LMFDB - Embedded newform 3234.2.e.a.2155.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3234,2,Mod(2155,3234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3234, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("3234.2155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3234.e (of order $2$, degree $1$, 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:	$25.8236200137$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 $ x^16 - 8x^15 + 74x^14 - 378x^13 + 1878x^12 - 6718x^11 + 22086x^10 - 56904x^9 + 130215x^8 - 239606x^7 + 378750x^6 - 477124x^5 + 493030x^4 - 386266x^3 + 223844x^2 - 82874*x + 13417
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 462)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2155.8
Root			$0.500000 - 2.40229i$ of defining polynomial
Character	$\chi$	$=$	3234.2155
Dual form			3234.2.e.a.2155.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +3.26832i q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +3.26832i q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +3.26832 q^{10} +(3.11438 - 1.14045i) q^{11} +1.00000i q^{12} +5.12518 q^{13} +3.26832 q^{15} +1.00000 q^{16} -5.32580 q^{17} +1.00000i q^{18} -4.27490 q^{19} -3.26832i q^{20} +(-1.14045 - 3.11438i) q^{22} +5.37186 q^{23} +1.00000 q^{24} -5.68190 q^{25} -5.12518i q^{26} +1.00000i q^{27} -4.77874i q^{29} -3.26832i q^{30} -6.46485i q^{31} -1.00000i q^{32} +(-1.14045 - 3.11438i) q^{33} +5.32580i q^{34} +1.00000 q^{36} +2.13093 q^{37} +4.27490i q^{38} -5.12518i q^{39} -3.26832 q^{40} -0.949652 q^{41} +6.20483i q^{43} +(-3.11438 + 1.14045i) q^{44} -3.26832i q^{45} -5.37186i q^{46} +12.0303i q^{47} -1.00000i q^{48} +5.68190i q^{50} +5.32580i q^{51} -5.12518 q^{52} +12.5399 q^{53} +1.00000 q^{54} +(3.72736 + 10.1788i) q^{55} +4.27490i q^{57} -4.77874 q^{58} +13.4844i q^{59} -3.26832 q^{60} +5.34060 q^{61} -6.46485 q^{62} -1.00000 q^{64} +16.7507i q^{65} +(-3.11438 + 1.14045i) q^{66} +6.19350 q^{67} +5.32580 q^{68} -5.37186i q^{69} -10.8061 q^{71} -1.00000i q^{72} +13.2295 q^{73} -2.13093i q^{74} +5.68190i q^{75} +4.27490 q^{76} -5.12518 q^{78} -9.16702i q^{79} +3.26832i q^{80} +1.00000 q^{81} +0.949652i q^{82} -0.835847 q^{83} -17.4064i q^{85} +6.20483 q^{86} -4.77874 q^{87} +(1.14045 + 3.11438i) q^{88} -6.22408i q^{89} -3.26832 q^{90} -5.37186 q^{92} -6.46485 q^{93} +12.0303 q^{94} -13.9717i q^{95} -1.00000 q^{96} +0.624337i q^{97} +(-3.11438 + 1.14045i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 16 q^{6} - 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 - 16 * q^6 - 16 * q^9	$ 16 q - 16 q^{4} - 16 q^{6} - 16 q^{9} - 4 q^{10} + 8 q^{11} - 4 q^{15} + 16 q^{16} + 20 q^{19} + 2 q^{22} + 8 q^{23} + 16 q^{24} - 20 q^{25} + 2 q^{33} + 16 q^{36} - 28 q^{37} + 4 q^{40} + 32 q^{41} - 8 q^{44} + 16 q^{54} - 14 q^{55} + 4 q^{60} - 56 q^{61} - 8 q^{62} - 16 q^{64} - 8 q^{66} + 32 q^{67} - 56 q^{71} + 88 q^{73} - 20 q^{76} + 16 q^{81} + 8 q^{83} + 24 q^{86} - 2 q^{88} + 4 q^{90} - 8 q^{92} - 8 q^{93} - 28 q^{94} - 16 q^{96} - 8 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 - 16 * q^6 - 16 * q^9 - 4 * q^10 + 8 * q^11 - 4 * q^15 + 16 * q^16 + 20 * q^19 + 2 * q^22 + 8 * q^23 + 16 * q^24 - 20 * q^25 + 2 * q^33 + 16 * q^36 - 28 * q^37 + 4 * q^40 + 32 * q^41 - 8 * q^44 + 16 * q^54 - 14 * q^55 + 4 * q^60 - 56 * q^61 - 8 * q^62 - 16 * q^64 - 8 * q^66 + 32 * q^67 - 56 * q^71 + 88 * q^73 - 20 * q^76 + 16 * q^81 + 8 * q^83 + 24 * q^86 - 2 * q^88 + 4 * q^90 - 8 * q^92 - 8 * q^93 - 28 * q^94 - 16 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times$.

$n$	$199$	$1079$	$2059$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.00000			−0.500000
$5$			3.26832i			1.46164i	0.682572	+	0.730818i	$0.260861\pi$
$5$			3.26832i			1.46164i	−0.682572	+	0.730818i	$0.739139\pi$
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−1.00000			−0.333333
$10$	3.26832			1.03353
$11$	3.11438	−	1.14045i	0.939021	−	0.343860i
$11$	3.11438	−	1.14045i	0.939021	−	0.343860i
$12$			1.00000i			0.288675i
$13$	5.12518			1.42147			0.710734	−	0.703461i	$-0.248363\pi$
$13$	5.12518			1.42147			0.710734	+	0.703461i	$0.248363\pi$
$14$		0			0
$15$	3.26832			0.843876
$16$	1.00000			0.250000
$17$	−5.32580			−1.29170			−0.645848	−	0.763466i	$-0.723496\pi$
$17$	−5.32580			−1.29170			−0.645848	+	0.763466i	$0.723496\pi$
$18$			1.00000i			0.235702i
$19$	−4.27490			−0.980729			−0.490364	−	0.871518i	$-0.663136\pi$
$19$	−4.27490			−0.980729			−0.490364	+	0.871518i	$0.663136\pi$
$20$		−	3.26832i		−	0.730818i
$21$		0			0
$22$	−1.14045	−	3.11438i	−0.243145	−	0.663988i
$23$	5.37186			1.12011			0.560055	−	0.828455i	$-0.310780\pi$
$23$	5.37186			1.12011			0.560055	+	0.828455i	$0.310780\pi$
$24$	1.00000			0.204124
$25$	−5.68190			−1.13638
$26$		−	5.12518i		−	1.00513i
$27$			1.00000i			0.192450i
$28$		0			0
$29$		−	4.77874i		−	0.887389i	−0.896178	−	0.443695i	$-0.853667\pi$
$29$		−	4.77874i		−	0.887389i	0.896178	−	0.443695i	$-0.146333\pi$
$30$		−	3.26832i		−	0.596711i
$31$		−	6.46485i		−	1.16112i	−0.814217	−	0.580561i	$-0.802833\pi$
$31$		−	6.46485i		−	1.16112i	0.814217	−	0.580561i	$-0.197167\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.14045	−	3.11438i	−0.198527	−	0.542144i
$34$			5.32580i			0.913367i
$35$		0			0
$36$	1.00000			0.166667
$37$	2.13093			0.350323			0.175161	−	0.984540i	$-0.443955\pi$
$37$	2.13093			0.350323			0.175161	+	0.984540i	$0.443955\pi$
$38$			4.27490i			0.693480i
$39$		−	5.12518i		−	0.820685i
$40$	−3.26832			−0.516767
$41$	−0.949652			−0.148311			−0.0741554	−	0.997247i	$-0.523626\pi$
$41$	−0.949652			−0.148311			−0.0741554	+	0.997247i	$0.523626\pi$
$42$		0			0
$43$			6.20483i			0.946228i	0.881001	+	0.473114i	$0.156870\pi$
$43$			6.20483i			0.946228i	−0.881001	+	0.473114i	$0.843130\pi$
$44$	−3.11438	+	1.14045i	−0.469511	+	0.171930i
$45$		−	3.26832i		−	0.487212i
$46$		−	5.37186i		−	0.792037i
$47$			12.0303i			1.75479i	0.479766	+	0.877397i	$0.340722\pi$
$47$			12.0303i			1.75479i	−0.479766	+	0.877397i	$0.659278\pi$
$48$		−	1.00000i		−	0.144338i
$49$		0			0
$50$			5.68190i			0.803543i
$51$			5.32580i			0.745761i
$52$	−5.12518			−0.710734
$53$	12.5399			1.72249			0.861246	−	0.508189i	$-0.169685\pi$
$53$	12.5399			1.72249			0.861246	+	0.508189i	$0.169685\pi$
$54$	1.00000			0.136083
$55$	3.72736	+	10.1788i	0.502598	+	1.37251i
$56$		0			0
$57$			4.27490i			0.566224i
$58$	−4.77874			−0.627479
$59$			13.4844i			1.75552i	0.479105	+	0.877758i	$0.340961\pi$
$59$			13.4844i			1.75552i	−0.479105	+	0.877758i	$0.659039\pi$
