LMFDB - Embedded newform 1205.2.b.c.724.28

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:	$46$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			724.28
Character	$\chi$	$=$	1205.724
Dual form			1205.2.b.c.724.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.636788i q^{2} +2.24729i q^{3} +1.59450 q^{4} +(-1.29399 - 1.82362i) q^{5} -1.43105 q^{6} -1.14493i q^{7} +2.28894i q^{8} -2.05030 q^{9} +O(q^{10})$	\(q+0.636788i q^{2} +2.24729i q^{3} +1.59450 q^{4} +(-1.29399 - 1.82362i) q^{5} -1.43105 q^{6} -1.14493i q^{7} +2.28894i q^{8} -2.05030 q^{9} +(1.16126 - 0.824000i) q^{10} -0.440443 q^{11} +3.58330i q^{12} +0.0742578i q^{13} +0.729079 q^{14} +(4.09819 - 2.90797i) q^{15} +1.73143 q^{16} +3.83474i q^{17} -1.30561i q^{18} +4.81267 q^{19} +(-2.06327 - 2.90776i) q^{20} +2.57299 q^{21} -0.280469i q^{22} +6.24519i q^{23} -5.14390 q^{24} +(-1.65117 + 4.71950i) q^{25} -0.0472865 q^{26} +2.13425i q^{27} -1.82559i q^{28} -2.54550 q^{29} +(1.85176 + 2.60968i) q^{30} -0.429517 q^{31} +5.68043i q^{32} -0.989801i q^{33} -2.44192 q^{34} +(-2.08792 + 1.48153i) q^{35} -3.26920 q^{36} +10.9158i q^{37} +3.06465i q^{38} -0.166878 q^{39} +(4.17415 - 2.96187i) q^{40} -4.91543 q^{41} +1.63845i q^{42} -1.72125i q^{43} -0.702286 q^{44} +(2.65307 + 3.73896i) q^{45} -3.97686 q^{46} -0.485128i q^{47} +3.89103i q^{48} +5.68913 q^{49} +(-3.00532 - 1.05144i) q^{50} -8.61777 q^{51} +0.118404i q^{52} -2.29994i q^{53} -1.35907 q^{54} +(0.569929 + 0.803199i) q^{55} +2.62068 q^{56} +10.8155i q^{57} -1.62094i q^{58} +1.98580 q^{59} +(6.53457 - 4.63676i) q^{60} +8.96972 q^{61} -0.273511i q^{62} +2.34745i q^{63} -0.154367 q^{64} +(0.135418 - 0.0960890i) q^{65} +0.630294 q^{66} -1.53915i q^{67} +6.11450i q^{68} -14.0347 q^{69} +(-0.943423 - 1.32956i) q^{70} +14.1657 q^{71} -4.69300i q^{72} -15.2643i q^{73} -6.95108 q^{74} +(-10.6061 - 3.71064i) q^{75} +7.67381 q^{76} +0.504277i q^{77} -0.106266i q^{78} -1.84814 q^{79} +(-2.24046 - 3.15747i) q^{80} -10.9472 q^{81} -3.13009i q^{82} -1.08755i q^{83} +4.10263 q^{84} +(6.99311 - 4.96213i) q^{85} +1.09608 q^{86} -5.72046i q^{87} -1.00815i q^{88} -1.27098 q^{89} +(-2.38093 + 1.68944i) q^{90} +0.0850201 q^{91} +9.95795i q^{92} -0.965247i q^{93} +0.308924 q^{94} +(-6.22756 - 8.77648i) q^{95} -12.7656 q^{96} +14.7657i q^{97} +3.62277i q^{98} +0.903038 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * 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 $

$2$			0.636788i			0.450277i	0.974327	+	0.225139i	$0.0722835\pi$
$2$			0.636788i			0.450277i	−0.974327	+	0.225139i	$0.927716\pi$
$3$			2.24729i			1.29747i	0.761014	+	0.648736i	$0.224702\pi$
$3$			2.24729i			1.29747i	−0.761014	+	0.648736i	$0.775298\pi$
$4$	1.59450			0.797250
$5$	−1.29399	−	1.82362i	−0.578691	−	0.815547i
$5$	−1.29399	−	1.82362i	−0.578691	−	0.815547i
$6$	−1.43105			−0.584222
$7$		−	1.14493i		−	0.432743i	−0.976311	−	0.216372i	$-0.930578\pi$
$7$		−	1.14493i		−	0.432743i	0.976311	−	0.216372i	$-0.0694223\pi$
$8$			2.28894i			0.809261i
$9$	−2.05030			−0.683433
$10$	1.16126	−	0.824000i	0.367222	−	0.260572i
$11$	−0.440443			−0.132798			−0.0663992	−	0.997793i	$-0.521151\pi$
$11$	−0.440443			−0.132798			−0.0663992	+	0.997793i	$0.521151\pi$
$12$			3.58330i			1.03441i
$13$			0.0742578i			0.0205954i	0.999947	+	0.0102977i	$0.00327792\pi$
$13$			0.0742578i			0.0205954i	−0.999947	+	0.0102977i	$0.996722\pi$
$14$	0.729079			0.194855
$15$	4.09819	−	2.90797i	1.05815	−	0.750835i
$16$	1.73143			0.432858
$17$			3.83474i			0.930062i	0.885294	+	0.465031i	$0.153957\pi$
$17$			3.83474i			0.930062i	−0.885294	+	0.465031i	$0.846043\pi$
$18$		−	1.30561i		−	0.307734i
$19$	4.81267			1.10410			0.552051	−	0.833810i	$-0.313845\pi$
$19$	4.81267			1.10410			0.552051	+	0.833810i	$0.313845\pi$
$20$	−2.06327	−	2.90776i	−0.461362	−	0.650195i
$21$	2.57299			0.561472
$22$		−	0.280469i		−	0.0597961i
$23$			6.24519i			1.30221i	0.758987	+	0.651106i	$0.225695\pi$
$23$			6.24519i			1.30221i	−0.758987	+	0.651106i	$0.774305\pi$
$24$	−5.14390			−1.04999
$25$	−1.65117	+	4.71950i	−0.330233	+	0.943899i
$26$	−0.0472865			−0.00927364
$27$			2.13425i			0.410737i
$28$		−	1.82559i		−	0.345005i
$29$	−2.54550			−0.472687			−0.236343	−	0.971670i	$-0.575949\pi$
$29$	−2.54550			−0.472687			−0.236343	+	0.971670i	$0.575949\pi$
$30$	1.85176	+	2.60968i	0.338084	+	0.476461i
$31$	−0.429517			−0.0771435			−0.0385717	−	0.999256i	$-0.512281\pi$
$31$	−0.429517			−0.0771435			−0.0385717	+	0.999256i	$0.512281\pi$
$32$			5.68043i			1.00417i
$33$		−	0.989801i		−	0.172302i
$34$	−2.44192			−0.418786
$35$	−2.08792	+	1.48153i	−0.352923	+	0.250425i
$36$	−3.26920			−0.544867
$37$			10.9158i			1.79455i	0.441470	+	0.897276i	$0.354457\pi$
$37$			10.9158i			1.79455i	−0.441470	+	0.897276i	$0.645543\pi$
$38$			3.06465i			0.497153i
$39$	−0.166878			−0.0267219
$40$	4.17415	−	2.96187i	0.659990	−	0.468312i
$41$	−4.91543			−0.767662			−0.383831	−	0.923403i	$-0.625395\pi$
$41$	−4.91543			−0.767662			−0.383831	+	0.923403i	$0.625395\pi$
$42$			1.63845i			0.252818i
$43$		−	1.72125i		−	0.262489i	−0.991350	−	0.131244i	$-0.958103\pi$
$43$		−	1.72125i		−	0.262489i	0.991350	−	0.131244i	$-0.0418973\pi$
$44$	−0.702286			−0.105874
$45$	2.65307	+	3.73896i	0.395496	+	0.557371i
$46$	−3.97686			−0.586356
$47$		−	0.485128i		−	0.0707631i	−0.999374	−	0.0353816i	$-0.988735\pi$
$47$		−	0.485128i		−	0.0707631i	0.999374	−	0.0353816i	$-0.0112647\pi$
$48$			3.89103i			0.561621i
$49$	5.68913			0.812733
$50$	−3.00532	−	1.05144i	−0.425017	−	0.148697i
$51$	−8.61777			−1.20673
$52$			0.118404i			0.0164197i
$53$		−	2.29994i		−	0.315921i	−0.987445	−	0.157960i	$-0.949508\pi$
$53$		−	2.29994i		−	0.315921i	0.987445	−	0.157960i	$-0.0504918\pi$
$54$	−1.35907			−0.184946
$55$	0.569929	+	0.803199i	0.0768493	+	0.108303i
$56$	2.62068			0.350203
$57$			10.8155i			1.43254i
$58$		−	1.62094i		−	0.212840i
$59$	1.98580			0.258530			0.129265	−	0.991610i	$-0.458738\pi$
$59$	1.98580			0.258530			0.129265	+	0.991610i	$0.458738\pi$
$60$	6.53457	−	4.63676i	0.843609	−	0.598604i
$61$	8.96972			1.14846			0.574228	−	0.818696i	$-0.305302\pi$
$61$	8.96972			1.14846			0.574228	+	0.818696i	$0.305302\pi$
$62$		−	0.273511i		−	0.0347360i
$63$			2.34745i			0.295751i
$64$	−0.154367			−0.0192959
$65$	0.135418	−	0.0960890i	0.0167965	−	0.0119184i
$66$	0.630294			0.0775838
$67$		−	1.53915i		−	0.188038i	−0.995570	−	0.0940188i	$-0.970029\pi$
$67$		−	1.53915i		−	0.188038i	0.995570	−	0.0940188i	$-0.0299714\pi$
$68$			6.11450i			0.741492i
$69$	−14.0347			−1.68958
$70$	−0.943423	−	1.32956i	−0.112761	−	0.158913i
$71$	14.1657			1.68116			0.840579	−	0.541688i	$-0.182215\pi$
$71$	14.1657			1.68116			0.840579	+	0.541688i	$0.182215\pi$
$72$		−	4.69300i		−	0.553075i
$73$		−	15.2643i		−	1.78656i	−0.449504	−	0.893278i	$-0.648399\pi$
$73$		−	15.2643i		−	1.78656i	0.449504	−	0.893278i	$-0.351601\pi$
$74$	−6.95108			−0.808046
