LMFDB - Embedded newform 1045.2.b.e.419.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(419,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.b (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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.15
Character	$\chi$	$=$	1045.419
Dual form			1045.2.b.e.419.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.202376i q^{2} +2.47875i q^{3} +1.95904 q^{4} +(-1.53426 - 1.62666i) q^{5} +0.501638 q^{6} +5.06314i q^{7} -0.801215i q^{8} -3.14418 q^{9} +O(q^{10})$	\(q-0.202376i q^{2} +2.47875i q^{3} +1.95904 q^{4} +(-1.53426 - 1.62666i) q^{5} +0.501638 q^{6} +5.06314i q^{7} -0.801215i q^{8} -3.14418 q^{9} +(-0.329197 + 0.310498i) q^{10} +1.00000 q^{11} +4.85597i q^{12} +1.72877i q^{13} +1.02466 q^{14} +(4.03208 - 3.80305i) q^{15} +3.75594 q^{16} +2.65088i q^{17} +0.636306i q^{18} -1.00000 q^{19} +(-3.00569 - 3.18670i) q^{20} -12.5502 q^{21} -0.202376i q^{22} -6.75421i q^{23} +1.98601 q^{24} +(-0.292065 + 4.99146i) q^{25} +0.349861 q^{26} -0.357381i q^{27} +9.91891i q^{28} -10.1690 q^{29} +(-0.769646 - 0.815996i) q^{30} +6.13793 q^{31} -2.36254i q^{32} +2.47875i q^{33} +0.536473 q^{34} +(8.23602 - 7.76819i) q^{35} -6.15958 q^{36} +7.01000i q^{37} +0.202376i q^{38} -4.28518 q^{39} +(-1.30331 + 1.22928i) q^{40} -3.72063 q^{41} +2.53986i q^{42} -0.935858i q^{43} +1.95904 q^{44} +(4.82400 + 5.11452i) q^{45} -1.36689 q^{46} +3.29300i q^{47} +9.31002i q^{48} -18.6354 q^{49} +(1.01015 + 0.0591069i) q^{50} -6.57085 q^{51} +3.38674i q^{52} +0.668027i q^{53} -0.0723253 q^{54} +(-1.53426 - 1.62666i) q^{55} +4.05666 q^{56} -2.47875i q^{57} +2.05796i q^{58} +3.35364 q^{59} +(7.89903 - 7.45034i) q^{60} +13.2751 q^{61} -1.24217i q^{62} -15.9194i q^{63} +7.03376 q^{64} +(2.81213 - 2.65239i) q^{65} +0.501638 q^{66} -12.8646i q^{67} +5.19318i q^{68} +16.7420 q^{69} +(-1.57209 - 1.66677i) q^{70} +0.833169 q^{71} +2.51916i q^{72} +1.38130i q^{73} +1.41865 q^{74} +(-12.3726 - 0.723955i) q^{75} -1.95904 q^{76} +5.06314i q^{77} +0.867217i q^{78} -11.3823 q^{79} +(-5.76261 - 6.10965i) q^{80} -8.54668 q^{81} +0.752965i q^{82} +14.3628i q^{83} -24.5865 q^{84} +(4.31208 - 4.06714i) q^{85} -0.189395 q^{86} -25.2064i q^{87} -0.801215i q^{88} +1.51234 q^{89} +(1.03505 - 0.976261i) q^{90} -8.75300 q^{91} -13.2318i q^{92} +15.2144i q^{93} +0.666425 q^{94} +(1.53426 + 1.62666i) q^{95} +5.85614 q^{96} -14.9617i q^{97} +3.77135i q^{98} -3.14418 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) $ 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9	$ 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9} + 10 q^{10} + 30 q^{11} + 4 q^{14} + 4 q^{15} + 66 q^{16} - 30 q^{19} + 10 q^{20} + 14 q^{21} - 22 q^{24} - 6 q^{25} - 30 q^{29} + 14 q^{30} + 26 q^{31} - 12 q^{34} + 6 q^{35} + 78 q^{36} - 64 q^{39} - 20 q^{40} + 22 q^{41} - 42 q^{44} + 6 q^{45} + 28 q^{46} - 60 q^{49} + 64 q^{51} - 62 q^{54} - 32 q^{56} + 14 q^{59} - 28 q^{60} + 78 q^{61} - 90 q^{64} + 40 q^{65} + 12 q^{66} + 28 q^{69} + 12 q^{70} + 20 q^{71} - 42 q^{74} + 50 q^{75} + 42 q^{76} - 102 q^{79} - 40 q^{80} + 42 q^{81} - 98 q^{84} - 2 q^{85} - 52 q^{86} + 8 q^{89} + 22 q^{90} + 56 q^{91} - 40 q^{94} - 74 q^{96} - 40 q^{99}+O(q^{100}) $ 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9 + 10 * q^10 + 30 * q^11 + 4 * q^14 + 4 * q^15 + 66 * q^16 - 30 * q^19 + 10 * q^20 + 14 * q^21 - 22 * q^24 - 6 * q^25 - 30 * q^29 + 14 * q^30 + 26 * q^31 - 12 * q^34 + 6 * q^35 + 78 * q^36 - 64 * q^39 - 20 * q^40 + 22 * q^41 - 42 * q^44 + 6 * q^45 + 28 * q^46 - 60 * q^49 + 64 * q^51 - 62 * q^54 - 32 * q^56 + 14 * q^59 - 28 * q^60 + 78 * q^61 - 90 * q^64 + 40 * q^65 + 12 * q^66 + 28 * q^69 + 12 * q^70 + 20 * q^71 - 42 * q^74 + 50 * q^75 + 42 * q^76 - 102 * q^79 - 40 * q^80 + 42 * q^81 - 98 * q^84 - 2 * q^85 - 52 * q^86 + 8 * q^89 + 22 * q^90 + 56 * q^91 - 40 * q^94 - 74 * q^96 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	0.202376i		−	0.143101i	−0.997437	−	0.0715507i	$-0.977205\pi$
$2$		−	0.202376i		−	0.143101i	0.997437	−	0.0715507i	$-0.0227948\pi$
$3$			2.47875i			1.43110i	0.698559	+	0.715552i	$0.253825\pi$
$3$			2.47875i			1.43110i	−0.698559	+	0.715552i	$0.746175\pi$
$4$	1.95904			0.979522
$5$	−1.53426	−	1.62666i	−0.686144	−	0.727466i
$5$	−1.53426	−	1.62666i	−0.686144	−	0.727466i
$6$	0.501638			0.204793
$7$			5.06314i			1.91369i	0.290605	+	0.956843i	$0.406143\pi$
$7$			5.06314i			1.91369i	−0.290605	+	0.956843i	$0.593857\pi$
$8$		−	0.801215i		−	0.283272i
$9$	−3.14418			−1.04806
$10$	−0.329197	+	0.310498i	−0.104101	+	0.0981881i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$			4.85597i			1.40180i
$13$			1.72877i			0.479474i	0.970838	+	0.239737i	$0.0770613\pi$
$13$			1.72877i			0.479474i	−0.970838	+	0.239737i	$0.922939\pi$
$14$	1.02466			0.273851
$15$	4.03208	−	3.80305i	1.04108	−	0.981944i
$16$	3.75594			0.938985
$17$			2.65088i			0.642932i	0.946921	+	0.321466i	$0.104176\pi$
$17$			2.65088i			0.642932i	−0.946921	+	0.321466i	$0.895824\pi$
$18$			0.636306i			0.149979i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−3.00569	−	3.18670i	−0.672093	−	0.712569i
$21$	−12.5502			−2.73868
$22$		−	0.202376i		−	0.0431467i
$23$		−	6.75421i		−	1.40835i	−0.710027	−	0.704175i	$-0.751317\pi$
$23$		−	6.75421i		−	1.40835i	0.710027	−	0.704175i	$-0.248683\pi$
$24$	1.98601			0.405392
$25$	−0.292065	+	4.99146i	−0.0584130	+	0.998293i
$26$	0.349861			0.0686134
$27$		−	0.357381i		−	0.0687780i
$28$			9.91891i			1.87450i
$29$	−10.1690			−1.88834			−0.944169	−	0.329462i	$-0.893133\pi$
$29$	−10.1690			−1.88834			−0.944169	+	0.329462i	$0.893133\pi$
$30$	−0.769646	−	0.815996i	−0.140517	−	0.148980i
$31$	6.13793			1.10240			0.551202	−	0.834372i	$-0.314169\pi$
$31$	6.13793			1.10240			0.551202	+	0.834372i	$0.314169\pi$
$32$		−	2.36254i		−	0.417642i
$33$			2.47875i			0.431494i
$34$	0.536473			0.0920044
$35$	8.23602	−	7.76819i	1.39214	−	1.31306i
$36$	−6.15958			−1.02660
$37$			7.01000i			1.15244i	0.817296	+	0.576218i	$0.195472\pi$
$37$			7.01000i			1.15244i	−0.817296	+	0.576218i	$0.804528\pi$
$38$			0.202376i			0.0328297i
$39$	−4.28518			−0.686178
$40$	−1.30331	+	1.22928i	−0.206071	+	0.194366i
$41$	−3.72063			−0.581064			−0.290532	−	0.956865i	$-0.593832\pi$
$41$	−3.72063			−0.581064			−0.290532	+	0.956865i	$0.593832\pi$
$42$			2.53986i			0.391909i
$43$		−	0.935858i		−	0.142717i	−0.997451	−	0.0713585i	$-0.977267\pi$
$43$		−	0.935858i		−	0.142717i	0.997451	−	0.0713585i	$-0.0227334\pi$
$44$	1.95904			0.295337
$45$	4.82400	+	5.11452i	0.719120	+	0.762427i
$46$	−1.36689			−0.201537
$47$			3.29300i			0.480334i	0.970732	+	0.240167i	$0.0772022\pi$
$47$			3.29300i			0.480334i	−0.970732	+	0.240167i	$0.922798\pi$
$48$			9.31002i			1.34379i
$49$	−18.6354			−2.66220
$50$	1.01015	+	0.0591069i	0.142857	+	0.00835898i
$51$	−6.57085			−0.920103
$52$			3.38674i			0.469656i
$53$			0.668027i			0.0917606i	0.998947	+	0.0458803i	$0.0146093\pi$
$53$			0.668027i			0.0917606i	−0.998947	+	0.0458803i	$0.985391\pi$
$54$	−0.0723253			−0.00984222
$55$	−1.53426	−	1.62666i	−0.206880	−	0.219339i
$56$	4.05666			0.542094
$57$		−	2.47875i		−	0.328318i
$58$			2.05796i			0.270224i
$59$	3.35364			0.436606			0.218303	−	0.975881i	$-0.429948\pi$
