LMFDB - Embedded newform 690.2.m.g.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			31.3
Character	$\chi$	$=$	690.31
Dual form			690.2.m.g.601.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-0.654861 - 0.755750i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(4.15900 + 2.67283i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-0.654861 - 0.755750i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(4.15900 + 2.67283i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(0.841254 - 0.540641i) q^{10} +(0.0610876 + 0.424874i) q^{11} +(-0.142315 - 0.989821i) q^{12} +(2.87340 - 1.84662i) q^{13} +(-3.23751 + 3.73629i) q^{14} +(0.415415 - 0.909632i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-0.972837 + 0.285651i) q^{17} +(-0.654861 - 0.755750i) q^{18} +(1.62118 + 0.476023i) q^{19} +(0.415415 + 0.909632i) q^{20} +(-0.703578 + 4.89350i) q^{21} -0.429243 q^{22} +(4.78984 - 0.239582i) q^{23} +1.00000 q^{24} +(-0.142315 + 0.989821i) q^{25} +(1.41890 + 3.10695i) q^{26} +(-0.959493 - 0.281733i) q^{27} +(-3.23751 - 3.73629i) q^{28} +(-5.78632 + 1.69902i) q^{29} +(0.841254 + 0.540641i) q^{30} +(-0.844104 + 1.84833i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-0.361102 + 0.232066i) q^{33} +(-0.144294 - 1.00359i) q^{34} +(-0.703578 - 4.89350i) q^{35} +(0.841254 - 0.540641i) q^{36} +(-5.19223 + 5.99216i) q^{37} +(-0.701896 + 1.53694i) q^{38} +(2.87340 + 1.84662i) q^{39} +(-0.959493 + 0.281733i) q^{40} +(4.09962 + 4.73121i) q^{41} +(-4.74356 - 1.39283i) q^{42} +(2.20967 + 4.83851i) q^{43} +(0.0610876 - 0.424874i) q^{44} +1.00000 q^{45} +(-0.444523 + 4.77519i) q^{46} +2.74912 q^{47} +(-0.142315 + 0.989821i) q^{48} +(7.24539 + 15.8652i) q^{49} +(-0.959493 - 0.281733i) q^{50} +(-0.663968 - 0.766260i) q^{51} +(-3.27726 + 0.962290i) q^{52} +(-10.9911 - 7.06355i) q^{53} +(0.415415 - 0.909632i) q^{54} +(0.281094 - 0.324400i) q^{55} +(4.15900 - 2.67283i) q^{56} +(0.240459 + 1.67243i) q^{57} +(-0.858244 - 5.96922i) q^{58} +(-6.23504 + 4.00702i) q^{59} +(-0.654861 + 0.755750i) q^{60} +(3.99747 - 8.75325i) q^{61} +(-1.70939 - 1.09856i) q^{62} +(-4.74356 + 1.39283i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-3.27726 - 0.962290i) q^{65} +(-0.178314 - 0.390453i) q^{66} +(1.06163 - 7.38379i) q^{67} +1.01391 q^{68} +(2.20770 + 4.25747i) q^{69} +4.94382 q^{70} +(0.922154 - 6.41373i) q^{71} +(0.415415 + 0.909632i) q^{72} +(-0.920722 - 0.270348i) q^{73} +(-5.19223 - 5.99216i) q^{74} +(-0.959493 + 0.281733i) q^{75} +(-1.42140 - 0.913481i) q^{76} +(-0.881551 + 1.93033i) q^{77} +(-2.23675 + 2.58135i) q^{78} +(-1.94012 + 1.24684i) q^{79} +(-0.142315 - 0.989821i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-5.26649 + 3.38457i) q^{82} +(5.00997 - 5.78181i) q^{83} +(2.05374 - 4.49705i) q^{84} +(0.852953 + 0.548160i) q^{85} +(-5.10373 + 1.49859i) q^{86} +(-3.94920 - 4.55762i) q^{87} +(0.411855 + 0.120932i) q^{88} +(-3.74388 - 8.19796i) q^{89} +(-0.142315 + 0.989821i) q^{90} +16.8862 q^{91} +(-4.66332 - 1.11958i) q^{92} -2.03195 q^{93} +(-0.391240 + 2.72114i) q^{94} +(-0.701896 - 1.53694i) q^{95} +(-0.959493 - 0.281733i) q^{96} +(-2.89043 - 3.33573i) q^{97} +(-16.7348 + 4.91379i) q^{98} +(-0.361102 - 0.232066i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	−0.654861	−	0.755750i	−0.292863	−	0.337981i
$5$	−0.654861	−	0.755750i	−0.292863	−	0.337981i
$6$	−0.959493	+	0.281733i	−0.391711	+	0.115017i
$7$	4.15900	+	2.67283i	1.57196	+	1.01023i	0.978719	+	0.205206i	$0.0657866\pi$
$7$	4.15900	+	2.67283i	1.57196	+	1.01023i	0.593237	+	0.805028i	$0.297850\pi$
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$	0.841254	−	0.540641i	0.266028	−	0.170966i
$11$	0.0610876	+	0.424874i	0.0184186	+	0.128104i	0.996956	−	0.0779644i	$-0.0248421\pi$
$11$	0.0610876	+	0.424874i	0.0184186	+	0.128104i	−0.978538	+	0.206069i	$0.933933\pi$
$12$	−0.142315	−	0.989821i	−0.0410828	−	0.285737i
$13$	2.87340	−	1.84662i	0.796937	−	0.512160i	−0.0776778	−	0.996979i	$-0.524751\pi$
$13$	2.87340	−	1.84662i	0.796937	−	0.512160i	0.874615	+	0.484818i	$0.161114\pi$
$14$	−3.23751	+	3.73629i	−0.865261	+	0.998565i
$15$	0.415415	−	0.909632i	0.107260	−	0.234866i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	−0.972837	+	0.285651i	−0.235948	+	0.0692805i	−0.397569	−	0.917572i	$-0.630146\pi$
$17$	−0.972837	+	0.285651i	−0.235948	+	0.0692805i	0.161621	+	0.986853i	$0.448328\pi$
$18$	−0.654861	−	0.755750i	−0.154352	−	0.178132i
$19$	1.62118	+	0.476023i	0.371925	+	0.109207i	0.462353	−	0.886696i	$-0.347005\pi$
$19$	1.62118	+	0.476023i	0.371925	+	0.109207i	−0.0904278	+	0.995903i	$0.528823\pi$
$20$	0.415415	+	0.909632i	0.0928896	+	0.203400i
$21$	−0.703578	+	4.89350i	−0.153533	+	1.06785i
$22$	−0.429243			−0.0915149
$23$	4.78984	−	0.239582i	0.998751	−	0.0499563i
$23$	4.78984	−	0.239582i	0.998751	−	0.0499563i
$24$	1.00000			0.204124
$25$	−0.142315	+	0.989821i	−0.0284630	+	0.197964i
$26$	1.41890	+	3.10695i	0.278269	+	0.609324i
$27$	−0.959493	−	0.281733i	−0.184655	−	0.0542195i
$28$	−3.23751	−	3.73629i	−0.611832	−	0.706092i
$29$	−5.78632	+	1.69902i	−1.07449	+	0.315499i	−0.770673	−	0.637230i	$-0.780080\pi$
$29$	−5.78632	+	1.69902i	−1.07449	+	0.315499i	−0.303819	+	0.952730i	$0.598262\pi$
$30$	0.841254	+	0.540641i	0.153591	+	0.0987071i
$31$	−0.844104	+	1.84833i	−0.151606	+	0.331970i	−0.970163	−	0.242455i	$-0.922047\pi$
$31$	−0.844104	+	1.84833i	−0.151606	+	0.331970i	0.818557	+	0.574425i	$0.194774\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$	−0.361102	+	0.232066i	−0.0628598	+	0.0403975i
$34$	−0.144294	−	1.00359i	−0.0247462	−	0.172114i
$35$	−0.703578	−	4.89350i	−0.118926	−	0.827152i
$36$	0.841254	−	0.540641i	0.140209	−	0.0901068i
$37$	−5.19223	+	5.99216i	−0.853598	+	0.985105i	−0.999992	−	0.00412179i	$-0.998688\pi$
$37$	−5.19223	+	5.99216i	−0.853598	+	0.985105i	0.146393	+	0.989226i	$0.453233\pi$
$38$	−0.701896	+	1.53694i	−0.113863	+	0.249324i
$39$	2.87340	+	1.84662i	0.460112	+	0.295696i
$40$	−0.959493	+	0.281733i	−0.151709	+	0.0445458i
$41$	4.09962	+	4.73121i	0.640252	+	0.738891i	0.979419	−	0.201835i	$-0.0646906\pi$
$41$	4.09962	+	4.73121i	0.640252	+	0.738891i	−0.339167	+	0.940726i	$0.610145\pi$
$42$	−4.74356	−	1.39283i	−0.731947	−	0.214919i
$43$	2.20967	+	4.83851i	0.336972	+	0.737866i	0.999942	−	0.0107803i	$-0.00343155\pi$
$43$	2.20967	+	4.83851i	0.336972	+	0.737866i	−0.662970	+	0.748646i	$0.730704\pi$
$44$	0.0610876	−	0.424874i	0.00920931	−	0.0640521i
$45$	1.00000			0.149071
$46$	−0.444523	+	4.77519i	−0.0655413	+	0.704063i
$47$	2.74912			0.401000			0.200500	−	0.979694i	$-0.435743\pi$
$47$	2.74912			0.401000			0.200500	+	0.979694i	$0.435743\pi$
$48$	−0.142315	+	0.989821i	−0.0205414	+	0.142868i
$49$	7.24539	+	15.8652i	1.03506	+	2.26646i
$50$	−0.959493	−	0.281733i	−0.135693	−	0.0398430i
$51$	−0.663968	−	0.766260i	−0.0929741	−	0.107298i
$52$	−3.27726	+	0.962290i	−0.454474	+	0.133446i
$53$	−10.9911	−	7.06355i	−1.50974	−	0.970253i	−0.993503	−	0.113809i	$-0.963695\pi$
$53$	−10.9911	−	7.06355i	−1.50974	−	0.970253i	−0.516240	−	0.856444i	$-0.672669\pi$
$54$	0.415415	−	0.909632i	0.0565308	−	0.123785i
$55$	0.281094	−	0.324400i	0.0379027	−	0.0437421i
$56$	4.15900	−	2.67283i	0.555770	−	0.357172i
$57$	0.240459	+	1.67243i	0.0318496	+	0.221519i
$58$	−0.858244	−	5.96922i	−0.112693	−	0.783797i
$59$	−6.23504	+	4.00702i	−0.811733	+	0.521669i	−0.879425	−	0.476037i	$-0.842073\pi$
$59$	−6.23504	+	4.00702i	−0.811733	+	0.521669i	0.0676921	+	0.997706i	$0.478436\pi$
$60$	−0.654861	+	0.755750i	−0.0845422	+	0.0975669i
$61$	3.99747	−	8.75325i	0.511824	−	1.12074i	−0.460619	−	0.887598i	$-0.652373\pi$
$61$	3.99747	−	8.75325i	0.511824	−	1.12074i	0.972443	−	0.233140i	$-0.0749002\pi$
$62$	−1.70939	−	1.09856i	−0.217093	−	0.139517i
$63$	−4.74356	+	1.39283i	−0.597632	+	0.175481i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−3.27726	−	0.962290i	−0.406494	−	0.119357i
$66$	−0.178314	−	0.390453i	−0.0219489	−	0.0480614i
$67$	1.06163	−	7.38379i	0.129699	−	0.902073i	−0.816237	−	0.577718i	$-0.803944\pi$
$67$	1.06163	−	7.38379i	0.129699	−	0.902073i	0.945935	−	0.324355i	$-0.105147\pi$
$68$	1.01391			0.122954
$69$	2.20770	+	4.25747i	0.265776	+	0.512539i
$70$	4.94382			0.590899
$71$	0.922154	−	6.41373i	0.109440	−	0.761169i	−0.859010	−	0.511959i	$-0.828920\pi$
$71$	0.922154	−	6.41373i	0.109440	−	0.761169i	0.968449	−	0.249210i	$-0.0801710\pi$
$72$	0.415415	+	0.909632i	0.0489571	+	0.107201i
$73$	−0.920722	−	0.270348i	−0.107762	−	0.0316419i	0.227407	−	0.973800i	$-0.426975\pi$
$73$	−0.920722	−	0.270348i	−0.107762	−	0.0316419i	−0.335169	+	0.942158i	$0.608793\pi$
$74$	−5.19223	−	5.99216i	−0.603585	−	0.696574i
$75$	−0.959493	+	0.281733i	−0.110793	+	0.0325317i
$76$	−1.42140	−	0.913481i	−0.163046	−	0.104783i
$77$	−0.881551	+	1.93033i	−0.100462	+	0.219981i
$78$	−2.23675	+	2.58135i	−0.253262	+	0.292280i
$79$	−1.94012	+	1.24684i	−0.218281	+	0.140280i	−0.645212	−	0.764004i	$-0.723231\pi$
$79$	−1.94012	+	1.24684i	−0.218281	+	0.140280i	0.426931	+	0.904284i	$0.359595\pi$
$80$	−0.142315	−	0.989821i	−0.0159113	−	0.110665i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	−5.26649	+	3.38457i	−0.581586	+	0.373763i
