LMFDB - Embedded newform 690.2.r.a.169.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(49,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 16]))

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

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

chi := DirichletCharacter("690.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.r (of order $22$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			169.7
Character	$\chi$	$=$	690.169
Dual form			690.2.r.a.49.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.989821 + 0.142315i) q^{2} +(0.909632 - 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(-1.51343 - 1.64607i) q^{5} +(0.959493 - 0.281733i) q^{6} +(0.692568 - 1.07766i) q^{7} +(0.909632 + 0.415415i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(0.989821 + 0.142315i) q^{2} +(0.909632 - 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(-1.51343 - 1.64607i) q^{5} +(0.959493 - 0.281733i) q^{6} +(0.692568 - 1.07766i) q^{7} +(0.909632 + 0.415415i) q^{8} +(0.654861 - 0.755750i) q^{9} +(-1.26376 - 1.84470i) q^{10} +(-0.442419 - 3.07709i) q^{11} +(0.989821 - 0.142315i) q^{12} +(-0.352273 - 0.548147i) q^{13} +(0.838885 - 0.968125i) q^{14} +(-2.06046 - 0.868614i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-0.722927 - 2.46206i) q^{17} +(0.755750 - 0.654861i) q^{18} +(0.879007 + 0.258100i) q^{19} +(-0.988373 - 2.00577i) q^{20} +(0.182307 - 1.26797i) q^{21} -3.10873i q^{22} +(4.62306 - 1.27568i) q^{23} +1.00000 q^{24} +(-0.419071 + 4.98241i) q^{25} +(-0.270678 - 0.592702i) q^{26} +(0.281733 - 0.959493i) q^{27} +(0.968125 - 0.838885i) q^{28} +(1.09111 - 0.320379i) q^{29} +(-1.91587 - 1.15301i) q^{30} +(-2.37387 + 5.19805i) q^{31} +(0.755750 + 0.654861i) q^{32} +(-1.68071 - 2.61523i) q^{33} +(-0.365181 - 2.53989i) q^{34} +(-2.82205 + 0.490943i) q^{35} +(0.841254 - 0.540641i) q^{36} +(-0.366219 - 0.317331i) q^{37} +(0.833329 + 0.380568i) q^{38} +(-0.548147 - 0.352273i) q^{39} +(-0.692862 - 2.12602i) q^{40} +(0.536349 + 0.618979i) q^{41} +(0.360903 - 1.22912i) q^{42} +(6.44417 - 2.94295i) q^{43} +(0.442419 - 3.07709i) q^{44} +(-2.23510 + 0.0658281i) q^{45} +(4.75755 - 0.604762i) q^{46} -1.67106i q^{47} +(0.989821 + 0.142315i) q^{48} +(2.22621 + 4.87472i) q^{49} +(-1.12388 + 4.87205i) q^{50} +(-1.68038 - 1.93926i) q^{51} +(-0.183572 - 0.625190i) q^{52} +(2.43574 - 3.79009i) q^{53} +(0.415415 - 0.909632i) q^{54} +(-4.39553 + 5.38521i) q^{55} +(1.07766 - 0.692568i) q^{56} +(0.906791 - 0.130377i) q^{57} +(1.12560 - 0.161837i) q^{58} +(-3.50406 + 2.25192i) q^{59} +(-1.73228 - 1.41393i) q^{60} +(-4.69390 + 10.2782i) q^{61} +(-3.08947 + 4.80731i) q^{62} +(-0.360903 - 1.22912i) q^{63} +(0.654861 + 0.755750i) q^{64} +(-0.369147 + 1.40945i) q^{65} +(-1.29142 - 2.82780i) q^{66} +(1.35954 + 0.195472i) q^{67} -2.56600i q^{68} +(3.67535 - 3.08088i) q^{69} +(-2.86319 + 0.0843267i) q^{70} +(-1.00604 + 6.99716i) q^{71} +(0.909632 - 0.415415i) q^{72} +(0.679223 - 2.31322i) q^{73} +(-0.317331 - 0.366219i) q^{74} +(1.68857 + 4.70625i) q^{75} +(0.770686 + 0.495290i) q^{76} +(-3.62246 - 1.65432i) q^{77} +(-0.492434 - 0.426697i) q^{78} +(-5.92615 + 3.80850i) q^{79} +(-0.383246 - 2.20298i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(0.442799 + 0.689009i) q^{82} +(4.33703 + 3.75806i) q^{83} +(0.532152 - 1.16525i) q^{84} +(-2.95862 + 4.91614i) q^{85} +(6.79741 - 1.99590i) q^{86} +(0.859419 - 0.744691i) q^{87} +(0.875832 - 2.98281i) q^{88} +(2.39366 + 5.24139i) q^{89} +(-2.22172 - 0.252930i) q^{90} -0.834688 q^{91} +(4.79519 + 0.0784636i) q^{92} +5.71446i q^{93} +(0.237816 - 1.65405i) q^{94} +(-0.905464 - 1.83752i) q^{95} +(0.959493 + 0.281733i) q^{96} +(-8.81752 + 7.64042i) q^{97} +(1.50981 + 5.14193i) q^{98} +(-2.61523 - 1.68071i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} + 12 q^{6} + 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^4 + 12 * q^6 + 12 * q^9	$ 120 q + 12 q^{4} + 12 q^{6} + 12 q^{9} + 18 q^{10} - 8 q^{14} - 4 q^{15} - 12 q^{16} + 22 q^{20} + 14 q^{21} + 120 q^{24} + 52 q^{25} + 16 q^{29} + 8 q^{31} - 36 q^{34} - 90 q^{35} - 12 q^{36} + 22 q^{39} + 4 q^{40} + 16 q^{41} - 4 q^{49} - 4 q^{50} + 8 q^{51} - 12 q^{54} - 56 q^{55} + 8 q^{56} + 138 q^{59} + 4 q^{60} - 36 q^{61} + 12 q^{64} + 52 q^{65} + 96 q^{70} + 8 q^{71} + 8 q^{74} - 4 q^{75} - 60 q^{79} - 12 q^{81} + 8 q^{84} + 24 q^{85} - 8 q^{86} - 104 q^{89} + 4 q^{90} - 144 q^{91} - 24 q^{94} - 14 q^{95} + 12 q^{96} - 44 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 + 12 * q^6 + 12 * q^9 + 18 * q^10 - 8 * q^14 - 4 * q^15 - 12 * q^16 + 22 * q^20 + 14 * q^21 + 120 * q^24 + 52 * q^25 + 16 * q^29 + 8 * q^31 - 36 * q^34 - 90 * q^35 - 12 * q^36 + 22 * q^39 + 4 * q^40 + 16 * q^41 - 4 * q^49 - 4 * q^50 + 8 * q^51 - 12 * q^54 - 56 * q^55 + 8 * q^56 + 138 * q^59 + 4 * q^60 - 36 * q^61 + 12 * q^64 + 52 * q^65 + 96 * q^70 + 8 * q^71 + 8 * q^74 - 4 * q^75 - 60 * q^79 - 12 * q^81 + 8 * q^84 + 24 * q^85 - 8 * q^86 - 104 * q^89 + 4 * q^90 - 144 * q^91 - 24 * q^94 - 14 * q^95 + 12 * q^96 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	0.989821	+	0.142315i	0.699909	+	0.100632i
$2$	0.989821	+	0.142315i	0.699909	+	0.100632i
$3$	0.909632	−	0.415415i	0.525176	−	0.239840i
$3$	0.909632	−	0.415415i	0.525176	−	0.239840i
$4$	0.959493	+	0.281733i	0.479746	+	0.140866i
$5$	−1.51343	−	1.64607i	−0.676826	−	0.736143i
$5$	−1.51343	−	1.64607i	−0.676826	−	0.736143i
$6$	0.959493	−	0.281733i	0.391711	−	0.115017i
$7$	0.692568	−	1.07766i	0.261766	−	0.407316i	−0.685347	−	0.728217i	$-0.740349\pi$
$7$	0.692568	−	1.07766i	0.261766	−	0.407316i	0.947113	+	0.320901i	$0.103986\pi$
$8$	0.909632	+	0.415415i	0.321603	+	0.146871i
$9$	0.654861	−	0.755750i	0.218287	−	0.251917i
$10$	−1.26376	−	1.84470i	−0.399637	−	0.583344i
$11$	−0.442419	−	3.07709i	−0.133394	−	0.927778i	−0.941085	−	0.338171i	$-0.890192\pi$
$11$	−0.442419	−	3.07709i	−0.133394	−	0.927778i	0.807690	−	0.589607i	$-0.200717\pi$
$12$	0.989821	−	0.142315i	0.285737	−	0.0410828i
$13$	−0.352273	−	0.548147i	−0.0977029	−	0.152029i	0.788961	−	0.614444i	$-0.210619\pi$
$13$	−0.352273	−	0.548147i	−0.0977029	−	0.152029i	−0.886664	+	0.462415i	$0.846983\pi$
$14$	0.838885	−	0.968125i	0.224202	−	0.258742i
$15$	−2.06046	−	0.868614i	−0.532009	−	0.224275i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	−0.722927	−	2.46206i	−0.175336	−	0.597138i	−0.999525	−	0.0308236i	$-0.990187\pi$
$17$	−0.722927	−	2.46206i	−0.175336	−	0.597138i	0.824189	−	0.566314i	$-0.191631\pi$
$18$	0.755750	−	0.654861i	0.178132	−	0.154352i
$19$	0.879007	+	0.258100i	0.201658	+	0.0592121i	0.381002	−	0.924574i	$-0.375579\pi$
$19$	0.879007	+	0.258100i	0.201658	+	0.0592121i	−0.179344	+	0.983786i	$0.557397\pi$
$20$	−0.988373	−	2.00577i	−0.221007	−	0.448504i
$21$	0.182307	−	1.26797i	0.0397827	−	0.276695i
$22$		−	3.10873i		−	0.662784i
$23$	4.62306	−	1.27568i	0.963974	−	0.265997i
$23$	4.62306	−	1.27568i	0.963974	−	0.265997i
$24$	1.00000			0.204124
$25$	−0.419071	+	4.98241i	−0.0838143	+	0.996481i
$26$	−0.270678	−	0.592702i	−0.0530843	−	0.116238i
$27$	0.281733	−	0.959493i	0.0542195	−	0.184655i
$28$	0.968125	−	0.838885i	0.182958	−	0.158534i
$29$	1.09111	−	0.320379i	0.202614	−	0.0594929i	−0.178851	−	0.983876i	$-0.557238\pi$
$29$	1.09111	−	0.320379i	0.202614	−	0.0594929i	0.381465	+	0.924383i	$0.375420\pi$
$30$	−1.91587	−	1.15301i	−0.349789	−	0.210509i
$31$	−2.37387	+	5.19805i	−0.426360	+	0.933598i	0.567543	+	0.823344i	$0.307894\pi$
$31$	−2.37387	+	5.19805i	−0.426360	+	0.933598i	−0.993903	+	0.110255i	$0.964833\pi$
$32$	0.755750	+	0.654861i	0.133599	+	0.115764i
$33$	−1.68071	−	2.61523i	−0.292574	−	0.455254i
$34$	−0.365181	−	2.53989i	−0.0626279	−	0.435587i
$35$	−2.82205	+	0.490943i	−0.477013	+	0.0829845i
$36$	0.841254	−	0.540641i	0.140209	−	0.0901068i
$37$	−0.366219	−	0.317331i	−0.0602061	−	0.0521688i	0.624238	−	0.781234i	$-0.285410\pi$
$37$	−0.366219	−	0.317331i	−0.0602061	−	0.0521688i	−0.684444	+	0.729065i	$0.739955\pi$
$38$	0.833329	+	0.380568i	0.135184	+	0.0617363i
$39$	−0.548147	−	0.352273i	−0.0877738	−	0.0564088i
$40$	−0.692862	−	2.12602i	−0.109551	−	0.336153i
$41$	0.536349	+	0.618979i	0.0837636	+	0.0966683i	0.796084	−	0.605186i	$-0.206901\pi$
$41$	0.536349	+	0.618979i	0.0837636	+	0.0966683i	−0.712321	+	0.701854i	$0.752356\pi$
$42$	0.360903	−	1.22912i	0.0556886	−	0.189658i
$43$	6.44417	−	2.94295i	0.982727	−	0.448796i	0.141771	−	0.989900i	$-0.454720\pi$
$43$	6.44417	−	2.94295i	0.982727	−	0.448796i	0.840956	+	0.541103i	$0.181993\pi$
$44$	0.442419	−	3.07709i	0.0666972	−	0.463889i
$45$	−2.23510	+	0.0658281i	−0.333189	+	0.00981307i
$46$	4.75755	−	0.604762i	0.701462	−	0.0891672i
$47$		−	1.67106i		−	0.243749i	−0.992546	−	0.121874i	$-0.961110\pi$
$47$		−	1.67106i		−	0.243749i	0.992546	−	0.121874i	$-0.0388905\pi$
$48$	0.989821	+	0.142315i	0.142868	+	0.0205414i
$49$	2.22621	+	4.87472i	0.318030	+	0.696389i
$50$	−1.12388	+	4.87205i	−0.158940	+	0.689012i
$51$	−1.68038	−	1.93926i	−0.235300	−	0.271550i
$52$	−0.183572	−	0.625190i	−0.0254569	−	0.0866983i
$53$	2.43574	−	3.79009i	0.334575	−	0.520609i	−0.632681	−	0.774413i	$-0.718045\pi$
$53$	2.43574	−	3.79009i	0.334575	−	0.520609i	0.967256	+	0.253804i	$0.0816818\pi$
$54$	0.415415	−	0.909632i	0.0565308	−	0.123785i
$55$	−4.39553	+	5.38521i	−0.592693	+	0.726141i
$56$	1.07766	−	0.692568i	0.144008	−	0.0925483i
$57$	0.906791	−	0.130377i	0.120107	−	0.0172688i
$58$	1.12560	−	0.161837i	0.147798	−	0.0212502i
$59$	−3.50406	+	2.25192i	−0.456190	+	0.293175i	−0.748484	−	0.663153i	$-0.769218\pi$
$59$	−3.50406	+	2.25192i	−0.456190	+	0.293175i	0.292294	+	0.956329i	$0.405581\pi$
$60$	−1.73228	−	1.41393i	−0.223637	−	0.182537i
$61$	−4.69390	+	10.2782i	−0.600993	+	1.31599i	0.327574	+	0.944826i	$0.393769\pi$
