LMFDB - Embedded newform 770.2.c.e.309.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(309,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("770.309");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.c (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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			309.5
Root			$-2.16053i$ of defining polynomial
Character	$\chi$	$=$	770.309
Dual form			770.2.c.e.309.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.41421i q^{3} -1.00000 q^{4} +(-1.63280 + 1.52773i) q^{5} +1.41421 q^{6} -1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.41421i q^{3} -1.00000 q^{4} +(-1.63280 + 1.52773i) q^{5} +1.41421 q^{6} -1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} +(-1.52773 - 1.63280i) q^{10} -1.00000 q^{11} +1.41421i q^{12} +1.56282i q^{13} +1.00000 q^{14} +(2.16053 + 2.30913i) q^{15} +1.00000 q^{16} -0.210157i q^{17} +1.00000i q^{18} +6.24264 q^{19} +(1.63280 - 1.52773i) q^{20} -1.41421 q^{21} -1.00000i q^{22} +8.79073i q^{23} -1.41421 q^{24} +(0.332104 - 4.98896i) q^{25} -1.56282 q^{26} -5.65685i q^{27} +1.00000i q^{28} +9.96230 q^{29} +(-2.30913 + 2.16053i) q^{30} +6.93933 q^{31} +1.00000i q^{32} +1.41421i q^{33} +0.210157 q^{34} +(1.52773 + 1.63280i) q^{35} -1.00000 q^{36} -0.358761i q^{37} +6.24264i q^{38} +2.21016 q^{39} +(1.52773 + 1.63280i) q^{40} -4.76687 q^{41} -1.41421i q^{42} +5.44670i q^{43} +1.00000 q^{44} +(-1.63280 + 1.52773i) q^{45} -8.79073 q^{46} +3.65685i q^{47} -1.41421i q^{48} -1.00000 q^{49} +(4.98896 + 0.332104i) q^{50} -0.297207 q^{51} -1.56282i q^{52} -2.76687i q^{53} +5.65685 q^{54} +(1.63280 - 1.52773i) q^{55} -1.00000 q^{56} -8.82843i q^{57} +9.96230i q^{58} +2.11612 q^{59} +(-2.16053 - 2.30913i) q^{60} +6.71231 q^{61} +6.93933i q^{62} -1.00000i q^{63} -1.00000 q^{64} +(-2.38756 - 2.55178i) q^{65} -1.41421 q^{66} +11.9779i q^{67} +0.210157i q^{68} +12.4320 q^{69} +(-1.63280 + 1.52773i) q^{70} +10.2751 q^{71} -1.00000i q^{72} -6.02386i q^{73} +0.358761 q^{74} +(-7.05545 - 0.469666i) q^{75} -6.24264 q^{76} +1.00000i q^{77} +2.21016i q^{78} +9.59530 q^{79} +(-1.63280 + 1.52773i) q^{80} -5.00000 q^{81} -4.76687i q^{82} +1.56282i q^{83} +1.41421 q^{84} +(0.321063 + 0.343146i) q^{85} -5.44670 q^{86} -14.0888i q^{87} +1.00000i q^{88} -8.59619 q^{89} +(-1.52773 - 1.63280i) q^{90} +1.56282 q^{91} -8.79073i q^{92} -9.81370i q^{93} -3.65685 q^{94} +(-10.1930 + 9.53705i) q^{95} +1.41421 q^{96} -14.1725i q^{97} -1.00000i q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 4 q^{5} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 4 * q^5 + 8 * q^9	$ 8 q - 8 q^{4} - 4 q^{5} + 8 q^{9} - 8 q^{11} + 8 q^{14} - 4 q^{15} + 8 q^{16} + 16 q^{19} + 4 q^{20} + 4 q^{25} - 8 q^{26} + 24 q^{29} - 4 q^{30} - 16 q^{31} + 8 q^{34} - 8 q^{36} + 24 q^{39} - 16 q^{41} + 8 q^{44} - 4 q^{45} + 8 q^{46} - 8 q^{49} - 4 q^{50} - 16 q^{51} + 4 q^{55} - 8 q^{56} + 64 q^{59} + 4 q^{60} - 16 q^{61} - 8 q^{64} + 4 q^{65} + 8 q^{69} - 4 q^{70} + 8 q^{71} + 16 q^{74} - 32 q^{75} - 16 q^{76} + 32 q^{79} - 4 q^{80} - 40 q^{81} - 40 q^{85} + 8 q^{86} + 48 q^{89} + 8 q^{91} + 16 q^{94} - 20 q^{95} - 8 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 4 * q^5 + 8 * q^9 - 8 * q^11 + 8 * q^14 - 4 * q^15 + 8 * q^16 + 16 * q^19 + 4 * q^20 + 4 * q^25 - 8 * q^26 + 24 * q^29 - 4 * q^30 - 16 * q^31 + 8 * q^34 - 8 * q^36 + 24 * q^39 - 16 * q^41 + 8 * q^44 - 4 * q^45 + 8 * q^46 - 8 * q^49 - 4 * q^50 - 16 * q^51 + 4 * q^55 - 8 * q^56 + 64 * q^59 + 4 * q^60 - 16 * q^61 - 8 * q^64 + 4 * q^65 + 8 * q^69 - 4 * q^70 + 8 * q^71 + 16 * q^74 - 32 * q^75 - 16 * q^76 + 32 * q^79 - 4 * q^80 - 40 * q^81 - 40 * q^85 + 8 * q^86 + 48 * q^89 + 8 * q^91 + 16 * q^94 - 20 * q^95 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		−	1.41421i		−	0.816497i	−0.912871	−	0.408248i	$-0.866140\pi$
$3$		−	1.41421i		−	0.816497i	0.912871	−	0.408248i	$-0.133860\pi$
$4$	−1.00000			−0.500000
$5$	−1.63280	+	1.52773i	−0.730213	+	0.683220i
$5$	−1.63280	+	1.52773i	−0.730213	+	0.683220i
$6$	1.41421			0.577350
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	1.00000i		−	0.353553i
$9$	1.00000			0.333333
$10$	−1.52773	−	1.63280i	−0.483109	−	0.516338i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$			1.41421i			0.408248i
$13$			1.56282i			0.433447i	0.976233	+	0.216724i	$0.0695371\pi$
$13$			1.56282i			0.433447i	−0.976233	+	0.216724i	$0.930463\pi$
$14$	1.00000			0.267261
$15$	2.16053	+	2.30913i	0.557847	+	0.596216i
$16$	1.00000			0.250000
$17$		−	0.210157i		−	0.0509706i	−0.999675	−	0.0254853i	$-0.991887\pi$
$17$		−	0.210157i		−	0.0509706i	0.999675	−	0.0254853i	$-0.00811310\pi$
$18$			1.00000i			0.235702i
$19$	6.24264			1.43216			0.716080	−	0.698018i	$-0.245935\pi$
$19$	6.24264			1.43216			0.716080	+	0.698018i	$0.245935\pi$
$20$	1.63280	−	1.52773i	0.365106	−	0.341610i
$21$	−1.41421			−0.308607
$22$		−	1.00000i		−	0.213201i
$23$			8.79073i			1.83299i	0.400042	+	0.916497i	$0.368996\pi$
$23$			8.79073i			1.83299i	−0.400042	+	0.916497i	$0.631004\pi$
$24$	−1.41421			−0.288675
$25$	0.332104	−	4.98896i	0.0664208	−	0.997792i
$26$	−1.56282			−0.306494
$27$		−	5.65685i		−	1.08866i
$28$			1.00000i			0.188982i
$29$	9.96230			1.84995			0.924977	−	0.380024i	$-0.124084\pi$
$29$	9.96230			1.84995			0.924977	+	0.380024i	$0.124084\pi$
$30$	−2.30913	+	2.16053i	−0.421588	+	0.394457i
$31$	6.93933			1.24634			0.623170	−	0.782086i	$-0.285844\pi$
$31$	6.93933			1.24634			0.623170	+	0.782086i	$0.285844\pi$
$32$			1.00000i			0.176777i
$33$			1.41421i			0.246183i
$34$	0.210157			0.0360417
$35$	1.52773	+	1.63280i	0.258233	+	0.275994i
$36$	−1.00000			−0.166667
$37$		−	0.358761i		−	0.0589799i	−0.999565	−	0.0294900i	$-0.990612\pi$
$37$		−	0.358761i		−	0.0589799i	0.999565	−	0.0294900i	$-0.00938831\pi$
$38$			6.24264i			1.01269i
$39$	2.21016			0.353908
$40$	1.52773	+	1.63280i	0.241555	+	0.258169i
$41$	−4.76687			−0.744461			−0.372230	−	0.928140i	$-0.621407\pi$
$41$	−4.76687			−0.744461			−0.372230	+	0.928140i	$0.621407\pi$
$42$		−	1.41421i		−	0.218218i
$43$			5.44670i			0.830614i	0.909681	+	0.415307i	$0.136326\pi$
$43$			5.44670i			0.830614i	−0.909681	+	0.415307i	$0.863674\pi$
$44$	1.00000			0.150756
$45$	−1.63280	+	1.52773i	−0.243404	+	0.227740i
$46$	−8.79073			−1.29612
$47$			3.65685i			0.533407i	0.963779	+	0.266704i	$0.0859344\pi$
$47$			3.65685i			0.533407i	−0.963779	+	0.266704i	$0.914066\pi$
$48$		−	1.41421i		−	0.204124i
$49$	−1.00000			−0.142857
$50$	4.98896	+	0.332104i	0.705545	+	0.0469666i
$51$	−0.297207			−0.0416173
$52$		−	1.56282i		−	0.216724i
$53$		−	2.76687i		−	0.380059i	−0.981778	−	0.190030i	$-0.939142\pi$
$53$		−	2.76687i		−	0.380059i	0.981778	−	0.190030i	$-0.0608584\pi$
$54$	5.65685			0.769800
$55$	1.63280	−	1.52773i	0.220167	−	0.205999i
$56$	−1.00000			−0.133631
$57$		−	8.82843i		−	1.16935i
$58$			9.96230i			1.30811i
$59$	2.11612			0.275495			0.137748	−	0.990467i	$-0.456014\pi$
$59$	2.11612			0.275495			0.137748	+	0.990467i	$0.456014\pi$
$60$	−2.16053	−	2.30913i	−0.278923	−	0.298108i
$61$	6.71231			0.859423			0.429711	−	0.902966i	$-0.358615\pi$
$61$	6.71231			0.859423			0.429711	+	0.902966i	$0.358615\pi$