$83$	5.00997	−	5.78181i	0.549916	−	0.634636i	−0.410948	−	0.911659i	$-0.634802\pi$
$83$	5.00997	−	5.78181i	0.549916	−	0.634636i	0.960863	+	0.277022i	$0.0893476\pi$
$84$	2.05374	−	4.49705i	0.224081	−	0.490669i
$85$	0.852953	+	0.548160i	0.0925157	+	0.0594563i
$86$	−5.10373	+	1.49859i	−0.550349	+	0.161597i
$87$	−3.94920	−	4.55762i	−0.423399	−	0.488629i
$88$	0.411855	+	0.120932i	0.0439039	+	0.0128914i
$89$	−3.74388	−	8.19796i	−0.396851	−	0.868982i	−0.997580	−	0.0695293i	$-0.977850\pi$
$89$	−3.74388	−	8.19796i	−0.396851	−	0.868982i	0.600729	−	0.799453i	$-0.294877\pi$
$90$	−0.142315	+	0.989821i	−0.0150013	+	0.104336i
$91$	16.8862			1.77015
$92$	−4.66332	−	1.11958i	−0.486185	−	0.116724i
$93$	−2.03195			−0.210704
$94$	−0.391240	+	2.72114i	−0.0403533	+	0.280664i
$95$	−0.701896	−	1.53694i	−0.0720130	−	0.157687i
$96$	−0.959493	−	0.281733i	−0.0979278	−	0.0287542i
$97$	−2.89043	−	3.33573i	−0.293478	−	0.338692i	0.589793	−	0.807555i	$-0.299209\pi$
$97$	−2.89043	−	3.33573i	−0.293478	−	0.338692i	−0.883271	+	0.468863i	$0.844664\pi$
$98$	−16.7348	+	4.91379i	−1.69047	+	0.496368i
$99$	−0.361102	−	0.232066i	−0.0362921	−	0.0233235i
$100$	0.415415	−	0.909632i	0.0415415	−	0.0909632i
$101$	8.07019	−	9.31350i	0.803014	−	0.926728i	−0.195529	−	0.980698i	$-0.562642\pi$
$101$	8.07019	−	9.31350i	0.803014	−	0.926728i	0.998543	+	0.0539704i	$0.0171877\pi$
$102$	0.852953	−	0.548160i	0.0844549	−	0.0542759i
$103$	1.45878	+	10.1460i	0.143738	+	0.999717i	0.926204	+	0.377024i	$0.123052\pi$
$103$	1.45878	+	10.1460i	0.143738	+	0.999717i	−0.782466	+	0.622693i	$0.786038\pi$
$104$	−0.486093	−	3.38085i	−0.0476653	−	0.331520i
$105$	4.15900	−	2.67283i	0.405877	−	0.260841i
$106$	8.55584	−	9.87397i	0.831017	−	0.959045i
$107$	−1.21341	+	2.65699i	−0.117304	+	0.256861i	−0.959172	−	0.282823i	$-0.908729\pi$
$107$	−1.21341	+	2.65699i	−0.117304	+	0.256861i	0.841868	+	0.539684i	$0.181456\pi$
$108$	0.841254	+	0.540641i	0.0809497	+	0.0520232i
$109$	8.62031	−	2.53115i	0.825676	−	0.242440i	0.158517	−	0.987356i	$-0.449329\pi$
$109$	8.62031	−	2.53115i	0.825676	−	0.242440i	0.667158	+	0.744916i	$0.267510\pi$
$110$	0.281094	+	0.324400i	0.0268013	+	0.0309303i
$111$	−7.60759	−	2.23379i	−0.722081	−	0.212022i
$112$	2.05374	+	4.49705i	0.194060	+	0.424932i
$113$	−0.761543	+	5.29665i	−0.0716400	+	0.498267i	0.922136	+	0.386867i	$0.126443\pi$
$113$	−0.761543	+	5.29665i	−0.0716400	+	0.498267i	−0.993776	+	0.111400i	$0.964466\pi$
$114$	−1.68963			−0.158248
$115$	−3.31774	−	3.46303i	−0.309381	−	0.322929i
$116$	6.03060			0.559927
$117$	−0.486093	+	3.38085i	−0.0449393	+	0.312560i
$118$	−3.07889	−	6.74183i	−0.283435	−	0.620636i
$119$	−4.80953	−	1.41220i	−0.440889	−	0.129457i
$120$	−0.654861	−	0.755750i	−0.0597803	−	0.0689902i
$121$	10.3776	−	3.04715i	0.943422	−	0.277014i
$122$	8.09525	+	5.20250i	0.732910	+	0.471012i
$123$	−2.60062	+	5.69456i	−0.234490	+	0.513461i
$124$	1.33065	−	1.53565i	0.119496	−	0.137905i
$125$	0.841254	−	0.540641i	0.0752440	−	0.0483564i
$126$	−0.703578	−	4.89350i	−0.0626798	−	0.435947i
$127$	−3.09550	−	21.5297i	−0.274682	−	1.91045i	−0.396743	−	0.917930i	$-0.629860\pi$
$127$	−3.09550	−	21.5297i	−0.274682	−	1.91045i	0.122062	−	0.992522i	$-0.461049\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	−3.48333	+	4.01998i	−0.306690	+	0.353939i
$130$	1.41890	−	3.10695i	0.124446	−	0.272498i
$131$	10.8147	+	6.95017i	0.944883	+	0.607239i	0.919775	−	0.392445i	$-0.128371\pi$
$131$	10.8147	+	6.95017i	0.944883	+	0.607239i	0.0251075	+	0.999685i	$0.492007\pi$
$132$	0.411855	−	0.120932i	0.0358474	−	0.0105258i
$133$	5.47018	+	6.31293i	0.474325	+	0.547400i
$134$	7.15754	+	2.10164i	0.618318	+	0.181554i
$135$	0.415415	+	0.909632i	0.0357532	+	0.0782887i
$136$	−0.144294	+	1.00359i	−0.0123731	+	0.0860569i
$137$	5.35070			0.457141			0.228570	−	0.973527i	$-0.426595\pi$
$137$	5.35070			0.457141			0.228570	+	0.973527i	$0.426595\pi$
$138$	−4.52832	+	1.57933i	−0.385476	+	0.134442i
$139$	−9.07846			−0.770025			−0.385013	−	0.922911i	$-0.625803\pi$
$139$	−9.07846			−0.770025			−0.385013	+	0.922911i	$0.625803\pi$
$140$	−0.703578	+	4.89350i	−0.0594632	+	0.413576i
$141$	1.14202	+	2.50069i	0.0961758	+	0.210596i
$142$	6.21721	+	1.82554i	0.521736	+	0.153196i
$143$	0.960110	+	1.10803i	0.0802884	+	0.0926578i
$144$	−0.959493	+	0.281733i	−0.0799577	+	0.0234777i
$145$	5.07326	+	3.26039i	0.421312	+	0.270761i
$146$	0.398629	−	0.872876i	0.0329908	−	0.0722397i
$147$	−11.4216	+	13.1813i	−0.942041	+	1.08717i
$148$	6.67010	−	4.28661i	0.548279	−	0.352357i
$149$	2.67081	+	18.5759i	0.218802	+	1.52180i	0.742472	+	0.669877i	$0.233653\pi$
$149$	2.67081	+	18.5759i	0.218802	+	1.52180i	−0.523670	+	0.851921i	$0.675438\pi$
$150$	−0.142315	−	0.989821i	−0.0116200	−	0.0808186i
$151$	13.6969	−	8.80244i	1.11464	−	0.716333i	0.152337	−	0.988329i	$-0.451320\pi$
$151$	13.6969	−	8.80244i	1.11464	−	0.716333i	0.962298	+	0.271996i	$0.0876838\pi$
$152$	1.10647	−	1.27693i	0.0897466	−	0.103573i
$153$	0.421192	−	0.922282i	0.0340514	−	0.0745621i
$154$	−1.78522	−	1.14729i	−0.143857	−	0.0924515i
$155$	1.94965	−	0.572468i	0.156599	−	0.0459817i
$156$	−2.23675	−	2.58135i	−0.179083	−	0.206673i
$157$	1.75372	+	0.514938i	0.139962	+	0.0410965i	0.350963	−	0.936389i	$-0.385854\pi$
$157$	1.75372	+	0.514938i	0.139962	+	0.0410965i	−0.211001	+	0.977486i	$0.567672\pi$
$158$	−0.958041	−	2.09782i	−0.0762176	−	0.166893i
$159$	1.85936	−	12.9322i	0.147457	−	1.02559i
$160$	1.00000			0.0790569
$161$	20.5613	+	11.8060i	1.62046	+	0.930444i
$162$	1.00000			0.0785674
$163$	0.681932	−	4.74294i	0.0534130	−	0.371496i	−0.945530	−	0.325534i	$-0.894456\pi$
$163$	0.681932	−	4.74294i	0.0534130	−	0.371496i	0.998943	−	0.0459614i	$-0.0146351\pi$
$164$	−2.60062	−	5.69456i	−0.203074	−	0.444670i
$165$	0.411855	+	0.120932i	0.0320629	+	0.00941452i
$166$	5.00997	+	5.78181i	0.388849	+	0.448756i
$167$	−14.3175	+	4.20399i	−1.10792	+	0.325314i	−0.783994	−	0.620769i	$-0.786821\pi$
$167$	−14.3175	+	4.20399i	−1.10792	+	0.325314i	−0.323925	+	0.946083i	$0.605002\pi$
$168$	4.15900	+	2.67283i	0.320874	+	0.206213i
$169$	−0.553987	+	1.21306i	−0.0426144	+	0.0933125i
$170$	−0.663968	+	0.766260i	−0.0509240	+	0.0587694i
$171$	−1.42140	+	0.913481i	−0.108697	+	0.0698556i
$172$	−0.757000	−	5.26505i	−0.0577207	−	0.401456i
$173$	−1.03043	−	7.16682i	−0.0783424	−	0.544884i	−0.990760	−	0.135624i	$-0.956696\pi$
$173$	−1.03043	−	7.16682i	−0.0783424	−	0.544884i	0.912418	−	0.409260i	$-0.134213\pi$
$174$	5.07326	−	3.26039i	0.384603	−	0.247169i
$175$	−3.23751	+	3.73629i	−0.244733	+	0.282437i
$176$	−0.178314	+	0.390453i	−0.0134409	+	0.0294315i
$177$	−6.23504	−	4.00702i	−0.468654	−	0.301186i
$178$	8.64733	−	2.53908i	0.648144	−	0.190312i
$179$	−16.1488	−	18.6367i	−1.20702	−	1.39297i	−0.896877	−	0.442280i	$-0.854170\pi$
$179$	−16.1488	−	18.6367i	−1.20702	−	1.39297i	−0.310139	−	0.950691i	$-0.600376\pi$
$180$	−0.959493	−	0.281733i	−0.0715164	−	0.0209991i
$181$	−6.80715	−	14.9056i	−0.505972	−	1.10792i	−0.974482	−	0.224466i	$-0.927936\pi$
$181$	−6.80715	−	14.9056i	−0.505972	−	1.10792i	0.468510	−	0.883458i	$-0.344791\pi$
$182$	−2.40315	+	16.7143i	−0.178134	+	1.23895i
$183$	9.62284			0.711341
$184$	1.77184	−	4.45652i	0.130622	−	0.328539i
$185$	7.92876			0.582934
$186$	0.289177	−	2.01127i	0.0212035	−	0.147474i
$187$	−0.180794	−	0.395883i	−0.0132209	−	0.0289498i
$188$	−2.63776	−	0.774516i	−0.192378	−	0.0564874i
$189$	−3.23751	−	3.73629i	−0.235494	−	0.271775i
$190$	1.62118	−	0.476023i	0.117613	−	0.0345343i
$191$	4.87146	+	3.13070i	0.352486	+	0.226529i	0.704886	−	0.709320i	$-0.250998\pi$
$191$	4.87146	+	3.13070i	0.352486	+	0.226529i	−0.352400	+	0.935849i	$0.614634\pi$
$192$	0.415415	−	0.909632i	0.0299800	−	0.0656470i
$193$	9.22234	−	10.6432i	0.663839	−	0.766111i	−0.319560	−	0.947566i	$-0.603535\pi$
$193$	9.22234	−	10.6432i	0.663839	−	0.766111i	0.983399	+	0.181455i	$0.0580807\pi$
$194$	3.71313	−	2.38628i	0.266587	−	0.171325i
$195$	−0.486093	−	3.38085i	−0.0348098	−	0.242108i
$196$	−2.48216	−	17.2638i	−0.177297	−	1.23313i
$197$	2.32049	−	1.49129i	0.165328	−	0.106250i	−0.455360	−	0.890307i	$-0.650490\pi$
$197$	2.32049	−	1.49129i	0.165328	−	0.106250i	0.620689	+	0.784057i	$0.286853\pi$
$198$	0.281094	−	0.324400i	0.0199765	−	0.0230541i
$199$	0.338266	−	0.740698i	0.0239790	−	0.0525067i	−0.897264	−	0.441495i	$-0.854448\pi$
$199$	0.338266	−	0.740698i	0.0239790	−	0.0525067i	0.921243	+	0.388989i	$0.127175\pi$
$200$	0.841254	+	0.540641i	0.0594856	+	0.0382291i
$201$	7.15754	−	2.10164i	0.504854	−	0.148239i
$202$	8.07019	+	9.31350i	0.567817	+	0.655295i
$203$	−28.6065	−	8.39963i	−2.00778	−	0.589538i
$204$	0.421192	+	0.922282i	0.0294894	+	0.0645727i
$205$	0.890932	−	6.19657i	0.0622254	−	0.432787i
$206$	−10.2504			−0.714176
$207$	−2.95562	+	3.77681i	−0.205430	+	0.262507i
$208$	3.41561			0.236830
$209$	−0.103215	+	0.717878i	−0.00713955	+	0.0496566i
$210$	2.05374	+	4.49705i	0.141721	+	0.310326i
$211$	−27.2936	−	8.01413i	−1.87897	−	0.551715i	−0.996719	−	0.0809349i	$-0.974209\pi$
$211$	−27.2936	−	8.01413i	−1.87897	−	0.551715i	−0.882250	−	0.470780i	$-0.843972\pi$
$212$	8.55584	+	9.87397i	0.587618	+	0.678147i
$213$	6.21721	−	1.82554i	0.425996	−	0.125084i
