LMFDB - Embedded newform 230.2.b.b.139.3

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			139.3
Root			$-0.386289 + 0.386289i$ of defining polynomial
Character	$\chi$	$=$	230.139
Dual form			230.2.b.b.139.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.44270i q^{3} -1.00000 q^{4} +(-0.386289 - 2.20245i) q^{5} +1.44270 q^{6} -3.25886i q^{7} +1.00000i q^{8} +0.918614 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.44270i q^{3} -1.00000 q^{4} +(-0.386289 - 2.20245i) q^{5} +1.44270 q^{6} -3.25886i q^{7} +1.00000i q^{8} +0.918614 q^{9} +(-2.20245 + 0.386289i) q^{10} +1.32988 q^{11} -1.44270i q^{12} -1.25886i q^{13} -3.25886 q^{14} +(3.17748 - 0.557299i) q^{15} +1.00000 q^{16} -4.62018i q^{17} -0.918614i q^{18} +3.37169 q^{19} +(0.386289 + 2.20245i) q^{20} +4.70156 q^{21} -1.32988i q^{22} +1.00000i q^{23} -1.44270 q^{24} +(-4.70156 + 1.70156i) q^{25} -1.25886 q^{26} +5.65339i q^{27} +3.25886i q^{28} -4.29207 q^{29} +(-0.557299 - 3.17748i) q^{30} +2.37346 q^{31} -1.00000i q^{32} +1.91861i q^{33} -4.62018 q^{34} +(-7.17748 + 1.25886i) q^{35} -0.918614 q^{36} +5.74514i q^{37} -3.37169i q^{38} +1.81616 q^{39} +(2.20245 - 0.386289i) q^{40} -5.13790 q^{41} -4.70156i q^{42} +10.4678i q^{43} -1.32988 q^{44} +(-0.354850 - 2.02320i) q^{45} +1.00000 q^{46} +6.06288i q^{47} +1.44270i q^{48} -3.62018 q^{49} +(1.70156 + 4.70156i) q^{50} +6.66553 q^{51} +1.25886i q^{52} -11.1275i q^{53} +5.65339 q^{54} +(-0.513716 - 2.92898i) q^{55} +3.25886 q^{56} +4.86433i q^{57} +4.29207i q^{58} +2.72263 q^{59} +(-3.17748 + 0.557299i) q^{60} +12.3653 q^{61} -2.37346i q^{62} -2.99364i q^{63} -1.00000 q^{64} +(-2.77258 + 0.486284i) q^{65} +1.91861 q^{66} +6.60981i q^{67} +4.62018i q^{68} -1.44270 q^{69} +(1.25886 + 7.17748i) q^{70} +0.265226 q^{71} +0.918614i q^{72} +5.26464i q^{73} +5.74514 q^{74} +(-2.45485 - 6.78295i) q^{75} -3.37169 q^{76} -4.33388i q^{77} -1.81616i q^{78} +15.3275 q^{79} +(-0.386289 - 2.20245i) q^{80} -5.40031 q^{81} +5.13790i q^{82} -2.02566i q^{83} -4.70156 q^{84} +(-10.1757 + 1.78472i) q^{85} +10.4678 q^{86} -6.19218i q^{87} +1.32988i q^{88} -16.1500 q^{89} +(-2.02320 + 0.354850i) q^{90} -4.10245 q^{91} -1.00000i q^{92} +3.42419i q^{93} +6.06288 q^{94} +(-1.30244 - 7.42597i) q^{95} +1.44270 q^{96} +8.62018i q^{97} +3.62018i q^{98} +1.22164 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$			1.44270i			0.832944i	0.909149	+	0.416472i	$0.136734\pi$
$3$			1.44270i			0.832944i	−0.909149	+	0.416472i	$0.863266\pi$
$4$	−1.00000			−0.500000
$5$	−0.386289	−	2.20245i	−0.172754	−	0.984965i
$5$	−0.386289	−	2.20245i	−0.172754	−	0.984965i
$6$	1.44270			0.588980
$7$		−	3.25886i		−	1.23173i	−0.787850	−	0.615867i	$-0.788806\pi$
$7$		−	3.25886i		−	1.23173i	0.787850	−	0.615867i	$-0.211194\pi$
$8$			1.00000i			0.353553i
$9$	0.918614			0.306205
$10$	−2.20245	+	0.386289i	−0.696475	+	0.122155i
$11$	1.32988			0.400973			0.200486	−	0.979696i	$-0.435748\pi$
$11$	1.32988			0.400973			0.200486	+	0.979696i	$0.435748\pi$
$12$		−	1.44270i		−	0.416472i
$13$		−	1.25886i		−	0.349145i	−0.984644	−	0.174573i	$-0.944146\pi$
$13$		−	1.25886i		−	0.349145i	0.984644	−	0.174573i	$-0.0558544\pi$
$14$	−3.25886			−0.870967
$15$	3.17748	−	0.557299i	0.820421	−	0.143894i
$16$	1.00000			0.250000
$17$		−	4.62018i		−	1.12056i	−0.828304	−	0.560279i	$-0.810694\pi$
$17$		−	4.62018i		−	1.12056i	0.828304	−	0.560279i	$-0.189306\pi$
$18$		−	0.918614i		−	0.216519i
$19$	3.37169			0.773518			0.386759	−	0.922181i	$-0.373595\pi$
$19$	3.37169			0.773518			0.386759	+	0.922181i	$0.373595\pi$
$20$	0.386289	+	2.20245i	0.0863768	+	0.492483i
$21$	4.70156			1.02596
$22$		−	1.32988i		−	0.283531i
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	−1.44270			−0.294490
$25$	−4.70156	+	1.70156i	−0.940312	+	0.340312i
$26$	−1.25886			−0.246883
$27$			5.65339i			1.08800i
$28$			3.25886i			0.615867i
$29$	−4.29207			−0.797018			−0.398509	−	0.917164i	$-0.630472\pi$
$29$	−4.29207			−0.797018			−0.398509	+	0.917164i	$0.630472\pi$
$30$	−0.557299	−	3.17748i	−0.101748	−	0.580125i
$31$	2.37346			0.426286			0.213143	−	0.977021i	$-0.431630\pi$
$31$	2.37346			0.426286			0.213143	+	0.977021i	$0.431630\pi$
$32$		−	1.00000i		−	0.176777i
$33$			1.91861i			0.333988i
$34$	−4.62018			−0.792354
$35$	−7.17748	+	1.25886i	−1.21321	+	0.212786i
$36$	−0.918614			−0.153102
$37$			5.74514i			0.944496i	0.881466	+	0.472248i	$0.156557\pi$
$37$			5.74514i			0.944496i	−0.881466	+	0.472248i	$0.843443\pi$
$38$		−	3.37169i		−	0.546960i
$39$	1.81616			0.290818
$40$	2.20245	−	0.386289i	0.348238	−	0.0610776i
$41$	−5.13790			−0.802405			−0.401202	−	0.915989i	$-0.631408\pi$
$41$	−5.13790			−0.802405			−0.401202	+	0.915989i	$0.631408\pi$
$42$		−	4.70156i		−	0.725467i
$43$			10.4678i			1.59632i	0.602445	+	0.798160i	$0.294193\pi$
$43$			10.4678i			1.59632i	−0.602445	+	0.798160i	$0.705807\pi$
$44$	−1.32988			−0.200486
$45$	−0.354850	−	2.02320i	−0.0528979	−	0.301601i
$46$	1.00000			0.147442
$47$			6.06288i			0.884362i	0.896926	+	0.442181i	$0.145795\pi$
$47$			6.06288i			0.884362i	−0.896926	+	0.442181i	$0.854205\pi$
$48$			1.44270i			0.208236i
$49$	−3.62018			−0.517168
$50$	1.70156	+	4.70156i	0.240637	+	0.664901i
$51$	6.66553			0.933361
$52$			1.25886i			0.174573i
$53$		−	11.1275i		−	1.52848i	−0.644930	−	0.764242i	$-0.723113\pi$
$53$		−	11.1275i		−	1.52848i	0.644930	−	0.764242i	$-0.276887\pi$
$54$	5.65339			0.769329
$55$	−0.513716	−	2.92898i	−0.0692695	−	0.394944i
$56$	3.25886			0.435484
$57$			4.86433i			0.644297i
$58$			4.29207i			0.563577i
$59$	2.72263			0.354456			0.177228	−	0.984170i	$-0.443287\pi$
$59$	2.72263			0.354456			0.177228	+	0.984170i	$0.443287\pi$
$60$	−3.17748	+	0.557299i	−0.410210	+	0.0719470i
$61$	12.3653			1.58322			0.791609	−	0.611029i	$-0.209244\pi$
$61$	12.3653			1.58322			0.791609	+	0.611029i	$0.209244\pi$
$62$		−	2.37346i		−	0.301430i
$63$		−	2.99364i		−	0.377163i
$64$	−1.00000			−0.125000
$65$	−2.77258	+	0.486284i	−0.343896	+	0.0603161i
$66$	1.91861			0.236165
$67$			6.60981i			0.807516i	0.914866	+	0.403758i	$0.132296\pi$
$67$			6.60981i			0.807516i	−0.914866	+	0.403758i	$0.867704\pi$
$68$			4.62018i			0.560279i
$69$	−1.44270			−0.173681
$70$	1.25886	+	7.17748i	0.150463	+	0.857872i
$71$	0.265226			0.0314765			0.0157383	−	0.999876i	$-0.494990\pi$
$71$	0.265226			0.0314765			0.0157383	+	0.999876i	$0.494990\pi$
$72$			0.918614i			0.108260i
$73$			5.26464i			0.616180i	0.951357	+	0.308090i	$0.0996897\pi$
$73$			5.26464i			0.616180i	−0.951357	+	0.308090i	$0.900310\pi$
$74$	5.74514			0.667860
$75$	−2.45485	−	6.78295i	−0.283461	−	0.783227i
$76$	−3.37169			−0.386759
$77$		−	4.33388i		−	0.493892i
$78$		−	1.81616i		−	0.205640i
$79$	15.3275			1.72448			0.862240	−	0.506500i	$-0.169061\pi$
$79$	15.3275			1.72448			0.862240	+	0.506500i	$0.169061\pi$
$80$	−0.386289	−	2.20245i	−0.0431884	−	0.246241i
$81$	−5.40031			−0.600034