$61$	−4.69390	+	10.2782i	−0.600993	+	1.31599i	−0.928567	+	0.371165i	$0.878958\pi$
$62$	−3.08947	+	4.80731i	−0.392363	+	0.610529i
$63$	−0.360903	−	1.22912i	−0.0454695	−	0.154855i
$64$	0.654861	+	0.755750i	0.0818576	+	0.0944687i
$65$	−0.369147	+	1.40945i	−0.0457871	+	0.174820i
$66$	−1.29142	−	2.82780i	−0.158962	−	0.348079i
$67$	1.35954	+	0.195472i	0.166094	+	0.0238808i	0.224860	−	0.974391i	$-0.427807\pi$
$67$	1.35954	+	0.195472i	0.166094	+	0.0238808i	−0.0587659	+	0.998272i	$0.518717\pi$
$68$		−	2.56600i		−	0.311174i
$69$	3.67535	−	3.08088i	0.442460	−	0.370895i
$70$	−2.86319	+	0.0843267i	−0.342217	+	0.0100790i
$71$	−1.00604	+	6.99716i	−0.119395	+	0.830410i	0.838830	+	0.544394i	$0.183240\pi$
$71$	−1.00604	+	6.99716i	−0.119395	+	0.830410i	−0.958225	+	0.286016i	$0.907669\pi$
$72$	0.909632	−	0.415415i	0.107201	−	0.0489571i
$73$	0.679223	−	2.31322i	0.0794970	−	0.270742i	−0.910147	−	0.414285i	$-0.864032\pi$
$73$	0.679223	−	2.31322i	0.0794970	−	0.270742i	0.989644	+	0.143544i	$0.0458497\pi$
$74$	−0.317331	−	0.366219i	−0.0368889	−	0.0425721i
$75$	1.68857	+	4.70625i	0.194979	+	0.543430i
$76$	0.770686	+	0.495290i	0.0884037	+	0.0568136i
$77$	−3.62246	−	1.65432i	−0.412817	−	0.188527i
$78$	−0.492434	−	0.426697i	−0.0557572	−	0.0483139i
$79$	−5.92615	+	3.80850i	−0.666744	+	0.428490i	−0.829750	−	0.558135i	$-0.811517\pi$
$79$	−5.92615	+	3.80850i	−0.666744	+	0.428490i	0.163007	+	0.986625i	$0.447881\pi$
$80$	−0.383246	−	2.20298i	−0.0428482	−	0.246301i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	0.442799	+	0.689009i	0.0488990	+	0.0760883i
$83$	4.33703	+	3.75806i	0.476051	+	0.412501i	0.859559	−	0.511037i	$-0.170738\pi$
$83$	4.33703	+	3.75806i	0.476051	+	0.412501i	−0.383507	+	0.923538i	$0.625284\pi$
$84$	0.532152	−	1.16525i	0.0580626	−	0.127139i
$85$	−2.95862	+	4.91614i	−0.320908	+	0.533230i
$86$	6.79741	−	1.99590i	0.732983	−	0.215223i
$87$	0.859419	−	0.744691i	0.0921394	−	0.0798392i
$88$	0.875832	−	2.98281i	0.0933640	−	0.317969i
$89$	2.39366	+	5.24139i	0.253728	+	0.555586i	0.993040	−	0.117777i	$-0.0375767\pi$
$89$	2.39366	+	5.24139i	0.253728	+	0.555586i	−0.739313	+	0.673362i	$0.764849\pi$
$90$	−2.22172	−	0.252930i	−0.234190	−	0.0266611i
$91$	−0.834688			−0.0874990
$92$	4.79519	+	0.0784636i	0.499933	+	0.00818040i
$93$			5.71446i			0.592562i
$94$	0.237816	−	1.65405i	0.0245289	−	0.170602i
$95$	−0.905464	−	1.83752i	−0.0928987	−	0.188526i
$96$	0.959493	+	0.281733i	0.0979278	+	0.0287542i
$97$	−8.81752	+	7.64042i	−0.895283	+	0.775767i	−0.975267	−	0.221029i	$-0.929058\pi$
$97$	−8.81752	+	7.64042i	−0.895283	+	0.775767i	0.0799841	+	0.996796i	$0.474513\pi$
$98$	1.50981	+	5.14193i	0.152513	+	0.519413i
$99$	−2.61523	−	1.68071i	−0.262841	−	0.168918i
$100$	−1.80580	+	4.66252i	−0.180580	+	0.466252i
$101$	−4.07320	+	4.70073i	−0.405299	+	0.467740i	−0.921302	−	0.388847i	$-0.872874\pi$
$101$	−4.07320	+	4.70073i	−0.405299	+	0.467740i	0.516004	+	0.856586i	$0.327419\pi$
$102$	−1.38729	−	2.15866i	−0.137362	−	0.213739i
$103$	10.5226	−	1.51293i	1.03683	−	0.149073i	0.397179	−	0.917741i	$-0.369989\pi$
$103$	10.5226	−	1.51293i	1.03683	−	0.149073i	0.639648	+	0.768668i	$0.279080\pi$
$104$	−0.0927301	−	0.644952i	−0.00909293	−	0.0632427i
$105$	−2.36308	+	1.61890i	−0.230613	+	0.157988i
$106$	2.95034	−	3.40487i	0.286562	−	0.330710i
$107$	−1.18786	−	0.542477i	−0.114835	−	0.0524433i	0.357169	−	0.934040i	$-0.383742\pi$
$107$	−1.18786	−	0.542477i	−0.114835	−	0.0524433i	−0.472004	+	0.881596i	$0.656469\pi$
$108$	0.540641	−	0.841254i	0.0520232	−	0.0809497i
$109$	11.2156	−	3.29318i	1.07426	−	0.315430i	0.303677	−	0.952775i	$-0.401786\pi$
$109$	11.2156	−	3.29318i	1.07426	−	0.315430i	0.770578	+	0.637345i	$0.219967\pi$
$110$	−5.11718	+	4.70485i	−0.487904	+	0.448589i
$111$	−0.464949	−	0.136521i	−0.0441310	−	0.0129580i
$112$	1.16525	−	0.532152i	0.110106	−	0.0502837i
$113$	3.35771	+	0.482767i	0.315867	+	0.0454149i	0.298425	−	0.954433i	$-0.403539\pi$
$113$	3.35771	+	0.482767i	0.315867	+	0.0454149i	0.0174420	+	0.999848i	$0.494448\pi$
$114$	0.916116			0.0858021
$115$	−9.09651	−	5.67922i	−0.848254	−	0.529590i
$116$	1.13717			0.105584
$117$	−0.644952	−	0.0927301i	−0.0596258	−	0.00857290i
$118$	−3.78888	+	1.73032i	−0.348794	+	0.159289i
$119$	−3.15394	−	0.926079i	−0.289121	−	0.0848935i
$120$	−1.51343	−	1.64607i	−0.138156	−	0.150265i
$121$	1.28166	−	0.376329i	0.116515	−	0.0342118i
$122$	−6.10887	+	9.50559i	−0.553071	+	0.860595i
$123$	0.745013	+	0.340236i	0.0671756	+	0.0306781i
$124$	−3.74217	+	4.31870i	−0.336057	+	0.387831i
$125$	8.83561	−	6.85069i	0.790281	−	0.612745i
$126$	−0.182307	−	1.26797i	−0.0162412	−	0.112960i
$127$	−16.7168	+	2.40352i	−1.48338	+	0.213278i	−0.835932	−	0.548834i	$-0.815072\pi$
$127$	−16.7168	+	2.40352i	−1.48338	+	0.213278i	−0.647446	+	0.762111i	$0.724163\pi$
$128$	0.540641	+	0.841254i	0.0477863	+	0.0743570i
$129$	4.63928	−	5.35401i	0.408466	−	0.471394i
$130$	−0.565975	+	1.34256i	−0.0496393	+	0.117751i
$131$	−3.33226	−	2.14151i	−0.291141	−	0.187105i	0.386915	−	0.922115i	$-0.373541\pi$
$131$	−3.33226	−	2.14151i	−0.291141	−	0.187105i	−0.678055	+	0.735011i	$0.737177\pi$
$132$	−0.875832	−	2.98281i	−0.0762314	−	0.259620i
$133$	0.886915	−	0.768516i	0.0769053	−	0.0666388i
$134$	1.31788	+	0.386965i	0.113848	+	0.0334287i
$135$	−2.00577	+	0.988373i	−0.172629	+	0.0850656i
$136$	0.365181	−	2.53989i	0.0313140	−	0.217793i
$137$		−	9.45939i		−	0.808171i	−0.914721	−	0.404085i	$-0.867590\pi$
$137$		−	9.45939i		−	0.808171i	0.914721	−	0.404085i	$-0.132410\pi$
$138$	4.07639	−	2.52647i	0.347005	−	0.215067i
$139$	9.95872			0.844688			0.422344	−	0.906436i	$-0.361207\pi$
$139$	9.95872			0.844688			0.422344	+	0.906436i	$0.361207\pi$
$140$	−2.84605	−	0.324006i	−0.240535	−	0.0273835i
$141$	−0.694182	−	1.52005i	−0.0584607	−	0.128011i
$142$	−1.99160	+	6.78277i	−0.167131	+	0.569197i
$143$	−1.53085	+	1.32649i	−0.128016	+	0.110926i
$144$	0.959493	−	0.281733i	0.0799577	−	0.0234777i
$145$	−2.17868	−	1.31117i	−0.180930	−	0.108887i
$146$	1.00151	−	2.19301i	0.0828859	−	0.181495i
$147$	4.05007	+	3.50940i	0.334044	+	0.289451i
$148$	−0.261982	−	0.407652i	−0.0215348	−	0.0335088i
$149$	−2.42225	−	16.8471i	−0.198438	−	1.38017i	−0.808817	−	0.588060i	$-0.799892\pi$
$149$	−2.42225	−	16.8471i	−0.198438	−	1.38017i	0.610379	−	0.792110i	$-0.291017\pi$
$150$	1.00161	+	4.89865i	0.0817811	+	0.399973i
$151$	−14.0718	+	9.04342i	−1.14515	+	0.735943i	−0.968668	−	0.248361i	$-0.920108\pi$
$151$	−14.0718	+	9.04342i	−1.14515	+	0.735943i	−0.176482	+	0.984304i	$0.556472\pi$
$152$	0.692354	+	0.599928i	0.0561574	+	0.0486606i
$153$	−2.33412	−	1.06596i	−0.188702	−	0.0861775i
$154$	−3.35015	−	2.15301i	−0.269963	−	0.173495i
$155$	12.1490	−	3.95933i	0.975834	−	0.318021i
$156$	−0.426697	−	0.492434i	−0.0341631	−	0.0394263i
$157$	−6.51447	+	22.1862i	−0.519911	+	1.77065i	0.109940	+	0.993938i	$0.464934\pi$
$157$	−6.51447	+	22.1862i	−0.519911	+	1.77065i	−0.629851	+	0.776716i	$0.716884\pi$
$158$	−6.40783	+	2.92636i	−0.509780	+	0.232809i
$159$	0.641170	−	4.45943i	0.0508481	−	0.353656i
$160$	−0.0658281	−	2.23510i	−0.00520417	−	0.176700i
$161$	1.82704	−	5.86556i	0.143991	−	0.462271i
$162$		−	1.00000i		−	0.0785674i
$163$	2.26717	+	0.325970i	0.177579	+	0.0255320i	0.230530	−	0.973065i	$-0.425954\pi$
$163$	2.26717	+	0.325970i	0.177579	+	0.0255320i	−0.0529518	+	0.998597i	$0.516863\pi$
$164$	0.340236	+	0.745013i	0.0265680	+	0.0581758i
$165$	−1.76122	+	6.72453i	−0.137111	+	0.523504i
$166$	3.75806	+	4.33703i	0.291682	+	0.336619i
$167$	2.85848	+	9.73509i	0.221196	+	0.753324i	0.993068	+	0.117545i	$0.0375026\pi$
$167$	2.85848	+	9.73509i	0.221196	+	0.753324i	−0.771872	+	0.635778i	$0.780679\pi$
$168$	0.692568	−	1.07766i	0.0534328	−	0.0831430i
$169$	5.22403	−	11.4390i	0.401848	−	0.879925i
$170$	−3.62815	+	4.44505i	−0.278266	+	0.340920i
$171$	0.770686	−	0.495290i	0.0589358	−	0.0378758i
$172$	7.01226	−	1.00821i	0.534680	−	0.0768754i
$173$	3.74841	−	0.538939i	0.284986	−	0.0409748i	0.00166055	−	0.999999i	$-0.499471\pi$
$173$	3.74841	−	0.538939i	0.284986	−	0.0409748i	0.283325	+	0.959024i	$0.408562\pi$
$174$	0.956652	−	0.614803i	0.0725236	−	0.0466081i
$175$	5.07909	+	3.90227i	0.383943	+	0.294984i
$176$	1.29142	−	2.82780i	0.0973441	−	0.213154i
$177$	−2.25192	+	3.50406i	−0.169265	+	0.263381i
$178$	1.62337	+	5.52869i	0.121677	+	0.414393i
$179$	4.30664	+	4.97012i	0.321893	+	0.371484i	0.893515	−	0.449032i	$-0.148231\pi$
$179$	4.30664	+	4.97012i	0.321893	+	0.371484i	−0.571622	+	0.820517i	$0.693686\pi$
$180$	−2.16311	−	0.566539i	−0.161229	−	0.0422273i
$181$	−3.50744	−	7.68023i	−0.260706	−	0.570867i	0.733335	−	0.679867i	$-0.237962\pi$
$181$	−3.50744	−	7.68023i	−0.260706	−	0.570867i	−0.994042	+	0.109000i	$0.965235\pi$
$182$	−0.826192	−	0.118788i	−0.0612414	−	0.00880519i
$183$			11.2993i			0.835269i
$184$	4.73521	+	0.760092i	0.349085	+	0.0560347i
$185$	0.0318988	+	1.08308i	0.00234525	+	0.0796295i
$186$	−0.813252	+	5.65629i	−0.0596306	+	0.414740i
$187$	−7.25616	+	3.31378i	−0.530623	+	0.242327i
$188$	0.470791	−	1.60337i	0.0343360	−	0.116938i
$189$	−0.838885	−	0.968125i	−0.0610199	−	0.0704208i
$190$	−0.634742	−	1.94768i	−0.0460490	−	0.141299i
$191$	−15.8055	−	10.1575i	−1.14364	−	0.734974i	−0.175279	−	0.984519i	$-0.556083\pi$
$191$	−15.8055	−	10.1575i	−1.14364	−	0.734974i	−0.968363	+	0.249544i	$0.919719\pi$
$192$	0.909632	+	0.415415i	0.0656470	+	0.0299800i
$193$	18.4315	+	15.9710i	1.32673	+	1.14962i	0.977113	+	0.212722i	$0.0682327\pi$
$193$	18.4315	+	15.9710i	1.32673	+	1.14962i	0.349614	+	0.936894i	$0.386313\pi$
$194$	−9.81511	+	6.30779i	−0.704684	+	0.452873i
$195$	0.249717	+	1.43543i	0.0178826	+	0.102793i
$196$	0.762666	+	5.30446i	0.0544761	+	0.378890i
