LMFDB - Embedded newform 670.2.k.c.491.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(81,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("670.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.k (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:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			491.1
Character	$\chi$	$=$	670.491
Dual form			670.2.k.c.131.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 - 0.281733i) q^{2} +(-0.442767 - 3.07951i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-1.29243 - 2.83003i) q^{6} +(0.952113 - 0.279566i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-6.40889 + 1.88182i) q^{9} +O(q^{10})$	\(q+(0.959493 - 0.281733i) q^{2} +(-0.442767 - 3.07951i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-1.29243 - 2.83003i) q^{6} +(0.952113 - 0.279566i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-6.40889 + 1.88182i) q^{9} +(0.142315 - 0.989821i) q^{10} +(0.513740 - 1.12493i) q^{11} +(-2.03739 - 2.35127i) q^{12} +(-1.87557 - 2.16452i) q^{13} +(0.834783 - 0.536483i) q^{14} +(-2.98516 - 0.876521i) q^{15} +(0.415415 - 0.909632i) q^{16} +(1.78534 + 1.14737i) q^{17} +(-5.61911 + 3.61119i) q^{18} +(0.440965 + 0.129479i) q^{19} +(-0.142315 - 0.989821i) q^{20} +(-1.28249 - 2.80826i) q^{21} +(0.175999 - 1.22410i) q^{22} +(0.346728 + 2.41154i) q^{23} +(-2.61729 - 1.68203i) q^{24} +(-0.654861 - 0.755750i) q^{25} +(-2.40941 - 1.54843i) q^{26} +(4.75544 + 10.4130i) q^{27} +(0.649824 - 0.749937i) q^{28} +1.15389 q^{29} -3.11118 q^{30} +(-0.121176 + 0.139844i) q^{31} +(0.142315 - 0.989821i) q^{32} +(-3.69172 - 1.08399i) q^{33} +(2.03627 + 0.597902i) q^{34} +(0.141220 - 0.982209i) q^{35} +(-4.37411 + 5.04800i) q^{36} +6.05545 q^{37} +0.459581 q^{38} +(-5.83524 + 6.73422i) q^{39} +(-0.415415 - 0.909632i) q^{40} +(-7.00594 - 4.50244i) q^{41} +(-2.02172 - 2.33319i) q^{42} +(6.91693 + 4.44524i) q^{43} +(-0.175999 - 1.22410i) q^{44} +(-0.950586 + 6.61147i) q^{45} +(1.01209 + 2.21618i) q^{46} +(1.16104 + 8.07518i) q^{47} +(-2.98516 - 0.876521i) q^{48} +(-5.06041 + 3.25213i) q^{49} +(-0.841254 - 0.540641i) q^{50} +(2.74284 - 6.00599i) q^{51} +(-2.74806 - 0.806903i) q^{52} +(4.98124 - 3.20125i) q^{53} +(7.49649 + 8.65141i) q^{54} +(-0.809860 - 0.934628i) q^{55} +(0.412220 - 0.902636i) q^{56} +(0.203487 - 1.41529i) q^{57} +(1.10715 - 0.325087i) q^{58} +(-0.771659 + 0.890541i) q^{59} +(-2.98516 + 0.876521i) q^{60} +(-4.23071 - 9.26395i) q^{61} +(-0.0768684 + 0.168318i) q^{62} +(-5.57590 + 3.58341i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-2.74806 + 0.806903i) q^{65} -3.84757 q^{66} +(-8.07475 + 1.34103i) q^{67} +2.12223 q^{68} +(7.27287 - 2.13551i) q^{69} +(-0.141220 - 0.982209i) q^{70} +(8.89297 - 5.71516i) q^{71} +(-2.77475 + 6.07585i) q^{72} +(-0.565644 - 1.23859i) q^{73} +(5.81016 - 1.70602i) q^{74} +(-2.03739 + 2.35127i) q^{75} +(0.440965 - 0.129479i) q^{76} +(0.174646 - 1.21469i) q^{77} +(-3.70162 + 8.10542i) q^{78} +(3.86533 + 4.46083i) q^{79} +(-0.654861 - 0.755750i) q^{80} +(13.1040 - 8.42143i) q^{81} +(-7.99063 - 2.34626i) q^{82} +(5.25951 - 11.5167i) q^{83} +(-2.59716 - 1.66910i) q^{84} +(1.78534 - 1.14737i) q^{85} +(7.88912 + 2.31645i) q^{86} +(-0.510903 - 3.55341i) q^{87} +(-0.513740 - 1.12493i) q^{88} +(2.24843 - 15.6381i) q^{89} +(0.950586 + 6.61147i) q^{90} +(-2.39088 - 1.53653i) q^{91} +(1.59547 + 1.84126i) q^{92} +(0.484304 + 0.311243i) q^{93} +(3.38905 + 7.42098i) q^{94} +(0.300961 - 0.347328i) q^{95} -3.11118 q^{96} +9.56820 q^{97} +(-3.93920 + 4.54608i) q^{98} +(-1.17558 + 8.17634i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9}+O(q^{10}) $ 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9	\( 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9} + 5 q^{10} - 12 q^{11} - 2 q^{12} + 24 q^{13} + 23 q^{14} - 2 q^{15} - 5 q^{16} + 31 q^{17} + q^{18} + 4 q^{19} - 5 q^{20} + 12 q^{21} + q^{22} + 27 q^{23} - 9 q^{24} - 5 q^{25} - 2 q^{26} - 14 q^{27} + 10 q^{28} - 36 q^{29} + 2 q^{30} - 13 q^{31} + 5 q^{32} - 42 q^{33} + 2 q^{34} + 21 q^{35} - q^{36} - 50 q^{37} - 26 q^{38} - 31 q^{39} + 5 q^{40} - 10 q^{41} + 21 q^{42} + 16 q^{43} - q^{44} - q^{45} + 17 q^{46} - 13 q^{47} - 2 q^{48} - 40 q^{49} + 5 q^{50} - 19 q^{51} - 20 q^{52} - 5 q^{53} + 47 q^{54} + 10 q^{55} + 12 q^{56} - 90 q^{57} - 8 q^{58} - 20 q^{59} - 2 q^{60} + 12 q^{61} + 13 q^{62} - 15 q^{63} - 5 q^{64} - 20 q^{65} + 20 q^{66} - 21 q^{67} - 24 q^{68} + 77 q^{69} - 21 q^{70} + 24 q^{71} + 12 q^{72} - 68 q^{73} - 16 q^{74} - 2 q^{75} + 4 q^{76} + 7 q^{77} + 53 q^{78} - 26 q^{79} - 5 q^{80} - 21 q^{81} + 21 q^{82} - 10 q^{83} + 12 q^{84} + 31 q^{85} - 27 q^{86} + 61 q^{87} + 12 q^{88} + 51 q^{89} + q^{90} - 10 q^{91} - 6 q^{92} - 38 q^{93} - 9 q^{94} + 15 q^{95} + 2 q^{96} + 72 q^{97} - 37 q^{98} - 32 q^{99}+O(q^{100}) \) 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9 + 5 * q^10 - 12 * q^11 - 2 * q^12 + 24 * q^13 + 23 * q^14 - 2 * q^15 - 5 * q^16 + 31 * q^17 + q^18 + 4 * q^19 - 5 * q^20 + 12 * q^21 + q^22 + 27 * q^23 - 9 * q^24 - 5 * q^25 - 2 * q^26 - 14 * q^27 + 10 * q^28 - 36 * q^29 + 2 * q^30 - 13 * q^31 + 5 * q^32 - 42 * q^33 + 2 * q^34 + 21 * q^35 - q^36 - 50 * q^37 - 26 * q^38 - 31 * q^39 + 5 * q^40 - 10 * q^41 + 21 * q^42 + 16 * q^43 - q^44 - q^45 + 17 * q^46 - 13 * q^47 - 2 * q^48 - 40 * q^49 + 5 * q^50 - 19 * q^51 - 20 * q^52 - 5 * q^53 + 47 * q^54 + 10 * q^55 + 12 * q^56 - 90 * q^57 - 8 * q^58 - 20 * q^59 - 2 * q^60 + 12 * q^61 + 13 * q^62 - 15 * q^63 - 5 * q^64 - 20 * q^65 + 20 * q^66 - 21 * q^67 - 24 * q^68 + 77 * q^69 - 21 * q^70 + 24 * q^71 + 12 * q^72 - 68 * q^73 - 16 * q^74 - 2 * q^75 + 4 * q^76 + 7 * q^77 + 53 * q^78 - 26 * q^79 - 5 * q^80 - 21 * q^81 + 21 * q^82 - 10 * q^83 + 12 * q^84 + 31 * q^85 - 27 * q^86 + 61 * q^87 + 12 * q^88 + 51 * q^89 + q^90 - 10 * q^91 - 6 * q^92 - 38 * q^93 - 9 * q^94 + 15 * q^95 + 2 * q^96 + 72 * q^97 - 37 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.959493	−	0.281733i	0.678464	−	0.199215i
$2$	0.959493	−	0.281733i	0.678464	−	0.199215i
$3$	−0.442767	−	3.07951i	−0.255632	−	1.77796i	−0.563088	−	0.826397i	$-0.690387\pi$
$3$	−0.442767	−	3.07951i	−0.255632	−	1.77796i	0.307457	−	0.951562i	$-0.400522\pi$
$4$	0.841254	−	0.540641i	0.420627	−	0.270320i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$6$	−1.29243	−	2.83003i	−0.527633	−	1.15536i
$7$	0.952113	−	0.279566i	0.359865	−	0.105666i	−0.0968019	−	0.995304i	$-0.530861\pi$
$7$	0.952113	−	0.279566i	0.359865	−	0.105666i	0.456667	+	0.889638i	$0.349043\pi$
$8$	0.654861	−	0.755750i	0.231528	−	0.267198i
$9$	−6.40889	+	1.88182i	−2.13630	+	0.627273i
$10$	0.142315	−	0.989821i	0.0450039	−	0.313009i
$11$	0.513740	−	1.12493i	0.154898	−	0.339180i	−0.816234	−	0.577722i	$-0.803942\pi$
$11$	0.513740	−	1.12493i	0.154898	−	0.339180i	0.971132	+	0.238541i	$0.0766692\pi$
$12$	−2.03739	−	2.35127i	−0.588144	−	0.678755i
$13$	−1.87557	−	2.16452i	−0.520189	−	0.600330i	0.433489	−	0.901159i	$-0.357282\pi$
$13$	−1.87557	−	2.16452i	−0.520189	−	0.600330i	−0.953678	+	0.300828i	$0.902737\pi$
$14$	0.834783	−	0.536483i	0.223105	−	0.143381i
$15$	−2.98516	−	0.876521i	−0.770764	−	0.226317i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	1.78534	+	1.14737i	0.433008	+	0.278277i	0.738934	−	0.673778i	$-0.235330\pi$
$17$	1.78534	+	1.14737i	0.433008	+	0.278277i	−0.305926	+	0.952055i	$0.598966\pi$
$18$	−5.61911	+	3.61119i	−1.32444	+	0.851165i
$19$	0.440965	+	0.129479i	0.101164	+	0.0297045i	0.331923	−	0.943307i	$-0.392303\pi$
$19$	0.440965	+	0.129479i	0.101164	+	0.0297045i	−0.230759	+	0.973011i	$0.574121\pi$
$20$	−0.142315	−	0.989821i	−0.0318226	−	0.221331i
$21$	−1.28249	−	2.80826i	−0.279863	−	0.612814i
$22$	0.175999	−	1.22410i	0.0375232	−	0.260980i
$23$	0.346728	+	2.41154i	0.0722977	+	0.502842i	0.993507	+	0.113774i	$0.0362938\pi$
$23$	0.346728	+	2.41154i	0.0722977	+	0.502842i	−0.921209	+	0.389068i	$0.872797\pi$
$24$	−2.61729	−	1.68203i	−0.534253	−	0.343343i
$25$	−0.654861	−	0.755750i	−0.130972	−	0.151150i
$26$	−2.40941	−	1.54843i	−0.472524	−	0.303673i
$27$	4.75544	+	10.4130i	0.915186	+	2.00398i
$28$	0.649824	−	0.749937i	0.122805	−	0.141725i
$29$	1.15389			0.214271			0.107136	−	0.994244i	$-0.465832\pi$
$29$	1.15389			0.214271			0.107136	+	0.994244i	$0.465832\pi$
$30$	−3.11118			−0.568022
$31$	−0.121176	+	0.139844i	−0.0217638	+	0.0251167i	−0.766527	−	0.642212i	$-0.778017\pi$
$31$	−0.121176	+	0.139844i	−0.0217638	+	0.0251167i	0.744763	+	0.667329i	$0.232562\pi$
$32$	0.142315	−	0.989821i	0.0251579	−	0.174977i
$33$	−3.69172	−	1.08399i	−0.642645	−	0.188698i
$34$	2.03627	+	0.597902i	0.349217	+	0.102539i
$35$	0.141220	−	0.982209i	0.0238706	−	0.166024i
$36$	−4.37411	+	5.04800i	−0.729019	+	0.841333i
$37$	6.05545			0.995510			0.497755	−	0.867318i	$-0.334158\pi$
$37$	6.05545			0.995510			0.497755	+	0.867318i	$0.334158\pi$
$38$	0.459581			0.0745539
$39$	−5.83524	+	6.73422i	−0.934386	+	1.07834i
$40$	−0.415415	−	0.909632i	−0.0656829	−	0.143825i
$41$	−7.00594	−	4.50244i	−1.09414	−	0.703163i	−0.136362	−	0.990659i	$-0.543541\pi$
$41$	−7.00594	−	4.50244i	−1.09414	−	0.703163i	−0.957782	+	0.287496i	$0.907177\pi$
$42$	−2.02172	−	2.33319i	−0.311958	−	0.360019i
$43$	6.91693	+	4.44524i	1.05482	+	0.677893i	0.948609	−	0.316450i	$-0.102491\pi$
$43$	6.91693	+	4.44524i	1.05482	+	0.677893i	0.106213	+	0.994343i	$0.466127\pi$
$44$	−0.175999	−	1.22410i	−0.0265329	−	0.184540i
$45$	−0.950586	+	6.61147i	−0.141705	+	0.985579i
$46$	1.01209	+	2.21618i	0.149225	+	0.326757i
$47$	1.16104	+	8.07518i	0.169354	+	1.17789i	0.880223	+	0.474561i	$0.157393\pi$
$47$	1.16104	+	8.07518i	0.169354	+	1.17789i	−0.710868	+	0.703325i	$0.751698\pi$
$48$	−2.98516	−	0.876521i	−0.430870	−	0.126515i
$49$	−5.06041	+	3.25213i	−0.722916	+	0.464590i