$60$	−3.26832			−0.421938
$61$	5.34060			0.683793			0.341897	−	0.939738i	$-0.388931\pi$
$61$	5.34060			0.683793			0.341897	+	0.939738i	$0.388931\pi$
$62$	−6.46485			−0.821037
$63$		0			0
$64$	−1.00000			−0.125000
$65$			16.7507i			2.07767i
$66$	−3.11438	+	1.14045i	−0.383354	+	0.140380i
$67$	6.19350			0.756656			0.378328	−	0.925672i	$-0.376499\pi$
$67$	6.19350			0.756656			0.378328	+	0.925672i	$0.376499\pi$
$68$	5.32580			0.645848
$69$		−	5.37186i		−	0.646696i
$70$		0			0
$71$	−10.8061			−1.28245			−0.641226	−	0.767352i	$-0.721574\pi$
$71$	−10.8061			−1.28245			−0.641226	+	0.767352i	$0.721574\pi$
$72$		−	1.00000i		−	0.117851i
$73$	13.2295			1.54840			0.774199	−	0.632943i	$-0.218153\pi$
$73$	13.2295			1.54840			0.774199	+	0.632943i	$0.218153\pi$
$74$		−	2.13093i		−	0.247716i
$75$			5.68190i			0.656090i
$76$	4.27490			0.490364
$77$		0			0
$78$	−5.12518			−0.580312
$79$		−	9.16702i		−	1.03137i	−0.856778	−	0.515685i	$-0.827537\pi$
$79$		−	9.16702i		−	1.03137i	0.856778	−	0.515685i	$-0.172463\pi$
$80$			3.26832i			0.365409i
$81$	1.00000			0.111111
$82$			0.949652i			0.104872i
$83$	−0.835847			−0.0917462			−0.0458731	−	0.998947i	$-0.514607\pi$
$83$	−0.835847			−0.0917462			−0.0458731	+	0.998947i	$0.514607\pi$
$84$		0			0
$85$		−	17.4064i		−	1.88799i
$86$	6.20483			0.669084
$87$	−4.77874			−0.512335
$88$	1.14045	+	3.11438i	0.121573	+	0.331994i
$89$		−	6.22408i		−	0.659751i	−0.944024	−	0.329875i	$-0.892993\pi$
$89$		−	6.22408i		−	0.659751i	0.944024	−	0.329875i	$-0.107007\pi$
$90$	−3.26832			−0.344511
$91$		0			0
$92$	−5.37186			−0.560055
$93$	−6.46485			−0.670374
$94$	12.0303			1.24083
$95$		−	13.9717i		−	1.43347i
$96$	−1.00000			−0.102062
$97$			0.624337i			0.0633919i	0.999498	+	0.0316959i	$0.0100908\pi$
$97$			0.624337i			0.0633919i	−0.999498	+	0.0316959i	$0.989909\pi$
$98$		0			0
$99$	−3.11438	+	1.14045i	−0.313007	+	0.114620i
$100$	5.68190			0.568190
$101$	13.1692			1.31039			0.655194	−	0.755460i	$-0.272587\pi$
$101$	13.1692			1.31039			0.655194	+	0.755460i	$0.272587\pi$
$102$	5.32580			0.527332
$103$			13.2122i			1.30183i	0.759150	+	0.650916i	$0.225615\pi$
$103$			13.2122i			1.30183i	−0.759150	+	0.650916i	$0.774385\pi$
$104$			5.12518i			0.502565i
$105$		0			0
$106$		−	12.5399i		−	1.21799i
$107$			11.1094i			1.07399i	0.843586	+	0.536994i	$0.180440\pi$
$107$			11.1094i			1.07399i	−0.843586	+	0.536994i	$0.819560\pi$
$108$		−	1.00000i		−	0.0962250i
$109$			7.13138i			0.683062i	0.939870	+	0.341531i	$0.110945\pi$
$109$			7.13138i			0.683062i	−0.939870	+	0.341531i	$0.889055\pi$
$110$	10.1788	−	3.72736i	0.970509	−	0.355390i
$111$		−	2.13093i		−	0.202259i
$112$		0			0
$113$	2.41436			0.227124			0.113562	−	0.993531i	$-0.463774\pi$
$113$	2.41436			0.227124			0.113562	+	0.993531i	$0.463774\pi$
$114$	4.27490			0.400381
$115$			17.5569i			1.63719i
$116$			4.77874i			0.443695i
$117$	−5.12518			−0.473823
$118$	13.4844			1.24134
$119$		0			0
$120$			3.26832i			0.298355i
$121$	8.39873	−	7.10361i	0.763521	−	0.645783i
$122$		−	5.34060i		−	0.483515i
$123$			0.949652i			0.0856273i
$124$			6.46485i			0.580561i
$125$		−	2.22868i		−	0.199339i
$126$		0			0
$127$		−	13.8100i		−	1.22544i	−0.790301	−	0.612719i	$-0.790076\pi$
$127$		−	13.8100i		−	1.22544i	0.790301	−	0.612719i	$-0.209924\pi$
$128$			1.00000i			0.0883883i
$129$	6.20483			0.546305
$130$	16.7507			1.46913
$131$	11.7866			1.02980			0.514902	−	0.857249i	$-0.327828\pi$
$131$	11.7866			1.02980			0.514902	+	0.857249i	$0.327828\pi$
$132$	1.14045	+	3.11438i	0.0992637	+	0.271072i
$133$		0			0
$134$		−	6.19350i		−	0.535037i
$135$	−3.26832			−0.281292
$136$		−	5.32580i		−	0.456683i
$137$	4.86111			0.415312			0.207656	−	0.978202i	$-0.433416\pi$
$137$	4.86111			0.415312			0.207656	+	0.978202i	$0.433416\pi$
$138$	−5.37186			−0.457283
$139$	−16.7827			−1.42349			−0.711744	−	0.702439i	$-0.752094\pi$
$139$	−16.7827			−1.42349			−0.711744	+	0.702439i	$0.752094\pi$
$140$		0			0
$141$	12.0303			1.01313
$142$			10.8061i			0.906830i
$143$	15.9618	−	5.84502i	1.33479	−	0.488785i
$144$	−1.00000			−0.0833333
$145$	15.6184			1.29704
$146$		−	13.2295i		−	1.09488i
$147$		0			0
$148$	−2.13093			−0.175161
$149$			7.22464i			0.591866i	0.955209	+	0.295933i	$0.0956305\pi$
$149$			7.22464i			0.591866i	−0.955209	+	0.295933i	$0.904370\pi$
$150$	5.68190			0.463926
$151$		−	4.88028i		−	0.397151i	−0.980086	−	0.198576i	$-0.936368\pi$
$151$		−	4.88028i		−	0.397151i	0.980086	−	0.198576i	$-0.0636315\pi$
$152$		−	4.27490i		−	0.346740i
$153$	5.32580			0.430565
$154$		0			0
$155$	21.1292			1.69714
$156$			5.12518i			0.410343i
$157$			3.30239i			0.263560i	0.991279	+	0.131780i	$0.0420692\pi$
$157$			3.30239i			0.263560i	−0.991279	+	0.131780i	$0.957931\pi$
$158$	−9.16702			−0.729289
$159$		−	12.5399i		−	0.994481i
$160$	3.26832			0.258383
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	−4.84536			−0.379518			−0.189759	−	0.981831i	$-0.560771\pi$
$163$	−4.84536			−0.379518			−0.189759	+	0.981831i	$0.560771\pi$
$164$	0.949652			0.0741554
$165$	10.1788	−	3.72736i	0.792418	−	0.290175i
$166$			0.835847i			0.0648743i
$167$	−2.13922			−0.165538			−0.0827688	−	0.996569i	$-0.526376\pi$
$167$	−2.13922			−0.165538			−0.0827688	+	0.996569i	$0.526376\pi$
$168$		0			0
$169$	13.2674			1.02057
$170$	−17.4064			−1.33501
$171$	4.27490			0.326910
$172$		−	6.20483i		−	0.473114i
$173$	17.7492			1.34944			0.674722	−	0.738072i	$-0.264264\pi$
$173$	17.7492			1.34944			0.674722	+	0.738072i	$0.264264\pi$
$174$			4.77874i			0.362275i
$175$		0			0
$176$	3.11438	−	1.14045i	0.234755	−	0.0859649i
$177$	13.4844			1.01355
$178$	−6.22408			−0.466514
$179$	2.88470			0.215612			0.107806	−	0.994172i	$-0.465617\pi$
$179$	2.88470			0.215612			0.107806	+	0.994172i	$0.465617\pi$
$180$			3.26832i			0.243606i
$181$			10.9351i			0.812803i	0.913695	+	0.406401i	$0.133217\pi$
$181$			10.9351i			0.812803i	−0.913695	+	0.406401i	$0.866783\pi$
$182$		0			0
$183$		−	5.34060i		−	0.394788i
$184$			5.37186i			0.396019i
$185$			6.96456i			0.512044i
$186$			6.46485i			0.474026i
$187$	−16.5866	+	6.07382i	−1.21293	+	0.444162i
$188$		−	12.0303i		−	0.877397i
$189$		0			0
$190$	−13.9717			−1.01362
$191$	12.8770			0.931744			0.465872	−	0.884852i	$-0.345741\pi$
$191$	12.8770			0.931744			0.465872	+	0.884852i	$0.345741\pi$
$192$			1.00000i			0.0721688i
$193$		−	6.04479i		−	0.435113i	−0.976048	−	0.217557i	$-0.930191\pi$
$193$		−	6.04479i		−	0.435113i	0.976048	−	0.217557i	$-0.0698087\pi$
$194$	0.624337			0.0448248
$195$	16.7507			1.19954
