LMFDB - Embedded newform 847.2.b.f.846.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(846,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("847.846");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.b (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:	$6.76332905120$
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} + 20x^{14} + 260x^{12} + 2030x^{10} + 11605x^{8} + 42100x^{6} + 106925x^{4} + 113575x^{2} + 87025 $ x^16 + 20x^14 + 260x^12 + 2030x^10 + 11605x^8 + 42100x^6 + 106925x^4 + 113575*x^2 + 87025
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			846.13
Root			$-1.29877 + 2.24954i$ of defining polynomial
Character	$\chi$	$=$	847.846
Dual form			847.2.b.f.846.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.22930i q^{2} -1.30593i q^{3} +0.488830 q^{4} -2.38605i q^{5} +1.60537 q^{6} +(2.59754 + 0.502754i) q^{7} +3.05951i q^{8} +1.29456 q^{9} +O(q^{10})$	\(q+1.22930i q^{2} -1.30593i q^{3} +0.488830 q^{4} -2.38605i q^{5} +1.60537 q^{6} +(2.59754 + 0.502754i) q^{7} +3.05951i q^{8} +1.29456 q^{9} +2.93316 q^{10} -0.638376i q^{12} +2.59754 q^{13} +(-0.618034 + 3.19315i) q^{14} -3.11600 q^{15} -2.78339 q^{16} +4.53853 q^{17} +1.59139i q^{18} -8.22214 q^{19} -1.16637i q^{20} +(0.656560 - 3.39220i) q^{21} -3.85410 q^{23} +3.99549 q^{24} -0.693216 q^{25} +3.19315i q^{26} -5.60837i q^{27} +(1.26976 + 0.245761i) q^{28} -2.82069i q^{29} -3.83049i q^{30} +4.13372i q^{31} +2.69741i q^{32} +5.57920i q^{34} +(1.19959 - 6.19786i) q^{35} +0.632818 q^{36} +4.02859 q^{37} -10.1075i q^{38} -3.39220i q^{39} +7.30013 q^{40} +0.808486 q^{41} +(4.17002 + 0.807107i) q^{42} +1.73205i q^{43} -3.08887i q^{45} -4.73783i q^{46} -1.84002i q^{47} +3.63490i q^{48} +(6.49448 + 2.61185i) q^{49} -0.852168i q^{50} -5.92699i q^{51} +1.26976 q^{52} -2.50361 q^{53} +6.89436 q^{54} +(-1.53818 + 7.94721i) q^{56} +10.7375i q^{57} +3.46747 q^{58} -10.7750i q^{59} -1.52319 q^{60} +6.21100 q^{61} -5.08156 q^{62} +(3.36267 + 0.650844i) q^{63} -8.88269 q^{64} -6.19786i q^{65} +11.5592 q^{67} +2.21857 q^{68} +5.03317i q^{69} +(7.61901 + 1.47466i) q^{70} -9.88834 q^{71} +3.96071i q^{72} -4.78931 q^{73} +4.95233i q^{74} +0.905289i q^{75} -4.01923 q^{76} +4.17002 q^{78} -4.82331i q^{79} +6.64129i q^{80} -3.44045 q^{81} +0.993869i q^{82} -10.3705 q^{83} +(0.320946 - 1.65821i) q^{84} -10.8291i q^{85} -2.12920 q^{86} -3.68361 q^{87} +1.52186i q^{89} +3.79714 q^{90} +(6.74724 + 1.30593i) q^{91} -1.88400 q^{92} +5.39833 q^{93} +2.26193 q^{94} +19.6184i q^{95} +3.52262 q^{96} +10.2290i q^{97} +(-3.21074 + 7.98364i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{9}+O(q^{10}) $ 16 * q - 32 * q^9	$ 16 q - 32 q^{9} + 8 q^{14} - 20 q^{15} + 16 q^{16} - 8 q^{23} - 40 q^{25} - 60 q^{36} - 36 q^{37} - 20 q^{42} + 48 q^{49} + 20 q^{53} - 4 q^{56} + 28 q^{58} - 140 q^{60} + 12 q^{64} - 4 q^{67} + 100 q^{70} + 44 q^{71} - 20 q^{78} - 56 q^{81} - 24 q^{86} + 80 q^{91} - 60 q^{92} - 20 q^{93}+O(q^{100}) $ 16 * q - 32 * q^9 + 8 * q^14 - 20 * q^15 + 16 * q^16 - 8 * q^23 - 40 * q^25 - 60 * q^36 - 36 * q^37 - 20 * q^42 + 48 * q^49 + 20 * q^53 - 4 * q^56 + 28 * q^58 - 140 * q^60 + 12 * q^64 - 4 * q^67 + 100 * q^70 + 44 * q^71 - 20 * q^78 - 56 * q^81 - 24 * q^86 + 80 * q^91 - 60 * q^92 - 20 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$-1$	$-1$

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 $

$2$			1.22930i			0.869244i	0.900613	+	0.434622i	$0.143118\pi$
$2$			1.22930i			0.869244i	−0.900613	+	0.434622i	$0.856882\pi$
$3$		−	1.30593i		−	0.753977i	−0.926218	−	0.376988i	$-0.876960\pi$
$3$		−	1.30593i		−	0.753977i	0.926218	−	0.376988i	$-0.123040\pi$
$4$	0.488830			0.244415
$5$		−	2.38605i		−	1.06707i	−0.845777	−	0.533536i	$-0.820863\pi$
$5$		−	2.38605i		−	1.06707i	0.845777	−	0.533536i	$-0.179137\pi$
$6$	1.60537			0.655390
$7$	2.59754	+	0.502754i	0.981780	+	0.190023i
$7$	2.59754	+	0.502754i	0.981780	+	0.190023i
$8$			3.05951i			1.08170i
$9$	1.29456			0.431519
$10$	2.93316			0.927546
$11$		0			0
$11$		0			0
$12$		−	0.638376i		−	0.184283i
$13$	2.59754			0.720429			0.360215	−	0.932869i	$-0.382703\pi$
$13$	2.59754			0.720429			0.360215	+	0.932869i	$0.382703\pi$
$14$	−0.618034	+	3.19315i	−0.165177	+	0.853406i
$15$	−3.11600			−0.804548
$16$	−2.78339			−0.695847
$17$	4.53853			1.10076			0.550378	−	0.834916i	$-0.314484\pi$
$17$	4.53853			1.10076			0.550378	+	0.834916i	$0.314484\pi$
$18$			1.59139i			0.375095i
$19$	−8.22214			−1.88629			−0.943145	−	0.332383i	$-0.892147\pi$
$19$	−8.22214			−1.88629			−0.943145	+	0.332383i	$0.892147\pi$
$20$		−	1.16637i		−	0.260808i
$21$	0.656560	−	3.39220i	0.143273	−	0.740239i
$22$		0			0
$23$	−3.85410			−0.803636			−0.401818	−	0.915720i	$-0.631622\pi$
$23$	−3.85410			−0.803636			−0.401818	+	0.915720i	$0.631622\pi$
$24$	3.99549			0.815577
$25$	−0.693216			−0.138643
$26$			3.19315i			0.626229i
$27$		−	5.60837i		−	1.07933i
$28$	1.26976	+	0.245761i	0.239962	+	0.0464445i
$29$		−	2.82069i		−	0.523789i	−0.965096	−	0.261895i	$-0.915653\pi$
$29$		−	2.82069i		−	0.523789i	0.965096	−	0.261895i	$-0.0843473\pi$
$30$		−	3.83049i		−	0.699348i
$31$			4.13372i			0.742437i	0.928545	+	0.371219i	$0.121060\pi$
$31$			4.13372i			0.742437i	−0.928545	+	0.371219i	$0.878940\pi$
$32$			2.69741i			0.476840i
$33$		0			0
$34$			5.57920i			0.956825i
$35$	1.19959	−	6.19786i	0.202768	−	1.04763i
$36$	0.632818			0.105470
$37$	4.02859			0.662296			0.331148	−	0.943579i	$-0.392564\pi$
$37$	4.02859			0.662296			0.331148	+	0.943579i	$0.392564\pi$
$38$		−	10.1075i		−	1.63965i
$39$		−	3.39220i		−	0.543187i
$40$	7.30013			1.15425
$41$	0.808486			0.126264			0.0631322	−	0.998005i	$-0.479891\pi$
$41$	0.808486			0.126264			0.0631322	+	0.998005i	$0.479891\pi$
$42$	4.17002	+	0.807107i	0.643448	+	0.124539i
$43$			1.73205i			0.264135i	0.991241	+	0.132068i	$0.0421616\pi$
$43$			1.73205i			0.264135i	−0.991241	+	0.132068i	$0.957838\pi$
$44$		0			0
$45$		−	3.08887i		−	0.460462i
$46$		−	4.73783i		−	0.698556i
$47$		−	1.84002i		−	0.268395i	−0.990955	−	0.134197i	$-0.957154\pi$
$47$		−	1.84002i		−	0.268395i	0.990955	−	0.134197i	$-0.0428456\pi$
$48$			3.63490i			0.524652i
$49$	6.49448	+	2.61185i	0.927782	+	0.373122i
$50$		−	0.852168i		−	0.120515i
$51$		−	5.92699i		−	0.829944i
$52$	1.26976			0.176084
$53$	−2.50361			−0.343898			−0.171949	−	0.985106i	$-0.555006\pi$
$53$	−2.50361			−0.343898			−0.171949	+	0.985106i	$0.555006\pi$
$54$	6.89436			0.938203
$55$		0			0
$56$	−1.53818	+	7.94721i	−0.205548	+	1.06199i
$57$			10.7375i			1.42222i
$58$	3.46747			0.455301
$59$		−	10.7750i		−	1.40279i	−0.712775	−	0.701393i	$-0.752562\pi$
$59$		−	10.7750i		−	1.40279i	0.712775	−	0.701393i	$-0.247438\pi$
$60$	−1.52319			−0.196643
$61$	6.21100			0.795237			0.397618	−	0.917551i	$-0.369837\pi$
$61$	6.21100			0.795237			0.397618	+	0.917551i	$0.369837\pi$
$62$	−5.08156			−0.645359
$63$	3.36267	+	0.650844i	0.423656	+	0.0819986i