$62$			6.93933i			0.881296i
$63$		−	1.00000i		−	0.125988i
$64$	−1.00000			−0.125000
$65$	−2.38756	−	2.55178i	−0.296140	−	0.316509i
$66$	−1.41421			−0.174078
$67$			11.9779i			1.46334i	0.681661	+	0.731668i	$0.261258\pi$
$67$			11.9779i			1.46334i	−0.681661	+	0.731668i	$0.738742\pi$
$68$			0.210157i			0.0254853i
$69$	12.4320			1.49663
$70$	−1.63280	+	1.52773i	−0.195158	+	0.182598i
$71$	10.2751			1.21943			0.609716	−	0.792620i	$-0.291283\pi$
$71$	10.2751			1.21943			0.609716	+	0.792620i	$0.291283\pi$
$72$		−	1.00000i		−	0.117851i
$73$		−	6.02386i		−	0.705039i	−0.935804	−	0.352519i	$-0.885325\pi$
$73$		−	6.02386i		−	0.705039i	0.935804	−	0.352519i	$-0.114675\pi$
$74$	0.358761			0.0417051
$75$	−7.05545	−	0.469666i	−0.814694	−	0.0542324i
$76$	−6.24264			−0.716080
$77$			1.00000i			0.113961i
$78$			2.21016i			0.250251i
$79$	9.59530			1.07956			0.539778	−	0.841808i	$-0.318508\pi$
$79$	9.59530			1.07956			0.539778	+	0.841808i	$0.318508\pi$
$80$	−1.63280	+	1.52773i	−0.182553	+	0.170805i
$81$	−5.00000			−0.555556
$82$		−	4.76687i		−	0.526413i
$83$			1.56282i			0.171541i	0.996315	+	0.0857707i	$0.0273353\pi$
$83$			1.56282i			0.171541i	−0.996315	+	0.0857707i	$0.972665\pi$
$84$	1.41421			0.154303
$85$	0.321063	+	0.343146i	0.0348241	+	0.0372194i
$86$	−5.44670			−0.587332
$87$		−	14.0888i		−	1.51048i
$88$			1.00000i			0.106600i
$89$	−8.59619			−0.911194			−0.455597	−	0.890186i	$-0.650574\pi$
$89$	−8.59619			−0.911194			−0.455597	+	0.890186i	$0.650574\pi$
$90$	−1.52773	−	1.63280i	−0.161036	−	0.172113i
$91$	1.56282			0.163828
$92$		−	8.79073i		−	0.916497i
$93$		−	9.81370i		−	1.01763i
$94$	−3.65685			−0.377176
$95$	−10.1930	+	9.53705i	−1.04578	+	0.978480i
$96$	1.41421			0.144338
$97$		−	14.1725i		−	1.43900i	−0.694495	−	0.719498i	$-0.744372\pi$
$97$		−	14.1725i		−	1.43900i	0.694495	−	0.719498i	$-0.255628\pi$
$98$		−	1.00000i		−	0.101015i
$99$	−1.00000			−0.100504
$100$	−0.332104	+	4.98896i	−0.0332104	+	0.498896i
$101$	−9.92982			−0.988054			−0.494027	−	0.869447i	$-0.664476\pi$
$101$	−9.92982			−0.988054			−0.494027	+	0.869447i	$0.664476\pi$
$102$		−	0.297207i		−	0.0294279i
$103$		−	10.9393i		−	1.07788i	−0.842343	−	0.538942i	$-0.818824\pi$
$103$		−	10.9393i		−	1.07788i	0.842343	−	0.538942i	$-0.181176\pi$
$104$	1.56282			0.153247
$105$	2.30913	−	2.16053i	0.225348	−	0.210846i
$106$	2.76687			0.268743
$107$			12.8523i			1.24248i	0.783622	+	0.621239i	$0.213370\pi$
$107$			12.8523i			1.24248i	−0.783622	+	0.621239i	$0.786630\pi$
$108$			5.65685i			0.544331i
$109$	−14.4476			−1.38383			−0.691914	−	0.721980i	$-0.743232\pi$
$109$	−14.4476			−1.38383			−0.691914	+	0.721980i	$0.743232\pi$
$110$	1.52773	+	1.63280i	0.145663	+	0.155682i
$111$	−0.507364			−0.0481569
$112$		−	1.00000i		−	0.0944911i
$113$			5.55760i			0.522815i	0.965228	+	0.261408i	$0.0841867\pi$
$113$			5.55760i			0.522815i	−0.965228	+	0.261408i	$0.915813\pi$
$114$	8.82843			0.826858
$115$	−13.4298	−	14.3535i	−1.25234	−	1.33848i
$116$	−9.96230			−0.924977
$117$			1.56282i			0.144482i
$118$			2.11612i			0.194805i
$119$	−0.210157			−0.0192651
$120$	2.30913	−	2.16053i	0.210794	−	0.197229i
$121$	1.00000			0.0909091
$122$			6.71231i			0.607704i
$123$			6.74138i			0.607850i
$124$	−6.93933			−0.623170
$125$	7.07950	+	8.65336i	0.633210	+	0.773980i
$126$	1.00000			0.0890871
$127$			1.07232i			0.0951531i	0.998868	+	0.0475766i	$0.0151498\pi$
$127$			1.07232i			0.0951531i	−0.998868	+	0.0475766i	$0.984850\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	7.70279			0.678193
$130$	2.55178	−	2.38756i	0.223806	−	0.209403i
$131$	−21.8700			−1.91079			−0.955397	−	0.295324i	$-0.904572\pi$
$131$	−21.8700			−1.91079			−0.955397	+	0.295324i	$0.904572\pi$
$132$		−	1.41421i		−	0.123091i
$133$		−	6.24264i		−	0.541306i
$134$	−11.9779			−1.03473
$135$	8.64213	+	9.23654i	0.743796	+	0.794955i
$136$	−0.210157			−0.0180208
$137$		−	8.22181i		−	0.702437i	−0.936294	−	0.351218i	$-0.885767\pi$
$137$		−	8.22181i		−	0.702437i	0.936294	−	0.351218i	$-0.114233\pi$
$138$			12.4320i			1.05828i
$139$	−9.71319			−0.823862			−0.411931	−	0.911215i	$-0.635146\pi$
$139$	−9.71319			−0.823862			−0.411931	+	0.911215i	$0.635146\pi$
$140$	−1.52773	−	1.63280i	−0.129116	−	0.137997i
$141$	5.17157			0.435525
$142$			10.2751i			0.862269i
$143$		−	1.56282i		−	0.130689i
$144$	1.00000			0.0833333
$145$	−16.2665	+	15.2197i	−1.35086	+	1.26392i
$146$	6.02386			0.498538
$147$			1.41421i			0.116642i
$148$			0.358761i			0.0294900i
$149$	5.02297			0.411498			0.205749	−	0.978605i	$-0.434037\pi$
$149$	5.02297			0.411498			0.205749	+	0.978605i	$0.434037\pi$
$150$	0.469666	−	7.05545i	0.0383481	−	0.576075i
$151$	2.56892			0.209056			0.104528	−	0.994522i	$-0.466667\pi$
$151$	2.56892			0.209056			0.104528	+	0.994522i	$0.466667\pi$
$152$		−	6.24264i		−	0.506345i
$153$		−	0.210157i		−	0.0169902i
$154$	−1.00000			−0.0805823
$155$	−11.3306	+	10.6014i	−0.910094	+	0.851525i
$156$	−2.21016			−0.176954
$157$		−	16.8692i		−	1.34630i	−0.739504	−	0.673152i	$-0.764940\pi$
$157$		−	16.8692i		−	1.34630i	0.739504	−	0.673152i	$-0.235060\pi$
$158$			9.59530i			0.763361i
$159$	−3.91295			−0.310317
$160$	−1.52773	−	1.63280i	−0.120777	−	0.129085i
$161$	8.79073			0.692807
$162$		−	5.00000i		−	0.392837i
$163$		−	12.5723i		−	0.984741i	−0.870386	−	0.492370i	$-0.836131\pi$
$163$		−	12.5723i		−	0.984741i	0.870386	−	0.492370i	$-0.163869\pi$
$164$	4.76687			0.372230
$165$	−2.16053	−	2.30913i	−0.168197	−	0.179766i
$166$	−1.56282			−0.121298
$167$		−	13.0962i		−	1.01341i	−0.862119	−	0.506706i	$-0.830863\pi$
$167$		−	13.0962i		−	1.01341i	0.862119	−	0.506706i	$-0.169137\pi$
$168$			1.41421i			0.109109i
$169$	10.5576			0.812123
$170$	−0.343146	+	0.321063i	−0.0263181	+	0.0246244i
$171$	6.24264			0.477387
$172$		−	5.44670i		−	0.415307i
$173$			0.461038i			0.0350521i	0.999846	+	0.0175260i	$0.00557900\pi$
$173$			0.461038i			0.0350521i	−0.999846	+	0.0175260i	$0.994421\pi$
$174$	14.0888			1.06807
$175$	−4.98896	−	0.332104i	−0.377130	−	0.0251047i
$176$	−1.00000			−0.0753778
$177$		−	2.99265i		−	0.224941i
$178$		−	8.59619i		−	0.644311i
$179$	4.69544			0.350954			0.175477	−	0.984484i	$-0.443853\pi$
$179$	4.69544			0.350954			0.175477	+	0.984484i	$0.443853\pi$
$180$	1.63280	−	1.52773i	0.121702	−	0.113870i
$181$	−15.4537			−1.14866			−0.574332	−	0.818623i	$-0.694738\pi$
$181$	−15.4537			−1.14866			−0.574332	+	0.818623i	$0.694738\pi$
$182$			1.56282i			0.115844i
$183$		−	9.49264i		−	0.701716i
$184$	8.79073			0.648061
$185$	0.548088	+	0.585786i	0.0402963	+	0.0430679i
$186$	9.81370			0.719575
$187$			0.210157i			0.0153682i
$188$		−	3.65685i		−	0.266704i
$189$	−5.65685			−0.411476
$190$	−9.53705	−	10.1930i	−0.691890	−	0.739479i
$191$	−14.6954			−1.06332			−0.531662	−	0.846956i	$-0.678432\pi$
$191$	−14.6954			−1.06332			−0.531662	+	0.846956i	$0.678432\pi$
$192$			1.41421i			0.102062i
$193$			18.2751i			1.31547i	0.753248	+	0.657736i	$0.228486\pi$
$193$			18.2751i			1.31547i	−0.753248	+	0.657736i	$0.771514\pi$
$194$	14.1725			1.01752
$195$	−3.60876	+	3.37652i	−0.258428	+	0.241797i
$196$	1.00000			0.0714286
$197$			19.8787i			1.41630i	0.706064	+	0.708148i	$0.250469\pi$