$82$			5.13790i			0.567386i
$83$		−	2.02566i		−	0.222345i	−0.993801	−	0.111172i	$-0.964539\pi$
$83$		−	2.02566i		−	0.222345i	0.993801	−	0.111172i	$-0.0354606\pi$
$84$	−4.70156			−0.512982
$85$	−10.1757	+	1.78472i	−1.10371	+	0.193580i
$86$	10.4678			1.12877
$87$		−	6.19218i		−	0.663871i
$88$			1.32988i			0.141765i
$89$	−16.1500			−1.71190			−0.855951	−	0.517058i	$-0.827027\pi$
$89$	−16.1500			−1.71190			−0.855951	+	0.517058i	$0.827027\pi$
$90$	−2.02320	+	0.354850i	−0.213264	+	0.0374045i
$91$	−4.10245			−0.430054
$92$		−	1.00000i		−	0.104257i
$93$			3.42419i			0.355072i
$94$	6.06288			0.625338
$95$	−1.30244	−	7.42597i	−0.133628	−	0.761888i
$96$	1.44270			0.147245
$97$			8.62018i			0.875246i	0.899158	+	0.437623i	$0.144180\pi$
$97$			8.62018i			0.875246i	−0.899158	+	0.437623i	$0.855820\pi$
$98$			3.62018i			0.365693i
$99$	1.22164			0.122780
$100$	4.70156	−	1.70156i	0.470156	−	0.170156i
$101$	14.4934			1.44215			0.721075	−	0.692857i	$-0.243648\pi$
$101$	14.4934			1.44215			0.721075	+	0.692857i	$0.243648\pi$
$102$		−	6.66553i		−	0.659986i
$103$		−	18.5410i		−	1.82690i	−0.406950	−	0.913451i	$-0.633408\pi$
$103$		−	18.5410i		−	1.82690i	0.406950	−	0.913451i	$-0.366592\pi$
$104$	1.25886			0.123441
$105$	−1.81616	−	10.3550i	−0.177239	−	1.01054i
$106$	−11.1275			−1.08080
$107$			4.48050i			0.433147i	0.976266	+	0.216573i	$0.0694880\pi$
$107$			4.48050i			0.433147i	−0.976266	+	0.216573i	$0.930512\pi$
$108$		−	5.65339i		−	0.543998i
$109$	−17.1298			−1.64073			−0.820367	−	0.571838i	$-0.806231\pi$
$109$	−17.1298			−1.64073			−0.820367	+	0.571838i	$0.806231\pi$
$110$	−2.92898	+	0.513716i	−0.279268	+	0.0489809i
$111$	−8.28853			−0.786712
$112$		−	3.25886i		−	0.307933i
$113$		−	9.77435i		−	0.919494i	−0.888050	−	0.459747i	$-0.847940\pi$
$113$		−	9.77435i		−	0.919494i	0.888050	−	0.459747i	$-0.152060\pi$
$114$	4.86433			0.455587
$115$	2.20245	−	0.386289i	0.205379	−	0.0360216i
$116$	4.29207			0.398509
$117$		−	1.15641i		−	0.106910i
$118$		−	2.72263i		−	0.250638i
$119$	−15.0565			−1.38023
$120$	0.557299	+	3.17748i	0.0508742	+	0.290062i
$121$	−9.23143			−0.839221
$122$		−	12.3653i		−	1.11950i
$123$		−	7.41245i		−	0.668358i
$124$	−2.37346			−0.213143
$125$	5.56376	+	9.69766i	0.497638	+	0.867385i
$126$	−2.99364			−0.266694
$127$		−	1.02743i		−	0.0911699i	−0.998960	−	0.0455849i	$-0.985485\pi$
$127$		−	1.02743i		−	0.0911699i	0.998960	−	0.0455849i	$-0.0145152\pi$
$128$			1.00000i			0.0883883i
$129$	−15.1019			−1.32965
$130$	0.486284	+	2.77258i	0.0426499	+	0.243171i
$131$	12.2885			1.07365			0.536827	−	0.843692i	$-0.319623\pi$
$131$	12.2885			1.07365			0.536827	+	0.843692i	$0.319623\pi$
$132$		−	1.91861i		−	0.166994i
$133$		−	10.9879i		−	0.952768i
$134$	6.60981			0.571000
$135$	12.4513	−	2.18384i	1.07164	−	0.187955i
$136$	4.62018			0.396177
$137$			8.82830i			0.754253i	0.926162	+	0.377126i	$0.123088\pi$
$137$			8.82830i			0.754253i	−0.926162	+	0.377126i	$0.876912\pi$
$138$			1.44270i			0.122811i
$139$	11.5532			0.979927			0.489963	−	0.871743i	$-0.337010\pi$
$139$	11.5532			0.979927			0.489963	+	0.871743i	$0.337010\pi$
$140$	7.17748	−	1.25886i	0.606607	−	0.106393i
$141$	−8.74692			−0.736623
$142$		−	0.265226i		−	0.0222573i
$143$		−	1.67413i		−	0.139998i
$144$	0.918614			0.0765512
$145$	1.65798	+	9.45307i	0.137688	+	0.785035i
$146$	5.26464			0.435705
$147$		−	5.22283i		−	0.430772i
$148$		−	5.74514i		−	0.472248i
$149$	11.1333			0.912076			0.456038	−	0.889960i	$-0.349268\pi$
$149$	11.1333			0.912076			0.456038	+	0.889960i	$0.349268\pi$
$150$	−6.78295	+	2.45485i	−0.553825	+	0.200437i
$151$	−3.23779			−0.263488			−0.131744	−	0.991284i	$-0.542058\pi$
$151$	−3.23779			−0.263488			−0.131744	+	0.991284i	$0.542058\pi$
$152$			3.37169i			0.273480i
$153$		−	4.24416i		−	0.343120i
$154$	−4.33388			−0.349234
$155$	−0.916840	−	5.22742i	−0.0736424	−	0.419877i
$156$	−1.81616			−0.145409
$157$			17.6452i			1.40824i	0.710079	+	0.704122i	$0.248659\pi$
$157$			17.6452i			1.40824i	−0.710079	+	0.704122i	$0.751341\pi$
$158$		−	15.3275i		−	1.21939i
$159$	16.0537			1.27314
$160$	−2.20245	+	0.386289i	−0.174119	+	0.0305388i
$161$	3.25886			0.256834
$162$			5.40031i			0.424288i
$163$			12.2107i			0.956415i	0.878247	+	0.478207i	$0.158713\pi$
$163$			12.2107i			0.956415i	−0.878247	+	0.478207i	$0.841287\pi$
$164$	5.13790			0.401202
$165$	4.22565	−	0.741139i	0.328966	−	0.0576976i
$166$	−2.02566			−0.157222
$167$		−	2.06288i		−	0.159630i	−0.996810	−	0.0798151i	$-0.974567\pi$
$167$		−	2.06288i		−	0.159630i	0.996810	−	0.0798151i	$-0.0254330\pi$
$168$			4.70156i			0.362733i
$169$	11.4153			0.878098
$170$	1.78472	+	10.1757i	0.136882	+	0.780441i
$171$	3.09728			0.236855
$172$		−	10.4678i		−	0.798160i
$173$		−	2.10245i		−	0.159847i	−0.996801	−	0.0799233i	$-0.974532\pi$
$173$		−	2.10245i		−	0.159847i	0.996801	−	0.0799233i	$-0.0254675\pi$
$174$	−6.19218			−0.469428
$175$	5.54515	+	15.3217i	0.419174	+	1.15821i
$176$	1.32988			0.100243
$177$			3.92794i			0.295242i
$178$			16.1500i			1.21050i
$179$	−20.4421			−1.52792			−0.763958	−	0.645266i	$-0.776746\pi$
$179$	−20.4421			−1.52792			−0.763958	+	0.645266i	$0.776746\pi$
$180$	0.354850	+	2.02320i	0.0264490	+	0.150800i
$181$	−7.12175			−0.529355			−0.264678	−	0.964337i	$-0.585266\pi$
$181$	−7.12175			−0.529355			−0.264678	+	0.964337i	$0.585266\pi$
$182$			4.10245i			0.304094i
$183$			17.8395i			1.31873i
$184$	−1.00000			−0.0737210
$185$	12.6534	−	2.21928i	0.930296	−	0.163165i
$186$	3.42419			0.251074
$187$		−	6.14426i		−	0.449313i
$188$		−	6.06288i		−	0.442181i
$189$	18.4236			1.34012
$190$	−7.42597	+	1.30244i	−0.538736	+	0.0944892i
$191$	−16.7191			−1.20975			−0.604875	−	0.796320i	$-0.706777\pi$
$191$	−16.7191			−1.20975			−0.604875	+	0.796320i	$0.706777\pi$
$192$		−	1.44270i		−	0.104118i
$193$		−	6.51772i		−	0.469156i	−0.972097	−	0.234578i	$-0.924629\pi$
$193$		−	6.51772i		−	0.469156i	0.972097	−	0.234578i	$-0.0753708\pi$
$194$	8.62018			0.618893
$195$	−0.701562	−	4.00000i	−0.0502399	−	0.286446i
$196$	3.62018			0.258584
$197$		−	17.8184i		−	1.26951i	−0.772714	−	0.634754i	$-0.781101\pi$
$197$		−	17.8184i		−	1.26951i	0.772714	−	0.634754i	$-0.218899\pi$
$198$		−	1.22164i		−	0.0868184i
$199$	3.77435			0.267557			0.133778	−	0.991011i	$-0.457289\pi$
$199$	3.77435			0.267557			0.133778	+	0.991011i	$0.457289\pi$
$200$	−1.70156	−	4.70156i	−0.120319	−	0.332451i
$201$	−9.53597			−0.672616
$202$		−	14.4934i		−	1.01975i
$203$			13.9873i			0.981714i
$204$	−6.66553			−0.466681
$205$	1.98471	+	11.3160i	0.138618	+	0.790341i
$206$	−18.5410			−1.29181
$207$			0.918614i			0.0638481i
$208$		−	1.25886i		−	0.0872863i
$209$	4.48393			0.310160
$210$	−10.3550	+	1.81616i	−0.714559	+	0.125327i
$211$	−23.9630			−1.64968			−0.824840	−	0.565366i	$-0.808735\pi$
$211$	−23.9630			−1.64968			−0.824840	+	0.565366i	$0.808735\pi$
$212$			11.1275i			0.764242i
$213$			0.382642i			0.0262182i
