LMFDB - Embedded newform 630.2.bv.c.523.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(73,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("630.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bv (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			523.4
Root			$0.587308 + 2.01725i$ of defining polynomial
Character	$\chi$	$=$	630.523
Dual form			630.2.bv.c.577.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(2.21323 + 0.318742i) q^{5} +(0.559876 - 2.58583i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(2.21323 + 0.318742i) q^{5} +(0.559876 - 2.58583i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.264946 + 2.22032i) q^{10} +(1.83557 + 3.17930i) q^{11} +(0.830578 - 0.830578i) q^{13} +(2.64263 - 0.128464i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.204036 - 0.761471i) q^{17} +(1.09461 - 1.89593i) q^{19} +(-2.07609 + 0.830578i) q^{20} +(-2.59589 + 2.59589i) q^{22} +(4.54529 - 1.21791i) q^{23} +(4.79681 + 1.41090i) q^{25} +(1.01725 + 0.587308i) q^{26} +(0.808050 + 2.51934i) q^{28} +2.62236i q^{29} +(0.0359651 - 0.0207644i) q^{31} +(0.965926 + 0.258819i) q^{32} +0.788333 q^{34} +(2.06335 - 5.54460i) q^{35} +(0.0664979 + 0.248174i) q^{37} +(2.11463 + 0.566614i) q^{38} +(-1.33961 - 1.79038i) q^{40} +8.98026i q^{41} +(-0.474569 - 0.474569i) q^{43} +(-3.17930 - 1.83557i) q^{44} +(2.35282 + 4.07520i) q^{46} +(-6.18205 + 1.65648i) q^{47} +(-6.37308 - 2.89549i) q^{49} +(-0.121320 + 4.99853i) q^{50} +(-0.304013 + 1.13459i) q^{52} +(-2.04824 + 7.64413i) q^{53} +(3.04917 + 7.62161i) q^{55} +(-2.22435 + 1.43257i) q^{56} +(-2.53301 + 0.678717i) q^{58} +(-5.35616 - 9.27713i) q^{59} +(1.72539 + 0.996157i) q^{61} +(0.0293654 + 0.0293654i) q^{62} +1.00000i q^{64} +(2.10300 - 1.57352i) q^{65} +(6.39671 + 1.71399i) q^{67} +(0.204036 + 0.761471i) q^{68} +(5.88971 + 0.557996i) q^{70} -8.11777 q^{71} +(9.52910 + 2.55331i) q^{73} +(-0.222506 + 0.128464i) q^{74} +2.18923i q^{76} +(9.24884 - 2.96647i) q^{77} +(-11.6145 - 6.70563i) q^{79} +(1.38266 - 1.75735i) q^{80} +(-8.67427 + 2.32426i) q^{82} +(9.73033 - 9.73033i) q^{83} +(0.694291 - 1.62028i) q^{85} +(0.335571 - 0.581226i) q^{86} +(0.950161 - 3.54605i) q^{88} +(-0.715130 + 1.23864i) q^{89} +(-1.68272 - 2.61276i) q^{91} +(-3.32739 + 3.32739i) q^{92} +(-3.20007 - 5.54268i) q^{94} +(3.02695 - 3.84723i) q^{95} +(-3.16693 - 3.16693i) q^{97} +(1.14736 - 6.90533i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) $ 16 * q + 12 * q^5 + 8 * q^7	$ 16 q + 12 q^{5} + 8 q^{7} - 12 q^{10} + 12 q^{11} + 8 q^{16} + 36 q^{17} - 8 q^{22} + 4 q^{23} + 12 q^{25} - 12 q^{26} + 4 q^{28} + 24 q^{31} - 8 q^{35} + 4 q^{37} - 24 q^{38} - 8 q^{43} - 8 q^{46} - 12 q^{47} + 32 q^{50} + 28 q^{53} + 4 q^{56} - 32 q^{58} - 12 q^{61} + 8 q^{65} + 32 q^{67} + 36 q^{68} - 12 q^{70} - 16 q^{71} - 12 q^{73} - 16 q^{77} + 12 q^{80} - 48 q^{82} + 24 q^{85} - 12 q^{86} - 4 q^{88} - 16 q^{91} - 8 q^{92} - 20 q^{95} - 40 q^{98}+O(q^{100}) $ 16 * q + 12 * q^5 + 8 * q^7 - 12 * q^10 + 12 * q^11 + 8 * q^16 + 36 * q^17 - 8 * q^22 + 4 * q^23 + 12 * q^25 - 12 * q^26 + 4 * q^28 + 24 * q^31 - 8 * q^35 + 4 * q^37 - 24 * q^38 - 8 * q^43 - 8 * q^46 - 12 * q^47 + 32 * q^50 + 28 * q^53 + 4 * q^56 - 32 * q^58 - 12 * q^61 + 8 * q^65 + 32 * q^67 + 36 * q^68 - 12 * q^70 - 16 * q^71 - 12 * q^73 - 16 * q^77 + 12 * q^80 - 48 * q^82 + 24 * q^85 - 12 * q^86 - 4 * q^88 - 16 * q^91 - 8 * q^92 - 20 * q^95 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	2.21323	+	0.318742i	0.989788	+	0.142546i
$5$	2.21323	+	0.318742i	0.989788	+	0.142546i
$6$		0			0
$7$	0.559876	−	2.58583i	0.211613	−	0.977353i
$7$	0.559876	−	2.58583i	0.211613	−	0.977353i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	0.264946	+	2.22032i	0.0837833	+	0.702126i
$11$	1.83557	+	3.17930i	0.553445	+	0.958596i	0.998023	+	0.0628551i	$0.0200206\pi$
$11$	1.83557	+	3.17930i	0.553445	+	0.958596i	−0.444577	+	0.895741i	$0.646646\pi$
$12$		0			0
$13$	0.830578	−	0.830578i	0.230361	−	0.230361i	−0.582482	−	0.812843i	$-0.697918\pi$
$13$	0.830578	−	0.830578i	0.230361	−	0.230361i	0.812843	+	0.582482i	$0.197918\pi$
$14$	2.64263	−	0.128464i	0.706273	−	0.0343335i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.204036	−	0.761471i	0.0494859	−	0.184684i	−0.936759	−	0.349976i	$-0.886190\pi$
$17$	0.204036	−	0.761471i	0.0494859	−	0.184684i	0.986245	+	0.165292i	$0.0528565\pi$
$18$		0			0
$19$	1.09461	−	1.89593i	0.251122	−	0.434955i	−0.712713	−	0.701455i	$-0.752534\pi$
$19$	1.09461	−	1.89593i	0.251122	−	0.434955i	0.963835	+	0.266500i	$0.0858673\pi$
$20$	−2.07609	+	0.830578i	−0.464227	+	0.185723i
$21$		0			0
$22$	−2.59589	+	2.59589i	−0.553445	+	0.553445i
$23$	4.54529	−	1.21791i	0.947759	−	0.253951i	0.248348	−	0.968671i	$-0.420112\pi$
$23$	4.54529	−	1.21791i	0.947759	−	0.253951i	0.699411	+	0.714719i	$0.253446\pi$
$24$		0			0
$25$	4.79681	+	1.41090i	0.959361	+	0.282180i
$26$	1.01725	+	0.587308i	0.199498	+	0.115180i
$27$		0			0
$28$	0.808050	+	2.51934i	0.152707	+	0.476110i
$29$			2.62236i			0.486960i	0.969906	+	0.243480i	$0.0782891\pi$
$29$			2.62236i			0.486960i	−0.969906	+	0.243480i	$0.921711\pi$
$30$		0			0
$31$	0.0359651	−	0.0207644i	0.00645952	−	0.00372940i	−0.496767	−	0.867884i	$-0.665480\pi$
$31$	0.0359651	−	0.0207644i	0.00645952	−	0.00372940i	0.503226	+	0.864155i	$0.332146\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$		0			0
$34$	0.788333			0.135198
$35$	2.06335	−	5.54460i	0.348770	−	0.937208i
$36$		0			0
$37$	0.0664979	+	0.248174i	0.0109322	+	0.0407995i	0.971176	−	0.238362i	$-0.0766103\pi$
$37$	0.0664979	+	0.248174i	0.0109322	+	0.0407995i	−0.960244	+	0.279161i	$0.909944\pi$
$38$	2.11463	+	0.566614i	0.343038	+	0.0919169i
$39$		0			0
$40$	−1.33961	−	1.79038i	−0.211811	−	0.283083i
$41$			8.98026i			1.40248i	0.712925	+	0.701241i	$0.247370\pi$
$41$			8.98026i			1.40248i	−0.712925	+	0.701241i	$0.752630\pi$
$42$		0			0
$43$	−0.474569	−	0.474569i	−0.0723711	−	0.0723711i	0.669995	−	0.742366i	$-0.266296\pi$
$43$	−0.474569	−	0.474569i	−0.0723711	−	0.0723711i	−0.742366	+	0.669995i	$0.766296\pi$
$44$	−3.17930	−	1.83557i	−0.479298	−	0.276723i
$45$		0			0
$46$	2.35282	+	4.07520i	0.346904	+	0.600855i
$47$	−6.18205	+	1.65648i	−0.901745	+	0.241622i	−0.679766	−	0.733429i	$-0.737919\pi$
$47$	−6.18205	+	1.65648i	−0.901745	+	0.241622i	−0.221980	+	0.975051i	$0.571252\pi$
$48$		0			0
$49$	−6.37308	−	2.89549i	−0.910440	−	0.413642i
$50$	−0.121320	+	4.99853i	−0.0171573	+	0.706899i
$51$		0			0
$52$	−0.304013	+	1.13459i	−0.0421590	+	0.157339i
$53$	−2.04824	+	7.64413i	−0.281347	+	1.05000i	0.670120	+	0.742252i	$0.266242\pi$
$53$	−2.04824	+	7.64413i	−0.281347	+	1.05000i	−0.951468	+	0.307749i	$0.900424\pi$
$54$		0			0
$55$	3.04917	+	7.62161i	0.411150	+	1.02770i
$56$	−2.22435	+	1.43257i	−0.297242	+	0.191435i
$57$		0			0
$58$	−2.53301	+	0.678717i	−0.332600	+	0.0891199i
$59$	−5.35616	−	9.27713i	−0.697312	−	1.20778i	−0.969395	−	0.245506i	$-0.921046\pi$
$59$	−5.35616	−	9.27713i	−0.697312	−	1.20778i	0.272083	−	0.962274i	$-0.412287\pi$
$60$		0			0
$61$	1.72539	+	0.996157i	0.220914	+	0.127545i	0.606373	−	0.795180i	$-0.292624\pi$
$61$	1.72539	+	0.996157i	0.220914	+	0.127545i	−0.385459	+	0.922725i	$0.625957\pi$
$62$	0.0293654	+	0.0293654i	0.00372940	+	0.00372940i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	2.10300	−	1.57352i	0.260846	−	0.195172i
$66$		0			0
$67$	6.39671	+	1.71399i	0.781482	+	0.209398i	0.627438	−	0.778666i	$-0.284103\pi$
$67$	6.39671	+	1.71399i	0.781482	+	0.209398i	0.154044	+	0.988064i	$0.450770\pi$
$68$	0.204036	+	0.761471i	0.0247430	+	0.0923420i
$69$		0			0
$70$	5.88971	+	0.557996i	0.703955	+	0.0666933i
$71$	−8.11777			−0.963402			−0.481701	−	0.876336i	$-0.659981\pi$
$71$	−8.11777			−0.963402			−0.481701	+	0.876336i	$0.659981\pi$
$72$		0			0
$73$	9.52910	+	2.55331i	1.11530	+	0.298843i	0.768979	−	0.639274i	$-0.220765\pi$
