LMFDB - Embedded newform 483.2.q.c.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 40 x^{18} - 117 x^{17} + 295 x^{16} - 575 x^{15} + 1777 x^{14} - 1560 x^{13} + \cdots + 2374681 $ x^20 - 8x^19 + 40x^18 - 117x^17 + 295x^16 - 575x^15 + 1777x^14 - 1560x^13 + 4383x^12 - 6446x^11 + 7261x^10 + 7700x^9 + 7852x^8 - 39430x^7 - 101709x^6 + 156742x^5 + 999838x^4 + 2029154x^3 + 3616480x^2 + 4299390*x + 2374681
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.2
Root			$3.28340 + 2.11011i$ of defining polynomial
Character	$\chi$	$=$	483.127
Dual form			483.2.q.c.232.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61435 + 1.03748i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.698939 - 1.53046i) q^{4} +(2.13054 - 0.625582i) q^{5} +(-0.797176 - 1.74557i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.0867074 - 0.603063i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-1.61435 + 1.03748i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.698939 - 1.53046i) q^{4} +(2.13054 - 0.625582i) q^{5} +(-0.797176 - 1.74557i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.0867074 - 0.603063i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-2.79041 + 3.22030i) q^{10} +(-1.39126 - 0.894108i) q^{11} +(1.41542 + 0.909632i) q^{12} +(-2.99062 + 3.45136i) q^{13} +(1.84125 + 0.540641i) q^{14} +(0.316007 + 2.19788i) q^{15} +(2.96926 + 3.42671i) q^{16} +(2.73620 + 5.99145i) q^{17} +(1.84125 - 0.540641i) q^{18} +(-2.49708 + 5.46784i) q^{19} +(0.531685 - 3.69795i) q^{20} +(0.841254 - 0.540641i) q^{21} +3.17361 q^{22} +(-0.317551 - 4.78531i) q^{23} +0.609264 q^{24} +(-0.0584382 + 0.0375559i) q^{25} +(1.24720 - 8.67443i) q^{26} +(0.415415 - 0.909632i) q^{27} +(-1.61435 + 0.474017i) q^{28} +(2.61680 + 5.73000i) q^{29} +(-2.79041 - 3.22030i) q^{30} +(1.43695 + 9.99423i) q^{31} +(-7.17941 - 2.10807i) q^{32} +(1.08300 - 1.24985i) q^{33} +(-10.6332 - 6.83356i) q^{34} +(-1.86799 - 1.20048i) q^{35} +(-1.10181 + 1.27155i) q^{36} +(-1.08170 - 0.317617i) q^{37} +(-1.64162 - 11.4177i) q^{38} +(-2.99062 - 3.45136i) q^{39} +(-0.561998 - 1.23060i) q^{40} +(2.60853 - 0.765934i) q^{41} +(-0.797176 + 1.74557i) q^{42} +(-0.992605 + 6.90372i) q^{43} +(-2.34080 + 1.50434i) q^{44} -2.22048 q^{45} +(5.47731 + 7.39572i) q^{46} -8.43638 q^{47} +(-3.81440 + 2.45137i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(0.0553763 - 0.121257i) q^{50} +(-6.31987 + 1.85568i) q^{51} +(3.19192 + 6.98932i) q^{52} +(-1.03957 - 1.19972i) q^{53} +(0.273100 + 1.89945i) q^{54} +(-3.52346 - 1.03458i) q^{55} +(-0.398983 + 0.460451i) q^{56} +(-5.05681 - 3.24981i) q^{57} +(-10.1692 - 6.53536i) q^{58} +(6.51293 - 7.51632i) q^{59} +(3.58464 + 1.05255i) q^{60} +(-1.71185 - 11.9062i) q^{61} +(-12.6886 - 14.6434i) q^{62} +(0.415415 + 0.909632i) q^{63} +(5.07616 - 1.49049i) q^{64} +(-4.21252 + 9.22412i) q^{65} +(-0.451651 + 3.14130i) q^{66} +(6.90761 - 4.43925i) q^{67} +11.0821 q^{68} +(4.78179 + 0.366702i) q^{69} +4.26107 q^{70} +(-0.127308 + 0.0818157i) q^{71} +(-0.0867074 + 0.603063i) q^{72} +(-5.86431 + 12.8410i) q^{73} +(2.07577 - 0.609502i) q^{74} +(-0.0288570 - 0.0631881i) q^{75} +(6.62301 + 7.64336i) q^{76} +(0.235359 + 1.63696i) q^{77} +(8.40864 + 2.46900i) q^{78} +(6.85970 - 7.91652i) q^{79} +(8.46980 + 5.44321i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-3.41645 + 3.94279i) q^{82} +(0.211247 + 0.0620278i) q^{83} +(-0.239446 - 1.66538i) q^{84} +(9.57772 + 11.0533i) q^{85} +(-5.56007 - 12.1749i) q^{86} +(-6.04409 + 1.77470i) q^{87} +(-0.418571 + 0.916543i) q^{88} +(-1.01376 + 7.05083i) q^{89} +(3.58464 - 2.30371i) q^{90} +4.56680 q^{91} +(-7.54568 - 2.85864i) q^{92} -10.0970 q^{93} +(13.6193 - 8.75260i) q^{94} +(-1.89953 + 13.2115i) q^{95} +(3.10835 - 6.80633i) q^{96} +(14.9531 - 4.39062i) q^{97} +(-0.797176 - 1.74557i) q^{98} +(1.08300 + 1.24985i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9} + 9 q^{10} + 3 q^{11} + 18 q^{12} - 2 q^{13} + 18 q^{14} - q^{15} + 8 q^{16} + 8 q^{17} + 18 q^{18} + 6 q^{19} - 2 q^{20} - 2 q^{21} + 6 q^{22} + 11 q^{23} + 9 q^{25} + 7 q^{26} - 2 q^{27} - 4 q^{28} + 23 q^{29} + 9 q^{30} + q^{31} - 28 q^{32} + 14 q^{33} - 28 q^{34} + 10 q^{35} - 4 q^{36} - 9 q^{37} + 34 q^{38} - 2 q^{39} - 15 q^{41} - 4 q^{42} - 23 q^{43} - 16 q^{44} - 12 q^{45} + 11 q^{46} - 66 q^{47} - 36 q^{48} - 2 q^{49} - 26 q^{50} - 14 q^{51} + 7 q^{52} + 9 q^{53} - 4 q^{54} - 62 q^{55} + 22 q^{56} - 27 q^{57} - 20 q^{58} + 49 q^{59} - 2 q^{60} + 46 q^{61} - 9 q^{62} - 2 q^{63} + 16 q^{64} + 11 q^{65} - 16 q^{66} + 14 q^{67} + 38 q^{68} + 11 q^{69} - 2 q^{70} + 36 q^{71} - q^{73} + 4 q^{74} - 2 q^{75} + 34 q^{76} - 8 q^{77} - 15 q^{78} - 22 q^{79} + 15 q^{80} - 2 q^{81} - 30 q^{82} + 8 q^{83} - 4 q^{84} - 32 q^{85} - 68 q^{86} + q^{87} - 11 q^{88} - 2 q^{89} - 2 q^{90} - 24 q^{91} + 11 q^{92} - 32 q^{93} + 33 q^{94} - 107 q^{95} + 16 q^{96} + 18 q^{97} - 4 q^{98} + 14 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9 + 9 * q^10 + 3 * q^11 + 18 * q^12 - 2 * q^13 + 18 * q^14 - q^15 + 8 * q^16 + 8 * q^17 + 18 * q^18 + 6 * q^19 - 2 * q^20 - 2 * q^21 + 6 * q^22 + 11 * q^23 + 9 * q^25 + 7 * q^26 - 2 * q^27 - 4 * q^28 + 23 * q^29 + 9 * q^30 + q^31 - 28 * q^32 + 14 * q^33 - 28 * q^34 + 10 * q^35 - 4 * q^36 - 9 * q^37 + 34 * q^38 - 2 * q^39 - 15 * q^41 - 4 * q^42 - 23 * q^43 - 16 * q^44 - 12 * q^45 + 11 * q^46 - 66 * q^47 - 36 * q^48 - 2 * q^49 - 26 * q^50 - 14 * q^51 + 7 * q^52 + 9 * q^53 - 4 * q^54 - 62 * q^55 + 22 * q^56 - 27 * q^57 - 20 * q^58 + 49 * q^59 - 2 * q^60 + 46 * q^61 - 9 * q^62 - 2 * q^63 + 16 * q^64 + 11 * q^65 - 16 * q^66 + 14 * q^67 + 38 * q^68 + 11 * q^69 - 2 * q^70 + 36 * q^71 - q^73 + 4 * q^74 - 2 * q^75 + 34 * q^76 - 8 * q^77 - 15 * q^78 - 22 * q^79 + 15 * q^80 - 2 * q^81 - 30 * q^82 + 8 * q^83 - 4 * q^84 - 32 * q^85 - 68 * q^86 + q^87 - 11 * q^88 - 2 * q^89 - 2 * q^90 - 24 * q^91 + 11 * q^92 - 32 * q^93 + 33 * q^94 - 107 * q^95 + 16 * q^96 + 18 * q^97 - 4 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	−1.61435	+	1.03748i	−1.14152	+	0.733611i	−0.967933	−	0.251208i	$-0.919172\pi$
$2$	−1.61435	+	1.03748i	−1.14152	+	0.733611i	−0.173587	+	0.984818i	$0.555536\pi$
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$4$	0.698939	−	1.53046i	0.349469	−	0.765231i
$5$	2.13054	−	0.625582i	0.952804	−	0.279769i	0.231850	−	0.972751i	$-0.425522\pi$
$5$	2.13054	−	0.625582i	0.952804	−	0.279769i	0.720954	+	0.692983i	$0.243704\pi$
$6$	−0.797176	−	1.74557i	−0.325446	−	0.712626i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$8$	−0.0867074	−	0.603063i	−0.0306557	−	0.213215i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	−2.79041	+	3.22030i	−0.882405	+	1.01835i
$11$	−1.39126	−	0.894108i	−0.419480	−	0.269584i	0.313828	−	0.949480i	$-0.398388\pi$
$11$	−1.39126	−	0.894108i	−0.419480	−	0.269584i	−0.733308	+	0.679896i	$0.762025\pi$
$12$	1.41542	+	0.909632i	0.408595	+	0.262588i
$13$	−2.99062	+	3.45136i	−0.829449	+	0.957235i	−0.999603	−	0.0281823i	$-0.991028\pi$
$13$	−2.99062	+	3.45136i	−0.829449	+	0.957235i	0.170154	+	0.985418i	$0.445574\pi$
$14$	1.84125	+	0.540641i	0.492096	+	0.144492i
$15$	0.316007	+	2.19788i	0.0815927	+	0.567490i
$16$	2.96926	+	3.42671i	0.742315	+	0.856677i
$17$	2.73620	+	5.99145i	0.663627	+	1.45314i	0.879104	+	0.476631i	$0.158142\pi$
$17$	2.73620	+	5.99145i	0.663627	+	1.45314i	−0.215477	+	0.976509i	$0.569131\pi$
$18$	1.84125	−	0.540641i	0.433988	−	0.127430i
$19$	−2.49708	+	5.46784i	−0.572869	+	1.25441i	0.372387	+	0.928077i	$0.378539\pi$
$19$	−2.49708	+	5.46784i	−0.572869	+	1.25441i	−0.945256	+	0.326330i	$0.894188\pi$
$20$	0.531685	−	3.69795i	0.118888	−	0.826886i
$21$	0.841254	−	0.540641i	0.183577	−	0.117977i
$22$	3.17361			0.676615
$23$	−0.317551	−	4.78531i	−0.0662139	−	0.997805i
$23$	−0.317551	−	4.78531i	−0.0662139	−	0.997805i
$24$	0.609264			0.124366
$25$	−0.0584382	+	0.0375559i	−0.0116876	+	0.00751118i
$26$	1.24720	−	8.67443i	0.244595	−	1.70120i
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$	−1.61435	+	0.474017i	−0.305084	+	0.0895808i
$29$	2.61680	+	5.73000i	0.485928	+	1.06403i	0.980791	+	0.195063i	$0.0624912\pi$
$29$	2.61680	+	5.73000i	0.485928	+	1.06403i	−0.494862	+	0.868971i	$0.664781\pi$
$30$	−2.79041	−	3.22030i	−0.509457	−	0.587944i
$31$	1.43695	+	9.99423i	0.258085	+	1.79502i	0.546445	+	0.837495i	$0.315981\pi$
$31$	1.43695	+	9.99423i	0.258085	+	1.79502i	−0.288360	+	0.957522i	$0.593110\pi$
$32$	−7.17941	−	2.10807i	−1.26915	−	0.372657i
$33$	1.08300	−	1.24985i	0.188527	−	0.217572i
$34$	−10.6332	−	6.83356i	−1.82358	−	1.17195i
$35$	−1.86799	−	1.20048i	−0.315747	−	0.202919i
$36$	−1.10181	+	1.27155i	−0.183635	+	0.211926i
$37$	−1.08170	−	0.317617i	−0.177831	−	0.0522159i	0.191605	−	0.981472i	$-0.438631\pi$
$37$	−1.08170	−	0.317617i	−0.177831	−	0.0522159i	−0.369436	+	0.929256i	$0.620449\pi$
$38$	−1.64162	−	11.4177i	−0.266305	−	1.85219i
$39$	−2.99062	−	3.45136i	−0.478883	−	0.552660i
$40$	−0.561998	−	1.23060i	−0.0888597	−	0.194576i
$41$	2.60853	−	0.765934i	0.407384	−	0.119619i	−0.0716187	−	0.997432i	$-0.522816\pi$
$41$	2.60853	−	0.765934i	0.407384	−	0.119619i	0.479003	+	0.877813i	$0.340998\pi$
$42$	−0.797176	+	1.74557i	−0.123007	+	0.269347i
$43$	−0.992605	+	6.90372i	−0.151371	+	1.05281i	0.762554	+	0.646925i	$0.223945\pi$
$43$	−0.992605	+	6.90372i	−0.151371	+	1.05281i	−0.913925	+	0.405883i	$0.866964\pi$
$44$	−2.34080	+	1.50434i	−0.352889	+	0.226788i
$45$	−2.22048			−0.331010
$46$	5.47731	+	7.39572i	0.807585	+	1.09044i
$47$	−8.43638			−1.23057			−0.615286	−	0.788304i	$-0.710960\pi$
$47$	−8.43638			−1.23057			−0.615286	+	0.788304i	$0.710960\pi$
$48$	−3.81440	+	2.45137i	−0.550561	+	0.353824i
$49$	−0.142315	+	0.989821i	−0.0203307	+	0.141403i
$50$	0.0553763	−	0.121257i	0.00783138	−	0.0171483i
