LMFDB - Embedded newform 1815.2.c.j.364.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,2,Mod(364,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1815.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1815.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.4928479669$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.9
Character	$\chi$	$=$	1815.364
Dual form			1815.2.c.j.364.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.784131i q^{2} +1.00000i q^{3} +1.38514 q^{4} +(-1.83964 - 1.27111i) q^{5} +0.784131 q^{6} +1.51801i q^{7} -2.65439i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.784131i q^{2} +1.00000i q^{3} +1.38514 q^{4} +(-1.83964 - 1.27111i) q^{5} +0.784131 q^{6} +1.51801i q^{7} -2.65439i q^{8} -1.00000 q^{9} +(-0.996719 + 1.44252i) q^{10} +1.38514i q^{12} -0.466512i q^{13} +1.19032 q^{14} +(1.27111 - 1.83964i) q^{15} +0.688885 q^{16} -1.69631i q^{17} +0.784131i q^{18} -5.60956 q^{19} +(-2.54816 - 1.76067i) q^{20} -1.51801 q^{21} -7.68641i q^{23} +2.65439 q^{24} +(1.76855 + 4.67678i) q^{25} -0.365807 q^{26} -1.00000i q^{27} +2.10265i q^{28} -2.66104 q^{29} +(-1.44252 - 0.996719i) q^{30} +3.95772 q^{31} -5.84896i q^{32} -1.33013 q^{34} +(1.92956 - 2.79258i) q^{35} -1.38514 q^{36} -3.05939i q^{37} +4.39863i q^{38} +0.466512 q^{39} +(-3.37403 + 4.88312i) q^{40} -1.35030 q^{41} +1.19032i q^{42} -12.0864i q^{43} +(1.83964 + 1.27111i) q^{45} -6.02716 q^{46} +2.55805i q^{47} +0.688885i q^{48} +4.69566 q^{49} +(3.66721 - 1.38677i) q^{50} +1.69631 q^{51} -0.646184i q^{52} -8.01711i q^{53} -0.784131 q^{54} +4.02938 q^{56} -5.60956i q^{57} +2.08661i q^{58} -7.54869 q^{59} +(1.76067 - 2.54816i) q^{60} -11.1178 q^{61} -3.10338i q^{62} -1.51801i q^{63} -3.20858 q^{64} +(-0.592989 + 0.858214i) q^{65} +6.89959i q^{67} -2.34962i q^{68} +7.68641 q^{69} +(-2.18975 - 1.51303i) q^{70} +14.5878 q^{71} +2.65439i q^{72} +2.26725i q^{73} -2.39896 q^{74} +(-4.67678 + 1.76855i) q^{75} -7.77002 q^{76} -0.365807i q^{78} -12.1809 q^{79} +(-1.26730 - 0.875650i) q^{80} +1.00000 q^{81} +1.05881i q^{82} -11.7808i q^{83} -2.10265 q^{84} +(-2.15620 + 3.12059i) q^{85} -9.47736 q^{86} -2.66104i q^{87} -1.47962 q^{89} +(0.996719 - 1.44252i) q^{90} +0.708168 q^{91} -10.6467i q^{92} +3.95772i q^{93} +2.00584 q^{94} +(10.3196 + 7.13038i) q^{95} +5.84896 q^{96} -14.2015i q^{97} -3.68201i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} - 2 q^{5} - 8 q^{6} - 24 q^{9}+O(q^{10}) $ 24 * q - 24 * q^4 - 2 * q^5 - 8 * q^6 - 24 * q^9	$ 24 q - 24 q^{4} - 2 q^{5} - 8 q^{6} - 24 q^{9} - 6 q^{10} - 12 q^{14} + 48 q^{16} + 32 q^{19} - 2 q^{20} - 16 q^{21} + 24 q^{24} + 2 q^{25} + 32 q^{26} - 8 q^{30} - 12 q^{34} + 10 q^{35} + 24 q^{36} + 36 q^{39} + 34 q^{40} + 2 q^{45} - 56 q^{46} - 24 q^{49} + 46 q^{50} - 36 q^{51} + 8 q^{54} + 12 q^{56} - 40 q^{59} - 26 q^{60} - 40 q^{61} + 12 q^{64} + 10 q^{65} - 2 q^{70} + 64 q^{71} - 136 q^{74} + 20 q^{75} - 68 q^{76} + 64 q^{79} + 76 q^{80} + 24 q^{81} + 60 q^{84} - 72 q^{86} + 20 q^{89} + 6 q^{90} - 4 q^{94} + 64 q^{95} - 56 q^{96}+O(q^{100}) $ 24 * q - 24 * q^4 - 2 * q^5 - 8 * q^6 - 24 * q^9 - 6 * q^10 - 12 * q^14 + 48 * q^16 + 32 * q^19 - 2 * q^20 - 16 * q^21 + 24 * q^24 + 2 * q^25 + 32 * q^26 - 8 * q^30 - 12 * q^34 + 10 * q^35 + 24 * q^36 + 36 * q^39 + 34 * q^40 + 2 * q^45 - 56 * q^46 - 24 * q^49 + 46 * q^50 - 36 * q^51 + 8 * q^54 + 12 * q^56 - 40 * q^59 - 26 * q^60 - 40 * q^61 + 12 * q^64 + 10 * q^65 - 2 * q^70 + 64 * q^71 - 136 * q^74 + 20 * q^75 - 68 * q^76 + 64 * q^79 + 76 * q^80 + 24 * q^81 + 60 * q^84 - 72 * q^86 + 20 * q^89 + 6 * q^90 - 4 * q^94 + 64 * q^95 - 56 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times$.

$n$	$727$	$1211$	$1696$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	0.784131i		−	0.554464i	−0.960803	−	0.277232i	$-0.910583\pi$
$2$		−	0.784131i		−	0.554464i	0.960803	−	0.277232i	$-0.0894171\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.38514			0.692569
$5$	−1.83964	−	1.27111i	−0.822712	−	0.568459i
$5$	−1.83964	−	1.27111i	−0.822712	−	0.568459i
$6$	0.784131			0.320120
$7$			1.51801i			0.573752i	0.957968	+	0.286876i	$0.0926168\pi$
$7$			1.51801i			0.573752i	−0.957968	+	0.286876i	$0.907383\pi$
$8$		−	2.65439i		−	0.938469i
$9$	−1.00000			−0.333333
$10$	−0.996719	+	1.44252i	−0.315190	+	0.456164i
$11$		0			0
$11$		0			0
$12$			1.38514i			0.399855i
$13$		−	0.466512i		−	0.129387i	−0.997905	−	0.0646936i	$-0.979393\pi$
$13$		−	0.466512i		−	0.129387i	0.997905	−	0.0646936i	$-0.0206070\pi$
$14$	1.19032			0.318125
$15$	1.27111	−	1.83964i	0.328200	−	0.474993i
$16$	0.688885			0.172221
$17$		−	1.69631i		−	0.411415i	−0.978614	−	0.205707i	$-0.934051\pi$
$17$		−	1.69631i		−	0.411415i	0.978614	−	0.205707i	$-0.0659495\pi$
$18$			0.784131i			0.184821i
$19$	−5.60956			−1.28692			−0.643461	−	0.765479i	$-0.722502\pi$
$19$	−5.60956			−1.28692			−0.643461	+	0.765479i	$0.722502\pi$
$20$	−2.54816	−	1.76067i	−0.569785	−	0.393697i
$21$	−1.51801			−0.331256
$22$		0			0
$23$		−	7.68641i		−	1.60273i	−0.598177	−	0.801364i	$-0.704108\pi$
$23$		−	7.68641i		−	1.60273i	0.598177	−	0.801364i	$-0.295892\pi$
$24$	2.65439			0.541826
$25$	1.76855	+	4.67678i	0.353709	+	0.935355i
$26$	−0.365807			−0.0717406
$27$		−	1.00000i		−	0.192450i
$28$			2.10265i			0.397363i
$29$	−2.66104			−0.494143			−0.247072	−	0.968997i	$-0.579468\pi$
$29$	−2.66104			−0.494143			−0.247072	+	0.968997i	$0.579468\pi$
$30$	−1.44252	−	0.996719i	−0.263367	−	0.181975i
$31$	3.95772			0.710828			0.355414	−	0.934709i	$-0.384340\pi$
$31$	3.95772			0.710828			0.355414	+	0.934709i	$0.384340\pi$
$32$		−	5.84896i		−	1.03396i
$33$		0			0
$34$	−1.33013			−0.228115
$35$	1.92956	−	2.79258i	0.326155	−	0.472033i
$36$	−1.38514			−0.230856
$37$		−	3.05939i		−	0.502960i	−0.967863	−	0.251480i	$-0.919083\pi$
$37$		−	3.05939i		−	0.502960i	0.967863	−	0.251480i	$-0.0809173\pi$
$38$			4.39863i			0.713552i
$39$	0.466512			0.0747017
$40$	−3.37403	+	4.88312i	−0.533481	+	0.772090i
$41$	−1.35030			−0.210882			−0.105441	−	0.994426i	$-0.533625\pi$
$41$	−1.35030			−0.210882			−0.105441	+	0.994426i	$0.533625\pi$
$42$			1.19032i			0.183670i
$43$		−	12.0864i		−	1.84317i	−0.388181	−	0.921583i	$-0.626896\pi$
$43$		−	12.0864i		−	1.84317i	0.388181	−	0.921583i	$-0.373104\pi$
$44$		0			0
$45$	1.83964	+	1.27111i	0.274237	+	0.189486i
$46$	−6.02716			−0.888656
$47$			2.55805i			0.373129i	0.982443	+	0.186565i	$0.0597354\pi$
$47$			2.55805i			0.373129i	−0.982443	+	0.186565i	$0.940265\pi$
$48$			0.688885i			0.0994320i
$49$	4.69566			0.670808
$50$	3.66721	−	1.38677i	0.518621	−	0.196119i
$51$	1.69631			0.237530
$52$		−	0.646184i		−	0.0896096i
$53$		−	8.01711i		−	1.10123i	−0.834758	−	0.550617i	$-0.814392\pi$
$53$		−	8.01711i		−	1.10123i	0.834758	−	0.550617i	$-0.185608\pi$
$54$	−0.784131			−0.106707
$55$		0			0
$56$	4.02938			0.538449
$57$		−	5.60956i		−	0.743005i
$58$			2.08661i			0.273985i
$59$	−7.54869			−0.982755			−0.491378	−	0.870947i	$-0.663507\pi$
$59$	−7.54869			−0.982755			−0.491378	+	0.870947i	$0.663507\pi$
$60$	1.76067	−	2.54816i	0.227301	−	0.328965i