$73$	9.52910	+	2.55331i	1.11530	+	0.298843i	0.346318	+	0.938117i	$0.387432\pi$
$74$	−0.222506	+	0.128464i	−0.0258658	+	0.0149336i
$75$		0			0
$76$			2.18923i			0.251122i
$77$	9.24884	−	2.96647i	1.05400	−	0.338060i
$78$		0			0
$79$	−11.6145	−	6.70563i	−1.30673	−	0.754443i	−0.325184	−	0.945651i	$-0.605426\pi$
$79$	−11.6145	−	6.70563i	−1.30673	−	0.754443i	−0.981550	+	0.191208i	$0.938760\pi$
$80$	1.38266	−	1.75735i	0.154586	−	0.196477i
$81$		0			0
$82$	−8.67427	+	2.32426i	−0.957912	+	0.256672i
$83$	9.73033	−	9.73033i	1.06804	−	1.06804i	0.0705331	−	0.997509i	$-0.477530\pi$
$83$	9.73033	−	9.73033i	1.06804	−	1.06804i	0.997509	−	0.0705331i	$-0.0224700\pi$
$84$		0			0
$85$	0.694291	−	1.62028i	0.0753065	−	0.175744i
$86$	0.335571	−	0.581226i	0.0361855	−	0.0626752i
$87$		0			0
$88$	0.950161	−	3.54605i	0.101288	−	0.378010i
$89$	−0.715130	+	1.23864i	−0.0758036	+	0.131296i	−0.901435	−	0.432914i	$-0.857486\pi$
$89$	−0.715130	+	1.23864i	−0.0758036	+	0.131296i	0.825632	+	0.564209i	$0.190819\pi$
$90$		0			0
$91$	−1.68272	−	2.61276i	−0.176397	−	0.273892i
$92$	−3.32739	+	3.32739i	−0.346904	+	0.346904i
$93$		0			0
$94$	−3.20007	−	5.54268i	−0.330062	−	0.571684i
$95$	3.02695	−	3.84723i	0.310558	−	0.394717i
$96$		0			0
$97$	−3.16693	−	3.16693i	−0.321553	−	0.321553i	0.527810	−	0.849363i	$-0.323013\pi$
$97$	−3.16693	−	3.16693i	−0.321553	−	0.321553i	−0.849363	+	0.527810i	$0.823013\pi$
$98$	1.14736	−	6.90533i	0.115901	−	0.697544i
$99$		0			0
$100$	−4.85961	+	1.17653i	−0.485961	+	0.117653i
$101$	0.0622734	−	0.0359536i	0.00619644	−	0.00357751i	−0.496899	−	0.867809i	$-0.665528\pi$
$101$	0.0622734	−	0.0359536i	0.00619644	−	0.00357751i	0.503095	+	0.864231i	$0.332195\pi$
$102$		0			0
$103$	−4.29116	−	16.0148i	−0.422820	−	1.57799i	−0.768638	−	0.639685i	$-0.779065\pi$
$103$	−4.29116	−	16.0148i	−0.422820	−	1.57799i	0.345817	−	0.938302i	$-0.387602\pi$
$104$	−1.17462			−0.115180
$105$		0			0
$106$	−7.91378			−0.768654
$107$	−1.18265	−	4.41372i	−0.114331	−	0.426690i	0.884905	−	0.465772i	$-0.154223\pi$
$107$	−1.18265	−	4.41372i	−0.114331	−	0.426690i	−0.999236	+	0.0390819i	$0.987557\pi$
$108$		0			0
$109$	−15.6773	+	9.05131i	−1.50162	+	0.866958i	−0.501617	+	0.865090i	$0.667261\pi$
$109$	−15.6773	+	9.05131i	−1.50162	+	0.866958i	−0.999998	+	0.00186842i	$0.999405\pi$
$110$	−6.57273	+	4.91789i	−0.626685	+	0.468902i
$111$		0			0
$112$	−1.95946	−	1.77778i	−0.185152	−	0.167985i
$113$	−1.52064	−	1.52064i	−0.143049	−	0.143049i	0.631955	−	0.775005i	$-0.282253\pi$
$113$	−1.52064	−	1.52064i	−0.143049	−	0.143049i	−0.775005	+	0.631955i	$0.782253\pi$
$114$		0			0
$115$	10.4480	−	1.24674i	0.974281	−	0.116259i
$116$	−1.31118	−	2.27103i	−0.121740	−	0.210860i
$117$		0			0
$118$	7.57475	−	7.57475i	0.697312	−	0.697312i
$119$	−1.85480	−	0.953932i	−0.170030	−	0.0874468i
$120$		0			0
$121$	−1.23864	+	2.14539i	−0.112604	+	0.195035i
$122$	−0.515649	+	1.92443i	−0.0466846	+	0.174229i
$123$		0			0
$124$	−0.0207644	+	0.0359651i	−0.00186470	+	0.00322976i
$125$	10.1667	+	4.65160i	0.909341	+	0.416051i
$126$		0			0
$127$	−13.2527	+	13.2527i	−1.17599	+	1.17599i	−0.195234	+	0.980757i	$0.562547\pi$
$127$	−13.2527	+	13.2527i	−1.17599	+	1.17599i	−0.980757	+	0.195234i	$0.937453\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$		0			0
$130$	2.06420	+	1.62409i	0.181043	+	0.142442i
$131$	−12.2929	−	7.09731i	−1.07404	−	0.620095i	−0.144755	−	0.989468i	$-0.546239\pi$
$131$	−12.2929	−	7.09731i	−1.07404	−	0.620095i	−0.929281	+	0.369372i	$0.879573\pi$
$132$		0			0
$133$	−4.28970	−	3.89197i	−0.371964	−	0.337477i
$134$			6.62236i			0.572085i
$135$		0			0
$136$	−0.682717	+	0.394167i	−0.0585425	+	0.0337995i
$137$	−18.3201	−	4.90887i	−1.56519	−	0.419393i	−0.630891	−	0.775871i	$-0.717311\pi$
$137$	−18.3201	−	4.90887i	−1.56519	−	0.419393i	−0.934303	+	0.356479i	$0.883977\pi$
$138$		0			0
$139$	8.23706			0.698658			0.349329	−	0.937000i	$-0.386409\pi$
$139$	8.23706			0.698658			0.349329	+	0.937000i	$0.386409\pi$
$140$	0.985385	+	5.83344i	0.0832803	+	0.493016i
$141$		0			0
$142$	−2.10103	−	7.84116i	−0.176315	−	0.658016i
$143$	4.16524	+	1.11607i	0.348315	+	0.0933308i
$144$		0			0
$145$	−0.835856	+	5.80390i	−0.0694141	+	0.481988i
$146$			9.86525i			0.816454i
$147$		0			0
$148$	−0.181676	−	0.181676i	−0.0149336	−	0.0149336i
$149$	−4.19317	−	2.42093i	−0.343518	−	0.198330i	0.318309	−	0.947987i	$-0.396885\pi$
$149$	−4.19317	−	2.42093i	−0.343518	−	0.198330i	−0.661826	+	0.749657i	$0.730218\pi$
$150$		0			0
$151$	−5.02292	−	8.69995i	−0.408759	−	0.707992i	0.585992	−	0.810317i	$-0.300705\pi$
$151$	−5.02292	−	8.69995i	−0.408759	−	0.707992i	−0.994751	+	0.102325i	$0.967372\pi$
$152$	−2.11463	+	0.566614i	−0.171519	+	0.0459584i
$153$		0			0
$154$	5.25916	+	8.16592i	0.423795	+	0.658028i
$155$	0.0862176	−	0.0344930i	0.00692516	−	0.00277054i
$156$		0			0
$157$	6.33762	−	23.6523i	0.505797	−	1.88766i	0.0474774	−	0.998872i	$-0.484882\pi$
$157$	6.33762	−	23.6523i	0.505797	−	1.88766i	0.458320	−	0.888788i	$-0.348452\pi$
$158$	3.47109	−	12.9543i	0.276145	−	1.03059i
$159$		0			0
$160$	2.05532	+	0.880708i	0.162488	+	0.0696261i
$161$	−0.604505	−	12.4353i	−0.0476417	−	0.980035i
$162$		0			0
$163$	21.2171	−	5.68510i	1.66185	−	0.445291i	0.698954	−	0.715166i	$-0.253649\pi$
$163$	21.2171	−	5.68510i	1.66185	−	0.445291i	0.962895	+	0.269875i	$0.0869823\pi$
$164$	−4.49013	−	7.77713i	−0.350620	−	0.607292i
$165$		0			0
$166$	11.9172	+	6.88038i	0.924952	+	0.534021i
$167$	3.14616	+	3.14616i	0.243457	+	0.243457i	0.818279	−	0.574821i	$-0.194928\pi$
$167$	3.14616	+	3.14616i	0.243457	+	0.243457i	−0.574821	+	0.818279i	$0.694928\pi$
$168$		0			0
$169$			11.6203i			0.893868i
$170$	1.74477	+	0.251275i	0.133817	+	0.0192719i
$171$		0			0
$172$	0.648273	+	0.173704i	0.0494304	+	0.0132448i
$173$	1.35273	+	5.04844i	0.102846	+	0.383826i	0.998092	−	0.0617463i	$-0.0196670\pi$
$173$	1.35273	+	5.04844i	0.102846	+	0.383826i	−0.895246	+	0.445572i	$0.853000\pi$
$174$		0			0
$175$	6.33397	−	11.6138i	0.478803	−	0.877922i
$176$	3.67114			0.276723
$177$		0			0
$178$	−1.38152	−	0.370178i	−0.103550	−	0.0277460i
$179$	−10.8847	+	6.28428i	−0.813560	+	0.469709i	−0.848191	−	0.529691i	$-0.822308\pi$
$179$	−10.8847	+	6.28428i	−0.813560	+	0.469709i	0.0346308	+	0.999400i	$0.488974\pi$
$180$		0			0
$181$			11.6742i			0.867740i	0.900976	+	0.433870i	$0.142852\pi$
$181$			11.6742i			0.867740i	−0.900976	+	0.433870i	$0.857148\pi$
$182$	2.08821	−	2.30161i	0.154789	−	0.170607i
$183$		0			0
$184$	−4.07520	−	2.35282i	−0.300428	−	0.173452i
$185$	0.0680721	+	0.570462i	0.00500476	+	0.0419412i
$186$		0			0
$187$	2.79547	−	0.749044i	0.204425	−	0.0547755i
$188$	4.52558	−	4.52558i	0.330062	−	0.330062i
$189$		0			0
$190$	4.49957	+	1.92807i	0.326433	+	0.139877i
$191$	7.75170	−	13.4263i	0.560894	−	0.971496i	−0.436525	−	0.899692i	$-0.643791\pi$
$191$	7.75170	−	13.4263i	0.560894	−	0.971496i	0.997419	−	0.0718040i	$-0.0228756\pi$
$192$		0			0
$193$	2.32883	−	8.69132i	0.167633	−	0.625615i	−0.830057	−	0.557679i	$-0.811692\pi$
$193$	2.32883	−	8.69132i	0.167633	−	0.625615i	0.997690	−	0.0679359i	$-0.0216413\pi$
$194$	2.23936	−	3.87868i	0.160776	−	0.278473i
$195$		0			0
$196$	6.96699	−	0.678966i	0.497642	−	0.0484976i
$197$	−12.1951	+	12.1951i	−0.868865	+	0.868865i	−0.992347	−	0.123482i	$-0.960594\pi$
$197$	−12.1951	+	12.1951i	−0.868865	+	0.868865i	0.123482	+	0.992347i	$0.460594\pi$
$198$		0			0
$199$	4.36557	+	7.56140i	0.309467	+	0.536013i	0.978246	−	0.207448i	$-0.0665159\pi$
$199$	4.36557	+	7.56140i	0.309467	+	0.536013i	−0.668779	+	0.743462i	$0.733183\pi$
$200$	−2.39420	−	4.38951i	−0.169295	−	0.310385i
$201$		0			0
$202$	0.0508460	+	0.0508460i	0.00357751	+	0.00357751i
$203$	6.78099	+	1.46820i	0.475932	+	0.103047i
$204$		0			0
$205$	−2.86239	+	19.8754i	−0.199918	+	1.38816i
$206$	14.3585	−	8.28988i	1.00040	−	0.577583i
$207$		0			0
$208$	−0.304013	−	1.13459i	−0.0210795	−	0.0786697i
$209$	8.03696			0.555928
