LMFDB - Embedded newform 138.2.e.b.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(13,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("138.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.e (of order $11$, degree $10$, 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:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.1
Root			$-0.841254 + 0.540641i$ of defining polynomial
Character	$\chi$	$=$	138.127
Dual form			138.2.e.b.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.186393 - 0.0547299i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-1.27819 - 1.47511i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.186393 - 0.0547299i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-1.27819 - 1.47511i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(0.127214 - 0.146813i) q^{10} +(5.30154 + 3.40709i) q^{11} +(-0.841254 - 0.540641i) q^{12} +(-3.15177 + 3.63733i) q^{13} +(-1.87279 - 0.549899i) q^{14} +(-0.0276463 - 0.192284i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-1.33259 - 2.91797i) q^{17} +(-0.959493 + 0.281733i) q^{18} +(0.357028 - 0.781782i) q^{19} +(0.0276463 - 0.192284i) q^{20} +(-1.64200 + 1.05525i) q^{21} +6.30195 q^{22} +(3.37782 + 3.40446i) q^{23} -1.00000 q^{24} +(-4.17452 + 2.68280i) q^{25} +(-0.684944 + 4.76389i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-1.87279 + 0.549899i) q^{28} +(2.25047 + 4.92785i) q^{29} +(-0.127214 - 0.146813i) q^{30} +(0.144265 + 1.00339i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(4.12690 - 4.76270i) q^{33} +(-2.69862 - 1.73430i) q^{34} +(-0.318978 - 0.204995i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(-6.61126 - 1.94124i) q^{37} +(-0.122312 - 0.850701i) q^{38} +(3.15177 + 3.63733i) q^{39} +(-0.0806993 - 0.176707i) q^{40} +(0.932638 - 0.273847i) q^{41} +(-0.810827 + 1.77546i) q^{42} +(0.731899 - 5.09047i) q^{43} +(5.30154 - 3.40709i) q^{44} -0.194262 q^{45} +(4.68219 + 1.03782i) q^{46} -7.41216 q^{47} +(-0.841254 + 0.540641i) q^{48} +(0.454025 - 3.15781i) q^{49} +(-2.06140 + 4.51383i) q^{50} +(-3.07792 + 0.903759i) q^{51} +(1.99934 + 4.37795i) q^{52} +(-1.31494 - 1.51752i) q^{53} +(0.142315 + 0.989821i) q^{54} +(1.17464 + 0.344905i) q^{55} +(-1.27819 + 1.47511i) q^{56} +(-0.723014 - 0.464653i) q^{57} +(4.55742 + 2.92887i) q^{58} +(5.63325 - 6.50112i) q^{59} +(-0.186393 - 0.0547299i) q^{60} +(-1.72487 - 11.9968i) q^{61} +(0.663836 + 0.766107i) q^{62} +(0.810827 + 1.77546i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-0.388396 + 0.850468i) q^{65} +(0.896861 - 6.23781i) q^{66} +(5.96723 - 3.83491i) q^{67} -3.20786 q^{68} +(3.85052 - 2.85894i) q^{69} -0.379170 q^{70} +(0.933267 - 0.599775i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(-5.47763 + 11.9943i) q^{73} +(-6.61126 + 1.94124i) q^{74} +(2.06140 + 4.51383i) q^{75} +(-0.562819 - 0.649528i) q^{76} +(-1.75054 - 12.1753i) q^{77} +(4.61792 + 1.35595i) q^{78} +(-0.739858 + 0.853842i) q^{79} +(-0.163423 - 0.105026i) q^{80} +(0.841254 + 0.540641i) q^{81} +(0.636532 - 0.734597i) q^{82} +(-3.84482 - 1.12894i) q^{83} +(0.277777 + 1.93198i) q^{84} +(-0.408086 - 0.470956i) q^{85} +(-2.13640 - 4.67807i) q^{86} +(5.19797 - 1.52626i) q^{87} +(2.61792 - 5.73246i) q^{88} +(1.35933 - 9.45436i) q^{89} +(-0.163423 + 0.105026i) q^{90} +9.39402 q^{91} +(4.50000 - 1.65831i) q^{92} +1.01371 q^{93} +(-6.23551 + 4.00732i) q^{94} +(0.0237606 - 0.165259i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(1.07554 - 0.315806i) q^{97} +(-1.32529 - 2.90199i) q^{98} +(-4.12690 - 4.76270i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 - q^8 - q^9	$ 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9} + 9 q^{10} + 11 q^{11} + q^{12} + 13 q^{13} - 11 q^{14} + 13 q^{15} - q^{16} - 24 q^{17} - q^{18} - 14 q^{19} - 13 q^{20} + 11 q^{21} + 22 q^{22} - 10 q^{23} - 10 q^{24} - 43 q^{25} - 9 q^{26} + q^{27} - 11 q^{28} + 13 q^{29} - 9 q^{30} + 8 q^{31} - q^{32} + 22 q^{33} + 9 q^{34} - q^{36} - 13 q^{37} - 3 q^{38} - 13 q^{39} + 9 q^{40} - 10 q^{41} - 8 q^{43} + 11 q^{44} - 2 q^{45} + q^{46} - 8 q^{47} + q^{48} + 29 q^{49} + 23 q^{50} - 9 q^{51} + 2 q^{52} - 35 q^{53} + q^{54} - 11 q^{55} + 3 q^{57} + 13 q^{58} + 37 q^{59} + 2 q^{60} - 2 q^{61} + 8 q^{62} - q^{64} + 37 q^{65} + 14 q^{67} - 2 q^{68} - q^{69} - 22 q^{70} + 44 q^{71} - q^{72} - 49 q^{73} - 13 q^{74} - 23 q^{75} + 8 q^{76} + 44 q^{77} + 20 q^{78} - 8 q^{79} - 2 q^{80} - q^{81} + 12 q^{82} - 17 q^{83} - 11 q^{84} - 37 q^{85} + 14 q^{86} - 2 q^{87} + 59 q^{89} - 2 q^{90} + 66 q^{91} + 45 q^{92} + 36 q^{93} - 19 q^{94} - 28 q^{95} + q^{96} - 21 q^{97} - 26 q^{98} - 22 q^{99}+O(q^{100}) $ 10 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 - q^8 - q^9 + 9 * q^10 + 11 * q^11 + q^12 + 13 * q^13 - 11 * q^14 + 13 * q^15 - q^16 - 24 * q^17 - q^18 - 14 * q^19 - 13 * q^20 + 11 * q^21 + 22 * q^22 - 10 * q^23 - 10 * q^24 - 43 * q^25 - 9 * q^26 + q^27 - 11 * q^28 + 13 * q^29 - 9 * q^30 + 8 * q^31 - q^32 + 22 * q^33 + 9 * q^34 - q^36 - 13 * q^37 - 3 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 - 8 * q^43 + 11 * q^44 - 2 * q^45 + q^46 - 8 * q^47 + q^48 + 29 * q^49 + 23 * q^50 - 9 * q^51 + 2 * q^52 - 35 * q^53 + q^54 - 11 * q^55 + 3 * q^57 + 13 * q^58 + 37 * q^59 + 2 * q^60 - 2 * q^61 + 8 * q^62 - q^64 + 37 * q^65 + 14 * q^67 - 2 * q^68 - q^69 - 22 * q^70 + 44 * q^71 - q^72 - 49 * q^73 - 13 * q^74 - 23 * q^75 + 8 * q^76 + 44 * q^77 + 20 * q^78 - 8 * q^79 - 2 * q^80 - q^81 + 12 * q^82 - 17 * q^83 - 11 * q^84 - 37 * q^85 + 14 * q^86 - 2 * q^87 + 59 * q^89 - 2 * q^90 + 66 * q^91 + 45 * q^92 + 36 * q^93 - 19 * q^94 - 28 * q^95 + q^96 - 21 * q^97 - 26 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{10}{11}\right)$

Coefficient data

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

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

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

$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	0.186393	−	0.0547299i	0.0833574	−	0.0244759i	−0.239788	−	0.970825i	$-0.577078\pi$
$5$	0.186393	−	0.0547299i	0.0833574	−	0.0244759i	0.323145	+	0.946349i	$0.395260\pi$
$6$	−0.415415	−	0.909632i	−0.169592	−	0.371356i
$7$	−1.27819	−	1.47511i	−0.483110	−	0.557539i	0.460901	−	0.887451i	$-0.347526\pi$
$7$	−1.27819	−	1.47511i	−0.483110	−	0.557539i	−0.944012	+	0.329913i	$0.892981\pi$
$8$	−0.142315	−	0.989821i	−0.0503159	−	0.349955i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	0.127214	−	0.146813i	0.0402287	−	0.0464264i
$11$	5.30154	+	3.40709i	1.59847	+	1.02728i	0.967962	+	0.251097i	$0.0807913\pi$
$11$	5.30154	+	3.40709i	1.59847	+	1.02728i	0.630512	+	0.776180i	$0.282845\pi$
$12$	−0.841254	−	0.540641i	−0.242849	−	0.156070i
$13$	−3.15177	+	3.63733i	−0.874143	+	1.00881i	0.125717	+	0.992066i	$0.459877\pi$
$13$	−3.15177	+	3.63733i	−0.874143	+	1.00881i	−0.999860	+	0.0167483i	$0.994669\pi$
$14$	−1.87279	−	0.549899i	−0.500523	−	0.146967i
$15$	−0.0276463	−	0.192284i	−0.00713825	−	0.0496476i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−1.33259	−	2.91797i	−0.323201	−	0.707712i	0.676383	−	0.736550i	$-0.263547\pi$
$17$	−1.33259	−	2.91797i	−0.323201	−	0.707712i	−0.999584	+	0.0288381i	$0.990819\pi$
$18$	−0.959493	+	0.281733i	−0.226155	+	0.0664050i
$19$	0.357028	−	0.781782i	0.0819078	−	0.179353i	−0.864247	−	0.503068i	$-0.832205\pi$
$19$	0.357028	−	0.781782i	0.0819078	−	0.179353i	0.946155	+	0.323715i	$0.104932\pi$
$20$	0.0276463	−	0.192284i	0.00618191	−	0.0429961i
$21$	−1.64200	+	1.05525i	−0.358314	+	0.230274i
$22$	6.30195			1.34358
$23$	3.37782	+	3.40446i	0.704324	+	0.709878i
$23$	3.37782	+	3.40446i	0.704324	+	0.709878i
$24$	−1.00000			−0.204124
$25$	−4.17452	+	2.68280i	−0.834904	+	0.536560i
$26$	−0.684944	+	4.76389i	−0.134329	+	0.934276i
$27$	−0.415415	+	0.909632i	−0.0799467	+	0.175059i
$28$	−1.87279	+	0.549899i	−0.353923	+	0.103921i
$29$	2.25047	+	4.92785i	0.417902	+	0.915079i	0.995137	+	0.0985003i	$0.0314045\pi$
$29$	2.25047	+	4.92785i	0.417902	+	0.915079i	−0.577235	+	0.816578i	$0.695868\pi$
$30$	−0.127214	−	0.146813i	−0.0232261	−	0.0268043i
$31$	0.144265	+	1.00339i	0.0259108	+	0.180214i	0.998667	−	0.0516171i	$-0.0164375\pi$
$31$	0.144265	+	1.00339i	0.0259108	+	0.180214i	−0.972756	+	0.231831i	$0.925528\pi$
$32$	−0.959493	−	0.281733i	−0.169616	−	0.0498038i
$33$	4.12690	−	4.76270i	0.718401	−	0.829079i
$34$	−2.69862	−	1.73430i	−0.462810	−	0.297430i
$35$	−0.318978	−	0.204995i	−0.0539171	−	0.0346504i
$36$	−0.654861	+	0.755750i	−0.109143	+	0.125958i
$37$	−6.61126	−	1.94124i	−1.08688	−	0.319138i	−0.311255	−	0.950326i	$-0.600749\pi$
$37$	−6.61126	−	1.94124i	−1.08688	−	0.319138i	−0.775630	+	0.631188i	$0.782567\pi$
$38$	−0.122312	−	0.850701i	−0.0198417	−	0.138002i
$39$	3.15177	+	3.63733i	0.504687	+	0.582439i
$40$	−0.0806993	−	0.176707i	−0.0127597	−	0.0279398i
$41$	0.932638	−	0.273847i	0.145654	−	0.0427677i	−0.208093	−	0.978109i	$-0.566726\pi$
$41$	0.932638	−	0.273847i	0.145654	−	0.0427677i	0.353747	+	0.935341i	$0.384908\pi$
$42$	−0.810827	+	1.77546i	−0.125113	+	0.273960i
$43$	0.731899	−	5.09047i	0.111614	−	0.776290i	−0.854737	−	0.519061i	$-0.826282\pi$
$43$	0.731899	−	5.09047i	0.111614	−	0.776290i	0.966351	−	0.257228i	$-0.0828093\pi$
$44$	5.30154	−	3.40709i	0.799237	−	0.513638i
$45$	−0.194262			−0.0289588
$46$	4.68219	+	1.03782i	0.690352	+	0.153019i
$47$	−7.41216			−1.08117			−0.540587	−	0.841288i	$-0.681798\pi$
$47$	−7.41216			−1.08117			−0.540587	+	0.841288i	$0.681798\pi$
$48$	−0.841254	+	0.540641i	−0.121424	+	0.0780348i
$49$	0.454025	−	3.15781i	0.0648607	−	0.451116i
$50$	−2.06140	+	4.51383i	−0.291526	+	0.638352i
$51$	−3.07792	+	0.903759i	−0.430995	+	0.126552i
$52$	1.99934	+	4.37795i	0.277259	+	0.607112i
$53$	−1.31494	−	1.51752i	−0.180621	−	0.208447i	0.658218	−	0.752827i	$-0.271310\pi$
$53$	−1.31494	−	1.51752i	−0.180621	−	0.208447i	−0.838839	+	0.544380i	$0.816765\pi$
