LMFDB - Embedded newform 925.2.bc.e.49.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(49,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 14]))

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

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

chi := DirichletCharacter("925.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.bc (of order $18$, degree $6$, not 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:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.19
Character	$\chi$	$=$	925.49
Dual form			925.2.bc.e.774.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.797210 + 0.950078i) q^{2} +(0.636268 - 0.758274i) q^{3} +(0.0801918 - 0.454791i) q^{4} +1.22766 q^{6} +(1.25175 + 3.43915i) q^{7} +(2.64417 - 1.52661i) q^{8} +(0.350801 + 1.98949i) q^{9} +O(q^{10})$	\(q+(0.797210 + 0.950078i) q^{2} +(0.636268 - 0.758274i) q^{3} +(0.0801918 - 0.454791i) q^{4} +1.22766 q^{6} +(1.25175 + 3.43915i) q^{7} +(2.64417 - 1.52661i) q^{8} +(0.350801 + 1.98949i) q^{9} +(1.23181 + 2.13355i) q^{11} +(-0.293833 - 0.350176i) q^{12} +(-4.70993 - 0.830487i) q^{13} +(-2.26956 + 3.93099i) q^{14} +(2.69045 + 0.979245i) q^{16} +(-2.52078 + 0.444482i) q^{17} +(-1.61051 + 1.91933i) q^{18} +(4.86848 + 4.08514i) q^{19} +(3.40427 + 1.23905i) q^{21} +(-1.04503 + 2.87121i) q^{22} +(5.03691 + 2.90806i) q^{23} +(0.524810 - 2.97635i) q^{24} +(-2.96578 - 5.13687i) q^{26} +(4.30351 + 2.48463i) q^{27} +(1.66447 - 0.293492i) q^{28} +(-5.09284 - 8.82106i) q^{29} +5.61333 q^{31} +(-0.874033 - 2.40139i) q^{32} +(2.40158 + 0.423463i) q^{33} +(-2.43189 - 2.04060i) q^{34} +0.932934 q^{36} +(-5.84622 - 1.67979i) q^{37} +7.88215i q^{38} +(-3.62651 + 3.04301i) q^{39} +(1.68317 - 9.54575i) q^{41} +(1.53672 + 4.22211i) q^{42} -4.94702i q^{43} +(1.06910 - 0.389121i) q^{44} +(1.25259 + 7.10380i) q^{46} +(1.04817 + 0.605159i) q^{47} +(2.45439 - 1.41704i) q^{48} +(-4.89859 + 4.11040i) q^{49} +(-1.26685 + 2.19426i) q^{51} +(-0.755396 + 2.07543i) q^{52} +(-2.59001 + 7.11598i) q^{53} +(1.07021 + 6.06944i) q^{54} +(8.56011 + 7.18278i) q^{56} +(6.19531 - 1.09240i) q^{57} +(4.32063 - 11.8708i) q^{58} +(7.33791 + 2.67078i) q^{59} +(1.46437 - 8.30484i) q^{61} +(4.47501 + 5.33310i) q^{62} +(-6.40305 + 3.69680i) q^{63} +(4.44784 - 7.70388i) q^{64} +(1.51224 + 2.61928i) q^{66} +(-2.14168 - 5.88423i) q^{67} +1.18207i q^{68} +(5.40993 - 1.96905i) q^{69} +(3.87040 + 3.24765i) q^{71} +(3.96477 + 4.72503i) q^{72} +15.6559i q^{73} +(-3.06473 - 6.89352i) q^{74} +(2.24829 - 1.88654i) q^{76} +(-5.79570 + 6.90705i) q^{77} +(-5.78219 - 1.01956i) q^{78} +(-6.99790 + 2.54703i) q^{79} +(-1.07284 + 0.390481i) q^{81} +(10.4111 - 6.01083i) q^{82} +(1.75704 - 0.309814i) q^{83} +(0.836504 - 1.44887i) q^{84} +(4.70006 - 3.94382i) q^{86} +(-9.92920 - 1.75079i) q^{87} +(6.51423 + 3.76099i) q^{88} +(-7.63255 - 2.77802i) q^{89} +(-3.03948 - 17.2377i) q^{91} +(1.72648 - 2.05754i) q^{92} +(3.57158 - 4.25645i) q^{93} +(0.260660 + 1.47828i) q^{94} +(-2.37703 - 0.865168i) q^{96} +(-13.1866 - 7.61326i) q^{97} +(-7.81041 - 1.37719i) q^{98} +(-3.81257 + 3.19912i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 6 q^{4}+O(q^{10}) $ 156 * q - 6 * q^4	$ 156 q - 6 q^{4} - 12 q^{14} + 42 q^{16} + 24 q^{19} + 30 q^{21} - 30 q^{24} + 6 q^{29} - 72 q^{31} + 42 q^{34} + 216 q^{36} - 18 q^{39} - 6 q^{41} + 30 q^{44} - 72 q^{46} + 60 q^{49} - 60 q^{51} - 54 q^{54} + 240 q^{56} - 30 q^{59} - 12 q^{61} + 108 q^{64} - 12 q^{66} - 90 q^{69} + 144 q^{71} - 192 q^{74} + 42 q^{76} - 96 q^{79} + 96 q^{81} - 54 q^{84} + 216 q^{86} + 42 q^{89} - 54 q^{91} + 156 q^{94} - 252 q^{96} - 282 q^{99}+O(q^{100}) $ 156 * q - 6 * q^4 - 12 * q^14 + 42 * q^16 + 24 * q^19 + 30 * q^21 - 30 * q^24 + 6 * q^29 - 72 * q^31 + 42 * q^34 + 216 * q^36 - 18 * q^39 - 6 * q^41 + 30 * q^44 - 72 * q^46 + 60 * q^49 - 60 * q^51 - 54 * q^54 + 240 * q^56 - 30 * q^59 - 12 * q^61 + 108 * q^64 - 12 * q^66 - 90 * q^69 + 144 * q^71 - 192 * q^74 + 42 * q^76 - 96 * q^79 + 96 * q^81 - 54 * q^84 + 216 * q^86 + 42 * q^89 - 54 * q^91 + 156 * q^94 - 252 * q^96 - 282 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

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 $

$2$	0.797210	+	0.950078i	0.563713	+	0.671807i	0.970328	−	0.241793i	$-0.0777354\pi$
$2$	0.797210	+	0.950078i	0.563713	+	0.671807i	−0.406615	+	0.913600i	$0.633291\pi$
$3$	0.636268	−	0.758274i	0.367349	−	0.437790i	−0.550430	−	0.834882i	$-0.685536\pi$
$3$	0.636268	−	0.758274i	0.367349	−	0.437790i	0.917779	+	0.397092i	$0.129980\pi$
$4$	0.0801918	−	0.454791i	0.0400959	−	0.227395i
$5$		0			0
$5$		0			0
$6$	1.22766			0.501190
$7$	1.25175	+	3.43915i	0.473117	+	1.29988i	0.915235	+	0.402921i	$0.132005\pi$
$7$	1.25175	+	3.43915i	0.473117	+	1.29988i	−0.442118	+	0.896957i	$0.645773\pi$
$8$	2.64417	−	1.52661i	0.934857	−	0.539740i
$9$	0.350801	+	1.98949i	0.116934	+	0.663164i
$10$		0			0
$11$	1.23181	+	2.13355i	0.371404	+	0.643291i	0.989782	−	0.142590i	$-0.0455432\pi$
$11$	1.23181	+	2.13355i	0.371404	+	0.643291i	−0.618378	+	0.785881i	$0.712210\pi$
$12$	−0.293833	−	0.350176i	−0.0848222	−	0.101087i
$13$	−4.70993	−	0.830487i	−1.30630	−	0.230336i	−0.523188	−	0.852217i	$-0.675257\pi$
$13$	−4.70993	−	0.830487i	−1.30630	−	0.230336i	−0.783111	+	0.621882i	$0.786369\pi$
$14$	−2.26956	+	3.93099i	−0.606565	+	1.05060i
$15$		0			0
$16$	2.69045	+	0.979245i	0.672614	+	0.244811i
$17$	−2.52078	+	0.444482i	−0.611380	+	0.107803i	−0.470761	−	0.882261i	$-0.656020\pi$
$17$	−2.52078	+	0.444482i	−0.611380	+	0.107803i	−0.140619	+	0.990064i	$0.544909\pi$
$18$	−1.61051	+	1.91933i	−0.379601	+	0.452391i
$19$	4.86848	+	4.08514i	1.11690	+	0.937194i	0.998444	−	0.0557642i	$-0.0177595\pi$
$19$	4.86848	+	4.08514i	1.11690	+	0.937194i	0.118461	+	0.992959i	$0.462204\pi$
$20$		0			0
$21$	3.40427	+	1.23905i	0.742873	+	0.270384i
$22$	−1.04503	+	2.87121i	−0.222802	+	0.612143i
$23$	5.03691	+	2.90806i	1.05027	+	0.606373i	0.922724	−	0.385460i	$-0.125957\pi$
$23$	5.03691	+	2.90806i	1.05027	+	0.606373i	0.127544	+	0.991833i	$0.459291\pi$
$24$	0.524810	−	2.97635i	0.107126	−	0.607544i
$25$		0			0
$26$	−2.96578	−	5.13687i	−0.581637	−	1.00742i
$27$	4.30351	+	2.48463i	0.828211	+	0.478168i
$28$	1.66447	−	0.293492i	0.314556	−	0.0554647i
$29$	−5.09284	−	8.82106i	−0.945717	−	1.63803i	−0.754309	−	0.656520i	$-0.772028\pi$
$29$	−5.09284	−	8.82106i	−0.945717	−	1.63803i	−0.191408	−	0.981511i	$-0.561305\pi$
$30$		0			0
$31$	5.61333			1.00818			0.504092	−	0.863650i	$-0.331827\pi$
$31$	5.61333			1.00818			0.504092	+	0.863650i	$0.331827\pi$
$32$	−0.874033	−	2.40139i	−0.154509	−	0.424509i
$33$	2.40158	+	0.423463i	0.418061	+	0.0737155i
$34$	−2.43189	−	2.04060i	−0.417065	−	0.349959i
$35$		0			0
$36$	0.932934			0.155489
$37$	−5.84622	−	1.67979i	−0.961113	−	0.276156i
$37$	−5.84622	−	1.67979i	−0.961113	−	0.276156i
$38$			7.88215i			1.27865i
$39$	−3.62651	+	3.04301i	−0.580707	+	0.487271i
$40$		0			0
$41$	1.68317	−	9.54575i	0.262868	−	1.49080i	−0.512172	−	0.858883i	$-0.671159\pi$
$41$	1.68317	−	9.54575i	0.262868	−	1.49080i	0.775039	−	0.631913i	$-0.217730\pi$
$42$	1.53672	+	4.22211i	0.237121	+	0.651486i
$43$		−	4.94702i		−	0.754414i	−0.926129	−	0.377207i	$-0.876885\pi$
$43$		−	4.94702i		−	0.754414i	0.926129	−	0.377207i	$-0.123115\pi$
$44$	1.06910	−	0.389121i	0.161173	−	0.0586622i
$45$		0			0
$46$	1.25259	+	7.10380i	0.184684	+	1.04740i
$47$	1.04817	+	0.605159i	0.152891	+	0.0882715i	0.574494	−	0.818509i	$-0.305199\pi$
$47$	1.04817	+	0.605159i	0.152891	+	0.0882715i	−0.421603	+	0.906781i	$0.638532\pi$
$48$	2.45439	−	1.41704i	0.354260	−	0.204532i
$49$	−4.89859	+	4.11040i	−0.699798	+	0.587201i
$50$		0			0
$51$	−1.26685	+	2.19426i	−0.177395	+	0.307257i
$52$	−0.755396	+	2.07543i	−0.104755	+	0.287811i
$53$	−2.59001	+	7.11598i	−0.355765	+	0.977455i	0.624718	+	0.780850i	$0.285214\pi$
$53$	−2.59001	+	7.11598i	−0.355765	+	0.977455i	−0.980483	+	0.196605i	$0.937008\pi$
$54$	1.07021	+	6.06944i	0.145637	+	0.825947i
$55$		0			0
$56$	8.56011	+	7.18278i	1.14389	+	0.959839i
$57$	6.19531	−	1.09240i	0.820589	−	0.144692i
$58$	4.32063	−	11.8708i	0.567327	−	1.55872i
$59$	7.33791	+	2.67078i	0.955314	+	0.347706i	0.772196	−	0.635385i	$-0.219159\pi$
$59$	7.33791	+	2.67078i	0.955314	+	0.347706i	0.183119	+	0.983091i	$0.441381\pi$
$60$		0			0
$61$	1.46437	−	8.30484i	0.187493	−	1.06333i	−0.735217	−	0.677831i	$-0.762920\pi$
$61$	1.46437	−	8.30484i	0.187493	−	1.06333i	0.922710	−	0.385494i	$-0.125969\pi$
$62$	4.47501	+	5.33310i	0.568326	+	0.677305i
