LMFDB - Embedded newform 84.2.o.a.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,2,Mod(19,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("84.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	84.o (of order $6$, degree $2$, 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:	$0.670743376979$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.2
Root			$0.856419 - 1.12541i$ of defining polynomial
Character	$\chi$	$=$	84.31
Dual form			84.2.o.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.546424 + 1.30439i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.40284 - 1.42549i) q^{4} +(-3.33878 + 1.92764i) q^{5} +(-0.856419 - 1.12541i) q^{6} +(1.59285 + 2.11254i) q^{7} +(2.62594 - 1.05092i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.546424 + 1.30439i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.40284 - 1.42549i) q^{4} +(-3.33878 + 1.92764i) q^{5} +(-0.856419 - 1.12541i) q^{6} +(1.59285 + 2.11254i) q^{7} +(2.62594 - 1.05092i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.690004 - 5.40836i) q^{10} +(1.17975 + 0.681127i) q^{11} +(1.93594 - 0.502151i) q^{12} +0.369798i q^{13} +(-3.62594 + 0.923343i) q^{14} -3.85529i q^{15} +(-0.0640649 + 3.99949i) q^{16} +(3.89853 + 2.25082i) q^{17} +(1.40284 - 0.178976i) q^{18} +(0.0330925 + 0.0573178i) q^{19} +(7.43162 + 2.05523i) q^{20} +(-2.62594 + 0.323174i) q^{21} +(-1.53309 + 1.16666i) q^{22} +(2.77902 - 1.60447i) q^{23} +(-0.402843 + 2.79959i) q^{24} +(4.93162 - 8.54182i) q^{25} +(-0.482359 - 0.202066i) q^{26} +1.00000 q^{27} +(0.776903 - 5.23416i) q^{28} -3.11951 q^{29} +(5.02878 + 2.10662i) q^{30} +(-3.01852 + 5.22824i) q^{31} +(-5.18187 - 2.26898i) q^{32} +(-1.17975 + 0.681127i) q^{33} +(-5.06618 + 3.85529i) q^{34} +(-9.39039 - 3.98287i) q^{35} +(-0.533092 + 1.92764i) q^{36} +(2.74593 + 4.75609i) q^{37} +(-0.0928470 + 0.0118455i) q^{38} +(-0.320254 - 0.184899i) q^{39} +(-6.74162 + 8.57068i) q^{40} -8.45017i q^{41} +(1.01333 - 3.60183i) q^{42} -6.30324i q^{43} +(-0.684056 - 2.63723i) q^{44} +(3.33878 + 1.92764i) q^{45} +(0.574323 + 4.50164i) q^{46} +(-0.712838 - 1.23467i) q^{47} +(-3.43162 - 2.05523i) q^{48} +(-1.92568 + 6.72992i) q^{49} +(8.44708 + 11.1002i) q^{50} +(-3.89853 + 2.25082i) q^{51} +(0.527144 - 0.518768i) q^{52} +(1.27259 - 2.20420i) q^{53} +(-0.546424 + 1.30439i) q^{54} -5.25188 q^{55} +(6.40284 + 3.87345i) q^{56} -0.0661849 q^{57} +(1.70457 - 4.06904i) q^{58} +(1.71879 - 2.97703i) q^{59} +(-5.49569 + 5.40836i) q^{60} +(1.23998 - 0.715904i) q^{61} +(-5.17024 - 6.79415i) q^{62} +(1.03309 - 2.43572i) q^{63} +(5.79112 - 5.51933i) q^{64} +(-0.712838 - 1.23467i) q^{65} +(-0.243811 - 1.91103i) q^{66} +(8.45877 + 4.88367i) q^{67} +(-2.26050 - 8.71488i) q^{68} +3.20894i q^{69} +(10.3263 - 10.0724i) q^{70} +12.9518i q^{71} +(-2.22310 - 1.74867i) q^{72} +(-1.56024 - 0.900803i) q^{73} +(-7.70422 + 0.982912i) q^{74} +(4.93162 + 8.54182i) q^{75} +(0.0352827 - 0.127581i) q^{76} +(0.440245 + 3.57719i) q^{77} +(0.416174 - 0.316702i) q^{78} +(10.8156 - 6.24438i) q^{79} +(-7.49569 - 13.4769i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(11.0223 + 4.61737i) q^{82} +12.2889 q^{83} +(4.14446 + 3.28990i) q^{84} -17.3551 q^{85} +(8.22186 + 3.44424i) q^{86} +(1.55975 - 2.70157i) q^{87} +(3.81375 + 0.548774i) q^{88} +(1.11951 - 0.646349i) q^{89} +(-4.33878 + 3.30174i) q^{90} +(-0.781213 + 0.589031i) q^{91} +(-6.18569 - 1.71066i) q^{92} +(-3.01852 - 5.22824i) q^{93} +(2.00000 - 0.255162i) q^{94} +(-0.220977 - 0.127581i) q^{95} +(4.55593 - 3.35314i) q^{96} +2.88422i q^{97} +(-7.72617 - 6.18921i) q^{98} -1.36225i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9	$ 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9} - 5 q^{10} + 6 q^{11} - q^{12} - 12 q^{14} - 17 q^{16} + q^{18} - 6 q^{19} + 22 q^{20} - 4 q^{21} - 6 q^{22} + 7 q^{24} + 2 q^{25} + 18 q^{26} + 8 q^{27} + 13 q^{28} - 16 q^{29} + 13 q^{30} + 6 q^{31} - 9 q^{32} - 6 q^{33} - 28 q^{34} - 12 q^{35} + 2 q^{36} + 6 q^{37} + 10 q^{38} - 6 q^{39} - 17 q^{40} + 9 q^{42} - 23 q^{44} + 24 q^{46} + 4 q^{47} + 10 q^{48} + 4 q^{49} + 2 q^{50} + 16 q^{52} - 4 q^{53} + q^{54} - 8 q^{55} + 41 q^{56} + 12 q^{57} + 37 q^{58} - 14 q^{59} - 23 q^{60} + 12 q^{61} - 48 q^{62} + 2 q^{63} + 2 q^{64} + 4 q^{65} - 15 q^{66} + 42 q^{67} - 26 q^{68} + 3 q^{70} - 11 q^{72} - 18 q^{73} - 10 q^{74} + 2 q^{75} + 44 q^{76} + 8 q^{77} - 6 q^{78} - 6 q^{79} - 39 q^{80} - 4 q^{81} - 10 q^{82} + 4 q^{83} - 14 q^{84} - 32 q^{85} + 36 q^{86} + 8 q^{87} - 37 q^{88} - 8 q^{90} - 34 q^{91} - 28 q^{92} + 6 q^{93} + 16 q^{94} - 24 q^{95} + 21 q^{96} - 53 q^{98}+O(q^{100}) $ 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9 - 5 * q^10 + 6 * q^11 - q^12 - 12 * q^14 - 17 * q^16 + q^18 - 6 * q^19 + 22 * q^20 - 4 * q^21 - 6 * q^22 + 7 * q^24 + 2 * q^25 + 18 * q^26 + 8 * q^27 + 13 * q^28 - 16 * q^29 + 13 * q^30 + 6 * q^31 - 9 * q^32 - 6 * q^33 - 28 * q^34 - 12 * q^35 + 2 * q^36 + 6 * q^37 + 10 * q^38 - 6 * q^39 - 17 * q^40 + 9 * q^42 - 23 * q^44 + 24 * q^46 + 4 * q^47 + 10 * q^48 + 4 * q^49 + 2 * q^50 + 16 * q^52 - 4 * q^53 + q^54 - 8 * q^55 + 41 * q^56 + 12 * q^57 + 37 * q^58 - 14 * q^59 - 23 * q^60 + 12 * q^61 - 48 * q^62 + 2 * q^63 + 2 * q^64 + 4 * q^65 - 15 * q^66 + 42 * q^67 - 26 * q^68 + 3 * q^70 - 11 * q^72 - 18 * q^73 - 10 * q^74 + 2 * q^75 + 44 * q^76 + 8 * q^77 - 6 * q^78 - 6 * q^79 - 39 * q^80 - 4 * q^81 - 10 * q^82 + 4 * q^83 - 14 * q^84 - 32 * q^85 + 36 * q^86 + 8 * q^87 - 37 * q^88 - 8 * q^90 - 34 * q^91 - 28 * q^92 + 6 * q^93 + 16 * q^94 - 24 * q^95 + 21 * q^96 - 53 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.546424	+	1.30439i	−0.386380	+	0.922340i
$2$	−0.546424	+	1.30439i	−0.386380	+	0.922340i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−1.40284	−	1.42549i	−0.701421	−	0.712747i
$5$	−3.33878	+	1.92764i	−1.49315	+	0.862069i	−0.999969	−	0.00785986i	$-0.997498\pi$
$5$	−3.33878	+	1.92764i	−1.49315	+	0.862069i	−0.493178	+	0.869929i	$0.664165\pi$
$6$	−0.856419	−	1.12541i	−0.349632	−	0.459446i
$7$	1.59285	+	2.11254i	0.602040	+	0.798466i
$7$	1.59285	+	2.11254i	0.602040	+	0.798466i
$8$	2.62594	−	1.05092i	0.928410	−	0.371558i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.690004	−	5.40836i	−0.218199	−	1.71027i
$11$	1.17975	+	0.681127i	0.355707	+	0.205367i	0.667196	−	0.744882i	$-0.267494\pi$
$11$	1.17975	+	0.681127i	0.355707	+	0.205367i	−0.311489	+	0.950250i	$0.600828\pi$
$12$	1.93594	−	0.502151i	0.558856	−	0.144958i
$13$			0.369798i			0.102563i	0.998684	+	0.0512817i	$0.0163306\pi$
$13$			0.369798i			0.102563i	−0.998684	+	0.0512817i	$0.983669\pi$
$14$	−3.62594	+	0.923343i	−0.969073	+	0.246774i
$15$		−	3.85529i		−	0.995431i
$16$	−0.0640649	+	3.99949i	−0.0160162	+	0.999872i
$17$	3.89853	+	2.25082i	0.945533	+	0.545904i	0.891690	−	0.452646i	$-0.149520\pi$
$17$	3.89853	+	2.25082i	0.945533	+	0.545904i	0.0538425	+	0.998549i	$0.482853\pi$
$18$	1.40284	−	0.178976i	0.330653	−	0.0421851i
$19$	0.0330925	+	0.0573178i	0.00759193	+	0.0131496i	0.869796	−	0.493411i	$-0.164250\pi$
$19$	0.0330925	+	0.0573178i	0.00759193	+	0.0131496i	−0.862204	+	0.506560i	$0.830917\pi$
$20$	7.43162	+	2.05523i	1.66176	+	0.459562i
$21$	−2.62594	+	0.323174i	−0.573027	+	0.0705224i
$22$	−1.53309	+	1.16666i	−0.326856	+	0.248733i
$23$	2.77902	−	1.60447i	0.579466	−	0.334555i	−0.181455	−	0.983399i	$-0.558081\pi$
$23$	2.77902	−	1.60447i	0.579466	−	0.334555i	0.760921	+	0.648844i	$0.224747\pi$
$24$	−0.402843	+	2.79959i	−0.0822299	+	0.571464i
$25$	4.93162	−	8.54182i	0.986325	−	1.70836i
$26$	−0.482359	−	0.202066i	−0.0945983	−	0.0396284i
$27$	1.00000			0.192450
$28$	0.776903	−	5.23416i	0.146821	−	0.989163i
$29$	−3.11951			−0.579278			−0.289639	−	0.957136i	$-0.593535\pi$
$29$	−3.11951			−0.579278			−0.289639	+	0.957136i	$0.593535\pi$
$30$	5.02878	+	2.10662i	0.918126	+	0.384614i
$31$	−3.01852	+	5.22824i	−0.542143	+	0.939019i	0.456638	+	0.889653i	$0.349054\pi$
$31$	−3.01852	+	5.22824i	−0.542143	+	0.939019i	−0.998781	+	0.0493663i	$0.984280\pi$
$32$	−5.18187	−	2.26898i	−0.916033	−	0.401103i
$33$	−1.17975	+	0.681127i	−0.205367	+	0.118569i
$34$	−5.06618	+	3.85529i	−0.868844	+	0.661177i
$35$	−9.39039	−	3.98287i	−1.58727	−	0.673228i
$36$	−0.533092	+	1.92764i	−0.0888487	+	0.321274i
$37$	2.74593	+	4.75609i	0.451428	+	0.781897i	0.998475	−	0.0552054i	$-0.0175814\pi$
$37$	2.74593	+	4.75609i	0.451428	+	0.781897i	−0.547047	+	0.837102i	$0.684248\pi$
$38$	−0.0928470	+	0.0118455i	−0.0150618	+	0.00192160i
$39$	−0.320254	−	0.184899i	−0.0512817	−	0.0296075i
$40$	−6.74162	+	8.57068i	−1.06594	+	1.35514i
$41$		−	8.45017i		−	1.31970i	−0.751399	−	0.659848i	$-0.770621\pi$
$41$		−	8.45017i		−	1.31970i	0.751399	−	0.659848i	$-0.229379\pi$
$42$	1.01333	−	3.60183i	0.156360	−	0.555774i
$43$		−	6.30324i		−	0.961236i	−0.876930	−	0.480618i	$-0.840412\pi$
$43$		−	6.30324i		−	0.961236i	0.876930	−	0.480618i	$-0.159588\pi$
$44$	−0.684056	−	2.63723i	−0.103125	−	0.397578i
$45$	3.33878	+	1.92764i	0.497716	+	0.287356i
$46$	0.574323	+	4.50164i	0.0846794	+	0.663730i
$47$	−0.712838	−	1.23467i	−0.103978	−	0.180095i	0.809342	−	0.587338i	$-0.199824\pi$
$47$	−0.712838	−	1.23467i	−0.103978	−	0.180095i	−0.913320	+	0.407242i	$0.866491\pi$
$48$	−3.43162	−	2.05523i	−0.495312	−	0.296646i
$49$	−1.92568	+	6.72992i	−0.275097	+	0.961417i
$50$	8.44708	+	11.1002i	1.19460	+	1.56980i
$51$	−3.89853	+	2.25082i	−0.545904	+	0.315178i
$52$	0.527144	−	0.518768i	0.0731018	−	0.0719402i
$53$	1.27259	−	2.20420i	0.174804	−	0.302770i	−0.765289	−	0.643686i	$-0.777404\pi$
$53$	1.27259	−	2.20420i	0.174804	−	0.302770i	0.940093	+	0.340917i	$0.110737\pi$
$54$	−0.546424	+	1.30439i	−0.0743588	+	0.177504i
