LMFDB - Embedded newform 345.2.m.c.151.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [345,2,Mod(16,345)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(345, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("345.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.m (of order $11$, degree $10$, 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:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			151.4
Character	$\chi$	$=$	345.151
Dual form			345.2.m.c.16.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707484 + 0.816480i) q^{2} +(0.841254 + 0.540641i) q^{3} +(0.118524 - 0.824351i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(0.153751 + 1.06936i) q^{6} +(2.39967 + 0.704607i) q^{7} +(2.57463 - 1.65461i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(0.707484 + 0.816480i) q^{2} +(0.841254 + 0.540641i) q^{3} +(0.118524 - 0.824351i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(0.153751 + 1.06936i) q^{6} +(2.39967 + 0.704607i) q^{7} +(2.57463 - 1.65461i) q^{8} +(0.415415 + 0.909632i) q^{9} +(-1.03660 + 0.304372i) q^{10} +(2.02946 - 2.34213i) q^{11} +(0.545386 - 0.629409i) q^{12} +(-4.85120 + 1.42444i) q^{13} +(1.12243 + 2.45778i) q^{14} +(-0.841254 + 0.540641i) q^{15} +(1.57428 + 0.462250i) q^{16} +(-0.628124 - 4.36869i) q^{17} +(-0.448797 + 0.982728i) q^{18} +(-1.19141 + 8.28644i) q^{19} +(0.700619 + 0.450261i) q^{20} +(1.63779 + 1.89011i) q^{21} +3.34811 q^{22} +(4.64395 + 1.19739i) q^{23} +3.06047 q^{24} +(-0.654861 - 0.755750i) q^{25} +(-4.59517 - 2.95314i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(0.865261 - 1.89466i) q^{28} +(0.149528 + 1.03999i) q^{29} +(-1.03660 - 0.304372i) q^{30} +(-4.73204 + 3.04109i) q^{31} +(-1.80637 - 3.95539i) q^{32} +(2.97354 - 0.873111i) q^{33} +(3.12256 - 3.60363i) q^{34} +(-1.63779 + 1.89011i) q^{35} +(0.799093 - 0.234635i) q^{36} +(-2.68007 - 5.86853i) q^{37} +(-7.60861 + 4.88976i) q^{38} +(-4.85120 - 1.42444i) q^{39} +(0.435550 + 3.02932i) q^{40} +(1.30560 - 2.85886i) q^{41} +(-0.384527 + 2.67445i) q^{42} +(-9.78386 - 6.28770i) q^{43} +(-1.69019 - 1.95059i) q^{44} -1.00000 q^{45} +(2.30787 + 4.63882i) q^{46} +8.62851 q^{47} +(1.07446 + 1.23999i) q^{48} +(-0.626829 - 0.402839i) q^{49} +(0.153751 - 1.06936i) q^{50} +(1.83348 - 4.01477i) q^{51} +(0.599256 + 4.16792i) q^{52} +(-8.97083 - 2.63407i) q^{53} +(-0.908854 + 0.584085i) q^{54} +(1.28740 + 2.81902i) q^{55} +(7.34411 - 2.15643i) q^{56} +(-5.48226 + 6.32687i) q^{57} +(-0.743341 + 0.857862i) q^{58} +(-10.9224 + 3.20709i) q^{59} +(0.345969 + 0.757567i) q^{60} +(10.1067 - 6.49516i) q^{61} +(-5.83083 - 1.71209i) q^{62} +(0.355926 + 2.47552i) q^{63} +(3.31470 - 7.25818i) q^{64} +(0.719544 - 5.00454i) q^{65} +(2.81661 + 1.81013i) q^{66} +(-4.59576 - 5.30379i) q^{67} -3.67579 q^{68} +(3.25938 + 3.51802i) q^{69} -2.70195 q^{70} +(4.10360 + 4.73581i) q^{71} +(2.57463 + 1.65461i) q^{72} +(-2.20088 + 15.3074i) q^{73} +(2.89543 - 6.34011i) q^{74} +(-0.142315 - 0.989821i) q^{75} +(6.68972 + 1.96428i) q^{76} +(6.52032 - 4.19036i) q^{77} +(-2.26912 - 4.96867i) q^{78} +(6.46832 - 1.89927i) q^{79} +(-1.07446 + 1.23999i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(3.25789 - 0.956604i) q^{82} +(-5.93120 - 12.9875i) q^{83} +(1.75223 - 1.12609i) q^{84} +(4.23484 + 1.24346i) q^{85} +(-1.78814 - 12.4368i) q^{86} +(-0.436470 + 0.955735i) q^{87} +(1.34980 - 9.38808i) q^{88} +(-4.99424 - 3.20960i) q^{89} +(-0.707484 - 0.816480i) q^{90} -12.6449 q^{91} +(1.53749 - 3.68632i) q^{92} -5.62498 q^{93} +(6.10453 + 7.04500i) q^{94} +(-7.04268 - 4.52606i) q^{95} +(0.618834 - 4.30409i) q^{96} +(-4.84371 + 10.6062i) q^{97} +(-0.114562 - 0.796795i) q^{98} +(2.97354 + 0.873111i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9}+O(q^{10}) $ 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9} + 15 q^{11} - 4 q^{12} - 19 q^{13} + 55 q^{14} + 5 q^{15} + 12 q^{16} + 5 q^{17} - 11 q^{19} + 4 q^{20} + 8 q^{21} - 18 q^{22} + 14 q^{23} + 66 q^{24} - 5 q^{25} - 18 q^{26} - 5 q^{27} + 10 q^{28} - 22 q^{29} + 6 q^{31} + 33 q^{32} + 4 q^{33} + 18 q^{34} - 8 q^{35} - 15 q^{36} + 25 q^{37} - 97 q^{38} - 19 q^{39} + 22 q^{40} - 42 q^{41} - 11 q^{42} - 25 q^{43} + 25 q^{44} - 50 q^{45} - 44 q^{46} + 86 q^{47} - 10 q^{48} - 8 q^{49} - 11 q^{50} - 17 q^{51} - 67 q^{52} - 26 q^{53} - 4 q^{55} - 132 q^{56} + 22 q^{57} + 8 q^{58} - 76 q^{59} + 4 q^{60} + 13 q^{61} - 8 q^{62} + 8 q^{63} + 76 q^{64} + 8 q^{65} + 4 q^{66} + 84 q^{67} + 66 q^{68} + 25 q^{69} + 22 q^{70} + 55 q^{71} - 59 q^{73} + 17 q^{74} - 5 q^{75} + 82 q^{76} - 56 q^{77} - 7 q^{78} + 7 q^{79} + 10 q^{80} - 5 q^{81} - 150 q^{82} + 19 q^{83} + 10 q^{84} + 6 q^{85} + 44 q^{86} - 11 q^{87} - 62 q^{88} - 74 q^{89} - 56 q^{91} + 41 q^{92} + 28 q^{93} - 161 q^{94} + 11 q^{95} - 44 q^{96} - 68 q^{97} - 198 q^{98} + 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9 + 15 * q^11 - 4 * q^12 - 19 * q^13 + 55 * q^14 + 5 * q^15 + 12 * q^16 + 5 * q^17 - 11 * q^19 + 4 * q^20 + 8 * q^21 - 18 * q^22 + 14 * q^23 + 66 * q^24 - 5 * q^25 - 18 * q^26 - 5 * q^27 + 10 * q^28 - 22 * q^29 + 6 * q^31 + 33 * q^32 + 4 * q^33 + 18 * q^34 - 8 * q^35 - 15 * q^36 + 25 * q^37 - 97 * q^38 - 19 * q^39 + 22 * q^40 - 42 * q^41 - 11 * q^42 - 25 * q^43 + 25 * q^44 - 50 * q^45 - 44 * q^46 + 86 * q^47 - 10 * q^48 - 8 * q^49 - 11 * q^50 - 17 * q^51 - 67 * q^52 - 26 * q^53 - 4 * q^55 - 132 * q^56 + 22 * q^57 + 8 * q^58 - 76 * q^59 + 4 * q^60 + 13 * q^61 - 8 * q^62 + 8 * q^63 + 76 * q^64 + 8 * q^65 + 4 * q^66 + 84 * q^67 + 66 * q^68 + 25 * q^69 + 22 * q^70 + 55 * q^71 - 59 * q^73 + 17 * q^74 - 5 * q^75 + 82 * q^76 - 56 * q^77 - 7 * q^78 + 7 * q^79 + 10 * q^80 - 5 * q^81 - 150 * q^82 + 19 * q^83 + 10 * q^84 + 6 * q^85 + 44 * q^86 - 11 * q^87 - 62 * q^88 - 74 * q^89 - 56 * q^91 + 41 * q^92 + 28 * q^93 - 161 * q^94 + 11 * q^95 - 44 * q^96 - 68 * q^97 - 198 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{7}{11}\right)$	$1$

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 $

$2$	0.707484	+	0.816480i	0.500266	+	0.577338i	0.948580	−	0.316538i	$-0.102521\pi$
$2$	0.707484	+	0.816480i	0.500266	+	0.577338i	−0.448313	+	0.893876i	$0.647975\pi$
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$4$	0.118524	−	0.824351i	0.0592619	−	0.412176i
$5$	−0.415415	+	0.909632i	−0.185779	+	0.406800i
$5$	−0.415415	+	0.909632i	−0.185779	+	0.406800i
$6$	0.153751	+	1.06936i	0.0627685	+	0.436565i
$7$	2.39967	+	0.704607i	0.906990	+	0.266316i	0.701773	−	0.712400i	$-0.252392\pi$
$7$	2.39967	+	0.704607i	0.906990	+	0.266316i	0.205217	+	0.978717i	$0.434210\pi$
$8$	2.57463	−	1.65461i	0.910269	−	0.584994i
$9$	0.415415	+	0.909632i	0.138472	+	0.303211i
$10$	−1.03660	+	0.304372i	−0.327800	+	0.0962508i
$11$	2.02946	−	2.34213i	0.611906	−	0.706178i	−0.362243	−	0.932084i	$-0.617989\pi$
$11$	2.02946	−	2.34213i	0.611906	−	0.706178i	0.974149	+	0.225906i	$0.0725343\pi$
$12$	0.545386	−	0.629409i	0.157439	−	0.181695i
$13$	−4.85120	+	1.42444i	−1.34548	+	0.395069i	−0.873622	−	0.486606i	$-0.838235\pi$
$13$	−4.85120	+	1.42444i	−1.34548	+	0.395069i	−0.471858	+	0.881674i	$0.656417\pi$
$14$	1.12243	+	2.45778i	0.299982	+	0.656869i
$15$	−0.841254	+	0.540641i	−0.217211	+	0.139593i
$16$	1.57428	+	0.462250i	0.393570	+	0.115563i
$17$	−0.628124	−	4.36869i	−0.152342	−	1.05956i	−0.912280	−	0.409568i	$-0.865680\pi$
$17$	−0.628124	−	4.36869i	−0.152342	−	1.05956i	0.759937	−	0.649996i	$-0.225230\pi$
$18$	−0.448797	+	0.982728i	−0.105782	+	0.231631i
$19$	−1.19141	+	8.28644i	−0.273328	+	1.90104i	0.139486	+	0.990224i	$0.455455\pi$
$19$	−1.19141	+	8.28644i	−0.273328	+	1.90104i	−0.412814	+	0.910815i	$0.635454\pi$
$20$	0.700619	+	0.450261i	0.156663	+	0.100681i
$21$	1.63779	+	1.89011i	0.357395	+	0.412456i
$22$	3.34811			0.713820
$23$	4.64395	+	1.19739i	0.968330	+	0.249673i
$23$	4.64395	+	1.19739i	0.968330	+	0.249673i
$24$	3.06047			0.624715
$25$	−0.654861	−	0.755750i	−0.130972	−	0.151150i
$26$	−4.59517	−	2.95314i	−0.901187	−	0.579157i
$27$	−0.142315	+	0.989821i	−0.0273885	+	0.190491i
$28$	0.865261	−	1.89466i	0.163519	−	0.358057i
$29$	0.149528	+	1.03999i	0.0277666	+	0.193121i	0.998984	−	0.0450755i	$-0.0143528\pi$
$29$	0.149528	+	1.03999i	0.0277666	+	0.193121i	−0.971217	+	0.238197i	$0.923444\pi$
$30$	−1.03660	−	0.304372i	−0.189256	−	0.0555704i
$31$	−4.73204	+	3.04109i	−0.849899	+	0.546197i	−0.891543	−	0.452936i	$-0.850377\pi$
$31$	−4.73204	+	3.04109i	−0.849899	+	0.546197i	0.0416444	+	0.999132i	$0.486740\pi$
$32$	−1.80637	−	3.95539i	−0.319324	−	0.699222i
$33$	2.97354	−	0.873111i	0.517627	−	0.151989i
$34$	3.12256	−	3.60363i	0.535515	−	0.618017i
$35$	−1.63779	+	1.89011i	−0.276837	+	0.319487i
$36$	0.799093	−	0.234635i	0.133182	−	0.0391058i
$37$	−2.68007	−	5.86853i	−0.440600	−	0.964780i	−0.991488	−	0.130201i	$-0.958438\pi$
$37$	−2.68007	−	5.86853i	−0.440600	−	0.964780i	0.550887	−	0.834580i	$-0.314289\pi$
$38$	−7.60861	+	4.88976i	−1.23428	+	0.793223i
$39$	−4.85120	−	1.42444i	−0.776813	−	0.228093i
$40$	0.435550	+	3.02932i	0.0688665	+	0.478977i
$41$	1.30560	−	2.85886i	0.203900	−	0.446480i	−0.779863	−	0.625950i	$-0.784711\pi$
$41$	1.30560	−	2.85886i	0.203900	−	0.446480i	0.983763	+	0.179471i	$0.0574385\pi$
$42$	−0.384527	+	2.67445i	−0.0593339	+	0.412676i
$43$	−9.78386	−	6.28770i	−1.49202	−	0.958866i	−0.995885	−	0.0906226i	$-0.971114\pi$
$43$	−9.78386	−	6.28770i	−1.49202	−	0.958866i	−0.496139	−	0.868243i	$-0.665249\pi$
$44$	−1.69019	−	1.95059i	−0.254806	−	0.294062i
$45$	−1.00000			−0.149071
$46$	2.30787	+	4.63882i	0.340277	+	0.683957i
$47$	8.62851			1.25860			0.629299	−	0.777163i	$-0.283342\pi$
$47$	8.62851			1.25860			0.629299	+	0.777163i	$0.283342\pi$
$48$	1.07446	+	1.23999i	0.155085	+	0.178977i
$49$	−0.626829	−	0.402839i	−0.0895470	−	0.0575484i
$50$	0.153751	−	1.06936i	0.0217437	−	0.151230i