$59$	3.35364			0.436606			0.218303	+	0.975881i	$0.429948\pi$
$60$	7.89903	−	7.45034i	1.01976	−	0.961835i
$61$	13.2751			1.69970			0.849850	−	0.527024i	$-0.176692\pi$
$61$	13.2751			1.69970			0.849850	+	0.527024i	$0.176692\pi$
$62$		−	1.24217i		−	0.157755i
$63$		−	15.9194i		−	2.00566i
$64$	7.03376			0.879220
$65$	2.81213	−	2.65239i	0.348801	−	0.328988i
$66$	0.501638			0.0617474
$67$		−	12.8646i		−	1.57166i	−0.618444	−	0.785829i	$-0.712236\pi$
$67$		−	12.8646i		−	1.57166i	0.618444	−	0.785829i	$-0.287764\pi$
$68$			5.19318i			0.629766i
$69$	16.7420			2.01550
$70$	−1.57209	−	1.66677i	−0.187901	−	0.199217i
$71$	0.833169			0.0988790			0.0494395	−	0.998777i	$-0.484257\pi$
$71$	0.833169			0.0988790			0.0494395	+	0.998777i	$0.484257\pi$
$72$			2.51916i			0.296886i
$73$			1.38130i			0.161669i	0.996728	+	0.0808345i	$0.0257585\pi$
$73$			1.38130i			0.161669i	−0.996728	+	0.0808345i	$0.974241\pi$
$74$	1.41865			0.164915
$75$	−12.3726	−	0.723955i	−1.42866	−	0.0835951i
$76$	−1.95904			−0.224718
$77$			5.06314i			0.576998i
$78$			0.867217i			0.0981930i
$79$	−11.3823			−1.28061			−0.640306	−	0.768120i	$-0.721193\pi$
$79$	−11.3823			−1.28061			−0.640306	+	0.768120i	$0.721193\pi$
$80$	−5.76261	−	6.10965i	−0.644279	−	0.683080i
$81$	−8.54668			−0.949631
$82$			0.752965i			0.0831511i
$83$			14.3628i			1.57652i	0.615341	+	0.788261i	$0.289018\pi$
$83$			14.3628i			1.57652i	−0.615341	+	0.788261i	$0.710982\pi$
$84$	−24.5865			−2.68260
$85$	4.31208	−	4.06714i	0.467711	−	0.441144i
$86$	−0.189395			−0.0204230
$87$		−	25.2064i		−	2.70241i
$88$		−	0.801215i		−	0.0854098i
$89$	1.51234			0.160308			0.0801540	−	0.996782i	$-0.474459\pi$
$89$	1.51234			0.160308			0.0801540	+	0.996782i	$0.474459\pi$
$90$	1.03505	−	0.976261i	0.109104	−	0.102907i
$91$	−8.75300			−0.917564
$92$		−	13.2318i		−	1.37951i
$93$			15.2144i			1.57765i
$94$	0.666425			0.0687364
$95$	1.53426	+	1.62666i	0.157412	+	0.166892i
$96$	5.85614			0.597690
$97$		−	14.9617i		−	1.51913i	−0.650434	−	0.759563i	$-0.725413\pi$
$97$		−	14.9617i		−	1.51913i	0.650434	−	0.759563i	$-0.274587\pi$
$98$			3.77135i			0.380964i
$99$	−3.14418			−0.316002
$100$	−0.572168	+	9.77849i	−0.0572168	+	0.977849i
$101$	6.11490			0.608455			0.304227	−	0.952599i	$-0.401602\pi$
$101$	6.11490			0.608455			0.304227	+	0.952599i	$0.401602\pi$
$102$			1.32978i			0.131668i
$103$			18.1934i			1.79265i	0.443394	+	0.896327i	$0.353774\pi$
$103$			18.1934i			1.79265i	−0.443394	+	0.896327i	$0.646226\pi$
$104$	1.38512			0.135822
$105$	19.2554	+	20.4150i	1.87913	+	1.99230i
$106$	0.135193			0.0131311
$107$			1.35532i			0.131023i	0.997852	+	0.0655117i	$0.0208680\pi$
$107$			1.35532i			0.131023i	−0.997852	+	0.0655117i	$0.979132\pi$
$108$		−	0.700125i		−	0.0673696i
$109$	5.01210			0.480072			0.240036	−	0.970764i	$-0.422841\pi$
$109$	5.01210			0.480072			0.240036	+	0.970764i	$0.422841\pi$
$110$	−0.329197	+	0.310498i	−0.0313877	+	0.0296048i
$111$	−17.3760			−1.64926
$112$			19.0169i			1.79692i
$113$		−	8.91136i		−	0.838310i	−0.907915	−	0.419155i	$-0.862326\pi$
$113$		−	8.91136i		−	0.838310i	0.907915	−	0.419155i	$-0.137674\pi$
$114$	−0.501638			−0.0469827
$115$	−10.9868	+	10.3627i	−1.02453	+	0.966331i
$116$	−19.9215			−1.84967
$117$		−	5.43556i		−	0.502518i
$118$		−	0.678695i		−	0.0624789i
$119$	−13.4218			−1.23037
$120$	−3.04706	−	3.23056i	−0.278157	−	0.294909i
$121$	1.00000			0.0909091
$122$		−	2.68656i		−	0.243229i
$123$		−	9.22249i		−	0.831564i
$124$	12.0245			1.07983
$125$	8.56753	−	7.18313i	0.766303	−	0.642479i
$126$	−3.22170			−0.287012
$127$			6.60871i			0.586428i	0.956047	+	0.293214i	$0.0947249\pi$
$127$			6.60871i			0.586428i	−0.956047	+	0.293214i	$0.905275\pi$
$128$		−	6.14855i		−	0.543460i
$129$	2.31975			0.204243
$130$	−0.536780	−	0.569106i	−0.0470787	−	0.0499139i
$131$	5.78122			0.505108			0.252554	−	0.967583i	$-0.418729\pi$
$131$	5.78122			0.505108			0.252554	+	0.967583i	$0.418729\pi$
$132$			4.85597i			0.422658i
$133$		−	5.06314i		−	0.439030i
$134$	−2.60348			−0.224906
$135$	−0.581338	+	0.548317i	−0.0500337	+	0.0471916i
$136$	2.12392			0.182125
$137$			9.55287i			0.816156i	0.912947	+	0.408078i	$0.133801\pi$
$137$			9.55287i			0.816156i	−0.912947	+	0.408078i	$0.866199\pi$
$138$		−	3.38817i		−	0.288420i
$139$	8.39417			0.711984			0.355992	−	0.934489i	$-0.384143\pi$
$139$	8.39417			0.711984			0.355992	+	0.934489i	$0.384143\pi$
$140$	16.1347	−	15.2182i	1.36363	−	1.28618i
$141$	−8.16252			−0.687408
$142$		−	0.168613i		−	0.0141497i
$143$			1.72877i			0.144567i
$144$	−11.8093			−0.984112
$145$	15.6020	+	16.5416i	1.29567	+	1.37370i
$146$	0.279542			0.0231350
$147$		−	46.1923i		−	3.80988i
$148$			13.7329i			1.12884i
$149$	9.09038			0.744713			0.372356	−	0.928090i	$-0.378550\pi$
$149$	9.09038			0.744713			0.372356	+	0.928090i	$0.378550\pi$
$150$	−0.146511	+	2.50391i	−0.0119626	+	0.204443i
$151$	11.6838			0.950815			0.475407	−	0.879766i	$-0.342301\pi$
$151$	11.6838			0.950815			0.475407	+	0.879766i	$0.342301\pi$
$152$			0.801215i			0.0649871i
$153$		−	8.33483i		−	0.673831i
$154$	1.02466			0.0825692
$155$	−9.41720	−	9.98434i	−0.756408	−	0.801961i
$156$	−8.39486			−0.672126
$157$		−	13.3380i		−	1.06449i	−0.846590	−	0.532246i	$-0.821348\pi$
$157$		−	13.3380i		−	1.06449i	0.846590	−	0.532246i	$-0.178652\pi$
$158$			2.30351i			0.183257i
$159$	−1.65587			−0.131319
$160$	−3.84306	+	3.62476i	−0.303820	+	0.286563i
$161$	34.1975			2.69514
$162$			1.72964i			0.135893i
$163$		−	2.77342i		−	0.217231i	−0.994084	−	0.108616i	$-0.965358\pi$
$163$		−	2.77342i		−	0.217231i	0.994084	−	0.108616i	$-0.0346418\pi$
$164$	−7.28887			−0.569165
$165$	4.03208	−	3.80305i	0.313897	−	0.296067i
$166$	2.90668			0.225602
$167$		−	9.90398i		−	0.766393i	−0.923667	−	0.383196i	$-0.874823\pi$
$167$		−	9.90398i		−	0.766393i	0.923667	−	0.383196i	$-0.125177\pi$
$168$			10.0554i			0.775793i
$169$	10.0114			0.770104
$170$	−0.823092	−	0.872661i	−0.0631283	−	0.0669301i
$171$	3.14418			0.240441
$172$		−	1.83339i		−	0.139795i
$173$			4.99846i			0.380026i	0.981782	+	0.190013i	$0.0608530\pi$
$173$			4.99846i			0.380026i	−0.981782	+	0.190013i	$0.939147\pi$
$174$	−5.10116			−0.386718
$175$	−25.2725	−	1.47877i	−1.91042	−	0.111784i
$176$	3.75594			0.283115
$177$			8.31281i			0.624829i
$178$		−	0.306061i		−	0.0229403i
$179$	12.8738			0.962234			0.481117	−	0.876656i	$-0.340231\pi$
$179$	12.8738			0.962234			0.481117	+	0.876656i	$0.340231\pi$
$180$	9.45043	+	10.0196i	0.704393	+	0.746814i
$181$	10.3518			0.769445			0.384723	−	0.923032i	$-0.374297\pi$
$181$	10.3518			0.769445			0.384723	+	0.923032i	$0.374297\pi$
$182$			1.77140i			0.131305i
$183$			32.9056i			2.43245i
$184$	−5.41157			−0.398946
$185$	11.4029	−	10.7552i	0.838358	−	0.790737i
$186$	3.07902			0.225764
$187$			2.65088i			0.193851i
$188$			6.45114i			0.470498i
$189$	1.80947			0.131620
$190$	0.329197	−	0.310498i	0.0238825	−	0.0225259i
$191$	20.5833			1.48936			0.744678	−	0.667424i	$-0.232603\pi$
$191$	20.5833			1.48936			0.744678	+	0.667424i	$0.232603\pi$
$192$			17.4349i			1.25826i
$193$		−	8.48648i		−	0.610870i	−0.952213	−	0.305435i	$-0.901198\pi$
$193$		−	8.48648i		−	0.610870i	0.952213	−	0.305435i	$-0.0988019\pi$
$194$	−3.02788			−0.217389