$75$	−10.6061	−	3.71064i	−1.22468	−	0.428468i
$76$	7.67381			0.880246
$77$			0.504277i			0.0574677i
$78$		−	0.106266i		−	0.0120323i
$79$	−1.84814			−0.207932			−0.103966	−	0.994581i	$-0.533153\pi$
$79$	−1.84814			−0.207932			−0.103966	+	0.994581i	$0.533153\pi$
$80$	−2.24046	−	3.15747i	−0.250491	−	0.353016i
$81$	−10.9472			−1.21635
$82$		−	3.13009i		−	0.345661i
$83$		−	1.08755i		−	0.119375i	−0.998217	−	0.0596873i	$-0.980990\pi$
$83$		−	1.08755i		−	0.119375i	0.998217	−	0.0596873i	$-0.0190104\pi$
$84$	4.10263			0.447634
$85$	6.99311	−	4.96213i	0.758509	−	0.538219i
$86$	1.09608			0.118193
$87$		−	5.72046i		−	0.613298i
$88$		−	1.00815i		−	0.107469i
$89$	−1.27098			−0.134723			−0.0673617	−	0.997729i	$-0.521458\pi$
$89$	−1.27098			−0.134723			−0.0673617	+	0.997729i	$0.521458\pi$
$90$	−2.38093	+	1.68944i	−0.250972	+	0.178083i
$91$	0.0850201			0.00891252
$92$			9.95795i			1.03819i
$93$		−	0.965247i		−	0.100091i
$94$	0.308924			0.0318630
$95$	−6.22756	−	8.77648i	−0.638934	−	0.900447i
$96$	−12.7656			−1.30288
$97$			14.7657i			1.49923i	0.661876	+	0.749614i	$0.269761\pi$
$97$			14.7657i			1.49923i	−0.661876	+	0.749614i	$0.730239\pi$
$98$			3.62277i			0.365955i
$99$	0.903038			0.0907588
$100$	−2.63279	+	7.52524i	−0.263279	+	0.752524i
$101$	−5.30890			−0.528255			−0.264127	−	0.964488i	$-0.585084\pi$
$101$	−5.30890			−0.528255			−0.264127	+	0.964488i	$0.585084\pi$
$102$		−	5.48770i		−	0.543363i
$103$		−	3.19134i		−	0.314452i	−0.987563	−	0.157226i	$-0.949745\pi$
$103$		−	3.19134i		−	0.314452i	0.987563	−	0.157226i	$-0.0502550\pi$
$104$	−0.169971			−0.0166671
$105$	−3.32943	−	4.69215i	−0.324919	−	0.457907i
$106$	1.46457			0.142252
$107$		−	9.30857i		−	0.899893i	−0.893055	−	0.449947i	$-0.851443\pi$
$107$		−	9.30857i		−	0.899893i	0.893055	−	0.449947i	$-0.148557\pi$
$108$			3.40307i			0.327460i
$109$	−3.00453			−0.287782			−0.143891	−	0.989594i	$-0.545961\pi$
$109$	−3.00453			−0.287782			−0.143891	+	0.989594i	$0.545961\pi$
$110$	−0.511468	+	0.362925i	−0.0487666	+	0.0346035i
$111$	−24.5310			−2.32838
$112$		−	1.98237i		−	0.187317i
$113$		−	5.77781i		−	0.543530i	−0.962364	−	0.271765i	$-0.912393\pi$
$113$		−	5.77781i		−	0.543530i	0.962364	−	0.271765i	$-0.0876074\pi$
$114$	−6.88716			−0.645041
$115$	11.3888	−	8.08122i	1.06201	−	0.753578i
$116$	−4.05879			−0.376850
$117$		−	0.152251i		−	0.0140756i
$118$			1.26454i			0.116410i
$119$	4.39052			0.402478
$120$	6.65616	+	9.38050i	0.607622	+	0.856319i
$121$	−10.8060			−0.982365
$122$			5.71182i			0.517124i
$123$		−	11.0464i		−	0.996019i
$124$	−0.684865			−0.0615027
$125$	10.7432	−	3.09590i	0.960897	−	0.276905i
$126$	−1.49483			−0.133170
$127$		−	19.2286i		−	1.70627i	−0.521694	−	0.853133i	$-0.674700\pi$
$127$		−	19.2286i		−	1.70627i	0.521694	−	0.853133i	$-0.325300\pi$
$128$			11.2626i			0.995479i
$129$	3.86815			0.340572
$130$	0.0611884	+	0.0862325i	0.00536657	+	0.00756309i
$131$	−15.0685			−1.31654			−0.658271	−	0.752781i	$-0.728712\pi$
$131$	−15.0685			−1.31654			−0.658271	+	0.752781i	$0.728712\pi$
$132$		−	1.57824i		−	0.137368i
$133$		−	5.51018i		−	0.477793i
$134$	0.980116			0.0846691
$135$	3.89206	−	2.76171i	0.334975	−	0.237690i
$136$	−8.77749			−0.752663
$137$			10.3778i			0.886638i	0.896364	+	0.443319i	$0.146199\pi$
$137$			10.3778i			0.886638i	−0.896364	+	0.443319i	$0.853801\pi$
$138$		−	8.93715i		−	0.760781i
$139$	2.30756			0.195725			0.0978623	−	0.995200i	$-0.468800\pi$
$139$	2.30756			0.195725			0.0978623	+	0.995200i	$0.468800\pi$
$140$	−3.32919	+	2.36230i	−0.281368	+	0.199651i
$141$	1.09022			0.0918132
$142$			9.02055i			0.756988i
$143$		−	0.0327063i		−	0.00273504i
$144$	−3.54995			−0.295829
$145$	3.29385	+	4.64201i	0.273540	+	0.385498i
$146$	9.72016			0.804446
$147$			12.7851i			1.05450i
$148$			17.4053i			1.43071i
$149$	11.1945			0.917092			0.458546	−	0.888671i	$-0.348370\pi$
$149$	11.1945			0.917092			0.458546	+	0.888671i	$0.348370\pi$
$150$	2.36290	−	6.75382i	0.192930	−	0.551447i
$151$	−6.66973			−0.542775			−0.271387	−	0.962470i	$-0.587482\pi$
$151$	−6.66973			−0.542775			−0.271387	+	0.962470i	$0.587482\pi$
$152$			11.0159i			0.893507i
$153$		−	7.86237i		−	0.635635i
$154$	−0.321118			−0.0258764
$155$	0.555792	+	0.783275i	0.0446423	+	0.0629141i
$156$	−0.266088			−0.0213041
$157$		−	22.8522i		−	1.82380i	−0.410410	−	0.911901i	$-0.634614\pi$
$157$		−	22.8522i		−	1.82380i	0.410410	−	0.911901i	$-0.365386\pi$
$158$		−	1.17687i		−	0.0936269i
$159$	5.16862			0.409898
$160$	10.3589	−	7.35043i	0.818946	−	0.581103i
$161$	7.15031			0.563523
$162$		−	6.97103i		−	0.547696i
$163$		−	6.90573i		−	0.540898i	−0.962734	−	0.270449i	$-0.912828\pi$
$163$		−	6.90573i		−	0.540898i	0.962734	−	0.270449i	$-0.0871722\pi$
$164$	−7.83766			−0.612018
$165$	−1.80502	+	1.28079i	−0.140521	+	0.0997098i
$166$	0.692542			0.0537517
$167$			2.49550i			0.193108i	0.995328	+	0.0965538i	$0.0307820\pi$
$167$			2.49550i			0.193108i	−0.995328	+	0.0965538i	$0.969218\pi$
$168$			5.88941i			0.454378i
$169$	12.9945			0.999576
$170$	3.15983	+	4.45313i	0.242348	+	0.341540i
$171$	−9.86741			−0.754580
$172$		−	2.74454i		−	0.209269i
$173$			0.427640i			0.0325129i	0.999868	+	0.0162565i	$0.00517482\pi$
$173$			0.427640i			0.0325129i	−0.999868	+	0.0162565i	$0.994825\pi$
$174$	3.64272			0.276154
$175$	5.40350	+	1.89047i	0.408466	+	0.142906i
$176$	−0.762597			−0.0574829
$177$			4.46267i			0.335435i
$178$		−	0.809344i		−	0.0606629i
$179$	−6.01228			−0.449379			−0.224689	−	0.974430i	$-0.572137\pi$
$179$	−6.01228			−0.449379			−0.224689	+	0.974430i	$0.572137\pi$
$180$	4.23032	+	5.96177i	0.315310	+	0.444364i
$181$	15.2285			1.13193			0.565963	−	0.824431i	$-0.308505\pi$
$181$	15.2285			1.13193			0.565963	+	0.824431i	$0.308505\pi$
$182$			0.0541398i			0.00401311i
$183$			20.1575i			1.49009i
$184$	−14.2948			−1.05383
$185$	19.9063	−	14.1250i	1.46354	−	1.03849i
$186$	0.614658			0.0450689
$187$		−	1.68898i		−	0.123511i
$188$		−	0.773536i		−	0.0564159i
$189$	2.44357			0.177744
$190$	5.58876	−	3.96564i	0.405451	−	0.287698i
$191$	−0.578755			−0.0418772			−0.0209386	−	0.999781i	$-0.506665\pi$
$191$	−0.578755			−0.0418772			−0.0209386	+	0.999781i	$0.506665\pi$
$192$		−	0.346907i		−	0.0250359i
$193$			2.26365i			0.162941i	0.996676	+	0.0814706i	$0.0259617\pi$
$193$			2.26365i			0.162941i	−0.996676	+	0.0814706i	$0.974038\pi$
$194$	−9.40261			−0.675068
$195$	0.215940	+	0.304323i	0.0154638	+	0.0217930i
$196$	9.07132			0.647952
$197$			12.3730i			0.881542i	0.897620	+	0.440771i	$0.145295\pi$
$197$			12.3730i			0.881542i	−0.897620	+	0.440771i	$0.854705\pi$
$198$			0.575044i			0.0408666i
$199$	−11.8775			−0.841976			−0.420988	−	0.907066i	$-0.638316\pi$
$199$	−11.8775			−0.841976			−0.420988	+	0.907066i	$0.638316\pi$
$200$	−10.8026	−	3.77942i	−0.763861	−	0.267245i
$201$	3.45892			0.243974
$202$		−	3.38064i		−	0.237861i
$203$			2.91442i			0.204552i
$204$	−13.7410			−0.962065