$54$	0.142315	+	0.989821i	0.0193666	+	0.134698i
$55$	1.17464	+	0.344905i	0.158388	+	0.0465070i
$56$	−1.27819	+	1.47511i	−0.170805	+	0.197120i
$57$	−0.723014	−	0.464653i	−0.0957656	−	0.0615448i
$58$	4.55742	+	2.92887i	0.598418	+	0.384580i
$59$	5.63325	−	6.50112i	0.733387	−	0.846373i	−0.259462	−	0.965753i	$-0.583545\pi$
$59$	5.63325	−	6.50112i	0.733387	−	0.846373i	0.992849	+	0.119380i	$0.0380907\pi$
$60$	−0.186393	−	0.0547299i	−0.0240632	−	0.00706560i
$61$	−1.72487	−	11.9968i	−0.220848	−	1.53603i	−0.734844	−	0.678236i	$-0.762745\pi$
$61$	−1.72487	−	11.9968i	−0.220848	−	1.53603i	0.513996	−	0.857792i	$-0.328165\pi$
$62$	0.663836	+	0.766107i	0.0843072	+	0.0972957i
$63$	0.810827	+	1.77546i	0.102155	+	0.223687i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	−0.388396	+	0.850468i	−0.0481746	+	0.105488i
$66$	0.896861	−	6.23781i	0.110396	−	0.767821i
$67$	5.96723	−	3.83491i	0.729014	−	0.468509i	−0.122748	−	0.992438i	$-0.539171\pi$
$67$	5.96723	−	3.83491i	0.729014	−	0.468509i	0.851762	+	0.523929i	$0.175534\pi$
$68$	−3.20786			−0.389010
$69$	3.85052	−	2.85894i	0.463548	−	0.344175i
$70$	−0.379170			−0.0453194
$71$	0.933267	−	0.599775i	0.110758	−	0.0711801i	−0.484089	−	0.875019i	$-0.660849\pi$
$71$	0.933267	−	0.599775i	0.110758	−	0.0711801i	0.594847	+	0.803839i	$0.297212\pi$
$72$	−0.142315	+	0.989821i	−0.0167720	+	0.116652i
$73$	−5.47763	+	11.9943i	−0.641109	+	1.40383i	0.258017	+	0.966141i	$0.416931\pi$
$73$	−5.47763	+	11.9943i	−0.641109	+	1.40383i	−0.899125	+	0.437692i	$0.855796\pi$
$74$	−6.61126	+	1.94124i	−0.768543	+	0.225665i
$75$	2.06140	+	4.51383i	0.238030	+	0.521212i
$76$	−0.562819	−	0.649528i	−0.0645598	−	0.0745060i
$77$	−1.75054	−	12.1753i	−0.199492	−	1.38750i
$78$	4.61792	+	1.35595i	0.522877	+	0.153531i
$79$	−0.739858	+	0.853842i	−0.0832405	+	0.0960647i	−0.795842	−	0.605504i	$-0.792971\pi$
$79$	−0.739858	+	0.853842i	−0.0832405	+	0.0960647i	0.712601	+	0.701569i	$0.247517\pi$
$80$	−0.163423	−	0.105026i	−0.0182713	−	0.0117422i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	0.636532	−	0.734597i	0.0702932	−	0.0811227i
$83$	−3.84482	−	1.12894i	−0.422024	−	0.123918i	0.0638230	−	0.997961i	$-0.479671\pi$
$83$	−3.84482	−	1.12894i	−0.422024	−	0.123918i	−0.485847	+	0.874044i	$0.661489\pi$
$84$	0.277777	+	1.93198i	0.0303080	+	0.210797i
$85$	−0.408086	−	0.470956i	−0.0442631	−	0.0510824i
$86$	−2.13640	−	4.67807i	−0.230374	−	0.504450i
$87$	5.19797	−	1.52626i	0.557281	−	0.163632i
$88$	2.61792	−	5.73246i	0.279072	−	0.611082i
$89$	1.35933	−	9.45436i	0.144089	−	1.00216i	−0.781575	−	0.623812i	$-0.785583\pi$
$89$	1.35933	−	9.45436i	0.144089	−	1.00216i	0.925663	−	0.378348i	$-0.123508\pi$
$90$	−0.163423	+	0.105026i	−0.0172263	+	0.0110707i
$91$	9.39402			0.984760
$92$	4.50000	−	1.65831i	0.469157	−	0.172891i
$93$	1.01371			0.105116
$94$	−6.23551	+	4.00732i	−0.643143	+	0.413323i
$95$	0.0237606	−	0.165259i	0.00243779	−	0.0169552i
$96$	−0.415415	+	0.909632i	−0.0423981	+	0.0928389i
$97$	1.07554	−	0.315806i	0.109204	−	0.0320653i	−0.226674	−	0.973971i	$-0.572785\pi$
$97$	1.07554	−	0.315806i	0.109204	−	0.0320653i	0.335878	+	0.941905i	$0.390967\pi$
$98$	−1.32529	−	2.90199i	−0.133875	−	0.293145i
$99$	−4.12690	−	4.76270i	−0.414769	−	0.478669i
$100$	0.706204	+	4.91175i	0.0706204	+	0.491175i
$101$	−12.0622	−	3.54178i	−1.20023	−	0.352420i	−0.380290	−	0.924867i	$-0.624176\pi$
$101$	−12.0622	−	3.54178i	−1.20023	−	0.352420i	−0.819942	+	0.572447i	$0.805994\pi$
$102$	−2.10070	+	2.42434i	−0.208000	+	0.240045i
$103$	16.3172	+	10.4864i	1.60778	+	1.03326i	0.963222	+	0.268706i	$0.0865959\pi$
$103$	16.3172	+	10.4864i	1.60778	+	1.03326i	0.644560	+	0.764553i	$0.277040\pi$
$104$	4.04885	+	2.60204i	0.397023	+	0.255151i
$105$	−0.248303	+	0.286557i	−0.0242319	+	0.0279651i
$106$	−1.92663	−	0.565710i	−0.187131	−	0.0549466i
$107$	−0.437753	−	3.04464i	−0.0423191	−	0.294336i	−0.999979	−	0.00643501i	$-0.997952\pi$
$107$	−0.437753	−	3.04464i	−0.0423191	−	0.294336i	0.957660	−	0.287901i	$-0.0929574\pi$
$108$	0.654861	+	0.755750i	0.0630140	+	0.0727220i
$109$	0.809766	+	1.77314i	0.0775615	+	0.169836i	0.944440	−	0.328683i	$-0.106605\pi$
$109$	0.809766	+	1.77314i	0.0775615	+	0.169836i	−0.866879	+	0.498519i	$0.833877\pi$
$110$	1.17464	−	0.344905i	0.111997	−	0.0328854i
$111$	−2.86236	+	6.26770i	−0.271683	+	0.594904i
$112$	−0.277777	+	1.93198i	−0.0262475	+	0.182555i
$113$	−14.4268	+	9.27157i	−1.35716	+	0.872196i	−0.998130	−	0.0611286i	$-0.980530\pi$
$113$	−14.4268	+	9.27157i	−1.35716	+	0.872196i	−0.359034	+	0.933325i	$0.616894\pi$
$114$	−0.859449			−0.0804947
$115$	0.815927	+	0.449698i	0.0760856	+	0.0419346i
$116$	5.41741			0.502994
$117$	4.04885	−	2.60204i	0.374317	−	0.240559i
$118$	1.22422	−	8.51465i	0.112699	−	0.783837i
$119$	−2.60102	+	5.69544i	−0.238435	+	0.522100i
$120$	−0.186393	+	0.0547299i	−0.0170153	+	0.00499613i
$121$	11.9285	+	26.1197i	1.08441	+	2.37452i
$122$	−7.93700	−	9.15979i	−0.718582	−	0.829288i
$123$	−0.138332	−	0.962117i	−0.0124729	−	0.0867512i
$124$	0.972643	+	0.285594i	0.0873459	+	0.0256471i
$125$	−1.26734	+	1.46259i	−0.113355	+	0.130818i
$126$	1.64200	+	1.05525i	0.146281	+	0.0940091i
$127$	−18.1810	−	11.6842i	−1.61330	−	1.03681i	−0.960113	−	0.279613i	$-0.909794\pi$
$127$	−18.1810	−	11.6842i	−1.61330	−	1.03681i	−0.653190	−	0.757194i	$-0.726570\pi$
$128$	−0.654861	+	0.755750i	−0.0578821	+	0.0667995i
$129$	−4.93450	−	1.44890i	−0.434458	−	0.127568i
$130$	0.133058	+	0.925442i	0.0116700	+	0.0811666i
$131$	9.79482	+	11.3038i	0.855777	+	0.987620i	0.999998	−	0.00192587i	$-0.000613023\pi$
$131$	9.79482	+	11.3038i	0.855777	+	0.987620i	−0.144221	+	0.989546i	$0.546068\pi$
$132$	−2.61792	−	5.73246i	−0.227861	−	0.498946i
$133$	−1.60956	+	0.472610i	−0.139567	+	0.0409805i
$134$	2.94665	−	6.45226i	0.254552	−	0.557390i
$135$	−0.0276463	+	0.192284i	−0.00237942	+	0.0165492i
$136$	−2.69862	+	1.73430i	−0.231405	+	0.148715i
$137$	18.1570			1.55126			0.775628	−	0.631190i	$-0.217433\pi$
$137$	18.1570			1.55126			0.775628	+	0.631190i	$0.217433\pi$
$138$	1.69360	−	4.48684i	0.144169	−	0.381945i
$139$	−7.36718			−0.624876			−0.312438	−	0.949938i	$-0.601146\pi$
$139$	−7.36718			−0.624876			−0.312438	+	0.949938i	$0.601146\pi$
$140$	−0.318978	+	0.204995i	−0.0269585	+	0.0173252i
$141$	−1.05486	+	7.33672i	−0.0888353	+	0.617863i
$142$	0.460852	−	1.00912i	0.0386738	−	0.0846839i
$143$	−29.1019	+	8.54510i	−2.43363	+	0.714577i
$144$	0.415415	+	0.909632i	0.0346179	+	0.0758027i
$145$	0.689173	+	0.795348i	0.0572327	+	0.0660500i
$146$	1.87655	+	13.0517i	0.155305	+	1.08017i
$147$	−3.06106	−	0.898807i	−0.252472	−	0.0741324i
$148$	−4.51223	+	5.20739i	−0.370903	+	0.428045i
$149$	13.1516	+	8.45201i	1.07742	+	0.692415i	0.953960	−	0.299934i	$-0.0969648\pi$
$149$	13.1516	+	8.45201i	1.07742	+	0.692415i	0.123459	+	0.992350i	$0.460601\pi$
$150$	4.17452	+	2.68280i	0.340848	+	0.219050i
$151$	−13.5583	+	15.6472i	−1.10336	+	1.27335i	−0.144491	+	0.989506i	$0.546154\pi$
$151$	−13.5583	+	15.6472i	−1.10336	+	1.27335i	−0.958871	+	0.283842i	$0.908391\pi$
$152$	−0.824635	−	0.242135i	−0.0668867	−	0.0196397i
$153$	0.456526	+	3.17521i	0.0369080	+	0.256700i
$154$	−8.05509	−	9.29606i	−0.649097	−	0.749098i
$155$	0.0818052	+	0.179129i	0.00657076	+	0.0143879i
$156$	4.61792	−	1.35595i	0.369730	−	0.108562i
$157$	−1.65182	+	3.61698i	−0.131830	+	0.288666i	−0.964023	−	0.265819i	$-0.914358\pi$
$157$	−1.65182	+	3.61698i	−0.131830	+	0.288666i	0.832193	+	0.554485i	$0.187085\pi$
$158$	−0.160787	+	1.11829i	−0.0127915	+	0.0889668i
$159$	−1.68921	+	1.08559i	−0.133963	+	0.0860928i
$160$	−0.194262			−0.0153577
$161$	0.704449	−	9.33420i	0.0555183	−	0.735638i
$162$	1.00000			0.0785674
$163$	20.6215	−	13.2526i	1.61520	−	1.03803i	0.656217	−	0.754572i	$-0.272156\pi$
$163$	20.6215	−	13.2526i	1.61520	−	1.03803i	0.958985	−	0.283455i	$-0.0914807\pi$
$164$	0.138332	−	0.962117i	0.0108019	−	0.0751288i
$165$	0.508563	−	1.11360i	0.0395915	−	0.0866934i
$166$	−3.84482	+	1.12894i	−0.298416	+	0.0876229i
$167$	−0.811902	−	1.77782i	−0.0628268	−	0.137572i	0.875614	−	0.483011i	$-0.160457\pi$
$167$	−0.811902	−	1.77782i	−0.0628268	−	0.137572i	−0.938441	+	0.345440i	$0.887730\pi$
$168$	1.27819	+	1.47511i	0.0986145	+	0.113807i
$169$	−1.44646	−	10.0604i	−0.111266	−	0.773874i
$170$	−0.597922	−	0.175566i	−0.0458585	−	0.0134653i
$171$	−0.562819	+	0.649528i	−0.0430399	+	0.0496706i
$172$	−4.32641	−	2.78042i	−0.329886	−	0.212005i
$173$	5.16669	+	3.32043i	0.392816	+	0.252447i	0.722108	−	0.691781i	$-0.243174\pi$
$173$	5.16669	+	3.32043i	0.392816	+	0.252447i	−0.329292	+	0.944228i	$0.606810\pi$
$174$	3.54765	−	4.09421i	0.268947	−	0.310381i
$175$	9.29325	+	2.72875i	0.702504	+	0.206274i
$176$	−0.896861	−	6.23781i	−0.0676034	−	0.470192i
$177$	−5.63325	−	6.50112i	−0.423421	−	0.488654i
$178$	−3.96787	−	8.68842i	−0.297404	−	0.651225i
$179$	−6.20879	+	1.82307i	−0.464067	+	0.136262i	−0.505404	−	0.862883i	$-0.668656\pi$
$179$	−6.20879	+	1.82307i	−0.464067	+	0.136262i	0.0413370	+	0.999145i	$0.486838\pi$
$180$	−0.0806993	+	0.176707i	−0.00601497	+	0.0131709i
$181$	−0.464155	+	3.22827i	−0.0345004	+	0.239955i	−0.999773	−	0.0212879i	$-0.993223\pi$
$181$	−0.464155	+	3.22827i	−0.0345004	+	0.239955i	0.965273	+	0.261243i	$0.0841324\pi$
$182$	7.90275	−	5.07879i	0.585791	−	0.376465i
$183$	−12.1201			−0.895946
$184$	2.88909	−	3.82794i	0.212987	−	0.282200i
$185$	−1.33853			−0.0984110
$186$	0.852783	−	0.548050i	0.0625291	−	0.0401850i
$187$	2.87700	−	20.0100i	0.210387	−	1.46328i
$188$	−3.07912	+	6.74234i	−0.224568	+	0.491736i
$189$	1.87279	−	0.549899i	0.136225	−	0.0399993i
$190$	−0.0693569	−	0.151870i	−0.00503167	−	0.0110178i
$191$	14.9659	+	17.2716i	1.08290	+	1.24973i	0.966538	+	0.256523i	$0.0825768\pi$
$191$	14.9659	+	17.2716i	1.08290	+	1.24973i	0.116359	+	0.993207i	$0.462878\pi$
$192$	0.142315	+	0.989821i	0.0102707	+	0.0714342i
$193$	16.2552	+	4.77294i	1.17007	+	0.343564i	0.808339	−	0.588718i	$-0.200367\pi$
