LMFDB - Embedded newform 230.2.b.b.139.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(139,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("230.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.11574317056.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 45x^{4} + 4 $ x^8 + 45*x^4 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.1
Root			$1.83051 - 1.83051i$ of defining polynomial
Character	$\chi$	$=$	230.139
Dual form			230.2.b.b.139.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -2.40815i q^{3} -1.00000 q^{4} +(1.83051 - 1.28422i) q^{5} -2.40815 q^{6} -0.706585i q^{7} +1.00000i q^{8} -2.79917 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -2.40815i q^{3} -1.00000 q^{4} +(1.83051 - 1.28422i) q^{5} -2.40815 q^{6} -0.706585i q^{7} +1.00000i q^{8} -2.79917 q^{9} +(-1.28422 - 1.83051i) q^{10} +0.747120 q^{11} +2.40815i q^{12} +1.29341i q^{13} -0.706585 q^{14} +(-3.09259 - 4.40815i) q^{15} +1.00000 q^{16} +5.50074i q^{17} +2.79917i q^{18} -2.44868 q^{19} +(-1.83051 + 1.28422i) q^{20} -1.70156 q^{21} -0.747120i q^{22} +1.00000i q^{23} +2.40815 q^{24} +(1.70156 - 4.70156i) q^{25} +1.29341 q^{26} -0.483617i q^{27} +0.706585i q^{28} -5.72371 q^{29} +(-4.40815 + 3.09259i) q^{30} +7.52288 q^{31} -1.00000i q^{32} -1.79917i q^{33} +5.50074 q^{34} +(-0.907411 - 1.29341i) q^{35} +2.79917 q^{36} +5.07420i q^{37} +2.44868i q^{38} +3.11473 q^{39} +(1.28422 + 1.83051i) q^{40} +10.0876 q^{41} +1.70156i q^{42} -5.34045i q^{43} -0.747120 q^{44} +(-5.12393 + 3.59475i) q^{45} +1.00000 q^{46} -7.90888i q^{47} -2.40815i q^{48} +6.50074 q^{49} +(-4.70156 - 1.70156i) q^{50} +13.2466 q^{51} -1.29341i q^{52} +5.84621i q^{53} -0.483617 q^{54} +(1.36761 - 0.959466i) q^{55} +0.706585 q^{56} +5.89679i q^{57} +5.72371i q^{58} -12.4146 q^{59} +(3.09259 + 4.40815i) q^{60} +1.57346 q^{61} -7.52288i q^{62} +1.97786i q^{63} -1.00000 q^{64} +(1.66103 + 2.36761i) q^{65} -1.79917 q^{66} -5.25938i q^{67} -5.50074i q^{68} +2.40815 q^{69} +(-1.29341 + 0.907411i) q^{70} +2.68444 q^{71} -2.79917i q^{72} +10.4589i q^{73} +5.07420 q^{74} +(-11.3221 - 4.09761i) q^{75} +2.44868 q^{76} -0.527904i q^{77} -3.11473i q^{78} +6.55005 q^{79} +(1.83051 - 1.28422i) q^{80} -9.56214 q^{81} -10.0876i q^{82} +12.7068i q^{83} +1.70156 q^{84} +(7.06415 + 10.0692i) q^{85} -5.34045 q^{86} +13.7835i q^{87} +0.747120i q^{88} -13.6426 q^{89} +(3.59475 + 5.12393i) q^{90} +0.913908 q^{91} -1.00000i q^{92} -18.1162i q^{93} -7.90888 q^{94} +(-4.48235 + 3.14464i) q^{95} -2.40815 q^{96} -1.50074i q^{97} -6.50074i q^{98} -2.09132 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 6 q^{6} - 14 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 + 6 * q^6 - 14 * q^9	$ 8 q - 8 q^{4} + 6 q^{6} - 14 q^{9} + 10 q^{11} - 6 q^{14} - 16 q^{15} + 8 q^{16} + 2 q^{19} + 12 q^{21} - 6 q^{24} - 12 q^{25} + 10 q^{26} - 4 q^{29} - 10 q^{30} + 10 q^{31} + 10 q^{34} - 16 q^{35} + 14 q^{36} + 46 q^{41} - 10 q^{44} - 26 q^{45} + 8 q^{46} + 18 q^{49} - 12 q^{50} + 14 q^{51} - 12 q^{54} - 18 q^{55} + 6 q^{56} - 32 q^{59} + 16 q^{60} + 18 q^{61} - 8 q^{64} - 16 q^{65} - 6 q^{66} - 6 q^{69} - 10 q^{70} + 38 q^{71} + 12 q^{74} - 32 q^{75} - 2 q^{76} + 12 q^{79} + 32 q^{81} - 12 q^{84} - 24 q^{85} - 4 q^{86} - 60 q^{89} - 24 q^{90} - 26 q^{91} - 4 q^{94} + 18 q^{95} + 6 q^{96} + 54 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 + 6 * q^6 - 14 * q^9 + 10 * q^11 - 6 * q^14 - 16 * q^15 + 8 * q^16 + 2 * q^19 + 12 * q^21 - 6 * q^24 - 12 * q^25 + 10 * q^26 - 4 * q^29 - 10 * q^30 + 10 * q^31 + 10 * q^34 - 16 * q^35 + 14 * q^36 + 46 * q^41 - 10 * q^44 - 26 * q^45 + 8 * q^46 + 18 * q^49 - 12 * q^50 + 14 * q^51 - 12 * q^54 - 18 * q^55 + 6 * q^56 - 32 * q^59 + 16 * q^60 + 18 * q^61 - 8 * q^64 - 16 * q^65 - 6 * q^66 - 6 * q^69 - 10 * q^70 + 38 * q^71 + 12 * q^74 - 32 * q^75 - 2 * q^76 + 12 * q^79 + 32 * q^81 - 12 * q^84 - 24 * q^85 - 4 * q^86 - 60 * q^89 - 24 * q^90 - 26 * q^91 - 4 * q^94 + 18 * q^95 + 6 * q^96 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	2.40815i		−	1.39034i	−0.718843	−	0.695172i	$-0.755328\pi$
$3$		−	2.40815i		−	1.39034i	0.718843	−	0.695172i	$-0.244672\pi$
$4$	−1.00000			−0.500000
$5$	1.83051	−	1.28422i	0.818631	−	0.574320i
$5$	1.83051	−	1.28422i	0.818631	−	0.574320i
$6$	−2.40815			−0.983122
$7$		−	0.706585i		−	0.267064i	−0.991044	−	0.133532i	$-0.957368\pi$
$7$		−	0.706585i		−	0.267064i	0.991044	−	0.133532i	$-0.0426319\pi$
$8$			1.00000i			0.353553i
$9$	−2.79917			−0.933058
$10$	−1.28422	−	1.83051i	−0.406106	−	0.578859i
$11$	0.747120			0.225265			0.112633	−	0.993637i	$-0.464072\pi$
$11$	0.747120			0.225265			0.112633	+	0.993637i	$0.464072\pi$
$12$			2.40815i			0.695172i
$13$			1.29341i			0.358729i	0.983783	+	0.179364i	$0.0574041\pi$
$13$			1.29341i			0.358729i	−0.983783	+	0.179364i	$0.942596\pi$
$14$	−0.706585			−0.188843
$15$	−3.09259	−	4.40815i	−0.798503	−	1.13818i
$16$	1.00000			0.250000
$17$			5.50074i			1.33412i	0.745002	+	0.667062i	$0.232449\pi$
$17$			5.50074i			1.33412i	−0.745002	+	0.667062i	$0.767551\pi$
$18$			2.79917i			0.659772i
$19$	−2.44868			−0.561766			−0.280883	−	0.959742i	$-0.590627\pi$
$19$	−2.44868			−0.561766			−0.280883	+	0.959742i	$0.590627\pi$
$20$	−1.83051	+	1.28422i	−0.409315	+	0.287160i
$21$	−1.70156			−0.371311
$22$		−	0.747120i		−	0.159286i
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	2.40815			0.491561
$25$	1.70156	−	4.70156i	0.340312	−	0.940312i
$26$	1.29341			0.253659
$27$		−	0.483617i		−	0.0930721i
$28$			0.706585i			0.133532i
$29$	−5.72371			−1.06287			−0.531433	−	0.847100i	$-0.678346\pi$
$29$	−5.72371			−1.06287			−0.531433	+	0.847100i	$0.678346\pi$
$30$	−4.40815	+	3.09259i	−0.804814	+	0.564627i
$31$	7.52288			1.35115			0.675575	−	0.737292i	$-0.263896\pi$
$31$	7.52288			1.35115			0.675575	+	0.737292i	$0.263896\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	1.79917i		−	0.313196i
$34$	5.50074			0.943369
$35$	−0.907411	−	1.29341i	−0.153380	−	0.218627i
$36$	2.79917			0.466529
$37$			5.07420i			0.834193i	0.908862	+	0.417097i	$0.136952\pi$
$37$			5.07420i			0.834193i	−0.908862	+	0.417097i	$0.863048\pi$
$38$			2.44868i			0.397229i
$39$	3.11473			0.498756
$40$	1.28422	+	1.83051i	0.203053	+	0.289430i
$41$	10.0876			1.57541			0.787707	−	0.616051i	$-0.211268\pi$
$41$	10.0876			1.57541			0.787707	+	0.616051i	$0.211268\pi$
$42$			1.70156i			0.262557i
$43$		−	5.34045i		−	0.814410i	−0.913337	−	0.407205i	$-0.866503\pi$
$43$		−	5.34045i		−	0.814410i	0.913337	−	0.407205i	$-0.133497\pi$
$44$	−0.747120			−0.112633
$45$	−5.12393	+	3.59475i	−0.763830	+	0.535874i
$46$	1.00000			0.147442
$47$		−	7.90888i		−	1.15363i	−0.816875	−	0.576815i	$-0.804295\pi$
$47$		−	7.90888i		−	1.15363i	0.816875	−	0.576815i	$-0.195705\pi$
$48$		−	2.40815i		−	0.347586i
$49$	6.50074			0.928677
$50$	−4.70156	−	1.70156i	−0.664901	−	0.240637i
$51$	13.2466			1.85489
$52$		−	1.29341i		−	0.179364i
$53$			5.84621i			0.803038i	0.915851	+	0.401519i	$0.131518\pi$
$53$			5.84621i			0.803038i	−0.915851	+	0.401519i	$0.868482\pi$
$54$	−0.483617			−0.0658119
$55$	1.36761	−	0.959466i	0.184409	−	0.129374i
$56$	0.706585			0.0944215
$57$			5.89679i			0.781049i
$58$			5.72371i			0.751559i