$214$	4.48050			0.306281
$215$	23.0547	−	4.04358i	1.57232	−	0.275770i
$216$	−5.65339			−0.384664
$217$		−	7.73477i		−	0.525071i
$218$			17.1298i			1.16017i
$219$	−7.59530			−0.513243
$220$	0.513716	+	2.92898i	0.0346347	+	0.197472i
$221$	−5.81616			−0.391237
$222$			8.28853i			0.556289i
$223$			20.2094i			1.35332i	0.736296	+	0.676660i	$0.236573\pi$
$223$			20.2094i			1.35332i	−0.736296	+	0.676660i	$0.763427\pi$
$224$	−3.25886			−0.217742
$225$	−4.31892	+	1.56308i	−0.287928	+	0.104205i
$226$	−9.77435			−0.650180
$227$			1.60666i			0.106638i	0.998578	+	0.0533189i	$0.0169800\pi$
$227$			1.60666i			0.106638i	−0.998578	+	0.0533189i	$0.983020\pi$
$228$		−	4.86433i		−	0.322148i
$229$	18.9019			1.24907			0.624536	−	0.780996i	$-0.285288\pi$
$229$	18.9019			1.24907			0.624536	+	0.780996i	$0.285288\pi$
$230$	−0.386289	−	2.20245i	−0.0254711	−	0.145225i
$231$	6.25250			0.411384
$232$		−	4.29207i		−	0.281788i
$233$		−	19.0112i		−	1.24546i	−0.782436	−	0.622731i	$-0.786023\pi$
$233$		−	19.0112i		−	1.24546i	0.782436	−	0.622731i	$-0.213977\pi$
$234$	−1.15641			−0.0755967
$235$	13.3532	−	2.34202i	0.871065	−	0.152777i
$236$	−2.72263			−0.177228
$237$			22.1130i			1.43640i
$238$			15.0565i			0.975969i
$239$	−28.3387			−1.83308			−0.916538	−	0.399947i	$-0.869028\pi$
$239$	−28.3387			−1.83308			−0.916538	+	0.399947i	$0.869028\pi$
$240$	3.17748	−	0.557299i	0.205105	−	0.0359735i
$241$	6.35140			0.409130			0.204565	−	0.978853i	$-0.434422\pi$
$241$	6.35140			0.409130			0.204565	+	0.978853i	$0.434422\pi$
$242$			9.23143i			0.593419i
$243$			9.16914i			0.588200i
$244$	−12.3653			−0.791609
$245$	1.39843	+	7.97325i	0.0893426	+	0.509392i
$246$	−7.41245			−0.472601
$247$		−	4.24448i		−	0.270070i
$248$			2.37346i			0.150715i
$249$	2.92242			0.185201
$250$	9.69766	−	5.56376i	0.613334	−	0.351883i
$251$	19.7231			1.24491			0.622455	−	0.782655i	$-0.286135\pi$
$251$	19.7231			1.24491			0.622455	+	0.782655i	$0.286135\pi$
$252$			2.99364i			0.188581i
$253$			1.32988i			0.0836086i
$254$	−1.02743			−0.0644668
$255$	−2.57482	−	14.6805i	−0.161241	−	0.919328i
$256$	1.00000			0.0625000
$257$		−	1.18102i		−	0.0736701i	−0.999321	−	0.0368351i	$-0.988272\pi$
$257$		−	1.18102i		−	0.0736701i	0.999321	−	0.0368351i	$-0.0117276\pi$
$258$			15.1019i			0.940201i
$259$	18.7226			1.16337
$260$	2.77258	−	0.486284i	0.171948	−	0.0301580i
$261$	−3.94276			−0.244051
$262$		−	12.2885i		−	0.759188i
$263$			24.3189i			1.49957i	0.661682	+	0.749784i	$0.269843\pi$
$263$			24.3189i			1.49957i	−0.661682	+	0.749784i	$0.730157\pi$
$264$	−1.91861			−0.118083
$265$	−24.5078	+	4.29844i	−1.50550	+	0.264051i
$266$	−10.9879			−0.673709
$267$		−	23.2997i		−	1.42592i
$268$		−	6.60981i		−	0.403758i
$269$	−7.91283			−0.482454			−0.241227	−	0.970469i	$-0.577550\pi$
$269$	−7.91283			−0.482454			−0.241227	+	0.970469i	$0.577550\pi$
$270$	−2.18384	−	12.4513i	−0.132904	−	0.757762i
$271$	−18.2979			−1.11152			−0.555758	−	0.831344i	$-0.687572\pi$
$271$	−18.2979			−1.11152			−0.555758	+	0.831344i	$0.687572\pi$
$272$		−	4.62018i		−	0.280139i
$273$		−	5.91861i		−	0.358211i
$274$	8.82830			0.533337
$275$	−6.25250	+	2.26287i	−0.377040	+	0.136456i
$276$	1.44270			0.0868404
$277$		−	28.6550i		−	1.72171i	−0.508847	−	0.860857i	$-0.669928\pi$
$277$		−	28.6550i		−	1.72171i	0.508847	−	0.860857i	$-0.330072\pi$
$278$		−	11.5532i		−	0.692913i
$279$	2.18029			0.130531
$280$	−1.25886	−	7.17748i	−0.0752313	−	0.428936i
$281$	2.74692			0.163867			0.0819337	−	0.996638i	$-0.473890\pi$
$281$	2.74692			0.163867			0.0819337	+	0.996638i	$0.473890\pi$
$282$			8.74692i			0.520871i
$283$		−	5.45307i		−	0.324151i	−0.986778	−	0.162076i	$-0.948181\pi$
$283$		−	5.45307i		−	0.324151i	0.986778	−	0.162076i	$-0.0518189\pi$
$284$	−0.265226			−0.0157383
$285$	10.7134	−	1.87904i	0.634610	−	0.111305i
$286$	−1.67413			−0.0989934
$287$			16.7437i			0.988349i
$288$		−	0.918614i		−	0.0541298i
$289$	−4.34603			−0.255649
$290$	9.45307	−	1.65798i	0.555103	−	0.0973599i
$291$	−12.4363			−0.729031
$292$		−	5.26464i		−	0.308090i
$293$			18.3806i			1.07381i	0.843644	+	0.536903i	$0.180406\pi$
$293$			18.3806i			1.07381i	−0.843644	+	0.536903i	$0.819594\pi$
$294$	−5.22283			−0.304602
$295$	−1.05172	−	5.99645i	−0.0612336	−	0.349127i
$296$	−5.74514			−0.333930
$297$			7.51831i			0.436256i
$298$		−	11.1333i		−	0.644935i
$299$	1.25886			0.0728018
$300$	2.45485	+	6.78295i	0.141731	+	0.391614i
$301$	34.1130			1.96624
$302$			3.23779i			0.186314i
$303$			20.9097i			1.20123i
$304$	3.37169			0.193379
$305$	−4.77658	−	27.2340i	−0.273506	−	1.55941i
$306$	−4.24416			−0.242622
$307$			15.9234i			0.908797i	0.890799	+	0.454398i	$0.150146\pi$
$307$			15.9234i			0.908797i	−0.890799	+	0.454398i	$0.849854\pi$
$308$			4.33388i			0.246946i
$309$	26.7492			1.52171
$310$	−5.22742	+	0.916840i	−0.296898	+	0.0520730i
$311$	−11.3518			−0.643702			−0.321851	−	0.946790i	$-0.604305\pi$
$311$	−11.3518			−0.643702			−0.321851	+	0.946790i	$0.604305\pi$
$312$			1.81616i			0.102820i
$313$		−	28.7913i		−	1.62738i	−0.581299	−	0.813690i	$-0.697455\pi$
$313$		−	28.7913i		−	1.62738i	0.581299	−	0.813690i	$-0.302545\pi$
$314$	17.6452			0.995779
$315$	−6.59333	+	1.15641i	−0.371492	+	0.0651562i
$316$	−15.3275			−0.862240
$317$			31.2299i			1.75404i	0.480451	+	0.877022i	$0.340473\pi$
$317$			31.2299i			1.75404i	−0.480451	+	0.877022i	$0.659527\pi$
$318$		−	16.0537i		−	0.900246i
$319$	−5.70793			−0.319583
$320$	0.386289	+	2.20245i	0.0215942	+	0.123121i
$321$	−6.46403			−0.360787
$322$		−	3.25886i		−	0.181609i
$323$		−	15.5778i		−	0.866771i
$324$	5.40031			0.300017
$325$	2.14203	+	5.91861i	0.118818	+	0.328306i
$326$	12.2107			0.676287
$327$		−	24.7131i		−	1.36664i
$328$		−	5.13790i		−	0.283693i
$329$	19.7581			1.08930
$330$	−0.741139	−	4.22565i	−0.0407984	−	0.232614i
$331$	17.6917			0.972421			0.486211	−	0.873842i	$-0.338379\pi$
$331$	17.6917			0.972421			0.486211	+	0.873842i	$0.338379\pi$
$332$			2.02566i			0.111172i
$333$			5.27757i			0.289209i
$334$	−2.06288			−0.112876
$335$	14.5578	−	2.55329i	0.795375	−	0.139501i
$336$	4.70156			0.256491
$337$			1.33801i			0.0728863i	0.999336	+	0.0364431i	$0.0116028\pi$
$337$			1.33801i			0.0728863i	−0.999336	+	0.0364431i	$0.988397\pi$
$338$		−	11.4153i		−	0.620909i
$339$	14.1015			0.765886
$340$	10.1757	−	1.78472i	0.551855	−	0.0967901i
$341$	3.15641			0.170929
$342$		−	3.09728i		−	0.167482i
$343$		−	11.0144i		−	0.594720i
$344$	−10.4678			−0.564385
$345$	0.557299	+	3.17748i	0.0300040	+	0.171070i
$346$	−2.10245			−0.113029
$347$			5.36355i			0.287930i	0.989583	+	0.143965i	$0.0459853\pi$
$347$			5.36355i			0.287930i	−0.989583	+	0.143965i	$0.954015\pi$
$348$			6.19218i			0.331936i
$349$	18.4306			0.986565			0.493283	−	0.869869i	$-0.335797\pi$
$349$	18.4306			0.986565			0.493283	+	0.869869i	$0.335797\pi$
$350$	15.3217	−	5.54515i	0.818981	−	0.296401i
$351$	7.11683			0.379868
$352$		−	1.32988i		−	0.0708826i