$197$			19.8787i			1.41630i	−0.706064	+	0.708148i	$0.749531\pi$
$198$		−	1.00000i		−	0.0710669i
$199$	22.7941			1.61583			0.807917	−	0.589296i	$-0.200595\pi$
$199$	22.7941			1.61583			0.807917	+	0.589296i	$0.200595\pi$
$200$	−4.98896	−	0.332104i	−0.352773	−	0.0234833i
$201$	16.9393			1.19481
$202$		−	9.92982i		−	0.698660i
$203$		−	9.96230i		−	0.699217i
$204$	0.297207			0.0208087
$205$	7.78337	−	7.28248i	0.543614	−	0.508630i
$206$	10.9393			0.762179
$207$			8.79073i			0.610998i
$208$			1.56282i			0.108362i
$209$	−6.24264			−0.431812
$210$	2.16053	+	2.30913i	0.149091	+	0.159345i
$211$	−13.8449			−0.953124			−0.476562	−	0.879141i	$-0.658117\pi$
$211$	−13.8449			−0.953124			−0.476562	+	0.879141i	$0.658117\pi$
$212$			2.76687i			0.190030i
$213$		−	14.5312i		−	0.995663i
$214$	−12.8523			−0.878564
$215$	−8.32106	−	8.89339i	−0.567492	−	0.606524i
$216$	−5.65685			−0.384900
$217$		−	6.93933i		−	0.471073i
$218$		−	14.4476i		−	0.978514i
$219$	−8.51902			−0.575662
$220$	−1.63280	+	1.52773i	−0.110084	+	0.102999i
$221$	0.328437			0.0220931
$222$		−	0.507364i		−	0.0340521i
$223$		−	11.1274i		−	0.745146i	−0.928003	−	0.372573i	$-0.878476\pi$
$223$		−	11.1274i		−	0.745146i	0.928003	−	0.372573i	$-0.121524\pi$
$224$	1.00000			0.0668153
$225$	0.332104	−	4.98896i	0.0221403	−	0.332597i
$226$	−5.55760			−0.369686
$227$			17.0021i			1.12847i	0.825614	+	0.564236i	$0.190829\pi$
$227$			17.0021i			1.12847i	−0.825614	+	0.564236i	$0.809171\pi$
$228$			8.82843i			0.584677i
$229$	−14.7895			−0.977316			−0.488658	−	0.872475i	$-0.662513\pi$
$229$	−14.7895			−0.977316			−0.488658	+	0.872475i	$0.662513\pi$
$230$	14.3535	−	13.4298i	0.946445	−	0.885537i
$231$	1.41421			0.0930484
$232$		−	9.96230i		−	0.654057i
$233$		−	22.0888i		−	1.44709i	−0.690279	−	0.723543i	$-0.742512\pi$
$233$		−	22.0888i		−	1.44709i	0.690279	−	0.723543i	$-0.257488\pi$
$234$	−1.56282			−0.102165
$235$	−5.58667	−	5.97093i	−0.364434	−	0.389501i
$236$	−2.11612			−0.137748
$237$		−	13.5698i		−	0.881454i
$238$		−	0.210157i		−	0.0136225i
$239$	12.3489			0.798783			0.399391	−	0.916781i	$-0.369221\pi$
$239$	12.3489			0.798783			0.399391	+	0.916781i	$0.369221\pi$
$240$	2.16053	+	2.30913i	0.139462	+	0.149054i
$241$	11.0659			0.712814			0.356407	−	0.934331i	$-0.384002\pi$
$241$	11.0659			0.712814			0.356407	+	0.934331i	$0.384002\pi$
$242$			1.00000i			0.0642824i
$243$		−	9.89949i		−	0.635053i
$244$	−6.71231			−0.429711
$245$	1.63280	−	1.52773i	0.104316	−	0.0976029i
$246$	−6.74138			−0.429815
$247$			9.75611i			0.620766i
$248$		−	6.93933i		−	0.440648i
$249$	2.21016			0.140063
$250$	−8.65336	+	7.07950i	−0.547287	+	0.447747i
$251$	21.9488			1.38540			0.692699	−	0.721226i	$-0.256421\pi$
$251$	21.9488			1.38540			0.692699	+	0.721226i	$0.256421\pi$
$252$			1.00000i			0.0629941i
$253$		−	8.79073i		−	0.552668i
$254$	−1.07232			−0.0672834
$255$	0.485281	−	0.454051i	0.0303895	−	0.0284338i
$256$	1.00000			0.0625000
$257$		−	3.93845i		−	0.245674i	−0.992427	−	0.122837i	$-0.960801\pi$
$257$		−	3.93845i		−	0.245674i	0.992427	−	0.122837i	$-0.0391992\pi$
$258$			7.70279i			0.479555i
$259$	−0.358761			−0.0222923
$260$	2.38756	+	2.55178i	0.148070	+	0.158254i
$261$	9.96230			0.616651
$262$		−	21.8700i		−	1.35114i
$263$			1.77996i			0.109757i	0.998493	+	0.0548786i	$0.0174772\pi$
$263$			1.77996i			0.109757i	−0.998493	+	0.0548786i	$0.982523\pi$
$264$	1.41421			0.0870388
$265$	4.22703	+	4.51776i	0.259664	+	0.277524i
$266$	6.24264			0.382761
$267$			12.1568i			0.743987i
$268$		−	11.9779i		−	0.731668i
$269$	19.0555			1.16183			0.580916	−	0.813964i	$-0.302695\pi$
$269$	19.0555			1.16183			0.580916	+	0.813964i	$0.302695\pi$
$270$	−9.23654	+	8.64213i	−0.562118	+	0.525943i
$271$	−12.5190			−0.760476			−0.380238	−	0.924889i	$-0.624158\pi$
$271$	−12.5190			−0.760476			−0.380238	+	0.924889i	$0.624158\pi$
$272$		−	0.210157i		−	0.0127427i
$273$		−	2.21016i		−	0.133765i
$274$	8.22181			0.496698
$275$	−0.332104	+	4.98896i	−0.0200266	+	0.300846i
$276$	−12.4320			−0.748317
$277$		−	2.75126i		−	0.165307i	−0.996578	−	0.0826535i	$-0.973661\pi$
$277$		−	2.75126i		−	0.165307i	0.996578	−	0.0826535i	$-0.0263395\pi$
$278$		−	9.71319i		−	0.582559i
$279$	6.93933			0.415447
$280$	1.63280	−	1.52773i	0.0975788	−	0.0912991i
$281$	9.75050			0.581666			0.290833	−	0.956774i	$-0.406068\pi$
$281$	9.75050			0.581666			0.290833	+	0.956774i	$0.406068\pi$
$282$			5.17157i			0.307963i
$283$			26.1608i			1.55510i	0.628823	+	0.777548i	$0.283537\pi$
$283$			26.1608i			1.55510i	−0.628823	+	0.777548i	$0.716463\pi$
$284$	−10.2751			−0.609716
$285$	13.4874	+	14.4151i	0.798926	+	0.853877i
$286$	1.56282			0.0924113
$287$			4.76687i			0.281380i
$288$			1.00000i			0.0589256i
$289$	16.9558			0.997402
$290$	−15.2197	−	16.2665i	−0.893730	−	0.955202i
$291$	−20.0429			−1.17493
$292$			6.02386i			0.352519i
$293$			0.814065i			0.0475582i	0.999717	+	0.0237791i	$0.00756984\pi$
$293$			0.814065i			0.0475582i	−0.999717	+	0.0237791i	$0.992430\pi$
$294$	−1.41421			−0.0824786
$295$	−3.45521	+	3.23285i	−0.201170	+	0.188224i
$296$	−0.358761			−0.0208525
$297$			5.65685i			0.328244i
$298$			5.02297i			0.290973i
$299$	−13.7383			−0.794507
$300$	7.05545	+	0.469666i	0.407347	+	0.0271162i
$301$	5.44670			0.313942
$302$			2.56892i			0.147825i
$303$			14.0429i			0.806743i
$304$	6.24264			0.358040
$305$	−10.9599	+	10.2546i	−0.627561	+	0.587175i
$306$	0.210157			0.0120139
$307$			24.8593i			1.41879i	0.704809	+	0.709397i	$0.251033\pi$
$307$			24.8593i			1.41879i	−0.704809	+	0.709397i	$0.748967\pi$
$308$		−	1.00000i		−	0.0569803i
$309$	−15.4706			−0.880089
$310$	−10.6014	−	11.3306i	−0.602119	−	0.643534i
$311$	−13.6447			−0.773717			−0.386859	−	0.922139i	$-0.626440\pi$
$311$	−13.6447			−0.773717			−0.386859	+	0.922139i	$0.626440\pi$
$312$		−	2.21016i		−	0.125126i
$313$		−	22.3943i		−	1.26580i	−0.774234	−	0.632899i	$-0.781865\pi$
$313$		−	22.3943i		−	1.26580i	0.774234	−	0.632899i	$-0.218135\pi$
$314$	16.8692			0.951981
$315$	1.52773	+	1.63280i	0.0860776	+	0.0919981i
$316$	−9.59530			−0.539778
$317$			19.3753i			1.08822i	0.839013	+	0.544112i	$0.183133\pi$
$317$			19.3753i			1.08822i	−0.839013	+	0.544112i	$0.816867\pi$
$318$		−	3.91295i		−	0.219427i
$319$	−9.96230			−0.557782
$320$	1.63280	−	1.52773i	0.0912766	−	0.0854025i
$321$	18.1759			1.01448
$322$			8.79073i			0.489888i
$323$		−	1.31194i		−	0.0729981i
$324$	5.00000			0.277778
$325$	7.79683	+	0.519018i	0.432490	+	0.0287899i
$326$	12.5723			0.696317
$327$			20.4320i			1.12989i
$328$			4.76687i			0.263207i
$329$	3.65685			0.201609
$330$	2.30913	−	2.16053i	0.127114	−	0.118933i
$331$	−33.1391			−1.82149			−0.910744	−	0.412972i	$-0.864491\pi$
$331$	−33.1391			−1.82149			−0.910744	+	0.412972i	$0.864491\pi$
$332$		−	1.56282i		−	0.0857707i
$333$		−	0.358761i		−	0.0196600i
$334$	13.0962			0.716591
$335$	−18.2990	−	19.5576i	−0.999780	−	1.06855i
$336$	−1.41421			−0.0771517
$337$		−	9.62740i		−	0.524438i	−0.965008	−	0.262219i	$-0.915546\pi$
$337$		−	9.62740i		−	0.524438i	0.965008	−	0.262219i	$-0.0844542\pi$
$338$			10.5576i			0.574258i
$339$	7.85964			0.426877
$340$	−0.321063	−	0.343146i	−0.0174121	−	0.0186097i
