$796$	−331.779	−	871.558i	−0.416808	−	1.09492i
$797$	−731.347	−	613.673i	−0.917625	−	0.769979i	0.0559292	−	0.998435i	$-0.482188\pi$
$797$	−731.347	−	613.673i	−0.917625	−	0.769979i	−0.973554	+	0.228456i	$0.926632\pi$
$798$		0			0
$799$	223.158	−	613.123i	0.279297	−	0.767363i
$800$	190.373	−	119.426i	0.237966	−	0.149283i
$801$		0			0
$802$	264.777	+	150.290i	0.330146	+	0.187395i
$803$	−85.1703	+	15.0178i	−0.106065	+	0.0187022i
$804$		0			0
$805$	139.511	−	50.7779i	0.173306	−	0.0630782i
$806$	422.041	−	157.125i	0.523624	−	0.194945i
$807$		0			0
$808$	118.904	+	135.533i	0.147159	+	0.167739i
$809$	303.198			0.374781			0.187390	−	0.982286i	$-0.439997\pi$
$809$	303.198			0.374781			0.187390	+	0.982286i	$0.439997\pi$
$810$		0			0
$811$		−	655.791i		−	0.808620i	−0.914622	−	0.404310i	$-0.867512\pi$
$811$		−	655.791i		−	0.808620i	0.914622	−	0.404310i	$-0.132488\pi$
$812$	441.927	−	84.6258i	0.544245	−	0.104219i
$813$		0			0
$814$	206.531	−	76.8914i	0.253724	−	0.0944612i
$815$	−239.126	−	656.994i	−0.293406	−	0.806127i
$816$		0			0
$817$	88.1260	+	499.787i	0.107865	+	0.611735i
$818$	576.105	+	327.004i	0.704285	+	0.399761i
$819$		0			0
$820$	−670.862	−	1123.58i	−0.818125	−	1.37021i
$821$	603.451	+	219.638i	0.735020	+	0.267525i	0.682288	−	0.731083i	$-0.260985\pi$
$821$	603.451	+	219.638i	0.735020	+	0.267525i	0.0527318	+	0.998609i	$0.483207\pi$
$822$		0			0
$823$	−191.436	+	228.144i	−0.232607	+	0.277210i	−0.869704	−	0.493573i	$-0.835691\pi$
$823$	−191.436	+	228.144i	−0.232607	+	0.277210i	0.637097	+	0.770783i	$0.280135\pi$
$824$	−1150.82	−	923.273i	−1.39662	−	1.12048i
$825$		0			0
$826$	467.996	−	86.0643i	0.566581	−	0.104194i
$827$	−945.876	−	546.102i	−1.14374	−	0.660340i	−0.196388	−	0.980526i	$-0.562921\pi$
$827$	−945.876	−	546.102i	−1.14374	−	0.660340i	−0.947355	+	0.320186i	$0.896255\pi$
$828$		0			0
$829$	−331.753	−	574.613i	−0.400184	−	0.693140i	0.593563	−	0.804787i	$-0.297721\pi$
$829$	−331.753	−	574.613i	−0.400184	−	0.693140i	−0.993748	+	0.111647i	$0.964387\pi$
$830$	−509.560	+	433.980i	−0.613927	+	0.522867i
$831$		0			0
$832$	−280.043	+	116.121i	−0.336591	+	0.139568i
$833$	−128.998	+	731.582i	−0.154859	+	0.878250i
$834$		0			0
$835$	−328.517	−	391.511i	−0.393433	−	0.468875i
$836$	−72.0804	+	129.187i	−0.0862205	+	0.154530i
$837$		0			0
$838$	−402.006	−	684.649i	−0.479721	−	0.817003i
$839$	−105.043	−	125.185i	−0.125200	−	0.149207i	0.699803	−	0.714336i	$-0.253271\pi$
$839$	−105.043	−	125.185i	−0.125200	−	0.149207i	−0.825003	+	0.565128i	$0.808827\pi$
$840$		0			0
$841$	182.923	−	1037.41i	0.217506	−	1.23354i
$842$	−830.538	+	1004.67i	−0.986387	+	1.19320i
$843$		0			0
$844$	27.3539	−	78.7289i	0.0324099	−	0.0932807i
$845$	310.706	+	538.159i	0.367700	+	0.636874i
$846$		0			0
