LMFDB - Embedded newform 370.2.b.d.149.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [370,2,Mod(149,370)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("370.149"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(370, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,0,-10,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.12837029094400.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 51x^{6} - 124x^{5} + 154x^{4} - 46x^{3} + x^{2} + 4x + 8 $ x^10 - 2x^9 + 2x^8 - 4x^7 + 51x^6 - 124x^5 + 154x^4 - 46x^3 + x^2 + 4x + 8
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			149.10
Root			$1.51933 + 1.51933i$ of defining polynomial
Character	$\chi$	$=$	370.149
Dual form			370.2.b.d.149.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +2.72987i q^{3} -1.00000 q^{4} +(-1.42149 + 1.72608i) q^{5} -2.72987 q^{6} -4.14336i q^{7} -1.00000i q^{8} -4.45216 q^{9} +(-1.72608 - 1.42149i) q^{10} -4.76853 q^{11} -2.72987i q^{12} +3.91744i q^{13} +4.14336 q^{14} +(-4.71197 - 3.88048i) q^{15} +1.00000 q^{16} +3.31637i q^{17} -4.45216i q^{18} +1.85109 q^{19} +(1.42149 - 1.72608i) q^{20} +11.3108 q^{21} -4.76853i q^{22} +1.54229i q^{23} +2.72987 q^{24} +(-0.958719 - 4.90723i) q^{25} -3.91744 q^{26} -3.96421i q^{27} +4.14336i q^{28} -8.87323 q^{29} +(3.88048 - 4.71197i) q^{30} +9.75286 q^{31} +1.00000i q^{32} -13.0174i q^{33} -3.31637 q^{34} +(7.15179 + 5.88976i) q^{35} +4.45216 q^{36} +1.00000i q^{37} +1.85109i q^{38} -10.6941 q^{39} +(1.72608 + 1.42149i) q^{40} -5.06977 q^{41} +11.3108i q^{42} +9.99446i q^{43} +4.76853 q^{44} +(6.32872 - 7.68480i) q^{45} -1.54229 q^{46} +4.82700i q^{47} +2.72987i q^{48} -10.1675 q^{49} +(4.90723 - 0.958719i) q^{50} -9.05324 q^{51} -3.91744i q^{52} +5.13611i q^{53} +3.96421 q^{54} +(6.77843 - 8.23088i) q^{55} -4.14336 q^{56} +5.05324i q^{57} -8.87323i q^{58} +1.05324 q^{59} +(4.71197 + 3.88048i) q^{60} -4.14422 q^{61} +9.75286i q^{62} +18.4469i q^{63} -1.00000 q^{64} +(-6.76182 - 5.56861i) q^{65} +13.0174 q^{66} +1.00811i q^{67} -3.31637i q^{68} -4.21025 q^{69} +(-5.88976 + 7.15179i) q^{70} +6.45248 q^{71} +4.45216i q^{72} -10.7714i q^{73} -1.00000 q^{74} +(13.3961 - 2.61717i) q^{75} -1.85109 q^{76} +19.7578i q^{77} -10.6941i q^{78} +1.19856 q^{79} +(-1.42149 + 1.72608i) q^{80} -2.53473 q^{81} -5.06977i q^{82} -10.6932i q^{83} -11.3108 q^{84} +(-5.72432 - 4.71419i) q^{85} -9.99446 q^{86} -24.2227i q^{87} +4.76853i q^{88} -7.29569 q^{89} +(7.68480 + 6.32872i) q^{90} +16.2314 q^{91} -1.54229i q^{92} +26.6240i q^{93} -4.82700 q^{94} +(-2.63131 + 3.19514i) q^{95} -2.72987 q^{96} +14.8988i q^{97} -10.1675i q^{98} +21.2303 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{4} + 6 q^{5} - 6 q^{9} + 2 q^{10} + 6 q^{11} + 2 q^{14} + 10 q^{16} - 8 q^{19} - 6 q^{20} + 32 q^{21} + 4 q^{25} - 12 q^{26} - 22 q^{29} + 20 q^{30} + 46 q^{31} - 18 q^{34} + 32 q^{35} + 6 q^{36}+ \cdots + 22 q^{99}+O(q^{100}) $ 10 * q - 10 * q^4 + 6 * q^5 - 6 * q^9 + 2 * q^10 + 6 * q^11 + 2 * q^14 + 10 * q^16 - 8 * q^19 - 6 * q^20 + 32 * q^21 + 4 * q^25 - 12 * q^26 - 22 * q^29 + 20 * q^30 + 46 * q^31 - 18 * q^34 + 32 * q^35 + 6 * q^36 - 40 * q^39 - 2 * q^40 - 14 * q^41 - 6 * q^44 + 2 * q^45 + 12 * q^46 - 60 * q^49 + 8 * q^50 - 40 * q^51 + 42 * q^55 - 2 * q^56 - 40 * q^59 - 18 * q^61 - 10 * q^64 + 4 * q^65 + 40 * q^66 - 32 * q^69 - 6 * q^70 + 12 * q^71 - 10 * q^74 + 50 * q^75 + 8 * q^76 - 40 * q^79 + 6 * q^80 - 14 * q^81 - 32 * q^84 + 36 * q^85 - 34 * q^86 - 24 * q^89 + 44 * q^90 + 32 * q^91 - 24 * q^94 + 12 * q^95 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$1$	$-1$

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
$3$			2.72987i			1.57609i	0.615619	+	0.788044i	$0.288906\pi$
$3$			2.72987i			1.57609i	−0.615619	+	0.788044i	$0.711094\pi$
$4$	−1.00000			−0.500000
$5$	−1.42149	+	1.72608i	−0.635711	+	0.771927i
$5$	−1.42149	+	1.72608i	−0.635711	+	0.771927i
$6$	−2.72987			−1.11446
$7$		−	4.14336i		−	1.56604i	−0.621994	−	0.783022i	$-0.713677\pi$
$7$		−	4.14336i		−	1.56604i	0.621994	−	0.783022i	$-0.286323\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−4.45216			−1.48405
$10$	−1.72608	−	1.42149i	−0.545835	−	0.449515i
$11$	−4.76853			−1.43777			−0.718883	−	0.695131i	$-0.755346\pi$
$11$	−4.76853			−1.43777			−0.718883	+	0.695131i	$0.755346\pi$
$12$		−	2.72987i		−	0.788044i
$13$			3.91744i			1.08650i	0.839570	+	0.543251i	$0.182807\pi$
$13$			3.91744i			1.08650i	−0.839570	+	0.543251i	$0.817193\pi$
$14$	4.14336			1.10736
$15$	−4.71197	−	3.88048i	−1.21663	−	1.00194i
$16$	1.00000			0.250000
$17$			3.31637i			0.804337i	0.915566	+	0.402169i	$0.131743\pi$
$17$			3.31637i			0.804337i	−0.915566	+	0.402169i	$0.868257\pi$
$18$		−	4.45216i		−	1.04939i
$19$	1.85109			0.424670			0.212335	−	0.977197i	$-0.431893\pi$
$19$	1.85109			0.424670			0.212335	+	0.977197i	$0.431893\pi$
$20$	1.42149	−	1.72608i	0.317855	−	0.385964i
$21$	11.3108			2.46822
$22$		−	4.76853i		−	1.01665i
$23$			1.54229i			0.321590i	0.986988	+	0.160795i	$0.0514058\pi$
$23$			1.54229i			0.321590i	−0.986988	+	0.160795i	$0.948594\pi$
$24$	2.72987			0.557231
$25$	−0.958719	−	4.90723i	−0.191744	−	0.981445i
$26$	−3.91744			−0.768273
$27$		−	3.96421i		−	0.762913i
$28$			4.14336i			0.783022i
$29$	−8.87323			−1.64772			−0.823859	−	0.566795i	$-0.808183\pi$
$29$	−8.87323			−1.64772			−0.823859	+	0.566795i	$0.808183\pi$
$30$	3.88048	−	4.71197i	0.708476	−	0.860284i
$31$	9.75286			1.75166			0.875832	−	0.482615i	$-0.160313\pi$
$31$	9.75286			1.75166			0.875832	+	0.482615i	$0.160313\pi$
$32$			1.00000i			0.176777i
$33$		−	13.0174i		−	2.26605i
$34$	−3.31637			−0.568752
$35$	7.15179	+	5.88976i	1.20887	+	0.995551i
$36$	4.45216			0.742027
$37$			1.00000i			0.164399i
$37$			1.00000i			0.164399i
$38$			1.85109i			0.300287i
$39$	−10.6941			−1.71242
$40$	1.72608	+	1.42149i	0.272918	+	0.224758i
$41$	−5.06977			−0.791764			−0.395882	−	0.918301i	$-0.629561\pi$
$41$	−5.06977			−0.791764			−0.395882	+	0.918301i	$0.629561\pi$
$42$			11.3108i			1.74530i
$43$			9.99446i			1.52414i	0.647494	+	0.762070i	$0.275817\pi$
$43$			9.99446i			1.52414i	−0.647494	+	0.762070i	$0.724183\pi$
$44$	4.76853			0.718883
$45$	6.32872	−	7.68480i	0.943429	−	1.14558i
$46$	−1.54229			−0.227399
$47$			4.82700i			0.704090i	0.935983	+	0.352045i	$0.114514\pi$
$47$			4.82700i			0.704090i	−0.935983	+	0.352045i	$0.885486\pi$
$48$			2.72987i			0.394022i
$49$	−10.1675			−1.45249
$50$	4.90723	−	0.958719i	0.693986	−	0.135583i
$51$	−9.05324			−1.26771
$52$		−	3.91744i		−	0.543251i
$53$			5.13611i			0.705499i	0.935718	+	0.352750i	$0.114753\pi$
$53$			5.13611i			0.705499i	−0.935718	+	0.352750i	$0.885247\pi$
$54$	3.96421			0.539461
$55$	6.77843	−	8.23088i	0.914003	−	1.10985i
$56$	−4.14336			−0.553680
$57$			5.05324i			0.669317i
$58$		−	8.87323i		−	1.16511i
$59$	1.05324			0.137120			0.0685598	−	0.997647i	$-0.478160\pi$
$59$	1.05324			0.137120			0.0685598	+	0.997647i	$0.478160\pi$
$60$	4.71197	+	3.88048i	0.608313	+	0.500968i
$61$	−4.14422			−0.530613			−0.265306	−	0.964164i	$-0.585473\pi$