$51$	1.83348	−	4.01477i	0.256739	−	0.562180i
$52$	0.599256	+	4.16792i	0.0831019	+	0.577986i
$53$	−8.97083	−	2.63407i	−1.23224	−	0.361818i	−0.400144	−	0.916452i	$-0.631040\pi$
$53$	−8.97083	−	2.63407i	−1.23224	−	0.361818i	−0.832094	+	0.554635i	$0.812858\pi$
$54$	−0.908854	+	0.584085i	−0.123679	+	0.0794839i
$55$	1.28740	+	2.81902i	0.173593	+	0.380117i
$56$	7.34411	−	2.15643i	0.981398	−	0.288164i
$57$	−5.48226	+	6.32687i	−0.726144	+	0.838014i
$58$	−0.743341	+	0.857862i	−0.0976055	+	0.112643i
$59$	−10.9224	+	3.20709i	−1.42197	+	0.417528i	−0.900169	−	0.435540i	$-0.856557\pi$
$59$	−10.9224	+	3.20709i	−1.42197	+	0.417528i	−0.521800	+	0.853068i	$0.674739\pi$
$60$	0.345969	+	0.757567i	0.0446644	+	0.0978015i
$61$	10.1067	−	6.49516i	1.29403	−	0.831620i	0.301477	−	0.953473i	$-0.402520\pi$
$61$	10.1067	−	6.49516i	1.29403	−	0.831620i	0.992548	+	0.121854i	$0.0388839\pi$
$62$	−5.83083	−	1.71209i	−0.740516	−	0.217435i
$63$	0.355926	+	2.47552i	0.0448425	+	0.311886i
$64$	3.31470	−	7.25818i	0.414338	−	0.907273i
$65$	0.719544	−	5.00454i	0.0892484	−	0.620736i
$66$	2.81661	+	1.81013i	0.346701	+	0.222811i
$67$	−4.59576	−	5.30379i	−0.561461	−	0.647961i	0.402054	−	0.915616i	$-0.368297\pi$
$67$	−4.59576	−	5.30379i	−0.561461	−	0.647961i	−0.963515	+	0.267655i	$0.913751\pi$
$68$	−3.67579			−0.445754
$69$	3.25938	+	3.51802i	0.392383	+	0.423520i
$70$	−2.70195			−0.322945
$71$	4.10360	+	4.73581i	0.487008	+	0.562037i	0.945064	−	0.326886i	$-0.105999\pi$
$71$	4.10360	+	4.73581i	0.487008	+	0.562037i	−0.458056	+	0.888923i	$0.651454\pi$
$72$	2.57463	+	1.65461i	0.303423	+	0.194998i
$73$	−2.20088	+	15.3074i	−0.257593	+	1.79160i	0.292259	+	0.956339i	$0.405593\pi$
$73$	−2.20088	+	15.3074i	−0.257593	+	1.79160i	−0.549853	+	0.835262i	$0.685316\pi$
$74$	2.89543	−	6.34011i	0.336587	−	0.737023i
$75$	−0.142315	−	0.989821i	−0.0164331	−	0.114295i
$76$	6.68972	+	1.96428i	0.767364	+	0.225318i
$77$	6.52032	−	4.19036i	0.743060	−	0.477535i
$78$	−2.26912	−	4.96867i	−0.256927	−	0.562591i
$79$	6.46832	−	1.89927i	0.727743	−	0.213685i	0.103184	−	0.994662i	$-0.467097\pi$
$79$	6.46832	−	1.89927i	0.727743	−	0.213685i	0.624559	+	0.780978i	$0.285279\pi$
$80$	−1.07446	+	1.23999i	−0.120128	+	0.138635i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	3.25789	−	0.956604i	0.359774	−	0.105639i
$83$	−5.93120	−	12.9875i	−0.651034	−	1.42557i	−0.890646	−	0.454697i	$-0.849748\pi$
$83$	−5.93120	−	12.9875i	−0.651034	−	1.42557i	0.239612	−	0.970869i	$-0.422980\pi$
$84$	1.75223	−	1.12609i	0.191184	−	0.122867i
$85$	4.23484	+	1.24346i	0.459333	+	0.134872i
$86$	−1.78814	−	12.4368i	−0.192820	−	1.34109i
$87$	−0.436470	+	0.955735i	−0.0467945	+	0.102466i
$88$	1.34980	−	9.38808i	0.143889	−	1.00077i
$89$	−4.99424	−	3.20960i	−0.529388	−	0.340217i	0.248488	−	0.968635i	$-0.420066\pi$
$89$	−4.99424	−	3.20960i	−0.529388	−	0.340217i	−0.777876	+	0.628418i	$0.783703\pi$
$90$	−0.707484	−	0.816480i	−0.0745753	−	0.0860645i
$91$	−12.6449			−1.32555
$92$	1.53749	−	3.68632i	0.160294	−	0.384326i
$93$	−5.62498			−0.583283
$94$	6.10453	+	7.04500i	0.629634	+	0.726637i
$95$	−7.04268	−	4.52606i	−0.722564	−	0.464363i
$96$	0.618834	−	4.30409i	0.0631595	−	0.439284i
$97$	−4.84371	+	10.6062i	−0.491804	+	1.07690i	0.487243	+	0.873266i	$0.338002\pi$
$97$	−4.84371	+	10.6062i	−0.491804	+	1.07690i	−0.979047	+	0.203634i	$0.934725\pi$
$98$	−0.114562	−	0.796795i	−0.0115725	−	0.0804884i
$99$	2.97354	+	0.873111i	0.298852	+	0.0877509i
$100$	−0.700619	+	0.450261i	−0.0700619	+	0.0450261i
$101$	1.72669	+	3.78092i	0.171812	+	0.376216i	0.975876	−	0.218328i	$-0.0700602\pi$
$101$	1.72669	+	3.78092i	0.171812	+	0.376216i	−0.804064	+	0.594543i	$0.797333\pi$
$102$	4.57514	−	1.34338i	0.453006	−	0.133015i
$103$	3.51924	−	4.06141i	0.346761	−	0.400183i	−0.555400	−	0.831583i	$-0.687435\pi$
$103$	3.51924	−	4.06141i	0.346761	−	0.400183i	0.902161	+	0.431400i	$0.141980\pi$
$104$	−10.1331	+	11.6943i	−0.993635	+	1.14672i
$105$	−2.39967	+	0.704607i	−0.234184	+	0.0687626i
$106$	−4.19605	−	9.18806i	−0.407556	−	0.892423i
$107$	3.60514	−	2.31689i	0.348522	−	0.223982i	−0.354653	−	0.934998i	$-0.615401\pi$
$107$	3.60514	−	2.31689i	0.348522	−	0.223982i	0.703176	+	0.711016i	$0.251765\pi$
$108$	0.799093	+	0.234635i	0.0768927	+	0.0225777i
$109$	0.422082	+	2.93565i	0.0404281	+	0.281184i	1.00000		0.000280043i	$-8.91405e-5\pi$
$109$	0.422082	+	2.93565i	0.0404281	+	0.281184i	−0.959572	+	0.281464i	$0.909180\pi$
$110$	−1.39086	+	3.04555i	−0.132613	+	0.290382i
$111$	0.918150	−	6.38587i	0.0871469	−	0.606120i
$112$	3.45205	+	2.21850i	0.326188	+	0.209628i
$113$	11.1969	+	12.9219i	1.05332	+	1.21559i	0.975814	+	0.218602i	$0.0701497\pi$
$113$	11.1969	+	12.9219i	1.05332	+	1.21559i	0.0775042	+	0.996992i	$0.475305\pi$
$114$	−9.04437			−0.847083
$115$	−3.01835	+	3.72687i	−0.281463	+	0.347532i
$116$	0.875039			0.0812453
$117$	−3.31098	−	3.82107i	−0.306100	−	0.353258i
$118$	−10.3459	−	6.64891i	−0.952418	−	0.612082i
$119$	1.57092	−	10.9260i	0.144006	−	1.00159i
$120$	−1.27136	+	2.78390i	−0.116059	+	0.254134i
$121$	0.198632	+	1.38151i	0.0180574	+	0.125592i
$122$	12.4535	+	3.65667i	1.12748	+	0.331059i
$123$	2.64396	−	1.69917i	0.238398	−	0.153209i
$124$	1.94607	+	4.26130i	0.174762	+	0.382676i
$125$	0.959493	−	0.281733i	0.0858197	−	0.0251989i
$126$	−1.76940	+	2.04200i	−0.157631	+	0.181916i
$127$	−0.107995	+	0.124633i	−0.00958300	+	0.0110594i	−0.760521	−	0.649314i	$-0.775056\pi$
$127$	−0.107995	+	0.124633i	−0.00958300	+	0.0110594i	0.750938	+	0.660373i	$0.229602\pi$
$128$	−0.0731612	+	0.0214821i	−0.00646660	+	0.00189876i
$129$	−4.83132	−	10.5791i	−0.425374	−	0.931438i
$130$	4.59517	−	2.95314i	0.403023	−	0.259007i
$131$	11.1709	+	3.28006i	0.976002	+	0.286580i	0.730573	−	0.682835i	$-0.239253\pi$
$131$	11.1709	+	3.28006i	0.976002	+	0.286580i	0.245429	+	0.969415i	$0.421071\pi$
$132$	−0.367314	−	2.55473i	−0.0319706	−	0.222360i
$133$	−8.69767	+	19.0452i	−0.754184	+	1.65143i
$134$	1.07901	−	7.50469i	0.0932123	−	0.648306i
$135$	−0.841254	−	0.540641i	−0.0724036	−	0.0465310i
$136$	−8.84568	−	10.2085i	−0.758511	−	0.875369i
$137$	−3.02846			−0.258739			−0.129369	−	0.991596i	$-0.541295\pi$
$137$	−3.02846			−0.258739			−0.129369	+	0.991596i	$0.541295\pi$
$138$	−0.566433	+	5.15016i	−0.0482179	+	0.438410i
$139$	9.83875			0.834512			0.417256	−	0.908789i	$-0.362992\pi$
$139$	9.83875			0.834512			0.417256	+	0.908789i	$0.362992\pi$
$140$	1.36400	+	1.57414i	0.115279	+	0.133039i
$141$	7.25877	+	4.66493i	0.611298	+	0.392858i
$142$	−0.963460	+	6.70101i	−0.0808518	+	0.562336i
$143$	−6.50911	+	14.2530i	−0.544319	+	1.19189i
$144$	0.233502	+	1.62404i	0.0194585	+	0.135337i
$145$	−1.00812	−	0.296012i	−0.0837201	−	0.0245824i
$146$	−14.0553	+	9.03279i	−1.16322	+	0.747559i
$147$	−0.309531	−	0.677779i	−0.0255297	−	0.0559022i
$148$	−5.15538	+	1.51376i	−0.423770	+	0.124430i
$149$	−10.5563	+	12.1826i	−0.864806	+	0.998039i	0.135168	+	0.990823i	$0.456843\pi$
$149$	−10.5563	+	12.1826i	−0.864806	+	0.998039i	−0.999974	+	0.00721648i	$0.997703\pi$
$150$	0.707484	−	0.816480i	0.0577658	−	0.0666653i
$151$	4.90056	−	1.43893i	0.398802	−	0.117099i	−0.0761807	−	0.997094i	$-0.524273\pi$
$151$	4.90056	−	1.43893i	0.398802	−	0.117099i	0.474982	+	0.879995i	$0.342454\pi$
$152$	10.6434	+	23.3058i	0.863295	+	1.89035i
$153$	3.71297	−	2.38618i	0.300176	−	0.192911i
$154$	8.03436	+	2.35910i	0.647427	+	0.190102i
$155$	−0.800518	−	5.56773i	−0.0642992	−	0.447211i
$156$	−1.74922	+	3.83026i	−0.140050	+	0.306666i
$157$	0.913149	−	6.35109i	0.0728772	−	0.506872i	−0.920388	−	0.391007i	$-0.872127\pi$
$157$	0.913149	−	6.35109i	0.0728772	−	0.506872i	0.993265	−	0.115865i	$-0.0369641\pi$
$158$	6.12694	+	3.93755i	0.487433	+	0.313254i
$159$	−6.12265	−	7.06592i	−0.485558	−	0.560364i
$160$	4.34835			0.343767
$161$	10.3003	+	6.14550i	0.811774	+	0.484333i
$162$	−1.08036			−0.0848809
$163$	9.78889	+	11.2970i	0.766725	+	0.884848i	0.996077	−	0.0884960i	$-0.0282061\pi$
$163$	9.78889	+	11.2970i	0.766725	+	0.884848i	−0.229352	+	0.973344i	$0.573661\pi$
$164$	−2.20196	−	1.41512i	−0.171944	−	0.110502i
$165$	−0.441045	+	3.06753i	−0.0343353	+	0.238807i
$166$	6.40782	−	14.0312i	0.497343	−	1.08903i
$167$	−0.923653	−	6.42415i	−0.0714744	−	0.497116i	−0.993842	−	0.110803i	$-0.964658\pi$
$167$	−0.923653	−	6.42415i	−0.0714744	−	0.497116i	0.922368	−	0.386313i	$-0.126251\pi$
$168$	7.34411	+	2.15643i	0.566610	+	0.166372i
$169$	10.5688	−	6.79215i	0.812983	−	0.522473i
$170$	1.98082	+	4.33739i	0.151922	+	0.332662i
$171$	−8.03254	+	2.35857i	−0.614264	+	0.180364i
$172$	−6.34289	+	7.32009i	−0.483641	+	0.558152i
$173$	−4.08917	+	4.71915i	−0.310894	+	0.358790i	−0.889596	−	0.456749i	$-0.849014\pi$
$173$	−4.08917	+	4.71915i	−0.310894	+	0.358790i	0.578702	+	0.815539i	$0.303559\pi$
$174$	−1.08913	+	0.319799i	−0.0825670	+	0.0242439i
$175$	−1.03894	−	2.27497i	−0.0785367	−	0.171971i
$176$	4.27759	−	2.74904i	0.322436	−	0.207217i
$177$	−10.9224	−	3.20709i	−0.820974	−	0.241060i
$178$	−0.912767	−	6.34844i	−0.0684148	−	0.475835i
$179$	1.52765	−	3.34508i	0.114182	−	0.250023i	−0.843910	−	0.536485i	$-0.819752\pi$
$179$	1.52765	−	3.34508i	0.114182	−	0.250023i	0.958092	+	0.286462i	$0.0924792\pi$
$180$	−0.118524	+	0.824351i	−0.00883424	+	0.0614435i
$181$	9.97798	+	6.41246i	0.741657	+	0.476634i	0.856109	−	0.516795i	$-0.172875\pi$
$181$	9.97798	+	6.41246i	0.741657	+	0.476634i	−0.114452	+	0.993429i	$0.536511\pi$
$182$	−8.94609	−	10.3243i	−0.663128	−	0.765291i
$183$	12.0138			0.888087
$184$	13.9377	−	4.60110i	1.02750	−	0.339198i
$185$	6.45154			0.474327
$186$	−3.97958	−	4.59268i	−0.291797	−	0.336752i
$187$	−11.5068	−	7.39496i	−0.841460	−	0.540773i
$188$	1.02268	−	7.11292i	0.0745869	−	0.518763i
$189$	−1.03894	+	2.27497i	−0.0755720	+	0.165480i
$190$	−1.28715	−	8.95231i	−0.0933796	−	0.649469i
