LMFDB - Embedded newform 845.2.d.a.844.6

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:	$6$
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:	$\Z[a_1, a_2, a_3]$
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			844.6
Root			$1.45161 - 1.45161i$ of defining polynomial
Character	$\chi$	$=$	845.844
Dual form			845.2.d.a.844.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.21432 q^{2} +1.31111i q^{3} -0.525428 q^{4} +(-0.311108 + 2.21432i) q^{5} +1.59210i q^{6} +2.90321 q^{7} -3.06668 q^{8} +1.28100 q^{9} +(-0.377784 + 2.68889i) q^{10} +0.214320i q^{11} -0.688892i q^{12} +3.52543 q^{14} +(-2.90321 - 0.407896i) q^{15} -2.67307 q^{16} +6.42864i q^{17} +1.55554 q^{18} +2.21432i q^{19} +(0.163465 - 1.16346i) q^{20} +3.80642i q^{21} +0.260253i q^{22} -4.68889i q^{23} -4.02074i q^{24} +(-4.80642 - 1.37778i) q^{25} +5.61285i q^{27} -1.52543 q^{28} -8.70964 q^{29} +(-3.52543 - 0.495316i) q^{30} +5.59210i q^{31} +2.88739 q^{32} -0.280996 q^{33} +7.80642i q^{34} +(-0.903212 + 6.42864i) q^{35} -0.673071 q^{36} +2.28100 q^{37} +2.68889i q^{38} +(0.954067 - 6.79060i) q^{40} -3.05086i q^{41} +4.62222i q^{42} -6.36196i q^{43} -0.112610i q^{44} +(-0.398528 + 2.83654i) q^{45} -5.69381i q^{46} +1.09679 q^{47} -3.50468i q^{48} +1.42864 q^{49} +(-5.83654 - 1.67307i) q^{50} -8.42864 q^{51} -6.23506i q^{53} +6.81579i q^{54} +(-0.474572 - 0.0666765i) q^{55} -8.90321 q^{56} -2.90321 q^{57} -10.5763 q^{58} +9.26517i q^{59} +(1.52543 + 0.214320i) q^{60} -0.280996 q^{61} +6.79060i q^{62} +3.71900 q^{63} +8.85236 q^{64} -0.341219 q^{66} +7.76049 q^{67} -3.37778i q^{68} +6.14764 q^{69} +(-1.09679 + 7.80642i) q^{70} +6.08097i q^{71} -3.92840 q^{72} +10.2810 q^{73} +2.76986 q^{74} +(1.80642 - 6.30174i) q^{75} -1.16346i q^{76} +0.622216i q^{77} +14.2351 q^{79} +(0.831613 - 5.91903i) q^{80} -3.51606 q^{81} -3.70471i q^{82} +9.52543 q^{83} -2.00000i q^{84} +(-14.2351 - 2.00000i) q^{85} -7.72546i q^{86} -11.4193i q^{87} -0.657249i q^{88} +5.61285i q^{89} +(-0.483940 + 3.44446i) q^{90} +2.46367i q^{92} -7.33185 q^{93} +1.33185 q^{94} +(-4.90321 - 0.688892i) q^{95} +3.78568i q^{96} +18.0415 q^{97} +1.73483 q^{98} +0.274543i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 10 q^{4} - 2 q^{5} + 4 q^{7} - 18 q^{8} - 6 q^{9} - 2 q^{10} + 8 q^{14} - 4 q^{15} + 10 q^{16} + 10 q^{18} + 14 q^{20} - 2 q^{25} + 4 q^{28} - 12 q^{29} - 8 q^{30} - 22 q^{32} + 12 q^{33}+ \cdots + 50 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 + 10 * q^4 - 2 * q^5 + 4 * q^7 - 18 * q^8 - 6 * q^9 - 2 * q^10 + 8 * q^14 - 4 * q^15 + 10 * q^16 + 10 * q^18 + 14 * q^20 - 2 * q^25 + 4 * q^28 - 12 * q^29 - 8 * q^30 - 22 * q^32 + 12 * q^33 + 8 * q^35 + 22 * q^36 - 34 * q^40 + 38 * q^45 + 20 * q^47 - 18 * q^49 - 22 * q^50 - 24 * q^51 - 16 * q^55 - 40 * q^56 - 4 * q^57 - 24 * q^58 - 4 * q^60 + 12 * q^61 + 36 * q^63 + 66 * q^64 - 16 * q^66 - 20 * q^67 + 24 * q^69 - 20 * q^70 - 90 * q^72 + 48 * q^73 + 4 * q^74 - 16 * q^75 + 32 * q^79 + 58 * q^80 + 46 * q^81 + 44 * q^83 - 32 * q^85 - 70 * q^90 - 4 * q^93 - 32 * q^94 - 16 * q^95 + 28 * q^97 + 50 * q^98

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 $

$2$	1.21432			0.858654			0.429327	−	0.903149i	$-0.358751\pi$
$2$	1.21432			0.858654			0.429327	+	0.903149i	$0.358751\pi$
$3$			1.31111i			0.756968i	0.925608	+	0.378484i	$0.123555\pi$
$3$			1.31111i			0.756968i	−0.925608	+	0.378484i	$0.876445\pi$
$4$	−0.525428			−0.262714
$5$	−0.311108	+	2.21432i	−0.139132	+	0.990274i
$5$	−0.311108	+	2.21432i	−0.139132	+	0.990274i
$6$			1.59210i			0.649974i
$7$	2.90321			1.09731			0.548655	−	0.836049i	$-0.315140\pi$
$7$	2.90321			1.09731			0.548655	+	0.836049i	$0.315140\pi$
$8$	−3.06668			−1.08423
$9$	1.28100			0.426999
$10$	−0.377784	+	2.68889i	−0.119466	+	0.850302i
$11$			0.214320i			0.0646198i	0.999478	+	0.0323099i	$0.0102864\pi$
$11$			0.214320i			0.0646198i	−0.999478	+	0.0323099i	$0.989714\pi$
$12$		−	0.688892i		−	0.198866i
$13$		0			0
$13$		0			0
$14$	3.52543			0.942210
$15$	−2.90321	−	0.407896i	−0.749606	−	0.105318i
$16$	−2.67307			−0.668268
$17$			6.42864i			1.55917i	0.626294	+	0.779587i	$0.284571\pi$
$17$			6.42864i			1.55917i	−0.626294	+	0.779587i	$0.715429\pi$
$18$	1.55554			0.366644
$19$			2.21432i			0.508000i	0.967204	+	0.254000i	$0.0817463\pi$
$19$			2.21432i			0.508000i	−0.967204	+	0.254000i	$0.918254\pi$
$20$	0.163465	−	1.16346i	0.0365518	−	0.260159i
$21$			3.80642i			0.830630i
$22$			0.260253i			0.0554861i
$23$		−	4.68889i		−	0.977702i	−0.872367	−	0.488851i	$-0.837416\pi$
$23$		−	4.68889i		−	0.977702i	0.872367	−	0.488851i	$-0.162584\pi$
$24$		−	4.02074i		−	0.820731i
$25$	−4.80642	−	1.37778i	−0.961285	−	0.275557i
$26$		0			0
$27$			5.61285i			1.08019i
$28$	−1.52543			−0.288279
$29$	−8.70964			−1.61734			−0.808669	−	0.588263i	$-0.799812\pi$
$29$	−8.70964			−1.61734			−0.808669	+	0.588263i	$0.799812\pi$
$30$	−3.52543	−	0.495316i	−0.643652	−	0.0904319i
$31$			5.59210i			1.00437i	0.864760	+	0.502186i	$0.167471\pi$
$31$			5.59210i			1.00437i	−0.864760	+	0.502186i	$0.832529\pi$
$32$	2.88739			0.510423
$33$	−0.280996			−0.0489152
$34$			7.80642i			1.33879i
$35$	−0.903212	+	6.42864i	−0.152671	+	1.08664i
$36$	−0.673071			−0.112178
$37$	2.28100			0.374993			0.187497	−	0.982265i	$-0.439963\pi$
$37$	2.28100			0.374993			0.187497	+	0.982265i	$0.439963\pi$
$38$			2.68889i			0.436196i
$39$		0			0
$40$	0.954067	−	6.79060i	0.150851	−	1.07369i
$41$		−	3.05086i		−	0.476464i	−0.971208	−	0.238232i	$-0.923432\pi$
$41$		−	3.05086i		−	0.476464i	0.971208	−	0.238232i	$-0.0765678\pi$
$42$			4.62222i			0.713223i
$43$		−	6.36196i		−	0.970190i	−0.874461	−	0.485095i	$-0.838785\pi$
$43$		−	6.36196i		−	0.970190i	0.874461	−	0.485095i	$-0.161215\pi$
$44$		−	0.112610i		−	0.0169765i
$45$	−0.398528	+	2.83654i	−0.0594090	+	0.422846i
$46$		−	5.69381i		−	0.839507i
$47$	1.09679			0.159983			0.0799915	−	0.996796i	$-0.474511\pi$
$47$	1.09679			0.159983			0.0799915	+	0.996796i	$0.474511\pi$
$48$		−	3.50468i		−	0.505858i
$49$	1.42864			0.204091
$50$	−5.83654	−	1.67307i	−0.825411	−	0.236608i
$51$	−8.42864			−1.18025
$52$		0			0
$53$		−	6.23506i		−	0.856452i	−0.903672	−	0.428226i	$-0.859139\pi$
$53$		−	6.23506i		−	0.856452i	0.903672	−	0.428226i	$-0.140861\pi$
$54$			6.81579i			0.927512i
$55$	−0.474572	−	0.0666765i	−0.0639913	−	0.00899066i
$56$	−8.90321			−1.18974
$57$	−2.90321			−0.384540
$58$	−10.5763			−1.38873
$59$			9.26517i			1.20622i	0.797657	+	0.603112i	$0.206073\pi$
$59$			9.26517i			1.20622i	−0.797657	+	0.603112i	$0.793927\pi$
$60$	1.52543	+	0.214320i	0.196932	+	0.0276686i
$61$	−0.280996			−0.0359779			−0.0179889	−	0.999838i	$-0.505726\pi$
$61$	−0.280996			−0.0359779			−0.0179889	+	0.999838i	$0.505726\pi$
$62$			6.79060i			0.862407i
$63$	3.71900			0.468550
$64$	8.85236			1.10654
$65$		0			0
$66$	−0.341219			−0.0420012
$67$	7.76049			0.948095			0.474047	−	0.880499i	$-0.342793\pi$
$67$	7.76049			0.948095			0.474047	+	0.880499i	$0.342793\pi$
$68$		−	3.37778i		−	0.409617i
$69$	6.14764			0.740089
$70$	−1.09679	+	7.80642i	−0.131091	+	0.933046i