$214$	−2.45726	−	1.57919i	−0.167975	−	0.107951i
$215$	2.20967	−	4.83851i	0.150698	−	0.329984i
$216$	−0.654861	+	0.755750i	−0.0445576	+	0.0514222i
$217$	−8.45090	+	5.43107i	−0.573685	+	0.368685i
$218$	1.27859	+	8.89279i	0.0865970	+	0.602296i
$219$	−0.136564	−	0.949825i	−0.00922815	−	0.0641832i
$220$	−0.361102	+	0.232066i	−0.0243455	+	0.0156459i
$221$	−2.26786	+	2.61725i	−0.152553	+	0.176055i
$222$	3.29373	−	7.21225i	0.221060	−	0.484055i
$223$	−0.538746	−	0.346231i	−0.0360771	−	0.0231854i	0.522478	−	0.852653i	$-0.325008\pi$
$223$	−0.538746	−	0.346231i	−0.0360771	−	0.0231854i	−0.558555	+	0.829467i	$0.688644\pi$
$224$	−4.74356	+	1.39283i	−0.316942	+	0.0930626i
$225$	−0.654861	−	0.755750i	−0.0436574	−	0.0503833i
$226$	−5.13436	−	1.50758i	−0.341532	−	0.100283i
$227$	−10.6806	−	23.3873i	−0.708898	−	1.55227i	−0.828838	−	0.559489i	$-0.810997\pi$
$227$	−10.6806	−	23.3873i	−0.708898	−	1.55227i	0.119940	−	0.992781i	$-0.461730\pi$
$228$	0.240459	−	1.67243i	0.0159248	−	0.110759i
$229$	20.9814			1.38649			0.693244	−	0.720703i	$-0.256181\pi$
$229$	20.9814			1.38649			0.693244	+	0.720703i	$0.256181\pi$
$230$	3.89995	−	2.79113i	0.257155	−	0.184042i
$231$	−2.12210			−0.139624
$232$	−0.858244	+	5.96922i	−0.0563465	+	0.391898i
$233$	−5.66657	−	12.4081i	−0.371230	−	0.812879i	−0.999394	−	0.0347991i	$-0.988921\pi$
$233$	−5.66657	−	12.4081i	−0.371230	−	0.812879i	0.628165	−	0.778080i	$-0.283806\pi$
$234$	−3.27726	−	0.962290i	−0.214241	−	0.0629069i
$235$	−1.80029	−	2.07764i	−0.117438	−	0.135531i
$236$	7.11138	−	2.08809i	0.462912	−	0.135923i
$237$	−1.94012	−	1.24684i	−0.126024	−	0.0809909i
$238$	2.08230	−	4.55959i	0.134975	−	0.295555i
$239$	12.3924	−	14.3016i	0.801597	−	0.925093i	−0.196870	−	0.980430i	$-0.563078\pi$
$239$	12.3924	−	14.3016i	0.801597	−	0.925093i	0.998468	+	0.0553368i	$0.0176233\pi$
$240$	0.841254	−	0.540641i	0.0543027	−	0.0348982i
$241$	3.51017	+	24.4138i	0.226110	+	1.57263i	0.714267	+	0.699873i	$0.246760\pi$
$241$	3.51017	+	24.4138i	0.226110	+	1.57263i	−0.488158	+	0.872756i	$0.662331\pi$
$242$	1.53924	+	10.7057i	0.0989462	+	0.688186i
$243$	0.841254	−	0.540641i	0.0539664	−	0.0346821i
$244$	−6.30162	+	7.27246i	−0.403420	+	0.465572i
$245$	7.24539	−	15.8652i	0.462891	−	1.01359i
$246$	−5.26649	−	3.38457i	−0.335779	−	0.215792i
$247$	5.53734	−	1.62591i	0.352333	−	0.103454i
$248$	1.33065	+	1.53565i	0.0844962	+	0.0975138i
$249$	7.34054	+	2.15538i	0.465188	+	0.136591i
$250$	0.415415	+	0.909632i	0.0262732	+	0.0575302i
$251$	−0.166998	+	1.16150i	−0.0105408	+	0.0733132i	−0.994413	−	0.105561i	$-0.966336\pi$
$251$	−0.166998	+	1.16150i	−0.0105408	+	0.0733132i	0.983872	+	0.178874i	$0.0572454\pi$
$252$	4.94382			0.311431
$253$	0.394392	+	2.02044i	0.0247952	+	0.127024i
$254$	21.7511			1.36479
$255$	−0.144294	+	1.00359i	−0.00903604	+	0.0628471i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−17.8826	−	5.25079i	−1.11548	−	0.327535i	−0.328496	−	0.944505i	$-0.606542\pi$
$257$	−17.8826	−	5.25079i	−1.11548	−	0.327535i	−0.786987	+	0.616970i	$0.788360\pi$
$258$	−3.48333	−	4.01998i	−0.216863	−	0.250273i
$259$	−37.6105	+	11.0434i	−2.33700	+	0.686207i
$260$	2.87340	+	1.84662i	0.178201	+	0.114523i
$261$	2.50520	−	5.48563i	0.155068	−	0.339552i
$262$	−8.41852	+	9.71549i	−0.520098	+	0.600225i
$263$	−2.58234	+	1.65957i	−0.159234	+	0.102333i	−0.617831	−	0.786311i	$-0.711988\pi$
$263$	−2.58234	+	1.65957i	−0.159234	+	0.102333i	0.458597	+	0.888644i	$0.348352\pi$
$264$	0.0610876	+	0.424874i	0.00375968	+	0.0261492i
$265$	1.85936	+	12.9322i	0.114220	+	0.794416i
$266$	−7.02716	+	4.51608i	−0.430863	+	0.276899i
$267$	5.90186	−	6.81111i	0.361188	−	0.416833i
$268$	−3.09888	+	6.78560i	−0.189294	+	0.414496i
$269$	24.9155	+	16.0122i	1.51913	+	0.976282i	0.991964	+	0.126517i	$0.0403798\pi$
$269$	24.9155	+	16.0122i	1.51913	+	0.976282i	0.527161	+	0.849766i	$0.323257\pi$
$270$	−0.959493	+	0.281733i	−0.0583929	+	0.0171457i
$271$	−9.76742	−	11.2722i	−0.593328	−	0.684738i	0.377087	−	0.926178i	$-0.376926\pi$
$271$	−9.76742	−	11.2722i	−0.593328	−	0.684738i	−0.970416	+	0.241440i	$0.922380\pi$
$272$	−0.972837	−	0.285651i	−0.0589869	−	0.0173201i
$273$	7.01477	+	15.3602i	0.424553	+	0.929642i
$274$	−0.761483	+	5.29623i	−0.0460029	+	0.319957i
$275$	−0.429243			−0.0258843
$276$	−0.918809	−	4.70699i	−0.0553058	−	0.283328i
$277$	−27.4424			−1.64886			−0.824428	−	0.565967i	$-0.808503\pi$
$277$	−27.4424			−1.64886			−0.824428	+	0.565967i	$0.808503\pi$
$278$	1.29200	−	8.98606i	0.0774890	−	0.538948i
$279$	−0.844104	−	1.84833i	−0.0505352	−	0.110657i
$280$	−4.74356	−	1.39283i	−0.283482	−	0.0832378i
$281$	6.58802	+	7.60298i	0.393008	+	0.453555i	0.917427	−	0.397905i	$-0.130263\pi$
$281$	6.58802	+	7.60298i	0.393008	+	0.453555i	−0.524418	+	0.851461i	$0.675717\pi$
$282$	−2.63776	+	0.774516i	−0.157076	+	0.0461218i
$283$	1.67015	+	1.07334i	0.0992800	+	0.0638034i	0.589339	−	0.807886i	$-0.299388\pi$
$283$	1.67015	+	1.07334i	0.0992800	+	0.0638034i	−0.490059	+	0.871689i	$0.663025\pi$
$284$	−2.69176	+	5.89412i	−0.159726	+	0.349752i
$285$	1.10647	−	1.27693i	0.0655416	−	0.0756391i
$286$	−1.23339	+	0.792649i	−0.0729316	+	0.0468703i
$287$	4.40460	+	30.6347i	0.259996	+	1.80831i
$288$	−0.142315	−	0.989821i	−0.00838598	−	0.0583258i
$289$	−13.4365	+	8.63511i	−0.790382	+	0.507948i
$290$	−3.94920	+	4.55762i	−0.231905	+	0.267633i
$291$	1.83356	−	4.01494i	0.107485	−	0.235360i
$292$	0.807260	+	0.518795i	0.0472413	+	0.0303602i
$293$	−14.6139	+	4.29101i	−0.853750	+	0.250684i	−0.679190	−	0.733963i	$-0.737669\pi$
$293$	−14.6139	+	4.29101i	−0.853750	+	0.250684i	−0.174561	+	0.984646i	$0.555850\pi$
$294$	−11.4216	−	13.1813i	−0.666123	−	0.768747i
$295$	7.11138	+	2.08809i	0.414041	+	0.121573i
$296$	3.29373	+	7.21225i	0.191444	+	0.419204i
$297$	0.0610876	−	0.424874i	0.00354466	−	0.0246537i
$298$	−18.7669			−1.08714
$299$	13.3207	−	9.53344i	0.770357	−	0.551333i
$300$	1.00000			0.0577350
$301$	−3.74247	+	26.0295i	−0.215712	+	1.50031i
$302$	6.76358	+	14.8102i	0.389200	+	0.852230i
$303$	11.8243	+	3.47194i	0.679290	+	0.199458i
$304$	1.10647	+	1.27693i	0.0634604	+	0.0732372i
$305$	−9.23305	+	2.71107i	−0.528683	+	0.155235i
$306$	0.852953	+	0.548160i	0.0487601	+	0.0313362i
$307$	−3.65617	+	8.00590i	−0.208669	+	0.456921i	−0.984809	−	0.173639i	$-0.944447\pi$
$307$	−3.65617	+	8.00590i	−0.208669	+	0.456921i	0.776141	+	0.630560i	$0.217175\pi$
$308$	1.38968	−	1.60377i	0.0791843	−	0.0913835i
$309$	−8.62314	+	5.54176i	−0.490554	+	0.315260i
$310$	0.289177	+	2.01127i	0.0164242	+	0.114233i
$311$	2.36908	+	16.4773i	0.134338	+	0.934343i	0.939807	+	0.341705i	$0.111004\pi$
$311$	2.36908	+	16.4773i	0.134338	+	0.934343i	−0.805469	+	0.592638i	$0.798086\pi$
$312$	2.87340	−	1.84662i	0.162674	−	0.104544i
$313$	21.3491	−	24.6382i	1.20672	−	1.39263i	0.309588	−	0.950871i	$-0.399809\pi$
$313$	21.3491	−	24.6382i	1.20672	−	1.39263i	0.897133	−	0.441760i	$-0.145646\pi$
$314$	−0.759276	+	1.66258i	−0.0428484	+	0.0938250i
$315$	4.15900	+	2.67283i	0.234333	+	0.150597i
$316$	2.21281	−	0.649739i	0.124480	−	0.0365507i
$317$	8.34540	+	9.63110i	0.468724	+	0.540937i	0.940056	−	0.341019i	$-0.110772\pi$
$317$	8.34540	+	9.63110i	0.468724	+	0.540937i	−0.471332	+	0.881956i	$0.656227\pi$
$318$	12.5359	+	3.68087i	0.702979	+	0.206413i
$319$	−1.07534	−	2.35467i	−0.0602075	−	0.131836i
$320$	−0.142315	+	0.989821i	−0.00795564	+	0.0553327i
$321$	−2.92095			−0.163032
$322$	−14.6120	+	18.6719i	−0.814296	+	1.04054i
$323$	−1.71312			−0.0953208
$324$	−0.142315	+	0.989821i	−0.00790638	+	0.0549901i
$325$	1.41890	+	3.10695i	0.0787063	+	0.172343i
$326$	4.59762	+	1.34998i	0.254638	+	0.0747686i
$327$	5.88342	+	6.78983i	0.325354	+	0.375479i
$328$	6.00670	−	1.76373i	0.331665	−	0.0973855i
$329$	11.4336	+	7.34792i	0.630354	+	0.405104i
$330$	−0.178314	+	0.390453i	−0.00981586	+	0.0214937i
$331$	−4.49792	+	5.19088i	−0.247228	+	0.285317i	−0.865777	−	0.500430i	$-0.833175\pi$
$331$	−4.49792	+	5.19088i	−0.247228	+	0.285317i	0.618549	+	0.785746i	$0.287721\pi$
$332$	−6.43596	+	4.13614i	−0.353219	+	0.227000i
$333$	−1.12838	−	7.84806i	−0.0618349	−	0.430071i
$334$	−2.12361	−	14.7700i	−0.116199	−	0.808179i
$335$	−6.27551	+	4.03303i	−0.342868	+	0.220348i
$336$	−3.23751	+	3.73629i	−0.176621	+	0.203831i
$337$	10.4755	−	22.9381i	0.570636	−	1.24952i	−0.375822	−	0.926692i	$-0.622640\pi$
$337$	10.4755	−	22.9381i	0.570636	−	1.24952i	0.946458	−	0.322827i	$-0.104633\pi$
$338$	−1.12187	−	0.720985i	−0.0610219	−	0.0392164i
$339$	−5.13436	+	1.50758i	−0.278860	+	0.0818807i
$340$	−0.663968	−	0.766260i	−0.0360087	−	0.0415563i
$341$	−0.836871	−	0.245728i	−0.0453191	−	0.0133069i
$342$	−0.701896	−	1.53694i	−0.0379542	−	0.0831081i
$343$	−7.34629	+	51.0946i	−0.396662	+	2.75885i
$344$	5.31919			0.286792
$345$	1.77184	−	4.45652i	0.0953927	−	0.239931i
$346$	7.24052			0.389253
$347$	3.92863	−	27.3242i	0.210900	−	1.46684i	−0.559262	−	0.828991i	$-0.688915\pi$
$347$	3.92863	−	27.3242i	0.210900	−	1.46684i	0.770162	−	0.637849i	$-0.220175\pi$
$348$	2.50520	+	5.48563i	0.134293	+	0.294060i
$349$	−24.0891	−	7.07319i	−1.28946	−	0.378619i	−0.436078	−	0.899909i	$-0.643633\pi$
$349$	−24.0891	−	7.07319i	−1.28946	−	0.378619i	−0.853380	+	0.521290i	$0.825451\pi$