$59$	−12.4146			−1.61625			−0.808125	−	0.589012i	$-0.799517\pi$
$59$	−12.4146			−1.61625			−0.808125	+	0.589012i	$0.799517\pi$
$60$	3.09259	+	4.40815i	0.399252	+	0.569089i
$61$	1.57346			0.201461			0.100731	−	0.994914i	$-0.467882\pi$
$61$	1.57346			0.201461			0.100731	+	0.994914i	$0.467882\pi$
$62$		−	7.52288i		−	0.955407i
$63$			1.97786i			0.249186i
$64$	−1.00000			−0.125000
$65$	1.66103	+	2.36761i	0.206025	+	0.293666i
$66$	−1.79917			−0.221463
$67$		−	5.25938i		−	0.642535i	−0.946988	−	0.321268i	$-0.895891\pi$
$67$		−	5.25938i		−	0.642535i	0.946988	−	0.321268i	$-0.104109\pi$
$68$		−	5.50074i		−	0.667062i
$69$	2.40815			0.289907
$70$	−1.29341	+	0.907411i	−0.154593	+	0.108456i
$71$	2.68444			0.318585			0.159292	−	0.987231i	$-0.449079\pi$
$71$	2.68444			0.318585			0.159292	+	0.987231i	$0.449079\pi$
$72$		−	2.79917i		−	0.329886i
$73$			10.4589i			1.22413i	0.790809	+	0.612063i	$0.209660\pi$
$73$			10.4589i			1.22413i	−0.790809	+	0.612063i	$0.790340\pi$
$74$	5.07420			0.589864
$75$	−11.3221	−	4.09761i	−1.30736	−	0.473152i
$76$	2.44868			0.280883
$77$		−	0.527904i		−	0.0601602i
$78$		−	3.11473i		−	0.352674i
$79$	6.55005			0.736938			0.368469	−	0.929640i	$-0.379882\pi$
$79$	6.55005			0.736938			0.368469	+	0.929640i	$0.379882\pi$
$80$	1.83051	−	1.28422i	0.204658	−	0.143580i
$81$	−9.56214			−1.06246
$82$		−	10.0876i		−	1.11399i
$83$			12.7068i			1.39475i	0.716706	+	0.697376i	$0.245649\pi$
$83$			12.7068i			1.39475i	−0.716706	+	0.697376i	$0.754351\pi$
$84$	1.70156			0.185656
$85$	7.06415	+	10.0692i	0.766215	+	1.09216i
$86$	−5.34045			−0.575875
$87$			13.7835i			1.47775i
$88$			0.747120i			0.0796432i
$89$	−13.6426			−1.44612			−0.723058	−	0.690787i	$-0.757264\pi$
$89$	−13.6426			−1.44612			−0.723058	+	0.690787i	$0.757264\pi$
$90$	3.59475	+	5.12393i	0.378920	+	0.540109i
$91$	0.913908			0.0958036
$92$		−	1.00000i		−	0.104257i
$93$		−	18.1162i		−	1.87856i
$94$	−7.90888			−0.815739
$95$	−4.48235	+	3.14464i	−0.459879	+	0.322634i
$96$	−2.40815			−0.245781
$97$		−	1.50074i		−	0.152377i	−0.997093	−	0.0761884i	$-0.975725\pi$
$97$		−	1.50074i		−	0.152377i	0.997093	−	0.0761884i	$-0.0242750\pi$
$98$		−	6.50074i		−	0.656674i
$99$	−2.09132			−0.210185
$100$	−1.70156	+	4.70156i	−0.170156	+	0.470156i
$101$	−16.0472			−1.59676			−0.798380	−	0.602154i	$-0.794309\pi$
$101$	−16.0472			−1.59676			−0.798380	+	0.602154i	$0.794309\pi$
$102$		−	13.2466i		−	1.31161i
$103$			9.49069i			0.935145i	0.883955	+	0.467573i	$0.154871\pi$
$103$			9.49069i			0.935145i	−0.883955	+	0.467573i	$0.845129\pi$
$104$	−1.29341			−0.126830
$105$	−3.11473	+	2.18518i	−0.303967	+	0.213252i
$106$	5.84621			0.567834
$107$		−	1.38473i		−	0.133867i	−0.997757	−	0.0669336i	$-0.978678\pi$
$107$		−	1.38473i		−	0.133867i	0.997757	−	0.0669336i	$-0.0213216\pi$
$108$			0.483617i			0.0465360i
$109$	14.0370			1.34450			0.672250	−	0.740325i	$-0.265328\pi$
$109$	14.0370			1.34450			0.672250	+	0.740325i	$0.265328\pi$
$110$	−0.959466	−	1.36761i	−0.0914815	−	0.130397i
$111$	12.2194			1.15982
$112$		−	0.706585i		−	0.0667661i
$113$		−	16.3105i		−	1.53437i	−0.641428	−	0.767183i	$-0.721658\pi$
$113$		−	16.3105i		−	1.53437i	0.641428	−	0.767183i	$-0.278342\pi$
$114$	5.89679			0.552285
$115$	1.28422	+	1.83051i	0.119754	+	0.170696i
$116$	5.72371			0.531433
$117$		−	3.62049i		−	0.334715i
$118$			12.4146i			1.14286i
$119$	3.88674			0.356297
$120$	4.40815	−	3.09259i	0.402407	−	0.282313i
$121$	−10.4418			−0.949256
$122$		−	1.57346i		−	0.142455i
$123$		−	24.2923i		−	2.19037i
$124$	−7.52288			−0.675575
$125$	−2.92310	−	10.7915i	−0.261450	−	0.965217i
$126$	1.97786			0.176201
$127$			2.73523i			0.242712i	0.992609	+	0.121356i	$0.0387243\pi$
$127$			2.73523i			0.242712i	−0.992609	+	0.121356i	$0.961276\pi$
$128$			1.00000i			0.0883883i
$129$	−12.8606			−1.13231
$130$	2.36761	−	1.66103i	0.207653	−	0.145682i
$131$	−8.21942			−0.718134			−0.359067	−	0.933312i	$-0.616905\pi$
$131$	−8.21942			−0.718134			−0.359067	+	0.933312i	$0.616905\pi$
$132$			1.79917i			0.156598i
$133$			1.73020i			0.150028i
$134$	−5.25938			−0.454341
$135$	−0.621070	−	0.885267i	−0.0534532	−	0.0761916i
$136$	−5.50074			−0.471684
$137$			22.8449i			1.95177i	0.218275	+	0.975887i	$0.429957\pi$
$137$			22.8449i			1.95177i	−0.218275	+	0.975887i	$0.570043\pi$
$138$		−	2.40815i		−	0.204995i
$139$	−3.76049			−0.318960			−0.159480	−	0.987201i	$-0.550982\pi$
$139$	−3.76049			−0.318960			−0.159480	+	0.987201i	$0.550982\pi$
$140$	0.907411	+	1.29341i	0.0766902	+	0.109313i
$141$	−19.0458			−1.60394
$142$		−	2.68444i		−	0.225273i
$143$			0.966336i			0.0808090i
$144$	−2.79917			−0.233265
$145$	−10.4773	+	7.35049i	−0.870094	+	0.610425i
$146$	10.4589			0.865587
$147$		−	15.6547i		−	1.29118i
$148$		−	5.07420i		−	0.417097i
$149$	1.90614			0.156157			0.0780785	−	0.996947i	$-0.475122\pi$
$149$	1.90614			0.156157			0.0780785	+	0.996947i	$0.475122\pi$
$150$	−4.09761	+	11.3221i	−0.334569	+	0.924442i
$151$	−9.41967			−0.766562			−0.383281	−	0.923632i	$-0.625206\pi$
$151$	−9.41967			−0.766562			−0.383281	+	0.923632i	$0.625206\pi$
$152$		−	2.44868i		−	0.198614i
$153$		−	15.3975i		−	1.24482i
$154$	−0.527904			−0.0425397
$155$	13.7707	−	9.66103i	1.10609	−	0.775992i
$156$	−3.11473			−0.249378
$157$		−	4.43304i		−	0.353795i	−0.984229	−	0.176897i	$-0.943394\pi$
$157$		−	4.43304i		−	0.353795i	0.984229	−	0.176897i	$-0.0566061\pi$
$158$		−	6.55005i		−	0.521094i
$159$	14.0785			1.11650
$160$	−1.28422	−	1.83051i	−0.101526	−	0.144715i
$161$	0.706585			0.0556867
$162$			9.56214i			0.751273i
$163$			9.92453i			0.777349i	0.921375	+	0.388675i	$0.127067\pi$
$163$			9.92453i			0.777349i	−0.921375	+	0.388675i	$0.872933\pi$
$164$	−10.0876			−0.787707
$165$	−2.31053	−	3.29341i	−0.179875	−	0.256392i
$166$	12.7068			0.986238
$167$			11.9089i			0.921537i	0.887520	+	0.460769i	$0.152426\pi$
$167$			11.9089i			0.921537i	−0.887520	+	0.460769i	$0.847574\pi$
$168$		−	1.70156i		−	0.131278i
$169$	11.3271			0.871314
$170$	10.0692	−	7.06415i	0.772270	−	0.541796i
$171$	6.85429			0.524161
$172$			5.34045i			0.407205i
$173$			2.91391i			0.221540i	0.993846	+	0.110770i	$0.0353317\pi$
$173$			2.91391i			0.221540i	−0.993846	+	0.110770i	$0.964668\pi$
$174$	13.7835			1.04493
$175$	−3.32206	−	1.20230i	−0.251124	−	0.0908853i
$176$	0.747120			0.0563163
$177$			29.8963i			2.24714i
$178$			13.6426i			1.02256i
$179$	−19.3663			−1.44751			−0.723754	−	0.690058i	$-0.757585\pi$
$179$	−19.3663			−1.44751			−0.723754	+	0.690058i	$0.757585\pi$
$180$	5.12393	−	3.59475i	0.381915	−	0.267937i
$181$	17.5986			1.30809			0.654045	−	0.756456i	$-0.273071\pi$
$181$	17.5986			1.30809			0.654045	+	0.756456i	$0.273071\pi$
$182$		−	0.913908i		−	0.0677434i
$183$		−	3.78913i		−	0.280100i
$184$	−1.00000			−0.0737210
$185$	6.51638	+	9.28839i	0.479094	+	0.682896i
$186$	−18.1162			−1.32834
$187$			4.10971i			0.300532i
$188$			7.90888i			0.576815i
$189$	−0.341716			−0.0248562
$190$	3.14464	+	4.48235i	0.228136	+	0.325184i
$191$	20.3578			1.47304			0.736518	−	0.676418i	$-0.236469\pi$
$191$	20.3578			1.47304			0.736518	+	0.676418i	$0.236469\pi$
$192$			2.40815i			0.173793i
$193$		−	1.41317i		−	0.101722i	−0.998706	−	0.0508611i	$-0.983803\pi$
$193$		−	1.41317i		−	0.101722i	0.998706	−	0.0508611i	$-0.0161966\pi$
$194$	−1.50074			−0.107747