$71$			6.08097i			0.721678i	0.932628	+	0.360839i	$0.117510\pi$
$71$			6.08097i			0.721678i	−0.932628	+	0.360839i	$0.882490\pi$
$72$	−3.92840			−0.462967
$73$	10.2810			1.20330			0.601650	−	0.798760i	$-0.294510\pi$
$73$	10.2810			1.20330			0.601650	+	0.798760i	$0.294510\pi$
$74$	2.76986			0.321990
$75$	1.80642	−	6.30174i	0.208588	−	0.727662i
$76$		−	1.16346i		−	0.133459i
$77$			0.622216i			0.0709081i
$78$		0			0
$79$	14.2351			1.60157			0.800785	−	0.598952i	$-0.204416\pi$
$79$	14.2351			1.60157			0.800785	+	0.598952i	$0.204416\pi$
$80$	0.831613	−	5.91903i	0.0929772	−	0.661768i
$81$	−3.51606			−0.390673
$82$		−	3.70471i		−	0.409117i
$83$	9.52543			1.04555			0.522776	−	0.852470i	$-0.324897\pi$
$83$	9.52543			1.04555			0.522776	+	0.852470i	$0.324897\pi$
$84$		−	2.00000i		−	0.218218i
$85$	−14.2351	−	2.00000i	−1.54401	−	0.216930i
$86$		−	7.72546i		−	0.833057i
$87$		−	11.4193i		−	1.22427i
$88$		−	0.657249i		−	0.0700630i
$89$			5.61285i			0.594961i	0.954728	+	0.297480i	$0.0961463\pi$
$89$			5.61285i			0.594961i	−0.954728	+	0.297480i	$0.903854\pi$
$90$	−0.483940	+	3.44446i	−0.0510118	+	0.363078i
$91$		0			0
$92$			2.46367i			0.256856i
$93$	−7.33185			−0.760278
$94$	1.33185			0.137370
$95$	−4.90321	−	0.688892i	−0.503059	−	0.0706788i
$96$			3.78568i			0.386374i
$97$	18.0415			1.83184			0.915918	−	0.401366i	$-0.131464\pi$
$97$	18.0415			1.83184			0.915918	+	0.401366i	$0.131464\pi$
$98$	1.73483			0.175244
$99$			0.274543i			0.0275926i
$100$	2.52543	+	0.723926i	0.252543	+	0.0723926i
$101$	−3.93978			−0.392022			−0.196011	−	0.980602i	$-0.562799\pi$
$101$	−3.93978			−0.392022			−0.196011	+	0.980602i	$0.562799\pi$
$102$	−10.2351			−1.01342
$103$		−	2.82225i		−	0.278084i	−0.990286	−	0.139042i	$-0.955598\pi$
$103$		−	2.82225i		−	0.278084i	0.990286	−	0.139042i	$-0.0444023\pi$
$104$		0			0
$105$	−8.42864	−	1.18421i	−0.822551	−	0.115567i
$106$		−	7.57136i		−	0.735396i
$107$		−	17.1175i		−	1.65481i	−0.561603	−	0.827407i	$-0.689815\pi$
$107$		−	17.1175i		−	1.65481i	0.561603	−	0.827407i	$-0.310185\pi$
$108$		−	2.94914i		−	0.283782i
$109$		−	16.7239i		−	1.60186i	−0.598757	−	0.800931i	$-0.704338\pi$
$109$		−	16.7239i		−	1.60186i	0.598757	−	0.800931i	$-0.295662\pi$
$110$	−0.576283	−	0.0809666i	−0.0549464	−	0.00771987i
$111$			2.99063i			0.283858i
$112$	−7.76049			−0.733297
$113$			1.18421i			0.111401i	0.998448	+	0.0557005i	$0.0177392\pi$
$113$			1.18421i			0.111401i	−0.998448	+	0.0557005i	$0.982261\pi$
$114$	−3.52543			−0.330187
$115$	10.3827	+	1.45875i	0.968192	+	0.136029i
$116$	4.57628			0.424897
$117$		0			0
$118$			11.2509i			1.03573i
$119$			18.6637i			1.71090i
$120$	8.90321	+	1.25088i	0.812748	+	0.114190i
$121$	10.9541			0.995824
$122$	−0.341219			−0.0308925
$123$	4.00000			0.360668
$124$		−	2.93825i		−	0.263862i
$125$	4.54617	−	10.2143i	0.406622	−	0.913597i
$126$	4.51606			0.402323
$127$			2.30174i			0.204246i	0.994772	+	0.102123i	$0.0325636\pi$
$127$			2.30174i			0.204246i	−0.994772	+	0.102123i	$0.967436\pi$
$128$	4.97481			0.439715
$129$	8.34122			0.734403
$130$		0			0
$131$	−13.4193			−1.17245			−0.586224	−	0.810149i	$-0.699386\pi$
$131$	−13.4193			−1.17245			−0.586224	+	0.810149i	$0.699386\pi$
$132$	0.147643			0.0128507
$133$			6.42864i			0.557434i
$134$	9.42372			0.814085
$135$	−12.4286	−	1.74620i	−1.06969	−	0.150289i
$136$		−	19.7146i		−	1.69051i
$137$	19.1526			1.63631			0.818157	−	0.574995i	$-0.194996\pi$
$137$	19.1526			1.63631			0.818157	+	0.574995i	$0.194996\pi$
$138$	7.46520			0.635480
$139$	−19.0923			−1.61939			−0.809696	−	0.586850i	$-0.800368\pi$
$139$	−19.0923			−1.61939			−0.809696	+	0.586850i	$0.800368\pi$
$140$	0.474572	−	3.37778i	0.0401087	−	0.285475i
$141$			1.43801i			0.121102i
$142$			7.38424i			0.619671i
$143$		0			0
$144$	−3.42419			−0.285349
$145$	2.70964	−	19.2859i	0.225023	−	1.60161i
$146$	12.4844			1.03322
$147$			1.87310i			0.154491i
$148$	−1.19850			−0.0985160
$149$		−	3.57136i		−	0.292577i	−0.989242	−	0.146289i	$-0.953267\pi$
$149$		−	3.57136i		−	0.292577i	0.989242	−	0.146289i	$-0.0467328\pi$
$150$	2.19358	−	7.65233i	0.179105	−	0.624810i
$151$		−	1.26517i		−	0.102958i	−0.998674	−	0.0514792i	$-0.983606\pi$
$151$		−	1.26517i		−	0.102958i	0.998674	−	0.0514792i	$-0.0163936\pi$
$152$		−	6.79060i		−	0.550791i
$153$			8.23506i			0.665765i
$154$			0.755569i			0.0608855i
$155$	−12.3827	−	1.73975i	−0.994603	−	0.139740i
$156$		0			0
$157$			5.61285i			0.447954i	0.974594	+	0.223977i	$0.0719041\pi$
$157$			5.61285i			0.447954i	−0.974594	+	0.223977i	$0.928096\pi$
$158$	17.2859			1.37519
$159$	8.17484			0.648307
$160$	−0.898290	+	6.39361i	−0.0710160	+	0.505459i
$161$		−	13.6128i		−	1.07284i
$162$	−4.26962			−0.335453
$163$	−3.71900			−0.291295			−0.145647	−	0.989337i	$-0.546527\pi$
$163$	−3.71900			−0.291295			−0.145647	+	0.989337i	$0.546527\pi$
$164$			1.60300i			0.125174i
$165$	0.0874201	−	0.622216i	0.00680565	−	0.0484394i
$166$	11.5669			0.897767
$167$	−7.03657			−0.544506			−0.272253	−	0.962226i	$-0.587769\pi$
$167$	−7.03657			−0.544506			−0.272253	+	0.962226i	$0.587769\pi$
$168$		−	11.6731i		−	0.900597i
$169$		0			0
$170$	−17.2859	−	2.42864i	−1.32577	−	0.186268i
$171$			2.83654i			0.216915i
$172$			3.34275i			0.254882i
$173$		−	0.723926i		−	0.0550391i	−0.999621	−	0.0275195i	$-0.991239\pi$
$173$		−	0.723926i		−	0.0550391i	0.999621	−	0.0275195i	$-0.00876085\pi$
$174$		−	13.8666i		−	1.05123i
$175$	−13.9541	−	4.00000i	−1.05483	−	0.302372i
$176$		−	0.572892i		−	0.0431833i
$177$	−12.1476			−0.913073
$178$			6.81579i			0.510865i
$179$	−4.04149			−0.302075			−0.151037	−	0.988528i	$-0.548261\pi$
$179$	−4.04149			−0.302075			−0.151037	+	0.988528i	$0.548261\pi$
$180$	0.209398	−	1.49039i	0.0156076	−	0.111087i
$181$	−2.34122			−0.174021			−0.0870107	−	0.996207i	$-0.527731\pi$
$181$	−2.34122			−0.174021			−0.0870107	+	0.996207i	$0.527731\pi$
$182$		0			0
$183$		−	0.368416i		−	0.0272341i
$184$			14.3793i			1.06006i
$185$	−0.709636	+	5.05086i	−0.0521735	+	0.371346i
$186$	−8.90321			−0.652815
$187$	−1.37778			−0.100754
$188$	−0.576283			−0.0420297
$189$			16.2953i			1.18531i
$190$	−5.95407	−	0.836535i	−0.431953	−	0.0606887i
$191$	−2.10171			−0.152074			−0.0760372	−	0.997105i	$-0.524227\pi$
$191$	−2.10171			−0.152074			−0.0760372	+	0.997105i	$0.524227\pi$
$192$			11.6064i			0.837619i
$193$	−13.5210			−0.973262			−0.486631	−	0.873608i	$-0.661774\pi$
$193$	−13.5210			−0.973262			−0.486631	+	0.873608i	$0.661774\pi$
$194$	21.9081			1.57291
$195$		0			0
$196$	−0.750647			−0.0536176
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$			0.333383i			0.0236925i
$199$	22.1432			1.56969			0.784845	−	0.619692i	$-0.212743\pi$
$199$	22.1432			1.56969			0.784845	+	0.619692i	$0.212743\pi$
$200$	14.7397	+	4.22522i	1.04226	+	0.298768i
$201$			10.1748i			0.717678i
$202$	−4.78415			−0.336612
$203$	−25.2859			−1.77472
$204$	4.42864			0.310067
$205$	6.75557	+	0.949145i	0.471829	+	0.0662912i
$206$		−	3.42711i		−	0.238778i
$207$		−	6.00645i		−	0.417477i
$208$		0			0
$209$	−0.474572			−0.0328269
$210$	−10.2351	−	1.43801i	−0.706286	−	0.0992319i
$211$	19.6543			1.35306			0.676530	−	0.736415i	$-0.263483\pi$