$51$	−6.31987	+	1.85568i	−0.884958	+	0.259847i
$52$	3.19192	+	6.98932i	0.442639	+	0.969245i
$53$	−1.03957	−	1.19972i	−0.142795	−	0.164795i	0.679847	−	0.733354i	$-0.262046\pi$
$53$	−1.03957	−	1.19972i	−0.142795	−	0.164795i	−0.822642	+	0.568560i	$0.807501\pi$
$54$	0.273100	+	1.89945i	0.0371642	+	0.258483i
$55$	−3.52346	−	1.03458i	−0.475104	−	0.139503i
$56$	−0.398983	+	0.460451i	−0.0533164	+	0.0615304i
$57$	−5.05681	−	3.24981i	−0.669791	−	0.430448i
$58$	−10.1692	−	6.53536i	−1.33528	−	0.858135i
$59$	6.51293	−	7.51632i	0.847911	−	0.978541i	−0.152041	−	0.988374i	$-0.548585\pi$
$59$	6.51293	−	7.51632i	0.847911	−	0.978541i	0.999952	+	0.00983316i	$0.00313004\pi$
$60$	3.58464	+	1.05255i	0.462775	+	0.135883i
$61$	−1.71185	−	11.9062i	−0.219180	−	1.52443i	−0.741074	−	0.671423i	$-0.765683\pi$
$61$	−1.71185	−	11.9062i	−0.219180	−	1.52443i	0.521894	−	0.853010i	$-0.325226\pi$
$62$	−12.6886	−	14.6434i	−1.61145	−	1.85972i
$63$	0.415415	+	0.909632i	0.0523374	+	0.114603i
$64$	5.07616	−	1.49049i	0.634520	−	0.186312i
$65$	−4.21252	+	9.22412i	−0.522498	+	1.14411i
$66$	−0.451651	+	3.14130i	−0.0555944	+	0.386668i
$67$	6.90761	−	4.43925i	0.843899	−	0.542341i	−0.0457675	−	0.998952i	$-0.514573\pi$
$67$	6.90761	−	4.43925i	0.843899	−	0.542341i	0.889666	+	0.456611i	$0.150937\pi$
$68$	11.0821			1.34390
$69$	4.78179	+	0.366702i	0.575660	+	0.0441457i
$70$	4.26107			0.509295
$71$	−0.127308	+	0.0818157i	−0.0151086	+	0.00970973i	−0.548173	−	0.836365i	$-0.684677\pi$
$71$	−0.127308	+	0.0818157i	−0.0151086	+	0.00970973i	0.533065	+	0.846074i	$0.321040\pi$
$72$	−0.0867074	+	0.603063i	−0.0102186	+	0.0710717i
$73$	−5.86431	+	12.8410i	−0.686365	+	1.50293i	0.169389	+	0.985549i	$0.445820\pi$
$73$	−5.86431	+	12.8410i	−0.686365	+	1.50293i	−0.855755	+	0.517381i	$0.826907\pi$
$74$	2.07577	−	0.609502i	0.241304	−	0.0708532i
$75$	−0.0288570	−	0.0631881i	−0.00333212	−	0.00729633i
$76$	6.62301	+	7.64336i	0.759712	+	0.876754i
$77$	0.235359	+	1.63696i	0.0268217	+	0.186549i
$78$	8.40864	+	2.46900i	0.952092	+	0.279559i
$79$	6.85970	−	7.91652i	0.771777	−	0.890678i	−0.224710	−	0.974426i	$-0.572144\pi$
$79$	6.85970	−	7.91652i	0.771777	−	0.890678i	0.996487	+	0.0837479i	$0.0266890\pi$
$80$	8.46980	+	5.44321i	0.946952	+	0.608569i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	−3.41645	+	3.94279i	−0.377284	+	0.435409i
$83$	0.211247	+	0.0620278i	0.0231874	+	0.00680844i	0.293306	−	0.956019i	$-0.405245\pi$
$83$	0.211247	+	0.0620278i	0.0231874	+	0.00680844i	−0.270118	+	0.962827i	$0.587063\pi$
$84$	−0.239446	−	1.66538i	−0.0261257	−	0.181708i
$85$	9.57772	+	11.0533i	1.03885	+	1.19890i
$86$	−5.56007	−	12.1749i	−0.599558	−	1.31285i
$87$	−6.04409	+	1.77470i	−0.647994	+	0.190268i
$88$	−0.418571	+	0.916543i	−0.0446198	+	0.0977038i
$89$	−1.01376	+	7.05083i	−0.107458	+	0.747386i	0.862841	+	0.505476i	$0.168683\pi$
$89$	−1.01376	+	7.05083i	−0.107458	+	0.747386i	−0.970299	+	0.241910i	$0.922226\pi$
$90$	3.58464	−	2.30371i	0.377854	−	0.242832i
$91$	4.56680			0.478731
$92$	−7.54568	−	2.85864i	−0.786692	−	0.298033i
$93$	−10.0970			−1.04701
$94$	13.6193	−	8.75260i	1.40472	−	0.902761i
$95$	−1.89953	+	13.2115i	−0.194888	+	1.35548i
$96$	3.10835	−	6.80633i	0.317244	−	0.694668i
$97$	14.9531	−	4.39062i	1.51826	−	0.445800i	0.586824	−	0.809715i	$-0.300378\pi$
$97$	14.9531	−	4.39062i	1.51826	−	0.445800i	0.931432	+	0.363914i	$0.118560\pi$
$98$	−0.797176	−	1.74557i	−0.0805269	−	0.176329i
$99$	1.08300	+	1.24985i	0.108846	+	0.125615i
$100$	0.0166332	+	0.115687i	0.00166332	+	0.0115687i
$101$	12.6694	+	3.72008i	1.26066	+	0.370162i	0.842739	−	0.538323i	$-0.180942\pi$
$101$	12.6694	+	3.72008i	1.26066	+	0.370162i	0.417918	+	0.908485i	$0.362760\pi$
$102$	8.27726	−	9.55247i	0.819571	−	0.945836i
$103$	−14.0682	−	9.04111i	−1.38618	−	0.890847i	−0.386677	−	0.922215i	$-0.626377\pi$
$103$	−14.0682	−	9.04111i	−1.38618	−	0.890847i	−0.999508	+	0.0313686i	$0.990013\pi$
$104$	2.34070	+	1.50427i	0.229524	+	0.147506i
$105$	1.45411	−	1.67813i	0.141906	−	0.163768i
$106$	2.92292	+	0.858246i	0.283899	+	0.0833602i
$107$	−1.75650	−	12.2167i	−0.169807	−	1.18104i	−0.879281	−	0.476304i	$-0.841976\pi$
$107$	−1.75650	−	12.2167i	−0.169807	−	1.18104i	0.709474	−	0.704732i	$-0.248933\pi$
$108$	−1.10181	−	1.27155i	−0.106022	−	0.122355i
$109$	8.56880	+	18.7631i	0.820742	+	1.79718i	0.551689	+	0.834050i	$0.313983\pi$
$109$	8.56880	+	18.7631i	0.820742	+	1.79718i	0.269053	+	0.963125i	$0.413289\pi$
$110$	6.76148	−	1.98535i	0.644682	−	0.189296i
$111$	0.468326	−	1.02549i	0.0444516	−	0.0973354i
$112$	0.645282	−	4.48803i	0.0609734	−	0.424079i
$113$	0.951797	−	0.611683i	0.0895375	−	0.0575423i	−0.495106	−	0.868833i	$-0.664871\pi$
$113$	0.951797	−	0.611683i	0.0895375	−	0.0575423i	0.584643	+	0.811290i	$0.301234\pi$
$114$	11.5351			1.08036
$115$	−3.67015	−	9.99661i	−0.342244	−	0.932189i
$116$	10.5985			0.984050
$117$	3.84184	−	2.46900i	0.355178	−	0.228259i
$118$	−2.71612	+	18.8910i	−0.250039	+	1.73906i
$119$	2.73620	−	5.99145i	0.250827	−	0.549235i
$120$	1.29806	−	0.381145i	0.118496	−	0.0347936i
$121$	−3.43339	−	7.51808i	−0.312127	−	0.683462i
$122$	15.1160	+	17.4448i	1.36854	+	1.57938i
$123$	0.386905	+	2.69098i	0.0348861	+	0.242638i
$124$	16.3001	+	4.78615i	1.46380	+	0.429809i
$125$	−7.37154	+	8.50721i	−0.659330	+	0.760908i
$126$	−1.61435	−	1.03748i	−0.143818	−	0.0924263i
$127$	−13.1102	−	8.42544i	−1.16335	−	0.747637i	−0.191094	−	0.981572i	$-0.561203\pi$
$127$	−13.1102	−	8.42544i	−1.16335	−	0.747637i	−0.972252	+	0.233935i	$0.924840\pi$
$128$	3.15165	−	3.63720i	0.278569	−	0.321486i
$129$	−6.69219	−	1.96500i	−0.589214	−	0.173009i
$130$	−2.76937	−	19.2614i	−0.242890	−	1.68934i
$131$	7.56009	+	8.72481i	0.660528	+	0.762290i	0.982863	−	0.184335i	$-0.0590132\pi$
$131$	7.56009	+	8.72481i	0.660528	+	0.762290i	−0.322335	+	0.946626i	$0.604468\pi$
$132$	−1.15590	−	2.53107i	−0.100608	−	0.220301i
$133$	5.76755	−	1.69351i	0.500110	−	0.146846i
$134$	−6.54568	+	14.3330i	−0.565461	+	1.23819i
$135$	0.316007	−	2.19788i	0.0271976	−	0.189163i
$136$	3.37597	−	2.16961i	0.289487	−	0.186042i
$137$	3.36578			0.287558			0.143779	−	0.989610i	$-0.454075\pi$
$137$	3.36578			0.287558			0.143779	+	0.989610i	$0.454075\pi$
$138$	−8.09995	+	4.36904i	−0.689513	+	0.371917i
$139$	2.14198			0.181680			0.0908400	−	0.995866i	$-0.471045\pi$
$139$	2.14198			0.181680			0.0908400	+	0.995866i	$0.471045\pi$
$140$	−3.14290	+	2.01982i	−0.265624	+	0.170706i
$141$	1.20062	−	8.35051i	0.101111	−	0.703240i
$142$	0.120637	−	0.264159i	0.0101237	−	0.0221677i
$143$	7.24662	−	2.12780i	0.605993	−	0.177935i
$144$	−1.88357	−	4.12444i	−0.156964	−	0.343703i
$145$	9.15978	+	10.5709i	0.760678	+	0.877870i
$146$	−3.85529	−	26.8141i	−0.319066	−	2.21915i
$147$	−0.959493	−	0.281733i	−0.0791376	−	0.0232369i
$148$	−1.24214	+	1.43351i	−0.102104	+	0.117834i
$149$	3.04390	+	1.95620i	0.249366	+	0.160258i	0.659353	−	0.751834i	$-0.270830\pi$
$149$	3.04390	+	1.95620i	0.249366	+	0.160258i	−0.409987	+	0.912091i	$0.634467\pi$
$150$	0.112142	+	0.0720693i	0.00915636	+	0.00588443i
$151$	3.41646	−	3.94281i	0.278028	−	0.320861i	−0.599511	−	0.800366i	$-0.704638\pi$
$151$	3.41646	−	3.94281i	0.278028	−	0.320861i	0.877539	+	0.479505i	$0.159184\pi$
$152$	3.51396	+	1.03179i	0.285020	+	0.0836895i
$153$	−0.937381	−	6.51963i	−0.0757828	−	0.527081i
$154$	−2.07827	−	2.39845i	−0.167472	−	0.193273i
$155$	9.31369	+	20.3941i	0.748094	+	1.63810i
$156$	−7.37244	+	2.16474i	−0.590267	+	0.173318i
$157$	−5.14677	+	11.2699i	−0.410757	+	0.899432i	0.585308	+	0.810811i	$0.300973\pi$
$157$	−5.14677	+	11.2699i	−0.410757	+	0.899432i	−0.996065	+	0.0886215i	$0.971754\pi$
$158$	−2.86074	+	19.8969i	−0.227588	+	1.58291i
$159$	1.33546	−	0.858246i	0.105909	−	0.0680633i
$160$	−16.6148			−1.31351
$161$	−3.40854	+	3.37370i	−0.268631	+	0.265885i
$162$	−1.91899			−0.150770
$163$	−7.44527	+	4.78478i	−0.583159	+	0.374773i	−0.798707	−	0.601720i	$-0.794482\pi$
$163$	−7.44527	+	4.78478i	−0.583159	+	0.374773i	0.215549	+	0.976493i	$0.430846\pi$
$164$	0.650971	−	4.52760i	0.0508323	−	0.353546i
$165$	1.52549	−	3.34036i	0.118759	−	0.260047i
$166$	−0.405381	+	0.119031i	−0.0314636	+	0.00923856i
$167$	1.00006	+	2.18983i	0.0773869	+	0.169454i	0.944371	−	0.328882i	$-0.106672\pi$
$167$	1.00006	+	2.18983i	0.0773869	+	0.169454i	−0.866984	+	0.498336i	$0.833945\pi$
$168$	−0.398983	−	0.460451i	−0.0307822	−	0.0355246i
$169$	−1.11798	−	7.77574i	−0.0859987	−	0.598134i
$170$	−26.9294	−	7.90719i	−2.06539	−	0.606453i
$171$	3.93639	−	4.54284i	0.301024	−	0.347400i
$172$	9.87212	+	6.34442i	0.752742	+	0.483758i
$173$	−1.68792	−	1.08476i	−0.128330	−	0.0824726i	0.474901	−	0.880039i	$-0.342484\pi$
$173$	−1.68792	−	1.08476i	−0.128330	−	0.0824726i	−0.603231	+	0.797567i	$0.706120\pi$
$174$	7.91607	−	9.13564i	0.600116	−	0.692571i
$175$	0.0666517	+	0.0195707i	0.00503840	+	0.00147941i
$176$	−1.06716	−	7.42228i	−0.0804404	−	0.559475i
$177$	6.51293	+	7.51632i	0.489541	+	0.564961i
$178$	−5.67855	−	12.4343i	−0.425625	−	0.931989i
$179$	−15.2099	+	4.46604i	−1.13684	+	0.333808i	−0.795394	−	0.606092i	$-0.792736\pi$
$179$	−15.2099	+	4.46604i	−1.13684	+	0.333808i	−0.341450	+	0.939900i	$0.610918\pi$
$180$	−1.55198	+	3.39836i	−0.115678	+	0.253299i
$181$	1.59855	−	11.1182i	0.118820	−	0.826409i	−0.840039	−	0.542526i	$-0.817468\pi$
$181$	1.59855	−	11.1182i	0.118820	−	0.826409i	0.958859	−	0.283883i	$-0.0916227\pi$
$182$	−7.37244	+	4.73798i	−0.546481	+	0.351202i
$183$	12.0286			0.889183
$184$	−2.85831	+	0.606425i	−0.210717	+	0.0447062i
$185$	−2.50330			−0.184046
$186$	16.3001	−	10.4755i	1.19518	−	0.768098i
$187$	1.55023	−	10.7821i	0.113364	−	0.788467i
$188$	−5.89651	+	12.9116i	−0.430048	+	0.941673i
$189$	−0.959493	+	0.281733i	−0.0697928	+	0.0204930i
$190$	−10.6402	−	23.2988i	−0.771923	−	1.69028i