$63$	−6.40305	+	3.69680i	−0.806709	+	0.465754i
$64$	4.44784	−	7.70388i	0.555980	−	0.962985i
$65$		0			0
$66$	1.51224	+	2.61928i	0.186144	+	0.322411i
$67$	−2.14168	−	5.88423i	−0.261648	−	0.718873i	−0.999057	−	0.0434257i	$-0.986173\pi$
$67$	−2.14168	−	5.88423i	−0.261648	−	0.718873i	0.737408	−	0.675447i	$-0.236049\pi$
$68$			1.18207i			0.143347i
$69$	5.40993	−	1.96905i	0.651279	−	0.237046i
$70$		0			0
$71$	3.87040	+	3.24765i	0.459332	+	0.385425i	0.842885	−	0.538094i	$-0.180855\pi$
$71$	3.87040	+	3.24765i	0.459332	+	0.385425i	−0.383553	+	0.923519i	$0.625300\pi$
$72$	3.96477	+	4.72503i	0.467252	+	0.556850i
$73$			15.6559i			1.83238i	0.400742	+	0.916191i	$0.368752\pi$
$73$			15.6559i			1.83238i	−0.400742	+	0.916191i	$0.631248\pi$
$74$	−3.06473	−	6.89352i	−0.356268	−	0.801355i
$75$		0			0
$76$	2.24829	−	1.88654i	0.257897	−	0.216401i
$77$	−5.79570	+	6.90705i	−0.660482	+	0.787131i
$78$	−5.78219	−	1.01956i	−0.654704	−	0.115442i
$79$	−6.99790	+	2.54703i	−0.787326	+	0.286563i	−0.704224	−	0.709978i	$-0.748705\pi$
$79$	−6.99790	+	2.54703i	−0.787326	+	0.286563i	−0.0831017	+	0.996541i	$0.526483\pi$
$80$		0			0
$81$	−1.07284	+	0.390481i	−0.119204	+	0.0433868i
$82$	10.4111	−	6.01083i	1.14971	−	0.663785i
$83$	1.75704	−	0.309814i	0.192861	−	0.0340065i	−0.0763834	−	0.997079i	$-0.524337\pi$
$83$	1.75704	−	0.309814i	0.192861	−	0.0340065i	0.269244	+	0.963072i	$0.413226\pi$
$84$	0.836504	−	1.44887i	0.0912701	−	0.158084i
$85$		0			0
$86$	4.70006	−	3.94382i	0.506821	−	0.425273i
$87$	−9.92920	−	1.75079i	−1.06452	−	0.187704i
$88$	6.51423	+	3.76099i	0.694419	+	0.400923i
$89$	−7.63255	−	2.77802i	−0.809049	−	0.294470i	−0.0958180	−	0.995399i	$-0.530547\pi$
$89$	−7.63255	−	2.77802i	−0.809049	−	0.294470i	−0.713231	+	0.700929i	$0.752769\pi$
$90$		0			0
$91$	−3.03948	−	17.2377i	−0.318624	−	1.80701i
$92$	1.72648	−	2.05754i	0.179998	−	0.214513i
$93$	3.57158	−	4.25645i	0.370356	−	0.441373i
$94$	0.260660	+	1.47828i	0.0268851	+	0.152473i
$95$		0			0
$96$	−2.37703	−	0.865168i	−0.242605	−	0.0883008i
$97$	−13.1866	−	7.61326i	−1.33889	−	0.773010i	−0.352249	−	0.935906i	$-0.614583\pi$
$97$	−13.1866	−	7.61326i	−1.33889	−	0.773010i	−0.986643	+	0.162897i	$0.947916\pi$
$98$	−7.81041	−	1.37719i	−0.788971	−	0.139117i
$99$	−3.81257	+	3.19912i	−0.383178	+	0.321524i
$100$		0			0
$101$	−3.34038	+	5.78571i	−0.332381	+	0.575700i	−0.982978	−	0.183723i	$-0.941185\pi$
$101$	−3.34038	+	5.78571i	−0.332381	+	0.575700i	0.650598	+	0.759423i	$0.274519\pi$
$102$	−3.09466	+	0.545673i	−0.306417	+	0.0540297i
$103$	−9.93095	+	5.73363i	−0.978525	+	0.564952i	−0.901825	−	0.432102i	$-0.857772\pi$
$103$	−9.93095	+	5.73363i	−0.978525	+	0.564952i	−0.0767006	+	0.997054i	$0.524439\pi$
$104$	−13.7217	+	4.99429i	−1.34552	+	0.489731i
$105$		0			0
$106$	−8.82552	+	3.21223i	−0.857210	+	0.311999i
$107$	−8.82877	−	1.55675i	−0.853509	−	0.150497i	−0.270257	−	0.962788i	$-0.587109\pi$
$107$	−8.82877	−	1.55675i	−0.853509	−	0.150497i	−0.583252	+	0.812291i	$0.698220\pi$
$108$	1.47509	−	1.75795i	0.141941	−	0.169159i
$109$	8.42520	−	7.06958i	0.806987	−	0.677143i	−0.142899	−	0.989737i	$-0.545643\pi$
$109$	8.42520	−	7.06958i	0.806987	−	0.677143i	0.949887	+	0.312594i	$0.101198\pi$
$110$		0			0
$111$	−4.99351	+	3.36424i	−0.473963	+	0.319320i
$112$			10.4787i			0.990140i
$113$	0.967770	+	1.15334i	0.0910402	+	0.108497i	0.809641	−	0.586925i	$-0.199662\pi$
$113$	0.967770	+	1.15334i	0.0910402	+	0.108497i	−0.718601	+	0.695423i	$0.755217\pi$
$114$	5.97683	+	5.01516i	0.559781	+	0.469712i
$115$		0			0
$116$	−4.42014	+	1.60880i	−0.410400	+	0.149373i
$117$		−	9.66170i		−	0.893225i
$118$	3.31241	+	9.10076i	0.304932	+	0.837793i
$119$	−4.68403	−	8.11298i	−0.429385	−	0.743716i
$120$		0			0
$121$	2.46530	−	4.27002i	0.224118	−	0.388184i
$122$	9.05766	−	5.22944i	0.820042	−	0.473451i
$123$	−6.16735	−	7.34996i	−0.556091	−	0.662724i
$124$	0.450143	−	2.55289i	0.0404241	−	0.229256i
$125$		0			0
$126$	−8.61684	−	3.13627i	−0.767649	−	0.279401i
$127$	3.61646	−	9.93615i	0.320909	−	0.881690i	−0.669412	−	0.742892i	$-0.733454\pi$
$127$	3.61646	−	9.93615i	0.320909	−	0.881690i	0.990321	−	0.138799i	$-0.0443241\pi$
$128$	5.83180	−	1.02830i	0.515463	−	0.0908901i
$129$	−3.75120	−	3.14763i	−0.330275	−	0.277134i
$130$		0			0
$131$	−2.78143	−	15.7743i	−0.243015	−	1.37821i	−0.825058	−	0.565048i	$-0.808858\pi$
$131$	−2.78143	−	15.7743i	−0.243015	−	1.37821i	0.582043	−	0.813158i	$-0.302253\pi$
$132$	0.385174	−	1.05826i	0.0335251	−	0.0921095i
$133$	−7.95530	+	21.8570i	−0.689812	+	1.89524i
$134$	3.88311	−	6.72574i	0.335449	−	0.581015i
$135$		0			0
$136$	−5.98684	+	5.02355i	−0.513367	+	0.430766i
$137$	13.4139	−	7.74451i	1.14603	−	0.661658i	0.198110	−	0.980180i	$-0.436520\pi$
$137$	13.4139	−	7.74451i	1.14603	−	0.661658i	0.947916	+	0.318521i	$0.103186\pi$
$138$	6.18361	+	3.57011i	0.526384	+	0.303908i
$139$	2.43285	+	13.7974i	0.206352	+	1.17028i	0.895299	+	0.445467i	$0.146962\pi$
$139$	2.43285	+	13.7974i	0.206352	+	1.17028i	−0.688947	+	0.724812i	$0.741927\pi$
$140$		0			0
$141$	1.12579	−	0.409754i	0.0948087	−	0.0345075i
$142$			6.26624i			0.525851i
$143$	−4.02984	−	11.0719i	−0.336992	−	0.925878i
$144$	−1.00439	+	5.69616i	−0.0836989	+	0.474680i
$145$		0			0
$146$	−14.8743	+	12.4810i	−1.23101	+	1.03294i
$147$			6.32979i			0.522072i
$148$	−1.23277	+	2.52410i	−0.101333	+	0.207480i
$149$	13.8513			1.13474			0.567372	−	0.823462i	$-0.307960\pi$
$149$	13.8513			1.13474			0.567372	+	0.823462i	$0.307960\pi$
$150$		0			0
$151$	−9.55115	−	8.01436i	−0.777261	−	0.652200i	0.165296	−	0.986244i	$-0.447142\pi$
$151$	−9.55115	−	8.01436i	−0.777261	−	0.652200i	−0.942557	+	0.334044i	$0.891586\pi$
$152$	19.1095	+	3.36952i	1.54999	+	0.273305i
$153$	−1.76859	−	4.85916i	−0.142982	−	0.392839i
$154$	−11.1826			−0.901122
$155$		0			0
$156$	1.09311	+	1.89333i	0.0875191	+	0.151588i
$157$	−15.4450	+	2.72336i	−1.23264	+	0.217348i	−0.751759	−	0.659437i	$-0.770795\pi$
$157$	−15.4450	+	2.72336i	−1.23264	+	0.217348i	−0.480882	+	0.876785i	$0.659683\pi$
$158$	−7.99868	−	4.61804i	−0.636341	−	0.367391i
$159$	3.74793	+	6.49160i	0.297230	+	0.514818i
$160$		0			0
$161$	−3.69632	+	20.9629i	−0.291311	+	1.65211i
$162$	−1.22626	−	0.707984i	−0.0963444	−	0.0556245i
$163$	5.47871	−	15.0526i	0.429125	−	1.17901i	−0.517219	−	0.855853i	$-0.673033\pi$
$163$	5.47871	−	15.0526i	0.429125	−	1.17901i	0.946345	−	0.323159i	$-0.104745\pi$
$164$	−4.20634	−	1.53098i	−0.328460	−	0.119550i
$165$		0			0
$166$	1.69508	+	1.42234i	0.131564	+	0.110395i
$167$	−3.89883	+	4.64644i	−0.301701	+	0.359553i	−0.895501	−	0.445060i	$-0.853182\pi$
$167$	−3.89883	+	4.64644i	−0.301701	+	0.359553i	0.593800	+	0.804612i	$0.297627\pi$
$168$	10.8930	−	1.92074i	0.840416	−	0.148188i
$169$	9.27771	+	3.37681i	0.713670	+	0.259755i
$170$		0			0
$171$	−6.41948	+	11.1189i	−0.490910	+	0.850281i
$172$	−2.24986	−	0.396711i	−0.171550	−	0.0302489i
$173$	−12.0443	−	14.3538i	−0.915711	−	1.09130i	−0.995526	−	0.0944922i	$-0.969877\pi$
$173$	−12.0443	−	14.3538i	−0.915711	−	1.09130i	0.0798146	−	0.996810i	$-0.474567\pi$
$174$	−6.25228	−	10.8293i	−0.473984	−	0.820964i
$175$		0			0
$176$	1.22485	+	6.94647i	0.0923266	+	0.523610i
$177$	6.69406	−	3.86482i	0.503156	−	0.290497i
$178$	−3.44541	−	9.46619i	−0.258245	−	0.709521i
$179$	7.14373			0.533948			0.266974	−	0.963704i	$-0.413976\pi$
$179$	7.14373			0.533948			0.266974	+	0.963704i	$0.413976\pi$
$180$		0			0
$181$	−0.470008	+	2.66555i	−0.0349355	+	0.198129i	−0.997280	−	0.0737030i	$-0.976518\pi$
$181$	−0.470008	+	2.66555i	−0.0349355	+	0.198129i	0.962345	+	0.271832i	$0.0876294\pi$
$182$	13.9541	−	16.6298i	1.03435	−	1.23269i
$183$	−5.36562	−	6.39449i	−0.396638	−	0.472695i
$184$	17.7580			1.30913
$185$		0			0
$186$	6.89126			0.505292
$187$	−4.05345	−	4.83071i	−0.296417	−	0.353257i
$188$	0.359275	−	0.428167i	0.0262028	−	0.0312273i
$189$	−3.15812	+	17.9106i	−0.229719	+	1.30280i
$190$		0			0
$191$	−1.27137			−0.0919933			−0.0459966	−	0.998942i	$-0.514646\pi$
$191$	−1.27137			−0.0919933			−0.0459966	+	0.998942i	$0.514646\pi$
$192$	−3.01164	−	8.27442i	−0.217346	−	0.597154i
$193$	5.02777	−	2.90279i	0.361907	−	0.208947i	−0.308010	−	0.951383i	$-0.599663\pi$
$193$	5.02777	−	2.90279i	0.361907	−	0.208947i	0.669917	+	0.742436i	$0.266330\pi$
$194$	−3.27927	−	18.5976i	−0.235438	−	1.33523i
$195$		0			0
$196$	1.47655	+	2.55745i	0.105468	+	0.182675i
$197$	2.05632	+	2.45062i	0.146507	+	0.174600i	0.834307	−	0.551300i	$-0.185868\pi$
$197$	2.05632	+	2.45062i	0.146507	+	0.174600i	−0.687800	+	0.725900i	$0.741424\pi$