$210$		0			0
$211$	−11.1745			−0.769288			−0.384644	−	0.923065i	$-0.625676\pi$
$211$	−11.1745			−0.769288			−0.384644	+	0.923065i	$0.625676\pi$
$212$	−2.04824	−	7.64413i	−0.140674	−	0.525001i
$213$		0			0
$214$	3.95723	−	2.28471i	0.270511	−	0.156179i
$215$	−0.899067	−	1.20160i	−0.0613158	−	0.0819482i
$216$		0			0
$217$	−0.0335574	−	0.104625i	−0.00227803	−	0.00710242i
$218$	−12.8005	−	12.8005i	−0.866958	−	0.866958i
$219$		0			0
$220$	−6.45147	−	5.07592i	−0.434958	−	0.342219i
$221$	−0.462994	−	0.801929i	−0.0311443	−	0.0539436i
$222$		0			0
$223$	0.746804	−	0.746804i	0.0500097	−	0.0500097i	−0.681660	−	0.731669i	$-0.738742\pi$
$223$	0.746804	−	0.746804i	0.0500097	−	0.0500097i	0.731669	+	0.681660i	$0.238742\pi$
$224$	1.21006	−	2.35282i	0.0808507	−	0.157204i
$225$		0			0
$226$	1.07525	−	1.86239i	0.0715247	−	0.123884i
$227$	0.807609	−	3.01404i	0.0536029	−	0.200049i	−0.933932	−	0.357452i	$-0.883646\pi$
$227$	0.807609	−	3.01404i	0.0536029	−	0.200049i	0.987534	+	0.157403i	$0.0503122\pi$
$228$		0			0
$229$	4.21091	−	7.29350i	0.278264	−	0.481968i	−0.692689	−	0.721236i	$-0.743574\pi$
$229$	4.21091	−	7.29350i	0.278264	−	0.481968i	0.970954	+	0.239268i	$0.0769075\pi$
$230$	3.90840	+	9.76931i	0.257712	+	0.644169i
$231$		0			0
$232$	1.85429	−	1.85429i	0.121740	−	0.121740i
$233$	−22.0201	+	5.90027i	−1.44259	+	0.386540i	−0.893439	−	0.449186i	$-0.851714\pi$
$233$	−22.0201	+	5.90027i	−1.44259	+	0.386540i	−0.549148	+	0.835725i	$0.685048\pi$
$234$		0			0
$235$	−14.2103	+	1.69569i	−0.926979	+	0.110615i
$236$	9.27713	+	5.35616i	0.603890	+	0.348656i
$237$		0			0
$238$	0.441369	−	2.03850i	0.0286097	−	0.132136i
$239$			23.9971i			1.55224i	0.630585	+	0.776120i	$0.282815\pi$
$239$			23.9971i			1.55224i	−0.630585	+	0.776120i	$0.717185\pi$
$240$		0			0
$241$	−21.4666	+	12.3937i	−1.38278	+	0.798350i	−0.992488	−	0.122340i	$-0.960960\pi$
$241$	−21.4666	+	12.3937i	−1.38278	+	0.798350i	−0.390295	+	0.920690i	$0.627627\pi$
$242$	−2.39287	−	0.641168i	−0.153820	−	0.0412158i
$243$		0			0
$244$	−1.99231			−0.127545
$245$	−13.1822	−	8.43977i	−0.842179	−	0.539197i
$246$		0			0
$247$	−0.665553	−	2.48388i	−0.0423481	−	0.158045i
$248$	−0.0401138	−	0.0107485i	−0.00254723	−	0.000682528i
$249$		0			0
$250$	−1.86175	+	11.0242i	−0.117747	+	0.697234i
$251$			11.1158i			0.701623i	0.936446	+	0.350811i	$0.114094\pi$
$251$			11.1158i			0.701623i	−0.936446	+	0.350811i	$0.885906\pi$
$252$		0			0
$253$	12.2153	+	12.2153i	0.767970	+	0.767970i
$254$	−16.2312	−	9.37110i	−1.01844	−	0.587995i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	24.4314	−	6.54637i	1.52399	−	0.408351i	0.602935	−	0.797790i	$-0.293998\pi$
$257$	24.4314	−	6.54637i	1.52399	−	0.408351i	0.921052	+	0.389439i	$0.127331\pi$
$258$		0			0
$259$	0.678966	−	0.0330060i	0.0421889	−	0.00205090i
$260$	−1.03449	+	2.41421i	−0.0641565	+	0.149723i
$261$		0			0
$262$	3.67384	−	13.7110i	0.226971	−	0.847066i
$263$	−2.93659	+	10.9595i	−0.181078	+	0.675792i	0.814358	+	0.580363i	$0.197089\pi$
$263$	−2.93659	+	10.9595i	−0.181078	+	0.675792i	−0.995436	+	0.0954297i	$0.969577\pi$
$264$		0			0
$265$	−6.96973	+	16.2654i	−0.428147	+	0.999174i
$266$	2.64910	−	5.15085i	0.162427	−	0.315819i
$267$		0			0
$268$	−6.39671	+	1.71399i	−0.390741	+	0.104699i
$269$	4.03346	+	6.98616i	0.245924	+	0.425954i	0.962391	−	0.271668i	$-0.0875752\pi$
$269$	4.03346	+	6.98616i	0.245924	+	0.425954i	−0.716467	+	0.697621i	$0.754242\pi$
$270$		0			0
$271$	7.27419	+	4.19976i	0.441876	+	0.255117i	0.704393	−	0.709810i	$-0.251219\pi$
$271$	7.27419	+	4.19976i	0.441876	+	0.255117i	−0.262517	+	0.964927i	$0.584553\pi$
$272$	−0.557436	−	0.557436i	−0.0337995	−	0.0337995i
$273$		0			0
$274$		−	18.9664i		−	1.14580i
$275$	4.31920	+	17.8403i	0.260458	+	1.07581i
$276$		0			0
$277$	−5.48646	−	1.47009i	−0.329650	−	0.0883293i	0.0901983	−	0.995924i	$-0.471250\pi$
$277$	−5.48646	−	1.47009i	−0.329650	−	0.0883293i	−0.419848	+	0.907594i	$0.637917\pi$
$278$	2.13191	+	7.95639i	0.127863	+	0.477193i
$279$		0			0
$280$	−5.37963	+	2.46161i	−0.321495	+	0.147110i
$281$	−7.27627			−0.434066			−0.217033	−	0.976164i	$-0.569638\pi$
$281$	−7.27627			−0.434066			−0.217033	+	0.976164i	$0.569638\pi$
$282$		0			0
$283$	−7.44729	−	1.99550i	−0.442696	−	0.118620i	0.0305840	−	0.999532i	$-0.490263\pi$
$283$	−7.44729	−	1.99550i	−0.442696	−	0.118620i	−0.473280	+	0.880912i	$0.656930\pi$
$284$	7.03019	−	4.05888i	0.417165	−	0.240850i
$285$		0			0
$286$			4.31218i			0.254984i
$287$	23.2215	+	5.02784i	1.37072	+	0.296784i
$288$		0			0
$289$	14.1842	+	8.18927i	0.834366	+	0.481721i
$290$	−5.82247	+	0.694784i	−0.341907	+	0.0407991i
$291$		0			0
$292$	−9.52910	+	2.55331i	−0.557648	+	0.149421i
$293$	−3.35198	+	3.35198i	−0.195824	+	0.195824i	−0.798207	−	0.602383i	$-0.794218\pi$
$293$	−3.35198	+	3.35198i	−0.195824	+	0.195824i	0.602383	+	0.798207i	$0.294218\pi$
$294$		0			0
$295$	−8.89741	−	22.2397i	−0.518027	−	1.29485i
$296$	0.128464	−	0.222506i	0.00746682	−	0.0129329i
$297$		0			0
$298$	1.25316	−	4.67687i	0.0725938	−	0.270924i
$299$	2.76365	−	4.78679i	0.159826	−	0.276827i
$300$		0			0
$301$	−1.49286	+	0.961456i	−0.0860468	+	0.0554174i
$302$	7.10348	−	7.10348i	0.408759	−	0.408759i
$303$		0			0
$304$	−1.09461	−	1.89593i	−0.0627804	−	0.108739i
$305$	3.50118	+	2.75468i	0.200477	+	0.157733i
$306$		0			0
$307$	−1.06546	−	1.06546i	−0.0608089	−	0.0608089i	0.676048	−	0.736857i	$-0.263691\pi$
$307$	−1.06546	−	1.06546i	−0.0608089	−	0.0608089i	−0.736857	+	0.676048i	$0.763691\pi$
$308$	−6.52650	+	7.19345i	−0.371882	+	0.409885i
$309$		0			0
$310$	0.0556324	+	0.0743524i	0.00315971	+	0.00422293i
$311$	−11.9584	+	6.90417i	−0.678097	+	0.391500i	−0.799138	−	0.601148i	$-0.794710\pi$
$311$	−11.9584	+	6.90417i	−0.678097	+	0.391500i	0.121040	+	0.992648i	$0.461377\pi$
$312$		0			0
$313$	6.04266	+	22.5515i	0.341551	+	1.27469i	0.896590	+	0.442863i	$0.146037\pi$
$313$	6.04266	+	22.5515i	0.341551	+	1.27469i	−0.555038	+	0.831825i	$0.687296\pi$
$314$	24.4867			1.38186
$315$		0			0
$316$	13.4113			0.754443
$317$	−3.41352	−	12.7394i	−0.191722	−	0.715518i	−0.993091	−	0.117347i	$-0.962561\pi$
$317$	−3.41352	−	12.7394i	−0.191722	−	0.715518i	0.801369	−	0.598171i	$-0.204106\pi$
$318$		0			0
$319$	−8.33728	+	4.81353i	−0.466798	+	0.269506i
$320$	−0.318742	+	2.21323i	−0.0178182	+	0.123724i
$321$		0			0
$322$	11.8551	−	3.80239i	0.660658	−	0.211899i
$323$	−1.22035	−	1.22035i	−0.0679023	−	0.0679023i
$324$		0			0
$325$	5.15599	−	2.81226i	0.286003	−	0.155996i
$326$	10.9828	+	19.0227i	0.608279	+	1.05357i
$327$		0			0
$328$	6.35000	−	6.35000i	0.350620	−	0.350620i
$329$	0.822187	+	16.9132i	0.0453286	+	0.932454i
$330$		0			0
$331$	9.54799	−	16.5376i	0.524805	−	0.908989i	−0.474778	−	0.880106i	$-0.657472\pi$
$331$	9.54799	−	16.5376i	0.524805	−	0.908989i	0.999583	−	0.0288830i	$-0.00919501\pi$
$332$	−3.56155	+	13.2919i	−0.195465	+	0.729487i
$333$		0			0
$334$	−2.22467	+	3.85325i	−0.121729	+	0.210840i
$335$	13.6111	+	5.83237i	0.743653	+	0.318656i
$336$		0			0
$337$	0.488226	−	0.488226i	0.0265953	−	0.0265953i	−0.693684	−	0.720279i	$-0.744014\pi$
$337$	0.488226	−	0.488226i	0.0265953	−	0.0265953i	0.720279	+	0.693684i	$0.244014\pi$
$338$	−11.2243	+	3.00755i	−0.610523	+	0.163589i
$339$		0			0
$340$	0.208866	+	1.75035i	0.0113273	+	0.0949260i
$341$	0.132033	+	0.0762292i	0.00714998	+	0.00412804i
$342$		0			0
$343$	−11.0554	+	14.8586i	−0.596936	+	0.802289i
$344$			0.671142i			0.0361855i
$345$		0			0
$346$	−4.52631	+	2.61327i	−0.243336	+	0.140490i
$347$	3.68015	+	0.986094i	0.197561	+	0.0529363i	0.356243	−	0.934393i	$-0.384058\pi$
$347$	3.68015	+	0.986094i	0.197561	+	0.0529363i	−0.158682	+	0.987330i	$0.550724\pi$
$348$		0			0
$349$	−7.91303			−0.423575			−0.211787	−	0.977316i	$-0.567928\pi$
$349$	−7.91303			−0.423575			−0.211787	+	0.977316i	$0.567928\pi$
$350$	12.8574	+	3.11227i	0.687259	+	0.166358i
$351$		0			0
$352$	0.950161	+	3.54605i	0.0506438	+	0.189005i