$205$	6.36053	+	8.96387i	0.444239	+	0.626064i
$206$	2.03221			0.141590
$207$		−	12.8045i		−	0.889974i
$208$			0.128572i			0.00891489i
$209$	−2.11971			−0.146623
$210$	2.98791	−	2.12014i	0.206185	−	0.146304i
$211$	−11.3488			−0.781281			−0.390641	−	0.920543i	$-0.627746\pi$
$211$	−11.3488			−0.781281			−0.390641	+	0.920543i	$0.627746\pi$
$212$		−	3.66725i		−	0.251868i
$213$			31.8344i			2.18126i
$214$	5.92759			0.405202
$215$	−3.13891	+	2.22729i	−0.214072	+	0.151900i
$216$	−4.88517			−0.332394
$217$			0.491767i			0.0333833i
$218$		−	1.91325i		−	0.129582i
$219$	34.3034			2.31801
$220$	0.908753	+	1.28070i	0.0612681	+	0.0863449i
$221$	−0.284760			−0.0191550
$222$		−	15.6211i		−	1.04842i
$223$			3.01780i			0.202087i	0.994882	+	0.101043i	$0.0322181\pi$
$223$			3.01780i			0.202087i	−0.994882	+	0.101043i	$0.967782\pi$
$224$	6.50370			0.434547
$225$	3.38538	−	9.67637i	0.225692	−	0.645092i
$226$	3.67924			0.244739
$227$			14.3773i			0.954257i	0.878833	+	0.477129i	$0.158322\pi$
$227$			14.3773i			0.954257i	−0.878833	+	0.477129i	$0.841678\pi$
$228$			17.2452i			1.14209i
$229$	26.5382			1.75369			0.876847	−	0.480769i	$-0.159642\pi$
$229$	26.5382			1.75369			0.876847	+	0.480769i	$0.159642\pi$
$230$	5.14603	+	7.25228i	0.339319	+	0.478201i
$231$	−1.13325			−0.0745627
$232$		−	5.82648i		−	0.382527i
$233$		−	15.2500i		−	0.999061i	−0.866296	−	0.499530i	$-0.833506\pi$
$233$		−	15.2500i		−	0.999061i	0.866296	−	0.499530i	$-0.166494\pi$
$234$	0.0969514			0.00633791
$235$	−0.884688	+	0.627752i	−0.0577107	+	0.0409500i
$236$	3.16636			0.206113
$237$		−	4.15329i		−	0.269785i
$238$			2.79583i			0.181227i
$239$	9.98370			0.645792			0.322896	−	0.946434i	$-0.395344\pi$
$239$	9.98370			0.645792			0.322896	+	0.946434i	$0.395344\pi$
$240$	7.09574	−	5.03496i	0.458028	−	0.325005i
$241$	1.00000			0.0644157
$241$	1.00000			0.0644157
$242$		−	6.88114i		−	0.442337i
$243$		−	18.1987i		−	1.16745i
$244$	14.3022			0.915606
$245$	−7.36169	−	10.3748i	−0.470321	−	0.662822i
$246$	7.03421			0.448485
$247$			0.357378i			0.0227394i
$248$		−	0.983137i		−	0.0624292i
$249$	2.44405			0.154885
$250$	1.97143	+	6.84112i	0.124684	+	0.432670i
$251$	−19.2151			−1.21285			−0.606424	−	0.795141i	$-0.707397\pi$
$251$	−19.2151			−1.21285			−0.606424	+	0.795141i	$0.707397\pi$
$252$			3.74301i			0.235788i
$253$		−	2.75065i		−	0.172932i
$254$	12.2446			0.768293
$255$	11.1513	+	15.7155i	0.698323	+	0.984144i
$256$	−7.48060			−0.467538
$257$		−	29.6396i		−	1.84887i	−0.381339	−	0.924435i	$-0.624537\pi$
$257$		−	29.6396i		−	1.84887i	0.381339	−	0.924435i	$-0.375463\pi$
$258$			2.46320i			0.153352i
$259$	12.4979			0.776580
$260$	0.215924	−	0.153214i	0.0133910	−	0.00950193i
$261$	5.21903			0.323050
$262$		−	9.59545i		−	0.592809i
$263$			24.3550i			1.50180i	0.660418	+	0.750898i	$0.270379\pi$
$263$			24.3550i			1.50180i	−0.660418	+	0.750898i	$0.729621\pi$
$264$	2.26559			0.139438
$265$	−4.19421	+	2.97610i	−0.257648	+	0.182821i
$266$	3.50882			0.215139
$267$		−	2.85625i		−	0.174800i
$268$		−	2.45418i		−	0.149913i
$269$	15.0768			0.919248			0.459624	−	0.888114i	$-0.347984\pi$
$269$	15.0768			0.919248			0.459624	+	0.888114i	$0.347984\pi$
$270$	1.75862	+	2.47842i	0.107026	+	0.150832i
$271$	23.5456			1.43029			0.715146	−	0.698975i	$-0.246360\pi$
$271$	23.5456			1.43029			0.715146	+	0.698975i	$0.246360\pi$
$272$			6.63960i			0.402585i
$273$			0.191064i			0.0115637i
$274$	−6.60848			−0.399233
$275$	0.727244	−	2.07867i	0.0438545	−	0.125348i
$276$	−22.3784			−1.34702
$277$			4.70682i			0.282806i	0.989952	+	0.141403i	$0.0451613\pi$
$277$			4.70682i			0.282806i	−0.989952	+	0.141403i	$0.954839\pi$
$278$			1.46943i			0.0881304i
$279$	0.880637			0.0527224
$280$	−3.39113	−	4.77911i	−0.202659	−	0.285607i
$281$	2.94319			0.175576			0.0877879	−	0.996139i	$-0.472020\pi$
$281$	2.94319			0.175576			0.0877879	+	0.996139i	$0.472020\pi$
$282$			0.694240i			0.0413414i
$283$		−	12.3920i		−	0.736628i	−0.929702	−	0.368314i	$-0.879935\pi$
$283$		−	12.3920i		−	0.736628i	0.929702	−	0.368314i	$-0.120065\pi$
$284$	22.5872			1.34030
$285$	19.7233	−	13.9951i	1.16830	−	0.828999i
$286$	0.0208270			0.00123153
$287$			5.62783i			0.332201i
$288$		−	11.6466i		−	0.686281i
$289$	2.29474			0.134985
$290$	−2.95598	+	2.09749i	−0.173581	+	0.123169i
$291$	−33.1827			−1.94521
$292$		−	24.3390i		−	1.42433i
$293$			11.0669i			0.646532i	0.946308	+	0.323266i	$0.104781\pi$
$293$			11.0669i			0.646532i	−0.946308	+	0.323266i	$0.895219\pi$
$294$	−8.14141			−0.474817
$295$	−2.56961	−	3.62135i	−0.149609	−	0.210843i
$296$	−24.9856			−1.45226
$297$		−	0.940016i		−	0.0545453i
$298$			7.12855i			0.412946i
$299$	−0.463754			−0.0268196
$300$	−16.9114	−	5.91662i	−0.976378	−	0.341596i
$301$	−1.97072			−0.113590
$302$		−	4.24720i		−	0.244399i
$303$		−	11.9306i		−	0.685396i
$304$	8.33282			0.477920
$305$	−11.6068	−	16.3574i	−0.664601	−	0.936619i
$306$	5.00666			0.286212
$307$		−	19.5529i		−	1.11595i	−0.829859	−	0.557973i	$-0.811579\pi$
$307$		−	19.5529i		−	1.11595i	0.829859	−	0.557973i	$-0.188421\pi$
$308$			0.804069i			0.0458161i
$309$	7.17184			0.407992
$310$	−0.498780	+	0.353922i	−0.0283288	+	0.0201014i
$311$	6.79509			0.385314			0.192657	−	0.981266i	$-0.438289\pi$
$311$	6.79509			0.385314			0.192657	+	0.981266i	$0.438289\pi$
$312$		−	0.381974i		−	0.0216250i
$313$		−	4.82490i		−	0.272719i	−0.990659	−	0.136360i	$-0.956460\pi$
$313$		−	4.82490i		−	0.272719i	0.990659	−	0.136360i	$-0.0435403\pi$
$314$	14.5520			0.821217
$315$	4.28085	−	3.03758i	0.241199	−	0.171148i
$316$	−2.94686			−0.165774
$317$			4.07296i			0.228760i	0.993437	+	0.114380i	$0.0364882\pi$
$317$			4.07296i			0.228760i	−0.993437	+	0.114380i	$0.963512\pi$
$318$			3.29132i			0.184568i
$319$	1.12115			0.0627721
$320$	0.199750	+	0.281507i	0.0111664	+	0.0157367i
$321$	20.9190			1.16759
$322$			4.55324i			0.253742i
$323$			18.4554i			1.02688i
$324$	−17.4553			−0.969737
$325$	−0.350459	−	0.122612i	−0.0194400	−	0.00680129i
$326$	4.39749			0.243554
$327$		−	6.75204i		−	0.373389i
$328$		−	11.2511i		−	0.621239i
$329$	−0.555438			−0.0306223
$330$	−0.815595	−	1.14942i	−0.0448971	−	0.0632732i
$331$	−29.2742			−1.60906			−0.804528	−	0.593915i	$-0.797582\pi$
$331$	−29.2742			−1.60906			−0.804528	+	0.593915i	$0.797582\pi$
$332$		−	1.73411i		−	0.0951714i
$333$		−	22.3807i		−	1.22645i
$334$	−1.58911			−0.0869520
$335$	−2.80683	+	1.99165i	−0.153354	+	0.108816i
$336$	4.45496			0.243038
$337$		−	3.70484i		−	0.201816i	−0.994896	−	0.100908i	$-0.967825\pi$
$337$		−	3.70484i		−	0.201816i	0.994896	−	0.100908i	$-0.0321747\pi$
$338$			8.27474i			0.450086i
$339$	12.9844			0.705215
$340$	11.1505	−	7.91212i	0.604722	−	0.429095i
$341$	0.189178			0.0102445
$342$		−	6.28345i		−	0.339770i
$343$		−	14.5282i		−	0.784448i
$344$	3.93984			0.212422
$345$	18.1608	+	25.5940i	0.977746	+	1.37793i
$346$	−0.272317			−0.0146398
$347$		−	20.8963i		−	1.12177i	−0.827893	−	0.560886i	$-0.810460\pi$