$61$	−4.14422			−0.530613			−0.265306	+	0.964164i	$0.585473\pi$
$62$			9.75286i			1.23861i
$63$			18.4469i			2.32410i
$64$	−1.00000			−0.125000
$65$	−6.76182	−	5.56861i	−0.838701	−	0.690701i
$66$	13.0174			1.60234
$67$			1.00811i			0.123160i	0.998102	+	0.0615800i	$0.0196139\pi$
$67$			1.00811i			0.123160i	−0.998102	+	0.0615800i	$0.980386\pi$
$68$		−	3.31637i		−	0.402169i
$69$	−4.21025			−0.506855
$70$	−5.88976	+	7.15179i	−0.703961	+	0.854802i
$71$	6.45248			0.765768			0.382884	−	0.923796i	$-0.374931\pi$
$71$	6.45248			0.765768			0.382884	+	0.923796i	$0.374931\pi$
$72$			4.45216i			0.524693i
$73$		−	10.7714i		−	1.26070i	−0.776312	−	0.630349i	$-0.782912\pi$
$73$		−	10.7714i		−	1.26070i	0.776312	−	0.630349i	$-0.217088\pi$
$74$	−1.00000			−0.116248
$75$	13.3961	−	2.61717i	1.54684	−	0.302205i
$76$	−1.85109			−0.212335
$77$			19.7578i			2.25161i
$78$		−	10.6941i		−	1.21087i
$79$	1.19856			0.134849			0.0674243	−	0.997724i	$-0.478522\pi$
$79$	1.19856			0.134849			0.0674243	+	0.997724i	$0.478522\pi$
$80$	−1.42149	+	1.72608i	−0.158928	+	0.192982i
$81$	−2.53473			−0.281636
$82$		−	5.06977i		−	0.559862i
$83$		−	10.6932i		−	1.17373i	−0.809683	−	0.586867i	$-0.800361\pi$
$83$		−	10.6932i		−	1.17373i	0.809683	−	0.586867i	$-0.199639\pi$
$84$	−11.3108			−1.23411
$85$	−5.72432	−	4.71419i	−0.620890	−	0.511326i
$86$	−9.99446			−1.07773
$87$		−	24.2227i		−	2.59695i
$88$			4.76853i			0.508327i
$89$	−7.29569			−0.773342			−0.386671	−	0.922218i	$-0.626375\pi$
$89$	−7.29569			−0.773342			−0.386671	+	0.922218i	$0.626375\pi$
$90$	7.68480	+	6.32872i	0.810049	+	0.667105i
$91$	16.2314			1.70151
$92$		−	1.54229i		−	0.160795i
$93$			26.6240i			2.76078i
$94$	−4.82700			−0.497867
$95$	−2.63131	+	3.19514i	−0.269967	+	0.327814i
$96$	−2.72987			−0.278616
$97$			14.8988i			1.51274i	0.654143	+	0.756371i	$0.273030\pi$
$97$			14.8988i			1.51274i	−0.654143	+	0.756371i	$0.726970\pi$
$98$		−	10.1675i		−	1.02707i
$99$	21.2303			2.13372
$100$	0.958719	+	4.90723i	0.0958719	+	0.490723i
$101$	18.5903			1.84980			0.924902	−	0.380206i	$-0.124147\pi$
$101$	18.5903			1.84980			0.924902	+	0.380206i	$0.124147\pi$
$102$		−	9.05324i		−	0.896404i
$103$			13.3033i			1.31081i	0.755278	+	0.655404i	$0.227502\pi$
$103$			13.3033i			1.31081i	−0.755278	+	0.655404i	$0.772498\pi$
$104$	3.91744			0.384136
$105$	−16.0782	+	19.5234i	−1.56908	+	1.90529i
$106$	−5.13611			−0.498863
$107$			12.4763i			1.20613i	0.797691	+	0.603066i	$0.206054\pi$
$107$			12.4763i			1.20613i	−0.797691	+	0.603066i	$0.793946\pi$
$108$			3.96421i			0.381457i
$109$	4.35447			0.417083			0.208541	−	0.978014i	$-0.433128\pi$
$109$	4.35447			0.417083			0.208541	+	0.978014i	$0.433128\pi$
$110$	8.23088	+	6.77843i	0.784783	+	0.646298i
$111$	−2.72987			−0.259107
$112$		−	4.14336i		−	0.391511i
$113$		−	9.54261i		−	0.897693i	−0.893609	−	0.448846i	$-0.851835\pi$
$113$		−	9.54261i		−	0.897693i	0.893609	−	0.448846i	$-0.148165\pi$
$114$	−5.05324			−0.473279
$115$	−2.66212	−	2.19236i	−0.248244	−	0.204438i
$116$	8.87323			0.823859
$117$		−	17.4411i		−	1.61243i
$118$			1.05324i			0.0969582i
$119$	13.7409			1.25963
$120$	−3.88048	+	4.71197i	−0.354238	+	0.430142i
$121$	11.7389			1.06717
$122$		−	4.14422i		−	0.375200i
$123$		−	13.8398i		−	1.24789i
$124$	−9.75286			−0.875832
$125$	9.83309	+	5.32076i	0.879498	+	0.475903i
$126$	−18.4469			−1.64338
$127$			8.33492i			0.739605i	0.929110	+	0.369802i	$0.120575\pi$
$127$			8.33492i			0.739605i	−0.929110	+	0.369802i	$0.879425\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−27.2835			−2.40218
$130$	5.56861	−	6.76182i	0.488399	−	0.593051i
$131$	3.68597			0.322045			0.161022	−	0.986951i	$-0.448521\pi$
$131$	3.68597			0.322045			0.161022	+	0.986951i	$0.448521\pi$
$132$			13.0174i			1.13302i
$133$		−	7.66975i		−	0.665052i
$134$	−1.00811			−0.0870873
$135$	6.84256	+	5.63510i	0.588914	+	0.484992i
$136$	3.31637			0.284376
$137$		−	12.3027i		−	1.05109i	−0.850765	−	0.525546i	$-0.823861\pi$
$137$		−	12.3027i		−	1.05109i	0.850765	−	0.525546i	$-0.176139\pi$
$138$		−	4.21025i		−	0.358400i
$139$	0.842442			0.0714550			0.0357275	−	0.999362i	$-0.488625\pi$
$139$	0.842442			0.0714550			0.0357275	+	0.999362i	$0.488625\pi$
$140$	−7.15179	−	5.88976i	−0.604436	−	0.497776i
$141$	−13.1770			−1.10971
$142$			6.45248i			0.541480i
$143$		−	18.6804i		−	1.56214i
$144$	−4.45216			−0.371014
$145$	12.6132	−	15.3159i	1.04747	−	1.27192i
$146$	10.7714			0.891448
$147$		−	27.7558i		−	2.28926i
$148$		−	1.00000i		−	0.0821995i
$149$	16.7723			1.37404			0.687019	−	0.726640i	$-0.258919\pi$
$149$	16.7723			1.37404			0.687019	+	0.726640i	$0.258919\pi$
$150$	2.61717	+	13.3961i	0.213691	+	1.09378i
$151$	−7.59755			−0.618280			−0.309140	−	0.951017i	$-0.600041\pi$
$151$	−7.59755			−0.618280			−0.309140	+	0.951017i	$0.600041\pi$
$152$		−	1.85109i		−	0.150143i
$153$		−	14.7650i		−	1.19368i
$154$	−19.7578			−1.59213
$155$	−13.8636	+	16.8342i	−1.11355	+	1.35216i
$156$	10.6941			0.856211
$157$			4.45631i			0.355652i	0.984062	+	0.177826i	$0.0569065\pi$
$157$			4.45631i			0.355652i	−0.984062	+	0.177826i	$0.943094\pi$
$158$			1.19856i			0.0953523i
$159$	−14.0209			−1.11193
$160$	−1.72608	−	1.42149i	−0.136459	−	0.112379i
$161$	6.39028			0.503624
$162$		−	2.53473i		−	0.199147i
$163$		−	19.4599i		−	1.52422i	−0.647447	−	0.762110i	$-0.724163\pi$
$163$		−	19.4599i		−	1.52422i	0.647447	−	0.762110i	$-0.275837\pi$
$164$	5.06977			0.395882
$165$	22.4692	+	18.5042i	1.74922	+	1.44055i
$166$	10.6932			0.829955
$167$			7.13813i			0.552365i	0.961105	+	0.276183i	$0.0890695\pi$
$167$			7.13813i			0.552365i	−0.961105	+	0.276183i	$0.910931\pi$
$168$		−	11.3108i		−	0.872649i
$169$	−2.34632			−0.180486
$170$	4.71419	−	5.72432i	0.361562	−	0.439035i
$171$	−8.24137			−0.630233
$172$		−	9.99446i		−	0.762070i
$173$			11.6199i			0.883448i	0.897151	+	0.441724i	$0.145633\pi$
$173$			11.6199i			0.883448i	−0.897151	+	0.441724i	$0.854367\pi$
$174$	24.2227			1.83632
$175$	−20.3324	+	3.97232i	−1.53699	+	0.300279i
$176$	−4.76853			−0.359442
$177$			2.87519i			0.216113i
$178$		−	7.29569i		−	0.546835i
$179$	17.2224			1.28726			0.643631	−	0.765336i	$-0.277427\pi$
$179$	17.2224			1.28726			0.643631	+	0.765336i	$0.277427\pi$
$180$	−6.32872	+	7.68480i	−0.471715	+	0.572791i
$181$	−23.5098			−1.74747			−0.873733	−	0.486405i	$-0.838308\pi$
$181$	−23.5098			−1.74747			−0.873733	+	0.486405i	$0.838308\pi$
$182$			16.2314i			1.20315i
$183$		−	11.3132i		−	0.836293i
$184$	1.54229			0.113699
$185$	−1.72608	−	1.42149i	−0.126904	−	0.104510i
$186$	−26.6240			−1.95217
$187$		−	15.8142i		−	1.15645i
$188$		−	4.82700i		−	0.352045i
$189$	−16.4252			−1.19476
$190$	−3.19514	−	2.63131i	−0.231800	−	0.190896i
$191$	1.16660			0.0844125			0.0422063	−	0.999109i	$-0.486561\pi$
$191$	1.16660			0.0844125			0.0422063	+	0.999109i	$0.486561\pi$
$192$		−	2.72987i		−	0.197011i
$193$			9.36727i			0.674271i	0.941456	+	0.337135i	$0.109458\pi$
$193$			9.36727i			0.674271i	−0.941456	+	0.337135i	$0.890542\pi$
$194$	−14.8988			−1.06967