$55$	−5.25188			−0.708163
$56$	6.40284	+	3.87345i	0.855616	+	0.517611i
$57$	−0.0661849			−0.00876641
$58$	1.70457	−	4.06904i	0.223821	−	0.534291i
$59$	1.71879	−	2.97703i	0.223767	−	0.387576i	−0.732182	−	0.681109i	$-0.761498\pi$
$59$	1.71879	−	2.97703i	0.223767	−	0.387576i	0.955949	+	0.293533i	$0.0948312\pi$
$60$	−5.49569	+	5.40836i	−0.709490	+	0.698217i
$61$	1.23998	−	0.715904i	0.158763	−	0.0916621i	−0.418513	−	0.908211i	$-0.637449\pi$
$61$	1.23998	−	0.715904i	0.158763	−	0.0916621i	0.577277	+	0.816549i	$0.304115\pi$
$62$	−5.17024	−	6.79415i	−0.656622	−	0.862858i
$63$	1.03309	−	2.43572i	0.130157	−	0.306872i
$64$	5.79112	−	5.51933i	0.723890	−	0.689916i
$65$	−0.712838	−	1.23467i	−0.0884167	−	0.153142i
$66$	−0.243811	−	1.91103i	−0.0300110	−	0.235231i
$67$	8.45877	+	4.88367i	1.03340	+	0.596636i	0.917958	−	0.396678i	$-0.129837\pi$
$67$	8.45877	+	4.88367i	1.03340	+	0.596636i	0.115445	+	0.993314i	$0.463170\pi$
$68$	−2.26050	−	8.71488i	−0.274126	−	1.05683i
$69$			3.20894i			0.386311i
$70$	10.3263	−	10.0724i	1.23423	−	1.20388i
$71$			12.9518i			1.53710i	0.639792	+	0.768549i	$0.279021\pi$
$71$			12.9518i			1.53710i	−0.639792	+	0.768549i	$0.720979\pi$
$72$	−2.22310	−	1.74867i	−0.261994	−	0.206083i
$73$	−1.56024	−	0.900803i	−0.182612	−	0.105431i	0.405907	−	0.913914i	$-0.366956\pi$
$73$	−1.56024	−	0.900803i	−0.182612	−	0.105431i	−0.588519	+	0.808483i	$0.700289\pi$
$74$	−7.70422	+	0.982912i	−0.895597	+	0.114261i
$75$	4.93162	+	8.54182i	0.569455	+	0.986325i
$76$	0.0352827	−	0.127581i	0.00404720	−	0.0146345i
$77$	0.440245	+	3.57719i	0.0501706	+	0.407659i
$78$	0.416174	−	0.316702i	0.0471224	−	0.0358594i
$79$	10.8156	−	6.24438i	1.21685	−	0.702548i	0.252606	−	0.967569i	$-0.418712\pi$
$79$	10.8156	−	6.24438i	1.21685	−	0.702548i	0.964243	+	0.265021i	$0.0853790\pi$
$80$	−7.49569	−	13.4769i	−0.838044	−	1.50676i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	11.0223	+	4.61737i	1.21721	+	0.509904i
$83$	12.2889			1.34888			0.674442	−	0.738327i	$-0.264384\pi$
$83$	12.2889			1.34888			0.674442	+	0.738327i	$0.264384\pi$
$84$	4.14446	+	3.28990i	0.452198	+	0.358957i
$85$	−17.3551			−1.88243
$86$	8.22186	+	3.44424i	0.886586	+	0.371402i
$87$	1.55975	−	2.70157i	0.167223	−	0.289639i
$88$	3.81375	+	0.548774i	0.406548	+	0.0584995i
$89$	1.11951	−	0.646349i	0.118668	−	0.0685128i	−0.439491	−	0.898247i	$-0.644841\pi$
$89$	1.11951	−	0.646349i	0.118668	−	0.0685128i	0.558159	+	0.829734i	$0.311508\pi$
$90$	−4.33878	+	3.30174i	−0.457347	+	0.348034i
$91$	−0.781213	+	0.589031i	−0.0818934	+	0.0617472i
$92$	−6.18569	−	1.71066i	−0.644903	−	0.178349i
$93$	−3.01852	−	5.22824i	−0.313006	−	0.542143i
$94$	2.00000	−	0.255162i	0.206284	−	0.0263179i
$95$	−0.220977	−	0.127581i	−0.0226717	−	0.0130895i
$96$	4.55593	−	3.35314i	0.464987	−	0.342228i
$97$			2.88422i			0.292848i	0.989222	+	0.146424i	$0.0467764\pi$
$97$			2.88422i			0.292848i	−0.989222	+	0.146424i	$0.953224\pi$
$98$	−7.72617	−	6.18921i	−0.780461	−	0.625205i
$99$		−	1.36225i		−	0.136912i
$100$	−19.0946	+	4.95284i	−1.90946	+	0.495284i
$101$	5.35949	+	3.09430i	0.533289	+	0.307895i	0.742355	−	0.670007i	$-0.233709\pi$
$101$	5.35949	+	3.09430i	0.533289	+	0.307895i	−0.209066	+	0.977902i	$0.567042\pi$
$102$	−0.805685	−	6.31509i	−0.0797747	−	0.625287i
$103$	−8.89634	−	15.4089i	−0.876583	−	1.51829i	−0.855067	−	0.518517i	$-0.826484\pi$
$103$	−8.89634	−	15.4089i	−0.876583	−	1.51829i	−0.0215154	−	0.999769i	$-0.506849\pi$
$104$	0.388629	+	0.971066i	0.0381082	+	0.0952209i
$105$	8.14446	−	6.14088i	0.794818	−	0.599289i
$106$	2.17975	+	2.86438i	0.211716	+	0.278213i
$107$	−5.27683	+	3.04658i	−0.510131	+	0.294524i	−0.732887	−	0.680350i	$-0.761828\pi$
$107$	−5.27683	+	3.04658i	−0.510131	+	0.294524i	0.222757	+	0.974874i	$0.428494\pi$
$108$	−1.40284	−	1.42549i	−0.134989	−	0.137168i
$109$	−3.93162	+	6.80977i	−0.376581	+	0.652258i	−0.990562	−	0.137063i	$-0.956234\pi$
$109$	−3.93162	+	6.80977i	−0.376581	+	0.652258i	0.613981	+	0.789321i	$0.289567\pi$
$110$	2.86975	−	6.85047i	0.273620	−	0.653167i
$111$	−5.49186			−0.521264
$112$	−8.55113	+	6.23523i	−0.808006	+	0.589174i
$113$	4.70669			0.442768			0.221384	−	0.975187i	$-0.428943\pi$
$113$	4.70669			0.442768			0.221384	+	0.975187i	$0.428943\pi$
$114$	0.0361650	−	0.0863307i	0.00338716	−	0.00808561i
$115$	−6.18569	+	10.7139i	−0.576819	+	0.999080i
$116$	4.37618	+	4.44684i	0.406318	+	0.412879i
$117$	0.320254	−	0.184899i	0.0296075	−	0.0170939i
$118$	2.94400	+	3.86868i	0.271017	+	0.356141i
$119$	1.45481	+	11.8210i	0.133363	+	1.08363i
$120$	−4.05162	−	10.1238i	−0.369860	−	0.924168i
$121$	−4.57213	−	7.91917i	−0.415648	−	0.719924i
$122$	0.256259	+	2.00860i	0.0232006	+	0.181850i
$123$	7.31806	+	4.22509i	0.659848	+	0.380963i
$124$	11.6873	−	3.03151i	1.04955	−	0.272237i
$125$			18.7492i			1.67698i
$126$	2.61261	+	2.67848i	0.232750	+	0.238618i
$127$			2.70312i			0.239863i	0.992782	+	0.119931i	$0.0382675\pi$
$127$			2.70312i			0.239863i	−0.992782	+	0.119931i	$0.961733\pi$
$128$	4.03493	+	10.5697i	0.356641	+	0.934242i
$129$	5.45877	+	3.15162i	0.480618	+	0.277485i
$130$	2.00000	−	0.255162i	0.175412	−	0.0223792i
$131$	−3.88644	−	6.73151i	−0.339560	−	0.588135i	0.644790	−	0.764360i	$-0.276945\pi$
$131$	−3.88644	−	6.73151i	−0.339560	−	0.588135i	−0.984350	+	0.176225i	$0.943611\pi$
$132$	2.62594	+	0.726207i	0.228559	+	0.0632082i
$133$	−0.0683751	+	0.161208i	−0.00592888	+	0.0139785i
$134$	−10.9923	+	8.36494i	−0.949587	+	0.722621i
$135$	−3.33878	+	1.92764i	−0.287356	+	0.165905i
$136$	12.6028	+	1.81345i	1.08068	+	0.155502i
$137$	−1.42568	+	2.46934i	−0.121804	+	0.210970i	−0.920479	−	0.390792i	$-0.872201\pi$
$137$	−1.42568	+	2.46934i	−0.121804	+	0.210970i	0.798675	+	0.601762i	$0.205535\pi$
$138$	−4.18569	−	1.75344i	−0.356310	−	0.149263i
$139$	−7.15656			−0.607011			−0.303506	−	0.952830i	$-0.598157\pi$
$139$	−7.15656			−0.607011			−0.303506	+	0.952830i	$0.598157\pi$
$140$	7.49569	+	18.9733i	0.633501	+	1.60354i
$141$	1.42568			0.120064
$142$	−16.8942	−	7.07717i	−1.41773	−	0.593903i
$143$	−0.251879	+	0.436267i	−0.0210632	+	0.0364825i
$144$	3.49569	−	1.94426i	0.291307	−	0.162022i
$145$	10.4153	−	6.01330i	0.864948	−	0.499378i
$146$	2.02754	−	1.54293i	0.167801	−	0.127694i
$147$	−4.86544	−	5.03264i	−0.401295	−	0.415085i
$148$	2.92767	−	10.5864i	0.240653	−	0.870193i
$149$	−10.6776	−	18.4941i	−0.874739	−	1.51509i	−0.857040	−	0.515250i	$-0.827699\pi$
$149$	−10.6776	−	18.4941i	−0.874739	−	1.51509i	−0.0176994	−	0.999843i	$-0.505634\pi$
$150$	−13.8366	+	1.76529i	−1.12975	+	0.144135i
$151$	−19.2373	−	11.1067i	−1.56551	−	0.903848i	−0.996682	−	0.0813911i	$-0.974064\pi$
$151$	−19.2373	−	11.1067i	−1.56551	−	0.903848i	−0.568828	−	0.822457i	$-0.692603\pi$
$152$	0.147136	+	0.115735i	0.0119343	+	0.00938739i
$153$		−	4.50164i		−	0.363936i
$154$	−4.90660	−	1.38041i	−0.395385	−	0.111237i
$155$		−	23.2746i		−	1.86946i
$156$	0.185694	+	0.715904i	0.0148674	+	0.0573182i
$157$	−4.71898	−	2.72451i	−0.376616	−	0.217439i	0.299729	−	0.954024i	$-0.403104\pi$
$157$	−4.71898	−	2.72451i	−0.376616	−	0.217439i	−0.676345	+	0.736585i	$0.736437\pi$
$158$	2.23519	+	17.5198i	0.177822	+	1.39380i
$159$	1.27259	+	2.20420i	0.100923	+	0.174804i
$160$	21.6749	−	2.41318i	1.71355	−	0.190778i
$161$	7.81607	+	3.31513i	0.615993	+	0.261269i
$162$	−0.856419	−	1.12541i	−0.0672866	−	0.0884205i
$163$	4.11951	−	2.37840i	0.322665	−	0.186291i	−0.329915	−	0.944011i	$-0.607020\pi$
$163$	4.11951	−	2.37840i	0.322665	−	0.186291i	0.652580	+	0.757720i	$0.273687\pi$
$164$	−12.0457	+	11.8543i	−0.940609	+	0.925662i
$165$	2.62594	−	4.54826i	0.204429	−	0.354082i
$166$	−6.71496	+	16.0295i	−0.521182	+	1.24413i
$167$	14.0618			1.08814			0.544068	−	0.839041i	$-0.316884\pi$
$167$	14.0618			1.08814			0.544068	+	0.839041i	$0.316884\pi$
$168$	−6.55593	+	3.60830i	−0.505801	+	0.278386i
$169$	12.8632			0.989481
$170$	9.48324	−	22.6378i	0.727331	−	1.73624i
$171$	0.0330925	−	0.0573178i	0.00253064	−	0.00438320i
$172$	−8.98523	+	8.84246i	−0.685118	+	0.674231i
$173$	1.53904	−	0.888566i	0.117011	−	0.0675564i	−0.440352	−	0.897825i	$-0.645146\pi$
$173$	1.53904	−	0.888566i	0.117011	−	0.0675564i	0.557363	+	0.830269i	$0.311813\pi$
$174$	2.67161	+	3.51072i	0.202534	+	0.266147i
$175$	25.9003	−	3.18755i	1.95788	−	0.240956i
$176$	−2.79974	+	4.67474i	−0.211038	+	0.352372i
$177$	1.71879	+	2.97703i	0.129192	+	0.223767i
$178$	0.231362	+	1.81345i	0.0173413	+	0.135924i
$179$	−2.81607	−	1.62586i	−0.210483	−	0.121522i	0.391053	−	0.920368i	$-0.372111\pi$
$179$	−2.81607	−	1.62586i	−0.210483	−	0.121522i	−0.601536	+	0.798846i	$0.705444\pi$
$180$	−1.93594	−	7.46359i	−0.144296	−	0.556303i
$181$		−	23.5015i		−	1.74685i	−0.486954	−	0.873427i	$-0.661892\pi$
$181$		−	23.5015i		−	1.74685i	0.486954	−	0.873427i	$-0.338108\pi$
$182$	−0.341450	−	1.34086i	−0.0253100	−	0.0993914i
$183$			1.43181i			0.105842i
$184$	5.61137	−	7.13378i	0.413676	−	0.525909i
$185$	−18.3361	−	10.5864i	−1.34810	−	0.778324i
$186$	8.46903	−	1.08049i	0.620979	−	0.0792251i
$187$	3.06618	+	5.31079i	0.224222	+	0.388363i
$188$	−0.760017	+	2.74820i	−0.0554300	+	0.200433i
$189$	1.59285	+	2.11254i	0.115863	+	0.153665i
$190$	0.287162	−	0.218526i	0.0208329	−	0.0158535i
$191$	−20.6956	+	11.9486i	−1.49748	+	0.864571i	−0.999996	−	0.00290157i	$-0.999076\pi$
$191$	−20.6956	+	11.9486i	−1.49748	+	0.864571i	−0.497485	+	0.867473i	$0.665743\pi$
$192$	1.88432	+	7.77492i	0.135989	+	0.561106i
$193$	−9.93757	+	17.2124i	−0.715322	+	1.23897i	0.247513	+	0.968885i	$0.420387\pi$
$193$	−9.93757	+	17.2124i	−0.715322	+	1.23897i	−0.962835	+	0.270090i	$0.912947\pi$
$194$	−3.76214	−	1.57601i	−0.270106	−	0.113151i
$195$	1.42568			0.102095
$196$	12.2949	−	6.69597i	0.878205	−	0.478284i