$64$	−8.88269			−1.11034
$65$		−	6.19786i		−	0.768750i
$66$		0			0
$67$	11.5592			1.41218			0.706091	−	0.708121i	$-0.250457\pi$
$67$	11.5592			1.41218			0.706091	+	0.708121i	$0.250457\pi$
$68$	2.21857			0.269041
$69$			5.03317i			0.605923i
$70$	7.61901	+	1.47466i	0.910646	+	0.176255i
$71$	−9.88834			−1.17353			−0.586765	−	0.809757i	$-0.699599\pi$
$71$	−9.88834			−1.17353			−0.586765	+	0.809757i	$0.699599\pi$
$72$			3.96071i			0.466774i
$73$	−4.78931			−0.560547			−0.280273	−	0.959920i	$-0.590425\pi$
$73$	−4.78931			−0.560547			−0.280273	+	0.959920i	$0.590425\pi$
$74$			4.95233i			0.575697i
$75$			0.905289i			0.104534i
$76$	−4.01923			−0.461037
$77$		0			0
$78$	4.17002			0.472162
$79$		−	4.82331i		−	0.542665i	−0.962486	−	0.271333i	$-0.912536\pi$
$79$		−	4.82331i		−	0.542665i	0.962486	−	0.271333i	$-0.0874643\pi$
$80$			6.64129i			0.742519i
$81$	−3.44045			−0.382273
$82$			0.993869i			0.109755i
$83$	−10.3705			−1.13832			−0.569158	−	0.822228i	$-0.692731\pi$
$83$	−10.3705			−1.13832			−0.569158	+	0.822228i	$0.692731\pi$
$84$	0.320946	−	1.65821i	0.0350181	−	0.180925i
$85$		−	10.8291i		−	1.17459i
$86$	−2.12920			−0.229598
$87$	−3.68361			−0.394925
$88$		0			0
$89$			1.52186i			0.161317i	0.996742	+	0.0806586i	$0.0257024\pi$
$89$			1.52186i			0.161317i	−0.996742	+	0.0806586i	$0.974298\pi$
$90$	3.79714			0.400254
$91$	6.74724	+	1.30593i	0.707303	+	0.136898i
$92$	−1.88400			−0.196421
$93$	5.39833			0.559781
$94$	2.26193			0.233300
$95$			19.6184i			2.01281i
$96$	3.52262			0.359526
$97$			10.2290i			1.03860i	0.854593	+	0.519298i	$0.173806\pi$
$97$			10.2290i			1.03860i	−0.854593	+	0.519298i	$0.826194\pi$
$98$	−3.21074	+	7.98364i	−0.324334	+	0.806469i
$99$		0			0
$100$	−0.338865			−0.0338865
$101$	−2.16804			−0.215728			−0.107864	−	0.994166i	$-0.534401\pi$
$101$	−2.16804			−0.215728			−0.107864	+	0.994166i	$0.534401\pi$
$102$	7.28602			0.721424
$103$			3.17512i			0.312854i	0.987690	+	0.156427i	$0.0499976\pi$
$103$			3.17512i			0.312854i	−0.987690	+	0.156427i	$0.950002\pi$
$104$			7.94721i			0.779288i
$105$	−8.09395	−	1.56658i	−0.789889	−	0.152883i
$106$		−	3.07768i		−	0.298931i
$107$			3.43325i			0.331904i	0.986134	+	0.165952i	$0.0530697\pi$
$107$			3.43325i			0.331904i	−0.986134	+	0.165952i	$0.946930\pi$
$108$		−	2.74154i		−	0.263805i
$109$			13.9559i			1.33673i	0.743834	+	0.668364i	$0.233005\pi$
$109$			13.9559i			1.33673i	−0.743834	+	0.668364i	$0.766995\pi$
$110$		0			0
$111$		−	5.26104i		−	0.499356i
$112$	−7.22997	−	1.39936i	−0.683168	−	0.132227i
$113$	−16.7016			−1.57116			−0.785578	−	0.618762i	$-0.787634\pi$
$113$	−16.7016			−1.57116			−0.785578	+	0.618762i	$0.787634\pi$
$114$	−13.1996			−1.23625
$115$			9.19607i			0.857537i
$116$		−	1.37884i		−	0.128022i
$117$	3.36267			0.310879
$118$	13.2457			1.21936
$119$	11.7890	+	2.28176i	1.08070	+	0.209169i
$120$		−	9.53343i		−	0.870280i
$121$		0			0
$122$			7.63516i			0.691255i
$123$		−	1.05582i		−	0.0952004i
$124$			2.02068i			0.181463i
$125$		−	10.2762i		−	0.919130i
$126$	−0.800080	+	4.13372i	−0.0712768	+	0.368261i
$127$		−	4.01872i		−	0.356604i	−0.983976	−	0.178302i	$-0.942940\pi$
$127$		−	4.01872i		−	0.356604i	0.983976	−	0.178302i	$-0.0570604\pi$
$128$		−	5.52464i		−	0.488314i
$129$	2.26193			0.199152
$130$	7.61901			0.668231
$131$	−8.32100			−0.727009			−0.363505	−	0.931592i	$-0.618420\pi$
$131$	−8.32100			−0.727009			−0.363505	+	0.931592i	$0.618420\pi$
$132$		0			0
$133$	−21.3574	−	4.13372i	−1.85192	−	0.358439i
$134$			14.2097i			1.22753i
$135$	−13.3818			−1.15173
$136$			13.8857i			1.19069i
$137$	0.773273			0.0660652			0.0330326	−	0.999454i	$-0.489483\pi$
$137$	0.773273			0.0660652			0.0330326	+	0.999454i	$0.489483\pi$
$138$	−6.18726			−0.526695
$139$	−3.76844			−0.319635			−0.159818	−	0.987147i	$-0.551091\pi$
$139$	−3.76844			−0.319635			−0.159818	+	0.987147i	$0.551091\pi$
$140$	0.586397	−	3.02970i	0.0495596	−	0.256056i
$141$	−2.40293			−0.202363
$142$		−	12.1557i		−	1.02008i
$143$		0			0
$144$	−3.60325			−0.300271
$145$	−6.73030			−0.558921
$146$		−	5.88749i		−	0.487252i
$147$	3.41089	−	8.48131i	0.281325	−	0.699526i
$148$	1.96929			0.161875
$149$			9.67554i			0.792651i	0.918110	+	0.396326i	$0.129715\pi$
$149$			9.67554i			0.792651i	−0.918110	+	0.396326i	$0.870285\pi$
$150$	−1.11287			−0.0908654
$151$			17.1192i			1.39314i	0.717489	+	0.696570i	$0.245291\pi$
$151$			17.1192i			1.39314i	−0.717489	+	0.696570i	$0.754709\pi$
$152$		−	25.1557i		−	2.04040i
$153$	5.87538			0.474997
$154$		0			0
$155$	9.86324			0.792234
$156$		−	1.65821i		−	0.132763i
$157$		−	20.1106i		−	1.60500i	−0.596650	−	0.802501i	$-0.703502\pi$
$157$		−	20.1106i		−	1.60500i	0.596650	−	0.802501i	$-0.296498\pi$
$158$	5.92928			0.471709
$159$			3.26953i			0.259291i
$160$	6.43615			0.508822
$161$	−10.0112	−	1.93767i	−0.788993	−	0.152709i
$162$		−	4.22934i		−	0.332288i
$163$	−0.191760			−0.0150198			−0.00750989	−	0.999972i	$-0.502390\pi$
$163$	−0.191760			−0.0150198			−0.00750989	+	0.999972i	$0.502390\pi$
$164$	0.395212			0.0308609
$165$		0			0
$166$		−	12.7485i		−	0.989474i
$167$	−20.7027			−1.60202			−0.801011	−	0.598649i	$-0.795704\pi$
$167$	−20.7027			−1.60202			−0.801011	+	0.598649i	$0.795704\pi$
$168$	10.3785	+	2.00875i	0.800717	+	0.154979i
$169$	−6.25276			−0.480982
$170$	13.3122			1.02100
$171$	−10.6440			−0.813969
$172$			0.846678i			0.0645586i
$173$	−9.29915			−0.707001			−0.353501	−	0.935434i	$-0.615009\pi$
$173$	−9.29915			−0.707001			−0.353501	+	0.935434i	$0.615009\pi$
$174$		−	4.52825i		−	0.343286i
$175$	−1.80066	−	0.348517i	−0.136117	−	0.0263454i
$176$		0			0
$177$	−14.0714			−1.05767
$178$	−1.87082			−0.140224
$179$	23.4794			1.75493			0.877465	−	0.479641i	$-0.159233\pi$
$179$	23.4794			1.75493			0.877465	+	0.479641i	$0.159233\pi$
$180$		−	1.50993i		−	0.112544i
$181$			13.5675i			1.00847i	0.863568	+	0.504233i	$0.168225\pi$
$181$			13.5675i			1.00847i	−0.863568	+	0.504233i	$0.831775\pi$
$182$	−1.60537	+	8.29436i	−0.118998	+	0.614819i
$183$		−	8.11110i		−	0.599590i
$184$		−	11.7917i		−	0.869293i
$185$		−	9.61240i		−	0.706718i
$186$			6.63615i			0.486586i
$187$		0			0
$188$		−	0.899457i		−	0.0655996i
$189$	2.81963	−	14.5680i	0.205098	−	1.05967i
$190$	−24.1169			−1.74962
$191$	11.7620			0.851070			0.425535	−	0.904942i	$-0.360086\pi$
$191$	11.7620			0.851070			0.425535	+	0.904942i	$0.360086\pi$
$192$			11.6001i			0.837168i
$193$			13.6080i			0.979525i	0.871856	+	0.489762i	$0.162916\pi$
$193$			13.6080i			0.979525i	−0.871856	+	0.489762i	$0.837084\pi$
$194$	−12.5744			−0.902793
$195$	−8.09395			−0.579620
$196$	3.17469	+	1.27675i	0.226764	+	0.0911965i
$197$		−	10.8493i		−	0.772978i	−0.922294	−	0.386489i	$-0.873688\pi$
$197$		−	10.8493i		−	0.772978i	0.922294	−	0.386489i	$-0.126312\pi$
$198$		0			0
$199$		−	18.0374i		−	1.27864i	−0.768941	−	0.639320i	$-0.779216\pi$
$199$		−	18.0374i		−	1.27864i	0.768941	−	0.639320i	$-0.220784\pi$