$195$	15.2015	−	18.4589i	1.08861	−	1.32187i
$196$	10.1675			0.726247
$197$			3.21836i			0.229299i	0.993406	+	0.114649i	$0.0365744\pi$
$197$			3.21836i			0.229299i	−0.993406	+	0.114649i	$0.963426\pi$
$198$			21.2303i			1.50877i
$199$	2.99104			0.212029			0.106014	−	0.994365i	$-0.466191\pi$
$199$	2.99104			0.212029			0.106014	+	0.994365i	$0.466191\pi$
$200$	−4.90723	+	0.958719i	−0.346993	+	0.0677917i
$201$	−2.75200			−0.194111
$202$			18.5903i			1.30801i
$203$			36.7650i			2.58040i
$204$	9.05324			0.633853
$205$	7.20663	−	8.75083i	0.503333	−	0.611185i
$206$	−13.3033			−0.926882
$207$		−	6.86654i		−	0.477257i
$208$			3.91744i			0.271625i
$209$	−8.82700			−0.610576
$210$	−19.5234	−	16.0782i	−1.34724	−	1.10950i
$211$	4.75340			0.327237			0.163619	−	0.986524i	$-0.447683\pi$
$211$	4.75340			0.327237			0.163619	+	0.986524i	$0.447683\pi$
$212$		−	5.13611i		−	0.352750i
$213$			17.6144i			1.20692i
$214$	−12.4763			−0.852864
$215$	−17.2513	−	14.2070i	−1.17653	−	0.968912i
$216$	−3.96421			−0.269731
$217$		−	40.4096i		−	2.74318i
$218$			4.35447i			0.294922i
$219$	29.4045			1.98697
$220$	−6.77843	+	8.23088i	−0.457002	+	0.554926i
$221$	−12.9917			−0.873914
$222$		−	2.72987i		−	0.183217i
$223$			6.95635i			0.465832i	0.972497	+	0.232916i	$0.0748267\pi$
$223$			6.95635i			0.465832i	−0.972497	+	0.232916i	$0.925173\pi$
$224$	4.14336			0.276840
$225$	4.26837	+	21.8478i	0.284558	+	1.45652i
$226$	9.54261			0.634765
$227$		−	22.2980i		−	1.47997i	−0.672622	−	0.739986i	$-0.734832\pi$
$227$		−	22.2980i		−	1.47997i	0.672622	−	0.739986i	$-0.265168\pi$
$228$		−	5.05324i		−	0.334659i
$229$	−12.9648			−0.856739			−0.428370	−	0.903604i	$-0.640912\pi$
$229$	−12.9648			−0.856739			−0.428370	+	0.903604i	$0.640912\pi$
$230$	2.19236	−	2.66212i	0.144560	−	0.175535i
$231$	−53.9360			−3.54873
$232$			8.87323i			0.582556i
$233$			10.4327i			0.683468i	0.939797	+	0.341734i	$0.111014\pi$
$233$			10.4327i			0.683468i	−0.939797	+	0.341734i	$0.888986\pi$
$234$	17.4411			1.14016
$235$	−8.33179	−	6.86154i	−0.543506	−	0.447597i
$236$	−1.05324			−0.0685598
$237$			3.27191i			0.212533i
$238$			13.7409i			0.890691i
$239$	−1.58711			−0.102661			−0.0513307	−	0.998682i	$-0.516346\pi$
$239$	−1.58711			−0.102661			−0.0513307	+	0.998682i	$0.516346\pi$
$240$	−4.71197	−	3.88048i	−0.304156	−	0.250484i
$241$	16.2576			1.04724			0.523622	−	0.851951i	$-0.324581\pi$
$241$	16.2576			1.04724			0.523622	+	0.851951i	$0.324581\pi$
$242$			11.7389i			0.754604i
$243$		−	18.8121i		−	1.20680i
$244$	4.14422			0.265306
$245$	14.4530	−	17.5499i	0.923366	−	1.12122i
$246$	13.8398			0.882392
$247$			7.25154i			0.461405i
$248$		−	9.75286i		−	0.619307i
$249$	29.1911			1.84991
$250$	−5.32076	+	9.83309i	−0.336514	+	0.621899i
$251$	14.9486			0.943547			0.471774	−	0.881720i	$-0.343614\pi$
$251$	14.9486			0.943547			0.471774	+	0.881720i	$0.343614\pi$
$252$		−	18.4469i		−	1.16205i
$253$		−	7.35447i		−	0.462372i
$254$	−8.33492			−0.522979
$255$	12.8691	−	15.6266i	0.805895	−	0.978577i
$256$	1.00000			0.0625000
$257$			14.9968i			0.935474i	0.883868	+	0.467737i	$0.154931\pi$
$257$			14.9968i			0.935474i	−0.883868	+	0.467737i	$0.845069\pi$
$258$		−	27.2835i		−	1.69860i
$259$	4.14336			0.257456
$260$	6.76182	+	5.56861i	0.419350	+	0.345350i
$261$	39.5051			2.44530
$262$			3.68597i			0.227720i
$263$		−	22.9610i		−	1.41583i	−0.706295	−	0.707917i	$-0.749635\pi$
$263$		−	22.9610i		−	1.41583i	0.706295	−	0.707917i	$-0.250365\pi$
$264$	−13.0174			−0.801169
$265$	−8.86535	−	7.30094i	−0.544594	−	0.448493i
$266$	7.66975			0.470263
$267$		−	19.9163i		−	1.21885i
$268$		−	1.00811i		−	0.0615800i
$269$	−10.0896			−0.615175			−0.307588	−	0.951520i	$-0.599522\pi$
$269$	−10.0896			−0.615175			−0.307588	+	0.951520i	$0.599522\pi$
$270$	−5.63510	+	6.84256i	−0.342941	+	0.416425i
$271$	3.30678			0.200872			0.100436	−	0.994943i	$-0.467976\pi$
$271$	3.30678			0.200872			0.100436	+	0.994943i	$0.467976\pi$
$272$			3.31637i			0.201084i
$273$			44.3095i			2.68173i
$274$	12.3027			0.743234
$275$	4.57168	+	23.4003i	0.275683	+	1.41109i
$276$	4.21025			0.253427
$277$		−	15.9046i		−	0.955617i	−0.878464	−	0.477809i	$-0.841431\pi$
$277$		−	15.9046i		−	0.955617i	0.878464	−	0.477809i	$-0.158569\pi$
$278$			0.842442i			0.0505263i
$279$	−43.4213			−2.59957
$280$	5.88976	−	7.15179i	0.351980	−	0.427401i
$281$	11.3609			0.677732			0.338866	−	0.940835i	$-0.389957\pi$
$281$	11.3609			0.677732			0.338866	+	0.940835i	$0.389957\pi$
$282$		−	13.1770i		−	0.784682i
$283$		−	20.1530i		−	1.19797i	−0.800761	−	0.598984i	$-0.795571\pi$
$283$		−	20.1530i		−	1.19797i	0.800761	−	0.598984i	$-0.204429\pi$
$284$	−6.45248			−0.382884
$285$	−8.72230	−	7.18314i	−0.516664	−	0.425492i
$286$	18.6804			1.10460
$287$			21.0059i			1.23994i
$288$		−	4.45216i		−	0.262346i
$289$	6.00171			0.353042
$290$	15.3159	+	12.6132i	0.899382	+	0.740674i
$291$	−40.6717			−2.38422
$292$			10.7714i			0.630349i
$293$			21.0517i			1.22986i	0.788583	+	0.614928i	$0.210815\pi$
$293$			21.0517i			1.22986i	−0.788583	+	0.614928i	$0.789185\pi$
$294$	27.7558			1.61875
$295$	−1.49717	+	1.81797i	−0.0871684	+	0.105846i
$296$	1.00000			0.0581238
$297$			18.9035i			1.09689i
$298$			16.7723i			0.971591i
$299$	−6.04184			−0.349408
$300$	−13.3961	+	2.61717i	−0.773422	+	0.151103i
$301$	41.4107			2.38687
$302$		−	7.59755i		−	0.437190i
$303$			50.7490i			2.91545i
$304$	1.85109			0.106167
$305$	5.89098	−	7.15326i	0.337316	−	0.409595i
$306$	14.7650			0.844059
$307$			17.0946i			0.975638i	0.872945	+	0.487819i	$0.162207\pi$
$307$			17.0946i			0.975638i	−0.872945	+	0.487819i	$0.837793\pi$
$308$		−	19.7578i		−	1.12580i
$309$	−36.3161			−2.06595
$310$	−16.8342	−	13.8636i	−0.956120	−	0.787400i
$311$	20.0503			1.13695			0.568473	−	0.822702i	$-0.307534\pi$
$311$	20.0503			1.13695			0.568473	+	0.822702i	$0.307534\pi$
$312$			10.6941i			0.605433i
$313$		−	13.3400i		−	0.754019i	−0.926209	−	0.377010i	$-0.876952\pi$
$313$		−	13.3400i		−	0.754019i	0.926209	−	0.377010i	$-0.123048\pi$
$314$	−4.45631			−0.251484
$315$	−31.8409	−	26.2222i	−1.79403	−	1.47745i
$316$	−1.19856			−0.0674243
$317$			12.8528i			0.721885i	0.932588	+	0.360943i	$0.117545\pi$
$317$			12.8528i			0.721885i	−0.932588	+	0.360943i	$0.882455\pi$
$318$		−	14.0209i		−	0.786252i
$319$	42.3123			2.36903
$320$	1.42149	−	1.72608i	0.0794638	−	0.0964909i
$321$	−34.0587			−1.90097
$322$			6.39028i			0.356116i
$323$			6.13890i			0.341578i
$324$	2.53473			0.140818
$325$	19.2238	−	3.75572i	1.06634	−	0.208330i
$326$	19.4599			1.07779
$327$			11.8871i			0.657359i
$328$			5.06977i			0.279931i
$329$	20.0000			1.10264
$330$	−18.5042	+	22.4692i	−1.01862	+	1.23689i
$331$	−23.5835			−1.29627			−0.648134	−	0.761526i	$-0.724451\pi$
$331$	−23.5835			−1.29627			−0.648134	+	0.761526i	$0.724451\pi$
$332$			10.6932i			0.586867i
$333$		−	4.45216i		−	0.243977i
$334$	−7.13813			−0.390581
$335$	−1.74008	−	1.43302i	−0.0950706	−	0.0782942i
$336$	11.3108			0.617056
$337$			26.6074i			1.44940i	0.689067	+	0.724698i	$0.258021\pi$
$337$			26.6074i			1.44940i	−0.689067	+	0.724698i	$0.741979\pi$