$347$		−	20.8963i		−	1.12177i	0.827893	−	0.560886i	$-0.189540\pi$
$348$		−	9.12128i		−	0.488952i
$349$	28.4273			1.52168			0.760840	−	0.648939i	$-0.224787\pi$
$349$	28.4273			1.52168			0.760840	+	0.648939i	$0.224787\pi$
$350$	−1.20383	+	3.44089i	−0.0643475	+	0.183923i
$351$	−0.158485			−0.00845930
$352$		−	2.50190i		−	0.133352i
$353$		−	11.3118i		−	0.602067i	−0.953614	−	0.301033i	$-0.902668\pi$
$353$		−	11.3118i		−	0.602067i	0.953614	−	0.301033i	$-0.0973316\pi$
$354$	−2.84178			−0.151039
$355$	−18.3303	−	25.8328i	−0.972872	−	1.37106i
$356$	−2.02657			−0.107408
$357$			9.86676i			0.522204i
$358$		−	3.82855i		−	0.202345i
$359$	−10.1228			−0.534263			−0.267132	−	0.963660i	$-0.586076\pi$
$359$	−10.1228			−0.534263			−0.267132	+	0.963660i	$0.586076\pi$
$360$	−8.55824	+	6.07271i	−0.451059	+	0.320060i
$361$	4.16181			0.219043
$362$			9.69733i			0.509680i
$363$		−	24.2842i		−	1.27459i
$364$	0.135565			0.00710551
$365$	−27.8363	+	19.7520i	−1.45702	+	1.03386i
$366$	−12.8361			−0.670953
$367$			3.11637i			0.162673i	0.996687	+	0.0813366i	$0.0259189\pi$
$367$			3.11637i			0.162673i	−0.996687	+	0.0813366i	$0.974081\pi$
$368$			10.8131i			0.563673i
$369$	10.0781			0.524645
$370$	8.99464	+	12.6761i	0.467609	+	0.658999i
$371$	−2.63327			−0.136713
$372$		−	1.53909i		−	0.0797980i
$373$		−	6.89555i		−	0.357038i	−0.983936	−	0.178519i	$-0.942869\pi$
$373$		−	6.89555i		−	0.357038i	0.983936	−	0.178519i	$-0.0571306\pi$
$374$	1.07553			0.0556141
$375$	6.95737	+	24.1430i	0.359277	+	1.24674i
$376$	1.11043			0.0572659
$377$		−	0.189023i		−	0.00973517i
$378$			1.55604i			0.0800341i
$379$	−26.3335			−1.35266			−0.676330	−	0.736599i	$-0.736431\pi$
$379$	−26.3335			−1.35266			−0.676330	+	0.736599i	$0.736431\pi$
$380$	−9.92985	−	13.9941i	−0.509391	−	0.717882i
$381$	43.2123			2.21383
$382$		−	0.368545i		−	0.0188564i
$383$		−	38.3736i		−	1.96080i	−0.197019	−	0.980400i	$-0.563126\pi$
$383$		−	38.3736i		−	1.96080i	0.197019	−	0.980400i	$-0.436874\pi$
$384$	−25.3102			−1.29161
$385$	0.919608	−	0.652530i	0.0468676	−	0.0332560i
$386$	−1.44147			−0.0733688
$387$			3.52908i			0.179393i
$388$			23.5439i			1.19526i
$389$	−7.49361			−0.379941			−0.189970	−	0.981790i	$-0.560839\pi$
$389$	−7.49361			−0.379941			−0.189970	+	0.981790i	$0.560839\pi$
$390$	−0.193789	+	0.137508i	−0.00981290	+	0.00696298i
$391$	−23.9487			−1.21114
$392$			13.0221i			0.657713i
$393$		−	33.8633i		−	1.70818i
$394$	−7.87901			−0.396939
$395$	2.39148	+	3.37030i	0.120328	+	0.169578i
$396$	1.43990			0.0723575
$397$			5.36992i			0.269509i	0.990879	+	0.134754i	$0.0430245\pi$
$397$			5.36992i			0.269509i	−0.990879	+	0.134754i	$0.956975\pi$
$398$		−	7.56347i		−	0.379123i
$399$	12.3830			0.619923
$400$	−2.85888	+	8.17149i	−0.142944	+	0.408574i
$401$	−24.6951			−1.23321			−0.616606	−	0.787272i	$-0.711493\pi$
$401$	−24.6951			−1.23321			−0.616606	+	0.787272i	$0.711493\pi$
$402$			2.20260i			0.109856i
$403$		−	0.0318950i		−	0.00158880i
$404$	−8.46504			−0.421151
$405$	14.1656	+	19.9635i	0.703892	+	0.991992i
$406$	−1.85587			−0.0921052
$407$		−	4.80780i		−	0.238314i
$408$		−	19.7255i		−	0.976559i
$409$	23.7785			1.17577			0.587885	−	0.808945i	$-0.299961\pi$
$409$	23.7785			1.17577			0.587885	+	0.808945i	$0.299961\pi$
$410$	−5.70809	+	4.05031i	−0.281903	+	0.200031i
$411$	−23.3220			−1.15039
$412$		−	5.08859i		−	0.250697i
$413$		−	2.27361i		−	0.111877i
$414$	8.15375			0.400735
$415$	−1.98328	+	1.40729i	−0.0973556	+	0.0690810i
$416$	−0.421816			−0.0206812
$417$			5.18575i			0.253947i
$418$		−	1.34980i		−	0.0660211i
$419$	31.0372			1.51627			0.758133	−	0.652100i	$-0.226112\pi$
$419$	31.0372			1.51627			0.758133	+	0.652100i	$0.226112\pi$
$420$	−5.30878	−	7.48164i	−0.259042	−	0.365066i
$421$	−2.89741			−0.141211			−0.0706055	−	0.997504i	$-0.522493\pi$
$421$	−2.89741			−0.141211			−0.0706055	+	0.997504i	$0.522493\pi$
$422$		−	7.22676i		−	0.351793i
$423$			0.994656i			0.0483618i
$424$	5.26441			0.255663
$425$	−18.0981	−	6.33180i	−0.877885	−	0.307137i
$426$	−20.2718			−0.982170
$427$		−	10.2697i		−	0.496987i
$428$		−	14.8425i		−	0.717440i
$429$	0.0735004			0.00354863
$430$	−1.41831	−	1.99882i	−0.0683971	−	0.0963918i
$431$	−30.6994			−1.47874			−0.739370	−	0.673299i	$-0.764877\pi$
$431$	−30.6994			−1.47874			−0.739370	+	0.673299i	$0.764877\pi$
$432$			3.69532i			0.177791i
$433$			26.8147i			1.28863i	0.764759	+	0.644316i	$0.222858\pi$
$433$			26.8147i			1.28863i	−0.764759	+	0.644316i	$0.777142\pi$
$434$	−0.313152			−0.0150318
$435$	−10.4319	+	7.40223i	−0.500173	+	0.354910i
$436$	−4.79073			−0.229434
$437$			30.0560i			1.43777i
$438$			21.8440i			1.04375i
$439$	16.8791			0.805594			0.402797	−	0.915289i	$-0.368038\pi$
$439$	16.8791			0.805594			0.402797	+	0.915289i	$0.368038\pi$
$440$	−1.83847	+	1.30453i	−0.0876457	+	0.0621911i
$441$	−11.6644			−0.555448
$442$		−	0.181332i		−	0.00862506i
$443$			16.8323i			0.799729i	0.916574	+	0.399864i	$0.130943\pi$
$443$			16.8323i			0.799729i	−0.916574	+	0.399864i	$0.869057\pi$
$444$	−39.1147			−1.85630
$445$	1.64463	+	2.31778i	0.0779632	+	0.109873i
$446$	−1.92170			−0.0909951
$447$			25.1573i			1.18990i
$448$			0.176740i			0.00835017i
$449$	−14.1492			−0.667741			−0.333870	−	0.942619i	$-0.608355\pi$
$449$	−14.1492			−0.667741			−0.333870	+	0.942619i	$0.608355\pi$
$450$	6.16180	+	2.15577i	0.290470	+	0.101624i
$451$	2.16497			0.101944
$452$		−	9.21272i		−	0.433330i
$453$		−	14.9888i		−	0.704235i
$454$	−9.15532			−0.429680
$455$	−0.110015	−	0.155044i	−0.00515760	−	0.00726858i
$456$	−24.7559			−1.15930
$457$			4.43915i			0.207655i	0.994595	+	0.103827i	$0.0331089\pi$
$457$			4.43915i			0.207655i	−0.994595	+	0.103827i	$0.966891\pi$
$458$			16.8992i			0.789649i
$459$	−8.18432			−0.382011
$460$	18.1595	−	12.8855i	0.846691	−	0.600790i
$461$	0.00973326			0.000453323			0.000226661	−	1.00000i	$-0.499928\pi$
$461$	0.00973326			0.000453323			0.000226661		1.00000i	$0.499928\pi$
$462$		−	0.721643i		−	0.0335739i
$463$			21.6957i			1.00829i	0.863620	+	0.504143i	$0.168191\pi$
$463$			21.6957i			1.00829i	−0.863620	+	0.504143i	$0.831809\pi$
$464$	−4.40735			−0.204606
$465$	−1.76024	+	1.24902i	−0.0816293	+	0.0579221i
$466$	9.71103			0.449855
$467$		−	24.0487i		−	1.11284i	−0.830900	−	0.556422i	$-0.812174\pi$
$467$		−	24.0487i		−	1.11284i	0.830900	−	0.556422i	$-0.187826\pi$
$468$		−	0.242764i		−	0.0112217i
$469$	−1.76223			−0.0813721
$470$	−0.399745	−	0.563359i	−0.0184389	−	0.0259858i
$471$	51.3554			2.36633
$472$			4.54538i			0.209218i
$473$			0.758114i			0.0348581i
$474$	2.64477			0.121478
$475$	−7.94652	+	22.7134i	−0.364611	+	1.04216i
$476$	7.00068			0.320876
$477$			4.71556i			0.215911i
$478$			6.35751i			0.290786i
$479$	−19.0129			−0.868720			−0.434360	−	0.900739i	$-0.643025\pi$
$479$	−19.0129			−0.868720			−0.434360	+	0.900739i	$0.643025\pi$
$480$	16.5185	+	23.2795i	0.753964	+	1.06256i