$200$		−	2.12090i		−	0.149970i
$201$		−	15.0955i		−	1.06475i
$202$		−	2.66516i		−	0.187520i
$203$	1.41811	−	7.32687i	0.0995321	−	0.514245i
$204$		−	2.89729i		−	0.202851i
$205$		−	1.92909i		−	0.134733i
$206$	−3.90317			−0.271947
$207$	−4.98935			−0.346784
$208$	−7.22997			−0.501308
$209$		0			0
$210$	1.92579	−	9.94987i	0.132892	−	0.686606i
$211$			23.0974i			1.59009i	0.606551	+	0.795045i	$0.292553\pi$
$211$			23.0974i			1.59009i	−0.606551	+	0.795045i	$0.707447\pi$
$212$	−1.22384			−0.0840537
$213$			12.9134i			0.884815i
$214$	−4.22048			−0.288506
$215$	4.13275			0.281851
$216$	17.1589			1.16751
$217$	−2.07824	+	10.7375i	−0.141080	+	0.728910i
$218$	−17.1559			−1.16194
$219$			6.25449i			0.422639i
$220$		0			0
$221$	11.7890			0.793016
$222$	6.46738			0.434062
$223$			4.97610i			0.333224i	0.986023	+	0.166612i	$0.0532828\pi$
$223$			4.97610i			0.333224i	−0.986023	+	0.166612i	$0.946717\pi$
$224$	−1.35614	+	7.00665i	−0.0906106	+	0.468152i
$225$	−0.897407			−0.0598272
$226$		−	20.5312i		−	1.36572i
$227$	8.40993			0.558187			0.279093	−	0.960264i	$-0.409966\pi$
$227$	8.40993			0.558187			0.279093	+	0.960264i	$0.409966\pi$
$228$			5.24882i			0.347611i
$229$			26.9958i			1.78393i	0.452105	+	0.891965i	$0.350673\pi$
$229$			26.9958i			1.78393i	−0.452105	+	0.891965i	$0.649327\pi$
$230$	−11.3047			−0.745409
$231$		0			0
$232$	8.62993			0.566583
$233$			13.1930i			0.864300i	0.901802	+	0.432150i	$0.142245\pi$
$233$			13.1930i			0.864300i	−0.901802	+	0.432150i	$0.857755\pi$
$234$			4.13372i			0.270230i
$235$	−4.39037			−0.286396
$236$		−	5.26714i		−	0.342862i
$237$	−6.29889			−0.409157
$238$	−2.80497	+	14.4922i	−0.181819	+	0.939391i
$239$		−	7.46545i		−	0.482900i	−0.970413	−	0.241450i	$-0.922377\pi$
$239$		−	7.46545i		−	0.482900i	0.970413	−	0.241450i	$-0.0776229\pi$
$240$	8.67303			0.559842
$241$	−1.08607			−0.0699599			−0.0349799	−	0.999388i	$-0.511137\pi$
$241$	−1.08607			−0.0699599			−0.0349799	+	0.999388i	$0.511137\pi$
$242$		0			0
$243$		−	12.3321i		−	0.791107i
$244$	3.03612			0.194368
$245$	6.23200	−	15.4961i	0.398148	−	0.990011i
$246$	1.29792			0.0827524
$247$	−21.3574			−1.35894
$248$	−12.6471			−0.803095
$249$			13.5432i			0.858264i
$250$	12.6325			0.798948
$251$		−	14.3117i		−	0.903348i	−0.892183	−	0.451674i	$-0.850827\pi$
$251$		−	14.3117i		−	0.903348i	0.892183	−	0.451674i	$-0.149173\pi$
$252$	1.64377	+	0.318152i	0.103548	+	0.0200417i
$253$		0			0
$254$	4.94020			0.309976
$255$	−14.1421			−0.885610
$256$	−10.9740			−0.685873
$257$		−	5.07428i		−	0.316525i	−0.987397	−	0.158262i	$-0.949411\pi$
$257$		−	5.07428i		−	0.316525i	0.987397	−	0.158262i	$-0.0505892\pi$
$258$			2.78058i			0.173112i
$259$	10.4644	+	2.02539i	0.650229	+	0.125852i
$260$		−	3.02970i		−	0.187894i
$261$		−	3.65154i		−	0.226025i
$262$		−	10.2290i		−	0.631948i
$263$			13.2482i			0.816922i	0.912776	+	0.408461i	$0.133934\pi$
$263$			13.2482i			0.816922i	−0.912776	+	0.408461i	$0.866066\pi$
$264$		0			0
$265$			5.97374i			0.366964i
$266$	5.08156	−	26.2546i	0.311571	−	1.60977i
$267$	1.98744			0.121629
$268$	5.65049			0.345158
$269$			6.89706i			0.420521i	0.977645	+	0.210261i	$0.0674312\pi$
$269$			6.89706i			0.420521i	−0.977645	+	0.210261i	$0.932569\pi$
$270$		−	16.4503i		−	1.00113i
$271$	−12.7320			−0.773413			−0.386706	−	0.922203i	$-0.626387\pi$
$271$	−12.7320			−0.773413			−0.386706	+	0.922203i	$0.626387\pi$
$272$	−12.6325			−0.765957
$273$	1.70544	−	8.81140i	0.103218	−	0.533290i
$274$			0.950582i			0.0574267i
$275$		0			0
$276$			2.46036i			0.148097i
$277$		−	20.6196i		−	1.23891i	−0.785031	−	0.619457i	$-0.787353\pi$
$277$		−	20.6196i		−	1.23891i	0.785031	−	0.619457i	$-0.212647\pi$
$278$		−	4.63254i		−	0.277841i
$279$			5.35133i			0.320376i
$280$	18.9624	+	3.67017i	1.13322	+	0.219335i
$281$		−	5.49339i		−	0.327708i	−0.986485	−	0.163854i	$-0.947607\pi$
$281$		−	5.49339i		−	0.327708i	0.986485	−	0.163854i	$-0.0523927\pi$
$282$		−	2.95391i		−	0.175903i
$283$	−24.7148			−1.46914			−0.734570	−	0.678533i	$-0.762616\pi$
$283$	−24.7148			−1.46914			−0.734570	+	0.678533i	$0.762616\pi$
$284$	−4.83371			−0.286828
$285$	25.6202			1.51761
$286$		0			0
$287$	2.10008	+	0.406470i	0.123964	+	0.0239932i
$288$			3.49195i			0.205765i
$289$	3.59825			0.211662
$290$		−	8.27353i		−	0.485839i
$291$	13.3583			0.783077
$292$	−2.34116			−0.137006
$293$	−10.6768			−0.623747			−0.311873	−	0.950124i	$-0.600956\pi$
$293$	−10.6768			−0.623747			−0.311873	+	0.950124i	$0.600956\pi$
$294$	10.4260	+	4.19299i	0.608059	+	0.244540i
$295$	−25.7097			−1.49687
$296$			12.3255i			0.716406i
$297$		0			0
$298$	−11.8941			−0.689007
$299$	−10.0112			−0.578963
$300$			0.442532i			0.0255496i
$301$	−0.870796	+	4.49908i	−0.0501918	+	0.259323i
$302$	−21.0446			−1.21098
$303$			2.83129i			0.162654i
$304$	22.8854			1.31257
$305$		−	14.8197i		−	0.848575i
$306$			7.22259i			0.412888i
$307$	12.1712			0.694648			0.347324	−	0.937745i	$-0.387090\pi$
$307$	12.1712			0.694648			0.347324	+	0.937745i	$0.387090\pi$
$308$		0			0
$309$	4.14648			0.235885
$310$			12.1248i			0.688645i
$311$			25.7979i			1.46286i	0.681915	+	0.731432i	$0.261148\pi$
$311$			25.7979i			1.46286i	−0.681915	+	0.731432i	$0.738852\pi$
$312$	10.3785			0.587566
$313$			9.93056i			0.561308i	0.959809	+	0.280654i	$0.0905514\pi$
$313$			9.93056i			0.561308i	−0.959809	+	0.280654i	$0.909449\pi$
$314$	24.7219			1.39514
$315$	1.55294	−	8.02348i	0.0874984	−	0.452072i
$316$		−	2.35778i		−	0.132635i
$317$	−10.2534			−0.575886			−0.287943	−	0.957647i	$-0.592971\pi$
$317$	−10.2534			−0.575886			−0.287943	+	0.957647i	$0.592971\pi$
$318$	−4.01923			−0.225387
$319$		0			0
$320$			21.1945i			1.18481i
$321$	4.48357			0.250248
$322$	2.38197	−	12.3067i	0.132742	−	0.685828i
$323$	−37.3164			−2.07634
$324$	−1.68180			−0.0934331
$325$	−1.80066			−0.0998826
$326$		−	0.235730i		−	0.0130559i
$327$	18.2253			1.00786
$328$			2.47357i			0.136580i
$329$	0.925078	−	4.77953i	0.0510012	−	0.263504i
$330$		0			0
$331$	−2.52904			−0.139009			−0.0695044	−	0.997582i	$-0.522142\pi$
$331$	−2.52904			−0.139009			−0.0695044	+	0.997582i	$0.522142\pi$
$332$	−5.06943			−0.278221
$333$	5.21524			0.285793
$334$		−	25.4498i		−	1.39255i
$335$		−	27.5808i		−	1.50690i
$336$	−1.82746	+	9.44181i	−0.0996961	+	0.515093i
$337$		−	23.4630i		−	1.27811i	−0.769161	−	0.639055i	$-0.779326\pi$
$337$		−	23.4630i		−	1.27811i	0.769161	−	0.639055i	$-0.220674\pi$
$338$		−	7.68650i		−	0.418090i
$339$			21.8111i			1.18462i
$340$		−	5.29361i		−	0.287086i
$341$		0			0
$342$		−	13.0847i		−	0.707538i
$343$	15.5566	+	10.0495i	0.839976	+	0.542624i
$344$	−5.29923			−0.285715
$345$	12.0094			0.646563
$346$		−	11.4314i		−	0.614556i
$347$		−	4.72103i		−	0.253438i	−0.991939	−	0.126719i	$-0.959555\pi$
$347$		−	4.72103i		−	0.253438i	0.991939	−	0.126719i	$-0.0404447\pi$
$348$	−1.80066			−0.0965255
$349$	16.4614			0.881157			0.440579	−	0.897714i	$-0.354773\pi$