$211$	19.6543			1.35306			0.676530	+	0.736415i	$0.263483\pi$
$212$			3.27607i			0.225002i
$213$	−7.97280			−0.546287
$214$		−	20.7862i		−	1.42091i
$215$	14.0874	+	1.97926i	0.960754	+	0.134984i
$216$		−	17.2128i		−	1.17118i
$217$			16.2351i			1.10211i
$218$		−	20.3082i		−	1.37544i
$219$			13.4795i			0.910860i
$220$	0.249353	+	0.0350337i	0.0168114	+	0.00236197i
$221$		0			0
$222$			3.63158i			0.243736i
$223$	−19.6686			−1.31711			−0.658554	−	0.752533i	$-0.728832\pi$
$223$	−19.6686			−1.31711			−0.658554	+	0.752533i	$0.728832\pi$
$224$	8.38271			0.560093
$225$	−6.15701	−	1.76494i	−0.410467	−	0.117662i
$226$			1.43801i			0.0956548i
$227$	−13.2716			−0.880869			−0.440434	−	0.897785i	$-0.645176\pi$
$227$	−13.2716			−0.880869			−0.440434	+	0.897785i	$0.645176\pi$
$228$	1.52543			0.101024
$229$			2.42864i			0.160489i	0.996775	+	0.0802445i	$0.0255701\pi$
$229$			2.42864i			0.160489i	−0.996775	+	0.0802445i	$0.974430\pi$
$230$	12.6079	+	1.77139i	0.831342	+	0.116802i
$231$	−0.815792			−0.0536752
$232$	26.7096			1.75357
$233$			16.1748i			1.05965i	0.848107	+	0.529825i	$0.177742\pi$
$233$			16.1748i			1.05965i	−0.848107	+	0.529825i	$0.822258\pi$
$234$		0			0
$235$	−0.341219	+	2.42864i	−0.0222587	+	0.158427i
$236$		−	4.86818i		−	0.316891i
$237$			18.6637i			1.21234i
$238$			22.6637i			1.46907i
$239$		−	12.7763i		−	0.826431i	−0.910633	−	0.413215i	$-0.864406\pi$
$239$		−	12.7763i		−	0.826431i	0.910633	−	0.413215i	$-0.135594\pi$
$240$	7.76049	+	1.09033i	0.500938	+	0.0703808i
$241$		−	5.89829i		−	0.379942i	−0.981790	−	0.189971i	$-0.939161\pi$
$241$		−	5.89829i		−	0.379942i	0.981790	−	0.189971i	$-0.0608394\pi$
$242$	13.3017			0.855068
$243$			12.2286i			0.784466i
$244$	0.147643			0.00945189
$245$	−0.444461	+	3.16346i	−0.0283956	+	0.202106i
$246$	4.85728			0.309689
$247$		0			0
$248$		−	17.1492i		−	1.08897i
$249$			12.4889i			0.791450i
$250$	5.52051	−	12.4035i	0.349147	−	0.784463i
$251$	2.07313			0.130855			0.0654274	−	0.997857i	$-0.479159\pi$
$251$	2.07313			0.130855			0.0654274	+	0.997857i	$0.479159\pi$
$252$	−1.95407			−0.123095
$253$	1.00492			0.0631789
$254$			2.79505i			0.175377i
$255$	2.62222	−	18.6637i	0.164210	−	1.16877i
$256$	−11.6637			−0.728981
$257$		−	18.3970i		−	1.14757i	−0.819005	−	0.573787i	$-0.805474\pi$
$257$		−	18.3970i		−	1.14757i	0.819005	−	0.573787i	$-0.194526\pi$
$258$	10.1289			0.630598
$259$	6.62222			0.411484
$260$		0			0
$261$	−11.1570			−0.690602
$262$	−16.2953			−1.00673
$263$		−	11.0257i		−	0.679872i	−0.940449	−	0.339936i	$-0.889595\pi$
$263$		−	11.0257i		−	0.679872i	0.940449	−	0.339936i	$-0.110405\pi$
$264$	0.861725			0.0530355
$265$	13.8064	+	1.93978i	0.848122	+	0.119160i
$266$			7.80642i			0.478643i
$267$	−7.35905			−0.450366
$268$	−4.07758			−0.249078
$269$	16.1432			0.984268			0.492134	−	0.870519i	$-0.336217\pi$
$269$	16.1432			0.984268			0.492134	+	0.870519i	$0.336217\pi$
$270$	−15.0923	−	2.12045i	−0.918491	−	0.129046i
$271$			13.0114i			0.790385i	0.918598	+	0.395192i	$0.129322\pi$
$271$			13.0114i			0.790385i	−0.918598	+	0.395192i	$0.870678\pi$
$272$		−	17.1842i		−	1.04195i
$273$		0			0
$274$	23.2573			1.40503
$275$	0.295286	−	1.03011i	0.0178064	−	0.0621181i
$276$	−3.23014			−0.194432
$277$		−	7.57136i		−	0.454919i	−0.973788	−	0.227459i	$-0.926958\pi$
$277$		−	7.57136i		−	0.454919i	0.973788	−	0.227459i	$-0.0730419\pi$
$278$	−23.1842			−1.39050
$279$			7.16346i			0.428865i
$280$	2.76986	−	19.7146i	0.165531	−	1.17817i
$281$			6.75557i			0.403003i	0.979488	+	0.201502i	$0.0645822\pi$
$281$			6.75557i			0.403003i	−0.979488	+	0.201502i	$0.935418\pi$
$282$			1.74620i			0.103985i
$283$			19.0859i			1.13454i	0.823532	+	0.567269i	$0.192000\pi$
$283$			19.0859i			1.13454i	−0.823532	+	0.567269i	$0.808000\pi$
$284$		−	3.19511i		−	0.189595i
$285$	0.903212	−	6.42864i	0.0535017	−	0.380800i
$286$		0			0
$287$		−	8.85728i		−	0.522829i
$288$	3.69874			0.217950
$289$	−24.3274			−1.43102
$290$	3.29036	−	23.4193i	0.193217	−	1.37523i
$291$			23.6543i			1.38664i
$292$	−5.40192			−0.316123
$293$	−8.08742			−0.472472			−0.236236	−	0.971696i	$-0.575914\pi$
$293$	−8.08742			−0.472472			−0.236236	+	0.971696i	$0.575914\pi$
$294$			2.27454i			0.132654i
$295$	−20.5161	−	2.88247i	−1.19449	−	0.167824i
$296$	−6.99508			−0.406581
$297$	−1.20294			−0.0698019
$298$		−	4.33677i		−	0.251223i
$299$		0			0
$300$	−0.949145	+	3.31111i	−0.0547989	+	0.191167i
$301$		−	18.4701i		−	1.06460i
$302$		−	1.53633i		−	0.0884057i
$303$		−	5.16547i		−	0.296749i
$304$		−	5.91903i		−	0.339480i
$305$	0.0874201	−	0.622216i	0.00500566	−	0.0356280i
$306$			10.0000i			0.571662i
$307$	13.4336			0.766694			0.383347	−	0.923604i	$-0.374771\pi$
$307$	13.4336			0.766694			0.383347	+	0.923604i	$0.374771\pi$
$308$		−	0.326929i		−	0.0186285i
$309$	3.70027			0.210501
$310$	−15.0366	−	2.11261i	−0.854020	−	0.119988i
$311$	−20.2034			−1.14563			−0.572815	−	0.819684i	$-0.694149\pi$
$311$	−20.2034			−1.14563			−0.572815	+	0.819684i	$0.694149\pi$
$312$		0			0
$313$		−	15.1111i		−	0.854129i	−0.904221	−	0.427064i	$-0.859548\pi$
$313$		−	15.1111i		−	0.854129i	0.904221	−	0.427064i	$-0.140452\pi$
$314$			6.81579i			0.384637i
$315$	−1.15701	+	8.23506i	−0.0651902	+	0.463993i
$316$	−7.47949			−0.420754
$317$	22.2810			1.25143			0.625713	−	0.780054i	$-0.284808\pi$
$317$	22.2810			1.25143			0.625713	+	0.780054i	$0.284808\pi$
$318$	9.92687			0.556671
$319$		−	1.86665i		−	0.104512i
$320$	−2.75404	+	19.6019i	−0.153955	+	1.09578i
$321$	22.4429			1.25264
$322$		−	16.5303i		−	0.921200i
$323$	−14.2351			−0.792060
$324$	1.84743			0.102635
$325$		0			0
$326$	−4.51606			−0.250121
$327$	21.9269			1.21256
$328$			9.35599i			0.516598i
$329$	3.18421			0.175551
$330$	0.106156	−	0.755569i	0.00584370	−	0.0415927i
$331$		−	8.25581i		−	0.453780i	−0.973920	−	0.226890i	$-0.927144\pi$
$331$		−	8.25581i		−	0.453780i	0.973920	−	0.226890i	$-0.0728558\pi$
$332$	−5.00492			−0.274681
$333$	2.92195			0.160122
$334$	−8.54464			−0.467542
$335$	−2.41435	+	17.1842i	−0.131910	+	0.938874i
$336$		−	10.1748i		−	0.555083i
$337$			13.7462i			0.748803i	0.927267	+	0.374402i	$0.122152\pi$
$337$			13.7462i			0.748803i	−0.927267	+	0.374402i	$0.877848\pi$
$338$		0			0
$339$	−1.55262			−0.0843270
$340$	7.47949	+	1.05086i	0.405633	+	0.0569906i
$341$	−1.19850			−0.0649023
$342$			3.44446i			0.186255i
$343$	−16.1748			−0.873359
$344$			19.5101i			1.05191i
$345$	−1.91258	+	13.6128i	−0.102970	+	0.732891i
$346$		−	0.879077i		−	0.0472595i
$347$			1.21924i			0.0654523i	0.999464	+	0.0327262i	$0.0104189\pi$
$347$			1.21924i			0.0654523i	−0.999464	+	0.0327262i	$0.989581\pi$
$348$			6.00000i			0.321634i
$349$		−	22.5116i		−	1.20502i	−0.798112	−	0.602510i	$-0.794168\pi$
$349$		−	22.5116i		−	1.20502i	0.798112	−	0.602510i	$-0.205832\pi$
$350$	−16.9447	−	4.85728i	−0.905732	−	0.259632i
$351$		0			0
$352$			0.618825i			0.0329835i
$353$	14.2810			0.760101			0.380050	−	0.924966i	$-0.375907\pi$
$353$	14.2810			0.760101			0.380050	+	0.924966i	$0.375907\pi$
$354$	−14.7511			−0.784013
$355$	−13.4652	−	1.89184i	−0.714659	−	0.100408i
$356$		−	2.94914i		−	0.156304i