$341$	−6.93933			−0.375786
$342$			6.24264i			0.337563i
$343$			1.00000i			0.0539949i
$344$	5.44670			0.293666
$345$	−20.2990	+	18.9926i	−1.09286	+	1.02253i
$346$	−0.461038			−0.0247856
$347$			29.9147i			1.60591i	0.596042	+	0.802953i	$0.296739\pi$
$347$			29.9147i			1.60591i	−0.596042	+	0.802953i	$0.703261\pi$
$348$			14.0888i			0.755240i
$349$	8.89861			0.476332			0.238166	−	0.971225i	$-0.423454\pi$
$349$	8.89861			0.476332			0.238166	+	0.971225i	$0.423454\pi$
$350$	0.332104	−	4.98896i	0.0177517	−	0.266671i
$351$	8.84063			0.471878
$352$		−	1.00000i		−	0.0533002i
$353$		−	13.6265i		−	0.725267i	−0.931932	−	0.362634i	$-0.881878\pi$
$353$		−	13.6265i		−	0.725267i	0.931932	−	0.362634i	$-0.118122\pi$
$354$	2.99265			0.159057
$355$	−16.7773	+	15.6976i	−0.890445	+	0.833141i
$356$	8.59619			0.455597
$357$			0.297207i			0.0157299i
$358$			4.69544i			0.248162i
$359$	23.2110			1.22503			0.612516	−	0.790458i	$-0.290157\pi$
$359$	23.2110			1.22503			0.612516	+	0.790458i	$0.290157\pi$
$360$	1.52773	+	1.63280i	0.0805182	+	0.0860564i
$361$	19.9706			1.05108
$362$		−	15.4537i		−	0.812228i
$363$		−	1.41421i		−	0.0742270i
$364$	−1.56282			−0.0819139
$365$	9.20280	+	9.83578i	0.481697	+	0.514828i
$366$	9.49264			0.496188
$367$			9.84316i			0.513809i	0.966437	+	0.256904i	$0.0827025\pi$
$367$			9.84316i			0.513809i	−0.966437	+	0.256904i	$0.917297\pi$
$368$			8.79073i			0.458248i
$369$	−4.76687			−0.248154
$370$	−0.585786	+	0.548088i	−0.0304536	+	0.0284938i
$371$	−2.76687			−0.143649
$372$			9.81370i			0.508817i
$373$			4.71929i			0.244356i	0.992508	+	0.122178i	$0.0389878\pi$
$373$			4.71929i			0.244356i	−0.992508	+	0.122178i	$0.961012\pi$
$374$	−0.210157			−0.0108670
$375$	12.2377	−	10.0119i	0.631952	−	0.517014i
$376$	3.65685			0.188588
$377$			15.5693i			0.801857i
$378$		−	5.65685i		−	0.290957i
$379$	−21.6906			−1.11417			−0.557085	−	0.830455i	$-0.688080\pi$
$379$	−21.6906			−1.11417			−0.557085	+	0.830455i	$0.688080\pi$
$380$	10.1930	−	9.53705i	0.522891	−	0.489240i
$381$	1.51649			0.0776922
$382$		−	14.6954i		−	0.751884i
$383$			20.1759i			1.03094i	0.856908	+	0.515469i	$0.172382\pi$
$383$			20.1759i			1.03094i	−0.856908	+	0.515469i	$0.827618\pi$
$384$	−1.41421			−0.0721688
$385$	−1.52773	−	1.63280i	−0.0778601	−	0.0832154i
$386$	−18.2751			−0.930179
$387$			5.44670i			0.276871i
$388$			14.1725i			0.719498i
$389$	15.3769			0.779640			0.389820	−	0.920891i	$-0.372537\pi$
$389$	15.3769			0.779640			0.389820	+	0.920891i	$0.372537\pi$
$390$	−3.37652	−	3.60876i	−0.170977	−	0.182736i
$391$	1.84744			0.0934288
$392$			1.00000i			0.0505076i
$393$			30.9289i			1.56016i
$394$	−19.8787			−1.00147
$395$	−15.6673	+	14.6590i	−0.788305	+	0.737574i
$396$	1.00000			0.0502519
$397$			1.42983i			0.0717610i	0.999356	+	0.0358805i	$0.0114236\pi$
$397$			1.42983i			0.0717610i	−0.999356	+	0.0358805i	$0.988576\pi$
$398$			22.7941i			1.14257i
$399$	−8.82843			−0.441974
$400$	0.332104	−	4.98896i	0.0166052	−	0.249448i
$401$	−32.3761			−1.61679			−0.808394	−	0.588642i	$-0.799663\pi$
$401$	−32.3761			−1.61679			−0.808394	+	0.588642i	$0.799663\pi$
$402$			16.9393i			0.844857i
$403$			10.8449i			0.540223i
$404$	9.92982			0.494027
$405$	8.16402	−	7.63863i	0.405674	−	0.379567i
$406$	9.96230			0.494421
$407$			0.358761i			0.0177831i
$408$			0.297207i			0.0147139i
$409$	19.1100			0.944930			0.472465	−	0.881350i	$-0.343364\pi$
$409$	19.1100			0.944930			0.472465	+	0.881350i	$0.343364\pi$
$410$	7.28248	+	7.78337i	0.359656	+	0.384393i
$411$	−11.6274			−0.573537
$412$			10.9393i			0.538942i
$413$		−	2.11612i		−	0.104127i
$414$	−8.79073			−0.432041
$415$	−2.38756	−	2.55178i	−0.117201	−	0.125262i
$416$	−1.56282			−0.0766234
$417$			13.7365i			0.672681i
$418$		−	6.24264i		−	0.305338i
$419$	34.7453			1.69742			0.848710	−	0.528859i	$-0.177380\pi$
$419$	34.7453			1.69742			0.848710	+	0.528859i	$0.177380\pi$
$420$	−2.30913	+	2.16053i	−0.112674	+	0.105423i
$421$	22.3787			1.09067			0.545334	−	0.838219i	$-0.316403\pi$
$421$	22.3787			1.09067			0.545334	+	0.838219i	$0.316403\pi$
$422$		−	13.8449i		−	0.673961i
$423$			3.65685i			0.177802i
$424$	−2.76687			−0.134371
$425$	−1.04847	−	0.0697941i	−0.0508581	−	0.00338551i
$426$	14.5312			0.704040
$427$		−	6.71231i		−	0.324831i
$428$		−	12.8523i		−	0.621239i
$429$	−2.21016			−0.106707
$430$	8.89339	−	8.32106i	0.428878	−	0.401277i
$431$	−12.6971			−0.611597			−0.305798	−	0.952096i	$-0.598923\pi$
$431$	−12.6971			−0.611597			−0.305798	+	0.952096i	$0.598923\pi$
$432$		−	5.65685i		−	0.272166i
$433$			15.0131i			0.721483i	0.932666	+	0.360741i	$0.117476\pi$
$433$			15.0131i			0.721483i	−0.932666	+	0.360741i	$0.882524\pi$
$434$	6.93933			0.333099
$435$	21.5239	+	23.0043i	1.03199	+	1.10297i
$436$	14.4476			0.691914
$437$			54.8774i			2.62514i
$438$		−	8.51902i		−	0.407054i
$439$	−4.29721			−0.205095			−0.102547	−	0.994728i	$-0.532699\pi$
$439$	−4.29721			−0.205095			−0.102547	+	0.994728i	$0.532699\pi$
$440$	−1.52773	−	1.63280i	−0.0728315	−	0.0778409i
$441$	−1.00000			−0.0476190
$442$			0.328437i			0.0156222i
$443$		−	41.8228i		−	1.98706i	−0.113555	−	0.993532i	$-0.536224\pi$
$443$		−	41.8228i		−	1.98706i	0.113555	−	0.993532i	$-0.463776\pi$
$444$	0.507364			0.0240784
$445$	14.0359	−	13.1326i	0.665365	−	0.622546i
$446$	11.1274			0.526898
$447$		−	7.10355i		−	0.335986i
$448$			1.00000i			0.0472456i
$449$	−15.4804			−0.730567			−0.365283	−	0.930896i	$-0.619028\pi$
$449$	−15.4804			−0.730567			−0.365283	+	0.930896i	$0.619028\pi$
$450$	4.98896	+	0.332104i	0.235182	+	0.0156555i
$451$	4.76687			0.224463
$452$		−	5.55760i		−	0.261408i
$453$		−	3.63300i		−	0.170693i
$454$	−17.0021			−0.797950
$455$	−2.55178	+	2.38756i	−0.119629	+	0.111930i
$456$	−8.82843			−0.413429
$457$		−	34.5980i		−	1.61842i	−0.587517	−	0.809212i	$-0.699894\pi$
$457$		−	34.5980i		−	1.61842i	0.587517	−	0.809212i	$-0.300106\pi$
$458$		−	14.7895i		−	0.691067i
$459$	−1.18883			−0.0554898
$460$	13.4298	+	14.3535i	0.626169	+	0.669238i
$461$	−30.8250			−1.43566			−0.717831	−	0.696217i	$-0.754865\pi$
$461$	−30.8250			−1.43566			−0.717831	+	0.696217i	$0.754865\pi$
$462$			1.41421i			0.0657952i
$463$		−	41.3648i		−	1.92239i	−0.275875	−	0.961193i	$-0.588968\pi$
$463$		−	41.3648i		−	1.92239i	0.275875	−	0.961193i	$-0.411032\pi$
$464$	9.96230			0.462488
$465$	14.9926	+	16.0239i	0.695267	+	0.743089i
$466$	22.0888			1.02324
$467$		−	8.74440i		−	0.404643i	−0.979319	−	0.202321i	$-0.935151\pi$
$467$		−	8.74440i		−	0.404643i	0.979319	−	0.202321i	$-0.0648485\pi$
$468$		−	1.56282i		−	0.0722412i
$469$	11.9779			0.553089
$470$	5.97093	−	5.58667i	0.275418	−	0.257694i
$471$	−23.8566			−1.09925
$472$		−	2.11612i		−	0.0974023i
$473$		−	5.44670i		−	0.250439i
$474$	13.5698			0.623282
$475$	2.07321	−	31.1443i	0.0951253	−	1.42900i
$476$	0.210157			0.00963254
$477$		−	2.76687i		−	0.126686i
$478$			12.3489i			0.564825i
$479$	4.87437			0.222715			0.111358	−	0.993780i	$-0.464480\pi$
$479$	4.87437			0.222715			0.111358	+	0.993780i	$0.464480\pi$
$480$	−2.30913	+	2.16053i	−0.105397	+	0.0986143i
$481$	0.560678			0.0255647
$482$			11.0659i			0.504036i
$483$		−	12.4320i		−	0.565674i