$350$	−3.23751	−	3.73629i	−0.173052	−	0.199713i
$351$	−3.27726	+	0.962290i	−0.174927	+	0.0513632i
$352$	−0.361102	−	0.232066i	−0.0192468	−	0.0123692i
$353$	4.76482	−	10.4335i	0.253606	−	0.555320i	−0.739416	−	0.673249i	$-0.764898\pi$
$353$	4.76482	−	10.4335i	0.253606	−	0.555320i	0.993022	+	0.117929i	$0.0376256\pi$
$354$	4.85357	−	5.60132i	0.257964	−	0.297707i
$355$	−5.45105	+	3.50318i	−0.289312	+	0.185929i
$356$	1.28260	+	8.92066i	0.0679775	+	0.472794i
$357$	−0.713363	−	4.96155i	−0.0377552	−	0.262593i
$358$	20.7452	−	13.3321i	1.09642	−	0.704625i
$359$	6.30783	−	7.27963i	0.332915	−	0.384204i	−0.564470	−	0.825454i	$-0.690919\pi$
$359$	6.30783	−	7.27963i	0.332915	−	0.384204i	0.897384	+	0.441250i	$0.145465\pi$
$360$	0.415415	−	0.909632i	0.0218943	−	0.0479418i
$361$	−13.5822	−	8.72873i	−0.714851	−	0.459407i
$362$	15.7226	−	4.61658i	0.826363	−	0.242642i
$363$	7.08281	+	8.17400i	0.371751	+	0.429024i
$364$	−16.2022	−	4.75739i	−0.849224	−	0.249355i
$365$	0.398629	+	0.872876i	0.0208652	+	0.0456884i
$366$	−1.36947	+	9.52490i	−0.0715835	+	0.497874i
$367$	−22.5530			−1.17726			−0.588628	−	0.808404i	$-0.700332\pi$
$367$	−22.5530			−1.17726			−0.588628	+	0.808404i	$0.700332\pi$
$368$	4.15900	+	2.38804i	0.216803	+	0.124485i
$369$	−6.26029			−0.325898
$370$	−1.12838	+	7.84806i	−0.0586617	+	0.408001i
$371$	−26.8323	−	58.7546i	−1.39307	−	3.05039i
$372$	1.94965	+	0.572468i	0.101084	+	0.0296811i
$373$	19.1385	+	22.0870i	0.990952	+	1.14362i	0.989633	+	0.143621i	$0.0458745\pi$
$373$	19.1385	+	22.0870i	0.990952	+	1.14362i	0.00131946	+	0.999999i	$0.499580\pi$
$374$	0.417583	−	0.122613i	0.0215927	−	0.00634019i
$375$	0.841254	+	0.540641i	0.0434421	+	0.0279186i
$376$	1.14202	−	2.50069i	0.0588954	−	0.128963i
$377$	−13.4890	+	15.5671i	−0.694717	+	0.801746i
$378$	4.15900	−	2.67283i	0.213916	−	0.137475i
$379$	4.10726	+	28.5666i	0.210976	+	1.46737i	0.769908	+	0.638155i	$0.220302\pi$
$379$	4.10726	+	28.5666i	0.210976	+	1.46737i	−0.558933	+	0.829213i	$0.688789\pi$
$380$	0.240459	+	1.67243i	0.0123353	+	0.0857938i
$381$	18.2982	−	11.7595i	0.937444	−	0.602459i
$382$	−3.79211	+	4.37633i	−0.194021	+	0.223912i
$383$	−10.6828	+	23.3920i	−0.545865	+	1.19528i	0.412822	+	0.910812i	$0.364543\pi$
$383$	−10.6828	+	23.3920i	−0.545865	+	1.19528i	−0.958686	+	0.284465i	$0.908184\pi$
$384$	0.841254	+	0.540641i	0.0429300	+	0.0275895i
$385$	2.03614	−	0.597864i	0.103771	−	0.0304700i
$386$	9.22234	+	10.6432i	0.469405	+	0.541722i
$387$	−5.10373	−	1.49859i	−0.259437	−	0.0761776i
$388$	1.83356	+	4.01494i	0.0930849	+	0.203827i
$389$	−2.62556	+	18.2612i	−0.133121	+	0.925877i	0.808331	+	0.588729i	$0.200371\pi$
$389$	−2.62556	+	18.2612i	−0.133121	+	0.925877i	−0.941452	+	0.337148i	$0.890538\pi$
$390$	3.41561			0.172956
$391$	−4.59130	+	1.60130i	−0.232192	+	0.0809810i
$392$	17.4413			0.880920
$393$	−1.82952	+	12.7246i	−0.0922870	+	0.641870i
$394$	1.14587	+	2.50911i	0.0577281	+	0.126407i
$395$	2.21281	+	0.649739i	0.111338	+	0.0326919i
$396$	0.281094	+	0.324400i	0.0141255	+	0.0163017i
$397$	−2.65532	+	0.779673i	−0.133267	+	0.0391307i	−0.347686	−	0.937611i	$-0.613032\pi$
$397$	−2.65532	+	0.779673i	−0.133267	+	0.0391307i	0.214419	+	0.976742i	$0.431214\pi$
$398$	0.685019	+	0.440235i	0.0343369	+	0.0220670i
$399$	−3.47005	+	7.59834i	−0.173720	+	0.380393i
$400$	−0.654861	+	0.755750i	−0.0327430	+	0.0377875i
$401$	−6.04461	+	3.88464i	−0.301853	+	0.193989i	−0.682796	−	0.730609i	$-0.739236\pi$
$401$	−6.04461	+	3.88464i	−0.301853	+	0.193989i	0.380942	+	0.924599i	$0.375600\pi$
$402$	1.06163	+	7.38379i	0.0529492	+	0.368270i
$403$	0.987718	+	6.86973i	0.0492017	+	0.342206i
$404$	−10.3672	+	6.66260i	−0.515788	+	0.331477i
$405$	−0.654861	+	0.755750i	−0.0325403	+	0.0375535i
$406$	12.3853	−	27.1199i	0.614670	−	1.34594i
$407$	−2.86309	−	1.84000i	−0.141918	−	0.0912053i
$408$	−0.972837	+	0.285651i	−0.0481626	+	0.0141418i
$409$	−23.2075	−	26.7829i	−1.14754	−	1.32433i	−0.938042	−	0.346521i	$-0.887363\pi$
$409$	−23.2075	−	26.7829i	−1.14754	−	1.32433i	−0.209497	−	0.977809i	$-0.567183\pi$
$410$	6.00670	+	1.76373i	0.296650	+	0.0871042i
$411$	2.22276	+	4.86716i	0.109641	+	0.240080i
$412$	1.45878	−	10.1460i	0.0718688	−	0.499858i
$413$	−36.6416			−1.80302
$414$	−3.31774	−	3.46303i	−0.163058	−	0.170199i
$415$	−7.65044			−0.375545
$416$	−0.486093	+	3.38085i	−0.0238327	+	0.165760i
$417$	−3.77133	−	8.25806i	−0.184683	−	0.404399i
$418$	−0.695882	−	0.204329i	−0.0340367	−	0.00999407i
$419$	−2.02917	−	2.34179i	−0.0991316	−	0.114404i	0.704016	−	0.710184i	$-0.251388\pi$
$419$	−2.02917	−	2.34179i	−0.0991316	−	0.114404i	−0.803147	+	0.595780i	$0.796843\pi$
$420$	−4.74356	+	1.39283i	−0.231462	+	0.0679633i
$421$	−17.6943	−	11.3714i	−0.862368	−	0.554210i	0.0330413	−	0.999454i	$-0.489481\pi$
$421$	−17.6943	−	11.3714i	−0.862368	−	0.554210i	−0.895409	+	0.445244i	$0.853117\pi$
$422$	11.8168	−	25.8753i	0.575235	−	1.25959i
$423$	−1.80029	+	2.07764i	−0.0875331	+	0.101019i
$424$	−10.9911	+	7.06355i	−0.533775	+	0.343036i
$425$	−0.144294	−	1.00359i	−0.00699929	−	0.0486811i
$426$	0.922154	+	6.41373i	0.0446785	+	0.310746i
$427$	40.0214	−	25.7202i	1.93677	−	1.24469i
$428$	1.91282	−	2.20751i	0.0924595	−	0.106704i
$429$	−0.609052	+	1.33364i	−0.0294053	+	0.0643886i
$430$	4.47479	+	2.87577i	0.215794	+	0.138682i
$431$	9.49263	−	2.78729i	0.457244	−	0.134259i	−0.0449961	−	0.998987i	$-0.514328\pi$
$431$	9.49263	−	2.78729i	0.457244	−	0.134259i	0.502240	+	0.864728i	$0.332509\pi$
$432$	−0.654861	−	0.755750i	−0.0315070	−	0.0363610i
$433$	−29.4737	−	8.65427i	−1.41642	−	0.415898i	−0.518128	−	0.855303i	$-0.673371\pi$
$433$	−29.4737	−	8.65427i	−1.41642	−	0.415898i	−0.898289	+	0.439405i	$0.855189\pi$
$434$	−4.17310	−	9.13781i	−0.200315	−	0.438629i
$435$	−0.858244	+	5.96922i	−0.0411496	+	0.286202i
$436$	−8.98423			−0.430267
$437$	7.87927	+	1.89167i	0.376916	+	0.0904908i
$438$	0.959592			0.0458511
$439$	−4.90948	+	34.1462i	−0.234317	+	1.62971i	0.444766	+	0.895647i	$0.353287\pi$
$439$	−4.90948	+	34.1462i	−0.234317	+	1.62971i	−0.679082	+	0.734062i	$0.737622\pi$
$440$	−0.178314	−	0.390453i	−0.00850078	−	0.0186141i
$441$	−16.7348	−	4.91379i	−0.796897	−	0.233990i
$442$	−2.26786	−	2.61725i	−0.107871	−	0.124490i
$443$	−3.15420	+	0.926156i	−0.149860	+	0.0440030i	−0.355802	−	0.934561i	$-0.615792\pi$
$443$	−3.15420	+	0.926156i	−0.149860	+	0.0440030i	0.205942	+	0.978564i	$0.433974\pi$
$444$	6.67010	+	4.28661i	0.316549	+	0.203434i
$445$	−3.74388	+	8.19796i	−0.177477	+	0.388621i
$446$	0.419379	−	0.483989i	0.0198582	−	0.0229175i
$447$	−15.7878	+	10.1462i	−0.746735	+	0.479897i
$448$	−0.703578	−	4.89350i	−0.0332410	−	0.231196i
$449$	4.83351	+	33.6178i	0.228108	+	1.58652i	0.706069	+	0.708143i	$0.250467\pi$
$449$	4.83351	+	33.6178i	0.228108	+	1.58652i	−0.477962	+	0.878381i	$0.658624\pi$
$450$	0.841254	−	0.540641i	0.0396571	−	0.0254861i
$451$	−1.75973	+	2.03084i	−0.0828625	+	0.0956284i
$452$	2.22293	−	4.86755i	0.104558	−	0.228950i
$453$	13.6969	+	8.80244i	0.643535	+	0.413575i
$454$	24.6693	−	7.24355i	1.15779	−	0.339957i
$455$	−11.0581	−	12.7617i	−0.518411	−	0.598279i
$456$	1.62118	+	0.476023i	0.0759189	+	0.0222918i
$457$	5.99345	+	13.1238i	0.280362	+	0.613907i	0.996458	−	0.0840950i	$-0.0267999\pi$
$457$	5.99345	+	13.1238i	0.280362	+	0.613907i	−0.716096	+	0.698002i	$0.754073\pi$
$458$	−2.98596	+	20.7678i	−0.139525	+	0.970416i
$459$	1.01391			0.0473251
$460$	2.20770	+	4.25747i	0.102935	+	0.198506i
$461$	11.5340			0.537192			0.268596	−	0.963253i	$-0.413440\pi$
$461$	11.5340			0.537192			0.268596	+	0.963253i	$0.413440\pi$
$462$	0.302006	−	2.10050i	0.0140506	−	0.0977240i
$463$	−3.25266	−	7.12233i	−0.151164	−	0.331003i	0.818867	−	0.573983i	$-0.194602\pi$
$463$	−3.25266	−	7.12233i	−0.151164	−	0.331003i	−0.970031	+	0.242980i	$0.921875\pi$
$464$	−5.78632	−	1.69902i	−0.268623	−	0.0788749i
$465$	1.33065	+	1.53565i	0.0617073	+	0.0712140i
$466$	13.0882	−	3.84304i	0.606300	−	0.178026i
$467$	−1.71860	−	1.10448i	−0.0795274	−	0.0511092i	0.500273	−	0.865868i	$-0.333233\pi$
$467$	−1.71860	−	1.10448i	−0.0795274	−	0.0511092i	−0.579800	+	0.814759i	$0.696869\pi$
$468$	1.41890	−	3.10695i	0.0655886	−	0.143619i
$469$	24.1509	−	27.8716i	1.11519	−	1.28699i
$470$	2.31270	−	1.48629i	0.106677	−	0.0685572i
$471$	0.260116	+	1.80915i	0.0119855	+	0.0833612i
$472$	1.05478	+	7.33617i	0.0485503	+	0.337674i
$473$	−1.92077	+	1.23441i	−0.0883172	+	0.0567580i
$474$	1.51026	−	1.74293i	0.0693684	−	0.0800554i
$475$	−0.701896	+	1.53694i	−0.0322052	+	0.0705196i
$476$	4.21684	+	2.71000i	0.193279	+	0.124213i
$477$	12.5359	−	3.68087i	0.573980	−	0.168536i
$478$	12.3924	+	14.3016i	0.566815	+	0.654139i
$479$	27.1060	+	7.95905i	1.23851	+	0.363658i	0.834454	−	0.551077i	$-0.185783\pi$
$479$	27.1060	+	7.95905i	1.23851	+	0.363658i	0.404052	+	0.914736i	$0.367601\pi$
$480$	0.415415	+	0.909632i	0.0189610	+	0.0415188i
$481$	−3.85411	+	26.8059i	−0.175732	+	1.22225i
$482$	−24.6648			−1.12345
$483$	−2.19764	+	23.6076i	−0.0999960	+	1.07418i
$484$	−10.8158			−0.491625
$485$	−0.628150	+	4.36888i	−0.0285228	+	0.198380i
$486$	0.415415	+	0.909632i	0.0188436	+	0.0412617i