$195$	5.70156	−	4.00000i	0.408297	−	0.286446i
$196$	−6.50074			−0.464338
$197$		−	4.92395i		−	0.350817i	−0.984496	−	0.175409i	$-0.943875\pi$
$197$		−	4.92395i		−	0.350817i	0.984496	−	0.175409i	$-0.0561247\pi$
$198$			2.09132i			0.148624i
$199$	10.3105			0.730894			0.365447	−	0.930832i	$-0.380916\pi$
$199$	10.3105			0.730894			0.365447	+	0.930832i	$0.380916\pi$
$200$	4.70156	+	1.70156i	0.332451	+	0.120319i
$201$	−12.6654			−0.893345
$202$			16.0472i			1.12908i
$203$			4.04429i			0.283853i
$204$	−13.2466			−0.927447
$205$	18.4654	−	12.9546i	1.28968	−	0.904792i
$206$	9.49069			0.661248
$207$		−	2.79917i		−	0.194556i
$208$			1.29341i			0.0896822i
$209$	−1.82946			−0.126546
$210$	2.18518	+	3.11473i	0.150792	+	0.214937i
$211$	11.4161			0.785918			0.392959	−	0.919556i	$-0.371451\pi$
$211$	11.4161			0.785918			0.392959	+	0.919556i	$0.371451\pi$
$212$		−	5.84621i		−	0.401519i
$213$		−	6.46453i		−	0.442942i
$214$	−1.38473			−0.0946584
$215$	−6.85830	−	9.77576i	−0.467732	−	0.666701i
$216$	0.483617			0.0329059
$217$		−	5.31556i		−	0.360844i
$218$		−	14.0370i		−	0.950705i
$219$	25.1867			1.70196
$220$	−1.36761	+	0.959466i	−0.0922045	+	0.0646872i
$221$	−7.11473			−0.478589
$222$		−	12.2194i		−	0.820114i
$223$		−	18.2094i		−	1.21939i	−0.792636	−	0.609695i	$-0.791292\pi$
$223$		−	18.2094i		−	1.21939i	0.792636	−	0.609695i	$-0.208708\pi$
$224$	−0.706585			−0.0472107
$225$	−4.76297	+	13.1605i	−0.317531	+	0.877366i
$226$	−16.3105			−1.08496
$227$			18.9363i			1.25684i	0.777873	+	0.628422i	$0.216299\pi$
$227$			18.9363i			1.25684i	−0.777873	+	0.628422i	$0.783701\pi$
$228$		−	5.89679i		−	0.390524i
$229$	8.46433			0.559339			0.279669	−	0.960096i	$-0.409775\pi$
$229$	8.46433			0.559339			0.279669	+	0.960096i	$0.409775\pi$
$230$	1.83051	−	1.28422i	0.120701	−	0.0846789i
$231$	−1.27127			−0.0836435
$232$		−	5.72371i		−	0.375780i
$233$			16.6341i			1.08973i	0.838523	+	0.544867i	$0.183420\pi$
$233$			16.6341i			1.08973i	−0.838523	+	0.544867i	$0.816580\pi$
$234$	−3.62049			−0.236679
$235$	−10.1567	−	14.4773i	−0.662553	−	0.944396i
$236$	12.4146			0.808125
$237$		−	15.7735i		−	1.02460i
$238$		−	3.88674i		−	0.251940i
$239$	16.0840			1.04039			0.520194	−	0.854048i	$-0.325860\pi$
$239$	16.0840			1.04039			0.520194	+	0.854048i	$0.325860\pi$
$240$	−3.09259	−	4.40815i	−0.199626	−	0.284545i
$241$	−28.1283			−1.81190			−0.905952	−	0.423381i	$-0.860843\pi$
$241$	−28.1283			−1.81190			−0.905952	+	0.423381i	$0.860843\pi$
$242$			10.4418i			0.671225i
$243$			21.5762i			1.38411i
$244$	−1.57346			−0.100731
$245$	11.8997	−	8.34837i	0.760243	−	0.533358i
$246$	−24.2923			−1.54882
$247$		−	3.16716i		−	0.201522i
$248$			7.52288i			0.477703i
$249$	30.5998			1.93919
$250$	−10.7915	+	2.92310i	−0.682511	+	0.184873i
$251$	−20.5770			−1.29881			−0.649404	−	0.760444i	$-0.724982\pi$
$251$	−20.5770			−1.29881			−0.649404	+	0.760444i	$0.724982\pi$
$252$		−	1.97786i		−	0.124593i
$253$			0.747120i			0.0469710i
$254$	2.73523			0.171623
$255$	24.2481	−	17.0115i	1.51847	−	1.06530i
$256$	1.00000			0.0625000
$257$		−	16.8505i		−	1.05111i	−0.850760	−	0.525554i	$-0.823858\pi$
$257$		−	16.8505i		−	1.05111i	0.850760	−	0.525554i	$-0.176142\pi$
$258$			12.8606i			0.800665i
$259$	3.58536			0.222783
$260$	−1.66103	−	2.36761i	−0.103013	−	0.146833i
$261$	16.0217			0.991715
$262$			8.21942i			0.507797i
$263$			24.7630i			1.52695i	0.645837	+	0.763475i	$0.276508\pi$
$263$			24.7630i			1.52695i	−0.645837	+	0.763475i	$0.723492\pi$
$264$	1.79917			0.110732
$265$	7.50781	+	10.7016i	0.461201	+	0.657392i
$266$	1.73020			0.106086
$267$			32.8535i			2.01060i
$268$			5.25938i			0.321268i
$269$	3.55152			0.216540			0.108270	−	0.994122i	$-0.465469\pi$
$269$	3.55152			0.216540			0.108270	+	0.994122i	$0.465469\pi$
$270$	−0.885267	+	0.621070i	−0.0538756	+	0.0377971i
$271$	−27.4761			−1.66905			−0.834526	−	0.550969i	$-0.814258\pi$
$271$	−27.4761			−1.66905			−0.834526	+	0.550969i	$0.814258\pi$
$272$			5.50074i			0.333531i
$273$		−	2.20083i		−	0.133200i
$274$	22.8449			1.38011
$275$	1.27127	−	3.51263i	0.0766605	−	0.211820i
$276$	−2.40815			−0.144953
$277$		−	11.1001i		−	0.666940i	−0.942761	−	0.333470i	$-0.891780\pi$
$277$		−	11.1001i		−	0.666940i	0.942761	−	0.333470i	$-0.108220\pi$
$278$			3.76049i			0.225539i
$279$	−21.0579			−1.26070
$280$	1.29341	−	0.907411i	0.0772963	−	0.0542282i
$281$	13.0458			0.778245			0.389122	−	0.921186i	$-0.372778\pi$
$281$	13.0458			0.778245			0.389122	+	0.921186i	$0.372778\pi$
$282$			19.0458i			1.13416i
$283$		−	3.35049i		−	0.199166i	−0.995029	−	0.0995831i	$-0.968249\pi$
$283$		−	3.35049i		−	0.199166i	0.995029	−	0.0995831i	$-0.0317509\pi$
$284$	−2.68444			−0.159292
$285$	7.57277	+	10.7942i	0.448572	+	0.639390i
$286$	0.966336			0.0571406
$287$		−	7.12773i		−	0.420736i
$288$			2.79917i			0.164943i
$289$	−13.2581			−0.779889
$290$	7.35049	+	10.4773i	0.431636	+	0.615250i
$291$	−3.61400			−0.211856
$292$		−	10.4589i		−	0.612063i
$293$		−	8.89197i		−	0.519474i	−0.965679	−	0.259737i	$-0.916364\pi$
$293$		−	8.89197i		−	0.519474i	0.965679	−	0.259737i	$-0.0836359\pi$
$294$	−15.6547			−0.913003
$295$	−22.7252	+	15.9431i	−1.32311	+	0.928245i
$296$	−5.07420			−0.294932
$297$		−	0.361320i		−	0.0209659i
$298$		−	1.90614i		−	0.110420i
$299$	−1.29341			−0.0748001
$300$	11.3221	+	4.09761i	0.653679	+	0.236576i
$301$	−3.77348			−0.217500
$302$			9.41967i			0.542041i
$303$			38.6441i			2.22005i
$304$	−2.44868			−0.140442
$305$	2.88024	−	2.02067i	0.164922	−	0.115703i
$306$	−15.3975			−0.880218
$307$		−	28.4111i		−	1.62151i	−0.585388	−	0.810753i	$-0.699058\pi$
$307$		−	28.4111i		−	1.62151i	0.585388	−	0.810753i	$-0.300942\pi$
$308$			0.527904i			0.0300801i
$309$	22.8550			1.30017
$310$	−9.66103	−	13.7707i	−0.548710	−	0.782125i
$311$	−28.0105			−1.58833			−0.794164	−	0.607704i	$-0.792091\pi$
$311$	−28.0105			−1.58833			−0.794164	+	0.607704i	$0.792091\pi$
$312$			3.11473i			0.176337i
$313$		−	7.42882i		−	0.419902i	−0.977712	−	0.209951i	$-0.932670\pi$
$313$		−	7.42882i		−	0.419902i	0.977712	−	0.209951i	$-0.0673304\pi$
$314$	−4.43304			−0.250171
$315$	2.54000	+	3.62049i	0.143113	+	0.203992i
$316$	−6.55005			−0.368469
$317$		−	13.1480i		−	0.738463i	−0.929337	−	0.369232i	$-0.879621\pi$
$317$		−	13.1480i		−	0.738463i	0.929337	−	0.369232i	$-0.120379\pi$
$318$		−	14.0785i		−	0.789485i
$319$	−4.27629			−0.239427
$320$	−1.83051	+	1.28422i	−0.102329	+	0.0717900i
$321$	−3.33464			−0.186122
$322$		−	0.706585i		−	0.0393765i
$323$		−	13.4696i		−	0.749466i
$324$	9.56214			0.531230
$325$	6.08107	+	2.20083i	0.337317	+	0.122080i
$326$	9.92453			0.549669
$327$		−	33.8031i		−	1.86932i
$328$			10.0876i			0.556993i
$329$	−5.58830			−0.308093
$330$	−3.29341	+	2.31053i	−0.181297	+	0.127191i
$331$	−15.6225			−0.858693			−0.429346	−	0.903140i	$-0.641256\pi$
$331$	−15.6225			−0.858693			−0.429346	+	0.903140i	$0.641256\pi$
$332$		−	12.7068i		−	0.697376i
$333$		−	14.2036i		−	0.778351i
$334$	11.9089			0.651625
$335$	−6.75419	−	9.62736i	−0.369021	−	0.525999i
$336$	−1.70156			−0.0928278
$337$			16.6965i			0.909518i	0.890614	+	0.454759i	$0.150275\pi$
$337$			16.6965i			0.909518i	−0.890614	+	0.454759i	$0.849725\pi$
$338$		−	11.3271i		−	0.616112i
$339$	−39.2782			−2.13330
