LMFDB - Embedded newform 349.2.b.b.348.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(348,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("349.348");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.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:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			348.10
Character	$\chi$	$=$	349.348
Dual form			349.2.b.b.348.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.19339i q^{2} -2.66615 q^{3} +0.575830 q^{4} -1.00436 q^{5} +3.18175i q^{6} +3.16046i q^{7} -3.07396i q^{8} +4.10838 q^{9} +O(q^{10})$	\(q-1.19339i q^{2} -2.66615 q^{3} +0.575830 q^{4} -1.00436 q^{5} +3.18175i q^{6} +3.16046i q^{7} -3.07396i q^{8} +4.10838 q^{9} +1.19859i q^{10} +0.0928732i q^{11} -1.53525 q^{12} +5.39489i q^{13} +3.77165 q^{14} +2.67778 q^{15} -2.51676 q^{16} +1.78063 q^{17} -4.90288i q^{18} +6.77818 q^{19} -0.578340 q^{20} -8.42627i q^{21} +0.110834 q^{22} +7.82106 q^{23} +8.19565i q^{24} -3.99126 q^{25} +6.43818 q^{26} -2.95510 q^{27} +1.81989i q^{28} -1.50524 q^{29} -3.19562i q^{30} +5.64457 q^{31} -3.14445i q^{32} -0.247614i q^{33} -2.12498i q^{34} -3.17424i q^{35} +2.36573 q^{36} -9.77605 q^{37} -8.08899i q^{38} -14.3836i q^{39} +3.08736i q^{40} +1.12663 q^{41} -10.0558 q^{42} +7.91594i q^{43} +0.0534792i q^{44} -4.12629 q^{45} -9.33354i q^{46} +12.5713i q^{47} +6.71007 q^{48} -2.98849 q^{49} +4.76312i q^{50} -4.74744 q^{51} +3.10654i q^{52} +6.18961i q^{53} +3.52658i q^{54} -0.0932781i q^{55} +9.71512 q^{56} -18.0717 q^{57} +1.79633i q^{58} +2.13858i q^{59} +1.54194 q^{60} +3.31836i q^{61} -6.73615i q^{62} +12.9843i q^{63} -8.78607 q^{64} -5.41841i q^{65} -0.295499 q^{66} +5.45587 q^{67} +1.02534 q^{68} -20.8521 q^{69} -3.78809 q^{70} -6.90898i q^{71} -12.6290i q^{72} +4.92337 q^{73} +11.6666i q^{74} +10.6413 q^{75} +3.90308 q^{76} -0.293522 q^{77} -17.1652 q^{78} -10.2115i q^{79} +2.52773 q^{80} -4.44637 q^{81} -1.34450i q^{82} -12.2987 q^{83} -4.85210i q^{84} -1.78839 q^{85} +9.44677 q^{86} +4.01319 q^{87} +0.285489 q^{88} +11.6838i q^{89} +4.92425i q^{90} -17.0503 q^{91} +4.50360 q^{92} -15.0493 q^{93} +15.0024 q^{94} -6.80773 q^{95} +8.38360i q^{96} -14.9553i q^{97} +3.56643i q^{98} +0.381558i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9}+O(q^{10}) $ 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9	$ 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9} + 12 q^{12} + 4 q^{14} + 12 q^{15} + 20 q^{16} - 14 q^{17} - 4 q^{19} - 2 q^{20} - 12 q^{22} - 18 q^{23} + 18 q^{25} + 22 q^{26} + 4 q^{27} - 18 q^{29} + 10 q^{31} - 54 q^{36} + 30 q^{37} - 16 q^{41} - 44 q^{45} - 74 q^{48} - 22 q^{49} + 32 q^{51} - 38 q^{56} - 16 q^{57} - 78 q^{60} - 96 q^{64} + 104 q^{66} + 72 q^{67} + 36 q^{68} - 40 q^{69} + 86 q^{70} + 72 q^{73} - 38 q^{75} + 96 q^{76} - 28 q^{77} - 30 q^{78} + 30 q^{80} - 6 q^{81} - 8 q^{83} - 22 q^{85} + 60 q^{86} + 32 q^{87} + 110 q^{88} - 12 q^{91} + 14 q^{92} + 84 q^{93} + 22 q^{94} - 10 q^{95}+O(q^{100}) $ 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9 + 12 * q^12 + 4 * q^14 + 12 * q^15 + 20 * q^16 - 14 * q^17 - 4 * q^19 - 2 * q^20 - 12 * q^22 - 18 * q^23 + 18 * q^25 + 22 * q^26 + 4 * q^27 - 18 * q^29 + 10 * q^31 - 54 * q^36 + 30 * q^37 - 16 * q^41 - 44 * q^45 - 74 * q^48 - 22 * q^49 + 32 * q^51 - 38 * q^56 - 16 * q^57 - 78 * q^60 - 96 * q^64 + 104 * q^66 + 72 * q^67 + 36 * q^68 - 40 * q^69 + 86 * q^70 + 72 * q^73 - 38 * q^75 + 96 * q^76 - 28 * q^77 - 30 * q^78 + 30 * q^80 - 6 * q^81 - 8 * q^83 - 22 * q^85 + 60 * q^86 + 32 * q^87 + 110 * q^88 - 12 * q^91 + 14 * q^92 + 84 * q^93 + 22 * q^94 - 10 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	1.19339i		−	0.843851i	−0.906630	−	0.421926i	$-0.861354\pi$
$2$		−	1.19339i		−	0.843851i	0.906630	−	0.421926i	$-0.138646\pi$
$3$	−2.66615			−1.53930			−0.769652	−	0.638463i	$-0.779570\pi$
$3$	−2.66615			−1.53930			−0.769652	+	0.638463i	$0.779570\pi$
$4$	0.575830			0.287915
$5$	−1.00436			−0.449163			−0.224582	−	0.974455i	$-0.572102\pi$
$5$	−1.00436			−0.449163			−0.224582	+	0.974455i	$0.572102\pi$
$6$			3.18175i			1.29894i
$7$			3.16046i			1.19454i	0.802040	+	0.597270i	$0.203748\pi$
$7$			3.16046i			1.19454i	−0.802040	+	0.597270i	$0.796252\pi$
$8$		−	3.07396i		−	1.08681i
$9$	4.10838			1.36946
$10$			1.19859i			0.379027i
$11$			0.0928732i			0.0280023i	0.999902	+	0.0140012i	$0.00445686\pi$
$11$			0.0928732i			0.0280023i	−0.999902	+	0.0140012i	$0.995543\pi$
$12$	−1.53525			−0.443189
$13$			5.39489i			1.49627i	0.663545	+	0.748136i	$0.269051\pi$
$13$			5.39489i			1.49627i	−0.663545	+	0.748136i	$0.730949\pi$
$14$	3.77165			1.00801
$15$	2.67778			0.691399
$16$	−2.51676			−0.629190
$17$	1.78063			0.431867			0.215933	−	0.976408i	$-0.430721\pi$
$17$	1.78063			0.431867			0.215933	+	0.976408i	$0.430721\pi$
$18$		−	4.90288i		−	1.15562i
$19$	6.77818			1.55502			0.777511	−	0.628870i	$-0.216482\pi$
$19$	6.77818			1.55502			0.777511	+	0.628870i	$0.216482\pi$
$20$	−0.578340			−0.129321
$21$		−	8.42627i		−	1.83876i
$22$	0.110834			0.0236298
$23$	7.82106			1.63080			0.815402	−	0.578896i	$-0.196516\pi$
$23$	7.82106			1.63080			0.815402	+	0.578896i	$0.196516\pi$
$24$			8.19565i			1.67293i
$25$	−3.99126			−0.798252
$26$	6.43818			1.26263
$27$	−2.95510			−0.568709
$28$			1.81989i			0.343926i
$29$	−1.50524			−0.279515			−0.139758	−	0.990186i	$-0.544632\pi$
$29$	−1.50524			−0.279515			−0.139758	+	0.990186i	$0.544632\pi$
$30$		−	3.19562i		−	0.583438i
$31$	5.64457			1.01380			0.506898	−	0.862006i	$-0.330792\pi$
$31$	5.64457			1.01380			0.506898	+	0.862006i	$0.330792\pi$
$32$		−	3.14445i		−	0.555866i
$33$		−	0.247614i		−	0.0431041i
$34$		−	2.12498i		−	0.364431i
$35$		−	3.17424i		−	0.536544i
$36$	2.36573			0.394288
$37$	−9.77605			−1.60717			−0.803586	−	0.595188i	$-0.797078\pi$
$37$	−9.77605			−1.60717			−0.803586	+	0.595188i	$0.797078\pi$
$38$		−	8.08899i		−	1.31221i
$39$		−	14.3836i		−	2.30322i
$40$			3.08736i			0.488154i
$41$	1.12663			0.175950			0.0879748	−	0.996123i	$-0.471961\pi$
$41$	1.12663			0.175950			0.0879748	+	0.996123i	$0.471961\pi$
$42$	−10.0558			−1.55164
$43$			7.91594i			1.20717i	0.797299	+	0.603585i	$0.206262\pi$
$43$			7.91594i			1.20717i	−0.797299	+	0.603585i	$0.793738\pi$
$44$			0.0534792i			0.00806229i
$45$	−4.12629			−0.615110
$46$		−	9.33354i		−	1.37616i
$47$			12.5713i			1.83371i	0.399222	+	0.916854i	$0.369280\pi$
$47$			12.5713i			1.83371i	−0.399222	+	0.916854i	$0.630720\pi$
$48$	6.71007			0.968515
$49$	−2.98849			−0.426928
$50$			4.76312i			0.673606i
$51$	−4.74744			−0.664774
$52$			3.10654i			0.430800i
$53$			6.18961i			0.850208i	0.905144	+	0.425104i	$0.139763\pi$
