LMFDB - Embedded newform 690.2.m.a.541.1

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:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			541.1
Root			$0.142315 + 0.989821i$ of defining polynomial
Character	$\chi$	$=$	690.541
Dual form			690.2.m.a.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 - 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(0.415415 + 0.909632i) q^{6} +(0.730471 + 0.843008i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(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} +(0.730471 + 0.843008i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(0.654861 - 0.755750i) q^{10} +(0.307599 + 0.197682i) q^{11} +(0.841254 + 0.540641i) q^{12} +(4.06250 - 4.68838i) q^{13} +(1.07028 + 0.314261i) q^{14} +(0.142315 + 0.989821i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(1.64231 + 3.59617i) q^{17} +(-0.959493 + 0.281733i) q^{18} +(-0.805836 + 1.76453i) q^{19} +(0.142315 - 0.989821i) q^{20} +(-0.938384 + 0.603063i) q^{21} +0.365644 q^{22} +(4.43274 - 1.83053i) q^{23} +1.00000 q^{24} +(0.841254 - 0.540641i) q^{25} +(0.882867 - 6.14047i) q^{26} +(0.415415 - 0.909632i) q^{27} +(1.07028 - 0.314261i) q^{28} +(2.03788 + 4.46234i) q^{29} +(0.654861 + 0.755750i) q^{30} +(0.0682430 + 0.474640i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-0.239446 + 0.276335i) q^{33} +(3.32584 + 2.13739i) q^{34} +(0.938384 + 0.603063i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(-6.87816 - 2.01961i) q^{37} +(0.276067 + 1.92009i) q^{38} +(4.06250 + 4.68838i) q^{39} +(-0.415415 - 0.909632i) q^{40} +(11.1841 - 3.28396i) q^{41} +(-0.463379 + 1.01466i) q^{42} +(-1.18767 + 8.26043i) q^{43} +(0.307599 - 0.197682i) q^{44} -1.00000 q^{45} +(2.73939 - 3.93646i) q^{46} -10.2150 q^{47} +(0.841254 - 0.540641i) q^{48} +(0.819129 - 5.69716i) q^{49} +(0.415415 - 0.909632i) q^{50} +(-3.79329 + 1.11381i) q^{51} +(-2.57708 - 5.64301i) q^{52} +(-1.51978 - 1.75392i) q^{53} +(-0.142315 - 0.989821i) q^{54} +(0.350833 + 0.103014i) q^{55} +(0.730471 - 0.843008i) q^{56} +(-1.63189 - 1.04875i) q^{57} +(4.12690 + 2.65220i) q^{58} +(-0.708833 + 0.818036i) q^{59} +(0.959493 + 0.281733i) q^{60} +(-1.05206 - 7.31727i) q^{61} +(0.314020 + 0.362398i) q^{62} +(-0.463379 - 1.01466i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(2.57708 - 5.64301i) q^{65} +(-0.0520365 + 0.361922i) q^{66} +(-3.02292 + 1.94271i) q^{67} +3.95343 q^{68} +(1.18106 + 4.64813i) q^{69} +1.11546 q^{70} +(-8.18185 + 5.25816i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(-0.843563 + 1.84715i) q^{73} +(-6.87816 + 2.01961i) q^{74} +(0.415415 + 0.909632i) q^{75} +(1.27032 + 1.46603i) q^{76} +(0.0580447 + 0.403709i) q^{77} +(5.95233 + 1.74776i) q^{78} +(8.57764 - 9.89913i) q^{79} +(-0.841254 - 0.540641i) q^{80} +(0.841254 + 0.540641i) q^{81} +(7.63325 - 8.80924i) q^{82} +(4.74056 + 1.39196i) q^{83} +(0.158746 + 1.10411i) q^{84} +(2.58895 + 2.98780i) q^{85} +(3.46679 + 7.59122i) q^{86} +(-4.70694 + 1.38208i) q^{87} +(0.151894 - 0.332601i) q^{88} +(-1.60617 + 11.1712i) q^{89} +(-0.841254 + 0.540641i) q^{90} +6.91988 q^{91} +(0.176312 - 4.79259i) q^{92} -0.479521 q^{93} +(-8.59341 + 5.52265i) q^{94} +(-0.276067 + 1.92009i) q^{95} +(0.415415 - 0.909632i) q^{96} +(-16.9563 + 4.97882i) q^{97} +(-2.39102 - 5.23561i) q^{98} +(-0.239446 - 0.276335i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 - q^3 - q^4 + q^5 - q^6 - q^8 - q^9	$ 10 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - q^{8} - q^{9} + q^{10} - 2 q^{11} - q^{12} + q^{15} - q^{16} + 16 q^{17} - q^{18} + 18 q^{19} + q^{20} + 20 q^{22} - q^{23} + 10 q^{24} - q^{25} + 11 q^{26} - q^{27} + 22 q^{29} + q^{30} + 8 q^{31} - q^{32} - 2 q^{33} + 5 q^{34} - q^{36} - 16 q^{37} - 4 q^{38} + q^{40} - 9 q^{41} - 11 q^{42} + 2 q^{43} - 2 q^{44} - 10 q^{45} - q^{46} - 48 q^{47} - q^{48} + 7 q^{49} - q^{50} - 17 q^{51} + 2 q^{53} - q^{54} - 9 q^{55} - 15 q^{57} + 22 q^{58} - 22 q^{59} + q^{60} + 13 q^{61} + 8 q^{62} - 11 q^{63} - q^{64} - 13 q^{66} + 2 q^{67} - 6 q^{68} - q^{69} - 45 q^{71} - q^{72} + 21 q^{73} - 16 q^{74} - q^{75} - 4 q^{76} + 22 q^{77} + 11 q^{78} + 66 q^{79} + q^{80} - q^{81} + 57 q^{82} + 15 q^{83} + 11 q^{84} - 5 q^{85} + 24 q^{86} - 2 q^{88} + 29 q^{89} + q^{90} + 22 q^{91} - 12 q^{92} - 58 q^{93} + 7 q^{94} + 4 q^{95} - q^{96} - 27 q^{97} + 7 q^{98} - 2 q^{99}+O(q^{100}) $ 10 * q - q^2 - q^3 - q^4 + q^5 - q^6 - q^8 - q^9 + q^10 - 2 * q^11 - q^12 + q^15 - q^16 + 16 * q^17 - q^18 + 18 * q^19 + q^20 + 20 * q^22 - q^23 + 10 * q^24 - q^25 + 11 * q^26 - q^27 + 22 * q^29 + q^30 + 8 * q^31 - q^32 - 2 * q^33 + 5 * q^34 - q^36 - 16 * q^37 - 4 * q^38 + q^40 - 9 * q^41 - 11 * q^42 + 2 * q^43 - 2 * q^44 - 10 * q^45 - q^46 - 48 * q^47 - q^48 + 7 * q^49 - q^50 - 17 * q^51 + 2 * q^53 - q^54 - 9 * q^55 - 15 * q^57 + 22 * q^58 - 22 * q^59 + q^60 + 13 * q^61 + 8 * q^62 - 11 * q^63 - q^64 - 13 * q^66 + 2 * q^67 - 6 * q^68 - q^69 - 45 * q^71 - q^72 + 21 * q^73 - 16 * q^74 - q^75 - 4 * q^76 + 22 * q^77 + 11 * q^78 + 66 * q^79 + q^80 - q^81 + 57 * q^82 + 15 * q^83 + 11 * q^84 - 5 * q^85 + 24 * q^86 - 2 * q^88 + 29 * q^89 + q^90 + 22 * q^91 - 12 * q^92 - 58 * q^93 + 7 * q^94 + 4 * q^95 - q^96 - 27 * q^97 + 7 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

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
$7$	0.730471	+	0.843008i	0.276092	+	0.318627i	0.876813	−	0.480832i	$-0.159665\pi$
$7$	0.730471	+	0.843008i	0.276092	+	0.318627i	−0.600721	+	0.799459i	$0.705120\pi$
$8$	−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
$11$	0.307599	+	0.197682i	0.0927446	+	0.0596033i	0.586191	−	0.810173i	$-0.300627\pi$
$11$	0.307599	+	0.197682i	0.0927446	+	0.0596033i	−0.493447	+	0.869776i	$0.664263\pi$
$12$	0.841254	+	0.540641i	0.242849	+	0.156070i
$13$	4.06250	−	4.68838i	1.12674	−	1.30032i	0.178079	−	0.984016i	$-0.443012\pi$
$13$	4.06250	−	4.68838i	1.12674	−	1.30032i	0.948657	−	0.316306i	$-0.102443\pi$
$14$	1.07028	+	0.314261i	0.286043	+	0.0839899i
$15$	0.142315	+	0.989821i	0.0367455	+	0.255571i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	1.64231	+	3.59617i	0.398320	+	0.872199i	0.997438	+	0.0715381i	$0.0227907\pi$
$17$	1.64231	+	3.59617i	0.398320	+	0.872199i	−0.599118	+	0.800661i	$0.704482\pi$
$18$	−0.959493	+	0.281733i	−0.226155	+	0.0664050i
$19$	−0.805836	+	1.76453i	−0.184871	+	0.404812i	−0.979263	−	0.202594i	$-0.935063\pi$
$19$	−0.805836	+	1.76453i	−0.184871	+	0.404812i	0.794391	+	0.607406i	$0.207790\pi$
$20$	0.142315	−	0.989821i	0.0318226	−	0.221331i
$21$	−0.938384	+	0.603063i	−0.204772	+	0.131599i
$22$	0.365644			0.0779555
$23$	4.43274	−	1.83053i	0.924289	−	0.381693i
$23$	4.43274	−	1.83053i	0.924289	−	0.381693i
$24$	1.00000			0.204124
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	0.882867	−	6.14047i	0.173144	−	1.20425i
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$	1.07028	−	0.314261i	0.202263	−	0.0593898i
$29$	2.03788	+	4.46234i	0.378425	+	0.828636i	0.999010	+	0.0444961i	$0.0141682\pi$
$29$	2.03788	+	4.46234i	0.378425	+	0.828636i	−0.620584	+	0.784140i	$0.713105\pi$
$30$	0.654861	+	0.755750i	0.119561	+	0.137980i
$31$	0.0682430	+	0.474640i	0.0122568	+	0.0852479i	0.995032	−	0.0995589i	$-0.0317432\pi$
$31$	0.0682430	+	0.474640i	0.0122568	+	0.0852479i	−0.982775	+	0.184807i	$0.940834\pi$
$32$	−0.959493	−	0.281733i	−0.169616	−	0.0498038i
$33$	−0.239446	+	0.276335i	−0.0416821	+	0.0481038i
$34$	3.32584	+	2.13739i	0.570377	+	0.366559i
$35$	0.938384	+	0.603063i	0.158616	+	0.101936i
$36$	−0.654861	+	0.755750i	−0.109143	+	0.125958i
$37$	−6.87816	−	2.01961i	−1.13076	−	0.332022i	−0.337756	−	0.941234i	$-0.609668\pi$
$37$	−6.87816	−	2.01961i	−1.13076	−	0.332022i	−0.793008	+	0.609212i	$0.791486\pi$
$38$	0.276067	+	1.92009i	0.0447840	+	0.311479i
$39$	4.06250	+	4.68838i	0.650521	+	0.750742i
$40$	−0.415415	−	0.909632i	−0.0656829	−	0.143825i
$41$	11.1841	−	3.28396i	1.74667	−	0.512868i	0.756652	−	0.653818i	$-0.226834\pi$
$41$	11.1841	−	3.28396i	1.74667	−	0.512868i	0.990017	+	0.140950i	$0.0450158\pi$
$42$	−0.463379	+	1.01466i	−0.0715009	+	0.156565i
$43$	−1.18767	+	8.26043i	−0.181118	+	1.25970i	0.673007	+	0.739636i	$0.265002\pi$
$43$	−1.18767	+	8.26043i	−0.181118	+	1.25970i	−0.854125	+	0.520068i	$0.825907\pi$
$44$	0.307599	−	0.197682i	0.0463723	−	0.0298017i
$45$	−1.00000			−0.149071
$46$	2.73939	−	3.93646i	0.403901	−	0.580400i
$47$	−10.2150			−1.49001			−0.745006	−	0.667058i	$-0.767553\pi$
$47$	−10.2150			−1.49001			−0.745006	+	0.667058i	$0.767553\pi$
$48$	0.841254	−	0.540641i	0.121424	−	0.0780348i
$49$	0.819129	−	5.69716i	0.117018	−	0.813881i
$50$	0.415415	−	0.909632i	0.0587486	−	0.128641i
$51$	−3.79329	+	1.11381i	−0.531167	+	0.155965i
$52$	−2.57708	−	5.64301i	−0.357376	−	0.782544i
$53$	−1.51978	−	1.75392i	−0.208757	−	0.240919i	0.641709	−	0.766948i	$-0.278226\pi$
$53$	−1.51978	−	1.75392i	−0.208757	−	0.240919i	−0.850466	+	0.526029i	$0.823680\pi$
$54$	−0.142315	−	0.989821i	−0.0193666	−	0.134698i
$55$	0.350833	+	0.103014i	0.0473063	+	0.0138904i
$56$	0.730471	−	0.843008i	0.0976133	−	0.112652i
$57$	−1.63189	−	1.04875i	−0.216149	−	0.138911i
$58$	4.12690	+	2.65220i	0.541888	+	0.348251i
$59$	−0.708833	+	0.818036i	−0.0922821	+	0.106499i	−0.800012	−	0.599984i	$-0.795174\pi$
$59$	−0.708833	+	0.818036i	−0.0922821	+	0.106499i	0.707730	+	0.706483i	$0.249719\pi$
$60$	0.959493	+	0.281733i	0.123870	+	0.0363715i
$61$	−1.05206	−	7.31727i	−0.134703	−	0.936880i	−0.939309	−	0.343071i	$-0.888533\pi$
$61$	−1.05206	−	7.31727i	−0.134703	−	0.936880i	0.804606	−	0.593809i	$-0.202376\pi$
$62$	0.314020	+	0.362398i	0.0398805	+	0.0460246i