$484$	−1.00000			−0.0454545
$485$	21.6516	+	23.1409i	0.983150	+	1.05077i
$486$	9.89949			0.449050
$487$			16.3704i			0.741814i	0.928670	+	0.370907i	$0.120953\pi$
$487$			16.3704i			0.741814i	−0.928670	+	0.370907i	$0.879047\pi$
$488$		−	6.71231i		−	0.303852i
$489$	−17.7800			−0.804038
$490$	1.52773	+	1.63280i	0.0690156	+	0.0737626i
$491$	9.39088			0.423804			0.211902	−	0.977291i	$-0.432034\pi$
$491$	9.39088			0.423804			0.211902	+	0.977291i	$0.432034\pi$
$492$		−	6.74138i		−	0.303925i
$493$		−	2.09365i		−	0.0942932i
$494$	−9.75611			−0.438948
$495$	1.63280	−	1.52773i	0.0733891	−	0.0686662i
$496$	6.93933			0.311585
$497$		−	10.2751i		−	0.460902i
$498$			2.21016i			0.0990395i
$499$	−35.6703			−1.59682			−0.798411	−	0.602113i	$-0.794325\pi$
$499$	−35.6703			−1.59682			−0.798411	+	0.602113i	$0.794325\pi$
$500$	−7.07950	−	8.65336i	−0.316605	−	0.386990i
$501$	−18.5208			−0.827448
$502$			21.9488i			0.979625i
$503$		−	0.313688i		−	0.0139867i	−0.999976	−	0.00699333i	$-0.997774\pi$
$503$		−	0.313688i		−	0.0139867i	0.999976	−	0.00699333i	$-0.00222606\pi$
$504$	−1.00000			−0.0445435
$505$	16.2135	−	15.1700i	0.721489	−	0.675058i
$506$	8.79073			0.390796
$507$		−	14.9307i		−	0.663096i
$508$		−	1.07232i		−	0.0475766i
$509$	−0.0922646			−0.00408956			−0.00204478	−	0.999998i	$-0.500651\pi$
$509$	−0.0922646			−0.00408956			−0.00204478	+	0.999998i	$0.500651\pi$
$510$	0.454051	+	0.485281i	0.0201057	+	0.0214886i
$511$	−6.02386			−0.266480
$512$			1.00000i			0.0441942i
$513$		−	35.3137i		−	1.55914i
$514$	3.93845			0.173717
$515$	16.7123	+	17.8618i	0.736432	+	0.787085i
$516$	−7.70279			−0.339097
$517$		−	3.65685i		−	0.160828i
$518$		−	0.358761i		−	0.0157630i
$519$	0.652007			0.0286199
$520$	−2.55178	+	2.38756i	−0.111903	+	0.104701i
$521$	−12.2850			−0.538216			−0.269108	−	0.963110i	$-0.586729\pi$
$521$	−12.2850			−0.538216			−0.269108	+	0.963110i	$0.586729\pi$
$522$			9.96230i			0.436038i
$523$			2.46841i			0.107936i	0.998543	+	0.0539681i	$0.0171869\pi$
$523$			2.46841i			0.107936i	−0.998543	+	0.0539681i	$0.982813\pi$
$524$	21.8700			0.955397
$525$	−0.469666	+	7.05545i	−0.0204979	+	0.307925i
$526$	−1.77996			−0.0776100
$527$		−	1.45835i		−	0.0635268i
$528$			1.41421i			0.0615457i
$529$	−54.2769			−2.35987
$530$	−4.51776	+	4.22703i	−0.196239	+	0.183610i
$531$	2.11612			0.0918318
$532$			6.24264i			0.270653i
$533$		−	7.44975i		−	0.322685i
$534$	−12.1568			−0.526078
$535$	−19.6348	−	20.9853i	−0.848885	−	0.907272i
$536$	11.9779			0.517367
$537$		−	6.64035i		−	0.286552i
$538$			19.0555i			0.821539i
$539$	1.00000			0.0430730
$540$	−8.64213	−	9.23654i	−0.371898	−	0.397477i
$541$	−38.8991			−1.67240			−0.836202	−	0.548421i	$-0.815229\pi$
$541$	−38.8991			−1.67240			−0.836202	+	0.548421i	$0.815229\pi$
$542$		−	12.5190i		−	0.537738i
$543$			21.8548i			0.937880i
$544$	0.210157			0.00901042
$545$	23.5901	−	22.0720i	1.01049	−	0.945459i
$546$	2.21016			0.0945860
$547$		−	34.2548i		−	1.46463i	−0.680966	−	0.732315i	$-0.738440\pi$
$547$		−	34.2548i		−	1.46463i	0.680966	−	0.732315i	$-0.261560\pi$
$548$			8.22181i			0.351218i
$549$	6.71231			0.286474
$550$	−4.98896	−	0.332104i	−0.212730	−	0.0141610i
$551$	62.1911			2.64943
$552$		−	12.4320i		−	0.529140i
$553$		−	9.59530i		−	0.408034i
$554$	2.75126			0.116890
$555$	0.828427	−	0.775114i	0.0351648	−	0.0329018i
$556$	9.71319			0.411931
$557$			29.2383i			1.23887i	0.785049	+	0.619434i	$0.212638\pi$
$557$			29.2383i			1.23887i	−0.785049	+	0.619434i	$0.787362\pi$
$558$			6.93933i			0.293765i
$559$	−8.51219			−0.360027
$560$	1.52773	+	1.63280i	0.0645582	+	0.0689986i
$561$	0.297207			0.0125481
$562$			9.75050i			0.411300i
$563$			26.8783i			1.13279i	0.824136	+	0.566393i	$0.191661\pi$
$563$			26.8783i			1.13279i	−0.824136	+	0.566393i	$0.808339\pi$
$564$	−5.17157			−0.217763
$565$	−8.49050	−	9.07448i	−0.357198	−	0.381766i
$566$	−26.1608			−1.09962
$567$			5.00000i			0.209980i
$568$		−	10.2751i		−	0.431135i
$569$	−6.92945			−0.290498			−0.145249	−	0.989395i	$-0.546398\pi$
$569$	−6.92945			−0.290498			−0.145249	+	0.989395i	$0.546398\pi$
$570$	−14.4151	+	13.4874i	−0.603782	+	0.564926i
$571$	29.3155			1.22681			0.613407	−	0.789767i	$-0.289798\pi$
$571$	29.3155			1.22681			0.613407	+	0.789767i	$0.289798\pi$
$572$			1.56282i			0.0653447i
$573$			20.7825i			0.868201i
$574$	−4.76687			−0.198965
$575$	43.8566	+	2.91944i	1.82895	+	0.121749i
$576$	−1.00000			−0.0416667
$577$		−	4.09278i		−	0.170385i	−0.996365	−	0.0851924i	$-0.972850\pi$
$577$		−	4.09278i		−	0.170385i	0.996365	−	0.0851924i	$-0.0271505\pi$
$578$			16.9558i			0.705270i
$579$	25.8449			1.07408
$580$	16.2665	−	15.2197i	0.675429	−	0.631962i
$581$	1.56282			0.0648366
$582$		−	20.0429i		−	0.830804i
$583$			2.76687i			0.114592i
$584$	−6.02386			−0.249269
$585$	−2.38756	−	2.55178i	−0.0987133	−	0.105503i
$586$	−0.814065			−0.0336287
$587$		−	42.7157i		−	1.76307i	−0.472122	−	0.881533i	$-0.656512\pi$
$587$		−	42.7157i		−	1.76307i	0.472122	−	0.881533i	$-0.343488\pi$
$588$		−	1.41421i		−	0.0583212i
$589$	43.3198			1.78496
$590$	−3.23285	−	3.45521i	−0.133094	−	0.142249i
$591$	28.1127			1.15640
$592$		−	0.358761i		−	0.0147450i
$593$		−	1.86952i		−	0.0767719i	−0.999263	−	0.0383860i	$-0.987778\pi$
$593$		−	1.86952i		−	0.0767719i	0.999263	−	0.0383860i	$-0.0122216\pi$
$594$	−5.65685			−0.232104
$595$	0.343146	−	0.321063i	0.0140676	−	0.0131623i
$596$	−5.02297			−0.205749
$597$		−	32.2358i		−	1.31932i
$598$		−	13.7383i		−	0.561801i
$599$	13.5264			0.552673			0.276336	−	0.961061i	$-0.410880\pi$
$599$	13.5264			0.552673			0.276336	+	0.961061i	$0.410880\pi$
$600$	−0.469666	+	7.05545i	−0.0191740	+	0.288038i
$601$	−11.9714			−0.488326			−0.244163	−	0.969734i	$-0.578513\pi$
$601$	−11.9714			−0.488326			−0.244163	+	0.969734i	$0.578513\pi$
$602$			5.44670i			0.221991i
$603$			11.9779i			0.487778i
$604$	−2.56892			−0.104528
$605$	−1.63280	+	1.52773i	−0.0663830	+	0.0621109i
$606$	−14.0429			−0.570453
$607$		−	8.99265i		−	0.365000i	−0.983206	−	0.182500i	$-0.941581\pi$
$607$		−	8.99265i		−	0.365000i	0.983206	−	0.182500i	$-0.0584190\pi$
$608$			6.24264i			0.253173i
$609$	−14.0888			−0.570908
$610$	−10.2546	−	10.9599i	−0.415195	−	0.443753i
$611$	−5.71499			−0.231204
$612$			0.210157i			0.00849510i
$613$		−	8.56245i		−	0.345834i	−0.984936	−	0.172917i	$-0.944681\pi$
$613$		−	8.56245i		−	0.345834i	0.984936	−	0.172917i	$-0.0553193\pi$
$614$	−24.8593			−1.00324
$615$	−10.2990	−	11.0074i	−0.415295	−	0.443859i
$616$	1.00000			0.0402911
$617$		−	3.97614i		−	0.160074i	−0.996792	−	0.0800368i	$-0.974496\pi$
$617$		−	3.97614i		−	0.160074i	0.996792	−	0.0800368i	$-0.0255038\pi$
$618$		−	15.4706i		−	0.622317i
$619$	−39.0450			−1.56935			−0.784676	−	0.619906i	$-0.787171\pi$
$619$	−39.0450			−1.56935			−0.784676	+	0.619906i	$0.787171\pi$
$620$	11.3306	−	10.6014i	0.455047	−	0.425763i
$621$	49.7279			1.99551
$622$		−	13.6447i		−	0.547101i
$623$			8.59619i			0.344399i
$624$	2.21016			0.0884771
$625$	−24.7794	−	3.31371i	−0.991177	−	0.132548i
$626$	22.3943			0.895055
$627$			8.82843i			0.352573i
$628$			16.8692i			0.673152i
$629$	−0.0753962			−0.00300624
$630$	−1.63280	+	1.52773i	−0.0650525	+	0.0608661i