$340$	−7.06415	−	10.0692i	−0.383107	−	0.546078i
$341$	5.62049			0.304367
$342$		−	6.85429i		−	0.370637i
$343$		−	9.53942i		−	0.515081i
$344$	5.34045			0.287938
$345$	4.40815	−	3.09259i	0.237327	−	0.166499i
$346$	2.91391			0.156653
$347$		−	16.3981i		−	0.880296i	−0.897925	−	0.440148i	$-0.854926\pi$
$347$		−	16.3981i		−	0.880296i	0.897925	−	0.440148i	$-0.145074\pi$
$348$		−	13.7835i		−	0.738875i
$349$	1.86165			0.0996518			0.0498259	−	0.998758i	$-0.484133\pi$
$349$	1.86165			0.0996518			0.0498259	+	0.998758i	$0.484133\pi$
$350$	−1.20230	+	3.32206i	−0.0642656	+	0.177571i
$351$	0.625517			0.0333876
$352$		−	0.747120i		−	0.0398216i
$353$		−	25.8408i		−	1.37537i	−0.726010	−	0.687684i	$-0.758628\pi$
$353$		−	25.8408i		−	1.37537i	0.726010	−	0.687684i	$-0.241372\pi$
$354$	29.8963			1.58897
$355$	4.91391	−	3.44741i	0.260803	−	0.182970i
$356$	13.6426			0.723058
$357$		−	9.35985i		−	0.495376i
$358$			19.3663i			1.02354i
$359$	−8.72223			−0.460342			−0.230171	−	0.973150i	$-0.573929\pi$
$359$	−8.72223			−0.460342			−0.230171	+	0.973150i	$0.573929\pi$
$360$	−3.59475	−	5.12393i	−0.189460	−	0.270055i
$361$	−13.0040			−0.684419
$362$		−	17.5986i		−	0.924959i
$363$			25.1454i			1.31979i
$364$	−0.913908			−0.0479018
$365$	13.4316	+	19.1452i	0.703040	+	1.00211i
$366$	−3.78913			−0.198061
$367$		−	25.5958i		−	1.33609i	−0.744121	−	0.668045i	$-0.767131\pi$
$367$		−	25.5958i		−	1.33609i	0.744121	−	0.668045i	$-0.232869\pi$
$368$			1.00000i			0.0521286i
$369$	−28.2369			−1.46995
$370$	9.28839	−	6.51638i	0.482880	−	0.338771i
$371$	4.13084			0.214463
$372$			18.1162i			0.939282i
$373$		−	17.2125i		−	0.891232i	−0.895224	−	0.445616i	$-0.852985\pi$
$373$		−	17.2125i		−	0.891232i	0.895224	−	0.445616i	$-0.147015\pi$
$374$	4.10971			0.212508
$375$	−25.9874	+	7.03926i	−1.34198	+	0.363506i
$376$	7.90888			0.407870
$377$		−	7.40312i		−	0.381280i
$378$			0.341716i			0.0175760i
$379$	−23.0339			−1.18317			−0.591585	−	0.806243i	$-0.701498\pi$
$379$	−23.0339			−1.18317			−0.591585	+	0.806243i	$0.701498\pi$
$380$	4.48235	−	3.14464i	0.229940	−	0.161317i
$381$	6.58683			0.337453
$382$		−	20.3578i		−	1.04159i
$383$			3.81777i			0.195079i	0.995232	+	0.0975394i	$0.0310972\pi$
$383$			3.81777i			0.195079i	−0.995232	+	0.0975394i	$0.968903\pi$
$384$	2.40815			0.122890
$385$	−0.677944	−	0.966336i	−0.0345513	−	0.0492490i
$386$	−1.41317			−0.0719285
$387$			14.9488i			0.759892i
$388$			1.50074i			0.0761884i
$389$	8.25435			0.418512			0.209256	−	0.977861i	$-0.432896\pi$
$389$	8.25435			0.418512			0.209256	+	0.977861i	$0.432896\pi$
$390$	−4.00000	−	5.70156i	−0.202548	−	0.288710i
$391$	−5.50074			−0.278184
$392$			6.50074i			0.328337i
$393$			19.7936i			0.998454i
$394$	−4.92395			−0.248065
$395$	11.9900	−	8.41170i	0.603280	−	0.423238i
$396$	2.09132			0.105093
$397$		−	12.4967i		−	0.627193i	−0.949556	−	0.313596i	$-0.898466\pi$
$397$		−	12.4967i		−	0.627193i	0.949556	−	0.313596i	$-0.101534\pi$
$398$		−	10.3105i		−	0.516820i
$399$	4.16658			0.208590
$400$	1.70156	−	4.70156i	0.0850781	−	0.235078i
$401$	34.5660			1.72614			0.863072	−	0.505082i	$-0.168538\pi$
$401$	34.5660			1.72614			0.863072	+	0.505082i	$0.168538\pi$
$402$			12.6654i			0.631691i
$403$			9.73020i			0.484696i
$404$	16.0472			0.798380
$405$	−17.5036	+	12.2799i	−0.869763	+	0.610193i
$406$	4.04429			0.200715
$407$			3.79103i			0.187915i
$408$			13.2466i			0.655804i
$409$	−12.0499			−0.595829			−0.297914	−	0.954593i	$-0.596291\pi$
$409$	−12.0499			−0.595829			−0.297914	+	0.954593i	$0.596291\pi$
$410$	−12.9546	−	18.4654i	−0.639784	−	0.911943i
$411$	55.0140			2.71364
$412$		−	9.49069i		−	0.467573i
$413$			8.77201i			0.431642i
$414$	−2.79917			−0.137572
$415$	16.3183	+	23.2600i	0.801034	+	1.14179i
$416$	1.29341			0.0634149
$417$			9.05581i			0.443465i
$418$			1.82946i			0.0894818i
$419$	−38.6157			−1.88650			−0.943250	−	0.332085i	$-0.892248\pi$
$419$	−38.6157			−1.88650			−0.943250	+	0.332085i	$0.892248\pi$
$420$	3.11473	−	2.18518i	0.151983	−	0.106626i
$421$	32.7384			1.59557			0.797785	−	0.602941i	$-0.206005\pi$
$421$	32.7384			1.59557			0.797785	+	0.602941i	$0.206005\pi$
$422$		−	11.4161i		−	0.555728i
$423$			22.1384i			1.07640i
$424$	−5.84621			−0.283917
$425$	25.8621	+	9.35985i	1.25449	+	0.454019i
$426$	−6.46453			−0.313208
$427$		−	1.11179i		−	0.0538031i
$428$			1.38473i			0.0669336i
$429$	2.32708			0.112352
$430$	−9.77576	+	6.85830i	−0.471429	+	0.330737i
$431$	−35.7739			−1.72317			−0.861584	−	0.507615i	$-0.830527\pi$
$431$	−35.7739			−1.72317			−0.861584	+	0.507615i	$0.830527\pi$
$432$		−	0.483617i		−	0.0232680i
$433$		−	10.5682i		−	0.507877i	−0.967220	−	0.253938i	$-0.918274\pi$
$433$		−	10.5682i		−	0.507877i	0.967220	−	0.253938i	$-0.0817261\pi$
$434$	−5.31556			−0.255155
$435$	17.7011	+	25.2309i	0.848701	+	1.20973i
$436$	−14.0370			−0.672250
$437$		−	2.44868i		−	0.117136i
$438$		−	25.1867i		−	1.20346i
$439$	27.6642			1.32034			0.660170	−	0.751117i	$-0.270484\pi$
$439$	27.6642			1.32034			0.660170	+	0.751117i	$0.270484\pi$
$440$	0.959466	+	1.36761i	0.0457407	+	0.0651984i
$441$	−18.1967			−0.866509
$442$			7.11473i			0.338413i
$443$			36.8082i			1.74881i	0.485198	+	0.874404i	$0.338747\pi$
$443$			36.8082i			1.74881i	−0.485198	+	0.874404i	$0.661253\pi$
$444$	−12.2194			−0.579908
$445$	−24.9730	+	17.5201i	−1.18384	+	0.830534i
$446$	−18.2094			−0.862239
$447$		−	4.59027i		−	0.217112i
$448$			0.706585i			0.0333830i
$449$	−18.2711			−0.862267			−0.431133	−	0.902288i	$-0.641886\pi$
$449$	−18.2711			−0.862267			−0.431133	+	0.902288i	$0.641886\pi$
$450$	13.1605	+	4.76297i	0.620392	+	0.224529i
$451$	7.53662			0.354886
$452$			16.3105i			0.767183i
$453$			22.6840i			1.06579i
$454$	18.9363			0.888722
$455$	1.67292	−	1.17366i	0.0784278	−	0.0550219i
$456$	−5.89679			−0.276142
$457$			27.6326i			1.29260i	0.763084	+	0.646299i	$0.223684\pi$
$457$			27.6326i			1.29260i	−0.763084	+	0.646299i	$0.776316\pi$
$458$		−	8.46433i		−	0.395512i
$459$	2.66025			0.124170
$460$	−1.28422	−	1.83051i	−0.0598770	−	0.0853481i
$461$	35.5515			1.65580			0.827900	−	0.560876i	$-0.189536\pi$
$461$	35.5515			1.65580			0.827900	+	0.560876i	$0.189536\pi$
$462$			1.27127i			0.0591449i
$463$		−	23.9331i		−	1.11226i	−0.831094	−	0.556132i	$-0.812285\pi$
$463$		−	23.9331i		−	1.11226i	0.831094	−	0.556132i	$-0.187715\pi$
$464$	−5.72371			−0.265716
$465$	−23.2652	−	33.1620i	−1.07890	−	1.53785i
$466$	16.6341			0.770558
$467$			19.9035i			0.921024i	0.887654	+	0.460512i	$0.152334\pi$
$467$			19.9035i			0.921024i	−0.887654	+	0.460512i	$0.847666\pi$
$468$			3.62049i			0.167357i
$469$	−3.71620			−0.171598
$470$	−14.4773	+	10.1567i	−0.667789	+	0.468496i
$471$	−10.6754			−0.491897
$472$		−	12.4146i		−	0.571430i
$473$		−	3.98995i		−	0.183458i
$474$	−15.7735			−0.724500
$475$	−4.16658	+	11.5126i	−0.191176	+	0.528236i
$476$	−3.88674			−0.178148
$477$		−	16.3646i		−	0.749281i
$478$		−	16.0840i		−	0.735666i
$479$	3.86206			0.176462			0.0882309	−	0.996100i	$-0.471879\pi$
$479$	3.86206			0.176462			0.0882309	+	0.996100i	$0.471879\pi$
$480$	−4.40815	+	3.09259i	−0.201203	+	0.141157i
$481$	−6.56304			−0.299249
$482$			28.1283i			1.28121i
$483$		−	1.70156i		−	0.0774238i
$484$	10.4418			0.474628
$485$	−1.92728	−	2.74712i	−0.0875131	−	0.124740i