$195$	6.57460	+	6.97054i	0.470817	+	0.499171i
$196$	−36.5075			−2.60768
$197$			3.74247i			0.266640i	0.991073	+	0.133320i	$0.0425638\pi$
$197$			3.74247i			0.266640i	−0.991073	+	0.133320i	$0.957436\pi$
$198$			0.636306i			0.0452203i
$199$	−1.18891			−0.0842795			−0.0421397	−	0.999112i	$-0.513417\pi$
$199$	−1.18891			−0.0842795			−0.0421397	+	0.999112i	$0.513417\pi$
$200$	3.99923	+	0.234007i	0.282789	+	0.0165468i
$201$	31.8880			2.24921
$202$		−	1.23751i		−	0.0870707i
$203$		−	51.4871i		−	3.61369i
$204$	−12.8726			−0.901261
$205$	5.70843	+	6.05221i	0.398694	+	0.422704i
$206$	3.68191			0.256531
$207$			21.2364i			1.47603i
$208$			6.49316i			0.450219i
$209$	−1.00000			−0.0691714
$210$	4.13150	−	3.89682i	0.285101	−	0.268906i
$211$	10.8311			0.745643			0.372822	−	0.927903i	$-0.378390\pi$
$211$	10.8311			0.745643			0.372822	+	0.927903i	$0.378390\pi$
$212$			1.30869i			0.0898815i
$213$			2.06521i			0.141506i
$214$	0.274283			0.0187496
$215$	−1.52233	+	1.43585i	−0.103822	+	0.0979244i
$216$	−0.286339			−0.0194829
$217$			31.0772i			2.10966i
$218$		−	1.01433i		−	0.0686990i
$219$	−3.42389			−0.231365
$220$	−3.00569	−	3.18670i	−0.202644	−	0.214848i
$221$	−4.58275			−0.308269
$222$			3.51648i			0.236011i
$223$			3.32216i			0.222468i	0.993794	+	0.111234i	$0.0354804\pi$
$223$			3.32216i			0.222468i	−0.993794	+	0.111234i	$0.964520\pi$
$224$	11.9619			0.799236
$225$	0.918305	−	15.6940i	0.0612203	−	1.04627i
$226$	−1.80344			−0.119963
$227$		−	24.5086i		−	1.62669i	−0.581781	−	0.813345i	$-0.697644\pi$
$227$		−	24.5086i		−	1.62669i	0.581781	−	0.813345i	$-0.302356\pi$
$228$		−	4.85597i		−	0.321595i
$229$	−14.9309			−0.986664			−0.493332	−	0.869841i	$-0.664221\pi$
$229$	−14.9309			−0.986664			−0.493332	+	0.869841i	$0.664221\pi$
$230$	2.09717	+	2.22347i	0.138283	+	0.146611i
$231$	−12.5502			−0.825744
$232$			8.14756i			0.534914i
$233$			27.0720i			1.77355i	0.462204	+	0.886773i	$0.347059\pi$
$233$			27.0720i			1.77355i	−0.462204	+	0.886773i	$0.652941\pi$
$234$	−1.10003			−0.0719109
$235$	5.35661	−	5.05234i	0.349427	−	0.329578i
$236$	6.56992			0.427665
$237$		−	28.2139i		−	1.83269i
$238$			2.71624i			0.176068i
$239$	−19.9281			−1.28904			−0.644519	−	0.764588i	$-0.722942\pi$
$239$	−19.9281			−1.28904			−0.644519	+	0.764588i	$0.722942\pi$
$240$	15.1443	−	14.2840i	0.977558	−	0.922031i
$241$	11.8613			0.764051			0.382026	−	0.924152i	$-0.375227\pi$
$241$	11.8613			0.764051			0.382026	+	0.924152i	$0.375227\pi$
$242$		−	0.202376i		−	0.0130092i
$243$		−	22.2572i		−	1.42780i
$244$	26.0065			1.66489
$245$	28.5916	+	30.3135i	1.82665	+	1.93666i
$246$	−1.86641			−0.118998
$247$		−	1.72877i		−	0.109999i
$248$		−	4.91780i		−	0.312280i
$249$	−35.6017			−2.25617
$250$	−1.45369	−	1.73386i	−0.0919396	−	0.109659i
$251$	12.8036			0.808158			0.404079	−	0.914724i	$-0.367592\pi$
$251$	12.8036			0.808158			0.404079	+	0.914724i	$0.367592\pi$
$252$		−	31.1868i		−	1.96459i
$253$		−	6.75421i		−	0.424633i
$254$	1.33744			0.0839187
$255$	10.0814	+	10.6886i	0.631323	+	0.669343i
$256$	12.8232			0.801450
$257$			7.75124i			0.483509i	0.970337	+	0.241754i	$0.0777228\pi$
$257$			7.75124i			0.483509i	−0.970337	+	0.241754i	$0.922277\pi$
$258$		−	0.469462i		−	0.0292274i
$259$	−35.4926			−2.20540
$260$	5.50908	−	5.19615i	0.341658	−	0.322251i
$261$	31.9732			1.97909
$262$		−	1.16998i		−	0.0722816i
$263$			16.9790i			1.04697i	0.852035	+	0.523485i	$0.175369\pi$
$263$			16.9790i			1.04697i	−0.852035	+	0.523485i	$0.824631\pi$
$264$	1.98601			0.122230
$265$	1.08666	−	1.02493i	0.0667527	−	0.0629610i
$266$	−1.02466			−0.0628257
$267$			3.74871i			0.229417i
$268$		−	25.2023i		−	1.53947i
$269$	24.5098			1.49439			0.747193	−	0.664607i	$-0.231401\pi$
$269$	24.5098			1.49439			0.747193	+	0.664607i	$0.231401\pi$
$270$	0.110966	+	0.117649i	0.00675318	+	0.00715988i
$271$	4.34679			0.264049			0.132024	−	0.991246i	$-0.457852\pi$
$271$	4.34679			0.264049			0.132024	+	0.991246i	$0.457852\pi$
$272$			9.95654i			0.603704i
$273$		−	21.6965i		−	1.31313i
$274$	1.93327			0.116793
$275$	−0.292065	+	4.99146i	−0.0176122	+	0.300997i
$276$	32.7982			1.97422
$277$		−	15.9348i		−	0.957432i	−0.877970	−	0.478716i	$-0.841102\pi$
$277$		−	15.9348i		−	0.957432i	0.877970	−	0.478716i	$-0.158898\pi$
$278$		−	1.69878i		−	0.101886i
$279$	−19.2987			−1.15538
$280$	−6.22399	−	6.59882i	−0.371955	−	0.394355i
$281$	−9.70532			−0.578971			−0.289485	−	0.957182i	$-0.593484\pi$
$281$	−9.70532			−0.578971			−0.289485	+	0.957182i	$0.593484\pi$
$282$			1.65190i			0.0983690i
$283$		−	19.9487i		−	1.18583i	−0.805266	−	0.592913i	$-0.797978\pi$
$283$		−	19.9487i		−	1.18583i	0.805266	−	0.592913i	$-0.202022\pi$
$284$	1.63221			0.0968541
$285$	−4.03208	+	3.80305i	−0.238840	+	0.225273i
$286$	0.349861			0.0206877
$287$		−	18.8380i		−	1.11197i
$288$			7.42825i			0.437714i
$289$	9.97286			0.586639
$290$	3.34761	−	3.15746i	0.196578	−	0.185412i
$291$	37.0861			2.17403
$292$			2.70603i			0.158358i
$293$			8.45190i			0.493765i	0.969045	+	0.246883i	$0.0794062\pi$
$293$			8.45190i			0.493765i	−0.969045	+	0.246883i	$0.920594\pi$
$294$	−9.34821			−0.545199
$295$	−5.14536	−	5.45524i	−0.299575	−	0.317616i
$296$	5.61651			0.326453
$297$		−	0.357381i		−	0.0207374i
$298$		−	1.83967i		−	0.106569i
$299$	11.6765			0.675268
$300$	−24.2384	−	1.41826i	−1.39940	−	0.0818833i
$301$	4.73838			0.273116
$302$		−	2.36452i		−	0.136063i
$303$			15.1573i			0.870762i
$304$	−3.75594			−0.215418
$305$	−20.3675	−	21.5941i	−1.16624	−	1.23647i
$306$	−1.68677			−0.0964261
$307$		−	14.1923i		−	0.809996i	−0.914318	−	0.404998i	$-0.867272\pi$
$307$		−	14.1923i		−	0.809996i	0.914318	−	0.404998i	$-0.132728\pi$
$308$			9.91891i			0.565182i
$309$	−45.0969			−2.56547
$310$	−2.02059	+	1.90581i	−0.114762	+	0.108243i
$311$	7.59809			0.430848			0.215424	−	0.976521i	$-0.430887\pi$
$311$	7.59809			0.430848			0.215424	+	0.976521i	$0.430887\pi$
$312$			3.43335i			0.194375i
$313$		−	31.8101i		−	1.79801i	−0.437937	−	0.899005i	$-0.644291\pi$
$313$		−	31.8101i		−	1.79801i	0.437937	−	0.899005i	$-0.355709\pi$
$314$	−2.69930			−0.152330
$315$	−25.8955	+	24.4246i	−1.45905	+	1.37617i
$316$	−22.2985			−1.25439
$317$			6.90608i			0.387884i	0.981013	+	0.193942i	$0.0621274\pi$
$317$			6.90608i			0.387884i	−0.981013	+	0.193942i	$0.937873\pi$
$318$			0.335108i			0.0187919i
$319$	−10.1690			−0.569355
$320$	−10.7917	−	11.4416i	−0.603272	−	0.639603i
$321$	−3.35948			−0.187508
$322$		−	6.92074i		−	0.385678i
$323$		−	2.65088i		−	0.147499i
$324$	−16.7433			−0.930184
$325$	−8.62909	−	0.504913i	−0.478656	−	0.0280075i
$326$	−0.561274			−0.0310861
$327$			12.4237i			0.687034i
$328$			2.98102i			0.164599i
$329$	−16.6729			−0.919209
$330$	−0.769646	−	0.815996i	−0.0423676	−	0.0449191i
$331$	−31.0030			−1.70408			−0.852038	−	0.523480i	$-0.824634\pi$
$331$	−31.0030			−1.70408			−0.852038	+	0.523480i	$0.824634\pi$
$332$			28.1373i			1.54424i
$333$		−	22.0407i		−	1.20782i
$334$	−2.00433			−0.109672
$335$	−20.9263	+	19.7377i	−1.14333	+	1.07838i
$336$	−47.1379			−2.57158
$337$			30.7881i			1.67714i	0.544797	+	0.838568i	$0.316607\pi$
$337$			30.7881i			1.67714i	−0.544797	+	0.838568i	$0.683393\pi$
$338$		−	2.02606i		−	0.110203i
$339$	22.0890			1.19971