$481$	−0.810585			−0.0369595
$482$			0.636788i			0.0290049i
$483$			16.0688i			0.731156i
$484$	−17.2302			−0.783190
$485$	26.9270	−	19.1067i	1.22269	−	0.867590i
$486$	11.5887			0.525674
$487$			23.1741i			1.05012i	0.851066	+	0.525058i	$0.175956\pi$
$487$			23.1741i			1.05012i	−0.851066	+	0.525058i	$0.824044\pi$
$488$			20.5311i			0.929401i
$489$	15.5191			0.701800
$490$	6.60656	−	4.68784i	0.298454	−	0.211775i
$491$	17.8038			0.803473			0.401736	−	0.915755i	$-0.368407\pi$
$491$	17.8038			0.803473			0.401736	+	0.915755i	$0.368407\pi$
$492$		−	17.6135i		−	0.794076i
$493$		−	9.76133i		−	0.439628i
$494$	−0.227574			−0.0102391
$495$	−1.16853	−	1.64680i	−0.0525213	−	0.0740180i
$496$	−0.743679			−0.0333922
$497$		−	16.2188i		−	0.727510i
$498$			1.55634i			0.0697413i
$499$	13.6724			0.612060			0.306030	−	0.952022i	$-0.400999\pi$
$499$	13.6724			0.612060			0.306030	+	0.952022i	$0.400999\pi$
$500$	17.1300	−	4.93641i	0.766075	−	0.220763i
$501$	−5.60810			−0.250552
$502$		−	12.2360i		−	0.546118i
$503$		−	13.1075i		−	0.584433i	−0.956352	−	0.292216i	$-0.905607\pi$
$503$		−	13.1075i		−	0.584433i	0.956352	−	0.292216i	$-0.0943927\pi$
$504$	−5.37317			−0.239340
$505$	6.86967	+	9.68140i	0.305696	+	0.430817i
$506$	1.75158			0.0778672
$507$			29.2023i			1.29692i
$508$		−	30.6601i		−	1.36032i
$509$	14.6586			0.649731			0.324865	−	0.945760i	$-0.394681\pi$
$509$	14.6586			0.649731			0.324865	+	0.945760i	$0.394681\pi$
$510$	−10.0075	+	7.10104i	−0.443138	+	0.314439i
$511$	−17.4766			−0.773121
$512$			17.7616i			0.784957i
$513$			10.2715i			0.453496i
$514$	18.8742			0.832505
$515$	−5.81978	+	4.12956i	−0.256450	+	0.181970i
$516$	6.16777			0.271521
$517$			0.213671i			0.00939723i
$518$			7.95851i			0.349677i
$519$	−0.961031			−0.0421846
$520$	0.219942	+	0.309963i	0.00964508	+	0.0135928i
$521$	5.24664			0.229859			0.114930	−	0.993374i	$-0.463336\pi$
$521$	5.24664			0.229859			0.114930	+	0.993374i	$0.463336\pi$
$522$			3.32342i			0.145462i
$523$			26.4312i			1.15575i	0.816124	+	0.577877i	$0.196119\pi$
$523$			26.4312i			1.15575i	−0.816124	+	0.577877i	$0.803881\pi$
$524$	−24.0267			−1.04961
$525$	−4.24843	+	12.1432i	−0.185417	+	0.529973i
$526$	−15.5090			−0.676225
$527$		−	1.64709i		−	0.0717482i
$528$		−	1.71377i		−	0.0745824i
$529$	−16.0023			−0.695754
$530$	−1.89515	−	2.67082i	−0.0823200	−	0.116013i
$531$	−4.07149			−0.176687
$532$		−	8.78598i		−	0.380921i
$533$		−	0.365009i		−	0.0158103i
$534$	1.81883			0.0787083
$535$	−16.9753	+	12.0452i	−0.733905	+	0.520760i
$536$	3.52303			0.152172
$537$		−	13.5113i		−	0.583056i
$538$			9.60072i			0.413916i
$539$	−2.50574			−0.107930
$540$	6.20590	−	4.40354i	0.267059	−	0.189498i
$541$	40.6899			1.74940			0.874698	−	0.484668i	$-0.161060\pi$
$541$	40.6899			1.74940			0.874698	+	0.484668i	$0.161060\pi$
$542$			14.9936i			0.644028i
$543$			34.2228i			1.46864i
$544$	−21.7830			−0.933938
$545$	3.88784	+	5.47912i	0.166537	+	0.234700i
$546$	−0.121668			−0.00520689
$547$		−	16.6696i		−	0.712740i	−0.934345	−	0.356370i	$-0.884014\pi$
$547$		−	16.6696i		−	0.712740i	0.934345	−	0.356370i	$-0.115986\pi$
$548$			16.5475i			0.706872i
$549$	−18.3906			−0.784892
$550$	1.32367	+	0.463101i	0.0564415	+	0.0197467i
$551$	−12.2506			−0.521895
$552$		−	32.1246i		−	1.36731i
$553$			2.11599i			0.0899811i
$554$	−2.99725			−0.127341
$555$	31.7429	+	44.7352i	1.34741	+	1.89890i
$556$	3.67940			0.156042
$557$			10.8329i			0.459006i	0.973308	+	0.229503i	$0.0737100\pi$
$557$			10.8329i			0.459006i	−0.973308	+	0.229503i	$0.926290\pi$
$558$			0.560780i			0.0237397i
$559$	0.127817			0.00540606
$560$	−3.61509	+	2.56517i	−0.152765	+	0.108398i
$561$	3.79563			0.160252
$562$			1.87419i			0.0790578i
$563$		−	28.6816i		−	1.20879i	−0.796686	−	0.604393i	$-0.793416\pi$
$563$		−	28.6816i		−	1.20879i	0.796686	−	0.604393i	$-0.206584\pi$
$564$	1.73836			0.0731981
$565$	−10.5365	+	7.47644i	−0.443274	+	0.314536i
$566$	7.89108			0.331687
$567$			12.5338i			0.526369i
$568$			32.4244i			1.36050i
$569$	−12.8372			−0.538161			−0.269081	−	0.963118i	$-0.586720\pi$
$569$	−12.8372			−0.538161			−0.269081	+	0.963118i	$0.586720\pi$
$570$	8.91193	+	12.5595i	0.373280	+	0.526061i
$571$	2.68924			0.112541			0.0562707	−	0.998416i	$-0.482079\pi$
$571$	2.68924			0.112541			0.0562707	+	0.998416i	$0.482079\pi$
$572$		−	0.0521502i		−	0.00218051i
$573$		−	1.30063i		−	0.0543345i
$574$	−3.58374			−0.149582
$575$	−29.4741	−	10.3118i	−1.22916	−	0.430033i
$576$	0.316498			0.0131874
$577$		−	3.19429i		−	0.132980i	−0.997787	−	0.0664900i	$-0.978820\pi$
$577$		−	3.19429i		−	0.132980i	0.997787	−	0.0664900i	$-0.0211801\pi$
$578$			1.46126i			0.0607806i
$579$	−5.08708			−0.211412
$580$	5.25205	+	7.40169i	0.218080	+	0.307339i
$581$	−1.24518			−0.0516586
$582$		−	21.1304i		−	0.875882i
$583$			1.01299i			0.0419538i
$584$	34.9391			1.44579
$585$	−0.277647	+	0.197011i	−0.0114793	+	0.00814540i
$586$	−7.04724			−0.291119
$587$		−	9.55051i		−	0.394192i	−0.980384	−	0.197096i	$-0.936849\pi$
$587$		−	9.55051i		−	0.394192i	0.980384	−	0.197096i	$-0.0631510\pi$
$588$			20.3859i			0.840699i
$589$	−2.06712			−0.0851743
$590$	2.30603	−	1.63630i	0.0949378	−	0.0673654i
$591$	−27.8058			−1.14378
$592$			18.9000i			0.776786i
$593$		−	21.1508i		−	0.868559i	−0.900778	−	0.434280i	$-0.857003\pi$
$593$		−	21.1508i		−	0.868559i	0.900778	−	0.434280i	$-0.142997\pi$
$594$	0.598591			0.0245605
$595$	−5.68130	−	8.00663i	−0.232911	−	0.328240i
$596$	17.8497			0.731152
$597$		−	26.6922i		−	1.09244i
$598$		−	0.295313i		−	0.0120762i
$599$	−2.77929			−0.113559			−0.0567793	−	0.998387i	$-0.518083\pi$
$599$	−2.77929			−0.113559			−0.0567793	+	0.998387i	$0.518083\pi$
$600$	8.49343	−	24.2766i	0.346743	−	0.991088i
$601$	−18.5051			−0.754837			−0.377418	−	0.926043i	$-0.623188\pi$
$601$	−18.5051			−0.754837			−0.377418	+	0.926043i	$0.623188\pi$
$602$		−	1.25493i		−	0.0511472i
$603$			3.15572i			0.128511i
$604$	−10.6349			−0.432727
$605$	13.9829	+	19.7060i	0.568486	+	0.801164i
$606$	7.59728			0.308618
$607$			14.5288i			0.589706i	0.955543	+	0.294853i	$0.0952707\pi$
$607$			14.5288i			0.589706i	−0.955543	+	0.294853i	$0.904729\pi$
$608$			27.3380i			1.10870i
$609$	−6.54954			−0.265401
$610$	10.4162	−	7.39105i	0.421739	−	0.299255i
$611$	0.0360245			0.00145739
$612$		−	12.5365i		−	0.506760i
$613$		−	14.9699i		−	0.604627i	−0.953209	−	0.302314i	$-0.902241\pi$
$613$		−	14.9699i		−	0.604627i	0.953209	−	0.302314i	$-0.0977590\pi$
$614$	12.4511			0.502485
$615$	−20.1444	+	14.2939i	−0.812300	+	0.576387i
$616$	−1.15426			−0.0465063
$617$			0.478194i			0.0192514i	0.999954	+	0.00962568i	$0.00306400\pi$
$617$			0.478194i			0.0192514i	−0.999954	+	0.00962568i	$0.996936\pi$
$618$			4.56695i			0.183710i
$619$	−29.2455			−1.17548			−0.587738	−	0.809052i	$-0.699981\pi$
$619$	−29.2455			−1.17548			−0.587738	+	0.809052i	$0.699981\pi$
$620$	0.886210	+	1.24893i	0.0355910	+	0.0501583i
