LMFDB - Embedded newform 85.2.d.a.16.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,2,Mod(16,85)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(85, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("85.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.d (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:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			16.6
Root			$0.403032 + 0.403032i$ of defining polynomial
Character	$\chi$	$=$	85.16
Dual form			85.2.d.a.16.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.48119 q^{2} +1.67513i q^{3} +0.193937 q^{4} -1.00000i q^{5} +2.48119i q^{6} -1.28726i q^{7} -2.67513 q^{8} +0.193937 q^{9} -1.48119i q^{10} -0.481194i q^{11} +0.324869i q^{12} -2.15633 q^{13} -1.90668i q^{14} +1.67513 q^{15} -4.35026 q^{16} +(-1.86907 - 3.67513i) q^{17} +0.287258 q^{18} +3.35026 q^{19} -0.193937i q^{20} +2.15633 q^{21} -0.712742i q^{22} +8.24965i q^{23} -4.48119i q^{24} -1.00000 q^{25} -3.19394 q^{26} +5.35026i q^{27} -0.249646i q^{28} +0.649738i q^{29} +2.48119 q^{30} +1.83146i q^{31} -1.09332 q^{32} +0.806063 q^{33} +(-2.76845 - 5.44358i) q^{34} -1.28726 q^{35} +0.0376114 q^{36} +4.31265i q^{37} +4.96239 q^{38} -3.61213i q^{39} +2.67513i q^{40} -11.2750i q^{41} +3.19394 q^{42} +8.15633 q^{43} -0.0933212i q^{44} -0.193937i q^{45} +12.2193i q^{46} -6.54420 q^{47} -7.28726i q^{48} +5.34297 q^{49} -1.48119 q^{50} +(6.15633 - 3.13093i) q^{51} -0.418190 q^{52} -8.57452 q^{53} +7.92478i q^{54} -0.481194 q^{55} +3.44358i q^{56} +5.61213i q^{57} +0.962389i q^{58} +4.96239 q^{59} +0.324869 q^{60} +2.83638i q^{61} +2.71274i q^{62} -0.249646i q^{63} +7.08110 q^{64} +2.15633i q^{65} +1.19394 q^{66} +4.93207 q^{67} +(-0.362481 - 0.712742i) q^{68} -13.8192 q^{69} -1.90668 q^{70} -14.5320i q^{71} -0.518806 q^{72} -13.3503i q^{73} +6.38787i q^{74} -1.67513i q^{75} +0.649738 q^{76} -0.619421 q^{77} -5.35026i q^{78} +9.05571i q^{79} +4.35026i q^{80} -8.38058 q^{81} -16.7005i q^{82} -13.4314 q^{83} +0.418190 q^{84} +(-3.67513 + 1.86907i) q^{85} +12.0811 q^{86} -1.08840 q^{87} +1.28726i q^{88} -16.7816 q^{89} -0.287258i q^{90} +2.77575i q^{91} +1.59991i q^{92} -3.06793 q^{93} -9.69323 q^{94} -3.35026i q^{95} -1.83146i q^{96} -3.66291i q^{97} +7.91397 q^{98} -0.0933212i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} + 2 q^{4} - 6 q^{8} + 2 q^{9} + 8 q^{13} - 6 q^{16} - 2 q^{17} - 10 q^{18} - 8 q^{21} - 6 q^{25} - 20 q^{26} + 4 q^{30} + 6 q^{32} + 4 q^{33} + 6 q^{34} + 4 q^{35} + 22 q^{36} + 8 q^{38} + 20 q^{42}+ \cdots + 86 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 + 2 * q^4 - 6 * q^8 + 2 * q^9 + 8 * q^13 - 6 * q^16 - 2 * q^17 - 10 * q^18 - 8 * q^21 - 6 * q^25 - 20 * q^26 + 4 * q^30 + 6 * q^32 + 4 * q^33 + 6 * q^34 + 4 * q^35 + 22 * q^36 + 8 * q^38 + 20 * q^42 + 28 * q^43 - 20 * q^47 - 14 * q^49 + 2 * q^50 + 16 * q^51 - 28 * q^53 + 8 * q^55 + 8 * q^59 + 12 * q^60 - 22 * q^64 + 8 * q^66 + 12 * q^67 - 34 * q^68 - 24 * q^70 - 14 * q^72 + 24 * q^76 - 28 * q^77 - 26 * q^81 + 4 * q^83 - 12 * q^85 + 8 * q^86 + 32 * q^87 + 4 * q^89 - 36 * q^93 + 8 * q^94 + 86 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.48119			1.04736			0.523681	−	0.851914i	$-0.324558\pi$
$2$	1.48119			1.04736			0.523681	+	0.851914i	$0.324558\pi$
$3$			1.67513i			0.967137i	0.875306	+	0.483569i	$0.160660\pi$
$3$			1.67513i			0.967137i	−0.875306	+	0.483569i	$0.839340\pi$
$4$	0.193937			0.0969683
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$			2.48119i			1.01294i
$7$		−	1.28726i		−	0.486538i	−0.969959	−	0.243269i	$-0.921780\pi$
$7$		−	1.28726i		−	0.486538i	0.969959	−	0.243269i	$-0.0782197\pi$
$8$	−2.67513			−0.945802
$9$	0.193937			0.0646455
$10$		−	1.48119i		−	0.468395i
$11$		−	0.481194i		−	0.145086i	−0.997365	−	0.0725428i	$-0.976889\pi$
$11$		−	0.481194i		−	0.145086i	0.997365	−	0.0725428i	$-0.0231114\pi$
$12$			0.324869i			0.0937816i
$13$	−2.15633			−0.598057			−0.299028	−	0.954244i	$-0.596663\pi$
$13$	−2.15633			−0.598057			−0.299028	+	0.954244i	$0.596663\pi$
$14$		−	1.90668i		−	0.509581i
$15$	1.67513			0.432517
$16$	−4.35026			−1.08757
$17$	−1.86907	−	3.67513i	−0.453315	−	0.891350i
$17$	−1.86907	−	3.67513i	−0.453315	−	0.891350i
$18$	0.287258			0.0677073
$19$	3.35026			0.768603			0.384301	−	0.923208i	$-0.374442\pi$
$19$	3.35026			0.768603			0.384301	+	0.923208i	$0.374442\pi$
$20$		−	0.193937i		−	0.0433655i
$21$	2.15633			0.470549
$22$		−	0.712742i		−	0.151957i
$23$			8.24965i			1.72017i	0.510151	+	0.860085i	$0.329590\pi$
$23$			8.24965i			1.72017i	−0.510151	+	0.860085i	$0.670410\pi$
$24$		−	4.48119i		−	0.914720i
$25$	−1.00000			−0.200000
$26$	−3.19394			−0.626382
$27$			5.35026i			1.02966i
$28$		−	0.249646i		−	0.0471787i
$29$			0.649738i			0.120653i	0.998179	+	0.0603267i	$0.0192142\pi$
$29$			0.649738i			0.120653i	−0.998179	+	0.0603267i	$0.980786\pi$
$30$	2.48119			0.453002
$31$			1.83146i			0.328939i	0.986382	+	0.164470i	$0.0525912\pi$
$31$			1.83146i			0.328939i	−0.986382	+	0.164470i	$0.947409\pi$
$32$	−1.09332			−0.193274
$33$	0.806063			0.140318
$34$	−2.76845	−	5.44358i	−0.474786	−	0.933567i
$35$	−1.28726			−0.217586
$36$	0.0376114			0.00626857
$37$			4.31265i			0.708995i	0.935057	+	0.354498i	$0.115348\pi$
$37$			4.31265i			0.708995i	−0.935057	+	0.354498i	$0.884652\pi$
$38$	4.96239			0.805006
$39$		−	3.61213i		−	0.578403i
$40$			2.67513i			0.422975i
$41$		−	11.2750i		−	1.76087i	−0.474171	−	0.880433i	$-0.657252\pi$
$41$		−	11.2750i		−	1.76087i	0.474171	−	0.880433i	$-0.342748\pi$
$42$	3.19394			0.492835
$43$	8.15633			1.24383			0.621914	−	0.783086i	$-0.286355\pi$
$43$	8.15633			1.24383			0.621914	+	0.783086i	$0.286355\pi$
$44$		−	0.0933212i		−	0.0140687i
$45$		−	0.193937i		−	0.0289104i
$46$			12.2193i			1.80164i
$47$	−6.54420			−0.954569			−0.477285	−	0.878749i	$-0.658379\pi$
$47$	−6.54420			−0.954569			−0.477285	+	0.878749i	$0.658379\pi$
$48$		−	7.28726i		−	1.05183i
$49$	5.34297			0.763281
$50$	−1.48119			−0.209473
$51$	6.15633	−	3.13093i	0.862058	−	0.438418i
$52$	−0.418190			−0.0579926
$53$	−8.57452			−1.17780			−0.588900	−	0.808206i	$-0.700439\pi$
$53$	−8.57452			−1.17780			−0.588900	+	0.808206i	$0.700439\pi$
$54$			7.92478i			1.07843i
$55$	−0.481194			−0.0648842
$56$			3.44358i			0.460168i
$57$			5.61213i			0.743344i
$58$			0.962389i			0.126368i
$59$	4.96239			0.646048			0.323024	−	0.946391i	$-0.395301\pi$
$59$	4.96239			0.646048			0.323024	+	0.946391i	$0.395301\pi$
$60$	0.324869			0.0419404
$61$			2.83638i			0.363161i	0.983376	+	0.181581i	$0.0581213\pi$
$61$			2.83638i			0.363161i	−0.983376	+	0.181581i	$0.941879\pi$
$62$			2.71274i			0.344519i
$63$		−	0.249646i		−	0.0314525i
$64$	7.08110			0.885138
$65$			2.15633i			0.267459i
$66$	1.19394			0.146963