$193$	16.2552	+	4.77294i	1.17007	+	0.343564i	0.361733	+	0.932282i	$0.382185\pi$
$194$	0.734062	−	0.847152i	0.0527025	−	0.0608220i
$195$	0.786537	+	0.505477i	0.0563251	+	0.0361979i
$196$	−2.68384	−	1.72480i	−0.191703	−	0.123200i
$197$	−0.821721	+	0.948317i	−0.0585452	+	0.0675648i	−0.784267	−	0.620424i	$-0.786961\pi$
$197$	−0.821721	+	0.948317i	−0.0585452	+	0.0675648i	0.725722	+	0.687989i	$0.241506\pi$
$198$	−6.04668	−	1.77546i	−0.429719	−	0.126177i
$199$	−3.53140	−	24.5614i	−0.250334	−	1.74111i	−0.596206	−	0.802832i	$-0.703326\pi$
$199$	−3.53140	−	24.5614i	−0.250334	−	1.74111i	0.345872	−	0.938282i	$-0.387583\pi$
$200$	3.24959	+	3.75023i	0.229781	+	0.265181i
$201$	−2.94665	−	6.45226i	−0.207841	−	0.455107i
$202$	−12.0622	+	3.54178i	−0.848692	+	0.249198i
$203$	4.39258	−	9.61842i	0.308299	−	0.675081i
$204$	−0.456526	+	3.17521i	−0.0319632	+	0.222309i
$205$	0.158849	−	0.102086i	0.0110945	−	0.00713002i
$206$	19.3963			1.35140
$207$	−2.28185	−	4.21819i	−0.158600	−	0.293185i
$208$	4.81288			0.333713
$209$	4.55640	−	2.92822i	0.315173	−	0.202549i
$210$	−0.0539615	+	0.375310i	−0.00372370	+	0.0258989i
$211$	3.01519	−	6.60235i	0.207575	−	0.454525i	−0.776998	−	0.629503i	$-0.783258\pi$
$211$	3.01519	−	6.60235i	0.207575	−	0.454525i	0.984572	+	0.174979i	$0.0559856\pi$
$212$	−1.92663	+	0.565710i	−0.132321	+	0.0388531i
$213$	−0.460852	−	1.00912i	−0.0315771	−	0.0691441i
$214$	−2.01432	−	2.32464i	−0.137696	−	0.158909i
$215$	−0.142180	−	0.988884i	−0.00969660	−	0.0674413i
$216$	0.959493	+	0.281733i	0.0652852	+	0.0191695i
$217$	1.29571	−	1.49533i	0.0879583	−	0.101509i
$218$	1.63985	+	1.05387i	0.111065	+	0.0713769i
$219$	11.0927	+	7.12885i	0.749576	+	0.481723i
$220$	0.801699	−	0.925210i	0.0540505	−	0.0623776i
$221$	14.8137	+	4.34968i	0.996474	+	0.292591i
$222$	0.980602	+	6.82023i	0.0658137	+	0.457744i
$223$	−13.5780	−	15.6698i	−0.909250	−	1.04933i	−0.998577	−	0.0533276i	$-0.983017\pi$
$223$	−13.5780	−	15.6698i	−0.909250	−	1.04933i	0.0893275	−	0.996002i	$-0.471528\pi$
$224$	0.810827	+	1.77546i	0.0541757	+	0.118628i
$225$	4.76126	−	1.39803i	0.317417	−	0.0932021i
$226$	−7.12405	+	15.5995i	−0.473884	+	1.03766i
$227$	2.99578	−	20.8361i	0.198837	−	1.38294i	−0.608829	−	0.793301i	$-0.708361\pi$
$227$	2.99578	−	20.8361i	0.198837	−	1.38294i	0.807666	−	0.589640i	$-0.200730\pi$
$228$	−0.723014	+	0.464653i	−0.0478828	+	0.0307724i
$229$	−1.91595			−0.126609			−0.0633047	−	0.997994i	$-0.520164\pi$
$229$	−1.91595			−0.126609			−0.0633047	+	0.997994i	$0.520164\pi$
$230$	0.929527	−	0.0628131i	0.0612912	−	0.00414177i
$231$	−12.3005			−0.809311
$232$	4.55742	−	2.92887i	0.299209	−	0.192290i
$233$	2.05368	−	14.2837i	0.134541	−	0.935756i	−0.804989	−	0.593290i	$-0.797829\pi$
$233$	2.05368	−	14.2837i	0.134541	−	0.935756i	0.939530	−	0.342466i	$-0.111262\pi$
$234$	1.99934	−	4.37795i	0.130701	−	0.286196i
$235$	−1.38157	+	0.405667i	−0.0901239	+	0.0264628i
$236$	−3.57349	−	7.82485i	−0.232614	−	0.509354i
$237$	0.739858	+	0.853842i	0.0480589	+	0.0554630i
$238$	0.891070	+	6.19753i	0.0577595	+	0.401726i
$239$	9.41935	+	2.76577i	0.609287	+	0.178903i	0.571798	−	0.820394i	$-0.306246\pi$
$239$	9.41935	+	2.76577i	0.609287	+	0.178903i	0.0374888	+	0.999297i	$0.488064\pi$
$240$	−0.127214	+	0.146813i	−0.00821165	+	0.00947675i
$241$	−12.5379	−	8.05765i	−0.807640	−	0.519039i	0.0704608	−	0.997515i	$-0.477553\pi$
$241$	−12.5379	−	8.05765i	−0.807640	−	0.519039i	−0.878101	+	0.478476i	$0.841189\pi$
$242$	24.1562	+	15.5243i	1.55282	+	0.997938i
$243$	0.654861	−	0.755750i	0.0420093	−	0.0484814i
$244$	−11.6292	−	3.41464i	−0.744482	−	0.218600i
$245$	−0.0881997	−	0.613442i	−0.00563487	−	0.0391914i
$246$	−0.636532	−	0.734597i	−0.0405838	−	0.0468362i
$247$	1.71833	+	3.76262i	0.109335	+	0.239410i
$248$	0.972643	−	0.285594i	0.0617629	−	0.0181352i
$249$	−1.66463	+	3.64502i	−0.105491	+	0.230994i
$250$	−0.275420	+	1.91559i	−0.0174191	+	0.121152i
$251$	−1.80424	+	1.15952i	−0.113883	+	0.0731880i	−0.596342	−	0.802730i	$-0.703380\pi$
$251$	−1.80424	+	1.15952i	−0.113883	+	0.0731880i	0.482460	+	0.875918i	$0.339744\pi$
$252$	1.95185			0.122955
$253$	6.30836	+	29.5574i	0.396603	+	1.85826i
$254$	−21.6118			−1.35604
$255$	−0.524239	+	0.336908i	−0.0328291	+	0.0210980i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−6.58383	+	14.4166i	−0.410688	+	0.899281i	0.585386	+	0.810755i	$0.300943\pi$
$257$	−6.58383	+	14.4166i	−0.410688	+	0.899281i	−0.996074	+	0.0885261i	$0.971784\pi$
$258$	−4.93450	+	1.44890i	−0.307208	+	0.0902045i
$259$	5.58690	+	12.2336i	0.347153	+	0.760159i
$260$	0.612268	+	0.706595i	0.0379712	+	0.0438211i
$261$	−0.770978	−	5.36227i	−0.0477223	−	0.331916i
$262$	14.3512	+	4.21390i	0.886622	+	0.260336i
$263$	−0.0855299	+	0.0987067i	−0.00527400	+	0.00608652i	−0.758380	−	0.651812i	$-0.774009\pi$
$263$	−0.0855299	+	0.0987067i	−0.00527400	+	0.00608652i	0.753106	+	0.657899i	$0.228555\pi$
$264$	−5.30154	−	3.40709i	−0.326287	−	0.209692i
$265$	−0.328149	−	0.210888i	−0.0201580	−	0.0129548i
$266$	−1.09854	+	1.26778i	−0.0673557	+	0.0777326i
$267$	−9.16467	−	2.69099i	−0.560869	−	0.164686i
$268$	−1.00948	−	7.02107i	−0.0616636	−	0.428880i
$269$	15.6962	+	18.1144i	0.957016	+	1.10446i	0.994456	+	0.105157i	$0.0335344\pi$
$269$	15.6962	+	18.1144i	0.957016	+	1.10446i	−0.0374396	+	0.999299i	$0.511920\pi$
$270$	0.0806993	+	0.176707i	0.00491120	+	0.0107540i
$271$	−3.09137	+	0.907707i	−0.187787	+	0.0551393i	−0.374274	−	0.927318i	$-0.622108\pi$
$271$	−3.09137	+	0.907707i	−0.187787	+	0.0551393i	0.186487	+	0.982457i	$0.440290\pi$
$272$	−1.33259	+	2.91797i	−0.0808003	+	0.176928i
$273$	1.33691	−	9.29840i	0.0809133	−	0.562765i
$274$	15.2746	−	9.81641i	0.922775	−	0.593031i
$275$	−31.2719			−1.88577
$276$	−1.00102	−	4.69020i	−0.0602541	−	0.282317i
$277$	−13.0026			−0.781250			−0.390625	−	0.920550i	$-0.627741\pi$
$277$	−13.0026			−0.781250			−0.390625	+	0.920550i	$0.627741\pi$
$278$	−6.19766	+	3.98300i	−0.371711	+	0.238884i
$279$	0.144265	−	1.00339i	0.00863694	−	0.0600712i
$280$	−0.157513	+	0.344905i	−0.00941319	+	0.0206120i
$281$	−9.32483	+	2.73802i	−0.556273	+	0.163336i	−0.547772	−	0.836627i	$-0.684524\pi$
$281$	−9.32483	+	2.73802i	−0.556273	+	0.163336i	−0.00850036	+	0.999964i	$0.502706\pi$
$282$	3.07912	+	6.74234i	0.183359	+	0.401500i
$283$	−13.0872	−	15.1035i	−0.777955	−	0.897808i	0.219005	−	0.975724i	$-0.429719\pi$
$283$	−13.0872	−	15.1035i	−0.777955	−	0.897808i	−0.996960	+	0.0779160i	$0.975173\pi$
$284$	−0.157881	−	1.09809i	−0.00936850	−	0.0651594i
$285$	−0.160195	−	0.0470375i	−0.00948913	−	0.00278626i
$286$	−19.8623	+	22.9223i	−1.17448	+	1.35542i
$287$	−1.59604	−	1.02571i	−0.0942114	−	0.0605460i
$288$	0.841254	+	0.540641i	0.0495713	+	0.0318576i
$289$	4.39387	−	5.07080i	0.258463	−	0.298282i
$290$	1.00977	+	0.296494i	0.0592955	+	0.0174107i
$291$	−0.159527	−	1.10953i	−0.00935163	−	0.0650420i
$292$	8.63495	+	9.96526i	0.505322	+	0.583173i
$293$	−7.42848	−	16.2661i	−0.433977	−	0.950276i	−0.992665	−	0.120898i	$-0.961422\pi$
$293$	−7.42848	−	16.2661i	−0.433977	−	0.950276i	0.558688	−	0.829378i	$-0.311305\pi$
$294$	−3.06106	+	0.898807i	−0.178524	+	0.0524195i
$295$	0.694192	−	1.52007i	0.0404174	−	0.0885018i
$296$	−0.980602	+	6.82023i	−0.0569963	+	0.396418i
$297$	−5.30154	+	3.40709i	−0.307626	+	0.197699i
$298$	15.6333			0.905613
$299$	−23.0292	+	1.55621i	−1.33182	+	0.0899979i
$300$	4.96226			0.286496
$301$	−8.44451	+	5.42696i	−0.486733	+	0.312805i
$302$	−2.94651	+	20.4934i	−0.169553	+	1.17926i
$303$	−5.22235	+	11.4354i	−0.300016	+	0.656944i
$304$	−0.824635	+	0.242135i	−0.0472960	+	0.0138874i
$305$	−0.978086	−	2.14171i	−0.0560050	−	0.122634i
$306$	2.10070	+	2.42434i	0.120089	+	0.138590i
$307$	1.78091	+	12.3865i	0.101642	+	0.706935i	0.975379	+	0.220536i	$0.0707807\pi$
$307$	1.78091	+	12.3865i	0.101642	+	0.706935i	−0.873737	+	0.486399i	$0.838310\pi$
$308$	−11.8022	−	3.46544i	−0.672493	−	0.197462i
$309$	12.7019	−	14.6588i	0.722585	−	0.833907i
$310$	0.165663	+	0.106465i	0.00940903	+	0.00604682i
$311$	4.59133	+	2.95067i	0.260350	+	0.167317i	0.664304	−	0.747462i	$-0.268728\pi$
$311$	4.59133	+	2.95067i	0.260350	+	0.167317i	−0.403954	+	0.914779i	$0.632364\pi$
$312$	3.15177	−	3.63733i	0.178434	−	0.205923i
$313$	22.9543	+	6.73999i	1.29745	+	0.380967i	0.856307	−	0.516468i	$-0.172753\pi$
$313$	22.9543	+	6.73999i	1.29745	+	0.380967i	0.441147	+	0.897435i	$0.354572\pi$
$314$	0.565888	+	3.93584i	0.0319349	+	0.222112i
$315$	0.248303	+	0.286557i	0.0139903	+	0.0161457i
$316$	0.469334	+	1.02770i	0.0264021	+	0.0578125i
$317$	15.4695	−	4.54224i	0.868852	−	0.255118i	0.183225	−	0.983071i	$-0.441346\pi$
$317$	15.4695	−	4.54224i	0.868852	−	0.255118i	0.685627	+	0.727953i	$0.259528\pi$
$318$	−0.834139	+	1.82651i	−0.0467762	+	0.102426i
$319$	−4.85866	+	33.7927i	−0.272033	+	1.89203i
$320$	−0.163423	+	0.105026i	−0.00913565	+	0.00587112i
$321$	−3.07594			−0.171682
$322$	−4.45383	−	8.23328i	−0.248202	−	0.458823i
$323$	−2.75699			−0.153403
$324$	0.841254	−	0.540641i	0.0467363	−	0.0300356i
$325$	3.39887	−	23.6397i	0.188536	−	1.31129i
$326$	10.1830	−	22.2977i	0.563985	−	1.23495i
$327$	1.87033	−	0.549179i	0.103430	−	0.0303697i
$328$	−0.403788	−	0.884172i	−0.0222955	−	0.0488203i
$329$	9.47415	+	10.9337i	0.522327	+	0.602797i
$330$	−0.174226	−	1.21177i	−0.00959081	−	0.0667056i
$331$	0.496914	+	0.145907i	0.0273129	+	0.00801979i	0.295360	−	0.955386i	$-0.404560\pi$
$331$	0.496914	+	0.145907i	0.0273129	+	0.00801979i	−0.268048	+	0.963406i	$0.586378\pi$
$332$	−2.62412	+	3.02840i	−0.144017	+	0.166205i
$333$	5.79655	+	3.72521i	0.317649	+	0.204140i
$334$	−1.64418	−	1.05665i	−0.0899653	−	0.0578172i
$335$	0.902365	−	1.04139i	0.0493015	−	0.0568970i
$336$	1.87279	+	0.549899i	0.102169	+	0.0299995i
$337$	0.0754437	+	0.524723i	0.00410968	+	0.0285835i	0.991773	−	0.128008i	$-0.0408584\pi$
$337$	0.0754437	+	0.524723i	0.00410968	+	0.0285835i	−0.987663	+	0.156592i	$0.949949\pi$