$198$	−6.07884	−	1.07186i	−0.432004	−	0.0761740i
$199$	−1.02492	+	1.77521i	−0.0726545	+	0.125841i	−0.900064	−	0.435758i	$-0.856480\pi$
$199$	−1.02492	+	1.77521i	−0.0726545	+	0.125841i	0.827409	+	0.561599i	$0.189814\pi$
$200$		0			0
$201$	−5.82454	−	2.11996i	−0.410832	−	0.149530i
$202$	−8.15987	+	1.43881i	−0.574126	+	0.101234i
$203$	23.9620	−	28.5568i	1.68180	−	2.00430i
$204$	0.896336	+	0.752115i	0.0627560	+	0.0526586i
$205$		0			0
$206$	−13.3645	−	4.86426i	−0.931146	−	0.338909i
$207$	−4.01861	+	11.0410i	−0.279313	+	0.767405i
$208$	−11.8586	−	6.84656i	−0.822246	−	0.474724i
$209$	−2.71883	+	15.4193i	−0.188065	+	1.06657i
$210$		0			0
$211$	−3.22049	−	5.57806i	−0.221708	−	0.384009i	0.733619	−	0.679561i	$-0.237830\pi$
$211$	−3.22049	−	5.57806i	−0.221708	−	0.384009i	−0.955327	+	0.295552i	$0.904496\pi$
$212$	3.02858	+	1.74855i	0.208004	+	0.120091i
$213$	4.92522	−	0.868449i	0.337470	−	0.0595051i
$214$	−5.55935	−	9.62908i	−0.380029	−	0.658230i
$215$		0			0
$216$	15.1723			1.03234
$217$	7.02648	+	19.3051i	0.476989	+	1.31052i
$218$	13.4333	+	2.36865i	0.909818	+	0.160426i
$219$	11.8714	+	9.96133i	0.802198	+	0.673124i
$220$		0			0
$221$	12.2419			0.823476
$222$	−7.17717	−	2.06221i	−0.481700	−	0.138407i
$223$			2.50828i			0.167967i	0.996467	+	0.0839834i	$0.0267643\pi$
$223$			2.50828i			0.167967i	−0.996467	+	0.0839834i	$0.973236\pi$
$224$	7.16467	−	6.01187i	0.478709	−	0.401685i
$225$		0			0
$226$	−0.324250	+	1.83892i	−0.0215688	+	0.122323i
$227$	2.87741	+	7.90562i	0.190981	+	0.524715i	0.997816	−	0.0660622i	$-0.0210436\pi$
$227$	2.87741	+	7.90562i	0.190981	+	0.524715i	−0.806835	+	0.590777i	$0.798821\pi$
$228$		−	2.90517i		−	0.192400i
$229$	2.52906	−	0.920501i	0.167125	−	0.0608284i	−0.257103	−	0.966384i	$-0.582768\pi$
$229$	2.52906	−	0.920501i	0.167125	−	0.0608284i	0.424228	+	0.905556i	$0.360546\pi$
$230$		0			0
$231$	1.54982	+	8.78947i	0.101971	+	0.578304i
$232$	−26.9327	−	15.5496i	−1.76822	−	1.02088i
$233$	1.40608	−	0.811802i	0.0921156	−	0.0531829i	−0.453235	−	0.891391i	$-0.649730\pi$
$233$	1.40608	−	0.811802i	0.0921156	−	0.0531829i	0.545350	+	0.838208i	$0.316397\pi$
$234$	9.17937	−	7.70241i	0.600074	−	0.503522i
$235$		0			0
$236$	1.80309	−	3.12304i	0.117371	−	0.203292i
$237$	−2.52119	+	6.92692i	−0.163769	+	0.449952i
$238$	3.97381	−	10.9180i	0.257584	−	0.707706i
$239$	1.43161	+	8.11908i	0.0926034	+	0.525180i	0.995455	+	0.0952285i	$0.0303582\pi$
$239$	1.43161	+	8.11908i	0.0926034	+	0.525180i	−0.902852	+	0.429951i	$0.858531\pi$
$240$		0			0
$241$	−15.2451	−	12.7922i	−0.982025	−	0.824017i	0.00236836	−	0.999997i	$-0.499246\pi$
$241$	−15.2451	−	12.7922i	−0.982025	−	0.824017i	−0.984394	+	0.175980i	$0.943691\pi$
$242$	6.02222	−	1.06188i	0.387123	−	0.0682602i
$243$	−5.48528	+	15.0707i	−0.351881	+	0.966786i
$244$	−3.65953	−	1.33196i	−0.234278	−	0.0852700i
$245$		0			0
$246$	2.06636	−	11.7189i	0.131747	−	0.747172i
$247$	−19.5375	−	23.2839i	−1.24314	−	1.48152i
$248$	14.8426	−	8.56939i	0.942508	−	0.544157i
$249$	0.883026	−	1.52945i	0.0559595	−	0.0969247i
$250$		0			0
$251$	7.00189	+	12.1276i	0.441955	+	0.765489i	0.997835	−	0.0657741i	$-0.0209517\pi$
$251$	7.00189	+	12.1276i	0.441955	+	0.765489i	−0.555879	+	0.831263i	$0.687618\pi$
$252$	1.16780	+	3.20850i	0.0735644	+	0.202117i
$253$			14.3287i			0.900837i
$254$	12.3232	−	4.48528i	0.773226	−	0.281431i
$255$		0			0
$256$	−8.00283	−	6.71517i	−0.500177	−	0.419698i
$257$	−8.56572	−	10.2082i	−0.534315	−	0.636772i	0.429588	−	0.903025i	$-0.358659\pi$
$257$	−8.56572	−	10.2082i	−0.534315	−	0.636772i	−0.963903	+	0.266253i	$0.914214\pi$
$258$		−	6.07326i		−	0.378105i
$259$	−1.54094	−	22.2087i	−0.0957491	−	1.37998i
$260$		0			0
$261$	15.7629	−	13.2266i	0.975696	−	0.818706i
$262$	12.7694	−	15.2180i	0.788897	−	0.940171i
$263$	4.84093	+	0.853587i	0.298505	+	0.0526344i	0.320895	−	0.947115i	$-0.396016\pi$
$263$	4.84093	+	0.853587i	0.298505	+	0.0526344i	−0.0223901	+	0.999749i	$0.507128\pi$
$264$	6.99666	−	2.54657i	0.430614	−	0.156731i
$265$		0			0
$266$	−27.1079	+	9.86647i	−1.66209	+	0.604952i
$267$	−6.96285	+	4.02000i	−0.426120	+	0.246020i
$268$	−2.84784	+	0.502151i	−0.173959	+	0.0306737i
$269$	−7.14311	+	12.3722i	−0.435523	+	0.754348i	−0.997338	−	0.0729148i	$-0.976770\pi$
$269$	−7.14311	+	12.3722i	−0.435523	+	0.754348i	0.561815	+	0.827263i	$0.310103\pi$
$270$		0			0
$271$	−12.4220	+	10.4233i	−0.754586	+	0.633172i	−0.936711	−	0.350103i	$-0.886147\pi$
$271$	−12.4220	+	10.4233i	−0.754586	+	0.633172i	0.182126	+	0.983275i	$0.441702\pi$
$272$	−7.21731	−	1.27261i	−0.437614	−	0.0771631i
$273$	−15.0049	−	8.66305i	−0.908135	−	0.524312i
$274$	18.0516	+	6.57024i	1.09054	+	0.396923i
$275$		0			0
$276$	−0.461675	−	2.61829i	−0.0277896	−	0.157602i
$277$	−4.68527	+	5.58368i	−0.281510	+	0.335491i	−0.888208	−	0.459442i	$-0.848049\pi$
$277$	−4.68527	+	5.58368i	−0.281510	+	0.335491i	0.606698	+	0.794933i	$0.292494\pi$
$278$	−11.1691	+	13.3108i	−0.669878	+	0.798330i
$279$	1.96916	+	11.1677i	0.117891	+	0.668591i
$280$		0			0
$281$	24.0504	+	8.75365i	1.43473	+	0.522199i	0.938283	−	0.345869i	$-0.112416\pi$
$281$	24.0504	+	8.75365i	1.43473	+	0.522199i	0.496446	+	0.868067i	$0.334638\pi$
$282$	1.28679	+	0.742929i	0.0766273	+	0.0442408i
$283$	4.28481	+	0.755528i	0.254706	+	0.0449115i	0.299543	−	0.954083i	$-0.403166\pi$
$283$	4.28481	+	0.755528i	0.254706	+	0.0449115i	−0.0448373	+	0.998994i	$0.514277\pi$
$284$	1.78737	−	1.49978i	0.106061	−	0.0889959i
$285$		0			0
$286$	7.30653	−	12.6553i	0.432044	−	0.748323i
$287$	34.9362	−	6.16020i	2.06222	−	0.363625i
$288$	4.47093	−	2.58129i	0.263452	−	0.152104i
$289$	−9.81799	+	3.57345i	−0.577529	+	0.210203i
$290$		0			0
$291$	−14.1631	+	5.15496i	−0.830257	+	0.302189i
$292$	7.12014	+	1.25547i	0.416675	+	0.0734710i
$293$	−1.15963	+	1.38199i	−0.0677460	+	0.0807366i	−0.798853	−	0.601526i	$-0.794560\pi$
$293$	−1.15963	+	1.38199i	−0.0677460	+	0.0807366i	0.731107	+	0.682263i	$0.239004\pi$
$294$	−6.01380	+	5.04618i	−0.350732	+	0.294299i
$295$		0			0
$296$	−18.0228	+	4.48326i	−1.04756	+	0.260584i
$297$			12.2424i			0.710373i
$298$	11.0424	+	13.1598i	0.639670	+	0.762329i
$299$	−21.3084	−	17.8798i	−1.23230	−	1.03402i
$300$		0			0
$301$	17.0136	−	6.19243i	0.980646	−	0.356926i
$302$		−	15.4635i		−	0.889823i
$303$	2.26178	+	6.21419i	0.129936	+	0.356996i
$304$	9.09806	+	15.7583i	0.521810	+	0.903801i
$305$		0			0
$306$	3.20664	−	5.55407i	0.183312	−	0.317505i
$307$	−1.79282	+	1.03508i	−0.102321	+	0.0590753i	−0.550287	−	0.834975i	$-0.685482\pi$
$307$	−1.79282	+	1.03508i	−0.102321	+	0.0590753i	0.447966	+	0.894051i	$0.352149\pi$
$308$	2.67649	+	3.18972i	0.152507	+	0.181751i
$309$	−1.97107	+	11.1785i	−0.112130	+	0.635923i
$310$		0			0
$311$	8.40758	+	3.06011i	0.476750	+	0.173523i	0.569208	−	0.822194i	$-0.307250\pi$
$311$	8.40758	+	3.06011i	0.476750	+	0.173523i	−0.0924575	+	0.995717i	$0.529472\pi$
$312$	−4.94363	+	13.5825i	−0.279878	+	0.768959i
$313$	0.217018	−	0.0382662i	0.0122666	−	0.00216293i	−0.167512	−	0.985870i	$-0.553573\pi$
$313$	0.217018	−	0.0382662i	0.0122666	−	0.00216293i	0.179778	+	0.983707i	$0.442462\pi$
$314$	−14.9003	−	12.5028i	−0.840872	−	0.705575i
$315$		0			0
$316$	0.597190	+	3.38683i	0.0335945	+	0.190524i
$317$	9.71763	−	26.6990i	0.545797	−	1.49956i	−0.293537	−	0.955948i	$-0.594832\pi$
$317$	9.71763	−	26.6990i	0.545797	−	1.49956i	0.839334	−	0.543616i	$-0.182945\pi$
$318$	−3.17964	+	8.73600i	−0.178306	+	0.489891i
$319$	12.5468	−	21.7317i	0.702486	−	1.21674i
$320$		0			0
$321$	−6.79790	+	5.70412i	−0.379422	+	0.318373i
$322$	−22.8631	+	13.2000i	−1.27411	+	0.735609i
$323$	−14.0881	−	8.13380i	−0.783886	−	0.452577i
$324$	0.0915542	+	0.519230i	0.00508634	+	0.0288461i
$325$		0			0
$326$	18.6689	−	6.79491i	1.03397	−	0.376335i
$327$		−	10.8868i		−	0.602039i
$328$	−10.1221	−	27.8102i	−0.558898	−	1.53556i
$329$	−0.769193	+	4.36231i	−0.0424070	+	0.240502i
$330$		0			0
$331$	−20.8378	+	17.4850i	−1.14535	+	0.961064i	−0.999601	−	0.0282577i	$-0.991004\pi$
$331$	−20.8378	+	17.4850i	−1.14535	+	0.961064i	−0.145750	+	0.989321i	$0.546560\pi$
$332$		−	0.823932i		−	0.0452191i
$333$	1.29108	−	12.2203i	0.0707505	−	0.669667i
$334$	−7.52267			−0.411622
$335$		0			0
$336$	7.94570	+	6.66723i	0.433473	+	0.363727i
$337$	2.47970	+	0.437238i	0.135078	+	0.0238179i	0.240778	−	0.970580i	$-0.422597\pi$
$337$	2.47970	+	0.437238i	0.135078	+	0.0238179i	−0.105700	+	0.994398i	$0.533708\pi$
$338$	4.18805	+	11.5066i	0.227800	+	0.625876i
$339$	1.49031			0.0809426
$340$		0			0