$191$	6.25399	+	1.83634i	0.452523	+	0.132873i	0.500049	−	0.865997i	$-0.333315\pi$
$191$	6.25399	+	1.83634i	0.452523	+	0.132873i	−0.0475257	+	0.998870i	$0.515134\pi$
$192$	6.71257	−	4.31391i	0.484438	−	0.311330i
$193$	−2.97134	−	6.50632i	−0.213882	−	0.468335i	0.772034	−	0.635582i	$-0.219240\pi$
$193$	−2.97134	−	6.50632i	−0.213882	−	0.468335i	−0.985915	+	0.167246i	$0.946512\pi$
$194$	−12.0866	+	3.54895i	−0.867768	+	0.254800i
$195$	3.31098	−	3.82107i	0.237104	−	0.273633i
$196$	−0.406374	+	0.468981i	−0.0290267	+	0.0334987i
$197$	2.74559	−	0.806179i	0.195615	−	0.0574379i	−0.182457	−	0.983214i	$-0.558405\pi$
$197$	2.74559	−	0.806179i	0.195615	−	0.0574379i	0.378073	+	0.925776i	$0.376587\pi$
$198$	1.39086	+	3.04555i	0.0988438	+	0.216438i
$199$	4.89013	−	3.14269i	0.346652	−	0.222780i	−0.355716	−	0.934594i	$-0.615763\pi$
$199$	4.89013	−	3.14269i	0.346652	−	0.222780i	0.702367	+	0.711815i	$0.252126\pi$
$200$	−2.93650	−	0.862233i	−0.207642	−	0.0609691i
$201$	−0.998754	−	6.94648i	−0.0704467	−	0.489967i
$202$	−1.86544	+	4.08474i	−0.131252	+	0.287402i
$203$	−0.373966	+	2.60099i	−0.0262473	+	0.182554i
$204$	−3.09227	−	1.98728i	−0.216502	−	0.139137i
$205$	2.05815	+	2.37523i	0.143747	+	0.165893i
$206$	5.80586			0.404514
$207$	0.839980	+	4.72170i	0.0583826	+	0.328181i
$208$	−8.29559			−0.575196
$209$	16.9900	+	19.6075i	1.17522	+	1.35628i
$210$	−2.27302	−	1.46078i	−0.156854	−	0.100804i
$211$	−2.09307	+	14.5576i	−0.144093	+	1.00219i	0.781565	+	0.623824i	$0.214422\pi$
$211$	−2.09307	+	14.5576i	−0.144093	+	1.00219i	−0.925657	+	0.378363i	$0.876487\pi$
$212$	−3.23466	+	7.08291i	−0.222157	+	0.486456i
$213$	0.891798	+	6.20259i	0.0611050	+	0.424994i
$214$	4.44227	+	1.30437i	0.303667	+	0.0891648i
$215$	9.78386	−	6.28770i	0.667254	−	0.428818i
$216$	1.27136	+	2.78390i	0.0865053	+	0.189420i
$217$	−13.4981	+	3.96340i	−0.916311	+	0.269053i
$218$	−2.09828	+	2.42154i	−0.142113	+	0.164008i
$219$	−10.1273	+	11.6876i	−0.684341	+	0.789772i
$220$	2.47645	−	0.727151i	0.166962	−	0.0490245i
$221$	9.27009	+	20.2987i	0.623574	+	1.36544i
$222$	5.86351	−	3.76825i	0.393533	−	0.252908i
$223$	−26.3039	−	7.72353i	−1.76144	−	0.517206i	−0.768927	−	0.639337i	$-0.779209\pi$
$223$	−26.3039	−	7.72353i	−1.76144	−	0.517206i	−0.992514	+	0.122131i	$0.961027\pi$
$224$	−1.54769	−	10.7644i	−0.103409	−	0.719228i
$225$	0.415415	−	0.909632i	0.0276943	−	0.0606421i
$226$	−2.62886	+	18.2841i	−0.174869	+	1.21624i
$227$	2.69783	+	1.73379i	0.179061	+	0.115076i	0.627101	−	0.778938i	$-0.284241\pi$
$227$	2.69783	+	1.73379i	0.179061	+	0.115076i	−0.448040	+	0.894014i	$0.647878\pi$
$228$	4.56578	+	5.26919i	0.302376	+	0.348961i
$229$	9.14163			0.604096			0.302048	−	0.953293i	$-0.402330\pi$
$229$	9.14163			0.604096			0.302048	+	0.953293i	$0.402330\pi$
$230$	−5.17835	+	0.172277i	−0.341450	+	0.0113596i
$231$	7.75072			0.509960
$232$	2.10576	+	2.43017i	0.138250	+	0.159549i
$233$	6.34613	+	4.07841i	0.415749	+	0.267186i	0.731750	−	0.681573i	$-0.238704\pi$
$233$	6.34613	+	4.07841i	0.415749	+	0.267186i	−0.316001	+	0.948759i	$0.602340\pi$
$234$	0.777364	−	5.40669i	0.0508179	−	0.353446i
$235$	−3.58441	+	7.84877i	−0.233821	+	0.511997i
$236$	1.34921	+	9.38397i	0.0878262	+	0.610844i
$237$	6.46832	+	1.89927i	0.420162	+	0.123371i
$238$	10.0323	−	6.44734i	0.650295	−	0.417919i
$239$	4.46122	+	9.76872i	0.288573	+	0.631886i	0.997287	−	0.0736096i	$-0.0234519\pi$
$239$	4.46122	+	9.76872i	0.288573	+	0.631886i	−0.708715	+	0.705495i	$0.750725\pi$
$240$	−1.57428	+	0.462250i	−0.101619	+	0.0298381i
$241$	2.23458	−	2.57884i	0.143942	−	0.166118i	−0.679201	−	0.733953i	$-0.737673\pi$
$241$	2.23458	−	2.57884i	0.143942	−	0.166118i	0.823142	+	0.567835i	$0.192219\pi$
$242$	−0.987450	+	1.13958i	−0.0634757	+	0.0732548i
$243$	−0.959493	+	0.281733i	−0.0615515	+	0.0180732i
$244$	−4.15641	−	9.10127i	−0.266087	−	0.582649i
$245$	0.626829	−	0.402839i	0.0400466	−	0.0257364i
$246$	3.25789	+	0.956604i	0.207716	+	0.0609909i
$247$	−6.02377	−	41.8962i	−0.383283	−	2.66579i
$248$	−7.15140	+	15.6594i	−0.454114	+	0.994372i
$249$	2.03194	−	14.1324i	0.128769	−	0.895607i
$250$	0.908854	+	0.584085i	0.0574810	+	0.0369408i
$251$	−17.0337	−	19.6579i	−1.07516	−	1.24080i	−0.969161	−	0.246430i	$-0.920742\pi$
$251$	−17.0337	−	19.6579i	−1.07516	−	1.24080i	−0.105996	−	0.994367i	$-0.533803\pi$
$252$	2.08288			0.131209
$253$	12.2292	−	8.44665i	0.768841	−	0.531036i
$254$	−0.178165			−0.0111790
$255$	2.89031	+	3.33559i	0.180998	+	0.208883i
$256$	−13.4944	−	8.67235i	−0.843403	−	0.542022i
$257$	−2.49867	+	17.3787i	−0.155863	+	1.08405i	0.750292	+	0.661106i	$0.229913\pi$
$257$	−2.49867	+	17.3787i	−0.155863	+	1.08405i	−0.906155	+	0.422945i	$0.860996\pi$
$258$	5.21955	−	11.4292i	0.324955	−	0.711552i
$259$	−2.29627	−	15.9709i	−0.142683	−	0.992385i
$260$	−4.04021	−	1.18631i	−0.250563	−	0.0735720i
$261$	−0.883891	+	0.568042i	−0.0547115	+	0.0351609i
$262$	5.22509	+	11.4414i	0.322807	+	0.706849i
$263$	19.9893	−	5.86940i	1.23259	−	0.361922i	0.400366	−	0.916355i	$-0.368883\pi$
$263$	19.9893	−	5.86940i	1.23259	−	0.361922i	0.832228	+	0.554433i	$0.187065\pi$
$264$	6.21111	−	7.16800i	0.382267	−	0.441160i
$265$	6.12265	−	7.06592i	0.376112	−	0.434056i
$266$	−21.7035	+	6.37273i	−1.33073	+	0.390737i
$267$	−2.46618	−	5.40018i	−0.150928	−	0.330486i
$268$	−4.91689	+	3.15989i	−0.300347	+	0.193021i
$269$	4.53536	+	1.33170i	0.276526	+	0.0811952i	0.417055	−	0.908881i	$-0.363062\pi$
$269$	4.53536	+	1.33170i	0.276526	+	0.0811952i	−0.140529	+	0.990077i	$0.544880\pi$
$270$	−0.153751	−	1.06936i	−0.00935698	−	0.0650792i
$271$	−9.01019	+	19.7296i	−0.547330	+	1.19849i	0.410688	+	0.911776i	$0.365289\pi$
$271$	−9.01019	+	19.7296i	−0.547330	+	1.19849i	−0.958018	+	0.286709i	$0.907439\pi$
$272$	1.03059	−	7.16790i	0.0624886	−	0.434618i
$273$	−10.6376	−	6.83637i	−0.643817	−	0.413756i
$274$	−2.14259	−	2.47268i	−0.129438	−	0.149380i
$275$	−3.09908			−0.186881
$276$	3.28640	−	2.26990i	0.197818	−	0.136632i
$277$	9.27565			0.557320			0.278660	−	0.960390i	$-0.410110\pi$
$277$	9.27565			0.557320			0.278660	+	0.960390i	$0.410110\pi$
$278$	6.96075	+	8.03314i	0.417478	+	0.481796i
$279$	−4.73204	−	3.04109i	−0.283300	−	0.182066i
$280$	−1.08930	+	7.57625i	−0.0650981	+	0.452767i
$281$	0.935042	−	2.04746i	0.0557799	−	0.122141i	−0.879690	−	0.475548i	$-0.842250\pi$
$281$	0.935042	−	2.04746i	0.0557799	−	0.122141i	0.935470	+	0.353407i	$0.114977\pi$
$282$	1.32664	+	9.22699i	0.0790003	+	0.549459i
$283$	10.2855	+	3.02008i	0.611407	+	0.179525i	0.572754	−	0.819728i	$-0.305875\pi$
$283$	10.2855	+	3.02008i	0.611407	+	0.179525i	0.0386529	+	0.999253i	$0.487693\pi$
$284$	4.39034	−	2.82150i	0.260519	−	0.167425i
$285$	−3.47771	−	7.61512i	−0.206002	−	0.451081i
$286$	−16.2423	+	4.76918i	−0.960430	+	0.282008i
$287$	5.14738	−	5.94040i	0.303840	−	0.350651i
$288$	2.84756	−	3.28626i	0.167794	−	0.193645i
$289$	−2.37958	+	0.698706i	−0.139975	+	0.0411004i
$290$	−0.471543	−	1.03254i	−0.0276900	−	0.0606326i
$291$	−9.80895	+	6.30383i	−0.575011	+	0.369537i
$292$	12.3578	+	3.62859i	0.723188	+	0.212347i
$293$	−2.39898	−	16.6853i	−0.140150	−	0.974763i	−0.931588	−	0.363515i	$-0.881577\pi$
$293$	−2.39898	−	16.6853i	−0.140150	−	0.974763i	0.791439	−	0.611249i	$-0.209332\pi$
$294$	0.334404	−	0.732243i	0.0195029	−	0.0427053i
$295$	1.62004	−	11.2676i	0.0943221	−	0.656025i
$296$	−16.6103	−	10.6748i	−0.965455	−	0.620460i
$297$	2.02946	+	2.34213i	0.117761	+	0.135904i
$298$	−17.4153			−1.00884
$299$	−24.2343	+	0.806243i	−1.40151	+	0.0466262i
$300$	−0.832828			−0.0480833
$301$	−19.0477	−	21.9822i	−1.09789	−	1.26703i
$302$	4.64192	+	2.98318i	0.267113	+	0.171663i
$303$	−0.591537	+	4.11423i	−0.0339829	+	0.236356i
$304$	−5.70602	+	12.4944i	−0.327263	+	0.716605i
$305$	1.70974	+	11.8915i	0.0978996	+	0.680907i
$306$	4.57514	+	1.34338i	0.261543	+	0.0767960i
$307$	−6.74486	+	4.33466i	−0.384950	+	0.247392i	−0.718775	−	0.695243i	$-0.755297\pi$
$307$	−6.74486	+	4.33466i	−0.384950	+	0.247392i	0.333825	+	0.942635i	$0.391660\pi$
$308$	−2.68151	−	5.87169i	−0.152793	−	0.334571i
$309$	5.15634	−	1.51404i	0.293334	−	0.0861306i
$310$	3.97958	−	4.59268i	0.226025	−	0.260847i
$311$	0.175579	−	0.202629i	0.00995618	−	0.0114900i	−0.750750	−	0.660587i	$-0.770308\pi$
$311$	0.175579	−	0.202629i	0.00995618	−	0.0114900i	0.760706	+	0.649097i	$0.224853\pi$
$312$	−14.8469	+	4.35945i	−0.840542	+	0.246805i
$313$	−1.13329	−	2.48156i	−0.0640575	−	0.140266i	0.874896	−	0.484312i	$-0.160930\pi$
$313$	−1.13329	−	2.48156i	−0.0640575	−	0.140266i	−0.938953	+	0.344045i	$0.888203\pi$
$314$	5.83157	−	3.74772i	0.329095	−	0.211496i
$315$	−2.39967	−	0.704607i	−0.135206	−	0.0397001i
$316$	−0.799015	−	5.55727i	−0.0449481	−	0.312621i
$317$	8.66321	−	18.9698i	0.486574	−	1.06545i	−0.494029	−	0.869445i	$-0.664476\pi$
$317$	8.66321	−	18.9698i	0.486574	−	1.06545i	0.980603	−	0.196003i	$-0.0627963\pi$
$318$	1.43750	−	9.99804i	0.0806111	−	0.560662i
$319$	2.73925	+	1.76041i	0.153368	+	0.0985639i
$320$	5.22530	+	6.03032i	0.292103	+	0.337105i
$321$	4.28544			0.239190
$322$	2.26958	+	12.7578i	0.126479	+	0.710964i
$323$	36.9493			2.05591
$324$	0.545386	+	0.629409i	0.0302992	+	0.0349672i
$325$	4.25338	+	2.73348i	0.235935	+	0.151626i
$326$	−2.29827	+	15.9849i	−0.127290	+	0.885319i
$327$	−1.23205	+	2.69782i	−0.0681326	+	0.149190i
$328$	−1.36888	−	9.52078i	−0.0755838	−	0.525697i
$329$	20.7056	+	6.07971i	1.14154	+	0.335185i
$330$	−2.81661	+	1.81013i	−0.155049	+	0.0996441i
$331$	3.22504	+	7.06186i	0.177264	+	0.388155i	0.977319	−	0.211772i	$-0.0679235\pi$
$331$	3.22504	+	7.06186i	0.177264	+	0.388155i	−0.800055	+	0.599927i	$0.795196\pi$
$332$	−11.4093	+	3.35006i	−0.626165	+	0.183859i
$333$	4.22486	−	4.87575i	0.231521	−	0.267189i
$334$	4.59172	−	5.29912i	0.251248	−	0.289955i
$335$	6.73364	−	1.97718i	0.367898	−	0.108025i
$336$	1.70464	+	3.73264i	0.0929956	+	0.203632i