$349$	16.4614			0.881157			0.440579	+	0.897714i	$0.354773\pi$
$350$	0.428431	−	2.21355i	0.0229006	−	0.118319i
$351$		−	14.5680i		−	0.777582i
$352$		0			0
$353$			27.9774i			1.48909i	0.667573	+	0.744544i	$0.267333\pi$
$353$			27.9774i			1.48909i	−0.667573	+	0.744544i	$0.732667\pi$
$354$		−	17.2979i		−	0.919372i
$355$			23.5940i			1.25224i
$356$			0.743932i			0.0394283i
$357$	2.97982	−	15.3956i	0.157709	−	0.814822i
$358$			28.8631i			1.52546i
$359$		−	12.1966i		−	0.643711i	−0.946789	−	0.321855i	$-0.895693\pi$
$359$		−	12.1966i		−	0.643711i	0.946789	−	0.321855i	$-0.104307\pi$
$360$	9.45043			0.498082
$361$	48.6036			2.55809
$362$	−16.6785			−0.876603
$363$		0			0
$364$	3.29825	+	0.638376i	0.172875	+	0.0334600i
$365$			11.4275i			0.598144i
$366$	9.97095			0.521190
$367$			2.02068i			0.105479i	0.998608	+	0.0527394i	$0.0167953\pi$
$367$			2.02068i			0.105479i	−0.998608	+	0.0527394i	$0.983205\pi$
$368$	10.7275			0.559207
$369$	1.04663			0.0544854
$370$	11.8165			0.614310
$371$	−6.50325	−	1.25870i	−0.337632	−	0.0653486i
$372$	2.63886			0.136819
$373$		−	16.8056i		−	0.870159i	−0.900392	−	0.435080i	$-0.856720\pi$
$373$		−	16.8056i		−	0.870159i	0.900392	−	0.435080i	$-0.143280\pi$
$374$		0			0
$375$	−13.4199			−0.693003
$376$	5.62956			0.290322
$377$		−	7.32687i		−	0.377353i
$378$	17.9084	+	3.46617i	0.921109	+	0.178280i
$379$	5.47851			0.281412			0.140706	−	0.990051i	$-0.455063\pi$
$379$	5.47851			0.281412			0.140706	+	0.990051i	$0.455063\pi$
$380$			9.59006i			0.491960i
$381$	−5.24816			−0.268871
$382$			14.4590i			0.739788i
$383$			11.4075i			0.582898i	0.956586	+	0.291449i	$0.0941374\pi$
$383$			11.4075i			0.582898i	−0.956586	+	0.291449i	$0.905863\pi$
$384$	−7.21477			−0.368177
$385$		0			0
$386$	−16.7283			−0.851446
$387$			2.24224i			0.113979i
$388$			5.00023i			0.253848i
$389$	20.5996			1.04444			0.522221	−	0.852810i	$-0.325103\pi$
$389$	20.5996			1.04444			0.522221	+	0.852810i	$0.325103\pi$
$390$		−	9.94987i		−	0.503831i
$391$	−17.4920			−0.884606
$392$	−7.99099	+	19.8699i	−0.403606	+	1.00358i
$393$			10.8666i			0.548148i
$394$	13.3370			0.671906
$395$	−11.5087			−0.579063
$396$		0			0
$397$			25.8101i			1.29537i	0.761908	+	0.647685i	$0.224263\pi$
$397$			25.8101i			1.29537i	−0.761908	+	0.647685i	$0.775737\pi$
$398$	22.1733			1.11145
$399$	−5.39833	+	27.8912i	−0.270255	+	1.39631i
$400$	1.92949			0.0964744
$401$	−0.183999			−0.00918845			−0.00459423	−	0.999989i	$-0.501462\pi$
$401$	−0.183999			−0.00918845			−0.00459423	+	0.999989i	$0.501462\pi$
$402$	18.5568			0.925530
$403$			10.7375i			0.534874i
$404$	−1.05980			−0.0527270
$405$			8.20908i			0.407913i
$406$	9.00690	+	1.74328i	0.447005	+	0.0865177i
$407$		0			0
$408$	18.1337			0.897750
$409$	21.6808			1.07205			0.536024	−	0.844203i	$-0.319926\pi$
$409$	21.6808			1.07205			0.536024	+	0.844203i	$0.319926\pi$
$410$	2.37142			0.117116
$411$		−	1.00984i		−	0.0498116i
$412$			1.55209i			0.0764662i
$413$	5.41718	−	27.9886i	0.266562	−	1.37723i
$414$		−	6.13339i		−	0.301440i
$415$			24.7446i			1.21467i
$416$			7.00665i			0.343529i
$417$			4.92131i			0.240998i
$418$		0			0
$419$			16.7097i			0.816322i	0.912910	+	0.408161i	$0.133830\pi$
$419$			16.7097i			0.816322i	−0.912910	+	0.408161i	$0.866170\pi$
$420$	−3.95656	−	0.765792i	−0.193061	−	0.0373668i
$421$	13.9025			0.677567			0.338784	−	0.940864i	$-0.389985\pi$
$421$	13.9025			0.677567			0.338784	+	0.940864i	$0.389985\pi$
$422$	−28.3935			−1.38218
$423$		−	2.38201i		−	0.115817i
$424$		−	7.65983i		−	0.371994i
$425$	−3.14618			−0.152612
$426$	−15.8745			−0.769120
$427$	16.1333	+	3.12260i	0.780747	+	0.151113i
$428$			1.67827i			0.0811223i
$429$		0			0
$430$			5.08038i			0.244998i
$431$		−	12.1194i		−	0.583769i	−0.956454	−	0.291884i	$-0.905718\pi$
$431$		−	12.1194i		−	0.583769i	0.956454	−	0.291884i	$-0.0942823\pi$
$432$			15.6103i			0.751050i
$433$			30.5842i			1.46978i	0.678184	+	0.734892i	$0.262767\pi$
$433$			30.5842i			1.46978i	−0.678184	+	0.734892i	$0.737233\pi$
$434$	−13.1996	−	2.55478i	−0.633601	−	0.122633i
$435$			8.78927i			0.421413i
$436$			6.82204i			0.326716i
$437$	31.6890			1.51589
$438$	−7.68862			−0.367377
$439$	−10.8777			−0.519165			−0.259583	−	0.965721i	$-0.583585\pi$
$439$	−10.8777			−0.519165			−0.259583	+	0.965721i	$0.583585\pi$
$440$		0			0
$441$	8.40747	+	3.38119i	0.400356	+	0.161009i
$442$			14.4922i			0.689325i
$443$	−26.2881			−1.24898			−0.624492	−	0.781032i	$-0.714694\pi$
$443$	−26.2881			−1.24898			−0.624492	+	0.781032i	$0.714694\pi$
$444$		−	2.57175i		−	0.122050i
$445$	3.63124			0.172137
$446$	−6.11710			−0.289653
$447$	12.6355			0.597641
$448$	−23.0732	−	4.46581i	−1.09011	−	0.210990i
$449$	11.3177			0.534118			0.267059	−	0.963680i	$-0.413948\pi$
$449$	11.3177			0.534118			0.267059	+	0.963680i	$0.413948\pi$
$450$		−	1.10318i		−	0.0520044i
$451$		0			0
$452$	−8.16425			−0.384014
$453$	22.3564			1.05039
$454$			10.3383i			0.485201i
$455$	3.11600	−	16.0992i	0.146080	−	0.754743i
$456$	−32.8515			−1.53841
$457$		−	10.6210i		−	0.496831i	−0.968654	−	0.248416i	$-0.920090\pi$
$457$		−	10.6210i		−	0.496831i	0.968654	−	0.248416i	$-0.0799099\pi$
$458$	−33.1858			−1.55067
$459$		−	25.4538i		−	1.18808i
$460$			4.49531i			0.209595i
$461$	26.2088			1.22067			0.610333	−	0.792145i	$-0.291036\pi$
$461$	26.2088			1.22067			0.610333	+	0.792145i	$0.291036\pi$
$462$		0			0
$463$	8.14781			0.378661			0.189330	−	0.981913i	$-0.439368\pi$
$463$	8.14781			0.378661			0.189330	+	0.981913i	$0.439368\pi$
$464$			7.85107i			0.364477i
$465$		−	12.8807i		−	0.597326i
$466$	−16.2181			−0.751287
$467$		−	18.1602i		−	0.840355i	−0.907442	−	0.420177i	$-0.861968\pi$
$467$		−	18.1602i		−	0.840355i	0.907442	−	0.420177i	$-0.138032\pi$
$468$	1.64377			0.0759834
$469$	30.0256	+	5.81144i	1.38645	+	0.268348i
$470$		−	5.39707i		−	0.248948i
$471$	−26.2630			−1.21013
$472$	32.9662			1.51739
$473$		0			0
$474$		−	7.74321i		−	0.355657i
$475$	5.69972			0.261521
$476$	5.76283	+	1.11539i	0.264139	+	0.0511240i
$477$	−3.24107			−0.148398
$478$	9.17725			0.419758
$479$	12.2615			0.560244			0.280122	−	0.959964i	$-0.409625\pi$
$479$	12.2615			0.560244			0.280122	+	0.959964i	$0.409625\pi$
$480$		−	8.40514i		−	0.383640i
$481$	10.4644			0.477138
$482$		−	1.33510i		−	0.0608122i
$483$	−2.53045	+	13.0739i	−0.115139	+	0.594883i
$484$		0			0
$485$	24.4068			1.10826
$486$	15.1599			0.687665
$487$	5.86851			0.265928			0.132964	−	0.991121i	$-0.457551\pi$
$487$	5.86851			0.265928			0.132964	+	0.991121i	$0.457551\pi$
$488$			19.0026i			0.860208i
$489$			0.250424i			0.0113246i
$490$	19.0493	+	7.66098i	0.860561	+	0.346088i
$491$			12.6196i			0.569514i	0.958600	+	0.284757i	$0.0919130\pi$
$491$			12.6196i			0.569514i	−0.958600	+	0.284757i	$0.908087\pi$
$492$		−	0.516118i		−	0.0232684i
$493$		−	12.8018i		−	0.576563i
$494$		−	26.2546i		−	1.18125i
$495$		0			0
$496$		−	11.5057i		−	0.516623i
$497$	−25.6854	−	4.97140i	−1.15215	−	0.222998i