$621$	−13.3288			−0.534867
$622$			4.32704i			0.173498i
$623$			1.45518i			0.0583006i
$624$	−0.288939			−0.0115668
$625$	−19.5473	−	15.5853i	−0.781892	−	0.623414i
$626$	3.07244			0.122799
$627$		−	4.76359i		−	0.190239i
$628$		−	36.4378i		−	1.45403i
$629$	−41.8594			−1.66904
$630$	1.93430	+	2.72600i	0.0770643	+	0.108606i
$631$	25.1784			1.00234			0.501168	−	0.865350i	$-0.332904\pi$
$631$	25.1784			1.00234			0.501168	+	0.865350i	$0.332904\pi$
$632$		−	4.23027i		−	0.168271i
$633$		−	25.5039i		−	1.01369i
$634$	−2.59362			−0.103006
$635$	−35.0657	+	24.8817i	−1.39154	+	0.987401i
$636$	8.24137			0.326792
$637$			0.422462i			0.0167386i
$638$			0.713932i			0.0282648i
$639$	−29.0439			−1.14896
$640$	20.5386	−	14.5737i	0.811860	−	0.576075i
$641$	−47.7764			−1.88705			−0.943527	−	0.331297i	$-0.892514\pi$
$641$	−47.7764			−1.88705			−0.943527	+	0.331297i	$0.892514\pi$
$642$			13.3210i			0.525738i
$643$		−	1.76572i		−	0.0696332i	−0.999394	−	0.0348166i	$-0.988915\pi$
$643$		−	1.76572i		−	0.0696332i	0.999394	−	0.0348166i	$-0.0110847\pi$
$644$	11.4012			0.449269
$645$	−5.00536	−	7.05403i	−0.197086	−	0.277752i
$646$	−11.7522			−0.462383
$647$		−	17.7016i		−	0.695921i	−0.937509	−	0.347961i	$-0.886874\pi$
$647$		−	17.7016i		−	0.695921i	0.937509	−	0.347961i	$-0.113126\pi$
$648$		−	25.0574i		−	0.984347i
$649$	−0.874632			−0.0343323
$650$	0.0780779	−	0.223168i	0.00306247	−	0.00875339i
$651$	−1.10514			−0.0433139
$652$		−	11.0112i		−	0.431231i
$653$		−	36.0403i		−	1.41037i	−0.709025	−	0.705183i	$-0.750865\pi$
$653$		−	36.0403i		−	1.41037i	0.709025	−	0.705183i	$-0.249135\pi$
$654$	4.29962			0.168129
$655$	19.4985	+	27.4792i	0.761871	+	1.07370i
$656$	−8.51074			−0.332289
$657$			31.2965i			1.22099i
$658$		−	0.353696i		−	0.0137885i
$659$	31.7767			1.23784			0.618922	−	0.785452i	$-0.287569\pi$
$659$	31.7767			1.23784			0.618922	+	0.785452i	$0.287569\pi$
$660$	−2.87810	+	2.04223i	−0.112030	+	0.0794936i
$661$	34.0434			1.32413			0.662067	−	0.749445i	$-0.269679\pi$
$661$	34.0434			1.32413			0.662067	+	0.749445i	$0.269679\pi$
$662$		−	18.6415i		−	0.724521i
$663$		−	0.639936i		−	0.0248531i
$664$	2.48934			0.0966052
$665$	−10.0485	+	7.13013i	−0.389663	+	0.276495i
$666$	14.2518			0.552245
$667$		−	15.8971i		−	0.615538i
$668$			3.97907i			0.153955i
$669$	−6.78186			−0.262202
$670$	−1.26826	−	1.78736i	−0.0489973	−	0.0690516i
$671$	−3.95065			−0.152513
$672$			14.6157i			0.563812i
$673$			36.3663i			1.40182i	0.713251	+	0.700909i	$0.247222\pi$
$673$			36.3663i			1.40182i	−0.713251	+	0.700909i	$0.752778\pi$
$674$	2.35920			0.0908731
$675$	−10.0726	−	3.52401i	−0.387695	−	0.135639i
$676$	20.7197			0.796912
$677$		−	27.7344i		−	1.06592i	−0.846141	−	0.532959i	$-0.821080\pi$
$677$		−	27.7344i		−	1.06592i	0.846141	−	0.532959i	$-0.178920\pi$
$678$			8.26831i			0.317543i
$679$	16.9057			0.648781
$680$	11.3580	+	16.0068i	0.435559	+	0.613832i
$681$	−32.3100			−1.23812
$682$			0.120466i			0.00461288i
$683$		−	31.2794i		−	1.19687i	−0.801170	−	0.598437i	$-0.795789\pi$
$683$		−	31.2794i		−	1.19687i	0.801170	−	0.598437i	$-0.204211\pi$
$684$	−15.7336			−0.601589
$685$	18.9252	−	13.4288i	0.723095	−	0.513089i
$686$	9.25138			0.353219
$687$			59.6390i			2.27537i
$688$		−	2.98024i		−	0.113620i
$689$	0.170788			0.00650652
$690$	−16.2979	+	11.5646i	−0.620452	+	0.440257i
$691$	48.1424			1.83142			0.915712	−	0.401836i	$-0.131628\pi$
$691$	48.1424			1.83142			0.915712	+	0.401836i	$0.131628\pi$
$692$			0.681873i			0.0259209i
$693$		−	1.03392i		−	0.0392753i
$694$	13.3065			0.505109
$695$	−2.98596	−	4.20811i	−0.113264	−	0.159623i
$696$	13.0938			0.496318
$697$		−	18.8494i		−	0.713973i
$698$			18.1022i			0.685179i
$699$	34.2711			1.29625
$700$	8.61588	+	3.01436i	0.325650	+	0.113932i
$701$	23.3483			0.881852			0.440926	−	0.897543i	$-0.354650\pi$
$701$	23.3483			0.881852			0.440926	+	0.897543i	$0.354650\pi$
$702$		−	0.100921i		−	0.00380903i
$703$			52.5343i			1.98137i
$704$	0.0679898			0.00256246
$705$	−1.41074	−	1.98815i	−0.0531315	−	0.0748779i
$706$	7.20323			0.271097
$707$			6.07832i			0.228599i
$708$			7.11573i			0.267425i
$709$	39.2625			1.47453			0.737267	−	0.675601i	$-0.236116\pi$
$709$	39.2625			1.47453			0.737267	+	0.675601i	$0.236116\pi$
$710$	16.4500	−	11.6725i	0.617359	−	0.438062i
$711$	3.78923			0.142107
$712$		−	2.90919i		−	0.109026i
$713$		−	2.68241i		−	0.100457i
$714$	−6.28304			−0.235137
$715$	−0.0596438	+	0.0423217i	−0.00223055	+	0.00158274i
$716$	−9.58658			−0.358267
$717$			22.4362i			0.837897i
$718$		−	6.44611i		−	0.240567i
$719$	−2.50667			−0.0934830			−0.0467415	−	0.998907i	$-0.514884\pi$
$719$	−2.50667			−0.0934830			−0.0467415	+	0.998907i	$0.514884\pi$
$720$	4.59361	+	6.47376i	0.171194	+	0.241263i
$721$	−3.65386			−0.136077
$722$			2.65019i			0.0986299i
$723$			2.24729i			0.0835775i
$724$	24.2818			0.902428
$725$	4.20304	−	12.0135i	0.156097	−	0.446169i
$726$	15.4639			0.573919
$727$		−	17.3890i		−	0.644922i	−0.946583	−	0.322461i	$-0.895490\pi$
$727$		−	17.3890i		−	0.644922i	0.946583	−	0.322461i	$-0.104510\pi$
$728$			0.194606i			0.00721256i
$729$	8.05612			0.298375
$730$	−12.5778	−	17.7259i	−0.465526	−	0.656064i
$731$	6.60057			0.244131
$732$			32.1412i			1.18797i
$733$		−	12.6365i		−	0.466739i	−0.972388	−	0.233370i	$-0.925025\pi$
$733$		−	12.6365i		−	0.466739i	0.972388	−	0.233370i	$-0.0749752\pi$
$734$	−1.98447			−0.0732481
$735$	23.3152	−	16.5438i	0.859993	−	0.610229i
$736$	−35.4753			−1.30764
$737$			0.677909i			0.0249711i
$738$			6.41762i			0.236236i
$739$	−49.2503			−1.81170			−0.905850	−	0.423598i	$-0.860767\pi$
$739$	−49.2503			−1.81170			−0.905850	+	0.423598i	$0.860767\pi$
$740$	31.7406	−	22.5223i	1.16681	−	0.827937i
$741$	−0.803131			−0.0295038
$742$		−	1.67684i		−	0.0615586i
$743$			42.2847i			1.55127i	0.631179	+	0.775637i	$0.282571\pi$
$743$			42.2847i			1.55127i	−0.631179	+	0.775637i	$0.717429\pi$
$744$	2.20939			0.0810002
$745$	−14.4857	−	20.4146i	−0.530713	−	0.747932i
$746$	4.39101			0.160766
$747$			2.22981i			0.0815845i
$748$		−	2.69309i		−	0.0984690i
$749$	−10.6577			−0.389423
$750$	−15.3740	+	4.43037i	−0.561377	+	0.161774i
$751$	−44.6401			−1.62894			−0.814471	−	0.580204i	$-0.802973\pi$
$751$	−44.6401			−1.62894			−0.814471	+	0.580204i	$0.802973\pi$
$752$		−	0.839966i		−	0.0306304i
$753$		−	43.1819i		−	1.57364i
$754$	0.120368			0.00438353
$755$	8.63058	+	12.1630i	0.314099	+	0.442658i
$756$	3.89628			0.141706
$757$			28.3936i			1.03198i	0.856593	+	0.515992i	$0.172577\pi$
$757$			28.3936i			1.03198i	−0.856593	+	0.515992i	$0.827423\pi$
$758$		−	16.7689i		−	0.609072i
$759$	6.18149			0.224374
$760$	20.0888	−	14.2545i	0.728697	−	0.517065i
$761$	27.7195			1.00483			0.502415	−	0.864627i	$-0.332445\pi$
$761$	27.7195			1.00483			0.502415	+	0.864627i	$0.332445\pi$
$762$			27.5171i			0.996838i
$763$			3.43998i			0.124536i
$764$	−0.922825			−0.0333866
