LMFDB - Embedded newform 1915.2.c.a.384.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1915,2,Mod(384,1915)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1915, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1915.384");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1915 = 5 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1915.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:	$15.2913519871$
Analytic rank:	$0$
Dimension:	$190$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			384.5
Character	$\chi$	$=$	1915.384
Dual form			1915.2.c.a.384.186

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68469i q^{2} +0.951315i q^{3} -5.20755 q^{4} +(1.01533 - 1.99226i) q^{5} +2.55398 q^{6} +3.51008i q^{7} +8.61126i q^{8} +2.09500 q^{9} +O(q^{10})$	\(q-2.68469i q^{2} +0.951315i q^{3} -5.20755 q^{4} +(1.01533 - 1.99226i) q^{5} +2.55398 q^{6} +3.51008i q^{7} +8.61126i q^{8} +2.09500 q^{9} +(-5.34860 - 2.72585i) q^{10} -4.92456 q^{11} -4.95402i q^{12} -1.97112i q^{13} +9.42348 q^{14} +(1.89527 + 0.965901i) q^{15} +12.7035 q^{16} -5.00455i q^{17} -5.62442i q^{18} +2.96615 q^{19} +(-5.28739 + 10.3748i) q^{20} -3.33920 q^{21} +13.2209i q^{22} +1.02971i q^{23} -8.19202 q^{24} +(-2.93820 - 4.04561i) q^{25} -5.29183 q^{26} +4.84695i q^{27} -18.2789i q^{28} +5.60306 q^{29} +(2.59314 - 5.08820i) q^{30} +2.32105 q^{31} -16.8823i q^{32} -4.68481i q^{33} -13.4356 q^{34} +(6.99300 + 3.56390i) q^{35} -10.9098 q^{36} -10.1216i q^{37} -7.96320i q^{38} +1.87515 q^{39} +(17.1559 + 8.74330i) q^{40} -11.8948 q^{41} +8.96470i q^{42} -11.7454i q^{43} +25.6449 q^{44} +(2.12712 - 4.17378i) q^{45} +2.76444 q^{46} +3.45950i q^{47} +12.0850i q^{48} -5.32069 q^{49} +(-10.8612 + 7.88815i) q^{50} +4.76090 q^{51} +10.2647i q^{52} -8.70143i q^{53} +13.0125 q^{54} +(-5.00007 + 9.81101i) q^{55} -30.2263 q^{56} +2.82175i q^{57} -15.0425i q^{58} -6.01579 q^{59} +(-9.86969 - 5.02998i) q^{60} -11.3176 q^{61} -6.23130i q^{62} +7.35363i q^{63} -19.9167 q^{64} +(-3.92698 - 2.00134i) q^{65} -12.5773 q^{66} -5.02134i q^{67} +26.0614i q^{68} -0.979577 q^{69} +(9.56797 - 18.7740i) q^{70} -4.05936 q^{71} +18.0406i q^{72} +0.376922i q^{73} -27.1732 q^{74} +(3.84865 - 2.79515i) q^{75} -15.4464 q^{76} -17.2856i q^{77} -5.03420i q^{78} +0.427569 q^{79} +(12.8982 - 25.3086i) q^{80} +1.67402 q^{81} +31.9339i q^{82} -2.04253i q^{83} +17.3890 q^{84} +(-9.97036 - 5.08128i) q^{85} -31.5328 q^{86} +5.33028i q^{87} -42.4067i q^{88} +7.12008 q^{89} +(-11.2053 - 5.71066i) q^{90} +6.91878 q^{91} -5.36225i q^{92} +2.20805i q^{93} +9.28769 q^{94} +(3.01163 - 5.90935i) q^{95} +16.0604 q^{96} -17.0240i q^{97} +14.2844i q^{98} -10.3170 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 190 q - 188 q^{4} - 4 q^{6} - 186 q^{9}+O(q^{10}) $ 190 * q - 188 * q^4 - 4 * q^6 - 186 * q^9	$ 190 q - 188 q^{4} - 4 q^{6} - 186 q^{9} - 6 q^{10} - 4 q^{11} + 12 q^{14} - 8 q^{15} + 192 q^{16} + 8 q^{19} - 24 q^{20} + 40 q^{24} - 4 q^{25} + 16 q^{26} + 8 q^{29} - 6 q^{30} - 12 q^{31} + 4 q^{35} + 136 q^{36} + 8 q^{39} + 12 q^{40} - 16 q^{41} - 16 q^{44} - 12 q^{45} - 154 q^{49} - 2 q^{50} + 16 q^{51} + 16 q^{54} + 4 q^{55} - 28 q^{59} + 34 q^{60} - 20 q^{61} - 204 q^{64} - 12 q^{65} + 40 q^{66} + 28 q^{69} + 2 q^{70} - 24 q^{71} - 20 q^{74} + 22 q^{75} - 64 q^{76} - 12 q^{79} + 46 q^{80} + 142 q^{81} - 8 q^{84} + 8 q^{85} + 12 q^{86} + 28 q^{89} + 32 q^{90} + 28 q^{91} + 16 q^{94} + 28 q^{95} - 84 q^{96} - 20 q^{99}+O(q^{100}) $ 190 * q - 188 * q^4 - 4 * q^6 - 186 * q^9 - 6 * q^10 - 4 * q^11 + 12 * q^14 - 8 * q^15 + 192 * q^16 + 8 * q^19 - 24 * q^20 + 40 * q^24 - 4 * q^25 + 16 * q^26 + 8 * q^29 - 6 * q^30 - 12 * q^31 + 4 * q^35 + 136 * q^36 + 8 * q^39 + 12 * q^40 - 16 * q^41 - 16 * q^44 - 12 * q^45 - 154 * q^49 - 2 * q^50 + 16 * q^51 + 16 * q^54 + 4 * q^55 - 28 * q^59 + 34 * q^60 - 20 * q^61 - 204 * q^64 - 12 * q^65 + 40 * q^66 + 28 * q^69 + 2 * q^70 - 24 * q^71 - 20 * q^74 + 22 * q^75 - 64 * q^76 - 12 * q^79 + 46 * q^80 + 142 * q^81 - 8 * q^84 + 8 * q^85 + 12 * q^86 + 28 * q^89 + 32 * q^90 + 28 * q^91 + 16 * q^94 + 28 * q^95 - 84 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1915\mathbb{Z}\right)^\times$.

$n$	$767$	$771$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	2.68469i		−	1.89836i	−0.314733	−	0.949180i	$-0.601915\pi$
$2$		−	2.68469i		−	1.89836i	0.314733	−	0.949180i	$-0.398085\pi$
$3$			0.951315i			0.549242i	0.961553	+	0.274621i	$0.0885524\pi$
$3$			0.951315i			0.549242i	−0.961553	+	0.274621i	$0.911448\pi$
$4$	−5.20755			−2.60377
$5$	1.01533	−	1.99226i	0.454071	−	0.890966i
$5$	1.01533	−	1.99226i	0.454071	−	0.890966i
$6$	2.55398			1.04266
$7$			3.51008i			1.32669i	0.748315	+	0.663344i	$0.230863\pi$
$7$			3.51008i			1.32669i	−0.748315	+	0.663344i	$0.769137\pi$
$8$			8.61126i			3.04454i
$9$	2.09500			0.698333
$10$	−5.34860	−	2.72585i	−1.69137	−	0.861990i
$11$	−4.92456			−1.48481			−0.742406	−	0.669951i	$-0.766315\pi$
$11$	−4.92456			−1.48481			−0.742406	+	0.669951i	$0.766315\pi$
$12$		−	4.95402i		−	1.43010i
$13$		−	1.97112i		−	0.546689i	−0.961916	−	0.273345i	$-0.911870\pi$
$13$		−	1.97112i		−	0.546689i	0.961916	−	0.273345i	$-0.0881300\pi$
$14$	9.42348			2.51853
$15$	1.89527	+	0.965901i	0.489356	+	0.249395i
$16$	12.7035			3.17586
$17$		−	5.00455i		−	1.21378i	−0.794786	−	0.606890i	$-0.792417\pi$
$17$		−	5.00455i		−	1.21378i	0.794786	−	0.606890i	$-0.207583\pi$
$18$		−	5.62442i		−	1.32569i
$19$	2.96615			0.680483			0.340241	−	0.940338i	$-0.389491\pi$
$19$	2.96615			0.680483			0.340241	+	0.940338i	$0.389491\pi$
$20$	−5.28739	+	10.3748i	−1.18230	+	2.31987i
$21$	−3.33920			−0.728672
$22$			13.2209i			2.81871i
$23$			1.02971i			0.214709i	0.994221	+	0.107354i	$0.0342380\pi$
$23$			1.02971i			0.214709i	−0.994221	+	0.107354i	$0.965762\pi$
$24$	−8.19202			−1.67219
$25$	−2.93820	−	4.04561i	−0.587640	−	0.809123i
$26$	−5.29183			−1.03781
$27$			4.84695i			0.932796i
$28$		−	18.2789i		−	3.45439i
$29$	5.60306			1.04046			0.520231	−	0.854025i	$-0.325846\pi$
$29$	5.60306			1.04046			0.520231	+	0.854025i	$0.325846\pi$
$30$	2.59314	−	5.08820i	0.473441	−	0.928974i
$31$	2.32105			0.416873			0.208437	−	0.978036i	$-0.433162\pi$
$31$	2.32105			0.416873			0.208437	+	0.978036i	$0.433162\pi$
$32$		−	16.8823i		−	2.98439i
$33$		−	4.68481i		−	0.815521i
$34$	−13.4356			−2.30419
$35$	6.99300	+	3.56390i	1.18203	+	0.602410i
$36$	−10.9098			−1.81830
$37$		−	10.1216i		−	1.66397i	−0.554795	−	0.831987i	$-0.687203\pi$
$37$		−	10.1216i		−	1.66397i	0.554795	−	0.831987i	$-0.312797\pi$
$38$		−	7.96320i		−	1.29180i
$39$	1.87515			0.300265
$40$	17.1559	+	8.74330i	2.71258	+	1.38244i
$41$	−11.8948			−1.85766			−0.928829	−	0.370508i	$-0.879184\pi$
$41$	−11.8948			−1.85766			−0.928829	+	0.370508i	$0.879184\pi$
$42$			8.96470i			1.38328i
$43$		−	11.7454i		−	1.79116i	−0.444899	−	0.895581i	$-0.646760\pi$
$43$		−	11.7454i		−	1.79116i	0.444899	−	0.895581i	$-0.353240\pi$
$44$	25.6449			3.86611
$45$	2.12712	−	4.17378i	0.317093	−	0.622191i
$46$	2.76444			0.407595
$47$			3.45950i			0.504621i	0.967646	+	0.252310i	$0.0811904\pi$
$47$			3.45950i			0.504621i	−0.967646	+	0.252310i	$0.918810\pi$
$48$			12.0850i			1.74432i