$197$	−8.39087	−	13.0564i	−0.597825	−	0.930234i	−0.999893	−	0.0146238i	$-0.995345\pi$
$197$	−8.39087	−	13.0564i	−0.597825	−	0.930234i	0.402068	−	0.915610i	$-0.368291\pi$
$198$	−2.34942	−	2.03579i	−0.166966	−	0.144677i
$199$	−9.54773	+	20.9066i	−0.676821	+	1.48203i	0.189157	+	0.981947i	$0.439425\pi$
$199$	−9.54773	+	20.9066i	−0.676821	+	1.48203i	−0.865977	+	0.500083i	$0.833303\pi$
$200$	−2.45097	+	4.35807i	−0.173310	+	0.308162i
$201$	1.31788	−	0.386965i	0.0929563	−	0.0272944i
$202$	−4.70073	+	4.07320i	−0.330742	+	0.286589i
$203$	0.410410	−	1.39773i	0.0288051	−	0.0981012i
$204$	−1.06596	−	2.33412i	−0.0746319	−	0.163421i
$205$	0.207156	−	1.81965i	0.0144684	−	0.127090i
$206$	10.6308			0.740686
$207$	2.06337	−	4.32926i	0.143414	−	0.300905i
$208$		−	0.651584i		−	0.0451792i
$209$	0.405307	−	2.81897i	0.0280357	−	0.194992i
$210$	−2.56942	+	1.26612i	−0.177307	+	0.0873705i
$211$	4.19265	+	1.23107i	0.288634	+	0.0847505i	0.422844	−	0.906202i	$-0.361032\pi$
$211$	4.19265	+	1.23107i	0.288634	+	0.0847505i	−0.134211	+	0.990953i	$0.542850\pi$
$212$	3.40487	−	2.95034i	0.233847	−	0.202630i
$213$	1.99160	+	6.78277i	0.136462	+	0.464747i
$214$	−1.09857	−	0.706006i	−0.0750965	−	0.0482616i
$215$	−14.5971	−	6.15359i	−0.995513	−	0.419671i
$216$	0.654861	−	0.755750i	0.0445576	−	0.0514222i
$217$	3.95765	+	6.15823i	0.268663	+	0.418048i
$218$	11.5701	−	1.66352i	0.783624	−	0.112668i
$219$	−0.343104	−	2.38634i	−0.0231848	−	0.161254i
$220$	−5.73467	+	3.92871i	−0.386631	+	0.264873i
$221$	−1.09491	+	1.26359i	−0.0736513	+	0.0849982i
$222$	−0.440787	−	0.201301i	−0.0295837	−	0.0135104i
$223$	1.11515	−	1.73520i	0.0746759	−	0.116198i	−0.801907	−	0.597449i	$-0.796181\pi$
$223$	1.11515	−	1.73520i	0.0746759	−	0.116198i	0.876583	+	0.481251i	$0.159817\pi$
$224$	1.22912	−	0.360903i	0.0821243	−	0.0241139i
$225$	3.49102	+	3.57950i	0.232735	+	0.238633i
$226$	3.25483	+	0.955705i	0.216508	+	0.0635726i
$227$	−12.7550	+	5.82499i	−0.846576	+	0.386618i	−0.790985	−	0.611835i	$-0.790431\pi$
$227$	−12.7550	+	5.82499i	−0.846576	+	0.386618i	−0.0555908	+	0.998454i	$0.517704\pi$
$228$	0.906791	+	0.130377i	0.0600537	+	0.00863442i
$229$	19.2053			1.26912			0.634561	−	0.772873i	$-0.281181\pi$
$229$	19.2053			1.26912			0.634561	+	0.772873i	$0.281181\pi$
$230$	−8.19568	−	6.91598i	−0.540407	−	0.456026i
$231$	−3.98233			−0.262018
$232$	1.12560	+	0.161837i	0.0738992	+	0.0106251i
$233$	17.8491	−	8.15140i	1.16933	−	0.534016i	0.266426	−	0.963855i	$-0.414157\pi$
$233$	17.8491	−	8.15140i	1.16933	−	0.534016i	0.902905	+	0.429839i	$0.141430\pi$
$234$	−0.625190	−	0.183572i	−0.0408700	−	0.0120005i
$235$	−2.75067	+	2.52902i	−0.179434	+	0.164975i
$236$	−3.99656	+	1.17350i	−0.260154	+	0.0763881i
$237$	−3.80850	+	5.92615i	−0.247389	+	0.384945i
$238$	−2.99004	−	1.36550i	−0.193815	−	0.0885125i
$239$	−16.8053	+	19.3943i	−1.08704	+	1.25451i	−0.121968	+	0.992534i	$0.538921\pi$
$239$	−16.8053	+	19.3943i	−1.08704	+	1.25451i	−0.965074	+	0.261979i	$0.915625\pi$
$240$	−1.26376	−	1.84470i	−0.0815756	−	0.119075i
$241$	−2.15447	−	14.9847i	−0.138782	−	0.965247i	−0.933579	−	0.358372i	$-0.883332\pi$
$241$	−2.15447	−	14.9847i	−0.138782	−	0.965247i	0.794797	−	0.606875i	$-0.207577\pi$
$242$	1.32217	−	0.190100i	0.0849924	−	0.0122201i
$243$	−0.540641	−	0.841254i	−0.0346821	−	0.0539664i
$244$	−7.39948	+	8.53945i	−0.473703	+	0.546682i
$245$	4.65491	−	11.0420i	0.297391	−	0.705450i
$246$	0.689009	+	0.442799i	0.0439296	+	0.0282319i
$247$	−0.168174	−	0.572747i	−0.0107006	−	0.0364430i
$248$	−4.31870	+	3.74217i	−0.274238	+	0.237628i
$249$	5.50626	+	1.61678i	0.348945	+	0.102460i
$250$	9.72063	−	5.52353i	0.614787	−	0.349338i
$251$	0.458819	−	3.19116i	0.0289604	−	0.201424i	−0.970204	−	0.242288i	$-0.922102\pi$
$251$	0.458819	−	3.19116i	0.0289604	−	0.201424i	0.999165	+	0.0408642i	$0.0130111\pi$
$252$		−	1.28101i		−	0.0806963i
$253$	−5.97070	−	13.6612i	−0.375375	−	0.858872i
$254$	−16.8887			−1.05969
$255$	−0.649019	+	5.70094i	−0.0406431	+	0.357006i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	5.46208	−	18.6021i	0.340715	−	1.16037i	−0.593850	−	0.804576i	$-0.702393\pi$
$257$	5.46208	−	18.6021i	0.340715	−	1.16037i	0.934565	−	0.355793i	$-0.115789\pi$
$258$	5.35401	−	4.63928i	0.333326	−	0.288829i
$259$	−0.595605	+	0.174886i	−0.0370091	+	0.0108669i
$260$	−0.751281	+	1.24835i	−0.0465925	+	0.0774196i
$261$	0.472399	−	1.03441i	0.0292408	−	0.0640284i
$262$	−2.99357	−	2.59394i	−0.184943	−	0.160254i
$263$	−3.45284	−	5.37272i	−0.212911	−	0.331296i	0.718328	−	0.695704i	$-0.244908\pi$
$263$	−3.45284	−	5.37272i	−0.212911	−	0.331296i	−0.931239	+	0.364408i	$0.881271\pi$
$264$	−0.442419	−	3.07709i	−0.0272290	−	0.189382i
$265$	−9.92506	+	1.72663i	−0.609692	+	0.106066i
$266$	0.987259	−	0.634473i	0.0605327	−	0.0389020i
$267$	4.35470	+	3.77337i	0.266503	+	0.230926i
$268$	1.24940	+	0.570581i	0.0763191	+	0.0348538i
$269$	−1.12146	−	0.720721i	−0.0683769	−	0.0439432i	0.506006	−	0.862530i	$-0.331121\pi$
$269$	−1.12146	−	0.720721i	−0.0683769	−	0.0439432i	−0.574383	+	0.818587i	$0.694758\pi$
$270$	−2.12602	+	0.692862i	−0.129385	+	0.0421662i
$271$	0.870767	+	1.00492i	0.0528954	+	0.0610445i	0.781581	−	0.623804i	$-0.214414\pi$
$271$	0.870767	+	1.00492i	0.0528954	+	0.0610445i	−0.728685	+	0.684849i	$0.759868\pi$
$272$	0.722927	−	2.46206i	0.0438339	−	0.149285i
$273$	−0.759259	+	0.346742i	−0.0459524	+	0.0209858i
$274$	1.34621	−	9.36311i	0.0813277	−	0.565646i
$275$	15.5167	−	0.914791i	0.935694	−	0.0551639i
$276$	4.39445	−	1.92062i	0.264515	−	0.115608i
$277$			1.75254i			0.105300i	0.998613	+	0.0526500i	$0.0167668\pi$
$277$			1.75254i			0.105300i	−0.998613	+	0.0526500i	$0.983233\pi$
$278$	9.85735	+	1.41727i	0.591205	+	0.0850024i
$279$	2.37387	+	5.19805i	0.142120	+	0.311199i
$280$	−2.77097	−	0.725743i	−0.165597	−	0.0433715i
$281$	−6.68264	−	7.71218i	−0.398653	−	0.460070i	0.520563	−	0.853823i	$-0.325722\pi$
$281$	−6.68264	−	7.71218i	−0.398653	−	0.460070i	−0.919216	+	0.393753i	$0.871177\pi$
$282$	−0.470791	−	1.60337i	−0.0280352	−	0.0954791i
$283$	12.9943	−	20.2195i	0.772430	−	1.20192i	−0.202472	−	0.979288i	$-0.564898\pi$
$283$	12.9943	−	20.2195i	0.772430	−	1.20192i	0.974902	−	0.222636i	$-0.0714661\pi$
$284$	−2.93662	+	6.43029i	−0.174256	+	0.381568i
$285$	−1.58697	−	1.29532i	−0.0940041	−	0.0767283i
$286$	−1.70404	+	1.09512i	−0.100762	+	0.0647560i
$287$	1.03851	−	0.149315i	0.0613010	−	0.00881376i
$288$	0.989821	−	0.142315i	0.0583258	−	0.00838598i
$289$	8.76218	−	5.63111i	0.515422	−	0.331242i
$290$	−1.96991	−	1.60788i	−0.115677	−	0.0944182i
$291$	−4.84675	+	10.6129i	−0.284121	+	0.622139i
$292$	1.30342	−	2.02816i	0.0762768	−	0.118689i
$293$	−4.26894	−	14.5387i	−0.249394	−	0.849358i	−0.985089	−	0.172045i	$-0.944962\pi$
$293$	−4.26894	−	14.5387i	−0.249394	−	0.849358i	0.735695	−	0.677313i	$-0.236856\pi$
$294$	3.50940	+	4.05007i	0.204672	+	0.236205i
$295$	9.00996	+	2.35979i	0.524580	+	0.137393i
$296$	−0.201301	−	0.440787i	−0.0117004	−	0.0256202i
$297$	−3.07709	−	0.442419i	−0.178551	−	0.0256718i
$298$		−	17.0204i		−	0.985963i
$299$	−2.32784	−	2.08473i	−0.134622	−	0.120563i
$300$	0.294265	+	4.99133i	0.0169894	+	0.288175i
$301$	1.29153	−	8.98280i	0.0744427	−	0.517760i
$302$	−15.2156	+	6.94874i	−0.875560	+	0.399855i
$303$	−1.75236	+	5.96800i	−0.100671	+	0.342853i
$304$	0.599928	+	0.692354i	0.0344083	+	0.0397092i
$305$	24.0225	−	7.82886i	1.37553	−	0.448279i
$306$	−2.15866	−	1.38729i	−0.123402	−	0.0793059i
$307$	−28.9747	−	13.2323i	−1.65367	−	0.755206i	−0.653672	−	0.756778i	$-0.726773\pi$
$307$	−28.9747	−	13.2323i	−1.65367	−	0.755206i	−0.999999	+	0.00157124i	$0.999500\pi$
$308$	−3.00964	−	2.60787i	−0.171490	−	0.148597i
$309$	8.94324	−	5.74747i	0.508763	−	0.326962i
$310$	12.5888	−	2.19004i	0.714998	−	0.124386i
$311$	2.32898	+	16.1984i	0.132064	+	0.918527i	0.942858	+	0.333195i	$0.108127\pi$
$311$	2.32898	+	16.1984i	0.132064	+	0.918527i	−0.810794	+	0.585332i	$0.800964\pi$
$312$	−0.352273	−	0.548147i	−0.0199435	−	0.0310327i
$313$	2.20523	+	1.91085i	0.124647	+	0.108007i	0.714954	−	0.699172i	$-0.246448\pi$
$313$	2.20523	+	1.91085i	0.124647	+	0.108007i	−0.590307	+	0.807179i	$0.700993\pi$
$314$	−9.60559	+	21.0333i	−0.542075	+	1.18698i
$315$	−1.47702	+	2.45426i	−0.0832205	+	0.138282i
$316$	−6.75908	+	1.98464i	−0.380228	+	0.111645i
$317$	18.7997	−	16.2900i	1.05590	−	0.914940i	0.0593724	−	0.998236i	$-0.481090\pi$
$317$	18.7997	−	16.2900i	1.05590	−	0.914940i	0.996525	+	0.0832958i	$0.0265446\pi$
$318$	1.26929	−	4.32279i	0.0711781	−	0.242410i
$319$	−1.46856	−	3.21571i	−0.0822238	−	0.180045i
$320$	0.252930	−	2.22172i	0.0141392	−	0.124198i
$321$	−1.30587			−0.0728865
$322$	2.64320	−	5.54584i	0.147300	−	0.309058i
$323$		−	2.35076i		−	0.130800i
$324$	0.142315	−	0.989821i	0.00790638	−	0.0549901i
$325$	2.87872	−	1.52545i	0.159683	−	0.0846170i
$326$	2.19771	+	0.645305i	0.121720	+	0.0357401i
$327$	8.83399	−	7.65470i	0.488521	−	0.423306i
$328$	0.230747	+	0.785851i	0.0127408	+	0.0433913i
$329$	−1.80083	−	1.15732i	−0.0992828	−	0.0638052i
$330$	−2.70029	+	6.40543i	−0.148646	+	0.352608i
$331$	−7.27654	+	8.39757i	−0.399955	+	0.461572i	−0.919627	−	0.392793i	$-0.871509\pi$
$331$	−7.27654	+	8.39757i	−0.399955	+	0.461572i	0.519672	+	0.854366i	$0.326054\pi$
$332$	3.10259	+	4.82772i	0.170277	+	0.264955i
$333$	−0.479645	+	0.0689626i	−0.0262844	+	0.00377912i
$334$	1.44394	+	10.0428i	0.0790087	+	0.549518i
$335$	−1.73581	−	2.53373i	−0.0948372	−	0.138432i
$336$	0.838885	−	0.968125i	0.0457649	−	0.0528156i
$337$	13.6438	+	6.23093i	0.743227	+	0.339420i	0.750781	−	0.660551i	$-0.229677\pi$
$337$	13.6438	+	6.23093i	0.743227	+	0.339420i	−0.00755433	+	0.999971i	$0.502405\pi$
$338$	6.79880	−	10.5791i	0.369806	−	0.575429i
$339$	3.25483	−	0.955705i	0.176778	−	0.0519068i
$340$	−4.22381	+	3.88346i	−0.229069	+	0.210610i
