LMFDB - Embedded newform 690.2.m.g.601.2

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			601.2
Character	$\chi$	$=$	690.601
Dual form			690.2.m.g.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-1.19214 + 0.766143i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-1.19214 + 0.766143i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(0.841254 + 0.540641i) q^{10} +(0.577515 - 4.01670i) q^{11} +(-0.142315 + 0.989821i) q^{12} +(-3.17730 - 2.04193i) q^{13} +(0.928004 + 1.07097i) q^{14} +(0.415415 + 0.909632i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-0.685140 - 0.201175i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(-5.06029 + 1.48584i) q^{19} +(0.415415 - 0.909632i) q^{20} +(0.201675 + 1.40268i) q^{21} -4.05801 q^{22} +(-1.59325 + 4.52345i) q^{23} +1.00000 q^{24} +(-0.142315 - 0.989821i) q^{25} +(-1.56897 + 3.43556i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(0.928004 - 1.07097i) q^{28} +(-6.08763 - 1.78749i) q^{29} +(0.841254 - 0.540641i) q^{30} +(-4.36442 - 9.55674i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-3.41381 - 2.19392i) q^{33} +(-0.101622 + 0.706796i) q^{34} +(0.201675 - 1.40268i) q^{35} +(0.841254 + 0.540641i) q^{36} +(1.24849 + 1.44083i) q^{37} +(2.19087 + 4.79733i) q^{38} +(-3.17730 + 2.04193i) q^{39} +(-0.959493 - 0.281733i) q^{40} +(-7.44001 + 8.58623i) q^{41} +(1.35970 - 0.399244i) q^{42} +(-0.495831 + 1.08572i) q^{43} +(0.577515 + 4.01670i) q^{44} +1.00000 q^{45} +(4.70415 + 0.933277i) q^{46} +6.23833 q^{47} +(-0.142315 - 0.989821i) q^{48} +(-2.07368 + 4.54072i) q^{49} +(-0.959493 + 0.281733i) q^{50} +(-0.467613 + 0.539654i) q^{51} +(3.62388 + 1.06407i) q^{52} +(10.2844 - 6.60938i) q^{53} +(0.415415 + 0.909632i) q^{54} +(2.65743 + 3.06684i) q^{55} +(-1.19214 - 0.766143i) q^{56} +(-0.750557 + 5.22024i) q^{57} +(-0.902936 + 6.28006i) q^{58} +(10.2213 + 6.56883i) q^{59} +(-0.654861 - 0.755750i) q^{60} +(-4.37254 - 9.57452i) q^{61} +(-8.83835 + 5.68006i) q^{62} +(1.35970 + 0.399244i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(3.62388 - 1.06407i) q^{65} +(-1.68576 + 3.69129i) q^{66} +(-1.53988 - 10.7101i) q^{67} +0.714064 q^{68} +(3.45281 + 3.32838i) q^{69} -1.41710 q^{70} +(-1.76050 - 12.2446i) q^{71} +(0.415415 - 0.909632i) q^{72} +(-2.26681 + 0.665597i) q^{73} +(1.24849 - 1.44083i) q^{74} +(-0.959493 - 0.281733i) q^{75} +(4.43670 - 2.85130i) q^{76} +(2.38889 + 5.23094i) q^{77} +(2.47332 + 2.85437i) q^{78} +(-6.51708 - 4.18827i) q^{79} +(-0.142315 + 0.989821i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(9.55765 + 6.14233i) q^{82} +(11.2250 + 12.9543i) q^{83} +(-0.588685 - 1.28904i) q^{84} +(0.600709 - 0.386052i) q^{85} +(1.14523 + 0.336270i) q^{86} +(-4.15485 + 4.79496i) q^{87} +(3.89363 - 1.14327i) q^{88} +(-3.42073 + 7.49036i) q^{89} +(-0.142315 - 0.989821i) q^{90} +5.35221 q^{91} +(0.254308 - 4.78908i) q^{92} -10.5062 q^{93} +(-0.887807 - 6.17483i) q^{94} +(2.19087 - 4.79733i) q^{95} +(-0.959493 + 0.281733i) q^{96} +(1.48686 - 1.71593i) q^{97} +(4.78962 + 1.40636i) q^{98} +(-3.41381 + 2.19392i) 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	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 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 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$6$	−0.959493	−	0.281733i	−0.391711	−	0.115017i
$7$	−1.19214	+	0.766143i	−0.450587	+	0.289575i	−0.746186	−	0.665737i	$-0.768117\pi$
$7$	−1.19214	+	0.766143i	−0.450587	+	0.289575i	0.295599	+	0.955312i	$0.404481\pi$
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$	0.841254	+	0.540641i	0.266028	+	0.170966i
$11$	0.577515	−	4.01670i	0.174127	−	1.21108i	−0.695922	−	0.718117i	$-0.745004\pi$
$11$	0.577515	−	4.01670i	0.174127	−	1.21108i	0.870050	−	0.492964i	$-0.164087\pi$
$12$	−0.142315	+	0.989821i	−0.0410828	+	0.285737i
$13$	−3.17730	−	2.04193i	−0.881226	−	0.566329i	0.0199416	−	0.999801i	$-0.493652\pi$
$13$	−3.17730	−	2.04193i	−0.881226	−	0.566329i	−0.901167	+	0.433472i	$0.857288\pi$
$14$	0.928004	+	1.07097i	0.248020	+	0.286230i
$15$	0.415415	+	0.909632i	0.107260	+	0.234866i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−0.685140	−	0.201175i	−0.166171	−	0.0487921i	0.197589	−	0.980285i	$-0.436689\pi$
$17$	−0.685140	−	0.201175i	−0.166171	−	0.0487921i	−0.363760	+	0.931493i	$0.618507\pi$
$18$	−0.654861	+	0.755750i	−0.154352	+	0.178132i
$19$	−5.06029	+	1.48584i	−1.16091	+	0.340874i	−0.804786	−	0.593565i	$-0.797720\pi$
$19$	−5.06029	+	1.48584i	−1.16091	+	0.340874i	−0.356124	+	0.934439i	$0.615902\pi$
$20$	0.415415	−	0.909632i	0.0928896	−	0.203400i
$21$	0.201675	+	1.40268i	0.0440090	+	0.306089i
$22$	−4.05801			−0.865170
$23$	−1.59325	+	4.52345i	−0.332215	+	0.943204i
$23$	−1.59325	+	4.52345i	−0.332215	+	0.943204i
$24$	1.00000			0.204124
$25$	−0.142315	−	0.989821i	−0.0284630	−	0.197964i
$26$	−1.56897	+	3.43556i	−0.307700	+	0.673769i
$27$	−0.959493	+	0.281733i	−0.184655	+	0.0542195i
$28$	0.928004	−	1.07097i	0.175376	−	0.202395i
$29$	−6.08763	−	1.78749i	−1.13044	−	0.331929i	−0.337562	−	0.941303i	$-0.609602\pi$
$29$	−6.08763	−	1.78749i	−1.13044	−	0.331929i	−0.792883	+	0.609375i	$0.791421\pi$
$30$	0.841254	−	0.540641i	0.153591	−	0.0987071i
$31$	−4.36442	−	9.55674i	−0.783873	−	1.71644i	−0.693412	−	0.720542i	$-0.743893\pi$
$31$	−4.36442	−	9.55674i	−0.783873	−	1.71644i	−0.0904611	−	0.995900i	$-0.528834\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	−3.41381	−	2.19392i	−0.594268	−	0.381913i
$34$	−0.101622	+	0.706796i	−0.0174280	+	0.121215i
$35$	0.201675	−	1.40268i	0.0340892	−	0.237096i
$36$	0.841254	+	0.540641i	0.140209	+	0.0901068i
$37$	1.24849	+	1.44083i	0.205250	+	0.236871i	0.849037	−	0.528334i	$-0.177183\pi$
$37$	1.24849	+	1.44083i	0.205250	+	0.236871i	−0.643787	+	0.765205i	$0.722638\pi$
$38$	2.19087	+	4.79733i	0.355405	+	0.778229i
$39$	−3.17730	+	2.04193i	−0.508776	+	0.326970i
$40$	−0.959493	−	0.281733i	−0.151709	−	0.0445458i
$41$	−7.44001	+	8.58623i	−1.16193	+	1.34094i	−0.232219	+	0.972664i	$0.574598\pi$
$41$	−7.44001	+	8.58623i	−1.16193	+	1.34094i	−0.929715	+	0.368279i	$0.879947\pi$
$42$	1.35970	−	0.399244i	0.209806	−	0.0616046i
$43$	−0.495831	+	1.08572i	−0.0756135	+	0.165570i	−0.943664	−	0.330906i	$-0.892646\pi$
$43$	−0.495831	+	1.08572i	−0.0756135	+	0.165570i	0.868050	+	0.496476i	$0.165373\pi$
$44$	0.577515	+	4.01670i	0.0870636	+	0.605541i
$45$	1.00000			0.149071
$46$	4.70415	+	0.933277i	0.693589	+	0.137604i
$47$	6.23833			0.909954			0.454977	−	0.890503i	$-0.349648\pi$
$47$	6.23833			0.909954			0.454977	+	0.890503i	$0.349648\pi$
$48$	−0.142315	−	0.989821i	−0.0205414	−	0.142868i
$49$	−2.07368	+	4.54072i	−0.296240	+	0.648675i
$50$	−0.959493	+	0.281733i	−0.135693	+	0.0398430i
$51$	−0.467613	+	0.539654i	−0.0654789	+	0.0755666i
$52$	3.62388	+	1.06407i	0.502542	+	0.147560i
$53$	10.2844	−	6.60938i	1.41267	−	0.907868i	0.412674	−	0.910879i	$-0.364595\pi$
$53$	10.2844	−	6.60938i	1.41267	−	0.907868i	0.999995	+	0.00301117i	$0.000958487\pi$
$54$	0.415415	+	0.909632i	0.0565308	+	0.123785i
$55$	2.65743	+	3.06684i	0.358328	+	0.413532i
$56$	−1.19214	−	0.766143i	−0.159307	−	0.102380i
$57$	−0.750557	+	5.22024i	−0.0994137	+	0.691438i
$58$	−0.902936	+	6.28006i	−0.118561	+	0.824612i
$59$	10.2213	+	6.56883i	1.33070	+	0.855189i	0.996190	−	0.0872037i	$-0.0277931\pi$
$59$	10.2213	+	6.56883i	1.33070	+	0.855189i	0.334509	+	0.942392i	$0.391429\pi$
$60$	−0.654861	−	0.755750i	−0.0845422	−	0.0975669i
$61$	−4.37254	−	9.57452i	−0.559846	−	1.22589i	−0.952030	−	0.306005i	$-0.901008\pi$
$61$	−4.37254	−	9.57452i	−0.559846	−	1.22589i	0.392184	−	0.919887i	$-0.371720\pi$
$62$	−8.83835	+	5.68006i	−1.12247	+	0.721368i
$63$	1.35970	+	0.399244i	0.171306	+	0.0503000i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	3.62388	−	1.06407i	0.449487	−	0.131981i
$66$	−1.68576	+	3.69129i	−0.207502	+	0.454367i
$67$	−1.53988	−	10.7101i	−0.188126	−	1.30845i	−0.836853	−	0.547427i	$-0.815607\pi$
$67$	−1.53988	−	10.7101i	−0.188126	−	1.30845i	0.648727	−	0.761021i	$-0.275302\pi$
$68$	0.714064			0.0865930
$69$	3.45281	+	3.32838i	0.415670	+	0.400689i
$70$	−1.41710			−0.169376
$71$	−1.76050	−	12.2446i	−0.208933	−	1.45316i	−0.776647	−	0.629937i	$-0.783081\pi$
$71$	−1.76050	−	12.2446i	−0.208933	−	1.45316i	0.567713	−	0.823226i	$-0.307828\pi$
$72$	0.415415	−	0.909632i	0.0489571	−	0.107201i
$73$	−2.26681	+	0.665597i	−0.265310	+	0.0779022i	−0.411682	−	0.911327i	$-0.635059\pi$
$73$	−2.26681	+	0.665597i	−0.265310	+	0.0779022i	0.146372	+	0.989230i	$0.453240\pi$
$74$	1.24849	−	1.44083i	0.145134	−	0.167493i
$75$	−0.959493	−	0.281733i	−0.110793	−	0.0325317i
$76$	4.43670	−	2.85130i	0.508925	−	0.327066i
$77$	2.38889	+	5.23094i	0.272239	+	0.596120i
$78$	2.47332	+	2.85437i	0.280049	+	0.323193i
$79$	−6.51708	−	4.18827i	−0.733229	−	0.471218i	0.119987	−	0.992775i	$-0.461715\pi$
$79$	−6.51708	−	4.18827i	−0.733229	−	0.471218i	−0.853216	+	0.521558i	$0.825351\pi$
$80$	−0.142315	+	0.989821i	−0.0159113	+	0.110665i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	9.55765	+	6.14233i	1.05547	+	0.678307i
$83$	11.2250	+	12.9543i	1.23210	+	1.42192i	0.872355	+	0.488874i	$0.162592\pi$