$49$	−5.32069			−0.760099
$50$	−10.8612	+	7.88815i	−1.53601	+	1.11555i
$51$	4.76090			0.666659
$52$			10.2647i			1.42346i
$53$		−	8.70143i		−	1.19523i	−0.801782	−	0.597617i	$-0.796115\pi$
$53$		−	8.70143i		−	1.19523i	0.801782	−	0.597617i	$-0.203885\pi$
$54$	13.0125			1.77078
$55$	−5.00007	+	9.81101i	−0.674209	+	1.32292i
$56$	−30.2263			−4.03915
$57$			2.82175i			0.373750i
$58$		−	15.0425i		−	1.97517i
$59$	−6.01579			−0.783189			−0.391595	−	0.920138i	$-0.628076\pi$
$59$	−6.01579			−0.783189			−0.391595	+	0.920138i	$0.628076\pi$
$60$	−9.86969	−	5.02998i	−1.27417	−	0.649367i
$61$	−11.3176			−1.44907			−0.724534	−	0.689239i	$-0.757945\pi$
$61$	−11.3176			−1.44907			−0.724534	+	0.689239i	$0.757945\pi$
$62$		−	6.23130i		−	0.791376i
$63$			7.35363i			0.926470i
$64$	−19.9167			−2.48959
$65$	−3.92698	−	2.00134i	−0.487081	−	0.248236i
$66$	−12.5773			−1.54815
$67$		−	5.02134i		−	0.613455i	−0.951797	−	0.306727i	$-0.900766\pi$
$67$		−	5.02134i		−	0.613455i	0.951797	−	0.306727i	$-0.0992340\pi$
$68$			26.0614i			3.16041i
$69$	−0.979577			−0.117927
$70$	9.56797	−	18.7740i	1.14359	−	2.24392i
$71$	−4.05936			−0.481758			−0.240879	−	0.970555i	$-0.577436\pi$
$71$	−4.05936			−0.481758			−0.240879	+	0.970555i	$0.577436\pi$
$72$			18.0406i			2.12610i
$73$			0.376922i			0.0441154i	0.999757	+	0.0220577i	$0.00702176\pi$
$73$			0.376922i			0.0441154i	−0.999757	+	0.0220577i	$0.992978\pi$
$74$	−27.1732			−3.15882
$75$	3.84865	−	2.79515i	0.444404	−	0.322756i
$76$	−15.4464			−1.77182
$77$		−	17.2856i		−	1.96988i
$78$		−	5.03420i		−	0.570011i
$79$	0.427569			0.0481052			0.0240526	−	0.999711i	$-0.492343\pi$
$79$	0.427569			0.0481052			0.0240526	+	0.999711i	$0.492343\pi$
$80$	12.8982	−	25.3086i	1.44207	−	2.82959i
$81$	1.67402			0.186003
$82$			31.9339i			3.52651i
$83$		−	2.04253i		−	0.224197i	−0.993697	−	0.112099i	$-0.964243\pi$
$83$		−	2.04253i		−	0.224197i	0.993697	−	0.112099i	$-0.0357572\pi$
$84$	17.3890			1.89730
$85$	−9.97036	−	5.08128i	−1.08144	−	0.551142i
$86$	−31.5328			−3.40027
$87$			5.33028i			0.571466i
$88$		−	42.4067i		−	4.52057i
$89$	7.12008			0.754727			0.377363	−	0.926065i	$-0.376831\pi$
$89$	7.12008			0.754727			0.377363	+	0.926065i	$0.376831\pi$
$90$	−11.2053	−	5.71066i	−1.18114	−	0.601956i
$91$	6.91878			0.725286
$92$		−	5.36225i		−	0.559053i
$93$			2.20805i			0.228964i
$94$	9.28769			0.957952
$95$	3.01163	−	5.90935i	0.308987	−	0.606287i
$96$	16.0604			1.63915
$97$		−	17.0240i		−	1.72852i	−0.503045	−	0.864260i	$-0.667787\pi$
$97$		−	17.0240i		−	1.72852i	0.503045	−	0.864260i	$-0.332213\pi$
$98$			14.2844i			1.44294i
$99$	−10.3170			−1.03689
$100$	15.3008	+	21.0677i	1.53008	+	2.10677i
$101$	−5.68996			−0.566172			−0.283086	−	0.959094i	$-0.591358\pi$
$101$	−5.68996			−0.566172			−0.283086	+	0.959094i	$0.591358\pi$
$102$		−	12.7815i		−	1.26556i
$103$		−	0.422683i		−	0.0416482i	−0.999783	−	0.0208241i	$-0.993371\pi$
$103$		−	0.422683i		−	0.0416482i	0.999783	−	0.0208241i	$-0.00662900\pi$
$104$	16.9738			1.66442
$105$	−3.39039	+	6.65255i	−0.330869	+	0.649222i
$106$	−23.3606			−2.26898
$107$		−	10.8960i		−	1.05335i	−0.850066	−	0.526677i	$-0.823438\pi$
$107$		−	10.8960i		−	1.05335i	0.850066	−	0.526677i	$-0.176562\pi$
$108$		−	25.2407i		−	2.42879i
$109$	13.8267			1.32436			0.662178	−	0.749347i	$-0.269632\pi$
$109$	13.8267			1.32436			0.662178	+	0.749347i	$0.269632\pi$
$110$	26.3395	+	13.4236i	2.51137	+	1.27989i
$111$	9.62880			0.913925
$112$			44.5902i			4.21338i
$113$			17.3812i			1.63509i	0.575865	+	0.817545i	$0.304665\pi$
$113$			17.3812i			1.63509i	−0.575865	+	0.817545i	$0.695335\pi$
$114$	7.57551			0.709512
$115$	2.05145	+	1.04550i	0.191298	+	0.0974930i
$116$	−29.1782			−2.70913
$117$		−	4.12949i		−	0.381771i
$118$			16.1505i			1.48678i
$119$	17.5664			1.61031
$120$	−8.31763	+	16.3206i	−0.759292	+	1.48986i
$121$	13.2513			1.20466
$122$			30.3842i			2.75085i
$123$		−	11.3157i		−	1.02030i
$124$	−12.0870			−1.08544
$125$	−11.0432	+	1.74601i	−0.987731	+	0.156168i
$126$	19.7422			1.75877
$127$			3.44698i			0.305870i	0.988236	+	0.152935i	$0.0488725\pi$
$127$			3.44698i			0.305870i	−0.988236	+	0.152935i	$0.951127\pi$
$128$			19.7057i			1.74175i
$129$	11.1736			0.983781
$130$	−5.37297	+	10.5427i	−0.471241	+	0.924656i
$131$	8.24131			0.720046			0.360023	−	0.932943i	$-0.382769\pi$
$131$	8.24131			0.720046			0.360023	+	0.932943i	$0.382769\pi$
$132$			24.3964i			2.12343i
$133$			10.4115i			0.902787i
$134$	−13.4807			−1.16456
$135$	9.65638	+	4.92127i	0.831089	+	0.423555i
$136$	43.0955			3.69540
$137$			21.5269i			1.83916i	0.392899	+	0.919582i	$0.371472\pi$
$137$			21.5269i			1.83916i	−0.392899	+	0.919582i	$0.628528\pi$
$138$			2.62986i			0.223868i
$139$	−1.73150			−0.146864			−0.0734320	−	0.997300i	$-0.523395\pi$
$139$	−1.73150			−0.146864			−0.0734320	+	0.997300i	$0.523395\pi$
$140$	−36.4164	−	18.5592i	−3.07775	−	1.56854i
$141$	−3.29108			−0.277159
$142$			10.8981i			0.914550i
$143$			9.70689i			0.811731i
$144$	26.6137			2.21781
$145$	5.68897	−	11.1628i	0.472443	−	0.927016i
$146$	1.01192			0.0837470
$147$		−	5.06165i		−	0.417478i
$148$			52.7085i			4.33261i
$149$	−20.2749			−1.66098			−0.830490	−	0.557033i	$-0.811940\pi$
$149$	−20.2749			−1.66098			−0.830490	+	0.557033i	$0.811940\pi$
$150$	−7.50411	−	10.3324i	−0.612708	−	0.843639i
$151$	20.4512			1.66429			0.832146	−	0.554556i	$-0.187112\pi$
$151$	20.4512			1.66429			0.832146	+	0.554556i	$0.187112\pi$
$152$			25.5423i			2.07176i
$153$		−	10.4845i		−	0.847623i
$154$	−46.4065			−3.73954
$155$	2.35664	−	4.62414i	0.189290	−	0.371420i
$156$	−9.76495			−0.781821
$157$		−	9.32993i		−	0.744610i	−0.928111	−	0.372305i	$-0.878568\pi$
$157$		−	9.32993i		−	0.744610i	0.928111	−	0.372305i	$-0.121432\pi$
$158$		−	1.14789i		−	0.0913211i
$159$	8.27780			0.656472
$160$	−33.6339	−	17.1411i	−2.65899	−	1.35513i
$161$	−3.61436			−0.284852
$162$		−	4.49423i		−	0.353100i
$163$		−	21.6693i		−	1.69727i	−0.528980	−	0.848634i	$-0.677425\pi$
$163$		−	21.6693i		−	1.69727i	0.528980	−	0.848634i	$-0.322575\pi$
$164$	61.9428			4.83692
$165$	−9.33336	−	4.75664i	−0.726601	−	0.370304i
$166$	−5.48356			−0.425607
$167$		−	3.80213i		−	0.294218i	−0.989120	−	0.147109i	$-0.953003\pi$
$167$		−	3.80213i		−	0.294218i	0.989120	−	0.147109i	$-0.0469968\pi$
$168$		−	28.7547i		−	2.21847i
$169$	9.11470			0.701131
$170$	−13.6416	+	26.7673i	−1.04627	+	2.05296i
$171$	6.21409			0.475204
$172$			61.1649i			4.66378i
$173$			8.12860i			0.618006i	0.951061	+	0.309003i	$0.0999953\pi$
$173$			8.12860i			0.618006i	−0.951061	+	0.309003i	$0.900005\pi$
$174$	14.3101			1.08485
$175$	14.2004	−	10.3133i	1.07345	−	0.779614i
$176$	−62.5589			−4.71556
$177$		−	5.72291i		−	0.430160i
$178$		−	19.1152i		−	1.43274i
$179$	−19.8399			−1.48290			−0.741450	−	0.671008i	$-0.765862\pi$
$179$	−19.8399			−1.48290			−0.741450	+	0.671008i	$0.765862\pi$
$180$	−11.0771	+	21.7352i	−0.825637	+	1.62004i
$181$	−16.4347			−1.22158			−0.610792	−	0.791791i	$-0.709149\pi$
$181$	−16.4347			−1.22158			−0.610792	+	0.791791i	$0.709149\pi$
$182$		−	18.5748i		−	1.37685i
$183$		−	10.7666i		−	0.795889i
$184$	−8.86708			−0.653690
$185$	−20.1648	−	10.2768i	−1.48254	−	0.755562i
$186$	5.92793			0.434657