$765$	−14.3380	+	10.1738i	−0.518390	+	0.367836i
$766$	24.4359			0.882904
$767$			0.147461i			0.00532452i
$768$		−	16.8111i		−	0.606617i
$769$	−35.1939			−1.26912			−0.634562	−	0.772872i	$-0.718819\pi$
$769$	−35.1939			−1.26912			−0.634562	+	0.772872i	$0.718819\pi$
$770$	0.415524	+	0.585596i	0.0149744	+	0.0211034i
$771$	66.6088			2.39886
$772$			3.60939i			0.129905i
$773$		−	0.165321i		−	0.00594618i	−0.999996	−	0.00297309i	$-0.999054\pi$
$773$		−	0.165321i		−	0.00594618i	0.999996	−	0.00297309i	$-0.000946365\pi$
$774$	−2.24728			−0.0807768
$775$	0.709204	−	2.02710i	0.0254753	−	0.0728157i
$776$	−33.7977			−1.21327
$777$			28.0863i			1.00759i
$778$		−	4.77184i		−	0.171079i
$779$	−23.6564			−0.847577
$780$	0.344316	+	0.485243i	0.0123285	+	0.0173745i
$781$	−6.23918			−0.223255
$782$		−	15.2502i		−	0.545348i
$783$		−	5.43273i		−	0.194150i
$784$	9.85035			0.351798
$785$	−41.6737	+	29.5706i	−1.48740	+	1.05542i
$786$	21.5637			0.769153
$787$		−	22.9720i		−	0.818863i	−0.912341	−	0.409431i	$-0.865727\pi$
$787$		−	22.9720i		−	0.818863i	0.912341	−	0.409431i	$-0.134273\pi$
$788$			19.7288i			0.702810i
$789$	−54.7328			−1.94854
$790$	−2.14617	+	1.52286i	−0.0763572	+	0.0541811i
$791$	−6.61519			−0.235209
$792$			2.06700i			0.0734476i
$793$			0.666072i			0.0236529i
$794$	−3.41950			−0.121354
$795$	−6.68816	−	9.42559i	−0.237205	−	0.334291i
$796$	−18.9387			−0.671265
$797$		−	32.6066i		−	1.15499i	−0.816395	−	0.577493i	$-0.804031\pi$
$797$		−	32.6066i		−	1.15499i	0.816395	−	0.577493i	$-0.195969\pi$
$798$			7.88532i			0.279137i
$799$	1.86034			0.0658141
$800$	−26.8088	−	9.37933i	−0.947833	−	0.331610i
$801$	2.60588			0.0920743
$802$		−	15.7255i		−	0.555288i
$803$			6.72307i			0.237252i
$804$	5.51525			0.194508
$805$	−9.25245	−	13.0394i	−0.326106	−	0.459580i
$806$	0.0203103			0.000715401
$807$			33.8818i			1.19270i
$808$		−	12.1517i		−	0.427496i
$809$	−19.3356			−0.679802			−0.339901	−	0.940461i	$-0.610394\pi$
$809$	−19.3356			−0.679802			−0.339901	+	0.940461i	$0.610394\pi$
$810$	−12.7125	+	9.02047i	−0.446672	+	0.316947i
$811$	−45.2010			−1.58722			−0.793612	−	0.608425i	$-0.791802\pi$
$811$	−45.2010			−1.58722			−0.793612	+	0.608425i	$0.791802\pi$
$812$			4.64704i			0.163079i
$813$			52.9137i			1.85576i
$814$	3.06155			0.107307
$815$	−12.5934	+	8.93596i	−0.441128	+	0.313013i
$816$	−14.9211			−0.522342
$817$		−	8.28383i		−	0.289815i
$818$			15.1419i			0.529423i
$819$	−0.174316			−0.00609111
$820$	10.1419	+	14.2929i	0.354170	+	0.499130i
$821$	29.4554			1.02800			0.514001	−	0.857790i	$-0.328163\pi$
$821$	29.4554			1.02800			0.514001	+	0.857790i	$0.328163\pi$
$822$		−	14.8512i		−	0.517994i
$823$		−	49.6297i		−	1.72998i	−0.501787	−	0.864991i	$-0.667324\pi$
$823$		−	49.6297i		−	1.72998i	0.501787	−	0.864991i	$-0.332676\pi$
$824$	7.30476			0.254473
$825$	4.67136	+	1.63433i	0.162636	+	0.0568999i
$826$	1.44781			0.0503757
$827$		−	8.61123i		−	0.299442i	−0.988728	−	0.149721i	$-0.952162\pi$
$827$		−	8.61123i		−	0.299442i	0.988728	−	0.149721i	$-0.0478375\pi$
$828$		−	20.4168i		−	0.709532i
$829$	9.81975			0.341054			0.170527	−	0.985353i	$-0.445453\pi$
$829$	9.81975			0.341054			0.170527	+	0.985353i	$0.445453\pi$
$830$	−0.896144	−	1.26293i	−0.0311056	−	0.0438370i
$831$	−10.5776			−0.366932
$832$		−	0.0114630i		−	0.000397406i
$833$			21.8164i			0.755892i
$834$	−3.30222			−0.114347
$835$	4.55084	−	3.22916i	0.157488	−	0.111750i
$836$	−3.37987			−0.116895
$837$		−	0.916698i		−	0.0316857i
$838$			19.7641i			0.682740i
$839$	5.45749			0.188414			0.0942068	−	0.995553i	$-0.469969\pi$
$839$	5.45749			0.188414			0.0942068	+	0.995553i	$0.469969\pi$
$840$	10.7400	−	7.62085i	0.370566	−	0.262944i
$841$	−22.5204			−0.776567
$842$		−	1.84504i		−	0.0635841i
$843$			6.61419i			0.227805i
$844$	−18.0956			−0.622876
$845$	−16.8148	−	23.6970i	−0.578446	−	0.815201i
$846$	−0.633386			−0.0217762
$847$			12.3721i			0.425112i
$848$		−	3.98219i		−	0.136749i
$849$	27.8484			0.955753
$850$	4.03202	−	11.5246i	0.138297	−	0.395292i
$851$	−68.1714			−2.33689
$852$			50.7599i			1.73901i
$853$			1.89562i			0.0649050i	0.999473	+	0.0324525i	$0.0103318\pi$
$853$			1.89562i			0.0649050i	−0.999473	+	0.0324525i	$0.989668\pi$
$854$	6.53964			0.223782
$855$	12.7684	+	17.9944i	0.436669	+	0.615395i
$856$	21.3067			0.728249
$857$			40.1087i			1.37009i	0.728502	+	0.685044i	$0.240217\pi$
$857$			40.1087i			1.37009i	−0.728502	+	0.685044i	$0.759783\pi$
$858$			0.0468042i			0.00159787i
$859$	−56.6142			−1.93165			−0.965825	−	0.259195i	$-0.916543\pi$
$859$	−56.6142			−1.93165			−0.965825	+	0.259195i	$0.916543\pi$
$860$	−5.00500	+	3.55142i	−0.170669	+	0.121102i
$861$	−12.6474			−0.431021
$862$		−	19.5491i		−	0.665843i
$863$			15.4130i			0.524664i	0.964978	+	0.262332i	$0.0844915\pi$
$863$			15.4130i			0.524664i	−0.964978	+	0.262332i	$0.915508\pi$
$864$	−12.1235			−0.412449
$865$	0.779853	−	0.553364i	0.0265158	−	0.0188149i
$866$	−17.0753			−0.580242
$867$			5.15694i			0.175139i
$868$			0.784123i			0.0266149i
$869$	0.813998			0.0276130
$870$	−4.71366	−	6.64294i	−0.159808	−	0.225217i
$871$	0.114294			0.00387271
$872$		−	6.87718i		−	0.232891i
$873$		−	30.2740i		−	1.02462i
$874$	−19.1393			−0.647398
$875$	−3.54459	−	12.3002i	−0.119829	−	0.415822i
$876$	54.6967			1.84803
$877$		−	2.57230i		−	0.0868603i	−0.999056	−	0.0434301i	$-0.986171\pi$
$877$		−	2.57230i		−	0.0868603i	0.999056	−	0.0434301i	$-0.0138286\pi$
$878$			10.7484i			0.362741i
$879$	−24.8704			−0.838857
$880$	0.986794	+	1.39069i	0.0332648	+	0.0468800i
$881$	−50.0812			−1.68728			−0.843639	−	0.536910i	$-0.819591\pi$
$881$	−50.0812			−1.68728			−0.843639	+	0.536910i	$0.819591\pi$
$882$		−	7.42776i		−	0.250106i
$883$			29.8568i			1.00476i	0.864646	+	0.502381i	$0.167543\pi$
$883$			29.8568i			1.00476i	−0.864646	+	0.502381i	$0.832457\pi$
$884$	−0.454049			−0.0152713
$885$	8.13820	−	5.77466i	0.273563	−	0.194113i
$886$	−10.7186			−0.360100
$887$		−	24.9301i		−	0.837072i	−0.908200	−	0.418536i	$-0.862543\pi$
$887$		−	24.9301i		−	0.837072i	0.908200	−	0.418536i	$-0.137457\pi$
$888$		−	56.1499i		−	1.88427i
$889$	−22.0155			−0.738375
$890$	−1.47593	+	1.04728i	−0.0494734	+	0.0351051i
$891$	4.82160			0.161530
$892$			4.81188i			0.161114i
$893$		−	2.33476i		−	0.0781298i
$894$	−16.0199			−0.535786
$895$	7.77984	+	10.9641i	0.260051	+	0.366489i
$896$	12.8949			0.430787
$897$		−	1.04219i		−	0.0347976i
$898$		−	9.01003i		−	0.300669i
$899$	1.09333			0.0364647
$900$	5.39799	−	15.4290i	0.179933	−	0.514299i
$901$	8.81968			0.293826
$902$			1.37863i			0.0459032i
$903$		−	4.42877i		−	0.147380i
$904$	13.2250			0.439858
$905$	−19.7056	−	27.7710i	−0.655035	−	0.923138i
$906$	9.54469			0.317101
$907$			27.8785i			0.925689i	0.886440	+	0.462844i	$0.153171\pi$
$907$			27.8785i			0.925689i	−0.886440	+	0.462844i	$0.846829\pi$
$908$			22.9247i			0.760782i
$909$	10.8848			0.361027
$910$	0.0987303	−	0.0700565i	0.00327288	−	0.00232235i