$53$			6.18961i			0.850208i	−0.905144	+	0.425104i	$0.860237\pi$
$54$			3.52658i			0.479906i
$55$		−	0.0932781i		−	0.0125776i
$56$	9.71512			1.29824
$57$	−18.0717			−2.39365
$58$			1.79633i			0.235869i
$59$			2.13858i			0.278420i	0.990263	+	0.139210i	$0.0444562\pi$
$59$			2.13858i			0.278420i	−0.990263	+	0.139210i	$0.955544\pi$
$60$	1.54194			0.199064
$61$			3.31836i			0.424872i	0.977175	+	0.212436i	$0.0681397\pi$
$61$			3.31836i			0.424872i	−0.977175	+	0.212436i	$0.931860\pi$
$62$		−	6.73615i		−	0.855492i
$63$			12.9843i			1.63587i
$64$	−8.78607			−1.09826
$65$		−	5.41841i		−	0.672071i
$66$	−0.295499			−0.0363735
$67$	5.45587			0.666541			0.333270	−	0.942831i	$-0.391848\pi$
$67$	5.45587			0.666541			0.333270	+	0.942831i	$0.391848\pi$
$68$	1.02534			0.124341
$69$	−20.8521			−2.51030
$70$	−3.78809			−0.452763
$71$		−	6.90898i		−	0.819946i	−0.912098	−	0.409973i	$-0.865538\pi$
$71$		−	6.90898i		−	0.819946i	0.912098	−	0.409973i	$-0.134462\pi$
$72$		−	12.6290i		−	1.48834i
$73$	4.92337			0.576237			0.288119	−	0.957595i	$-0.406970\pi$
$73$	4.92337			0.576237			0.288119	+	0.957595i	$0.406970\pi$
$74$			11.6666i			1.35621i
$75$	10.6413			1.22875
$76$	3.90308			0.447714
$77$	−0.293522			−0.0334499
$78$	−17.1652			−1.94357
$79$		−	10.2115i		−	1.14888i	−0.818546	−	0.574441i	$-0.805220\pi$
$79$		−	10.2115i		−	1.14888i	0.818546	−	0.574441i	$-0.194780\pi$
$80$	2.52773			0.282609
$81$	−4.44637			−0.494042
$82$		−	1.34450i		−	0.148475i
$83$	−12.2987			−1.34996			−0.674979	−	0.737837i	$-0.735847\pi$
$83$	−12.2987			−1.34996			−0.674979	+	0.737837i	$0.735847\pi$
$84$		−	4.85210i		−	0.529407i
$85$	−1.78839			−0.193979
$86$	9.44677			1.01867
$87$	4.01319			0.430259
$88$	0.285489			0.0304332
$89$			11.6838i			1.23848i	0.785201	+	0.619242i	$0.212560\pi$
$89$			11.6838i			1.23848i	−0.785201	+	0.619242i	$0.787440\pi$
$90$			4.92425i			0.519062i
$91$	−17.0503			−1.78736
$92$	4.50360			0.469533
$93$	−15.0493			−1.56054
$94$	15.0024			1.54738
$95$	−6.80773			−0.698458
$96$			8.38360i			0.855647i
$97$		−	14.9553i		−	1.51848i	−0.650809	−	0.759241i	$-0.725570\pi$
$97$		−	14.9553i		−	1.51848i	0.650809	−	0.759241i	$-0.274430\pi$
$98$			3.56643i			0.360263i
$99$			0.381558i			0.0383480i
$100$	−2.29829			−0.229829
$101$		−	2.33098i		−	0.231942i	−0.993253	−	0.115971i	$-0.963002\pi$
$101$		−	2.33098i		−	0.231942i	0.993253	−	0.115971i	$-0.0369979\pi$
$102$			5.66553i			0.560971i
$103$			1.50938i			0.148724i	0.997231	+	0.0743619i	$0.0236920\pi$
$103$			1.50938i			0.148724i	−0.997231	+	0.0743619i	$0.976308\pi$
$104$	16.5837			1.62616
$105$			8.46300i			0.825904i
$106$	7.38659			0.717449
$107$		−	8.47222i		−	0.819040i	−0.912301	−	0.409520i	$-0.865696\pi$
$107$		−	8.47222i		−	0.819040i	0.912301	−	0.409520i	$-0.134304\pi$
$108$	−1.70164			−0.163740
$109$	−2.71282			−0.259841			−0.129920	−	0.991524i	$-0.541472\pi$
$109$	−2.71282			−0.259841			−0.129920	+	0.991524i	$0.541472\pi$
$110$	−0.111317			−0.0106136
$111$	26.0645			2.47393
$112$		−	7.95411i		−	0.751593i
$113$		−	11.4065i		−	1.07304i	−0.843888	−	0.536519i	$-0.819739\pi$
$113$		−	11.4065i		−	1.07304i	0.843888	−	0.536519i	$-0.180261\pi$
$114$			21.5665i			2.01989i
$115$	−7.85515			−0.732497
$116$	−0.866760			−0.0804767
$117$			22.1642i			2.04908i
$118$	2.55215			0.234945
$119$			5.62761i			0.515882i
$120$		−	8.23138i		−	0.751418i
$121$	10.9914			0.999216
$122$	3.96008			0.358529
$123$	−3.00376			−0.270840
$124$	3.25032			0.291887
$125$	9.03046			0.807709
$126$	15.4953			1.38043
$127$			21.3625i			1.89562i	0.318837	+	0.947810i	$0.396708\pi$
$127$			21.3625i			1.89562i	−0.318837	+	0.947810i	$0.603292\pi$
$128$			4.19626i			0.370900i
$129$		−	21.1051i		−	1.85820i
$130$	−6.46625			−0.567128
$131$		−	1.11322i		−	0.0972624i	−0.998817	−	0.0486312i	$-0.984514\pi$
$131$		−	1.11322i		−	0.0972624i	0.998817	−	0.0486312i	$-0.0154859\pi$
$132$		−	0.142584i		−	0.0124103i
$133$			21.4222i			1.85754i
$134$		−	6.51096i		−	0.562461i
$135$	2.96798			0.255443
$136$		−	5.47359i		−	0.469356i
$137$		−	12.4166i		−	1.06082i	−0.847740	−	0.530412i	$-0.822037\pi$
$137$		−	12.4166i		−	1.06082i	0.847740	−	0.530412i	$-0.177963\pi$
$138$			24.8846i			2.11832i
$139$	−8.34582			−0.707883			−0.353942	−	0.935268i	$-0.615159\pi$
$139$	−8.34582			−0.707883			−0.353942	+	0.935268i	$0.615159\pi$
$140$		−	1.82782i		−	0.154479i
$141$		−	33.5169i		−	2.82264i
$142$	−8.24508			−0.691912
$143$	−0.501041			−0.0418991
$144$	−10.3398			−0.861649
$145$	1.51180			0.125548
$146$		−	5.87548i		−	0.486258i
$147$	7.96778			0.657172
$148$	−5.62935			−0.462729
$149$			0.506123i			0.0414632i	0.999785	+	0.0207316i	$0.00659954\pi$
$149$			0.506123i			0.0414632i	−0.999785	+	0.0207316i	$0.993400\pi$
$150$		−	12.6992i		−	1.03689i
$151$	9.19746			0.748479			0.374239	−	0.927332i	$-0.377904\pi$
$151$	9.19746			0.748479			0.374239	+	0.927332i	$0.377904\pi$
$152$		−	20.8359i		−	1.69001i
$153$	7.31551			0.591424
$154$			0.350285i			0.0282268i
$155$	−5.66918			−0.455360
$156$		−	8.28251i		−	0.663132i
$157$	5.78636			0.461802			0.230901	−	0.972977i	$-0.425833\pi$
$157$	5.78636			0.461802			0.230901	+	0.972977i	$0.425833\pi$
$158$	−12.1862			−0.969485
$159$		−	16.5025i		−	1.30873i
$160$			3.15816i			0.249675i
$161$			24.7181i			1.94806i
$162$			5.30624i			0.416898i
$163$		−	11.9982i		−	0.939775i	−0.882726	−	0.469887i	$-0.844295\pi$
$163$		−	11.9982i		−	0.939775i	0.882726	−	0.469887i	$-0.155705\pi$
$164$	0.648746			0.0506585
$165$			0.248694i			0.0193608i
$166$			14.6771i			1.13916i
$167$			5.63265i			0.435868i	0.975964	+	0.217934i	$0.0699317\pi$
$167$			5.63265i			0.435868i	−0.975964	+	0.217934i	$0.930068\pi$
$168$	−25.9020			−1.99838
$169$	−16.1048			−1.23883
$170$			2.13424i			0.163689i
$171$	27.8473			2.12954
$172$			4.55824i			0.347562i
$173$		−	16.1601i		−	1.22863i	−0.789061	−	0.614315i	$-0.789432\pi$
$173$		−	16.1601i		−	1.22863i	0.789061	−	0.614315i	$-0.210568\pi$
$174$		−	4.78928i		−	0.363075i
$175$		−	12.6142i		−	0.953545i
$176$		−	0.233740i		−	0.0176188i
$177$		−	5.70179i		−	0.428572i
$178$	13.9433			1.04510
$179$		−	24.0828i		−	1.80003i	−0.435854	−	0.900017i	$-0.643554\pi$
$179$		−	24.0828i		−	1.80003i	0.435854	−	0.900017i	$-0.356446\pi$
$180$	−2.37604			−0.177100
$181$	−2.90382			−0.215839			−0.107920	−	0.994160i	$-0.534419\pi$
$181$	−2.90382			−0.215839			−0.107920	+	0.994160i	$0.534419\pi$
$182$			20.3476i			1.50826i
$183$		−	8.84725i		−	0.654007i
$184$		−	24.0416i		−	1.77237i
$185$	9.81867			0.721883
$186$			17.9596i			1.31686i
$187$			0.165373i			0.0120933i
$188$			7.23892i			0.527952i
$189$		−	9.33947i		−	0.679347i