$63$	−0.463379	−	1.01466i	−0.0583802	−	0.127835i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	2.57708	−	5.64301i	0.319647	−	0.699929i
$66$	−0.0520365	+	0.361922i	−0.00640525	+	0.0445495i
$67$	−3.02292	+	1.94271i	−0.369308	+	0.237340i	−0.712110	−	0.702068i	$-0.752260\pi$
$67$	−3.02292	+	1.94271i	−0.369308	+	0.237340i	0.342802	+	0.939408i	$0.388624\pi$
$68$	3.95343			0.479424
$69$	1.18106	+	4.64813i	0.142183	+	0.559569i
$70$	1.11546			0.133323
$71$	−8.18185	+	5.25816i	−0.971007	+	0.624028i	−0.927023	−	0.375004i	$-0.877641\pi$
$71$	−8.18185	+	5.25816i	−0.971007	+	0.624028i	−0.0439837	+	0.999032i	$0.514005\pi$
$72$	−0.142315	+	0.989821i	−0.0167720	+	0.116652i
$73$	−0.843563	+	1.84715i	−0.0987316	+	0.216192i	−0.952552	−	0.304375i	$-0.901552\pi$
$73$	−0.843563	+	1.84715i	−0.0987316	+	0.216192i	0.853821	+	0.520567i	$0.174280\pi$
$74$	−6.87816	+	2.01961i	−0.799570	+	0.234775i
$75$	0.415415	+	0.909632i	0.0479680	+	0.105035i
$76$	1.27032	+	1.46603i	0.145716	+	0.168165i
$77$	0.0580447	+	0.403709i	0.00661480	+	0.0460070i
$78$	5.95233	+	1.74776i	0.673968	+	0.197895i
$79$	8.57764	−	9.89913i	0.965060	−	1.11374i	−0.0284042	−	0.999597i	$-0.509043\pi$
$79$	8.57764	−	9.89913i	0.965060	−	1.11374i	0.993464	−	0.114142i	$-0.0364120\pi$
$80$	−0.841254	−	0.540641i	−0.0940550	−	0.0604455i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	7.63325	−	8.80924i	0.842951	−	0.972818i
$83$	4.74056	+	1.39196i	0.520345	+	0.152787i	0.531350	−	0.847152i	$-0.321685\pi$
$83$	4.74056	+	1.39196i	0.520345	+	0.152787i	−0.0110053	+	0.999939i	$0.503503\pi$
$84$	0.158746	+	1.10411i	0.0173207	+	0.120468i
$85$	2.58895	+	2.98780i	0.280811	+	0.324073i
$86$	3.46679	+	7.59122i	0.373834	+	0.818582i
$87$	−4.70694	+	1.38208i	−0.504637	+	0.148175i
$88$	0.151894	−	0.332601i	0.0161919	−	0.0354554i
$89$	−1.60617	+	11.1712i	−0.170254	+	1.18414i	0.708094	+	0.706118i	$0.249555\pi$
$89$	−1.60617	+	11.1712i	−0.170254	+	1.18414i	−0.878348	+	0.478022i	$0.841354\pi$
$90$	−0.841254	+	0.540641i	−0.0886759	+	0.0569885i
$91$	6.91988			0.725401
$92$	0.176312	−	4.79259i	0.0183818	−	0.499662i
$93$	−0.479521			−0.0497240
$94$	−8.59341	+	5.52265i	−0.886342	+	0.569618i
$95$	−0.276067	+	1.92009i	−0.0283239	+	0.196997i
$96$	0.415415	−	0.909632i	0.0423981	−	0.0928389i
$97$	−16.9563	+	4.97882i	−1.72165	+	0.505523i	−0.985265	−	0.171036i	$-0.945288\pi$
$97$	−16.9563	+	4.97882i	−1.72165	+	0.505523i	−0.736388	+	0.676559i	$0.763470\pi$
$98$	−2.39102	−	5.23561i	−0.241530	−	0.528877i
$99$	−0.239446	−	0.276335i	−0.0240652	−	0.0277727i
$100$	−0.142315	−	0.989821i	−0.0142315	−	0.0989821i
$101$	−8.56954	−	2.51625i	−0.852701	−	0.250376i	−0.173960	−	0.984753i	$-0.555656\pi$
$101$	−8.56954	−	2.51625i	−0.852701	−	0.250376i	−0.678742	+	0.734377i	$0.737474\pi$
$102$	−2.58895	+	2.98780i	−0.256344	+	0.295837i
$103$	−12.5818	−	8.08584i	−1.23972	−	0.796722i	−0.254347	−	0.967113i	$-0.581860\pi$
$103$	−12.5818	−	8.08584i	−1.23972	−	0.796722i	−0.985376	+	0.170391i	$0.945497\pi$
$104$	−5.21881	−	3.35393i	−0.511747	−	0.328880i
$105$	−0.730471	+	0.843008i	−0.0712866	+	0.0822692i
$106$	−2.22676	−	0.653835i	−0.216282	−	0.0635061i
$107$	1.60227	+	11.1441i	0.154898	+	1.07734i	0.907860	+	0.419273i	$0.137715\pi$
$107$	1.60227	+	11.1441i	0.154898	+	1.07734i	−0.752963	+	0.658063i	$0.771376\pi$
$108$	−0.654861	−	0.755750i	−0.0630140	−	0.0727220i
$109$	−3.67708	−	8.05167i	−0.352200	−	0.771210i	−0.999956	−	0.00936262i	$-0.997020\pi$
$109$	−3.67708	−	8.05167i	−0.352200	−	0.771210i	0.647756	−	0.761848i	$-0.275708\pi$
$110$	0.350833	−	0.103014i	0.0334506	−	0.00982197i
$111$	2.97792	−	6.52073i	0.282652	−	0.618921i
$112$	0.158746	−	1.10411i	0.0150001	−	0.104328i
$113$	−5.84147	+	3.75408i	−0.549519	+	0.353154i	−0.785752	−	0.618542i	$-0.787724\pi$
$113$	−5.84147	+	3.75408i	−0.549519	+	0.353154i	0.236233	+	0.971697i	$0.424087\pi$
$114$	−1.93983			−0.181682
$115$	3.73746	−	3.00523i	0.348520	−	0.280239i
$116$	4.90566			0.455479
$117$	−5.21881	+	3.35393i	−0.482479	+	0.310071i
$118$	−0.154044	+	1.07140i	−0.0141809	+	0.0986303i
$119$	−1.83194	+	4.01138i	−0.167933	+	0.367723i
$120$	0.959493	−	0.281733i	0.0875893	−	0.0257185i
$121$	−4.51403	−	9.88434i	−0.410366	−	0.898576i
$122$	−4.84107	−	5.58689i	−0.438290	−	0.505813i
$123$	1.65886	+	11.5377i	0.149575	+	1.04031i
$124$	0.460097	+	0.135097i	0.0413179	+	0.0121320i
$125$	0.654861	−	0.755750i	0.0585725	−	0.0675963i
$126$	−0.938384	−	0.603063i	−0.0835979	−	0.0537251i
$127$	−9.76760	−	6.27726i	−0.866735	−	0.557017i	0.0300176	−	0.999549i	$-0.490444\pi$
$127$	−9.76760	−	6.27726i	−0.866735	−	0.557017i	−0.896752	+	0.442533i	$0.854080\pi$
$128$	−0.654861	+	0.755750i	−0.0578821	+	0.0667995i
$129$	−8.00733	−	2.35116i	−0.705006	−	0.207008i
$130$	−0.882867	−	6.14047i	−0.0774325	−	0.538555i
$131$	5.95694	+	6.87468i	0.520461	+	0.600644i	0.953746	−	0.300613i	$-0.0971913\pi$
$131$	5.95694	+	6.87468i	0.520461	+	0.600644i	−0.433286	+	0.901257i	$0.642646\pi$
$132$	0.151894	+	0.332601i	0.0132207	+	0.0289492i
$133$	−2.07616	+	0.609614i	−0.180026	+	0.0528603i
$134$	−1.49273	+	3.26862i	−0.128952	+	0.282366i
$135$	0.142315	−	0.989821i	0.0122485	−	0.0851903i
$136$	3.32584	−	2.13739i	0.285188	−	0.183279i
$137$	3.70944			0.316919			0.158459	−	0.987366i	$-0.449347\pi$
$137$	3.70944			0.316919			0.158459	+	0.987366i	$0.449347\pi$
$138$	3.50654	+	3.27173i	0.298496	+	0.278508i
$139$	−9.09958			−0.771816			−0.385908	−	0.922537i	$-0.626112\pi$
$139$	−9.09958			−0.771816			−0.385908	+	0.922537i	$0.626112\pi$
$140$	0.938384	−	0.603063i	0.0793080	−	0.0509681i
$141$	1.45375	−	10.1110i	0.122428	−	0.851502i
$142$	−4.04024	+	8.84688i	−0.339049	+	0.742414i
$143$	2.17643	−	0.639058i	0.182002	−	0.0534407i
$144$	0.415415	+	0.909632i	0.0346179	+	0.0758027i
$145$	3.21252	+	3.70745i	0.266785	+	0.307887i
$146$	0.288992	+	2.00998i	0.0239171	+	0.166347i
$147$	5.52260	+	1.62158i	0.455496	+	0.133746i
$148$	−4.69440	+	5.41762i	−0.385877	+	0.445326i
$149$	2.26820	+	1.45768i	0.185818	+	0.119418i	0.630243	−	0.776398i	$-0.282955\pi$
$149$	2.26820	+	1.45768i	0.185818	+	0.119418i	−0.444425	+	0.895816i	$0.646592\pi$
$150$	0.841254	+	0.540641i	0.0686881	+	0.0441431i
$151$	−11.5141	+	13.2880i	−0.937007	+	1.08136i	0.0595310	+	0.998226i	$0.481039\pi$
$151$	−11.5141	+	13.2880i	−0.937007	+	1.08136i	−0.996538	+	0.0831374i	$0.973506\pi$
$152$	1.86126	+	0.546514i	0.150968	+	0.0443281i
$153$	−0.562632	−	3.91319i	−0.0454861	−	0.316363i
$154$	0.267092	+	0.308241i	0.0215229	+	0.0248387i
$155$	0.199200	+	0.436188i	0.0160001	+	0.0350354i
$156$	5.95233	−	1.74776i	0.476567	−	0.139933i
$157$	−5.22802	+	11.4478i	−0.417241	+	0.913631i	0.577986	+	0.816047i	$0.303839\pi$
$157$	−5.22802	+	11.4478i	−0.417241	+	0.913631i	−0.995227	+	0.0975845i	$0.968888\pi$
$158$	1.86410	−	12.9651i	0.148300	−	1.03145i
$159$	1.95235	−	1.25470i	0.154832	−	0.0995042i
$160$	−1.00000			−0.0790569
$161$	4.78114	+	2.39968i	0.376807	+	0.189121i
$162$	1.00000			0.0785674
$163$	1.85623	−	1.19293i	0.145391	−	0.0934372i	−0.465923	−	0.884825i	$-0.654278\pi$
$163$	1.85623	−	1.19293i	0.145391	−	0.0934372i	0.611314	+	0.791388i	$0.290641\pi$
$164$	1.65886	−	11.5377i	0.129536	−	0.900939i
$165$	−0.151894	+	0.332601i	−0.0118249	+	0.0258930i
$166$	4.74056	−	1.39196i	0.367939	−	0.108037i
$167$	0.478173	+	1.04705i	0.0370022	+	0.0810234i	0.927231	−	0.374491i	$-0.122183\pi$
$167$	0.478173	+	1.04705i	0.0370022	+	0.0810234i	−0.890228	+	0.455515i	$0.849455\pi$
$168$	0.730471	+	0.843008i	0.0563570	+	0.0650395i
$169$	−3.62687	−	25.2254i	−0.278990	−	1.94042i
$170$	3.79329	+	1.11381i	0.290932	+	0.0854254i
$171$	1.27032	−	1.46603i	0.0971438	−	0.112110i
$172$	7.02058	+	4.51185i	0.535314	+	0.344025i
$173$	−12.1011	−	7.77687i	−0.920026	−	0.591265i	−0.00736073	−	0.999973i	$-0.502343\pi$
$173$	−12.1011	−	7.77687i	−0.920026	−	0.591265i	−0.912665	+	0.408708i	$0.865979\pi$
$174$	−3.21252	+	3.70745i	−0.243541	+	0.281061i
$175$	1.07028	+	0.314261i	0.0809052	+	0.0237559i
$176$	−0.0520365	−	0.361922i	−0.00392240	−	0.0272809i
$177$	−0.708833	−	0.818036i	−0.0532791	−	0.0614874i
$178$	4.68839	+	10.2661i	0.351409	+	0.769479i
$179$	−17.8282	+	5.23484i	−1.33255	+	0.391271i	−0.869004	−	0.494805i	$-0.835240\pi$
$179$	−17.8282	+	5.23484i	−1.33255	+	0.391271i	−0.463541	+	0.886075i	$0.653421\pi$
$180$	−0.415415	+	0.909632i	−0.0309632	+	0.0678000i
$181$	2.23138	−	15.5196i	0.165857	−	1.15356i	−0.721478	−	0.692437i	$-0.756537\pi$
$181$	2.23138	−	15.5196i	0.165857	−	1.15356i	0.887335	−	0.461125i	$-0.152554\pi$
$182$	5.82138	−	3.74117i	0.431509	−	0.277314i
$183$	7.39251			0.546470
$184$	−2.44275	−	4.12710i	−0.180082	−	0.304254i
$185$	−7.16854			−0.527042
$186$	−0.403399	+	0.259249i	−0.0295786	+	0.0190090i
$187$	−0.205723	+	1.43083i	−0.0150439	+	0.104633i
$188$	−4.24347	+	9.29189i	−0.309487	+	0.677681i
$189$	1.07028	−	0.314261i	0.0778511	−	0.0228591i
$190$	0.805836	+	1.76453i	0.0584615	+	0.128013i
$191$	12.8261	+	14.8021i	0.928061	+	1.07104i	0.997300	+	0.0734392i	$0.0233975\pi$
$191$	12.8261	+	14.8021i	0.928061	+	1.07104i	−0.0692388	+	0.997600i	$0.522057\pi$
$192$	−0.142315	−	0.989821i	−0.0102707	−	0.0714342i
$193$	15.3441	+	4.50545i	1.10450	+	0.324309i	0.782637	−	0.622479i	$-0.213874\pi$
$193$	15.3441	+	4.50545i	1.10450	+	0.324309i	0.321858	+	0.946788i	$0.395692\pi$
$194$	−11.5728	+	13.3557i	−0.830879	+	0.958885i
$195$	5.21881	+	3.35393i	0.373727	+	0.240180i
$196$	−4.84204	−	3.11179i	−0.345860	−	0.222271i
$197$	−3.56175	+	4.11048i	−0.253764	+	0.292859i	−0.868310	−	0.496021i	$-0.834794\pi$
$197$	−3.56175	+	4.11048i	−0.253764	+	0.292859i	0.614546	+	0.788881i	$0.289339\pi$
$198$	−0.350833	−	0.103014i	−0.0249326	−	0.00732087i
