LMFDB - Embedded newform 845.2.d.d.844.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(844,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, 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("845.844");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 22x^{10} + 147x^{8} + 390x^{6} + 413x^{4} + 128x^{2} + 4 $ x^12 + 22x^10 + 147x^8 + 390x^6 + 413x^4 + 128*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			844.11
Root			$1.54574i$ of defining polynomial
Character	$\chi$	$=$	845.844
Dual form			845.2.d.d.844.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.54574 q^{2} -2.15293i q^{3} +4.48079 q^{4} +(2.08125 + 0.817544i) q^{5} -5.48079i q^{6} -2.93855 q^{7} +6.31544 q^{8} -1.63509 q^{9} +O(q^{10})$	\(q+2.54574 q^{2} -2.15293i q^{3} +4.48079 q^{4} +(2.08125 + 0.817544i) q^{5} -5.48079i q^{6} -2.93855 q^{7} +6.31544 q^{8} -1.63509 q^{9} +(5.29833 + 2.08125i) q^{10} -0.635089i q^{11} -9.64680i q^{12} -7.48079 q^{14} +(1.76011 - 4.48079i) q^{15} +7.11588 q^{16} -1.22396i q^{17} -4.16251 q^{18} +1.36491i q^{19} +(9.32566 + 3.66324i) q^{20} +6.32648i q^{21} -1.61677i q^{22} -2.15293i q^{23} -13.5967i q^{24} +(3.66324 + 3.40304i) q^{25} -2.93855i q^{27} -13.1670 q^{28} -3.00000 q^{29} +(4.48079 - 11.4069i) q^{30} +8.96157i q^{31} +5.48429 q^{32} -1.36730 q^{33} -3.11588i q^{34} +(-6.11588 - 2.40240i) q^{35} -7.32648 q^{36} +1.22396 q^{37} +3.47471i q^{38} +(13.1440 + 5.16315i) q^{40} +9.96157i q^{41} +16.1056i q^{42} +1.36730i q^{43} -2.84570i q^{44} +(-3.40304 - 1.33676i) q^{45} -5.48079i q^{46} -6.16379 q^{47} -15.3200i q^{48} +1.63509 q^{49} +(9.32566 + 8.66324i) q^{50} -2.63509 q^{51} +0.642285i q^{53} -7.48079i q^{54} +(0.519213 - 1.32178i) q^{55} -18.5582 q^{56} +2.93855 q^{57} -7.63722 q^{58} -7.59666i q^{59} +(7.88669 - 20.0774i) q^{60} -2.27018 q^{61} +22.8138i q^{62} +4.80479 q^{63} -0.270178 q^{64} -3.48079 q^{66} -8.03003 q^{67} -5.48429i q^{68} -4.63509 q^{69} +(-15.5694 - 6.11588i) q^{70} -2.63509i q^{71} -10.3263 q^{72} +10.3263 q^{73} +3.11588 q^{74} +(7.32648 - 7.88669i) q^{75} +6.11588i q^{76} +1.86624i q^{77} -1.03843 q^{79} +(14.8099 + 5.81754i) q^{80} -11.2318 q^{81} +25.3596i q^{82} +11.8452 q^{83} +28.3476i q^{84} +(1.00064 - 2.54737i) q^{85} +3.48079i q^{86} +6.45878i q^{87} -4.01086i q^{88} +12.5582i q^{89} +(-8.66324 - 3.40304i) q^{90} -9.64680i q^{92} +19.2936 q^{93} -15.6914 q^{94} +(-1.11588 + 2.84073i) q^{95} -11.8073i q^{96} +14.7838 q^{97} +4.16251 q^{98} +1.03843i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4} - 12 q^{9}+O(q^{10}) $ 12 * q + 8 * q^4 - 12 * q^9	$ 12 q + 8 q^{4} - 12 q^{9} + 14 q^{10} - 44 q^{14} + 32 q^{16} + 2 q^{25} - 36 q^{29} + 8 q^{30} - 20 q^{35} - 4 q^{36} + 70 q^{40} + 12 q^{49} - 24 q^{51} + 52 q^{55} - 32 q^{56} - 12 q^{61} + 12 q^{64} + 4 q^{66} - 48 q^{69} - 16 q^{74} + 4 q^{75} - 104 q^{79} - 28 q^{81} - 62 q^{90} - 112 q^{94} + 40 q^{95}+O(q^{100}) $ 12 * q + 8 * q^4 - 12 * q^9 + 14 * q^10 - 44 * q^14 + 32 * q^16 + 2 * q^25 - 36 * q^29 + 8 * q^30 - 20 * q^35 - 4 * q^36 + 70 * q^40 + 12 * q^49 - 24 * q^51 + 52 * q^55 - 32 * q^56 - 12 * q^61 + 12 * q^64 + 4 * q^66 - 48 * q^69 - 16 * q^74 + 4 * q^75 - 104 * q^79 - 28 * q^81 - 62 * q^90 - 112 * q^94 + 40 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$-1$	$-1$

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 $

$2$	2.54574			1.80011			0.900055	−	0.435777i	$-0.143526\pi$
$2$	2.54574			1.80011			0.900055	+	0.435777i	$0.143526\pi$
$3$		−	2.15293i		−	1.24299i	−0.783417	−	0.621496i	$-0.786525\pi$
$3$		−	2.15293i		−	1.24299i	0.783417	−	0.621496i	$-0.213475\pi$
$4$	4.48079			2.24039
$5$	2.08125	+	0.817544i	0.930765	+	0.365617i
$5$	2.08125	+	0.817544i	0.930765	+	0.365617i
$6$		−	5.48079i		−	2.23752i
$7$	−2.93855			−1.11067			−0.555334	−	0.831627i	$-0.687410\pi$
$7$	−2.93855			−1.11067			−0.555334	+	0.831627i	$0.687410\pi$
$8$	6.31544			2.23284
$9$	−1.63509			−0.545030
$10$	5.29833	+	2.08125i	1.67548	+	0.658151i
$11$		−	0.635089i		−	0.191487i	−0.995406	−	0.0957433i	$-0.969477\pi$
$11$		−	0.635089i		−	0.191487i	0.995406	−	0.0957433i	$-0.0305228\pi$
$12$		−	9.64680i		−	2.78479i
$13$		0			0
$13$		0			0
$14$	−7.48079			−1.99932
$15$	1.76011	−	4.48079i	0.454459	−	1.15693i
$16$	7.11588			1.77897
$17$		−	1.22396i		−	0.296853i	−0.988923	−	0.148427i	$-0.952579\pi$
$17$		−	1.22396i		−	0.296853i	0.988923	−	0.148427i	$-0.0474209\pi$
$18$	−4.16251			−0.981113
$19$			1.36491i			0.313132i	0.987667	+	0.156566i	$0.0500424\pi$
$19$			1.36491i			0.313132i	−0.987667	+	0.156566i	$0.949958\pi$
$20$	9.32566	+	3.66324i	2.08528	+	0.819126i
$21$			6.32648i			1.38055i
$22$		−	1.61677i		−	0.344697i
$23$		−	2.15293i		−	0.448916i	−0.974484	−	0.224458i	$-0.927939\pi$
$23$		−	2.15293i		−	0.448916i	0.974484	−	0.224458i	$-0.0720612\pi$
$24$		−	13.5967i		−	2.77541i
$25$	3.66324	+	3.40304i	0.732648	+	0.680607i
$26$		0			0
$27$		−	2.93855i		−	0.565525i
$28$	−13.1670			−2.48833
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$	4.48079	−	11.4069i	0.818076	−	2.08261i
$31$			8.96157i			1.60955i	0.593583	+	0.804773i	$0.297713\pi$
$31$			8.96157i			1.60955i	−0.593583	+	0.804773i	$0.702287\pi$
$32$	5.48429			0.969495
$33$	−1.36730			−0.238016
$34$		−	3.11588i		−	0.534368i
$35$	−6.11588	−	2.40240i	−1.03377	−	0.406079i
$36$	−7.32648			−1.22108
$37$	1.22396			0.201217			0.100609	−	0.994926i	$-0.467921\pi$
$37$	1.22396			0.201217			0.100609	+	0.994926i	$0.467921\pi$
$38$			3.47471i			0.563672i
$39$		0			0
$40$	13.1440	+	5.16315i	2.07825	+	0.816366i
$41$			9.96157i			1.55574i	0.628427	+	0.777868i	$0.283699\pi$
$41$			9.96157i			1.55574i	−0.628427	+	0.777868i	$0.716301\pi$
$42$			16.1056i			2.48514i
$43$			1.36730i			0.208511i	0.994551	+	0.104256i	$0.0332460\pi$
$43$			1.36730i			0.208511i	−0.994551	+	0.104256i	$0.966754\pi$
$44$		−	2.84570i		−	0.429005i
$45$	−3.40304	−	1.33676i	−0.507295	−	0.199272i
$46$		−	5.48079i		−	0.808098i
$47$	−6.16379			−0.899081			−0.449540	−	0.893260i	$-0.648412\pi$
$47$	−6.16379			−0.899081			−0.449540	+	0.893260i	$0.648412\pi$
$48$		−	15.3200i		−	2.21124i
$49$	1.63509			0.233584
$50$	9.32566	+	8.66324i	1.31885	+	1.22517i
$51$	−2.63509			−0.368986
$52$		0			0
$53$			0.642285i			0.0882246i	0.999027	+	0.0441123i	$0.0140459\pi$
$53$			0.642285i			0.0882246i	−0.999027	+	0.0441123i	$0.985954\pi$
$54$		−	7.48079i		−	1.01801i
$55$	0.519213	−	1.32178i	0.0700107	−	0.178229i
$56$	−18.5582			−2.47995
$57$	2.93855			0.389221
$58$	−7.63722			−1.00282
$59$		−	7.59666i		−	0.989001i	−0.869177	−	0.494501i	$-0.835351\pi$
$59$		−	7.59666i		−	0.989001i	0.869177	−	0.494501i	$-0.164649\pi$
$60$	7.88669	−	20.0774i	1.01817	−	2.59199i
$61$	−2.27018			−0.290666			−0.145333	−	0.989383i	$-0.546425\pi$
$61$	−2.27018			−0.290666			−0.145333	+	0.989383i	$0.546425\pi$
$62$			22.8138i			2.89736i
$63$	4.80479			0.605347
$64$	−0.270178			−0.0337722
$65$		0			0
$66$	−3.48079			−0.428455
$67$	−8.03003			−0.981024			−0.490512	−	0.871434i	$-0.663190\pi$
$67$	−8.03003			−0.981024			−0.490512	+	0.871434i	$0.663190\pi$
$68$		−	5.48429i		−	0.665068i