$61$	−11.1178			−1.42348			−0.711742	−	0.702441i	$-0.752093\pi$
$61$	−11.1178			−1.42348			−0.711742	+	0.702441i	$0.752093\pi$
$62$		−	3.10338i		−	0.394129i
$63$		−	1.51801i		−	0.191251i
$64$	−3.20858			−0.401073
$65$	−0.592989	+	0.858214i	−0.0735513	+	0.106448i
$66$		0			0
$67$			6.89959i			0.842919i	0.906847	+	0.421460i	$0.138482\pi$
$67$			6.89959i			0.842919i	−0.906847	+	0.421460i	$0.861518\pi$
$68$		−	2.34962i		−	0.284933i
$69$	7.68641			0.925335
$70$	−2.18975	−	1.51303i	−0.261725	−	0.180841i
$71$	14.5878			1.73126			0.865629	−	0.500686i	$-0.166919\pi$
$71$	14.5878			1.73126			0.865629	+	0.500686i	$0.166919\pi$
$72$			2.65439i			0.312823i
$73$			2.26725i			0.265361i	0.991159	+	0.132681i	$0.0423584\pi$
$73$			2.26725i			0.265361i	−0.991159	+	0.132681i	$0.957642\pi$
$74$	−2.39896			−0.278873
$75$	−4.67678	+	1.76855i	−0.540028	+	0.204214i
$76$	−7.77002			−0.891282
$77$		0			0
$78$		−	0.365807i		−	0.0414195i
$79$	−12.1809			−1.37046			−0.685230	−	0.728326i	$-0.740298\pi$
$79$	−12.1809			−1.37046			−0.685230	+	0.728326i	$0.740298\pi$
$80$	−1.26730	−	0.875650i	−0.141688	−	0.0979007i
$81$	1.00000			0.111111
$82$			1.05881i			0.116926i
$83$		−	11.7808i		−	1.29311i	−0.762867	−	0.646555i	$-0.776209\pi$
$83$		−	11.7808i		−	1.29311i	0.762867	−	0.646555i	$-0.223791\pi$
$84$	−2.10265			−0.229418
$85$	−2.15620	+	3.12059i	−0.233872	+	0.338476i
$86$	−9.47736			−1.02197
$87$		−	2.66104i		−	0.285294i
$88$		0			0
$89$	−1.47962			−0.156840			−0.0784199	−	0.996920i	$-0.524987\pi$
$89$	−1.47962			−0.156840			−0.0784199	+	0.996920i	$0.524987\pi$
$90$	0.996719	−	1.44252i	0.105063	−	0.152055i
$91$	0.708168			0.0742362
$92$		−	10.6467i		−	1.11000i
$93$			3.95772i			0.410397i
$94$	2.00584			0.206887
$95$	10.3196	+	7.13038i	1.05877	+	0.731562i
$96$	5.84896			0.596957
$97$		−	14.2015i		−	1.44195i	−0.692963	−	0.720973i	$-0.743695\pi$
$97$		−	14.2015i		−	1.44195i	0.692963	−	0.720973i	$-0.256305\pi$
$98$		−	3.68201i		−	0.371939i
$99$		0			0
$100$	2.44968	+	6.47798i	0.244968	+	0.647798i
$101$	−2.62410			−0.261107			−0.130554	−	0.991441i	$-0.541675\pi$
$101$	−2.62410			−0.261107			−0.130554	+	0.991441i	$0.541675\pi$
$102$		−	1.33013i		−	0.131702i
$103$			0.0180806i			0.00178154i	1.00000		0.000890769i	$0.000283541\pi$
$103$			0.0180806i			0.00178154i	−1.00000		0.000890769i	$0.999716\pi$
$104$	−1.23831			−0.121426
$105$	2.79258	+	1.92956i	0.272528	+	0.188305i
$106$	−6.28647			−0.610596
$107$		−	14.6980i		−	1.42091i	−0.703742	−	0.710456i	$-0.748489\pi$
$107$		−	14.6980i		−	1.42091i	0.703742	−	0.710456i	$-0.251511\pi$
$108$		−	1.38514i		−	0.133285i
$109$	5.31791			0.509364			0.254682	−	0.967025i	$-0.418029\pi$
$109$	5.31791			0.509364			0.254682	+	0.967025i	$0.418029\pi$
$110$		0			0
$111$	3.05939			0.290384
$112$			1.04573i			0.0988123i
$113$			9.57689i			0.900918i	0.892797	+	0.450459i	$0.148740\pi$
$113$			9.57689i			0.900918i	−0.892797	+	0.450459i	$0.851260\pi$
$114$	−4.39863			−0.411970
$115$	−9.77029	+	14.1402i	−0.911085	+	1.31858i
$116$	−3.68591			−0.342228
$117$			0.466512i			0.0431291i
$118$			5.91916i			0.544903i
$119$	2.57500			0.236050
$120$	−4.88312	−	3.37403i	−0.445766	−	0.308006i
$121$		0			0
$122$			8.71779i			0.789271i
$123$		−	1.35030i		−	0.121753i
$124$	5.48200			0.492298
$125$	2.69122	−	10.8516i	0.240710	−	0.970597i
$126$	−1.19032			−0.106042
$127$			18.1340i			1.60913i	0.593865	+	0.804565i	$0.297602\pi$
$127$			18.1340i			1.60913i	−0.593865	+	0.804565i	$0.702398\pi$
$128$		−	9.18197i		−	0.811579i
$129$	12.0864			1.06415
$130$	0.672952	+	0.464981i	0.0590218	+	0.0407816i
$131$	−8.67183			−0.757661			−0.378831	−	0.925466i	$-0.623674\pi$
$131$	−8.67183			−0.757661			−0.378831	+	0.925466i	$0.623674\pi$
$132$		0			0
$133$		−	8.51535i		−	0.738374i
$134$	5.41018			0.467369
$135$	−1.27111	+	1.83964i	−0.109400	+	0.158331i
$136$	−4.50266			−0.386100
$137$		−	1.56076i		−	0.133345i	−0.997775	−	0.0666723i	$-0.978762\pi$
$137$		−	1.56076i		−	0.133345i	0.997775	−	0.0666723i	$-0.0212382\pi$
$138$		−	6.02716i		−	0.513066i
$139$	14.2883			1.21192			0.605959	−	0.795496i	$-0.292789\pi$
$139$	14.2883			1.21192			0.605959	+	0.795496i	$0.292789\pi$
$140$	2.67270	−	3.86812i	0.225885	−	0.326915i
$141$	−2.55805			−0.215426
$142$		−	11.4388i		−	0.959921i
$143$		0			0
$144$	−0.688885			−0.0574071
$145$	4.89536	+	3.38248i	0.406537	+	0.280900i
$146$	1.77782			0.147133
$147$			4.69566i			0.387291i
$148$		−	4.23767i		−	0.348335i
$149$	11.0147			0.902358			0.451179	−	0.892433i	$-0.351004\pi$
$149$	11.0147			0.902358			0.451179	+	0.892433i	$0.351004\pi$
$150$	1.38677	+	3.66721i	0.113229	+	0.299426i
$151$	−4.32201			−0.351720			−0.175860	−	0.984415i	$-0.556271\pi$
$151$	−4.32201			−0.351720			−0.175860	+	0.984415i	$0.556271\pi$
$152$			14.8900i			1.20774i
$153$			1.69631i			0.137138i
$154$		0			0
$155$	−7.28079	−	5.03071i	−0.584807	−	0.404077i
$156$	0.646184			0.0517361
$157$		−	0.931491i		−	0.0743411i	−0.999309	−	0.0371705i	$-0.988166\pi$
$157$		−	0.931491i		−	0.0743411i	0.999309	−	0.0371705i	$-0.0118345\pi$
$158$			9.55144i			0.759872i
$159$	8.01711			0.635798
$160$	−7.43469	+	10.7600i	−0.587764	+	0.850651i
$161$	11.6680			0.919569
$162$		−	0.784131i		−	0.0616072i
$163$		−	16.9584i		−	1.32828i	−0.747608	−	0.664141i	$-0.768798\pi$
$163$		−	16.9584i		−	1.32828i	0.747608	−	0.664141i	$-0.231202\pi$
$164$	−1.87035			−0.146050
$165$		0			0
$166$	−9.23769			−0.716984
$167$			2.50053i			0.193497i	0.995309	+	0.0967484i	$0.0308442\pi$
$167$			2.50053i			0.193497i	−0.995309	+	0.0967484i	$0.969156\pi$
$168$			4.02938i			0.310874i
$169$	12.7824			0.983259
$170$	2.44695	+	1.69074i	0.187673	+	0.129674i
$171$	5.60956			0.428974
$172$		−	16.7414i		−	1.27652i
$173$		−	5.61755i		−	0.427094i	−0.976933	−	0.213547i	$-0.931498\pi$
$173$		−	5.61755i		−	0.427094i	0.976933	−	0.213547i	$-0.0685017\pi$
$174$	−2.08661			−0.158185
$175$	−7.09938	+	2.68466i	−0.536662	+	0.202942i
$176$		0			0
$177$		−	7.54869i		−	0.567394i
$178$			1.16022i			0.0869621i
$179$	7.96904			0.595634			0.297817	−	0.954623i	$-0.403741\pi$
$179$	7.96904			0.595634			0.297817	+	0.954623i	$0.403741\pi$
$180$	2.54816	+	1.76067i	0.189928	+	0.131232i
$181$	−17.3472			−1.28941			−0.644704	−	0.764432i	$-0.723020\pi$
$181$	−17.3472			−1.28941			−0.644704	+	0.764432i	$0.723020\pi$
$182$		−	0.555297i		−	0.0411613i
$183$		−	11.1178i		−	0.821849i
$184$	−20.4028			−1.50411
$185$	−3.88882	+	5.62817i	−0.285912	+	0.413791i
$186$	3.10338			0.227551
$187$		0			0
$188$			3.54325i			0.258418i
$189$	1.51801			0.110419
$190$	5.59116	−	8.09190i	0.405625	−	0.587048i
$191$	−22.1873			−1.60541			−0.802707	−	0.596373i	$-0.796608\pi$
$191$	−22.1873			−1.60541			−0.802707	+	0.596373i	$0.796608\pi$
$192$		−	3.20858i		−	0.231560i
$193$		−	26.2954i		−	1.89278i	−0.323025	−	0.946391i	$-0.604700\pi$
$193$		−	26.2954i		−	1.89278i	0.323025	−	0.946391i	$-0.395300\pi$
$194$	−11.1359			−0.799508
$195$	−0.858214	−	0.592989i	−0.0614580	−	0.0424649i
$196$	6.50413			0.464581
$197$			11.5966i			0.826227i	0.910680	+	0.413113i	$0.135559\pi$