$486$	21.5762			0.978717
$487$			15.1499i			0.686506i	0.939243	+	0.343253i	$0.111529\pi$
$487$			15.1499i			0.686506i	−0.939243	+	0.343253i	$0.888471\pi$
$488$			1.57346i			0.0712273i
$489$	23.8997			1.08078
$490$	−8.34837	−	11.8997i	−0.377141	−	0.537573i
$491$	−6.86312			−0.309728			−0.154864	−	0.987936i	$-0.549494\pi$
$491$	−6.86312			−0.309728			−0.154864	+	0.987936i	$0.549494\pi$
$492$			24.2923i			1.09518i
$493$		−	31.4846i		−	1.41800i
$494$	−3.16716			−0.142497
$495$	−3.82819	+	2.68571i	−0.172064	+	0.120714i
$496$	7.52288			0.337787
$497$		−	1.89679i		−	0.0850826i
$498$		−	30.5998i		−	1.37121i
$499$	18.6809			0.836272			0.418136	−	0.908385i	$-0.362684\pi$
$499$	18.6809			0.836272			0.418136	+	0.908385i	$0.362684\pi$
$500$	2.92310	+	10.7915i	0.130725	+	0.482608i
$501$	28.6784			1.28125
$502$			20.5770i			0.918396i
$503$			23.1886i			1.03393i	0.856008	+	0.516963i	$0.172938\pi$
$503$			23.1886i			1.03393i	−0.856008	+	0.516963i	$0.827062\pi$
$504$	−1.97786			−0.0881007
$505$	−29.3747	+	20.6082i	−1.30716	+	0.917051i
$506$	0.747120			0.0332135
$507$		−	27.2773i		−	1.21143i
$508$		−	2.73523i		−	0.121356i
$509$	−11.5385			−0.511436			−0.255718	−	0.966751i	$-0.582312\pi$
$509$	−11.5385			−0.511436			−0.255718	+	0.966751i	$0.582312\pi$
$510$	−17.0115	−	24.2481i	−0.753283	−	1.07372i
$511$	7.39013			0.326920
$512$		−	1.00000i		−	0.0441942i
$513$			1.18422i			0.0522847i
$514$	−16.8505			−0.743245
$515$	12.1881	+	17.3728i	0.537073	+	0.765539i
$516$	12.8606			0.566156
$517$		−	5.90888i		−	0.259872i
$518$		−	3.58536i		−	0.157531i
$519$	7.01712			0.308017
$520$	−2.36761	+	1.66103i	−0.103827	+	0.0728409i
$521$	−16.2792			−0.713207			−0.356603	−	0.934256i	$-0.616065\pi$
$521$	−16.2792			−0.713207			−0.356603	+	0.934256i	$0.616065\pi$
$522$		−	16.0217i		−	0.701249i
$523$			30.8347i			1.34831i	0.738591	+	0.674153i	$0.235491\pi$
$523$			30.8347i			1.34831i	−0.738591	+	0.674153i	$0.764509\pi$
$524$	8.21942			0.359067
$525$	−2.89531	+	8.00000i	−0.126362	+	0.349149i
$526$	24.7630			1.07972
$527$			41.3814i			1.80260i
$528$		−	1.79917i		−	0.0782990i
$529$	−1.00000			−0.0434783
$530$	10.7016	−	7.50781i	0.464846	−	0.326118i
$531$	34.7508			1.50805
$532$		−	1.73020i		−	0.0750138i
$533$			13.0474i			0.565146i
$534$	32.8535			1.42171
$535$	−1.77830	−	2.53477i	−0.0768827	−	0.109588i
$536$	5.25938			0.227171
$537$			46.6370i			2.01254i
$538$		−	3.55152i		−	0.153117i
$539$	4.85683			0.209198
$540$	0.621070	+	0.885267i	0.0267266	+	0.0380958i
$541$	−30.5199			−1.31215			−0.656077	−	0.754694i	$-0.727785\pi$
$541$	−30.5199			−1.31215			−0.656077	+	0.754694i	$0.727785\pi$
$542$			27.4761i			1.18020i
$543$		−	42.3799i		−	1.81870i
$544$	5.50074			0.235842
$545$	25.6949	−	18.0266i	1.10065	−	0.772173i
$546$	−2.20083			−0.0941866
$547$		−	28.0416i		−	1.19897i	−0.800385	−	0.599487i	$-0.795371\pi$
$547$		−	28.0416i		−	1.19897i	0.800385	−	0.599487i	$-0.204629\pi$
$548$		−	22.8449i		−	0.975887i
$549$	−4.40439			−0.187975
$550$	−3.51263	−	1.27127i	−0.149779	−	0.0542072i
$551$	14.0155			0.597082
$552$			2.40815i			0.102498i
$553$		−	4.62817i		−	0.196810i
$554$	−11.1001			−0.471598
$555$	22.3678	−	15.6924i	0.949461	−	0.666106i
$556$	3.76049			0.159480
$557$			4.15674i			0.176127i	0.996115	+	0.0880634i	$0.0280678\pi$
$557$			4.15674i			0.176127i	−0.996115	+	0.0880634i	$0.971932\pi$
$558$			21.0579i			0.891450i
$559$	6.90741			0.292152
$560$	−0.907411	−	1.29341i	−0.0383451	−	0.0546567i
$561$	9.89679			0.417843
$562$		−	13.0458i		−	0.550302i
$563$		−	21.3480i		−	0.899709i	−0.893102	−	0.449854i	$-0.851476\pi$
$563$		−	21.3480i		−	0.899709i	0.893102	−	0.449854i	$-0.148524\pi$
$564$	19.0458			0.801971
$565$	−20.9463	−	29.8567i	−0.881218	−	1.25608i
$566$	−3.35049			−0.140832
$567$			6.75647i			0.283745i
$568$			2.68444i			0.112637i
$569$	25.6430			1.07501			0.537506	−	0.843260i	$-0.319366\pi$
$569$	25.6430			1.07501			0.537506	+	0.843260i	$0.319366\pi$
$570$	10.7942	−	7.57277i	0.452117	−	0.317188i
$571$	−7.10743			−0.297437			−0.148718	−	0.988880i	$-0.547515\pi$
$571$	−7.10743			−0.297437			−0.148718	+	0.988880i	$0.547515\pi$
$572$		−	0.966336i		−	0.0404045i
$573$		−	49.0245i		−	2.04803i
$574$	−7.12773			−0.297506
$575$	4.70156	+	1.70156i	0.196069	+	0.0709600i
$576$	2.79917			0.116632
$577$			22.7226i			0.945956i	0.881074	+	0.472978i	$0.156821\pi$
$577$			22.7226i			0.945956i	−0.881074	+	0.472978i	$0.843179\pi$
$578$			13.2581i			0.551465i
$579$	−3.40312			−0.141429
$580$	10.4773	−	7.35049i	0.435047	−	0.305213i
$581$	8.97843			0.372488
$582$			3.61400i			0.149805i
$583$			4.36782i			0.180896i
$584$	−10.4589			−0.432794
$585$	−4.64951	−	6.62736i	−0.192233	−	0.274008i
$586$	−8.89197			−0.367324
$587$			7.06600i			0.291645i	0.989311	+	0.145822i	$0.0465828\pi$
$587$			7.06600i			0.291645i	−0.989311	+	0.145822i	$0.953417\pi$
$588$			15.6547i			0.645590i
$589$	−18.4211			−0.759030
$590$	15.9431	+	22.7252i	0.656368	+	0.935581i
$591$	−11.8576			−0.487757
$592$			5.07420i			0.208548i
$593$		−	14.9914i		−	0.615624i	−0.951447	−	0.307812i	$-0.900403\pi$
$593$		−	14.9914i		−	0.615624i	0.951447	−	0.307812i	$-0.0995968\pi$
$594$	−0.361320			−0.0148251
$595$	7.11473	−	4.99143i	0.291676	−	0.204629i
$596$	−1.90614			−0.0780785
$597$		−	24.8293i		−	1.01620i
$598$			1.29341i			0.0528917i
$599$	4.03069			0.164690			0.0823448	−	0.996604i	$-0.473759\pi$
$599$	4.03069			0.164690			0.0823448	+	0.996604i	$0.473759\pi$
$600$	4.09761	−	11.3221i	0.167284	−	0.462221i
$601$	13.9320			0.568300			0.284150	−	0.958780i	$-0.408289\pi$
$601$	13.9320			0.568300			0.284150	+	0.958780i	$0.408289\pi$
$602$			3.77348i			0.153796i
$603$			14.7219i			0.599523i
$604$	9.41967			0.383281
$605$	−19.1139	+	13.4096i	−0.777090	+	0.545177i
$606$	38.6441			1.56981
$607$		−	31.0588i		−	1.26064i	−0.776337	−	0.630318i	$-0.782925\pi$
$607$		−	31.0588i		−	1.26064i	0.776337	−	0.630318i	$-0.217075\pi$
$608$			2.44868i			0.0993072i
$609$	9.73924			0.394654
$610$	−2.02067	−	2.88024i	−0.0818145	−	0.116618i
$611$	10.2295			0.413840
$612$			15.3975i			0.622408i
$613$		−	19.6722i		−	0.794554i	−0.917699	−	0.397277i	$-0.869955\pi$
$613$		−	19.6722i		−	0.794554i	0.917699	−	0.397277i	$-0.130045\pi$
$614$	−28.4111			−1.14658
$615$	−31.1967	−	44.4675i	−1.25797	−	1.79310i
$616$	0.527904			0.0212699
$617$		−	40.9043i		−	1.64674i	−0.567502	−	0.823372i	$-0.692090\pi$
$617$		−	40.9043i		−	1.64674i	0.567502	−	0.823372i	$-0.307910\pi$
$618$		−	22.8550i		−	0.919362i
$619$	3.58556			0.144116			0.0720579	−	0.997400i	$-0.477043\pi$
$619$	3.58556			0.144116			0.0720579	+	0.997400i	$0.477043\pi$
$620$	−13.7707	+	9.66103i	−0.553046	+	0.387996i
$621$	0.483617			0.0194069
$622$			28.0105i			1.12312i
$623$			9.63969i			0.386206i
$624$	3.11473			0.124689
$625$	−19.2094	−	16.0000i	−0.768375	−	0.640000i
$626$	−7.42882			−0.296915
$627$			4.40561i			0.175943i
$628$			4.43304i			0.176897i
$629$	−27.9118			−1.11292
$630$	3.62049	−	2.54000i	0.144244	−	0.101196i
$631$	−7.19670			−0.286496			−0.143248	−	0.989687i	$-0.545755\pi$
$631$	−7.19670			−0.286496			−0.143248	+	0.989687i	$0.545755\pi$
$632$			6.55005i			0.260547i
$633$		−	27.4917i		−	1.09270i
$634$	−13.1480			−0.522172
$635$	3.51263	+	5.00687i	0.139394	+	0.198692i
