LMFDB - Embedded newform 714.2.b.f.169.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [714,2,Mod(169,714)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(714, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("714.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	714.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:	$5.70131870432$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.415622617344.23
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 21x^{6} + 104x^{4} + 21x^{2} + 1 $ x^8 + 21x^6 + 104x^4 + 21*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			169.4
Root			$-3.64652i$ of defining polynomial
Character	$\chi$	$=$	714.169
Dual form			714.2.b.f.169.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +3.51142i q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +3.51142i q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} -3.51142i q^{10} -6.05989i q^{11} -1.00000i q^{12} +3.78161 q^{13} -1.00000i q^{14} +3.51142 q^{15} +1.00000 q^{16} +(-2.37228 + 3.37228i) q^{17} +1.00000 q^{18} +5.29303 q^{19} +3.51142i q^{20} +1.00000 q^{21} +6.05989i q^{22} +6.74456i q^{23} +1.00000i q^{24} -7.33008 q^{25} -3.78161 q^{26} +1.00000i q^{27} +1.00000i q^{28} -1.72981i q^{29} -3.51142 q^{30} +7.02284i q^{31} -1.00000 q^{32} -6.05989 q^{33} +(2.37228 - 3.37228i) q^{34} -3.51142 q^{35} -1.00000 q^{36} +5.78161i q^{37} -5.29303 q^{38} -3.78161i q^{39} -3.51142i q^{40} +11.8415i q^{41} -1.00000 q^{42} +3.23314 q^{43} -6.05989i q^{44} -3.51142i q^{45} -6.74456i q^{46} +7.02284 q^{47} -1.00000i q^{48} -1.00000 q^{49} +7.33008 q^{50} +(3.37228 + 2.37228i) q^{51} +3.78161 q^{52} -2.76686 q^{53} -1.00000i q^{54} +21.2788 q^{55} -1.00000i q^{56} -5.29303i q^{57} +1.72981i q^{58} -1.45153 q^{59} +3.51142 q^{60} -7.84150i q^{61} -7.02284i q^{62} -1.00000i q^{63} +1.00000 q^{64} +13.2788i q^{65} +6.05989 q^{66} +3.23314 q^{67} +(-2.37228 + 3.37228i) q^{68} +6.74456 q^{69} +3.51142 q^{70} +3.18134i q^{71} +1.00000 q^{72} +11.0746i q^{73} -5.78161i q^{74} +7.33008i q^{75} +5.29303 q^{76} +6.05989 q^{77} +3.78161i q^{78} -7.78970i q^{79} +3.51142i q^{80} +1.00000 q^{81} -11.8415i q^{82} -6.33817 q^{83} +1.00000 q^{84} +(-11.8415 - 8.33008i) q^{85} -3.23314 q^{86} -1.72981 q^{87} +6.05989i q^{88} -8.53426 q^{89} +3.51142i q^{90} +3.78161i q^{91} +6.74456i q^{92} +7.02284 q^{93} -7.02284 q^{94} +18.5861i q^{95} +1.00000i q^{96} -18.0975i q^{97} +1.00000 q^{98} +6.05989i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 - 8 * q^9	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 8 q^{9} + 6 q^{13} - 2 q^{15} + 8 q^{16} + 4 q^{17} + 8 q^{18} - 12 q^{19} + 8 q^{21} - 26 q^{25} - 6 q^{26} + 2 q^{30} - 8 q^{32} - 10 q^{33} - 4 q^{34} + 2 q^{35} - 8 q^{36} + 12 q^{38} - 8 q^{42} + 10 q^{43} - 4 q^{47} - 8 q^{49} + 26 q^{50} + 4 q^{51} + 6 q^{52} - 38 q^{53} + 34 q^{55} - 20 q^{59} - 2 q^{60} + 8 q^{64} + 10 q^{66} + 10 q^{67} + 4 q^{68} + 8 q^{69} - 2 q^{70} + 8 q^{72} - 12 q^{76} + 10 q^{77} + 8 q^{81} + 2 q^{83} + 8 q^{84} - 32 q^{85} - 10 q^{86} - 8 q^{87} + 22 q^{89} - 4 q^{93} + 4 q^{94} + 8 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 - 8 * q^9 + 6 * q^13 - 2 * q^15 + 8 * q^16 + 4 * q^17 + 8 * q^18 - 12 * q^19 + 8 * q^21 - 26 * q^25 - 6 * q^26 + 2 * q^30 - 8 * q^32 - 10 * q^33 - 4 * q^34 + 2 * q^35 - 8 * q^36 + 12 * q^38 - 8 * q^42 + 10 * q^43 - 4 * q^47 - 8 * q^49 + 26 * q^50 + 4 * q^51 + 6 * q^52 - 38 * q^53 + 34 * q^55 - 20 * q^59 - 2 * q^60 + 8 * q^64 + 10 * q^66 + 10 * q^67 + 4 * q^68 + 8 * q^69 - 2 * q^70 + 8 * q^72 - 12 * q^76 + 10 * q^77 + 8 * q^81 + 2 * q^83 + 8 * q^84 - 32 * q^85 - 10 * q^86 - 8 * q^87 + 22 * q^89 - 4 * q^93 + 4 * q^94 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/714\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$547$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.00000			0.500000
$5$			3.51142i			1.57036i	0.619271	+	0.785178i	$0.287428\pi$
$5$			3.51142i			1.57036i	−0.619271	+	0.785178i	$0.712572\pi$
$6$			1.00000i			0.408248i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−1.00000			−0.353553
$9$	−1.00000			−0.333333
$10$		−	3.51142i		−	1.11041i
$11$		−	6.05989i		−	1.82713i	−0.406698	−	0.913563i	$-0.633320\pi$
$11$		−	6.05989i		−	1.82713i	0.406698	−	0.913563i	$-0.366680\pi$
$12$		−	1.00000i		−	0.288675i
$13$	3.78161			1.04883			0.524415	−	0.851463i	$-0.324284\pi$
$13$	3.78161			1.04883			0.524415	+	0.851463i	$0.324284\pi$
$14$		−	1.00000i		−	0.267261i
$15$	3.51142			0.906645
$16$	1.00000			0.250000
$17$	−2.37228	+	3.37228i	−0.575363	+	0.817898i
$17$	−2.37228	+	3.37228i	−0.575363	+	0.817898i
$18$	1.00000			0.235702
$19$	5.29303			1.21430			0.607152	−	0.794585i	$-0.292312\pi$
$19$	5.29303			1.21430			0.607152	+	0.794585i	$0.292312\pi$
$20$			3.51142i			0.785178i
$21$	1.00000			0.218218
$22$			6.05989i			1.29197i
$23$			6.74456i			1.40634i	0.711022	+	0.703169i	$0.248232\pi$
$23$			6.74456i			1.40634i	−0.711022	+	0.703169i	$0.751768\pi$
$24$			1.00000i			0.204124i
$25$	−7.33008			−1.46602
$26$	−3.78161			−0.741635
$27$			1.00000i			0.192450i
$28$			1.00000i			0.188982i
$29$		−	1.72981i		−	0.321218i	−0.987018	−	0.160609i	$-0.948654\pi$
$29$		−	1.72981i		−	0.321218i	0.987018	−	0.160609i	$-0.0513458\pi$
$30$	−3.51142			−0.641095
$31$			7.02284i			1.26134i	0.776051	+	0.630670i	$0.217220\pi$
$31$			7.02284i			1.26134i	−0.776051	+	0.630670i	$0.782780\pi$
$32$	−1.00000			−0.176777
$33$	−6.05989			−1.05489
$34$	2.37228	−	3.37228i	0.406843	−	0.578341i
$35$	−3.51142			−0.593539
$36$	−1.00000			−0.166667
$37$			5.78161i			0.950491i	0.879853	+	0.475245i	$0.157641\pi$
$37$			5.78161i			0.950491i	−0.879853	+	0.475245i	$0.842359\pi$
$38$	−5.29303			−0.858643
$39$		−	3.78161i		−	0.605542i
$40$		−	3.51142i		−	0.555204i
$41$			11.8415i			1.84933i	0.380780	+	0.924666i	$0.375656\pi$
$41$			11.8415i			1.84933i	−0.380780	+	0.924666i	$0.624344\pi$
$42$	−1.00000			−0.154303
$43$	3.23314			0.493049			0.246525	−	0.969137i	$-0.420711\pi$
$43$	3.23314			0.493049			0.246525	+	0.969137i	$0.420711\pi$
$44$		−	6.05989i		−	0.913563i
$45$		−	3.51142i		−	0.523452i
$46$		−	6.74456i		−	0.994432i
$47$	7.02284			1.02439			0.512193	−	0.858870i	$-0.328833\pi$
$47$	7.02284			1.02439			0.512193	+	0.858870i	$0.328833\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−1.00000			−0.142857
$50$	7.33008			1.03663
$51$	3.37228	+	2.37228i	0.472214	+	0.332186i
$52$	3.78161			0.524415
$53$	−2.76686			−0.380057			−0.190029	−	0.981779i	$-0.560858\pi$
$53$	−2.76686			−0.380057			−0.190029	+	0.981779i	$0.560858\pi$
$54$		−	1.00000i		−	0.136083i
$55$	21.2788			2.86924
$56$		−	1.00000i		−	0.133631i
$57$		−	5.29303i		−	0.701079i
$58$			1.72981i			0.227135i