$197$			11.5966i			0.826227i	−0.910680	+	0.413113i	$0.864441\pi$
$198$		0			0
$199$	−14.4208			−1.02226			−0.511131	−	0.859503i	$-0.670773\pi$
$199$	−14.4208			−1.02226			−0.511131	+	0.859503i	$0.670773\pi$
$200$	12.4140	−	4.69442i	0.877802	−	0.331945i
$201$	−6.89959			−0.486660
$202$			2.05764i			0.144775i
$203$		−	4.03948i		−	0.283516i
$204$	2.34962			0.164506
$205$	2.48407	+	1.71639i	0.173495	+	0.119878i
$206$	0.0141776			0.000987799
$207$			7.68641i			0.534243i
$208$		−	0.321373i		−	0.0222832i
$209$		0			0
$210$	1.51303	−	2.18975i	0.104409	−	0.151107i
$211$	−3.26706			−0.224914			−0.112457	−	0.993657i	$-0.535872\pi$
$211$	−3.26706			−0.224914			−0.112457	+	0.993657i	$0.535872\pi$
$212$		−	11.1048i		−	0.762681i
$213$			14.5878i			0.999542i
$214$	−11.5252			−0.787845
$215$	−15.3632	+	22.2347i	−1.04776	+	1.51639i
$216$	−2.65439			−0.180609
$217$			6.00785i			0.407839i
$218$		−	4.16994i		−	0.282424i
$219$	−2.26725			−0.153206
$220$		0			0
$221$	−0.791347			−0.0532318
$222$		−	2.39896i		−	0.161008i
$223$			18.1284i			1.21397i	0.794714	+	0.606984i	$0.207621\pi$
$223$			18.1284i			1.21397i	−0.794714	+	0.606984i	$0.792379\pi$
$224$	8.87876			0.593237
$225$	−1.76855	−	4.67678i	−0.117903	−	0.311785i
$226$	7.50954			0.499527
$227$			28.1483i			1.86827i	0.356920	+	0.934135i	$0.383827\pi$
$227$			28.1483i			1.86827i	−0.356920	+	0.934135i	$0.616173\pi$
$228$		−	7.77002i		−	0.514582i
$229$	18.3614			1.21335			0.606677	−	0.794948i	$-0.292502\pi$
$229$	18.3614			1.21335			0.606677	+	0.794948i	$0.292502\pi$
$230$	11.0878	+	7.66119i	0.731107	+	0.505164i
$231$		0			0
$232$			7.06345i			0.463738i
$233$			9.03910i			0.592171i	0.955161	+	0.296086i	$0.0956814\pi$
$233$			9.03910i			0.592171i	−0.955161	+	0.296086i	$0.904319\pi$
$234$	0.365807			0.0239135
$235$	3.25156	−	4.70588i	0.212109	−	0.306978i
$236$	−10.4560			−0.680626
$237$		−	12.1809i		−	0.791236i
$238$		−	2.01914i		−	0.130881i
$239$	11.9238			0.771283			0.385642	−	0.922649i	$-0.373980\pi$
$239$	11.9238			0.771283			0.385642	+	0.922649i	$0.373980\pi$
$240$	0.875650	−	1.26730i	0.0565230	−	0.0818038i
$241$	25.4155			1.63715			0.818577	−	0.574396i	$-0.194763\pi$
$241$	25.4155			1.63715			0.818577	+	0.574396i	$0.194763\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$	−15.3996			−0.985861
$245$	−8.63832	−	5.96871i	−0.551882	−	0.381327i
$246$	−1.05881			−0.0675075
$247$			2.61693i			0.166511i
$248$		−	10.5054i		−	0.667091i
$249$	11.7808			0.746578
$250$	−8.50908	−	2.11027i	−0.538162	−	0.133465i
$251$	−14.7981			−0.934047			−0.467024	−	0.884245i	$-0.654674\pi$
$251$	−14.7981			−0.934047			−0.467024	+	0.884245i	$0.654674\pi$
$252$		−	2.10265i		−	0.132454i
$253$		0			0
$254$	14.2194			0.892205
$255$	−3.12059	−	2.15620i	−0.195419	−	0.135026i
$256$	−13.6170			−0.851065
$257$			8.16954i			0.509602i	0.966994	+	0.254801i	$0.0820099\pi$
$257$			8.16954i			0.509602i	−0.966994	+	0.254801i	$0.917990\pi$
$258$		−	9.47736i		−	0.590035i
$259$	4.64417			0.288574
$260$	−0.821372	+	1.18875i	−0.0509393	+	0.0737228i
$261$	2.66104			0.164714
$262$			6.79985i			0.420096i
$263$			9.66161i			0.595761i	0.954603	+	0.297880i	$0.0962796\pi$
$263$			9.66161i			0.595761i	−0.954603	+	0.297880i	$0.903720\pi$
$264$		0			0
$265$	−10.1906	+	14.7486i	−0.626007	+	0.905999i
$266$	−6.67715			−0.409402
$267$		−	1.47962i		−	0.0905515i
$268$			9.55689i			0.583780i
$269$	−0.379875			−0.0231614			−0.0115807	−	0.999933i	$-0.503686\pi$
$269$	−0.379875			−0.0231614			−0.0115807	+	0.999933i	$0.503686\pi$
$270$	1.44252	+	0.996719i	0.0877889	+	0.0606584i
$271$	−8.96837			−0.544790			−0.272395	−	0.962186i	$-0.587816\pi$
$271$	−8.96837			−0.544790			−0.272395	+	0.962186i	$0.587816\pi$
$272$		−	1.16856i		−	0.0708543i
$273$			0.708168i			0.0428603i
$274$	−1.22384			−0.0739349
$275$		0			0
$276$	10.6467			0.640859
$277$			3.37910i			0.203030i	0.994834	+	0.101515i	$0.0323690\pi$
$277$			3.37910i			0.203030i	−0.994834	+	0.101515i	$0.967631\pi$
$278$		−	11.2039i		−	0.671966i
$279$	−3.95772			−0.236943
$280$	−7.41261	−	5.12180i	−0.442988	−	0.306086i
$281$	−5.07550			−0.302779			−0.151390	−	0.988474i	$-0.548375\pi$
$281$	−5.07550			−0.302779			−0.151390	+	0.988474i	$0.548375\pi$
$282$			2.00584i			0.119446i
$283$			22.2980i			1.32548i	0.748849	+	0.662741i	$0.230607\pi$
$283$			22.2980i			1.32548i	−0.748849	+	0.662741i	$0.769393\pi$
$284$	20.2062			1.19902
$285$	−7.13038	+	10.3196i	−0.422367	+	0.611279i
$286$		0			0
$287$		−	2.04977i		−	0.120994i
$288$			5.84896i			0.344653i
$289$	14.1225			0.830738
$290$	2.65231	−	3.83860i	0.155749	−	0.225410i
$291$	14.2015			0.832508
$292$			3.14045i			0.183781i
$293$		−	16.2166i		−	0.947382i	−0.880691	−	0.473691i	$-0.842921\pi$
$293$		−	16.2166i		−	0.947382i	0.880691	−	0.473691i	$-0.157079\pi$
$294$	3.68201			0.214739
$295$	13.8869	+	9.59523i	0.808524	+	0.558656i
$296$	−8.12081			−0.472012
$297$		0			0
$298$		−	8.63696i		−	0.500325i
$299$	−3.58580			−0.207372
$300$	−6.47798	+	2.44968i	−0.374007	+	0.141432i
$301$	18.3473			1.05752
$302$			3.38902i			0.195016i
$303$		−	2.62410i		−	0.150750i
$304$	−3.86434			−0.221635
$305$	20.4527	+	14.1319i	1.17112	+	0.809192i
$306$	1.33013			0.0760383
$307$			29.9543i			1.70958i	0.518973	+	0.854791i	$0.326314\pi$
$307$			29.9543i			1.70958i	−0.518973	+	0.854791i	$0.673686\pi$
$308$		0			0
$309$	−0.0180806			−0.00102857
$310$	−3.94474	+	5.70909i	−0.224046	+	0.324255i
$311$	5.11022			0.289774			0.144887	−	0.989448i	$-0.453718\pi$
$311$	5.11022			0.289774			0.144887	+	0.989448i	$0.453718\pi$
$312$		−	1.23831i		−	0.0701053i
$313$			25.1105i			1.41933i	0.704538	+	0.709666i	$0.251154\pi$
$313$			25.1105i			1.41933i	−0.704538	+	0.709666i	$0.748846\pi$
$314$	−0.730411			−0.0412195
$315$	−1.92956	+	2.79258i	−0.108718	+	0.157344i
$316$	−16.8723			−0.949139
$317$			12.4189i			0.697516i	0.937213	+	0.348758i	$0.113396\pi$
$317$			12.4189i			0.697516i	−0.937213	+	0.348758i	$0.886604\pi$
$318$		−	6.28647i		−	0.352528i
$319$		0			0
$320$	5.90264	+	4.07847i	0.329967	+	0.227993i
$321$	14.6980			0.820364
$322$		−	9.14926i		−	0.509868i
$323$			9.51553i			0.529458i
$324$	1.38514			0.0769521
$325$	2.18177	−	0.825048i	0.121023	−	0.0457654i
$326$	−13.2976			−0.736485
$327$			5.31791i			0.294081i
$328$			3.58423i			0.197906i
$329$	−3.88313			−0.214084
$330$		0			0
$331$	8.35534			0.459251			0.229626	−	0.973279i	$-0.426250\pi$
$331$	8.35534			0.459251			0.229626	+	0.973279i	$0.426250\pi$
$332$		−	16.3180i		−	0.895569i
$333$			3.05939i			0.167653i
$334$	1.96074			0.107287
$335$	8.77016	−	12.6928i	0.479165	−	0.693480i
$336$	−1.04573			−0.0570493
$337$			3.93359i			0.214276i	0.994244	+	0.107138i	$0.0341687\pi$
$337$			3.93359i			0.214276i	−0.994244	+	0.107138i	$0.965831\pi$
$338$		−	10.0231i		−	0.545182i
$339$	−9.57689			−0.520145
$340$	−2.98663	+	4.32245i	−0.161973	+	0.234418i
$341$		0			0
$342$		−	4.39863i		−	0.237851i
$343$			17.7541i			0.958630i
$344$	−32.0822			−1.72976
$345$	−14.1402	−	9.77029i	−0.761284	−	0.526015i
$346$	−4.40489			−0.236809
$347$			9.19932i			0.493845i	0.969035	+	0.246923i	$0.0794194\pi$
