LMFDB - Embedded newform 912.2.ci.a.319.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(79,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))

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

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

chi := DirichletCharacter("912.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.ci (of order $18$, degree $6$, 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:	$7.28235666434$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			319.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	912.319
Dual form			912.2.ci.a.223.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{3} +(-1.93969 + 1.62760i) q^{5} +(-0.386659 - 0.223238i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{3} +(-1.93969 + 1.62760i) q^{5} +(-0.386659 - 0.223238i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(-2.02094 + 1.16679i) q^{11} +(0.358441 + 0.0632028i) q^{13} +(-1.93969 - 1.62760i) q^{15} +(-5.58512 - 2.03282i) q^{17} +(-0.354570 - 4.34445i) q^{19} +(0.152704 - 0.419550i) q^{21} +(2.14543 - 2.55682i) q^{23} +(0.245100 - 1.39003i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(0.449493 + 1.23497i) q^{29} +(3.35117 - 5.80439i) q^{31} +(-1.50000 - 1.78763i) q^{33} +(1.11334 - 0.196312i) q^{35} +7.52974i q^{37} +0.363970i q^{39} +(-11.2947 + 1.99157i) q^{41} +(-4.52481 - 5.39246i) q^{43} +(1.26604 - 2.19285i) q^{45} +(-2.66978 - 7.33515i) q^{47} +(-3.40033 - 5.88954i) q^{49} +(1.03209 - 5.85327i) q^{51} +(-1.13176 + 1.34878i) q^{53} +(2.02094 - 5.55250i) q^{55} +(4.21688 - 1.10359i) q^{57} +(5.69119 + 2.07142i) q^{59} +(5.19459 + 4.35878i) q^{61} +(0.439693 + 0.0775297i) q^{63} +(-0.798133 + 0.460802i) q^{65} +(-8.71688 + 3.17269i) q^{67} +(2.89053 + 1.66885i) q^{69} +(-4.11334 + 3.45150i) q^{71} +(-0.591052 - 3.35202i) q^{73} +1.41147 q^{75} +1.04189 q^{77} +(-0.442219 - 2.50795i) q^{79} +(0.766044 - 0.642788i) q^{81} +(-1.39053 - 0.802823i) q^{83} +(14.1420 - 5.14728i) q^{85} +(-1.13816 + 0.657115i) q^{87} +(-6.14930 - 1.08429i) q^{89} +(-0.124485 - 0.104455i) q^{91} +(6.29813 + 2.29233i) q^{93} +(7.75877 + 7.84981i) q^{95} +(0.368241 - 1.01173i) q^{97} +(1.50000 - 1.78763i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{5} - 9 q^{7}+O(q^{10}) $ 6 * q - 6 * q^5 - 9 * q^7	$ 6 q - 6 q^{5} - 9 q^{7} - 9 q^{11} - 6 q^{13} - 6 q^{15} - 12 q^{17} - 18 q^{19} + 3 q^{21} - 3 q^{23} - 3 q^{27} - 6 q^{31} - 9 q^{33} - 12 q^{41} + 3 q^{45} - 39 q^{47} - 6 q^{49} - 3 q^{51} - 12 