$196$		0			0
$197$			6.18237i			0.440476i	0.975446	+	0.220238i	$0.0706833\pi$
$197$			6.18237i			0.440476i	−0.975446	+	0.220238i	$0.929317\pi$
$198$	1.14045	+	3.11438i	0.0810485	+	0.221329i
$199$			3.88246i			0.275220i	0.990486	+	0.137610i	$0.0439421\pi$
$199$			3.88246i			0.275220i	−0.990486	+	0.137610i	$0.956058\pi$
$200$		−	5.68190i		−	0.401771i
$201$		−	6.19350i		−	0.436856i
$202$		−	13.1692i		−	0.926585i
$203$		0			0
$204$		−	5.32580i		−	0.372880i
$205$		−	3.10377i		−	0.216776i
$206$	13.2122			0.920534
$207$	−5.37186			−0.373370
$208$	5.12518			0.355367
$209$	−13.3137	+	4.87532i	−0.920925	+	0.337233i
$210$		0			0
$211$			9.04700i			0.622821i	0.950276	+	0.311410i	$0.100801\pi$
$211$			9.04700i			0.622821i	−0.950276	+	0.311410i	$0.899199\pi$
$212$	−12.5399			−0.861246
$213$			10.8061i			0.740424i
$214$	11.1094			0.759424
$215$	−20.2794			−1.38304
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	7.13138			0.482998
$219$		−	13.2295i		−	0.893968i
$220$	−3.72736	−	10.1788i	−0.251299	−	0.686254i
$221$	−27.2956			−1.83610
$222$	−2.13093			−0.143019
$223$		−	5.42935i		−	0.363576i	−0.983338	−	0.181788i	$-0.941812\pi$
$223$		−	5.42935i		−	0.363576i	0.983338	−	0.181788i	$-0.0581885\pi$
$224$		0			0
$225$	5.68190			0.378794
$226$		−	2.41436i		−	0.160601i
$227$	11.8564			0.786934			0.393467	−	0.919339i	$-0.371276\pi$
$227$	11.8564			0.786934			0.393467	+	0.919339i	$0.371276\pi$
$228$		−	4.27490i		−	0.283112i
$229$		−	6.42701i		−	0.424708i	−0.977193	−	0.212354i	$-0.931887\pi$
$229$		−	6.42701i		−	0.424708i	0.977193	−	0.212354i	$-0.0681131\pi$
$230$	17.5569			1.15767
$231$		0			0
$232$	4.77874			0.313740
$233$		−	2.00886i		−	0.131605i	−0.997833	−	0.0658023i	$-0.979039\pi$
$233$		−	2.00886i		−	0.131605i	0.997833	−	0.0658023i	$-0.0209607\pi$
$234$			5.12518i			0.335043i
$235$	−39.3187			−2.56487
$236$		−	13.4844i		−	0.877758i
$237$	−9.16702			−0.595462
$238$		0			0
$239$			4.65869i			0.301346i	0.988584	+	0.150673i	$0.0481440\pi$
$239$			4.65869i			0.301346i	−0.988584	+	0.150673i	$0.951856\pi$
$240$	3.26832			0.210969
$241$	−5.96996			−0.384559			−0.192279	−	0.981340i	$-0.561588\pi$
$241$	−5.96996			−0.384559			−0.192279	+	0.981340i	$0.561588\pi$
$242$	−7.10361	−	8.39873i	−0.456637	−	0.539891i
$243$		−	1.00000i		−	0.0641500i
$244$	−5.34060			−0.341897
$245$		0			0
$246$	0.949652			0.0605476
$247$	−21.9096			−1.39407
$248$	6.46485			0.410519
$249$			0.835847i			0.0529697i
$250$	−2.22868			−0.140954
$251$		−	1.45699i		−	0.0919645i	−0.998942	−	0.0459822i	$-0.985358\pi$
$251$		−	1.45699i		−	0.0919645i	0.998942	−	0.0459822i	$-0.0146418\pi$
$252$		0			0
$253$	16.7300	−	6.12635i	1.05181	−	0.385161i
$254$	−13.8100			−0.866516
$255$	−17.4064			−1.09003
$256$	1.00000			0.0625000
$257$			26.3742i			1.64518i	0.568636	+	0.822589i	$0.307471\pi$
$257$			26.3742i			1.64518i	−0.568636	+	0.822589i	$0.692529\pi$
$258$		−	6.20483i		−	0.386296i
$259$		0			0
$260$		−	16.7507i		−	1.03883i
$261$			4.77874i			0.295796i
$262$		−	11.7866i		−	0.728181i
$263$		−	31.3179i		−	1.93114i	−0.260141	−	0.965571i	$-0.583769\pi$
$263$		−	31.3179i		−	1.93114i	0.260141	−	0.965571i	$-0.416231\pi$
$264$	3.11438	−	1.14045i	0.191677	−	0.0701900i
$265$			40.9845i			2.51766i
$266$		0			0
$267$	−6.22408			−0.380907
$268$	−6.19350			−0.378328
$269$		−	3.05002i		−	0.185963i	−0.995668	−	0.0929815i	$-0.970360\pi$
$269$		−	3.05002i		−	0.185963i	0.995668	−	0.0929815i	$-0.0296397\pi$
$270$			3.26832i			0.198904i
$271$	−22.4492			−1.36369			−0.681847	−	0.731495i	$-0.738823\pi$
$271$	−22.4492			−1.36369			−0.681847	+	0.731495i	$0.738823\pi$
$272$	−5.32580			−0.322924
$273$		0			0
$274$		−	4.86111i		−	0.293670i
$275$	−17.6956	+	6.47995i	−1.06709	+	0.390755i
$276$			5.37186i			0.323348i
$277$		−	20.5218i		−	1.23304i	−0.787341	−	0.616518i	$-0.788543\pi$
$277$		−	20.5218i		−	1.23304i	0.787341	−	0.616518i	$-0.211457\pi$
$278$			16.7827i			1.00656i
$279$			6.46485i			0.387041i
$280$		0			0
$281$		−	13.8822i		−	0.828141i	−0.910245	−	0.414071i	$-0.864107\pi$
$281$		−	13.8822i		−	0.828141i	0.910245	−	0.414071i	$-0.135893\pi$
$282$		−	12.0303i		−	0.716391i
$283$	29.7862			1.77061			0.885304	−	0.465013i	$-0.153950\pi$
$283$	29.7862			1.77061			0.885304	+	0.465013i	$0.153950\pi$
$284$	10.8061			0.641226
$285$	−13.9717			−0.827614
$286$	−5.84502	−	15.9618i	−0.345624	−	0.943838i
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	11.3641			0.668477
$290$		−	15.6184i		−	0.917146i
$291$	0.624337			0.0365993
$292$	−13.2295			−0.774199
$293$	−10.3943			−0.607243			−0.303621	−	0.952793i	$-0.598196\pi$
$293$	−10.3943			−0.607243			−0.303621	+	0.952793i	$0.598196\pi$
$294$		0			0
$295$	−44.0712			−2.56593
$296$			2.13093i			0.123858i
$297$	1.14045	+	3.11438i	0.0661758	+	0.180715i
$298$	7.22464			0.418512
$299$	27.5317			1.59220
$300$		−	5.68190i		−	0.328045i
$301$		0			0
$302$	−4.88028			−0.280828
$303$		−	13.1692i		−	0.756553i
$304$	−4.27490			−0.245182
$305$			17.4548i			0.999457i
$306$		−	5.32580i		−	0.304456i
$307$	1.37847			0.0786736			0.0393368	−	0.999226i	$-0.487475\pi$
$307$	1.37847			0.0786736			0.0393368	+	0.999226i	$0.487475\pi$
$308$		0			0
$309$	13.2122			0.751613
$310$		−	21.1292i		−	1.20006i
$311$		−	10.5210i		−	0.596594i	−0.954473	−	0.298297i	$-0.903581\pi$
$311$		−	10.5210i		−	0.596594i	0.954473	−	0.298297i	$-0.0964185\pi$
$312$	5.12518			0.290156
$313$			2.26694i			0.128135i	0.997946	+	0.0640676i	$0.0204073\pi$
$313$			2.26694i			0.128135i	−0.997946	+	0.0640676i	$0.979593\pi$
$314$	3.30239			0.186365
$315$		0			0
$316$			9.16702i			0.515685i
$317$	−4.94169			−0.277553			−0.138777	−	0.990324i	$-0.544317\pi$
$317$	−4.94169			−0.277553			−0.138777	+	0.990324i	$0.544317\pi$
$318$	−12.5399			−0.703204
$319$	−5.44993	−	14.8828i	−0.305137	−	0.833277i
$320$		−	3.26832i		−	0.182705i
$321$	11.1094			0.620067
$322$		0			0
$323$	22.7672			1.26680
$324$	−1.00000			−0.0555556
$325$	−29.1208			−1.61533
$326$			4.84536i			0.268360i
$327$	7.13138			0.394366
$328$		−	0.949652i		−	0.0524358i
$329$		0			0
$330$	−3.72736	−	10.1788i	−0.205185	−	0.560324i
$331$	12.9489			0.711737			0.355869	−	0.934536i	$-0.384185\pi$
$331$	12.9489			0.711737			0.355869	+	0.934536i	$0.384185\pi$
$332$	0.835847			0.0458731
$333$	−2.13093			−0.116774
$334$			2.13922i			0.117053i
$335$			20.2423i			1.10596i
$336$		0			0
$337$		−	8.22142i		−	0.447849i	−0.974606	−	0.223925i	$-0.928113\pi$
$337$		−	8.22142i		−	0.447849i	0.974606	−	0.223925i	$-0.0718869\pi$
$338$		−	13.2674i		−	0.721654i