$340$	8.44756	−	7.96772i	0.458133	−	0.432110i
$341$	6.13793			0.332387
$342$		−	0.636306i		−	0.0344075i
$343$		−	58.9115i		−	3.18092i
$344$	−0.749824			−0.0404278
$345$	−25.6866	−	27.2335i	−1.38292	−	1.46620i
$346$	1.01157			0.0543822
$347$			8.35559i			0.448551i	0.974526	+	0.224276i	$0.0720016\pi$
$347$			8.35559i			0.448551i	−0.974526	+	0.224276i	$0.927998\pi$
$348$		−	49.3804i		−	2.64707i
$349$	16.7466			0.896425			0.448213	−	0.893927i	$-0.352061\pi$
$349$	16.7466			0.896425			0.448213	+	0.893927i	$0.352061\pi$
$350$	−0.299266	+	5.11454i	−0.0159965	+	0.273383i
$351$	0.617829			0.0329773
$352$		−	2.36254i		−	0.125924i
$353$		−	28.1372i		−	1.49759i	−0.662799	−	0.748797i	$-0.730632\pi$
$353$		−	28.1372i		−	1.49759i	0.662799	−	0.748797i	$-0.269368\pi$
$354$	1.68231			0.0894138
$355$	−1.27830	−	1.35529i	−0.0678452	−	0.0719311i
$356$	2.96274			0.157025
$357$		−	33.2691i		−	1.76079i
$358$		−	2.60535i		−	0.137697i
$359$	29.6897			1.56696			0.783480	−	0.621417i	$-0.213442\pi$
$359$	29.6897			1.56696			0.783480	+	0.621417i	$0.213442\pi$
$360$	4.09783	−	3.86506i	0.215974	−	0.203707i
$361$	1.00000			0.0526316
$362$		−	2.09496i		−	0.110109i
$363$			2.47875i			0.130100i
$364$	−17.1475			−0.898774
$365$	2.24691	−	2.11928i	0.117609	−	0.110928i
$366$	6.65929			0.348087
$367$		−	12.5412i		−	0.654645i	−0.944913	−	0.327322i	$-0.893854\pi$
$367$		−	12.5412i		−	0.654645i	0.944913	−	0.327322i	$-0.106146\pi$
$368$		−	25.3684i		−	1.32242i
$369$	11.6983			0.608990
$370$	−2.17659	−	2.30767i	−0.113156	−	0.119970i
$371$	−3.38231			−0.175601
$372$			29.8056i			1.54535i
$373$			13.7844i			0.713727i	0.934157	+	0.356864i	$0.116154\pi$
$373$			13.7844i			0.713727i	−0.934157	+	0.356864i	$0.883846\pi$
$374$	0.536473			0.0277404
$375$	17.8052	+	21.2367i	0.919454	+	1.09666i
$376$	2.63840			0.136065
$377$		−	17.5799i		−	0.905410i
$378$		−	0.366193i		−	0.0188349i
$379$	−20.8733			−1.07219			−0.536094	−	0.844158i	$-0.680101\pi$
$379$	−20.8733			−1.07219			−0.536094	+	0.844158i	$0.680101\pi$
$380$	3.00569	+	3.18670i	0.154189	+	0.163474i
$381$	−16.3813			−0.839240
$382$		−	4.16556i		−	0.213129i
$383$			21.9844i			1.12335i	0.827357	+	0.561676i	$0.189843\pi$
$383$			21.9844i			1.12335i	−0.827357	+	0.561676i	$0.810157\pi$
$384$	15.2407			0.777748
$385$	8.23602	−	7.76819i	0.419746	−	0.395904i
$386$	−1.71746			−0.0874163
$387$			2.94251i			0.149576i
$388$		−	29.3105i		−	1.48802i
$389$	10.7856			0.546854			0.273427	−	0.961893i	$-0.411843\pi$
$389$	10.7856			0.546854			0.273427	+	0.961893i	$0.411843\pi$
$390$	1.41067	−	1.33054i	0.0714320	−	0.0673745i
$391$	17.9046			0.905473
$392$			14.9309i			0.754126i
$393$			14.3302i			0.722862i
$394$	0.757386			0.0381565
$395$	17.4635	+	18.5152i	0.878685	+	0.931602i
$396$	−6.15958			−0.309531
$397$			3.66005i			0.183692i	0.995773	+	0.0918462i	$0.0292768\pi$
$397$			3.66005i			0.183692i	−0.995773	+	0.0918462i	$0.970723\pi$
$398$			0.240606i			0.0120605i
$399$	12.5502			0.628297
$400$	−1.09698	+	18.7476i	−0.0548490	+	0.937382i
$401$	−2.69857			−0.134760			−0.0673801	−	0.997727i	$-0.521464\pi$
$401$	−2.69857			−0.134760			−0.0673801	+	0.997727i	$0.521464\pi$
$402$		−	6.45336i		−	0.321864i
$403$			10.6111i			0.528574i
$404$	11.9793			0.595995
$405$	13.1129	+	13.9026i	0.651583	+	0.690824i
$406$	−10.4197			−0.517123
$407$			7.01000i			0.347473i
$408$			5.26466i			0.260639i
$409$	0.352613			0.0174356			0.00871780	−	0.999962i	$-0.497225\pi$
$409$	0.352613			0.0174356			0.00871780	+	0.999962i	$0.497225\pi$
$410$	1.22482	−	1.15525i	0.0604896	−	0.0570536i
$411$	−23.6791			−1.16800
$412$			35.6418i			1.75594i
$413$			16.9799i			0.835527i
$414$	4.29774			0.211222
$415$	23.3634	−	22.0363i	1.14687	−	1.08172i
$416$	4.08429			0.200249
$417$			20.8070i			1.01892i
$418$			0.202376i			0.00989852i
$419$	13.7803			0.673214			0.336607	−	0.941645i	$-0.390721\pi$
$419$	13.7803			0.673214			0.336607	+	0.941645i	$0.390721\pi$
$420$	37.7221	+	39.9939i	1.84065	+	1.95150i
$421$	−24.9174			−1.21440			−0.607200	−	0.794549i	$-0.707707\pi$
$421$	−24.9174			−1.21440			−0.607200	+	0.794549i	$0.707707\pi$
$422$		−	2.19195i		−	0.106703i
$423$		−	10.3538i		−	0.503419i
$424$	0.535233			0.0259932
$425$	−13.2317	−	0.774228i	−0.641834	−	0.0375556i
$426$	0.417949			0.0202497
$427$			67.2136i			3.25269i
$428$			2.65512i			0.128340i
$429$	−4.28518			−0.206890
$430$	0.290582	+	0.308082i	0.0140131	+	0.0148570i
$431$	−33.8426			−1.63014			−0.815070	−	0.579362i	$-0.803302\pi$
$431$	−33.8426			−1.63014			−0.815070	+	0.579362i	$0.803302\pi$
$432$		−	1.34230i		−	0.0645815i
$433$			25.4495i			1.22302i	0.791235	+	0.611512i	$0.209438\pi$
$433$			25.4495i			1.22302i	−0.791235	+	0.611512i	$0.790562\pi$
$434$	6.28927			0.301894
$435$	−41.0023	+	38.6733i	−1.96591	+	1.85424i
$436$	9.81893			0.470241
$437$			6.75421i			0.323098i
$438$			0.692913i			0.0331086i
$439$	−33.8978			−1.61785			−0.808927	−	0.587910i	$-0.799951\pi$
$439$	−33.8978			−1.61785			−0.808927	+	0.587910i	$0.799951\pi$
$440$	−1.30331	+	1.22928i	−0.0621327	+	0.0586034i
$441$	58.5929			2.79014
$442$			0.927439i			0.0441138i
$443$		−	29.9900i		−	1.42487i	−0.701740	−	0.712433i	$-0.747593\pi$
$443$		−	29.9900i		−	1.42487i	0.701740	−	0.712433i	$-0.252407\pi$
$444$	−34.0403			−1.61548
$445$	−2.32033	−	2.46007i	−0.109994	−	0.116619i
$446$	0.672325			0.0318355
$447$			22.5327i			1.06576i
$448$			35.6129i			1.68255i
$449$	−25.6195			−1.20906			−0.604530	−	0.796583i	$-0.706639\pi$
$449$	−25.6195			−1.20906			−0.604530	+	0.796583i	$0.706639\pi$
$450$	−3.17610	−	0.185843i	−0.149723	−	0.00876071i
$451$	−3.72063			−0.175197
$452$		−	17.4577i		−	0.821143i
$453$			28.9612i			1.36071i
$454$	−4.95994			−0.232782
$455$	13.4294	+	14.2382i	0.629581	+	0.667496i
$456$	−1.98601			−0.0930033
$457$			33.0797i			1.54740i	0.633550	+	0.773702i	$0.281597\pi$
$457$			33.0797i			1.54740i	−0.633550	+	0.773702i	$0.718403\pi$
$458$			3.02166i			0.141193i
$459$	0.947373			0.0442196
$460$	−21.5237	+	20.3011i	−1.00355	+	0.946542i
$461$	42.3987			1.97470			0.987352	−	0.158540i	$-0.0506788\pi$
$461$	42.3987			1.97470			0.987352	+	0.158540i	$0.0506788\pi$
$462$			2.53986i			0.118165i
$463$		−	22.5364i		−	1.04736i	−0.851916	−	0.523678i	$-0.824560\pi$
$463$		−	22.5364i		−	1.04736i	0.851916	−	0.523678i	$-0.175440\pi$
$464$	−38.1942			−1.77312
$465$	24.7486	−	23.3428i	1.14769	−	1.08250i
$466$	5.47872			0.253797
$467$			9.25897i			0.428454i	0.976784	+	0.214227i	$0.0687232\pi$
$467$			9.25897i			0.428454i	−0.976784	+	0.214227i	$0.931277\pi$
$468$		−	10.6485i		−	0.492227i
$469$	65.1351			3.00766
$470$	−1.02247	−	1.08405i	−0.0471631	−	0.0500034i
$471$	33.0616			1.52340
$472$		−	2.68698i		−	0.123678i
$473$		−	0.935858i		−	0.0430308i
$474$	−5.70981			−0.262260
$475$	0.292065	−	4.99146i	0.0134009	−	0.229024i
$476$	−26.2938			−1.20517
$477$		−	2.10040i		−	0.0961706i
$478$			4.03296i			0.184463i
$479$	−7.87129			−0.359649			−0.179824	−	0.983699i	$-0.557553\pi$
$479$	−7.87129			−0.359649			−0.179824	+	0.983699i	$0.557553\pi$
$480$	−8.98486	−	9.52596i	−0.410101	−	0.434799i
$481$	−12.1187			−0.552564
$482$		−	2.40043i		−	0.109337i
$483$			84.7669i			3.85703i
$484$	1.95904			0.0890475