q^{53} + 9 q^{55} + 9 q^{57} - 12 q^{59} + 27 q^{61} - 3 q^{63} + 9 q^{65} - 36 q^{67} - 18 q^{71} - 9 q^{73} - 12 q^{75} + 18 q^{79} + 9 q^{83} + 27 q^{85} + 27 q^{87} + 3 q^{89} + 12 q^{91} + 24 q^{93} + 24 q^{95} - 3 q^{97} + 9 q^{99}+O(q^{100}) $ 6 * q - 6 * q^5 - 9 * q^7 - 9 * q^11 - 6 * q^13 - 6 * q^15 - 12 * q^17 - 18 * q^19 + 3 * q^21 - 3 * q^23 - 3 * q^27 - 6 * q^31 - 9 * q^33 - 12 * q^41 + 3 * q^45 - 39 * q^47 - 6 * q^49 - 3 * q^51 - 12 * q^53 + 9 * q^55 + 9 * q^57 - 12 * q^59 + 27 * q^61 - 3 * q^63 + 9 * q^65 - 36 * q^67 - 18 * q^71 - 9 * q^73 - 12 * q^75 + 18 * q^79 + 9 * q^83 + 27 * q^85 + 27 * q^87 + 3 * q^89 + 12 * q^91 + 24 * q^93 + 24 * q^95 - 3 * q^97 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$4$		0			0
$5$	−1.93969	+	1.62760i	−0.867457	+	0.727883i	−0.963561	−	0.267489i	$-0.913806\pi$
$5$	−1.93969	+	1.62760i	−0.867457	+	0.727883i	0.0961041	+	0.995371i	$0.469362\pi$
$6$		0			0
$7$	−0.386659	−	0.223238i	−0.146143	−	0.0843760i	0.425145	−	0.905125i	$-0.360223\pi$
$7$	−0.386659	−	0.223238i	−0.146143	−	0.0843760i	−0.571289	+	0.820749i	$0.693556\pi$
$8$		0			0
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$		0			0
$11$	−2.02094	+	1.16679i	−0.609338	+	0.351801i	−0.772706	−	0.634764i	$-0.781097\pi$
$11$	−2.02094	+	1.16679i	−0.609338	+	0.351801i	0.163369	+	0.986565i	$0.447764\pi$
$12$		0			0
$13$	0.358441	+	0.0632028i	0.0994136	+	0.0175293i	0.223134	−	0.974788i	$-0.428371\pi$
$13$	0.358441	+	0.0632028i	0.0994136	+	0.0175293i	−0.123720	+	0.992317i	$0.539482\pi$
$14$		0			0
$15$	−1.93969	−	1.62760i	−0.500826	−	0.420243i
$16$		0			0
$17$	−5.58512	−	2.03282i	−1.35459	−	0.493031i	−0.440213	−	0.897893i	$-0.645097\pi$
$17$	−5.58512	−	2.03282i	−1.35459	−	0.493031i	−0.914378	+	0.404862i	$0.867319\pi$
$18$		0			0
$19$	−0.354570	−	4.34445i	−0.0813440	−	0.996686i
$19$	−0.354570	−	4.34445i	−0.0813440	−	0.996686i
$20$		0			0
$21$	0.152704	−	0.419550i	0.0333227	−	0.0915533i
$22$		0			0
$23$	2.14543	−	2.55682i	0.447353	−	0.533135i	−0.494492	−	0.869182i	$-0.664646\pi$
$23$	2.14543	−	2.55682i	0.447353	−	0.533135i	0.941845	+	0.336048i	$0.109090\pi$
$24$		0			0
$25$	0.245100	−	1.39003i	0.0490200	−	0.278006i
$26$		0			0
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$		0			0
$29$	0.449493	+	1.23497i	0.0834687	+	0.229328i	0.974405	−	0.224800i	$-0.0721729\pi$
$29$	0.449493	+	1.23497i	0.0834687	+	0.229328i	−0.890936	+	0.454129i	$0.849951\pi$
$30$		0			0
$31$	3.35117	−	5.80439i	0.601887	−	1.04250i	−0.390648	−	0.920540i	$-0.627749\pi$