$190$			8.12425i			0.589395i
$191$	19.5889			1.41741			0.708703	−	0.705507i	$-0.249281\pi$
$191$	19.5889			1.41741			0.708703	+	0.705507i	$0.249281\pi$
$192$	23.4250			1.69055
$193$		−	3.30753i		−	0.238081i	−0.992889	−	0.119041i	$-0.962018\pi$
$193$		−	3.30753i		−	0.238081i	0.992889	−	0.119041i	$-0.0379818\pi$
$194$	−17.8475			−1.28137
$195$			14.4463i			1.03452i
$196$	−1.72086			−0.122919
$197$			5.91774i			0.421621i	0.977527	+	0.210811i	$0.0676104\pi$
$197$			5.91774i			0.421621i	−0.977527	+	0.210811i	$0.932390\pi$
$198$	0.455346			0.0323600
$199$		−	10.4370i		−	0.739860i	−0.929060	−	0.369930i	$-0.879382\pi$
$199$		−	10.4370i		−	0.739860i	0.929060	−	0.369930i	$-0.120618\pi$
$200$			12.2690i			0.867548i
$201$	−14.5462			−1.02601
$202$	−2.78176			−0.195724
$203$		−	4.75723i		−	0.333892i
$204$	−2.73372			−0.191399
$205$	−1.13154			−0.0790301
$206$	1.80127			0.125501
$207$	32.1318			2.23332
$208$		−	13.5776i		−	0.941440i
$209$			0.629512i			0.0435442i
$210$	10.0996			0.696940
$211$			21.0239i			1.44734i	0.690145	+	0.723671i	$0.257547\pi$
$211$			21.0239i			1.44734i	−0.690145	+	0.723671i	$0.742453\pi$
$212$			3.56416i			0.244788i
$213$			18.4204i			1.26215i
$214$	−10.1106			−0.691148
$215$		−	7.95045i		−	0.542216i
$216$			9.08386i			0.618078i
$217$			17.8394i			1.21102i
$218$			3.23744i			0.219267i
$219$	−13.1265			−0.887005
$220$		−	0.0537123i		−	0.00362129i
$221$			9.60631i			0.646190i
$222$		−	31.1050i		−	2.08763i
$223$	−16.6811			−1.11705			−0.558524	−	0.829489i	$-0.688632\pi$
$223$	−16.6811			−1.11705			−0.558524	+	0.829489i	$0.688632\pi$
$224$	9.93791			0.664005
$225$	−16.3976			−1.09317
$226$	−13.6124			−0.905484
$227$	3.88358			0.257762			0.128881	−	0.991660i	$-0.458861\pi$
$227$	3.88358			0.257762			0.128881	+	0.991660i	$0.458861\pi$
$228$	−10.4062			−0.689168
$229$			24.0626i			1.59010i	0.606544	+	0.795050i	$0.292555\pi$
$229$			24.0626i			1.59010i	−0.606544	+	0.795050i	$0.707445\pi$
$230$			9.37423i			0.618118i
$231$	0.782575			0.0514896
$232$			4.62703i			0.303780i
$233$	−11.4625			−0.750930			−0.375465	−	0.926836i	$-0.622517\pi$
$233$	−11.4625			−0.750930			−0.375465	+	0.926836i	$0.622517\pi$
$234$	26.4505			1.72912
$235$		−	12.6261i		−	0.823634i
$236$			1.23146i			0.0801612i
$237$			27.2254i			1.76848i
$238$	6.71591			0.435328
$239$	−5.72612			−0.370392			−0.185196	−	0.982702i	$-0.559292\pi$
$239$	−5.72612			−0.370392			−0.185196	+	0.982702i	$0.559292\pi$
$240$	−6.73932			−0.435021
$241$	27.9599			1.80106			0.900529	−	0.434796i	$-0.143179\pi$
$241$	27.9599			1.80106			0.900529	+	0.434796i	$0.143179\pi$
$242$		−	13.1170i		−	0.843190i
$243$	20.7200			1.32919
$244$			1.91081i			0.122327i
$245$	3.00152			0.191760
$246$			3.58465i			0.228549i
$247$			36.5675i			2.32674i
$248$		−	17.3512i		−	1.10180i
$249$	32.7902			2.07800
$250$		−	10.7768i		−	0.681586i
$251$		−	13.1855i		−	0.832261i	−0.909305	−	0.416130i	$-0.863386\pi$
$251$		−	13.1855i		−	0.832261i	0.909305	−	0.416130i	$-0.136614\pi$
$252$			7.47678i			0.470993i
$253$			0.726367i			0.0456663i
$254$	25.4938			1.59962
$255$	4.76813			0.298592
$256$	−12.5644			−0.785273
$257$	−20.5287			−1.28054			−0.640272	−	0.768149i	$-0.721178\pi$
$257$	−20.5287			−1.28054			−0.640272	+	0.768149i	$0.721178\pi$
$258$	−25.1865			−1.56805
$259$		−	30.8968i		−	1.91983i
$260$		−	3.12008i		−	0.193499i
$261$	−6.18407			−0.382785
$262$	−1.32850			−0.0820750
$263$	21.8471			1.34715			0.673574	−	0.739120i	$-0.264758\pi$
$263$	21.8471			1.34715			0.673574	+	0.739120i	$0.264758\pi$
$264$	−0.761156			−0.0468459
$265$		−	6.21659i		−	0.381882i
$266$	25.5649			1.56748
$267$		−	31.1509i		−	1.90640i
$268$	3.14166			0.191907
$269$	−16.7897			−1.02369			−0.511843	−	0.859079i	$-0.671037\pi$
$269$	−16.7897			−1.02369			−0.511843	+	0.859079i	$0.671037\pi$
$270$		−	3.54195i		−	0.215556i
$271$	6.64680			0.403764			0.201882	−	0.979410i	$-0.435294\pi$
$271$	6.64680			0.403764			0.201882	+	0.979410i	$0.435294\pi$
$272$	−4.48142			−0.271726
$273$	45.4588			2.75129
$274$	−14.8178			−0.895178
$275$		−	0.370681i		−	0.0223529i
$276$	−12.0073			−0.722754
$277$		−	10.2582i		−	0.616358i	−0.951328	−	0.308179i	$-0.900280\pi$
$277$		−	10.2582i		−	0.616358i	0.951328	−	0.308179i	$-0.0997196\pi$
$278$			9.95978i			0.597348i
$279$	23.1900			1.38835
$280$	−9.75747			−0.583120
$281$	8.95547			0.534239			0.267119	−	0.963663i	$-0.413928\pi$
$281$	8.95547			0.534239			0.267119	+	0.963663i	$0.413928\pi$
$282$	−39.9986			−2.38188
$283$	3.74494			0.222613			0.111307	−	0.993786i	$-0.464496\pi$
$283$	3.74494			0.222613			0.111307	+	0.993786i	$0.464496\pi$
$284$		−	3.97840i		−	0.236075i
$285$	18.1505			1.07514
$286$			0.597935i			0.0353566i
$287$			3.56066i			0.210179i
$288$		−	12.9186i		−	0.761236i
$289$	−13.8293			−0.813491
$290$		−	1.80416i		−	0.105944i
$291$			39.8732i			2.33741i
$292$	2.83503			0.165907
$293$	−25.5850			−1.49469			−0.747345	−	0.664436i	$-0.768672\pi$
$293$	−25.5850			−1.49469			−0.747345	+	0.664436i	$0.768672\pi$
$294$		−	9.50864i		−	0.554555i
$295$		−	2.14790i		−	0.125056i
$296$			30.0512i			1.74669i
$297$		−	0.274450i		−	0.0159252i
$298$	0.604000			0.0349888
$299$			42.1937i			2.44013i
$300$	6.12759			0.353777
$301$	−25.0180			−1.44201
$302$		−	10.9761i		−	0.631605i
$303$			6.21476i			0.357029i
$304$	−17.0591			−0.978404
$305$		−	3.33282i		−	0.190837i
$306$		−	8.73022i		−	0.499074i
$307$	−19.8517			−1.13299			−0.566497	−	0.824064i	$-0.691702\pi$
$307$	−19.8517			−1.13299			−0.566497	+	0.824064i	$0.691702\pi$
$308$	−0.169019			−0.00963074
$309$		−	4.02424i		−	0.228931i
$310$			6.76552i			0.384256i
$311$			12.5009i			0.708861i	0.935082	+	0.354431i	$0.115325\pi$
$311$			12.5009i			0.708861i	−0.935082	+	0.354431i	$0.884675\pi$
$312$	−44.2146			−2.50316
$313$	−0.192079			−0.0108569			−0.00542847	−	0.999985i	$-0.501728\pi$
$313$	−0.192079			−0.0108569			−0.00542847	+	0.999985i	$0.501728\pi$
$314$		−	6.90536i		−	0.389692i
$315$		−	13.0410i		−	0.734774i
$316$		−	5.88008i		−	0.330780i
$317$		−	3.08067i		−	0.173028i	−0.996251	−	0.0865138i	$-0.972427\pi$
$317$		−	3.08067i		−	0.173028i	0.996251	−	0.0865138i	$-0.0275727\pi$
$318$	−19.6938			−1.10437
$319$		−	0.139796i		−	0.00782708i
$320$	8.82437			0.493297
$321$			22.5882i			1.26075i
$322$	29.4983			1.64387
$323$	12.0694			0.671562
$324$	−2.56036			−0.142242
$325$		−	21.5324i		−	1.19440i
$326$	−14.3185			−0.793030
$327$	7.23279			0.399974
$328$		−	3.46321i		−	0.191224i
$329$	−39.7310			−2.19044
$330$	0.296788			0.0163376
$331$		−	14.8351i		−	0.815412i	−0.913113	−	0.407706i	$-0.866329\pi$
$331$		−	14.8351i		−	0.815412i	0.913113	−	0.407706i	$-0.133671\pi$