$357$	−24.4701			−1.29510
$358$	−4.90766			−0.259378
$359$			12.1541i			0.641469i	0.947169	+	0.320734i	$0.103930\pi$
$359$			12.1541i			0.641469i	−0.947169	+	0.320734i	$0.896070\pi$
$360$	1.22216	−	8.69874i	0.0644133	−	0.458464i
$361$	14.0968			0.741936
$362$	−2.84299			−0.149424
$363$			14.3620i			0.753808i
$364$		0			0
$365$	−3.19850	+	22.7654i	−0.167417	+	1.19160i
$366$		−	0.447375i		−	0.0233847i
$367$		−	4.65725i		−	0.243106i	−0.992585	−	0.121553i	$-0.961212\pi$
$367$		−	4.65725i		−	0.243106i	0.992585	−	0.121553i	$-0.0387875\pi$
$368$			12.5337i			0.653366i
$369$		−	3.90813i		−	0.203449i
$370$	−0.861725	+	6.13335i	−0.0447989	+	0.318858i
$371$		−	18.1017i		−	0.939794i
$372$	3.85236			0.199735
$373$		−	34.9403i		−	1.80914i	−0.426328	−	0.904569i	$-0.640193\pi$
$373$		−	34.9403i		−	1.80914i	0.426328	−	0.904569i	$-0.359807\pi$
$374$	−1.67307			−0.0865124
$375$	13.3921	+	5.96052i	0.691564	+	0.307800i
$376$	−3.36349			−0.173459
$377$		0			0
$378$			19.7877i			1.01777i
$379$		−	17.4717i		−	0.897459i	−0.893668	−	0.448729i	$-0.851877\pi$
$379$		−	17.4717i		−	0.897459i	0.893668	−	0.448729i	$-0.148123\pi$
$380$	2.57628	+	0.361963i	0.132161	+	0.0185683i
$381$	−3.01783			−0.154608
$382$	−2.55215			−0.130579
$383$	18.6780			0.954401			0.477200	−	0.878794i	$-0.341652\pi$
$383$	18.6780			0.954401			0.477200	+	0.878794i	$0.341652\pi$
$384$			6.52251i			0.332851i
$385$	−1.37778	−	0.193576i	−0.0702184	−	0.00986555i
$386$	−16.4188			−0.835695
$387$		−	8.14965i		−	0.414270i
$388$	−9.47949			−0.481248
$389$	1.61285			0.0817746			0.0408873	−	0.999164i	$-0.486982\pi$
$389$	1.61285			0.0817746			0.0408873	+	0.999164i	$0.486982\pi$
$390$		0			0
$391$	30.1432			1.52441
$392$	−4.38118			−0.221283
$393$		−	17.5941i		−	0.887506i
$394$	−2.42864			−0.122353
$395$	−4.42864	+	31.5210i	−0.222829	+	1.58599i
$396$		−	0.144252i		−	0.00724895i
$397$	−6.57628			−0.330054			−0.165027	−	0.986289i	$-0.552771\pi$
$397$	−6.57628			−0.330054			−0.165027	+	0.986289i	$0.552771\pi$
$398$	26.8889			1.34782
$399$	−8.42864			−0.421960
$400$	12.8479	+	3.68292i	0.642396	+	0.184146i
$401$		−	21.9081i		−	1.09404i	−0.837120	−	0.547020i	$-0.815762\pi$
$401$		−	21.9081i		−	1.09404i	0.837120	−	0.547020i	$-0.184238\pi$
$402$			12.3555i			0.616237i
$403$		0			0
$404$	2.07007			0.102990
$405$	1.09387	−	7.78568i	0.0543550	−	0.386874i
$406$	−30.7052			−1.52387
$407$			0.488863i			0.0242320i
$408$	25.8479			1.27966
$409$		−	10.1936i		−	0.504040i	−0.967722	−	0.252020i	$-0.918905\pi$
$409$		−	10.1936i		−	0.504040i	0.967722	−	0.252020i	$-0.0810949\pi$
$410$	8.20342	+	1.15257i	0.405138	+	0.0569211i
$411$			25.1111i			1.23864i
$412$			1.48289i			0.0730565i
$413$			26.8988i			1.32360i
$414$		−	7.29376i		−	0.358469i
$415$	−2.96343	+	21.0923i	−0.145469	+	1.03538i
$416$		0			0
$417$		−	25.0321i		−	1.22583i
$418$	−0.576283			−0.0281869
$419$	−7.31756			−0.357486			−0.178743	−	0.983896i	$-0.557203\pi$
$419$	−7.31756			−0.357486			−0.178743	+	0.983896i	$0.557203\pi$
$420$	4.42864	+	0.622216i	0.216095	+	0.0303610i
$421$			7.86665i			0.383397i	0.981454	+	0.191698i	$0.0613996\pi$
$421$			7.86665i			0.383397i	−0.981454	+	0.191698i	$0.938600\pi$
$422$	23.8666			1.16181
$423$	1.40498			0.0683125
$424$			19.1209i			0.928594i
$425$	8.85728	−	30.8988i	0.429641	−	1.49881i
$426$	−9.68153			−0.469072
$427$	−0.815792			−0.0394789
$428$			8.99402i			0.434743i
$429$		0			0
$430$	17.1066	+	2.40345i	0.824955	+	0.115905i
$431$			38.9195i			1.87469i	0.348407	+	0.937343i	$0.386723\pi$
$431$			38.9195i			1.87469i	−0.348407	+	0.937343i	$0.613277\pi$
$432$		−	15.0035i		−	0.721858i
$433$		−	20.2034i		−	0.970914i	−0.874260	−	0.485457i	$-0.838653\pi$
$433$		−	20.2034i		−	0.970914i	0.874260	−	0.485457i	$-0.161347\pi$
$434$			19.7146i			0.946329i
$435$	25.2859	+	3.55262i	1.21237	+	0.170335i
$436$			8.78721i			0.420831i
$437$	10.3827			0.496672
$438$			16.3684i			0.782113i
$439$	10.8889			0.519700			0.259850	−	0.965649i	$-0.416327\pi$
$439$	10.8889			0.519700			0.259850	+	0.965649i	$0.416327\pi$
$440$	1.45536	+	0.204475i	0.0693816	+	0.00974798i
$441$	1.83008			0.0871468
$442$		0			0
$443$			28.6287i			1.36019i	0.733124	+	0.680095i	$0.238061\pi$
$443$			28.6287i			1.36019i	−0.733124	+	0.680095i	$0.761939\pi$
$444$		−	1.57136i		−	0.0745735i
$445$	−12.4286	−	1.74620i	−0.589174	−	0.0827779i
$446$	−23.8840			−1.13094
$447$	4.68244			0.221472
$448$	25.7003			1.21422
$449$			10.9304i			0.515838i	0.966167	+	0.257919i	$0.0830368\pi$
$449$			10.9304i			0.515838i	−0.966167	+	0.257919i	$0.916963\pi$
$450$	−7.47658	−	2.14320i	−0.352449	−	0.101031i
$451$	0.653858			0.0307890
$452$		−	0.622216i		−	0.0292666i
$453$	1.65878			0.0779363
$454$	−16.1160			−0.756361
$455$		0			0
$456$	8.90321			0.416931
$457$	−11.4064			−0.533567			−0.266784	−	0.963756i	$-0.585961\pi$
$457$	−11.4064			−0.533567			−0.266784	+	0.963756i	$0.585961\pi$
$458$			2.94914i			0.137804i
$459$	−36.0830			−1.68421
$460$	−5.45536	−	0.766468i	−0.254357	−	0.0357368i
$461$			26.1334i			1.21715i	0.793496	+	0.608576i	$0.208259\pi$
$461$			26.1334i			1.21715i	−0.793496	+	0.608576i	$0.791741\pi$
$462$	−0.990632			−0.0460884
$463$	−7.92242			−0.368186			−0.184093	−	0.982909i	$-0.558935\pi$
$463$	−7.92242			−0.368186			−0.184093	+	0.982909i	$0.558935\pi$
$464$	23.2815			1.08082
$465$	2.28100	−	16.2351i	0.105779	−	0.752883i
$466$			19.6414i			0.909872i
$467$		−	10.8923i		−	0.504036i	−0.967723	−	0.252018i	$-0.918906\pi$
$467$		−	10.8923i		−	0.504036i	0.967723	−	0.252018i	$-0.0810942\pi$
$468$		0			0
$469$	22.5303			1.04035
$470$	−0.414349	+	2.94914i	−0.0191125	+	0.136034i
$471$	−7.35905			−0.339087
$472$		−	28.4133i		−	1.30783i
$473$	1.36349			0.0626935
$474$			22.6637i			1.04098i
$475$	3.05086	−	10.6430i	0.139983	−	0.488332i
$476$		−	9.80642i		−	0.449477i
$477$		−	7.98709i		−	0.365704i
$478$		−	15.5145i		−	0.709618i
$479$			9.13182i			0.417244i	0.977996	+	0.208622i	$0.0668978\pi$
$479$			9.13182i			0.417244i	−0.977996	+	0.208622i	$0.933102\pi$
$480$	−8.38271	−	1.17775i	−0.382616	−	0.0537569i
$481$		0			0
$482$		−	7.16241i		−	0.326239i
$483$	17.8479			0.812108
$484$	−5.75557			−0.261617
$485$	−5.61285	+	39.9496i	−0.254866	+	1.81402i
$486$			14.8494i			0.673584i
$487$	−16.1891			−0.733600			−0.366800	−	0.930300i	$-0.619547\pi$
$487$	−16.1891			−0.733600			−0.366800	+	0.930300i	$0.619547\pi$
$488$	0.861725			0.0390084
$489$		−	4.87601i		−	0.220501i
$490$	−0.539718	+	3.84146i	−0.0243820	+	0.173539i
$491$	−26.2636			−1.18526			−0.592631	−	0.805474i	$-0.701911\pi$
$491$	−26.2636			−1.18526			−0.592631	+	0.805474i	$0.701911\pi$
$492$	−2.10171			−0.0947524
$493$		−	55.9911i		−	2.52171i
$494$		0			0
$495$	−0.607926	−	0.0854124i	−0.0273242	−	0.00383900i
$496$		−	14.9481i		−	0.671189i
$497$			17.6543i			0.791905i
$498$			15.1655i			0.679581i
$499$			30.0306i			1.34435i	0.740391	+	0.672177i	$0.234641\pi$
$499$			30.0306i			1.34435i	−0.740391	+	0.672177i	$0.765359\pi$
$500$	−2.38868	+	5.36689i	−0.106825	+	0.240014i
$501$		−	9.22570i		−	0.412174i
$502$	2.51744			0.112359