$353$	24.9004	+	6.67203i	1.32531	+	0.355116i	0.850965	−	0.525222i	$-0.176018\pi$
$353$	24.9004	+	6.67203i	1.32531	+	0.355116i	0.474347	+	0.880338i	$0.342684\pi$
$354$		0			0
$355$	−17.9665	−	2.58747i	−0.953564	−	0.137329i
$356$		−	1.43026i		−	0.0758036i
$357$		0			0
$358$	−8.88731	−	8.88731i	−0.469709	−	0.469709i
$359$	−8.99497	−	5.19325i	−0.474737	−	0.274089i	0.243484	−	0.969905i	$-0.421710\pi$
$359$	−8.99497	−	5.19325i	−0.474737	−	0.274089i	−0.718220	+	0.695816i	$0.755043\pi$
$360$		0			0
$361$	7.10364	+	12.3039i	0.373876	+	0.647572i
$362$	−11.2765	+	3.02152i	−0.592677	+	0.158807i
$363$		0			0
$364$	2.76365	+	1.42136i	0.144855	+	0.0744994i
$365$	20.2763	+	8.68840i	1.06131	+	0.454772i
$366$		0			0
$367$	−2.24811	+	8.39004i	−0.117350	+	0.437957i	−0.999452	−	0.0331020i	$-0.989461\pi$
$367$	−2.24811	+	8.39004i	−0.117350	+	0.437957i	0.882102	+	0.471059i	$0.156128\pi$
$368$	1.21791	−	4.54529i	0.0634878	−	0.236940i
$369$		0			0
$370$	−0.533405	+	0.213399i	−0.0277304	+	0.0110941i
$371$	18.6197	+	9.57617i	0.966686	+	0.497170i
$372$		0			0
$373$	−12.8560	+	3.44476i	−0.665660	+	0.178363i	−0.575799	−	0.817591i	$-0.695309\pi$
$373$	−12.8560	+	3.44476i	−0.665660	+	0.178363i	−0.0898611	+	0.995954i	$0.528642\pi$
$374$	1.44704	+	2.50635i	0.0748247	+	0.129600i
$375$		0			0
$376$	5.54268	+	3.20007i	0.285842	+	0.165031i
$377$	2.17808	+	2.17808i	0.112177	+	0.112177i
$378$		0			0
$379$			25.3453i			1.30190i	0.759121	+	0.650949i	$0.225629\pi$
$379$			25.3453i			1.30190i	−0.759121	+	0.650949i	$0.774371\pi$
$380$	−0.697798	+	4.84527i	−0.0357963	+	0.248557i
$381$		0			0
$382$	14.9751	+	4.01258i	0.766195	+	0.205301i
$383$	−4.76251	−	17.7739i	−0.243353	−	0.908205i	−0.974204	−	0.225668i	$-0.927543\pi$
$383$	−4.76251	−	17.7739i	−0.243353	−	0.908205i	0.730851	−	0.682537i	$-0.239123\pi$
$384$		0			0
$385$	21.4154	−	3.61749i	1.09143	−	0.184364i
$386$	8.99792			0.457982
$387$		0			0
$388$	4.32611	+	1.15918i	0.219625	+	0.0588483i
$389$	19.3621	−	11.1787i	0.981699	−	0.566784i	0.0789164	−	0.996881i	$-0.474854\pi$
$389$	19.3621	−	11.1787i	0.981699	−	0.566784i	0.902783	+	0.430097i	$0.141521\pi$
$390$		0			0
$391$		−	3.70961i		−	0.187603i
$392$	2.45902	+	6.55387i	0.124199	+	0.331020i
$393$		0			0
$394$	−14.9359	−	8.62324i	−0.752459	−	0.434432i
$395$	−23.5682	−	18.5432i	−1.18585	−	0.933008i
$396$		0			0
$397$	−15.2461	+	4.08518i	−0.765181	+	0.205029i	−0.620241	−	0.784411i	$-0.712965\pi$
$397$	−15.2461	+	4.08518i	−0.765181	+	0.205029i	−0.144939	+	0.989441i	$0.546299\pi$
$398$	−6.17385	+	6.17385i	−0.309467	+	0.309467i
$399$		0			0
$400$	3.62028	−	3.44871i	0.181014	−	0.172435i
$401$	6.98528	−	12.0989i	0.348828	−	0.604188i	−0.637213	−	0.770687i	$-0.719913\pi$
$401$	6.98528	−	12.0989i	0.348828	−	0.604188i	0.986042	+	0.166499i	$0.0532463\pi$
$402$		0			0
$403$	0.0126253	−	0.0471183i	0.000628911	−	0.00234713i
$404$	−0.0359536	+	0.0622734i	−0.00178876	+	0.00309822i
$405$		0			0
$406$	0.336879	+	6.92993i	0.0167190	+	0.343927i
$407$	−0.666957	+	0.666957i	−0.0330598	+	0.0330598i
$408$		0			0
$409$	−0.156681	−	0.271379i	−0.00774737	−	0.0134188i	0.862126	−	0.506694i	$-0.169133\pi$
$409$	−0.156681	−	0.271379i	−0.00774737	−	0.0134188i	−0.869873	+	0.493276i	$0.835799\pi$
$410$	−19.9390	+	2.37928i	−0.984718	+	0.117504i
$411$		0			0
$412$	11.7237	+	11.7237i	0.577583	+	0.577583i
$413$	−26.9879	+	8.65608i	−1.32799	+	0.425938i
$414$		0			0
$415$	24.6370	−	18.4340i	1.20938	−	0.904891i
$416$	1.01725	−	0.587308i	0.0498746	−	0.0287951i
$417$		0			0
$418$	2.08012	+	7.76311i	0.101742	+	0.379706i
$419$	−31.6254			−1.54500			−0.772501	−	0.635014i	$-0.780994\pi$
$419$	−31.6254			−1.54500			−0.772501	+	0.635014i	$0.780994\pi$
$420$		0			0
$421$	24.2137			1.18011			0.590053	−	0.807365i	$-0.299107\pi$
$421$	24.2137			1.18011			0.590053	+	0.807365i	$0.299107\pi$
$422$	−2.89219	−	10.7938i	−0.140789	−	0.525433i
$423$		0			0
$424$	6.85354	−	3.95689i	0.332837	−	0.192164i
$425$	2.05308	−	3.36476i	0.0995890	−	0.163215i
$426$		0			0
$427$	3.54190	−	3.90386i	0.171405	−	0.188921i
$428$	3.23107	+	3.23107i	0.156179	+	0.156179i
$429$		0			0
$430$	0.927958	−	1.17943i	0.0447501	−	0.0568771i
$431$	0.779037	+	1.34933i	0.0375249	+	0.0649950i	0.884178	−	0.467150i	$-0.154719\pi$
$431$	0.779037	+	1.34933i	0.0375249	+	0.0649950i	−0.846653	+	0.532145i	$0.821386\pi$
$432$		0			0
$433$	6.28166	−	6.28166i	0.301877	−	0.301877i	−0.539871	−	0.841748i	$-0.681527\pi$
$433$	6.28166	−	6.28166i	0.301877	−	0.301877i	0.841748	+	0.539871i	$0.181527\pi$
$434$	0.0923749	−	0.0594930i	0.00443414	−	0.00285575i
$435$		0			0
$436$	9.05131	−	15.6773i	0.433479	−	0.750808i
$437$	2.66628	−	9.95068i	0.127545	−	0.476006i
$438$		0			0
$439$	11.9571	−	20.7103i	0.570681	−	0.988449i	−0.425815	−	0.904810i	$-0.640012\pi$
$439$	11.9571	−	20.7103i	0.570681	−	0.988449i	0.996496	−	0.0836389i	$-0.0266542\pi$
$440$	3.23320	−	7.54538i	0.154137	−	0.359712i
$441$		0			0
$442$	0.654772	−	0.654772i	0.0311443	−	0.0311443i
$443$	12.4238	−	3.32895i	0.590272	−	0.158163i	0.0486946	−	0.998814i	$-0.484494\pi$
$443$	12.4238	−	3.32895i	0.590272	−	0.158163i	0.541578	+	0.840651i	$0.317827\pi$
$444$		0			0
$445$	−1.97756	+	2.51346i	−0.0937451	+	0.119149i
$446$	0.914645	+	0.528070i	0.0433097	+	0.0250049i
$447$		0			0
$448$	2.58583	+	0.559876i	0.122169	+	0.0264517i
$449$			17.8932i			0.844435i	0.906495	+	0.422217i	$0.138748\pi$
$449$			17.8932i			0.844435i	−0.906495	+	0.422217i	$0.861252\pi$
$450$		0			0
$451$	−28.5510	+	16.4839i	−1.34441	+	0.776197i
$452$	2.07723	+	0.556592i	0.0977046	+	0.0261799i
$453$		0			0
$454$	3.12036			0.146446
$455$	−2.89145	−	6.31900i	−0.135553	−	0.296239i
$456$		0			0
$457$	8.85449	+	33.0454i	0.414196	+	1.54580i	0.786442	+	0.617665i	$0.211921\pi$
$457$	8.85449	+	33.0454i	0.414196	+	1.54580i	−0.372246	+	0.928134i	$0.621412\pi$
$458$	8.13485	+	2.17973i	0.380116	+	0.101852i
$459$		0			0
$460$	−8.42486	+	6.30371i	−0.392811	+	0.293912i
$461$		−	23.3471i		−	1.08738i	−0.839286	−	0.543690i	$-0.817027\pi$
$461$		−	23.3471i		−	1.08738i	0.839286	−	0.543690i	$-0.182973\pi$
$462$		0			0
$463$	3.98510	+	3.98510i	0.185203	+	0.185203i	0.793619	−	0.608415i	$-0.208195\pi$
$463$	3.98510	+	3.98510i	0.185203	+	0.185203i	−0.608415	+	0.793619i	$0.708195\pi$
$464$	2.27103	+	1.31118i	0.105430	+	0.0608700i
$465$		0			0
$466$	−11.3985	−	19.7427i	−0.528023	−	0.914563i
$467$	4.71932	−	1.26454i	0.218384	−	0.0585159i	−0.147968	−	0.988992i	$-0.547273\pi$
$467$	4.71932	−	1.26454i	0.218384	−	0.0585159i	0.366352	+	0.930476i	$0.380607\pi$
$468$		0			0
$469$	8.01347	−	15.5812i	0.370028	−	0.719473i
$470$	−5.31581	−	13.2872i	−0.245200	−	0.612895i
$471$		0			0
$472$	−2.77255	+	10.3473i	−0.127617	+	0.476273i
$473$	0.637693	−	2.37990i	0.0293212	−	0.109428i
$474$		0			0
$475$	7.92561	−	7.55000i	0.363652	−	0.346418i
$476$	2.08327	−	0.101272i	0.0954867	−	0.00464182i
$477$		0			0
$478$	−23.1794	+	6.21090i	−1.06020	+	0.284080i
$479$	8.55572	+	14.8189i	0.390921	+	0.677094i	0.992571	−	0.121665i	$-0.0388234\pi$
$479$	8.55572	+	14.8189i	0.390921	+	0.677094i	−0.601651	+	0.798759i	$0.705490\pi$
$480$		0			0
$481$	0.261359	+	0.150896i	0.0119170	+	0.00688026i
$482$	−17.5274	−	17.5274i	−0.798350	−	0.798350i
$483$		0			0
$484$		−	2.47728i		−	0.112604i
$485$	−5.99972	−	8.01859i	−0.272433	−	0.364105i
$486$		0			0
$487$	−0.125860	−	0.0337240i	−0.00570325	−	0.00152818i	0.255966	−	0.966686i	$-0.417606\pi$
$487$	−0.125860	−	0.0337240i	−0.00570325	−	0.00152818i	−0.261670	+	0.965158i	$0.584273\pi$
$488$	−0.515649	−	1.92443i	−0.0233423	−	0.0871147i
$489$		0			0
$490$	4.74039	−	14.9174i	0.214149	−	0.673899i
$491$	−26.9895			−1.21802			−0.609011	−	0.793162i	$-0.708433\pi$
$491$	−26.9895			−1.21802			−0.609011	+	0.793162i	$0.708433\pi$
$492$		0			0
$493$	1.99685	+	0.535055i	0.0899337	+	0.0240977i
$494$	2.22698	−	1.28575i	0.100197	−	0.0578486i
$495$		0			0