$83$	11.2250	+	12.9543i	1.23210	+	1.42192i	0.359749	+	0.933049i	$0.382862\pi$
$84$	−0.588685	−	1.28904i	−0.0642308	−	0.140646i
$85$	0.600709	−	0.386052i	0.0651560	−	0.0418732i
$86$	1.14523	+	0.336270i	0.123493	+	0.0362609i
$87$	−4.15485	+	4.79496i	−0.445447	+	0.514073i
$88$	3.89363	−	1.14327i	0.415062	−	0.121873i
$89$	−3.42073	+	7.49036i	−0.362597	+	0.793976i	0.637133	+	0.770754i	$0.280120\pi$
$89$	−3.42073	+	7.49036i	−0.362597	+	0.793976i	−0.999730	+	0.0232229i	$0.992607\pi$
$90$	−0.142315	−	0.989821i	−0.0150013	−	0.104336i
$91$	5.35221			0.561064
$92$	0.254308	−	4.78908i	0.0265134	−	0.499297i
$93$	−10.5062			−1.08944
$94$	−0.887807	−	6.17483i	−0.0915703	−	0.636885i
$95$	2.19087	−	4.79733i	0.224778	−	0.492195i
$96$	−0.959493	+	0.281733i	−0.0979278	+	0.0287542i
$97$	1.48686	−	1.71593i	0.150968	−	0.174226i	−0.675228	−	0.737609i	$-0.735955\pi$
$97$	1.48686	−	1.71593i	0.150968	−	0.174226i	0.826196	+	0.563383i	$0.190500\pi$
$98$	4.78962	+	1.40636i	0.483825	+	0.142064i
$99$	−3.41381	+	2.19392i	−0.343101	+	0.220498i
$100$	0.415415	+	0.909632i	0.0415415	+	0.0909632i
$101$	−10.8581	−	12.5309i	−1.08042	−	1.24687i	−0.967394	−	0.253276i	$-0.918492\pi$
$101$	−10.8581	−	12.5309i	−1.08042	−	1.24687i	−0.113024	−	0.993592i	$-0.536054\pi$
$102$	0.600709	+	0.386052i	0.0594791	+	0.0382249i
$103$	1.58152	−	10.9997i	0.155832	−	1.08383i	−0.750380	−	0.661007i	$-0.770129\pi$
$103$	1.58152	−	10.9997i	0.155832	−	1.08383i	0.906211	−	0.422825i	$-0.138962\pi$
$104$	0.537504	−	3.73843i	0.0527066	−	0.366583i
$105$	−1.19214	−	0.766143i	−0.116341	−	0.0747679i
$106$	−8.00572	−	9.23910i	−0.777585	−	0.897380i
$107$	6.22630	+	13.6337i	0.601919	+	1.31802i	0.927966	+	0.372665i	$0.121556\pi$
$107$	6.22630	+	13.6337i	0.601919	+	1.31802i	−0.326047	+	0.945354i	$0.605717\pi$
$108$	0.841254	−	0.540641i	0.0809497	−	0.0520232i
$109$	−5.32138	−	1.56250i	−0.509695	−	0.149660i	0.0167654	−	0.999859i	$-0.494663\pi$
$109$	−5.32138	−	1.56250i	−0.509695	−	0.149660i	−0.526461	+	0.850199i	$0.676481\pi$
$110$	2.65743	−	3.06684i	0.253376	−	0.292411i
$111$	1.82927	−	0.537121i	0.173626	−	0.0509813i
$112$	−0.588685	+	1.28904i	−0.0556255	+	0.121803i
$113$	−0.667574	−	4.64308i	−0.0628001	−	0.436784i	−0.996828	−	0.0795846i	$-0.974641\pi$
$113$	−0.667574	−	4.64308i	−0.0628001	−	0.436784i	0.934028	−	0.357200i	$-0.116268\pi$
$114$	5.27392			0.493948
$115$	−2.37524	−	4.16632i	−0.221492	−	0.388512i
$116$	6.34463			0.589085
$117$	0.537504	+	3.73843i	0.0496923	+	0.345618i
$118$	5.04733	−	11.0521i	0.464644	−	1.01743i
$119$	0.970912	−	0.285086i	0.0890034	−	0.0261337i
$120$	−0.654861	+	0.755750i	−0.0597803	+	0.0689902i
$121$	−5.24595	−	1.54035i	−0.476904	−	0.140032i
$122$	−8.85479	+	5.69063i	−0.801675	+	0.515205i
$123$	4.71961	+	10.3345i	0.425553	+	0.931832i
$124$	6.88007	+	7.94003i	0.617849	+	0.713036i
$125$	0.841254	+	0.540641i	0.0752440	+	0.0483564i
$126$	0.201675	−	1.40268i	0.0179666	−	0.124960i
$127$	−0.820780	+	5.70865i	−0.0728325	+	0.506561i	0.920451	+	0.390857i	$0.127821\pi$
$127$	−0.820780	+	5.70865i	−0.0728325	+	0.506561i	−0.993284	+	0.115704i	$0.963088\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	0.781628	+	0.902047i	0.0688185	+	0.0794208i
$130$	−1.56897	−	3.43556i	−0.137608	−	0.301319i
$131$	6.96485	−	4.47604i	0.608522	−	0.391073i	−0.199781	−	0.979841i	$-0.564023\pi$
$131$	6.96485	−	4.47604i	0.608522	−	0.391073i	0.808303	+	0.588767i	$0.200387\pi$
$132$	3.89363	+	1.14327i	0.338897	+	0.0995091i
$133$	4.89422	−	5.64823i	0.424383	−	0.489764i
$134$	−10.3819	+	3.04842i	−0.896864	+	0.263343i
$135$	0.415415	−	0.909632i	0.0357532	−	0.0782887i
$136$	−0.101622	−	0.706796i	−0.00871401	−	0.0606073i
$137$	1.82545			0.155958			0.0779792	−	0.996955i	$-0.475153\pi$
$137$	1.82545			0.155958			0.0779792	+	0.996955i	$0.475153\pi$
$138$	2.80311	−	3.89134i	0.238617	−	0.331253i
$139$	−2.84016			−0.240899			−0.120450	−	0.992719i	$-0.538434\pi$
$139$	−2.84016			−0.240899			−0.120450	+	0.992719i	$0.538434\pi$
$140$	0.201675	+	1.40268i	0.0170446	+	0.118548i
$141$	2.59150	−	5.67458i	0.218243	−	0.477886i
$142$	−11.8694	+	3.48517i	−0.996057	+	0.292469i
$143$	−10.0368	+	11.5830i	−0.839316	+	0.968622i
$144$	−0.959493	−	0.281733i	−0.0799577	−	0.0234777i
$145$	5.33745	−	3.43017i	0.443251	−	0.284860i
$146$	0.981423	+	2.14902i	0.0812231	+	0.177854i
$147$	3.26895	+	3.77257i	0.269618	+	0.311156i
$148$	−1.60384	−	1.03073i	−0.131835	−	0.0847253i
$149$	2.54268	−	17.6847i	0.208304	−	1.44879i	−0.570385	−	0.821377i	$-0.693206\pi$
$149$	2.54268	−	17.6847i	0.208304	−	1.44879i	0.778689	−	0.627410i	$-0.215885\pi$
$150$	−0.142315	+	0.989821i	−0.0116200	+	0.0808186i
$151$	13.6369	+	8.76392i	1.10976	+	0.713198i	0.961240	−	0.275712i	$-0.0889136\pi$
$151$	13.6369	+	8.76392i	1.10976	+	0.713198i	0.148517	+	0.988910i	$0.452550\pi$
$152$	−3.45368	−	3.98576i	−0.280131	−	0.323288i
$153$	0.296633	+	0.649536i	0.0239814	+	0.0525118i
$154$	4.83772	−	3.10901i	0.389834	−	0.250531i
$155$	10.0806	+	2.95993i	0.809693	+	0.237747i
$156$	2.47332	−	2.85437i	0.198024	−	0.228532i
$157$	−2.64486	+	0.776601i	−0.211083	+	0.0619795i	−0.385564	−	0.922681i	$-0.625993\pi$
$157$	−2.64486	+	0.776601i	−0.211083	+	0.0619795i	0.174482	+	0.984660i	$0.444175\pi$
$158$	−3.21817	+	7.04680i	−0.256023	+	0.560613i
$159$	−1.73981	−	12.1006i	−0.137976	−	0.959643i
$160$	1.00000			0.0790569
$161$	−1.56623	−	6.61324i	−0.123436	−	0.521197i
$162$	1.00000			0.0785674
$163$	−2.71703	−	18.8974i	−0.212814	−	1.48016i	−0.763698	−	0.645574i	$-0.776618\pi$
$163$	−2.71703	−	18.8974i	−0.212814	−	1.48016i	0.550884	−	0.834582i	$-0.314291\pi$
$164$	4.71961	−	10.3345i	0.368540	−	0.806990i
$165$	3.89363	−	1.14327i	0.303119	−	0.0890037i
$166$	11.2250	−	12.9543i	0.871229	−	1.00545i
$167$	−10.5886	−	3.10908i	−0.819368	−	0.240588i	−0.154924	−	0.987926i	$-0.549513\pi$
$167$	−10.5886	−	3.10908i	−0.819368	−	0.240588i	−0.664444	+	0.747338i	$0.731331\pi$
$168$	−1.19214	+	0.766143i	−0.0919757	+	0.0591092i
$169$	0.525390	+	1.15044i	0.0404146	+	0.0884956i
$170$	−0.467613	−	0.539654i	−0.0358642	−	0.0413895i
$171$	4.43670	+	2.85130i	0.339283	+	0.218044i
$172$	0.169864	−	1.18143i	0.0129520	−	0.0900832i
$173$	−0.388336	+	2.70093i	−0.0295246	+	0.205348i	−0.999244	−	0.0388730i	$-0.987623\pi$
$173$	−0.388336	+	2.70093i	−0.0295246	+	0.205348i	0.969720	+	0.244221i	$0.0785323\pi$
$174$	5.33745	+	3.43017i	0.404631	+	0.260040i
$175$	0.928004	+	1.07097i	0.0701505	+	0.0809580i
$176$	−1.68576	−	3.69129i	−0.127069	−	0.278242i
$177$	10.2213	−	6.56883i	0.768280	−	0.493743i
$178$	7.90094	+	2.31992i	0.592200	+	0.173886i
$179$	1.59016	−	1.83514i	0.118854	−	0.137165i	−0.693204	−	0.720741i	$-0.743802\pi$
$179$	1.59016	−	1.83514i	0.118854	−	0.137165i	0.812058	+	0.583576i	$0.198347\pi$
$180$	−0.959493	+	0.281733i	−0.0715164	+	0.0209991i
$181$	2.82229	−	6.17996i	0.209779	−	0.459353i	−0.775269	−	0.631631i	$-0.782386\pi$
$181$	2.82229	−	6.17996i	0.209779	−	0.459353i	0.985048	+	0.172279i	$0.0551130\pi$
$182$	−0.761698	−	5.29773i	−0.0564608	−	0.392694i
$183$	−10.5257			−0.778083
$184$	−4.77653	+	0.429838i	−0.352130	+	0.0316881i
$185$	−1.90649			−0.140168
$186$	1.49518	+	10.3992i	0.109632	+	0.762508i
$187$	−1.20374	+	2.63582i	−0.0880261	+	0.192750i
$188$	−5.98563	+	1.75754i	−0.436547	+	0.128182i
$189$	0.928004	−	1.07097i	0.0675024	−	0.0779019i
$190$	−5.06029	−	1.48584i	−0.367112	−	0.107794i
$191$	16.3378	−	10.4997i	1.18216	−	0.759729i	0.206379	−	0.978472i	$-0.433832\pi$
$191$	16.3378	−	10.4997i	1.18216	−	0.759729i	0.975783	+	0.218743i	$0.0701956\pi$
$192$	0.415415	+	0.909632i	0.0299800	+	0.0656470i
$193$	1.86365	+	2.15077i	0.134149	+	0.154816i	0.818849	−	0.574009i	$-0.194612\pi$
$193$	1.86365	+	2.15077i	0.134149	+	0.154816i	−0.684701	+	0.728825i	$0.740067\pi$
$194$	−1.91006	−	1.22752i	−0.137135	−	0.0881311i
$195$	0.537504	−	3.73843i	0.0384915	−	0.267714i
$196$	0.710411	−	4.94101i	0.0507436	−	0.352930i
$197$	−6.61652	−	4.25218i	−0.471407	−	0.302955i	0.283283	−	0.959036i	$-0.408576\pi$
$197$	−6.61652	−	4.25218i	−0.471407	−	0.302955i	−0.754690	+	0.656081i	$0.772213\pi$
$198$	2.65743	+	3.06684i	0.188855	+	0.217951i
$199$	7.97996	+	17.4737i	0.565685	+	1.23868i	0.949063	+	0.315085i	$0.102033\pi$
$199$	7.97996	+	17.4737i	0.565685	+	1.23868i	−0.383379	+	0.923591i	$0.625240\pi$
$200$	0.841254	−	0.540641i	0.0594856	−	0.0382291i
$201$	−10.3819	−	3.04842i	−0.732286	−	0.215019i
$202$	−10.8581	+	12.5309i	−0.763971	+	0.881669i
$203$	8.62679	−	2.53305i	0.605482	−	0.177786i
$204$	0.296633	−	0.649536i	0.0207685	−	0.0454766i
$205$	−1.61687	−	11.2456i	−0.112927	−	0.785424i
$206$	−11.1128			−0.774266
$207$	4.46195	−	1.75813i	0.310127	−	0.122199i
$208$	−3.77687			−0.261879
$209$	3.04577	+	21.1838i	0.210680	+	1.46531i
$210$	−0.588685	+	1.28904i	−0.0406231	+	0.0889523i
$211$	−0.798256	+	0.234389i	−0.0549542	+	0.0161360i	−0.309094	−	0.951031i	$-0.600026\pi$
$211$	−0.798256	+	0.234389i	−0.0549542	+	0.0161360i	0.254140	+	0.967167i	$0.418208\pi$
$212$	−8.00572	+	9.23910i	−0.549835	+	0.634544i
$213$	−11.8694	−	3.48517i	−0.813277	−	0.238800i
$214$	12.6088	−	8.10320i	0.861922	−	0.553923i
$215$	−0.495831	−	1.08572i	−0.0338154	−	0.0740453i
$216$	−0.654861	−	0.755750i	−0.0445576	−	0.0514222i