$50$	−0.841254	−	0.540641i	−0.118971	−	0.0764582i
$51$	2.74284	−	6.00599i	0.384075	−	0.841006i
$52$	−2.74806	−	0.806903i	−0.381087	−	0.111897i
$53$	4.98124	−	3.20125i	0.684226	−	0.439726i	−0.151803	−	0.988411i	$-0.548508\pi$
$53$	4.98124	−	3.20125i	0.684226	−	0.439726i	0.836029	+	0.548685i	$0.184871\pi$
$54$	7.49649	+	8.65141i	1.02014	+	1.17731i
$55$	−0.809860	−	0.934628i	−0.109202	−	0.126025i
$56$	0.412220	−	0.902636i	0.0550852	−	0.120620i
$57$	0.203487	−	1.41529i	0.0269526	−	0.187459i
$58$	1.10715	−	0.325087i	0.145375	−	0.0426860i
$59$	−0.771659	+	0.890541i	−0.100461	+	0.115939i	−0.803754	−	0.594962i	$-0.797167\pi$
$59$	−0.771659	+	0.890541i	−0.100461	+	0.115939i	0.703292	+	0.710901i	$0.251712\pi$
$60$	−2.98516	+	0.876521i	−0.385382	+	0.113158i
$61$	−4.23071	−	9.26395i	−0.541686	−	1.18613i	−0.960557	−	0.278082i	$-0.910301\pi$
$61$	−4.23071	−	9.26395i	−0.541686	−	1.18613i	0.418871	−	0.908046i	$-0.362426\pi$
$62$	−0.0768684	+	0.168318i	−0.00976230	+	0.0213765i
$63$	−5.57590	+	3.58341i	−0.702497	+	0.451467i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	−2.74806	+	0.806903i	−0.340855	+	0.100084i
$66$	−3.84757			−0.473603
$67$	−8.07475	+	1.34103i	−0.986488	+	0.163833i
$67$	−8.07475	+	1.34103i	−0.986488	+	0.163833i
$68$	2.12223			0.257359
$69$	7.27287	−	2.13551i	0.875550	−	0.257085i
$70$	−0.141220	−	0.982209i	−0.0168791	−	0.117396i
$71$	8.89297	−	5.71516i	1.05540	−	0.678265i	0.106652	−	0.994296i	$-0.465987\pi$
$71$	8.89297	−	5.71516i	1.05540	−	0.678265i	0.948749	+	0.316031i	$0.102350\pi$
$72$	−2.77475	+	6.07585i	−0.327007	+	0.716045i
$73$	−0.565644	−	1.23859i	−0.0662036	−	0.144966i	0.873638	−	0.486577i	$-0.161755\pi$
$73$	−0.565644	−	1.23859i	−0.0662036	−	0.144966i	−0.939841	+	0.341611i	$0.889027\pi$
$74$	5.81016	−	1.70602i	0.675418	−	0.198321i
$75$	−2.03739	+	2.35127i	−0.235258	+	0.271502i
$76$	0.440965	−	0.129479i	0.0505821	−	0.0148522i
$77$	0.174646	−	1.21469i	0.0199027	−	0.138427i
$78$	−3.70162	+	8.10542i	−0.419126	+	0.917758i
$79$	3.86533	+	4.46083i	0.434884	+	0.501883i	0.930313	−	0.366765i	$-0.119535\pi$
$79$	3.86533	+	4.46083i	0.434884	+	0.501883i	−0.495430	+	0.868648i	$0.664989\pi$
$80$	−0.654861	−	0.755750i	−0.0732157	−	0.0844954i
$81$	13.1040	−	8.42143i	1.45600	−	0.935714i
$82$	−7.99063	−	2.34626i	−0.882418	−	0.259101i
$83$	5.25951	−	11.5167i	0.577306	−	1.26412i	−0.365510	−	0.930808i	$-0.619105\pi$
$83$	5.25951	−	11.5167i	0.577306	−	1.26412i	0.942815	−	0.333316i	$-0.108167\pi$
$84$	−2.59716	−	1.66910i	−0.283374	−	0.182113i
$85$	1.78534	−	1.14737i	0.193647	−	0.124449i
$86$	7.88912	+	2.31645i	0.850705	+	0.249790i
$87$	−0.510903	−	3.55341i	−0.0547745	−	0.380965i
$88$	−0.513740	−	1.12493i	−0.0547649	−	0.119918i
$89$	2.24843	−	15.6381i	0.238333	−	1.65764i	−0.421947	−	0.906620i	$-0.638653\pi$
$89$	2.24843	−	15.6381i	0.238333	−	1.65764i	0.660280	−	0.751019i	$-0.270438\pi$
$90$	0.950586	+	6.61147i	0.100201	+	0.696910i
$91$	−2.39088	−	1.53653i	−0.250632	−	0.161072i
$92$	1.59547	+	1.84126i	0.166339	+	0.191965i
$93$	0.484304	+	0.311243i	0.0502200	+	0.0322744i
$94$	3.38905	+	7.42098i	0.349553	+	0.765415i
$95$	0.300961	−	0.347328i	0.0308780	−	0.0356351i
$96$	−3.11118			−0.317534
$97$	9.56820			0.971503			0.485752	−	0.874097i	$-0.338546\pi$
$97$	9.56820			0.971503			0.485752	+	0.874097i	$0.338546\pi$
$98$	−3.93920	+	4.54608i	−0.397919	+	0.459223i
$99$	−1.17558	+	8.17634i	−0.118150	+	0.821753i
$100$	−0.959493	−	0.281733i	−0.0959493	−	0.0281733i
$101$	12.9302	+	3.79665i	1.28660	+	0.377781i	0.852332	−	0.523002i	$-0.175188\pi$
$101$	12.9302	+	3.79665i	1.28660	+	0.377781i	0.434271	+	0.900782i	$0.357006\pi$
$102$	0.939656	−	6.53545i	0.0930398	−	0.647106i
$103$	−1.78868	+	2.06425i	−0.176244	+	0.203397i	−0.836998	−	0.547206i	$-0.815691\pi$
$103$	−1.78868	+	2.06425i	−0.176244	+	0.203397i	0.660754	+	0.750603i	$0.270237\pi$
$104$	−2.86407			−0.280845
$105$	−3.08725			−0.301285
$106$	3.87757	−	4.47496i	0.376623	−	0.434646i
$107$	4.23857	+	9.28117i	0.409758	+	0.897245i	0.996187	+	0.0872440i	$0.0278060\pi$
$107$	4.23857	+	9.28117i	0.409758	+	0.897245i	−0.586429	+	0.810001i	$0.699467\pi$
$108$	9.63021	+	6.18896i	0.926667	+	0.595533i
$109$	−4.14382	−	4.78223i	−0.396906	−	0.458054i	0.521758	−	0.853094i	$-0.325276\pi$
$109$	−4.14382	−	4.78223i	−0.396906	−	0.458054i	−0.918664	+	0.395039i	$0.870731\pi$
$110$	−1.04037	−	0.668605i	−0.0991954	−	0.0637490i
$111$	−2.68116	−	18.6479i	−0.254484	−	1.76998i
$112$	0.141220	−	0.982209i	0.0133441	−	0.0928100i
$113$	7.20928	+	15.7861i	0.678192	+	1.48503i	0.864547	+	0.502552i	$0.167605\pi$
$113$	7.20928	+	15.7861i	0.678192	+	1.48503i	−0.186355	+	0.982482i	$0.559667\pi$
$114$	−0.203487	−	1.41529i	−0.0190583	−	0.132554i
$115$	2.33765	+	0.686397i	0.217987	+	0.0640069i
$116$	0.970710	−	0.623838i	0.0901282	−	0.0579219i
$117$	16.0936	+	10.3427i	1.48785	+	0.956183i
$118$	−0.489506	+	1.07187i	−0.0450627	+	0.0986736i
$119$	2.02061	+	0.593304i	0.185229	+	0.0543881i
$120$	−2.61729	+	1.68203i	−0.238925	+	0.153548i
$121$	6.20192	+	7.15740i	0.563811	+	0.650673i
$122$	−6.66929	−	7.69677i	−0.603809	−	0.696833i
$123$	−10.7633	+	23.5684i	−0.970497	+	2.12509i
$124$	−0.0263340	+	0.183157i	−0.00236486	+	0.0164480i
$125$	−0.959493	+	0.281733i	−0.0858197	+	0.0251989i
$126$	−4.34047	+	5.00917i	−0.386680	+	0.446252i
$127$	−7.00395	+	2.05655i	−0.621500	+	0.182489i	−0.577298	−	0.816534i	$-0.695893\pi$
$127$	−7.00395	+	2.05655i	−0.621500	+	0.182489i	−0.0442024	+	0.999023i	$0.514075\pi$
$128$	−0.415415	−	0.909632i	−0.0367178	−	0.0804009i
$129$	10.6266	−	23.2690i	0.935620	−	2.04872i
$130$	−2.40941	+	1.54843i	−0.211319	+	0.135807i
$131$	−1.18637	−	8.25140i	−0.103654	−	0.720928i	−0.973679	−	0.227922i	$-0.926807\pi$
$131$	−1.18637	−	8.25140i	−0.103654	−	0.720928i	0.870026	−	0.493006i	$-0.164102\pi$
$132$	−3.69172	+	1.08399i	−0.321323	+	0.0943488i
$133$	0.456046			0.0395442
$134$	−7.36986	+	3.56163i	−0.636659	+	0.307678i
$135$	11.4475			0.985240
$136$	2.03627	−	0.597902i	0.174609	−	0.0512697i
$137$	−2.89653	−	20.1458i	−0.247467	−	1.72117i	−0.612752	−	0.790275i	$-0.709938\pi$
$137$	−2.89653	−	20.1458i	−0.247467	−	1.72117i	0.365285	−	0.930896i	$-0.380971\pi$
$138$	6.37662	−	4.09801i	0.542814	−	0.348845i
$139$	−1.99672	+	4.37221i	−0.169360	+	0.370846i	−0.975213	−	0.221270i	$-0.928980\pi$
$139$	−1.99672	+	4.37221i	−0.169360	+	0.370846i	0.805853	+	0.592116i	$0.201707\pi$
$140$	−0.412220	−	0.902636i	−0.0348389	−	0.0762867i
$141$	24.3536	−	7.15085i	2.05094	−	0.602210i
$142$	6.92259	−	7.98910i	0.580931	−	0.670430i
$143$	−3.39850	+	0.997889i	−0.284197	+	0.0834477i
$144$	−0.950586	+	6.61147i	−0.0792155	+	0.550956i
$145$	0.479341	−	1.04961i	0.0398071	−	0.0871655i
$146$	−0.891681	−	1.02906i	−0.0737961	−	0.0851652i
$147$	12.2556	+	14.1437i	1.01082	+	1.16655i
$148$	5.09417	−	3.27382i	0.418738	−	0.269107i
$149$	7.07520	+	2.07747i	0.579623	+	0.170193i	0.558385	−	0.829582i	$-0.311421\pi$
$149$	7.07520	+	2.07747i	0.579623	+	0.170193i	0.0212379	+	0.999774i	$0.493239\pi$
$150$	−1.29243	+	2.83003i	−0.105527	+	0.231071i
$151$	−10.0740	−	6.47418i	−0.819812	−	0.526861i	0.0622132	−	0.998063i	$-0.480184\pi$
$151$	−10.0740	−	6.47418i	−0.819812	−	0.526861i	−0.882026	+	0.471201i	$0.843820\pi$
$152$	0.386624	−	0.248468i	0.0313594	−	0.0201534i
$153$	−13.6012	−	3.99366i	−1.09959	−	0.322868i
$154$	−0.174646	−	1.21469i	−0.0140734	−	0.0978824i
$155$	0.0768684	+	0.168318i	0.00617422	+	0.0135197i
$156$	−1.26812	+	8.81996i	−0.101531	+	0.706162i
$157$	−1.83878	−	12.7890i	−0.146751	−	1.02067i	−0.921493	−	0.388396i	$-0.873029\pi$
$157$	−1.83878	−	12.7890i	−0.146751	−	1.02067i	0.774742	−	0.632278i	$-0.217880\pi$
$158$	4.96552	+	3.19115i	0.395036	+	0.253874i
$159$	−12.0638	−	13.9224i	−0.956724	−	1.10412i
$160$	−0.841254	−	0.540641i	−0.0665069	−	0.0427414i
$161$	1.00431	+	2.19913i	0.0791507	+	0.173316i
$162$	10.2006	−	11.7721i	0.801435	−	0.924905i
$163$	12.9267			1.01249			0.506247	−	0.862388i	$-0.331032\pi$
$163$	12.9267			1.01249			0.506247	+	0.862388i	$0.331032\pi$
$164$	−8.32797			−0.650305
$165$	−2.51962	+	2.90780i	−0.196152	+	0.226372i
$166$	1.80183	−	12.5320i	0.139849	−	0.972670i
$167$	7.35287	+	2.15900i	0.568982	+	0.167068i	0.553555	−	0.832813i	$-0.313271\pi$
$167$	7.35287	+	2.15900i	0.568982	+	0.167068i	0.0154274	+	0.999881i	$0.495089\pi$
$168$	−2.96220	−	0.869780i	−0.228539	−	0.0671050i
$169$	0.682696	−	4.74826i	0.0525151	−	0.365251i
$170$	1.38977	−	1.60388i	0.106590	−	0.123012i
$171$	−3.06975			−0.234750
$172$	8.22217			0.626935
$173$	−9.39527	+	10.8427i	−0.714309	+	0.824357i	−0.990611	−	0.136714i	$-0.956346\pi$
$173$	−9.39527	+	10.8427i	−0.714309	+	0.824357i	0.276301	+	0.961071i	$0.410891\pi$
$174$	−1.49132	−	3.26553i	−0.113057	−	0.247559i
$175$	−0.834783	−	0.536483i	−0.0631037	−	0.0405543i
$176$	−0.809860	−	0.934628i	−0.0610455	−	0.0704503i
$177$	3.08410	+	1.98203i	0.231815	+	0.148979i
$178$	−2.24843	−	15.6381i	−0.168527	−	1.17213i
$179$	−2.70551	+	18.8173i	−0.202219	+	1.40647i	0.595460	+	0.803385i	$0.296970\pi$
$179$	−2.70551	+	18.8173i	−0.202219	+	1.40647i	−0.797679	+	0.603082i	$0.793939\pi$
$180$	2.77475	+	6.07585i	0.206817	+	0.452867i
$181$	0.615384	+	4.28009i	0.0457411	+	0.318136i	0.999827	+	0.0186031i	$0.00592189\pi$
$181$	0.615384	+	4.28009i	0.0457411	+	0.318136i	−0.954086	+	0.299533i	$0.903169\pi$
$182$	−2.72692	−	0.800697i	−0.202133	−	0.0593516i
$183$	−26.6553	+	17.1303i	−1.97041	+	1.26631i
$184$	2.04958	+	1.31719i	0.151097	+	0.0971043i
$185$	2.51553	−	5.50823i	0.184945	−	0.404973i
$186$	0.552374	+	0.162192i	0.0405020	+	0.0118925i
$187$	2.20791	−	1.41894i	0.161458	−	0.103763i
$188$	5.34250	+	6.16557i	0.389642	+	0.449670i
$189$	7.43883	+	8.58487i	0.541095	+	0.624457i
$190$	0.190917	−	0.418050i	0.0138506	−	0.0303285i
$191$	0.124306	−	0.864566i	0.00899445	−	0.0625578i	−0.984830	−	0.173523i	$-0.944485\pi$