$59$	−1.45153			−0.188973			−0.0944866	−	0.995526i	$-0.530121\pi$
$59$	−1.45153			−0.188973			−0.0944866	+	0.995526i	$0.530121\pi$
$60$	3.51142			0.453323
$61$		−	7.84150i		−	1.00400i	−0.864867	−	0.502001i	$-0.832598\pi$
$61$		−	7.84150i		−	1.00400i	0.864867	−	0.502001i	$-0.167402\pi$
$62$		−	7.02284i		−	0.891902i
$63$		−	1.00000i		−	0.125988i
$64$	1.00000			0.125000
$65$			13.2788i			1.64704i
$66$	6.05989			0.745921
$67$	3.23314			0.394991			0.197496	−	0.980304i	$-0.436719\pi$
$67$	3.23314			0.394991			0.197496	+	0.980304i	$0.436719\pi$
$68$	−2.37228	+	3.37228i	−0.287681	+	0.408949i
$69$	6.74456			0.811950
$70$	3.51142			0.419695
$71$			3.18134i			0.377556i	0.982020	+	0.188778i	$0.0604526\pi$
$71$			3.18134i			0.377556i	−0.982020	+	0.188778i	$0.939547\pi$
$72$	1.00000			0.117851
$73$			11.0746i			1.29619i	0.761560	+	0.648094i	$0.224434\pi$
$73$			11.0746i			1.29619i	−0.761560	+	0.648094i	$0.775566\pi$
$74$		−	5.78161i		−	0.672099i
$75$			7.33008i			0.846405i
$76$	5.29303			0.607152
$77$	6.05989			0.690589
$78$			3.78161i			0.428183i
$79$		−	7.78970i		−	0.876410i	−0.898875	−	0.438205i	$-0.855614\pi$
$79$		−	7.78970i		−	0.876410i	0.898875	−	0.438205i	$-0.144386\pi$
$80$			3.51142i			0.392589i
$81$	1.00000			0.111111
$82$		−	11.8415i		−	1.30767i
$83$	−6.33817			−0.695705			−0.347852	−	0.937549i	$-0.613089\pi$
$83$	−6.33817			−0.695705			−0.347852	+	0.937549i	$0.613089\pi$
$84$	1.00000			0.109109
$85$	−11.8415	−	8.33008i	−1.28439	−	0.903524i
$86$	−3.23314			−0.348639
$87$	−1.72981			−0.185455
$88$			6.05989i			0.645986i
$89$	−8.53426			−0.904630			−0.452315	−	0.891858i	$-0.649402\pi$
$89$	−8.53426			−0.904630			−0.452315	+	0.891858i	$0.649402\pi$
$90$			3.51142i			0.370136i
$91$			3.78161i			0.396420i
$92$			6.74456i			0.703169i
$93$	7.02284			0.728235
$94$	−7.02284			−0.724351
$95$			18.5861i			1.90689i
$96$			1.00000i			0.102062i
$97$		−	18.0975i		−	1.83752i	−0.394815	−	0.918761i	$-0.629191\pi$
$97$		−	18.0975i		−	1.83752i	0.394815	−	0.918761i	$-0.370809\pi$
$98$	1.00000			0.101015
$99$			6.05989i			0.609042i
$100$	−7.33008			−0.733008
$101$	11.8496			1.17908			0.589539	−	0.807740i	$-0.299309\pi$
$101$	11.8496			1.17908			0.589539	+	0.807740i	$0.299309\pi$
$102$	−3.37228	−	2.37228i	−0.333906	−	0.234891i
$103$	7.51142			0.740122			0.370061	−	0.929007i	$-0.379337\pi$
$103$	7.51142			0.740122			0.370061	+	0.929007i	$0.379337\pi$
$104$	−3.78161			−0.370817
$105$			3.51142i			0.342680i
$106$	2.76686			0.268741
$107$			0.196094i			0.0189571i	0.999955	+	0.00947856i	$0.00301716\pi$
$107$			0.196094i			0.0189571i	−0.999955	+	0.00947856i	$0.996983\pi$
$108$			1.00000i			0.0962250i
$109$		−	5.01475i		−	0.480326i	−0.970733	−	0.240163i	$-0.922799\pi$
$109$		−	5.01475i		−	0.480326i	0.970733	−	0.240163i	$-0.0772009\pi$
$110$	−21.2788			−2.02886
$111$	5.78161			0.548766
$112$			1.00000i			0.0944911i
$113$		−	0.488579i		−	0.0459616i	−0.999736	−	0.0229808i	$-0.992684\pi$
$113$		−	0.488579i		−	0.0459616i	0.999736	−	0.0229808i	$-0.00731566\pi$
$114$			5.29303i			0.495738i
$115$	−23.6830			−2.20845
$116$		−	1.72981i		−	0.160609i
$117$	−3.78161			−0.349610
$118$	1.45153			0.133624
$119$	−3.37228	−	2.37228i	−0.309137	−	0.217467i
$120$	−3.51142			−0.320547
$121$	−25.7223			−2.33839
$122$			7.84150i			0.709936i
$123$	11.8415			1.06771
$124$			7.02284i			0.630670i
$125$		−	8.18189i		−	0.731810i
$126$			1.00000i			0.0890871i
$127$	−3.45962			−0.306992			−0.153496	−	0.988149i	$-0.549053\pi$
$127$	−3.45962			−0.306992			−0.153496	+	0.988149i	$0.549053\pi$
$128$	−1.00000			−0.0883883
$129$		−	3.23314i		−	0.284662i
$130$		−	13.2788i		−	1.16463i
$131$		−	7.45962i		−	0.651750i	−0.945413	−	0.325875i	$-0.894341\pi$
$131$		−	7.45962i		−	0.651750i	0.945413	−	0.325875i	$-0.105659\pi$
$132$	−6.05989			−0.527446
$133$			5.29303i			0.458964i
$134$	−3.23314			−0.279301
$135$	−3.51142			−0.302215
$136$	2.37228	−	3.37228i	0.203421	−	0.289171i
$137$	20.0457			1.71262			0.856309	−	0.516463i	$-0.172752\pi$
$137$	20.0457			1.71262			0.856309	+	0.516463i	$0.172752\pi$
$138$	−6.74456			−0.574135
$139$		−	2.25598i		−	0.191350i	−0.995413	−	0.0956750i	$-0.969499\pi$
$139$		−	2.25598i		−	0.191350i	0.995413	−	0.0956750i	$-0.0305010\pi$
$140$	−3.51142			−0.296769
$141$		−	7.02284i		−	0.591430i
$142$		−	3.18134i		−	0.266972i
$143$		−	22.9161i		−	1.91634i
$144$	−1.00000			−0.0833333
$145$	6.07410			0.504426
$146$		−	11.0746i		−	0.916544i
$147$			1.00000i			0.0824786i
$148$			5.78161i			0.475245i
$149$	3.86380			0.316535			0.158267	−	0.987396i	$-0.449409\pi$
$149$	3.86380			0.316535			0.158267	+	0.987396i	$0.449409\pi$
$150$		−	7.33008i		−	0.598498i
$151$	5.09694			0.414783			0.207391	−	0.978258i	$-0.433503\pi$
$151$	5.09694			0.414783			0.207391	+	0.978258i	$0.433503\pi$
$152$	−5.29303			−0.429322
$153$	2.37228	−	3.37228i	0.191788	−	0.272633i
$154$	−6.05989			−0.488320
$155$	−24.6602			−1.98075
$156$		−	3.78161i		−	0.302771i
$157$	8.54847			0.682242			0.341121	−	0.940019i	$-0.389193\pi$
$157$	8.54847			0.682242			0.341121	+	0.940019i	$0.389193\pi$
$158$			7.78970i			0.619715i
$159$			2.76686i			0.219426i
$160$		−	3.51142i		−	0.277602i
$161$	−6.74456			−0.531546
$162$	−1.00000			−0.0785674
$163$			20.5942i			1.61306i	0.591194	+	0.806529i	$0.298657\pi$
$163$			20.5942i			1.61306i	−0.591194	+	0.806529i	$0.701343\pi$
$164$			11.8415i			0.924666i
$165$		−	21.2788i		−	1.65655i
$166$	6.33817			0.491937
$167$		−	18.7964i		−	1.45451i	−0.686369	−	0.727253i	$-0.740797\pi$
$167$		−	18.7964i		−	1.45451i	0.686369	−	0.727253i	$-0.259203\pi$
$168$	−1.00000			−0.0771517
$169$	1.30058			0.100044
$170$	11.8415	+	8.33008i	0.908202	+	0.638888i
$171$	−5.29303			−0.404768
$172$	3.23314			0.246525
$173$		−	6.86434i		−	0.521886i	−0.965354	−	0.260943i	$-0.915966\pi$
$173$		−	6.86434i		−	0.521886i	0.965354	−	0.260943i	$-0.0840335\pi$
$174$	1.72981			0.131137
$175$		−	7.33008i		−	0.554102i
$176$		−	6.05989i		−	0.456781i
$177$			1.45153i			0.109104i
$178$	8.53426			0.639670
$179$	6.90306			0.515959			0.257980	−	0.966150i	$-0.416943\pi$
$179$	6.90306			0.515959			0.257980	+	0.966150i	$0.416943\pi$
$180$		−	3.51142i		−	0.261726i
$181$			11.8577i			0.881375i	0.897661	+	0.440687i	$0.145265\pi$
$181$			11.8577i			0.881375i	−0.897661	+	0.440687i	$0.854735\pi$
$182$		−	3.78161i		−	0.280312i
$183$	−7.84150			−0.579660
$184$		−	6.74456i		−	0.497216i
$185$	−20.3017			−1.49261
$186$	−7.02284			−0.514940
$187$	20.4357	+	14.3758i	1.49440	+	1.05126i
$188$	7.02284			0.512193
$189$	−1.00000			−0.0727393
$190$		−	18.5861i		−	1.34837i
$191$	−25.3986			−1.83778			−0.918889	−	0.394515i	$-0.870912\pi$
$191$	−25.3986			−1.83778			−0.918889	+	0.394515i	$0.870912\pi$
$192$		−	1.00000i		−	0.0721688i