$487$	1.46122	+	0.429052i	0.0662140	+	0.0194422i	0.314672	−	0.949201i	$-0.398106\pi$
$487$	1.46122	+	0.429052i	0.0662140	+	0.0194422i	−0.248458	+	0.968643i	$0.579924\pi$
$488$	−6.30162	−	7.27246i	−0.285261	−	0.329209i
$489$	4.59762	−	1.34998i	0.207911	−	0.0610483i
$490$	14.6726	+	9.42949i	0.662839	+	0.425981i
$491$	14.0623	−	30.7921i	0.634621	−	1.38963i	−0.269771	−	0.962924i	$-0.586948\pi$
$491$	14.0623	−	30.7921i	0.634621	−	1.38963i	0.904392	−	0.426702i	$-0.140325\pi$
$492$	4.09962	−	4.73121i	0.184825	−	0.213299i
$493$	5.14382	−	3.30573i	0.231666	−	0.148883i
$494$	0.821315	+	5.71237i	0.0369527	+	0.257012i
$495$	0.0610876	+	0.424874i	0.00274568	+	0.0190967i
$496$	−1.70939	+	1.09856i	−0.0767538	+	0.0493267i
$497$	20.9780	−	24.2099i	0.940993	−	1.08596i
$498$	−3.17811	+	6.95908i	−0.142414	+	0.311844i
$499$	5.72884	+	3.68170i	0.256458	+	0.164816i	0.662552	−	0.749016i	$-0.269473\pi$
$499$	5.72884	+	3.68170i	0.256458	+	0.164816i	−0.406094	+	0.913831i	$0.633110\pi$
$500$	−0.959493	+	0.281733i	−0.0429098	+	0.0125995i
$501$	−9.77177	−	11.2772i	−0.436570	−	0.503829i
$502$	−1.12591	−	0.330597i	−0.0502518	−	0.0147553i
$503$	5.64361	+	12.3578i	0.251636	+	0.551006i	0.992725	−	0.120400i	$-0.0384178\pi$
$503$	5.64361	+	12.3578i	0.251636	+	0.551006i	−0.741089	+	0.671406i	$0.765691\pi$
$504$	−0.703578	+	4.89350i	−0.0313399	+	0.217974i
$505$	−12.3235			−0.548390
$506$	−2.05601	+	0.102839i	−0.0914006	+	0.00457174i
$507$	−1.33357			−0.0592261
$508$	−3.09550	+	21.5297i	−0.137341	+	0.955226i
$509$	−3.10273	−	6.79404i	−0.137526	−	0.301141i	0.828320	−	0.560255i	$-0.189297\pi$
$509$	−3.10273	−	6.79404i	−0.137526	−	0.301141i	−0.965847	+	0.259114i	$0.916569\pi$
$510$	−0.972837	−	0.285651i	−0.0430779	−	0.0126488i
$511$	−3.10669	−	3.58531i	−0.137432	−	0.158605i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	−1.42140	−	0.913481i	−0.0627565	−	0.0403312i
$514$	7.74230	−	16.9533i	0.341498	−	0.747777i
$515$	6.71255	−	7.74670i	0.295790	−	0.341360i
$516$	4.47479	−	2.87577i	0.196992	−	0.126599i
$517$	0.167937	+	1.16803i	0.00738586	+	0.0513698i
$518$	−5.57851	−	38.7994i	−0.245105	−	1.70475i
$519$	6.09111	−	3.91452i	0.267370	−	0.171828i
$520$	−2.23675	+	2.58135i	−0.0980881	+	0.113200i
$521$	−14.9359	+	32.7051i	−0.654354	+	1.43284i	0.233337	+	0.972396i	$0.425036\pi$
$521$	−14.9359	+	32.7051i	−0.654354	+	1.43284i	−0.887691	+	0.460440i	$0.847692\pi$
$522$	5.07326	+	3.26039i	0.222051	+	0.142703i
$523$	31.1015	−	9.13222i	1.35997	−	0.399324i	0.481220	−	0.876600i	$-0.340194\pi$
$523$	31.1015	−	9.13222i	1.35997	−	0.399324i	0.878753	+	0.477276i	$0.158376\pi$
$524$	−8.41852	−	9.71549i	−0.367765	−	0.424423i
$525$	−4.74356	−	1.39283i	−0.207026	−	0.0607883i
$526$	−1.27517	−	2.79224i	−0.0556001	−	0.121747i
$527$	0.293199	−	2.03924i	0.0127719	−	0.0888308i
$528$	−0.429243			−0.0186804
$529$	22.8852	−	2.29512i	0.995009	−	0.0997878i
$530$	−13.0651			−0.567513
$531$	1.05478	−	7.33617i	0.0457736	−	0.318363i
$532$	−3.47005	−	7.59834i	−0.150446	−	0.329430i
$533$	20.5166	+	6.02421i	0.888672	+	0.260938i
$534$	5.90186	+	6.81111i	0.255399	+	0.294746i
$535$	2.80263	−	0.822927i	0.121168	−	0.0355782i
$536$	−6.27551	−	4.03303i	−0.271061	−	0.174200i
$537$	10.2441	−	22.4314i	0.442065	−	0.967986i
$538$	−19.3951	+	22.3831i	−0.836182	+	0.965005i
$539$	−6.29810	+	4.04754i	−0.271278	+	0.174340i
$540$	−0.142315	−	0.989821i	−0.00612426	−	0.0425951i
$541$	−1.43497	−	9.98046i	−0.0616943	−	0.429094i	−0.997137	−	0.0756153i	$-0.975908\pi$
$541$	−1.43497	−	9.98046i	−0.0616943	−	0.429094i	0.935443	−	0.353478i	$-0.115001\pi$
$542$	12.5475	−	8.06380i	0.538962	−	0.346370i
$543$	10.7308	−	12.3840i	0.460503	−	0.531449i
$544$	0.421192	−	0.922282i	0.0180585	−	0.0395425i
$545$	−7.55802	−	4.85724i	−0.323750	−	0.208061i
$546$	−16.2022	+	4.75739i	−0.693389	+	0.203597i
$547$	−13.1173	−	15.1381i	−0.560854	−	0.647260i	0.402524	−	0.915410i	$-0.368133\pi$
$547$	−13.1173	−	15.1381i	−0.560854	−	0.647260i	−0.963377	+	0.268150i	$0.913588\pi$
$548$	−5.13396	−	1.50747i	−0.219312	−	0.0643957i
$549$	3.99747	+	8.75325i	0.170608	+	0.373579i
$550$	0.0610876	−	0.424874i	0.00260478	−	0.0181167i
$551$	−10.1895			−0.434086
$552$	4.78984	−	0.239582i	0.203869	−	0.0101973i
$553$	−11.4016			−0.484843
$554$	3.90547	−	27.1631i	0.165927	−	1.15405i
$555$	3.29373	+	7.21225i	0.139811	+	0.306143i
$556$	8.71072	+	2.55770i	0.369417	+	0.108471i
$557$	18.7665	+	21.6577i	0.795162	+	0.917666i	0.998106	−	0.0615242i	$-0.0195961\pi$
$557$	18.7665	+	21.6577i	0.795162	+	0.917666i	−0.202943	+	0.979191i	$0.565051\pi$
$558$	1.94965	−	0.572468i	0.0825351	−	0.0242345i
$559$	15.2842	+	9.82253i	0.646451	+	0.415449i
$560$	2.05374	−	4.49705i	0.0867862	−	0.190035i
$561$	0.285003	−	0.328912i	0.0120329	−	0.0138867i
$562$	−8.46316	+	5.43894i	−0.356997	+	0.229428i
$563$	−3.06320	−	21.3050i	−0.129098	−	0.897898i	−0.946701	−	0.322115i	$-0.895606\pi$
$563$	−3.06320	−	21.3050i	−0.129098	−	0.897898i	0.817602	−	0.575783i	$-0.195303\pi$
$564$	−0.391240	−	2.72114i	−0.0164742	−	0.114580i
$565$	4.50165	−	2.89303i	0.189386	−	0.121711i
$566$	−1.30010	+	1.50040i	−0.0546473	+	0.0630663i
$567$	2.05374	−	4.49705i	0.0862488	−	0.188859i
$568$	−5.45105	−	3.50318i	−0.228721	−	0.146990i
$569$	2.95667	−	0.868155i	0.123950	−	0.0363950i	−0.219169	−	0.975687i	$-0.570335\pi$
$569$	2.95667	−	0.868155i	0.123950	−	0.0363950i	0.343119	+	0.939292i	$0.388517\pi$
$570$	1.10647	+	1.27693i	0.0463449	+	0.0534849i
$571$	−43.3114	−	12.7174i	−1.81253	−	0.532205i	−0.813729	−	0.581245i	$-0.802566\pi$
$571$	−43.3114	−	12.7174i	−1.81253	−	0.532205i	−0.998797	+	0.0490397i	$0.984384\pi$
$572$	−0.609052	−	1.33364i	−0.0254657	−	0.0557622i
$573$	−0.824104	+	5.73177i	−0.0344275	+	0.239448i
$574$	−30.9497			−1.29182
$575$	−0.444523	+	4.77519i	−0.0185379	+	0.199139i
$576$	1.00000			0.0416667
$577$	2.82374	−	19.6396i	0.117554	−	0.817606i	−0.842681	−	0.538413i	$-0.819024\pi$
$577$	2.82374	−	19.6396i	0.117554	−	0.817606i	0.960235	−	0.279193i	$-0.0900669\pi$
$578$	−6.63501	−	14.5286i	−0.275980	−	0.604312i
$579$	13.5125	+	3.96761i	0.561558	+	0.164888i
$580$	−3.94920	−	4.55762i	−0.163982	−	0.189245i
$581$	36.2903	−	10.6558i	1.50557	−	0.442077i
$582$	3.71313	+	2.38628i	0.153914	+	0.0989146i
$583$	2.32970	−	5.10132i	0.0964861	−	0.211275i
$584$	−0.628399	+	0.725211i	−0.0260033	+	0.0300095i
$585$	2.87340	−	1.84662i	0.118800	−	0.0763484i
$586$	−2.16757	−	15.0758i	−0.0895415	−	0.622775i
$587$	−2.88301	−	20.0518i	−0.118995	−	0.827625i	−0.958667	−	0.284532i	$-0.908162\pi$
$587$	−2.88301	−	20.0518i	−0.118995	−	0.827625i	0.839672	−	0.543094i	$-0.182747\pi$
$588$	14.6726	−	9.42949i	0.605087	−	0.388866i
$589$	−2.24830	+	2.59467i	−0.0926394	+	0.106912i
$590$	−3.07889	+	6.74183i	−0.126756	+	0.277557i
$591$	2.32049	+	1.49129i	0.0954523	+	0.0613435i
$592$	−7.60759	+	2.23379i	−0.312670	+	0.0918082i
$593$	21.7465	+	25.0968i	0.893022	+	1.03060i	0.999342	+	0.0362709i	$0.0115479\pi$
$593$	21.7465	+	25.0968i	0.893022	+	1.03060i	−0.106320	+	0.994332i	$0.533907\pi$
$594$	0.411855	+	0.120932i	0.0168986	+	0.00496189i
$595$	2.08230	+	4.55959i	0.0853659	+	0.186925i
$596$	2.67081	−	18.5759i	0.109401	−	0.760899i
$597$	0.814283			0.0333264
$598$	7.54067	+	14.5419i	0.308361	+	0.594661i
$599$	39.9968			1.63423			0.817113	−	0.576478i	$-0.195573\pi$
$599$	39.9968			1.63423			0.817113	+	0.576478i	$0.195573\pi$
$600$	−0.142315	+	0.989821i	−0.00580998	+	0.0404093i
$601$	2.72865	+	5.97491i	0.111304	+	0.243722i	0.957084	−	0.289810i	$-0.0935920\pi$
$601$	2.72865	+	5.97491i	0.111304	+	0.243722i	−0.845780	+	0.533531i	$0.820865\pi$
$602$	−25.2319	−	7.40876i	−1.02838	−	0.301958i
$603$	4.88507	+	5.63768i	0.198936	+	0.229584i
$604$	−15.6220	+	4.58703i	−0.635649	+	0.186644i
$605$	−9.09879	−	5.84744i	−0.369918	−	0.237732i
$606$	−5.11938	+	11.2099i	−0.207960	+	0.455370i
$607$	26.8866	−	31.0288i	1.09130	−	1.25942i	0.127770	−	0.991804i	$-0.459218\pi$
$607$	26.8866	−	31.0288i	1.09130	−	1.25942i	0.963525	−	0.267618i	$-0.0862366\pi$
$608$	−1.42140	+	0.913481i	−0.0576455	+	0.0370465i
$609$	−4.24300	−	29.5107i	−0.171935	−	1.19583i
$610$	−1.36947	−	9.52490i	−0.0554484	−	0.385652i
$611$	7.89931	−	5.07658i	0.319572	−	0.205376i
$612$	−0.663968	+	0.766260i	−0.0268393	+	0.0309742i
$613$	15.8201	−	34.6412i	0.638969	−	1.39915i	−0.261917	−	0.965090i	$-0.584355\pi$
$613$	15.8201	−	34.6412i	0.638969	−	1.39915i	0.900886	−	0.434056i	$-0.142918\pi$
$614$	−7.40409	−	4.75832i	−0.298805	−	0.192030i
$615$	6.00670	−	1.76373i	0.242214	−	0.0711203i
$616$	1.38968	+	1.60377i	0.0559917	+	0.0646179i
$617$	−30.1793	−	8.86145i	−1.21497	−	0.356749i	−0.389414	−	0.921063i	$-0.627323\pi$
$617$	−30.1793	−	8.86145i	−1.21497	−	0.356749i	−0.825560	+	0.564314i	$0.809141\pi$
$618$	−4.25815	−	9.32405i	−0.171288	−	0.375068i
$619$	−2.86414	+	19.9206i	−0.115120	+	0.800675i	0.847689	+	0.530493i	$0.177993\pi$
$619$	−2.86414	+	19.9206i	−0.115120	+	0.800675i	−0.962809	+	0.270182i	$0.912916\pi$
$620$	−2.03195			−0.0816052
$621$	−4.66332	−	1.11958i	−0.187133	−	0.0449271i
$622$	−16.6468			−0.667475
$623$	6.34092	−	44.1021i	0.254044	−	1.76691i
$624$	1.41890	+	3.10695i	0.0568014	+	0.124378i
$625$	−0.959493	−	0.281733i	−0.0383797	−	0.0112693i
