LMFDB - Embedded newform 357.2.d.b.188.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(188,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("357.188");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.d (of order $2$, degree $1$, 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			188.1
Character	$\chi$	$=$	357.188
Dual form			357.2.d.b.188.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67583i q^{2} +(1.42596 + 0.983178i) q^{3} -5.16008 q^{4} +2.78395 q^{5} +(2.63082 - 3.81563i) q^{6} +(1.08035 + 2.41513i) q^{7} +8.45583i q^{8} +(1.06672 + 2.80394i) q^{9} +O(q^{10})$	\(q-2.67583i q^{2} +(1.42596 + 0.983178i) q^{3} -5.16008 q^{4} +2.78395 q^{5} +(2.63082 - 3.81563i) q^{6} +(1.08035 + 2.41513i) q^{7} +8.45583i q^{8} +(1.06672 + 2.80394i) q^{9} -7.44937i q^{10} -5.34689i q^{11} +(-7.35806 - 5.07327i) q^{12} -2.98095i q^{13} +(6.46247 - 2.89084i) q^{14} +(3.96979 + 2.73712i) q^{15} +12.3062 q^{16} +1.00000 q^{17} +(7.50289 - 2.85437i) q^{18} +0.834999i q^{19} -14.3654 q^{20} +(-0.833962 + 4.50605i) q^{21} -14.3074 q^{22} -1.99584i q^{23} +(-8.31359 + 12.0577i) q^{24} +2.75036 q^{25} -7.97653 q^{26} +(-1.23568 + 5.04709i) q^{27} +(-5.57470 - 12.4622i) q^{28} +8.46598i q^{29} +(7.32406 - 10.6225i) q^{30} -2.71996i q^{31} -16.0177i q^{32} +(5.25695 - 7.62445i) q^{33} -2.67583i q^{34} +(3.00764 + 6.72358i) q^{35} +(-5.50436 - 14.4686i) q^{36} -6.32140 q^{37} +2.23432 q^{38} +(2.93081 - 4.25072i) q^{39} +23.5406i q^{40} -4.31944 q^{41} +(12.0574 + 2.23154i) q^{42} -6.73365 q^{43} +27.5904i q^{44} +(2.96969 + 7.80603i) q^{45} -5.34053 q^{46} +6.90600 q^{47} +(17.5482 + 12.0992i) q^{48} +(-4.66568 + 5.21838i) q^{49} -7.35949i q^{50} +(1.42596 + 0.983178i) q^{51} +15.3819i q^{52} +0.951595i q^{53} +(13.5052 + 3.30647i) q^{54} -14.8855i q^{55} +(-20.4219 + 9.13528i) q^{56} +(-0.820953 + 1.19067i) q^{57} +22.6535 q^{58} -4.99982 q^{59} +(-20.4844 - 14.1237i) q^{60} +1.79277i q^{61} -7.27815 q^{62} +(-5.61945 + 5.60551i) q^{63} -18.2483 q^{64} -8.29881i q^{65} +(-20.4018 - 14.0667i) q^{66} -2.35890 q^{67} -5.16008 q^{68} +(1.96227 - 2.84599i) q^{69} +(17.9912 - 8.04794i) q^{70} -2.43325i q^{71} +(-23.7097 + 9.02001i) q^{72} -1.83657i q^{73} +16.9150i q^{74} +(3.92189 + 2.70409i) q^{75} -4.30866i q^{76} +(12.9134 - 5.77653i) q^{77} +(-11.3742 - 7.84235i) q^{78} -1.09758 q^{79} +34.2599 q^{80} +(-6.72421 + 5.98205i) q^{81} +11.5581i q^{82} +11.9874 q^{83} +(4.30331 - 23.2516i) q^{84} +2.78395 q^{85} +18.0181i q^{86} +(-8.32357 + 12.0721i) q^{87} +45.2124 q^{88} -13.9468 q^{89} +(20.8876 - 7.94640i) q^{90} +(7.19938 - 3.22048i) q^{91} +10.2987i q^{92} +(2.67420 - 3.87855i) q^{93} -18.4793i q^{94} +2.32459i q^{95} +(15.7483 - 22.8407i) q^{96} +15.3525i q^{97} +(13.9635 + 12.4846i) q^{98} +(14.9924 - 5.70364i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 24 q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 22 * q - 24 * q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	$ 22 q - 24 q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} - 8 q^{14} - 4 q^{15} + 20 q^{16} + 22 q^{17} + 8 q^{18} - 30 q^{20} - 4 q^{21} - 12 q^{22} - 44 q^{24} + 14 q^{25} - 24 q^{26} + 6 q^{27} + 8 q^{28} + 5 q^{30} + 28 q^{33} + 10 q^{35} - 3 q^{36} - 16 q^{37} + 88 q^{38} - 14 q^{39} - 16 q^{41} + 19 q^{42} - 24 q^{43} - 46 q^{45} + 4 q^{46} - 16 q^{47} + 25 q^{48} + 6 q^{49} + 36 q^{54} - 40 q^{56} - 6 q^{57} + 24 q^{58} + 24 q^{59} - 21 q^{60} - 20 q^{62} - 6 q^{63} - 20 q^{64} - 116 q^{66} + 8 q^{67} - 24 q^{68} + 6 q^{69} + 4 q^{70} - 7 q^{72} + 54 q^{75} + 6 q^{77} + 2 q^{78} + 16 q^{79} + 128 q^{80} - 4 q^{81} + 8 q^{83} + 42 q^{84} - 48 q^{87} + 32 q^{88} - 100 q^{89} + 47 q^{90} + 18 q^{91} + 20 q^{93} + 88 q^{96} - 8 q^{98} + 18 q^{99}+O(q^{100}) $ 22 * q - 24 * q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 - 8 * q^14 - 4 * q^15 + 20 * q^16 + 22 * q^17 + 8 * q^18 - 30 * q^20 - 4 * q^21 - 12 * q^22 - 44 * q^24 + 14 * q^25 - 24 * q^26 + 6 * q^27 + 8 * q^28 + 5 * q^30 + 28 * q^33 + 10 * q^35 - 3 * q^36 - 16 * q^37 + 88 * q^38 - 14 * q^39 - 16 * q^41 + 19 * q^42 - 24 * q^43 - 46 * q^45 + 4 * q^46 - 16 * q^47 + 25 * q^48 + 6 * q^49 + 36 * q^54 - 40 * q^56 - 6 * q^57 + 24 * q^58 + 24 * q^59 - 21 * q^60 - 20 * q^62 - 6 * q^63 - 20 * q^64 - 116 * q^66 + 8 * q^67 - 24 * q^68 + 6 * q^69 + 4 * q^70 - 7 * q^72 + 54 * q^75 + 6 * q^77 + 2 * q^78 + 16 * q^79 + 128 * q^80 - 4 * q^81 + 8 * q^83 + 42 * q^84 - 48 * q^87 + 32 * q^88 - 100 * q^89 + 47 * q^90 + 18 * q^91 + 20 * q^93 + 88 * q^96 - 8 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	2.67583i		−	1.89210i	−0.324022	−	0.946049i	$-0.605035\pi$
$2$		−	2.67583i		−	1.89210i	0.324022	−	0.946049i	$-0.394965\pi$
$3$	1.42596	+	0.983178i	0.823278	+	0.567638i
$3$	1.42596	+	0.983178i	0.823278	+	0.567638i
$4$	−5.16008			−2.58004
$5$	2.78395			1.24502			0.622509	−	0.782612i	$-0.286113\pi$
$5$	2.78395			1.24502			0.622509	+	0.782612i	$0.286113\pi$
$6$	2.63082	−	3.81563i	1.07403	−	1.55772i
$7$	1.08035	+	2.41513i	0.408335	+	0.912832i
$7$	1.08035	+	2.41513i	0.408335	+	0.912832i
$8$			8.45583i			2.98959i
$9$	1.06672	+	2.80394i	0.355574	+	0.934648i
$10$		−	7.44937i		−	2.35570i
$11$		−	5.34689i		−	1.61215i	−0.591814	−	0.806075i	$-0.701588\pi$
$11$		−	5.34689i		−	1.61215i	0.591814	−	0.806075i	$-0.298412\pi$
$12$	−7.35806	−	5.07327i	−2.12409	−	1.46453i
$13$		−	2.98095i		−	0.826767i	−0.910557	−	0.413384i	$-0.864347\pi$
$13$		−	2.98095i		−	0.826767i	0.910557	−	0.413384i	$-0.135653\pi$
$14$	6.46247	−	2.89084i	1.72717	−	0.772610i
$15$	3.96979	+	2.73712i	1.02500	+	0.706720i
$16$	12.3062			3.07656
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$	7.50289	−	2.85437i	1.76845	−	0.672780i
$19$			0.834999i			0.191562i	0.995402	+	0.0957810i	$0.0305348\pi$
$19$			0.834999i			0.191562i	−0.995402	+	0.0957810i	$0.969465\pi$
$20$	−14.3654			−3.21219
$21$	−0.833962	+	4.50605i	−0.181986	+	0.983301i
$22$	−14.3074			−3.05035
$23$		−	1.99584i		−	0.416161i	−0.978112	−	0.208081i	$-0.933278\pi$
$23$		−	1.99584i		−	0.416161i	0.978112	−	0.208081i	$-0.0667216\pi$
$24$	−8.31359	+	12.0577i	−1.69700	+	2.46126i
$25$	2.75036			0.550071
$26$	−7.97653			−1.56433
$27$	−1.23568	+	5.04709i	−0.237806	+	0.971313i
$28$	−5.57470	−	12.4622i	−1.05352	−	2.35514i
$29$			8.46598i			1.57209i	0.618167	+	0.786047i	$0.287875\pi$
$29$			8.46598i			1.57209i	−0.618167	+	0.786047i	$0.712125\pi$
$30$	7.32406	−	10.6225i	1.33718	−	1.93939i
$31$		−	2.71996i		−	0.488519i	−0.969710	−	0.244259i	$-0.921455\pi$
$31$		−	2.71996i		−	0.488519i	0.969710	−	0.244259i	$-0.0785448\pi$
$32$		−	16.0177i		−	2.83156i
$33$	5.25695	−	7.62445i	0.915118	−	1.32725i
$34$		−	2.67583i		−	0.458901i
$35$	3.00764	+	6.72358i	0.508384	+	1.13649i
$36$	−5.50436	−	14.4686i	−0.917393	−	2.41143i
$37$	−6.32140			−1.03923			−0.519616	−	0.854400i	$-0.673925\pi$
$37$	−6.32140			−1.03923			−0.519616	+	0.854400i	$0.673925\pi$
$38$	2.23432			0.362454
$39$	2.93081	−	4.25072i	0.469305	−	0.680660i
$40$			23.5406i			3.72209i
$41$	−4.31944			−0.674583			−0.337292	−	0.941400i	$-0.609511\pi$
$41$	−4.31944			−0.674583			−0.337292	+	0.941400i	$0.609511\pi$
$42$	12.0574	+	2.23154i	1.86050	+	0.344335i
$43$	−6.73365			−1.02687			−0.513436	−	0.858128i	$-0.671627\pi$
$43$	−6.73365			−1.02687			−0.513436	+	0.858128i	$0.671627\pi$
$44$			27.5904i			4.15941i
$45$	2.96969	+	7.80603i	0.442696	+	1.16365i
$46$	−5.34053			−0.787418
$47$	6.90600			1.00734			0.503672	−	0.863895i	$-0.331982\pi$
$47$	6.90600			1.00734			0.503672	+	0.863895i	$0.331982\pi$
$48$	17.5482	+	12.0992i	2.53286	+	1.74637i
$49$	−4.66568	+	5.21838i	−0.666525	+	0.745482i
$50$		−	7.35949i		−	1.04079i
$51$	1.42596	+	0.983178i	0.199674	+	0.137673i
$52$			15.3819i			2.13309i
$53$			0.951595i			0.130712i	0.997862	+	0.0653558i	$0.0208182\pi$
