LMFDB - Embedded newform 690.2.d.d.139.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(139,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, 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("690.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.5161984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 4x^{3} + 25x^{2} - 20x + 8 $ x^6 - 4x^3 + 25x^2 - 20*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.3
Root			$1.32001 - 1.32001i$ of defining polynomial
Character	$\chi$	$=$	690.139
Dual form			690.2.d.d.139.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(1.32001 + 1.80487i) q^{5} -1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(1.32001 + 1.80487i) q^{5} -1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(1.80487 - 1.32001i) q^{10} -2.64002 q^{11} +1.00000i q^{12} +4.24977i q^{13} +2.00000 q^{14} +(1.80487 - 1.32001i) q^{15} +1.00000 q^{16} +6.24977i q^{17} +1.00000i q^{18} -3.67030 q^{19} +(-1.32001 - 1.80487i) q^{20} +2.00000 q^{21} +2.64002i q^{22} -1.00000i q^{23} +1.00000 q^{24} +(-1.51514 + 4.76491i) q^{25} +4.24977 q^{26} +1.00000i q^{27} -2.00000i q^{28} +2.00000 q^{29} +(-1.32001 - 1.80487i) q^{30} +2.96972 q^{31} -1.00000i q^{32} +2.64002i q^{33} +6.24977 q^{34} +(-3.60975 + 2.64002i) q^{35} +1.00000 q^{36} +3.35998i q^{37} +3.67030i q^{38} +4.24977 q^{39} +(-1.80487 + 1.32001i) q^{40} -6.24977 q^{41} -2.00000i q^{42} +0.640023i q^{43} +2.64002 q^{44} +(-1.32001 - 1.80487i) q^{45} -1.00000 q^{46} -4.24977i q^{47} -1.00000i q^{48} +3.00000 q^{49} +(4.76491 + 1.51514i) q^{50} +6.24977 q^{51} -4.24977i q^{52} -12.8898i q^{53} +1.00000 q^{54} +(-3.48486 - 4.76491i) q^{55} -2.00000 q^{56} +3.67030i q^{57} -2.00000i q^{58} +8.31032 q^{59} +(-1.80487 + 1.32001i) q^{60} +11.8595 q^{61} -2.96972i q^{62} -2.00000i q^{63} -1.00000 q^{64} +(-7.67030 + 5.60975i) q^{65} +2.64002 q^{66} +11.8595i q^{67} -6.24977i q^{68} -1.00000 q^{69} +(2.64002 + 3.60975i) q^{70} +7.52982 q^{71} -1.00000i q^{72} -9.03028i q^{73} +3.35998 q^{74} +(4.76491 + 1.51514i) q^{75} +3.67030 q^{76} -5.28005i q^{77} -4.24977i q^{78} -9.52982 q^{79} +(1.32001 + 1.80487i) q^{80} +1.00000 q^{81} +6.24977i q^{82} -17.2001i q^{83} -2.00000 q^{84} +(-11.2800 + 8.24977i) q^{85} +0.640023 q^{86} -2.00000i q^{87} -2.64002i q^{88} +11.2195 q^{89} +(-1.80487 + 1.32001i) q^{90} -8.49954 q^{91} +1.00000i q^{92} -2.96972i q^{93} -4.24977 q^{94} +(-4.84484 - 6.62443i) q^{95} -1.00000 q^{96} +18.4995i q^{97} -3.00000i q^{98} +2.64002 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9	$ 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} + 12 q^{14} + 2 q^{15} + 6 q^{16} - 8 q^{19} + 12 q^{21} + 6 q^{24} - 10 q^{25} - 8 q^{26} + 12 q^{29} + 16 q^{31} + 4 q^{34} - 4 q^{35} + 6 q^{36} - 8 q^{39} - 2 q^{40} - 4 q^{41} - 6 q^{46} + 18 q^{49} - 4 q^{50} + 4 q^{51} + 6 q^{54} - 20 q^{55} - 12 q^{56} + 20 q^{59} - 2 q^{60} + 20 q^{61} - 6 q^{64} - 32 q^{65} - 6 q^{69} - 20 q^{71} + 36 q^{74} - 4 q^{75} + 8 q^{76} + 8 q^{79} + 6 q^{81} - 12 q^{84} - 36 q^{85} - 12 q^{86} + 32 q^{89} - 2 q^{90} + 16 q^{91} + 8 q^{94} - 44 q^{95} - 6 q^{96}+O(q^{100}) $ 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 + 12 * q^14 + 2 * q^15 + 6 * q^16 - 8 * q^19 + 12 * q^21 + 6 * q^24 - 10 * q^25 - 8 * q^26 + 12 * q^29 + 16 * q^31 + 4 * q^34 - 4 * q^35 + 6 * q^36 - 8 * q^39 - 2 * q^40 - 4 * q^41 - 6 * q^46 + 18 * q^49 - 4 * q^50 + 4 * q^51 + 6 * q^54 - 20 * q^55 - 12 * q^56 + 20 * q^59 - 2 * q^60 + 20 * q^61 - 6 * q^64 - 32 * q^65 - 6 * q^69 - 20 * q^71 + 36 * q^74 - 4 * q^75 + 8 * q^76 + 8 * q^79 + 6 * q^81 - 12 * q^84 - 36 * q^85 - 12 * q^86 + 32 * q^89 - 2 * q^90 + 16 * q^91 + 8 * q^94 - 44 * q^95 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.00000			−0.500000
$5$	1.32001	+	1.80487i	0.590327	+	0.807164i
$5$	1.32001	+	1.80487i	0.590327	+	0.807164i
$6$	−1.00000			−0.408248
$7$			2.00000i			0.755929i	0.925820	+	0.377964i	$0.123376\pi$
$7$			2.00000i			0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$			1.00000i			0.353553i
$9$	−1.00000			−0.333333
$10$	1.80487	−	1.32001i	0.570751	−	0.417424i
$11$	−2.64002			−0.795997			−0.397999	−	0.917386i	$-0.630295\pi$
$11$	−2.64002			−0.795997			−0.397999	+	0.917386i	$0.630295\pi$
$12$			1.00000i			0.288675i
$13$			4.24977i			1.17867i	0.807887	+	0.589337i	$0.200611\pi$
$13$			4.24977i			1.17867i	−0.807887	+	0.589337i	$0.799389\pi$
$14$	2.00000			0.534522
$15$	1.80487	−	1.32001i	0.466016	−	0.340826i
$16$	1.00000			0.250000
$17$			6.24977i			1.51579i	0.652375	+	0.757896i	$0.273773\pi$
$17$			6.24977i			1.51579i	−0.652375	+	0.757896i	$0.726227\pi$
$18$			1.00000i			0.235702i
$19$	−3.67030			−0.842024			−0.421012	−	0.907055i	$-0.638325\pi$
$19$	−3.67030			−0.842024			−0.421012	+	0.907055i	$0.638325\pi$
$20$	−1.32001	−	1.80487i	−0.295164	−	0.403582i
$21$	2.00000			0.436436
$22$			2.64002i			0.562855i
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$	1.00000			0.204124
$25$	−1.51514	+	4.76491i	−0.303028	+	0.952982i
$26$	4.24977			0.833449
$27$			1.00000i			0.192450i
$28$		−	2.00000i		−	0.377964i
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$	−1.32001	−	1.80487i	−0.241000	−	0.329523i
$31$	2.96972			0.533378			0.266689	−	0.963783i	$-0.414070\pi$
$31$	2.96972			0.533378			0.266689	+	0.963783i	$0.414070\pi$
$32$		−	1.00000i		−	0.176777i
$33$			2.64002i			0.459569i
$34$	6.24977			1.07183
$35$	−3.60975	+	2.64002i	−0.610159	+	0.446245i
$36$	1.00000			0.166667
$37$			3.35998i			0.552377i	0.961104	+	0.276188i	$0.0890714\pi$
$37$			3.35998i			0.552377i	−0.961104	+	0.276188i	$0.910929\pi$
$38$			3.67030i			0.595401i
$39$	4.24977			0.680508
$40$	−1.80487	+	1.32001i	−0.285376	+	0.208712i
$41$	−6.24977			−0.976050			−0.488025	−	0.872830i	$-0.662283\pi$
$41$	−6.24977			−0.976050			−0.488025	+	0.872830i	$0.662283\pi$
$42$		−	2.00000i		−	0.308607i
$43$			0.640023i			0.0976027i	0.998809	+	0.0488013i	$0.0155401\pi$
$43$			0.640023i			0.0976027i	−0.998809	+	0.0488013i	$0.984460\pi$
$44$	2.64002			0.397999
$45$	−1.32001	−	1.80487i	−0.196776	−	0.269055i
$46$	−1.00000			−0.147442
$47$		−	4.24977i		−	0.619893i	−0.950754	−	0.309946i	$-0.899689\pi$
$47$		−	4.24977i		−	0.619893i	0.950754	−	0.309946i	$-0.100311\pi$
$48$		−	1.00000i		−	0.144338i
$49$	3.00000			0.428571
$50$	4.76491	+	1.51514i	0.673860	+	0.214273i
$51$	6.24977			0.875143
$52$		−	4.24977i		−	0.589337i
$53$		−	12.8898i		−	1.77055i	−0.465068	−	0.885275i	$-0.653970\pi$
$53$		−	12.8898i		−	1.77055i	0.465068	−	0.885275i	$-0.346030\pi$
$54$	1.00000			0.136083
$55$	−3.48486	−	4.76491i	−0.469899	−	0.642500i
$56$	−2.00000			−0.267261
$57$			3.67030i			0.486143i
$58$		−	2.00000i		−	0.262613i
$59$	8.31032			1.08191			0.540956	−	0.841051i	$-0.318063\pi$
$59$	8.31032			1.08191			0.540956	+	0.841051i	$0.318063\pi$
$60$	−1.80487	+	1.32001i	−0.233008	+	0.170413i
$61$	11.8595			1.51846			0.759228	−	0.650825i	$-0.225577\pi$
$61$	11.8595			1.51846			0.759228	+	0.650825i	$0.225577\pi$
$62$		−	2.96972i		−	0.377155i
$63$		−	2.00000i		−	0.251976i
$64$	−1.00000			−0.125000