$191$	0.124306	−	0.864566i	0.00899445	−	0.0625578i	0.993824	+	0.110965i	$0.0353941\pi$
$192$	−2.98516	+	0.876521i	−0.215435	+	0.0632575i
$193$	−9.81479	+	11.3269i	−0.706484	+	0.815326i	−0.989613	−	0.143756i	$-0.954082\pi$
$193$	−9.81479	+	11.3269i	−0.706484	+	0.815326i	0.283129	+	0.959082i	$0.408627\pi$
$194$	9.18062	−	2.69567i	0.659130	−	0.193538i
$195$	3.70162	+	8.10542i	0.265078	+	0.580441i
$196$	−2.49886	+	5.47173i	−0.178490	+	0.390838i
$197$	8.98020	−	5.77122i	0.639812	−	0.411183i	−0.180118	−	0.983645i	$-0.557648\pi$
$197$	8.98020	−	5.77122i	0.639812	−	0.411183i	0.819931	+	0.572462i	$0.194012\pi$
$198$	1.17558	+	8.17634i	0.0835448	+	0.581067i
$199$	−25.6127	+	7.52055i	−1.81563	+	0.533118i	−0.999028	−	0.0440789i	$-0.985965\pi$
$199$	−25.6127	+	7.52055i	−1.81563	+	0.533118i	−0.816605	+	0.577197i	$0.804147\pi$
$200$	−1.00000			−0.0707107
$201$	7.70496	+	24.2726i	0.543466	+	1.71205i
$202$	13.4761			0.948173
$203$	1.09863	−	0.322587i	0.0771087	−	0.0226412i
$204$	−0.939656	−	6.53545i	−0.0657891	−	0.457573i
$205$	−7.00594	+	4.50244i	−0.489316	+	0.314464i
$206$	−1.13466	+	2.48456i	−0.0790557	+	0.173108i
$207$	−6.76023	−	14.8028i	−0.469869	−	1.02887i
$208$	−2.74806	+	0.806903i	−0.190544	+	0.0559486i
$209$	0.372196	−	0.429537i	0.0257454	−	0.0297117i
$210$	−2.96220	+	0.869780i	−0.204411	+	0.0600205i
$211$	−3.26700	+	22.7225i	−0.224909	+	1.56428i	0.494179	+	0.869360i	$0.335469\pi$
$211$	−3.26700	+	22.7225i	−0.224909	+	1.56428i	−0.719088	+	0.694919i	$0.755440\pi$
$212$	2.45976	−	5.38613i	0.168937	−	0.369921i
$213$	−21.5374	−	24.8555i	−1.47572	−	1.70307i
$214$	6.68168	+	7.71108i	0.456751	+	0.527118i
$215$	6.91693	−	4.44524i	0.471731	−	0.303163i
$216$	10.9838	+	3.22512i	0.747350	+	0.219442i
$217$	−0.0762772	+	0.167024i	−0.00517804	+	0.0113383i
$218$	−5.32328	−	3.42106i	−0.360538	−	0.231704i
$219$	−3.56380	+	2.29031i	−0.240819	+	0.154765i
$220$	−1.18660	−	0.348416i	−0.0800003	−	0.0234902i
$221$	−0.865023	−	6.01636i	−0.0581877	−	0.404704i
$222$	−7.82626	−	17.1371i	−0.525264	−	1.15017i
$223$	−1.63209	+	11.3515i	−0.109293	+	0.760150i	0.859295	+	0.511480i	$0.170903\pi$
$223$	−1.63209	+	11.3515i	−0.109293	+	0.760150i	−0.968588	+	0.248670i	$0.920007\pi$
$224$	−0.141220	−	0.982209i	−0.00943568	−	0.0656266i
$225$	5.61911	+	3.61119i	0.374608	+	0.240746i
$226$	11.3647	+	13.1156i	0.755970	+	0.872436i
$227$	−3.56298	−	2.28979i	−0.236484	−	0.151979i	0.417032	−	0.908892i	$-0.363070\pi$
$227$	−3.56298	−	2.28979i	−0.236484	−	0.151979i	−0.653516	+	0.756913i	$0.726707\pi$
$228$	−0.593977	−	1.30063i	−0.0393371	−	0.0861362i
$229$	−5.11341	+	5.90119i	−0.337903	+	0.389961i	−0.899116	−	0.437710i	$-0.855790\pi$
$229$	−5.11341	+	5.90119i	−0.337903	+	0.389961i	0.561213	+	0.827672i	$0.310335\pi$
$230$	2.43634			0.160648
$231$	−3.81798			−0.251204
$232$	0.755634	−	0.872048i	0.0496098	−	0.0572528i
$233$	−1.31214	+	9.12610i	−0.0859609	+	0.597871i	0.900621	+	0.434605i	$0.143112\pi$
$233$	−1.31214	+	9.12610i	−0.0859609	+	0.597871i	−0.986582	+	0.163266i	$0.947797\pi$
$234$	18.3555	+	5.38967i	1.19994	+	0.352334i
$235$	7.82775	+	2.29844i	0.510626	+	0.149933i
$236$	−0.167697	+	1.16636i	−0.0109162	+	0.0759236i
$237$	12.0258	−	13.8785i	0.781156	−	0.901503i
$238$	2.10591			0.136506
$239$	−12.4397			−0.804657			−0.402328	−	0.915495i	$-0.631799\pi$
$239$	−12.4397			−0.804657			−0.402328	+	0.915495i	$0.631799\pi$
$240$	−2.03739	+	2.35127i	−0.131513	+	0.151774i
$241$	0.866573	+	1.89753i	0.0558209	+	0.122231i	0.935487	−	0.353361i	$-0.114961\pi$
$241$	0.866573	+	1.89753i	0.0558209	+	0.122231i	−0.879666	+	0.475592i	$0.842234\pi$
$242$	7.96717	+	5.12019i	0.512149	+	0.329138i
$243$	−9.24647	−	10.6710i	−0.593161	−	0.684545i
$244$	−8.56757	−	5.50604i	−0.548482	−	0.352488i
$245$	0.856070	+	5.95410i	0.0546923	+	0.380393i
$246$	−3.68735	+	25.6461i	−0.235097	+	1.63514i
$247$	−0.546800	−	1.19732i	−0.0347920	−	0.0761839i
$248$	0.0263340	+	0.183157i	0.00167221	+	0.0116305i
$249$	−37.7946	−	11.0975i	−2.39514	−	0.703276i
$250$	−0.841254	+	0.540641i	−0.0532055	+	0.0341931i
$251$	20.8603	+	13.4061i	1.31669	+	0.846185i	0.994923	−	0.100635i	$-0.0320874\pi$
$251$	20.8603	+	13.4061i	1.31669	+	0.846185i	0.321766	+	0.946819i	$0.395724\pi$
$252$	−2.75340	+	6.02912i	−0.173448	+	0.379799i
$253$	2.89095	+	0.848861i	0.181753	+	0.0533674i
$254$	−6.14085	+	3.94648i	−0.385311	+	0.247624i
$255$	−4.32382	−	4.98995i	−0.270768	−	0.312483i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	−9.02112	+	19.7535i	−0.562722	+	1.23219i	0.387861	+	0.921718i	$0.373214\pi$
$257$	−9.02112	+	19.7535i	−0.562722	+	1.23219i	−0.950583	+	0.310471i	$0.899513\pi$
$258$	3.64051	−	25.3203i	0.226648	−	1.57637i
$259$	5.76548	−	1.69290i	0.358249	−	0.105191i
$260$	−1.87557	+	2.16452i	−0.116318	+	0.134238i
$261$	−7.39512	+	2.17140i	−0.457747	+	0.134407i
$262$	−3.46300	−	7.58292i	−0.213945	−	0.468474i
$263$	0.577317	−	1.26415i	0.0355989	−	0.0779507i	−0.890997	−	0.454009i	$-0.849993\pi$
$263$	0.577317	−	1.26415i	0.0355989	−	0.0779507i	0.926596	+	0.376058i	$0.122721\pi$
$264$	−3.23678	+	2.08015i	−0.199210	+	0.128025i
$265$	−0.842677	−	5.86094i	−0.0517652	−	0.360035i
$266$	0.437573	−	0.128483i	0.0268293	−	0.00787780i
$267$	−49.1534			−3.00814
$268$	−6.06790	+	5.49369i	−0.370656	+	0.335580i
$269$	12.9076			0.786992			0.393496	−	0.919326i	$-0.371266\pi$
$269$	12.9076			0.786992			0.393496	+	0.919326i	$0.371266\pi$
$270$	10.9838	−	3.22512i	0.668450	−	0.196275i
$271$	−0.869109	−	6.04478i	−0.0527946	−	0.367194i	−0.999042	−	0.0437519i	$-0.986069\pi$
$271$	−0.869109	−	6.04478i	−0.0527946	−	0.367194i	0.946248	−	0.323442i	$-0.104840\pi$
$272$	1.78534	−	1.14737i	0.108252	−	0.0695693i
$273$	−3.67315	+	8.04308i	−0.222309	+	0.486789i
$274$	−8.45492	−	18.5137i	−0.510780	−	1.11845i
$275$	−1.18660	+	0.348416i	−0.0715544	+	0.0210103i
$276$	4.96378	−	5.72851i	0.298785	−	0.344816i
$277$	−22.8074	+	6.69685i	−1.37036	+	0.402375i	−0.882404	−	0.470492i	$-0.844077\pi$
$277$	−22.8074	+	6.69685i	−1.37036	+	0.402375i	−0.487959	+	0.872867i	$0.662258\pi$
$278$	−0.684046	+	4.75764i	−0.0410263	+	0.285344i
$279$	0.513439	−	1.12428i	0.0307388	−	0.0673086i
$280$	−0.649824	−	0.749937i	−0.0388344	−	0.0448173i
$281$	16.2899	+	18.7995i	0.971773	+	1.12149i	0.992567	+	0.121702i	$0.0388353\pi$
$281$	16.2899	+	18.7995i	0.971773	+	1.12149i	−0.0207934	+	0.999784i	$0.506619\pi$
$282$	21.3524	−	13.7224i	1.27152	−	0.817156i
$283$	20.1727	+	5.92325i	1.19914	+	0.352101i	0.819526	−	0.573042i	$-0.194237\pi$
$283$	20.1727	+	5.92325i	1.19914	+	0.352101i	0.379619	+	0.925143i	$0.376055\pi$
$284$	4.39139	−	9.61580i	0.260581	−	0.570593i
$285$	−1.20286	−	0.773030i	−0.0712512	−	0.0457903i
$286$	−2.97970	+	1.91493i	−0.176193	+	0.113232i
$287$	−7.92917	−	2.32822i	−0.468044	−	0.137430i
$288$	0.950586	+	6.61147i	0.0560138	+	0.389584i
$289$	−5.19108	−	11.3669i	−0.305358	−	0.668640i
$290$	0.164215	−	1.14214i	0.00964304	−	0.0670688i
$291$	−4.23649	−	29.4654i	−0.248347	−	1.72729i
$292$	−1.14548	−	0.736156i	−0.0670342	−	0.0430802i
$293$	−8.17938	−	9.43951i	−0.477844	−	0.551462i	0.464732	−	0.885451i	$-0.346151\pi$
$293$	−8.17938	−	9.43951i	−0.477844	−	0.551462i	−0.942577	+	0.333989i	$0.891605\pi$
$294$	15.7439	+	10.1180i	0.918201	+	0.590092i
$295$	0.489506	+	1.07187i	0.0285002	+	0.0624067i
$296$	3.96548	−	4.57641i	0.230489	−	0.265998i
$297$	14.1570			0.821470
$298$	7.37390			0.427158
$299$	4.56953	−	5.27352i	0.264263	−	0.304975i
$300$	−0.442767	+	3.07951i	−0.0255632	+	0.177796i
$301$	7.82844	+	2.29864i	0.451224	+	0.132491i
$302$	−11.4899	−	3.37375i	−0.661172	−	0.194138i
$303$	5.96676	−	41.4998i	0.342782	−	2.38410i
$304$	0.300961	−	0.347328i	0.0172613	−	0.0199206i
$305$	−10.1843			−0.583151
$306$	−14.1754			−0.810352
$307$	9.26734	−	10.6951i	0.528915	−	0.610400i	−0.426925	−	0.904287i	$-0.640403\pi$
$307$	9.26734	−	10.6951i	0.528915	−	0.610400i	0.955840	+	0.293886i	$0.0949488\pi$
$308$	−0.509789	−	1.11628i	−0.0290479	−	0.0636060i
$309$	7.14886	+	4.59429i	0.406684	+	0.261360i
$310$	0.121176	+	0.139844i	0.00688231	+	0.00794260i
$311$	−2.61404	−	1.67994i	−0.148228	−	0.0952606i	0.464424	−	0.885613i	$-0.346261\pi$
$311$	−2.61404	−	1.67994i	−0.148228	−	0.0952606i	−0.612653	+	0.790352i	$0.709898\pi$
$312$	1.26812	+	8.81996i	0.0717931	+	0.499332i
$313$	0.405190	−	2.81816i	0.0229027	−	0.159292i	−0.975161	−	0.221499i	$-0.928905\pi$
$313$	0.405190	−	2.81816i	0.0229027	−	0.159292i	0.998063	+	0.0622074i	$0.0198140\pi$
$314$	−5.36737	−	11.7529i	−0.302898	−	0.663255i
$315$	0.943274	+	6.56062i	0.0531475	+	0.369649i
$316$	5.66343	+	1.66293i	0.318593	+	0.0935473i
$317$	−22.6821	+	14.5769i	−1.27395	+	0.818720i	−0.990129	−	0.140156i	$-0.955239\pi$
$317$	−22.6821	+	14.5769i	−1.27395	+	0.818720i	−0.283824	+	0.958876i	$0.591603\pi$
$318$	−15.4976	−	9.95967i	−0.869060	−	0.558511i
$319$	0.592797	−	1.29804i	0.0331903	−	0.0726765i
$320$	−0.959493	−	0.281733i	−0.0536373	−	0.0157493i
$321$	26.7048	−	17.1621i	1.49052	−	0.957897i
$322$	1.58319	+	1.82710i	0.0882280	+	0.101820i
$323$	0.638711	+	0.737111i	0.0355388	+	0.0410140i
$324$	6.47082	−	14.1691i	0.359490	−	0.787173i
$325$	−0.407600	+	2.83492i	−0.0226096	+	0.157253i
$326$	12.4030	−	3.64186i	0.686941	−	0.201704i
$327$	−12.8922	+	14.8784i	−0.712940	+	0.822776i
$328$	−7.99063	+	2.34626i	−0.441209	+	0.129551i
$329$	3.36298	+	7.36390i	0.185407	+	0.405985i
$330$	−1.59834	+	3.49987i	−0.0879856	+	0.192662i
$331$	−5.64721	+	3.62924i	−0.310399	+	0.199481i	−0.686560	−	0.727073i	$-0.740880\pi$
$331$	−5.64721	+	3.62924i	−0.310399	+	0.199481i	0.376161	+	0.926554i	$0.377244\pi$
$332$	−1.80183	−	12.5320i	−0.0988881	−	0.687782i
$333$	−38.8087	+	11.3953i	−2.12671	+	0.624457i
$334$	7.66329			0.419317
$335$	−2.13453	+	7.90214i	−0.116622	+	0.431740i
$336$	−3.08725			−0.168423