$341$	17.0451	+	5.00491i	0.923046	+	0.271031i
$342$	0.833329	−	0.380568i	0.0450612	−	0.0205788i
$343$	15.6709	+	2.25314i	0.846149	+	0.121658i
$344$	7.08437			0.381964
$345$	−10.6337	−	1.38717i	−0.572500	−	0.0746827i
$346$	3.78695			0.203588
$347$	33.4555	+	4.81018i	1.79599	+	0.258224i	0.957856	−	0.287248i	$-0.0927403\pi$
$347$	33.4555	+	4.81018i	1.79599	+	0.258224i	0.838129	+	0.545471i	$0.183649\pi$
$348$	1.03441	−	0.472399i	0.0554502	−	0.0253233i
$349$	4.78972	+	1.40639i	0.256388	+	0.0752823i	0.407401	−	0.913250i	$-0.366435\pi$
$349$	4.78972	+	1.40639i	0.256388	+	0.0752823i	−0.151013	+	0.988532i	$0.548253\pi$
$350$	4.47204	+	4.58538i	0.239041	+	0.245099i
$351$	−0.625190	+	0.183572i	−0.0333702	+	0.00979837i
$352$	1.68071	−	2.61523i	0.0895821	−	0.139392i
$353$	−19.6315	−	8.96543i	−1.04488	−	0.477182i	−0.182376	−	0.983229i	$-0.558379\pi$
$353$	−19.6315	−	8.96543i	−1.04488	−	0.477182i	−0.862506	+	0.506047i	$0.831106\pi$
$354$	−2.72768	+	3.14791i	−0.144975	+	0.167310i
$355$	13.0404	−	8.93369i	0.692111	−	0.474151i
$356$	0.820032	+	5.70345i	0.0434616	+	0.302282i
$357$	−3.25363	+	0.467801i	−0.172200	+	0.0247587i
$358$	3.55548	+	5.53243i	0.187913	+	0.292398i
$359$	−24.5656	+	28.3502i	−1.29652	+	1.49627i	−0.541239	+	0.840869i	$0.682045\pi$
$359$	−24.5656	+	28.3502i	−1.29652	+	1.49627i	−0.755284	+	0.655398i	$0.772501\pi$
$360$	−2.06046	−	0.868614i	−0.108596	−	0.0457800i
$361$	−15.2778	−	9.81843i	−0.804094	−	0.516760i
$362$	−2.37873	−	8.10122i	−0.125023	−	0.425791i
$363$	1.00951	−	0.874742i	0.0529853	−	0.0459121i
$364$	−0.800877	−	0.235159i	−0.0419774	−	0.0123257i
$365$	−4.83567	+	2.38285i	−0.253110	+	0.124724i
$366$	−1.60806	+	11.1843i	−0.0840546	+	0.584613i
$367$			1.02746i			0.0536329i	0.999640	+	0.0268164i	$0.00853696\pi$
$367$			1.02746i			0.0536329i	−0.999640	+	0.0268164i	$0.991463\pi$
$368$	4.57884	+	1.42625i	0.238689	+	0.0743482i
$369$	0.819027			0.0426368
$370$	−0.122564	+	1.07659i	−0.00637180	+	0.0559695i
$371$	−2.39750	−	5.24979i	−0.124472	−	0.272556i
$372$	−1.60995	+	5.48298i	−0.0834720	+	0.284279i
$373$	11.1821	−	9.68930i	0.578985	−	0.501693i	−0.315420	−	0.948952i	$-0.602145\pi$
$373$	11.1821	−	9.68930i	0.578985	−	0.501693i	0.894404	+	0.447259i	$0.147600\pi$
$374$	−7.65390	+	2.24739i	−0.395774	+	0.116210i
$375$	5.19127	−	9.90206i	0.268076	−	0.511340i
$376$	0.694182	−	1.52005i	0.0357997	−	0.0783904i
$377$	−0.559984	−	0.485229i	−0.0288406	−	0.0249905i
$378$	−0.692568	−	1.07766i	−0.0356219	−	0.0554287i
$379$	−5.27072	−	36.6587i	−0.270739	−	1.88303i	−0.440815	−	0.897598i	$-0.645311\pi$
$379$	−5.27072	−	36.6587i	−0.270739	−	1.88303i	0.170077	−	0.985431i	$-0.445598\pi$
$380$	−0.351098	−	2.01819i	−0.0180109	−	0.103531i
$381$	−14.2077	+	9.13073i	−0.727882	+	0.467782i
$382$	−14.1990	−	12.3035i	−0.726484	−	0.629502i
$383$	−1.69606	−	0.774563i	−0.0866644	−	0.0395783i	0.371611	−	0.928388i	$-0.378805\pi$
$383$	−1.69606	−	0.774563i	−0.0866644	−	0.0395783i	−0.458276	+	0.888810i	$0.651533\pi$
$384$	0.841254	+	0.540641i	0.0429300	+	0.0275895i
$385$	2.75920	+	8.46650i	0.140622	+	0.431493i
$386$	15.9710	+	18.4315i	0.812901	+	0.938138i
$387$	1.99590	−	6.79741i	0.101457	−	0.345532i
$388$	−10.6129	+	4.84675i	−0.538788	+	0.246056i
$389$	−0.589482	+	4.09994i	−0.0298879	+	0.207875i	−0.999293	−	0.0375906i	$-0.988032\pi$
$389$	−0.589482	+	4.09994i	−0.0298879	+	0.207875i	0.969405	+	0.245466i	$0.0789408\pi$
$390$	0.0428925	+	1.45635i	0.00217195	+	0.0737454i
$391$	−6.48293	−	10.4600i	−0.327856	−	0.528987i
$392$			5.35900i			0.270671i
$393$	−3.92074	−	0.563718i	−0.197775	−	0.0284358i
$394$	−6.44734	−	14.1177i	−0.324812	−	0.711239i
$395$	15.2378	+	3.99094i	0.766699	+	0.200806i
$396$	−2.03579	−	2.34942i	−0.102302	−	0.118063i
$397$	−2.51379	−	8.56118i	−0.126163	−	0.429673i	0.872050	−	0.489416i	$-0.162790\pi$
$397$	−2.51379	−	8.56118i	−0.126163	−	0.429673i	−0.998214	+	0.0597430i	$0.980972\pi$
$398$	−12.4259	+	19.3350i	−0.622852	+	0.969177i
$399$	0.487513	−	1.06750i	0.0244062	−	0.0534421i
$400$	−3.04624	+	3.96490i	−0.152312	+	0.198245i
$401$	29.2511	−	18.7986i	1.46073	−	0.938755i	0.462080	−	0.886838i	$-0.347103\pi$
$401$	29.2511	−	18.7986i	1.46073	−	0.938755i	0.998651	−	0.0519166i	$-0.0165330\pi$
$402$	1.35954	−	0.195472i	0.0678077	−	0.00974928i
$403$	3.68555	−	0.529902i	0.183590	−	0.0263963i
$404$	−5.23256	+	3.36276i	−0.260329	+	0.167304i
$405$	−1.41393	+	1.73228i	−0.0702587	+	0.0860778i
$406$	0.605150	−	1.32509i	0.0300331	−	0.0657633i
$407$	−0.814434	+	1.26728i	−0.0403700	+	0.0628169i
$408$	−0.722927	−	2.46206i	−0.0357902	−	0.121890i
$409$	−3.02882	−	3.49545i	−0.149766	−	0.172839i	0.675909	−	0.736985i	$-0.263751\pi$
$409$	−3.02882	−	3.49545i	−0.149766	−	0.172839i	−0.825675	+	0.564146i	$0.809206\pi$
$410$	0.464010	−	1.77164i	0.0229158	−	0.0874952i
$411$	−3.92957	−	8.60457i	−0.193832	−	0.424432i
$412$	10.5226	+	1.51293i	0.518413	+	0.0745366i
$413$			5.33579i			0.262557i
$414$	2.65848	−	3.99155i	0.130657	−	0.196174i
$415$	−0.377769	−	12.8266i	−0.0185439	−	0.629633i
$416$	0.0927301	−	0.644952i	0.00454647	−	0.0316214i
$417$	9.05877	−	4.13700i	0.443610	−	0.202590i
$418$	0.802364	−	2.73260i	0.0392449	−	0.133656i
$419$	−0.304385	−	0.351279i	−0.0148702	−	0.0171611i	0.748266	−	0.663399i	$-0.230887\pi$
$419$	−0.304385	−	0.351279i	−0.0148702	−	0.0171611i	−0.763136	+	0.646238i	$0.776341\pi$
$420$	−2.72345	+	0.887565i	−0.132891	+	0.0433087i
$421$	−9.29231	−	5.97181i	−0.452880	−	0.291048i	0.294248	−	0.955729i	$-0.404931\pi$
$421$	−9.29231	−	5.97181i	−0.452880	−	0.291048i	−0.747127	+	0.664681i	$0.768567\pi$
$422$	3.97477	+	1.81522i	0.193489	+	0.0883634i
$423$	−1.26290	−	1.09431i	−0.0614043	−	0.0532071i
$424$	3.79009	−	2.43574i	0.184063	−	0.118290i
$425$	12.5700	−	2.57014i	0.609733	−	0.124670i
$426$	1.00604	+	6.99716i	0.0487428	+	0.339014i
$427$	7.82554	+	12.1768i	0.378705	+	0.589276i
$428$	−0.986910	−	0.855162i	−0.0477041	−	0.0413358i
$429$	−0.841465	+	1.84255i	−0.0406263	+	0.0889593i
$430$	−13.5728	−	8.16833i	−0.654537	−	0.393912i
$431$	4.94095	−	1.45079i	0.237997	−	0.0698822i	−0.160559	−	0.987026i	$-0.551330\pi$
$431$	4.94095	−	1.45079i	0.237997	−	0.0698822i	0.398556	+	0.917144i	$0.369511\pi$
$432$	0.755750	−	0.654861i	0.0363610	−	0.0315070i
$433$	−3.05542	+	10.4058i	−0.146834	+	0.500071i	−0.999759	−	0.0219628i	$-0.993008\pi$
$433$	−3.05542	+	10.4058i	−0.146834	+	0.500071i	0.852925	+	0.522034i	$0.174827\pi$
$434$	3.04096	+	6.65878i	0.145971	+	0.319632i
$435$	−2.52648	−	0.287625i	−0.121135	−	0.0137906i
$436$	11.6890			0.559804
$437$	4.39295	+	0.0718818i	0.210143	+	0.00343857i
$438$		−	2.41088i		−	0.115196i
$439$	4.50478	−	31.3315i	0.215002	−	1.49537i	−0.541124	−	0.840943i	$-0.682001\pi$
$439$	4.50478	−	31.3315i	0.215002	−	1.49537i	0.756126	−	0.654426i	$-0.227090\pi$
$440$	−6.23541	+	3.07259i	−0.297262	+	0.146480i
$441$	5.14193	+	1.50981i	0.244854	+	0.0718955i
$442$	−1.26359	+	1.09491i	−0.0601028	+	0.0520794i
$443$	8.57888	+	29.2170i	0.407595	+	1.38814i	0.866288	+	0.499545i	$0.166500\pi$
$443$	8.57888	+	29.2170i	0.407595	+	1.38814i	−0.458693	+	0.888595i	$0.651682\pi$
$444$	−0.407652	−	0.261982i	−0.0193463	−	0.0124331i
$445$	5.00504	−	11.8726i	0.237262	−	0.562815i
$446$	1.35074	−	1.55884i	0.0639595	−	0.0738132i
$447$	−9.20190	−	14.3184i	−0.435235	−	0.677239i
$448$	1.26797	−	0.182307i	0.0599062	−	0.00861321i
$449$	4.53960	+	31.5736i	0.214237	+	1.49005i	0.758796	+	0.651328i	$0.225788\pi$
$449$	4.53960	+	31.5736i	0.214237	+	1.49005i	−0.544559	+	0.838722i	$0.683303\pi$
$450$	2.94607	+	4.03989i	0.138879	+	0.190442i
$451$	1.66737	−	1.92424i	0.0785132	−	0.0906090i
$452$	3.08569	+	1.40919i	0.145139	+	0.0662827i
$453$	−9.04342	+	14.0718i	−0.424897	+	0.661152i
$454$	−13.4541	+	3.95048i	−0.631433	+	0.185405i
$455$	1.26324	+	1.37395i	0.0592216	+	0.0644118i
$456$	0.879007	+	0.258100i	0.0411633	+	0.0120866i
$457$	14.8606	−	6.78661i	0.695150	−	0.317464i	−0.0363181	−	0.999340i	$-0.511563\pi$
$457$	14.8606	−	6.78661i	0.695150	−	0.317464i	0.731468	+	0.681876i	$0.238836\pi$
$458$	19.0098	+	2.73320i	0.888270	+	0.127714i
$459$	−2.56600			−0.119771
$460$	−7.12802	−	8.01195i	−0.332346	−	0.373559i
$461$	−13.8184			−0.643586			−0.321793	−	0.946810i	$-0.604286\pi$
$461$	−13.8184			−0.643586			−0.321793	+	0.946810i	$0.604286\pi$
$462$	−3.94180	−	0.566745i	−0.183389	−	0.0263674i
$463$	−2.31737	+	1.05831i	−0.107697	+	0.0491838i	−0.468535	−	0.883445i	$-0.655218\pi$
$463$	−2.31737	+	1.05831i	−0.107697	+	0.0491838i	0.360838	+	0.932629i	$0.382491\pi$
$464$	1.09111	+	0.320379i	0.0506535	+	0.0148732i
$465$	9.40638	−	8.64842i	0.436210	−	0.401061i
$466$	18.8275	−	5.52824i	0.872165	−	0.256091i
$467$	−5.53538	+	8.61322i	−0.256147	+	0.398572i	−0.945382	−	0.325966i	$-0.894311\pi$
$467$	−5.53538	+	8.61322i	−0.256147	+	0.398572i	0.689235	+	0.724538i	$0.257947\pi$
$468$	−0.592702	−	0.270678i	−0.0273976	−	0.0125121i
$469$	1.15223	−	1.32974i	0.0532049	−	0.0614017i
$470$	−3.08259	+	2.11182i	−0.142189	+	0.0974110i
$471$	3.29073	+	22.8875i	0.151629	+	1.05460i
$472$	−4.12289	+	0.592782i	−0.189771	+	0.0272850i
$473$	−11.9068	−	18.5273i	−0.547474	−	0.851886i
$474$	−4.61312	+	5.32382i	−0.211887	+	0.244531i
$475$	−1.65432	+	4.27141i	−0.0759056	+	0.195986i
$476$	−2.76527	−	1.77713i	−0.126746	−	0.0814548i
$477$	−1.26929	−	4.32279i	−0.0581166	−	0.197927i
$478$	−19.3943	+	16.8053i	−0.887075	+	0.768654i
$479$	−29.0948	−	8.54300i	−1.32937	−	0.390340i	−0.461508	−	0.887136i	$-0.652691\pi$
$479$	−29.0948	−	8.54300i	−1.32937	−	0.390340i	−0.867867	+	0.496797i	$0.834510\pi$
$480$	−0.988373	−	2.00577i	−0.0451128	−	0.0915505i
$481$	−0.0449349	+	0.312529i	−0.00204885	+	0.0142501i
$482$		−	15.1387i		−	0.689551i
$483$	−0.774708	−	6.09448i	−0.0352504	−	0.277309i