$65$	−7.67030	+	5.60975i	−0.951384	+	0.695804i
$66$	2.64002			0.324964
$67$			11.8595i			1.44887i	0.689343	+	0.724435i	$0.257899\pi$
$67$			11.8595i			1.44887i	−0.689343	+	0.724435i	$0.742101\pi$
$68$		−	6.24977i		−	0.757896i
$69$	−1.00000			−0.120386
$70$	2.64002	+	3.60975i	0.315543	+	0.431447i
$71$	7.52982			0.893625			0.446812	−	0.894628i	$-0.352559\pi$
$71$	7.52982			0.893625			0.446812	+	0.894628i	$0.352559\pi$
$72$		−	1.00000i		−	0.117851i
$73$		−	9.03028i		−	1.05691i	−0.848960	−	0.528457i	$-0.822771\pi$
$73$		−	9.03028i		−	1.05691i	0.848960	−	0.528457i	$-0.177229\pi$
$74$	3.35998			0.390589
$75$	4.76491	+	1.51514i	0.550204	+	0.174953i
$76$	3.67030			0.421012
$77$		−	5.28005i		−	0.601717i
$78$		−	4.24977i		−	0.481192i
$79$	−9.52982			−1.07219			−0.536094	−	0.844158i	$-0.680101\pi$
$79$	−9.52982			−1.07219			−0.536094	+	0.844158i	$0.680101\pi$
$80$	1.32001	+	1.80487i	0.147582	+	0.201791i
$81$	1.00000			0.111111
$82$			6.24977i			0.690172i
$83$		−	17.2001i		−	1.88796i	−0.330005	−	0.943979i	$-0.607051\pi$
$83$		−	17.2001i		−	1.88796i	0.330005	−	0.943979i	$-0.392949\pi$
$84$	−2.00000			−0.218218
$85$	−11.2800	+	8.24977i	−1.22349	+	0.894813i
$86$	0.640023			0.0690155
$87$		−	2.00000i		−	0.214423i
$88$		−	2.64002i		−	0.281427i
$89$	11.2195			1.18926			0.594632	−	0.803998i	$-0.297298\pi$
$89$	11.2195			1.18926			0.594632	+	0.803998i	$0.297298\pi$
$90$	−1.80487	+	1.32001i	−0.190250	+	0.139141i
$91$	−8.49954			−0.890994
$92$			1.00000i			0.104257i
$93$		−	2.96972i		−	0.307946i
$94$	−4.24977			−0.438330
$95$	−4.84484	−	6.62443i	−0.497070	−	0.679652i
$96$	−1.00000			−0.102062
$97$			18.4995i			1.87834i	0.343447	+	0.939172i	$0.388405\pi$
$97$			18.4995i			1.87834i	−0.343447	+	0.939172i	$0.611595\pi$
$98$		−	3.00000i		−	0.303046i
$99$	2.64002			0.265332
$100$	1.51514	−	4.76491i	0.151514	−	0.476491i
$101$	−10.4995			−1.04474			−0.522372	−	0.852718i	$-0.674953\pi$
$101$	−10.4995			−1.04474			−0.522372	+	0.852718i	$0.674953\pi$
$102$		−	6.24977i		−	0.618820i
$103$			11.7796i			1.16068i	0.814375	+	0.580339i	$0.197080\pi$
$103$			11.7796i			1.16068i	−0.814375	+	0.580339i	$0.802920\pi$
$104$	−4.24977			−0.416724
$105$	2.64002	+	3.60975i	0.257640	+	0.352275i
$106$	−12.8898			−1.25197
$107$		−	8.57947i		−	0.829409i	−0.909956	−	0.414704i	$-0.863885\pi$
$107$		−	8.57947i		−	0.829409i	0.909956	−	0.414704i	$-0.136115\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	−9.13957			−0.875412			−0.437706	−	0.899118i	$-0.644209\pi$
$109$	−9.13957			−0.875412			−0.437706	+	0.899118i	$0.644209\pi$
$110$	−4.76491	+	3.48486i	−0.454316	+	0.332269i
$111$	3.35998			0.318915
$112$			2.00000i			0.188982i
$113$			7.52982i			0.708346i	0.935180	+	0.354173i	$0.115238\pi$
$113$			7.52982i			0.708346i	−0.935180	+	0.354173i	$0.884762\pi$
$114$	3.67030			0.343755
$115$	1.80487	−	1.32001i	0.168305	−	0.123092i
$116$	−2.00000			−0.185695
$117$		−	4.24977i		−	0.392891i
$118$		−	8.31032i		−	0.765027i
$119$	−12.4995			−1.14583
$120$	1.32001	+	1.80487i	0.120500	+	0.164762i
$121$	−4.03028			−0.366389
$122$		−	11.8595i		−	1.07371i
$123$			6.24977i			0.563523i
$124$	−2.96972			−0.266689
$125$	−10.6001	+	3.55510i	−0.948098	+	0.317978i
$126$	−2.00000			−0.178174
$127$			6.96972i			0.618463i	0.950987	+	0.309231i	$0.100072\pi$
$127$			6.96972i			0.618463i	−0.950987	+	0.309231i	$0.899928\pi$
$128$			1.00000i			0.0883883i
$129$	0.640023			0.0563509
$130$	5.60975	+	7.67030i	0.492007	+	0.672730i
$131$	1.09083			0.0953061			0.0476531	−	0.998864i	$-0.484826\pi$
$131$	1.09083			0.0953061			0.0476531	+	0.998864i	$0.484826\pi$
$132$		−	2.64002i		−	0.229785i
$133$		−	7.34060i		−	0.636511i
$134$	11.8595			1.02451
$135$	−1.80487	+	1.32001i	−0.155339	+	0.113609i
$136$	−6.24977			−0.535913
$137$			10.2498i			0.875697i	0.899049	+	0.437849i	$0.144259\pi$
$137$			10.2498i			0.875697i	−0.899049	+	0.437849i	$0.855741\pi$
$138$			1.00000i			0.0851257i
$139$	10.5601			0.895695			0.447848	−	0.894110i	$-0.352191\pi$
$139$	10.5601			0.895695			0.447848	+	0.894110i	$0.352191\pi$
$140$	3.60975	−	2.64002i	0.305079	−	0.223123i
$141$	−4.24977			−0.357895
$142$		−	7.52982i		−	0.631888i
$143$		−	11.2195i		−	0.938221i
$144$	−1.00000			−0.0833333
$145$	2.64002	+	3.60975i	0.219242	+	0.299773i
$146$	−9.03028			−0.747351
$147$		−	3.00000i		−	0.247436i
$148$		−	3.35998i		−	0.276188i
$149$	10.6400			0.871665			0.435832	−	0.900028i	$-0.356454\pi$
$149$	10.6400			0.871665			0.435832	+	0.900028i	$0.356454\pi$
$150$	1.51514	−	4.76491i	0.123711	−	0.389053i
$151$	−7.59037			−0.617696			−0.308848	−	0.951111i	$-0.599943\pi$
$151$	−7.59037			−0.617696			−0.308848	+	0.951111i	$0.599943\pi$
$152$		−	3.67030i		−	0.297701i
$153$		−	6.24977i		−	0.505264i
$154$	−5.28005			−0.425478
$155$	3.92007	+	5.35998i	0.314868	+	0.430524i
$156$	−4.24977			−0.340254
$157$			19.0790i			1.52267i	0.648358	+	0.761336i	$0.275456\pi$
$157$			19.0790i			1.52267i	−0.648358	+	0.761336i	$0.724544\pi$
$158$			9.52982i			0.758152i
$159$	−12.8898			−1.02223
$160$	1.80487	−	1.32001i	0.142688	−	0.104356i
$161$	2.00000			0.157622
$162$		−	1.00000i		−	0.0785674i
$163$		−	5.15894i		−	0.404080i	−0.979377	−	0.202040i	$-0.935243\pi$
$163$		−	5.15894i		−	0.404080i	0.979377	−	0.202040i	$-0.0647570\pi$
$164$	6.24977			0.488025
$165$	−4.76491	+	3.48486i	−0.370948	+	0.271296i
$166$	−17.2001			−1.33499
$167$		−	22.8099i		−	1.76508i	−0.470237	−	0.882540i	$-0.655832\pi$
$167$		−	22.8099i		−	1.76508i	0.470237	−	0.882540i	$-0.344168\pi$
$168$			2.00000i			0.154303i
$169$	−5.06055			−0.389273
$170$	8.24977	+	11.2800i	0.632729	+	0.865140i
$171$	3.67030			0.280675
$172$		−	0.640023i		−	0.0488013i
$173$			9.71904i			0.738925i	0.929246	+	0.369462i	$0.120458\pi$
$173$			9.71904i			0.738925i	−0.929246	+	0.369462i	$0.879542\pi$
$174$	−2.00000			−0.151620
$175$	−9.52982	−	3.03028i	−0.720387	−	0.229067i
$176$	−2.64002			−0.198999
$177$		−	8.31032i		−	0.624642i
$178$		−	11.2195i		−	0.840937i
$179$	−21.9688			−1.64203			−0.821013	−	0.570910i	$-0.806591\pi$
$179$	−21.9688			−1.64203			−0.821013	+	0.570910i	$0.806591\pi$
$180$	1.32001	+	1.80487i	0.0983879	+	0.134527i
$181$	2.70058			0.200732			0.100366	−	0.994951i	$-0.467999\pi$
$181$	2.70058			0.200732			0.100366	+	0.994951i	$0.467999\pi$
$182$			8.49954i			0.630028i
$183$		−	11.8595i		−	0.876681i
$184$	1.00000			0.0737210
$185$	−6.06433	+	4.43521i	−0.445859	+	0.326083i
$186$	−2.96972			−0.217751
$187$		−	16.4995i		−	1.20657i
$188$			4.24977i			0.309946i
$189$	−2.00000			−0.145479
$190$	−6.62443	+	4.84484i	−0.480586	+	0.351482i
$191$	3.34060			0.241717			0.120859	−	0.992670i	$-0.461435\pi$
$191$	3.34060			0.241717			0.120859	+	0.992670i	$0.461435\pi$
$192$			1.00000i			0.0721688i
$193$		−	14.5601i		−	1.04806i	−0.851700	−	0.524029i	$-0.824428\pi$
$193$		−	14.5601i		−	1.04806i	0.851700	−	0.524029i	$-0.175572\pi$
$194$	18.4995			1.32819
$195$	5.60975	+	7.67030i	0.401722	+	0.549282i
$196$	−3.00000			−0.214286
$197$			2.00000i			0.142494i	0.997459	+	0.0712470i	$0.0226979\pi$
$197$			2.00000i			0.142494i	−0.997459	+	0.0712470i	$0.977302\pi$