$337$	−16.2267	+	4.76458i	−0.883923	+	0.259543i	−0.692027	−	0.721872i	$-0.743282\pi$
$337$	−16.2267	+	4.76458i	−0.883923	+	0.259543i	−0.191896	+	0.981415i	$0.561464\pi$
$338$	−0.682696	−	4.74826i	−0.0371338	−	0.258271i
$339$	45.4216	−	29.1907i	2.46696	−	1.58542i
$340$	0.881608	−	1.93045i	0.0478119	−	0.104693i
$341$	0.0950625	+	0.208158i	0.00514792	+	0.0112724i
$342$	−2.94540	+	0.864848i	−0.159269	+	0.0467657i
$343$	−8.45767	+	9.76067i	−0.456671	+	0.527027i
$344$	7.88912	−	2.31645i	0.425353	−	0.124895i
$345$	1.07873	−	7.50275i	0.0580770	−	0.403935i
$346$	−5.95995	+	13.0505i	−0.320409	+	0.701598i
$347$	14.2239	+	16.4152i	0.763578	+	0.881216i	0.995810	−	0.0914444i	$-0.0291484\pi$
$347$	14.2239	+	16.4152i	0.763578	+	0.881216i	−0.232232	+	0.972660i	$0.574603\pi$
$348$	−2.35092	−	2.71310i	−0.126022	−	0.145438i
$349$	−8.15346	+	5.23991i	−0.436445	+	0.280486i	−0.740357	−	0.672214i	$-0.765343\pi$
$349$	−8.15346	+	5.23991i	−0.436445	+	0.280486i	0.303912	+	0.952700i	$0.401707\pi$
$350$	−0.952113	−	0.279566i	−0.0508926	−	0.0149434i
$351$	13.6199	−	29.8235i	0.726979	−	1.59186i
$352$	−1.04037	−	0.668605i	−0.0554519	−	0.0356368i
$353$	27.4179	−	17.6204i	1.45931	−	0.937842i	0.460572	−	0.887622i	$-0.347644\pi$
$353$	27.4179	−	17.6204i	1.45931	−	0.937842i	0.998738	−	0.0502192i	$-0.0159920\pi$
$354$	3.51758	+	1.03285i	0.186957	+	0.0548955i
$355$	−1.50442	−	10.4635i	−0.0798465	−	0.555345i
$356$	−6.56312	−	14.3712i	−0.347845	−	0.761674i
$357$	0.932429	−	6.48519i	0.0493494	−	0.343232i
$358$	2.70551	+	18.8173i	0.142991	+	0.994523i
$359$	12.1399	+	7.80185i	0.640721	+	0.411766i	0.820265	−	0.571984i	$-0.193826\pi$
$359$	12.1399	+	7.80185i	0.640721	+	0.411766i	−0.179544	+	0.983750i	$0.557462\pi$
$360$	4.37411	+	5.04800i	0.230536	+	0.266053i
$361$	−15.8061	−	10.1580i	−0.831902	−	0.534631i
$362$	1.79630	+	3.93334i	0.0944112	+	0.206732i
$363$	19.2953	−	22.2680i	1.01274	−	1.16877i
$364$	−2.84205			−0.148964
$365$	−1.36164			−0.0712712
$366$	−20.7494	+	23.9461i	−1.08459	+	1.25168i
$367$	3.15222	−	21.9242i	0.164545	−	1.14443i	−0.725388	−	0.688340i	$-0.758340\pi$
$367$	3.15222	−	21.9242i	0.164545	−	1.14443i	0.889932	−	0.456092i	$-0.150751\pi$
$368$	2.33765	+	0.686397i	0.121859	+	0.0357809i
$369$	53.3731	+	15.6717i	2.77849	+	0.815838i
$370$	0.861781	−	5.99382i	0.0448018	−	0.311604i
$371$	3.84775	−	4.44054i	0.199765	−	0.230541i
$372$	0.575694			0.0298483
$373$	22.4159			1.16065			0.580325	−	0.814385i	$-0.302926\pi$
$373$	22.4159			1.16065			0.580325	+	0.814385i	$0.302926\pi$
$374$	1.71871	−	1.98350i	0.0888725	−	0.102564i
$375$	1.29243	+	2.83003i	0.0667409	+	0.146142i
$376$	6.86313	+	4.41067i	0.353939	+	0.227463i
$377$	−2.16419	−	2.49761i	−0.111462	−	0.128633i
$378$	9.55614	+	6.14136i	0.491515	+	0.315878i
$379$	3.74372	+	26.0381i	0.192302	+	1.33749i	0.825896	+	0.563823i	$0.190670\pi$
$379$	3.74372	+	26.0381i	0.192302	+	1.33749i	−0.633594	+	0.773666i	$0.718421\pi$
$380$	0.0654052	−	0.454903i	0.00335522	−	0.0233360i
$381$	9.43428	+	20.6582i	0.483333	+	1.05835i
$382$	−0.124306	−	0.864566i	−0.00636004	−	0.0442351i
$383$	11.2230	+	3.29537i	0.573468	+	0.168385i	0.555592	−	0.831455i	$-0.312491\pi$
$383$	11.2230	+	3.29537i	0.573468	+	0.168385i	0.0178758	+	0.999840i	$0.494310\pi$
$384$	−2.61729	+	1.68203i	−0.133563	+	0.0858358i
$385$	−1.03237	−	0.663463i	−0.0526144	−	0.0338132i
$386$	−6.22607	+	13.6332i	−0.316899	+	0.693911i
$387$	−52.6950	−	15.4726i	−2.67864	−	0.786519i
$388$	8.04928	−	5.17296i	0.408640	−	0.262617i
$389$	−13.1898	−	15.2219i	−0.668750	−	0.771778i	0.315430	−	0.948949i	$-0.397851\pi$
$389$	−13.1898	−	15.2219i	−0.668750	−	0.771778i	−0.984180	+	0.177170i	$0.943306\pi$
$390$	5.83524	+	6.73422i	0.295479	+	0.341001i
$391$	−2.14790	+	4.70324i	−0.108624	+	0.237853i
$392$	−0.856070	+	5.95410i	−0.0432381	+	0.300727i
$393$	−24.8850	+	7.30690i	−1.25528	+	0.368584i
$394$	6.99049	−	8.06746i	0.352176	−	0.406433i
$395$	5.66343	−	1.66293i	0.284958	−	0.0836713i
$396$	3.43150	+	7.51394i	0.172439	+	0.377590i
$397$	−5.30087	+	11.6073i	−0.266043	+	0.582553i	−0.994757	−	0.102265i	$-0.967391\pi$
$397$	−5.30087	+	11.6073i	−0.266043	+	0.582553i	0.728714	+	0.684818i	$0.240118\pi$
$398$	−22.4564	+	14.4318i	−1.12564	+	0.723403i
$399$	−0.201922	−	1.40440i	−0.0101088	−	0.0703080i
$400$	−0.959493	+	0.281733i	−0.0479746	+	0.0140866i
$401$	18.5484			0.926262			0.463131	−	0.886290i	$-0.346726\pi$
$401$	18.5484			0.926262			0.463131	+	0.886290i	$0.346726\pi$
$402$	14.2312	+	21.1186i	0.709789	+	1.05330i
$403$	0.529968			0.0263996
$404$	12.9302	−	3.79665i	0.643301	−	0.188890i
$405$	−2.21680	−	15.4182i	−0.110154	−	0.766137i
$406$	0.963244	−	0.619040i	0.0478050	−	0.0307224i
$407$	3.11093	−	6.81198i	0.154203	−	0.337657i
$408$	−2.74284	−	6.00599i	−0.135791	−	0.297341i
$409$	−5.44342	+	1.59833i	−0.269160	+	0.0790325i	−0.413527	−	0.910492i	$-0.635703\pi$
$409$	−5.44342	+	1.59833i	−0.269160	+	0.0790325i	0.144368	+	0.989524i	$0.453885\pi$
$410$	−5.45366	+	6.29386i	−0.269337	+	0.310832i
$411$	−60.7568	+	17.8398i	−2.99691	+	0.879972i
$412$	−0.388718	+	2.70359i	−0.0191508	+	0.133196i
$413$	−0.485742	+	1.06363i	−0.0239018	+	0.0523376i
$414$	−10.6568	−	12.2986i	−0.523755	−	0.604445i
$415$	−8.29109	−	9.56843i	−0.406994	−	0.469696i
$416$	−2.40941	+	1.54843i	−0.118131	+	0.0759183i
$417$	14.3484	+	4.21306i	0.702642	+	0.206314i
$418$	0.236105	−	0.516998i	0.0115483	−	0.0252872i
$419$	−8.10614	−	5.20950i	−0.396011	−	0.254501i	0.327447	−	0.944870i	$-0.393812\pi$
$419$	−8.10614	−	5.20950i	−0.396011	−	0.254501i	−0.723457	+	0.690369i	$0.757448\pi$
$420$	−2.59716	+	1.66910i	−0.126729	+	0.0814435i
$421$	−7.26666	−	2.13368i	−0.354155	−	0.103989i	0.0998155	−	0.995006i	$-0.468175\pi$
$421$	−7.26666	−	2.13368i	−0.354155	−	0.103989i	−0.453971	+	0.891017i	$0.649993\pi$
$422$	3.26700	+	22.7225i	0.159035	+	1.10611i
$423$	−22.6370	−	49.5681i	−1.10065	−	2.41008i
$424$	0.842677	−	5.86094i	0.0409240	−	0.284633i
$425$	−0.302025	−	2.10063i	−0.0146504	−	0.101896i
$426$	−27.6676	−	17.7809i	−1.34050	−	0.861488i
$427$	−6.61799	−	7.63757i	−0.320267	−	0.369608i
$428$	8.58349	+	5.51627i	0.414899	+	0.266639i
$429$	4.57776	+	10.0239i	0.221016	+	0.483958i
$430$	5.38438	−	6.21390i	0.259658	−	0.299661i
$431$	−20.6011			−0.992322			−0.496161	−	0.868231i	$-0.665257\pi$
$431$	−20.6011			−0.992322			−0.496161	+	0.868231i	$0.665257\pi$
$432$	11.4475			0.550766
$433$	−19.9270	+	22.9969i	−0.957628	+	1.10516i	0.0367551	+	0.999324i	$0.488298\pi$
$433$	−19.9270	+	22.9969i	−0.957628	+	1.10516i	−0.994383	+	0.105838i	$0.966248\pi$
$434$	−0.0261314	+	0.181748i	−0.00125435	+	0.00872418i
$435$	−3.44453	−	1.01141i	−0.165153	−	0.0484932i
$436$	−6.07147	−	1.78275i	−0.290771	−	0.0853780i
$437$	−0.159349	+	1.10830i	−0.00762272	+	0.0530172i
$438$	−2.77418	+	3.20158i	−0.132556	+	0.152977i
$439$	−39.2376			−1.87271			−0.936353	−	0.351060i	$-0.885821\pi$
$439$	−39.2376			−1.87271			−0.936353	+	0.351060i	$0.885821\pi$
$440$	−1.23669			−0.0589569
$441$	26.3117	−	30.3653i	1.25294	−	1.44597i
$442$	−2.52499	−	5.52895i	−0.120101	−	0.262986i
$443$	20.1955	+	12.9789i	0.959519	+	0.616646i	0.923865	−	0.382719i	$-0.125012\pi$
$443$	20.1955	+	12.9789i	0.959519	+	0.616646i	0.0356543	+	0.999364i	$0.488648\pi$
$444$	−12.3373	−	14.2380i	−0.585504	−	0.675707i
$445$	−13.2909	−	8.54156i	−0.630050	−	0.404909i
$446$	1.63209	+	11.3515i	0.0772819	+	0.537507i
$447$	3.26492	−	22.7080i	0.154425	−	1.07405i
$448$	−0.412220	−	0.902636i	−0.0194756	−	0.0426455i
$449$	−4.92789	−	34.2743i	−0.232562	−	1.61750i	−0.686954	−	0.726701i	$-0.741053\pi$
$449$	−4.92789	−	34.2743i	−0.232562	−	1.61750i	0.454393	−	0.890801i	$-0.349856\pi$
$450$	6.40889	+	1.88182i	0.302118	+	0.0887098i
$451$	−8.66418	+	5.56813i	−0.407980	+	0.262193i
$452$	14.5995	+	9.38250i	0.686701	+	0.441316i
$453$	−15.4769	+	33.8897i	−0.727168	+	1.59228i
$454$	−4.06377	−	1.19323i	−0.190722	−	0.0560010i
$455$	−2.39088	+	1.53653i	−0.112086	+	0.0720334i
$456$	−0.936346	−	1.08060i	−0.0438484	−	0.0506038i
$457$	−3.73073	−	4.30549i	−0.174516	−	0.201402i	0.661752	−	0.749722i	$-0.269813\pi$
$457$	−3.73073	−	4.30549i	−0.174516	−	0.201402i	−0.836269	+	0.548320i	$0.815268\pi$
$458$	−3.24372	+	7.10276i	−0.151569	+	0.331890i
$459$	−3.45742	+	24.0469i	−0.161379	+	1.12241i
$460$	2.33765	−	0.686397i	0.108994	−	0.0320034i
$461$	5.26947	−	6.08130i	0.245424	−	0.283234i	−0.619651	−	0.784878i	$-0.712726\pi$
$461$	5.26947	−	6.08130i	0.245424	−	0.283234i	0.865074	+	0.501644i	$0.167271\pi$
$462$	−3.66332	+	1.07565i	−0.170433	+	0.0500437i
$463$	6.87792	+	15.0606i	0.319644	+	0.699923i	0.999439	−	0.0334787i	$-0.0106586\pi$
$463$	6.87792	+	15.0606i	0.319644	+	0.699923i	−0.679795	+	0.733402i	$0.737931\pi$
$464$	0.479341	−	1.04961i	0.0222529	−	0.0487270i
$465$	0.484304	−	0.311243i	0.0224591	−	0.0144336i
$466$	1.31214	+	9.12610i	0.0607835	+	0.422759i
$467$	−20.1364	+	5.91259i	−0.931803	+	0.273602i	−0.712191	−	0.701985i	$-0.752297\pi$
$467$	−20.1364	+	5.91259i	−0.931803	+	0.273602i	−0.219611	+	0.975587i	$0.570479\pi$
$468$	19.1304			0.884305
$469$	−7.31318	+	3.53424i	−0.337691	+	0.163196i
$470$	8.15822			0.376311
$471$	−38.5698	+	11.3251i	−1.77720	+	0.521833i
$472$	0.167697	+	1.16636i	0.00771890	+	0.0536861i
$473$	8.55410	−	5.49739i	0.393318	−	0.252770i
$474$	7.62861	−	16.7043i	0.350394	−	0.767255i
$475$	−0.190917	−	0.418050i	−0.00875986	−	0.0191814i
$476$	2.02061	−	0.593304i	0.0926144	−	0.0271940i
$477$	−25.9001	+	29.8903i	−1.18588	+	1.36858i
$478$	−11.9358	+	3.50467i	−0.545931	+	0.160300i
$479$	−1.40730	+	9.78796i	−0.0643010	+	0.447224i	0.932082	+	0.362247i	$0.117990\pi$
$479$	−1.40730	+	9.78796i	−0.0643010	+	0.447224i	−0.996383	+	0.0849761i	$0.972919\pi$
$480$	−1.29243	+	2.83003i	−0.0589912	+	0.129173i
$481$	−11.3574	−	13.1072i	−0.517854	−	0.597635i
$482$	1.36607	+	1.57652i	0.0622226	+	0.0718087i