$341$	6.91454	+	11.9763i	0.374444	+	0.648555i
$342$	−15.6815	+	2.76507i	−0.847957	+	0.149518i
$343$	1.91867	+	1.10775i	0.103599	+	0.0598127i
$344$	−7.55220	−	13.0808i	−0.407187	−	0.705269i
$345$		0			0
$346$	4.03543	−	22.8861i	0.216946	−	1.23036i
$347$	23.6379	+	13.6474i	1.26895	+	0.732629i	0.974790	−	0.223126i	$-0.0716263\pi$
$347$	23.6379	+	13.6474i	1.26895	+	0.732629i	0.294162	+	0.955756i	$0.404960\pi$
$348$	−1.59248	+	4.37531i	−0.0853660	+	0.234541i
$349$	−10.2193	−	3.71954i	−0.547029	−	0.199102i	0.0536970	−	0.998557i	$-0.482900\pi$
$349$	−10.2193	−	3.71954i	−0.547029	−	0.199102i	−0.600726	+	0.799455i	$0.705122\pi$
$350$		0			0
$351$	−18.2058	−	15.2764i	−0.971752	−	0.815396i
$352$	4.04685	−	4.82284i	0.215698	−	0.257058i
$353$	18.9422	−	3.34001i	1.00819	−	0.177771i	0.354920	−	0.934897i	$-0.384508\pi$
$353$	18.9422	−	3.34001i	1.00819	−	0.177771i	0.653269	+	0.757126i	$0.273397\pi$
$354$	9.00845	+	3.27881i	0.478794	+	0.174267i
$355$		0			0
$356$	−1.87549	+	3.24844i	−0.0994006	+	0.172167i
$357$	−9.13217	−	1.61025i	−0.483326	−	0.0852233i
$358$	5.69506	+	6.78711i	0.300993	+	0.358710i
$359$	8.17874	+	14.1660i	0.431658	+	0.747653i	0.997016	−	0.0771923i	$-0.0245955\pi$
$359$	8.17874	+	14.1660i	0.431658	+	0.747653i	−0.565359	+	0.824845i	$0.691262\pi$
$360$		0			0
$361$	3.71440	+	21.0654i	0.195495	+	1.10871i
$362$	−2.90718	+	1.67846i	−0.152798	+	0.0882179i
$363$	−1.66926	−	4.58625i	−0.0876134	−	0.240716i
$364$	−8.08330			−0.423680
$365$		0			0
$366$	1.79774	−	10.1955i	0.0939696	−	0.532928i
$367$	−5.65205	+	6.73585i	−0.295035	+	0.351609i	−0.893116	−	0.449827i	$-0.851486\pi$
$367$	−5.65205	+	6.73585i	−0.295035	+	0.351609i	0.598081	+	0.801436i	$0.295930\pi$
$368$	10.7039	+	12.7564i	0.557978	+	0.664972i
$369$	19.5817			1.01938
$370$		0			0
$371$	−27.7150			−1.43889
$372$	−1.64938	−	1.96565i	−0.0855163	−	0.101914i
$373$	3.64465	−	4.34352i	0.188713	−	0.224899i	−0.663390	−	0.748274i	$-0.730883\pi$
$373$	3.64465	−	4.34352i	0.188713	−	0.224899i	0.852102	+	0.523375i	$0.175327\pi$
$374$	1.35810	−	7.70219i	0.0702259	−	0.398271i
$375$		0			0
$376$	3.69538			0.190575
$377$	16.6611	+	45.7761i	0.858093	+	2.35759i
$378$	−19.5341	+	11.2780i	−1.00473	+	0.580079i
$379$	1.04036	+	5.90015i	0.0534395	+	0.303071i	0.999799	−	0.0200448i	$-0.00638090\pi$
$379$	1.04036	+	5.90015i	0.0534395	+	0.303071i	−0.946360	+	0.323115i	$0.895270\pi$
$380$		0			0
$381$	−5.23329	−	9.06432i	−0.268109	−	0.464379i
$382$	−1.01355	−	1.20790i	−0.0518578	−	0.0618017i
$383$	4.45222	+	0.785047i	0.227498	+	0.0401140i	0.286235	−	0.958159i	$-0.407596\pi$
$383$	4.45222	+	0.785047i	0.227498	+	0.0401140i	−0.0587369	+	0.998273i	$0.518707\pi$
$384$	2.93085	−	5.07638i	0.149564	−	0.259053i
$385$		0			0
$386$	6.76607	+	2.46265i	0.344384	+	0.125345i
$387$	9.84206	−	1.73542i	0.500300	−	0.0882164i
$388$	−4.51989	+	5.38660i	−0.229463	+	0.273463i
$389$	−16.0606	−	13.4765i	−0.814306	−	0.683284i	0.137325	−	0.990526i	$-0.456149\pi$
$389$	−16.0606	−	13.4765i	−0.814306	−	0.683284i	−0.951631	+	0.307242i	$0.900594\pi$
$390$		0			0
$391$	−13.9895	−	5.09178i	−0.707482	−	0.257502i
$392$	−6.67772	+	18.3469i	−0.337276	+	0.926657i
$393$	−13.7310	−	7.92758i	−0.692636	−	0.399894i
$394$	−0.688967	+	3.90733i	−0.0347096	+	0.196848i
$395$		0			0
$396$	1.14919	+	1.99046i	0.0577492	+	0.100025i
$397$	−30.8124	−	17.7895i	−1.54643	−	0.892832i	−0.998410	−	0.0563660i	$-0.982049\pi$
$397$	−30.8124	−	17.7895i	−1.54643	−	0.892832i	−0.548019	−	0.836466i	$-0.684618\pi$
$398$	−2.50366	+	0.441463i	−0.125497	+	0.0221286i
$399$	11.5119	+	19.9392i	0.576316	+	0.998209i
$400$		0			0
$401$	39.1144			1.95328			0.976639	−	0.214887i	$-0.0689384\pi$
$401$	39.1144			1.95328			0.976639	+	0.214887i	$0.0689384\pi$
$402$	−2.62926	−	7.22383i	−0.131136	−	0.360292i
$403$	−26.4384	−	4.66180i	−1.31699	−	0.232221i
$404$	2.36342	+	1.98314i	0.117584	+	0.0986650i
$405$		0			0
$406$	46.2340			2.29455
$407$	−3.61749	−	14.5424i	−0.179312	−	0.720840i
$408$			7.73599i			0.382989i
$409$	−13.6766	+	11.4760i	−0.676265	+	0.567454i	−0.914912	−	0.403652i	$-0.867741\pi$
$409$	−13.6766	+	11.4760i	−0.676265	+	0.567454i	0.238647	+	0.971106i	$0.423296\pi$
$410$		0			0
$411$	2.66236	−	15.0990i	0.131325	−	0.744778i
$412$	1.81122	+	4.97629i	0.0892325	+	0.245164i
$413$			28.5793i			1.40630i
$414$	−13.6935	+	4.98404i	−0.673000	+	0.244952i
$415$		0			0
$416$	2.12231	+	12.0362i	0.104055	+	0.590125i
$417$	12.0101	+	6.93406i	0.588139	+	0.339562i
$418$	−16.8170	+	9.70929i	−0.822545	+	0.474897i
$419$	21.7756	−	18.2719i	1.06381	−	0.892639i	0.0693287	−	0.997594i	$-0.477914\pi$
$419$	21.7756	−	18.2719i	1.06381	−	0.892639i	0.994477	+	0.104955i	$0.0334698\pi$
$420$		0			0
$421$	12.9197	−	22.3776i	0.629668	−	1.09062i	−0.357950	−	0.933741i	$-0.616524\pi$
$421$	12.9197	−	22.3776i	0.629668	−	1.09062i	0.987618	−	0.156877i	$-0.0501426\pi$
$422$	2.73218	−	7.50661i	0.133000	−	0.365416i
$423$	−0.836261	+	2.29761i	−0.0406604	+	0.111714i
$424$	4.01494	+	22.7698i	0.194983	+	1.10580i
$425$		0			0
$426$	4.75153	+	3.98701i	0.230212	+	0.193171i
$427$	30.3946	−	5.35939i	1.47090	−	0.259359i
$428$	−1.41599	+	3.89040i	−0.0684445	+	0.188050i
$429$	−10.9596	−	3.98896i	−0.529134	−	0.192589i
$430$		0			0
$431$	2.73557	−	15.5142i	0.131768	−	0.747291i	−0.845289	−	0.534310i	$-0.820572\pi$
$431$	2.73557	−	15.5142i	0.131768	−	0.747291i	0.977056	−	0.212981i	$-0.0683174\pi$
$432$	9.14533	+	10.8990i	0.440005	+	0.524377i
$433$	8.60283	−	4.96684i	0.413426	−	0.238691i	−0.278835	−	0.960339i	$-0.589948\pi$
$433$	8.60283	−	4.96684i	0.413426	−	0.238691i	0.692261	+	0.721648i	$0.256615\pi$
$434$	−12.7398	+	22.0659i	−0.611529	+	1.05920i
$435$		0			0
$436$	−2.53955	−	4.39862i	−0.121622	−	0.210656i
$437$	12.6422	+	34.7343i	0.604761	+	1.66157i
$438$			19.2201i			0.918371i
$439$	−23.9716	+	8.72495i	−1.14410	+	0.416419i	−0.843393	−	0.537297i	$-0.819446\pi$
$439$	−23.9716	+	8.72495i	−1.14410	+	0.416419i	−0.300709	+	0.953716i	$0.597223\pi$
$440$		0			0
$441$	−9.89605	−	8.30377i	−0.471240	−	0.395418i
$442$	9.75933	+	11.6307i	0.464204	+	0.553217i
$443$			8.54985i			0.406215i	0.979156	+	0.203108i	$0.0651042\pi$
$443$			8.54985i			0.406215i	−0.979156	+	0.203108i	$0.934896\pi$
$444$	1.12959	+	2.54078i	0.0536078	+	0.120580i
$445$		0			0
$446$	−2.38306	+	1.99963i	−0.112841	+	0.0946851i
$447$	8.81314	−	10.5031i	0.416847	−	0.496779i
$448$	32.0624	+	5.65347i	1.51481	+	0.267101i
$449$	−27.3838	+	9.96691i	−1.29232	+	0.470367i	−0.894489	−	0.447090i	$-0.852460\pi$
$449$	−27.3838	+	9.96691i	−1.29232	+	0.470367i	−0.397835	+	0.917457i	$0.630238\pi$
$450$		0			0
$451$	22.4397	−	8.16739i	1.05665	−	0.384587i
$452$	0.602137	−	0.347644i	0.0283222	−	0.0163518i
$453$	−12.1542	+	2.14311i	−0.571053	+	0.100692i
$454$	−5.21706	+	9.03621i	−0.244849	+	0.424090i
$455$		0			0
$456$	14.7138	−	12.3463i	0.689037	−	0.578171i
$457$	−0.106590	−	0.0187947i	−0.00498606	−	0.000879177i	0.171155	−	0.985244i	$-0.445250\pi$
$457$	−0.106590	−	0.0187947i	−0.00498606	−	0.000879177i	−0.176141	+	0.984365i	$0.556361\pi$
$458$	2.89074	+	1.66897i	0.135075	+	0.0779858i
$459$	−11.9526	−	4.35039i	−0.557899	−	0.203059i
$460$		0			0
$461$	−1.31931	−	7.48215i	−0.0614462	−	0.348479i	−0.999994	−	0.00333056i	$-0.998940\pi$
$461$	−1.31931	−	7.48215i	−0.0614462	−	0.348479i	0.938548	−	0.345148i	$-0.112171\pi$
$462$	−7.11515	+	8.47951i	−0.331027	+	0.394502i
$463$	−6.99000	+	8.33036i	−0.324853	+	0.387145i	−0.903611	−	0.428355i	$-0.859093\pi$
$463$	−6.99000	+	8.33036i	−0.324853	+	0.387145i	0.578758	+	0.815500i	$0.303538\pi$
$464$	−5.06408	−	28.7198i	−0.235094	−	1.33328i
$465$		0			0
$466$	1.89222	+	0.688712i	0.0876554	+	0.0319040i
$467$	−24.1671	−	13.9529i	−1.11832	−	0.645664i	−0.177350	−	0.984148i	$-0.556752\pi$
$467$	−24.1671	−	13.9529i	−1.11832	−	0.645664i	−0.940972	+	0.338484i	$0.890086\pi$
$468$	−4.39405	−	0.774790i	−0.203115	−	0.0358147i
$469$	17.5559	−	14.7312i	0.810657	−	0.680222i
$470$		0			0
$471$	−7.76207	+	13.4443i	−0.357657	+	0.619481i
$472$	23.4800	−	4.14015i	1.08075	−	0.190566i
$473$	10.5547	−	6.09378i	0.485307	−	0.280192i
$474$	−8.59104	+	3.12688i	−0.394600	+	0.143623i
$475$		0			0
$476$	−4.06533	+	1.47966i	−0.186334	+	0.0678201i
$477$	−15.0658	−	2.65650i	−0.689814	−	0.121633i
$478$	−6.57247	+	7.83276i	−0.300618	+	0.358262i
$479$	10.9884	−	9.22039i	0.502074	−	0.421290i	−0.356256	−	0.934389i	$-0.615947\pi$
$479$	10.9884	−	9.22039i	0.502074	−	0.421290i	0.858330	+	0.513098i	$0.171502\pi$
$480$		0			0
$481$	26.1402	+	12.7669i	1.19189	+	0.582121i