$484$	1.33577			0.0607167
$485$	25.9213	+	2.95099i	1.17703	+	0.133998i
$486$	−0.415415	−	0.909632i	−0.0188436	−	0.0412617i
$487$	0.119278	−	0.406223i	0.00540500	−	0.0184077i	−0.956746	−	0.290923i	$-0.906037\pi$
$487$	0.119278	−	0.406223i	0.00540500	−	0.0184077i	0.962151	+	0.272516i	$0.0878557\pi$
$488$	−8.53945	+	7.39948i	−0.386563	+	0.334959i
$489$	2.19771	−	0.645305i	0.0993837	−	0.0291817i
$490$	6.17897	−	10.2672i	0.279138	−	0.463824i
$491$	3.67080	−	8.03794i	0.165661	−	0.362747i	−0.808536	−	0.588447i	$-0.799740\pi$
$491$	3.67080	−	8.03794i	0.165661	−	0.362747i	0.974197	+	0.225700i	$0.0724669\pi$
$492$	0.618979	+	0.536349i	0.0279057	+	0.0241805i
$493$	−1.57759	−	2.45477i	−0.0710509	−	0.110557i
$494$	−0.0849515	−	0.590851i	−0.00382215	−	0.0265836i
$495$	1.19141	+	6.84848i	0.0535499	+	0.307816i
$496$	−4.80731	+	3.08947i	−0.215855	+	0.138721i
$497$	6.84379	+	5.93018i	0.306986	+	0.266005i
$498$	5.22012	+	2.38395i	0.233919	+	0.106827i
$499$	−34.1089	−	21.9205i	−1.52692	−	0.981295i	−0.990525	−	0.137330i	$-0.956148\pi$
$499$	−34.1089	−	21.9205i	−1.52692	−	0.981295i	−0.536399	−	0.843964i	$-0.680216\pi$
$500$	10.4078	−	4.08391i	0.465450	−	0.182638i
$501$	6.64427	+	7.66789i	0.296844	+	0.342576i
$502$	0.908298	−	3.09338i	0.0405393	−	0.138064i
$503$	−32.2749	+	14.7395i	−1.43907	+	0.657201i	−0.973683	−	0.227907i	$-0.926812\pi$
$503$	−32.2749	+	14.7395i	−1.43907	+	0.657201i	−0.465386	+	0.885108i	$0.654084\pi$
$504$	0.182307	−	1.26797i	0.00812061	−	0.0564801i
$505$	13.9022	−	0.409448i	0.618640	−	0.0182202i
$506$	−3.96574	−	14.3719i	−0.176299	−	0.638907i
$507$		−	12.5754i		−	0.558495i
$508$	−16.7168	−	2.40352i	−0.741689	−	0.106639i
$509$	16.6921	+	36.5506i	0.739865	+	1.62008i	0.783776	+	0.621043i	$0.213291\pi$
$509$	16.6921	+	36.5506i	0.739865	+	1.62008i	−0.0439112	+	0.999035i	$0.513982\pi$
$510$	−1.45374	+	5.55054i	−0.0643727	+	0.245782i
$511$	−2.02245	−	2.33403i	−0.0894679	−	0.103251i
$512$	0.281733	+	0.959493i	0.0124509	+	0.0424040i
$513$	0.495290	−	0.770686i	0.0218676	−	0.0340266i
$514$	8.05384	−	17.6354i	0.355240	−	0.777866i
$515$	−18.4156	−	15.0313i	−0.811490	−	0.662356i
$516$	5.95975	−	3.83010i	0.262363	−	0.168611i
$517$	−5.14200	+	0.739307i	−0.226145	+	0.0325147i
$518$	−0.614432	+	0.0883420i	−0.0269966	+	0.00388152i
$519$	3.18579	−	2.04738i	0.139840	−	0.0898700i
$520$	−0.921293	+	1.12873i	−0.0404014	+	0.0494980i
$521$	−8.16189	+	17.8720i	−0.357579	+	0.782988i	0.642285	+	0.766466i	$0.277987\pi$
$521$	−8.16189	+	17.8720i	−0.357579	+	0.782988i	−0.999863	+	0.0165222i	$0.994741\pi$
$522$	0.614803	−	0.956652i	0.0269092	−	0.0418715i
$523$	−4.23447	−	14.4213i	−0.185161	−	0.630599i	−0.998788	−	0.0492130i	$-0.984329\pi$
$523$	−4.23447	−	14.4213i	−0.185161	−	0.630599i	0.813628	−	0.581386i	$-0.197489\pi$
$524$	−2.59394	−	2.99357i	−0.113317	−	0.130775i
$525$	6.24117	+	1.43970i	0.272387	+	0.0628337i
$526$	−2.65308	−	5.80942i	−0.115680	−	0.253303i
$527$	14.5141	+	2.08681i	0.632243	+	0.0909028i
$528$		−	3.10873i		−	0.135290i
$529$	19.7453	−	11.7950i	0.858491	−	0.512828i
$530$	−10.0698	+	0.296575i	−0.437403	+	0.0128824i
$531$	−0.592782	+	4.12289i	−0.0257245	+	0.178918i
$532$	1.06750	−	0.487513i	0.0462822	−	0.0211364i
$533$	0.150351	−	0.512048i	0.00651241	−	0.0221792i
$534$	3.77337	+	4.35470i	0.163290	+	0.188446i
$535$	0.904786	+	2.77630i	0.0391173	+	0.120030i
$536$	1.15548	+	0.742581i	0.0499091	+	0.0320746i
$537$	5.98212	+	2.73194i	0.258147	+	0.117892i
$538$	−1.00748	−	0.872986i	−0.0434355	−	0.0376371i
$539$	14.0151	−	9.00693i	0.603671	−	0.387956i
$540$	−2.20298	+	0.383246i	−0.0948012	+	0.0164923i
$541$	0.532784	+	3.70559i	0.0229062	+	0.159316i	0.998064	−	0.0621953i	$-0.0198102\pi$
$541$	0.532784	+	3.70559i	0.0229062	+	0.159316i	−0.975158	+	0.221511i	$0.928901\pi$
$542$	0.718889	+	1.11861i	0.0308789	+	0.0480486i
$543$	−6.38097	−	5.52914i	−0.273834	−	0.237278i
$544$	1.06596	−	2.33412i	0.0457025	−	0.100075i
$545$	−22.3947	−	13.4776i	−0.959285	−	0.577315i
$546$	−0.800877	+	0.235159i	−0.0342744	+	0.0100639i
$547$	9.18415	−	7.95811i	0.392686	−	0.340264i	−0.436032	−	0.899931i	$-0.643616\pi$
$547$	9.18415	−	7.95811i	0.392686	−	0.340264i	0.828718	+	0.559667i	$0.189071\pi$
$548$	2.66502	−	9.07622i	0.113844	−	0.387717i
$549$	4.69390	+	10.2782i	0.200331	+	0.438664i
$550$	15.4890	+	1.30278i	0.660452	+	0.0555508i
$551$	1.04178			0.0443815
$552$	4.62306	−	1.27568i	0.196770	−	0.0542964i
$553$			9.02400i			0.383740i
$554$	−0.249413	+	1.73470i	−0.0105965	+	0.0737005i
$555$	0.478943	+	0.971952i	0.0203300	+	0.0412570i
$556$	9.55532	+	2.80570i	0.405236	+	0.118988i
$557$	16.1912	−	14.0298i	0.686043	−	0.594460i	−0.240499	−	0.970649i	$-0.577311\pi$
$557$	16.1912	−	14.0298i	0.686043	−	0.594460i	0.926543	+	0.376189i	$0.122766\pi$
$558$	1.60995	+	5.48298i	0.0681546	+	0.232113i
$559$	−3.88328	−	2.49563i	−0.164245	−	0.105554i
$560$	−2.63948	−	1.11271i	−0.111538	−	0.0470204i
$561$	−5.22384	+	6.02864i	−0.220551	+	0.254529i
$562$	−5.51706	−	8.58472i	−0.232723	−	0.362125i
$563$	−19.6803	+	2.82960i	−0.829426	+	0.119253i	−0.543934	−	0.839128i	$-0.683066\pi$
$563$	−19.6803	+	2.82960i	−0.829426	+	0.119253i	−0.285491	+	0.958381i	$0.592157\pi$
$564$	−0.237816	−	1.65405i	−0.0100139	−	0.0696480i
$565$	−4.28699	−	6.25765i	−0.180355	−	0.263262i
$566$	15.7395	−	18.1644i	0.661583	−	0.763507i
$567$	−1.16525	−	0.532152i	−0.0489359	−	0.0223483i
$568$	−3.82185	+	5.94692i	−0.160361	+	0.249527i
$569$	−28.3438	+	8.32250i	−1.18824	+	0.348897i	−0.815344	−	0.578978i	$-0.803452\pi$
$569$	−28.3438	+	8.32250i	−1.18824	+	0.348897i	−0.372892	+	0.927875i	$0.621634\pi$
$570$	−1.38648	−	1.50799i	−0.0580731	−	0.0631627i
$571$	21.8117	+	6.40449i	0.912791	+	0.268019i	0.704215	−	0.709987i	$-0.251299\pi$
$571$	21.8117	+	6.40449i	0.912791	+	0.268019i	0.208576	+	0.978006i	$0.433117\pi$
$572$	−1.84255	+	0.841465i	−0.0770410	+	0.0351834i
$573$	−18.5967	−	2.67381i	−0.776890	−	0.111700i
$574$	1.04918			0.0437921
$575$	4.41854	+	23.5685i	0.184266	+	0.982876i
$576$	1.00000			0.0416667
$577$	−2.19973	−	0.316273i	−0.0915758	−	0.0131666i	0.0963746	−	0.995345i	$-0.469275\pi$
$577$	−2.19973	−	0.316273i	−0.0915758	−	0.0131666i	−0.187950	+	0.982179i	$0.560184\pi$
$578$	9.47438	−	4.32681i	0.394082	−	0.179971i
$579$	23.4004	+	6.87099i	0.972489	+	0.285549i
$580$	−1.72103	−	1.87186i	−0.0714619	−	0.0777250i
$581$	7.05359	−	2.07112i	0.292632	−	0.0859246i
$582$	−6.30779	+	9.81511i	−0.261466	+	0.406849i
$583$	−12.7401	−	5.81820i	−0.527640	−	0.240965i
$584$	1.57879	−	1.82202i	0.0653307	−	0.0753957i
$585$	0.823448	+	1.20197i	0.0340454	+	0.0496955i
$586$	−2.15642	−	14.9982i	−0.0890809	−	0.619571i
$587$	−30.4068	+	4.37183i	−1.25502	+	0.180445i	−0.737572	−	0.675269i	$-0.764028\pi$
$587$	−30.4068	+	4.37183i	−1.25502	+	0.180445i	−0.517450	+	0.855714i	$0.673119\pi$
$588$	2.89730	+	4.50828i	0.119483	+	0.185918i
$589$	−3.42827	+	3.95643i	−0.141259	+	0.163022i
$590$	8.58242	+	3.61803i	0.353332	+	0.148952i
$591$	−13.0564	−	8.39087i	−0.537071	−	0.345154i
$592$	−0.136521	−	0.464949i	−0.00561099	−	0.0191093i
$593$	−19.2840	+	16.7097i	−0.791900	+	0.686185i	−0.953740	−	0.300632i	$-0.902802\pi$
$593$	−19.2840	+	16.7097i	−0.791900	+	0.686185i	0.161840	+	0.986817i	$0.448257\pi$
$594$	−2.98281	−	0.875832i	−0.122386	−	0.0359358i
$595$	3.24887	+	6.59314i	0.133191	+	0.270293i
$596$	2.42225	−	16.8471i	0.0992192	−	0.690085i
$597$			22.9836i			0.940656i
$598$	−2.00745	−	2.39480i	−0.0820909	−	0.0979305i
$599$	−33.1178			−1.35316			−0.676578	−	0.736371i	$-0.736538\pi$
$599$	−33.1178			−1.35316			−0.676578	+	0.736371i	$0.736538\pi$
$600$	−0.419071	+	4.98241i	−0.0171085	+	0.203406i
$601$	7.23861	+	15.8503i	0.295269	+	0.646549i	0.997884	−	0.0650214i	$-0.0207116\pi$
$601$	7.23861	+	15.8503i	0.295269	+	0.646549i	−0.702615	+	0.711570i	$0.747984\pi$
$602$	2.55677	−	8.70757i	0.104206	−	0.354894i
$603$	1.03804	−	0.899465i	0.0422722	−	0.0366290i
$604$	−16.0497	+	4.71260i	−0.653051	+	0.191753i
$605$	−2.55916	−	1.54015i	−0.104045	−	0.0626160i
$606$	−2.58386	+	5.65787i	−0.104962	+	0.229835i
$607$	33.8252	+	29.3097i	1.37292	+	1.18964i	0.960377	+	0.278706i	$0.0899054\pi$
$607$	33.8252	+	29.3097i	1.37292	+	1.18964i	0.412545	+	0.910937i	$0.364640\pi$
$608$	0.495290	+	0.770686i	0.0200867	+	0.0312554i
$609$	−0.207315	−	1.44191i	−0.00840083	−	0.0584291i
$610$	24.8922	−	4.33041i	1.00785	−	0.175333i
$611$	−0.915985	+	0.588668i	−0.0370568	+	0.0238150i
$612$	−1.93926	−	1.68038i	−0.0783898	−	0.0679252i
$613$	−43.6926	−	19.9537i	−1.76473	−	0.805924i	−0.983316	−	0.181907i	$-0.941773\pi$
$613$	−43.6926	−	19.9537i	−1.76473	−	0.805924i	−0.781411	−	0.624017i	$-0.785500\pi$
$614$	−26.7966	−	17.2211i	−1.08142	−	0.694988i
$615$	−0.567472	−	1.74126i	−0.0228827	−	0.0702145i
$616$	−2.60787	−	3.00964i	−0.105074	−	0.121262i
$617$	−8.49136	+	28.9189i	−0.341849	+	1.16423i	0.591812	+	0.806076i	$0.298413\pi$
$617$	−8.49136	+	28.9189i	−0.341849	+	1.16423i	−0.933662	+	0.358156i	$0.883405\pi$
$618$	9.67016	−	4.41621i	0.388991	−	0.177646i
$619$	1.67235	−	11.6315i	0.0672176	−	0.467509i	−0.928215	−	0.372044i	$-0.878657\pi$
$619$	1.67235	−	11.6315i	0.0672176	−	0.467509i	0.995433	−	0.0954649i	$-0.0304338\pi$
$620$	12.7724	−	0.376172i	0.512951	−	0.0151074i
$621$	0.0784636	−	4.79519i	0.00314864	−	0.192424i
$622$			16.3650i			0.656176i
$623$	7.30619	+	1.05047i	0.292716	+	0.0420863i
$624$	−0.270678	−	0.592702i	−0.0108358	−	0.0237271i
$625$	−24.6488	−	4.17597i	−0.985950	−	0.167039i
$626$	1.91085	+	2.20523i	0.0763728	+	0.0881389i
$627$	−0.802364	−	2.73260i	−0.0320433	−	0.109130i
$628$	−12.5012	+	19.4522i	−0.498851	+	0.776227i
$629$	−0.516539	+	1.13106i	−0.0205957	+	0.0450984i
$630$	−1.81126	+	2.21908i	−0.0721624	+	0.0884102i