$193$		−	4.43678i		−	0.319366i	−0.987168	−	0.159683i	$-0.948953\pi$
$193$		−	4.43678i		−	0.319366i	0.987168	−	0.159683i	$-0.0510473\pi$
$194$			18.0975i			1.29932i
$195$	13.2788			0.950917
$196$	−1.00000			−0.0714286
$197$			3.36713i			0.239898i	0.992780	+	0.119949i	$0.0382731\pi$
$197$			3.36713i			0.239898i	−0.992780	+	0.119949i	$0.961727\pi$
$198$		−	6.05989i		−	0.430658i
$199$		−	14.0457i		−	0.995672i	−0.867271	−	0.497836i	$-0.834128\pi$
$199$		−	14.0457i		−	0.995672i	0.867271	−	0.497836i	$-0.165872\pi$
$200$	7.33008			0.518315
$201$		−	3.23314i		−	0.228048i
$202$	−11.8496			−0.833734
$203$	1.72981			0.121409
$204$	3.37228	+	2.37228i	0.236107	+	0.166093i
$205$	−41.5805			−2.90411
$206$	−7.51142			−0.523346
$207$		−	6.74456i		−	0.468780i
$208$	3.78161			0.262207
$209$		−	32.0752i		−	2.21869i
$210$		−	3.51142i		−	0.242311i
$211$		−	2.98525i		−	0.205513i	−0.994707	−	0.102756i	$-0.967234\pi$
$211$		−	2.98525i		−	0.205513i	0.994707	−	0.102756i	$-0.0327662\pi$
$212$	−2.76686			−0.190029
$213$	3.18134			0.217982
$214$		−	0.196094i		−	0.0134047i
$215$			11.3529i			0.774263i
$216$		−	1.00000i		−	0.0680414i
$217$	−7.02284			−0.476742
$218$			5.01475i			0.339642i
$219$	11.0746			0.748355
$220$	21.2788			1.43462
$221$	−8.97104	+	12.7527i	−0.603458	+	0.857836i
$222$	−5.78161			−0.388036
$223$	3.84150			0.257246			0.128623	−	0.991694i	$-0.458944\pi$
$223$	3.84150			0.257246			0.128623	+	0.991694i	$0.458944\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	7.33008			0.488672
$226$			0.488579i			0.0324998i
$227$		−	26.7058i		−	1.77253i	−0.463179	−	0.886265i	$-0.653291\pi$
$227$		−	26.7058i		−	1.77253i	0.463179	−	0.886265i	$-0.346709\pi$
$228$		−	5.29303i		−	0.350540i
$229$	−25.3905			−1.67785			−0.838926	−	0.544245i	$-0.816816\pi$
$229$	−25.3905			−1.67785			−0.838926	+	0.544245i	$0.816816\pi$
$230$	23.6830			1.56161
$231$		−	6.05989i		−	0.398711i
$232$			1.72981i			0.113568i
$233$		−	23.1944i		−	1.51952i	−0.650205	−	0.759759i	$-0.725317\pi$
$233$		−	23.1944i		−	1.51952i	0.650205	−	0.759759i	$-0.274683\pi$
$234$	3.78161			0.247212
$235$			24.6602i			1.60865i
$236$	−1.45153			−0.0944866
$237$	−7.78970			−0.505995
$238$	3.37228	+	2.37228i	0.218593	+	0.153772i
$239$	27.9095			1.80531			0.902657	−	0.430360i	$-0.141614\pi$
$239$	27.9095			1.80531			0.902657	+	0.430360i	$0.141614\pi$
$240$	3.51142			0.226661
$241$			5.21085i			0.335660i	0.985816	+	0.167830i	$0.0536760\pi$
$241$			5.21085i			0.335660i	−0.985816	+	0.167830i	$0.946324\pi$
$242$	25.7223			1.65349
$243$		−	1.00000i		−	0.0641500i
$244$		−	7.84150i		−	0.502001i
$245$		−	3.51142i		−	0.224336i
$246$	−11.8415			−0.754986
$247$	20.0162			1.27360
$248$		−	7.02284i		−	0.445951i
$249$			6.33817i			0.401665i
$250$			8.18189i			0.517468i
$251$	8.26407			0.521624			0.260812	−	0.965390i	$-0.416010\pi$
$251$	8.26407			0.521624			0.260812	+	0.965390i	$0.416010\pi$
$252$		−	1.00000i		−	0.0629941i
$253$	40.8713			2.56956
$254$	3.45962			0.217076
$255$	−8.33008	+	11.8415i	−0.521650	+	0.741544i
$256$	1.00000			0.0625000
$257$	−18.4886			−1.15329			−0.576643	−	0.816996i	$-0.695638\pi$
$257$	−18.4886			−1.15329			−0.576643	+	0.816996i	$0.695638\pi$
$258$			3.23314i			0.201287i
$259$	−5.78161			−0.359252
$260$			13.2788i			0.823518i
$261$			1.72981i			0.107073i
$262$			7.45962i			0.460857i
$263$	8.84205			0.545224			0.272612	−	0.962124i	$-0.412112\pi$
$263$	8.84205			0.545224			0.272612	+	0.962124i	$0.412112\pi$
$264$	6.05989			0.372960
$265$		−	9.71561i		−	0.596825i
$266$		−	5.29303i		−	0.324537i
$267$			8.53426i			0.522288i
$268$	3.23314			0.197496
$269$		−	17.2108i		−	1.04936i	−0.851298	−	0.524682i	$-0.824184\pi$
$269$		−	17.2108i		−	1.04936i	0.851298	−	0.524682i	$-0.175816\pi$
$270$	3.51142			0.213698
$271$	−22.1137			−1.34331			−0.671655	−	0.740864i	$-0.734416\pi$
$271$	−22.1137			−1.34331			−0.671655	+	0.740864i	$0.734416\pi$
$272$	−2.37228	+	3.37228i	−0.143841	+	0.204475i
$273$	3.78161			0.228873
$274$	−20.0457			−1.21100
$275$			44.4195i			2.67859i
$276$	6.74456			0.405975
$277$			2.42869i			0.145926i	0.997335	+	0.0729629i	$0.0232455\pi$
$277$			2.42869i			0.145926i	−0.997335	+	0.0729629i	$0.976755\pi$
$278$			2.25598i			0.135305i
$279$		−	7.02284i		−	0.420447i
$280$	3.51142			0.209848
$281$	−26.7515			−1.59586			−0.797931	−	0.602749i	$-0.794072\pi$
$281$	−26.7515			−1.59586			−0.797931	+	0.602749i	$0.794072\pi$
$282$			7.02284i			0.418204i
$283$			21.1590i			1.25777i	0.777496	+	0.628887i	$0.216489\pi$
$283$			21.1590i			1.25777i	−0.777496	+	0.628887i	$0.783511\pi$
$284$			3.18134i			0.188778i
$285$	18.5861			1.10094
$286$			22.9161i			1.35506i
$287$	−11.8415			−0.698982
$288$	1.00000			0.0589256
$289$	−5.74456	−	16.0000i	−0.337915	−	0.941176i
$290$	−6.07410			−0.356683
$291$	−18.0975			−1.06089
$292$			11.0746i			0.648094i
$293$	18.1961			1.06303			0.531514	−	0.847050i	$-0.321623\pi$
$293$	18.1961			1.06303			0.531514	+	0.847050i	$0.321623\pi$
$294$		−	1.00000i		−	0.0583212i
$295$		−	5.09694i		−	0.296755i
$296$		−	5.78161i		−	0.336049i
$297$	6.05989			0.351630
$298$	−3.86380			−0.223824
$299$			25.5053i			1.47501i
$300$			7.33008i			0.423202i
$301$			3.23314i			0.186355i
$302$	−5.09694			−0.293296
$303$		−	11.8496i		−	0.680741i
$304$	5.29303			0.303576
$305$	27.5348			1.57664
$306$	−2.37228	+	3.37228i	−0.135614	+	0.192780i
$307$	−14.5097			−0.828115			−0.414058	−	0.910251i	$-0.635889\pi$
$307$	−14.5097			−0.828115			−0.414058	+	0.910251i	$0.635889\pi$
$308$	6.05989			0.345294
$309$		−	7.51142i		−	0.427310i
$310$	24.6602			1.40060
$311$		−	7.12954i		−	0.404279i	−0.979357	−	0.202140i	$-0.935211\pi$
$311$		−	7.12954i		−	0.404279i	0.979357	−	0.202140i	$-0.0647895\pi$
$312$			3.78161i			0.214092i
$313$			5.21085i			0.294534i	0.989097	+	0.147267i	$0.0470477\pi$
$313$			5.21085i			0.294534i	−0.989097	+	0.147267i	$0.952952\pi$
$314$	−8.54847			−0.482418
$315$	3.51142			0.197846
$316$		−	7.78970i		−	0.438205i
$317$			1.41281i			0.0793514i	0.999213	+	0.0396757i	$0.0126325\pi$
$317$			1.41281i			0.0793514i	−0.999213	+	0.0396757i	$0.987368\pi$
$318$		−	2.76686i		−	0.155158i
$319$	−10.4825			−0.586905
$320$			3.51142i			0.196294i
$321$	0.196094			0.0109449
$322$	6.74456			0.375860
$323$	−12.5566	+	17.8496i	−0.698666	+	0.993178i
$324$	1.00000			0.0555556
$325$	−27.7195			−1.53760
$326$		−	20.5942i		−	1.14060i
$327$	−5.01475			−0.277316
$328$		−	11.8415i		−	0.653837i
$329$			7.02284i			0.387182i
$330$			21.2788i			1.17136i
$331$	−6.69276			−0.367868			−0.183934	−	0.982939i	$-0.558883\pi$
$331$	−6.69276			−0.367868			−0.183934	+	0.982939i	$0.558883\pi$
$332$	−6.33817			−0.347852
$333$		−	5.78161i		−	0.316830i
$334$			18.7964i			1.02849i
$335$			11.3529i			0.620276i