$67$	4.93207			0.602548			0.301274	−	0.953538i	$-0.402588\pi$
$67$	4.93207			0.602548			0.301274	+	0.953538i	$0.402588\pi$
$68$	−0.362481	−	0.712742i	−0.0439572	−	0.0864327i
$69$	−13.8192			−1.66364
$70$	−1.90668			−0.227892
$71$		−	14.5320i		−	1.72463i	−0.506373	−	0.862314i	$-0.669014\pi$
$71$		−	14.5320i		−	1.72463i	0.506373	−	0.862314i	$-0.330986\pi$
$72$	−0.518806			−0.0611418
$73$		−	13.3503i		−	1.56253i	−0.624200	−	0.781265i	$-0.714575\pi$
$73$		−	13.3503i		−	1.56253i	0.624200	−	0.781265i	$-0.285425\pi$
$74$			6.38787i			0.742575i
$75$		−	1.67513i		−	0.193427i
$76$	0.649738			0.0745301
$77$	−0.619421			−0.0705896
$78$		−	5.35026i		−	0.605798i
$79$			9.05571i			1.01885i	0.860516	+	0.509423i	$0.170141\pi$
$79$			9.05571i			1.01885i	−0.860516	+	0.509423i	$0.829859\pi$
$80$			4.35026i			0.486374i
$81$	−8.38058			−0.931175
$82$		−	16.7005i		−	1.84426i
$83$	−13.4314			−1.47428			−0.737142	−	0.675738i	$-0.763825\pi$
$83$	−13.4314			−1.47428			−0.737142	+	0.675738i	$0.763825\pi$
$84$	0.418190			0.0456283
$85$	−3.67513	+	1.86907i	−0.398624	+	0.202729i
$86$	12.0811			1.30274
$87$	−1.08840			−0.116688
$88$			1.28726i			0.137222i
$89$	−16.7816			−1.77885			−0.889424	−	0.457082i	$-0.848894\pi$
$89$	−16.7816			−1.77885			−0.889424	+	0.457082i	$0.848894\pi$
$90$		−	0.287258i		−	0.0302796i
$91$			2.77575i			0.290977i
$92$			1.59991i			0.166802i
$93$	−3.06793			−0.318129
$94$	−9.69323			−0.999780
$95$		−	3.35026i		−	0.343730i
$96$		−	1.83146i		−	0.186922i
$97$		−	3.66291i		−	0.371912i	−0.982558	−	0.185956i	$-0.940462\pi$
$97$		−	3.66291i		−	0.371912i	0.982558	−	0.185956i	$-0.0595383\pi$
$98$	7.91397			0.799432
$99$		−	0.0933212i		−	0.00937913i
$100$	−0.193937			−0.0193937
$101$	6.85685			0.682282			0.341141	−	0.940012i	$-0.389187\pi$
$101$	6.85685			0.682282			0.341141	+	0.940012i	$0.389187\pi$
$102$	9.11871	−	4.63752i	0.902887	−	0.459183i
$103$	7.04349			0.694016			0.347008	−	0.937862i	$-0.387198\pi$
$103$	7.04349			0.694016			0.347008	+	0.937862i	$0.387198\pi$
$104$	5.76845			0.565643
$105$		−	2.15633i		−	0.210436i
$106$	−12.7005			−1.23358
$107$		−	5.86177i		−	0.566679i	−0.959020	−	0.283340i	$-0.908558\pi$
$107$		−	5.86177i		−	0.566679i	0.959020	−	0.283340i	$-0.0914423\pi$
$108$			1.03761i			0.0998442i
$109$			12.7005i			1.21649i	0.793750	+	0.608245i	$0.208126\pi$
$109$			12.7005i			1.21649i	−0.793750	+	0.608245i	$0.791874\pi$
$110$	−0.712742			−0.0679573
$111$	−7.22425			−0.685696
$112$			5.59991i			0.529142i
$113$			4.88717i			0.459746i	0.973221	+	0.229873i	$0.0738311\pi$
$113$			4.88717i			0.459746i	−0.973221	+	0.229873i	$0.926169\pi$
$114$			8.31265i			0.778551i
$115$	8.24965			0.769283
$116$			0.126008i			0.0116995i
$117$	−0.418190			−0.0386617
$118$	7.35026			0.676646
$119$	−4.73084	+	2.40597i	−0.433675	+	0.220555i
$120$	−4.48119			−0.409075
$121$	10.7685			0.978950
$122$			4.20123i			0.380362i
$123$	18.8872			1.70300
$124$			0.355186i			0.0318967i
$125$			1.00000i			0.0894427i
$126$		−	0.369775i		−	0.0329422i
$127$	1.76845			0.156925			0.0784624	−	0.996917i	$-0.474999\pi$
$127$	1.76845			0.156925			0.0784624	+	0.996917i	$0.474999\pi$
$128$	12.6751			1.12033
$129$			13.6629i			1.20295i
$130$			3.19394i			0.280127i
$131$			11.1065i			0.970379i	0.874409	+	0.485189i	$0.161249\pi$
$131$			11.1065i			0.970379i	−0.874409	+	0.485189i	$0.838751\pi$
$132$	0.156325			0.0136064
$133$		−	4.31265i		−	0.373954i
$134$	7.30536			0.631087
$135$	5.35026			0.460477
$136$	5.00000	+	9.83146i	0.428746	+	0.843040i
$137$	11.7685			1.00545			0.502723	−	0.864447i	$-0.332331\pi$
$137$	11.7685			1.00545			0.502723	+	0.864447i	$0.332331\pi$
$138$	−20.4690			−1.74243
$139$		−	11.7054i		−	0.992843i	−0.868082	−	0.496422i	$-0.834647\pi$
$139$		−	11.7054i		−	0.992843i	0.868082	−	0.496422i	$-0.165353\pi$
$140$	−0.249646			−0.0210990
$141$		−	10.9624i		−	0.923200i
$142$		−	21.5247i		−	1.80631i
$143$			1.03761i			0.0867694i
$144$	−0.843675			−0.0703062
$145$	0.649738			0.0539578
$146$		−	19.7743i		−	1.63654i
$147$			8.95017i			0.738198i
$148$			0.836381i			0.0687501i
$149$	17.1998			1.40906			0.704532	−	0.709672i	$-0.251157\pi$
$149$	17.1998			1.40906			0.704532	+	0.709672i	$0.251157\pi$
$150$		−	2.48119i		−	0.202589i
$151$	−13.5877			−1.10575			−0.552875	−	0.833264i	$-0.686469\pi$
$151$	−13.5877			−1.10575			−0.552875	+	0.833264i	$0.686469\pi$
$152$	−8.96239			−0.726946
$153$	−0.362481	−	0.712742i	−0.0293048	−	0.0576218i
$154$	−0.917483			−0.0739329
$155$	1.83146			0.147106
$156$		−	0.700523i		−	0.0560868i
$157$	−8.57452			−0.684321			−0.342160	−	0.939642i	$-0.611159\pi$
$157$	−8.57452			−0.684321			−0.342160	+	0.939642i	$0.611159\pi$
$158$			13.4133i			1.06710i
$159$		−	14.3634i		−	1.13909i
$160$			1.09332i			0.0864346i
$161$	10.6194			0.836928
$162$	−12.4133			−0.975278
$163$			14.3757i			1.12599i	0.826461	+	0.562994i	$0.190351\pi$
$163$			14.3757i			1.12599i	−0.826461	+	0.562994i	$0.809649\pi$
$164$		−	2.18664i		−	0.170748i
$165$		−	0.806063i		−	0.0627520i
$166$	−19.8945			−1.54411
$167$			7.54912i			0.584169i	0.956393	+	0.292084i	$0.0943488\pi$
$167$			7.54912i			0.584169i	−0.956393	+	0.292084i	$0.905651\pi$
$168$	−5.76845			−0.445046
$169$	−8.35026			−0.642328
$170$	−5.44358	+	2.76845i	−0.417504	+	0.212331i
$171$	0.649738			0.0496867
$172$	1.58181			0.120612
$173$		−	11.8496i		−	0.900905i	−0.892800	−	0.450452i	$-0.851263\pi$
$173$		−	11.8496i		−	0.900905i	0.892800	−	0.450452i	$-0.148737\pi$
$174$	−1.61213			−0.122215
$175$			1.28726i			0.0973075i
$176$			2.09332i			0.157790i
$177$			8.31265i			0.624817i
$178$	−24.8568			−1.86310
$179$	−3.22425			−0.240992			−0.120496	−	0.992714i	$-0.538449\pi$
$179$	−3.22425			−0.240992			−0.120496	+	0.992714i	$0.538449\pi$
$180$		−	0.0376114i		−	0.00280339i
$181$			6.88717i			0.511919i	0.966688	+	0.255960i	$0.0823914\pi$
$181$			6.88717i			0.511919i	−0.966688	+	0.255960i	$0.917609\pi$
$182$			4.11142i			0.304759i
$183$	−4.75131			−0.351227
$184$		−	22.0689i		−	1.62694i
$185$	4.31265			0.317072
$186$	−4.54420			−0.333197
$187$	−1.76845	+	0.899385i	−0.129322	+	0.0657695i
$188$	−1.26916			−0.0925630
$189$	6.88717			0.500968
$190$		−	4.96239i		−	0.360010i
$191$	7.19982			0.520960			0.260480	−	0.965479i	$-0.416119\pi$
$191$	7.19982			0.520960			0.260480	+	0.965479i	$0.416119\pi$
$192$			11.8618i			0.856050i
$193$		−	20.1114i		−	1.44765i	−0.689983	−	0.723826i	$-0.742382\pi$
$193$		−	20.1114i		−	1.44765i	0.689983	−	0.723826i	$-0.257618\pi$
$194$		−	5.42548i		−	0.389527i
$195$	−3.61213			−0.258670
$196$	1.03620			0.0740141
$197$			3.16362i			0.225399i	0.993629	+	0.112699i	$0.0359497\pi$
$197$			3.16362i			0.225399i	−0.993629	+	0.112699i	$0.964050\pi$
$198$		−	0.138227i		−	0.00982335i
$199$		−	21.4944i		−	1.52370i	−0.647756	−	0.761848i	$-0.724292\pi$