$69$	−4.63509			−0.557999
$70$	−15.5694	−	6.11588i	−1.86090	−	0.730987i
$71$		−	2.63509i		−	0.312728i	−0.987700	−	0.156364i	$-0.950023\pi$
$71$		−	2.63509i		−	0.312728i	0.987700	−	0.156364i	$-0.0499772\pi$
$72$	−10.3263			−1.21697
$73$	10.3263			1.20860			0.604301	−	0.796756i	$-0.293453\pi$
$73$	10.3263			1.20860			0.604301	+	0.796756i	$0.293453\pi$
$74$	3.11588			0.362213
$75$	7.32648	−	7.88669i	0.845990	−	0.910676i
$76$			6.11588i			0.701539i
$77$			1.86624i			0.212678i
$78$		0			0
$79$	−1.03843			−0.116832			−0.0584161	−	0.998292i	$-0.518605\pi$
$79$	−1.03843			−0.116832			−0.0584161	+	0.998292i	$0.518605\pi$
$80$	14.8099	+	5.81754i	1.65580	+	0.650421i
$81$	−11.2318			−1.24797
$82$			25.3596i			2.80050i
$83$	11.8452			1.30018			0.650092	−	0.759855i	$-0.274730\pi$
$83$	11.8452			1.30018			0.650092	+	0.759855i	$0.274730\pi$
$84$			28.3476i			3.09298i
$85$	1.00064	−	2.54737i	0.108535	−	0.276301i
$86$			3.48079i			0.375343i
$87$			6.45878i			0.692454i
$88$		−	4.01086i		−	0.427559i
$89$			12.5582i			1.33117i	0.746322	+	0.665585i	$0.231818\pi$
$89$			12.5582i			1.33117i	−0.746322	+	0.665585i	$0.768182\pi$
$90$	−8.66324	−	3.40304i	−0.913186	−	0.358712i
$91$		0			0
$92$		−	9.64680i		−	1.00575i
$93$	19.2936			2.00065
$94$	−15.6914			−1.61844
$95$	−1.11588	+	2.84073i	−0.114486	+	0.291453i
$96$		−	11.8073i		−	1.20507i
$97$	14.7838			1.50107			0.750534	−	0.660832i	$-0.229797\pi$
$97$	14.7838			1.50107			0.750534	+	0.660832i	$0.229797\pi$
$98$	4.16251			0.420477
$99$			1.03843i			0.104366i
$100$	16.4142	+	15.2483i	1.64142	+	1.52483i
$101$	−13.2318			−1.31661			−0.658304	−	0.752752i	$-0.728726\pi$
$101$	−13.2318			−1.31661			−0.658304	+	0.752752i	$0.728726\pi$
$102$	−6.70825			−0.664216
$103$		−	10.9686i		−	1.08077i	−0.841419	−	0.540383i	$-0.818279\pi$
$103$		−	10.9686i		−	1.08077i	0.841419	−	0.540383i	$-0.181721\pi$
$104$		0			0
$105$	−5.17218	+	13.1670i	−0.504753	+	1.28497i
$106$			1.63509i			0.158814i
$107$			10.6736i			1.03186i	0.856632	+	0.515928i	$0.172553\pi$
$107$			10.6736i			1.03186i	−0.856632	+	0.515928i	$0.827447\pi$
$108$		−	13.1670i		−	1.26700i
$109$		−	3.27018i		−	0.313226i	−0.987660	−	0.156613i	$-0.949942\pi$
$109$		−	3.27018i		−	0.313226i	0.987660	−	0.156613i	$-0.0500576\pi$
$110$	1.32178	−	3.36491i	0.126027	−	0.320832i
$111$		−	2.63509i		−	0.250112i
$112$	−20.9104			−1.97584
$113$		−	5.52981i		−	0.520201i	−0.965582	−	0.260100i	$-0.916244\pi$
$113$		−	5.52981i		−	0.520201i	0.965582	−	0.260100i	$-0.0837556\pi$
$114$	7.48079			0.700640
$115$	1.76011	−	4.48079i	0.164131	−	0.417836i
$116$	−13.4424			−1.24809
$117$		0			0
$118$		−	19.3391i		−	1.78031i
$119$			3.59666i			0.329705i
$120$	11.1159	−	28.2981i	1.01474	−	2.58325i
$121$	10.5967			0.963333
$122$	−5.77928			−0.523231
$123$	21.4465			1.93377
$124$			40.1549i			3.60602i
$125$	4.84201	+	10.0774i	0.433082	+	0.901354i
$126$	12.2318			1.08969
$127$		−	17.2317i		−	1.52907i	−0.644584	−	0.764534i	$-0.722969\pi$
$127$		−	17.2317i		−	1.52907i	0.644584	−	0.764534i	$-0.277031\pi$
$128$	−11.6564			−1.03029
$129$	2.94369			0.259178
$130$		0			0
$131$	10.0000			0.873704			0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000			0.873704			0.436852	+	0.899533i	$0.356093\pi$
$132$	−6.12658			−0.533250
$133$		−	4.01086i		−	0.347786i
$134$	−20.4424			−1.76595
$135$	2.40240	−	6.11588i	0.206765	−	0.526371i
$136$		−	7.72982i		−	0.662827i
$137$	−8.67231			−0.740926			−0.370463	−	0.928847i	$-0.620801\pi$
$137$	−8.67231			−0.740926			−0.370463	+	0.928847i	$0.620801\pi$
$138$	−11.7997			−1.00446
$139$	−14.3265			−1.21516			−0.607578	−	0.794260i	$-0.707859\pi$
$139$	−14.3265			−1.21516			−0.607578	+	0.794260i	$0.707859\pi$
$140$	−27.4039	−	10.7646i	−2.31606	−	0.909777i
$141$			13.2702i			1.11755i
$142$		−	6.70825i		−	0.562944i
$143$		0			0
$144$	−11.6351			−0.969591
$145$	−6.24376	−	2.45263i	−0.518516	−	0.203680i
$146$	26.2881			2.17562
$147$		−	3.52022i		−	0.290343i
$148$	5.48429			0.450806
$149$		−	17.1549i		−	1.40538i	−0.711494	−	0.702692i	$-0.751981\pi$
$149$		−	17.1549i		−	1.40538i	0.711494	−	0.702692i	$-0.248019\pi$
$150$	18.6513	−	20.0774i	1.52287	−	1.63932i
$151$		−	21.3828i		−	1.74011i	−0.492957	−	0.870053i	$-0.664084\pi$
$151$		−	21.3828i		−	1.74011i	0.492957	−	0.870053i	$-0.335916\pi$
$152$			8.62001i			0.699175i
$153$			2.00128i			0.161794i
$154$			4.75096i			0.382844i
$155$	−7.32648	+	18.6513i	−0.588477	+	1.49811i
$156$		0			0
$157$			18.3646i			1.46566i	0.680413	+	0.732829i	$0.261800\pi$
$157$			18.3646i			1.46566i	−0.680413	+	0.732829i	$0.738200\pi$
$158$	−2.64356			−0.210311
$159$	1.38279			0.109662
$160$	11.4142	+	4.48365i	0.902372	+	0.354464i
$161$			6.32648i			0.498597i
$162$	−28.5931			−2.24649
$163$	4.01086			0.314155			0.157078	−	0.987586i	$-0.449793\pi$
$163$	4.01086			0.314155			0.157078	+	0.987586i	$0.449793\pi$
$164$			44.6357i			3.48546i
$165$	−2.84570	−	1.11783i	−0.221537	−	0.0870228i
$166$	30.1549			2.34047
$167$	2.93855			0.227392			0.113696	−	0.993516i	$-0.463731\pi$
$167$	2.93855			0.227392			0.113696	+	0.993516i	$0.463731\pi$
$168$			39.9545i			3.08256i
$169$		0			0
$170$	2.54737	−	6.48493i	0.195374	−	0.497371i
$171$		−	2.23175i		−	0.170666i
$172$			6.12658i			0.467147i
$173$		−	1.36730i		−	0.103954i	−0.998648	−	0.0519769i	$-0.983448\pi$
$173$		−	1.36730i		−	0.103954i	0.998648	−	0.0519769i	$-0.0165522\pi$
$174$			16.4424i			1.24649i
$175$	−10.7646	−	10.0000i	−0.813729	−	0.755929i
$176$		−	4.51921i		−	0.340649i
$177$	−16.3550			−1.22932
$178$			31.9700i			2.39625i
$179$	7.78613			0.581963			0.290981	−	0.956729i	$-0.406018\pi$
$179$	7.78613			0.581963			0.290981	+	0.956729i	$0.406018\pi$
$180$	−15.2483	−	5.98973i	−1.13654	−	0.446448i
$181$	3.86684			0.287420			0.143710	−	0.989620i	$-0.454097\pi$
$181$	3.86684			0.287420			0.143710	+	0.989620i	$0.454097\pi$
$182$		0			0
$183$			4.88752i			0.361296i
$184$		−	13.5967i		−	1.00236i
$185$	2.54737	+	1.00064i	0.187286	+	0.0735685i
$186$	49.1165			3.60139
$187$	−0.777322			−0.0568434
$188$	−27.6186			−2.01429
$189$			8.63509i			0.628110i
$190$	−2.84073	+	7.23175i	−0.206088	+	0.524646i
$191$	4.94369			0.357713			0.178857	−	0.983875i	$-0.442760\pi$
$191$	4.94369			0.357713			0.178857	+	0.983875i	$0.442760\pi$
$192$			0.581673i			0.0419786i
$193$	−4.95644			−0.356772			−0.178386	−	0.983961i	$-0.557088\pi$
$193$	−4.95644			−0.356772			−0.178386	+	0.983961i	$0.557088\pi$
$194$	37.6357			2.70208
$195$		0			0
$196$	7.32648			0.523320
$197$	−6.74546			−0.480594			−0.240297	−	0.970699i	$-0.577245\pi$
$197$	−6.74546			−0.480594			−0.240297	+	0.970699i	$0.577245\pi$
$198$			2.64356i			0.187870i
$199$	5.17544			0.366878			0.183439	−	0.983031i	$-0.441277\pi$
$199$	5.17544			0.366878			0.183439	+	0.983031i	$0.441277\pi$
$200$	23.1350	+	21.4917i	1.63589	+	1.51969i
$201$			17.2881i			1.21941i
$202$	−33.6846			−2.37004
$203$	8.81566			0.618738
$204$	−11.8073			−0.826674
$205$	−8.14403	+	20.7326i	−0.568804	+	1.44803i
$206$		−	27.9231i		−	1.94550i
$207$			3.52022i			0.244673i
$208$		0			0
$209$	0.866840			0.0599606
$210$	−13.1670	+	33.5198i	−0.908611	+	2.31309i