$198$		−	2.64002i		−	0.187618i
$199$	10.0294			0.710962			0.355481	−	0.934683i	$-0.384317\pi$
$199$	10.0294			0.710962			0.355481	+	0.934683i	$0.384317\pi$
$200$	−4.76491	−	1.51514i	−0.336930	−	0.107136i
$201$	11.8595			0.836506
$202$			10.4995i			0.738745i
$203$			4.00000i			0.280745i
$204$	−6.24977			−0.437571
$205$	−8.24977	−	11.2800i	−0.576189	−	0.787833i
$206$	11.7796			0.820723
$207$			1.00000i			0.0695048i
$208$			4.24977i			0.294669i
$209$	9.68968			0.670249
$210$	3.60975	−	2.64002i	0.249096	−	0.182179i
$211$	15.3406			1.05609			0.528045	−	0.849216i	$-0.322925\pi$
$211$	15.3406			1.05609			0.528045	+	0.849216i	$0.322925\pi$
$212$			12.8898i			0.885275i
$213$		−	7.52982i		−	0.515935i
$214$	−8.57947			−0.586481
$215$	−1.15516	+	0.844838i	−0.0787814	+	0.0576175i
$216$	−1.00000			−0.0680414
$217$			5.93945i			0.403196i
$218$			9.13957i			0.619009i
$219$	−9.03028			−0.610210
$220$	3.48486	+	4.76491i	0.234949	+	0.321250i
$221$	−26.5601			−1.78663
$222$		−	3.35998i		−	0.225507i
$223$		−	8.62065i		−	0.577281i	−0.957438	−	0.288641i	$-0.906797\pi$
$223$		−	8.62065i		−	0.577281i	0.957438	−	0.288641i	$-0.0932033\pi$
$224$	2.00000			0.133631
$225$	1.51514	−	4.76491i	0.101009	−	0.317661i
$226$	7.52982			0.500876
$227$			20.4196i			1.35530i	0.735386	+	0.677649i	$0.237001\pi$
$227$			20.4196i			1.35530i	−0.735386	+	0.677649i	$0.762999\pi$
$228$		−	3.67030i		−	0.243072i
$229$	16.4802			1.08904			0.544520	−	0.838748i	$-0.316712\pi$
$229$	16.4802			1.08904			0.544520	+	0.838748i	$0.316712\pi$
$230$	−1.32001	−	1.80487i	−0.0870390	−	0.119010i
$231$	−5.28005			−0.347402
$232$			2.00000i			0.131306i
$233$		−	10.1287i		−	0.663551i	−0.943358	−	0.331776i	$-0.892352\pi$
$233$		−	10.1287i		−	0.663551i	0.943358	−	0.331776i	$-0.107648\pi$
$234$	−4.24977			−0.277816
$235$	7.67030	−	5.60975i	0.500355	−	0.365940i
$236$	−8.31032			−0.540956
$237$			9.52982i			0.619028i
$238$			12.4995i			0.810225i
$239$	5.21949			0.337621			0.168811	−	0.985649i	$-0.446007\pi$
$239$	5.21949			0.337621			0.168811	+	0.985649i	$0.446007\pi$
$240$	1.80487	−	1.32001i	0.116504	−	0.0852064i
$241$	5.21949			0.336217			0.168109	−	0.985768i	$-0.446234\pi$
$241$	5.21949			0.336217			0.168109	+	0.985768i	$0.446234\pi$
$242$			4.03028i			0.259076i
$243$		−	1.00000i		−	0.0641500i
$244$	−11.8595			−0.759228
$245$	3.96004	+	5.41462i	0.252997	+	0.345927i
$246$	6.24977			0.398471
$247$		−	15.5979i		−	0.992473i
$248$			2.96972i			0.188578i
$249$	−17.2001			−1.09001
$250$	3.55510	+	10.6001i	0.224844	+	0.670407i
$251$	13.8595			0.874805			0.437403	−	0.899266i	$-0.355899\pi$
$251$	13.8595			0.874805			0.437403	+	0.899266i	$0.355899\pi$
$252$			2.00000i			0.125988i
$253$			2.64002i			0.165977i
$254$	6.96972			0.437319
$255$	8.24977	+	11.2800i	0.516621	+	0.706384i
$256$	1.00000			0.0625000
$257$		−	10.9991i		−	0.686104i	−0.939316	−	0.343052i	$-0.888539\pi$
$257$		−	10.9991i		−	0.686104i	0.939316	−	0.343052i	$-0.111461\pi$
$258$		−	0.640023i		−	0.0398461i
$259$	−6.71995			−0.417558
$260$	7.67030	−	5.60975i	0.475692	−	0.347902i
$261$	−2.00000			−0.123797
$262$		−	1.09083i		−	0.0673916i
$263$			2.43899i			0.150395i	0.997169	+	0.0751973i	$0.0239586\pi$
$263$			2.43899i			0.150395i	−0.997169	+	0.0751973i	$0.976041\pi$
$264$	−2.64002			−0.162482
$265$	23.2645	−	17.0147i	1.42912	−	1.04520i
$266$	−7.34060			−0.450081
$267$		−	11.2195i		−	0.686622i
$268$		−	11.8595i		−	0.724435i
$269$	−11.1589			−0.680373			−0.340186	−	0.940358i	$-0.610490\pi$
$269$	−11.1589			−0.680373			−0.340186	+	0.940358i	$0.610490\pi$
$270$	1.32001	+	1.80487i	0.0803334	+	0.109841i
$271$	4.62065			0.280684			0.140342	−	0.990103i	$-0.455180\pi$
$271$	4.62065			0.280684			0.140342	+	0.990103i	$0.455180\pi$
$272$			6.24977i			0.378948i
$273$			8.49954i			0.514416i
$274$	10.2498			0.619211
$275$	4.00000	−	12.5795i	0.241209	−	0.758571i
$276$	1.00000			0.0601929
$277$		−	14.6888i		−	0.882562i	−0.897369	−	0.441281i	$-0.854524\pi$
$277$		−	14.6888i		−	0.882562i	0.897369	−	0.441281i	$-0.145476\pi$
$278$		−	10.5601i		−	0.633352i
$279$	−2.96972			−0.177793
$280$	−2.64002	−	3.60975i	−0.157772	−	0.215724i
$281$	1.15894			0.0691367			0.0345684	−	0.999402i	$-0.488994\pi$
$281$	1.15894			0.0691367			0.0345684	+	0.999402i	$0.488994\pi$
$282$			4.24977i			0.253070i
$283$		−	11.7384i		−	0.697776i	−0.937164	−	0.348888i	$-0.886559\pi$
$283$		−	11.7384i		−	0.697776i	0.937164	−	0.348888i	$-0.113441\pi$
$284$	−7.52982			−0.446812
$285$	−6.62443	+	4.84484i	−0.392397	+	0.286983i
$286$	−11.2195			−0.663423
$287$		−	12.4995i		−	0.737825i
$288$			1.00000i			0.0589256i
$289$	−22.0596			−1.29763
$290$	3.60975	−	2.64002i	0.211972	−	0.155028i
$291$	18.4995			1.08446
$292$			9.03028i			0.528457i
$293$		−	26.1698i		−	1.52886i	−0.644708	−	0.764429i	$-0.723021\pi$
$293$		−	26.1698i		−	1.52886i	0.644708	−	0.764429i	$-0.276979\pi$
$294$	−3.00000			−0.174964
$295$	10.9697	+	14.9991i	0.638682	+	0.873280i
$296$	−3.35998			−0.195295
$297$		−	2.64002i		−	0.153190i
$298$		−	10.6400i		−	0.616360i
$299$	4.24977			0.245771
$300$	−4.76491	−	1.51514i	−0.275102	−	0.0874765i
$301$	−1.28005			−0.0737807
$302$			7.59037i			0.436777i
$303$			10.4995i			0.603183i
$304$	−3.67030			−0.210506
$305$	15.6547	+	21.4049i	0.896386	+	1.22564i
$306$	−6.24977			−0.357276
$307$		−	4.65940i		−	0.265926i	−0.991121	−	0.132963i	$-0.957551\pi$
$307$		−	4.65940i		−	0.265926i	0.991121	−	0.132963i	$-0.0424492\pi$
$308$			5.28005i			0.300859i
$309$	11.7796			0.670117
$310$	5.35998	−	3.92007i	0.304426	−	0.222645i
$311$	15.1589			0.859585			0.429792	−	0.902928i	$-0.358587\pi$
$311$	15.1589			0.859585			0.429792	+	0.902928i	$0.358587\pi$
$312$			4.24977i			0.240596i
$313$			26.6206i			1.50469i	0.658771	+	0.752344i	$0.271077\pi$
$313$			26.6206i			1.50469i	−0.658771	+	0.752344i	$0.728923\pi$
$314$	19.0790			1.07669
$315$	3.60975	−	2.64002i	0.203386	−	0.148748i
$316$	9.52982			0.536094
$317$			15.1589i			0.851411i	0.904862	+	0.425706i	$0.139974\pi$
$317$			15.1589i			0.851411i	−0.904862	+	0.425706i	$0.860026\pi$
$318$			12.8898i			0.722824i
$319$	−5.28005			−0.295626
$320$	−1.32001	−	1.80487i	−0.0737909	−	0.100896i
$321$	−8.57947			−0.478859
$322$		−	2.00000i		−	0.111456i
$323$		−	22.9385i		−	1.27633i
$324$	−1.00000			−0.0555556
$325$	−20.2498	−	6.43899i	−1.12326	−	0.357171i
$326$	−5.15894			−0.285727
$327$			9.13957i			0.505419i
$328$		−	6.24977i		−	0.345086i
$329$	8.49954			0.468595
$330$	3.48486	+	4.76491i	0.191835	+	0.262300i
$331$	23.7190			1.30372			0.651858	−	0.758341i	$-0.273990\pi$
$331$	23.7190			1.30372			0.651858	+	0.758341i	$0.273990\pi$
$332$			17.2001i			0.943979i
$333$		−	3.35998i		−	0.184126i
$334$	−22.8099			−1.24810
$335$	−21.4049	+	15.6547i	−1.16948	+	0.855308i
$336$	2.00000			0.109109
$337$		−	15.1589i		−	0.825760i	−0.910785	−	0.412880i	$-0.864523\pi$
$337$		−	15.1589i		−	0.825760i	0.910785	−	0.412880i	$-0.135477\pi$
$338$			5.06055i			0.275258i
$339$	7.52982			0.408964
$340$	11.2800	−	8.24977i	0.611746	−	0.447407i
$341$	−7.84014			−0.424567
$342$		−	3.67030i		−	0.198467i