$631$	4.56351	−	2.93279i	0.181670	−	0.116752i	−0.446645	−	0.894711i	$-0.647381\pi$
$631$	4.56351	−	2.93279i	0.181670	−	0.116752i	0.628315	+	0.777959i	$0.283745\pi$
$632$	−6.97272	+	1.00253i	−0.277360	+	0.0398783i
$633$	4.32517	−	0.621866i	0.171910	−	0.0247169i
$634$	20.9267	−	13.4488i	0.831105	−	0.534118i
$635$	29.2561	+	23.8795i	1.16099	+	0.947627i
$636$	1.87156	−	4.09816i	0.0742124	−	0.162502i
$637$	1.88783	−	2.93752i	0.0747986	−	0.116389i
$638$	−0.995973	−	3.39197i	−0.0394310	−	0.134290i
$639$	4.62929	+	5.34248i	0.183132	+	0.211345i
$640$	0.566539	−	2.16311i	0.0223944	−	0.0855043i
$641$	−11.6024	−	25.4056i	−0.458266	−	1.00346i	−0.987879	−	0.155223i	$-0.950390\pi$
$641$	−11.6024	−	25.4056i	−0.458266	−	1.00346i	0.529614	−	0.848239i	$-0.322337\pi$
$642$	−1.29258	−	0.185845i	−0.0510139	−	0.00733470i
$643$			40.4315i			1.59446i	0.603675	+	0.797231i	$0.293703\pi$
$643$			40.4315i			1.59446i	−0.603675	+	0.797231i	$0.706297\pi$
$644$	3.40555	−	5.11323i	0.134198	−	0.201489i
$645$	−15.8343	+	0.466351i	−0.623474	+	0.0183625i
$646$	0.334548	−	2.32683i	0.0131626	−	0.0915479i
$647$	−24.9327	+	11.3864i	−0.980205	+	0.447645i	−0.840064	−	0.542487i	$-0.817483\pi$
$647$	−24.9327	+	11.3864i	−0.980205	+	0.447645i	−0.140141	+	0.990132i	$0.544756\pi$
$648$	0.281733	−	0.959493i	0.0110675	−	0.0376924i
$649$	8.47964	+	9.78602i	0.332855	+	0.384135i
$650$	3.06651	−	1.10024i	0.120279	−	0.0431551i
$651$	6.15823	+	3.95765i	0.241360	+	0.155113i
$652$	2.08350	+	0.951503i	0.0815962	+	0.0372637i
$653$	−1.03848	−	0.899846i	−0.0406388	−	0.0352137i	0.634305	−	0.773083i	$-0.281287\pi$
$653$	−1.03848	−	0.899846i	−0.0406388	−	0.0352137i	−0.674943	+	0.737870i	$0.735832\pi$
$654$	9.83345	−	6.31957i	0.384518	−	0.247115i
$655$	1.51806	+	8.72614i	0.0593155	+	0.340959i
$656$	0.116560	+	0.810690i	0.00455089	+	0.0316521i
$657$	−1.30342	−	2.02816i	−0.0508512	−	0.0791260i
$658$	−1.61779	−	1.40183i	−0.0630681	−	0.0546488i
$659$	−7.41133	+	16.2285i	−0.288704	+	0.632175i	−0.997300	−	0.0734407i	$-0.976602\pi$
$659$	−7.41133	+	16.2285i	−0.288704	+	0.632175i	0.708595	+	0.705615i	$0.249329\pi$
$660$	−3.58439	+	5.95594i	−0.139522	+	0.231835i
$661$	−35.0297	+	10.2856i	−1.36250	+	0.400065i	−0.879642	−	0.475636i	$-0.842218\pi$
$661$	−35.0297	+	10.2856i	−1.36250	+	0.400065i	−0.482854	+	0.875701i	$0.660400\pi$
$662$	−8.39757	+	7.27654i	−0.326381	+	0.282811i
$663$	−0.471048	+	1.60424i	−0.0182940	+	0.0623036i
$664$	2.38395	+	5.22012i	0.0925152	+	0.202580i
$665$	−2.60731	−	0.296827i	−0.101107	−	0.0115105i
$666$	−0.484577			−0.0187770
$667$	4.63557	−	2.87303i	0.179490	−	0.111244i
$668$			10.1461i			0.392563i
$669$	0.293545	−	2.04165i	0.0113491	−	0.0789346i
$670$	−1.35755	−	2.75497i	−0.0524468	−	0.106434i
$671$	33.7037	+	9.89630i	1.30112	+	0.382042i
$672$	0.968125	−	0.838885i	0.0373462	−	0.0323607i
$673$	−0.0423067	−	0.144083i	−0.00163080	−	0.00555400i	0.958674	−	0.284508i	$-0.0918304\pi$
$673$	−0.0423067	−	0.144083i	−0.00163080	−	0.00555400i	−0.960304	+	0.278954i	$0.910012\pi$
$674$	12.6182	+	8.10922i	0.486035	+	0.312356i
$675$	4.66252	+	1.80580i	0.179460	+	0.0695054i
$676$	8.23516	−	9.50388i	0.316737	−	0.365534i
$677$	26.7417	+	41.6108i	1.02777	+	1.59923i	0.775264	+	0.631638i	$0.217617\pi$
$677$	26.7417	+	41.6108i	1.02777	+	1.59923i	0.252502	+	0.967596i	$0.418747\pi$
$678$	3.35771	−	0.482767i	0.128952	−	0.0185405i
$679$	2.12702	+	14.7938i	0.0816277	+	0.567733i
$680$	−4.73350	+	3.24282i	−0.181521	+	0.124357i
$681$	−9.18252	+	10.5972i	−0.351875	+	0.406085i
$682$	16.1594	+	7.37974i	0.618774	+	0.282585i
$683$	−20.7301	+	32.2567i	−0.793216	+	1.23427i	0.175103	+	0.984550i	$0.443974\pi$
$683$	−20.7301	+	32.2567i	−0.793216	+	1.23427i	−0.968319	+	0.249717i	$0.919662\pi$
$684$	0.879007	−	0.258100i	0.0336097	−	0.00986869i
$685$	−15.5708	+	14.3161i	−0.594930	+	0.546991i
$686$	15.1907	+	4.46040i	0.579985	+	0.170299i
$687$	17.4698	−	7.97817i	0.666513	−	0.304386i
$688$	7.01226	+	1.00821i	0.267340	+	0.0384377i
$689$	−2.93557			−0.111836
$690$	−10.3281	−	2.88638i	−0.393182	−	0.109883i
$691$	22.8459			0.869100			0.434550	−	0.900648i	$-0.356907\pi$
$691$	22.8459			0.869100			0.434550	+	0.900648i	$0.356907\pi$
$692$	3.74841	+	0.538939i	0.142493	+	0.0204874i
$693$	−3.62246	+	1.65432i	−0.137606	+	0.0628424i
$694$	32.4304	+	9.52243i	1.23104	+	0.361467i
$695$	−15.0718	−	16.3927i	−0.571706	−	0.621811i
$696$	1.09111	−	0.320379i	0.0413584	−	0.0121439i
$697$	1.13623	−	1.76800i	0.0430376	−	0.0669678i
$698$	4.54082	+	2.07372i	0.171873	+	0.0784916i
$699$	12.8499	−	14.8295i	0.486027	−	0.560905i
$700$	3.77395	+	5.17515i	0.142642	+	0.195602i
$701$	3.49494	+	24.3079i	0.132002	+	0.918095i	0.942940	+	0.332963i	$0.108048\pi$
$701$	3.49494	+	24.3079i	0.132002	+	0.918095i	−0.810938	+	0.585132i	$0.801043\pi$
$702$	−0.644952	+	0.0927301i	−0.0243421	+	0.00349987i
$703$	−0.240006	−	0.373457i	−0.00905201	−	0.0140852i
$704$	2.03579	−	2.34942i	0.0767267	−	0.0885473i
$705$	−1.45150	+	3.44315i	−0.0546668	+	0.129677i
$706$	−18.1558	−	11.6680i	−0.683303	−	0.439132i
$707$	2.24480	+	7.64509i	0.0844244	+	0.287523i
$708$	−3.14791	+	2.72768i	−0.118306	+	0.102513i
$709$	8.67654	+	2.54766i	0.325854	+	0.0956794i	0.440568	−	0.897719i	$-0.354777\pi$
$709$	8.67654	+	2.54766i	0.325854	+	0.0956794i	−0.114714	+	0.993399i	$0.536595\pi$
$710$	14.1790	−	6.98692i	0.532129	−	0.262215i
$711$	−1.00253	+	6.97272i	−0.0375977	+	0.261498i
$712$			5.76210i			0.215944i
$713$	−4.34351	+	27.0592i	−0.162666	+	1.01337i
$714$	−3.28709			−0.123016
$715$	4.50031	+	0.512335i	0.168302	+	0.0191602i
$716$	2.73194	+	5.98212i	0.102097	+	0.223562i
$717$	−7.22992	+	24.6228i	−0.270006	+	0.919556i
$718$	−28.3502	+	24.5656i	−1.05802	+	0.916780i
$719$	−4.65232	+	1.36604i	−0.173502	+	0.0509449i	−0.367330	−	0.930091i	$-0.619728\pi$
$719$	−4.65232	+	1.36604i	−0.173502	+	0.0509449i	0.193828	+	0.981036i	$0.437910\pi$
$720$	−1.91587	−	1.15301i	−0.0714004	−	0.0429701i
$721$	5.65723	−	12.3876i	0.210686	−	0.461338i
$722$	−13.7250	−	11.8927i	−0.510790	−	0.442602i
$723$	−8.18463	−	12.7355i	−0.304389	−	0.473639i
$724$	−1.20160	−	8.35729i	−0.0446570	−	0.310596i
$725$	1.13901	+	5.57062i	0.0423016	+	0.206888i
$726$	1.12372	−	0.722171i	0.0417052	−	0.0268023i
$727$	−22.2030	−	19.2390i	−0.823464	−	0.713536i	0.137412	−	0.990514i	$-0.456122\pi$
$727$	−22.2030	−	19.2390i	−0.823464	−	0.713536i	−0.960876	+	0.276978i	$0.910667\pi$
$728$	−0.759259	−	0.346742i	−0.0281400	−	0.0128511i
$729$	−0.841254	−	0.540641i	−0.0311575	−	0.0200237i
$730$	−5.12556	+	1.67040i	−0.189706	+	0.0618244i
$731$	−11.9044	−	13.7384i	−0.440300	−	0.508134i
$732$	−3.18338	+	10.8416i	−0.117661	+	0.400717i
$733$	−8.04975	+	3.67620i	−0.297324	+	0.135783i	−0.558492	−	0.829510i	$-0.688620\pi$
$733$	−8.04975	+	3.67620i	−0.297324	+	0.135783i	0.261167	+	0.965294i	$0.415893\pi$
$734$	−0.146223	+	1.01700i	−0.00539717	+	0.0375382i
$735$	−0.352773	−	11.9779i	−0.0130122	−	0.441812i
$736$	4.32926	+	2.06337i	0.159579	+	0.0760567i
$737$		−	4.26991i		−	0.157284i
$738$	0.810690	+	0.116560i	0.0298419	+	0.00429062i
$739$	18.9436	+	41.4807i	0.696851	+	1.52589i	0.843748	+	0.536739i	$0.180344\pi$
$739$	18.9436	+	41.4807i	0.696851	+	1.52589i	−0.146897	+	0.989152i	$0.546929\pi$
$740$	−0.274532	+	1.04819i	−0.0100920	+	0.0385323i
$741$	−0.390904	−	0.451127i	−0.0143602	−	0.0165726i
$742$	−1.62597	−	5.53756i	−0.0596914	−	0.203290i
$743$	−8.56150	+	13.3220i	−0.314091	+	0.488735i	−0.962025	−	0.272961i	$-0.911997\pi$
$743$	−8.56150	+	13.3220i	−0.314091	+	0.488735i	0.647934	+	0.761696i	$0.275633\pi$
$744$	−2.37387	+	5.19805i	−0.0870304	+	0.190570i
$745$	−24.0656	+	29.4841i	−0.881695	+	1.08021i
$746$	12.4472	−	7.99931i	0.455723	−	0.292875i
$747$	5.68031	−	0.816705i	0.207832	−	0.0298817i
$748$	−7.89583	+	1.13525i	−0.288700	+	0.0415088i
$749$	−1.40728	+	0.904403i	−0.0514208	+	0.0330462i
$750$	6.54764	−	9.06247i	0.239086	−	0.330915i
$751$	−22.1111	+	48.4166i	−0.806846	+	1.76675i	−0.186438	+	0.982467i	$0.559694\pi$
$751$	−22.1111	+	48.4166i	−0.806846	+	1.76675i	−0.620408	+	0.784279i	$0.713033\pi$
$752$	0.903442	−	1.40578i	0.0329451	−	0.0512636i
$753$	−0.908298	−	3.09338i	−0.0331002	−	0.112729i
$754$	−0.485229	−	0.559984i	−0.0176710	−	0.0203934i
$755$	36.1828	+	9.47662i	1.31683	+	0.344889i
$756$	−0.532152	−	1.16525i	−0.0193542	−	0.0423798i
$757$	−26.1881	−	3.76528i	−0.951823	−	0.136851i	−0.351126	−	0.936328i	$-0.614201\pi$
$757$	−26.1881	−	3.76528i	−0.951823	−	0.136851i	−0.600697	+	0.799477i	$0.705110\pi$
$758$		−	37.0356i		−	1.34519i
$759$	−11.1062	−	9.94634i	−0.403130	−	0.361029i
$760$	−0.0603062	−	2.04761i	−0.00218753	−	0.0742746i
$761$	−3.26052	+	22.6774i	−0.118194	+	0.822056i	0.841349	+	0.540492i	$0.181762\pi$
$761$	−3.26052	+	22.6774i	−0.118194	+	0.822056i	−0.959543	+	0.281563i	$0.909147\pi$
$762$	−15.3625	+	7.01583i	−0.556525	+	0.254157i
$763$	4.21861	−	14.3673i	0.152724	−	0.520130i
$764$	−12.3035	−	14.1990i	−0.445125	−	0.513702i
$765$	1.77789	+	5.45537i	0.0642796	+	0.197239i
$766$	−1.56856	−	1.00805i	−0.0566744	−	0.0364224i
$767$	2.46877	+	1.12745i	0.0891421	+	0.0407099i
$768$	0.755750	+	0.654861i	0.0272708	+	0.0236303i
$769$	5.25071	−	3.37443i	0.189346	−	0.121685i	−0.442534	−	0.896752i	$-0.645920\pi$
$769$	5.25071	−	3.37443i	0.189346	−	0.121685i	0.631879	+	0.775067i	$0.282284\pi$
$770$	1.52621	+	8.77300i	0.0550008	+	0.316157i
$771$	−2.75912	−	19.1901i	−0.0993674	−	0.691115i
$772$	13.1853	+	20.5168i	0.474551	+	0.738415i
$773$	−4.58743	−	3.97503i	−0.164998	−	0.142972i	0.568448	−	0.822719i	$-0.307544\pi$
$773$	−4.58743	−	3.97503i	−0.164998	−	0.142972i	−0.733446	+	0.679747i	$0.762089\pi$
$774$	2.94295	−	6.44417i	0.105782	−	0.231631i
$775$	−24.9040	−	14.0060i	−0.894578	−	0.503109i
$776$	−11.1946	+	3.28704i	−0.401864	+	0.117998i
