LMFDB - Embedded newform 1205.2.b.d.724.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(724,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1205.724");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.b (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:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			724.3
Character	$\chi$	$=$	1205.724
Dual form			1205.2.b.d.724.64

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70326i q^{2} +3.35528i q^{3} -5.30763 q^{4} +(0.474898 + 2.18506i) q^{5} +9.07021 q^{6} +3.43095i q^{7} +8.94141i q^{8} -8.25791 q^{9} +O(q^{10})$	\(q-2.70326i q^{2} +3.35528i q^{3} -5.30763 q^{4} +(0.474898 + 2.18506i) q^{5} +9.07021 q^{6} +3.43095i q^{7} +8.94141i q^{8} -8.25791 q^{9} +(5.90678 - 1.28377i) q^{10} +4.01571 q^{11} -17.8086i q^{12} -0.273217i q^{13} +9.27475 q^{14} +(-7.33148 + 1.59342i) q^{15} +13.5557 q^{16} +6.77517i q^{17} +22.3233i q^{18} +5.41206 q^{19} +(-2.52058 - 11.5975i) q^{20} -11.5118 q^{21} -10.8555i q^{22} -2.33987i q^{23} -30.0009 q^{24} +(-4.54894 + 2.07536i) q^{25} -0.738577 q^{26} -17.6418i q^{27} -18.2102i q^{28} -3.85012 q^{29} +(4.30742 + 19.8189i) q^{30} +0.673699 q^{31} -18.7618i q^{32} +13.4738i q^{33} +18.3151 q^{34} +(-7.49681 + 1.62935i) q^{35} +43.8300 q^{36} -4.50226i q^{37} -14.6302i q^{38} +0.916720 q^{39} +(-19.5375 + 4.24625i) q^{40} -3.57192 q^{41} +31.1194i q^{42} -0.816401i q^{43} -21.3139 q^{44} +(-3.92166 - 18.0440i) q^{45} -6.32529 q^{46} +1.60364i q^{47} +45.4832i q^{48} -4.77138 q^{49} +(5.61024 + 12.2970i) q^{50} -22.7326 q^{51} +1.45014i q^{52} +4.44393i q^{53} -47.6904 q^{54} +(1.90705 + 8.77455i) q^{55} -30.6775 q^{56} +18.1590i q^{57} +10.4079i q^{58} -0.529530 q^{59} +(38.9128 - 8.45726i) q^{60} -6.64845 q^{61} -1.82119i q^{62} -28.3324i q^{63} -23.6068 q^{64} +(0.596994 - 0.129750i) q^{65} +36.4233 q^{66} +7.41240i q^{67} -35.9601i q^{68} +7.85093 q^{69} +(4.40456 + 20.2659i) q^{70} +14.8394 q^{71} -73.8373i q^{72} -3.73531i q^{73} -12.1708 q^{74} +(-6.96340 - 15.2630i) q^{75} -28.7252 q^{76} +13.7777i q^{77} -2.47813i q^{78} -3.17183 q^{79} +(6.43757 + 29.6200i) q^{80} +34.4194 q^{81} +9.65585i q^{82} -13.2562i q^{83} +61.1003 q^{84} +(-14.8041 + 3.21751i) q^{85} -2.20695 q^{86} -12.9182i q^{87} +35.9061i q^{88} -1.74820 q^{89} +(-48.7777 + 10.6013i) q^{90} +0.937392 q^{91} +12.4192i q^{92} +2.26045i q^{93} +4.33506 q^{94} +(2.57017 + 11.8256i) q^{95} +62.9513 q^{96} -1.39934i q^{97} +12.8983i q^{98} -33.1614 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 78 q^{4} + 16 q^{6} - 90 q^{9}+O(q^{10}) $ 66 * q - 78 * q^4 + 16 * q^6 - 90 * q^9	$ 66 q - 78 q^{4} + 16 q^{6} - 90 q^{9} + q^{10} + 48 q^{11} - 30 q^{14} - 3 q^{15} + 98 q^{16} - 12 q^{19} - 10 q^{20} + 18 q^{21} - 42 q^{24} + 6 q^{25} + 48 q^{26} - 56 q^{29} - 5 q^{30} + 48 q^{31} - 8 q^{34} + 3 q^{35} + 158 q^{36} - 84 q^{39} - 6 q^{40} + 56 q^{41} - 144 q^{44} - 13 q^{45} + 36 q^{46} - 98 q^{49} + 2 q^{50} + 44 q^{51} - 86 q^{54} + 3 q^{55} + 104 q^{56} - 108 q^{59} + 7 q^{60} + 22 q^{61} - 136 q^{64} + 15 q^{65} + 74 q^{66} - 20 q^{69} - 32 q^{70} + 212 q^{71} - 84 q^{74} - 9 q^{75} + 6 q^{76} - 66 q^{79} - 21 q^{80} + 162 q^{81} + 52 q^{84} - 48 q^{85} + 100 q^{86} - 54 q^{89} - 155 q^{90} + 72 q^{91} + 96 q^{94} - 5 q^{95} + 122 q^{96} - 112 q^{99}+O(q^{100}) $ 66 * q - 78 * q^4 + 16 * q^6 - 90 * q^9 + q^10 + 48 * q^11 - 30 * q^14 - 3 * q^15 + 98 * q^16 - 12 * q^19 - 10 * q^20 + 18 * q^21 - 42 * q^24 + 6 * q^25 + 48 * q^26 - 56 * q^29 - 5 * q^30 + 48 * q^31 - 8 * q^34 + 3 * q^35 + 158 * q^36 - 84 * q^39 - 6 * q^40 + 56 * q^41 - 144 * q^44 - 13 * q^45 + 36 * q^46 - 98 * q^49 + 2 * q^50 + 44 * q^51 - 86 * q^54 + 3 * q^55 + 104 * q^56 - 108 * q^59 + 7 * q^60 + 22 * q^61 - 136 * q^64 + 15 * q^65 + 74 * q^66 - 20 * q^69 - 32 * q^70 + 212 * q^71 - 84 * q^74 - 9 * q^75 + 6 * q^76 - 66 * q^79 - 21 * q^80 + 162 * q^81 + 52 * q^84 - 48 * q^85 + 100 * q^86 - 54 * q^89 - 155 * q^90 + 72 * q^91 + 96 * q^94 - 5 * q^95 + 122 * q^96 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1205\mathbb{Z}\right)^\times$.

$n$	$242$	$971$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	2.70326i		−	1.91150i	−0.294187	−	0.955748i	$-0.595049\pi$
$2$		−	2.70326i		−	1.91150i	0.294187	−	0.955748i	$-0.404951\pi$
$3$			3.35528i			1.93717i	0.248678	+	0.968586i	$0.420004\pi$
$3$			3.35528i			1.93717i	−0.248678	+	0.968586i	$0.579996\pi$
$4$	−5.30763			−2.65382
$5$	0.474898	+	2.18506i	0.212381	+	0.977187i
$5$	0.474898	+	2.18506i	0.212381	+	0.977187i
$6$	9.07021			3.70290
$7$			3.43095i			1.29678i	0.761310	+	0.648388i	$0.224556\pi$
$7$			3.43095i			1.29678i	−0.761310	+	0.648388i	$0.775444\pi$
$8$			8.94141i			3.16126i
$9$	−8.25791			−2.75264
$10$	5.90678	−	1.28377i	1.86789	−	0.405965i
$11$	4.01571			1.21078			0.605391	−	0.795928i	$-0.293017\pi$
$11$	4.01571			1.21078			0.605391	+	0.795928i	$0.293017\pi$
$12$		−	17.8086i		−	5.14090i
$13$		−	0.273217i		−	0.0757767i	−0.999282	−	0.0378884i	$-0.987937\pi$
$13$		−	0.273217i		−	0.0757767i	0.999282	−	0.0378884i	$-0.0120631\pi$
$14$	9.27475			2.47878
$15$	−7.33148	+	1.59342i	−1.89298	+	0.411418i
$16$	13.5557			3.38893
$17$			6.77517i			1.64322i	0.570049	+	0.821610i	$0.306924\pi$
$17$			6.77517i			1.64322i	−0.570049	+	0.821610i	$0.693076\pi$
$18$			22.3233i			5.26166i
$19$	5.41206			1.24161			0.620805	−	0.783965i	$-0.286806\pi$
$19$	5.41206			1.24161			0.620805	+	0.783965i	$0.286806\pi$
$20$	−2.52058	−	11.5975i	−0.563619	−	2.59328i
$21$	−11.5118			−2.51208
$22$		−	10.8555i		−	2.31441i
$23$		−	2.33987i		−	0.487897i	−0.969788	−	0.243949i	$-0.921557\pi$
$23$		−	2.33987i		−	0.487897i	0.969788	−	0.243949i	$-0.0784428\pi$
$24$	−30.0009			−6.12391
$25$	−4.54894	+	2.07536i	−0.909789	+	0.415071i
$26$	−0.738577			−0.144847
$27$		−	17.6418i		−	3.39516i
$28$		−	18.2102i		−	3.44140i
$29$	−3.85012			−0.714949			−0.357474	−	0.933923i	$-0.616362\pi$
$29$	−3.85012			−0.714949			−0.357474	+	0.933923i	$0.616362\pi$
$30$	4.30742	+	19.8189i	0.786424	+	3.61842i
$31$	0.673699			0.121000			0.0604999	−	0.998168i	$-0.480731\pi$
$31$	0.673699			0.121000			0.0604999	+	0.998168i	$0.480731\pi$
$32$		−	18.7618i		−	3.31666i
$33$			13.4738i			2.34549i
$34$	18.3151			3.14101
$35$	−7.49681	+	1.62935i	−1.26719	+	0.275410i
$36$	43.8300			7.30500
$37$		−	4.50226i		−	0.740168i	−0.928998	−	0.370084i	$-0.879329\pi$
$37$		−	4.50226i		−	0.740168i	0.928998	−	0.370084i	$-0.120671\pi$
$38$		−	14.6302i		−	2.37333i
$39$	0.916720			0.146793
$40$	−19.5375	+	4.24625i	−3.08915	+	0.671391i
$41$	−3.57192			−0.557841			−0.278920	−	0.960314i	$-0.589977\pi$
$41$	−3.57192			−0.557841			−0.278920	+	0.960314i	$0.589977\pi$
$42$			31.1194i			4.80183i
$43$		−	0.816401i		−	0.124500i	−0.998061	−	0.0622500i	$-0.980172\pi$
$43$		−	0.816401i		−	0.124500i	0.998061	−	0.0622500i	$-0.0198276\pi$
$44$	−21.3139			−3.21319
$45$	−3.92166	−	18.0440i	−0.584607	−	2.68984i
$46$	−6.32529			−0.932613
$47$			1.60364i			0.233915i	0.993137	+	0.116957i	$0.0373141\pi$
$47$			1.60364i			0.233915i	−0.993137	+	0.116957i	$0.962686\pi$
$48$			45.4832i			6.56494i
$49$	−4.77138			−0.681626
$50$	5.61024	+	12.2970i	0.793407	+	1.73906i