$31$	3.35117	−	5.80439i	0.601887	−	1.04250i	0.992535	−	0.121959i	$-0.0389177\pi$
$32$		0			0
$33$	−1.50000	−	1.78763i	−0.261116	−	0.311187i
$34$		0			0
$35$	1.11334	−	0.196312i	0.188189	−	0.0331828i
$36$		0			0
$37$			7.52974i			1.23788i	0.785438	+	0.618941i	$0.212438\pi$
$37$			7.52974i			1.23788i	−0.785438	+	0.618941i	$0.787562\pi$
$38$		0			0
$39$			0.363970i			0.0582819i
$40$		0			0
$41$	−11.2947	+	1.99157i	−1.76394	+	0.311030i	−0.959228	−	0.282634i	$-0.908792\pi$
$41$	−11.2947	+	1.99157i	−1.76394	+	0.311030i	−0.804713	+	0.593664i	$0.797681\pi$
$42$		0			0
$43$	−4.52481	−	5.39246i	−0.690028	−	0.822343i	0.301331	−	0.953520i	$-0.402569\pi$
$43$	−4.52481	−	5.39246i	−0.690028	−	0.822343i	−0.991359	+	0.131176i	$0.958125\pi$
$44$		0			0
$45$	1.26604	−	2.19285i	0.188731	−	0.326891i
$46$		0			0
$47$	−2.66978	−	7.33515i	−0.389427	−	1.06994i	−0.967260	−	0.253787i	$-0.918324\pi$
$47$	−2.66978	−	7.33515i	−0.389427	−	1.06994i	0.577833	−	0.816155i	$-0.303899\pi$
$48$		0			0
$49$	−3.40033	−	5.88954i	−0.485761	−	0.841363i
$50$		0			0
$51$	1.03209	−	5.85327i	0.144521	−	0.819621i
$52$		0			0
$53$	−1.13176	+	1.34878i	−0.155459	+	0.185269i	−0.838152	−	0.545436i	$-0.816364\pi$
$53$	−1.13176	+	1.34878i	−0.155459	+	0.185269i	0.682693	+	0.730705i	$0.260808\pi$
$54$		0			0
$55$	2.02094	−	5.55250i	0.272504	−	0.748699i
$56$		0			0
$57$	4.21688	−	1.10359i	0.558540	−	0.146174i
$58$		0			0
$59$	5.69119	+	2.07142i	0.740930	+	0.269676i	0.684784	−	0.728746i	$-0.259897\pi$
$59$	5.69119	+	2.07142i	0.740930	+	0.269676i	0.0561458	+	0.998423i	$0.482119\pi$
$60$		0			0
$61$	5.19459	+	4.35878i	0.665099	+	0.558085i	0.911610	−	0.411055i	$-0.134840\pi$
$61$	5.19459	+	4.35878i	0.665099	+	0.558085i	−0.246511	+	0.969140i	$0.579284\pi$
$62$		0			0
$63$	0.439693	+	0.0775297i	0.0553961	+	0.00976782i
$64$		0			0
$65$	−0.798133	+	0.460802i	−0.0989963	+	0.0571555i
$66$		0			0
$67$	−8.71688	+	3.17269i	−1.06494	+	0.387605i	−0.814281	−	0.580471i	$-0.802868\pi$
$67$	−8.71688	+	3.17269i	−1.06494	+	0.387605i	−0.250656	+	0.968076i	$0.580646\pi$
$68$		0			0
$69$	2.89053	+	1.66885i	0.347979	+	0.200906i
$70$		0			0
$71$	−4.11334	+	3.45150i	−0.488164	+	0.409618i	−0.853368	−	0.521310i	$-0.825444\pi$
$71$	−4.11334	+	3.45150i	−0.488164	+	0.409618i	0.365204	+	0.930928i	$0.380999\pi$
$72$		0			0
$73$	−0.591052	−	3.35202i	−0.0691774	−	0.392325i	−0.999662	−	0.0259938i	$-0.991725\pi$
$73$	−0.591052	−	3.35202i	−0.0691774	−	0.392325i	0.930485	−	0.366331i	$-0.119386\pi$
$74$		0			0
$75$	1.41147			0.162983
