LMFDB - Embedded newform 690.2.m.h.301.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			301.3
Character	$\chi$	$=$	690.301
Dual form			690.2.m.h.541.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 - 0.540641i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(2.94698 - 3.40099i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.841254 - 0.540641i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(2.94698 - 3.40099i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(-0.654861 - 0.755750i) q^{10} +(3.15964 - 2.03058i) q^{11} +(0.841254 - 0.540641i) q^{12} +(4.55681 + 5.25884i) q^{13} +(-4.31787 + 1.26784i) q^{14} +(0.142315 - 0.989821i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-2.91086 + 6.37389i) q^{17} +(0.959493 + 0.281733i) q^{18} +(-0.990383 - 2.16864i) q^{19} +(0.142315 + 0.989821i) q^{20} +(-3.78577 - 2.43297i) q^{21} -3.75587 q^{22} +(1.30885 - 4.61377i) q^{23} -1.00000 q^{24} +(0.841254 + 0.540641i) q^{25} +(-0.990289 - 6.88761i) q^{26} +(0.415415 + 0.909632i) q^{27} +(4.31787 + 1.26784i) q^{28} +(-2.07904 + 4.55246i) q^{29} +(-0.654861 + 0.755750i) q^{30} +(0.564660 - 3.92729i) q^{31} +(0.959493 - 0.281733i) q^{32} +(-2.45957 - 2.83850i) q^{33} +(5.89475 - 3.78833i) q^{34} +(3.78577 - 2.43297i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(7.21215 - 2.11768i) q^{37} +(-0.339290 + 2.35981i) q^{38} +(4.55681 - 5.25884i) q^{39} +(0.415415 - 0.909632i) q^{40} +(-2.11326 - 0.620508i) q^{41} +(1.86943 + 4.09349i) q^{42} +(1.26125 + 8.77220i) q^{43} +(3.15964 + 2.03058i) q^{44} -1.00000 q^{45} +(-3.59547 + 3.17373i) q^{46} -4.07475 q^{47} +(0.841254 + 0.540641i) q^{48} +(-1.88587 - 13.1165i) q^{49} +(-0.415415 - 0.909632i) q^{50} +(6.72327 + 1.97413i) q^{51} +(-2.89064 + 6.32962i) q^{52} +(2.56761 - 2.96318i) q^{53} +(0.142315 - 0.989821i) q^{54} +(3.60373 - 1.05815i) q^{55} +(-2.94698 - 3.40099i) q^{56} +(-2.00562 + 1.28893i) q^{57} +(4.21025 - 2.70576i) q^{58} +(-7.13771 - 8.23736i) q^{59} +(0.959493 - 0.281733i) q^{60} +(1.89566 - 13.1846i) q^{61} +(-2.59828 + 2.99857i) q^{62} +(-1.86943 + 4.09349i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(2.89064 + 6.32962i) q^{65} +(0.534516 + 3.71764i) q^{66} +(0.866222 + 0.556687i) q^{67} -7.00711 q^{68} +(-4.75308 - 0.638921i) q^{69} -4.50016 q^{70} +(-4.19300 - 2.69468i) q^{71} +(0.142315 + 0.989821i) q^{72} +(-2.59043 - 5.67225i) q^{73} +(-7.21215 - 2.11768i) q^{74} +(0.415415 - 0.909632i) q^{75} +(1.56124 - 1.80177i) q^{76} +(2.40540 - 16.7300i) q^{77} +(-6.67657 + 1.96042i) q^{78} +(-2.60645 - 3.00801i) q^{79} +(-0.841254 + 0.540641i) q^{80} +(0.841254 - 0.540641i) q^{81} +(1.44231 + 1.66452i) q^{82} +(-14.6281 + 4.29519i) q^{83} +(0.640439 - 4.45435i) q^{84} +(-4.58868 + 5.29562i) q^{85} +(3.68158 - 8.06153i) q^{86} +(4.80200 + 1.41000i) q^{87} +(-1.56024 - 3.41646i) q^{88} +(1.83561 + 12.7670i) q^{89} +(0.841254 + 0.540641i) q^{90} +31.3141 q^{91} +(4.74055 - 0.726057i) q^{92} -3.96768 q^{93} +(3.42790 + 2.20298i) q^{94} +(-0.339290 - 2.35981i) q^{95} +(-0.415415 - 0.909632i) q^{96} +(6.25556 + 1.83680i) q^{97} +(-5.50484 + 12.0539i) q^{98} +(-2.45957 + 2.83850i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.841254	−	0.540641i	−0.594856	−	0.382291i
$2$	−0.841254	−	0.540641i	−0.594856	−	0.382291i
$3$	−0.142315	−	0.989821i	−0.0821655	−	0.571474i
$3$	−0.142315	−	0.989821i	−0.0821655	−	0.571474i
$4$	0.415415	+	0.909632i	0.207708	+	0.454816i
$5$	0.959493	+	0.281733i	0.429098	+	0.125995i
$5$	0.959493	+	0.281733i	0.429098	+	0.125995i
$6$	−0.415415	+	0.909632i	−0.169592	+	0.371356i
$7$	2.94698	−	3.40099i	1.11385	−	1.28545i	0.159360	−	0.987221i	$-0.449057\pi$
$7$	2.94698	−	3.40099i	1.11385	−	1.28545i	0.954493	−	0.298234i	$-0.0963975\pi$
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$	−0.959493	+	0.281733i	−0.319831	+	0.0939109i
$10$	−0.654861	−	0.755750i	−0.207085	−	0.238989i
$11$	3.15964	−	2.03058i	0.952666	−	0.612241i	0.0307071	−	0.999528i	$-0.490224\pi$
$11$	3.15964	−	2.03058i	0.952666	−	0.612241i	0.921959	+	0.387287i	$0.126588\pi$
$12$	0.841254	−	0.540641i	0.242849	−	0.156070i
$13$	4.55681	+	5.25884i	1.26383	+	1.45854i	0.830216	+	0.557441i	$0.188217\pi$
$13$	4.55681	+	5.25884i	1.26383	+	1.45854i	0.433615	+	0.901098i	$0.357238\pi$
$14$	−4.31787	+	1.26784i	−1.15400	+	0.338845i
$15$	0.142315	−	0.989821i	0.0367455	−	0.255571i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−2.91086	+	6.37389i	−0.705987	+	1.54589i	0.126572	+	0.991957i	$0.459603\pi$
$17$	−2.91086	+	6.37389i	−0.705987	+	1.54589i	−0.832558	+	0.553937i	$0.813125\pi$
$18$	0.959493	+	0.281733i	0.226155	+	0.0664050i
$19$	−0.990383	−	2.16864i	−0.227209	−	0.497519i	0.761352	−	0.648339i	$-0.224536\pi$
$19$	−0.990383	−	2.16864i	−0.227209	−	0.497519i	−0.988561	+	0.150820i	$0.951809\pi$
$20$	0.142315	+	0.989821i	0.0318226	+	0.221331i
$21$	−3.78577	−	2.43297i	−0.826124	−	0.530917i
$22$	−3.75587			−0.800754
$23$	1.30885	−	4.61377i	0.272914	−	0.962038i
$23$	1.30885	−	4.61377i	0.272914	−	0.962038i
$24$	−1.00000			−0.204124
$25$	0.841254	+	0.540641i	0.168251	+	0.108128i
$26$	−0.990289	−	6.88761i	−0.194212	−	1.35077i
$27$	0.415415	+	0.909632i	0.0799467	+	0.175059i
$28$	4.31787	+	1.26784i	0.816001	+	0.239599i
$29$	−2.07904	+	4.55246i	−0.386068	+	0.845371i	0.612427	+	0.790527i	$0.290193\pi$
$29$	−2.07904	+	4.55246i	−0.386068	+	0.845371i	−0.998495	+	0.0548438i	$0.982534\pi$
$30$	−0.654861	+	0.755750i	−0.119561	+	0.137980i
$31$	0.564660	−	3.92729i	0.101416	−	0.705363i	−0.874150	−	0.485656i	$-0.838581\pi$
$31$	0.564660	−	3.92729i	0.101416	−	0.705363i	0.975566	−	0.219707i	$-0.0705101\pi$
$32$	0.959493	−	0.281733i	0.169616	−	0.0498038i
$33$	−2.45957	−	2.83850i	−0.428156	−	0.494119i
$34$	5.89475	−	3.78833i	1.01094	−	0.649693i
$35$	3.78577	−	2.43297i	0.639913	−	0.411247i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	7.21215	−	2.11768i	1.18567	−	0.348144i	0.371313	−	0.928508i	$-0.378908\pi$
$37$	7.21215	−	2.11768i	1.18567	−	0.348144i	0.814357	+	0.580364i	$0.197090\pi$
$38$	−0.339290	+	2.35981i	−0.0550401	+	0.382812i
$39$	4.55681	−	5.25884i	0.729673	−	0.842088i
$40$	0.415415	−	0.909632i	0.0656829	−	0.143825i
$41$	−2.11326	−	0.620508i	−0.330035	−	0.0969070i	0.112517	−	0.993650i	$-0.464109\pi$
$41$	−2.11326	−	0.620508i	−0.330035	−	0.0969070i	−0.442552	+	0.896743i	$0.645927\pi$
$42$	1.86943	+	4.09349i	0.288460	+	0.631639i
$43$	1.26125	+	8.77220i	0.192339	+	1.33775i	0.825796	+	0.563969i	$0.190726\pi$
$43$	1.26125	+	8.77220i	0.192339	+	1.33775i	−0.633457	+	0.773778i	$0.718365\pi$
$44$	3.15964	+	2.03058i	0.476333	+	0.306121i
$45$	−1.00000			−0.149071
$46$	−3.59547	+	3.17373i	−0.530123	+	0.467942i
$47$	−4.07475			−0.594364			−0.297182	−	0.954821i	$-0.596047\pi$
$47$	−4.07475			−0.594364			−0.297182	+	0.954821i	$0.596047\pi$
$48$	0.841254	+	0.540641i	0.121424	+	0.0780348i
$49$	−1.88587	−	13.1165i	−0.269411	−	1.87379i
$50$	−0.415415	−	0.909632i	−0.0587486	−	0.128641i
$51$	6.72327	+	1.97413i	0.941446	+	0.276433i
$52$	−2.89064	+	6.32962i	−0.400860	+	0.877760i
$53$	2.56761	−	2.96318i	0.352688	−	0.407024i	−0.551489	−	0.834182i	$-0.685940\pi$
$53$	2.56761	−	2.96318i	0.352688	−	0.407024i	0.904177	+	0.427159i	$0.140485\pi$
$54$	0.142315	−	0.989821i	0.0193666	−	0.134698i
$55$	3.60373	−	1.05815i	0.485927	−	0.142681i
$56$	−2.94698	−	3.40099i	−0.393806	−	0.454477i
$57$	−2.00562	+	1.28893i	−0.265650	+	0.170723i
$58$	4.21025	−	2.70576i	0.552832	−	0.355284i
$59$	−7.13771	−	8.23736i	−0.929251	−	1.07241i	−0.997204	−	0.0747241i	$-0.976192\pi$
$59$	−7.13771	−	8.23736i	−0.929251	−	1.07241i	0.0679535	−	0.997688i	$-0.478353\pi$
$60$	0.959493	−	0.281733i	0.123870	−	0.0363715i
$61$	1.89566	−	13.1846i	0.242714	−	1.68811i	−0.395669	−	0.918393i	$-0.629487\pi$
$61$	1.89566	−	13.1846i	0.242714	−	1.68811i	0.638383	−	0.769719i	$-0.279604\pi$
$62$	−2.59828	+	2.99857i	−0.329982	+	0.380819i
$63$	−1.86943	+	4.09349i	−0.235526	+	0.515731i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	2.89064	+	6.32962i	0.358540	+	0.785093i
$66$	0.534516	+	3.71764i	0.0657943	+	0.457610i
$67$	0.866222	+	0.556687i	0.105826	+	0.0680101i	0.592483	−	0.805583i	$-0.298148\pi$
$67$	0.866222	+	0.556687i	0.105826	+	0.0680101i	−0.486657	+	0.873593i	$0.661784\pi$
$68$	−7.00711			−0.849736
$69$	−4.75308	−	0.638921i	−0.572204	−	0.0769171i
$70$	−4.50016			−0.537872
$71$	−4.19300	−	2.69468i	−0.497617	−	0.319799i	0.267645	−	0.963518i	$-0.413755\pi$
$71$	−4.19300	−	2.69468i	−0.497617	−	0.319799i	−0.765263	+	0.643718i	$0.777391\pi$
$72$	0.142315	+	0.989821i	0.0167720	+	0.116652i
$73$	−2.59043	−	5.67225i	−0.303187	−	0.663886i	0.695309	−	0.718711i	$-0.255267\pi$
$73$	−2.59043	−	5.67225i	−0.303187	−	0.663886i	−0.998496	+	0.0548245i	$0.982540\pi$
$74$	−7.21215	−	2.11768i	−0.838395	−	0.246175i
$75$	0.415415	−	0.909632i	0.0479680	−	0.105035i
$76$	1.56124	−	1.80177i	0.179087	−	0.206677i
$77$	2.40540	−	16.7300i	0.274121	−	1.90656i
$78$	−6.67657	+	1.96042i	−0.755973	+	0.221974i
$79$	−2.60645	−	3.00801i	−0.293249	−	0.338427i	0.589938	−	0.807449i	$-0.299152\pi$
$79$	−2.60645	−	3.00801i	−0.293249	−	0.338427i	−0.883187	+	0.469021i	$0.844607\pi$