$51$	−22.7326			−3.18320
$52$			1.45014i			0.201098i
$53$			4.44393i			0.610421i	0.952285	+	0.305210i	$0.0987268\pi$
$53$			4.44393i			0.610421i	−0.952285	+	0.305210i	$0.901273\pi$
$54$	−47.6904			−6.48984
$55$	1.90705	+	8.77455i	0.257147	+	1.18316i
$56$	−30.6775			−4.09945
$57$			18.1590i			2.40521i
$58$			10.4079i			1.36662i
$59$	−0.529530			−0.0689390			−0.0344695	−	0.999406i	$-0.510974\pi$
$59$	−0.529530			−0.0689390			−0.0344695	+	0.999406i	$0.510974\pi$
$60$	38.9128	−	8.45726i	5.02362	−	1.09183i
$61$	−6.64845			−0.851246			−0.425623	−	0.904900i	$-0.639945\pi$
$61$	−6.64845			−0.851246			−0.425623	+	0.904900i	$0.639945\pi$
$62$		−	1.82119i		−	0.231291i
$63$		−	28.3324i		−	3.56955i
$64$	−23.6068			−2.95085
$65$	0.596994	−	0.129750i	0.0740480	−	0.0160935i
$66$	36.4233			4.48340
$67$			7.41240i			0.905568i	0.891620	+	0.452784i	$0.149569\pi$
$67$			7.41240i			0.905568i	−0.891620	+	0.452784i	$0.850431\pi$
$68$		−	35.9601i		−	4.36081i
$69$	7.85093			0.945141
$70$	4.40456	+	20.2659i	0.526445	+	2.42223i
$71$	14.8394			1.76112			0.880559	−	0.473937i	$-0.157168\pi$
$71$	14.8394			1.76112			0.880559	+	0.473937i	$0.157168\pi$
$72$		−	73.8373i		−	8.70181i
$73$		−	3.73531i		−	0.437184i	−0.975816	−	0.218592i	$-0.929854\pi$
$73$		−	3.73531i		−	0.437184i	0.975816	−	0.218592i	$-0.0701465\pi$
$74$	−12.1708			−1.41483
$75$	−6.96340	−	15.2630i	−0.804065	−	1.76242i
$76$	−28.7252			−3.29501
$77$			13.7777i			1.57011i
$78$		−	2.47813i		−	0.280593i
$79$	−3.17183			−0.356859			−0.178430	−	0.983953i	$-0.557102\pi$
$79$	−3.17183			−0.356859			−0.178430	+	0.983953i	$0.557102\pi$
$80$	6.43757	+	29.6200i	0.719743	+	3.31162i
$81$	34.4194			3.82437
$82$			9.65585i			1.06631i
$83$		−	13.2562i		−	1.45506i	−0.686077	−	0.727529i	$-0.740669\pi$
$83$		−	13.2562i		−	1.45506i	0.686077	−	0.727529i	$-0.259331\pi$
$84$	61.1003			6.66659
$85$	−14.8041	+	3.21751i	−1.60573	+	0.348988i
$86$	−2.20695			−0.237981
$87$		−	12.9182i		−	1.38498i
$88$			35.9061i			3.82760i
$89$	−1.74820			−0.185309			−0.0926547	−	0.995698i	$-0.529535\pi$
$89$	−1.74820			−0.185309			−0.0926547	+	0.995698i	$0.529535\pi$
$90$	−48.7777	+	10.6013i	−5.14162	+	1.11747i
$91$	0.937392			0.0982654
$92$			12.4192i			1.29479i
$93$			2.26045i			0.234398i
$94$	4.33506			0.447127
$95$	2.57017	+	11.8256i	0.263694	+	1.21329i
$96$	62.9513			6.42494
$97$		−	1.39934i		−	0.142081i	−0.997473	−	0.0710407i	$-0.977368\pi$
$97$		−	1.39934i		−	0.142081i	0.997473	−	0.0710407i	$-0.0226320\pi$
$98$			12.8983i			1.30293i
$99$	−33.1614			−3.33284
$100$	24.1441	−	11.0152i	2.41441	−	1.10152i
$101$	5.84086			0.581187			0.290593	−	0.956847i	$-0.406147\pi$
$101$	5.84086			0.581187			0.290593	+	0.956847i	$0.406147\pi$
$102$			61.4522i			6.08468i
$103$		−	0.444988i		−	0.0438460i	−0.999760	−	0.0219230i	$-0.993021\pi$
$103$		−	0.444988i		−	0.0438460i	0.999760	−	0.0219230i	$-0.00697887\pi$
$104$	2.44294			0.239550
$105$	−5.46692	−	25.1539i	−0.533517	−	2.45477i
$106$	12.0131			1.16682
$107$			1.92184i			0.185792i	0.995676	+	0.0928959i	$0.0296124\pi$
$107$			1.92184i			0.185792i	−0.995676	+	0.0928959i	$0.970388\pi$
$108$			93.6361i			9.01014i
$109$	7.36107			0.705063			0.352531	−	0.935800i	$-0.385321\pi$
$109$	7.36107			0.705063			0.352531	+	0.935800i	$0.385321\pi$
$110$	23.7199	−	5.15526i	2.26161	−	0.491535i
$111$	15.1064			1.43383
$112$			46.5089i			4.39468i
$113$		−	14.6826i		−	1.38122i	−0.723228	−	0.690609i	$-0.757342\pi$
$113$		−	14.6826i		−	1.38122i	0.723228	−	0.690609i	$-0.242658\pi$
$114$	49.0885			4.59756
$115$	5.11275	−	1.11120i	0.476767	−	0.103620i
$116$	20.4350			1.89734
$117$			2.25620i			0.208586i
$118$			1.43146i			0.131777i
$119$	−23.2452			−2.13089
$120$	−14.2474	−	65.5537i	−1.30060	−	5.98421i
$121$	5.12592			0.465993
$122$			17.9725i			1.62715i
$123$		−	11.9848i		−	1.08063i
$124$	−3.57575			−0.321112
$125$	−6.69505	−	8.95412i	−0.598824	−	0.800881i
$126$	−76.5901			−6.82318
$127$			19.1178i			1.69643i	0.529649	+	0.848217i	$0.322324\pi$
$127$			19.1178i			1.69643i	−0.529649	+	0.848217i	$0.677676\pi$
$128$			26.2917i			2.32388i
$129$	2.73925			0.241178
$130$	−0.350749	−	1.61383i	−0.0307627	−	0.141543i
$131$	−15.4821			−1.35267			−0.676337	−	0.736592i	$-0.736434\pi$
$131$	−15.4821			−1.35267			−0.676337	+	0.736592i	$0.736434\pi$
$132$		−	71.5142i		−	6.22451i
$133$			18.5685i			1.61009i
$134$	20.0377			1.73099
$135$	38.5483	−	8.37804i	3.31771	−	0.721067i
$136$	−60.5796			−5.19466
$137$		−	9.02561i		−	0.771110i	−0.922685	−	0.385555i	$-0.874010\pi$
$137$		−	9.02561i		−	0.771110i	0.922685	−	0.385555i	$-0.125990\pi$
$138$		−	21.2231i		−	1.80663i
$139$	−2.06894			−0.175485			−0.0877427	−	0.996143i	$-0.527965\pi$
$139$	−2.06894			−0.175485			−0.0877427	+	0.996143i	$0.527965\pi$
$140$	39.7903	−	8.64798i	3.36290	−	0.730888i
$141$	−5.38066			−0.453134
$142$		−	40.1149i		−	3.36637i
$143$		−	1.09716i		−	0.0917491i
$144$	−111.942			−9.32849
$145$	−1.82841	−	8.41273i	−0.151841	−	0.698639i
$146$	−10.0975			−0.835676
$147$		−	16.0093i		−	1.32043i
$148$			23.8964i			1.96427i
$149$	21.0000			1.72039			0.860195	−	0.509965i	$-0.170342\pi$
$149$	21.0000			1.72039			0.860195	+	0.509965i	$0.170342\pi$
$150$	−41.2599	+	18.8239i	−3.36886	+	1.53697i
$151$	19.8081			1.61196			0.805979	−	0.591944i	$-0.201640\pi$
$151$	19.8081			1.61196			0.805979	+	0.591944i	$0.201640\pi$
$152$			48.3914i			3.92506i
$153$		−	55.9488i		−	4.52319i
$154$	37.2447			3.00126
$155$	0.319938	+	1.47207i	0.0256980	+	0.118240i
$156$	−4.86561			−0.389561
$157$		−	5.88284i		−	0.469502i	−0.972056	−	0.234751i	$-0.924573\pi$
$157$		−	5.88284i		−	0.469502i	0.972056	−	0.234751i	$-0.0754274\pi$
$158$			8.57430i			0.682135i
$159$	−14.9106			−1.18249
$160$	40.9957	−	8.90995i	3.24099	−	0.704394i
$161$	8.02797			0.632693
$162$		−	93.0446i		−	7.31028i
$163$			4.04268i			0.316647i	0.987387	+	0.158324i	$0.0506089\pi$
$163$			4.04268i			0.316647i	−0.987387	+	0.158324i	$0.949391\pi$
$164$	18.9585			1.48041
$165$	−29.4411	+	6.39869i	−2.29199	+	0.498138i
$166$	−35.8350			−2.78134
$167$		−	5.11166i		−	0.395552i	−0.980247	−	0.197776i	$-0.936628\pi$
$167$		−	5.11166i		−	0.395552i	0.980247	−	0.197776i	$-0.0633719\pi$
$168$		−	102.932i		−	7.94134i
$169$	12.9254			0.994258
$170$	8.69779	+	40.0195i	0.667090	+	3.06935i
$171$	−44.6923			−3.41770
$172$			4.33316i			0.330400i
$173$		−	8.24097i		−	0.626549i	−0.949663	−	0.313275i	$-0.898574\pi$
$173$		−	8.24097i		−	0.626549i	0.949663	−	0.313275i	$-0.101426\pi$
$174$	−34.9214			−2.64738
$175$	−7.12043	−	15.6072i	−0.538254	−	1.17979i
$176$	54.4358			4.10325
$177$		−	1.77672i		−	0.133547i
$178$			4.72586i			0.354218i
$179$	−8.47962			−0.633797			−0.316898	−	0.948460i	$-0.602641\pi$
$179$	−8.47962			−0.633797			−0.316898	+	0.948460i	$0.602641\pi$
$180$	20.8148	+	95.7710i	1.55144	+	7.13835i
$181$	4.59151			0.341284			0.170642	−	0.985333i	$-0.445416\pi$
$181$	4.59151			0.341284			0.170642	+	0.985333i	$0.445416\pi$
$182$		−	2.53402i		−	0.187834i
$183$		−	22.3074i		−	1.64901i
$184$	20.9217			1.54237
$185$	9.83770	−	2.13811i	0.723282	−	0.157197i
$186$	6.11059			0.448050
$187$			27.2071i			1.98958i
$188$		−	8.51153i		−	0.620767i
$189$	60.5280			4.40276