$197$	19.0198			1.35511			0.677553	−	0.735474i	$-0.263041\pi$
$197$	19.0198			1.35511			0.677553	+	0.735474i	$0.263041\pi$
$198$	1.77690	+	0.744367i	0.126279	+	0.0528999i
$199$	7.42568	−	12.8616i	0.526392	−	0.911738i	−0.473135	−	0.880990i	$-0.656878\pi$
$199$	7.42568	−	12.8616i	0.526392	−	0.911738i	0.999527	−	0.0307481i	$-0.00978898\pi$
$200$	3.97334	−	27.6131i	0.280957	−	1.95254i
$201$	−8.45877	+	4.88367i	−0.596636	+	0.344468i
$202$	−6.96472	+	5.30004i	−0.490036	+	0.372910i
$203$	−4.96890	−	6.59010i	−0.348748	−	0.462534i
$204$	8.67756	+	2.39979i	0.607550	+	0.168019i
$205$	16.2889	+	28.2132i	1.13767	+	1.97050i
$206$	24.9603	−	3.18446i	1.73907	−	0.221872i
$207$	−2.77902	−	1.60447i	−0.193155	−	0.111518i
$208$	−1.47900	−	0.0236910i	−0.102550	−	0.00164268i
$209$			0.0901606i			0.00623654i
$210$	3.55975	+	13.9790i	0.245646	+	0.964646i
$211$			19.6676i			1.35398i	0.735994	+	0.676988i	$0.236715\pi$
$211$			19.6676i			1.35398i	−0.735994	+	0.676988i	$0.763285\pi$
$212$	−4.92731	+	1.27807i	−0.338409	+	0.0877780i
$213$	−11.2166	−	6.47590i	−0.768549	−	0.443722i
$214$	−1.09053	−	8.54775i	−0.0745471	−	0.584312i
$215$	12.1504	+	21.0451i	0.828651	+	1.43527i
$216$	2.62594	−	1.05092i	0.178673	−	0.0715063i
$217$	−15.8529	+	1.95102i	−1.07617	+	0.132444i
$218$	−6.73424	−	8.84937i	−0.456100	−	0.599355i
$219$	1.56024	−	0.900803i	0.105431	−	0.0608706i
$220$	7.36756	+	7.48652i	0.496721	+	0.504741i
$221$	−0.832347	+	1.44167i	−0.0559897	+	0.0969771i
$222$	3.00088	−	7.16350i	0.201406	−	0.480783i
$223$	−8.10323			−0.542633			−0.271316	−	0.962490i	$-0.587459\pi$
$223$	−8.10323			−0.542633			−0.271316	+	0.962490i	$0.587459\pi$
$224$	−3.46060	−	14.5611i	−0.231221	−	0.972901i
$225$	−9.86325			−0.657550
$226$	−2.57185	+	6.13934i	−0.171077	+	0.408383i
$227$	6.04300	−	10.4668i	0.401088	−	0.694704i	−0.592770	−	0.805372i	$-0.701966\pi$
$227$	6.04300	−	10.4668i	0.401088	−	0.694704i	0.993857	+	0.110668i	$0.0352989\pi$
$228$	0.0928470	+	0.0943462i	0.00614895	+	0.00624823i
$229$	20.5963	−	11.8913i	1.36104	−	0.785799i	0.371280	−	0.928521i	$-0.378919\pi$
$229$	20.5963	−	11.8913i	1.36104	−	0.785799i	0.989763	+	0.142722i	$0.0455856\pi$
$230$	−10.5951	−	13.9229i	−0.698620	−	0.918047i
$231$	−3.31806	−	1.40733i	−0.218313	−	0.0925957i
$232$	−8.19164	+	3.27837i	−0.537808	+	0.215235i
$233$	9.96472	+	17.2594i	0.652810	+	1.13070i	0.982438	+	0.186590i	$0.0597435\pi$
$233$	9.96472	+	17.2594i	0.652810	+	1.13070i	−0.329628	+	0.944111i	$0.606923\pi$
$234$	0.0661849	+	0.518768i	0.00432664	+	0.0339129i
$235$	4.76002	+	2.74820i	0.310509	+	0.179273i
$236$	−6.65492	+	1.72618i	−0.433198	+	0.112365i
$237$			12.4888i			0.811233i
$238$	−16.2141	−	4.56165i	−1.05101	−	0.295688i
$239$			9.60993i			0.621615i	0.950473	+	0.310807i	$0.100599\pi$
$239$			9.60993i			0.621615i	−0.950473	+	0.310807i	$0.899401\pi$
$240$	15.4192	+	0.246989i	0.995304	+	0.0159430i
$241$	−9.01386	−	5.20415i	−0.580634	−	0.335229i	0.180752	−	0.983529i	$-0.442147\pi$
$241$	−9.01386	−	5.20415i	−0.580634	−	0.335229i	−0.761385	+	0.648300i	$0.775480\pi$
$242$	12.8280	−	1.63660i	0.824613	−	0.105205i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−2.76002	−	0.763286i	−0.176692	−	0.0488644i
$245$	−6.54348	−	26.1817i	−0.418047	−	1.67269i
$246$	−9.50990	+	7.23689i	−0.606329	+	0.461407i
$247$	−0.0211960	+	0.0122375i	−0.00134867	+	0.000778654i
$248$	−2.43198	+	16.9013i	−0.154431	+	1.07323i
$249$	−6.14446	+	10.6425i	−0.389390	+	0.674442i
$250$	−24.4562	−	10.2450i	−1.54675	−	0.647952i
$251$	−20.6860			−1.30569			−0.652846	−	0.757491i	$-0.726425\pi$
$251$	−20.6860			−1.30569			−0.652846	+	0.757491i	$0.726425\pi$
$252$	−4.92137	+	1.94426i	−0.310017	+	0.122477i
$253$	4.37139			0.274827
$254$	−3.52591	−	1.47705i	−0.221235	−	0.0926782i
$255$	8.67756	−	15.0300i	0.543410	−	0.941213i
$256$	−15.9918	−	0.512453i	−0.999487	−	0.0320283i
$257$	−15.3732	+	8.87569i	−0.958951	+	0.553651i	−0.895850	−	0.444357i	$-0.853432\pi$
$257$	−15.3732	+	8.87569i	−0.958951	+	0.553651i	−0.0631009	+	0.998007i	$0.520099\pi$
$258$	−7.09373	+	5.39822i	−0.441636	+	0.336078i
$259$	−5.67360	+	13.3766i	−0.352540	+	0.831183i
$260$	−0.760017	+	2.74820i	−0.0471343	+	0.170436i
$261$	1.55975	+	2.70157i	0.0965464	+	0.167223i
$262$	10.9041	−	1.39116i	0.673659	−	0.0859461i
$263$	−1.80241	−	1.04062i	−0.111141	−	0.0641675i	0.443399	−	0.896324i	$-0.353773\pi$
$263$	−1.80241	−	1.04062i	−0.111141	−	0.0641675i	−0.554540	+	0.832157i	$0.687106\pi$
$264$	−2.38213	+	3.02842i	−0.146610	+	0.186386i
$265$			9.81243i			0.602773i
$266$	−0.172915	−	0.177275i	−0.0106021	−	0.0108694i
$267$			1.29270i			0.0791118i
$268$	−4.90468	−	18.9089i	−0.299601	−	1.15505i
$269$	3.08075	+	1.77867i	0.187837	+	0.108448i	0.590970	−	0.806694i	$-0.298745\pi$
$269$	3.08075	+	1.77867i	0.187837	+	0.108448i	−0.403133	+	0.915142i	$0.632079\pi$
$270$	−0.690004	−	5.40836i	−0.0419923	−	0.329143i
$271$	6.18399	+	10.7110i	0.375650	+	0.650646i	0.990424	−	0.138058i	$-0.0440860\pi$
$271$	6.18399	+	10.7110i	0.375650	+	0.650646i	−0.614774	+	0.788704i	$0.710753\pi$
$272$	−9.25188	+	15.4479i	−0.560978	+	0.936668i
$273$	−0.119509	−	0.971066i	−0.00723302	−	0.0587716i
$274$	−2.44195	−	3.20894i	−0.147524	−	0.193859i
$275$	11.6361	−	6.71812i	0.701685	−	0.405118i
$276$	4.57432	−	4.50164i	0.275342	−	0.270967i
$277$	5.93162	−	10.2739i	0.356397	−	0.617297i	−0.630959	−	0.775816i	$-0.717338\pi$
$277$	5.93162	−	10.2739i	0.356397	−	0.617297i	0.987356	+	0.158519i	$0.0506718\pi$
$278$	3.91051	−	9.33491i	0.234537	−	0.559871i
$279$	6.03705			0.361429
$280$	−28.8443	−	0.590182i	−1.72378	−	0.0352701i
$281$	−19.3428			−1.15390			−0.576948	−	0.816781i	$-0.695756\pi$
$281$	−19.3428			−1.15390			−0.576948	+	0.816781i	$0.695756\pi$
$282$	−0.779023	+	1.85963i	−0.0463902	+	0.110739i
$283$	−12.4707	+	21.5998i	−0.741304	+	1.28398i	0.210598	+	0.977573i	$0.432459\pi$
$283$	−12.4707	+	21.5998i	−0.741304	+	1.28398i	−0.951902	+	0.306404i	$0.900874\pi$
$284$	18.4627	−	18.1694i	1.09556	−	1.07815i
$285$	0.220977	−	0.127581i	0.0130895	−	0.00755725i
$286$	−0.431428	−	0.566934i	−0.0255109	−	0.0335235i
$287$	17.8514	−	13.4598i	1.05373	−	0.794509i
$288$	0.625940	+	5.62212i	0.0368838	+	0.331286i
$289$	1.63237	+	2.82735i	0.0960218	+	0.166315i
$290$	2.15247	+	16.8714i	0.126398	+	0.990725i
$291$	−2.49781	−	1.44211i	−0.146424	−	0.0845381i
$292$	0.904677	+	3.48779i	0.0529422	+	0.204108i
$293$		−	6.88234i		−	0.402071i	−0.979584	−	0.201035i	$-0.935569\pi$
$293$		−	6.88234i		−	0.402071i	0.979584	−	0.201035i	$-0.0644306\pi$
$294$	9.22310	−	3.59645i	0.537902	−	0.209749i
$295$			13.2528i			0.771610i
$296$	12.2089	+	9.60344i	0.709630	+	0.558189i
$297$	1.17975	+	0.681127i	0.0684558	+	0.0395230i
$298$	29.9579	−	3.82205i	1.73541	−	0.221406i
$299$	0.593329	+	1.02768i	0.0343131	+	0.0594321i
$300$	5.25802	−	19.0128i	0.303572	−	1.09771i
$301$	13.3159	−	10.0401i	0.767514	−	0.578702i
$302$	24.9991	−	19.0239i	1.43854	−	1.09470i
$303$	−5.35949	+	3.09430i	−0.307895	+	0.177763i
$304$	−0.231362	+	0.128681i	−0.0132695	+	0.00738035i
$305$	−2.76002	+	4.78049i	−0.158038	+	0.273730i
$306$	5.87187	+	2.45980i	0.335672	+	0.140617i
$307$	17.4213			0.994286			0.497143	−	0.867669i	$-0.334382\pi$
$307$	17.4213			0.994286			0.497143	+	0.867669i	$0.334382\pi$
$308$	4.48167	−	5.64581i	0.255367	−	0.321700i
$309$	17.7927			1.01219
$310$	30.3590	+	12.7178i	1.72428	+	0.722321i
$311$	12.5580	−	21.7512i	0.712101	−	1.23340i	−0.251965	−	0.967736i	$-0.581077\pi$
$311$	12.5580	−	21.7512i	0.712101	−	1.23340i	0.964067	−	0.265660i	$-0.0855898\pi$
$312$	−1.03528	−	0.148970i	−0.0586113	−	0.00843378i
$313$	−19.1361	+	11.0482i	−1.08164	+	0.624484i	−0.931338	−	0.364156i	$-0.881357\pi$
$313$	−19.1361	+	11.0482i	−1.08164	+	0.624484i	−0.150300	+	0.988640i	$0.548024\pi$
$314$	6.13237	−	4.66664i	0.346070	−	0.263354i
$315$	1.24593	+	10.1238i	0.0702002	+	0.570409i
$316$	−24.0739	−	6.65767i	−1.35426	−	0.374523i
$317$	0.811634	+	1.40579i	0.0455859	+	0.0789571i	0.887918	−	0.460002i	$-0.152151\pi$
$317$	0.811634	+	1.40579i	0.0455859	+	0.0789571i	−0.842332	+	0.538959i	$0.818818\pi$
$318$	−3.57050	+	0.455527i	−0.200223	+	0.0255447i
$319$	−3.68023	−	2.12478i	−0.206053	−	0.118965i
$320$	−8.69595	+	29.5910i	−0.486119	+	1.65419i
$321$		−	6.09316i		−	0.340087i
$322$	−8.59509	+	8.38370i	−0.478986	+	0.467205i
$323$			0.297941i			0.0165779i
$324$	1.93594	−	0.502151i	0.107552	−	0.0278973i
$325$	3.15875	+	1.82370i	0.175216	+	0.101161i
$326$	0.851353	+	6.67304i	0.0471521	+	0.369586i
$327$	−3.93162	−	6.80977i	−0.217419	−	0.376581i
$328$	−8.88049	−	22.1896i	−0.490343	−	1.22522i
$329$	1.47286	−	3.47255i	0.0812012	−	0.191448i
$330$	4.49781	+	5.91051i	0.247596	+	0.325363i
$331$	23.0949	−	13.3338i	1.26941	−	0.732894i	0.294534	−	0.955641i	$-0.404836\pi$
$331$	23.0949	−	13.3338i	1.26941	−	0.732894i	0.974876	+	0.222747i	$0.0715023\pi$
$332$	−17.2394	−	17.5178i	−0.946137	−	0.961413i
$333$	2.74593	−	4.75609i	0.150476	−	0.260632i
$334$	−7.68370	+	18.3420i	−0.420433	+	1.00363i
$335$	−37.6559			−2.05736
$336$	−1.12430	−	10.5231i	−0.0613357	−	0.574083i
$337$	29.8426			1.62563			0.812815	−	0.582522i	$-0.197934\pi$
$337$	29.8426			1.62563			0.812815	+	0.582522i	$0.197934\pi$
$338$	−7.02878	+	16.7786i	−0.382315	+	0.912637i
$339$	−2.35335	+	4.07612i	−0.127816	+	0.221384i
$340$	24.3465	+	24.7396i	1.32037	+	1.34169i
$341$	−7.12218	+	4.11199i	−0.385688	+	0.222677i
$342$	0.0566820	+	0.0744851i	0.00306501	+	0.00402769i
$343$	−17.2845	+	6.65165i	−0.933278	+	0.359155i
$344$	−6.62423	−	16.5519i	−0.357155	−	0.892421i
$345$	−6.18569	−	10.7139i	−0.333027	−	0.576819i
$346$	0.318064	+	2.49304i	0.0170992	+	0.134026i
$347$	0.820451	+	0.473688i	0.0440441	+	0.0254289i	0.521860	−	0.853031i	$-0.325238\pi$