$496$		−	0.0415289i		−	0.00186470i
$497$	−4.54495	+	20.9912i	−0.203869	+	0.941584i
$498$		0			0
$499$	−0.0833977	−	0.0481497i	−0.00373339	−	0.00215548i	0.498132	−	0.867101i	$-0.334019\pi$
$499$	−0.0833977	−	0.0481497i	−0.00373339	−	0.00215548i	−0.501866	+	0.864946i	$0.667353\pi$
$500$	−11.1305	+	1.05497i	−0.497769	+	0.0471797i
$501$		0			0
$502$	−10.7370	+	2.87698i	−0.479217	+	0.128406i
$503$	13.6334	−	13.6334i	0.607883	−	0.607883i	−0.334509	−	0.942392i	$-0.608571\pi$
$503$	13.6334	−	13.6334i	0.607883	−	0.607883i	0.942392	+	0.334509i	$0.108571\pi$
$504$		0			0
$505$	0.149286	−	0.0597245i	0.00664312	−	0.00265771i
$506$	−8.63753	+	14.9606i	−0.383985	+	0.665081i
$507$		0			0
$508$	4.85084	−	18.1036i	0.215221	−	0.803217i
$509$	6.16366	−	10.6758i	0.273199	−	0.473195i	−0.696480	−	0.717576i	$-0.745251\pi$
$509$	6.16366	−	10.6758i	0.273199	−	0.473195i	0.969679	+	0.244381i	$0.0785848\pi$
$510$		0			0
$511$	11.9376	−	23.2111i	0.528087	−	1.02680i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	12.6466	+	21.9046i	0.557818	+	0.966169i
$515$	−4.39274	−	36.8123i	−0.193567	−	1.62214i
$516$		0			0
$517$	−16.6140	−	16.6140i	−0.730684	−	0.730684i
$518$	0.207611	+	0.647288i	0.00912189	+	0.0284402i
$519$		0			0
$520$	−2.59970	−	0.374399i	−0.114004	−	0.0164185i
$521$	−14.1415	+	8.16461i	−0.619551	+	0.357698i	−0.776694	−	0.629878i	$-0.783105\pi$
$521$	−14.1415	+	8.16461i	−0.619551	+	0.357698i	0.157143	+	0.987576i	$0.449772\pi$
$522$		0			0
$523$	−7.09270	−	26.4703i	−0.310142	−	1.15747i	−0.928428	−	0.371512i	$-0.878839\pi$
$523$	−7.09270	−	26.4703i	−0.310142	−	1.15747i	0.618286	−	0.785953i	$-0.287827\pi$
$524$	14.1946			0.620095
$525$		0			0
$526$	−11.3461			−0.494714
$527$	−0.00847337	−	0.0316231i	−0.000369106	−	0.00137752i
$528$		0			0
$529$	−0.742186	+	0.428501i	−0.0322689	+	0.0186305i
$530$	−17.5151	−	2.52245i	−0.760805	−	0.109568i
$531$		0			0
$532$	5.66098	+	1.22570i	0.245435	+	0.0531407i
$533$	7.45881	+	7.45881i	0.323077	+	0.323077i
$534$		0			0
$535$	−1.21065	−	10.1456i	−0.0523409	−	0.438630i
$536$	−3.31118	−	5.73513i	−0.143021	−	0.247720i
$537$		0			0
$538$	−5.70417	+	5.70417i	−0.245924	+	0.245924i
$539$	−2.49258	−	25.5768i	−0.107363	−	1.10167i
$540$		0			0
$541$	20.5773	−	35.6410i	0.884689	−	1.53233i	0.0386200	−	0.999254i	$-0.487704\pi$
$541$	20.5773	−	35.6410i	0.884689	−	1.53233i	0.846069	−	0.533073i	$-0.178963\pi$
$542$	−2.17395	+	8.11330i	−0.0933793	+	0.348496i
$543$		0			0
$544$	0.394167	−	0.682717i	0.0168998	−	0.0292712i
$545$	−37.5826	+	15.0356i	−1.60986	+	0.644056i
$546$		0			0
$547$	8.06541	−	8.06541i	0.344852	−	0.344852i	−0.513336	−	0.858188i	$-0.671590\pi$
$547$	8.06541	−	8.06541i	0.344852	−	0.344852i	0.858188	+	0.513336i	$0.171590\pi$
$548$	18.3201	−	4.90887i	0.782597	−	0.209696i
$549$		0			0
$550$	−16.1145	+	8.78944i	−0.687126	+	0.374783i
$551$	4.97180	+	2.87047i	0.211806	+	0.122286i
$552$		0			0
$553$	−23.8423	+	26.2788i	−1.01388	+	1.11749i
$554$		−	5.68000i		−	0.241320i
$555$		0			0
$556$	−7.13350	+	4.11853i	−0.302528	+	0.174665i
$557$	−24.7826	−	6.64049i	−1.05007	−	0.281367i	−0.307792	−	0.951454i	$-0.599590\pi$
$557$	−24.7826	−	6.64049i	−1.05007	−	0.281367i	−0.742282	+	0.670087i	$0.766257\pi$
$558$		0			0
$559$	−0.788333			−0.0333429
$560$	−3.77009	−	4.55921i	−0.159315	−	0.192662i
$561$		0			0
$562$	−1.88324	−	7.02834i	−0.0794396	−	0.296473i
$563$	12.3749	+	3.31584i	0.521539	+	0.139746i	0.509978	−	0.860187i	$-0.329653\pi$
$563$	12.3749	+	3.31584i	0.521539	+	0.139746i	0.0115606	+	0.999933i	$0.496320\pi$
$564$		0			0
$565$	−2.88083	−	3.85022i	−0.121198	−	0.161980i
$566$		−	7.71000i		−	0.324076i
$567$		0			0
$568$	5.74013	+	5.74013i	0.240850	+	0.240850i
$569$	29.8291	+	17.2218i	1.25050	+	0.721977i	0.971209	−	0.238229i	$-0.0765669\pi$
$569$	29.8291	+	17.2218i	1.25050	+	0.721977i	0.279292	+	0.960206i	$0.409900\pi$
$570$		0			0
$571$	4.11985	+	7.13579i	0.172410	+	0.298623i	0.939262	−	0.343201i	$-0.111511\pi$
$571$	4.11985	+	7.13579i	0.172410	+	0.298623i	−0.766852	+	0.641824i	$0.778178\pi$
$572$	−4.16524	+	1.11607i	−0.174158	+	0.0466654i
$573$		0			0
$574$	1.15364	+	23.7315i	0.0481520	+	0.990534i
$575$	23.5212	+	0.570889i	0.980904	+	0.0238077i
$576$		0			0
$577$	−0.910086	+	3.39649i	−0.0378874	+	0.141398i	−0.982279	−	0.187426i	$-0.939985\pi$
$577$	−0.910086	+	3.39649i	−0.0378874	+	0.141398i	0.944391	+	0.328824i	$0.106652\pi$
$578$	−4.23908	+	15.8204i	−0.176322	+	0.658044i
$579$		0			0
$580$	−2.17808	−	5.44425i	−0.0904397	−	0.226060i
$581$	−19.7132	−	30.6088i	−0.817843	−	1.26987i
$582$		0			0
$583$	−28.0627	+	7.51937i	−1.16224	+	0.311421i
$584$	−4.93262	−	8.54355i	−0.204113	−	0.353535i
$585$		0			0
$586$	−4.10531	−	2.37020i	−0.169589	−	0.0979122i
$587$	5.37485	+	5.37485i	0.221844	+	0.221844i	0.809275	−	0.587431i	$-0.199861\pi$
$587$	5.37485	+	5.37485i	0.221844	+	0.221844i	−0.587431	+	0.809275i	$0.699861\pi$
$588$		0			0
$589$		−	0.0909162i		−	0.00374613i
$590$	19.1791	−	14.3503i	0.789590	−	0.590792i
$591$		0			0
$592$	0.248174	+	0.0664979i	0.0101999	+	0.00273305i
$593$	−0.190155	−	0.709668i	−0.00780872	−	0.0291426i	0.961912	−	0.273361i	$-0.0881353\pi$
$593$	−0.190155	−	0.709668i	−0.00780872	−	0.0291426i	−0.969720	+	0.244218i	$0.921469\pi$
$594$		0			0
$595$	−3.80106	−	2.70248i	−0.155828	−	0.110791i
$596$	4.84185			0.198330
$597$		0			0
$598$	5.33897	+	1.43057i	0.218327	+	0.0585005i
$599$	−7.23778	+	4.17873i	−0.295727	+	0.170738i	−0.640522	−	0.767940i	$-0.721282\pi$
$599$	−7.23778	+	4.17873i	−0.295727	+	0.170738i	0.344794	+	0.938678i	$0.387949\pi$
$600$		0			0
$601$		−	39.9236i		−	1.62852i	−0.580501	−	0.814259i	$-0.697143\pi$
$601$		−	39.9236i		−	1.62852i	0.580501	−	0.814259i	$-0.302857\pi$
$602$	−1.31508	−	1.19315i	−0.0535985	−	0.0486290i
$603$		0			0
$604$	8.69995	+	5.02292i	0.353996	+	0.204380i
$605$	−3.42523	+	4.35344i	−0.139255	+	0.176993i
$606$		0			0
$607$	33.2758	−	8.91623i	1.35062	−	0.361899i	0.490259	−	0.871577i	$-0.336902\pi$
$607$	33.2758	−	8.91623i	1.35062	−	0.361899i	0.860365	+	0.509678i	$0.170235\pi$
$608$	1.54802	−	1.54802i	0.0627804	−	0.0627804i
$609$		0			0
$610$	−1.75465	+	4.09485i	−0.0710436	+	0.165796i
$611$	−3.75885	+	6.51051i	−0.152067	+	0.263387i
$612$		0			0
$613$	−8.46832	+	31.6042i	−0.342032	+	1.27648i	0.554009	+	0.832510i	$0.313097\pi$
$613$	−8.46832	+	31.6042i	−0.342032	+	1.27648i	−0.896041	+	0.443971i	$0.853569\pi$
$614$	0.753393	−	1.30491i	0.0304044	−	0.0526620i
$615$		0			0
$616$	−8.63753	−	4.44231i	−0.348016	−	0.178986i
$617$	15.5005	−	15.5005i	0.624025	−	0.624025i	−0.322533	−	0.946558i	$-0.604534\pi$
$617$	15.5005	−	15.5005i	0.624025	−	0.624025i	0.946558	+	0.322533i	$0.104534\pi$
$618$		0			0
$619$	4.31138	+	7.46752i	0.173289	+	0.300145i	0.939568	−	0.342363i	$-0.111227\pi$
$619$	4.31138	+	7.46752i	0.173289	+	0.300145i	−0.766279	+	0.642508i	$0.777894\pi$
$620$	−0.0574201	+	0.0729806i	−0.00230605	+	0.00293097i
$621$		0			0
$622$	−9.76397	−	9.76397i	−0.391500	−	0.391500i
$623$	2.80254	+	2.54269i	0.112281	+	0.101871i
$624$		0			0
$625$	21.0187	+	13.5356i	0.840749	+	0.541425i
$626$	−20.2191	+	11.6735i	−0.808119	+	0.466568i
$627$		0			0
$628$	6.33762	+	23.6523i	0.252898	+	0.943830i
$629$	0.202545			0.00807600
$630$		0			0
$631$	−4.13675			−0.164682			−0.0823408	−	0.996604i	$-0.526240\pi$
$631$	−4.13675			−0.164682			−0.0823408	+	0.996604i	$0.526240\pi$
$632$	3.47109	+	12.9543i	0.138073	+	0.515294i
$633$		0			0
$634$	11.4219	−	6.59442i	0.453620	−	0.261898i
$635$	−33.5556	+	25.1072i	−1.33161	+	0.996349i
$636$		0			0
$637$	−7.69827	+	2.88840i	−0.305017	+	0.114443i
$638$	−6.80736	−	6.80736i	−0.269506	−	0.269506i
$639$		0			0
$640$	−2.22032	+	0.264946i	−0.0877657	+	0.0104729i
$641$	5.42807	+	9.40169i	0.214396	+	0.371345i	0.953086	−	0.302701i	$-0.0978884\pi$
$641$	5.42807	+	9.40169i	0.214396	+	0.371345i	−0.738690	+	0.674046i	$0.764555\pi$
$642$		0			0