$187$			24.6452i			1.80224i
$188$		−	18.0155i		−	1.31392i
$189$	−17.0132			−1.23753
$190$	−15.8648	−	8.08530i	−1.15095	−	0.586569i
$191$	−3.37404			−0.244137			−0.122068	−	0.992522i	$-0.538953\pi$
$191$	−3.37404			−0.244137			−0.122068	+	0.992522i	$0.538953\pi$
$192$		−	18.9471i		−	1.36739i
$193$		−	5.42069i		−	0.390190i	−0.980784	−	0.195095i	$-0.937498\pi$
$193$		−	5.42069i		−	0.390190i	0.980784	−	0.195095i	$-0.0625015\pi$
$194$	−45.7040			−3.28136
$195$	1.90390	−	3.73579i	0.136341	−	0.267526i
$196$	27.7078			1.97913
$197$			6.04877i			0.430957i	0.976509	+	0.215479i	$0.0691311\pi$
$197$			6.04877i			0.430957i	−0.976509	+	0.215479i	$0.930869\pi$
$198$			27.6978i			1.96840i
$199$	5.59390			0.396541			0.198271	−	0.980147i	$-0.436468\pi$
$199$	5.59390			0.396541			0.198271	+	0.980147i	$0.436468\pi$
$200$	34.8378	−	25.3016i	2.46341	−	1.78909i
$201$	4.77688			0.336935
$202$			15.2758i			1.07480i
$203$			19.6672i			1.38037i
$204$	−24.7926			−1.73583
$205$	−12.0772	+	23.6976i	−0.843508	+	1.65511i
$206$	−1.13477			−0.0790633
$207$			2.15724i			0.149938i
$208$		−	25.0400i		−	1.73621i
$209$	−14.6070			−1.01039
$210$	17.8600	+	9.10215i	1.23246	+	0.628108i
$211$	1.93152			0.132971			0.0664857	−	0.997787i	$-0.478821\pi$
$211$	1.93152			0.132971			0.0664857	+	0.997787i	$0.478821\pi$
$212$			45.3131i			3.11212i
$213$		−	3.86173i		−	0.264601i
$214$	−29.2523			−1.99965
$215$	−23.4000	−	11.9255i	−1.59586	−	0.813314i
$216$	−41.7384			−2.83994
$217$			8.14709i			0.553060i
$218$		−	37.1203i		−	2.51411i
$219$	−0.358572			−0.0242300
$220$	26.0381	−	51.0913i	1.75549	−	3.44457i
$221$	−9.86454			−0.663561
$222$		−	25.8503i		−	1.73496i
$223$		−	8.16868i		−	0.547015i	−0.961870	−	0.273508i	$-0.911816\pi$
$223$		−	8.16868i		−	0.547015i	0.961870	−	0.273508i	$-0.0881839\pi$
$224$	59.2582			3.95936
$225$	−6.15553	−	8.47556i	−0.410368	−	0.565037i
$226$	46.6632			3.10399
$227$			6.91929i			0.459250i	0.973279	+	0.229625i	$0.0737499\pi$
$227$			6.91929i			0.459250i	−0.973279	+	0.229625i	$0.926250\pi$
$228$		−	14.6944i		−	0.973159i
$229$	25.6939			1.69790			0.848951	−	0.528471i	$-0.177235\pi$
$229$	25.6939			1.69790			0.848951	+	0.528471i	$0.177235\pi$
$230$	2.80683	−	5.50749i	0.185077	−	0.363153i
$231$	16.4441			1.08194
$232$			48.2494i			3.16773i
$233$		−	28.4652i		−	1.86481i	−0.361410	−	0.932407i	$-0.617704\pi$
$233$		−	28.4652i		−	1.86481i	0.361410	−	0.932407i	$-0.382296\pi$
$234$	−11.0864			−0.724740
$235$	6.89223	+	3.51255i	0.449600	+	0.229133i
$236$	31.3275			2.03925
$237$			0.406752i			0.0264214i
$238$		−	47.1602i		−	3.05694i
$239$	−8.18158			−0.529222			−0.264611	−	0.964355i	$-0.585244\pi$
$239$	−8.18158			−0.529222			−0.264611	+	0.964355i	$0.585244\pi$
$240$	24.0764	+	12.2703i	1.55413	+	0.792043i
$241$	16.3751			1.05481			0.527405	−	0.849614i	$-0.323165\pi$
$241$	16.3751			1.05481			0.527405	+	0.849614i	$0.323165\pi$
$242$		−	35.5756i		−	2.28689i
$243$			16.1334i			1.03496i
$244$	58.9368			3.77304
$245$	−5.40227	+	10.6002i	−0.345139	+	0.677222i
$246$	−30.3792			−1.93691
$247$		−	5.84664i		−	0.372013i
$248$			19.9872i			1.26919i
$249$	1.94309			0.123138
$250$	4.68750	+	29.6474i	0.296463	+	1.87507i
$251$	8.20379			0.517819			0.258909	−	0.965902i	$-0.416637\pi$
$251$	8.20379			0.517819			0.258909	+	0.965902i	$0.416637\pi$
$252$		−	38.2944i		−	2.41232i
$253$		−	5.07086i		−	0.318802i
$254$	9.25406			0.580651
$255$	4.83390	−	9.48495i	0.302710	−	0.593971i
$256$	13.0701			0.816879
$257$			7.09933i			0.442844i	0.975178	+	0.221422i	$0.0710699\pi$
$257$			7.09933i			0.442844i	−0.975178	+	0.221422i	$0.928930\pi$
$258$		−	29.9976i		−	1.86757i
$259$	35.5275			2.20757
$260$	20.4499	+	10.4221i	1.26825	+	0.646349i
$261$	11.7384			0.726590
$262$		−	22.1253i		−	1.36691i
$263$			18.5057i			1.14111i	0.821260	+	0.570555i	$0.193272\pi$
$263$			18.5057i			1.14111i	−0.821260	+	0.570555i	$0.806728\pi$
$264$	40.3421			2.48289
$265$	−17.3355	−	8.83485i	−1.06491	−	0.542720i
$266$	27.9515			1.71382
$267$			6.77344i			0.414528i
$268$			26.1489i			1.59730i
$269$	−26.5205			−1.61698			−0.808492	−	0.588507i	$-0.799716\pi$
$269$	−26.5205			−1.61698			−0.808492	+	0.588507i	$0.799716\pi$
$270$	13.2121	−	25.9244i	0.804061	−	1.57771i
$271$	11.5336			0.700615			0.350307	−	0.936635i	$-0.386077\pi$
$271$	11.5336			0.700615			0.350307	+	0.936635i	$0.386077\pi$
$272$		−	63.5750i		−	3.85480i
$273$			6.58194i			0.398357i
$274$	57.7929			3.49140
$275$	14.4693	+	19.9229i	0.872534	+	1.20139i
$276$	5.10119			0.307056
$277$			3.67489i			0.220803i	0.993887	+	0.110401i	$0.0352136\pi$
$277$			3.67489i			0.220803i	−0.993887	+	0.110401i	$0.964786\pi$
$278$			4.64854i			0.278801i
$279$	4.86260			0.291116
$280$	−30.6897	+	60.2186i	−1.83406	+	3.59875i
$281$	15.7337			0.938594			0.469297	−	0.883040i	$-0.344507\pi$
$281$	15.7337			0.938594			0.469297	+	0.883040i	$0.344507\pi$
$282$			8.83552i			0.526147i
$283$		−	10.1979i		−	0.606202i	−0.952958	−	0.303101i	$-0.901978\pi$
$283$		−	10.1979i		−	0.606202i	0.952958	−	0.303101i	$-0.0980220\pi$
$284$	21.1393			1.25439
$285$	5.62165	+	2.86501i	0.332998	+	0.169709i
$286$	26.0600			1.54096
$287$		−	41.7518i		−	2.46453i
$288$		−	35.3684i		−	2.08410i
$289$	−8.04548			−0.473263
$290$	−29.9685	−	15.2731i	−1.75981	−	0.896868i
$291$	16.1951			0.949376
$292$		−	1.96284i		−	0.114867i
$293$			7.01424i			0.409776i	0.978785	+	0.204888i	$0.0656830\pi$
$293$			7.01424i			0.409776i	−0.978785	+	0.204888i	$0.934317\pi$
$294$	−13.5890			−0.792524
$295$	−6.10803	+	11.9850i	−0.355623	+	0.697795i
$296$	87.1594			5.06604
$297$		−	23.8691i		−	1.38503i
$298$			54.4317i			3.15314i
$299$	2.02967			0.117379
$300$	−20.0420	+	14.5559i	−1.15713	+	0.840385i
$301$	41.2275			2.37631
$302$		−	54.9050i		−	3.15943i
$303$		−	5.41295i		−	0.310966i
$304$	37.6804			2.16112
$305$	−11.4911	+	22.5476i	−0.657979	+	1.29107i
$306$	−28.1477			−1.60909
$307$		−	17.1829i		−	0.980683i	−0.871530	−	0.490341i	$-0.836872\pi$
$307$		−	17.1829i		−	0.980683i	0.871530	−	0.490341i	$-0.163128\pi$
$308$			90.0157i			5.12912i
$309$	0.402105			0.0228750
$310$	−12.4144	−	6.32684i	−0.705089	−	0.359341i
$311$	−22.0697			−1.25146			−0.625729	−	0.780041i	$-0.715198\pi$
$311$	−22.0697			−1.25146			−0.625729	+	0.780041i	$0.715198\pi$
$312$			16.1474i			0.914168i
$313$		−	13.8324i		−	0.781855i	−0.920421	−	0.390927i	$-0.872154\pi$
$313$		−	13.8324i		−	0.781855i	0.920421	−	0.390927i	$-0.127846\pi$
$314$	−25.0480			−1.41354
$315$	14.6503	+	7.46638i	0.825453	+	0.420683i
$316$	−2.22658			−0.125255
$317$		−	7.45140i		−	0.418512i	−0.977861	−	0.209256i	$-0.932896\pi$
$317$		−	7.45140i		−	0.418512i	0.977861	−	0.209256i	$-0.0671043\pi$
$318$		−	22.2233i		−	1.24622i
$319$	−27.5926			−1.54489
$320$	−20.2221	+	39.6793i	−1.13045	+	2.21814i
$321$	10.3655			0.578546
$322$			9.70343i			0.540751i
$323$		−	14.8443i		−	0.825956i
$324$	−8.71755			−0.484309
$325$	−7.97438	+	5.79153i	−0.442339	+	0.321256i
$326$	−58.1752			−3.22203
$327$			13.1535i			0.727392i
$328$		−	102.429i		−	5.65572i
$329$	−12.1432			−0.669474
$330$	−12.7701	+	25.0572i	−0.702971	+	1.37935i
$331$	−17.0507			−0.937192			−0.468596	−	0.883413i	$-0.655240\pi$
$331$	−17.0507			−0.937192			−0.468596	+	0.883413i	$0.655240\pi$