$343$			20.0000i			1.07990i
$344$	−0.640023			−0.0345078
$345$	−1.32001	−	1.80487i	−0.0710670	−	0.0971711i
$346$	9.71904			0.522499
$347$			18.2791i			0.981275i	0.871364	+	0.490638i	$0.163236\pi$
$347$			18.2791i			0.981275i	−0.871364	+	0.490638i	$0.836764\pi$
$348$			2.00000i			0.107211i
$349$	−15.9394			−0.853219			−0.426610	−	0.904436i	$-0.640292\pi$
$349$	−15.9394			−0.853219			−0.426610	+	0.904436i	$0.640292\pi$
$350$	−3.03028	+	9.52982i	−0.161975	+	0.509390i
$351$	−4.24977			−0.226836
$352$			2.64002i			0.140714i
$353$			22.6282i			1.20438i	0.798354	+	0.602189i	$0.205705\pi$
$353$			22.6282i			1.20438i	−0.798354	+	0.602189i	$0.794295\pi$
$354$	−8.31032			−0.441689
$355$	9.93945	+	13.5904i	0.527531	+	0.721302i
$356$	−11.2195			−0.594632
$357$			12.4995i			0.661546i
$358$			21.9688i			1.16109i
$359$	31.8401			1.68046			0.840229	−	0.542231i	$-0.182420\pi$
$359$	31.8401			1.68046			0.840229	+	0.542231i	$0.182420\pi$
$360$	1.80487	−	1.32001i	0.0951252	−	0.0695707i
$361$	−5.52890			−0.290995
$362$		−	2.70058i		−	0.141939i
$363$			4.03028i			0.211535i
$364$	8.49954			0.445497
$365$	16.2985	−	11.9201i	0.853103	−	0.623925i
$366$	−11.8595			−0.619907
$367$		−	6.49954i		−	0.339273i	−0.985507	−	0.169637i	$-0.945741\pi$
$367$		−	6.49954i		−	0.339273i	0.985507	−	0.169637i	$-0.0542594\pi$
$368$		−	1.00000i		−	0.0521286i
$369$	6.24977			0.325350
$370$	4.43521	+	6.06433i	0.230576	+	0.315270i
$371$	25.7796			1.33841
$372$			2.96972i			0.153973i
$373$		−	20.6400i		−	1.06870i	−0.845263	−	0.534350i	$-0.820556\pi$
$373$		−	20.6400i		−	1.06870i	0.845263	−	0.534350i	$-0.179444\pi$
$374$	−16.4995			−0.853171
$375$	3.55510	+	10.6001i	0.183585	+	0.547385i
$376$	4.24977			0.219165
$377$			8.49954i			0.437749i
$378$			2.00000i			0.102869i
$379$	23.8889			1.22709			0.613545	−	0.789660i	$-0.289743\pi$
$379$	23.8889			1.22709			0.613545	+	0.789660i	$0.289743\pi$
$380$	4.84484	+	6.62443i	0.248535	+	0.339826i
$381$	6.96972			0.357070
$382$		−	3.34060i		−	0.170920i
$383$			10.0606i			0.514070i	0.966402	+	0.257035i	$0.0827456\pi$
$383$			10.0606i			0.514070i	−0.966402	+	0.257035i	$0.917254\pi$
$384$	1.00000			0.0510310
$385$	9.52982	−	6.96972i	0.485684	−	0.355210i
$386$	−14.5601			−0.741089
$387$		−	0.640023i		−	0.0325342i
$388$		−	18.4995i		−	0.939172i
$389$	−1.20012			−0.0608484			−0.0304242	−	0.999537i	$-0.509686\pi$
$389$	−1.20012			−0.0608484			−0.0304242	+	0.999537i	$0.509686\pi$
$390$	7.67030	−	5.60975i	0.388401	−	0.284061i
$391$	6.24977			0.316064
$392$			3.00000i			0.151523i
$393$		−	1.09083i		−	0.0550250i
$394$	2.00000			0.100759
$395$	−12.5795	−	17.2001i	−0.632942	−	0.865432i
$396$	−2.64002			−0.132666
$397$		−	18.4702i		−	0.926992i	−0.886099	−	0.463496i	$-0.846595\pi$
$397$		−	18.4702i		−	0.926992i	0.886099	−	0.463496i	$-0.153405\pi$
$398$		−	10.0294i		−	0.502726i
$399$	−7.34060			−0.367490
$400$	−1.51514	+	4.76491i	−0.0757569	+	0.238245i
$401$	20.9991			1.04864			0.524322	−	0.851520i	$-0.324319\pi$
$401$	20.9991			1.04864			0.524322	+	0.851520i	$0.324319\pi$
$402$		−	11.8595i		−	0.591499i
$403$			12.6206i			0.628679i
$404$	10.4995			0.522372
$405$	1.32001	+	1.80487i	0.0655919	+	0.0896849i
$406$	4.00000			0.198517
$407$		−	8.87042i		−	0.439690i
$408$			6.24977i			0.309410i
$409$	−2.00000			−0.0988936			−0.0494468	−	0.998777i	$-0.515746\pi$
$409$	−2.00000			−0.0988936			−0.0494468	+	0.998777i	$0.515746\pi$
$410$	−11.2800	+	8.24977i	−0.557082	+	0.407427i
$411$	10.2498			0.505584
$412$		−	11.7796i		−	0.580339i
$413$			16.6206i			0.817849i
$414$	1.00000			0.0491473
$415$	31.0440	−	22.7044i	1.52389	−	1.11451i
$416$	4.24977			0.208362
$417$		−	10.5601i		−	0.517130i
$418$		−	9.68968i		−	0.473938i
$419$	4.41961			0.215912			0.107956	−	0.994156i	$-0.465569\pi$
$419$	4.41961			0.215912			0.107956	+	0.994156i	$0.465569\pi$
$420$	−2.64002	−	3.60975i	−0.128820	−	0.176138i
$421$	24.3591			1.18719			0.593594	−	0.804765i	$-0.297709\pi$
$421$	24.3591			1.18719			0.593594	+	0.804765i	$0.297709\pi$
$422$		−	15.3406i		−	0.746769i
$423$			4.24977i			0.206631i
$424$	12.8898			0.625984
$425$	−29.7796	−	9.46927i	−1.44452	−	0.459327i
$426$	−7.52982			−0.364821
$427$			23.7190i			1.14784i
$428$			8.57947i			0.414704i
$429$	−11.2195			−0.541682
$430$	0.844838	+	1.15516i	0.0407417	+	0.0557068i
$431$	−34.1580			−1.64533			−0.822667	−	0.568523i	$-0.807515\pi$
$431$	−34.1580			−1.64533			−0.822667	+	0.568523i	$0.807515\pi$
$432$			1.00000i			0.0481125i
$433$			5.87890i			0.282522i	0.989972	+	0.141261i	$0.0451156\pi$
$433$			5.87890i			0.282522i	−0.989972	+	0.141261i	$0.954884\pi$
$434$	5.93945			0.285103
$435$	3.60975	−	2.64002i	0.173074	−	0.126579i
$436$	9.13957			0.437706
$437$			3.67030i			0.175574i
$438$			9.03028i			0.431483i
$439$	18.9385			0.903887			0.451943	−	0.892047i	$-0.350731\pi$
$439$	18.9385			0.903887			0.451943	+	0.892047i	$0.350731\pi$
$440$	4.76491	−	3.48486i	0.227158	−	0.166134i
$441$	−3.00000			−0.142857
$442$			26.5601i			1.26333i
$443$		−	4.00000i		−	0.190046i	−0.995475	−	0.0950229i	$-0.969708\pi$
$443$		−	4.00000i		−	0.190046i	0.995475	−	0.0950229i	$-0.0302924\pi$
$444$	−3.35998			−0.159457
$445$	14.8099	+	20.2498i	0.702055	+	0.959931i
$446$	−8.62065			−0.408199
$447$		−	10.6400i		−	0.503256i
$448$		−	2.00000i		−	0.0944911i
$449$	14.6282			0.690348			0.345174	−	0.938539i	$-0.387820\pi$
$449$	14.6282			0.690348			0.345174	+	0.938539i	$0.387820\pi$
$450$	−4.76491	−	1.51514i	−0.224620	−	0.0714243i
$451$	16.4995			0.776933
$452$		−	7.52982i		−	0.354173i
$453$			7.59037i			0.356627i
$454$	20.4196			0.958340
$455$	−11.2195	−	15.3406i	−0.525978	−	0.719178i
$456$	−3.67030			−0.171878
$457$			12.0606i			0.564169i	0.959390	+	0.282084i	$0.0910258\pi$
$457$			12.0606i			0.564169i	−0.959390	+	0.282084i	$0.908974\pi$
$458$		−	16.4802i		−	0.770068i
$459$	−6.24977			−0.291714
$460$	−1.80487	+	1.32001i	−0.0841527	+	0.0615459i
$461$	9.34060			0.435035			0.217518	−	0.976056i	$-0.430204\pi$
$461$	9.34060			0.435035			0.217518	+	0.976056i	$0.430204\pi$
$462$			5.28005i			0.245650i
$463$			17.5298i			0.814680i	0.913277	+	0.407340i	$0.133544\pi$
$463$			17.5298i			0.814680i	−0.913277	+	0.407340i	$0.866456\pi$
$464$	2.00000			0.0928477
$465$	5.35998	−	3.92007i	0.248563	−	0.181789i
$466$	−10.1287			−0.469201
$467$		−	27.0185i		−	1.25027i	−0.780519	−	0.625133i	$-0.785045\pi$
$467$		−	27.0185i		−	1.25027i	0.780519	−	0.625133i	$-0.214955\pi$
$468$			4.24977i			0.196446i
$469$	−23.7190			−1.09524
$470$	−5.60975	−	7.67030i	−0.258758	−	0.353805i
$471$	19.0790			0.879115
$472$			8.31032i			0.382514i
$473$		−	1.68968i		−	0.0776914i
$474$	9.52982			0.437719
$475$	5.56101	−	17.4886i	0.255157	−	0.802434i
$476$	12.4995			0.572916
$477$			12.8898i			0.590183i
$478$		−	5.21949i		−	0.238734i
$479$	−40.0587			−1.83033			−0.915165	−	0.403080i	$-0.867940\pi$
$479$	−40.0587			−1.83033			−0.915165	+	0.403080i	$0.867940\pi$
$480$	−1.32001	−	1.80487i	−0.0602500	−	0.0823808i
$481$	−14.2791			−0.651072
$482$		−	5.21949i		−	0.237741i
$483$		−	2.00000i		−	0.0910032i
$484$	4.03028			0.183194