$911$	−12.1116			−0.401275			−0.200638	−	0.979666i	$-0.564301\pi$
$911$	−12.1116			−0.401275			−0.200638	+	0.979666i	$0.564301\pi$
$912$			18.7262i			0.620087i
$913$			0.479005i			0.0158528i
$914$	−2.82680			−0.0935022
$915$	36.7597	−	26.0837i	1.21524	−	0.862301i
$916$	42.3152			1.39813
$917$			17.2524i			0.569725i
$918$		−	5.21168i		−	0.172011i
$919$	15.4282			0.508928			0.254464	−	0.967082i	$-0.418101\pi$
$919$	15.4282			0.508928			0.254464	+	0.967082i	$0.418101\pi$
$920$	18.4974	+	26.0683i	0.609841	+	0.859447i
$921$	43.9411			1.44791
$922$			0.00619803i			0.000204121i
$923$			1.05191i			0.0346241i
$924$	−1.80697			−0.0594451
$925$	−51.5172	−	18.0239i	−1.69388	−	0.592621i
$926$	−13.8156			−0.454008
$927$			6.54319i			0.214906i
$928$		−	14.4595i		−	0.474657i
$929$	17.1882			0.563925			0.281963	−	0.959425i	$-0.409015\pi$
$929$	17.1882			0.563925			0.281963	+	0.959425i	$0.409015\pi$
$930$	−0.795363	−	1.12090i	−0.0260810	−	0.0367558i
$931$	27.3799			0.897341
$932$		−	24.3161i		−	0.796501i
$933$			15.2705i			0.499935i
$934$	15.3140			0.501088
$935$	−3.08006	+	2.18553i	−0.100729	+	0.0714746i
$936$	0.348492			0.0113908
$937$		−	55.7620i		−	1.82167i	−0.412775	−	0.910833i	$-0.635440\pi$
$937$		−	55.7620i		−	1.82167i	0.412775	−	0.910833i	$-0.364560\pi$
$938$		−	1.12217i		−	0.0366400i
$939$	10.8429			0.353846
$940$	−1.41063	+	1.00095i	−0.0460098	+	0.0326474i
$941$	16.8053			0.547836			0.273918	−	0.961753i	$-0.411680\pi$
$941$	16.8053			0.547836			0.273918	+	0.961753i	$0.411680\pi$
$942$			32.7025i			1.06551i
$943$		−	30.6978i		−	0.999658i
$944$	3.43828			0.111907
$945$	−3.16197	−	4.45615i	−0.102859	−	0.144958i
$946$	−0.482758			−0.0156958
$947$			13.5446i			0.440139i	0.975484	+	0.220069i	$0.0706284\pi$
$947$			13.5446i			0.440139i	−0.975484	+	0.220069i	$0.929372\pi$
$948$		−	6.62243i		−	0.215087i
$949$	1.13350			0.0367949
$950$	−14.4636	−	5.06025i	−0.469262	−	0.164176i
$951$	−9.15312			−0.296810
$952$			10.0496i			0.325710i
$953$		−	25.8635i		−	0.837802i	−0.908032	−	0.418901i	$-0.862416\pi$
$953$		−	25.8635i		−	0.837802i	0.908032	−	0.418901i	$-0.137584\pi$
$954$	−3.00281			−0.0972197
$955$	0.748905	+	1.05543i	0.0242340	+	0.0341529i
$956$	15.9190			0.514858
$957$			2.51953i			0.0814450i
$958$		−	12.1072i		−	0.391165i
$959$	11.8819			0.383687
$960$	−0.632626	+	0.448895i	−0.0204179	+	0.0144880i
$961$	−30.8155			−0.994049
$962$		−	0.516171i		−	0.0166420i
$963$			19.0853i			0.615016i
$964$	1.59450			0.0513554
$965$	4.12804	−	2.92915i	0.132886	−	0.0942927i
$966$	−10.2324			−0.329223
$967$			2.77504i			0.0892392i	0.999004	+	0.0446196i	$0.0142076\pi$
$967$			2.77504i			0.0892392i	−0.999004	+	0.0446196i	$0.985792\pi$
$968$		−	24.7343i		−	0.794990i
$969$	−41.4745			−1.33235
$970$	12.1669	+	17.1468i	0.390656	+	0.550550i
$971$	50.6358			1.62498			0.812490	−	0.582975i	$-0.198111\pi$
$971$	50.6358			1.62498			0.812490	+	0.582975i	$0.198111\pi$
$972$		−	29.0178i		−	0.930746i
$973$		−	2.64200i		−	0.0846986i
$974$	−14.7570			−0.472844
$975$	0.275544	−	0.787582i	0.00882448	−	0.0252228i
$976$	15.5305			0.497118
$977$			45.4183i			1.45306i	0.687135	+	0.726529i	$0.258868\pi$
$977$			45.4183i			1.45306i	−0.687135	+	0.726529i	$0.741132\pi$
$978$			9.88241i			0.316005i
$979$	0.559792			0.0178910
$980$	−11.7382	−	16.5426i	−0.374964	−	0.528435i
$981$	6.16018			0.196680
$982$			11.3372i			0.361786i
$983$			22.6856i			0.723559i	0.932264	+	0.361780i	$0.117831\pi$
$983$			22.6856i			0.723559i	−0.932264	+	0.361780i	$0.882169\pi$
$984$	25.2845			0.806040
$985$	22.5637	−	16.0106i	0.718939	−	0.510141i
$986$	6.21590			0.197955
$987$		−	1.24823i		−	0.0397315i
$988$			0.569840i			0.0181290i
$989$	10.7496			0.341816
$990$	1.04866	−	0.744103i	0.0333287	−	0.0236492i
$991$	−42.6339			−1.35431			−0.677155	−	0.735841i	$-0.736787\pi$
$991$	−42.6339			−1.35431			−0.677155	+	0.735841i	$0.736787\pi$
$992$		−	2.43984i		−	0.0774650i
$993$		−	65.7875i		−	2.08770i
$994$	10.3279			0.327582
$995$	15.3694	+	21.6601i	0.487244	+	0.686671i
$996$	3.89703			0.123482
$997$		−	48.2019i		−	1.52657i	−0.646062	−	0.763285i	$-0.723585\pi$
$997$		−	48.2019i		−	1.52657i	0.646062	−	0.763285i	$-0.276415\pi$
$998$			8.70642i			0.275597i
$999$	−23.2971			−0.737089

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.b.c.724.28	yes	46
5.2	odd	4		6025.2.a.p.1.19		46
5.3	odd	4		6025.2.a.p.1.28		46
5.4	even	2	inner	1205.2.b.c.724.19	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.c.724.19	✓	46	5.4	even	2	inner
1205.2.b.c.724.28	yes	46	1.1	even	1	trivial
6025.2.a.p.1.19		46	5.2	odd	4
6025.2.a.p.1.28		46	5.3	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)

\(f(q)\)	\(=\)	\(q+0.636788i q^{2} +2.24729i q^{3} +1.59450 q^{4} +(-1.29399 - 1.82362i) q^{5} -1.43105 q^{6} -1.14493i q^{7} +2.28894i q^{8} -2.05030 q^{9} +O(q^{10})\)	\(q+0.636788i q^{2} +2.24729i q^{3} +1.59450 q^{4} +(-1.29399 - 1.82362i) q^{5} -1.43105 q^{6} -1.14493i q^{7} +2.28894i q^{8} -2.05030 q^{9} +(1.16126 - 0.824000i) q^{10} -0.440443 q^{11} +3.58330i q^{12} +0.0742578i q^{13} +0.729079 q^{14} +(4.09819 - 2.90797i) q^{15} +1.73143 q^{16} +3.83474i q^{17} -1.30561i q^{18} +4.81267 q^{19} +(-2.06327 - 2.90776i) q^{20} +2.57299 q^{21} -0.280469i q^{22} +6.24519i q^{23} -5.14390 q^{24} +(-1.65117 + 4.71950i) q^{25} -0.0472865 q^{26} +2.13425i q^{27} -1.82559i q^{28} -2.54550 q^{29} +(1.85176 + 2.60968i) q^{30} -0.429517 q^{31} +5.68043i q^{32} -0.989801i q^{33} -2.44192 q^{34} +(-2.08792 + 1.48153i) q^{35} -3.26920 q^{36} +10.9158i q^{37} +3.06465i q^{38} -0.166878 q^{39} +(4.17415 - 2.96187i) q^{40} -4.91543 q^{41} +1.63845i q^{42} -1.72125i q^{43} -0.702286 q^{44} +(2.65307 + 3.73896i) q^{45} -3.97686 q^{46} -0.485128i q^{47} +3.89103i q^{48} +5.68913 q^{49} +(-3.00532 - 1.05144i) q^{50} -8.61777 q^{51} +0.118404i q^{52} -2.29994i q^{53} -1.35907 q^{54} +(0.569929 + 0.803199i) q^{55} +2.62068 q^{56} +10.8155i q^{57} -1.62094i q^{58} +1.98580 q^{59} +(6.53457 - 4.63676i) q^{60} +8.96972 q^{61} -0.273511i q^{62} +2.34745i q^{63} -0.154367 q^{64} +(0.135418 - 0.0960890i) q^{65} +0.630294 q^{66} -1.53915i q^{67} +6.11450i q^{68} -14.0347 q^{69} +(-0.943423 - 1.32956i) q^{70} +14.1657 q^{71} -4.69300i q^{72} -15.2643i q^{73} -6.95108 q^{74} +(-10.6061 - 3.71064i) q^{75} +7.67381 q^{76} +0.504277i q^{77} -0.106266i q^{78} -1.84814 q^{79} +(-2.24046 - 3.15747i) q^{80} -10.9472 q^{81} -3.13009i q^{82} -1.08755i q^{83} +4.10263 q^{84} +(6.99311 - 4.96213i) q^{85} +1.09608 q^{86} -5.72046i q^{87} -1.00815i q^{88} -1.27098 q^{89} +(-2.38093 + 1.68944i) q^{90} +0.0850201 q^{91} +9.95795i q^{92} -0.965247i q^{93} +0.308924 q^{94} +(-6.22756 - 8.77648i) q^{95} -12.7656 q^{96} +14.7657i q^{97} +3.62277i q^{98} +0.903038 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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