$211$	−14.0179			−0.965031			−0.482515	−	0.875888i	$-0.660277\pi$
$211$	−14.0179			−0.965031			−0.482515	+	0.875888i	$0.660277\pi$
$212$			2.87794i			0.197658i
$213$	−5.67315			−0.388718
$214$			27.1722i			1.85745i
$215$	−1.11783	+	2.84570i	−0.0762352	+	0.194075i
$216$		−	18.5582i		−	1.26273i
$217$		−	26.3341i		−	1.78767i
$218$		−	8.32502i		−	0.563841i
$219$		−	22.2318i		−	1.50228i
$220$	2.32648	−	5.92262i	0.156852	−	0.399303i
$221$		0			0
$222$		−	6.70825i		−	0.450228i
$223$	−0.00830491			−0.000556138			−0.000278069	−	1.00000i	$-0.500089\pi$
$223$	−0.00830491			−0.000556138			−0.000278069		1.00000i	$0.500089\pi$
$224$	−16.1159			−1.07679
$225$	−5.98973	−	5.56427i	−0.399315	−	0.370951i
$226$		−	14.0774i		−	0.936418i
$227$	−11.2636			−0.747589			−0.373795	−	0.927511i	$-0.621944\pi$
$227$	−11.2636			−0.747589			−0.373795	+	0.927511i	$0.621944\pi$
$228$	13.1670			0.872008
$229$			16.5404i			1.09302i	0.837453	+	0.546509i	$0.184043\pi$
$229$			16.5404i			1.09302i	−0.837453	+	0.546509i	$0.815957\pi$
$230$	4.48079	−	11.4069i	0.295454	−	0.752150i
$231$	4.01788			0.264357
$232$	−18.9463			−1.24389
$233$		−	6.94941i		−	0.455271i	−0.973746	−	0.227636i	$-0.926900\pi$
$233$		−	6.94941i		−	0.455271i	0.973746	−	0.227636i	$-0.0730995\pi$
$234$		0			0
$235$	−12.8284	−	5.03917i	−0.836833	−	0.328719i
$236$		−	34.0390i		−	2.21575i
$237$			2.23566i			0.145221i
$238$			9.15616i			0.593506i
$239$			4.00000i			0.258738i	0.991596	+	0.129369i	$0.0412952\pi$
$239$			4.00000i			0.258738i	−0.991596	+	0.129369i	$0.958705\pi$
$240$	12.5247	−	31.8847i	0.808469	−	2.05815i
$241$			19.7721i			1.27363i	0.771015	+	0.636817i	$0.219749\pi$
$241$			19.7721i			1.27363i	−0.771015	+	0.636817i	$0.780251\pi$
$242$	26.9763			1.73410
$243$			15.3655i			0.985695i
$244$	−10.1722			−0.651207
$245$	3.40304	+	1.33676i	0.217412	+	0.0854023i
$246$	54.5973			3.48099
$247$		0			0
$248$			56.5962i			3.59386i
$249$		−	25.5019i		−	1.61612i
$250$	12.3265	+	25.6546i	0.779595	+	1.62254i
$251$	−3.67352			−0.231870			−0.115935	−	0.993257i	$-0.536986\pi$
$251$	−3.67352			−0.231870			−0.115935	+	0.993257i	$0.536986\pi$
$252$	21.5293			1.35622
$253$	−1.36730			−0.0859614
$254$		−	43.8674i		−	2.75249i
$255$	−5.48429	−	2.15430i	−0.343440	−	0.134908i
$256$	−29.1338			−1.82086
$257$		−	13.2648i		−	0.827439i	−0.910404	−	0.413719i	$-0.864229\pi$
$257$		−	13.2648i		−	0.827439i	0.910404	−	0.413719i	$-0.135771\pi$
$258$	7.49387			0.466548
$259$	−3.59666			−0.223486
$260$		0			0
$261$	4.90527			0.303628
$262$	25.4574			1.57276
$263$		−	30.2705i		−	1.86656i	−0.359152	−	0.933279i	$-0.616934\pi$
$263$		−	30.2705i		−	1.86656i	0.359152	−	0.933279i	$-0.383066\pi$
$264$	−8.63509			−0.531453
$265$	−0.525096	+	1.33676i	−0.0322564	+	0.0821164i
$266$		−	10.2106i		−	0.626053i
$267$	27.0369			1.65463
$268$	−35.9809			−2.19788
$269$	22.2496			1.35658			0.678292	−	0.734792i	$-0.262720\pi$
$269$	22.2496			1.35658			0.678292	+	0.734792i	$0.262720\pi$
$270$	6.11588	−	15.5694i	0.372200	−	0.947525i
$271$		−	11.8284i		−	0.718525i	−0.933237	−	0.359262i	$-0.883028\pi$
$271$		−	11.8284i		−	0.718525i	0.933237	−	0.359262i	$-0.116972\pi$
$272$		−	8.70953i		−	0.528093i
$273$		0			0
$274$	−22.0774			−1.33375
$275$	2.16123	−	2.32648i	0.130327	−	0.140292i
$276$	−20.7688			−1.25014
$277$		−	16.7851i		−	1.00852i	−0.863553	−	0.504259i	$-0.831766\pi$
$277$		−	16.7851i		−	1.00852i	0.863553	−	0.504259i	$-0.168234\pi$
$278$	−36.4715			−2.18741
$279$		−	14.6530i		−	0.877250i
$280$	−38.6244	−	15.1722i	−2.30825	−	0.906711i
$281$		−	10.5967i		−	0.632144i	−0.948735	−	0.316072i	$-0.897636\pi$
$281$		−	10.5967i		−	0.632144i	0.948735	−	0.316072i	$-0.102364\pi$
$282$			33.7824i			2.01171i
$283$		−	8.81566i		−	0.524036i	−0.965063	−	0.262018i	$-0.915612\pi$
$283$		−	8.81566i		−	0.524036i	0.965063	−	0.262018i	$-0.0843880\pi$
$284$		−	11.8073i		−	0.700633i
$285$	6.11588	+	2.40240i	0.362273	+	0.142306i
$286$		0			0
$287$		−	29.2726i		−	1.72791i
$288$	−8.96730			−0.528403
$289$	15.5019			0.911878
$290$	−15.8950	−	6.24376i	−0.933386	−	0.366646i
$291$		−	31.8284i		−	1.86581i
$292$	46.2699			2.70774
$293$	−28.2526			−1.65053			−0.825267	−	0.564742i	$-0.808976\pi$
$293$	−28.2526			−1.65053			−0.825267	+	0.564742i	$0.808976\pi$
$294$		−	8.96157i		−	0.522650i
$295$	6.21061	−	15.8106i	0.361596	−	0.920528i
$296$	7.72982			0.449287
$297$	−1.86624			−0.108290
$298$		−	43.6719i		−	2.52984i
$299$		0			0
$300$	32.8284	−	35.3386i	1.89535	−	2.04027i
$301$		−	4.01788i		−	0.231587i
$302$		−	54.4350i		−	3.13238i
$303$			28.4870i			1.63653i
$304$			9.71254i			0.557052i
$305$	−4.72482	−	1.85597i	−0.270542	−	0.106273i
$306$			5.09473i			0.291247i
$307$	−12.7219			−0.726077			−0.363039	−	0.931774i	$-0.618261\pi$
$307$	−12.7219			−0.726077			−0.363039	+	0.931774i	$0.618261\pi$
$308$			8.36223i			0.476482i
$309$	−23.6145			−1.34338
$310$	−18.6513	+	47.4814i	−1.05932	+	2.69676i
$311$	−27.9231			−1.58338			−0.791688	−	0.610925i	$-0.790798\pi$
$311$	−27.9231			−1.58338			−0.791688	+	0.610925i	$0.790798\pi$
$312$		0			0
$313$		−	24.5807i		−	1.38938i	−0.719307	−	0.694692i	$-0.755540\pi$
$313$		−	24.5807i		−	1.38938i	0.719307	−	0.694692i	$-0.244460\pi$
$314$			46.7516i			2.63834i
$315$	10.0000	+	3.92813i	0.563436	+	0.221325i
$316$	−4.65297			−0.261750
$317$	−0.234377			−0.0131639			−0.00658196	−	0.999978i	$-0.502095\pi$
$317$	−0.234377			−0.0131639			−0.00658196	+	0.999978i	$0.502095\pi$
$318$	3.52022			0.197404
$319$			1.90527i			0.106674i
$320$	−0.562309	−	0.220882i	−0.0314340	−	0.0123477i
$321$	22.9795			1.28259
$322$			16.1056i			0.897529i
$323$	1.67059			0.0929543
$324$	−50.3271			−2.79595
$325$		0			0
$326$	10.2106			0.565513
$327$	−7.04045			−0.389338
$328$			62.9117i			3.47372i
$329$	18.1126			0.998581
$330$	−7.24440	−	2.84570i	−0.398791	−	0.156651i
$331$			18.3265i			1.00731i	0.863904	+	0.503657i	$0.168013\pi$
$331$			18.3265i			1.00731i	−0.863904	+	0.503657i	$0.831987\pi$
$332$	53.0760			2.91292
$333$	−2.00128			−0.109669
$334$	7.48079			0.409330
$335$	−16.7125	−	6.56491i	−0.913103	−	0.358679i
$336$			45.0185i			2.45596i
$337$			21.2949i			1.16001i	0.814614	+	0.580003i	$0.196949\pi$
$337$			21.2949i			1.16001i	−0.814614	+	0.580003i	$0.803051\pi$
$338$		0			0
$339$	−11.9053			−0.646605
$340$	4.48365	−	11.4142i	0.243160	−	0.619022i
$341$	5.69140			0.308206
$342$		−	5.68146i		−	0.307218i
$343$	15.7651			0.851234
$344$			8.63509i			0.465573i
$345$	−9.64680	−	3.78939i	−0.519366	−	0.204014i
$346$		−	3.48079i		−	0.187128i
$347$		−	3.81521i		−	0.204811i	−0.994743	−	0.102406i	$-0.967346\pi$
$347$		−	3.81521i		−	0.204811i	0.994743	−	0.102406i	$-0.0326540\pi$
$348$			28.9404i			1.55137i
$349$		−	24.3265i		−	1.30217i	−0.759006	−	0.651083i	$-0.774315\pi$
$349$		−	24.3265i		−	1.30217i	0.759006	−	0.651083i	$-0.225685\pi$
$350$	−27.4039	−	25.4574i	−1.46480	−	1.36075i
$351$		0			0
$352$		−	3.48301i		−	0.185645i
$353$	27.0591			1.44021			0.720104	−	0.693866i	$-0.244094\pi$
$353$	27.0591			1.44021			0.720104	+	0.693866i	$0.244094\pi$
$354$	−41.6357			−2.21291
$355$	2.15430	−	5.48429i	0.114338	−	0.291076i