$485$	−33.3893	+	24.4196i	−1.51613	+	1.10884i
$486$	−1.00000			−0.0453609
$487$			14.9697i			0.678343i	0.940725	+	0.339171i	$0.110147\pi$
$487$			14.9697i			0.678343i	−0.940725	+	0.339171i	$0.889853\pi$
$488$			11.8595i			0.536855i
$489$	−5.15894			−0.233295
$490$	5.41462	−	3.96004i	0.244608	−	0.178896i
$491$	−28.5289			−1.28749			−0.643746	−	0.765240i	$-0.722621\pi$
$491$	−28.5289			−1.28749			−0.643746	+	0.765240i	$0.722621\pi$
$492$		−	6.24977i		−	0.281761i
$493$			12.4995i			0.562951i
$494$	−15.5979			−0.701784
$495$	3.48486	+	4.76491i	0.156633	+	0.214167i
$496$	2.96972			0.133345
$497$			15.0596i			0.675517i
$498$			17.2001i			0.770756i
$499$	−33.2800			−1.48982			−0.744910	−	0.667165i	$-0.767507\pi$
$499$	−33.2800			−1.48982			−0.744910	+	0.667165i	$0.767507\pi$
$500$	10.6001	−	3.55510i	0.474049	−	0.158989i
$501$	−22.8099			−1.01907
$502$		−	13.8595i		−	0.618581i
$503$			15.2195i			0.678604i	0.940678	+	0.339302i	$0.110191\pi$
$503$			15.2195i			0.678604i	−0.940678	+	0.339302i	$0.889809\pi$
$504$	2.00000			0.0890871
$505$	−13.8595	−	18.9503i	−0.616740	−	0.843279i
$506$	2.64002			0.117363
$507$			5.06055i			0.224747i
$508$		−	6.96972i		−	0.309231i
$509$	26.0000			1.15243			0.576215	−	0.817298i	$-0.304529\pi$
$509$	26.0000			1.15243			0.576215	+	0.817298i	$0.304529\pi$
$510$	11.2800	−	8.24977i	0.499489	−	0.365306i
$511$	18.0606			0.798952
$512$		−	1.00000i		−	0.0441942i
$513$		−	3.67030i		−	0.162048i
$514$	−10.9991			−0.485149
$515$	−21.2607	+	15.5492i	−0.936857	+	0.685179i
$516$	−0.640023			−0.0281755
$517$			11.2195i			0.493433i
$518$			6.71995i			0.295258i
$519$	9.71904			0.426618
$520$	−5.60975	−	7.67030i	−0.246004	−	0.336365i
$521$	15.1807			0.665080			0.332540	−	0.943089i	$-0.392094\pi$
$521$	15.1807			0.665080			0.332540	+	0.943089i	$0.392094\pi$
$522$			2.00000i			0.0875376i
$523$		−	20.2380i		−	0.884944i	−0.896782	−	0.442472i	$-0.854102\pi$
$523$		−	20.2380i		−	0.884944i	0.896782	−	0.442472i	$-0.145898\pi$
$524$	−1.09083			−0.0476531
$525$	−3.03028	+	9.52982i	−0.132252	+	0.415915i
$526$	2.43899			0.106345
$527$			18.5601i			0.808490i
$528$			2.64002i			0.114892i
$529$	−1.00000			−0.0434783
$530$	−17.0147	−	23.2645i	−0.739070	−	1.01054i
$531$	−8.31032			−0.360637
$532$			7.34060i			0.318255i
$533$		−	26.5601i		−	1.15045i
$534$	−11.2195			−0.485515
$535$	15.4849	−	11.3250i	0.669469	−	0.489623i
$536$	−11.8595			−0.512253
$537$			21.9688i			0.948024i
$538$			11.1589i			0.481096i
$539$	−7.92007			−0.341142
$540$	1.80487	−	1.32001i	0.0776694	−	0.0568043i
$541$	25.0596			1.07740			0.538699	−	0.842498i	$-0.318916\pi$
$541$	25.0596			1.07740			0.538699	+	0.842498i	$0.318916\pi$
$542$		−	4.62065i		−	0.198474i
$543$		−	2.70058i		−	0.115893i
$544$	6.24977			0.267957
$545$	−12.0643	−	16.4958i	−0.516779	−	0.706601i
$546$	8.49954			0.363747
$547$		−	38.4002i		−	1.64188i	−0.571018	−	0.820938i	$-0.693451\pi$
$547$		−	38.4002i		−	1.64188i	0.571018	−	0.820938i	$-0.306549\pi$
$548$		−	10.2498i		−	0.437849i
$549$	−11.8595			−0.506152
$550$	−12.5795	−	4.00000i	−0.536390	−	0.170561i
$551$	−7.34060			−0.312720
$552$		−	1.00000i		−	0.0425628i
$553$		−	19.0596i		−	0.810498i
$554$	−14.6888			−0.624066
$555$	4.43521	+	6.06433i	0.188264	+	0.257417i
$556$	−10.5601			−0.447848
$557$		−	12.7299i		−	0.539385i	−0.962947	−	0.269692i	$-0.913078\pi$
$557$		−	12.7299i		−	0.539385i	0.962947	−	0.269692i	$-0.0869220\pi$
$558$			2.96972i			0.125718i
$559$	−2.71995			−0.115042
$560$	−3.60975	+	2.64002i	−0.152540	+	0.111561i
$561$	−16.4995			−0.696611
$562$		−	1.15894i		−	0.0488870i
$563$		−	21.0403i		−	0.886741i	−0.896338	−	0.443371i	$-0.853783\pi$
$563$		−	21.0403i		−	0.886741i	0.896338	−	0.443371i	$-0.146217\pi$
$564$	4.24977			0.178948
$565$	−13.5904	+	9.93945i	−0.571751	+	0.418156i
$566$	−11.7384			−0.493402
$567$			2.00000i			0.0839921i
$568$			7.52982i			0.315944i
$569$	20.0000			0.838444			0.419222	−	0.907884i	$-0.362303\pi$
$569$	20.0000			0.838444			0.419222	+	0.907884i	$0.362303\pi$
$570$	4.84484	+	6.62443i	0.202928	+	0.277467i
$571$	−11.1708			−0.467482			−0.233741	−	0.972299i	$-0.575097\pi$
$571$	−11.1708			−0.467482			−0.233741	+	0.972299i	$0.575097\pi$
$572$			11.2195i			0.469111i
$573$		−	3.34060i		−	0.139556i
$574$	−12.4995			−0.521721
$575$	4.76491	+	1.51514i	0.198710	+	0.0631856i
$576$	1.00000			0.0416667
$577$		−	23.5904i		−	0.982080i	−0.871137	−	0.491040i	$-0.836617\pi$
$577$		−	23.5904i		−	0.982080i	0.871137	−	0.491040i	$-0.163383\pi$
$578$			22.0596i			0.917560i
$579$	−14.5601			−0.605097
$580$	−2.64002	−	3.60975i	−0.109621	−	0.149887i
$581$	34.4002			1.42716
$582$		−	18.4995i		−	0.766831i
$583$			34.0294i			1.40935i
$584$	9.03028			0.373675
$585$	7.67030	−	5.60975i	0.317128	−	0.231935i
$586$	−26.1698			−1.08107
$587$			12.6594i			0.522509i	0.965270	+	0.261255i	$0.0841362\pi$
$587$			12.6594i			0.522509i	−0.965270	+	0.261255i	$0.915864\pi$
$588$			3.00000i			0.123718i
$589$	−10.8998			−0.449117
$590$	14.9991	−	10.9697i	0.617502	−	0.451616i
$591$	2.00000			0.0822690
$592$			3.35998i			0.138094i
$593$			18.4995i			0.759685i	0.925051	+	0.379843i	$0.124022\pi$
$593$			18.4995i			0.759685i	−0.925051	+	0.379843i	$0.875978\pi$
$594$	−2.64002			−0.108321
$595$	−16.4995	−	22.5601i	−0.676415	−	0.924874i
$596$	−10.6400			−0.435832
$597$		−	10.0294i		−	0.410474i
$598$		−	4.24977i		−	0.173786i
$599$	−7.15894			−0.292506			−0.146253	−	0.989247i	$-0.546721\pi$
$599$	−7.15894			−0.292506			−0.146253	+	0.989247i	$0.546721\pi$
$600$	−1.51514	+	4.76491i	−0.0618553	+	0.194527i
$601$	−7.40871			−0.302208			−0.151104	−	0.988518i	$-0.548283\pi$
$601$	−7.40871			−0.302208			−0.151104	+	0.988518i	$0.548283\pi$
$602$			1.28005i			0.0521708i
$603$		−	11.8595i		−	0.482957i
$604$	7.59037			0.308848
$605$	−5.32001	−	7.27414i	−0.216289	−	0.295736i
$606$	10.4995			0.426515
$607$			16.9991i			0.689972i	0.938608	+	0.344986i	$0.112116\pi$
$607$			16.9991i			0.689972i	−0.938608	+	0.344986i	$0.887884\pi$
$608$			3.67030i			0.148850i
$609$	4.00000			0.162088
$610$	21.4049	−	15.6547i	0.866660	−	0.633840i
$611$	18.0606			0.730652
$612$			6.24977i			0.252632i
$613$		−	2.91915i		−	0.117904i	−0.998261	−	0.0589518i	$-0.981224\pi$
$613$		−	2.91915i		−	0.117904i	0.998261	−	0.0589518i	$-0.0187758\pi$
$614$	−4.65940			−0.188038
$615$	−11.2800	+	8.24977i	−0.454855	+	0.332663i
$616$	5.28005			0.212739
$617$			41.0284i			1.65174i	0.563858	+	0.825871i	$0.309316\pi$
$617$			41.0284i			1.65174i	−0.563858	+	0.825871i	$0.690684\pi$
$618$		−	11.7796i		−	0.473845i
$619$	−42.1093			−1.69252			−0.846258	−	0.532774i	$-0.821150\pi$
$619$	−42.1093			−1.69252			−0.846258	+	0.532774i	$0.821150\pi$
$620$	−3.92007	−	5.35998i	−0.157434	−	0.215262i
$621$	1.00000			0.0401286
$622$		−	15.1589i		−	0.607818i
$623$			22.4390i			0.898999i
$624$	4.24977			0.170127
$625$	−20.4087	−	14.4390i	−0.816349	−	0.577560i
$626$	26.6206			1.06398
$627$		−	9.68968i		−	0.386968i
$628$		−	19.0790i		−	0.761336i
$629$	−20.9991			−0.837288
$630$	−2.64002	−	3.60975i	−0.105181	−	0.143816i
$631$	−37.4911			−1.49250			−0.746248	−	0.665668i	$-0.768147\pi$