$336$	1.00000			0.0545545
$337$			28.5120i			1.55315i	0.630027	+	0.776573i	$0.283044\pi$
$337$			28.5120i			1.55315i	−0.630027	+	0.776573i	$0.716956\pi$
$338$	−1.30058			−0.0707420
$339$	−0.488579			−0.0265360
$340$	−11.8415	−	8.33008i	−0.642196	−	0.451762i
$341$	42.5577			2.30463
$342$	5.29303			0.286214
$343$		−	1.00000i		−	0.0539949i
$344$	−3.23314			−0.174319
$345$			23.6830i			1.27505i
$346$			6.86434i			0.369029i
$347$			4.94677i			0.265557i	0.991146	+	0.132778i	$0.0423898\pi$
$347$			4.94677i			0.265557i	−0.991146	+	0.132778i	$0.957610\pi$
$348$	−1.72981			−0.0927276
$349$	13.1955			0.706341			0.353171	−	0.935559i	$-0.385103\pi$
$349$	13.1955			0.706341			0.353171	+	0.935559i	$0.385103\pi$
$350$			7.33008i			0.391809i
$351$			3.78161i			0.201847i
$352$			6.05989i			0.322993i
$353$	24.6379			1.31134			0.655671	−	0.755047i	$-0.272386\pi$
$353$	24.6379			1.31134			0.655671	+	0.755047i	$0.272386\pi$
$354$		−	1.45153i		−	0.0771480i
$355$	−11.1710			−0.592897
$356$	−8.53426			−0.452315
$357$	−2.37228	+	3.37228i	−0.125554	+	0.178480i
$358$	−6.90306			−0.364838
$359$	13.7287			0.724572			0.362286	−	0.932067i	$-0.381996\pi$
$359$	13.7287			0.724572			0.362286	+	0.932067i	$0.381996\pi$
$360$			3.51142i			0.185068i
$361$	9.01618			0.474536
$362$		−	11.8577i		−	0.623226i
$363$			25.7223i			1.35007i
$364$			3.78161i			0.198210i
$365$	−38.8877			−2.03548
$366$	7.84150			0.409882
$367$			29.0685i			1.51736i	0.651461	+	0.758682i	$0.274157\pi$
$367$			29.0685i			1.51736i	−0.651461	+	0.758682i	$0.725843\pi$
$368$			6.74456i			0.351585i
$369$		−	11.8415i		−	0.616444i
$370$	20.3017			1.05543
$371$		−	2.76686i		−	0.143648i
$372$	7.02284			0.364117
$373$	5.45962			0.282689			0.141344	−	0.989961i	$-0.454858\pi$
$373$	5.45962			0.282689			0.141344	+	0.989961i	$0.454858\pi$
$374$	−20.4357	−	14.3758i	−1.05670	−	0.743353i
$375$	−8.18189			−0.422511
$376$	−7.02284			−0.362175
$377$		−	6.54147i		−	0.336903i
$378$	1.00000			0.0514344
$379$		−	16.1574i		−	0.829949i	−0.909833	−	0.414974i	$-0.863791\pi$
$379$		−	16.1574i		−	0.829949i	0.909833	−	0.414974i	$-0.136209\pi$
$380$			18.5861i			0.953445i
$381$			3.45962i			0.177242i
$382$	25.3986			1.29951
$383$	34.5861			1.76727			0.883633	−	0.468181i	$-0.155090\pi$
$383$	34.5861			1.76727			0.883633	+	0.468181i	$0.155090\pi$
$384$			1.00000i			0.0510310i
$385$			21.2788i			1.08447i
$386$			4.43678i			0.225826i
$387$	−3.23314			−0.164350
$388$		−	18.0975i		−	0.918761i
$389$	−25.1426			−1.27478			−0.637391	−	0.770541i	$-0.719986\pi$
$389$	−25.1426			−1.27478			−0.637391	+	0.770541i	$0.719986\pi$
$390$	−13.2788			−0.672400
$391$	−22.7446	−	16.0000i	−1.15024	−	0.809155i
$392$	1.00000			0.0505076
$393$	−7.45962			−0.376288
$394$		−	3.36713i		−	0.169633i
$395$	27.3529			1.37627
$396$			6.05989i			0.304521i
$397$		−	37.3306i		−	1.87357i	−0.349905	−	0.936785i	$-0.613786\pi$
$397$		−	37.3306i		−	1.87357i	0.349905	−	0.936785i	$-0.386214\pi$
$398$			14.0457i			0.704047i
$399$	5.29303			0.264983
$400$	−7.33008			−0.366504
$401$		−	23.9613i		−	1.19657i	−0.801284	−	0.598285i	$-0.795849\pi$
$401$		−	23.9613i		−	1.19657i	0.801284	−	0.598285i	$-0.204151\pi$
$402$			3.23314i			0.161254i
$403$			26.5577i			1.32293i
$404$	11.8496			0.589539
$405$			3.51142i			0.174484i
$406$	−1.72981			−0.0858491
$407$	35.0359			1.73667
$408$	−3.37228	−	2.37228i	−0.166953	−	0.117445i
$409$	21.2462			1.05056			0.525279	−	0.850930i	$-0.323961\pi$
$409$	21.2462			1.05056			0.525279	+	0.850930i	$0.323961\pi$
$410$	41.5805			2.05351
$411$		−	20.0457i		−	0.988781i
$412$	7.51142			0.370061
$413$		−	1.45153i		−	0.0714252i
$414$			6.74456i			0.331477i
$415$		−	22.2560i		−	1.09250i
$416$	−3.78161			−0.185409
$417$	−2.25598			−0.110476
$418$			32.0752i			1.56885i
$419$		−	28.2396i		−	1.37959i	−0.724003	−	0.689796i	$-0.757700\pi$
$419$		−	28.2396i		−	1.37959i	0.724003	−	0.689796i	$-0.242300\pi$
$420$			3.51142i			0.171340i
$421$	−4.04568			−0.197175			−0.0985873	−	0.995128i	$-0.531432\pi$
$421$	−4.04568			−0.197175			−0.0985873	+	0.995128i	$0.531432\pi$
$422$			2.98525i			0.145320i
$423$	−7.02284			−0.341462
$424$	2.76686			0.134371
$425$	17.3890	−	24.7191i	0.843491	−	1.19905i
$426$	−3.18134			−0.154137
$427$	7.84150			0.379477
$428$			0.196094i			0.00947856i
$429$	−22.9161			−1.10640
$430$		−	11.3529i		−	0.547486i
$431$			27.4961i			1.32444i	0.749309	+	0.662220i	$0.230386\pi$
$431$			27.4961i			1.32444i	−0.749309	+	0.662220i	$0.769614\pi$
$432$			1.00000i			0.0481125i
$433$	15.6089			0.750116			0.375058	−	0.927001i	$-0.377623\pi$
$433$	15.6089			0.750116			0.375058	+	0.927001i	$0.377623\pi$
$434$	7.02284			0.337107
$435$		−	6.07410i		−	0.291231i
$436$		−	5.01475i		−	0.240163i
$437$			35.6992i			1.70772i
$438$	−11.0746			−0.529167
$439$		−	21.7287i		−	1.03705i	−0.855061	−	0.518527i	$-0.826481\pi$
$439$		−	21.7287i		−	1.03705i	0.855061	−	0.518527i	$-0.173519\pi$
$440$	−21.2788			−1.01443
$441$	1.00000			0.0476190
$442$	8.97104	−	12.7527i	0.426709	−	0.606582i
$443$	−7.72759			−0.367149			−0.183574	−	0.983006i	$-0.558767\pi$
$443$	−7.72759			−0.367149			−0.183574	+	0.983006i	$0.558767\pi$
$444$	5.78161			0.274383
$445$		−	29.9674i		−	1.42059i
$446$	−3.84150			−0.181900
$447$		−	3.86380i		−	0.182751i
$448$			1.00000i			0.0472456i
$449$		−	30.9265i		−	1.45951i	−0.683709	−	0.729755i	$-0.739634\pi$
$449$		−	30.9265i		−	1.45951i	0.683709	−	0.729755i	$-0.260366\pi$
$450$	−7.33008			−0.345543
$451$	71.7582			3.37896
$452$		−	0.488579i		−	0.0229808i
$453$		−	5.09694i		−	0.239475i
$454$			26.7058i			1.25337i
$455$	−13.2788			−0.622521
$456$			5.29303i			0.247869i
$457$	−37.8487			−1.77049			−0.885244	−	0.465127i	$-0.846009\pi$
$457$	−37.8487			−1.77049			−0.885244	+	0.465127i	$0.846009\pi$
$458$	25.3905			1.18642
$459$	−3.37228	−	2.37228i	−0.157405	−	0.110729i
$460$	−23.6830			−1.10423
$461$	37.9989			1.76978			0.884892	−	0.465796i	$-0.154232\pi$
$461$	37.9989			1.76978			0.884892	+	0.465796i	$0.154232\pi$
$462$			6.05989i			0.281932i
$463$	−17.2167			−0.800129			−0.400064	−	0.916487i	$-0.631012\pi$
$463$	−17.2167			−0.800129			−0.400064	+	0.916487i	$0.631012\pi$
$464$		−	1.72981i		−	0.0803045i
$465$			24.6602i			1.14359i
$466$			23.1944i			1.07446i
$467$	1.97573			0.0914258			0.0457129	−	0.998955i	$-0.485444\pi$
$467$	1.97573			0.0914258			0.0457129	+	0.998955i	$0.485444\pi$
$468$	−3.78161			−0.174805
$469$			3.23314i			0.149293i
$470$		−	24.6602i		−	1.13749i
$471$		−	8.54847i		−	0.393893i
$472$	1.45153			0.0668121
$473$		−	19.5925i		−	0.900863i
$474$	7.78970			0.357793
$475$	−38.7983			−1.78019
$476$	−3.37228	−	2.37228i	−0.154568	−	0.108733i
$477$	2.76686			0.126686
$478$	−27.9095			−1.27655
$479$			17.0064i			0.777043i	0.921440	+	0.388522i	$0.127014\pi$