$485$	−24.3376	+	22.9551i	−1.10511	+	1.04234i
$486$	−4.50432			−0.204320
$487$			8.22682i			0.372793i	0.982475	+	0.186396i	$0.0596809\pi$
$487$			8.22682i			0.372793i	−0.982475	+	0.186396i	$0.940319\pi$
$488$		−	10.6362i		−	0.481478i
$489$	6.87461			0.310881
$490$	6.13471	−	5.78624i	0.277138	−	0.261396i
$491$	−10.7584			−0.485518			−0.242759	−	0.970087i	$-0.578052\pi$
$491$	−10.7584			−0.485518			−0.242759	+	0.970087i	$0.578052\pi$
$492$		−	18.0673i		−	0.814535i
$493$		−	26.9568i		−	1.21407i
$494$	−0.349861			−0.0157410
$495$	4.82400	+	5.11452i	0.216823	+	0.229881i
$496$	23.0537			1.03514
$497$			4.21845i			0.189223i
$498$			7.20492i			0.322860i
$499$	−1.56834			−0.0702085			−0.0351043	−	0.999384i	$-0.511176\pi$
$499$	−1.56834			−0.0702085			−0.0351043	+	0.999384i	$0.511176\pi$
$500$	16.7842	−	14.0721i	0.750611	−	0.629322i
$501$	24.5494			1.09679
$502$		−	2.59114i		−	0.115648i
$503$			29.2811i			1.30558i	0.757539	+	0.652790i	$0.226401\pi$
$503$			29.2811i			1.30558i	−0.757539	+	0.652790i	$0.773599\pi$
$504$	−12.7549			−0.568147
$505$	−9.38187	−	9.94687i	−0.417488	−	0.442630i
$506$	−1.36689			−0.0607656
$507$			24.8156i			1.10210i
$508$			12.9468i			0.574419i
$509$	10.8216			0.479659			0.239830	−	0.970815i	$-0.422908\pi$
$509$	10.8216			0.479659			0.239830	+	0.970815i	$0.422908\pi$
$510$	2.16310	−	2.04023i	0.0957839	−	0.0903431i
$511$	−6.99371			−0.309384
$512$		−	14.8922i		−	0.658148i
$513$			0.357381i			0.0157788i
$514$	1.56866			0.0691908
$515$	29.5946	−	27.9136i	1.30409	−	1.23002i
$516$	4.54450			0.200061
$517$			3.29300i			0.144826i
$518$			7.18284i			0.315596i
$519$	−12.3899			−0.543857
$520$	−2.12513	−	2.25312i	−0.0931933	−	0.0988057i
$521$	−33.0597			−1.44837			−0.724186	−	0.689605i	$-0.757784\pi$
$521$	−33.0597			−1.44837			−0.724186	+	0.689605i	$0.757784\pi$
$522$		−	6.47060i		−	0.283210i
$523$		−	3.69508i		−	0.161574i	−0.996731	−	0.0807872i	$-0.974257\pi$
$523$		−	3.69508i		−	0.161574i	0.996731	−	0.0807872i	$-0.0257434\pi$
$524$	11.3257			0.494764
$525$	3.66548	−	62.6440i	0.159975	−	2.73401i
$526$	3.43614			0.149823
$527$			16.2709i			0.708771i
$528$			9.31002i			0.405167i
$529$	−22.6193			−0.983449
$530$	−0.207421	−	0.219913i	−0.00900980	−	0.00955240i
$531$	−10.5444			−0.457589
$532$		−	9.91891i		−	0.430039i
$533$		−	6.43211i		−	0.278605i
$534$	0.758648			0.0328299
$535$	2.20464	−	2.07941i	0.0953150	−	0.0899009i
$536$	−10.3073			−0.445207
$537$			31.9109i			1.37706i
$538$		−	4.96018i		−	0.213849i
$539$	−18.6354			−0.802682
$540$	−1.13887	+	1.07418i	−0.0490091	+	0.0462252i
$541$	7.84255			0.337178			0.168589	−	0.985686i	$-0.446079\pi$
$541$	7.84255			0.337178			0.168589	+	0.985686i	$0.446079\pi$
$542$		−	0.879685i		−	0.0377857i
$543$			25.6595i			1.10116i
$544$	6.26280			0.268516
$545$	−7.68989	−	8.15300i	−0.329399	−	0.349236i
$546$	−4.39084			−0.187911
$547$		−	33.9101i		−	1.44989i	−0.688806	−	0.724946i	$-0.741865\pi$
$547$		−	33.9101i		−	1.44989i	0.688806	−	0.724946i	$-0.258135\pi$
$548$			18.7145i			0.799443i
$549$	−41.7392			−1.78139
$550$	1.01015	+	0.0591069i	0.0430730	+	0.00252033i
$551$	10.1690			0.433214
$552$		−	13.4139i		−	0.570934i
$553$		−	57.6303i		−	2.45069i
$554$	−3.22483			−0.137010
$555$	26.6594	+	28.2649i	1.13163	+	1.19978i
$556$	16.4445			0.697404
$557$		−	24.5959i		−	1.04216i	−0.853508	−	0.521081i	$-0.825529\pi$
$557$		−	24.5959i		−	1.04216i	0.853508	−	0.521081i	$-0.174471\pi$
$558$			3.90560i			0.165337i
$559$	1.61788			0.0684292
$560$	30.9340	−	29.1769i	1.30720	−	1.23295i
$561$	−6.57085			−0.277421
$562$			1.96412i			0.0828515i
$563$		−	0.155899i		−	0.00657035i	−0.999995	−	0.00328517i	$-0.998954\pi$
$563$		−	0.155899i		−	0.00657035i	0.999995	−	0.00328517i	$-0.00104571\pi$
$564$	−15.9907			−0.673331
$565$	−14.4958	+	13.6724i	−0.609842	+	0.575202i
$566$	−4.03713			−0.169693
$567$		−	43.2730i		−	1.81730i
$568$		−	0.667547i		−	0.0280097i
$569$	−12.1528			−0.509472			−0.254736	−	0.967011i	$-0.581989\pi$
$569$	−12.1528			−0.509472			−0.254736	+	0.967011i	$0.581989\pi$
$570$	0.769646	+	0.815996i	0.0322369	+	0.0341783i
$571$	21.6646			0.906636			0.453318	−	0.891349i	$-0.350240\pi$
$571$	21.6646			0.906636			0.453318	+	0.891349i	$0.350240\pi$
$572$			3.38674i			0.141607i
$573$			51.0208i			2.13142i
$574$	−3.81237			−0.159125
$575$	33.7134	+	1.97267i	1.40594	+	0.0822660i
$576$	−22.1154			−0.921475
$577$			5.43970i			0.226458i	0.993569	+	0.113229i	$0.0361193\pi$
$577$			5.43970i			0.226458i	−0.993569	+	0.113229i	$0.963881\pi$
$578$		−	2.01826i		−	0.0839488i
$579$	21.0358			0.874219
$580$	30.5649	+	32.4056i	1.26914	+	1.34557i
$581$	−72.7208			−3.01697
$582$		−	7.50533i		−	0.311106i
$583$			0.668027i			0.0276669i
$584$	1.10672			0.0457963
$585$	−8.84182	+	8.33959i	−0.365564	+	0.344799i
$586$	1.71046			0.0706584
$587$		−	7.30061i		−	0.301329i	−0.988585	−	0.150664i	$-0.951859\pi$
$587$		−	7.30061i		−	0.301329i	0.988585	−	0.150664i	$-0.0481413\pi$
$588$		−	90.4928i		−	3.73186i
$589$	−6.13793			−0.252909
$590$	−1.10401	+	1.04130i	−0.0454513	+	0.0428695i
$591$	−9.27663			−0.381590
$592$			26.3291i			1.08212i
$593$			5.19172i			0.213198i	0.994302	+	0.106599i	$0.0339962\pi$
$593$			5.19172i			0.213198i	−0.994302	+	0.106599i	$0.966004\pi$
$594$	−0.0723253			−0.00296754
$595$	20.5925	+	21.8327i	0.844211	+	0.895052i
$596$	17.8085			0.729463
$597$		−	2.94700i		−	0.120613i
$598$		−	2.36304i		−	0.0966317i
$599$	−26.5360			−1.08423			−0.542116	−	0.840303i	$-0.682377\pi$
$599$	−26.5360			−1.08423			−0.542116	+	0.840303i	$0.682377\pi$
$600$	−0.580043	+	9.91308i	−0.0236802	+	0.404700i
$601$	−17.3856			−0.709175			−0.354587	−	0.935023i	$-0.615379\pi$
$601$	−17.3856			−0.709175			−0.354587	+	0.935023i	$0.615379\pi$
$602$		−	0.958934i		−	0.0390832i
$603$			40.4485i			1.64719i
$604$	22.8891			0.931344
$605$	−1.53426	−	1.62666i	−0.0623767	−	0.0661333i
$606$	3.06746			0.124607
$607$		−	8.31498i		−	0.337494i	−0.985659	−	0.168747i	$-0.946028\pi$
$607$		−	8.31498i		−	0.337494i	0.985659	−	0.168747i	$-0.0539722\pi$
$608$			2.36254i			0.0958137i
$609$	127.623			5.17156
$610$	−4.37012	+	4.12189i	−0.176941	+	0.166890i
$611$	−5.69285			−0.230308
$612$		−	16.3283i		−	0.660032i
$613$		−	5.99839i		−	0.242273i	−0.992636	−	0.121136i	$-0.961346\pi$
$613$		−	5.99839i		−	0.242273i	0.992636	−	0.121136i	$-0.0386538\pi$
$614$	−2.87217			−0.115912
$615$	−15.0019	+	14.1497i	−0.604934	+	0.570572i
$616$	4.05666			0.163448
$617$		−	39.3159i		−	1.58280i	−0.611299	−	0.791400i	$-0.709353\pi$
$617$		−	39.3159i		−	1.58280i	0.611299	−	0.791400i	$-0.290647\pi$
$618$			9.12652i			0.367123i
$619$	−23.1425			−0.930177			−0.465089	−	0.885264i	$-0.653978\pi$
$619$	−23.1425			−0.930177			−0.465089	+	0.885264i	$0.653978\pi$
$620$	−18.4487	−	19.5598i	−0.740918	−	0.785539i
$621$	−2.41383			−0.0968635
$622$		−	1.53767i		−	0.0616549i
$623$			7.65720i			0.306779i
$624$	−16.0949			−0.644311
$625$	−24.8294	−	2.91566i	−0.993176	−	0.116627i
$626$	−6.43759			−0.257298
$627$		−	2.47875i		−	0.0989916i
$628$		−	26.1298i		−	1.04269i
$629$	−18.5826			−0.740938
$630$	4.94294	+	5.24063i	0.196932	+	0.208792i
$631$	12.3052			0.489862			0.244931	−	0.969540i	$-0.421235\pi$
$631$	12.3052			0.489862			0.244931	+	0.969540i	$0.421235\pi$