$339$		−	2.41436i		−	0.131130i
$340$			17.4064i			0.943994i
$341$	−7.37286	−	20.1340i	−0.399263	−	1.09032i
$342$		−	4.27490i		−	0.231160i
$343$		0			0
$344$	−6.20483			−0.334542
$345$	17.5569			0.945234
$346$		−	17.7492i		−	0.954201i
$347$			31.3657i			1.68380i	0.539632	+	0.841901i	$0.318563\pi$
$347$			31.3657i			1.68380i	−0.539632	+	0.841901i	$0.681437\pi$
$348$	4.77874			0.256167
$349$	−3.15342			−0.168799			−0.0843993	−	0.996432i	$-0.526897\pi$
$349$	−3.15342			−0.168799			−0.0843993	+	0.996432i	$0.526897\pi$
$350$		0			0
$351$			5.12518i			0.273562i
$352$	−1.14045	−	3.11438i	−0.0607864	−	0.165997i
$353$			8.15423i			0.434006i	0.976171	+	0.217003i	$0.0696281\pi$
$353$			8.15423i			0.434006i	−0.976171	+	0.217003i	$0.930372\pi$
$354$		−	13.4844i		−	0.716686i
$355$		−	35.3179i		−	1.87448i
$356$			6.22408i			0.329875i
$357$		0			0
$358$		−	2.88470i		−	0.152461i
$359$			9.54046i			0.503526i	0.967789	+	0.251763i	$0.0810104\pi$
$359$			9.54046i			0.503526i	−0.967789	+	0.251763i	$0.918990\pi$
$360$	3.26832			0.172256
$361$	−0.725250			−0.0381710
$362$	10.9351			0.574738
$363$	−7.10361	−	8.39873i	−0.372843	−	0.440819i
$364$		0			0
$365$			43.2383i			2.26319i
$366$	−5.34060			−0.279158
$367$			6.76680i			0.353224i	0.984281	+	0.176612i	$0.0565138\pi$
$367$			6.76680i			0.353224i	−0.984281	+	0.176612i	$0.943486\pi$
$368$	5.37186			0.280028
$369$	0.949652			0.0494369
$370$	6.96456			0.362070
$371$		0			0
$372$	6.46485			0.335187
$373$			0.476776i			0.0246865i	0.999924	+	0.0123433i	$0.00392908\pi$
$373$			0.476776i			0.0246865i	−0.999924	+	0.0123433i	$0.996071\pi$
$374$	6.07382	+	16.5866i	0.314070	+	0.857670i
$375$	−2.22868			−0.115089
$376$	−12.0303			−0.620413
$377$		−	24.4919i		−	1.26140i
$378$		0			0
$379$	−15.2564			−0.783669			−0.391835	−	0.920036i	$-0.628160\pi$
$379$	−15.2564			−0.783669			−0.391835	+	0.920036i	$0.628160\pi$
$380$			13.9717i			0.716734i
$381$	−13.8100			−0.707507
$382$		−	12.8770i		−	0.658843i
$383$			12.2197i			0.624396i	0.950017	+	0.312198i	$0.101065\pi$
$383$			12.2197i			0.624396i	−0.950017	+	0.312198i	$0.898935\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−6.04479			−0.307672
$387$		−	6.20483i		−	0.315409i
$388$		−	0.624337i		−	0.0316959i
$389$	28.0321			1.42128			0.710641	−	0.703554i	$-0.248405\pi$
$389$	28.0321			1.42128			0.710641	+	0.703554i	$0.248405\pi$
$390$		−	16.7507i		−	0.848205i
$391$	−28.6094			−1.44684
$392$		0			0
$393$		−	11.7866i		−	0.594557i
$394$	6.18237			0.311463
$395$	29.9607			1.50749
$396$	3.11438	−	1.14045i	0.156504	−	0.0573099i
$397$		−	30.1481i		−	1.51309i	−0.653941	−	0.756546i	$-0.726886\pi$
$397$		−	30.1481i		−	1.51309i	0.653941	−	0.756546i	$-0.273114\pi$
$398$	3.88246			0.194610
$399$		0			0
$400$	−5.68190			−0.284095
$401$	−3.21065			−0.160332			−0.0801661	−	0.996782i	$-0.525545\pi$
$401$	−3.21065			−0.160332			−0.0801661	+	0.996782i	$0.525545\pi$
$402$	−6.19350			−0.308904
$403$		−	33.1335i		−	1.65050i
$404$	−13.1692			−0.655194
$405$			3.26832i			0.162404i
$406$		0			0
$407$	6.63653	−	2.43023i	0.328960	−	0.120462i
$408$	−5.32580			−0.263666
$409$	−34.3043			−1.69624			−0.848120	−	0.529805i	$-0.822265\pi$
$409$	−34.3043			−1.69624			−0.848120	+	0.529805i	$0.822265\pi$
$410$	−3.10377			−0.153284
$411$		−	4.86111i		−	0.239781i
$412$		−	13.2122i		−	0.650916i
$413$		0			0
$414$			5.37186i			0.264012i
$415$		−	2.73181i		−	0.134100i
$416$		−	5.12518i		−	0.251282i
$417$			16.7827i			0.821851i
$418$	4.87532	+	13.3137i	0.238460	+	0.651192i
$419$			12.7969i			0.625168i	0.949890	+	0.312584i	$0.101195\pi$
$419$			12.7969i			0.625168i	−0.949890	+	0.312584i	$0.898805\pi$
$420$		0			0
$421$	35.0356			1.70753			0.853766	−	0.520657i	$-0.174313\pi$
$421$	35.0356			1.70753			0.853766	+	0.520657i	$0.174313\pi$
$422$	9.04700			0.440401
$423$		−	12.0303i		−	0.584931i
$424$			12.5399i			0.608993i
$425$	30.2607			1.46786
$426$	10.8061			0.523559
$427$		0			0
$428$		−	11.1094i		−	0.536994i
$429$	−5.84502	−	15.9618i	−0.282200	−	0.770641i
$430$			20.2794i			0.977958i
$431$			25.9217i			1.24860i	0.781183	+	0.624302i	$0.214616\pi$
$431$			25.9217i			1.24860i	−0.781183	+	0.624302i	$0.785384\pi$
$432$			1.00000i			0.0481125i
$433$		−	29.5108i		−	1.41820i	−0.705110	−	0.709098i	$-0.749102\pi$
$433$		−	29.5108i		−	1.41820i	0.705110	−	0.709098i	$-0.250898\pi$
$434$		0			0
$435$		−	15.6184i		−	0.748847i
$436$		−	7.13138i		−	0.341531i
$437$	−22.9641			−1.09852
$438$	−13.2295			−0.632131
$439$	−11.4208			−0.545085			−0.272542	−	0.962144i	$-0.587864\pi$
$439$	−11.4208			−0.545085			−0.272542	+	0.962144i	$0.587864\pi$
$440$	−10.1788	+	3.72736i	−0.485255	+	0.177695i
$441$		0			0
$442$			27.2956i			1.29832i
$443$	25.5212			1.21255			0.606273	−	0.795256i	$-0.292664\pi$
$443$	25.5212			1.21255			0.606273	+	0.795256i	$0.292664\pi$
$444$			2.13093i			0.101129i
$445$	20.3423			0.964316
$446$	−5.42935			−0.257087
$447$	7.22464			0.341714
$448$		0			0
$449$	25.9959			1.22682			0.613412	−	0.789763i	$-0.289797\pi$
$449$	25.9959			1.22682			0.613412	+	0.789763i	$0.289797\pi$
$450$		−	5.68190i		−	0.267848i
$451$	−2.95758	+	1.08303i	−0.139267	+	0.0509981i
$452$	−2.41436			−0.113562
$453$	−4.88028			−0.229295
$454$		−	11.8564i		−	0.556446i
$455$		0			0
$456$	−4.27490			−0.200190
$457$			8.03248i			0.375743i	0.982194	+	0.187872i	$0.0601589\pi$
$457$			8.03248i			0.375743i	−0.982194	+	0.187872i	$0.939841\pi$
$458$	−6.42701			−0.300314
$459$		−	5.32580i		−	0.248587i
$460$		−	17.5569i		−	0.818597i
$461$	33.5115			1.56078			0.780392	−	0.625290i	$-0.215019\pi$
$461$	33.5115			1.56078			0.780392	+	0.625290i	$0.215019\pi$
$462$		0			0
$463$	−15.7419			−0.731587			−0.365793	−	0.930696i	$-0.619202\pi$
$463$	−15.7419			−0.731587			−0.365793	+	0.930696i	$0.619202\pi$
$464$		−	4.77874i		−	0.221847i
$465$		−	21.1292i		−	0.979843i
$466$	−2.00886			−0.0930585
$467$			10.2329i			0.473521i	0.971568	+	0.236760i	$0.0760857\pi$
$467$			10.2329i			0.473521i	−0.971568	+	0.236760i	$0.923914\pi$
$468$	5.12518			0.236911
$469$		0			0
$470$			39.3187i			1.81364i
$471$	3.30239			0.152166
$472$	−13.4844			−0.620668
$473$	7.07632	+	19.3242i	0.325370	+	0.888528i
$474$			9.16702i			0.421055i
$475$	24.2896			1.11448
$476$		0			0
$477$	−12.5399			−0.574164
$478$	4.65869			0.213083
$479$	−5.19626			−0.237423			−0.118712	−	0.992929i	$-0.537876\pi$
$479$	−5.19626			−0.237423			−0.118712	+	0.992929i	$0.537876\pi$
$480$		−	3.26832i		−	0.149178i
$481$	10.9214			0.497973
$482$			5.96996i			0.271924i
$483$		0			0