$80$	−0.841254	+	0.540641i	−0.0940550	+	0.0604455i
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$	1.44231	+	1.66452i	0.159277	+	0.183815i
$83$	−14.6281	+	4.29519i	−1.60564	+	0.471458i	−0.957108	−	0.289730i	$-0.906435\pi$
$83$	−14.6281	+	4.29519i	−1.60564	+	0.471458i	−0.648531	+	0.761188i	$0.724616\pi$
$84$	0.640439	−	4.45435i	0.0698777	−	0.486010i
$85$	−4.58868	+	5.29562i	−0.497712	+	0.574390i
$86$	3.68158	−	8.06153i	0.396995	−	0.869297i
$87$	4.80200	+	1.41000i	0.514829	+	0.151167i
$88$	−1.56024	−	3.41646i	−0.166323	−	0.364196i
$89$	1.83561	+	12.7670i	0.194574	+	1.35329i	0.819710	+	0.572779i	$0.194135\pi$
$89$	1.83561	+	12.7670i	0.194574	+	1.35329i	−0.625136	+	0.780516i	$0.714956\pi$
$90$	0.841254	+	0.540641i	0.0886759	+	0.0569885i
$91$	31.3141			3.28261
$92$	4.74055	−	0.726057i	0.494237	−	0.0756967i
$93$	−3.96768			−0.411429
$94$	3.42790	+	2.20298i	0.353561	+	0.227220i
$95$	−0.339290	−	2.35981i	−0.0348104	−	0.242112i
$96$	−0.415415	−	0.909632i	−0.0423981	−	0.0928389i
$97$	6.25556	+	1.83680i	0.635156	+	0.186499i	0.583431	−	0.812163i	$-0.301710\pi$
$97$	6.25556	+	1.83680i	0.635156	+	0.186499i	0.0517252	+	0.998661i	$0.483528\pi$
$98$	−5.50484	+	12.0539i	−0.556073	+	1.21763i
$99$	−2.45957	+	2.83850i	−0.247196	+	0.285280i
$100$	−0.142315	+	0.989821i	−0.0142315	+	0.0989821i
$101$	4.20064	−	1.23342i	0.417979	−	0.122730i	−0.0659786	−	0.997821i	$-0.521017\pi$
$101$	4.20064	−	1.23342i	0.417979	−	0.122730i	0.483958	+	0.875091i	$0.339199\pi$
$102$	−4.58868	−	5.29562i	−0.454347	−	0.524344i
$103$	0.0990437	−	0.0636515i	0.00975907	−	0.00627177i	−0.535752	−	0.844375i	$-0.679972\pi$
$103$	0.0990437	−	0.0636515i	0.00975907	−	0.00627177i	0.545511	+	0.838103i	$0.316336\pi$
$104$	5.85381	−	3.76202i	0.574014	−	0.368896i
$105$	−2.94698	−	3.40099i	−0.287595	−	0.331903i
$106$	−3.76202	+	1.10463i	−0.365400	+	0.107291i
$107$	−1.48069	+	10.2984i	−0.143144	+	0.995587i	0.783968	+	0.620802i	$0.213193\pi$
$107$	−1.48069	+	10.2984i	−0.143144	+	0.995587i	−0.927112	+	0.374785i	$0.877716\pi$
$108$	−0.654861	+	0.755750i	−0.0630140	+	0.0727220i
$109$	−8.35340	+	18.2914i	−0.800110	+	1.75200i	−0.154990	+	0.987916i	$0.549534\pi$
$109$	−8.35340	+	18.2914i	−0.800110	+	1.75200i	−0.645121	+	0.764081i	$0.723193\pi$
$110$	−3.60373	−	1.05815i	−0.343602	−	0.100891i
$111$	−3.12252	−	6.83736i	−0.296376	−	0.648974i
$112$	0.640439	+	4.45435i	0.0605158	+	0.420897i
$113$	−6.50827	−	4.18261i	−0.612246	−	0.393467i	0.197452	−	0.980312i	$-0.436733\pi$
$113$	−6.50827	−	4.18261i	−0.612246	−	0.393467i	−0.809699	+	0.586846i	$0.800370\pi$
$114$	2.38408			0.223290
$115$	2.55568	−	4.05814i	0.238319	−	0.378423i
$116$	−5.00473			−0.464677
$117$	−5.85381	−	3.76202i	−0.541185	−	0.347799i
$118$	1.55117	+	10.7886i	0.142797	+	0.993175i
$119$	13.0993	+	28.6835i	1.20081	+	2.62941i
$120$	−0.959493	−	0.281733i	−0.0875893	−	0.0257185i
$121$	1.29050	−	2.82581i	0.117318	−	0.256892i
$122$	−8.72285	+	10.0667i	−0.789729	+	0.911396i
$123$	−0.313444	+	2.18005i	−0.0282623	+	0.196569i
$124$	3.80696	−	1.11782i	0.341875	−	0.100384i
$125$	0.654861	+	0.755750i	0.0585725	+	0.0675963i
$126$	3.78577	−	2.43297i	0.337264	−	0.216746i
$127$	−11.1862	+	7.18893i	−0.992615	+	0.637915i	−0.932838	−	0.360297i	$-0.882675\pi$
$127$	−11.1862	+	7.18893i	−0.992615	+	0.637915i	−0.0597771	+	0.998212i	$0.519039\pi$
$128$	0.654861	+	0.755750i	0.0578821	+	0.0667995i
$129$	8.50341	−	2.49683i	0.748684	−	0.219833i
$130$	0.990289	−	6.88761i	0.0868541	−	0.604084i
$131$	4.98808	−	5.75656i	0.435811	−	0.502953i	−0.494778	−	0.869020i	$-0.664750\pi$
$131$	4.98808	−	5.75656i	0.435811	−	0.502953i	0.930588	+	0.366067i	$0.119296\pi$
$132$	1.56024	−	3.41646i	0.135802	−	0.297364i
$133$	−10.2941	−	3.02263i	−0.892616	−	0.262096i
$134$	−0.427744	−	0.936629i	−0.0369515	−	0.0809125i
$135$	0.142315	+	0.989821i	0.0122485	+	0.0851903i
$136$	5.89475	+	3.78833i	0.505471	+	0.324846i
$137$	0.457151			0.0390571			0.0195285	−	0.999809i	$-0.493783\pi$
$137$	0.457151			0.0390571			0.0195285	+	0.999809i	$0.493783\pi$
$138$	3.65312	+	3.10720i	0.310974	+	0.264503i
$139$	−3.56577			−0.302445			−0.151222	−	0.988500i	$-0.548321\pi$
$139$	−3.56577			−0.302445			−0.151222	+	0.988500i	$0.548321\pi$
$140$	3.78577	+	2.43297i	0.319956	+	0.205623i
$141$	0.579898	+	4.03328i	0.0488362	+	0.339663i
$142$	2.07052	+	4.53381i	0.173754	+	0.380469i
$143$	25.0763	+	7.36307i	2.09699	+	0.615731i
$144$	0.415415	−	0.909632i	0.0346179	−	0.0758027i
$145$	−3.27740	+	3.78232i	−0.272173	+	0.314105i
$146$	−0.887441	+	6.17229i	−0.0734451	+	0.510822i
$147$	−12.7146	+	3.73336i	−1.04869	+	0.307922i
$148$	4.92234	+	5.68069i	0.404614	+	0.466949i
$149$	3.18680	−	2.04803i	0.261073	−	0.167781i	−0.403556	−	0.914955i	$-0.632226\pi$
$149$	3.18680	−	2.04803i	0.261073	−	0.167781i	0.664629	+	0.747173i	$0.268590\pi$
$150$	−0.841254	+	0.540641i	−0.0686881	+	0.0441431i
$151$	8.19411	+	9.45651i	0.666827	+	0.769560i	0.983876	−	0.178849i	$-0.0572375\pi$
$151$	8.19411	+	9.45651i	0.666827	+	0.769560i	−0.317049	+	0.948409i	$0.602692\pi$
$152$	−2.28751	+	0.671673i	−0.185541	+	0.0544799i
$153$	0.997215	−	6.93578i	0.0806201	−	0.560725i
$154$	−11.0685	+	12.7737i	−0.891921	+	1.02933i
$155$	1.64823	−	3.60913i	0.132389	−	0.289892i
$156$	6.67657	+	1.96042i	0.534554	+	0.156959i
$157$	1.83361	+	4.01505i	0.146338	+	0.320436i	0.968580	−	0.248702i	$-0.0800041\pi$
$157$	1.83361	+	4.01505i	0.146338	+	0.320436i	−0.822242	+	0.569139i	$0.807277\pi$
$158$	0.566437	+	3.93965i	0.0450633	+	0.313422i
$159$	−3.29843	−	2.11977i	−0.261582	−	0.168109i
$160$	1.00000			0.0790569
$161$	−11.8343	−	18.0481i	−0.932670	−	1.42239i
$162$	−1.00000			−0.0785674
$163$	4.73056	+	3.04014i	0.370526	+	0.238122i	0.712631	−	0.701539i	$-0.247504\pi$
$163$	4.73056	+	3.04014i	0.370526	+	0.238122i	−0.342105	+	0.939662i	$0.611140\pi$
$164$	−0.313444	−	2.18005i	−0.0244759	−	0.170234i
$165$	−1.56024	−	3.41646i	−0.121465	−	0.265971i
$166$	14.6281	+	4.29519i	1.13536	+	0.333371i
$167$	6.75084	−	14.7823i	0.522395	−	1.14389i	−0.446129	−	0.894969i	$-0.647198\pi$
$167$	6.75084	−	14.7823i	0.522395	−	1.14389i	0.968525	−	0.248918i	$-0.0800749\pi$
$168$	−2.94698	+	3.40099i	−0.227364	+	0.262392i
$169$	−5.04078	+	35.0594i	−0.387752	+	2.69687i
$170$	6.72327	−	1.97413i	0.515651	−	0.151409i
$171$	1.56124	+	1.80177i	0.119391	+	0.137785i
$172$	−7.45553	+	4.79138i	−0.568479	+	0.365339i
$173$	1.43265	−	0.920706i	0.108922	−	0.0700000i	−0.485046	−	0.874489i	$-0.661197\pi$
$173$	1.43265	−	0.920706i	0.108922	−	0.0700000i	0.593968	+	0.804489i	$0.297561\pi$
$174$	−3.27740	−	3.78232i	−0.248459	−	0.286737i
$175$	4.31787	−	1.26784i	0.326400	−	0.0958398i
$176$	−0.534516	+	3.71764i	−0.0402906	+	0.280228i
$177$	−7.13771	+	8.23736i	−0.536503	+	0.619158i
$178$	5.35812	−	11.7327i	0.401608	−	0.879400i
$179$	−12.5417	−	3.68258i	−0.937411	−	0.275249i	−0.222875	−	0.974847i	$-0.571544\pi$
$179$	−12.5417	−	3.68258i	−0.937411	−	0.275249i	−0.714536	+	0.699598i	$0.753362\pi$
$180$	−0.415415	−	0.909632i	−0.0309632	−	0.0678000i
$181$	−2.82585	−	19.6542i	−0.210043	−	1.46088i	−0.773004	−	0.634401i	$-0.781247\pi$
$181$	−2.82585	−	19.6542i	−0.210043	−	1.46088i	0.562961	−	0.826484i	$-0.309662\pi$
$182$	−26.3431	−	16.9297i	−1.95268	−	1.25491i
$183$	−13.3202			−0.984654
$184$	−4.38054	−	1.95214i	−0.322938	−	0.143914i
$185$	7.51662			0.552633
$186$	3.33782	+	2.14509i	0.244741	+	0.157286i
$187$	3.74541	+	26.0499i	0.273891	+	1.90496i
$188$	−1.69271	−	3.70652i	−0.123454	−	0.270326i
$189$	4.31787	+	1.26784i	0.314079	+	0.0922219i
$190$	−0.990383	+	2.16864i	−0.0718499	+	0.157329i
$191$	4.27913	−	4.93837i	0.309627	−	0.357328i	−0.579514	−	0.814962i	$-0.696758\pi$
$191$	4.27913	−	4.93837i	0.309627	−	0.357328i	0.889141	+	0.457634i	$0.151303\pi$
$192$	−0.142315	+	0.989821i	−0.0102707	+	0.0714342i
$193$	−3.55126	+	1.04275i	−0.255626	+	0.0750584i	−0.407035	−	0.913413i	$-0.633437\pi$
$193$	−3.55126	+	1.04275i	−0.255626	+	0.0750584i	0.151409	+	0.988471i	$0.451619\pi$
$194$	−4.26947	−	4.92723i	−0.306530	−	0.353754i
$195$	5.85381	−	3.76202i	0.419200	−	0.269404i
$196$	11.1478	−	7.16426i	0.796272	−	0.511733i
$197$	8.30675	+	9.58650i	0.591831	+	0.683010i	0.970105	−	0.242684i	$-0.0780278\pi$
$197$	8.30675	+	9.58650i	0.591831	+	0.683010i	−0.378274	+	0.925694i	$0.623482\pi$
$198$	3.60373	−	1.05815i	0.256106	−	0.0751995i
$199$	−0.731905	+	5.09051i	−0.0518833	+	0.360857i	0.947296	+	0.320359i	$0.103803\pi$
$199$	−0.731905	+	5.09051i	−0.0518833	+	0.360857i	−0.999180	+	0.0404978i	$0.987106\pi$
$200$	0.654861	−	0.755750i	0.0463056	−	0.0534396i
$201$	0.427744	−	0.936629i	0.0301708	−	0.0660647i
$202$	−4.20064	−	1.23342i	−0.295556	−	0.0867831i
$203$	9.35601	+	20.4868i	0.656663	+	1.43789i
$204$	0.997215	+	6.93578i	0.0698190	+	0.485602i
$205$	−1.85284	−	1.19075i	−0.129408	−	0.0831653i
$206$	−0.117733			−0.00820288
$207$	0.0440162	+	4.79563i	0.00305933	+	0.333319i
$208$	−6.95844			−0.482481
$209$	−7.53283	−	4.84105i	−0.521057	−	0.334863i
$210$	0.640439	+	4.45435i	0.0441945	+	0.307380i
$211$	0.942067	+	2.06284i	0.0648546	+	0.142012i	0.939284	−	0.343142i	$-0.111491\pi$