$191$	−3.57685	−	4.12790i	−0.258811	−	0.298684i	0.611441	−	0.791290i	$-0.290590\pi$
$191$	−3.57685	−	4.12790i	−0.258811	−	0.298684i	−0.870253	+	0.492605i	$0.836045\pi$
$192$	0.752911	+	5.23661i	0.0543366	+	0.377920i
$193$	0.746975	+	0.219332i	0.0537685	+	0.0157878i	0.308506	−	0.951222i	$-0.400171\pi$
$193$	0.746975	+	0.219332i	0.0537685	+	0.0157878i	−0.254738	+	0.967010i	$0.581989\pi$
$194$	−19.5844	+	22.6016i	−1.40608	+	1.62270i
$195$	−8.53073	−	5.48237i	−0.610898	−	0.392601i
$196$	1.41542	+	0.909632i	0.101101	+	0.0649737i
$197$	0.725272	−	0.837008i	0.0516735	−	0.0596344i	−0.729324	−	0.684168i	$-0.760165\pi$
$197$	0.725272	−	0.837008i	0.0516735	−	0.0596344i	0.780998	+	0.624534i	$0.214711\pi$
$198$	−3.04505	−	0.894108i	−0.216402	−	0.0635415i
$199$	0.0277213	+	0.192806i	0.00196511	+	0.0136676i	0.990780	−	0.135478i	$-0.0432569\pi$
$199$	0.0277213	+	0.192806i	0.00196511	+	0.0136676i	−0.988815	+	0.149145i	$0.952348\pi$
$200$	0.0277156	+	0.0319855i	0.00195979	+	0.00226172i
$201$	3.41101	+	7.46907i	0.240594	+	0.526828i
$202$	−24.3125	+	7.13879i	−1.71062	+	0.502283i
$203$	2.61680	−	5.73000i	0.183664	−	0.402167i
$204$	−1.57715	+	10.9693i	−0.110423	+	0.768006i
$205$	5.07842	−	3.26370i	0.354692	−	0.227947i
$206$	32.0911			2.23589
$207$	−1.04349	+	4.68093i	−0.0725275	+	0.325347i
$208$	−20.7067			−1.43575
$209$	8.36292	−	5.37452i	0.578475	−	0.371763i
$210$	−0.606414	+	4.21770i	−0.0418465	+	0.291049i
$211$	1.79959	−	3.94056i	0.123889	−	0.271279i	−0.837518	−	0.546410i	$-0.815994\pi$
$211$	1.79959	−	3.94056i	0.123889	−	0.271279i	0.961407	+	0.275131i	$0.0887212\pi$
$212$	−2.56272	+	0.752484i	−0.176009	+	0.0516808i
$213$	−0.0628651	−	0.137655i	−0.00430745	−	0.00943199i
$214$	15.5103	+	17.8998i	1.06026	+	1.22360i
$215$	2.20406	+	15.3296i	0.150316	+	1.04547i
$216$	−0.584585	−	0.171650i	−0.0397760	−	0.0116793i
$217$	6.61213	−	7.63081i	0.448861	−	0.518013i
$218$	−33.2994	−	21.4002i	−2.25532	−	1.44941i
$219$	−11.8758	−	7.63209i	−0.802490	−	0.515729i
$220$	−4.04608	+	4.66942i	−0.272786	+	0.314812i
$221$	−28.8616	−	8.47453i	−1.94144	−	0.570058i
$222$	0.307885	+	2.14139i	0.0206639	+	0.143720i
$223$	0.767942	+	0.886252i	0.0514252	+	0.0593478i	0.780879	−	0.624682i	$-0.214771\pi$
$223$	0.767942	+	0.886252i	0.0514252	+	0.0593478i	−0.729454	+	0.684030i	$0.760226\pi$
$224$	3.10835	+	6.80633i	0.207685	+	0.454767i
$225$	0.0666517	−	0.0195707i	0.00444345	−	0.00130471i
$226$	−0.901927	+	1.97494i	−0.0599953	+	0.131371i
$227$	3.25591	−	22.6453i	0.216102	−	1.50302i	−0.536136	−	0.844132i	$-0.680116\pi$
$227$	3.25591	−	22.6453i	0.216102	−	1.50302i	0.752238	−	0.658892i	$-0.228974\pi$
$228$	−8.50812	+	5.46784i	−0.563464	+	0.362116i
$229$	8.02239			0.530135			0.265067	−	0.964230i	$-0.414606\pi$
$229$	8.02239			0.530135			0.265067	+	0.964230i	$0.414606\pi$
$230$	16.2962	+	12.3303i	1.07454	+	0.813039i
$231$	−1.65379			−0.108812
$232$	3.22866	−	2.07493i	0.211972	−	0.136226i
$233$	−3.48466	+	24.2364i	−0.228288	+	1.58778i	0.477031	+	0.878886i	$0.341713\pi$
$233$	−3.48466	+	24.2364i	−0.228288	+	1.58778i	−0.705319	+	0.708890i	$0.749196\pi$
$234$	−3.64054	+	7.97168i	−0.237990	+	0.521125i
$235$	−17.9740	+	5.27765i	−1.17250	+	0.344276i
$236$	−6.95130	−	15.2212i	−0.452491	−	0.990818i
$237$	6.85970	+	7.91652i	0.445585	+	0.514233i
$238$	1.79882	+	12.5111i	0.116600	+	0.810973i
$239$	−15.6263	−	4.58829i	−1.01078	−	0.296792i	−0.265907	−	0.963999i	$-0.585672\pi$
$239$	−15.6263	−	4.58829i	−1.01078	−	0.296792i	−0.744872	+	0.667207i	$0.767490\pi$
$240$	−6.59318	+	7.60894i	−0.425588	+	0.491155i
$241$	18.3461	+	11.7903i	1.18178	+	0.759481i	0.975712	−	0.219057i	$-0.0702982\pi$
$241$	18.3461	+	11.7903i	1.18178	+	0.759481i	0.206064	+	0.978539i	$0.433935\pi$
$242$	13.3426	+	8.57476i	0.857694	+	0.551206i
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$	−19.4185	−	5.70178i	−1.24314	−	0.365019i
$245$	0.316007	+	2.19788i	0.0201890	+	0.140417i
$246$	−3.41645	−	3.94279i	−0.217825	−	0.251383i
$247$	−11.4037	−	24.9705i	−0.725598	−	1.58884i
$248$	5.90256	−	1.73315i	0.374813	−	0.110055i
$249$	−0.0914601	+	0.200270i	−0.00579605	+	0.0126916i
$250$	3.07419	−	21.3815i	0.194429	−	1.35228i
$251$	3.97710	−	2.55592i	0.251032	−	0.161328i	−0.409073	−	0.912502i	$-0.634148\pi$
$251$	3.97710	−	2.55592i	0.251032	−	0.161328i	0.660105	+	0.751173i	$0.270512\pi$
$252$	1.68251			0.105988
$253$	−3.83679	+	6.94153i	−0.241217	+	0.436410i
$254$	29.9058			1.87646
$255$	−12.3038	+	7.90719i	−0.770495	+	0.495167i
$256$	−2.82017	+	19.6147i	−0.176261	+	1.22592i
$257$	8.40154	−	18.3968i	0.524074	−	1.14756i	−0.443800	−	0.896126i	$-0.646370\pi$
$257$	8.40154	−	18.3968i	0.524074	−	1.14756i	0.967874	−	0.251436i	$-0.0809027\pi$
$258$	12.8422	−	3.77082i	0.799522	−	0.234761i
$259$	0.468326	+	1.02549i	0.0291004	+	0.0637209i
$260$	11.1729	+	12.8942i	0.692913	+	0.799664i
$261$	−0.896477	−	6.23514i	−0.0554905	−	0.385945i
$262$	−21.2565	−	6.24147i	−1.31323	−	0.385599i
$263$	−9.97309	+	11.5096i	−0.614967	+	0.709710i	−0.974743	−	0.223329i	$-0.928308\pi$
$263$	−9.97309	+	11.5096i	−0.614967	+	0.709710i	0.359776	+	0.933039i	$0.382853\pi$
$264$	−0.847645	−	0.544748i	−0.0521689	−	0.0335269i
$265$	−2.96536	−	1.90572i	−0.182160	−	0.117067i
$266$	−7.55389	+	8.71765i	−0.463158	+	0.534513i
$267$	−6.83479	−	2.00688i	−0.418282	−	0.122819i
$268$	−1.96611	−	13.6746i	−0.120099	−	0.835309i
$269$	−14.1946	−	16.3815i	−0.865462	−	0.998796i	−0.999969	−	0.00788335i	$-0.997491\pi$
$269$	−14.1946	−	16.3815i	−0.865462	−	0.998796i	0.134507	−	0.990913i	$-0.457055\pi$
$270$	1.77011	+	3.87601i	0.107726	+	0.235886i
$271$	22.4856	−	6.60236i	1.36590	−	0.401065i	0.485061	−	0.874480i	$-0.338797\pi$
$271$	22.4856	−	6.60236i	1.36590	−	0.401065i	0.880839	+	0.473415i	$0.156979\pi$
$272$	−12.4064	+	27.1663i	−0.752251	+	1.64720i
$273$	−0.649924	+	4.52032i	−0.0393352	+	0.273582i
$274$	−5.43355	+	3.49193i	−0.328253	+	0.210955i
$275$	0.114882			0.00692763
$276$	3.90340	−	7.06205i	0.234957	−	0.425085i
$277$	−13.3919			−0.804643			−0.402321	−	0.915498i	$-0.631797\pi$
$277$	−13.3919			−0.804643			−0.402321	+	0.915498i	$0.631797\pi$
$278$	−3.45791	+	2.22226i	−0.207391	+	0.133282i
$279$	1.43695	−	9.99423i	0.0860282	−	0.598339i
$280$	−0.561998	+	1.23060i	−0.0335858	+	0.0735427i
$281$	12.4131	−	3.64480i	0.740501	−	0.217431i	0.110338	−	0.993894i	$-0.464807\pi$
$281$	12.4131	−	3.64480i	0.740501	−	0.217431i	0.630162	+	0.776463i	$0.282988\pi$
$282$	6.72528	+	14.7263i	0.400484	+	0.876939i
$283$	5.90666	+	6.81665i	0.351115	+	0.405208i	0.903643	−	0.428286i	$-0.140882\pi$
$283$	5.90666	+	6.81665i	0.351115	+	0.405208i	−0.552529	+	0.833494i	$0.686337\pi$
$284$	0.0362355	+	0.252024i	0.00215018	+	0.0149549i
$285$	−12.8067	−	3.76040i	−0.758606	−	0.222747i
$286$	−9.49105	+	10.9533i	−0.561218	+	0.647680i
$287$	−2.28708	−	1.46982i	−0.135002	−	0.0867605i
$288$	6.29469	+	4.04535i	0.370918	+	0.238374i
$289$	−17.2780	+	19.9399i	−1.01635	+	1.17293i
$290$	−25.7543	−	7.56214i	−1.51234	−	0.444064i
$291$	2.21789	+	15.4257i	0.130015	+	0.904273i
$292$	15.5539	+	17.9502i	0.910226	+	1.05046i
$293$	4.97609	+	10.8961i	0.290706	+	0.636558i	0.997485	−	0.0708765i	$-0.0225796\pi$
$293$	4.97609	+	10.8961i	0.290706	+	0.636558i	−0.706779	+	0.707435i	$0.749852\pi$
$294$	1.84125	−	0.540641i	0.107384	−	0.0315308i
$295$	9.17395	−	20.0881i	0.534128	−	1.16958i
$296$	−0.0977513	+	0.679875i	−0.00568168	+	0.0395169i
$297$	−1.39126	+	0.894108i	−0.0807290	+	0.0518814i
$298$	−6.94345			−0.402223
$299$	17.4655	+	13.2151i	1.01006	+	0.764246i
$300$	−0.116876			−0.00674786
$301$	5.86750	−	3.77082i	0.338197	−	0.217346i
$302$	−1.42479	+	9.90960i	−0.0819872	+	0.570234i
$303$	−5.48527	+	12.0111i	−0.315120	+	0.690018i
$304$	−26.1511	+	7.67867i	−1.49987	+	0.440402i
$305$	−11.0955	−	24.2957i	−0.635325	−	1.39117i
$306$	8.27726	+	9.55247i	0.473180	+	0.546079i
$307$	4.21571	+	29.3209i	0.240603	+	1.67343i	0.649123	+	0.760684i	$0.275136\pi$
$307$	4.21571	+	29.3209i	0.240603	+	1.67343i	−0.408519	+	0.912750i	$0.633955\pi$
$308$	2.66981	+	0.783926i	0.152126	+	0.0446683i
$309$	10.9512	−	12.6384i	0.622992	−	0.718971i
$310$	−36.1941	−	23.2606i	−2.05569	−	1.32111i
$311$	−6.58395	−	4.23125i	−0.373342	−	0.239932i	0.340492	−	0.940247i	$-0.389406\pi$
$311$	−6.58395	−	4.23125i	−0.373342	−	0.239932i	−0.713834	+	0.700315i	$0.753043\pi$
$312$	−1.82208	+	2.10279i	−0.103155	+	0.119047i
$313$	13.0261	+	3.82482i	0.736281	+	0.216192i	0.628311	−	0.777963i	$-0.283747\pi$
$313$	13.0261	+	3.82482i	0.736281	+	0.216192i	0.107970	+	0.994154i	$0.465565\pi$
$314$	−3.38356	−	23.5332i	−0.190946	−	1.32806i
$315$	1.45411	+	1.67813i	0.0819296	+	0.0945518i
$316$	−7.32142	−	16.0317i	−0.411862	−	0.901852i
$317$	3.11670	−	0.915147i	0.175051	−	0.0513998i	−0.193032	−	0.981192i	$-0.561832\pi$
$317$	3.11670	−	0.915147i	0.175051	−	0.0513998i	0.368084	+	0.929793i	$0.380014\pi$
$318$	−1.26549	+	2.77103i	−0.0709649	+	0.155391i
$319$	1.48259	−	10.3116i	0.0830090	−	0.577340i
$320$	9.88251	−	6.35110i	0.552449	−	0.355037i
$321$	12.3424			0.688883
$322$	2.00244	−	8.98264i	0.111592	−	0.500583i
$323$	−39.5928			−2.20300
$324$	1.41542	−	0.909632i	0.0786342	−	0.0505351i
$325$	0.0451473	−	0.314007i	0.00250432	−	0.0174180i
$326$	7.05517	−	15.4487i	0.390750	−	0.855623i
$327$	−19.7915	+	5.81132i	−1.09447	+	0.321367i
$328$	−0.688086	−	1.50670i	−0.0379932	−	0.0831934i
$329$	5.52466	+	6.37579i	0.304584	+	0.351509i
$330$	1.00288	+	6.97520i	0.0552069	+	0.383972i
$331$	21.8924	+	6.42819i	1.20332	+	0.353325i	0.821120	−	0.570756i	$-0.193350\pi$
$331$	21.8924	+	6.42819i	1.20332	+	0.353325i	0.382196	+	0.924081i	$0.375168\pi$
$332$	0.242580	−	0.279952i	0.0133133	−	0.0153644i
$333$	0.948404	+	0.609502i	0.0519722	+	0.0334005i
$334$	−3.88635	−	2.49761i	−0.212652	−	0.136663i
$335$	11.9398	−	13.7793i	0.652341	−	0.752841i