$632$			9.11970i			0.362762i
$633$			26.8475i			1.06709i
$634$	1.39762			0.0555067
$635$	10.7501	−	10.1395i	0.426607	−	0.402374i
$636$	−3.24392			−0.128630
$637$		−	32.2163i		−	1.27645i
$638$			2.05796i			0.0814755i
$639$	−2.61963			−0.103631
$640$	−10.0016	+	9.43350i	−0.395348	+	0.372892i
$641$	−11.6616			−0.460604			−0.230302	−	0.973119i	$-0.573971\pi$
$641$	−11.6616			−0.460604			−0.230302	+	0.973119i	$0.573971\pi$
$642$			0.679878i			0.0268327i
$643$			9.76053i			0.384918i	0.981305	+	0.192459i	$0.0616462\pi$
$643$			9.76053i			0.384918i	−0.981305	+	0.192459i	$0.938354\pi$
$644$	66.9944			2.63995
$645$	−3.55912	−	3.77346i	−0.140140	−	0.148580i
$646$	−0.536473			−0.0211073
$647$			6.56903i			0.258255i	0.991628	+	0.129128i	$0.0412177\pi$
$647$			6.56903i			0.258255i	−0.991628	+	0.129128i	$0.958782\pi$
$648$			6.84772i			0.269004i
$649$	3.35364			0.131642
$650$	−0.102182	+	1.74632i	−0.00400792	+	0.0684963i
$651$	−77.0324			−3.01914
$652$		−	5.43326i		−	0.212783i
$653$		−	9.88177i		−	0.386704i	−0.981129	−	0.193352i	$-0.938064\pi$
$653$		−	9.88177i		−	0.386704i	0.981129	−	0.193352i	$-0.0619359\pi$
$654$	2.51426			0.0983154
$655$	−8.86993	−	9.40410i	−0.346577	−	0.367449i
$656$	−13.9745			−0.545611
$657$		−	4.34305i		−	0.169439i
$658$			3.37420i			0.131540i
$659$	−20.7690			−0.809047			−0.404523	−	0.914528i	$-0.632563\pi$
$659$	−20.7690			−0.809047			−0.404523	+	0.914528i	$0.632563\pi$
$660$	7.89903	−	7.45034i	0.307469	−	0.290004i
$661$	−27.5222			−1.07049			−0.535244	−	0.844697i	$-0.679781\pi$
$661$	−27.5222			−1.07049			−0.535244	+	0.844697i	$0.679781\pi$
$662$			6.27425i			0.243856i
$663$		−	11.3595i		−	0.441166i
$664$	11.5077			0.446585
$665$	−8.23602	+	7.76819i	−0.319379	+	0.301238i
$666$	−4.46050			−0.172841
$667$			68.6836i			2.65944i
$668$		−	19.4023i		−	0.750699i
$669$	−8.23479			−0.318375
$670$	3.99443	+	4.23498i	0.154318	+	0.163612i
$671$	13.2751			0.512479
$672$			29.6504i			1.14379i
$673$		−	14.9080i		−	0.574660i	−0.957832	−	0.287330i	$-0.907232\pi$
$673$		−	14.9080i		−	0.574660i	0.957832	−	0.287330i	$-0.0927676\pi$
$674$	6.23077			0.240000
$675$	1.78385	+	0.104379i	0.0686606	+	0.00401753i
$676$	19.6127			0.754334
$677$			21.3317i			0.819842i	0.912121	+	0.409921i	$0.134444\pi$
$677$			21.3317i			0.819842i	−0.912121	+	0.409921i	$0.865556\pi$
$678$		−	4.47028i		−	0.171680i
$679$	75.7529			2.90713
$680$	−3.25866	−	3.45490i	−0.124964	−	0.132490i
$681$	60.7505			2.32796
$682$		−	1.24217i		−	0.0475651i
$683$			2.64869i			0.101349i	0.998715	+	0.0506747i	$0.0161372\pi$
$683$			2.64869i			0.101349i	−0.998715	+	0.0506747i	$0.983863\pi$
$684$	6.15958			0.235518
$685$	15.5393	−	14.6566i	0.593726	−	0.560001i
$686$	−11.9223			−0.455194
$687$		−	37.0100i		−	1.41202i
$688$		−	3.51503i		−	0.134009i
$689$	−1.15487			−0.0439969
$690$	−5.51141	+	5.19835i	−0.209816	+	0.197898i
$691$	−25.2356			−0.960009			−0.480005	−	0.877266i	$-0.659365\pi$
$691$	−25.2356			−0.960009			−0.480005	+	0.877266i	$0.659365\pi$
$692$			9.79220i			0.372244i
$693$		−	15.9194i		−	0.604728i
$694$	1.69097			0.0641883
$695$	−12.8789	−	13.6545i	−0.488523	−	0.517944i
$696$	−20.1957			−0.765517
$697$		−	9.86292i		−	0.373585i
$698$		−	3.38911i		−	0.128280i
$699$	−67.1046			−2.53813
$700$	−49.5099	−	2.89697i	−1.87130	−	0.109495i
$701$	−25.1770			−0.950924			−0.475462	−	0.879736i	$-0.657719\pi$
$701$	−25.1770			−0.950924			−0.475462	+	0.879736i	$0.657719\pi$
$702$		−	0.125034i		−	0.00471909i
$703$		−	7.01000i		−	0.264387i
$704$	7.03376			0.265095
$705$	12.5235	+	13.2777i	0.471661	+	0.500066i
$706$	−5.69430			−0.214308
$707$			30.9606i			1.16439i
$708$			16.2852i			0.612034i
$709$	38.3670			1.44090			0.720451	−	0.693506i	$-0.243935\pi$
$709$	38.3670			1.44090			0.720451	+	0.693506i	$0.243935\pi$
$710$	−0.274277	+	0.258697i	−0.0102934	+	0.00970874i
$711$	35.7881			1.34216
$712$		−	1.21171i		−	0.0454108i
$713$		−	41.4568i		−	1.55257i
$714$	−6.73286			−0.251971
$715$	2.81213	−	2.65239i	0.105168	−	0.0991938i
$716$	25.2204			0.942529
$717$		−	49.3966i		−	1.84475i
$718$		−	6.00847i		−	0.224234i
$719$	−38.1597			−1.42312			−0.711559	−	0.702626i	$-0.752011\pi$
$719$	−38.1597			−1.42312			−0.711559	+	0.702626i	$0.752011\pi$
$720$	18.1187	+	19.2098i	0.675243	+	0.715908i
$721$	−92.1159			−3.43058
$722$		−	0.202376i		−	0.00753165i
$723$			29.4011i			1.09344i
$724$	20.2797			0.753689
$725$	2.97001	−	50.7582i	0.110304	−	1.88511i
$726$	0.501638			0.0186175
$727$		−	4.76411i		−	0.176691i	−0.996090	−	0.0883455i	$-0.971842\pi$
$727$		−	4.76411i		−	0.176691i	0.996090	−	0.0883455i	$-0.0281580\pi$
$728$			7.01303i			0.259920i
$729$	29.5298			1.09370
$730$	−0.428891	−	0.454720i	−0.0158740	−	0.0168299i
$731$	2.48084			0.0917574
$732$			64.4634i			2.38264i
$733$			25.4352i			0.939472i	0.882807	+	0.469736i	$0.155651\pi$
$733$			25.4352i			0.939472i	−0.882807	+	0.469736i	$0.844349\pi$
$734$	−2.53803			−0.0936806
$735$	−75.1393	+	70.8712i	−2.77156	+	2.61413i
$736$	−15.9571			−0.588186
$737$		−	12.8646i		−	0.473873i
$738$		−	2.36746i		−	0.0871472i
$739$	2.13812			0.0786518			0.0393259	−	0.999226i	$-0.487479\pi$
$739$	2.13812			0.0786518			0.0393259	+	0.999226i	$0.487479\pi$
$740$	22.3388	−	21.0699i	0.821190	−	0.774544i
$741$	4.28518			0.157420
$742$			0.684499i			0.0251287i
$743$		−	7.85670i		−	0.288234i	−0.989561	−	0.144117i	$-0.953966\pi$
$743$		−	7.85670i		−	0.288234i	0.989561	−	0.144117i	$-0.0460342\pi$
$744$	12.1900			0.446906
$745$	−13.9470	−	14.7870i	−0.510980	−	0.541753i
$746$	2.78962			0.102135
$747$		−	45.1592i		−	1.65229i
$748$			5.19318i			0.189882i
$749$	−6.86215			−0.250738
$750$	4.29780	−	3.60333i	0.156933	−	0.131575i
$751$	−44.5610			−1.62605			−0.813027	−	0.582226i	$-0.802182\pi$
$751$	−44.5610			−1.62605			−0.813027	+	0.582226i	$0.802182\pi$
$752$			12.3683i			0.451027i
$753$			31.7369i			1.15656i
$754$	−3.55774			−0.129565
$755$	−17.9260	−	19.0056i	−0.652396	−	0.691685i
$756$	3.54483			0.128924
$757$			10.6657i			0.387652i	0.981036	+	0.193826i	$0.0620896\pi$
$757$			10.6657i			0.387652i	−0.981036	+	0.193826i	$0.937910\pi$
$758$			4.22424i			0.153431i
$759$	16.7420			0.607695
$760$	1.30331	−	1.22928i	0.0472759	−	0.0445905i
$761$	−26.5797			−0.963514			−0.481757	−	0.876305i	$-0.660001\pi$
$761$	−26.5797			−0.963514			−0.481757	+	0.876305i	$0.660001\pi$
$762$			3.31518i			0.120096i
$763$			25.3770i			0.918708i
$764$	40.3236			1.45886
$765$	−13.5580	+	12.7878i	−0.490189	+	0.462345i
$766$	4.44912			0.160753
$767$			5.79766i			0.209341i
$768$			31.7855i			1.14696i
$769$	37.5326			1.35346			0.676731	−	0.736230i	$-0.263396\pi$
$769$	37.5326			1.35346			0.676731	+	0.736230i	$0.263396\pi$
$770$	−1.57209	−	1.66677i	−0.0566543	−	0.0600663i
$771$	−19.2133			−0.691952
$772$		−	16.6254i		−	0.598361i
$773$			41.3888i			1.48865i	0.667816	+	0.744326i	$0.267229\pi$
$773$			41.3888i			1.48865i	−0.667816	+	0.744326i	$0.732771\pi$
$774$	0.595492			0.0214045
$775$	−1.79267	+	30.6372i	−0.0643947	+	1.10052i
$776$	−11.9875			−0.430326
$777$		−	87.9771i		−	3.15616i
$778$		−	2.18275i		−	0.0782555i
$779$	3.72063			0.133305
$780$	12.8799	+	13.6556i	0.461175	+	0.488949i
$781$	0.833169			0.0298131
$782$		−	3.62345i		−	0.129574i