$332$			10.6366i			0.583758i
$333$		−	21.2047i		−	1.16201i
$334$	−10.2075			−0.558532
$335$	−10.0038	−	5.09833i	−0.546567	−	0.278552i
$336$	−42.4193			−2.31416
$337$		−	2.01323i		−	0.109668i	−0.998495	−	0.0548339i	$-0.982537\pi$
$337$		−	2.01323i		−	0.109668i	0.998495	−	0.0548339i	$-0.0174629\pi$
$338$		−	24.4701i		−	1.33100i
$339$	−16.5350			−0.898060
$340$	51.9211	+	26.4610i	2.81582	+	1.43505i
$341$	−11.4302			−0.618978
$342$		−	16.6829i		−	0.902108i
$343$			5.89451i			0.318274i
$344$	101.143			5.45326
$345$	−0.994596	+	1.95157i	−0.0535473	+	0.105069i
$346$	21.8227			1.17320
$347$		−	14.6797i		−	0.788049i	−0.919100	−	0.394024i	$-0.871083\pi$
$347$		−	14.6797i		−	0.788049i	0.919100	−	0.394024i	$-0.128917\pi$
$348$		−	27.7577i		−	1.48797i
$349$	30.6560			1.64098			0.820488	−	0.571664i	$-0.193702\pi$
$349$	30.6560			1.64098			0.820488	+	0.571664i	$0.193702\pi$
$350$	−27.6881	−	38.1238i	−1.47999	−	2.03780i
$351$	9.55390			0.509950
$352$			83.1378i			4.43126i
$353$		−	12.8367i		−	0.683229i	−0.939840	−	0.341615i	$-0.889026\pi$
$353$		−	12.8367i		−	0.683229i	0.939840	−	0.341615i	$-0.110974\pi$
$354$	−15.3642			−0.816600
$355$	−4.12160	+	8.08730i	−0.218752	+	0.429229i
$356$	−37.0781			−1.96514
$357$			16.7112i			0.884448i
$358$			53.2638i			2.81508i
$359$	15.6170			0.824235			0.412118	−	0.911131i	$-0.364789\pi$
$359$	15.6170			0.824235			0.412118	+	0.911131i	$0.364789\pi$
$360$	35.9415	+	18.3172i	1.89429	+	0.965401i
$361$	−10.2019			−0.536944
$362$			44.1221i			2.31901i
$363$			12.6062i			0.661652i
$364$	−36.0299			−1.88848
$365$	0.750927	+	0.382701i	0.0393053	+	0.0200315i
$366$	−28.9049			−1.51088
$367$		−	26.0784i		−	1.36128i	−0.732617	−	0.680641i	$-0.761701\pi$
$367$		−	26.0784i		−	1.36128i	0.732617	−	0.680641i	$-0.238299\pi$
$368$			13.0808i			0.681886i
$369$	−24.9196			−1.29726
$370$	−27.5899	+	54.1361i	−1.43433	+	2.81440i
$371$	30.5427			1.58570
$372$		−	11.4985i		−	0.596171i
$373$			4.48454i			0.232201i	0.993237	+	0.116100i	$0.0370394\pi$
$373$			4.48454i			0.232201i	−0.993237	+	0.116100i	$0.962961\pi$
$374$	66.1646			3.42129
$375$	−1.66101	−	10.5055i	−0.0857740	−	0.542503i
$376$	−29.7907			−1.53634
$377$		−	11.0443i		−	0.568810i
$378$			45.6751i			2.34928i
$379$	−20.9436			−1.07580			−0.537900	−	0.843008i	$-0.680782\pi$
$379$	−20.9436			−1.07580			−0.537900	+	0.843008i	$0.680782\pi$
$380$	−15.6832	+	30.7732i	−0.804532	+	1.57863i
$381$	−3.27916			−0.167997
$382$			9.05823i			0.463460i
$383$			1.00000i			0.0510976i
$383$			1.00000i			0.0510976i
$384$	−18.7463			−0.956642
$385$	−34.4375	−	17.5507i	−1.75510	−	0.894465i
$386$	−14.5529			−0.740721
$387$		−	24.6067i		−	1.25083i
$388$			88.6531i			4.50068i
$389$	16.0723			0.814898			0.407449	−	0.913228i	$-0.366418\pi$
$389$	16.0723			0.814898			0.407449	+	0.913228i	$0.366418\pi$
$390$	−10.0294	−	5.11139i	−0.507860	−	0.258825i
$391$	5.15322			0.260610
$392$		−	45.8179i		−	2.31415i
$393$			7.84008i			0.395480i
$394$	16.2391			0.818112
$395$	0.434124	−	0.851828i	0.0218432	−	0.0428601i
$396$	53.7260			2.69983
$397$		−	6.75273i		−	0.338910i	−0.985538	−	0.169455i	$-0.945799\pi$
$397$		−	6.75273i		−	0.338910i	0.985538	−	0.169455i	$-0.0542007\pi$
$398$		−	15.0179i		−	0.752778i
$399$	−9.90457			−0.495849
$400$	−37.3253	−	51.3933i	−1.86626	−	2.56966i
$401$	28.4554			1.42100			0.710498	−	0.703699i	$-0.248470\pi$
$401$	28.4554			1.42100			0.710498	+	0.703699i	$0.248470\pi$
$402$		−	12.8244i		−	0.639624i
$403$		−	4.57506i		−	0.227900i
$404$	29.6307			1.47418
$405$	1.69969	−	3.33509i	0.0844583	−	0.165722i
$406$	52.8003			2.62044
$407$			49.8443i			2.47069i
$408$			40.9974i			2.02967i
$409$	−4.85707			−0.240167			−0.120083	−	0.992764i	$-0.538316\pi$
$409$	−4.85707			−0.240167			−0.120083	+	0.992764i	$0.538316\pi$
$410$	63.6206	+	32.4235i	3.14200	+	1.60128i
$411$	−20.4788			−1.01015
$412$			2.20114i			0.108443i
$413$		−	21.1159i		−	1.03905i
$414$	5.79151			0.284637
$415$	−4.06926	−	2.07385i	−0.199752	−	0.101801i
$416$	−33.2769			−1.63154
$417$		−	1.64720i		−	0.0806639i
$418$			39.2153i			1.91808i
$419$	21.2754			1.03937			0.519685	−	0.854358i	$-0.326049\pi$
$419$	21.2754			1.03937			0.519685	+	0.854358i	$0.326049\pi$
$420$	17.6556	−	34.6434i	0.861507	−	1.69043i
$421$	−2.64181			−0.128754			−0.0643769	−	0.997926i	$-0.520506\pi$
$421$	−2.64181			−0.128754			−0.0643769	+	0.997926i	$0.520506\pi$
$422$		−	5.18553i		−	0.252428i
$423$			7.24766i			0.352393i
$424$	74.9303			3.63894
$425$	−20.2465	+	14.7043i	−0.982097	+	0.713266i
$426$	−10.3675			−0.502309
$427$		−	39.7257i		−	1.92246i
$428$			56.7413i			2.74269i
$429$	−9.23431			−0.445836
$430$	−32.0163	+	62.8216i	−1.54396	+	3.02952i
$431$	−10.8780			−0.523976			−0.261988	−	0.965071i	$-0.584378\pi$
$431$	−10.8780			−0.523976			−0.261988	+	0.965071i	$0.584378\pi$
$432$			61.5730i			2.96243i
$433$		−	9.26405i		−	0.445202i	−0.974910	−	0.222601i	$-0.928545\pi$
$433$		−	9.26405i		−	0.445202i	0.974910	−	0.222601i	$-0.0714547\pi$
$434$	21.8724			1.04991
$435$	10.6193	+	5.41200i	0.509156	+	0.259486i
$436$	−72.0031			−3.44832
$437$			3.05427i			0.146106i
$438$			0.962653i			0.0459973i
$439$	−19.0622			−0.909788			−0.454894	−	0.890546i	$-0.650323\pi$
$439$	−19.0622			−0.909788			−0.454894	+	0.890546i	$0.650323\pi$
$440$	−84.4852	−	43.0569i	−4.02767	−	2.05266i
$441$	−11.1468			−0.530802
$442$			26.4832i			1.25968i
$443$		−	38.8062i		−	1.84374i	−0.387501	−	0.921869i	$-0.626662\pi$
$443$		−	38.8062i		−	1.84374i	0.387501	−	0.921869i	$-0.373338\pi$
$444$	−50.1424			−2.37965
$445$	7.22925	−	14.1850i	0.342699	−	0.672436i
$446$	−21.9304			−1.03843
$447$		−	19.2878i		−	0.912280i
$448$		−	69.9094i		−	3.30291i
$449$	−0.906478			−0.0427793			−0.0213897	−	0.999771i	$-0.506809\pi$
$449$	−0.906478			−0.0427793			−0.0213897	+	0.999771i	$0.506809\pi$
$450$	−22.7542	+	16.5257i	−1.07264	+	0.779027i
$451$	58.5768			2.75827
$452$		−	90.5136i		−	4.25740i
$453$			19.4555i			0.914100i
$454$	18.5761			0.871821
$455$	7.02487	−	13.7840i	0.329331	−	0.646205i
$456$	−24.2988			−1.13790
$457$			31.0318i			1.45161i	0.687902	+	0.725803i	$0.258532\pi$
$457$			31.0318i			1.45161i	−0.687902	+	0.725803i	$0.741468\pi$
$458$		−	68.9802i		−	3.22323i
$459$	24.2568			1.13221
$460$	−10.6830	−	5.44447i	−0.498097	−	0.253850i
$461$	10.4564			0.487002			0.243501	−	0.969901i	$-0.421704\pi$
$461$	10.4564			0.487002			0.243501	+	0.969901i	$0.421704\pi$
$462$		−	44.1472i		−	2.05391i
$463$			39.3475i			1.82863i	0.404999	+	0.914317i	$0.367272\pi$
$463$			39.3475i			1.82863i	−0.404999	+	0.914317i	$0.632728\pi$
$464$	71.1782			3.30437
$465$	4.39901	+	2.24191i	0.203999	+	0.103966i
$466$	−76.4200			−3.54009
$467$			30.5138i			1.41201i	0.708206	+	0.706005i	$0.249505\pi$
$467$			30.5138i			1.41201i	−0.708206	+	0.706005i	$0.750495\pi$
$468$			21.5045i			0.994046i
$469$	17.6253			0.813862
$470$	9.43009	−	18.5035i	0.434978	−	0.853502i
$471$	8.87570			0.408971
$472$		−	51.8036i		−	2.38445i
$473$			57.8411i			2.65954i
$474$	1.09200			0.0501574
$475$	−8.71515	−	11.9999i	−0.399879	−	0.550594i
$476$	−91.4777			−4.19288
$477$		−	18.2295i		−	0.834671i
$478$			21.9650i			1.00465i