$356$			56.2708i			2.98235i
$357$	7.74335			0.409821
$358$	19.8215			1.04760
$359$		−	27.0039i		−	1.42521i	−0.701566	−	0.712605i	$-0.747515\pi$
$359$		−	27.0039i		−	1.42521i	0.701566	−	0.712605i	$-0.252485\pi$
$360$	−21.4917	−	8.44221i	−1.13271	−	0.444943i
$361$	17.1370			0.901948
$362$	9.84396			0.517387
$363$		−	22.8138i		−	1.19742i
$364$		0			0
$365$	21.4917	+	8.44221i	1.12492	+	0.441885i
$366$			12.4424i			0.650373i
$367$		−	6.94111i		−	0.362323i	−0.983453	−	0.181161i	$-0.942014\pi$
$367$		−	6.94111i		−	0.362323i	0.983453	−	0.181161i	$-0.0579857\pi$
$368$		−	15.3200i		−	0.798608i
$369$		−	16.2881i		−	0.847922i
$370$	6.48493	+	2.54737i	0.337135	+	0.132431i
$371$		−	1.88739i		−	0.0979882i
$372$	86.4505			4.48225
$373$		−	2.31288i		−	0.119756i	−0.998206	−	0.0598781i	$-0.980929\pi$
$373$		−	2.31288i		−	0.119756i	0.998206	−	0.0598781i	$-0.0190712\pi$
$374$	−1.97886			−0.102324
$375$	21.6960	−	10.4245i	1.12038	−	0.538318i
$376$	−38.9270			−2.00751
$377$		0			0
$378$			21.9827i			1.13067i
$379$			5.17544i			0.265845i	0.991126	+	0.132922i	$0.0424361\pi$
$379$			5.17544i			0.265845i	−0.991126	+	0.132922i	$0.957564\pi$
$380$	−5.00000	+	12.7287i	−0.256495	+	0.652968i
$381$	−37.0986			−1.90062
$382$	12.5854			0.643923
$383$	20.6609			1.05572			0.527861	−	0.849331i	$-0.322994\pi$
$383$	20.6609			1.05572			0.527861	+	0.849331i	$0.322994\pi$
$384$			25.0953i			1.28064i
$385$	−1.52574	+	3.88412i	−0.0777587	+	0.197953i
$386$	−12.6178			−0.642229
$387$		−	2.23566i		−	0.113645i
$388$	66.2430			3.36298
$389$	19.7477			1.00125			0.500624	−	0.865665i	$-0.333104\pi$
$389$	19.7477			1.00125			0.500624	+	0.865665i	$0.333104\pi$
$390$		0			0
$391$	−2.63509			−0.133262
$392$	10.3263			0.521557
$393$		−	21.5293i		−	1.08601i
$394$	−17.1722			−0.865122
$395$	−2.16123	−	0.848960i	−0.108743	−	0.0427158i
$396$			4.65297i			0.233820i
$397$	9.38902			0.471222			0.235611	−	0.971847i	$-0.424291\pi$
$397$	9.38902			0.471222			0.235611	+	0.971847i	$0.424291\pi$
$398$	13.1753			0.660420
$399$	−8.63509			−0.432295
$400$	26.0672	+	24.2156i	1.30336	+	1.21078i
$401$			24.5019i			1.22357i	0.791025	+	0.611784i	$0.209548\pi$
$401$			24.5019i			1.22357i	−0.791025	+	0.611784i	$0.790452\pi$
$402$			44.0109i			2.19506i
$403$		0			0
$404$	−59.2887			−2.94972
$405$	−23.3761	−	9.18246i	−1.16157	−	0.456280i
$406$	22.4424			1.11380
$407$		−	0.777322i		−	0.0385304i
$408$	−16.6417			−0.823889
$409$			36.1165i			1.78584i	0.450211	+	0.892922i	$0.351349\pi$
$409$			36.1165i			1.78584i	−0.450211	+	0.892922i	$0.648651\pi$
$410$	−20.7326	+	52.7797i	−1.02391	+	2.60660i
$411$			18.6708i			0.920965i
$412$		−	49.1479i		−	2.42134i
$413$			22.3232i			1.09845i
$414$			8.96157i			0.440437i
$415$	24.6530	+	9.68401i	1.21017	+	0.475370i
$416$		0			0
$417$			30.8439i			1.51043i
$418$	2.20675			0.107936
$419$	6.86684			0.335467			0.167734	−	0.985832i	$-0.446355\pi$
$419$	6.86684			0.335467			0.167734	+	0.985832i	$0.446355\pi$
$420$	−23.1754	+	58.9986i	−1.13085	+	2.87884i
$421$		−	33.9795i		−	1.65606i	−0.560686	−	0.828029i	$-0.689462\pi$
$421$		−	33.9795i		−	1.65606i	0.560686	−	0.828029i	$-0.310538\pi$
$422$	−35.6859			−1.73716
$423$	10.0783			0.490026
$424$			4.05631i			0.196992i
$425$	4.16517	−	4.48365i	0.202040	−	0.217489i
$426$	−14.4424			−0.699735
$427$	6.67104			0.322834
$428$			47.8261i			2.31176i
$429$		0			0
$430$	−2.84570	+	7.24440i	−0.137232	+	0.349356i
$431$			16.2496i			0.782717i	0.920238	+	0.391359i	$0.127995\pi$
$431$			16.2496i			0.782717i	−0.920238	+	0.391359i	$0.872005\pi$
$432$		−	20.9104i		−	1.00605i
$433$			0.256261i			0.0123151i	0.999981	+	0.00615756i	$0.00196002\pi$
$433$			0.256261i			0.0123151i	−0.999981	+	0.00615756i	$0.998040\pi$
$434$		−	67.0396i		−	3.21800i
$435$	−5.28034	+	13.4424i	−0.253173	+	0.644512i
$436$		−	14.6530i		−	0.701750i
$437$	2.93855			0.140570
$438$		−	56.5962i		−	2.70427i
$439$	−7.59666			−0.362569			−0.181284	−	0.983431i	$-0.558025\pi$
$439$	−7.59666			−0.362569			−0.181284	+	0.983431i	$0.558025\pi$
$440$	3.27906	−	8.34763i	0.156323	−	0.397957i
$441$	−2.67352			−0.127310
$442$		0			0
$443$		−	4.32246i		−	0.205366i	−0.994714	−	0.102683i	$-0.967257\pi$
$443$		−	4.32246i		−	0.205366i	0.994714	−	0.102683i	$-0.0327428\pi$
$444$		−	11.8073i		−	0.560348i
$445$	−10.2669	+	26.1369i	−0.486698	+	1.23901i
$446$	−0.0211421			−0.00100111
$447$	−36.9332			−1.74688
$448$	0.793931			0.0375097
$449$		−	3.28806i		−	0.155173i	−0.996986	−	0.0775865i	$-0.975279\pi$
$449$		−	3.28806i		−	0.155173i	0.996986	−	0.0775865i	$-0.0247214\pi$
$450$	−15.2483	−	14.1652i	−0.718811	−	0.667753i
$451$	6.32648			0.297903
$452$		−	24.7779i		−	1.16545i
$453$	−46.0356			−2.16294
$454$	−28.6741			−1.34574
$455$		0			0
$456$	18.5582			0.869069
$457$	−15.4261			−0.721602			−0.360801	−	0.932643i	$-0.617497\pi$
$457$	−15.4261			−0.721602			−0.360801	+	0.932643i	$0.617497\pi$
$458$			42.1074i			1.96755i
$459$	−3.59666			−0.167878
$460$	7.88669	−	20.0774i	0.367719	−	0.936116i
$461$		−	25.8847i		−	1.20557i	−0.797903	−	0.602786i	$-0.794057\pi$
$461$		−	25.8847i		−	1.20557i	0.797903	−	0.602786i	$-0.205943\pi$
$462$	10.2285			0.475872
$463$	7.04045			0.327197			0.163599	−	0.986527i	$-0.447690\pi$
$463$	7.04045			0.327197			0.163599	+	0.986527i	$0.447690\pi$
$464$	−21.3476			−0.991039
$465$	40.1549	+	15.7734i	1.86214	+	0.731473i
$466$		−	17.6914i		−	0.819538i
$467$		−	18.8113i		−	0.870482i	−0.900314	−	0.435241i	$-0.856663\pi$
$467$		−	18.8113i		−	0.870482i	0.900314	−	0.435241i	$-0.143337\pi$
$468$		0			0
$469$	23.5967			1.08959
$470$	−32.6578	−	12.8284i	−1.50639	−	0.591731i
$471$	39.5377			1.82180
$472$		−	47.9762i		−	2.20828i
$473$	0.868356			0.0399271
$474$			5.69140i			0.261414i
$475$	−4.64484	+	5.00000i	−0.213120	+	0.229416i
$476$			16.1159i			0.738670i
$477$		−	1.05019i		−	0.0480850i
$478$			10.1830i			0.465758i
$479$			19.4775i			0.889951i	0.895543	+	0.444975i	$0.146788\pi$
$479$			19.4775i			0.889951i	−0.895543	+	0.444975i	$0.853212\pi$
$480$	9.65297	−	24.5739i	0.440596	−	1.12164i
$481$		0			0
$482$			50.3346i			2.29268i
$483$	13.6205			0.619752
$484$	47.4814			2.15824
$485$	30.7688	+	12.0864i	1.39714	+	0.548816i
$486$			39.1165i			1.77436i
$487$	−32.3241			−1.46474			−0.732372	−	0.680905i	$-0.761587\pi$
$487$	−32.3241			−1.46474			−0.732372	+	0.680905i	$0.761587\pi$
$488$	−14.3372			−0.649013
$489$		−	8.63509i		−	0.390492i
$490$	8.66324	+	3.40304i	0.391365	+	0.153734i
$491$	−28.6708			−1.29390			−0.646949	−	0.762534i	$-0.723955\pi$
$491$	−28.6708			−1.29390			−0.646949	+	0.762534i	$0.723955\pi$
$492$	96.0973			4.33240
$493$			3.67187i			0.165373i
$494$		0			0
$495$	−0.848960	+	2.16123i	−0.0381579	+	0.0971401i
$496$			63.7694i			2.86333i
$497$			7.74335i			0.347337i
$498$		−	64.9213i		−	2.90919i
$499$			28.9616i			1.29650i	0.761428	+	0.648249i	$0.224498\pi$
$499$			28.9616i			1.29650i	−0.761428	+	0.648249i	$0.775502\pi$
$500$	21.6960	+	45.1549i	0.970275	+	2.01939i
$501$		−	6.32648i		−	0.282646i
$502$	−9.35181			−0.417392
$503$			28.1093i			1.25333i	0.779289	+	0.626665i	$0.215581\pi$