$76$		0			0
$77$	1.04189			0.118734
$78$		0			0
$79$	−0.442219	−	2.50795i	−0.0497535	−	0.282166i	0.949773	−	0.312940i	$-0.101314\pi$
$79$	−0.442219	−	2.50795i	−0.0497535	−	0.282166i	−0.999526	+	0.0307739i	$0.990203\pi$
$80$		0			0
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$		0			0
$83$	−1.39053	−	0.802823i	−0.152630	−	0.0881212i	0.421740	−	0.906717i	$-0.361420\pi$
$83$	−1.39053	−	0.802823i	−0.152630	−	0.0881212i	−0.574370	+	0.818596i	$0.694753\pi$
$84$		0			0
$85$	14.1420	−	5.14728i	1.53392	−	0.558301i
$86$		0			0
$87$	−1.13816	+	0.657115i	−0.122023	+	0.0704501i
$88$		0			0
$89$	−6.14930	−	1.08429i	−0.651825	−	0.114934i	−0.162049	−	0.986783i	$-0.551810\pi$
$89$	−6.14930	−	1.08429i	−0.651825	−	0.114934i	−0.489776	+	0.871848i	$0.662921\pi$
$90$		0			0
$91$	−0.124485	−	0.104455i	−0.0130496	−	0.0109499i
$92$		0			0
$93$	6.29813	+	2.29233i	0.653086	+	0.237704i
$94$		0			0
$95$	7.75877	+	7.84981i	0.796033	+	0.805373i
$96$		0			0
$97$	0.368241	−	1.01173i	0.0373892	−	0.102726i	−0.919593	−	0.392872i	$-0.871482\pi$
$97$	0.368241	−	1.01173i	0.0373892	−	0.102726i	0.956982	+	0.290146i	$0.0937038\pi$
$98$		0			0
$99$	1.50000	−	1.78763i	0.150756	−	0.179664i
$100$		0			0
$101$	−2.84090	+	16.1115i	−0.282680	+	1.60316i	0.430776	+	0.902459i	$0.358240\pi$
$101$	−2.84090	+	16.1115i	−0.282680	+	1.60316i	−0.713456	+	0.700700i	$0.752871\pi$
$102$		0			0
$103$	−0.794263	−	1.37570i	−0.0782611	−	0.135552i	0.824239	−	0.566243i	$-0.191603\pi$
$103$	−0.794263	−	1.37570i	−0.0782611	−	0.135552i	−0.902500	+	0.430690i	$0.858270\pi$
$104$		0			0
$105$	0.386659	+	1.06234i	0.0377341	+	0.103674i
$106$		0			0
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	−0.973814	−	0.227345i	$-0.926996\pi$
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	0.683793	+	0.729676i	$0.260329\pi$
$108$		0			0
$109$	−9.56418	−	11.3981i	−0.916082	−	1.09174i	−0.995487	−	0.0949016i	$-0.969746\pi$
$109$	−9.56418	−	11.3981i	−0.916082	−	1.09174i	0.0794046	−	0.996842i	$-0.474698\pi$
$110$		0			0
$111$	−7.41534	+	1.30753i	−0.703833	+	0.124105i
$112$		0			0
$113$			8.51860i			0.801363i	0.916217	+	0.400681i	$0.131227\pi$
$113$			8.51860i			0.801363i	−0.916217	+	0.400681i	$0.868773\pi$
$114$		0			0
$115$			8.45134i			0.788092i
$116$		0			0
$117$	−0.358441	+	0.0632028i	−0.0331379	+	0.00584310i
$118$		0			0
$119$	1.70574	+	2.03282i	0.156365	+	0.186348i
$120$		0			0
$121$	−2.77719	+	4.81023i	−0.252472	+	0.437294i
$122$		0			0
$123$	−3.92262	−	10.7773i	−0.353691	−	0.971757i