$332$	−7.08197			−0.388673
$333$	−40.1637			−2.20096
$334$	6.72192			0.367807
$335$	−5.47966			−0.299386
$336$			21.2069i			1.15693i
$337$	12.9316			0.704427			0.352214	−	0.935920i	$-0.385429\pi$
$337$	12.9316			0.704427			0.352214	+	0.935920i	$0.385429\pi$
$338$			19.2193i			1.04539i
$339$			30.4116i			1.65173i
$340$	−1.02981			−0.0558494
$341$			0.524230i			0.0283886i
$342$		−	33.2326i		−	1.79701i
$343$			12.6782i			0.684558i
$344$	24.3333			1.31196
$345$	20.9430			1.12754
$346$	−19.2852			−1.03678
$347$		−	5.95915i		−	0.319904i	−0.987125	−	0.159952i	$-0.948866\pi$
$347$		−	5.95915i		−	0.319904i	0.987125	−	0.159952i	$-0.0511339\pi$
$348$	2.31092			0.123878
$349$	−18.6714	−	0.616110i	−0.999456	−	0.0329796i
$349$	−18.6714	−	0.616110i	−0.999456	−	0.0329796i
$350$	−15.0536			−0.804650
$351$		−	15.9424i		−	0.850944i
$352$	0.292036			0.0155655
$353$	0.793622			0.0422402			0.0211201	−	0.999777i	$-0.493277\pi$
$353$	0.793622			0.0422402			0.0211201	+	0.999777i	$0.493277\pi$
$354$	−6.80443			−0.361651
$355$			6.93910i			0.368289i
$356$			6.72790i			0.356578i
$357$		−	15.0041i		−	0.794100i
$358$	−28.7401			−1.51896
$359$			5.46131i			0.288237i	0.989560	+	0.144119i	$0.0460347\pi$
$359$			5.46131i			0.288237i	−0.989560	+	0.144119i	$0.953965\pi$
$360$			12.6840i			0.668507i
$361$	26.9437			1.41809
$362$			3.46538i			0.182136i
$363$	−29.3047			−1.53810
$364$	−9.81809			−0.514608
$365$	−4.94484			−0.258825
$366$	−10.5582			−0.551885
$367$		−	18.0993i		−	0.944777i	−0.881390	−	0.472388i	$-0.843392\pi$
$367$		−	18.0993i		−	0.944777i	0.881390	−	0.472388i	$-0.156608\pi$
$368$	−19.6837			−1.02608
$369$	4.62861			0.240956
$370$		−	11.7175i		−	0.609162i
$371$	−19.5620			−1.01561
$372$	−8.66584			−0.449303
$373$			9.91344i			0.513298i	0.966505	+	0.256649i	$0.0826185\pi$
$373$			9.91344i			0.513298i	−0.966505	+	0.256649i	$0.917382\pi$
$374$	0.197354			0.0102049
$375$	−24.0766			−1.24331
$376$	38.6436			1.99289
$377$		−	8.12058i		−	0.418231i
$378$	−11.1456			−0.573267
$379$			2.37451i			0.121970i	0.998139	+	0.0609851i	$0.0194242\pi$
$379$			2.37451i			0.121970i	−0.998139	+	0.0609851i	$0.980576\pi$
$380$	−3.92010			−0.201097
$381$		−	56.9558i		−	2.91794i
$382$		−	23.3772i		−	1.19608i
$383$		−	34.4565i		−	1.76065i	−0.474374	−	0.880324i	$-0.657325\pi$
$383$		−	34.4565i		−	1.76065i	0.474374	−	0.880324i	$-0.342675\pi$
$384$		−	11.1879i		−	0.570929i
$385$	0.294801			0.0150245
$386$	−3.94716			−0.200905
$387$			32.5217i			1.65317i
$388$		−	8.61173i		−	0.437194i
$389$		−	4.85455i		−	0.246136i	−0.992398	−	0.123068i	$-0.960727\pi$
$389$		−	4.85455i		−	0.246136i	0.992398	−	0.123068i	$-0.0392733\pi$
$390$	17.2400			0.872982
$391$	13.9264			0.704290
$392$			9.18651i			0.463989i
$393$			2.96801i			0.149716i
$394$	7.06215			0.355786
$395$			10.2560i			0.516035i
$396$			0.219713i			0.0110410i
$397$	14.3753			0.721475			0.360738	−	0.932667i	$-0.382525\pi$
$397$	14.3753			0.721475			0.360738	+	0.932667i	$0.382525\pi$
$398$	−12.4554			−0.624332
$399$		−	57.1148i		−	2.85931i
$400$	10.0450			0.502252
$401$		−	32.1479i		−	1.60539i	−0.596391	−	0.802694i	$-0.703399\pi$
$401$		−	32.1479i		−	1.60539i	0.596391	−	0.802694i	$-0.296601\pi$
$402$			17.3592i			0.865799i
$403$			30.4518i			1.51691i
$404$		−	1.34225i		−	0.0667795i
$405$	4.46576			0.221905
$406$	−5.67722			−0.281755
$407$		−	0.907933i		−	0.0450046i
$408$			14.5934i			0.722483i
$409$	22.4720			1.11117			0.555585	−	0.831460i	$-0.312494\pi$
$409$	22.4720			1.11117			0.555585	+	0.831460i	$0.312494\pi$
$410$			1.35036i			0.0666896i
$411$			33.1047i			1.63293i
$412$			0.869148i			0.0428198i
$413$	−6.75889			−0.332583
$414$		−	38.3457i		−	1.88459i
$415$	12.3523			0.606352
$416$	16.9640			0.831727
$417$	22.2512			1.08965
$418$	0.751250			0.0367448
$419$	−10.3581			−0.506024			−0.253012	−	0.967463i	$-0.581421\pi$
$419$	−10.3581			−0.506024			−0.253012	+	0.967463i	$0.581421\pi$
$420$			4.87325i			0.237790i
$421$		−	30.2536i		−	1.47447i	−0.675637	−	0.737234i	$-0.736132\pi$
$421$		−	30.2536i		−	1.47447i	0.675637	−	0.737234i	$-0.263868\pi$
$422$	25.0896			1.22134
$423$			51.6475i			2.51119i
$424$	19.0266			0.924014
$425$	−7.10697			−0.344739
$426$	21.9827			1.06506
$427$	−10.4875			−0.507527
$428$		−	4.87856i		−	0.235814i
$429$	1.33585			0.0644955
$430$	−9.48795			−0.457550
$431$			28.6916i			1.38203i	0.722842	+	0.691013i	$0.242835\pi$
$431$			28.6916i			1.38203i	−0.722842	+	0.691013i	$0.757165\pi$
$432$	7.43728			0.357826
$433$			12.7232i			0.611438i	0.952122	+	0.305719i	$0.0988968\pi$
$433$			12.7232i			0.611438i	−0.952122	+	0.305719i	$0.901103\pi$
$434$	21.2893			1.02192
$435$	−4.03068			−0.193257
$436$	−1.56212			−0.0748121
$437$	53.0125			2.53593
$438$			15.6649i			0.748500i
$439$		−	19.8930i		−	0.949440i	−0.880137	−	0.474720i	$-0.842549\pi$
$439$		−	19.8930i		−	0.949440i	0.880137	−	0.474720i	$-0.157451\pi$
$440$	−0.286733			−0.0136695
$441$	−12.2779			−0.584660
$442$	11.4640			0.545289
$443$	27.6449			1.31345			0.656724	−	0.754131i	$-0.271942\pi$
$443$	27.6449			1.31345			0.656724	+	0.754131i	$0.271942\pi$
$444$	15.0087			0.712281
$445$		−	11.7348i		−	0.556281i
$446$			19.9070i			0.942622i
$447$		−	1.34940i		−	0.0638245i
$448$		−	27.7680i		−	1.31191i
$449$	−16.7408			−0.790049			−0.395025	−	0.918671i	$-0.629264\pi$
$449$	−16.7408			−0.790049			−0.395025	+	0.918671i	$0.629264\pi$
$450$			19.5687i			0.922476i
$451$			0.104633i			0.00492700i
$452$		−	6.56823i		−	0.308944i
$453$	−24.5218			−1.15214
$454$		−	4.63460i		−	0.217513i
$455$	17.1246			0.802816
$456$			55.5516i			2.60144i
$457$	−2.31993			−0.108522			−0.0542609	−	0.998527i	$-0.517280\pi$
$457$	−2.31993			−0.108522			−0.0542609	+	0.998527i	$0.517280\pi$
$458$	28.7159			1.34181
$459$	−5.26195			−0.245607
$460$	−4.52323			−0.210897
$461$			30.7042i			1.43004i	0.699104	+	0.715020i	$0.253582\pi$
$461$			30.7042i			1.43004i	−0.699104	+	0.715020i	$0.746418\pi$
$462$		−	0.933913i		−	0.0434496i
$463$		−	24.1966i		−	1.12451i	−0.826964	−	0.562255i	$-0.809934\pi$
$463$		−	24.1966i		−	1.12451i	0.826964	−	0.562255i	$-0.190066\pi$
$464$	3.78832			0.175868
$465$	15.1149			0.700937
$466$			13.6791i			0.633674i
$467$	−31.7381			−1.46866			−0.734331	−	0.678791i	$-0.762504\pi$
$467$	−31.7381			−1.46866			−0.734331	+	0.678791i	$0.762504\pi$
$468$			12.7628i			0.589962i
$469$			17.2430i			0.796210i
$470$	−15.0678			−0.695025
$471$	−15.4273			−0.710854
$472$	6.57391			0.302589
$473$	−0.735179			−0.0338036
$474$	32.4904			1.49233
$475$	−27.0535			−1.24130
$476$			3.24055i			0.148530i
$477$			25.4292i			1.16433i