$503$			28.1093i			1.25333i	−0.779289	+	0.626665i	$0.784419\pi$
$504$	30.3444			1.35165
$505$	−27.5386	−	10.8175i	−1.22545	−	0.481374i
$506$	−3.48079			−0.154740
$507$		0			0
$508$		−	77.2116i		−	3.42571i
$509$			21.1126i			0.935800i	0.883781	+	0.467900i	$0.154989\pi$
$509$			21.1126i			0.935800i	−0.883781	+	0.467900i	$0.845011\pi$
$510$	−13.9616	−	5.48429i	−0.618229	−	0.242848i
$511$	−30.3444			−1.34236
$512$	−50.8542			−2.24746
$513$	4.01086			0.177084
$514$		−	33.7688i		−	1.48948i
$515$	8.96730	−	22.8284i	0.395147	−	1.00594i
$516$	13.1901			0.580660
$517$			3.91455i			0.172162i
$518$	−9.15616			−0.402299
$519$	−2.94369			−0.129214
$520$		0			0
$521$	0.673516			0.0295073			0.0147536	−	0.999891i	$-0.495304\pi$
$521$	0.673516			0.0295073			0.0147536	+	0.999891i	$0.495304\pi$
$522$	12.4875			0.546564
$523$			29.8626i			1.30580i	0.757444	+	0.652900i	$0.226448\pi$
$523$			29.8626i			1.30580i	−0.757444	+	0.652900i	$0.773552\pi$
$524$	44.8079			1.95744
$525$	−21.5293	+	23.1754i	−0.939614	+	1.01146i
$526$		−	77.0608i		−	3.36001i
$527$	10.9686			0.477799
$528$	−9.72953			−0.423423
$529$	18.3649			0.798474
$530$	−1.33676	+	3.40304i	−0.0580650	+	0.147818i
$531$			12.4212i			0.539035i
$532$		−	17.9718i		−	0.779177i
$533$		0			0
$534$	68.8290			2.97852
$535$	−8.72614	+	22.2145i	−0.377264	+	0.960415i
$536$	−50.7131			−2.19047
$537$		−	16.7630i		−	0.723375i
$538$	56.6418			2.44200
$539$		−	1.03843i		−	0.0447282i
$540$	10.7646	−	27.4039i	0.463236	−	1.17928i
$541$			6.28806i			0.270345i	0.990822	+	0.135172i	$0.0431588\pi$
$541$			6.28806i			0.270345i	−0.990822	+	0.135172i	$0.956841\pi$
$542$		−	30.1121i		−	1.29342i
$543$		−	8.32502i		−	0.357261i
$544$		−	6.71254i		−	0.287798i
$545$	2.67352	−	6.80607i	0.114521	−	0.291540i
$546$		0			0
$547$		−	3.03789i		−	0.129891i	−0.997889	−	0.0649454i	$-0.979313\pi$
$547$		−	3.03789i		−	0.129891i	0.997889	−	0.0649454i	$-0.0206873\pi$
$548$	−38.8588			−1.65997
$549$	3.71194			0.158422
$550$	5.50193	−	5.92262i	0.234603	−	0.252541i
$551$		−	4.09473i		−	0.174442i
$552$	−29.2726			−1.24592
$553$	3.05147			0.129762
$554$		−	42.7304i		−	1.81544i
$555$	2.15430	−	5.48429i	0.0914450	−	0.232795i
$556$	−64.1939			−2.72243
$557$	−20.6996			−0.877071			−0.438536	−	0.898714i	$-0.644503\pi$
$557$	−20.6996			−0.877071			−0.438536	+	0.898714i	$0.644503\pi$
$558$		−	37.3026i		−	1.57915i
$559$		0			0
$560$	−43.5198	−	17.0952i	−1.83905	−	0.722402i
$561$			1.67352i			0.0706559i
$562$		−	26.9763i		−	1.13793i
$563$			10.9603i			0.461921i	0.972963	+	0.230960i	$0.0741868\pi$
$563$			10.9603i			0.461921i	−0.972963	+	0.230960i	$0.925813\pi$
$564$			59.4608i			2.50375i
$565$	4.52086	−	11.5089i	0.190194	−	0.484185i
$566$		−	22.4424i		−	0.943323i
$567$	33.0051			1.38608
$568$		−	16.6417i		−	0.698272i
$569$	42.7131			1.79063			0.895314	−	0.445436i	$-0.146951\pi$
$569$	42.7131			1.79063			0.895314	+	0.445436i	$0.146951\pi$
$570$	15.5694	+	6.11588i	0.652131	+	0.256166i
$571$	23.6145			0.988238			0.494119	−	0.869394i	$-0.335491\pi$
$571$	23.6145			0.988238			0.494119	+	0.869394i	$0.335491\pi$
$572$		0			0
$573$		−	10.6434i		−	0.444635i
$574$		−	74.5204i		−	3.11042i
$575$	7.32648	−	7.88669i	0.305536	−	0.328898i
$576$	0.441765			0.0184069
$577$	−18.3646			−0.764530			−0.382265	−	0.924053i	$-0.624856\pi$
$577$	−18.3646			−0.764530			−0.382265	+	0.924053i	$0.624856\pi$
$578$	39.4639			1.64148
$579$			10.6708i			0.443465i
$580$	−27.9770	−	10.9897i	−1.16168	−	0.456324i
$581$	−34.8079			−1.44407
$582$		−	81.0268i		−	3.35867i
$583$	0.407908			0.0168938
$584$	65.2151			2.69862
$585$		0			0
$586$	−71.9237			−2.97114
$587$	−0.702897			−0.0290116			−0.0145058	−	0.999895i	$-0.504618\pi$
$587$	−0.702897			−0.0290116			−0.0145058	+	0.999895i	$0.504618\pi$
$588$		−	15.7734i		−	0.650483i
$589$	−12.2318			−0.504001
$590$	15.8106	−	40.2496i	0.650912	−	1.65705i
$591$			14.5225i			0.597375i
$592$	8.70953			0.357959
$593$	−37.1593			−1.52595			−0.762975	−	0.646428i	$-0.776262\pi$
$593$	−37.1593			−1.52595			−0.762975	+	0.646428i	$0.776262\pi$
$594$	−4.75096			−0.194934
$595$	−2.94043	+	7.48557i	−0.120546	+	0.306878i
$596$		−	76.8674i		−	3.14861i
$597$		−	11.1423i		−	0.456026i
$598$		0			0
$599$	15.6914			0.641133			0.320567	−	0.947226i	$-0.396127\pi$
$599$	15.6914			0.641133			0.320567	+	0.947226i	$0.396127\pi$
$600$	46.2699	−	49.8079i	1.88896	−	2.03340i
$601$	12.0039			0.489648			0.244824	−	0.969568i	$-0.421270\pi$
$601$	12.0039			0.489648			0.244824	+	0.969568i	$0.421270\pi$
$602$		−	10.2285i		−	0.416881i
$603$	13.1298			0.534687
$604$		−	95.8117i		−	3.89852i
$605$	22.0544	+	8.66324i	0.896637	+	0.352211i
$606$			72.5204i			2.94594i
$607$			38.6865i			1.57024i	0.619345	+	0.785119i	$0.287398\pi$
$607$			38.6865i			1.57024i	−0.619345	+	0.785119i	$0.712602\pi$
$608$			7.48557i			0.303580i
$609$		−	18.9795i		−	0.769086i
$610$	−12.0282	−	4.72482i	−0.487006	−	0.191302i
$611$		0			0
$612$			8.96730i			0.362482i
$613$	17.2840			0.698095			0.349047	−	0.937105i	$-0.386505\pi$
$613$	17.2840			0.698095			0.349047	+	0.937105i	$0.386505\pi$
$614$	−32.3866			−1.30702
$615$	44.6357	+	17.5335i	1.79988	+	0.707018i
$616$			11.7861i			0.474877i
$617$	26.4691			1.06561			0.532803	−	0.846240i	$-0.321139\pi$
$617$	26.4691			1.06561			0.532803	+	0.846240i	$0.321139\pi$
$618$	−60.1165			−2.41824
$619$			31.0039i			1.24615i	0.782162	+	0.623075i	$0.214117\pi$
$619$			31.0039i			1.24615i	−0.782162	+	0.623075i	$0.785883\pi$
$620$	−32.8284	+	83.5726i	−1.31842	+	3.35636i
$621$	−6.32648			−0.253873
$622$	−71.0850			−2.85025
$623$		−	36.9030i		−	1.47849i
$624$		0			0
$625$	1.83869	+	24.9323i	0.0735475	+	0.997292i
$626$		−	62.5761i		−	2.50104i
$627$		−	1.86624i		−	0.0745305i
$628$			82.2880i			3.28365i
$629$		−	1.49807i		−	0.0597320i
$630$	25.4574	+	10.0000i	1.01425	+	0.398410i
$631$		−	20.7131i		−	0.824577i	−0.911053	−	0.412288i	$-0.864730\pi$
$631$		−	20.7131i		−	0.824577i	0.911053	−	0.412288i	$-0.135270\pi$
$632$	−6.55812			−0.260868
$633$			30.1795i			1.19953i
$634$	−0.596662			−0.0236965
$635$	14.0877	−	35.8636i	0.559053	−	1.42320i
$636$	6.19599			0.245687
$637$		0			0
$638$			4.85031i			0.192026i
$639$			4.30860i			0.170446i
$640$	−24.2599	−	9.52961i	−0.958957	−	0.376691i
$641$	−21.1895			−0.836934			−0.418467	−	0.908232i	$-0.637432\pi$
$641$	−21.1895			−0.836934			−0.418467	+	0.908232i	$0.637432\pi$
$642$	58.4997			2.30880
$643$	11.5336			0.454843			0.227421	−	0.973796i	$-0.426971\pi$
$643$	11.5336			0.454843			0.227421	+	0.973796i	$0.426971\pi$
$644$			28.3476i			1.11705i
$645$	6.12658	+	2.40660i	0.241234	+	0.0947598i
$646$	4.25289			0.167328
$647$			34.8464i			1.36995i	0.728565	+	0.684977i	$0.240188\pi$
$647$			34.8464i			1.36995i	−0.728565	+	0.684977i	$0.759812\pi$
$648$	−70.9334			−2.78653
$649$	−4.82456			−0.189380
$650$		0			0
$651$	−56.6953			−2.22206
$652$	17.9718			0.703831
$653$		−	22.3232i		−	0.873574i	−0.899565	−	0.436787i	$-0.856116\pi$
$653$		−	22.3232i		−	0.873574i	0.899565	−	0.436787i	$-0.143884\pi$
$654$	−17.9231			−0.700850
$655$	20.8125	+	8.17544i	0.813214	+	0.319441i
$656$			70.8853i			2.76761i