$631$	−37.4911			−1.49250			−0.746248	+	0.665668i	$0.768147\pi$
$632$		−	9.52982i		−	0.379076i
$633$		−	15.3406i		−	0.609734i
$634$	15.1589			0.602039
$635$	−12.5795	+	9.20012i	−0.499201	+	0.365096i
$636$	12.8898			0.511114
$637$			12.7493i			0.505146i
$638$			5.28005i			0.209039i
$639$	−7.52982			−0.297875
$640$	−1.80487	+	1.32001i	−0.0713439	+	0.0521780i
$641$	−21.2413			−0.838981			−0.419490	−	0.907760i	$-0.637791\pi$
$641$	−21.2413			−0.838981			−0.419490	+	0.907760i	$0.637791\pi$
$642$			8.57947i			0.338605i
$643$		−	23.6997i		−	0.934623i	−0.884093	−	0.467312i	$-0.845223\pi$
$643$		−	23.6997i		−	0.934623i	0.884093	−	0.467312i	$-0.154777\pi$
$644$	−2.00000			−0.0788110
$645$	0.844838	+	1.15516i	0.0332655	+	0.0454844i
$646$	−22.9385			−0.902504
$647$		−	50.5601i		−	1.98772i	−0.110634	−	0.993861i	$-0.535288\pi$
$647$		−	50.5601i		−	1.98772i	0.110634	−	0.993861i	$-0.464712\pi$
$648$			1.00000i			0.0392837i
$649$	−21.9394			−0.861199
$650$	−6.43899	+	20.2498i	−0.252558	+	0.794261i
$651$	5.93945			0.232785
$652$			5.15894i			0.202040i
$653$			40.2791i			1.57624i	0.615519	+	0.788122i	$0.288946\pi$
$653$			40.2791i			1.57624i	−0.615519	+	0.788122i	$0.711054\pi$
$654$	9.13957			0.357385
$655$	1.43991	+	1.96881i	0.0562618	+	0.0769277i
$656$	−6.24977			−0.244013
$657$			9.03028i			0.352305i
$658$		−	8.49954i		−	0.331347i
$659$	−7.79897			−0.303805			−0.151902	−	0.988396i	$-0.548540\pi$
$659$	−7.79897			−0.303805			−0.151902	+	0.988396i	$0.548540\pi$
$660$	4.76491	−	3.48486i	0.185474	−	0.135648i
$661$	16.9797			0.660434			0.330217	−	0.943905i	$-0.392878\pi$
$661$	16.9797			0.660434			0.330217	+	0.943905i	$0.392878\pi$
$662$		−	23.7190i		−	0.921867i
$663$			26.5601i			1.03151i
$664$	17.2001			0.667494
$665$	13.2489	−	9.68968i	0.513769	−	0.375750i
$666$	−3.35998			−0.130196
$667$		−	2.00000i		−	0.0774403i
$668$			22.8099i			0.882540i
$669$	−8.62065			−0.333293
$670$	15.6547	+	21.4049i	0.604794	+	0.826945i
$671$	−31.3094			−1.20869
$672$		−	2.00000i		−	0.0771517i
$673$			37.6509i			1.45134i	0.688045	+	0.725668i	$0.258469\pi$
$673$			37.6509i			1.45134i	−0.688045	+	0.725668i	$0.741531\pi$
$674$	−15.1589			−0.583901
$675$	−4.76491	−	1.51514i	−0.183401	−	0.0583177i
$676$	5.06055			0.194637
$677$		−	16.8898i		−	0.649128i	−0.945864	−	0.324564i	$-0.894783\pi$
$677$		−	16.8898i		−	0.649128i	0.945864	−	0.324564i	$-0.105217\pi$
$678$		−	7.52982i		−	0.289181i
$679$	−36.9991			−1.41989
$680$	−8.24977	−	11.2800i	−0.316364	−	0.432570i
$681$	20.4196			0.782481
$682$			7.84014i			0.300215i
$683$		−	32.4608i		−	1.24208i	−0.783780	−	0.621039i	$-0.786711\pi$
$683$		−	32.4608i		−	1.24208i	0.783780	−	0.621039i	$-0.213289\pi$
$684$	−3.67030			−0.140337
$685$	−18.4995	+	13.5298i	−0.706831	+	0.516948i
$686$	20.0000			0.763604
$687$		−	16.4802i		−	0.628757i
$688$			0.640023i			0.0244007i
$689$	54.7787			2.08690
$690$	−1.80487	+	1.32001i	−0.0687104	+	0.0502520i
$691$	36.9603			1.40604			0.703019	−	0.711171i	$-0.251835\pi$
$691$	36.9603			1.40604			0.703019	+	0.711171i	$0.251835\pi$
$692$		−	9.71904i		−	0.369462i
$693$			5.28005i			0.200572i
$694$	18.2791			0.693866
$695$	13.9394	+	19.0596i	0.528753	+	0.722973i
$696$	2.00000			0.0758098
$697$		−	39.0596i		−	1.47949i
$698$			15.9394i			0.603317i
$699$	−10.1287			−0.383101
$700$	9.52982	+	3.03028i	0.360193	+	0.114534i
$701$	7.92007			0.299137			0.149568	−	0.988751i	$-0.452212\pi$
$701$	7.92007			0.299137			0.149568	+	0.988751i	$0.452212\pi$
$702$			4.24977i			0.160397i
$703$		−	12.3321i		−	0.465115i
$704$	2.64002			0.0994996
$705$	−5.60975	−	7.67030i	−0.211275	−	0.288880i
$706$	22.6282			0.851624
$707$		−	20.9991i		−	0.789752i
$708$			8.31032i			0.312321i
$709$	52.8586			1.98515			0.992573	−	0.121649i	$-0.0388181\pi$
$709$	52.8586			1.98515			0.992573	+	0.121649i	$0.0388181\pi$
$710$	13.5904	−	9.93945i	0.510037	−	0.373021i
$711$	9.52982			0.357396
$712$			11.2195i			0.420468i
$713$		−	2.96972i		−	0.111217i
$714$	12.4995			0.467784
$715$	20.2498	−	14.8099i	0.757298	−	0.553858i
$716$	21.9688			0.821013
$717$		−	5.21949i		−	0.194926i
$718$		−	31.8401i		−	1.18826i
$719$	−16.7200			−0.623549			−0.311775	−	0.950156i	$-0.600923\pi$
$719$	−16.7200			−0.623549			−0.311775	+	0.950156i	$0.600923\pi$
$720$	−1.32001	−	1.80487i	−0.0491939	−	0.0672637i
$721$	−23.5592			−0.877390
$722$			5.52890i			0.205764i
$723$		−	5.21949i		−	0.194115i
$724$	−2.70058			−0.100366
$725$	−3.03028	+	9.52982i	−0.112542	+	0.353929i
$726$	4.03028			0.149578
$727$			13.5592i			0.502882i	0.967873	+	0.251441i	$0.0809044\pi$
$727$			13.5592i			0.502882i	−0.967873	+	0.251441i	$0.919096\pi$
$728$		−	8.49954i		−	0.315014i
$729$	−1.00000			−0.0370370
$730$	−11.9201	−	16.2985i	−0.441182	−	0.603235i
$731$	−4.00000			−0.147945
$732$			11.8595i			0.438340i
$733$		−	0.640023i		−	0.0236398i	−0.999930	−	0.0118199i	$-0.996238\pi$
$733$		−	0.640023i		−	0.0236398i	0.999930	−	0.0118199i	$-0.00376248\pi$
$734$	−6.49954			−0.239902
$735$	5.41462	−	3.96004i	0.199721	−	0.146068i
$736$	−1.00000			−0.0368605
$737$		−	31.3094i		−	1.15330i
$738$		−	6.24977i		−	0.230057i
$739$	31.1807			1.14700			0.573501	−	0.819205i	$-0.305585\pi$
$739$	31.1807			1.14700			0.573501	+	0.819205i	$0.305585\pi$
$740$	6.06433	−	4.43521i	0.222929	−	0.163042i
$741$	−15.5979			−0.573004
$742$		−	25.7796i		−	0.946398i
$743$			34.5601i			1.26789i	0.773379	+	0.633943i	$0.218565\pi$
$743$			34.5601i			1.26789i	−0.773379	+	0.633943i	$0.781435\pi$
$744$	2.96972			0.108875
$745$	14.0450	+	19.2039i	0.514567	+	0.703576i
$746$	−20.6400			−0.755685
$747$			17.2001i			0.629319i
$748$			16.4995i			0.603283i
$749$	17.1589			0.626974
$750$	10.6001	−	3.55510i	0.387059	−	0.129814i
$751$	−18.1892			−0.663734			−0.331867	−	0.943326i	$-0.607679\pi$
$751$	−18.1892			−0.663734			−0.331867	+	0.943326i	$0.607679\pi$
$752$		−	4.24977i		−	0.154973i
$753$		−	13.8595i		−	0.505069i
$754$	8.49954			0.309535
$755$	−10.0194	−	13.6997i	−0.364642	−	0.498582i
$756$	2.00000			0.0727393
$757$		−	51.0403i		−	1.85509i	−0.373712	−	0.927545i	$-0.621915\pi$
$757$		−	51.0403i		−	1.85509i	0.373712	−	0.927545i	$-0.378085\pi$
$758$		−	23.8889i		−	0.867683i
$759$	2.64002			0.0958268
$760$	6.62443	−	4.84484i	0.240293	−	0.175741i
$761$	−14.6206			−0.529998			−0.264999	−	0.964249i	$-0.585372\pi$
$761$	−14.6206			−0.529998			−0.264999	+	0.964249i	$0.585372\pi$
$762$		−	6.96972i		−	0.252486i
$763$		−	18.2791i		−	0.661749i
$764$	−3.34060			−0.120859
$765$	11.2800	−	8.24977i	0.407831	−	0.298271i
$766$	10.0606			0.363503
$767$			35.3170i			1.27522i
$768$		−	1.00000i		−	0.0360844i
$769$	−40.6576			−1.46615			−0.733075	−	0.680148i	$-0.761915\pi$
$769$	−40.6576			−1.46615			−0.733075	+	0.680148i	$0.761915\pi$
$770$	−6.96972	−	9.52982i	−0.251171	−	0.343431i
$771$	−10.9991			−0.396122
$772$			14.5601i			0.524029i
$773$			38.7905i			1.39520i	0.716489	+	0.697598i	$0.245748\pi$
$773$			38.7905i			1.39520i	−0.716489	+	0.697598i	$0.754252\pi$
$774$	−0.640023			−0.0230052
$775$	−4.49954	+	14.1505i	−0.161628	+	0.508300i