$199$		−	21.4944i		−	1.52370i	0.647756	−	0.761848i	$-0.275708\pi$
$200$	2.67513			0.189160
$201$			8.26187i			0.582747i
$202$	10.1563			0.714597
$203$	0.836381			0.0587024
$204$	1.19394	−	0.607202i	0.0835923	−	0.0425127i
$205$	−11.2750			−0.787483
$206$	10.4328			0.726886
$207$			1.59991i			0.111201i
$208$	9.38058			0.650426
$209$		−	1.61213i		−	0.111513i
$210$		−	3.19394i		−	0.220403i
$211$			20.8691i			1.43669i	0.695689	+	0.718343i	$0.255099\pi$
$211$			20.8691i			1.43669i	−0.695689	+	0.718343i	$0.744901\pi$
$212$	−1.66291			−0.114209
$213$	24.3430			1.66795
$214$		−	8.68243i		−	0.593518i
$215$		−	8.15633i		−	0.556257i
$216$		−	14.3127i		−	0.973853i
$217$	2.35756			0.160041
$218$			18.8119i			1.27411i
$219$	22.3634			1.51118
$220$	−0.0933212			−0.00629171
$221$	4.03032	+	7.92478i	0.271108	+	0.533078i
$222$	−10.7005			−0.718172
$223$	−24.3430			−1.63013			−0.815063	−	0.579373i	$-0.803298\pi$
$223$	−24.3430			−1.63013			−0.815063	+	0.579373i	$0.803298\pi$
$224$			1.40739i			0.0940349i
$225$	−0.193937			−0.0129291
$226$			7.23884i			0.481521i
$227$			11.2120i			0.744169i	0.928199	+	0.372084i	$0.121357\pi$
$227$			11.2120i			0.744169i	−0.928199	+	0.372084i	$0.878643\pi$
$228$			1.08840i			0.0720808i
$229$	12.1563			0.803313			0.401656	−	0.915790i	$-0.368435\pi$
$229$	12.1563			0.803313			0.401656	+	0.915790i	$0.368435\pi$
$230$	12.2193			0.805719
$231$		−	1.03761i		−	0.0682698i
$232$		−	1.73813i		−	0.114114i
$233$			11.9756i			0.784545i	0.919849	+	0.392273i	$0.128311\pi$
$233$			11.9756i			0.784545i	−0.919849	+	0.392273i	$0.871689\pi$
$234$	−0.619421			−0.0404928
$235$			6.54420i			0.426896i
$236$	0.962389			0.0626462
$237$	−15.1695			−0.985365
$238$	−7.00729	+	3.56371i	−0.454215	+	0.231001i
$239$	−8.83638			−0.571578			−0.285789	−	0.958293i	$-0.592256\pi$
$239$	−8.83638			−0.571578			−0.285789	+	0.958293i	$0.592256\pi$
$240$	−7.28726			−0.470390
$241$		−	0.261865i		−	0.0168682i	−0.999964	−	0.00843411i	$-0.997315\pi$
$241$		−	0.261865i		−	0.0168682i	0.999964	−	0.00843411i	$-0.00268469\pi$
$242$	15.9502			1.02532
$243$			2.01222i			0.129084i
$244$			0.550078i			0.0352151i
$245$		−	5.34297i		−	0.341350i
$246$	27.9756			1.78366
$247$	−7.22425			−0.459668
$248$		−	4.89938i		−	0.311111i
$249$		−	22.4993i		−	1.42583i
$250$			1.48119i			0.0936790i
$251$	−23.6629			−1.49359			−0.746795	−	0.665054i	$-0.768408\pi$
$251$	−23.6629			−1.49359			−0.746795	+	0.665054i	$0.768408\pi$
$252$		−	0.0484156i		−	0.00304989i
$253$	3.96968			0.249572
$254$	2.61942			0.164357
$255$	−3.13093	−	6.15633i	−0.196067	−	0.385524i
$256$	4.61213			0.288258
$257$	19.2447			1.20045			0.600226	−	0.799830i	$-0.295077\pi$
$257$	19.2447			1.20045			0.600226	+	0.799830i	$0.295077\pi$
$258$			20.2374i			1.25993i
$259$	5.55149			0.344953
$260$			0.418190i			0.0259351i
$261$			0.126008i			0.00779970i
$262$			16.4509i			1.01634i
$263$	−17.2447			−1.06336			−0.531678	−	0.846947i	$-0.678438\pi$
$263$	−17.2447			−1.06336			−0.531678	+	0.846947i	$0.678438\pi$
$264$	−2.15633			−0.132713
$265$			8.57452i			0.526728i
$266$		−	6.38787i		−	0.391666i
$267$		−	28.1114i		−	1.72039i
$268$	0.956509			0.0584281
$269$			26.6253i			1.62337i	0.584093	+	0.811687i	$0.301450\pi$
$269$			26.6253i			1.62337i	−0.584093	+	0.811687i	$0.698550\pi$
$270$	7.92478			0.482287
$271$	−6.70052			−0.407028			−0.203514	−	0.979072i	$-0.565236\pi$
$271$	−6.70052			−0.407028			−0.203514	+	0.979072i	$0.565236\pi$
$272$	8.13093	+	15.9878i	0.493010	+	0.969402i
$273$	−4.64974			−0.281415
$274$	17.4314			1.05307
$275$			0.481194i			0.0290171i
$276$	−2.68006			−0.161320
$277$		−	16.7005i		−	1.00344i	−0.865031	−	0.501719i	$-0.832701\pi$
$277$		−	16.7005i		−	1.00344i	0.865031	−	0.501719i	$-0.167299\pi$
$278$		−	17.3380i		−	1.03987i
$279$			0.355186i			0.0212644i
$280$	3.44358			0.205793
$281$	−28.4241			−1.69564			−0.847819	−	0.530286i	$-0.822085\pi$
$281$	−28.4241			−1.69564			−0.847819	+	0.530286i	$0.822085\pi$
$282$		−	16.2374i		−	0.966925i
$283$			10.0630i			0.598183i	0.954224	+	0.299092i	$0.0966837\pi$
$283$			10.0630i			0.598183i	−0.954224	+	0.299092i	$0.903316\pi$
$284$		−	2.81828i		−	0.167234i
$285$	5.61213			0.332434
$286$			1.53690i			0.0908790i
$287$	−14.5139			−0.856727
$288$	−0.212035			−0.0124943
$289$	−10.0132	+	13.7381i	−0.589010	+	0.808126i
$290$	0.962389			0.0565134
$291$	6.13586			0.359690
$292$		−	2.58910i		−	0.151516i
$293$	14.3127			0.836154			0.418077	−	0.908412i	$-0.362704\pi$
$293$	14.3127			0.836154			0.418077	+	0.908412i	$0.362704\pi$
$294$			13.2569i			0.773160i
$295$		−	4.96239i		−	0.288921i
$296$		−	11.5369i		−	0.670569i
$297$	2.57452			0.149389
$298$	25.4763			1.47580
$299$		−	17.7889i		−	1.02876i
$300$		−	0.324869i		−	0.0187563i
$301$		−	10.4993i		−	0.605169i
$302$	−20.1260			−1.15812
$303$			11.4861i			0.659860i
$304$	−14.5745			−0.835906
$305$	2.83638			0.162411
$306$	−0.536904	−	1.05571i	−0.0306928	−	0.0603509i
$307$	29.2809			1.67115			0.835575	−	0.549376i	$-0.185135\pi$
$307$	29.2809			1.67115			0.835575	+	0.549376i	$0.185135\pi$
$308$	−0.120128			−0.00684495
$309$			11.7988i			0.671209i
$310$	2.71274			0.154073
$311$			4.54183i			0.257543i	0.991674	+	0.128772i	$0.0411035\pi$
$311$			4.54183i			0.257543i	−0.991674	+	0.128772i	$0.958897\pi$
$312$			9.66291i			0.547055i
$313$		−	0.826531i		−	0.0467183i	−0.999727	−	0.0233592i	$-0.992564\pi$
$313$		−	0.826531i		−	0.0467183i	0.999727	−	0.0233592i	$-0.00743613\pi$
$314$	−12.7005			−0.716732
$315$	−0.249646			−0.0140660
$316$			1.75623i			0.0987958i
$317$		−	32.2374i		−	1.81063i	−0.424736	−	0.905317i	$-0.639633\pi$
$317$		−	32.2374i		−	1.81063i	0.424736	−	0.905317i	$-0.360367\pi$
$318$		−	21.2750i		−	1.19304i
$319$	0.312650			0.0175051
$320$		−	7.08110i		−	0.395846i
$321$	9.81924			0.548056
$322$	15.7294			0.876567
$323$	−6.26187	−	12.3127i	−0.348419	−	0.685094i
$324$	−1.62530			−0.0902945
$325$	2.15633			0.119611
$326$			21.2931i			1.17932i
$327$	−21.2750			−1.17651
$328$			30.1622i			1.66543i
$329$			8.42407i			0.464434i
$330$		−	1.19394i		−	0.0657240i
$331$	−6.82653			−0.375220			−0.187610	−	0.982244i	$-0.560074\pi$
$331$	−6.82653			−0.375220			−0.187610	+	0.982244i	$0.560074\pi$
$332$	−2.60483			−0.142959
$333$			0.836381i			0.0458334i
$334$			11.1817i			0.611836i
$335$		−	4.93207i		−	0.269468i
$336$	−9.38058			−0.511753
$337$			18.0508i			0.983289i	0.870796	+	0.491644i	$0.163604\pi$
$337$			18.0508i			0.983289i	−0.870796	+	0.491644i	$0.836396\pi$
$338$	−12.3684			−0.672750
$339$	−8.18664			−0.444637
$340$	−0.712742	+	0.362481i	−0.0386539	+	0.0196583i
$341$	0.881286			0.0477243
$342$	0.962389			0.0520400
$343$		−	15.8886i		−	0.857903i
$344$	−21.8192			−1.17641
$345$			13.8192i			0.744003i
$346$		−	17.5515i		−	0.943574i