$657$	−16.8844			−0.658724
$658$	46.1100			1.79755
$659$	0.866840			0.0337673			0.0168836	−	0.999857i	$-0.494626\pi$
$659$	0.866840			0.0337673			0.0168836	+	0.999857i	$0.494626\pi$
$660$	−12.7510	−	5.00875i	−0.496331	−	0.194965i
$661$			13.3086i			0.517645i	0.965925	+	0.258822i	$0.0833344\pi$
$661$			13.3086i			0.517645i	−0.965925	+	0.258822i	$0.916666\pi$
$662$			46.6544i			1.81328i
$663$		0			0
$664$	74.8079			2.90311
$665$	3.27906	−	8.34763i	0.127156	−	0.323707i
$666$	−5.09473			−0.197417
$667$			6.45878i			0.250085i
$668$	13.1670			0.509448
$669$			0.0178799i			0.000691275i
$670$	−42.5458	−	16.7125i	−1.64369	−	0.645662i
$671$			1.44176i			0.0556587i
$672$			34.6963i			1.33844i
$673$		−	5.51320i		−	0.212518i	−0.994338	−	0.106259i	$-0.966113\pi$
$673$		−	5.51320i		−	0.212518i	0.994338	−	0.106259i	$-0.0338873\pi$
$674$			54.2112i			2.08814i
$675$	10.0000	−	10.7646i	0.384900	−	0.414331i
$676$		0			0
$677$		−	4.80479i		−	0.184663i	−0.995728	−	0.0923316i	$-0.970568\pi$
$677$		−	4.80479i		−	0.184663i	0.995728	−	0.0923316i	$-0.0294320\pi$
$678$	−30.3077			−1.16396
$679$	−43.4430			−1.66719
$680$	6.31947	−	16.0877i	0.242341	−	0.616936i
$681$			24.2496i			0.929248i
$682$	14.4888			0.554805
$683$	11.7625			0.450080			0.225040	−	0.974350i	$-0.427749\pi$
$683$	11.7625			0.450080			0.225040	+	0.974350i	$0.427749\pi$
$684$		−	10.0000i		−	0.382360i
$685$	−18.0493	−	7.09000i	−0.689628	−	0.270895i
$686$	40.1338			1.53231
$687$	35.6102			1.35861
$688$			9.72953i			0.370935i
$689$		0			0
$690$	−24.5582	−	9.64680i	−0.934916	−	0.367247i
$691$		−	4.86684i		−	0.185143i	−0.995706	−	0.0925717i	$-0.970491\pi$
$691$		−	4.86684i		−	0.185143i	0.995706	−	0.0925717i	$-0.0295087\pi$
$692$		−	6.12658i		−	0.232897i
$693$		−	3.05147i		−	0.115916i
$694$		−	9.71254i		−	0.368683i
$695$	−29.8171	−	11.7125i	−1.13103	−	0.444282i
$696$			40.7900i			1.54614i
$697$	12.1925			0.461825
$698$		−	61.9289i		−	2.34404i
$699$	−14.9616			−0.565899
$700$	−48.2340	−	44.8079i	−1.82307	−	1.69358i
$701$	−21.3828			−0.807617			−0.403808	−	0.914844i	$-0.632314\pi$
$701$	−21.3828			−0.807617			−0.403808	+	0.914844i	$0.632314\pi$
$702$		0			0
$703$			1.67059i			0.0630076i
$704$			0.171587i			0.00646692i
$705$	−10.8490	+	27.6186i	−0.408595	+	1.04018i
$706$	68.8853			2.59253
$707$	38.8822			1.46232
$708$	−73.2835			−2.75416
$709$			26.1165i			0.980825i	0.871491	+	0.490412i	$0.163154\pi$
$709$			26.1165i			0.980825i	−0.871491	+	0.490412i	$0.836846\pi$
$710$	5.48429	−	13.9616i	0.205822	−	0.523969i
$711$	1.69792			0.0636770
$712$			79.3107i			2.97229i
$713$	19.2936			0.722551
$714$	19.7125			0.737723
$715$		0			0
$716$	34.8880			1.30383
$717$	8.61170			0.321610
$718$		−	68.7448i		−	2.56553i
$719$	36.6774			1.36784			0.683918	−	0.729559i	$-0.260275\pi$
$719$	36.6774			1.36784			0.683918	+	0.729559i	$0.260275\pi$
$720$	−24.2156	−	9.51220i	−0.902462	−	0.354499i
$721$			32.2318i			1.20037i
$722$	43.6264			1.62361
$723$	42.5679			1.58312
$724$	17.3265			0.643934
$725$	−10.9897	−	10.2091i	−0.408148	−	0.379157i
$726$		−	58.0780i		−	2.15548i
$727$			26.2596i			0.973916i	0.873425	+	0.486958i	$0.161893\pi$
$727$			26.2596i			0.973916i	−0.873425	+	0.486958i	$0.838107\pi$
$728$		0			0
$729$	−0.614542			−0.0227608
$730$	54.7121	+	21.4917i	2.02499	+	0.795442i
$731$	1.67352			0.0618972
$732$			21.9000i			0.809446i
$733$	−31.7811			−1.17386			−0.586931	−	0.809637i	$-0.699664\pi$
$733$	−31.7811			−1.17386			−0.586931	+	0.809637i	$0.699664\pi$
$734$		−	17.6703i		−	0.652221i
$735$	2.87794	−	7.32648i	0.106154	−	0.270241i
$736$		−	11.8073i		−	0.435222i
$737$			5.09978i			0.187853i
$738$		−	41.4651i		−	1.52635i
$739$			34.1370i			1.25575i	0.778314	+	0.627875i	$0.216075\pi$
$739$			34.1370i			1.25575i	−0.778314	+	0.627875i	$0.783925\pi$
$740$	11.4142	+	4.48365i	0.419595	+	0.164822i
$741$		0			0
$742$		−	4.80479i		−	0.176390i
$743$	−3.12062			−0.114485			−0.0572423	−	0.998360i	$-0.518231\pi$
$743$	−3.12062			−0.114485			−0.0572423	+	0.998360i	$0.518231\pi$
$744$	121.847			4.46715
$745$	14.0249	−	35.7037i	0.513832	−	1.30808i
$746$		−	5.88798i		−	0.215574i
$747$	−19.3680			−0.708639
$748$	−3.48301			−0.127352
$749$		−	31.3649i		−	1.14605i
$750$	55.2323	−	26.5380i	2.01680	−	0.969031i
$751$	−1.48405			−0.0541537			−0.0270769	−	0.999633i	$-0.508620\pi$
$751$	−1.48405			−0.0541537			−0.0270769	+	0.999633i	$0.508620\pi$
$752$	−43.8607			−1.59944
$753$			7.90881i			0.288213i
$754$		0			0
$755$	17.4814	−	44.5030i	0.636213	−	1.61963i
$756$			38.6920i			1.40721i
$757$			5.09978i			0.185355i	0.995696	+	0.0926774i	$0.0295425\pi$
$757$			5.09978i			0.185355i	−0.995696	+	0.0926774i	$0.970457\pi$
$758$			13.1753i			0.478550i
$759$			2.94369i			0.106849i
$760$	−7.04724	+	17.9404i	−0.255630	+	0.650768i
$761$		−	29.7861i		−	1.07975i	−0.841746	−	0.539873i	$-0.818472\pi$
$761$		−	29.7861i		−	1.07975i	0.841746	−	0.539873i	$-0.181528\pi$
$762$	−94.4433			−3.42132
$763$			9.60959i			0.347890i
$764$	22.1516			0.801418
$765$	−1.63613	+	4.16517i	−0.0591546	+	0.150592i
$766$	52.5973			1.90042
$767$		0			0
$768$			62.7228i			2.26331i
$769$			19.0986i			0.688713i	0.938839	+	0.344356i	$0.111903\pi$
$769$			19.0986i			0.688713i	−0.938839	+	0.344356i	$0.888097\pi$
$770$	−3.88412	+	9.88797i	−0.139974	+	0.356338i
$771$	−28.5582			−1.02850
$772$	−22.2088			−0.799311
$773$	−49.2306			−1.77070			−0.885351	−	0.464923i	$-0.846082\pi$
$773$	−49.2306			−1.77070			−0.885351	+	0.464923i	$0.846082\pi$
$774$		−	5.69140i		−	0.204573i
$775$	−30.4966	+	32.8284i	−1.09547	+	1.17923i
$776$	93.3661			3.35165
$777$			7.74335i			0.277791i
$778$	50.2725			1.80236
$779$	−13.5967			−0.487151
$780$		0			0
$781$	−1.67352			−0.0598831
$782$	−6.70825			−0.239886
$783$			8.81566i			0.315046i
$784$	11.6351			0.415539
$785$	−15.0139	+	38.2215i	−0.535869	+	1.36418i
$786$		−	54.8079i		−	1.95493i
$787$	9.78335			0.348739			0.174369	−	0.984680i	$-0.444211\pi$
$787$	9.78335			0.348739			0.174369	+	0.984680i	$0.444211\pi$
$788$	−30.2250			−1.07672
$789$	−65.1701			−2.32012
$790$	−5.50193	−	2.16123i	−0.195750	−	0.0768931i
$791$			16.2496i			0.577770i
$792$			6.55812i			0.233033i
$793$		0			0
$794$	23.9020			0.848250
$795$	2.87794	+	1.13049i	0.102070	+	0.0400945i
$796$	23.1901			0.821950
$797$		−	16.5371i		−	0.585775i	−0.956147	−	0.292887i	$-0.905384\pi$
$797$		−	16.5371i		−	0.585775i	0.956147	−	0.292887i	$-0.0946161\pi$
$798$	−21.9827			−0.778178
$799$			7.54421i			0.266895i
$800$	20.0903	+	18.6632i	0.710299	+	0.659845i
$801$		−	20.5338i		−	0.725527i
$802$			62.3755i			2.20256i
$803$		−	6.55812i		−	0.231431i
$804$			77.4641i			2.73195i
$805$	−5.17218	+	13.1670i	−0.182295	+	0.464077i
$806$		0			0
$807$		−	47.9018i		−	1.68622i
$808$	−83.5643			−2.93978
$809$	31.8424			1.11952			0.559760	−	0.828655i	$-0.310893\pi$
$809$	31.8424			1.11952			0.559760	+	0.828655i	$0.310893\pi$
$810$	−59.5095	−	23.3761i	−2.09095	−	0.821354i
$811$		−	13.3470i		−	0.468678i	−0.972155	−	0.234339i	$-0.924707\pi$
$811$		−	13.3470i		−	0.468678i	0.972155	−	0.234339i	$-0.0752925\pi$
$812$	39.5011			1.38622
$813$	−25.4657			−0.893121