$347$	0.820451	+	0.473688i	0.0440441	+	0.0254289i	−0.477816	+	0.878460i	$0.658572\pi$
$348$	−6.03917	+	1.56646i	−0.323733	+	0.0839712i
$349$		−	6.41788i		−	0.343541i	−0.985137	−	0.171771i	$-0.945051\pi$
$349$		−	6.41788i		−	0.343541i	0.985137	−	0.171771i	$-0.0549488\pi$
$350$	−9.99474	+	35.5257i	−0.534241	+	1.89893i
$351$			0.369798i			0.0197383i
$352$	−4.56782	−	6.20633i	−0.243466	−	0.330798i
$353$	12.0146	+	6.93665i	0.639474	+	0.369200i	0.784412	−	0.620240i	$-0.212965\pi$
$353$	12.0146	+	6.93665i	0.639474	+	0.369200i	−0.144938	+	0.989441i	$0.546298\pi$
$354$	−4.82237	+	0.615243i	−0.256306	+	0.0326998i
$355$	−24.9665	−	43.2432i	−1.32508	−	2.29511i
$356$	−2.49186	−	0.689127i	−0.132068	−	0.0365237i
$357$	−10.9647	−	4.65061i	−0.580314	−	0.246136i
$358$	3.65951	−	2.78483i	0.193411	−	0.147183i
$359$	6.00000	−	3.46410i	0.316668	−	0.182828i	−0.333238	−	0.942843i	$-0.608141\pi$
$359$	6.00000	−	3.46410i	0.316668	−	0.182828i	0.649906	+	0.760014i	$0.274808\pi$
$360$	10.7932	+	1.55307i	0.568854	+	0.0818542i
$361$	9.49781	−	16.4507i	0.499885	−	0.865826i
$362$	30.6551	+	12.8418i	1.61119	+	0.674949i
$363$	9.14427			0.479950
$364$	1.93558	+	0.287297i	0.101452	+	0.0150585i
$365$	6.94571			0.363555
$366$	−1.86763	−	0.782374i	−0.0976226	−	0.0408953i
$367$	9.65903	−	16.7299i	0.504197	−	0.873295i	−0.495791	−	0.868442i	$-0.665122\pi$
$367$	9.65903	−	16.7299i	0.504197	−	0.873295i	0.999988	−	0.00485350i	$-0.00154492\pi$
$368$	6.23902	+	11.2175i	0.325231	+	0.584750i
$369$	−7.31806	+	4.22509i	−0.380963	+	0.219949i
$370$	23.8280	−	18.1327i	1.23876	−	0.942675i
$371$	6.68350	−	0.822539i	0.346990	−	0.0427041i
$372$	−3.21830	+	11.6373i	−0.166861	+	0.603365i
$373$	−5.63832	−	9.76585i	−0.291941	−	0.505657i	0.682328	−	0.731047i	$-0.260968\pi$
$373$	−5.63832	−	9.76585i	−0.291941	−	0.505657i	−0.974269	+	0.225390i	$0.927634\pi$
$374$	−8.60275	+	1.09755i	−0.444838	+	0.0567528i
$375$	−16.2373	−	9.37462i	−0.838491	−	0.484103i
$376$	−3.16942	−	2.49304i	−0.163450	−	0.128568i
$377$		−	1.15359i		−	0.0594128i
$378$	−3.62594	+	0.923343i	−0.186498	+	0.0474917i
$379$		−	25.1457i		−	1.29165i	−0.763486	−	0.645824i	$-0.776514\pi$
$379$		−	25.1457i		−	1.29165i	0.763486	−	0.645824i	$-0.223486\pi$
$380$	0.128130	+	0.493977i	0.00657292	+	0.0253405i
$381$	−2.34097	−	1.35156i	−0.119931	−	0.0692424i
$382$	−4.27703	−	33.5240i	−0.218832	−	1.71524i
$383$	8.88226	+	15.3845i	0.453862	+	0.786112i	0.998622	−	0.0524799i	$-0.0167126\pi$
$383$	8.88226	+	15.3845i	0.453862	+	0.786112i	−0.544760	+	0.838592i	$0.683379\pi$
$384$	−11.1711	−	1.79052i	−0.570074	−	0.0913721i
$385$	−8.36544	−	11.0948i	−0.426342	−	0.565444i
$386$	−17.0215	−	22.3677i	−0.866369	−	1.13848i
$387$	−5.45877	+	3.15162i	−0.277485	+	0.160206i
$388$	4.11144	−	4.04611i	0.208727	−	0.205410i
$389$	−7.07233	+	12.2496i	−0.358581	+	0.621081i	−0.987724	−	0.156209i	$-0.950073\pi$
$389$	−7.07233	+	12.2496i	−0.358581	+	0.621081i	0.629143	+	0.777290i	$0.283406\pi$
$390$	−0.779023	+	1.85963i	−0.0394474	+	0.0941661i
$391$	14.4455			0.730539
$392$	2.01592	+	19.6961i	0.101819	+	0.994803i
$393$	7.77288			0.392090
$394$	−10.3929	+	24.8092i	−0.523585	+	1.24987i
$395$	−24.0739	+	41.6972i	−1.21129	+	2.09801i
$396$	−1.94188	+	1.91103i	−0.0975833	+	0.0960327i
$397$	−10.9558	+	6.32534i	−0.549856	+	0.317460i	−0.749064	−	0.662498i	$-0.769497\pi$
$397$	−10.9558	+	6.32534i	−0.549856	+	0.317460i	0.199208	+	0.979957i	$0.436163\pi$
$398$	12.7190	+	16.7139i	0.637545	+	0.837790i
$399$	−0.105422	−	0.139819i	−0.00527772	−	0.00699968i
$400$	33.8470	+	20.2712i	1.69235	+	1.01356i
$401$	12.3904	+	21.4608i	0.618747	+	1.07170i	0.989715	+	0.143055i	$0.0456926\pi$
$401$	12.3904	+	21.4608i	0.618747	+	1.07170i	−0.370968	+	0.928646i	$0.620974\pi$
$402$	−1.74812	−	13.7020i	−0.0871884	−	0.683396i
$403$	−1.93339	−	1.11624i	−0.0963090	−	0.0556040i
$404$	−3.10761	−	11.9807i	−0.154610	−	0.596064i
$405$		−	3.85529i		−	0.191571i
$406$	11.3112	−	2.88038i	0.561363	−	0.142951i
$407$			7.48131i			0.370835i
$408$	−7.87187	+	10.0076i	−0.389716	+	0.495449i
$409$	−5.02003	−	2.89832i	−0.248225	−	0.143313i	0.370726	−	0.928742i	$-0.379109\pi$
$409$	−5.02003	−	2.89832i	−0.248225	−	0.143313i	−0.618951	+	0.785430i	$0.712442\pi$
$410$	−45.7016	+	5.83066i	−2.25704	+	0.287956i
$411$	−1.42568	−	2.46934i	−0.0703234	−	0.121804i
$412$	−9.48515	+	34.2980i	−0.467300	+	1.68974i
$413$	9.02686	−	1.11094i	0.444183	−	0.0546656i
$414$	3.61137	−	2.74820i	0.177489	−	0.135067i
$415$	−41.0300	+	23.6887i	−2.01408	+	1.16283i
$416$	0.839063	−	1.91624i	0.0411385	−	0.0939515i
$417$	3.57828	−	6.19776i	0.175229	−	0.303506i
$418$	−0.117604	−	0.0492659i	−0.00575221	−	0.00240967i
$419$	2.42966			0.118697			0.0593484	−	0.998237i	$-0.481098\pi$
$419$	2.42966			0.118697			0.0593484	+	0.998237i	$0.481098\pi$
$420$	−20.1792	−	2.99519i	−0.984644	−	0.146150i
$421$	−25.9373			−1.26411			−0.632054	−	0.774924i	$-0.717788\pi$
$421$	−25.9373			−1.26411			−0.632054	+	0.774924i	$0.717788\pi$
$422$	−25.6542	−	10.7469i	−1.24883	−	0.523149i
$423$	−0.712838	+	1.23467i	−0.0346594	+	0.0600318i
$424$	1.02531	−	7.12548i	0.0497934	−	0.346044i
$425$	38.4522	−	22.2004i	1.86521	−	1.07688i
$426$	14.5761	−	11.0922i	0.706214	−	0.537418i
$427$	3.48748	+	1.47919i	0.168771	+	0.0715830i
$428$	11.7454	+	3.24822i	0.567738	+	0.157009i
$429$	−0.251879	−	0.436267i	−0.0121608	−	0.0210632i
$430$	−34.0902	+	4.34927i	−1.64398	+	0.209740i
$431$	−12.7781	−	7.37742i	−0.615497	−	0.355358i	0.159616	−	0.987179i	$-0.448974\pi$
$431$	−12.7781	−	7.37742i	−0.615497	−	0.355358i	−0.775114	+	0.631821i	$0.782308\pi$
$432$	−0.0640649	+	3.99949i	−0.00308232	+	0.192425i
$433$			35.7396i			1.71754i	0.512364	+	0.858769i	$0.328770\pi$
$433$			35.7396i			1.71754i	−0.512364	+	0.858769i	$0.671230\pi$
$434$	6.11753	−	21.7444i	0.293651	−	1.04376i
$435$			12.0266i			0.576632i
$436$	15.2227	−	3.94853i	0.729037	−	0.189101i
$437$	0.183929	+	0.106192i	0.00879854	+	0.00507984i
$438$	0.322444	+	2.52737i	0.0154070	+	0.120762i
$439$	9.91925	+	17.1806i	0.473420	+	0.819987i	0.999537	−	0.0304249i	$-0.00968604\pi$
$439$	9.91925	+	17.1806i	0.473420	+	0.819987i	−0.526117	+	0.850412i	$0.676353\pi$
$440$	−13.7911	+	5.51933i	−0.657466	+	0.263124i
$441$	6.79112	−	1.69727i	0.323387	−	0.0808225i
$442$	−1.42568	−	1.87346i	−0.0678125	−	0.0891116i
$443$	16.4378	−	9.49035i	0.780982	−	0.450900i	−0.0557962	−	0.998442i	$-0.517770\pi$
$443$	16.4378	−	9.49035i	0.780982	−	0.450900i	0.836778	+	0.547542i	$0.184436\pi$
$444$	7.70422	+	7.82861i	0.365626	+	0.371530i
$445$	−2.49186	+	4.31603i	−0.118126	+	0.204599i
$446$	4.42780	−	10.5697i	0.209662	−	0.500492i
$447$	21.3551			1.01006
$448$	20.8842	+	3.44254i	0.986685	+	0.162645i
$449$	−25.2845			−1.19325			−0.596626	−	0.802520i	$-0.703492\pi$
$449$	−25.2845			−1.19325			−0.596626	+	0.802520i	$0.703492\pi$
$450$	5.38951	−	12.8655i	0.254064	−	0.606485i
$451$	5.75564	−	9.96906i	0.271022	−	0.469425i
$452$	−6.60275	−	6.70936i	−0.310567	−	0.315582i
$453$	19.2373	−	11.1067i	0.903848	−	0.521837i
$454$	10.3507	+	13.6017i	0.485781	+	0.638359i
$455$	1.47286	−	3.47255i	0.0690485	−	0.162795i
$456$	−0.173798	+	0.0695553i	−0.00813882	+	0.00325723i
$457$	−11.4837	−	19.8904i	−0.537186	−	0.930433i	−0.999054	−	0.0434847i	$-0.986154\pi$
$457$	−11.4837	−	19.8904i	−0.537186	−	0.930433i	0.461868	−	0.886949i	$-0.347179\pi$
$458$	4.25651	+	33.3632i	0.198894	+	1.55896i
$459$	3.89853	+	2.25082i	0.181968	+	0.105059i
$460$	23.9502	−	6.21230i	1.11668	−	0.289650i
$461$			2.95838i			0.137786i	0.997624	+	0.0688928i	$0.0219466\pi$
$461$			2.95838i			0.137786i	−0.997624	+	0.0688928i	$0.978053\pi$
$462$	3.64877	−	3.55903i	0.169756	−	0.165581i
$463$			3.30669i			0.153675i	0.997044	+	0.0768374i	$0.0244822\pi$
$463$			3.30669i			0.153675i	−0.997044	+	0.0768374i	$0.975518\pi$
$464$	0.199851	−	12.4764i	0.00927785	−	0.579204i
$465$	20.1564	+	11.6373i	0.934729	+	0.539666i
$466$	−27.9579	+	3.56689i	−1.29512	+	0.165233i
$467$	−5.95282	−	10.3106i	−0.275464	−	0.477117i	0.694788	−	0.719214i	$-0.255498\pi$
$467$	−5.95282	−	10.3106i	−0.275464	−	0.477117i	−0.970252	+	0.242097i	$0.922165\pi$
$468$	−0.712838	−	0.197136i	−0.0329510	−	0.00911263i
$469$	3.15656	+	25.6485i	0.145756	+	1.18434i
$470$	−6.18569	+	4.70722i	−0.285325	+	0.217128i
$471$	4.71898	−	2.72451i	0.217439	−	0.125539i
$472$	1.38480	−	9.62380i	0.0637406	−	0.442971i
$473$	4.29331	−	7.43623i	0.197406	−	0.341918i
$474$	−16.2902	−	6.82416i	−0.748232	−	0.313444i
$475$	0.652798			0.0299524
$476$	14.8099	−	18.6569i	0.678812	−	0.855136i
$477$	−2.54519			−0.116536
$478$	−12.5351	−	5.25109i	−0.573340	−	0.240179i
$479$	5.95186	−	10.3089i	0.271947	−	0.471026i	−0.697413	−	0.716669i	$-0.745666\pi$
$479$	5.95186	−	10.3089i	0.271947	−	0.471026i	0.969360	+	0.245643i	$0.0789990\pi$
$480$	−8.74757	+	19.9776i	−0.399270	+	0.911848i
$481$	−1.75879	+	1.01544i	−0.0801940	+	0.0463000i
$482$	11.7136	−	8.91387i	0.533540	−	0.406016i
$483$	−6.77902	+	5.11135i	−0.308456	+	0.232574i
$484$	−4.87474	+	17.6269i	−0.221579	+	0.801222i
$485$	−5.55975	−	9.62978i	−0.252455	−	0.437266i
$486$	1.40284	−	0.178976i	0.0636342	−	0.00811852i
$487$	−6.50151	−	3.75365i	−0.294612	−	0.170094i	0.345408	−	0.938453i	$-0.387740\pi$
$487$	−6.50151	−	3.75365i	−0.294612	−	0.170094i	−0.640020	+	0.768358i	$0.721074\pi$
$488$	2.50376	−	3.18305i	0.113340	−	0.144090i
$489$			4.75680i			0.215110i
$490$	37.7266	+	5.77109i	1.70431	+	0.260711i
$491$		−	22.0031i		−	0.992988i	−0.868040	−	0.496494i	$-0.834620\pi$
$491$		−	22.0031i		−	0.992988i	0.868040	−	0.496494i	$-0.165380\pi$
$492$	−4.24326	−	16.3590i	−0.191301	−	0.737520i
$493$	−12.1615	−	7.02145i	−0.547727	−	0.316230i