$847$	−257.995	−	148.954i	−0.304599	−	0.175860i
$848$	114.787	+	555.213i	0.135362	+	0.654732i
$849$		0			0
$850$	−243.113	−	41.0310i	−0.286015	−	0.0482718i
$851$	400.809	−	477.665i	0.470986	−	0.561299i
$852$		0			0
$853$	443.225	+	161.321i	0.519607	+	0.189121i	0.588492	−	0.808503i	$-0.299722\pi$
$853$	443.225	+	161.321i	0.519607	+	0.189121i	−0.0688849	+	0.997625i	$0.521944\pi$
$854$	−518.482	+	3.80298i	−0.607122	+	0.00445314i
$855$		0			0
$856$	−843.271	−	1389.08i	−0.985130	−	1.62276i
$857$	−164.122	−	930.785i	−0.191508	−	1.08610i	−0.917304	−	0.398187i	$-0.869640\pi$
$857$	−164.122	−	930.785i	−0.191508	−	1.08610i	0.725796	−	0.687910i	$-0.241472\pi$
$858$		0			0
$859$	−326.269	−	896.417i	−0.379824	−	1.04356i	−0.971429	−	0.237330i	$-0.923728\pi$
$859$	−326.269	−	896.417i	−0.379824	−	1.04356i	0.591605	−	0.806228i	$-0.298495\pi$
$860$	−351.857	+	432.042i	−0.409136	+	0.502374i
$861$		0			0
$862$	−467.940	−	166.440i	−0.542854	−	0.193085i
$863$			1620.35i			1.87758i	0.344486	+	0.938791i	$0.388053\pi$
$863$			1620.35i			1.87758i	−0.344486	+	0.938791i	$0.611947\pi$
$864$		0			0
$865$	−13.2244			−0.0152883
$866$	285.762	−	803.411i	0.329979	−	0.927726i
$867$		0			0
$868$	381.038	+	310.318i	0.438983	+	0.357510i
$869$	−205.970	+	74.9669i	−0.237020	+	0.0862681i
$870$		0			0
$871$	−131.764	+	23.2335i	−0.151279	+	0.0266745i
$872$	−94.4678	+	57.3487i	−0.108335	+	0.0657669i
$873$		0			0
$874$	3.07006	+	418.559i	0.00351266	+	0.478901i
$875$	−120.018	+	329.746i	−0.137163	+	0.376853i
$876$		0			0
$877$	−736.316	−	617.843i	−0.839585	−	0.704496i	0.117885	−	0.993027i	$-0.462389\pi$
$877$	−736.316	−	617.843i	−0.839585	−	0.704496i	−0.957470	+	0.288532i	$0.906833\pi$
$878$	−257.080	+	1523.22i	−0.292802	+	1.73488i
$879$		0			0
$880$	−159.058	+	32.8842i	−0.180747	+	0.0373684i
$881$	−692.400	+	1199.27i	−0.785925	+	1.36126i	0.142520	+	0.989792i	$0.454480\pi$
$881$	−692.400	+	1199.27i	−0.785925	+	1.36126i	−0.928445	+	0.371470i	$0.878854\pi$
$882$		0			0
$883$	−810.077	+	467.698i	−0.917415	+	0.529670i	−0.882809	−	0.469731i	$-0.844351\pi$
$883$	−810.077	+	467.698i	−0.917415	+	0.529670i	−0.0346053	+	0.999401i	$0.511017\pi$
$884$	314.174	+	109.158i	0.355401	+	0.123482i
$885$		0			0
$886$	−1106.13	−	914.416i	−1.24846	−	1.03207i
$887$	815.590	+	143.810i	0.919492	+	0.162131i	0.613311	−	0.789842i	$-0.289837\pi$
$887$	815.590	+	143.810i	0.919492	+	0.162131i	0.306182	+	0.951973i	$0.400948\pi$
$888$		0			0
$889$	39.9783	−	33.5458i	0.0449700	−	0.0377343i
$890$	463.541	−	272.178i	0.520832	−	0.305818i
$891$		0			0
$892$	937.211	+	522.920i	1.05068	+	0.586234i
$893$	439.848	−	369.077i	0.492551	−	0.413300i
$894$		0			0
$895$	−985.515	−	173.773i	−1.10113	−	0.194160i
$896$	−263.997	−	199.357i	−0.294639	−	0.222497i