$338$		−	2.34632i		−	0.127623i
$339$	26.0500			1.41484
$340$	5.72432	+	4.71419i	0.310445	+	0.255663i
$341$	−46.5068			−2.51848
$342$		−	8.24137i		−	0.445642i
$343$			13.1239i			0.708626i
$344$	9.99446			0.538865
$345$	5.98484	−	7.26724i	0.322213	−	0.391255i
$346$	−11.6199			−0.624692
$347$		−	17.2626i		−	0.926707i	−0.886174	−	0.463353i	$-0.846646\pi$
$347$		−	17.2626i		−	0.926707i	0.886174	−	0.463353i	$-0.153354\pi$
$348$			24.2227i			1.29847i
$349$	−11.1619			−0.597484			−0.298742	−	0.954334i	$-0.596567\pi$
$349$	−11.1619			−0.597484			−0.298742	+	0.954334i	$0.596567\pi$
$350$	−3.97232	−	20.3324i	−0.212330	−	1.08681i
$351$	15.5296			0.828906
$352$		−	4.76853i		−	0.254164i
$353$			12.6563i			0.673628i	0.941571	+	0.336814i	$0.109349\pi$
$353$			12.6563i			0.673628i	−0.941571	+	0.336814i	$0.890651\pi$
$354$	−2.87519			−0.152815
$355$	−9.17215	+	11.1375i	−0.486807	+	0.591117i
$356$	7.29569			0.386671
$357$			37.5108i			1.98528i
$358$			17.2224i			0.910232i
$359$	23.2778			1.22855			0.614277	−	0.789091i	$-0.289448\pi$
$359$	23.2778			1.22855			0.614277	+	0.789091i	$0.289448\pi$
$360$	−7.68480	−	6.32872i	−0.405025	−	0.333553i
$361$	−15.5735			−0.819655
$362$		−	23.5098i		−	1.23565i
$363$			32.0456i			1.68196i
$364$	−16.2314			−0.850755
$365$	18.5923	+	15.3115i	0.973167	+	0.801439i
$366$	11.3132			0.591348
$367$		−	9.09417i		−	0.474712i	−0.971423	−	0.237356i	$-0.923719\pi$
$367$		−	9.09417i		−	0.474712i	0.971423	−	0.237356i	$-0.0762808\pi$
$368$			1.54229i			0.0803976i
$369$	22.5714			1.17502
$370$	1.42149	−	1.72608i	0.0738999	−	0.0897347i
$371$	21.2808			1.10484
$372$		−	26.6240i		−	1.38039i
$373$		−	5.75976i		−	0.298229i	−0.988820	−	0.149114i	$-0.952358\pi$
$373$		−	5.75976i		−	0.298229i	0.988820	−	0.149114i	$-0.0476423\pi$
$374$	15.8142			0.817733
$375$	−14.5249	+	26.8430i	−0.750065	+	1.38617i
$376$	4.82700			0.248933
$377$		−	34.7603i		−	1.79025i
$378$		−	16.4252i		−	0.844820i
$379$	−18.0902			−0.929229			−0.464614	−	0.885513i	$-0.653807\pi$
$379$	−18.0902			−0.929229			−0.464614	+	0.885513i	$0.653807\pi$
$380$	2.63131	−	3.19514i	0.134984	−	0.163907i
$381$	−22.7532			−1.16568
$382$			1.16660i			0.0596887i
$383$		−	3.54752i		−	0.181270i	−0.995884	−	0.0906350i	$-0.971110\pi$
$383$		−	3.54752i		−	0.181270i	0.995884	−	0.0906350i	$-0.0288896\pi$
$384$	2.72987			0.139308
$385$	−34.1035	−	28.0855i	−1.73808	−	1.43137i
$386$	−9.36727			−0.476781
$387$		−	44.4970i		−	2.26191i
$388$		−	14.8988i		−	0.756371i
$389$	−25.6053			−1.29824			−0.649119	−	0.760687i	$-0.724862\pi$
$389$	−25.6053			−1.29824			−0.649119	+	0.760687i	$0.724862\pi$
$390$	18.4589	+	15.2015i	0.934701	+	0.769760i
$391$	−5.11481			−0.258667
$392$			10.1675i			0.513534i
$393$			10.0622i			0.507571i
$394$	−3.21836			−0.162139
$395$	−1.70374	+	2.06881i	−0.0857247	+	0.104093i
$396$	−21.2303			−1.06686
$397$			31.4597i			1.57892i	0.613803	+	0.789459i	$0.289639\pi$
$397$			31.4597i			1.57892i	−0.613803	+	0.789459i	$0.710361\pi$
$398$			2.99104i			0.149927i
$399$	20.9374			1.04818
$400$	−0.958719	−	4.90723i	−0.0479360	−	0.245361i
$401$	−22.9940			−1.14826			−0.574132	−	0.818763i	$-0.694660\pi$
$401$	−22.9940			−1.14826			−0.574132	+	0.818763i	$0.694660\pi$
$402$		−	2.75200i		−	0.137257i
$403$			38.2062i			1.90319i
$404$	−18.5903			−0.924902
$405$	3.60309	−	4.37515i	0.179039	−	0.217403i
$406$	−36.7650			−1.82462
$407$		−	4.76853i		−	0.236367i
$408$			9.05324i			0.448202i
$409$	33.3828			1.65067			0.825337	−	0.564640i	$-0.190985\pi$
$409$	33.3828			1.65067			0.825337	+	0.564640i	$0.190985\pi$
$410$	8.75083	+	7.20663i	0.432173	+	0.355910i
$411$	33.5848			1.65661
$412$		−	13.3033i		−	0.655404i
$413$		−	4.36394i		−	0.214735i
$414$	6.86654			0.337472
$415$	18.4574	+	15.2003i	0.906037	+	0.746155i
$416$	−3.91744			−0.192068
$417$			2.29975i			0.112619i
$418$		−	8.82700i		−	0.431743i
$419$	−8.32565			−0.406734			−0.203367	−	0.979103i	$-0.565189\pi$
$419$	−8.32565			−0.406734			−0.203367	+	0.979103i	$0.565189\pi$
$420$	16.0782	−	19.5234i	0.784538	−	0.952645i
$421$	−8.41521			−0.410132			−0.205066	−	0.978748i	$-0.565741\pi$
$421$	−8.41521			−0.410132			−0.205066	+	0.978748i	$0.565741\pi$
$422$			4.75340i			0.231392i
$423$		−	21.4906i		−	1.04491i
$424$	5.13611			0.249432
$425$	16.2742	−	3.17946i	0.789413	−	0.154227i
$426$	−17.6144			−0.853420
$427$			17.1710i			0.830963i
$428$		−	12.4763i		−	0.603066i
$429$	50.9950			2.46206
$430$	14.2070	−	17.2513i	0.685124	−	0.831929i
$431$	3.04769			0.146802			0.0734011	−	0.997303i	$-0.476615\pi$
$431$	3.04769			0.146802			0.0734011	+	0.997303i	$0.476615\pi$
$432$		−	3.96421i		−	0.190728i
$433$		−	22.9439i		−	1.10262i	−0.834302	−	0.551308i	$-0.814129\pi$
$433$		−	22.9439i		−	1.10262i	0.834302	−	0.551308i	$-0.185871\pi$
$434$	40.4096			1.93972
$435$	41.8104	+	34.4324i	2.00466	+	1.65091i
$436$	−4.35447			−0.208541
$437$			2.85493i			0.136570i
$438$			29.4045i			1.40500i
$439$	−10.3033			−0.491751			−0.245875	−	0.969301i	$-0.579075\pi$
$439$	−10.3033			−0.491751			−0.245875	+	0.969301i	$0.579075\pi$
$440$	−8.23088	−	6.77843i	−0.392392	−	0.323149i
$441$	45.2672			2.15558
$442$		−	12.9917i		−	0.617950i
$443$			4.84236i			0.230067i	0.993362	+	0.115034i	$0.0366976\pi$
$443$			4.84236i			0.230067i	−0.993362	+	0.115034i	$0.963302\pi$
$444$	2.72987			0.129554
$445$	10.3708	−	12.5930i	0.491622	−	0.596964i
$446$	−6.95635			−0.329393
$447$			45.7860i			2.16560i
$448$			4.14336i			0.195756i
$449$	−25.3149			−1.19468			−0.597341	−	0.801987i	$-0.703776\pi$
$449$	−25.3149			−1.19468			−0.597341	+	0.801987i	$0.703776\pi$
$450$	−21.8478	+	4.26837i	−1.02991	+	0.201213i
$451$	24.1753			1.13837
$452$			9.54261i			0.448846i
$453$		−	20.7403i		−	0.974464i
$454$	22.2980			1.04650
$455$	−23.0728	+	28.0167i	−1.08167	+	1.31344i
$456$	5.05324			0.236639
$457$			11.9945i			0.561077i	0.959843	+	0.280539i	$0.0905130\pi$
$457$			11.9945i			0.561077i	−0.959843	+	0.280539i	$0.909487\pi$
$458$		−	12.9648i		−	0.605806i
$459$	13.1468			0.613639
$460$	2.66212	+	2.19236i	0.124122	+	0.102219i
$461$	−23.6570			−1.10182			−0.550909	−	0.834565i	$-0.685719\pi$
$461$	−23.6570			−1.10182			−0.550909	+	0.834565i	$0.685719\pi$
$462$		−	53.9360i		−	2.50933i
$463$			17.3667i			0.807099i	0.914958	+	0.403550i	$0.132224\pi$
$463$			17.3667i			0.807099i	−0.914958	+	0.403550i	$0.867776\pi$
$464$	−8.87323			−0.411929
$465$	−45.9552	−	37.8458i	−2.13112	−	1.75506i
$466$	−10.4327			−0.483285
$467$		−	20.4476i		−	0.946200i	−0.881009	−	0.473100i	$-0.843135\pi$
$467$		−	20.4476i		−	0.946200i	0.881009	−	0.473100i	$-0.156865\pi$
$468$			17.4411i			0.806214i
$469$	4.17696			0.192874
$470$	6.86154	−	8.33179i	0.316499	−	0.384317i
$471$	−12.1651			−0.560539
$472$		−	1.05324i		−	0.0484791i
$473$		−	47.6589i		−	2.19136i
$474$	−3.27191			−0.150284
$475$	−1.77468	−	9.08373i	−0.0814278	−	0.416790i
$476$	−13.7409			−0.629814
$477$		−	22.8668i		−	1.04700i
$478$		−	1.58711i		−	0.0725925i
$479$	34.1325			1.55955			0.779777	−	0.626057i	$-0.215332\pi$