$353$			6.76477i			0.360052i	0.983662	+	0.180026i	$0.0576182\pi$
$353$			6.76477i			0.360052i	−0.983662	+	0.180026i	$0.942382\pi$
$354$	3.92794			0.208768
$355$	−0.102454	−	0.584146i	−0.00543768	−	0.0310033i
$356$	16.1500			0.855951
$357$		−	21.7220i		−	1.14965i
$358$			20.4421i			1.08040i
$359$	−27.5324			−1.45311			−0.726553	−	0.687111i	$-0.758879\pi$
$359$	−27.5324			−1.45311			−0.726553	+	0.687111i	$0.758879\pi$
$360$	2.02320	−	0.354850i	0.106632	−	0.0187022i
$361$	−7.63174			−0.401670
$362$			7.12175i			0.374311i
$363$		−	13.3182i		−	0.699024i
$364$	4.10245			0.215027
$365$	11.5951	−	2.03367i	0.606915	−	0.106447i
$366$	17.8395			0.932484
$367$		−	24.0744i		−	1.25668i	−0.777941	−	0.628338i	$-0.783736\pi$
$367$		−	24.0744i		−	1.25668i	0.777941	−	0.628338i	$-0.216264\pi$
$368$			1.00000i			0.0521286i
$369$	−4.71975			−0.245700
$370$	−2.21928	−	12.6534i	−0.115375	−	0.657818i
$371$	−36.2631			−1.88268
$372$		−	3.42419i		−	0.177536i
$373$		−	1.31459i		−	0.0680668i	−0.999421	−	0.0340334i	$-0.989165\pi$
$373$		−	1.31459i		−	0.0680668i	0.999421	−	0.0340334i	$-0.0108353\pi$
$374$	−6.14426			−0.317712
$375$	−13.9908	+	8.02685i	−0.722483	+	0.414505i
$376$	−6.06288			−0.312669
$377$			5.40312i			0.278275i
$378$		−	18.4236i		−	0.947608i
$379$	−8.38961			−0.430945			−0.215473	−	0.976510i	$-0.569129\pi$
$379$	−8.38961			−0.430945			−0.215473	+	0.976510i	$0.569129\pi$
$380$	1.30244	+	7.42597i	0.0668140	+	0.380944i
$381$	1.48228			0.0759394
$382$			16.7191i			0.855423i
$383$		−	24.1258i		−	1.23277i	−0.787446	−	0.616384i	$-0.788597\pi$
$383$		−	24.1258i		−	1.23277i	0.787446	−	0.616384i	$-0.211403\pi$
$384$	−1.44270			−0.0736225
$385$	−9.54515	+	1.67413i	−0.486466	+	0.0853216i
$386$	−6.51772			−0.331743
$387$			9.61584i			0.488801i
$388$		−	8.62018i		−	0.437623i
$389$	−12.5702			−0.637336			−0.318668	−	0.947866i	$-0.603235\pi$
$389$	−12.5702			−0.637336			−0.318668	+	0.947866i	$0.603235\pi$
$390$	−4.00000	+	0.701562i	−0.202548	+	0.0355250i
$391$	4.62018			0.233652
$392$		−	3.62018i		−	0.182847i
$393$			17.7287i			0.894293i
$394$	−17.8184			−0.897678
$395$	−5.92085	−	33.7581i	−0.297910	−	1.69855i
$396$	−1.22164			−0.0613899
$397$		−	28.5318i		−	1.43197i	−0.698115	−	0.715986i	$-0.745977\pi$
$397$		−	28.5318i		−	1.43197i	0.698115	−	0.715986i	$-0.254023\pi$
$398$		−	3.77435i		−	0.189191i
$399$	15.8522			0.793602
$400$	−4.70156	+	1.70156i	−0.235078	+	0.0850781i
$401$	−19.7130			−0.984422			−0.492211	−	0.870476i	$-0.663811\pi$
$401$	−19.7130			−0.984422			−0.492211	+	0.870476i	$0.663811\pi$
$402$			9.53597i			0.475611i
$403$		−	2.98786i		−	0.148836i
$404$	−14.4934			−0.721075
$405$	2.08608	+	11.8939i	0.103658	+	0.591013i
$406$	13.9873			0.694177
$407$			7.64033i			0.378717i
$408$			6.66553i			0.329993i
$409$	−20.3400			−1.00575			−0.502874	−	0.864360i	$-0.667724\pi$
$409$	−20.3400			−1.00575			−0.502874	+	0.864360i	$0.667724\pi$
$410$	11.3160	−	1.98471i	0.558855	−	0.0980179i
$411$	−12.7366			−0.628250
$412$			18.5410i			0.913451i
$413$		−	8.87267i		−	0.436596i
$414$	0.918614			0.0451474
$415$	−4.46141	+	0.782489i	−0.219002	+	0.0384109i
$416$	−1.25886			−0.0617207
$417$			16.6678i			0.816224i
$418$		−	4.48393i		−	0.219316i
$419$	−9.91146			−0.484207			−0.242103	−	0.970250i	$-0.577837\pi$
$419$	−9.91146			−0.484207			−0.242103	+	0.970250i	$0.577837\pi$
$420$	1.81616	+	10.3550i	0.0886195	+	0.505270i
$421$	−28.7927			−1.40327			−0.701634	−	0.712537i	$-0.747546\pi$
$421$	−28.7927			−1.40327			−0.701634	+	0.712537i	$0.747546\pi$
$422$			23.9630i			1.16650i
$423$			5.56944i			0.270796i
$424$	11.1275			0.540401
$425$	7.86152	+	21.7220i	0.381340	+	1.05367i
$426$	0.382642			0.0185390
$427$		−	40.2969i		−	1.95010i
$428$		−	4.48050i		−	0.216573i
$429$	2.41527			0.116610
$430$	−4.04358	−	23.0547i	−0.194999	−	1.11180i
$431$	36.6821			1.76691			0.883456	−	0.468513i	$-0.155210\pi$
$431$	36.6821			1.76691			0.883456	+	0.468513i	$0.155210\pi$
$432$			5.65339i			0.271999i
$433$		−	29.6894i		−	1.42678i	−0.700766	−	0.713391i	$-0.747158\pi$
$433$		−	29.6894i		−	1.42678i	0.700766	−	0.713391i	$-0.252842\pi$
$434$	−7.73477			−0.371281
$435$	−13.6380	+	2.39197i	−0.653890	+	0.114686i
$436$	17.1298			0.820367
$437$			3.37169i			0.161290i
$438$			7.59530i			0.362918i
$439$	−34.5378			−1.64840			−0.824200	−	0.566299i	$-0.808375\pi$
$439$	−34.5378			−1.64840			−0.824200	+	0.566299i	$0.808375\pi$
$440$	2.92898	−	0.513716i	0.139634	−	0.0244905i
$441$	−3.32554			−0.158359
$442$			5.81616i			0.276647i
$443$			36.6735i			1.74241i	0.490917	+	0.871206i	$0.336662\pi$
$443$			36.6735i			1.74241i	−0.490917	+	0.871206i	$0.663338\pi$
$444$	8.28853			0.393356
$445$	6.23858	+	35.5696i	0.295737	+	1.68616i
$446$	20.2094			0.956942
$447$			16.0620i			0.759708i
$448$			3.25886i			0.153967i
$449$	13.2138			0.623599			0.311800	−	0.950148i	$-0.399068\pi$
$449$	13.2138			0.623599			0.311800	+	0.950148i	$0.399068\pi$
$450$	1.56308	+	4.31892i	0.0736842	+	0.203596i
$451$	−6.83277			−0.321743
$452$			9.77435i			0.459747i
$453$		−	4.67117i		−	0.219471i
$454$	1.60666			0.0754044
$455$	1.58473	+	9.03544i	0.0742934	+	0.423588i
$456$	−4.86433			−0.227793
$457$			12.2292i			0.572058i	0.958221	+	0.286029i	$0.0923353\pi$
$457$			12.2292i			0.572058i	−0.958221	+	0.286029i	$0.907665\pi$
$458$		−	18.9019i		−	0.883227i
$459$	26.1196			1.21916
$460$	−2.20245	+	0.386289i	−0.102690	+	0.0180108i
$461$	24.0872			1.12185			0.560926	−	0.827866i	$-0.310445\pi$
$461$	24.0872			1.12185			0.560926	+	0.827866i	$0.310445\pi$
$462$		−	6.25250i		−	0.290892i
$463$			15.9173i			0.739740i	0.929084	+	0.369870i	$0.120598\pi$
$463$			15.9173i			0.739740i	−0.929084	+	0.369870i	$0.879402\pi$
$464$	−4.29207			−0.199254
$465$	7.54161	−	1.32273i	0.349734	−	0.0613400i
$466$	−19.0112			−0.880675
$467$		−	9.70011i		−	0.448868i	−0.974489	−	0.224434i	$-0.927947\pi$
$467$		−	9.70011i		−	0.448868i	0.974489	−	0.224434i	$-0.0720533\pi$
$468$			1.15641i			0.0534550i
$469$	21.5404			0.994645
$470$	−2.34202	−	13.3532i	−0.108029	−	0.615936i
$471$	−25.4568			−1.17299
$472$			2.72263i			0.125319i
$473$			13.9208i			0.640081i
$474$	22.1130			1.01568
$475$	−15.8522	+	5.73713i	−0.727348	+	0.263238i
$476$	15.0565			0.690114
$477$		−	10.2219i		−	0.468029i
$478$			28.3387i			1.29618i
$479$	−14.1385			−0.646004			−0.323002	−	0.946398i	$-0.604692\pi$
$479$	−14.1385			−0.646004			−0.323002	+	0.946398i	$0.604692\pi$
$480$	−0.557299	−	3.17748i	−0.0254371	−	0.145031i
$481$	7.23234			0.329766
$482$		−	6.35140i		−	0.289298i
$483$			4.70156i			0.213928i
$484$	9.23143			0.419610
$485$	18.9855	−	3.32988i	0.862087	−	0.151202i
$486$	9.16914			0.415920
$487$		−	3.75006i		−	0.169932i	−0.996384	−	0.0849658i	$-0.972922\pi$
$487$		−	3.75006i		−	0.169932i	0.996384	−	0.0849658i	$-0.0270781\pi$
$488$			12.3653i			0.559752i
$489$	−17.6164			−0.796640