$483$	6.32758	−	4.06649i	0.287915	−	0.185032i
$484$	9.08697	+	2.66818i	0.413044	+	0.121281i
$485$	3.97477	−	8.70354i	0.180485	−	0.395207i
$486$	−11.8783	−	7.63371i	−0.538810	−	0.346272i
$487$	−21.7957	+	14.0072i	−0.987656	+	0.634728i	−0.931518	−	0.363695i	$-0.881515\pi$
$487$	−21.7957	+	14.0072i	−0.987656	+	0.634728i	−0.0561376	+	0.998423i	$0.517879\pi$
$488$	−9.77175	−	2.86924i	−0.442346	−	0.129885i
$489$	−5.72351	−	39.8079i	−0.258826	−	1.80017i
$490$	2.49886	+	5.47173i	0.112887	+	0.247188i
$491$	2.06615	−	14.3704i	0.0932439	−	0.648526i	−0.888579	−	0.458724i	$-0.848306\pi$
$491$	2.06615	−	14.3704i	0.0932439	−	0.648526i	0.981823	−	0.189801i	$-0.0607844\pi$
$492$	3.68735	+	25.6461i	0.166239	+	1.15622i
$493$	2.06007	+	1.32393i	0.0927811	+	0.0596268i
$494$	−0.861976	−	0.994773i	−0.0387821	−	0.0447570i
$495$	6.94911	+	4.46592i	0.312339	+	0.200728i
$496$	0.0768684	+	0.168318i	0.00345149	+	0.00755772i
$497$	6.86935	−	7.92765i	0.308132	−	0.355604i
$498$	−39.3902			−1.76512
$499$	−21.5998			−0.966939			−0.483469	−	0.875361i	$-0.660624\pi$
$499$	−21.5998			−0.966939			−0.483469	+	0.875361i	$0.660624\pi$
$500$	−0.654861	+	0.755750i	−0.0292863	+	0.0337981i
$501$	3.39305	−	23.5992i	0.151590	−	1.05434i
$502$	23.7922	+	6.98603i	1.06190	+	0.311802i
$503$	37.1786	+	10.9166i	1.65771	+	0.486748i	0.970780	−	0.239973i	$-0.0771386\pi$
$503$	37.1786	+	10.9166i	1.65771	+	0.486748i	0.686933	+	0.726721i	$0.258957\pi$
$504$	−0.943274	+	6.56062i	−0.0420168	+	0.292233i
$505$	8.82495	−	10.1845i	0.392705	−	0.453206i
$506$	3.01300			0.133944
$507$	−14.9246			−0.662825
$508$	−4.78025	+	5.51670i	−0.212089	+	0.244764i
$509$	17.7345	+	38.8331i	0.786067	+	1.72125i	0.687581	+	0.726107i	$0.258672\pi$
$509$	17.7345	+	38.8331i	0.786067	+	1.72125i	0.0984852	+	0.995139i	$0.468600\pi$
$510$	−5.55451	−	3.56967i	−0.245958	−	0.158067i
$511$	−0.884823	−	1.02114i	−0.0391423	−	0.0451726i
$512$	−0.841254	−	0.540641i	−0.0371785	−	0.0238932i
$513$	0.748723	+	5.20748i	0.0330569	+	0.229916i
$514$	−3.09050	+	21.4949i	−0.136316	+	0.948098i
$515$	1.13466	+	2.48456i	0.0499992	+	0.109483i
$516$	−3.64051	−	25.3203i	−0.160264	−	1.11466i
$517$	9.68051	+	2.84245i	0.425748	+	0.125011i
$518$	5.05499	−	3.24865i	0.222104	−	0.142737i
$519$	37.5503	+	24.1321i	1.64827	+	1.05928i
$520$	−1.18978	+	2.60525i	−0.0521753	+	0.114248i
$521$	2.55640	+	0.750628i	0.111998	+	0.0328856i	0.337251	−	0.941415i	$-0.390503\pi$
$521$	2.55640	+	0.750628i	0.111998	+	0.0328856i	−0.225253	+	0.974300i	$0.572321\pi$
$522$	−6.48382	+	4.16689i	−0.283789	+	0.182380i
$523$	5.20076	+	6.00199i	0.227413	+	0.262449i	0.857976	−	0.513689i	$-0.171722\pi$
$523$	5.20076	+	6.00199i	0.227413	+	0.262449i	−0.630563	+	0.776138i	$0.717176\pi$
$524$	−5.45908	−	6.30012i	−0.238481	−	0.275222i
$525$	−1.28249	+	2.80826i	−0.0559725	+	0.122563i
$526$	0.197780	−	1.37559i	0.00862362	−	0.0599786i
$527$	−0.376791	+	0.110636i	−0.0164133	+	0.00481938i
$528$	−2.51962	+	2.90780i	−0.109652	+	0.126546i
$529$	16.3730	−	4.80755i	0.711870	−	0.209024i
$530$	−2.45976	−	5.38613i	−0.106845	−	0.233958i
$531$	3.26964	−	7.15950i	0.141890	−	0.310696i
$532$	0.383650	−	0.246557i	0.0166334	−	0.0106896i
$533$	3.39448	+	23.6091i	0.147031	+	1.02263i
$534$	−47.1624	+	13.8481i	−2.04092	+	0.599267i
$535$	10.2032			0.441123
$536$	−4.27436	+	6.98068i	−0.184624	+	0.301519i
$537$	59.1459			2.55233
$538$	12.3848	−	3.63650i	0.533946	−	0.156781i
$539$	1.05869	+	7.36337i	0.0456012	+	0.317163i
$540$	9.63021	−	6.18896i	0.414418	−	0.266330i
$541$	−10.3406	+	22.6428i	−0.444578	+	0.973490i	0.546157	+	0.837683i	$0.316090\pi$
$541$	−10.3406	+	22.6428i	−0.444578	+	0.973490i	−0.990735	+	0.135807i	$0.956637\pi$
$542$	−2.53692	−	5.55507i	−0.108970	−	0.238611i
$543$	12.9081	−	3.79017i	0.553941	−	0.162652i
$544$	1.38977	−	1.60388i	0.0595858	−	0.0687657i
$545$	−6.07147	+	1.78275i	−0.260073	+	0.0763644i
$546$	−1.25836	+	8.75212i	−0.0538530	+	0.374556i
$547$	10.8899	−	23.8455i	0.465617	−	1.01956i	−0.520554	−	0.853829i	$-0.674274\pi$
$547$	10.8899	−	23.8455i	0.465617	−	1.01956i	0.986171	−	0.165731i	$-0.0529982\pi$
$548$	−13.3283	−	15.3817i	−0.569359	−	0.657075i
$549$	44.5472	+	51.4102i	1.90123	+	2.19413i
$550$	−1.04037	+	0.668605i	−0.0443615	+	0.0285094i
$551$	0.508823	+	0.149404i	0.0216766	+	0.00636482i
$552$	3.14881	−	6.89492i	0.134022	−	0.293467i
$553$	4.92733	+	3.16660i	0.209531	+	0.134658i
$554$	−19.9968	+	12.8512i	−0.849583	+	0.545994i
$555$	−18.0765	−	5.30773i	−0.767304	−	0.225301i
$556$	0.684046	+	4.75764i	0.0290100	+	0.201769i
$557$	−2.08661	−	4.56903i	−0.0884124	−	0.193596i	0.860261	−	0.509854i	$-0.170301\pi$
$557$	−2.08661	−	4.56903i	−0.0884124	−	0.193596i	−0.948673	+	0.316258i	$0.897573\pi$
$558$	0.175896	−	1.22339i	0.00744629	−	0.0517901i
$559$	−3.35136	−	23.3092i	−0.141747	−	0.985874i
$560$	−0.834783	−	0.536483i	−0.0352760	−	0.0226705i
$561$	−5.34723	−	6.17103i	−0.225760	−	0.260541i
$562$	20.9265	+	13.4486i	0.882730	+	0.567296i
$563$	9.71964	+	21.2830i	0.409634	+	0.896973i	0.996202	+	0.0870734i	$0.0277515\pi$
$563$	9.71964	+	21.2830i	0.409634	+	0.896973i	−0.586568	+	0.809900i	$0.699521\pi$
$564$	16.6215	−	19.1822i	0.699891	−	0.807717i
$565$	17.3544			0.730106
$566$	21.0244			0.883720
$567$	10.1221	−	11.6816i	0.425090	−	0.490580i
$568$	1.50442	−	10.4635i	0.0631242	−	0.439038i
$569$	−18.9831	−	5.57393i	−0.795811	−	0.233671i	−0.141541	−	0.989932i	$-0.545206\pi$
$569$	−18.9831	−	5.57393i	−0.795811	−	0.233671i	−0.654270	+	0.756261i	$0.727024\pi$
$570$	−1.37192	−	0.402832i	−0.0574635	−	0.0168728i
$571$	−3.42441	+	23.8173i	−0.143307	+	0.996724i	0.783555	+	0.621322i	$0.213404\pi$
$571$	−3.42441	+	23.8173i	−0.143307	+	0.996724i	−0.926862	+	0.375402i	$0.877505\pi$
$572$	−2.31950	+	2.67684i	−0.0969831	+	0.111924i
$573$	−2.71748			−0.113524
$574$	−8.26392			−0.344929
$575$	1.59547	−	1.84126i	0.0665355	−	0.0767861i
$576$	2.77475	+	6.07585i	0.115614	+	0.253160i
$577$	−2.89875	−	1.86291i	−0.120676	−	0.0775540i	0.478910	−	0.877864i	$-0.341032\pi$
$577$	−2.89875	−	1.86291i	−0.120676	−	0.0775540i	−0.599587	+	0.800310i	$0.704668\pi$
$578$	−8.18322	−	9.44394i	−0.340377	−	0.392816i
$579$	39.2269	+	25.2096i	1.63022	+	1.04768i
$580$	−0.164215	−	1.14214i	−0.00681866	−	0.0474248i
$581$	1.78797	−	12.4356i	0.0741774	−	0.515915i
$582$	−12.3662	−	27.0783i	−0.512597	−	1.12243i
$583$	−1.04213	−	7.24818i	−0.0431606	−	0.300189i
$584$	−1.30648	−	0.383617i	−0.0540625	−	0.0158742i
$585$	16.0936	−	10.3427i	0.665387	−	0.427618i
$586$	−10.5075	−	6.75274i	−0.434060	−	0.278953i
$587$	−1.93479	+	4.23661i	−0.0798575	+	0.174863i	−0.945349	−	0.326060i	$-0.894279\pi$
$587$	−1.93479	+	4.23661i	−0.0798575	+	0.174863i	0.865492	+	0.500923i	$0.167006\pi$
$588$	17.9567	+	5.27256i	0.740521	+	0.217437i
$589$	−0.0715410	+	0.0459766i	−0.00294779	+	0.00189443i
$590$	0.771659	+	0.890541i	0.0317687	+	0.0366630i
$591$	−21.7487	−	25.0993i	−0.894622	−	1.03245i
$592$	2.51553	−	5.50823i	0.103387	−	0.226387i
$593$	2.75916	−	19.1904i	0.113305	−	0.788055i	−0.851361	−	0.524580i	$-0.824222\pi$
$593$	2.75916	−	19.1904i	0.113305	−	0.788055i	0.964666	−	0.263475i	$-0.0848686\pi$
$594$	13.5835	−	3.98848i	0.557338	−	0.163649i
$595$	1.37908	−	1.59154i	0.0565367	−	0.0652468i
$596$	7.07520	−	2.07747i	0.289812	−	0.0850964i
$597$	34.5001	+	75.5447i	1.41200	+	3.09184i
$598$	2.89871	−	6.34729i	0.118537	−	0.259560i
$599$	−21.5081	+	13.8224i	−0.878796	+	0.564768i	−0.900431	−	0.434998i	$-0.856749\pi$
$599$	−21.5081	+	13.8224i	−0.878796	+	0.564768i	0.0216357	+	0.999766i	$0.493113\pi$
$600$	0.442767	+	3.07951i	0.0180759	+	0.125721i
$601$	10.1534	−	2.98131i	0.414166	−	0.121610i	−0.0680099	−	0.997685i	$-0.521665\pi$
$601$	10.1534	−	2.98131i	0.414166	−	0.121610i	0.482176	+	0.876075i	$0.339847\pi$
$602$	8.15893			0.332533
$603$	49.2266	−	23.7897i	2.00466	−	0.968793i
$604$	−11.9750			−0.487256
$605$	9.08697	−	2.66818i	0.369438	−	0.108477i
$606$	−5.96676	−	41.4998i	−0.242383	−	1.68581i
$607$	29.1716	−	18.7475i	1.18404	−	0.760937i	0.207916	−	0.978147i	$-0.433332\pi$
$607$	29.1716	−	18.7475i	1.18404	−	0.760937i	0.976125	+	0.217210i	$0.0696957\pi$
$608$	0.190917	−	0.418050i	0.00774270	−	0.0169541i
$609$	−1.47985	−	3.24042i	−0.0599665	−	0.131308i
$610$	−9.77175	+	2.86924i	−0.395647	+	0.116172i
$611$	15.3013	−	17.6586i	0.619024	−	0.714392i
$612$	−13.6012	+	3.99366i	−0.549794	+	0.161434i
$613$	2.75603	−	19.1686i	0.111315	−	0.774214i	−0.855328	−	0.518087i	$-0.826644\pi$
$613$	2.75603	−	19.1686i	0.111315	−	0.774214i	0.966643	−	0.256127i	$-0.0824465\pi$
$614$	5.87879	−	12.8728i	0.237249	−	0.519502i
$615$	16.9673	+	19.5814i	0.684189	+	0.789596i
$616$	−0.803631	−	0.927440i	−0.0323792	−	0.0373676i
$617$	2.13693	−	1.37332i	0.0860295	−	0.0552878i	−0.496919	−	0.867797i	$-0.665535\pi$
$617$	2.13693	−	1.37332i	0.0860295	−	0.0552878i	0.582948	+	0.812509i	$0.301899\pi$
$618$	8.15364	+	2.39413i	0.327988	+	0.0963058i
$619$	4.58184	−	10.0328i	0.184160	−	0.403253i	−0.794925	−	0.606708i	$-0.792490\pi$
$619$	4.58184	−	10.0328i	0.184160	−	0.403253i	0.979084	+	0.203455i	$0.0652170\pi$
$620$	0.155666	+	0.100040i	0.00625168	+	0.00401771i
$621$	−23.4625	+	15.0784i	−0.941517	+	0.605077i
$622$	−2.98144	−	0.875430i	−0.119545	−	0.0351016i
$623$	−2.23113	−	15.5179i	−0.0893884	−	0.621710i
$624$	3.70162	+	8.10542i	0.148183	+	0.324476i
$625$	−0.142315	+	0.989821i	−0.00569259	+	0.0395929i
$626$	−0.405190	−	2.81816i	−0.0161947	−	0.112636i
$627$	−1.48756	−	0.955999i	−0.0594075	−	0.0381789i
$628$	−8.46114	−	9.76467i	−0.337636	−	0.389653i
$629$	10.8110	+	6.94782i	0.431064	+	0.277028i
$630$	2.75340	+	6.02912i	0.109698	+	0.240206i
$631$	0.154591	−	0.178407i	0.00615417	−	0.00710229i	−0.752664	−	0.658405i	$-0.771232\pi$
$631$	0.154591	−	0.178407i	0.00615417	−	0.00710229i	0.758818	+	0.651302i	$0.225777\pi$