$53$			0.951595i			0.130712i	−0.997862	+	0.0653558i	$0.979182\pi$
$54$	13.5052	+	3.30647i	1.83782	+	0.449953i
$55$		−	14.8855i		−	2.00716i
$56$	−20.4219	+	9.13528i	−2.72899	+	1.22075i
$57$	−0.820953	+	1.19067i	−0.108738	+	0.157709i
$58$	22.6535			2.97456
$59$	−4.99982			−0.650921			−0.325460	−	0.945556i	$-0.605519\pi$
$59$	−4.99982			−0.650921			−0.325460	+	0.945556i	$0.605519\pi$
$60$	−20.4844	−	14.1237i	−2.64453	−	1.82336i
$61$			1.79277i			0.229541i	0.993392	+	0.114770i	$0.0366132\pi$
$61$			1.79277i			0.229541i	−0.993392	+	0.114770i	$0.963387\pi$
$62$	−7.27815			−0.924326
$63$	−5.61945	+	5.60551i	−0.707984	+	0.706228i
$64$	−18.2483			−2.28104
$65$		−	8.29881i		−	1.02934i
$66$	−20.4018	−	14.0667i	−2.51128	−	1.73149i
$67$	−2.35890			−0.288186			−0.144093	−	0.989564i	$-0.546026\pi$
$67$	−2.35890			−0.288186			−0.144093	+	0.989564i	$0.546026\pi$
$68$	−5.16008			−0.625751
$69$	1.96227	−	2.84599i	0.236229	−	0.342616i
$70$	17.9912	−	8.04794i	2.15036	−	0.961913i
$71$		−	2.43325i		−	0.288774i	−0.989521	−	0.144387i	$-0.953879\pi$
$71$		−	2.43325i		−	0.288774i	0.989521	−	0.144387i	$-0.0461210\pi$
$72$	−23.7097	+	9.02001i	−2.79421	+	1.06302i
$73$		−	1.83657i		−	0.214954i	−0.994208	−	0.107477i	$-0.965723\pi$
$73$		−	1.83657i		−	0.214954i	0.994208	−	0.107477i	$-0.0342772\pi$
$74$			16.9150i			1.96633i
$75$	3.92189	+	2.70409i	0.452861	+	0.312241i
$76$		−	4.30866i		−	0.494237i
$77$	12.9134	−	5.77653i	1.47162	−	0.658297i
$78$	−11.3742	−	7.84235i	−1.28788	−	0.887971i
$79$	−1.09758			−0.123487			−0.0617436	−	0.998092i	$-0.519666\pi$
$79$	−1.09758			−0.123487			−0.0617436	+	0.998092i	$0.519666\pi$
$80$	34.2599			3.83037
$81$	−6.72421	+	5.98205i	−0.747135	+	0.664672i
$82$			11.5581i			1.27638i
$83$	11.9874			1.31579			0.657896	−	0.753108i	$-0.271446\pi$
$83$	11.9874			1.31579			0.657896	+	0.753108i	$0.271446\pi$
$84$	4.30331	−	23.2516i	0.469530	−	2.53695i
$85$	2.78395			0.301961
$86$			18.0181i			1.94294i
$87$	−8.32357	+	12.0721i	−0.892380	+	1.29427i
$88$	45.2124			4.81966
$89$	−13.9468			−1.47836			−0.739178	−	0.673510i	$-0.764786\pi$
$89$	−13.9468			−1.47836			−0.739178	+	0.673510i	$0.764786\pi$
$90$	20.8876	−	7.94640i	2.20175	−	0.837624i
$91$	7.19938	−	3.22048i	0.754700	−	0.337598i
$92$			10.2987i			1.07371i
$93$	2.67420	−	3.87855i	0.277302	−	0.402187i
$94$		−	18.4793i		−	1.90599i
$95$			2.32459i			0.238498i
$96$	15.7483	−	22.8407i	1.60730	−	2.33116i
$97$			15.3525i			1.55881i	0.626517	+	0.779407i	$0.284480\pi$
$97$			15.3525i			1.55881i	−0.626517	+	0.779407i	$0.715520\pi$
$98$	13.9635	+	12.4846i	1.41053	+	1.26113i
$99$	14.9924	−	5.70364i	1.50679	−	0.573238i
$100$	−14.1920			−1.41920
$101$	12.0693			1.20094			0.600470	−	0.799647i	$-0.294980\pi$
$101$	12.0693			1.20094			0.600470	+	0.799647i	$0.294980\pi$
$102$	2.63082	−	3.81563i	0.260490	−	0.377803i
$103$		−	5.94173i		−	0.585456i	−0.956196	−	0.292728i	$-0.905437\pi$
$103$		−	5.94173i		−	0.585456i	0.956196	−	0.292728i	$-0.0945630\pi$
$104$	25.2064			2.47169
$105$	−2.32171	+	12.5446i	−0.226575	+	1.22423i
$106$	2.54631			0.247319
$107$		−	15.5721i		−	1.50541i	−0.658355	−	0.752707i	$-0.728747\pi$
$107$		−	15.5721i		−	1.50541i	0.658355	−	0.752707i	$-0.271253\pi$
$108$	6.37619	−	26.0434i	0.613549	−	2.50602i
$109$	−15.3573			−1.47096			−0.735479	−	0.677547i	$-0.763043\pi$
$109$	−15.3573			−1.47096			−0.735479	+	0.677547i	$0.763043\pi$
$110$	−39.8310			−3.79774
$111$	−9.01405	−	6.21506i	−0.855576	−	0.589907i
$112$	13.2951	+	29.7211i	1.25627	+	2.80838i
$113$			2.15854i			0.203058i	0.994833	+	0.101529i	$0.0323735\pi$
$113$			2.15854i			0.203058i	−0.994833	+	0.101529i	$0.967626\pi$
$114$	3.18605	+	2.19673i	0.298400	+	0.205743i
$115$		−	5.55631i		−	0.518128i
$116$		−	43.6851i		−	4.05606i
$117$	8.35843	−	3.17984i	0.772737	−	0.293977i
$118$			13.3787i			1.23161i
$119$	1.08035	+	2.41513i	0.0990357	+	0.221394i
$120$	−23.1446	+	33.5679i	−2.11280	+	3.06432i
$121$	−17.5893			−1.59903
$122$	4.79715			0.434313
$123$	−6.15935	−	4.24678i	−0.555370	−	0.382919i
$124$			14.0352i			1.26040i
$125$	−6.26289			−0.560170
$126$	14.9994	+	15.0367i	1.33625	+	1.33958i
$127$	1.44766			0.128459			0.0642297	−	0.997935i	$-0.479541\pi$
$127$	1.44766			0.128459			0.0642297	+	0.997935i	$0.479541\pi$
$128$			16.7940i			1.48439i
$129$	−9.60190	−	6.62037i	−0.845401	−	0.582891i
$130$	−22.2062			−1.94761
$131$	20.1637			1.76171			0.880857	−	0.473382i	$-0.156967\pi$
$131$	20.1637			1.76171			0.880857	+	0.473382i	$0.156967\pi$
$132$	−27.1263	+	39.3428i	−2.36104	+	3.42435i
$133$	−2.01663	+	0.902093i	−0.174864	+	0.0782214i
$134$			6.31203i			0.545276i
$135$	−3.44006	+	14.0508i	−0.296073	+	1.20930i
$136$			8.45583i			0.725082i
$137$			0.525958i			0.0449357i	0.999748	+	0.0224678i	$0.00715233\pi$
$137$			0.525958i			0.0449357i	−0.999748	+	0.0224678i	$0.992848\pi$
$138$	−7.61538	−	5.25069i	−0.648264	−	0.446969i
$139$		−	0.0693433i		−	0.00588162i	−0.999996	−	0.00294081i	$-0.999064\pi$
$139$		−	0.0693433i		−	0.00588162i	0.999996	−	0.00294081i	$-0.000936091\pi$
$140$	−15.5197	−	34.6942i	−1.31165	−	2.93220i
$141$	9.84767	+	6.78983i	0.829324	+	0.571807i
$142$	−6.51098			−0.546389
$143$	−15.9388			−1.33287
$144$	13.1273	+	34.5060i	1.09394	+	2.87550i
$145$			23.5688i			1.95729i
$146$	−4.91435			−0.406714
$147$	−11.7837	+	2.85400i	−0.971900	+	0.235394i
$148$	32.6189			2.68126
$149$		−	11.6950i		−	0.958091i	−0.877790	−	0.479045i	$-0.840983\pi$
$149$		−	11.6950i		−	0.958091i	0.877790	−	0.479045i	$-0.159017\pi$
$150$	7.23569	−	10.4943i	0.590792	−	0.856859i
$151$	0.152068			0.0123751			0.00618757	−	0.999981i	$-0.498030\pi$
$151$	0.152068			0.0123751			0.00618757	+	0.999981i	$0.498030\pi$
$152$	−7.06061			−0.572691
$153$	1.06672	+	2.80394i	0.0862393	+	0.226686i
$154$	−15.4570	−	34.5542i	−1.24556	−	2.78445i
$155$		−	7.57221i		−	0.608215i
$156$	−15.1232	+	21.9340i	−1.21082	+	1.75613i
$157$			1.77515i			0.141672i	0.997488	+	0.0708362i	$0.0225668\pi$
$157$			1.77515i			0.141672i	−0.997488	+	0.0708362i	$0.977433\pi$
$158$			2.93693i			0.233650i
$159$	−0.935588	+	1.35694i	−0.0741970	+	0.107612i
$160$		−	44.5925i		−	3.52535i
$161$	4.82020	−	2.15621i	0.379885	−	0.169933i
$162$	16.0070	+	17.9929i	1.25763	+	1.41365i
$163$	−12.5338			−0.981724			−0.490862	−	0.871237i	$-0.663318\pi$
$163$	−12.5338			−0.981724			−0.490862	+	0.871237i	$0.663318\pi$
$164$	22.2886			1.74045
$165$	14.6351	−	21.2261i	1.13934	−	1.65245i
$166$		−	32.0764i		−	2.48961i
$167$	−17.9445			−1.38859			−0.694293	−	0.719693i	$-0.744283\pi$
$167$	−17.9445			−1.38859			−0.694293	+	0.719693i	$0.744283\pi$
$168$	−38.1024	−	7.05185i	−2.93967	−	0.544062i
$169$	4.11392			0.316456
$170$		−	7.44937i		−	0.571341i
$171$	−2.34129	+	0.890711i	−0.179043	+	0.0681144i
$172$	34.7461			2.64937
$173$	−1.23096			−0.0935883			−0.0467941	−	0.998905i	$-0.514900\pi$
$173$	−1.23096			−0.0935883			−0.0467941	+	0.998905i	$0.514900\pi$
$174$	32.3030	+	22.2725i	2.44889	+	1.68847i
$175$	2.97135	+	6.64246i	0.224613	+	0.502123i
$176$		−	65.8001i		−	4.95987i
$177$	−7.12954	−	4.91571i	−0.535889	−	0.369488i
$178$			37.3193i			2.79720i
$179$			10.9374i			0.817497i	0.912647	+	0.408748i	$0.134035\pi$
$179$			10.9374i			0.817497i	−0.912647	+	0.408748i	$0.865965\pi$
$180$	−15.3238	−	40.2797i	−1.14217	−	3.00227i
$181$			14.4451i			1.07370i	0.843679	+	0.536849i	$0.180385\pi$
$181$			14.4451i			1.07370i	−0.843679	+	0.536849i	$0.819615\pi$
$182$	−8.61746	−	19.2643i	−0.638769	−	1.42797i
$183$	−1.76261	+	2.55642i	−0.130296	+	0.188976i
$184$	16.8765			1.24415
$185$	−17.5984			−1.29386
$186$	−10.3783	−	7.15572i	−0.760977	−	0.524683i
$187$		−	5.34689i		−	0.391004i
$188$	−35.6355			−2.59898
$189$	−13.5243	+	2.46831i	−0.983750	+	0.179543i
$190$	6.22022			0.451262
$191$			9.59596i			0.694339i	0.937802	+	0.347170i	$0.112857\pi$
$191$			9.59596i			0.694339i	−0.937802	+	0.347170i	$0.887143\pi$