$337$	10.6082	−	6.81747i	0.577865	−	0.371371i	−0.218821	−	0.975765i	$-0.570221\pi$
$337$	10.6082	−	6.81747i	0.577865	−	0.371371i	0.796686	+	0.604394i	$0.206585\pi$
$338$	13.0229	+	3.82387i	0.708352	+	0.207991i
$339$	2.43332	+	16.9241i	0.132160	+	0.919193i
$340$	1.52698	−	3.34361i	0.0828119	−	0.181333i
$341$	−2.48087	+	17.2548i	−0.134347	+	0.934401i
$342$	−7.60861	−	4.88976i	−0.411427	−	0.264408i
$343$	−12.6849	−	14.6391i	−0.684919	−	0.790439i
$344$	−35.5935			−1.91907
$345$	−4.55410	+	1.50340i	−0.245184	+	0.0809402i
$346$	−6.74611			−0.362673
$347$	−19.1121	−	22.0566i	−1.02599	−	1.18406i	−0.982739	−	0.184995i	$-0.940773\pi$
$347$	−19.1121	−	22.0566i	−1.02599	−	1.18406i	−0.0432541	−	0.999064i	$-0.513772\pi$
$348$	0.736129	+	0.473082i	0.0394607	+	0.0253598i
$349$	0.137285	−	0.954841i	0.00734872	−	0.0511115i	−0.985817	−	0.167823i	$-0.946326\pi$
$349$	0.137285	−	0.954841i	0.00734872	−	0.0511115i	0.993166	+	0.116712i	$0.0372353\pi$
$350$	1.12243	−	2.45778i	0.0599964	−	0.131374i
$351$	−0.719544	−	5.00454i	−0.0384064	−	0.267122i
$352$	−12.9300	−	3.79659i	−0.689171	−	0.202359i
$353$	19.4428	−	12.4951i	1.03483	−	0.665048i	0.0911306	−	0.995839i	$-0.470952\pi$
$353$	19.4428	−	12.4951i	1.03483	−	0.665048i	0.943704	+	0.330791i	$0.107316\pi$
$354$	−5.10886	−	11.1868i	−0.271533	−	0.594574i
$355$	−6.01254	+	1.76544i	−0.319112	+	0.0936999i
$356$	−3.23778	+	3.73659i	−0.171602	+	0.198039i
$357$	7.22859	−	8.34224i	0.382578	−	0.441518i
$358$	3.81197	−	1.11930i	0.201469	−	0.0591566i
$359$	−3.32072	−	7.27135i	−0.175261	−	0.383767i	0.801533	−	0.597951i	$-0.204018\pi$
$359$	−3.32072	−	7.27135i	−0.175261	−	0.383767i	−0.976793	+	0.214184i	$0.931291\pi$
$360$	−2.57463	+	1.65461i	−0.135695	+	0.0872058i
$361$	−49.0152	−	14.3922i	−2.57975	−	0.757483i
$362$	1.82362	+	12.6835i	0.0958471	+	0.666631i
$363$	−0.579803	+	1.26959i	−0.0304318	+	0.0666363i
$364$	−1.49873	+	10.4239i	−0.0785546	+	0.546359i
$365$	−13.0099	−	8.36093i	−0.680967	−	0.437631i
$366$	8.49957	+	9.80903i	0.444280	+	0.512726i
$367$	−15.5771			−0.813119			−0.406559	−	0.913624i	$-0.633272\pi$
$367$	−15.5771			−0.813119			−0.406559	+	0.913624i	$0.633272\pi$
$368$	6.75738	+	4.03170i	0.352253	+	0.210167i
$369$	3.14288			0.163612
$370$	4.56436	+	5.26755i	0.237290	+	0.273847i
$371$	−19.6710	−	12.6418i	−1.02127	−	0.656330i
$372$	−0.666694	+	4.63696i	−0.0345665	+	0.240415i
$373$	3.94580	−	8.64010i	0.204306	−	0.447367i	−0.779548	−	0.626343i	$-0.784551\pi$
$373$	3.94580	−	8.64010i	0.204306	−	0.447367i	0.983854	+	0.178975i	$0.0572783\pi$
$374$	−2.10303	−	14.6269i	−0.108745	−	0.756338i
$375$	0.959493	+	0.281733i	0.0495480	+	0.0145486i
$376$	22.2152	−	14.2768i	1.14566	−	0.736272i
$377$	−2.20679	−	4.83220i	−0.113656	−	0.248871i
$378$	−2.59250	+	0.761227i	−0.133344	+	0.0391533i
$379$	−20.6598	+	23.8427i	−1.06122	+	1.22472i	−0.0876951	+	0.996147i	$0.527950\pi$
$379$	−20.6598	+	23.8427i	−1.06122	+	1.22472i	−0.973528	+	0.228569i	$0.926595\pi$
$380$	−4.56578	+	5.26919i	−0.234220	+	0.270304i
$381$	−0.158233	+	0.0464613i	−0.00810650	+	0.00238028i
$382$	2.92527	+	6.40544i	0.149670	+	0.327731i
$383$	16.5393	−	10.6292i	0.845120	−	0.543126i	−0.0449291	−	0.998990i	$-0.514306\pi$
$383$	16.5393	−	10.6292i	0.845120	−	0.543126i	0.890049	+	0.455864i	$0.150670\pi$
$384$	−0.0731612	−	0.0214821i	−0.00373349	−	0.00109625i
$385$	1.10304	+	7.67183i	0.0562163	+	0.390993i
$386$	3.21011	−	7.02915i	0.163390	−	0.357774i
$387$	1.65513	−	11.5117i	0.0841352	−	0.585173i
$388$	8.16917	+	5.25000i	0.414727	+	0.266529i
$389$	9.71959	+	11.2170i	0.492803	+	0.568725i	0.946612	−	0.322374i	$-0.104481\pi$
$389$	9.71959	+	11.2170i	0.492803	+	0.568725i	−0.453809	+	0.891099i	$0.649935\pi$
$390$	5.46229			0.276594
$391$	2.31407	−	21.0401i	0.117027	−	1.06404i
$392$	−2.28039			−0.115177
$393$	7.62418	+	8.79878i	0.384589	+	0.443840i
$394$	2.60069	+	1.67136i	0.131021	+	0.0842020i
$395$	−0.959400	+	6.67277i	−0.0482727	+	0.335744i
$396$	1.07219	−	2.34776i	0.0538793	−	0.117979i
$397$	0.750568	+	5.22032i	0.0376699	+	0.262000i	0.999949	−	0.0100629i	$-0.00320316\pi$
$397$	0.750568	+	5.22032i	0.0376699	+	0.262000i	−0.962279	+	0.272063i	$0.912294\pi$
$398$	6.02563	+	1.76928i	0.302037	+	0.0886862i
$399$	−17.6136	+	11.3196i	−0.881782	+	0.566687i
$400$	−0.681589	−	1.49247i	−0.0340794	−	0.0746235i
$401$	−6.92609	+	2.03368i	−0.345872	+	0.101557i	−0.450055	−	0.893001i	$-0.648596\pi$
$401$	−6.92609	+	2.03368i	−0.345872	+	0.101557i	0.104183	+	0.994558i	$0.466777\pi$
$402$	4.96506	−	5.72999i	0.247635	−	0.285786i
$403$	18.6242	−	21.4935i	0.927737	−	1.07067i
$404$	3.32146	−	0.975268i	0.165249	−	0.0485214i
$405$	−0.415415	−	0.909632i	−0.0206421	−	0.0452000i
$406$	−2.38823	+	1.53482i	−0.118526	+	0.0761719i
$407$	−19.1839	−	5.63291i	−0.950912	−	0.279213i
$408$	−1.92235	−	13.3702i	−0.0951706	−	0.661926i
$409$	−3.91433	+	8.57119i	−0.193551	+	0.423818i	−0.981380	−	0.192076i	$-0.938478\pi$
$409$	−3.91433	+	8.57119i	−0.193551	+	0.423818i	0.787829	+	0.615894i	$0.211205\pi$
$410$	−0.483221	+	3.36087i	−0.0238646	+	0.165982i
$411$	−2.54770	−	1.63731i	−0.125669	−	0.0807625i
$412$	−2.93092	−	3.38246i	−0.144396	−	0.166642i
$413$	−28.4698			−1.40091
$414$	−3.26090	+	4.02635i	−0.160264	+	0.197884i
$415$	14.2778			0.700868
$416$	14.3973	+	16.6153i	0.705884	+	0.814634i
$417$	8.27688	+	5.31923i	0.405321	+	0.260484i
$418$	−3.98897	+	27.7439i	−0.195107	+	1.35700i
$419$	9.00006	−	19.7074i	0.439682	−	0.962769i	−0.551975	−	0.833861i	$-0.686126\pi$
$419$	9.00006	−	19.7074i	0.439682	−	0.962769i	0.991657	−	0.128908i	$-0.0411472\pi$
$420$	0.296425	+	2.06168i	0.0144641	+	0.100600i
$421$	21.4952	+	6.31156i	1.04761	+	0.307607i	0.759852	−	0.650096i	$-0.225271\pi$
$421$	21.4952	+	6.31156i	1.04761	+	0.307607i	0.287760	+	0.957703i	$0.407089\pi$
$422$	−13.3668	+	8.59032i	−0.650685	+	0.418170i
$423$	3.58441	+	7.84877i	0.174280	+	0.381620i
$424$	−27.4549	+	8.06149i	−1.33333	+	0.391501i
$425$	−2.89031	+	3.33559i	−0.140200	+	0.161800i
$426$	−4.43336	+	5.11636i	−0.214797	+	0.247889i
$427$	28.8292	−	8.46501i	1.39514	−	0.409651i
$428$	−1.48263	−	3.24651i	−0.0716657	−	0.156926i
$429$	−13.1815	+	8.47127i	−0.636411	+	0.408997i
$430$	12.0557	+	3.53987i	0.581377	+	0.170708i
$431$	−0.556516	−	3.87065i	−0.0268064	−	0.186443i	0.972019	−	0.234904i	$-0.0754775\pi$
$431$	−0.556516	−	3.87065i	−0.0268064	−	0.186443i	−0.998825	+	0.0484608i	$0.984568\pi$
$432$	−0.681589	+	1.49247i	−0.0327930	+	0.0718065i
$433$	0.568406	−	3.95335i	0.0273159	−	0.189986i	−0.971595	−	0.236651i	$-0.923950\pi$
$433$	0.568406	−	3.95335i	0.0273159	−	0.189986i	0.998911	+	0.0466650i	$0.0148593\pi$
$434$	−12.7857	−	8.21688i	−0.613734	−	0.394423i
$435$	−0.688051	−	0.794054i	−0.0329895	−	0.0380720i
$436$	2.47003			0.118293
$437$	−15.4550	+	37.0552i	−0.739311	+	1.77259i
$438$	−16.7076			−0.798318
$439$	18.8871	+	21.7969i	0.901431	+	1.04031i	0.998984	+	0.0450766i	$0.0143532\pi$
$439$	18.8871	+	21.7969i	0.901431	+	1.04031i	−0.0975524	+	0.995230i	$0.531101\pi$
$440$	7.97897	+	5.12777i	0.380383	+	0.244457i
$441$	0.106041	−	0.737529i	0.00504955	−	0.0351204i
$442$	−10.0150	+	21.9298i	−0.476366	+	1.04310i
$443$	−4.82406	−	33.5521i	−0.229198	−	1.59411i	−0.701500	−	0.712669i	$-0.747486\pi$
$443$	−4.82406	−	33.5521i	−0.229198	−	1.59411i	0.472302	−	0.881437i	$-0.343423\pi$
$444$	−5.15538	−	1.51376i	−0.244663	−	0.0718397i
$445$	4.99424	−	3.20960i	0.236750	−	0.152150i
$446$	−12.3035	−	26.9409i	−0.582587	−	1.27569i
$447$	−15.4669	+	4.54151i	−0.731562	+	0.214806i
$448$	13.0684	−	15.0817i	0.617422	−	0.712542i
$449$	−21.6233	+	24.9546i	−1.02047	+	1.17768i	−0.0364975	+	0.999334i	$0.511620\pi$
$449$	−21.6233	+	24.9546i	−1.02047	+	1.17768i	−0.983968	+	0.178346i	$0.942925\pi$
$450$	1.03660	−	0.304372i	0.0488656	−	0.0143482i
$451$	−4.04615	−	8.85984i	−0.190526	−	0.417194i
$452$	11.9793	−	7.69864i	0.563460	−	0.362114i
$453$	4.90056	+	1.43893i	0.230248	+	0.0676070i
$454$	0.493066	+	3.42935i	0.0231407	+	0.160947i
$455$	5.25290	−	11.5022i	0.246260	−	0.539233i
$456$	−3.64627	+	25.3604i	−0.170752	+	1.18761i
$457$	23.5271	+	15.1199i	1.10055	+	0.707281i	0.959214	−	0.282681i	$-0.0912236\pi$
$457$	23.5271	+	15.1199i	1.10055	+	0.707281i	0.141337	+	0.989962i	$0.454860\pi$
$458$	6.46755	+	7.46395i	0.302209	+	0.348768i
$459$	4.41362			0.206010
$460$	2.71450	+	2.92990i	0.126564	+	0.136607i
$461$	33.4177			1.55642			0.778209	−	0.628005i	$-0.216128\pi$
$461$	33.4177			1.55642			0.778209	+	0.628005i	$0.216128\pi$
$462$	5.48351	+	6.32831i	0.255116	+	0.294419i
$463$	14.0177	+	9.00861i	0.651456	+	0.418666i	0.824198	−	0.566302i	$-0.191626\pi$
$463$	14.0177	+	9.00861i	0.651456	+	0.418666i	−0.172742	+	0.984967i	$0.555263\pi$
$464$	−0.245337	+	1.70635i	−0.0113895	+	0.0792155i
$465$	2.33670	−	5.11666i	0.108362	−	0.237280i
$466$	1.15984	+	8.06689i	0.0537288	+	0.373692i
$467$	−14.8962	−	4.37393i	−0.689315	−	0.202401i	−0.0817285	−	0.996655i	$-0.526044\pi$
$467$	−14.8962	−	4.37393i	−0.689315	−	0.202401i	−0.607587	+	0.794253i	$0.707862\pi$
$468$	−3.54233	+	2.27652i	−0.163744	+	0.105232i
$469$	−7.29122	−	15.9655i	−0.336677	−	0.737220i
$470$	−8.94427	+	2.62628i	−0.412569	+	0.121141i
$471$	4.20185	−	4.84919i	0.193611	−	0.223439i
$472$	−22.8145	+	26.3293i	−1.05012	+	1.21191i
$473$	−34.5826	+	10.1544i	−1.59011	+	0.466898i
$474$	3.02551	+	6.62495i	0.138966	+	0.304294i
$475$	7.04268	−	4.52606i	0.323140	−	0.207670i
$476$	−8.82067	−	2.58998i	−0.404295	−	0.118712i
$477$	−1.33058	−	9.25438i	−0.0609230	−	0.423729i
$478$	−4.81972	+	10.5537i	−0.220449	+	0.482715i
$479$	4.49018	−	31.2299i	0.205162	−	1.42693i	−0.583505	−	0.812110i	$-0.698319\pi$
$479$	4.49018	−	31.2299i	0.205162	−	1.42693i	0.788666	−	0.614821i	$-0.210772\pi$
$480$	3.65806	+	2.35089i	0.166967	+	0.107303i
$481$	21.3609	+	24.6518i	0.973973	+	1.12402i
$482$	3.68650			0.167915