$347$		−	18.3512i		−	0.985145i	−0.870271	−	0.492572i	$-0.836057\pi$
$347$		−	18.3512i		−	0.985145i	0.870271	−	0.492572i	$-0.163943\pi$
$348$	−0.211080			−0.0113151
$349$	−13.6023			−0.728113			−0.364057	−	0.931377i	$-0.618609\pi$
$349$	−13.6023			−0.728113			−0.364057	+	0.931377i	$0.618609\pi$
$350$			1.90668i			0.101916i
$351$		−	11.5369i		−	0.615794i
$352$			0.526100i			0.0280412i
$353$	27.4010			1.45841			0.729205	−	0.684295i	$-0.239890\pi$
$353$	27.4010			1.45841			0.729205	+	0.684295i	$0.239890\pi$
$354$			12.3127i			0.654410i
$355$	−14.5320			−0.771277
$356$	−3.25457			−0.172492
$357$	−4.03032	−	7.92478i	−0.213307	−	0.419424i
$358$	−4.77575			−0.252406
$359$	−9.08840			−0.479667			−0.239834	−	0.970814i	$-0.577093\pi$
$359$	−9.08840			−0.479667			−0.239834	+	0.970814i	$0.577093\pi$
$360$			0.518806i			0.0273435i
$361$	−7.77575			−0.409250
$362$			10.2012i			0.536165i
$363$			18.0386i			0.946779i
$364$			0.538319i			0.0282156i
$365$	−13.3503			−0.698785
$366$	−7.03761			−0.367862
$367$		−	12.7635i		−	0.666251i	−0.942883	−	0.333125i	$-0.891897\pi$
$367$		−	12.7635i		−	0.666251i	0.942883	−	0.333125i	$-0.108103\pi$
$368$		−	35.8881i		−	1.87080i
$369$		−	2.18664i		−	0.113832i
$370$	6.38787			0.332090
$371$			11.0376i			0.573044i
$372$	−0.594984			−0.0308485
$373$	10.0957			0.522735			0.261368	−	0.965239i	$-0.415827\pi$
$373$	10.0957			0.522735			0.261368	+	0.965239i	$0.415827\pi$
$374$	−2.61942	+	1.33216i	−0.135447	+	0.0688845i
$375$	−1.67513			−0.0865034
$376$	17.5066			0.902833
$377$		−	1.40105i		−	0.0721576i
$378$	10.2012			0.524695
$379$			9.18172i			0.471633i	0.971798	+	0.235817i	$0.0757765\pi$
$379$			9.18172i			0.471633i	−0.971798	+	0.235817i	$0.924224\pi$
$380$		−	0.649738i		−	0.0333309i
$381$			2.96239i			0.151768i
$382$	10.6643			0.545634
$383$	−1.83383			−0.0937041			−0.0468521	−	0.998902i	$-0.514919\pi$
$383$	−1.83383			−0.0937041			−0.0468521	+	0.998902i	$0.514919\pi$
$384$			21.2325i			1.08352i
$385$			0.619421i			0.0315686i
$386$		−	29.7889i		−	1.51622i
$387$	1.58181			0.0804079
$388$		−	0.710373i		−	0.0360637i
$389$	11.6570			0.591035			0.295518	−	0.955337i	$-0.404508\pi$
$389$	11.6570			0.591035			0.295518	+	0.955337i	$0.404508\pi$
$390$	−5.35026			−0.270921
$391$	30.3185	−	15.4191i	1.53327	−	0.779780i
$392$	−14.2931			−0.721912
$393$	−18.6048			−0.938490
$394$			4.68594i			0.236074i
$395$	9.05571			0.455642
$396$		−	0.0180984i		−	0.000909478i
$397$		−	9.37470i		−	0.470503i	−0.971935	−	0.235251i	$-0.924409\pi$
$397$		−	9.37470i		−	0.470503i	0.971935	−	0.235251i	$-0.0755913\pi$
$398$		−	31.8373i		−	1.59586i
$399$	7.22425			0.361665
$400$	4.35026			0.217513
$401$			7.93937i			0.396473i	0.980154	+	0.198237i	$0.0635214\pi$
$401$			7.93937i			0.396473i	−0.980154	+	0.198237i	$0.936479\pi$
$402$			12.2374i			0.610347i
$403$		−	3.94921i		−	0.196724i
$404$	1.32979			0.0661597
$405$			8.38058i			0.416434i
$406$	1.23884			0.0614827
$407$	2.07522			0.102865
$408$	−16.4690	+	8.37565i	−0.815336	+	0.414657i
$409$	9.07381			0.448671			0.224335	−	0.974512i	$-0.427979\pi$
$409$	9.07381			0.448671			0.224335	+	0.974512i	$0.427979\pi$
$410$	−16.7005			−0.824780
$411$			19.7137i			0.972405i
$412$	1.36599			0.0672975
$413$		−	6.38787i		−	0.314327i
$414$			2.36977i			0.116468i
$415$			13.4314i			0.659320i
$416$	2.35756			0.115589
$417$	19.6082			0.960216
$418$		−	2.38787i		−	0.116795i
$419$		−	8.99508i		−	0.439438i	−0.975563	−	0.219719i	$-0.929486\pi$
$419$		−	8.99508i		−	0.439438i	0.975563	−	0.219719i	$-0.0705141\pi$
$420$		−	0.418190i		−	0.0204056i
$421$	16.9076			0.824028			0.412014	−	0.911178i	$-0.364826\pi$
$421$	16.9076			0.824028			0.412014	+	0.911178i	$0.364826\pi$
$422$			30.9111i			1.50473i
$423$	−1.26916			−0.0617086
$424$	22.9380			1.11397
$425$	1.86907	+	3.67513i	0.0906631	+	0.178270i
$426$	36.0567			1.74695
$427$	3.65115			0.176692
$428$		−	1.13681i		−	0.0549499i
$429$	−1.73813			−0.0839179
$430$		−	12.0811i		−	0.582602i
$431$			14.6678i			0.706525i	0.935524	+	0.353262i	$0.114928\pi$
$431$			14.6678i			0.706525i	−0.935524	+	0.353262i	$0.885072\pi$
$432$		−	23.2750i		−	1.11982i
$433$	−6.68006			−0.321023			−0.160511	−	0.987034i	$-0.551314\pi$
$433$	−6.68006			−0.321023			−0.160511	+	0.987034i	$0.551314\pi$
$434$	3.49200			0.167621
$435$			1.08840i			0.0521846i
$436$			2.46310i			0.117961i
$437$			27.6385i			1.32213i
$438$	33.1246			1.58275
$439$			9.56959i			0.456732i	0.973575	+	0.228366i	$0.0733382\pi$
$439$			9.56959i			0.456732i	−0.973575	+	0.228366i	$0.926662\pi$
$440$	1.28726			0.0613676
$441$	1.03620			0.0493427
$442$	5.96968	+	11.7381i	0.283949	+	0.558326i
$443$	−14.7915			−0.702764			−0.351382	−	0.936232i	$-0.614288\pi$
$443$	−14.7915			−0.702764			−0.351382	+	0.936232i	$0.614288\pi$
$444$	−1.40105			−0.0664907
$445$			16.7816i			0.795525i
$446$	−36.0567			−1.70733
$447$			28.8119i			1.36276i
$448$		−	9.11520i		−	0.430653i
$449$			10.9018i			0.514486i	0.966347	+	0.257243i	$0.0828140\pi$
$449$			10.9018i			0.514486i	−0.966347	+	0.257243i	$0.917186\pi$
$450$	−0.287258			−0.0135415
$451$	−5.42548			−0.255476
$452$			0.947800i			0.0445808i
$453$		−	22.7612i		−	1.06941i
$454$			16.6072i			0.779415i
$455$	2.77575			0.130129
$456$		−	15.0132i		−	0.703056i
$457$	7.61801			0.356355			0.178178	−	0.983998i	$-0.442980\pi$
$457$	7.61801			0.356355			0.178178	+	0.983998i	$0.442980\pi$
$458$	18.0059			0.841360
$459$	19.6629	−	10.0000i	0.917786	−	0.466760i
$460$	1.59991			0.0745961
$461$	4.57452			0.213056			0.106528	−	0.994310i	$-0.466027\pi$
$461$	4.57452			0.213056			0.106528	+	0.994310i	$0.466027\pi$
$462$		−	1.53690i		−	0.0715032i
$463$	2.56864			0.119375			0.0596873	−	0.998217i	$-0.480990\pi$
$463$	2.56864			0.119375			0.0596873	+	0.998217i	$0.480990\pi$
$464$		−	2.82653i		−	0.131218i
$465$			3.06793i			0.142272i
$466$			17.7381i			0.821703i
$467$	1.55737			0.0720666			0.0360333	−	0.999351i	$-0.488528\pi$
$467$	1.55737			0.0720666			0.0360333	+	0.999351i	$0.488528\pi$
$468$	−0.0811024			−0.00374896
$469$		−	6.34885i		−	0.293163i
$470$			9.69323i			0.447115i
$471$		−	14.3634i		−	0.661832i
$472$	−13.2750			−0.611033
$473$		−	3.92478i		−	0.180461i
$474$	−22.4690			−1.03203
$475$	−3.35026			−0.153721
$476$	−0.917483	+	0.466606i	−0.0420528	+	0.0213868i
$477$	−1.66291			−0.0761395
$478$	−13.0884			−0.598649
$479$		−	20.4060i		−	0.932373i	−0.884687	−	0.466186i	$-0.845628\pi$
$479$		−	20.4060i		−	0.932373i	0.884687	−	0.466186i	$-0.154372\pi$
$480$	−1.83146			−0.0835941
$481$		−	9.29948i		−	0.424020i
$482$		−	0.387873i		−	0.0176671i
$483$			17.7889i			0.809424i
$484$	2.08840			0.0949271
$485$	−3.66291			−0.166324
$486$			2.98049i			0.135198i
$487$			0.162664i			0.00737103i	0.999993	+	0.00368551i	$0.00117314\pi$