$482$		−	24.6821i		−	1.12424i
$483$	13.5438	+	16.1408i	0.616262	+	0.734433i
$484$	−1.74427	−	1.46362i	−0.0792850	−	0.0665280i
$485$		0			0
$486$	−18.6913	+	6.80307i	−0.847853	+	0.308593i
$487$			42.5477i			1.92802i	0.265865	+	0.964010i	$0.414342\pi$
$487$			42.5477i			1.92802i	−0.265865	+	0.964010i	$0.585658\pi$
$488$	−8.80625	−	24.1950i	−0.398640	−	1.09525i
$489$	−7.92809	−	13.7319i	−0.358521	−	0.620976i
$490$		0			0
$491$	−7.16458	+	12.4094i	−0.323333	+	0.560029i	−0.981174	−	0.193128i	$-0.938137\pi$
$491$	−7.16458	+	12.4094i	−0.323333	+	0.560029i	0.657840	+	0.753157i	$0.271470\pi$
$492$	−3.83726	+	2.21545i	−0.172997	+	0.0998800i
$493$	16.7588	+	19.9723i	0.754777	+	0.899508i
$494$	6.54602	−	37.1243i	0.294520	−	1.67030i
$495$		0			0
$496$	15.1024	+	5.49683i	0.678118	+	0.246815i
$497$	−6.32439	+	17.3761i	−0.283688	+	0.779426i
$498$	2.15705	−	0.380346i	0.0966598	−	0.0170437i
$499$	−12.7933	−	10.7348i	−0.572705	−	0.480556i	0.309837	−	0.950790i	$-0.399725\pi$
$499$	−12.7933	−	10.7348i	−0.572705	−	0.480556i	−0.882542	+	0.470233i	$0.844170\pi$
$500$		0			0
$501$	1.04258	+	5.91277i	0.0465790	+	0.264163i
$502$	−5.94022	+	16.3206i	−0.265125	+	0.728425i
$503$	−3.64205	+	10.0065i	−0.162391	+	0.446166i	−0.994024	−	0.109160i	$-0.965184\pi$
$503$	−3.64205	+	10.0065i	−0.162391	+	0.446166i	0.831633	+	0.555325i	$0.187406\pi$
$504$	−11.2872	+	19.5500i	−0.502771	+	0.870826i
$505$		0			0
$506$	−13.6134	+	11.4230i	−0.605188	+	0.507813i
$507$	8.46366	−	4.88650i	0.375884	−	0.217017i
$508$	−4.22885	−	2.44153i	−0.187625	−	0.108325i
$509$	−4.34768	−	24.6569i	−0.192707	−	1.09290i	−0.915646	−	0.401986i	$-0.868320\pi$
$509$	−4.34768	−	24.6569i	−0.192707	−	1.09290i	0.722938	−	0.690912i	$-0.242791\pi$
$510$		0			0
$511$	−53.8430	+	19.5972i	−2.38187	+	0.866931i
$512$		−	24.8002i		−	1.09603i
$513$	10.8015	+	29.6768i	0.476896	+	1.31026i
$514$	2.86994	−	16.2762i	0.126587	−	0.717913i
$515$		0			0
$516$	−1.73233	+	1.45360i	−0.0762615	+	0.0639910i
$517$			2.98176i			0.131138i
$518$	19.8716	−	19.1690i	0.873107	−	0.842239i
$519$	−18.5475			−0.814147
$520$		0			0
$521$	25.5968	+	21.4783i	1.12142	+	0.940980i	0.998675	−	0.0514589i	$-0.0163871\pi$
$521$	25.5968	+	21.4783i	1.12142	+	0.940980i	0.122741	+	0.992439i	$0.460832\pi$
$522$	25.1326	+	4.43156i	1.10003	+	0.193964i
$523$	2.91797	+	8.01707i	0.127594	+	0.350562i	0.986997	−	0.160737i	$-0.0513869\pi$
$523$	2.91797	+	8.01707i	0.127594	+	0.350562i	−0.859403	+	0.511298i	$0.829165\pi$
$524$	−7.39704			−0.323141
$525$		0			0
$526$	3.04827	+	5.27975i	0.132911	+	0.230208i
$527$	−14.1500	+	2.49503i	−0.616384	+	0.108685i
$528$	6.04666	+	3.49104i	0.263147	+	0.151928i
$529$	5.41364	+	9.37669i	0.235375	+	0.407682i
$530$		0			0
$531$	−2.73935	+	15.5356i	−0.118878	+	0.674188i
$532$	9.30241	+	5.37075i	0.403311	+	0.232851i
$533$	−15.8553	+	43.5620i	−0.686767	+	1.88688i
$534$	−9.37018	−	3.41046i	−0.405487	−	0.147585i
$535$		0			0
$536$	−14.6459	−	12.2894i	−0.632608	−	0.530821i
$537$	4.54533	−	5.41691i	0.196145	−	0.233757i
$538$	−17.4491	+	3.07676i	−0.752286	+	0.132648i
$539$	−14.8039	−	5.38817i	−0.637648	−	0.232085i
$540$		0			0
$541$	20.7028	−	35.8583i	0.890083	−	1.54167i	0.0503095	−	0.998734i	$-0.483979\pi$
$541$	20.7028	−	35.8583i	0.890083	−	1.54167i	0.839774	−	0.542936i	$-0.182687\pi$
$542$	−19.8060	−	3.49233i	−0.850739	−	0.150008i
$543$	1.72217	+	2.05240i	0.0739053	+	0.0880769i
$544$	3.27062	+	5.66488i	0.140227	+	0.242880i
$545$		0			0
$546$	−3.73144	−	21.1621i	−0.159691	−	0.905653i
$547$	26.4787	−	15.2875i	1.13215	−	0.653645i	0.187673	−	0.982232i	$-0.439906\pi$
$547$	26.4787	−	15.2875i	1.13215	−	0.653645i	0.944474	+	0.328587i	$0.106572\pi$
$548$	−2.44645	−	6.72156i	−0.104507	−	0.287131i
$549$	17.0361			0.727084
$550$		0			0
$551$	11.2409	−	63.7501i	0.478877	−	2.71584i
$552$	11.2988	−	13.4654i	0.480909	−	0.573126i
$553$	−17.5192	−	20.8786i	−0.744994	−	0.887849i
$554$	−9.04008			−0.384076
$555$		0			0
$556$	6.47001			0.274390
$557$	−12.3110	−	14.6716i	−0.521632	−	0.621657i	0.439334	−	0.898324i	$-0.355215\pi$
$557$	−12.3110	−	14.6716i	−0.521632	−	0.621657i	−0.960966	+	0.276667i	$0.910770\pi$
$558$	−9.04033	+	10.7738i	−0.382708	+	0.456093i
$559$	−4.10844	+	23.3001i	−0.173769	+	0.985490i
$560$		0			0
$561$	−6.24208			−0.263541
$562$	10.8566	+	29.8283i	0.457959	+	1.25823i
$563$	−6.52364	+	3.76642i	−0.274938	+	0.158736i	−0.631130	−	0.775677i	$-0.717408\pi$
$563$	−6.52364	+	3.76642i	−0.274938	+	0.158736i	0.356191	+	0.934413i	$0.384075\pi$
$564$	−0.0960731	−	0.544858i	−0.00404541	−	0.0229427i
$565$		0			0
$566$	2.69809	+	4.67322i	0.113409	+	0.196430i
$567$	−2.68585	−	3.20087i	−0.112795	−	0.134424i
$568$	15.1919	+	2.67874i	0.637438	+	0.112398i
$569$	1.46065	−	2.52993i	0.0612338	−	0.106060i	−0.833783	−	0.552092i	$-0.813830\pi$
$569$	1.46065	−	2.52993i	0.0612338	−	0.106060i	0.895017	+	0.446032i	$0.147163\pi$
$570$		0			0
$571$	12.6815	+	4.61568i	0.530703	+	0.193160i	0.593452	−	0.804869i	$-0.297765\pi$
$571$	12.6815	+	4.61568i	0.530703	+	0.193160i	−0.0627490	+	0.998029i	$0.519987\pi$
$572$	−5.35855	+	0.944857i	−0.224052	+	0.0395064i
$573$	−0.808933	+	0.964049i	−0.0337937	+	0.0402737i
$574$	33.7042	+	28.2812i	1.40679	+	1.18043i
$575$		0			0
$576$	16.8871	+	6.14641i	0.703630	+	0.256100i
$577$	−8.00728	+	21.9998i	−0.333347	+	0.915864i	0.653887	+	0.756592i	$0.273137\pi$
$577$	−8.00728	+	21.9998i	−0.333347	+	0.915864i	−0.987235	+	0.159272i	$0.949085\pi$
$578$	−11.2221	−	6.47906i	−0.466776	−	0.269493i
$579$	0.997902	−	5.65938i	0.0414714	−	0.235196i
$580$		0			0
$581$	3.26488	+	5.65493i	0.135450	+	0.234606i
$582$	−16.1886	−	9.34650i	−0.671039	−	0.387425i
$583$	−18.3727	+	3.23961i	−0.760920	+	0.134171i
$584$	23.9005	+	41.3969i	0.989009	+	1.71301i
$585$		0			0
$586$	−2.23746			−0.0924287
$587$	2.41780	+	6.64286i	0.0997935	+	0.274180i	0.979536	−	0.201271i	$-0.0645071\pi$
$587$	2.41780	+	6.64286i	0.0997935	+	0.274180i	−0.879742	+	0.475451i	$0.842285\pi$
$588$	2.87873	+	0.507598i	0.118717	+	0.0209330i
$589$	27.3284	+	22.9312i	1.12605	+	0.944865i
$590$		0			0
$591$	3.16661			0.130257
$592$	−14.0841	−	10.2443i	−0.578851	−	0.421038i
$593$		−	18.9348i		−	0.777560i	−0.921331	−	0.388780i	$-0.872897\pi$
$593$		−	18.9348i		−	0.777560i	0.921331	−	0.388780i	$-0.127103\pi$
$594$	−11.6312	+	9.75973i	−0.477234	+	0.400447i
$595$		0			0
$596$	1.11076	−	6.29945i	0.0454986	−	0.258035i
$597$	0.693974	+	1.90668i	0.0284025	+	0.0780351i
$598$		−	34.4986i		−	1.41075i
$599$	−27.8106	+	10.1222i	−1.13631	+	0.413584i	−0.840580	−	0.541688i	$-0.817786\pi$
$599$	−27.8106	+	10.1222i	−1.13631	+	0.413584i	−0.295731	+	0.955271i	$0.595563\pi$
$600$		0			0
$601$	4.28444	+	24.2983i	0.174766	+	0.991147i	0.938414	+	0.345514i	$0.112295\pi$
$601$	4.28444	+	24.2983i	0.174766	+	0.991147i	−0.763648	+	0.645633i	$0.776594\pi$
$602$	19.4467	+	11.2276i	0.792588	+	0.457601i
$603$	10.9553	−	6.32506i	0.446135	−	0.257576i
$604$	−4.41078	+	3.70109i	−0.179472	+	0.150595i
$605$		0			0
$606$	−4.10085	+	7.10289i	−0.166586	+	0.288535i
$607$	−3.90283	+	10.7229i	−0.158411	+	0.435230i	−0.993353	−	0.115107i	$-0.963279\pi$
$607$	−3.90283	+	10.7229i	−0.158411	+	0.435230i	0.834942	+	0.550338i	$0.185501\pi$
$608$	5.55478	−	15.2616i	0.225276	−	0.618941i
$609$	−6.40765	−	36.3396i	−0.259651	−	1.47255i
$610$		0			0
$611$	−4.43421	−	3.72074i	−0.179389	−	0.150525i
$612$	−2.35172	+	0.414672i	−0.0950628	+	0.0167621i
$613$	5.50889	−	15.1356i	0.222502	−	0.611319i	−0.777340	−	0.629080i	$-0.783432\pi$
$613$	5.50889	−	15.1356i	0.222502	−	0.611319i	0.999842	+	0.0177611i	$0.00565383\pi$
$614$	−2.41266	−	0.878137i	−0.0973671	−	0.0354387i
$615$		0			0
$616$	−4.78044	+	27.1112i	−0.192610	+	1.09234i
$617$	13.0690	+	15.5751i	0.526140	+	0.627029i	0.962021	−	0.272975i	$-0.0880077\pi$
$617$	13.0690	+	15.5751i	0.526140	+	0.627029i	−0.435881	+	0.900004i	$0.643563\pi$
$618$	−12.1918	+	7.03895i	−0.490427	+	0.283148i
$619$	−8.72715	+	15.1159i	−0.350774	+	0.607558i	−0.986385	−	0.164451i	$-0.947415\pi$
$619$	−8.72715	+	15.1159i	−0.350774	+	0.607558i	0.635611	+	0.772009i	$0.280748\pi$
$620$		0			0
$621$	14.4509	+	25.0297i	0.579895	+	1.00441i
$622$	3.79527	+	10.4274i	0.152176	+	0.418101i
$623$		−	29.7269i		−	1.19098i
$624$	−12.7368	+	4.63582i	−0.509881	+	0.185581i
$625$		0			0
$626$	0.209365	+	0.175678i	0.00836792	+	0.00702152i
$627$	9.96212	+	11.8724i	0.397849	+	0.474138i
$628$			7.24261i			0.289012i
$629$	15.4837	+	1.63586i	0.617376	+	0.0652259i
$630$		0			0