$777$	−0.469132	+	0.406505i	−0.0168300	+	0.0145833i
$778$	−1.16696	+	3.97431i	−0.0418377	+	0.142486i
$779$	0.311696	+	0.682519i	0.0111677	+	0.0244538i
$780$	−0.164805	+	1.44764i	−0.00590096	+	0.0518337i
$781$	21.9760			0.786363
$782$	−4.92832	−	11.2762i	−0.176236	−	0.403236i
$783$		−	1.13717i		−	0.0406393i
$784$	−0.762666	+	5.30446i	−0.0272381	+	0.189445i
$785$	46.3792	−	22.8540i	1.65534	−	0.815695i
$786$	−3.80061	−	1.11596i	−0.135563	−	0.0398050i
$787$	−3.87706	+	3.35949i	−0.138202	+	0.119753i	−0.721219	−	0.692707i	$-0.756418\pi$
$787$	−3.87706	+	3.35949i	−0.138202	+	0.119753i	0.583016	+	0.812460i	$0.301872\pi$
$788$	−4.37255	−	14.8916i	−0.155766	−	0.530490i
$789$	−5.37272	−	3.45284i	−0.191274	−	0.122924i
$790$	14.5148	+	6.11889i	0.516413	+	0.217700i
$791$	2.84570	−	3.28412i	0.101182	−	0.116770i
$792$	−1.68071	−	2.61523i	−0.0597214	−	0.0929283i
$793$	7.28751	−	1.04779i	0.258787	−	0.0372080i
$794$	−1.26982	−	8.83179i	−0.0450642	−	0.313428i
$795$	−8.31089	+	5.69362i	−0.294757	+	0.201932i
$796$	−15.0511	+	17.3698i	−0.533470	+	0.615658i
$797$	−16.9655	−	7.74790i	−0.600950	−	0.274445i	0.0916216	−	0.995794i	$-0.470795\pi$
$797$	−16.9655	−	7.74790i	−0.600950	−	0.274445i	−0.692571	+	0.721349i	$0.743522\pi$
$798$	0.634473	−	0.987259i	0.0224601	−	0.0349486i
$799$	−4.11425	+	1.20805i	−0.145552	+	0.0427378i
$800$	−3.57950	+	3.49102i	−0.126554	+	0.123426i
$801$	5.52869	+	1.62337i	0.195347	+	0.0573590i
$802$	31.6287	−	14.4443i	1.11685	−	0.510047i
$803$	−7.41849	−	1.06662i	−0.261793	−	0.0376401i
$804$	1.37352			0.0484403
$805$	−12.4202	+	5.86967i	−0.437755	+	0.206879i
$806$	3.72345			0.131153
$807$	−1.31952	−	0.189718i	−0.0464492	−	0.00667839i
$808$	−5.65787	+	2.58386i	−0.199043	+	0.0908999i
$809$	38.8523	+	11.4081i	1.36597	+	0.401086i	0.880865	−	0.473367i	$-0.156962\pi$
$809$	38.8523	+	11.4081i	1.36597	+	0.401086i	0.485109	+	0.874453i	$0.338780\pi$
$810$	−1.64607	+	1.51343i	−0.0578369	+	0.0531764i
$811$	0.778788	−	0.228673i	0.0273470	−	0.00802979i	−0.268030	−	0.963410i	$-0.586373\pi$
$811$	0.778788	−	0.228673i	0.0273470	−	0.00802979i	0.295377	+	0.955381i	$0.404555\pi$
$812$	0.787571	−	1.22548i	0.0276383	−	0.0430061i
$813$	1.20954	+	0.552377i	0.0424203	+	0.0193727i
$814$	−0.986497	+	1.13848i	−0.0345767	+	0.0399036i
$815$	−2.89463	−	4.22525i	−0.101395	−	0.148004i
$816$	−0.365181	−	2.53989i	−0.0127839	−	0.0889138i
$817$	6.42405	−	0.923639i	0.224749	−	0.0323140i
$818$	−2.50054	−	3.89092i	−0.0874293	−	0.136043i
$819$	−0.546604	+	0.630815i	−0.0190999	+	0.0220425i
$820$	0.711418	−	1.68758i	0.0248438	−	0.0589327i
$821$	−39.9712	−	25.6880i	−1.39501	−	0.896516i	−0.395249	−	0.918574i	$-0.629342\pi$
$821$	−39.9712	−	25.6880i	−1.39501	−	0.896516i	−0.999757	+	0.0220584i	$0.992978\pi$
$822$	−2.66502	−	9.07622i	−0.0929532	−	0.316570i
$823$	15.1600	−	13.1362i	0.528446	−	0.457901i	−0.349311	−	0.937007i	$-0.613584\pi$
$823$	15.1600	−	13.1362i	0.528446	−	0.457901i	0.877757	+	0.479106i	$0.159039\pi$
$824$	10.2002	+	2.99505i	0.355342	+	0.104338i
$825$	13.7345	−	7.27801i	0.478174	−	0.253388i
$826$	−0.759361	+	5.28147i	−0.0264216	+	0.183766i
$827$		−	13.1567i		−	0.457504i	−0.973485	−	0.228752i	$-0.926536\pi$
$827$		−	13.1567i		−	0.457504i	0.973485	−	0.228752i	$-0.0734644\pi$
$828$	3.19948	−	3.57258i	0.111190	−	0.124156i
$829$	−1.18029			−0.0409931			−0.0204965	−	0.999790i	$-0.506525\pi$
$829$	−1.18029			−0.0409931			−0.0204965	+	0.999790i	$0.506525\pi$
$830$	1.45149	−	12.7498i	0.0503820	−	0.442552i
$831$	0.728032	+	1.59417i	0.0252552	+	0.0553011i
$832$	0.183572	−	0.625190i	0.00636423	−	0.0216746i
$833$	10.3925	−	9.00514i	0.360078	−	0.312010i
$834$	9.55532	−	2.80570i	0.330874	−	0.0971533i
$835$	11.6985	−	19.4386i	0.404843	−	0.672701i
$836$	1.18309	−	2.59060i	0.0409179	−	0.0895977i
$837$	4.31870	+	3.74217i	0.149276	+	0.129348i
$838$	−0.251294	−	0.391022i	−0.00868082	−	0.0135076i
$839$	−3.44435	−	23.9560i	−0.118912	−	0.827053i	−0.958757	−	0.284226i	$-0.908263\pi$
$839$	−3.44435	−	23.9560i	−0.118912	−	0.827053i	0.839845	−	0.542826i	$-0.182646\pi$
$840$	−2.82205	+	0.490943i	−0.0973699	+	0.0169391i
$841$	−23.3085	+	14.9794i	−0.803740	+	0.516533i
$842$	−8.34785	−	7.23345i	−0.287686	−	0.249281i
$843$	−9.28250	−	4.23918i	−0.319706	−	0.146005i
$844$	3.67598	+	2.36241i	0.126533	+	0.0813175i
$845$	−26.7356	+	8.71304i	−0.919732	+	0.299738i
$846$	−1.09431	−	1.26290i	−0.0376231	−	0.0434194i
$847$	0.482083	−	1.64182i	0.0165646	−	0.0564137i
$848$	4.09816	−	1.87156i	0.140731	−	0.0642698i
$849$	3.42053	−	23.7903i	0.117392	−	0.816481i
$850$	12.8078	−	0.755084i	0.439303	−	0.0258992i
$851$	−2.09786	−	0.999861i	−0.0719138	−	0.0342748i
$852$			7.06911i			0.242184i
$853$	−48.5509	−	6.98057i	−1.66235	−	0.239010i	−0.753897	−	0.656993i	$-0.771828\pi$
$853$	−48.5509	−	6.98057i	−1.66235	−	0.239010i	−0.908455	+	0.417983i	$0.862737\pi$
$854$	6.01295	+	13.1665i	0.205759	+	0.450549i
$855$	−1.98166	−	0.519015i	−0.0677713	−	0.0177499i
$856$	−0.855162	−	0.986910i	−0.0292288	−	0.0337319i
$857$	−6.23658	−	21.2398i	−0.213037	−	0.725539i	−0.994790	−	0.101949i	$-0.967492\pi$
$857$	−6.23658	−	21.2398i	−0.213037	−	0.725539i	0.781752	−	0.623589i	$-0.214326\pi$
$858$	−1.09512	+	1.70404i	−0.0373869	+	0.0581751i
$859$	2.31404	−	5.06704i	0.0789540	−	0.172885i	−0.866038	−	0.499978i	$-0.833342\pi$
$859$	2.31404	−	5.06704i	0.0789540	−	0.172885i	0.944992	+	0.327092i	$0.106069\pi$
$860$	−12.2721	−	10.0168i	−0.418476	−	0.341570i
$861$	0.882630	−	0.567232i	0.0300800	−	0.0193312i
$862$	5.09712	−	0.732856i	0.173609	−	0.0249612i
$863$	−1.03978	+	0.149497i	−0.0353944	+	0.00508895i	−0.159989	−	0.987119i	$-0.551146\pi$
$863$	−1.03978	+	0.149497i	−0.0353944	+	0.00508895i	0.124595	+	0.992208i	$0.460237\pi$
$864$	0.841254	−	0.540641i	0.0286200	−	0.0183930i
$865$	−6.56007	−	5.35448i	−0.223049	−	0.182058i
$866$	−4.50522	+	9.86506i	−0.153094	+	0.335229i
$867$	5.63111	−	8.76218i	0.191243	−	0.297579i
$868$	2.06237	+	7.02378i	0.0700013	+	0.238402i
$869$	14.3410	+	16.5503i	0.486484	+	0.561432i
$870$	−2.45983	−	0.644253i	−0.0833961	−	0.0218422i
$871$	−0.371781	−	0.814088i	−0.0125973	−	0.0275843i
$872$	11.5701	+	1.66352i	0.391812	+	0.0563340i
$873$			11.6672i			0.394876i
$874$	4.33801	+	0.696332i	0.146735	+	0.0235538i
$875$	−1.26344	−	14.2663i	−0.0427120	−	0.482290i
$876$	0.343104	−	2.38634i	0.0115924	−	0.0806269i
$877$	23.8943	−	10.9122i	0.806852	−	0.368477i	0.0311014	−	0.999516i	$-0.490099\pi$
$877$	23.8943	−	10.9122i	0.806852	−	0.368477i	0.775751	+	0.631039i	$0.217371\pi$
$878$	8.91786	−	30.3714i	0.300963	−	1.02499i
$879$	−9.92275	−	11.4515i	−0.334686	−	0.386248i
$880$	−6.60922	+	2.15392i	−0.222797	+	0.0726087i
$881$	−6.99488	−	4.49534i	−0.235663	−	0.151452i	0.417479	−	0.908686i	$-0.362914\pi$
$881$	−6.99488	−	4.49534i	−0.235663	−	0.151452i	−0.653143	+	0.757235i	$0.726550\pi$
$882$	4.87472	+	2.22621i	0.164140	+	0.0749604i
$883$	24.0271	+	20.8196i	0.808576	+	0.700635i	0.957569	−	0.288203i	$-0.0930577\pi$
$883$	24.0271	+	20.8196i	0.808576	+	0.700635i	−0.148993	+	0.988838i	$0.547603\pi$
$884$	−1.40655	+	0.903934i	−0.0473073	+	0.0304026i
$885$	9.17604	−	1.59633i	0.308449	−	0.0536600i
$886$	4.33355	+	30.1405i	0.145588	+	1.01259i
$887$	−5.60946	−	8.72849i	−0.188347	−	0.293074i	0.734219	−	0.678913i	$-0.237548\pi$
$887$	−5.60946	−	8.72849i	−0.188347	−	0.293074i	−0.922566	+	0.385839i	$0.873912\pi$
$888$	−0.366219	−	0.317331i	−0.0122895	−	0.0106489i
$889$	−8.98737	+	19.6796i	−0.301427	+	0.660032i
$890$	6.64374	−	11.0394i	0.222699	−	0.370043i
$891$	−2.98281	+	0.875832i	−0.0999279	+	0.0293415i
$892$	1.55884	−	1.35074i	0.0521938	−	0.0452262i
$893$	0.431299	−	1.46887i	0.0144329	−	0.0491539i
$894$	−7.07051	−	15.4823i	−0.236473	−	0.517804i
$895$	1.66337	−	14.6109i	0.0556004	−	0.488390i
$896$	1.28101			0.0427957
$897$	−2.98350	−	0.929319i	−0.0996162	−	0.0310291i
$898$			31.8983i			1.06446i
$899$	−0.924810	+	6.43219i	−0.0308441	+	0.214526i
$900$	2.34115	+	4.41803i	0.0780382	+	0.147268i
$901$	−11.0923	−	3.25700i	−0.369538	−	0.108506i
$902$	1.92424	−	1.66737i	0.0640703	−	0.0555172i
$903$	−2.55677	−	8.70757i	−0.0850841	−	0.289770i
$904$	2.85374	+	1.83398i	0.0949139	+	0.0609974i
$905$	−7.33391	+	17.3970i	−0.243787	+	0.578295i
$906$	−10.9540	+	12.6416i	−0.363922	+	0.419989i
$907$	−2.46978	−	3.84306i	−0.0820079	−	0.127607i	0.797827	−	0.602887i	$-0.205983\pi$
$907$	−2.46978	−	3.84306i	−0.0820079	−	0.127607i	−0.879834	+	0.475280i	$0.842347\pi$
$908$	−13.8794	+	1.99555i	−0.460603	+	0.0662248i
$909$	0.885191	+	6.15664i	0.0293599	+	0.204203i
$910$	1.05485	+	1.53974i	0.0349679	+	0.0510420i
$911$	−4.09728	+	4.72851i	−0.135749	+	0.156662i	−0.819554	−	0.573003i	$-0.805779\pi$
$911$	−4.09728	+	4.72851i	−0.135749	+	0.156662i	0.683805	+	0.729665i	$0.260324\pi$
$912$	0.833329	+	0.380568i	0.0275943	+	0.0126019i
$913$	9.64512	−	15.0081i	0.319207	−	0.496695i
$914$	15.6752	−	4.60265i	0.518489	−	0.152242i
$915$	18.5994	−	17.1007i	0.614878	−	0.565332i
$916$	18.4273	+	5.41076i	0.608857	+	0.178776i
$917$	−4.61563	+	2.10789i	−0.152422	+	0.0696086i
$918$	−2.53989	−	0.365181i	−0.0838287	−	0.0120528i
$919$	−0.149898			−0.00494466			−0.00247233	−	0.999997i	$-0.500787\pi$
$919$	−0.149898			−0.00494466			−0.00247233	+	0.999997i	$0.500787\pi$
$920$	−5.91525	−	8.94482i	−0.195020	−	0.294902i
$921$	−31.8532			−1.04960
$922$	−13.6777	−	1.96656i	−0.450452	−	0.0647653i
$923$	4.18988	−	1.91345i	0.137911	−	0.0629820i
$924$	−3.82102	−	1.12195i	−0.125702	−	0.0369095i
$925$	1.73454	−	1.69167i	0.0570314	−	0.0556217i
$926$	−2.44440	+	0.717740i	−0.0803279	+	0.0235864i
$927$	5.74747	−	8.94324i	0.188772	−	0.293734i
$928$	1.03441	+	0.472399i	0.0339562	+	0.0155073i
$929$	16.9133	−	19.5190i	0.554908	−	0.640398i	−0.407111	−	0.913379i	$-0.633464\pi$