$487$			0.162664i			0.00737103i	−0.999993	+	0.00368551i	$0.998827\pi$
$488$		−	7.58769i		−	0.343479i
$489$	−24.0811			−1.08899
$490$		−	7.91397i		−	0.357517i
$491$	12.8364			0.579298			0.289649	−	0.957133i	$-0.406461\pi$
$491$	12.8364			0.579298			0.289649	+	0.957133i	$0.406461\pi$
$492$	3.66291			0.165137
$493$	2.38787	−	1.21440i	0.107544	−	0.0546940i
$494$	−10.7005			−0.481439
$495$	−0.0933212			−0.00419447
$496$		−	7.96731i		−	0.357743i
$497$	−18.7064			−0.839097
$498$		−	33.3258i		−	1.49337i
$499$		−	17.7416i		−	0.794225i	−0.917770	−	0.397113i	$-0.870012\pi$
$499$		−	17.7416i		−	0.794225i	0.917770	−	0.397113i	$-0.129988\pi$
$500$			0.193937i			0.00867311i
$501$	−12.6458			−0.564971
$502$	−35.0494			−1.56433
$503$		−	11.2120i		−	0.499920i	−0.968256	−	0.249960i	$-0.919583\pi$
$503$		−	11.2120i		−	0.499920i	0.968256	−	0.249960i	$-0.0804175\pi$
$504$			0.667837i			0.0297478i
$505$		−	6.85685i		−	0.305126i
$506$	5.87987			0.261392
$507$		−	13.9878i		−	0.621219i
$508$	0.342968			0.0152167
$509$	−6.37328			−0.282491			−0.141245	−	0.989975i	$-0.545111\pi$
$509$	−6.37328			−0.282491			−0.141245	+	0.989975i	$0.545111\pi$
$510$	−4.63752	−	9.11871i	−0.205353	−	0.403783i
$511$	−17.1852			−0.760230
$512$	−18.5188			−0.818423
$513$			17.9248i			0.791398i
$514$	28.5052			1.25731
$515$		−	7.04349i		−	0.310373i
$516$			2.64974i			0.116648i
$517$			3.14903i			0.138494i
$518$	8.22284			0.361291
$519$	19.8496			0.871299
$520$		−	5.76845i		−	0.252963i
$521$		−	0.986826i		−	0.0432336i	−0.999766	−	0.0216168i	$-0.993119\pi$
$521$		−	0.986826i		−	0.0432336i	0.999766	−	0.0216168i	$-0.00688138\pi$
$522$			0.186642i			0.00816911i
$523$	8.99271			0.393224			0.196612	−	0.980481i	$-0.437006\pi$
$523$	8.99271			0.393224			0.196612	+	0.980481i	$0.437006\pi$
$524$			2.15396i			0.0940960i
$525$	−2.15633			−0.0941097
$526$	−25.5428			−1.11372
$527$	6.73084	−	3.42311i	0.293200	−	0.149113i
$528$	−3.50659			−0.152605
$529$	−45.0567			−1.95899
$530$			12.7005i			0.551675i
$531$	0.962389			0.0417641
$532$		−	0.836381i		−	0.0362617i
$533$			24.3127i			1.05310i
$534$		−	41.6385i		−	1.80187i
$535$	−5.86177			−0.253427
$536$	−13.1939			−0.569891
$537$		−	5.40105i		−	0.233072i
$538$			39.4372i			1.70026i
$539$		−	2.57101i		−	0.110741i
$540$	1.03761			0.0446517
$541$		−	37.3766i		−	1.60695i	−0.595341	−	0.803473i	$-0.702983\pi$
$541$		−	37.3766i		−	1.60695i	0.595341	−	0.803473i	$-0.297017\pi$
$542$	−9.92478			−0.426306
$543$	−11.5369			−0.495096
$544$	2.04349	+	4.01810i	0.0876140	+	0.172275i
$545$	12.7005			0.544031
$546$	−6.88717			−0.294743
$547$		−	22.1744i		−	0.948110i	−0.880495	−	0.474055i	$-0.842790\pi$
$547$		−	22.1744i		−	0.948110i	0.880495	−	0.474055i	$-0.157210\pi$
$548$	2.28233			0.0974964
$549$			0.550078i			0.0234768i
$550$			0.712742i			0.0303914i
$551$			2.17679i			0.0927345i
$552$	36.9683			1.57347
$553$	11.6570			0.495707
$554$		−	24.7367i		−	1.05096i
$555$			7.22425i			0.306652i
$556$		−	2.27011i		−	0.0962743i
$557$	1.16950			0.0495533			0.0247766	−	0.999693i	$-0.492113\pi$
$557$	1.16950			0.0495533			0.0247766	+	0.999693i	$0.492113\pi$
$558$			0.526100i			0.0222716i
$559$	−17.5877			−0.743880
$560$	5.59991			0.236639
$561$	−1.50659	−	2.96239i	−0.0636081	−	0.125072i
$562$	−42.1016			−1.77595
$563$	−11.1333			−0.469213			−0.234606	−	0.972090i	$-0.575380\pi$
$563$	−11.1333			−0.469213			−0.234606	+	0.972090i	$0.575380\pi$
$564$		−	2.12601i		−	0.0895211i
$565$	4.88717			0.205605
$566$			14.9053i			0.626515i
$567$			10.7880i			0.453052i
$568$			38.8749i			1.63116i
$569$	16.7005			0.700122			0.350061	−	0.936727i	$-0.386161\pi$
$569$	16.7005			0.700122			0.350061	+	0.936727i	$0.386161\pi$
$570$	8.31265			0.348179
$571$			37.2833i			1.56026i	0.625619	+	0.780129i	$0.284846\pi$
$571$			37.2833i			1.56026i	−0.625619	+	0.780129i	$0.715154\pi$
$572$			0.201231i			0.00841388i
$573$			12.0606i			0.503840i
$574$	−21.4979			−0.897304
$575$		−	8.24965i		−	0.344034i
$576$	1.37328			0.0572202
$577$	−1.63259			−0.0679658			−0.0339829	−	0.999422i	$-0.510819\pi$
$577$	−1.63259			−0.0679658			−0.0339829	+	0.999422i	$0.510819\pi$
$578$	−14.8315	+	20.3488i	−0.616907	+	0.846400i
$579$	33.6893			1.40008
$580$	0.126008			0.00523220
$581$			17.2896i			0.717295i
$582$	9.08840			0.376726
$583$			4.12601i			0.170882i
$584$			35.7137i			1.47784i
$585$			0.418190i			0.0172900i
$586$	21.1998			0.875756
$587$	23.0435			0.951107			0.475553	−	0.879687i	$-0.342248\pi$
$587$	23.0435			0.951107			0.475553	+	0.879687i	$0.342248\pi$
$588$			1.73577i			0.0715818i
$589$			6.13586i			0.252824i
$590$		−	7.35026i		−	0.302605i
$591$	−5.29948			−0.217991
$592$		−	18.7612i		−	0.771079i
$593$	44.2130			1.81561			0.907805	−	0.419393i	$-0.137757\pi$
$593$	44.2130			1.81561			0.907805	+	0.419393i	$0.137757\pi$
$594$	3.81336			0.156464
$595$	2.40597	+	4.73084i	0.0986352	+	0.193946i
$596$	3.33567			0.136635
$597$	36.0059			1.47362
$598$		−	26.3488i		−	1.07748i
$599$	15.4518			0.631345			0.315672	−	0.948868i	$-0.397770\pi$
$599$	15.4518			0.631345			0.315672	+	0.948868i	$0.397770\pi$
$600$			4.48119i			0.182944i
$601$		−	43.0640i		−	1.75662i	−0.478096	−	0.878308i	$-0.658673\pi$
$601$		−	43.0640i		−	1.75662i	0.478096	−	0.878308i	$-0.341327\pi$
$602$		−	15.5515i		−	0.633832i
$603$	0.956509			0.0389521
$604$	−2.63515			−0.107223
$605$		−	10.7685i		−	0.437800i
$606$			17.0132i			0.691113i
$607$			41.5002i			1.68444i	0.539132	+	0.842222i	$0.318753\pi$
$607$			41.5002i			1.68444i	−0.539132	+	0.842222i	$0.681247\pi$
$608$	−3.66291			−0.148551
$609$			1.40105i			0.0567733i
$610$	4.20123			0.170103
$611$	14.1114			0.570887
$612$	−0.0702982	−	0.138227i	−0.00284164	−	0.00558749i
$613$	−27.7137			−1.11935			−0.559673	−	0.828714i	$-0.689073\pi$
$613$	−27.7137			−1.11935			−0.559673	+	0.828714i	$0.689073\pi$
$614$	43.3707			1.75030
$615$		−	18.8872i		−	0.761604i
$616$	1.65703			0.0667637
$617$		−	29.6629i		−	1.19418i	−0.802173	−	0.597092i	$-0.796323\pi$
$617$		−	29.6629i		−	1.19418i	0.802173	−	0.597092i	$-0.203677\pi$
$618$			17.4763i			0.702999i
$619$			26.4422i			1.06280i	0.847121	+	0.531400i	$0.178334\pi$
$619$			26.4422i			1.06280i	−0.847121	+	0.531400i	$0.821666\pi$
$620$	0.355186			0.0142646
$621$	−44.1378			−1.77119
$622$			6.72733i			0.269741i
$623$			21.6023i			0.865477i
$624$			15.7137i			0.629051i
$625$	1.00000			0.0400000
$626$		−	1.22425i		−	0.0489310i
$627$	2.70052			0.107849
$628$	−1.66291			−0.0663574
$629$	15.8496	−	8.06063i	0.631963	−	0.321399i
$630$	−0.369775			−0.0147322
$631$	37.7499			1.50280			0.751400	−	0.659847i	$-0.229379\pi$
$631$	37.7499			1.50280			0.751400	+	0.659847i	$0.229379\pi$
$632$		−	24.2252i		−	0.963627i
$633$	−34.9584			−1.38947
$634$		−	47.7499i		−	1.89639i
$635$		−	1.76845i		−	0.0701789i