$347$			9.19932i			0.493845i	−0.969035	+	0.246923i	$0.920581\pi$
$348$		−	3.68591i		−	0.197586i
$349$	20.1952			1.08102			0.540511	−	0.841337i	$-0.318231\pi$
$349$	20.1952			1.08102			0.540511	+	0.841337i	$0.318231\pi$
$350$	2.10513	+	5.56684i	0.112524	+	0.297560i
$351$	−0.466512			−0.0249006
$352$		0			0
$353$		−	34.8561i		−	1.85520i	−0.373572	−	0.927601i	$-0.621867\pi$
$353$		−	34.8561i		−	1.85520i	0.373572	−	0.927601i	$-0.378133\pi$
$354$	−5.91916			−0.314600
$355$	−26.8364	−	18.5428i	−1.42433	−	0.984149i
$356$	−2.04948			−0.108622
$357$			2.57500i			0.136284i
$358$		−	6.24877i		−	0.330258i
$359$	−28.4295			−1.50045			−0.750226	−	0.661181i	$-0.770055\pi$
$359$	−28.4295			−1.50045			−0.750226	+	0.661181i	$0.770055\pi$
$360$	3.37403	−	4.88312i	0.177827	−	0.257363i
$361$	12.4672			0.656167
$362$			13.6025i			0.714931i
$363$		0			0
$364$	0.980911			0.0514137
$365$	2.88192	−	4.17092i	0.150847	−	0.218316i
$366$	−8.71779			−0.455686
$367$		−	26.5774i		−	1.38733i	−0.720299	−	0.693663i	$-0.755996\pi$
$367$		−	26.5774i		−	1.38733i	0.720299	−	0.693663i	$-0.244004\pi$
$368$		−	5.29505i		−	0.276024i
$369$	1.35030			0.0702939
$370$	4.41322	+	3.04935i	0.229432	+	0.158528i
$371$	12.1700			0.631836
$372$			5.48200i			0.284228i
$373$		−	19.1900i		−	0.993621i	−0.867859	−	0.496811i	$-0.834504\pi$
$373$		−	19.1900i		−	0.993621i	0.867859	−	0.496811i	$-0.165496\pi$
$374$		0			0
$375$	10.8516	+	2.69122i	0.560374	+	0.138974i
$376$	6.79006			0.350171
$377$			1.24141i			0.0639358i
$378$		−	1.19032i		−	0.0612232i
$379$	3.04089			0.156200			0.0781001	−	0.996946i	$-0.475115\pi$
$379$	3.04089			0.156200			0.0781001	+	0.996946i	$0.475115\pi$
$380$	14.2940	+	9.87657i	0.733268	+	0.506657i
$381$	−18.1340			−0.929032
$382$			17.3977i			0.890145i
$383$			8.69345i			0.444215i	0.975022	+	0.222107i	$0.0712935\pi$
$383$			8.69345i			0.444215i	−0.975022	+	0.222107i	$0.928706\pi$
$384$	9.18197			0.468566
$385$		0			0
$386$	−20.6190			−1.04948
$387$			12.0864i			0.614389i
$388$		−	19.6711i		−	0.998647i
$389$	13.6919			0.694206			0.347103	−	0.937827i	$-0.387165\pi$
$389$	13.6919			0.694206			0.347103	+	0.937827i	$0.387165\pi$
$390$	−0.464981	+	0.672952i	−0.0235453	+	0.0340763i
$391$	−13.0385			−0.659386
$392$		−	12.4641i		−	0.629533i
$393$		−	8.67183i		−	0.437436i
$394$	9.09329			0.458113
$395$	22.4085	+	15.4833i	1.12749	+	0.779050i
$396$		0			0
$397$		−	8.96241i		−	0.449811i	−0.974381	−	0.224905i	$-0.927793\pi$
$397$		−	8.96241i		−	0.449811i	0.974381	−	0.224905i	$-0.0722073\pi$
$398$			11.3078i			0.566808i
$399$	8.51535			0.426301
$400$	1.21832	+	3.22176i	0.0609162	+	0.161088i
$401$	7.39627			0.369352			0.184676	−	0.982799i	$-0.440876\pi$
$401$	7.39627			0.369352			0.184676	+	0.982799i	$0.440876\pi$
$402$			5.41018i			0.269835i
$403$		−	1.84633i		−	0.0919721i
$404$	−3.63474			−0.180835
$405$	−1.83964	−	1.27111i	−0.0914124	−	0.0631621i
$406$	−3.16748			−0.157199
$407$		0			0
$408$		−	4.50266i		−	0.222915i
$409$	27.9054			1.37984			0.689918	−	0.723888i	$-0.257647\pi$
$409$	27.9054			1.37984			0.689918	+	0.723888i	$0.257647\pi$
$410$	1.34587	−	1.94784i	0.0664679	−	0.0961967i
$411$	1.56076			0.0769866
$412$			0.0250442i			0.00123384i
$413$		−	11.4590i		−	0.563858i
$414$	6.02716			0.296219
$415$	−14.9747	+	21.6724i	−0.735080	+	1.06386i
$416$	−2.72861			−0.133781
$417$			14.2883i			0.699702i
$418$		0			0
$419$	25.4267			1.24218			0.621088	−	0.783741i	$-0.286691\pi$
$419$	25.4267			1.24218			0.621088	+	0.783741i	$0.286691\pi$
$420$	3.86812	+	2.67270i	0.188745	+	0.130415i
$421$	−3.35560			−0.163542			−0.0817711	−	0.996651i	$-0.526058\pi$
$421$	−3.35560			−0.163542			−0.0817711	+	0.996651i	$0.526058\pi$
$422$			2.56180i			0.124707i
$423$		−	2.55805i		−	0.124376i
$424$	−21.2806			−1.03348
$425$	7.93324	−	3.00000i	0.384819	−	0.145521i
$426$	11.4388			0.554211
$427$		−	16.8768i		−	0.816727i
$428$		−	20.3588i		−	0.984079i
$429$		0			0
$430$	17.4349	+	12.0468i	0.840787	+	0.580948i
$431$	10.3766			0.499825			0.249913	−	0.968268i	$-0.419598\pi$
$431$	10.3766			0.499825			0.249913	+	0.968268i	$0.419598\pi$
$432$		−	0.688885i		−	0.0331440i
$433$			27.1667i			1.30555i	0.757553	+	0.652774i	$0.226395\pi$
$433$			27.1667i			1.30555i	−0.757553	+	0.652774i	$0.773605\pi$
$434$	4.71094			0.226132
$435$	−3.38248	+	4.89536i	−0.162178	+	0.234714i
$436$	7.36605			0.352770
$437$			43.1174i			2.06258i
$438$			1.77782i			0.0849474i
$439$	30.5785			1.45943			0.729715	−	0.683751i	$-0.239653\pi$
$439$	30.5785			1.45943			0.729715	+	0.683751i	$0.239653\pi$
$440$		0			0
$441$	−4.69566			−0.223603
$442$			0.620520i			0.0295151i
$443$			4.08492i			0.194080i	0.995280	+	0.0970401i	$0.0309375\pi$
$443$			4.08492i			0.194080i	−0.995280	+	0.0970401i	$0.969062\pi$
$444$	4.23767			0.201111
$445$	2.72197	+	1.88077i	0.129034	+	0.0891569i
$446$	14.2151			0.673103
$447$			11.0147i			0.520977i
$448$		−	4.87065i		−	0.230117i
$449$	−20.3031			−0.958165			−0.479082	−	0.877770i	$-0.659031\pi$
$449$	−20.3031			−0.958165			−0.479082	+	0.877770i	$0.659031\pi$
$450$	−3.66721	+	1.38677i	−0.172874	+	0.0653731i
$451$		0			0
$452$			13.2653i			0.623948i
$453$		−	4.32201i		−	0.203066i
$454$	22.0720			1.03589
$455$	−1.30277	−	0.900161i	−0.0610750	−	0.0422002i
$456$	−14.8900			−0.697287
$457$			25.8142i			1.20754i	0.797160	+	0.603768i	$0.206335\pi$
$457$			25.8142i			1.20754i	−0.797160	+	0.603768i	$0.793665\pi$
$458$		−	14.3977i		−	0.672762i
$459$	−1.69631			−0.0791768
$460$	−13.5332	+	19.5862i	−0.630989	+	0.913210i
$461$	2.54024			0.118311			0.0591553	−	0.998249i	$-0.481159\pi$
$461$	2.54024			0.118311			0.0591553	+	0.998249i	$0.481159\pi$
$462$		0			0
$463$		−	2.87598i		−	0.133658i	−0.997764	−	0.0668290i	$-0.978712\pi$
$463$		−	2.87598i		−	0.133658i	0.997764	−	0.0668290i	$-0.0212882\pi$
$464$	−1.83315			−0.0851019
$465$	5.03071	−	7.28079i	0.233294	−	0.337638i
$466$	7.08784			0.328338
$467$		−	22.8326i		−	1.05657i	−0.849068	−	0.528283i	$-0.822836\pi$
$467$		−	22.8326i		−	1.05657i	0.849068	−	0.528283i	$-0.177164\pi$
$468$			0.646184i			0.0298699i
$469$	−10.4736			−0.483627
$470$	−3.69003	−	2.54965i	−0.170208	−	0.117607i
$471$	0.931491			0.0429208
$472$			20.0372i			0.922286i
$473$		0			0
$474$	−9.55144			−0.438712
$475$	−9.92077	−	26.2347i	−0.455196	−	1.20373i
$476$	3.56673			0.163481
$477$			8.01711i			0.367078i
$478$		−	9.34979i		−	0.427649i
$479$	23.9065			1.09231			0.546157	−	0.837683i	$-0.316090\pi$
$479$	23.9065			1.09231			0.546157	+	0.837683i	$0.316090\pi$
$480$	−10.7600	−	7.43469i	−0.491124	−	0.339345i
$481$	−1.42724			−0.0650766
$482$		−	19.9291i		−	0.907744i
$483$			11.6680i			0.530913i
$484$		0			0
$485$	−18.0517	+	26.1257i	−0.819687	+	1.18631i
$486$	0.784131			0.0355689
$487$			13.6526i			0.618658i	0.950955	+	0.309329i	$0.100104\pi$
$487$			13.6526i			0.618658i	−0.950955	+	0.309329i	$0.899896\pi$
$488$			29.5109i			1.33590i
$489$	16.9584			0.766884
$490$	−4.68025	+	6.77357i	−0.211432	+	0.305999i
$491$	43.1224			1.94609			0.973043	−	0.230622i	$-0.0740762\pi$