$626$	21.3491	+	24.6382i	0.853281	+	0.984739i
$627$	−0.695882	+	0.204329i	−0.0277908	+	0.00816013i
$628$	−1.53760	−	0.988158i	−0.0613571	−	0.0394318i
$629$	3.33953	−	7.31256i	0.133156	−	0.291571i
$630$	−3.23751	+	3.73629i	−0.128986	+	0.148857i
$631$	8.63522	−	5.54952i	0.343762	−	0.220923i	−0.357355	−	0.933969i	$-0.616321\pi$
$631$	8.63522	−	5.54952i	0.343762	−	0.220923i	0.701117	+	0.713046i	$0.252685\pi$
$632$	0.328210	+	2.28275i	0.0130555	+	0.0908030i
$633$	−4.04827	−	28.1563i	−0.160904	−	1.11911i
$634$	−10.7207	+	6.88981i	−0.425775	+	0.273629i
$635$	−14.2439	+	16.4384i	−0.565253	+	0.652337i
$636$	−5.42745	+	11.8845i	−0.215213	+	0.471250i
$637$	50.1159	+	32.2075i	1.98566	+	1.27611i
$638$	2.48374	−	0.729291i	0.0983320	−	0.0288729i
$639$	4.24329	+	4.89701i	0.167862	+	0.193723i
$640$	−0.959493	−	0.281733i	−0.0379273	−	0.0111365i
$641$	18.0930	+	39.6182i	0.714632	+	1.56483i	0.821277	+	0.570529i	$0.193262\pi$
$641$	18.0930	+	39.6182i	0.714632	+	1.56483i	−0.106645	+	0.994297i	$0.534011\pi$
$642$	0.415695	−	2.89122i	0.0164062	−	0.114107i
$643$	−33.4506			−1.31916			−0.659581	−	0.751633i	$-0.729266\pi$
$643$	−33.4506			−1.31916			−0.659581	+	0.751633i	$0.729266\pi$
$644$	−16.4023	−	17.1206i	−0.646342	−	0.674645i
$645$	5.31919			0.209443
$646$	0.243803	−	1.69569i	0.00959230	−	0.0667159i
$647$	4.45434	+	9.75364i	0.175118	+	0.383455i	0.976756	−	0.214355i	$-0.0687649\pi$
$647$	4.45434	+	9.75364i	0.175118	+	0.383455i	−0.801638	+	0.597810i	$0.796038\pi$
$648$	−0.959493	−	0.281733i	−0.0376924	−	0.0110675i
$649$	−2.08336	−	2.40433i	−0.0817790	−	0.0943780i
$650$	−3.27726	+	0.962290i	−0.128545	+	0.0377441i
$651$	−8.45090	−	5.43107i	−0.331217	−	0.212860i
$652$	−1.99055	+	4.35870i	−0.0779560	+	0.170700i
$653$	13.2044	−	15.2387i	0.516728	−	0.596336i	−0.436080	−	0.899908i	$-0.643634\pi$
$653$	13.2044	−	15.2387i	0.516728	−	0.596336i	0.952809	+	0.303572i	$0.0981791\pi$
$654$	−7.55802	+	4.85724i	−0.295542	+	0.189933i
$655$	−1.82952	−	12.7246i	−0.0714852	−	0.497191i
$656$	0.890932	+	6.19657i	0.0347850	+	0.241935i
$657$	0.807260	−	0.518795i	0.0314942	−	0.0202401i
$658$	−8.90030	+	10.2715i	−0.346970	+	0.400425i
$659$	12.6381	−	27.6735i	0.492309	−	1.07801i	−0.486584	−	0.873634i	$-0.661757\pi$
$659$	12.6381	−	27.6735i	0.492309	−	1.07801i	0.978893	−	0.204372i	$-0.0655153\pi$
$660$	−0.361102	−	0.232066i	−0.0140559	−	0.00903316i
$661$	−42.9885	+	12.6226i	−1.67206	+	0.490961i	−0.974278	−	0.225349i	$-0.927648\pi$
$661$	−42.9885	+	12.6226i	−1.67206	+	0.490961i	−0.697782	+	0.716310i	$0.745830\pi$
$662$	−4.49792	−	5.19088i	−0.174817	−	0.201749i
$663$	−3.32284	−	0.975673i	−0.129048	−	0.0378920i
$664$	−3.17811	−	6.95908i	−0.123334	−	0.270065i
$665$	1.18878	−	8.26818i	0.0460991	−	0.320626i
$666$	7.92876			0.307233
$667$	−27.3085	+	9.52432i	−1.05739	+	0.368783i
$668$	14.9219			0.577346
$669$	0.0911397	−	0.633891i	0.00352367	−	0.0245076i
$670$	−3.09888	−	6.78560i	−0.119720	−	0.262150i
$671$	3.96322	+	1.16371i	0.152998	+	0.0449244i
$672$	−3.23751	−	3.73629i	−0.124890	−	0.144130i
$673$	−7.01063	+	2.05851i	−0.270240	+	0.0793496i	−0.414045	−	0.910256i	$-0.635884\pi$
$673$	−7.01063	+	2.05851i	−0.270240	+	0.0793496i	0.143805	+	0.989606i	$0.454066\pi$
$674$	21.2138	+	13.6333i	0.817126	+	0.525135i
$675$	0.415415	−	0.909632i	0.0159893	−	0.0350118i
$676$	0.873306	−	1.00785i	0.0335887	−	0.0387634i
$677$	4.97302	−	3.19597i	0.191129	−	0.122831i	−0.441577	−	0.897223i	$-0.645581\pi$
$677$	4.97302	−	3.19597i	0.191129	−	0.122831i	0.632706	+	0.774392i	$0.281944\pi$
$678$	−0.761543	−	5.29665i	−0.0292469	−	0.203417i
$679$	−3.10546	−	21.5989i	−0.119176	−	0.828891i
$680$	0.852953	−	0.548160i	0.0327093	−	0.0210210i
$681$	16.8370	−	19.4309i	0.645193	−	0.744593i
$682$	0.362326	−	0.793383i	0.0138742	−	0.0303802i
$683$	−6.97546	−	4.48286i	−0.266909	−	0.171532i	0.400340	−	0.916367i	$-0.368892\pi$
$683$	−6.97546	−	4.48286i	−0.266909	−	0.171532i	−0.667249	+	0.744835i	$0.732528\pi$
$684$	1.62118	−	0.476023i	0.0619875	−	0.0182012i
$685$	−3.50396	−	4.04379i	−0.133879	−	0.154505i
$686$	−49.5290	−	14.5430i	−1.89103	−	0.555256i
$687$	8.71597	+	19.0853i	0.332535	+	0.728150i
$688$	−0.757000	+	5.26505i	−0.0288604	+	0.200728i
$689$	−44.6255			−1.70010
$690$	4.15900	+	2.38804i	0.158330	+	0.0909110i
$691$	−10.1646			−0.386681			−0.193340	−	0.981132i	$-0.561932\pi$
$691$	−10.1646			−0.386681			−0.193340	+	0.981132i	$0.561932\pi$
$692$	−1.03043	+	7.16682i	−0.0391712	+	0.272442i
$693$	−0.881551	−	1.93033i	−0.0334874	−	0.0733271i
$694$	26.4870	+	7.77728i	1.00543	+	0.295221i
$695$	5.94513	+	6.86105i	0.225512	+	0.260254i
$696$	−5.78632	+	1.69902i	−0.219330	+	0.0644010i
$697$	−5.33973	−	3.43164i	−0.202257	−	0.129982i
$698$	10.4294	−	22.8373i	0.394759	−	0.864403i
$699$	8.93279	−	10.3090i	0.337869	−	0.389922i
$700$	4.15900	−	2.67283i	0.157196	−	0.101023i
$701$	5.79830	+	40.3281i	0.218999	+	1.52317i	0.741745	+	0.670682i	$0.233999\pi$
$701$	5.79830	+	40.3281i	0.218999	+	1.52317i	−0.522746	+	0.852489i	$0.675092\pi$
$702$	−0.486093	−	3.38085i	−0.0183464	−	0.127602i
$703$	−11.2700	+	7.24277i	−0.425055	+	0.273166i
$704$	0.281094	−	0.324400i	0.0105941	−	0.0122263i
$705$	1.14202	−	2.50069i	0.0430111	−	0.0941813i
$706$	9.64921	+	6.20117i	0.363153	+	0.233384i
$707$	58.4573	−	17.1646i	2.19851	−	0.645542i
$708$	4.85357	+	5.60132i	0.182408	+	0.210510i
$709$	40.8911	+	12.0067i	1.53570	+	0.450922i	0.936789	−	0.349894i	$-0.113783\pi$
$709$	40.8911	+	12.0067i	1.53570	+	0.450922i	0.598910	+	0.800816i	$0.295601\pi$
$710$	−2.69176	−	5.89412i	−0.101020	−	0.221203i
$711$	0.328210	−	2.28275i	0.0123088	−	0.0856099i
$712$	−9.01239			−0.337754
$713$	−3.60030	+	9.05545i	−0.134832	+	0.339129i
$714$	5.01257			0.187591
$715$	0.208652	−	1.45121i	0.00780313	−	0.0542720i
$716$	10.2441	+	22.4314i	0.382839	+	0.838301i
$717$	18.1572	+	5.33143i	0.678092	+	0.199106i
$718$	6.30783	+	7.27963i	0.235406	+	0.271673i
$719$	−37.7625	+	11.0881i	−1.40830	+	0.413515i	−0.895527	−	0.445008i	$-0.853201\pi$
$719$	−37.7625	+	11.0881i	−1.40830	+	0.413515i	−0.512776	+	0.858523i	$0.671383\pi$
$720$	0.841254	+	0.540641i	0.0313517	+	0.0201485i
$721$	−21.0515	+	46.0964i	−0.783999	+	1.71672i
$722$	10.5728	−	12.2017i	0.393480	−	0.454100i
$723$	−20.7494	+	13.3348i	−0.771677	+	0.495927i
$724$	2.33203	+	16.2196i	0.0866691	+	0.602797i
$725$	−0.858244	−	5.96922i	−0.0318744	−	0.221691i
$726$	−9.09879	+	5.84744i	−0.337688	+	0.217019i
$727$	10.5877	−	12.2189i	0.392677	−	0.453173i	−0.524644	−	0.851322i	$-0.675802\pi$
$727$	10.5877	−	12.2189i	0.392677	−	0.453173i	0.917321	+	0.398149i	$0.130347\pi$
$728$	7.01477	−	15.3602i	0.259985	−	0.569287i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	−0.920722	+	0.270348i	−0.0340774	+	0.0100060i
$731$	−3.53177	−	4.07588i	−0.130627	−	0.150752i
$732$	−9.23305	−	2.71107i	−0.341263	−	0.100204i
$733$	0.756532	+	1.65657i	0.0279431	+	0.0611870i	0.923089	−	0.384587i	$-0.125656\pi$
$733$	0.756532	+	1.65657i	0.0279431	+	0.0611870i	−0.895146	+	0.445773i	$0.852929\pi$
$734$	3.20963	−	22.3234i	0.118469	−	0.823973i
$735$	17.4413			0.643333
$736$	−2.95562	+	3.77681i	−0.108945	+	0.139215i
$737$	3.20203			0.117948
$738$	0.890932	−	6.19657i	0.0327956	−	0.228099i
$739$	2.83891	+	6.21636i	0.104431	+	0.228672i	0.954633	−	0.297784i	$-0.0962476\pi$
$739$	2.83891	+	6.21636i	0.104431	+	0.228672i	−0.850202	+	0.526457i	$0.823520\pi$
$740$	−7.60759	−	2.23379i	−0.279661	−	0.0821158i
$741$	3.77927	+	4.36152i	0.138835	+	0.160224i
$742$	61.9752	−	18.1976i	2.27518	−	0.668054i
$743$	15.9605	+	10.2572i	0.585532	+	0.376299i	0.799612	−	0.600518i	$-0.205039\pi$
$743$	15.9605	+	10.2572i	0.585532	+	0.376299i	−0.214079	+	0.976816i	$0.568675\pi$
$744$	−0.844104	+	1.84833i	−0.0309464	+	0.0677631i
$745$	12.2897	−	14.1831i	0.450261	−	0.519629i
$746$	−24.5858	+	15.8004i	−0.900152	+	0.578492i
$747$	1.08877	+	7.57256i	0.0398360	+	0.277066i
$748$	0.0619372	+	0.430782i	0.00226465	+	0.0157510i
$749$	−12.1482	+	7.80720i	−0.443887	+	0.285269i
$750$	−0.654861	+	0.755750i	−0.0239121	+	0.0275961i
$751$	−18.6423	+	40.8209i	−0.680266	+	1.48958i	0.182094	+	0.983281i	$0.441712\pi$
$751$	−18.6423	+	40.8209i	−0.680266	+	1.48958i	−0.862361	+	0.506294i	$0.831015\pi$
$752$	2.31270	+	1.48629i	0.0843357	+	0.0541992i
$753$	−1.12591	+	0.330597i	−0.0410304	+	0.0120476i
$754$	−13.4890	−	15.5671i	−0.491239	−	0.566920i
$755$	−15.6220	−	4.58703i	−0.568542	−	0.166939i
$756$	2.05374	+	4.49705i	0.0746936	+	0.163556i
$757$	1.43607	−	9.98805i	0.0521947	−	0.363022i	−0.946939	−	0.321413i	$-0.895842\pi$
$757$	1.43607	−	9.98805i	0.0521947	−	0.363022i	0.999134	−	0.0416095i	$-0.0132485\pi$
$758$	−28.8604			−1.04826
$759$	−1.67402	+	1.19807i	−0.0607632	+	0.0434873i
$760$	−1.68963			−0.0612892
$761$	−3.67073	+	25.5305i	−0.133064	+	0.925479i	0.808464	+	0.588545i	$0.200299\pi$
$761$	−3.67073	+	25.5305i	−0.133064	+	0.925479i	−0.941528	+	0.336934i	$0.890610\pi$
$762$	9.03573	+	19.7855i	0.327330	+	0.716753i
$763$	42.6172	+	12.5135i	1.54285	+	0.453021i
$764$	−3.79211	−	4.37633i	−0.137194	−	0.158330i
$765$	−0.972837	+	0.285651i	−0.0351730	+	0.0103277i
$766$	−21.6336	−	13.9031i	−0.781654	−	0.502339i