$124$		0			0
$125$	−4.54323	−	7.86911i	−0.406359	−	0.703835i
$126$		0			0
$127$	−2.28359	+	12.9509i	−0.202635	+	1.14920i	0.698482	+	0.715628i	$0.253859\pi$
$127$	−2.28359	+	12.9509i	−0.202635	+	1.14920i	−0.901117	+	0.433575i	$0.857252\pi$
$128$		0			0
$129$	4.52481	−	5.39246i	0.398388	−	0.474780i
$130$		0			0
$131$	−1.52481	+	4.18939i	−0.133224	+	0.366029i	−0.988310	−	0.152456i	$-0.951282\pi$
$131$	−1.52481	+	4.18939i	−0.133224	+	0.366029i	0.855087	+	0.518485i	$0.173504\pi$
$132$		0			0
$133$	−0.832748	+	1.75898i	−0.0722084	+	0.152523i
$134$		0			0
$135$	2.37939	+	0.866025i	0.204785	+	0.0745356i
$136$		0			0
$137$	0.701867	+	0.588936i	0.0599645	+	0.0503162i	0.672277	−	0.740299i	$-0.265316\pi$
$137$	0.701867	+	0.588936i	0.0599645	+	0.0503162i	−0.612313	+	0.790616i	$0.709761\pi$
$138$		0			0
$139$	12.0778	+	2.12965i	1.02443	+	0.180635i	0.660527	−	0.750802i	$-0.270333\pi$
$139$	12.0778	+	2.12965i	1.02443	+	0.180635i	0.363903	+	0.931437i	$0.381444\pi$
$140$		0			0
$141$	6.76011	−	3.90295i	0.569304	−	0.328688i
$142$		0			0
$143$	−0.798133	+	0.290497i	−0.0667433	+	0.0242926i
$144$		0			0
$145$	−2.88191	−	1.66387i	−0.239330	−	0.138177i
$146$		0			0
$147$	5.20961	−	4.37138i	0.429681	−	0.360545i
$148$		0			0
$149$	0.187319	+	1.06234i	0.0153457	+	0.0870301i	0.991519	−	0.129964i	$-0.0414860\pi$
$149$	0.187319	+	1.06234i	0.0153457	+	0.0870301i	−0.976173	+	0.216994i	$0.930375\pi$
$150$		0			0
$151$	11.0300			0.897611			0.448806	−	0.893629i	$-0.351850\pi$
$151$	11.0300			0.897611			0.448806	+	0.893629i	$0.351850\pi$
$152$		0			0
$153$	5.94356			0.480509
$154$		0			0
$155$	2.94697	+	16.7131i	0.236706	+	1.34243i
$156$		0			0
$157$	4.06805	−	3.41350i	0.324666	−	0.272427i	−0.465857	−	0.884860i	$-0.654254\pi$
$157$	4.06805	−	3.41350i	0.324666	−	0.272427i	0.790522	+	0.612433i	$0.209809\pi$
$158$		0			0
$159$	−1.52481	−	0.880352i	−0.120926	−	0.0698165i
$160$		0			0
$161$	−1.40033	+	0.509678i	−0.110361	+	0.0401683i
$162$		0			0
$163$	−11.5201	+	6.65111i	−0.902321	+	0.520955i	−0.877953	−	0.478748i	$-0.841091\pi$
$163$	−11.5201	+	6.65111i	−0.902321	+	0.520955i	−0.0243687	+	0.999703i	$0.507758\pi$
$164$		0			0
$165$	5.81908	+	1.02606i	0.453015	+	0.0798787i
$166$		0			0
$167$	3.87939	+	3.25519i	0.300196	+	0.251894i	0.780426	−	0.625248i	$-0.215002\pi$
$167$	3.87939	+	3.25519i	0.300196	+	0.251894i	−0.480230	+	0.877143i	$0.659447\pi$
$168$		0			0
$169$	−12.0915	−	4.40095i	−0.930117	−	0.338535i
$170$		0			0
$171$	1.81908	+	3.96118i	0.139108	+	0.302919i
$172$		0			0