$336$	4.35052	+	1.27743i	0.237340	+	0.0696894i
$337$	−1.07754	−	7.49448i	−0.0586975	−	0.408250i	−0.997894	−	0.0648693i	$-0.979337\pi$
$337$	−1.07754	−	7.49448i	−0.0586975	−	0.408250i	0.939196	−	0.343381i	$-0.111572\pi$
$338$	9.87201	+	11.3929i	0.536967	+	0.619693i
$339$	0.470002	+	1.02916i	0.0255270	+	0.0558963i
$340$	23.6109	−	6.93277i	1.28048	−	0.375982i
$341$	6.93675	−	15.1894i	0.375646	−	0.822550i
$342$	−1.64162	+	11.4177i	−0.0887684	+	0.617398i
$343$	0.841254	−	0.540641i	0.0454234	−	0.0291919i
$344$	4.24945			0.229115
$345$	10.4172	−	2.21013i	0.560842	−	0.118989i
$346$	3.85031			0.206994
$347$	17.6081	−	11.3161i	0.945255	−	0.607478i	0.0253746	−	0.999678i	$-0.491922\pi$
$347$	17.6081	−	11.3161i	0.945255	−	0.607478i	0.919880	+	0.392200i	$0.128286\pi$
$348$	−1.50833	+	10.4907i	−0.0808549	+	0.562358i
$349$	7.08754	−	15.5196i	0.379387	−	0.830743i	−0.619563	−	0.784947i	$-0.712690\pi$
$349$	7.08754	−	15.5196i	0.379387	−	0.830743i	0.998951	−	0.0457959i	$-0.0145824\pi$
$350$	−0.127904	+	0.0375559i	−0.00683674	+	0.00200745i
$351$	1.89712	+	4.15411i	0.101261	+	0.221730i
$352$	8.10359	+	9.35204i	0.431923	+	0.498465i
$353$	−3.76323	−	26.1738i	−0.200296	−	1.39309i	−0.803405	−	0.595433i	$-0.796981\pi$
$353$	−3.76323	−	26.1738i	−0.200296	−	1.39309i	0.603109	−	0.797659i	$-0.293928\pi$
$354$	−18.3122	−	5.37695i	−0.973283	−	0.285782i
$355$	−0.220051	+	0.253952i	−0.0116791	+	0.0134784i
$356$	10.0825	+	6.47961i	0.534370	+	0.343419i
$357$	5.54106	+	3.56102i	0.293264	+	0.188469i
$358$	19.9208	−	22.9898i	1.05285	−	1.21505i
$359$	14.1513	+	4.15518i	0.746875	+	0.219302i	0.632956	−	0.774188i	$-0.281841\pi$
$359$	14.1513	+	4.15518i	0.746875	+	0.219302i	0.113919	+	0.993490i	$0.463660\pi$
$360$	0.192532	+	1.33909i	0.0101473	+	0.0705762i
$361$	−11.2195	−	12.9480i	−0.590499	−	0.681472i
$362$	8.95429	+	19.6072i	0.470627	+	1.03053i
$363$	7.93018	−	2.32851i	0.416226	−	0.122215i
$364$	3.19192	−	6.98932i	0.167302	−	0.366340i
$365$	−4.46100	+	31.0269i	−0.233499	+	1.62402i
$366$	−19.4185	+	12.4795i	−1.01502	+	0.652314i
$367$	5.98625			0.312479			0.156240	−	0.987719i	$-0.450063\pi$
$367$	5.98625			0.312479			0.156240	+	0.987719i	$0.450063\pi$
$368$	15.4550	−	15.2970i	0.805645	−	0.797410i
$369$	−2.71866			−0.141528
$370$	4.04122	−	2.59713i	0.210093	−	0.135018i
$371$	−0.225919	+	1.57130i	−0.0117291	+	0.0815780i
$372$	−7.05719	+	15.4531i	−0.365898	+	0.801205i
$373$	11.5151	−	3.38114i	0.596230	−	0.175069i	0.0303258	−	0.999540i	$-0.490346\pi$
$373$	11.5151	−	3.38114i	0.596230	−	0.175069i	0.565904	+	0.824471i	$0.308527\pi$
$374$	8.68363	+	19.0145i	0.449020	+	0.983216i
$375$	−7.37154	−	8.50721i	−0.380665	−	0.439310i
$376$	0.731497	+	5.08767i	0.0377241	+	0.262377i
$377$	−27.6022	−	8.10473i	−1.42158	−	0.417415i
$378$	1.25667	−	1.45027i	0.0646361	−	0.0745940i
$379$	16.1324	+	10.3677i	0.828665	+	0.532551i	0.884854	−	0.465869i	$-0.154258\pi$
$379$	16.1324	+	10.3677i	0.828665	+	0.532551i	−0.0561882	+	0.998420i	$0.517895\pi$
$380$	18.8921	+	12.1412i	0.969145	+	0.622832i
$381$	10.2055	−	11.7777i	0.522842	−	0.603392i
$382$	10.0569	+	2.95298i	0.514557	+	0.151087i
$383$	0.635938	+	4.42305i	0.0324949	+	0.226007i	0.999597	−	0.0283808i	$-0.00903509\pi$
$383$	0.635938	+	4.42305i	0.0324949	+	0.226007i	−0.967102	+	0.254388i	$0.918126\pi$
$384$	3.15165	+	3.63720i	0.160832	+	0.185610i
$385$	1.52549	+	3.34036i	0.0777463	+	0.170241i
$386$	−1.43344	+	0.420895i	−0.0729599	+	0.0214230i
$387$	2.89740	−	6.34442i	0.147283	−	0.322505i
$388$	3.73161	−	25.9539i	0.189444	−	1.31761i
$389$	6.70426	−	4.30857i	0.339920	−	0.218453i	−0.359532	−	0.933133i	$-0.617064\pi$
$389$	6.70426	−	4.30857i	0.339920	−	0.218453i	0.699452	+	0.714679i	$0.253427\pi$
$390$	19.4595			0.985369
$391$	27.8020	−	14.9962i	1.40601	−	0.758388i
$392$	0.609264			0.0307725
$393$	−9.71192	+	6.24147i	−0.489902	+	0.314841i
$394$	−0.302464	+	2.10368i	−0.0152379	+	0.105982i
$395$	9.66241	−	21.1577i	0.486169	−	1.06456i
$396$	2.66981	−	0.783926i	0.134163	−	0.0393938i
$397$	3.68150	+	8.06136i	0.184769	+	0.404588i	0.979237	−	0.202718i	$-0.0649774\pi$
$397$	3.68150	+	8.06136i	0.184769	+	0.404588i	−0.794468	+	0.607306i	$0.792250\pi$
$398$	−0.244785	−	0.282497i	−0.0122699	−	0.0141603i
$399$	0.855460	+	5.94986i	0.0428266	+	0.297865i
$400$	−0.302211	−	0.0887372i	−0.0151106	−	0.00443686i
$401$	12.2732	−	14.1640i	0.612894	−	0.707317i	−0.361447	−	0.932392i	$-0.617717\pi$
$401$	12.2732	−	14.1640i	0.612894	−	0.707317i	0.974341	+	0.225075i	$0.0722628\pi$
$402$	−13.2556	−	8.51886i	−0.661130	−	0.424882i
$403$	−38.7911	−	24.9295i	−1.93232	−	1.24183i
$404$	14.5486	−	16.7900i	0.723821	−	0.835333i
$405$	2.13054	+	0.625582i	0.105867	+	0.0310854i
$406$	1.72033	+	11.9651i	0.0853784	+	0.593820i
$407$	1.22095	+	1.40905i	0.0605200	+	0.0698439i
$408$	1.66707	+	3.65038i	0.0825323	+	0.180721i
$409$	10.5400	−	3.09482i	0.521168	−	0.153029i	−0.0105593	−	0.999944i	$-0.503361\pi$
$409$	10.5400	−	3.09482i	0.521168	−	0.153029i	0.531728	+	0.846915i	$0.321543\pi$
$410$	−4.81233	+	10.5375i	−0.237664	+	0.520412i
$411$	−0.479000	+	3.33152i	−0.0236273	+	0.164332i
$412$	−23.6699	+	15.2117i	−1.16613	+	0.749428i
$413$	−9.94551			−0.489387
$414$	−3.17182	−	8.63928i	−0.155887	−	0.424598i
$415$	0.488874			0.0239979
$416$	28.7466	−	18.4743i	1.40942	−	0.905778i
$417$	−0.304835	+	2.12017i	−0.0149278	+	0.103825i
$418$	−7.92474	+	17.3528i	−0.387612	+	0.848751i
$419$	−15.6334	+	4.59039i	−0.763743	+	0.224255i	−0.640330	−	0.768100i	$-0.721202\pi$
$419$	−15.6334	+	4.59039i	−0.763743	+	0.224255i	−0.123413	+	0.992355i	$0.539384\pi$
$420$	−1.55198	−	3.39836i	−0.0757289	−	0.165823i
$421$	−10.8050	−	12.4697i	−0.526606	−	0.607735i	0.428667	−	0.903463i	$-0.358983\pi$
$421$	−10.8050	−	12.4697i	−0.526606	−	0.607735i	−0.955272	+	0.295727i	$0.904438\pi$
$422$	1.18308	+	8.22850i	0.0575914	+	0.400557i
$423$	8.09465	+	2.37680i	0.393575	+	0.115564i
$424$	−0.633371	+	0.730949i	−0.0307592	+	0.0354980i
$425$	−0.384913	−	0.247369i	−0.0186710	−	0.0119991i
$426$	0.244302	+	0.157003i	0.0118365	+	0.00760682i
$427$	−7.87708	+	9.09064i	−0.381199	+	0.439927i
$428$	−19.9249	−	5.85049i	−0.963108	−	0.282794i
$429$	1.07484	+	7.47567i	0.0518938	+	0.360929i
$430$	−19.4623	−	22.4607i	−0.938556	−	1.08315i
$431$	−3.10329	−	6.79526i	−0.149480	−	0.327316i	0.820048	−	0.572294i	$-0.193947\pi$
$431$	−3.10329	−	6.79526i	−0.149480	−	0.327316i	−0.969529	+	0.244978i	$0.921219\pi$
$432$	4.35052	−	1.27743i	0.209314	−	0.0614602i
$433$	−6.55130	+	14.3453i	−0.314835	+	0.689393i	−0.999210	−	0.0397373i	$-0.987348\pi$
$433$	−6.55130	+	14.3453i	−0.314835	+	0.689393i	0.684375	+	0.729130i	$0.260075\pi$
$434$	−2.75749	+	19.1788i	−0.132364	+	0.920612i
$435$	−11.7669	+	7.56214i	−0.564181	+	0.362577i
$436$	34.7052			1.66208
$437$	26.9582	+	10.2130i	1.28959	+	0.488552i
$438$	27.0898			1.29440
$439$	−3.20867	+	2.06209i	−0.153142	+	0.0984181i	−0.614967	−	0.788553i	$-0.710831\pi$
$439$	−3.20867	+	2.06209i	−0.153142	+	0.0984181i	0.461826	+	0.886971i	$0.347194\pi$
$440$	−0.318408	+	2.21458i	−0.0151795	+	0.105576i
$441$	0.415415	−	0.909632i	0.0197817	−	0.0433158i
$442$	55.3850	−	16.2625i	2.63440	−	0.773528i
$443$	−8.78350	−	19.2332i	−0.417317	−	0.913796i	−0.995217	−	0.0976885i	$-0.968855\pi$
$443$	−8.78350	−	19.2332i	−0.417317	−	0.913796i	0.577901	−	0.816107i	$-0.303872\pi$
$444$	−1.24214	−	1.43351i	−0.0589496	−	0.0680314i
$445$	2.25103	+	15.6562i	0.106709	+	0.742177i
$446$	−2.15920	−	0.633998i	−0.102241	−	0.0300207i
$447$	−2.36948	+	2.73452i	−0.112072	+	0.129338i
$448$	−4.45062	−	2.86024i	−0.210272	−	0.135133i
$449$	−19.5553	−	12.5674i	−0.922872	−	0.593094i	−0.00938215	−	0.999956i	$-0.502986\pi$
$449$	−19.5553	−	12.5674i	−0.922872	−	0.593094i	−0.913489	+	0.406862i	$0.866623\pi$
$450$	−0.0872952	+	0.100744i	−0.00411513	+	0.00474912i
$451$	−4.31397	−	1.26670i	−0.203137	−	0.0596464i
$452$	−0.270910	−	1.88422i	−0.0127425	−	0.0886261i
$453$	3.41646	+	3.94281i	0.160519	+	0.185249i
$454$	18.2379	+	39.9355i	0.855949	+	1.87427i
$455$	9.72974	−	2.85691i	0.456137	−	0.133934i
$456$	−1.52138	+	3.33136i	−0.0712451	+	0.156005i
$457$	2.01232	−	13.9960i	0.0941323	−	0.654705i	−0.887057	−	0.461659i	$-0.847254\pi$
$457$	2.01232	−	13.9960i	0.0941323	−	0.654705i	0.981190	−	0.193046i	$-0.0618365\pi$
$458$	−12.9510	+	8.32309i	−0.605159	+	0.388912i
$459$	6.58667			0.307440
$460$	−17.8647	−	1.36999i	−0.832944	−	0.0638760i
$461$	31.1928			1.45279			0.726397	−	0.687275i	$-0.241193\pi$
$461$	31.1928			1.45279			0.726397	+	0.687275i	$0.241193\pi$
$462$	2.66981	−	1.71578i	0.124211	−	0.0798253i
$463$	−1.88819	+	13.1326i	−0.0877516	+	0.610326i	0.897730	+	0.440545i	$0.145215\pi$
$463$	−1.88819	+	13.1326i	−0.0877516	+	0.610326i	−0.985482	+	0.169780i	$0.945694\pi$
$464$	−11.8651	+	25.9809i	−0.550822	+	1.20613i
$465$	−21.5120	+	6.31650i	−0.997597	+	0.292921i
$466$	−19.5193	−	42.7413i	−0.904214	−	1.97995i
$467$	16.9423	+	19.5524i	0.783995	+	0.904779i	0.997391	−	0.0721868i	$-0.0229978\pi$
$467$	16.9423	+	19.5524i	0.783995	+	0.904779i	−0.213396	+	0.976966i	$0.568452\pi$
$468$	−1.09350	−	7.60547i	−0.0505471	−	0.351563i
$469$	−7.87848	−	2.31333i	−0.363795	−	0.106820i
$470$	23.5410	−	27.1677i	1.08586	−	1.25315i
$471$	−10.4227	−	6.69825i	−0.480252	−	0.308639i
$472$	−5.09753	−	3.27598i	−0.234633	−	0.150789i
$473$	7.55364	−	8.71737i	0.347317	−	0.400825i
$474$	−19.2872	−	5.66324i	−0.885892	−	0.260121i
$475$	−0.0594250	−	0.413310i	−0.00272661	−	0.0189640i
$476$	−7.25725	−	8.37531i	−0.332635	−	0.383882i
$477$	0.659455	+	1.44401i	0.0301944	+	0.0661165i
$478$	29.9866	−	8.80486i	1.37156	−	0.402725i
$479$	−16.0348	+	35.1113i	−0.732648	+	1.60428i	0.0626349	+	0.998037i	$0.480050\pi$
$479$	−16.0348	+	35.1113i	−0.732648	+	1.60428i	−0.795283	+	0.606239i	$0.792678\pi$
$480$	2.36453	−	16.4456i	0.107925	−	0.750638i