$490$	7.97325	−	1.39843i	0.360195	−	0.0631748i
$491$	−3.19020			−0.143972			−0.0719860	−	0.997406i	$-0.522934\pi$
$491$	−3.19020			−0.143972			−0.0719860	+	0.997406i	$0.522934\pi$
$492$			7.41245i			0.334179i
$493$			19.8301i			0.893104i
$494$	−4.24448			−0.190968
$495$	−0.471907	−	2.69061i	−0.0212106	−	0.120934i
$496$	2.37346			0.106571
$497$		−	0.864334i		−	0.0387707i
$498$		−	2.92242i		−	0.130957i
$499$	−12.9355			−0.579075			−0.289537	−	0.957167i	$-0.593501\pi$
$499$	−12.9355			−0.579075			−0.289537	+	0.957167i	$0.593501\pi$
$500$	−5.56376	−	9.69766i	−0.248819	−	0.433692i
$501$	2.97611			0.132963
$502$		−	19.7231i		−	0.880285i
$503$			15.8845i			0.708254i	0.935197	+	0.354127i	$0.115222\pi$
$503$			15.8845i			0.708254i	−0.935197	+	0.354127i	$0.884778\pi$
$504$	2.99364			0.133347
$505$	−5.59865	−	31.9210i	−0.249137	−	1.42047i
$506$	1.32988			0.0591202
$507$			16.4688i			0.731406i
$508$			1.02743i			0.0455849i
$509$	−22.6470			−1.00381			−0.501906	−	0.864922i	$-0.667368\pi$
$509$	−22.6470			−1.00381			−0.501906	+	0.864922i	$0.667368\pi$
$510$	−14.6805	+	2.57482i	−0.650063	+	0.114015i
$511$	17.1567			0.758969
$512$		−	1.00000i		−	0.0441942i
$513$			19.0614i			0.841583i
$514$	−1.18102			−0.0520927
$515$	−40.8357	+	7.16219i	−1.79943	+	0.315604i
$516$	15.1019			0.664823
$517$			8.06288i			0.354605i
$518$		−	18.7226i		−	0.822625i
$519$	3.03321			0.133143
$520$	−0.486284	−	2.77258i	−0.0213250	−	0.121586i
$521$	22.7728			0.997693			0.498847	−	0.866690i	$-0.333757\pi$
$521$	22.7728			0.997693			0.498847	+	0.866690i	$0.333757\pi$
$522$			3.94276i			0.172570i
$523$			16.1920i			0.708026i	0.935241	+	0.354013i	$0.115183\pi$
$523$			16.1920i			0.708026i	−0.935241	+	0.354013i	$0.884817\pi$
$524$	−12.2885			−0.536827
$525$	−22.1047	+	8.00000i	−0.964728	+	0.349149i
$526$	24.3189			1.06036
$527$		−	10.9658i		−	0.477678i
$528$			1.91861i			0.0834970i
$529$	−1.00000			−0.0434783
$530$	4.29844	+	24.5078i	0.186712	+	1.06455i
$531$	2.50105			0.108536
$532$			10.9879i			0.476384i
$533$			6.46790i			0.280156i
$534$	−23.2997			−1.00828
$535$	9.86808	−	1.73077i	0.426634	−	0.0748276i
$536$	−6.60981			−0.285500
$537$		−	29.4919i		−	1.27267i
$538$			7.91283i			0.341147i
$539$	−4.81439			−0.207370
$540$	−12.4513	+	2.18384i	−0.535819	+	0.0939775i
$541$	14.4350			0.620610			0.310305	−	0.950637i	$-0.399569\pi$
$541$	14.4350			0.620610			0.310305	+	0.950637i	$0.399569\pi$
$542$			18.2979i			0.785960i
$543$		−	10.2746i		−	0.440923i
$544$	−4.62018			−0.198088
$545$	6.61703	+	37.7274i	0.283443	+	1.61607i
$546$	−5.91861			−0.253293
$547$			0.846151i			0.0361788i	0.999836	+	0.0180894i	$0.00575835\pi$
$547$			0.846151i			0.0361788i	−0.999836	+	0.0180894i	$0.994242\pi$
$548$		−	8.82830i		−	0.377126i
$549$	11.3590			0.484788
$550$	2.26287	+	6.25250i	0.0964890	+	0.266607i
$551$	−14.4715			−0.616508
$552$		−	1.44270i		−	0.0614054i
$553$		−	49.9503i		−	2.12410i
$554$	−28.6550			−1.21744
$555$	3.20176	+	18.2551i	0.135907	+	0.774884i
$556$	−11.5532			−0.489963
$557$		−	19.3532i		−	0.820020i	−0.912081	−	0.410010i	$-0.865525\pi$
$557$		−	19.3532i		−	0.820020i	0.912081	−	0.410010i	$-0.134475\pi$
$558$		−	2.18029i		−	0.0922992i
$559$	13.1775			0.557348
$560$	−7.17748	+	1.25886i	−0.303304	+	0.0531966i
$561$	8.86433			0.374252
$562$		−	2.74692i		−	0.115872i
$563$		−	29.3647i		−	1.23758i	−0.785558	−	0.618788i	$-0.787624\pi$
$563$		−	29.3647i		−	1.23758i	0.785558	−	0.618788i	$-0.212376\pi$
$564$	8.74692			0.368312
$565$	−21.5275	+	3.77572i	−0.905669	+	0.158846i
$566$	−5.45307			−0.229210
$567$			17.5988i			0.739082i
$568$			0.265226i			0.0111286i
$569$	−6.41900			−0.269098			−0.134549	−	0.990907i	$-0.542959\pi$
$569$	−6.41900			−0.269098			−0.134549	+	0.990907i	$0.542959\pi$
$570$	−1.87904	−	10.7134i	−0.0787042	−	0.448737i
$571$	35.3009			1.47730			0.738648	−	0.674092i	$-0.235465\pi$
$571$	35.3009			1.47730			0.738648	+	0.674092i	$0.235465\pi$
$572$			1.67413i			0.0699989i
$573$		−	24.1206i		−	1.00765i
$574$	16.7437			0.698868
$575$	−1.70156	−	4.70156i	−0.0709600	−	0.196069i
$576$	−0.918614			−0.0382756
$577$			6.96339i			0.289890i	0.989440	+	0.144945i	$0.0463004\pi$
$577$			6.96339i			0.289890i	−0.989440	+	0.144945i	$0.953700\pi$
$578$			4.34603i			0.180771i
$579$	9.40312			0.390781
$580$	−1.65798	−	9.45307i	−0.0688438	−	0.392517i
$581$	−6.60134			−0.273870
$582$			12.4363i			0.515503i
$583$		−	14.7982i		−	0.612880i
$584$	−5.26464			−0.217852
$585$	−2.54693	+	0.446707i	−0.105303	+	0.0184691i
$586$	18.3806			0.759296
$587$		−	23.7392i		−	0.979823i	−0.871772	−	0.489912i	$-0.837029\pi$
$587$		−	23.7392i		−	0.979823i	0.871772	−	0.489912i	$-0.162971\pi$
$588$			5.22283i			0.215386i
$589$	8.00256			0.329740
$590$	−5.99645	+	1.05172i	−0.246870	+	0.0432987i
$591$	25.7066			1.05743
$592$			5.74514i			0.236124i
$593$			23.1612i			0.951116i	0.879684	+	0.475558i	$0.157754\pi$
$593$			23.1612i			0.951116i	−0.879684	+	0.475558i	$0.842246\pi$
$594$	7.51831			0.308480
$595$	5.81616	+	33.1612i	0.238439	+	1.35948i
$596$	−11.1333			−0.456038
$597$			5.44526i			0.222860i
$598$		−	1.25886i		−	0.0514787i
$599$	−33.1344			−1.35383			−0.676916	−	0.736060i	$-0.736684\pi$
$599$	−33.1344			−1.35383			−0.676916	+	0.736060i	$0.736684\pi$
$600$	6.78295	−	2.45485i	0.276913	−	0.100219i
$601$	40.0432			1.63340			0.816698	−	0.577065i	$-0.195802\pi$
$601$	40.0432			1.63340			0.816698	+	0.577065i	$0.195802\pi$
$602$		−	34.1130i		−	1.39034i
$603$			6.07186i			0.247265i
$604$	3.23779			0.131744
$605$	3.56600	+	20.3317i	0.144978	+	0.826603i
$606$	20.9097			0.849398
$607$			1.81294i			0.0735849i	0.999323	+	0.0367925i	$0.0117140\pi$
$607$			1.81294i			0.0735849i	−0.999323	+	0.0367925i	$0.988286\pi$
$608$		−	3.37169i		−	0.136740i
$609$	−20.1794			−0.817713
$610$	−27.2340	+	4.77658i	−1.10267	+	0.193398i
$611$	7.63232			0.308771
$612$			4.24416i			0.171560i
$613$		−	11.9329i		−	0.481964i	−0.970530	−	0.240982i	$-0.922531\pi$
$613$		−	11.9329i		−	0.481964i	0.970530	−	0.240982i	$-0.0774694\pi$
$614$	15.9234			0.642616
$615$	−16.3255	+	2.86335i	−0.658309	+	0.115461i
$616$	4.33388			0.174617
$617$			16.5923i			0.667982i	0.942576	+	0.333991i	$0.108396\pi$
$617$			16.5923i			0.667982i	−0.942576	+	0.333991i	$0.891604\pi$
$618$		−	26.7492i		−	1.07601i
$619$	1.43811			0.0578025			0.0289013	−	0.999582i	$-0.490799\pi$
$619$	1.43811			0.0578025			0.0289013	+	0.999582i	$0.490799\pi$
$620$	0.916840	+	5.22742i	0.0368212	+	0.209938i
$621$	−5.65339			−0.226863
$622$			11.3518i			0.455166i
$623$			52.6307i			2.10861i
$624$	1.81616			0.0727046
$625$	19.2094	−	16.0000i	0.768375	−	0.640000i
$626$	−28.7913			−1.15073
$627$			6.46896i			0.258346i
$628$		−	17.6452i		−	0.704122i
$629$	26.5436			1.05836
$630$	1.15641	+	6.59333i	0.0460724	+	0.262685i
$631$	7.67446			0.305515			0.152758	−	0.988264i	$-0.451185\pi$
$631$	7.67446			0.305515			0.152758	+	0.988264i	$0.451185\pi$