$631$	30.2727	−	25.4018i	1.20514	−	1.01123i	0.205668	−	0.978622i	$-0.434063\pi$
$631$	30.2727	−	25.4018i	1.20514	−	1.01123i	0.999468	−	0.0326075i	$-0.0103811\pi$
$632$	−14.6153	+	17.4179i	−0.581367	+	0.692846i
$633$	−6.27879	−	1.10712i	−0.249560	−	0.0440041i
$634$	33.1131	−	12.0522i	1.31509	−	0.478654i
$635$		0			0
$636$	3.25287	−	1.18395i	0.128985	−	0.0469466i
$637$	26.4856	−	15.2915i	1.04940	−	0.605871i
$638$	30.6493	−	5.40429i	1.21342	−	0.213958i
$639$	−5.10343	+	8.83940i	−0.201889	+	0.349681i
$640$		0			0
$641$	−17.2485	+	14.4732i	−0.681276	+	0.571659i	−0.916379	−	0.400312i	$-0.868902\pi$
$641$	−17.2485	+	14.4732i	−0.681276	+	0.571659i	0.235103	+	0.971971i	$0.424457\pi$
$642$	−10.8387	−	1.91116i	−0.427770	−	0.0754274i
$643$	36.4249	+	21.0300i	1.43646	+	0.829340i	0.997602	−	0.0692162i	$-0.0220498\pi$
$643$	36.4249	+	21.0300i	1.43646	+	0.829340i	0.438858	+	0.898557i	$0.355383\pi$
$644$	9.23730	+	3.36210i	0.364001	+	0.132485i
$645$		0			0
$646$	−3.50347	−	19.8692i	−0.137842	−	0.781743i
$647$	13.7686	−	16.4087i	0.541299	−	0.645095i	−0.424180	−	0.905578i	$-0.639438\pi$
$647$	13.7686	−	16.4087i	0.541299	−	0.645095i	0.965478	+	0.260484i	$0.0838820\pi$
$648$	−2.24065	+	2.67031i	−0.0880212	+	0.104900i
$649$	3.34064	+	18.9457i	0.131132	+	0.743684i
$650$		0			0
$651$	19.1093	+	6.95521i	0.748952	+	0.272596i
$652$	−6.40644	−	3.69876i	−0.250896	−	0.144855i
$653$	12.2740	+	2.16424i	0.480319	+	0.0846933i	0.408565	−	0.912729i	$-0.366029\pi$
$653$	12.2740	+	2.16424i	0.480319	+	0.0846933i	0.0717541	+	0.997422i	$0.477140\pi$
$654$	10.3433	−	8.67903i	0.404454	−	0.339377i
$655$		0			0
$656$	13.8761	−	24.0342i	0.541772	−	0.938377i
$657$	−31.1472	+	5.49210i	−1.21517	+	0.214267i
$658$	−4.75775	+	2.74689i	−0.185476	+	0.107085i
$659$	36.0072	−	13.1056i	1.40264	−	0.510520i	0.473681	−	0.880696i	$-0.342925\pi$
$659$	36.0072	−	13.1056i	1.40264	−	0.510520i	0.928962	+	0.370176i	$0.120703\pi$
$660$		0			0
$661$	−20.8014	+	7.57108i	−0.809079	+	0.294481i	−0.713243	−	0.700916i	$-0.752775\pi$
$661$	−20.8014	+	7.57108i	−0.809079	+	0.294481i	−0.0958358	+	0.995397i	$0.530552\pi$
$662$	−33.2243	−	5.85834i	−1.29130	−	0.227691i
$663$	7.78910	−	9.28268i	0.302503	−	0.360510i
$664$	4.17296	−	3.50153i	0.161942	−	0.135886i
$665$		0			0
$666$	12.6395	−	8.51551i	0.489770	−	0.329969i
$667$		−	59.2412i		−	2.29383i
$668$	1.80050	+	2.14576i	0.0696636	+	0.0830219i
$669$	1.90197	+	1.59594i	0.0735342	+	0.0617025i
$670$		0			0
$671$	19.5226	−	7.10566i	0.753663	−	0.274311i
$672$		−	9.25794i		−	0.357133i
$673$	−5.13260	−	14.1017i	−0.197847	−	0.543581i	0.800605	−	0.599192i	$-0.204511\pi$
$673$	−5.13260	−	14.1017i	−0.197847	−	0.543581i	−0.998452	+	0.0556114i	$0.982289\pi$
$674$	1.56143	+	2.70448i	0.0601442	+	0.104173i
$675$		0			0
$676$	2.27974	−	3.94862i	0.0876823	−	0.151870i
$677$	2.38960	−	1.37964i	0.0918398	−	0.0530238i	−0.453377	−	0.891319i	$-0.649781\pi$
$677$	2.38960	−	1.37964i	0.0918398	−	0.0530238i	0.545217	+	0.838295i	$0.316447\pi$
$678$	1.18809	+	1.41591i	0.0456284	+	0.0543778i
$679$	9.67691	−	54.8805i	0.371366	−	2.10612i
$680$		0			0
$681$	7.82544	+	2.84823i	0.299871	+	0.109144i
$682$	−5.86612	+	16.1170i	−0.224625	+	0.617153i
$683$	45.6942	−	8.05713i	1.74844	−	0.308297i	0.794271	−	0.607563i	$-0.207853\pi$
$683$	45.6942	−	8.05713i	1.74844	−	0.308297i	0.954170	+	0.299266i	$0.0967418\pi$
$684$	4.54196	+	3.81116i	0.173666	+	0.145723i
$685$		0			0
$686$	0.477140	+	2.70600i	0.0182173	+	0.103315i
$687$	0.911164	−	2.50340i	0.0347631	−	0.0955108i
$688$	4.84435	−	13.3097i	0.184689	−	0.507429i
$689$	18.1085	−	31.3648i	0.689878	−	1.19490i
$690$		0			0
$691$	−27.9174	+	23.4255i	−1.06203	+	0.891147i	−0.994307	−	0.106558i	$-0.966017\pi$
$691$	−27.9174	+	23.4255i	−1.06203	+	0.891147i	−0.0677208	+	0.997704i	$0.521573\pi$
$692$	−7.49384	+	4.32657i	−0.284873	+	0.164472i
$693$	−15.7747	−	9.10750i	−0.599230	−	0.345965i
$694$	5.87834	+	33.3377i	0.223139	+	1.26548i
$695$		0			0
$696$	−28.9273	+	10.5287i	−1.09649	+	0.399088i
$697$			24.8109i			0.939781i
$698$	−4.61312	−	12.6744i	−0.174609	−	0.479734i
$699$	0.279076	−	1.58272i	0.0105556	−	0.0598640i
$700$		0			0
$701$	12.9285	−	10.8483i	0.488305	−	0.409736i	−0.365114	−	0.930963i	$-0.618970\pi$
$701$	12.9285	−	10.8483i	0.488305	−	0.409736i	0.853418	+	0.521227i	$0.174525\pi$
$702$		−	29.4754i		−	1.11248i
$703$	−21.6000	−	32.0606i	−0.814659	−	1.20919i
$704$	21.9155			0.825973
$705$		0			0
$706$	18.2742	+	15.3338i	0.687757	+	0.577097i
$707$	−24.0793	−	4.24583i	−0.905595	−	0.159681i
$708$	−1.22087	−	3.35432i	−0.0458832	−	0.126063i
$709$	−33.5312			−1.25929			−0.629645	−	0.776883i	$-0.716800\pi$
$709$	−33.5312			−1.25929			−0.629645	+	0.776883i	$0.716800\pi$
$710$		0			0
$711$	−7.52216	−	13.0288i	−0.282103	−	0.488617i
$712$	−24.4228	+	4.30639i	−0.915282	+	0.161389i
$713$	28.2738	+	16.3239i	1.05886	+	0.611335i
$714$	−5.75040	−	9.95998i	−0.215203	−	0.372743i
$715$		0			0
$716$	0.572869	−	3.24890i	0.0214091	−	0.121417i
$717$	7.06738	+	4.08035i	0.263936	+	0.152384i
$718$	−6.93863	+	19.0637i	−0.258947	+	0.711452i
$719$	12.4813	+	4.54283i	0.465475	+	0.169419i	0.564101	−	0.825705i	$-0.309223\pi$
$719$	12.4813	+	4.54283i	0.465475	+	0.169419i	−0.0986265	+	0.995125i	$0.531445\pi$
$720$		0			0
$721$	−32.1499	−	26.9770i	−1.19733	−	1.00467i
$722$	−17.0526	+	20.3225i	−0.634634	+	0.756327i
$723$	−19.4000	+	3.42074i	−0.721493	+	0.127219i
$724$	1.17458	+	0.427511i	0.0436528	+	0.0158883i
$725$		0			0
$726$	3.02655	−	5.24214i	0.112326	−	0.194554i
$727$	15.3378	+	2.70446i	0.568847	+	0.100303i	0.450672	−	0.892690i	$-0.351185\pi$
$727$	15.3378	+	2.70446i	0.568847	+	0.100303i	0.118175	+	0.992993i	$0.462296\pi$
$728$	−34.3523	−	40.9394i	−1.27318	−	1.51732i
$729$	6.22508	+	10.7822i	0.230558	+	0.399339i
$730$		0			0
$731$	2.19886	+	12.4704i	0.0813279	+	0.461234i
$732$	−3.33843	+	1.92745i	−0.123392	+	0.0712404i
$733$	−13.4718	−	37.0134i	−0.497592	−	1.36712i	−0.893595	−	0.448873i	$-0.851825\pi$
$733$	−13.4718	−	37.0134i	−0.497592	−	1.36712i	0.396004	−	0.918249i	$-0.370397\pi$
$734$	−10.9055			−0.402528
$735$		0			0
$736$	2.58095	−	14.6373i	0.0951352	−	0.539538i
$737$	9.91617	−	11.8176i	0.365267	−	0.435308i
$738$	15.6107	+	18.6041i	0.574638	+	0.684827i
$739$	3.94898			0.145266			0.0726329	−	0.997359i	$-0.476860\pi$
$739$	3.94898			0.145266			0.0726329	+	0.997359i	$0.476860\pi$
$740$		0			0
$741$	−30.0867			−1.10526
$742$	−22.0947	−	26.3314i	−0.811121	−	0.966657i
$743$	7.85345	−	9.35938i	0.288115	−	0.343362i	−0.602501	−	0.798118i	$-0.705829\pi$
$743$	7.85345	−	9.35938i	0.288115	−	0.343362i	0.890616	+	0.454756i	$0.150273\pi$
$744$	2.94593	−	16.7072i	0.108003	−	0.612516i
$745$		0			0
$746$	7.03224			0.257468
$747$	1.23275	+	3.38694i	0.0451038	+	0.123922i
$748$	−2.52202	+	1.45609i	−0.0922140	+	0.0532398i
$749$	−5.69750	−	32.3121i	−0.208182	−	1.18066i
$750$		0			0
$751$	15.5196	+	26.8807i	0.566317	+	0.980890i	0.996926	+	0.0783515i	$0.0249656\pi$
$751$	15.5196	+	26.8807i	0.566317	+	0.980890i	−0.430609	+	0.902539i	$0.641701\pi$
$752$	2.22744	+	2.65456i	0.0812265	+	0.0968020i
$753$	13.6511	+	2.40707i	0.497475	+	0.0877183i
$754$	−30.2085	+	52.3226i	−1.10013	+	1.90548i
$755$		0			0
$756$	7.89230	+	2.87256i	0.287040	+	0.104474i
$757$	−3.40414	+	0.600241i	−0.123725	+	0.0218161i	−0.235168	−	0.971955i	$-0.575564\pi$
$757$	−3.40414	+	0.600241i	−0.123725	+	0.0218161i	0.111443	+	0.993771i	$0.464453\pi$
$758$	−4.77623	+	5.69209i	−0.173480	+	0.206746i
$759$	10.8651	+	9.11688i	0.394377	+	0.330922i
$760$		0			0
$761$	45.0175	+	16.3850i	1.63188	+	0.593956i	0.985593	−	0.169136i	$-0.0540978\pi$
$761$	45.0175	+	16.3850i	1.63188	+	0.593956i	0.646289	+	0.763093i	$0.276320\pi$
$762$	4.43978	−	12.1982i	0.160836	−	0.441894i
$763$	34.8596	+	20.1262i	1.26200	+	0.728617i
$764$	−0.101954	+	0.578208i	−0.00368856	+	0.0209188i
$765$		0			0
$766$	2.80350	+	4.85581i	0.101295	+	0.175448i
$767$	−32.3430	−	18.6732i	−1.16784	−	0.674251i
$768$	−10.1839	+	1.79569i	−0.367479	+	0.0647965i
$769$	−0.558267	−	0.966946i	−0.0201316	−	0.0348690i	0.855784	−	0.517333i	$-0.173075\pi$
$769$	−0.558267	−	0.966946i	−0.0201316	−	0.0348690i	−0.875916	+	0.482464i	$0.839742\pi$
$770$		0			0
$771$	−13.1907			−0.475053
$772$	−0.916973	−	2.51936i	−0.0330026	−	0.0906739i
$773$	40.4497	+	7.13236i	1.45487	+	0.256533i	0.844489	−	0.535573i	$-0.179904\pi$
$773$	40.4497	+	7.13236i	1.45487	+	0.256533i	0.610384	+	0.792106i	$0.291015\pi$
$774$	9.49498	+	7.96724i	0.341290	+	0.286376i
$775$		0			0