$481$	4.33117	−	2.78348i	0.197485	−	0.126916i
$482$	−41.8493			−1.90618
$483$	−2.85427	−	3.85398i	−0.129874	−	0.175362i
$484$	−13.9059			−0.632085
$485$	29.1114	−	18.7088i	1.32188	−	0.849521i
$486$	0.273100	−	1.89945i	0.0123881	−	0.0861610i
$487$	0.820898	−	1.79752i	0.0371984	−	0.0814532i	−0.890121	−	0.455725i	$-0.849380\pi$
$487$	0.820898	−	1.79752i	0.0371984	−	0.0814532i	0.927319	+	0.374272i	$0.122107\pi$
$488$	−7.03176	+	2.06471i	−0.318313	+	0.0934651i
$489$	−3.67651	−	8.05043i	−0.166258	−	0.364053i
$490$	−2.79041	−	3.22030i	−0.126058	−	0.145478i
$491$	−1.93627	−	13.4671i	−0.0873828	−	0.607761i	−0.985712	−	0.168438i	$-0.946128\pi$
$491$	−1.93627	−	13.4671i	−0.0873828	−	0.607761i	0.898329	−	0.439323i	$-0.144782\pi$
$492$	4.38887	+	1.28869i	0.197866	+	0.0580986i
$493$	−27.1709	+	31.3569i	−1.22372	+	1.41224i
$494$	44.3160	+	28.4802i	1.99387	+	1.28138i
$495$	3.08926	+	1.98535i	0.138852	+	0.0892348i
$496$	−29.9806	+	34.5995i	−1.34617	+	1.55356i
$497$	0.145201	+	0.0426348i	0.00651315	+	0.00191243i
$498$	−0.0601273	−	0.418194i	−0.00269437	−	0.0187397i
$499$	27.8761	+	32.1707i	1.24790	+	1.44016i	0.853395	+	0.521265i	$0.174540\pi$
$499$	27.8761	+	32.1707i	1.24790	+	1.44016i	0.394509	+	0.918892i	$0.370915\pi$
$500$	7.86771	+	17.2279i	0.351855	+	0.770454i
$501$	−2.30986	+	0.678236i	−0.103197	+	0.0303013i
$502$	−3.76871	+	8.25233i	−0.168206	+	0.368320i
$503$	1.21335	−	8.43900i	0.0541004	−	0.376277i	−0.944727	−	0.327859i	$-0.893673\pi$
$503$	1.21335	−	8.43900i	0.0541004	−	0.376277i	0.998827	−	0.0484178i	$-0.0154179\pi$
$504$	0.512546	−	0.329393i	0.0228306	−	0.0146723i
$505$	29.3199			1.30472
$506$	−1.00778	−	15.1867i	−0.0448013	−	0.675130i
$507$	7.85570			0.348884
$508$	−22.0581	+	14.1759i	−0.978669	+	0.628952i
$509$	2.60165	−	18.0949i	0.115316	−	0.802041i	−0.847289	−	0.531132i	$-0.821767\pi$
$509$	2.60165	−	18.0949i	0.115316	−	0.802041i	0.962605	−	0.270909i	$-0.0873241\pi$
$510$	11.6592	−	25.5300i	0.516276	−	1.13049i
$511$	13.5449	−	3.97715i	0.599192	−	0.175939i
$512$	−11.7986	−	25.8354i	−0.521431	−	1.14177i
$513$	3.93639	+	4.54284i	0.173796	+	0.200571i
$514$	5.52330	+	38.4154i	0.243622	+	1.69443i
$515$	−35.6288	−	10.4616i	−1.56999	−	0.460992i
$516$	−7.68480	+	8.86873i	−0.338304	+	0.390424i
$517$	11.7372	+	7.54304i	0.516201	+	0.331742i
$518$	−1.81997	−	1.16963i	−0.0799650	−	0.0513904i
$519$	1.31393	−	1.51636i	0.0576752	−	0.0665607i
$520$	5.92798	+	1.74061i	0.259959	+	0.0763309i
$521$	2.86801	+	19.9474i	0.125650	+	0.873913i	0.950978	+	0.309259i	$0.100081\pi$
$521$	2.86801	+	19.9474i	0.125650	+	0.873913i	−0.825328	+	0.564654i	$0.809010\pi$
$522$	7.91607	+	9.13564i	0.346477	+	0.399856i
$523$	0.242100	+	0.530124i	0.0105863	+	0.0231807i	0.914851	−	0.403791i	$-0.132308\pi$
$523$	0.242100	+	0.530124i	0.0105863	+	0.0231807i	−0.904265	+	0.426972i	$0.859580\pi$
$524$	18.6370	−	5.47233i	0.814163	−	0.239060i
$525$	−0.0288570	+	0.0631881i	−0.00125942	+	0.00275775i
$526$	4.15913	−	28.9274i	0.181347	−	1.26129i
$527$	−55.9481	+	35.9557i	−2.43714	+	1.56625i
$528$	7.49860			0.326335
$529$	−22.7983	+	3.03916i	−0.991231	+	0.132137i
$530$	6.76428			0.293822
$531$	−8.36670	+	5.37695i	−0.363084	+	0.233340i
$532$	1.43932	−	10.0107i	0.0624023	−	0.434018i
$533$	−5.15762	+	11.2936i	−0.223401	+	0.489180i
$534$	13.1159	−	3.85117i	0.567579	−	0.166656i
$535$	−11.3848	−	24.9293i	−0.492210	−	1.07779i
$536$	−3.27609	−	3.78081i	−0.141505	−	0.163306i
$537$	−2.25598	−	15.6907i	−0.0973529	−	0.677104i
$538$	39.9106	+	11.7188i	1.72067	+	0.505234i
$539$	1.08300	−	1.24985i	0.0466483	−	0.0538350i
$540$	−3.14290	−	2.01982i	−0.135249	−	0.0869192i
$541$	−16.5386	−	10.6287i	−0.711052	−	0.456965i	0.134462	−	0.990919i	$-0.457069\pi$
$541$	−16.5386	−	10.6287i	−0.711052	−	0.456965i	−0.845514	+	0.533954i	$0.820706\pi$
$542$	−29.4498	+	33.9869i	−1.26498	+	1.45986i
$543$	10.7775	+	3.16457i	0.462508	+	0.135805i
$544$	−7.01396	−	48.7832i	−0.300721	−	2.09156i
$545$	29.9940	+	34.6149i	1.28480	+	1.48274i
$546$	−3.64054	−	7.97168i	−0.155801	−	0.341156i
$547$	−9.83884	+	2.88894i	−0.420678	+	0.123522i	−0.485219	−	0.874393i	$-0.661260\pi$
$547$	−9.83884	+	2.88894i	−0.420678	+	0.123522i	0.0645404	+	0.997915i	$0.479442\pi$
$548$	2.35247	−	5.15119i	0.100493	−	0.220048i
$549$	−1.71185	+	11.9062i	−0.0730601	+	0.508144i
$550$	−0.185460	+	0.119188i	−0.00790803	+	0.00508218i
$551$	−37.8651			−1.61311
$552$	−0.193472	−	2.91552i	−0.00823473	−	0.124093i
$553$	−10.4751			−0.445445
$554$	21.6193	−	13.8939i	0.918516	−	0.590295i
$555$	0.356257	−	2.47782i	0.0151223	−	0.105178i
$556$	1.49711	−	3.27821i	0.0634916	−	0.139027i
$557$	39.3703	−	11.5602i	1.66817	−	0.489820i	0.694830	−	0.719174i	$-0.255479\pi$
$557$	39.3703	−	11.5602i	1.66817	−	0.489820i	0.973343	+	0.229354i	$0.0736613\pi$
$558$	8.04909	+	17.6250i	0.340745	+	0.746128i
$559$	−20.8587	−	24.0723i	−0.882230	−	1.01815i
$560$	−1.43284	−	9.96559i	−0.0605484	−	0.421123i
$561$	10.4518	+	3.06891i	0.441273	+	0.129570i
$562$	−16.2576	+	18.7623i	−0.685787	+	0.791441i
$563$	−5.40046	−	3.47066i	−0.227602	−	0.146271i	0.421870	−	0.906656i	$-0.361374\pi$
$563$	−5.40046	−	3.47066i	−0.227602	−	0.146271i	−0.649472	+	0.760385i	$0.725010\pi$
$564$	−11.9410	−	7.67400i	−0.502806	−	0.323134i
$565$	1.64518	−	1.89864i	0.0692132	−	0.0798763i
$566$	−16.6076	−	4.87643i	−0.698070	−	0.204972i
$567$	−0.142315	−	0.989821i	−0.00597666	−	0.0415686i
$568$	0.0603785	+	0.0696805i	0.00253343	+	0.00292373i
$569$	−6.44667	−	14.1162i	−0.270259	−	0.591784i	0.725032	−	0.688715i	$-0.241825\pi$
$569$	−6.44667	−	14.1162i	−0.270259	−	0.591784i	−0.995291	+	0.0969308i	$0.969097\pi$
$570$	24.5759	−	7.21615i	1.02937	−	0.302251i
$571$	−6.92831	+	15.1709i	−0.289941	+	0.634881i	−0.997415	−	0.0718577i	$-0.977107\pi$
$571$	−6.92831	+	15.1709i	−0.289941	+	0.634881i	0.707474	+	0.706739i	$0.249835\pi$
$572$	1.80843	−	12.5779i	0.0756141	−	0.525907i
$573$	4.59492	−	2.95298i	0.191956	−	0.123362i
$574$	5.21706			0.217756
$575$	0.198274	+	0.267719i	0.00826858	+	0.0111646i
$576$	−5.29046			−0.220436
$577$	10.9293	−	7.02381i	0.454991	−	0.292405i	−0.293001	−	0.956112i	$-0.594654\pi$
$577$	10.9293	−	7.02381i	0.454991	−	0.292405i	0.747993	+	0.663707i	$0.231018\pi$
$578$	7.20555	−	50.1157i	0.299711	−	2.08454i
$579$	−0.323405	+	0.708158i	−0.0134403	+	0.0294300i
$580$	22.5806	−	6.63025i	0.937607	−	0.275306i
$581$	−0.0914601	−	0.200270i	−0.00379440	−	0.00830859i
$582$	−19.5844	−	22.6016i	−0.811799	−	0.936866i
$583$	0.373624	+	2.59861i	0.0154739	+	0.107623i
$584$	8.25244	+	2.42313i	0.341488	+	0.100270i
$585$	6.64062	−	7.66368i	0.274556	−	0.316854i
$586$	−19.3377	−	12.4276i	−0.798833	−	0.513379i
$587$	2.48862	+	1.59934i	0.102716	+	0.0660119i	0.590991	−	0.806678i	$-0.298737\pi$
$587$	2.48862	+	1.59934i	0.102716	+	0.0660119i	−0.488274	+	0.872690i	$0.662373\pi$
$588$	−1.10181	+	1.27155i	−0.0454378	+	0.0524380i
$589$	−58.2350	−	17.0993i	−2.39953	−	0.704566i
$590$	6.03109	+	41.9472i	0.248296	+	1.72694i
$591$	0.725272	+	0.837008i	0.0298337	+	0.0344299i
$592$	−2.12348	−	4.64977i	−0.0872744	−	0.191104i
$593$	−36.5268	+	10.7252i	−1.49998	+	0.440433i	−0.925709	−	0.378236i	$-0.876531\pi$
$593$	−36.5268	+	10.7252i	−1.49998	+	0.440433i	−0.574266	+	0.818669i	$0.694713\pi$
$594$	1.31836	−	2.88681i	0.0540931	−	0.118447i
$595$	2.08144	−	14.4767i	0.0853306	−	0.593487i
$596$	5.12139	−	3.29131i	0.209780	−	0.134817i
$597$	−0.194789			−0.00797217
$598$	−41.9059	−	3.21364i	−1.71366	−	0.131415i
$599$	−19.9298			−0.814311			−0.407155	−	0.913359i	$-0.633479\pi$
$599$	−19.9298			−0.814311			−0.407155	+	0.913359i	$0.633479\pi$
$600$	−0.0356043	+	0.0228815i	−0.00145354	+	0.000934133i
$601$	−1.61954	+	11.2642i	−0.0660626	+	0.459475i	0.929760	+	0.368166i	$0.120014\pi$
$601$	−1.61954	+	11.2642i	−0.0660626	+	0.459475i	−0.995823	+	0.0913091i	$0.970895\pi$
$602$	−5.56007	+	12.1749i	−0.226612	+	0.496210i
$603$	−7.87848	+	2.31333i	−0.320837	+	0.0942062i
$604$	−3.64642	−	7.98455i	−0.148371	−	0.324887i
$605$	−12.0181	−	13.8697i	−0.488607	−	0.563882i
$606$	−3.60610	−	25.0810i	−0.146488	−	1.01884i
$607$	−7.43277	−	2.18246i	−0.301687	−	0.0885832i	0.127386	−	0.991853i	$-0.459341\pi$
$607$	−7.43277	−	2.18246i	−0.301687	−	0.0885832i	−0.429073	+	0.903270i	$0.641160\pi$
$608$	29.4541	−	33.9918i	1.19452	−	1.37855i
$609$	5.29927	+	3.40563i	0.214737	+	0.138003i
$610$	43.1184	+	27.7105i	1.74581	+	1.12196i
$611$	25.2300	−	29.1170i	1.02070	−	1.17795i
$612$	−10.6332	−	3.12219i	−0.429822	−	0.126207i
$613$	5.34148	+	37.1508i	0.215740	+	1.50051i	0.753522	+	0.657423i	$0.228353\pi$
$613$	5.34148	+	37.1508i	0.215740	+	1.50051i	−0.537781	+	0.843084i	$0.680737\pi$
$614$	−37.2256	−	42.9606i	−1.50230	−	1.73375i
$615$	2.50775	+	5.49120i	0.101122	+	0.221426i
$616$	0.966783	−	0.283873i	0.0389528	−	0.0114376i
$617$	−18.0325	+	39.4857i	−0.725961	+	1.58963i	0.0793968	+	0.996843i	$0.474701\pi$
$617$	−18.0325	+	39.4857i	−0.725961	+	1.58963i	−0.805358	+	0.592789i	$0.798027\pi$
$618$	−4.56704	+	31.7645i	−0.183713	+	1.27775i
$619$	−13.1217	+	8.43283i	−0.527407	+	0.338944i	−0.777096	−	0.629382i	$-0.783308\pi$
$619$	−13.1217	+	8.43283i	−0.527407	+	0.338944i	0.249689	+	0.968326i	$0.419672\pi$
$620$	37.7222			1.51496
$621$	−4.48478	−	1.69903i	−0.179968	−	0.0681799i
$622$	15.0187			0.602194
$623$	5.99253	−	3.85117i	0.240086	−	0.154294i
$624$	2.94688	−	20.4960i	0.117969	−	0.820495i
$625$	−10.2391	+	22.4205i	−0.409563	+	0.896819i
$626$	−24.9970	+	7.33977i	−0.999080	+	0.293356i
$627$	4.12965	+	9.04267i	0.164922	+	0.361129i
$628$	13.6508	+	15.7539i	0.544727	+	0.628648i
$629$	−1.05678	−	7.35003i	−0.0421364	−	0.293065i
$630$	−4.08847	−	1.20048i	−0.162888	−	0.0478284i
$631$	−0.181754	+	0.209755i	−0.00723550	+	0.00835021i	−0.759356	−	0.650676i	$-0.774486\pi$