$632$			15.3275i			0.609696i
$633$		−	34.5714i		−	1.37409i
$634$	31.2299			1.24030
$635$	−2.26287	+	0.396885i	−0.0897991	+	0.0157499i
$636$	−16.0537			−0.636570
$637$			4.55730i			0.180567i
$638$			5.70793i			0.225979i
$639$	0.243640			0.00963826
$640$	2.20245	−	0.386289i	0.0870594	−	0.0152694i
$641$	−23.0562			−0.910665			−0.455332	−	0.890322i	$-0.650480\pi$
$641$	−23.0562			−0.910665			−0.455332	+	0.890322i	$0.650480\pi$
$642$			6.46403i			0.255115i
$643$		−	9.51595i		−	0.375272i	−0.982239	−	0.187636i	$-0.939917\pi$
$643$		−	9.51595i		−	0.375272i	0.982239	−	0.187636i	$-0.0600826\pi$
$644$	−3.25886			−0.128417
$645$	5.83368	+	33.2611i	0.229701	+	1.30965i
$646$	−15.5778			−0.612900
$647$		−	38.9857i		−	1.53269i	−0.642432	−	0.766343i	$-0.722074\pi$
$647$		−	38.9857i		−	1.53269i	0.642432	−	0.766343i	$-0.277926\pi$
$648$		−	5.40031i		−	0.212144i
$649$	3.62076			0.142127
$650$	5.91861	−	2.14203i	0.232147	−	0.0840173i
$651$	11.1590			0.437354
$652$		−	12.2107i		−	0.478207i
$653$			7.32529i			0.286661i	0.989675	+	0.143330i	$0.0457811\pi$
$653$			7.32529i			0.286661i	−0.989675	+	0.143330i	$0.954219\pi$
$654$	−24.7131			−0.966360
$655$	−4.74692	−	27.0649i	−0.185477	−	1.05751i
$656$	−5.13790			−0.200601
$657$			4.83617i			0.188677i
$658$		−	19.7581i		−	0.770250i
$659$	20.7177			0.807048			0.403524	−	0.914969i	$-0.367785\pi$
$659$	20.7177			0.807048			0.403524	+	0.914969i	$0.367785\pi$
$660$	−4.22565	+	0.741139i	−0.164483	+	0.0288488i
$661$	12.9749			0.504666			0.252333	−	0.967640i	$-0.418802\pi$
$661$	12.9749			0.504666			0.252333	+	0.967640i	$0.418802\pi$
$662$		−	17.6917i		−	0.687606i
$663$		−	8.39098i		−	0.325879i
$664$	2.02566			0.0786108
$665$	−24.2002	+	4.24448i	−0.938443	+	0.164594i
$666$	5.27757			0.204502
$667$		−	4.29207i		−	0.166190i
$668$			2.06288i			0.0798151i
$669$	−29.1561			−1.12724
$670$	−2.55329	−	14.5578i	−0.0986423	−	0.562415i
$671$	16.4443			0.634827
$672$		−	4.70156i		−	0.181367i
$673$		−	15.8660i		−	0.611589i	−0.952098	−	0.305794i	$-0.901078\pi$
$673$		−	15.8660i		−	0.611589i	0.952098	−	0.305794i	$-0.0989220\pi$
$674$	1.33801			0.0515384
$675$	−9.61959	−	26.5798i	−0.370258	−	1.02306i
$676$	−11.4153			−0.439049
$677$		−	23.2787i		−	0.894675i	−0.894365	−	0.447337i	$-0.852372\pi$
$677$		−	23.2787i		−	0.894675i	0.894365	−	0.447337i	$-0.147628\pi$
$678$		−	14.1015i		−	0.541564i
$679$	28.0920			1.07807
$680$	−1.78472	−	10.1757i	−0.0684410	−	0.390220i
$681$	−2.31793			−0.0888234
$682$		−	3.15641i		−	0.120865i
$683$		−	27.5797i		−	1.05531i	−0.849460	−	0.527654i	$-0.823072\pi$
$683$		−	27.5797i		−	1.05531i	0.849460	−	0.527654i	$-0.176928\pi$
$684$	−3.09728			−0.118427
$685$	19.4439	−	3.41027i	0.742913	−	0.130300i
$686$	−11.0144			−0.420531
$687$			27.2698i			1.04041i
$688$			10.4678i			0.399080i
$689$	−14.0080			−0.533663
$690$	3.17748	−	0.557299i	0.120964	−	0.0212160i
$691$	8.61472			0.327719			0.163860	−	0.986484i	$-0.447606\pi$
$691$	8.61472			0.327719			0.163860	+	0.986484i	$0.447606\pi$
$692$			2.10245i			0.0799233i
$693$		−	3.98116i		−	0.151232i
$694$	5.36355			0.203597
$695$	−4.46286	−	25.4453i	−0.169286	−	0.965194i
$696$	6.19218			0.234714
$697$			23.7380i			0.899141i
$698$		−	18.4306i		−	0.697607i
$699$	27.4274			1.03740
$700$	−5.54515	−	15.3217i	−0.209587	−	0.579107i
$701$	17.4254			0.658148			0.329074	−	0.944304i	$-0.393264\pi$
$701$	17.4254			0.658148			0.329074	+	0.944304i	$0.393264\pi$
$702$		−	7.11683i		−	0.268607i
$703$			19.3708i			0.730584i
$704$	−1.32988			−0.0501216
$705$	3.37884	+	19.2646i	0.127254	+	0.725548i
$706$	6.76477			0.254595
$707$		−	47.2321i		−	1.77635i
$708$		−	3.92794i		−	0.147621i
$709$	6.42019			0.241115			0.120558	−	0.992706i	$-0.461532\pi$
$709$	6.42019			0.241115			0.120558	+	0.992706i	$0.461532\pi$
$710$	−0.584146	+	0.102454i	−0.0219226	+	0.00384502i
$711$	14.0801			0.528044
$712$		−	16.1500i		−	0.605248i
$713$			2.37346i			0.0888867i
$714$	−21.7220			−0.812927
$715$	−3.68719	+	0.646697i	−0.137893	+	0.0241851i
$716$	20.4421			0.763958
$717$		−	40.8842i		−	1.52685i
$718$			27.5324i			1.02750i
$719$	−1.50079			−0.0559699			−0.0279849	−	0.999608i	$-0.508909\pi$
$719$	−1.50079			−0.0559699			−0.0279849	+	0.999608i	$0.508909\pi$
$720$	−0.354850	−	2.02320i	−0.0132245	−	0.0754002i
$721$	−60.4226			−2.25026
$722$			7.63174i			0.284024i
$723$			9.16318i			0.340782i
$724$	7.12175			0.264678
$725$	20.1794	−	7.30323i	0.749446	−	0.271235i
$726$	−13.3182			−0.494284
$727$		−	6.97867i		−	0.258825i	−0.991591	−	0.129412i	$-0.958691\pi$
$727$		−	6.97867i		−	0.258825i	0.991591	−	0.129412i	$-0.0413091\pi$
$728$		−	4.10245i		−	0.152047i
$729$	−29.4292			−1.08997
$730$	−2.03367	−	11.5951i	−0.0752695	−	0.429154i
$731$	48.3630			1.78877
$732$		−	17.8395i		−	0.659365i
$733$		−	3.61138i		−	0.133389i	−0.997773	−	0.0666947i	$-0.978755\pi$
$733$		−	3.61138i		−	0.133389i	0.997773	−	0.0666947i	$-0.0212453\pi$
$734$	−24.0744			−0.888604
$735$	−11.5030	+	2.01752i	−0.424295	+	0.0744174i
$736$	1.00000			0.0368605
$737$			8.79022i			0.323792i
$738$			4.71975i			0.173736i
$739$	−5.24953			−0.193107			−0.0965536	−	0.995328i	$-0.530782\pi$
$739$	−5.24953			−0.193107			−0.0965536	+	0.995328i	$0.530782\pi$
$740$	−12.6534	+	2.21928i	−0.465148	+	0.0815825i
$741$	6.12352			0.224953
$742$			36.2631i			1.33126i
$743$			2.72603i			0.100008i	0.998749	+	0.0500042i	$0.0159235\pi$
$743$			2.72603i			0.100008i	−0.998749	+	0.0500042i	$0.984077\pi$
$744$	−3.42419			−0.125537
$745$	−4.30067	−	24.5205i	−0.157564	−	0.898363i
$746$	−1.31459			−0.0481305
$747$		−	1.86080i		−	0.0680831i
$748$			6.14426i			0.224657i
$749$	14.6013			0.533521
$750$	8.02685	+	13.9908i	0.293099	+	0.510872i
$751$	−20.6729			−0.754364			−0.377182	−	0.926139i	$-0.623107\pi$
$751$	−20.6729			−0.754364			−0.377182	+	0.926139i	$0.623107\pi$
$752$			6.06288i			0.221090i
$753$			28.4545i			1.03694i
$754$	5.40312			0.196770
$755$	1.25072	+	7.13107i	0.0455185	+	0.259526i
$756$	−18.4236			−0.670060
$757$		−	8.87759i		−	0.322661i	−0.986900	−	0.161331i	$-0.948421\pi$
$757$		−	8.87759i		−	0.322661i	0.986900	−	0.161331i	$-0.0515786\pi$
$758$			8.38961i			0.304724i
$759$	−1.91861			−0.0696413
$760$	7.42597	−	1.30244i	0.269368	−	0.0472446i
$761$	31.8816			1.15571			0.577853	−	0.816141i	$-0.303891\pi$
$761$	31.8816			1.15571			0.577853	+	0.816141i	$0.303891\pi$
$762$		−	1.48228i		−	0.0536973i
$763$			55.8235i			2.02095i
$764$	16.7191			0.604875
$765$	−9.34754	+	1.63947i	−0.337961	+	0.0592752i
$766$	−24.1258			−0.871699
$767$		−	3.42741i		−	0.123757i
$768$			1.44270i			0.0520590i
$769$	−37.6697			−1.35841			−0.679203	−	0.733951i	$-0.737674\pi$
$769$	−37.6697			−1.35841			−0.679203	+	0.733951i	$0.737674\pi$
$770$	1.67413	+	9.54515i	0.0603314	+	0.343983i
$771$	1.70386			0.0613631
$772$			6.51772i			0.234578i
$773$		−	6.14066i		−	0.220864i	−0.993884	−	0.110432i	$-0.964777\pi$