$491$	43.1224			1.94609			0.973043	+	0.230622i	$0.0740762\pi$
$492$		−	1.87035i		−	0.0843221i
$493$			4.51394i			0.203298i
$494$	2.05202			0.0923245
$495$		0			0
$496$	2.72642			0.122420
$497$			22.1444i			0.993314i
$498$		−	9.23769i		−	0.413951i
$499$	−11.9384			−0.534436			−0.267218	−	0.963636i	$-0.586104\pi$
$499$	−11.9384			−0.534436			−0.267218	+	0.963636i	$0.586104\pi$
$500$	3.72771	−	15.0310i	0.166708	−	0.672206i
$501$	−2.50053			−0.111715
$502$			11.6036i			0.517896i
$503$			17.5270i			0.781490i	0.920499	+	0.390745i	$0.127783\pi$
$503$			17.5270i			0.781490i	−0.920499	+	0.390745i	$0.872217\pi$
$504$	−4.02938			−0.179483
$505$	4.82739	+	3.33552i	0.214816	+	0.148429i
$506$		0			0
$507$			12.7824i			0.567685i
$508$			25.1181i			1.11443i
$509$	−26.6433			−1.18094			−0.590472	−	0.807058i	$-0.701059\pi$
$509$	−26.6433			−1.18094			−0.590472	+	0.807058i	$0.701059\pi$
$510$	−1.69074	+	2.44695i	−0.0748672	+	0.108353i
$511$	−3.44169			−0.152252
$512$		−	7.68640i		−	0.339694i
$513$			5.60956i			0.247668i
$514$	6.40599			0.282556
$515$	0.0229825	−	0.0332618i	0.00101273	−	0.00146569i
$516$	16.7414			0.736999
$517$		0			0
$518$		−	3.64164i		−	0.160004i
$519$	5.61755			0.246583
$520$	2.27804	+	1.57403i	0.0998985	+	0.0690256i
$521$	26.4986			1.16093			0.580463	−	0.814287i	$-0.302872\pi$
$521$	26.4986			1.16093			0.580463	+	0.814287i	$0.302872\pi$
$522$		−	2.08661i		−	0.0913282i
$523$		−	8.92785i		−	0.390388i	−0.980765	−	0.195194i	$-0.937466\pi$
$523$		−	8.92785i		−	0.390388i	0.980765	−	0.195194i	$-0.0625336\pi$
$524$	−12.0117			−0.524733
$525$	−2.68466	−	7.09938i	−0.117168	−	0.309842i
$526$	7.57597			0.330328
$527$		−	6.71351i		−	0.292445i
$528$		0			0
$529$	−36.0809			−1.56874
$530$	11.5648	+	7.99081i	0.502344	+	0.347098i
$531$	7.54869			0.327585
$532$		−	11.7949i		−	0.511375i
$533$			0.629932i			0.0272854i
$534$	−1.16022			−0.0502076
$535$	−18.6828	+	27.0391i	−0.807730	+	1.16900i
$536$	18.3142			0.791054
$537$			7.96904i			0.343889i
$538$			0.297872i			0.0128422i
$539$		0			0
$540$	−1.76067	+	2.54816i	−0.0757670	+	0.109655i
$541$	17.7832			0.764559			0.382279	−	0.924047i	$-0.375139\pi$
$541$	17.7832			0.764559			0.382279	+	0.924047i	$0.375139\pi$
$542$			7.03238i			0.302067i
$543$		−	17.3472i		−	0.744441i
$544$	−9.92163			−0.425386
$545$	−9.78305	−	6.75967i	−0.419060	−	0.289552i
$546$	0.555297			0.0237645
$547$		−	15.3492i		−	0.656283i	−0.944629	−	0.328141i	$-0.893578\pi$
$547$		−	15.3492i		−	0.656283i	0.944629	−	0.328141i	$-0.106422\pi$
$548$		−	2.16187i		−	0.0923504i
$549$	11.1178			0.474495
$550$		0			0
$551$	14.9273			0.635923
$552$		−	20.4028i		−	0.868399i
$553$		−	18.4907i		−	0.786305i
$554$	2.64966			0.112573
$555$	−5.62817	−	3.88882i	−0.238902	−	0.165071i
$556$	19.7913			0.839337
$557$			16.9072i			0.716382i	0.933648	+	0.358191i	$0.116606\pi$
$557$			16.9072i			0.716382i	−0.933648	+	0.358191i	$0.883394\pi$
$558$			3.10338i			0.131376i
$559$	−5.63848			−0.238482
$560$	1.32924	−	1.92377i	0.0561707	−	0.0812941i
$561$		0			0
$562$			3.97986i			0.167880i
$563$		−	11.8428i		−	0.499116i	−0.968360	−	0.249558i	$-0.919715\pi$
$563$		−	11.8428i		−	0.499116i	0.968360	−	0.249558i	$-0.0802854\pi$
$564$	−3.54325			−0.149198
$565$	12.1733	−	17.6180i	0.512135	−	0.741196i
$566$	17.4846			0.734932
$567$			1.51801i			0.0637503i
$568$		−	38.7219i		−	1.62473i
$569$	−27.5579			−1.15529			−0.577644	−	0.816289i	$-0.696028\pi$
$569$	−27.5579			−1.15529			−0.577644	+	0.816289i	$0.696028\pi$
$570$	8.09190	+	5.59116i	0.338932	+	0.234188i
$571$	18.4594			0.772502			0.386251	−	0.922394i	$-0.373770\pi$
$571$	18.4594			0.772502			0.386251	+	0.922394i	$0.373770\pi$
$572$		0			0
$573$		−	22.1873i		−	0.926887i
$574$	−1.60729			−0.0670868
$575$	35.9476	−	13.5938i	1.49912	−	0.566900i
$576$	3.20858			0.133691
$577$		−	18.4637i		−	0.768654i	−0.923197	−	0.384327i	$-0.874434\pi$
$577$		−	18.4637i		−	0.768654i	0.923197	−	0.384327i	$-0.125566\pi$
$578$		−	11.0739i		−	0.460615i
$579$	26.2954			1.09280
$580$	6.78075	+	4.68521i	0.281555	+	0.194543i
$581$	17.8833			0.741925
$582$		−	11.1359i		−	0.461596i
$583$		0			0
$584$	6.01816			0.249033
$585$	0.592989	−	0.858214i	0.0245171	−	0.0354828i
$586$	−12.7159			−0.525290
$587$			9.88975i			0.408194i	0.978951	+	0.204097i	$0.0654257\pi$
$587$			9.88975i			0.408194i	−0.978951	+	0.204097i	$0.934574\pi$
$588$			6.50413i			0.268226i
$589$	−22.2011			−0.914780
$590$	7.52392	−	10.8891i	0.309755	−	0.448298i
$591$	−11.5966			−0.477022
$592$		−	2.10756i		−	0.0866204i
$593$		−	20.5782i		−	0.845047i	−0.906352	−	0.422523i	$-0.861144\pi$
$593$		−	20.5782i		−	0.845047i	0.906352	−	0.422523i	$-0.138856\pi$
$594$		0			0
$595$	−4.73708	−	3.27312i	−0.194201	−	0.134185i
$596$	15.2569			0.624945
$597$		−	14.4208i		−	0.590203i
$598$			2.81174i			0.114981i
$599$	−20.4682			−0.836308			−0.418154	−	0.908376i	$-0.637323\pi$
$599$	−20.4682			−0.836308			−0.418154	+	0.908376i	$0.637323\pi$
$600$	4.69442	+	12.4140i	0.191649	+	0.506799i
$601$	8.12230			0.331315			0.165658	−	0.986183i	$-0.447025\pi$
$601$	8.12230			0.331315			0.165658	+	0.986183i	$0.447025\pi$
$602$		−	14.3867i		−	0.586358i
$603$		−	6.89959i		−	0.280973i
$604$	−5.98658			−0.243591
$605$		0			0
$606$	−2.05764			−0.0835857
$607$			18.1757i			0.737727i	0.929484	+	0.368864i	$0.120253\pi$
$607$			18.1757i			0.737727i	−0.929484	+	0.368864i	$0.879747\pi$
$608$			32.8101i			1.33063i
$609$	4.03948			0.163688
$610$	11.0813	−	16.0376i	0.448668	−	0.649343i
$611$	1.19336			0.0482782
$612$			2.34962i			0.0949777i
$613$		−	30.2791i		−	1.22296i	−0.791259	−	0.611482i	$-0.790574\pi$
$613$		−	30.2791i		−	1.22296i	0.791259	−	0.611482i	$-0.209426\pi$
$614$	23.4881			0.947902
$615$	−1.71639	+	2.48407i	−0.0692113	+	0.100167i
$616$		0			0
$617$		−	29.0856i		−	1.17094i	−0.810694	−	0.585471i	$-0.800910\pi$
$617$		−	29.0856i		−	1.17094i	0.810694	−	0.585471i	$-0.199090\pi$
$618$			0.0141776i			0.000570306i
$619$	−14.7296			−0.592031			−0.296016	−	0.955183i	$-0.595658\pi$
$619$	−14.7296			−0.592031			−0.296016	+	0.955183i	$0.595658\pi$
$620$	−10.0849	−	6.96823i	−0.405019	−	0.279851i
$621$	−7.68641			−0.308445
$622$		−	4.00708i		−	0.160669i
$623$		−	2.24608i		−	0.0899872i
$624$	0.321373			0.0128652
$625$	−18.7445	+	16.5422i	−0.749780	+	0.661688i
$626$	19.6900			0.786969
$627$		0			0
$628$		−	1.29024i		−	0.0514863i
$629$	−5.18965			−0.206925
$630$	2.18975	+	1.51303i	0.0872418	+	0.0602804i
$631$	9.89021			0.393723			0.196862	−	0.980431i	$-0.436925\pi$
$631$	9.89021			0.393723			0.196862	+	0.980431i	$0.436925\pi$
$632$			32.3329i			1.28614i
$633$		−	3.26706i		−	0.129854i
$634$	9.73806			0.386748
$635$	23.0503	−	33.3600i	0.914724	−	1.32385i
$636$	11.1048			0.440334
$637$		−	2.19058i		−	0.0867940i
$638$		0			0
$639$	−14.5878			−0.577086
$640$	−11.6713	+	16.8915i	−0.461349	+	0.667696i
$641$	44.2429			1.74749			0.873745	−	0.486384i	$-0.161684\pi$
$641$	44.2429			1.74749			0.873745	+	0.486384i	$0.161684\pi$
$642$		−	11.5252i		−	0.454862i
$643$			1.27504i			0.0502825i	0.999684	+	0.0251413i	$0.00800355\pi$