$211$	0.942067	+	2.06284i	0.0648546	+	0.142012i	−0.874429	+	0.485153i	$0.838764\pi$
$212$	3.76202	+	1.10463i	0.258377	+	0.0758663i
$213$	−2.07052	+	4.53381i	−0.141870	+	0.310652i
$214$	6.81339	−	7.86307i	0.465754	−	0.537508i
$215$	−1.26125	+	8.77220i	−0.0860166	+	0.598259i
$216$	0.959493	−	0.281733i	0.0652852	−	0.0191695i
$217$	−11.6927	−	13.4940i	−0.793749	−	0.916036i
$218$	16.9164	−	10.8715i	1.14572	−	0.736311i
$219$	−5.24585	+	3.37131i	−0.354482	+	0.227812i
$220$	2.45957	+	2.83850i	0.165824	+	0.191371i
$221$	−46.7835	+	13.7369i	−3.14700	+	0.924042i
$222$	−1.06973	+	7.44012i	−0.0717954	+	0.499348i
$223$	−8.05267	+	9.29328i	−0.539247	+	0.622324i	−0.958344	−	0.285618i	$-0.907801\pi$
$223$	−8.05267	+	9.29328i	−0.539247	+	0.622324i	0.419097	+	0.907941i	$0.362347\pi$
$224$	1.86943	−	4.09349i	0.124907	−	0.273508i
$225$	−0.959493	−	0.281733i	−0.0639662	−	0.0187822i
$226$	3.21381	+	7.03727i	0.213780	+	0.468112i
$227$	0.581482	+	4.04429i	0.0385943	+	0.268429i	0.999977	−	0.00678591i	$-0.00216004\pi$
$227$	0.581482	+	4.04429i	0.0385943	+	0.268429i	−0.961383	+	0.275215i	$0.911251\pi$
$228$	−2.00562	−	1.28893i	−0.132825	−	0.0853615i
$229$	−12.1403			−0.802253			−0.401126	−	0.916023i	$-0.631381\pi$
$229$	−12.1403			−0.802253			−0.401126	+	0.916023i	$0.631381\pi$
$230$	−4.34397	+	2.03222i	−0.286433	+	0.134000i
$231$	−16.9020			−1.11207
$232$	4.21025	+	2.70576i	0.276416	+	0.177642i
$233$	2.65323	+	18.4536i	0.173819	+	1.20894i	0.870724	+	0.491772i	$0.163651\pi$
$233$	2.65323	+	18.4536i	0.173819	+	1.20894i	−0.696905	+	0.717163i	$0.745440\pi$
$234$	2.89064	+	6.32962i	0.188967	+	0.413780i
$235$	−3.90970	−	1.14799i	−0.255040	−	0.0748866i
$236$	4.52785	−	9.91461i	0.294738	−	0.645386i
$237$	−2.60645	+	3.00801i	−0.169307	+	0.195391i
$238$	4.48763	−	31.2121i	0.290890	−	2.02318i
$239$	−2.19543	+	0.644637i	−0.142011	+	0.0416981i	−0.351965	−	0.936013i	$-0.614487\pi$
$239$	−2.19543	+	0.644637i	−0.142011	+	0.0416981i	0.209955	+	0.977711i	$0.432668\pi$
$240$	0.654861	+	0.755750i	0.0422711	+	0.0487834i
$241$	−11.0338	+	7.09102i	−0.710752	+	0.456772i	−0.845409	−	0.534120i	$-0.820643\pi$
$241$	−11.0338	+	7.09102i	−0.710752	+	0.456772i	0.134657	+	0.990892i	$0.457007\pi$
$242$	−2.61339	+	1.67952i	−0.167995	+	0.107964i
$243$	−0.654861	−	0.755750i	−0.0420093	−	0.0484814i
$244$	12.7806	−	3.75272i	0.818194	−	0.240243i
$245$	1.88587	−	13.1165i	0.120484	−	0.837985i
$246$	1.44231	−	1.66452i	0.0919584	−	0.106126i
$247$	6.89152	−	15.0903i	0.438497	−	0.960174i
$248$	−3.80696	−	1.11782i	−0.241742	−	0.0709819i
$249$	6.33326	+	13.8679i	0.401354	+	0.878843i
$250$	−0.142315	−	0.989821i	−0.00900078	−	0.0626018i
$251$	−3.60795	−	2.31869i	−0.227731	−	0.146354i	0.421800	−	0.906689i	$-0.361398\pi$
$251$	−3.60795	−	2.31869i	−0.227731	−	0.146354i	−0.649531	+	0.760335i	$0.725035\pi$
$252$	−4.50016			−0.283483
$253$	−5.23312	−	17.2356i	−0.329003	−	1.08359i
$254$	13.2971			0.834332
$255$	5.89475	+	3.78833i	0.369144	+	0.237234i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	8.12908	+	17.8002i	0.507078	+	1.11035i	0.974104	+	0.226102i	$0.0725984\pi$
$257$	8.12908	+	17.8002i	0.507078	+	1.11035i	−0.467025	+	0.884244i	$0.654674\pi$
$258$	−8.50341	−	2.49683i	−0.529399	−	0.155446i
$259$	14.0518	−	30.7692i	0.873138	−	1.91191i
$260$	−4.55681	+	5.25884i	−0.282601	+	0.326139i
$261$	0.712247	−	4.95379i	0.0440870	−	0.306632i
$262$	−7.30847	+	2.14596i	−0.451519	+	0.132578i
$263$	11.8728	+	13.7019i	0.732108	+	0.844898i	0.992707	−	0.120549i	$-0.0384655\pi$
$263$	11.8728	+	13.7019i	0.732108	+	0.844898i	−0.260599	+	0.965447i	$0.583920\pi$
$264$	−3.15964	+	2.03058i	−0.194462	+	0.124973i
$265$	3.29843	−	2.11977i	0.202621	−	0.130216i
$266$	7.02583	+	8.10824i	0.430781	+	0.497148i
$267$	12.3758	−	3.63385i	0.757385	−	0.222388i
$268$	−0.146539	+	1.01920i	−0.00895127	+	0.0622575i
$269$	5.24425	−	6.05218i	0.319747	−	0.369008i	−0.573008	−	0.819550i	$-0.694224\pi$
$269$	5.24425	−	6.05218i	0.319747	−	0.369008i	0.892755	+	0.450542i	$0.148769\pi$
$270$	0.415415	−	0.909632i	0.0252814	−	0.0553584i
$271$	−25.3828	−	7.45305i	−1.54189	−	0.452741i	−0.603227	−	0.797569i	$-0.706119\pi$
$271$	−25.3828	−	7.45305i	−1.54189	−	0.452741i	−0.938666	+	0.344829i	$0.887937\pi$
$272$	−2.91086	−	6.37389i	−0.176497	−	0.386474i
$273$	−4.45646	−	30.9953i	−0.269717	−	1.87592i
$274$	−0.384580	−	0.247155i	−0.0232333	−	0.0149312i
$275$	3.75587			0.226487
$276$	−1.39332	−	4.58897i	−0.0838679	−	0.276224i
$277$	−2.76068			−0.165873			−0.0829365	−	0.996555i	$-0.526430\pi$
$277$	−2.76068			−0.165873			−0.0829365	+	0.996555i	$0.526430\pi$
$278$	2.99972	+	1.92780i	0.179911	+	0.115622i
$279$	0.564660	+	3.92729i	0.0338053	+	0.235121i
$280$	−1.86943	−	4.09349i	−0.111720	−	0.244633i
$281$	27.1941	+	7.98491i	1.62227	+	0.476340i	0.961626	−	0.274363i	$-0.0884671\pi$
$281$	27.1941	+	7.98491i	1.62227	+	0.476340i	0.660639	+	0.750704i	$0.270285\pi$
$282$	1.69271	−	3.70652i	0.100800	−	0.220720i
$283$	13.5748	−	15.6662i	0.806939	−	0.931258i	−0.191801	−	0.981434i	$-0.561433\pi$
$283$	13.5748	−	15.6662i	0.806939	−	0.931258i	0.998740	+	0.0501762i	$0.0159783\pi$
$284$	0.709330	−	4.93350i	0.0420910	−	0.292749i
$285$	−2.28751	+	0.671673i	−0.135500	+	0.0397865i
$286$	−17.1148	−	19.7515i	−1.01202	−	1.16793i
$287$	−8.33806	+	5.35854i	−0.492180	+	0.316305i
$288$	−0.841254	+	0.540641i	−0.0495713	+	0.0318576i
$289$	−21.0207	−	24.2592i	−1.23651	−	1.42701i
$290$	4.80200	−	1.41000i	0.281983	−	0.0827978i
$291$	0.927844	−	6.45330i	0.0543912	−	0.378299i
$292$	4.08355	−	4.71267i	0.238972	−	0.275788i
$293$	3.82530	−	8.37623i	0.223476	−	0.489345i	−0.764370	−	0.644778i	$-0.776950\pi$
$293$	3.82530	−	8.37623i	0.223476	−	0.489345i	0.987846	+	0.155433i	$0.0496772\pi$
$294$	12.7146	+	3.73336i	0.741533	+	0.217734i
$295$	−4.52785	−	9.91461i	−0.263622	−	0.577251i
$296$	−1.06973	−	7.44012i	−0.0621766	−	0.432448i
$297$	3.15964	+	2.03058i	0.183341	+	0.117826i
$298$	−3.78816			−0.219442
$299$	30.2273	−	14.1410i	1.74809	−	0.817798i
$300$	1.00000			0.0577350
$301$	33.5511	+	21.5620i	1.93385	+	1.24281i
$302$	−1.78075	−	12.3854i	−0.102471	−	0.712699i
$303$	−1.81868	−	3.98235i	−0.104480	−	0.228780i
$304$	2.28751	+	0.671673i	0.131198	+	0.0385231i
$305$	5.53339	−	12.1164i	0.316841	−	0.693785i
$306$	−4.58868	+	5.29562i	−0.262317	+	0.302730i
$307$	−1.33473	+	9.28328i	−0.0761773	+	0.529825i	0.915624	+	0.402036i	$0.131697\pi$
$307$	−1.33473	+	9.28328i	−0.0761773	+	0.529825i	−0.991801	+	0.127789i	$0.959212\pi$
$308$	16.2173	−	4.76184i	0.924069	−	0.271331i
$309$	−0.0770990	−	0.0889770i	−0.00438601	−	0.00506173i
$310$	−3.33782	+	2.14509i	−0.189576	+	0.121833i
$311$	−6.99976	+	4.49847i	−0.396920	+	0.255085i	−0.723841	−	0.689967i	$-0.757625\pi$
$311$	−6.99976	+	4.49847i	−0.396920	+	0.255085i	0.326921	+	0.945052i	$0.393989\pi$
$312$	−4.55681	−	5.25884i	−0.257979	−	0.297723i
$313$	−19.6564	+	5.77163i	−1.11104	+	0.326232i	−0.785232	−	0.619202i	$-0.787456\pi$
$313$	−19.6564	+	5.77163i	−1.11104	+	0.326232i	−0.325813	+	0.945434i	$0.605638\pi$
$314$	0.628168	−	4.36900i	0.0354496	−	0.246557i
$315$	−2.94698	+	3.40099i	−0.166043	+	0.191624i
$316$	1.65342	−	3.62049i	0.0930122	−	0.203668i
$317$	28.9344	+	8.49590i	1.62512	+	0.477177i	0.962387	−	0.271682i	$-0.0875797\pi$
$317$	28.9344	+	8.49590i	1.62512	+	0.477177i	0.662730	+	0.748859i	$0.269398\pi$
$318$	1.62878	+	3.56653i	0.0913373	+	0.200001i
$319$	2.67511	+	18.6058i	0.149777	+	1.04172i
$320$	−0.841254	−	0.540641i	−0.0470275	−	0.0302227i
$321$	10.4043			0.580713
$322$	0.198080	+	21.5811i	0.0110385	+	1.20267i
$323$	16.7055			0.929519
$324$	0.841254	+	0.540641i	0.0467363	+	0.0300356i
$325$	0.990289	+	6.88761i	0.0549314	+	0.382056i
$326$	−2.33597	−	5.11506i	−0.129377	−	0.283297i
$327$	19.2940	+	5.66523i	1.06696	+	0.313288i
$328$	−0.914940	+	2.00344i	−0.0505191	+	0.110621i
$329$	−12.0082	+	13.8582i	−0.662033	+	0.764027i
$330$	−0.534516	+	3.71764i	−0.0294241	+	0.204649i
$331$	−20.1419	+	5.91420i	−1.10710	+	0.325074i	−0.783670	−	0.621178i	$-0.786655\pi$
$331$	−20.1419	+	5.91420i	−1.10710	+	0.325074i	−0.323431	+	0.946252i	$0.604836\pi$
$332$	−9.98376	−	11.5219i	−0.547930	−	0.632345i
$333$	−6.32339	+	4.06379i	−0.346519	+	0.222695i
$334$	−13.6711	+	8.78586i	−0.748047	+	0.480741i
$335$	0.674297	+	0.778180i	0.0368408	+	0.0425165i
$336$	4.31787	−	1.26784i	0.235559	−	0.0691664i
$337$	4.82099	−	33.5307i	0.262616	−	1.82653i	−0.250386	−	0.968146i	$-0.580557\pi$
$337$	4.82099	−	33.5307i	0.262616	−	1.82653i	0.513001	−	0.858388i	$-0.328534\pi$
$338$	23.1951	−	26.7686i	1.26165	−	1.45602i
$339$	−3.21381	+	7.03727i	−0.174550	+	0.382212i
$340$	−6.72327	−	1.97413i	−0.364620	−	0.107062i
$341$	−6.19055	−	13.5554i	−0.335237	−	0.734067i
$342$	−0.339290	−	2.35981i	−0.0183467	−	0.127604i
$343$	−23.6665	−	15.2095i	−1.27787	−	0.821237i
$344$	8.86240			0.477829
$345$	−4.38054	−	1.95214i	−0.235841	−	0.105100i
$346$	−1.70299			−0.0915533
$347$	−7.31702	−	4.70236i	−0.392798	−	0.252436i	0.329302	−	0.944225i	$-0.393187\pi$
$347$	−7.31702	−	4.70236i	−0.392798	−	0.252436i	−0.722100	+	0.691789i	$0.756823\pi$
$348$	0.712247	+	4.95379i	0.0381805	+	0.265551i