$190$	31.9678	−	6.94785i	2.31919	−	0.504050i
$191$	5.24071			0.379205			0.189602	−	0.981861i	$-0.439280\pi$
$191$	5.24071			0.379205			0.189602	+	0.981861i	$0.439280\pi$
$192$		−	79.2074i		−	5.71630i
$193$			19.6142i			1.41186i	0.708283	+	0.705929i	$0.249470\pi$
$193$			19.6142i			1.41186i	−0.708283	+	0.705929i	$0.750530\pi$
$194$	−3.78279			−0.271588
$195$	0.435348	+	2.00308i	0.0311759	+	0.143444i
$196$	25.3248			1.80891
$197$			23.3595i			1.66430i	0.554554	+	0.832148i	$0.312889\pi$
$197$			23.3595i			1.66430i	−0.554554	+	0.832148i	$0.687111\pi$
$198$			89.6439i			6.37072i
$199$	−2.25607			−0.159928			−0.0799642	−	0.996798i	$-0.525481\pi$
$199$	−2.25607			−0.159928			−0.0799642	+	0.996798i	$0.525481\pi$
$200$	−18.5566	−	40.6740i	−1.31215	−	2.87608i
$201$	−24.8707			−1.75424
$202$		−	15.7894i		−	1.11094i
$203$		−	13.2095i		−	0.927128i
$204$	120.656			8.44764
$205$	−1.69630	−	7.80486i	−0.118475	−	0.545115i
$206$	−1.20292			−0.0838115
$207$			19.3225i			1.34300i
$208$		−	3.70365i		−	0.256802i
$209$	21.7332			1.50332
$210$	−67.9976	+	14.7785i	−4.69228	+	1.01982i
$211$	−8.17208			−0.562589			−0.281294	−	0.959622i	$-0.590764\pi$
$211$	−8.17208			−0.562589			−0.281294	+	0.959622i	$0.590764\pi$
$212$		−	23.5868i		−	1.61995i
$213$			49.7905i			3.41159i
$214$	5.19525			0.355140
$215$	1.78388	−	0.387707i	0.121660	−	0.0264414i
$216$	157.742			10.7330
$217$			2.31142i			0.156910i
$218$		−	19.8989i		−	1.34772i
$219$	12.5330			0.846902
$220$	−10.1219	−	46.5721i	−0.682420	−	3.13989i
$221$	1.85109			0.124518
$222$		−	40.8365i		−	2.74076i
$223$			7.17999i			0.480807i	0.970673	+	0.240404i	$0.0772798\pi$
$223$			7.17999i			0.480807i	−0.970673	+	0.240404i	$0.922720\pi$
$224$	64.3709			4.30096
$225$	37.5648	−	17.1381i	2.50432	−	1.14254i
$226$	−39.6908			−2.64019
$227$			7.51999i			0.499119i	0.968359	+	0.249560i	$0.0802858\pi$
$227$			7.51999i			0.499119i	−0.968359	+	0.249560i	$0.919714\pi$
$228$		−	96.3812i		−	6.38300i
$229$	−24.0760			−1.59098			−0.795492	−	0.605964i	$-0.792788\pi$
$229$	−24.0760			−1.59098			−0.795492	+	0.605964i	$0.792788\pi$
$230$	−3.00387	−	13.8211i	−0.198069	−	0.911338i
$231$	−46.2280			−3.04158
$232$		−	34.4255i		−	2.26014i
$233$		−	6.80438i		−	0.445770i	−0.974845	−	0.222885i	$-0.928453\pi$
$233$		−	6.80438i		−	0.445770i	0.974845	−	0.222885i	$-0.0715474\pi$
$234$	6.09911			0.398711
$235$	−3.50404	+	0.761565i	−0.228579	+	0.0496790i
$236$	2.81055			0.182951
$237$		−	10.6424i		−	0.691298i
$238$			62.8380i			4.07318i
$239$	−11.7624			−0.760846			−0.380423	−	0.924813i	$-0.624222\pi$
$239$	−11.7624			−0.760846			−0.380423	+	0.924813i	$0.624222\pi$
$240$	−99.3834	+	21.5999i	−6.41517	+	1.39427i
$241$	−1.00000			−0.0644157
$241$	−1.00000			−0.0644157
$242$		−	13.8567i		−	0.890744i
$243$			62.5614i			4.01331i
$244$	35.2875			2.25905
$245$	−2.26592	−	10.4257i	−0.144764	−	0.666076i
$246$	−32.3981			−2.06563
$247$		−	1.47866i		−	0.0940852i
$248$			6.02381i			0.382513i
$249$	44.4783			2.81870
$250$	−24.2053	+	18.0985i	−1.53088	+	1.14465i
$251$	3.13511			0.197886			0.0989431	−	0.995093i	$-0.468454\pi$
$251$	3.13511			0.197886			0.0989431	+	0.995093i	$0.468454\pi$
$252$			150.378i			9.47294i
$253$		−	9.39625i		−	0.590737i
$254$	51.6805			3.24273
$255$	−10.7957	−	49.6720i	−0.676051	−	3.11058i
$256$	23.8598			1.49124
$257$			12.7199i			0.793444i	0.917939	+	0.396722i	$0.129852\pi$
$257$			12.7199i			0.793444i	−0.917939	+	0.396722i	$0.870148\pi$
$258$		−	7.40493i		−	0.461011i
$259$	15.4470			0.959831
$260$	−3.16863	+	0.688666i	−0.196510	+	0.0427092i
$261$	31.7939			1.96800
$262$			41.8521i			2.58563i
$263$			24.6778i			1.52170i	0.648930	+	0.760848i	$0.275217\pi$
$263$			24.6778i			1.52170i	−0.648930	+	0.760848i	$0.724783\pi$
$264$	−120.475			−7.41473
$265$	−9.71024	+	2.11041i	−0.596495	+	0.129642i
$266$	50.1955			3.07768
$267$		−	5.86572i		−	0.358976i
$268$		−	39.3423i		−	2.40321i
$269$	8.25882			0.503549			0.251775	−	0.967786i	$-0.418986\pi$
$269$	8.25882			0.503549			0.251775	+	0.967786i	$0.418986\pi$
$270$	−22.6480	−	104.206i	−1.37832	−	6.34178i
$271$	−32.7163			−1.98737			−0.993687	−	0.112184i	$-0.964215\pi$
$271$	−32.7163			−1.98737			−0.993687	+	0.112184i	$0.964215\pi$
$272$			91.8423i			5.56876i
$273$			3.14521i			0.190357i
$274$	−24.3986			−1.47397
$275$	−18.2672	+	8.33403i	−1.10156	+	0.502561i
$276$	−41.6699			−2.50823
$277$		−	28.7866i		−	1.72962i	−0.502099	−	0.864810i	$-0.667439\pi$
$277$		−	28.7866i		−	1.72962i	0.502099	−	0.864810i	$-0.332561\pi$
$278$			5.59290i			0.335440i
$279$	−5.56335			−0.333069
$280$	−14.5687	−	67.0320i	−0.870644	−	4.00593i
$281$	27.8460			1.66115			0.830577	−	0.556903i	$-0.188011\pi$
$281$	27.8460			1.66115			0.830577	+	0.556903i	$0.188011\pi$
$282$			14.5454i			0.866163i
$283$		−	20.2368i		−	1.20295i	−0.798891	−	0.601476i	$-0.794580\pi$
$283$		−	20.2368i		−	1.20295i	0.798891	−	0.601476i	$-0.205420\pi$
$284$	−78.7623			−4.67368
$285$	−39.6784	+	8.62365i	−2.35034	+	0.510821i
$286$	−2.96591			−0.175378
$287$		−	12.2551i		−	0.723394i
$288$			154.934i			9.12955i
$289$	−28.9030			−1.70017
$290$	−22.7418	+	4.94268i	−1.33545	+	0.290244i
$291$	4.69518			0.275236
$292$			19.8256i			1.16021i
$293$			11.8673i			0.693294i	0.937996	+	0.346647i	$0.112680\pi$
$293$			11.8673i			0.693294i	−0.937996	+	0.346647i	$0.887320\pi$
$294$	−43.2775			−2.52399
$295$	−0.251473	−	1.15705i	−0.0146413	−	0.0673663i
$296$	40.2566			2.33987
$297$		−	70.8442i		−	4.11080i
$298$		−	56.7686i		−	3.28852i
$299$	−0.639293			−0.0369712
$300$	36.9592	+	81.0104i	2.13384	+	4.67713i
$301$	2.80103			0.161449
$302$		−	53.5464i		−	3.08125i
$303$			19.5977i			1.12586i
$304$	73.3643			4.20773
$305$	−3.15733	−	14.5272i	−0.180788	−	0.831827i
$306$	−151.244			−8.64606
$307$			4.23151i			0.241505i	0.992683	+	0.120753i	$0.0385308\pi$
$307$			4.23151i			0.241505i	−0.992683	+	0.120753i	$0.961469\pi$
$308$		−	73.1269i		−	4.16679i
$309$	1.49306			0.0849373
$310$	3.97939	−	0.864877i	0.226014	−	0.0491217i
$311$	29.4486			1.66988			0.834938	−	0.550344i	$-0.185503\pi$
$311$	29.4486			1.66988			0.834938	+	0.550344i	$0.185503\pi$
$312$			8.19676i			0.464050i
$313$			25.7917i			1.45783i	0.684602	+	0.728917i	$0.259976\pi$
$313$			25.7917i			1.45783i	−0.684602	+	0.728917i	$0.740024\pi$
$314$	−15.9029			−0.897451
$315$	61.9080	−	13.4550i	3.48812	−	0.758104i
$316$	16.8349			0.947039
$317$			20.4033i			1.14597i	0.819568	+	0.572983i	$0.194214\pi$
$317$			20.4033i			1.14597i	−0.819568	+	0.572983i	$0.805786\pi$
$318$			40.3074i			2.26033i
$319$	−15.4610			−0.865647
$320$	−11.2108	−	51.5822i	−0.626703	−	2.88353i
$321$	−6.44833			−0.359911
$322$		−	21.7017i		−	1.20939i
$323$			36.6676i			2.04024i
$324$	−182.685			−10.1492
$325$	0.567022	+	1.24285i	0.0314527	+	0.0689408i
$326$	10.9284			0.605270
$327$			24.6985i			1.36583i
$328$		−	31.9380i		−	1.76348i
$329$	−5.50200			−0.303335
$330$	17.2974	+	79.5870i	0.952188	+	4.38112i
$331$	−2.39711			−0.131757			−0.0658784	−	0.997828i	$-0.520985\pi$
$331$	−2.39711			−0.131757			−0.0658784	+	0.997828i	$0.520985\pi$
$332$			70.3591i			3.86146i
$333$			37.1793i			2.03741i
$334$	−13.8182			−0.756097