$484$	−8.39873	+	7.10361i	−0.381761	+	0.322891i
$485$	−2.04053			−0.0926558
$486$	−1.00000			−0.0453609
$487$	−31.5483			−1.42959			−0.714794	−	0.699335i	$-0.753479\pi$
$487$	−31.5483			−1.42959			−0.714794	+	0.699335i	$0.753479\pi$
$488$			5.34060i			0.241758i
$489$			4.84536i			0.219115i
$490$		0			0
$491$		−	7.14182i		−	0.322306i	−0.986929	−	0.161153i	$-0.948479\pi$
$491$		−	7.14182i		−	0.322306i	0.986929	−	0.161153i	$-0.0515212\pi$
$492$		−	0.949652i		−	0.0428136i
$493$			25.4506i			1.14624i
$494$			21.9096i			0.985760i
$495$	−3.72736	−	10.1788i	−0.167533	−	0.457502i
$496$		−	6.46485i		−	0.290281i
$497$		0			0
$498$	0.835847			0.0374552
$499$	−34.7635			−1.55623			−0.778114	−	0.628123i	$-0.783824\pi$
$499$	−34.7635			−1.55623			−0.778114	+	0.628123i	$0.783824\pi$
$500$			2.22868i			0.0996697i
$501$			2.13922i			0.0955732i
$502$	−1.45699			−0.0650287
$503$	3.06150			0.136506			0.0682529	−	0.997668i	$-0.478258\pi$
$503$	3.06150			0.136506			0.0682529	+	0.997668i	$0.478258\pi$
$504$		0			0
$505$			43.0413i			1.91531i
$506$	−6.12635	−	16.7300i	−0.272350	−	0.743740i
$507$		−	13.2674i		−	0.589228i
$508$			13.8100i			0.612719i
$509$		−	28.4354i		−	1.26038i	−0.776442	−	0.630188i	$-0.782978\pi$
$509$		−	28.4354i		−	1.26038i	0.776442	−	0.630188i	$-0.217022\pi$
$510$			17.4064i			0.770768i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		−	4.27490i		−	0.188741i
$514$	26.3742			1.16332
$515$	−43.1815			−1.90281
$516$	−6.20483			−0.273152
$517$	13.7199	+	37.4668i	0.603402	+	1.64779i
$518$		0			0
$519$		−	17.7492i		−	0.779101i
$520$	−16.7507			−0.734567
$521$			3.64587i			0.159728i	0.996806	+	0.0798642i	$0.0254487\pi$
$521$			3.64587i			0.159728i	−0.996806	+	0.0798642i	$0.974551\pi$
$522$	4.77874			0.209160
$523$	−23.9460			−1.04708			−0.523542	−	0.852000i	$-0.675390\pi$
$523$	−23.9460			−1.04708			−0.523542	+	0.852000i	$0.675390\pi$
$524$	−11.7866			−0.514902
$525$		0			0
$526$	−31.3179			−1.36552
$527$			34.4305i			1.49982i
$528$	−1.14045	−	3.11438i	−0.0496318	−	0.135536i
$529$	5.85687			0.254647
$530$	40.9845			1.78025
$531$		−	13.4844i		−	0.585172i
$532$		0			0
$533$	−4.86714			−0.210819
$534$			6.22408i			0.269342i
$535$	−36.3091			−1.56978
$536$			6.19350i			0.267518i
$537$		−	2.88470i		−	0.124484i
$538$	−3.05002			−0.131496
$539$		0			0
$540$	3.26832			0.140646
$541$			43.0569i			1.85116i	0.378552	+	0.925580i	$0.376422\pi$
$541$			43.0569i			1.85116i	−0.378552	+	0.925580i	$0.623578\pi$
$542$			22.4492i			0.964278i
$543$	10.9351			0.469272
$544$			5.32580i			0.228342i
$545$	−23.3076			−0.998389
$546$		0			0
$547$			8.00013i			0.342061i	0.985266	+	0.171030i	$0.0547097\pi$
$547$			8.00013i			0.342061i	−0.985266	+	0.171030i	$0.945290\pi$
$548$	−4.86111			−0.207656
$549$	−5.34060			−0.227931
$550$	6.47995	+	17.6956i	0.276306	+	0.754544i
$551$			20.4286i			0.870288i
$552$	5.37186			0.228642
$553$		0			0
$554$	−20.5218			−0.871888
$555$	6.96456			0.295629
$556$	16.7827			0.711744
$557$		−	23.3405i		−	0.988967i	−0.869187	−	0.494484i	$-0.835357\pi$
$557$		−	23.3405i		−	0.988967i	0.869187	−	0.494484i	$-0.164643\pi$
$558$	6.46485			0.273679
$559$			31.8009i			1.34503i
$560$		0			0
$561$	6.07382	+	16.5866i	0.256437	+	0.700285i
$562$	−13.8822			−0.585584
$563$	−26.4381			−1.11423			−0.557116	−	0.830435i	$-0.688092\pi$
$563$	−26.4381			−1.11423			−0.557116	+	0.830435i	$0.688092\pi$
$564$	−12.0303			−0.506565
$565$			7.89089i			0.331972i
$566$		−	29.7862i		−	1.25201i
$567$		0			0
$568$		−	10.8061i		−	0.453415i
$569$		−	24.9986i		−	1.04799i	−0.851720	−	0.523997i	$-0.824440\pi$
$569$		−	24.9986i		−	1.04799i	0.851720	−	0.523997i	$-0.175560\pi$
$570$			13.9717i			0.585211i
$571$			43.4852i			1.81980i	0.414830	+	0.909899i	$0.363841\pi$
$571$			43.4852i			1.81980i	−0.414830	+	0.909899i	$0.636159\pi$
$572$	−15.9618	+	5.84502i	−0.667394	+	0.244393i
$573$		−	12.8770i		−	0.537943i
$574$		0			0
$575$	−30.5224			−1.27287
$576$	1.00000			0.0416667
$577$		−	27.7990i		−	1.15729i	−0.815581	−	0.578643i	$-0.803582\pi$
$577$		−	27.7990i		−	1.15729i	0.815581	−	0.578643i	$-0.196418\pi$
$578$		−	11.3641i		−	0.472685i
$579$	−6.04479			−0.251213
$580$	−15.6184			−0.648520
$581$		0			0
$582$		−	0.624337i		−	0.0258796i
$583$	39.0541	−	14.3012i	1.61746	−	0.592295i
$584$			13.2295i			0.547441i
$585$		−	16.7507i		−	0.692557i
$586$			10.3943i			0.429385i
$587$		−	11.2683i		−	0.465091i	−0.972585	−	0.232546i	$-0.925294\pi$
$587$		−	11.2683i		−	0.465091i	0.972585	−	0.232546i	$-0.0747055\pi$
$588$		0			0
$589$			27.6366i			1.13875i
$590$			44.0712i			1.81438i
$591$	6.18237			0.254309
$592$	2.13093			0.0875807
$593$	−15.7021			−0.644809			−0.322405	−	0.946602i	$-0.604491\pi$
$593$	−15.7021			−0.644809			−0.322405	+	0.946602i	$0.604491\pi$
$594$	3.11438	−	1.14045i	0.127785	−	0.0467934i
$595$		0			0
$596$		−	7.22464i		−	0.295933i
$597$	3.88246			0.158898
$598$		−	27.5317i		−	1.12586i
$599$	9.58002			0.391429			0.195714	−	0.980661i	$-0.437297\pi$
$599$	9.58002			0.391429			0.195714	+	0.980661i	$0.437297\pi$
$600$	−5.68190			−0.231963
$601$	−36.7398			−1.49865			−0.749324	−	0.662204i	$-0.769621\pi$
$601$	−36.7398			−1.49865			−0.749324	+	0.662204i	$0.769621\pi$
$602$		0			0
$603$	−6.19350			−0.252219
$604$			4.88028i			0.198576i
$605$	23.2169	+	27.4497i	0.943900	+	1.11599i
$606$	−13.1692			−0.534964
$607$	40.4651			1.64243			0.821215	−	0.570619i	$-0.193297\pi$
$607$	40.4651			1.64243			0.821215	+	0.570619i	$0.193297\pi$
$608$			4.27490i			0.173370i
$609$		0			0
$610$	17.4548			0.706723
$611$			61.6572i			2.49438i
$612$	−5.32580			−0.215283
$613$		−	10.4735i		−	0.423019i	−0.977376	−	0.211509i	$-0.932162\pi$
$613$		−	10.4735i		−	0.423019i	0.977376	−	0.211509i	$-0.0678379\pi$
$614$		−	1.37847i		−	0.0556307i
$615$	−3.10377			−0.125156
$616$		0			0
$617$	−14.4244			−0.580706			−0.290353	−	0.956920i	$-0.593773\pi$
$617$	−14.4244			−0.580706			−0.290353	+	0.956920i	$0.593773\pi$
$618$		−	13.2122i		−	0.531471i
$619$		−	44.7946i		−	1.80045i	−0.435430	−	0.900223i	$-0.643404\pi$
$619$		−	44.7946i		−	1.80045i	0.435430	−	0.900223i	$-0.356596\pi$
$620$	−21.1292			−0.848569
$621$			5.37186i			0.215565i
$622$	−10.5210			−0.421855
$623$		0			0
$624$		−	5.12518i		−	0.205171i
$625$	−21.1255			−0.845019
$626$	2.26694			0.0906052
$627$	4.87532	+	13.3137i	0.194702	+	0.531696i
$628$		−	3.30239i		−	0.131780i
$629$	−11.3489			−0.452510
$630$		0			0
$631$	13.1975			0.525383			0.262692	−	0.964880i	$-0.415390\pi$
$631$	13.1975			0.525383			0.262692	+	0.964880i	$0.415390\pi$