$483$	5.34262	+	10.7387i	0.243097	+	0.488626i
$484$	1.16240			0.0528362
$485$	−7.63562	−	8.81198i	−0.346716	−	0.400131i
$486$	−0.908854	−	0.584085i	−0.0412265	−	0.0264946i
$487$	4.07805	−	28.3635i	0.184794	−	1.28527i	−0.660442	−	0.750877i	$-0.729631\pi$
$487$	4.07805	−	28.3635i	0.184794	−	1.28527i	0.845236	−	0.534394i	$-0.179460\pi$
$488$	15.2739	−	33.4452i	0.691418	−	1.51399i
$489$	2.12733	+	14.7959i	0.0962011	+	0.669093i
$490$	0.772381	+	0.226791i	0.0348926	+	0.0102454i
$491$	8.89089	−	5.71383i	0.401240	−	0.257861i	−0.324422	−	0.945912i	$-0.605170\pi$
$491$	8.89089	−	5.71383i	0.401240	−	0.257861i	0.725662	+	0.688051i	$0.241533\pi$
$492$	−1.08734	−	2.38094i	−0.0490211	−	0.107341i
$493$	4.44947	−	1.30648i	0.200394	−	0.0588410i
$494$	29.9457	−	34.5592i	1.34732	−	1.55489i
$495$	−2.02946	+	2.34213i	−0.0912176	+	0.105271i
$496$	−8.85530	+	2.60015i	−0.397615	+	0.116750i
$497$	6.51041	+	14.2558i	0.292032	+	0.639460i
$498$	12.9764	−	8.33944i	0.581487	−	0.373699i
$499$	33.2493	+	9.76287i	1.48844	+	0.437046i	0.922044	−	0.387085i	$-0.126518\pi$
$499$	33.2493	+	9.76287i	1.48844	+	0.437046i	0.566398	+	0.824132i	$0.308336\pi$
$500$	−0.118524	−	0.824351i	−0.00530054	−	0.0368661i
$501$	2.69613	−	5.90370i	0.120454	−	0.263758i
$502$	3.99924	−	27.8153i	0.178495	−	1.24146i
$503$	18.5980	+	11.9522i	0.829245	+	0.532923i	0.885038	−	0.465519i	$-0.154132\pi$
$503$	18.5980	+	11.9522i	0.829245	+	0.532923i	−0.0557931	+	0.998442i	$0.517769\pi$
$504$	5.01241	+	5.78463i	0.223270	+	0.257668i
$505$	−4.15654			−0.184963
$506$	15.5485	+	4.00900i	0.691213	+	0.178222i
$507$	12.5631			0.557949
$508$	0.0899412	+	0.103798i	0.00399049	+	0.00460528i
$509$	3.53306	+	2.27056i	0.156600	+	0.100641i	0.616594	−	0.787281i	$-0.288512\pi$
$509$	3.53306	+	2.27056i	0.156600	+	0.100641i	−0.459994	+	0.887922i	$0.652148\pi$
$510$	−0.678598	+	4.71975i	−0.0300488	+	0.208994i
$511$	−16.0671	+	35.1821i	−0.710767	+	1.55636i
$512$	−2.44460	−	17.0025i	−0.108037	−	0.751413i
$513$	−8.03254	−	2.35857i	−0.354645	−	0.104133i
$514$	−15.9571	+	10.2550i	−0.703837	+	0.452329i
$515$	2.23245	+	4.88838i	0.0983735	+	0.215408i
$516$	−9.29352	+	2.72882i	−0.409124	+	0.120130i
$517$	17.5113	−	20.2091i	0.770144	−	0.888794i
$518$	11.4154	−	13.1740i	0.501562	−	0.578834i
$519$	−5.99139	+	1.75923i	−0.262993	+	0.0772217i
$520$	−6.42802	−	14.0754i	−0.281887	−	0.617247i
$521$	24.3267	−	15.6338i	1.06577	−	0.684930i	0.114544	−	0.993418i	$-0.463459\pi$
$521$	24.3267	−	15.6338i	1.06577	−	0.684930i	0.951228	+	0.308488i	$0.0998231\pi$
$522$	−1.08913	−	0.319799i	−0.0476701	−	0.0139972i
$523$	1.83305	+	12.7491i	0.0801536	+	0.557480i	0.989840	+	0.142185i	$0.0454128\pi$
$523$	1.83305	+	12.7491i	0.0801536	+	0.557480i	−0.909687	+	0.415296i	$0.863678\pi$
$524$	4.02793	−	8.81994i	0.175961	−	0.385301i
$525$	0.355926	−	2.47552i	0.0155339	−	0.108041i
$526$	18.9344	+	12.1684i	0.825577	+	0.530566i
$527$	16.2579	+	18.7626i	0.708206	+	0.817313i
$528$	5.08478			0.221287
$529$	20.1325	+	11.1212i	0.875326	+	0.483533i
$530$	10.1009			0.438753
$531$	−7.45458	−	8.60305i	−0.323501	−	0.373340i
$532$	14.6691	+	9.42725i	0.635985	+	0.408723i
$533$	−2.26144	+	15.7287i	−0.0979538	+	0.681284i
$534$	2.66435	−	5.83412i	0.115298	−	0.252467i
$535$	0.609882	+	4.24182i	0.0263675	+	0.183390i
$536$	−20.6081	−	6.05108i	−0.890134	−	0.261367i
$537$	3.09362	−	1.98815i	0.133500	−	0.0857951i
$538$	2.12138	+	4.64518i	0.0914593	+	0.200268i
$539$	−2.21563	+	0.650566i	−0.0954337	+	0.0280219i
$540$	−0.545386	+	0.629409i	−0.0234697	+	0.0270855i
$541$	−9.46242	+	10.9202i	−0.406821	+	0.469497i	−0.921777	−	0.387720i	$-0.873263\pi$
$541$	−9.46242	+	10.9202i	−0.406821	+	0.469497i	0.514956	+	0.857217i	$0.327808\pi$
$542$	−22.4833	+	6.60170i	−0.965742	+	0.283567i
$543$	4.92717	+	10.7890i	0.211445	+	0.463001i
$544$	−16.1453	+	10.3759i	−0.692224	+	0.444865i
$545$	−2.84570	−	0.835572i	−0.121896	−	0.0357920i
$546$	−1.94417	−	13.5220i	−0.0832028	−	0.578688i
$547$	−11.7296	+	25.6842i	−0.501521	+	1.09818i	0.474451	+	0.880282i	$0.342647\pi$
$547$	−11.7296	+	25.6842i	−0.501521	+	1.09818i	−0.975972	+	0.217896i	$0.930081\pi$
$548$	−0.358945	+	2.49652i	−0.0153334	+	0.106646i
$549$	10.1067	+	6.49516i	0.431342	+	0.277207i
$550$	−2.19255	−	2.53033i	−0.0934905	−	0.107894i
$551$	−8.79595			−0.374720
$552$	14.2126	+	3.66458i	0.604930	+	0.155975i
$553$	16.8601			0.716963
$554$	6.56237	+	7.57338i	0.278808	+	0.321762i
$555$	5.42738	+	3.48797i	0.230380	+	0.148056i
$556$	1.16613	−	8.11058i	0.0494547	−	0.343965i
$557$	1.69790	−	3.71789i	0.0719424	−	0.157532i	−0.870244	−	0.492621i	$-0.836039\pi$
$557$	1.69790	−	3.71789i	0.0719424	−	0.157532i	0.942187	+	0.335089i	$0.108766\pi$
$558$	−0.864846	−	6.01514i	−0.0366118	−	0.254641i
$559$	56.4199	+	16.5664i	2.38631	+	0.700683i
$560$	−3.45205	+	2.21850i	−0.145876	+	0.0937486i
$561$	−5.68211	−	12.4421i	−0.239899	−	0.525305i
$562$	2.33323	−	0.685099i	0.0984215	−	0.0288992i
$563$	−10.4992	+	12.1167i	−0.442487	+	0.510657i	−0.932556	−	0.361027i	$-0.882426\pi$
$563$	−10.4992	+	12.1167i	−0.442487	+	0.510657i	0.490068	+	0.871684i	$0.336972\pi$
$564$	4.70587	−	5.43087i	0.198153	−	0.228681i
$565$	−16.4056	+	4.81711i	−0.690188	+	0.202658i
$566$	4.81095	+	10.5345i	0.202219	+	0.442799i
$567$	−2.10396	+	1.35213i	−0.0883578	+	0.0567841i
$568$	18.4012	+	5.40307i	0.772096	+	0.226708i
$569$	1.94557	+	13.5317i	0.0815624	+	0.567279i	0.989093	+	0.147293i	$0.0470559\pi$
$569$	1.94557	+	13.5317i	0.0815624	+	0.567279i	−0.907531	+	0.419986i	$0.862035\pi$
$570$	3.75717	−	8.22705i	0.157370	−	0.344593i
$571$	−0.289610	+	2.01428i	−0.0121198	+	0.0842951i	−0.994984	−	0.100038i	$-0.968103\pi$
$571$	−0.289610	+	2.01428i	−0.0121198	+	0.0842951i	0.982864	+	0.184333i	$0.0590126\pi$
$572$	10.9780	+	7.05511i	0.459012	+	0.294989i
$573$	4.26839	+	4.92599i	0.178315	+	0.205786i
$574$	8.49190			0.354445
$575$	−2.13621	−	4.29379i	−0.0890862	−	0.179063i
$576$	7.97925			0.332469
$577$	−6.12073	−	7.06370i	−0.254809	−	0.294065i	0.613904	−	0.789381i	$-0.289598\pi$
$577$	−6.12073	−	7.06370i	−0.254809	−	0.294065i	−0.868713	+	0.495315i	$0.835053\pi$
$578$	−2.25399	−	1.44855i	−0.0937536	−	0.0602518i
$579$	1.01793	−	7.07989i	0.0423039	−	0.294230i
$580$	−0.363504	+	0.795963i	−0.0150937	+	0.0330506i
$581$	−5.08183	−	35.3449i	−0.210830	−	1.46635i
$582$	−12.0866	−	3.54895i	−0.501006	−	0.147109i
$583$	−24.3753	+	15.6651i	−1.00952	+	0.648780i
$584$	19.6615	+	43.0526i	0.813597	+	1.78153i
$585$	4.85120	−	1.42444i	0.200572	−	0.0588933i
$586$	11.9259	−	13.7633i	0.492656	−	0.568555i
$587$	−27.6197	+	31.8748i	−1.13999	+	1.31561i	−0.197908	+	0.980221i	$0.563415\pi$
$587$	−27.6197	+	31.8748i	−1.13999	+	1.31561i	−0.942078	+	0.335393i	$0.891131\pi$
$588$	−0.595414	+	0.174829i	−0.0245545	+	0.00720984i
$589$	−19.5620	−	42.8349i	−0.806040	−	1.76498i
$590$	10.3459	−	6.64891i	0.425934	−	0.273731i
$591$	2.74559	+	0.806179i	0.112939	+	0.0331618i
$592$	−1.50645	−	10.4776i	−0.0619146	−	0.430625i
$593$	5.07808	−	11.1194i	0.208532	−	0.456621i	−0.776248	−	0.630428i	$-0.782880\pi$
$593$	5.07808	−	11.1194i	0.208532	−	0.456621i	0.984780	+	0.173807i	$0.0556069\pi$
$594$	−0.476486	+	3.31403i	−0.0195505	+	0.135976i
$595$	9.28606	+	5.96779i	0.380691	+	0.244655i
$596$	8.79158	+	10.1460i	0.360117	+	0.415597i
$597$	5.81290			0.237906
$598$	−17.8037	−	19.2164i	−0.728046	−	0.785818i
$599$	−25.6961			−1.04991			−0.524957	−	0.851129i	$-0.675919\pi$
$599$	−25.6961			−1.04991			−0.524957	+	0.851129i	$0.675919\pi$
$600$	−2.00418	−	2.31295i	−0.0818203	−	0.0944256i
$601$	5.16181	+	3.31729i	0.210555	+	0.135315i	0.641668	−	0.766983i	$-0.278243\pi$
$601$	5.16181	+	3.31729i	0.210555	+	0.135315i	−0.431113	+	0.902298i	$0.641879\pi$
$602$	4.47209	−	31.1041i	0.182269	−	1.26771i
$603$	2.91535	−	6.38372i	0.118722	−	0.259965i
$604$	−0.605354	−	4.21033i	−0.0246315	−	0.171316i
$605$	−1.33918	−	0.393220i	−0.0544456	−	0.0159867i
$606$	−3.77769	+	2.42777i	−0.153458	+	0.0986215i
$607$	−2.58566	−	5.66180i	−0.104949	−	0.229805i	0.849871	−	0.526990i	$-0.176680\pi$
$607$	−2.58566	−	5.66180i	−0.104949	−	0.229805i	−0.954820	+	0.297185i	$0.903952\pi$
$608$	34.9283	−	10.2559i	1.41653	−	0.415930i
$609$	−1.72080	+	1.98591i	−0.0697304	+	0.0804731i
$610$	−8.49957	+	9.80903i	−0.344138	+	0.397156i
$611$	−41.8586	+	12.2908i	−1.69342	+	0.497232i
$612$	−1.52698	−	3.34361i	−0.0617244	−	0.135158i
$613$	−24.6338	+	15.8312i	−0.994950	+	0.639415i	−0.933456	−	0.358692i	$-0.883223\pi$
$613$	−24.6338	+	15.8312i	−0.994950	+	0.639415i	−0.0614938	+	0.998107i	$0.519586\pi$
$614$	−8.31104	−	2.44034i	−0.335406	−	0.0984842i
$615$	0.447279	+	3.11089i	0.0180360	+	0.125443i
$616$	9.85399	−	21.5772i	0.397028	−	0.869371i
$617$	−2.51454	+	17.4890i	−0.101231	+	0.704080i	0.874487	+	0.485050i	$0.161199\pi$
$617$	−2.51454	+	17.4890i	−0.101231	+	0.704080i	−0.975718	+	0.219031i	$0.929711\pi$
$618$	4.88420	+	3.13889i	0.196471	+	0.126265i
$619$	−18.8469	−	21.7505i	−0.757521	−	0.874226i	0.237753	−	0.971326i	$-0.423589\pi$
$619$	−18.8469	−	21.7505i	−0.757521	−	0.874226i	−0.995275	+	0.0970993i	$0.969044\pi$
$620$	−4.68464			−0.188140
$621$	−1.84611	+	4.42627i	−0.0740817	+	0.177620i
$622$	0.289662			0.0116144
$623$	−9.72302	−	11.2210i	−0.389545	−	0.449558i
$624$	−6.97869	−	4.48493i	−0.279371	−	0.179541i
$625$	−0.142315	+	0.989821i	−0.00569259	+	0.0395929i
$626$	1.22436	−	2.68098i	0.0489353	−	0.107153i
$627$	3.69227	+	25.6803i	0.147455	+	1.02557i
$628$	−5.12730	−	1.50551i	−0.204601	−	0.0600764i
$629$	−23.9544	+	15.3946i	−0.955124	+	0.613821i
$630$	−1.12243	−	2.45778i	−0.0447187	−	0.0979203i
$631$	−11.1748	+	3.28121i	−0.444861	+	0.130623i	−0.496488	−	0.868043i	$-0.665377\pi$
$631$	−11.1748	+	3.28121i	−0.444861	+	0.130623i	0.0516271	+	0.998666i	$0.483559\pi$
$632$	13.5110	−	15.5925i	0.537437	−	0.620235i
$633$	−9.63123	+	11.1150i	−0.382807	+	0.441783i