$335$	−16.1965	+	3.52013i	−0.884910	+	0.192325i
$336$	−156.050			−8.51325
$337$		−	26.9613i		−	1.46868i	−0.678783	−	0.734339i	$-0.737492\pi$
$337$		−	26.9613i		−	1.46868i	0.678783	−	0.734339i	$-0.262508\pi$
$338$		−	34.9406i		−	1.90052i
$339$	49.2641			2.67566
$340$	78.5749	−	17.0774i	4.26132	−	0.926151i
$341$	2.70538			0.146504
$342$			120.815i			6.53293i
$343$			7.64626i			0.412859i
$344$	7.29977			0.393577
$345$	3.72839	+	17.1547i	0.200730	+	0.923579i
$346$	−22.2775			−1.19765
$347$			24.7328i			1.32773i	0.747854	+	0.663863i	$0.231084\pi$
$347$			24.7328i			1.32773i	−0.747854	+	0.663863i	$0.768916\pi$
$348$			68.5652i			3.67548i
$349$	12.1569			0.650745			0.325373	−	0.945586i	$-0.394510\pi$
$349$	12.1569			0.650745			0.325373	+	0.945586i	$0.394510\pi$
$350$	−42.1903	+	19.2484i	−2.25517	+	1.02887i
$351$	−4.82003			−0.257274
$352$		−	75.3421i		−	4.01575i
$353$			35.0021i			1.86297i	0.363775	+	0.931487i	$0.381488\pi$
$353$			35.0021i			1.86297i	−0.363775	+	0.931487i	$0.618512\pi$
$354$	−4.80295			−0.255274
$355$	7.04722	+	32.4250i	0.374027	+	1.72094i
$356$	9.27883			0.491777
$357$		−	77.9943i		−	4.12790i
$358$			22.9226i			1.21150i
$359$	8.10869			0.427960			0.213980	−	0.976838i	$-0.431357\pi$
$359$	8.10869			0.427960			0.213980	+	0.976838i	$0.431357\pi$
$360$	161.339	−	35.0652i	8.50330	−	1.84810i
$361$	10.2903			0.541597
$362$		−	12.4121i		−	0.652363i
$363$			17.1989i			0.902709i
$364$	−4.97533			−0.260778
$365$	8.16185	−	1.77389i	0.427211	−	0.0928495i
$366$	−60.3028			−3.15208
$367$		−	17.4433i		−	0.910531i	−0.890356	−	0.455266i	$-0.849544\pi$
$367$		−	17.4433i		−	0.910531i	0.890356	−	0.455266i	$-0.150456\pi$
$368$		−	31.7186i		−	1.65345i
$369$	29.4966			1.53553
$370$	−5.77989	−	26.5939i	−0.300482	−	1.38255i
$371$	−15.2469			−0.791579
$372$		−	11.9976i		−	0.622048i
$373$			3.19117i			0.165233i	0.996581	+	0.0826163i	$0.0263276\pi$
$373$			3.19117i			0.165233i	−0.996581	+	0.0826163i	$0.973672\pi$
$374$	73.5480			3.80308
$375$	30.0436	−	22.4638i	1.55144	−	1.16003i
$376$	−14.3388			−0.739467
$377$			1.05192i			0.0541765i
$378$		−	163.623i		−	8.41586i
$379$	0.832901			0.0427833			0.0213916	−	0.999771i	$-0.493190\pi$
$379$	0.832901			0.0427833			0.0213916	+	0.999771i	$0.493190\pi$
$380$	−13.6415	−	62.7662i	−0.699796	−	3.21984i
$381$	−64.1457			−3.28628
$382$		−	14.1670i		−	0.724849i
$383$			26.4615i			1.35212i	0.736846	+	0.676061i	$0.236314\pi$
$383$			26.4615i			1.35212i	−0.736846	+	0.676061i	$0.763686\pi$
$384$	−88.2160			−4.50175
$385$	−30.1050	+	6.54299i	−1.53429	+	0.333462i
$386$	53.0222			2.69876
$387$			6.74177i			0.342703i
$388$			7.42719i			0.377058i
$389$	−15.4436			−0.783021			−0.391510	−	0.920174i	$-0.628047\pi$
$389$	−15.4436			−0.783021			−0.391510	+	0.920174i	$0.628047\pi$
$390$	5.41486	−	1.17686i	0.274192	−	0.0595926i
$391$	15.8530			0.801723
$392$		−	42.6629i		−	2.15480i
$393$		−	51.9467i		−	2.62036i
$394$	63.1469			3.18130
$395$	−1.50630	−	6.93064i	−0.0757900	−	0.348718i
$396$	176.008			8.84476
$397$			18.9929i			0.953226i	0.879113	+	0.476613i	$0.158136\pi$
$397$			18.9929i			0.953226i	−0.879113	+	0.476613i	$0.841864\pi$
$398$			6.09874i			0.305702i
$399$	−62.3024			−3.11902
$400$	−61.6642	+	28.1329i	−3.08321	+	1.40665i
$401$	15.9990			0.798952			0.399476	−	0.916744i	$-0.369192\pi$
$401$	15.9990			0.798952			0.399476	+	0.916744i	$0.369192\pi$
$402$			67.2320i			3.35323i
$403$		−	0.184066i		−	0.00916898i
$404$	−31.0011			−1.54236
$405$	16.3457	+	75.2083i	0.812223	+	3.73713i
$406$	−35.7089			−1.77220
$407$		−	18.0798i		−	0.896182i
$408$		−	203.262i		−	10.0629i
$409$	−33.9863			−1.68051			−0.840257	−	0.542189i	$-0.817596\pi$
$409$	−33.9863			−1.68051			−0.840257	+	0.542189i	$0.817596\pi$
$410$	−21.0986	+	4.58554i	−1.04198	+	0.226464i
$411$	30.2835			1.49377
$412$			2.36184i			0.116359i
$413$		−	1.81679i		−	0.0893984i
$414$	52.2337			2.56715
$415$	28.9655	−	6.29534i	1.42186	−	0.309026i
$416$	−5.12605			−0.251325
$417$		−	6.94189i		−	0.339946i
$418$		−	58.7507i		−	2.87359i
$419$	13.0756			0.638787			0.319394	−	0.947622i	$-0.396521\pi$
$419$	13.0756			0.638787			0.319394	+	0.947622i	$0.396521\pi$
$420$	29.0164	+	133.508i	1.41586	+	6.51451i
$421$	−5.32603			−0.259575			−0.129787	−	0.991542i	$-0.541430\pi$
$421$	−5.32603			−0.259575			−0.129787	+	0.991542i	$0.541430\pi$
$422$			22.0913i			1.07539i
$423$		−	13.2427i		−	0.643883i
$424$	−39.7350			−1.92970
$425$	−14.0609	−	30.8199i	−0.682054	−	1.49498i
$426$	134.597			6.52124
$427$		−	22.8105i		−	1.10388i
$428$		−	10.2004i		−	0.493057i
$429$	3.68128			0.177734
$430$	−1.04807	−	4.82230i	−0.0505426	−	0.232552i
$431$	10.5429			0.507831			0.253916	−	0.967226i	$-0.418281\pi$
$431$	10.5429			0.507831			0.253916	+	0.967226i	$0.418281\pi$
$432$		−	239.147i		−	11.5060i
$433$		−	33.9409i		−	1.63110i	−0.578689	−	0.815548i	$-0.696435\pi$
$433$		−	33.9409i		−	1.63110i	0.578689	−	0.815548i	$-0.303565\pi$
$434$	6.24839			0.299932
$435$	28.2271	−	6.13484i	1.35338	−	0.294143i
$436$	−39.0699			−1.87111
$437$		−	12.6635i		−	0.605778i
$438$		−	33.8800i		−	1.61885i
$439$	−16.5413			−0.789473			−0.394736	−	0.918794i	$-0.629164\pi$
$439$	−16.5413			−0.789473			−0.394736	+	0.918794i	$0.629164\pi$
$440$	−78.4568	+	17.0517i	−3.74028	+	0.812909i
$441$	39.4017			1.87627
$442$		−	5.00399i		−	0.238015i
$443$			3.26455i			0.155104i	0.996988	+	0.0775518i	$0.0247103\pi$
$443$			3.26455i			0.155104i	−0.996988	+	0.0775518i	$0.975290\pi$
$444$	−80.1790			−3.80513
$445$	−0.830218	−	3.81993i	−0.0393561	−	0.181082i
$446$	19.4094			0.919061
$447$			70.4610i			3.33269i
$448$		−	80.9936i		−	3.82659i
$449$	−18.7302			−0.883934			−0.441967	−	0.897031i	$-0.645719\pi$
$449$	−18.7302			−0.883934			−0.441967	+	0.897031i	$0.645719\pi$
$450$	−46.3288	−	101.548i	−2.18396	−	4.78700i
$451$	−14.3438			−0.675424
$452$			77.9296i			3.66550i
$453$			66.4616i			3.12264i
$454$	20.3285			0.954064
$455$	0.445165	+	2.04825i	0.0208697	+	0.0960237i
$456$	−162.367			−7.60352
$457$			26.0758i			1.21978i	0.792487	+	0.609888i	$0.208786\pi$
$457$			26.0758i			1.21978i	−0.792487	+	0.609888i	$0.791214\pi$
$458$			65.0837i			3.04116i
$459$	119.526			5.57900
$460$	−27.1366	+	5.89784i	−1.26525	+	0.274988i
$461$	20.1258			0.937353			0.468676	−	0.883370i	$-0.344731\pi$
$461$	20.1258			0.937353			0.468676	+	0.883370i	$0.344731\pi$
$462$			124.966i			5.81396i
$463$			3.72503i			0.173117i	0.996247	+	0.0865585i	$0.0275869\pi$
$463$			3.72503i			0.173117i	−0.996247	+	0.0865585i	$0.972413\pi$
$464$	−52.1911			−2.42291
$465$	−4.93921	+	1.07348i	−0.229050	+	0.0497815i
$466$	−18.3940			−0.852087
$467$		−	42.7555i		−	1.97849i	−0.146269	−	0.989245i	$-0.546727\pi$
$467$		−	42.7555i		−	1.97849i	0.146269	−	0.989245i	$-0.453273\pi$
$468$		−	11.9751i		−	0.553549i
$469$	−25.4315			−1.17432
$470$	2.05871	+	9.47236i	0.0949612	+	0.436927i
$471$	19.7386			0.909506
$472$		−	4.73475i		−	0.217934i
$473$		−	3.27843i		−	0.150742i
$474$	−28.7692			−1.32141
$475$	−24.6191	+	11.2319i	−1.12960	+	0.515357i
$476$	123.377			5.65499
$477$		−	36.6976i		−	1.68027i
$478$			31.7968i			1.45435i
$479$	−19.0042			−0.868326			−0.434163	−	0.900834i	$-0.642956\pi$
$479$	−19.0042			−0.868326			−0.434163	+	0.900834i	$0.642956\pi$