$929$	16.9133	−	19.5190i	0.554908	−	0.640398i	0.962020	+	0.272980i	$0.0880094\pi$
$930$	10.5414	−	7.22173i	0.345667	−	0.236810i
$931$	0.698691	+	4.85950i	0.0228987	+	0.159264i
$932$	19.4226	−	2.79255i	0.636208	−	0.0914729i
$933$	8.84757	+	13.7671i	0.289656	+	0.450714i
$934$	−6.70483	+	7.73779i	−0.219389	+	0.253188i
$935$	16.4364	+	6.92896i	0.537527	+	0.226601i
$936$	−0.548147	−	0.352273i	−0.0179168	−	0.0115144i
$937$	−11.4634	−	39.0407i	−0.374492	−	1.27540i	−0.904158	−	0.427197i	$-0.859501\pi$
$937$	−11.4634	−	39.0407i	−0.374492	−	1.27540i	0.529666	−	0.848206i	$-0.322317\pi$
$938$	1.32974	−	1.15223i	0.0434176	−	0.0376215i
$939$	2.79975	+	0.822079i	0.0913662	+	0.0268275i
$940$	−3.35176	+	1.65163i	−0.109322	+	0.0538701i
$941$	4.56820	−	31.7725i	0.148919	−	1.03575i	−0.769074	−	0.639159i	$-0.779282\pi$
$941$	4.56820	−	31.7725i	0.148919	−	1.03575i	0.917993	−	0.396595i	$-0.129808\pi$
$942$			23.1229i			0.753384i
$943$	3.26919	+	2.17737i	0.106459	+	0.0709049i
$944$	−4.16528			−0.135568
$945$	−0.324006	+	2.84605i	−0.0105399	+	0.0925820i
$946$	−9.14887	−	20.0332i	−0.297455	−	0.651336i
$947$	4.17889	−	14.2320i	0.135796	−	0.462478i	−0.863314	−	0.504667i	$-0.831615\pi$
$947$	4.17889	−	14.2320i	0.135796	−	0.462478i	0.999110	+	0.0421895i	$0.0134333\pi$
$948$	−5.32382	+	4.61312i	−0.172910	+	0.149827i
$949$	−1.50726	+	0.442571i	−0.0489276	+	0.0143664i
$950$	−2.24537	+	3.99250i	−0.0728494	+	0.129534i
$951$	10.3337	−	22.6276i	0.335093	−	0.733751i
$952$	−2.48421	−	2.15258i	−0.0805138	−	0.0697656i
$953$	20.1984	+	31.4293i	0.654289	+	1.01809i	0.996905	+	0.0786185i	$0.0250509\pi$
$953$	20.1984	+	31.4293i	0.654289	+	1.01809i	−0.342615	+	0.939476i	$0.611313\pi$
$954$	−0.641170	−	4.45943i	−0.0207586	−	0.144379i
$955$	7.20041	+	41.3895i	0.233000	+	1.33933i
$956$	−21.5885	+	13.8741i	−0.698223	+	0.448721i
$957$	−2.67171	−	2.31505i	−0.0863640	−	0.0748348i
$958$	−27.5828	−	12.5967i	−0.891161	−	0.406980i
$959$	−10.1940	−	6.55128i	−0.329181	−	0.211552i
$960$	−0.692862	−	2.12602i	−0.0223620	−	0.0686169i
$961$	−1.08382	−	1.25080i	−0.0349620	−	0.0403484i
$962$	−0.0889550	+	0.302953i	−0.00286803	+	0.00976760i
$963$	−1.18786	+	0.542477i	−0.0382783	+	0.0174811i
$964$	2.15447	−	14.9847i	0.0693908	−	0.482623i
$965$	−1.60544	−	54.5104i	−0.0516809	−	1.75475i
$966$	0.100513	−	6.14270i	0.00323395	−	0.197638i
$967$		−	33.6175i		−	1.08107i	−0.841322	−	0.540534i	$-0.818222\pi$
$967$		−	33.6175i		−	1.08107i	0.841322	−	0.540534i	$-0.181778\pi$
$968$	1.32217	+	0.190100i	0.0424962	+	0.00611003i
$969$	−0.976540	−	2.13832i	−0.0313710	−	0.0686929i
$970$	25.2375	+	6.60994i	0.810328	+	0.212233i
$971$	20.0257	+	23.1109i	0.642655	+	0.741664i	0.979842	−	0.199774i	$-0.0640208\pi$
$971$	20.0257	+	23.1109i	0.642655	+	0.741664i	−0.337187	+	0.941438i	$0.609475\pi$
$972$	−0.281733	−	0.959493i	−0.00903658	−	0.0307758i
$973$	6.89709	−	10.7321i	0.221111	−	0.344055i
$974$	0.175875	−	0.385113i	0.00563541	−	0.0123398i
$975$	1.98488	−	2.58347i	0.0635670	−	0.0827371i
$976$	−9.50559	+	6.10887i	−0.304266	+	0.195540i
$977$	−43.1758	+	6.20775i	−1.38132	+	0.198603i	−0.792603	−	0.609738i	$-0.791275\pi$
$977$	−43.1758	+	6.20775i	−1.38132	+	0.198603i	−0.588714	+	0.808341i	$0.700366\pi$
$978$	2.26717	−	0.325970i	0.0724962	−	0.0104234i
$979$	15.0692	−	9.68441i	0.481615	−	0.309515i
$980$	7.57725	−	9.28331i	0.242046	−	0.296545i
$981$	4.85580	−	10.6327i	0.155034	−	0.339477i
$982$	4.77736	−	7.43371i	0.152452	−	0.237219i
$983$	8.00197	+	27.2522i	0.255223	+	0.869211i	0.983033	+	0.183431i	$0.0587204\pi$
$983$	8.00197	+	27.2522i	0.255223	+	0.869211i	−0.727809	+	0.685780i	$0.759461\pi$
$984$	0.536349	+	0.618979i	0.0170982	+	0.0197323i
$985$	−8.79281	+	33.5719i	−0.280162	+	1.06969i
$986$	−1.21218	−	2.65430i	−0.0386036	−	0.0845302i
$987$	−2.11886	−	0.304646i	−0.0674440	−	0.00969698i
$988$		−	0.596927i		−	0.0189908i
$989$	26.0375	−	21.8261i	0.827945	−	0.694030i
$990$	0.204642	+	6.94833i	0.00650395	+	0.220832i
$991$	6.02617	−	41.9129i	0.191428	−	1.33141i	−0.636805	−	0.771025i	$-0.719745\pi$
$991$	6.02617	−	41.9129i	0.191428	−	1.33141i	0.828233	−	0.560384i	$-0.189346\pi$
$992$	−5.19805	+	2.37387i	−0.165038	+	0.0753705i
$993$	−3.13049	+	10.6615i	−0.0993433	+	0.338332i
$994$	5.93018	+	6.84379i	0.188094	+	0.217072i
$995$	48.8635	−	15.9245i	1.54908	−	0.504839i
$996$	4.82772	+	3.10259i	0.152972	+	0.0983092i
$997$	22.7288	+	10.3799i	0.719829	+	0.328735i	0.741429	−	0.671032i	$-0.234149\pi$
$997$	22.7288	+	10.3799i	0.719829	+	0.328735i	−0.0215994	+	0.999767i	$0.506876\pi$
$998$	−30.6421	−	26.5515i	−0.969959	−	0.840475i
$999$	−0.407652	+	0.261982i	−0.0128976	+	0.00828875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.r.a.169.7	yes	120
5.4	even	2	inner	690.2.r.a.169.2	yes	120
23.3	even	11	inner	690.2.r.a.49.2	✓	120
115.49	even	22	inner	690.2.r.a.49.7	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.r.a.49.2	✓	120	23.3	even	11	inner
690.2.r.a.49.7	yes	120	115.49	even	22	inner
690.2.r.a.169.2	yes	120	5.4	even	2	inner
690.2.r.a.169.7	yes	120	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.989821 + 0.142315i) q^{2} +(0.909632 - 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(-1.51343 - 1.64607i) q^{5} +(0.959493 - 0.281733i) q^{6} +(0.692568 - 1.07766i) q^{7} +(0.909632 + 0.415415i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.989821 + 0.142315i) q^{2} +(0.909632 - 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(-1.51343 - 1.64607i) q^{5} +(0.959493 - 0.281733i) q^{6} +(0.692568 - 1.07766i) q^{7} +(0.909632 + 0.415415i) q^{8} +(0.654861 - 0.755750i) q^{9} +(-1.26376 - 1.84470i) q^{10} +(-0.442419 - 3.07709i) q^{11} +(0.989821 - 0.142315i) q^{12} +(-0.352273 - 0.548147i) q^{13} +(0.838885 - 0.968125i) q^{14} +(-2.06046 - 0.868614i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-0.722927 - 2.46206i) q^{17} +(0.755750 - 0.654861i) q^{18} +(0.879007 + 0.258100i) q^{19} +(-0.988373 - 2.00577i) q^{20} +(0.182307 - 1.26797i) q^{21} -3.10873i q^{22} +(4.62306 - 1.27568i) q^{23} +1.00000 q^{24} +(-0.419071 + 4.98241i) q^{25} +(-0.270678 - 0.592702i) q^{26} +(0.281733 - 0.959493i) q^{27} +(0.968125 - 0.838885i) q^{28} +(1.09111 - 0.320379i) q^{29} +(-1.91587 - 1.15301i) q^{30} +(-2.37387 + 5.19805i) q^{31} +(0.755750 + 0.654861i) q^{32} +(-1.68071 - 2.61523i) q^{33} +(-0.365181 - 2.53989i) q^{34} +(-2.82205 + 0.490943i) q^{35} +(0.841254 - 0.540641i) q^{36} +(-0.366219 - 0.317331i) q^{37} +(0.833329 + 0.380568i) q^{38} +(-0.548147 - 0.352273i) q^{39} +(-0.692862 - 2.12602i) q^{40} +(0.536349 + 0.618979i) q^{41} +(0.360903 - 1.22912i) q^{42} +(6.44417 - 2.94295i) q^{43} +(0.442419 - 3.07709i) q^{44} +(-2.23510 + 0.0658281i) q^{45} +(4.75755 - 0.604762i) q^{46} -1.67106i q^{47} +(0.989821 + 0.142315i) q^{48} +(2.22621 + 4.87472i) q^{49} +(-1.12388 + 4.87205i) q^{50} +(-1.68038 - 1.93926i) q^{51} +(-0.183572 - 0.625190i) q^{52} +(2.43574 - 3.79009i) q^{53} +(0.415415 - 0.909632i) q^{54} +(-4.39553 + 5.38521i) q^{55} +(1.07766 - 0.692568i) q^{56} +(0.906791 - 0.130377i) q^{57} +(1.12560 - 0.161837i) q^{58} +(-3.50406 + 2.25192i) q^{59} +(-1.73228 - 1.41393i) q^{60} +(-4.69390 + 10.2782i) q^{61} +(-3.08947 + 4.80731i) q^{62} +(-0.360903 - 1.22912i) q^{63} +(0.654861 + 0.755750i) q^{64} +(-0.369147 + 1.40945i) q^{65} +(-1.29142 - 2.82780i) q^{66} +(1.35954 + 0.195472i) q^{67} -2.56600i q^{68} +(3.67535 - 3.08088i) q^{69} +(-2.86319 + 0.0843267i) q^{70} +(-1.00604 + 6.99716i) q^{71} +(0.909632 - 0.415415i) q^{72} +(0.679223 - 2.31322i) q^{73} +(-0.317331 - 0.366219i) q^{74} +(1.68857 + 4.70625i) q^{75} +(0.770686 + 0.495290i) q^{76} +(-3.62246 - 1.65432i) q^{77} +(-0.492434 - 0.426697i) q^{78} +(-5.92615 + 3.80850i) q^{79} +(-0.383246 - 2.20298i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(0.442799 + 0.689009i) q^{82} +(4.33703 + 3.75806i) q^{83} +(0.532152 - 1.16525i) q^{84} +(-2.95862 + 4.91614i) q^{85} +(6.79741 - 1.99590i) q^{86} +(0.859419 - 0.744691i) q^{87} +(0.875832 - 2.98281i) q^{88} +(2.39366 + 5.24139i) q^{89} +(-2.22172 - 0.252930i) q^{90} -0.834688 q^{91} +(4.79519 + 0.0784636i) q^{92} +5.71446i q^{93} +(0.237816 - 1.65405i) q^{94} +(-0.905464 - 1.83752i) q^{95} +(0.959493 + 0.281733i) q^{96} +(-8.81752 + 7.64042i) q^{97} +(1.50981 + 5.14193i) q^{98} +(-2.61523 - 1.68071i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} + 12 q^{6} + 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^4 + 12 * q^6 + 12 * q^9	\( 120 q + 12 q^{4} + 12 q^{6} + 12 q^{9} + 18 q^{10} - 8 q^{14} - 4 q^{15} - 12 q^{16} + 22 q^{20} + 14 q^{21} + 120 q^{24} + 52 q^{25} + 16 q^{29} + 8 q^{31} - 36 q^{34} - 90 q^{35} - 12 q^{36} + 22 q^{39} + 4 q^{40} + 16 q^{41} - 4 q^{49} - 4 q^{50} + 8 q^{51} - 12 q^{54} - 56 q^{55} + 8 q^{56} + 138 q^{59} + 4 q^{60} - 36 q^{61} + 12 q^{64} + 52 q^{65} + 96 q^{70} + 8 q^{71} + 8 q^{74} - 4 q^{75} - 60 q^{79} - 12 q^{81} + 8 q^{84} + 24 q^{85} - 8 q^{86} - 104 q^{89} + 4 q^{90} - 144 q^{91} - 24 q^{94} - 14 q^{95} + 12 q^{96} - 44 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 + 12 * q^6 + 12 * q^9 + 18 * q^10 - 8 * q^14 - 4 * q^15 - 12 * q^16 + 22 * q^20 + 14 * q^21 + 120 * q^24 + 52 * q^25 + 16 * q^29 + 8 * q^31 - 36 * q^34 - 90 * q^35 - 12 * q^36 + 22 * q^39 + 4 * q^40 + 16 * q^41 - 4 * q^49 - 4 * q^50 + 8 * q^51 - 12 * q^54 - 56 * q^55 + 8 * q^56 + 138 * q^59 + 4 * q^60 - 36 * q^61 + 12 * q^64 + 52 * q^65 + 96 * q^70 + 8 * q^71 + 8 * q^74 - 4 * q^75 - 60 * q^79 - 12 * q^81 + 8 * q^84 + 24 * q^85 - 8 * q^86 - 104 * q^89 + 4 * q^90 - 144 * q^91 - 24 * q^94 - 14 * q^95 + 12 * q^96 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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