$173$	4.58765	−	12.6045i	0.348792	−	0.958299i	−0.633959	−	0.773367i	$-0.718571\pi$
$173$	4.58765	−	12.6045i	0.348792	−	0.958299i	0.982751	−	0.184933i	$-0.0592067\pi$
$174$		0			0
$175$	−0.405078	+	0.482753i	−0.0306210	+	0.0364927i
$176$		0			0
$177$	−1.05169	+	5.96443i	−0.0790498	+	0.448314i
$178$		0			0
$179$	5.92855	+	10.2685i	0.443121	+	0.767507i	0.997919	−	0.0644774i	$-0.0205380\pi$
$179$	5.92855	+	10.2685i	0.443121	+	0.767507i	−0.554799	+	0.831985i	$0.687205\pi$
$180$		0			0
$181$	6.74170	+	18.5227i	0.501106	+	1.37678i	0.890196	+	0.455578i	$0.150568\pi$
$181$	6.74170	+	18.5227i	0.501106	+	1.37678i	−0.389089	+	0.921200i	$0.627210\pi$
$182$		0			0
$183$	−3.39053	+	5.87257i	−0.250635	+	0.434113i
$184$		0			0
$185$	−12.2554	−	14.6054i	−0.901032	−	1.07381i
$186$		0			0
$187$	13.6591	−	2.40847i	0.998852	−	0.176125i
$188$		0			0
$189$			0.446476i			0.0324763i
$190$		0			0
$191$		−	9.45545i		−	0.684173i	−0.939669	−	0.342086i	$-0.888866\pi$
$191$		−	9.45545i		−	0.684173i	0.939669	−	0.342086i	$-0.111134\pi$
$192$		0			0
$193$	4.93969	−	0.871001i	0.355567	−	0.0626960i	0.00698825	−	0.999976i	$-0.497776\pi$
$193$	4.93969	−	0.871001i	0.355567	−	0.0626960i	0.348579	+	0.937280i	$0.386664\pi$
$194$		0			0
$195$	−0.592396	−	0.705990i	−0.0424224	−	0.0505570i
$196$		0			0
$197$	−8.26651	+	14.3180i	−0.588965	+	1.02012i	0.405404	+	0.914138i	$0.367131\pi$
$197$	−8.26651	+	14.3180i	−0.588965	+	1.02012i	−0.994368	+	0.105979i	$0.966202\pi$
$198$		0			0
$199$	−2.35638	−	6.47410i	−0.167039	−	0.458937i	0.827725	−	0.561134i	$-0.189635\pi$
$199$	−2.35638	−	6.47410i	−0.167039	−	0.458937i	−0.994764	+	0.102197i	$0.967413\pi$
$200$		0			0
$201$	−4.63816	−	8.03352i	−0.327150	−	0.566641i
$202$		0			0
$203$	0.101892	−	0.577857i	0.00715140	−	0.0405576i
$204$		0			0
$205$	18.6668	−	22.2463i	1.30375	−	1.55375i
$206$		0			0
$207$	−1.14156	+	3.13641i	−0.0793439	+	0.217995i
$208$		0			0
$209$	5.78564	+	8.36619i	0.400201	+	0.578701i
$210$		0			0
$211$	−20.7665	−	7.55839i	−1.42963	−	0.520341i	−0.492801	−	0.870142i	$-0.664027\pi$
$211$	−20.7665	−	7.55839i	−1.42963	−	0.520341i	−0.936824	+	0.349801i	$0.886249\pi$
$212$		0			0
$213$	−4.11334	−	3.45150i	−0.281841	−	0.236493i
$214$		0			0
$215$	17.5535	+	3.09516i	1.19714	+	0.211088i
$216$		0			0
$217$	−2.59152	+	1.49621i	−0.175924	+	0.101570i
$218$		0			0
$219$	3.19846	−	1.16415i	0.216132	−	0.0786657i
$220$		0			0
$221$	−1.87346	−	1.08164i	−0.126022	−	0.0727590i
$222$		0			0
$223$	−17.5797	+	14.7511i	−1.17722	+	0.987806i	−0.177228	+	0.984170i	$0.556713\pi$