$480$	29.8954	+	137.552i	1.36453	+	6.27836i
$481$	−1.23009			−0.0560875
$482$			2.70326i			0.123130i
$483$			26.9361i			1.22564i
$484$	−27.2065			−1.23666
$485$	3.05764	−	0.664543i	0.138840	−	0.0301754i
$486$	169.120			7.67143
$487$			13.8722i			0.628609i	0.949322	+	0.314305i	$0.101771\pi$
$487$			13.8722i			0.628609i	−0.949322	+	0.314305i	$0.898229\pi$
$488$		−	59.4465i		−	2.69101i
$489$	−13.5643			−0.613400
$490$	−28.1835	+	6.12538i	−1.27320	+	0.276716i
$491$	8.57923			0.387175			0.193588	−	0.981083i	$-0.437988\pi$
$491$	8.57923			0.387175			0.193588	+	0.981083i	$0.437988\pi$
$492$			63.6110i			2.86780i
$493$		−	26.0852i		−	1.17482i
$494$	−3.99722			−0.179843
$495$	−15.7483	−	72.4595i	−0.707832	−	3.25681i
$496$	9.13247			0.410060
$497$			50.9133i			2.28377i
$498$		−	120.237i		−	5.38793i
$499$	−16.5238			−0.739706			−0.369853	−	0.929090i	$-0.620592\pi$
$499$	−16.5238			−0.739706			−0.369853	+	0.929090i	$0.620592\pi$
$500$	35.5349	+	47.5252i	1.58917	+	2.12539i
$501$	17.1511			0.766253
$502$		−	8.47502i		−	0.378259i
$503$		−	41.3259i		−	1.84263i	−0.388814	−	0.921316i	$-0.627115\pi$
$503$		−	41.3259i		−	1.84263i	0.388814	−	0.921316i	$-0.372885\pi$
$504$	253.332			11.2843
$505$	2.77381	+	12.7626i	0.123433	+	0.567928i
$506$	−25.4005			−1.12919
$507$			43.3682i			1.92605i
$508$		−	101.470i		−	4.50202i
$509$	38.9093			1.72462			0.862311	−	0.506378i	$-0.169016\pi$
$509$	38.9093			1.72462			0.862311	+	0.506378i	$0.169016\pi$
$510$	−134.277	+	29.1835i	−5.94587	+	1.29227i
$511$	12.8156			0.566930
$512$		−	11.9159i		−	0.526613i
$513$		−	95.4783i		−	4.21547i
$514$	34.3852			1.51667
$515$	0.972325	−	0.211324i	0.0428458	−	0.00931205i
$516$	−14.5390			−0.640042
$517$			6.43975i			0.283220i
$518$		−	41.7574i		−	1.83471i
$519$	27.6508			1.21373
$520$	1.16015	+	5.33797i	0.0508759	+	0.234085i
$521$	−11.4043			−0.499631			−0.249815	−	0.968294i	$-0.580370\pi$
$521$	−11.4043			−0.499631			−0.249815	+	0.968294i	$0.580370\pi$
$522$		−	85.9474i		−	3.76181i
$523$			26.0626i			1.13964i	0.821770	+	0.569819i	$0.192987\pi$
$523$			26.0626i			1.13964i	−0.821770	+	0.569819i	$0.807013\pi$
$524$	82.1731			3.58975
$525$	52.3665	−	23.8911i	2.28546	−	1.04269i
$526$	66.7105			2.90872
$527$			4.56443i			0.198830i
$528$			182.647i			7.94871i
$529$	17.5250			0.761956
$530$	5.70500	+	26.2493i	0.247809	+	1.14020i
$531$	4.37282			0.189764
$532$		−	98.5546i		−	4.27288i
$533$			0.975910i			0.0422714i
$534$	−15.8566			−0.686181
$535$	−4.19934	+	0.912680i	−0.181553	+	0.0394586i
$536$	−66.2772			−2.86274
$537$		−	28.4515i		−	1.22777i
$538$		−	22.3258i		−	0.962532i
$539$	−19.1605			−0.825301
$540$	−204.600	+	44.4675i	−8.80459	+	1.91358i
$541$	16.0881			0.691682			0.345841	−	0.938293i	$-0.387594\pi$
$541$	16.0881			0.691682			0.345841	+	0.938293i	$0.387594\pi$
$542$			88.4408i			3.79886i
$543$			15.4058i			0.661126i
$544$	127.115			5.45000
$545$	3.49576	+	16.0844i	0.149742	+	0.688978i
$546$	8.50234			0.363867
$547$			32.6032i			1.39401i	0.717064	+	0.697007i	$0.245485\pi$
$547$			32.6032i			1.39401i	−0.717064	+	0.697007i	$0.754515\pi$
$548$			47.9047i			2.04639i
$549$	54.9023			2.34317
$550$	22.5291	+	49.3812i	0.960643	+	2.10562i
$551$	−20.8371			−0.887688
$552$			70.1983i			2.98784i
$553$		−	10.8824i		−	0.462766i
$554$	−77.8178			−3.30616
$555$	7.17398	+	33.0083i	0.304518	+	1.40112i
$556$	10.9812			0.465706
$557$		−	25.3965i		−	1.07608i	−0.842918	−	0.538042i	$-0.819164\pi$
$557$		−	25.3965i		−	1.07608i	0.842918	−	0.538042i	$-0.180836\pi$
$558$			15.0392i			0.636660i
$559$	−0.223055			−0.00943420
$560$	−101.625	+	22.0870i	−4.29442	+	0.933345i
$561$	−91.2876			−3.85416
$562$		−	75.2752i		−	3.17529i
$563$		−	20.7748i		−	0.875553i	−0.899084	−	0.437776i	$-0.855766\pi$
$563$		−	20.7748i		−	0.875553i	0.899084	−	0.437776i	$-0.144234\pi$
$564$	28.5586			1.20253
$565$	32.0822	−	6.97271i	1.34971	−	0.293344i
$566$	−54.7054			−2.29944
$567$			118.091i			4.95935i
$568$			132.685i			5.56736i
$569$	31.7927			1.33282			0.666409	−	0.745586i	$-0.267831\pi$
$569$	31.7927			1.33282			0.666409	+	0.745586i	$0.267831\pi$
$570$	23.3120	+	107.261i	0.976432	+	4.49267i
$571$	5.77539			0.241693			0.120846	−	0.992671i	$-0.461439\pi$
$571$	5.77539			0.241693			0.120846	+	0.992671i	$0.461439\pi$
$572$			5.82332i			0.243485i
$573$			17.5841i			0.734585i
$574$	−33.1287			−1.38277
$575$	4.85607	+	10.6439i	0.202512	+	0.443883i
$576$	194.943			8.12262
$577$			24.5448i			1.02181i	0.859636	+	0.510907i	$0.170690\pi$
$577$			24.5448i			1.02181i	−0.859636	+	0.510907i	$0.829310\pi$
$578$			78.1323i			3.24988i
$579$	−65.8110			−2.73501
$580$	9.70454	+	44.6517i	0.402959	+	1.85406i
$581$	45.4813			1.88688
$582$		−	12.6923i		−	0.526113i
$583$			17.8455i			0.739087i
$584$	33.3989			1.38206
$585$	−4.92993	+	1.07146i	−0.203827	+	0.0442996i
$586$	32.0804			1.32523
$587$		−	7.25772i		−	0.299558i	−0.988719	−	0.149779i	$-0.952144\pi$
$587$		−	7.25772i		−	0.299558i	0.988719	−	0.149779i	$-0.0478563\pi$
$588$			84.9717i			3.50417i
$589$	3.64610			0.150235
$590$	−3.12782	+	0.679797i	−0.128770	+	0.0279868i
$591$	−78.3777			−3.22403
$592$		−	61.0314i		−	2.50837i
$593$		−	30.2173i		−	1.24087i	−0.784256	−	0.620437i	$-0.786955\pi$
$593$		−	30.2173i		−	1.24087i	0.784256	−	0.620437i	$-0.213045\pi$
$594$	−191.511			−7.85778
$595$	−11.0391	−	50.7922i	−0.452559	−	2.08228i
$596$	−111.461			−4.56560
$597$		−	7.56974i		−	0.309809i
$598$			1.72818i			0.0706704i
$599$	−23.3204			−0.952846			−0.476423	−	0.879216i	$-0.658067\pi$
$599$	−23.3204			−0.952846			−0.476423	+	0.879216i	$0.658067\pi$
$600$	136.473	−	62.2626i	5.57147	−	2.54186i
$601$	−7.46795			−0.304624			−0.152312	−	0.988332i	$-0.548672\pi$
$601$	−7.46795			−0.304624			−0.152312	+	0.988332i	$0.548672\pi$
$602$		−	7.57191i		−	0.308608i
$603$		−	61.2109i		−	2.49270i
$604$	−105.134			−4.27784
$605$	2.43429	+	11.2004i	0.0989679	+	0.455362i
$606$	52.9778			2.15208
$607$		−	44.1118i		−	1.79044i	−0.445622	−	0.895221i	$-0.647017\pi$
$607$		−	44.1118i		−	1.79044i	0.445622	−	0.895221i	$-0.352983\pi$
$608$		−	101.540i		−	4.11800i
$609$	44.3217			1.79601
$610$	−39.2709	+	8.53510i	−1.59003	+	0.345576i
$611$	0.438142			0.0177253
$612$			296.956i			12.0037i
$613$			19.5991i			0.791598i	0.918337	+	0.395799i	$0.129532\pi$
$613$			19.5991i			0.791598i	−0.918337	+	0.395799i	$0.870468\pi$
$614$	11.4389			0.461636
$615$	26.1875	−	5.69156i	1.05598	−	0.229506i
$616$	−123.192			−4.96354
$617$			10.8947i			0.438605i	0.975657	+	0.219302i	$0.0703781\pi$
$617$			10.8947i			0.438605i	−0.975657	+	0.219302i	$0.929622\pi$
$618$		−	4.03614i		−	0.162357i
$619$	−12.2713			−0.493225			−0.246613	−	0.969114i	$-0.579318\pi$
$619$	−12.2713			−0.493225			−0.246613	+	0.969114i	$0.579318\pi$
$620$	−1.69811	−	7.81321i	−0.0681979	−	0.313786i
$621$	−41.2795			−1.65649
$622$		−	79.6073i		−	3.19196i
$623$		−	5.99799i		−	0.240305i
$624$	12.4268			0.497469
$625$	16.3858	−	18.8814i	0.655432	−	0.755254i
$626$	69.7218			2.78664
$627$			72.9211i			2.91219i
$628$			31.2240i			1.24597i
$629$	30.5036			1.21626
$630$	−36.3724	−	167.354i	−1.44911	−	6.66753i
$631$	31.3350			1.24743			0.623713	−	0.781654i	$-0.285623\pi$