$776$	−46.4901			−1.66890
$777$	−17.8208	−	12.9622i	−0.639316	−	0.465018i
$778$		−	26.0024i		−	0.932233i
$779$	47.1902	−	39.5973i	1.69076	−	1.41872i
$780$		0			0
$781$	−2.16145	+	12.2582i	−0.0773427	+	0.438632i
$782$	−6.31502	−	17.3504i	−0.225825	−	0.620448i
$783$		−	50.6154i		−	1.80885i
$784$	−17.2045	+	6.26193i	−0.614447	+	0.223641i
$785$		0			0
$786$	−3.41465	−	19.3655i	−0.121797	−	0.690743i
$787$	18.2080	+	10.5124i	0.649044	+	0.374726i	0.788090	−	0.615560i	$-0.211070\pi$
$787$	18.2080	+	10.5124i	0.649044	+	0.374726i	−0.139046	+	0.990286i	$0.544404\pi$
$788$	1.27942	−	0.738674i	0.0455775	−	0.0263142i
$789$	3.72738	−	3.12764i	0.132698	−	0.111347i
$790$		0			0
$791$	−2.75512	+	4.77201i	−0.0979608	+	0.169673i
$792$	−5.19726	+	14.2794i	−0.184677	+	0.507395i
$793$	−13.7941	+	37.8991i	−0.489844	+	1.34583i
$794$	−7.66250	−	43.4562i	−0.271932	−	1.54220i
$795$		0			0
$796$	0.725159	+	0.608480i	0.0257026	+	0.0215670i
$797$	28.3049	−	4.99091i	1.00261	−	0.176787i	0.351838	−	0.936061i	$-0.385557\pi$
$797$	28.3049	−	4.99091i	1.00261	−	0.176787i	0.650772	+	0.759274i	$0.274446\pi$
$798$	−9.76640	+	26.8330i	−0.345727	+	0.949876i
$799$	−2.91118	−	1.05958i	−0.102990	−	0.0374854i
$800$		0			0
$801$	2.84934	−	16.1594i	0.100677	−	0.570966i
$802$	31.1824	+	37.1617i	1.10109	+	1.31223i
$803$	−33.4026	+	19.2850i	−1.17875	+	0.680554i
$804$	−1.43122	+	2.47894i	−0.0504752	+	0.0874256i
$805$		0			0
$806$	−16.6479	−	28.8350i	−0.586397	−	1.01567i
$807$	4.83661	+	13.2885i	0.170257	+	0.467777i
$808$			20.3979i			0.717596i
$809$	−39.8492	+	14.5039i	−1.40102	+	0.509930i	−0.928481	−	0.371379i	$-0.878885\pi$
$809$	−39.8492	+	14.5039i	−1.40102	+	0.509930i	−0.472540	+	0.881309i	$0.656663\pi$
$810$		0			0
$811$	−25.1317	−	21.0880i	−0.882492	−	0.740499i	0.0841981	−	0.996449i	$-0.473167\pi$
$811$	−25.1317	−	21.0880i	−0.882492	−	0.740499i	−0.966690	+	0.255951i	$0.917612\pi$
$812$	−11.0658	−	13.1877i	−0.388334	−	0.462798i
$813$			16.0514i			0.562945i
$814$	10.9325	−	15.0303i	0.383185	−	0.526810i
$815$		0			0
$816$	−5.55713	+	4.66299i	−0.194538	+	0.163237i
$817$	20.2093	−	24.0845i	0.707033	−	0.842609i
$818$	−21.8063	−	3.84504i	−0.762439	−	0.134439i
$819$	33.2281	−	12.0940i	1.16108	−	0.422600i
$820$		0			0
$821$	−25.1835	+	9.16606i	−0.878911	+	0.319898i	−0.741770	−	0.670654i	$-0.766014\pi$
$821$	−25.1835	+	9.16606i	−0.878911	+	0.319898i	−0.137141	+	0.990552i	$0.543791\pi$
$822$	16.4677	−	9.50762i	0.574377	−	0.331616i
$823$	−54.6474	+	9.63581i	−1.90489	+	0.335883i	−0.996595	−	0.0824499i	$-0.973726\pi$
$823$	−54.6474	+	9.63581i	−1.90489	+	0.335883i	−0.908294	+	0.418333i	$0.862614\pi$
$824$	−17.5061	+	30.3215i	−0.609854	+	1.05630i
$825$		0			0
$826$	−27.1526	+	22.7837i	−0.944760	+	0.792748i
$827$	−3.72119	−	0.656146i	−0.129398	−	0.0228164i	0.108574	−	0.994088i	$-0.465372\pi$
$827$	−3.72119	−	0.656146i	−0.129398	−	0.0228164i	−0.237972	+	0.971272i	$0.576483\pi$
$828$	4.69910	+	2.71303i	0.163305	+	0.0942842i
$829$	−24.6966	−	8.98884i	−0.857749	−	0.312195i	−0.124554	−	0.992213i	$-0.539750\pi$
$829$	−24.6966	−	8.98884i	−0.857749	−	0.312195i	−0.733196	+	0.680018i	$0.761972\pi$
$830$		0			0
$831$	1.25288	+	7.10543i	0.0434619	+	0.246485i
$832$	−27.3470	+	32.5909i	−0.948086	+	1.12988i
$833$	10.5213	−	12.5388i	0.364541	−	0.434443i
$834$	2.98671	+	16.9385i	0.103421	+	0.586532i
$835$		0			0
$836$	6.79450	+	2.47300i	0.234993	+	0.0855304i
$837$	24.1570	+	13.9471i	0.834989	+	0.482081i
$838$	34.7194	+	6.12197i	1.19936	+	0.211480i
$839$	−42.8912	+	35.9900i	−1.48077	+	1.24251i	−0.575413	+	0.817863i	$0.695159\pi$
$839$	−42.8912	+	35.9900i	−1.48077	+	1.24251i	−0.905357	+	0.424651i	$0.860397\pi$
$840$		0			0
$841$	−37.3741	+	64.7338i	−1.28876	+	2.23220i
$842$	31.5602	−	5.56492i	1.08764	−	0.191780i
$843$	21.9402	−	12.6672i	0.755660	−	0.436281i
$844$	−2.79510	+	1.01733i	−0.0962115	+	0.0350181i
$845$		0			0
$846$	−2.84958	+	1.03716i	−0.0979707	+	0.0356584i
$847$	17.7712	+	3.13354i	0.610626	+	0.107670i
$848$	−13.9366	+	16.6090i	−0.478584	+	0.570354i
$849$	3.29919	−	2.76835i	0.113228	−	0.0950094i
$850$		0			0
$851$	−24.5619	−	25.4621i	−0.841972	−	0.872831i
$852$		−	2.30958i		−	0.0791251i
$853$	−4.80759	−	5.72947i	−0.164609	−	0.196173i	0.677434	−	0.735583i	$-0.263092\pi$
$853$	−4.80759	−	5.72947i	−0.164609	−	0.196173i	−0.842043	+	0.539410i	$0.818647\pi$
$854$	29.3228	+	24.6047i	1.00340	+	0.841956i
$855$		0			0
$856$	−25.7214	+	9.36181i	−0.879138	+	0.319980i
$857$		−	8.23982i		−	0.281467i	−0.990048	−	0.140733i	$-0.955054\pi$
$857$		−	8.23982i		−	0.281467i	0.990048	−	0.140733i	$-0.0449461\pi$
$858$	−4.94727	−	13.5925i	−0.168897	−	0.464040i
$859$	27.7933	+	48.1394i	0.948295	+	1.64250i	0.749015	+	0.662552i	$0.230527\pi$
$859$	27.7933	+	48.1394i	0.948295	+	1.64250i	0.199280	+	0.979943i	$0.436140\pi$
$860$		0			0
$861$	17.5577	−	30.4108i	0.598364	−	1.03640i
$862$	16.9205	−	9.76906i	0.576315	−	0.332735i
$863$	8.33184	+	9.92950i	0.283619	+	0.338004i	0.888979	−	0.457948i	$-0.151415\pi$
$863$	8.33184	+	9.92950i	0.283619	+	0.338004i	−0.605360	+	0.795952i	$0.706971\pi$
$864$	2.20515	−	12.5060i	0.0750208	−	0.425464i
$865$		0			0
$866$	11.5772	+	4.21374i	0.393408	+	0.143189i
$867$	−3.53721	+	9.71840i	−0.120130	+	0.330054i
$868$	9.34325	−	1.64747i	0.317130	−	0.0559187i
$869$	−14.0543	−	11.7929i	−0.476759	−	0.400048i
$870$		0			0
$871$	5.20040	+	29.4929i	0.176209	+	0.999330i
$872$	11.4852	−	31.5552i	0.388937	−	1.06859i
$873$	10.5207	−	28.9053i	0.356071	−	0.978296i
$874$	−22.9218	+	39.7017i	−0.775340	+	1.34293i
$875$		0			0
$876$	5.48231	−	4.60021i	0.185230	−	0.155427i
$877$	−28.6898	+	16.5641i	−0.968786	+	0.559329i	−0.898866	−	0.438224i	$-0.855608\pi$
$877$	−28.6898	+	16.5641i	−0.968786	+	0.559329i	−0.0699198	+	0.997553i	$0.522274\pi$
$878$	−27.3998	−	15.8193i	−0.924699	−	0.533875i
$879$	0.310094	+	1.75863i	0.0104592	+	0.0593171i
$880$		0			0
$881$	−18.3415	+	6.67576i	−0.617941	+	0.224912i	−0.631974	−	0.774989i	$-0.717755\pi$
$881$	−18.3415	+	6.67576i	−0.617941	+	0.224912i	0.0140332	+	0.999902i	$0.495533\pi$
$882$		−	16.0219i		−	0.539484i
$883$	−6.44966	−	17.7203i	−0.217048	−	0.596335i	0.782609	−	0.622514i	$-0.213888\pi$
$883$	−6.44966	−	17.7203i	−0.217048	−	0.596335i	−0.999657	+	0.0261784i	$0.991666\pi$
$884$	0.981697	−	5.56748i	0.0330180	−	0.187255i
$885$		0			0
$886$	−8.12302	+	6.81603i	−0.272898	+	0.228989i
$887$		−	45.5256i		−	1.52860i	−0.644861	−	0.764299i	$-0.723085\pi$
$887$		−	45.5256i		−	1.52860i	0.644861	−	0.764299i	$-0.276915\pi$
$888$	−8.06780	+	16.5188i	−0.270738	+	0.554335i
$889$	38.6988			1.29792
$890$		0			0
$891$	−2.15464	−	1.80796i	−0.0721832	−	0.0605689i
$892$	1.14074	+	0.201144i	0.0381949	+	0.00673479i
$893$	2.63081	+	7.22810i	0.0880368	+	0.241879i
$894$	17.0047			0.568722
$895$		0			0
$896$	10.8364	+	18.7693i	0.362020	+	0.627038i
$897$	−27.1157	+	4.78122i	−0.905366	+	0.159640i
$898$	−31.3000	−	18.0711i	−1.04450	−	0.603040i
$899$	−28.5878	−	49.5155i	−0.953457	−	1.65144i
$900$		0			0
$901$	3.36592	−	19.0891i	0.112135	−	0.635949i
$902$	25.6488	+	14.8084i	0.854013	+	0.493065i
$903$	6.12962	−	16.8410i	0.203981	−	0.560434i
$904$	4.31966	+	1.57223i	0.143670	+	0.0522916i
$905$		0			0
$906$	−11.7256	−	9.83891i	−0.389556	−	0.326876i
$907$	30.5261	−	36.3796i	1.01360	−	1.20796i	0.0356010	−	0.999366i	$-0.488665\pi$
$907$	30.5261	−	36.3796i	1.01360	−	1.20796i	0.978001	−	0.208598i	$-0.0668901\pi$
$908$	3.82615	−	0.674653i	0.126975	−	0.0223891i
$909$	−12.6824	−	4.61603i	−0.420650	−	0.153104i
$910$		0			0
$911$	−24.5172	+	42.4650i	−0.812290	+	1.40693i	0.0989670	+	0.995091i	$0.468446\pi$
$911$	−24.5172	+	42.4650i	−0.812290	+	1.40693i	−0.911257	+	0.411837i	$0.864887\pi$
$912$	17.7379	+	3.12767i	0.587361	+	0.103568i
$913$	2.82535	+	3.36712i	0.0935053	+	0.111435i
$914$	−0.0671181	−	0.116252i	−0.00222007	−	0.00384527i
$915$		0			0
$916$	−0.215825	−	1.22401i	−0.00713108	−	0.0404423i
$917$	50.7685	−	29.3112i	1.67652	−	0.967942i
$918$	−5.39552	−	14.8241i	−0.178079	−	0.489267i
$919$	17.3447			0.572147			0.286074	−	0.958208i	$-0.407650\pi$
$919$	17.3447			0.572147			0.286074	+	0.958208i	$0.407650\pi$
$920$		0			0
$921$	−0.355834	+	2.01804i	−0.0117251	+	0.0664965i
$922$	6.05687	−	7.21829i	0.199472	−	0.237722i
$923$	−15.5322	−	18.5105i	−0.511247	−	0.609281i
$924$	4.12165			0.135592
$925$		0			0
$926$	−13.4870			−0.443210
$927$	−14.8908	−	17.7462i	−0.489078	−	0.582861i
$928$	−16.7315	+	19.9398i	−0.549237	+	0.654555i
$929$	−3.42676	+	19.4341i	−0.112428	+	0.637613i	0.875563	+	0.483104i	$0.160491\pi$