$636$	−14.0785			−0.558250
$637$			8.40815i			0.333143i
$638$			4.27629i			0.169300i
$639$	−7.51422			−0.297258
$640$	1.28422	+	1.83051i	0.0507632	+	0.0723574i
$641$	−16.3436			−0.645534			−0.322767	−	0.946478i	$-0.604613\pi$
$641$	−16.3436			−0.645534			−0.322767	+	0.946478i	$0.604613\pi$
$642$			3.33464i			0.131608i
$643$			6.55839i			0.258638i	0.991603	+	0.129319i	$0.0412791\pi$
$643$			6.55839i			0.258638i	−0.991603	+	0.129319i	$0.958721\pi$
$644$	−0.706585			−0.0278434
$645$	−23.5415	+	16.5158i	−0.926945	+	0.650309i
$646$	−13.4696			−0.529953
$647$			16.5455i			0.650470i	0.945633	+	0.325235i	$0.105443\pi$
$647$			16.5455i			0.650470i	−0.945633	+	0.325235i	$0.894557\pi$
$648$		−	9.56214i		−	0.375637i
$649$	−9.27523			−0.364085
$650$	2.20083	−	6.08107i	0.0863235	−	0.238519i
$651$	−12.8006			−0.501697
$652$		−	9.92453i		−	0.388675i
$653$			12.7408i			0.498587i	0.968428	+	0.249294i	$0.0801984\pi$
$653$			12.7408i			0.498587i	−0.968428	+	0.249294i	$0.919802\pi$
$654$	−33.8031			−1.32181
$655$	−15.0458	+	10.5555i	−0.587887	+	0.412439i
$656$	10.0876			0.393853
$657$		−	29.2764i		−	1.14218i
$658$			5.58830i			0.217855i
$659$	23.8094			0.927484			0.463742	−	0.885970i	$-0.346507\pi$
$659$	23.8094			0.927484			0.463742	+	0.885970i	$0.346507\pi$
$660$	2.31053	+	3.29341i	0.0899374	+	0.128196i
$661$	24.9323			0.969754			0.484877	−	0.874582i	$-0.338864\pi$
$661$	24.9323			0.969754			0.484877	+	0.874582i	$0.338864\pi$
$662$			15.6225i			0.607187i
$663$			17.1333i			0.665403i
$664$	−12.7068			−0.493119
$665$	2.22196	+	3.16716i	0.0861639	+	0.122817i
$666$	−14.2036			−0.550377
$667$		−	5.72371i		−	0.221623i
$668$		−	11.9089i		−	0.460769i
$669$	−43.8509			−1.69537
$670$	−9.62736	+	6.75419i	−0.371937	+	0.260937i
$671$	1.17556			0.0453822
$672$			1.70156i			0.0656392i
$673$		−	5.48050i		−	0.211258i	−0.994406	−	0.105629i	$-0.966314\pi$
$673$		−	5.48050i		−	0.211258i	0.994406	−	0.105629i	$-0.0336856\pi$
$674$	16.6965			0.643127
$675$	−2.27375	−	0.822904i	−0.0875168	−	0.0316736i
$676$	−11.3271			−0.435657
$677$			1.75255i			0.0673560i	0.999433	+	0.0336780i	$0.0107221\pi$
$677$			1.75255i			0.0673560i	−0.999433	+	0.0336780i	$0.989278\pi$
$678$			39.2782i			1.50847i
$679$	−1.06040			−0.0406944
$680$	−10.0692	+	7.06415i	−0.386135	+	0.270898i
$681$	45.6013			1.74745
$682$		−	5.62049i		−	0.215220i
$683$		−	23.5091i		−	0.899552i	−0.893141	−	0.449776i	$-0.851504\pi$
$683$		−	23.5091i		−	0.899552i	0.893141	−	0.449776i	$-0.148496\pi$
$684$	−6.85429			−0.262080
$685$	29.3379	+	41.8180i	1.12094	+	1.59778i
$686$	−9.53942			−0.364217
$687$		−	20.3834i		−	0.777673i
$688$		−	5.34045i		−	0.203603i
$689$	−7.56157			−0.288073
$690$	−3.09259	−	4.40815i	−0.117733	−	0.167815i
$691$	−21.4834			−0.817269			−0.408634	−	0.912698i	$-0.633995\pi$
$691$	−21.4834			−0.817269			−0.408634	+	0.912698i	$0.633995\pi$
$692$		−	2.91391i		−	0.110770i
$693$			1.47770i			0.0561330i
$694$	−16.3981			−0.622463
$695$	−6.88362	+	4.82929i	−0.261111	+	0.183185i
$696$	−13.7835			−0.522463
$697$			55.4890i			2.10180i
$698$		−	1.86165i		−	0.0704645i
$699$	40.0573			1.51511
$700$	3.32206	+	1.20230i	0.125562	+	0.0454426i
$701$	9.62985			0.363714			0.181857	−	0.983325i	$-0.441789\pi$
$701$	9.62985			0.363714			0.181857	+	0.983325i	$0.441789\pi$
$702$		−	0.625517i		−	0.0236086i
$703$		−	12.4251i		−	0.468621i
$704$	−0.747120			−0.0281581
$705$	−34.8635	+	24.4589i	−1.31304	+	0.921177i
$706$	−25.8408			−0.972532
$707$			11.3387i			0.426437i
$708$		−	29.8963i		−	1.12357i
$709$	−11.8970			−0.446801			−0.223400	−	0.974727i	$-0.571716\pi$
$709$	−11.8970			−0.446801			−0.223400	+	0.974727i	$0.571716\pi$
$710$	−3.44741	−	4.91391i	−0.129379	−	0.184416i
$711$	−18.3347			−0.687606
$712$		−	13.6426i		−	0.511279i
$713$			7.52288i			0.281734i
$714$	−9.35985			−0.350283
$715$	1.24099	+	1.76889i	0.0464103	+	0.0661528i
$716$	19.3663			0.723754
$717$		−	38.7327i		−	1.44650i
$718$			8.72223i			0.325511i
$719$	−24.2949			−0.906046			−0.453023	−	0.891499i	$-0.649655\pi$
$719$	−24.2949			−0.906046			−0.453023	+	0.891499i	$0.649655\pi$
$720$	−5.12393	+	3.59475i	−0.190958	+	0.133969i
$721$	6.70598			0.249744
$722$			13.0040i			0.483957i
$723$			67.7371i			2.51917i
$724$	−17.5986			−0.654045
$725$	−9.73924	+	26.9104i	−0.361706	+	0.999426i
$726$	25.1454			0.933234
$727$		−	6.25721i		−	0.232067i	−0.993245	−	0.116034i	$-0.962982\pi$
$727$		−	6.25721i		−	0.232067i	0.993245	−	0.116034i	$-0.0370180\pi$
$728$			0.913908i			0.0338717i
$729$	23.2723			0.861935
$730$	19.1452	−	13.4316i	0.708596	−	0.497124i
$731$	29.3764			1.08653
$732$			3.78913i			0.140050i
$733$		−	37.3304i		−	1.37883i	−0.724367	−	0.689415i	$-0.757868\pi$
$733$		−	37.3304i		−	1.37883i	0.724367	−	0.689415i	$-0.242132\pi$
$734$	−25.5958			−0.944759
$735$	−20.1041	−	28.6562i	−0.741551	−	1.05700i
$736$	1.00000			0.0368605
$737$		−	3.92939i		−	0.144741i
$738$			28.2369i			1.03941i
$739$	26.9889			0.992802			0.496401	−	0.868093i	$-0.334655\pi$
$739$	26.9889			0.992802			0.496401	+	0.868093i	$0.334655\pi$
$740$	−6.51638	−	9.28839i	−0.239547	−	0.341448i
$741$	−7.62699			−0.280185
$742$		−	4.13084i		−	0.151648i
$743$		−	32.1544i		−	1.17963i	−0.807538	−	0.589815i	$-0.799201\pi$
$743$		−	32.1544i		−	1.17963i	0.807538	−	0.589815i	$-0.200799\pi$
$744$	18.1162			0.664172
$745$	3.48922	−	2.44790i	0.127835	−	0.0896842i
$746$	−17.2125			−0.630196
$747$		−	35.5685i		−	1.30138i
$748$		−	4.10971i		−	0.150266i
$749$	−0.978433			−0.0357512
$750$	7.03926	+	25.9874i	0.257038	+	0.948926i
$751$	39.7865			1.45183			0.725915	−	0.687785i	$-0.241417\pi$
$751$	39.7865			1.45183			0.725915	+	0.687785i	$0.241417\pi$
$752$		−	7.90888i		−	0.288407i
$753$			49.5524i			1.80579i
$754$	−7.40312			−0.269606
$755$	−17.2428	+	12.0969i	−0.627531	+	0.440252i
$756$	0.341716			0.0124281
$757$			26.9961i			0.981189i	0.871388	+	0.490595i	$0.163220\pi$
$757$			26.9961i			0.981189i	−0.871388	+	0.490595i	$0.836780\pi$
$758$			23.0339i			0.836628i
$759$	1.79917			0.0653059
$760$	−3.14464	−	4.48235i	−0.114068	−	0.162592i
$761$	−7.21529			−0.261554			−0.130777	−	0.991412i	$-0.541747\pi$
$761$	−7.21529			−0.261554			−0.130777	+	0.991412i	$0.541747\pi$
$762$		−	6.58683i		−	0.238616i
$763$		−	9.91833i		−	0.359068i
$764$	−20.3578			−0.736518
$765$	−19.7738	−	28.1854i	−0.714923	−	1.01904i
$766$	3.81777			0.137942
$767$		−	16.0573i		−	0.579795i
$768$		−	2.40815i		−	0.0868965i
$769$	−6.40916			−0.231120			−0.115560	−	0.993300i	$-0.536866\pi$
$769$	−6.40916			−0.231120			−0.115560	+	0.993300i	$0.536866\pi$
$770$	−0.966336	+	0.677944i	−0.0348243	+	0.0244314i
$771$	−40.5786			−1.46140
$772$			1.41317i			0.0508611i
$773$		−	50.2483i		−	1.80730i	−0.428267	−	0.903652i	$-0.640876\pi$
$773$		−	50.2483i		−	1.80730i	0.428267	−	0.903652i	$-0.359124\pi$
$774$	14.9488			0.537325
$775$	12.8006	−	35.3693i	0.459813	−	1.27050i
$776$	1.50074			0.0538733
$777$		−	8.63406i		−	0.309745i
$778$		−	8.25435i		−	0.295933i
$779$	−24.7012			−0.885014
$780$	−5.70156	+	4.00000i	−0.204149	+	0.143223i
$781$	2.00560			0.0717660
$782$			5.50074i			0.196706i
$783$			2.76808i			0.0989231i
$784$	6.50074			0.232169
$785$	−5.69299	−	8.11473i	−0.203192	−	0.289627i
$786$	19.7936			0.706013