$783$			3.63421i			0.129876i
$784$	−69.9933			−2.49976
$785$	−21.6965	+	20.4641i	−0.774381	+	0.730394i
$786$	2.90008			0.103443
$787$		−	12.0371i		−	0.429076i	−0.976716	−	0.214538i	$-0.931175\pi$
$787$		−	12.0371i		−	0.429076i	0.976716	−	0.214538i	$-0.0688245\pi$
$788$			7.33167i			0.261180i
$789$	−42.0867			−1.49832
$790$	3.74703	−	3.53419i	0.133313	−	0.125741i
$791$	45.1194			1.60426
$792$			2.51916i			0.0895145i
$793$			22.9496i			0.814963i
$794$	0.740705			0.0262866
$795$	2.54054	+	2.69354i	0.0901037	+	0.0955301i
$796$	−2.32912			−0.0825536
$797$		−	13.1219i		−	0.464802i	−0.972620	−	0.232401i	$-0.925342\pi$
$797$		−	13.1219i		−	0.464802i	0.972620	−	0.232401i	$-0.0746582\pi$
$798$		−	2.53986i		−	0.0899102i
$799$	−8.72935			−0.308822
$800$	11.7925	+	0.690016i	0.416929	+	0.0243957i
$801$	−4.75507			−0.168012
$802$			0.546126i			0.0192844i
$803$			1.38130i			0.0487450i
$804$	62.4700			2.20315
$805$	−52.4680	−	55.6278i	−1.84925	−	1.96062i
$806$	2.14742			0.0756397
$807$			60.7534i			2.13862i
$808$		−	4.89934i		−	0.172358i
$809$	−12.3579			−0.434482			−0.217241	−	0.976118i	$-0.569706\pi$
$809$	−12.3579			−0.434482			−0.217241	+	0.976118i	$0.569706\pi$
$810$	2.81354	−	2.65373i	0.0988578	−	0.0932425i
$811$	28.6174			1.00489			0.502447	−	0.864608i	$-0.332433\pi$
$811$	28.6174			1.00489			0.502447	+	0.864608i	$0.332433\pi$
$812$		−	100.866i		−	3.53969i
$813$			10.7746i			0.377881i
$814$	1.41865			0.0497238
$815$	−4.51142	+	4.25516i	−0.158028	+	0.149052i
$816$	−24.6797			−0.863963
$817$			0.935858i			0.0327415i
$818$		−	0.0713604i		−	0.00249506i
$819$	27.5210			0.961661
$820$	11.1831	+	11.8565i	0.390529	+	0.414048i
$821$	−51.3323			−1.79151			−0.895755	−	0.444549i	$-0.853364\pi$
$821$	−51.3323			−1.79151			−0.895755	+	0.444549i	$0.853364\pi$
$822$			4.79208i			0.167143i
$823$		−	16.9859i		−	0.592091i	−0.955174	−	0.296046i	$-0.904332\pi$
$823$		−	16.9859i		−	0.592091i	0.955174	−	0.296046i	$-0.0956681\pi$
$824$	14.5769			0.507809
$825$	−12.3726	−	0.723955i	−0.430757	−	0.0252049i
$826$	3.43633			0.119565
$827$		−	47.9770i		−	1.66832i	−0.551520	−	0.834162i	$-0.685952\pi$
$827$		−	47.9770i		−	1.66832i	0.551520	−	0.834162i	$-0.314048\pi$
$828$			41.6031i			1.44581i
$829$	16.9407			0.588376			0.294188	−	0.955748i	$-0.404951\pi$
$829$	16.9407			0.588376			0.294188	+	0.955748i	$0.404951\pi$
$830$	−4.45962	−	4.72819i	−0.154796	−	0.164118i
$831$	39.4984			1.37018
$832$			12.1598i			0.421564i
$833$		−	49.4000i		−	1.71161i
$834$	4.21083			0.145809
$835$	−16.1104	+	15.1953i	−0.557525	+	0.525856i
$836$	−1.95904			−0.0677550
$837$		−	2.19358i		−	0.0758211i
$838$		−	2.78881i		−	0.0963378i
$839$	2.36980			0.0818145			0.0409073	−	0.999163i	$-0.486975\pi$
$839$	2.36980			0.0818145			0.0409073	+	0.999163i	$0.486975\pi$
$840$	16.3568	−	15.4277i	0.564363	−	0.532306i
$841$	74.4088			2.56582
$842$			5.04268i			0.173782i
$843$		−	24.0570i		−	0.828567i
$844$	21.2186			0.730374
$845$	−15.3601	−	16.2851i	−0.528402	−	0.560225i
$846$	−2.09536			−0.0720399
$847$			5.06314i			0.173971i
$848$			2.50907i			0.0861619i
$849$	49.4477			1.69704
$850$	−0.156685	+	2.67779i	−0.00537425	+	0.0918473i
$851$	47.3470			1.62303
$852$			4.04584i			0.138608i
$853$		−	4.76117i		−	0.163019i	−0.996673	−	0.0815097i	$-0.974026\pi$
$853$		−	4.76117i		−	0.163019i	0.996673	−	0.0815097i	$-0.0259741\pi$
$854$	13.6024			0.465465
$855$	−4.82400	−	5.11452i	−0.164977	−	0.174913i
$856$	1.08590			0.0371153
$857$		−	15.5789i		−	0.532165i	−0.963950	−	0.266082i	$-0.914271\pi$
$857$		−	15.5789i		−	0.532165i	0.963950	−	0.266082i	$-0.0857293\pi$
$858$			0.867217i			0.0296063i
$859$	−39.9404			−1.36275			−0.681374	−	0.731935i	$-0.738617\pi$
$859$	−39.9404			−1.36275			−0.681374	+	0.731935i	$0.738617\pi$
$860$	−2.98230	+	2.81290i	−0.101696	+	0.0959192i
$861$	46.6947			1.59135
$862$			6.84892i			0.233275i
$863$		−	28.0580i		−	0.955105i	−0.878603	−	0.477552i	$-0.841524\pi$
$863$		−	28.0580i		−	0.955105i	0.878603	−	0.477552i	$-0.158476\pi$
$864$	−0.844327			−0.0287246
$865$	8.13081	−	7.66896i	0.276456	−	0.260752i
$866$	5.15036			0.175016
$867$			24.7202i			0.839541i
$868$			60.8815i			2.06645i
$869$	−11.3823			−0.386119
$870$	7.82653	+	8.29787i	0.265344	+	0.281324i
$871$	22.2399			0.753570
$872$		−	4.01577i		−	0.135991i
$873$			47.0421i			1.59213i
$874$	1.36689			0.0462357
$875$	36.3692	+	43.3786i	1.22950	+	1.46646i
$876$	−6.70755			−0.226627
$877$		−	35.8593i		−	1.21088i	−0.795890	−	0.605441i	$-0.792997\pi$
$877$		−	35.8593i		−	1.21088i	0.795890	−	0.605441i	$-0.207003\pi$
$878$			6.86009i			0.231517i
$879$	−20.9501			−0.706629
$880$	−5.76261	−	6.10965i	−0.194257	−	0.205956i
$881$	−4.98649			−0.167999			−0.0839996	−	0.996466i	$-0.526769\pi$
$881$	−4.98649			−0.167999			−0.0839996	+	0.996466i	$0.526769\pi$
$882$		−	11.8578i		−	0.399273i
$883$		−	36.4602i		−	1.22698i	−0.789701	−	0.613492i	$-0.789764\pi$
$883$		−	36.4602i		−	1.22698i	0.789701	−	0.613492i	$-0.210236\pi$
$884$	−8.97782			−0.301957
$885$	13.5221	−	12.7540i	0.454542	−	0.428723i
$886$	−6.06924			−0.203900
$887$			2.52582i			0.0848089i	0.999101	+	0.0424044i	$0.0135018\pi$
$887$			2.52582i			0.0848089i	−0.999101	+	0.0424044i	$0.986498\pi$
$888$			13.9219i			0.467189i
$889$	−33.4608			−1.12224
$890$	−0.497859	+	0.469579i	−0.0166883	+	0.0157403i
$891$	−8.54668			−0.286324
$892$			6.50826i			0.217913i
$893$		−	3.29300i		−	0.110196i
$894$	4.56008			0.152512
$895$	−19.7518	−	20.9414i	−0.660231	−	0.699992i
$896$	31.1309			1.04001
$897$			28.9430i			0.966378i
$898$			5.18477i			0.173018i
$899$	−62.4166			−2.08171
$900$	1.79900	−	30.7453i	0.0599666	−	1.02484i
$901$	−1.77086			−0.0589958
$902$			0.752965i			0.0250710i
$903$			11.7452i			0.390857i
$904$	−7.13991			−0.237470
$905$	−15.8824	−	16.8389i	−0.527950	−	0.559745i
$906$	5.86104			0.194720
$907$		−	20.7383i		−	0.688604i	−0.938859	−	0.344302i	$-0.888116\pi$
$907$		−	20.7383i		−	0.688604i	0.938859	−	0.344302i	$-0.111884\pi$
$908$		−	48.0134i		−	1.59338i
$909$	−19.2263			−0.637697
$910$	2.88146	−	2.71779i	0.0955196	−	0.0900938i
$911$	24.6244			0.815843			0.407921	−	0.913017i	$-0.366254\pi$
$911$	24.6244			0.815843			0.407921	+	0.913017i	$0.366254\pi$
$912$		−	9.31002i		−	0.308286i
$913$			14.3628i			0.475339i
$914$	6.69453			0.221435
$915$	53.5263	−	50.4858i	1.76952	−	1.66901i
$916$	−29.2504			−0.966460
$917$			29.2711i			0.966618i
$918$		−	0.191725i		−	0.00632788i
$919$	−25.1599			−0.829948			−0.414974	−	0.909833i	$-0.636209\pi$
$919$	−25.1599			−0.829948			−0.414974	+	0.909833i	$0.636209\pi$
$920$	8.30278	+	8.80280i	0.273735	+	0.290220i
$921$	35.1790			1.15919
$922$		−	8.58047i		−	0.282583i
$923$			1.44036i			0.0474099i
$924$	−24.5865			−0.808835
$925$	−34.9901	−	2.04738i	−1.15047	−	0.0673173i
$926$	−4.56082			−0.149878
$927$		−	57.2034i		−	1.87881i
$928$			24.0247i			0.788650i
$929$	10.0752			0.330556			0.165278	−	0.986247i	$-0.447148\pi$
$929$	10.0752			0.330556			0.165278	+	0.986247i	$0.447148\pi$
$930$	−4.72403	−	5.00852i	−0.154907	−	0.164236i
$931$	18.6354			0.610749
$932$			53.0353i			1.73723i
$933$			18.8337i			0.616589i
$934$	1.87379			0.0613123
$935$	4.31208	−	4.06714i	0.141020	−	0.133010i