$349$	−3.81184	−	8.34677i	−0.204043	−	0.446792i	0.779752	−	0.626089i	$-0.215345\pi$
$349$	−3.81184	−	8.34677i	−0.204043	−	0.446792i	−0.983795	+	0.179296i	$0.942618\pi$
$350$	−4.31787	−	1.26784i	−0.230800	−	0.0677690i
$351$	−2.89064	+	6.32962i	−0.154291	+	0.337850i
$352$	2.45957	−	2.83850i	0.131096	−	0.151292i
$353$	−0.547749	+	3.80968i	−0.0291537	+	0.202769i	−0.999192	−	0.0401820i	$-0.987206\pi$
$353$	−0.547749	+	3.80968i	−0.0291537	+	0.202769i	0.970039	+	0.242951i	$0.0781153\pi$
$354$	10.4581	−	3.07077i	0.555840	−	0.163209i
$355$	−3.26398	−	3.76683i	−0.173234	−	0.199922i
$356$	−10.8507	+	6.97332i	−0.575086	+	0.369585i
$357$	26.5273	−	17.0481i	1.40397	−	0.902280i
$358$	8.55980	+	9.87854i	0.452400	+	0.522097i
$359$	−12.0921	+	3.55056i	−0.638196	+	0.187391i	−0.584794	−	0.811182i	$-0.698825\pi$
$359$	−12.0921	+	3.55056i	−0.638196	+	0.187391i	−0.0534020	+	0.998573i	$0.517006\pi$
$360$	−0.142315	+	0.989821i	−0.00750065	+	0.0521682i
$361$	8.72023	−	10.0637i	0.458960	−	0.529668i
$362$	−8.24860	+	18.0619i	−0.433537	+	0.949314i
$363$	−2.98070	−	0.875214i	−0.156446	−	0.0459368i
$364$	13.0083	+	28.4843i	0.681822	+	1.49298i
$365$	−0.887441	−	6.17229i	−0.0464508	−	0.323072i
$366$	11.2056	+	7.20142i	0.585728	+	0.376424i
$367$	−9.04072			−0.471922			−0.235961	−	0.971763i	$-0.575824\pi$
$367$	−9.04072			−0.471922			−0.235961	+	0.971763i	$0.575824\pi$
$368$	2.62974	+	4.01054i	0.137085	+	0.209064i
$369$	2.20247			0.114656
$370$	−6.32339	−	4.06379i	−0.328737	−	0.211267i
$371$	−2.51106	−	17.4648i	−0.130368	−	0.906729i
$372$	−1.64823	−	3.60913i	−0.0854569	−	0.187125i
$373$	22.6519	+	6.65120i	1.17287	+	0.344386i	0.809421	−	0.587228i	$-0.199781\pi$
$373$	22.6519	+	6.65120i	1.17287	+	0.344386i	0.363449	+	0.931614i	$0.381599\pi$
$374$	10.9328	−	23.9395i	0.565321	−	1.23788i
$375$	0.654861	−	0.755750i	0.0338169	−	0.0390267i
$376$	−0.579898	+	4.03328i	−0.0299059	+	0.208000i
$377$	−33.4144	+	9.81137i	−1.72093	+	0.505311i
$378$	−2.94698	−	3.40099i	−0.151576	−	0.174928i
$379$	−24.7485	+	15.9049i	−1.27124	+	0.816979i	−0.989781	−	0.142593i	$-0.954456\pi$
$379$	−24.7485	+	15.9049i	−1.27124	+	0.816979i	−0.281463	+	0.959572i	$0.590820\pi$
$380$	2.00562	−	1.28893i	0.102886	−	0.0661208i
$381$	8.70772	+	10.0492i	0.446110	+	0.514839i
$382$	−6.26972	+	1.84095i	−0.320787	+	0.0941914i
$383$	−1.91168	+	13.2961i	−0.0976825	+	0.679396i	0.880864	+	0.473370i	$0.156963\pi$
$383$	−1.91168	+	13.2961i	−0.0976825	+	0.679396i	−0.978546	+	0.206027i	$0.933947\pi$
$384$	0.654861	−	0.755750i	0.0334182	−	0.0385667i
$385$	7.02134	−	15.3746i	0.357841	−	0.783562i
$386$	3.55126	+	1.04275i	0.180755	+	0.0530743i
$387$	−3.68158	−	8.06153i	−0.187145	−	0.409790i
$388$	0.927844	+	6.45330i	0.0471041	+	0.327616i
$389$	−14.7126	−	9.45523i	−0.745959	−	0.479399i	0.111620	−	0.993751i	$-0.464396\pi$
$389$	−14.7126	−	9.45523i	−0.745959	−	0.479399i	−0.857579	+	0.514352i	$0.828032\pi$
$390$	−6.95844			−0.352354
$391$	25.5978	+	21.7725i	1.29454	+	1.10108i
$392$	−13.2514			−0.669298
$393$	−6.40784	−	4.11807i	−0.323233	−	0.207729i
$394$	−1.80523	−	12.5556i	−0.0909461	−	0.632544i
$395$	−1.65342	−	3.62049i	−0.0831926	−	0.182166i
$396$	−3.60373	−	1.05815i	−0.181094	−	0.0531740i
$397$	8.11992	−	17.7802i	0.407527	−	0.892360i	−0.588924	−	0.808188i	$-0.700448\pi$
$397$	8.11992	−	17.7802i	0.407527	−	0.892360i	0.996451	−	0.0841718i	$-0.0268245\pi$
$398$	3.36785	−	3.88671i	0.168815	−	0.194823i
$399$	−1.52686	+	10.6195i	−0.0764385	+	0.531642i
$400$	−0.959493	+	0.281733i	−0.0479746	+	0.0140866i
$401$	13.5061	+	15.5869i	0.674464	+	0.778373i	0.985068	−	0.172167i	$-0.0550768\pi$
$401$	13.5061	+	15.5869i	0.674464	+	0.778373i	−0.310604	+	0.950539i	$0.600531\pi$
$402$	−0.866222	+	0.556687i	−0.0432032	+	0.0277650i
$403$	23.2261	−	14.9265i	1.15697	−	0.743541i
$404$	2.86697	+	3.30866i	0.142637	+	0.164612i
$405$	0.959493	−	0.281733i	0.0476776	−	0.0139994i
$406$	3.20523	−	22.2928i	0.159073	−	1.10637i
$407$	18.4877	−	21.3359i	0.916400	−	1.05758i
$408$	2.91086	−	6.37389i	0.144109	−	0.315554i
$409$	−6.72040	−	1.97329i	−0.332303	−	0.0975728i	0.111325	−	0.993784i	$-0.464491\pi$
$409$	−6.72040	−	1.97329i	−0.332303	−	0.0975728i	−0.443628	+	0.896211i	$0.646309\pi$
$410$	0.914940	+	2.00344i	0.0451856	+	0.0989428i
$411$	−0.0650594	−	0.452498i	−0.00320915	−	0.0223201i
$412$	0.0990437	+	0.0636515i	0.00487953	+	0.00313589i
$413$	−49.0499			−2.41359
$414$	2.55568	−	4.05814i	0.125605	−	0.199447i
$415$	−15.2456			−0.748378
$416$	5.85381	+	3.76202i	0.287007	+	0.184448i
$417$	0.507462	+	3.52947i	0.0248505	+	0.172839i
$418$	3.71975	+	8.14511i	0.181939	+	0.398390i
$419$	−31.9607	−	9.38450i	−1.56138	−	0.458463i	−0.616904	−	0.787038i	$-0.711613\pi$
$419$	−31.9607	−	9.38450i	−1.56138	−	0.458463i	−0.944478	+	0.328575i	$0.893432\pi$
$420$	1.86943	−	4.09349i	0.0912190	−	0.199742i
$421$	−14.5762	+	16.8218i	−0.710400	+	0.819846i	−0.990118	−	0.140237i	$-0.955214\pi$
$421$	−14.5762	+	16.8218i	−0.710400	+	0.819846i	0.279718	+	0.960082i	$0.409759\pi$
$422$	0.322738	−	2.24469i	0.0157106	−	0.109270i
$423$	3.90970	−	1.14799i	0.190096	−	0.0558172i
$424$	−2.56761	−	2.96318i	−0.124694	−	0.143905i
$425$	−5.89475	+	3.78833i	−0.285938	+	0.183761i
$426$	4.19300	−	2.69468i	0.203151	−	0.130558i
$427$	−39.2542	−	45.3018i	−1.89964	−	2.19231i
$428$	−9.98288	+	2.93124i	−0.482541	+	0.141687i
$429$	3.71940	−	25.8690i	0.179574	−	1.24897i
$430$	5.80364	−	6.69776i	0.279876	−	0.322995i
$431$	0.409021	−	0.895632i	0.0197019	−	0.0431411i	−0.899525	−	0.436869i	$-0.856087\pi$
$431$	0.409021	−	0.895632i	0.0197019	−	0.0431411i	0.919227	+	0.393728i	$0.128815\pi$
$432$	−0.959493	−	0.281733i	−0.0461636	−	0.0135549i
$433$	−2.31200	−	5.06257i	−0.111108	−	0.243292i	0.845908	−	0.533329i	$-0.179059\pi$
$433$	−2.31200	−	5.06257i	−0.111108	−	0.243292i	−0.957015	+	0.290038i	$0.906332\pi$
$434$	2.54106	+	17.6734i	0.121975	+	0.848353i
$435$	4.21025	+	2.70576i	0.201866	+	0.129731i
$436$	−20.1086			−0.963025
$437$	−11.3019	+	1.73098i	−0.540641	+	0.0828040i
$438$	6.23576			0.297956
$439$	23.3856	+	15.0290i	1.11613	+	0.717295i	0.962621	−	0.270852i	$-0.0873055\pi$
$439$	23.3856	+	15.0290i	1.11613	+	0.717295i	0.153511	+	0.988147i	$0.450942\pi$
$440$	−0.534516	−	3.71764i	−0.0254820	−	0.177231i
$441$	5.50484	+	12.0539i	0.262135	+	0.573996i
$442$	46.7835	+	13.7369i	2.22526	+	0.653396i
$443$	7.35780	−	16.1113i	0.349580	−	0.765473i	−0.650403	−	0.759589i	$-0.725400\pi$
$443$	7.35780	−	16.1113i	0.349580	−	0.765473i	0.999983	−	0.00588337i	$-0.00187275\pi$
$444$	4.92234	−	5.68069i	0.233604	−	0.269593i
$445$	−1.83561	+	12.7670i	−0.0870163	+	0.605212i
$446$	11.7987	−	3.46440i	0.558683	−	0.164044i
$447$	−2.48072	−	2.86290i	−0.117334	−	0.135411i
$448$	−3.78577	+	2.43297i	−0.178861	+	0.114947i
$449$	20.5880	−	13.2311i	0.971609	−	0.624415i	0.0444217	−	0.999013i	$-0.485855\pi$
$449$	20.5880	−	13.2311i	0.971609	−	0.624415i	0.927187	+	0.374598i	$0.122219\pi$
$450$	0.654861	+	0.755750i	0.0308704	+	0.0356264i
$451$	−7.93711	+	2.33054i	−0.373744	+	0.109741i
$452$	1.10100	−	7.65765i	0.0517869	−	0.360185i
$453$	8.19411	−	9.45651i	0.384993	−	0.444306i
$454$	1.69734	−	3.71665i	0.0796599	−	0.174431i
$455$	30.0456	+	8.82220i	1.40856	+	0.413591i
$456$	0.990383	+	2.16864i	0.0463789	+	0.101556i
$457$	2.29012	+	15.9281i	0.107127	+	0.745087i	0.970601	+	0.240694i	$0.0773749\pi$
$457$	2.29012	+	15.9281i	0.107127	+	0.745087i	−0.863474	+	0.504394i	$0.831716\pi$
$458$	10.2131	+	6.56353i	0.477225	+	0.306694i
$459$	−7.00711			−0.327064
$460$	4.75308	+	0.638921i	0.221614	+	0.0297898i
$461$	7.38655			0.344026			0.172013	−	0.985095i	$-0.444973\pi$
$461$	7.38655			0.344026			0.172013	+	0.985095i	$0.444973\pi$
$462$	14.2189	+	9.13791i	0.661521	+	0.425134i
$463$	0.0233132	+	0.162147i	0.00108346	+	0.00753560i	0.990356	−	0.138546i	$-0.0442429\pi$
$463$	0.0233132	+	0.162147i	0.00108346	+	0.00753560i	−0.989273	+	0.146082i	$0.953334\pi$
$464$	−2.07904	−	4.55246i	−0.0965170	−	0.211343i
$465$	−3.80696	−	1.11782i	−0.176544	−	0.0518379i
$466$	7.74473	−	16.9586i	0.358768	−	0.785592i
$467$	10.6615	−	12.3040i	0.493354	−	0.569361i	−0.453405	−	0.891305i	$-0.649791\pi$
$467$	10.6615	−	12.3040i	0.493354	−	0.569361i	0.946759	+	0.321944i	$0.104336\pi$
$468$	0.990289	−	6.88761i	0.0457761	−	0.318380i
$469$	4.44602	−	1.30547i	0.205298	−	0.0602810i
$470$	2.66840	+	3.07949i	0.123084	+	0.142046i
$471$	3.71324	−	2.38635i	0.171097	−	0.109957i
$472$	−9.16931	+	5.89276i	−0.422052	+	0.271236i
$473$	21.7977	+	25.1559i	1.00226	+	1.15667i
$474$	3.81894	−	1.12134i	0.175410	−	0.0515050i
$475$	0.339290	−	2.35981i	0.0155677	−	0.108276i
$476$	−20.6498	+	23.8311i	−0.946481	+	1.09230i
$477$	−1.62878	+	3.56653i	−0.0745766	+	0.163300i
$478$	2.19543	+	0.644637i	0.100417	+	0.0294850i
$479$	5.15018	+	11.2773i	0.235318	+	0.515274i	0.990043	−	0.140767i	$-0.0449569\pi$
$479$	5.15018	+	11.2773i	0.235318	+	0.515274i	−0.754725	+	0.656042i	$0.772230\pi$
$480$	−0.142315	−	0.989821i	−0.00649575	−	0.0451790i
$481$	44.0009	+	28.2777i	2.00627	+	1.28935i
$482$	13.1159			0.597415
$483$	−16.1802	+	14.2823i	−0.736224	+	0.649867i
$484$	3.10654			0.141206
$485$	5.48468	+	3.52479i	0.249047	+	0.160053i