$479$			17.0064i			0.777043i	−0.921440	+	0.388522i	$0.872986\pi$
$480$	−3.51142			−0.160274
$481$			21.8638i			0.996903i
$482$		−	5.21085i		−	0.237348i
$483$			6.74456i			0.306888i
$484$	−25.7223			−1.16919
$485$	63.5479			2.88556
$486$			1.00000i			0.0453609i
$487$		−	38.8877i		−	1.76217i	−0.472957	−	0.881086i	$-0.656813\pi$
$487$		−	38.8877i		−	1.76217i	0.472957	−	0.881086i	$-0.343187\pi$
$488$			7.84150i			0.354968i
$489$	20.5942			0.931300
$490$			3.51142i			0.158630i
$491$	8.67634			0.391558			0.195779	−	0.980648i	$-0.437277\pi$
$491$	8.67634			0.391558			0.195779	+	0.980648i	$0.437277\pi$
$492$	11.8415			0.533856
$493$	5.83341	+	4.10360i	0.262724	+	0.184817i
$494$	−20.0162			−0.900571
$495$	−21.2788			−0.956412
$496$			7.02284i			0.315335i
$497$	−3.18134			−0.142703
$498$		−	6.33817i		−	0.284020i
$499$		−	9.55513i		−	0.427746i	−0.976861	−	0.213873i	$-0.931392\pi$
$499$		−	9.55513i		−	0.427746i	0.976861	−	0.213873i	$-0.0686079\pi$
$500$		−	8.18189i		−	0.365905i
$501$	−18.7964			−0.839760
$502$	−8.26407			−0.368844
$503$			23.6830i			1.05597i	0.849253	+	0.527986i	$0.177053\pi$
$503$			23.6830i			1.05597i	−0.849253	+	0.527986i	$0.822947\pi$
$504$			1.00000i			0.0445435i
$505$			41.6089i			1.85157i
$506$	−40.8713			−1.81695
$507$		−	1.30058i		−	0.0577606i
$508$	−3.45962			−0.153496
$509$	−38.0151			−1.68499			−0.842494	−	0.538706i	$-0.818913\pi$
$509$	−38.0151			−1.68499			−0.842494	+	0.538706i	$0.818913\pi$
$510$	8.33008	−	11.8415i	0.368862	−	0.524350i
$511$	−11.0746			−0.489913
$512$	−1.00000			−0.0441942
$513$			5.29303i			0.233693i
$514$	18.4886			0.815496
$515$			26.3758i			1.16226i
$516$		−	3.23314i		−	0.142331i
$517$		−	42.5577i		−	1.87168i
$518$	5.78161			0.254029
$519$	−6.86434			−0.301311
$520$		−	13.2788i		−	0.582315i
$521$			19.0287i			0.833663i	0.908984	+	0.416832i	$0.136860\pi$
$521$			19.0287i			0.833663i	−0.908984	+	0.416832i	$0.863140\pi$
$522$		−	1.72981i		−	0.0757118i
$523$	33.7014			1.47366			0.736830	−	0.676078i	$-0.236322\pi$
$523$	33.7014			1.47366			0.736830	+	0.676078i	$0.236322\pi$
$524$		−	7.45962i		−	0.325875i
$525$	−7.33008			−0.319911
$526$	−8.84205			−0.385532
$527$	−23.6830	−	16.6602i	−1.03165	−	0.725728i
$528$	−6.05989			−0.263723
$529$	−22.4891			−0.977788
$530$			9.71561i			0.422019i
$531$	1.45153			0.0629911
$532$			5.29303i			0.229482i
$533$			44.7799i			1.93963i
$534$		−	8.53426i		−	0.369314i
$535$	−0.688568			−0.0297694
$536$	−3.23314			−0.139650
$537$		−	6.90306i		−	0.297889i
$538$			17.2108i			0.742012i
$539$			6.05989i			0.261018i
$540$	−3.51142			−0.151108
$541$		−	24.3393i		−	1.04643i	−0.852202	−	0.523213i	$-0.824733\pi$
$541$		−	24.3393i		−	1.04643i	0.852202	−	0.523213i	$-0.175267\pi$
$542$	22.1137			0.949863
$543$	11.8577			0.508862
$544$	2.37228	−	3.37228i	0.101711	−	0.144585i
$545$	17.6089			0.754283
$546$	−3.78161			−0.161838
$547$			11.3284i			0.484368i	0.970230	+	0.242184i	$0.0778637\pi$
$547$			11.3284i			0.484368i	−0.970230	+	0.242184i	$0.922136\pi$
$548$	20.0457			0.856309
$549$			7.84150i			0.334667i
$550$		−	44.4195i		−	1.89405i
$551$		−	9.15594i		−	0.390056i
$552$	−6.74456			−0.287068
$553$	7.78970			0.331252
$554$		−	2.42869i		−	0.103185i
$555$			20.3017i			0.861758i
$556$		−	2.25598i		−	0.0956750i
$557$	−15.8769			−0.672725			−0.336362	−	0.941733i	$-0.609197\pi$
$557$	−15.8769			−0.672725			−0.336362	+	0.941733i	$0.609197\pi$
$558$			7.02284i			0.297301i
$559$	12.2265			0.517125
$560$	−3.51142			−0.148385
$561$	14.3758	−	20.4357i	0.606945	−	0.862794i
$562$	26.7515			1.12845
$563$	−10.3220			−0.435020			−0.217510	−	0.976058i	$-0.569793\pi$
$563$	−10.3220			−0.435020			−0.217510	+	0.976058i	$0.569793\pi$
$564$		−	7.02284i		−	0.295715i
$565$	1.71561			0.0721761
$566$		−	21.1590i		−	0.889381i
$567$			1.00000i			0.0419961i
$568$		−	3.18134i		−	0.133486i
$569$	−13.1264			−0.550289			−0.275145	−	0.961403i	$-0.588726\pi$
$569$	−13.1264			−0.550289			−0.275145	+	0.961403i	$0.588726\pi$
$570$	−18.5861			−0.778485
$571$		−	3.64541i		−	0.152556i	−0.997087	−	0.0762778i	$-0.975696\pi$
$571$		−	3.64541i		−	0.152556i	0.997087	−	0.0762778i	$-0.0243036\pi$
$572$		−	22.9161i		−	0.958172i
$573$			25.3986i			1.06104i
$574$	11.8415			0.494255
$575$		−	49.4382i		−	2.06171i
$576$	−1.00000			−0.0416667
$577$	−7.38553			−0.307464			−0.153732	−	0.988113i	$-0.549129\pi$
$577$	−7.38553			−0.307464			−0.153732	+	0.988113i	$0.549129\pi$
$578$	5.74456	+	16.0000i	0.238942	+	0.665512i
$579$	−4.43678			−0.184386
$580$	6.07410			0.252213
$581$		−	6.33817i		−	0.262952i
$582$	18.0975			0.750165
$583$			16.7669i			0.694412i
$584$		−	11.0746i		−	0.458272i
$585$		−	13.2788i		−	0.549012i
$586$	−18.1961			−0.751674
$587$	−17.8730			−0.737697			−0.368848	−	0.929490i	$-0.620248\pi$
$587$	−17.8730			−0.737697			−0.368848	+	0.929490i	$0.620248\pi$
$588$			1.00000i			0.0412393i
$589$			37.1721i			1.53165i
$590$			5.09694i			0.209838i
$591$	3.36713			0.138505
$592$			5.78161i			0.237623i
$593$	1.13675			0.0466807			0.0233404	−	0.999728i	$-0.492570\pi$
$593$	1.13675			0.0466807			0.0233404	+	0.999728i	$0.492570\pi$
$594$	−6.05989			−0.248640
$595$	8.33008	−	11.8415i	0.341500	−	0.485454i
$596$	3.86380			0.158267
$597$	−14.0457			−0.574852
$598$		−	25.5053i		−	1.04299i
$599$	−13.4891			−0.551151			−0.275575	−	0.961279i	$-0.588868\pi$
$599$	−13.4891			−0.551151			−0.275575	+	0.961279i	$0.588868\pi$
$600$		−	7.33008i		−	0.299249i
$601$			27.8131i			1.13452i	0.823539	+	0.567260i	$0.191996\pi$
$601$			27.8131i			1.13452i	−0.823539	+	0.567260i	$0.808004\pi$
$602$		−	3.23314i		−	0.131773i
$603$	−3.23314			−0.131664
$604$	5.09694			0.207391
$605$		−	90.3217i		−	3.67210i
$606$			11.8496i			0.481357i
$607$			5.26131i			0.213550i	0.994283	+	0.106775i	$0.0340524\pi$
$607$			5.26131i			0.213550i	−0.994283	+	0.106775i	$0.965948\pi$
$608$	−5.29303			−0.214661
$609$		−	1.72981i		−	0.0700955i
$610$	−27.5348			−1.11485
$611$	26.5577			1.07441
$612$	2.37228	−	3.37228i	0.0958938	−	0.136316i
$613$	−23.0685			−0.931729			−0.465865	−	0.884856i	$-0.654257\pi$
$613$	−23.0685			−0.931729			−0.465865	+	0.884856i	$0.654257\pi$
$614$	14.5097			0.585566
$615$			41.5805i			1.67669i
$616$	−6.05989			−0.244160
$617$		−	38.0813i		−	1.53310i	−0.642187	−	0.766548i	$-0.721973\pi$
$617$		−	38.0813i		−	1.53310i	0.642187	−	0.766548i	$-0.278027\pi$
$618$			7.51142i			0.302154i
$619$		−	19.1295i		−	0.768881i	−0.923150	−	0.384441i	$-0.874394\pi$
$619$		−	19.1295i		−	0.768881i	0.923150	−	0.384441i	$-0.125606\pi$
$620$	−24.6602			−0.990376
$621$	−6.74456			−0.270650
$622$			7.12954i			0.285869i
$623$		−	8.53426i		−	0.341918i
$624$		−	3.78161i		−	0.151386i
$625$	−7.92034			−0.316813