$494$	−0.00438044	−	0.0343346i	−0.000197086	−	0.00154479i
$495$	2.62594	+	4.54826i	0.118027	+	0.204429i
$496$	−20.7169	−	12.4075i	−0.930215	−	0.557113i
$497$	−27.3613	+	20.6303i	−1.22732	+	0.925393i
$498$	−10.5245	−	13.8301i	−0.471613	−	0.619740i
$499$	−1.22277	+	0.705968i	−0.0547389	+	0.0316035i	−0.527120	−	0.849791i	$-0.676728\pi$
$499$	−1.22277	+	0.705968i	−0.0547389	+	0.0316035i	0.472381	+	0.881395i	$0.343395\pi$
$500$	26.7269	−	26.3022i	1.19526	−	1.17627i
$501$	−7.03090	+	12.1779i	−0.314118	+	0.544068i
$502$	11.3033	−	26.9826i	0.504493	−	1.20429i
$503$	26.2303			1.16955			0.584775	−	0.811196i	$-0.301183\pi$
$503$	26.2303			1.16955			0.584775	+	0.811196i	$0.301183\pi$
$504$	0.153084	−	7.48175i	0.00681889	−	0.333264i
$505$	−23.8589			−1.06171
$506$	−2.38863	+	5.70197i	−0.106188	+	0.253484i
$507$	−6.43162	+	11.1399i	−0.285638	+	0.494740i
$508$	3.85328	−	3.79205i	0.170961	−	0.168245i
$509$	−4.38419	+	2.53121i	−0.194326	+	0.112194i	−0.594006	−	0.804461i	$-0.702455\pi$
$509$	−4.38419	+	2.53121i	−0.194326	+	0.112194i	0.399680	+	0.916655i	$0.369121\pi$
$510$	14.8632	+	19.5316i	0.658156	+	0.864874i
$511$	−0.582233	−	4.73091i	−0.0257565	−	0.209283i
$512$	9.40673	−	20.5794i	0.415723	−	0.909491i
$513$	0.0330925	+	0.0573178i	0.00146107	+	0.00253064i
$514$	−3.17707	−	24.9024i	−0.140135	−	1.09840i
$515$	59.4058	+	34.2980i	2.61773	+	1.51135i
$516$	−3.16518	−	12.2027i	−0.139339	−	0.537193i
$517$		−	1.94213i		−	0.0854149i
$518$	−14.3481	−	14.7099i	−0.630419	−	0.646314i
$519$			1.77713i			0.0780074i
$520$	−3.16942	−	2.49304i	−0.138988	−	0.109327i
$521$	−8.60044	−	4.96547i	−0.376792	−	0.217541i	0.299630	−	0.954056i	$-0.403137\pi$
$521$	−8.60044	−	4.96547i	−0.376792	−	0.217541i	−0.676422	+	0.736515i	$0.736470\pi$
$522$	−4.37618	+	0.558317i	−0.191540	+	0.0244369i
$523$	15.6686	+	27.1389i	0.685142	+	1.18670i	0.973392	+	0.229146i	$0.0735933\pi$
$523$	15.6686	+	27.1389i	0.685142	+	1.18670i	−0.288250	+	0.957555i	$0.593073\pi$
$524$	−4.14366	+	14.9833i	−0.181017	+	0.654550i
$525$	−10.1896	+	24.0241i	−0.444713	+	1.04850i
$526$	2.34225	−	1.78242i	0.102127	−	0.0777171i
$527$	−23.5356	+	13.5883i	−1.02523	+	0.591916i
$528$	−2.64858	−	4.76201i	−0.115265	−	0.207240i
$529$	−6.35135	+	11.0009i	−0.276146	+	0.478299i
$530$	−12.7992	−	5.36174i	−0.555961	−	0.232899i
$531$	−3.43757			−0.149178
$532$	0.325720	−	0.128681i	0.0141218	−	0.00557902i
$533$	3.12485			0.135352
$534$	−1.68618	−	0.706360i	−0.0729680	−	0.0305672i
$535$	11.7454	−	20.3437i	0.507800	−	0.879535i
$536$	27.3446	+	3.93470i	1.18111	+	0.169953i
$537$	2.81607	−	1.62586i	0.121522	−	0.0701610i
$538$	−4.00347	+	3.04658i	−0.172602	+	0.131347i
$539$	−6.85573	+	6.62796i	−0.295297	+	0.285486i
$540$	7.43162	+	2.05523i	0.319806	+	0.0884428i
$541$	2.09313	+	3.62541i	0.0899908	+	0.155869i	0.907507	−	0.420037i	$-0.137983\pi$
$541$	2.09313	+	3.62541i	0.0899908	+	0.155869i	−0.817516	+	0.575906i	$0.804650\pi$
$542$	−17.3503	+	2.21357i	−0.745260	+	0.0950810i
$543$	20.3529	+	11.7508i	0.873427	+	0.504274i
$544$	−15.0946	−	20.5091i	−0.647176	−	0.879322i
$545$		−	30.3151i		−	1.29856i
$546$	1.33195	+	0.374727i	0.0570021	+	0.0160369i
$547$		−	12.4674i		−	0.533067i	−0.963826	−	0.266533i	$-0.914122\pi$
$547$		−	12.4674i		−	0.533067i	0.963826	−	0.266533i	$-0.0858782\pi$
$548$	5.52003	−	1.43181i	0.235804	−	0.0611638i
$549$	−1.23998	−	0.715904i	−0.0529212	−	0.0305540i
$550$	2.40477	+	18.8489i	0.102540	+	0.803721i
$551$	−0.103232	−	0.178803i	−0.00439784	−	0.00761728i
$552$	3.37235	+	8.42648i	0.143537	+	0.358655i
$553$	30.4191	+	12.9020i	1.29355	+	0.548651i
$554$	10.1599	+	13.3510i	0.431653	+	0.567230i
$555$	18.3361	−	10.5864i	0.778324	−	0.449366i
$556$	10.0395	+	10.2016i	0.425771	+	0.432645i
$557$	18.2744	−	31.6521i	0.774309	−	1.34114i	−0.160872	−	0.986975i	$-0.551431\pi$
$557$	18.2744	−	31.6521i	0.774309	−	1.34114i	0.935182	−	0.354168i	$-0.115236\pi$
$558$	−3.29878	+	7.87464i	−0.139649	+	0.333360i
$559$	2.33092			0.0985876
$560$	16.5310	−	37.3016i	0.698563	−	1.57628i
$561$	−6.13237			−0.258909
$562$	10.5694	−	25.2305i	0.445842	−	1.06428i
$563$	−21.3672	+	37.0091i	−0.900520	+	1.55975i	−0.0737002	+	0.997280i	$0.523481\pi$
$563$	−21.3672	+	37.0091i	−0.900520	+	1.55975i	−0.826820	+	0.562466i	$0.809853\pi$
$564$	−2.00000	−	2.03229i	−0.0842152	−	0.0855750i
$565$	−15.7146	+	9.07283i	−0.661118	+	0.381697i
$566$	−21.3602	−	28.0692i	−0.897838	−	1.17984i
$567$	−2.62594	+	0.323174i	−0.110279	+	0.0135721i
$568$	13.6114	+	34.0107i	0.571120	+	1.42706i
$569$	−10.7265	−	18.5788i	−0.449678	−	0.778866i	0.548687	−	0.836028i	$-0.315128\pi$
$569$	−10.7265	−	18.5788i	−0.449678	−	0.778866i	−0.998365	+	0.0571625i	$0.981795\pi$
$570$	0.0456679	+	0.357952i	0.00191282	+	0.0149930i
$571$	18.3349	+	10.5856i	0.767291	+	0.442996i	0.831907	−	0.554915i	$-0.187249\pi$
$571$	18.3349	+	10.5856i	0.767291	+	0.442996i	−0.0646165	+	0.997910i	$0.520582\pi$
$572$	0.975243	−	0.252962i	0.0407770	−	0.0105769i
$573$		−	23.8972i		−	0.998321i
$574$	7.80241	+	30.6398i	0.325666	+	1.27888i
$575$		−	31.6506i		−	1.31992i
$576$	−7.67544	−	2.25559i	−0.319810	−	0.0939829i
$577$	4.10289	+	2.36880i	0.170806	+	0.0986146i	0.582966	−	0.812497i	$-0.301892\pi$
$577$	4.10289	+	2.36880i	0.170806	+	0.0986146i	−0.412160	+	0.911111i	$0.635226\pi$
$578$	−4.57992	+	0.584310i	−0.190499	+	0.0243041i
$579$	−9.93757	−	17.2124i	−0.412991	−	0.715322i
$580$	−23.1830	−	6.41129i	−0.962623	−	0.266214i
$581$	19.5744	+	25.9609i	0.812082	+	1.07704i
$582$	3.24593	−	2.47010i	0.134548	−	0.102389i
$583$	3.00267	−	1.73359i	0.124358	−	0.0717981i
$584$	−5.04376	−	0.725764i	−0.208712	−	0.0300323i
$585$	−0.712838	+	1.23467i	−0.0294722	+	0.0510474i
$586$	8.97722	+	3.76067i	0.370846	+	0.155352i
$587$	−29.8450			−1.23184			−0.615918	−	0.787810i	$-0.711215\pi$
$587$	−29.8450			−1.23184			−0.615918	+	0.787810i	$0.711215\pi$
$588$	−0.348554	+	13.9957i	−0.0143741	+	0.577171i
$589$	−0.399562			−0.0164636
$590$	−17.2868	−	7.24166i	−0.711687	−	0.298134i
$591$	−9.50990	+	16.4716i	−0.391185	+	0.677553i
$592$	−19.1978	+	10.6776i	−0.789027	+	0.438847i
$593$	22.9586	−	13.2551i	0.942796	−	0.544323i	0.0519600	−	0.998649i	$-0.483453\pi$
$593$	22.9586	−	13.2551i	0.942796	−	0.544323i	0.890836	+	0.454326i	$0.150120\pi$
$594$	−1.53309	+	1.16666i	−0.0629035	+	0.0478686i
$595$	−27.6440	−	36.6634i	−1.13330	−	1.50305i
$596$	−11.3842	+	41.1651i	−0.466317	+	1.68619i
$597$	7.42568	+	12.8616i	0.303913	+	0.526392i
$598$	−1.66469	+	0.212383i	−0.0680744	+	0.00868500i
$599$	−18.0000	−	10.3923i	−0.735460	−	0.424618i	0.0849563	−	0.996385i	$-0.472925\pi$
$599$	−18.0000	−	10.3923i	−0.735460	−	0.424618i	−0.820416	+	0.571767i	$0.806258\pi$
$600$	21.9270	+	17.2476i	0.895164	+	0.704128i
$601$		−	10.8255i		−	0.441581i	−0.975321	−	0.220790i	$-0.929136\pi$
$601$		−	10.8255i		−	0.441581i	0.975321	−	0.220790i	$-0.0708637\pi$
$602$	5.82006	+	22.8552i	0.237208	+	0.931508i
$603$		−	9.76735i		−	0.397757i
$604$	11.1544	+	43.0036i	0.453868	+	1.74979i
$605$	30.5307	+	17.6269i	1.24125	+	0.716635i
$606$	−1.10761	−	8.68164i	−0.0449937	−	0.352668i
$607$	−6.95330	−	12.0435i	−0.282226	−	0.488830i	0.689707	−	0.724089i	$-0.257739\pi$
$607$	−6.95330	−	12.0435i	−0.282226	−	0.488830i	−0.971933	+	0.235259i	$0.924406\pi$
$608$	−0.0414278	−	0.372099i	−0.00168012	−	0.0150906i
$609$	8.19164	−	1.00815i	0.331942	−	0.0408521i
$610$	−4.72746	−	6.21230i	−0.191409	−	0.251529i
$611$	0.456579	−	0.263606i	0.0184712	−	0.0106644i
$612$	−6.41706	+	6.31509i	−0.259394	+	0.255272i
$613$	−0.322444	+	0.558490i	−0.0130234	+	0.0225572i	−0.872464	−	0.488679i	$-0.837479\pi$
$613$	−0.322444	+	0.558490i	−0.0130234	+	0.0225572i	0.859440	+	0.511236i	$0.170812\pi$
$614$	−9.51941	+	22.7241i	−0.384172	+	0.917069i
$615$	−32.5779			−1.31367
$616$	4.91542	+	8.93083i	0.198048	+	0.359833i
$617$	12.3626			0.497701			0.248850	−	0.968542i	$-0.419947\pi$
$617$	12.3626			0.497701			0.248850	+	0.968542i	$0.419947\pi$
$618$	−9.72234	+	23.2085i	−0.391090	+	0.933584i
$619$	−5.69875	+	9.87053i	−0.229052	+	0.396730i	−0.957527	−	0.288342i	$-0.906896\pi$
$619$	−5.69875	+	9.87053i	−0.229052	+	0.396730i	0.728475	+	0.685072i	$0.240229\pi$
$620$	−33.1777	+	32.6505i	−1.33245	+	1.31128i
$621$	2.77902	−	1.60447i	0.111518	−	0.0643852i
$622$	21.5099	+	28.2659i	0.862469	+	1.13336i
$623$	3.14865	+	1.33548i	0.126148	+	0.0535047i
$624$	0.760017	−	1.26901i	0.0304250	−	0.0508009i
$625$	−11.4837	−	19.8904i	−0.459349	−	0.795616i
$626$	−3.95474	−	30.9979i	−0.158063	−	1.23893i
$627$	−0.0780814	−	0.0450803i	−0.00311827	−	0.00180033i
$628$	2.73622	+	10.5489i	0.109187	+	0.420948i
$629$			24.7224i			0.985745i
$630$	−13.8861	−	3.90668i	−0.553235	−	0.155646i
$631$			10.8050i			0.430140i	0.976599	+	0.215070i	$0.0689979\pi$
$631$			10.8050i			0.430140i	−0.976599	+	0.215070i	$0.931002\pi$
$632$	21.8387	−	27.7637i	0.868697	−	1.10438i
$633$	−17.0327	−	9.83381i	−0.676988	−	0.390859i
$634$	−2.27719	+	0.290526i	−0.0904387	+	0.0115383i
$635$	−5.21065	−	9.02511i	−0.206778	−	0.358150i
$636$	1.35682	−	4.90621i	0.0538014	−	0.194544i
$637$	−2.48871	−	0.712111i	−0.0986062	−	0.0282149i
$638$	4.78250	−	3.63941i	0.189341	−	0.144085i
$639$	11.2166	−	6.47590i	0.443722	−	0.256183i
$640$	−33.8464	−	27.5121i	−1.33790	−	1.08751i
$641$	−1.12662	+	1.95136i	−0.0444988	+	0.0770741i	−0.887417	−	0.460968i	$-0.847502\pi$
$641$	−1.12662	+	1.95136i	−0.0444988	+	0.0770741i	0.842918	+	0.538042i	$0.180836\pi$
$642$	7.94783	+	3.32945i	0.313676	+	0.131403i
$643$	−22.0574			−0.869860			−0.434930	−	0.900464i	$-0.643227\pi$
$643$	−22.0574			−0.869860			−0.434930	+	0.900464i	$0.643227\pi$
$644$	−6.23902	−	15.7924i	−0.245852	−	0.622306i
$645$	−24.3008			−0.956844
$646$	−0.388629	−	0.162802i	−0.0152904	−	0.00640535i