$486$	0.142315	+	0.989821i	0.00645553	+	0.0448992i
$487$	15.8612	+	34.7313i	0.718742	+	1.57382i	0.815659	+	0.578532i	$0.196374\pi$
$487$	15.8612	+	34.7313i	0.718742	+	1.57382i	−0.0969178	+	0.995292i	$0.530898\pi$
$488$	−12.7806	−	3.75272i	−0.578550	−	0.169878i
$489$	2.33597	−	5.11506i	0.105636	−	0.231311i
$490$	−8.67784	+	10.0148i	−0.392025	+	0.452421i
$491$	3.61330	−	25.1311i	0.163066	−	1.13415i	−0.729746	−	0.683719i	$-0.760362\pi$
$491$	3.61330	−	25.1311i	0.163066	−	1.13415i	0.892812	−	0.450430i	$-0.148729\pi$
$492$	−2.11326	+	0.620508i	−0.0952729	+	0.0279747i
$493$	−22.9651	−	26.5031i	−1.03430	−	1.19364i
$494$	−13.9560	+	8.96895i	−0.627908	+	0.403532i
$495$	−3.15964	+	2.03058i	−0.142015	+	0.0912676i
$496$	2.59828	+	2.99857i	0.116666	+	0.134640i
$497$	−21.5212	+	6.31921i	−0.965360	+	0.283455i
$498$	2.16968	−	15.0904i	0.0972256	−	0.676219i
$499$	23.8043	−	27.4716i	1.06563	−	1.22980i	0.0934322	−	0.995626i	$-0.470216\pi$
$499$	23.8043	−	27.4716i	1.06563	−	1.22980i	0.972195	−	0.234173i	$-0.0752384\pi$
$500$	−0.415415	+	0.909632i	−0.0185779	+	0.0406800i
$501$	−15.5926	−	4.57839i	−0.696624	−	0.204547i
$502$	1.78162	+	3.90121i	0.0795176	+	0.174119i
$503$	1.24830	+	8.68212i	0.0556590	+	0.387117i	0.998541	+	0.0539910i	$0.0171942\pi$
$503$	1.24830	+	8.68212i	0.0556590	+	0.387117i	−0.942882	+	0.333126i	$0.891897\pi$
$504$	3.78577	+	2.43297i	0.168632	+	0.108373i
$505$	4.37798			0.194818
$506$	−4.91587	+	17.3287i	−0.218537	+	0.770356i
$507$	35.4199			1.57305
$508$	−11.1862	−	7.18893i	−0.496307	−	0.318957i
$509$	0.746880	+	5.19467i	0.0331049	+	0.230250i	0.999656	−	0.0262242i	$-0.00834838\pi$
$509$	0.746880	+	5.19467i	0.0331049	+	0.230250i	−0.966551	+	0.256474i	$0.917439\pi$
$510$	−2.91086	−	6.37389i	−0.128895	−	0.282240i
$511$	−26.9252	−	7.90595i	−1.19110	−	0.349739i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$	1.56124	−	1.80177i	0.0689304	−	0.0795500i
$514$	2.78490	−	19.3694i	0.122837	−	0.854347i
$515$	0.112964	−	0.0331694i	0.00497781	−	0.00146162i
$516$	5.80364	+	6.69776i	0.255491	+	0.294852i
$517$	−12.8747	+	8.27409i	−0.566230	+	0.363894i
$518$	−28.4562	+	18.2877i	−1.25030	+	0.803516i
$519$	−1.11522	−	1.28703i	−0.0489528	−	0.0564945i
$520$	6.67657	−	1.96042i	0.292787	−	0.0859701i
$521$	3.31202	−	23.0356i	0.145102	−	1.00921i	−0.778989	−	0.627038i	$-0.784267\pi$
$521$	3.31202	−	23.0356i	0.145102	−	1.00921i	0.924091	−	0.382172i	$-0.124824\pi$
$522$	−3.27740	+	3.78232i	−0.143448	+	0.165548i
$523$	−17.4732	+	38.2610i	−0.764051	+	1.67304i	−0.0247216	+	0.999694i	$0.507870\pi$
$523$	−17.4732	+	38.2610i	−0.764051	+	1.67304i	−0.739329	+	0.673344i	$0.764857\pi$
$524$	7.30847	+	2.14596i	0.319272	+	0.0937467i
$525$	−1.86943	−	4.09349i	−0.0815888	−	0.178654i
$526$	−2.58021	−	17.9457i	−0.112502	−	0.782471i
$527$	23.3885	+	15.0309i	1.01882	+	0.654755i
$528$	3.75587			0.163453
$529$	−19.5738	−	12.0775i	−0.851035	−	0.525108i
$530$	−3.92085			−0.170311
$531$	9.16931	+	5.89276i	0.397914	+	0.255724i
$532$	−1.52686	−	10.6195i	−0.0661977	−	0.460415i
$533$	−6.36655	−	13.9408i	−0.275766	−	0.603843i
$534$	−12.3758	−	3.63385i	−0.535552	−	0.157252i
$535$	−4.32212	+	9.46411i	−0.186861	+	0.409169i
$536$	0.674297	−	0.778180i	0.0291252	−	0.0336123i
$537$	−1.86022	+	12.9381i	−0.0802746	+	0.558322i
$538$	−7.68380	+	2.25617i	−0.331272	+	0.0972702i
$539$	−32.5928	−	37.6141i	−1.40387	−	1.62015i
$540$	−0.841254	+	0.540641i	−0.0362018	+	0.0232655i
$541$	−15.5404	+	9.98719i	−0.668133	+	0.429383i	−0.830252	−	0.557388i	$-0.811803\pi$
$541$	−15.5404	+	9.98719i	−0.668133	+	0.429383i	0.162119	+	0.986771i	$0.448167\pi$
$542$	17.3239	+	19.9929i	0.744126	+	0.858767i
$543$	−19.0520	+	5.59417i	−0.817599	+	0.240069i
$544$	−0.997215	+	6.93578i	−0.0427552	+	0.297369i
$545$	−13.1683	+	15.1970i	−0.564068	+	0.650969i
$546$	−13.0083	+	28.4843i	−0.556706	+	1.21902i
$547$	−17.4482	−	5.12325i	−0.746031	−	0.219054i	−0.113445	−	0.993544i	$-0.536188\pi$
$547$	−17.4482	−	5.12325i	−0.746031	−	0.219054i	−0.632586	+	0.774490i	$0.718007\pi$
$548$	0.189908	+	0.415840i	0.00811245	+	0.0177638i
$549$	1.89566	+	13.1846i	0.0809046	+	0.562704i
$550$	−3.15964	−	2.03058i	−0.134727	−	0.0865840i
$551$	11.9317			0.508306
$552$	−1.30885	+	4.61377i	−0.0557084	+	0.196375i
$553$	−17.9114			−0.761669
$554$	2.32243	+	1.49253i	0.0986705	+	0.0634117i
$555$	−1.06973	−	7.44012i	−0.0454074	−	0.315815i
$556$	−1.48127	−	3.24354i	−0.0628200	−	0.137557i
$557$	−22.4784	−	6.60026i	−0.952441	−	0.279662i	−0.231638	−	0.972802i	$-0.574409\pi$
$557$	−22.4784	−	6.60026i	−0.952441	−	0.279662i	−0.720803	+	0.693140i	$0.756227\pi$
$558$	1.64823	−	3.60913i	0.0697753	−	0.152787i
$559$	−40.3843	+	46.6060i	−1.70807	+	1.97122i
$560$	−0.640439	+	4.45435i	−0.0270635	+	0.188231i
$561$	25.2517	−	7.41457i	1.06613	−	0.313043i
$562$	−18.5602	−	21.4196i	−0.782914	−	0.903531i
$563$	34.7450	−	22.3293i	1.46433	−	0.941067i	0.465911	−	0.884832i	$-0.345727\pi$
$563$	34.7450	−	22.3293i	1.46433	−	0.941067i	0.998418	−	0.0562351i	$-0.0179096\pi$
$564$	−3.42790	+	2.20298i	−0.144341	+	0.0927621i
$565$	−5.06626	−	5.84678i	−0.213139	−	0.245976i
$566$	−19.8896	+	5.84013i	−0.836024	+	0.245479i
$567$	0.640439	−	4.45435i	0.0268959	−	0.187065i
$568$	−3.26398	+	3.76683i	−0.136953	+	0.158053i
$569$	18.9572	−	41.5106i	0.794729	−	1.74021i	0.132140	−	0.991231i	$-0.457815\pi$
$569$	18.9572	−	41.5106i	0.794729	−	1.74021i	0.662589	−	0.748983i	$-0.269458\pi$
$570$	2.28751	+	0.671673i	0.0958132	+	0.0281333i
$571$	13.2347	+	28.9800i	0.553856	+	1.21278i	0.954957	+	0.296743i	$0.0959004\pi$
$571$	13.2347	+	28.9800i	0.553856	+	1.21278i	−0.401101	+	0.916034i	$0.631372\pi$
$572$	3.71940	+	25.8690i	0.155516	+	1.08164i
$573$	−5.49709	−	3.53277i	−0.229644	−	0.147583i
$574$	9.91147			0.413697
$575$	3.59547	−	3.17373i	0.149941	−	0.132354i
$576$	1.00000			0.0416667
$577$	16.3426	+	10.5027i	0.680350	+	0.437234i	0.834643	−	0.550791i	$-0.185674\pi$
$577$	16.3426	+	10.5027i	0.680350	+	0.437234i	−0.154294	+	0.988025i	$0.549310\pi$
$578$	4.56824	+	31.7728i	0.190014	+	1.32157i
$579$	1.53753	+	3.36672i	0.0638975	+	0.139916i
$580$	−4.80200	−	1.41000i	−0.199392	−	0.0585469i
$581$	−28.5007	+	62.4078i	−1.18241	+	2.58911i
$582$	−4.26947	+	4.92723i	−0.176975	+	0.204240i
$583$	2.09575	−	14.5763i	0.0867972	−	0.603688i
$584$	−5.98317	+	1.75682i	−0.247585	+	0.0726976i
$585$	−4.55681	−	5.25884i	−0.188401	−	0.217426i
$586$	−7.74658	+	4.97842i	−0.320008	+	0.205657i
$587$	−5.06170	+	3.25296i	−0.208919	+	0.134264i	−0.640916	−	0.767611i	$-0.721445\pi$
$587$	−5.06170	+	3.25296i	−0.208919	+	0.134264i	0.431997	+	0.901875i	$0.357809\pi$
$588$	−8.67784	−	10.0148i	−0.357868	−	0.413002i
$589$	−9.07610	+	2.66498i	−0.373974	+	0.109809i
$590$	−1.55117	+	10.7886i	−0.0638608	+	0.444161i
$591$	8.30675	−	9.58650i	0.341694	−	0.394336i
$592$	−3.12252	+	6.83736i	−0.128335	+	0.281014i
$593$	−10.2187	−	3.00048i	−0.419631	−	0.123215i	0.0650985	−	0.997879i	$-0.479264\pi$
$593$	−10.2187	−	3.00048i	−0.419631	−	0.123215i	−0.484730	+	0.874664i	$0.661082\pi$
$594$	−1.56024	−	3.41646i	−0.0640176	−	0.140179i
$595$	4.48763	+	31.2121i	0.183975	+	1.27957i
$596$	3.18680	+	2.04803i	0.130537	+	0.0838907i
$597$	5.14286			0.210483
$598$	−33.0740	−	4.44589i	−1.35250	−	0.181806i
$599$	18.2925			0.747411			0.373705	−	0.927547i	$-0.378087\pi$
$599$	18.2925			0.747411			0.373705	+	0.927547i	$0.378087\pi$
$600$	−0.841254	−	0.540641i	−0.0343440	−	0.0220716i
$601$	1.18991	+	8.27598i	0.0485373	+	0.337584i	0.999592	+	0.0285617i	$0.00909272\pi$
$601$	1.18991	+	8.27598i	0.0485373	+	0.337584i	−0.951055	+	0.309022i	$0.899998\pi$
$602$	−16.5677	−	36.2781i	−0.675248	−	1.47859i
$603$	−0.987970	−	0.290094i	−0.0402333	−	0.0118136i
$604$	−5.19799	+	11.3820i	−0.211503	+	0.463127i
$605$	2.03435	−	2.34777i	0.0827081	−	0.0954503i
$606$	−0.623052	+	4.33342i	−0.0253097	+	0.176033i
$607$	15.9623	−	4.68697i	0.647891	−	0.190238i	0.0587560	−	0.998272i	$-0.481287\pi$
$607$	15.9623	−	4.68697i	0.647891	−	0.190238i	0.589135	+	0.808034i	$0.299468\pi$
$608$	−1.56124	−	1.80177i	−0.0633167	−	0.0730713i
$609$	18.9468	−	12.1764i	0.767762	−	0.493411i
$610$	−11.2056	+	7.20142i	−0.453703	+	0.291577i
$611$	−18.5679	−	21.4285i	−0.751176	−	0.866903i
$612$	6.72327	−	1.97413i	0.271772	−	0.0797995i
$613$	−1.64374	+	11.4325i	−0.0663900	+	0.461752i	0.929324	+	0.369266i	$0.120391\pi$
$613$	−1.64374	+	11.4325i	−0.0663900	+	0.461752i	−0.995714	+	0.0924869i	$0.970518\pi$
$614$	6.14177	−	7.08798i	0.247862	−	0.286048i
$615$	−0.914940	+	2.00344i	−0.0368939	+	0.0807864i
$616$	−16.2173	−	4.76184i	−0.653416	−	0.191860i
$617$	5.31964	+	11.6484i	0.214161	+	0.468947i	0.985973	−	0.166904i	$-0.0533768\pi$
$617$	5.31964	+	11.6484i	0.214161	+	0.468947i	−0.771812	+	0.635850i	$0.780650\pi$
$618$	0.0167552	+	0.116535i	0.000673994	+	0.00468773i
$619$	8.13572	+	5.22851i	0.327002	+	0.210152i	0.693833	−	0.720136i	$-0.255921\pi$
$619$	8.13572	+	5.22851i	0.327002	+	0.210152i	−0.366830	+	0.930288i	$0.619557\pi$
$620$	3.96768			0.159346
$621$	4.74055	−	0.726057i	0.190232	−	0.0291357i
$622$	8.32063			0.333627
$623$	48.8298	+	31.3810i	1.95633	+	1.25725i