$478$			6.83347i			0.312556i
$479$	−42.8701			−1.95879			−0.979394	−	0.201961i	$-0.935269\pi$
$479$	−42.8701			−1.95879			−0.979394	+	0.201961i	$0.935269\pi$
$480$		−	8.42015i		−	0.384325i
$481$		−	52.7407i		−	2.40477i
$482$		−	33.3670i		−	1.51983i
$483$		−	65.9023i		−	2.99866i
$484$	6.32917			0.287689
$485$			15.0205i			0.682047i
$486$		−	24.7270i		−	1.12164i
$487$		−	12.8388i		−	0.581779i	−0.956757	−	0.290890i	$-0.906049\pi$
$487$		−	12.8388i		−	0.581779i	0.956757	−	0.290890i	$-0.0939513\pi$
$488$	10.2005			0.461754
$489$			31.9892i			1.44660i
$490$		−	3.58197i		−	0.161817i
$491$	27.2001			1.22752			0.613762	−	0.789491i	$-0.289655\pi$
$491$	27.2001			1.22752			0.613762	+	0.789491i	$0.289655\pi$
$492$	−1.72966			−0.0779789
$493$	−2.68027			−0.120713
$494$	43.6392			1.96342
$495$		−	0.383222i		−	0.0172245i
$496$	−14.2060			−0.637870
$497$	21.8356			0.979458
$498$		−	39.1314i		−	1.75352i
$499$			36.3112i			1.62551i	0.582603	+	0.812757i	$0.302034\pi$
$499$			36.3112i			1.62551i	−0.582603	+	0.812757i	$0.697966\pi$
$500$	5.20001			0.232552
$501$		−	15.0175i		−	0.670933i
$502$	−15.7354			−0.702304
$503$			5.44068i			0.242588i	0.992617	+	0.121294i	$0.0387044\pi$
$503$			5.44068i			0.242588i	−0.992617	+	0.121294i	$0.961296\pi$
$504$	39.9134			1.77788
$505$			2.34115i			0.104180i
$506$	0.866836			0.0385356
$507$	42.9379			1.90694
$508$			12.3012i			0.545777i
$509$		−	12.7398i		−	0.564683i	−0.959314	−	0.282342i	$-0.908889\pi$
$509$		−	12.7398i		−	0.564683i	0.959314	−	0.282342i	$-0.0911112\pi$
$510$		−	5.69022i		−	0.251967i
$511$			15.5601i			0.688339i
$512$			23.3867i			1.03355i
$513$	−20.0302			−0.884355
$514$			24.4986i			1.08059i
$515$		−	1.51596i		−	0.0668013i
$516$		−	12.1530i		−	0.535004i
$517$	−1.16753			−0.0513481
$518$	−36.8718			−1.62005
$519$			43.0853i			1.89124i
$520$	−16.6560			−0.730412
$521$			14.7645i			0.646844i	0.946255	+	0.323422i	$0.104833\pi$
$521$			14.7645i			0.646844i	−0.946255	+	0.323422i	$0.895167\pi$
$522$			7.37999i			0.323013i
$523$		−	22.3869i		−	0.978910i	−0.872029	−	0.489455i	$-0.837196\pi$
$523$		−	22.3869i		−	0.978910i	0.872029	−	0.489455i	$-0.162804\pi$
$524$		−	0.641025i		−	0.0280033i
$525$			33.6314i			1.46780i
$526$		−	26.0720i		−	1.13679i
$527$	10.0509			0.437824
$528$			0.623186i			0.0271207i
$529$	38.1689			1.65952
$530$	−7.41879			−0.322252
$531$			8.78609i			0.381284i
$532$			12.3355i			0.534813i
$533$			6.07803i			0.263269i
$534$	−37.1750			−1.60872
$535$			8.50915i			0.367883i
$536$		−	16.7711i		−	0.724402i
$537$			64.2085i			2.77080i
$538$			20.0366i			0.863839i
$539$		−	0.277551i		−	0.0119550i
$540$	1.70905			0.0735460
$541$	33.8149			1.45382			0.726908	−	0.686735i	$-0.240957\pi$
$541$	33.8149			1.45382			0.726908	+	0.686735i	$0.240957\pi$
$542$		−	7.93219i		−	0.340717i
$543$	7.74204			0.332243
$544$		−	5.59911i		−	0.240060i
$545$	2.72464			0.116711
$546$		−	54.2498i		−	2.32168i
$547$	17.4754			0.747194			0.373597	−	0.927591i	$-0.378124\pi$
$547$	17.4754			0.747194			0.373597	+	0.927591i	$0.378124\pi$
$548$		−	7.14987i		−	0.305427i
$549$			13.6331i			0.581844i
$550$	−0.442366			−0.0188625
$551$	−10.2028			−0.434652
$552$			64.0986i			2.72822i
$553$	32.2730			1.37239
$554$	−12.2420			−0.520114
$555$	−26.1781			−1.11120
$556$	−4.80577			−0.203810
$557$		−	18.0126i		−	0.763219i	−0.924324	−	0.381610i	$-0.875370\pi$
$557$		−	18.0126i		−	0.763219i	0.924324	−	0.381610i	$-0.124630\pi$
$558$		−	27.6747i		−	1.17156i
$559$	−42.7056			−1.80625
$560$			7.98879i			0.337588i
$561$		−	0.440910i		−	0.0186152i
$562$		−	10.6873i		−	0.450818i
$563$	20.8594			0.879117			0.439559	−	0.898214i	$-0.355135\pi$
$563$	20.8594			0.879117			0.439559	+	0.898214i	$0.355135\pi$
$564$		−	19.3001i		−	0.812679i
$565$			11.4563i			0.481969i
$566$		−	4.46916i		−	0.187853i
$567$		−	14.0526i		−	0.590153i
$568$	−21.2379			−0.891124
$569$		−	2.00845i		−	0.0841985i	−0.999113	−	0.0420993i	$-0.986595\pi$
$569$		−	2.00845i		−	0.0841985i	0.999113	−	0.0420993i	$-0.0134046\pi$
$570$		−	21.6605i		−	0.907258i
$571$			2.67823i			0.112081i	0.998429	+	0.0560403i	$0.0178475\pi$
$571$			2.67823i			0.112081i	−0.998429	+	0.0560403i	$0.982152\pi$
$572$	−0.288514			−0.0120634
$573$	−52.2271			−2.18182
$574$	4.24924			0.177360
$575$	−31.2159			−1.30179
$576$	−36.0965			−1.50402
$577$	−7.22840			−0.300922			−0.150461	−	0.988616i	$-0.548076\pi$
$577$	−7.22840			−0.300922			−0.150461	+	0.988616i	$0.548076\pi$
$578$			16.5038i			0.686466i
$579$			8.81838i			0.366479i
$580$	0.870539			0.0361472
$581$		−	38.8696i		−	1.61258i
$582$	47.5841			1.97242
$583$	−0.574849			−0.0238078
$584$		−	15.1342i		−	0.626260i
$585$		−	22.2609i		−	0.920373i
$586$			30.5327i			1.26130i
$587$	5.20621			0.214883			0.107442	−	0.994211i	$-0.465734\pi$
$587$	5.20621			0.214883			0.107442	+	0.994211i	$0.465734\pi$
$588$	4.58809			0.189210
$589$	38.2599			1.57647
$590$	−2.56328			−0.105528
$591$		−	15.7776i		−	0.649004i
$592$	24.6040			1.01122
$593$		−	36.2996i		−	1.49065i	−0.666703	−	0.745324i	$-0.732295\pi$
$593$		−	36.2996i		−	1.49065i	0.666703	−	0.745324i	$-0.267705\pi$
$594$	−0.327524			−0.0134385
$595$		−	5.65215i		−	0.231715i
$596$			0.291441i			0.0119379i
$597$			27.8267i			1.13887i
$598$	50.3534			2.05910
$599$			18.9550i			0.774479i	0.921979	+	0.387240i	$0.126571\pi$
$599$			18.9550i			0.774479i	−0.921979	+	0.387240i	$0.873429\pi$
$600$		−	32.7110i		−	1.33542i
$601$			24.7931i			1.01133i	0.862730	+	0.505665i	$0.168753\pi$
$601$			24.7931i			1.01133i	−0.862730	+	0.505665i	$0.831247\pi$
$602$			29.8561i			1.21684i
$603$	22.4148			0.912800
$604$	5.29618			0.215498
$605$	−11.0393			−0.448811
$606$	7.41661			0.301279
$607$	31.4933			1.27827			0.639137	−	0.769093i	$-0.279292\pi$
$607$	31.4933			1.27827			0.639137	+	0.769093i	$0.279292\pi$
$608$		−	21.3137i		−	0.864384i
$609$			12.6835i			0.513962i
$610$	−3.97734			−0.161038
$611$	−67.8206			−2.74373
$612$	4.21249			0.170280
$613$	−21.6938			−0.876206			−0.438103	−	0.898925i	$-0.644349\pi$
$613$	−21.6938			−0.876206			−0.438103	+	0.898925i	$0.644349\pi$
$614$			23.6907i			0.956079i
$615$	3.01686			0.121651
$616$			0.902274i			0.0363537i
$617$	−30.5646			−1.23048			−0.615242	−	0.788338i	$-0.710942\pi$
$617$	−30.5646			−1.23048			−0.615242	+	0.788338i	$0.710942\pi$
$618$	−4.80248			−0.193184
$619$			10.5878i			0.425558i	0.977100	+	0.212779i	$0.0682514\pi$
$619$			10.5878i			0.425558i	−0.977100	+	0.212779i	$0.931749\pi$
$620$	−3.26449			−0.131105
$621$	−23.1120			−0.927453
$622$	14.9184			0.598173
$623$	−36.9262			−1.47942
$624$			36.2001i			1.44916i
$625$	10.8865			0.435459
$626$			0.229224i			0.00916164i