$479$	34.1325			1.55955			0.779777	+	0.626057i	$0.215332\pi$
$480$	3.88048	−	4.71197i	0.177119	−	0.215071i
$481$	−3.91744			−0.178620
$482$			16.2576i			0.740513i
$483$			17.4446i			0.793757i
$484$	−11.7389			−0.533586
$485$	−25.7165	−	21.1785i	−1.16773	−	0.961667i
$486$	18.8121			0.853334
$487$			6.16917i			0.279552i	0.990183	+	0.139776i	$0.0446382\pi$
$487$			6.16917i			0.279552i	−0.990183	+	0.139776i	$0.955362\pi$
$488$			4.14422i			0.187600i
$489$	53.1230			2.40231
$490$	17.5499	+	14.4530i	0.792822	+	0.652918i
$491$	−11.8290			−0.533836			−0.266918	−	0.963719i	$-0.586005\pi$
$491$	−11.8290			−0.533836			−0.266918	+	0.963719i	$0.586005\pi$
$492$			13.8398i			0.623945i
$493$		−	29.4269i		−	1.32532i
$494$	−7.25154			−0.326262
$495$	−30.1787	+	36.6452i	−1.35643	+	1.64708i
$496$	9.75286			0.437916
$497$		−	26.7350i		−	1.19923i
$498$			29.1911i			1.30808i
$499$	−31.4004			−1.40568			−0.702839	−	0.711349i	$-0.748084\pi$
$499$	−31.4004			−1.40568			−0.702839	+	0.711349i	$0.748084\pi$
$500$	−9.83309	−	5.32076i	−0.439749	−	0.237951i
$501$	−19.4861			−0.870577
$502$			14.9486i			0.667189i
$503$		−	39.7743i		−	1.77345i	−0.462299	−	0.886724i	$-0.652975\pi$
$503$		−	39.7743i		−	1.77345i	0.462299	−	0.886724i	$-0.347025\pi$
$504$	18.4469			0.821692
$505$	−26.4260	+	32.0884i	−1.17594	+	1.42791i
$506$	7.35447			0.326946
$507$		−	6.40514i		−	0.284462i
$508$		−	8.33492i		−	0.369802i
$509$	6.82812			0.302651			0.151326	−	0.988484i	$-0.451646\pi$
$509$	6.82812			0.302651			0.151326	+	0.988484i	$0.451646\pi$
$510$	15.6266	+	12.8691i	0.691959	+	0.569854i
$511$	−44.6299			−1.97431
$512$			1.00000i			0.0441942i
$513$		−	7.33813i		−	0.323986i
$514$	−14.9968			−0.661480
$515$	−22.9625	−	18.9105i	−1.01185	−	0.833295i
$516$	27.2835			1.20109
$517$		−	23.0177i		−	1.01232i
$518$			4.14336i			0.182049i
$519$	−31.7209			−1.39239
$520$	−5.56861	+	6.76182i	−0.244200	+	0.296525i
$521$	−30.6638			−1.34341			−0.671703	−	0.740821i	$-0.734437\pi$
$521$	−30.6638			−1.34341			−0.671703	+	0.740821i	$0.734437\pi$
$522$			39.5051i			1.72909i
$523$		−	12.1618i		−	0.531800i	−0.964001	−	0.265900i	$-0.914331\pi$
$523$		−	12.1618i		−	0.531800i	0.964001	−	0.265900i	$-0.0856690\pi$
$524$	−3.68597			−0.161022
$525$	−10.8439	−	55.5048i	−0.473267	−	2.42243i
$526$	22.9610			1.00115
$527$			32.3441i			1.40893i
$528$		−	13.0174i		−	0.566512i
$529$	20.6213			0.896580
$530$	7.30094	−	8.86535i	0.317133	−	0.385086i
$531$	−4.68918			−0.203493
$532$			7.66975i			0.332526i
$533$		−	19.8605i		−	0.860253i
$534$	19.9163			0.861861
$535$	−21.5352	−	17.7350i	−0.931046	−	0.766751i
$536$	1.00811			0.0435437
$537$			47.0148i			2.02884i
$538$		−	10.0896i		−	0.434995i
$539$	48.4839			2.08835
$540$	−6.84256	−	5.63510i	−0.294457	−	0.242496i
$541$	10.5469			0.453446			0.226723	−	0.973959i	$-0.427199\pi$
$541$	10.5469			0.453446			0.226723	+	0.973959i	$0.427199\pi$
$542$			3.30678i			0.142038i
$543$		−	64.1785i		−	2.75416i
$544$	−3.31637			−0.142188
$545$	−6.18985	+	7.51617i	−0.265144	+	0.321957i
$546$	−44.3095			−1.89627
$547$			4.09517i			0.175097i	0.996160	+	0.0875484i	$0.0279032\pi$
$547$			4.09517i			0.175097i	−0.996160	+	0.0875484i	$0.972097\pi$
$548$			12.3027i			0.525546i
$549$	18.4507			0.787459
$550$	−23.4003	+	4.57168i	−0.997790	+	0.194937i
$551$	−16.4252			−0.699736
$552$			4.21025i			0.179200i
$553$		−	4.96607i		−	0.211179i
$554$	15.9046			0.675723
$555$	3.88048	−	4.71197i	0.164717	−	0.200012i
$556$	−0.842442			−0.0357275
$557$		−	2.50711i		−	0.106230i	−0.998588	−	0.0531149i	$-0.983085\pi$
$557$		−	2.50711i		−	0.106230i	0.998588	−	0.0531149i	$-0.0169149\pi$
$558$		−	43.4213i		−	1.83817i
$559$	−39.1527			−1.65598
$560$	7.15179	+	5.88976i	0.302218	+	0.248888i
$561$	43.1706			1.82267
$562$			11.3609i			0.479229i
$563$		−	9.87532i		−	0.416195i	−0.978108	−	0.208097i	$-0.933273\pi$
$563$		−	9.87532i		−	0.416195i	0.978108	−	0.208097i	$-0.0667271\pi$
$564$	13.1770			0.554854
$565$	16.4713	+	13.5647i	0.692954	+	0.570673i
$566$	20.1530			0.847092
$567$			10.5023i			0.441055i
$568$		−	6.45248i		−	0.270740i
$569$	−12.5198			−0.524858			−0.262429	−	0.964951i	$-0.584523\pi$
$569$	−12.5198			−0.524858			−0.262429	+	0.964951i	$0.584523\pi$
$570$	7.18314	−	8.72230i	0.300868	−	0.365337i
$571$	20.3156			0.850179			0.425090	−	0.905151i	$-0.360243\pi$
$571$	20.3156			0.850179			0.425090	+	0.905151i	$0.360243\pi$
$572$			18.6804i			0.781068i
$573$			3.18467i			0.133042i
$574$	−21.0059			−0.876769
$575$	7.56838	−	1.47863i	0.315623	−	0.0616629i
$576$	4.45216			0.185507
$577$			20.0756i			0.835759i	0.908502	+	0.417880i	$0.137227\pi$
$577$			20.0756i			0.835759i	−0.908502	+	0.417880i	$0.862773\pi$
$578$			6.00171i			0.249638i
$579$	−25.5714			−1.06271
$580$	−12.6132	+	15.3159i	−0.523736	+	0.635959i
$581$	−44.3059			−1.83812
$582$		−	40.6717i		−	1.68590i
$583$		−	24.4917i		−	1.01434i
$584$	−10.7714			−0.445724
$585$	30.1047	+	24.7924i	1.24468	+	1.02504i
$586$	−21.0517			−0.869639
$587$			3.71178i			0.153201i	0.997062	+	0.0766007i	$0.0244067\pi$
$587$			3.71178i			0.153201i	−0.997062	+	0.0766007i	$0.975593\pi$
$588$			27.7558i			1.14463i
$589$	18.0534			0.743879
$590$	−1.81797	−	1.49717i	−0.0748447	−	0.0616373i
$591$	−8.78569			−0.361395
$592$			1.00000i			0.0410997i
$593$		−	36.2899i		−	1.49025i	−0.666926	−	0.745124i	$-0.732390\pi$
$593$		−	36.2899i		−	1.49025i	0.666926	−	0.745124i	$-0.267610\pi$
$594$	−18.9035			−0.775619
$595$	−19.5326	+	23.7179i	−0.800759	+	0.972341i
$596$	−16.7723			−0.687019
$597$			8.16512i			0.334176i
$598$		−	6.04184i		−	0.247069i
$599$	−23.7528			−0.970515			−0.485257	−	0.874371i	$-0.661274\pi$
$599$	−23.7528			−0.970515			−0.485257	+	0.874371i	$0.661274\pi$
$600$	−2.61717	−	13.3961i	−0.106846	−	0.546892i
$601$	15.9718			0.651502			0.325751	−	0.945456i	$-0.394383\pi$
$601$	15.9718			0.651502			0.325751	+	0.945456i	$0.394383\pi$
$602$			41.4107i			1.68777i
$603$		−	4.48827i		−	0.182776i
$604$	7.59755			0.309140
$605$	−16.6867	+	20.2623i	−0.678413	+	0.823779i
$606$	−50.7490			−2.06154
$607$			38.0139i			1.54294i	0.636267	+	0.771469i	$0.280478\pi$
$607$			38.0139i			1.54294i	−0.636267	+	0.771469i	$0.719522\pi$
$608$			1.85109i			0.0750717i
$609$	−100.364			−4.06694
$610$	7.15326	+	5.89098i	0.289627	+	0.238519i
$611$	−18.9095			−0.764995
$612$			14.7650i			0.596840i
$613$			8.40204i			0.339355i	0.985500	+	0.169678i	$0.0542726\pi$
$613$			8.40204i			0.339355i	−0.985500	+	0.169678i	$0.945727\pi$
$614$	−17.0946			−0.689880
$615$	23.8886	+	19.6731i	0.963281	+	0.793298i
$616$	19.7578			0.796063
$617$		−	6.72707i		−	0.270822i	−0.990790	−	0.135411i	$-0.956765\pi$
$617$		−	6.72707i		−	0.270822i	0.990790	−	0.135411i	$-0.0432354\pi$
$618$		−	36.3161i		−	1.46085i
$619$	−24.3689			−0.979470			−0.489735	−	0.871871i	$-0.662906\pi$
$619$	−24.3689			−0.979470			−0.489735	+	0.871871i	$0.662906\pi$
$620$	13.8636	−	16.8342i	0.556776	−	0.676079i
$621$	6.11398			0.245345
$622$			20.0503i			0.803943i
$623$			30.2287i			1.21109i
$624$	−10.6941			−0.428106