$498$	−16.6486			−0.746041
$499$	−18.3676			−0.822248			−0.411124	−	0.911579i	$-0.634864\pi$
$499$	−18.3676			−0.822248			−0.411124	+	0.911579i	$0.634864\pi$
$500$		−	5.02330i		−	0.224649i
$501$			27.0362i			1.20789i
$502$	17.5933			0.785230
$503$	−22.5302			−1.00457			−0.502285	−	0.864702i	$-0.667507\pi$
$503$	−22.5302			−1.00457			−0.502285	+	0.864702i	$0.667507\pi$
$504$	−1.99126	+	10.2881i	−0.0886979	+	0.458269i
$505$			5.17303i			0.230197i
$506$		0			0
$507$			8.16565i			0.362649i
$508$		−	1.96447i		−	0.0871594i
$509$			19.9878i			0.885945i	0.896535	+	0.442972i	$0.146076\pi$
$509$			19.9878i			0.885945i	−0.896535	+	0.442972i	$0.853924\pi$
$510$		−	17.3848i		−	0.769811i
$511$	−12.4405	−	2.40785i	−0.550333	−	0.106517i
$512$		−	24.5395i		−	1.08450i
$513$			46.1129i			2.03593i
$514$	6.23780			0.275137
$515$	7.57599			0.333838
$516$	1.10570			0.0486757
$517$		0			0
$518$	−2.48981	+	12.8639i	−0.109396	+	0.565208i
$519$			12.1440i			0.533063i
$520$	18.9624			0.831557
$521$		−	19.7575i		−	0.865590i	−0.901492	−	0.432795i	$-0.857527\pi$
$521$		−	19.7575i		−	0.865590i	0.901492	−	0.432795i	$-0.142473\pi$
$522$	4.48883			0.196471
$523$	−14.8782			−0.650577			−0.325289	−	0.945615i	$-0.605461\pi$
$523$	−14.8782			−0.650577			−0.325289	+	0.945615i	$0.605461\pi$
$524$	−4.06755			−0.177692
$525$	−0.455138	+	2.35153i	−0.0198638	+	0.102629i
$526$	−16.2860			−0.710104
$527$			18.7610i			0.817242i
$528$		0			0
$529$	−8.14590			−0.354169
$530$	−7.34349			−0.318981
$531$		−	13.9489i		−	0.605329i
$532$	−10.4401	−	2.02068i	−0.452637	−	0.0876077i
$533$	2.10008			0.0909645
$534$			2.44316i			0.105726i
$535$	8.19188			0.354166
$536$			35.3655i			1.52756i
$537$		−	30.6623i		−	1.32318i
$538$	−8.47853			−0.365535
$539$		0			0
$540$	−6.54144			−0.281499
$541$		−	27.8718i		−	1.19830i	−0.800635	−	0.599152i	$-0.795505\pi$
$541$		−	27.8718i		−	1.19830i	0.800635	−	0.599152i	$-0.204495\pi$
$542$		−	15.6514i		−	0.672284i
$543$	17.7182			0.760360
$544$			12.2423i			0.524884i
$545$	33.2993			1.42639
$546$	10.8318	+	2.09650i	0.463559	+	0.0897218i
$547$		−	33.3955i		−	1.42789i	−0.700203	−	0.713944i	$-0.746907\pi$
$547$		−	33.3955i		−	1.42789i	0.700203	−	0.713944i	$-0.253093\pi$
$548$	0.377999			0.0161473
$549$	8.04049			0.343160
$550$		0			0
$551$			23.1921i			0.988018i
$552$	−15.3990			−0.655427
$553$	2.42494	−	12.5288i	0.103119	−	0.532778i
$554$	25.3476			1.07692
$555$	−12.5531			−0.532849
$556$	−1.84213			−0.0781236
$557$		−	35.0500i		−	1.48512i	−0.669782	−	0.742558i	$-0.733612\pi$
$557$		−	35.0500i		−	1.48512i	0.669782	−	0.742558i	$-0.266388\pi$
$558$	−6.57837			−0.278485
$559$			4.49908i			0.190291i
$560$	−3.33893	+	17.2510i	−0.141096	+	0.728990i
$561$		0			0
$562$	6.75301			0.284859
$563$	9.38587			0.395567			0.197784	−	0.980246i	$-0.436626\pi$
$563$	9.38587			0.395567			0.197784	+	0.980246i	$0.436626\pi$
$564$	−1.17462			−0.0494606
$565$			39.8508i			1.67654i
$566$		−	30.3818i		−	1.27704i
$567$	−8.93673	−	1.72970i	−0.375308	−	0.0726407i
$568$		−	30.2535i		−	1.26941i
$569$			38.2790i			1.60474i	0.596826	+	0.802370i	$0.296428\pi$
$569$			38.2790i			1.60474i	−0.596826	+	0.802370i	$0.703572\pi$
$570$			31.4948i			1.31917i
$571$		−	15.2363i		−	0.637620i	−0.947819	−	0.318810i	$-0.896717\pi$
$571$		−	15.2363i		−	0.637620i	0.947819	−	0.318810i	$-0.103283\pi$
$572$		0			0
$573$		−	15.3603i		−	0.641687i
$574$	−0.499672	+	2.58162i	−0.0208559	+	0.107755i
$575$	2.67173			0.111419
$576$	−11.4991			−0.479131
$577$		−	38.0950i		−	1.58592i	−0.609276	−	0.792958i	$-0.708540\pi$
$577$		−	38.0950i		−	1.58592i	0.609276	−	0.792958i	$-0.291460\pi$
$578$			4.42332i			0.183986i
$579$	17.7710			0.738539
$580$	−3.28997			−0.136609
$581$	−26.9380	−	5.21384i	−1.11758	−	0.216306i
$582$			16.4213i			0.680685i
$583$		0			0
$584$		−	14.6530i		−	0.606343i
$585$		−	8.02348i		−	0.331730i
$586$		−	13.1250i		−	0.542188i
$587$			4.22984i			0.174584i	0.996183	+	0.0872920i	$0.0278213\pi$
$587$			4.22984i			0.174584i	−0.996183	+	0.0872920i	$0.972179\pi$
$588$	1.66734	−	4.14592i	0.0687601	−	0.170975i
$589$		−	33.9880i		−	1.40045i
$590$		−	31.6048i		−	1.30115i
$591$	−14.1683			−0.582807
$592$	−11.2131			−0.460857
$593$	−12.7441			−0.523338			−0.261669	−	0.965158i	$-0.584273\pi$
$593$	−12.7441			−0.523338			−0.261669	+	0.965158i	$0.584273\pi$
$594$		0			0
$595$	5.44440	−	28.1292i	0.223198	−	1.15318i
$596$			4.72969i			0.193736i
$597$	−23.5555			−0.964064
$598$		−	12.3067i		−	0.503260i
$599$	16.2990			0.665960			0.332980	−	0.942934i	$-0.391946\pi$
$599$	16.2990			0.665960			0.332980	+	0.942934i	$0.391946\pi$
$600$	−2.76974			−0.113074
$601$	−25.9155			−1.05712			−0.528558	−	0.848897i	$-0.677267\pi$
$601$	−25.9155			−1.05712			−0.528558	+	0.848897i	$0.677267\pi$
$602$	−5.53070	−	1.07047i	−0.225415	−	0.0436289i
$603$	14.9641			0.609383
$604$			8.36837i			0.340504i
$605$		0			0
$606$	−3.48050			−0.141386
$607$	−4.71315			−0.191301			−0.0956505	−	0.995415i	$-0.530493\pi$
$607$	−4.71315			−0.191301			−0.0956505	+	0.995415i	$0.530493\pi$
$608$		−	22.1785i		−	0.899458i
$609$	−9.56835	−	1.85195i	−0.387729	−	0.0750449i
$610$	18.2178			0.737619
$611$		−	4.77953i		−	0.193359i
$612$	2.87206			0.116096
$613$		−	37.5760i		−	1.51768i	−0.651278	−	0.758840i	$-0.725767\pi$
$613$		−	37.5760i		−	1.51768i	0.651278	−	0.758840i	$-0.274233\pi$
$614$			14.9620i			0.603818i
$615$	−2.51924			−0.101586
$616$		0			0
$617$	−2.93775			−0.118269			−0.0591346	−	0.998250i	$-0.518834\pi$
$617$	−2.93775			−0.118269			−0.0591346	+	0.998250i	$0.518834\pi$
$618$			5.09725i			0.205041i
$619$			31.0117i			1.24647i	0.782036	+	0.623233i	$0.214181\pi$
$619$			31.0117i			1.24647i	−0.782036	+	0.623233i	$0.785819\pi$
$620$	4.82144			0.193634
$621$			21.6152i			0.867390i
$622$	−31.7132			−1.27159
$623$	−0.765123	+	3.95311i	−0.0306540	+	0.158378i
$624$			9.44181i			0.377975i
$625$	−27.9855			−1.11942
$626$	−12.2076			−0.487914
$627$		0			0
$628$		−	9.83067i		−	0.392286i
$629$	18.2839			0.729026
$630$	9.86324	+	1.90903i	0.392961	+	0.0760575i
$631$	38.0775			1.51584			0.757920	−	0.652347i	$-0.226216\pi$
$631$	38.0775			1.51584			0.757920	+	0.652347i	$0.226216\pi$
$632$	14.7570			0.587001
$633$	30.1635			1.19889
$634$		−	12.6044i		−	0.500586i
$635$	−9.58886			−0.380522
$636$			1.59825i			0.0633746i
$637$	16.8697	+	6.78440i	0.668402	+	0.268808i
$638$		0			0
$639$	−12.8010			−0.506400
$640$	−13.1820			−0.521066
$641$	7.67316			0.303072			0.151536	−	0.988452i	$-0.451578\pi$
$641$	7.67316			0.303072			0.151536	+	0.988452i	$0.451578\pi$
$642$			5.51163i			0.217527i
$643$		−	2.20666i		−	0.0870221i	−0.999053	−	0.0435110i	$-0.986146\pi$
$643$		−	2.20666i		−	0.0870221i	0.999053	−	0.0435110i	$-0.0138544\pi$
$644$	−4.89377	−	0.947189i	−0.192842	−	0.0373245i
$645$		−	5.39707i		−	0.212509i
$646$		−	45.8730i		−	1.80485i
$647$		−	25.8963i		−	1.01809i	−0.860740	−	0.509045i	$-0.829999\pi$