$631$	31.3350			1.24743			0.623713	+	0.781654i	$0.285623\pi$
$632$		−	28.3607i		−	1.12813i
$633$		−	27.4196i		−	1.08983i
$634$	55.1556			2.19051
$635$	−41.7736	+	9.07902i	−1.65773	+	0.360290i
$636$	79.1402			3.13811
$637$			1.30362i			0.0516514i
$638$			41.7950i			1.65468i
$639$	−122.543			−4.84772
$640$	−57.4488	+	12.4859i	−2.27086	+	0.493547i
$641$	−4.50609			−0.177980			−0.0889899	−	0.996033i	$-0.528364\pi$
$641$	−4.50609			−0.177980			−0.0889899	+	0.996033i	$0.528364\pi$
$642$			17.4315i			0.687968i
$643$		−	27.3969i		−	1.08043i	−0.841527	−	0.540214i	$-0.818343\pi$
$643$		−	27.3969i		−	1.08043i	0.841527	−	0.540214i	$-0.181657\pi$
$644$	−42.6095			−1.67905
$645$	1.30087	+	5.98543i	0.0512215	+	0.235676i
$646$	99.1222			3.89991
$647$			10.4356i			0.410267i	0.978734	+	0.205133i	$0.0657628\pi$
$647$			10.4356i			0.410267i	−0.978734	+	0.205133i	$0.934237\pi$
$648$			307.758i			12.0899i
$649$	−2.12644			−0.0834701
$650$	3.35975	−	1.53281i	0.131780	−	0.0601218i
$651$	−7.75548			−0.303961
$652$		−	21.4571i		−	0.840324i
$653$		−	32.4173i		−	1.26859i	−0.773093	−	0.634293i	$-0.781291\pi$
$653$		−	32.4173i		−	1.26859i	0.773093	−	0.634293i	$-0.218709\pi$
$654$	66.7665			2.61078
$655$	−7.35240	−	33.8292i	−0.287282	−	1.32182i
$656$	−48.4200			−1.89048
$657$			30.8458i			1.20341i
$658$			14.8734i			0.579824i
$659$	19.7610			0.769780			0.384890	−	0.922962i	$-0.374239\pi$
$659$	19.7610			0.769780			0.384890	+	0.922962i	$0.374239\pi$
$660$	156.263	−	33.9619i	6.08251	−	1.32197i
$661$	−13.6618			−0.531381			−0.265690	−	0.964058i	$-0.585600\pi$
$661$	−13.6618			−0.531381			−0.265690	+	0.964058i	$0.585600\pi$
$662$			6.48001i			0.251853i
$663$			6.21093i			0.241213i
$664$	118.529			4.59982
$665$	−40.5731	+	8.81812i	−1.57336	+	0.341952i
$666$	100.505			3.89451
$667$			9.00878i			0.348822i
$668$			27.1308i			1.04972i
$669$	−24.0909			−0.931407
$670$	9.51584	+	43.7834i	0.367629	+	1.69150i
$671$	−26.6982			−1.03067
$672$			215.982i			8.33170i
$673$			42.3140i			1.63109i	0.578697	+	0.815543i	$0.303561\pi$
$673$			42.3140i			1.63109i	−0.578697	+	0.815543i	$0.696439\pi$
$674$	−72.8836			−2.80737
$675$	36.6130	+	80.2514i	1.40923	+	3.08888i
$676$	−68.6030			−2.63858
$677$			5.90240i			0.226848i	0.993547	+	0.113424i	$0.0361818\pi$
$677$			5.90240i			0.226848i	−0.993547	+	0.113424i	$0.963818\pi$
$678$		−	133.174i		−	5.11451i
$679$	4.80106			0.184248
$680$	−28.7691	−	132.370i	−1.10324	−	5.07615i
$681$	−25.2317			−0.966880
$682$		−	7.31335i		−	0.280043i
$683$		−	46.3854i		−	1.77489i	−0.460917	−	0.887443i	$-0.652479\pi$
$683$		−	46.3854i		−	1.77489i	0.460917	−	0.887443i	$-0.347521\pi$
$684$	237.210			9.06996
$685$	19.7215	−	4.28624i	0.753519	−	0.163769i
$686$	20.6699			0.789179
$687$		−	80.7816i		−	3.08201i
$688$		−	11.0669i		−	0.421921i
$689$	1.21416			0.0462557
$690$	46.3737	−	10.0788i	1.76542	−	0.383694i
$691$	−7.70227			−0.293008			−0.146504	−	0.989210i	$-0.546802\pi$
$691$	−7.70227			−0.293008			−0.146504	+	0.989210i	$0.546802\pi$
$692$			43.7400i			1.66275i
$693$		−	113.775i		−	4.32195i
$694$	66.8592			2.53794
$695$	−0.982536	−	4.52076i	−0.0372697	−	0.171482i
$696$	115.507			4.37829
$697$		−	24.2004i		−	0.916656i
$698$		−	32.8634i		−	1.24390i
$699$	22.8306			0.863533
$700$	37.7927	+	82.8372i	1.42843	+	3.13095i
$701$	−1.53294			−0.0578983			−0.0289491	−	0.999581i	$-0.509216\pi$
$701$	−1.53294			−0.0578983			−0.0289491	+	0.999581i	$0.509216\pi$
$702$			13.0298i			0.491779i
$703$		−	24.3665i		−	0.919000i
$704$	−94.7980			−3.57283
$705$	−2.55526	−	11.7571i	−0.0962368	−	0.442796i
$706$	94.6199			3.56107
$707$			20.0397i			0.753669i
$708$			9.43020i			0.354409i
$709$	46.3315			1.74002			0.870009	−	0.493037i	$-0.164113\pi$
$709$	46.3315			1.74002			0.870009	+	0.493037i	$0.164113\pi$
$710$	87.6534	−	19.0505i	3.28957	−	0.714952i
$711$	26.1927			0.982304
$712$		−	15.6314i		−	0.585812i
$713$		−	1.57637i		−	0.0590355i
$714$	−210.839			−7.89046
$715$	2.39736	−	0.521039i	0.0896560	−	0.0194857i
$716$	45.0067			1.68198
$717$		−	39.4661i		−	1.47389i
$718$		−	21.9199i		−	0.818045i
$719$	36.5081			1.36152			0.680762	−	0.732505i	$-0.261649\pi$
$719$	36.5081			1.36152			0.680762	+	0.732505i	$0.261649\pi$
$720$	−53.1609	−	244.599i	−1.98119	−	9.11568i
$721$	1.52673			0.0568584
$722$		−	27.8175i		−	1.03526i
$723$		−	3.35528i		−	0.124784i
$724$	−24.3700			−0.905705
$725$	17.5140	−	7.99037i	0.650453	−	0.296755i
$726$	46.4932			1.72552
$727$		−	11.1877i		−	0.414930i	−0.978242	−	0.207465i	$-0.933479\pi$
$727$		−	11.1877i		−	0.414930i	0.978242	−	0.207465i	$-0.0665214\pi$
$728$			8.38160i			0.310643i
$729$	−106.653			−3.95010
$730$	−4.79529	−	22.0636i	−0.177482	−	0.816612i
$731$	5.53126			0.204581
$732$			118.400i			4.37617i
$733$		−	28.4274i		−	1.04999i	−0.851106	−	0.524994i	$-0.824068\pi$
$733$		−	28.4274i		−	1.04999i	0.851106	−	0.524994i	$-0.175932\pi$
$734$	−47.1538			−1.74048
$735$	34.9813	−	7.60279i	1.29030	−	0.280433i
$736$	−43.9003			−1.61819
$737$			29.7660i			1.09645i
$738$		−	79.7372i		−	2.93517i
$739$	−29.4807			−1.08447			−0.542233	−	0.840228i	$-0.682421\pi$
$739$	−29.4807			−1.08447			−0.542233	+	0.840228i	$0.682421\pi$
$740$	−52.2149	+	11.3483i	−1.91946	+	0.417173i
$741$	4.96134			0.182259
$742$			41.2164i			1.51310i
$743$			16.0342i			0.588237i	0.955769	+	0.294118i	$0.0950260\pi$
$743$			16.0342i			0.588237i	−0.955769	+	0.294118i	$0.904974\pi$
$744$	−20.2116			−0.740993
$745$	9.97287	+	45.8863i	0.365378	+	1.68114i
$746$	8.62657			0.315841
$747$			109.469i			4.00524i
$748$		−	144.405i		−	5.27999i
$749$	−6.59374			−0.240930
$750$	−60.7255	−	81.2157i	−2.21738	−	2.96558i
$751$	−21.1700			−0.772503			−0.386251	−	0.922394i	$-0.626230\pi$
$751$	−21.1700			−0.772503			−0.386251	+	0.922394i	$0.626230\pi$
$752$			21.7385i			0.792721i
$753$			10.5192i			0.383340i
$754$	2.84361			0.103558
$755$	9.40680	+	43.2817i	0.342349	+	1.57518i
$756$	−321.260			−11.6841
$757$			3.46802i			0.126048i	0.998012	+	0.0630238i	$0.0200744\pi$
$757$			3.46802i			0.126048i	−0.998012	+	0.0630238i	$0.979926\pi$
$758$		−	2.25155i		−	0.0817800i
$759$	31.5271			1.14436
$760$	−105.738	+	22.9810i	−3.83552	+	0.833607i
$761$	−8.94564			−0.324279			−0.162140	−	0.986768i	$-0.551840\pi$
$761$	−8.94564			−0.324279			−0.162140	+	0.986768i	$0.551840\pi$
$762$			173.403i			6.28172i
$763$			25.2554i			0.914308i
$764$	−27.8158			−1.00634
$765$	122.251	−	26.5699i	4.42000	−	0.960638i
$766$	71.5325			2.58458
$767$			0.144677i			0.00522397i
$768$			80.0563i			2.88878i
$769$	−19.5376			−0.704544			−0.352272	−	0.935898i	$-0.614591\pi$
$769$	−19.5376			−0.704544			−0.352272	+	0.935898i	$0.614591\pi$
$770$	17.6874	+	81.3818i	0.637410	+	2.93280i
$771$	−42.6788			−1.53704
$772$		−	104.105i		−	3.74681i
$773$			35.1299i			1.26354i	0.775158	+	0.631768i	$0.217670\pi$
$773$			35.1299i			1.26354i	−0.775158	+	0.631768i	$0.782330\pi$
$774$	18.2248			0.655076
$775$	−3.06462	+	1.39817i	−0.110084	+	0.0502236i
$776$	12.5121			0.449157
$777$			51.8291i			1.85936i
$778$			41.7481i			1.49674i
$779$	−19.3314			−0.692621
$780$	−2.31067	−	10.6316i	−0.0827352	−	0.380674i
$781$	59.5909			2.13233
$782$		−	42.8549i		−	1.53249i