$627$		−	1.67837i		−	0.0670278i
$628$	3.33196			0.132960
$629$	−17.4075			−0.694084
$630$	−15.5629			−0.620040
$631$	4.32223			0.172065			0.0860326	−	0.996292i	$-0.472581\pi$
$631$	4.32223			0.172065			0.0860326	+	0.996292i	$0.472581\pi$
$632$	−31.3897			−1.24861
$633$		−	56.0529i		−	2.22790i
$634$	−3.67642			−0.146009
$635$		−	21.4557i		−	0.851442i
$636$		−	9.50261i		−	0.376803i
$637$		−	16.1226i		−	0.638800i
$638$	−0.166831			−0.00660489
$639$		−	28.3847i		−	1.12288i
$640$		−	4.21455i		−	0.166595i
$641$	−29.7435			−1.17480			−0.587399	−	0.809298i	$-0.699848\pi$
$641$	−29.7435			−1.17480			−0.587399	+	0.809298i	$0.699848\pi$
$642$	26.9565			1.06389
$643$			38.1013i			1.50257i	0.659978	+	0.751285i	$0.270566\pi$
$643$			38.1013i			1.50257i	−0.659978	+	0.751285i	$0.729434\pi$
$644$			14.2334i			0.560876i
$645$			21.1971i			0.834636i
$646$		−	14.4035i		−	0.566698i
$647$	13.3902			0.526423			0.263212	−	0.964738i	$-0.415218\pi$
$647$	13.3902			0.526423			0.263212	+	0.964738i	$0.415218\pi$
$648$			13.6680i			0.536929i
$649$	−0.198617			−0.00779640
$650$	−25.6965			−1.00790
$651$		−	47.5627i		−	1.86413i
$652$		−	6.90895i		−	0.270575i
$653$	17.3835			0.680270			0.340135	−	0.940377i	$-0.389527\pi$
$653$	17.3835			0.680270			0.340135	+	0.940377i	$0.389527\pi$
$654$		−	8.63150i		−	0.337518i
$655$			1.11807i			0.0436867i
$656$	−2.83545			−0.110706
$657$	20.2271			0.789133
$658$			47.4144i			1.84840i
$659$		−	24.4882i		−	0.953924i	−0.878924	−	0.476962i	$-0.841738\pi$
$659$		−	24.4882i		−	0.953924i	0.878924	−	0.476962i	$-0.158262\pi$
$660$			0.143205i			0.00557426i
$661$	38.6980			1.50518			0.752589	−	0.658490i	$-0.228805\pi$
$661$	38.6980			1.50518			0.752589	+	0.658490i	$0.228805\pi$
$662$	−17.7040			−0.688086
$663$		−	25.6119i		−	0.994684i
$664$			37.8057i			1.46715i
$665$		−	21.5155i		−	0.834337i
$666$			47.9308i			1.85728i
$667$	−11.7725			−0.455834
$668$			3.24345i			0.125493i
$669$	44.4743			1.71948
$670$			6.53934i			0.252637i
$671$	−0.308186			−0.0118974
$672$	−26.4960			−1.02211
$673$	28.2505			1.08898			0.544489	−	0.838768i	$-0.316724\pi$
$673$	28.2505			1.08898			0.544489	+	0.838768i	$0.316724\pi$
$674$		−	15.4324i		−	0.594432i
$675$	11.7946			0.453974
$676$	−9.27364			−0.356678
$677$		−	11.8240i		−	0.454433i	−0.973844	−	0.227216i	$-0.927038\pi$
$677$		−	11.8240i		−	0.454433i	0.973844	−	0.227216i	$-0.0729625\pi$
$678$	36.2928			1.39382
$679$	47.2657			1.81389
$680$			5.49745i			0.210818i
$681$	−10.3542			−0.396774
$682$	0.625608			0.0239558
$683$	31.5590			1.20757			0.603785	−	0.797147i	$-0.293658\pi$
$683$	31.5590			1.20757			0.603785	+	0.797147i	$0.293658\pi$
$684$	16.0353			0.613126
$685$			12.4708i			0.476483i
$686$	15.1300			0.577665
$687$		−	64.1545i		−	2.44765i
$688$		−	19.9225i		−	0.759539i
$689$	−33.3923			−1.27214
$690$		−	24.9931i		−	0.951472i
$691$		−	30.4677i		−	1.15905i	−0.814956	−	0.579523i	$-0.803239\pi$
$691$		−	30.4677i		−	1.15905i	0.814956	−	0.579523i	$-0.196761\pi$
$692$		−	9.30548i		−	0.353741i
$693$	−1.20590			−0.0458083
$694$	−7.11156			−0.269951
$695$	8.38220			0.317955
$696$		−	12.3364i		−	0.467609i
$697$	2.00611			0.0759868
$698$	−0.735257	+	22.2822i	−0.0278299	+	0.843392i
$699$	30.5607			1.15591
$700$		−	7.26365i		−	0.274540i
$701$	−25.7820			−0.973773			−0.486887	−	0.873465i	$-0.661868\pi$
$701$	−25.7820			−0.973773			−0.486887	+	0.873465i	$0.661868\pi$
$702$	−19.0255			−0.718071
$703$	−66.2639			−2.49919
$704$		−	0.815990i		−	0.0307538i
$705$			33.6631i			1.26782i
$706$		−	0.947097i		−	0.0356445i
$707$	7.36698			0.277064
$708$		−	3.28326i		−	0.123392i
$709$			15.5810i			0.585157i	0.956241	+	0.292579i	$0.0945133\pi$
$709$			15.5810i			0.585157i	−0.956241	+	0.292579i	$0.905487\pi$
$710$	8.28103			0.310781
$711$		−	41.9526i		−	1.57335i
$712$	35.9156			1.34599
$713$	44.1465			1.65330
$714$	−17.9057			−0.670102
$715$	0.503225			0.0188195
$716$		−	13.8676i		−	0.518257i
$717$	15.2667			0.570146
$718$	6.51745			0.243229
$719$			34.4302i			1.28403i	0.766692	+	0.642015i	$0.221901\pi$
$719$			34.4302i			1.28403i	−0.766692	+	0.642015i	$0.778099\pi$
$720$	10.3849			0.387021
$721$	−4.77034			−0.177657
$722$		−	32.1543i		−	1.19666i
$723$	−74.5455			−2.77238
$724$	−1.67211			−0.0621434
$725$	6.00779			0.223124
$726$			34.9718i			1.29793i
$727$	−2.38880			−0.0885955			−0.0442978	−	0.999018i	$-0.514105\pi$
$727$	−2.38880			−0.0885955			−0.0442978	+	0.999018i	$0.514105\pi$
$728$			52.4120i			1.94252i
$729$	−41.9036			−1.55199
$730$			5.90110i			0.218409i
$731$			14.0954i			0.521336i
$732$		−	5.09451i		−	0.188299i
$733$		−	4.90527i		−	0.181180i	−0.995888	−	0.0905901i	$-0.971125\pi$
$733$		−	4.90527i		−	0.181180i	0.995888	−	0.0905901i	$-0.0288753\pi$
$734$	−21.5995			−0.797251
$735$	−8.00252			−0.295177
$736$		−	24.5930i		−	0.906508i
$737$			0.506704i			0.0186647i
$738$		−	5.52372i		−	0.203331i
$739$	−14.8094			−0.544771			−0.272385	−	0.962188i	$-0.587813\pi$
$739$	−14.8094			−0.544771			−0.272385	+	0.962188i	$0.587813\pi$
$740$	5.65389			0.207841
$741$		−	97.4947i		−	3.58156i
$742$			23.3450i			0.857022i
$743$	3.50652			0.128642			0.0643208	−	0.997929i	$-0.479512\pi$
$743$	3.50652			0.128642			0.0643208	+	0.997929i	$0.479512\pi$
$744$			46.2609i			1.69601i
$745$		−	0.508329i		−	0.0186237i
$746$	11.8306			0.433147
$747$	−50.5277			−1.84871
$748$			0.0952268i			0.00348184i
$749$	26.7761			0.978377
$750$			28.7327i			1.04917i
$751$		−	30.0028i		−	1.09482i	−0.836865	−	0.547409i	$-0.815614\pi$
$751$		−	30.0028i		−	1.09482i	0.836865	−	0.547409i	$-0.184386\pi$
$752$		−	31.6389i		−	1.15375i
$753$			35.1545i			1.28110i
$754$	−9.69098			−0.352925
$755$	−9.23756			−0.336189
$756$		−	5.37795i		−	0.195594i
$757$			28.9322i			1.05156i	0.850621	+	0.525780i	$0.176226\pi$
$757$			28.9322i			1.05156i	−0.850621	+	0.525780i	$0.823774\pi$
$758$	2.83370			0.102925
$759$		−	1.93661i		−	0.0702943i
$760$			20.9267i			0.759091i
$761$		−	37.7572i		−	1.36870i	−0.729155	−	0.684349i	$-0.760087\pi$
$761$		−	37.7572i		−	1.36870i	0.729155	−	0.684349i	$-0.239913\pi$
$762$	−67.9703			−2.46230
$763$		−	8.57374i		−	0.310390i
$764$	11.2799			0.408092
$765$	−7.34740			−0.265646
$766$	−41.1200			−1.48572
$767$	−11.5374			−0.416592
$768$	33.4986			1.20878
$769$			34.7299i			1.25239i	0.779666	+	0.626196i	$0.215389\pi$
$769$			34.7299i			1.25239i	−0.779666	+	0.626196i	$0.784611\pi$
$770$		−	0.351812i		−	0.0126784i
$771$	54.7326			1.97115
$772$		−	1.90457i		−	0.0685471i
$773$	3.44106			0.123766			0.0618831	−	0.998083i	$-0.480289\pi$
$773$	3.44106			0.123766			0.0618831	+	0.998083i	$0.480289\pi$
$774$	38.8109			1.39503