$897$		0			0
$898$	263.074	+	308.890i	0.292956	+	0.343976i
$899$	1791.77	−	1034.48i	1.99306	−	1.15070i
$900$		0			0
$901$	310.999	−	538.667i	0.345171	−	0.597854i
$902$	−66.8258	−	363.382i	−0.0740862	−	0.402862i
$903$		0			0
$904$	−137.864	+	171.841i	−0.152505	+	0.190090i
$905$	−428.612	−	359.648i	−0.473604	−	0.397401i
$906$		0			0
$907$	−185.561	+	509.825i	−0.204588	+	0.562100i	−0.998973	−	0.0453144i	$-0.985571\pi$
$907$	−185.561	+	509.825i	−0.204588	+	0.562100i	0.794385	+	0.607414i	$0.207793\pi$
$908$	−941.550	+	562.179i	−1.03695	+	0.619140i
$909$		0			0
$910$	51.2468	−	90.2849i	0.0563152	−	0.0992142i
$911$	−33.3668	+	5.88346i	−0.0366265	+	0.00645824i	−0.191931	−	0.981408i	$-0.561475\pi$
$911$	−33.3668	+	5.88346i	−0.0366265	+	0.00645824i	0.155305	+	0.987867i	$0.450364\pi$
$912$		0			0
$913$	−177.579	+	64.6336i	−0.194501	+	0.0707925i
$914$	−564.296	−	1515.71i	−0.617392	−	1.65832i
$915$		0			0
$916$	−148.088	−	773.332i	−0.161668	−	0.844249i
$917$	274.162			0.298977
$918$		0			0
$919$			745.594i			0.811310i	0.914026	+	0.405655i	$0.132956\pi$
$919$			745.594i			0.811310i	−0.914026	+	0.405655i	$0.867044\pi$
$920$	−345.457	+	303.072i	−0.375497	+	0.329426i
$921$		0			0
$922$	129.137	+	346.864i	0.140062	+	0.376208i
$923$	−75.3348	−	206.981i	−0.0816195	−	0.224248i
$924$		0			0
$925$	56.1261	+	318.307i	0.0606769	+	0.344116i
$926$	503.042	−	886.243i	0.543242	−	0.957065i
$927$		0			0
$928$	−1179.85	+	740.154i	−1.27139	+	0.797580i
$929$	669.948	+	243.841i	0.721149	+	0.262477i	0.676414	−	0.736522i	$-0.263533\pi$
$929$	669.948	+	243.841i	0.721149	+	0.262477i	0.0447356	+	0.998999i	$0.485755\pi$
$930$		0			0
$931$	−420.210	+	500.787i	−0.451354	+	0.537902i
$932$	1027.83	−	391.267i	1.10282	−	0.419814i
$933$		0			0
$934$	149.733	+	814.212i	0.160314	+	0.871747i
$935$	154.317	+	89.0952i	0.165045	+	0.0952890i
$936$		0			0
$937$	−430.456	−	745.572i	−0.459398	−	0.795701i	0.539531	−	0.841966i	$-0.318602\pi$
$937$	−430.456	−	745.572i	−0.459398	−	0.795701i	−0.998929	+	0.0462645i	$0.985268\pi$
$938$	−94.6643	−	111.151i	−0.100921	−	0.118497i
$939$		0			0
$940$	622.368	+	100.350i	0.662093	+	0.106756i
$941$	−87.2608	+	494.881i	−0.0927320	+	0.525909i	0.902687	+	0.430298i	$0.141592\pi$
$941$	−87.2608	+	494.881i	−0.0927320	+	0.525909i	−0.995419	+	0.0956111i	$0.969519\pi$
$942$		0			0
$943$	−671.970	−	800.823i	−0.712587	−	0.849229i
$944$	−1253.44	+	773.565i	−1.32779	+	0.819454i
$945$		0			0
$946$	−135.661	+	79.6560i	−0.143404	+	0.0842030i
$947$	157.029	+	187.140i	0.165817	+	0.197613i	0.842554	−	0.538612i	$-0.181051\pi$
$947$	157.029	+	187.140i	0.165817	+	0.197613i	−0.676737	+	0.736225i	$0.736607\pi$
$948$		0			0
$949$	−29.7127	+	168.509i	−0.0313095	+	0.177565i