$217$	12.5248	+	8.04922i	0.850241	+	0.546417i
$218$	−0.789282	+	5.48958i	−0.0534569	+	0.371801i
$219$	−0.336221	+	2.33847i	−0.0227197	+	0.158019i
$220$	−3.41381	−	2.19392i	−0.230159	−	0.147914i
$221$	1.76611	+	2.03820i	0.118801	+	0.137104i
$222$	−0.791986	−	1.73421i	−0.0531546	−	0.116392i
$223$	8.99042	−	5.77779i	0.602043	−	0.386910i	−0.203823	−	0.979008i	$-0.565337\pi$
$223$	8.99042	−	5.77779i	0.602043	−	0.386910i	0.805866	+	0.592098i	$0.201700\pi$
$224$	1.35970	+	0.399244i	0.0908487	+	0.0266756i
$225$	−0.654861	+	0.755750i	−0.0436574	+	0.0503833i
$226$	−4.50082	+	1.32156i	−0.299390	+	0.0879088i
$227$	6.69886	−	14.6684i	0.444619	−	0.973579i	−0.546109	−	0.837714i	$-0.683891\pi$
$227$	6.69886	−	14.6684i	0.444619	−	0.973579i	0.990727	−	0.135865i	$-0.0433813\pi$
$228$	−0.750557	−	5.22024i	−0.0497069	−	0.345719i
$229$	5.24813			0.346806			0.173403	−	0.984851i	$-0.444524\pi$
$229$	5.24813			0.346806			0.173403	+	0.984851i	$0.444524\pi$
$230$	−3.78588	+	2.94399i	−0.249634	+	0.194121i
$231$	5.75061			0.378362
$232$	−0.902936	−	6.28006i	−0.0592806	−	0.412306i
$233$	−8.73917	+	19.1361i	−0.572522	+	1.25365i	0.372922	+	0.927863i	$0.378356\pi$
$233$	−8.73917	+	19.1361i	−0.572522	+	1.25365i	−0.945444	+	0.325785i	$0.894371\pi$
$234$	3.62388	−	1.06407i	0.236900	−	0.0695602i
$235$	−4.08524	+	4.71461i	−0.266491	+	0.307548i
$236$	−11.6579	−	3.42307i	−0.758866	−	0.222823i
$237$	−6.51708	+	4.18827i	−0.423330	+	0.272058i
$238$	−0.420359	−	0.920458i	−0.0272478	−	0.0596644i
$239$	2.10204	+	2.42588i	0.135969	+	0.156917i	0.819651	−	0.572864i	$-0.194168\pi$
$239$	2.10204	+	2.42588i	0.135969	+	0.156917i	−0.683681	+	0.729781i	$0.739622\pi$
$240$	0.841254	+	0.540641i	0.0543027	+	0.0348982i
$241$	0.643600	−	4.47633i	0.0414579	−	0.288346i	−0.958536	−	0.284970i	$-0.908016\pi$
$241$	0.643600	−	4.47633i	0.0414579	−	0.288346i	0.999994	−	0.00337589i	$-0.00107458\pi$
$242$	−0.778095	+	5.41177i	−0.0500178	+	0.347882i
$243$	0.841254	+	0.540641i	0.0539664	+	0.0346821i
$244$	6.89287	+	7.95480i	0.441271	+	0.509254i
$245$	−2.07368	−	4.54072i	−0.132482	−	0.290096i
$246$	9.55765	−	6.14233i	0.609374	−	0.391621i
$247$	19.1120	+	5.61180i	1.21607	+	0.357071i
$248$	6.88007	−	7.94003i	0.436885	−	0.504192i
$249$	16.4467	−	4.82919i	1.04227	−	0.306037i
$250$	0.415415	−	0.909632i	0.0262732	−	0.0575302i
$251$	−0.0130087	−	0.0904775i	−0.000821102	−	0.00571089i	0.989407	−	0.145170i	$-0.0463728\pi$
$251$	−0.0130087	−	0.0904775i	−0.000821102	−	0.00571089i	−0.990228	+	0.139459i	$0.955464\pi$
$252$	−1.41710			−0.0892690
$253$	17.2492	+	9.01196i	1.08445	+	0.566577i
$254$	5.76736			0.361876
$255$	−0.101622	−	0.706796i	−0.00636381	−	0.0442613i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−24.5989	+	7.22290i	−1.53444	+	0.450552i	−0.936406	−	0.350919i	$-0.885869\pi$
$257$	−24.5989	+	7.22290i	−1.53444	+	0.450552i	−0.598033	+	0.801471i	$0.704051\pi$
$258$	0.781628	−	0.902047i	0.0486620	−	0.0561590i
$259$	−2.59226	−	0.761155i	−0.161075	−	0.0472959i
$260$	−3.17730	+	2.04193i	−0.197048	+	0.126635i
$261$	2.63566	+	5.77128i	0.163143	+	0.357233i
$262$	−5.42168	−	6.25695i	−0.334953	−	0.386556i
$263$	2.26320	+	1.45447i	0.139555	+	0.0896863i	0.608555	−	0.793512i	$-0.291749\pi$
$263$	2.26320	+	1.45447i	0.139555	+	0.0896863i	−0.469001	+	0.883198i	$0.655386\pi$
$264$	0.577515	−	4.01670i	0.0355436	−	0.247211i
$265$	−1.73981	+	12.1006i	−0.106876	+	0.743337i
$266$	−6.28726	−	4.04058i	−0.385497	−	0.247744i
$267$	5.39245	+	6.22321i	0.330012	+	0.380855i
$268$	4.49489	+	9.84244i	0.274569	+	0.601223i
$269$	−9.06953	+	5.82863i	−0.552979	+	0.355378i	−0.787096	−	0.616830i	$-0.788416\pi$
$269$	−9.06953	+	5.82863i	−0.552979	+	0.355378i	0.234117	+	0.972208i	$0.424780\pi$
$270$	−0.959493	−	0.281733i	−0.0583929	−	0.0171457i
$271$	−18.0403	+	20.8196i	−1.09587	+	1.26470i	−0.134062	+	0.990973i	$0.542802\pi$
$271$	−18.0403	+	20.8196i	−1.09587	+	1.26470i	−0.961807	+	0.273727i	$0.911743\pi$
$272$	−0.685140	+	0.201175i	−0.0415427	+	0.0121980i
$273$	2.22339	−	4.86854i	0.134565	−	0.294657i
$274$	−0.259788	−	1.80687i	−0.0156944	−	0.109157i
$275$	−4.05801			−0.244707
$276$	−4.25066	−	2.22078i	−0.255860	−	0.133675i
$277$	1.21105			0.0727648			0.0363824	−	0.999338i	$-0.488417\pi$
$277$	1.21105			0.0727648			0.0363824	+	0.999338i	$0.488417\pi$
$278$	0.404197	+	2.81125i	0.0242421	+	0.168608i
$279$	−4.36442	+	9.55674i	−0.261291	+	0.572147i
$280$	1.35970	−	0.399244i	0.0812575	−	0.0238594i
$281$	19.1395	−	22.0882i	1.14177	−	1.31767i	0.200625	−	0.979668i	$-0.435703\pi$
$281$	19.1395	−	22.0882i	1.14177	−	1.31767i	0.941145	−	0.338004i	$-0.109752\pi$
$282$	−5.98563	−	1.75754i	−0.356439	−	0.104660i
$283$	−19.2446	+	12.3677i	−1.14397	+	0.735186i	−0.968430	−	0.249286i	$-0.919804\pi$
$283$	−19.2446	+	12.3677i	−1.14397	+	0.735186i	−0.175542	+	0.984472i	$0.556168\pi$
$284$	5.13888	+	11.2526i	0.304937	+	0.667718i
$285$	−3.45368	−	3.98576i	−0.204579	−	0.236096i
$286$	12.8935	+	8.28616i	0.762410	+	0.489971i
$287$	2.29127	−	15.9361i	0.135249	−	0.940678i
$288$	−0.142315	+	0.989821i	−0.00838598	+	0.0583258i
$289$	−13.8724	−	8.91523i	−0.816021	−	0.524425i
$290$	−4.15485	−	4.79496i	−0.243981	−	0.281569i
$291$	−0.943199	−	2.06532i	−0.0552913	−	0.121071i
$292$	1.98747	−	1.27727i	0.116308	−	0.0747466i
$293$	22.6294	+	6.64458i	1.32202	+	0.388181i	0.865222	−	0.501389i	$-0.167177\pi$
$293$	22.6294	+	6.64458i	1.32202	+	0.388181i	0.456800	+	0.889570i	$0.348996\pi$
$294$	3.26895	−	3.77257i	0.190649	−	0.220021i
$295$	−11.6579	+	3.42307i	−0.678750	+	0.199299i
$296$	−0.791986	+	1.73421i	−0.0460332	+	0.100799i
$297$	0.577515	+	4.01670i	0.0335108	+	0.233073i
$298$	−17.8666			−1.03498
$299$	14.2988	−	11.1191i	0.826920	−	0.643032i
$300$	1.00000			0.0577350
$301$	−0.240715	−	1.67421i	−0.0138746	−	0.0964996i
$302$	6.73398	−	14.7454i	0.387497	−	0.848500i
$303$	−15.9091	+	4.67133i	−0.913953	+	0.268361i
$304$	−3.45368	+	3.98576i	−0.198082	+	0.228599i
$305$	10.0993	+	2.96543i	0.578287	+	0.169800i
$306$	0.600709	−	0.386052i	0.0343402	−	0.0220691i
$307$	8.71841	+	19.0907i	0.497586	+	1.08956i	0.977246	+	0.212107i	$0.0680325\pi$
$307$	8.71841	+	19.0907i	0.497586	+	1.08956i	−0.479661	+	0.877454i	$0.659240\pi$
$308$	−3.76585	−	4.34602i	−0.214579	−	0.247637i
$309$	−9.34869	−	6.00804i	−0.531828	−	0.341785i
$310$	1.49518	−	10.3992i	0.0849207	−	0.590636i
$311$	0.334808	−	2.32864i	0.0189852	−	0.132045i	−0.978124	−	0.208021i	$-0.933298\pi$
$311$	0.334808	−	2.32864i	0.0189852	−	0.132045i	0.997110	+	0.0759753i	$0.0242070\pi$
$312$	−3.17730	−	2.04193i	−0.179879	−	0.115601i
$313$	−21.7103	−	25.0550i	−1.22714	−	1.41619i	−0.877685	−	0.479237i	$-0.840913\pi$
$313$	−21.7103	−	25.0550i	−1.22714	−	1.41619i	−0.349451	−	0.936954i	$-0.613632\pi$
$314$	1.14510	+	2.50742i	0.0646217	+	0.141502i
$315$	−1.19214	+	0.766143i	−0.0671696	+	0.0431673i
$316$	7.43307	+	2.18255i	0.418143	+	0.122778i
$317$	−8.30392	+	9.58324i	−0.466395	+	0.538248i	−0.939405	−	0.342808i	$-0.888622\pi$
$317$	−8.30392	+	9.58324i	−0.466395	+	0.538248i	0.473010	+	0.881057i	$0.343167\pi$
$318$	−11.7299	+	3.44420i	−0.657779	+	0.193141i
$319$	−10.6955	+	23.4199i	−0.598834	+	1.31126i
$320$	−0.142315	−	0.989821i	−0.00795564	−	0.0553327i
$321$	14.9881			0.836556
$322$	−6.32303	+	2.49145i	−0.352369	+	0.138843i
$323$	3.76592			0.209541
$324$	−0.142315	−	0.989821i	−0.00790638	−	0.0549901i
$325$	−1.56897	+	3.43556i	−0.0870307	+	0.190571i
$326$	−18.3183	+	5.37875i	−1.01456	+	0.297901i
$327$	−3.63188	+	4.19141i	−0.200843	+	0.231785i
$328$	−10.9010	−	3.20082i	−0.601907	−	0.176736i
$329$	−7.43697	+	4.77945i	−0.410013	+	0.263500i
$330$	−1.68576	−	3.69129i	−0.0927979	−	0.203199i
$331$	20.3168	+	23.4469i	1.11671	+	1.28876i	0.953242	+	0.302208i	$0.0977237\pi$
$331$	20.3168	+	23.4469i	1.11671	+	1.28876i	0.163472	+	0.986548i	$0.447731\pi$
$332$	−14.4200	−	9.26715i	−0.791398	−	0.508601i
$333$	0.271322	−	1.88709i	0.0148684	−	0.103412i
$334$	−1.57053	+	10.9233i	−0.0859354	+	0.597694i
$335$	9.10257	+	5.84987i	0.497326	+	0.319612i
$336$	0.928004	+	1.07097i	0.0506268	+	0.0584264i
$337$	3.95785	+	8.66647i	0.215598	+	0.472093i	0.986270	−	0.165138i	$-0.0528070\pi$
$337$	3.95785	+	8.66647i	0.215598	+	0.472093i	−0.770673	+	0.637231i	$0.780080\pi$
$338$	1.06396	−	0.683767i	0.0578719	−	0.0371920i
$339$	−4.50082	−	1.32156i	−0.244451	−	0.0717772i
$340$	−0.467613	+	0.539654i	−0.0253599	+	0.0292668i
$341$	−40.9071	+	12.0114i	−2.21524	+	0.650454i
$342$	2.19087	−	4.79733i	0.118468	−	0.259410i
$343$	−2.41845	−	16.8207i	−0.130584	−	0.908230i
$344$	−1.19358			−0.0643535
$345$	−4.77653	+	0.429838i	−0.257160	+	0.0231417i
$346$	2.72871			0.146696
$347$	3.83443	+	26.6690i	0.205843	+	1.43167i	0.786535	+	0.617546i	$0.211873\pi$
$347$	3.83443	+	26.6690i	0.205843	+	1.43167i	−0.580692	+	0.814123i	$0.697218\pi$
$348$	2.63566	−	5.77128i	0.141286	−	0.309373i
$349$	−27.8893	+	8.18904i	−1.49288	+	0.438349i	−0.923459	−	0.383697i	$-0.874651\pi$
$349$	−27.8893	+	8.18904i	−1.49288	+	0.438349i	−0.569421	+	0.822046i	$0.692832\pi$
$350$	0.928004	−	1.07097i	0.0496039	−	0.0572460i
$351$	3.62388	+	1.06407i	0.193428	+	0.0567957i
$352$	−3.41381	+	2.19392i	−0.181957	+	0.116937i