$199$	0.733438	+	5.10117i	0.0519920	+	0.361612i	0.999164	+	0.0408858i	$0.0130180\pi$
$199$	0.733438	+	5.10117i	0.0519920	+	0.361612i	−0.947172	+	0.320727i	$0.896073\pi$
$200$	−0.654861	−	0.755750i	−0.0463056	−	0.0534396i
$201$	−1.49273	−	3.26862i	−0.105289	−	0.230551i
$202$	−8.56954	+	2.51625i	−0.602951	+	0.177042i
$203$	−2.27318	+	4.97756i	−0.159546	+	0.349356i
$204$	−0.562632	+	3.91319i	−0.0393921	+	0.273978i
$205$	9.80590	−	6.30187i	0.684874	−	0.440142i
$206$	−14.9560			−1.04204
$207$	−4.76890	+	0.507539i	−0.331461	+	0.0352764i
$208$	−6.20362			−0.430143
$209$	−0.596691	+	0.383470i	−0.0412740	+	0.0265252i
$210$	−0.158746	+	1.10411i	−0.0109545	+	0.0761905i
$211$	10.7843	−	23.6143i	0.742420	−	1.62567i	−0.0371133	−	0.999311i	$-0.511816\pi$
$211$	10.7843	−	23.6143i	0.742420	−	1.62567i	0.779533	−	0.626361i	$-0.215456\pi$
$212$	−2.22676	+	0.653835i	−0.152934	+	0.0449056i
$213$	−4.04024	−	8.84688i	−0.276832	−	0.606178i
$214$	7.37285	+	8.50872i	0.503998	+	0.581644i
$215$	1.18767	+	8.26043i	0.0809985	+	0.563357i
$216$	−0.959493	−	0.281733i	−0.0652852	−	0.0191695i
$217$	−0.350276	+	0.404240i	−0.0237783	+	0.0274416i
$218$	−7.44641	−	4.78552i	−0.504335	−	0.324116i
$219$	−1.70829	−	1.09785i	−0.115436	−	0.0741860i
$220$	0.239446	−	0.276335i	0.0161434	−	0.0186305i
$221$	23.5321	+	6.90965i	1.58294	+	0.464793i
$222$	−1.02019	−	7.09557i	−0.0684706	−	0.476224i
$223$	7.49304	+	8.64742i	0.501771	+	0.579074i	0.948973	−	0.315359i	$-0.102125\pi$
$223$	7.49304	+	8.64742i	0.501771	+	0.579074i	−0.447202	+	0.894433i	$0.647579\pi$
$224$	−0.463379	−	1.01466i	−0.0309608	−	0.0677947i
$225$	−0.959493	+	0.281733i	−0.0639662	+	0.0187822i
$226$	−2.88454	+	6.31627i	−0.191877	+	0.420152i
$227$	−1.96987	+	13.7007i	−0.130745	+	0.909349i	0.813842	+	0.581087i	$0.197372\pi$
$227$	−1.96987	+	13.7007i	−0.130745	+	0.909349i	−0.944586	+	0.328263i	$0.893537\pi$
$228$	−1.63189	+	1.04875i	−0.108075	+	0.0694554i
$229$	3.73656			0.246919			0.123459	−	0.992350i	$-0.460601\pi$
$229$	3.73656			0.246919			0.123459	+	0.992350i	$0.460601\pi$
$230$	1.51940	−	4.54878i	0.100186	−	0.299938i
$231$	−0.407861			−0.0268353
$232$	4.12690	−	2.65220i	0.270944	−	0.174125i
$233$	2.53624	−	17.6400i	0.166155	−	1.15563i	−0.720586	−	0.693365i	$-0.756127\pi$
$233$	2.53624	−	17.6400i	0.166155	−	1.15563i	0.886741	−	0.462266i	$-0.152964\pi$
$234$	−2.57708	+	5.64301i	−0.168469	+	0.368895i
$235$	−9.80122	+	2.87790i	−0.639361	+	0.187733i
$236$	0.449652	+	0.984601i	0.0292699	+	0.0640921i
$237$	8.57764	+	9.89913i	0.557178	+	0.643017i
$238$	0.627593	+	4.36501i	0.0406808	+	0.282941i
$239$	24.3595	+	7.15260i	1.57569	+	0.462663i	0.948650	−	0.316327i	$-0.102450\pi$
$239$	24.3595	+	7.15260i	1.57569	+	0.462663i	0.627036	+	0.778990i	$0.284268\pi$
$240$	0.654861	−	0.755750i	0.0422711	−	0.0487834i
$241$	14.2647	+	9.16736i	0.918870	+	0.590522i	0.912329	−	0.409457i	$-0.134282\pi$
$241$	14.2647	+	9.16736i	0.918870	+	0.590522i	0.00654019	+	0.999979i	$0.497918\pi$
$242$	−9.14132	−	5.87477i	−0.587626	−	0.377644i
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$	−7.09306	−	2.08271i	−0.454087	−	0.133332i
$245$	−0.819129	−	5.69716i	−0.0523322	−	0.363978i
$246$	7.63325	+	8.80924i	0.486678	+	0.561657i
$247$	4.99910	+	10.9465i	0.318085	+	0.696509i
$248$	0.460097	−	0.135097i	0.0292162	−	0.00857865i
$249$	−2.05244	+	4.49422i	−0.130068	+	0.284809i
$250$	0.142315	−	0.989821i	0.00900078	−	0.0626018i
$251$	−2.59926	+	1.67044i	−0.164064	+	0.105437i	−0.620096	−	0.784526i	$-0.712906\pi$
$251$	−2.59926	+	1.67044i	−0.164064	+	0.105437i	0.456032	+	0.889963i	$0.349270\pi$
$252$	−1.11546			−0.0702674
$253$	1.72537	+	0.313201i	0.108473	+	0.0196908i
$254$	−11.6108			−0.728525
$255$	−3.32584	+	2.13739i	−0.208272	+	0.133848i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−8.83026	+	19.3356i	−0.550817	+	1.20612i	0.405583	+	0.914058i	$0.367069\pi$
$257$	−8.83026	+	19.3356i	−0.550817	+	1.20612i	−0.956399	+	0.292062i	$0.905659\pi$
$258$	−8.00733	+	2.35116i	−0.498515	+	0.146377i
$259$	−3.32175	−	7.27362i	−0.206403	−	0.451960i
$260$	−4.06250	−	4.68838i	−0.251946	−	0.290761i
$261$	−0.698147	−	4.85572i	−0.0432142	−	0.300562i
$262$	8.72803	+	2.56278i	0.539220	+	0.158329i
$263$	7.49027	−	8.64423i	0.461870	−	0.533026i	−0.476263	−	0.879303i	$-0.658009\pi$
$263$	7.49027	−	8.64423i	0.461870	−	0.533026i	0.938132	+	0.346277i	$0.112554\pi$
$264$	0.307599	+	0.197682i	0.0189314	+	0.0121665i
$265$	−1.95235	−	1.25470i	−0.119932	−	0.0770756i
$266$	−1.41699	+	1.63530i	−0.0868813	+	0.100266i
$267$	−10.8289	−	3.17964i	−0.662716	−	0.194591i
$268$	0.511387	+	3.55677i	0.0312379	+	0.217264i
$269$	−3.10298	−	3.58103i	−0.189192	−	0.218339i	0.653227	−	0.757162i	$-0.273415\pi$
$269$	−3.10298	−	3.58103i	−0.189192	−	0.218339i	−0.842419	+	0.538823i	$0.818869\pi$
$270$	−0.415415	−	0.909632i	−0.0252814	−	0.0553584i
$271$	16.5550	−	4.86098i	1.00564	−	0.295283i	0.262873	−	0.964830i	$-0.415330\pi$
$271$	16.5550	−	4.86098i	1.00564	−	0.295283i	0.742770	+	0.669547i	$0.233512\pi$
$272$	1.64231	−	3.59617i	0.0995800	−	0.218050i
$273$	−0.984802	+	6.84945i	−0.0596029	+	0.414548i
$274$	3.12058	−	2.00547i	0.188521	−	0.121155i
$275$	0.365644			0.0220491
$276$	4.71872	+	0.856574i	0.284033	+	0.0515597i
$277$	−4.24328			−0.254954			−0.127477	−	0.991842i	$-0.540688\pi$
$277$	−4.24328			−0.254954			−0.127477	+	0.991842i	$0.540688\pi$
$278$	−7.65505	+	4.91960i	−0.459119	+	0.295058i
$279$	0.0682430	−	0.474640i	0.00408560	−	0.0284160i
$280$	0.463379	−	1.01466i	0.0276922	−	0.0606374i
$281$	16.8021	−	4.93353i	1.00233	−	0.294310i	0.260916	−	0.965361i	$-0.415975\pi$
$281$	16.8021	−	4.93353i	1.00233	−	0.294310i	0.741411	+	0.671052i	$0.234157\pi$
$282$	−4.24347	−	9.29189i	−0.252695	−	0.553324i
$283$	13.2652	+	15.3088i	0.788532	+	0.910014i	0.997694	−	0.0678669i	$-0.0216193\pi$
$283$	13.2652	+	15.3088i	0.788532	+	0.910014i	−0.209163	+	0.977881i	$0.567074\pi$
$284$	1.38412	+	9.62679i	0.0821326	+	0.571245i
$285$	−1.86126	−	0.546514i	−0.110251	−	0.0323727i
$286$	1.48543	−	1.71428i	0.0878353	−	0.101367i
$287$	10.9381	+	7.02948i	0.645655	+	0.414937i
$288$	0.841254	+	0.540641i	0.0495713	+	0.0318576i
$289$	0.897407	−	1.03566i	0.0527887	−	0.0609214i
$290$	4.70694	+	1.38208i	0.276401	+	0.0811587i
$291$	−2.51501	−	17.4923i	−0.147433	−	1.02542i
$292$	1.32979	+	1.53466i	0.0778203	+	0.0898094i
$293$	−8.94057	−	19.5771i	−0.522314	−	1.14371i	−0.968556	−	0.248795i	$-0.919965\pi$
$293$	−8.94057	−	19.5771i	−0.522314	−	1.14371i	0.446242	−	0.894912i	$-0.352762\pi$
$294$	5.52260	−	1.62158i	0.322085	−	0.0945726i
$295$	−0.449652	+	0.984601i	−0.0261798	+	0.0573257i
$296$	−1.02019	+	7.09557i	−0.0592973	+	0.412422i
$297$	0.307599	−	0.197682i	0.0178487	−	0.0114707i
$298$	2.69621			0.156187
$299$	9.42576	−	28.2189i	0.545106	−	1.63194i
$300$	1.00000			0.0577350
$301$	−7.83117	+	5.03279i	−0.451381	+	0.290085i
$302$	−2.50226	+	17.4036i	−0.143989	+	1.00147i
$303$	3.71021	−	8.12422i	0.213146	−	0.466724i
$304$	1.86126	−	0.546514i	0.106750	−	0.0313447i
$305$	−3.07096	−	6.72447i	−0.175843	−	0.385042i
$306$	−2.58895	−	2.98780i	−0.148000	−	0.170801i
$307$	−2.45314	−	17.0619i	−0.140008	−	0.973776i	−0.931797	−	0.362981i	$-0.881759\pi$
$307$	−2.45314	−	17.0619i	−0.140008	−	0.973776i	0.791789	−	0.610795i	$-0.209150\pi$
$308$	0.391340	+	0.114908i	0.0222986	+	0.00654747i
$309$	9.79412	−	11.3030i	0.557168	−	0.643006i
$310$	0.403399	+	0.259249i	0.0229115	+	0.0147243i
$311$	−14.1368	−	9.08514i	−0.801622	−	0.515171i	0.0745227	−	0.997219i	$-0.476257\pi$
$311$	−14.1368	−	9.08514i	−0.801622	−	0.515171i	−0.876145	+	0.482048i	$0.839893\pi$
$312$	4.06250	−	4.68838i	0.229994	−	0.265427i
$313$	−16.6348	−	4.88442i	−0.940255	−	0.276084i	−0.224531	−	0.974467i	$-0.572085\pi$
$313$	−16.6348	−	4.88442i	−0.940255	−	0.276084i	−0.715724	+	0.698383i	$0.753903\pi$
$314$	1.79104	+	12.4570i	0.101074	+	0.702987i
$315$	−0.730471	−	0.843008i	−0.0411574	−	0.0474981i
$316$	−5.44128	−	11.9147i	−0.306096	−	0.670257i
$317$	9.00069	−	2.64284i	0.505529	−	0.148437i	−0.0190165	−	0.999819i	$-0.506054\pi$
$317$	9.00069	−	2.64284i	0.505529	−	0.148437i	0.524545	+	0.851383i	$0.324235\pi$
$318$	0.964080	−	2.11104i	0.0540629	−	0.118381i
$319$	−0.255273	+	1.77546i	−0.0142926	+	0.0994069i
$320$	−0.841254	+	0.540641i	−0.0470275	+	0.0302227i
$321$	−11.2587			−0.628397
$322$	5.31952	−	0.566140i	0.296445	−	0.0315497i
$323$	−7.66900			−0.426714
$324$	0.841254	−	0.540641i	0.0467363	−	0.0300356i
$325$	0.882867	−	6.14047i	0.0489726	−	0.340612i
$326$	0.916615	−	2.00711i	0.0507666	−	0.111163i
$327$	8.49302	−	2.49378i	0.469665	−	0.137906i
$328$	−4.84220	−	10.6029i	−0.267366	−	0.585449i
$329$	−7.46176	−	8.61133i	−0.411380	−	0.474758i
$330$	0.0520365	+	0.361922i	0.00286452	+	0.0199232i
$331$	7.12206	+	2.09122i	0.391464	+	0.114944i	0.471540	−	0.881845i	$-0.343698\pi$
$331$	7.12206	+	2.09122i	0.391464	+	0.114944i	−0.0800764	+	0.996789i	$0.525516\pi$
$332$	3.23547	−	3.73393i	0.177569	−	0.204926i
$333$	6.03056	+	3.87561i	0.330473	+	0.212382i
$334$	0.968345	+	0.622318i	0.0529855	+	0.0340517i
$335$	−2.35314	+	2.71567i	−0.128566	+	0.148373i
$336$	1.07028	+	0.314261i	0.0583883	+	0.0171444i
$337$	0.791772	+	5.50689i	0.0431305	+	0.299980i	0.999957	+	0.00931833i	$0.00296616\pi$
$337$	0.791772	+	5.50689i	0.0431305	+	0.299980i	−0.956826	+	0.290661i	$0.906125\pi$
$338$	−16.6890	−	19.2602i	−0.907763	−	1.04761i
$339$	−2.88454	−	6.31627i	−0.156667	−	0.343053i
$340$	3.79329	−	1.11381i	0.205720	−	0.0604048i
$341$	−0.0728363	+	0.159489i	−0.00394431	+	0.00863683i
$342$	0.276067	−	1.92009i	0.0149280	−	0.103826i
$343$	11.9698	−	7.69252i	0.646308	−	0.415357i
$344$	8.34538			0.449952