$503$			16.7304i			0.745971i	0.927837	+	0.372985i	$0.121666\pi$
$503$			16.7304i			0.745971i	−0.927837	+	0.372985i	$0.878334\pi$
$504$	−11.4050			−0.508018
$505$	1.22570	−	8.72393i	0.0545427	−	0.388210i
$506$	1.22030			0.0542488
$507$		0			0
$508$		−	1.20940i		−	0.0536583i
$509$		−	11.9684i		−	0.530488i	−0.964181	−	0.265244i	$-0.914547\pi$
$509$		−	11.9684i		−	0.530488i	0.964181	−	0.265244i	$-0.0854525\pi$
$510$	3.18421	−	22.6637i	0.140999	−	1.00357i
$511$	29.8479			1.32039
$512$	−24.1131			−1.06566
$513$	−12.4286			−0.548738
$514$		−	22.3398i		−	0.985368i
$515$	6.24935	+	0.878023i	0.275379	+	0.0386903i
$516$	−4.38271			−0.192938
$517$			0.235063i			0.0103381i
$518$	8.04149			0.353323
$519$	0.949145			0.0416628
$520$		0			0
$521$	5.75065			0.251940			0.125970	−	0.992034i	$-0.459796\pi$
$521$	5.75065			0.251940			0.125970	+	0.992034i	$0.459796\pi$
$522$	−13.5482			−0.592988
$523$			20.8035i			0.909674i	0.890575	+	0.454837i	$0.150302\pi$
$523$			20.8035i			0.909674i	−0.890575	+	0.454837i	$0.849698\pi$
$524$	7.05086			0.308018
$525$	5.24443	−	18.2953i	0.228886	−	0.798472i
$526$		−	13.3887i		−	0.583774i
$527$	−35.9496			−1.56599
$528$	0.751123			0.0326884
$529$	1.01429			0.0440996
$530$	16.7654	+	2.35551i	0.728243	+	0.102317i
$531$			11.8687i			0.515056i
$532$		−	3.37778i		−	0.146446i
$533$		0			0
$534$	−8.93624			−0.386709
$535$	37.9037	+	5.32540i	1.63872	+	0.230237i
$536$	−23.7989			−1.02796
$537$		−	5.29883i		−	0.228661i
$538$	19.6030			0.845145
$539$			0.306186i			0.0131883i
$540$	6.53035	+	0.917502i	0.281022	+	0.0394830i
$541$			16.6222i			0.714645i	0.933981	+	0.357322i	$0.116310\pi$
$541$			16.6222i			0.714645i	−0.933981	+	0.357322i	$0.883690\pi$
$542$			15.8000i			0.678667i
$543$		−	3.06959i		−	0.131729i
$544$			18.5620i			0.795839i
$545$	37.0321	+	5.20294i	1.58628	+	0.222870i
$546$		0			0
$547$		−	29.9748i		−	1.28163i	−0.767695	−	0.640815i	$-0.778596\pi$
$547$		−	29.9748i		−	1.28163i	0.767695	−	0.640815i	$-0.221404\pi$
$548$	−10.0633			−0.429882
$549$	−0.359955			−0.0153625
$550$	0.358572	−	1.25088i	0.0152896	−	0.0533379i
$551$		−	19.2859i		−	0.821608i
$552$	−18.8528			−0.802430
$553$	41.3274			1.75742
$554$		−	9.19405i		−	0.390618i
$555$	−6.62222	−	0.930409i	−0.281097	−	0.0394937i
$556$	10.0316			0.425436
$557$	5.03657			0.213406			0.106703	−	0.994291i	$-0.465971\pi$
$557$	5.03657			0.213406			0.106703	+	0.994291i	$0.465971\pi$
$558$			8.69874i			0.368247i
$559$		0			0
$560$	2.41435	−	17.1842i	0.102025	−	0.726165i
$561$		−	1.80642i		−	0.0762673i
$562$			8.20342i			0.346040i
$563$			2.88247i			0.121482i	0.998154	+	0.0607408i	$0.0193463\pi$
$563$			2.88247i			0.121482i	−0.998154	+	0.0607408i	$0.980654\pi$
$564$		−	0.755569i		−	0.0318152i
$565$	−2.62222	−	0.368416i	−0.110317	−	0.0154994i
$566$			23.1764i			0.974176i
$567$	−10.2079			−0.428690
$568$		−	18.6484i		−	0.782468i
$569$	−4.37286			−0.183320			−0.0916600	−	0.995790i	$-0.529217\pi$
$569$	−4.37286			−0.183320			−0.0916600	+	0.995790i	$0.529217\pi$
$570$	1.09679	−	7.80642i	0.0459394	−	0.326975i
$571$	1.58120			0.0661714			0.0330857	−	0.999453i	$-0.489467\pi$
$571$	1.58120			0.0661714			0.0330857	+	0.999453i	$0.489467\pi$
$572$		0			0
$573$		−	2.75557i		−	0.115116i
$574$		−	10.7556i		−	0.448929i
$575$	−6.46028	+	22.5368i	−0.269412	+	0.939850i
$576$	11.3398			0.472493
$577$	−7.61729			−0.317112			−0.158556	−	0.987350i	$-0.550684\pi$
$577$	−7.61729			−0.317112			−0.158556	+	0.987350i	$0.550684\pi$
$578$	−29.5412			−1.22875
$579$		−	17.7275i		−	0.736728i
$580$	−1.42372	+	10.1334i	−0.0591166	+	0.420765i
$581$	27.6543			1.14730
$582$			28.7239i			1.19065i
$583$	1.33630			0.0553438
$584$	−31.5285			−1.30466
$585$		0			0
$586$	−9.82071			−0.405690
$587$	−46.8243			−1.93264			−0.966322	−	0.257336i	$-0.917155\pi$
$587$	−46.8243			−1.93264			−0.966322	+	0.257336i	$0.917155\pi$
$588$		−	0.984179i		−	0.0405868i
$589$	−12.3827			−0.510221
$590$	−24.9131	−	3.50024i	−1.02565	−	0.144103i
$591$		−	2.62222i		−	0.107864i
$592$	−6.09726			−0.250596
$593$	−15.9398			−0.654568			−0.327284	−	0.944926i	$-0.606133\pi$
$593$	−15.9398			−0.654568			−0.327284	+	0.944926i	$0.606133\pi$
$594$	−1.46076			−0.0599357
$595$	−41.3274	−	5.80642i	−1.69426	−	0.238040i
$596$			1.87649i			0.0768641i
$597$			29.0321i			1.18821i
$598$		0			0
$599$	−18.4889			−0.755434			−0.377717	−	0.925921i	$-0.623291\pi$
$599$	−18.4889			−0.755434			−0.377717	+	0.925921i	$0.623291\pi$
$600$	−5.53972	+	19.3254i	−0.226158	+	0.788956i
$601$	20.7556			0.846637			0.423319	−	0.905981i	$-0.360865\pi$
$601$	20.7556			0.846637			0.423319	+	0.905981i	$0.360865\pi$
$602$		−	22.4286i		−	0.914123i
$603$	9.94116			0.404835
$604$			0.664758i			0.0270486i
$605$	−3.40790	+	24.2558i	−0.138551	+	0.986139i
$606$		−	6.27254i		−	0.254804i
$607$			36.0765i			1.46430i	0.681143	+	0.732150i	$0.261483\pi$
$607$			36.0765i			1.46430i	−0.681143	+	0.732150i	$0.738517\pi$
$608$			6.39361i			0.259295i
$609$		−	33.1526i		−	1.34341i
$610$	0.106156	−	0.755569i	0.00429813	−	0.0305921i
$611$		0			0
$612$		−	4.32693i		−	0.174906i
$613$	−9.94962			−0.401861			−0.200931	−	0.979605i	$-0.564397\pi$
$613$	−9.94962			−0.401861			−0.200931	+	0.979605i	$0.564397\pi$
$614$	16.3126			0.658325
$615$	−1.24443	+	8.85728i	−0.0501803	+	0.357160i
$616$		−	1.90813i		−	0.0768809i
$617$	2.09187			0.0842154			0.0421077	−	0.999113i	$-0.486593\pi$
$617$	2.09187			0.0842154			0.0421077	+	0.999113i	$0.486593\pi$
$618$	4.49331			0.180747
$619$		−	18.4681i		−	0.742296i	−0.928574	−	0.371148i	$-0.878964\pi$
$619$		−	18.4681i		−	0.742296i	0.928574	−	0.371148i	$-0.121036\pi$
$620$	6.50622	+	0.914111i	0.261296	+	0.0367116i
$621$	26.3180			1.05611
$622$	−24.5334			−0.983700
$623$			16.2953i			0.652857i
$624$		0			0
$625$	21.2034	+	13.2444i	0.848137	+	0.529777i
$626$		−	18.3497i		−	0.733401i
$627$		−	0.622216i		−	0.0248489i
$628$		−	2.94914i		−	0.117684i
$629$			14.6637i			0.584680i
$630$	−1.40498	+	10.0000i	−0.0559758	+	0.398410i
$631$		−	38.6657i		−	1.53926i	−0.638492	−	0.769629i	$-0.720441\pi$
$631$		−	38.6657i		−	1.53926i	0.638492	−	0.769629i	$-0.279559\pi$
$632$	−43.6543			−1.73648
$633$			25.7690i			1.02422i
$634$	27.0563			1.07454
$635$	−5.09679	−	0.716089i	−0.202260	−	0.0284171i
$636$	−4.29529			−0.170319
$637$		0			0
$638$		−	2.26671i		−	0.0897398i
$639$			7.78970i			0.308156i
$640$	−1.54770	+	11.0158i	−0.0611783	+	0.435439i
$641$	−24.5718			−0.970529			−0.485265	−	0.874367i	$-0.661277\pi$
$641$	−24.5718			−0.970529			−0.485265	+	0.874367i	$0.661277\pi$
$642$	27.2529			1.07559
$643$	−27.4938			−1.08425			−0.542125	−	0.840298i	$-0.682380\pi$
$643$	−27.4938			−1.08425			−0.542125	+	0.840298i	$0.682380\pi$
$644$			7.15257i			0.281851i
$645$	−2.59502	+	18.4701i	−0.102179	+	0.727261i
$646$	−17.2859			−0.680105
$647$		−	13.7812i		−	0.541796i	−0.962608	−	0.270898i	$-0.912679\pi$
$647$		−	13.7812i		−	0.541796i	0.962608	−	0.270898i	$-0.0873207\pi$
$648$	10.7826			0.423581
$649$	−1.98571			−0.0779459
$650$		0			0
$651$	−21.2859			−0.834261
$652$	1.95407			0.0765272
$653$			2.12045i			0.0829795i	0.999139	+	0.0414897i	$0.0132104\pi$