$192$	−26.0214	−	17.9414i	−1.87793	−	1.29481i
$193$	−1.91128			−0.137577			−0.0687885	−	0.997631i	$-0.521913\pi$
$193$	−1.91128			−0.137577			−0.0687885	+	0.997631i	$0.521913\pi$
$194$	41.0808			2.94943
$195$	8.15921	−	11.8338i	0.584293	−	0.847434i
$196$	24.0753	−	26.9272i	1.71966	−	1.92337i
$197$			4.67680i			0.333208i	0.986024	+	0.166604i	$0.0532802\pi$
$197$			4.67680i			0.333208i	−0.986024	+	0.166604i	$0.946720\pi$
$198$	−15.2620	−	40.1171i	−1.08462	−	2.85100i
$199$			10.2974i			0.729964i	0.931015	+	0.364982i	$0.118925\pi$
$199$			10.2974i			0.729964i	−0.931015	+	0.364982i	$0.881075\pi$
$200$			23.2565i			1.64449i
$201$	−3.36370	−	2.31922i	−0.237257	−	0.163585i
$202$		−	32.2954i		−	2.27230i
$203$	−20.4464	+	9.14624i	−1.43506	+	0.641940i
$204$	−7.35806	−	5.07327i	−0.515167	−	0.355200i
$205$	−12.0251			−0.839869
$206$	−15.8991			−1.10774
$207$	5.59622	−	2.12900i	0.388964	−	0.147976i
$208$		−	36.6843i		−	2.54360i
$209$	4.46465			0.308826
$210$	33.5673	+	6.21250i	2.31636	+	0.428703i
$211$	21.4556			1.47707			0.738533	−	0.674217i	$-0.235519\pi$
$211$	21.4556			1.47707			0.738533	+	0.674217i	$0.235519\pi$
$212$		−	4.91030i		−	0.337241i
$213$	2.39232	−	3.46972i	0.163919	−	0.237741i
$214$	−41.6684			−2.84839
$215$	−18.7461			−1.27847
$216$	−42.6773	−	10.4487i	−2.90382	−	0.710943i
$217$	6.56904	−	2.93851i	0.445936	−	0.199479i
$218$			41.0935i			2.78320i
$219$	1.80567	−	2.61887i	0.122016	−	0.176967i
$220$			76.8101i			5.17854i
$221$		−	2.98095i		−	0.200521i
$222$	−16.6305	+	24.1201i	−1.11616	+	1.61883i
$223$			2.44145i			0.163491i	0.996653	+	0.0817457i	$0.0260495\pi$
$223$			2.44145i			0.163491i	−0.996653	+	0.0817457i	$0.973950\pi$
$224$	38.6849	−	17.3048i	2.58474	−	1.15623i
$225$	2.93386	+	7.71184i	0.195591	+	0.514123i
$226$	5.77589			0.384207
$227$	4.20785			0.279285			0.139642	−	0.990202i	$-0.455405\pi$
$227$	4.20785			0.279285			0.139642	+	0.990202i	$0.455405\pi$
$228$	4.23618	−	6.14397i	0.280548	−	0.406894i
$229$			5.07308i			0.335238i	0.985852	+	0.167619i	$0.0536079\pi$
$229$			5.07308i			0.335238i	−0.985852	+	0.167619i	$0.946392\pi$
$230$	−14.8677			−0.980350
$231$	24.0934	+	4.45911i	1.58523	+	0.293388i
$232$	−71.5869			−4.69991
$233$		−	13.5072i		−	0.884883i	−0.896797	−	0.442442i	$-0.854112\pi$
$233$		−	13.5072i		−	0.884883i	0.896797	−	0.442442i	$-0.145888\pi$
$234$	−8.50873	−	22.3657i	−0.556233	−	1.46209i
$235$	19.2259			1.25416
$236$	25.7994			1.67940
$237$	−1.56510	−	1.07911i	−0.101664	−	0.0700960i
$238$	6.46247	−	2.89084i	0.418900	−	0.187385i
$239$		−	9.24657i		−	0.598111i	−0.954236	−	0.299055i	$-0.903328\pi$
$239$		−	9.24657i		−	0.598111i	0.954236	−	0.299055i	$-0.0966715\pi$
$240$	48.8532	+	33.6836i	3.15346	+	2.17427i
$241$		−	27.8414i		−	1.79342i	−0.442615	−	0.896712i	$-0.645949\pi$
$241$		−	27.8414i		−	1.79342i	0.442615	−	0.896712i	$-0.354051\pi$
$242$			47.0660i			3.02551i
$243$	−15.4699	+	1.91906i	−0.992393	+	0.123108i
$244$		−	9.25082i		−	0.592223i
$245$	−12.9890	+	14.5277i	−0.829837	+	0.928139i
$246$	−11.3637	+	16.4814i	−0.724521	+	1.05081i
$247$	2.48909			0.158377
$248$	22.9995			1.46047
$249$	17.0936	+	11.7858i	1.08326	+	0.746894i
$250$			16.7584i			1.05990i
$251$	17.7364			1.11951			0.559756	−	0.828658i	$-0.310895\pi$
$251$	17.7364			1.11951			0.559756	+	0.828658i	$0.310895\pi$
$252$	28.9968	−	28.9249i	1.82663	−	1.82210i
$253$	−10.6715			−0.670914
$254$		−	3.87371i		−	0.243058i
$255$	3.96979	+	2.73712i	0.248598	+	0.171405i
$256$	8.44116			0.527573
$257$	17.8810			1.11539			0.557693	−	0.830047i	$-0.311687\pi$
$257$	17.8810			1.11539			0.557693	+	0.830047i	$0.311687\pi$
$258$	−17.7150	+	25.6931i	−1.10289	+	1.59958i
$259$	−6.82933	−	15.2670i	−0.424354	−	0.948644i
$260$			42.8225i			2.65574i
$261$	−23.7381	+	9.03084i	−1.46935	+	0.558995i
$262$		−	53.9548i		−	3.33334i
$263$		−	20.9548i		−	1.29213i	−0.763283	−	0.646065i	$-0.776414\pi$
$263$		−	20.9548i		−	1.29213i	0.763283	−	0.646065i	$-0.223586\pi$
$264$	64.4711	+	44.4519i	3.96792	+	2.73582i
$265$			2.64919i			0.162738i
$266$	2.41385	+	5.39616i	0.148003	+	0.330860i
$267$	−19.8876	−	13.7122i	−1.21710	−	0.839172i
$268$	12.1721			0.743531
$269$	24.1813			1.47436			0.737181	−	0.675695i	$-0.236156\pi$
$269$	24.1813			1.47436			0.737181	+	0.675695i	$0.236156\pi$
$270$	37.5976	+	9.20502i	2.28812	+	0.560200i
$271$		−	30.6013i		−	1.85890i	−0.368949	−	0.929450i	$-0.620282\pi$
$271$		−	30.6013i		−	1.85890i	0.368949	−	0.929450i	$-0.379718\pi$
$272$	12.3062			0.746175
$273$	13.4323	+	2.48600i	0.812961	+	0.150460i
$274$	1.40738			0.0850227
$275$		−	14.7059i		−	0.886797i
$276$	−10.1254	+	14.6855i	−0.609480	+	0.883963i
$277$	27.3358			1.64245			0.821225	−	0.570605i	$-0.193291\pi$
$277$	27.3358			1.64245			0.821225	+	0.570605i	$0.193291\pi$
$278$	−0.185551			−0.0111286
$279$	7.62661	−	2.90143i	0.456593	−	0.173704i
$280$	−56.8535	+	25.4321i	−3.39765	+	1.51986i
$281$			9.76503i			0.582533i	0.956642	+	0.291267i	$0.0940767\pi$
$281$			9.76503i			0.582533i	−0.956642	+	0.291267i	$0.905923\pi$
$282$	18.1684	−	26.3507i	1.08191	−	1.56916i
$283$			12.9271i			0.768435i	0.923243	+	0.384218i	$0.125529\pi$
$283$			12.9271i			0.768435i	−0.923243	+	0.384218i	$0.874471\pi$
$284$			12.5558i			0.745048i
$285$	−2.28549	+	3.31477i	−0.135381	+	0.196350i
$286$			42.6497i			2.52193i
$287$	−4.66652	−	10.4320i	−0.275456	−	0.615782i
$288$	44.9129	−	17.0865i	2.64652	−	1.00683i
$289$	1.00000			0.0588235
$290$	63.0662			3.70338
$291$	−15.0943	+	21.8921i	−0.884843	+	1.28334i
$292$			9.47683i			0.554590i
$293$	11.7510			0.686501			0.343251	−	0.939244i	$-0.388472\pi$
$293$	11.7510			0.686501			0.343251	+	0.939244i	$0.388472\pi$
$294$	7.63682	+	31.5311i	0.445388	+	1.83893i
$295$	−13.9192			−0.810408
$296$		−	53.4527i		−	3.10687i
$297$	26.9862	+	6.60704i	1.56590	+	0.383379i
$298$	−31.2938			−1.81280
$299$	−5.94950			−0.344069
$300$	−20.2373	−	13.9533i	−1.16840	−	0.805595i
$301$	−7.27471	−	16.2626i	−0.419307	−	0.937361i
$302$		−	0.406909i		−	0.0234150i
$303$	17.2103	+	11.8663i	0.988707	+	0.681699i
$304$			10.2757i			0.589351i
$305$			4.99097i			0.285782i
$306$	7.50289	−	2.85437i	0.428911	−	0.163173i
$307$		−	2.04712i		−	0.116835i	−0.998292	−	0.0584177i	$-0.981394\pi$
$307$		−	2.04712i		−	0.116835i	0.998292	−	0.0584177i	$-0.0186055\pi$
$308$	−66.6343	+	29.8073i	−3.79684	+	1.69843i
$309$	5.84178	−	8.47266i	0.332327	−	0.481993i
$310$	−20.2620			−1.15080
$311$	−18.3400			−1.03996			−0.519982	−	0.854177i	$-0.674061\pi$
$311$	−18.3400			−1.03996			−0.519982	+	0.854177i	$0.674061\pi$
$312$	35.9434	+	24.7824i	2.03489	+	1.40303i
$313$			21.4288i			1.21123i	0.795758	+	0.605614i	$0.207073\pi$
$313$			21.4288i			1.21123i	−0.795758	+	0.605614i	$0.792927\pi$
$314$	4.75000			0.268058
$315$	−15.6442	+	15.6054i	−0.881453	+	0.879267i
$316$	5.66358			0.318602
$317$			1.47209i			0.0826806i	0.999145	+	0.0413403i	$0.0131628\pi$
$317$			1.47209i			0.0826806i	−0.999145	+	0.0413403i	$0.986837\pi$
$318$	3.63093	+	2.50348i	0.203613	+	0.140388i
$319$	45.2667			2.53445
$320$	−50.8023			−2.83994
$321$	15.3102	−	22.2052i	0.854531	−	1.23938i
$322$	−5.76965	−	12.8981i	−0.321530	−	0.718781i
$323$			0.834999i			0.0464606i
$324$	34.6975	−	30.8678i	1.92764	−	1.71488i
$325$		−	8.19868i		−	0.454781i
$326$			33.5384i			1.85752i
$327$	−21.8988	−	15.0989i	−1.21101	−	0.834973i
$328$		−	36.5245i		−	2.01673i
$329$	7.46091	+	16.6789i	0.411333	+	0.919535i
$330$	−56.7974	−	39.1610i	−3.12659	−	2.15574i
$331$	−0.256112			−0.0140772			−0.00703859	−	0.999975i	$-0.502240\pi$
$331$	−0.256112			−0.0140772			−0.00703859	+	0.999975i	$0.502240\pi$
$332$	−61.8561			−3.39480
$333$	−6.74316	−	17.7248i	−0.369523	−	0.971315i
$334$			48.0164i			2.62734i
$335$	−6.56706			−0.358797
$336$	−10.2629	+	55.4525i	−0.559889	+	3.02518i
$337$	−23.8694			−1.30025			−0.650126	−	0.759827i	$-0.725284\pi$
$337$	−23.8694			−1.30025			−0.650126	+	0.759827i	$0.725284\pi$