$353$	−3.95418	−	8.65845i	−0.210460	−	0.460843i	0.774734	−	0.632287i	$-0.217884\pi$
$353$	−3.95418	−	8.65845i	−0.210460	−	0.460843i	−0.985194	+	0.171445i	$0.945157\pi$
$354$	−7.95661	−	9.18242i	−0.422889	−	0.488040i
$355$	10.4067	+	6.68799i	0.552331	+	0.354962i
$356$	1.17189	−	8.15068i	0.0621101	−	0.431985i
$357$	0.144009	−	1.00160i	0.00762174	−	0.0530104i
$358$	−2.04276	−	1.31280i	−0.107963	−	0.0693838i
$359$	−15.7334	−	18.1573i	−0.830377	−	0.958306i	0.169251	−	0.985573i	$-0.445865\pi$
$359$	−15.7334	−	18.1573i	−0.830377	−	0.958306i	−0.999628	+	0.0272665i	$0.991320\pi$
$360$	0.415415	+	0.909632i	0.0218943	+	0.0479418i
$361$	7.41501	−	4.76534i	0.390264	−	0.250807i
$362$	−6.51871	−	1.91407i	−0.342616	−	0.100601i
$363$	−3.58040	+	4.13200i	−0.187922	+	0.216874i
$364$	−5.13540	+	1.50789i	−0.269168	+	0.0790349i
$365$	0.981423	−	2.14902i	0.0513700	−	0.112485i
$366$	1.49796	+	10.4186i	0.0782999	+	0.544587i
$367$	13.0566			0.681548			0.340774	−	0.940145i	$-0.389311\pi$
$367$	13.0566			0.681548			0.340774	+	0.940145i	$0.389311\pi$
$368$	1.10523	+	4.66674i	0.0576143	+	0.243271i
$369$	11.3612			0.591441
$370$	0.271322	+	1.88709i	0.0141054	+	0.0981050i
$371$	−7.19672	+	15.7586i	−0.373635	+	0.818147i
$372$	10.0806	−	2.95993i	0.522654	−	0.153465i
$373$	−0.111637	+	0.128836i	−0.00578035	+	0.00667088i	−0.758632	−	0.651519i	$-0.774132\pi$
$373$	−0.111637	+	0.128836i	−0.00578035	+	0.00667088i	0.752852	+	0.658190i	$0.228678\pi$
$374$	2.78030	+	0.816370i	0.143766	+	0.0422135i
$375$	0.841254	−	0.540641i	0.0434421	−	0.0279186i
$376$	2.59150	+	5.67458i	0.133646	+	0.292644i
$377$	15.6923	+	18.1099i	0.808196	+	0.932708i
$378$	−1.19214	−	0.766143i	−0.0613171	−	0.0394061i
$379$	1.27004	−	8.83332i	0.0652375	−	0.453737i	−0.930853	−	0.365395i	$-0.880934\pi$
$379$	1.27004	−	8.83332i	0.0652375	−	0.453737i	0.996090	−	0.0883422i	$-0.0281569\pi$
$380$	−0.750557	+	5.22024i	−0.0385028	+	0.267793i
$381$	4.85181	+	3.11807i	0.248566	+	0.159743i
$382$	−12.7179	−	14.6772i	−0.650705	−	0.750953i
$383$	8.79040	+	19.2483i	0.449169	+	0.983542i	0.989824	+	0.142298i	$0.0454490\pi$
$383$	8.79040	+	19.2483i	0.449169	+	0.983542i	−0.540655	+	0.841244i	$0.681824\pi$
$384$	0.841254	−	0.540641i	0.0429300	−	0.0275895i
$385$	−5.51767	−	1.62013i	−0.281206	−	0.0825696i
$386$	1.86365	−	2.15077i	0.0948574	−	0.109471i
$387$	1.14523	−	0.336270i	0.0582153	−	0.0170936i
$388$	−0.943199	+	2.06532i	−0.0478837	+	0.104851i
$389$	−2.78719	−	19.3853i	−0.141316	−	0.982876i	−0.929864	−	0.367903i	$-0.880076\pi$
$389$	−2.78719	−	19.3853i	−0.141316	−	0.982876i	0.788548	−	0.614973i	$-0.210833\pi$
$390$	−3.77687			−0.191249
$391$	2.00160	−	2.77867i	0.101225	−	0.140523i
$392$	−4.99182			−0.252125
$393$	−1.17824	−	8.19486i	−0.0594345	−	0.413376i
$394$	−3.26727	+	7.15432i	−0.164603	+	0.360429i
$395$	7.43307	−	2.18255i	0.373998	−	0.109816i
$396$	2.65743	−	3.06684i	0.133541	−	0.154114i
$397$	−2.26408	−	0.664794i	−0.113631	−	0.0333651i	0.224423	−	0.974492i	$-0.427950\pi$
$397$	−2.26408	−	0.664794i	−0.113631	−	0.0333651i	−0.338054	+	0.941127i	$0.609769\pi$
$398$	16.1602	−	10.3855i	0.810036	−	0.520578i
$399$	−3.10468	−	6.79830i	−0.155428	−	0.340341i
$400$	−0.654861	−	0.755750i	−0.0327430	−	0.0377875i
$401$	−27.3245	−	17.5604i	−1.36452	−	0.876925i	−0.365966	−	0.930628i	$-0.619261\pi$
$401$	−27.3245	−	17.5604i	−1.36452	−	0.876925i	−0.998557	+	0.0537030i	$0.982898\pi$
$402$	−1.53988	+	10.7101i	−0.0768023	+	0.534172i
$403$	−5.64711	+	39.2765i	−0.281303	+	1.95650i
$404$	13.9486	+	8.96421i	0.693968	+	0.445986i
$405$	−0.654861	−	0.755750i	−0.0325403	−	0.0375535i
$406$	−3.73499	−	8.17849i	−0.185365	−	0.405892i
$407$	6.50841	−	4.18270i	0.322610	−	0.207329i
$408$	−0.685140	−	0.201175i	−0.0339195	−	0.00995965i
$409$	12.8845	−	14.8695i	0.637095	−	0.735247i	−0.341763	−	0.939786i	$-0.611024\pi$
$409$	12.8845	−	14.8695i	0.637095	−	0.735247i	0.978858	+	0.204539i	$0.0655695\pi$
$410$	−10.9010	+	3.20082i	−0.538362	+	0.158077i
$411$	0.758318	−	1.66048i	0.0374051	−	0.0819057i
$412$	1.58152	+	10.9997i	0.0779158	+	0.541916i
$413$	−17.2179			−0.847237
$414$	−2.37524	−	4.16632i	−0.116737	−	0.204764i
$415$	−17.1410			−0.841421
$416$	0.537504	+	3.73843i	0.0263533	+	0.183291i
$417$	−1.17985	+	2.58350i	−0.0577773	+	0.126515i
$418$	20.5347	−	6.02953i	1.00438	−	0.294914i
$419$	−5.13772	+	5.92925i	−0.250994	+	0.289663i	−0.867239	−	0.497892i	$-0.834108\pi$
$419$	−5.13772	+	5.92925i	−0.250994	+	0.289663i	0.616245	+	0.787554i	$0.288653\pi$
$420$	1.35970	+	0.399244i	0.0663465	+	0.0194811i
$421$	−22.7087	+	14.5940i	−1.10675	+	0.711268i	−0.960584	−	0.277991i	$-0.910331\pi$
$421$	−22.7087	+	14.5940i	−1.10675	+	0.711268i	−0.146171	+	0.989259i	$0.546695\pi$
$422$	0.345607	+	0.756774i	0.0168239	+	0.0368392i
$423$	−4.08524	−	4.71461i	−0.198631	−	0.229232i
$424$	10.2844	+	6.60938i	0.499454	+	0.320980i
$425$	−0.101622	+	0.706796i	−0.00492939	+	0.0342846i
$426$	−1.76050	+	12.2446i	−0.0852967	+	0.593251i
$427$	12.5481	+	8.06420i	0.607247	+	0.390254i
$428$	−9.81515	−	11.3273i	−0.474433	−	0.547525i
$429$	6.36688	+	13.9415i	0.307396	+	0.673103i
$430$	−1.00410	+	0.645298i	−0.0484221	+	0.0311190i
$431$	17.5620	+	5.15666i	0.845931	+	0.248388i	0.675847	−	0.737042i	$-0.263778\pi$
$431$	17.5620	+	5.15666i	0.845931	+	0.248388i	0.170084	+	0.985430i	$0.445596\pi$
$432$	−0.654861	+	0.755750i	−0.0315070	+	0.0363610i
$433$	−23.7125	+	6.96261i	−1.13955	+	0.334602i	−0.796454	−	0.604699i	$-0.793293\pi$
$433$	−23.7125	+	6.96261i	−1.13955	+	0.334602i	−0.343095	+	0.939301i	$0.611475\pi$
$434$	6.18482	−	13.5429i	0.296881	−	0.650079i
$435$	−0.902936	−	6.28006i	−0.0432925	−	0.301106i
$436$	5.54603			0.265607
$437$	1.34120	−	25.2573i	0.0641582	−	1.20822i
$438$	2.36251			0.112885
$439$	−0.849097	−	5.90560i	−0.0405252	−	0.281859i	−1.00000		6.45386e-5i	$-0.999979\pi$
$439$	−0.849097	−	5.90560i	−0.0405252	−	0.281859i	0.959475	−	0.281794i	$-0.0909296\pi$
$440$	−1.68576	+	3.69129i	−0.0803653	+	0.175975i
$441$	4.78962	−	1.40636i	0.228077	−	0.0669695i
$442$	1.76611	−	2.03820i	0.0840053	−	0.0969473i
$443$	−23.5065	−	6.90213i	−1.11683	−	0.327930i	−0.329310	−	0.944222i	$-0.606816\pi$
$443$	−23.5065	−	6.90213i	−1.11683	−	0.327930i	−0.787518	+	0.616292i	$0.788634\pi$
$444$	−1.60384	+	1.03073i	−0.0761151	+	0.0489162i
$445$	−3.42073	−	7.49036i	−0.162158	−	0.355077i
$446$	−6.99846	−	8.07665i	−0.331386	−	0.382440i
$447$	−15.0303	−	9.65939i	−0.710909	−	0.456873i
$448$	0.201675	−	1.40268i	0.00952823	−	0.0662703i
$449$	−1.45278	+	10.1043i	−0.0685609	+	0.476852i	0.926396	+	0.376550i	$0.122890\pi$
$449$	−1.45278	+	10.1043i	−0.0685609	+	0.476852i	−0.994957	+	0.100301i	$0.968019\pi$
$450$	0.841254	+	0.540641i	0.0396571	+	0.0254861i
$451$	30.1916	+	34.8430i	1.42167	+	1.64069i
$452$	1.94864	+	4.26693i	0.0916563	+	0.200699i
$453$	13.6369	−	8.76392i	0.640719	−	0.411765i
$454$	−15.4725	−	4.54313i	−0.726160	−	0.213220i
$455$	−3.50495	+	4.04493i	−0.164315	+	0.189629i
$456$	−5.06029	+	1.48584i	−0.236970	+	0.0695806i
$457$	1.95891	−	4.28942i	0.0916340	−	0.200651i	−0.858266	−	0.513206i	$-0.828458\pi$
$457$	1.95891	−	4.28942i	0.0916340	−	0.200651i	0.949900	+	0.312555i	$0.101185\pi$
$458$	−0.746887	−	5.19471i	−0.0348997	−	0.242733i
$459$	0.714064			0.0333297
$460$	3.45281	+	3.32838i	0.160988	+	0.155186i
$461$	9.58668			0.446496			0.223248	−	0.974762i	$-0.428334\pi$
$461$	9.58668			0.446496			0.223248	+	0.974762i	$0.428334\pi$
$462$	−0.818397	−	5.69207i	−0.0380753	−	0.264819i
$463$	−6.74867	+	14.7775i	−0.313637	+	0.686770i	−0.999147	−	0.0412937i	$-0.986852\pi$
$463$	−6.74867	+	14.7775i	−0.313637	+	0.686770i	0.685510	+	0.728063i	$0.259579\pi$
$464$	−6.08763	+	1.78749i	−0.282611	+	0.0829821i
$465$	6.88007	−	7.94003i	0.319056	−	0.368210i
$466$	20.1850	+	5.92686i	0.935054	+	0.274557i
$467$	21.6105	−	13.8882i	1.00001	−	0.642670i	0.0652238	−	0.997871i	$-0.479224\pi$
$467$	21.6105	−	13.8882i	1.00001	−	0.642670i	0.934790	+	0.355201i	$0.115588\pi$
$468$	−1.56897	−	3.43556i	−0.0725256	−	0.158809i
$469$	10.0412	+	11.5882i	0.463661	+	0.535093i
$470$	5.24802	+	3.37270i	0.242073	+	0.155571i
$471$	−0.392293	+	2.72846i	−0.0180759	+	0.125721i
$472$	−1.72914	+	12.0264i	−0.0795900	+	0.553560i
$473$	4.07465	+	2.61862i	0.187353	+	0.120404i
$474$	5.07312	+	5.85469i	0.233016	+	0.268915i
$475$	2.19087	+	4.79733i	0.100524	+	0.220116i
$476$	−0.851266	+	0.547075i	−0.0390177	+	0.0250751i
$477$	−11.7299	−	3.44420i	−0.537074	−	0.157699i
$478$	2.10204	−	2.42588i	0.0961449	−	0.110957i
$479$	−17.7817	+	5.22117i	−0.812465	+	0.238561i	−0.661468	−	0.749973i	$-0.730066\pi$
$479$	−17.7817	+	5.22117i	−0.812465	+	0.238561i	−0.150997	+	0.988534i	$0.548248\pi$
$480$	0.415415	−	0.909632i	0.0189610	−	0.0415188i
$481$	−1.02475	−	7.12728i	−0.0467245	−	0.324976i
$482$	−4.52236			−0.205988
$483$	−6.66625	−	1.32255i	−0.303325	−	0.0601780i
$484$	5.46742			0.248519
$485$	0.323125	+	2.24739i	0.0146724	+	0.102049i
$486$	0.415415	−	0.909632i	0.0188436	−	0.0412617i
$487$	−16.4244	+	4.82265i	−0.744263	+	0.218535i	−0.631812	−	0.775122i	$-0.717688\pi$
$487$	−16.4244	+	4.82265i	−0.744263	+	0.218535i	−0.112451	+	0.993657i	$0.535870\pi$