$632$	9.16702			0.364644
$633$	9.04700			0.359586
$634$			4.94169i			0.196260i
$635$	45.1354			1.79114
$636$			12.5399i			0.497240i
$637$		0			0
$638$	−14.8828	+	5.44993i	−0.589216	+	0.215765i
$639$	10.8061			0.427484
$640$	−3.26832			−0.129192
$641$	21.5850			0.852555			0.426278	−	0.904592i	$-0.359825\pi$
$641$	21.5850			0.852555			0.426278	+	0.904592i	$0.359825\pi$
$642$		−	11.1094i		−	0.438454i
$643$		−	28.9651i		−	1.14227i	−0.820855	−	0.571137i	$-0.806503\pi$
$643$		−	28.9651i		−	1.14227i	0.820855	−	0.571137i	$-0.193497\pi$
$644$		0			0
$645$			20.2794i			0.798499i
$646$		−	22.7672i		−	0.895765i
$647$		−	29.3639i		−	1.15442i	−0.816597	−	0.577208i	$-0.804142\pi$
$647$		−	29.3639i		−	1.15442i	0.816597	−	0.577208i	$-0.195858\pi$
$648$			1.00000i			0.0392837i
$649$	15.3783	+	41.9955i	0.603651	+	1.64847i
$650$			29.1208i			1.14221i
$651$		0			0
$652$	4.84536			0.189759
$653$	−38.2449			−1.49664			−0.748320	−	0.663338i	$-0.769139\pi$
$653$	−38.2449			−1.49664			−0.748320	+	0.663338i	$0.769139\pi$
$654$		−	7.13138i		−	0.278859i
$655$			38.5225i			1.50520i
$656$	−0.949652			−0.0370777
$657$	−13.2295			−0.516133
$658$		0			0
$659$			0.210272i			0.00819105i	0.999992	+	0.00409553i	$0.00130365\pi$
$659$			0.210272i			0.00819105i	−0.999992	+	0.00409553i	$0.998696\pi$
$660$	−10.1788	+	3.72736i	−0.396209	+	0.145087i
$661$		−	9.32692i		−	0.362775i	−0.983412	−	0.181388i	$-0.941941\pi$
$661$		−	9.32692i		−	0.362775i	0.983412	−	0.181388i	$-0.0580588\pi$
$662$		−	12.9489i		−	0.503274i
$663$			27.2956i			1.06008i
$664$		−	0.835847i		−	0.0324372i
$665$		0			0
$666$			2.13093i			0.0825718i
$667$		−	25.6707i		−	0.993974i
$668$	2.13922			0.0827688
$669$	−5.42935			−0.209911
$670$	20.2423			0.782029
$671$	16.6327	−	6.09070i	0.642096	−	0.235129i
$672$		0			0
$673$		−	15.7351i		−	0.606545i	−0.952904	−	0.303273i	$-0.901921\pi$
$673$		−	15.7351i		−	0.606545i	0.952904	−	0.303273i	$-0.0980793\pi$
$674$	−8.22142			−0.316677
$675$		−	5.68190i		−	0.218697i
$676$	−13.2674			−0.510286
$677$	−13.0789			−0.502661			−0.251331	−	0.967901i	$-0.580868\pi$
$677$	−13.0789			−0.502661			−0.251331	+	0.967901i	$0.580868\pi$
$678$	−2.41436			−0.0927229
$679$		0			0
$680$	17.4064			0.667505
$681$		−	11.8564i		−	0.454337i
$682$	−20.1340	+	7.37286i	−0.770971	+	0.282322i
$683$	−25.1709			−0.963136			−0.481568	−	0.876409i	$-0.659933\pi$
$683$	−25.1709			−0.963136			−0.481568	+	0.876409i	$0.659933\pi$
$684$	−4.27490			−0.163455
$685$			15.8876i			0.607036i
$686$		0			0
$687$	−6.42701			−0.245206
$688$			6.20483i			0.236557i
$689$	64.2693			2.44847
$690$		−	17.5569i		−	0.668381i
$691$			0.792464i			0.0301468i	0.999886	+	0.0150734i	$0.00479819\pi$
$691$			0.792464i			0.0301468i	−0.999886	+	0.0150734i	$0.995202\pi$
$692$	−17.7492			−0.674722
$693$		0			0
$694$	31.3657			1.19063
$695$		−	54.8511i		−	2.08062i
$696$		−	4.77874i		−	0.181138i
$697$	5.05766			0.191572
$698$			3.15342i			0.119359i
$699$	−2.00886			−0.0759820
$700$		0			0
$701$			39.5754i			1.49474i	0.664406	+	0.747372i	$0.268685\pi$
$701$			39.5754i			1.49474i	−0.664406	+	0.747372i	$0.731315\pi$
$702$	5.12518			0.193437
$703$	−9.10951			−0.343572
$704$	−3.11438	+	1.14045i	−0.117378	+	0.0429824i
$705$			39.3187i			1.48083i
$706$	8.15423			0.306889
$707$		0			0
$708$	−13.4844			−0.506774
$709$	36.4422			1.36861			0.684307	−	0.729194i	$-0.260105\pi$
$709$	36.4422			1.36861			0.684307	+	0.729194i	$0.260105\pi$
$710$	−35.3179			−1.32546
$711$			9.16702i			0.343790i
$712$	6.22408			0.233257
$713$		−	34.7283i		−	1.30058i
$714$		0			0
$715$	19.1034	+	52.1681i	0.714427	+	1.95098i
$716$	−2.88470			−0.107806
$717$	4.65869			0.173982
$718$	9.54046			0.356047
$719$		−	14.1604i		−	0.528092i	−0.964510	−	0.264046i	$-0.914943\pi$
$719$		−	14.1604i		−	0.528092i	0.964510	−	0.264046i	$-0.0850571\pi$
$720$		−	3.26832i		−	0.121803i
$721$		0			0
$722$			0.725250i			0.0269910i
$723$			5.96996i			0.222025i
$724$		−	10.9351i		−	0.406401i
$725$			27.1523i			1.00841i
$726$	−8.39873	+	7.10361i	−0.311706	+	0.263640i
$727$		−	8.58699i		−	0.318474i	−0.987240	−	0.159237i	$-0.949097\pi$
$727$		−	8.58699i		−	0.318474i	0.987240	−	0.159237i	$-0.0509033\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	43.2383			1.60032
$731$		−	33.0457i		−	1.22224i
$732$			5.34060i			0.197394i
$733$	−42.7196			−1.57788			−0.788942	−	0.614468i	$-0.789371\pi$
$733$	−42.7196			−1.57788			−0.788942	+	0.614468i	$0.789371\pi$
$734$	6.76680			0.249767
$735$		0			0
$736$		−	5.37186i		−	0.198009i
$737$	19.2889	−	7.06340i	0.710516	−	0.260184i
$738$		−	0.949652i		−	0.0349572i
$739$		−	33.2019i		−	1.22135i	−0.791881	−	0.610675i	$-0.790898\pi$
$739$		−	33.2019i		−	1.22135i	0.791881	−	0.610675i	$-0.209102\pi$
$740$		−	6.96456i		−	0.256022i
$741$			21.9096i			0.804870i
$742$		0			0
$743$			8.11448i			0.297691i	0.988860	+	0.148846i	$0.0475557\pi$
$743$			8.11448i			0.297691i	−0.988860	+	0.148846i	$0.952444\pi$
$744$		−	6.46485i		−	0.237013i
$745$	−23.6124			−0.865093
$746$	0.476776			0.0174560
$747$	0.835847			0.0305821
$748$	16.5866	−	6.07382i	0.606465	−	0.222081i
$749$		0			0
$750$			2.22868i			0.0813800i
$751$	0.0753513			0.00274961			0.00137480	−	0.999999i	$-0.499562\pi$
$751$	0.0753513			0.00274961			0.00137480	+	0.999999i	$0.499562\pi$
$752$			12.0303i			0.438698i
$753$	−1.45699			−0.0530957
$754$	−24.4919			−0.891942
$755$	15.9503			0.580491
$756$		0			0
$757$	−0.134400			−0.00488484			−0.00244242	−	0.999997i	$-0.500777\pi$
$757$	−0.134400			−0.00488484			−0.00244242	+	0.999997i	$0.500777\pi$
$758$			15.2564i			0.554138i
$759$	−6.12635	−	16.7300i	−0.222373	−	0.607261i
$760$	13.9717			0.506808
$761$	−14.7028			−0.532978			−0.266489	−	0.963838i	$-0.585864\pi$
$761$	−14.7028			−0.532978			−0.266489	+	0.963838i	$0.585864\pi$
$762$			13.8100i			0.500283i
$763$		0			0
$764$	−12.8770			−0.465872
$765$			17.4064i			0.629330i
$766$	12.2197			0.441515
$767$			69.1098i			2.49541i
$768$		−	1.00000i		−	0.0360844i
$769$	7.17040			0.258571			0.129286	−	0.991607i	$-0.458732\pi$
$769$	7.17040			0.258571			0.129286	+	0.991607i	$0.458732\pi$
$770$		0			0
$771$	26.3742			0.949844
$772$			6.04479i			0.217557i
$773$			37.2109i			1.33838i	0.743090	+	0.669192i	$0.233359\pi$
$773$			37.2109i			1.33838i	−0.743090	+	0.669192i	$0.766641\pi$
$774$	−6.20483			−0.223028
$775$			36.7327i			1.31948i
$776$	−0.624337			−0.0224124
$777$		0			0
$778$		−	28.0321i		−	1.00500i
$779$	4.05967			0.145453
$780$	−16.7507			−0.599772
$781$	−33.6544	+	12.3239i	−1.20425	+	0.440983i