$950$	−167.225	−	138.241i	−0.176026	−	0.145517i
$951$		0			0
$952$	70.8712	+	355.945i	0.0744445	+	0.373892i
$953$	−263.010	−	455.547i	−0.275981	−	0.478014i	0.694401	−	0.719588i	$-0.255669\pi$
$953$	−263.010	−	455.547i	−0.275981	−	0.478014i	−0.970382	+	0.241575i	$0.922336\pi$
$954$		0			0
$955$	287.757	+	166.136i	0.301316	+	0.173965i
$956$	−652.997	−	755.424i	−0.683051	−	0.790193i
$957$		0			0
$958$	−228.675	+	1354.92i	−0.238700	+	1.41432i
$959$	147.873	−	176.228i	0.154195	−	0.183762i
$960$		0			0
$961$	1220.26	+	444.140i	1.26978	+	0.462164i
$962$	−3.19805	−	436.009i	−0.00332438	−	0.453232i
$963$		0			0
$964$	76.1322	−	1.11689i	0.0789753	−	0.00115860i
$965$	−18.9493	−	107.467i	−0.0196366	−	0.111365i
$966$		0			0
$967$	−569.494	−	1564.67i	−0.588929	−	1.61807i	−0.772467	−	0.635055i	$-0.780977\pi$
$967$	−569.494	−	1564.67i	−0.588929	−	1.61807i	0.183538	−	0.983013i	$-0.441245\pi$
$968$	911.436	+	140.108i	0.941566	+	0.144740i
$969$		0			0
$970$	−226.619	+	637.134i	−0.233628	+	0.656839i
$971$		−	25.8021i		−	0.0265727i	−0.999912	−	0.0132863i	$-0.995771\pi$
$971$		−	25.8021i		−	0.0265727i	0.999912	−	0.0132863i	$-0.00422930\pi$
$972$		0			0
$973$	−511.046			−0.525227
$974$	−28.6816	−	10.2017i	−0.0294473	−	0.0104740i
$975$		0			0
$976$	1491.41	−	592.931i	1.52808	−	0.607511i
$977$	677.223	−	246.489i	0.693165	−	0.252292i	0.0286755	−	0.999589i	$-0.490871\pi$
$977$	677.223	−	246.489i	0.693165	−	0.252292i	0.664490	+	0.747297i	$0.268649\pi$
$978$		0			0
$979$	149.464	−	26.3545i	0.152670	−	0.0269198i
$980$	−717.668	+	10.5285i	−0.732315	+	0.0107434i
$981$		0			0
$982$	956.935	−	7.01895i	0.974475	−	0.00714761i
$983$	212.414	−	583.604i	0.216088	−	0.593697i	−0.783530	−	0.621355i	$-0.786583\pi$
$983$	212.414	−	583.604i	0.216088	−	0.593697i	0.999617	+	0.0276579i	$0.00880491\pi$
$984$		0			0
$985$	−467.646	−	392.402i	−0.474768	−	0.398377i
$986$	1506.71	+	254.293i	1.52810	+	0.257904i
$987$		0			0
$988$	191.406	+	221.429i	0.193730	+	0.224118i
$989$	−222.559	+	385.483i	−0.225034	+	0.389771i
$990$		0			0
$991$	441.847	−	255.101i	0.445860	−	0.257417i	−0.260220	−	0.965549i	$-0.583795\pi$
$991$	441.847	−	255.101i	0.445860	−	0.257417i	0.706080	+	0.708132i	$0.250462\pi$
$992$	−1447.50	−	467.495i	−1.45917	−	0.471265i
$993$		0			0
$994$	153.141	−	185.249i	0.154066	−	0.186368i
$995$	−973.496	−	171.654i	−0.978388	−	0.172516i
$996$		0			0
$997$	−698.282	+	585.928i	−0.700383	+	0.587691i	−0.921883	−	0.387469i	$-0.873349\pi$
$997$	−698.282	+	585.928i	−0.700383	+	0.587691i	0.221499	+	0.975161i	$0.428905\pi$
$998$	505.898	+	861.585i	0.506912	+	0.863312i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.199.13		204
3.2	odd	2		108.3.j.a.103.22	yes	204
4.3	odd	2	inner	324.3.j.a.199.2		204
12.11	even	2		108.3.j.a.103.33	yes	204