$647$		−	25.8963i		−	1.01809i	0.860740	−	0.509045i	$-0.170001\pi$
$648$		−	10.5261i		−	0.413504i
$649$		0			0
$650$		−	2.21355i		−	0.0868224i
$651$	14.0224	+	2.71403i	0.549581	+	0.106371i
$652$	−0.0937379			−0.00367106
$653$	29.8983			1.17001			0.585005	−	0.811030i	$-0.301092\pi$
$653$	29.8983			1.17001			0.585005	+	0.811030i	$0.301092\pi$
$654$			22.4043i			0.876078i
$655$			19.8543i			0.775771i
$656$	−2.25033			−0.0878606
$657$	−6.20004			−0.241886
$658$	5.87547	+	1.13720i	0.229050	+	0.0443325i
$659$		−	38.2797i		−	1.49116i	−0.666414	−	0.745582i	$-0.732172\pi$
$659$		−	38.2797i		−	1.49116i	0.666414	−	0.745582i	$-0.267828\pi$
$660$		0			0
$661$		−	47.8663i		−	1.86178i	−0.365297	−	0.930891i	$-0.619032\pi$
$661$		−	47.8663i		−	1.86178i	0.365297	−	0.930891i	$-0.380968\pi$
$662$		−	3.10895i		−	0.120833i
$663$		−	15.3956i		−	0.597916i
$664$		−	31.7288i		−	1.23132i
$665$	−9.86324	+	50.9597i	−0.382480	+	1.97613i
$666$			6.41107i			0.248424i
$667$			10.8712i			0.420936i
$668$	−10.1201			−0.391558
$669$	6.49842			0.251243
$670$	33.9050			1.30986
$671$		0			0
$672$	9.15017	+	1.77101i	0.352975	+	0.0683183i
$673$		−	36.4467i		−	1.40492i	−0.711724	−	0.702459i	$-0.752085\pi$
$673$		−	36.4467i		−	1.40492i	0.711724	−	0.702459i	$-0.247915\pi$
$674$	28.8430			1.11099
$675$			3.88782i			0.149642i
$676$	−3.05654			−0.117559
$677$	17.0978			0.657121			0.328561	−	0.944483i	$-0.393437\pi$
$677$	17.0978			0.657121			0.328561	+	0.944483i	$0.393437\pi$
$678$	−26.8123			−1.02972
$679$	−5.14266	+	26.5702i	−0.197357	+	1.01967i
$680$	33.1319			1.27055
$681$		−	10.9828i		−	0.420860i
$682$		0			0
$683$	−18.7353			−0.716886			−0.358443	−	0.933552i	$-0.616692\pi$
$683$	−18.7353			−0.716886			−0.358443	+	0.933552i	$0.616692\pi$
$684$	−5.20312			−0.198946
$685$		−	1.84506i		−	0.0704963i
$686$	−12.3539	+	19.1236i	−0.471672	+	0.730144i
$687$	35.2545			1.34504
$688$		−	4.82097i		−	0.183798i
$689$	−6.50325			−0.247754
$690$			14.7631i			0.562021i
$691$		−	42.2501i		−	1.60727i	−0.595123	−	0.803635i	$-0.702897\pi$
$691$		−	42.2501i		−	1.60727i	0.595123	−	0.803635i	$-0.297103\pi$
$692$	−4.54570			−0.172802
$693$		0			0
$694$	5.80354			0.220299
$695$			8.99168i			0.341074i
$696$		−	11.2701i		−	0.427190i
$697$	3.66934			0.138986
$698$			20.2359i			0.765941i
$699$	17.2290			0.651662
$700$	−0.880216	−	0.170366i	−0.0332690	−	0.00643921i
$701$		−	8.02644i		−	0.303154i	−0.988445	−	0.151577i	$-0.951565\pi$
$701$		−	8.02644i		−	0.303154i	0.988445	−	0.151577i	$-0.0484352\pi$
$702$	17.9084			0.675909
$703$	−33.1237			−1.24928
$704$		0			0
$705$			5.73350i			0.215936i
$706$	−34.3926			−1.29438
$707$	−5.63157	−	1.08999i	−0.211797	−	0.0409932i
$708$	−6.87850			−0.258510
$709$	−31.9571			−1.20017			−0.600087	−	0.799935i	$-0.704867\pi$
$709$	−31.9571			−1.20017			−0.600087	+	0.799935i	$0.704867\pi$
$710$	−29.0041			−1.08850
$711$		−	6.24405i		−	0.234170i
$712$	−4.65616			−0.174497
$713$		−	15.9318i		−	0.596649i
$714$	18.9258	+	3.66308i	0.708279	+	0.137087i
$715$		0			0
$716$	11.4774			0.428931
$717$	−9.74932			−0.364095
$718$	14.9932			0.559542
$719$		−	43.3512i		−	1.61673i	−0.588683	−	0.808364i	$-0.700353\pi$
$719$		−	43.3512i		−	1.61673i	0.588683	−	0.808364i	$-0.299647\pi$
$720$			8.59752i			0.320411i
$721$	−1.59631	+	8.24752i	−0.0594495	+	0.307154i
$722$			59.7483i			2.22360i
$723$			1.41833i			0.0527481i
$724$			6.63221i			0.246484i
$725$			1.95535i			0.0726198i
$726$		0			0
$727$			5.57920i			0.206921i	0.994634	+	0.103461i	$0.0329915\pi$
$727$			5.57920i			0.206921i	−0.994634	+	0.103461i	$0.967008\pi$
$728$	−3.99549	+	20.6432i	−0.148083	+	0.765090i
$729$	−26.4262			−0.978749
$730$	−14.0478			−0.519933
$731$			7.86096i			0.290748i
$732$		−	3.96495i		−	0.146549i
$733$	−2.34422			−0.0865859			−0.0432930	−	0.999062i	$-0.513785\pi$
$733$	−2.34422			−0.0865859			−0.0432930	+	0.999062i	$0.513785\pi$
$734$	−2.48402			−0.0916868
$735$	−20.2368	−	8.13853i	−0.746445	−	0.300194i
$736$		−	10.3961i		−	0.383205i
$737$		0			0
$738$			1.28662i			0.0473611i
$739$			18.2120i			0.669940i	0.942229	+	0.334970i	$0.108726\pi$
$739$			18.2120i			0.669940i	−0.942229	+	0.334970i	$0.891274\pi$
$740$		−	4.69883i		−	0.172732i
$741$			27.8912i			1.02461i
$742$	1.54732	−	7.99442i	0.0568038	−	0.293484i
$743$			33.4497i			1.22715i	0.789636	+	0.613575i	$0.210269\pi$
$743$			33.4497i			1.22715i	−0.789636	+	0.613575i	$0.789731\pi$
$744$			16.5162i			0.605515i
$745$	23.0863			0.845816
$746$	20.6590			0.756381
$747$	−13.4253			−0.491205
$748$		0			0
$749$	−1.72608	+	8.91801i	−0.0630695	+	0.325857i
$750$		−	16.4971i		−	0.602388i
$751$	−23.7858			−0.867957			−0.433978	−	0.900923i	$-0.642891\pi$
$751$	−23.7858			−0.867957			−0.433978	+	0.900923i	$0.642891\pi$
$752$			5.12149i			0.186761i
$753$	−18.6901			−0.681103
$754$	9.00690			0.328012
$755$	40.8472			1.48658
$756$	1.37832	−	7.12127i	0.0501290	−	0.258998i
$757$	−22.8585			−0.830806			−0.415403	−	0.909638i	$-0.636359\pi$
$757$	−22.8585			−0.830806			−0.415403	+	0.909638i	$0.636359\pi$
$758$			6.73472i			0.244616i
$759$		0			0
$760$	−60.0227			−2.17725
$761$	−10.2065			−0.369985			−0.184993	−	0.982740i	$-0.559226\pi$
$761$	−10.2065			−0.369985			−0.184993	+	0.982740i	$0.559226\pi$
$762$		−	6.45154i		−	0.233715i
$763$	−7.01636	+	36.2510i	−0.254009	+	1.31237i
$764$	5.74963			0.208014
$765$		−	14.0189i		−	0.506856i
$766$	−14.0233			−0.506681
$767$		−	27.9886i		−	1.01061i
$768$			14.3312i			0.517132i
$769$	−17.9851			−0.648559			−0.324280	−	0.945961i	$-0.605122\pi$
$769$	−17.9851			−0.648559			−0.324280	+	0.945961i	$0.605122\pi$
$770$		0			0
$771$	−6.62664			−0.238652
$772$			6.65199i			0.239410i
$773$		−	36.1492i		−	1.30020i	−0.759851	−	0.650098i	$-0.774728\pi$
$773$		−	36.1492i		−	1.30020i	0.759851	−	0.650098i	$-0.225272\pi$
$774$	−2.75638			−0.0990759
$775$		−	2.86556i		−	0.102934i
$776$	−31.2957			−1.12345
$777$	2.64501	−	13.6658i	0.0948892	−	0.490258i
$778$			25.3231i			0.907876i
$779$	−6.64749			−0.238171
$780$	−3.95656			−0.141668
$781$		0			0
$782$		−	21.5028i		−	0.768939i
$783$	−15.8195			−0.565342
$784$	−18.0766	−	7.26979i	−0.645594	−	0.259636i
$785$	−47.9849			−1.71265
$786$	−13.3583			−0.476475
$787$	−30.9744			−1.10412			−0.552059	−	0.833805i	$-0.686158\pi$
$787$	−30.9744			−1.10412			−0.552059	+	0.833805i	$0.686158\pi$
$788$		−	5.30344i		−	0.188927i
$789$	17.3012			0.615940
$790$		−	14.1475i		−	0.503347i
$791$	−43.3832	−	8.39681i	−1.54253	−	0.298556i
$792$		0			0
$793$	16.1333			0.572912
$794$	−31.7282			−1.12599
$795$	7.80126			0.276682
$796$		−	8.81723i		−	0.312518i
$797$			37.2440i			1.31925i	0.751594	+	0.659626i	$0.229285\pi$
$797$			37.2440i			1.31925i	−0.751594	+	0.659626i	$0.770715\pi$
$798$	−34.2865	−	6.63615i	−1.21373	−	0.234917i
$799$		−	8.35099i		−	0.295437i
$800$		−	1.86989i		−	0.0661106i
$801$			1.97014i			0.0696114i
$802$		−	0.226189i		−	0.00798701i