$936$	−4.35505			−0.142349
$937$			3.95364i			0.129160i	0.997913	+	0.0645800i	$0.0205708\pi$
$937$			3.95364i			0.129160i	−0.997913	+	0.0645800i	$0.979429\pi$
$938$		−	13.1818i		−	0.430400i
$939$	78.8490			2.57314
$940$	10.4938	−	9.89776i	0.342271	−	0.322829i
$941$	1.92792			0.0628483			0.0314242	−	0.999506i	$-0.489996\pi$
$941$	1.92792			0.0628483			0.0314242	+	0.999506i	$0.489996\pi$
$942$		−	6.69087i		−	0.218000i
$943$			25.1299i			0.818342i
$944$	12.5961			0.409967
$945$	−2.77620	−	2.94340i	−0.0903099	−	0.0957487i
$946$	−0.189395			−0.00615777
$947$		−	18.2213i		−	0.592113i	−0.955170	−	0.296057i	$-0.904328\pi$
$947$		−	18.2213i		−	0.592113i	0.955170	−	0.296057i	$-0.0956717\pi$
$948$		−	55.2723i		−	1.79516i
$949$	−2.38795			−0.0775161
$950$	−1.01015	−	0.0591069i	−0.0327736	−	0.00191768i
$951$	−17.1184			−0.555103
$952$			10.7537i			0.348530i
$953$			25.0122i			0.810224i	0.914267	+	0.405112i	$0.132768\pi$
$953$			25.0122i			0.810224i	−0.914267	+	0.405112i	$0.867232\pi$
$954$	−0.425070			−0.0137621
$955$	−31.5802	−	33.4821i	−1.02191	−	1.08346i
$956$	−39.0399			−1.26264
$957$		−	25.2064i		−	0.814807i
$958$			1.59296i			0.0514662i
$959$	−48.3675			−1.56187
$960$	28.3607	−	26.7498i	0.915338	−	0.863345i
$961$	6.67413			0.215294
$962$			2.45253i			0.0790726i
$963$		−	4.26136i		−	0.137320i
$964$	23.2367			0.748405
$965$	−13.8046	+	13.0205i	−0.444387	+	0.419145i
$966$	17.1548			0.551945
$967$		−	27.9282i		−	0.898111i	−0.893504	−	0.449055i	$-0.851761\pi$
$967$		−	27.9282i		−	0.898111i	0.893504	−	0.449055i	$-0.148239\pi$
$968$		−	0.801215i		−	0.0257520i
$969$	6.57085			0.211086
$970$	4.64556	+	4.92533i	0.149160	+	0.158143i
$971$	24.1677			0.775577			0.387789	−	0.921748i	$-0.373239\pi$
$971$	24.1677			0.775577			0.387789	+	0.921748i	$0.373239\pi$
$972$		−	43.6028i		−	1.39856i
$973$			42.5008i			1.36251i
$974$	1.66491			0.0533471
$975$	1.25155	−	21.3893i	0.0400817	−	0.685006i
$976$	49.8604			1.59599
$977$			17.7154i			0.566766i	0.959007	+	0.283383i	$0.0914568\pi$
$977$			17.7154i			0.566766i	−0.959007	+	0.283383i	$0.908543\pi$
$978$		−	1.39125i		−	0.0444874i
$979$	1.51234			0.0483347
$980$	56.0122	+	59.3854i	1.78924	+	1.89700i
$981$	−15.7589			−0.503144
$982$			2.17723i			0.0694782i
$983$		−	19.0942i		−	0.609010i	−0.952511	−	0.304505i	$-0.901509\pi$
$983$		−	19.0942i		−	0.609010i	0.952511	−	0.304505i	$-0.0984910\pi$
$984$	−7.38919			−0.235559
$985$	6.08774	−	5.74194i	0.193971	−	0.182953i
$986$	−5.45540			−0.173735
$987$		−	41.3280i		−	1.31548i
$988$		−	3.38674i		−	0.107746i
$989$	−6.32098			−0.200996
$990$	1.03505	−	0.976261i	0.0328962	−	0.0310276i
$991$	53.1833			1.68942			0.844711	−	0.535222i	$-0.179772\pi$
$991$	53.1833			1.68942			0.844711	+	0.535222i	$0.179772\pi$
$992$		−	14.5011i		−	0.460410i
$993$		−	76.8484i		−	2.43871i
$994$	0.853712			0.0270781
$995$	1.82410	+	1.93395i	0.0578278	+	0.0613104i
$996$	−69.7453			−2.20996
$997$			38.2718i			1.21208i	0.795435	+	0.606039i	$0.207243\pi$
$997$			38.2718i			1.21208i	−0.795435	+	0.606039i	$0.792757\pi$
$998$			0.317394i			0.0100469i
$999$	2.50524			0.0792623

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.b.e.419.15	✓	30
5.2	odd	4		5225.2.a.bc.1.16		30
5.3	odd	4		5225.2.a.bc.1.15		30
5.4	even	2	inner	1045.2.b.e.419.16	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.b.e.419.15	✓	30	1.1	even	1	trivial
1045.2.b.e.419.16	yes	30	5.4	even	2	inner
5225.2.a.bc.1.15		30	5.3	odd	4
5225.2.a.bc.1.16		30	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.202376i q^{2} +2.47875i q^{3} +1.95904 q^{4} +(-1.53426 - 1.62666i) q^{5} +0.501638 q^{6} +5.06314i q^{7} -0.801215i q^{8} -3.14418 q^{9} +O(q^{10})\)	\(q-0.202376i q^{2} +2.47875i q^{3} +1.95904 q^{4} +(-1.53426 - 1.62666i) q^{5} +0.501638 q^{6} +5.06314i q^{7} -0.801215i q^{8} -3.14418 q^{9} +(-0.329197 + 0.310498i) q^{10} +1.00000 q^{11} +4.85597i q^{12} +1.72877i q^{13} +1.02466 q^{14} +(4.03208 - 3.80305i) q^{15} +3.75594 q^{16} +2.65088i q^{17} +0.636306i q^{18} -1.00000 q^{19} +(-3.00569 - 3.18670i) q^{20} -12.5502 q^{21} -0.202376i q^{22} -6.75421i q^{23} +1.98601 q^{24} +(-0.292065 + 4.99146i) q^{25} +0.349861 q^{26} -0.357381i q^{27} +9.91891i q^{28} -10.1690 q^{29} +(-0.769646 - 0.815996i) q^{30} +6.13793 q^{31} -2.36254i q^{32} +2.47875i q^{33} +0.536473 q^{34} +(8.23602 - 7.76819i) q^{35} -6.15958 q^{36} +7.01000i q^{37} +0.202376i q^{38} -4.28518 q^{39} +(-1.30331 + 1.22928i) q^{40} -3.72063 q^{41} +2.53986i q^{42} -0.935858i q^{43} +1.95904 q^{44} +(4.82400 + 5.11452i) q^{45} -1.36689 q^{46} +3.29300i q^{47} +9.31002i q^{48} -18.6354 q^{49} +(1.01015 + 0.0591069i) q^{50} -6.57085 q^{51} +3.38674i q^{52} +0.668027i q^{53} -0.0723253 q^{54} +(-1.53426 - 1.62666i) q^{55} +4.05666 q^{56} -2.47875i q^{57} +2.05796i q^{58} +3.35364 q^{59} +(7.89903 - 7.45034i) q^{60} +13.2751 q^{61} -1.24217i q^{62} -15.9194i q^{63} +7.03376 q^{64} +(2.81213 - 2.65239i) q^{65} +0.501638 q^{66} -12.8646i q^{67} +5.19318i q^{68} +16.7420 q^{69} +(-1.57209 - 1.66677i) q^{70} +0.833169 q^{71} +2.51916i q^{72} +1.38130i q^{73} +1.41865 q^{74} +(-12.3726 - 0.723955i) q^{75} -1.95904 q^{76} +5.06314i q^{77} +0.867217i q^{78} -11.3823 q^{79} +(-5.76261 - 6.10965i) q^{80} -8.54668 q^{81} +0.752965i q^{82} +14.3628i q^{83} -24.5865 q^{84} +(4.31208 - 4.06714i) q^{85} -0.189395 q^{86} -25.2064i q^{87} -0.801215i q^{88} +1.51234 q^{89} +(1.03505 - 0.976261i) q^{90} -8.75300 q^{91} -13.2318i q^{92} +15.2144i q^{93} +0.666425 q^{94} +(1.53426 + 1.62666i) q^{95} +5.85614 q^{96} -14.9617i q^{97} +3.77135i q^{98} -3.14418 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) \) 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9	\( 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9} + 10 q^{10} + 30 q^{11} + 4 q^{14} + 4 q^{15} + 66 q^{16} - 30 q^{19} + 10 q^{20} + 14 q^{21} - 22 q^{24} - 6 q^{25} - 30 q^{29} + 14 q^{30} + 26 q^{31} - 12 q^{34} + 6 q^{35} + 78 q^{36} - 64 q^{39} - 20 q^{40} + 22 q^{41} - 42 q^{44} + 6 q^{45} + 28 q^{46} - 60 q^{49} + 64 q^{51} - 62 q^{54} - 32 q^{56} + 14 q^{59} - 28 q^{60} + 78 q^{61} - 90 q^{64} + 40 q^{65} + 12 q^{66} + 28 q^{69} + 12 q^{70} + 20 q^{71} - 42 q^{74} + 50 q^{75} + 42 q^{76} - 102 q^{79} - 40 q^{80} + 42 q^{81} - 98 q^{84} - 2 q^{85} - 52 q^{86} + 8 q^{89} + 22 q^{90} + 56 q^{91} - 40 q^{94} - 74 q^{96} - 40 q^{99}+O(q^{100}) \) 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9 + 10 * q^10 + 30 * q^11 + 4 * q^14 + 4 * q^15 + 66 * q^16 - 30 * q^19 + 10 * q^20 + 14 * q^21 - 22 * q^24 - 6 * q^25 - 30 * q^29 + 14 * q^30 + 26 * q^31 - 12 * q^34 + 6 * q^35 + 78 * q^36 - 64 * q^39 - 20 * q^40 + 22 * q^41 - 42 * q^44 + 6 * q^45 + 28 * q^46 - 60 * q^49 + 64 * q^51 - 62 * q^54 - 32 * q^56 + 14 * q^59 - 28 * q^60 + 78 * q^61 - 90 * q^64 + 40 * q^65 + 12 * q^66 + 28 * q^69 + 12 * q^70 + 20 * q^71 - 42 * q^74 + 50 * q^75 + 42 * q^76 - 102 * q^79 - 40 * q^80 + 42 * q^81 - 98 * q^84 - 2 * q^85 - 52 * q^86 + 8 * q^89 + 22 * q^90 + 56 * q^91 - 40 * q^94 - 74 * q^96 - 40 * q^99

Introduction

L-functions

Modular forms

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Database

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