$626$		−	5.21085i		−	0.208267i
$627$	−32.0752			−1.28096
$628$	8.54847			0.341121
$629$	−19.4972	−	13.7156i	−0.777405	−	0.546877i
$630$	−3.51142			−0.139898
$631$	−11.6992			−0.465737			−0.232869	−	0.972508i	$-0.574811\pi$
$631$	−11.6992			−0.465737			−0.232869	+	0.972508i	$0.574811\pi$
$632$			7.78970i			0.309858i
$633$	−2.98525			−0.118653
$634$		−	1.41281i		−	0.0561099i
$635$		−	12.1482i		−	0.482086i
$636$			2.76686i			0.109713i
$637$	−3.78161			−0.149833
$638$	10.4825			0.415005
$639$		−	3.18134i		−	0.125852i
$640$		−	3.51142i		−	0.138801i
$641$		−	5.48192i		−	0.216523i	−0.994122	−	0.108261i	$-0.965472\pi$
$641$		−	5.48192i		−	0.216523i	0.994122	−	0.108261i	$-0.0345283\pi$
$642$	−0.196094			−0.00773921
$643$		−	34.4955i		−	1.36037i	−0.733040	−	0.680186i	$-0.761899\pi$
$643$		−	34.4955i		−	1.36037i	0.733040	−	0.680186i	$-0.238101\pi$
$644$	−6.74456			−0.265773
$645$	11.3529			0.447021
$646$	12.5566	−	17.8496i	0.494031	−	0.702283i
$647$	−39.4902			−1.55252			−0.776260	−	0.630412i	$-0.782886\pi$
$647$	−39.4902			−1.55252			−0.776260	+	0.630412i	$0.782886\pi$
$648$	−1.00000			−0.0392837
$649$			8.79612i			0.345278i
$650$	27.7195			1.08725
$651$			7.02284i			0.275247i
$652$			20.5942i			0.806529i
$653$			23.8791i			0.934461i	0.884135	+	0.467231i	$0.154748\pi$
$653$			23.8791i			0.934461i	−0.884135	+	0.467231i	$0.845252\pi$
$654$	5.01475			0.196092
$655$	26.1939			1.02348
$656$			11.8415i			0.462333i
$657$		−	11.0746i		−	0.432063i
$658$		−	7.02284i		−	0.273779i
$659$	37.6089			1.46503			0.732517	−	0.680748i	$-0.238345\pi$
$659$	37.6089			1.46503			0.732517	+	0.680748i	$0.238345\pi$
$660$		−	21.2788i		−	0.828277i
$661$	8.38410			0.326104			0.163052	−	0.986618i	$-0.447866\pi$
$661$	8.38410			0.326104			0.163052	+	0.986618i	$0.447866\pi$
$662$	6.69276			0.260122
$663$	12.7527	+	8.97104i	0.495272	+	0.348406i
$664$	6.33817			0.245969
$665$	−18.5861			−0.720737
$666$			5.78161i			0.224033i
$667$	11.6668			0.451741
$668$		−	18.7964i		−	0.727253i
$669$		−	3.84150i		−	0.148521i
$670$		−	11.3529i		−	0.438602i
$671$	−47.5186			−1.83444
$672$	−1.00000			−0.0385758
$673$			14.4379i			0.556539i	0.960503	+	0.278270i	$0.0897608\pi$
$673$			14.4379i			0.556539i	−0.960503	+	0.278270i	$0.910239\pi$
$674$		−	28.5120i		−	1.09824i
$675$		−	7.33008i		−	0.282135i
$676$	1.30058			0.0500221
$677$			45.4635i			1.74730i	0.486552	+	0.873652i	$0.338255\pi$
$677$			45.4635i			1.74730i	−0.486552	+	0.873652i	$0.661745\pi$
$678$	0.488579			0.0187638
$679$	18.0975			0.694518
$680$	11.8415	+	8.33008i	0.454101	+	0.319444i
$681$	−26.7058			−1.02337
$682$	−42.5577			−1.62962
$683$			12.7365i			0.487348i	0.969857	+	0.243674i	$0.0783526\pi$
$683$			12.7365i			0.487348i	−0.969857	+	0.243674i	$0.921647\pi$
$684$	−5.29303			−0.202384
$685$			70.3888i			2.68942i
$686$			1.00000i			0.0381802i
$687$			25.3905i			0.968709i
$688$	3.23314			0.123262
$689$	−10.4632			−0.398615
$690$		−	23.6830i		−	0.901596i
$691$		−	11.2047i		−	0.426248i	−0.977025	−	0.213124i	$-0.931636\pi$
$691$		−	11.2047i		−	0.426248i	0.977025	−	0.213124i	$-0.0683638\pi$
$692$		−	6.86434i		−	0.260943i
$693$	−6.05989			−0.230196
$694$		−	4.94677i		−	0.187777i
$695$	7.92171			0.300488
$696$	1.72981			0.0655683
$697$	−39.9329	−	28.0914i	−1.51257	−	1.06404i
$698$	−13.1955			−0.499459
$699$	−23.1944			−0.877294
$700$		−	7.33008i		−	0.277051i
$701$	3.98358			0.150458			0.0752288	−	0.997166i	$-0.476031\pi$
$701$	3.98358			0.150458			0.0752288	+	0.997166i	$0.476031\pi$
$702$		−	3.78161i		−	0.142728i
$703$			30.6022i			1.15419i
$704$		−	6.05989i		−	0.228391i
$705$	24.6602			0.928755
$706$	−24.6379			−0.927258
$707$			11.8496i			0.445650i
$708$			1.45153i			0.0545519i
$709$			30.4134i			1.14220i	0.820881	+	0.571099i	$0.193483\pi$
$709$			30.4134i			1.14220i	−0.820881	+	0.571099i	$0.806517\pi$
$710$	11.1710			0.419241
$711$			7.78970i			0.292137i
$712$	8.53426			0.319835
$713$	−47.3660			−1.77387
$714$	2.37228	−	3.37228i	0.0887804	−	0.126204i
$715$	80.4682			3.00934
$716$	6.90306			0.257980
$717$		−	27.9095i		−	1.04230i
$718$	−13.7287			−0.512350
$719$		−	49.1883i		−	1.83441i	−0.398411	−	0.917207i	$-0.630438\pi$
$719$		−	49.1883i		−	1.83441i	0.398411	−	0.917207i	$-0.369562\pi$
$720$		−	3.51142i		−	0.130863i
$721$			7.51142i			0.279740i
$722$	−9.01618			−0.335548
$723$	5.21085			0.193793
$724$			11.8577i			0.440687i
$725$			12.6797i			0.470910i
$726$		−	25.7223i		−	0.954643i
$727$	28.8479			1.06991			0.534955	−	0.844881i	$-0.320329\pi$
$727$	28.8479			1.06991			0.534955	+	0.844881i	$0.320329\pi$
$728$		−	3.78161i		−	0.140156i
$729$	−1.00000			−0.0370370
$730$	38.8877			1.43930
$731$	−7.66992	+	10.9031i	−0.283682	+	0.403264i
$732$	−7.84150			−0.289830
$733$	−26.0376			−0.961720			−0.480860	−	0.876797i	$-0.659676\pi$
$733$	−26.0376			−0.961720			−0.480860	+	0.876797i	$0.659676\pi$
$734$		−	29.0685i		−	1.07294i
$735$	−3.51142			−0.129521
$736$		−	6.74456i		−	0.248608i
$737$		−	19.5925i		−	0.721698i
$738$			11.8415i			0.435892i
$739$	15.6992			0.577504			0.288752	−	0.957404i	$-0.406760\pi$
$739$	15.6992			0.577504			0.288752	+	0.957404i	$0.406760\pi$
$740$	−20.3017			−0.746304
$741$		−	20.0162i		−	0.735313i
$742$			2.76686i			0.101575i
$743$		−	26.9679i		−	0.989358i	−0.869076	−	0.494679i	$-0.835286\pi$
$743$		−	26.9679i		−	0.989358i	0.869076	−	0.494679i	$-0.164714\pi$
$744$	−7.02284			−0.257470
$745$			13.5674i			0.497072i
$746$	−5.45962			−0.199891
$747$	6.33817			0.231902
$748$	20.4357	+	14.3758i	0.747202	+	0.525630i
$749$	−0.196094			−0.00716511
$750$	8.18189			0.298760
$751$		−	34.6613i		−	1.26481i	−0.774639	−	0.632404i	$-0.782068\pi$
$751$		−	34.6613i		−	1.26481i	0.774639	−	0.632404i	$-0.217932\pi$
$752$	7.02284			0.256097
$753$		−	8.26407i		−	0.301160i
$754$			6.54147i			0.238226i
$755$			17.8975i			0.651357i
$756$	−1.00000			−0.0363696
$757$	−16.7504			−0.608805			−0.304402	−	0.952544i	$-0.598457\pi$
$757$	−16.7504			−0.608805			−0.304402	+	0.952544i	$0.598457\pi$
$758$			16.1574i			0.586862i
$759$		−	40.8713i		−	1.48353i
$760$		−	18.5861i		−	0.674187i
$761$	42.9721			1.55774			0.778869	−	0.627186i	$-0.215793\pi$
$761$	42.9721			1.55774			0.778869	+	0.627186i	$0.215793\pi$
$762$		−	3.45962i		−	0.125329i
$763$	5.01475			0.181546
$764$	−25.3986			−0.918889
$765$	11.8415	+	8.33008i	0.428130	+	0.301175i
$766$	−34.5861			−1.24965
$767$	−5.48913			−0.198201
$768$		−	1.00000i		−	0.0360844i
$769$	−14.0162			−0.505436			−0.252718	−	0.967540i	$-0.581325\pi$
$769$	−14.0162			−0.505436			−0.252718	+	0.967540i	$0.581325\pi$
$770$		−	21.2788i		−	0.766836i
$771$			18.4886i			0.665850i
$772$		−	4.43678i		−	0.159683i
$773$	10.7365			0.386164			0.193082	−	0.981183i	$-0.438152\pi$