$643$	−8.06230	+	8.06230i	−0.317946	+	0.317946i	−0.847978	−	0.530032i	$-0.822180\pi$
$643$	−8.06230	+	8.06230i	−0.317946	+	0.317946i	0.530032	+	0.847978i	$0.322180\pi$
$644$	6.74114	+	10.4670i	0.265638	+	0.412457i
$645$		0			0
$646$	0.862920	−	1.49462i	0.0339511	−	0.0588051i
$647$	2.69865	−	10.0715i	0.106095	−	0.395951i	−0.892372	−	0.451300i	$-0.850960\pi$
$647$	2.69865	−	10.0715i	0.106095	−	0.395951i	0.998467	+	0.0553490i	$0.0176271\pi$
$648$		0			0
$649$	19.6632	−	34.0577i	0.771848	−	1.33688i
$650$	4.05090	+	4.25243i	0.158889	+	0.166794i
$651$		0			0
$652$	−15.5320	+	15.5320i	−0.608279	+	0.608279i
$653$	−6.41946	+	1.72009i	−0.251213	+	0.0673123i	−0.382228	−	0.924068i	$-0.624843\pi$
$653$	−6.41946	+	1.72009i	−0.251213	+	0.0673123i	0.131015	+	0.991380i	$0.458176\pi$
$654$		0			0
$655$	−24.9449	−	19.6263i	−0.974677	−	0.766862i
$656$	7.77713	+	4.49013i	0.303646	+	0.175310i
$657$		0			0
$658$	−16.1241	+	5.17163i	−0.628582	+	0.201611i
$659$		−	22.0345i		−	0.858343i	−0.903223	−	0.429172i	$-0.858806\pi$
$659$		−	22.0345i		−	0.858343i	0.903223	−	0.429172i	$-0.141194\pi$
$660$		0			0
$661$	−9.94278	+	5.74047i	−0.386729	+	0.223278i	−0.680742	−	0.732523i	$-0.738343\pi$
$661$	−9.94278	+	5.74047i	−0.386729	+	0.223278i	0.294013	+	0.955802i	$0.405009\pi$
$662$	18.4453	+	4.94240i	0.716897	+	0.192092i
$663$		0			0
$664$	−13.7608			−0.534021
$665$	−8.25358	−	9.98115i	−0.320060	−	0.387053i
$666$		0			0
$667$	3.19379	+	11.9194i	0.123664	+	0.461521i
$668$	−4.29774	−	1.15158i	−0.166285	−	0.0445558i
$669$		0			0
$670$	−2.11082	+	14.6568i	−0.0815482	+	0.566243i
$671$			7.31407i			0.282356i
$672$		0			0
$673$	−15.2073	−	15.2073i	−0.586198	−	0.586198i	0.350402	−	0.936600i	$-0.386045\pi$
$673$	−15.2073	−	15.2073i	−0.586198	−	0.586198i	−0.936600	+	0.350402i	$0.886045\pi$
$674$	0.597952	+	0.345228i	0.0230322	+	0.0132977i
$675$		0			0
$676$	−5.81014	−	10.0635i	−0.223467	−	0.387056i
$677$	5.54296	−	1.48523i	0.213033	−	0.0570821i	−0.150724	−	0.988576i	$-0.548160\pi$
$677$	5.54296	−	1.48523i	0.213033	−	0.0570821i	0.363757	+	0.931494i	$0.381494\pi$
$678$		0			0
$679$	−9.96224	+	6.41606i	−0.382316	+	0.246226i
$680$	−1.63665	+	0.654772i	−0.0627626	+	0.0251094i
$681$		0			0
$682$	−0.0394591	+	0.147264i	−0.00151097	+	0.00563901i
$683$	−5.02900	+	18.7685i	−0.192430	+	0.718157i	0.800488	+	0.599349i	$0.204574\pi$
$683$	−5.02900	+	18.7685i	−0.192430	+	0.718157i	−0.992917	+	0.118808i	$0.962093\pi$
$684$		0			0
$685$	−38.9821	−	16.7039i	−1.48943	−	0.638222i
$686$	−17.2137	−	6.83301i	−0.657220	−	0.260886i
$687$		0			0
$688$	−0.648273	+	0.173704i	−0.0247152	+	0.00662241i
$689$	4.64782	+	8.05027i	0.177068	+	0.306691i
$690$		0			0
$691$	19.0914	+	11.0224i	0.726270	+	0.419312i	0.817056	−	0.576558i	$-0.195605\pi$
$691$	19.0914	+	11.0224i	0.726270	+	0.419312i	−0.0907861	+	0.995870i	$0.528938\pi$
$692$	−3.69572	−	3.69572i	−0.140490	−	0.140490i
$693$		0			0
$694$			3.80998i			0.144625i
$695$	18.2305	+	2.62550i	0.691524	+	0.0995908i
$696$		0			0
$697$	6.83821	+	1.83229i	0.259016	+	0.0694031i
$698$	−2.04804	−	7.64340i	−0.0775196	−	0.289307i
$699$		0			0
$700$	0.321526	+	13.2248i	0.0121526	+	0.499852i
$701$	18.0270			0.680870			0.340435	−	0.940268i	$-0.389426\pi$
$701$	18.0270			0.680870			0.340435	+	0.940268i	$0.389426\pi$
$702$		0			0
$703$	0.543308	+	0.145579i	0.0204913	+	0.00549062i
$704$	−3.17930	+	1.83557i	−0.119824	+	0.0691807i
$705$		0			0
$706$			25.7787i			0.970196i
$707$	−0.0581046	−	0.181158i	−0.00218525	−	0.00681316i
$708$		0			0
$709$	−37.0614	−	21.3974i	−1.39187	−	0.803597i	−0.398349	−	0.917234i	$-0.630417\pi$
$709$	−37.0614	−	21.3974i	−1.39187	−	0.803597i	−0.993522	+	0.113637i	$0.963750\pi$
$710$	−2.15077	−	18.0240i	−0.0807170	−	0.676429i
$711$		0			0
$712$	1.38152	−	0.370178i	0.0517748	−	0.0138730i
$713$	0.138183	−	0.138183i	0.00517498	−	0.00517498i
$714$		0			0
$715$	8.86292	+	3.79777i	0.331454	+	0.142029i
$716$	6.28428	−	10.8847i	0.234854	−	0.406780i
$717$		0			0
$718$	2.68822	−	10.0326i	0.100324	−	0.374413i
$719$	2.72691	−	4.72315i	0.101697	−	0.176144i	−0.810687	−	0.585480i	$-0.800906\pi$
$719$	2.72691	−	4.72315i	0.101697	−	0.176144i	0.912384	+	0.409336i	$0.134240\pi$
$720$		0			0
$721$	−43.8142	+	2.12990i	−1.63172	+	0.0793217i
$722$	−10.0461	+	10.0461i	−0.373876	+	0.373876i
$723$		0			0
$724$	−5.83712	−	10.1102i	−0.216935	−	0.375742i
$725$	−3.69989	+	12.5790i	−0.137411	+	0.467171i
$726$		0			0
$727$	16.6781	+	16.6781i	0.618555	+	0.618555i	0.945161	−	0.326606i	$-0.105905\pi$
$727$	16.6781	+	16.6781i	0.618555	+	0.618555i	−0.326606	+	0.945161i	$0.605905\pi$
$728$	−0.657639	+	3.03736i	−0.0243737	+	0.112572i
$729$		0			0
$730$	−3.14447	+	21.8341i	−0.116382	+	0.808116i
$731$	−0.458200	+	0.264542i	−0.0169471	+	0.00978443i
$732$		0			0
$733$	−8.79960	−	32.8405i	−0.325021	−	1.21299i	−0.914291	−	0.405057i	$-0.867252\pi$
$733$	−8.79960	−	32.8405i	−0.325021	−	1.21299i	0.589271	−	0.807936i	$-0.299415\pi$
$734$	−8.68601			−0.320607
$735$		0			0
$736$	4.70563			0.173452
$737$	6.29231	+	23.4832i	0.231780	+	0.865016i
$738$		0			0
$739$	25.0733	−	14.4761i	0.922335	−	0.532510i	0.0379557	−	0.999279i	$-0.487915\pi$
$739$	25.0733	−	14.4761i	0.922335	−	0.532510i	0.884379	+	0.466769i	$0.154582\pi$
$740$	−0.344183	−	0.459998i	−0.0126524	−	0.0169099i
$741$		0			0
$742$	−4.43074	+	20.4637i	−0.162658	+	0.751247i
$743$	−34.0351	−	34.0351i	−1.24863	−	1.24863i	−0.956327	−	0.292300i	$-0.905579\pi$
$743$	−34.0351	−	34.0351i	−1.24863	−	1.24863i	−0.292300	−	0.956327i	$-0.594421\pi$
$744$		0			0
$745$	−8.50881	−	6.69461i	−0.311739	−	0.245272i
$746$	−6.65477	−	11.5264i	−0.243649	−	0.422012i
$747$		0			0
$748$	−2.04643	+	2.04643i	−0.0748247	+	0.0748247i
$749$	−12.0753	+	0.587006i	−0.441221	+	0.0214487i
$750$		0			0
$751$	9.30569	−	16.1179i	0.339569	−	0.588151i	−0.644782	−	0.764366i	$-0.723052\pi$
$751$	9.30569	−	16.1179i	0.339569	−	0.588151i	0.984352	+	0.176215i	$0.0563853\pi$
$752$	−1.65648	+	6.18205i	−0.0604055	+	0.225436i
$753$		0			0
$754$	−1.54013	+	2.66759i	−0.0560883	+	0.0971478i
$755$	−8.34385	−	20.8560i	−0.303664	−	0.759029i
$756$		0			0
$757$	29.7422	−	29.7422i	1.08100	−	1.08100i	0.0845825	−	0.996416i	$-0.473044\pi$
$757$	29.7422	−	29.7422i	1.08100	−	1.08100i	0.996416	−	0.0845825i	$-0.0269557\pi$
$758$	−24.4816	+	6.55984i	−0.889213	+	0.238264i
$759$		0			0
$760$	−4.86078	+	0.580027i	−0.176319	+	0.0210398i
$761$	−17.6474	−	10.1887i	−0.639718	−	0.369341i	0.144788	−	0.989463i	$-0.453750\pi$
$761$	−17.6474	−	10.1887i	−0.639718	−	0.369341i	−0.784506	+	0.620122i	$0.787083\pi$
$762$		0			0
$763$	14.6278	+	45.6066i	0.529563	+	1.65107i
$764$			15.5034i			0.560894i
$765$		0			0
$766$	15.9357	−	9.20046i	0.575779	−	0.332426i
$767$	−12.1541	−	3.25668i	−0.438859	−	0.117592i
$768$		0			0
$769$	40.9728			1.47752			0.738759	−	0.673970i	$-0.235412\pi$
$769$	40.9728			1.47752			0.738759	+	0.673970i	$0.235412\pi$
$770$	9.03694	+	19.7494i	0.325669	+	0.711719i
$771$		0			0
$772$	2.32883	+	8.69132i	0.0838165	+	0.312808i
$773$	−23.8577	−	6.39265i	−0.858101	−	0.229928i	−0.197166	−	0.980370i	$-0.563174\pi$
$773$	−23.8577	−	6.39265i	−0.858101	−	0.229928i	−0.660936	+	0.750443i	$0.729840\pi$
$774$		0			0
$775$	0.201814	−	0.0488599i	0.00724938	−	0.00175510i
$776$			4.47871i			0.160776i
$777$		0			0
$778$	15.8091	+	15.8091i	0.566784	+	0.566784i
$779$	17.0259	+	9.82991i	0.610017	+	0.352193i
$780$		0			0
$781$	−14.9007	−	25.8088i	−0.533190	−	0.923513i
$782$	3.58321	−	0.960117i	0.128135	−	0.0343337i
$783$		0			0
$784$	−5.69411	+	4.07150i	−0.203361	+	0.145411i
$785$	21.5656	−	50.3280i	0.769710	−	1.79628i
$786$		0			0
$787$	2.12442	−	7.92843i	0.0757273	−	0.282618i	−0.917670	−	0.397343i	$-0.869932\pi$
$787$	2.12442	−	7.92843i	0.0757273	−	0.282618i	0.993397	+	0.114725i	$0.0365988\pi$
$788$	4.46372	−	16.6588i	0.159013	−	0.593446i
$789$		0			0
$790$	11.8114	−	27.5645i	0.420231	−	0.980701i