$338$		−	11.0082i		−	0.598765i
$339$	−2.12223	+	3.07799i	−0.115264	+	0.167174i
$340$	−14.3654			−0.779072
$341$	−14.5433			−0.787565
$342$	2.38339	+	6.26490i	0.128879	+	0.338767i
$343$	−17.6436	−	5.63052i	−0.952666	−	0.304020i
$344$		−	56.9386i		−	3.06992i
$345$	5.46284	−	7.92307i	0.294109	−	0.426564i
$346$			3.29385i			0.177078i
$347$		−	27.5960i		−	1.48143i	−0.671818	−	0.740716i	$-0.734487\pi$
$347$		−	27.5960i		−	1.48143i	0.671818	−	0.740716i	$-0.265513\pi$
$348$	42.9503	−	62.2932i	2.30238	−	3.33927i
$349$		−	4.87320i		−	0.260856i	−0.991458	−	0.130428i	$-0.958365\pi$
$349$		−	4.87320i		−	0.260856i	0.991458	−	0.130428i	$-0.0416352\pi$
$350$	17.7741	−	7.95084i	0.950066	−	0.424990i
$351$	15.0451	+	3.68350i	0.803050	+	0.196610i
$352$	−85.6452			−4.56490
$353$	9.41827			0.501284			0.250642	−	0.968080i	$-0.419358\pi$
$353$	9.41827			0.501284			0.250642	+	0.968080i	$0.419358\pi$
$354$	−13.1536	+	19.0774i	−0.699107	+	1.01395i
$355$		−	6.77404i		−	0.359529i
$356$	71.9665			3.81422
$357$	−0.833962	+	4.50605i	−0.0441380	+	0.238486i
$358$	29.2665			1.54678
$359$		−	23.0062i		−	1.21422i	−0.794618	−	0.607110i	$-0.792329\pi$
$359$		−	23.0062i		−	1.21422i	0.794618	−	0.607110i	$-0.207671\pi$
$360$	−66.0065	+	25.1112i	−3.47885	+	1.32348i
$361$	18.3028			0.963304
$362$	38.6527			2.03154
$363$	−25.0816	−	17.2934i	−1.31644	−	0.907668i
$364$	−37.1493	+	16.6179i	−1.94715	+	0.871015i
$365$		−	5.11291i		−	0.267622i
$366$	6.84054	+	4.71645i	0.357561	+	0.246533i
$367$		−	23.5934i		−	1.23156i	−0.787916	−	0.615782i	$-0.788840\pi$
$367$		−	23.5934i		−	1.23156i	0.787916	−	0.615782i	$-0.211160\pi$
$368$		−	24.5613i		−	1.28034i
$369$	−4.60764	−	12.1115i	−0.239864	−	0.630498i
$370$			47.0904i			2.44811i
$371$	−2.29822	+	1.02806i	−0.119318	+	0.0533741i
$372$	−13.7991	+	20.0136i	−0.715450	+	1.03766i
$373$	−2.39810			−0.124169			−0.0620846	−	0.998071i	$-0.519775\pi$
$373$	−2.39810			−0.124169			−0.0620846	+	0.998071i	$0.519775\pi$
$374$	−14.3074			−0.739818
$375$	−8.93063	−	6.15754i	−0.461176	−	0.317974i
$376$			58.3960i			3.01154i
$377$	25.2367			1.29976
$378$	6.60479	+	36.1888i	0.339714	+	1.86135i
$379$	13.1355			0.674725			0.337362	−	0.941375i	$-0.390465\pi$
$379$	13.1355			0.674725			0.337362	+	0.941375i	$0.390465\pi$
$380$		−	11.9951i		−	0.615334i
$381$	2.06431	+	1.42331i	0.105758	+	0.0729185i
$382$	25.6772			1.31376
$383$	−6.10135			−0.311764			−0.155882	−	0.987776i	$-0.549822\pi$
$383$	−6.10135			−0.311764			−0.155882	+	0.987776i	$0.549822\pi$
$384$	−16.5115	+	23.9475i	−0.842597	+	1.22207i
$385$	35.9503	−	16.0815i	1.83220	−	0.819591i
$386$			5.11427i			0.260309i
$387$	−7.18292	−	18.8808i	−0.365128	−	0.959763i
$388$		−	79.2203i		−	4.02180i
$389$		−	2.41930i		−	0.122663i	−0.998117	−	0.0613316i	$-0.980465\pi$
$389$		−	2.41930i		−	0.122663i	0.998117	−	0.0613316i	$-0.0195347\pi$
$390$	−31.6652	−	21.8327i	−1.60343	−	1.10554i
$391$		−	1.99584i		−	0.100934i
$392$	−44.1257	−	39.4522i	−2.22868	−	1.99264i
$393$	28.7527	+	19.8246i	1.45038	+	1.00002i
$394$	12.5143			0.630463
$395$	−3.05560			−0.153744
$396$	−77.3619	+	29.4312i	−3.88758	+	1.47898i
$397$			2.29296i			0.115080i	0.998343	+	0.0575401i	$0.0183257\pi$
$397$			2.29296i			0.115080i	−0.998343	+	0.0575401i	$0.981674\pi$
$398$	27.5541			1.38116
$399$	−3.76255	−	0.696358i	−0.188363	−	0.0348615i
$400$	33.8465			1.69233
$401$			34.4071i			1.71821i	0.511800	+	0.859105i	$0.328979\pi$
$401$			34.4071i			1.71821i	−0.511800	+	0.859105i	$0.671021\pi$
$402$	−6.20585	+	9.00070i	−0.309520	+	0.448914i
$403$	−8.10806			−0.403891
$404$	−62.2785			−3.09847
$405$	−18.7198	+	16.6537i	−0.930197	+	0.827529i
$406$	24.4738	+	54.7112i	1.21461	+	2.71527i
$407$			33.7998i			1.67540i
$408$	−8.31359	+	12.0577i	−0.411584	+	0.596944i
$409$			14.3380i			0.708969i	0.935062	+	0.354485i	$0.115344\pi$
$409$			14.3380i			0.708969i	−0.935062	+	0.354485i	$0.884656\pi$
$410$			32.1771i			1.58911i
$411$	−0.517111	+	0.749995i	−0.0255072	+	0.0369945i
$412$			30.6598i			1.51050i
$413$	−5.40156	−	12.0752i	−0.265794	−	0.594182i
$414$	−5.69685	−	14.9745i	−0.279985	−	0.735959i
$415$	33.3724			1.63819
$416$	−47.7481			−2.34104
$417$	0.0681768	−	0.0988807i	0.00333863	−	0.00484221i
$418$		−	11.9467i		−	0.584330i
$419$	30.6994			1.49976			0.749882	−	0.661572i	$-0.230110\pi$
$419$	30.6994			1.49976			0.749882	+	0.661572i	$0.230110\pi$
$420$	11.9802	−	64.7311i	0.584573	−	3.15856i
$421$	37.7143			1.83808			0.919042	−	0.394159i	$-0.128964\pi$
$421$	37.7143			1.83808			0.919042	+	0.394159i	$0.128964\pi$
$422$		−	57.4117i		−	2.79476i
$423$	7.36677	+	19.3640i	0.358185	+	0.941512i
$424$	−8.04653			−0.390774
$425$	2.75036			0.133412
$426$	−9.28439	−	6.40145i	−0.449830	−	0.310151i
$427$	−4.32976	+	1.93682i	−0.209532	+	0.0937294i
$428$			80.3534i			3.88403i
$429$	−22.7281	−	15.6707i	−1.09732	−	0.756590i
$430$			50.1614i			2.41900i
$431$		−	28.2977i		−	1.36305i	−0.731794	−	0.681526i	$-0.761317\pi$
$431$		−	28.2977i		−	1.36305i	0.731794	−	0.681526i	$-0.238683\pi$
$432$	−15.2065	+	62.1106i	−0.731625	+	2.98830i
$433$			24.2985i			1.16771i	0.811858	+	0.583855i	$0.198456\pi$
$433$			24.2985i			1.16771i	−0.811858	+	0.583855i	$0.801544\pi$
$434$	−7.86296	−	17.5777i	−0.377434	−	0.843754i
$435$	−23.1724	+	33.6082i	−1.11103	+	1.61139i
$436$	79.2446			3.79513
$437$	1.66652			0.0797206
$438$	−7.00766	−	4.83168i	−0.334839	−	0.230867i
$439$		−	31.1810i		−	1.48819i	−0.668075	−	0.744094i	$-0.732881\pi$
$439$		−	31.1810i		−	1.48819i	0.668075	−	0.744094i	$-0.267119\pi$
$440$	125.869			6.00057
$441$	−19.6090	−	7.51576i	−0.933763	−	0.357893i
$442$	−7.97653			−0.379405
$443$		−	1.31714i		−	0.0625794i	−0.999510	−	0.0312897i	$-0.990039\pi$
$443$		−	1.31714i		−	0.0625794i	0.999510	−	0.0312897i	$-0.00996145\pi$
$444$	46.5132	+	32.0702i	2.20742	+	1.52198i
$445$	−38.8271			−1.84058
$446$	6.53290			0.309342
$447$	11.4983	−	16.6766i	0.543849	−	0.788775i
$448$	−19.7146	−	44.0720i	−0.931428	−	2.08221i
$449$		−	9.27554i		−	0.437740i	−0.975754	−	0.218870i	$-0.929763\pi$
$449$		−	9.27554i		−	0.437740i	0.975754	−	0.218870i	$-0.0702370\pi$
$450$	20.6356	−	7.85052i	0.972771	−	0.370077i
$451$			23.0956i			1.08753i
$452$		−	11.1382i		−	0.523899i
$453$	0.216843	+	0.149510i	0.0101882	+	0.00702460i
$454$		−	11.2595i		−	0.528435i
$455$	20.0427	−	8.96564i	0.939615	−	0.420316i
$456$	−10.0681	−	6.94184i	−0.471484	−	0.325081i
$457$	−17.0243			−0.796362			−0.398181	−	0.917307i	$-0.630358\pi$
$457$	−17.0243			−0.796362			−0.398181	+	0.917307i	$0.630358\pi$
$458$	13.5747			0.634304
$459$	−1.23568	+	5.04709i	−0.0576765	+	0.235578i
$460$			28.6710i			1.33679i
$461$	−24.6313			−1.14719			−0.573597	−	0.819138i	$-0.694452\pi$
$461$	−24.6313			−1.14719			−0.573597	+	0.819138i	$0.694452\pi$
$462$	11.9318	−	64.4698i	0.555119	−	2.99941i
$463$	−19.3382			−0.898721			−0.449361	−	0.893350i	$-0.648348\pi$
$463$	−19.3382			−0.898721			−0.449361	+	0.893350i	$0.648348\pi$
$464$			104.184i			4.83664i
$465$	7.44484	−	10.7977i	0.345246	−	0.500730i
$466$	−36.1429			−1.67429
$467$	5.05465			0.233901			0.116951	−	0.993138i	$-0.462688\pi$
$467$	5.05465			0.233901			0.116951	+	0.993138i	$0.462688\pi$
$468$	−43.1301	+	16.4082i	−1.99369	+	0.758471i
$469$	−2.54845	−	5.69705i	−0.117676	−	0.263065i
$470$		−	51.4453i		−	2.37300i
$471$	−1.74529	+	2.53129i	−0.0804187	+	0.116636i
$472$		−	42.2776i		−	1.94599i
$473$			36.0041i			1.65547i
$474$	−2.88753	+	4.18795i	−0.132629	+	0.192359i
$475$			2.29654i			0.105373i
$476$	−5.57470	−	12.4622i	−0.255516	−	0.571206i
$477$	−2.66822	+	1.01509i	−0.122169	+	0.0464776i
$478$	−24.7423			−1.13168
$479$	13.5467			0.618964			0.309482	−	0.950905i	$-0.399844\pi$
$479$	13.5467			0.618964			0.309482	+	0.950905i	$0.399844\pi$
$480$	43.8424	−	63.5871i	2.00112	−	2.90234i
$481$			18.8438i			0.859202i
$482$	−74.4990			−3.39333