$773$	10.7365			0.386164			0.193082	+	0.981183i	$0.438152\pi$
$774$	3.23314			0.116213
$775$		−	51.4780i		−	1.84914i
$776$			18.0975i			0.649662i
$777$			5.78161i			0.207414i
$778$	25.1426			0.901407
$779$			62.6774i			2.24565i
$780$	13.2788			0.475458
$781$	19.2786			0.689842
$782$	22.7446	+	16.0000i	0.813344	+	0.572159i
$783$	1.72981			0.0618184
$784$	−1.00000			−0.0357143
$785$			30.0173i			1.07136i
$786$	7.45962			0.266076
$787$		−	3.78970i		−	0.135088i	−0.997716	−	0.0675441i	$-0.978484\pi$
$787$		−	3.78970i		−	0.135088i	0.997716	−	0.0675441i	$-0.0215163\pi$
$788$			3.36713i			0.119949i
$789$		−	8.84205i		−	0.314785i
$790$	−27.3529			−0.973173
$791$	0.488579			0.0173719
$792$		−	6.05989i		−	0.215329i
$793$		−	29.6535i		−	1.05303i
$794$			37.3306i			1.32481i
$795$	−9.71561			−0.344577
$796$		−	14.0457i		−	0.497836i
$797$	9.48691			0.336043			0.168022	−	0.985783i	$-0.446262\pi$
$797$	9.48691			0.336043			0.168022	+	0.985783i	$0.446262\pi$
$798$	−5.29303			−0.187371
$799$	−16.6602	+	23.6830i	−0.589394	+	0.837844i
$800$	7.33008			0.259157
$801$	8.53426			0.301543
$802$			23.9613i			0.846102i
$803$	67.1111			2.36830
$804$		−	3.23314i		−	0.114024i
$805$		−	23.6830i		−	0.834716i
$806$		−	26.5577i		−	0.935453i
$807$	−17.2108			−0.605850
$808$	−11.8496			−0.416867
$809$			37.4504i			1.31669i	0.752718	+	0.658343i	$0.228742\pi$
$809$			37.4504i			1.31669i	−0.752718	+	0.658343i	$0.771258\pi$
$810$		−	3.51142i		−	0.123379i
$811$		−	18.4955i		−	0.649466i	−0.945806	−	0.324733i	$-0.894725\pi$
$811$		−	18.4955i		−	0.649466i	0.945806	−	0.324733i	$-0.105275\pi$
$812$	1.72981			0.0607045
$813$			22.1137i			0.775560i
$814$	−35.0359			−1.22801
$815$	−72.3147			−2.53308
$816$	3.37228	+	2.37228i	0.118053	+	0.0830465i
$817$	17.1131			0.598712
$818$	−21.2462			−0.742857
$819$		−	3.78161i		−	0.132140i
$820$	−41.5805			−1.45205
$821$			21.2930i			0.743132i	0.928407	+	0.371566i	$0.121179\pi$
$821$			21.2930i			0.743132i	−0.928407	+	0.371566i	$0.878821\pi$
$822$			20.0457i			0.699174i
$823$			42.0304i			1.46509i	0.680721	+	0.732543i	$0.261667\pi$
$823$			42.0304i			1.46509i	−0.680721	+	0.732543i	$0.738333\pi$
$824$	−7.51142			−0.261673
$825$	44.4195			1.54649
$826$			1.45153i			0.0505052i
$827$		−	52.7373i		−	1.83386i	−0.399052	−	0.916928i	$-0.630661\pi$
$827$		−	52.7373i		−	1.83386i	0.399052	−	0.916928i	$-0.369339\pi$
$828$		−	6.74456i		−	0.234390i
$829$	−1.53871			−0.0534415			−0.0267207	−	0.999643i	$-0.508506\pi$
$829$	−1.53871			−0.0534415			−0.0267207	+	0.999643i	$0.508506\pi$
$830$			22.2560i			0.772516i
$831$	2.42869			0.0842503
$832$	3.78161			0.131104
$833$	2.37228	−	3.37228i	0.0821947	−	0.116843i
$834$	2.25598			0.0781183
$835$	66.0019			2.28409
$836$		−	32.0752i		−	1.10934i
$837$	−7.02284			−0.242745
$838$			28.2396i			0.975519i
$839$			47.8649i			1.65248i	0.563319	+	0.826240i	$0.309524\pi$
$839$			47.8649i			1.65248i	−0.563319	+	0.826240i	$0.690476\pi$
$840$		−	3.51142i		−	0.121156i
$841$	26.0078			0.896819
$842$	4.04568			0.139424
$843$			26.7515i			0.921372i
$844$		−	2.98525i		−	0.102756i
$845$			4.56687i			0.157105i
$846$	7.02284			0.241450
$847$		−	25.7223i		−	0.883828i
$848$	−2.76686			−0.0950143
$849$	21.1590			0.726177
$850$	−17.3890	+	24.7191i	−0.596438	+	0.847858i
$851$	−38.9944			−1.33671
$852$	3.18134			0.108991
$853$			2.58019i			0.0883441i	0.999024	+	0.0441720i	$0.0140650\pi$
$853$			2.58019i			0.0883441i	−0.999024	+	0.0441720i	$0.985935\pi$
$854$	−7.84150			−0.268331
$855$		−	18.5861i		−	0.635630i
$856$		−	0.196094i		−	0.00670235i
$857$			33.4342i			1.14209i	0.820918	+	0.571046i	$0.193462\pi$
$857$			33.4342i			1.14209i	−0.820918	+	0.571046i	$0.806538\pi$
$858$	22.9161			0.782344
$859$	12.6329			0.431028			0.215514	−	0.976501i	$-0.430857\pi$
$859$	12.6329			0.431028			0.215514	+	0.976501i	$0.430857\pi$
$860$			11.3529i			0.387131i
$861$			11.8415i			0.403557i
$862$		−	27.4961i		−	0.936521i
$863$	47.3083			1.61039			0.805197	−	0.593007i	$-0.202059\pi$
$863$	47.3083			1.61039			0.805197	+	0.593007i	$0.202059\pi$
$864$		−	1.00000i		−	0.0340207i
$865$	24.1036			0.819547
$866$	−15.6089			−0.530412
$867$	−16.0000	+	5.74456i	−0.543388	+	0.195096i
$868$	−7.02284			−0.238371
$869$	−47.2047			−1.60131
$870$			6.07410i			0.205931i
$871$	12.2265			0.414278
$872$			5.01475i			0.169821i
$873$			18.0975i			0.612507i
$874$		−	35.6992i		−	1.20754i
$875$	8.18189			0.276598
$876$	11.0746			0.374177
$877$		−	21.1966i		−	0.715760i	−0.933768	−	0.357880i	$-0.883500\pi$
$877$		−	21.1966i		−	0.715760i	0.933768	−	0.357880i	$-0.116500\pi$
$878$			21.7287i			0.733308i
$879$		−	18.1961i		−	0.613739i
$880$	21.2788			0.717309
$881$			1.88719i			0.0635809i	0.999495	+	0.0317904i	$0.0101209\pi$
$881$			1.88719i			0.0635809i	−0.999495	+	0.0317904i	$0.989879\pi$
$882$	−1.00000			−0.0336718
$883$	−33.8931			−1.14059			−0.570296	−	0.821439i	$-0.693172\pi$
$883$	−33.8931			−1.14059			−0.570296	+	0.821439i	$0.693172\pi$
$884$	−8.97104	+	12.7527i	−0.301729	+	0.428918i
$885$	−5.09694			−0.171332
$886$	7.72759			0.259614
$887$			15.3367i			0.514957i	0.966284	+	0.257479i	$0.0828917\pi$
$887$			15.3367i			0.514957i	−0.966284	+	0.257479i	$0.917108\pi$
$888$	−5.78161			−0.194018
$889$		−	3.45962i		−	0.116032i
$890$			29.9674i			1.00451i
$891$		−	6.05989i		−	0.203014i
$892$	3.84150			0.128623
$893$	37.1721			1.24392
$894$			3.86380i			0.129225i
$895$			24.2396i			0.810239i
$896$		−	1.00000i		−	0.0334077i
$897$	25.5053			0.851597
$898$			30.9265i			1.03203i
$899$	12.1482			0.405165
$900$	7.33008			0.244336
$901$	6.56377	−	9.33063i	0.218671	−	0.310848i
$902$	−71.7582			−2.38929
$903$	3.23314			0.107592
$904$			0.488579i			0.0162499i
$905$	−41.6373			−1.38407
$906$			5.09694i			0.169334i
$907$		−	48.0538i		−	1.59560i	−0.602923	−	0.797800i	$-0.705997\pi$
$907$		−	48.0538i		−	1.59560i	0.602923	−	0.797800i	$-0.294003\pi$
$908$		−	26.7058i		−	0.886265i
$909$	−11.8496			−0.393026
$910$	13.2788			0.440189
$911$		−	52.9690i		−	1.75494i	−0.479629	−	0.877471i	$-0.659229\pi$
$911$		−	52.9690i		−	1.75494i	0.479629	−	0.877471i	$-0.340771\pi$
$912$		−	5.29303i		−	0.175270i
$913$			38.4086i			1.27114i
$914$	37.8487			1.25192
$915$		−	27.5348i		−	0.910273i
$916$	−25.3905			−0.838926
$917$	7.45962			0.246338
$918$	3.37228	+	2.37228i	0.111302	+	0.0782970i
$919$	−0.720931			−0.0237813			−0.0118907	−	0.999929i	$-0.503785\pi$
$919$	−0.720931			−0.0237813			−0.0118907	+	0.999929i	$0.503785\pi$
$920$	23.6830			0.780805
$921$			14.5097i			0.478112i
$922$	−37.9989			−1.25143
$923$			12.0306i			0.395992i
$924$		−	6.05989i		−	0.199356i
$925$		−	42.3797i		−	1.39343i
$926$	17.2167			0.565776
$927$	−7.51142			−0.246707
$928$			1.72981i			0.0567838i
$929$			6.74456i			0.221282i	0.993860	+	0.110641i	$0.0352904\pi$