$643$			1.27504i			0.0502825i	−0.999684	+	0.0251413i	$0.991996\pi$
$644$	16.1618			0.636865
$645$	−22.2347	−	15.3632i	−0.875491	−	0.604927i
$646$	7.46142			0.293566
$647$			43.0951i			1.69424i	0.531400	+	0.847121i	$0.321666\pi$
$647$			43.0951i			1.69424i	−0.531400	+	0.847121i	$0.678334\pi$
$648$		−	2.65439i		−	0.104274i
$649$		0			0
$650$	−0.646946	−	1.71080i	−0.0253753	−	0.0671030i
$651$	−6.00785			−0.235466
$652$		−	23.4897i		−	0.919927i
$653$			19.2900i			0.754876i	0.926035	+	0.377438i	$0.123195\pi$
$653$			19.2900i			0.754876i	−0.926035	+	0.377438i	$0.876805\pi$
$654$	4.16994			0.163058
$655$	15.9530	+	11.0229i	0.623337	+	0.430699i
$656$	−0.930202			−0.0363183
$657$		−	2.26725i		−	0.0884537i
$658$			3.04488i			0.118702i
$659$	−33.4717			−1.30387			−0.651937	−	0.758273i	$-0.726043\pi$
$659$	−33.4717			−1.30387			−0.651937	+	0.758273i	$0.726043\pi$
$660$		0			0
$661$	−6.94932			−0.270297			−0.135149	−	0.990825i	$-0.543151\pi$
$661$	−6.94932			−0.270297			−0.135149	+	0.990825i	$0.543151\pi$
$662$		−	6.55168i		−	0.254638i
$663$		−	0.791347i		−	0.0307334i
$664$	−31.2709			−1.21354
$665$	−10.8240	+	15.6652i	−0.419735	+	0.607469i
$666$	2.39896			0.0929578
$667$			20.4539i			0.791977i
$668$			3.46358i			0.134010i
$669$	−18.1284			−0.700885
$670$	−9.95279	−	6.87695i	−0.384510	−	0.265680i
$671$		0			0
$672$			8.87876i			0.342506i
$673$		−	21.8549i		−	0.842446i	−0.906957	−	0.421223i	$-0.861601\pi$
$673$		−	21.8549i		−	0.842446i	0.906957	−	0.421223i	$-0.138399\pi$
$674$	3.08445			0.118809
$675$	4.67678	−	1.76855i	0.180009	−	0.0680714i
$676$	17.7053			0.680975
$677$		−	1.25855i		−	0.0483700i	−0.999708	−	0.0241850i	$-0.992301\pi$
$677$		−	1.25855i		−	0.0483700i	0.999708	−	0.0241850i	$-0.00769908\pi$
$678$			7.50954i			0.288402i
$679$	21.5580			0.827320
$680$	8.28327	+	5.72339i	0.317649	+	0.219482i
$681$	−28.1483			−1.07865
$682$		0			0
$683$			19.8677i			0.760215i	0.924942	+	0.380108i	$0.124113\pi$
$683$			19.8677i			0.760215i	−0.924942	+	0.380108i	$0.875887\pi$
$684$	7.77002			0.297094
$685$	−1.98390	+	2.87123i	−0.0758009	+	0.109704i
$686$	13.9215			0.531526
$687$			18.3614i			0.700531i
$688$		−	8.32617i		−	0.317432i
$689$	−3.74008			−0.142486
$690$	−7.66119	+	11.0878i	−0.291657	+	0.422105i
$691$	7.43730			0.282928			0.141464	−	0.989943i	$-0.454819\pi$
$691$	7.43730			0.282928			0.141464	+	0.989943i	$0.454819\pi$
$692$		−	7.78108i		−	0.295792i
$693$		0			0
$694$	7.21347			0.273820
$695$	−26.2853	−	18.1620i	−0.997060	−	0.688926i
$696$	−7.06345			−0.267739
$697$			2.29053i			0.0867598i
$698$		−	15.8356i		−	0.599388i
$699$	−9.03910			−0.341890
$700$	−9.83362	+	3.71863i	−0.371676	+	0.140551i
$701$	−28.9650			−1.09399			−0.546997	−	0.837135i	$-0.684229\pi$
$701$	−28.9650			−1.09399			−0.546997	+	0.837135i	$0.684229\pi$
$702$			0.365807i			0.0138065i
$703$			17.1618i			0.647270i
$704$		0			0
$705$	4.70588	+	3.25156i	0.177234	+	0.122461i
$706$	−27.3317			−1.02864
$707$		−	3.98339i		−	0.149811i
$708$		−	10.4560i		−	0.392960i
$709$	26.6222			0.999818			0.499909	−	0.866078i	$-0.333367\pi$
$709$	26.6222			0.999818			0.499909	+	0.866078i	$0.333367\pi$
$710$	−14.5400	+	21.0432i	−0.545676	+	0.789738i
$711$	12.1809			0.456820
$712$			3.92750i			0.147189i
$713$		−	30.4207i		−	1.13926i
$714$	2.01914			0.0755644
$715$		0			0
$716$	11.0382			0.412518
$717$			11.9238i			0.445301i
$718$			22.2925i			0.831947i
$719$	−12.5985			−0.469846			−0.234923	−	0.972014i	$-0.575484\pi$
$719$	−12.5985			−0.469846			−0.234923	+	0.972014i	$0.575484\pi$
$720$	1.26730	+	0.875650i	0.0472295	+	0.0326336i
$721$	−0.0274465			−0.00102216
$722$		−	9.77590i		−	0.363821i
$723$			25.4155i			0.945212i
$724$	−24.0283			−0.893005
$725$	−4.70618	−	12.4451i	−0.174783	−	0.462199i
$726$		0			0
$727$		−	15.2116i		−	0.564169i	−0.959390	−	0.282084i	$-0.908974\pi$
$727$		−	15.2116i		−	0.564169i	0.959390	−	0.282084i	$-0.0910258\pi$
$728$		−	1.87976i		−	0.0696684i
$729$	−1.00000			−0.0370370
$730$	−3.27054	−	2.25981i	−0.121048	−	0.0836392i
$731$	−20.5023			−0.758305
$732$		−	15.3996i		−	0.569187i
$733$		−	30.5557i		−	1.12860i	−0.825570	−	0.564299i	$-0.809146\pi$
$733$		−	30.5557i		−	1.12860i	0.825570	−	0.564299i	$-0.190854\pi$
$734$	−20.8401			−0.769223
$735$	5.96871	−	8.63832i	0.220159	−	0.318629i
$736$	−44.9575			−1.65716
$737$		0			0
$738$		−	1.05881i		−	0.0389755i
$739$	−8.75876			−0.322196			−0.161098	−	0.986938i	$-0.551504\pi$
$739$	−8.75876			−0.322196			−0.161098	+	0.986938i	$0.551504\pi$
$740$	−5.38656	+	7.79579i	−0.198014	+	0.286579i
$741$	−2.61693			−0.0961353
$742$		−	9.54289i		−	0.350331i
$743$		−	30.3075i		−	1.11187i	−0.831224	−	0.555937i	$-0.812359\pi$
$743$		−	30.3075i		−	1.11187i	0.831224	−	0.555937i	$-0.187641\pi$
$744$	10.5054			0.385145
$745$	−20.2630	−	14.0009i	−0.742381	−	0.512953i
$746$	−15.0475			−0.550928
$747$			11.7808i			0.431037i
$748$		0			0
$749$	22.3117			0.815251
$750$	2.11027	−	8.50908i	0.0770562	−	0.310708i
$751$	1.24651			0.0454859			0.0227430	−	0.999741i	$-0.492760\pi$
$751$	1.24651			0.0454859			0.0227430	+	0.999741i	$0.492760\pi$
$752$			1.76220i			0.0642608i
$753$		−	14.7981i		−	0.539273i
$754$	0.973427			0.0354501
$755$	7.95094	+	5.49376i	0.289364	+	0.199938i
$756$	2.10265			0.0764726
$757$		−	13.9362i		−	0.506521i	−0.967398	−	0.253260i	$-0.918497\pi$
$757$		−	13.9362i		−	0.506521i	0.967398	−	0.253260i	$-0.0815029\pi$
$758$		−	2.38446i		−	0.0866075i
$759$		0			0
$760$	18.9268	−	27.3922i	0.686548	−	0.993619i
$761$	−3.16515			−0.114737			−0.0573683	−	0.998353i	$-0.518271\pi$
$761$	−3.16515			−0.114737			−0.0573683	+	0.998353i	$0.518271\pi$
$762$			14.2194i			0.515115i
$763$			8.07263i			0.292249i
$764$	−30.7324			−1.11186
$765$	2.15620	−	3.12059i	0.0779574	−	0.112825i
$766$	6.81681			0.246301
$767$			3.52155i			0.127156i
$768$		−	13.6170i		−	0.491362i
$769$	−1.39451			−0.0502874			−0.0251437	−	0.999684i	$-0.508004\pi$
$769$	−1.39451			−0.0502874			−0.0251437	+	0.999684i	$0.508004\pi$
$770$		0			0
$771$	−8.16954			−0.294219
$772$		−	36.4227i		−	1.31088i
$773$		−	3.33684i		−	0.120018i	−0.998198	−	0.0600089i	$-0.980887\pi$
$773$		−	3.33684i		−	0.120018i	0.998198	−	0.0600089i	$-0.0191129\pi$
$774$	9.47736			0.340657
$775$	6.99942	+	18.5094i	0.251427	+	0.664877i
$776$	−37.6964			−1.35322
$777$			4.64417i			0.166609i
$778$		−	10.7362i		−	0.384913i
$779$	7.57460			0.271388
$780$	−1.18875	−	0.821372i	−0.0425639	−	0.0294098i
$781$		0			0
$782$			10.2239i			0.365606i
$783$			2.66104i			0.0950979i
$784$	3.23477			0.115527
$785$	−1.18403	+	1.71361i	−0.0422598	+	0.0611613i
$786$	−6.79985			−0.242543
$787$			15.7494i			0.561405i	0.959795	+	0.280703i	$0.0905675\pi$
$787$			15.7494i			0.561405i	−0.959795	+	0.280703i	$0.909433\pi$
$788$			16.0630i			0.572219i
$789$	−9.66161			−0.343963
$790$	12.1410	−	17.5712i	0.431956	−	0.625155i
$791$	−14.5378			−0.516904
$792$		0			0
$793$			5.18657i			0.184181i
$794$	−7.02771			−0.249404
$795$	−14.7486	−	10.1906i	−0.523079	−	0.361425i
$796$	−19.9748			−0.707987
$797$			25.1030i			0.889193i	0.895731	+	0.444597i	$0.146653\pi$