$767$	−10.5163	+	23.0275i	−0.379722	+	0.831475i
$768$	−0.654861	+	0.755750i	−0.0236303	+	0.0272708i
$769$	18.9330	−	12.1675i	0.682741	−	0.438771i	−0.152758	−	0.988264i	$-0.548815\pi$
$769$	18.9330	−	12.1675i	0.682741	−	0.438771i	0.835498	+	0.549493i	$0.185179\pi$
$770$	0.302006	+	2.10050i	0.0108835	+	0.0756967i
$771$	−2.65239	−	18.4478i	−0.0955236	−	0.664381i
$772$	−11.8473	+	7.61380i	−0.426394	+	0.274027i
$773$	4.46673	−	5.15488i	0.160657	−	0.185408i	−0.669714	−	0.742619i	$-0.733583\pi$
$773$	4.46673	−	5.15488i	0.160657	−	0.185408i	0.830371	+	0.557211i	$0.188129\pi$
$774$	2.20967	−	4.83851i	0.0794251	−	0.173917i
$775$	−1.70939	−	1.09856i	−0.0614030	−	0.0394613i
$776$	−4.23501	+	1.24351i	−0.152028	+	0.0446395i
$777$	−25.6695	−	29.6241i	−0.920887	−	1.06276i
$778$	−17.7016	−	5.19767i	−0.634634	−	0.186345i
$779$	4.39407	+	9.62167i	0.157434	+	0.344732i
$780$	−0.486093	+	3.38085i	−0.0174049	+	0.121054i
$781$	2.78136			0.0995247
$782$	−0.931587	−	4.77245i	−0.0333135	−	0.170663i
$783$	6.03060			0.215516
$784$	−2.48216	+	17.2638i	−0.0886485	+	0.616564i
$785$	−0.759276	−	1.66258i	−0.0270997	−	0.0593401i
$786$	−12.3347	−	3.62179i	−0.439964	−	0.129185i
$787$	−12.4554	−	14.3743i	−0.443988	−	0.512390i	0.489006	−	0.872280i	$-0.337360\pi$
$787$	−12.4554	−	14.3743i	−0.443988	−	0.512390i	−0.932995	+	0.359890i	$0.882814\pi$
$788$	−2.64664	+	0.777124i	−0.0942827	+	0.0276839i
$789$	−2.58234	−	1.65957i	−0.0919337	−	0.0590822i
$790$	−0.958041	+	2.09782i	−0.0340856	+	0.0746370i
$791$	−17.3243	+	19.9933i	−0.615981	+	0.710880i
$792$	−0.361102	+	0.232066i	−0.0128312	+	0.00824611i
$793$	−4.67759	−	32.5334i	−0.166106	−	1.15529i
$794$	−0.393845	−	2.73925i	−0.0139770	−	0.0972125i
$795$	−10.9911	+	7.06355i	−0.389814	+	0.250518i
$796$	−0.533242	+	0.615394i	−0.0189003	+	0.0218121i
$797$	12.8298	−	28.0933i	0.454454	−	0.995116i	−0.534263	−	0.845319i	$-0.679411\pi$
$797$	12.8298	−	28.0933i	0.454454	−	0.995116i	0.988717	−	0.149797i	$-0.0478620\pi$
$798$	−7.02716	−	4.51608i	−0.248759	−	0.159868i
$799$	−2.67444	+	0.785287i	−0.0946150	+	0.0277815i
$800$	−0.654861	−	0.755750i	−0.0231528	−	0.0267198i
$801$	8.64733	+	2.53908i	0.305538	+	0.0897141i
$802$	−2.98486	−	6.53593i	−0.105399	−	0.230792i
$803$	0.0586192	−	0.407705i	0.00206863	−	0.0143876i
$804$	−7.45972			−0.263084
$805$	−4.54242	−	23.2705i	−0.160099	−	0.820178i
$806$	−6.94037			−0.244464
$807$	−4.21496	+	29.3157i	−0.148373	+	1.03196i
$808$	−5.11938	−	11.2099i	−0.180099	−	0.394362i
$809$	−49.8524	−	14.6380i	−1.75272	−	0.514644i	−0.761647	−	0.647992i	$-0.775609\pi$
$809$	−49.8524	−	14.6380i	−1.75272	−	0.514644i	−0.991069	+	0.133348i	$0.957427\pi$
$810$	−0.654861	−	0.755750i	−0.0230095	−	0.0265543i
$811$	−22.2257	+	6.52607i	−0.780451	+	0.229161i	−0.647606	−	0.761976i	$-0.724230\pi$
$811$	−22.2257	+	6.52607i	−0.780451	+	0.229161i	−0.132845	+	0.991137i	$0.542411\pi$
$812$	25.0813	+	16.1188i	0.880181	+	0.565658i
$813$	6.19602	−	13.5674i	0.217304	−	0.475829i
$814$	2.22873	−	2.57209i	0.0781169	−	0.0901517i
$815$	−4.03105	+	2.59060i	−0.141201	+	0.0907446i
$816$	−0.144294	−	1.00359i	−0.00505130	−	0.0351326i
$817$	1.27905	+	8.89597i	0.0447482	+	0.311231i
$818$	29.8131	−	19.1597i	1.04239	−	0.669904i
$819$	−11.0581	+	12.7617i	−0.386401	+	0.445931i
$820$	−2.60062	+	5.69456i	−0.0908175	+	0.198863i
$821$	−0.136279	−	0.0875812i	−0.00475617	−	0.00305661i	0.538261	−	0.842778i	$-0.319082\pi$
$821$	−0.136279	−	0.0875812i	−0.00475617	−	0.00305661i	−0.543017	+	0.839722i	$0.682718\pi$
$822$	−5.13396	+	1.50747i	−0.179067	+	0.0525789i
$823$	−7.38271	−	8.52011i	−0.257345	−	0.296992i	0.612344	−	0.790591i	$-0.290227\pi$
$823$	−7.38271	−	8.52011i	−0.257345	−	0.296992i	−0.869690	+	0.493599i	$0.835681\pi$
$824$	9.83514	+	2.88786i	0.342623	+	0.100603i
$825$	−0.178314	−	0.390453i	−0.00620809	−	0.0135938i
$826$	5.21465	−	36.2687i	0.181441	−	1.26195i
$827$	31.6378			1.10016			0.550078	−	0.835113i	$-0.314598\pi$
$827$	31.6378			1.10016			0.550078	+	0.835113i	$0.314598\pi$
$828$	3.89995	−	2.79113i	0.135532	−	0.0969986i
$829$	9.12753			0.317012			0.158506	−	0.987358i	$-0.449332\pi$
$829$	9.12753			0.317012			0.158506	+	0.987358i	$0.449332\pi$
$830$	1.08877	−	7.57256i	0.0377918	−	0.262848i
$831$	−11.4000	−	24.9625i	−0.395462	−	0.865940i
$832$	−3.27726	−	0.962290i	−0.113618	−	0.0333614i
$833$	−11.5805	−	13.3646i	−0.401240	−	0.463055i
$834$	8.71072	−	2.55770i	0.301628	−	0.0885659i
$835$	12.5531	+	8.06739i	0.434418	+	0.279184i
$836$	0.301284	−	0.659720i	0.0104201	−	0.0228169i
$837$	1.33065	−	1.53565i	0.0459939	−	0.0530798i
$838$	2.60674	−	1.67525i	0.0900482	−	0.0578705i
$839$	1.90041	+	13.2177i	0.0656096	+	0.456325i	0.995971	+	0.0896801i	$0.0285845\pi$
$839$	1.90041	+	13.2177i	0.0656096	+	0.456325i	−0.930361	+	0.366645i	$0.880506\pi$
$840$	−0.703578	−	4.89350i	−0.0242758	−	0.168842i
$841$	6.19847	−	3.98351i	0.213740	−	0.137363i
$842$	13.7739	−	15.8959i	0.474679	−	0.547808i
$843$	−4.17915	+	9.15106i	−0.143938	+	0.315179i
$844$	23.9302	+	15.3790i	0.823711	+	0.529367i
$845$	1.27956	−	0.375711i	0.0440181	−	0.0129249i
$846$	−1.80029	−	2.07764i	−0.0618952	−	0.0714309i
$847$	51.3051	+	15.0645i	1.76287	+	0.517624i
$848$	−5.42745	−	11.8845i	−0.186380	−	0.408114i
$849$	−0.282539	+	1.96510i	−0.00969671	+	0.0674421i
$850$	1.01391			0.0347767
$851$	−23.4344	+	29.9455i	−0.803320	+	1.02652i
$852$	−6.47968			−0.221990
$853$	−1.48617	+	10.3365i	−0.0508855	+	0.353916i	0.948432	+	0.316980i	$0.102669\pi$
$853$	−1.48617	+	10.3365i	−0.0508855	+	0.353916i	−0.999318	+	0.0369360i	$0.988240\pi$
$854$	19.7628	+	43.2744i	0.676268	+	1.48082i
$855$	1.62118	+	0.476023i	0.0554433	+	0.0162796i
$856$	1.91282	+	2.20751i	0.0653787	+	0.0754511i
$857$	−21.4619	+	6.30178i	−0.733125	+	0.215265i	−0.626925	−	0.779080i	$-0.715687\pi$
$857$	−21.4619	+	6.30178i	−0.733125	+	0.215265i	−0.106200	+	0.994345i	$0.533868\pi$
$858$	−1.23339	−	0.792649i	−0.0421071	−	0.0270606i
$859$	15.1041	−	33.0734i	0.515345	−	1.12845i	−0.455826	−	0.890069i	$-0.650656\pi$
$859$	15.1041	−	33.0734i	0.515345	−	1.12845i	0.971172	−	0.238380i	$-0.0766165\pi$
$860$	−3.48333	+	4.01998i	−0.118781	+	0.137080i
$861$	−26.0366	+	16.7327i	−0.887323	+	0.570248i
$862$	1.40798	+	9.79268i	0.0479558	+	0.333540i
$863$	−2.17536	−	15.1300i	−0.0740503	−	0.515031i	−0.992762	−	0.120101i	$-0.961678\pi$
$863$	−2.17536	−	15.1300i	−0.0740503	−	0.515031i	0.918711	−	0.394930i	$-0.129231\pi$
$864$	0.841254	−	0.540641i	0.0286200	−	0.0183930i
$865$	−4.74153	+	5.47202i	−0.161217	+	0.186054i
$866$	12.7607	−	27.9421i	0.433627	−	0.949511i
$867$	−13.4365	−	8.63511i	−0.456327	−	0.293264i
$868$	9.63869	−	2.83017i	0.327158	−	0.0960624i
$869$	−0.648267	−	0.748140i	−0.0219909	−	0.0253789i
$870$	−5.78632	−	1.69902i	−0.196175	−	0.0576020i
$871$	−10.5846	−	23.1770i	−0.358645	−	0.785322i
$872$	1.27859	−	8.89279i	0.0432985	−	0.301148i
$873$	4.41380			0.149385
$874$	−2.99375	+	7.52985i	−0.101265	+	0.254701i
$875$	4.94382			0.167132
$876$	−0.136564	+	0.949825i	−0.00461408	+	0.0320916i
$877$	−18.7146	−	40.9793i	−0.631948	−	1.38377i	−0.906502	−	0.422202i	$-0.861257\pi$
$877$	−18.7146	−	40.9793i	−0.631948	−	1.38377i	0.274554	−	0.961572i	$-0.411470\pi$
$878$	−33.0999	−	9.71902i	−1.11707	−	0.328001i
$879$	−9.97406	−	11.5107i	−0.336417	−	0.388245i
$880$	0.411855	−	0.120932i	0.0138836	−	0.00407661i
$881$	12.1202	+	7.78916i	0.408339	+	0.262423i	0.728646	−	0.684890i	$-0.240150\pi$
$881$	12.1202	+	7.78916i	0.408339	+	0.262423i	−0.320308	+	0.947314i	$0.603786\pi$
$882$	7.24539	−	15.8652i	0.243965	−	0.534209i
$883$	15.3038	−	17.6616i	0.515015	−	0.594359i	−0.437361	−	0.899286i	$-0.644087\pi$
$883$	15.3038	−	17.6616i	0.515015	−	0.594359i	0.952376	+	0.304927i	$0.0986322\pi$
$884$	2.91336	−	1.87230i	0.0979869	−	0.0629723i
$885$	1.05478	+	7.33617i	0.0354561	+	0.246603i
$886$	−0.467840	−	3.25390i	−0.0157174	−	0.109317i
$887$	−16.4284	+	10.5579i	−0.551612	+	0.354499i	−0.786565	−	0.617507i	$-0.788143\pi$
$887$	−16.4284	+	10.5579i	−0.551612	+	0.354499i	0.234954	+	0.972007i	$0.424506\pi$
$888$	−5.19223	+	5.99216i	−0.174240	+	0.201084i
$889$	44.6710	−	97.8158i	1.49822	−	3.28064i
$890$	−7.58171	−	4.87247i	−0.254139	−	0.163325i
$891$	0.411855	−	0.120932i	0.0137977	−	0.00405136i
$892$	0.419379	+	0.483989i	0.0140418	+	0.0162051i
$893$	4.45683	+	1.30864i	0.149142	+	0.0437920i
$894$	−7.79607	−	17.0710i	−0.260740	−	0.570940i
$895$	−3.50946	+	24.4089i	−0.117308	+	0.815898i
$896$	4.94382			0.165161
$897$	14.2055	+	8.15661i	0.474309	+	0.272341i
$898$	−33.9635			−1.13338
$899$	1.74391	−	12.1292i	0.0581627	−	0.404531i
$900$	0.415415	+	0.909632i	0.0138472	+	0.0303211i
$901$	12.7102	+	3.73206i	0.423440	+	0.124333i
$902$	−1.75973	−	2.03084i	−0.0585926	−	0.0676195i
$903$	−25.2319	+	7.40876i	−0.839665	+	0.246548i
$904$	4.50165	+	2.89303i	0.149723	+	0.0962208i
$905$	−6.80715	+	14.9056i	−0.226277	+	0.495479i
$906$	−10.6621	+	12.3047i	−0.354225	+	0.408797i
$907$	10.8207	−	6.95404i	0.359295	−	0.230905i	−0.348522	−	0.937301i	$-0.613316\pi$
$907$	10.8207	−	6.95404i	0.359295	−	0.230905i	0.707817	+	0.706396i	$0.249680\pi$
$908$	3.65902	+	25.4490i	0.121429	+	0.844556i
$909$	1.75382	+	12.1981i	0.0581705	+	0.404585i