$338$	−6.65588	−	7.68130i	−0.362032	−	0.417808i
$339$	7.12405	+	15.5995i	0.386925	+	0.847248i
$340$	−0.597922	+	0.175566i	−0.0324269	+	0.00952139i
$341$	−2.65380	+	5.81102i	−0.143712	+	0.314684i
$342$	−0.122312	+	0.850701i	−0.00661389	+	0.0460006i
$343$	−16.7324	+	10.7533i	−0.903467	+	0.580623i
$344$	−5.14282			−0.277282
$345$	0.561240	−	0.743623i	0.0302161	−	0.0400353i
$346$	6.14165			0.330177
$347$	22.5562	−	14.4960i	1.21088	−	0.778185i	0.230073	−	0.973173i	$-0.426103\pi$
$347$	22.5562	−	14.4960i	1.21088	−	0.778185i	0.980805	+	0.194989i	$0.0624670\pi$
$348$	0.770978	−	5.36227i	0.0413287	−	0.287448i
$349$	0.605377	−	1.32559i	0.0324051	−	0.0709573i	−0.892737	−	0.450578i	$-0.851218\pi$
$349$	0.605377	−	1.32559i	0.0324051	−	0.0709573i	0.925142	+	0.379620i	$0.123945\pi$
$350$	9.29325	−	2.72875i	0.496745	−	0.145858i
$351$	−1.99934	−	4.37795i	−0.106717	−	0.233678i
$352$	−4.12690	−	4.76270i	−0.219964	−	0.253853i
$353$	−3.19550	−	22.2252i	−0.170079	−	1.18293i	−0.878713	−	0.477350i	$-0.841597\pi$
$353$	−3.19550	−	22.2252i	−0.170079	−	1.18293i	0.708634	−	0.705576i	$-0.249312\pi$
$354$	−8.25376	−	2.42352i	−0.438682	−	0.128809i
$355$	0.141129	−	0.162871i	0.00749034	−	0.00864431i
$356$	−8.03530	−	5.16397i	−0.425870	−	0.273690i
$357$	5.26731	+	3.38509i	0.278775	+	0.179158i
$358$	−4.23754	+	4.89039i	−0.223961	+	0.258465i
$359$	−0.162153	−	0.0476124i	−0.00855811	−	0.00251289i	0.277451	−	0.960740i	$-0.410510\pi$
$359$	−0.162153	−	0.0476124i	−0.00855811	−	0.00251289i	−0.286009	+	0.958227i	$0.592329\pi$
$360$	0.0276463	+	0.192284i	0.00145709	+	0.0101343i
$361$	11.9586	+	13.8010i	0.629402	+	0.726369i
$362$	1.35486	+	2.96673i	0.0712099	+	0.155928i
$363$	27.5514	−	8.08983i	1.44608	−	0.424606i
$364$	3.90242	−	8.54510i	0.204542	−	0.447885i
$365$	−0.364543	+	2.53545i	−0.0190810	+	0.132712i
$366$	−10.1961	+	6.55264i	−0.532959	+	0.342512i
$367$	17.8312			0.930782			0.465391	−	0.885105i	$-0.345914\pi$
$367$	17.8312			0.930782			0.465391	+	0.885105i	$0.345914\pi$
$368$	0.360914	−	4.78223i	0.0188139	−	0.249291i
$369$	−0.972011			−0.0506009
$370$	−1.12605	+	0.723667i	−0.0585404	+	0.0376216i
$371$	−0.557767	+	3.87936i	−0.0289578	+	0.201406i
$372$	0.421108	−	0.922099i	0.0218335	−	0.0478086i
$373$	26.2789	−	7.71619i	1.36067	−	0.399529i	0.481672	−	0.876352i	$-0.340030\pi$
$373$	26.2789	−	7.71619i	1.36067	−	0.399529i	0.879000	+	0.476822i	$0.158211\pi$
$374$	−8.39794	−	18.3889i	−0.434247	−	0.950868i
$375$	1.26734	+	1.46259i	0.0654453	+	0.0755279i
$376$	1.05486	+	7.33672i	0.0544003	+	0.378362i
$377$	−25.0172	−	7.34571i	−1.28845	−	0.378323i
$378$	1.27819	−	1.47511i	0.0657430	−	0.0758714i
$379$	−2.30170	−	1.47921i	−0.118230	−	0.0759821i	0.480189	−	0.877165i	$-0.340568\pi$
$379$	−2.30170	−	1.47921i	−0.118230	−	0.0759821i	−0.598420	+	0.801183i	$0.704204\pi$
$380$	−0.140454	−	0.0902643i	−0.00720514	−	0.00463046i
$381$	−14.1527	+	16.3331i	−0.725066	+	0.836770i
$382$	21.9279	+	6.43861i	1.12193	+	0.329428i
$383$	2.05088	+	14.2642i	0.104795	+	0.728867i	0.972688	+	0.232116i	$0.0745649\pi$
$383$	2.05088	+	14.2642i	0.104795	+	0.728867i	−0.867893	+	0.496751i	$0.834526\pi$
$384$	0.654861	+	0.755750i	0.0334182	+	0.0385667i
$385$	−0.992638	−	2.17357i	−0.0505895	−	0.110776i
$386$	16.2552	−	4.77294i	0.827365	−	0.242936i
$387$	−2.13640	+	4.67807i	−0.108600	+	0.237800i
$388$	0.159527	−	1.10953i	0.00809875	−	0.0563280i
$389$	0.911952	−	0.586076i	0.0462378	−	0.0297152i	−0.517318	−	0.855793i	$-0.673069\pi$
$389$	0.911952	−	0.586076i	0.0462378	−	0.0297152i	0.563556	+	0.826078i	$0.309433\pi$
$390$	0.934959			0.0473435
$391$	5.43285	−	14.3931i	0.274751	−	0.727893i
$392$	−3.19028			−0.161134
$393$	12.5827	−	8.08642i	0.634714	−	0.407906i
$394$	−0.178577	+	1.24203i	−0.00899658	+	0.0625726i
$395$	−0.0911736	+	0.199642i	−0.00458744	+	0.0100451i
$396$	−6.04668	+	1.77546i	−0.303857	+	0.0892204i
$397$	−11.2262	−	24.5819i	−0.563427	−	1.23373i	−0.950224	−	0.311568i	$-0.899146\pi$
$397$	−11.2262	−	24.5819i	−0.563427	−	1.23373i	0.386797	−	0.922165i	$-0.373581\pi$
$398$	−16.2497	−	18.7532i	−0.814524	−	0.940011i
$399$	0.238735	+	1.66044i	0.0119517	+	0.0831259i
$400$	4.76126	+	1.39803i	0.238063	+	0.0699015i
$401$	−6.07324	+	7.00889i	−0.303283	+	0.350007i	−0.886850	−	0.462058i	$-0.847111\pi$
$401$	−6.07324	+	7.00889i	−0.303283	+	0.350007i	0.583567	+	0.812065i	$0.301657\pi$
$402$	−5.96723	−	3.83491i	−0.297619	−	0.191268i
$403$	−4.10434	−	2.63770i	−0.204452	−	0.131393i
$404$	−8.23252	+	9.50084i	−0.409583	+	0.472684i
$405$	0.186393	+	0.0547299i	0.00926193	+	0.00271955i
$406$	−1.50483	−	10.4663i	−0.0746836	−	0.519436i
$407$	−28.4359	−	32.8167i	−1.40951	−	1.62666i
$408$	1.33259	+	2.91797i	0.0659732	+	0.144461i
$409$	−35.2765	+	10.3581i	−1.74431	+	0.512175i	−0.989595	−	0.143879i	$-0.954042\pi$
$409$	−35.2765	+	10.3581i	−1.74431	+	0.512175i	−0.754714	+	0.656054i	$0.772224\pi$
$410$	0.0784406	−	0.171761i	0.00387390	−	0.00848267i
$411$	2.58401	−	17.9722i	0.127460	−	0.886502i
$412$	16.3172	−	10.4864i	0.803891	−	0.516630i
$413$	−16.7902			−0.826193
$414$	−4.20014	−	2.31491i	−0.206426	−	0.113772i
$415$	−0.778434			−0.0382118
$416$	4.04885	−	2.60204i	0.198511	−	0.127575i
$417$	−1.04846	+	7.29219i	−0.0513432	+	0.357100i
$418$	2.24997	−	4.92675i	0.110050	−	0.240975i
$419$	25.4226	−	7.46473i	1.24197	−	0.364676i	0.406217	−	0.913777i	$-0.366848\pi$
$419$	25.4226	−	7.46473i	1.24197	−	0.364676i	0.835756	+	0.549101i	$0.185030\pi$
$420$	0.157513	+	0.344905i	0.00768584	+	0.0168296i
$421$	−6.51649	−	7.52043i	−0.317594	−	0.366523i	0.574396	−	0.818577i	$-0.305237\pi$
$421$	−6.51649	−	7.52043i	−0.317594	−	0.366523i	−0.891991	+	0.452054i	$0.850691\pi$
$422$	−1.03296	−	7.18439i	−0.0502837	−	0.349731i
$423$	7.11192	+	2.08825i	0.345793	+	0.101534i
$424$	−1.31494	+	1.51752i	−0.0638591	+	0.0736973i
$425$	13.3913	+	8.60605i	0.649572	+	0.417455i
$426$	−0.933267	−	0.599775i	−0.0452170	−	0.0290592i
$427$	−15.4918	+	17.8785i	−0.749702	+	0.865202i
$428$	−2.95135	−	0.866594i	−0.142659	−	0.0418884i
$429$	4.31648	+	30.0218i	0.208402	+	1.44947i
$430$	−0.654241	−	0.755034i	−0.0315503	−	0.0364110i
$431$	3.64438	+	7.98009i	0.175544	+	0.384387i	0.976868	−	0.213843i	$-0.0685981\pi$
$431$	3.64438	+	7.98009i	0.175544	+	0.384387i	−0.801324	+	0.598230i	$0.795871\pi$
$432$	0.959493	−	0.281733i	0.0461636	−	0.0135549i
$433$	−3.31942	+	7.26851i	−0.159521	+	0.349303i	−0.972468	−	0.233035i	$-0.925134\pi$
$433$	−3.31942	+	7.26851i	−0.159521	+	0.349303i	0.812947	+	0.582337i	$0.197862\pi$
$434$	0.281584	−	1.95846i	0.0135165	−	0.0940091i
$435$	0.885331	−	0.568968i	0.0424484	−	0.0272799i
$436$	1.94929			0.0933542
$437$	3.86752	−	1.42523i	0.185008	−	0.0681782i
$438$	13.1859			0.630048
$439$	−1.18670	+	0.762644i	−0.0566380	+	0.0363990i	−0.568653	−	0.822577i	$-0.692535\pi$
$439$	−1.18670	+	0.762644i	−0.0566380	+	0.0363990i	0.512015	+	0.858976i	$0.328899\pi$
$440$	0.174226	−	1.21177i	0.00830589	−	0.0577687i
$441$	−1.32529	+	2.90199i	−0.0631092	+	0.138190i
$442$	14.8137	−	4.34968i	0.704614	−	0.206893i
$443$	5.23153	+	11.4554i	0.248557	+	0.544265i	0.992250	−	0.124257i	$-0.0396547\pi$
$443$	5.23153	+	11.4554i	0.248557	+	0.544265i	−0.743693	+	0.668522i	$0.766927\pi$
$444$	4.51223	+	5.20739i	0.214141	+	0.247132i
$445$	−0.264066	−	1.83662i	−0.0125179	−	0.0870641i
$446$	−19.8943	−	5.84149i	−0.942022	−	0.276603i
$447$	10.2376	−	11.8149i	0.484224	−	0.558824i
$448$	1.64200	+	1.05525i	0.0775772	+	0.0498558i
$449$	−32.2649	−	20.7354i	−1.52267	−	0.978562i	−0.991329	−	0.131406i	$-0.958051\pi$
$449$	−32.2649	−	20.7354i	−1.52267	−	0.978562i	−0.531344	−	0.847156i	$-0.678313\pi$
$450$	3.24959	−	3.75023i	0.153187	−	0.176787i
$451$	5.87744	+	1.72577i	0.276758	+	0.0812634i
$452$	2.44059	+	16.9747i	0.114796	+	0.798421i
$453$	13.5583	+	15.6472i	0.637026	+	0.735168i
$454$	−8.74464	−	19.1481i	−0.410406	−	0.898664i
$455$	1.75098	−	0.514133i	0.0820871	−	0.0241029i
$456$	−0.357028	+	0.781782i	−0.0167194	+	0.0366103i
$457$	−3.79066	+	26.3646i	−0.177319	+	1.23328i	0.685614	+	0.727966i	$0.259534\pi$
$457$	−3.79066	+	26.3646i	−0.177319	+	1.23328i	−0.862933	+	0.505318i	$0.831375\pi$
$458$	−1.61180	+	1.03584i	−0.0753144	+	0.0484016i
$459$	3.20786			0.149730
$460$	0.748008	−	0.555382i	0.0348761	−	0.0258948i
$461$	7.65301			0.356436			0.178218	−	0.983991i	$-0.442967\pi$
$461$	7.65301			0.356436			0.178218	+	0.983991i	$0.442967\pi$
$462$	−10.3478	+	6.65013i	−0.481423	+	0.309392i
$463$	0.590819	−	4.10924i	0.0274577	−	0.190972i	−0.971476	−	0.237137i	$-0.923791\pi$
$463$	0.590819	−	4.10924i	0.0274577	−	0.190972i	0.998934	+	0.0461649i	$0.0147000\pi$
$464$	2.25047	−	4.92785i	0.104476	−	0.228770i
$465$	0.188947	−	0.0554799i	0.00876222	−	0.00257282i
$466$	−5.99468	−	13.1265i	−0.277698	−	0.608074i
$467$	21.0312	+	24.2712i	0.973206	+	1.12314i	0.992367	+	0.123323i	$0.0393551\pi$
$467$	21.0312	+	24.2712i	0.973206	+	1.12314i	−0.0191607	+	0.999816i	$0.506099\pi$
$468$	−0.684944	−	4.76389i	−0.0316616	−	0.220211i
$469$	−13.2842	−	3.90058i	−0.613406	−	0.180112i
$470$	−0.942934	+	1.08820i	−0.0434943	+	0.0501951i
$471$	3.34509	+	2.14976i	0.154133	+	0.0990555i
$472$	−7.23664	−	4.65071i	−0.333093	−	0.214066i
$473$	21.2239	−	24.4937i	0.975876	−	1.12622i
$474$	1.08403	+	0.318300i	0.0497911	+	0.0146200i
$475$	0.606946	+	4.22140i	0.0278486	+	0.193691i
$476$	4.10025	+	4.73194i	0.187935	+	0.216888i
$477$	0.834139	+	1.82651i	0.0381926	+	0.0836302i
$478$	9.41935	−	2.76577i	0.430831	−	0.126503i
$479$	0.754017	−	1.65107i	0.0344519	−	0.0754391i	−0.891624	−	0.452777i	$-0.850433\pi$
$479$	0.754017	−	1.65107i	0.0344519	−	0.0754391i	0.926076	+	0.377338i	$0.123161\pi$
$480$	−0.0276463	+	0.192284i	−0.00126188	+	0.00877654i
$481$	27.8981	−	17.9290i	1.27204	−	0.817492i
$482$	−14.9039			−0.678853
$483$	−9.13893	−	2.02567i	−0.415836	−	0.0921713i
$484$	28.7146			1.30521
$485$	0.183188	−	0.117728i	0.00831815	−	0.00534575i