$776$	−18.4995			−0.664095
$777$			6.71995i			0.241077i
$778$			1.20012i			0.0430263i
$779$	22.9385			0.821858
$780$	−5.60975	−	7.67030i	−0.200861	−	0.274641i
$781$	−19.8789			−0.711323
$782$		−	6.24977i		−	0.223491i
$783$			2.00000i			0.0714742i
$784$	3.00000			0.107143
$785$	−34.4352	+	25.1845i	−1.22905	+	0.898874i
$786$	−1.09083			−0.0389086
$787$		−	12.1992i		−	0.434855i	−0.976077	−	0.217427i	$-0.930234\pi$
$787$		−	12.1992i		−	0.434855i	0.976077	−	0.217427i	$-0.0697665\pi$
$788$		−	2.00000i		−	0.0712470i
$789$	2.43899			0.0868303
$790$	−17.2001	+	12.5795i	−0.611953	+	0.447558i
$791$	−15.0596			−0.535459
$792$			2.64002i			0.0938091i
$793$			50.4002i			1.78976i
$794$	−18.4702			−0.655482
$795$	−17.0147	−	23.2645i	−0.603449	−	0.825105i
$796$	−10.0294			−0.355481
$797$		−	46.8292i		−	1.65878i	−0.558672	−	0.829388i	$-0.688689\pi$
$797$		−	46.8292i		−	1.65878i	0.558672	−	0.829388i	$-0.311311\pi$
$798$			7.34060i			0.259854i
$799$	26.5601			0.939629
$800$	4.76491	+	1.51514i	0.168465	+	0.0535682i
$801$	−11.2195			−0.396421
$802$		−	20.9991i		−	0.741503i
$803$			23.8401i			0.841300i
$804$	−11.8595			−0.418253
$805$	2.64002	+	3.60975i	0.0930486	+	0.127227i
$806$	12.6206			0.444543
$807$			11.1589i			0.392813i
$808$		−	10.4995i		−	0.369373i
$809$	51.1202			1.79729			0.898645	−	0.438677i	$-0.144553\pi$
$809$	51.1202			1.79729			0.898645	+	0.438677i	$0.144553\pi$
$810$	1.80487	−	1.32001i	0.0634168	−	0.0463805i
$811$	16.2810			0.571702			0.285851	−	0.958274i	$-0.407724\pi$
$811$	16.2810			0.571702			0.285851	+	0.958274i	$0.407724\pi$
$812$		−	4.00000i		−	0.140372i
$813$		−	4.62065i		−	0.162053i
$814$	−8.87042			−0.310908
$815$	9.31124	−	6.80986i	0.326158	−	0.238539i
$816$	6.24977			0.218786
$817$		−	2.34908i		−	0.0821838i
$818$			2.00000i			0.0699284i
$819$	8.49954			0.296998
$820$	8.24977	+	11.2800i	0.288094	+	0.393916i
$821$	−51.6197			−1.80154			−0.900770	−	0.434295i	$-0.856997\pi$
$821$	−51.6197			−1.80154			−0.900770	+	0.434295i	$0.856997\pi$
$822$		−	10.2498i		−	0.357502i
$823$			15.8789i			0.553504i	0.960941	+	0.276752i	$0.0892580\pi$
$823$			15.8789i			0.553504i	−0.960941	+	0.276752i	$0.910742\pi$
$824$	−11.7796			−0.410361
$825$	−12.5795	−	4.00000i	−0.437961	−	0.139262i
$826$	16.6206			0.578306
$827$			10.1017i			0.351271i	0.984455	+	0.175636i	$0.0561981\pi$
$827$			10.1017i			0.351271i	−0.984455	+	0.175636i	$0.943802\pi$
$828$		−	1.00000i		−	0.0347524i
$829$	3.56101			0.123679			0.0618395	−	0.998086i	$-0.480303\pi$
$829$	3.56101			0.123679			0.0618395	+	0.998086i	$0.480303\pi$
$830$	−22.7044	−	31.0440i	−0.788080	−	1.07755i
$831$	−14.6888			−0.509547
$832$		−	4.24977i		−	0.147334i
$833$			18.7493i			0.649625i
$834$	−10.5601			−0.365666
$835$	41.1689	−	30.1093i	1.42471	−	1.04197i
$836$	−9.68968			−0.335124
$837$			2.96972i			0.102649i
$838$		−	4.41961i		−	0.152673i
$839$	−40.0587			−1.38298			−0.691490	−	0.722386i	$-0.743046\pi$
$839$	−40.0587			−1.38298			−0.691490	+	0.722386i	$0.743046\pi$
$840$	−3.60975	+	2.64002i	−0.124548	+	0.0910895i
$841$	−25.0000			−0.862069
$842$		−	24.3591i		−	0.839469i
$843$		−	1.15894i		−	0.0399161i
$844$	−15.3406			−0.528045
$845$	−6.67999	−	9.13366i	−0.229799	−	0.314207i
$846$	4.24977			0.146110
$847$		−	8.06055i		−	0.276964i
$848$		−	12.8898i		−	0.442637i
$849$	−11.7384			−0.402861
$850$	−9.46927	+	29.7796i	−0.324793	+	1.02143i
$851$	3.35998			0.115179
$852$			7.52982i			0.257967i
$853$			32.0899i			1.09874i	0.835580	+	0.549369i	$0.185132\pi$
$853$			32.0899i			1.09874i	−0.835580	+	0.549369i	$0.814868\pi$
$854$	23.7190			0.811649
$855$	4.84484	+	6.62443i	0.165690	+	0.226551i
$856$	8.57947			0.293240
$857$		−	18.0076i		−	0.615127i	−0.951528	−	0.307563i	$-0.900486\pi$
$857$		−	18.0076i		−	0.615127i	0.951528	−	0.307563i	$-0.0995136\pi$
$858$			11.2195i			0.383027i
$859$	10.4390			0.356174			0.178087	−	0.984015i	$-0.443009\pi$
$859$	10.4390			0.356174			0.178087	+	0.984015i	$0.443009\pi$
$860$	1.15516	−	0.844838i	0.0393907	−	0.0288088i
$861$	−12.4995			−0.425983
$862$			34.1580i			1.16343i
$863$			21.1202i			0.718940i	0.933157	+	0.359470i	$0.117042\pi$
$863$			21.1202i			0.718940i	−0.933157	+	0.359470i	$0.882958\pi$
$864$	1.00000			0.0340207
$865$	−17.5416	+	12.8292i	−0.596433	+	0.436207i
$866$	5.87890			0.199773
$867$			22.0596i			0.749185i
$868$		−	5.93945i		−	0.201598i
$869$	25.1589			0.853459
$870$	−2.64002	−	3.60975i	−0.0895052	−	0.122382i
$871$	−50.4002			−1.70775
$872$		−	9.13957i		−	0.309505i
$873$		−	18.4995i		−	0.626115i
$874$	3.67030			0.124150
$875$	−7.11021	−	21.2001i	−0.240369	−	0.716695i
$876$	9.03028			0.305105
$877$		−	32.1287i		−	1.08491i	−0.840086	−	0.542454i	$-0.817495\pi$
$877$		−	32.1287i		−	1.08491i	0.840086	−	0.542454i	$-0.182505\pi$
$878$		−	18.9385i		−	0.639144i
$879$	−26.1698			−0.882687
$880$	−3.48486	−	4.76491i	−0.117475	−	0.160625i
$881$	44.2186			1.48976			0.744881	−	0.667197i	$-0.232506\pi$
$881$	44.2186			1.48976			0.744881	+	0.667197i	$0.232506\pi$
$882$			3.00000i			0.101015i
$883$			46.6576i			1.57015i	0.619399	+	0.785076i	$0.287376\pi$
$883$			46.6576i			1.57015i	−0.619399	+	0.785076i	$0.712624\pi$
$884$	26.5601			0.893313
$885$	14.9991	−	10.9697i	0.504189	−	0.368743i
$886$	−4.00000			−0.134383
$887$			7.62912i			0.256161i	0.991764	+	0.128080i	$0.0408816\pi$
$887$			7.62912i			0.256161i	−0.991764	+	0.128080i	$0.959118\pi$
$888$			3.35998i			0.112753i
$889$	−13.9394			−0.467514
$890$	20.2498	−	14.8099i	0.678774	−	0.496428i
$891$	−2.64002			−0.0884441
$892$			8.62065i			0.288641i
$893$			15.5979i			0.521965i
$894$	−10.6400			−0.355856
$895$	−28.9991	−	39.6509i	−0.969332	−	1.32538i
$896$	−2.00000			−0.0668153
$897$		−	4.24977i		−	0.141896i
$898$		−	14.6282i		−	0.488150i
$899$	5.93945			0.198092
$900$	−1.51514	+	4.76491i	−0.0505046	+	0.158830i
$901$	80.5583			2.68378
$902$		−	16.4995i		−	0.549375i
$903$			1.28005i			0.0425973i
$904$	−7.52982			−0.250438
$905$	3.56479	+	4.87420i	0.118498	+	0.162024i
$906$	7.59037			0.252173
$907$			11.0790i			0.367873i	0.982938	+	0.183936i	$0.0588840\pi$
$907$			11.0790i			0.367873i	−0.982938	+	0.183936i	$0.941116\pi$
$908$		−	20.4196i		−	0.677649i
$909$	10.4995			0.348248
$910$	−15.3406	+	11.2195i	−0.508536	+	0.371923i
$911$	−0.280964			−0.00930874			−0.00465437	−	0.999989i	$-0.501482\pi$
$911$	−0.280964			−0.00930874			−0.00465437	+	0.999989i	$0.501482\pi$
$912$			3.67030i			0.121536i
$913$			45.4087i			1.50281i
$914$	12.0606			0.398928
$915$	21.4049	−	15.6547i	0.707625	−	0.517529i
$916$	−16.4802			−0.544520
$917$			2.18166i			0.0720446i
$918$			6.24977i			0.206273i
$919$	12.4096			0.409356			0.204678	−	0.978829i	$-0.434385\pi$
$919$	12.4096			0.409356			0.204678	+	0.978829i	$0.434385\pi$
$920$	1.32001	+	1.80487i	0.0435195	+	0.0595049i
$921$	−4.65940			−0.153532
$922$		−	9.34060i		−	0.307616i
$923$			32.0000i			1.05329i
$924$	5.28005			0.173701
$925$	−16.0100	−	5.09083i	−0.526405	−	0.167385i
$926$	17.5298			0.576066
$927$		−	11.7796i		−	0.386892i
$928$		−	2.00000i		−	0.0656532i
$929$	45.0672			1.47861			0.739303	−	0.673372i	$-0.235155\pi$