$479$	−3.48339			−0.159160			−0.0795801	−	0.996828i	$-0.525358\pi$
$479$	−3.48339			−0.159160			−0.0795801	+	0.996828i	$0.525358\pi$
$480$	16.3066	−	31.9964i	0.744292	−	1.46043i
$481$	−19.9508			−0.909677
$482$		−	43.9619i		−	2.00241i
$483$		−	3.43840i		−	0.156452i
$484$	−69.0068			−3.13667
$485$	−33.9161	−	17.2850i	−1.54005	−	0.784871i
$486$	43.3131			1.96472
$487$			22.5586i			1.02223i	0.859513	+	0.511114i	$0.170767\pi$
$487$			22.5586i			1.02223i	−0.859513	+	0.511114i	$0.829233\pi$
$488$		−	97.4586i		−	4.41174i
$489$	20.6143			0.932211
$490$	28.4582	+	14.5034i	1.28561	+	0.655197i
$491$	19.8969			0.897935			0.448967	−	0.893548i	$-0.351792\pi$
$491$	19.8969			0.897935			0.448967	+	0.893548i	$0.351792\pi$
$492$			58.9271i			2.65664i
$493$		−	28.0408i		−	1.26289i
$494$	−15.6964			−0.706214
$495$	−10.4751	+	20.5541i	−0.470823	+	0.923836i
$496$	29.4854			1.32393
$497$		−	14.2487i		−	0.639142i
$498$		−	5.21659i		−	0.233761i
$499$	−28.9136			−1.29435			−0.647175	−	0.762342i	$-0.724050\pi$
$499$	−28.9136			−1.29435			−0.647175	+	0.762342i	$0.724050\pi$
$500$	57.5078	−	9.09244i	2.57183	−	0.406626i
$501$	3.61703			0.161597
$502$		−	22.0246i		−	0.983007i
$503$			22.9597i			1.02372i	0.859069	+	0.511860i	$0.171044\pi$
$503$			22.9597i			1.02372i	−0.859069	+	0.511860i	$0.828956\pi$
$504$	−63.3240			−2.82067
$505$	−5.77720	+	11.3359i	−0.257082	+	0.504440i
$506$	−13.6137			−0.605202
$507$			8.67095i			0.385090i
$508$		−	17.9503i		−	0.796416i
$509$	15.8294			0.701627			0.350814	−	0.936445i	$-0.385905\pi$
$509$	15.8294			0.701627			0.350814	+	0.936445i	$0.385905\pi$
$510$	−25.4641	−	12.9775i	−1.12757	−	0.574653i
$511$	−1.32303			−0.0585273
$512$			4.32229i			0.191020i
$513$			14.3768i			0.634751i
$514$	19.0595			0.840678
$515$	−0.842095	−	0.429164i	−0.0371071	−	0.0189112i
$516$	−58.1871			−2.56154
$517$		−	17.0365i		−	0.749266i
$518$		−	95.3803i		−	4.19077i
$519$	−7.73286			−0.339435
$520$	17.2341	−	33.8162i	0.755763	−	1.48294i
$521$	10.3264			0.452410			0.226205	−	0.974080i	$-0.427368\pi$
$521$	10.3264			0.452410			0.226205	+	0.974080i	$0.427368\pi$
$522$		−	31.5140i		−	1.37933i
$523$			13.9385i			0.609488i	0.952434	+	0.304744i	$0.0985709\pi$
$523$			13.9385i			0.609488i	−0.952434	+	0.304744i	$0.901429\pi$
$524$	−42.9170			−1.87484
$525$	9.81122	+	13.5091i	0.428197	+	0.589585i
$526$	49.6820			2.16624
$527$		−	11.6158i		−	0.505993i
$528$		−	59.5133i		−	2.58998i
$529$	21.9397			0.953900
$530$	−23.7188	+	46.5404i	−1.03028	+	2.02159i
$531$	−12.6031			−0.546927
$532$		−	54.2181i		−	2.35065i
$533$			23.4461i			1.01556i
$534$	18.1846			0.786923
$535$	−21.7076	−	11.0630i	−0.938502	−	0.478297i
$536$	43.2401			1.86769
$537$		−	18.8739i		−	0.814471i
$538$			71.1993i			3.06962i
$539$	26.2021			1.12860
$540$	−50.2861	−	25.6277i	−2.16397	−	1.10284i
$541$	14.3426			0.616639			0.308319	−	0.951283i	$-0.400233\pi$
$541$	14.3426			0.616639			0.308319	+	0.951283i	$0.400233\pi$
$542$		−	30.9640i		−	1.33002i
$543$		−	15.6346i		−	0.670945i
$544$	−84.4881			−3.62240
$545$	14.0387	−	27.5463i	0.601351	−	1.17996i
$546$	17.6705			0.756226
$547$		−	8.71359i		−	0.372566i	−0.982496	−	0.186283i	$-0.940356\pi$
$547$		−	8.71359i		−	0.372566i	0.982496	−	0.186283i	$-0.0596442\pi$
$548$		−	112.102i		−	4.78877i
$549$	−23.7103			−1.01193
$550$	53.4867	−	38.8457i	2.28068	−	1.65638i
$551$	16.6195			0.708017
$552$		−	8.43539i		−	0.359034i
$553$			1.50080i			0.0638206i
$554$	9.86593			0.419163
$555$	9.77643	−	19.1831i	0.414986	−	0.814276i
$556$	9.01688			0.382401
$557$			2.39626i			0.101533i	0.998711	+	0.0507664i	$0.0161664\pi$
$557$			2.39626i			0.101533i	−0.998711	+	0.0507664i	$0.983834\pi$
$558$		−	13.0546i		−	0.552644i
$559$	−23.1516			−0.979209
$560$	88.8352	+	45.2739i	3.75397	+	1.91317i
$561$	−23.4453			−0.989863
$562$		−	42.2401i		−	1.78179i
$563$			29.3468i			1.23682i	0.785856	+	0.618410i	$0.212223\pi$
$563$			29.3468i			1.23682i	−0.785856	+	0.618410i	$0.787777\pi$
$564$	17.1384			0.721659
$565$	34.6280	+	17.6477i	1.45681	+	0.742446i
$566$	−27.3782			−1.15079
$567$			5.87596i			0.246767i
$568$		−	34.9562i		−	1.46673i
$569$	−0.943498			−0.0395535			−0.0197767	−	0.999804i	$-0.506296\pi$
$569$	−0.943498			−0.0395535			−0.0197767	+	0.999804i	$0.506296\pi$
$570$	7.69166	−	15.0924i	0.322168	−	0.632150i
$571$	2.76378			0.115660			0.0578302	−	0.998326i	$-0.481582\pi$
$571$	2.76378			0.115660			0.0578302	+	0.998326i	$0.481582\pi$
$572$		−	50.5491i		−	2.11356i
$573$		−	3.20977i		−	0.134090i
$574$	−112.091			−4.67857
$575$	4.16580	−	3.02549i	0.173726	−	0.126172i
$576$	−41.7256			−1.73856
$577$		−	16.9595i		−	0.706033i	−0.935617	−	0.353017i	$-0.885156\pi$
$577$		−	16.9595i		−	0.706033i	0.935617	−	0.353017i	$-0.114844\pi$
$578$			21.5996i			0.898424i
$579$	5.15679			0.214309
$580$	−29.6256	+	58.1306i	−1.23014	+	2.41374i
$581$	7.16946			0.297439
$582$		−	43.4789i		−	1.80226i
$583$			42.8507i			1.77470i
$584$	−3.24578			−0.134311
$585$	−8.22701	−	4.19280i	−0.340145	−	0.173351i
$586$	18.8310			0.777903
$587$			26.3959i			1.08948i	0.838606	+	0.544739i	$0.183371\pi$
$587$			26.3959i			1.08948i	−0.838606	+	0.544739i	$0.816629\pi$
$588$			26.3588i			1.08702i
$589$	6.88460			0.283675
$590$	32.1760	+	16.3982i	1.32467	+	0.675101i
$591$	−5.75429			−0.236700
$592$		−	128.579i		−	5.28456i
$593$		−	41.2596i		−	1.69433i	−0.531330	−	0.847165i	$-0.678307\pi$
$593$		−	41.2596i		−	1.69433i	0.531330	−	0.847165i	$-0.321693\pi$
$594$	−64.0811			−2.62928
$595$	17.8357	−	34.9968i	0.731193	−	1.43473i
$596$	105.582			4.32482
$597$			5.32156i			0.217797i
$598$		−	5.44904i		−	0.222828i
$599$	7.65074			0.312601			0.156300	−	0.987710i	$-0.450043\pi$
$599$	7.65074			0.312601			0.156300	+	0.987710i	$0.450043\pi$
$600$	24.0698	+	33.1418i	0.982645	+	1.35301i
$601$	−39.1676			−1.59768			−0.798839	−	0.601545i	$-0.794552\pi$
$601$	−39.1676			−1.59768			−0.798839	+	0.601545i	$0.794552\pi$
$602$		−	110.683i		−	4.51110i
$603$		−	10.5197i		−	0.428396i
$604$	−106.500			−4.33344
$605$	13.4545	−	26.4001i	0.547003	−	1.07331i
$606$	−14.5321			−0.590325
$607$			42.1375i			1.71031i	0.518375	+	0.855154i	$0.326537\pi$
$607$			42.1375i			1.71031i	−0.518375	+	0.855154i	$0.673463\pi$
$608$		−	50.0754i		−	2.03083i
$609$	−18.7097			−0.758156
$610$	60.5331	+	30.8500i	2.45092	+	1.24908i
$611$	6.81909			0.275871
$612$			54.5986i			2.20702i
$613$		−	4.01513i		−	0.162170i	−0.996707	−	0.0810848i	$-0.974162\pi$
$613$		−	4.01513i		−	0.162170i	0.996707	−	0.0810848i	$-0.0258384\pi$
$614$	−46.1308			−1.86169
$615$	−22.5439	−	11.4892i	−0.909056	−	0.463290i
$616$	148.851			5.99738
$617$			29.0811i			1.17076i	0.810758	+	0.585381i	$0.199055\pi$
$617$			29.0811i			1.17076i	−0.810758	+	0.585381i	$0.800945\pi$
$618$		−	1.07953i		−	0.0434249i
$619$	−30.2752			−1.21686			−0.608432	−	0.793606i	$-0.708201\pi$
$619$	−30.2752			−1.21686			−0.608432	+	0.793606i	$0.708201\pi$
$620$	−12.2723	+	24.0804i	−0.492868	+	0.967093i
$621$	−4.99094			−0.200280
$622$			59.2502i			2.37572i
$623$			24.9921i			1.00129i
$624$	23.8209			0.953600
$625$	−7.73398	+	23.7736i	−0.309359	+	0.950945i
$626$	−37.1357			−1.48424
$627$		−	13.8959i		−	0.554948i
$628$			48.5861i			1.93879i
$629$	−50.6538			−2.01970