$653$			2.12045i			0.0829795i	−0.999139	+	0.0414897i	$0.986790\pi$
$654$	26.6262			1.04117
$655$	4.17484	−	29.7146i	0.163125	−	1.16104i
$656$			8.15515i			0.318405i
$657$	13.1699			0.513807
$658$	3.86665			0.150738
$659$	−33.8894			−1.32014			−0.660072	−	0.751203i	$-0.729474\pi$
$659$	−33.8894			−1.32014			−0.660072	+	0.751203i	$0.729474\pi$
$660$	−0.0459330	+	0.326929i	−0.00178794	+	0.0127257i
$661$		−	37.3689i		−	1.45348i	−0.686912	−	0.726741i	$-0.741034\pi$
$661$		−	37.3689i		−	1.45348i	0.686912	−	0.726741i	$-0.258966\pi$
$662$		−	10.0252i		−	0.389640i
$663$		0			0
$664$	−29.2114			−1.13362
$665$	−14.2351	−	2.00000i	−0.552012	−	0.0775567i
$666$	3.54818			0.137489
$667$			40.8385i			1.58127i
$668$	3.69721			0.143049
$669$		−	25.7877i		−	0.997010i
$670$	−2.93179	+	20.8671i	−0.113265	+	0.806167i
$671$		−	0.0602231i		−	0.00232489i
$672$			10.9906i			0.423973i
$673$		−	35.4608i		−	1.36691i	−0.729992	−	0.683456i	$-0.760476\pi$
$673$		−	35.4608i		−	1.36691i	0.729992	−	0.683456i	$-0.239524\pi$
$674$			16.6923i			0.642963i
$675$	7.73329	−	26.9777i	0.297655	−	1.03837i
$676$		0			0
$677$			15.3047i			0.588206i	0.955774	+	0.294103i	$0.0950208\pi$
$677$			15.3047i			0.588206i	−0.955774	+	0.294103i	$0.904979\pi$
$678$	−1.88538			−0.0724077
$679$	52.3783			2.01009
$680$	43.6543	+	6.13335i	1.67407	+	0.235203i
$681$		−	17.4005i		−	0.666790i
$682$	−1.45536			−0.0557286
$683$	−13.0968			−0.501135			−0.250567	−	0.968099i	$-0.580617\pi$
$683$	−13.0968			−0.501135			−0.250567	+	0.968099i	$0.580617\pi$
$684$		−	1.49039i		−	0.0569866i
$685$	−5.95851	+	42.4099i	−0.227663	+	1.62040i
$686$	−19.6414			−0.749913
$687$	−3.18421			−0.121485
$688$			17.0060i			0.648347i
$689$		0			0
$690$	−2.32248	+	16.5303i	−0.0884154	+	0.629300i
$691$			18.4079i			0.700269i	0.936699	+	0.350135i	$0.113864\pi$
$691$			18.4079i			0.700269i	−0.936699	+	0.350135i	$0.886136\pi$
$692$			0.380371i			0.0144595i
$693$			0.797056i			0.0302777i
$694$			1.48055i			0.0562009i
$695$	5.93978	−	42.2766i	0.225309	−	1.60364i
$696$			35.0192i			1.32740i
$697$	19.6128			0.742890
$698$		−	27.3363i		−	1.03469i
$699$	−21.2070			−0.802121
$700$	7.33185	+	2.10171i	0.277118	+	0.0794372i
$701$	31.3689			1.18479			0.592393	−	0.805649i	$-0.298183\pi$
$701$	31.3689			1.18479			0.592393	+	0.805649i	$0.298183\pi$
$702$		0			0
$703$			5.05086i			0.190497i
$704$			1.89723i			0.0715047i
$705$	−3.18421	−	0.447375i	−0.119924	−	0.0168491i
$706$	17.3417			0.652663
$707$	−11.4380			−0.430171
$708$	6.38271			0.239877
$709$		−	9.47949i		−	0.356010i	−0.984030	−	0.178005i	$-0.943036\pi$
$709$		−	9.47949i		−	0.356010i	0.984030	−	0.178005i	$-0.0569643\pi$
$710$	−16.3511	−	2.29729i	−0.613644	−	0.0862159i
$711$	18.2351			0.683868
$712$		−	17.2128i		−	0.645077i
$713$	26.2208			0.981976
$714$	−29.7146			−1.11204
$715$		0			0
$716$	2.12351			0.0793592
$717$	16.7511			0.625582
$718$			14.7590i			0.550799i
$719$	−29.6227			−1.10474			−0.552370	−	0.833599i	$-0.686276\pi$
$719$	−29.6227			−1.10474			−0.552370	+	0.833599i	$0.686276\pi$
$720$	1.06529	−	7.58226i	0.0397011	−	0.282574i
$721$		−	8.19358i		−	0.305145i
$722$	17.1180			0.637066
$723$	7.73329			0.287604
$724$	1.23014			0.0457178
$725$	41.8622	+	12.0000i	1.55472	+	0.445669i
$726$			17.4400i			0.647260i
$727$		−	42.6702i		−	1.58255i	−0.611461	−	0.791274i	$-0.709418\pi$
$727$		−	42.6702i		−	1.58255i	0.611461	−	0.791274i	$-0.290582\pi$
$728$		0			0
$729$	−26.5812			−0.984489
$730$	−3.88400	+	27.6445i	−0.143753	+	1.02317i
$731$	40.8988			1.51270
$732$			0.193576i			0.00715478i
$733$	−26.0830			−0.963397			−0.481698	−	0.876337i	$-0.659980\pi$
$733$	−26.0830			−0.963397			−0.481698	+	0.876337i	$0.659980\pi$
$734$		−	5.65539i		−	0.208744i
$735$	−4.14764	−	0.582736i	−0.152988	−	0.0214945i
$736$		−	13.5387i		−	0.499042i
$737$			1.66323i			0.0612657i
$738$		−	4.74572i		−	0.174693i
$739$			28.2687i			1.03988i	0.854202	+	0.519941i	$0.174046\pi$
$739$			28.2687i			1.03988i	−0.854202	+	0.519941i	$0.825954\pi$
$740$	0.372862	−	2.65386i	0.0137067	−	0.0975578i
$741$		0			0
$742$		−	21.9813i		−	0.806958i
$743$	−20.6681			−0.758241			−0.379120	−	0.925347i	$-0.623773\pi$
$743$	−20.6681			−0.758241			−0.379120	+	0.925347i	$0.623773\pi$
$744$	22.4844			0.824319
$745$	7.90813	+	1.11108i	0.289732	+	0.0407068i
$746$		−	42.4286i		−	1.55342i
$747$	12.2020			0.446449
$748$	0.723926			0.0264694
$749$		−	49.6958i		−	1.81585i
$750$	16.2623	+	7.23798i	0.593814	+	0.264294i
$751$	−2.46028			−0.0897770			−0.0448885	−	0.998992i	$-0.514293\pi$
$751$	−2.46028			−0.0897770			−0.0448885	+	0.998992i	$0.514293\pi$
$752$	−2.93179			−0.106911
$753$			2.71810i			0.0990530i
$754$		0			0
$755$	2.80150	+	0.393606i	0.101957	+	0.0143248i
$756$		−	8.56199i		−	0.311397i
$757$		−	48.6035i		−	1.76652i	−0.468880	−	0.883262i	$-0.655342\pi$
$757$		−	48.6035i		−	1.76652i	0.468880	−	0.883262i	$-0.344658\pi$
$758$		−	21.2162i		−	0.770606i
$759$			1.31756i			0.0478244i
$760$	15.0366	+	2.11261i	0.545434	+	0.0766324i
$761$		−	13.8252i		−	0.501162i	−0.968096	−	0.250581i	$-0.919378\pi$
$761$		−	13.8252i		−	0.501162i	0.968096	−	0.250581i	$-0.0806216\pi$
$762$	−3.66461			−0.132755
$763$		−	48.5531i		−	1.75774i
$764$	1.10430			0.0399520
$765$	−18.2351	−	2.56199i	−0.659290	−	0.0926290i
$766$	22.6811			0.819500
$767$		0			0
$768$		−	15.2924i		−	0.551816i
$769$		−	38.9688i		−	1.40525i	−0.711559	−	0.702626i	$-0.752011\pi$
$769$		−	38.9688i		−	1.40525i	0.711559	−	0.702626i	$-0.247989\pi$
$770$	−1.67307	−	0.235063i	−0.0602933	−	0.00847109i
$771$	24.1204			0.868677
$772$	7.10430			0.255689
$773$	0.445992			0.0160412			0.00802061	−	0.999968i	$-0.497447\pi$
$773$	0.445992			0.0160412			0.00802061	+	0.999968i	$0.497447\pi$
$774$		−	9.89628i		−	0.355715i
$775$	7.70471	−	26.8780i	0.276761	−	0.965487i
$776$	−55.3274			−1.98614
$777$			8.68244i			0.311481i
$778$	1.95851			0.0702161
$779$	6.75557			0.242043
$780$		0			0
$781$	−1.30327			−0.0466347
$782$	36.6035			1.30894
$783$		−	48.8859i		−	1.74704i
$784$	−3.81885			−0.136388
$785$	−12.4286	−	1.74620i	−0.443597	−	0.0623246i
$786$		−	21.3649i		−	0.762060i
$787$	33.9037			1.20854			0.604268	−	0.796781i	$-0.293466\pi$
$787$	33.9037			1.20854			0.604268	+	0.796781i	$0.293466\pi$
$788$	1.05086			0.0374352
$789$	14.4558			0.514641
$790$	−5.37778	+	38.2766i	−0.191333	+	1.36182i
$791$			3.43801i			0.122241i
$792$		−	0.841934i		−	0.0299168i
$793$		0			0
$794$	−7.98571			−0.283402
$795$	−2.54326	+	18.1017i	−0.0902000	+	0.642002i
$796$	−11.6346			−0.412379
$797$		−	10.2953i		−	0.364678i	−0.983236	−	0.182339i	$-0.941633\pi$
$797$		−	10.2953i		−	0.364678i	0.983236	−	0.182339i	$-0.0583668\pi$
$798$	−10.2351			−0.362317
$799$			7.05086i			0.249441i
$800$	−13.8780	−	3.97820i	−0.490662	−	0.140651i
$801$			7.19004i			0.254047i
$802$		−	26.6035i		−	0.939402i
$803$			2.20342i			0.0777570i
$804$		−	5.34614i		−	0.188544i
$805$	30.1432	+	4.23506i	1.06241	+	0.149266i
$806$		0			0
$807$			21.1655i			0.745060i
$808$	12.0820			0.425044
$809$	−7.94422			−0.279304			−0.139652	−	0.990201i	$-0.544598\pi$