$632$	5.90252			0.234790
$633$	71.4207			2.83872
$634$	−17.6565	+	20.3767i	−0.701230	+	0.809263i
$635$	−1.03885	+	7.22534i	−0.0412254	+	0.286729i
$636$	−17.6758	−	5.19007i	−0.700889	−	0.205800i
$637$	16.5305	+	4.85378i	0.654961	+	0.192314i
$638$	0.203083	−	1.41247i	0.00804014	−	0.0559204i
$639$	−46.2391	+	53.3628i	−1.82919	+	2.11100i
$640$	−1.00000			−0.0395285
$641$	21.7320			0.858361			0.429180	−	0.903219i	$-0.358802\pi$
$641$	21.7320			0.858361			0.429180	+	0.903219i	$0.358802\pi$
$642$	20.7879	−	23.9906i	0.820434	−	0.946832i
$643$	−11.7139	−	25.6499i	−0.461951	−	1.01153i	−0.987038	−	0.160484i	$-0.948694\pi$
$643$	−11.7139	−	25.6499i	−0.461951	−	1.01153i	0.525087	−	0.851049i	$-0.324033\pi$
$644$	2.03382	+	1.30706i	0.0801437	+	0.0515052i
$645$	−16.7518	−	19.3326i	−0.659601	−	0.761220i
$646$	0.820507	+	0.527308i	0.0322824	+	0.0207466i
$647$	3.04745	+	21.1955i	0.119808	+	0.833282i	0.957766	+	0.287548i	$0.0928400\pi$
$647$	3.04745	+	21.1955i	0.119808	+	0.833282i	−0.837959	+	0.545734i	$0.816251\pi$
$648$	2.21680	−	15.4182i	0.0870842	−	0.605684i
$649$	0.605368	+	1.32557i	0.0237628	+	0.0520332i
$650$	0.407600	+	2.83492i	0.0159874	+	0.111195i
$651$	0.548126	+	0.160944i	0.0214827	+	0.00630790i
$652$	10.8746	−	6.98868i	0.425882	−	0.273698i
$653$	−28.7917	−	18.5033i	−1.12671	−	0.724091i	−0.161837	−	0.986817i	$-0.551742\pi$
$653$	−28.7917	−	18.5033i	−1.12671	−	0.724091i	−0.964870	+	0.262726i	$0.915378\pi$
$654$	−8.17824	+	17.9079i	−0.319795	+	0.700253i
$655$	−7.99857	−	2.34859i	−0.312530	−	0.0917671i
$656$	−7.00594	+	4.50244i	−0.273536	+	0.175791i
$657$	5.95595	+	6.87353i	0.232364	+	0.268162i
$658$	5.30141	+	6.11815i	0.206670	+	0.238510i
$659$	17.6900	−	38.7356i	0.689103	−	1.50892i	−0.163599	−	0.986527i	$-0.552310\pi$
$659$	17.6900	−	38.7356i	0.689103	−	1.50892i	0.852702	−	0.522398i	$-0.174962\pi$
$660$	−0.547566	+	3.80841i	−0.0213140	+	0.148242i
$661$	−35.8211	+	10.5180i	−1.39328	+	0.409104i	−0.890371	−	0.455235i	$-0.849555\pi$
$661$	−35.8211	+	10.5180i	−1.39328	+	0.409104i	−0.502909	+	0.864339i	$0.667737\pi$
$662$	−4.39598	+	5.07324i	−0.170855	+	0.197177i
$663$	−18.1445	+	5.32770i	−0.704673	+	0.206911i
$664$	−5.25951	−	11.5167i	−0.204108	−	0.446935i
$665$	0.189448	−	0.414834i	0.00734650	−	0.0160866i
$666$	−34.0263	+	21.8674i	−1.31849	+	0.847343i
$667$	0.400084	+	2.78265i	0.0154913	+	0.107744i
$668$	7.35287	−	2.15900i	0.284491	−	0.0835341i
$669$	35.6796			1.37945
$670$	0.178222	+	8.18341i	0.00688531	+	0.316153i
$671$	−12.5948			−0.486217
$672$	−2.96220	+	0.869780i	−0.114269	+	0.0335525i
$673$	5.58262	+	38.8280i	0.215194	+	1.49671i	0.755449	+	0.655207i	$0.227419\pi$
$673$	5.58262	+	38.8280i	0.215194	+	1.49671i	−0.540255	+	0.841501i	$0.681672\pi$
$674$	−14.2270	+	9.14316i	−0.548005	+	0.352181i
$675$	4.75544	−	10.4130i	0.183037	−	0.400795i
$676$	−1.99278	−	4.36358i	−0.0766454	−	0.167830i
$677$	−15.3378	+	4.50358i	−0.589479	+	0.173087i	−0.562850	−	0.826559i	$-0.690295\pi$
$677$	−15.3378	+	4.50358i	−0.589479	+	0.173087i	−0.0266285	+	0.999645i	$0.508477\pi$
$678$	35.3577	−	40.8050i	1.35791	−	1.56711i
$679$	9.11001	−	2.67494i	0.349610	−	0.102655i
$680$	0.302025	−	2.10063i	0.0115821	−	0.0805556i
$681$	−5.47387	+	11.9861i	−0.209759	+	0.459309i
$682$	0.149857	+	0.172944i	0.00573831	+	0.00662236i
$683$	6.83564	+	7.88875i	0.261559	+	0.301855i	0.871305	−	0.490742i	$-0.163274\pi$
$683$	6.83564	+	7.88875i	0.261559	+	0.301855i	−0.609746	+	0.792597i	$0.708729\pi$
$684$	−2.58244	+	1.65963i	−0.0987420	+	0.0634576i
$685$	−19.5285	−	5.73409i	−0.746146	−	0.219088i
$686$	−5.36518	+	11.7481i	−0.204843	+	0.448544i
$687$	20.4368	+	13.1340i	0.779714	+	0.501092i
$688$	6.91693	−	4.44524i	0.263706	−	0.169473i
$689$	−16.2718	−	4.77784i	−0.619908	−	0.182021i
$690$	−1.07873	−	7.50275i	−0.0410667	−	0.285625i
$691$	0.890296	+	1.94948i	0.0338685	+	0.0741616i	0.925810	−	0.377989i	$-0.123384\pi$
$691$	0.890296	+	1.94948i	0.0338685	+	0.0741616i	−0.891942	+	0.452150i	$0.850657\pi$
$692$	−2.04179	+	14.2009i	−0.0776171	+	0.539839i
$693$	1.16654	+	8.11345i	0.0443131	+	0.308205i
$694$	18.2724	+	11.7430i	0.693612	+	0.445757i
$695$	3.14763	+	3.63256i	0.119396	+	0.137791i
$696$	−3.02006	−	1.94087i	−0.114475	−	0.0735686i
$697$	−7.34201	−	16.0767i	−0.278098	−	0.608950i
$698$	−6.34693	+	7.32475i	−0.240235	+	0.277246i
$699$	28.6849			1.08496
$700$	−0.992309			−0.0375058
$701$	17.9008	−	20.6587i	0.676105	−	0.780267i	−0.309214	−	0.950993i	$-0.600066\pi$
$701$	17.9008	−	20.6587i	0.676105	−	0.780267i	0.985319	+	0.170726i	$0.0546113\pi$
$702$	4.66598	−	32.4526i	0.176106	−	1.22485i
$703$	2.67024	+	0.784053i	0.100710	+	0.0295711i
$704$	−1.18660	−	0.348416i	−0.0447215	−	0.0131314i
$705$	3.61219	−	25.1234i	0.136043	−	0.946200i
$706$	21.3431	−	24.6312i	0.803257	−	0.927008i
$707$	13.3724			0.502922
$708$	3.66608			0.137780
$709$	−30.8980	+	35.6582i	−1.16040	+	1.33917i	−0.229755	+	0.973248i	$0.573793\pi$
$709$	−30.8980	+	35.6582i	−1.16040	+	1.33917i	−0.930645	+	0.365925i	$0.880753\pi$
$710$	−4.39139	−	9.61580i	−0.164806	−	0.360875i
$711$	−33.1670	−	21.3151i	−1.24386	−	0.799379i
$712$	−10.3461	−	11.9401i	−0.387737	−	0.447472i
$713$	−0.379255	−	0.243732i	−0.0142032	−	0.00912785i
$714$	−0.932429	−	6.48519i	−0.0348953	−	0.242702i
$715$	−0.504075	+	3.50592i	−0.0188513	+	0.131114i
$716$	7.89735	+	17.2928i	0.295138	+	0.646262i
$717$	5.50789	+	38.3082i	0.205696	+	1.43065i
$718$	13.8462	+	4.06561i	0.516736	+	0.151727i
$719$	9.69680	−	6.23175i	0.361629	−	0.232405i	−0.347190	−	0.937795i	$-0.612864\pi$
$719$	9.69680	−	6.23175i	0.361629	−	0.232405i	0.708820	+	0.705389i	$0.249228\pi$
$720$	5.61911	+	3.61119i	0.209412	+	0.134581i
$721$	−1.12594	+	2.46545i	−0.0419320	+	0.0918183i
$722$	−18.0277	−	5.29341i	−0.670922	−	0.197000i
$723$	5.45978	−	3.50879i	0.203051	−	0.130493i
$724$	2.83168	+	3.26794i	0.105239	+	0.121452i
$725$	−0.755634	−	0.872048i	−0.0280636	−	0.0323871i
$726$	12.2401	−	26.8021i	0.454273	−	0.994718i
$727$	4.68652	−	32.5954i	0.173813	−	1.20890i	−0.696922	−	0.717147i	$-0.745448\pi$
$727$	4.68652	−	32.5954i	0.173813	−	1.20890i	0.870736	−	0.491751i	$-0.163643\pi$
$728$	−2.72692	+	0.800697i	−0.101066	+	0.0296758i
$729$	1.83436	−	2.11696i	0.0679392	−	0.0784060i
$730$	−1.30648	+	0.383617i	−0.0483550	+	0.0141983i
$731$	7.24873	+	15.8725i	0.268104	+	0.587066i
$732$	−13.1625	+	28.8218i	−0.486500	+	1.06529i
$733$	−16.8711	+	10.8424i	−0.623149	+	0.400474i	−0.813768	−	0.581190i	$-0.802587\pi$
$733$	−16.8711	+	10.8424i	−0.623149	+	0.400474i	0.190618	+	0.981664i	$0.438951\pi$
$734$	−3.15222	−	21.9242i	−0.116351	−	0.809236i
$735$	17.9567	−	5.27256i	0.662342	−	0.194481i
$736$	2.43634			0.0898048
$737$	−2.63975	+	9.77250i	−0.0972366	+	0.359975i
$738$	55.6263			2.04763
$739$	26.9911	−	7.92530i	0.992883	−	0.291537i	0.255351	−	0.966848i	$-0.417809\pi$
$739$	26.9911	−	7.92530i	0.992883	−	0.291537i	0.737533	+	0.675312i	$0.235991\pi$
$740$	−0.861781	−	5.99382i	−0.0316797	−	0.220337i
$741$	−3.44507	+	2.21401i	−0.126558	+	0.0813338i
$742$	2.44084	−	5.34470i	0.0896062	−	0.196210i
$743$	16.8776	+	36.9568i	0.619179	+	1.35581i	0.916115	+	0.400916i	$0.131308\pi$
$743$	16.8776	+	36.9568i	0.619179	+	1.35581i	−0.296935	+	0.954898i	$0.595965\pi$
$744$	0.552374	−	0.162192i	0.0202510	−	0.00594623i
$745$	4.82888	−	5.57282i	0.176916	−	0.204172i
$746$	21.5079	−	6.31528i	0.787459	−	0.231219i
$747$	−12.0352	+	83.7068i	−0.440346	+	3.06267i
$748$	1.09028	−	2.38737i	0.0398644	−	0.0872909i
$749$	6.63030	+	7.65177i	0.242266	+	0.279590i
$750$	2.03739	+	2.35127i	0.0743950	+	0.0858564i
$751$	−31.2110	+	20.0581i	−1.13891	+	0.731931i	−0.967400	−	0.253253i	$-0.918500\pi$
$751$	−31.2110	+	20.0581i	−1.13891	+	0.731931i	−0.171506	+	0.985183i	$0.554863\pi$
$752$	7.82775	+	2.29844i	0.285449	+	0.0838153i
$753$	32.0480	−	70.1753i	1.16789	−	2.55733i
$754$	−2.78019	−	1.78672i	−0.101248	−	0.0650684i
$755$	−10.0740	+	6.47418i	−0.366631	+	0.235620i
$756$	10.8993	+	3.20032i	0.396403	+	0.116394i
$757$	−3.60169	−	25.0503i	−0.130906	−	0.910469i	−0.944377	−	0.328864i	$-0.893334\pi$
$757$	−3.60169	−	25.0503i	−0.130906	−	0.910469i	0.813472	−	0.581605i	$-0.197575\pi$
$758$	10.9279	+	23.9287i	0.396918	+	0.869128i
$759$	1.33406	−	9.27858i	0.0484233	−	0.336791i
$760$	−0.0654052	−	0.454903i	−0.00237250	−	0.0165011i
$761$	19.4598	+	12.5061i	0.705418	+	0.453344i	0.843537	−	0.537071i	$-0.180469\pi$
$761$	19.4598	+	12.5061i	0.705418	+	0.453344i	−0.138119	+	0.990416i	$0.544106\pi$
$762$	14.8722	+	17.1635i	0.538764	+	0.621766i
$763$	−5.28234	−	3.39475i	−0.191233	−	0.122898i
$764$	−0.362847	−	0.794524i	−0.0131273	−	0.0287449i
$765$	−9.28289	+	10.7130i	−0.335624	+	0.387330i
$766$	11.6968			0.422622
$767$	3.37490			0.121860
$768$	−2.03739	+	2.35127i	−0.0735180	+	0.0848443i
$769$	4.68109	−	32.5577i	0.168804	−	1.17406i	−0.712556	−	0.701615i	$-0.752463\pi$
$769$	4.68109	−	32.5577i	0.168804	−	1.17406i	0.881360	−	0.472445i	$-0.156628\pi$
$770$	−1.17747	−	0.345736i	−0.0424331	−	0.0124595i
$771$	64.8254	+	19.0345i	2.33463	+	0.685509i
$772$	−2.13296	+	14.8350i	−0.0767668	+	0.533925i
$773$	29.0608	−	33.5380i	1.04525	−	1.20628i	0.0672325	−	0.997737i	$-0.478583\pi$
$773$	29.0608	−	33.5380i	1.04525	−	1.20628i	0.978014	−	0.208541i	$-0.0668715\pi$
$774$	−54.9196			−1.97405
$775$	0.185040			0.00664684
$776$	6.26584	−	7.23116i	0.224930	−	0.259584i
$777$	−7.76607	−	17.0053i	−0.278606	−	0.610062i
$778$	−16.9440	−	10.8893i	−0.607473	−	0.390399i
$779$	−2.50640	−	2.89254i	−0.0898011	−	0.103636i
$780$	7.49612	+	4.81746i	0.268404	+	0.172493i
$781$	−1.86051	−	12.9401i	−0.0665741	−	0.463033i
$782$	−0.735837	+	5.11786i	−0.0263135	+	0.183014i
$783$	5.48724	+	12.0154i	0.196098	+	0.429394i
$784$	0.856070	+	5.95410i	0.0305739	+	0.212646i
$785$	−12.3971	−	3.64013i	−0.442473	−	0.129922i