$486$	0.142315	−	0.989821i	0.00645553	−	0.0448992i
$487$	−6.72443	+	14.7245i	−0.304713	+	0.667229i	−0.998602	−	0.0528530i	$-0.983169\pi$
$487$	−6.72443	+	14.7245i	−0.304713	+	0.667229i	0.693889	+	0.720082i	$0.255896\pi$
$488$	−11.6292	+	3.41464i	−0.526428	+	0.154573i
$489$	−10.1830	−	22.2977i	−0.460491	−	1.00834i
$490$	−0.405850	−	0.468376i	−0.0183344	−	0.0211591i
$491$	0.202307	+	1.40708i	0.00913000	+	0.0635006i	0.993877	−	0.110491i	$-0.0352424\pi$
$491$	0.202307	+	1.40708i	0.00913000	+	0.0635006i	−0.984747	+	0.173992i	$0.944333\pi$
$492$	−0.932638	−	0.273847i	−0.0420466	−	0.0123460i
$493$	11.3804	−	13.1336i	0.512546	−	0.591509i
$494$	3.47978	+	2.23632i	0.156563	+	0.100617i
$495$	−1.02989	−	0.661868i	−0.0462899	−	0.0297487i
$496$	0.663836	−	0.766107i	0.0298071	−	0.0343992i
$497$	−2.07763	−	0.610046i	−0.0931942	−	0.0273643i
$498$	0.570276	+	3.96635i	0.0255547	+	0.177737i
$499$	−13.4737	−	15.5495i	−0.603167	−	0.696092i	0.369253	−	0.929329i	$-0.379614\pi$
$499$	−13.4737	−	15.5495i	−0.603167	−	0.696092i	−0.972420	+	0.233237i	$0.925068\pi$
$500$	0.803947	+	1.76040i	0.0359536	+	0.0787274i
$501$	−1.87527	+	0.550628i	−0.0837808	+	0.0246002i
$502$	−0.890944	+	1.95089i	−0.0397648	+	0.0870727i
$503$	−2.10448	+	14.6370i	−0.0938342	+	0.652631i	0.887569	+	0.460674i	$0.152392\pi$
$503$	−2.10448	+	14.6370i	−0.0938342	+	0.652631i	−0.981403	+	0.191957i	$0.938517\pi$
$504$	1.64200	−	1.05525i	0.0731405	−	0.0470045i
$505$	−2.44214			−0.108674
$506$	21.2869	+	21.4547i	0.946316	+	0.953778i
$507$	−10.1638			−0.451391
$508$	−18.1810	+	11.6842i	−0.806652	+	0.518403i
$509$	−4.71769	+	32.8122i	−0.209108	+	1.45438i	0.566969	+	0.823739i	$0.308116\pi$
$509$	−4.71769	+	32.8122i	−0.209108	+	1.45438i	−0.776077	+	0.630638i	$0.782793\pi$
$510$	−0.258872	+	0.566850i	−0.0114630	+	0.0251006i
$511$	24.6944	−	7.25094i	1.09242	−	0.320763i
$512$	0.415415	+	0.909632i	0.0183589	+	0.0402004i
$513$	0.562819	+	0.649528i	0.0248491	+	0.0286774i
$514$	2.25552	+	15.6875i	0.0994866	+	0.691945i
$515$	3.61533	+	1.06156i	0.159311	+	0.0467778i
$516$	−3.36783	+	3.88668i	−0.148260	+	0.171102i
$517$	−39.2959	−	25.2539i	−1.72823	−	1.11067i
$518$	11.3140	+	7.27106i	0.497108	+	0.319472i
$519$	4.02193	−	4.64155i	0.176543	−	0.203742i
$520$	0.897086	+	0.263408i	0.0393398	+	0.0115512i
$521$	4.12229	+	28.6712i	0.180601	+	1.25611i	0.855347	+	0.518056i	$0.173344\pi$
$521$	4.12229	+	28.6712i	0.180601	+	1.25611i	−0.674746	+	0.738050i	$0.735747\pi$
$522$	−3.54765	−	4.09421i	−0.155276	−	0.179198i
$523$	13.9867	+	30.6266i	0.611595	+	1.33921i	0.921477	+	0.388432i	$0.126983\pi$
$523$	13.9867	+	30.6266i	0.611595	+	1.33921i	−0.309882	+	0.950775i	$0.600290\pi$
$524$	14.3512	−	4.21390i	0.626937	−	0.184085i
$525$	4.02354	−	8.81032i	0.175602	−	0.384514i
$526$	−0.0185874	+	0.129278i	−0.000810450	+	0.00563680i
$527$	2.73561	−	1.75807i	0.119165	−	0.0765827i
$528$	−6.30195			−0.274257
$529$	−0.180643	+	22.9993i	−0.00785404	+	0.999969i
$530$	−0.390071			−0.0169436
$531$	−7.23664	+	4.65071i	−0.314043	+	0.201823i
$532$	−0.238735	+	1.66044i	−0.0103505	+	0.0719892i
$533$	−1.94338	+	4.25542i	−0.0841773	+	0.184323i
$534$	−9.16467	+	2.69099i	−0.396594	+	0.116451i
$535$	−0.248226	−	0.543540i	−0.0107318	−	0.0234993i
$536$	−4.64510	−	5.36073i	−0.200638	−	0.231548i
$537$	0.920906	+	6.40504i	0.0397400	+	0.276398i
$538$	22.9979	+	6.75279i	0.991510	+	0.291134i
$539$	13.1660	−	15.1944i	0.567099	−	0.654467i
$540$	0.163423	+	0.105026i	0.00703262	+	0.00451959i
$541$	−33.8175	−	21.7332i	−1.45393	−	0.934383i	−0.999039	−	0.0438352i	$-0.986042\pi$
$541$	−33.8175	−	21.7332i	−1.45393	−	0.934383i	−0.454890	−	0.890548i	$-0.650321\pi$
$542$	−2.10988	+	2.43493i	−0.0906271	+	0.104589i
$543$	3.12935	+	0.918861i	0.134293	+	0.0394321i
$544$	0.456526	+	3.17521i	0.0195734	+	0.136136i
$545$	0.247978	+	0.286182i	0.0106222	+	0.0122587i
$546$	−3.90242	−	8.54510i	−0.167008	−	0.365696i
$547$	−21.7806	+	6.39537i	−0.931272	+	0.273446i	−0.711969	−	0.702211i	$-0.752196\pi$
$547$	−21.7806	+	6.39537i	−0.931272	+	0.273446i	−0.219303	+	0.975657i	$0.570378\pi$
$548$	7.54269	−	16.5162i	0.322208	−	0.705536i
$549$	−1.72487	+	11.9968i	−0.0736159	+	0.512010i
$550$	−26.3076	+	16.9069i	−1.12176	+	0.720912i
$551$	4.65598			0.198352
$552$	−3.37782	−	3.40446i	−0.143770	−	0.144903i
$553$	2.20519			0.0937741
$554$	−10.9385	+	7.02973i	−0.464731	+	0.298665i
$555$	−0.190493	+	1.32491i	−0.00808599	+	0.0562393i
$556$	−3.06044	+	6.70142i	−0.129791	+	0.284203i
$557$	−3.79597	+	1.11460i	−0.160841	+	0.0472270i	−0.361162	−	0.932503i	$-0.617620\pi$
$557$	−3.79597	+	1.11460i	−0.160841	+	0.0472270i	0.200321	+	0.979730i	$0.435802\pi$
$558$	−0.421108	−	0.922099i	−0.0178269	−	0.0390355i
$559$	16.2090	+	18.7061i	0.685566	+	0.791185i
$560$	0.0539615	+	0.375310i	0.00228029	+	0.0158598i
$561$	−19.3969	−	5.69544i	−0.818938	−	0.240462i
$562$	−6.36426	+	7.34475i	−0.268460	+	0.309820i
$563$	−22.8941	−	14.7132i	−0.964873	−	0.620086i	−0.0395303	−	0.999218i	$-0.512586\pi$
$563$	−22.8941	−	14.7132i	−0.964873	−	0.620086i	−0.925342	+	0.379132i	$0.876223\pi$
$564$	6.23551	+	4.00732i	0.262562	+	0.168738i
$565$	−2.18163	+	2.51773i	−0.0917818	+	0.105922i
$566$	−19.1752	−	5.63035i	−0.805995	−	0.236661i
$567$	−0.277777	−	1.93198i	−0.0116655	−	0.0811356i
$568$	−0.726488	−	0.838411i	−0.0304827	−	0.0351790i
$569$	−8.57486	−	18.7763i	−0.359477	−	0.787144i	−0.999818	−	0.0190542i	$-0.993935\pi$
$569$	−8.57486	−	18.7763i	−0.359477	−	0.787144i	0.640342	−	0.768090i	$-0.278793\pi$
$570$	−0.160195	+	0.0470375i	−0.00670983	+	0.00197018i
$571$	12.6110	−	27.6142i	0.527753	−	1.15562i	−0.438667	−	0.898650i	$-0.644549\pi$
$571$	12.6110	−	27.6142i	0.527753	−	1.15562i	0.966420	−	0.256968i	$-0.0827235\pi$
$572$	−4.31648	+	30.0218i	−0.180481	+	1.25527i
$573$	19.2257	−	12.3556i	0.803165	−	0.516162i
$574$	−1.89722			−0.0791884
$575$	−23.2343	−	5.14995i	−0.968936	−	0.214768i
$576$	1.00000			0.0416667
$577$	−11.8754	+	7.63182i	−0.494377	+	0.317717i	−0.763964	−	0.645259i	$-0.776749\pi$
$577$	−11.8754	+	7.63182i	−0.494377	+	0.317717i	0.269586	+	0.962976i	$0.413113\pi$
$578$	0.954880	−	6.64134i	0.0397178	−	0.276243i
$579$	7.03771	−	15.4104i	0.292477	−	0.640436i
$580$	1.00977	−	0.296494i	0.0419283	−	0.0123112i
$581$	3.24910	+	7.11454i	0.134795	+	0.295161i
$582$	−0.734062	−	0.847152i	−0.0304278	−	0.0351156i
$583$	−1.80087	−	12.5253i	−0.0745843	−	0.518745i
$584$	12.6518	+	3.71491i	0.523536	+	0.153724i
$585$	0.612268	−	0.706595i	0.0253142	−	0.0292141i
$586$	−15.0434	−	9.66778i	−0.621435	−	0.399372i
$587$	30.7510	+	19.7625i	1.26923	+	0.815685i	0.989520	−	0.144399i	$-0.0461249\pi$
$587$	30.7510	+	19.7625i	1.26923	+	0.815685i	0.279711	+	0.960084i	$0.409761\pi$
$588$	−2.08919	+	2.41106i	−0.0861568	+	0.0994303i
$589$	0.835937	+	0.245453i	0.0344442	+	0.0101137i
$590$	−0.237820	−	1.65407i	−0.00979088	−	0.0680970i
$591$	0.821721	+	0.948317i	0.0338011	+	0.0390085i
$592$	2.86236	+	6.26770i	0.117642	+	0.257601i
$593$	−6.37440	+	1.87169i	−0.261765	+	0.0768612i	−0.409982	−	0.912094i	$-0.634465\pi$
$593$	−6.37440	+	1.87169i	−0.261765	+	0.0768612i	0.148216	+	0.988955i	$0.452647\pi$
$594$	−2.61792	+	5.73246i	−0.107415	+	0.235205i
$595$	−0.173101	+	1.20394i	−0.00709644	+	0.0493568i
$596$	13.1516	−	8.45201i	0.538710	−	0.346208i
$597$	−24.8140			−1.01557
$598$	−18.5321	+	13.7597i	−0.757833	+	0.562677i
$599$	28.0099			1.14445			0.572226	−	0.820096i	$-0.306080\pi$
$599$	28.0099			1.14445			0.572226	+	0.820096i	$0.306080\pi$
$600$	4.17452	−	2.68280i	0.170424	−	0.109525i
$601$	−2.50280	+	17.4074i	−0.102091	+	0.710061i	0.872913	+	0.487876i	$0.162228\pi$
$601$	−2.50280	+	17.4074i	−0.102091	+	0.710061i	−0.975004	+	0.222185i	$0.928681\pi$
$602$	−4.16994	+	9.13089i	−0.169954	+	0.372147i
$603$	−6.80594	+	1.99840i	−0.277159	+	0.0813813i
$604$	8.60082	+	18.8332i	0.349962	+	0.766311i
$605$	3.65291	+	4.21568i	0.148512	+	0.171392i
$606$	1.78910	+	12.4435i	0.0726772	+	0.505481i
$607$	22.6391	+	6.64743i	0.918891	+	0.269811i	0.706779	−	0.707435i	$-0.250148\pi$
$607$	22.6391	+	6.64743i	0.918891	+	0.269811i	0.212112	+	0.977245i	$0.431966\pi$
$608$	−0.562819	+	0.649528i	−0.0228253	+	0.0263418i
$609$	−8.89539	−	5.71672i	−0.360459	−	0.231653i
$610$	−1.98071	−	1.27293i	−0.0801967	−	0.0515393i
$611$	23.3614	−	26.9605i	0.945101	−	1.09070i
$612$	3.07792	+	0.903759i	0.124418	+	0.0365323i
$613$	−4.69550	−	32.6579i	−0.189650	−	1.31904i	−0.832916	−	0.553399i	$-0.813330\pi$
$613$	−4.69550	−	32.6579i	−0.189650	−	1.31904i	0.643267	−	0.765642i	$-0.277579\pi$
$614$	8.19485	+	9.45736i	0.330717	+	0.381668i
$615$	−0.0784406	−	0.171761i	−0.00316303	−	0.00692607i
$616$	−11.8022	+	3.46544i	−0.475524	+	0.139627i
$617$	−15.8099	+	34.6189i	−0.636484	+	1.39371i	0.266418	+	0.963858i	$0.414160\pi$
$617$	−15.8099	+	34.6189i	−0.636484	+	1.39371i	−0.902901	+	0.429848i	$0.858567\pi$
$618$	2.76038	−	19.1989i	0.111039	−	0.772292i
$619$	−7.14317	+	4.59063i	−0.287108	+	0.184513i	−0.676265	−	0.736658i	$-0.736403\pi$
$619$	−7.14317	+	4.59063i	−0.287108	+	0.184513i	0.389157	+	0.921171i	$0.372766\pi$
$620$	0.196924			0.00790866
$621$	−4.50000	+	1.65831i	−0.180579	+	0.0665458i
$622$	5.45773			0.218835
$623$	−15.6837	+	10.0793i	−0.628354	+	0.403818i
$624$	0.684944	−	4.76389i	0.0274197	−	0.190708i
$625$	10.1508	−	22.2272i	0.406033	−	0.889087i
$626$	22.9543	−	6.73999i	0.917438	−	0.269384i
$627$	−2.24997	−	4.92675i	−0.0898552	−	0.196755i
$628$	2.60393	+	3.00510i	0.103908	+	0.119916i
$629$	3.14563	+	21.8784i	0.125425	+	0.872347i
$630$	0.363811	+	0.106824i	0.0144946	+	0.00425599i
$631$	−7.29960	+	8.42419i	−0.290593	+	0.335362i	−0.882209	−	0.470858i	$-0.843945\pi$
$631$	−7.29960	+	8.42419i	−0.290593	+	0.335362i	0.591617	+	0.806220i	$0.298490\pi$
$632$	0.950444	+	0.610813i	0.0378066	+	0.0242968i
$633$	−6.10604	−	3.92412i	−0.242693	−	0.155970i
$634$	10.5580	−	12.1846i	0.419313	−	0.483912i