$631$	−0.181754	+	0.209755i	−0.00723550	+	0.00835021i	0.752120	+	0.659026i	$0.229031\pi$
$632$	−5.36895	−	3.45041i	−0.213565	−	0.137250i
$633$	3.64434	+	2.34208i	0.144850	+	0.0930891i
$634$	−4.08201	+	4.71089i	−0.162117	+	0.187093i
$635$	−33.2026	−	9.74918i	−1.31761	−	0.386884i
$636$	−0.380111	−	2.64373i	−0.0150724	−	0.104831i
$637$	−2.99062	−	3.45136i	−0.118493	−	0.136748i
$638$	8.30470	+	18.1848i	0.328786	+	0.719942i
$639$	0.145201	−	0.0426348i	0.00574406	−	0.00168661i
$640$	4.43934	−	9.72079i	0.175480	−	0.384248i
$641$	0.583637	−	4.05929i	0.0230523	−	0.160332i	−0.975044	−	0.222013i	$-0.928737\pi$
$641$	0.583637	−	4.05929i	0.0230523	−	0.160332i	0.998096	+	0.0616812i	$0.0196462\pi$
$642$	−19.9249	+	12.8050i	−0.786374	+	0.505372i
$643$	−10.8401			−0.427491			−0.213745	−	0.976889i	$-0.568566\pi$
$643$	−10.8401			−0.427491			−0.213745	+	0.976889i	$0.568566\pi$
$644$	2.78096	+	7.57465i	0.109585	+	0.298483i
$645$	−15.4872			−0.609809
$646$	63.9167	−	41.0768i	2.51477	−	1.61614i
$647$	6.14973	−	42.7723i	0.241771	−	1.68155i	−0.401456	−	0.915878i	$-0.631496\pi$
$647$	6.14973	−	42.7723i	0.241771	−	1.68155i	0.643227	−	0.765675i	$-0.277595\pi$
$648$	0.253098	−	0.554206i	0.00994261	−	0.0217713i
$649$	−15.7816	+	4.63389i	−0.619481	+	0.181896i
$650$	0.252893	+	0.553757i	0.00991926	+	0.0217202i
$651$	6.61213	+	7.63081i	0.259150	+	0.299075i
$652$	2.11914	+	14.7390i	0.0829921	+	0.577223i
$653$	12.5539	+	3.68617i	0.491274	+	0.144251i	0.517981	−	0.855392i	$-0.326684\pi$
$653$	12.5539	+	3.68617i	0.491274	+	0.144251i	−0.0267069	+	0.999643i	$0.508502\pi$
$654$	25.9214	−	29.9149i	1.01361	−	1.16977i
$655$	21.5651	+	13.8591i	0.842619	+	0.541519i
$656$	10.3700	+	6.66442i	0.404882	+	0.260202i
$657$	9.24450	−	10.6687i	0.360662	−	0.416227i
$658$	−15.5335	−	4.56105i	−0.605560	−	0.177808i
$659$	5.32669	+	37.0480i	0.207498	+	1.44318i	0.781283	+	0.624177i	$0.214566\pi$
$659$	5.32669	+	37.0480i	0.207498	+	1.44318i	−0.573784	+	0.819006i	$0.694525\pi$
$660$	−4.04608	−	4.66942i	−0.157493	−	0.181757i
$661$	4.90335	+	10.7368i	0.190718	+	0.417615i	0.980701	−	0.195515i	$-0.0626377\pi$
$661$	4.90335	+	10.7368i	0.190718	+	0.417615i	−0.789982	+	0.613129i	$0.789910\pi$
$662$	−42.0112	+	12.3356i	−1.63281	+	0.479437i
$663$	12.4957	−	27.3618i	0.485293	−	1.06264i
$664$	0.0190900	−	0.132774i	0.000740835	−	0.00515262i
$665$	11.2285	−	7.21615i	0.435424	−	0.279830i
$666$	−2.16341			−0.0838303
$667$	26.5889	−	14.3418i	1.02952	−	0.555316i
$668$	4.05043			0.156716
$669$	−0.986520	+	0.633998i	−0.0381411	+	0.0245118i
$670$	−4.97932	+	34.6319i	−0.192368	+	1.33795i
$671$	−8.26380	+	18.0952i	−0.319020	+	0.698557i
$672$	−7.17941	+	2.10807i	−0.276952	+	0.0813204i
$673$	9.79518	+	21.4485i	0.377576	+	0.826777i	0.999060	+	0.0433499i	$0.0138030\pi$
$673$	9.79518	+	21.4485i	0.377576	+	0.826777i	−0.621484	+	0.783427i	$0.713470\pi$
$674$	9.51492	+	10.9808i	0.366501	+	0.422965i
$675$	0.00988598	+	0.0687585i	0.000380512	+	0.00264652i
$676$	−12.6819	−	3.72374i	−0.487765	−	0.143221i
$677$	−3.01064	+	3.47447i	−0.115708	+	0.133535i	−0.810649	−	0.585533i	$-0.800885\pi$
$677$	−3.01064	+	3.47447i	−0.115708	+	0.133535i	0.694940	+	0.719067i	$0.255431\pi$
$678$	−1.82648	−	1.17381i	−0.0701457	−	0.0450799i
$679$	−13.1104	−	8.42554i	−0.503131	−	0.323343i
$680$	5.83536	−	6.73437i	0.223776	−	0.258251i
$681$	21.9515	+	6.44553i	0.841182	+	0.246993i
$682$	4.56032	+	31.7178i	0.174624	+	1.21454i
$683$	1.28101	+	1.47837i	0.0490166	+	0.0565681i	0.779728	−	0.626118i	$-0.215357\pi$
$683$	1.28101	+	1.47837i	0.0490166	+	0.0565681i	−0.730712	+	0.682686i	$0.760812\pi$
$684$	−4.20135	−	9.19967i	−0.160643	−	0.351758i
$685$	7.17090	−	2.10557i	0.273986	−	0.0804496i
$686$	−0.797176	+	1.74557i	−0.0304363	+	0.0666462i
$687$	−1.14171	+	7.94073i	−0.0435588	+	0.302958i
$688$	−26.6043	+	17.0976i	−1.01428	+	0.651839i
$689$	7.24962			0.276189
$690$	−14.5240	+	14.3756i	−0.552921	+	0.547269i
$691$	41.1852			1.56676			0.783379	−	0.621544i	$-0.213494\pi$
$691$	41.1852			1.56676			0.783379	+	0.621544i	$0.213494\pi$
$692$	−2.83993	+	1.82511i	−0.107958	+	0.0693804i
$693$	0.235359	−	1.63696i	0.00894056	−	0.0621830i
$694$	−16.6856	+	36.5363i	−0.633375	+	1.38690i
$695$	4.56356	−	1.33998i	0.173106	−	0.0508284i
$696$	1.59433	+	3.49109i	0.0604328	+	0.132329i
$697$	11.7265	+	13.5331i	0.444174	+	0.512604i
$698$	4.65946	+	32.4072i	0.176363	+	1.22663i
$699$	−23.4937	−	6.89839i	−0.888615	−	0.260921i
$700$	0.0765377	−	0.0883292i	0.00289285	−	0.00333853i
$701$	−13.4752	−	8.66000i	−0.508952	−	0.327084i	0.260836	−	0.965383i	$-0.416002\pi$
$701$	−13.4752	−	8.66000i	−0.508952	−	0.327084i	−0.769788	+	0.638299i	$0.779638\pi$
$702$	−7.37244	−	4.73798i	−0.278255	−	0.178823i
$703$	4.43777	−	5.12146i	0.167374	−	0.193160i
$704$	−8.39491	−	2.46497i	−0.316395	−	0.0929020i
$705$	−2.66596	−	18.5422i	−0.100406	−	0.698338i
$706$	33.2300	+	38.3495i	1.25063	+	1.44330i
$707$	−5.48527	−	12.0111i	−0.206295	−	0.451723i
$708$	16.0556	−	4.71434i	0.603405	−	0.177176i
$709$	−2.95328	+	6.46677i	−0.110913	+	0.242865i	−0.956946	−	0.290264i	$-0.906257\pi$
$709$	−2.95328	+	6.46677i	−0.110913	+	0.242865i	0.846034	+	0.533129i	$0.178984\pi$
$710$	0.0917691	−	0.638268i	0.00344403	−	0.0239538i
$711$	−8.81218	+	5.66324i	−0.330482	+	0.212388i
$712$	4.33999			0.162648
$713$	47.3692	−	10.0499i	1.77399	−	0.376373i
$714$	−12.6397			−0.473030
$715$	14.1081	−	9.06670i	0.527612	−	0.339075i
$716$	−3.79571	+	26.3997i	−0.141852	+	0.986604i
$717$	6.76544	−	14.8142i	0.252660	−	0.553248i
$718$	−27.1561	+	7.97374i	−1.01345	+	0.297577i
$719$	12.2303	+	26.7806i	0.456113	+	0.998747i	0.988356	+	0.152156i	$0.0486217\pi$
$719$	12.2303	+	26.7806i	0.456113	+	0.998747i	−0.532244	+	0.846591i	$0.678651\pi$
$720$	−6.59318	−	7.60894i	−0.245713	−	0.283568i
$721$	2.37992	+	16.5527i	0.0886330	+	0.616456i
$722$	31.5455	+	9.26259i	1.17400	+	0.344718i
$723$	−14.2812	+	16.4814i	−0.531125	+	0.612951i
$724$	−15.8987	−	10.2175i	−0.590870	−	0.379729i
$725$	−0.368117	−	0.236574i	−0.0136715	−	0.00878615i
$726$	−10.3863	+	11.9865i	−0.385473	+	0.444859i
$727$	−23.0402	−	6.76520i	−0.854513	−	0.250908i	−0.174997	−	0.984569i	$-0.555992\pi$
$727$	−23.0402	−	6.76520i	−0.854513	−	0.250908i	−0.679515	+	0.733661i	$0.737810\pi$
$728$	−0.395976	−	2.75407i	−0.0146758	−	0.102073i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	−24.9882	−	54.7166i	−0.924856	−	2.02515i
$731$	−44.0793	+	12.9428i	−1.63033	+	0.478708i
$732$	8.40728	−	18.4094i	0.310742	−	0.680430i
$733$	5.54102	−	38.5387i	0.204662	−	1.42346i	−0.585556	−	0.810632i	$-0.699124\pi$
$733$	5.54102	−	38.5387i	0.204662	−	1.42346i	0.790218	−	0.612826i	$-0.209967\pi$
$734$	−9.66392	+	6.21062i	−0.356702	+	0.229238i
$735$	−2.22048			−0.0819037
$736$	−7.80791	+	35.0251i	−0.287803	+	1.29104i
$737$	−13.5794			−0.500205
$738$	4.38887	−	2.82056i	0.161557	−	0.103826i
$739$	−1.83148	+	12.7382i	−0.0673720	+	0.468583i	0.928007	+	0.372562i	$0.121521\pi$
$739$	−1.83148	+	12.7382i	−0.0673720	+	0.468583i	−0.995379	+	0.0960208i	$0.969388\pi$
$740$	−1.74966	+	3.83121i	−0.0643186	+	0.140838i
$741$	26.3393	−	7.73391i	0.967598	−	0.284112i
$742$	−1.26549	−	2.77103i	−0.0464574	−	0.101728i
$743$	−7.20669	−	8.31696i	−0.264388	−	0.305120i	0.607997	−	0.793939i	$-0.291973\pi$
$743$	−7.20669	−	8.31696i	−0.264388	−	0.305120i	−0.872385	+	0.488819i	$0.837428\pi$
$744$	0.875485	+	6.08913i	0.0320968	+	0.223238i
$745$	7.70890	+	2.26354i	0.282432	+	0.0829296i
$746$	−15.0816	+	17.4051i	−0.552176	+	0.637245i
$747$	−0.185215	−	0.119031i	−0.00677667	−	0.00435510i
$748$	−15.4181	−	9.90861i	−0.563742	−	0.362295i
$749$	−8.08252	+	9.32773i	−0.295329	+	0.340828i
$750$	20.7263	+	6.08580i	0.756819	+	0.222222i
$751$	−0.846691	−	5.88886i	−0.0308962	−	0.214888i	0.968525	−	0.248918i	$-0.0800749\pi$
$751$	−0.846691	−	5.88886i	−0.0308962	−	0.214888i	−0.999421	+	0.0340301i	$0.989166\pi$
$752$	−25.0498	−	28.9090i	−0.913472	−	1.05420i
$753$	1.96391	+	4.30036i	0.0715688	+	0.156714i
$754$	52.9682	−	15.5529i	1.92899	−	0.566402i
$755$	4.81234	−	10.5376i	0.175139	−	0.383501i
$756$	−0.239446	+	1.66538i	−0.00870856	+	0.0605693i
$757$	28.3983	−	18.2505i	1.03215	−	0.663324i	0.0891190	−	0.996021i	$-0.471595\pi$
$757$	28.3983	−	18.2505i	1.03215	−	0.663324i	0.943034	+	0.332697i	$0.107958\pi$
$758$	−36.7996			−1.33662
$759$	−6.32484	−	4.78561i	−0.229577	−	0.173707i
$760$	8.13210			0.294982
$761$	−10.3884	+	6.67619i	−0.376578	+	0.242012i	−0.715214	−	0.698906i	$-0.753671\pi$
$761$	−10.3884	+	6.67619i	−0.376578	+	0.242012i	0.338636	+	0.940917i	$0.390034\pi$
$762$	−4.25604	+	29.6014i	−0.154180	+	1.07235i
$763$	8.56880	−	18.7631i	0.310211	−	0.679268i
$764$	−8.81759	+	2.58908i	−0.319009	+	0.0936696i
$765$	−6.07569	−	13.3039i	−0.219667	−	0.481003i
$766$	−5.61546	−	6.48059i	−0.202895	−	0.234153i
$767$	6.46383	+	44.9569i	0.233395	+	1.62330i
$768$	−19.0137	−	5.58293i	−0.686098	−	0.201457i
$769$	10.7760	−	12.4362i	0.388593	−	0.448460i	−0.527423	−	0.849603i	$-0.676842\pi$
$769$	10.7760	−	12.4362i	0.388593	−	0.448460i	0.916015	+	0.401143i	$0.131387\pi$
$770$	−5.92825	−	3.80986i	−0.213639	−	0.137298i
$771$	17.0139	+	10.9342i	0.612740	+	0.393784i
$772$	0.857769	−	0.989918i	0.0308718	−	0.0356279i
$773$	17.6749	+	5.18982i	0.635722	+	0.186665i	0.583685	−	0.811980i	$-0.301610\pi$
$773$	17.6749	+	5.18982i	0.635722	+	0.186665i	0.0520374	+	0.998645i	$0.483428\pi$
$774$	1.90480	+	13.2481i	0.0684665	+	0.476195i
$775$	−0.459316	−	0.530078i	−0.0164991	−	0.0190410i
$776$	−3.94437	−	8.63696i	−0.141594	−	0.310049i
$777$	−1.08170	+	0.317617i	−0.0388059	+	0.0113944i
$778$	−6.35299	+	13.9111i	−0.227766	+	0.498737i
$779$	−2.32570	+	16.1756i	−0.0833270	+	0.579552i
$780$	−14.3530	+	9.22412i	−0.513920	+	0.330277i
$781$	0.250270			0.00895536
$782$	−29.3241	+	53.0532i	−1.04863	+	1.89718i