$223$	−17.5797	+	14.7511i	−1.17722	+	0.987806i	−0.999993	+	0.00363588i	$0.998843\pi$
$224$		0			0
$225$	0.245100	+	1.39003i	0.0163400	+	0.0926687i
$226$		0			0
$227$	13.4338			0.891630			0.445815	−	0.895125i	$-0.352914\pi$
$227$	13.4338			0.891630			0.445815	+	0.895125i	$0.352914\pi$
$228$		0			0
$229$	21.5526			1.42424			0.712119	−	0.702059i	$-0.247736\pi$
$229$	21.5526			1.42424			0.712119	+	0.702059i	$0.247736\pi$
$230$		0			0
$231$	0.180922	+	1.02606i	0.0119038	+	0.0675098i
$232$		0			0
$233$	−14.5719	+	12.2273i	−0.954638	+	0.801036i	−0.980073	−	0.198640i	$-0.936348\pi$
$233$	−14.5719	+	12.2273i	−0.954638	+	0.801036i	0.0254344	+	0.999676i	$0.491903\pi$
$234$		0			0
$235$	17.1172	+	9.88263i	1.11660	+	0.644671i
$236$		0			0
$237$	2.39306	−	0.871001i	0.155446	−	0.0565776i
$238$		0			0
$239$	−14.3229	+	8.26936i	−0.926475	+	0.534900i	−0.885695	−	0.464268i	$-0.846318\pi$
$239$	−14.3229	+	8.26936i	−0.926475	+	0.534900i	−0.0407797	+	0.999168i	$0.512984\pi$
$240$		0			0
$241$	16.1780	+	2.85262i	1.04212	+	0.183753i	0.668409	−	0.743794i	$-0.266976\pi$
$241$	16.1780	+	2.85262i	1.04212	+	0.183753i	0.373707	+	0.927547i	$0.378087\pi$
$242$		0			0
$243$	0.766044	+	0.642788i	0.0491418	+	0.0412348i
$244$		0			0
$245$	16.1814	+	5.88954i	1.03379	+	0.376269i
$246$		0			0
$247$	0.147489	−	1.57964i	0.00938451	−	0.100510i
$248$		0			0
$249$	0.549163	−	1.50881i	0.0348018	−	0.0956171i
$250$		0			0
$251$	−14.0522	+	16.7467i	−0.886964	+	1.05704i	0.111035	+	0.993816i	$0.464583\pi$
$251$	−14.0522	+	16.7467i	−0.886964	+	1.05704i	−0.997999	+	0.0632263i	$0.979861\pi$
$252$		0			0
$253$	−1.35251	+	7.67047i	−0.0850316	+	0.482238i
$254$		0			0
$255$	7.52481	+	13.0334i	0.471222	+	0.816181i
$256$		0			0
$257$	−0.637222	−	1.75075i	−0.0397488	−	0.109209i	0.918230	−	0.396047i	$-0.129618\pi$
$257$	−0.637222	−	1.75075i	−0.0397488	−	0.109209i	−0.957979	+	0.286838i	$0.907396\pi$
$258$		0			0
$259$	1.68092	−	2.91144i	0.104447	−	0.180908i
$260$		0			0
$261$	−0.844770	−	1.00676i	−0.0522900	−	0.0623167i
$262$		0			0
$263$	−11.4757	+	2.02347i	−0.707619	+	0.124772i	−0.515864	−	0.856670i	$-0.672529\pi$
$263$	−11.4757	+	2.02347i	−0.707619	+	0.124772i	−0.191755	+	0.981443i	$0.561418\pi$
$264$		0			0
$265$		−	4.45826i		−	0.273869i
$266$		0			0
$267$		−	6.24416i		−	0.382137i
$268$		0			0
$269$	−5.61856	+	0.990703i	−0.342569	+	0.0604042i	−0.342286	−	0.939596i	$-0.611201\pi$
$269$	−5.61856	+	0.990703i	−0.342569	+	0.0604042i	−0.000283157		1.00000i	$0.500090\pi$