$787$			2.70933i			0.0965772i	0.998833	+	0.0482886i	$0.0153767\pi$
$787$			2.70933i			0.0965772i	−0.998833	+	0.0482886i	$0.984623\pi$
$788$			4.92395i			0.175409i
$789$	59.6329			2.12299
$790$	−8.41170	−	11.9900i	−0.299275	−	0.426583i
$791$	−11.5248			−0.409774
$792$		−	2.09132i		−	0.0743118i
$793$			2.03514i			0.0722699i
$794$	−12.4967			−0.443492
$795$	25.7709	−	18.0799i	0.914001	−	0.641229i
$796$	−10.3105			−0.365447
$797$		−	15.1452i		−	0.536471i	−0.963353	−	0.268236i	$-0.913559\pi$
$797$		−	15.1452i		−	0.536471i	0.963353	−	0.268236i	$-0.0864406\pi$
$798$		−	4.16658i		−	0.147495i
$799$	43.5047			1.53909
$800$	−4.70156	−	1.70156i	−0.166225	−	0.0601593i
$801$	38.1881			1.34931
$802$		−	34.5660i		−	1.22057i
$803$			7.81408i			0.275753i
$804$	12.6654			0.446673
$805$	1.29341	−	0.907411i	0.0455869	−	0.0319820i
$806$	9.73020			0.342732
$807$		−	8.55259i		−	0.301065i
$808$		−	16.0472i		−	0.564540i
$809$	3.94373			0.138654			0.0693270	−	0.997594i	$-0.477915\pi$
$809$	3.94373			0.138654			0.0693270	+	0.997594i	$0.477915\pi$
$810$	12.2799	+	17.5036i	0.431471	+	0.615015i
$811$	−14.1521			−0.496947			−0.248474	−	0.968639i	$-0.579929\pi$
$811$	−14.1521			−0.496947			−0.248474	+	0.968639i	$0.579929\pi$
$812$		−	4.04429i		−	0.141927i
$813$			66.1664i			2.32056i
$814$	3.79103			0.132876
$815$	12.7453	+	18.1670i	0.446447	+	0.636362i
$816$	13.2466			0.463723
$817$			13.0771i			0.457508i
$818$			12.0499i			0.421314i
$819$	−2.55819			−0.0893903
$820$	−18.4654	+	12.9546i	−0.644841	+	0.452396i
$821$	37.0094			1.29164			0.645818	−	0.763491i	$-0.276516\pi$
$821$	37.0094			1.29164			0.645818	+	0.763491i	$0.276516\pi$
$822$		−	55.0140i		−	1.91883i
$823$			18.1208i			0.631651i	0.948817	+	0.315826i	$0.102281\pi$
$823$			18.1208i			0.631651i	−0.948817	+	0.315826i	$0.897719\pi$
$824$	−9.49069			−0.330624
$825$	−8.45893	−	3.06141i	−0.294502	−	0.106585i
$826$	8.77201			0.305217
$827$		−	41.5398i		−	1.44448i	−0.691643	−	0.722240i	$-0.743113\pi$
$827$		−	41.5398i		−	1.44448i	0.691643	−	0.722240i	$-0.256887\pi$
$828$			2.79917i			0.0972781i
$829$	−21.3976			−0.743171			−0.371585	−	0.928399i	$-0.621186\pi$
$829$	−21.3976			−0.743171			−0.371585	+	0.928399i	$0.621186\pi$
$830$	23.2600	−	16.3183i	0.807365	−	0.566417i
$831$	−26.7307			−0.927277
$832$		−	1.29341i		−	0.0448411i
$833$			35.7588i			1.23897i
$834$	9.05581			0.313577
$835$	15.2936	+	21.7994i	0.529257	+	0.754399i
$836$	1.82946			0.0632732
$837$		−	3.63819i		−	0.125754i
$838$			38.6157i			1.33396i
$839$	41.3437			1.42734			0.713672	−	0.700480i	$-0.247031\pi$
$839$	41.3437			1.42734			0.713672	+	0.700480i	$0.247031\pi$
$840$	−2.18518	−	3.11473i	−0.0753958	−	0.107469i
$841$	3.76081			0.129683
$842$		−	32.7384i		−	1.12824i
$843$		−	31.4161i		−	1.08203i
$844$	−11.4161			−0.392959
$845$	20.7344	−	14.5465i	0.713284	−	0.500413i
$846$	22.1384			0.761132
$847$			7.37803i			0.253512i
$848$			5.84621i			0.200760i
$849$	−8.06848			−0.276910
$850$	9.35985	−	25.8621i	0.321040	−	0.887061i
$851$	−5.07420			−0.173941
$852$			6.46453i			0.221471i
$853$			56.0373i			1.91868i	0.282252	+	0.959340i	$0.408919\pi$
$853$			56.0373i			1.91868i	−0.282252	+	0.959340i	$0.591081\pi$
$854$	−1.11179			−0.0380445
$855$	12.5469	−	8.80241i	0.429094	−	0.301036i
$856$	1.38473			0.0473292
$857$		−	43.4734i		−	1.48502i	−0.669833	−	0.742512i	$-0.733634\pi$
$857$		−	43.4734i		−	1.48502i	0.669833	−	0.742512i	$-0.266366\pi$
$858$		−	2.32708i		−	0.0794452i
$859$	−11.1599			−0.380771			−0.190386	−	0.981709i	$-0.560974\pi$
$859$	−11.1599			−0.380771			−0.190386	+	0.981709i	$0.560974\pi$
$860$	6.85830	+	9.77576i	0.233866	+	0.333351i
$861$	−17.1646			−0.584969
$862$			35.7739i			1.21846i
$863$		−	32.2767i		−	1.09871i	−0.835589	−	0.549356i	$-0.814873\pi$
$863$		−	32.2767i		−	1.09871i	0.835589	−	0.549356i	$-0.185127\pi$
$864$	−0.483617			−0.0164530
$865$	3.74210	+	5.33395i	0.127235	+	0.181360i
$866$	−10.5682			−0.359123
$867$			31.9275i			1.08431i
$868$			5.31556i			0.180422i
$869$	4.89367			0.166006
$870$	25.2309	−	17.7011i	0.855409	−	0.600123i
$871$	6.80256			0.230496
$872$			14.0370i			0.475352i
$873$			4.20083i			0.142176i
$874$	−2.44868			−0.0828279
$875$	−7.62508	+	2.06542i	−0.257775	+	0.0698240i
$876$	−25.1867			−0.850978
$877$		−	9.52493i		−	0.321634i	−0.986984	−	0.160817i	$-0.948587\pi$
$877$		−	9.52493i		−	0.321634i	0.986984	−	0.160817i	$-0.0514129\pi$
$878$		−	27.6642i		−	0.933621i
$879$	−21.4132			−0.722248
$880$	1.36761	−	0.959466i	0.0461022	−	0.0323436i
$881$	49.1585			1.65619			0.828096	−	0.560586i	$-0.189424\pi$
$881$	49.1585			1.65619			0.828096	+	0.560586i	$0.189424\pi$
$882$			18.1967i			0.612715i
$883$		−	33.1379i		−	1.11518i	−0.830117	−	0.557590i	$-0.811726\pi$
$883$		−	33.1379i		−	1.11518i	0.830117	−	0.557590i	$-0.188274\pi$
$884$	7.11473			0.239294
$885$	38.3934	+	54.7256i	1.29058	+	1.83958i
$886$	36.8082			1.23659
$887$		−	1.59084i		−	0.0534153i	−0.999643	−	0.0267076i	$-0.991498\pi$
$887$		−	1.59084i		−	0.0534153i	0.999643	−	0.0267076i	$-0.00850232\pi$
$888$			12.2194i			0.410057i
$889$	1.93267			0.0648197
$890$	17.5201	+	24.9730i	0.587276	+	0.837098i
$891$	−7.14407			−0.239335
$892$			18.2094i			0.609695i
$893$			19.3663i			0.648070i
$894$	−4.59027			−0.153522
$895$	−35.4504	+	24.8706i	−1.18497	+	0.831333i
$896$	0.706585			0.0236054
$897$			3.11473i			0.103998i
$898$			18.2711i			0.609715i
$899$	−43.0588			−1.43609
$900$	4.76297	−	13.1605i	0.158766	−	0.438683i
$901$	−32.1584			−1.07135
$902$		−	7.53662i		−	0.250942i
$903$			9.08710i			0.302400i
$904$	16.3105			0.542480
$905$	32.2144	−	22.6004i	1.07084	−	0.751263i
$906$	22.6840			0.753624
$907$			17.4658i			0.579942i	0.957035	+	0.289971i	$0.0936457\pi$
$907$			17.4658i			0.579942i	−0.957035	+	0.289971i	$0.906354\pi$
$908$		−	18.9363i		−	0.628422i
$909$	44.9190			1.48987
$910$	−1.17366	−	1.67292i	−0.0389064	−	0.0554568i
$911$	−21.6050			−0.715805			−0.357903	−	0.933759i	$-0.616508\pi$
$911$	−21.6050			−0.715805			−0.357903	+	0.933759i	$0.616508\pi$
$912$			5.89679i			0.195262i
$913$			9.49349i			0.314189i
$914$	27.6326			0.914005
$915$	−4.86607	−	6.93605i	−0.160867	−	0.229299i
$916$	−8.46433			−0.279669
$917$			5.80772i			0.191788i
$918$		−	2.66025i		−	0.0878013i
$919$	41.7396			1.37686			0.688432	−	0.725301i	$-0.258299\pi$
$919$	41.7396			1.37686			0.688432	+	0.725301i	$0.258299\pi$
$920$	−1.83051	+	1.28422i	−0.0603503	+	0.0423395i
$921$	−68.4181			−2.25445
$922$		−	35.5515i		−	1.17083i
$923$			3.47210i			0.114285i
$924$	1.27127			0.0418217
$925$	23.8567	+	8.63406i	0.784402	+	0.283886i
$926$	−23.9331			−0.786490
$927$		−	26.5661i		−	0.872545i
$928$			5.72371i			0.187890i
$929$	−38.8505			−1.27464			−0.637322	−	0.770597i	$-0.719958\pi$
$929$	−38.8505			−1.27464			−0.637322	+	0.770597i	$0.719958\pi$
$930$	−33.1620	+	23.2652i	−1.08742	+	0.762895i
$931$	−15.9182			−0.521699
$932$		−	16.6341i		−	0.544867i
$933$			67.4533i			2.20832i
$934$	19.9035			0.651262
$935$	5.27777	+	7.52288i	0.172601	+	0.246025i
$936$	3.62049			0.118340
$937$			33.1555i			1.08314i	0.840655	+	0.541571i	$0.182170\pi$
$937$			33.1555i			1.08314i	−0.840655	+	0.541571i	$0.817830\pi$
$938$			3.71620i			0.121338i
$939$	−17.8897			−0.583808