$929$	45.0672			1.47861			0.739303	+	0.673372i	$0.235155\pi$
$930$	−3.92007	−	5.35998i	−0.128544	−	0.175761i
$931$	−11.0109			−0.360868
$932$			10.1287i			0.331776i
$933$		−	15.1589i		−	0.496281i
$934$	−27.0185			−0.884071
$935$	29.7796	−	21.7796i	0.973897	−	0.712269i
$936$	4.24977			0.138908
$937$			6.78051i			0.221509i	0.993848	+	0.110755i	$0.0353268\pi$
$937$			6.78051i			0.221509i	−0.993848	+	0.110755i	$0.964673\pi$
$938$			23.7190i			0.774454i
$939$	26.6206			0.868732
$940$	−7.67030	+	5.60975i	−0.250178	+	0.182970i
$941$	18.0781			0.589329			0.294665	−	0.955601i	$-0.404792\pi$
$941$	18.0781			0.589329			0.294665	+	0.955601i	$0.404792\pi$
$942$		−	19.0790i		−	0.621628i
$943$			6.24977i			0.203521i
$944$	8.31032			0.270478
$945$	−2.64002	−	3.60975i	−0.0858800	−	0.117425i
$946$	−1.68968			−0.0549361
$947$			50.7787i			1.65009i	0.565071	+	0.825043i	$0.308849\pi$
$947$			50.7787i			1.65009i	−0.565071	+	0.825043i	$0.691151\pi$
$948$		−	9.52982i		−	0.309514i
$949$	38.3766			1.24576
$950$	−17.4886	−	5.56101i	−0.567407	−	0.180423i
$951$	15.1589			0.491562
$952$		−	12.4995i		−	0.405112i
$953$		−	51.6273i		−	1.67237i	−0.548446	−	0.836186i	$-0.684780\pi$
$953$		−	51.6273i		−	1.67237i	0.548446	−	0.836186i	$-0.315220\pi$
$954$	12.8898			0.417322
$955$	4.40963	+	6.02936i	0.142692	+	0.195105i
$956$	−5.21949			−0.168811
$957$			5.28005i			0.170680i
$958$			40.0587i			1.29424i
$959$	−20.4995			−0.661965
$960$	−1.80487	+	1.32001i	−0.0582520	+	0.0426032i
$961$	−22.1807			−0.715508
$962$			14.2791i			0.460378i
$963$			8.57947i			0.276470i
$964$	−5.21949			−0.168109
$965$	26.2791	−	19.2195i	0.845955	−	0.618697i
$966$	−2.00000			−0.0643489
$967$			50.1193i			1.61173i	0.592101	+	0.805864i	$0.298299\pi$
$967$			50.1193i			1.61173i	−0.592101	+	0.805864i	$0.701701\pi$
$968$		−	4.03028i		−	0.129538i
$969$	−22.9385			−0.736892
$970$	24.4196	+	33.3893i	0.784066	+	1.07207i
$971$	17.5786			0.564123			0.282061	−	0.959396i	$-0.408982\pi$
$971$	17.5786			0.564123			0.282061	+	0.959396i	$0.408982\pi$
$972$			1.00000i			0.0320750i
$973$			21.1202i			0.677082i
$974$	14.9697			0.479661
$975$	−6.43899	+	20.2498i	−0.206213	+	0.648512i
$976$	11.8595			0.379614
$977$			20.1892i			0.645910i	0.946414	+	0.322955i	$0.104676\pi$
$977$			20.1892i			0.645910i	−0.946414	+	0.322955i	$0.895324\pi$
$978$			5.15894i			0.164965i
$979$	−29.6197			−0.946651
$980$	−3.96004	−	5.41462i	−0.126499	−	0.172964i
$981$	9.13957			0.291804
$982$			28.5289i			0.910394i
$983$		−	49.6585i		−	1.58386i	−0.610612	−	0.791930i	$-0.709077\pi$
$983$		−	49.6585i		−	1.58386i	0.610612	−	0.791930i	$-0.290923\pi$
$984$	−6.24977			−0.199235
$985$	−3.60975	+	2.64002i	−0.115016	+	0.0841181i
$986$	12.4995			0.398067
$987$		−	8.49954i		−	0.270543i
$988$			15.5979i			0.496236i
$989$	0.640023			0.0203516
$990$	4.76491	−	3.48486i	0.151439	−	0.110756i
$991$	1.90826			0.0606177			0.0303089	−	0.999541i	$-0.490351\pi$
$991$	1.90826			0.0606177			0.0303089	+	0.999541i	$0.490351\pi$
$992$		−	2.96972i		−	0.0942888i
$993$		−	23.7190i		−	0.752701i
$994$	15.0596			0.477663
$995$	13.2389	+	18.1017i	0.419700	+	0.573863i
$996$	17.2001			0.545007
$997$		−	57.5298i		−	1.82199i	−0.412420	−	0.910994i	$-0.635316\pi$
$997$		−	57.5298i		−	1.82199i	0.412420	−	0.910994i	$-0.364684\pi$
$998$			33.2800i			1.05346i
$999$	−3.35998			−0.106305

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.d.d.139.3	✓	6
3.2	odd	2		2070.2.d.d.829.4		6
5.2	odd	4		3450.2.a.br.1.1		3
5.3	odd	4		3450.2.a.bq.1.1		3
5.4	even	2	inner	690.2.d.d.139.6	yes	6
15.14	odd	2		2070.2.d.d.829.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.d.d.139.3	✓	6	1.1	even	1	trivial
690.2.d.d.139.6	yes	6	5.4	even	2	inner
2070.2.d.d.829.1		6	15.14	odd	2
2070.2.d.d.829.4		6	3.2	odd	2
3450.2.a.bq.1.1		3	5.3	odd	4
3450.2.a.br.1.1		3	5.2	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(1.32001 + 1.80487i) q^{5} -1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(1.32001 + 1.80487i) q^{5} -1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(1.80487 - 1.32001i) q^{10} -2.64002 q^{11} +1.00000i q^{12} +4.24977i q^{13} +2.00000 q^{14} +(1.80487 - 1.32001i) q^{15} +1.00000 q^{16} +6.24977i q^{17} +1.00000i q^{18} -3.67030 q^{19} +(-1.32001 - 1.80487i) q^{20} +2.00000 q^{21} +2.64002i q^{22} -1.00000i q^{23} +1.00000 q^{24} +(-1.51514 + 4.76491i) q^{25} +4.24977 q^{26} +1.00000i q^{27} -2.00000i q^{28} +2.00000 q^{29} +(-1.32001 - 1.80487i) q^{30} +2.96972 q^{31} -1.00000i q^{32} +2.64002i q^{33} +6.24977 q^{34} +(-3.60975 + 2.64002i) q^{35} +1.00000 q^{36} +3.35998i q^{37} +3.67030i q^{38} +4.24977 q^{39} +(-1.80487 + 1.32001i) q^{40} -6.24977 q^{41} -2.00000i q^{42} +0.640023i q^{43} +2.64002 q^{44} +(-1.32001 - 1.80487i) q^{45} -1.00000 q^{46} -4.24977i q^{47} -1.00000i q^{48} +3.00000 q^{49} +(4.76491 + 1.51514i) q^{50} +6.24977 q^{51} -4.24977i q^{52} -12.8898i q^{53} +1.00000 q^{54} +(-3.48486 - 4.76491i) q^{55} -2.00000 q^{56} +3.67030i q^{57} -2.00000i q^{58} +8.31032 q^{59} +(-1.80487 + 1.32001i) q^{60} +11.8595 q^{61} -2.96972i q^{62} -2.00000i q^{63} -1.00000 q^{64} +(-7.67030 + 5.60975i) q^{65} +2.64002 q^{66} +11.8595i q^{67} -6.24977i q^{68} -1.00000 q^{69} +(2.64002 + 3.60975i) q^{70} +7.52982 q^{71} -1.00000i q^{72} -9.03028i q^{73} +3.35998 q^{74} +(4.76491 + 1.51514i) q^{75} +3.67030 q^{76} -5.28005i q^{77} -4.24977i q^{78} -9.52982 q^{79} +(1.32001 + 1.80487i) q^{80} +1.00000 q^{81} +6.24977i q^{82} -17.2001i q^{83} -2.00000 q^{84} +(-11.2800 + 8.24977i) q^{85} +0.640023 q^{86} -2.00000i q^{87} -2.64002i q^{88} +11.2195 q^{89} +(-1.80487 + 1.32001i) q^{90} -8.49954 q^{91} +1.00000i q^{92} -2.96972i q^{93} -4.24977 q^{94} +(-4.84484 - 6.62443i) q^{95} -1.00000 q^{96} +18.4995i q^{97} -3.00000i q^{98} +2.64002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9	\( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} + 12 q^{14} + 2 q^{15} + 6 q^{16} - 8 q^{19} + 12 q^{21} + 6 q^{24} - 10 q^{25} - 8 q^{26} + 12 q^{29} + 16 q^{31} + 4 q^{34} - 4 q^{35} + 6 q^{36} - 8 q^{39} - 2 q^{40} - 4 q^{41} - 6 q^{46} + 18 q^{49} - 4 q^{50} + 4 q^{51} + 6 q^{54} - 20 q^{55} - 12 q^{56} + 20 q^{59} - 2 q^{60} + 20 q^{61} - 6 q^{64} - 32 q^{65} - 6 q^{69} - 20 q^{71} + 36 q^{74} - 4 q^{75} + 8 q^{76} + 8 q^{79} + 6 q^{81} - 12 q^{84} - 36 q^{85} - 12 q^{86} + 32 q^{89} - 2 q^{90} + 16 q^{91} + 8 q^{94} - 44 q^{95} - 6 q^{96}+O(q^{100}) \) 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 + 12 * q^14 + 2 * q^15 + 6 * q^16 - 8 * q^19 + 12 * q^21 + 6 * q^24 - 10 * q^25 - 8 * q^26 + 12 * q^29 + 16 * q^31 + 4 * q^34 - 4 * q^35 + 6 * q^36 - 8 * q^39 - 2 * q^40 - 4 * q^41 - 6 * q^46 + 18 * q^49 - 4 * q^50 + 4 * q^51 + 6 * q^54 - 20 * q^55 - 12 * q^56 + 20 * q^59 - 2 * q^60 + 20 * q^61 - 6 * q^64 - 32 * q^65 - 6 * q^69 - 20 * q^71 + 36 * q^74 - 4 * q^75 + 8 * q^76 + 8 * q^79 + 6 * q^81 - 12 * q^84 - 36 * q^85 - 12 * q^86 + 32 * q^89 - 2 * q^90 + 16 * q^91 + 8 * q^94 - 44 * q^95 - 6 * q^96

Introduction

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