$786$	−21.8184	+	14.0218i	−0.778237	+	0.500142i
$787$	14.3322	+	9.21071i	0.510886	+	0.328327i	0.770557	−	0.637370i	$-0.219978\pi$
$787$	14.3322	+	9.21071i	0.510886	+	0.328327i	−0.259671	+	0.965697i	$0.583614\pi$
$788$	4.43446	−	9.71012i	0.157971	−	0.345909i
$789$	−4.14858	−	1.21813i	−0.147693	−	0.0433667i
$790$	4.96552	−	3.19115i	0.176665	−	0.113536i
$791$	11.2773	+	13.0147i	0.400975	+	0.462750i
$792$	5.40942	+	6.24281i	0.192216	+	0.221829i
$793$	−12.1170	+	26.5326i	−0.430289	+	0.942202i
$794$	−1.81600	+	12.6305i	−0.0644473	+	0.448241i
$795$	−17.6758	+	5.19007i	−0.626894	+	0.184073i
$796$	−17.4808	+	20.1739i	−0.619591	+	0.715046i
$797$	−50.5550	+	14.8443i	−1.79075	+	0.525812i	−0.996636	−	0.0819555i	$-0.973883\pi$
$797$	−50.5550	+	14.8443i	−1.79075	+	0.525812i	−0.794115	+	0.607767i	$0.792065\pi$
$798$	−0.589409	−	1.29062i	−0.0208648	−	0.0456876i
$799$	−7.19235	+	15.7490i	−0.254447	+	0.557161i
$800$	−0.841254	+	0.540641i	−0.0297428	+	0.0191145i
$801$	15.0183	+	104.454i	0.530644	+	3.69071i
$802$	17.7970	−	5.22568i	0.628435	−	0.184525i
$803$	−1.68392			−0.0594243
$804$	19.6046	+	16.2538i	0.691399	+	0.573226i
$805$	2.41760			0.0852094
$806$	0.508501	−	0.149309i	0.0179112	−	0.00525920i
$807$	−5.71508	−	39.7492i	−0.201180	−	1.39924i
$808$	11.3368	−	7.28571i	0.398827	−	0.256311i
$809$	10.8219	−	23.6965i	0.380476	−	0.833126i	−0.618406	−	0.785859i	$-0.712221\pi$
$809$	10.8219	−	23.6965i	0.380476	−	0.833126i	0.998882	−	0.0472677i	$-0.0150514\pi$
$810$	−6.47082	−	14.1691i	−0.227361	−	0.497852i
$811$	4.84720	−	1.42327i	0.170208	−	0.0499776i	−0.195518	−	0.980700i	$-0.562639\pi$
$811$	4.84720	−	1.42327i	0.170208	−	0.0499776i	0.365726	+	0.930722i	$0.380821\pi$
$812$	0.749823	−	0.865341i	0.0263136	−	0.0303675i
$813$	−18.2302	+	5.35287i	−0.639361	+	0.187733i
$814$	1.06576	−	7.41250i	0.0373547	−	0.259808i
$815$	5.36993	−	11.7585i	0.188100	−	0.411883i
$816$	−4.32382	−	4.98995i	−0.151364	−	0.174683i
$817$	2.47456	+	2.85579i	0.0865738	+	0.0999115i
$818$	−4.77262	+	3.06718i	−0.166871	+	0.107241i
$819$	18.2144	+	5.34822i	0.636461	+	0.186882i
$820$	−3.45957	+	7.57539i	−0.120813	+	0.264544i
$821$	−37.5644	−	24.1412i	−1.31101	−	0.842534i	−0.316643	−	0.948545i	$-0.602556\pi$
$821$	−37.5644	−	24.1412i	−1.31101	−	0.842534i	−0.994365	+	0.106011i	$0.966192\pi$
$822$	−53.2696	+	34.2343i	−1.85799	+	1.19406i
$823$	33.6397	+	9.87752i	1.17261	+	0.344309i	0.809320	−	0.587368i	$-0.199836\pi$
$823$	33.6397	+	9.87752i	1.17261	+	0.344309i	0.363288	+	0.931677i	$0.381654\pi$
$824$	0.388718	+	2.70359i	0.0135416	+	0.0941841i
$825$	1.59834	+	3.49987i	0.0556470	+	0.121850i
$826$	−0.166408	+	1.15739i	−0.00579006	+	0.0402708i
$827$	6.37576	+	44.3444i	0.221707	+	1.54201i	0.731580	+	0.681756i	$0.238783\pi$
$827$	6.37576	+	44.3444i	0.221707	+	1.54201i	−0.509873	+	0.860250i	$0.670307\pi$
$828$	−13.6901	−	8.79809i	−0.475763	−	0.305755i
$829$	−31.0985	−	35.8896i	−1.08010	−	1.24650i	−0.967504	−	0.252857i	$-0.918630\pi$
$829$	−31.0985	−	35.8896i	−1.08010	−	1.24650i	−0.112594	−	0.993641i	$-0.535916\pi$
$830$	−10.6510	−	6.84497i	−0.369701	−	0.237592i
$831$	30.7214	+	67.2705i	1.06571	+	2.33359i
$832$	−1.87557	+	2.16452i	−0.0650237	+	0.0750413i
$833$	−12.7659			−0.442313
$834$	14.9541			0.517818
$835$	5.01839	−	5.79153i	0.173668	−	0.200424i
$836$	0.0808860	−	0.562574i	0.00279750	−	0.0194570i
$837$	−2.03243	−	0.596777i	−0.0702512	−	0.0206276i
$838$	−9.24547	−	2.71471i	−0.319379	−	0.0937782i
$839$	−3.31713	+	23.0711i	−0.114520	+	0.796504i	0.848909	+	0.528539i	$0.177260\pi$
$839$	−3.31713	+	23.0711i	−0.114520	+	0.796504i	−0.963429	+	0.267965i	$0.913649\pi$
$840$	−2.02172	+	2.33319i	−0.0697560	+	0.0805027i
$841$	−27.6685			−0.954088
$842$	−7.57344			−0.260998
$843$	50.6808	−	58.4888i	1.74554	−	2.01446i
$844$	9.53632	+	20.8816i	0.328254	+	0.718775i
$845$	−4.03557	−	2.59350i	−0.138828	−	0.0892191i
$846$	−35.6850	−	41.1826i	−1.22687	−	1.41589i
$847$	7.90590	+	5.08081i	0.271650	+	0.174579i
$848$	−0.842677	−	5.86094i	−0.0289376	−	0.201266i
$849$	9.30891	−	64.7449i	0.319481	−	2.22204i
$850$	−0.881608	−	1.93045i	−0.0302389	−	0.0662139i
$851$	2.09959	+	14.6030i	0.0719731	+	0.500584i
$852$	−31.5564	−	9.26579i	−1.08110	−	0.317441i
$853$	−4.47831	+	2.87804i	−0.153334	+	0.0985421i	−0.615058	−	0.788482i	$-0.710868\pi$
$853$	−4.47831	+	2.87804i	−0.153334	+	0.0985421i	0.461724	+	0.887024i	$0.347231\pi$
$854$	−8.50167	−	5.46369i	−0.290921	−	0.186964i
$855$	−1.27522	+	2.79234i	−0.0436116	+	0.0954961i
$856$	9.78991	+	2.87458i	0.334612	+	0.0982510i
$857$	4.36939	−	2.80804i	0.149256	−	0.0959207i	−0.463882	−	0.885897i	$-0.653544\pi$
$857$	4.36939	−	2.80804i	0.149256	−	0.0959207i	0.613137	+	0.789977i	$0.289907\pi$
$858$	7.21638	+	8.32815i	0.246363	+	0.284318i
$859$	3.70738	+	4.27854i	0.126494	+	0.145982i	0.815464	−	0.578808i	$-0.196482\pi$
$859$	3.70738	+	4.27854i	0.126494	+	0.145982i	−0.688969	+	0.724790i	$0.741937\pi$
$860$	3.41561	−	7.47915i	0.116471	−	0.255037i
$861$	−3.65900	+	25.4489i	−0.124698	+	0.867295i
$862$	−19.7666	+	5.80401i	−0.673255	+	0.197685i
$863$	33.4791	−	38.6369i	1.13964	−	1.31522i	0.197383	−	0.980327i	$-0.436756\pi$
$863$	33.4791	−	38.6369i	1.13964	−	1.31522i	0.942258	−	0.334889i	$-0.108699\pi$
$864$	10.9838	−	3.22512i	0.373675	−	0.109721i
$865$	5.95995	+	13.0505i	0.202644	+	0.443729i
$866$	−12.6408	+	27.6795i	−0.429551	+	0.940586i
$867$	−32.7060	+	21.0189i	−1.11075	+	0.713839i
$868$	0.0261314	+	0.181748i	0.000886958	+	0.00616893i
$869$	7.00391	−	2.05653i	0.237591	−	0.0697631i
$870$	−3.58995			−0.121711
$871$	18.0474	+	14.9628i	0.611514	+	0.506995i
$872$	−6.32779			−0.214286
$873$	−61.3215	+	18.0056i	−2.07542	+	0.609398i
$874$	0.159349	+	1.10830i	0.00539008	+	0.0374888i
$875$	−0.834783	+	0.536483i	−0.0282208	+	0.0181364i
$876$	−1.75982	+	3.85347i	−0.0594588	+	0.130197i
$877$	−3.94531	−	8.63903i	−0.133224	−	0.291719i	0.831250	−	0.555899i	$-0.187626\pi$
$877$	−3.94531	−	8.63903i	−0.133224	−	0.291719i	−0.964473	+	0.264180i	$0.914899\pi$
$878$	−37.6482	+	11.0545i	−1.27056	+	0.373071i
$879$	−25.4475	+	29.3680i	−0.858324	+	0.990559i
$880$	−1.18660	+	0.348416i	−0.0400001	+	0.0117451i
$881$	6.59898	−	45.8969i	0.222325	−	1.54631i	−0.506884	−	0.862014i	$-0.669203\pi$
$881$	6.59898	−	45.8969i	0.222325	−	1.54631i	0.729209	−	0.684291i	$-0.239888\pi$
$882$	16.6910	−	36.5482i	0.562015	−	1.23064i
$883$	−19.2259	−	22.1879i	−0.647003	−	0.746681i	0.333594	−	0.942717i	$-0.391739\pi$
$883$	−19.2259	−	22.1879i	−0.647003	−	0.746681i	−0.980597	+	0.196036i	$0.937193\pi$
$884$	−3.98040	−	4.59362i	−0.133875	−	0.154500i
$885$	3.08410	−	1.98203i	0.103671	−	0.0666253i
$886$	23.0341	+	6.76341i	0.773844	+	0.227221i
$887$	0.265133	−	0.580561i	0.00890230	−	0.0194933i	−0.905129	−	0.425138i	$-0.860226\pi$
$887$	0.265133	−	0.580561i	0.00890230	−	0.0194933i	0.914031	+	0.405645i	$0.132953\pi$
$888$	−15.8489	−	10.1855i	−0.531854	−	0.341802i
$889$	−6.09362	+	3.91613i	−0.204373	+	0.131343i
$890$	−15.1590	−	4.45108i	−0.508130	−	0.149201i
$891$	−2.74150	−	19.0675i	−0.0918437	−	0.638787i
$892$	4.76406	+	10.4318i	0.159512	+	0.349284i
$893$	−0.533590	+	3.71120i	−0.0178559	+	0.124191i
$894$	−3.26492	−	22.7080i	−0.109195	−	0.759470i
$895$	15.9929	+	10.2780i	0.534582	+	0.343555i
$896$	−0.649824	−	0.749937i	−0.0217091	−	0.0250536i
$897$	−18.2631	−	11.7370i	−0.609788	−	0.391887i
$898$	−14.3845	−	31.4976i	−0.480015	−	1.05109i
$899$	−0.139823	+	0.161364i	−0.00466335	+	0.00538179i
$900$	6.67945			0.222648
$901$	12.5662			0.418641
$902$	−6.74449	+	7.78356i	−0.224567	+	0.259164i
$903$	3.61251	−	25.1256i	0.120217	−	0.836126i
$904$	16.6514	+	4.88930i	0.553819	+	0.162616i
$905$	4.14894	+	1.21824i	0.137916	+	0.0404957i
$906$	−5.30215	+	36.8772i	−0.176152	+	1.22516i
$907$	33.0353	−	38.1247i	1.09692	−	1.26591i	0.135512	−	0.990776i	$-0.456732\pi$
$907$	33.0353	−	38.1247i	1.09692	−	1.26591i	0.961406	−	0.275135i	$-0.0887224\pi$
$908$	−4.23533			−0.140554
$909$	−90.0128			−2.98554
$910$	−1.86114	+	2.14787i	−0.0616963	+	0.0712013i
$911$	−18.7254	−	41.0030i	−0.620401	−	1.35849i	−0.915227	−	0.402938i	$-0.867989\pi$
$911$	−18.7254	−	41.0030i	−0.620401	−	1.35849i	0.294826	−	0.955551i	$-0.404738\pi$
$912$	−1.20286	−	0.773030i	−0.0398306	−	0.0255976i
$913$	−10.2535	−	11.8332i	−0.339342	−	0.391621i
$914$	−4.79260	−	3.08002i	−0.158525	−	0.101878i
$915$	4.50927	+	31.3627i	0.149072	+	1.03682i
$916$	−1.11125	+	7.72891i	−0.0367167	+	0.255370i
$917$	−3.43637	−	7.52460i	−0.113479	−	0.248484i
$918$	3.45742	+	24.0469i	0.114112	+	0.793666i
$919$	−50.9413	−	14.9577i	−1.68040	−	0.493410i	−0.704148	−	0.710053i	$-0.748671\pi$
$919$	−50.9413	−	14.9577i	−1.68040	−	0.493410i	−0.976251	+	0.216643i	$0.930489\pi$
$920$	2.04958	−	1.31719i	0.0675727	−	0.0434263i
$921$	−37.0389	−	23.8035i	−1.22047	−	0.784351i
$922$	3.34272	−	7.31954i	0.110087	−	0.241056i
$923$	−29.0500	−	8.52984i	−0.956191	−	0.280763i
$924$	−3.21189	+	2.06415i	−0.105663	+	0.0679057i
$925$	−3.96548	−	4.57641i	−0.130384	−	0.150471i
$926$	10.8424	+	12.5128i	0.356302	+	0.411195i
$927$	7.57892	−	16.5955i	0.248925	−	0.545069i
$928$	0.164215	−	1.14214i	0.00539062	−	0.0374926i
$929$	−35.0405	+	10.2888i	−1.14964	+	0.337566i	−0.800400	−	0.599467i	$-0.795379\pi$
$929$	−35.0405	+	10.2888i	−1.14964	+	0.337566i	−0.349243	+	0.937032i	$0.613561\pi$
$930$	0.376999	−	0.435080i	0.0123623	−	0.0142668i
$931$	−2.65254	+	0.778857i	−0.0869336	+	0.0255260i
$932$	3.83011	+	8.38676i	0.125459	+	0.274717i
$933$	−4.01599	+	8.79378i	−0.131477	+	0.287895i
$934$	−17.6550	+	11.3462i	−0.577689	+	0.371258i
$935$	−0.373512	−	2.59783i	−0.0122151	−	0.0849582i
$936$	18.3555	−	5.38967i	0.599969	−	0.176167i
$937$	−52.2116			−1.70568			−0.852839	−	0.522175i	$-0.825121\pi$
$937$	−52.2116			−1.70568			−0.852839	+	0.522175i	$0.825121\pi$
$938$	−6.02123	+	5.45143i	−0.196600	+	0.177996i