$797$			25.1030i			0.889193i	−0.895731	+	0.444597i	$0.853347\pi$
$798$		−	6.67715i		−	0.236369i
$799$	4.33923			0.153511
$800$	27.3543	−	10.3442i	0.967120	−	0.365721i
$801$	1.47962			0.0522799
$802$		−	5.79964i		−	0.204793i
$803$		0			0
$804$	−9.55689			−0.337045
$805$	−21.4650	−	14.8314i	−0.756540	−	0.522737i
$806$	−1.44776			−0.0509952
$807$		−	0.379875i		−	0.0133722i
$808$			6.96538i			0.245041i
$809$	−47.5170			−1.67061			−0.835305	−	0.549787i	$-0.814709\pi$
$809$	−47.5170			−1.67061			−0.835305	+	0.549787i	$0.814709\pi$
$810$	−0.996719	+	1.44252i	−0.0350211	+	0.0506849i
$811$	6.57091			0.230736			0.115368	−	0.993323i	$-0.463195\pi$
$811$	6.57091			0.230736			0.115368	+	0.993323i	$0.463195\pi$
$812$		−	5.59524i		−	0.196354i
$813$		−	8.96837i		−	0.314535i
$814$		0			0
$815$	−21.5560	+	31.1973i	−0.755073	+	1.09279i
$816$	1.16856			0.0409078
$817$			67.7997i			2.37201i
$818$		−	21.8815i		−	0.765070i
$819$	−0.708168			−0.0247454
$820$	3.44078	+	2.37743i	0.120157	+	0.0830235i
$821$	−16.3101			−0.569225			−0.284613	−	0.958643i	$-0.591865\pi$
$821$	−16.3101			−0.569225			−0.284613	+	0.958643i	$0.591865\pi$
$822$		−	1.22384i		−	0.0426863i
$823$		−	29.7724i		−	1.03780i	−0.854835	−	0.518900i	$-0.826342\pi$
$823$		−	29.7724i		−	1.03780i	0.854835	−	0.518900i	$-0.173658\pi$
$824$	0.0479931			0.00167192
$825$		0			0
$826$	−8.98532			−0.312639
$827$		−	17.1006i		−	0.594646i	−0.954777	−	0.297323i	$-0.903906\pi$
$827$		−	17.1006i		−	0.594646i	0.954777	−	0.297323i	$-0.0960938\pi$
$828$			10.6467i			0.370000i
$829$	−38.4218			−1.33445			−0.667223	−	0.744858i	$-0.732517\pi$
$829$	−38.4218			−1.33445			−0.667223	+	0.744858i	$0.732517\pi$
$830$	16.9940	+	11.7421i	0.589871	+	0.407576i
$831$	−3.37910			−0.117220
$832$			1.49684i			0.0518937i
$833$		−	7.96527i		−	0.275980i
$834$	11.2039			0.387960
$835$	3.17845	−	4.60007i	0.109995	−	0.159192i
$836$		0			0
$837$		−	3.95772i		−	0.136799i
$838$		−	19.9379i		−	0.688742i
$839$	−39.5772			−1.36636			−0.683178	−	0.730252i	$-0.739403\pi$
$839$	−39.5772			−1.36636			−0.683178	+	0.730252i	$0.739403\pi$
$840$	5.12180	−	7.41261i	0.176719	−	0.255759i
$841$	−21.9189			−0.755823
$842$			2.63123i			0.0906783i
$843$		−	5.07550i		−	0.174810i
$844$	−4.52533			−0.155768
$845$	−23.5149	−	16.2478i	−0.808939	−	0.558942i
$846$	−2.00584			−0.0689623
$847$		0			0
$848$		−	5.52287i		−	0.189656i
$849$	−22.2980			−0.765267
$850$	−2.35239	−	6.22070i	−0.0806863	−	0.213368i
$851$	−23.5157			−0.806108
$852$			20.2062i			0.692252i
$853$		−	43.4532i		−	1.48781i	−0.668285	−	0.743905i	$-0.732971\pi$
$853$		−	43.4532i		−	1.48781i	0.668285	−	0.743905i	$-0.267029\pi$
$854$	−13.2337			−0.452846
$855$	−10.3196	−	7.13038i	−0.352922	−	0.243854i
$856$	−39.0143			−1.33348
$857$		−	22.0266i		−	0.752415i	−0.926536	−	0.376207i	$-0.877228\pi$
$857$		−	22.0266i		−	0.752415i	0.926536	−	0.376207i	$-0.122772\pi$
$858$		0			0
$859$	42.4022			1.44675			0.723373	−	0.690458i	$-0.242591\pi$
$859$	42.4022			1.44675			0.723373	+	0.690458i	$0.242591\pi$
$860$	−21.2802	+	30.7981i	−0.725649	+	1.05021i
$861$	2.04977			0.0698559
$862$		−	8.13665i		−	0.277135i
$863$			8.04150i			0.273736i	0.990589	+	0.136868i	$0.0437036\pi$
$863$			8.04150i			0.273736i	−0.990589	+	0.136868i	$0.956296\pi$
$864$	−5.84896			−0.198986
$865$	−7.14053	+	10.3343i	−0.242785	+	0.351375i
$866$	21.3023			0.723880
$867$			14.1225i			0.479627i
$868$			8.32170i			0.282457i
$869$		0			0
$870$	3.83860	+	2.65231i	0.130141	+	0.0899217i
$871$	3.21874			0.109063
$872$		−	14.1158i		−	0.478022i
$873$			14.2015i			0.480649i
$874$	33.8097			1.14363
$875$	16.4728	+	4.08529i	0.556882	+	0.138108i
$876$	−3.14045			−0.106106
$877$		−	57.4518i		−	1.94001i	−0.243088	−	0.970004i	$-0.578161\pi$
$877$		−	57.4518i		−	1.94001i	0.243088	−	0.970004i	$-0.421839\pi$
$878$		−	23.9775i		−	0.809202i
$879$	16.2166			0.546971
$880$		0			0
$881$	−49.5171			−1.66827			−0.834137	−	0.551557i	$-0.814034\pi$
$881$	−49.5171			−1.66827			−0.834137	+	0.551557i	$0.814034\pi$
$882$			3.68201i			0.123980i
$883$			26.0946i			0.878153i	0.898450	+	0.439076i	$0.144694\pi$
$883$			26.0946i			0.878153i	−0.898450	+	0.439076i	$0.855306\pi$
$884$	−1.09613			−0.0368667
$885$	−9.59523	+	13.8869i	−0.322540	+	0.466802i
$886$	3.20311			0.107611
$887$		−	10.5321i		−	0.353632i	−0.984244	−	0.176816i	$-0.943420\pi$
$887$		−	10.5321i		−	0.353632i	0.984244	−	0.176816i	$-0.0565798\pi$
$888$		−	8.12081i		−	0.272517i
$889$	−27.5275			−0.923242
$890$	1.47477	−	2.13438i	0.0494343	−	0.0715447i
$891$		0			0
$892$			25.1104i			0.840757i
$893$		−	14.3495i		−	0.480188i
$894$	8.63696			0.288863
$895$	−14.6602	−	10.1295i	−0.490035	−	0.338593i
$896$	13.9383			0.465646
$897$		−	3.58580i		−	0.119727i
$898$			15.9203i			0.531268i
$899$	−10.5317			−0.351251
$900$	−2.44968	−	6.47798i	−0.0816560	−	0.215933i
$901$	−13.5995			−0.453064
$902$		0			0
$903$			18.3473i			0.610560i
$904$	25.4208			0.845484
$905$	31.9126	+	22.0503i	1.06081	+	0.732976i
$906$	−3.38902			−0.112593
$907$		−	14.9671i		−	0.496973i	−0.968635	−	0.248487i	$-0.920067\pi$
$907$		−	14.9671i		−	0.496973i	0.968635	−	0.248487i	$-0.0799332\pi$
$908$			38.9893i			1.29391i
$909$	2.62410			0.0870358
$910$	−0.705845	+	1.02155i	−0.0233985	+	0.0338639i
$911$	2.00811			0.0665316			0.0332658	−	0.999447i	$-0.489409\pi$
$911$	2.00811			0.0665316			0.0332658	+	0.999447i	$0.489409\pi$
$912$		−	3.86434i		−	0.127961i
$913$		0			0
$914$	20.2417			0.669535
$915$	−14.1319	+	20.4527i	−0.467187	+	0.676145i
$916$	25.4331			0.840332
$917$		−	13.1639i		−	0.434710i
$918$			1.33013i			0.0439007i
$919$	16.7985			0.554133			0.277066	−	0.960851i	$-0.410638\pi$
$919$	16.7985			0.554133			0.277066	+	0.960851i	$0.410638\pi$
$920$	37.5337	+	25.9342i	1.23745	+	0.855025i
$921$	−29.9543			−0.987027
$922$		−	1.99188i		−	0.0655990i
$923$		−	6.80541i		−	0.224003i
$924$		0			0
$925$	14.3081	−	5.41067i	0.470446	−	0.177902i
$926$	−2.25514			−0.0741086
$927$		−	0.0180806i		−	0.000593846i
$928$			15.5643i			0.510924i
$929$	−33.9165			−1.11276			−0.556382	−	0.830926i	$-0.687811\pi$
$929$	−33.9165			−1.11276			−0.556382	+	0.830926i	$0.687811\pi$
$930$	−5.70909	−	3.94474i	−0.187208	−	0.129353i
$931$	−26.3406			−0.863278
$932$			12.5204i			0.410120i
$933$			5.11022i			0.167301i
$934$	−17.9037			−0.585828
$935$		0			0
$936$	1.23831			0.0404753
$937$			20.5419i			0.671075i	0.942027	+	0.335538i	$0.108918\pi$
$937$			20.5419i			0.671075i	−0.942027	+	0.335538i	$0.891082\pi$
$938$			8.21269i			0.268154i
$939$	−25.1105			−0.819452
$940$	4.50387	−	6.51830i	0.146900	−	0.212603i
$941$	52.8643			1.72333			0.861663	−	0.507481i	$-0.169423\pi$
$941$	52.8643			1.72333			0.861663	+	0.507481i	$0.169423\pi$
$942$		−	0.730411i		−	0.0237981i
$943$			10.3790i			0.337986i
$944$	−5.20018			−0.169251
$945$	−2.79258	−	1.92956i	−0.0908428	−	0.0627685i
$946$		0			0
$947$			28.1947i			0.916206i	0.888899	+	0.458103i	$0.151471\pi$
$947$			28.1947i			0.916206i	−0.888899	+	0.458103i	$0.848529\pi$
$948$		−	16.8723i		−	0.547986i
$949$	1.05770			0.0343343