$773$		−	6.14066i		−	0.220864i	0.993884	−	0.110432i	$-0.0352235\pi$
$774$	9.61584			0.345634
$775$	−11.1590	+	4.03859i	−0.400842	+	0.145070i
$776$	−8.62018			−0.309446
$777$			27.0112i			0.969020i
$778$			12.5702i			0.450665i
$779$	−17.3234			−0.620674
$780$	0.701562	+	4.00000i	0.0251200	+	0.143223i
$781$	0.352718			0.0126212
$782$		−	4.62018i		−	0.165217i
$783$		−	24.2648i		−	0.867152i
$784$	−3.62018			−0.129292
$785$	38.8628	−	6.81616i	1.38707	−	0.243279i
$786$	17.7287			0.632361
$787$		−	17.9373i		−	0.639397i	−0.947519	−	0.319698i	$-0.896418\pi$
$787$		−	17.9373i		−	0.639397i	0.947519	−	0.319698i	$-0.103582\pi$
$788$			17.8184i			0.634754i
$789$	−35.0849			−1.24906
$790$	−33.7581	+	5.92085i	−1.20106	+	0.210654i
$791$	−31.8533			−1.13257
$792$			1.22164i			0.0434092i
$793$		−	15.5662i		−	0.552773i
$794$	−28.5318			−1.01256
$795$	−6.20136	−	35.3574i	−0.219940	−	1.25400i
$796$	−3.77435			−0.133778
$797$			6.03367i			0.213724i	0.994274	+	0.106862i	$0.0340802\pi$
$797$			6.03367i			0.213724i	−0.994274	+	0.106862i	$0.965920\pi$
$798$		−	15.8522i		−	0.561161i
$799$	28.0116			0.990978
$800$	1.70156	+	4.70156i	0.0601593	+	0.166225i
$801$	−14.8357			−0.524192
$802$			19.7130i			0.696092i
$803$			7.00132i			0.247071i
$804$	9.53597			0.336308
$805$	−1.25886	−	7.17748i	−0.0443690	−	0.252973i
$806$	−2.98786			−0.105243
$807$		−	11.4159i		−	0.401857i
$808$			14.4934i			0.509877i
$809$	51.6850			1.81715			0.908574	−	0.417723i	$-0.137172\pi$
$809$	51.6850			1.81715			0.908574	+	0.417723i	$0.137172\pi$
$810$	11.8939	−	2.08608i	0.417909	−	0.0732973i
$811$	11.6368			0.408623			0.204311	−	0.978906i	$-0.434504\pi$
$811$	11.6368			0.408623			0.204311	+	0.978906i	$0.434504\pi$
$812$		−	13.9873i		−	0.490857i
$813$		−	26.3983i		−	0.925830i
$814$	7.64033			0.267794
$815$	26.8934	−	4.71685i	0.942035	−	0.165224i
$816$	6.66553			0.233340
$817$			35.2940i			1.23478i
$818$			20.3400i			0.711171i
$819$	−3.76857			−0.131685
$820$	−1.98471	−	11.3160i	−0.0693091	−	0.395170i
$821$	6.02312			0.210208			0.105104	−	0.994461i	$-0.466482\pi$
$821$	6.02312			0.210208			0.105104	+	0.994461i	$0.466482\pi$
$822$			12.7366i			0.444240i
$823$		−	40.1839i		−	1.40072i	−0.713788	−	0.700362i	$-0.753022\pi$
$823$		−	40.1839i		−	1.40072i	0.713788	−	0.700362i	$-0.246978\pi$
$824$	18.5410			0.645907
$825$	−3.26464	−	9.02048i	−0.113660	−	0.314053i
$826$	−8.87267			−0.308720
$827$			30.5980i			1.06400i	0.846745	+	0.531998i	$0.178559\pi$
$827$			30.5980i			1.06400i	−0.846745	+	0.531998i	$0.821441\pi$
$828$		−	0.918614i		−	0.0319240i
$829$	−54.9892			−1.90986			−0.954928	−	0.296838i	$-0.904068\pi$
$829$	−54.9892			−1.90986			−0.954928	+	0.296838i	$0.904068\pi$
$830$	0.782489	+	4.46141i	0.0271606	+	0.154858i
$831$	41.3406			1.43409
$832$			1.25886i			0.0436432i
$833$			16.7259i			0.579516i
$834$	16.6678			0.577158
$835$	−4.54338	+	0.796866i	−0.157230	+	0.0275767i
$836$	−4.48393			−0.155080
$837$			13.4181i			0.463797i
$838$			9.91146i			0.342386i
$839$	12.5121			0.431965			0.215983	−	0.976397i	$-0.430705\pi$
$839$	12.5121			0.431965			0.215983	+	0.976397i	$0.430705\pi$
$840$	10.3550	−	1.81616i	0.357280	−	0.0626635i
$841$	−10.5781			−0.364762
$842$			28.7927i			0.992260i
$843$			3.96298i			0.136492i
$844$	23.9630			0.824840
$845$	−4.40959	−	25.1415i	−0.151694	−	0.864895i
$846$	5.56944			0.191481
$847$			30.0839i			1.03370i
$848$		−	11.1275i		−	0.382121i
$849$	7.86715			0.270000
$850$	21.7220	−	7.86152i	0.745060	−	0.269648i
$851$	−5.74514			−0.196941
$852$		−	0.382642i		−	0.0131091i
$853$			52.3308i			1.79177i	0.444283	+	0.895886i	$0.353458\pi$
$853$			52.3308i			1.79177i	−0.444283	+	0.895886i	$0.646542\pi$
$854$	−40.2969			−1.37893
$855$	−1.19644	−	6.82160i	−0.0409175	−	0.233294i
$856$	−4.48050			−0.153140
$857$			4.53557i			0.154932i	0.996995	+	0.0774660i	$0.0246829\pi$
$857$			4.53557i			0.154932i	−0.996995	+	0.0774660i	$0.975317\pi$
$858$		−	2.41527i		−	0.0824559i
$859$	−10.1708			−0.347023			−0.173511	−	0.984832i	$-0.555511\pi$
$859$	−10.1708			−0.347023			−0.173511	+	0.984832i	$0.555511\pi$
$860$	−23.0547	+	4.04358i	−0.786160	+	0.137885i
$861$	−24.1561			−0.823239
$862$		−	36.6821i		−	1.24940i
$863$			0.861113i			0.0293126i	0.999893	+	0.0146563i	$0.00466542\pi$
$863$			0.861113i			0.0293126i	−0.999893	+	0.0146563i	$0.995335\pi$
$864$	5.65339			0.192332
$865$	−4.63055	+	0.812154i	−0.157443	+	0.0276141i
$866$	−29.6894			−1.00889
$867$		−	6.27002i		−	0.212941i
$868$			7.73477i			0.262535i
$869$	20.3837			0.691470
$870$	2.39197	+	13.6380i	0.0810953	+	0.462370i
$871$	8.32083			0.281940
$872$		−	17.1298i		−	0.580087i
$873$			7.91861i			0.268004i
$874$	3.37169			0.114049
$875$	31.6033	−	18.1315i	1.06839	−	0.612958i
$876$	7.59530			0.256621
$877$			26.4746i			0.893984i	0.894538	+	0.446992i	$0.147505\pi$
$877$			26.4746i			0.893984i	−0.894538	+	0.446992i	$0.852495\pi$
$878$			34.5378i			1.16559i
$879$	−26.5177			−0.894421
$880$	−0.513716	−	2.92898i	−0.0173174	−	0.0987361i
$881$	32.8670			1.10732			0.553659	−	0.832743i	$-0.313231\pi$
$881$	32.8670			1.10732			0.553659	+	0.832743i	$0.313231\pi$
$882$			3.32554i			0.111977i
$883$			29.1507i			0.980999i	0.871441	+	0.490500i	$0.163186\pi$
$883$			29.1507i			0.980999i	−0.871441	+	0.490500i	$0.836814\pi$
$884$	5.81616			0.195619
$885$	8.65109	−	1.51732i	0.290803	−	0.0510041i
$886$	36.6735			1.23207
$887$			29.6697i			0.996212i	0.867116	+	0.498106i	$0.165971\pi$
$887$			29.6697i			0.996212i	−0.867116	+	0.498106i	$0.834029\pi$
$888$		−	8.28853i		−	0.278145i
$889$	−3.34826			−0.112297
$890$	35.5696	−	6.23858i	1.19230	−	0.209118i
$891$	−7.18174			−0.240597
$892$		−	20.2094i		−	0.676660i
$893$			20.4421i			0.684069i
$894$	16.0620			0.537195
$895$	7.89656	+	45.0227i	0.263953	+	1.50494i
$896$	3.25886			0.108871
$897$			1.81616i			0.0606398i
$898$		−	13.2138i		−	0.440951i
$899$	−10.1871			−0.339757
$900$	4.31892	−	1.56308i	0.143964	−	0.0521026i
$901$	−51.4111			−1.71275
$902$			6.83277i			0.227506i
$903$			49.2149i			1.63777i
$904$	9.77435			0.325090
$905$	2.75105	+	15.6853i	0.0914480	+	0.521397i
$906$	−4.67117			−0.155189
$907$			7.66153i			0.254397i	0.991877	+	0.127198i	$0.0405985\pi$
$907$			7.66153i			0.254397i	−0.991877	+	0.127198i	$0.959402\pi$
$908$		−	1.60666i		−	0.0533189i
$909$	13.3139			0.441593
$910$	9.03544	−	1.58473i	0.299522	−	0.0525333i
$911$	53.4450			1.77071			0.885356	−	0.464914i	$-0.153915\pi$
$911$	53.4450			1.77071			0.885356	+	0.464914i	$0.153915\pi$
$912$			4.86433i			0.161074i
$913$		−	2.69388i		−	0.0891543i
$914$	12.2292			0.404506
$915$	39.2905	−	6.89118i	1.29890	−	0.227815i
$916$	−18.9019			−0.624536
$917$		−	40.0466i		−	1.32246i
$918$		−	26.1196i		−	0.862077i
$919$	−22.7485			−0.750403			−0.375202	−	0.926943i	$-0.622427\pi$
$919$	−22.7485			−0.750403			−0.375202	+	0.926943i	$0.622427\pi$
$920$	0.386289	+	2.20245i	0.0127356	+	0.0726126i