$634$	21.6175	−	6.34747i	0.858541	−	0.252090i
$635$	−0.0685072	−	0.150010i	−0.00271863	−	0.00595296i
$636$	−6.55048	+	4.20974i	−0.259743	+	0.166927i
$637$	3.61469	+	1.06137i	0.143219	+	0.0420530i
$638$	0.500636	+	3.48200i	0.0198204	+	0.137854i
$639$	−2.60314	+	5.70009i	−0.102979	+	0.225492i
$640$	0.0108515	−	0.0754737i	0.000428943	−	0.00298336i
$641$	16.7053	+	10.7359i	0.659821	+	0.424041i	0.827243	−	0.561844i	$-0.189908\pi$
$641$	16.7053	+	10.7359i	0.659821	+	0.424041i	−0.167422	+	0.985885i	$0.553544\pi$
$642$	3.03188	+	3.49898i	0.119659	+	0.138094i
$643$	−13.5334			−0.533705			−0.266853	−	0.963737i	$-0.585984\pi$
$643$	−13.5334			−0.533705			−0.266853	+	0.963737i	$0.585984\pi$
$644$	6.28688	−	7.76264i	0.247738	−	0.305891i
$645$	11.6301			0.457934
$646$	26.1410	+	30.1683i	1.02850	+	1.18696i
$647$	−4.84456	−	3.11341i	−0.190459	−	0.122401i	0.441936	−	0.897047i	$-0.354292\pi$
$647$	−4.84456	−	3.11341i	−0.190459	−	0.122401i	−0.632395	+	0.774646i	$0.717928\pi$
$648$	−0.435550	+	3.02932i	−0.0171100	+	0.119003i
$649$	−14.6551	+	32.0902i	−0.575263	+	1.25965i
$650$	0.777364	+	5.40669i	0.0304907	+	0.212068i
$651$	−13.4981	−	3.96340i	−0.529032	−	0.155338i
$652$	10.4729	−	6.73052i	0.410150	−	0.263587i
$653$	−11.0950	−	24.2946i	−0.434180	−	0.950722i	−0.992630	−	0.121184i	$-0.961331\pi$
$653$	−11.0950	−	24.2946i	−0.434180	−	0.950722i	0.558450	−	0.829538i	$-0.311396\pi$
$654$	−3.07437	+	0.902716i	−0.120217	+	0.0352990i
$655$	−7.62418	+	8.79878i	−0.297902	+	0.343797i
$656$	3.37689	−	3.89714i	0.131845	−	0.152158i
$657$	−14.8384	+	4.35695i	−0.578902	+	0.169981i
$658$	9.68490	+	21.2070i	0.377557	+	0.826734i
$659$	0.630832	−	0.405411i	0.0245737	−	0.0157926i	−0.528296	−	0.849060i	$-0.677169\pi$
$659$	0.630832	−	0.405411i	0.0245737	−	0.0157926i	0.552870	+	0.833268i	$0.313533\pi$
$660$	2.47645	+	0.727151i	0.0963957	+	0.0283043i
$661$	0.269130	+	1.87184i	0.0104680	+	0.0728063i	0.994386	−	0.105815i	$-0.0337453\pi$
$661$	0.269130	+	1.87184i	0.0104680	+	0.0728063i	−0.983918	+	0.178622i	$0.942836\pi$
$662$	−3.48420	+	7.62933i	−0.135417	+	0.296522i
$663$	−3.17579	+	22.0881i	−0.123338	+	0.857832i
$664$	−36.7600	−	23.6242i	−1.42656	−	0.916796i
$665$	−13.7110	−	15.8234i	−0.531690	−	0.613604i
$666$	6.96997			0.270081
$667$	−0.550875	+	5.00870i	−0.0213300	+	0.193938i
$668$	−5.40523			−0.209135
$669$	−17.9526	−	20.7184i	−0.694088	−	0.801020i
$670$	6.37826	+	4.09906i	0.246414	+	0.158361i
$671$	5.29863	−	36.8528i	0.204551	−	1.42269i
$672$	4.51769	−	9.89235i	0.174274	−	0.381606i
$673$	−4.23121	−	29.4287i	−0.163101	−	1.13439i	−0.892744	−	0.450564i	$-0.851223\pi$
$673$	−4.23121	−	29.4287i	−0.163101	−	1.13439i	0.729643	−	0.683828i	$-0.239686\pi$
$674$	13.0714	+	3.83812i	0.503493	+	0.147839i
$675$	0.841254	−	0.540641i	0.0323799	−	0.0208093i
$676$	−4.34646	−	9.51742i	−0.167172	−	0.366055i
$677$	−3.60179	+	1.05758i	−0.138428	+	0.0406462i	−0.350213	−	0.936670i	$-0.613891\pi$
$677$	−3.60179	+	1.05758i	−0.138428	+	0.0406462i	0.211784	+	0.977316i	$0.432073\pi$
$678$	−12.0967	+	13.9603i	−0.464570	+	0.536143i
$679$	−19.0965	+	22.0386i	−0.732857	+	0.845762i
$680$	12.9606	−	3.80557i	0.497015	−	0.145937i
$681$	1.33220	+	2.91711i	0.0510500	+	0.111784i
$682$	−15.8434	+	10.1819i	−0.606674	+	0.389886i
$683$	−44.7511	−	13.1401i	−1.71236	−	0.502793i	−0.729004	−	0.684509i	$-0.760016\pi$
$683$	−44.7511	−	13.1401i	−1.71236	−	0.502793i	−0.983351	+	0.181717i	$0.941835\pi$
$684$	0.992239	+	6.90118i	0.0379392	+	0.263873i
$685$	1.25807	−	2.75479i	0.0480683	−	0.105255i
$686$	2.97821	−	20.7139i	0.113709	−	0.790860i
$687$	7.69043	+	4.94234i	0.293408	+	0.188562i
$688$	−12.4960	−	14.4212i	−0.476407	−	0.549803i
$689$	47.2713			1.80089
$690$	−4.44944	−	2.65470i	−0.169387	−	0.101063i
$691$	−39.2320			−1.49245			−0.746227	−	0.665692i	$-0.768137\pi$
$691$	−39.2320			−1.49245			−0.746227	+	0.665692i	$0.768137\pi$
$692$	3.40557	+	3.93024i	0.129460	+	0.149405i
$693$	6.52032	+	4.19036i	0.247687	+	0.159178i
$694$	4.48723	−	31.2093i	0.170333	−	1.18469i
$695$	−4.08716	+	8.94964i	−0.155035	+	0.339479i
$696$	0.457625	+	3.18285i	0.0173462	+	0.120646i
$697$	−13.3096	−	3.90805i	−0.504136	−	0.148028i
$698$	0.876735	−	0.563444i	0.0331849	−	0.0213267i
$699$	3.13375	+	6.86195i	0.118529	+	0.259543i
$700$	−1.99851	+	0.586816i	−0.0755367	+	0.0221796i
$701$	4.30521	−	4.96848i	0.162606	−	0.187657i	−0.668600	−	0.743623i	$-0.733106\pi$
$701$	4.30521	−	4.96848i	0.162606	−	0.187657i	0.831205	+	0.555966i	$0.187651\pi$
$702$	3.57704	−	4.12812i	0.135007	−	0.155806i
$703$	51.8223	−	15.2164i	1.95451	−	0.573897i
$704$	−10.2725	−	22.4937i	−0.387160	−	0.847762i
$705$	−7.25877	+	4.66493i	−0.273381	+	0.175691i
$706$	23.9575	+	7.03454i	0.901651	+	0.264748i
$707$	1.47942	+	10.2896i	0.0556393	+	0.386980i
$708$	−3.93833	+	8.62374i	−0.148011	+	0.324100i
$709$	−1.66976	+	11.6135i	−0.0627093	+	0.436153i	0.934145	+	0.356894i	$0.116164\pi$
$709$	−1.66976	+	11.6135i	−0.0627093	+	0.436153i	−0.996854	+	0.0792584i	$0.974745\pi$
$710$	−5.69522	−	3.66010i	−0.213738	−	0.137361i
$711$	4.41467	+	5.09480i	0.165563	+	0.191070i
$712$	−18.1690			−0.680911
$713$	−25.6167	+	8.45659i	−0.959353	+	0.316702i
$714$	11.9254			0.446296
$715$	−10.2610	−	11.8418i	−0.383739	−	0.442858i
$716$	−2.57646	−	1.65579i	−0.0962867	−	0.0618797i
$717$	−1.52835	+	10.6299i	−0.0570772	+	0.396980i
$718$	3.58756	−	7.85566i	0.133887	−	0.293171i
$719$	−1.47490	−	10.2581i	−0.0550044	−	0.382564i	−0.998665	−	0.0516500i	$-0.983552\pi$
$719$	−1.47490	−	10.2581i	−0.0550044	−	0.382564i	0.943661	−	0.330914i	$-0.107357\pi$
$720$	−1.57428	−	0.462250i	−0.0586700	−	0.0172271i
$721$	11.3067	−	7.26638i	0.421084	−	0.270614i
$722$	−22.9266	−	50.2022i	−0.853238	−	1.86833i
$723$	3.27407	−	0.961355i	0.121764	−	0.0357532i
$724$	6.46874	−	7.46533i	0.240409	−	0.277447i
$725$	0.688051	−	0.794054i	0.0255536	−	0.0294904i
$726$	−1.44680	+	0.424818i	−0.0536957	+	0.0157665i
$727$	14.1901	+	31.0721i	0.526283	+	1.15240i	0.967005	+	0.254756i	$0.0819950\pi$
$727$	14.1901	+	31.0721i	0.526283	+	1.15240i	−0.440722	+	0.897643i	$0.645278\pi$
$728$	−32.5560	+	20.9225i	−1.20661	+	0.775439i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	−2.37773	−	16.5375i	−0.0880039	−	0.612081i
$731$	−21.3236	+	46.6921i	−0.788681	+	1.72697i
$732$	1.42392	−	9.90360i	0.0526297	−	0.366048i
$733$	10.9298	+	7.02418i	0.403703	+	0.259444i	0.726699	−	0.686956i	$-0.241054\pi$
$733$	10.9298	+	7.02418i	0.403703	+	0.259444i	−0.322996	+	0.946400i	$0.604690\pi$
$734$	−11.0206	−	12.7184i	−0.406776	−	0.469444i
$735$	0.745113			0.0274839
$736$	−3.65252	−	20.5316i	−0.134634	−	0.756804i
$737$	−21.7491			−0.801137
$738$	2.22354	+	2.56610i	0.0818495	+	0.0944594i
$739$	−19.9072	−	12.7936i	−0.732298	−	0.470619i	0.120597	−	0.992701i	$-0.461519\pi$
$739$	−19.9072	−	12.7936i	−0.732298	−	0.470619i	−0.852895	+	0.522082i	$0.825155\pi$
$740$	0.764661	−	5.31833i	0.0281095	−	0.195506i
$741$	17.5833	−	38.5020i	0.645939	−	1.41441i
$742$	−3.59516	−	25.0049i	−0.131982	−	0.917958i
$743$	6.55913	+	1.92594i	0.240631	+	0.0706557i	0.399824	−	0.916592i	$-0.369071\pi$
$743$	6.55913	+	1.92594i	0.240631	+	0.0706557i	−0.159193	+	0.987247i	$0.550889\pi$
$744$	−14.4822	+	9.30717i	−0.530945	+	0.341217i
$745$	−6.69646	−	14.6632i	−0.245339	−	0.537218i
$746$	9.84605	−	2.89106i	0.360490	−	0.105849i
$747$	9.34995	−	10.7904i	0.342097	−	0.394801i
$748$	−7.45987	+	8.60915i	−0.272760	+	0.314782i
$749$	10.2837	−	3.01955i	0.375756	−	0.110332i
$750$	0.448797	+	0.982728i	0.0163877	+	0.0358841i
$751$	−31.1945	+	20.0475i	−1.13830	+	0.731544i	−0.967277	−	0.253723i	$-0.918345\pi$
$751$	−31.1945	+	20.0475i	−1.13830	+	0.731544i	−0.171027	+	0.985266i	$0.554709\pi$
$752$	13.5837	+	3.98853i	0.495346	+	0.145447i
$753$	−3.70177	−	25.7464i	−0.134900	−	0.938251i
$754$	2.38412	−	5.22050i	0.0868246	−	0.190119i
$755$	−0.726865	+	5.05546i	−0.0264533	+	0.183987i
$756$	1.75223	+	1.12609i	0.0637281	+	0.0409556i
$757$	−27.4880	−	31.7228i	−0.999067	−	1.15299i	−0.988219	−	0.153044i	$-0.951092\pi$
$757$	−27.4880	−	31.7228i	−0.999067	−	1.15299i	−0.0108479	−	0.999941i	$-0.503453\pi$
$758$	−34.0835			−1.23797
$759$	14.8544	−	0.494187i	0.539182	−	0.0179378i
$760$	−25.6212			−0.929377
$761$	−12.2467	−	14.1335i	−0.443944	−	0.512338i	0.489038	−	0.872263i	$-0.337348\pi$
$761$	−12.2467	−	14.1335i	−0.443944	−	0.512338i	−0.932982	+	0.359924i	$0.882803\pi$
$762$	−0.149882	−	0.0963231i	−0.00542964	−	0.00348942i
$763$	−1.05562	+	7.34198i	−0.0382159	+	0.265798i
$764$	2.25503	−	4.93784i	0.0815843	−	0.178645i
$765$	0.628124	+	4.36869i	0.0227099	+	0.157950i
$766$	20.3798	+	5.98405i	0.736352	+	0.216213i
$767$	48.4182	−	31.1165i	1.74828	−	1.12355i
$768$	−6.66362	−	14.5913i	−0.240453	−	0.526518i
$769$	−47.7352	+	14.0163i	−1.72138	+	0.505442i	−0.985209	−	0.171357i	$-0.945185\pi$
$769$	−47.7352	+	14.0163i	−1.72138	+	0.505442i	−0.736168	+	0.676799i	$0.763367\pi$
$770$	−5.48351	+	6.32831i	−0.197612	+	0.228056i
$771$	−11.4976	+	13.2690i	−0.414077	+	0.477870i
$772$	−5.71567	+	1.67827i	−0.205711	+	0.0604023i
$773$	−2.06267	−	4.51662i	−0.0741891	−	0.162451i	0.868904	−	0.494981i	$-0.164825\pi$
$773$	−2.06267	−	4.51662i	−0.0741891	−	0.162451i	−0.943093	+	0.332530i	$0.892098\pi$
$774$	10.5701	−	6.79297i	0.379933	−	0.244168i
$775$	5.39713	+	1.58474i	0.193871	+	0.0569256i
$776$	5.07847	+	35.3216i	0.182307	+	1.26797i
$777$	6.70279	−	14.6771i	0.240461	−	0.526536i
$778$	−2.28201	+	15.8717i	−0.0818139	+	0.569028i
$779$	22.1343	+	14.2248i	0.793044	+	0.509658i
$780$	−2.75747	−	3.18229i	−0.0987334	−	0.113944i
$781$	19.4200			0.694901
$782$	18.8160	−	12.9961i	0.672858	−	0.464741i
$783$	−1.05068			−0.0375484
$784$	−0.800592	−	0.923932i	−0.0285926	−	0.0329976i
$785$	5.39782	+	3.46897i	0.192656	+	0.123813i
$786$	−1.79004	+	12.4500i	−0.0638485	+	0.444076i