$783$			67.9229i			2.42737i
$784$	−64.6795			−2.30998
$785$	12.8543	−	2.79375i	0.458791	−	0.0997131i
$786$	−140.426			−5.00881
$787$		−	15.7786i		−	0.562447i	−0.959642	−	0.281223i	$-0.909260\pi$
$787$		−	15.7786i		−	0.562447i	0.959642	−	0.281223i	$-0.0907402\pi$
$788$		−	123.984i		−	4.41674i
$789$	−82.8008			−2.94779
$790$	−18.7353	+	4.07192i	−0.666573	+	0.144872i
$791$	50.3750			1.79113
$792$		−	296.509i		−	10.5360i
$793$			1.81647i			0.0645047i
$794$	51.3428			1.82209
$795$	−7.08103	−	32.5806i	−0.251138	−	1.15551i
$796$	11.9744			0.424420
$797$			14.1788i			0.502240i	0.967956	+	0.251120i	$0.0807989\pi$
$797$			14.1788i			0.502240i	−0.967956	+	0.251120i	$0.919201\pi$
$798$			168.420i			5.96200i
$799$	−10.8649			−0.384374
$800$	38.9375	+	85.3466i	1.37665	+	3.01746i
$801$	14.4365			0.510089
$802$		−	43.2495i		−	1.52719i
$803$		−	14.9999i		−	0.529335i
$804$	132.004			4.65544
$805$	3.81247	+	17.5416i	0.134372	+	0.618259i
$806$	−0.497579			−0.0175265
$807$			27.7107i			0.975461i
$808$			52.2255i			1.83729i
$809$	40.1751			1.41248			0.706241	−	0.707972i	$-0.250390\pi$
$809$	40.1751			1.41248			0.706241	+	0.707972i	$0.250390\pi$
$810$	203.308	−	44.1867i	7.14351	−	1.55256i
$811$	16.1770			0.568050			0.284025	−	0.958817i	$-0.408330\pi$
$811$	16.1770			0.568050			0.284025	+	0.958817i	$0.408330\pi$
$812$			70.1114i			2.46043i
$813$		−	109.772i		−	3.84989i
$814$	−48.8744			−1.71305
$815$	−8.83349	+	1.91986i	−0.309424	+	0.0672498i
$816$	−308.157			−10.7876
$817$		−	4.41841i		−	0.154581i
$818$			91.8739i			3.21229i
$819$	−7.74090			−0.270489
$820$	9.00333	+	41.4253i	0.314410	+	1.44663i
$821$	21.1039			0.736532			0.368266	−	0.929720i	$-0.379951\pi$
$821$	21.1039			0.736532			0.368266	+	0.929720i	$0.379951\pi$
$822$		−	81.8642i		−	2.85534i
$823$			20.7635i			0.723769i	0.932223	+	0.361884i	$0.117866\pi$
$823$			20.7635i			0.723769i	−0.932223	+	0.361884i	$0.882134\pi$
$824$	3.97882			0.138609
$825$	−27.9630	−	61.2917i	−0.973547	−	2.13390i
$826$	−4.91126			−0.170885
$827$		−	20.4952i		−	0.712688i	−0.934355	−	0.356344i	$-0.884023\pi$
$827$		−	20.4952i		−	0.712688i	0.934355	−	0.356344i	$-0.115977\pi$
$828$		−	102.557i		−	3.56409i
$829$	−19.0011			−0.659937			−0.329968	−	0.943992i	$-0.607038\pi$
$829$	−19.0011			−0.659937			−0.329968	+	0.943992i	$0.607038\pi$
$830$	−17.0180	−	78.3015i	−0.590702	−	2.71789i
$831$	96.5872			3.35057
$832$			6.44977i			0.223606i
$833$		−	32.3270i		−	1.12006i
$834$	−18.7657			−0.649805
$835$	11.1693	−	2.42752i	0.386529	−	0.0840077i
$836$	−115.352			−3.98954
$837$		−	11.8852i		−	0.410814i
$838$		−	35.3469i		−	1.22104i
$839$	7.58955			0.262020			0.131010	−	0.991381i	$-0.458178\pi$
$839$	7.58955			0.262020			0.131010	+	0.991381i	$0.458178\pi$
$840$	224.911	−	48.8819i	7.76018	−	1.68659i
$841$	−14.1766			−0.488848
$842$			14.3977i			0.496176i
$843$			93.4313i			3.21794i
$844$	43.3744			1.49301
$845$	6.13822	+	28.2426i	0.211161	+	0.971576i
$846$	−35.7986			−1.23078
$847$			17.5868i			0.604288i
$848$			60.2407i			2.06867i
$849$	67.9001			2.33033
$850$	−83.3143	+	38.0103i	−2.85766	+	1.30374i
$851$	−10.5347			−0.361126
$852$		−	264.270i		−	9.05373i
$853$			32.7092i			1.11994i	0.828512	+	0.559971i	$0.189188\pi$
$853$			32.7092i			1.11994i	−0.828512	+	0.559971i	$0.810812\pi$
$854$	−61.6627			−2.11005
$855$	−21.2243	−	97.6552i	−0.725854	−	3.33974i
$856$	−17.1840			−0.587337
$857$		−	36.8104i		−	1.25742i	−0.777641	−	0.628709i	$-0.783584\pi$
$857$		−	36.8104i		−	1.25742i	0.777641	−	0.628709i	$-0.216416\pi$
$858$		−	9.95147i		−	0.339738i
$859$	−35.0252			−1.19504			−0.597522	−	0.801853i	$-0.703848\pi$
$859$	−35.0252			−1.19504			−0.597522	+	0.801853i	$0.703848\pi$
$860$	−9.46819	+	2.05781i	−0.322863	+	0.0701706i
$861$	41.1192			1.40134
$862$		−	28.5001i		−	0.970718i
$863$			13.0144i			0.443016i	0.975159	+	0.221508i	$0.0710979\pi$
$863$			13.0144i			0.443016i	−0.975159	+	0.221508i	$0.928902\pi$
$864$	−330.992			−11.2606
$865$	18.0070	−	3.91362i	0.612256	−	0.133067i
$866$	−91.7513			−3.11784
$867$		−	96.9776i		−	3.29353i
$868$		−	12.2682i		−	0.416410i
$869$	−12.7372			−0.432079
$870$	−16.5841	−	76.3052i	−0.562253	−	2.58699i
$871$	2.02519			0.0686210
$872$			65.8183i			2.22889i
$873$			11.5556i			0.391099i
$874$	−34.2328			−1.15794
$875$	30.7211	−	22.9704i	1.03856	−	0.776540i
$876$	−66.5206			−2.24752
$877$			11.0175i			0.372033i	0.982547	+	0.186016i	$0.0595578\pi$
$877$			11.0175i			0.372033i	−0.982547	+	0.186016i	$0.940442\pi$
$878$			44.7155i			1.50907i
$879$	−39.8180			−1.34303
$880$	25.8514	+	118.945i	0.871452	+	4.00964i
$881$	12.4699			0.420123			0.210062	−	0.977688i	$-0.432634\pi$
$881$	12.4699			0.420123			0.210062	+	0.977688i	$0.432634\pi$
$882$		−	106.513i		−	3.58648i
$883$		−	16.6123i		−	0.559047i	−0.960139	−	0.279524i	$-0.909823\pi$
$883$		−	16.6123i		−	0.559047i	0.960139	−	0.279524i	$-0.0901765\pi$
$884$	−9.82492			−0.330448
$885$	3.88224	−	0.843762i	0.130500	−	0.0283627i
$886$	8.82495			0.296480
$887$		−	20.2890i		−	0.681239i	−0.940201	−	0.340619i	$-0.889363\pi$
$887$		−	20.2890i		−	0.681239i	0.940201	−	0.340619i	$-0.110637\pi$
$888$			135.072i			4.53272i
$889$	−65.5922			−2.19989
$890$	−10.3263	+	2.24430i	−0.346137	+	0.0752291i
$891$	138.218			4.63048
$892$		−	38.1087i		−	1.27597i
$893$			8.67899i			0.290431i
$894$	190.475			6.37043
$895$	−4.02695	−	18.5284i	−0.134606	−	0.619338i
$896$	−90.2053			−3.01355
$897$		−	2.14501i		−	0.0716197i
$898$			50.6327i			1.68964i
$899$	−2.59382			−0.0865087
$900$	−199.380	+	90.9628i	−6.64600	+	3.03209i
$901$	−30.1084			−1.00306
$902$			38.7751i			1.29107i
$903$			9.39823i			0.312754i
$904$	131.283			4.36640
$905$	2.18050	+	10.0327i	0.0724821	+	0.333498i
$906$	179.663			5.96891
$907$			2.41862i			0.0803091i	0.999193	+	0.0401546i	$0.0127850\pi$
$907$			2.41862i			0.0803091i	−0.999193	+	0.0401546i	$0.987215\pi$
$908$		−	39.9133i		−	1.32457i
$909$	−48.2333			−1.59980
$910$	5.53697	−	1.20340i	0.183549	−	0.0398923i
$911$	−13.9040			−0.460662			−0.230331	−	0.973112i	$-0.573981\pi$
$911$	−13.9040			−0.460662			−0.230331	+	0.973112i	$0.573981\pi$
$912$			246.158i			8.15110i
$913$		−	53.2331i		−	1.76176i
$914$	70.4899			2.33160
$915$	48.7430	−	10.5937i	1.61139	−	0.350218i
$916$	127.786			4.22218
$917$		−	53.1181i		−	1.75411i
$918$		−	323.110i		−	10.6642i
$919$	−34.2519			−1.12987			−0.564933	−	0.825137i	$-0.691098\pi$
$919$	−34.2519			−1.12987			−0.564933	+	0.825137i	$0.691098\pi$
$920$	9.93569	+	45.7152i	0.327570	+	1.50719i
$921$	−14.1979			−0.467837
$922$		−	54.4054i		−	1.79175i
$923$		−	4.05439i		−	0.133452i
$924$	245.361			8.07179
$925$	9.34380	+	20.4805i	0.307222	+	0.673396i
$926$	10.0697			0.330912
$927$			3.67467i			0.120692i
$928$			72.2353i			2.37124i
$929$	45.2370			1.48418			0.742090	−	0.670301i	$-0.233835\pi$
$929$	45.2370			1.48418			0.742090	+	0.670301i	$0.233835\pi$
$930$	2.90190	+	13.3520i	0.0951572	+	0.437829i
$931$	−25.8230			−0.846314
$932$			36.1151i			1.18299i
$933$			98.8083i			3.23484i
$934$	−115.579			−3.78187
$935$	−59.4491	+	12.9206i	−1.94419	+	0.422549i
$936$	−20.1736			−0.659395
$937$		−	6.24872i		−	0.204137i	−0.994777	−	0.102068i	$-0.967454\pi$