$635$	−4.02828	−	1.18281i	−0.159858	−	0.0469384i
$636$	0.285763	+	1.98753i	0.0113313	+	0.0788106i
$637$	10.0550	+	11.6041i	0.398395	+	0.459772i
$638$	14.1824	+	31.0551i	0.561485	+	1.22948i
$639$	−1.06444	+	0.312548i	−0.0421086	+	0.0123642i
$640$	−0.0806993	+	0.176707i	−0.00318992	+	0.00698495i
$641$	5.38460	−	37.4507i	0.212679	−	1.47921i	−0.551482	−	0.834187i	$-0.685937\pi$
$641$	5.38460	−	37.4507i	0.212679	−	1.47921i	0.764160	−	0.645026i	$-0.223154\pi$
$642$	−2.58765	+	1.66298i	−0.102126	+	0.0656326i
$643$	−22.3733			−0.882317			−0.441158	−	0.897429i	$-0.645432\pi$
$643$	−22.3733			−0.882317			−0.441158	+	0.897429i	$0.645432\pi$
$644$	−8.19804	−	4.51835i	−0.323048	−	0.178048i
$645$	−0.999053			−0.0393377
$646$	−2.31933	+	1.49054i	−0.0912528	+	0.0586446i
$647$	1.55788	−	10.8353i	0.0612465	−	0.425979i	−0.936011	−	0.351970i	$-0.885512\pi$
$647$	1.55788	−	10.8353i	0.0612465	−	0.425979i	0.997258	−	0.0740083i	$-0.0235791\pi$
$648$	0.415415	−	0.909632i	0.0163190	−	0.0357337i
$649$	52.0148	−	15.2729i	2.04176	−	0.599515i
$650$	−9.92126	−	21.7245i	−0.389144	−	0.852106i
$651$	−1.29571	−	1.49533i	−0.0507828	−	0.0586064i
$652$	−3.48854	−	24.2633i	−0.136622	−	0.950226i
$653$	−5.55361	−	1.63069i	−0.217329	−	0.0638137i	0.171255	−	0.985227i	$-0.445218\pi$
$653$	−5.55361	−	1.63069i	−0.217329	−	0.0638137i	−0.388585	+	0.921413i	$0.627036\pi$
$654$	1.27652	−	1.47318i	0.0499157	−	0.0576058i
$655$	2.44434	+	1.57088i	0.0955083	+	0.0613794i
$656$	−0.817708	−	0.525509i	−0.0319261	−	0.0205177i
$657$	8.63495	−	9.96526i	0.336881	−	0.388782i
$658$	13.8814	+	4.07594i	0.541153	+	0.158897i
$659$	1.18327	+	8.22980i	0.0460935	+	0.320588i	0.999803	+	0.0198575i	$0.00632124\pi$
$659$	1.18327	+	8.22980i	0.0460935	+	0.320588i	−0.953709	+	0.300730i	$0.902770\pi$
$660$	−0.801699	−	0.925210i	−0.0312061	−	0.0360137i
$661$	−5.05499	−	11.0689i	−0.196616	−	0.430530i	0.785486	−	0.618880i	$-0.212413\pi$
$661$	−5.05499	−	11.0689i	−0.196616	−	0.430530i	−0.982102	+	0.188350i	$0.939686\pi$
$662$	0.496914	−	0.145907i	0.0193131	−	0.00567085i
$663$	6.41361	−	14.0439i	0.249084	−	0.545418i
$664$	−0.570276	+	3.96635i	−0.0221310	+	0.153924i
$665$	−0.274145	+	0.176182i	−0.0106309	+	0.00683206i
$666$	6.89037			0.266996
$667$	−9.17495	+	24.3070i	−0.355255	+	0.941172i
$668$	−1.95444			−0.0756194
$669$	−17.4427	+	11.2097i	−0.674373	+	0.433393i
$670$	0.196103	−	1.36392i	0.00757611	−	0.0526930i
$671$	31.7296	−	69.4781i	1.22491	−	2.68217i
$672$	1.87279	−	0.549899i	0.0722443	−	0.0212128i
$673$	2.02362	+	4.43110i	0.0780047	+	0.170807i	0.944616	−	0.328177i	$-0.106434\pi$
$673$	2.02362	+	4.43110i	0.0780047	+	0.170807i	−0.866612	+	0.498983i	$0.833707\pi$
$674$	0.347154	+	0.400637i	0.0133719	+	0.0154320i
$675$	−0.706204	−	4.91175i	−0.0271818	−	0.189053i
$676$	−9.75211	−	2.86348i	−0.375081	−	0.110134i
$677$	13.1011	−	15.1195i	0.503517	−	0.581090i	−0.445910	−	0.895078i	$-0.647120\pi$
$677$	13.1011	−	15.1195i	0.503517	−	0.581090i	0.949427	+	0.313988i	$0.101665\pi$
$678$	14.4268	+	9.27157i	0.554060	+	0.356073i
$679$	−1.84059	−	1.18287i	−0.0706353	−	0.0453946i
$680$	−0.408086	+	0.470956i	−0.0156494	+	0.0180604i
$681$	−20.1977	−	5.93057i	−0.773977	−	0.227260i
$682$	0.909153	+	6.32330i	0.0348133	+	0.242131i
$683$	15.7090	+	18.1292i	0.601089	+	0.693693i	0.972002	−	0.234974i	$-0.0755006\pi$
$683$	15.7090	+	18.1292i	0.601089	+	0.693693i	−0.370913	+	0.928668i	$0.620955\pi$
$684$	0.357028	+	0.781782i	0.0136513	+	0.0298922i
$685$	3.38433	−	0.993730i	0.129309	−	0.0379685i
$686$	−8.26256	+	18.0925i	−0.315466	+	0.690774i
$687$	−0.272668	+	1.89645i	−0.0104029	+	0.0723540i
$688$	−4.32641	+	2.78042i	−0.164943	+	0.106002i
$689$	9.66410			0.368173
$690$	0.0701117	−	0.929005i	0.00266911	−	0.0353666i
$691$	16.5438			0.629356			0.314678	−	0.949199i	$-0.398104\pi$
$691$	16.5438			0.629356			0.314678	+	0.949199i	$0.398104\pi$
$692$	5.16669	−	3.32043i	0.196408	−	0.126224i
$693$	−1.75054	+	12.1753i	−0.0664974	+	0.462500i
$694$	11.1383	−	24.3896i	0.422806	−	0.925816i
$695$	−1.37319	+	0.403204i	−0.0520880	+	0.0152944i
$696$	−2.25047	−	4.92785i	−0.0853040	−	0.186790i
$697$	−2.04191	−	2.35648i	−0.0773427	−	0.0892582i
$698$	−0.207393	−	1.44245i	−0.00784994	−	0.0545975i
$699$	−13.8460	−	4.06556i	−0.523705	−	0.153774i
$700$	6.34271	−	7.31988i	0.239732	−	0.276665i
$701$	−13.4451	−	8.64063i	−0.507814	−	0.326352i	0.261521	−	0.965198i	$-0.415776\pi$
$701$	−13.4451	−	8.64063i	−0.507814	−	0.326352i	−0.769335	+	0.638846i	$0.779412\pi$
$702$	−4.04885	−	2.60204i	−0.152814	−	0.0982076i
$703$	−3.87803	+	4.47549i	−0.146263	+	0.168796i
$704$	−6.04668	−	1.77546i	−0.227893	−	0.0669153i
$705$	0.204919	+	1.42524i	0.00771770	+	0.0536778i
$706$	−14.7041	−	16.9694i	−0.553394	−	0.638651i
$707$	10.1932	+	22.3201i	0.383356	+	0.839434i
$708$	−8.25376	+	2.42352i	−0.310195	+	0.0910816i
$709$	2.66064	−	5.82599i	0.0999224	−	0.218800i	−0.853068	−	0.521800i	$-0.825261\pi$
$709$	2.66064	−	5.82599i	0.0999224	−	0.218800i	0.952991	+	0.303000i	$0.0979882\pi$
$710$	0.0306702	−	0.213316i	0.00115103	−	0.00800561i
$711$	0.950444	−	0.610813i	0.0356444	−	0.0229073i
$712$	−9.55158			−0.357960
$713$	−2.92868	+	3.88041i	−0.109680	+	0.145322i
$714$	6.26126			0.234322
$715$	−4.95672	+	3.18549i	−0.185371	+	0.119131i
$716$	−0.920906	+	6.40504i	−0.0344159	+	0.239368i
$717$	4.07813	−	8.92987i	0.152301	−	0.333492i
$718$	−0.162153	+	0.0476124i	−0.00605149	+	0.00177688i
$719$	−17.3216	−	37.9290i	−0.645986	−	1.41451i	−0.895024	−	0.446019i	$-0.852841\pi$
$719$	−17.3216	−	37.9290i	−0.645986	−	1.41451i	0.249037	−	0.968494i	$-0.419886\pi$
$720$	0.127214	+	0.146813i	0.00474100	+	0.00547141i
$721$	−5.38785	−	37.4733i	−0.200654	−	1.39558i
$722$	17.5216	+	5.14482i	0.652088	+	0.191470i
$723$	−9.75997	+	11.2636i	−0.362977	+	0.418898i
$724$	2.74372	+	1.76328i	0.101969	+	0.0655318i
$725$	−22.6151	−	14.5338i	−0.839903	−	0.539773i
$726$	18.8040	−	21.7010i	0.697884	−	0.805401i
$727$	9.60066	+	2.81901i	0.356069	+	0.104551i	0.454875	−	0.890555i	$-0.349684\pi$
$727$	9.60066	+	2.81901i	0.356069	+	0.104551i	−0.0988057	+	0.995107i	$0.531502\pi$
$728$	−1.33691	−	9.29840i	−0.0495491	−	0.344622i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	1.06409	+	2.33004i	0.0393839	+	0.0862388i
$731$	−15.8292	+	4.64787i	−0.585463	+	0.171908i
$732$	−5.03489	+	11.0249i	−0.186095	+	0.407491i
$733$	3.32462	−	23.1232i	0.122798	−	0.854076i	−0.831565	−	0.555427i	$-0.812555\pi$
$733$	3.32462	−	23.1232i	0.122798	−	0.854076i	0.954363	−	0.298649i	$-0.0965360\pi$
$734$	15.0006	−	9.64029i	0.553682	−	0.355830i
$735$	−0.619750			−0.0228598
$736$	−2.28185	−	4.21819i	−0.0841101	−	0.155485i
$737$	44.7014			1.64660
$738$	−0.817708	+	0.525509i	−0.0301002	+	0.0193442i
$739$	−3.80336	+	26.4530i	−0.139909	+	0.973088i	0.792033	+	0.610479i	$0.209023\pi$
$739$	−3.80336	+	26.4530i	−0.139909	+	0.973088i	−0.931941	+	0.362609i	$0.881886\pi$
$740$	−0.556048	+	1.21757i	−0.0204407	+	0.0447589i
$741$	3.96887	−	1.16536i	0.145800	−	0.0428108i
$742$	1.62811	+	3.56507i	0.0597700	+	0.130878i
$743$	9.93499	+	11.4656i	0.364479	+	0.420632i	0.908135	−	0.418676i	$-0.137506\pi$
$743$	9.93499	+	11.4656i	0.364479	+	0.420632i	−0.543656	+	0.839308i	$0.682960\pi$
$744$	−0.144265	−	1.00339i	−0.00528902	−	0.0367860i
$745$	2.91394	+	0.855609i	0.106758	+	0.0313471i
$746$	17.9356	−	20.6987i	0.656667	−	0.757835i
$747$	3.37102	+	2.16642i	0.123339	+	0.0792653i
$748$	−17.0066	−	10.9295i	−0.621823	−	0.399621i
$749$	−3.93164	+	4.53735i	−0.143659	+	0.165791i
$750$	1.85689	+	0.545233i	0.0678042	+	0.0199091i
$751$	−3.08374	−	21.4478i	−0.112527	−	0.782643i	−0.965447	−	0.260601i	$-0.916079\pi$
$751$	−3.08374	−	21.4478i	−0.112527	−	0.782643i	0.852920	−	0.522042i	$-0.174830\pi$
$752$	4.85393	+	5.60174i	0.177005	+	0.204274i
$753$	0.890944	+	1.95089i	0.0324678	+	0.0710946i
$754$	−25.0172	+	7.34571i	−0.911072	+	0.267515i
$755$	−1.67081	+	3.65856i	−0.0608070	+	0.133149i
$756$	0.277777	−	1.93198i	0.0101027	−	0.0702655i
$757$	−3.40872	+	2.19065i	−0.123892	+	0.0796206i	−0.601119	−	0.799159i	$-0.705278\pi$
$757$	−3.40872	+	2.19065i	−0.123892	+	0.0796206i	0.477227	+	0.878780i	$0.341642\pi$
$758$	−2.73604			−0.0993774
$759$	30.1543	−	2.03769i	1.09453	−	0.0739634i
$760$	−0.166958			−0.00605620
$761$	−37.1929	+	23.9024i	−1.34824	+	0.866461i	−0.997545	−	0.0700285i	$-0.977691\pi$
$761$	−37.1929	+	23.9024i	−1.34824	+	0.866461i	−0.350695	+	0.936490i	$0.614055\pi$
$762$	−3.07568	+	21.3918i	−0.111420	+	0.774944i
$763$	1.58054	−	3.46090i	0.0572194	−	0.125293i
$764$	21.9279	−	6.43861i	0.793323	−	0.232941i
$765$	0.258872	+	0.566850i	0.00935953	+	0.0204945i
$766$	9.43713	+	10.8910i	0.340977	+	0.393509i
$767$	5.89204	+	40.9800i	0.212749	+	1.47970i
$768$	0.959493	+	0.281733i	0.0346227	+	0.0101661i
$769$	−5.76963	+	6.65850i	−0.208058	+	0.240112i	−0.850182	−	0.526489i	$-0.823508\pi$
$769$	−5.76963	+	6.65850i	−0.208058	+	0.240112i	0.642124	+	0.766601i	$0.278054\pi$
$770$	−2.01018	−	1.29187i	−0.0724419	−	0.0465556i
$771$	13.3329	+	8.56850i	0.480171	+	0.308587i
$772$	11.0943	−	12.8035i	0.399291	−	0.460806i
$773$	0.608433	+	0.178652i	0.0218838	+	0.00642566i	0.292656	−	0.956218i	$-0.405461\pi$
$773$	0.608433	+	0.178652i	0.0218838	+	0.00642566i	−0.270772	+	0.962643i	$0.587279\pi$
$774$	0.731899	+	5.09047i	0.0263076	+	0.182973i
$775$	−3.29413	−	3.80163i	−0.118329	−	0.136558i
$776$	−0.465657	−	1.01965i	−0.0167161	−	0.0366031i
$777$	12.9042	−	3.78901i	0.462935	−	0.135930i
$778$	0.450326	−	0.986077i	0.0161450	−	0.0353526i
$779$	0.118889	−	0.826890i	0.00425964	−	0.0296264i
$780$	0.786537	−	0.505477i	0.0281625	−	0.0180990i
$781$	6.99124			0.250166
$782$	−3.21112	−	15.0455i	−0.114829	−	0.538026i
$783$	−5.41741			−0.193602
$784$	−2.68384	+	1.72480i	−0.0958514	+	0.0615999i
$785$	−0.109930	+	0.764583i	−0.00392359	+	0.0272891i
$786$	6.21340	−	13.6055i	0.221625	−	0.485291i