$791$	−4.78348	+	3.08075i	−0.170081	+	0.109539i
$792$		0			0
$793$	2.26046	−	0.605689i	0.0802713	−	0.0215086i
$794$	−7.89197	−	13.6693i	−0.280076	−	0.485105i
$795$		0			0
$796$	−7.56140	−	4.36557i	−0.268007	−	0.154734i
$797$	−11.7928	−	11.7928i	−0.417722	−	0.417722i	0.466696	−	0.884418i	$-0.345444\pi$
$797$	−11.7928	−	11.7928i	−0.417722	−	0.417722i	−0.884418	+	0.466696i	$0.845444\pi$
$798$		0			0
$799$			5.04544i			0.178495i
$800$	4.26819	+	2.60433i	0.150903	+	0.0920770i
$801$		0			0
$802$	13.4945	+	3.61585i	0.476508	+	0.127680i
$803$	9.37358	+	34.9827i	0.330786	+	1.23451i
$804$		0			0
$805$	2.62573	−	27.7148i	0.0925447	−	0.976819i
$806$	0.0487805			0.00171822
$807$		0			0
$808$	−0.0694570	−	0.0186109i	−0.00244349	−	0.000654730i
$809$	28.8498	−	16.6564i	1.01430	−	0.585609i	0.101855	−	0.994799i	$-0.467522\pi$
$809$	28.8498	−	16.6564i	1.01430	−	0.585609i	0.912449	+	0.409191i	$0.134189\pi$
$810$		0			0
$811$			55.2368i			1.93963i	0.243850	+	0.969813i	$0.421590\pi$
$811$			55.2368i			1.93963i	−0.243850	+	0.969813i	$0.578410\pi$
$812$	−6.60661	+	2.11900i	−0.231847	+	0.0743623i
$813$		0			0
$814$	−0.816852	−	0.471610i	−0.0286307	−	0.0165299i
$815$	48.7704	−	5.81968i	1.70835	−	0.203855i
$816$		0			0
$817$	−1.41922	+	0.380278i	−0.0496521	+	0.0133042i
$818$	0.221580	−	0.221580i	0.00774737	−	0.00774737i
$819$		0			0
$820$	−7.45881	−	18.6438i	−0.260473	−	0.651070i
$821$	9.31457	−	16.1333i	0.325081	−	0.563056i	−0.656448	−	0.754371i	$-0.727942\pi$
$821$	9.31457	−	16.1333i	0.325081	−	0.563056i	0.981529	+	0.191315i	$0.0612752\pi$
$822$		0			0
$823$	−4.37130	+	16.3139i	−0.152374	+	0.568668i	0.846942	+	0.531685i	$0.178441\pi$
$823$	−4.37130	+	16.3139i	−0.152374	+	0.568668i	−0.999316	+	0.0369821i	$0.988226\pi$
$824$	−8.28988	+	14.3585i	−0.288792	+	0.500202i
$825$		0			0
$826$	−15.3461	−	23.8280i	−0.533960	−	0.829081i
$827$	5.62716	−	5.62716i	0.195675	−	0.195675i	−0.602468	−	0.798143i	$-0.705816\pi$
$827$	5.62716	−	5.62716i	0.195675	−	0.195675i	0.798143	+	0.602468i	$0.205816\pi$
$828$		0			0
$829$	3.29757	+	5.71155i	0.114529	+	0.198370i	0.917591	−	0.397525i	$-0.130131\pi$
$829$	3.29757	+	5.71155i	0.114529	+	0.198370i	−0.803062	+	0.595895i	$0.796797\pi$
$830$	24.1824	+	19.0264i	0.839384	+	0.660416i
$831$		0			0
$832$	0.830578	+	0.830578i	0.0287951	+	0.0287951i
$833$	−3.50517	+	4.26213i	−0.121447	+	0.147674i
$834$		0			0
$835$	5.96038	+	7.96601i	0.206268	+	0.275675i
$836$	−6.96021	+	4.01848i	−0.240724	+	0.138982i
$837$		0			0
$838$	−8.18525	−	30.5478i	−0.282755	−	1.05526i
$839$	−46.0930			−1.59131			−0.795654	−	0.605752i	$-0.792872\pi$
$839$	−46.0930			−1.59131			−0.795654	+	0.605752i	$0.792872\pi$
$840$		0			0
$841$	22.1232			0.762870
$842$	6.26698	+	23.3887i	0.215974	+	0.806027i
$843$		0			0
$844$	9.67744	−	5.58727i	0.333111	−	0.192322i
$845$	−3.70387	+	25.7184i	−0.127417	+	0.884740i
$846$		0			0
$847$	4.85413	+	4.40407i	0.166790	+	0.151326i
$848$	5.59589	+	5.59589i	0.192164	+	0.192164i
$849$		0			0
$850$	3.78148	+	1.11226i	0.129704	+	0.0381502i
$851$	0.604505	+	1.04703i	0.0207222	+	0.0358918i
$852$		0			0
$853$	14.9594	−	14.9594i	0.512200	−	0.512200i	−0.403000	−	0.915200i	$-0.632032\pi$
$853$	14.9594	−	14.9594i	0.512200	−	0.512200i	0.915200	+	0.403000i	$0.132032\pi$
$854$	4.68755	+	2.41082i	0.160405	+	0.0824967i
$855$		0			0
$856$	−2.28471	+	3.95723i	−0.0780897	+	0.135255i
$857$	−3.12136	+	11.6491i	−0.106623	+	0.397924i	−0.998524	−	0.0543068i	$-0.982705\pi$
$857$	−3.12136	+	11.6491i	−0.106623	+	0.397924i	0.891901	+	0.452231i	$0.149372\pi$
$858$		0			0
$859$	−2.90061	+	5.02401i	−0.0989677	+	0.171417i	−0.911258	−	0.411837i	$-0.864887\pi$
$859$	−2.90061	+	5.02401i	−0.0989677	+	0.171417i	0.812290	+	0.583254i	$0.198221\pi$
$860$	1.37941	+	0.591080i	0.0470376	+	0.0201557i
$861$		0			0
$862$	−1.10172	+	1.10172i	−0.0375249	+	0.0375249i
$863$	−2.90586	+	0.778623i	−0.0989167	+	0.0265046i	−0.307938	−	0.951406i	$-0.599639\pi$
$863$	−2.90586	+	0.778623i	−0.0989167	+	0.0265046i	0.209021	+	0.977911i	$0.432972\pi$
$864$		0			0
$865$	1.38475	+	11.6046i	0.0470829	+	0.394567i
$866$	7.69343	+	4.44180i	0.261433	+	0.150939i
$867$		0			0
$868$	0.0813742	+	0.0738294i	0.00276202	+	0.00250593i
$869$		−	49.2347i		−	1.67017i
$870$		0			0
$871$	6.73657	−	3.88936i	0.228260	−	0.131786i
$872$	17.4858	+	4.68530i	0.592143	+	0.158664i
$873$		0			0
$874$	10.3017			0.348460
$875$	17.7204	−	23.6852i	0.599058	−	0.800706i
$876$		0			0
$877$	9.07228	+	33.8582i	0.306349	+	1.14331i	0.931778	+	0.363030i	$0.118258\pi$
$877$	9.07228	+	33.8582i	0.306349	+	1.14331i	−0.625428	+	0.780282i	$0.715076\pi$
$878$	23.0994	+	6.18945i	0.779565	+	0.208884i
$879$		0			0
$880$	8.12509	+	1.17015i	0.273897	+	0.0394456i
$881$			23.7116i			0.798864i	0.916763	+	0.399432i	$0.130793\pi$
$881$			23.7116i			0.798864i	−0.916763	+	0.399432i	$0.869207\pi$
$882$		0			0
$883$	−7.95370	−	7.95370i	−0.267663	−	0.267663i	0.560495	−	0.828158i	$-0.310611\pi$
$883$	−7.95370	−	7.95370i	−0.267663	−	0.267663i	−0.828158	+	0.560495i	$0.810611\pi$
$884$	0.801929	+	0.462994i	0.0269718	+	0.0155722i
$885$		0			0
$886$	6.43103	+	11.1389i	0.216055	+	0.374218i
$887$	19.6954	−	5.27738i	0.661308	−	0.177197i	0.0874718	−	0.996167i	$-0.472121\pi$
$887$	19.6954	−	5.27738i	0.661308	−	0.177197i	0.573836	+	0.818970i	$0.305455\pi$
$888$		0			0
$889$	26.8495	+	41.6893i	0.900503	+	1.39821i
$890$	−2.93964	−	1.25964i	−0.0985371	−	0.0422233i
$891$		0			0
$892$	−0.273349	+	1.02015i	−0.00915241	+	0.0341573i
$893$	−3.62640	+	13.5339i	−0.121353	+	0.452895i
$894$		0			0
$895$	−26.0934	+	10.4392i	−0.872207	+	0.348943i
$896$	0.128464	+	2.64263i	0.00429168	+	0.0882841i
$897$		0			0
$898$	−17.2836	+	4.63111i	−0.576760	+	0.154542i
$899$	0.0544519	+	0.0943134i	0.00181607	+	0.00314553i
$900$		0			0
$901$	5.40287	+	3.11935i	0.179996	+	0.103921i
$902$	−23.3118	−	23.3118i	−0.776197	−	0.776197i
$903$		0			0
$904$			2.15051i			0.0715247i
$905$	−3.72107	+	25.8378i	−0.123693	+	0.858879i
$906$		0			0
$907$	6.29276	+	1.68614i	0.208948	+	0.0559874i	0.361775	−	0.932266i	$-0.382171\pi$
$907$	6.29276	+	1.68614i	0.208948	+	0.0559874i	−0.152827	+	0.988253i	$0.548838\pi$
$908$	0.807609	+	3.01404i	0.0268014	+	0.100024i
$909$		0			0
$910$	5.35532	−	4.42840i	0.177527	−	0.146800i
$911$	24.2528			0.803531			0.401765	−	0.915743i	$-0.368397\pi$
$911$	24.2528			0.803531			0.401765	+	0.915743i	$0.368397\pi$
$912$		0			0
$913$	48.7964	+	13.0749i	1.61492	+	0.432718i
$914$	−29.6277	+	17.1056i	−0.979997	+	0.565802i
$915$		0			0
$916$			8.42181i			0.278264i
$917$	−25.2350	+	27.8138i	−0.833333	+	0.918493i
$918$		0			0
$919$	−31.2542	−	18.0446i	−1.03098	−	0.595236i	−0.113714	−	0.993513i	$-0.536275\pi$
$919$	−31.2542	−	18.0446i	−1.03098	−	0.595236i	−0.917265	+	0.398277i	$0.869608\pi$
$920$	−8.26943	−	6.50627i	−0.272635	−	0.214505i
$921$		0			0
$922$	22.5515	−	6.04266i	0.742695	−	0.199004i
$923$	−6.74244	+	6.74244i	−0.221930	+	0.221930i
$924$		0			0
$925$	−0.0311706	+	1.28426i	−0.00102488	+	0.0422263i
$926$	−2.81789	+	4.88073i	−0.0926017	+	0.160391i
$927$		0			0
$928$	−0.678717	+	2.53301i	−0.0222800	+	0.0831500i
$929$	21.2041	−	36.7266i	0.695685	−	1.20496i	−0.274264	−	0.961654i	$-0.588434\pi$
$929$	21.2041	−	36.7266i	0.695685	−	1.20496i	0.969949	−	0.243307i	$-0.0782323\pi$
$930$		0			0
$931$	−12.4657	+	8.91344i	−0.408547	+	0.292126i
$932$	16.1198	−	16.1198i	0.528023	−	0.528023i
$933$		0			0
$934$	2.44290	+	4.23123i	0.0799342	+	0.138450i
$935$	6.42578	−	0.766776i	0.210145	−	0.0250762i
$936$		0			0
$937$	4.06709	+	4.06709i	0.132866	+	0.132866i	0.770412	−	0.637546i	$-0.220050\pi$
$937$	4.06709	+	4.06709i	0.132866	+	0.132866i	−0.637546	+	0.770412i	$0.720050\pi$
$938$	17.1243	+	3.70770i	0.559129	+	0.121061i
$939$		0			0
$940$	11.4587	−	8.57367i	0.373740	−	0.279642i
$941$	17.4071	−	10.0500i	0.567455	−	0.327621i	−0.188677	−	0.982039i	$-0.560420\pi$