$488$	6.89287	−	7.95480i	0.312026	−	0.360097i
$489$	−18.3183	−	5.37875i	−0.828384	−	0.243236i
$490$	−4.19939	+	2.69878i	−0.189709	+	0.121919i
$491$	−1.94137	−	4.25100i	−0.0876126	−	0.191845i	0.860754	−	0.509021i	$-0.169993\pi$
$491$	−1.94137	−	4.25100i	−0.0876126	−	0.191845i	−0.948367	+	0.317176i	$0.897265\pi$
$492$	−7.44001	−	8.58623i	−0.335421	−	0.387097i
$493$	3.81128	+	2.44936i	0.171651	+	0.110314i
$494$	2.83476	−	19.7162i	0.127542	−	0.887072i
$495$	0.577515	−	4.01670i	0.0259573	−	0.180537i
$496$	−8.83835	−	5.68006i	−0.396854	−	0.255042i
$497$	11.4799	+	13.2485i	0.514942	+	0.594275i
$498$	−7.12065	−	15.5920i	−0.319084	−	0.698696i
$499$	−10.8612	+	6.98007i	−0.486214	+	0.312471i	−0.760681	−	0.649126i	$-0.775135\pi$
$499$	−10.8612	+	6.98007i	−0.486214	+	0.312471i	0.274467	+	0.961597i	$0.411499\pi$
$500$	−0.959493	−	0.281733i	−0.0429098	−	0.0125995i
$501$	−7.22677	+	8.34014i	−0.322868	+	0.372610i
$502$	−0.0877053	+	0.0257526i	−0.00391448	+	0.00114939i
$503$	6.61485	−	14.4845i	0.294941	−	0.645832i	−0.702915	−	0.711274i	$-0.748119\pi$
$503$	6.61485	−	14.4845i	0.294941	−	0.645832i	0.997856	+	0.0654422i	$0.0208458\pi$
$504$	0.201675	+	1.40268i	0.00898330	+	0.0624802i
$505$	16.5807			0.737832
$506$	6.46541	−	18.3562i	0.287422	−	0.816031i
$507$	1.26473			0.0561688
$508$	−0.820780	−	5.70865i	−0.0364162	−	0.253281i
$509$	5.41142	−	11.8494i	0.239857	−	0.525214i	−0.750972	−	0.660334i	$-0.770415\pi$
$509$	5.41142	−	11.8494i	0.239857	−	0.525214i	0.990829	+	0.135120i	$0.0431420\pi$
$510$	−0.685140	+	0.201175i	−0.0303385	+	0.00890818i
$511$	2.19242	−	2.53019i	0.0969870	−	0.111929i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	4.43670	−	2.85130i	0.195885	−	0.125888i
$514$	10.6502	+	23.3206i	0.469759	+	1.02863i
$515$	7.27734	+	8.39850i	0.320678	+	0.370082i
$516$	−1.00410	−	0.645298i	−0.0442032	−	0.0284076i
$517$	3.60273	−	25.0575i	0.158448	−	1.10203i
$518$	−0.384491	+	2.67419i	−0.0168936	+	0.117497i
$519$	2.29553	+	1.47525i	0.100763	+	0.0647563i
$520$	2.47332	+	2.85437i	0.108462	+	0.125172i
$521$	−1.09982	−	2.40827i	−0.0481841	−	0.105508i	0.884009	−	0.467470i	$-0.154834\pi$
$521$	−1.09982	−	2.40827i	−0.0481841	−	0.105508i	−0.932193	+	0.361962i	$0.882107\pi$
$522$	5.33745	−	3.43017i	0.233614	−	0.150134i
$523$	0.221422	+	0.0650154i	0.00968212	+	0.00284293i	0.286570	−	0.958059i	$-0.407485\pi$
$523$	0.221422	+	0.0650154i	0.00968212	+	0.00284293i	−0.276888	+	0.960902i	$0.589303\pi$
$524$	−5.42168	+	6.25695i	−0.236847	+	0.273336i
$525$	1.35970	−	0.399244i	0.0593421	−	0.0174244i
$526$	1.11758	−	2.44715i	0.0487287	−	0.106701i
$527$	1.06766	+	7.42572i	0.0465079	+	0.323469i
$528$	−4.05801			−0.176602
$529$	−17.9231	−	14.4139i	−0.779266	−	0.626693i
$530$	12.2251			0.531023
$531$	−1.72914	−	12.0264i	−0.0750381	−	0.521902i
$532$	−3.10468	+	6.79830i	−0.134605	+	0.294744i
$533$	41.1716	−	12.0891i	1.78334	−	0.523636i
$534$	5.39245	−	6.22321i	0.233354	−	0.269305i
$535$	−14.3810	−	4.22265i	−0.621746	−	0.182561i
$536$	9.10257	−	5.84987i	0.393171	−	0.252676i
$537$	−1.00873	−	2.20880i	−0.0435297	−	0.0953168i
$538$	7.06003	+	8.14771i	0.304380	+	0.351273i
$539$	17.0412	+	10.9517i	0.734014	+	0.471722i
$540$	−0.142315	+	0.989821i	−0.00612426	+	0.0425951i
$541$	−1.92186	+	13.3668i	−0.0826270	+	0.574683i	0.905883	+	0.423528i	$0.139208\pi$
$541$	−1.92186	+	13.3668i	−0.0826270	+	0.574683i	−0.988510	+	0.151155i	$0.951701\pi$
$542$	23.1751	+	14.8937i	0.995455	+	0.639740i
$543$	−4.44906	−	5.13449i	−0.190928	−	0.220342i
$544$	0.296633	+	0.649536i	0.0127180	+	0.0278486i
$545$	4.66562	−	2.99841i	0.199853	−	0.128438i
$546$	−5.13540	−	1.50789i	−0.219775	−	0.0645318i
$547$	25.4593	−	29.3816i	1.08856	−	1.25627i	0.124037	−	0.992278i	$-0.460416\pi$
$547$	25.4593	−	29.3816i	1.08856	−	1.25627i	0.964525	−	0.263990i	$-0.0850387\pi$
$548$	−1.75150	+	0.514288i	−0.0748205	+	0.0219693i
$549$	−4.37254	+	9.57452i	−0.186615	+	0.408631i
$550$	0.577515	+	4.01670i	0.0246253	+	0.171273i
$551$	33.4611			1.42549
$552$	−1.59325	+	4.52345i	−0.0678131	+	0.192531i
$553$	10.9781			0.466836
$554$	−0.172350	−	1.19872i	−0.00732246	−	0.0509288i
$555$	−0.791986	+	1.73421i	−0.0336179	+	0.0736130i
$556$	2.72511	−	0.800165i	0.115571	−	0.0339346i
$557$	6.25564	−	7.21939i	0.265060	−	0.305895i	−0.607581	−	0.794258i	$-0.707860\pi$
$557$	6.25564	−	7.21939i	0.265060	−	0.305895i	0.872641	+	0.488362i	$0.162405\pi$
$558$	10.0806	+	2.95993i	0.426745	+	0.125304i
$559$	3.79236	−	2.43720i	0.160400	−	0.103083i
$560$	−0.588685	−	1.28904i	−0.0248765	−	0.0544719i
$561$	1.89758	+	2.18992i	0.0801157	+	0.0924584i
$562$	−24.5872	−	15.8012i	−1.03715	−	0.666535i
$563$	1.58100	−	10.9961i	0.0666314	−	0.463431i	−0.929001	−	0.370076i	$-0.879332\pi$
$563$	1.58100	−	10.9961i	0.0666314	−	0.463431i	0.995633	−	0.0933554i	$-0.0297593\pi$
$564$	−0.887807	+	6.17483i	−0.0373834	+	0.260007i
$565$	3.94618	+	2.53605i	0.166017	+	0.106693i
$566$	14.9806	+	17.2886i	0.629684	+	0.726694i
$567$	−0.588685	−	1.28904i	−0.0247225	−	0.0541346i
$568$	10.4067	−	6.68799i	0.436656	−	0.280622i
$569$	−30.0764	−	8.83122i	−1.26087	−	0.370224i	−0.418050	−	0.908424i	$-0.637286\pi$
$569$	−30.0764	−	8.83122i	−1.26087	−	0.370224i	−0.842817	+	0.538200i	$0.819104\pi$
$570$	−3.45368	+	3.98576i	−0.144659	+	0.166945i
$571$	11.4986	−	3.37629i	0.481201	−	0.141293i	−0.0321306	−	0.999484i	$-0.510229\pi$
$571$	11.4986	−	3.37629i	0.481201	−	0.141293i	0.513332	+	0.858190i	$0.328411\pi$
$572$	6.36688	−	13.9415i	0.266213	−	0.582925i
$573$	−2.76387	−	19.2231i	−0.115462	−	0.803057i
$574$	−16.1000			−0.672000
$575$	4.70415	+	0.933277i	0.196176	+	0.0389203i
$576$	1.00000			0.0416667
$577$	−2.08892	−	14.5288i	−0.0869628	−	0.604840i	−0.985972	−	0.166910i	$-0.946621\pi$
$577$	−2.08892	−	14.5288i	−0.0869628	−	0.604840i	0.899009	−	0.437930i	$-0.144288\pi$
$578$	−6.85024	+	14.9999i	−0.284932	+	0.623915i
$579$	2.73060	−	0.801776i	0.113480	−	0.0333207i
$580$	−4.15485	+	4.79496i	−0.172521	+	0.199100i
$581$	−23.3067	−	6.84345i	−0.966923	−	0.283914i
$582$	−1.91006	+	1.22752i	−0.0791747	+	0.0508825i
$583$	−20.6085	−	45.1263i	−0.853517	−	1.86894i
$584$	−1.54712	−	1.78547i	−0.0640201	−	0.0738832i
$585$	−3.17730	−	2.04193i	−0.131365	−	0.0844234i
$586$	3.35645	−	23.3447i	0.138654	−	0.964359i
$587$	5.43721	−	37.8166i	0.224417	−	1.56086i	−0.496624	−	0.867966i	$-0.665427\pi$
$587$	5.43721	−	37.8166i	0.224417	−	1.56086i	0.721041	−	0.692892i	$-0.243664\pi$
$588$	−4.19939	−	2.69878i	−0.173180	−	0.111296i
$589$	36.2850	+	41.8751i	1.49510	+	1.72543i
$590$	5.04733	+	11.0521i	0.207795	+	0.455008i
$591$	−6.61652	+	4.25218i	−0.272167	+	0.174911i
$592$	1.82927	+	0.537121i	0.0751824	+	0.0220755i
$593$	−9.51998	+	10.9866i	−0.390939	+	0.451167i	−0.916766	−	0.399424i	$-0.869210\pi$
$593$	−9.51998	+	10.9866i	−0.390939	+	0.451167i	0.525828	+	0.850591i	$0.323756\pi$
$594$	3.89363	−	1.14327i	0.159758	−	0.0469090i
$595$	−0.420359	+	0.920458i	−0.0172330	+	0.0377351i
$596$	2.54268	+	17.6847i	0.104152	+	0.724394i
$597$	19.2096			0.786197
$598$	−13.0408	−	12.5708i	−0.533279	−	0.514060i
$599$	22.2124			0.907573			0.453787	−	0.891110i	$-0.350073\pi$
$599$	22.2124			0.907573			0.453787	+	0.891110i	$0.350073\pi$
$600$	−0.142315	−	0.989821i	−0.00580998	−	0.0404093i
$601$	−14.8989	+	32.6241i	−0.607740	+	1.33077i	0.316369	+	0.948636i	$0.397536\pi$
$601$	−14.8989	+	32.6241i	−0.607740	+	1.33077i	−0.924109	+	0.382129i	$0.875191\pi$
$602$	−1.62291	+	0.476529i	−0.0661448	+	0.0194219i
$603$	−7.08575	+	8.17740i	−0.288554	+	0.333009i
$604$	−15.5536	−	4.56695i	−0.632868	−	0.185827i
$605$	4.59948	−	2.95591i	0.186996	−	0.120175i
$606$	6.88788	+	15.0824i	0.279801	+	0.612679i
$607$	−24.0284	−	27.7303i	−0.975283	−	1.12554i	−0.992071	−	0.125677i	$-0.959890\pi$
$607$	−24.0284	−	27.7303i	−0.975283	−	1.12554i	0.0167883	−	0.999859i	$-0.494656\pi$
$608$	4.43670	+	2.85130i	0.179932	+	0.115635i
$609$	1.27955	−	8.89948i	0.0518500	−	0.360625i
$610$	1.49796	−	10.4186i	0.0606508	−	0.421836i
$611$	−19.8211	−	12.7382i	−0.801874	−	0.515333i
$612$	−0.467613	−	0.539654i	−0.0189021	−	0.0218142i
$613$	8.80916	+	19.2894i	0.355799	+	0.779090i	0.999900	+	0.0141502i	$0.00450429\pi$
$613$	8.80916	+	19.2894i	0.355799	+	0.779090i	−0.644101	+	0.764940i	$0.722768\pi$
$614$	17.6556	−	11.3466i	0.712521	−	0.457910i
$615$	−10.9010	−	3.20082i	−0.439571	−	0.129070i
$616$	−3.76585	+	4.34602i	−0.151730	+	0.175106i
$617$	1.46014	−	0.428735i	0.0587829	−	0.0172602i	−0.252209	−	0.967673i	$-0.581157\pi$
$617$	1.46014	−	0.428735i	0.0587829	−	0.0172602i	0.310992	+	0.950413i	$0.399339\pi$
$618$	−4.61643	+	10.1086i	−0.185700	+	0.406626i
$619$	−1.85317	−	12.8891i	−0.0744854	−	0.518057i	−0.992570	−	0.121673i	$-0.961174\pi$
$619$	−1.85317	−	12.8891i	−0.0744854	−	0.518057i	0.918085	−	0.396384i	$-0.129735\pi$
$620$	−10.5062			−0.421938
$621$	0.254308	−	4.78908i	0.0102050	−	0.192179i
$622$	−2.35259			−0.0943302
$623$	−1.66069	−	11.5503i	−0.0665341	−	0.462754i
$624$	−1.56897	+	3.43556i	−0.0628090	+	0.137532i
$625$	−0.959493	+	0.281733i	−0.0383797	+	0.0112693i
$626$	−21.7103	+	25.0550i	−0.867717	+	1.00140i
$627$	20.5347	+	6.02953i	0.820077	+	0.240796i
$628$	2.31893	−	1.49029i	0.0925354	−	0.0594689i