$775$	−22.5290			−0.809265
$776$	−45.9720			−1.65030
$777$			82.3756i			2.95521i
$778$	−5.79335			−0.207702
$779$	7.63648			0.273605
$780$			8.31862i			0.297854i
$781$	0.641660			0.0229604
$782$		−	16.6196i		−	0.594316i
$783$	4.44812			0.158963
$784$	7.52132			0.268619
$785$	−5.81158			−0.207424
$786$	3.54198			0.126338
$787$			8.65747i			0.308605i	0.988024	+	0.154303i	$0.0493131\pi$
$787$			8.65747i			0.308605i	−0.988024	+	0.154303i	$0.950687\pi$
$788$			3.40761i			0.121391i
$789$	−58.2477			−2.07367
$790$	12.2394			0.435457
$791$	36.0499			1.28179
$792$	1.17289			0.0416770
$793$	−17.9022			−0.635724
$794$		−	17.1553i		−	0.608818i
$795$			16.5744i			0.587833i
$796$		−	6.00995i		−	0.213017i
$797$		−	29.6813i		−	1.05137i	−0.850680	−	0.525684i	$-0.823810\pi$
$797$		−	29.6813i		−	1.05137i	0.850680	−	0.525684i	$-0.176190\pi$
$798$	−68.1599			−2.41284
$799$			22.3848i			0.791918i
$800$			12.5503i			0.443722i
$801$			48.0015i			1.69605i
$802$	−38.3648			−1.35471
$803$			0.457250i			0.0161360i
$804$	−8.37614			−0.295404
$805$		−	24.8259i		−	0.874997i
$806$	36.3408			1.28005
$807$	44.7640			1.57577
$808$	−7.16535			−0.252076
$809$	21.9724			0.772508			0.386254	−	0.922392i	$-0.373769\pi$
$809$	21.9724			0.772508			0.386254	+	0.922392i	$0.373769\pi$
$810$		−	5.32937i		−	0.187255i
$811$		−	25.3362i		−	0.889675i	−0.895611	−	0.444837i	$-0.853261\pi$
$811$		−	25.3362i		−	0.889675i	0.895611	−	0.444837i	$-0.146739\pi$
$812$		−	2.73936i		−	0.0961326i
$813$	−17.7214			−0.621516
$814$	−1.08351			−0.0379772
$815$			12.0505i			0.422112i
$816$	11.9482			0.418269
$817$			53.6557i			1.87717i
$818$		−	26.8178i		−	0.937663i
$819$	−70.0491			−2.44771
$820$	−0.651574			−0.0227540
$821$	−36.6670			−1.27969			−0.639843	−	0.768505i	$-0.721001\pi$
$821$	−36.6670			−1.27969			−0.639843	+	0.768505i	$0.721001\pi$
$822$	39.5066			1.37795
$823$	45.0251			1.56948			0.784739	−	0.619827i	$-0.212797\pi$
$823$	45.0251			1.56948			0.784739	+	0.619827i	$0.212797\pi$
$824$	4.63978			0.161634
$825$			0.988294i			0.0344080i
$826$			8.06597i			0.280651i
$827$		−	29.3804i		−	1.02166i	−0.859683	−	0.510829i	$-0.829339\pi$
$827$		−	29.3804i		−	1.02166i	0.859683	−	0.510829i	$-0.170661\pi$
$828$	18.5025			0.643006
$829$		−	51.1960i		−	1.77811i	−0.457801	−	0.889055i	$-0.651363\pi$
$829$		−	51.1960i		−	1.77811i	0.457801	−	0.889055i	$-0.348637\pi$
$830$		−	14.7411i		−	0.511671i
$831$			27.3500i			0.948763i
$832$		−	47.3998i		−	1.64329i
$833$	−5.32141			−0.184376
$834$		−	26.5543i		−	0.919501i
$835$		−	5.65720i		−	0.195776i
$836$			0.362492i			0.0125370i
$837$	−16.6803			−0.576555
$838$			12.3612i			0.427009i
$839$			34.8334i			1.20258i	0.799030	+	0.601291i	$0.205347\pi$
$839$			34.8334i			1.20258i	−0.799030	+	0.601291i	$0.794653\pi$
$840$	26.0149			0.897600
$841$	−26.7343			−0.921871
$842$	−36.1042			−1.24423
$843$	−23.8767			−0.822356
$844$			12.1062i			0.416712i
$845$	16.1750			0.556438
$846$	61.6354			2.11907
$847$			34.7378i			1.19360i
$848$		−	15.5778i		−	0.534942i
$849$	−9.98458			−0.342670
$850$			8.48136i			0.290908i
$851$	−76.4591			−2.62098
$852$			10.6070i			0.363391i
$853$	7.21155			0.246919			0.123459	−	0.992350i	$-0.460601\pi$
$853$	7.21155			0.246919			0.123459	+	0.992350i	$0.460601\pi$
$854$			12.5157i			0.428277i
$855$	−27.9687			−0.956510
$856$	−26.0433			−0.890140
$857$		−	25.7415i		−	0.879313i	−0.898166	−	0.439656i	$-0.855100\pi$
$857$		−	25.7415i		−	0.879313i	0.898166	−	0.439656i	$-0.144900\pi$
$858$		−	1.59419i		−	0.0544246i
$859$			19.1279i			0.652636i	0.945260	+	0.326318i	$0.105808\pi$
$859$			19.1279i			0.652636i	−0.945260	+	0.326318i	$0.894192\pi$
$860$		−	4.57811i		−	0.156112i
$861$		−	9.49326i		−	0.323529i
$862$	34.2402			1.16622
$863$			41.8592i			1.42490i	0.701721	+	0.712452i	$0.252415\pi$
$863$			41.8592i			1.42490i	−0.701721	+	0.712452i	$0.747585\pi$
$864$			9.29218i			0.316126i
$865$			16.2306i			0.551856i
$866$	15.1837			0.515963
$867$	36.8712			1.25221
$868$			10.2725i			0.348671i
$869$	0.948373			0.0321714
$870$			4.81016i			0.163080i
$871$			29.4338i			0.997327i
$872$			8.33909i			0.282397i
$873$		−	61.4421i		−	2.07950i
$874$		−	63.2644i		−	2.13995i
$875$			28.5404i			0.964841i
$876$	−7.55862			−0.255382
$877$		−	14.8940i		−	0.502934i	−0.967866	−	0.251467i	$-0.919087\pi$
$877$		−	14.8940i		−	0.502934i	0.967866	−	0.251467i	$-0.0809130\pi$
$878$	−23.7400			−0.801186
$879$	68.2135			2.30078
$880$			0.234759i			0.00791371i
$881$			49.4155i			1.66485i	0.554138	+	0.832425i	$0.313048\pi$
$881$			49.4155i			1.66485i	−0.554138	+	0.832425i	$0.686952\pi$
$882$			14.6522i			0.493366i
$883$	−29.4150			−0.989894			−0.494947	−	0.868923i	$-0.664813\pi$
$883$	−29.4150			−0.989894			−0.494947	+	0.868923i	$0.664813\pi$
$884$			5.53160i			0.186048i
$885$			5.72664i			0.192499i
$886$		−	32.9910i		−	1.10836i
$887$		−	19.1690i		−	0.643633i	−0.946802	−	0.321816i	$-0.895707\pi$
$887$		−	19.1690i		−	0.643633i	0.946802	−	0.321816i	$-0.104293\pi$
$888$		−	80.1211i		−	2.68869i
$889$	−67.5154			−2.26439
$890$	−14.0041			−0.469418
$891$		−	0.412949i		−	0.0138343i
$892$	−9.60547			−0.321615
$893$			85.2104i			2.85146i
$894$	−1.61036			−0.0538584
$895$			24.1878i			0.808509i
$896$	−13.2621			−0.443056
$897$		−	112.495i		−	3.75610i
$898$			19.9783i			0.666684i
$899$	−8.49641			−0.283371
$900$	−9.44224			−0.314741
$901$			11.0214i			0.367177i
$902$	0.124868			0.00415765
$903$	66.7018			2.21970
$904$	−35.0633			−1.16619
$905$	2.91648			0.0969471
$906$			29.2640i			0.972232i
$907$		−	7.12964i		−	0.236736i	−0.992970	−	0.118368i	$-0.962234\pi$
$907$		−	7.12964i		−	0.236736i	0.992970	−	0.118368i	$-0.0377662\pi$
$908$	2.23628			0.0742136
$909$		−	9.57656i		−	0.317634i
$910$		−	20.4363i		−	0.677457i
$911$			39.9763i			1.32447i	0.749295	+	0.662237i	$0.230393\pi$
$911$			39.9763i			1.32447i	−0.749295	+	0.662237i	$0.769607\pi$
$912$	45.4821			1.50606
$913$		−	1.14222i		−	0.0378020i
$914$			2.76857i			0.0915763i
$915$			8.88581i			0.293756i
$916$			13.8560i			0.457814i
$917$	3.51828			0.116184
$918$			6.27953i			0.207255i
$919$		−	49.5607i		−	1.63486i	−0.576030	−	0.817428i	$-0.695399\pi$
$919$		−	49.5607i		−	1.63486i	0.576030	−	0.817428i	$-0.304601\pi$
$920$			24.1464i			0.796084i
$921$	52.9276			1.74402
$922$	36.6420			1.20674
$923$	37.2732			1.22686
$924$	0.450630			0.0148246
$925$	39.0188			1.28293
$926$	−28.8759			−0.948919
$927$			6.20111i			0.203671i
$928$			4.73314i			0.155373i
$929$	−48.7762			−1.60030			−0.800148	−	0.599802i	$-0.795246\pi$
$929$	−48.7762			−1.60030			−0.800148	+	0.599802i	$0.795246\pi$
$930$		−	18.0379i		−	0.591487i