27.11	odd	18		108.3.j.a.43.33	yes	204
27.16	even	9	inner	324.3.j.a.127.2		204
108.11	even	18		108.3.j.a.43.22	✓	204
108.43	odd	18	inner	324.3.j.a.127.13		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.43.22	✓	204	108.11	even	18
108.3.j.a.43.33	yes	204	27.11	odd	18
108.3.j.a.103.22	yes	204	3.2	odd	2
108.3.j.a.103.33	yes	204	12.11	even	2
324.3.j.a.127.2		204	27.16	even	9	inner
324.3.j.a.127.13		204	108.43	odd	18	inner
324.3.j.a.199.2		204	4.3	odd	2	inner
324.3.j.a.199.13		204	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.j (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.670237 + 1.88435i) q^{2} +(-3.10156 - 2.52593i) q^{4} +(-3.98424 + 1.45015i) q^{5} +(-2.54522 + 0.448791i) q^{7} +(6.83852 - 4.15147i) q^{8} +O(q^{10})\)	\(q+(-0.670237 + 1.88435i) q^{2} +(-3.10156 - 2.52593i) q^{4} +(-3.98424 + 1.45015i) q^{5} +(-2.54522 + 0.448791i) q^{7} +(6.83852 - 4.15147i) q^{8} +(-0.0621969 - 8.47966i) q^{10} +(0.818869 - 2.24982i) q^{11} +(-3.62870 - 3.04484i) q^{13} +(0.860220 - 5.09688i) q^{14} +(3.23940 + 15.6686i) q^{16} +(8.77670 - 15.2017i) q^{17} +(13.3776 - 7.72359i) q^{19} +(16.0204 + 5.56618i) q^{20} +(3.69062 + 3.05095i) q^{22} +(13.3426 + 2.35266i) q^{23} +(-5.37983 + 4.51422i) q^{25} +(8.16965 - 4.79699i) q^{26} +(9.02777 + 5.03708i) q^{28} +(33.3419 - 27.9772i) q^{29} +(46.8128 + 8.25437i) q^{31} +(-31.6964 - 4.39754i) q^{32} +(22.7629 + 26.7271i) q^{34} +(9.48996 - 5.47903i) q^{35} +(23.0118 - 39.8576i) q^{37} +(5.58776 + 30.3848i) q^{38} +(-21.2261 + 26.4573i) q^{40} +(-59.1080 - 49.5975i) q^{41} +(-11.2366 + 30.8724i) q^{43} +(-8.22266 + 4.90957i) q^{44} +(-13.3760 + 23.5654i) q^{46} +(36.6059 - 6.45461i) q^{47} +(-39.7682 + 14.4744i) q^{49} +(-4.90061 - 13.1631i) q^{50} +(3.56361 + 18.6096i) q^{52} +35.4346 q^{53} +10.1513i q^{55} +(-15.5424 + 13.6355i) q^{56} +(30.3719 + 81.5793i) q^{58} +(31.4856 + 86.5061i) q^{59} +(-17.4186 - 98.7856i) q^{61} +(-46.9298 + 82.6795i) q^{62} +(29.5306 - 56.7798i) q^{64} +(18.8731 + 6.86925i) q^{65} +(18.1558 - 21.6372i) q^{67} +(-65.6199 + 24.9797i) q^{68} +(3.96390 + 21.5547i) q^{70} +(40.2696 + 23.2497i) q^{71} +(-18.0611 - 31.2827i) q^{73} +(59.6823 + 70.0763i) q^{74} +(-61.0008 - 9.83574i) q^{76} +(-1.07450 + 6.09379i) q^{77} +(-58.8468 - 70.1309i) q^{79} +(-35.6284 - 57.7301i) q^{80} +(133.076 - 78.1382i) q^{82} +(-50.7354 - 60.4641i) q^{83} +(-12.9238 + 73.2948i) q^{85} +(-50.6433 - 41.8656i) q^{86} +(-3.74022 - 18.7850i) q^{88} +(31.6951 + 54.8975i) q^{89} +(10.6023 + 6.12126i) q^{91} +(-35.4403 - 40.9994i) q^{92} +(-12.3719 + 73.3046i) q^{94} +(-42.0995 + 50.1722i) q^{95} +(-74.9366 - 27.2747i) q^{97} +(-0.620810 - 84.6386i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more