$345$	2.44275	+	4.12710i	0.131513	+	0.222196i
$346$	−14.3845			−0.773318
$347$	−14.4924	+	9.31372i	−0.777994	+	0.499986i	−0.868367	−	0.495921i	$-0.834830\pi$
$347$	−14.4924	+	9.31372i	−0.777994	+	0.499986i	0.0903732	+	0.995908i	$0.471194\pi$
$348$	−0.698147	+	4.85572i	−0.0374246	+	0.260294i
$349$	−2.82697	+	6.19021i	−0.151324	+	0.331354i	−0.970079	−	0.242789i	$-0.921938\pi$
$349$	−2.82697	+	6.19021i	−0.151324	+	0.331354i	0.818755	+	0.574144i	$0.194665\pi$
$350$	1.07028	−	0.314261i	0.0572086	−	0.0167980i
$351$	−2.57708	−	5.64301i	−0.137554	−	0.301201i
$352$	−0.239446	−	0.276335i	−0.0127625	−	0.0147287i
$353$	−3.61232	−	25.1242i	−0.192264	−	1.33723i	−0.825997	−	0.563675i	$-0.809387\pi$
$353$	−3.61232	−	25.1242i	−0.192264	−	1.33723i	0.633732	−	0.773552i	$-0.281522\pi$
$354$	−1.03857	−	0.304952i	−0.0551995	−	0.0162080i
$355$	−6.36903	+	7.35026i	−0.338033	+	0.390111i
$356$	9.49442	+	6.10169i	0.503203	+	0.323389i
$357$	−3.70984	−	2.38417i	−0.196345	−	0.126184i
$358$	−12.1679	+	14.0425i	−0.643093	+	0.742169i
$359$	13.7441	+	4.03563i	0.725386	+	0.212993i	0.623522	−	0.781806i	$-0.285701\pi$
$359$	13.7441	+	4.03563i	0.725386	+	0.212993i	0.101864	+	0.994798i	$0.467519\pi$
$360$	0.142315	+	0.989821i	0.00750065	+	0.0521682i
$361$	9.97814	+	11.5154i	0.525165	+	0.606073i
$362$	−6.51337	−	14.2623i	−0.342335	−	0.749609i
$363$	10.4261	−	3.06139i	0.547231	−	0.160681i
$364$	2.87462	−	6.29455i	0.150671	−	0.329924i
$365$	−0.288992	+	2.00998i	−0.0151265	+	0.105207i
$366$	6.21898	−	3.99669i	0.325071	−	0.208911i
$367$	19.1166			0.997877			0.498939	−	0.866637i	$-0.333723\pi$
$367$	19.1166			0.997877			0.498939	+	0.866637i	$0.333723\pi$
$368$	−4.28625	−	2.15129i	−0.223436	−	0.112144i
$369$	−11.6563			−0.606803
$370$	−6.03056	+	3.87561i	−0.313514	+	0.201483i
$371$	0.368413	−	2.56237i	0.0191271	−	0.133032i
$372$	−0.199200	+	0.436188i	−0.0103281	+	0.0226153i
$373$	−24.8125	+	7.28559i	−1.28474	+	0.377234i	−0.851647	−	0.524115i	$-0.824396\pi$
$373$	−24.8125	+	7.28559i	−1.28474	+	0.377234i	−0.433093	+	0.901349i	$0.642578\pi$
$374$	0.600502	+	1.31492i	0.0310512	+	0.0679927i
$375$	0.654861	+	0.755750i	0.0338169	+	0.0390267i
$376$	1.45375	+	10.1110i	0.0749712	+	0.521436i
$377$	29.2001	+	8.57391i	1.50388	+	0.441579i
$378$	0.730471	−	0.843008i	0.0375714	−	0.0433597i
$379$	−8.95645	−	5.75596i	−0.460062	−	0.295664i	0.290006	−	0.957025i	$-0.406343\pi$
$379$	−8.95645	−	5.75596i	−0.460062	−	0.295664i	−0.750068	+	0.661361i	$0.769979\pi$
$380$	1.63189	+	1.04875i	0.0837143	+	0.0537999i
$381$	7.60344	−	8.77484i	0.389536	−	0.449549i
$382$	18.7926	+	5.51799i	0.961511	+	0.282325i
$383$	1.02469	+	7.12684i	0.0523590	+	0.364165i	0.999109	+	0.0421961i	$0.0134354\pi$
$383$	1.02469	+	7.12684i	0.0523590	+	0.364165i	−0.946750	+	0.321968i	$0.895655\pi$
$384$	−0.654861	−	0.755750i	−0.0334182	−	0.0385667i
$385$	0.169432	+	0.371003i	0.00863503	+	0.0189081i
$386$	15.3441	−	4.50545i	0.780996	−	0.229321i
$387$	3.46679	−	7.59122i	0.176227	−	0.385883i
$388$	−2.51501	+	17.4923i	−0.127680	+	0.888036i
$389$	16.8502	−	10.8289i	0.854337	−	0.549049i	−0.0385874	−	0.999255i	$-0.512286\pi$
$389$	16.8502	−	10.8289i	0.854337	−	0.549049i	0.892925	+	0.450206i	$0.148649\pi$
$390$	6.20362			0.314132
$391$	13.8629	+	12.9345i	0.701075	+	0.654128i
$392$	−5.75575			−0.290709
$393$	−7.65247	+	4.91794i	−0.386016	+	0.248077i
$394$	−0.774042	+	5.38358i	−0.0389957	+	0.271221i
$395$	5.44128	−	11.9147i	0.273781	−	0.599496i
$396$	−0.350833	+	0.103014i	−0.0176300	+	0.00517664i
$397$	−4.38740	−	9.60707i	−0.220197	−	0.482165i	0.767004	−	0.641642i	$-0.221746\pi$
$397$	−4.38740	−	9.60707i	−0.220197	−	0.482165i	−0.987202	+	0.159477i	$0.949019\pi$
$398$	3.37491	+	3.89485i	0.169169	+	0.195231i
$399$	−0.307942	−	2.14178i	−0.0154164	−	0.107223i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	10.0108	−	11.5531i	0.499916	−	0.576933i	−0.448572	−	0.893747i	$-0.648067\pi$
$401$	10.0108	−	11.5531i	0.499916	−	0.576933i	0.948488	+	0.316813i	$0.102613\pi$
$402$	−3.02292	−	1.94271i	−0.150769	−	0.0968936i
$403$	2.50253	+	1.60828i	0.124660	+	0.0801141i
$404$	−5.84877	+	6.74985i	−0.290987	+	0.335817i
$405$	0.959493	+	0.281733i	0.0476776	+	0.0139994i
$406$	0.778755	+	5.41636i	0.0386490	+	0.268810i
$407$	−1.71648	−	1.98092i	−0.0850826	−	0.0981905i
$408$	1.64231	+	3.59617i	0.0813067	+	0.178037i
$409$	9.53580	−	2.79996i	0.471515	−	0.138449i	−0.0373382	−	0.999303i	$-0.511888\pi$
$409$	9.53580	−	2.79996i	0.471515	−	0.138449i	0.508853	+	0.860853i	$0.330070\pi$
$410$	4.84220	−	10.6029i	0.239139	−	0.523642i
$411$	−0.527908	+	3.67168i	−0.0260398	+	0.181111i
$412$	−12.5818	+	8.08584i	−0.619862	+	0.398361i
$413$	−1.20739			−0.0594119
$414$	−3.73746	+	3.00523i	−0.183686	+	0.147699i
$415$	4.94070			0.242529
$416$	−5.21881	+	3.35393i	−0.255873	+	0.164440i
$417$	1.29500	−	9.00695i	0.0634166	−	0.441072i
$418$	−0.294649	+	0.645191i	−0.0144117	+	0.0315573i
$419$	−23.8814	+	7.01221i	−1.16668	+	0.342569i	−0.807026	−	0.590516i	$-0.798924\pi$
$419$	−23.8814	+	7.01221i	−1.16668	+	0.342569i	−0.359657	+	0.933085i	$0.617106\pi$
$420$	0.463379	+	1.01466i	0.0226106	+	0.0495102i
$421$	4.18311	+	4.82756i	0.203872	+	0.235281i	0.848474	−	0.529238i	$-0.177522\pi$
$421$	4.18311	+	4.82756i	0.203872	+	0.235281i	−0.644601	+	0.764519i	$0.722977\pi$
$422$	−3.69453	−	25.6960i	−0.179847	−	1.25086i
$423$	9.80122	+	2.87790i	0.476552	+	0.139928i
$424$	−1.51978	+	1.75392i	−0.0738069	+	0.0851777i
$425$	3.32584	+	2.13739i	0.161327	+	0.103678i
$426$	−8.18185	−	5.25816i	−0.396412	−	0.254758i
$427$	5.40001	−	6.23195i	0.261325	−	0.301585i
$428$	10.8026	+	3.17193i	0.522163	+	0.153321i
$429$	0.322815	+	2.24522i	0.0155856	+	0.108400i
$430$	5.46506	+	6.30701i	0.263549	+	0.304151i
$431$	−0.224164	−	0.490851i	−0.0107976	−	0.0236434i	0.904156	−	0.427202i	$-0.140501\pi$
$431$	−0.224164	−	0.490851i	−0.0107976	−	0.0236434i	−0.914954	+	0.403558i	$0.867773\pi$
$432$	−0.959493	+	0.281733i	−0.0461636	+	0.0135549i
$433$	−0.728751	+	1.59574i	−0.0350216	+	0.0766865i	−0.926334	−	0.376703i	$-0.877058\pi$
$433$	−0.728751	+	1.59574i	−0.0350216	+	0.0766865i	0.891313	+	0.453389i	$0.149785\pi$
$434$	−0.0761223	+	0.529442i	−0.00365399	+	0.0254140i
$435$	−4.12690	+	2.65220i	−0.197870	+	0.127163i
$436$	−8.85157			−0.423913
$437$	−0.342016	+	9.29682i	−0.0163608	+	0.444727i
$438$	−2.03065			−0.0970283
$439$	11.1824	−	7.18650i	0.533707	−	0.342993i	−0.245866	−	0.969304i	$-0.579072\pi$
$439$	11.1824	−	7.18650i	0.533707	−	0.342993i	0.779573	+	0.626311i	$0.215436\pi$
$440$	0.0520365	−	0.361922i	0.00248074	−	0.0172540i
$441$	−2.39102	+	5.23561i	−0.113858	+	0.249315i
$442$	23.5321	−	6.90965i	1.11931	−	0.328659i
$443$	−13.6816	−	29.9584i	−0.650031	−	1.42337i	−0.891527	−	0.452967i	$-0.850366\pi$
$443$	−13.6816	−	29.9584i	−0.650031	−	1.42337i	0.241497	−	0.970402i	$-0.422362\pi$
$444$	−4.69440	−	5.41762i	−0.222786	−	0.257109i
$445$	1.60617	+	11.1712i	0.0761398	+	0.529564i
$446$	10.9787	+	3.22364i	0.519856	+	0.152644i
$447$	−1.76564	+	2.03766i	−0.0835121	+	0.0963781i
$448$	−0.938384	−	0.603063i	−0.0443345	−	0.0284921i
$449$	35.5362	+	22.8377i	1.67706	+	1.07778i	0.882007	+	0.471237i	$0.156192\pi$
$449$	35.5362	+	22.8377i	1.67706	+	1.07778i	0.795051	+	0.606543i	$0.207444\pi$
$450$	−0.654861	+	0.755750i	−0.0308704	+	0.0356264i
$451$	4.08941	+	1.20076i	0.192563	+	0.0565415i
$452$	0.988201	+	6.87309i	0.0464811	+	0.323283i
$453$	−11.5141	−	13.2880i	−0.540981	−	0.624326i
$454$	5.75002	+	12.5908i	0.269862	+	0.590914i
$455$	6.63958	−	1.94956i	0.311268	−	0.0913966i
$456$	−0.805836	+	1.76453i	−0.0377367	+	0.0826319i
$457$	1.49561	−	10.4022i	0.0699619	−	0.486596i	−0.924473	−	0.381247i	$-0.875495\pi$
$457$	1.49561	−	10.4022i	0.0699619	−	0.486596i	0.994435	−	0.105349i	$-0.0335960\pi$
$458$	3.14340	−	2.02014i	0.146881	−	0.0943948i
$459$	3.95343			0.184530
$460$	−1.18106	−	4.64813i	−0.0550671	−	0.216720i
$461$	5.26503			0.245217			0.122608	−	0.992455i	$-0.460874\pi$
$461$	5.26503			0.245217			0.122608	+	0.992455i	$0.460874\pi$
$462$	−0.343114	+	0.220506i	−0.0159631	+	0.0102589i
$463$	−3.98399	+	27.7093i	−0.185152	+	1.28776i	0.659199	+	0.751969i	$0.270896\pi$
$463$	−3.98399	+	27.7093i	−0.185152	+	1.28776i	−0.844351	+	0.535791i	$0.820013\pi$
$464$	2.03788	−	4.46234i	0.0946063	−	0.207159i
$465$	−0.460097	+	0.135097i	−0.0213365	+	0.00626496i
$466$	−7.40326	−	16.2109i	−0.342949	−	0.750954i
$467$	16.6499	+	19.2150i	0.770466	+	0.889165i	0.996383	−	0.0849817i	$-0.0270832\pi$
$467$	16.6499	+	19.2150i	0.770466	+	0.889165i	−0.225917	+	0.974147i	$0.572538\pi$
$468$	0.882867	+	6.14047i	0.0408105	+	0.283843i
$469$	−3.84587	−	1.12925i	−0.177586	−	0.0521439i
$470$	−6.68940	+	7.71998i	−0.308559	+	0.356096i
$471$	−10.5872	−	6.80399i	−0.487833	−	0.313511i
$472$	0.910587	+	0.585199i	0.0419132	+	0.0269360i
$473$	−1.99826	+	2.30612i	−0.0918803	+	0.106036i
$474$	12.5678	+	3.69025i	0.577260	+	0.169499i
$475$	0.276067	+	1.92009i	0.0126668	+	0.0880997i
$476$	2.88787	+	3.33278i	0.132365	+	0.152758i
$477$	0.964080	+	2.11104i	0.0441422	+	0.0966579i
$478$	24.3595	−	7.15260i	1.11418	−	0.327152i
$479$	−2.73806	+	5.99551i	−0.125105	+	0.273942i	−0.961813	−	0.273708i	$-0.911750\pi$
$479$	−2.73806	+	5.99551i	−0.125105	+	0.273942i	0.836708	+	0.547649i	$0.184477\pi$
$480$	0.142315	−	0.989821i	0.00649575	−	0.0451790i
$481$	−37.4113	+	24.0428i	−1.70581	+	1.09626i
$482$	16.9565			0.772346
$483$	−3.05568	+	4.39096i	−0.139038	+	0.199796i
$484$	−10.8663			−0.493923
$485$	−14.8668	+	9.55429i	−0.675065	+	0.433838i
$486$	−0.142315	+	0.989821i	−0.00645553	+	0.0448992i
$487$	5.26780	−	11.5349i	0.238707	−	0.522695i	−0.751926	−	0.659247i	$-0.770875\pi$