$937$		−	6.24872i		−	0.204137i	0.994777	−	0.102068i	$-0.0325461\pi$
$938$			68.7481i			2.24471i
$939$	−86.5385			−2.82408
$940$	18.5982	−	4.04211i	0.606606	−	0.131839i
$941$	−27.6223			−0.900461			−0.450231	−	0.892912i	$-0.648658\pi$
$941$	−27.6223			−0.900461			−0.450231	+	0.892912i	$0.648658\pi$
$942$		−	53.3586i		−	1.73852i
$943$			8.35785i			0.272169i
$944$	−7.17816			−0.233629
$945$	28.7446	+	132.257i	0.935061	+	4.30232i
$946$	−8.86246			−0.288143
$947$			37.9618i			1.23359i	0.787123	+	0.616796i	$0.211570\pi$
$947$			37.9618i			1.23359i	−0.787123	+	0.616796i	$0.788430\pi$
$948$			56.4859i			1.83458i
$949$	−1.02055			−0.0331284
$950$	30.3629	+	66.5520i	0.985103	+	2.15923i
$951$	−68.4589			−2.21993
$952$		−	207.845i		−	6.73630i
$953$			31.8263i			1.03096i	0.856903	+	0.515478i	$0.172386\pi$
$953$			31.8263i			1.03096i	−0.856903	+	0.515478i	$0.827614\pi$
$954$	−99.2033			−3.21182
$955$	2.48880	+	11.4513i	0.0805358	+	0.370554i
$956$	62.4304			2.01915
$957$		−	51.8759i		−	1.67691i
$958$			51.3735i			1.65980i
$959$	30.9664			0.999957
$960$	173.073	−	37.6154i	5.58590	−	1.21403i
$961$	−30.5461			−0.985359
$962$			3.32527i			0.107211i
$963$		−	15.8704i		−	0.511417i
$964$	5.30763			0.170947
$965$	−42.8580	+	9.31471i	−1.37965	+	0.299851i
$966$	72.8154			2.34280
$967$			42.8008i			1.37638i	0.725529	+	0.688191i	$0.241595\pi$
$967$			42.8008i			1.37638i	−0.725529	+	0.688191i	$0.758405\pi$
$968$			45.8330i			1.47313i
$969$	−123.030			−3.95230
$970$	−1.79644	−	8.26560i	−0.0576801	−	0.265392i
$971$	−40.4234			−1.29725			−0.648625	−	0.761108i	$-0.724655\pi$
$971$	−40.4234			−1.29725			−0.648625	+	0.761108i	$0.724655\pi$
$972$		−	332.053i		−	10.6506i
$973$		−	7.09843i		−	0.227565i
$974$	37.5002			1.20158
$975$	−4.17011	+	1.90252i	−0.133550	+	0.0609294i
$976$	−90.1244			−2.88481
$977$			4.42215i			0.141477i	0.997495	+	0.0707385i	$0.0225356\pi$
$977$			4.42215i			0.141477i	−0.997495	+	0.0707385i	$0.977464\pi$
$978$			36.6680i			1.17251i
$979$	−7.02028			−0.224369
$980$	12.0267	+	55.3360i	0.384178	+	1.76764i
$981$	−60.7871			−1.94078
$982$		−	23.1919i		−	0.740084i
$983$		−	15.8123i		−	0.504334i	−0.967684	−	0.252167i	$-0.918857\pi$
$983$		−	15.8123i		−	0.504334i	0.967684	−	0.252167i	$-0.0811432\pi$
$984$	107.161			3.41617
$985$	−51.0418	+	11.0934i	−1.62633	+	0.353464i
$986$	−70.5152			−2.24566
$987$		−	18.4608i		−	0.587612i
$988$			7.84821i			0.249685i
$989$	−1.91027			−0.0607432
$990$	−195.877	+	42.5717i	−6.22538	+	1.35302i
$991$	38.6286			1.22708			0.613538	−	0.789665i	$-0.289746\pi$
$991$	38.6286			1.22708			0.613538	+	0.789665i	$0.289746\pi$
$992$		−	12.6398i		−	0.401315i
$993$		−	8.04296i		−	0.255236i
$994$	137.632			4.36542
$995$	−1.07140	−	4.92963i	−0.0339657	−	0.156280i
$996$	−236.074			−7.48030
$997$		−	44.4049i		−	1.40632i	−0.711033	−	0.703159i	$-0.751772\pi$
$997$		−	44.4049i		−	1.40632i	0.711033	−	0.703159i	$-0.248228\pi$
$998$			44.6681i			1.41394i
$999$	−79.4279			−2.51299

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.b.d.724.3	✓	66
5.2	odd	4		6025.2.a.q.1.64		66
5.3	odd	4		6025.2.a.q.1.3		66
5.4	even	2	inner	1205.2.b.d.724.64	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.d.724.3	✓	66	1.1	even	1	trivial
1205.2.b.d.724.64	yes	66	5.4	even	2	inner
6025.2.a.q.1.3		66	5.3	odd	4
6025.2.a.q.1.64		66	5.2	odd	4

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:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.70326i q^{2} +3.35528i q^{3} -5.30763 q^{4} +(0.474898 + 2.18506i) q^{5} +9.07021 q^{6} +3.43095i q^{7} +8.94141i q^{8} -8.25791 q^{9} +O(q^{10})\)	\(q-2.70326i q^{2} +3.35528i q^{3} -5.30763 q^{4} +(0.474898 + 2.18506i) q^{5} +9.07021 q^{6} +3.43095i q^{7} +8.94141i q^{8} -8.25791 q^{9} +(5.90678 - 1.28377i) q^{10} +4.01571 q^{11} -17.8086i q^{12} -0.273217i q^{13} +9.27475 q^{14} +(-7.33148 + 1.59342i) q^{15} +13.5557 q^{16} +6.77517i q^{17} +22.3233i q^{18} +5.41206 q^{19} +(-2.52058 - 11.5975i) q^{20} -11.5118 q^{21} -10.8555i q^{22} -2.33987i q^{23} -30.0009 q^{24} +(-4.54894 + 2.07536i) q^{25} -0.738577 q^{26} -17.6418i q^{27} -18.2102i q^{28} -3.85012 q^{29} +(4.30742 + 19.8189i) q^{30} +0.673699 q^{31} -18.7618i q^{32} +13.4738i q^{33} +18.3151 q^{34} +(-7.49681 + 1.62935i) q^{35} +43.8300 q^{36} -4.50226i q^{37} -14.6302i q^{38} +0.916720 q^{39} +(-19.5375 + 4.24625i) q^{40} -3.57192 q^{41} +31.1194i q^{42} -0.816401i q^{43} -21.3139 q^{44} +(-3.92166 - 18.0440i) q^{45} -6.32529 q^{46} +1.60364i q^{47} +45.4832i q^{48} -4.77138 q^{49} +(5.61024 + 12.2970i) q^{50} -22.7326 q^{51} +1.45014i q^{52} +4.44393i q^{53} -47.6904 q^{54} +(1.90705 + 8.77455i) q^{55} -30.6775 q^{56} +18.1590i q^{57} +10.4079i q^{58} -0.529530 q^{59} +(38.9128 - 8.45726i) q^{60} -6.64845 q^{61} -1.82119i q^{62} -28.3324i q^{63} -23.6068 q^{64} +(0.596994 - 0.129750i) q^{65} +36.4233 q^{66} +7.41240i q^{67} -35.9601i q^{68} +7.85093 q^{69} +(4.40456 + 20.2659i) q^{70} +14.8394 q^{71} -73.8373i q^{72} -3.73531i q^{73} -12.1708 q^{74} +(-6.96340 - 15.2630i) q^{75} -28.7252 q^{76} +13.7777i q^{77} -2.47813i q^{78} -3.17183 q^{79} +(6.43757 + 29.6200i) q^{80} +34.4194 q^{81} +9.65585i q^{82} -13.2562i q^{83} +61.1003 q^{84} +(-14.8041 + 3.21751i) q^{85} -2.20695 q^{86} -12.9182i q^{87} +35.9061i q^{88} -1.74820 q^{89} +(-48.7777 + 10.6013i) q^{90} +0.937392 q^{91} +12.4192i q^{92} +2.26045i q^{93} +4.33506 q^{94} +(2.57017 + 11.8256i) q^{95} +62.9513 q^{96} -1.39934i q^{97} +12.8983i q^{98} -33.1614 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 78 q^{4} + 16 q^{6} - 90 q^{9}+O(q^{10}) \) 66 * q - 78 * q^4 + 16 * q^6 - 90 * q^9	\( 66 q - 78 q^{4} + 16 q^{6} - 90 q^{9} + q^{10} + 48 q^{11} - 30 q^{14} - 3 q^{15} + 98 q^{16} - 12 q^{19} - 10 q^{20} + 18 q^{21} - 42 q^{24} + 6 q^{25} + 48 q^{26} - 56 q^{29} - 5 q^{30} + 48 q^{31} - 8 q^{34} + 3 q^{35} + 158 q^{36} - 84 q^{39} - 6 q^{40} + 56 q^{41} - 144 q^{44} - 13 q^{45} + 36 q^{46} - 98 q^{49} + 2 q^{50} + 44 q^{51} - 86 q^{54} + 3 q^{55} + 104 q^{56} - 108 q^{59} + 7 q^{60} + 22 q^{61} - 136 q^{64} + 15 q^{65} + 74 q^{66} - 20 q^{69} - 32 q^{70} + 212 q^{71} - 84 q^{74} - 9 q^{75} + 6 q^{76} - 66 q^{79} - 21 q^{80} + 162 q^{81} + 52 q^{84} - 48 q^{85} + 100 q^{86} - 54 q^{89} - 155 q^{90} + 72 q^{91} + 96 q^{94} - 5 q^{95} + 122 q^{96} - 112 q^{99}+O(q^{100}) \) 66 * q - 78 * q^4 + 16 * q^6 - 90 * q^9 + q^10 + 48 * q^11 - 30 * q^14 - 3 * q^15 + 98 * q^16 - 12 * q^19 - 10 * q^20 + 18 * q^21 - 42 * q^24 + 6 * q^25 + 48 * q^26 - 56 * q^29 - 5 * q^30 + 48 * q^31 - 8 * q^34 + 3 * q^35 + 158 * q^36 - 84 * q^39 - 6 * q^40 + 56 * q^41 - 144 * q^44 - 13 * q^45 + 36 * q^46 - 98 * q^49 + 2 * q^50 + 44 * q^51 - 86 * q^54 + 3 * q^55 + 104 * q^56 - 108 * q^59 + 7 * q^60 + 22 * q^61 - 136 * q^64 + 15 * q^65 + 74 * q^66 - 20 * q^69 - 32 * q^70 + 212 * q^71 - 84 * q^74 - 9 * q^75 + 6 * q^76 - 66 * q^79 - 21 * q^80 + 162 * q^81 + 52 * q^84 - 48 * q^85 + 100 * q^86 - 54 * q^89 - 155 * q^90 + 72 * q^91 + 96 * q^94 - 5 * q^95 + 122 * q^96 - 112 * q^99

Introduction

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Modular forms

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