$629$	−0.565529	−	1.23834i	−0.0225491	−	0.0493757i
$630$	0.928004	+	1.07097i	0.0369726	+	0.0426686i
$631$	−23.1084	−	14.8509i	−0.919930	−	0.591203i	−0.00729265	−	0.999973i	$-0.502321\pi$
$631$	−23.1084	−	14.8509i	−0.919930	−	0.591203i	−0.912637	+	0.408770i	$0.865958\pi$
$632$	1.10249	−	7.66802i	0.0438549	−	0.305017i
$633$	−0.118400	+	0.823488i	−0.00470596	+	0.0327307i
$634$	10.6675	+	6.85557i	0.423659	+	0.272269i
$635$	−3.77682	−	4.35868i	−0.149878	−	0.172969i
$636$	5.07848	+	11.1203i	0.201375	+	0.440949i
$637$	15.8605	−	10.1930i	0.628418	−	0.403859i
$638$	24.7037	+	7.25365i	0.978027	+	0.287175i
$639$	−8.10094	+	9.34899i	−0.320468	+	0.369840i
$640$	−0.959493	+	0.281733i	−0.0379273	+	0.0111365i
$641$	−0.0353686	+	0.0774463i	−0.00139697	+	0.00305895i	−0.910329	−	0.413885i	$-0.864172\pi$
$641$	−0.0353686	+	0.0774463i	−0.00139697	+	0.00305895i	0.908932	+	0.416944i	$0.136899\pi$
$642$	−2.13303	−	14.8356i	−0.0841842	−	0.585514i
$643$	−21.2929			−0.839708			−0.419854	−	0.907592i	$-0.637919\pi$
$643$	−21.2929			−0.839708			−0.419854	+	0.907592i	$0.637919\pi$
$644$	3.36595	+	5.90410i	0.132637	+	0.232654i
$645$	−1.19358			−0.0469971
$646$	−0.535946	−	3.72759i	−0.0210865	−	0.146660i
$647$	−8.30915	+	18.1945i	−0.326666	+	0.715300i	−0.999705	−	0.0243082i	$-0.992262\pi$
$647$	−8.30915	+	18.1945i	−0.326666	+	0.715300i	0.673038	+	0.739608i	$0.264989\pi$
$648$	−0.959493	+	0.281733i	−0.0376924	+	0.0110675i
$649$	32.2880	−	37.2623i	1.26741	−	1.46267i
$650$	3.62388	+	1.06407i	0.142140	+	0.0417361i
$651$	12.5248	−	8.04922i	0.490887	−	0.315474i
$652$	7.93098	+	17.3664i	0.310601	+	0.680121i
$653$	20.8583	+	24.0718i	0.816250	+	0.942002i	0.999154	−	0.0411283i	$-0.0130952\pi$
$653$	20.8583	+	24.0718i	0.816250	+	0.942002i	−0.182904	+	0.983131i	$0.558550\pi$
$654$	4.66562	+	2.99841i	0.182440	+	0.117247i
$655$	−1.17824	+	8.19486i	−0.0460378	+	0.320200i
$656$	−1.61687	+	11.2456i	−0.0631281	+	0.439065i
$657$	1.98747	+	1.27727i	0.0775387	+	0.0498311i
$658$	5.78919	+	6.68109i	0.225686	+	0.260456i
$659$	−8.86826	−	19.4188i	−0.345458	−	0.756448i	−1.00000		0.000422106i	$-0.999866\pi$
$659$	−8.86826	−	19.4188i	−0.345458	−	0.756448i	0.654542	−	0.756026i	$-0.272862\pi$
$660$	−3.41381	+	2.19392i	−0.132882	+	0.0853984i
$661$	11.8204	+	3.47079i	0.459762	+	0.134998i	0.503408	−	0.864049i	$-0.332079\pi$
$661$	11.8204	+	3.47079i	0.459762	+	0.134998i	−0.0436462	+	0.999047i	$0.513897\pi$
$662$	20.3168	−	23.4469i	0.789636	−	0.911288i
$663$	2.58768	−	0.759812i	0.100497	−	0.0295087i
$664$	−7.12065	+	15.5920i	−0.276335	+	0.605089i
$665$	1.06362	+	7.39761i	0.0412452	+	0.286867i
$666$	−1.90649			−0.0738751
$667$	17.7847	−	24.6892i	0.688627	−	0.955968i
$668$	11.0356			0.426980
$669$	−1.52091	−	10.5782i	−0.0588018	−	0.408975i
$670$	4.49489	−	9.84244i	0.173653	−	0.380247i
$671$	−40.9832	+	12.0338i	−1.58214	+	0.464558i
$672$	0.928004	−	1.07097i	0.0357985	−	0.0413137i
$673$	1.80276	+	0.529339i	0.0694914	+	0.0204045i	0.316293	−	0.948661i	$-0.397562\pi$
$673$	1.80276	+	0.529339i	0.0694914	+	0.0204045i	−0.246802	+	0.969066i	$0.579380\pi$
$674$	8.01500	−	5.15093i	0.308726	−	0.198406i
$675$	0.415415	+	0.909632i	0.0159893	+	0.0350118i
$676$	−0.828225	−	0.955823i	−0.0318548	−	0.0367624i
$677$	−11.4947	−	7.38722i	−0.441779	−	0.283914i	0.300782	−	0.953693i	$-0.402752\pi$
$677$	−11.4947	−	7.38722i	−0.441779	−	0.283914i	−0.742560	+	0.669779i	$0.766389\pi$
$678$	−0.667574	+	4.64308i	−0.0256380	+	0.178316i
$679$	−0.457902	+	3.18477i	−0.0175726	+	0.122220i
$680$	0.600709	+	0.386052i	0.0230361	+	0.0148044i
$681$	−10.5601	−	12.1870i	−0.404663	−	0.467006i
$682$	17.7108	+	38.7813i	0.678183	+	1.48501i
$683$	−12.7842	+	8.21593i	−0.489175	+	0.314374i	−0.761874	−	0.647726i	$-0.775720\pi$
$683$	−12.7842	+	8.21593i	−0.489175	+	0.314374i	0.272698	+	0.962100i	$0.412084\pi$
$684$	−5.06029	−	1.48584i	−0.193485	−	0.0568123i
$685$	−1.19541	+	1.37958i	−0.0456744	+	0.0527111i
$686$	−16.3053	+	4.78766i	−0.622538	+	0.182794i
$687$	2.18015	−	4.77387i	0.0831780	−	0.182134i
$688$	0.169864	+	1.18143i	0.00647600	+	0.0450416i
$689$	−46.1725			−1.75903
$690$	1.10523	+	4.66674i	0.0420756	+	0.177660i
$691$	−10.1343			−0.385527			−0.192763	−	0.981245i	$-0.561745\pi$
$691$	−10.1343			−0.385527			−0.192763	+	0.981245i	$0.561745\pi$
$692$	−0.388336	−	2.70093i	−0.0147623	−	0.102674i
$693$	2.38889	−	5.23094i	0.0907464	−	0.198707i
$694$	25.8519	−	7.59080i	0.981324	−	0.288143i
$695$	1.85991	−	2.14645i	0.0705504	−	0.0814195i
$696$	−6.08763	−	1.78749i	−0.230751	−	0.0677546i
$697$	6.82478	−	4.38602i	0.258507	−	0.166132i
$698$	12.0747	+	26.4400i	0.457036	+	1.00077i
$699$	13.7764	+	15.8989i	0.521073	+	0.601350i
$700$	−1.19214	−	0.766143i	−0.0450587	−	0.0289575i
$701$	0.499188	−	3.47193i	0.0188541	−	0.131133i	−0.978220	−	0.207569i	$-0.933445\pi$
$701$	0.499188	−	3.47193i	0.0188541	−	0.131133i	0.997075	+	0.0764358i	$0.0243540\pi$
$702$	0.537504	−	3.73843i	0.0202868	−	0.141098i
$703$	−8.45855	−	5.43598i	−0.319020	−	0.205022i
$704$	2.65743	+	3.06684i	0.100156	+	0.115586i
$705$	2.59150	+	5.67458i	0.0976014	+	0.213717i
$706$	−8.00758	+	5.14616i	−0.301369	+	0.193678i
$707$	22.5448	+	6.61975i	0.847884	+	0.248961i
$708$	−7.95661	+	9.18242i	−0.299028	+	0.345096i
$709$	27.7501	−	8.14817i	1.04218	−	0.306011i	0.284525	−	0.958669i	$-0.408164\pi$
$709$	27.7501	−	8.14817i	1.04218	−	0.306011i	0.757653	+	0.652658i	$0.226346\pi$
$710$	5.13888	−	11.2526i	0.192859	−	0.422302i
$711$	1.10249	+	7.66802i	0.0413468	+	0.287573i
$712$	−8.23449			−0.308601
$713$	50.1830	−	4.51595i	1.87937	−	0.169124i
$714$	−1.01190			−0.0378695
$715$	−2.18120	−	15.1706i	−0.0815721	−	0.567347i
$716$	−1.00873	+	2.20880i	−0.0376979	+	0.0825468i
$717$	3.07987	−	0.904333i	0.115020	−	0.0337729i
$718$	−15.7334	+	18.1573i	−0.587165	+	0.677625i
$719$	−6.98501	−	2.05098i	−0.260497	−	0.0764888i	0.148876	−	0.988856i	$-0.452434\pi$
$719$	−6.98501	−	2.05098i	−0.260497	−	0.0764888i	−0.409373	+	0.912367i	$0.634253\pi$
$720$	0.841254	−	0.540641i	0.0313517	−	0.0201485i
$721$	6.54194	+	14.3249i	0.243635	+	0.533486i
$722$	−5.77210	−	6.66136i	−0.214815	−	0.247910i
$723$	−3.80446	−	2.44497i	−0.141489	−	0.0909296i
$724$	−0.966874	+	6.72476i	−0.0359336	+	0.249924i
$725$	−0.902936	+	6.28006i	−0.0335342	+	0.233235i
$726$	4.59948	+	2.95591i	0.170703	+	0.109704i
$727$	17.7978	+	20.5398i	0.660084	+	0.761778i	0.982791	−	0.184721i	$-0.0591383\pi$
$727$	17.7978	+	20.5398i	0.660084	+	0.761778i	−0.322707	+	0.946499i	$0.604593\pi$
$728$	2.22339	+	4.86854i	0.0824042	+	0.180440i
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$	−2.26681	−	0.665597i	−0.0838985	−	0.0246348i
$731$	0.558133	−	0.644119i	0.0206433	−	0.0238236i
$732$	10.0993	−	2.96543i	0.373282	−	0.109606i
$733$	0.166065	−	0.363632i	0.00613376	−	0.0134311i	−0.906540	−	0.422119i	$-0.861286\pi$
$733$	0.166065	−	0.363632i	0.00613376	−	0.0134311i	0.912674	+	0.408688i	$0.134014\pi$
$734$	−1.85815	−	12.9237i	−0.0685854	−	0.477022i
$735$	−4.99182			−0.184126
$736$	4.46195	−	1.75813i	0.164470	−	0.0648056i
$737$	−43.9086			−1.61739
$738$	−1.61687	−	11.2456i	−0.0595177	−	0.413955i
$739$	13.4977	−	29.5558i	0.496520	−	1.08723i	−0.481064	−	0.876685i	$-0.659750\pi$
$739$	13.4977	−	29.5558i	0.496520	−	1.08723i	0.977585	−	0.210543i	$-0.0675231\pi$
$740$	1.82927	−	0.537121i	0.0672452	−	0.0197450i
$741$	13.0441	−	15.0537i	0.479187	−	0.553012i
$742$	16.6224	+	4.88078i	0.610228	+	0.179179i
$743$	−1.50703	+	0.968512i	−0.0552877	+	0.0355313i	−0.567993	−	0.823034i	$-0.692280\pi$
$743$	−1.50703	+	0.968512i	−0.0552877	+	0.0355313i	0.512705	+	0.858565i	$0.328643\pi$
$744$	−4.36442	−	9.55674i	−0.160007	−	0.350367i
$745$	11.7001	+	13.5026i	0.428659	+	0.494699i
$746$	0.143412	+	0.0921655i	0.00525070	+	0.00337442i
$747$	2.43942	−	16.9666i	0.0892539	−	0.620774i
$748$	0.412382	−	2.86818i	0.0150782	−	0.104871i
$749$	−17.8680	−	11.4831i	−0.652882	−	0.419582i
$750$	−0.654861	−	0.755750i	−0.0239121	−	0.0275961i
$751$	16.4228	+	35.9610i	0.599278	+	1.31224i	0.929670	+	0.368392i	$0.120092\pi$
$751$	16.4228	+	35.9610i	0.599278	+	1.31224i	−0.330392	+	0.943844i	$0.607181\pi$
$752$	5.24802	−	3.37270i	0.191375	−	0.122990i
$753$	−0.0877053	−	0.0257526i	−0.00319616	−	0.000938476i
$754$	15.6923	−	18.1099i	0.571481	−	0.659524i
$755$	−15.5536	+	4.56695i	−0.566054	+	0.166208i
$756$	−0.588685	+	1.28904i	−0.0214103	+	0.0468820i
$757$	0.563747	+	3.92094i	0.0204897	+	0.142509i	0.997498	−	0.0706910i	$-0.0225204\pi$
$757$	0.563747	+	3.92094i	0.0204897	+	0.142509i	−0.977009	+	0.213200i	$0.931611\pi$
$758$	−8.92415			−0.324140
$759$	15.3631	−	11.9467i	0.557647	−	0.433639i
$760$	5.27392			0.191305
$761$	2.94904	+	20.5110i	0.106902	+	0.743523i	0.970806	+	0.239866i	$0.0771034\pi$
$761$	2.94904	+	20.5110i	0.106902	+	0.743523i	−0.863904	+	0.503657i	$0.831988\pi$
$762$	2.39585	−	5.24617i	0.0867924	−	0.190049i
$763$	7.54093	−	2.21422i	0.273000	−	0.0801600i
$764$	−12.7179	+	14.6772i	−0.460118	+	0.531004i
$765$	−0.685140	−	0.201175i	−0.0247713	−	0.00727350i
$766$	17.8014	−	11.4402i	0.643190	−	0.413353i
$767$	−19.0631	−	41.7423i	−0.688328	−	1.50723i
$768$	−0.654861	−	0.755750i	−0.0236303	−	0.0272708i