$483$	8.99335	+	1.66445i	0.409212	+	0.0757353i
$484$	90.7620			4.12555
$485$			42.7407i			1.94075i
$486$	5.13509	+	41.3948i	0.232932	+	1.87771i
$487$	−6.64214			−0.300984			−0.150492	−	0.988611i	$-0.548086\pi$
$487$	−6.64214			−0.300984			−0.150492	+	0.988611i	$0.548086\pi$
$488$	−15.1594			−0.686232
$489$	−17.8727	−	12.3230i	−0.808232	−	0.557264i
$490$	38.8736	+	34.7564i	1.75613	+	1.57013i
$491$			3.69105i			0.166575i	0.996526	+	0.0832874i	$0.0265420\pi$
$491$			3.69105i			0.166575i	−0.996526	+	0.0832874i	$0.973458\pi$
$492$	31.7827	+	21.9137i	1.43288	+	0.987947i
$493$			8.46598i			0.381289i
$494$		−	6.66039i		−	0.299665i
$495$	41.7380	−	15.8786i	1.87598	−	0.713692i
$496$		−	33.4724i		−	1.50296i
$497$	5.87662	−	2.62877i	0.263602	−	0.117916i
$498$	31.5368	−	45.7396i	1.41320	−	2.04964i
$499$	−27.1625			−1.21596			−0.607981	−	0.793952i	$-0.708020\pi$
$499$	−27.1625			−1.21596			−0.607981	+	0.793952i	$0.708020\pi$
$500$	32.3170			1.44526
$501$	−25.5881	−	17.6426i	−1.14319	−	0.788214i
$502$		−	47.4596i		−	2.11823i
$503$	31.4733			1.40332			0.701662	−	0.712510i	$-0.252442\pi$
$503$	31.4733			1.40332			0.701662	+	0.712510i	$0.252442\pi$
$504$	−47.3993	−	47.5171i	−2.11133	−	2.11658i
$505$	33.6003			1.49519
$506$			28.5552i			1.26944i
$507$	5.86629	+	4.04472i	0.260531	+	0.179632i
$508$	−7.47006			−0.331430
$509$	−24.4060			−1.08178			−0.540888	−	0.841095i	$-0.681912\pi$
$509$	−24.4060			−1.08178			−0.540888	+	0.841095i	$0.681912\pi$
$510$	7.32406	−	10.6225i	0.324315	−	0.470372i
$511$	4.43555	−	1.98414i	0.196217	−	0.0877732i
$512$			11.0008i			0.486171i
$513$	−4.21431	−	1.03179i	−0.186067	−	0.0455546i
$514$		−	47.8466i		−	2.11042i
$515$		−	16.5415i		−	0.728903i
$516$	49.5466	+	34.1616i	2.18117	+	1.50388i
$517$		−	36.9256i		−	1.62399i
$518$	−40.8519	+	18.2741i	−1.79493	+	0.802920i
$519$	−1.75530	−	1.21025i	−0.0770492	−	0.0531243i
$520$	70.1733			3.07730
$521$	38.5229			1.68772			0.843860	−	0.536564i	$-0.180278\pi$
$521$	38.5229			1.68772			0.843860	+	0.536564i	$0.180278\pi$
$522$	24.1650	+	63.5193i	1.05767	+	2.78016i
$523$			27.4237i			1.19915i	0.800317	+	0.599577i	$0.204664\pi$
$523$			27.4237i			1.19915i	−0.800317	+	0.599577i	$0.795336\pi$
$524$	−104.046			−4.54529
$525$	−2.29369	+	12.3932i	−0.100105	+	0.540885i
$526$	−56.0716			−2.44484
$527$		−	2.71996i		−	0.118483i
$528$	64.6933	−	93.8283i	2.81541	−	4.08335i
$529$	19.0166			0.826810
$530$	7.08879			0.307917
$531$	−5.33341	−	14.0192i	−0.231450	−	0.608382i
$532$	10.4060	−	4.65487i	0.451155	−	0.201814i
$533$			12.8761i			0.557724i
$534$	−36.6915	+	53.2158i	−1.58780	+	2.30287i
$535$		−	43.3520i		−	1.87427i
$536$		−	19.9465i		−	0.861557i
$537$	−10.7534	+	15.5962i	−0.464043	+	0.673027i
$538$		−	64.7052i		−	2.78964i
$539$	27.9021	+	24.9469i	1.20183	+	1.07454i
$540$	17.7510	−	72.5033i	0.763880	−	3.12005i
$541$	8.35543			0.359228			0.179614	−	0.983737i	$-0.442515\pi$
$541$	8.35543			0.359228			0.179614	+	0.983737i	$0.442515\pi$
$542$	−81.8841			−3.51722
$543$	−14.2021	+	20.5982i	−0.609472	+	0.883952i
$544$		−	16.0177i		−	0.686755i
$545$	−42.7538			−1.83137
$546$	6.65212	−	35.9427i	0.284685	−	1.53820i
$547$	14.8411			0.634561			0.317281	−	0.948332i	$-0.397230\pi$
$547$	14.8411			0.634561			0.317281	+	0.948332i	$0.397230\pi$
$548$		−	2.71399i		−	0.115936i
$549$	−5.02683	+	1.91238i	−0.214540	+	0.0816185i
$550$	−39.3504			−1.67791
$551$	−7.06909			−0.301153
$552$	24.0652	+	16.5926i	1.02428	+	0.706227i
$553$	−1.18577	−	2.65079i	−0.0504241	−	0.112723i
$554$		−	73.1460i		−	3.10768i
$555$	−25.0946	−	17.3024i	−1.06521	−	0.734445i
$556$			0.357817i			0.0151748i
$557$		−	18.8736i		−	0.799702i	−0.916580	−	0.399851i	$-0.869062\pi$
$557$		−	18.8736i		−	0.799702i	0.916580	−	0.399851i	$-0.130938\pi$
$558$	−7.76375	−	20.4075i	−0.328666	−	0.863920i
$559$			20.0727i			0.848984i
$560$	37.0127	+	82.7420i	1.56407	+	3.49649i
$561$	5.25695	−	7.62445i	0.221949	−	0.321905i
$562$	26.1296			1.10221
$563$	−29.3812			−1.23827			−0.619135	−	0.785284i	$-0.712517\pi$
$563$	−29.3812			−1.23827			−0.619135	+	0.785284i	$0.712517\pi$
$564$	−50.8147	−	35.0360i	−2.13969	−	1.47528i
$565$			6.00926i			0.252812i
$566$	34.5907			1.45396
$567$	−21.7119	−	9.77711i	−0.911816	−	0.410600i
$568$	20.5752			0.863315
$569$			14.7047i			0.616455i	0.951313	+	0.308227i	$0.0997358\pi$
$569$			14.7047i			0.616455i	−0.951313	+	0.308227i	$0.900264\pi$
$570$	8.86978	+	6.11558i	0.371514	+	0.256154i
$571$	−8.48454			−0.355067			−0.177534	−	0.984115i	$-0.556812\pi$
$571$	−8.48454			−0.355067			−0.177534	+	0.984115i	$0.556812\pi$
$572$	82.2456			3.43886
$573$	−9.43454	+	13.6835i	−0.394134	+	0.571634i
$574$	−27.9143	+	12.4868i	−1.16512	+	0.521190i
$575$		−	5.48927i		−	0.228918i
$576$	−19.4659	−	51.1673i	−0.811078	−	2.13197i
$577$		−	11.7737i		−	0.490147i	−0.969505	−	0.245073i	$-0.921188\pi$
$577$		−	11.7737i		−	0.490147i	0.969505	−	0.245073i	$-0.0788121\pi$
$578$		−	2.67583i		−	0.111300i
$579$	−2.72541	−	1.87913i	−0.113264	−	0.0780940i
$580$		−	121.617i		−	5.04987i
$581$	12.9507	+	28.9512i	0.537284	+	1.20110i
$582$	58.5796	+	40.3898i	2.42820	+	1.67421i
$583$	5.08808			0.210727
$584$	15.5297			0.642624
$585$	23.2694	−	8.85251i	0.962072	−	0.366006i
$586$		−	31.4437i		−	1.29893i
$587$	−2.32336			−0.0958952			−0.0479476	−	0.998850i	$-0.515268\pi$
$587$	−2.32336			−0.0958952			−0.0479476	+	0.998850i	$0.515268\pi$
$588$	60.8046	−	14.7268i	2.50754	−	0.607325i
$589$	2.27116			0.0935816
$590$			37.2455i			1.53337i
$591$	−4.59813	+	6.66893i	−0.189142	+	0.274323i
$592$	−77.7926			−3.19725
$593$	−37.1240			−1.52450			−0.762250	−	0.647282i	$-0.775905\pi$
$593$	−37.1240			−1.52450			−0.762250	+	0.647282i	$0.775905\pi$
$594$	17.6793	−	72.2107i	0.725391	−	2.96284i
$595$	3.00764	+	6.72358i	0.123301	+	0.275640i
$596$			60.3470i			2.47191i
$597$	−10.1242	+	14.6837i	−0.414356	+	0.600964i
$598$			15.9199i			0.651012i
$599$		−	9.41234i		−	0.384578i	−0.981338	−	0.192289i	$-0.938409\pi$
$599$		−	9.41234i		−	0.384578i	0.981338	−	0.192289i	$-0.0615911\pi$
$600$	−22.8653	+	33.1629i	−0.933473	+	1.35387i
$601$			33.9641i			1.38542i	0.721214	+	0.692712i	$0.243584\pi$
$601$			33.9641i			1.38542i	−0.721214	+	0.692712i	$0.756416\pi$
$602$	−43.5160	+	19.4659i	−1.77358	+	0.793371i
$603$	−2.51629	−	6.61424i	−0.102471	−	0.269353i
$604$	−0.784683			−0.0319283
$605$	−48.9676			−1.99082
$606$	31.7521	−	46.0519i	1.28984	−	1.87073i
$607$			2.01854i			0.0819302i	0.999161	+	0.0409651i	$0.0130432\pi$
$607$			2.01854i			0.0819302i	−0.999161	+	0.0409651i	$0.986957\pi$
$608$	13.3748			0.542420
$609$	−38.1482	−	7.06031i	−1.54584	−	0.286098i
$610$	13.3550			0.540728
$611$		−	20.5864i		−	0.832839i
$612$	−5.50436	−	14.4686i	−0.222501	−	0.584857i
$613$	−4.44209			−0.179415			−0.0897073	−	0.995968i	$-0.528593\pi$
$613$	−4.44209			−0.179415			−0.0897073	+	0.995968i	$0.528593\pi$
$614$	−5.47776			−0.221064
$615$	−17.1473	−	11.8228i	−0.691446	−	0.476742i
$616$	48.8454	+	109.194i	1.96804	+	4.39954i
$617$		−	35.1073i		−	1.41337i	−0.707530	−	0.706683i	$-0.750190\pi$
$617$		−	35.1073i		−	1.41337i	0.707530	−	0.706683i	$-0.249810\pi$
$618$	−22.6714	−	15.6316i	−0.911978	−	0.628796i
$619$			39.0447i			1.56934i	0.619914	+	0.784670i	$0.287167\pi$
$619$			39.0447i			1.56934i	−0.619914	+	0.784670i	$0.712833\pi$
$620$			39.0732i			1.56922i
$621$	10.0732	+	2.46621i	0.404223	+	0.0989657i
$622$			49.0747i			1.96771i
$623$	−15.0674	−	33.6833i	−0.603664	−	1.34949i
$624$	36.0672	−	52.3103i	1.44384	−	2.09409i
$625$	−31.1873			−1.24749
$626$	57.3399			2.29176
$627$	6.36641	+	4.38955i	0.254250	+	0.175302i
$628$		−	9.15991i		−	0.365520i
$629$	−6.32140			−0.252051
$630$	41.7576	+	41.8614i	1.66366	+	1.66780i
$631$	−19.6543			−0.782425			−0.391212	−	0.920300i	$-0.627944\pi$
$631$	−19.6543			−0.782425			−0.391212	+	0.920300i	$0.627944\pi$
$632$		−	9.28093i		−	0.369176i