$787$	−0.556856	+	1.21935i	−0.0198498	+	0.0434650i	−0.919297	−	0.393564i	$-0.871242\pi$
$787$	−0.556856	+	1.21935i	−0.0198498	+	0.0434650i	0.899447	+	0.437029i	$0.143969\pi$
$788$	−0.339156	−	2.35888i	−0.0120819	−	0.0840318i
$789$	19.9893	+	5.86940i	0.711639	+	0.208956i
$790$	−6.12694	+	3.93755i	−0.217987	+	0.140092i
$791$	17.7640	+	38.8978i	0.631617	+	1.38305i
$792$	9.10043	−	2.67213i	0.323370	−	0.0949499i
$793$	−39.7774	+	45.9056i	−1.41254	+	1.63016i
$794$	−3.73127	+	4.30611i	−0.132418	+	0.152818i
$795$	8.97083	−	2.63407i	0.318162	−	0.0934209i
$796$	−2.01109	−	4.40366i	−0.0712810	−	0.156084i
$797$	4.56531	−	2.93395i	0.161712	−	0.103926i	−0.457282	−	0.889322i	$-0.651177\pi$
$797$	4.56531	−	2.93395i	0.161712	−	0.103926i	0.618994	+	0.785396i	$0.287541\pi$
$798$	−21.7035	−	6.37273i	−0.768296	−	0.225592i
$799$	−5.41977	−	37.6953i	−0.191738	−	1.33357i
$800$	−1.80637	+	3.95539i	−0.0638648	+	0.139844i
$801$	0.844875	−	5.87624i	0.0298522	−	0.207627i
$802$	−6.56055	−	4.21621i	−0.231661	−	0.148880i
$803$	31.3854	+	36.2206i	1.10757	+	1.27820i
$804$	−5.84472			−0.206127
$805$	−9.86902	+	6.81651i	−0.347837	+	0.240250i
$806$	30.7253			1.08225
$807$	3.09541	+	3.57230i	0.108964	+	0.125751i
$808$	10.7015	+	6.87746i	0.376479	+	0.241948i
$809$	−0.200280	+	1.39298i	−0.00704147	+	0.0489745i	−0.993039	−	0.117784i	$-0.962421\pi$
$809$	−0.200280	+	1.39298i	−0.00704147	+	0.0489745i	0.985998	+	0.166759i	$0.0533300\pi$
$810$	0.448797	−	0.982728i	0.0157691	−	0.0345295i
$811$	−3.44276	−	23.9449i	−0.120892	−	0.840820i	−0.956550	−	0.291570i	$-0.905822\pi$
$811$	−3.44276	−	23.9449i	−0.120892	−	0.840820i	0.835658	−	0.549250i	$-0.185087\pi$
$812$	2.09980	+	0.616558i	0.0736887	+	0.0216370i
$813$	−18.2465	+	11.7263i	−0.639931	+	0.411259i
$814$	−8.97316	−	19.6485i	−0.314509	−	0.688679i
$815$	−14.3425	+	4.21135i	−0.502397	+	0.147517i
$816$	4.74224	−	5.47284i	0.166012	−	0.191588i
$817$	63.7592	−	73.5821i	2.23065	−	2.57431i
$818$	−9.76752	+	2.86800i	−0.341513	+	0.100277i
$819$	−5.25290	−	11.5022i	−0.183551	−	0.401921i
$820$	2.20196	−	1.41512i	0.0768959	−	0.0494180i
$821$	−4.53985	−	1.33302i	−0.158442	−	0.0465227i	0.201550	−	0.979478i	$-0.435402\pi$
$821$	−4.53985	−	1.33302i	−0.158442	−	0.0465227i	−0.359991	+	0.932956i	$0.617220\pi$
$822$	−0.465629	−	3.23852i	−0.0162407	−	0.112956i
$823$	−0.223106	+	0.488535i	−0.00777700	+	0.0170292i	−0.913481	−	0.406882i	$-0.866616\pi$
$823$	−0.223106	+	0.488535i	−0.00777700	+	0.0170292i	0.905704	+	0.423911i	$0.139343\pi$
$824$	2.34065	−	16.2796i	0.0815406	−	0.567127i
$825$	−2.60711	−	1.67549i	−0.0907679	−	0.0583330i
$826$	−20.1419	−	23.2450i	−0.700826	−	0.808797i
$827$	−17.4962			−0.608401			−0.304200	−	0.952608i	$-0.598389\pi$
$827$	−17.4962			−0.608401			−0.304200	+	0.952608i	$0.598389\pi$
$828$	3.99189	−	0.132805i	0.138728	−	0.00461529i
$829$	10.9294			0.379594			0.189797	−	0.981823i	$-0.439217\pi$
$829$	10.9294			0.379594			0.189797	+	0.981823i	$0.439217\pi$
$830$	10.1013	+	11.6575i	0.350621	+	0.404638i
$831$	7.80317	+	5.01480i	0.270689	+	0.173961i
$832$	−5.74142	+	39.9325i	−0.199048	+	1.38441i
$833$	−1.36615	+	2.99146i	−0.0473344	+	0.103648i
$834$	1.51272	+	10.5212i	0.0523811	+	0.364318i
$835$	6.22731	+	1.82850i	0.215505	+	0.0632780i
$836$	18.1771	−	11.6817i	0.628670	−	0.404021i
$837$	−2.33670	−	5.11666i	−0.0807682	−	0.176858i
$838$	22.4581	−	6.59428i	0.775801	−	0.227796i
$839$	17.6786	−	20.4022i	0.610335	−	0.704364i	−0.363507	−	0.931591i	$-0.618421\pi$
$839$	17.6786	−	20.4022i	0.610335	−	0.704364i	0.973842	+	0.227228i	$0.0729662\pi$
$840$	−5.01241	+	5.78463i	−0.172944	+	0.199589i
$841$	26.7661	−	7.85923i	0.922968	−	0.271008i
$842$	10.0542	+	22.0157i	0.346492	+	0.758712i
$843$	1.89355	−	1.21691i	0.0652172	−	0.0419125i
$844$	11.7525	+	3.45084i	0.404538	+	0.118783i
$845$	1.78792	+	12.4353i	0.0615064	+	0.427786i
$846$	−3.87245	+	8.47948i	−0.133137	+	0.291530i
$847$	−0.496774	+	3.45514i	−0.0170693	+	0.118720i
$848$	−12.9050	−	8.29353i	−0.443159	−	0.284801i
$849$	7.01989	+	8.10139i	0.240922	+	0.278039i
$850$	−4.76829			−0.163551
$851$	−5.41917	−	30.4622i	−0.185767	−	1.04423i
$852$	5.21881			0.178793
$853$	18.3304	+	21.1544i	0.627620	+	0.724312i	0.977135	−	0.212618i	$-0.0681991\pi$
$853$	18.3304	+	21.1544i	0.627620	+	0.724312i	−0.349515	+	0.936931i	$0.613654\pi$
$854$	27.3077	+	17.5496i	0.934450	+	0.600534i
$855$	1.19141	−	8.28644i	0.0407454	−	0.283390i
$856$	5.44836	−	11.9302i	0.186221	−	0.407767i
$857$	3.79427	+	26.3897i	0.129610	+	0.901456i	0.946049	+	0.324024i	$0.105036\pi$
$857$	3.79427	+	26.3897i	0.129610	+	0.901456i	−0.816439	+	0.577432i	$0.804055\pi$
$858$	−16.2423	−	4.76918i	−0.554504	−	0.162817i
$859$	−6.81391	+	4.37903i	−0.232487	+	0.149411i	−0.651698	−	0.758478i	$-0.725943\pi$
$859$	−6.81391	+	4.37903i	−0.232487	+	0.149411i	0.419211	+	0.907889i	$0.362307\pi$
$860$	−4.02365	−	8.81057i	−0.137205	−	0.300438i
$861$	7.54188	−	2.21449i	0.257026	−	0.0754698i
$862$	2.76658	−	3.19281i	0.0942302	−	0.108747i
$863$	12.5323	−	14.4630i	0.426604	−	0.492328i	−0.501233	−	0.865312i	$-0.667120\pi$
$863$	12.5323	−	14.4630i	0.426604	−	0.492328i	0.927838	+	0.372985i	$0.121666\pi$
$864$	4.17221	−	1.22507i	0.141941	−	0.0416777i
$865$	−2.59399	−	5.68004i	−0.0881983	−	0.193127i
$866$	3.62997	−	2.33284i	0.123351	−	0.0792731i
$867$	−2.37958	−	0.698706i	−0.0808146	−	0.0237293i
$868$	1.66739	+	11.5969i	0.0565948	+	0.393625i
$869$	8.67889	−	19.0041i	0.294411	−	0.644671i
$870$	0.161544	−	1.12356i	0.00547684	−	0.0380923i
$871$	29.8499	+	19.1833i	1.01142	+	0.650003i
$872$	5.94406	+	6.85981i	0.201291	+	0.232303i
$873$	−11.6599			−0.394628
$874$	−41.1889	+	13.5973i	−1.39324	+	0.459935i
$875$	2.50098			0.0845485
$876$	8.43432	+	9.73372i	0.284969	+	0.328872i
$877$	−12.6924	−	8.15690i	−0.428592	−	0.275439i	0.308510	−	0.951221i	$-0.400170\pi$
$877$	−12.6924	−	8.15690i	−0.428592	−	0.275439i	−0.737101	+	0.675782i	$0.763806\pi$
$878$	−4.43439	+	30.8418i	−0.149653	+	1.04086i
$879$	7.00258	−	15.3335i	0.236191	−	0.517187i
$880$	0.723640	+	5.03303i	0.0243939	+	0.169663i
$881$	−31.1776	−	9.15456i	−1.05040	−	0.308425i	−0.289420	−	0.957202i	$-0.593463\pi$
$881$	−31.1776	−	9.15456i	−1.05040	−	0.308425i	−0.760978	+	0.648777i	$0.775281\pi$
$882$	0.677199	−	0.435210i	0.0228025	−	0.0146543i
$883$	−2.55962	−	5.60479i	−0.0861381	−	0.188616i	0.861661	−	0.507484i	$-0.169425\pi$
$883$	−2.55962	−	5.60479i	−0.0861381	−	0.188616i	−0.947799	+	0.318868i	$0.896697\pi$
$884$	17.8320	−	5.23594i	0.599754	−	0.176104i
$885$	7.45458	−	8.60305i	0.250583	−	0.289188i
$886$	23.9816	−	27.6763i	0.805678	−	0.929802i
$887$	−4.03127	+	1.18369i	−0.135357	+	0.0397443i	−0.348709	−	0.937231i	$-0.613380\pi$
$887$	−4.03127	+	1.18369i	−0.135357	+	0.0397443i	0.213353	+	0.976975i	$0.431562\pi$
$888$	−8.20226	−	17.9604i	−0.275250	−	0.602713i
$889$	−0.346969	+	0.222984i	−0.0116370	+	0.00747863i
$890$	6.15392	+	1.80695i	0.206280	+	0.0605692i
$891$	0.441045	+	3.06753i	0.0147756	+	0.102766i
$892$	−9.48454	+	20.7682i	−0.317566	+	0.695372i
$893$	−10.2801	+	71.4996i	−0.344010	+	2.39264i
$894$	−14.6507	−	9.41541i	−0.489991	−	0.314898i
$895$	2.40818	+	2.77919i	0.0804967	+	0.0928981i
$896$	−0.190699			−0.00637081
$897$	−20.8231	−	12.4238i	−0.695263	−	0.414819i
$898$	−35.6730			−1.19042
$899$	−3.87028	−	4.46654i	−0.129081	−	0.148967i
$900$	−0.700619	−	0.450261i	−0.0233540	−	0.0150087i
$901$	−5.87267	+	40.8453i	−0.195647	+	1.36076i
$902$	4.37129	−	9.57179i	0.145548	−	0.318706i
$903$	−4.13945	−	28.7905i	−0.137752	−	0.958089i
$904$	50.2087	+	14.7426i	1.66992	+	0.490332i
$905$	−9.97798	+	6.41246i	−0.331679	+	0.213157i
$906$	2.29220	+	5.01923i	0.0761534	+	0.166753i
$907$	9.20830	−	2.70380i	0.305757	−	0.0897782i	−0.125255	−	0.992125i	$-0.539975\pi$
$907$	9.20830	−	2.70380i	0.305757	−	0.0897782i	0.431012	+	0.902346i	$0.358157\pi$
$908$	1.74901	−	2.01846i	0.0580428	−	0.0669850i
$909$	−2.72195	+	3.14130i	−0.0902815	+	0.104190i
$910$	13.1077	−	3.84876i	0.434516	−	0.127585i
$911$	−2.13404	−	4.67291i	−0.0707040	−	0.154820i	0.870980	−	0.491318i	$-0.163485\pi$
$911$	−2.13404	−	4.67291i	−0.0707040	−	0.154820i	−0.941684	+	0.336498i	$0.890757\pi$
$912$	−11.5552	+	7.42609i	−0.382631	+	0.245902i
$913$	−42.4556	−	12.4661i	−1.40507	−	0.412567i
$914$	4.29991	+	29.9065i	0.142228	+	0.989219i
$915$	−4.99072	+	10.9281i	−0.164988	+	0.361273i
$916$	1.08350	−	7.53591i	0.0357999	−	0.248994i
$917$	24.4952	+	15.7421i	0.808903	+	0.519850i
$918$	3.12256	+	3.60363i	0.103060	+	0.118938i
$919$	36.9375			1.21846			0.609228	−	0.792995i	$-0.291479\pi$
$919$	36.9375			1.21846			0.609228	+	0.792995i	$0.291479\pi$
$920$	−1.60461	+	14.5895i	−0.0529023	+	0.481002i
$921$	−8.01764			−0.264190
$922$	23.6425	+	27.2849i	0.778624	+	0.898580i
$923$	−26.6532	−	17.1290i	−0.877302	−	0.563808i
$924$	0.918645	−	6.38931i	0.0302212	−	0.210193i
$925$	−2.68007	+	5.86853i	−0.0881201	+	0.192956i
$926$	2.56193	+	17.8186i	0.0841901	+	0.585555i
$927$	5.15634	+	1.51404i	0.169356	+	0.0497275i
$928$	3.84347	−	2.47005i	0.126168	−	0.0810832i
$929$	4.82155	+	10.5577i	0.158190	+	0.346388i	0.972087	−	0.234622i	$-0.0753852\pi$
$929$	4.82155	+	10.5577i	0.158190	+	0.346388i	−0.813897	+	0.581009i	$0.802658\pi$
$930$	5.83083	−	1.71209i	0.191200	−	0.0561415i
$931$	4.08491	−	4.71423i	0.133877	−	0.154503i
$932$	4.11421	−	4.74805i	0.134765	−	0.155528i
$933$	0.257256	−	0.0755373i	0.00842219	−	0.00247298i
$934$	−6.96761	−	15.2569i	−0.227987	−	0.499222i
$935$	11.5068	−	7.39496i	0.376312	−	0.241841i
$936$	−14.8469	−	4.35945i	−0.485287	−	0.142493i
$937$	3.71658	+	25.8494i	0.121415	+	0.844462i	0.955955	+	0.293514i	$0.0948248\pi$
$937$	3.71658	+	25.8494i	0.121415	+	0.844462i	−0.834539	+	0.550948i	$0.814266\pi$
$938$	7.87712	−	17.2485i	0.257197	−	0.563183i
$939$	0.388249	−	2.70033i	0.0126700	−	0.0881219i