$769$	−10.8500	−	6.97287i	−0.391261	−	0.251448i	0.330189	−	0.943915i	$-0.392888\pi$
$769$	−10.8500	−	6.97287i	−0.391261	−	0.251448i	−0.721450	+	0.692467i	$0.756524\pi$
$770$	−0.818397	+	5.69207i	−0.0294930	+	0.205128i
$771$	−3.64859	+	25.3765i	−0.131401	+	0.913911i
$772$	−2.39410	−	1.53860i	−0.0861657	−	0.0553753i
$773$	20.8600	+	24.0737i	0.750281	+	0.865871i	0.994596	−	0.103825i	$-0.0331083\pi$
$773$	20.8600	+	24.0737i	0.750281	+	0.865871i	−0.244314	+	0.969696i	$0.578563\pi$
$774$	−0.495831	−	1.08572i	−0.0178223	−	0.0390253i
$775$	−8.83835	+	5.68006i	−0.317483	+	0.204034i
$776$	2.17853	+	0.639673i	0.0782045	+	0.0229629i
$777$	−1.76923	+	2.04180i	−0.0634709	+	0.0732493i
$778$	−18.7914	+	5.51765i	−0.673703	+	0.197817i
$779$	24.8909	−	54.5034i	0.891808	−	1.95279i
$780$	0.537504	+	3.73843i	0.0192457	+	0.133857i
$781$	−50.1995			−1.79628
$782$	−3.03524	−	1.58578i	−0.108540	−	0.0567075i
$783$	6.34463			0.226739
$784$	0.710411	+	4.94101i	0.0253718	+	0.176465i
$785$	1.14510	−	2.50742i	0.0408703	−	0.0894935i
$786$	−7.94377	+	2.33250i	−0.283345	+	0.0831976i
$787$	−4.93886	+	5.69975i	−0.176051	+	0.203174i	−0.836917	−	0.547331i	$-0.815644\pi$
$787$	−4.93886	+	5.69975i	−0.176051	+	0.203174i	0.660865	+	0.750505i	$0.270190\pi$
$788$	7.54648	+	2.21585i	0.268832	+	0.0789363i
$789$	2.26320	−	1.45447i	0.0805719	−	0.0517804i
$790$	−3.21817	−	7.04680i	−0.114497	−	0.250714i
$791$	4.35311	+	5.02375i	0.154779	+	0.178624i
$792$	−3.41381	−	2.19392i	−0.121305	−	0.0779577i
$793$	−5.65761	+	39.3496i	−0.200908	+	1.39734i
$794$	−0.335815	+	2.33565i	−0.0119176	+	0.0828890i
$795$	10.2844	+	6.60938i	0.364750	+	0.234410i
$796$	−12.5796	−	14.5177i	−0.445873	−	0.514565i
$797$	3.65099	+	7.99454i	0.129325	+	0.283181i	0.963207	−	0.268761i	$-0.0866142\pi$
$797$	3.65099	+	7.99454i	0.129325	+	0.283181i	−0.833882	+	0.551942i	$0.813887\pi$
$798$	−6.28726	+	4.04058i	−0.222567	+	0.143035i
$799$	−4.27413	−	1.25500i	−0.151208	−	0.0443986i
$800$	−0.654861	+	0.755750i	−0.0231528	+	0.0267198i
$801$	7.90094	−	2.31992i	0.279166	−	0.0819705i
$802$	−13.4930	+	29.5455i	−0.476454	+	1.04329i
$803$	1.36439	+	9.48951i	0.0481481	+	0.334877i
$804$	10.8202			0.381601
$805$	6.02362	+	3.14708i	0.212305	+	0.110920i
$806$	39.6804			1.39768
$807$	1.53429	+	10.6712i	0.0540096	+	0.375645i
$808$	6.88788	−	15.0824i	0.242315	−	0.530595i
$809$	−5.66123	+	1.66229i	−0.199038	+	0.0584429i	−0.379732	−	0.925096i	$-0.623984\pi$
$809$	−5.66123	+	1.66229i	−0.199038	+	0.0584429i	0.180694	+	0.983539i	$0.442166\pi$
$810$	−0.654861	+	0.755750i	−0.0230095	+	0.0265543i
$811$	36.6361	+	10.7573i	1.28647	+	0.377741i	0.852281	−	0.523083i	$-0.175218\pi$
$811$	36.6361	+	10.7573i	1.28647	+	0.377741i	0.434185	+	0.900824i	$0.357037\pi$
$812$	−7.56370	+	4.86090i	−0.265434	+	0.170584i
$813$	11.4440	+	25.0588i	0.401357	+	0.878850i
$814$	−5.06637	−	5.84690i	−0.177576	−	0.204934i
$815$	16.0610	+	10.3217i	0.562591	+	0.361555i
$816$	−0.101622	+	0.706796i	−0.00355748	+	0.0247428i
$817$	0.895849	−	6.23077i	0.0313418	−	0.217987i
$818$	−16.5518	−	10.6372i	−0.578718	−	0.371920i
$819$	−3.50495	−	4.04493i	−0.122473	−	0.141341i
$820$	4.71961	+	10.3345i	0.164816	+	0.360897i
$821$	28.1631	−	18.0993i	0.982898	−	0.631670i	0.0526541	−	0.998613i	$-0.483232\pi$
$821$	28.1631	−	18.0993i	0.982898	−	0.631670i	0.930243	+	0.366943i	$0.119596\pi$
$822$	−1.75150	−	0.514288i	−0.0610907	−	0.0179378i
$823$	16.3550	−	18.8747i	0.570101	−	0.657931i	−0.395346	−	0.918532i	$-0.629375\pi$
$823$	16.3550	−	18.8747i	0.570101	−	0.657931i	0.965447	+	0.260601i	$0.0839207\pi$
$824$	10.6627	−	3.13084i	0.371451	−	0.109068i
$825$	−1.68576	+	3.69129i	−0.0586905	+	0.128514i
$826$	2.45036	+	17.0426i	0.0852590	+	0.592989i
$827$	−6.00426			−0.208788			−0.104394	−	0.994536i	$-0.533290\pi$
$827$	−6.00426			−0.208788			−0.104394	+	0.994536i	$0.533290\pi$
$828$	−3.78588	+	2.94399i	−0.131569	+	0.102311i
$829$	−40.3640			−1.40190			−0.700950	−	0.713211i	$-0.747240\pi$
$829$	−40.3640			−1.40190			−0.700950	+	0.713211i	$0.747240\pi$
$830$	2.43942	+	16.9666i	0.0846737	+	0.588918i
$831$	0.503088	−	1.10161i	0.0174519	−	0.0382144i
$832$	3.62388	−	1.06407i	0.125635	−	0.0368899i
$833$	2.33424	−	2.69386i	0.0808766	−	0.0933366i
$834$	2.72511	+	0.800165i	0.0943630	+	0.0277075i
$835$	9.28372	−	5.96629i	0.321277	−	0.206472i
$836$	−8.89055	−	19.4676i	−0.307486	−	0.673300i
$837$	6.88007	+	7.94003i	0.237810	+	0.274448i
$838$	6.60007	+	4.24161i	0.227996	+	0.146524i
$839$	4.24392	−	29.5171i	0.146516	−	1.01904i	−0.775349	−	0.631533i	$-0.782426\pi$
$839$	4.24392	−	29.5171i	0.146516	−	1.01904i	0.921865	−	0.387511i	$-0.126665\pi$
$840$	0.201675	−	1.40268i	0.00695843	−	0.0483970i
$841$	9.46780	+	6.08458i	0.326476	+	0.209813i
$842$	17.6772	+	20.4006i	0.609198	+	0.703052i
$843$	−12.1413	−	26.5857i	−0.418168	−	0.915661i
$844$	0.699886	−	0.449789i	0.0240911	−	0.0154824i
$845$	−1.21350	−	0.356317i	−0.0417458	−	0.0122577i
$846$	−4.08524	+	4.71461i	−0.140453	+	0.162092i
$847$	7.43404	−	2.18283i	0.255437	−	0.0750030i
$848$	5.07848	−	11.1203i	0.174396	−	0.381873i
$849$	3.25561	+	22.6432i	0.111732	+	0.777114i
$850$	0.714064			0.0244922
$851$	−8.50667	+	3.35186i	−0.291605	+	0.114900i
$852$	12.3705			0.423806
$853$	−0.710604	−	4.94236i	−0.0243306	−	0.169223i	0.974033	−	0.226406i	$-0.0726975\pi$
$853$	−0.710604	−	4.94236i	−0.0243306	−	0.169223i	−0.998364	+	0.0571823i	$0.981788\pi$
$854$	6.19633	−	13.5681i	0.212034	−	0.464290i
$855$	−5.06029	+	1.48584i	−0.173058	+	0.0508145i
$856$	−9.81515	+	11.3273i	−0.335475	+	0.387159i
$857$	−22.3617	−	6.56599i	−0.763862	−	0.224290i	−0.123480	−	0.992347i	$-0.539406\pi$
$857$	−22.3617	−	6.56599i	−0.763862	−	0.224290i	−0.640381	+	0.768057i	$0.721224\pi$
$858$	12.8935	−	8.28616i	0.440178	−	0.282885i
$859$	−11.4046	−	24.9726i	−0.389121	−	0.852055i	−0.998259	−	0.0589910i	$-0.981212\pi$
$859$	−11.4046	−	24.9726i	−0.389121	−	0.852055i	0.609138	−	0.793064i	$-0.291516\pi$
$860$	0.781628	+	0.902047i	0.0266533	+	0.0307595i
$861$	−13.5442	−	8.70431i	−0.461584	−	0.296642i
$862$	2.60485	−	18.1171i	0.0887214	−	0.617071i
$863$	2.34829	−	16.3327i	0.0799368	−	0.555972i	−0.910016	−	0.414573i	$-0.863931\pi$
$863$	2.34829	−	16.3327i	0.0799368	−	0.555972i	0.989953	−	0.141399i	$-0.0451601\pi$
$864$	0.841254	+	0.540641i	0.0286200	+	0.0183930i
$865$	−1.78692	−	2.06222i	−0.0607572	−	0.0701176i
$866$	10.2664	+	22.4802i	0.348866	+	0.763910i
$867$	−13.8724	+	8.91523i	−0.471130	+	0.302777i
$868$	−14.2852	−	4.19452i	−0.484872	−	0.142371i
$869$	−20.5868	+	23.7584i	−0.698358	+	0.805948i
$870$	−6.08763	+	1.78749i	−0.206390	+	0.0606016i
$871$	−16.9766	+	37.1736i	−0.575231	+	1.25958i
$872$	−0.789282	−	5.48958i	−0.0267285	−	0.185901i
$873$	−2.27050			−0.0768447
$874$	−25.1910	+	2.26693i	−0.852100	+	0.0766802i
$875$	−1.41710			−0.0479068
$876$	−0.336221	−	2.33847i	−0.0113598	−	0.0790094i
$877$	19.6612	−	43.0520i	0.663911	−	1.45376i	−0.214920	−	0.976632i	$-0.568949\pi$
$877$	19.6612	−	43.0520i	0.663911	−	1.45376i	0.878832	−	0.477132i	$-0.158324\pi$
$878$	−5.72465	+	1.68091i	−0.193198	+	0.0567280i
$879$	15.4447	−	17.8241i	0.520937	−	0.601193i
$880$	3.89363	+	1.14327i	0.131254	+	0.0385397i
$881$	−39.2718	+	25.2384i	−1.32310	+	0.850305i	−0.995523	−	0.0945195i	$-0.969869\pi$
$881$	−39.2718	+	25.2384i	−1.32310	+	0.850305i	−0.327577	+	0.944824i	$0.606232\pi$
$882$	−2.07368	−	4.54072i	−0.0698244	−	0.152894i
$883$	17.2126	+	19.8644i	0.579249	+	0.668489i	0.967443	−	0.253089i	$-0.0814465\pi$
$883$	17.2126	+	19.8644i	0.579249	+	0.668489i	−0.388194	+	0.921578i	$0.626901\pi$
$884$	−2.26880	−	1.45807i	−0.0763080	−	0.0490402i
$885$	−1.72914	+	12.0264i	−0.0581243	+	0.404263i
$886$	−3.48655	+	24.2495i	−0.117133	+	0.814678i
$887$	−29.5698	−	19.0034i	−0.992857	−	0.638070i	−0.0599551	−	0.998201i	$-0.519096\pi$
$887$	−29.5698	−	19.0034i	−0.992857	−	0.638070i	−0.932902	+	0.360131i	$0.882732\pi$
$888$	1.24849	+	1.44083i	0.0418965	+	0.0483511i
$889$	−3.39516	−	7.43436i	−0.113870	−	0.249340i
$890$	−6.92730	+	4.45190i	−0.232204	+	0.149228i
$891$	3.89363	+	1.14327i	0.130441	+	0.0383011i
$892$	−6.99846	+	8.07665i	−0.234326	+	0.270426i
$893$	−31.5678	+	9.26913i	−1.05637	+	0.310180i
$894$	−7.42204	+	16.2520i	−0.248230	+	0.543548i
$895$	0.345574	+	2.40352i	0.0115513	+	0.0803408i
$896$	−1.41710			−0.0473420
$897$	−4.17432	−	17.6257i	−0.139377	−	0.588504i
$898$	10.2082			0.340652
$899$	9.48639	+	65.9793i	0.316389	+	2.20053i
$900$	0.415415	−	0.909632i	0.0138472	−	0.0303211i
$901$	−8.37588	+	2.45938i	−0.279041	+	0.0819339i
$902$	30.1916	−	34.8430i	1.00527	−	1.16014i
$903$	−1.62291	−	0.476529i	−0.0540070	−	0.0158579i
$904$	3.94618	−	2.53605i	0.131248	−	0.0843479i
$905$	2.82229	+	6.17996i	0.0938161	+	0.205429i
$906$	−10.6155	−	12.2509i	−0.352675	−	0.407008i
$907$	−47.7865	−	30.7105i	−1.58673	−	1.01973i	−0.973174	−	0.230072i	$-0.926104\pi$
$907$	−47.7865	−	30.7105i	−1.58673	−	1.01973i	−0.613552	−	0.789654i	$-0.710260\pi$
$908$	−2.29493	+	15.9616i	−0.0761598	+	0.529703i
$909$	−2.35968	+	16.4120i	−0.0782657	+	0.544350i
$910$	4.50256	+	2.89362i	0.149258	+	0.0959226i
$911$	−26.3151	−	30.3692i	−0.871858	−	1.00618i	−0.999896	−	0.0144081i	$-0.995414\pi$