$787$	−15.3336	+	4.50235i	−0.546584	+	0.160491i	−0.543355	−	0.839503i	$-0.682846\pi$
$787$	−15.3336	+	4.50235i	−0.546584	+	0.160491i	−0.00322916	+	0.999995i	$0.501028\pi$
$788$	0.521264	+	1.14141i	0.0185693	+	0.0406610i
$789$	0.0855299	+	0.0987067i	0.00304494	+	0.00351405i
$790$	0.0312347	+	0.217242i	0.00111128	+	0.00772912i
$791$	32.1168	+	9.43035i	1.14194	+	0.335305i
$792$	−4.12690	+	4.76270i	−0.146643	+	0.169235i
$793$	49.0726	+	31.5371i	1.74262	+	1.11991i
$794$	−22.7341	−	14.6103i	−0.806802	−	0.518500i
$795$	−0.255442	+	0.294796i	−0.00905960	+	0.0104553i
$796$	−23.8089	−	6.99091i	−0.843883	−	0.247786i
$797$	5.83086	+	40.5546i	0.206540	+	1.43652i	0.784337	+	0.620335i	$0.213004\pi$
$797$	5.83086	+	40.5546i	0.206540	+	1.43652i	−0.577797	+	0.816181i	$0.696087\pi$
$798$	1.09854	+	1.26778i	0.0388878	+	0.0448789i
$799$	9.87740	+	21.6285i	0.349437	+	0.765161i
$800$	4.76126	−	1.39803i	0.168336	−	0.0494279i
$801$	−3.96787	+	8.68842i	−0.140198	+	0.306990i
$802$	−1.31984	+	9.17969i	−0.0466052	+	0.324146i
$803$	−69.9057	+	44.9257i	−2.46692	+	1.58539i
$804$	−7.09327			−0.250160
$805$	−0.379555	−	1.77838i	−0.0133776	−	0.0626797i
$806$	−4.87884			−0.171850
$807$	20.1638	−	12.9585i	0.709801	−	0.456161i
$808$	−1.78910	+	12.4435i	−0.0629403	+	0.437759i
$809$	−11.7254	+	25.6750i	−0.412242	+	0.902685i	0.583638	+	0.812014i	$0.301629\pi$
$809$	−11.7254	+	25.6750i	−0.412242	+	0.902685i	−0.995881	+	0.0906713i	$0.971099\pi$
$810$	0.186393	−	0.0547299i	0.00654918	−	0.00192301i
$811$	−1.50266	−	3.29037i	−0.0527657	−	0.115541i	0.881413	−	0.472347i	$-0.156593\pi$
$811$	−1.50266	−	3.29037i	−0.0527657	−	0.115541i	−0.934178	+	0.356806i	$0.883866\pi$
$812$	−6.92448	−	7.99127i	−0.243001	−	0.280439i
$813$	0.458521	+	3.18908i	0.0160810	+	0.111846i
$814$	−41.6638	−	12.2336i	−1.46032	−	0.428788i
$815$	3.11839	−	3.59881i	0.109232	−	0.126061i
$816$	2.69862	+	1.73430i	0.0944707	+	0.0607127i
$817$	−3.71833	−	2.38963i	−0.130088	−	0.0836024i
$818$	−24.0764	+	27.7857i	−0.841813	+	0.971504i
$819$	−9.01349	−	2.64660i	−0.314957	−	0.0924797i
$820$	−0.0268725	−	0.186903i	−0.000938430	−	0.00652692i
$821$	−20.2317	−	23.3487i	−0.706092	−	0.814874i	0.283470	−	0.958981i	$-0.408514\pi$
$821$	−20.2317	−	23.3487i	−0.706092	−	0.814874i	−0.989562	+	0.144107i	$0.953969\pi$
$822$	−7.54269	−	16.5162i	−0.263081	−	0.576068i
$823$	−3.84377	+	1.12863i	−0.133985	+	0.0393416i	−0.348038	−	0.937481i	$-0.613152\pi$
$823$	−3.84377	+	1.12863i	−0.133985	+	0.0393416i	0.214052	+	0.976822i	$0.431334\pi$
$824$	8.05752	−	17.6435i	0.280697	−	0.614641i
$825$	−4.45046	+	30.9536i	−0.154945	+	1.07767i
$826$	−14.1248	+	9.07748i	−0.491466	+	0.315846i
$827$	−26.0104			−0.904469			−0.452234	−	0.891899i	$-0.649373\pi$
$827$	−26.0104			−0.904469			−0.452234	+	0.891899i	$0.649373\pi$
$828$	−4.78492	+	0.323343i	−0.166287	+	0.0112369i
$829$	39.4460			1.37002			0.685008	−	0.728535i	$-0.259798\pi$
$829$	39.4460			1.37002			0.685008	+	0.728535i	$0.259798\pi$
$830$	−0.654861	+	0.420853i	−0.0227305	+	0.0146080i
$831$	−1.85046	+	12.8702i	−0.0641918	+	0.446464i
$832$	1.99934	−	4.37795i	0.0693147	−	0.151778i
$833$	−9.81944	+	2.88325i	−0.340223	+	0.0998986i
$834$	3.06044	+	6.70142i	0.105974	+	0.232051i
$835$	−0.248632	−	0.286937i	−0.00860428	−	0.00992986i
$836$	−0.770806	−	5.36107i	−0.0266589	−	0.185417i
$837$	−0.972643	−	0.285594i	−0.0336195	−	0.00987156i
$838$	17.3511	−	20.0242i	0.599383	−	0.691725i
$839$	2.74335	+	1.76304i	0.0947110	+	0.0608670i	0.587139	−	0.809486i	$-0.300254\pi$
$839$	2.74335	+	1.76304i	0.0947110	+	0.0608670i	−0.492428	+	0.870353i	$0.663891\pi$
$840$	0.318978	+	0.204995i	0.0110058	+	0.00707299i
$841$	−0.228106	+	0.263249i	−0.00786573	+	0.00907754i
$842$	−9.54787	−	2.80351i	−0.329041	−	0.0966152i
$843$	1.38309	+	9.61958i	0.0476360	+	0.331316i
$844$	−4.75316	−	5.48543i	−0.163610	−	0.188816i
$845$	−0.820212	−	1.79601i	−0.0282162	−	0.0617848i
$846$	7.11192	−	2.08825i	0.244513	−	0.0717954i
$847$	23.2826	−	50.9817i	0.799998	−	1.75175i
$848$	−0.285763	+	1.98753i	−0.00981316	+	0.0682520i
$849$	−16.8122	+	10.8046i	−0.576995	+	0.370812i
$850$	15.9182			0.545991
$851$	−15.7228	−	29.0649i	−0.538970	−	0.996332i
$852$	−1.10938			−0.0380066
$853$	−6.49153	+	4.17185i	−0.222266	+	0.142842i	−0.647035	−	0.762460i	$-0.723991\pi$
$853$	−6.49153	+	4.17185i	−0.222266	+	0.142842i	0.424770	+	0.905301i	$0.360355\pi$
$854$	−3.36670	+	23.4159i	−0.115206	+	0.801275i
$855$	−0.0693569	+	0.151870i	−0.00237195	+	0.00519386i
$856$	−2.95135	+	0.866594i	−0.100875	+	0.0296196i
$857$	1.92561	+	4.21649i	0.0657775	+	0.144033i	0.939665	−	0.342095i	$-0.111136\pi$
$857$	1.92561	+	4.21649i	0.0657775	+	0.144033i	−0.873888	+	0.486127i	$0.838409\pi$
$858$	19.8623	+	22.9223i	0.678087	+	0.782554i
$859$	6.99219	+	48.6318i	0.238571	+	1.65929i	0.659130	+	0.752029i	$0.270925\pi$
$859$	6.99219	+	48.6318i	0.238571	+	1.65929i	−0.420559	+	0.907265i	$0.638166\pi$
$860$	−0.958584	−	0.281466i	−0.0326875	−	0.00959790i
$861$	−1.24241	+	1.43382i	−0.0423414	+	0.0488645i
$862$	7.38021	+	4.74297i	0.251371	+	0.161546i
$863$	−34.3280	−	22.0613i	−1.16854	−	0.750975i	−0.195295	−	0.980745i	$-0.562566\pi$
$863$	−34.3280	−	22.0613i	−1.16854	−	0.750975i	−0.973245	+	0.229770i	$0.926203\pi$
$864$	0.654861	−	0.755750i	0.0222788	−	0.0257111i
$865$	1.14476	+	0.336132i	0.0389230	+	0.0114288i
$866$	1.13718	+	7.90928i	0.0386430	+	0.268768i
$867$	−4.39387	−	5.07080i	−0.149224	−	0.172213i
$868$	−0.821940	−	1.79980i	−0.0278985	−	0.0610891i
$869$	−6.83150	+	2.00591i	−0.231743	+	0.0680458i
$870$	0.437181	−	0.957293i	0.0148218	−	0.0324553i
$871$	−4.85849	+	33.7915i	−0.164624	+	1.14498i
$872$	1.63985	−	1.05387i	0.0555323	−	0.0356885i
$873$	−1.12094			−0.0379382
$874$	2.48302	−	3.28992i	0.0839895	−	0.111283i
$875$	3.77739			0.127699
$876$	11.0927	−	7.12885i	0.374788	−	0.240862i
$877$	−3.64997	+	25.3861i	−0.123251	+	0.857228i	0.830583	+	0.556894i	$0.188007\pi$
$877$	−3.64997	+	25.3861i	−0.123251	+	0.857228i	−0.953834	+	0.300334i	$0.902902\pi$
$878$	−0.585997	+	1.28315i	−0.0197764	+	0.0433043i
$879$	−17.1577	+	5.03796i	−0.578716	+	0.169926i
$880$	−0.508563	−	1.11360i	−0.0171436	−	0.0375393i
$881$	−28.1778	−	32.5190i	−0.949336	−	1.09559i	−0.995318	−	0.0966497i	$-0.969187\pi$
$881$	−28.1778	−	32.5190i	−0.949336	−	1.09559i	0.0459826	−	0.998942i	$-0.485358\pi$
$882$	0.454025	+	3.15781i	0.0152878	+	0.106329i
$883$	9.63039	+	2.82774i	0.324089	+	0.0951610i	0.439730	−	0.898130i	$-0.355074\pi$
$883$	9.63039	+	2.82774i	0.324089	+	0.0951610i	−0.115641	+	0.993291i	$0.536892\pi$
$884$	10.1104	−	11.6681i	0.340050	−	0.392439i
$885$	−1.40580	−	0.903454i	−0.0472555	−	0.0303693i
$886$	10.5943	+	6.80856i	0.355923	+	0.228738i
$887$	6.89056	−	7.95213i	0.231362	−	0.267007i	−0.628183	−	0.778065i	$-0.716201\pi$
$887$	6.89056	−	7.95213i	0.231362	−	0.267007i	0.859546	+	0.511059i	$0.170747\pi$
$888$	6.61126	+	1.94124i	0.221859	+	0.0651438i
$889$	6.00326	+	41.7536i	0.201343	+	1.40037i
$890$	−1.21510	−	1.40230i	−0.0407302	−	0.0470051i
$891$	2.61792	+	5.73246i	0.0877038	+	0.192044i
$892$	−19.8943	+	5.84149i	−0.666110	+	0.195588i
$893$	−2.64635	+	5.79469i	−0.0885566	+	0.193912i
$894$	2.22485	−	15.4742i	0.0744102	−	0.517534i
$895$	−1.05750	+	0.679612i	−0.0353482	+	0.0227169i
$896$	1.95185			0.0652067
$897$	−1.73703	+	23.0163i	−0.0579979	+	0.768492i
$898$	−38.3533			−1.27987
$899$	−4.61988	+	2.96901i	−0.154081	+	0.0990221i
$900$	0.706204	−	4.91175i	0.0235401	−	0.163725i
$901$	−2.67580	+	5.85919i	−0.0891439	+	0.195198i
$902$	5.87744	−	1.72577i	0.195697	−	0.0574619i
$903$	4.16994	+	9.13089i	0.138767	+	0.303857i
$904$	11.2304	+	12.9605i	0.373516	+	0.431060i
$905$	0.0901675	+	0.627129i	0.00299727	+	0.0208465i
$906$	19.8655	+	5.83304i	0.659987	+	0.193790i
$907$	−25.5472	+	29.4830i	−0.848281	+	0.978968i	−0.999955	−	0.00946225i	$-0.996988\pi$
$907$	−25.5472	+	29.4830i	−0.848281	+	0.978968i	0.151674	+	0.988431i	$0.451533\pi$
$908$	−17.7087	−	11.3807i	−0.587684	−	0.377681i
$909$	10.5757	+	6.79662i	0.350775	+	0.225430i
$910$	1.19505	−	1.37917i	0.0396157	−	0.0457189i
$911$	21.8445	+	6.41412i	0.723740	+	0.212509i	0.622798	−	0.782383i	$-0.285996\pi$
$911$	21.8445	+	6.41412i	0.723740	+	0.212509i	0.100942	+	0.994892i	$0.467814\pi$
$912$	0.122312	+	0.850701i	0.00405016	+	0.0281695i
$913$	−16.5371	−	19.0848i	−0.547297	−	0.631615i
$914$	11.0649	+	24.2287i	0.365993	+	0.801414i
$915$	−2.25911	+	0.663333i	−0.0746837	+	0.0219291i
$916$	−0.795914	+	1.74281i	−0.0262977	+	0.0575840i
$917$	4.15474	−	28.8969i	0.137202	−	0.954258i
$918$	2.69862	−	1.73430i	0.0890679	−	0.0572404i
$919$	−21.7361			−0.717007			−0.358504	−	0.933528i	$-0.616713\pi$
$919$	−21.7361			−0.717007			−0.358504	+	0.933528i	$0.616713\pi$
$920$	0.329003	−	0.871621i	0.0108469	−	0.0287365i
$921$	12.5139			0.412346
$922$	6.43813	−	4.13753i	0.212028	−	0.136262i
$923$	−0.759861	+	5.28495i	−0.0250111	+	0.173956i
$924$	−5.10979	+	11.1889i	−0.168100	+	0.368087i
$925$	32.8068	−	9.63295i	1.07868	−	0.316729i
$926$	−1.72459	−	3.77633i	−0.0566736	−	0.124098i
$927$	−12.7019	−	14.6588i	−0.417184	−	0.481457i
$928$	−0.770978	−	5.36227i	−0.0253086	−	0.176025i
$929$	39.1306	+	11.4898i	1.28383	+	0.376967i	0.851314	−	0.524657i	$-0.175806\pi$
$929$	39.1306	+	11.4898i	1.28383	+	0.376967i	0.432520	+	0.901625i	$0.357625\pi$
$930$	0.128958	−	0.148825i	0.00422870	−	0.00488018i
$931$	−2.30662	−	1.48238i	−0.0755964	−	0.0485829i
$932$	−12.1398	−	7.80176i	−0.397651	−	0.255555i
$933$	3.57405	−	4.12467i	0.117009	−	0.135036i
$934$	30.8146	+	9.04797i	1.00828	+	0.296059i
$935$	−0.558892	−	3.88718i	−0.0182777	−	0.127124i
$936$	−3.15177	−	3.63733i	−0.103019	−	0.118890i
$937$	−3.00027	−	6.56968i	−0.0980146	−	0.214622i	0.854273	−	0.519825i	$-0.174003\pi$
$937$	−3.00027	−	6.56968i	−0.0980146	−	0.214622i	−0.952287	+	0.305203i	$0.901276\pi$
$938$	−13.2842	+	3.90058i	−0.433743	+	0.127359i
$939$	9.93813	−	21.7615i	0.324318	−	0.710158i