$929$			6.74456i			0.221282i	−0.993860	+	0.110641i	$0.964710\pi$
$930$		−	24.6602i		−	0.808638i
$931$	−5.29303			−0.173472
$932$		−	23.1944i		−	0.759759i
$933$	−7.12954			−0.233411
$934$	−1.97573			−0.0646478
$935$	−50.4794	+	71.7582i	−1.65085	+	2.34674i
$936$	3.78161			0.123606
$937$	−0.193875			−0.00633362			−0.00316681	−	0.999995i	$-0.501008\pi$
$937$	−0.193875			−0.00633362			−0.00316681	+	0.999995i	$0.501008\pi$
$938$		−	3.23314i		−	0.105566i
$939$	5.21085			0.170050
$940$			24.6602i			0.804326i
$941$		−	5.99389i		−	0.195395i	−0.995216	−	0.0976975i	$-0.968852\pi$
$941$		−	5.99389i		−	0.195395i	0.995216	−	0.0976975i	$-0.0311478\pi$
$942$			8.54847i			0.278524i
$943$	−79.8657			−2.60079
$944$	−1.45153			−0.0472433
$945$		−	3.51142i		−	0.114227i
$946$			19.5925i			0.637007i
$947$			6.61335i			0.214905i	0.994210	+	0.107452i	$0.0342693\pi$
$947$			6.61335i			0.214905i	−0.994210	+	0.107452i	$0.965731\pi$
$948$	−7.78970			−0.252998
$949$			41.8800i			1.35948i
$950$	38.7983			1.25878
$951$	1.41281			0.0458135
$952$	3.37228	+	2.37228i	0.109296	+	0.0768861i
$953$	−26.8997			−0.871367			−0.435684	−	0.900100i	$-0.643493\pi$
$953$	−26.8997			−0.871367			−0.435684	+	0.900100i	$0.643493\pi$
$954$	−2.76686			−0.0895804
$955$		−	89.1852i		−	2.88597i
$956$	27.9095			0.902657
$957$			10.4825i			0.338850i
$958$		−	17.0064i		−	0.549452i
$959$			20.0457i			0.647309i
$960$	3.51142			0.113331
$961$	−18.3203			−0.590978
$962$		−	21.8638i		−	0.704917i
$963$		−	0.196094i		−	0.00631904i
$964$			5.21085i			0.167830i
$965$	15.5794			0.501519
$966$		−	6.74456i		−	0.217003i
$967$	8.78438			0.282486			0.141243	−	0.989975i	$-0.454890\pi$
$967$	8.78438			0.282486			0.141243	+	0.989975i	$0.454890\pi$
$968$	25.7223			0.826745
$969$	17.8496	+	12.5566i	0.573411	+	0.403375i
$970$	−63.5479			−2.04040
$971$	−14.8947			−0.477995			−0.238997	−	0.971020i	$-0.576819\pi$
$971$	−14.8947			−0.477995			−0.238997	+	0.971020i	$0.576819\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	2.25598			0.0723235
$974$			38.8877i			1.24604i
$975$			27.7195i			0.887735i
$976$		−	7.84150i		−	0.251000i
$977$	59.3671			1.89932			0.949661	−	0.313280i	$-0.101428\pi$
$977$	59.3671			1.89932			0.949661	+	0.313280i	$0.101428\pi$
$978$	−20.5942			−0.658528
$979$			51.7167i			1.65287i
$980$		−	3.51142i		−	0.112168i
$981$			5.01475i			0.160109i
$982$	−8.67634			−0.276873
$983$		−	7.62843i		−	0.243309i	−0.992572	−	0.121655i	$-0.961180\pi$
$983$		−	7.62843i		−	0.243309i	0.992572	−	0.121655i	$-0.0388200\pi$
$984$	−11.8415			−0.377493
$985$	−11.8234			−0.376725
$986$	−5.83341	−	4.10360i	−0.185774	−	0.130685i
$987$	7.02284			0.223540
$988$	20.0162			0.636800
$989$			21.8061i			0.693394i
$990$	21.2788			0.676285
$991$			16.6633i			0.529326i	0.964341	+	0.264663i	$0.0852607\pi$
$991$			16.6633i			0.529326i	−0.964341	+	0.264663i	$0.914739\pi$
$992$		−	7.02284i		−	0.222975i
$993$			6.69276i			0.212388i
$994$	3.18134			0.100906
$995$	49.3203			1.56356
$996$			6.33817i			0.200833i
$997$			10.1880i			0.322657i	0.986901	+	0.161329i	$0.0515779\pi$
$997$			10.1880i			0.322657i	−0.986901	+	0.161329i	$0.948422\pi$
$998$			9.55513i			0.302462i
$999$	−5.78161			−0.182922

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.b.f.169.4	✓	8
3.2	odd	2		2142.2.b.j.883.2		8
17.16	even	2	inner	714.2.b.f.169.5	yes	8
51.50	odd	2		2142.2.b.j.883.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.b.f.169.4	✓	8	1.1	even	1	trivial
714.2.b.f.169.5	yes	8	17.16	even	2	inner
2142.2.b.j.883.2		8	3.2	odd	2
2142.2.b.j.883.7		8	51.50	odd	2

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:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +3.51142i q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +3.51142i q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} -3.51142i q^{10} -6.05989i q^{11} -1.00000i q^{12} +3.78161 q^{13} -1.00000i q^{14} +3.51142 q^{15} +1.00000 q^{16} +(-2.37228 + 3.37228i) q^{17} +1.00000 q^{18} +5.29303 q^{19} +3.51142i q^{20} +1.00000 q^{21} +6.05989i q^{22} +6.74456i q^{23} +1.00000i q^{24} -7.33008 q^{25} -3.78161 q^{26} +1.00000i q^{27} +1.00000i q^{28} -1.72981i q^{29} -3.51142 q^{30} +7.02284i q^{31} -1.00000 q^{32} -6.05989 q^{33} +(2.37228 - 3.37228i) q^{34} -3.51142 q^{35} -1.00000 q^{36} +5.78161i q^{37} -5.29303 q^{38} -3.78161i q^{39} -3.51142i q^{40} +11.8415i q^{41} -1.00000 q^{42} +3.23314 q^{43} -6.05989i q^{44} -3.51142i q^{45} -6.74456i q^{46} +7.02284 q^{47} -1.00000i q^{48} -1.00000 q^{49} +7.33008 q^{50} +(3.37228 + 2.37228i) q^{51} +3.78161 q^{52} -2.76686 q^{53} -1.00000i q^{54} +21.2788 q^{55} -1.00000i q^{56} -5.29303i q^{57} +1.72981i q^{58} -1.45153 q^{59} +3.51142 q^{60} -7.84150i q^{61} -7.02284i q^{62} -1.00000i q^{63} +1.00000 q^{64} +13.2788i q^{65} +6.05989 q^{66} +3.23314 q^{67} +(-2.37228 + 3.37228i) q^{68} +6.74456 q^{69} +3.51142 q^{70} +3.18134i q^{71} +1.00000 q^{72} +11.0746i q^{73} -5.78161i q^{74} +7.33008i q^{75} +5.29303 q^{76} +6.05989 q^{77} +3.78161i q^{78} -7.78970i q^{79} +3.51142i q^{80} +1.00000 q^{81} -11.8415i q^{82} -6.33817 q^{83} +1.00000 q^{84} +(-11.8415 - 8.33008i) q^{85} -3.23314 q^{86} -1.72981 q^{87} +6.05989i q^{88} -8.53426 q^{89} +3.51142i q^{90} +3.78161i q^{91} +6.74456i q^{92} +7.02284 q^{93} -7.02284 q^{94} +18.5861i q^{95} +1.00000i q^{96} -18.0975i q^{97} +1.00000 q^{98} +6.05989i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 - 8 * q^9	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 8 q^{9} + 6 q^{13} - 2 q^{15} + 8 q^{16} + 4 q^{17} + 8 q^{18} - 12 q^{19} + 8 q^{21} - 26 q^{25} - 6 q^{26} + 2 q^{30} - 8 q^{32} - 10 q^{33} - 4 q^{34} + 2 q^{35} - 8 q^{36} + 12 q^{38} - 8 q^{42} + 10 q^{43} - 4 q^{47} - 8 q^{49} + 26 q^{50} + 4 q^{51} + 6 q^{52} - 38 q^{53} + 34 q^{55} - 20 q^{59} - 2 q^{60} + 8 q^{64} + 10 q^{66} + 10 q^{67} + 4 q^{68} + 8 q^{69} - 2 q^{70} + 8 q^{72} - 12 q^{76} + 10 q^{77} + 8 q^{81} + 2 q^{83} + 8 q^{84} - 32 q^{85} - 10 q^{86} - 8 q^{87} + 22 q^{89} - 4 q^{93} + 4 q^{94} + 8 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 - 8 * q^9 + 6 * q^13 - 2 * q^15 + 8 * q^16 + 4 * q^17 + 8 * q^18 - 12 * q^19 + 8 * q^21 - 26 * q^25 - 6 * q^26 + 2 * q^30 - 8 * q^32 - 10 * q^33 - 4 * q^34 + 2 * q^35 - 8 * q^36 + 12 * q^38 - 8 * q^42 + 10 * q^43 - 4 * q^47 - 8 * q^49 + 26 * q^50 + 4 * q^51 + 6 * q^52 - 38 * q^53 + 34 * q^55 - 20 * q^59 - 2 * q^60 + 8 * q^64 + 10 * q^66 + 10 * q^67 + 4 * q^68 + 8 * q^69 - 2 * q^70 + 8 * q^72 - 12 * q^76 + 10 * q^77 + 8 * q^81 + 2 * q^83 + 8 * q^84 - 32 * q^85 - 10 * q^86 - 8 * q^87 + 22 * q^89 - 4 * q^93 + 4 * q^94 + 8 * q^98

Introduction

L-functions

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