$487$	5.26780	−	11.5349i	0.238707	−	0.522695i	0.990633	+	0.136553i	$0.0436023\pi$
$488$	−7.09306	+	2.08271i	−0.321088	+	0.0942799i
$489$	0.916615	+	2.00711i	0.0414507	+	0.0907645i
$490$	−3.76921	−	4.34991i	−0.170276	−	0.196509i
$491$	−5.40194	−	37.5713i	−0.243786	−	1.69557i	−0.632783	−	0.774330i	$-0.718087\pi$
$491$	−5.40194	−	37.5713i	−0.243786	−	1.69557i	0.388997	−	0.921239i	$-0.372822\pi$
$492$	11.1841	+	3.28396i	0.504220	+	0.148052i
$493$	−12.7005	+	14.6571i	−0.572001	+	0.660124i
$494$	10.1236	+	6.50606i	0.455483	+	0.292721i
$495$	−0.307599	−	0.197682i	−0.0138256	−	0.00888514i
$496$	0.314020	−	0.362398i	0.0140999	−	0.0162721i
$497$	−10.4093	−	3.05644i	−0.466920	−	0.137100i
$498$	0.703135	+	4.89041i	0.0315082	+	0.219144i
$499$	1.57621	+	1.81905i	0.0705610	+	0.0814317i	0.789932	−	0.613194i	$-0.210116\pi$
$499$	1.57621	+	1.81905i	0.0705610	+	0.0814317i	−0.719372	+	0.694626i	$0.755570\pi$
$500$	−0.415415	−	0.909632i	−0.0185779	−	0.0406800i
$501$	−1.10445	+	0.324295i	−0.0493431	+	0.0144884i
$502$	−1.28353	+	2.81053i	−0.0572866	+	0.125440i
$503$	−1.92833	+	13.4119i	−0.0859802	+	0.598005i	0.900590	+	0.434669i	$0.143135\pi$
$503$	−1.92833	+	13.4119i	−0.0859802	+	0.598005i	−0.986570	+	0.163336i	$0.947774\pi$
$504$	−0.938384	+	0.603063i	−0.0417990	+	0.0268626i
$505$	−8.93133			−0.397439
$506$	1.62080	−	0.669324i	0.0720534	−	0.0297551i
$507$	25.4848			1.13182
$508$	−9.76760	+	6.27726i	−0.433367	+	0.278508i
$509$	1.46996	−	10.2238i	0.0651547	−	0.453161i	−0.930962	−	0.365116i	$-0.881029\pi$
$509$	1.46996	−	10.2238i	0.0651547	−	0.453161i	0.996117	−	0.0880443i	$-0.0280617\pi$
$510$	−1.64231	+	3.59617i	−0.0727229	+	0.159241i
$511$	−2.17336	+	0.638155i	−0.0961436	+	0.0282303i
$512$	0.415415	+	0.909632i	0.0183589	+	0.0402004i
$513$	1.27032	+	1.46603i	0.0560860	+	0.0647267i
$514$	3.02511	+	21.0401i	0.133432	+	0.928040i
$515$	−14.3502	−	4.21360i	−0.632346	−	0.185673i
$516$	−5.46506	+	6.30701i	−0.240586	+	0.277651i
$517$	−3.14213	−	2.01932i	−0.138191	−	0.0888096i
$518$	−6.72685	−	4.32308i	−0.295561	−	0.189945i
$519$	9.41987	−	10.8711i	0.413487	−	0.477189i
$520$	−5.95233	−	1.74776i	−0.261027	−	0.0766444i
$521$	3.72906	+	25.9362i	0.163373	+	1.13628i	0.892218	+	0.451605i	$0.149148\pi$
$521$	3.72906	+	25.9362i	0.163373	+	1.13628i	−0.728845	+	0.684679i	$0.759942\pi$
$522$	−3.21252	−	3.70745i	−0.140608	−	0.162271i
$523$	15.8551	+	34.7178i	0.693295	+	1.51810i	0.847917	+	0.530130i	$0.177857\pi$
$523$	15.8551	+	34.7178i	0.693295	+	1.51810i	−0.154622	+	0.987974i	$0.549416\pi$
$524$	8.72803	−	2.56278i	0.381286	−	0.111956i
$525$	−0.463379	+	1.01466i	−0.0202235	+	0.0442833i
$526$	1.62779	−	11.3215i	0.0709750	−	0.493642i
$527$	−1.59481	+	1.02492i	−0.0694710	+	0.0446463i
$528$	0.365644			0.0159126
$529$	16.2983	−	16.2286i	0.708621	−	0.705589i
$530$	−2.32076			−0.100808
$531$	0.910587	−	0.585199i	0.0395161	−	0.0253955i
$532$	−0.307942	+	2.14178i	−0.0133510	+	0.0928580i
$533$	30.0391	−	65.7766i	1.30114	−	2.84910i
$534$	−10.8289	+	3.17964i	−0.468611	+	0.137597i
$535$	4.67701	+	10.2412i	0.202205	+	0.442767i
$536$	2.35314	+	2.71567i	0.101640	+	0.117299i
$537$	−2.64434	−	18.3918i	−0.114112	−	0.793663i
$538$	−4.54644	−	1.33496i	−0.196011	−	0.0575540i
$539$	1.37819	−	1.59052i	0.0593628	−	0.0685084i
$540$	−0.841254	−	0.540641i	−0.0362018	−	0.0232655i
$541$	10.3810	+	6.67147i	0.446315	+	0.286829i	0.744430	−	0.667701i	$-0.232722\pi$
$541$	10.3810	+	6.67147i	0.446315	+	0.286829i	−0.298115	+	0.954530i	$0.596358\pi$
$542$	11.2989	−	13.0396i	0.485329	−	0.560099i
$543$	15.0441	+	4.41734i	0.645603	+	0.189566i
$544$	−0.562632	−	3.91319i	−0.0241226	−	0.167777i
$545$	−5.79655	−	6.68957i	−0.248297	−	0.286550i
$546$	2.87462	+	6.29455i	0.123023	+	0.269382i
$547$	−24.6102	+	7.22622i	−1.05226	+	0.308971i	−0.761729	−	0.647896i	$-0.775649\pi$
$547$	−24.6102	+	7.22622i	−1.05226	+	0.308971i	−0.290529	+	0.956866i	$0.593831\pi$
$548$	1.54096	−	3.37422i	0.0658264	−	0.144140i
$549$	−1.05206	+	7.31727i	−0.0449010	+	0.312293i
$550$	0.307599	−	0.197682i	0.0131161	−	0.00842919i
$551$	−9.51615			−0.405402
$552$	4.43274	−	1.83053i	0.188670	−	0.0779127i
$553$	14.6108			0.621313
$554$	−3.56967	+	2.29409i	−0.151661	+	0.0974665i
$555$	1.02019	−	7.09557i	0.0433046	−	0.301190i
$556$	−3.78010	+	8.27727i	−0.160312	+	0.351034i
$557$	−30.5000	+	8.95561i	−1.29233	+	0.379461i	−0.854431	−	0.519564i	$-0.826094\pi$
$557$	−30.5000	+	8.95561i	−1.29233	+	0.379461i	−0.437896	+	0.899026i	$0.644276\pi$
$558$	−0.199200	−	0.436188i	−0.00843282	−	0.0184653i
$559$	33.9031	+	39.1263i	1.43395	+	1.65487i
$560$	−0.158746	−	1.10411i	−0.00670826	−	0.0466570i
$561$	−1.38699	−	0.407258i	−0.0585589	−	0.0171944i
$562$	11.4675	−	13.2342i	0.483728	−	0.558252i
$563$	2.23112	+	1.43385i	0.0940304	+	0.0604296i	0.586811	−	0.809724i	$-0.300383\pi$
$563$	2.23112	+	1.43385i	0.0940304	+	0.0604296i	−0.492781	+	0.870154i	$0.664020\pi$
$564$	−8.59341	−	5.52265i	−0.361848	−	0.232545i
$565$	−4.54720	+	5.24775i	−0.191302	+	0.220774i
$566$	19.4359	+	5.70690i	0.816953	+	0.239879i
$567$	0.158746	+	1.10411i	0.00666672	+	0.0463681i
$568$	6.36903	+	7.35026i	0.267239	+	0.308410i
$569$	−3.32089	−	7.27173i	−0.139219	−	0.304847i	0.827161	−	0.561965i	$-0.189954\pi$
$569$	−3.32089	−	7.27173i	−0.139219	−	0.304847i	−0.966380	+	0.257118i	$0.917227\pi$
$570$	−1.86126	+	0.546514i	−0.0779594	+	0.0228910i
$571$	−15.9468	+	34.9187i	−0.667353	+	1.46130i	0.208154	+	0.978096i	$0.433254\pi$
$571$	−15.9468	+	34.9187i	−0.667353	+	1.46130i	−0.875508	+	0.483204i	$0.839473\pi$
$572$	0.322815	−	2.24522i	0.0134976	−	0.0938776i
$573$	−16.4767	+	10.5890i	−0.688325	+	0.442360i
$574$	13.0021			0.542698
$575$	2.73939	−	3.93646i	0.114241	−	0.164162i
$576$	1.00000			0.0416667
$577$	−27.1579	+	17.4533i	−1.13060	+	0.726592i	−0.965685	−	0.259716i	$-0.916371\pi$
$577$	−27.1579	+	17.4533i	−1.13060	+	0.726592i	−0.164914	+	0.986308i	$0.552735\pi$
$578$	0.195025	−	1.35643i	0.00811198	−	0.0564201i
$579$	−6.64328	+	14.5468i	−0.276085	+	0.604543i
$580$	4.70694	−	1.38208i	0.195445	−	0.0573879i
$581$	2.28941	+	5.01312i	0.0949809	+	0.207979i
$582$	−11.5728	−	13.3557i	−0.479708	−	0.553613i
$583$	−0.120765	−	0.839936i	−0.00500156	−	0.0347866i
$584$	1.94840	+	0.572101i	0.0806252	+	0.0236737i
$585$	−4.06250	+	4.68838i	−0.167964	+	0.193841i
$586$	−18.1055	−	11.6357i	−0.747930	−	0.480666i
$587$	−0.0700101	−	0.0449928i	−0.00288963	−	0.00185705i	0.539195	−	0.842181i	$-0.318729\pi$
$587$	−0.0700101	−	0.0449928i	−0.00288963	−	0.00185705i	−0.542085	+	0.840324i	$0.682365\pi$
$588$	3.76921	−	4.34991i	0.155440	−	0.179387i
$589$	−0.892511	−	0.262065i	−0.0367753	−	0.0107982i
$590$	0.154044	+	1.07140i	0.00634189	+	0.0441088i
$591$	−3.56175	−	4.11048i	−0.146511	−	0.169082i
$592$	2.97792	+	6.52073i	0.122392	+	0.268001i
$593$	−23.9151	+	7.02211i	−0.982075	+	0.288363i	−0.733081	−	0.680141i	$-0.761918\pi$
$593$	−23.9151	+	7.02211i	−0.982075	+	0.288363i	−0.248995	+	0.968505i	$0.580100\pi$
$594$	0.151894	−	0.332601i	0.00623228	−	0.0136468i
$595$	−0.627593	+	4.36501i	−0.0257288	+	0.178948i
$596$	2.26820	−	1.45768i	0.0929090	−	0.0597090i
$597$	−5.15363			−0.210924
$598$	−7.32683	−	28.8352i	−0.299616	−	1.17916i
$599$	0.629631			0.0257260			0.0128630	−	0.999917i	$-0.495905\pi$
$599$	0.629631			0.0257260			0.0128630	+	0.999917i	$0.495905\pi$
$600$	0.841254	−	0.540641i	0.0343440	−	0.0220716i
$601$	−1.80103	+	12.5264i	−0.0734656	+	0.510964i	0.919549	+	0.392975i	$0.128554\pi$
$601$	−1.80103	+	12.5264i	−0.0734656	+	0.510964i	−0.993015	+	0.117989i	$0.962355\pi$
$602$	−3.86707	+	8.46770i	−0.157610	+	0.345118i
$603$	3.44779	−	1.01236i	0.140405	−	0.0412266i
$604$	7.30406	+	15.9937i	0.297198	+	0.650773i
$605$	−7.11592	−	8.21221i	−0.289303	−	0.333874i
$606$	−1.27106	−	8.84042i	−0.0516333	−	0.359117i
$607$	−29.9619	−	8.79760i	−1.21611	−	0.357084i	−0.390122	−	0.920763i	$-0.627567\pi$
$607$	−29.9619	−	8.79760i	−1.21611	−	0.357084i	−0.825993	+	0.563680i	$0.809385\pi$
$608$	1.27032	−	1.46603i	0.0515183	−	0.0594553i
$609$	−4.60339	−	2.95842i	−0.186539	−	0.119881i
$610$	−6.21898	−	3.99669i	−0.251799	−	0.161821i
$611$	−41.4985	+	47.8918i	−1.67885	+	1.93750i
$612$	−3.79329	−	1.11381i	−0.153335	−	0.0450231i
$613$	−1.35236	−	9.40589i	−0.0546214	−	0.379900i	−0.998735	−	0.0502804i	$-0.983988\pi$
$613$	−1.35236	−	9.40589i	−0.0546214	−	0.379900i	0.944114	−	0.329620i	$-0.106921\pi$
$614$	−11.2881	−	13.0271i	−0.455550	−	0.525733i
$615$	4.84220	+	10.6029i	0.195256	+	0.427552i
$616$	0.391340	−	0.114908i	0.0157675	−	0.00462976i
$617$	18.5120	−	40.5357i	0.745267	−	1.63191i	−0.0294251	−	0.999567i	$-0.509368\pi$
$617$	18.5120	−	40.5357i	0.745267	−	1.63191i	0.774692	−	0.632339i	$-0.217905\pi$
$618$	2.12847	−	14.8038i	0.0856194	−	0.595496i
$619$	−32.9628	+	21.1839i	−1.32489	+	0.851453i	−0.995684	−	0.0928064i	$-0.970416\pi$
$619$	−32.9628	+	21.1839i	−1.32489	+	0.851453i	−0.329203	+	0.944259i	$0.606780\pi$
$620$	0.479521			0.0192580
$621$	0.176312	−	4.79259i	0.00707515	−	0.192320i
$622$	−16.8044			−0.673795
$623$	−10.5906	+	6.80619i	−0.424305	+	0.272684i
$624$	0.882867	−	6.14047i	0.0353429	−	0.245816i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−16.6348	+	4.88442i	−0.664861	+	0.195221i
$627$	−0.294649	−	0.645191i	−0.0117671	−	0.0257664i
$628$	8.24146	+	9.51115i	0.328870	+	0.379536i
$629$	−4.03325	−	28.0519i	−0.160816	−	1.11850i
$630$	−1.07028	−	0.314261i	−0.0426408	−	0.0125205i
$631$	24.4286	−	28.1921i	0.972488	−	1.12231i	−0.0199790	−	0.999800i	$-0.506360\pi$
$631$	24.4286	−	28.1921i	0.972488	−	1.12231i	0.992467	−	0.122511i	$-0.0390946\pi$
$632$	−11.0191	−	7.08154i	−0.438316	−	0.281689i