$625$	−23.1617	+	9.40930i	−0.926469	+	0.376372i
$626$	13.3400			0.533172
$627$		−	24.0965i		−	0.962322i
$628$		−	4.45631i		−	0.177826i
$629$	−3.31637			−0.132232
$630$	26.2222	−	31.8409i	1.04472	−	1.26857i
$631$	34.7737			1.38432			0.692160	−	0.721744i	$-0.256659\pi$
$631$	34.7737			1.38432			0.692160	+	0.721744i	$0.256659\pi$
$632$		−	1.19856i		−	0.0476762i
$633$			12.9761i			0.515755i
$634$	−12.8528			−0.510450
$635$	−14.3868	−	11.8480i	−0.570921	−	0.470175i
$636$	14.0209			0.555964
$637$		−	39.8304i		−	1.57814i
$638$			42.3123i			1.67516i
$639$	−28.7275			−1.13644
$640$	1.72608	+	1.42149i	0.0682294	+	0.0561894i
$641$	−27.8544			−1.10018			−0.550091	−	0.835105i	$-0.685407\pi$
$641$	−27.8544			−1.10018			−0.550091	+	0.835105i	$0.685407\pi$
$642$		−	34.0587i		−	1.34419i
$643$			35.4013i			1.39609i	0.716054	+	0.698045i	$0.245947\pi$
$643$			35.4013i			1.39609i	−0.716054	+	0.698045i	$0.754053\pi$
$644$	−6.39028			−0.251812
$645$	38.7833	−	47.0936i	1.52709	−	1.85431i
$646$	−6.13890			−0.241532
$647$			16.1343i			0.634305i	0.948375	+	0.317152i	$0.102727\pi$
$647$			16.1343i			0.634305i	−0.948375	+	0.317152i	$0.897273\pi$
$648$			2.53473i			0.0995734i
$649$	−5.02239			−0.197146
$650$	3.75572	+	19.2238i	0.147312	+	0.754018i
$651$	110.313			4.32350
$652$			19.4599i			0.762110i
$653$		−	11.9146i		−	0.466256i	−0.972446	−	0.233128i	$-0.925104\pi$
$653$		−	11.9146i		−	0.466256i	0.972446	−	0.233128i	$-0.0748961\pi$
$654$	−11.8871			−0.464823
$655$	−5.23958	+	6.36229i	−0.204727	+	0.248595i
$656$	−5.06977			−0.197941
$657$			47.9561i			1.87095i
$658$			20.0000i			0.779681i
$659$	30.5124			1.18859			0.594297	−	0.804246i	$-0.297431\pi$
$659$	30.5124			1.18859			0.594297	+	0.804246i	$0.297431\pi$
$660$	−22.4692	−	18.5042i	−0.874612	−	0.720275i
$661$	42.0973			1.63740			0.818698	−	0.574224i	$-0.194696\pi$
$661$	42.0973			1.63740			0.818698	+	0.574224i	$0.194696\pi$
$662$		−	23.5835i		−	0.916600i
$663$		−	35.4655i		−	1.37737i
$664$	−10.6932			−0.414977
$665$	13.2386	+	10.9025i	0.513372	+	0.422781i
$666$	4.45216			0.172518
$667$		−	13.6851i		−	0.529890i
$668$		−	7.13813i		−	0.276183i
$669$	−18.9899			−0.734192
$670$	1.43302	−	1.74008i	0.0553623	−	0.0672251i
$671$	19.7618			0.762897
$672$			11.3108i			0.436324i
$673$			41.1540i			1.58637i	0.608982	+	0.793184i	$0.291578\pi$
$673$			41.1540i			1.58637i	−0.608982	+	0.793184i	$0.708422\pi$
$674$	−26.6074			−1.02488
$675$	−19.4533	+	3.80057i	−0.748757	+	0.146284i
$676$	2.34632			0.0902431
$677$		−	10.3914i		−	0.399373i	−0.979860	−	0.199686i	$-0.936008\pi$
$677$		−	10.3914i		−	0.399373i	0.979860	−	0.199686i	$-0.0639923\pi$
$678$			26.0500i			1.00045i
$679$	61.7311			2.36902
$680$	−4.71419	+	5.72432i	−0.180781	+	0.219518i
$681$	60.8706			2.33257
$682$		−	46.5068i		−	1.78084i
$683$		−	5.05345i		−	0.193365i	−0.995315	−	0.0966824i	$-0.969177\pi$
$683$		−	5.05345i		−	0.193365i	0.995315	−	0.0966824i	$-0.0308231\pi$
$684$	8.24137			0.315117
$685$	21.2355	+	17.4882i	0.811367	+	0.668190i
$686$	−13.1239			−0.501074
$687$		−	35.3922i		−	1.35030i
$688$			9.99446i			0.381035i
$689$	−20.1204			−0.766526
$690$	7.26724	+	5.98484i	0.276659	+	0.227839i
$691$	13.7857			0.524432			0.262216	−	0.965009i	$-0.415547\pi$
$691$	13.7857			0.524432			0.262216	+	0.965009i	$0.415547\pi$
$692$		−	11.6199i		−	0.441724i
$693$		−	87.9648i		−	3.34151i
$694$	17.2626			0.655280
$695$	−1.19753	+	1.45412i	−0.0454247	+	0.0551581i
$696$	−24.2227			−0.918160
$697$		−	16.8132i		−	0.636846i
$698$		−	11.1619i		−	0.422485i
$699$	−28.4798			−1.07721
$700$	20.3324	−	3.97232i	0.768493	−	0.150140i
$701$	−2.20512			−0.0832862			−0.0416431	−	0.999133i	$-0.513259\pi$
$701$	−2.20512			−0.0832862			−0.0416431	+	0.999133i	$0.513259\pi$
$702$			15.5296i			0.586125i
$703$			1.85109i			0.0698153i
$704$	4.76853			0.179721
$705$	18.7311	−	22.7447i	0.705453	−	0.856614i
$706$	−12.6563			−0.476327
$707$		−	77.0264i		−	2.89687i
$708$		−	2.87519i		−	0.108056i
$709$	12.7194			0.477687			0.238843	−	0.971058i	$-0.423232\pi$
$709$	12.7194			0.477687			0.238843	+	0.971058i	$0.423232\pi$
$710$	−11.1375	−	9.17215i	−0.417983	−	0.344225i
$711$	−5.33619			−0.200123
$712$			7.29569i			0.273418i
$713$			15.0418i			0.563318i
$714$	−37.5108			−1.40381
$715$	32.2439	+	26.5541i	1.20586	+	0.993066i
$716$	−17.2224			−0.643631
$717$		−	4.33258i		−	0.161803i
$718$			23.2778i			0.868718i
$719$	−34.9654			−1.30399			−0.651996	−	0.758223i	$-0.726068\pi$
$719$	−34.9654			−1.30399			−0.651996	+	0.758223i	$0.726068\pi$
$720$	6.32872	−	7.68480i	0.235857	−	0.286396i
$721$	55.1202			2.05278
$722$		−	15.5735i		−	0.579584i
$723$			44.3810i			1.65055i
$724$	23.5098			0.873733
$725$	8.50693	+	43.5429i	0.315940	+	1.61714i
$726$	−32.0456			−1.18932
$727$		−	9.90635i		−	0.367406i	−0.982982	−	0.183703i	$-0.941191\pi$
$727$		−	9.90635i		−	0.367406i	0.982982	−	0.183703i	$-0.0588085\pi$
$728$		−	16.2314i		−	0.601575i
$729$	43.7503			1.62038
$730$	−15.3115	+	18.5923i	−0.566703	+	0.688133i
$731$	−33.1453			−1.22592
$732$			11.3132i			0.418146i
$733$		−	37.3826i		−	1.38076i	−0.723448	−	0.690379i	$-0.757444\pi$
$733$		−	37.3826i		−	1.38076i	0.723448	−	0.690379i	$-0.242556\pi$
$734$	9.09417			0.335672
$735$	47.9088	+	39.4547i	1.76714	+	1.45531i
$736$	−1.54229			−0.0568497
$737$		−	4.80720i		−	0.177075i
$738$			22.5714i			0.830866i
$739$	−14.4487			−0.531506			−0.265753	−	0.964041i	$-0.585620\pi$
$739$	−14.4487			−0.531506			−0.265753	+	0.964041i	$0.585620\pi$
$740$	1.72608	+	1.42149i	0.0634520	+	0.0522551i
$741$	−19.7957			−0.727215
$742$			21.2808i			0.781242i
$743$		−	45.1826i		−	1.65759i	−0.559553	−	0.828794i	$-0.689027\pi$
$743$		−	45.1826i		−	1.65759i	0.559553	−	0.828794i	$-0.310973\pi$
$744$	26.6240			0.976083
$745$	−23.8416	+	28.9503i	−0.873490	+	1.06066i
$746$	5.75976			0.210880
$747$			47.6080i			1.74188i
$748$			15.8142i			0.578224i
$749$	51.6939			1.88886
$750$	−26.8430	−	14.5249i	−0.980168	−	0.530376i
$751$	49.3127			1.79945			0.899723	−	0.436461i	$-0.143768\pi$
$751$	49.3127			1.79945			0.899723	+	0.436461i	$0.143768\pi$
$752$			4.82700i			0.176022i
$753$			40.8077i			1.48711i
$754$	34.7603			1.26590
$755$	10.7999	−	13.1140i	0.393047	−	0.477267i
$756$	16.4252			0.597378
$757$			21.5911i			0.784741i	0.919807	+	0.392370i	$0.128345\pi$
$757$			21.5911i			0.784741i	−0.919807	+	0.392370i	$0.871655\pi$
$758$		−	18.0902i		−	0.657064i
$759$	20.0767			0.728738
$760$	3.19514	+	2.63131i	0.115900	+	0.0954478i
$761$	18.4253			0.667917			0.333959	−	0.942588i	$-0.391615\pi$
$761$	18.4253			0.667917			0.333959	+	0.942588i	$0.391615\pi$
$762$		−	22.7532i		−	0.824262i
$763$		−	18.0422i		−	0.653170i
$764$	−1.16660			−0.0422063
$765$	25.4856	+	20.9884i	0.921435	+	0.758835i
$766$	3.54752			0.128177
$767$			4.12598i			0.148981i
$768$			2.72987i			0.0985055i
$769$	−6.50829			−0.234695			−0.117348	−	0.993091i	$-0.537439\pi$
$769$	−6.50829			−0.234695			−0.117348	+	0.993091i	$0.537439\pi$
$770$	28.0855	−	34.1035i	1.01213	−	1.22901i
$771$	−40.9392			−1.47439
$772$		−	9.36727i		−	0.337135i