$940$	6.04530	+	3.88508i	0.197176	+	0.126717i
$941$	33.3734	+	38.5150i	1.08794	+	1.25555i	0.964750	+	0.263169i	$0.0847677\pi$
$941$	33.3734	+	38.5150i	1.08794	+	1.25555i	0.123192	+	0.992383i	$0.460687\pi$
$942$	6.93200			0.225857
$943$	9.48632	−	11.7131i	0.308917	−	0.381431i
$944$	−18.6773			−0.607895
$945$	−1.63779	−	1.89011i	−0.0532774	−	0.0614854i
$946$	−32.7574	−	21.0519i	−1.06504	−	0.684457i
$947$	−5.79275	+	40.2895i	−0.188239	+	1.30923i	0.648325	+	0.761363i	$0.275470\pi$
$947$	−5.79275	+	40.2895i	−0.188239	+	1.30923i	−0.836565	+	0.547868i	$0.815439\pi$
$948$	2.33231	−	5.10706i	0.0757500	−	0.165869i
$949$	−11.1276	−	77.3944i	−0.361218	−	2.51233i
$950$	8.67801	+	2.54809i	0.281552	+	0.0826711i
$951$	17.5438	−	11.2747i	0.568896	−	0.365607i
$952$	−14.0338	−	30.7297i	−0.454837	−	0.995954i
$953$	−2.50773	+	0.736335i	−0.0812332	+	0.0238522i	−0.322097	−	0.946707i	$-0.604388\pi$
$953$	−2.50773	+	0.736335i	−0.0812332	+	0.0238522i	0.240863	+	0.970559i	$0.422569\pi$
$954$	6.61465	−	7.63372i	0.214157	−	0.247151i
$955$	−4.26839	+	4.92599i	−0.138122	+	0.159401i
$956$	8.58161	−	2.51979i	0.277549	−	0.0814958i
$957$	1.35265	+	2.96190i	0.0437251	+	0.0957446i
$958$	28.6753	−	18.4285i	0.926457	−	0.595398i
$959$	−7.26731	−	2.13387i	−0.234674	−	0.0689064i
$960$	1.13557	+	7.89803i	0.0366502	+	0.254908i
$961$	0.266042	−	0.582550i	0.00858199	−	0.0187919i
$962$	−5.01520	+	34.8815i	−0.161697	+	1.12462i
$963$	3.60514	+	2.31689i	0.116174	+	0.0746606i
$964$	−1.86102	−	2.14773i	−0.0599394	−	0.0691738i
$965$	7.15270			0.230253
$966$	−4.98809	+	11.9596i	−0.160489	+	0.384793i
$967$	−18.2175			−0.585834			−0.292917	−	0.956138i	$-0.594626\pi$
$967$	−18.2175			−0.585834			−0.292917	+	0.956138i	$0.594626\pi$
$968$	2.79728	+	3.22823i	0.0899078	+	0.103759i
$969$	31.0837	+	19.9763i	0.998552	+	0.641731i
$970$	1.79272	−	12.4687i	0.0575609	−	0.400345i
$971$	−6.86379	+	15.0296i	−0.220269	+	0.482323i	−0.987216	−	0.159388i	$-0.949048\pi$
$971$	−6.86379	+	15.0296i	−0.220269	+	0.482323i	0.766947	+	0.641711i	$0.221775\pi$
$972$	0.118524	+	0.824351i	0.00380165	+	0.0264411i
$973$	23.6097	+	6.93245i	0.756894	+	0.222244i
$974$	26.0433	−	16.7370i	0.834483	−	0.536289i
$975$	2.10034	+	4.59910i	0.0672647	+	0.147289i
$976$	18.9131	−	5.55339i	0.605394	−	0.177760i
$977$	−20.6690	+	23.8533i	−0.661261	+	0.763136i	−0.982983	−	0.183698i	$-0.941193\pi$
$977$	−20.6690	+	23.8533i	−0.661261	+	0.763136i	0.321722	+	0.946834i	$0.395739\pi$
$978$	−10.5755	+	12.2048i	−0.338167	+	0.390266i
$979$	−17.6529	+	5.18337i	−0.564190	+	0.165661i
$980$	−0.257786	−	0.564473i	−0.00823468	−	0.0180314i
$981$	−2.49502	+	1.60345i	−0.0796598	+	0.0511942i
$982$	10.9554	+	3.21679i	0.349600	+	0.102652i
$983$	2.15677	+	15.0006i	0.0687902	+	0.478446i	0.994874	+	0.101127i	$0.0322449\pi$
$983$	2.15677	+	15.0006i	0.0687902	+	0.478446i	−0.926083	+	0.377319i	$0.876846\pi$
$984$	3.99574	−	8.74946i	0.127380	−	0.278923i
$985$	−0.407235	+	2.83238i	−0.0129756	+	0.0902471i
$986$	4.21465	+	2.70859i	0.134222	+	0.0862590i
$987$	14.1317	+	16.3089i	0.449817	+	0.519117i
$988$	−35.2512			−1.12149
$989$	−37.9069	−	40.9149i	−1.20537	−	1.30102i
$990$	−3.34811			−0.106410
$991$	−16.9186	−	19.5251i	−0.537436	−	0.620234i	0.420474	−	0.907305i	$-0.361864\pi$
$991$	−16.9186	−	19.5251i	−0.537436	−	0.620234i	−0.957909	+	0.287071i	$0.907318\pi$
$992$	20.5765	+	13.2237i	0.653305	+	0.419854i
$993$	−1.10485	+	7.68440i	−0.0350614	+	0.243857i
$994$	−7.03356	+	15.4014i	−0.223091	+	0.488501i
$995$	0.827262	+	5.75374i	0.0262260	+	0.182406i
$996$	−11.4093	−	3.35006i	−0.361516	−	0.106151i
$997$	47.8504	−	30.7516i	1.51544	−	0.973912i	0.522844	−	0.852428i	$-0.324871\pi$
$997$	47.8504	−	30.7516i	1.51544	−	0.973912i	0.992593	−	0.121484i	$-0.0387654\pi$
$998$	15.5521	+	34.0544i	0.492294	+	1.07797i
$999$	6.19021	−	1.81761i	0.195850	−	0.0575066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.m.c.151.4	yes	50
23.4	even	11		7935.2.a.bv.1.8		25
23.16	even	11	inner	345.2.m.c.16.4	✓	50
23.19	odd	22		7935.2.a.bw.1.8		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.c.16.4	✓	50	23.16	even	11	inner
345.2.m.c.151.4	yes	50	1.1	even	1	trivial
7935.2.a.bv.1.8		25	23.4	even	11
7935.2.a.bw.1.8		25	23.19	odd	22

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:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707484 + 0.816480i) q^{2} +(0.841254 + 0.540641i) q^{3} +(0.118524 - 0.824351i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(0.153751 + 1.06936i) q^{6} +(2.39967 + 0.704607i) q^{7} +(2.57463 - 1.65461i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.707484 + 0.816480i) q^{2} +(0.841254 + 0.540641i) q^{3} +(0.118524 - 0.824351i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(0.153751 + 1.06936i) q^{6} +(2.39967 + 0.704607i) q^{7} +(2.57463 - 1.65461i) q^{8} +(0.415415 + 0.909632i) q^{9} +(-1.03660 + 0.304372i) q^{10} +(2.02946 - 2.34213i) q^{11} +(0.545386 - 0.629409i) q^{12} +(-4.85120 + 1.42444i) q^{13} +(1.12243 + 2.45778i) q^{14} +(-0.841254 + 0.540641i) q^{15} +(1.57428 + 0.462250i) q^{16} +(-0.628124 - 4.36869i) q^{17} +(-0.448797 + 0.982728i) q^{18} +(-1.19141 + 8.28644i) q^{19} +(0.700619 + 0.450261i) q^{20} +(1.63779 + 1.89011i) q^{21} +3.34811 q^{22} +(4.64395 + 1.19739i) q^{23} +3.06047 q^{24} +(-0.654861 - 0.755750i) q^{25} +(-4.59517 - 2.95314i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(0.865261 - 1.89466i) q^{28} +(0.149528 + 1.03999i) q^{29} +(-1.03660 - 0.304372i) q^{30} +(-4.73204 + 3.04109i) q^{31} +(-1.80637 - 3.95539i) q^{32} +(2.97354 - 0.873111i) q^{33} +(3.12256 - 3.60363i) q^{34} +(-1.63779 + 1.89011i) q^{35} +(0.799093 - 0.234635i) q^{36} +(-2.68007 - 5.86853i) q^{37} +(-7.60861 + 4.88976i) q^{38} +(-4.85120 - 1.42444i) q^{39} +(0.435550 + 3.02932i) q^{40} +(1.30560 - 2.85886i) q^{41} +(-0.384527 + 2.67445i) q^{42} +(-9.78386 - 6.28770i) q^{43} +(-1.69019 - 1.95059i) q^{44} -1.00000 q^{45} +(2.30787 + 4.63882i) q^{46} +8.62851 q^{47} +(1.07446 + 1.23999i) q^{48} +(-0.626829 - 0.402839i) q^{49} +(0.153751 - 1.06936i) q^{50} +(1.83348 - 4.01477i) q^{51} +(0.599256 + 4.16792i) q^{52} +(-8.97083 - 2.63407i) q^{53} +(-0.908854 + 0.584085i) q^{54} +(1.28740 + 2.81902i) q^{55} +(7.34411 - 2.15643i) q^{56} +(-5.48226 + 6.32687i) q^{57} +(-0.743341 + 0.857862i) q^{58} +(-10.9224 + 3.20709i) q^{59} +(0.345969 + 0.757567i) q^{60} +(10.1067 - 6.49516i) q^{61} +(-5.83083 - 1.71209i) q^{62} +(0.355926 + 2.47552i) q^{63} +(3.31470 - 7.25818i) q^{64} +(0.719544 - 5.00454i) q^{65} +(2.81661 + 1.81013i) q^{66} +(-4.59576 - 5.30379i) q^{67} -3.67579 q^{68} +(3.25938 + 3.51802i) q^{69} -2.70195 q^{70} +(4.10360 + 4.73581i) q^{71} +(2.57463 + 1.65461i) q^{72} +(-2.20088 + 15.3074i) q^{73} +(2.89543 - 6.34011i) q^{74} +(-0.142315 - 0.989821i) q^{75} +(6.68972 + 1.96428i) q^{76} +(6.52032 - 4.19036i) q^{77} +(-2.26912 - 4.96867i) q^{78} +(6.46832 - 1.89927i) q^{79} +(-1.07446 + 1.23999i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(3.25789 - 0.956604i) q^{82} +(-5.93120 - 12.9875i) q^{83} +(1.75223 - 1.12609i) q^{84} +(4.23484 + 1.24346i) q^{85} +(-1.78814 - 12.4368i) q^{86} +(-0.436470 + 0.955735i) q^{87} +(1.34980 - 9.38808i) q^{88} +(-4.99424 - 3.20960i) q^{89} +(-0.707484 - 0.816480i) q^{90} -12.6449 q^{91} +(1.53749 - 3.68632i) q^{92} -5.62498 q^{93} +(6.10453 + 7.04500i) q^{94} +(-7.04268 - 4.52606i) q^{95} +(0.618834 - 4.30409i) q^{96} +(-4.84371 + 10.6062i) q^{97} +(-0.114562 - 0.796795i) q^{98} +(2.97354 + 0.873111i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9}+O(q^{10}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9} + 15 q^{11} - 4 q^{12} - 19 q^{13} + 55 q^{14} + 5 q^{15} + 12 q^{16} + 5 q^{17} - 11 q^{19} + 4 q^{20} + 8 q^{21} - 18 q^{22} + 14 q^{23} + 66 q^{24} - 5 q^{25} - 18 q^{26} - 5 q^{27} + 10 q^{28} - 22 q^{29} + 6 q^{31} + 33 q^{32} + 4 q^{33} + 18 q^{34} - 8 q^{35} - 15 q^{36} + 25 q^{37} - 97 q^{38} - 19 q^{39} + 22 q^{40} - 42 q^{41} - 11 q^{42} - 25 q^{43} + 25 q^{44} - 50 q^{45} - 44 q^{46} + 86 q^{47} - 10 q^{48} - 8 q^{49} - 11 q^{50} - 17 q^{51} - 67 q^{52} - 26 q^{53} - 4 q^{55} - 132 q^{56} + 22 q^{57} + 8 q^{58} - 76 q^{59} + 4 q^{60} + 13 q^{61} - 8 q^{62} + 8 q^{63} + 76 q^{64} + 8 q^{65} + 4 q^{66} + 84 q^{67} + 66 q^{68} + 25 q^{69} + 22 q^{70} + 55 q^{71} - 59 q^{73} + 17 q^{74} - 5 q^{75} + 82 q^{76} - 56 q^{77} - 7 q^{78} + 7 q^{79} + 10 q^{80} - 5 q^{81} - 150 q^{82} + 19 q^{83} + 10 q^{84} + 6 q^{85} + 44 q^{86} - 11 q^{87} - 62 q^{88} - 74 q^{89} - 56 q^{91} + 41 q^{92} + 28 q^{93} - 161 q^{94} + 11 q^{95} - 44 q^{96} - 68 q^{97} - 198 q^{98} + 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9 + 15 * q^11 - 4 * q^12 - 19 * q^13 + 55 * q^14 + 5 * q^15 + 12 * q^16 + 5 * q^17 - 11 * q^19 + 4 * q^20 + 8 * q^21 - 18 * q^22 + 14 * q^23 + 66 * q^24 - 5 * q^25 - 18 * q^26 - 5 * q^27 + 10 * q^28 - 22 * q^29 + 6 * q^31 + 33 * q^32 + 4 * q^33 + 18 * q^34 - 8 * q^35 - 15 * q^36 + 25 * q^37 - 97 * q^38 - 19 * q^39 + 22 * q^40 - 42 * q^41 - 11 * q^42 - 25 * q^43 + 25 * q^44 - 50 * q^45 - 44 * q^46 + 86 * q^47 - 10 * q^48 - 8 * q^49 - 11 * q^50 - 17 * q^51 - 67 * q^52 - 26 * q^53 - 4 * q^55 - 132 * q^56 + 22 * q^57 + 8 * q^58 - 76 * q^59 + 4 * q^60 + 13 * q^61 - 8 * q^62 + 8 * q^63 + 76 * q^64 + 8 * q^65 + 4 * q^66 + 84 * q^67 + 66 * q^68 + 25 * q^69 + 22 * q^70 + 55 * q^71 - 59 * q^73 + 17 * q^74 - 5 * q^75 + 82 * q^76 - 56 * q^77 - 7 * q^78 + 7 * q^79 + 10 * q^80 - 5 * q^81 - 150 * q^82 + 19 * q^83 + 10 * q^84 + 6 * q^85 + 44 * q^86 - 11 * q^87 - 62 * q^88 - 74 * q^89 - 56 * q^91 + 41 * q^92 + 28 * q^93 - 161 * q^94 + 11 * q^95 - 44 * q^96 - 68 * q^97 - 198 * q^98 + 4 * q^99

Introduction

L-functions

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