$940$	−0.204919	+	1.42524i	−0.00668372	+	0.0464863i
$941$	11.1082	−	7.13881i	0.362117	−	0.232718i	−0.346912	−	0.937898i	$-0.612770\pi$
$941$	11.1082	−	7.13881i	0.362117	−	0.232718i	0.709029	+	0.705179i	$0.249133\pi$
$942$	3.97631			0.129555
$943$	4.08258	+	2.25012i	0.132947	+	0.0732739i
$944$	−8.60221			−0.279978
$945$	0.318978	−	0.204995i	0.0103763	−	0.00666847i
$946$	4.61239	−	32.0799i	0.149962	−	1.04301i
$947$	14.0374	−	30.7376i	0.456154	−	0.998837i	−0.532194	−	0.846623i	$-0.678632\pi$
$947$	14.0374	−	30.7376i	0.456154	−	0.998837i	0.988347	−	0.152215i	$-0.0486405\pi$
$948$	1.08403	−	0.318300i	0.0352077	−	0.0103379i
$949$	−26.3632	−	57.7274i	−0.855786	−	1.87391i
$950$	2.79286	+	3.22313i	0.0906122	+	0.104572i
$951$	−2.29448	−	15.9584i	−0.0744035	−	0.517488i
$952$	6.00763	+	1.76400i	0.194709	+	0.0571716i
$953$	14.7742	−	17.0503i	0.478582	−	0.552313i	−0.464197	−	0.885732i	$-0.653657\pi$
$953$	14.7742	−	17.0503i	0.478582	−	0.552313i	0.942779	+	0.333419i	$0.108202\pi$
$954$	1.68921	+	1.08559i	0.0546902	+	0.0351472i
$955$	3.73482	+	2.40022i	0.120856	+	0.0776693i
$956$	6.42877	−	7.41920i	0.207921	−	0.239954i
$957$	32.7573	+	9.61842i	1.05889	+	0.310919i
$958$	−0.258315	−	1.79662i	−0.00834576	−	0.0580461i
$959$	−23.2081	−	26.7836i	−0.749428	−	0.864886i
$960$	0.0806993	+	0.176707i	0.00260456	+	0.00570318i
$961$	28.7583	−	8.44420i	0.927687	−	0.272394i
$962$	13.7762	−	30.1657i	0.444163	−	0.972581i
$963$	−0.437753	+	3.04464i	−0.0141064	+	0.0981120i
$964$	−12.5379	+	8.05765i	−0.403820	+	0.259519i
$965$	3.29107			0.105943
$966$	−8.78332	+	3.23678i	−0.282599	+	0.104142i
$967$	−15.9309			−0.512303			−0.256152	−	0.966637i	$-0.582455\pi$
$967$	−15.9309			−0.512303			−0.256152	+	0.966637i	$0.582455\pi$
$968$	24.1562	−	15.5243i	0.776411	−	0.498969i
$969$	−0.392361	+	2.72893i	−0.0126044	+	0.0876658i
$970$	0.0904593	−	0.198078i	0.00290447	−	0.00635991i
$971$	−40.4422	+	11.8749i	−1.29785	+	0.381084i	−0.856452	−	0.516227i	$-0.827336\pi$
$971$	−40.4422	+	11.8749i	−1.29785	+	0.381084i	−0.441400	+	0.897310i	$0.645518\pi$
$972$	−0.415415	−	0.909632i	−0.0133244	−	0.0291765i
$973$	9.41665	+	10.8674i	0.301884	+	0.348392i
$974$	2.30369	+	16.0225i	0.0738149	+	0.513394i
$975$	−22.9154	−	6.72855i	−0.733879	−	0.215486i
$976$	−7.93700	+	9.15979i	−0.254057	+	0.293198i
$977$	−26.7606	−	17.1980i	−0.856147	−	0.550212i	0.0373392	−	0.999303i	$-0.488112\pi$
$977$	−26.7606	−	17.1980i	−0.856147	−	0.550212i	−0.893486	+	0.449090i	$0.851748\pi$
$978$	−20.6215	−	13.2526i	−0.659404	−	0.423773i
$979$	39.4184	−	45.4913i	1.25982	−	1.45391i
$980$	−0.594646	−	0.174604i	−0.0189953	−	0.00557752i
$981$	−0.277413	−	1.92945i	−0.00885713	−	0.0616027i
$982$	0.930916	+	1.07433i	0.0297067	+	0.0342834i
$983$	8.23740	+	18.0374i	0.262732	+	0.575303i	0.994319	−	0.106446i	$-0.0339470\pi$
$983$	8.23740	+	18.0374i	0.262732	+	0.575303i	−0.731586	+	0.681749i	$0.761220\pi$
$984$	−0.932638	+	0.273847i	−0.0297314	+	0.00872993i
$985$	−0.101262	+	0.221732i	−0.00322646	+	0.00706497i
$986$	2.47319	−	17.2014i	0.0787624	−	0.547804i
$987$	12.1708	−	7.82168i	0.387400	−	0.248967i
$988$	4.13642			0.131597
$989$	19.8025	−	14.7030i	0.629683	−	0.467528i
$990$	−1.22423			−0.0389085
$991$	5.30776	−	3.41109i	0.168606	−	0.108357i	−0.453616	−	0.891197i	$-0.649866\pi$
$991$	5.30776	−	3.41109i	0.168606	−	0.108357i	0.622223	+	0.782840i	$0.286230\pi$
$992$	0.144265	−	1.00339i	0.00458043	−	0.0318576i
$993$	0.215140	−	0.471092i	0.00682728	−	0.0149496i
$994$	−2.07763	+	0.610046i	−0.0658983	+	0.0193495i
$995$	−2.00247	−	4.38480i	−0.0634826	−	0.139008i
$996$	2.62412	+	3.02840i	0.0831484	+	0.0959584i
$997$	6.33856	+	44.0856i	0.200744	+	1.39621i	0.802083	+	0.597212i	$0.203725\pi$
$997$	6.33856	+	44.0856i	0.200744	+	1.39621i	−0.601339	+	0.798994i	$0.705366\pi$
$998$	−19.7415	−	5.79663i	−0.624907	−	0.183489i
$999$	4.51223	−	5.20739i	0.142761	−	0.164755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.e.b.127.1	yes	10
3.2	odd	2		414.2.i.e.127.1		10
23.2	even	11	inner	138.2.e.b.25.1	✓	10
23.5	odd	22		3174.2.a.bb.1.3		5
23.18	even	11		3174.2.a.ba.1.3		5
69.2	odd	22		414.2.i.e.163.1		10
69.5	even	22		9522.2.a.br.1.3		5
69.41	odd	22		9522.2.a.bs.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.b.25.1	✓	10	23.2	even	11	inner
138.2.e.b.127.1	yes	10	1.1	even	1	trivial
414.2.i.e.127.1		10	3.2	odd	2
414.2.i.e.163.1		10	69.2	odd	22
3174.2.a.ba.1.3		5	23.18	even	11
3174.2.a.bb.1.3		5	23.5	odd	22
9522.2.a.br.1.3		5	69.5	even	22
9522.2.a.bs.1.3		5	69.41	odd	22

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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.186393 - 0.0547299i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-1.27819 - 1.47511i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.186393 - 0.0547299i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-1.27819 - 1.47511i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(0.127214 - 0.146813i) q^{10} +(5.30154 + 3.40709i) q^{11} +(-0.841254 - 0.540641i) q^{12} +(-3.15177 + 3.63733i) q^{13} +(-1.87279 - 0.549899i) q^{14} +(-0.0276463 - 0.192284i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-1.33259 - 2.91797i) q^{17} +(-0.959493 + 0.281733i) q^{18} +(0.357028 - 0.781782i) q^{19} +(0.0276463 - 0.192284i) q^{20} +(-1.64200 + 1.05525i) q^{21} +6.30195 q^{22} +(3.37782 + 3.40446i) q^{23} -1.00000 q^{24} +(-4.17452 + 2.68280i) q^{25} +(-0.684944 + 4.76389i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-1.87279 + 0.549899i) q^{28} +(2.25047 + 4.92785i) q^{29} +(-0.127214 - 0.146813i) q^{30} +(0.144265 + 1.00339i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(4.12690 - 4.76270i) q^{33} +(-2.69862 - 1.73430i) q^{34} +(-0.318978 - 0.204995i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(-6.61126 - 1.94124i) q^{37} +(-0.122312 - 0.850701i) q^{38} +(3.15177 + 3.63733i) q^{39} +(-0.0806993 - 0.176707i) q^{40} +(0.932638 - 0.273847i) q^{41} +(-0.810827 + 1.77546i) q^{42} +(0.731899 - 5.09047i) q^{43} +(5.30154 - 3.40709i) q^{44} -0.194262 q^{45} +(4.68219 + 1.03782i) q^{46} -7.41216 q^{47} +(-0.841254 + 0.540641i) q^{48} +(0.454025 - 3.15781i) q^{49} +(-2.06140 + 4.51383i) q^{50} +(-3.07792 + 0.903759i) q^{51} +(1.99934 + 4.37795i) q^{52} +(-1.31494 - 1.51752i) q^{53} +(0.142315 + 0.989821i) q^{54} +(1.17464 + 0.344905i) q^{55} +(-1.27819 + 1.47511i) q^{56} +(-0.723014 - 0.464653i) q^{57} +(4.55742 + 2.92887i) q^{58} +(5.63325 - 6.50112i) q^{59} +(-0.186393 - 0.0547299i) q^{60} +(-1.72487 - 11.9968i) q^{61} +(0.663836 + 0.766107i) q^{62} +(0.810827 + 1.77546i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-0.388396 + 0.850468i) q^{65} +(0.896861 - 6.23781i) q^{66} +(5.96723 - 3.83491i) q^{67} -3.20786 q^{68} +(3.85052 - 2.85894i) q^{69} -0.379170 q^{70} +(0.933267 - 0.599775i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(-5.47763 + 11.9943i) q^{73} +(-6.61126 + 1.94124i) q^{74} +(2.06140 + 4.51383i) q^{75} +(-0.562819 - 0.649528i) q^{76} +(-1.75054 - 12.1753i) q^{77} +(4.61792 + 1.35595i) q^{78} +(-0.739858 + 0.853842i) q^{79} +(-0.163423 - 0.105026i) q^{80} +(0.841254 + 0.540641i) q^{81} +(0.636532 - 0.734597i) q^{82} +(-3.84482 - 1.12894i) q^{83} +(0.277777 + 1.93198i) q^{84} +(-0.408086 - 0.470956i) q^{85} +(-2.13640 - 4.67807i) q^{86} +(5.19797 - 1.52626i) q^{87} +(2.61792 - 5.73246i) q^{88} +(1.35933 - 9.45436i) q^{89} +(-0.163423 + 0.105026i) q^{90} +9.39402 q^{91} +(4.50000 - 1.65831i) q^{92} +1.01371 q^{93} +(-6.23551 + 4.00732i) q^{94} +(0.0237606 - 0.165259i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(1.07554 - 0.315806i) q^{97} +(-1.32529 - 2.90199i) q^{98} +(-4.12690 - 4.76270i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 - q^8 - q^9	\( 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9} + 9 q^{10} + 11 q^{11} + q^{12} + 13 q^{13} - 11 q^{14} + 13 q^{15} - q^{16} - 24 q^{17} - q^{18} - 14 q^{19} - 13 q^{20} + 11 q^{21} + 22 q^{22} - 10 q^{23} - 10 q^{24} - 43 q^{25} - 9 q^{26} + q^{27} - 11 q^{28} + 13 q^{29} - 9 q^{30} + 8 q^{31} - q^{32} + 22 q^{33} + 9 q^{34} - q^{36} - 13 q^{37} - 3 q^{38} - 13 q^{39} + 9 q^{40} - 10 q^{41} - 8 q^{43} + 11 q^{44} - 2 q^{45} + q^{46} - 8 q^{47} + q^{48} + 29 q^{49} + 23 q^{50} - 9 q^{51} + 2 q^{52} - 35 q^{53} + q^{54} - 11 q^{55} + 3 q^{57} + 13 q^{58} + 37 q^{59} + 2 q^{60} - 2 q^{61} + 8 q^{62} - q^{64} + 37 q^{65} + 14 q^{67} - 2 q^{68} - q^{69} - 22 q^{70} + 44 q^{71} - q^{72} - 49 q^{73} - 13 q^{74} - 23 q^{75} + 8 q^{76} + 44 q^{77} + 20 q^{78} - 8 q^{79} - 2 q^{80} - q^{81} + 12 q^{82} - 17 q^{83} - 11 q^{84} - 37 q^{85} + 14 q^{86} - 2 q^{87} + 59 q^{89} - 2 q^{90} + 66 q^{91} + 45 q^{92} + 36 q^{93} - 19 q^{94} - 28 q^{95} + q^{96} - 21 q^{97} - 26 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 - q^8 - q^9 + 9 * q^10 + 11 * q^11 + q^12 + 13 * q^13 - 11 * q^14 + 13 * q^15 - q^16 - 24 * q^17 - q^18 - 14 * q^19 - 13 * q^20 + 11 * q^21 + 22 * q^22 - 10 * q^23 - 10 * q^24 - 43 * q^25 - 9 * q^26 + q^27 - 11 * q^28 + 13 * q^29 - 9 * q^30 + 8 * q^31 - q^32 + 22 * q^33 + 9 * q^34 - q^36 - 13 * q^37 - 3 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 - 8 * q^43 + 11 * q^44 - 2 * q^45 + q^46 - 8 * q^47 + q^48 + 29 * q^49 + 23 * q^50 - 9 * q^51 + 2 * q^52 - 35 * q^53 + q^54 - 11 * q^55 + 3 * q^57 + 13 * q^58 + 37 * q^59 + 2 * q^60 - 2 * q^61 + 8 * q^62 - q^64 + 37 * q^65 + 14 * q^67 - 2 * q^68 - q^69 - 22 * q^70 + 44 * q^71 - q^72 - 49 * q^73 - 13 * q^74 - 23 * q^75 + 8 * q^76 + 44 * q^77 + 20 * q^78 - 8 * q^79 - 2 * q^80 - q^81 + 12 * q^82 - 17 * q^83 - 11 * q^84 - 37 * q^85 + 14 * q^86 - 2 * q^87 + 59 * q^89 - 2 * q^90 + 66 * q^91 + 45 * q^92 + 36 * q^93 - 19 * q^94 - 28 * q^95 + q^96 - 21 * q^97 - 26 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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