$941$	17.4071	−	10.0500i	0.567455	−	0.327621i	0.756132	+	0.654419i	$0.227087\pi$
$942$		0			0
$943$	10.9371	+	40.8179i	0.356162	+	1.32921i
$944$	−10.7123			−0.348656
$945$		0			0
$946$	2.46386			0.0801069
$947$	15.2583	+	56.9449i	0.495830	+	1.85046i	0.525333	+	0.850897i	$0.323941\pi$
$947$	15.2583	+	56.9449i	0.495830	+	1.85046i	−0.0295030	+	0.999565i	$0.509392\pi$
$948$		0			0
$949$	10.0354	−	5.79393i	0.325762	−	0.188079i
$950$	9.34404	+	5.70147i	0.303161	+	0.184980i
$951$		0			0
$952$	0.637013	+	1.98608i	0.0206457	+	0.0643691i
$953$	31.1044	+	31.1044i	1.00757	+	1.00757i	0.999971	+	0.00759828i	$0.00241863\pi$
$953$	31.1044	+	31.1044i	1.00757	+	1.00757i	0.00759828	+	0.999971i	$0.497581\pi$
$954$		0			0
$955$	21.4359	−	27.2448i	0.693648	−	0.881622i
$956$	−11.9985	−	20.7821i	−0.388060	−	0.672140i
$957$		0			0
$958$	−12.0996	+	12.0996i	−0.390921	+	0.390921i
$959$	−22.9505	+	44.6245i	−0.741111	+	1.44100i
$960$		0			0
$961$	−15.4991	+	26.8453i	−0.499972	+	0.865977i
$962$	−0.0781094	+	0.291508i	−0.00251835	+	0.00939861i
$963$		0			0
$964$	12.3937	−	21.4666i	0.399175	−	0.691391i
$965$	7.92454	−	18.4936i	0.255100	−	0.595331i
$966$		0			0
$967$	−21.5036	+	21.5036i	−0.691510	+	0.691510i	−0.962564	−	0.271054i	$-0.912628\pi$
$967$	−21.5036	+	21.5036i	−0.691510	+	0.691510i	0.271054	+	0.962564i	$0.412628\pi$
$968$	2.39287	−	0.641168i	0.0769098	−	0.0206079i
$969$		0			0
$970$	6.19252	−	7.87065i	0.198830	−	0.252711i
$971$	45.3034	+	26.1559i	1.45385	+	0.839384i	0.998697	−	0.0510273i	$-0.0162496\pi$
$971$	45.3034	+	26.1559i	1.45385	+	0.839384i	0.455158	+	0.890411i	$0.349583\pi$
$972$		0			0
$973$	4.61174	−	21.2997i	0.147845	−	0.682836i
$974$		−	0.130300i		−	0.00417507i
$975$		0			0
$976$	1.72539	−	0.996157i	0.0552285	−	0.0318862i
$977$	54.6658	+	14.6477i	1.74891	+	0.468620i	0.984394	−	0.175979i	$-0.0563092\pi$
$977$	54.6658	+	14.6477i	1.74891	+	0.468620i	0.764520	+	0.644599i	$0.222976\pi$
$978$		0			0
$979$	−5.25068			−0.167813
$980$	15.6360	+	0.717962i	0.499474	+	0.0229345i
$981$		0			0
$982$	−6.98541	−	26.0699i	−0.222913	−	0.831924i
$983$	−14.9514	−	4.00621i	−0.476875	−	0.127778i	0.0123723	−	0.999923i	$-0.496062\pi$
$983$	−14.9514	−	4.00621i	−0.476875	−	0.127778i	−0.489247	+	0.872145i	$0.662728\pi$
$984$		0			0
$985$	−30.8777	+	23.1035i	−0.983845	+	0.736139i
$986$			2.06729i			0.0658361i
$987$		0			0
$988$	1.81832	+	1.81832i	0.0578486	+	0.0578486i
$989$	−2.73504	−	1.57907i	−0.0869691	−	0.0502116i
$990$		0			0
$991$	26.8648	+	46.5311i	0.853388	+	1.47811i	0.878133	+	0.478417i	$0.158789\pi$
$991$	26.8648	+	46.5311i	0.853388	+	1.47811i	−0.0247453	+	0.999694i	$0.507877\pi$
$992$	0.0401138	−	0.0107485i	0.00127362	−	0.000341264i
$993$		0			0
$994$	−21.4523	+	1.04284i	−0.680424	+	0.0330769i
$995$	7.25190	+	18.1266i	0.229901	+	0.574653i
$996$		0			0
$997$	9.97217	−	37.2167i	0.315822	−	1.17866i	−0.607400	−	0.794396i	$-0.707787\pi$
$997$	9.97217	−	37.2167i	0.315822	−	1.17866i	0.923222	−	0.384267i	$-0.125546\pi$
$998$	0.0249241	−	0.0930180i	0.000788959	−	0.00294443i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bv.c.523.4		16
3.2	odd	2		70.2.k.a.33.1	yes	16
5.2	odd	4	inner	630.2.bv.c.397.1		16
7.3	odd	6	inner	630.2.bv.c.73.1		16
12.11	even	2		560.2.ci.c.33.4		16
15.2	even	4		70.2.k.a.47.3	yes	16
15.8	even	4		350.2.o.c.257.2		16
15.14	odd	2		350.2.o.c.243.4		16
21.2	odd	6		490.2.g.c.293.4		16
21.5	even	6		490.2.g.c.293.1		16
21.11	odd	6		490.2.l.c.423.4		16
21.17	even	6		70.2.k.a.3.3	✓	16
21.20	even	2		490.2.l.c.313.2		16
35.17	even	12	inner	630.2.bv.c.577.4		16
60.47	odd	4		560.2.ci.c.257.4		16
84.59	odd	6		560.2.ci.c.353.4		16
105.2	even	12		490.2.g.c.97.1		16
105.17	odd	12		70.2.k.a.17.1	yes	16
105.32	even	12		490.2.l.c.227.2		16
105.38	odd	12		350.2.o.c.157.4		16
105.47	odd	12		490.2.g.c.97.4		16
105.59	even	6		350.2.o.c.143.2		16
105.62	odd	4		490.2.l.c.117.4		16
420.227	even	12		560.2.ci.c.17.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.3	✓	16	21.17	even	6
70.2.k.a.17.1	yes	16	105.17	odd	12
70.2.k.a.33.1	yes	16	3.2	odd	2
70.2.k.a.47.3	yes	16	15.2	even	4
350.2.o.c.143.2		16	105.59	even	6
350.2.o.c.157.4		16	105.38	odd	12
350.2.o.c.243.4		16	15.14	odd	2
350.2.o.c.257.2		16	15.8	even	4
490.2.g.c.97.1		16	105.2	even	12
490.2.g.c.97.4		16	105.47	odd	12
490.2.g.c.293.1		16	21.5	even	6
490.2.g.c.293.4		16	21.2	odd	6
490.2.l.c.117.4		16	105.62	odd	4
490.2.l.c.227.2		16	105.32	even	12
490.2.l.c.313.2		16	21.20	even	2
490.2.l.c.423.4		16	21.11	odd	6
560.2.ci.c.17.4		16	420.227	even	12
560.2.ci.c.33.4		16	12.11	even	2
560.2.ci.c.257.4		16	60.47	odd	4
560.2.ci.c.353.4		16	84.59	odd	6
630.2.bv.c.73.1		16	7.3	odd	6	inner
630.2.bv.c.397.1		16	5.2	odd	4	inner
630.2.bv.c.523.4		16	1.1	even	1	trivial
630.2.bv.c.577.4		16	35.17	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(2.21323 + 0.318742i) q^{5} +(0.559876 - 2.58583i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(2.21323 + 0.318742i) q^{5} +(0.559876 - 2.58583i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.264946 + 2.22032i) q^{10} +(1.83557 + 3.17930i) q^{11} +(0.830578 - 0.830578i) q^{13} +(2.64263 - 0.128464i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.204036 - 0.761471i) q^{17} +(1.09461 - 1.89593i) q^{19} +(-2.07609 + 0.830578i) q^{20} +(-2.59589 + 2.59589i) q^{22} +(4.54529 - 1.21791i) q^{23} +(4.79681 + 1.41090i) q^{25} +(1.01725 + 0.587308i) q^{26} +(0.808050 + 2.51934i) q^{28} +2.62236i q^{29} +(0.0359651 - 0.0207644i) q^{31} +(0.965926 + 0.258819i) q^{32} +0.788333 q^{34} +(2.06335 - 5.54460i) q^{35} +(0.0664979 + 0.248174i) q^{37} +(2.11463 + 0.566614i) q^{38} +(-1.33961 - 1.79038i) q^{40} +8.98026i q^{41} +(-0.474569 - 0.474569i) q^{43} +(-3.17930 - 1.83557i) q^{44} +(2.35282 + 4.07520i) q^{46} +(-6.18205 + 1.65648i) q^{47} +(-6.37308 - 2.89549i) q^{49} +(-0.121320 + 4.99853i) q^{50} +(-0.304013 + 1.13459i) q^{52} +(-2.04824 + 7.64413i) q^{53} +(3.04917 + 7.62161i) q^{55} +(-2.22435 + 1.43257i) q^{56} +(-2.53301 + 0.678717i) q^{58} +(-5.35616 - 9.27713i) q^{59} +(1.72539 + 0.996157i) q^{61} +(0.0293654 + 0.0293654i) q^{62} +1.00000i q^{64} +(2.10300 - 1.57352i) q^{65} +(6.39671 + 1.71399i) q^{67} +(0.204036 + 0.761471i) q^{68} +(5.88971 + 0.557996i) q^{70} -8.11777 q^{71} +(9.52910 + 2.55331i) q^{73} +(-0.222506 + 0.128464i) q^{74} +2.18923i q^{76} +(9.24884 - 2.96647i) q^{77} +(-11.6145 - 6.70563i) q^{79} +(1.38266 - 1.75735i) q^{80} +(-8.67427 + 2.32426i) q^{82} +(9.73033 - 9.73033i) q^{83} +(0.694291 - 1.62028i) q^{85} +(0.335571 - 0.581226i) q^{86} +(0.950161 - 3.54605i) q^{88} +(-0.715130 + 1.23864i) q^{89} +(-1.68272 - 2.61276i) q^{91} +(-3.32739 + 3.32739i) q^{92} +(-3.20007 - 5.54268i) q^{94} +(3.02695 - 3.84723i) q^{95} +(-3.16693 - 3.16693i) q^{97} +(1.14736 - 6.90533i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) \) 16 * q + 12 * q^5 + 8 * q^7	\( 16 q + 12 q^{5} + 8 q^{7} - 12 q^{10} + 12 q^{11} + 8 q^{16} + 36 q^{17} - 8 q^{22} + 4 q^{23} + 12 q^{25} - 12 q^{26} + 4 q^{28} + 24 q^{31} - 8 q^{35} + 4 q^{37} - 24 q^{38} - 8 q^{43} - 8 q^{46} - 12 q^{47} + 32 q^{50} + 28 q^{53} + 4 q^{56} - 32 q^{58} - 12 q^{61} + 8 q^{65} + 32 q^{67} + 36 q^{68} - 12 q^{70} - 16 q^{71} - 12 q^{73} - 16 q^{77} + 12 q^{80} - 48 q^{82} + 24 q^{85} - 12 q^{86} - 4 q^{88} - 16 q^{91} - 8 q^{92} - 20 q^{95} - 40 q^{98}+O(q^{100}) \) 16 * q + 12 * q^5 + 8 * q^7 - 12 * q^10 + 12 * q^11 + 8 * q^16 + 36 * q^17 - 8 * q^22 + 4 * q^23 + 12 * q^25 - 12 * q^26 + 4 * q^28 + 24 * q^31 - 8 * q^35 + 4 * q^37 - 24 * q^38 - 8 * q^43 - 8 * q^46 - 12 * q^47 + 32 * q^50 + 28 * q^53 + 4 * q^56 - 32 * q^58 - 12 * q^61 + 8 * q^65 + 32 * q^67 + 36 * q^68 - 12 * q^70 - 16 * q^71 - 12 * q^73 - 16 * q^77 + 12 * q^80 - 48 * q^82 + 24 * q^85 - 12 * q^86 - 4 * q^88 - 16 * q^91 - 8 * q^92 - 20 * q^95 - 40 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more