$636$		−	2.78560i		−	0.110456i
$637$	−11.5212			−0.456486
$638$	0.463096			0.0183341
$639$		−	2.81828i		−	0.111490i
$640$		−	12.6751i		−	0.501029i
$641$			46.3488i			1.83067i	0.402694	+	0.915335i	$0.368074\pi$
$641$			46.3488i			1.83067i	−0.402694	+	0.915335i	$0.631926\pi$
$642$	14.5442			0.574014
$643$		−	34.9502i		−	1.37830i	−0.724619	−	0.689150i	$-0.757984\pi$
$643$		−	34.9502i		−	1.37830i	0.724619	−	0.689150i	$-0.242016\pi$
$644$	2.05949			0.0811554
$645$	13.6629			0.537977
$646$	−9.27504	−	18.2374i	−0.364922	−	0.717542i
$647$	36.5296			1.43613			0.718064	−	0.695978i	$-0.245029\pi$
$647$	36.5296			1.43613			0.718064	+	0.695978i	$0.245029\pi$
$648$	22.4191			0.880707
$649$		−	2.38787i		−	0.0937322i
$650$	3.19394			0.125276
$651$			3.94921i			0.154782i
$652$			2.78797i			0.109185i
$653$		−	0.926192i		−	0.0362447i	−0.999836	−	0.0181223i	$-0.994231\pi$
$653$		−	0.926192i		−	0.0362447i	0.999836	−	0.0181223i	$-0.00576884\pi$
$654$	−31.5125			−1.23223
$655$	11.1065			0.433967
$656$			49.0494i			1.91506i
$657$		−	2.58910i		−	0.101011i
$658$			12.4777i			0.486431i
$659$	−24.0118			−0.935365			−0.467683	−	0.883896i	$-0.654911\pi$
$659$	−24.0118			−0.935365			−0.467683	+	0.883896i	$0.654911\pi$
$660$		−	0.156325i		−	0.00608495i
$661$	−20.9478			−0.814775			−0.407387	−	0.913255i	$-0.633560\pi$
$661$	−20.9478			−0.814775			−0.407387	+	0.913255i	$0.633560\pi$
$662$	−10.1114			−0.392991
$663$	−13.2750	+	6.75131i	−0.515560	+	0.262199i
$664$	35.9307			1.39438
$665$	−4.31265			−0.167237
$666$			1.23884i			0.0480042i
$667$	−5.36011			−0.207544
$668$			1.46405i			0.0566458i
$669$		−	40.7777i		−	1.57656i
$670$		−	7.30536i		−	0.282231i
$671$	1.36485			0.0526895
$672$	−2.35756			−0.0909447
$673$			0.513881i			0.0198087i	0.999951	+	0.00990433i	$0.00315270\pi$
$673$			0.513881i			0.0198087i	−0.999951	+	0.00990433i	$0.996847\pi$
$674$			26.7367i			1.02986i
$675$		−	5.35026i		−	0.205932i
$676$	−1.61942			−0.0622854
$677$		−	3.67276i		−	0.141156i	−0.997506	−	0.0705778i	$-0.977516\pi$
$677$		−	3.67276i		−	0.141156i	0.997506	−	0.0705778i	$-0.0224843\pi$
$678$	−12.1260			−0.465697
$679$	−4.71511			−0.180949
$680$	9.83146	−	5.00000i	0.377019	−	0.191741i
$681$	−18.7816			−0.719713
$682$	1.30536			0.0499847
$683$			10.5115i			0.402212i	0.979570	+	0.201106i	$0.0644535\pi$
$683$			10.5115i			0.402212i	−0.979570	+	0.201106i	$0.935546\pi$
$684$	0.126008			0.00481804
$685$		−	11.7685i		−	0.449649i
$686$		−	23.5341i		−	0.898535i
$687$			20.3634i			0.776914i
$688$	−35.4821			−1.35274
$689$	18.4894			0.704392
$690$			20.4690i			0.779241i
$691$			25.5940i			0.973643i	0.873502	+	0.486821i	$0.161844\pi$
$691$			25.5940i			0.973643i	−0.873502	+	0.486821i	$0.838156\pi$
$692$		−	2.29806i		−	0.0873592i
$693$	−0.120128			−0.00456330
$694$		−	27.1817i		−	1.03180i
$695$	−11.7054			−0.444013
$696$	2.91160			0.110364
$697$	−41.4372	+	21.0738i	−1.56955	+	0.798227i
$698$	−20.1476			−0.762599
$699$	−20.0606			−0.758763
$700$			0.249646i			0.00943574i
$701$	30.8324			1.16452			0.582262	−	0.813001i	$-0.302168\pi$
$701$	30.8324			1.16452			0.582262	+	0.813001i	$0.302168\pi$
$702$		−	17.0884i		−	0.644960i
$703$			14.4485i			0.544936i
$704$		−	3.40739i		−	0.128421i
$705$	−10.9624			−0.412867
$706$	40.5863			1.52748
$707$		−	8.82653i		−	0.331956i
$708$			1.61213i			0.0605874i
$709$			28.1866i			1.05857i	0.848444	+	0.529286i	$0.177540\pi$
$709$			28.1866i			1.05857i	−0.848444	+	0.529286i	$0.822460\pi$
$710$	−21.5247			−0.807807
$711$			1.75623i			0.0658639i
$712$	44.8930			1.68244
$713$	−15.1089			−0.565831
$714$	−5.96968	−	11.7381i	−0.223410	−	0.439289i
$715$	1.03761			0.0388045
$716$	−0.625301			−0.0233686
$717$		−	14.8021i		−	0.552794i
$718$	−13.4617			−0.502385
$719$			17.7200i			0.660846i	0.943833	+	0.330423i	$0.107191\pi$
$719$			17.7200i			0.660846i	−0.943833	+	0.330423i	$0.892809\pi$
$720$			0.843675i			0.0314419i
$721$		−	9.06679i		−	0.337665i
$722$	−11.5174			−0.428633
$723$	0.438658			0.0163139
$724$			1.33567i			0.0496399i
$725$		−	0.649738i		−	0.0241307i
$726$			26.7186i			0.991621i
$727$	−9.68338			−0.359137			−0.179568	−	0.983746i	$-0.557470\pi$
$727$	−9.68338			−0.359137			−0.179568	+	0.983746i	$0.557470\pi$
$728$		−	7.42548i		−	0.275207i
$729$	−28.5125			−1.05602
$730$	−19.7743			−0.731881
$731$	−15.2447	−	29.9756i	−0.563846	−	1.10869i
$732$	−0.921452			−0.0340579
$733$	32.7123			1.20826			0.604128	−	0.796887i	$-0.293522\pi$
$733$	32.7123			1.20826			0.604128	+	0.796887i	$0.293522\pi$
$734$		−	18.9053i		−	0.697806i
$735$	8.95017			0.330132
$736$		−	9.01951i		−	0.332464i
$737$		−	2.37328i		−	0.0874211i
$738$		−	3.23884i		−	0.119223i
$739$	1.42548			0.0524373			0.0262186	−	0.999656i	$-0.491653\pi$
$739$	1.42548			0.0524373			0.0262186	+	0.999656i	$0.491653\pi$
$740$	0.836381			0.0307460
$741$		−	12.1016i		−	0.444562i
$742$			16.3488i			0.600185i
$743$			16.8143i			0.616857i	0.951247	+	0.308429i	$0.0998031\pi$
$743$			16.8143i			0.616857i	−0.951247	+	0.308429i	$0.900197\pi$
$744$	8.20711			0.300887
$745$		−	17.1998i		−	0.630153i
$746$	14.9537			0.547493
$747$	−2.60483			−0.0953058
$748$	−0.342968	+	0.174424i	−0.0125401	+	0.00637756i
$749$	−7.54561			−0.275711
$750$	−2.48119			−0.0906004
$751$		−	44.0835i		−	1.60863i	−0.594204	−	0.804314i	$-0.702533\pi$
$751$		−	44.0835i		−	1.60863i	0.594204	−	0.804314i	$-0.297467\pi$
$752$	28.4690			1.03816
$753$		−	39.6385i		−	1.44451i
$754$		−	2.07522i		−	0.0755752i
$755$			13.5877i			0.494507i
$756$	1.33567			0.0485780
$757$	−39.8094			−1.44690			−0.723448	−	0.690378i	$-0.757444\pi$
$757$	−39.8094			−1.44690			−0.723448	+	0.690378i	$0.757444\pi$
$758$			13.5999i			0.493971i
$759$			6.64974i			0.241370i
$760$			8.96239i			0.325100i
$761$	2.81591			0.102077			0.0510384	−	0.998697i	$-0.483747\pi$
$761$	2.81591			0.102077			0.0510384	+	0.998697i	$0.483747\pi$
$762$			4.38787i			0.158956i
$763$	16.3488			0.591868
$764$	1.39631			0.0505166
$765$	−0.712742	+	0.362481i	−0.0257693	+	0.0131055i
$766$	−2.71625			−0.0981422
$767$	−10.7005			−0.386374
$768$			7.72592i			0.278785i
$769$	36.0665			1.30059			0.650296	−	0.759681i	$-0.274645\pi$
$769$	36.0665			1.30059			0.650296	+	0.759681i	$0.274645\pi$
$770$			0.917483i			0.0330638i
$771$			32.2374i			1.16100i
$772$		−	3.90034i		−	0.140376i
$773$	11.6180			0.417871			0.208935	−	0.977929i	$-0.433000\pi$
$773$	11.6180			0.417871			0.208935	+	0.977929i	$0.433000\pi$
$774$	2.34297			0.0842162
$775$		−	1.83146i		−	0.0657878i
$776$			9.79877i			0.351755i
$777$			9.29948i			0.333617i
$778$	17.2663			0.619028
$779$		−	37.7743i		−	1.35341i
$780$	−0.700523			−0.0250828
$781$	−6.99271			−0.250219
$782$	44.9076	−	22.8388i	1.60589	−	0.816712i
$783$	−3.47627			−0.124232
$784$	−23.2433			−0.830118