$911$	−26.3151	−	30.3692i	−0.871858	−	1.00618i	0.128039	−	0.991769i	$-0.459132\pi$
$912$	2.19087	+	4.79733i	0.0725468	+	0.158855i
$913$	58.5163	−	37.6061i	1.93661	−	1.24458i
$914$	−4.52454	−	1.32853i	−0.149659	−	0.0439437i
$915$	6.89287	−	7.95480i	0.227871	−	0.262978i
$916$	−5.03554	+	1.47857i	−0.166379	+	0.0488533i
$917$	−4.87380	+	10.6721i	−0.160947	+	0.352425i
$918$	−0.101622	−	0.706796i	−0.00335402	−	0.0233277i
$919$	−4.69115			−0.154747			−0.0773733	−	0.997002i	$-0.524653\pi$
$919$	−4.69115			−0.154747			−0.0773733	+	0.997002i	$0.524653\pi$
$920$	2.80311	−	3.89134i	0.0924159	−	0.128294i
$921$	20.9872			0.691553
$922$	−1.36433	−	9.48910i	−0.0449317	−	0.312507i
$923$	−19.4089	+	42.4995i	−0.638851	+	1.39889i
$924$	−5.51767	+	1.62013i	−0.181518	+	0.0532985i
$925$	1.24849	−	1.44083i	0.0410500	−	0.0473742i
$926$	15.5875	+	4.57692i	0.512238	+	0.150407i
$927$	−9.34869	+	6.00804i	−0.307051	+	0.197330i
$928$	2.63566	+	5.77128i	0.0865197	+	0.189452i
$929$	22.1596	+	25.5735i	0.727032	+	0.839040i	0.992134	−	0.125181i	$-0.0399510\pi$
$929$	22.1596	+	25.5735i	0.727032	+	0.839040i	−0.265102	+	0.964220i	$0.585406\pi$
$930$	−8.83835	−	5.68006i	−0.289821	−	0.186257i
$931$	3.74665	−	26.0585i	0.122791	−	0.854033i
$932$	2.99390	−	20.8231i	0.0980686	−	0.682082i
$933$	−1.97912	−	1.27191i	−0.0647936	−	0.0416403i
$934$	−16.8223	−	19.4140i	−0.550444	−	0.635246i
$935$	−1.20374	−	2.63582i	−0.0393665	−	0.0862005i
$936$	−3.17730	+	2.04193i	−0.103853	+	0.0667425i
$937$	25.7980	+	7.57498i	0.842784	+	0.247464i	0.674500	−	0.738275i	$-0.264359\pi$
$937$	25.7980	+	7.57498i	0.842784	+	0.247464i	0.168284	+	0.985739i	$0.446177\pi$
$938$	10.0412	−	11.5882i	0.327858	−	0.378368i
$939$	−31.8096	+	9.34014i	−1.03807	+	0.304804i
$940$	2.59150	−	5.67458i	0.0845253	−	0.185085i
$941$	3.62421	+	25.2069i	0.118146	+	0.821722i	0.959595	+	0.281386i	$0.0907940\pi$
$941$	3.62421	+	25.2069i	0.118146	+	0.821722i	−0.841449	+	0.540337i	$0.818297\pi$
$942$	2.75652			0.0898122
$943$	−26.9856	−	47.3344i	−0.878771	−	1.54142i
$944$	12.1501			0.395451
$945$	0.201675	+	1.40268i	0.00656047	+	0.0456291i
$946$	2.01208	−	4.40585i	0.0654185	−	0.143247i
$947$	14.3358	−	4.20938i	0.465852	−	0.136786i	−0.0403790	−	0.999184i	$-0.512857\pi$
$947$	14.3358	−	4.20938i	0.465852	−	0.136786i	0.506231	+	0.862398i	$0.331038\pi$
$948$	5.07312	−	5.85469i	0.164767	−	0.190152i
$949$	8.56146	+	2.51387i	0.277917	+	0.0816037i
$950$	4.43670	−	2.85130i	0.143946	−	0.0925083i
$951$	5.26765	+	11.5345i	0.170815	+	0.374033i
$952$	0.662654	+	0.764744i	0.0214768	+	0.0247855i
$953$	−24.0104	−	15.4306i	−0.777773	−	0.499845i	0.0905206	−	0.995895i	$-0.471147\pi$
$953$	−24.0104	−	15.4306i	−0.777773	−	0.499845i	−0.868294	+	0.496050i	$0.834783\pi$
$954$	−1.73981	+	12.1006i	−0.0563284	+	0.391773i
$955$	−2.76387	+	19.2231i	−0.0894366	+	0.622045i
$956$	−2.70034	−	1.73540i	−0.0873352	−	0.0561269i
$957$	16.8604	+	19.4580i	0.545020	+	0.628987i
$958$	7.69862	+	16.8576i	0.248731	+	0.544645i
$959$	−2.17619	+	1.39855i	−0.0702729	+	0.0451616i
$960$	−0.959493	−	0.281733i	−0.0309675	−	0.00909288i
$961$	−51.9825	+	59.9910i	−1.67686	+	1.93519i
$962$	−6.90890	+	2.02864i	−0.222752	+	0.0654058i
$963$	6.22630	−	13.6337i	0.200640	−	0.439340i
$964$	0.643600	+	4.47633i	0.0207289	+	0.144173i
$965$	−2.84588			−0.0916120
$966$	−0.360380	+	6.78662i	−0.0115950	+	0.218356i
$967$	−38.4775			−1.23735			−0.618676	−	0.785646i	$-0.712331\pi$
$967$	−38.4775			−1.23735			−0.618676	+	0.785646i	$0.712331\pi$
$968$	−0.778095	−	5.41177i	−0.0250089	−	0.173941i
$969$	1.56442	−	3.42560i	0.0502564	−	0.110046i
$970$	2.17853	−	0.639673i	0.0699483	−	0.0205387i
$971$	2.67557	−	3.08777i	0.0858630	−	0.0990912i	−0.711192	−	0.702998i	$-0.751844\pi$
$971$	2.67557	−	3.08777i	0.0858630	−	0.0990912i	0.797055	+	0.603906i	$0.206390\pi$
$972$	−0.959493	−	0.281733i	−0.0307758	−	0.00903658i
$973$	3.38587	−	2.17597i	0.108546	−	0.0697583i
$974$	7.11101	+	15.5709i	0.227851	+	0.498925i
$975$	2.47332	+	2.85437i	0.0792097	+	0.0914129i
$976$	−8.85479	−	5.69063i	−0.283435	−	0.182153i
$977$	−0.939614	+	6.53516i	−0.0300609	+	0.209078i	−0.999316	−	0.0369798i	$-0.988226\pi$
$977$	−0.939614	+	6.53516i	−0.0300609	+	0.209078i	0.969255	+	0.246058i	$0.0791354\pi$
$978$	−2.71703	+	18.8974i	−0.0868811	+	0.604271i
$979$	28.1110	+	18.0659i	0.898432	+	0.577387i
$980$	3.26895	+	3.77257i	0.104423	+	0.120510i
$981$	2.30390	+	5.04485i	0.0735580	+	0.161070i
$982$	−3.93144	+	2.52659i	−0.125457	+	0.0806266i
$983$	9.07920	+	2.66589i	0.289582	+	0.0850288i	0.423297	−	0.905991i	$-0.360873\pi$
$983$	9.07920	+	2.66589i	0.289582	+	0.0850288i	−0.133716	+	0.991020i	$0.542691\pi$
$984$	−7.44001	+	8.58623i	−0.237179	+	0.273719i
$985$	7.54648	−	2.21585i	0.240451	−	0.0706027i
$986$	1.88203	−	4.12107i	0.0599360	−	0.131241i
$987$	1.25811	+	8.75036i	0.0400462	+	0.278527i
$988$	−19.9189			−0.633705
$989$	−4.12120	−	3.97268i	−0.131047	−	0.126324i
$990$	−4.05801			−0.128972
$991$	−8.48781	−	59.0340i	−0.269624	−	1.87528i	−0.451957	−	0.892040i	$-0.649274\pi$
$991$	−8.48781	−	59.0340i	−0.269624	−	1.87528i	0.182333	−	0.983237i	$-0.441635\pi$
$992$	−4.36442	+	9.55674i	−0.138570	+	0.303427i
$993$	29.7679	−	8.74065i	0.944657	−	0.277376i
$994$	11.4799	−	13.2485i	0.364119	−	0.420216i
$995$	−18.4315	−	5.41198i	−0.584318	−	0.171571i
$996$	−14.4200	+	9.26715i	−0.456914	+	0.293641i
$997$	−15.5587	−	34.0688i	−0.492749	−	1.07897i	−0.978758	−	0.205017i	$-0.934275\pi$
$997$	−15.5587	−	34.0688i	−0.492749	−	1.07897i	0.486009	−	0.873954i	$-0.338452\pi$
$998$	8.45474	+	9.75729i	0.267630	+	0.308861i
$999$	−1.60384	−	1.03073i	−0.0507434	−	0.0326108i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.g.601.2	yes	30
23.8	even	11	inner	690.2.m.g.31.2	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.g.31.2	✓	30	23.8	even	11	inner
690.2.m.g.601.2	yes	30	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)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-1.19214 + 0.766143i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-1.19214 + 0.766143i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(0.841254 + 0.540641i) q^{10} +(0.577515 - 4.01670i) q^{11} +(-0.142315 + 0.989821i) q^{12} +(-3.17730 - 2.04193i) q^{13} +(0.928004 + 1.07097i) q^{14} +(0.415415 + 0.909632i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-0.685140 - 0.201175i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(-5.06029 + 1.48584i) q^{19} +(0.415415 - 0.909632i) q^{20} +(0.201675 + 1.40268i) q^{21} -4.05801 q^{22} +(-1.59325 + 4.52345i) q^{23} +1.00000 q^{24} +(-0.142315 - 0.989821i) q^{25} +(-1.56897 + 3.43556i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(0.928004 - 1.07097i) q^{28} +(-6.08763 - 1.78749i) q^{29} +(0.841254 - 0.540641i) q^{30} +(-4.36442 - 9.55674i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-3.41381 - 2.19392i) q^{33} +(-0.101622 + 0.706796i) q^{34} +(0.201675 - 1.40268i) q^{35} +(0.841254 + 0.540641i) q^{36} +(1.24849 + 1.44083i) q^{37} +(2.19087 + 4.79733i) q^{38} +(-3.17730 + 2.04193i) q^{39} +(-0.959493 - 0.281733i) q^{40} +(-7.44001 + 8.58623i) q^{41} +(1.35970 - 0.399244i) q^{42} +(-0.495831 + 1.08572i) q^{43} +(0.577515 + 4.01670i) q^{44} +1.00000 q^{45} +(4.70415 + 0.933277i) q^{46} +6.23833 q^{47} +(-0.142315 - 0.989821i) q^{48} +(-2.07368 + 4.54072i) q^{49} +(-0.959493 + 0.281733i) q^{50} +(-0.467613 + 0.539654i) q^{51} +(3.62388 + 1.06407i) q^{52} +(10.2844 - 6.60938i) q^{53} +(0.415415 + 0.909632i) q^{54} +(2.65743 + 3.06684i) q^{55} +(-1.19214 - 0.766143i) q^{56} +(-0.750557 + 5.22024i) q^{57} +(-0.902936 + 6.28006i) q^{58} +(10.2213 + 6.56883i) q^{59} +(-0.654861 - 0.755750i) q^{60} +(-4.37254 - 9.57452i) q^{61} +(-8.83835 + 5.68006i) q^{62} +(1.35970 + 0.399244i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(3.62388 - 1.06407i) q^{65} +(-1.68576 + 3.69129i) q^{66} +(-1.53988 - 10.7101i) q^{67} +0.714064 q^{68} +(3.45281 + 3.32838i) q^{69} -1.41710 q^{70} +(-1.76050 - 12.2446i) q^{71} +(0.415415 - 0.909632i) q^{72} +(-2.26681 + 0.665597i) q^{73} +(1.24849 - 1.44083i) q^{74} +(-0.959493 - 0.281733i) q^{75} +(4.43670 - 2.85130i) q^{76} +(2.38889 + 5.23094i) q^{77} +(2.47332 + 2.85437i) q^{78} +(-6.51708 - 4.18827i) q^{79} +(-0.142315 + 0.989821i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(9.55765 + 6.14233i) q^{82} +(11.2250 + 12.9543i) q^{83} +(-0.588685 - 1.28904i) q^{84} +(0.600709 - 0.386052i) q^{85} +(1.14523 + 0.336270i) q^{86} +(-4.15485 + 4.79496i) q^{87} +(3.89363 - 1.14327i) q^{88} +(-3.42073 + 7.49036i) q^{89} +(-0.142315 - 0.989821i) q^{90} +5.35221 q^{91} +(0.254308 - 4.78908i) q^{92} -10.5062 q^{93} +(-0.887807 - 6.17483i) q^{94} +(2.19087 - 4.79733i) q^{95} +(-0.959493 + 0.281733i) q^{96} +(1.48686 - 1.71593i) q^{97} +(4.78962 + 1.40636i) q^{98} +(-3.41381 + 2.19392i) 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	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 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 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * q^99

Introduction

L-functions

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