$940$	10.1567	+	14.4773i	0.331276	+	0.472198i
$941$	−33.8004			−1.10186			−0.550931	−	0.834551i	$-0.685727\pi$
$941$	−33.8004			−1.10186			−0.550931	+	0.834551i	$0.685727\pi$
$942$			10.6754i			0.347823i
$943$			10.0876i			0.328496i
$944$	−12.4146			−0.404062
$945$	−0.625517	+	0.438839i	−0.0203481	+	0.0142754i
$946$	−3.98995			−0.129725
$947$		−	20.2406i		−	0.657730i	−0.944377	−	0.328865i	$-0.893334\pi$
$947$		−	20.2406i		−	0.657730i	0.944377	−	0.328865i	$-0.106666\pi$
$948$			15.7735i			0.512299i
$949$	−13.5277			−0.439129
$950$	11.5126	+	4.16658i	0.373519	+	0.135182i
$951$	−31.6622			−1.02672
$952$			3.88674i			0.125970i
$953$		−	28.3885i		−	0.919592i	−0.888024	−	0.459796i	$-0.847922\pi$
$953$		−	28.3885i		−	0.919592i	0.888024	−	0.459796i	$-0.152078\pi$
$954$	−16.3646			−0.529822
$955$	37.2652	−	26.1438i	1.20587	−	0.845995i
$956$	−16.0840			−0.520194
$957$			10.2979i			0.332885i
$958$		−	3.86206i		−	0.124777i
$959$	16.1419			0.521249
$960$	3.09259	+	4.40815i	0.0998129	+	0.142272i
$961$	25.5937			0.825604
$962$			6.56304i			0.211601i
$963$			3.87611i			0.124906i
$964$	28.1283			0.905952
$965$	−1.81482	−	2.58683i	−0.0584212	−	0.0832730i
$966$	−1.70156			−0.0547469
$967$			57.6163i			1.85282i	0.376522	+	0.926408i	$0.377120\pi$
$967$			57.6163i			1.85282i	−0.376522	+	0.926408i	$0.622880\pi$
$968$		−	10.4418i		−	0.335613i
$969$	−32.4367			−1.04202
$970$	−2.74712	+	1.92728i	−0.0882047	+	0.0618811i
$971$	−1.47686			−0.0473946			−0.0236973	−	0.999719i	$-0.507544\pi$
$971$	−1.47686			−0.0473946			−0.0236973	+	0.999719i	$0.507544\pi$
$972$		−	21.5762i		−	0.692057i
$973$			2.65711i			0.0851829i
$974$	15.1499			0.485433
$975$	5.29991	−	14.6441i	0.169733	−	0.468987i
$976$	1.57346			0.0503653
$977$			11.5709i			0.370185i	0.982721	+	0.185092i	$0.0592584\pi$
$977$			11.5709i			0.370185i	−0.982721	+	0.185092i	$0.940742\pi$
$978$		−	23.8997i		−	0.764229i
$979$	−10.1927			−0.325760
$980$	−11.8997	+	8.34837i	−0.380122	+	0.266679i
$981$	−39.2920			−1.25450
$982$			6.86312i			0.219011i
$983$			37.5275i			1.19694i	0.801145	+	0.598470i	$0.204225\pi$
$983$			37.5275i			1.19694i	−0.801145	+	0.598470i	$0.795775\pi$
$984$	24.2923			0.774412
$985$	−6.32344	−	9.01337i	−0.201481	−	0.287190i
$986$	−31.4846			−1.00267
$987$			13.4575i			0.428356i
$988$			3.16716i			0.100761i
$989$	5.34045			0.169816
$990$	2.68571	+	3.82819i	0.0853575	+	0.121668i
$991$	9.87860			0.313804			0.156902	−	0.987614i	$-0.449849\pi$
$991$	9.87860			0.313804			0.156902	+	0.987614i	$0.449849\pi$
$992$		−	7.52288i		−	0.238852i
$993$			37.6214i			1.19388i
$994$	−1.89679			−0.0601624
$995$	18.8736	−	13.2410i	0.598333	−	0.419768i
$996$	−30.5998			−0.969593
$997$			53.6506i			1.69913i	0.527484	+	0.849565i	$0.323135\pi$
$997$			53.6506i			1.69913i	−0.527484	+	0.849565i	$0.676865\pi$
$998$		−	18.6809i		−	0.591333i
$999$	2.45397			0.0776401

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.b.b.139.1	✓	8
3.2	odd	2		2070.2.d.f.829.5		8
4.3	odd	2		1840.2.e.e.369.7		8
5.2	odd	4		1150.2.a.s.1.1		4
5.3	odd	4		1150.2.a.r.1.4		4
5.4	even	2	inner	230.2.b.b.139.8	yes	8
15.14	odd	2		2070.2.d.f.829.1		8
20.3	even	4		9200.2.a.cr.1.1		4
20.7	even	4		9200.2.a.cj.1.4		4
20.19	odd	2		1840.2.e.e.369.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.b.b.139.1	✓	8	1.1	even	1	trivial
230.2.b.b.139.8	yes	8	5.4	even	2	inner
1150.2.a.r.1.4		4	5.3	odd	4
1150.2.a.s.1.1		4	5.2	odd	4
1840.2.e.e.369.2		8	20.19	odd	2
1840.2.e.e.369.7		8	4.3	odd	2
2070.2.d.f.829.1		8	15.14	odd	2
2070.2.d.f.829.5		8	3.2	odd	2
9200.2.a.cj.1.4		4	20.7	even	4
9200.2.a.cr.1.1		4	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -2.40815i q^{3} -1.00000 q^{4} +(1.83051 - 1.28422i) q^{5} -2.40815 q^{6} -0.706585i q^{7} +1.00000i q^{8} -2.79917 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -2.40815i q^{3} -1.00000 q^{4} +(1.83051 - 1.28422i) q^{5} -2.40815 q^{6} -0.706585i q^{7} +1.00000i q^{8} -2.79917 q^{9} +(-1.28422 - 1.83051i) q^{10} +0.747120 q^{11} +2.40815i q^{12} +1.29341i q^{13} -0.706585 q^{14} +(-3.09259 - 4.40815i) q^{15} +1.00000 q^{16} +5.50074i q^{17} +2.79917i q^{18} -2.44868 q^{19} +(-1.83051 + 1.28422i) q^{20} -1.70156 q^{21} -0.747120i q^{22} +1.00000i q^{23} +2.40815 q^{24} +(1.70156 - 4.70156i) q^{25} +1.29341 q^{26} -0.483617i q^{27} +0.706585i q^{28} -5.72371 q^{29} +(-4.40815 + 3.09259i) q^{30} +7.52288 q^{31} -1.00000i q^{32} -1.79917i q^{33} +5.50074 q^{34} +(-0.907411 - 1.29341i) q^{35} +2.79917 q^{36} +5.07420i q^{37} +2.44868i q^{38} +3.11473 q^{39} +(1.28422 + 1.83051i) q^{40} +10.0876 q^{41} +1.70156i q^{42} -5.34045i q^{43} -0.747120 q^{44} +(-5.12393 + 3.59475i) q^{45} +1.00000 q^{46} -7.90888i q^{47} -2.40815i q^{48} +6.50074 q^{49} +(-4.70156 - 1.70156i) q^{50} +13.2466 q^{51} -1.29341i q^{52} +5.84621i q^{53} -0.483617 q^{54} +(1.36761 - 0.959466i) q^{55} +0.706585 q^{56} +5.89679i q^{57} +5.72371i q^{58} -12.4146 q^{59} +(3.09259 + 4.40815i) q^{60} +1.57346 q^{61} -7.52288i q^{62} +1.97786i q^{63} -1.00000 q^{64} +(1.66103 + 2.36761i) q^{65} -1.79917 q^{66} -5.25938i q^{67} -5.50074i q^{68} +2.40815 q^{69} +(-1.29341 + 0.907411i) q^{70} +2.68444 q^{71} -2.79917i q^{72} +10.4589i q^{73} +5.07420 q^{74} +(-11.3221 - 4.09761i) q^{75} +2.44868 q^{76} -0.527904i q^{77} -3.11473i q^{78} +6.55005 q^{79} +(1.83051 - 1.28422i) q^{80} -9.56214 q^{81} -10.0876i q^{82} +12.7068i q^{83} +1.70156 q^{84} +(7.06415 + 10.0692i) q^{85} -5.34045 q^{86} +13.7835i q^{87} +0.747120i q^{88} -13.6426 q^{89} +(3.59475 + 5.12393i) q^{90} +0.913908 q^{91} -1.00000i q^{92} -18.1162i q^{93} -7.90888 q^{94} +(-4.48235 + 3.14464i) q^{95} -2.40815 q^{96} -1.50074i q^{97} -6.50074i q^{98} -2.09132 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 6 q^{6} - 14 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 + 6 * q^6 - 14 * q^9	\( 8 q - 8 q^{4} + 6 q^{6} - 14 q^{9} + 10 q^{11} - 6 q^{14} - 16 q^{15} + 8 q^{16} + 2 q^{19} + 12 q^{21} - 6 q^{24} - 12 q^{25} + 10 q^{26} - 4 q^{29} - 10 q^{30} + 10 q^{31} + 10 q^{34} - 16 q^{35} + 14 q^{36} + 46 q^{41} - 10 q^{44} - 26 q^{45} + 8 q^{46} + 18 q^{49} - 12 q^{50} + 14 q^{51} - 12 q^{54} - 18 q^{55} + 6 q^{56} - 32 q^{59} + 16 q^{60} + 18 q^{61} - 8 q^{64} - 16 q^{65} - 6 q^{66} - 6 q^{69} - 10 q^{70} + 38 q^{71} + 12 q^{74} - 32 q^{75} - 2 q^{76} + 12 q^{79} + 32 q^{81} - 12 q^{84} - 24 q^{85} - 4 q^{86} - 60 q^{89} - 24 q^{90} - 26 q^{91} - 4 q^{94} + 18 q^{95} + 6 q^{96} + 54 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 + 6 * q^6 - 14 * q^9 + 10 * q^11 - 6 * q^14 - 16 * q^15 + 8 * q^16 + 2 * q^19 + 12 * q^21 - 6 * q^24 - 12 * q^25 + 10 * q^26 - 4 * q^29 - 10 * q^30 + 10 * q^31 + 10 * q^34 - 16 * q^35 + 14 * q^36 + 46 * q^41 - 10 * q^44 - 26 * q^45 + 8 * q^46 + 18 * q^49 - 12 * q^50 + 14 * q^51 - 12 * q^54 - 18 * q^55 + 6 * q^56 - 32 * q^59 + 16 * q^60 + 18 * q^61 - 8 * q^64 - 16 * q^65 - 6 * q^66 - 6 * q^69 - 10 * q^70 + 38 * q^71 + 12 * q^74 - 32 * q^75 - 2 * q^76 + 12 * q^79 + 32 * q^81 - 12 * q^84 - 24 * q^85 - 4 * q^86 - 60 * q^89 - 24 * q^90 - 26 * q^91 - 4 * q^94 + 18 * q^95 + 6 * q^96 + 54 * q^99

Introduction

L-functions

Modular forms

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