$631$	−28.2769			−1.12569			−0.562843	−	0.826564i	$-0.690292\pi$
$631$	−28.2769			−1.12569			−0.562843	+	0.826564i	$0.690292\pi$
$632$		−	9.59530i		−	0.381681i
$633$			19.5797i			0.778223i
$634$	−19.3753			−0.769490
$635$	−1.63821	−	1.75089i	−0.0650105	−	0.0694820i
$636$	3.91295			0.155159
$637$		−	1.56282i		−	0.0619211i
$638$		−	9.96230i		−	0.394411i
$639$	10.2751			0.406478
$640$	1.52773	+	1.63280i	0.0603887	+	0.0645423i
$641$	−6.78909			−0.268153			−0.134076	−	0.990971i	$-0.542807\pi$
$641$	−6.78909			−0.268153			−0.134076	+	0.990971i	$0.542807\pi$
$642$			18.1759i			0.717344i
$643$			12.7861i			0.504233i	0.967697	+	0.252117i	$0.0811266\pi$
$643$			12.7861i			0.504233i	−0.967697	+	0.252117i	$0.918873\pi$
$644$	−8.79073			−0.346403
$645$	−12.5772	+	11.7678i	−0.495225	+	0.463355i
$646$	1.31194			0.0516174
$647$		−	34.0312i		−	1.33791i	−0.743305	−	0.668953i	$-0.766743\pi$
$647$		−	34.0312i		−	1.33791i	0.743305	−	0.668953i	$-0.233257\pi$
$648$			5.00000i			0.196419i
$649$	−2.11612			−0.0830650
$650$	−0.519018	+	7.79683i	−0.0203576	+	0.305817i
$651$	−9.81370			−0.384629
$652$			12.5723i			0.492370i
$653$		−	6.01812i		−	0.235507i	−0.993043	−	0.117754i	$-0.962431\pi$
$653$		−	6.01812i		−	0.235507i	0.993043	−	0.117754i	$-0.0375693\pi$
$654$	−20.4320			−0.798953
$655$	35.7095	−	33.4114i	1.39529	−	1.30549i
$656$	−4.76687			−0.186115
$657$		−	6.02386i		−	0.235013i
$658$			3.65685i			0.142559i
$659$	−16.9498			−0.660269			−0.330134	−	0.943934i	$-0.607094\pi$
$659$	−16.9498			−0.660269			−0.330134	+	0.943934i	$0.607094\pi$
$660$	2.16053	+	2.30913i	0.0840986	+	0.0898830i
$661$	40.0714			1.55860			0.779299	−	0.626653i	$-0.215576\pi$
$661$	40.0714			1.55860			0.779299	+	0.626653i	$0.215576\pi$
$662$		−	33.1391i		−	1.28799i
$663$		−	0.464480i		−	0.0180389i
$664$	1.56282			0.0606491
$665$	9.53705	+	10.1930i	0.369831	+	0.395268i
$666$	0.358761			0.0139017
$667$			87.5759i			3.39095i
$668$			13.0962i			0.506706i
$669$	−15.7365			−0.608409
$670$	19.5576	−	18.2990i	0.755576	−	0.706951i
$671$	−6.71231			−0.259126
$672$		−	1.41421i		−	0.0545545i
$673$		−	24.4797i		−	0.943622i	−0.881700	−	0.471811i	$-0.843600\pi$
$673$		−	24.4797i		−	0.943622i	0.881700	−	0.471811i	$-0.156400\pi$
$674$	9.62740			0.370833
$675$	−28.2218	−	1.87867i	−1.08626	−	0.0723099i
$676$	−10.5576			−0.406062
$677$		−	33.0788i		−	1.27132i	−0.771969	−	0.635660i	$-0.780728\pi$
$677$		−	33.0788i		−	1.27132i	0.771969	−	0.635660i	$-0.219272\pi$
$678$			7.85964i			0.301848i
$679$	−14.1725			−0.543889
$680$	0.343146	−	0.321063i	0.0131590	−	0.0123122i
$681$	24.0447			0.921393
$682$		−	6.93933i		−	0.265721i
$683$		−	33.6175i		−	1.28634i	−0.765724	−	0.643169i	$-0.777619\pi$
$683$		−	33.6175i		−	1.28634i	0.765724	−	0.643169i	$-0.222381\pi$
$684$	−6.24264			−0.238693
$685$	12.5607	+	13.4246i	0.479919	+	0.512928i
$686$	−1.00000			−0.0381802
$687$			20.9155i			0.797975i
$688$			5.44670i			0.207653i
$689$	4.32412			0.164736
$690$	−18.9926	−	20.2990i	−0.723038	−	0.772769i
$691$	16.7877			0.638634			0.319317	−	0.947648i	$-0.396546\pi$
$691$	16.7877			0.638634			0.319317	+	0.947648i	$0.396546\pi$
$692$		−	0.461038i		−	0.0175260i
$693$			1.00000i			0.0379869i
$694$	−29.9147			−1.13555
$695$	15.8598	−	14.8391i	0.601595	−	0.562879i
$696$	−14.0888			−0.534035
$697$			1.00179i			0.0379456i
$698$			8.89861i			0.336817i
$699$	−31.2383			−1.18154
$700$	4.98896	+	0.332104i	0.188565	+	0.0125524i
$701$	−4.99606			−0.188699			−0.0943493	−	0.995539i	$-0.530077\pi$
$701$	−4.99606			−0.188699			−0.0943493	+	0.995539i	$0.530077\pi$
$702$			8.84063i			0.333668i
$703$		−	2.23961i		−	0.0844687i
$704$	1.00000			0.0376889
$705$	−8.44417	+	7.90075i	−0.318026	+	0.297559i
$706$	13.6265			0.512841
$707$			9.92982i			0.373449i
$708$			2.99265i			0.112471i
$709$	13.3310			0.500655			0.250327	−	0.968161i	$-0.419462\pi$
$709$	13.3310			0.500655			0.250327	+	0.968161i	$0.419462\pi$
$710$	−15.6976	−	16.7773i	−0.589120	−	0.629640i
$711$	9.59530			0.359852
$712$			8.59619i			0.322156i
$713$			61.0018i			2.28454i
$714$	−0.297207			−0.0111227
$715$	2.38756	+	2.55178i	0.0892896	+	0.0954310i
$716$	−4.69544			−0.175477
$717$		−	17.4640i		−	0.652203i
$718$			23.2110i			0.866228i
$719$	6.39823			0.238614			0.119307	−	0.992857i	$-0.461933\pi$
$719$	6.39823			0.238614			0.119307	+	0.992857i	$0.461933\pi$
$720$	−1.63280	+	1.52773i	−0.0608510	+	0.0569350i
$721$	−10.9393			−0.407402
$722$			19.9706i			0.743227i
$723$		−	15.6495i		−	0.582010i
$724$	15.4537			0.574332
$725$	3.30852	−	49.7015i	0.122875	−	1.84587i
$726$	1.41421			0.0524864
$727$		−	2.00000i		−	0.0741759i	−0.999312	−	0.0370879i	$-0.988192\pi$
$727$		−	2.00000i		−	0.0741759i	0.999312	−	0.0370879i	$-0.0118082\pi$
$728$		−	1.56282i		−	0.0579219i
$729$	−29.0000			−1.07407
$730$	−9.83578	+	9.20280i	−0.364039	+	0.340611i
$731$	1.14466			0.0423369
$732$			9.49264i			0.350858i
$733$		−	22.4463i		−	0.829074i	−0.910032	−	0.414537i	$-0.863944\pi$
$733$		−	22.4463i		−	0.829074i	0.910032	−	0.414537i	$-0.136056\pi$
$734$	−9.84316			−0.363318
$735$	−2.16053	−	2.30913i	−0.0796924	−	0.0851737i
$736$	−8.79073			−0.324031
$737$		−	11.9779i		−	0.441212i
$738$		−	4.76687i		−	0.175471i
$739$	37.6127			1.38361			0.691803	−	0.722087i	$-0.256817\pi$
$739$	37.6127			1.38361			0.691803	+	0.722087i	$0.256817\pi$
$740$	−0.548088	−	0.585786i	−0.0201481	−	0.0215339i
$741$	13.7972			0.506853
$742$		−	2.76687i		−	0.101575i
$743$		−	23.4779i		−	0.861322i	−0.902514	−	0.430661i	$-0.858281\pi$
$743$		−	23.4779i		−	0.861322i	0.902514	−	0.430661i	$-0.141719\pi$
$744$	−9.81370			−0.359788
$745$	−8.20153	+	7.67372i	−0.300481	+	0.281143i
$746$	−4.71929			−0.172786
$747$			1.56282i			0.0571805i
$748$		−	0.210157i		−	0.00768411i
$749$	12.8523			0.469612
$750$	10.0119	+	12.2377i	0.365584	+	0.446858i
$751$	10.9540			0.399719			0.199859	−	0.979825i	$-0.435951\pi$
$751$	10.9540			0.399719			0.199859	+	0.979825i	$0.435951\pi$
$752$			3.65685i			0.133352i
$753$		−	31.0404i		−	1.13117i
$754$	−15.5693			−0.566999
$755$	−4.19454	+	3.92460i	−0.152655	+	0.142831i
$756$	5.65685			0.205738
$757$		−	4.62223i		−	0.167998i	−0.996466	−	0.0839989i	$-0.973231\pi$
$757$		−	4.62223i		−	0.167998i	0.996466	−	0.0839989i	$-0.0267692\pi$
$758$		−	21.6906i		−	0.787838i
$759$	−12.4320			−0.451252
$760$	9.53705	+	10.1930i	0.345945	+	0.369740i
$761$	−42.6932			−1.54763			−0.773815	−	0.633412i	$-0.781654\pi$
$761$	−42.6932			−1.54763			−0.773815	+	0.633412i	$0.781654\pi$
$762$			1.51649i			0.0549367i
$763$			14.4476i			0.523038i
$764$	14.6954			0.531662
$765$	0.321063	+	0.343146i	0.0116080	+	0.0124065i
$766$	−20.1759			−0.728984
$767$			3.30711i			0.119413i
$768$		−	1.41421i		−	0.0510310i
$769$	−48.9133			−1.76386			−0.881929	−	0.471382i	$-0.843755\pi$
$769$	−48.9133			−1.76386			−0.881929	+	0.471382i	$0.843755\pi$
$770$	1.63280	−	1.52773i	0.0588422	−	0.0550554i
$771$	−5.56980			−0.200592
$772$		−	18.2751i		−	0.657736i
$773$			48.4801i			1.74371i	0.489767	+	0.871853i	$0.337082\pi$
$773$			48.4801i			1.74371i	−0.489767	+	0.871853i	$0.662918\pi$
$774$	−5.44670			−0.195777