$782$			28.6094i			1.02307i
$783$	4.77874			0.170778
$784$		0			0
$785$	−10.7933			−0.385229
$786$	−11.7866			−0.420416
$787$	−43.1199			−1.53706			−0.768529	−	0.639815i	$-0.779011\pi$
$787$	−43.1199			−1.53706			−0.768529	+	0.639815i	$0.779011\pi$
$788$		−	6.18237i		−	0.220238i
$789$	−31.3179			−1.11494
$790$		−	29.9607i		−	1.06596i
$791$		0			0
$792$	−1.14045	−	3.11438i	−0.0405242	−	0.110665i
$793$	27.3715			0.971991
$794$	−30.1481			−1.06992
$795$	40.9845			1.45357
$796$		−	3.88246i		−	0.137610i
$797$		−	30.1768i		−	1.06892i	−0.845195	−	0.534458i	$-0.820516\pi$
$797$		−	30.1768i		−	1.06892i	0.845195	−	0.534458i	$-0.179484\pi$
$798$		0			0
$799$		−	64.0707i		−	2.26666i
$800$			5.68190i			0.200886i
$801$			6.22408i			0.219917i
$802$			3.21065i			0.113372i
$803$	41.2017	−	15.0876i	1.45398	−	0.532431i
$804$			6.19350i			0.218428i
$805$		0			0
$806$	−33.1335			−1.16708
$807$	−3.05002			−0.107366
$808$			13.1692i			0.463292i
$809$			46.2479i			1.62599i	0.582270	+	0.812996i	$0.302165\pi$
$809$			46.2479i			1.62599i	−0.582270	+	0.812996i	$0.697835\pi$
$810$	3.26832			0.114837
$811$	22.9534			0.806003			0.403001	−	0.915199i	$-0.367967\pi$
$811$	22.9534			0.806003			0.403001	+	0.915199i	$0.367967\pi$
$812$		0			0
$813$			22.4492i			0.787329i
$814$	−2.43023	−	6.63653i	−0.0851794	−	0.232610i
$815$		−	15.8362i		−	0.554717i
$816$			5.32580i			0.186440i
$817$		−	26.5250i		−	0.927993i
$818$			34.3043i			1.19942i
$819$		0			0
$820$			3.10377i			0.108388i
$821$		−	16.4705i		−	0.574823i	−0.957807	−	0.287412i	$-0.907205\pi$
$821$		−	16.4705i		−	0.574823i	0.957807	−	0.287412i	$-0.0927948\pi$
$822$	−4.86111			−0.169551
$823$	12.2157			0.425812			0.212906	−	0.977073i	$-0.431707\pi$
$823$	12.2157			0.425812			0.212906	+	0.977073i	$0.431707\pi$
$824$	−13.2122			−0.460267
$825$	6.47995	+	17.6956i	0.225603	+	0.616082i
$826$		0			0
$827$			4.55524i			0.158401i	0.996859	+	0.0792007i	$0.0252368\pi$
$827$			4.55524i			0.158401i	−0.996859	+	0.0792007i	$0.974763\pi$
$828$	5.37186			0.186685
$829$			37.1759i			1.29117i	0.763688	+	0.645585i	$0.223387\pi$
$829$			37.1759i			1.29117i	−0.763688	+	0.645585i	$0.776613\pi$
$830$	−2.73181			−0.0948227
$831$	−20.5218			−0.711894
$832$	−5.12518			−0.177684
$833$		0			0
$834$	16.7827			0.581136
$835$		−	6.99164i		−	0.241956i
$836$	13.3137	−	4.87532i	0.460463	−	0.168616i
$837$	6.46485			0.223458
$838$	12.7969			0.442061
$839$			39.5086i			1.36399i	0.731358	+	0.681994i	$0.238887\pi$
$839$			39.5086i			1.36399i	−0.731358	+	0.681994i	$0.761113\pi$
$840$		0			0
$841$	6.16366			0.212540
$842$		−	35.0356i		−	1.20741i
$843$	−13.8822			−0.478128
$844$		−	9.04700i		−	0.311410i
$845$			43.3622i			1.49171i
$846$	−12.0303			−0.413609
$847$		0			0
$848$	12.5399			0.430623
$849$		−	29.7862i		−	1.02226i
$850$		−	30.2607i		−	1.03793i
$851$	11.4471			0.392400
$852$		−	10.8061i		−	0.370212i
$853$	34.2280			1.17194			0.585972	−	0.810331i	$-0.300713\pi$
$853$	34.2280			1.17194			0.585972	+	0.810331i	$0.300713\pi$
$854$		0			0
$855$			13.9717i			0.477823i
$856$	−11.1094			−0.379712
$857$	1.64415			0.0561629			0.0280815	−	0.999606i	$-0.491060\pi$
$857$	1.64415			0.0561629			0.0280815	+	0.999606i	$0.491060\pi$
$858$	−15.9618	+	5.84502i	−0.544925	+	0.199546i
$859$		−	21.9701i		−	0.749610i	−0.927104	−	0.374805i	$-0.877710\pi$
$859$		−	21.9701i		−	0.749610i	0.927104	−	0.374805i	$-0.122290\pi$
$860$	20.2794			0.691521
$861$		0			0
$862$	25.9217			0.882896
$863$	9.52205			0.324134			0.162067	−	0.986780i	$-0.448184\pi$
$863$	9.52205			0.324134			0.162067	+	0.986780i	$0.448184\pi$
$864$	1.00000			0.0340207
$865$			58.0099i			1.97240i
$866$	−29.5108			−1.00282
$867$		−	11.3641i		−	0.385945i
$868$		0			0
$869$	−10.4546	−	28.5496i	−0.354646	−	0.968478i
$870$	−15.6184			−0.529515
$871$	31.7428			1.07556
$872$	−7.13138			−0.241499
$873$		−	0.624337i		−	0.0211306i
$874$			22.9641i			0.776774i
$875$		0			0
$876$			13.2295i			0.446984i
$877$		−	34.6691i		−	1.17069i	−0.810783	−	0.585347i	$-0.800958\pi$
$877$		−	34.6691i		−	1.17069i	0.810783	−	0.585347i	$-0.199042\pi$
$878$			11.4208i			0.385433i
$879$			10.3943i			0.350592i
$880$	3.72736	+	10.1788i	0.125649	+	0.343127i
$881$		−	9.30311i		−	0.313430i	−0.987644	−	0.156715i	$-0.949910\pi$
$881$		−	9.30311i		−	0.313430i	0.987644	−	0.156715i	$-0.0500904\pi$
$882$		0			0
$883$	−40.2050			−1.35301			−0.676503	−	0.736440i	$-0.736505\pi$
$883$	−40.2050			−1.35301			−0.676503	+	0.736440i	$0.736505\pi$
$884$	27.2956			0.918052
$885$			44.0712i			1.48144i
$886$		−	25.5212i		−	0.857400i
$887$	−15.0891			−0.506643			−0.253322	−	0.967382i	$-0.581523\pi$
$887$	−15.0891			−0.506643			−0.253322	+	0.967382i	$0.581523\pi$
$888$	2.13093			0.0715093
$889$		0			0
$890$		−	20.3423i		−	0.681874i
$891$	3.11438	−	1.14045i	0.104336	−	0.0382066i
$892$			5.42935i			0.181788i
$893$		−	51.4281i		−	1.72098i
$894$		−	7.22464i		−	0.241628i
$895$			9.42811i			0.315147i
$896$		0			0
$897$		−	27.5317i		−	0.919258i
$898$		−	25.9959i		−	0.867495i
$899$	−30.8938			−1.03037
$900$	−5.68190			−0.189397
$901$	−66.7851			−2.22493
$902$	1.08303	+	2.95758i	0.0360611	+	0.0984766i
$903$		0			0
$904$			2.41436i			0.0803004i
$905$	−35.7395			−1.18802
$906$			4.88028i			0.162136i
$907$	−18.5370			−0.615512			−0.307756	−	0.951465i	$-0.599578\pi$
$907$	−18.5370			−0.615512			−0.307756	+	0.951465i	$0.599578\pi$
$908$	−11.8564			−0.393467
$909$	−13.1692			−0.436796
$910$		0			0
$911$	−33.6539			−1.11500			−0.557502	−	0.830176i	$-0.688240\pi$
$911$	−33.6539			−1.11500			−0.557502	+	0.830176i	$0.688240\pi$
$912$			4.27490i			0.141556i
$913$	−2.60315	+	0.953245i	−0.0861516	+	0.0315478i
$914$	8.03248			0.265691
$915$	17.4548			0.577037
$916$			6.42701i			0.212354i
$917$		0			0
$918$	−5.32580			−0.175777
$919$			13.7982i			0.455160i	0.973759	+	0.227580i	$0.0730813\pi$
$919$			13.7982i			0.455160i	−0.973759	+	0.227580i	$0.926919\pi$
$920$	−17.5569			−0.578835
$921$		−	1.37847i		−	0.0454222i
$922$		−	33.5115i		−	1.10364i
$923$	−55.3833			−1.82296
$924$		0			0
$925$	−12.1077			−0.398100
$926$			15.7419i			0.517310i
$927$		−	13.2122i		−	0.433944i
$928$	−4.77874			−0.156870
$929$		−	31.4371i		−	1.03142i	−0.856764	−	0.515709i	$-0.827529\pi$
$929$		−	31.4371i		−	1.03142i	0.856764	−	0.515709i	$-0.172471\pi$
$930$	−21.1292			−0.692854
$931$		0			0
$932$			2.00886i			0.0658023i
$933$	−10.5210			−0.344444
$934$	10.2329			0.334830
$935$	−19.8512	−	54.2102i	−0.649203	−	1.77286i
$936$		−	5.12518i		−	0.167522i