$773$			40.5853i			1.45975i	0.683581	+	0.729875i	$0.260422\pi$
$773$			40.5853i			1.45975i	−0.683581	+	0.729875i	$0.739578\pi$
$774$	44.4970			1.59941
$775$	−9.35025	−	47.8595i	−0.335871	−	1.71916i
$776$	14.8988			0.534835
$777$			11.3108i			0.405774i
$778$		−	25.6053i		−	0.917993i
$779$	−9.38461			−0.336239
$780$	−15.2015	+	18.4589i	−0.544303	+	0.660933i
$781$	−30.7688			−1.10100
$782$		−	5.11481i		−	0.182905i
$783$			35.1754i			1.25707i
$784$	−10.1675			−0.363124
$785$	−7.69196	−	6.33461i	−0.274538	−	0.226092i
$786$	−10.0622			−0.358907
$787$		−	37.5389i		−	1.33812i	−0.743210	−	0.669059i	$-0.766698\pi$
$787$		−	37.5389i		−	1.33812i	0.743210	−	0.669059i	$-0.233302\pi$
$788$		−	3.21836i		−	0.114649i
$789$	62.6804			2.23148
$790$	−2.06881	−	1.70374i	−0.0736051	−	0.0606165i
$791$	−39.5385			−1.40583
$792$		−	21.2303i		−	0.754385i
$793$		−	16.2347i		−	0.576512i
$794$	−31.4597			−1.11646
$795$	19.9306	−	24.2012i	0.706865	−	0.858328i
$796$	−2.99104			−0.106014
$797$			28.8746i			1.02279i	0.859345	+	0.511396i	$0.170871\pi$
$797$			28.8746i			1.02279i	−0.859345	+	0.511396i	$0.829129\pi$
$798$			20.9374i			0.741176i
$799$	−16.0081			−0.566326
$800$	4.90723	−	0.958719i	0.173497	−	0.0338958i
$801$	32.4816			1.14768
$802$		−	22.9940i		−	0.811945i
$803$			51.3638i			1.81259i
$804$	2.75200			0.0970556
$805$	−9.08373	+	11.0301i	−0.320159	+	0.388762i
$806$	−38.2062			−1.34576
$807$		−	27.5433i		−	0.969571i
$808$		−	18.5903i		−	0.654004i
$809$	8.98633			0.315943			0.157971	−	0.987444i	$-0.449505\pi$
$809$	8.98633			0.315943			0.157971	+	0.987444i	$0.449505\pi$
$810$	4.37515	+	3.60309i	0.153727	+	0.126600i
$811$	−24.4949			−0.860134			−0.430067	−	0.902797i	$-0.641510\pi$
$811$	−24.4949			−0.860134			−0.430067	+	0.902797i	$0.641510\pi$
$812$		−	36.7650i		−	1.29020i
$813$			9.02706i			0.316593i
$814$	4.76853			0.167137
$815$	33.5895	+	27.6622i	1.17659	+	0.968963i
$816$	−9.05324			−0.316927
$817$			18.5007i			0.647257i
$818$			33.3828i			1.16720i
$819$	−72.2647			−2.52513
$820$	−7.20663	+	8.75083i	−0.251667	+	0.305592i
$821$	27.1346			0.947005			0.473502	−	0.880793i	$-0.342990\pi$
$821$	27.1346			0.947005			0.473502	+	0.880793i	$0.342990\pi$
$822$			33.5848i			1.17140i
$823$			10.7460i			0.374584i	0.982304	+	0.187292i	$0.0599710\pi$
$823$			10.7460i			0.374584i	−0.982304	+	0.187292i	$0.940029\pi$
$824$	13.3033			0.463441
$825$	−63.8795	+	12.4801i	−2.22400	+	0.434500i
$826$	4.36394			0.151841
$827$			19.1035i			0.664293i	0.943228	+	0.332147i	$0.107773\pi$
$827$			19.1035i			0.664293i	−0.943228	+	0.332147i	$0.892227\pi$
$828$			6.86654i			0.238629i
$829$	−51.1250			−1.77565			−0.887823	−	0.460185i	$-0.847783\pi$
$829$	−51.1250			−1.77565			−0.887823	+	0.460185i	$0.847783\pi$
$830$	−15.2003	+	18.4574i	−0.527611	+	0.640665i
$831$	43.4175			1.50614
$832$		−	3.91744i		−	0.135813i
$833$		−	33.7190i		−	1.16830i
$834$	−2.29975			−0.0796340
$835$	−12.3210	−	10.1468i	−0.426386	−	0.351145i
$836$	8.82700			0.305288
$837$		−	38.6624i		−	1.33637i
$838$		−	8.32565i		−	0.287605i
$839$	42.1947			1.45672			0.728361	−	0.685193i	$-0.240282\pi$
$839$	42.1947			1.45672			0.728361	+	0.685193i	$0.240282\pi$
$840$	19.5234	+	16.0782i	0.673622	+	0.554752i
$841$	49.7342			1.71497
$842$		−	8.41521i		−	0.290007i
$843$			31.0136i			1.06816i
$844$	−4.75340			−0.163619
$845$	3.33528	−	4.04994i	0.114737	−	0.139322i
$846$	21.4906			0.738861
$847$		−	48.6385i		−	1.67124i
$848$			5.13611i			0.176375i
$849$	55.0148			1.88810
$850$	3.17946	+	16.2742i	0.109055	+	0.558199i
$851$	−1.54229			−0.0528691
$852$		−	17.6144i		−	0.603459i
$853$		−	42.5489i		−	1.45685i	−0.685128	−	0.728423i	$-0.740254\pi$
$853$		−	42.5489i		−	1.45685i	0.685128	−	0.728423i	$-0.259746\pi$
$854$	−17.1710			−0.587580
$855$	11.7150	−	14.2253i	0.400646	−	0.486494i
$856$	12.4763			0.426432
$857$			29.7588i			1.01654i	0.861197	+	0.508271i	$0.169715\pi$
$857$			29.7588i			1.01654i	−0.861197	+	0.508271i	$0.830285\pi$
$858$			50.9950i			1.74094i
$859$	−8.40182			−0.286666			−0.143333	−	0.989674i	$-0.545782\pi$
$859$	−8.40182			−0.286666			−0.143333	+	0.989674i	$0.545782\pi$
$860$	17.2513	+	14.2070i	0.588263	+	0.484456i
$861$	−57.3432			−1.95425
$862$			3.04769i			0.103805i
$863$			36.3794i			1.23837i	0.785245	+	0.619185i	$0.212537\pi$
$863$			36.3794i			1.23837i	−0.785245	+	0.619185i	$0.787463\pi$
$864$	3.96421			0.134865
$865$	−20.0570	−	16.5177i	−0.681957	−	0.561617i
$866$	22.9439			0.779667
$867$			16.3839i			0.556425i
$868$			40.4096i			1.37159i
$869$	−5.71537			−0.193881
$870$	−34.4324	+	41.8104i	−1.16737	+	1.41751i
$871$	−3.94920			−0.133814
$872$		−	4.35447i		−	0.147461i
$873$		−	66.3318i		−	2.24499i
$874$	−2.85493			−0.0965694
$875$	22.0458	−	40.7420i	0.745285	−	1.37733i
$876$	−29.4045			−0.993486
$877$			41.3380i			1.39588i	0.716154	+	0.697942i	$0.245901\pi$
$877$			41.3380i			1.39588i	−0.716154	+	0.697942i	$0.754099\pi$
$878$		−	10.3033i		−	0.347720i
$879$	−57.4684			−1.93836
$880$	6.77843	−	8.23088i	0.228501	−	0.277463i
$881$	21.1354			0.712071			0.356035	−	0.934472i	$-0.384128\pi$
$881$	21.1354			0.712071			0.356035	+	0.934472i	$0.384128\pi$
$882$			45.2672i			1.52423i
$883$			10.7365i			0.361312i	0.983546	+	0.180656i	$0.0578221\pi$
$883$			10.7365i			0.361312i	−0.983546	+	0.180656i	$0.942178\pi$
$884$	12.9917			0.436957
$885$	−4.96281	−	4.08706i	−0.166823	−	0.137385i
$886$	−4.84236			−0.162682
$887$		−	11.1798i		−	0.375379i	−0.982228	−	0.187690i	$-0.939900\pi$
$887$		−	11.1798i		−	0.375379i	0.982228	−	0.187690i	$-0.0600999\pi$
$888$			2.72987i			0.0916083i
$889$	34.5346			1.15825
$890$	12.5930	+	10.3708i	0.422117	+	0.347629i
$891$	12.0869			0.404927
$892$		−	6.95635i		−	0.232916i
$893$			8.93522i			0.299006i
$894$	−45.7860			−1.53131
$895$	−24.4815	+	29.7273i	−0.818327	+	0.993674i
$896$	−4.14336			−0.138420
$897$		−	16.4934i		−	0.550698i
$898$		−	25.3149i		−	0.844768i
$899$	−86.5393			−2.88625
$900$	−4.26837	−	21.8478i	−0.142279	−	0.728259i
$901$	−17.0332			−0.567459
$902$			24.1753i			0.804951i
$903$			113.046i			3.76192i
$904$	−9.54261			−0.317382
$905$	33.4189	−	40.5798i	1.11088	−	1.34892i
$906$	20.7403			0.689050
$907$		−	20.5343i		−	0.681831i	−0.940094	−	0.340915i	$-0.889263\pi$
$907$		−	20.5343i		−	0.681831i	0.940094	−	0.340915i	$-0.110737\pi$
$908$			22.2980i			0.739986i
$909$	−82.7671			−2.74521
$910$	−28.0167	−	23.0728i	−0.928744	−	0.764855i
$911$	17.5197			0.580454			0.290227	−	0.956958i	$-0.406269\pi$
$911$	17.5197			0.580454			0.290227	+	0.956958i	$0.406269\pi$
$912$			5.05324i			0.167329i
$913$			50.9910i			1.68755i
$914$	−11.9945			−0.396741
$915$	19.5274	+	16.0816i	0.645557	+	0.531640i
$916$	12.9648			0.428370
$917$		−	15.2723i		−	0.504336i
$918$			13.1468i			0.433909i
$919$	−43.8760			−1.44734			−0.723668	−	0.690149i	$-0.757545\pi$
$919$	−43.8760			−1.44734			−0.723668	+	0.690149i	$0.757545\pi$
$920$	−2.19236	+	2.66212i	−0.0722799	+	0.0877676i
$921$	−46.6658			−1.53769
$922$		−	23.6570i		−	0.779103i
$923$			25.2772i			0.832009i