$931$	−20.2566			−0.663882
$932$	−6.60043			−0.216204
$933$		−	33.3293i		−	1.09115i
$934$			37.8758i			1.23933i
$935$		−	0.166094i		−	0.00543185i
$936$	68.1319			2.22696
$937$	8.27932			0.270474			0.135237	−	0.990813i	$-0.456820\pi$
$937$	8.27932			0.270474			0.135237	+	0.990813i	$0.456820\pi$
$938$	20.5776			0.671883
$939$	0.512111			0.0167121
$940$		−	7.27047i		−	0.237137i
$941$	0.918164			0.0299313			0.0149657	−	0.999888i	$-0.495236\pi$
$941$	0.918164			0.0299313			0.0149657	+	0.999888i	$0.495236\pi$
$942$			18.4108i			0.599855i
$943$	8.81141			0.286939
$944$		−	5.38229i		−	0.175179i
$945$			9.38019i			0.305137i
$946$			0.877352i			0.0285252i
$947$	−49.6453			−1.61326			−0.806628	−	0.591060i	$-0.798710\pi$
$947$	−49.6453			−1.61326			−0.806628	+	0.591060i	$0.798710\pi$
$948$			15.6772i			0.509172i
$949$			26.5610i			0.862208i
$950$			32.2853i			1.04747i
$951$			8.21353i			0.266342i
$952$	17.2991			0.560665
$953$	−49.7899			−1.61285			−0.806426	−	0.591335i	$-0.798601\pi$
$953$	−49.7899			−1.61285			−0.806426	+	0.591335i	$0.798601\pi$
$954$	30.3469			0.982517
$955$	−19.6743			−0.636646
$956$	−3.29727			−0.106641
$957$			0.372718i			0.0120483i
$958$			51.1606i			1.65292i
$959$	39.2423			1.26720
$960$	−23.5271			−0.759335
$961$	0.861209			0.0277809
$962$	−62.9400			−2.02927
$963$		−	34.8071i		−	1.12164i
$964$	16.1002			0.518552
$965$			3.32195i			0.106937i
$966$	−78.6469			−2.53042
$967$	32.8942			1.05781			0.528903	−	0.848682i	$-0.322603\pi$
$967$	32.8942			1.05781			0.528903	+	0.848682i	$0.322603\pi$
$968$		−	33.7870i		−	1.08596i
$969$	−32.1790			−1.03374
$970$	17.9253			0.575546
$971$	13.8297			0.443815			0.221908	−	0.975068i	$-0.428772\pi$
$971$	13.8297			0.443815			0.221908	+	0.975068i	$0.428772\pi$
$972$	11.9312			0.382694
$973$		−	26.3766i		−	0.845595i
$974$	−15.3216			−0.490935
$975$			57.4087i			1.83855i
$976$		−	8.35150i		−	0.267325i
$977$	−15.3632			−0.491514			−0.245757	−	0.969332i	$-0.579036\pi$
$977$	−15.3632			−0.491514			−0.245757	+	0.969332i	$0.579036\pi$
$978$	38.1754			1.22072
$979$	−1.08511			−0.0346804
$980$	1.72837			0.0552107
$981$	−11.1453			−0.355841
$982$		−	32.4603i		−	1.03585i
$983$	2.29977			0.0733513			0.0366757	−	0.999327i	$-0.488323\pi$
$983$	2.29977			0.0733513			0.0366757	+	0.999327i	$0.488323\pi$
$984$			9.23344i			0.294351i
$985$		−	5.94354i		−	0.189377i
$986$			3.19860i			0.101864i
$987$	105.929			3.37175
$988$			21.0567i			0.669902i
$989$			61.9110i			1.96866i
$990$	−0.457331			−0.0145349
$991$	−32.1980			−1.02280			−0.511402	−	0.859341i	$-0.670874\pi$
$991$	−32.1980			−1.02280			−0.511402	+	0.859341i	$0.670874\pi$
$992$		−	17.7491i		−	0.563534i
$993$			39.5527i			1.25517i
$994$		−	26.0582i		−	0.826517i
$995$			10.4825i			0.332318i
$996$	18.8816			0.598287
$997$		−	12.3946i		−	0.392540i	−0.980550	−	0.196270i	$-0.937117\pi$
$997$		−	12.3946i		−	0.392540i	0.980550	−	0.196270i	$-0.0628828\pi$
$998$	43.3333			1.37169
$999$	28.8892			0.914014

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.b.b.348.10	✓	26
349.348	even	2	inner	349.2.b.b.348.17	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.b.b.348.10	✓	26	1.1	even	1	trivial
349.2.b.b.348.17	yes	26	349.348	even	2	inner

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:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.19339i q^{2} -2.66615 q^{3} +0.575830 q^{4} -1.00436 q^{5} +3.18175i q^{6} +3.16046i q^{7} -3.07396i q^{8} +4.10838 q^{9} +O(q^{10})\)	\(q-1.19339i q^{2} -2.66615 q^{3} +0.575830 q^{4} -1.00436 q^{5} +3.18175i q^{6} +3.16046i q^{7} -3.07396i q^{8} +4.10838 q^{9} +1.19859i q^{10} +0.0928732i q^{11} -1.53525 q^{12} +5.39489i q^{13} +3.77165 q^{14} +2.67778 q^{15} -2.51676 q^{16} +1.78063 q^{17} -4.90288i q^{18} +6.77818 q^{19} -0.578340 q^{20} -8.42627i q^{21} +0.110834 q^{22} +7.82106 q^{23} +8.19565i q^{24} -3.99126 q^{25} +6.43818 q^{26} -2.95510 q^{27} +1.81989i q^{28} -1.50524 q^{29} -3.19562i q^{30} +5.64457 q^{31} -3.14445i q^{32} -0.247614i q^{33} -2.12498i q^{34} -3.17424i q^{35} +2.36573 q^{36} -9.77605 q^{37} -8.08899i q^{38} -14.3836i q^{39} +3.08736i q^{40} +1.12663 q^{41} -10.0558 q^{42} +7.91594i q^{43} +0.0534792i q^{44} -4.12629 q^{45} -9.33354i q^{46} +12.5713i q^{47} +6.71007 q^{48} -2.98849 q^{49} +4.76312i q^{50} -4.74744 q^{51} +3.10654i q^{52} +6.18961i q^{53} +3.52658i q^{54} -0.0932781i q^{55} +9.71512 q^{56} -18.0717 q^{57} +1.79633i q^{58} +2.13858i q^{59} +1.54194 q^{60} +3.31836i q^{61} -6.73615i q^{62} +12.9843i q^{63} -8.78607 q^{64} -5.41841i q^{65} -0.295499 q^{66} +5.45587 q^{67} +1.02534 q^{68} -20.8521 q^{69} -3.78809 q^{70} -6.90898i q^{71} -12.6290i q^{72} +4.92337 q^{73} +11.6666i q^{74} +10.6413 q^{75} +3.90308 q^{76} -0.293522 q^{77} -17.1652 q^{78} -10.2115i q^{79} +2.52773 q^{80} -4.44637 q^{81} -1.34450i q^{82} -12.2987 q^{83} -4.85210i q^{84} -1.78839 q^{85} +9.44677 q^{86} +4.01319 q^{87} +0.285489 q^{88} +11.6838i q^{89} +4.92425i q^{90} -17.0503 q^{91} +4.50360 q^{92} -15.0493 q^{93} +15.0024 q^{94} -6.80773 q^{95} +8.38360i q^{96} -14.9553i q^{97} +3.56643i q^{98} +0.381558i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9}+O(q^{10}) \) 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9	\( 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9} + 12 q^{12} + 4 q^{14} + 12 q^{15} + 20 q^{16} - 14 q^{17} - 4 q^{19} - 2 q^{20} - 12 q^{22} - 18 q^{23} + 18 q^{25} + 22 q^{26} + 4 q^{27} - 18 q^{29} + 10 q^{31} - 54 q^{36} + 30 q^{37} - 16 q^{41} - 44 q^{45} - 74 q^{48} - 22 q^{49} + 32 q^{51} - 38 q^{56} - 16 q^{57} - 78 q^{60} - 96 q^{64} + 104 q^{66} + 72 q^{67} + 36 q^{68} - 40 q^{69} + 86 q^{70} + 72 q^{73} - 38 q^{75} + 96 q^{76} - 28 q^{77} - 30 q^{78} + 30 q^{80} - 6 q^{81} - 8 q^{83} - 22 q^{85} + 60 q^{86} + 32 q^{87} + 110 q^{88} - 12 q^{91} + 14 q^{92} + 84 q^{93} + 22 q^{94} - 10 q^{95}+O(q^{100}) \) 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9 + 12 * q^12 + 4 * q^14 + 12 * q^15 + 20 * q^16 - 14 * q^17 - 4 * q^19 - 2 * q^20 - 12 * q^22 - 18 * q^23 + 18 * q^25 + 22 * q^26 + 4 * q^27 - 18 * q^29 + 10 * q^31 - 54 * q^36 + 30 * q^37 - 16 * q^41 - 44 * q^45 - 74 * q^48 - 22 * q^49 + 32 * q^51 - 38 * q^56 - 16 * q^57 - 78 * q^60 - 96 * q^64 + 104 * q^66 + 72 * q^67 + 36 * q^68 - 40 * q^69 + 86 * q^70 + 72 * q^73 - 38 * q^75 + 96 * q^76 - 28 * q^77 - 30 * q^78 + 30 * q^80 - 6 * q^81 - 8 * q^83 - 22 * q^85 + 60 * q^86 + 32 * q^87 + 110 * q^88 - 12 * q^91 + 14 * q^92 + 84 * q^93 + 22 * q^94 - 10 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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