$783$	6.29925			0.225117
$784$	−3.81440	+	2.45137i	−0.136229	+	0.0875488i
$785$	−3.91516	+	27.2305i	−0.139738	+	0.971900i
$786$	9.20306	−	20.1519i	0.328262	−	0.718794i
$787$	22.3082	−	6.55027i	0.795200	−	0.233492i	0.141195	−	0.989982i	$-0.454906\pi$
$787$	22.3082	−	6.55027i	0.795200	−	0.233492i	0.654005	+	0.756490i	$0.273087\pi$
$788$	−0.774089	−	1.69502i	−0.0275758	−	0.0603825i
$789$	−9.97309	−	11.5096i	−0.355051	−	0.409751i
$790$	6.35222	+	44.1806i	0.226002	+	1.57188i
$791$	−1.08557	−	0.318753i	−0.0385985	−	0.0113336i
$792$	0.659836	−	0.761491i	0.0234462	−	0.0270584i
$793$	46.2121	+	29.6987i	1.64104	+	1.05463i
$794$	−14.3068	−	9.19440i	−0.507728	−	0.326297i
$795$	2.30834	−	2.66396i	0.0818682	−	0.0944810i
$796$	0.314458	+	0.0923331i	0.0111457	+	0.00327266i
$797$	−3.06358	−	21.3077i	−0.108518	−	0.754757i	−0.969317	−	0.245813i	$-0.920945\pi$
$797$	−3.06358	−	21.3077i	−0.108518	−	0.754757i	0.860800	−	0.508944i	$-0.169964\pi$
$798$	−7.55389	−	8.71765i	−0.267405	−	0.308601i
$799$	−23.0837	−	50.5462i	−0.816641	−	1.78819i
$800$	0.498722	−	0.146438i	0.0176325	−	0.00517736i
$801$	2.95914	−	6.47961i	0.104556	−	0.228946i
$802$	−5.11836	+	35.5990i	−0.180735	+	1.25704i
$803$	19.6401	−	12.6219i	0.693082	−	0.445417i
$804$	13.8152			0.487225
$805$	−5.15150	+	9.32011i	−0.181566	+	0.328491i
$806$	88.4865			3.11680
$807$	18.2348	−	11.7188i	0.641897	−	0.412522i
$808$	1.14491	−	7.96303i	0.0402778	−	0.280138i
$809$	−11.4454	+	25.0620i	−0.402400	+	0.881132i	0.594622	+	0.804006i	$0.297302\pi$
$809$	−11.4454	+	25.0620i	−0.402400	+	0.881132i	−0.997021	+	0.0771266i	$0.975425\pi$
$810$	−4.08847	+	1.20048i	−0.143654	+	0.0421807i
$811$	−13.2543	−	29.0229i	−0.465421	−	1.01913i	−0.986218	−	0.165450i	$-0.947092\pi$
$811$	−13.2543	−	29.0229i	−0.465421	−	1.01913i	0.520797	−	0.853681i	$-0.325635\pi$
$812$	−6.94057	−	8.00984i	−0.243566	−	0.281090i
$813$	3.33513	+	23.1963i	0.116968	+	0.813530i
$814$	−3.43290	−	1.00799i	−0.120323	−	0.0353300i
$815$	−12.8691	+	14.8518i	−0.450786	+	0.520235i
$816$	−25.1242	−	16.1463i	−0.879523	−	0.565235i
$817$	−35.2698	−	22.6665i	−1.23393	−	0.793001i
$818$	−13.8044	+	15.9312i	−0.482661	+	0.557020i
$819$	−4.38182	−	1.28662i	−0.153113	−	0.0449581i
$820$	−1.44547	−	10.0534i	−0.0504779	−	0.351082i
$821$	−0.712677	−	0.822473i	−0.0248726	−	0.0287045i	0.743177	−	0.669095i	$-0.233318\pi$
$821$	−0.712677	−	0.822473i	−0.0248726	−	0.0287045i	−0.768050	+	0.640390i	$0.778773\pi$
$822$	−2.68311	−	5.87520i	−0.0935843	−	0.204921i
$823$	29.6901	−	8.71780i	1.03493	−	0.303883i	0.280217	−	0.959937i	$-0.409594\pi$
$823$	29.6901	−	8.71780i	1.03493	−	0.303883i	0.754715	+	0.656053i	$0.227775\pi$
$824$	−4.23254	+	9.26796i	−0.147447	+	0.322865i
$825$	−0.0163494	+	0.113712i	−0.000569212	+	0.00395896i
$826$	16.0556	−	10.3183i	0.558645	−	0.359019i
$827$	18.8416			0.655186			0.327593	−	0.944819i	$-0.393763\pi$
$827$	18.8416			0.655186			0.327593	+	0.944819i	$0.393763\pi$
$828$	6.43466	+	4.86871i	0.223620	+	0.169199i
$829$	50.0517			1.73837			0.869183	−	0.494490i	$-0.164645\pi$
$829$	50.0517			1.73837			0.869183	+	0.494490i	$0.164645\pi$
$830$	−0.789215	+	0.507198i	−0.0273940	+	0.0176051i
$831$	1.90587	−	13.2556i	0.0661139	−	0.459832i
$832$	−10.0366	+	21.9771i	−0.347957	+	0.761920i
$833$	−6.31987	+	1.85568i	−0.218970	+	0.0642955i
$834$	−1.70753	−	3.73897i	−0.0591270	−	0.129470i
$835$	3.50058	+	4.03988i	0.121142	+	0.139806i
$836$	−2.38033	−	16.5556i	−0.0823256	−	0.572587i
$837$	9.68801	+	2.84466i	0.334867	+	0.0983257i
$838$	20.4754	−	23.6299i	0.707313	−	0.816282i
$839$	−32.1478	−	20.6601i	−1.10986	−	0.713267i	−0.148601	−	0.988897i	$-0.547477\pi$
$839$	−32.1478	−	20.6601i	−1.10986	−	0.713267i	−0.961264	+	0.275631i	$0.911113\pi$
$840$	−1.13810	−	0.731411i	−0.0392681	−	0.0252361i
$841$	−6.99430	+	8.07186i	−0.241183	+	0.278340i
$842$	30.3802	+	8.92045i	1.04697	+	0.307419i
$843$	1.84114	+	12.8054i	0.0634123	+	0.441042i
$844$	−4.77307	−	5.50842i	−0.164296	−	0.189608i
$845$	−7.24627	−	15.8671i	−0.249279	−	0.545845i
$846$	−15.5335	+	4.56105i	−0.534053	+	0.156812i
$847$	−3.43339	+	7.51808i	−0.117973	+	0.258324i
$848$	1.02436	−	7.12458i	0.0351766	−	0.244659i
$849$	−7.58788	+	4.87643i	−0.260415	+	0.167359i
$850$	0.878026			0.0301160
$851$	−1.17640	+	5.27714i	−0.0403264	+	0.180898i
$852$	−0.254615			−0.00872298
$853$	−11.0373	+	7.09322i	−0.377909	+	0.242867i	−0.715781	−	0.698325i	$-0.753929\pi$
$853$	−11.0373	+	7.09322i	−0.377909	+	0.242867i	0.337872	+	0.941192i	$0.390293\pi$
$854$	3.28502	−	22.8478i	0.112411	−	0.781837i
$855$	5.54471	−	12.1412i	0.189625	−	0.415221i
$856$	−7.21516	+	2.11856i	−0.246609	+	0.0724109i
$857$	−3.82665	−	8.37918i	−0.130716	−	0.286227i	0.832945	−	0.553355i	$-0.186653\pi$
$857$	−3.82665	−	8.37918i	−0.130716	−	0.286227i	−0.963661	+	0.267128i	$0.913925\pi$
$858$	−9.49105	−	10.9533i	−0.324019	−	0.373938i
$859$	2.44688	+	17.0184i	0.0834863	+	0.580660i	0.988028	+	0.154275i	$0.0493041\pi$
$859$	2.44688	+	17.0184i	0.0834863	+	0.580660i	−0.904542	+	0.426385i	$0.859787\pi$
$860$	25.0019	+	7.34121i	0.852556	+	0.250333i
$861$	1.78034	−	2.05462i	0.0606739	−	0.0700214i
$862$	12.0598	+	7.75035i	0.410758	+	0.263978i
$863$	46.3647	+	29.7968i	1.57827	+	1.01429i	0.976471	+	0.215649i	$0.0691866\pi$
$863$	46.3647	+	29.7968i	1.57827	+	1.01429i	0.601802	+	0.798646i	$0.294450\pi$
$864$	−4.90000	+	5.65490i	−0.166701	+	0.192384i
$865$	−4.27477	−	1.25519i	−0.145346	−	0.0426776i
$866$	−4.30692	−	29.9553i	−0.146355	−	1.01792i
$867$	−17.2780	−	19.9399i	−0.586792	−	0.677194i
$868$	−7.05719	−	15.4531i	−0.239537	−	0.524512i
$869$	−16.6218	+	4.88061i	−0.563857	+	0.165563i
$870$	11.1504	−	24.4159i	0.378034	−	0.827778i
$871$	−5.33659	+	37.1168i	−0.180823	+	1.25765i
$872$	10.5723	−	6.79442i	0.358024	−	0.230088i
$873$	−15.5844			−0.527451
$874$	−54.1159	+	11.4813i	−1.83050	+	0.388362i
$875$	11.2567			0.380544
$876$	−19.9811	+	12.8410i	−0.675097	+	0.433859i
$877$	1.03116	−	7.17189i	0.0348199	−	0.242178i	−0.964977	−	0.262335i	$-0.915508\pi$
$877$	1.03116	−	7.17189i	0.0348199	−	0.242178i	0.999797	+	0.0201571i	$0.00641665\pi$
$878$	3.04055	−	6.65788i	0.102614	−	0.224693i
$879$	−11.4934	+	3.37476i	−0.387662	+	0.113828i
$880$	−6.91687	−	15.1458i	−0.233168	−	0.510566i
$881$	−12.5025	−	14.4287i	−0.421220	−	0.486114i	0.504988	−	0.863126i	$-0.331497\pi$
$881$	−12.5025	−	14.4287i	−0.421220	−	0.486114i	−0.926208	+	0.377013i	$0.876951\pi$
$882$	0.273100	+	1.89945i	0.00919576	+	0.0639579i
$883$	44.7607	+	13.1429i	1.50632	+	0.442295i	0.927707	−	0.373310i	$-0.121777\pi$
$883$	44.7607	+	13.1429i	1.50632	+	0.442295i	0.578610	+	0.815604i	$0.303595\pi$
$884$	−33.1424	+	38.2484i	−1.11470	+	1.28643i
$885$	18.5781	+	11.9394i	0.624496	+	0.401339i
$886$	34.1337	+	21.9364i	1.14675	+	0.736969i
$887$	29.0702	−	33.5488i	0.976082	−	1.12646i	−0.0158734	−	0.999874i	$-0.505053\pi$
$887$	29.0702	−	33.5488i	0.976082	−	1.12646i	0.991956	−	0.126585i	$-0.0404017\pi$
$888$	−0.659043	−	0.193513i	−0.0221160	−	0.00649386i
$889$	2.21786	+	15.4256i	0.0743846	+	0.517357i
$890$	−19.8770	−	22.9393i	−0.666279	−	0.768927i
$891$	−0.687010	−	1.50434i	−0.0230157	−	0.0503974i
$892$	1.89312	−	0.555870i	0.0633863	−	0.0186119i
$893$	21.0663	−	46.1288i	0.704957	−	1.54364i
$894$	0.988156	−	6.87278i	0.0330489	−	0.229860i
$895$	−29.6115	+	19.0301i	−0.989802	+	0.636107i
$896$	−4.81270			−0.160781
$897$	−15.5661	+	15.4070i	−0.519738	+	0.514425i
$898$	44.6076			1.48858
$899$	−53.5068	+	34.3867i	−1.78455	+	1.14686i
$900$	0.0166332	−	0.115687i	0.000554441	−	0.00385622i
$901$	4.34362	−	9.51119i	0.144707	−	0.316864i
$902$	8.27845	−	2.43077i	0.275642	−	0.0809359i
$903$	2.89740	+	6.34442i	0.0964195	+	0.211129i
$904$	−0.451411	−	0.520956i	−0.0150137	−	0.0173267i
$905$	−3.54956	−	24.6877i	−0.117991	−	0.820648i
$906$	−9.60597	−	2.82057i	−0.319137	−	0.0937071i
$907$	−34.0258	+	39.2679i	−1.12981	+	1.30387i	−0.182623	+	0.983183i	$0.558459\pi$
$907$	−34.0258	+	39.2679i	−1.12981	+	1.30387i	−0.947186	+	0.320686i	$0.896087\pi$
$908$	−32.3821	−	20.8107i	−1.07464	−	0.690629i
$909$	−11.1082	−	7.13879i	−0.368435	−	0.236779i
$910$	−12.7432	+	14.7065i	−0.422435	+	0.487515i
$911$	17.6376	+	5.17888i	0.584361	+	0.171584i	0.560533	−	0.828132i	$-0.310596\pi$
$911$	17.6376	+	5.17888i	0.584361	+	0.171584i	0.0238282	+	0.999716i	$0.492415\pi$
$912$	−3.87881	−	26.9777i	−0.128440	−	0.893322i
$913$	−0.238440	−	0.275175i	−0.00789122	−	0.00910695i
$914$	11.2720	+	24.6822i	0.372844	+	0.816415i
$915$	25.6274	−	7.52490i	0.847217	−	0.248765i
$916$	5.60716	−	12.2780i	0.185266	−	0.405675i
$917$	1.64297	−	11.4271i	0.0542555	−	0.377355i
$918$	−10.6332	+	6.83356i	−0.350949	+	0.225541i
$919$	−26.4523			−0.872580			−0.436290	−	0.899806i	$-0.643708\pi$
$919$	−26.4523			−0.872580			−0.436290	+	0.899806i	$0.643708\pi$
$920$	−5.71036	+	3.08011i	−0.188265	+	0.101548i
$921$	−29.6224			−0.976093
$922$	−50.3562	+	32.3620i	−1.65839	+	1.06579i
$923$	0.0983536	−	0.684064i	0.00323735	−	0.0225162i
$924$	−1.15590	+	2.53107i	−0.0380263	+	0.0832660i
$925$	0.0751411	−	0.0220634i	0.00247063	−	0.000725441i
$926$	−10.5767	−	23.1597i	−0.347571	−	0.761075i
$927$	10.9512	+	12.6384i	0.359685	+	0.415098i
$928$	−6.70790	−	46.6544i	−0.220198	−	1.53151i
$929$	−27.1053	−	7.95883i	−0.889295	−	0.261121i	−0.194993	−	0.980805i	$-0.562469\pi$
$929$	−27.1053	−	7.95883i	−0.889295	−	0.261121i	−0.694302	+	0.719684i	$0.744287\pi$
$930$	28.1748	−	32.5154i	0.923887	−	1.06622i
$931$	−5.05681	−	3.24981i	−0.165730	−	0.106508i
$932$	34.6573	+	22.2729i	1.13524	+	0.729572i
$933$	5.12517	−	5.91477i	0.167791	−	0.193641i
$934$	−47.6361	−	13.9872i	−1.55870	−	0.457676i
$935$	−3.44227	−	23.9415i	−0.112574	−	0.782970i
$936$	−1.82208	−	2.10279i	−0.0595565	−	0.0687319i
$937$	0.617309	+	1.35172i	0.0201666	+	0.0441587i	0.919447	−	0.393213i	$-0.128637\pi$