$633$	30.5949	+	21.0947i	1.21604	+	0.838440i
$634$	3.93905			0.156440
$635$	4.03022			0.159934
$636$	4.82771	−	7.00190i	0.191431	−	0.277643i
$637$	15.5557	+	13.9082i	0.616340	+	0.551062i
$638$		−	121.126i		−	4.79543i
$639$	6.82271	−	2.59560i	0.269902	−	0.102680i
$640$			46.7535i			1.84809i
$641$		−	33.4883i		−	1.32271i	−0.750075	−	0.661353i	$-0.769982\pi$
$641$		−	33.4883i		−	1.32271i	0.750075	−	0.661353i	$-0.230018\pi$
$642$	−59.4175	−	40.9675i	−2.34502	−	1.61686i
$643$			48.2882i			1.90430i	0.305632	+	0.952150i	$0.401132\pi$
$643$			48.2882i			1.90430i	−0.305632	+	0.952150i	$0.598868\pi$
$644$	−24.8726	+	11.1262i	−0.980119	+	0.438434i
$645$	−26.7312	−	18.4308i	−1.05254	−	0.725711i
$646$	2.23432			0.0879080
$647$	4.30338			0.169183			0.0845916	−	0.996416i	$-0.473041\pi$
$647$	4.30338			0.169183			0.0845916	+	0.996416i	$0.473041\pi$
$648$	−50.5832	−	56.8588i	−1.98710	−	2.23363i
$649$			26.7335i			1.04938i
$650$	−21.9383			−0.860490
$651$	12.2563	+	2.26834i	0.480361	+	0.0889033i
$652$	64.6754			2.53289
$653$			43.7684i			1.71279i	0.516322	+	0.856395i	$0.327301\pi$
$653$			43.7684i			1.71279i	−0.516322	+	0.856395i	$0.672699\pi$
$654$	−40.4022	+	58.5976i	−1.57985	+	2.29135i
$655$	56.1348			2.19337
$656$	−53.1561			−2.07540
$657$	5.14964	−	1.95911i	0.200906	−	0.0764320i
$658$	44.6298	−	19.9641i	1.73985	−	0.778283i
$659$		−	0.350007i		−	0.0136343i	−0.999977	−	0.00681717i	$-0.997830\pi$
$659$		−	0.350007i		−	0.0136343i	0.999977	−	0.00681717i	$-0.00216999\pi$
$660$	−75.5181	+	109.528i	−2.93954	+	4.26338i
$661$		−	10.0415i		−	0.390568i	−0.980747	−	0.195284i	$-0.937437\pi$
$661$		−	10.0415i		−	0.390568i	0.980747	−	0.195284i	$-0.0625628\pi$
$662$			0.685312i			0.0266354i
$663$	2.93081	−	4.25072i	0.113823	−	0.165084i
$664$			101.364i			3.93368i
$665$	−5.61419	+	2.51138i	−0.217709	+	0.0973871i
$666$	−47.4287	+	18.0436i	−1.83782	+	0.699174i
$667$	16.8967			0.654244
$668$	92.5949			3.58260
$669$	−2.40038	+	3.48140i	−0.0928040	+	0.134599i
$670$			17.5723i			0.678879i
$671$	9.58575			0.370054
$672$	72.1768	+	13.3582i	2.78428	+	0.515304i
$673$	25.4136			0.979622			0.489811	−	0.871829i	$-0.337066\pi$
$673$	25.4136			0.979622			0.489811	+	0.871829i	$0.337066\pi$
$674$			63.8706i			2.46020i
$675$	−3.39855	+	13.8813i	−0.130810	+	0.534291i
$676$	−21.2281			−0.816467
$677$	17.4256			0.669718			0.334859	−	0.942268i	$-0.391311\pi$
$677$	17.4256			0.669718			0.334859	+	0.942268i	$0.391311\pi$
$678$	8.23619	+	5.67873i	0.316309	+	0.218090i
$679$	−37.0784	+	16.5862i	−1.42294	+	0.636518i
$680$			23.5406i			0.902740i
$681$	6.00022	+	4.13707i	0.229929	+	0.158533i
$682$			38.9155i			1.49015i
$683$		−	11.3809i		−	0.435477i	−0.976007	−	0.217739i	$-0.930132\pi$
$683$		−	11.3809i		−	0.435477i	0.976007	−	0.217739i	$-0.0698680\pi$
$684$	12.0812	−	4.59614i	0.461938	−	0.175738i
$685$			1.46424i			0.0559457i
$686$	−15.0663	+	47.2114i	−0.575235	+	1.80254i
$687$	−4.98774	+	7.23400i	−0.190294	+	0.275994i
$688$	−82.8658			−3.15923
$689$	2.83666			0.108068
$690$	−21.2008	−	14.6176i	−0.807101	−	0.556484i
$691$			8.92081i			0.339364i	0.985499	+	0.169682i	$0.0542740\pi$
$691$			8.92081i			0.339364i	−0.985499	+	0.169682i	$0.945726\pi$
$692$	6.35185			0.241461
$693$	29.9721	+	30.0466i	1.13855	+	1.14138i
$694$	−73.8423			−2.80302
$695$		−	0.193048i		−	0.00732273i
$696$	−102.080	−	70.3827i	−3.86933	−	2.66785i
$697$	−4.31944			−0.163611
$698$	−13.0399			−0.493566
$699$	13.2799	−	19.2607i	0.502294	−	0.728505i
$700$	−15.3324	−	34.2756i	−0.579510	−	1.29550i
$701$		−	34.0846i		−	1.28736i	−0.765295	−	0.643680i	$-0.777407\pi$
$701$		−	34.0846i		−	1.28736i	0.765295	−	0.643680i	$-0.222593\pi$
$702$	9.85642	−	40.2582i	0.372006	−	1.51945i
$703$		−	5.27836i		−	0.199077i
$704$			97.5719i			3.67738i
$705$	27.4154	+	18.9025i	1.03252	+	0.711910i
$706$		−	25.2017i		−	0.948479i
$707$	13.0391	+	29.1489i	0.490385	+	1.09626i
$708$	36.7890	+	25.3654i	1.38261	+	0.953292i
$709$	42.4252			1.59331			0.796656	−	0.604433i	$-0.206600\pi$
$709$	42.4252			1.59331			0.796656	+	0.604433i	$0.206600\pi$
$710$	−18.1262			−0.680264
$711$	−1.17081	−	3.07755i	−0.0439088	−	0.115417i
$712$		−	117.932i		−	4.41968i
$713$	−5.42860			−0.203303
$714$	12.0574	+	2.23154i	0.451238	+	0.0835134i
$715$	−44.3729			−1.65945
$716$		−	56.4376i		−	2.10917i
$717$	9.09103	−	13.1852i	0.339511	−	0.492412i
$718$	−61.5607			−2.29742
$719$	−13.6896			−0.510536			−0.255268	−	0.966870i	$-0.582164\pi$
$719$	−13.6896			−0.510536			−0.255268	+	0.966870i	$0.582164\pi$
$720$	36.5457	+	96.0628i	1.36198	+	3.58005i
$721$	14.3500	−	6.41916i	0.534423	−	0.239062i
$722$		−	48.9752i		−	1.82267i
$723$	27.3731	−	39.7007i	1.01802	−	1.47649i
$724$		−	74.5379i		−	2.77018i
$725$			23.2845i			0.864763i
$726$	−46.2742	+	67.1141i	−1.71740	+	2.49084i
$727$			38.6730i			1.43430i	0.696917	+	0.717151i	$0.254554\pi$
$727$			38.6730i			1.43430i	−0.696917	+	0.717151i	$0.745446\pi$
$728$	27.2318	+	60.8767i	1.00928	+	2.25624i
$729$	−23.9462	−	12.4731i	−0.886896	−	0.461968i
$730$	−13.6813			−0.506367
$731$	−6.73365			−0.249053
$732$	9.09521	−	13.1913i	0.336169	−	0.487564i
$733$		−	9.04798i		−	0.334195i	−0.985940	−	0.167097i	$-0.946561\pi$
$733$		−	9.04798i		−	0.334195i	0.985940	−	0.167097i	$-0.0534394\pi$
$734$	−63.1319			−2.33024
$735$	−32.8051	+	7.94538i	−1.21003	+	0.293070i
$736$	−31.9688			−1.17839
$737$			12.6128i			0.464599i
$738$	−32.4083	+	12.3293i	−1.19297	+	0.453846i
$739$	53.0480			1.95140			0.975701	−	0.219105i	$-0.0703139\pi$
$739$	53.0480			1.95140			0.975701	+	0.219105i	$0.0703139\pi$
$740$	90.8092			3.33821
$741$	3.54934	+	2.44722i	0.130388	+	0.0899009i
$742$	2.75091	+	6.14966i	0.100989	+	0.225761i
$743$		−	24.2270i		−	0.888801i	−0.895828	−	0.444401i	$-0.853417\pi$
$743$		−	24.2270i		−	0.888801i	0.895828	−	0.444401i	$-0.146583\pi$
$744$	32.7964	+	22.6126i	1.20237	+	0.829019i
$745$		−	32.5582i		−	1.19284i
$746$			6.41692i			0.234940i
$747$	12.7873	+	33.6121i	0.467861	+	1.22980i
$748$			27.5904i			1.00880i
$749$	37.6087	−	16.8234i	1.37419	−	0.614713i
$750$	−16.4765	+	23.8969i	−0.601638	+	0.872590i
$751$	−42.1734			−1.53893			−0.769464	−	0.638690i	$-0.779476\pi$
$751$	−42.1734			−1.53893			−0.769464	+	0.638690i	$0.779476\pi$
$752$	84.9868			3.09915
$753$	25.2914	+	17.4380i	0.921669	+	0.635478i
$754$		−	67.5291i		−	2.45927i
$755$	0.423350			0.0154073
$756$	69.7866	−	12.7367i	2.53811	−	0.463229i
$757$	−35.2391			−1.28079			−0.640393	−	0.768047i	$-0.721229\pi$
$757$	−35.2391			−1.28079			−0.640393	+	0.768047i	$0.721229\pi$
$758$		−	35.1484i		−	1.27665i
$759$	−15.2172	−	10.4920i	−0.552349	−	0.380836i
$760$	−19.6564			−0.713011
$761$	−28.9698			−1.05015			−0.525077	−	0.851055i	$-0.675964\pi$
$761$	−28.9698			−1.05015			−0.525077	+	0.851055i	$0.675964\pi$
$762$	3.80854	−	5.52375i	0.137969	−	0.200104i
$763$	−16.5913	−	37.0897i	−0.600644	−	1.34274i
$764$		−	49.5159i		−	1.79142i
$765$	2.96969	+	7.80603i	0.107369	+	0.282228i
$766$			16.3262i			0.589889i
$767$			14.9042i			0.538160i
$768$	12.0368	+	8.29917i	0.434339	+	0.299470i
$769$			16.3597i			0.589946i	0.955506	+	0.294973i	$0.0953107\pi$
$769$			16.3597i			0.589946i	−0.955506	+	0.294973i	$0.904689\pi$
$770$	−43.0315	−	96.1969i	−1.55075	−	3.46670i
$771$	25.4976	+	17.5802i	0.918273	+	0.633136i
$772$	9.86236			0.354954
$773$	−20.0990			−0.722910			−0.361455	−	0.932390i	$-0.617720\pi$
$773$	−20.0990			−0.722910			−0.361455	+	0.932390i	$0.617720\pi$
$774$	−50.5218	+	19.2203i	−1.81597	+	0.690859i
$775$		−	7.48085i		−	0.268720i
$776$	−129.819			−4.66021
$777$	5.27181	−	28.4845i	0.189125	−	1.02188i
$778$	−6.47363			−0.232091
$779$		−	3.60673i		−	0.129224i
$780$	−42.1021	+	61.0631i	−1.50750	+	2.18641i
$781$	−13.0103			−0.465547
$782$	−5.34053			−0.190977
$783$	−42.7286	−	10.4612i	−1.52699	−	0.373854i
$784$	−57.4169	+	64.2185i	−2.05060	+	2.29352i