$785$			8.57452i			0.306038i
$786$	−27.5574			−0.982939
$787$			28.4626i			1.01458i	0.861774	+	0.507292i	$0.169353\pi$
$787$			28.4626i			1.01458i	−0.861774	+	0.507292i	$0.830647\pi$
$788$			0.613541i			0.0218565i
$789$		−	28.8872i		−	1.02841i
$790$	13.4133			0.477223
$791$	6.29104			0.223684
$792$			0.249646i			0.00887080i
$793$		−	6.11616i		−	0.217191i
$794$		−	13.8858i		−	0.492787i
$795$	−14.3634			−0.509419
$796$		−	4.16854i		−	0.147750i
$797$	−50.5355			−1.79006			−0.895029	−	0.446007i	$-0.852846\pi$
$797$	−50.5355			−1.79006			−0.895029	+	0.446007i	$0.852846\pi$
$798$	10.7005			0.378794
$799$	12.2315	+	24.0508i	0.432721	+	0.850856i
$800$	1.09332			0.0386547
$801$	−3.25457			−0.114995
$802$			11.7597i			0.415251i
$803$	−6.42407			−0.226701
$804$			1.60228i			0.0565080i
$805$		−	10.6194i		−	0.374285i
$806$		−	5.84955i		−	0.206042i
$807$	−44.6009			−1.57002
$808$	−18.3430			−0.645303
$809$			2.50914i			0.0882167i	0.999027	+	0.0441084i	$0.0140447\pi$
$809$			2.50914i			0.0882167i	−0.999027	+	0.0441084i	$0.985955\pi$
$810$			12.4133i			0.436158i
$811$		−	18.0933i		−	0.635342i	−0.948201	−	0.317671i	$-0.897099\pi$
$811$		−	18.0933i		−	0.635342i	0.948201	−	0.317671i	$-0.102901\pi$
$812$	0.162205			0.00569227
$813$		−	11.2243i		−	0.393652i
$814$	3.07381			0.107737
$815$	14.3757			0.503557
$816$	−26.7816	+	13.6204i	−0.937544	+	0.476809i
$817$	27.3258			0.956010
$818$	13.4401			0.469921
$819$			0.538319i			0.0188104i
$820$	−2.18664			−0.0763609
$821$			7.02776i			0.245271i	0.992452	+	0.122635i	$0.0391345\pi$
$821$			7.02776i			0.245271i	−0.992452	+	0.122635i	$0.960865\pi$
$822$			29.1998i			1.01846i
$823$		−	28.5379i		−	0.994767i	−0.867531	−	0.497384i	$-0.834294\pi$
$823$		−	28.5379i		−	0.994767i	0.867531	−	0.497384i	$-0.165706\pi$
$824$	−18.8423			−0.656401
$825$	−0.806063			−0.0280635
$826$		−	9.46168i		−	0.329214i
$827$			26.3004i			0.914556i	0.889324	+	0.457278i	$0.151175\pi$
$827$			26.3004i			0.914556i	−0.889324	+	0.457278i	$0.848825\pi$
$828$			0.310281i			0.0107830i
$829$	−27.2506			−0.946453			−0.473226	−	0.880941i	$-0.656911\pi$
$829$	−27.2506			−0.946453			−0.473226	+	0.880941i	$0.656911\pi$
$830$			19.8945i			0.690547i
$831$	27.9756			0.970462
$832$	−15.2692			−0.529363
$833$	−9.98637	−	19.6361i	−0.346007	−	0.680351i
$834$	29.0435			1.00569
$835$	7.54912			0.261248
$836$		−	0.312650i		−	0.0108132i
$837$	−9.79877			−0.338695
$838$		−	13.3235i		−	0.460251i
$839$			38.6580i			1.33462i	0.744779	+	0.667311i	$0.232555\pi$
$839$			38.6580i			1.33462i	−0.744779	+	0.667311i	$0.767445\pi$
$840$			5.76845i			0.199031i
$841$	28.5778			0.985443
$842$	25.0435			0.863056
$843$		−	47.6140i		−	1.63991i
$844$			4.04728i			0.139313i
$845$			8.35026i			0.287258i
$846$	−1.87987			−0.0646313
$847$		−	13.8618i		−	0.476296i
$848$	37.3014			1.28093
$849$	−16.8568			−0.578526
$850$	2.76845	+	5.44358i	0.0949571	+	0.186713i
$851$	−35.5778			−1.21959
$852$	4.72099			0.161739
$853$		−	5.46168i		−	0.187004i	−0.995619	−	0.0935022i	$-0.970194\pi$
$853$		−	5.46168i		−	0.187004i	0.995619	−	0.0935022i	$-0.0298062\pi$
$854$	5.40807			0.185060
$855$		−	0.649738i		−	0.0222206i
$856$			15.6810i			0.535966i
$857$			8.30280i			0.283618i	0.989894	+	0.141809i	$0.0452919\pi$
$857$			8.30280i			0.283618i	−0.989894	+	0.141809i	$0.954708\pi$
$858$	−2.57452			−0.0878925
$859$	10.7612			0.367166			0.183583	−	0.983004i	$-0.441230\pi$
$859$	10.7612			0.367166			0.183583	+	0.983004i	$0.441230\pi$
$860$		−	1.58181i		−	0.0539393i
$861$		−	24.3127i		−	0.828573i
$862$			21.7259i			0.739988i
$863$	43.7342			1.48873			0.744364	−	0.667774i	$-0.232753\pi$
$863$	43.7342			1.48873			0.744364	+	0.667774i	$0.232753\pi$
$864$		−	5.84955i		−	0.199006i
$865$	−11.8496			−0.402897
$866$	−9.89446			−0.336227
$867$	−23.0132	−	16.7734i	−0.781568	−	0.569654i
$868$	0.457216			0.0155189
$869$	4.35756			0.147820
$870$			1.61213i			0.0546562i
$871$	−10.6351			−0.360358
$872$		−	33.9756i		−	1.15056i
$873$		−	0.710373i		−	0.0240425i
$874$			40.9380i			1.38475i
$875$	1.28726			0.0435173
$876$	4.33709			0.146537
$877$			43.5633i			1.47103i	0.677510	+	0.735513i	$0.263059\pi$
$877$			43.5633i			1.47103i	−0.677510	+	0.735513i	$0.736941\pi$
$878$			14.1744i			0.478364i
$879$			23.9756i			0.808676i
$880$	2.09332			0.0705658
$881$		−	43.4372i		−	1.46344i	−0.681606	−	0.731719i	$-0.738718\pi$
$881$		−	43.4372i		−	1.46344i	0.681606	−	0.731719i	$-0.261282\pi$
$882$	1.53481			0.0516797
$883$	−6.56864			−0.221052			−0.110526	−	0.993873i	$-0.535254\pi$
$883$	−6.56864			−0.221052			−0.110526	+	0.993873i	$0.535254\pi$
$884$	0.781626	+	1.53690i	0.0262889	+	0.0516917i
$885$	8.31265			0.279427
$886$	−21.9090			−0.736049
$887$			21.4396i			0.719872i	0.932977	+	0.359936i	$0.117201\pi$
$887$			21.4396i			0.719872i	−0.932977	+	0.359936i	$0.882799\pi$
$888$	19.3258			0.648532
$889$		−	2.27645i		−	0.0763498i
$890$			24.8568i			0.833203i
$891$			4.03269i			0.135100i
$892$	−4.72099			−0.158070
$893$	−21.9248			−0.733685
$894$			42.6761i			1.42730i
$895$			3.22425i			0.107775i
$896$		−	16.3162i		−	0.545085i
$897$	29.7988			0.994952
$898$			16.1476i			0.538853i
$899$	−1.18997			−0.0396876
$900$	−0.0376114			−0.00125371
$901$	16.0263	+	31.5125i	0.533915	+	1.04983i
$902$	−8.03620			−0.267576
$903$	17.5877			0.585282
$904$		−	13.0738i		−	0.434828i
$905$	6.88717			0.228937
$906$		−	33.7137i		−	1.12006i
$907$		−	21.2628i		−	0.706020i	−0.935619	−	0.353010i	$-0.885158\pi$
$907$		−	21.2628i		−	0.706020i	0.935619	−	0.353010i	$-0.114842\pi$
$908$			2.17442i			0.0721608i
$909$	1.32979			0.0441065
$910$	4.11142			0.136292
$911$		−	48.6678i		−	1.61244i	−0.591618	−	0.806219i	$-0.701510\pi$
$911$		−	48.6678i		−	1.61244i	0.591618	−	0.806219i	$-0.298490\pi$
$912$		−	24.4142i		−	0.808436i
$913$			6.46310i			0.213897i
$914$	11.2837			0.373233
$915$			4.75131i			0.157073i
$916$	2.35756			0.0778958
$917$	14.2969			0.472126
$918$	29.1246	−	14.8119i	0.961255	−	0.488867i
$919$	4.55993			0.150418			0.0752091	−	0.997168i	$-0.476038\pi$
$919$	4.55993			0.150418			0.0752091	+	0.997168i	$0.476038\pi$
$920$	−22.0689			−0.727590
$921$			49.0494i			1.61623i
$922$	6.77575			0.223147
$923$			31.3357i			1.03143i
$924$		−	0.201231i		−	0.00662001i
$925$		−	4.31265i		−	0.141799i
$926$	3.80465			0.125029
$927$	1.36599			0.0448650
$928$		−	0.710373i		−	0.0233191i
$929$		−	23.3963i		−	0.767608i	−0.923415	−	0.383804i	$-0.874614\pi$
$929$		−	23.3963i		−	0.767608i	0.923415	−	0.383804i	$-0.125386\pi$
$930$			4.54420i			0.149010i
$931$	17.9003			0.586660
$932$			2.32250i			0.0760760i
$933$	−7.60816			−0.249080
$934$	2.30677			0.0754798
$935$	0.899385	+	1.76845i	0.0294130	+	0.0578346i
$936$	1.11871			0.0365663
$937$	−30.3898			−0.992791			−0.496395	−	0.868097i	$-0.665343\pi$