$809$	−7.94422			−0.279304			−0.139652	+	0.990201i	$0.544598\pi$
$810$	1.32831	−	9.45431i	0.0466721	−	0.332190i
$811$			8.12245i			0.285218i	0.989779	+	0.142609i	$0.0455491\pi$
$811$			8.12245i			0.285218i	−0.989779	+	0.142609i	$0.954451\pi$
$812$	13.2859			0.466244
$813$	−17.0593			−0.598296
$814$			0.593635i			0.0208069i
$815$	1.15701	−	8.23506i	0.0405283	−	0.288462i
$816$	22.5303			0.788720
$817$	14.0874			0.492856
$818$		−	12.3783i		−	0.432796i
$819$		0			0
$820$	−3.54956	−	0.498707i	−0.123956	−	0.0174156i
$821$			22.2065i			0.775012i	0.921867	+	0.387506i	$0.126663\pi$
$821$			22.2065i			0.775012i	−0.921867	+	0.387506i	$0.873337\pi$
$822$			30.4929i			1.06356i
$823$		−	11.1175i		−	0.387533i	−0.981048	−	0.193766i	$-0.937930\pi$
$823$		−	11.1175i		−	0.387533i	0.981048	−	0.193766i	$-0.0620704\pi$
$824$			8.65491i			0.301508i
$825$	1.35059	+	0.387152i	0.0470214	+	0.0134789i
$826$			32.6637i			1.13652i
$827$	23.1570			0.805248			0.402624	−	0.915365i	$-0.368098\pi$
$827$	23.1570			0.805248			0.402624	+	0.915365i	$0.368098\pi$
$828$			3.15596i			0.109677i
$829$	−27.1195			−0.941901			−0.470950	−	0.882160i	$-0.656089\pi$
$829$	−27.1195			−0.941901			−0.470950	+	0.882160i	$0.656089\pi$
$830$	−3.59856	+	25.6128i	−0.124908	+	0.889035i
$831$	9.92687			0.344359
$832$		0			0
$833$			9.18421i			0.318214i
$834$		−	30.3970i		−	1.05256i
$835$	2.18913	−	15.5812i	0.0757580	−	0.539210i
$836$	0.249353			0.00862407
$837$	−31.3876			−1.08492
$838$	−8.88586			−0.306957
$839$		−	25.3955i		−	0.876749i	−0.898792	−	0.438374i	$-0.855554\pi$
$839$		−	25.3955i		−	0.876749i	0.898792	−	0.438374i	$-0.144446\pi$
$840$	25.8479	+	3.63158i	0.891838	+	0.125302i
$841$	46.8578			1.61578
$842$			9.55262i			0.329205i
$843$	−8.85728			−0.305061
$844$	−10.3269			−0.355468
$845$		0			0
$846$	1.70610			0.0586568
$847$	31.8020			1.09273
$848$			16.6668i			0.572339i
$849$	−25.0237			−0.858810
$850$	10.7556	−	37.5210i	0.368913	−	1.28696i
$851$		−	10.6953i		−	0.366632i
$852$	4.18913			0.143517
$853$	−25.0651			−0.858214			−0.429107	−	0.903254i	$-0.641172\pi$
$853$	−25.0651			−0.858214			−0.429107	+	0.903254i	$0.641172\pi$
$854$	−0.990632			−0.0338987
$855$	−6.28100	−	0.882468i	−0.214806	−	0.0301798i
$856$			52.4939i			1.79421i
$857$			7.61285i			0.260050i	0.991511	+	0.130025i	$0.0415057\pi$
$857$			7.61285i			0.260050i	−0.991511	+	0.130025i	$0.958494\pi$
$858$		0			0
$859$	−42.1432			−1.43791			−0.718954	−	0.695058i	$-0.755379\pi$
$859$	−42.1432			−1.43791			−0.718954	+	0.695058i	$0.755379\pi$
$860$	−7.40192	−	1.03996i	−0.252403	−	0.0354622i
$861$	11.6128			0.395765
$862$			47.2607i			1.60971i
$863$	51.5768			1.75569			0.877847	−	0.478942i	$-0.158980\pi$
$863$	51.5768			1.75569			0.877847	+	0.478942i	$0.158980\pi$
$864$			16.2065i			0.551356i
$865$	1.60300	+	0.225219i	0.0545037	+	0.00765768i
$866$		−	24.5334i		−	0.833679i
$867$		−	31.8959i		−	1.08324i
$868$		−	8.53035i		−	0.289539i
$869$			3.05086i			0.103493i
$870$	30.7052	+	4.31402i	1.04100	+	0.146259i
$871$		0			0
$872$			51.2869i			1.73679i
$873$	23.1111			0.782191
$874$	12.6079			0.426469
$875$	13.1985	−	29.6543i	0.446191	−	1.00250i
$876$		−	7.08250i		−	0.239295i
$877$	34.0701			1.15046			0.575232	−	0.817990i	$-0.304912\pi$
$877$	34.0701			1.15046			0.575232	+	0.817990i	$0.304912\pi$
$878$	13.2226			0.446242
$879$		−	10.6035i		−	0.357646i
$880$	1.26857	+	0.178231i	0.0427633	+	0.00600817i
$881$	−3.71900			−0.125296			−0.0626482	−	0.998036i	$-0.519955\pi$
$881$	−3.71900			−0.125296			−0.0626482	+	0.998036i	$0.519955\pi$
$882$	2.22230			0.0748289
$883$			42.0163i			1.41396i	0.707233	+	0.706981i	$0.249943\pi$
$883$			42.0163i			1.41396i	−0.707233	+	0.706981i	$0.750057\pi$
$884$		0			0
$885$	3.77923	−	26.8988i	0.127037	−	0.904192i
$886$			34.7644i			1.16793i
$887$			40.3116i			1.35353i	0.736199	+	0.676765i	$0.236619\pi$
$887$			40.3116i			1.35353i	−0.736199	+	0.676765i	$0.763381\pi$
$888$		−	9.17130i		−	0.307769i
$889$			6.68244i			0.224122i
$890$	−15.0923	−	2.12045i	−0.505896	−	0.0710775i
$891$		−	0.753561i		−	0.0252452i
$892$	10.3344			0.346023
$893$			2.42864i			0.0812713i
$894$	5.68598			0.190168
$895$	1.25734	−	8.94914i	0.0420282	−	0.299137i
$896$	14.4429			0.482504
$897$		0			0
$898$			13.2730i			0.442926i
$899$		−	48.7052i		−	1.62441i
$900$	3.23506	+	0.927346i	0.107835	+	0.0309115i
$901$	40.0830			1.33536
$902$	0.793993			0.0264371
$903$	24.2163			0.805869
$904$		−	3.63158i		−	0.120785i
$905$	0.728372	−	5.18421i	0.0242119	−	0.172329i
$906$	2.01429			0.0669203
$907$			34.8419i			1.15691i	0.815715	+	0.578454i	$0.196344\pi$
$907$			34.8419i			1.15691i	−0.815715	+	0.578454i	$0.803656\pi$
$908$	6.97328			0.231416
$909$	−5.04684			−0.167393
$910$		0			0
$911$	23.2672			0.770876			0.385438	−	0.922734i	$-0.374050\pi$
$911$	23.2672			0.770876			0.385438	+	0.922734i	$0.374050\pi$
$912$	7.76049			0.256976
$913$			2.04149i			0.0675634i
$914$	−13.8510			−0.458149
$915$	0.815792	+	0.114617i	0.0269692	+	0.00378913i
$916$		−	1.27607i		−	0.0421627i
$917$	−38.9590			−1.28654
$918$	−43.8163			−1.44615
$919$	3.22570			0.106406			0.0532029	−	0.998584i	$-0.483057\pi$
$919$	3.22570			0.106406			0.0532029	+	0.998584i	$0.483057\pi$
$920$	−31.8404	−	4.47352i	−1.04975	−	0.147488i
$921$			17.6128i			0.580363i
$922$			31.7342i			1.04511i
$923$		0			0
$924$	0.428639			0.0141012
$925$	−10.9634	−	3.14272i	−0.360476	−	0.103332i
$926$	−9.62036			−0.316145
$927$		−	3.61529i		−	0.118742i
$928$	−25.1481			−0.825527
$929$		−	39.3461i		−	1.29091i	−0.763800	−	0.645453i	$-0.776669\pi$
$929$		−	39.3461i		−	1.29091i	0.763800	−	0.645453i	$-0.223331\pi$
$930$	2.76986	−	19.7146i	0.0908272	−	0.646466i
$931$			3.16346i			0.103678i
$932$		−	8.49871i		−	0.278384i
$933$		−	26.4889i		−	0.867206i
$934$		−	13.2268i		−	0.432792i
$935$	0.428639	−	3.05086i	0.0140180	−	0.0997736i
$936$		0			0
$937$			51.6040i			1.68583i	0.538048	+	0.842914i	$0.319162\pi$
$937$			51.6040i			1.68583i	−0.538048	+	0.842914i	$0.680838\pi$
$938$	27.3590			0.893305
$939$	19.8123			0.646548
$940$	0.179286	−	1.27607i	0.00584767	−	0.0416209i
$941$		−	37.5081i		−	1.22273i	−0.791349	−	0.611364i	$-0.790621\pi$
$941$		−	37.5081i		−	1.22273i	0.791349	−	0.611364i	$-0.209379\pi$
$942$	−8.93624			−0.291158
$943$	−14.3051			−0.465839
$944$		−	24.7665i		−	0.806080i
$945$	−36.0830	−	5.06959i	−1.17378	−	0.164914i
$946$	1.65572			0.0538320
$947$	38.1160			1.23860			0.619302	−	0.785153i	$-0.287416\pi$
$947$	38.1160			1.23860			0.619302	+	0.785153i	$0.287416\pi$
$948$		−	9.80642i		−	0.318498i
$949$		0			0
$950$	3.70471	−	12.9240i	0.120197	−	0.419308i
$951$			29.2128i			0.947290i
$952$		−	57.2355i		−	1.85501i
$953$		−	28.7368i		−	0.930877i	−0.885080	−	0.465439i	$-0.845897\pi$
$953$		−	28.7368i		−	0.930877i	0.885080	−	0.465439i	$-0.154103\pi$
$954$		−	9.69888i		−	0.314013i
$955$	0.653858	−	4.65386i	0.0211584	−	0.150595i
$956$			6.71303i			0.217115i
$957$	2.44738			0.0791124
$958$			11.0890i			0.358268i
$959$	55.6040			1.79555
$960$	−25.7003	−	3.61084i	−0.829473	−	0.116539i
$961$	−0.271628			−0.00876221
$962$		0			0
$963$		−	21.9275i		−	0.706604i