$785$			4.94192i			0.176385i
$786$	53.0472	−	76.9373i	1.89213	−	2.74426i
$787$			20.0156i			0.713480i	0.934204	+	0.356740i	$0.116112\pi$
$787$			20.0156i			0.713480i	−0.934204	+	0.356740i	$0.883888\pi$
$788$		−	24.1327i		−	0.859690i
$789$	20.6023	−	29.8807i	0.733462	−	1.06378i
$790$			8.17626i			0.290898i
$791$	−5.21315	+	2.33198i	−0.185358	+	0.0829158i
$792$	48.2290	+	126.773i	1.71374	+	4.50469i
$793$	5.34416			0.189777
$794$	6.13557			0.217743
$795$	−2.60463	+	3.77764i	−0.0923766	+	0.133979i
$796$		−	53.1354i		−	1.88334i
$797$	−3.60608			−0.127734			−0.0638669	−	0.997958i	$-0.520343\pi$
$797$	−3.60608			−0.127734			−0.0638669	+	0.997958i	$0.520343\pi$
$798$	−1.86334	+	10.0679i	−0.0659614	+	0.356402i
$799$	6.90600			0.244317
$800$		−	44.0545i		−	1.55756i
$801$	−14.8773	−	39.1060i	−0.525665	−	1.38174i
$802$	92.0677			3.25102
$803$	−9.81994			−0.346538
$804$	17.3570	+	11.9674i	0.612133	+	0.422057i
$805$	13.4192	−	6.00277i	0.472964	−	0.211570i
$806$			21.6958i			0.764202i
$807$	34.4816	+	23.7746i	1.21381	+	0.836904i
$808$			102.056i			3.59031i
$809$			10.0198i			0.352278i	0.984365	+	0.176139i	$0.0563608\pi$
$809$			10.0198i			0.352278i	−0.984365	+	0.176139i	$0.943639\pi$
$810$	44.5625	+	50.0912i	1.56577	+	1.76002i
$811$			6.19756i			0.217626i	0.994062	+	0.108813i	$0.0347050\pi$
$811$			6.19756i			0.217626i	−0.994062	+	0.108813i	$0.965295\pi$
$812$	105.505	−	47.1953i	3.70250	−	1.65623i
$813$	30.0866	−	43.6363i	1.05518	−	1.53039i
$814$	90.4427			3.17001
$815$	−34.8935			−1.22226
$816$	17.5482	+	12.0992i	0.614309	+	0.423557i
$817$		−	5.62259i		−	0.196709i
$818$	38.3661			1.34144
$819$	16.7098	+	16.7513i	0.583887	+	0.585338i
$820$	62.0504			2.16689
$821$			15.7554i			0.549869i	0.961463	+	0.274934i	$0.0886561\pi$
$821$			15.7554i			0.549869i	−0.961463	+	0.274934i	$0.911344\pi$
$822$	2.00686	+	1.38370i	0.0699973	+	0.0482621i
$823$	−27.5267			−0.959520			−0.479760	−	0.877400i	$-0.659276\pi$
$823$	−27.5267			−0.959520			−0.479760	+	0.877400i	$0.659276\pi$
$824$	50.2423			1.75027
$825$	14.4585	−	20.9700i	0.503380	−	0.730080i
$826$	−32.3112	+	14.4537i	−1.12425	+	0.502908i
$827$			40.0214i			1.39168i	0.718197	+	0.695840i	$0.244968\pi$
$827$			40.0214i			1.39168i	−0.718197	+	0.695840i	$0.755032\pi$
$828$	−28.8769	+	10.9858i	−1.00354	+	0.381783i
$829$			14.6599i			0.509158i	0.967052	+	0.254579i	$0.0819370\pi$
$829$			14.6599i			0.509158i	−0.967052	+	0.254579i	$0.918063\pi$
$830$		−	89.2989i		−	3.09961i
$831$	38.9798	+	26.8760i	1.35219	+	0.932317i
$832$			54.3974i			1.88589i
$833$	−4.66568	+	5.21838i	−0.161656	+	0.180806i
$834$	−0.264588	−	0.182430i	−0.00916194	−	0.00631703i
$835$	−49.9564			−1.72881
$836$	−23.0379			−0.796784
$837$	13.7279	+	3.36099i	0.474504	+	0.116173i
$838$		−	82.1464i		−	2.83770i
$839$	4.27731			0.147669			0.0738346	−	0.997271i	$-0.476476\pi$
$839$	4.27731			0.147669			0.0738346	+	0.997271i	$0.476476\pi$
$840$	−106.075	−	19.6320i	−3.65994	−	0.677367i
$841$	−42.6729			−1.47148
$842$		−	100.917i		−	3.47784i
$843$	−9.60077	+	13.9245i	−0.330668	+	0.479587i
$844$	−110.713			−3.81089
$845$	11.4529			0.393993
$846$	51.8149	−	19.7122i	1.78143	−	0.677721i
$847$	−19.0026	−	42.4804i	−0.652938	−	1.45964i
$848$			11.7106i			0.402142i
$849$	−12.7096	+	18.4335i	−0.436193	+	0.632636i
$850$		−	7.35949i		−	0.252428i
$851$			12.6165i			0.432488i
$852$	−12.3446	+	17.9040i	−0.422918	+	0.613382i
$853$		−	9.07391i		−	0.310685i	−0.987861	−	0.155342i	$-0.950352\pi$
$853$		−	9.07391i		−	0.310685i	0.987861	−	0.155342i	$-0.0496481\pi$
$854$	5.18261	+	11.5857i	0.177345	+	0.396455i
$855$	−6.51803	+	2.47969i	−0.222912	+	0.0848036i
$856$	131.675			4.50057
$857$	17.6436			0.602695			0.301348	−	0.953514i	$-0.402564\pi$
$857$	17.6436			0.602695			0.301348	+	0.953514i	$0.402564\pi$
$858$	−41.9322	+	60.8167i	−1.43154	+	2.07625i
$859$		−	7.44018i		−	0.253856i	−0.991912	−	0.126928i	$-0.959488\pi$
$859$		−	7.44018i		−	0.253856i	0.991912	−	0.126928i	$-0.0405117\pi$
$860$	96.7313			3.29851
$861$	3.60225	−	19.4636i	0.122764	−	0.663319i
$862$	−75.7198			−2.57903
$863$			7.07664i			0.240892i	0.992720	+	0.120446i	$0.0384324\pi$
$863$			7.07664i			0.240892i	−0.992720	+	0.120446i	$0.961568\pi$
$864$	80.8430	+	19.7928i	2.75033	+	0.673364i
$865$	−3.42693			−0.116519
$866$	65.0186			2.20942
$867$	1.42596	+	0.983178i	0.0484281	+	0.0333905i
$868$	−33.8968	+	15.1629i	−1.15053	+	0.514664i
$869$			5.86863i			0.199080i
$870$	89.9299	+	62.0054i	3.04891	+	2.10218i
$871$			7.03178i			0.238263i
$872$		−	129.858i		−	4.39756i
$873$	−43.0477	+	16.3769i	−1.45694	+	0.554273i
$874$		−	4.45934i		−	0.150839i
$875$	−6.76613	−	15.1257i	−0.228737	−	0.511341i
$876$	−9.31742	+	13.5136i	−0.314806	+	0.456582i
$877$	1.32320			0.0446812			0.0223406	−	0.999750i	$-0.492888\pi$
$877$	1.32320			0.0446812			0.0223406	+	0.999750i	$0.492888\pi$
$878$	−83.4351			−2.81580
$879$	16.7565	+	11.5533i	0.565182	+	0.389684i
$880$		−	183.184i		−	6.17513i
$881$	39.4411			1.32880			0.664402	−	0.747376i	$-0.268686\pi$
$881$	39.4411			1.32880			0.664402	+	0.747376i	$0.268686\pi$
$882$	−20.1109	+	52.4704i	−0.677169	+	1.76677i
$883$	−3.86785			−0.130164			−0.0650818	−	0.997880i	$-0.520731\pi$
$883$	−3.86785			−0.130164			−0.0650818	+	0.997880i	$0.520731\pi$
$884$			15.3819i			0.517351i
$885$	−19.8482	−	13.6851i	−0.667191	−	0.460019i
$886$	−3.52446			−0.118406
$887$	0.620685			0.0208406			0.0104203	−	0.999946i	$-0.496683\pi$
$887$	0.620685			0.0208406			0.0104203	+	0.999946i	$0.496683\pi$
$888$	52.5535	−	76.2213i	1.76358	−	2.55782i
$889$	1.56399	+	3.49629i	0.0524544	+	0.117262i
$890$			103.895i			3.48256i
$891$	31.9854	+	35.9537i	1.07155	+	1.20449i
$892$		−	12.5981i		−	0.421814i
$893$			5.76650i			0.192969i
$894$	−44.6237	−	30.7674i	−1.49244	−	1.02902i
$895$			30.4490i			1.01780i
$896$	−40.5595	+	18.1434i	−1.35500	+	0.606128i
$897$	−8.48375	−	5.84942i	−0.283264	−	0.195306i
$898$	−24.8198			−0.828247
$899$	23.0271			0.767997
$900$	−15.1389	−	39.7937i	−0.504631	−	1.32646i
$901$			0.951595i			0.0317022i
$902$	61.7999			2.05771
$903$	5.61561	−	30.3422i	0.186876	−	1.00972i
$904$	−18.2523			−0.607061
$905$			40.2144i			1.33677i
$906$	0.400064	−	0.580236i	0.0132912	−	0.0192770i
$907$	−37.9541			−1.26025			−0.630123	−	0.776495i	$-0.716996\pi$
$907$	−37.9541			−1.26025			−0.630123	+	0.776495i	$0.716996\pi$
$908$	−21.7128			−0.720565
$909$	12.8746	+	33.8416i	0.427022	+	1.12246i
$910$	−23.9905	−	53.6309i	−0.795279	−	1.77785i
$911$			4.01300i			0.132957i	0.997788	+	0.0664784i	$0.0211763\pi$
$911$			4.01300i			0.132957i	−0.997788	+	0.0664784i	$0.978824\pi$
$912$	−10.1028	+	14.6527i	−0.334538	+	0.485200i
$913$		−	64.0956i		−	2.12125i
$914$			45.5541i			1.50679i
$915$	−4.90702	+	7.11692i	−0.162221	+	0.235278i
$916$		−	26.1775i		−	0.864928i
$917$	21.7839	+	48.6980i	0.719369	+	1.60815i
$918$	13.5052	+	3.30647i	0.445737	+	0.109130i
$919$	38.3621			1.26545			0.632725	−	0.774376i	$-0.281936\pi$
$919$	38.3621			1.26545			0.632725	+	0.774376i	$0.281936\pi$
$920$	46.9832			1.54899
$921$	2.01269	−	2.91911i	0.0663203	−	0.0961881i
$922$			65.9092i			2.17060i
$923$	−7.25341			−0.238749
$924$	−124.324	−	23.0093i	−4.08995	−	0.756952i
$925$	−17.3861			−0.571651
$926$			51.7457i			1.70047i
$927$	16.6603	−	6.33816i	0.547195	−	0.208173i
$928$	135.606			4.45148
$929$	9.42548			0.309240			0.154620	−	0.987974i	$-0.450585\pi$
$929$	9.42548			0.309240			0.154620	+	0.987974i	$0.450585\pi$
$930$	−28.8928	−	19.9211i	−0.947431	−	0.653240i
$931$	−4.35734	−	3.89584i	−0.142806	−	0.127681i
$932$			69.6980i			2.28303i
$933$	−26.1520	−	18.0315i	−0.856179	−	0.590323i
$934$		−	13.5254i		−	0.442564i
$935$		−	14.8855i		−	0.486807i
$936$	26.8882	+	70.6775i	0.878869	+	2.31016i
$937$			27.7413i			0.906267i	0.891443	+	0.453134i	$0.149694\pi$
$937$			27.7413i			0.906267i	−0.891443	+	0.453134i	$0.850306\pi$