$939$	−8.85797			−0.289069
$940$	7.82775	−	2.29844i	0.255313	−	0.0749667i
$941$	−5.10901	−	35.5340i	−0.166549	−	1.15837i	−0.885951	−	0.463780i	$-0.846493\pi$
$941$	−5.10901	−	35.5340i	−0.166549	−	1.15837i	0.719402	−	0.694594i	$-0.244416\pi$
$942$	−33.8168	+	21.7327i	−1.10181	+	0.708090i
$943$	8.42869	−	18.4562i	0.274476	−	0.601018i
$944$	0.489506	+	1.07187i	0.0159321	+	0.0348864i
$945$	10.8993	−	3.20032i	0.354553	−	0.104106i
$946$	6.65881	−	7.68468i	0.216497	−	0.249850i
$947$	−16.7758	+	4.92581i	−0.545139	+	0.160067i	−0.542695	−	0.839930i	$-0.682596\pi$
$947$	−16.7758	+	4.92581i	−0.545139	+	0.160067i	−0.00244385	+	0.999997i	$0.500778\pi$
$948$	2.61345	−	18.1769i	0.0848808	−	0.590359i
$949$	−1.62004	+	3.54740i	−0.0525889	+	0.115154i
$950$	−0.300961	−	0.347328i	−0.00976448	−	0.0112688i
$951$	54.9327	+	63.3957i	1.78131	+	2.05575i
$952$	1.77161	−	1.13854i	0.0574181	−	0.0369003i
$953$	46.9924	+	13.7982i	1.52223	+	0.446968i	0.932663	−	0.360748i	$-0.117479\pi$
$953$	46.9924	+	13.7982i	1.52223	+	0.446968i	0.589571	+	0.807717i	$0.299297\pi$
$954$	−16.4299	+	35.9764i	−0.531936	+	1.16478i
$955$	−0.734798	−	0.472226i	−0.0237775	−	0.0152809i
$956$	−10.4649	+	6.72540i	−0.338460	+	0.217515i
$957$	−4.25982	−	1.25080i	−0.137700	−	0.0404325i
$958$	1.40730	+	9.78796i	0.0454677	+	0.316235i
$959$	−8.38989	−	18.3713i	−0.270924	−	0.593240i
$960$	−0.442767	+	3.07951i	−0.0142903	+	0.0993909i
$961$	4.40689	+	30.6506i	0.142158	+	0.988728i
$962$	−14.5901	−	9.37647i	−0.470403	−	0.302310i
$963$	−44.6300	−	51.5058i	−1.43818	−	1.65975i
$964$	1.75489	+	1.12780i	0.0565212	+	0.0363240i
$965$	6.22607	+	13.6332i	0.200424	+	0.438868i
$966$	4.92561	−	5.68445i	0.158479	−	0.182894i
$967$	21.4077			0.688426			0.344213	−	0.938892i	$-0.388146\pi$
$967$	21.4077			0.688426			0.344213	+	0.938892i	$0.388146\pi$
$968$	9.47060			0.304396
$969$	1.98715	−	2.29329i	0.0638363	−	0.0736710i
$970$	1.36170	−	9.47081i	0.0437214	−	0.304089i
$971$	−37.2589	−	10.9402i	−1.19569	−	0.351087i	−0.377489	−	0.926014i	$-0.623212\pi$
$971$	−37.2589	−	10.9402i	−1.19569	−	0.351087i	−0.818205	+	0.574927i	$0.805031\pi$
$972$	−13.5478	−	3.97799i	−0.434546	−	0.127594i
$973$	−0.678785	+	4.72105i	−0.0217608	+	0.151350i
$974$	−16.9665	+	19.5804i	−0.543641	+	0.627396i
$975$	8.91065			0.285369
$976$	−10.1843			−0.325991
$977$	−15.0793	+	17.4025i	−0.482431	+	0.556755i	−0.943827	−	0.330439i	$-0.892803\pi$
$977$	−15.0793	+	17.4025i	−0.482431	+	0.556755i	0.461396	+	0.887194i	$0.347349\pi$
$978$	−16.7068	−	36.5829i	−0.534226	−	1.16979i
$979$	−16.4368	−	10.5633i	−0.525321	−	0.337603i
$980$	3.93920	+	4.54608i	0.125833	+	0.145219i
$981$	35.5566	+	22.8508i	1.13524	+	0.729571i
$982$	−2.06615	−	14.3704i	−0.0659334	−	0.458577i
$983$	3.42687	−	23.8344i	0.109300	−	0.760199i	−0.859282	−	0.511503i	$-0.829089\pi$
$983$	3.42687	−	23.8344i	0.109300	−	0.760199i	0.968582	−	0.248696i	$-0.0800020\pi$
$984$	10.7633	+	23.5684i	0.343123	+	0.751334i
$985$	−1.51918	−	10.5661i	−0.0484051	−	0.336665i
$986$	2.34962	+	0.689911i	0.0748272	+	0.0219712i
$987$	21.1882	−	13.6168i	0.674429	−	0.433429i
$988$	−1.10732	−	0.711631i	−0.0352285	−	0.0226400i
$989$	−8.32160	+	18.2218i	−0.264612	+	0.579419i
$990$	7.92581	+	2.32723i	0.251899	+	0.0739642i
$991$	−2.48955	+	1.59993i	−0.0790831	+	0.0508236i	−0.579585	−	0.814912i	$-0.696785\pi$
$991$	−2.48955	+	1.59993i	−0.0790831	+	0.0508236i	0.500502	+	0.865736i	$0.333149\pi$
$992$	0.121176	+	0.139844i	0.00384733	+	0.00444005i
$993$	13.6767	+	15.7838i	0.434017	+	0.500883i
$994$	4.35762	−	9.54185i	0.138215	−	0.302649i
$995$	−3.79895	+	26.4222i	−0.120435	+	0.837641i
$996$	−37.7946	+	11.0975i	−1.19757	+	0.351638i
$997$	16.2636	−	18.7692i	0.515072	−	0.594425i	−0.437318	−	0.899307i	$-0.644072\pi$
$997$	16.2636	−	18.7692i	0.515072	−	0.594425i	0.952390	+	0.304882i	$0.0986170\pi$
$998$	−20.7248	+	6.08536i	−0.656033	+	0.192629i
$999$	28.7964	+	63.0552i	0.911077	+	1.99498i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.k.c.491.1	yes	50
67.64	even	11	inner	670.2.k.c.131.1	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.k.c.131.1	✓	50	67.64	even	11	inner
670.2.k.c.491.1	yes	50	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:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.959493 - 0.281733i) q^{2} +(-0.442767 - 3.07951i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-1.29243 - 2.83003i) q^{6} +(0.952113 - 0.279566i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-6.40889 + 1.88182i) q^{9} +O(q^{10})\)	\(q+(0.959493 - 0.281733i) q^{2} +(-0.442767 - 3.07951i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-1.29243 - 2.83003i) q^{6} +(0.952113 - 0.279566i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-6.40889 + 1.88182i) q^{9} +(0.142315 - 0.989821i) q^{10} +(0.513740 - 1.12493i) q^{11} +(-2.03739 - 2.35127i) q^{12} +(-1.87557 - 2.16452i) q^{13} +(0.834783 - 0.536483i) q^{14} +(-2.98516 - 0.876521i) q^{15} +(0.415415 - 0.909632i) q^{16} +(1.78534 + 1.14737i) q^{17} +(-5.61911 + 3.61119i) q^{18} +(0.440965 + 0.129479i) q^{19} +(-0.142315 - 0.989821i) q^{20} +(-1.28249 - 2.80826i) q^{21} +(0.175999 - 1.22410i) q^{22} +(0.346728 + 2.41154i) q^{23} +(-2.61729 - 1.68203i) q^{24} +(-0.654861 - 0.755750i) q^{25} +(-2.40941 - 1.54843i) q^{26} +(4.75544 + 10.4130i) q^{27} +(0.649824 - 0.749937i) q^{28} +1.15389 q^{29} -3.11118 q^{30} +(-0.121176 + 0.139844i) q^{31} +(0.142315 - 0.989821i) q^{32} +(-3.69172 - 1.08399i) q^{33} +(2.03627 + 0.597902i) q^{34} +(0.141220 - 0.982209i) q^{35} +(-4.37411 + 5.04800i) q^{36} +6.05545 q^{37} +0.459581 q^{38} +(-5.83524 + 6.73422i) q^{39} +(-0.415415 - 0.909632i) q^{40} +(-7.00594 - 4.50244i) q^{41} +(-2.02172 - 2.33319i) q^{42} +(6.91693 + 4.44524i) q^{43} +(-0.175999 - 1.22410i) q^{44} +(-0.950586 + 6.61147i) q^{45} +(1.01209 + 2.21618i) q^{46} +(1.16104 + 8.07518i) q^{47} +(-2.98516 - 0.876521i) q^{48} +(-5.06041 + 3.25213i) q^{49} +(-0.841254 - 0.540641i) q^{50} +(2.74284 - 6.00599i) q^{51} +(-2.74806 - 0.806903i) q^{52} +(4.98124 - 3.20125i) q^{53} +(7.49649 + 8.65141i) q^{54} +(-0.809860 - 0.934628i) q^{55} +(0.412220 - 0.902636i) q^{56} +(0.203487 - 1.41529i) q^{57} +(1.10715 - 0.325087i) q^{58} +(-0.771659 + 0.890541i) q^{59} +(-2.98516 + 0.876521i) q^{60} +(-4.23071 - 9.26395i) q^{61} +(-0.0768684 + 0.168318i) q^{62} +(-5.57590 + 3.58341i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-2.74806 + 0.806903i) q^{65} -3.84757 q^{66} +(-8.07475 + 1.34103i) q^{67} +2.12223 q^{68} +(7.27287 - 2.13551i) q^{69} +(-0.141220 - 0.982209i) q^{70} +(8.89297 - 5.71516i) q^{71} +(-2.77475 + 6.07585i) q^{72} +(-0.565644 - 1.23859i) q^{73} +(5.81016 - 1.70602i) q^{74} +(-2.03739 + 2.35127i) q^{75} +(0.440965 - 0.129479i) q^{76} +(0.174646 - 1.21469i) q^{77} +(-3.70162 + 8.10542i) q^{78} +(3.86533 + 4.46083i) q^{79} +(-0.654861 - 0.755750i) q^{80} +(13.1040 - 8.42143i) q^{81} +(-7.99063 - 2.34626i) q^{82} +(5.25951 - 11.5167i) q^{83} +(-2.59716 - 1.66910i) q^{84} +(1.78534 - 1.14737i) q^{85} +(7.88912 + 2.31645i) q^{86} +(-0.510903 - 3.55341i) q^{87} +(-0.513740 - 1.12493i) q^{88} +(2.24843 - 15.6381i) q^{89} +(0.950586 + 6.61147i) q^{90} +(-2.39088 - 1.53653i) q^{91} +(1.59547 + 1.84126i) q^{92} +(0.484304 + 0.311243i) q^{93} +(3.38905 + 7.42098i) q^{94} +(0.300961 - 0.347328i) q^{95} -3.11118 q^{96} +9.56820 q^{97} +(-3.93920 + 4.54608i) q^{98} +(-1.17558 + 8.17634i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9	\( 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9} + 5 q^{10} - 12 q^{11} - 2 q^{12} + 24 q^{13} + 23 q^{14} - 2 q^{15} - 5 q^{16} + 31 q^{17} + q^{18} + 4 q^{19} - 5 q^{20} + 12 q^{21} + q^{22} + 27 q^{23} - 9 q^{24} - 5 q^{25} - 2 q^{26} - 14 q^{27} + 10 q^{28} - 36 q^{29} + 2 q^{30} - 13 q^{31} + 5 q^{32} - 42 q^{33} + 2 q^{34} + 21 q^{35} - q^{36} - 50 q^{37} - 26 q^{38} - 31 q^{39} + 5 q^{40} - 10 q^{41} + 21 q^{42} + 16 q^{43} - q^{44} - q^{45} + 17 q^{46} - 13 q^{47} - 2 q^{48} - 40 q^{49} + 5 q^{50} - 19 q^{51} - 20 q^{52} - 5 q^{53} + 47 q^{54} + 10 q^{55} + 12 q^{56} - 90 q^{57} - 8 q^{58} - 20 q^{59} - 2 q^{60} + 12 q^{61} + 13 q^{62} - 15 q^{63} - 5 q^{64} - 20 q^{65} + 20 q^{66} - 21 q^{67} - 24 q^{68} + 77 q^{69} - 21 q^{70} + 24 q^{71} + 12 q^{72} - 68 q^{73} - 16 q^{74} - 2 q^{75} + 4 q^{76} + 7 q^{77} + 53 q^{78} - 26 q^{79} - 5 q^{80} - 21 q^{81} + 21 q^{82} - 10 q^{83} + 12 q^{84} + 31 q^{85} - 27 q^{86} + 61 q^{87} + 12 q^{88} + 51 q^{89} + q^{90} - 10 q^{91} - 6 q^{92} - 38 q^{93} - 9 q^{94} + 15 q^{95} + 2 q^{96} + 72 q^{97} - 37 q^{98} - 32 q^{99}+O(q^{100}) \) 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9 + 5 * q^10 - 12 * q^11 - 2 * q^12 + 24 * q^13 + 23 * q^14 - 2 * q^15 - 5 * q^16 + 31 * q^17 + q^18 + 4 * q^19 - 5 * q^20 + 12 * q^21 + q^22 + 27 * q^23 - 9 * q^24 - 5 * q^25 - 2 * q^26 - 14 * q^27 + 10 * q^28 - 36 * q^29 + 2 * q^30 - 13 * q^31 + 5 * q^32 - 42 * q^33 + 2 * q^34 + 21 * q^35 - q^36 - 50 * q^37 - 26 * q^38 - 31 * q^39 + 5 * q^40 - 10 * q^41 + 21 * q^42 + 16 * q^43 - q^44 - q^45 + 17 * q^46 - 13 * q^47 - 2 * q^48 - 40 * q^49 + 5 * q^50 - 19 * q^51 - 20 * q^52 - 5 * q^53 + 47 * q^54 + 10 * q^55 + 12 * q^56 - 90 * q^57 - 8 * q^58 - 20 * q^59 - 2 * q^60 + 12 * q^61 + 13 * q^62 - 15 * q^63 - 5 * q^64 - 20 * q^65 + 20 * q^66 - 21 * q^67 - 24 * q^68 + 77 * q^69 - 21 * q^70 + 24 * q^71 + 12 * q^72 - 68 * q^73 - 16 * q^74 - 2 * q^75 + 4 * q^76 + 7 * q^77 + 53 * q^78 - 26 * q^79 - 5 * q^80 - 21 * q^81 + 21 * q^82 - 10 * q^83 + 12 * q^84 + 31 * q^85 - 27 * q^86 + 61 * q^87 + 12 * q^88 + 51 * q^89 + q^90 - 10 * q^91 - 6 * q^92 - 38 * q^93 - 9 * q^94 + 15 * q^95 + 2 * q^96 + 72 * q^97 - 37 * q^98 - 32 * q^99

Introduction

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