$814$		−	1.97886i		−	0.0693589i
$815$	8.34763	+	3.27906i	0.292405	+	0.114860i
$816$	−18.7510			−0.656415
$817$	−1.86624			−0.0652915
$818$			91.9431i			3.21472i
$819$		0			0
$820$	−36.4917	+	92.8982i	−1.27434	+	3.24415i
$821$		−	11.6735i		−	0.407409i	−0.979032	−	0.203704i	$-0.934702\pi$
$821$		−	11.6735i		−	0.407409i	0.979032	−	0.203704i	$-0.0652981\pi$
$822$			47.5311i			1.65784i
$823$			32.4317i			1.13050i	0.824920	+	0.565249i	$0.191220\pi$
$823$			32.4317i			1.13050i	−0.824920	+	0.565249i	$0.808780\pi$
$824$		−	69.2714i		−	2.41318i
$825$	−5.00875	−	4.65297i	−0.174382	−	0.161996i
$826$			56.8290i			1.97733i
$827$	−27.3319			−0.950425			−0.475212	−	0.879871i	$-0.657629\pi$
$827$	−27.3319			−0.950425			−0.475212	+	0.879871i	$0.657629\pi$
$828$			15.7734i			0.548163i
$829$	3.54036			0.122962			0.0614808	−	0.998108i	$-0.480418\pi$
$829$	3.54036			0.122962			0.0614808	+	0.998108i	$0.480418\pi$
$830$	62.7600	+	24.6530i	2.17843	+	0.855717i
$831$	−36.1370			−1.25358
$832$		0			0
$833$		−	2.00128i		−	0.0693402i
$834$			78.5204i			2.71894i
$835$	6.11588	+	2.40240i	0.211649	+	0.0831384i
$836$	3.88412			0.134335
$837$	26.3341			0.910238
$838$	17.4812			0.603877
$839$		−	44.7900i		−	1.54632i	−0.634210	−	0.773161i	$-0.718674\pi$
$839$		−	44.7900i		−	1.54632i	0.634210	−	0.773161i	$-0.281326\pi$
$840$	−32.6646	+	83.1555i	−1.12704	+	2.86914i
$841$	−20.0000			−0.689655
$842$		−	86.5028i		−	2.98108i
$843$	−22.8138			−0.785750
$844$	−62.8111			−2.16205
$845$		0			0
$846$	25.6568			0.882100
$847$	−31.1388			−1.06994
$848$			4.57042i			0.156949i
$849$	−18.9795			−0.651373
$850$	10.6034	−	11.4142i	0.363695	−	0.391504i
$851$		−	2.63509i		−	0.0903297i
$852$	−25.4202			−0.870881
$853$	−31.3732			−1.07420			−0.537099	−	0.843519i	$-0.680480\pi$
$853$	−31.3732			−1.07420			−0.537099	+	0.843519i	$0.680480\pi$
$854$	16.9827			0.581137
$855$	1.82456	−	4.64484i	0.0623985	−	0.158850i
$856$			67.4084i			2.30397i
$857$			21.2813i			0.726955i	0.931603	+	0.363478i	$0.118411\pi$
$857$			21.2813i			0.726955i	−0.931603	+	0.363478i	$0.881589\pi$
$858$		0			0
$859$	−56.8502			−1.93970			−0.969851	−	0.243698i	$-0.921639\pi$
$859$	−56.8502			−1.93970			−0.969851	+	0.243698i	$0.921639\pi$
$860$	−5.00875	+	12.7510i	−0.170797	+	0.434804i
$861$	−63.0217			−2.14778
$862$			41.3673i			1.40898i
$863$	−32.8011			−1.11656			−0.558282	−	0.829651i	$-0.688539\pi$
$863$	−32.8011			−1.11656			−0.558282	+	0.829651i	$0.688539\pi$
$864$		−	16.1159i		−	0.548273i
$865$	1.11783	−	2.84570i	0.0380073	−	0.0967566i
$866$			0.652374i			0.0221686i
$867$		−	33.3745i		−	1.13346i
$868$		−	117.997i		−	4.00509i
$869$			0.659493i			0.0223718i
$870$	−13.4424	+	34.2207i	−0.455739	+	1.16019i
$871$		0			0
$872$		−	20.6526i		−	0.699385i
$873$	−24.1728			−0.818126
$874$	7.48079			0.253041
$875$	−14.2285	−	29.6131i	−0.481011	−	1.00111i
$876$		−	99.6157i		−	3.36570i
$877$	−36.0651			−1.21783			−0.608916	−	0.793235i	$-0.708395\pi$
$877$	−36.0651			−1.21783			−0.608916	+	0.793235i	$0.708395\pi$
$878$	−19.3391			−0.652664
$879$			60.8257i			2.05160i
$880$	3.69466	−	9.40563i	0.124547	−	0.317064i
$881$	46.0396			1.55111			0.775557	−	0.631277i	$-0.217469\pi$
$881$	46.0396			1.55111			0.775557	+	0.631277i	$0.217469\pi$
$882$	−6.80607			−0.229172
$883$			0.802236i			0.0269974i	0.999909	+	0.0134987i	$0.00429690\pi$
$883$			0.802236i			0.0269974i	−0.999909	+	0.0134987i	$0.995703\pi$
$884$		0			0
$885$	−34.0390	−	13.3710i	−1.14421	−	0.449461i
$886$		−	11.0039i		−	0.369682i
$887$			8.22568i			0.276191i	0.990419	+	0.138096i	$0.0440981\pi$
$887$			8.22568i			0.276191i	−0.990419	+	0.138096i	$0.955902\pi$
$888$		−	16.6417i		−	0.558460i
$889$			50.6363i			1.69829i
$890$	−26.1369	+	66.5377i	−0.876110	+	2.23035i
$891$			7.13316i			0.238970i
$892$	−0.0372125			−0.00124597
$893$		−	8.41302i		−	0.281531i
$894$	−94.0223			−3.14458
$895$	16.2049	+	6.36551i	0.541671	+	0.212775i
$896$	34.2529			1.14431
$897$		0			0
$898$		−	8.37054i		−	0.279328i
$899$		−	26.8847i		−	0.896656i
$900$	−26.8387	−	24.9323i	−0.894623	−	0.831076i
$901$	0.786129			0.0261897
$902$	16.1056			0.536257
$903$	−8.65020			−0.287861
$904$		−	34.9231i		−	1.16153i
$905$	8.04788	+	3.16131i	0.267521	+	0.105086i
$906$	−117.195			−3.89353
$907$			30.4359i			1.01061i	0.862941	+	0.505305i	$0.168620\pi$
$907$			30.4359i			1.01061i	−0.862941	+	0.505305i	$0.831380\pi$
$908$	−50.4697			−1.67489
$909$	21.6351			0.717591
$910$		0			0
$911$	43.6145			1.44501			0.722507	−	0.691363i	$-0.242990\pi$
$911$	43.6145			1.44501			0.722507	+	0.691363i	$0.242990\pi$
$912$	20.9104			0.692412
$913$		−	7.52278i		−	0.248968i
$914$	−39.2708			−1.29896
$915$	−3.99577	+	10.1722i	−0.132096	+	0.336282i
$916$			74.1138i			2.44879i
$917$	−29.3855			−0.970395
$918$	−9.15616			−0.302198
$919$	37.0217			1.22123			0.610617	−	0.791926i	$-0.290921\pi$
$919$	37.0217			1.22123			0.610617	+	0.791926i	$0.290921\pi$
$920$	11.1159	−	28.2981i	0.366480	−	0.932961i
$921$			27.3893i			0.902509i
$922$		−	65.8957i		−	2.17016i
$923$		0			0
$924$	18.0033			0.592264
$925$	4.48365	+	4.16517i	0.147422	+	0.136950i
$926$	17.9231			0.588991
$927$			17.9346i			0.589050i
$928$	−16.4529			−0.540092
$929$		−	4.76825i		−	0.156441i	−0.996936	−	0.0782206i	$-0.975076\pi$
$929$		−	4.76825i		−	0.156441i	0.996936	−	0.0782206i	$-0.0249238\pi$
$930$	102.224	+	40.1549i	3.35205	+	1.31673i
$931$			2.23175i			0.0731427i
$932$		−	31.1388i		−	1.01999i
$933$			60.1165i			1.96812i
$934$		−	47.8886i		−	1.56696i
$935$	−1.61780	−	0.635495i	−0.0529079	−	0.0207829i
$936$		0			0
$937$			43.6264i			1.42521i	0.701565	+	0.712606i	$0.252485\pi$
$937$			43.6264i			1.42521i	−0.701565	+	0.712606i	$0.747515\pi$
$938$	60.0709			1.96139
$939$	−52.9205			−1.72699
$940$	−57.4814	−	22.5794i	−1.87484	−	0.736460i
$941$		−	18.2675i		−	0.595504i	−0.954643	−	0.297752i	$-0.903763\pi$
$941$		−	18.2675i		−	0.595504i	0.954643	−	0.297752i	$-0.0962368\pi$
$942$	100.653			3.27944
$943$	21.4465			0.698395
$944$		−	54.0569i		−	1.75940i
$945$	−7.05957	+	17.9718i	−0.229648	+	0.584623i
$946$	2.21061			0.0718731
$947$	19.9829			0.649358			0.324679	−	0.945824i	$-0.394744\pi$
$947$	19.9829			0.649358			0.324679	+	0.945824i	$0.394744\pi$
$948$			10.0175i			0.325353i
$949$		0			0
$950$	−11.8246	+	12.7287i	−0.383639	+	0.412973i
$951$			0.504596i			0.0163626i
$952$			22.7145i			0.736181i
$953$		−	39.8635i		−	1.29130i	−0.763632	−	0.645652i	$-0.776586\pi$
$953$		−	39.8635i		−	1.29130i	0.763632	−	0.645652i	$-0.223414\pi$
$954$		−	2.67352i		−	0.0865583i
$955$	10.2891	+	4.04169i	0.332947	+	0.130786i
$956$			17.9231i			0.579676i
$957$	4.10190			0.132596
$958$			49.5847i			1.60201i
$959$	25.4840			0.822923
$960$	−0.475543	+	1.21061i	−0.0153481	+	0.0390722i
$961$	−49.3098			−1.59064
$962$		0			0
$963$		−	17.4523i		−	0.562392i
$964$			88.5946i			2.85344i
$965$	−10.3156	−	4.05211i	−0.332071	−	0.130442i
$966$	34.6741			1.11562
$967$	−43.8607			−1.41047			−0.705233	−	0.708975i	$-0.749158\pi$
$967$	−43.8607			−1.41047			−0.705233	+	0.708975i	$0.749158\pi$
$968$	66.9225			2.15097
$969$		−	3.59666i		−	0.115541i