$647$	−2.26417	+	3.92166i	−0.0890137	+	0.154176i	−0.907094	−	0.420927i	$-0.861705\pi$
$647$	−2.26417	+	3.92166i	−0.0890137	+	0.154176i	0.818081	+	0.575103i	$0.195038\pi$
$648$	−0.402843	+	2.79959i	−0.0158252	+	0.109978i
$649$	4.05546	−	2.34142i	0.159191	−	0.0919089i
$650$	−4.10483	+	3.12371i	−0.161004	+	0.122522i
$651$	6.23683	−	14.7045i	0.244441	−	0.576316i
$652$	−9.16942	−	2.53581i	−0.359102	−	0.0993101i
$653$	−20.6749	−	35.8099i	−0.809071	−	1.40135i	−0.913508	−	0.406820i	$-0.866638\pi$
$653$	−20.6749	−	35.8099i	−0.809071	−	1.40135i	0.104438	−	0.994531i	$-0.466696\pi$
$654$	11.0309	−	1.40733i	0.431342	−	0.0550311i
$655$	25.9519	+	14.9833i	1.01403	+	0.585448i
$656$	33.7964	+	0.541359i	1.31953	+	0.0211365i
$657$			1.80161i			0.0702874i
$658$	3.72473	+	3.81865i	0.145205	+	0.148867i
$659$			10.6413i			0.414526i	0.978285	+	0.207263i	$0.0664556\pi$
$659$			10.6413i			0.414526i	−0.978285	+	0.207263i	$0.933544\pi$
$660$	−10.1673	+	2.63723i	−0.395762	+	0.102654i
$661$	41.7871	+	24.1258i	1.62533	+	0.938384i	0.985462	+	0.169899i	$0.0543441\pi$
$661$	41.7871	+	24.1258i	1.62533	+	0.938384i	0.639867	+	0.768485i	$0.278989\pi$
$662$	4.77288	+	37.4106i	0.185503	+	1.45400i
$663$	−0.832347	−	1.44167i	−0.0323257	−	0.0559897i
$664$	32.2700	−	12.9147i	1.25232	−	0.501189i
$665$	−0.0824618	−	0.670040i	−0.00319773	−	0.0259830i
$666$	4.70334	+	6.18059i	0.182251	+	0.239493i
$667$	−8.66919	+	5.00516i	−0.335672	+	0.193801i
$668$	−19.7265	−	20.0450i	−0.763241	−	0.775565i
$669$	4.05162	−	7.01760i	0.156645	−	0.271316i
$670$	20.5761	−	49.1179i	0.794924	−	1.89759i
$671$	1.95049			0.0752977
$672$	14.3405	+	4.28355i	0.553198	+	0.165242i
$673$	−0.148647			−0.00572991			−0.00286496	−	0.999996i	$-0.500912\pi$
$673$	−0.148647			−0.00572991			−0.00286496	+	0.999996i	$0.500912\pi$
$674$	−16.3067	+	38.9262i	−0.628110	+	1.49938i
$675$	4.93162	−	8.54182i	0.189818	−	0.328775i
$676$	−18.0451	−	18.3365i	−0.694043	−	0.705249i
$677$	−34.3935	+	19.8571i	−1.32185	+	0.763170i	−0.984023	−	0.178039i	$-0.943025\pi$
$677$	−34.3935	+	19.8571i	−1.32185	+	0.763170i	−0.337825	+	0.941209i	$0.609691\pi$
$678$	−4.03090	−	5.29696i	−0.154806	−	0.203428i
$679$	−6.09304	+	4.59412i	−0.233830	+	0.176306i
$680$	−45.5735	+	18.2389i	−1.74766	+	0.699430i
$681$	6.04300	+	10.4668i	0.231568	+	0.401088i
$682$	−1.47190	−	11.5370i	−0.0563618	−	0.441773i
$683$	−36.9070	−	21.3083i	−1.41221	−	0.815339i	−0.416613	−	0.909084i	$-0.636783\pi$
$683$	−36.9070	−	21.3083i	−1.41221	−	0.815339i	−0.995596	+	0.0937450i	$0.970116\pi$
$684$	−0.128130	+	0.0332348i	−0.00489916	+	0.00127076i
$685$		−	10.9928i		−	0.420013i
$686$	0.768365	−	26.1803i	0.0293363	−	0.999570i
$687$			23.7826i			0.907362i
$688$	25.2097	+	0.403816i	0.961112	+	0.0153954i
$689$	0.815106	+	0.470602i	0.0310531	+	0.0179285i
$690$	17.3551	−	2.21418i	0.660698	−	0.0842925i
$691$	−2.22317	−	3.85064i	−0.0845733	−	0.146485i	0.820636	−	0.571451i	$-0.193619\pi$
$691$	−2.22317	−	3.85064i	−0.0845733	−	0.146485i	−0.905209	+	0.424966i	$0.860286\pi$
$692$	−3.42568	−	0.947375i	−0.130225	−	0.0360138i
$693$	2.87782	−	2.16986i	0.109319	−	0.0824262i
$694$	−1.06618	+	0.811350i	−0.0404718	+	0.0307984i
$695$	23.8942	−	13.7953i	0.906357	−	0.523285i
$696$	1.25667	−	8.73335i	0.0476340	−	0.331037i
$697$	19.0198	−	32.9433i	0.720427	−	1.24782i
$698$	8.37139	+	3.50688i	0.316862	+	0.132737i
$699$	−19.9294			−0.753800
$700$	−40.8779	−	32.4491i	−1.54504	−	1.22646i
$701$	−24.9907			−0.943885			−0.471942	−	0.881629i	$-0.656447\pi$
$701$	−24.9907			−0.943885			−0.471942	+	0.881629i	$0.656447\pi$
$702$	−0.482359	−	0.202066i	−0.0182055	−	0.00762649i
$703$	−0.181739	+	0.314782i	−0.00685442	+	0.0118722i
$704$	10.5914	−	2.56692i	0.399179	−	0.0967444i
$705$	−4.76002	+	2.74820i	−0.179273	+	0.103503i
$706$	−15.6131	+	11.8814i	−0.587608	+	0.447161i
$707$	2.00000	+	16.2509i	0.0752177	+	0.611178i
$708$	1.83254	−	6.62642i	0.0688712	−	0.249036i
$709$	−9.07409	−	15.7168i	−0.340785	−	0.590257i	0.643794	−	0.765199i	$-0.277359\pi$
$709$	−9.07409	−	15.7168i	−0.340785	−	0.590257i	−0.984579	+	0.174942i	$0.944026\pi$
$710$	70.0481	−	8.93681i	2.62886	−	0.335392i
$711$	−10.8156	−	6.24438i	−0.405616	−	0.234183i
$712$	2.26050	−	2.87379i	0.0847158	−	0.107700i
$713$			19.3725i			0.725507i
$714$	12.0576	−	11.7610i	0.451243	−	0.440145i
$715$		−	1.94213i		−	0.0726316i
$716$	1.63285	+	6.29512i	0.0610225	+	0.235260i
$717$	−8.32244	−	4.80497i	−0.310807	−	0.179445i
$718$	1.23998	+	9.71918i	0.0462757	+	0.362717i
$719$	−20.5818	−	35.6488i	−0.767573	−	1.32948i	−0.938875	−	0.344257i	$-0.888131\pi$
$719$	−20.5818	−	35.6488i	−0.767573	−	1.32948i	0.171302	−	0.985219i	$-0.445203\pi$
$720$	−7.92349	+	13.2299i	−0.295291	+	0.493049i
$721$	18.3815	−	43.3380i	0.684562	−	1.61399i
$722$	16.2682	+	21.3778i	0.605440	+	0.795601i
$723$	9.01386	−	5.20415i	0.335229	−	0.193545i
$724$	−33.5013	+	32.9689i	−1.24507	+	1.22528i
$725$	−15.3842	+	26.6463i	−0.571357	+	0.989619i
$726$	−4.99664	+	11.9276i	−0.185443	+	0.442677i
$727$	−5.77231			−0.214083			−0.107042	−	0.994255i	$-0.534138\pi$
$727$	−5.77231			−0.214083			−0.107042	+	0.994255i	$0.534138\pi$
$728$	−1.43239	+	2.36776i	−0.0530880	+	0.0877549i
$729$	1.00000			0.0370370
$730$	−3.79530	+	9.05988i	−0.140470	+	0.335321i
$731$	14.1875	−	24.5734i	0.524742	−	0.908880i
$732$	2.04103	−	2.00860i	0.0754388	−	0.0742401i
$733$	−6.63928	+	3.83319i	−0.245227	+	0.141582i	−0.617577	−	0.786510i	$-0.711886\pi$
$733$	−6.63928	+	3.83319i	−0.245227	+	0.141582i	0.372350	+	0.928093i	$0.378552\pi$
$734$	16.5444	+	21.7407i	0.610663	+	0.802465i
$735$	25.9458	+	7.42404i	0.957024	+	0.273840i
$736$	−18.0410	+	2.00860i	−0.665001	+	0.0740381i
$737$	6.65280	+	11.5230i	0.245059	+	0.424455i
$738$	−1.51238	−	11.8543i	−0.0556714	−	0.436361i
$739$	17.3753	+	10.0317i	0.639162	+	0.369021i	0.784292	−	0.620392i	$-0.213027\pi$
$739$	17.3753	+	10.0317i	0.639162	+	0.369021i	−0.145129	+	0.989413i	$0.546360\pi$
$740$	10.6319	+	40.9890i	0.390836	+	1.50679i
$741$		−	0.0244750i		−	0.000899113i
$742$	−2.57912	+	9.16732i	−0.0946823	+	0.336543i
$743$			8.26368i			0.303165i	0.988445	+	0.151583i	$0.0484369\pi$
$743$			8.26368i			0.303165i	−0.988445	+	0.151583i	$0.951563\pi$
$744$	−13.4209	−	10.5568i	−0.492036	−	0.387031i
$745$	71.3000	+	41.1651i	2.61223	+	1.50817i
$746$	15.8193	−	2.01825i	0.579187	−	0.0738933i
$747$	−6.14446	−	10.6425i	−0.224814	−	0.389390i
$748$	3.26912	−	11.8210i	0.119531	−	0.432220i
$749$	−14.8412	−	6.29480i	−0.542286	−	0.230007i
$750$	21.1006	−	16.0572i	0.770484	−	0.586326i
$751$	23.4113	−	13.5165i	0.854289	−	0.493224i	−0.00780684	−	0.999970i	$-0.502485\pi$
$751$	23.4113	−	13.5165i	0.854289	−	0.493224i	0.862096	+	0.506746i	$0.169152\pi$
$752$	4.98372	−	2.77189i	0.181738	−	0.101080i
$753$	10.3430	−	17.9146i	0.376921	−	0.652846i
$754$	1.50472	+	0.630347i	0.0547988	+	0.0229559i
$755$	85.6388			3.11672
$756$	0.776903	−	5.23416i	0.0282557	−	0.190365i
$757$	21.9417			0.797486			0.398743	−	0.917063i	$-0.369447\pi$
$757$	21.9417			0.797486			0.398743	+	0.917063i	$0.369447\pi$
$758$	32.7997	+	13.7402i	1.19134	+	0.499067i
$759$	−2.18569	+	3.78573i	−0.0793357	+	0.137413i
$760$	−0.714350	−	0.102790i	−0.0259122	−	0.00372859i
$761$	1.02680	−	0.592825i	0.0372216	−	0.0214899i	−0.481274	−	0.876570i	$-0.659826\pi$
$761$	1.02680	−	0.592825i	0.0372216	−	0.0214899i	0.518495	+	0.855080i	$0.326492\pi$
$762$	3.04211	−	2.31500i	0.110204	−	0.0838636i
$763$	−20.6484	+	2.54120i	−0.747523	+	0.0919977i
$764$	46.0653	+	12.7394i	1.66659	+	0.460896i
$765$	8.67756	+	15.0300i	0.313738	+	0.543410i
$766$	−24.9208	+	3.17942i	−0.900426	+	0.114877i
$767$	1.10090	+	0.635603i	0.0397511	+	0.0229503i
$768$	8.43969	−	13.5931i	0.304541	−	0.490498i
$769$		−	19.0892i		−	0.688373i	−0.938901	−	0.344186i	$-0.888155\pi$
$769$		−	19.0892i		−	0.688373i	0.938901	−	0.344186i	$-0.111845\pi$
$770$	19.0430	−	4.84929i	0.686262	−	0.174756i
$771$		−	17.7514i		−	0.639301i
$772$	38.4770	−	9.98031i	1.38482	−	0.359199i
$773$	−30.7887	−	17.7759i	−1.10739	−	0.639353i	−0.169240	−	0.985575i	$-0.554131\pi$
$773$	−30.7887	−	17.7759i	−1.10739	−	0.639353i	−0.938153	+	0.346222i	$0.887465\pi$
$774$	−1.12813	−	8.84246i	−0.0405498	−	0.317836i
$775$	29.7725	+	51.5674i	1.06946	+	1.85236i
$776$	3.03110	+	7.57379i	0.108810	+	0.271883i
$777$	−8.74770	−	11.6018i	−0.313822	−	0.416212i
$778$	−12.1138	−	15.9185i	−0.434299	−	0.570707i
$779$	0.484346	−	0.279637i	0.0173535	−	0.0100190i
$780$	−2.00000	−	2.03229i	−0.0716115	−	0.0727678i
$781$	−8.82182	+	15.2798i	−0.315670	+	0.546756i
$782$	−7.89335	+	18.8425i	−0.282266	+	0.673806i
$783$	−3.11951			−0.111482
$784$	−26.7928	−	8.13287i	−0.956887	−	0.290460i
$785$	21.0075			0.749790
$786$	−4.24728	+	10.1388i	−0.151496	+	0.361640i
$787$	−21.3018	+	36.8958i	−0.759327	+	1.31519i	0.183868	+	0.982951i	$0.441138\pi$
$787$	−21.3018	+	36.8958i	−0.759327	+	1.31519i	−0.943194	+	0.332241i	$0.892195\pi$
$788$	−26.6818	−	27.1126i	−0.950500	−	0.965847i
$789$	1.80241	−	1.04062i	0.0641675	−	0.0370471i
$790$	−41.2347	−	54.1860i	−1.46706	−	1.92785i
$791$	7.49704	+	9.94309i	0.266564	+	0.353536i
$792$	−1.43162	−	3.57719i	−0.0508706	−	0.127110i
$793$	0.264740	+	0.458543i	0.00940118	+	0.0162833i
$794$	−2.26417	−	17.7469i	−0.0803524	−	0.629814i
$795$	−8.49781	−	4.90621i	−0.301386	−	0.174005i
$796$	−28.7513	+	7.45761i	−1.01906	+	0.264328i
$797$			23.1179i			0.818879i	0.912337	+	0.409440i	$0.134276\pi$
$797$			23.1179i			0.818879i	−0.912337	+	0.409440i	$0.865724\pi$
$798$	0.239983	−	0.0611114i	0.00849529	−	0.00216332i
$799$		−	6.41788i		−	0.227048i
$800$	−44.9362	+	33.0728i	−1.58874	+	1.16930i
$801$	−1.11951	−	0.646349i	−0.0395559	−	0.0228376i