$633$	21.8391	+	14.0352i	0.868028	+	0.557847i
$634$	6.14303	−	7.08944i	0.243971	−	0.281557i
$635$	−11.1405	−	3.27113i	−0.442096	−	0.129811i
$636$	−0.330279	−	2.29714i	−0.0130964	−	0.0910876i
$637$	−23.3828	−	26.9851i	−0.926459	−	1.06919i
$638$	0.745139	+	1.63163i	0.0295003	+	0.0645967i
$639$	9.33182	−	2.74007i	0.369161	−	0.108395i
$640$	−0.415415	+	0.909632i	−0.0164207	+	0.0359564i
$641$	−5.95025	+	41.3849i	−0.235021	+	1.63460i	0.440848	+	0.897582i	$0.354678\pi$
$641$	−5.95025	+	41.3849i	−0.235021	+	1.63460i	−0.675869	+	0.737022i	$0.736231\pi$
$642$	−9.47138	+	6.08689i	−0.373806	+	0.240230i
$643$	−11.4610			−0.451977			−0.225988	−	0.974130i	$-0.572561\pi$
$643$	−11.4610			−0.451977			−0.225988	+	0.974130i	$0.572561\pi$
$644$	4.16898	−	3.35221i	0.164281	−	0.132096i
$645$	−8.34538			−0.328599
$646$	−6.45157	+	4.14617i	−0.253834	+	0.163129i
$647$	1.43253	−	9.96346i	0.0563186	−	0.391704i	−0.942092	−	0.335353i	$-0.891144\pi$
$647$	1.43253	−	9.96346i	0.0563186	−	0.391704i	0.998411	−	0.0563510i	$-0.0179466\pi$
$648$	0.415415	−	0.909632i	0.0163190	−	0.0357337i
$649$	−0.379747	+	0.111504i	−0.0149064	+	0.00437691i
$650$	−2.57708	−	5.64301i	−0.101081	−	0.221337i
$651$	−0.350276	−	0.404240i	−0.0137284	−	0.0158434i
$652$	−0.314018	−	2.18404i	−0.0122979	−	0.0855338i
$653$	33.5101	+	9.83947i	1.31135	+	0.385048i	0.861365	−	0.507986i	$-0.169610\pi$
$653$	33.5101	+	9.83947i	1.31135	+	0.385048i	0.449988	+	0.893034i	$0.351428\pi$
$654$	5.79655	−	6.68957i	0.226663	−	0.261583i
$655$	7.65247	+	4.91794i	0.299007	+	0.192160i
$656$	−9.80590	−	6.30187i	−0.382856	−	0.246047i
$657$	1.32979	−	1.53466i	0.0518802	−	0.0598729i
$658$	−10.9329	−	3.21018i	−0.426208	−	0.125146i
$659$	−4.15733	−	28.9149i	−0.161947	−	1.12636i	−0.894959	−	0.446149i	$-0.852795\pi$
$659$	−4.15733	−	28.9149i	−0.161947	−	1.12636i	0.733012	−	0.680216i	$-0.238114\pi$
$660$	0.239446	+	0.276335i	0.00932041	+	0.0107563i
$661$	5.60869	+	12.2813i	0.218153	+	0.477688i	0.986792	−	0.161995i	$-0.0517928\pi$
$661$	5.60869	+	12.2813i	0.218153	+	0.477688i	−0.768639	+	0.639683i	$0.779066\pi$
$662$	7.12206	−	2.09122i	0.276807	−	0.0812778i
$663$	−10.1883	+	22.3092i	−0.395680	+	0.866419i
$664$	0.703135	−	4.89041i	0.0272869	−	0.189785i
$665$	−1.82031	+	1.16984i	−0.0705886	+	0.0453645i
$666$	7.16854			0.277775
$667$	17.2019	+	16.0500i	0.666059	+	0.621457i
$668$	1.15107			0.0445364
$669$	−9.62578	+	6.18611i	−0.372154	+	0.239169i
$670$	−0.511387	+	3.55677i	−0.0197566	+	0.137410i
$671$	1.12288	−	2.45876i	0.0433482	−	0.0949193i
$672$	1.07028	−	0.314261i	0.0412868	−	0.0121229i
$673$	−8.22529	−	18.0109i	−0.317062	−	0.694268i	0.682259	−	0.731110i	$-0.260997\pi$
$673$	−8.22529	−	18.0109i	−0.317062	−	0.694268i	−0.999321	+	0.0368420i	$0.988270\pi$
$674$	3.64333	+	4.20463i	0.140336	+	0.161956i
$675$	−0.142315	−	0.989821i	−0.00547770	−	0.0380982i
$676$	−24.4525	−	7.17991i	−0.940482	−	0.276150i
$677$	30.2997	−	34.9677i	1.16451	−	1.34392i	0.236381	−	0.971661i	$-0.424039\pi$
$677$	30.2997	−	34.9677i	1.16451	−	1.34392i	0.928130	−	0.372256i	$-0.121416\pi$
$678$	−5.84147	−	3.75408i	−0.224340	−	0.144175i
$679$	−16.5833	−	10.6574i	−0.636408	−	0.408995i
$680$	2.58895	−	2.98780i	0.0992816	−	0.114577i
$681$	−13.2809	−	3.89963i	−0.508927	−	0.149434i
$682$	0.0249526	+	0.173549i	0.000955485	+	0.00664554i
$683$	−19.7921	−	22.8413i	−0.757324	−	0.873998i	0.237933	−	0.971282i	$-0.423530\pi$
$683$	−19.7921	−	22.8413i	−0.757324	−	0.873998i	−0.995257	+	0.0972833i	$0.968985\pi$
$684$	−0.805836	−	1.76453i	−0.0308119	−	0.0674686i
$685$	3.55918	−	1.04507i	0.135989	−	0.0399300i
$686$	5.91074	−	12.9427i	0.225673	−	0.494155i
$687$	−0.531768	+	3.69853i	−0.0202882	+	0.141108i
$688$	7.02058	−	4.51185i	0.267657	−	0.172013i
$689$	−14.3971			−0.548487
$690$	4.28625	+	2.15129i	0.163175	+	0.0818983i
$691$	−35.1356			−1.33662			−0.668311	−	0.743882i	$-0.732983\pi$
$691$	−35.1356			−1.33662			−0.668311	+	0.743882i	$0.732983\pi$
$692$	−12.1011	+	7.77687i	−0.460013	+	0.295632i
$693$	0.0580447	−	0.403709i	0.00220493	−	0.0153357i
$694$	−7.15643	+	15.6704i	−0.271654	+	0.594840i
$695$	−8.73098	+	2.56365i	−0.331185	+	0.0972447i
$696$	2.03788	+	4.46234i	0.0772457	+	0.169145i
$697$	30.1775	+	34.8267i	1.14306	+	1.31916i
$698$	0.968478	+	6.73591i	0.0366574	+	0.254958i
$699$	17.0995	+	5.02085i	0.646761	+	0.189906i
$700$	0.730471	−	0.843008i	0.0276092	−	0.0318627i
$701$	2.86253	+	1.83964i	0.108116	+	0.0694822i	0.593582	−	0.804774i	$-0.297713\pi$
$701$	2.86253	+	1.83964i	0.108116	+	0.0694822i	−0.485465	+	0.874256i	$0.661350\pi$
$702$	−5.21881	−	3.35393i	−0.196971	−	0.126586i
$703$	9.10634	−	10.5093i	0.343452	−	0.396365i
$704$	−0.350833	−	0.103014i	−0.0132225	−	0.00388248i
$705$	−1.45375	−	10.1110i	−0.0547513	−	0.380803i
$706$	−16.6221	−	19.1829i	−0.625579	−	0.721957i
$707$	−4.13859	−	9.06224i	−0.155648	−	0.340821i
$708$	−1.03857	+	0.304952i	−0.0390319	+	0.0114608i
$709$	−9.68883	+	21.2156i	−0.363872	+	0.796768i	0.635817	+	0.771839i	$0.280663\pi$
$709$	−9.68883	+	21.2156i	−0.363872	+	0.796768i	−0.999689	+	0.0249285i	$0.992064\pi$
$710$	−1.38412	+	9.62679i	−0.0519452	+	0.361287i
$711$	−11.0191	+	7.08154i	−0.413248	+	0.265579i
$712$	11.2860			0.422962
$713$	1.17135	+	1.97903i	0.0438673	+	0.0741154i
$714$	−4.40989			−0.165036
$715$	1.90823	−	1.22634i	0.0713636	−	0.0458626i
$716$	−2.64434	+	18.3918i	−0.0988235	+	0.687333i
$717$	−10.5465	+	23.0937i	−0.393867	+	0.862449i
$718$	13.7441	−	4.03563i	0.512926	−	0.150609i
$719$	−10.5119	−	23.0179i	−0.392029	−	0.858423i	−0.998017	−	0.0629495i	$-0.979949\pi$
$719$	−10.5119	−	23.0179i	−0.392029	−	0.858423i	0.605988	−	0.795474i	$-0.292778\pi$
$720$	0.654861	+	0.755750i	0.0244052	+	0.0281651i
$721$	−2.37422	−	16.5130i	−0.0884205	−	0.614978i
$722$	14.6198	+	4.29277i	0.544094	+	0.159760i
$723$	−11.1041	+	12.8148i	−0.412967	+	0.476589i
$724$	−13.1902	−	8.47681i	−0.490209	−	0.315038i
$725$	4.12690	+	2.65220i	0.153269	+	0.0985001i
$726$	7.11592	−	8.21221i	0.264096	−	0.304784i
$727$	18.4056	+	5.40436i	0.682625	+	0.200437i	0.604617	−	0.796516i	$-0.293326\pi$
$727$	18.4056	+	5.40436i	0.682625	+	0.200437i	0.0780074	+	0.996953i	$0.475144\pi$
$728$	−0.984802	−	6.84945i	−0.0364992	−	0.253857i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	0.843563	+	1.84715i	0.0312217	+	0.0683659i
$731$	−31.6564	+	9.29517i	−1.17086	+	0.343794i
$732$	3.07096	−	6.72447i	0.113506	−	0.248543i
$733$	−7.00203	+	48.7002i	−0.258626	+	1.79878i	0.284017	+	0.958819i	$0.408333\pi$
$733$	−7.00203	+	48.7002i	−0.258626	+	1.79878i	−0.542643	+	0.839964i	$0.682576\pi$
$734$	16.0819	−	10.3352i	0.593593	−	0.381479i
$735$	5.75575			0.212304
$736$	−4.76890	+	0.507539i	−0.175784	+	0.0187081i
$737$	−1.31388			−0.0483976
$738$	−9.80590	+	6.30187i	−0.360960	+	0.231975i
$739$	3.02329	−	21.0275i	0.111214	−	0.773508i	−0.855529	−	0.517756i	$-0.826768\pi$
$739$	3.02329	−	21.0275i	0.111214	−	0.773508i	0.966742	−	0.255753i	$-0.0823232\pi$
$740$	−2.97792	+	6.52073i	−0.109470	+	0.239707i
$741$	−11.5465	+	3.39036i	−0.424172	+	0.124548i
$742$	−1.07539	−	2.35478i	−0.0394789	−	0.0864468i
$743$	−19.4673	−	22.4665i	−0.714187	−	0.824215i	0.276409	−	0.961040i	$-0.410856\pi$
$743$	−19.4673	−	22.4665i	−0.714187	−	0.824215i	−0.990595	+	0.136825i	$0.956310\pi$
$744$	0.0682430	+	0.474640i	0.00250191	+	0.0174012i
$745$	2.58700	+	0.759611i	0.0947802	+	0.0278300i
$746$	−16.9347	+	19.5437i	−0.620023	+	0.715544i
$747$	−4.15638	−	2.67114i	−0.152074	−	0.0977320i
$748$	1.21607	+	0.781522i	0.0444640	+	0.0285753i
$749$	−8.22412	+	9.49114i	−0.300503	+	0.346799i
$750$	0.959493	+	0.281733i	0.0350357	+	0.0102874i
$751$	−4.73233	−	32.9141i	−0.172685	−	1.20105i	−0.873181	−	0.487395i	$-0.837947\pi$
$751$	−4.73233	−	32.9141i	−0.172685	−	1.20105i	0.700496	−	0.713656i	$-0.252962\pi$
$752$	6.68940	+	7.71998i	0.243937	+	0.281519i
$753$	−1.28353	−	2.81053i	−0.0467743	−	0.102422i
$754$	29.2001	−	8.57391i	1.06340	−	0.312243i
$755$	−7.30406	+	15.9937i	−0.265822	+	0.582069i
$756$	0.158746	−	1.10411i	0.00577355	−	0.0401559i
$757$	44.2065	−	28.4098i	1.60671	−	1.03257i	0.642917	−	0.765936i	$-0.277724\pi$
$757$	44.2065	−	28.4098i	1.60671	−	1.03257i	0.963797	−	0.266637i	$-0.0859123\pi$
$758$	−10.6465			−0.386700
$759$	−0.555559	+	1.66323i	−0.0201655	+	0.0603716i
$760$	1.93983			0.0703651
$761$	−36.3379	+	23.3530i	−1.31725	+	0.846544i	−0.994977	−	0.100103i	$-0.968083\pi$
$761$	−36.3379	+	23.3530i	−1.31725	+	0.846544i	−0.322271	+	0.946647i	$0.604446\pi$
$762$	1.65239	−	11.4926i	0.0598596	−	0.416333i
$763$	4.10163	−	8.98132i	0.148489	−	0.325145i
$764$	18.7926	−	5.51799i	0.679891	−	0.199634i
$765$	−1.64231	−	3.59617i	−0.0593780	−	0.130020i
$766$	4.71508	+	5.44149i	0.170363	+	0.196609i
$767$	0.955630	+	6.64655i	0.0345058	+	0.239993i
$768$	−0.959493	−	0.281733i	−0.0346227	−	0.0101661i
$769$	−12.3270	+	14.2261i	−0.444522	+	0.513006i	−0.933151	−	0.359486i	$-0.882952\pi$
$769$	−12.3270	+	14.2261i	−0.444522	+	0.513006i	0.488628	+	0.872492i	$0.337498\pi$
$770$	0.343114	+	0.220506i	0.0123650	+	0.00794649i
$771$	−17.8821	−	11.4921i	−0.644008	−	0.413879i
$772$	10.4725	−	12.0859i	0.376913	−	0.434981i
$773$	22.9779	+	6.74692i	0.826457	+	0.242670i	0.667495	−	0.744615i	$-0.267367\pi$
$773$	22.9779	+	6.74692i	0.826457	+	0.242670i	0.158963	+	0.987285i	$0.449185\pi$
$774$	−1.18767	−	8.26043i	−0.0426899	−	0.296915i
$775$	0.314020	+	0.362398i	0.0112799	+	0.0130177i
$776$	7.34128	+	16.0752i	0.263537	+	0.577065i
$777$	7.67231	−	2.25279i	0.275243	−	0.0808186i
$778$	8.32069	−	18.2198i	0.298311	−	0.653211i
$779$	−3.21792	+	22.3811i	−0.115294	+	0.801887i
$780$	5.21881	−	3.35393i	0.186864	−	0.120090i
$781$	−3.55617			−0.127250