$624$	0.990289	+	6.88761i	0.0396433	+	0.275725i
$625$	0.415415	+	0.909632i	0.0166166	+	0.0363853i
$626$	19.6564	+	5.77163i	0.785627	+	0.230681i
$627$	−3.71975	+	8.14511i	−0.148552	+	0.325284i
$628$	−2.89051	+	3.33583i	−0.115344	+	0.133114i
$629$	−7.49569	+	52.1337i	−0.298873	+	2.07871i
$630$	4.31787	−	1.26784i	0.172028	−	0.0505120i
$631$	11.8139	+	13.6339i	0.470303	+	0.542758i	0.940496	−	0.339805i	$-0.110361\pi$
$631$	11.8139	+	13.6339i	0.470303	+	0.542758i	−0.470193	+	0.882564i	$0.655816\pi$
$632$	−3.34833	+	2.15184i	−0.133189	+	0.0855956i
$633$	1.90777	−	1.22605i	0.0758271	−	0.0487311i
$634$	−19.7479	−	22.7903i	−0.784290	−	0.905119i
$635$	−12.7584	+	3.74622i	−0.506303	+	0.148664i
$636$	0.557995	−	3.88094i	0.0221259	−	0.153889i
$637$	60.3842	−	69.6871i	2.39251	−	2.76110i
$638$	7.80860	−	17.0984i	0.309145	−	0.676934i
$639$	4.78233	+	1.40422i	0.189186	+	0.0555501i
$640$	0.415415	+	0.909632i	0.0164207	+	0.0359564i
$641$	6.03028	+	41.9415i	0.238182	+	1.65659i	0.661008	+	0.750379i	$0.270129\pi$
$641$	6.03028	+	41.9415i	0.238182	+	1.65659i	−0.422826	+	0.906211i	$0.638962\pi$
$642$	−8.75268	−	5.62501i	−0.345441	−	0.222001i
$643$	−10.4846			−0.413471			−0.206735	−	0.978397i	$-0.566284\pi$
$643$	−10.4846			−0.413471			−0.206735	+	0.978397i	$0.566284\pi$
$644$	11.5010	−	18.2623i	0.453202	−	0.719634i
$645$	8.86240			0.348957
$646$	−14.0536	−	9.03168i	−0.552930	−	0.355347i
$647$	3.25231	+	22.6203i	0.127862	+	0.889297i	0.948258	+	0.317502i	$0.102844\pi$
$647$	3.25231	+	22.6203i	0.127862	+	0.889297i	−0.820396	+	0.571796i	$0.806247\pi$
$648$	−0.415415	−	0.909632i	−0.0163190	−	0.0357337i
$649$	−39.2791	−	11.5334i	−1.54184	−	0.452725i
$650$	2.89064	−	6.32962i	0.113380	−	0.248268i
$651$	−11.6927	+	13.4940i	−0.458271	+	0.528873i
$652$	−0.800268	+	5.56599i	−0.0313409	+	0.217981i
$653$	8.01077	−	2.35218i	0.313486	−	0.0920477i	−0.121205	−	0.992627i	$-0.538676\pi$
$653$	8.01077	−	2.35218i	0.313486	−	0.0920477i	0.434691	+	0.900580i	$0.356858\pi$
$654$	−13.1683	−	15.1970i	−0.514921	−	0.594251i
$655$	6.40784	−	4.11807i	0.250375	−	0.160906i
$656$	1.85284	−	1.19075i	0.0723411	−	0.0464908i
$657$	4.08355	+	4.71267i	0.159315	+	0.183859i
$658$	17.5942	−	5.16614i	0.685895	−	0.201397i
$659$	−1.53180	+	10.6539i	−0.0596705	+	0.415018i	0.937990	+	0.346661i	$0.112685\pi$
$659$	−1.53180	+	10.6539i	−0.0596705	+	0.415018i	−0.997661	+	0.0683565i	$0.978224\pi$
$660$	2.45957	−	2.83850i	0.0957386	−	0.110488i
$661$	−6.03448	+	13.2137i	−0.234714	+	0.513953i	−0.989936	−	0.141517i	$-0.954802\pi$
$661$	−6.03448	+	13.2137i	−0.234714	+	0.513953i	0.755222	+	0.655470i	$0.227529\pi$
$662$	20.1419	+	5.91420i	0.782838	+	0.229862i
$663$	20.2550	+	44.3523i	0.786640	+	1.72250i
$664$	2.16968	+	15.0904i	0.0841999	+	0.585623i
$665$	−9.02559	−	5.80039i	−0.349997	−	0.224930i
$666$	7.51662			0.291263
$667$	18.2829	+	15.5507i	0.707916	+	0.602126i
$668$	16.2508			0.628763
$669$	10.3447	+	6.64813i	0.399949	+	0.257032i
$670$	−0.146539	−	1.01920i	−0.00566128	−	0.0393751i
$671$	−20.7827	−	45.5077i	−0.802307	−	1.75681i
$672$	−4.31787	−	1.26784i	−0.166565	−	0.0489080i
$673$	8.40678	−	18.4083i	0.324057	−	0.709587i	−0.675558	−	0.737307i	$-0.736097\pi$
$673$	8.40678	−	18.4083i	0.324057	−	0.709587i	0.999616	+	0.0277198i	$0.00882461\pi$
$674$	−22.1837	+	25.6014i	−0.854486	+	0.986129i
$675$	−0.142315	+	0.989821i	−0.00547770	+	0.0380982i
$676$	−33.9851	+	9.97894i	−1.30712	+	0.383805i
$677$	1.14274	+	1.31879i	0.0439191	+	0.0506853i	0.777284	−	0.629150i	$-0.216597\pi$
$677$	1.14274	+	1.31879i	0.0439191	+	0.0506853i	−0.733365	+	0.679835i	$0.762051\pi$
$678$	6.50827	−	4.18261i	0.249949	−	0.160632i
$679$	24.6819	−	15.8621i	0.947206	−	0.608732i
$680$	4.58868	+	5.29562i	0.175968	+	0.203078i
$681$	3.92037	−	1.15113i	0.150229	−	0.0441112i
$682$	−2.12079	+	14.7504i	−0.0812091	+	0.564822i
$683$	31.6833	−	36.5644i	1.21233	−	1.39910i	0.320178	−	0.947357i	$-0.396257\pi$
$683$	31.6833	−	36.5644i	1.21233	−	1.39910i	0.892148	−	0.451742i	$-0.149197\pi$
$684$	−0.990383	+	2.16864i	−0.0378682	+	0.0829199i
$685$	0.438634	+	0.128794i	0.0167593	+	0.00492098i
$686$	11.6866	+	25.5901i	0.446197	+	0.977035i
$687$	1.72774	+	12.0167i	0.0659175	+	0.458466i
$688$	−7.45553	−	4.79138i	−0.284239	−	0.182670i
$689$	27.2830			1.03940
$690$	2.62974	+	4.01054i	0.100113	+	0.152679i
$691$	4.72484			0.179742			0.0898708	−	0.995953i	$-0.471355\pi$
$691$	4.72484			0.179742			0.0898708	+	0.995953i	$0.471355\pi$
$692$	1.43265	+	0.920706i	0.0544610	+	0.0350000i
$693$	2.40540	+	16.7300i	0.0913738	+	0.635519i
$694$	3.61318	+	7.91176i	0.137154	+	0.300326i
$695$	−3.42133	−	1.00459i	−0.129778	−	0.0381064i
$696$	2.07904	−	4.55246i	0.0788058	−	0.172561i
$697$	10.1064	−	11.6634i	0.382808	−	0.441784i
$698$	−1.30588	+	9.08259i	−0.0494282	+	0.343781i
$699$	17.8882	−	5.25244i	0.676593	−	0.198666i
$700$	2.94698	+	3.40099i	0.111385	+	0.128545i
$701$	−34.1016	+	21.9157i	−1.28800	+	0.827746i	−0.991852	−	0.127396i	$-0.959338\pi$
$701$	−34.1016	+	21.9157i	−1.28800	+	0.827746i	−0.296146	+	0.955143i	$0.595702\pi$
$702$	5.85381	−	3.76202i	0.220938	−	0.141988i
$703$	−11.7353	−	13.5432i	−0.442604	−	0.510792i
$704$	−3.60373	+	1.05815i	−0.135821	+	0.0398805i
$705$	−0.579898	+	4.03328i	−0.0218402	+	0.151902i
$706$	2.52046	−	2.90877i	0.0948589	−	0.109473i
$707$	8.18434	−	17.9212i	0.307804	−	0.673996i
$708$	−10.4581	−	3.07077i	−0.393039	−	0.115407i
$709$	−14.0992	−	30.8729i	−0.529505	−	1.15945i	−0.965714	−	0.259609i	$-0.916406\pi$
$709$	−14.0992	−	30.8729i	−0.529505	−	1.15945i	0.436208	−	0.899846i	$-0.356321\pi$
$710$	0.709330	+	4.93350i	0.0266207	+	0.185151i
$711$	3.34833	+	2.15184i	0.125572	+	0.0807003i
$712$	12.8982			0.483382
$713$	−17.3806	−	7.74546i	−0.650908	−	0.290070i
$714$	−31.5331			−1.18010
$715$	21.9861	+	14.1296i	0.822235	+	0.528418i
$716$	−1.86022	−	12.9381i	−0.0695198	−	0.483521i
$717$	0.950518	+	2.08135i	0.0354978	+	0.0777293i
$718$	12.0921	+	3.55056i	0.451273	+	0.132506i
$719$	−3.66978	+	8.03570i	−0.136860	+	0.299681i	−0.965636	−	0.259900i	$-0.916310\pi$
$719$	−3.66978	+	8.03570i	−0.136860	+	0.299681i	0.828776	+	0.559581i	$0.189038\pi$
$720$	0.654861	−	0.755750i	0.0244052	−	0.0281651i
$721$	0.0754011	−	0.524426i	0.00280809	−	0.0195307i
$722$	−12.7768	+	3.75160i	−0.475502	+	0.139620i
$723$	8.58912	+	9.91237i	0.319433	+	0.368645i
$724$	16.7042	−	10.7351i	0.620806	−	0.398968i
$725$	−4.21025	+	2.70576i	−0.156365	+	0.100489i
$726$	2.03435	+	2.34777i	0.0755019	+	0.0871338i
$727$	−25.6959	+	7.54500i	−0.953009	+	0.279829i	−0.721039	−	0.692894i	$-0.756335\pi$
$727$	−25.6959	+	7.54500i	−0.953009	+	0.279829i	−0.231970	+	0.972723i	$0.574517\pi$
$728$	4.45646	−	30.9953i	0.165167	−	1.14876i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	−2.59043	+	5.67225i	−0.0958760	+	0.209939i
$731$	−59.5843	−	17.4955i	−2.20381	−	0.647096i
$732$	−5.53339	−	12.1164i	−0.204520	−	0.447837i
$733$	−5.35920	−	37.2740i	−0.197946	−	1.37675i	−0.810231	−	0.586110i	$-0.800658\pi$
$733$	−5.35920	−	37.2740i	−0.197946	−	1.37675i	0.612285	−	0.790637i	$-0.290251\pi$
$734$	7.60554	+	4.88778i	0.280726	+	0.180411i
$735$	−13.2514			−0.488786
$736$	−0.0440162	−	4.79563i	−0.00162246	−	0.176769i
$737$	3.86734			0.142455
$738$	−1.85284	−	1.19075i	−0.0682039	−	0.0438320i
$739$	−7.18194	−	49.9515i	−0.264192	−	1.83750i	−0.500402	−	0.865793i	$-0.666814\pi$
$739$	−7.18194	−	49.9515i	−0.264192	−	1.83750i	0.236210	−	0.971702i	$-0.424095\pi$
$740$	3.12252	+	6.83736i	0.114786	+	0.251346i
$741$	−15.9175	−	4.67380i	−0.584744	−	0.171696i
$742$	−7.32976	+	16.0499i	−0.269084	+	0.589212i
$743$	−16.5935	+	19.1499i	−0.608757	+	0.702543i	−0.973531	−	0.228553i	$-0.926601\pi$
$743$	−16.5935	+	19.1499i	−0.608757	+	0.702543i	0.364775	+	0.931096i	$0.381146\pi$
$744$	−0.564660	+	3.92729i	−0.0207014	+	0.143982i
$745$	3.63471	−	1.06725i	0.133166	−	0.0391009i
$746$	−15.4601	−	17.8419i	−0.566034	−	0.653238i
$747$	12.8254	−	8.24241i	0.469258	−	0.301574i
$748$	−22.1399	+	14.2285i	−0.809515	+	0.520244i
$749$	30.6613	+	35.3851i	1.12034	+	1.29294i
$750$	−0.959493	+	0.281733i	−0.0350357	+	0.0102874i
$751$	−3.23661	+	22.5111i	−0.118106	+	0.821442i	0.841533	+	0.540206i	$0.181654\pi$
$751$	−3.23661	+	22.5111i	−0.118106	+	0.821442i	−0.959638	+	0.281237i	$0.909255\pi$
$752$	2.66840	−	3.07949i	0.0973064	−	0.112298i
$753$	−1.78162	+	3.90121i	−0.0649259	+	0.142168i
$754$	33.4144	+	9.81137i	1.21688	+	0.357309i
$755$	5.19799	+	11.3820i	0.189174	+	0.414233i
$756$	0.640439	+	4.45435i	0.0232926	+	0.162003i
$757$	23.9947	+	15.4204i	0.872102	+	0.560466i	0.898395	−	0.439189i	$-0.144734\pi$
$757$	23.9947	+	15.4204i	0.872102	+	0.560466i	−0.0262932	+	0.999654i	$0.508370\pi$
$758$	29.4186			1.06853
$759$	−16.3154	+	7.63273i	−0.592211	+	0.277051i
$760$	−2.38408			−0.0864797
$761$	−34.6233	−	22.2511i	−1.25509	−	0.806600i	−0.267490	−	0.963561i	$-0.586194\pi$
$761$	−34.6233	−	22.2511i	−1.25509	−	0.806600i	−0.987605	+	0.156961i	$0.949830\pi$
$762$	−1.89237	−	13.1617i	−0.0685533	−	0.476799i
$763$	37.5916	+	82.3141i	1.36091	+	2.97997i
$764$	6.26972	+	1.84095i	0.226830	+	0.0666034i
$765$	2.91086	−	6.37389i	0.105242	−	0.230448i