$964$			3.09912i			0.0998161i
$965$	4.20648	−	29.9398i	0.135411	−	0.963796i
$966$	21.6731			0.697320
$967$	29.0593			0.934485			0.467242	−	0.884129i	$-0.345248\pi$
$967$	29.0593			0.934485			0.467242	+	0.884129i	$0.345248\pi$
$968$	−33.5926			−1.07971
$969$		−	18.6637i		−	0.599565i
$970$	−6.81579	+	48.5116i	−0.218842	+	1.55761i
$971$	−39.8578			−1.27910			−0.639548	−	0.768751i	$-0.720879\pi$
$971$	−39.8578			−1.27910			−0.639548	+	0.768751i	$0.720879\pi$
$972$		−	6.42525i		−	0.206090i
$973$	−55.4291			−1.77698
$974$	−19.6588			−0.629908
$975$		0			0
$976$	0.751123			0.0240429
$977$	−12.8617			−0.411483			−0.205742	−	0.978606i	$-0.565961\pi$
$977$	−12.8617			−0.411483			−0.205742	+	0.978606i	$0.565961\pi$
$978$		−	5.92104i		−	0.189334i
$979$	−1.20294			−0.0384463
$980$	0.233532	−	1.66217i	0.00745991	−	0.0530961i
$981$		−	21.4233i		−	0.683993i
$982$	−31.8925			−1.01773
$983$	45.4880			1.45084			0.725420	−	0.688306i	$-0.241645\pi$
$983$	45.4880			1.45084			0.725420	+	0.688306i	$0.241645\pi$
$984$	−12.2667			−0.391048
$985$	0.622216	−	4.42864i	0.0198254	−	0.141108i
$986$		−	67.9911i		−	2.16528i
$987$			4.17484i			0.132887i
$988$		0			0
$989$	−29.8306			−0.948557
$990$	−0.738216	−	0.103718i	−0.0234620	−	0.00329637i
$991$	8.07007			0.256354			0.128177	−	0.991751i	$-0.459087\pi$
$991$	8.07007			0.256354			0.128177	+	0.991751i	$0.459087\pi$
$992$			16.1466i			0.512655i
$993$	10.8243			0.343497
$994$			21.4380i			0.679972i
$995$	−6.88892	+	49.0321i	−0.218394	+	1.55442i
$996$		−	6.56199i		−	0.207925i
$997$		−	32.8158i		−	1.03929i	−0.854383	−	0.519643i	$-0.826065\pi$
$997$		−	32.8158i		−	1.03929i	0.854383	−	0.519643i	$-0.173935\pi$
$998$			36.4667i			1.15433i
$999$			12.8029i			0.405065i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.d.a.844.6		6
5.4	even	2		845.2.d.b.844.1		6
13.2	odd	12		845.2.n.g.529.4		12
13.3	even	3		845.2.l.e.654.1		12
13.4	even	6		845.2.l.d.699.6		12
13.5	odd	4		845.2.b.c.339.3		6
13.6	odd	12		845.2.n.g.484.3		12
13.7	odd	12		845.2.n.f.484.4		12
13.8	odd	4		65.2.b.a.14.4	yes	6
13.9	even	3		845.2.l.e.699.2		12
13.10	even	6		845.2.l.d.654.5		12
13.11	odd	12		845.2.n.f.529.3		12
13.12	even	2		845.2.d.b.844.2		6
39.8	even	4		585.2.c.b.469.3		6
52.47	even	4		1040.2.d.c.209.2		6
65.4	even	6		845.2.l.e.699.1		12
65.8	even	4		325.2.a.j.1.3		3
65.9	even	6		845.2.l.d.699.5		12
65.18	even	4		4225.2.a.bh.1.1		3
65.19	odd	12		845.2.n.g.484.4		12
65.24	odd	12		845.2.n.f.529.4		12
65.29	even	6		845.2.l.d.654.6		12
65.34	odd	4		65.2.b.a.14.3	✓	6
65.44	odd	4		845.2.b.c.339.4		6
65.47	even	4		325.2.a.k.1.1		3
65.49	even	6		845.2.l.e.654.2		12
65.54	odd	12		845.2.n.g.529.3		12
65.57	even	4		4225.2.a.ba.1.3		3
65.59	odd	12		845.2.n.f.484.3		12
65.64	even	2	inner	845.2.d.a.844.5		6
195.8	odd	4		2925.2.a.bj.1.1		3
195.47	odd	4		2925.2.a.bf.1.3		3
195.164	even	4		585.2.c.b.469.4		6
260.47	odd	4		5200.2.a.cb.1.2		3
260.99	even	4		1040.2.d.c.209.5		6
260.203	odd	4		5200.2.a.cj.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.b.a.14.3	✓	6	65.34	odd	4
65.2.b.a.14.4	yes	6	13.8	odd	4
325.2.a.j.1.3		3	65.8	even	4
325.2.a.k.1.1		3	65.47	even	4
585.2.c.b.469.3		6	39.8	even	4
585.2.c.b.469.4		6	195.164	even	4
845.2.b.c.339.3		6	13.5	odd	4
845.2.b.c.339.4		6	65.44	odd	4
845.2.d.a.844.5		6	65.64	even	2	inner
845.2.d.a.844.6		6	1.1	even	1	trivial
845.2.d.b.844.1		6	5.4	even	2
845.2.d.b.844.2		6	13.12	even	2
845.2.l.d.654.5		12	13.10	even	6
845.2.l.d.654.6		12	65.29	even	6
845.2.l.d.699.5		12	65.9	even	6
845.2.l.d.699.6		12	13.4	even	6
845.2.l.e.654.1		12	13.3	even	3
845.2.l.e.654.2		12	65.49	even	6
845.2.l.e.699.1		12	65.4	even	6
845.2.l.e.699.2		12	13.9	even	3
845.2.n.f.484.3		12	65.59	odd	12
845.2.n.f.484.4		12	13.7	odd	12
845.2.n.f.529.3		12	13.11	odd	12
845.2.n.f.529.4		12	65.24	odd	12
845.2.n.g.484.3		12	13.6	odd	12
845.2.n.g.484.4		12	65.19	odd	12
845.2.n.g.529.3		12	65.54	odd	12
845.2.n.g.529.4		12	13.2	odd	12
1040.2.d.c.209.2		6	52.47	even	4
1040.2.d.c.209.5		6	260.99	even	4
2925.2.a.bf.1.3		3	195.47	odd	4
2925.2.a.bj.1.1		3	195.8	odd	4
4225.2.a.ba.1.3		3	65.57	even	4
4225.2.a.bh.1.1		3	65.18	even	4
5200.2.a.cb.1.2		3	260.47	odd	4
5200.2.a.cj.1.2		3	260.203	odd	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)

\(f(q)\)	\(=\)	\(q+1.21432 q^{2} +1.31111i q^{3} -0.525428 q^{4} +(-0.311108 + 2.21432i) q^{5} +1.59210i q^{6} +2.90321 q^{7} -3.06668 q^{8} +1.28100 q^{9} +(-0.377784 + 2.68889i) q^{10} +0.214320i q^{11} -0.688892i q^{12} +3.52543 q^{14} +(-2.90321 - 0.407896i) q^{15} -2.67307 q^{16} +6.42864i q^{17} +1.55554 q^{18} +2.21432i q^{19} +(0.163465 - 1.16346i) q^{20} +3.80642i q^{21} +0.260253i q^{22} -4.68889i q^{23} -4.02074i q^{24} +(-4.80642 - 1.37778i) q^{25} +5.61285i q^{27} -1.52543 q^{28} -8.70964 q^{29} +(-3.52543 - 0.495316i) q^{30} +5.59210i q^{31} +2.88739 q^{32} -0.280996 q^{33} +7.80642i q^{34} +(-0.903212 + 6.42864i) q^{35} -0.673071 q^{36} +2.28100 q^{37} +2.68889i q^{38} +(0.954067 - 6.79060i) q^{40} -3.05086i q^{41} +4.62222i q^{42} -6.36196i q^{43} -0.112610i q^{44} +(-0.398528 + 2.83654i) q^{45} -5.69381i q^{46} +1.09679 q^{47} -3.50468i q^{48} +1.42864 q^{49} +(-5.83654 - 1.67307i) q^{50} -8.42864 q^{51} -6.23506i q^{53} +6.81579i q^{54} +(-0.474572 - 0.0666765i) q^{55} -8.90321 q^{56} -2.90321 q^{57} -10.5763 q^{58} +9.26517i q^{59} +(1.52543 + 0.214320i) q^{60} -0.280996 q^{61} +6.79060i q^{62} +3.71900 q^{63} +8.85236 q^{64} -0.341219 q^{66} +7.76049 q^{67} -3.37778i q^{68} +6.14764 q^{69} +(-1.09679 + 7.80642i) q^{70} +6.08097i q^{71} -3.92840 q^{72} +10.2810 q^{73} +2.76986 q^{74} +(1.80642 - 6.30174i) q^{75} -1.16346i q^{76} +0.622216i q^{77} +14.2351 q^{79} +(0.831613 - 5.91903i) q^{80} -3.51606 q^{81} -3.70471i q^{82} +9.52543 q^{83} -2.00000i q^{84} +(-14.2351 - 2.00000i) q^{85} -7.72546i q^{86} -11.4193i q^{87} -0.657249i q^{88} +5.61285i q^{89} +(-0.483940 + 3.44446i) q^{90} +2.46367i q^{92} -7.33185 q^{93} +1.33185 q^{94} +(-4.90321 - 0.688892i) q^{95} +3.78568i q^{96} +18.0415 q^{97} +1.73483 q^{98} +0.274543i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 10 q^{4} - 2 q^{5} + 4 q^{7} - 18 q^{8} - 6 q^{9} - 2 q^{10} + 8 q^{14} - 4 q^{15} + 10 q^{16} + 10 q^{18} + 14 q^{20} - 2 q^{25} + 4 q^{28} - 12 q^{29} - 8 q^{30} - 22 q^{32} + 12 q^{33}+ \cdots + 50 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 + 10 * q^4 - 2 * q^5 + 4 * q^7 - 18 * q^8 - 6 * q^9 - 2 * q^10 + 8 * q^14 - 4 * q^15 + 10 * q^16 + 10 * q^18 + 14 * q^20 - 2 * q^25 + 4 * q^28 - 12 * q^29 - 8 * q^30 - 22 * q^32 + 12 * q^33 + 8 * q^35 + 22 * q^36 - 34 * q^40 + 38 * q^45 + 20 * q^47 - 18 * q^49 - 22 * q^50 - 24 * q^51 - 16 * q^55 - 40 * q^56 - 4 * q^57 - 24 * q^58 - 4 * q^60 + 12 * q^61 + 36 * q^63 + 66 * q^64 - 16 * q^66 - 20 * q^67 + 24 * q^69 - 20 * q^70 - 90 * q^72 + 48 * q^73 + 4 * q^74 - 16 * q^75 + 32 * q^79 + 58 * q^80 + 46 * q^81 + 44 * q^83 - 32 * q^85 - 70 * q^90 - 4 * q^93 - 32 * q^94 - 16 * q^95 + 28 * q^97 + 50 * q^98

Introduction

L-functions

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