$782$	18.6551	+	3.38641i	0.667106	+	0.121098i
$783$	4.90566			0.175314
$784$	−4.84204	+	3.11179i	−0.172930	+	0.111135i
$785$	−1.79104	+	12.4570i	−0.0639249	+	0.444608i
$786$	−3.77883	+	8.27447i	−0.134786	+	0.295141i
$787$	−12.9076	+	3.79002i	−0.460108	+	0.135100i	−0.503568	−	0.863955i	$-0.667980\pi$
$787$	−12.9076	+	3.79002i	−0.460108	+	0.135100i	0.0434609	+	0.999055i	$0.486162\pi$
$788$	2.25942	+	4.94744i	0.0804884	+	0.176245i
$789$	7.49027	+	8.64423i	0.266661	+	0.307743i
$790$	−1.86410	−	12.9651i	−0.0663217	−	0.461278i
$791$	−7.43175	−	2.18216i	−0.264242	−	0.0775886i
$792$	−0.239446	+	0.276335i	−0.00850833	+	0.00981914i
$793$	−38.5801	−	24.7940i	−1.37002	−	0.880459i
$794$	−8.88489	−	5.70997i	−0.315313	−	0.202639i
$795$	1.51978	−	1.75392i	0.0539009	−	0.0622050i
$796$	4.94487	+	1.45194i	0.175266	+	0.0514628i
$797$	2.61244	+	18.1699i	0.0925375	+	0.643612i	0.982318	+	0.187223i	$0.0599486\pi$
$797$	2.61244	+	18.1699i	0.0925375	+	0.643612i	−0.889780	+	0.456390i	$0.849142\pi$
$798$	−1.41699	−	1.63530i	−0.0501609	−	0.0578888i
$799$	−16.7762	−	36.7349i	−0.593501	−	1.29959i
$800$	−0.959493	+	0.281733i	−0.0339232	+	0.00996075i
$801$	4.68839	−	10.2661i	0.165656	−	0.362736i
$802$	2.17556	−	15.1313i	0.0768215	−	0.534306i
$803$	−0.624626	+	0.401423i	−0.0220426	+	0.0141659i
$804$	−3.59335			−0.126728
$805$	5.26354	+	0.955474i	0.185515	+	0.0336760i
$806$	2.97476			0.104782
$807$	3.98618	−	2.56176i	0.140320	−	0.0901782i
$808$	−1.27106	+	8.84042i	−0.0447157	+	0.311005i
$809$	−8.29583	+	18.1653i	−0.291666	+	0.638659i	−0.997572	−	0.0696466i	$-0.977813\pi$
$809$	−8.29583	+	18.1653i	−0.291666	+	0.638659i	0.705906	+	0.708306i	$0.250540\pi$
$810$	0.959493	−	0.281733i	0.0337131	−	0.00989907i
$811$	−3.20544	−	7.01894i	−0.112558	−	0.246468i	0.844967	−	0.534819i	$-0.179620\pi$
$811$	−3.20544	−	7.01894i	−0.112558	−	0.246468i	−0.957525	+	0.288351i	$0.906893\pi$
$812$	3.58344	+	4.13551i	0.125754	+	0.145128i
$813$	2.45548	+	17.0783i	0.0861175	+	0.598960i
$814$	−2.51496	−	0.738458i	−0.0881492	−	0.0258829i
$815$	1.44495	−	1.66756i	0.0506145	−	0.0584122i
$816$	3.32584	+	2.13739i	0.116428	+	0.0748235i
$817$	−13.6187	−	8.75224i	−0.476460	−	0.306202i
$818$	6.50825	−	7.51092i	0.227556	−	0.262613i
$819$	−6.63958	−	1.94956i	−0.232006	−	0.0681230i
$820$	−1.65886	−	11.5377i	−0.0579300	−	0.402912i
$821$	−8.59945	−	9.92430i	−0.300123	−	0.346360i	0.585578	−	0.810616i	$-0.300867\pi$
$821$	−8.59945	−	9.92430i	−0.300123	−	0.346360i	−0.885701	+	0.464255i	$0.846322\pi$
$822$	1.54096	+	3.37422i	0.0537470	+	0.117690i
$823$	37.6173	−	11.0454i	1.31126	−	0.385020i	0.449928	−	0.893065i	$-0.351450\pi$
$823$	37.6173	−	11.0454i	1.31126	−	0.385020i	0.861331	+	0.508045i	$0.169632\pi$
$824$	−6.21296	+	13.6045i	−0.216439	+	0.473935i
$825$	−0.0520365	+	0.361922i	−0.00181168	+	0.0126005i
$826$	−1.01572	+	0.652766i	−0.0353415	+	0.0227126i
$827$	−44.5002			−1.54742			−0.773712	−	0.633538i	$-0.781602\pi$
$827$	−44.5002			−1.54742			−0.773712	+	0.633538i	$0.781602\pi$
$828$	−1.51940	+	4.54878i	−0.0528027	+	0.158081i
$829$	−36.7595			−1.27671			−0.638355	−	0.769742i	$-0.720385\pi$
$829$	−36.7595			−1.27671			−0.638355	+	0.769742i	$0.720385\pi$
$830$	4.15638	−	2.67114i	0.144270	−	0.0927167i
$831$	0.603881	−	4.20009i	0.0209484	−	0.145699i
$832$	−2.57708	+	5.64301i	−0.0893440	+	0.195636i
$833$	21.8332	−	6.41081i	0.756476	−	0.222122i
$834$	−3.78010	−	8.27727i	−0.130894	−	0.286618i
$835$	0.753793	+	0.869924i	0.0260861	+	0.0301049i
$836$	0.100942	+	0.702068i	0.00349116	+	0.0242815i
$837$	0.460097	+	0.135097i	0.0159033	+	0.00466962i
$838$	−16.2992	+	18.8103i	−0.563048	+	0.649792i
$839$	18.2225	+	11.7109i	0.629111	+	0.404305i	0.815980	−	0.578080i	$-0.196198\pi$
$839$	18.2225	+	11.7109i	0.629111	+	0.404305i	−0.186869	+	0.982385i	$0.559834\pi$
$840$	0.938384	+	0.603063i	0.0323773	+	0.0208077i
$841$	3.23144	−	3.72928i	0.111429	−	0.128596i
$842$	6.12903	+	1.79965i	0.211220	+	0.0620199i
$843$	2.49213	+	17.3332i	0.0858336	+	0.596985i
$844$	−17.0003	−	19.6194i	−0.585176	−	0.675329i
$845$	−10.5868	−	23.1818i	−0.364197	−	0.797479i
$846$	9.80122	−	2.87790i	0.336973	−	0.0989442i
$847$	5.03521	−	11.0256i	0.173012	−	0.378843i
$848$	−0.330279	+	2.29714i	−0.0113418	+	0.0788842i
$849$	−17.0408	+	10.9515i	−0.584839	+	0.375853i
$850$	3.95343			0.135602
$851$	−34.1860	+	3.63832i	−1.17188	+	0.124720i
$852$	−9.72578			−0.333200
$853$	−1.28590	+	0.826399i	−0.0440284	+	0.0282954i	−0.562470	−	0.826818i	$-0.690149\pi$
$853$	−1.28590	+	0.826399i	−0.0440284	+	0.0282954i	0.518441	+	0.855113i	$0.326512\pi$
$854$	1.17354	−	8.16212i	0.0401576	−	0.279302i
$855$	0.805836	−	1.76453i	0.0275590	−	0.0603458i
$856$	10.8026	−	3.17193i	0.369225	−	0.108414i
$857$	17.3019	+	37.8858i	0.591021	+	1.29416i	0.934823	+	0.355113i	$0.115558\pi$
$857$	17.3019	+	37.8858i	0.591021	+	1.29416i	−0.343802	+	0.939042i	$0.611715\pi$
$858$	1.48543	+	1.71428i	0.0507117	+	0.0585244i
$859$	−0.573566	−	3.98924i	−0.0195698	−	0.136111i	0.977694	−	0.210034i	$-0.0673573\pi$
$859$	−0.573566	−	3.98924i	−0.0195698	−	0.136111i	−0.997264	+	0.0739225i	$0.976448\pi$
$860$	8.00733	+	2.35116i	0.273048	+	0.0801740i
$861$	−8.51458	+	9.82635i	−0.290176	+	0.334881i
$862$	−0.453953	−	0.291738i	−0.0154617	−	0.00993662i
$863$	45.2847	+	29.1027i	1.54151	+	0.990669i	0.987403	+	0.158224i	$0.0505767\pi$
$863$	45.2847	+	29.1027i	1.54151	+	0.990669i	0.554108	+	0.832445i	$0.313060\pi$
$864$	−0.654861	+	0.755750i	−0.0222788	+	0.0257111i
$865$	−13.8019	−	4.05260i	−0.469278	−	0.137792i
$866$	0.249659	+	1.73642i	0.00848376	+	0.0590059i
$867$	0.897407	+	1.03566i	0.0304775	+	0.0351730i
$868$	0.222200	+	0.486550i	0.00754195	+	0.0165146i
$869$	4.59535	−	1.34932i	0.155887	−	0.0457725i
$870$	−2.03788	+	4.46234i	−0.0690907	+	0.151288i
$871$	−3.17245	+	22.0648i	−0.107494	+	0.747639i
$872$	−7.44641	+	4.78552i	−0.252167	+	0.162058i
$873$	17.6722			0.598112
$874$	4.73852	+	8.00589i	0.160283	+	0.270803i
$875$	1.11546			0.0377094
$876$	−1.70829	+	1.09785i	−0.0577179	+	0.0370930i
$877$	−4.79960	+	33.3820i	−0.162071	+	1.12723i	0.732650	+	0.680605i	$0.238283\pi$
$877$	−4.79960	+	33.3820i	−0.162071	+	1.12723i	−0.894722	+	0.446624i	$0.852626\pi$
$878$	5.52193	−	12.0913i	0.186356	−	0.408063i
$879$	20.6502	−	6.06345i	0.696515	−	0.204515i
$880$	−0.151894	−	0.332601i	−0.00512034	−	0.0112120i
$881$	19.1279	+	22.0748i	0.644435	+	0.743718i	0.980152	−	0.198245i	$-0.0635242\pi$
$881$	19.1279	+	22.0748i	0.644435	+	0.743718i	−0.335717	+	0.941963i	$0.608979\pi$
$882$	0.819129	+	5.69716i	0.0275815	+	0.191834i
$883$	14.1779	+	4.16302i	0.477126	+	0.140097i	0.511448	−	0.859314i	$-0.329109\pi$
$883$	14.1779	+	4.16302i	0.477126	+	0.140097i	−0.0343227	+	0.999411i	$0.510927\pi$
$884$	16.0608	−	18.5352i	0.540184	−	0.623406i
$885$	−0.910587	−	0.585199i	−0.0306091	−	0.0196712i
$886$	−27.7064	−	17.8058i	−0.930815	−	0.598199i
$887$	−3.95102	+	4.55972i	−0.132662	+	0.153100i	−0.818194	−	0.574942i	$-0.805024\pi$
$887$	−3.95102	+	4.55972i	−0.132662	+	0.153100i	0.685532	+	0.728043i	$0.259570\pi$
$888$	−6.87816	−	2.01961i	−0.230816	−	0.0677737i
$889$	−1.84317	−	12.8195i	−0.0618179	−	0.429953i
$890$	7.39078	+	8.52941i	0.247740	+	0.285907i
$891$	0.151894	+	0.332601i	0.00508864	+	0.0111426i
$892$	10.9787	−	3.22364i	0.367594	−	0.107935i
$893$	8.23161	−	18.0247i	0.275460	−	0.603174i
$894$	−0.383711	+	2.66877i	−0.0128332	+	0.0892570i
$895$	−15.6312	+	10.0456i	−0.522495	+	0.335787i
$896$	−1.11546			−0.0372649
$897$	26.5902	+	13.3458i	0.887823	+	0.445603i
$898$	42.2420			1.40963
$899$	−1.97894	+	1.27178i	−0.0660012	+	0.0424164i
$900$	−0.142315	+	0.989821i	−0.00474383	+	0.0329940i
$901$	3.81143	−	8.34586i	0.126977	−	0.278041i
$902$	4.08941	−	1.20076i	0.136162	−	0.0399809i
$903$	−3.86707	−	8.46770i	−0.128688	−	0.281787i
$904$	4.54720	+	5.24775i	0.151238	+	0.174538i
$905$	−2.23138	−	15.5196i	−0.0741736	−	0.515889i
$906$	−16.8704	−	4.95358i	−0.560480	−	0.164572i
$907$	25.8447	−	29.8264i	0.858160	−	0.990370i	−0.141839	−	0.989890i	$-0.545302\pi$
$907$	25.8447	−	29.8264i	0.858160	−	0.990370i	1.00000		0.000480285i	$-0.000152879\pi$
$908$	11.6443	+	7.48334i	0.386430	+	0.248343i
$909$	7.51351	+	4.82864i	0.249207	+	0.160156i
$910$	4.53156	−	5.22970i	0.150220	−	0.173363i
$911$	−34.8509	−	10.2332i	−1.15466	−	0.339040i	−0.352307	−	0.935885i	$-0.614603\pi$
$911$	−34.8509	−	10.2332i	−1.15466	−	0.339040i	−0.802357	+	0.596845i	$0.796421\pi$
$912$	0.276067	+	1.92009i	0.00914149	+	0.0635805i
$913$	1.18303	+	1.36529i	0.0391525	+	0.0451844i
$914$	−4.36568	−	9.55950i	−0.144404	−	0.316200i
$915$	7.09306	−	2.08271i	0.234489	−	0.0688523i
$916$	1.55222	−	3.39890i	0.0512869	−	0.112303i
$917$	−1.44404	+	10.0435i	−0.0476863	+	0.331666i
$918$	3.32584	−	2.13739i	0.109769	−	0.0705443i
$919$	29.0778			0.959187			0.479594	−	0.877491i	$-0.340784\pi$
$919$	29.0778			0.959187			0.479594	+	0.877491i	$0.340784\pi$
$920$	−3.50654	−	3.27173i	−0.115607	−	0.107866i
$921$	17.2374			0.567991
$922$	4.42922	−	2.84649i	0.145869	−	0.0937441i
$923$	−8.58657	+	59.7209i	−0.282630	+	1.96574i
$924$	−0.169432	+	0.371003i	−0.00557389	+	0.0122051i
$925$	−6.87816	+	2.01961i	−0.226153	+	0.0664044i
$926$	11.6292	+	25.4644i	0.382160	+	0.836814i
$927$	9.79412	+	11.3030i	0.321681	+	0.371240i
$928$	−0.698147	−	4.85572i	−0.0229178	−	0.159397i
$929$	14.9243	+	4.38217i	0.489651	+	0.143774i	0.517232	−	0.855845i	$-0.326962\pi$
$929$	14.9243	+	4.38217i	0.489651	+	0.143774i	−0.0275813	+	0.999620i	$0.508781\pi$
$930$	−0.314020	+	0.362398i	−0.0102971	+	0.0118835i
$931$	9.39276	+	6.03636i	0.307835	+	0.197834i
$932$	−14.9923	−	9.63495i	−0.491088	−	0.315603i