$924$	53.9360			1.77436
$925$	4.90723	−	0.958719i	0.161349	−	0.0315225i
$926$	−17.3667			−0.570705
$927$		−	59.2283i		−	1.94531i
$928$		−	8.87323i		−	0.291278i
$929$	21.9800			0.721142			0.360571	−	0.932732i	$-0.382582\pi$
$929$	21.9800			0.721142			0.360571	+	0.932732i	$0.382582\pi$
$930$	37.8458	−	45.9552i	1.24101	−	1.50693i
$931$	−18.8209			−0.616831
$932$		−	10.4327i		−	0.341734i
$933$			54.7346i			1.79193i
$934$	20.4476			0.669065
$935$	27.2966	+	22.4798i	0.892695	+	0.735167i
$936$	−17.4411			−0.570079
$937$		−	9.62735i		−	0.314512i	−0.987558	−	0.157256i	$-0.949735\pi$
$937$		−	9.62735i		−	0.314512i	0.987558	−	0.157256i	$-0.0502648\pi$
$938$			4.17696i			0.136383i
$939$	36.4163			1.18840
$940$	8.33179	+	6.86154i	0.271753	+	0.223799i
$941$	−28.3548			−0.924340			−0.462170	−	0.886791i	$-0.652929\pi$
$941$	−28.3548			−0.924340			−0.462170	+	0.886791i	$0.652929\pi$
$942$		−	12.1651i		−	0.396361i
$943$		−	7.81906i		−	0.254624i
$944$	1.05324			0.0342799
$945$	23.3483	−	28.3512i	0.759519	−	0.922265i
$946$	47.6589			1.54952
$947$		−	12.5179i		−	0.406778i	−0.979098	−	0.203389i	$-0.934804\pi$
$947$		−	12.5179i		−	0.406778i	0.979098	−	0.203389i	$-0.0651956\pi$
$948$		−	3.27191i		−	0.106267i
$949$	42.1963			1.36975
$950$	9.08373	−	1.77468i	0.294715	−	0.0575782i
$951$	−35.0864			−1.13776
$952$		−	13.7409i		−	0.445346i
$953$			3.39730i			0.110049i	0.998485	+	0.0550247i	$0.0175238\pi$
$953$			3.39730i			0.110049i	−0.998485	+	0.0550247i	$0.982476\pi$
$954$	22.8668			0.740340
$955$	−1.65832	+	2.01366i	−0.0536620	+	0.0651603i
$956$	1.58711			0.0513307
$957$			115.507i			3.73380i
$958$			34.1325i			1.10277i
$959$	−50.9746			−1.64606
$960$	4.71197	+	3.88048i	0.152078	+	0.125242i
$961$	64.1182			2.06833
$962$		−	3.91744i		−	0.126303i
$963$		−	55.5466i		−	1.78997i
$964$	−16.2576			−0.523622
$965$	−16.1687	−	13.3155i	−0.520488	−	0.428641i
$966$	−17.4446			−0.561271
$967$			2.54955i			0.0819879i	0.999159	+	0.0409940i	$0.0130524\pi$
$967$			2.54955i			0.0819879i	−0.999159	+	0.0409940i	$0.986948\pi$
$968$		−	11.7389i		−	0.377302i
$969$	−16.7584			−0.538357
$970$	21.1785	−	25.7165i	0.680001	−	0.825708i
$971$	−35.2223			−1.13034			−0.565168	−	0.824976i	$-0.691189\pi$
$971$	−35.2223			−1.13034			−0.565168	+	0.824976i	$0.691189\pi$
$972$			18.8121i			0.603398i
$973$		−	3.49054i		−	0.111902i
$974$	−6.16917			−0.197673
$975$	10.2526	+	52.4782i	0.328346	+	1.68065i
$976$	−4.14422			−0.132653
$977$		−	5.79786i		−	0.185490i	−0.995690	−	0.0927450i	$-0.970436\pi$
$977$		−	5.79786i		−	0.185490i	0.995690	−	0.0927450i	$-0.0295641\pi$
$978$			53.1230i			1.69869i
$979$	34.7897			1.11188
$980$	−14.4530	+	17.5499i	−0.461683	+	0.560610i
$981$	−19.3868			−0.618973
$982$		−	11.8290i		−	0.377479i
$983$			20.6825i			0.659671i	0.944038	+	0.329835i	$0.106993\pi$
$983$			20.6825i			0.659671i	−0.944038	+	0.329835i	$0.893007\pi$
$984$	−13.8398			−0.441196
$985$	−5.55515	−	4.57487i	−0.177002	−	0.145768i
$986$	29.4269			0.937143
$987$			54.5973i			1.73785i
$988$		−	7.25154i		−	0.230702i
$989$	−15.4144			−0.490149
$990$	−36.6452	−	30.1787i	−1.16466	−	0.959142i
$991$	49.7158			1.57927			0.789637	−	0.613574i	$-0.210269\pi$
$991$	49.7158			1.57927			0.789637	+	0.613574i	$0.210269\pi$
$992$			9.75286i			0.309654i
$993$		−	64.3799i		−	2.04303i
$994$	26.7350			0.847981
$995$	−4.25173	+	5.16277i	−0.134789	+	0.163671i
$996$	−29.1911			−0.924954
$997$		−	53.1550i		−	1.68344i	−0.539918	−	0.841718i	$-0.681545\pi$
$997$		−	53.1550i		−	1.68344i	0.539918	−	0.841718i	$-0.318455\pi$
$998$		−	31.4004i		−	0.993964i
$999$	3.96421			0.125422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.b.d.149.10	yes	10
3.2	odd	2		3330.2.d.p.1999.5		10
5.2	odd	4		1850.2.a.bd.1.5		5
5.3	odd	4		1850.2.a.be.1.1		5
5.4	even	2	inner	370.2.b.d.149.1	✓	10
15.14	odd	2		3330.2.d.p.1999.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.b.d.149.1	✓	10	5.4	even	2	inner
370.2.b.d.149.10	yes	10	1.1	even	1	trivial
1850.2.a.bd.1.5		5	5.2	odd	4
1850.2.a.be.1.1		5	5.3	odd	4
3330.2.d.p.1999.5		10	3.2	odd	2
3330.2.d.p.1999.10		10	15.14	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +2.72987i q^{3} -1.00000 q^{4} +(-1.42149 + 1.72608i) q^{5} -2.72987 q^{6} -4.14336i q^{7} -1.00000i q^{8} -4.45216 q^{9} +(-1.72608 - 1.42149i) q^{10} -4.76853 q^{11} -2.72987i q^{12} +3.91744i q^{13} +4.14336 q^{14} +(-4.71197 - 3.88048i) q^{15} +1.00000 q^{16} +3.31637i q^{17} -4.45216i q^{18} +1.85109 q^{19} +(1.42149 - 1.72608i) q^{20} +11.3108 q^{21} -4.76853i q^{22} +1.54229i q^{23} +2.72987 q^{24} +(-0.958719 - 4.90723i) q^{25} -3.91744 q^{26} -3.96421i q^{27} +4.14336i q^{28} -8.87323 q^{29} +(3.88048 - 4.71197i) q^{30} +9.75286 q^{31} +1.00000i q^{32} -13.0174i q^{33} -3.31637 q^{34} +(7.15179 + 5.88976i) q^{35} +4.45216 q^{36} +1.00000i q^{37} +1.85109i q^{38} -10.6941 q^{39} +(1.72608 + 1.42149i) q^{40} -5.06977 q^{41} +11.3108i q^{42} +9.99446i q^{43} +4.76853 q^{44} +(6.32872 - 7.68480i) q^{45} -1.54229 q^{46} +4.82700i q^{47} +2.72987i q^{48} -10.1675 q^{49} +(4.90723 - 0.958719i) q^{50} -9.05324 q^{51} -3.91744i q^{52} +5.13611i q^{53} +3.96421 q^{54} +(6.77843 - 8.23088i) q^{55} -4.14336 q^{56} +5.05324i q^{57} -8.87323i q^{58} +1.05324 q^{59} +(4.71197 + 3.88048i) q^{60} -4.14422 q^{61} +9.75286i q^{62} +18.4469i q^{63} -1.00000 q^{64} +(-6.76182 - 5.56861i) q^{65} +13.0174 q^{66} +1.00811i q^{67} -3.31637i q^{68} -4.21025 q^{69} +(-5.88976 + 7.15179i) q^{70} +6.45248 q^{71} +4.45216i q^{72} -10.7714i q^{73} -1.00000 q^{74} +(13.3961 - 2.61717i) q^{75} -1.85109 q^{76} +19.7578i q^{77} -10.6941i q^{78} +1.19856 q^{79} +(-1.42149 + 1.72608i) q^{80} -2.53473 q^{81} -5.06977i q^{82} -10.6932i q^{83} -11.3108 q^{84} +(-5.72432 - 4.71419i) q^{85} -9.99446 q^{86} -24.2227i q^{87} +4.76853i q^{88} -7.29569 q^{89} +(7.68480 + 6.32872i) q^{90} +16.2314 q^{91} -1.54229i q^{92} +26.6240i q^{93} -4.82700 q^{94} +(-2.63131 + 3.19514i) q^{95} -2.72987 q^{96} +14.8988i q^{97} -10.1675i q^{98} +21.2303 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{4} + 6 q^{5} - 6 q^{9} + 2 q^{10} + 6 q^{11} + 2 q^{14} + 10 q^{16} - 8 q^{19} - 6 q^{20} + 32 q^{21} + 4 q^{25} - 12 q^{26} - 22 q^{29} + 20 q^{30} + 46 q^{31} - 18 q^{34} + 32 q^{35} + 6 q^{36}+ \cdots + 22 q^{99}+O(q^{100}) \) 10 * q - 10 * q^4 + 6 * q^5 - 6 * q^9 + 2 * q^10 + 6 * q^11 + 2 * q^14 + 10 * q^16 - 8 * q^19 - 6 * q^20 + 32 * q^21 + 4 * q^25 - 12 * q^26 - 22 * q^29 + 20 * q^30 + 46 * q^31 - 18 * q^34 + 32 * q^35 + 6 * q^36 - 40 * q^39 - 2 * q^40 - 14 * q^41 - 6 * q^44 + 2 * q^45 + 12 * q^46 - 60 * q^49 + 8 * q^50 - 40 * q^51 + 42 * q^55 - 2 * q^56 - 40 * q^59 - 18 * q^61 - 10 * q^64 + 4 * q^65 + 40 * q^66 - 32 * q^69 - 6 * q^70 + 12 * q^71 - 10 * q^74 + 50 * q^75 + 8 * q^76 - 40 * q^79 + 6 * q^80 - 14 * q^81 - 32 * q^84 + 36 * q^85 - 34 * q^86 - 24 * q^89 + 44 * q^90 + 32 * q^91 - 24 * q^94 + 12 * q^95 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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