$950$	−20.5714	+	7.77918i	−0.667425	+	0.252390i
$951$	−12.4189			−0.402711
$952$		−	6.83507i		−	0.221526i
$953$			11.0184i			0.356922i	0.983947	+	0.178461i	$0.0571119\pi$
$953$			11.0184i			0.356922i	−0.983947	+	0.178461i	$0.942888\pi$
$954$	6.28647			0.203532
$955$	40.8166	+	28.2025i	1.32079	+	0.912612i
$956$	16.5160			0.534167
$957$		0			0
$958$		−	18.7458i		−	0.605649i
$959$	2.36924			0.0765068
$960$	−4.07847	+	5.90264i	−0.131632	+	0.190507i
$961$	−15.3364			−0.494723
$962$			1.11914i			0.0360826i
$963$			14.6980i			0.473637i
$964$	35.2040			1.13384
$965$	−33.4244	+	48.3740i	−1.07597	+	1.55721i
$966$	9.14926			0.294373
$967$		−	49.0215i		−	1.57643i	−0.615403	−	0.788213i	$-0.711007\pi$
$967$		−	49.0215i		−	1.57643i	0.615403	−	0.788213i	$-0.288993\pi$
$968$		0			0
$969$	−9.51553			−0.305683
$970$	20.4860	+	14.1549i	0.657764	+	0.454487i
$971$	1.02042			0.0327467			0.0163733	−	0.999866i	$-0.494788\pi$
$971$	1.02042			0.0327467			0.0163733	+	0.999866i	$0.494788\pi$
$972$			1.38514i			0.0444283i
$973$			21.6897i			0.695341i
$974$	10.7054			0.343024
$975$	0.825048	+	2.18177i	0.0264227	+	0.0698727i
$976$	−7.65886			−0.245154
$977$		−	48.3788i		−	1.54778i	−0.633323	−	0.773888i	$-0.718309\pi$
$977$		−	48.3788i		−	1.54778i	0.633323	−	0.773888i	$-0.281691\pi$
$978$		−	13.2976i		−	0.425210i
$979$		0			0
$980$	−11.9653	−	8.26749i	−0.382216	−	0.264095i
$981$	−5.31791			−0.169788
$982$		−	33.8136i		−	1.07904i
$983$		−	61.5170i		−	1.96209i	−0.193785	−	0.981044i	$-0.562076\pi$
$983$		−	61.5170i		−	1.96209i	0.193785	−	0.981044i	$-0.437924\pi$
$984$	−3.58423			−0.114261
$985$	14.7406	−	21.3336i	0.469676	−	0.679746i
$986$	3.53952			0.112721
$987$		−	3.88313i		−	0.123601i
$988$			3.62481i			0.115320i
$989$	−92.9014			−2.95409
$990$		0			0
$991$	31.0431			0.986117			0.493059	−	0.869996i	$-0.335879\pi$
$991$	31.0431			0.986117			0.493059	+	0.869996i	$0.335879\pi$
$992$		−	23.1486i		−	0.734968i
$993$			8.35534i			0.265149i
$994$	17.3641			0.550757
$995$	26.5290	+	18.3304i	0.841026	+	0.581113i
$996$	16.3180			0.517057
$997$		−	47.6034i		−	1.50761i	−0.657095	−	0.753807i	$-0.728215\pi$
$997$		−	47.6034i		−	1.50761i	0.657095	−	0.753807i	$-0.271785\pi$
$998$			9.36127i			0.296326i
$999$	−3.05939			−0.0967947

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.c.j.364.9		24
5.2	odd	4		9075.2.a.dy.1.9		12
5.3	odd	4		9075.2.a.dz.1.4		12
5.4	even	2	inner	1815.2.c.j.364.16		24
11.5	even	5		165.2.s.a.124.8	yes	48
11.9	even	5		165.2.s.a.4.5	✓	48
11.10	odd	2		1815.2.c.k.364.16		24
33.5	odd	10		495.2.ba.c.289.5		48
33.20	odd	10		495.2.ba.c.334.8		48
55.9	even	10		165.2.s.a.4.8	yes	48
55.27	odd	20		825.2.n.p.751.2		24
55.32	even	4		9075.2.a.ea.1.4		12
55.38	odd	20		825.2.n.o.751.5		24
55.42	odd	20		825.2.n.p.301.2		24
55.43	even	4		9075.2.a.dx.1.9		12
55.49	even	10		165.2.s.a.124.5	yes	48
55.53	odd	20		825.2.n.o.301.5		24
55.54	odd	2		1815.2.c.k.364.9		24
165.104	odd	10		495.2.ba.c.289.8		48
165.119	odd	10		495.2.ba.c.334.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.4.5	✓	48	11.9	even	5
165.2.s.a.4.8	yes	48	55.9	even	10
165.2.s.a.124.5	yes	48	55.49	even	10
165.2.s.a.124.8	yes	48	11.5	even	5
495.2.ba.c.289.5		48	33.5	odd	10
495.2.ba.c.289.8		48	165.104	odd	10
495.2.ba.c.334.5		48	165.119	odd	10
495.2.ba.c.334.8		48	33.20	odd	10
825.2.n.o.301.5		24	55.53	odd	20
825.2.n.o.751.5		24	55.38	odd	20
825.2.n.p.301.2		24	55.42	odd	20
825.2.n.p.751.2		24	55.27	odd	20
1815.2.c.j.364.9		24	1.1	even	1	trivial
1815.2.c.j.364.16		24	5.4	even	2	inner
1815.2.c.k.364.9		24	55.54	odd	2
1815.2.c.k.364.16		24	11.10	odd	2
9075.2.a.dx.1.9		12	55.43	even	4
9075.2.a.dy.1.9		12	5.2	odd	4
9075.2.a.dz.1.4		12	5.3	odd	4
9075.2.a.ea.1.4		12	55.32	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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.784131i q^{2} +1.00000i q^{3} +1.38514 q^{4} +(-1.83964 - 1.27111i) q^{5} +0.784131 q^{6} +1.51801i q^{7} -2.65439i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.784131i q^{2} +1.00000i q^{3} +1.38514 q^{4} +(-1.83964 - 1.27111i) q^{5} +0.784131 q^{6} +1.51801i q^{7} -2.65439i q^{8} -1.00000 q^{9} +(-0.996719 + 1.44252i) q^{10} +1.38514i q^{12} -0.466512i q^{13} +1.19032 q^{14} +(1.27111 - 1.83964i) q^{15} +0.688885 q^{16} -1.69631i q^{17} +0.784131i q^{18} -5.60956 q^{19} +(-2.54816 - 1.76067i) q^{20} -1.51801 q^{21} -7.68641i q^{23} +2.65439 q^{24} +(1.76855 + 4.67678i) q^{25} -0.365807 q^{26} -1.00000i q^{27} +2.10265i q^{28} -2.66104 q^{29} +(-1.44252 - 0.996719i) q^{30} +3.95772 q^{31} -5.84896i q^{32} -1.33013 q^{34} +(1.92956 - 2.79258i) q^{35} -1.38514 q^{36} -3.05939i q^{37} +4.39863i q^{38} +0.466512 q^{39} +(-3.37403 + 4.88312i) q^{40} -1.35030 q^{41} +1.19032i q^{42} -12.0864i q^{43} +(1.83964 + 1.27111i) q^{45} -6.02716 q^{46} +2.55805i q^{47} +0.688885i q^{48} +4.69566 q^{49} +(3.66721 - 1.38677i) q^{50} +1.69631 q^{51} -0.646184i q^{52} -8.01711i q^{53} -0.784131 q^{54} +4.02938 q^{56} -5.60956i q^{57} +2.08661i q^{58} -7.54869 q^{59} +(1.76067 - 2.54816i) q^{60} -11.1178 q^{61} -3.10338i q^{62} -1.51801i q^{63} -3.20858 q^{64} +(-0.592989 + 0.858214i) q^{65} +6.89959i q^{67} -2.34962i q^{68} +7.68641 q^{69} +(-2.18975 - 1.51303i) q^{70} +14.5878 q^{71} +2.65439i q^{72} +2.26725i q^{73} -2.39896 q^{74} +(-4.67678 + 1.76855i) q^{75} -7.77002 q^{76} -0.365807i q^{78} -12.1809 q^{79} +(-1.26730 - 0.875650i) q^{80} +1.00000 q^{81} +1.05881i q^{82} -11.7808i q^{83} -2.10265 q^{84} +(-2.15620 + 3.12059i) q^{85} -9.47736 q^{86} -2.66104i q^{87} -1.47962 q^{89} +(0.996719 - 1.44252i) q^{90} +0.708168 q^{91} -10.6467i q^{92} +3.95772i q^{93} +2.00584 q^{94} +(10.3196 + 7.13038i) q^{95} +5.84896 q^{96} -14.2015i q^{97} -3.68201i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 2 q^{5} - 8 q^{6} - 24 q^{9}+O(q^{10}) \) 24 * q - 24 * q^4 - 2 * q^5 - 8 * q^6 - 24 * q^9	\( 24 q - 24 q^{4} - 2 q^{5} - 8 q^{6} - 24 q^{9} - 6 q^{10} - 12 q^{14} + 48 q^{16} + 32 q^{19} - 2 q^{20} - 16 q^{21} + 24 q^{24} + 2 q^{25} + 32 q^{26} - 8 q^{30} - 12 q^{34} + 10 q^{35} + 24 q^{36} + 36 q^{39} + 34 q^{40} + 2 q^{45} - 56 q^{46} - 24 q^{49} + 46 q^{50} - 36 q^{51} + 8 q^{54} + 12 q^{56} - 40 q^{59} - 26 q^{60} - 40 q^{61} + 12 q^{64} + 10 q^{65} - 2 q^{70} + 64 q^{71} - 136 q^{74} + 20 q^{75} - 68 q^{76} + 64 q^{79} + 76 q^{80} + 24 q^{81} + 60 q^{84} - 72 q^{86} + 20 q^{89} + 6 q^{90} - 4 q^{94} + 64 q^{95} - 56 q^{96}+O(q^{100}) \) 24 * q - 24 * q^4 - 2 * q^5 - 8 * q^6 - 24 * q^9 - 6 * q^10 - 12 * q^14 + 48 * q^16 + 32 * q^19 - 2 * q^20 - 16 * q^21 + 24 * q^24 + 2 * q^25 + 32 * q^26 - 8 * q^30 - 12 * q^34 + 10 * q^35 + 24 * q^36 + 36 * q^39 + 34 * q^40 + 2 * q^45 - 56 * q^46 - 24 * q^49 + 46 * q^50 - 36 * q^51 + 8 * q^54 + 12 * q^56 - 40 * q^59 - 26 * q^60 - 40 * q^61 + 12 * q^64 + 10 * q^65 - 2 * q^70 + 64 * q^71 - 136 * q^74 + 20 * q^75 - 68 * q^76 + 64 * q^79 + 76 * q^80 + 24 * q^81 + 60 * q^84 - 72 * q^86 + 20 * q^89 + 6 * q^90 - 4 * q^94 + 64 * q^95 - 56 * q^96

Introduction

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