$929$	−3.42676	+	19.4341i	−0.112428	+	0.637613i	−0.987991	+	0.154509i	$0.950620\pi$
$930$		0			0
$931$	−40.6402			−1.33193
$932$	−0.256444	−	0.704573i	−0.00840009	−	0.0230791i
$933$	7.66988	−	4.42821i	0.251100	−	0.144973i
$934$	−6.00994	−	34.0841i	−0.196651	−	1.11527i
$935$		0			0
$936$	−14.7497	−	25.5472i	−0.482109	−	0.835037i
$937$	3.41806	+	4.07348i	0.111663	+	0.133075i	0.818981	−	0.573821i	$-0.194539\pi$
$937$	3.41806	+	4.07348i	0.111663	+	0.133075i	−0.707318	+	0.706896i	$0.750095\pi$
$938$	27.9915	+	4.93566i	0.913955	+	0.161155i
$939$	0.109066	−	0.188907i	0.00355922	−	0.00616475i
$940$		0			0
$941$	4.11175	+	1.49656i	0.134039	+	0.0487863i	0.408169	−	0.912906i	$-0.366167\pi$
$941$	4.11175	+	1.49656i	0.134039	+	0.0487863i	−0.274130	+	0.961693i	$0.588390\pi$
$942$	−18.9611	+	3.34336i	−0.617787	+	0.108933i
$943$	36.2376	−	43.1863i	1.18006	−	1.40634i
$944$	17.1270	+	14.3712i	0.557435	+	0.467743i
$945$		0			0
$946$	14.2039	+	5.16980i	0.461809	+	0.168085i
$947$	−14.3194	+	39.3421i	−0.465317	+	1.27845i	0.456120	+	0.889918i	$0.349239\pi$
$947$	−14.3194	+	39.3421i	−0.465317	+	1.27845i	−0.921437	+	0.388529i	$0.872983\pi$
$948$	2.94812	+	1.70210i	0.0957505	+	0.0552816i
$949$	13.0020	−	73.7381i	0.422063	−	2.39364i
$950$		0			0
$951$	−14.0621	−	24.3563i	−0.455996	−	0.789808i
$952$	−24.7708	−	14.3014i	−0.802826	−	0.463512i
$953$	−26.6216	+	4.69411i	−0.862359	+	0.152057i	−0.587299	−	0.809370i	$-0.699809\pi$
$953$	−26.6216	+	4.69411i	−0.862359	+	0.152057i	−0.275060	+	0.961427i	$0.588698\pi$
$954$	−9.48670	−	16.4314i	−0.307143	−	0.531988i
$955$		0			0
$956$	3.80729			0.123136
$957$	−8.49547	−	23.3411i	−0.274619	−	0.754511i
$958$	17.5202	+	3.08928i	0.566052	+	0.0998102i
$959$	43.4254	+	36.4382i	1.40228	+	1.17665i
$960$		0			0
$961$	0.509486			0.0164350
$962$	8.70969	+	35.0132i	0.280812	+	1.12887i
$963$		−	18.1109i		−	0.583615i
$964$	−7.04030	+	5.90751i	−0.226753	+	0.190268i
$965$		0			0
$966$	−4.53782	+	25.7353i	−0.146002	+	0.828019i
$967$	−18.5936	−	51.0854i	−0.597929	−	1.64280i	−0.755394	−	0.655271i	$-0.772554\pi$
$967$	−18.5936	−	51.0854i	−0.597929	−	1.64280i	0.157465	−	0.987525i	$-0.449668\pi$
$968$		−	15.0542i		−	0.483862i
$969$	−15.1315	+	5.50741i	−0.486093	+	0.176923i
$970$		0			0
$971$	−2.41080	−	13.6723i	−0.0773661	−	0.438765i	−0.998744	−	0.0500978i	$-0.984047\pi$
$971$	−2.41080	−	13.6723i	−0.0773661	−	0.438765i	0.921378	−	0.388667i	$-0.127064\pi$
$972$	6.41414	+	3.70320i	0.205733	+	0.118780i
$973$	−44.4060	+	25.6378i	−1.42359	+	0.821910i
$974$	−40.4237	+	33.9195i	−1.29526	+	1.08685i
$975$		0			0
$976$	12.0723	−	20.9098i	0.386425	−	0.669307i
$977$	−18.4638	+	50.7289i	−0.590709	+	1.62296i	0.178483	+	0.983943i	$0.442881\pi$
$977$	−18.4638	+	50.7289i	−0.590709	+	1.62296i	−0.769192	+	0.639017i	$0.779341\pi$
$978$	6.72599	−	18.4795i	0.215073	−	0.590909i
$979$	−3.47478	−	19.7064i	−0.111054	−	0.629821i
$980$		0			0
$981$	17.0204	+	14.2818i	0.543421	+	0.455984i
$982$	−17.5016	+	3.08601i	−0.558499	+	0.0984784i
$983$	2.96631	−	8.14987i	0.0946107	−	0.259941i	−0.883356	−	0.468703i	$-0.844721\pi$
$983$	2.96631	−	8.14987i	0.0946107	−	0.259941i	0.977966	+	0.208763i	$0.0669436\pi$
$984$	−27.5281	−	10.0194i	−0.877564	−	0.319407i
$985$		0			0
$986$	−5.61501	+	31.8443i	−0.178818	+	1.01413i
$987$	2.81842	+	3.35886i	0.0897112	+	0.106914i
$988$	−12.1561	+	7.01830i	−0.386736	+	0.223282i
$989$	14.3862	−	24.9177i	0.457456	−	0.792337i
$990$		0			0
$991$	−20.8815	−	36.1678i	−0.663322	−	1.14891i	−0.979737	−	0.200287i	$-0.935812\pi$
$991$	−20.8815	−	36.1678i	−0.663322	−	1.14891i	0.316415	−	0.948621i	$-0.397521\pi$
$992$	−4.90624	−	13.4798i	−0.155773	−	0.427983i
$993$			26.9260i			0.854469i
$994$	−21.5506	+	7.84376i	−0.683542	+	0.248789i
$995$		0			0
$996$	−0.624766	−	0.524241i	−0.0197965	−	0.0166112i
$997$	9.93106	+	11.8354i	0.314520	+	0.374830i	0.900025	−	0.435839i	$-0.143548\pi$
$997$	9.93106	+	11.8354i	0.314520	+	0.374830i	−0.585505	+	0.810669i	$0.699104\pi$
$998$		−	20.7125i		−	0.655643i
$999$	−20.9856	−	21.7547i	−0.663955	−	0.688289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.bc.e.49.19		156
5.2	odd	4		925.2.p.f.826.4	yes	78
5.3	odd	4		925.2.p.e.826.10	yes	78
5.4	even	2	inner	925.2.bc.e.49.8		156
37.34	even	9	inner	925.2.bc.e.774.8		156
185.34	even	18	inner	925.2.bc.e.774.19		156
185.108	odd	36		925.2.p.e.626.10	✓	78
185.182	odd	36		925.2.p.f.626.4	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.p.e.626.10	✓	78	185.108	odd	36
925.2.p.e.826.10	yes	78	5.3	odd	4
925.2.p.f.626.4	yes	78	185.182	odd	36
925.2.p.f.826.4	yes	78	5.2	odd	4
925.2.bc.e.49.8		156	5.4	even	2	inner
925.2.bc.e.49.19		156	1.1	even	1	trivial
925.2.bc.e.774.8		156	37.34	even	9	inner
925.2.bc.e.774.19		156	185.34	even	18	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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.bc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.797210 + 0.950078i) q^{2} +(0.636268 - 0.758274i) q^{3} +(0.0801918 - 0.454791i) q^{4} +1.22766 q^{6} +(1.25175 + 3.43915i) q^{7} +(2.64417 - 1.52661i) q^{8} +(0.350801 + 1.98949i) q^{9} +O(q^{10})\)	\(q+(0.797210 + 0.950078i) q^{2} +(0.636268 - 0.758274i) q^{3} +(0.0801918 - 0.454791i) q^{4} +1.22766 q^{6} +(1.25175 + 3.43915i) q^{7} +(2.64417 - 1.52661i) q^{8} +(0.350801 + 1.98949i) q^{9} +(1.23181 + 2.13355i) q^{11} +(-0.293833 - 0.350176i) q^{12} +(-4.70993 - 0.830487i) q^{13} +(-2.26956 + 3.93099i) q^{14} +(2.69045 + 0.979245i) q^{16} +(-2.52078 + 0.444482i) q^{17} +(-1.61051 + 1.91933i) q^{18} +(4.86848 + 4.08514i) q^{19} +(3.40427 + 1.23905i) q^{21} +(-1.04503 + 2.87121i) q^{22} +(5.03691 + 2.90806i) q^{23} +(0.524810 - 2.97635i) q^{24} +(-2.96578 - 5.13687i) q^{26} +(4.30351 + 2.48463i) q^{27} +(1.66447 - 0.293492i) q^{28} +(-5.09284 - 8.82106i) q^{29} +5.61333 q^{31} +(-0.874033 - 2.40139i) q^{32} +(2.40158 + 0.423463i) q^{33} +(-2.43189 - 2.04060i) q^{34} +0.932934 q^{36} +(-5.84622 - 1.67979i) q^{37} +7.88215i q^{38} +(-3.62651 + 3.04301i) q^{39} +(1.68317 - 9.54575i) q^{41} +(1.53672 + 4.22211i) q^{42} -4.94702i q^{43} +(1.06910 - 0.389121i) q^{44} +(1.25259 + 7.10380i) q^{46} +(1.04817 + 0.605159i) q^{47} +(2.45439 - 1.41704i) q^{48} +(-4.89859 + 4.11040i) q^{49} +(-1.26685 + 2.19426i) q^{51} +(-0.755396 + 2.07543i) q^{52} +(-2.59001 + 7.11598i) q^{53} +(1.07021 + 6.06944i) q^{54} +(8.56011 + 7.18278i) q^{56} +(6.19531 - 1.09240i) q^{57} +(4.32063 - 11.8708i) q^{58} +(7.33791 + 2.67078i) q^{59} +(1.46437 - 8.30484i) q^{61} +(4.47501 + 5.33310i) q^{62} +(-6.40305 + 3.69680i) q^{63} +(4.44784 - 7.70388i) q^{64} +(1.51224 + 2.61928i) q^{66} +(-2.14168 - 5.88423i) q^{67} +1.18207i q^{68} +(5.40993 - 1.96905i) q^{69} +(3.87040 + 3.24765i) q^{71} +(3.96477 + 4.72503i) q^{72} +15.6559i q^{73} +(-3.06473 - 6.89352i) q^{74} +(2.24829 - 1.88654i) q^{76} +(-5.79570 + 6.90705i) q^{77} +(-5.78219 - 1.01956i) q^{78} +(-6.99790 + 2.54703i) q^{79} +(-1.07284 + 0.390481i) q^{81} +(10.4111 - 6.01083i) q^{82} +(1.75704 - 0.309814i) q^{83} +(0.836504 - 1.44887i) q^{84} +(4.70006 - 3.94382i) q^{86} +(-9.92920 - 1.75079i) q^{87} +(6.51423 + 3.76099i) q^{88} +(-7.63255 - 2.77802i) q^{89} +(-3.03948 - 17.2377i) q^{91} +(1.72648 - 2.05754i) q^{92} +(3.57158 - 4.25645i) q^{93} +(0.260660 + 1.47828i) q^{94} +(-2.37703 - 0.865168i) q^{96} +(-13.1866 - 7.61326i) q^{97} +(-7.81041 - 1.37719i) q^{98} +(-3.81257 + 3.19912i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 6 q^{4}+O(q^{10}) \) 156 * q - 6 * q^4	\( 156 q - 6 q^{4} - 12 q^{14} + 42 q^{16} + 24 q^{19} + 30 q^{21} - 30 q^{24} + 6 q^{29} - 72 q^{31} + 42 q^{34} + 216 q^{36} - 18 q^{39} - 6 q^{41} + 30 q^{44} - 72 q^{46} + 60 q^{49} - 60 q^{51} - 54 q^{54} + 240 q^{56} - 30 q^{59} - 12 q^{61} + 108 q^{64} - 12 q^{66} - 90 q^{69} + 144 q^{71} - 192 q^{74} + 42 q^{76} - 96 q^{79} + 96 q^{81} - 54 q^{84} + 216 q^{86} + 42 q^{89} - 54 q^{91} + 156 q^{94} - 252 q^{96} - 282 q^{99}+O(q^{100}) \) 156 * q - 6 * q^4 - 12 * q^14 + 42 * q^16 + 24 * q^19 + 30 * q^21 - 30 * q^24 + 6 * q^29 - 72 * q^31 + 42 * q^34 + 216 * q^36 - 18 * q^39 - 6 * q^41 + 30 * q^44 - 72 * q^46 + 60 * q^49 - 60 * q^51 - 54 * q^54 + 240 * q^56 - 30 * q^59 - 12 * q^61 + 108 * q^64 - 12 * q^66 - 90 * q^69 + 144 * q^71 - 192 * q^74 + 42 * q^76 - 96 * q^79 + 96 * q^81 - 54 * q^84 + 216 * q^86 + 42 * q^89 - 54 * q^91 + 156 * q^94 - 252 * q^96 - 282 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more