$766$	8.79660	−	10.1518i	0.317834	−	0.366800i
$767$	10.7937	−	75.0721i	0.389739	−	2.71070i
$768$	−0.959493	+	0.281733i	−0.0346227	+	0.0101661i
$769$	3.46075	+	3.99392i	0.124798	+	0.144024i	0.814710	−	0.579869i	$-0.196896\pi$
$769$	3.46075	+	3.99392i	0.124798	+	0.144024i	−0.689912	+	0.723893i	$0.742351\pi$
$770$	−14.2189	+	9.13791i	−0.512412	+	0.329307i
$771$	16.4621	−	10.5796i	0.592869	−	0.381014i
$772$	−2.42376	−	2.79717i	−0.0872331	−	0.100672i
$773$	−12.9377	+	3.79884i	−0.465336	+	0.136635i	−0.505992	−	0.862538i	$-0.668873\pi$
$773$	−12.9377	+	3.79884i	−0.465336	+	0.136635i	0.0406559	+	0.999173i	$0.487055\pi$
$774$	−1.26125	+	8.77220i	−0.0453348	+	0.315310i
$775$	2.59828	−	2.99857i	0.0933329	−	0.107712i
$776$	2.70836	−	5.93049i	0.0972246	−	0.212892i
$777$	−32.4558	−	9.52988i	−1.16435	−	0.341883i
$778$	7.26516	+	15.9085i	0.260469	+	0.570347i
$779$	0.747276	+	5.19742i	0.0267740	+	0.186217i
$780$	5.85381	+	3.76202i	0.209600	+	0.134702i
$781$	−18.7201			−0.669858
$782$	−9.76313	−	32.1554i	−0.349129	−	1.14988i
$783$	−5.00473			−0.178854
$784$	11.1478	+	7.16426i	0.398136	+	0.255866i
$785$	0.628168	+	4.36900i	0.0224203	+	0.155936i
$786$	3.16422	+	6.92868i	0.112864	+	0.247138i
$787$	−15.4100	−	4.52478i	−0.549306	−	0.161291i	−0.00470960	−	0.999989i	$-0.501499\pi$
$787$	−15.4100	−	4.52478i	−0.549306	−	0.161291i	−0.544597	+	0.838698i	$0.683317\pi$
$788$	−5.26944	+	11.5385i	−0.187716	+	0.411041i
$789$	11.8728	−	13.7019i	0.422683	−	0.487802i
$790$	−0.566437	+	3.93965i	−0.0201529	+	0.140167i
$791$	−33.4047	+	9.80852i	−1.18774	+	0.348751i
$792$	2.45957	+	2.83850i	0.0873970	+	0.100862i
$793$	77.9737	−	50.1107i	2.76893	−	1.77948i
$794$	−16.4436	+	10.5677i	−0.583561	+	0.375032i
$795$	−2.56761	−	2.96318i	−0.0910637	−	0.105093i
$796$	−4.93453	+	1.44891i	−0.174900	+	0.0513553i
$797$	4.70548	−	32.7274i	0.166677	−	1.15926i	−0.719017	−	0.694993i	$-0.755408\pi$
$797$	4.70548	−	32.7274i	0.166677	−	1.15926i	0.885694	−	0.464270i	$-0.153683\pi$
$798$	7.02583	−	8.10824i	0.248712	−	0.287029i
$799$	11.8610	−	25.9720i	0.419613	−	0.918824i
$800$	0.959493	+	0.281733i	0.0339232	+	0.00996075i
$801$	−5.35812	−	11.7327i	−0.189320	−	0.414553i
$802$	−2.93516	−	20.4145i	−0.103644	−	0.720861i
$803$	−19.7027	−	12.6622i	−0.695294	−	0.446838i
$804$	1.02968			0.0363140
$805$	−6.27015	−	20.6511i	−0.220994	−	0.727856i
$806$	−27.6089			−0.972481
$807$	−6.73691	−	4.32955i	−0.237151	−	0.152407i
$808$	−0.623052	−	4.33342i	−0.0219189	−	0.152449i
$809$	−7.46690	−	16.3502i	−0.262522	−	0.574843i	0.731768	−	0.681554i	$-0.238695\pi$
$809$	−7.46690	−	16.3502i	−0.262522	−	0.574843i	−0.994290	+	0.106710i	$0.965968\pi$
$810$	−0.959493	−	0.281733i	−0.0337131	−	0.00989907i
$811$	−4.34586	+	9.51610i	−0.152604	+	0.334155i	−0.970458	−	0.241270i	$-0.922436\pi$
$811$	−4.34586	+	9.51610i	−0.152604	+	0.334155i	0.817854	+	0.575425i	$0.195163\pi$
$812$	−14.7488	+	17.0210i	−0.517582	+	0.597322i
$813$	−3.76485	+	26.1851i	−0.132039	+	0.918351i
$814$	−27.0879	+	7.95372i	−0.949429	+	0.278778i
$815$	3.68243	+	4.24975i	0.128990	+	0.148862i
$816$	−5.89475	+	3.78833i	−0.206358	+	0.132618i
$817$	17.7746	−	11.4230i	0.621854	−	0.399641i
$818$	4.58672	+	5.29336i	0.160371	+	0.185078i
$819$	−30.0456	+	8.82220i	−1.04988	+	0.308272i
$820$	0.313444	−	2.18005i	0.0109459	−	0.0761308i
$821$	−12.8797	+	14.8639i	−0.449504	+	0.518755i	−0.934597	−	0.355707i	$-0.884240\pi$
$821$	−12.8797	+	14.8639i	−0.449504	+	0.518755i	0.485094	+	0.874462i	$0.338785\pi$
$822$	−0.189908	+	0.415840i	−0.00662379	+	0.0145041i
$823$	−35.7243	−	10.4896i	−1.24527	−	0.365644i	−0.408277	−	0.912858i	$-0.633870\pi$
$823$	−35.7243	−	10.4896i	−1.24527	−	0.365644i	−0.836993	+	0.547214i	$0.815688\pi$
$824$	−0.0489083	−	0.107094i	−0.00170380	−	0.00373080i
$825$	−0.534516	−	3.71764i	−0.0186094	−	0.129432i
$826$	41.2634	+	26.5184i	1.43574	+	0.922692i
$827$	−11.3148			−0.393455			−0.196728	−	0.980458i	$-0.563031\pi$
$827$	−11.3148			−0.393455			−0.196728	+	0.980458i	$0.563031\pi$
$828$	−4.34397	+	2.03222i	−0.150964	+	0.0706244i
$829$	46.9665			1.63121			0.815607	−	0.578607i	$-0.196403\pi$
$829$	46.9665			1.63121			0.815607	+	0.578607i	$0.196403\pi$
$830$	12.8254	+	8.24241i	0.445177	+	0.286098i
$831$	0.392885	+	2.73258i	0.0136290	+	0.0947920i
$832$	−2.89064	−	6.32962i	−0.100215	−	0.219440i
$833$	89.0929	+	26.1600i	3.08689	+	0.906391i
$834$	1.48127	−	3.24354i	0.0512923	−	0.112314i
$835$	10.6420	−	12.2816i	0.368283	−	0.425021i
$836$	1.27433	−	8.86315i	0.0440736	−	0.306538i
$837$	3.80696	−	1.11782i	0.131588	−	0.0386377i
$838$	21.8134	+	25.1740i	0.753531	+	0.869621i
$839$	−20.3748	+	13.0941i	−0.703415	+	0.452057i	−0.842832	−	0.538176i	$-0.819113\pi$
$839$	−20.3748	+	13.0941i	−0.703415	+	0.452057i	0.139417	+	0.990234i	$0.455477\pi$
$840$	−3.78577	+	2.43297i	−0.130622	+	0.0839454i
$841$	2.58846	+	2.98724i	0.0892572	+	0.103008i
$842$	21.3568	−	6.27094i	0.736005	−	0.216111i
$843$	4.03351	−	28.0537i	0.138922	−	0.966221i
$844$	−1.48508	+	1.71387i	−0.0511184	+	0.0589938i
$845$	−14.7140	+	32.2191i	−0.506175	+	1.10837i
$846$	−3.90970	−	1.14799i	−0.134418	−	0.0394687i
$847$	−5.80747	−	12.7166i	−0.199547	−	0.436947i
$848$	0.557995	+	3.88094i	0.0191616	+	0.133272i
$849$	−17.4386	−	11.2071i	−0.598492	−	0.384627i
$850$	7.00711			0.240342
$851$	−0.330853	−	36.0469i	−0.0113415	−	1.23567i
$852$	−4.98423			−0.170757
$853$	−2.83745	−	1.82352i	−0.0971525	−	0.0624361i	0.491162	−	0.871068i	$-0.336572\pi$
$853$	−2.83745	−	1.82352i	−0.0971525	−	0.0624361i	−0.588315	+	0.808632i	$0.700208\pi$
$854$	8.53075	+	59.3327i	0.291916	+	2.03032i
$855$	0.990383	+	2.16864i	0.0338704	+	0.0741658i
$856$	9.98288	+	2.93124i	0.341208	+	0.100188i
$857$	3.93252	−	8.61102i	0.134332	−	0.294147i	−0.830497	−	0.557023i	$-0.811944\pi$
$857$	3.93252	−	8.61102i	0.134332	−	0.294147i	0.964830	+	0.262876i	$0.0846709\pi$
$858$	−17.1148	+	19.7515i	−0.584289	+	0.674305i
$859$	6.60896	−	45.9663i	0.225495	−	1.56835i	−0.491253	−	0.871017i	$-0.663461\pi$
$859$	6.60896	−	45.9663i	0.225495	−	1.56835i	0.716747	−	0.697333i	$-0.245630\pi$
$860$	−8.50341	+	2.49683i	−0.289964	+	0.0851411i
$861$	6.49063	+	7.49059i	0.221200	+	0.255279i
$862$	−0.828306	+	0.532320i	−0.0282122	+	0.0181309i
$863$	−29.9048	+	19.2186i	−1.01797	+	0.654209i	−0.939444	−	0.342703i	$-0.888658\pi$
$863$	−29.9048	+	19.2186i	−1.01797	+	0.654209i	−0.0785259	+	0.996912i	$0.525021\pi$
$864$	0.654861	+	0.755750i	0.0222788	+	0.0257111i
$865$	1.63401	−	0.479788i	0.0555579	−	0.0163133i
$866$	−0.792056	+	5.50887i	−0.0269151	+	0.187199i
$867$	−21.0207	+	24.2592i	−0.713901	+	0.823886i
$868$	7.41731	−	16.2416i	0.251760	−	0.551277i
$869$	−14.3434	−	4.21161i	−0.486568	−	0.142869i
$870$	−2.07904	−	4.55246i	−0.0704860	−	0.154343i
$871$	1.01968	+	7.09203i	0.0345506	+	0.240304i
$872$	16.9164	+	10.8715i	0.572861	+	0.368156i
$873$	−6.51966			−0.220657
$874$	10.4436	+	4.65405i	0.353259	+	0.157426i
$875$	4.50016			0.152133
$876$	−5.24585	−	3.37131i	−0.177241	−	0.113906i
$877$	5.22016	+	36.3070i	0.176272	+	1.22600i	0.865296	+	0.501262i	$0.167131\pi$
$877$	5.22016	+	36.3070i	0.176272	+	1.22600i	−0.689023	+	0.724739i	$0.741960\pi$
$878$	−11.5479	−	25.2864i	−0.389723	−	0.853374i
$879$	−8.83537	−	2.59430i	−0.298010	−	0.0875035i
$880$	−1.56024	+	3.41646i	−0.0525958	+	0.115169i
$881$	−0.227274	+	0.262288i	−0.00765705	+	0.00883671i	−0.759565	−	0.650431i	$-0.774588\pi$
$881$	−0.227274	+	0.262288i	−0.00765705	+	0.00883671i	0.751908	+	0.659268i	$0.229134\pi$
$882$	1.88587	−	13.1165i	0.0635007	−	0.441657i
$883$	−51.8074	+	15.2120i	−1.74346	+	0.511926i	−0.989442	−	0.144930i	$-0.953704\pi$
$883$	−51.8074	+	15.2120i	−1.74346	+	0.511926i	−0.754016	+	0.656856i	$0.771886\pi$
$884$	−31.9300	−	36.8492i	−1.07392	−	1.23937i
$885$	−9.16931	+	5.89276i	−0.308223	+	0.198083i
$886$	−14.9002	+	9.57579i	−0.500583	+	0.321705i
$887$	−10.6475	−	12.2879i	−0.357510	−	0.412588i	0.548294	−	0.836286i	$-0.315277\pi$
$887$	−10.6475	−	12.2879i	−0.357510	−	0.412588i	−0.905804	+	0.423698i	$0.860732\pi$
$888$	−7.21215	+	2.11768i	−0.242024	+	0.0710646i
$889$	−8.51596	+	59.2298i	−0.285616	+	1.98650i
$890$	8.44655	−	9.74784i	0.283129	−	0.326748i
$891$	1.56024	−	3.41646i	0.0522701	−	0.114456i
$892$	−11.7987	−	3.46440i	−0.395048	−	0.115997i
$893$	4.03556	+	8.83665i	0.135045	+	0.295707i
$894$	0.539111	+	3.74960i	0.0180306	+	0.125405i
$895$	−10.9962	−	7.06681i	−0.367562	−	0.236218i
$896$	4.50016			0.150340
$897$	−18.2989	−	27.9071i	−0.610983	−	0.931792i
$898$	−24.4730			−0.816676
$899$	16.7049	+	10.7356i	0.557140	+	0.358052i
$900$	−0.142315	−	0.989821i	−0.00474383	−	0.0329940i
$901$	11.4130	+	24.9910i	0.380223	+	0.832572i
$902$	7.93711	+	2.33054i	0.264277	+	0.0775987i
$903$	16.5677	−	36.2781i	0.551338	−	1.20726i
$904$	−5.06626	+	5.84678i	−0.168501	+	0.194461i
$905$	2.82585	−	19.6542i	0.0939343	−	0.653327i
$906$	−12.0059	+	3.52525i	−0.398869	+	0.117119i
$907$	−16.8892	−	19.4912i	−0.560797	−	0.647194i	0.402567	−	0.915390i	$-0.368118\pi$
$907$	−16.8892	−	19.4912i	−0.560797	−	0.647194i	−0.963364	+	0.268196i	$0.913572\pi$
$908$	−3.43726	+	2.20899i	−0.114070	+	0.0733080i
$909$	−3.68299	+	2.36691i	−0.122157	+	0.0785056i