$802$	−34.7635	+	4.43517i	−1.22754	+	0.156611i
$803$	−1.22712	−	2.12544i	−0.0433042	−	0.0750051i
$804$	18.8280	+	5.20690i	0.664011	+	0.183633i
$805$	−32.4865	+	3.99812i	−1.14500	+	0.140915i
$806$	2.51246	−	1.91194i	0.0884976	−	0.0673453i
$807$	−3.08075	+	1.77867i	−0.108448	+	0.0626123i
$808$	17.3256	+	2.49304i	0.609512	+	0.0877047i
$809$	16.0852	−	27.8604i	0.565525	−	0.979518i	−0.431475	−	0.902125i	$-0.642007\pi$
$809$	16.0852	−	27.8604i	0.565525	−	0.979518i	0.997001	−	0.0773937i	$-0.0246598\pi$
$810$	5.02878	+	2.10662i	0.176693	+	0.0740191i
$811$	41.0797			1.44250			0.721251	−	0.692673i	$-0.243567\pi$
$811$	41.0797			1.44250			0.721251	+	0.692673i	$0.243567\pi$
$812$	−2.42356	+	16.3280i	−0.0850502	+	0.573001i
$813$	−12.3680			−0.433764
$814$	−9.75851	−	4.08796i	−0.342035	−	0.143283i
$815$	−9.16942	+	15.8819i	−0.321191	+	0.556319i
$816$	−8.75236	−	15.7363i	−0.306394	−	0.550882i
$817$	0.361288	−	0.208590i	0.0126399	−	0.00729764i
$818$	6.52359	−	4.96435i	0.228092	−	0.173574i
$819$	0.900723	+	0.382035i	0.0314738	+	0.0133494i
$820$	17.3670	−	62.7985i	0.606482	−	2.19302i
$821$	14.6233	+	25.3283i	0.510358	+	0.883965i	0.999928	+	0.0120014i	$0.00382026\pi$
$821$	14.6233	+	25.3283i	0.510358	+	0.883965i	−0.489570	+	0.871964i	$0.662846\pi$
$822$	4.00000	−	0.510324i	0.139516	−	0.0177996i
$823$	−17.0790	−	9.86059i	−0.595338	−	0.343719i	0.171867	−	0.985120i	$-0.445020\pi$
$823$	−17.0790	−	9.86059i	−0.595338	−	0.343719i	−0.767205	+	0.641401i	$0.778353\pi$
$824$	−39.5549	−	31.1135i	−1.37796	−	1.08389i
$825$			13.4362i			0.467790i
$826$	−3.48340	+	12.3815i	−0.121203	+	0.430809i
$827$			16.1125i			0.560286i	0.959958	+	0.280143i	$0.0903819\pi$
$827$			16.1125i			0.560286i	−0.959958	+	0.280143i	$0.909618\pi$
$828$	1.61137	+	6.21230i	0.0559990	+	0.215892i
$829$	−40.9056	−	23.6169i	−1.42071	−	0.820248i	−0.424351	−	0.905498i	$-0.639498\pi$
$829$	−40.9056	−	23.6169i	−1.42071	−	0.820248i	−0.996360	+	0.0852497i	$0.972831\pi$
$830$	−8.47941	−	66.4630i	−0.294325	−	2.30696i
$831$	5.93162	+	10.2739i	0.205766	+	0.356397i
$832$	2.04103	+	2.14154i	0.0707601	+	0.0742446i
$833$	−22.6551	+	21.9024i	−0.784954	+	0.758875i
$834$	6.12901	+	8.05406i	0.212230	+	0.278889i
$835$	−46.9492	+	27.1062i	−1.62475	+	0.938047i
$836$	0.128523	−	0.126481i	0.00444508	−	0.00437444i
$837$	−3.01852	+	5.22824i	−0.104335	+	0.180714i
$838$	−1.32763	+	3.16922i	−0.0458621	+	0.109479i
$839$	−25.3551			−0.875356			−0.437678	−	0.899132i	$-0.644199\pi$
$839$	−25.3551			−0.875356			−0.437678	+	0.899132i	$0.644199\pi$
$840$	14.9333	−	24.6848i	0.515247	−	0.851707i
$841$	−19.2687			−0.664437
$842$	14.1728	−	33.8323i	0.488426	−	1.16594i
$843$	9.67141	−	16.7514i	0.333101	−	0.576948i
$844$	28.0361	−	27.5906i	0.965042	−	0.949707i
$845$	−42.9475	+	24.7958i	−1.47744	+	0.853000i
$846$	−1.22098	−	1.60447i	−0.0419780	−	0.0551628i
$847$	9.44687	−	22.2728i	0.324598	−	0.765304i
$848$	8.73412	+	5.23093i	0.299931	+	0.179631i
$849$	−12.4707	−	21.5998i	−0.427992	−	0.741304i
$850$	7.94668	+	62.2873i	0.272569	+	2.13644i
$851$	15.2620	+	8.81153i	0.523175	+	0.302055i
$852$	6.50376	+	25.0739i	0.222815	+	0.859016i
$853$			24.3802i			0.834763i	0.908731	+	0.417382i	$0.137052\pi$
$853$			24.3802i			0.834763i	−0.908731	+	0.417382i	$0.862948\pi$
$854$	−3.83508	+	3.74075i	−0.131234	+	0.128006i
$855$			0.255162i			0.00872636i
$856$	−10.6549	+	13.5457i	−0.364178	+	0.462982i
$857$	−22.4742	−	12.9755i	−0.767705	−	0.443235i	0.0643503	−	0.997927i	$-0.479502\pi$
$857$	−22.4742	−	12.9755i	−0.767705	−	0.443235i	−0.832055	+	0.554693i	$0.812836\pi$
$858$	0.706693	−	0.0901606i	0.0241261	−	0.00307803i
$859$	28.4213	+	49.2271i	0.969722	+	1.67961i	0.696354	+	0.717698i	$0.254804\pi$
$859$	28.4213	+	49.2271i	0.969722	+	1.67961i	0.273368	+	0.961909i	$0.411862\pi$
$860$	12.9546	−	46.8433i	0.441748	−	1.59734i
$861$	2.73088	+	22.1896i	0.0930681	+	0.756221i
$862$	16.6052	−	12.6363i	0.565576	−	0.430395i
$863$	15.3044	−	8.83597i	0.520966	−	0.300780i	−0.216364	−	0.976313i	$-0.569420\pi$
$863$	15.3044	−	8.83597i	0.520966	−	0.300780i	0.737330	+	0.675533i	$0.236086\pi$
$864$	−5.18187	−	2.26898i	−0.176291	−	0.0771922i
$865$	−3.42568	+	5.93345i	−0.116476	+	0.201743i
$866$	−46.6183	−	19.5290i	−1.58415	−	0.663622i
$867$	−3.26474			−0.110876
$868$	25.0203	+	19.8613i	0.849245	+	0.674135i
$869$	17.0129			0.577122
$870$	−15.6873	−	6.57162i	−0.531850	−	0.222799i
$871$	−1.80597	+	3.12803i	−0.0611930	+	0.105989i
$872$	−3.16765	+	22.0139i	−0.107270	+	0.745485i
$873$	2.49781	−	1.44211i	0.0845381	−	0.0488081i
$874$	−0.239018	+	0.181889i	−0.00808491	+	0.00615250i
$875$	−39.6086	+	29.8647i	−1.33901	+	1.00961i
$876$	−3.47286	−	0.960423i	−0.117337	−	0.0324497i
$877$	6.17283	+	10.6917i	0.208442	+	0.361032i	0.951224	−	0.308502i	$-0.0998275\pi$
$877$	6.17283	+	10.6917i	0.208442	+	0.361032i	−0.742782	+	0.669533i	$0.766494\pi$
$878$	−27.8303	+	3.55062i	−0.939227	+	0.119827i
$879$	5.96028	+	3.44117i	0.201035	+	0.116068i
$880$	0.336461	−	21.0048i	0.0113421	−	0.708072i
$881$		−	33.0442i		−	1.11329i	−0.830751	−	0.556644i	$-0.812089\pi$
$881$		−	33.0442i		−	1.11329i	0.830751	−	0.556644i	$-0.187911\pi$
$882$	−1.49693	+	9.78566i	−0.0504042	+	0.329500i
$883$		−	39.2680i		−	1.32147i	−0.750618	−	0.660737i	$-0.770244\pi$
$883$		−	39.2680i		−	1.32147i	0.750618	−	0.660737i	$-0.229756\pi$
$884$	3.22274	−	0.835927i	0.108393	−	0.0281153i
$885$	−11.4773	−	6.62642i	−0.385805	−	0.222745i
$886$	3.39709	+	26.6269i	0.114128	+	0.894549i
$887$	−19.7517	−	34.2109i	−0.663196	−	1.14869i	−0.979771	−	0.200121i	$-0.935866\pi$
$887$	−19.7517	−	34.2109i	−0.663196	−	1.14869i	0.316576	−	0.948567i	$-0.397467\pi$
$888$	−14.4213	+	5.77153i	−0.483947	+	0.193680i
$889$	−5.71045	+	4.30565i	−0.191522	+	0.144407i
$890$	−4.26816	−	5.60873i	−0.143069	−	0.188005i
$891$	−1.17975	+	0.681127i	−0.0395230	+	0.0228186i
$892$	11.3676	+	11.5511i	0.380614	+	0.386760i
$893$	0.0471792	−	0.0817167i	0.00157879	−	0.00273454i
$894$	−11.6689	+	27.8553i	−0.390268	+	0.931620i
$895$	12.5363			0.419043
$896$	−15.9020	+	25.3599i	−0.531249	+	0.847216i
$897$	−1.18666			−0.0396214
$898$	13.8161	−	32.9808i	0.461048	−	1.10058i
$899$	9.41631	−	16.3095i	0.314052	−	0.543953i
$900$	13.8366	+	14.0600i	0.461220	+	0.468667i
$901$	9.92249	−	5.72875i	0.330566	−	0.190852i
$902$	9.85848	+	12.9549i	0.328251	+	0.431351i
$903$	2.03705	+	16.5519i	0.0677887	+	0.550814i
$904$	12.3595	−	4.94638i	0.411071	−	0.164514i
$905$	45.3026	+	78.4664i	1.50591	+	2.60831i
$906$	3.97565	+	31.1618i	0.132082	+	1.03528i
$907$	−4.46372	−	2.57713i	−0.148215	−	0.0855722i	0.424058	−	0.905635i	$-0.360605\pi$
$907$	−4.46372	−	2.57713i	−0.148215	−	0.0855722i	−0.572274	+	0.820063i	$0.693938\pi$
$908$	−23.3977	+	6.06899i	−0.776480	+	0.201406i
$909$		−	6.18861i		−	0.205263i
$910$	3.72473	+	3.81865i	0.123474	+	0.126587i
$911$			25.8365i			0.856002i	0.903778	+	0.428001i	$0.140782\pi$
$911$			25.8365i			0.856002i	−0.903778	+	0.428001i	$0.859218\pi$
$912$	0.00424013	−	0.264706i	0.000140405	−	0.00876528i
$913$	14.4978	+	8.37031i	0.479807	+	0.277017i
$914$	32.2197	−	4.11062i	1.06573	−	0.135967i
$915$	−2.76002	−	4.78049i	−0.0912434	−	0.158038i
$916$	−45.8444	−	12.6783i	−1.51474	−	0.418903i
$917$	8.03010	−	18.9325i	0.265177	−	0.625207i
$918$	−5.06618	+	3.85529i	−0.167209	+	0.127243i
$919$	−30.6881	+	17.7178i	−1.01231	+	0.584455i	−0.911866	−	0.410488i	$-0.865358\pi$
$919$	−30.6881	+	17.7178i	−1.01231	+	0.584455i	−0.100440	+	0.994943i	$0.532025\pi$
$920$	−4.98372	+	34.6348i	−0.164308	+	1.14188i
$921$	−8.71065	+	15.0873i	−0.287026	+	0.497143i
$922$	−3.85887	−	1.61653i	−0.127085	−	0.0532375i
$923$	−4.78955			−0.157650
$924$	2.64858	+	6.70415i	0.0871318	+	0.220550i
$925$	54.1676			1.78102
$926$	−4.31319	−	1.80685i	−0.141740	−	0.0593768i
$927$	−8.89634	+	15.4089i	−0.292194	+	0.506095i
$928$	16.1649	+	7.07810i	0.530638	+	0.232350i
$929$	47.6452	−	27.5080i	1.56319	−	0.902508i	0.566258	−	0.824228i	$-0.308391\pi$
$929$	47.6452	−	27.5080i	1.56319	−	0.902508i	0.996931	−	0.0782797i	$-0.0249427\pi$
$930$	−26.1934	+	19.9328i	−0.858916	+	0.653622i
$931$	−0.449470	+	0.112334i	−0.0147308	+	0.00368159i
$932$	10.6242	−	38.4169i	0.348008	−	1.25839i
$933$	12.5580	+	21.7512i	0.411132	+	0.712101i
$934$	16.7017	−	2.13082i	0.546498	−	0.0697227i
$935$	−20.4746	−	11.8210i	−0.669592	−	0.386589i
$936$	0.646653	−	0.822096i	0.0211365	−	0.0268710i
$937$		−	6.90001i		−	0.225414i	−0.993628	−	0.112707i	$-0.964048\pi$
$937$		−	6.90001i		−	0.225414i	0.993628	−	0.112707i	$-0.0359521\pi$
$938$	−35.1803	−	9.89755i	−1.14868	−	0.323167i
$939$		−	22.0965i		−	0.721092i
$940$	−2.76002	−	10.6407i	−0.0900218	−	0.347060i
$941$	16.2597	+	9.38756i	0.530052	+	0.306026i	0.741038	−	0.671463i	$-0.234334\pi$
$941$	16.2597	+	9.38756i	0.530052	+	0.306026i	−0.210986	+	0.977489i	$0.567667\pi$
$942$	0.975243	+	7.64411i	0.0317751	+	0.249058i
$943$	−13.5580	−	23.4832i	−0.441511	−	0.764719i
$944$	11.7965	+	7.06499i	0.383942	+	0.229946i
$945$	−9.39039	−	3.98287i	−0.305470	−	0.129563i
$946$	7.35374	+	9.66346i	0.239091	+	0.314186i
$947$	−25.7931	+	14.8916i	−0.838162	+	0.483913i	−0.856639	−	0.515916i	$-0.827452\pi$
$947$	−25.7931	+	14.8916i	−0.838162	+	0.483913i	0.0184768	+	0.999829i	$0.494118\pi$
$948$	17.8027	−	17.5198i	0.578203	−	0.569016i
$949$	0.333115	−	0.576972i	0.0108134	−	0.0187293i
$950$	−0.356704	+	0.851501i	−0.0115730	+	0.0276263i
$951$	−1.62327			−0.0526380
$952$	16.2433	+	29.5124i	0.526447	+	0.956503i
$953$	−23.2676			−0.753711			−0.376856	−	0.926272i	$-0.622995\pi$
$953$	−23.2676			−0.753711			−0.376856	+	0.926272i	$0.622995\pi$
$954$	1.39075	−	3.31990i	0.0450272	−	0.107486i
$955$	46.0653	−	79.7875i	1.49064	−	2.58186i