$937$	−13.0822			−0.427377			−0.213689	−	0.976902i	$-0.568548\pi$
$937$	−13.0822			−0.427377			−0.213689	+	0.976902i	$0.568548\pi$
$938$		0			0
$939$	2.26694			0.0739788
$940$	39.3187			1.28243
$941$	−38.3447			−1.25000			−0.625001	−	0.780624i	$-0.714901\pi$
$941$	−38.3447			−1.25000			−0.625001	+	0.780624i	$0.714901\pi$
$942$		−	3.30239i		−	0.107598i
$943$	−5.10140			−0.166124
$944$			13.4844i			0.438879i
$945$		0			0
$946$	19.3242	−	7.07632i	0.628284	−	0.230071i
$947$	40.9405			1.33039			0.665193	−	0.746671i	$-0.268349\pi$
$947$	40.9405			1.33039			0.665193	+	0.746671i	$0.268349\pi$
$948$	9.16702			0.297731
$949$	67.8036			2.20100
$950$		−	24.2896i		−	0.788057i
$951$			4.94169i			0.160245i
$952$		0			0
$953$			19.7503i			0.639776i	0.947455	+	0.319888i	$0.103645\pi$
$953$			19.7503i			0.639776i	−0.947455	+	0.319888i	$0.896355\pi$
$954$			12.5399i			0.405995i
$955$			42.0860i			1.36187i
$956$		−	4.65869i		−	0.150673i
$957$	−14.8828	+	5.44993i	−0.481093	+	0.176171i
$958$			5.19626i			0.167883i
$959$		0			0
$960$	−3.26832			−0.105485
$961$	−10.7943			−0.348205
$962$		−	10.9214i		−	0.352120i
$963$		−	11.1094i		−	0.357996i
$964$	5.96996			0.192279
$965$	19.7563			0.635977
$966$		0			0
$967$		−	36.4927i		−	1.17352i	−0.809759	−	0.586762i	$-0.800402\pi$
$967$		−	36.4927i		−	1.17352i	0.809759	−	0.586762i	$-0.199598\pi$
$968$	7.10361	+	8.39873i	0.228319	+	0.269946i
$969$		−	22.7672i		−	0.731389i
$970$			2.04053i			0.0655176i
$971$		−	51.4179i		−	1.65008i	−0.565075	−	0.825039i	$-0.691153\pi$
$971$		−	51.4179i		−	1.65008i	0.565075	−	0.825039i	$-0.308847\pi$
$972$			1.00000i			0.0320750i
$973$		0			0
$974$			31.5483i			1.01087i
$975$			29.1208i			0.932611i
$976$	5.34060			0.170948
$977$	7.81628			0.250065			0.125033	−	0.992153i	$-0.460096\pi$
$977$	7.81628			0.250065			0.125033	+	0.992153i	$0.460096\pi$
$978$	4.84536			0.154938
$979$	−7.09827	−	19.3841i	−0.226862	−	0.619520i
$980$		0			0
$981$		−	7.13138i		−	0.227687i
$982$	−7.14182			−0.227905
$983$		−	14.7755i		−	0.471264i	−0.971842	−	0.235632i	$-0.924284\pi$
$983$		−	14.7755i		−	0.471264i	0.971842	−	0.235632i	$-0.0757160\pi$
$984$	−0.949652			−0.0302738
$985$	−20.2060			−0.643815
$986$	25.4506			0.810512
$987$		0			0
$988$	21.9096			0.697037
$989$			33.3315i			1.05988i
$990$	−10.1788	+	3.72736i	−0.323503	+	0.118463i
$991$	−0.545492			−0.0173281			−0.00866407	−	0.999962i	$-0.502758\pi$
$991$	−0.545492			−0.0173281			−0.00866407	+	0.999962i	$0.502758\pi$
$992$	−6.46485			−0.205259
$993$		−	12.9489i		−	0.410922i
$994$		0			0
$995$	−12.6891			−0.402272
$996$		−	0.835847i		−	0.0264848i
$997$	−37.9225			−1.20102			−0.600508	−	0.799619i	$-0.705035\pi$
$997$	−37.9225			−1.20102			−0.600508	+	0.799619i	$0.705035\pi$
$998$			34.7635i			1.10042i
$999$			2.13093i			0.0674196i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3234.2.e.a.2155.8		16
7.2	even	3		462.2.p.a.241.4	✓	16
7.3	odd	6		462.2.p.b.439.8	yes	16
7.6	odd	2		3234.2.e.b.2155.1		16
11.10	odd	2		3234.2.e.b.2155.16		16
21.2	odd	6		1386.2.bk.a.703.5		16
21.17	even	6		1386.2.bk.b.901.1		16
77.10	even	6		462.2.p.a.439.4	yes	16
77.65	odd	6		462.2.p.b.241.8	yes	16
77.76	even	2	inner	3234.2.e.a.2155.9		16
231.65	even	6		1386.2.bk.b.703.1		16
231.164	odd	6		1386.2.bk.a.901.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.4	✓	16	7.2	even	3
462.2.p.a.439.4	yes	16	77.10	even	6
462.2.p.b.241.8	yes	16	77.65	odd	6
462.2.p.b.439.8	yes	16	7.3	odd	6
1386.2.bk.a.703.5		16	21.2	odd	6
1386.2.bk.a.901.5		16	231.164	odd	6
1386.2.bk.b.703.1		16	231.65	even	6
1386.2.bk.b.901.1		16	21.17	even	6
3234.2.e.a.2155.8		16	1.1	even	1	trivial
3234.2.e.a.2155.9		16	77.76	even	2	inner
3234.2.e.b.2155.1		16	7.6	odd	2
3234.2.e.b.2155.16		16	11.10	odd	2

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:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +3.26832i q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +3.26832i q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +3.26832 q^{10} +(3.11438 - 1.14045i) q^{11} +1.00000i q^{12} +5.12518 q^{13} +3.26832 q^{15} +1.00000 q^{16} -5.32580 q^{17} +1.00000i q^{18} -4.27490 q^{19} -3.26832i q^{20} +(-1.14045 - 3.11438i) q^{22} +5.37186 q^{23} +1.00000 q^{24} -5.68190 q^{25} -5.12518i q^{26} +1.00000i q^{27} -4.77874i q^{29} -3.26832i q^{30} -6.46485i q^{31} -1.00000i q^{32} +(-1.14045 - 3.11438i) q^{33} +5.32580i q^{34} +1.00000 q^{36} +2.13093 q^{37} +4.27490i q^{38} -5.12518i q^{39} -3.26832 q^{40} -0.949652 q^{41} +6.20483i q^{43} +(-3.11438 + 1.14045i) q^{44} -3.26832i q^{45} -5.37186i q^{46} +12.0303i q^{47} -1.00000i q^{48} +5.68190i q^{50} +5.32580i q^{51} -5.12518 q^{52} +12.5399 q^{53} +1.00000 q^{54} +(3.72736 + 10.1788i) q^{55} +4.27490i q^{57} -4.77874 q^{58} +13.4844i q^{59} -3.26832 q^{60} +5.34060 q^{61} -6.46485 q^{62} -1.00000 q^{64} +16.7507i q^{65} +(-3.11438 + 1.14045i) q^{66} +6.19350 q^{67} +5.32580 q^{68} -5.37186i q^{69} -10.8061 q^{71} -1.00000i q^{72} +13.2295 q^{73} -2.13093i q^{74} +5.68190i q^{75} +4.27490 q^{76} -5.12518 q^{78} -9.16702i q^{79} +3.26832i q^{80} +1.00000 q^{81} +0.949652i q^{82} -0.835847 q^{83} -17.4064i q^{85} +6.20483 q^{86} -4.77874 q^{87} +(1.14045 + 3.11438i) q^{88} -6.22408i q^{89} -3.26832 q^{90} -5.37186 q^{92} -6.46485 q^{93} +12.0303 q^{94} -13.9717i q^{95} -1.00000 q^{96} +0.624337i q^{97} +(-3.11438 + 1.14045i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 16 q^{6} - 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 - 16 * q^6 - 16 * q^9	\( 16 q - 16 q^{4} - 16 q^{6} - 16 q^{9} - 4 q^{10} + 8 q^{11} - 4 q^{15} + 16 q^{16} + 20 q^{19} + 2 q^{22} + 8 q^{23} + 16 q^{24} - 20 q^{25} + 2 q^{33} + 16 q^{36} - 28 q^{37} + 4 q^{40} + 32 q^{41} - 8 q^{44} + 16 q^{54} - 14 q^{55} + 4 q^{60} - 56 q^{61} - 8 q^{62} - 16 q^{64} - 8 q^{66} + 32 q^{67} - 56 q^{71} + 88 q^{73} - 20 q^{76} + 16 q^{81} + 8 q^{83} + 24 q^{86} - 2 q^{88} + 4 q^{90} - 8 q^{92} - 8 q^{93} - 28 q^{94} - 16 q^{96} - 8 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 - 16 * q^6 - 16 * q^9 - 4 * q^10 + 8 * q^11 - 4 * q^15 + 16 * q^16 + 20 * q^19 + 2 * q^22 + 8 * q^23 + 16 * q^24 - 20 * q^25 + 2 * q^33 + 16 * q^36 - 28 * q^37 + 4 * q^40 + 32 * q^41 - 8 * q^44 + 16 * q^54 - 14 * q^55 + 4 * q^60 - 56 * q^61 - 8 * q^62 - 16 * q^64 - 8 * q^66 + 32 * q^67 - 56 * q^71 + 88 * q^73 - 20 * q^76 + 16 * q^81 + 8 * q^83 + 24 * q^86 - 2 * q^88 + 4 * q^90 - 8 * q^92 - 8 * q^93 - 28 * q^94 - 16 * q^96 - 8 * q^99

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