$910$	−20.5064	−	23.6656i	−0.679779	−	0.784507i
$911$	32.5387	−	9.55421i	1.07805	−	0.316545i	0.305954	−	0.952046i	$-0.401025\pi$
$911$	32.5387	−	9.55421i	1.07805	−	0.316545i	0.772100	+	0.635501i	$0.219206\pi$
$912$	0.339290	−	2.35981i	0.0112350	−	0.0781412i
$913$	−37.4977	+	43.2746i	−1.24099	+	1.43218i
$914$	6.68483	−	14.6377i	0.221115	−	0.484174i
$915$	−12.7806	−	3.75272i	−0.422513	−	0.124061i
$916$	−5.04326	−	11.0432i	−0.166634	−	0.364877i
$917$	−4.87824	−	33.9289i	−0.161094	−	1.12043i
$918$	5.89475	+	3.78833i	0.194556	+	0.125033i
$919$	53.3110			1.75857			0.879284	−	0.476297i	$-0.158021\pi$
$919$	53.3110			1.75857			0.879284	+	0.476297i	$0.158021\pi$
$920$	−3.65312	−	3.10720i	−0.120440	−	0.102441i
$921$	9.37874			0.309040
$922$	−6.21396	−	3.99347i	−0.204646	−	0.131518i
$923$	−4.93583	−	34.3294i	−0.162465	−	1.12997i
$924$	−7.02134	−	15.3746i	−0.230985	−	0.505787i
$925$	7.21215	+	2.11768i	0.237134	+	0.0696288i
$926$	0.0680509	−	0.149011i	0.00223629	−	0.00489679i
$927$	−0.0770990	+	0.0889770i	−0.00253226	+	0.00292239i
$928$	−0.712247	+	4.95379i	−0.0233807	+	0.162616i
$929$	37.4324	−	10.9911i	1.22812	−	0.360607i	0.397578	−	0.917569i	$-0.369851\pi$
$929$	37.4324	−	10.9911i	1.22812	−	0.360607i	0.830539	+	0.556961i	$0.188033\pi$
$930$	2.59828	+	2.99857i	0.0852009	+	0.0983271i
$931$	−26.5773	+	17.0802i	−0.871035	+	0.559780i
$932$	−15.6838	+	10.0794i	−0.513740	+	0.330160i
$933$	5.44885	+	6.28831i	0.178387	+	0.205870i
$934$	−15.6210	+	4.58675i	−0.511136	+	0.150083i
$935$	−3.74541	+	26.0499i	−0.122488	+	0.851922i
$936$	−4.55681	+	5.25884i	−0.148944	+	0.171891i
$937$	−4.51553	+	9.88763i	−0.147516	+	0.323015i	−0.968937	−	0.247307i	$-0.920454\pi$
$937$	−4.51553	+	9.88763i	−0.147516	+	0.323015i	0.821421	+	0.570322i	$0.193182\pi$
$938$	−4.44602	−	1.30547i	−0.145168	−	0.0426251i
$939$	8.51028	+	18.6349i	0.277723	+	0.608128i
$940$	−0.579898	−	4.03328i	−0.0189142	−	0.131551i
$941$	−38.3338	−	24.6356i	−1.24964	−	0.803098i	−0.262813	−	0.964847i	$-0.584650\pi$
$941$	−38.3338	−	24.6356i	−1.24964	−	0.803098i	−0.986832	+	0.161749i	$0.948287\pi$
$942$	−4.41393			−0.143814
$943$	−5.62882	+	8.93793i	−0.183300	+	0.291059i
$944$	10.8996			0.354751
$945$	3.78577	+	2.43297i	0.123151	+	0.0791445i
$946$	−4.73709	−	32.9472i	−0.154016	−	1.07121i
$947$	3.59941	+	7.88160i	0.116965	+	0.256118i	0.959055	−	0.283219i	$-0.0914023\pi$
$947$	3.59941	+	7.88160i	0.116965	+	0.256118i	−0.842090	+	0.539337i	$0.818675\pi$
$948$	−3.81894	−	1.12134i	−0.124033	−	0.0364195i
$949$	18.0253	−	39.4700i	0.585127	−	1.28125i
$950$	−1.56124	+	1.80177i	−0.0506533	+	0.0584571i
$951$	4.29163	−	29.8490i	0.139166	−	0.967919i
$952$	30.2558	−	8.88390i	0.980595	−	0.287929i
$953$	−14.5255	−	16.7634i	−0.470528	−	0.543019i	0.470030	−	0.882650i	$-0.344243\pi$
$953$	−14.5255	−	16.7634i	−0.470528	−	0.543019i	−0.940558	+	0.339632i	$0.889698\pi$
$954$	3.29843	−	2.11977i	0.106790	−	0.0686301i
$955$	5.49709	−	3.53277i	0.177882	−	0.114318i
$956$	−1.49840	−	1.72924i	−0.0484617	−	0.0559277i
$957$	18.0357	−	5.29575i	0.583011	−	0.171187i
$958$	1.76437	−	12.2715i	0.0570043	−	0.396474i
$959$	1.34721	−	1.55477i	0.0435038	−	0.0502061i
$960$	−0.415415	+	0.909632i	−0.0134075	+	0.0293582i
$961$	14.6395	+	4.29854i	0.472241	+	0.138663i
$962$	−21.7279	−	47.5774i	−0.700534	−	1.53396i
$963$	−1.48069	−	10.2984i	−0.0477146	−	0.331862i
$964$	−11.0338	−	7.09102i	−0.355376	−	0.228386i
$965$	−3.70119			−0.119145
$966$	21.3332	−	3.26737i	0.686386	−	0.105126i
$967$	−20.1255			−0.647192			−0.323596	−	0.946195i	$-0.604892\pi$
$967$	−20.1255			−0.647192			−0.323596	+	0.946195i	$0.604892\pi$
$968$	−2.61339	−	1.67952i	−0.0839975	−	0.0539819i
$969$	−2.37744	−	16.5355i	−0.0763744	−	0.531196i
$970$	−2.70836	−	5.93049i	−0.0869603	−	0.190416i
$971$	17.5976	+	5.16711i	0.564733	+	0.165820i	0.551623	−	0.834094i	$-0.314009\pi$
$971$	17.5976	+	5.16711i	0.564733	+	0.165820i	0.0131097	+	0.999914i	$0.495827\pi$
$972$	0.415415	−	0.909632i	0.0133244	−	0.0291765i
$973$	−10.5082	+	12.1272i	−0.336879	+	0.388779i
$974$	5.43382	−	37.7931i	0.174111	−	1.21097i
$975$	6.67657	−	1.96042i	0.213822	−	0.0627837i
$976$	8.72285	+	10.0667i	0.279212	+	0.322227i
$977$	−2.38644	+	1.53367i	−0.0763490	+	0.0490665i	−0.578258	−	0.815854i	$-0.696267\pi$
$977$	−2.38644	+	1.53367i	−0.0763490	+	0.0490665i	0.501909	+	0.864920i	$0.332631\pi$
$978$	−4.73056	+	3.04014i	−0.151266	+	0.0972131i
$979$	31.7241	+	36.6116i	1.01391	+	1.17011i
$980$	12.7146	−	3.73336i	0.406154	−	0.119258i
$981$	2.86175	−	19.9039i	0.0913685	−	0.635482i
$982$	−16.6266	+	19.1881i	−0.530575	+	0.612317i
$983$	15.4219	−	33.7692i	0.491882	−	1.07707i	−0.487142	−	0.873323i	$-0.661960\pi$
$983$	15.4219	−	33.7692i	0.491882	−	1.07707i	0.979023	−	0.203748i	$-0.0653122\pi$
$984$	2.11326	+	0.620508i	0.0673681	+	0.0197811i
$985$	5.26944	+	11.5385i	0.167898	+	0.367646i
$986$	4.99079	+	34.7117i	0.158939	+	1.10545i
$987$	15.4261	+	9.91375i	0.491018	+	0.315558i
$988$	16.5895			0.527782
$989$	42.1237	+	5.66238i	1.33946	+	0.180053i
$990$	3.75587			0.119369
$991$	−2.76575	−	1.77744i	−0.0878569	−	0.0564622i	0.495975	−	0.868337i	$-0.334811\pi$
$991$	−2.76575	−	1.77744i	−0.0878569	−	0.0564622i	−0.583832	+	0.811875i	$0.698447\pi$
$992$	−0.564660	−	3.92729i	−0.0179280	−	0.124692i
$993$	8.72050	+	19.0952i	0.276737	+	0.605969i
$994$	21.5212	+	6.31921i	0.682613	+	0.200433i
$995$	−2.13642	+	4.67811i	−0.0677291	+	0.148306i
$996$	−9.98376	+	11.5219i	−0.316348	+	0.365085i
$997$	−2.63942	+	18.3576i	−0.0835913	+	0.581391i	0.904377	+	0.426734i	$0.140336\pi$
$997$	−2.63942	+	18.3576i	−0.0835913	+	0.581391i	−0.987968	+	0.154656i	$0.950573\pi$
$998$	−34.8777	+	10.2410i	−1.10404	+	0.324174i
$999$	4.92234	+	5.68069i	0.155736	+	0.179729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.h.301.3	✓	30
23.12	even	11	inner	690.2.m.h.541.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.h.301.3	✓	30	1.1	even	1	trivial
690.2.m.h.541.3	yes	30	23.12	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841254 - 0.540641i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(2.94698 - 3.40099i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.841254 - 0.540641i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(2.94698 - 3.40099i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(-0.654861 - 0.755750i) q^{10} +(3.15964 - 2.03058i) q^{11} +(0.841254 - 0.540641i) q^{12} +(4.55681 + 5.25884i) q^{13} +(-4.31787 + 1.26784i) q^{14} +(0.142315 - 0.989821i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-2.91086 + 6.37389i) q^{17} +(0.959493 + 0.281733i) q^{18} +(-0.990383 - 2.16864i) q^{19} +(0.142315 + 0.989821i) q^{20} +(-3.78577 - 2.43297i) q^{21} -3.75587 q^{22} +(1.30885 - 4.61377i) q^{23} -1.00000 q^{24} +(0.841254 + 0.540641i) q^{25} +(-0.990289 - 6.88761i) q^{26} +(0.415415 + 0.909632i) q^{27} +(4.31787 + 1.26784i) q^{28} +(-2.07904 + 4.55246i) q^{29} +(-0.654861 + 0.755750i) q^{30} +(0.564660 - 3.92729i) q^{31} +(0.959493 - 0.281733i) q^{32} +(-2.45957 - 2.83850i) q^{33} +(5.89475 - 3.78833i) q^{34} +(3.78577 - 2.43297i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(7.21215 - 2.11768i) q^{37} +(-0.339290 + 2.35981i) q^{38} +(4.55681 - 5.25884i) q^{39} +(0.415415 - 0.909632i) q^{40} +(-2.11326 - 0.620508i) q^{41} +(1.86943 + 4.09349i) q^{42} +(1.26125 + 8.77220i) q^{43} +(3.15964 + 2.03058i) q^{44} -1.00000 q^{45} +(-3.59547 + 3.17373i) q^{46} -4.07475 q^{47} +(0.841254 + 0.540641i) q^{48} +(-1.88587 - 13.1165i) q^{49} +(-0.415415 - 0.909632i) q^{50} +(6.72327 + 1.97413i) q^{51} +(-2.89064 + 6.32962i) q^{52} +(2.56761 - 2.96318i) q^{53} +(0.142315 - 0.989821i) q^{54} +(3.60373 - 1.05815i) q^{55} +(-2.94698 - 3.40099i) q^{56} +(-2.00562 + 1.28893i) q^{57} +(4.21025 - 2.70576i) q^{58} +(-7.13771 - 8.23736i) q^{59} +(0.959493 - 0.281733i) q^{60} +(1.89566 - 13.1846i) q^{61} +(-2.59828 + 2.99857i) q^{62} +(-1.86943 + 4.09349i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(2.89064 + 6.32962i) q^{65} +(0.534516 + 3.71764i) q^{66} +(0.866222 + 0.556687i) q^{67} -7.00711 q^{68} +(-4.75308 - 0.638921i) q^{69} -4.50016 q^{70} +(-4.19300 - 2.69468i) q^{71} +(0.142315 + 0.989821i) q^{72} +(-2.59043 - 5.67225i) q^{73} +(-7.21215 - 2.11768i) q^{74} +(0.415415 - 0.909632i) q^{75} +(1.56124 - 1.80177i) q^{76} +(2.40540 - 16.7300i) q^{77} +(-6.67657 + 1.96042i) q^{78} +(-2.60645 - 3.00801i) q^{79} +(-0.841254 + 0.540641i) q^{80} +(0.841254 - 0.540641i) q^{81} +(1.44231 + 1.66452i) q^{82} +(-14.6281 + 4.29519i) q^{83} +(0.640439 - 4.45435i) q^{84} +(-4.58868 + 5.29562i) q^{85} +(3.68158 - 8.06153i) q^{86} +(4.80200 + 1.41000i) q^{87} +(-1.56024 - 3.41646i) q^{88} +(1.83561 + 12.7670i) q^{89} +(0.841254 + 0.540641i) q^{90} +31.3141 q^{91} +(4.74055 - 0.726057i) q^{92} -3.96768 q^{93} +(3.42790 + 2.20298i) q^{94} +(-0.339290 - 2.35981i) q^{95} +(-0.415415 - 0.909632i) q^{96} +(6.25556 + 1.83680i) q^{97} +(-5.50484 + 12.0539i) q^{98} +(-2.45957 + 2.83850i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Introduction

L-functions

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