$775$	2.30458	−	34.6200i	0.0827830	−	1.24359i
$776$	−14.1725			−0.508762
$777$			0.507364i			0.0182016i
$778$			15.3769i			0.551289i
$779$	−29.7579			−1.06619
$780$	3.60876	−	3.37652i	0.129214	−	0.120899i
$781$	−10.2751			−0.367673
$782$			1.84744i			0.0660641i
$783$		−	56.3553i		−	2.01397i
$784$	−1.00000			−0.0357143
$785$	25.7714	+	27.5440i	0.919822	+	0.983089i
$786$	−30.9289			−1.10320
$787$			10.5021i			0.374361i	0.982326	+	0.187181i	$0.0599350\pi$
$787$			10.5021i			0.374361i	−0.982326	+	0.187181i	$0.940065\pi$
$788$		−	19.8787i		−	0.708148i
$789$	2.51725			0.0896163
$790$	−14.6590	−	15.6673i	−0.521544	−	0.557416i
$791$	5.55760			0.197606
$792$			1.00000i			0.0355335i
$793$			10.4901i			0.372515i
$794$	−1.42983			−0.0507427
$795$	6.38908	−	5.97792i	0.226597	−	0.212015i
$796$	−22.7941			−0.807917
$797$		−	37.1872i		−	1.31724i	−0.752477	−	0.658618i	$-0.771141\pi$
$797$		−	37.1872i		−	1.31724i	0.752477	−	0.658618i	$-0.228859\pi$
$798$		−	8.82843i		−	0.312523i
$799$	0.768514			0.0271881
$800$	4.98896	+	0.332104i	0.176386	+	0.0117417i
$801$	−8.59619			−0.303731
$802$		−	32.3761i		−	1.14324i
$803$			6.02386i			0.212577i
$804$	−16.9393			−0.597404
$805$	−14.3535	+	13.4298i	−0.505896	+	0.473339i
$806$	−10.8449			−0.381996
$807$		−	26.9485i		−	0.948631i
$808$			9.92982i			0.349330i
$809$	−43.5403			−1.53080			−0.765399	−	0.643557i	$-0.777458\pi$
$809$	−43.5403			−1.53080			−0.765399	+	0.643557i	$0.777458\pi$
$810$	7.63863	+	8.16402i	0.268394	+	0.286855i
$811$	−47.0147			−1.65091			−0.825455	−	0.564468i	$-0.809081\pi$
$811$	−47.0147			−1.65091			−0.825455	+	0.564468i	$0.809081\pi$
$812$			9.96230i			0.349608i
$813$			17.7046i			0.620926i
$814$	−0.358761			−0.0125746
$815$	19.2071	+	20.5282i	0.672795	+	0.719070i
$816$	−0.297207			−0.0104043
$817$			34.0018i			1.18957i
$818$			19.1100i			0.668166i
$819$	1.56282			0.0546093
$820$	−7.78337	+	7.28248i	−0.271807	+	0.254315i
$821$	−42.5126			−1.48370			−0.741849	−	0.670567i	$-0.766051\pi$
$821$	−42.5126			−1.48370			−0.741849	+	0.670567i	$0.766051\pi$
$822$		−	11.6274i		−	0.405552i
$823$			23.9262i			0.834016i	0.908903	+	0.417008i	$0.136921\pi$
$823$			23.9262i			0.834016i	−0.908903	+	0.417008i	$0.863079\pi$
$824$	−10.9393			−0.381090
$825$	7.05545	+	0.469666i	0.245639	+	0.0163517i
$826$	2.11612			0.0736292
$827$			12.5944i			0.437951i	0.975730	+	0.218975i	$0.0702714\pi$
$827$			12.5944i			0.437951i	−0.975730	+	0.218975i	$0.929729\pi$
$828$		−	8.79073i		−	0.305499i
$829$	−11.6836			−0.405788			−0.202894	−	0.979201i	$-0.565035\pi$
$829$	−11.6836			−0.405788			−0.202894	+	0.979201i	$0.565035\pi$
$830$	2.55178	−	2.38756i	0.0885734	−	0.0828733i
$831$	−3.89087			−0.134973
$832$		−	1.56282i		−	0.0541809i
$833$			0.210157i			0.00728152i
$834$	−13.7365			−0.475657
$835$	20.0074	+	21.3835i	0.692384	+	0.740007i
$836$	6.24264			0.215906
$837$		−	39.2548i		−	1.35684i
$838$			34.7453i			1.20026i
$839$	−40.3302			−1.39235			−0.696177	−	0.717870i	$-0.745117\pi$
$839$	−40.3302			−1.39235			−0.696177	+	0.717870i	$0.745117\pi$
$840$	−2.16053	−	2.30913i	−0.0745454	−	0.0796727i
$841$	70.2475			2.42233
$842$			22.3787i			0.771219i
$843$		−	13.7893i		−	0.474929i
$844$	13.8449			0.476562
$845$	−17.2385	+	16.1291i	−0.593023	+	0.554859i
$846$	−3.65685			−0.125725
$847$		−	1.00000i		−	0.0343604i
$848$		−	2.76687i		−	0.0950148i
$849$	36.9969			1.26973
$850$	0.0697941	−	1.04847i	0.00239392	−	0.0359621i
$851$	3.15377			0.108110
$852$			14.5312i			0.497831i
$853$			30.2920i			1.03718i	0.855024	+	0.518589i	$0.173543\pi$
$853$			30.2920i			1.03718i	−0.855024	+	0.518589i	$0.826457\pi$
$854$	6.71231			0.229690
$855$	−10.1930	+	9.53705i	−0.348594	+	0.326160i
$856$	12.8523			0.439282
$857$		−	34.0134i		−	1.16188i	−0.813948	−	0.580938i	$-0.802686\pi$
$857$		−	34.0134i		−	1.16188i	0.813948	−	0.580938i	$-0.197314\pi$
$858$		−	2.21016i		−	0.0754535i
$859$	19.3250			0.659360			0.329680	−	0.944093i	$-0.393059\pi$
$859$	19.3250			0.659360			0.329680	+	0.944093i	$0.393059\pi$
$860$	8.32106	+	8.89339i	0.283746	+	0.303262i
$861$	6.74138			0.229746
$862$		−	12.6971i		−	0.432464i
$863$		−	23.2331i		−	0.790865i	−0.918495	−	0.395432i	$-0.870595\pi$
$863$		−	23.2331i		−	0.790865i	0.918495	−	0.395432i	$-0.129405\pi$
$864$	5.65685			0.192450
$865$	−0.704340	−	0.752786i	−0.0239483	−	0.0255955i
$866$	−15.0131			−0.510165
$867$		−	23.9792i		−	0.814375i
$868$			6.93933i			0.235536i
$869$	−9.59530			−0.325498
$870$	−23.0043	+	21.5239i	−0.779919	+	0.729727i
$871$	−18.7193			−0.634279
$872$			14.4476i			0.489257i
$873$		−	14.1725i		−	0.479665i
$874$	−54.8774			−1.85625
$875$	8.65336	−	7.07950i	0.292537	−	0.239331i
$876$	8.51902			0.287831
$877$		−	2.37260i		−	0.0801171i	−0.999197	−	0.0400586i	$-0.987246\pi$
$877$		−	2.37260i		−	0.0801171i	0.999197	−	0.0400586i	$-0.0127544\pi$
$878$		−	4.29721i		−	0.145024i
$879$	1.15126			0.0388311
$880$	1.63280	−	1.52773i	0.0550418	−	0.0514996i
$881$	10.6665			0.359364			0.179682	−	0.983725i	$-0.442493\pi$
$881$	10.6665			0.359364			0.179682	+	0.983725i	$0.442493\pi$
$882$		−	1.00000i		−	0.0336718i
$883$		−	33.1018i		−	1.11396i	−0.830525	−	0.556982i	$-0.811959\pi$
$883$		−	33.1018i		−	1.11396i	0.830525	−	0.556982i	$-0.188041\pi$
$884$	−0.328437			−0.0110465
$885$	4.57194	+	4.88641i	0.153684	+	0.164255i
$886$	41.8228			1.40507
$887$			18.4246i			0.618637i	0.950958	+	0.309319i	$0.100101\pi$
$887$			18.4246i			0.618637i	−0.950958	+	0.309319i	$0.899899\pi$
$888$			0.507364i			0.0170260i
$889$	1.07232			0.0359645
$890$	13.1326	+	14.0359i	0.440206	+	0.470484i
$891$	5.00000			0.167506
$892$			11.1274i			0.372573i
$893$			22.8284i			0.763924i
$894$	7.10355			0.237578
$895$	−7.66674	+	7.17335i	−0.256271	+	0.239778i
$896$	−1.00000			−0.0334077
$897$			19.4289i			0.648712i
$898$		−	15.4804i		−	0.516589i
$899$	69.1317			2.30567
$900$	−0.332104	+	4.98896i	−0.0110701	+	0.166299i
$901$	−0.581478			−0.0193719
$902$			4.76687i			0.158720i
$903$		−	7.70279i		−	0.256333i
$904$	5.55760			0.184843
$905$	25.2329	−	23.6090i	0.838768	−	0.784790i
$906$	3.63300			0.120698
$907$		−	2.13048i		−	0.0707415i	−0.999374	−	0.0353707i	$-0.988739\pi$
$907$		−	2.13048i		−	0.0707415i	0.999374	−	0.0353707i	$-0.0112612\pi$
$908$		−	17.0021i		−	0.564236i
$909$	−9.92982			−0.329351
$910$	−2.38756	−	2.55178i	−0.0791467	−	0.0845905i
$911$	−18.0330			−0.597460			−0.298730	−	0.954338i	$-0.596563\pi$
$911$	−18.0330			−0.597460			−0.298730	+	0.954338i	$0.596563\pi$
$912$		−	8.82843i		−	0.292338i
$913$		−	1.56282i		−	0.0517217i
$914$	34.5980			1.14440
$915$	14.5021	+	15.4996i	0.479426	+	0.512402i
$916$	14.7895			0.488658
$917$			21.8700i			0.722212i
$918$		−	1.18883i		−	0.0392372i
$919$	31.1326			1.02697			0.513485	−	0.858099i	$-0.328354\pi$
$919$	31.1326			1.02697			0.513485	+	0.858099i	$0.328354\pi$
$920$	−14.3535	+	13.4298i	−0.473222	+	0.442768i
$921$	35.1563			1.15844
$922$		−	30.8250i		−	1.01517i
$923$			16.0581i			0.528560i
$924$	−1.41421			−0.0465242
$925$	−1.78984	−	0.119146i	−0.0588497	−	0.00391750i
$926$	41.3648			1.35933
$927$		−	10.9393i		−	0.359295i
$928$			9.96230i			0.327029i
$929$	−40.0911			−1.31535			−0.657674	−	0.753303i	$-0.728459\pi$