$970$	78.3294	+	30.7688i	2.51501	+	0.987928i
$971$	60.9795			1.95692			0.978462	−	0.206428i	$-0.0661838\pi$
$971$	60.9795			1.95692			0.978462	+	0.206428i	$0.0661838\pi$
$972$			68.8494i			2.20835i
$973$	42.0991			1.34964
$974$	−82.2887			−2.63670
$975$		0			0
$976$	−16.1543			−0.517087
$977$	51.3697			1.64346			0.821731	−	0.569875i	$-0.193008\pi$
$977$	51.3697			1.64346			0.821731	+	0.569875i	$0.193008\pi$
$978$		−	21.9827i		−	0.702929i
$979$	7.97560			0.254901
$980$	15.2483	+	5.98973i	0.487088	+	0.191335i
$981$			5.34703i			0.170718i
$982$	−72.9885			−2.32916
$983$	37.3026			1.18977			0.594885	−	0.803811i	$-0.297198\pi$
$983$	37.3026			1.18977			0.594885	+	0.803811i	$0.297198\pi$
$984$	135.444			4.31780
$985$	−14.0390	−	5.51471i	−0.447320	−	0.175713i
$986$			9.34763i			0.297689i
$987$		−	38.9951i		−	1.24123i
$988$		0			0
$989$	2.94369			0.0936040
$990$	−2.16123	+	5.50193i	−0.0686884	+	0.174863i
$991$	−51.5621			−1.63792			−0.818962	−	0.573848i	$-0.805450\pi$
$991$	−51.5621			−1.63792			−0.818962	+	0.573848i	$0.805450\pi$
$992$			49.1479i			1.56045i
$993$	39.4556			1.25208
$994$			19.7125i			0.625244i
$995$	10.7714	+	4.23116i	0.341477	+	0.134137i
$996$		−	114.269i		−	3.62074i
$997$			22.9489i			0.726798i	0.931634	+	0.363399i	$0.118384\pi$
$997$			22.9489i			0.726798i	−0.931634	+	0.363399i	$0.881616\pi$
$998$			73.7286i			2.33384i
$999$		−	3.59666i		−	0.113793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.d.d.844.11		12
5.4	even	2	inner	845.2.d.d.844.2		12
13.2	odd	12		845.2.n.e.529.6		12
13.3	even	3		845.2.l.f.654.2		24
13.4	even	6		845.2.l.f.699.11		24
13.5	odd	4		845.2.b.e.339.1		6
13.6	odd	12		845.2.n.e.484.1		12
13.7	odd	12		65.2.n.a.29.6	yes	12
13.8	odd	4		845.2.b.d.339.6		6
13.9	even	3		845.2.l.f.699.1		24
13.10	even	6		845.2.l.f.654.12		24
13.11	odd	12		65.2.n.a.9.1	✓	12
13.12	even	2	inner	845.2.d.d.844.1		12
39.11	even	12		585.2.bs.a.334.6		12
39.20	even	12		585.2.bs.a.289.1		12
52.7	even	12		1040.2.dh.a.289.5		12
52.11	even	12		1040.2.dh.a.529.2		12
65.4	even	6		845.2.l.f.699.2		24
65.7	even	12		325.2.e.e.276.6		12
65.8	even	4		4225.2.a.br.1.6		6
65.9	even	6		845.2.l.f.699.12		24
65.18	even	4		4225.2.a.bq.1.1		6
65.19	odd	12		845.2.n.e.484.6		12
65.24	odd	12		65.2.n.a.9.6	yes	12
65.29	even	6		845.2.l.f.654.11		24
65.33	even	12		325.2.e.e.276.1		12
65.34	odd	4		845.2.b.d.339.1		6
65.37	even	12		325.2.e.e.126.6		12
65.44	odd	4		845.2.b.e.339.6		6
65.47	even	4		4225.2.a.br.1.1		6
65.49	even	6		845.2.l.f.654.1		24
65.54	odd	12		845.2.n.e.529.1		12
65.57	even	4		4225.2.a.bq.1.6		6
65.59	odd	12		65.2.n.a.29.1	yes	12
65.63	even	12		325.2.e.e.126.1		12
65.64	even	2	inner	845.2.d.d.844.12		12
195.59	even	12		585.2.bs.a.289.6		12
195.89	even	12		585.2.bs.a.334.1		12
260.59	even	12		1040.2.dh.a.289.2		12
260.219	even	12		1040.2.dh.a.529.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.1	✓	12	13.11	odd	12
65.2.n.a.9.6	yes	12	65.24	odd	12
65.2.n.a.29.1	yes	12	65.59	odd	12
65.2.n.a.29.6	yes	12	13.7	odd	12
325.2.e.e.126.1		12	65.63	even	12
325.2.e.e.126.6		12	65.37	even	12
325.2.e.e.276.1		12	65.33	even	12
325.2.e.e.276.6		12	65.7	even	12
585.2.bs.a.289.1		12	39.20	even	12
585.2.bs.a.289.6		12	195.59	even	12
585.2.bs.a.334.1		12	195.89	even	12
585.2.bs.a.334.6		12	39.11	even	12
845.2.b.d.339.1		6	65.34	odd	4
845.2.b.d.339.6		6	13.8	odd	4
845.2.b.e.339.1		6	13.5	odd	4
845.2.b.e.339.6		6	65.44	odd	4
845.2.d.d.844.1		12	13.12	even	2	inner
845.2.d.d.844.2		12	5.4	even	2	inner
845.2.d.d.844.11		12	1.1	even	1	trivial
845.2.d.d.844.12		12	65.64	even	2	inner
845.2.l.f.654.1		24	65.49	even	6
845.2.l.f.654.2		24	13.3	even	3
845.2.l.f.654.11		24	65.29	even	6
845.2.l.f.654.12		24	13.10	even	6
845.2.l.f.699.1		24	13.9	even	3
845.2.l.f.699.2		24	65.4	even	6
845.2.l.f.699.11		24	13.4	even	6
845.2.l.f.699.12		24	65.9	even	6
845.2.n.e.484.1		12	13.6	odd	12
845.2.n.e.484.6		12	65.19	odd	12
845.2.n.e.529.1		12	65.54	odd	12
845.2.n.e.529.6		12	13.2	odd	12
1040.2.dh.a.289.2		12	260.59	even	12
1040.2.dh.a.289.5		12	52.7	even	12
1040.2.dh.a.529.2		12	52.11	even	12
1040.2.dh.a.529.5		12	260.219	even	12
4225.2.a.bq.1.1		6	65.18	even	4
4225.2.a.bq.1.6		6	65.57	even	4
4225.2.a.br.1.1		6	65.47	even	4
4225.2.a.br.1.6		6	65.8	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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.54574 q^{2} -2.15293i q^{3} +4.48079 q^{4} +(2.08125 + 0.817544i) q^{5} -5.48079i q^{6} -2.93855 q^{7} +6.31544 q^{8} -1.63509 q^{9} +O(q^{10})\)	\(q+2.54574 q^{2} -2.15293i q^{3} +4.48079 q^{4} +(2.08125 + 0.817544i) q^{5} -5.48079i q^{6} -2.93855 q^{7} +6.31544 q^{8} -1.63509 q^{9} +(5.29833 + 2.08125i) q^{10} -0.635089i q^{11} -9.64680i q^{12} -7.48079 q^{14} +(1.76011 - 4.48079i) q^{15} +7.11588 q^{16} -1.22396i q^{17} -4.16251 q^{18} +1.36491i q^{19} +(9.32566 + 3.66324i) q^{20} +6.32648i q^{21} -1.61677i q^{22} -2.15293i q^{23} -13.5967i q^{24} +(3.66324 + 3.40304i) q^{25} -2.93855i q^{27} -13.1670 q^{28} -3.00000 q^{29} +(4.48079 - 11.4069i) q^{30} +8.96157i q^{31} +5.48429 q^{32} -1.36730 q^{33} -3.11588i q^{34} +(-6.11588 - 2.40240i) q^{35} -7.32648 q^{36} +1.22396 q^{37} +3.47471i q^{38} +(13.1440 + 5.16315i) q^{40} +9.96157i q^{41} +16.1056i q^{42} +1.36730i q^{43} -2.84570i q^{44} +(-3.40304 - 1.33676i) q^{45} -5.48079i q^{46} -6.16379 q^{47} -15.3200i q^{48} +1.63509 q^{49} +(9.32566 + 8.66324i) q^{50} -2.63509 q^{51} +0.642285i q^{53} -7.48079i q^{54} +(0.519213 - 1.32178i) q^{55} -18.5582 q^{56} +2.93855 q^{57} -7.63722 q^{58} -7.59666i q^{59} +(7.88669 - 20.0774i) q^{60} -2.27018 q^{61} +22.8138i q^{62} +4.80479 q^{63} -0.270178 q^{64} -3.48079 q^{66} -8.03003 q^{67} -5.48429i q^{68} -4.63509 q^{69} +(-15.5694 - 6.11588i) q^{70} -2.63509i q^{71} -10.3263 q^{72} +10.3263 q^{73} +3.11588 q^{74} +(7.32648 - 7.88669i) q^{75} +6.11588i q^{76} +1.86624i q^{77} -1.03843 q^{79} +(14.8099 + 5.81754i) q^{80} -11.2318 q^{81} +25.3596i q^{82} +11.8452 q^{83} +28.3476i q^{84} +(1.00064 - 2.54737i) q^{85} +3.48079i q^{86} +6.45878i q^{87} -4.01086i q^{88} +12.5582i q^{89} +(-8.66324 - 3.40304i) q^{90} -9.64680i q^{92} +19.2936 q^{93} -15.6914 q^{94} +(-1.11588 + 2.84073i) q^{95} -11.8073i q^{96} +14.7838 q^{97} +4.16251 q^{98} +1.03843i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4} - 12 q^{9}+O(q^{10}) \) 12 * q + 8 * q^4 - 12 * q^9	\( 12 q + 8 q^{4} - 12 q^{9} + 14 q^{10} - 44 q^{14} + 32 q^{16} + 2 q^{25} - 36 q^{29} + 8 q^{30} - 20 q^{35} - 4 q^{36} + 70 q^{40} + 12 q^{49} - 24 q^{51} + 52 q^{55} - 32 q^{56} - 12 q^{61} + 12 q^{64} + 4 q^{66} - 48 q^{69} - 16 q^{74} + 4 q^{75} - 104 q^{79} - 28 q^{81} - 62 q^{90} - 112 q^{94} + 40 q^{95}+O(q^{100}) \) 12 * q + 8 * q^4 - 12 * q^9 + 14 * q^10 - 44 * q^14 + 32 * q^16 + 2 * q^25 - 36 * q^29 + 8 * q^30 - 20 * q^35 - 4 * q^36 + 70 * q^40 + 12 * q^49 - 24 * q^51 + 52 * q^55 - 32 * q^56 - 12 * q^61 + 12 * q^64 + 4 * q^66 - 48 * q^69 - 16 * q^74 + 4 * q^75 - 104 * q^79 - 28 * q^81 - 62 * q^90 - 112 * q^94 + 40 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more