$956$	13.6989	−	13.4812i	0.443054	−	0.436014i
$957$	3.68023	−	2.12478i	0.118965	−	0.0686844i
$958$	10.1946	+	13.3966i	0.329372	+	0.432823i
$959$	−7.48748	+	0.921485i	−0.241783	+	0.0297563i
$960$	−21.2786	−	22.3264i	−0.686764	−	0.720582i
$961$	−2.72297	−	4.71632i	−0.0878377	−	0.152139i
$962$	−0.363478	−	2.84900i	−0.0117190	−	0.0918555i
$963$	5.27683	+	3.04658i	0.170044	+	0.0981747i
$964$	5.22654	+	20.1498i	0.168335	+	0.648982i
$965$		−	76.6244i		−	2.46663i
$966$	−2.96295	−	11.6354i	−0.0953314	−	0.374364i
$967$		−	16.9691i		−	0.545690i	−0.962058	−	0.272845i	$-0.912035\pi$
$967$		−	16.9691i		−	0.545690i	0.962058	−	0.272845i	$-0.0879646\pi$
$968$	−20.3286	−	15.9903i	−0.653386	−	0.513947i
$969$	−0.258024	−	0.148970i	−0.00828893	−	0.00478561i
$970$	15.5989	−	1.99013i	0.500851	−	0.0638991i
$971$	22.8349	+	39.5512i	0.732806	+	1.26926i	0.955679	+	0.294410i	$0.0951231\pi$
$971$	22.8349	+	39.5512i	0.732806	+	1.26926i	−0.222873	+	0.974847i	$0.571544\pi$
$972$	−0.533092	+	1.92764i	−0.0170989	+	0.0618292i
$973$	−11.3993	−	15.1185i	−0.365445	−	0.484678i
$974$	8.44878	−	6.42939i	0.270717	−	0.206011i
$975$	−3.15875	+	1.82370i	−0.101161	+	0.0584052i
$976$	2.78381	+	5.00516i	0.0891076	+	0.160211i
$977$	23.7102	−	41.0673i	0.758557	−	1.31386i	−0.185029	−	0.982733i	$-0.559238\pi$
$977$	23.7102	−	41.0673i	0.758557	−	1.31386i	0.943586	−	0.331127i	$-0.107429\pi$
$978$	−6.20470	−	2.59923i	−0.198404	−	0.0831141i
$979$	1.76098			0.0562812
$980$	−28.1424	+	46.0565i	−0.898976	+	1.47122i
$981$	7.86325			0.251054
$982$	28.7006	+	12.0230i	0.915873	+	0.383671i
$983$	17.6956	−	30.6497i	0.564402	−	0.977573i	−0.432703	−	0.901536i	$-0.642440\pi$
$983$	17.6956	−	30.6497i	0.564402	−	0.977573i	0.997105	−	0.0760363i	$-0.0242265\pi$
$984$	23.6570	+	3.40409i	0.754159	+	0.108518i
$985$	−63.5029	+	36.6634i	−2.02337	+	1.16819i
$986$	15.8040	−	12.0266i	0.503302	−	0.383005i
$987$	2.27088	+	3.01180i	0.0722831	+	0.0958668i
$988$	0.0471792	+	0.0130475i	0.00150097	+	0.000415095i
$989$	−10.1134	−	17.5169i	−0.321586	−	0.557004i
$990$	−7.36756	+	0.939961i	−0.234156	+	0.0298739i
$991$	−10.0136	−	5.78134i	−0.318092	−	0.183650i	0.332450	−	0.943121i	$-0.392125\pi$
$991$	−10.0136	−	5.78134i	−0.318092	−	0.183650i	−0.650542	+	0.759471i	$0.725458\pi$
$992$	27.5043	−	20.2431i	0.873264	−	0.642718i
$993$			26.6677i			0.846274i
$994$	−11.9590	−	46.9625i	−0.379315	−	1.48956i
$995$			57.2563i			1.81515i
$996$	23.7906	−	6.17089i	0.753833	−	0.195532i
$997$	−10.6832	−	6.16793i	−0.338339	−	0.195340i	0.321198	−	0.947012i	$-0.395914\pi$
$997$	−10.6832	−	6.16793i	−0.338339	−	0.195340i	−0.659537	+	0.751672i	$0.729248\pi$
$998$	−0.252703	−	1.98073i	−0.00799917	−	0.0626988i
$999$	2.74593	+	4.75609i	0.0868774	+	0.150476i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.2.o.a.31.2	yes	8
3.2	odd	2		252.2.bf.g.199.3		8
4.3	odd	2		84.2.o.b.31.4	yes	8
7.2	even	3		588.2.o.b.19.4		8
7.3	odd	6		588.2.b.a.391.3		8
7.4	even	3		588.2.b.b.391.3		8
7.5	odd	6		84.2.o.b.19.4	yes	8
7.6	odd	2		588.2.o.d.31.2		8
8.3	odd	2		1344.2.bl.i.703.4		8
8.5	even	2		1344.2.bl.j.703.4		8
12.11	even	2		252.2.bf.f.199.1		8
21.5	even	6		252.2.bf.f.19.1		8
21.11	odd	6		1764.2.b.i.1567.6		8
21.17	even	6		1764.2.b.j.1567.6		8
28.3	even	6		588.2.b.b.391.4		8
28.11	odd	6		588.2.b.a.391.4		8
28.19	even	6	inner	84.2.o.a.19.2	✓	8
28.23	odd	6		588.2.o.d.19.2		8
28.27	even	2		588.2.o.b.31.4		8
56.5	odd	6		1344.2.bl.i.1279.4		8
56.19	even	6		1344.2.bl.j.1279.4		8
84.11	even	6		1764.2.b.j.1567.5		8
84.47	odd	6		252.2.bf.g.19.3		8
84.59	odd	6		1764.2.b.i.1567.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.2	✓	8	28.19	even	6	inner
84.2.o.a.31.2	yes	8	1.1	even	1	trivial
84.2.o.b.19.4	yes	8	7.5	odd	6
84.2.o.b.31.4	yes	8	4.3	odd	2
252.2.bf.f.19.1		8	21.5	even	6
252.2.bf.f.199.1		8	12.11	even	2
252.2.bf.g.19.3		8	84.47	odd	6
252.2.bf.g.199.3		8	3.2	odd	2
588.2.b.a.391.3		8	7.3	odd	6
588.2.b.a.391.4		8	28.11	odd	6
588.2.b.b.391.3		8	7.4	even	3
588.2.b.b.391.4		8	28.3	even	6
588.2.o.b.19.4		8	7.2	even	3
588.2.o.b.31.4		8	28.27	even	2
588.2.o.d.19.2		8	28.23	odd	6
588.2.o.d.31.2		8	7.6	odd	2
1344.2.bl.i.703.4		8	8.3	odd	2
1344.2.bl.i.1279.4		8	56.5	odd	6
1344.2.bl.j.703.4		8	8.5	even	2
1344.2.bl.j.1279.4		8	56.19	even	6
1764.2.b.i.1567.5		8	84.59	odd	6
1764.2.b.i.1567.6		8	21.11	odd	6
1764.2.b.j.1567.5		8	84.11	even	6
1764.2.b.j.1567.6		8	21.17	even	6

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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	84.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.546424 + 1.30439i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.40284 - 1.42549i) q^{4} +(-3.33878 + 1.92764i) q^{5} +(-0.856419 - 1.12541i) q^{6} +(1.59285 + 2.11254i) q^{7} +(2.62594 - 1.05092i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.546424 + 1.30439i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.40284 - 1.42549i) q^{4} +(-3.33878 + 1.92764i) q^{5} +(-0.856419 - 1.12541i) q^{6} +(1.59285 + 2.11254i) q^{7} +(2.62594 - 1.05092i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.690004 - 5.40836i) q^{10} +(1.17975 + 0.681127i) q^{11} +(1.93594 - 0.502151i) q^{12} +0.369798i q^{13} +(-3.62594 + 0.923343i) q^{14} -3.85529i q^{15} +(-0.0640649 + 3.99949i) q^{16} +(3.89853 + 2.25082i) q^{17} +(1.40284 - 0.178976i) q^{18} +(0.0330925 + 0.0573178i) q^{19} +(7.43162 + 2.05523i) q^{20} +(-2.62594 + 0.323174i) q^{21} +(-1.53309 + 1.16666i) q^{22} +(2.77902 - 1.60447i) q^{23} +(-0.402843 + 2.79959i) q^{24} +(4.93162 - 8.54182i) q^{25} +(-0.482359 - 0.202066i) q^{26} +1.00000 q^{27} +(0.776903 - 5.23416i) q^{28} -3.11951 q^{29} +(5.02878 + 2.10662i) q^{30} +(-3.01852 + 5.22824i) q^{31} +(-5.18187 - 2.26898i) q^{32} +(-1.17975 + 0.681127i) q^{33} +(-5.06618 + 3.85529i) q^{34} +(-9.39039 - 3.98287i) q^{35} +(-0.533092 + 1.92764i) q^{36} +(2.74593 + 4.75609i) q^{37} +(-0.0928470 + 0.0118455i) q^{38} +(-0.320254 - 0.184899i) q^{39} +(-6.74162 + 8.57068i) q^{40} -8.45017i q^{41} +(1.01333 - 3.60183i) q^{42} -6.30324i q^{43} +(-0.684056 - 2.63723i) q^{44} +(3.33878 + 1.92764i) q^{45} +(0.574323 + 4.50164i) q^{46} +(-0.712838 - 1.23467i) q^{47} +(-3.43162 - 2.05523i) q^{48} +(-1.92568 + 6.72992i) q^{49} +(8.44708 + 11.1002i) q^{50} +(-3.89853 + 2.25082i) q^{51} +(0.527144 - 0.518768i) q^{52} +(1.27259 - 2.20420i) q^{53} +(-0.546424 + 1.30439i) q^{54} -5.25188 q^{55} +(6.40284 + 3.87345i) q^{56} -0.0661849 q^{57} +(1.70457 - 4.06904i) q^{58} +(1.71879 - 2.97703i) q^{59} +(-5.49569 + 5.40836i) q^{60} +(1.23998 - 0.715904i) q^{61} +(-5.17024 - 6.79415i) q^{62} +(1.03309 - 2.43572i) q^{63} +(5.79112 - 5.51933i) q^{64} +(-0.712838 - 1.23467i) q^{65} +(-0.243811 - 1.91103i) q^{66} +(8.45877 + 4.88367i) q^{67} +(-2.26050 - 8.71488i) q^{68} +3.20894i q^{69} +(10.3263 - 10.0724i) q^{70} +12.9518i q^{71} +(-2.22310 - 1.74867i) q^{72} +(-1.56024 - 0.900803i) q^{73} +(-7.70422 + 0.982912i) q^{74} +(4.93162 + 8.54182i) q^{75} +(0.0352827 - 0.127581i) q^{76} +(0.440245 + 3.57719i) q^{77} +(0.416174 - 0.316702i) q^{78} +(10.8156 - 6.24438i) q^{79} +(-7.49569 - 13.4769i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(11.0223 + 4.61737i) q^{82} +12.2889 q^{83} +(4.14446 + 3.28990i) q^{84} -17.3551 q^{85} +(8.22186 + 3.44424i) q^{86} +(1.55975 - 2.70157i) q^{87} +(3.81375 + 0.548774i) q^{88} +(1.11951 - 0.646349i) q^{89} +(-4.33878 + 3.30174i) q^{90} +(-0.781213 + 0.589031i) q^{91} +(-6.18569 - 1.71066i) q^{92} +(-3.01852 - 5.22824i) q^{93} +(2.00000 - 0.255162i) q^{94} +(-0.220977 - 0.127581i) q^{95} +(4.55593 - 3.35314i) q^{96} +2.88422i q^{97} +(-7.72617 - 6.18921i) q^{98} -1.36225i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9	\( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9} - 5 q^{10} + 6 q^{11} - q^{12} - 12 q^{14} - 17 q^{16} + q^{18} - 6 q^{19} + 22 q^{20} - 4 q^{21} - 6 q^{22} + 7 q^{24} + 2 q^{25} + 18 q^{26} + 8 q^{27} + 13 q^{28} - 16 q^{29} + 13 q^{30} + 6 q^{31} - 9 q^{32} - 6 q^{33} - 28 q^{34} - 12 q^{35} + 2 q^{36} + 6 q^{37} + 10 q^{38} - 6 q^{39} - 17 q^{40} + 9 q^{42} - 23 q^{44} + 24 q^{46} + 4 q^{47} + 10 q^{48} + 4 q^{49} + 2 q^{50} + 16 q^{52} - 4 q^{53} + q^{54} - 8 q^{55} + 41 q^{56} + 12 q^{57} + 37 q^{58} - 14 q^{59} - 23 q^{60} + 12 q^{61} - 48 q^{62} + 2 q^{63} + 2 q^{64} + 4 q^{65} - 15 q^{66} + 42 q^{67} - 26 q^{68} + 3 q^{70} - 11 q^{72} - 18 q^{73} - 10 q^{74} + 2 q^{75} + 44 q^{76} + 8 q^{77} - 6 q^{78} - 6 q^{79} - 39 q^{80} - 4 q^{81} - 10 q^{82} + 4 q^{83} - 14 q^{84} - 32 q^{85} + 36 q^{86} + 8 q^{87} - 37 q^{88} - 8 q^{90} - 34 q^{91} - 28 q^{92} + 6 q^{93} + 16 q^{94} - 24 q^{95} + 21 q^{96} - 53 q^{98}+O(q^{100}) \) 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9 - 5 * q^10 + 6 * q^11 - q^12 - 12 * q^14 - 17 * q^16 + q^18 - 6 * q^19 + 22 * q^20 - 4 * q^21 - 6 * q^22 + 7 * q^24 + 2 * q^25 + 18 * q^26 + 8 * q^27 + 13 * q^28 - 16 * q^29 + 13 * q^30 + 6 * q^31 - 9 * q^32 - 6 * q^33 - 28 * q^34 - 12 * q^35 + 2 * q^36 + 6 * q^37 + 10 * q^38 - 6 * q^39 - 17 * q^40 + 9 * q^42 - 23 * q^44 + 24 * q^46 + 4 * q^47 + 10 * q^48 + 4 * q^49 + 2 * q^50 + 16 * q^52 - 4 * q^53 + q^54 - 8 * q^55 + 41 * q^56 + 12 * q^57 + 37 * q^58 - 14 * q^59 - 23 * q^60 + 12 * q^61 - 48 * q^62 + 2 * q^63 + 2 * q^64 + 4 * q^65 - 15 * q^66 + 42 * q^67 - 26 * q^68 + 3 * q^70 - 11 * q^72 - 18 * q^73 - 10 * q^74 + 2 * q^75 + 44 * q^76 + 8 * q^77 - 6 * q^78 - 6 * q^79 - 39 * q^80 - 4 * q^81 - 10 * q^82 + 4 * q^83 - 14 * q^84 - 32 * q^85 + 36 * q^86 + 8 * q^87 - 37 * q^88 - 8 * q^90 - 34 * q^91 - 28 * q^92 + 6 * q^93 + 16 * q^94 - 24 * q^95 + 21 * q^96 - 53 * q^98

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