$910$	14.2056	−	9.12936i	0.470910	−	0.302635i
$911$	24.3587	−	28.1114i	0.807040	−	0.931374i	−0.191705	−	0.981453i	$-0.561402\pi$
$911$	24.3587	−	28.1114i	0.807040	−	0.931374i	0.998745	+	0.0500787i	$0.0159472\pi$
$912$	−0.701896	+	1.53694i	−0.0232421	+	0.0508931i
$913$	2.76259	+	1.77541i	0.0914283	+	0.0587574i
$914$	−13.8432	+	4.06473i	−0.457893	+	0.134449i
$915$	−6.30162	−	7.27246i	−0.208325	−	0.240420i
$916$	−20.1315	−	5.91113i	−0.665163	−	0.195309i
$917$	26.4017	+	57.8116i	0.871860	+	1.90911i
$918$	−0.144294	+	1.00359i	−0.00476241	+	0.0331233i
$919$	25.1179			0.828563			0.414281	−	0.910149i	$-0.364033\pi$
$919$	25.1179			0.828563			0.414281	+	0.910149i	$0.364033\pi$
$920$	−4.52832	+	1.57933i	−0.149294	+	0.0520690i
$921$	−8.80125			−0.290011
$922$	−1.64146	+	11.4166i	−0.0540586	+	0.375986i
$923$	−9.19400	−	20.1321i	−0.302624	−	0.662655i
$924$	2.03614	+	0.597864i	0.0669840	+	0.0196683i
$925$	−5.19223	−	5.99216i	−0.170720	−	0.197021i
$926$	7.51273	−	2.20594i	0.246884	−	0.0724916i
$927$	−8.62314	−	5.54176i	−0.283221	−	0.182015i
$928$	2.50520	−	5.48563i	0.0822373	−	0.180075i
$929$	3.60254	−	4.15755i	0.118195	−	0.136405i	−0.693568	−	0.720391i	$-0.743962\pi$
$929$	3.60254	−	4.15755i	0.118195	−	0.136405i	0.811764	+	0.583986i	$0.198508\pi$
$930$	−1.70939	+	1.09856i	−0.0560531	+	0.0360231i
$931$	4.19392	+	29.1694i	0.137450	+	0.955987i
$932$	1.94128	+	13.5019i	0.0635888	+	0.442270i
$933$	−14.0042	+	8.99992i	−0.458475	+	0.294644i
$934$	1.33782	−	1.54393i	0.0437748	−	0.0505188i
$935$	−0.180794	+	0.395883i	−0.00591259	+	0.0129468i
$936$	2.87340	+	1.84662i	0.0939200	+	0.0603587i
$937$	−42.8141	+	12.5714i	−1.39868	+	0.410688i	−0.892229	−	0.451583i	$-0.850860\pi$
$937$	−42.8141	+	12.5714i	−1.39868	+	0.410688i	−0.506447	+	0.862271i	$0.669041\pi$
$938$	24.1509	+	27.8716i	0.788555	+	0.910041i
$939$	31.2804	+	9.18475i	1.02080	+	0.299733i
$940$	1.14202	+	2.50069i	0.0372487	+	0.0815634i
$941$	−1.65983	+	11.5443i	−0.0541088	+	0.376335i	0.944717	+	0.327887i	$0.106337\pi$
$941$	−1.65983	+	11.5443i	−0.0541088	+	0.376335i	−0.998826	+	0.0484479i	$0.984573\pi$
$942$	−1.82775			−0.0595514
$943$	20.7700	+	21.6796i	0.676365	+	0.705984i
$944$	−7.41161			−0.241227
$945$	−0.703578	+	4.89350i	−0.0228874	+	0.159185i
$946$	−0.948486	−	2.07690i	−0.0308379	−	0.0675257i
$947$	−15.6746	−	4.60247i	−0.509356	−	0.149560i	0.0169490	−	0.999856i	$-0.494605\pi$
$947$	−15.6746	−	4.60247i	−0.509356	−	0.149560i	−0.526305	+	0.850296i	$0.676423\pi$
$948$	1.51026	+	1.74293i	0.0490509	+	0.0566077i
$949$	−3.14483	+	0.923406i	−0.102086	+	0.0299750i
$950$	−1.42140	−	0.913481i	−0.0461164	−	0.0296372i
$951$	−5.29396	+	11.5921i	−0.171668	+	0.375901i
$952$	−3.28254	+	3.78825i	−0.106388	+	0.122778i
$953$	−42.4102	+	27.2554i	−1.37380	+	0.882888i	−0.999022	−	0.0442262i	$-0.985918\pi$
$953$	−42.4102	+	27.2554i	−1.37380	+	0.882888i	−0.374779	+	0.927114i	$0.622281\pi$
$954$	1.85936	+	12.9322i	0.0601991	+	0.418694i
$955$	−0.824104	−	5.73177i	−0.0266674	−	0.185476i
$956$	−15.9196	+	10.2309i	−0.514878	+	0.330892i
$957$	1.69517	−	1.95633i	0.0547970	−	0.0632391i
$958$	−11.7356	+	25.6974i	−0.379161	+	0.830247i
$959$	22.2536	+	14.3015i	0.718605	+	0.461819i
$960$	−0.959493	+	0.281733i	−0.0309675	+	0.00909288i
$961$	17.5969	+	20.3079i	0.567641	+	0.655093i
$962$	−25.9846	−	7.62977i	−0.837777	−	0.245994i
$963$	−1.21341	−	2.65699i	−0.0391015	−	0.0856203i
$964$	3.51017	−	24.4138i	0.113055	−	0.786314i
$965$	−14.0829			−0.453345
$966$	−23.0546	−	5.53499i	−0.741769	−	0.178085i
$967$	11.8386			0.380702			0.190351	−	0.981716i	$-0.439037\pi$
$967$	11.8386			0.380702			0.190351	+	0.981716i	$0.439037\pi$
$968$	1.53924	−	10.7057i	0.0494731	−	0.344093i
$969$	−0.711657	−	1.55831i	−0.0228617	−	0.0500602i
$970$	−4.23501	−	1.24351i	−0.135978	−	0.0399268i
$971$	15.2467	+	17.5957i	0.489291	+	0.564672i	0.945676	−	0.325110i	$-0.105401\pi$
$971$	15.2467	+	17.5957i	0.489291	+	0.564672i	−0.456385	+	0.889783i	$0.650856\pi$
$972$	−0.959493	+	0.281733i	−0.0307758	+	0.00903658i
$973$	−37.7574	−	24.2652i	−1.21045	−	0.777906i
$974$	−0.632637	+	1.38528i	−0.0202710	+	0.0443873i
$975$	−2.23675	+	2.58135i	−0.0716334	+	0.0826693i
$976$	8.09525	−	5.20250i	0.259123	−	0.166528i
$977$	2.74480	+	19.0905i	0.0878139	+	0.610759i	0.985443	+	0.170007i	$0.0543790\pi$
$977$	2.74480	+	19.0905i	0.0878139	+	0.610759i	−0.897629	+	0.440752i	$0.854712\pi$
$978$	0.681932	+	4.74294i	0.0218058	+	0.151663i
$979$	3.25439	−	2.09147i	0.104011	−	0.0668437i
$980$	−11.4216	+	13.1813i	−0.364851	+	0.421060i
$981$	−3.73219	+	8.17235i	−0.119160	+	0.260923i
$982$	28.4774	+	18.3013i	0.908749	+	0.584018i
$983$	8.28027	−	2.43131i	0.264100	−	0.0775467i	−0.147002	−	0.989136i	$-0.546962\pi$
$983$	8.28027	−	2.43131i	0.264100	−	0.0775467i	0.411102	+	0.911590i	$0.365144\pi$
$984$	4.09962	+	4.73121i	0.130691	+	0.150825i
$985$	−2.64664	−	0.777124i	−0.0843290	−	0.0247612i
$986$	2.54004	+	5.56192i	0.0808914	+	0.177127i
$987$	−1.93422	+	13.4528i	−0.0615669	+	0.428207i
$988$	−5.77111			−0.183604
$989$	11.7432	+	22.6463i	0.373412	+	0.720111i
$990$	−0.429243			−0.0136422
$991$	−4.81943	+	33.5199i	−0.153094	+	1.06479i	0.757899	+	0.652372i	$0.226226\pi$
$991$	−4.81943	+	33.5199i	−0.153094	+	1.06479i	−0.910993	+	0.412422i	$0.864683\pi$
$992$	−0.844104	−	1.84833i	−0.0268003	−	0.0586845i
$993$	−6.59029	−	1.93509i	−0.209137	−	0.0614081i
$994$	20.9780	+	24.2099i	0.665383	+	0.767893i
$995$	−0.781299	+	0.229410i	−0.0247688	+	0.00727279i
$996$	−6.43596	−	4.13614i	−0.203931	−	0.131059i
$997$	−23.2480	+	50.9061i	−0.736273	+	1.61221i	0.0533170	+	0.998578i	$0.483021\pi$
$997$	−23.2480	+	50.9061i	−0.736273	+	1.61221i	−0.789590	+	0.613635i	$0.789707\pi$
$998$	−4.45953	+	5.14657i	−0.141164	+	0.162912i
$999$	6.67010	−	4.28661i	0.211033	−	0.135622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.g.31.3	✓	30
23.3	even	11	inner	690.2.m.g.601.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.g.31.3	✓	30	1.1	even	1	trivial
690.2.m.g.601.3	yes	30	23.3	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-0.654861 - 0.755750i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(4.15900 + 2.67283i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-0.654861 - 0.755750i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(4.15900 + 2.67283i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(0.841254 - 0.540641i) q^{10} +(0.0610876 + 0.424874i) q^{11} +(-0.142315 - 0.989821i) q^{12} +(2.87340 - 1.84662i) q^{13} +(-3.23751 + 3.73629i) q^{14} +(0.415415 - 0.909632i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-0.972837 + 0.285651i) q^{17} +(-0.654861 - 0.755750i) q^{18} +(1.62118 + 0.476023i) q^{19} +(0.415415 + 0.909632i) q^{20} +(-0.703578 + 4.89350i) q^{21} -0.429243 q^{22} +(4.78984 - 0.239582i) q^{23} +1.00000 q^{24} +(-0.142315 + 0.989821i) q^{25} +(1.41890 + 3.10695i) q^{26} +(-0.959493 - 0.281733i) q^{27} +(-3.23751 - 3.73629i) q^{28} +(-5.78632 + 1.69902i) q^{29} +(0.841254 + 0.540641i) q^{30} +(-0.844104 + 1.84833i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-0.361102 + 0.232066i) q^{33} +(-0.144294 - 1.00359i) q^{34} +(-0.703578 - 4.89350i) q^{35} +(0.841254 - 0.540641i) q^{36} +(-5.19223 + 5.99216i) q^{37} +(-0.701896 + 1.53694i) q^{38} +(2.87340 + 1.84662i) q^{39} +(-0.959493 + 0.281733i) q^{40} +(4.09962 + 4.73121i) q^{41} +(-4.74356 - 1.39283i) q^{42} +(2.20967 + 4.83851i) q^{43} +(0.0610876 - 0.424874i) q^{44} +1.00000 q^{45} +(-0.444523 + 4.77519i) q^{46} +2.74912 q^{47} +(-0.142315 + 0.989821i) q^{48} +(7.24539 + 15.8652i) q^{49} +(-0.959493 - 0.281733i) q^{50} +(-0.663968 - 0.766260i) q^{51} +(-3.27726 + 0.962290i) q^{52} +(-10.9911 - 7.06355i) q^{53} +(0.415415 - 0.909632i) q^{54} +(0.281094 - 0.324400i) q^{55} +(4.15900 - 2.67283i) q^{56} +(0.240459 + 1.67243i) q^{57} +(-0.858244 - 5.96922i) q^{58} +(-6.23504 + 4.00702i) q^{59} +(-0.654861 + 0.755750i) q^{60} +(3.99747 - 8.75325i) q^{61} +(-1.70939 - 1.09856i) q^{62} +(-4.74356 + 1.39283i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-3.27726 - 0.962290i) q^{65} +(-0.178314 - 0.390453i) q^{66} +(1.06163 - 7.38379i) q^{67} +1.01391 q^{68} +(2.20770 + 4.25747i) q^{69} +4.94382 q^{70} +(0.922154 - 6.41373i) q^{71} +(0.415415 + 0.909632i) q^{72} +(-0.920722 - 0.270348i) q^{73} +(-5.19223 - 5.99216i) q^{74} +(-0.959493 + 0.281733i) q^{75} +(-1.42140 - 0.913481i) q^{76} +(-0.881551 + 1.93033i) q^{77} +(-2.23675 + 2.58135i) q^{78} +(-1.94012 + 1.24684i) q^{79} +(-0.142315 - 0.989821i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-5.26649 + 3.38457i) q^{82} +(5.00997 - 5.78181i) q^{83} +(2.05374 - 4.49705i) q^{84} +(0.852953 + 0.548160i) q^{85} +(-5.10373 + 1.49859i) q^{86} +(-3.94920 - 4.55762i) q^{87} +(0.411855 + 0.120932i) q^{88} +(-3.74388 - 8.19796i) q^{89} +(-0.142315 + 0.989821i) q^{90} +16.8862 q^{91} +(-4.66332 - 1.11958i) q^{92} -2.03195 q^{93} +(-0.391240 + 2.72114i) q^{94} +(-0.701896 - 1.53694i) q^{95} +(-0.959493 - 0.281733i) q^{96} +(-2.89043 - 3.33573i) q^{97} +(-16.7348 + 4.91379i) q^{98} +(-0.361102 - 0.232066i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more