$933$	11.0045	−	12.6999i	0.360272	−	0.415777i
$934$	24.3952	+	7.16308i	0.798236	+	0.234383i
$935$	0.205723	+	1.43083i	0.00672786	+	0.0467933i
$936$	4.06250	+	4.68838i	0.132787	+	0.153244i
$937$	−5.86046	−	12.8326i	−0.191453	−	0.419224i	0.789425	−	0.613847i	$-0.210379\pi$
$937$	−5.86046	−	12.8326i	−0.191453	−	0.419224i	−0.980878	+	0.194623i	$0.937652\pi$
$938$	−3.84587	+	1.12925i	−0.125572	+	0.0368713i
$939$	7.20208	−	15.7704i	0.235031	−	0.514646i
$940$	−1.45375	+	10.1110i	−0.0474160	+	0.329785i
$941$	12.3215	−	7.91855i	0.401670	−	0.258137i	−0.324174	−	0.945998i	$-0.605086\pi$
$941$	12.3215	−	7.91855i	0.401670	−	0.258137i	0.725843	+	0.687860i	$0.241450\pi$
$942$	−12.5851			−0.410043
$943$	43.5649	−	35.0299i	1.41867	−	1.14073i
$944$	1.08242			0.0352297
$945$	0.938384	−	0.603063i	0.0305256	−	0.0196176i
$946$	−0.434264	+	3.02037i	−0.0141192	+	0.0982009i
$947$	21.2836	−	46.6045i	0.691623	−	1.51444i	−0.158218	−	0.987404i	$-0.550575\pi$
$947$	21.2836	−	46.6045i	0.691623	−	1.51444i	0.849841	−	0.527039i	$-0.176698\pi$
$948$	12.5678	−	3.69025i	0.408185	−	0.119854i
$949$	5.23314	+	11.4590i	0.169875	+	0.371974i
$950$	1.27032	+	1.46603i	0.0412146	+	0.0475642i
$951$	1.33501	+	9.28519i	0.0432906	+	0.301093i
$952$	4.23126	+	1.24241i	0.137136	+	0.0402668i
$953$	−31.9181	+	36.8355i	−1.03393	+	1.19322i	−0.0530517	+	0.998592i	$0.516895\pi$
$953$	−31.9181	+	36.8355i	−1.03393	+	1.19322i	−0.980878	+	0.194626i	$0.937651\pi$
$954$	1.95235	+	1.25470i	0.0632097	+	0.0406224i
$955$	16.4767	+	10.5890i	0.533175	+	0.342650i
$956$	16.6255	−	19.1869i	0.537709	−	0.620549i
$957$	−1.72106	−	0.505350i	−0.0556341	−	0.0163356i
$958$	0.938016	+	6.52405i	0.0303059	+	0.210782i
$959$	2.70964	+	3.12709i	0.0874987	+	0.100979i
$960$	−0.415415	−	0.909632i	−0.0134075	−	0.0293582i
$961$	29.5237	−	8.66893i	0.952376	−	0.279643i
$962$	−18.4739	+	40.4521i	−0.595621	+	1.30423i
$963$	1.60227	−	11.1441i	0.0516325	−	0.359112i
$964$	14.2647	−	9.16736i	0.459435	−	0.295261i
$965$	15.9919			0.514798
$966$	−0.196669	+	5.34594i	−0.00632771	+	0.172003i
$967$	15.2695			0.491035			0.245518	−	0.969392i	$-0.421042\pi$
$967$	15.2695			0.491035			0.245518	+	0.969392i	$0.421042\pi$
$968$	−9.14132	+	5.87477i	−0.293813	+	0.188822i
$969$	1.09141	−	7.59094i	0.0350612	−	0.243856i
$970$	−7.34128	+	16.0752i	−0.235714	+	0.516142i
$971$	1.17346	−	0.344559i	0.0376581	−	0.0110574i	−0.262849	−	0.964837i	$-0.584662\pi$
$971$	1.17346	−	0.344559i	0.0376581	−	0.0110574i	0.300507	+	0.953780i	$0.402844\pi$
$972$	0.415415	+	0.909632i	0.0133244	+	0.0291765i
$973$	−6.64697	−	7.67102i	−0.213092	−	0.245922i
$974$	−1.80467	−	12.5517i	−0.0578253	−	0.402184i
$975$	5.95233	+	1.74776i	0.190627	+	0.0559731i
$976$	−4.84107	+	5.58689i	−0.154959	+	0.178832i
$977$	23.6960	+	15.2285i	0.758102	+	0.487202i	0.861701	−	0.507417i	$-0.169400\pi$
$977$	23.6960	+	15.2285i	0.758102	+	0.487202i	−0.103599	+	0.994619i	$0.533036\pi$
$978$	1.85623	+	1.19293i	0.0593556	+	0.0381456i
$979$	−2.70239	+	3.11873i	−0.0863688	+	0.0996749i
$980$	−5.52260	−	1.62158i	−0.176413	−	0.0517995i
$981$	1.25971	+	8.76147i	0.0402194	+	0.279732i
$982$	−24.8570	−	28.6865i	−0.793218	−	0.915422i
$983$	−4.48079	−	9.81156i	−0.142915	−	0.312940i	0.824616	−	0.565693i	$-0.191391\pi$
$983$	−4.48079	−	9.81156i	−0.142915	−	0.312940i	−0.967531	+	0.252753i	$0.918664\pi$
$984$	11.1841	−	3.28396i	0.356537	−	0.104689i
$985$	−2.25942	+	4.94744i	−0.0719910	+	0.157638i
$986$	−2.76008	+	19.1968i	−0.0878988	+	0.611350i
$987$	9.58560	−	6.16029i	0.305113	−	0.196084i
$988$	12.0340			0.382852
$989$	9.85638	+	38.7904i	0.313415	+	1.23346i
$990$	−0.365644			−0.0116209
$991$	−12.8402	+	8.25188i	−0.407882	+	0.262130i	−0.728454	−	0.685094i	$-0.759761\pi$
$991$	−12.8402	+	8.25188i	−0.407882	+	0.262130i	0.320573	+	0.947224i	$0.396125\pi$
$992$	0.0682430	−	0.474640i	0.00216672	−	0.0150698i
$993$	−3.08351	+	6.75195i	−0.0978524	+	0.214267i
$994$	−10.4093	+	3.05644i	−0.330162	+	0.0969443i
$995$	2.14089	+	4.68790i	0.0678709	+	0.148617i
$996$	3.23547	+	3.73393i	0.102520	+	0.118314i
$997$	4.44410	+	30.9094i	0.140746	+	0.978911i	0.930710	+	0.365758i	$0.119190\pi$
$997$	4.44410	+	30.9094i	0.140746	+	0.978911i	−0.789964	+	0.613153i	$0.789901\pi$
$998$	2.30944	+	0.678114i	0.0731042	+	0.0214653i
$999$	−4.69440	+	5.41762i	−0.148524	+	0.171406i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.a.541.1	yes	10
23.2	even	11	inner	690.2.m.a.301.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.a.301.1	✓	10	23.2	even	11	inner
690.2.m.a.541.1	yes	10	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.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 - 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(0.415415 + 0.909632i) q^{6} +(0.730471 + 0.843008i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(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} +(0.730471 + 0.843008i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(0.654861 - 0.755750i) q^{10} +(0.307599 + 0.197682i) q^{11} +(0.841254 + 0.540641i) q^{12} +(4.06250 - 4.68838i) q^{13} +(1.07028 + 0.314261i) q^{14} +(0.142315 + 0.989821i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(1.64231 + 3.59617i) q^{17} +(-0.959493 + 0.281733i) q^{18} +(-0.805836 + 1.76453i) q^{19} +(0.142315 - 0.989821i) q^{20} +(-0.938384 + 0.603063i) q^{21} +0.365644 q^{22} +(4.43274 - 1.83053i) q^{23} +1.00000 q^{24} +(0.841254 - 0.540641i) q^{25} +(0.882867 - 6.14047i) q^{26} +(0.415415 - 0.909632i) q^{27} +(1.07028 - 0.314261i) q^{28} +(2.03788 + 4.46234i) q^{29} +(0.654861 + 0.755750i) q^{30} +(0.0682430 + 0.474640i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-0.239446 + 0.276335i) q^{33} +(3.32584 + 2.13739i) q^{34} +(0.938384 + 0.603063i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(-6.87816 - 2.01961i) q^{37} +(0.276067 + 1.92009i) q^{38} +(4.06250 + 4.68838i) q^{39} +(-0.415415 - 0.909632i) q^{40} +(11.1841 - 3.28396i) q^{41} +(-0.463379 + 1.01466i) q^{42} +(-1.18767 + 8.26043i) q^{43} +(0.307599 - 0.197682i) q^{44} -1.00000 q^{45} +(2.73939 - 3.93646i) q^{46} -10.2150 q^{47} +(0.841254 - 0.540641i) q^{48} +(0.819129 - 5.69716i) q^{49} +(0.415415 - 0.909632i) q^{50} +(-3.79329 + 1.11381i) q^{51} +(-2.57708 - 5.64301i) q^{52} +(-1.51978 - 1.75392i) q^{53} +(-0.142315 - 0.989821i) q^{54} +(0.350833 + 0.103014i) q^{55} +(0.730471 - 0.843008i) q^{56} +(-1.63189 - 1.04875i) q^{57} +(4.12690 + 2.65220i) q^{58} +(-0.708833 + 0.818036i) q^{59} +(0.959493 + 0.281733i) q^{60} +(-1.05206 - 7.31727i) q^{61} +(0.314020 + 0.362398i) q^{62} +(-0.463379 - 1.01466i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(2.57708 - 5.64301i) q^{65} +(-0.0520365 + 0.361922i) q^{66} +(-3.02292 + 1.94271i) q^{67} +3.95343 q^{68} +(1.18106 + 4.64813i) q^{69} +1.11546 q^{70} +(-8.18185 + 5.25816i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(-0.843563 + 1.84715i) q^{73} +(-6.87816 + 2.01961i) q^{74} +(0.415415 + 0.909632i) q^{75} +(1.27032 + 1.46603i) q^{76} +(0.0580447 + 0.403709i) q^{77} +(5.95233 + 1.74776i) q^{78} +(8.57764 - 9.89913i) q^{79} +(-0.841254 - 0.540641i) q^{80} +(0.841254 + 0.540641i) q^{81} +(7.63325 - 8.80924i) q^{82} +(4.74056 + 1.39196i) q^{83} +(0.158746 + 1.10411i) q^{84} +(2.58895 + 2.98780i) q^{85} +(3.46679 + 7.59122i) q^{86} +(-4.70694 + 1.38208i) q^{87} +(0.151894 - 0.332601i) q^{88} +(-1.60617 + 11.1712i) q^{89} +(-0.841254 + 0.540641i) q^{90} +6.91988 q^{91} +(0.176312 - 4.79259i) q^{92} -0.479521 q^{93} +(-8.59341 + 5.52265i) q^{94} +(-0.276067 + 1.92009i) q^{95} +(0.415415 - 0.909632i) q^{96} +(-16.9563 + 4.97882i) q^{97} +(-2.39102 - 5.23561i) q^{98} +(-0.239446 - 0.276335i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 - q^3 - q^4 + q^5 - q^6 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - q^{8} - q^{9} + q^{10} - 2 q^{11} - q^{12} + q^{15} - q^{16} + 16 q^{17} - q^{18} + 18 q^{19} + q^{20} + 20 q^{22} - q^{23} + 10 q^{24} - q^{25} + 11 q^{26} - q^{27} + 22 q^{29} + q^{30} + 8 q^{31} - q^{32} - 2 q^{33} + 5 q^{34} - q^{36} - 16 q^{37} - 4 q^{38} + q^{40} - 9 q^{41} - 11 q^{42} + 2 q^{43} - 2 q^{44} - 10 q^{45} - q^{46} - 48 q^{47} - q^{48} + 7 q^{49} - q^{50} - 17 q^{51} + 2 q^{53} - q^{54} - 9 q^{55} - 15 q^{57} + 22 q^{58} - 22 q^{59} + q^{60} + 13 q^{61} + 8 q^{62} - 11 q^{63} - q^{64} - 13 q^{66} + 2 q^{67} - 6 q^{68} - q^{69} - 45 q^{71} - q^{72} + 21 q^{73} - 16 q^{74} - q^{75} - 4 q^{76} + 22 q^{77} + 11 q^{78} + 66 q^{79} + q^{80} - q^{81} + 57 q^{82} + 15 q^{83} + 11 q^{84} - 5 q^{85} + 24 q^{86} - 2 q^{88} + 29 q^{89} + q^{90} + 22 q^{91} - 12 q^{92} - 58 q^{93} + 7 q^{94} + 4 q^{95} - q^{96} - 27 q^{97} + 7 q^{98} - 2 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 + q^5 - q^6 - q^8 - q^9 + q^10 - 2 * q^11 - q^12 + q^15 - q^16 + 16 * q^17 - q^18 + 18 * q^19 + q^20 + 20 * q^22 - q^23 + 10 * q^24 - q^25 + 11 * q^26 - q^27 + 22 * q^29 + q^30 + 8 * q^31 - q^32 - 2 * q^33 + 5 * q^34 - q^36 - 16 * q^37 - 4 * q^38 + q^40 - 9 * q^41 - 11 * q^42 + 2 * q^43 - 2 * q^44 - 10 * q^45 - q^46 - 48 * q^47 - q^48 + 7 * q^49 - q^50 - 17 * q^51 + 2 * q^53 - q^54 - 9 * q^55 - 15 * q^57 + 22 * q^58 - 22 * q^59 + q^60 + 13 * q^61 + 8 * q^62 - 11 * q^63 - q^64 - 13 * q^66 + 2 * q^67 - 6 * q^68 - q^69 - 45 * q^71 - q^72 + 21 * q^73 - 16 * q^74 - q^75 - 4 * q^76 + 22 * q^77 + 11 * q^78 + 66 * q^79 + q^80 - q^81 + 57 * q^82 + 15 * q^83 + 11 * q^84 - 5 * q^85 + 24 * q^86 - 2 * q^88 + 29 * q^89 + q^90 + 22 * q^91 - 12 * q^92 - 58 * q^93 + 7 * q^94 + 4 * q^95 - q^96 - 27 * q^97 + 7 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

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