$630$	20.0449	−	39.3316i	0.798607	−	1.56701i
$631$	−5.72805			−0.228030			−0.114015	−	0.993479i	$-0.536371\pi$
$631$	−5.72805			−0.228030			−0.114015	+	0.993479i	$0.536371\pi$
$632$			3.68191i			0.146458i
$633$			1.83748i			0.0730335i
$634$	−20.0047			−0.794487
$635$	6.86728	+	3.49983i	0.272520	+	0.138887i
$636$	−43.1070			−1.70931
$637$			10.4877i			0.415538i
$638$			74.0776i			2.93276i
$639$	−8.50436			−0.336427
$640$	39.2588	+	20.0078i	1.55184	+	0.790878i
$641$	23.2121			0.916824			0.458412	−	0.888740i	$-0.348418\pi$
$641$	23.2121			0.916824			0.458412	+	0.888740i	$0.348418\pi$
$642$		−	27.8281i		−	1.09829i
$643$			38.3370i			1.51187i	0.654649	+	0.755933i	$0.272816\pi$
$643$			38.3370i			1.51187i	−0.654649	+	0.755933i	$0.727184\pi$
$644$	18.8220			0.741689
$645$	11.3449	−	22.2607i	0.446706	−	0.876515i
$646$	−39.8522			−1.56796
$647$		−	4.25044i		−	0.167102i	−0.996503	−	0.0835511i	$-0.973374\pi$
$647$		−	4.25044i		−	0.167102i	0.996503	−	0.0835511i	$-0.0266262\pi$
$648$			14.4155i			0.566292i
$649$	29.6251			1.16289
$650$	15.5485	+	21.4087i	0.609861	+	0.839719i
$651$	−7.75045			−0.303764
$652$			112.844i			4.41930i
$653$			31.6602i			1.23896i	0.785012	+	0.619480i	$0.212657\pi$
$653$			31.6602i			1.23896i	−0.785012	+	0.619480i	$0.787343\pi$
$654$	35.3131			1.38085
$655$	8.36767	−	16.4188i	0.326952	−	0.641537i
$656$	−151.105			−5.89967
$657$			0.789652i			0.0308073i
$658$			32.6006i			1.27090i
$659$	4.01189			0.156281			0.0781405	−	0.996942i	$-0.475102\pi$
$659$	4.01189			0.156281			0.0781405	+	0.996942i	$0.475102\pi$
$660$	48.6039	+	24.7704i	1.89190	+	0.964188i
$661$	17.3396			0.674431			0.337216	−	0.941427i	$-0.390515\pi$
$661$	17.3396			0.674431			0.337216	+	0.941427i	$0.390515\pi$
$662$			45.7758i			1.77913i
$663$		−	9.38429i		−	0.364456i
$664$	17.5888			0.682577
$665$	20.7423	+	10.5711i	0.804353	+	0.409929i
$666$	−56.9279			−2.20591
$667$			5.76952i			0.223397i
$668$			19.7998i			0.766077i
$669$	7.77099			0.300444
$670$	−13.6874	+	26.8571i	−0.528792	+	1.03758i
$671$	55.7341			2.15159
$672$			56.3732i			2.17464i
$673$		−	18.6658i		−	0.719515i	−0.933046	−	0.359757i	$-0.882859\pi$
$673$		−	18.6658i		−	0.719515i	0.933046	−	0.359757i	$-0.117141\pi$
$674$	−5.40491			−0.208189
$675$	19.6089	−	14.2413i	0.754746	−	0.548148i
$676$	−47.4652			−1.82559
$677$			10.5332i			0.404823i	0.979301	+	0.202411i	$0.0648778\pi$
$677$			10.5332i			0.404823i	−0.979301	+	0.202411i	$0.935122\pi$
$678$			44.3914i			1.70484i
$679$	59.7555			2.29321
$680$	43.7562	−	85.8573i	1.67797	−	3.29248i
$681$	−6.58243			−0.252239
$682$			30.6864i			1.17504i
$683$			16.1414i			0.617634i	0.951122	+	0.308817i	$0.0999330\pi$
$683$			16.1414i			0.617634i	−0.951122	+	0.308817i	$0.900067\pi$
$684$	−32.3602			−1.23732
$685$	42.8871	+	21.8569i	1.63863	+	0.835110i
$686$	15.8249			0.604199
$687$			24.4430i			0.932559i
$688$		−	149.208i		−	5.68848i
$689$	−17.1515			−0.653421
$690$	5.23936	+	2.67018i	0.199459	+	0.101652i
$691$	−20.5844			−0.783068			−0.391534	−	0.920164i	$-0.628055\pi$
$691$	−20.5844			−0.783068			−0.391534	+	0.920164i	$0.628055\pi$
$692$		−	42.3301i		−	1.60915i
$693$		−	36.2134i		−	1.37563i
$694$	−39.4105			−1.49600
$695$	−1.75805	+	3.44960i	−0.0666867	+	0.130851i
$696$	−45.9004			−1.73985
$697$			59.5282i			2.25479i
$698$		−	82.3017i		−	3.11516i
$699$	27.0793			1.02423
$700$	−73.9495	+	53.7071i	−2.79503	+	2.02994i
$701$	11.7943			0.445466			0.222733	−	0.974880i	$-0.428502\pi$
$701$	11.7943			0.445466			0.222733	+	0.974880i	$0.428502\pi$
$702$		−	25.6492i		−	0.968068i
$703$		−	30.0221i		−	1.13231i
$704$	98.0812			3.69657
$705$	−3.34154	+	6.55668i	−0.125850	+	0.246939i
$706$	−34.4626			−1.29702
$707$		−	19.9722i		−	0.751134i
$708$			29.8023i			1.12004i
$709$	13.9558			0.524119			0.262060	−	0.965052i	$-0.415598\pi$
$709$	13.9558			0.524119			0.262060	+	0.965052i	$0.415598\pi$
$710$	21.7119	+	11.0652i	0.814832	+	0.415270i
$711$	0.895756			0.0335935
$712$			61.3128i			2.29780i
$713$			2.39001i			0.0895064i
$714$	44.8642			1.67900
$715$	19.3386	+	9.85572i	0.723224	+	0.368583i
$716$	103.317			3.86114
$717$		−	7.78326i		−	0.290671i
$718$		−	41.9269i		−	1.56470i
$719$	29.2684			1.09153			0.545764	−	0.837939i	$-0.316239\pi$
$719$	29.2684			1.09153			0.545764	+	0.837939i	$0.316239\pi$
$720$	27.0218	−	53.0215i	1.00704	−	1.97599i
$721$	1.48365			0.0552542
$722$			27.3890i			1.01931i
$723$			15.5778i			0.579346i
$724$	85.5846			3.18073
$725$	−16.4629	−	22.6678i	−0.611417	−	0.841862i
$726$	33.8436			1.25605
$727$		−	47.8606i		−	1.77505i	−0.460758	−	0.887526i	$-0.652422\pi$
$727$		−	47.8606i		−	1.77505i	0.460758	−	0.887526i	$-0.347578\pi$
$728$			59.5795i			2.20816i
$729$	−10.3259			−0.382439
$730$	1.02743	−	2.01600i	0.0380270	−	0.0746157i
$731$	−58.7805			−2.17408
$732$			56.0675i			2.07231i
$733$		−	31.8197i		−	1.17529i	−0.809120	−	0.587644i	$-0.800056\pi$
$733$		−	31.8197i		−	1.17529i	0.809120	−	0.587644i	$-0.199944\pi$
$734$	−70.0124			−2.58420
$735$	−10.0841	−	5.13926i	−0.371959	−	0.189565i
$736$	17.3838			0.640776
$737$			24.7279i			0.910864i
$738$			66.9014i			2.46268i
$739$	−26.2155			−0.964354			−0.482177	−	0.876074i	$-0.660154\pi$
$739$	−26.2155			−0.964354			−0.482177	+	0.876074i	$0.660154\pi$
$740$	105.009	+	53.5167i	3.86021	+	1.96731i
$741$	5.56199			0.204325
$742$		−	81.9977i		−	3.01023i
$743$		−	8.18860i		−	0.300411i	−0.988655	−	0.150205i	$-0.952007\pi$
$743$		−	8.18860i		−	0.300411i	0.988655	−	0.150205i	$-0.0479935\pi$
$744$	−19.0141			−0.697091
$745$	−20.5857	+	40.3928i	−0.754203	+	1.47988i
$746$	12.0396			0.440801
$747$		−	4.27910i		−	0.156564i
$748$		−	128.341i		−	4.69261i
$749$	38.2458			1.39747
$750$	−28.2041	+	4.45929i	−1.02987	+	0.162830i
$751$	36.0551			1.31567			0.657835	−	0.753162i	$-0.271472\pi$
$751$	36.0551			1.31567			0.657835	+	0.753162i	$0.271472\pi$
$752$			43.9477i			1.60261i
$753$			7.80439i			0.284408i
$754$	−29.6505			−1.07981
$755$	20.7647	−	40.7441i	0.755706	−	1.48283i
$756$	88.5971			3.22224
$757$			4.45517i			0.161926i	0.996717	+	0.0809629i	$0.0257995\pi$
$757$			4.45517i			0.161926i	−0.996717	+	0.0809629i	$0.974200\pi$
$758$			56.2270i			2.04226i
$759$	4.82399			0.175100
$760$	50.8870	+	25.9340i	1.84586	+	0.940724i
$761$	−22.8677			−0.828955			−0.414477	−	0.910060i	$-0.636036\pi$
$761$	−22.8677			−0.828955			−0.414477	+	0.910060i	$0.636036\pi$
$762$			8.80353i			0.318918i
$763$			48.5328i			1.75701i
$764$	17.5705			0.635677
$765$	−20.8879	−	10.6453i	−0.755203	−	0.384881i
$766$	2.68469			0.0970017
$767$			11.8578i			0.428161i
$768$			12.4337i			0.448664i
$769$	31.5666			1.13832			0.569160	−	0.822227i	$-0.307269\pi$
$769$	31.5666			1.13832			0.569160	+	0.822227i	$0.307269\pi$
$770$	−47.1180	+	92.4538i	−1.69802	+	3.33180i
$771$	−6.75370			−0.243229
$772$			28.2285i			1.01597i
$773$			3.63008i			0.130565i	0.997867	+	0.0652824i	$0.0207948\pi$
$773$			3.63008i			0.130565i	−0.997867	+	0.0652824i	$0.979205\pi$
$774$	−66.0612			−2.37452
$775$	−6.81971	−	9.39008i	−0.244971	−	0.337302i
$776$	146.598			5.26255
$777$			33.7979i			1.21249i
$778$		−	43.1491i		−	1.54697i
$779$	−35.2819			−1.26410
$780$	−9.91467	+	19.4543i	−0.355002	+	0.696576i