$921$	−22.9727			−0.756977
$922$		−	24.0872i		−	0.793269i
$923$		−	0.333883i		−	0.0109899i
$924$	−6.25250			−0.205692
$925$	−9.77572	−	27.0112i	−0.321424	−	0.888121i
$926$	15.9173			0.523075
$927$		−	17.0320i		−	0.559406i
$928$			4.29207i			0.140894i
$929$	−23.1810			−0.760545			−0.380272	−	0.924875i	$-0.624170\pi$
$929$	−23.1810			−0.760545			−0.380272	+	0.924875i	$0.624170\pi$
$930$	−1.32273	−	7.54161i	−0.0433739	−	0.247299i
$931$	−12.2061			−0.400039
$932$			19.0112i			0.622731i
$933$		−	16.3773i		−	0.536167i
$934$	−9.70011			−0.317397
$935$	−13.5324	+	2.37346i	−0.442558	+	0.0776204i
$936$	1.15641			0.0377984
$937$			12.6027i			0.411711i	0.978582	+	0.205855i	$0.0659977\pi$
$937$			12.6027i			0.411711i	−0.978582	+	0.205855i	$0.934002\pi$
$938$		−	21.5404i		−	0.703320i
$939$	41.5372			1.35552
$940$	−13.3532	+	2.34202i	−0.435533	+	0.0763883i
$941$	−47.9093			−1.56180			−0.780899	−	0.624657i	$-0.785239\pi$
$941$	−47.9093			−1.56180			−0.780899	+	0.624657i	$0.785239\pi$
$942$			25.4568i			0.829428i
$943$		−	5.13790i		−	0.167313i
$944$	2.72263			0.0886141
$945$	−7.11683	−	40.5771i	−0.231511	−	1.31997i
$946$	13.9208			0.452606
$947$			30.4073i			0.988105i	0.869432	+	0.494053i	$0.164485\pi$
$947$			30.4073i			0.988105i	−0.869432	+	0.494053i	$0.835515\pi$
$948$		−	22.1130i		−	0.718198i
$949$	6.62745			0.215136
$950$	5.73713	+	15.8522i	0.186137	+	0.514313i
$951$	−45.0553			−1.46102
$952$		−	15.0565i		−	0.487984i
$953$			45.8534i			1.48534i	0.669658	+	0.742669i	$0.266441\pi$
$953$			45.8534i			1.48534i	−0.669658	+	0.742669i	$0.733559\pi$
$954$	−10.2219			−0.330946
$955$	6.45839	+	36.8229i	0.208989	+	1.19156i
$956$	28.3387			0.916538
$957$		−	8.23483i		−	0.266194i
$958$			14.1385i			0.456794i
$959$	28.7702			0.929039
$960$	−3.17748	+	0.557299i	−0.102553	+	0.0179867i
$961$	−25.3667			−0.818280
$962$		−	7.23234i		−	0.233180i
$963$			4.11585i			0.132632i
$964$	−6.35140			−0.204565
$965$	−14.3550	+	2.51772i	−0.462102	+	0.0810483i
$966$	4.70156			0.151270
$967$			57.3471i			1.84416i	0.387002	+	0.922079i	$0.373511\pi$
$967$			57.3471i			1.84416i	−0.387002	+	0.922079i	$0.626489\pi$
$968$		−	9.23143i		−	0.296709i
$969$	22.4741			0.721971
$970$	−3.32988	−	18.9855i	−0.106916	−	0.609588i
$971$	−44.6948			−1.43432			−0.717162	−	0.696906i	$-0.754559\pi$
$971$	−44.6948			−1.43432			−0.717162	+	0.696906i	$0.754559\pi$
$972$		−	9.16914i		−	0.294100i
$973$		−	37.6502i		−	1.20701i
$974$	−3.75006			−0.120160
$975$	−8.53879	+	3.09031i	−0.273460	+	0.0989691i
$976$	12.3653			0.395804
$977$		−	10.7663i		−	0.344446i	−0.985058	−	0.172223i	$-0.944905\pi$
$977$		−	10.7663i		−	0.344446i	0.985058	−	0.172223i	$-0.0550950\pi$
$978$			17.6164i			0.563309i
$979$	−21.4776			−0.686426
$980$	−1.39843	−	7.97325i	−0.0446713	−	0.254696i
$981$	−15.7356			−0.502400
$982$			3.19020i			0.101804i
$983$		−	4.38626i		−	0.139900i	−0.997550	−	0.0699500i	$-0.977716\pi$
$983$		−	4.38626i		−	0.139900i	0.997550	−	0.0699500i	$-0.0222840\pi$
$984$	7.41245			0.236300
$985$	−39.2441	+	6.88304i	−1.25042	+	0.219312i
$986$	19.8301			0.631520
$987$			28.5050i			0.907324i
$988$			4.24448i			0.135035i
$989$	−10.4678			−0.332856
$990$	−2.69061	+	0.471907i	−0.0855131	+	0.0149982i
$991$	−1.49757			−0.0475717			−0.0237859	−	0.999717i	$-0.507572\pi$
$991$	−1.49757			−0.0475717			−0.0237859	+	0.999717i	$0.507572\pi$
$992$		−	2.37346i		−	0.0753574i
$993$			25.5238i			0.809972i
$994$	−0.864334			−0.0274150
$995$	−1.45799	−	8.31281i	−0.0462214	−	0.263534i
$996$	−2.92242			−0.0926004
$997$			45.4135i			1.43826i	0.694875	+	0.719130i	$0.255460\pi$
$997$			45.4135i			1.43826i	−0.694875	+	0.719130i	$0.744540\pi$
$998$			12.9355i			0.409468i
$999$	−32.4795			−1.02761

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.b.b.139.3	✓	8
3.2	odd	2		2070.2.d.f.829.7		8
4.3	odd	2		1840.2.e.e.369.3		8
5.2	odd	4		1150.2.a.s.1.3		4
5.3	odd	4		1150.2.a.r.1.2		4
5.4	even	2	inner	230.2.b.b.139.6	yes	8
15.14	odd	2		2070.2.d.f.829.3		8
20.3	even	4		9200.2.a.cr.1.3		4
20.7	even	4		9200.2.a.cj.1.2		4
20.19	odd	2		1840.2.e.e.369.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.b.b.139.3	✓	8	1.1	even	1	trivial
230.2.b.b.139.6	yes	8	5.4	even	2	inner
1150.2.a.r.1.2		4	5.3	odd	4
1150.2.a.s.1.3		4	5.2	odd	4
1840.2.e.e.369.3		8	4.3	odd	2
1840.2.e.e.369.6		8	20.19	odd	2
2070.2.d.f.829.3		8	15.14	odd	2
2070.2.d.f.829.7		8	3.2	odd	2
9200.2.a.cj.1.2		4	20.7	even	4
9200.2.a.cr.1.3		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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.44270i q^{3} -1.00000 q^{4} +(-0.386289 - 2.20245i) q^{5} +1.44270 q^{6} -3.25886i q^{7} +1.00000i q^{8} +0.918614 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.44270i q^{3} -1.00000 q^{4} +(-0.386289 - 2.20245i) q^{5} +1.44270 q^{6} -3.25886i q^{7} +1.00000i q^{8} +0.918614 q^{9} +(-2.20245 + 0.386289i) q^{10} +1.32988 q^{11} -1.44270i q^{12} -1.25886i q^{13} -3.25886 q^{14} +(3.17748 - 0.557299i) q^{15} +1.00000 q^{16} -4.62018i q^{17} -0.918614i q^{18} +3.37169 q^{19} +(0.386289 + 2.20245i) q^{20} +4.70156 q^{21} -1.32988i q^{22} +1.00000i q^{23} -1.44270 q^{24} +(-4.70156 + 1.70156i) q^{25} -1.25886 q^{26} +5.65339i q^{27} +3.25886i q^{28} -4.29207 q^{29} +(-0.557299 - 3.17748i) q^{30} +2.37346 q^{31} -1.00000i q^{32} +1.91861i q^{33} -4.62018 q^{34} +(-7.17748 + 1.25886i) q^{35} -0.918614 q^{36} +5.74514i q^{37} -3.37169i q^{38} +1.81616 q^{39} +(2.20245 - 0.386289i) q^{40} -5.13790 q^{41} -4.70156i q^{42} +10.4678i q^{43} -1.32988 q^{44} +(-0.354850 - 2.02320i) q^{45} +1.00000 q^{46} +6.06288i q^{47} +1.44270i q^{48} -3.62018 q^{49} +(1.70156 + 4.70156i) q^{50} +6.66553 q^{51} +1.25886i q^{52} -11.1275i q^{53} +5.65339 q^{54} +(-0.513716 - 2.92898i) q^{55} +3.25886 q^{56} +4.86433i q^{57} +4.29207i q^{58} +2.72263 q^{59} +(-3.17748 + 0.557299i) q^{60} +12.3653 q^{61} -2.37346i q^{62} -2.99364i q^{63} -1.00000 q^{64} +(-2.77258 + 0.486284i) q^{65} +1.91861 q^{66} +6.60981i q^{67} +4.62018i q^{68} -1.44270 q^{69} +(1.25886 + 7.17748i) q^{70} +0.265226 q^{71} +0.918614i q^{72} +5.26464i q^{73} +5.74514 q^{74} +(-2.45485 - 6.78295i) q^{75} -3.37169 q^{76} -4.33388i q^{77} -1.81616i q^{78} +15.3275 q^{79} +(-0.386289 - 2.20245i) q^{80} -5.40031 q^{81} +5.13790i q^{82} -2.02566i q^{83} -4.70156 q^{84} +(-10.1757 + 1.78472i) q^{85} +10.4678 q^{86} -6.19218i q^{87} +1.32988i q^{88} -16.1500 q^{89} +(-2.02320 + 0.354850i) q^{90} -4.10245 q^{91} -1.00000i q^{92} +3.42419i q^{93} +6.06288 q^{94} +(-1.30244 - 7.42597i) q^{95} +1.44270 q^{96} +8.62018i q^{97} +3.62018i q^{98} +1.22164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 6 q^{6} - 14 q^{9}+O(q^{10}) \) 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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Database

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