$938$	−15.2444	+	6.81921i	−0.497746	+	0.222655i
$939$	−21.0684	+	30.5566i	−0.687540	+	0.997178i
$940$	−99.2072			−3.23578
$941$	16.4317			0.535657			0.267828	−	0.963467i	$-0.413694\pi$
$941$	16.4317			0.535657			0.267828	+	0.963467i	$0.413694\pi$
$942$	6.77331	+	4.67010i	0.220686	+	0.152160i
$943$			8.62091i			0.280735i
$944$	−61.5289			−2.00260
$945$	−37.6510	+	6.87165i	−1.22479	+	0.223535i
$946$	96.3409			3.13231
$947$			47.2282i			1.53471i	0.641221	+	0.767356i	$0.278428\pi$
$947$			47.2282i			1.53471i	−0.641221	+	0.767356i	$0.721572\pi$
$948$	8.07604	+	5.56831i	0.262298	+	0.180850i
$949$	−5.47472			−0.177717
$950$	6.14516			0.199375
$951$	−1.44732	+	2.09913i	−0.0469327	+	0.0680691i
$952$	−20.4219	+	9.13528i	−0.661878	+	0.296076i
$953$		−	2.50359i		−	0.0810992i	−0.999178	−	0.0405496i	$-0.987089\pi$
$953$		−	2.50359i		−	0.0810992i	0.999178	−	0.0405496i	$-0.0129109\pi$
$954$	2.71620	+	7.13971i	0.0879402	+	0.231157i
$955$			26.7146i			0.864465i
$956$			47.7130i			1.54315i
$957$	64.5485	+	44.5053i	2.08656	+	1.43865i
$958$		−	36.2487i		−	1.17114i
$959$	−1.27026	+	0.568220i	−0.0410187	+	0.0183488i
$960$	−72.4421	−	49.9478i	−2.33806	−	1.61206i
$961$	23.6018			0.761349
$962$	50.4228			1.62570
$963$	43.6634	−	16.6111i	1.40703	−	0.535286i
$964$			143.664i			4.62710i
$965$	−5.32090			−0.171286
$966$	4.45380	−	24.0647i	0.143299	−	0.774269i
$967$	−19.7627			−0.635526			−0.317763	−	0.948170i	$-0.602932\pi$
$967$	−19.7627			−0.635526			−0.317763	+	0.948170i	$0.602932\pi$
$968$		−	148.732i		−	4.78043i
$969$	−0.820953	+	1.19067i	−0.0263728	+	0.0382500i
$970$	114.367			3.67210
$971$	10.9235			0.350553			0.175276	−	0.984519i	$-0.443918\pi$
$971$	10.9235			0.350553			0.175276	+	0.984519i	$0.443918\pi$
$972$	79.8258	−	9.90251i	2.56041	−	0.317623i
$973$	0.167473	−	0.0749152i	0.00536893	−	0.00240167i
$974$			17.7733i			0.569492i
$975$	8.06076	−	11.6910i	0.258151	−	0.374411i
$976$			22.0622i			0.706195i
$977$		−	37.3927i		−	1.19630i	−0.801385	−	0.598149i	$-0.795903\pi$
$977$		−	37.3927i		−	1.19630i	0.801385	−	0.598149i	$-0.204097\pi$
$978$	−32.9742	+	47.8244i	−1.05440	+	1.52925i
$979$			74.5720i			2.38333i
$980$	67.0242	−	74.9639i	2.14101	−	2.39463i
$981$	−16.3819	−	43.0609i	−0.523034	−	1.37483i
$982$	9.87664			0.315176
$983$	−52.4255			−1.67211			−0.836057	−	0.548643i	$-0.815145\pi$
$983$	−52.4255			−1.67211			−0.836057	+	0.548643i	$0.815145\pi$
$984$	35.9101	−	52.0824i	1.14477	−	1.66033i
$985$			13.0200i			0.414851i
$986$	22.6535			0.721436
$987$	−5.75934	+	31.1188i	−0.183322	+	0.990522i
$988$	−12.8439			−0.408619
$989$			13.4393i			0.427344i
$990$	−42.4886	−	111.684i	−1.35037	−	3.54955i
$991$	33.6866			1.07009			0.535045	−	0.844824i	$-0.320295\pi$
$991$	33.6866			1.07009			0.535045	+	0.844824i	$0.320295\pi$
$992$	−43.5676			−1.38327
$993$	−0.365205	−	0.251804i	−0.0115894	−	0.00799074i
$994$	−7.03415	−	15.7248i	−0.223110	−	0.498761i
$995$			28.6674i			0.908819i
$996$	−88.2043	−	60.8156i	−2.79486	−	1.92702i
$997$		−	16.5867i		−	0.525308i	−0.964890	−	0.262654i	$-0.915402\pi$
$997$		−	16.5867i		−	0.525308i	0.964890	−	0.262654i	$-0.0845977\pi$
$998$			72.6824i			2.30072i
$999$	7.81121	−	31.9046i	0.247136	−	1.00942i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.d.b.188.1	yes	22
3.2	odd	2		357.2.d.a.188.22	yes	22
7.6	odd	2		357.2.d.a.188.1	✓	22
21.20	even	2	inner	357.2.d.b.188.22	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.d.a.188.1	✓	22	7.6	odd	2
357.2.d.a.188.22	yes	22	3.2	odd	2
357.2.d.b.188.1	yes	22	1.1	even	1	trivial
357.2.d.b.188.22	yes	22	21.20	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.67583i q^{2} +(1.42596 + 0.983178i) q^{3} -5.16008 q^{4} +2.78395 q^{5} +(2.63082 - 3.81563i) q^{6} +(1.08035 + 2.41513i) q^{7} +8.45583i q^{8} +(1.06672 + 2.80394i) q^{9} +O(q^{10})\)	\(q-2.67583i q^{2} +(1.42596 + 0.983178i) q^{3} -5.16008 q^{4} +2.78395 q^{5} +(2.63082 - 3.81563i) q^{6} +(1.08035 + 2.41513i) q^{7} +8.45583i q^{8} +(1.06672 + 2.80394i) q^{9} -7.44937i q^{10} -5.34689i q^{11} +(-7.35806 - 5.07327i) q^{12} -2.98095i q^{13} +(6.46247 - 2.89084i) q^{14} +(3.96979 + 2.73712i) q^{15} +12.3062 q^{16} +1.00000 q^{17} +(7.50289 - 2.85437i) q^{18} +0.834999i q^{19} -14.3654 q^{20} +(-0.833962 + 4.50605i) q^{21} -14.3074 q^{22} -1.99584i q^{23} +(-8.31359 + 12.0577i) q^{24} +2.75036 q^{25} -7.97653 q^{26} +(-1.23568 + 5.04709i) q^{27} +(-5.57470 - 12.4622i) q^{28} +8.46598i q^{29} +(7.32406 - 10.6225i) q^{30} -2.71996i q^{31} -16.0177i q^{32} +(5.25695 - 7.62445i) q^{33} -2.67583i q^{34} +(3.00764 + 6.72358i) q^{35} +(-5.50436 - 14.4686i) q^{36} -6.32140 q^{37} +2.23432 q^{38} +(2.93081 - 4.25072i) q^{39} +23.5406i q^{40} -4.31944 q^{41} +(12.0574 + 2.23154i) q^{42} -6.73365 q^{43} +27.5904i q^{44} +(2.96969 + 7.80603i) q^{45} -5.34053 q^{46} +6.90600 q^{47} +(17.5482 + 12.0992i) q^{48} +(-4.66568 + 5.21838i) q^{49} -7.35949i q^{50} +(1.42596 + 0.983178i) q^{51} +15.3819i q^{52} +0.951595i q^{53} +(13.5052 + 3.30647i) q^{54} -14.8855i q^{55} +(-20.4219 + 9.13528i) q^{56} +(-0.820953 + 1.19067i) q^{57} +22.6535 q^{58} -4.99982 q^{59} +(-20.4844 - 14.1237i) q^{60} +1.79277i q^{61} -7.27815 q^{62} +(-5.61945 + 5.60551i) q^{63} -18.2483 q^{64} -8.29881i q^{65} +(-20.4018 - 14.0667i) q^{66} -2.35890 q^{67} -5.16008 q^{68} +(1.96227 - 2.84599i) q^{69} +(17.9912 - 8.04794i) q^{70} -2.43325i q^{71} +(-23.7097 + 9.02001i) q^{72} -1.83657i q^{73} +16.9150i q^{74} +(3.92189 + 2.70409i) q^{75} -4.30866i q^{76} +(12.9134 - 5.77653i) q^{77} +(-11.3742 - 7.84235i) q^{78} -1.09758 q^{79} +34.2599 q^{80} +(-6.72421 + 5.98205i) q^{81} +11.5581i q^{82} +11.9874 q^{83} +(4.30331 - 23.2516i) q^{84} +2.78395 q^{85} +18.0181i q^{86} +(-8.32357 + 12.0721i) q^{87} +45.2124 q^{88} -13.9468 q^{89} +(20.8876 - 7.94640i) q^{90} +(7.19938 - 3.22048i) q^{91} +10.2987i q^{92} +(2.67420 - 3.87855i) q^{93} -18.4793i q^{94} +2.32459i q^{95} +(15.7483 - 22.8407i) q^{96} +15.3525i q^{97} +(13.9635 + 12.4846i) q^{98} +(14.9924 - 5.70364i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 24 q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 22 * q - 24 * q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	\( 22 q - 24 q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} - 8 q^{14} - 4 q^{15} + 20 q^{16} + 22 q^{17} + 8 q^{18} - 30 q^{20} - 4 q^{21} - 12 q^{22} - 44 q^{24} + 14 q^{25} - 24 q^{26} + 6 q^{27} + 8 q^{28} + 5 q^{30} + 28 q^{33} + 10 q^{35} - 3 q^{36} - 16 q^{37} + 88 q^{38} - 14 q^{39} - 16 q^{41} + 19 q^{42} - 24 q^{43} - 46 q^{45} + 4 q^{46} - 16 q^{47} + 25 q^{48} + 6 q^{49} + 36 q^{54} - 40 q^{56} - 6 q^{57} + 24 q^{58} + 24 q^{59} - 21 q^{60} - 20 q^{62} - 6 q^{63} - 20 q^{64} - 116 q^{66} + 8 q^{67} - 24 q^{68} + 6 q^{69} + 4 q^{70} - 7 q^{72} + 54 q^{75} + 6 q^{77} + 2 q^{78} + 16 q^{79} + 128 q^{80} - 4 q^{81} + 8 q^{83} + 42 q^{84} - 48 q^{87} + 32 q^{88} - 100 q^{89} + 47 q^{90} + 18 q^{91} + 20 q^{93} + 88 q^{96} - 8 q^{98} + 18 q^{99}+O(q^{100}) \) 22 * q - 24 * q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 - 8 * q^14 - 4 * q^15 + 20 * q^16 + 22 * q^17 + 8 * q^18 - 30 * q^20 - 4 * q^21 - 12 * q^22 - 44 * q^24 + 14 * q^25 - 24 * q^26 + 6 * q^27 + 8 * q^28 + 5 * q^30 + 28 * q^33 + 10 * q^35 - 3 * q^36 - 16 * q^37 + 88 * q^38 - 14 * q^39 - 16 * q^41 + 19 * q^42 - 24 * q^43 - 46 * q^45 + 4 * q^46 - 16 * q^47 + 25 * q^48 + 6 * q^49 + 36 * q^54 - 40 * q^56 - 6 * q^57 + 24 * q^58 + 24 * q^59 - 21 * q^60 - 20 * q^62 - 6 * q^63 - 20 * q^64 - 116 * q^66 + 8 * q^67 - 24 * q^68 + 6 * q^69 + 4 * q^70 - 7 * q^72 + 54 * q^75 + 6 * q^77 + 2 * q^78 + 16 * q^79 + 128 * q^80 - 4 * q^81 + 8 * q^83 + 42 * q^84 - 48 * q^87 + 32 * q^88 - 100 * q^89 + 47 * q^90 + 18 * q^91 + 20 * q^93 + 88 * q^96 - 8 * q^98 + 18 * q^99

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