$937$	−30.3898			−0.992791			−0.496395	+	0.868097i	$0.665343\pi$
$938$		−	9.40388i		−	0.307047i
$939$	1.38455			0.0451830
$940$			1.26916i			0.0413954i
$941$			25.9610i			0.846304i	0.906059	+	0.423152i	$0.139076\pi$
$941$			25.9610i			0.846304i	−0.906059	+	0.423152i	$0.860924\pi$
$942$		−	21.2750i		−	0.693178i
$943$	93.0151			3.02899
$944$	−21.5877			−0.702619
$945$		−	6.88717i		−	0.224040i
$946$		−	5.81336i		−	0.189009i
$947$		−	16.8289i		−	0.546866i	−0.961891	−	0.273433i	$-0.911841\pi$
$947$		−	16.8289i		−	0.546866i	0.961891	−	0.273433i	$-0.0881592\pi$
$948$	−2.94192			−0.0955491
$949$			28.7875i			0.934482i
$950$	−4.96239			−0.161001
$951$	54.0019			1.75113
$952$	12.6556	−	6.43629i	0.410171	−	0.208601i
$953$	−12.7553			−0.413184			−0.206592	−	0.978427i	$-0.566237\pi$
$953$	−12.7553			−0.413184			−0.206592	+	0.978427i	$0.566237\pi$
$954$	−2.46310			−0.0797457
$955$		−	7.19982i		−	0.232981i
$956$	−1.71370			−0.0554249
$957$			0.523730i			0.0169298i
$958$		−	30.2252i		−	0.976532i
$959$		−	15.1490i		−	0.489188i
$960$	11.8618			0.382837
$961$	27.6458			0.891799
$962$		−	13.7743i		−	0.444102i
$963$		−	1.13681i		−	0.0366333i
$964$		−	0.0507852i		−	0.00163568i
$965$	−20.1114			−0.647410
$966$			26.3488i			0.847760i
$967$	42.5560			1.36851			0.684254	−	0.729244i	$-0.260128\pi$
$967$	42.5560			1.36851			0.684254	+	0.729244i	$0.260128\pi$
$968$	−28.8070			−0.925893
$969$	20.6253	−	10.4894i	0.662580	−	0.336969i
$970$	−5.42548			−0.174202
$971$	−18.4485			−0.592041			−0.296020	−	0.955182i	$-0.595660\pi$
$971$	−18.4485			−0.592041			−0.296020	+	0.955182i	$0.595660\pi$
$972$			0.390243i			0.0125170i
$973$	−15.0679			−0.483056
$974$			0.240938i			0.00772014i
$975$			3.61213i			0.115681i
$976$		−	12.3390i		−	0.394962i
$977$	24.8383			0.794647			0.397324	−	0.917679i	$-0.369939\pi$
$977$	24.8383			0.794647			0.397324	+	0.917679i	$0.369939\pi$
$978$	−35.6688			−1.14056
$979$			8.07522i			0.258085i
$980$		−	1.03620i		−	0.0331001i
$981$			2.46310i			0.0786406i
$982$	19.0132			0.606735
$983$			4.32487i			0.137942i	0.997619	+	0.0689710i	$0.0219716\pi$
$983$			4.32487i			0.137942i	−0.997619	+	0.0689710i	$0.978028\pi$
$984$	−50.5256			−1.61070
$985$	3.16362			0.100801
$986$	3.53690	−	1.79877i	0.112638	−	0.0572845i
$987$	−14.1114			−0.449171
$988$	−1.40105			−0.0445732
$989$			67.2868i			2.13960i
$990$	−0.138227			−0.00439314
$991$		−	31.8432i		−	1.01153i	−0.862670	−	0.505767i	$-0.831210\pi$
$991$		−	31.8432i		−	1.01153i	0.862670	−	0.505767i	$-0.168790\pi$
$992$		−	2.00237i		−	0.0635753i
$993$		−	11.4353i		−	0.362889i
$994$	−27.7078			−0.878839
$995$	−21.4944			−0.681417
$996$		−	4.36344i		−	0.138261i
$997$			29.0278i			0.919318i	0.888095	+	0.459659i	$0.152028\pi$
$997$			29.0278i			0.919318i	−0.888095	+	0.459659i	$0.847972\pi$
$998$		−	26.2788i		−	0.831842i
$999$	−23.0738			−0.730023

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.d.a.16.6	yes	6
3.2	odd	2		765.2.g.b.271.2		6
4.3	odd	2		1360.2.c.f.1121.2		6
5.2	odd	4		425.2.c.a.424.5		6
5.3	odd	4		425.2.c.b.424.2		6
5.4	even	2		425.2.d.c.101.1		6
17.4	even	4		1445.2.a.j.1.1		3
17.13	even	4		1445.2.a.k.1.1		3
17.16	even	2	inner	85.2.d.a.16.5	✓	6
51.50	odd	2		765.2.g.b.271.1		6
68.67	odd	2		1360.2.c.f.1121.5		6
85.4	even	4		7225.2.a.q.1.3		3
85.33	odd	4		425.2.c.a.424.2		6
85.64	even	4		7225.2.a.r.1.3		3
85.67	odd	4		425.2.c.b.424.5		6
85.84	even	2		425.2.d.c.101.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.d.a.16.5	✓	6	17.16	even	2	inner
85.2.d.a.16.6	yes	6	1.1	even	1	trivial
425.2.c.a.424.2		6	85.33	odd	4
425.2.c.a.424.5		6	5.2	odd	4
425.2.c.b.424.2		6	5.3	odd	4
425.2.c.b.424.5		6	85.67	odd	4
425.2.d.c.101.1		6	5.4	even	2
425.2.d.c.101.2		6	85.84	even	2
765.2.g.b.271.1		6	51.50	odd	2
765.2.g.b.271.2		6	3.2	odd	2
1360.2.c.f.1121.2		6	4.3	odd	2
1360.2.c.f.1121.5		6	68.67	odd	2
1445.2.a.j.1.1		3	17.4	even	4
1445.2.a.k.1.1		3	17.13	even	4
7225.2.a.q.1.3		3	85.4	even	4
7225.2.a.r.1.3		3	85.64	even	4

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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.48119 q^{2} +1.67513i q^{3} +0.193937 q^{4} -1.00000i q^{5} +2.48119i q^{6} -1.28726i q^{7} -2.67513 q^{8} +0.193937 q^{9} -1.48119i q^{10} -0.481194i q^{11} +0.324869i q^{12} -2.15633 q^{13} -1.90668i q^{14} +1.67513 q^{15} -4.35026 q^{16} +(-1.86907 - 3.67513i) q^{17} +0.287258 q^{18} +3.35026 q^{19} -0.193937i q^{20} +2.15633 q^{21} -0.712742i q^{22} +8.24965i q^{23} -4.48119i q^{24} -1.00000 q^{25} -3.19394 q^{26} +5.35026i q^{27} -0.249646i q^{28} +0.649738i q^{29} +2.48119 q^{30} +1.83146i q^{31} -1.09332 q^{32} +0.806063 q^{33} +(-2.76845 - 5.44358i) q^{34} -1.28726 q^{35} +0.0376114 q^{36} +4.31265i q^{37} +4.96239 q^{38} -3.61213i q^{39} +2.67513i q^{40} -11.2750i q^{41} +3.19394 q^{42} +8.15633 q^{43} -0.0933212i q^{44} -0.193937i q^{45} +12.2193i q^{46} -6.54420 q^{47} -7.28726i q^{48} +5.34297 q^{49} -1.48119 q^{50} +(6.15633 - 3.13093i) q^{51} -0.418190 q^{52} -8.57452 q^{53} +7.92478i q^{54} -0.481194 q^{55} +3.44358i q^{56} +5.61213i q^{57} +0.962389i q^{58} +4.96239 q^{59} +0.324869 q^{60} +2.83638i q^{61} +2.71274i q^{62} -0.249646i q^{63} +7.08110 q^{64} +2.15633i q^{65} +1.19394 q^{66} +4.93207 q^{67} +(-0.362481 - 0.712742i) q^{68} -13.8192 q^{69} -1.90668 q^{70} -14.5320i q^{71} -0.518806 q^{72} -13.3503i q^{73} +6.38787i q^{74} -1.67513i q^{75} +0.649738 q^{76} -0.619421 q^{77} -5.35026i q^{78} +9.05571i q^{79} +4.35026i q^{80} -8.38058 q^{81} -16.7005i q^{82} -13.4314 q^{83} +0.418190 q^{84} +(-3.67513 + 1.86907i) q^{85} +12.0811 q^{86} -1.08840 q^{87} +1.28726i q^{88} -16.7816 q^{89} -0.287258i q^{90} +2.77575i q^{91} +1.59991i q^{92} -3.06793 q^{93} -9.69323 q^{94} -3.35026i q^{95} -1.83146i q^{96} -3.66291i q^{97} +7.91397 q^{98} -0.0933212i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} + 2 q^{4} - 6 q^{8} + 2 q^{9} + 8 q^{13} - 6 q^{16} - 2 q^{17} - 10 q^{18} - 8 q^{21} - 6 q^{25} - 20 q^{26} + 4 q^{30} + 6 q^{32} + 4 q^{33} + 6 q^{34} + 4 q^{35} + 22 q^{36} + 8 q^{38} + 20 q^{42}+ \cdots + 86 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 + 2 * q^4 - 6 * q^8 + 2 * q^9 + 8 * q^13 - 6 * q^16 - 2 * q^17 - 10 * q^18 - 8 * q^21 - 6 * q^25 - 20 * q^26 + 4 * q^30 + 6 * q^32 + 4 * q^33 + 6 * q^34 + 4 * q^35 + 22 * q^36 + 8 * q^38 + 20 * q^42 + 28 * q^43 - 20 * q^47 - 14 * q^49 + 2 * q^50 + 16 * q^51 - 28 * q^53 + 8 * q^55 + 8 * q^59 + 12 * q^60 - 22 * q^64 + 8 * q^66 + 12 * q^67 - 34 * q^68 - 24 * q^70 - 14 * q^72 + 24 * q^76 - 28 * q^77 - 26 * q^81 + 4 * q^83 - 12 * q^85 + 8 * q^86 + 32 * q^87 + 4 * q^89 - 36 * q^93 + 8 * q^94 + 86 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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