$803$		0			0
$804$		−	7.37912i		−	0.260242i
$805$	−4.62336	+	23.8872i	−0.162952	+	0.841913i
$806$	−13.1996			−0.464936
$807$	9.00705			0.317063
$808$		−	6.63313i		−	0.233353i
$809$			6.95116i			0.244390i	0.992506	+	0.122195i	$0.0389933\pi$
$809$			6.95116i			0.244390i	−0.992506	+	0.122195i	$0.961007\pi$
$810$	−10.0914			−0.354576
$811$	49.4879			1.73775			0.868877	−	0.495028i	$-0.164842\pi$
$811$	49.4879			1.73775			0.868877	+	0.495028i	$0.164842\pi$
$812$	0.693216	−	3.58159i	0.0243271	−	0.125689i
$813$			16.6270i			0.583135i
$814$		0			0
$815$			0.457548i			0.0160272i
$816$			16.4971i			0.577514i
$817$		−	14.2412i		−	0.498235i
$818$			26.6522i			0.931872i
$819$	8.73468	+	1.69060i	0.305214	+	0.0590742i
$820$		−	0.942994i		−	0.0329308i
$821$		−	5.67636i		−	0.198106i	−0.995082	−	0.0990532i	$-0.968419\pi$
$821$		−	5.67636i		−	0.198106i	0.995082	−	0.0990532i	$-0.0315814\pi$
$822$	1.24139			0.0432984
$823$	3.26136			0.113684			0.0568420	−	0.998383i	$-0.481897\pi$
$823$	3.26136			0.113684			0.0568420	+	0.998383i	$0.481897\pi$
$824$	−9.71432			−0.338414
$825$		0			0
$826$	34.4062	+	6.65932i	1.19715	+	0.231707i
$827$		−	22.3699i		−	0.777877i	−0.921264	−	0.388938i	$-0.872842\pi$
$827$		−	22.3699i		−	0.777877i	0.921264	−	0.388938i	$-0.127158\pi$
$828$	−2.43894			−0.0847592
$829$		−	28.8517i		−	1.00206i	−0.865429	−	0.501031i	$-0.832954\pi$
$829$		−	28.8517i		−	1.00206i	0.865429	−	0.501031i	$-0.167046\pi$
$830$	−30.4185			−1.05584
$831$	−26.9277			−0.934112
$832$	−23.0732			−0.799919
$833$	29.4754	+	11.8540i	1.02126	+	0.410716i
$834$	−6.04975			−0.209486
$835$			49.3976i			1.70947i
$836$		0			0
$837$	23.1834			0.801337
$838$	−20.5412			−0.709583
$839$			37.2937i			1.28752i	0.765226	+	0.643761i	$0.222627\pi$
$839$			37.2937i			1.28752i	−0.765226	+	0.643761i	$0.777373\pi$
$840$	4.79297	−	24.7635i	0.165373	−	0.854423i
$841$	21.0437			0.725645
$842$			17.0903i			0.588971i
$843$	−7.17397			−0.247085
$844$			11.2907i			0.388641i
$845$			14.9194i			0.513242i
$846$	2.92820			0.100673
$847$		0			0
$848$	6.96852			0.239300
$849$			32.2756i			1.10770i
$850$		−	3.86759i		−	0.132657i
$851$	−15.5266			−0.532245
$852$			6.31247i			0.216262i
$853$	−18.9742			−0.649664			−0.324832	−	0.945772i	$-0.605308\pi$
$853$	−18.9742			−0.649664			−0.324832	+	0.945772i	$0.605308\pi$
$854$	−3.83861	+	19.8327i	−0.131354	+	0.678660i
$855$			25.3971i			0.868564i
$856$	−10.5040			−0.359021
$857$	30.0580			1.02676			0.513381	−	0.858161i	$-0.328393\pi$
$857$	30.0580			1.02676			0.513381	+	0.858161i	$0.328393\pi$
$858$		0			0
$859$		−	36.6092i		−	1.24909i	−0.780989	−	0.624545i	$-0.785284\pi$
$859$		−	36.6092i		−	1.24909i	0.780989	−	0.624545i	$-0.214716\pi$
$860$	2.02021			0.0688887
$861$	0.530820	−	2.74255i	0.0180903	−	0.0934658i
$862$	14.8983			0.507438
$863$	19.1456			0.651723			0.325862	−	0.945418i	$-0.394346\pi$
$863$	19.1456			0.651723			0.325862	+	0.945418i	$0.394346\pi$
$864$	15.1281			0.514668
$865$			22.1882i			0.754421i
$866$	−37.5971			−1.27760
$867$		−	4.69905i		−	0.159588i
$868$	−1.01591	+	5.24882i	−0.0344821	+	0.178156i
$869$		0			0
$870$	−10.8046			−0.366311
$871$	30.0256			1.01738
$872$	−42.6981			−1.44594
$873$			13.2420i			0.448173i
$874$			38.9552i			1.31768i
$875$	5.16639	−	26.6928i	0.174656	−	0.902383i
$876$			3.05738i			0.103299i
$877$			8.20800i			0.277164i	0.990351	+	0.138582i	$0.0442545\pi$
$877$			8.20800i			0.277164i	−0.990351	+	0.138582i	$0.955745\pi$
$878$		−	13.3719i		−	0.451281i
$879$			13.9431i			0.470291i
$880$		0			0
$881$			17.7233i			0.597113i	0.954392	+	0.298557i	$0.0965052\pi$
$881$			17.7233i			0.597113i	−0.954392	+	0.298557i	$0.903495\pi$
$882$	−4.15649	+	10.3353i	−0.139956	+	0.348007i
$883$	53.6778			1.80640			0.903202	−	0.429216i	$-0.141210\pi$
$883$	53.6778			1.80640			0.903202	+	0.429216i	$0.141210\pi$
$884$	5.76283			0.193825
$885$			33.5749i			1.12861i
$886$		−	32.3158i		−	1.08567i
$887$	2.92873			0.0983370			0.0491685	−	0.998790i	$-0.484343\pi$
$887$	2.92873			0.0983370			0.0491685	+	0.998790i	$0.484343\pi$
$888$	16.0962			0.540154
$889$	2.02043	−	10.4388i	0.0677631	−	0.350107i
$890$			4.46387i			0.149629i
$891$		0			0
$892$			2.43246i			0.0814449i
$893$			15.1289i			0.506270i
$894$			15.5328i			0.519496i
$895$		−	56.0228i		−	1.87264i
$896$	2.77754	−	14.3505i	0.0927909	−	0.479416i
$897$			13.0739i			0.436525i
$898$			13.9129i			0.464278i
$899$	11.6599			0.388881
$900$	−0.438679			−0.0146226
$901$	−11.3627			−0.378547
$902$		0			0
$903$	5.87547	+	1.13720i	0.195523	+	0.0378435i
$904$		−	51.0988i		−	1.69952i
$905$	32.3727			1.07611
$906$			27.4826i			0.913050i
$907$	35.6229			1.18284			0.591419	−	0.806365i	$-0.298568\pi$
$907$	35.6229			1.18284			0.591419	+	0.806365i	$0.298568\pi$
$908$	4.11103			0.136429
$909$	−2.80664			−0.0930905
$910$	19.7907	+	3.83049i	0.656056	+	0.126979i
$911$	51.4959			1.70614			0.853068	−	0.521800i	$-0.174739\pi$
$911$	51.4959			1.70614			0.853068	+	0.521800i	$0.174739\pi$
$912$		−	29.8866i		−	0.989646i
$913$		0			0
$914$	13.0564			0.431868
$915$	−19.3535			−0.639806
$916$			13.1963i			0.436019i
$917$	−21.6142	−	4.18342i	−0.713763	−	0.138149i
$918$	31.2902			1.03273
$919$			18.5014i			0.610306i	0.952303	+	0.305153i	$0.0987076\pi$
$919$			18.5014i			0.610306i	−0.952303	+	0.305153i	$0.901292\pi$
$920$	−28.1355			−0.927598
$921$		−	15.8947i		−	0.523748i
$922$			32.2184i			1.06106i
$923$	−25.6854			−0.845445
$924$		0			0
$925$	−2.79268			−0.0918229
$926$			10.0161i			0.329149i
$927$			4.11037i			0.135002i
$928$	7.60857			0.249763
$929$			16.2934i			0.534568i	0.963618	+	0.267284i	$0.0861261\pi$
$929$			16.2934i			0.534568i	−0.963618	+	0.267284i	$0.913874\pi$
$930$	15.8342			0.519222
$931$	−53.3985	−	21.4750i	−1.75007	−	0.703816i
$932$			6.44911i			0.211248i
$933$	33.6901			1.10297
$934$	22.3243			0.730474
$935$		0			0
$936$			10.2881i			0.336278i
$937$	43.9101			1.43448			0.717240	−	0.696826i	$-0.245405\pi$
$937$	43.9101			1.43448			0.717240	+	0.696826i	$0.245405\pi$
$938$	−7.14399	+	36.9103i	−0.233259	+	1.20517i
$939$	12.9686			0.423214
$940$	−2.14614			−0.0699995
$941$	−10.0037			−0.326111			−0.163056	−	0.986617i	$-0.552135\pi$
$941$	−10.0037			−0.326111			−0.163056	+	0.986617i	$0.552135\pi$
$942$		−	32.2850i		−	1.05190i
$943$	−3.11599			−0.101471
$944$			29.9910i			0.976124i
$945$	−34.7599	−	6.72778i	−1.13074	−	0.218855i
$946$		0			0
$947$	−33.5561			−1.09043			−0.545214	−	0.838297i	$-0.683552\pi$
$947$	−33.5561			−1.09043			−0.545214	+	0.838297i	$0.683552\pi$
$948$	−3.07909			−0.100004
$949$	−12.4405			−0.403834
$950$			7.00665i			0.227326i
$951$			13.3901i			0.434205i
$952$	−6.98108	+	36.0687i	−0.226258	+	1.16899i
$953$			13.9315i			0.451287i	0.974210	+	0.225643i	$0.0724484\pi$
$953$			13.9315i			0.451287i	−0.974210	+	0.225643i	$0.927552\pi$
$954$		−	3.98423i		−	0.128994i
$955$		−	28.0647i		−	0.908153i
$956$		−	3.64933i		−	0.118028i