$929$	−40.0911			−1.31535			−0.657674	+	0.753303i	$0.728459\pi$
$930$	−16.0239	+	14.9926i	−0.525443	+	0.491628i
$931$	−6.24264			−0.204594
$932$			22.0888i			0.723543i
$933$			19.2965i			0.631737i
$934$	8.74440			0.286126
$935$	−0.321063	−	0.343146i	−0.0104999	−	0.0112221i
$936$	1.56282			0.0510823
$937$		−	2.48834i		−	0.0812904i	−0.999174	−	0.0406452i	$-0.987059\pi$
$937$		−	2.48834i		−	0.0812904i	0.999174	−	0.0406452i	$-0.0129413\pi$
$938$			11.9779i			0.391093i
$939$	−31.6703			−1.03352
$940$	5.58667	+	5.97093i	0.182217	+	0.194750i
$941$	−23.3300			−0.760537			−0.380269	−	0.924876i	$-0.624168\pi$
$941$	−23.3300			−0.760537			−0.380269	+	0.924876i	$0.624168\pi$
$942$		−	23.8566i		−	0.777289i
$943$		−	41.9043i		−	1.36459i
$944$	2.11612			0.0688738
$945$	9.23654	−	8.64213i	0.300465	−	0.281128i
$946$	5.44670			0.177087
$947$			25.6556i			0.833694i	0.908977	+	0.416847i	$0.136865\pi$
$947$			25.6556i			0.833694i	−0.908977	+	0.416847i	$0.863135\pi$
$948$			13.5698i			0.440727i
$949$	9.41418			0.305597
$950$	31.1443	+	2.07321i	1.01045	+	0.0672637i
$951$	27.4008			0.888530
$952$			0.210157i			0.00681123i
$953$		−	9.07970i		−	0.294120i	−0.989128	−	0.147060i	$-0.953019\pi$
$953$		−	9.07970i		−	0.294120i	0.989128	−	0.147060i	$-0.0469811\pi$
$954$	2.76687			0.0895808
$955$	23.9948	−	22.4506i	0.776453	−	0.726485i
$956$	−12.3489			−0.399391
$957$			14.0888i			0.455427i
$958$			4.87437i			0.157484i
$959$	−8.22181			−0.265496
$960$	−2.16053	−	2.30913i	−0.0697308	−	0.0745270i
$961$	17.1543			0.553366
$962$			0.560678i			0.0180770i
$963$			12.8523i			0.414159i
$964$	−11.0659			−0.356407
$965$	−27.9194	−	29.8397i	−0.898757	−	0.960574i
$966$	12.4320			0.399992
$967$			52.3419i			1.68320i	0.540101	+	0.841600i	$0.318386\pi$
$967$			52.3419i			1.68320i	−0.540101	+	0.841600i	$0.681614\pi$
$968$		−	1.00000i		−	0.0321412i
$969$	−1.85536			−0.0596027
$970$	−23.1409	+	21.6516i	−0.743008	+	0.695192i
$971$	23.2600			0.746449			0.373225	−	0.927741i	$-0.378252\pi$
$971$	23.2600			0.746449			0.373225	+	0.927741i	$0.378252\pi$
$972$			9.89949i			0.317526i
$973$			9.71319i			0.311391i
$974$	−16.3704			−0.524542
$975$	0.734003	−	11.0264i	0.0235069	−	0.353127i
$976$	6.71231			0.214856
$977$		−	48.4436i		−	1.54985i	−0.632054	−	0.774924i	$-0.717788\pi$
$977$		−	48.4436i		−	1.54985i	0.632054	−	0.774924i	$-0.282212\pi$
$978$		−	17.7800i		−	0.568540i
$979$	8.59619			0.274735
$980$	−1.63280	+	1.52773i	−0.0521580	+	0.0488014i
$981$	−14.4476			−0.461276
$982$			9.39088i			0.299675i
$983$		−	2.25304i		−	0.0718609i	−0.999354	−	0.0359304i	$-0.988561\pi$
$983$		−	2.25304i		−	0.0718609i	0.999354	−	0.0359304i	$-0.0114395\pi$
$984$	6.74138			0.214907
$985$	−30.3692	−	32.4580i	−0.967642	−	1.03420i
$986$	2.09365			0.0666754
$987$		−	5.17157i		−	0.164613i
$988$		−	9.75611i		−	0.310383i
$989$	−47.8804			−1.52251
$990$	1.52773	+	1.63280i	0.0485543	+	0.0518939i
$991$	27.8254			0.883901			0.441951	−	0.897039i	$-0.354287\pi$
$991$	27.8254			0.883901			0.441951	+	0.897039i	$0.354287\pi$
$992$			6.93933i			0.220324i
$993$			46.8657i			1.48724i
$994$	10.2751			0.325907
$995$	−37.2184	+	34.8232i	−1.17990	+	1.10397i
$996$	−2.21016			−0.0700315
$997$		−	39.9966i		−	1.26670i	−0.773864	−	0.633352i	$-0.781679\pi$
$997$		−	39.9966i		−	1.26670i	0.773864	−	0.633352i	$-0.218321\pi$
$998$		−	35.6703i		−	1.12912i
$999$	−2.02946			−0.0642092

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.c.e.309.5	yes	8
5.2	odd	4		3850.2.a.bx.1.1		4
5.3	odd	4		3850.2.a.by.1.4		4
5.4	even	2	inner	770.2.c.e.309.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.c.e.309.3	✓	8	5.4	even	2	inner
770.2.c.e.309.5	yes	8	1.1	even	1	trivial
3850.2.a.bx.1.1		4	5.2	odd	4
3850.2.a.by.1.4		4	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.41421i q^{3} -1.00000 q^{4} +(-1.63280 + 1.52773i) q^{5} +1.41421 q^{6} -1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.41421i q^{3} -1.00000 q^{4} +(-1.63280 + 1.52773i) q^{5} +1.41421 q^{6} -1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} +(-1.52773 - 1.63280i) q^{10} -1.00000 q^{11} +1.41421i q^{12} +1.56282i q^{13} +1.00000 q^{14} +(2.16053 + 2.30913i) q^{15} +1.00000 q^{16} -0.210157i q^{17} +1.00000i q^{18} +6.24264 q^{19} +(1.63280 - 1.52773i) q^{20} -1.41421 q^{21} -1.00000i q^{22} +8.79073i q^{23} -1.41421 q^{24} +(0.332104 - 4.98896i) q^{25} -1.56282 q^{26} -5.65685i q^{27} +1.00000i q^{28} +9.96230 q^{29} +(-2.30913 + 2.16053i) q^{30} +6.93933 q^{31} +1.00000i q^{32} +1.41421i q^{33} +0.210157 q^{34} +(1.52773 + 1.63280i) q^{35} -1.00000 q^{36} -0.358761i q^{37} +6.24264i q^{38} +2.21016 q^{39} +(1.52773 + 1.63280i) q^{40} -4.76687 q^{41} -1.41421i q^{42} +5.44670i q^{43} +1.00000 q^{44} +(-1.63280 + 1.52773i) q^{45} -8.79073 q^{46} +3.65685i q^{47} -1.41421i q^{48} -1.00000 q^{49} +(4.98896 + 0.332104i) q^{50} -0.297207 q^{51} -1.56282i q^{52} -2.76687i q^{53} +5.65685 q^{54} +(1.63280 - 1.52773i) q^{55} -1.00000 q^{56} -8.82843i q^{57} +9.96230i q^{58} +2.11612 q^{59} +(-2.16053 - 2.30913i) q^{60} +6.71231 q^{61} +6.93933i q^{62} -1.00000i q^{63} -1.00000 q^{64} +(-2.38756 - 2.55178i) q^{65} -1.41421 q^{66} +11.9779i q^{67} +0.210157i q^{68} +12.4320 q^{69} +(-1.63280 + 1.52773i) q^{70} +10.2751 q^{71} -1.00000i q^{72} -6.02386i q^{73} +0.358761 q^{74} +(-7.05545 - 0.469666i) q^{75} -6.24264 q^{76} +1.00000i q^{77} +2.21016i q^{78} +9.59530 q^{79} +(-1.63280 + 1.52773i) q^{80} -5.00000 q^{81} -4.76687i q^{82} +1.56282i q^{83} +1.41421 q^{84} +(0.321063 + 0.343146i) q^{85} -5.44670 q^{86} -14.0888i q^{87} +1.00000i q^{88} -8.59619 q^{89} +(-1.52773 - 1.63280i) q^{90} +1.56282 q^{91} -8.79073i q^{92} -9.81370i q^{93} -3.65685 q^{94} +(-10.1930 + 9.53705i) q^{95} +1.41421 q^{96} -14.1725i q^{97} -1.00000i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 4 q^{5} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 4 * q^5 + 8 * q^9	\( 8 q - 8 q^{4} - 4 q^{5} + 8 q^{9} - 8 q^{11} + 8 q^{14} - 4 q^{15} + 8 q^{16} + 16 q^{19} + 4 q^{20} + 4 q^{25} - 8 q^{26} + 24 q^{29} - 4 q^{30} - 16 q^{31} + 8 q^{34} - 8 q^{36} + 24 q^{39} - 16 q^{41} + 8 q^{44} - 4 q^{45} + 8 q^{46} - 8 q^{49} - 4 q^{50} - 16 q^{51} + 4 q^{55} - 8 q^{56} + 64 q^{59} + 4 q^{60} - 16 q^{61} - 8 q^{64} + 4 q^{65} + 8 q^{69} - 4 q^{70} + 8 q^{71} + 16 q^{74} - 32 q^{75} - 16 q^{76} + 32 q^{79} - 4 q^{80} - 40 q^{81} - 40 q^{85} + 8 q^{86} + 48 q^{89} + 8 q^{91} + 16 q^{94} - 20 q^{95} - 8 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 4 * q^5 + 8 * q^9 - 8 * q^11 + 8 * q^14 - 4 * q^15 + 8 * q^16 + 16 * q^19 + 4 * q^20 + 4 * q^25 - 8 * q^26 + 24 * q^29 - 4 * q^30 - 16 * q^31 + 8 * q^34 - 8 * q^36 + 24 * q^39 - 16 * q^41 + 8 * q^44 - 4 * q^45 + 8 * q^46 - 8 * q^49 - 4 * q^50 - 16 * q^51 + 4 * q^55 - 8 * q^56 + 64 * q^59 + 4 * q^60 - 16 * q^61 - 8 * q^64 + 4 * q^65 + 8 * q^69 - 4 * q^70 + 8 * q^71 + 16 * q^74 - 32 * q^75 - 16 * q^76 + 32 * q^79 - 4 * q^80 - 40 * q^81 - 40 * q^85 + 8 * q^86 + 48 * q^89 + 8 * q^91 + 16 * q^94 - 20 * q^95 - 8 * q^99

Introduction

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