$781$	19.9906			0.715319
$782$		−	13.8348i		−	0.494731i
$783$			27.1578i			0.970539i
$784$	−67.5912			−2.41397
$785$	−18.5876	−	9.47299i	−0.663422	−	0.338105i
$786$	21.0482			0.750763
$787$			28.6941i			1.02283i	0.859332	+	0.511417i	$0.170879\pi$
$787$			28.6941i			1.02283i	−0.859332	+	0.511417i	$0.829121\pi$
$788$		−	31.4993i		−	1.12211i
$789$	−17.6047			−0.626745
$790$	−2.28689	−	1.16549i	−0.0813640	−	0.0414662i
$791$	−61.0096			−2.16925
$792$		−	88.8420i		−	3.15686i
$793$			22.3083i			0.792190i
$794$	−18.1290			−0.643373
$795$	8.40472	−	16.4915i	0.298085	−	0.584894i
$796$	−29.1305			−1.03250
$797$			29.2770i			1.03704i	0.855065	+	0.518521i	$0.173517\pi$
$797$			29.2770i			1.03704i	−0.855065	+	0.518521i	$0.826483\pi$
$798$			26.5907i			0.941300i
$799$	17.3132			0.612499
$800$	−68.2992	+	49.6035i	−2.41474	+	1.75375i
$801$	14.9166			0.527051
$802$		−	76.3939i		−	2.69756i
$803$		−	1.85618i		−	0.0655031i
$804$	−24.8758			−0.877303
$805$	−3.66978	+	7.20075i	−0.129343	+	0.253793i
$806$	−12.2826			−0.432637
$807$		−	25.2294i		−	0.888115i
$808$		−	48.9977i		−	1.72373i
$809$	18.6448			0.655517			0.327759	−	0.944762i	$-0.393707\pi$
$809$	18.6448			0.655517			0.327759	+	0.944762i	$0.393707\pi$
$810$	−8.95367	−	4.56314i	−0.314600	−	0.160332i
$811$	54.1968			1.90311			0.951554	−	0.307482i	$-0.0994863\pi$
$811$	54.1968			1.90311			0.951554	+	0.307482i	$0.0994863\pi$
$812$		−	102.418i		−	3.59417i
$813$			10.9721i			0.384807i
$814$	133.816			4.69026
$815$	−43.1708	−	22.0015i	−1.51221	−	0.770680i
$816$	60.4799			2.11722
$817$		−	34.8388i		−	1.21885i
$818$			13.0397i			0.455923i
$819$	14.4949			0.506491
$820$	62.8926	−	123.406i	2.19630	−	4.30953i
$821$	−38.6870			−1.35019			−0.675093	−	0.737733i	$-0.735896\pi$
$821$	−38.6870			−1.35019			−0.675093	+	0.737733i	$0.735896\pi$
$822$			54.9792i			1.91762i
$823$		−	40.3106i		−	1.40514i	−0.711615	−	0.702570i	$-0.752036\pi$
$823$		−	40.3106i		−	1.40514i	0.711615	−	0.702570i	$-0.247964\pi$
$824$	3.63984			0.126800
$825$	−18.9529	+	13.7649i	−0.659856	+	0.479232i
$826$	−56.6897			−1.97249
$827$			36.4492i			1.26746i	0.773553	+	0.633731i	$0.218477\pi$
$827$			36.4492i			1.26746i	−0.773553	+	0.633731i	$0.781523\pi$
$828$		−	11.2339i		−	0.390406i
$829$	21.9158			0.761168			0.380584	−	0.924746i	$-0.375723\pi$
$829$	21.9158			0.761168			0.380584	+	0.924746i	$0.375723\pi$
$830$	−5.56764	+	10.9247i	−0.193256	+	0.379201i
$831$	−3.49598			−0.121274
$832$			39.2582i			1.36103i
$833$			26.6276i			0.922593i
$834$	−4.42223			−0.153129
$835$	−7.57484	−	3.86043i	−0.262138	−	0.133596i
$836$	76.0667			2.63082
$837$			11.2500i			0.388858i
$838$		−	57.1177i		−	1.97310i
$839$	−6.75410			−0.233177			−0.116589	−	0.993180i	$-0.537196\pi$
$839$	−6.75410			−0.233177			−0.116589	+	0.993180i	$0.537196\pi$
$840$	−57.2868	−	29.1956i	−1.97658	−	1.00734i
$841$	2.39430			0.0825621
$842$			7.09243i			0.244421i
$843$			14.9677i			0.515515i
$844$	−10.0585			−0.346227
$845$	9.25445	−	18.1589i	0.318363	−	0.624683i
$846$	19.4577			0.668970
$847$			46.5132i			1.59821i
$848$		−	110.538i		−	3.79590i
$849$	9.70141			0.332952
$850$	39.4766	+	54.3554i	1.35404	+	1.86438i
$851$	10.4223			0.357270
$852$			20.1101i			0.688962i
$853$			30.1503i			1.03233i	0.856491	+	0.516163i	$0.172640\pi$
$853$			30.1503i			1.03233i	−0.856491	+	0.516163i	$0.827360\pi$
$854$	−106.651			−3.64952
$855$	6.30937	−	12.3801i	0.215776	−	0.423390i
$856$	93.8281			3.20698
$857$			18.6751i			0.637928i	0.947767	+	0.318964i	$0.103335\pi$
$857$			18.6751i			0.637928i	−0.947767	+	0.318964i	$0.896665\pi$
$858$			24.7912i			0.846358i
$859$	−38.9335			−1.32839			−0.664197	−	0.747558i	$-0.731226\pi$
$859$	−38.9335			−1.32839			−0.664197	+	0.747558i	$0.731226\pi$
$860$	121.856	+	62.1027i	4.15527	+	2.11769i
$861$	39.7191			1.35362
$862$			29.2041i			0.994695i
$863$			10.2262i			0.348103i	0.984737	+	0.174051i	$0.0556859\pi$
$863$			10.2262i			0.348103i	−0.984737	+	0.174051i	$0.944314\pi$
$864$	81.8276			2.78383
$865$	16.1943	+	8.25323i	0.550622	+	0.280618i
$866$	−24.8711			−0.845153
$867$		−	7.65378i		−	0.259936i
$868$		−	42.4264i		−	1.44004i
$869$	−2.10559			−0.0714272
$870$	14.5295	−	28.5095i	0.492598	−	0.966562i
$871$	−9.89765			−0.335369
$872$			119.065i			4.03206i
$873$		−	35.6652i		−	1.20708i
$874$	8.19977			0.277361
$875$	−6.12865	−	38.7624i	−0.207186	−	1.31041i
$876$	1.86728			0.0630895
$877$		−	25.0694i		−	0.846533i	−0.906005	−	0.423267i	$-0.860883\pi$
$877$		−	25.0694i		−	0.846533i	0.906005	−	0.423267i	$-0.139117\pi$
$878$			51.1760i			1.72711i
$879$	−6.67275			−0.225066
$880$	−63.5181	+	124.634i	−2.14120	+	4.20140i
$881$	17.8794			0.602372			0.301186	−	0.953565i	$-0.402618\pi$
$881$	17.8794			0.602372			0.301186	+	0.953565i	$0.402618\pi$
$882$			29.9258i			1.00765i
$883$			36.2131i			1.21867i	0.792914	+	0.609334i	$0.208563\pi$
$883$			36.2131i			1.21867i	−0.792914	+	0.609334i	$0.791437\pi$
$884$	51.3701			1.72776
$885$	−11.4015	−	5.81066i	−0.383258	−	0.195323i
$886$	−104.183			−3.50008
$887$			46.2703i			1.55361i	0.629744	+	0.776803i	$0.283160\pi$
$887$			46.2703i			1.55361i	−0.629744	+	0.776803i	$0.716840\pi$
$888$			82.9161i			2.78248i
$889$	−12.0992			−0.405794
$890$	−38.0824	−	19.4083i	−1.27653	−	0.650567i
$891$	−8.24383			−0.276179
$892$			42.5388i			1.42430i
$893$			10.2614i			0.343386i
$894$	−51.7817			−1.73184
$895$	−20.1441	+	39.5261i	−0.673341	+	1.32121i
$896$	−69.1685			−2.31076
$897$			1.93086i			0.0644695i
$898$			2.43361i			0.0812106i
$899$	13.0050			0.433741
$900$	32.0552	+	44.1369i	1.06851	+	1.47123i
$901$	−43.5467			−1.45075
$902$		−	157.260i		−	5.23620i
$903$			39.2203i			1.30517i
$904$	−149.674			−4.97810
$905$	−16.6867	+	32.7422i	−0.554685	+	1.08839i
$906$	52.2320			1.73529
$907$		−	26.1644i		−	0.868773i	−0.900726	−	0.434387i	$-0.856965\pi$
$907$		−	26.1644i		−	0.868773i	0.900726	−	0.434387i	$-0.143035\pi$
$908$		−	36.0325i		−	1.19578i
$909$	−11.9205			−0.395377
$910$	−37.0058	−	18.8596i	−1.22673	−	0.625189i
$911$	−17.4349			−0.577645			−0.288823	−	0.957383i	$-0.593264\pi$
$911$	−17.4349			−0.577645			−0.288823	+	0.957383i	$0.593264\pi$
$912$			35.8459i			1.18698i
$913$			10.0586i			0.332890i
$914$	83.3107			2.75567
$915$	−21.4498	−	10.9317i	−0.709109	−	0.361390i
$916$	−133.802			−4.42095
$917$			28.9277i			0.955276i
$918$		−	65.1219i		−	2.14934i
$919$	−21.3770			−0.705161			−0.352580	−	0.935782i	$-0.614696\pi$
$919$	−21.3770			−0.705161			−0.352580	+	0.935782i	$0.614696\pi$
$920$	−9.00304	+	17.6655i	−0.296821	+	0.582415i
$921$	16.3464			0.538632
$922$		−	28.0721i		−	0.924505i
$923$			8.00147i			0.263372i
$924$	−85.6333			−2.81713
$925$	−40.9479	+	29.7392i	−1.34636	+	0.977818i
$926$	105.636			3.47141
$927$		−	0.885521i		−	0.0290843i
$928$		−	94.5924i		−	3.10515i
$929$	31.4460			1.03171			0.515854	−	0.856676i	$-0.327475\pi$
$929$	31.4460			1.03171			0.515854	+	0.856676i	$0.327475\pi$
$930$	6.01882	−	11.8100i	0.197365	−	0.387264i
$931$	−15.7820			−0.517234
$932$			148.234i			4.85555i
$933$		−	20.9952i		−	0.687353i
$934$	81.9200			2.68051
$935$	49.0996	+	25.0231i	1.60573	+	0.818342i
$936$	35.5601			1.16232
$937$			0.369082i			0.0120574i	0.999982	+	0.00602869i	$0.00191900\pi$