$957$		0			0
$958$			15.0731i			0.486988i
$959$	2.00861	+	0.388766i	0.0648614	+	0.0125539i
$960$	27.6785			0.893319
$961$	13.9124			0.448787
$962$			12.8639i			0.414749i
$963$			4.44453i			0.143223i
$964$	−0.530903			−0.0170992
$965$	32.4693			1.04522
$966$	−16.0717	−	3.11067i	−0.517098	−	0.100084i
$967$			21.2211i			0.682423i	0.939987	+	0.341212i	$0.110837\pi$
$967$			21.2211i			0.682423i	−0.939987	+	0.341212i	$0.889163\pi$
$968$		0			0
$969$			48.7325i			1.56551i
$970$			30.0032i			0.963345i
$971$		−	8.08848i		−	0.259572i	−0.991542	−	0.129786i	$-0.958571\pi$
$971$		−	8.08848i		−	0.259572i	0.991542	−	0.129786i	$-0.0414290\pi$
$972$		−	6.02832i		−	0.193358i
$973$	−9.78870	−	1.89460i	−0.313811	−	0.0607381i
$974$			7.21414i			0.231156i
$975$			2.35153i			0.0753092i
$976$	−17.2876			−0.553363
$977$	−40.8199			−1.30594			−0.652972	−	0.757382i	$-0.726478\pi$
$977$	−40.8199			−1.30594			−0.652972	+	0.757382i	$0.726478\pi$
$978$	−0.307845			−0.00984381
$979$		0			0
$980$	3.04639	−	7.57496i	0.0973133	−	0.241973i
$981$			18.0666i			0.576823i
$982$	−15.5132			−0.495047
$983$			55.6262i			1.77420i	0.461576	+	0.887101i	$0.347284\pi$
$983$			55.6262i			1.77420i	−0.461576	+	0.887101i	$0.652716\pi$
$984$	3.23030			0.102978
$985$	−25.8868			−0.824823
$986$	15.7372			0.501174
$987$	−6.24172	−	1.20808i	−0.198676	−	0.0384537i
$988$	−10.4401			−0.332145
$989$		−	6.67550i		−	0.212269i
$990$		0			0
$991$	10.4439			0.331761			0.165880	−	0.986146i	$-0.446953\pi$
$991$	10.4439			0.331761			0.165880	+	0.986146i	$0.446953\pi$
$992$	−11.1503			−0.354024
$993$			3.30275i			0.104809i
$994$	6.11133	−	31.5750i	0.193840	−	1.00150i
$995$	−43.0381			−1.36440
$996$			6.62031i			0.209772i
$997$	15.3425			0.485902			0.242951	−	0.970039i	$-0.421885\pi$
$997$	15.3425			0.485902			0.242951	+	0.970039i	$0.421885\pi$
$998$		−	22.5793i		−	0.714734i
$999$		−	22.5938i		−	0.714838i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.b.f.846.13		16
7.6	odd	2	inner	847.2.b.f.846.14		16
11.2	odd	10		847.2.l.j.524.1		16
11.3	even	5		847.2.l.i.475.4		16
11.4	even	5		77.2.l.b.6.1	✓	16
11.5	even	5		847.2.l.j.118.2		16
11.6	odd	10		847.2.l.e.118.4		16
11.7	odd	10		847.2.l.i.699.3		16
11.8	odd	10		77.2.l.b.13.2	yes	16
11.9	even	5		847.2.l.e.524.3		16
11.10	odd	2	inner	847.2.b.f.846.3		16
33.8	even	10		693.2.bu.d.244.3		16
33.26	odd	10		693.2.bu.d.622.4		16
77.4	even	15		539.2.s.c.215.2		16
77.6	even	10		847.2.l.e.118.3		16
77.13	even	10		847.2.l.j.524.2		16
77.19	even	30		539.2.s.c.178.2		16
77.20	odd	10		847.2.l.e.524.4		16
77.26	odd	30		539.2.s.b.325.2		16
77.27	odd	10		847.2.l.j.118.1		16
77.30	odd	30		539.2.s.c.178.1		16
77.37	even	15		539.2.s.b.325.1		16
77.41	even	10		77.2.l.b.13.1	yes	16
77.48	odd	10		77.2.l.b.6.2	yes	16
77.52	even	30		539.2.s.b.68.1		16
77.59	odd	30		539.2.s.c.215.1		16
77.62	even	10		847.2.l.i.699.4		16
77.69	odd	10		847.2.l.i.475.3		16
77.74	odd	30		539.2.s.b.68.2		16
77.76	even	2	inner	847.2.b.f.846.4		16
231.41	odd	10		693.2.bu.d.244.4		16
231.125	even	10		693.2.bu.d.622.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.l.b.6.1	✓	16	11.4	even	5
77.2.l.b.6.2	yes	16	77.48	odd	10
77.2.l.b.13.1	yes	16	77.41	even	10
77.2.l.b.13.2	yes	16	11.8	odd	10
539.2.s.b.68.1		16	77.52	even	30
539.2.s.b.68.2		16	77.74	odd	30
539.2.s.b.325.1		16	77.37	even	15
539.2.s.b.325.2		16	77.26	odd	30
539.2.s.c.178.1		16	77.30	odd	30
539.2.s.c.178.2		16	77.19	even	30
539.2.s.c.215.1		16	77.59	odd	30
539.2.s.c.215.2		16	77.4	even	15
693.2.bu.d.244.3		16	33.8	even	10
693.2.bu.d.244.4		16	231.41	odd	10
693.2.bu.d.622.3		16	231.125	even	10
693.2.bu.d.622.4		16	33.26	odd	10
847.2.b.f.846.3		16	11.10	odd	2	inner
847.2.b.f.846.4		16	77.76	even	2	inner
847.2.b.f.846.13		16	1.1	even	1	trivial
847.2.b.f.846.14		16	7.6	odd	2	inner
847.2.l.e.118.3		16	77.6	even	10
847.2.l.e.118.4		16	11.6	odd	10
847.2.l.e.524.3		16	11.9	even	5
847.2.l.e.524.4		16	77.20	odd	10
847.2.l.i.475.3		16	77.69	odd	10
847.2.l.i.475.4		16	11.3	even	5
847.2.l.i.699.3		16	11.7	odd	10
847.2.l.i.699.4		16	77.62	even	10
847.2.l.j.118.1		16	77.27	odd	10
847.2.l.j.118.2		16	11.5	even	5
847.2.l.j.524.1		16	11.2	odd	10
847.2.l.j.524.2		16	77.13	even	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.22930i q^{2} -1.30593i q^{3} +0.488830 q^{4} -2.38605i q^{5} +1.60537 q^{6} +(2.59754 + 0.502754i) q^{7} +3.05951i q^{8} +1.29456 q^{9} +O(q^{10})\)	\(q+1.22930i q^{2} -1.30593i q^{3} +0.488830 q^{4} -2.38605i q^{5} +1.60537 q^{6} +(2.59754 + 0.502754i) q^{7} +3.05951i q^{8} +1.29456 q^{9} +2.93316 q^{10} -0.638376i q^{12} +2.59754 q^{13} +(-0.618034 + 3.19315i) q^{14} -3.11600 q^{15} -2.78339 q^{16} +4.53853 q^{17} +1.59139i q^{18} -8.22214 q^{19} -1.16637i q^{20} +(0.656560 - 3.39220i) q^{21} -3.85410 q^{23} +3.99549 q^{24} -0.693216 q^{25} +3.19315i q^{26} -5.60837i q^{27} +(1.26976 + 0.245761i) q^{28} -2.82069i q^{29} -3.83049i q^{30} +4.13372i q^{31} +2.69741i q^{32} +5.57920i q^{34} +(1.19959 - 6.19786i) q^{35} +0.632818 q^{36} +4.02859 q^{37} -10.1075i q^{38} -3.39220i q^{39} +7.30013 q^{40} +0.808486 q^{41} +(4.17002 + 0.807107i) q^{42} +1.73205i q^{43} -3.08887i q^{45} -4.73783i q^{46} -1.84002i q^{47} +3.63490i q^{48} +(6.49448 + 2.61185i) q^{49} -0.852168i q^{50} -5.92699i q^{51} +1.26976 q^{52} -2.50361 q^{53} +6.89436 q^{54} +(-1.53818 + 7.94721i) q^{56} +10.7375i q^{57} +3.46747 q^{58} -10.7750i q^{59} -1.52319 q^{60} +6.21100 q^{61} -5.08156 q^{62} +(3.36267 + 0.650844i) q^{63} -8.88269 q^{64} -6.19786i q^{65} +11.5592 q^{67} +2.21857 q^{68} +5.03317i q^{69} +(7.61901 + 1.47466i) q^{70} -9.88834 q^{71} +3.96071i q^{72} -4.78931 q^{73} +4.95233i q^{74} +0.905289i q^{75} -4.01923 q^{76} +4.17002 q^{78} -4.82331i q^{79} +6.64129i q^{80} -3.44045 q^{81} +0.993869i q^{82} -10.3705 q^{83} +(0.320946 - 1.65821i) q^{84} -10.8291i q^{85} -2.12920 q^{86} -3.68361 q^{87} +1.52186i q^{89} +3.79714 q^{90} +(6.74724 + 1.30593i) q^{91} -1.88400 q^{92} +5.39833 q^{93} +2.26193 q^{94} +19.6184i q^{95} +3.52262 q^{96} +10.2290i q^{97} +(-3.21074 + 7.98364i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{9}+O(q^{10}) \) 16 * q - 32 * q^9	\( 16 q - 32 q^{9} + 8 q^{14} - 20 q^{15} + 16 q^{16} - 8 q^{23} - 40 q^{25} - 60 q^{36} - 36 q^{37} - 20 q^{42} + 48 q^{49} + 20 q^{53} - 4 q^{56} + 28 q^{58} - 140 q^{60} + 12 q^{64} - 4 q^{67} + 100 q^{70} + 44 q^{71} - 20 q^{78} - 56 q^{81} - 24 q^{86} + 80 q^{91} - 60 q^{92} - 20 q^{93}+O(q^{100}) \) 16 * q - 32 * q^9 + 8 * q^14 - 20 * q^15 + 16 * q^16 - 8 * q^23 - 40 * q^25 - 60 * q^36 - 36 * q^37 - 20 * q^42 + 48 * q^49 + 20 * q^53 - 4 * q^56 + 28 * q^58 - 140 * q^60 + 12 * q^64 - 4 * q^67 + 100 * q^70 + 44 * q^71 - 20 * q^78 - 56 * q^81 - 24 * q^86 + 80 * q^91 - 60 * q^92 - 20 * q^93

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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