$937$	0.617309	+	1.35172i	0.0201666	+	0.0441587i	−0.899281	+	0.437372i	$0.855909\pi$
$938$	15.1187	−	4.43925i	0.493643	−	0.144947i
$939$	−5.63970	+	12.3492i	−0.184045	+	0.403002i
$940$	−4.48549	+	31.1973i	−0.146301	+	1.01754i
$941$	−0.575918	+	0.370120i	−0.0187744	+	0.0120656i	−0.549994	−	0.835168i	$-0.685370\pi$
$941$	−0.575918	+	0.370120i	−0.0187744	+	0.0120656i	0.531220	+	0.847234i	$0.321734\pi$
$942$	23.7752			0.774638
$943$	−4.49357	−	12.2394i	−0.146331	−	0.398570i
$944$	45.0948			1.46771
$945$	−1.86799	+	1.20048i	−0.0607656	+	0.0390517i
$946$	−3.15014	+	21.9097i	−0.102420	+	0.712346i
$947$	21.2073	−	46.4375i	0.689144	−	1.50901i	−0.163512	−	0.986541i	$-0.552282\pi$
$947$	21.2073	−	46.4375i	0.689144	−	1.50901i	0.852656	−	0.522473i	$-0.174991\pi$
$948$	16.9104	−	4.96535i	0.549226	−	0.161267i
$949$	−26.7812	−	58.6425i	−0.869353	−	1.90362i
$950$	0.524735	+	0.605576i	0.0170247	+	0.0196475i
$951$	0.462279	+	3.21522i	0.0149904	+	0.104261i
$952$	−3.85047	−	1.13060i	−0.124794	−	0.0366430i
$953$	−13.5781	+	15.6700i	−0.439839	+	0.507601i	−0.931778	−	0.363028i	$-0.881743\pi$
$953$	−13.5781	+	15.6700i	−0.439839	+	0.507601i	0.491939	+	0.870630i	$0.336288\pi$
$954$	−2.56272	−	1.64696i	−0.0829712	−	0.0533224i
$955$	−10.2029	−	6.55703i	−0.330159	−	0.212180i
$956$	−17.9440	+	20.7085i	−0.580351	+	0.669761i
$957$	9.99567	+	2.93499i	0.323114	+	0.0948749i
$958$	−10.5415	−	73.3178i	−0.340581	−	2.36879i
$959$	−2.20411	−	2.54368i	−0.0711746	−	0.0821398i
$960$	4.88003	+	10.6858i	0.157502	+	0.344882i
$961$	−68.0756	+	19.9888i	−2.19599	+	0.644800i
$962$	−4.10424	+	8.98703i	−0.132326	+	0.289754i
$963$	−1.75650	+	12.2167i	−0.0566024	+	0.393679i
$964$	30.8674	−	19.8373i	0.994173	−	0.638916i
$965$	1.72867			0.0556478
$966$	8.60624	+	3.26042i	0.276901	+	0.104902i
$967$	−37.7036			−1.21247			−0.606233	−	0.795287i	$-0.707320\pi$
$967$	−37.7036			−1.21247			−0.606233	+	0.795287i	$0.707320\pi$
$968$	−4.23618	+	2.72242i	−0.136156	+	0.0875021i
$969$	5.63464	−	39.1898i	0.181011	−	1.25896i
$970$	−27.5861	+	60.4051i	−0.885736	+	1.93949i
$971$	−14.8266	+	4.35347i	−0.475807	+	0.139709i	−0.510838	−	0.859677i	$-0.670665\pi$
$971$	−14.8266	+	4.35347i	−0.475807	+	0.139709i	0.0350316	+	0.999386i	$0.488847\pi$
$972$	0.698939	+	1.53046i	0.0224185	+	0.0490896i
$973$	−1.40270	−	1.61880i	−0.0449684	−	0.0518963i
$974$	0.539671	+	3.75349i	0.0172922	+	0.120270i
$975$	0.304385	+	0.0893756i	0.00974813	+	0.00286231i
$976$	35.7161	−	41.2186i	1.14325	−	1.31938i
$977$	18.7108	+	12.0247i	0.598611	+	0.384704i	0.804571	−	0.593856i	$-0.202395\pi$
$977$	18.7108	+	12.0247i	0.598611	+	0.384704i	−0.205960	+	0.978560i	$0.566032\pi$
$978$	14.2874	+	9.18193i	0.456860	+	0.293606i
$979$	7.71460	−	8.90312i	0.246560	−	0.284545i
$980$	3.58464	+	1.05255i	0.114507	+	0.0336223i
$981$	−2.93554	−	20.4171i	−0.0937246	−	0.651869i
$982$	17.0977	+	19.7318i	0.545609	+	0.629667i
$983$	−4.38798	−	9.60834i	−0.139955	−	0.306459i	0.826656	−	0.562708i	$-0.190240\pi$
$983$	−4.38798	−	9.60834i	−0.139955	−	0.306459i	−0.966611	+	0.256249i	$0.917513\pi$
$984$	1.58929	−	0.466656i	0.0506646	−	0.0148765i
$985$	1.02160	−	2.23699i	0.0325509	−	0.0712765i
$986$	11.3312	−	78.8105i	0.360860	−	2.50984i
$987$	−7.09714	+	4.56105i	−0.225904	+	0.145180i
$988$	−46.1869			−1.46940
$989$	33.3516	+	2.55764i	1.06052	+	0.0813282i
$990$	−7.04693			−0.223966
$991$	16.2600	−	10.4496i	0.516515	−	0.331944i	−0.256277	−	0.966603i	$-0.582496\pi$
$991$	16.2600	−	10.4496i	0.516515	−	0.331944i	0.772792	+	0.634659i	$0.218860\pi$
$992$	10.7520	−	74.7819i	0.341377	−	2.37433i
$993$	−9.47838	+	20.7548i	−0.300787	+	0.658632i
$994$	−0.278639	+	0.0818157i	−0.00883788	+	0.00259504i
$995$	0.179677	+	0.393438i	0.00569615	+	0.0124728i
$996$	0.242580	+	0.279952i	0.00768645	+	0.00887063i
$997$	3.19603	+	22.2289i	0.101219	+	0.703995i	0.975728	+	0.218986i	$0.0702748\pi$
$997$	3.19603	+	22.2289i	0.101219	+	0.703995i	−0.874509	+	0.485010i	$0.838816\pi$
$998$	−78.3783	−	23.0139i	−2.48102	−	0.728494i
$999$	−0.738270	+	0.852009i	−0.0233578	+	0.0269564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.c.127.2	✓	20
23.2	even	11	inner	483.2.q.c.232.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.c.127.2	✓	20	1.1	even	1	trivial
483.2.q.c.232.2	yes	20	23.2	even	11	inner

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61435 + 1.03748i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.698939 - 1.53046i) q^{4} +(2.13054 - 0.625582i) q^{5} +(-0.797176 - 1.74557i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.0867074 - 0.603063i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-1.61435 + 1.03748i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.698939 - 1.53046i) q^{4} +(2.13054 - 0.625582i) q^{5} +(-0.797176 - 1.74557i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.0867074 - 0.603063i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-2.79041 + 3.22030i) q^{10} +(-1.39126 - 0.894108i) q^{11} +(1.41542 + 0.909632i) q^{12} +(-2.99062 + 3.45136i) q^{13} +(1.84125 + 0.540641i) q^{14} +(0.316007 + 2.19788i) q^{15} +(2.96926 + 3.42671i) q^{16} +(2.73620 + 5.99145i) q^{17} +(1.84125 - 0.540641i) q^{18} +(-2.49708 + 5.46784i) q^{19} +(0.531685 - 3.69795i) q^{20} +(0.841254 - 0.540641i) q^{21} +3.17361 q^{22} +(-0.317551 - 4.78531i) q^{23} +0.609264 q^{24} +(-0.0584382 + 0.0375559i) q^{25} +(1.24720 - 8.67443i) q^{26} +(0.415415 - 0.909632i) q^{27} +(-1.61435 + 0.474017i) q^{28} +(2.61680 + 5.73000i) q^{29} +(-2.79041 - 3.22030i) q^{30} +(1.43695 + 9.99423i) q^{31} +(-7.17941 - 2.10807i) q^{32} +(1.08300 - 1.24985i) q^{33} +(-10.6332 - 6.83356i) q^{34} +(-1.86799 - 1.20048i) q^{35} +(-1.10181 + 1.27155i) q^{36} +(-1.08170 - 0.317617i) q^{37} +(-1.64162 - 11.4177i) q^{38} +(-2.99062 - 3.45136i) q^{39} +(-0.561998 - 1.23060i) q^{40} +(2.60853 - 0.765934i) q^{41} +(-0.797176 + 1.74557i) q^{42} +(-0.992605 + 6.90372i) q^{43} +(-2.34080 + 1.50434i) q^{44} -2.22048 q^{45} +(5.47731 + 7.39572i) q^{46} -8.43638 q^{47} +(-3.81440 + 2.45137i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(0.0553763 - 0.121257i) q^{50} +(-6.31987 + 1.85568i) q^{51} +(3.19192 + 6.98932i) q^{52} +(-1.03957 - 1.19972i) q^{53} +(0.273100 + 1.89945i) q^{54} +(-3.52346 - 1.03458i) q^{55} +(-0.398983 + 0.460451i) q^{56} +(-5.05681 - 3.24981i) q^{57} +(-10.1692 - 6.53536i) q^{58} +(6.51293 - 7.51632i) q^{59} +(3.58464 + 1.05255i) q^{60} +(-1.71185 - 11.9062i) q^{61} +(-12.6886 - 14.6434i) q^{62} +(0.415415 + 0.909632i) q^{63} +(5.07616 - 1.49049i) q^{64} +(-4.21252 + 9.22412i) q^{65} +(-0.451651 + 3.14130i) q^{66} +(6.90761 - 4.43925i) q^{67} +11.0821 q^{68} +(4.78179 + 0.366702i) q^{69} +4.26107 q^{70} +(-0.127308 + 0.0818157i) q^{71} +(-0.0867074 + 0.603063i) q^{72} +(-5.86431 + 12.8410i) q^{73} +(2.07577 - 0.609502i) q^{74} +(-0.0288570 - 0.0631881i) q^{75} +(6.62301 + 7.64336i) q^{76} +(0.235359 + 1.63696i) q^{77} +(8.40864 + 2.46900i) q^{78} +(6.85970 - 7.91652i) q^{79} +(8.46980 + 5.44321i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-3.41645 + 3.94279i) q^{82} +(0.211247 + 0.0620278i) q^{83} +(-0.239446 - 1.66538i) q^{84} +(9.57772 + 11.0533i) q^{85} +(-5.56007 - 12.1749i) q^{86} +(-6.04409 + 1.77470i) q^{87} +(-0.418571 + 0.916543i) q^{88} +(-1.01376 + 7.05083i) q^{89} +(3.58464 - 2.30371i) q^{90} +4.56680 q^{91} +(-7.54568 - 2.85864i) q^{92} -10.0970 q^{93} +(13.6193 - 8.75260i) q^{94} +(-1.89953 + 13.2115i) q^{95} +(3.10835 - 6.80633i) q^{96} +(14.9531 - 4.39062i) q^{97} +(-0.797176 - 1.74557i) q^{98} +(1.08300 + 1.24985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9} + 9 q^{10} + 3 q^{11} + 18 q^{12} - 2 q^{13} + 18 q^{14} - q^{15} + 8 q^{16} + 8 q^{17} + 18 q^{18} + 6 q^{19} - 2 q^{20} - 2 q^{21} + 6 q^{22} + 11 q^{23} + 9 q^{25} + 7 q^{26} - 2 q^{27} - 4 q^{28} + 23 q^{29} + 9 q^{30} + q^{31} - 28 q^{32} + 14 q^{33} - 28 q^{34} + 10 q^{35} - 4 q^{36} - 9 q^{37} + 34 q^{38} - 2 q^{39} - 15 q^{41} - 4 q^{42} - 23 q^{43} - 16 q^{44} - 12 q^{45} + 11 q^{46} - 66 q^{47} - 36 q^{48} - 2 q^{49} - 26 q^{50} - 14 q^{51} + 7 q^{52} + 9 q^{53} - 4 q^{54} - 62 q^{55} + 22 q^{56} - 27 q^{57} - 20 q^{58} + 49 q^{59} - 2 q^{60} + 46 q^{61} - 9 q^{62} - 2 q^{63} + 16 q^{64} + 11 q^{65} - 16 q^{66} + 14 q^{67} + 38 q^{68} + 11 q^{69} - 2 q^{70} + 36 q^{71} - q^{73} + 4 q^{74} - 2 q^{75} + 34 q^{76} - 8 q^{77} - 15 q^{78} - 22 q^{79} + 15 q^{80} - 2 q^{81} - 30 q^{82} + 8 q^{83} - 4 q^{84} - 32 q^{85} - 68 q^{86} + q^{87} - 11 q^{88} - 2 q^{89} - 2 q^{90} - 24 q^{91} + 11 q^{92} - 32 q^{93} + 33 q^{94} - 107 q^{95} + 16 q^{96} + 18 q^{97} - 4 q^{98} + 14 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9 + 9 * q^10 + 3 * q^11 + 18 * q^12 - 2 * q^13 + 18 * q^14 - q^15 + 8 * q^16 + 8 * q^17 + 18 * q^18 + 6 * q^19 - 2 * q^20 - 2 * q^21 + 6 * q^22 + 11 * q^23 + 9 * q^25 + 7 * q^26 - 2 * q^27 - 4 * q^28 + 23 * q^29 + 9 * q^30 + q^31 - 28 * q^32 + 14 * q^33 - 28 * q^34 + 10 * q^35 - 4 * q^36 - 9 * q^37 + 34 * q^38 - 2 * q^39 - 15 * q^41 - 4 * q^42 - 23 * q^43 - 16 * q^44 - 12 * q^45 + 11 * q^46 - 66 * q^47 - 36 * q^48 - 2 * q^49 - 26 * q^50 - 14 * q^51 + 7 * q^52 + 9 * q^53 - 4 * q^54 - 62 * q^55 + 22 * q^56 - 27 * q^57 - 20 * q^58 + 49 * q^59 - 2 * q^60 + 46 * q^61 - 9 * q^62 - 2 * q^63 + 16 * q^64 + 11 * q^65 - 16 * q^66 + 14 * q^67 + 38 * q^68 + 11 * q^69 - 2 * q^70 + 36 * q^71 - q^73 + 4 * q^74 - 2 * q^75 + 34 * q^76 - 8 * q^77 - 15 * q^78 - 22 * q^79 + 15 * q^80 - 2 * q^81 - 30 * q^82 + 8 * q^83 - 4 * q^84 - 32 * q^85 - 68 * q^86 + q^87 - 11 * q^88 - 2 * q^89 - 2 * q^90 - 24 * q^91 + 11 * q^92 - 32 * q^93 + 33 * q^94 - 107 * q^95 + 16 * q^96 + 18 * q^97 - 4 * q^98 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more