$937$			0.369082i			0.0120574i	−0.999982	+	0.00602869i	$0.998081\pi$
$938$		−	47.3185i		−	1.54500i
$939$	13.1590			0.429428
$940$	−35.8916	−	18.2918i	−1.17066	−	0.596611i
$941$	15.0915			0.491970			0.245985	−	0.969274i	$-0.420889\pi$
$941$	15.0915			0.491970			0.245985	+	0.969274i	$0.420889\pi$
$942$		−	23.8285i		−	0.776374i
$943$		−	12.2482i		−	0.398856i
$944$	−76.4213			−2.48730
$945$	−17.2741	+	33.8947i	−0.561925	+	1.10260i
$946$	155.285			5.04876
$947$		−	15.5802i		−	0.506289i	−0.967429	−	0.253144i	$-0.918535\pi$
$947$		−	15.5802i		−	0.506289i	0.967429	−	0.253144i	$-0.0814647\pi$
$948$		−	2.11818i		−	0.0687954i
$949$	0.742958			0.0241174
$950$	−32.2160	+	23.3975i	−1.04523	+	0.759114i
$951$	7.08863			0.229865
$952$			151.269i			4.90265i
$953$		−	7.81036i		−	0.253002i	−0.991966	−	0.126501i	$-0.959625\pi$
$953$		−	7.81036i		−	0.253002i	0.991966	−	0.126501i	$-0.0403748\pi$
$954$	−48.9405			−1.58451
$955$	−3.42577	+	6.72196i	−0.110855	+	0.217517i
$956$	42.6060			1.37797
$957$		−	26.2493i		−	0.848519i
$958$			9.35182i			0.302143i
$959$	−75.5611			−2.43999
$960$	−37.7475	−	19.2376i	−1.21830	−	0.620891i
$961$	−25.6127			−0.826217
$962$			53.5616i			1.72690i
$963$		−	22.8271i		−	0.735592i
$964$	−85.2739			−2.74649
$965$	−10.7994	−	5.50381i	−0.347646	−	0.177174i
$966$	−9.23102			−0.297003
$967$			25.3357i			0.814742i	0.913263	+	0.407371i	$0.133554\pi$
$967$			25.3357i			0.814742i	−0.913263	+	0.407371i	$0.866446\pi$
$968$			114.110i			3.66765i
$969$	14.1216			0.453650
$970$	−46.4048	+	91.0543i	−1.48997	+	2.92358i
$971$	26.0874			0.837186			0.418593	−	0.908174i	$-0.362523\pi$
$971$	26.0874			0.837186			0.418593	+	0.908174i	$0.362523\pi$
$972$		−	84.0153i		−	2.69479i
$973$		−	6.07772i		−	0.194843i
$974$	60.5628			1.94056
$975$	−5.50957	−	7.58614i	−0.176448	−	0.242951i
$976$	−143.772			−4.60204
$977$			32.5265i			1.04062i	0.853979	+	0.520308i	$0.174183\pi$
$977$			32.5265i			1.04062i	−0.853979	+	0.520308i	$0.825817\pi$
$978$		−	55.3430i		−	1.76967i
$979$	−35.0633			−1.12063
$980$	28.1326	−	55.2010i	0.898663	−	1.76333i
$981$	28.9669			0.924842
$982$		−	53.4170i		−	1.70460i
$983$		−	10.9881i		−	0.350465i	−0.984527	−	0.175232i	$-0.943932\pi$
$983$		−	10.9881i		−	0.350465i	0.984527	−	0.175232i	$-0.0560677\pi$
$984$	97.4426			3.10636
$985$	12.0507	+	6.14151i	0.383968	+	0.195685i
$986$	−75.2807			−2.39743
$987$		−	11.5520i		−	0.367703i
$988$			30.4466i			0.968636i
$989$	12.0944			0.384578
$990$	55.1812	+	28.1225i	1.75377	+	0.893791i
$991$	−11.2414			−0.357094			−0.178547	−	0.983931i	$-0.557140\pi$
$991$	−11.2414			−0.357094			−0.178547	+	0.983931i	$0.557140\pi$
$992$		−	39.1846i		−	1.24411i
$993$		−	16.2206i		−	0.514745i
$994$	−38.2533			−1.21332
$995$	5.67967	−	11.1445i	0.180058	−	0.353304i
$996$	−10.1187			−0.320625
$997$			9.71011i			0.307522i	0.988108	+	0.153761i	$0.0491386\pi$
$997$			9.71011i			0.307522i	−0.988108	+	0.153761i	$0.950861\pi$
$998$			77.6239i			2.45714i
$999$	49.0587			1.55215

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1915.2.c.a.384.5	✓	190
5.2	odd	4		9575.2.a.m.1.94		95
5.3	odd	4		9575.2.a.n.1.2		95
5.4	even	2	inner	1915.2.c.a.384.186	yes	190

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1915.2.c.a.384.5	✓	190	1.1	even	1	trivial
1915.2.c.a.384.186	yes	190	5.4	even	2	inner
9575.2.a.m.1.94		95	5.2	odd	4
9575.2.a.n.1.2		95	5.3	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:	\( N \)	\(=\)	\( 1915 = 5 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1915.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.68469i q^{2} +0.951315i q^{3} -5.20755 q^{4} +(1.01533 - 1.99226i) q^{5} +2.55398 q^{6} +3.51008i q^{7} +8.61126i q^{8} +2.09500 q^{9} +O(q^{10})\)	\(q-2.68469i q^{2} +0.951315i q^{3} -5.20755 q^{4} +(1.01533 - 1.99226i) q^{5} +2.55398 q^{6} +3.51008i q^{7} +8.61126i q^{8} +2.09500 q^{9} +(-5.34860 - 2.72585i) q^{10} -4.92456 q^{11} -4.95402i q^{12} -1.97112i q^{13} +9.42348 q^{14} +(1.89527 + 0.965901i) q^{15} +12.7035 q^{16} -5.00455i q^{17} -5.62442i q^{18} +2.96615 q^{19} +(-5.28739 + 10.3748i) q^{20} -3.33920 q^{21} +13.2209i q^{22} +1.02971i q^{23} -8.19202 q^{24} +(-2.93820 - 4.04561i) q^{25} -5.29183 q^{26} +4.84695i q^{27} -18.2789i q^{28} +5.60306 q^{29} +(2.59314 - 5.08820i) q^{30} +2.32105 q^{31} -16.8823i q^{32} -4.68481i q^{33} -13.4356 q^{34} +(6.99300 + 3.56390i) q^{35} -10.9098 q^{36} -10.1216i q^{37} -7.96320i q^{38} +1.87515 q^{39} +(17.1559 + 8.74330i) q^{40} -11.8948 q^{41} +8.96470i q^{42} -11.7454i q^{43} +25.6449 q^{44} +(2.12712 - 4.17378i) q^{45} +2.76444 q^{46} +3.45950i q^{47} +12.0850i q^{48} -5.32069 q^{49} +(-10.8612 + 7.88815i) q^{50} +4.76090 q^{51} +10.2647i q^{52} -8.70143i q^{53} +13.0125 q^{54} +(-5.00007 + 9.81101i) q^{55} -30.2263 q^{56} +2.82175i q^{57} -15.0425i q^{58} -6.01579 q^{59} +(-9.86969 - 5.02998i) q^{60} -11.3176 q^{61} -6.23130i q^{62} +7.35363i q^{63} -19.9167 q^{64} +(-3.92698 - 2.00134i) q^{65} -12.5773 q^{66} -5.02134i q^{67} +26.0614i q^{68} -0.979577 q^{69} +(9.56797 - 18.7740i) q^{70} -4.05936 q^{71} +18.0406i q^{72} +0.376922i q^{73} -27.1732 q^{74} +(3.84865 - 2.79515i) q^{75} -15.4464 q^{76} -17.2856i q^{77} -5.03420i q^{78} +0.427569 q^{79} +(12.8982 - 25.3086i) q^{80} +1.67402 q^{81} +31.9339i q^{82} -2.04253i q^{83} +17.3890 q^{84} +(-9.97036 - 5.08128i) q^{85} -31.5328 q^{86} +5.33028i q^{87} -42.4067i q^{88} +7.12008 q^{89} +(-11.2053 - 5.71066i) q^{90} +6.91878 q^{91} -5.36225i q^{92} +2.20805i q^{93} +9.28769 q^{94} +(3.01163 - 5.90935i) q^{95} +16.0604 q^{96} -17.0240i q^{97} +14.2844i q^{98} -10.3170 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 190 q - 188 q^{4} - 4 q^{6} - 186 q^{9}+O(q^{10}) \) 190 * q - 188 * q^4 - 4 * q^6 - 186 * q^9	\( 190 q - 188 q^{4} - 4 q^{6} - 186 q^{9} - 6 q^{10} - 4 q^{11} + 12 q^{14} - 8 q^{15} + 192 q^{16} + 8 q^{19} - 24 q^{20} + 40 q^{24} - 4 q^{25} + 16 q^{26} + 8 q^{29} - 6 q^{30} - 12 q^{31} + 4 q^{35} + 136 q^{36} + 8 q^{39} + 12 q^{40} - 16 q^{41} - 16 q^{44} - 12 q^{45} - 154 q^{49} - 2 q^{50} + 16 q^{51} + 16 q^{54} + 4 q^{55} - 28 q^{59} + 34 q^{60} - 20 q^{61} - 204 q^{64} - 12 q^{65} + 40 q^{66} + 28 q^{69} + 2 q^{70} - 24 q^{71} - 20 q^{74} + 22 q^{75} - 64 q^{76} - 12 q^{79} + 46 q^{80} + 142 q^{81} - 8 q^{84} + 8 q^{85} + 12 q^{86} + 28 q^{89} + 32 q^{90} + 28 q^{91} + 16 q^{94} + 28 q^{95} - 84 q^{96} - 20 q^{99}+O(q^{100}) \) 190 * q - 188 * q^4 - 4 * q^6 - 186 * q^9 - 6 * q^10 - 4 * q^11 + 12 * q^14 - 8 * q^15 + 192 * q^16 + 8 * q^19 - 24 * q^20 + 40 * q^24 - 4 * q^25 + 16 * q^26 + 8 * q^29 - 6 * q^30 - 12 * q^31 + 4 * q^35 + 136 * q^36 + 8 * q^39 + 12 * q^40 - 16 * q^41 - 16 * q^44 - 12 * q^45 - 154 * q^49 - 2 * q^50 + 16 * q^51 + 16 * q^54 + 4 * q^55 - 28 * q^59 + 34 * q^60 - 20 * q^61 - 204 * q^64 - 12 * q^65 + 40 * q^66 + 28 * q^69 + 2 * q^70 - 24 * q^71 - 20 * q^74 + 22 * q^75 - 64 * q^76 - 12 * q^79 + 46 * q^80 + 142 * q^81 - 8 * q^84 + 8 * q^85 + 12 * q^86 + 28 * q^89 + 32 * q^90 + 28 * q^91 + 16 * q^94 + 28 * q^95 - 84 * q^96 - 20 * q^99

Introduction

L-functions

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