$270$		0			0
$271$	16.7306	+	19.9387i	1.01631	+	1.21119i	0.977280	+	0.211951i	$0.0679819\pi$
$271$	16.7306	+	19.9387i	1.01631	+	1.21119i	0.0390284	+	0.999238i	$0.487574\pi$
$272$		0			0
$273$	0.0812519	−	0.140732i	0.00491759	−	0.00851751i
$274$		0			0
$275$	1.12654	+	3.09516i	0.0679332	+	0.186645i
$276$		0			0
$277$	1.28833	+	2.23146i	0.0774084	+	0.134075i	0.902131	−	0.431462i	$-0.142002\pi$
$277$	1.28833	+	2.23146i	0.0774084	+	0.134075i	−0.824723	+	0.565537i	$0.808669\pi$
$278$		0			0
$279$	−1.16385	+	6.60051i	−0.0696778	+	0.395162i
$280$		0			0
$281$	21.4111	−	25.5167i	1.27728	−	1.52220i	0.551740	−	0.834016i	$-0.313964\pi$
$281$	21.4111	−	25.5167i	1.27728	−	1.52220i	0.725537	−	0.688183i	$-0.241592\pi$
$282$		0			0
$283$	6.91581	−	19.0010i	0.411102	−	1.12949i	−0.545503	−	0.838109i	$-0.683661\pi$
$283$	6.91581	−	19.0010i	0.411102	−	1.12949i	0.956606	−	0.291386i	$-0.0941163\pi$
$284$		0			0
$285$	−6.38326	+	9.00400i	−0.378111	+	0.533351i
$286$		0			0
$287$	4.81180	+	1.75135i	0.284032	+	0.103379i
$288$		0			0
$289$	14.0385	+	11.7797i	0.825793	+	0.692923i
$290$		0			0
$291$	1.06031	+	0.186961i	0.0621563	+	0.0109598i
$292$		0			0
$293$	11.6964	−	6.75292i	0.683311	−	0.394510i	−0.117790	−	0.993038i	$-0.537581\pi$
$293$	11.6964	−	6.75292i	0.683311	−	0.394510i	0.801101	+	0.598529i	$0.204248\pi$
$294$		0			0
$295$	−14.4106	+	5.24503i	−0.839017	+	0.305377i
$296$		0			0
$297$	2.02094	+	1.16679i	0.117267	+	0.0677042i
$298$		0			0
$299$	0.930608	−	0.780873i	0.0538184	−	0.0451590i
$300$		0			0
$301$	0.545759	+	3.09516i	0.0314571	+	0.178402i
$302$		0			0
$303$	−16.3601			−0.939863
$304$		0			0
$305$	−17.1702			−0.983165
$306$		0			0
$307$	−1.54576	−	8.76644i	−0.0882212	−	0.500327i	−0.996615	−	0.0822113i	$-0.973802\pi$
$307$	−1.54576	−	8.76644i	−0.0882212	−	0.500327i	0.908394	−	0.418116i	$-0.137309\pi$
$308$		0			0
$309$	1.21688	−	1.02108i	0.0692260	−	0.0580875i
$310$		0			0
$311$	1.62108	+	0.935932i	0.0919231	+	0.0530718i	0.545257	−	0.838269i	$-0.316432\pi$
$311$	1.62108	+	0.935932i	0.0919231	+	0.0530718i	−0.453334	+	0.891341i	$0.649765\pi$
$312$		0			0
$313$	14.0881	−	5.12765i	0.796307	−	0.289832i	0.0883520	−	0.996089i	$-0.471840\pi$
$313$	14.0881	−	5.12765i	0.796307	−	0.289832i	0.707955	+	0.706257i	$0.249618\pi$
$314$		0			0
$315$	−0.979055	+	0.565258i	−0.0551635	+	0.0318487i
$316$		0			0
$317$	8.38460	+	1.47843i	0.470926	+	0.0830370i	0.404075	−	0.914726i	$-0.367594\pi$
$317$	8.38460	+	1.47843i	0.470926	+	0.0830370i	0.0668513	+	0.997763i	$0.478705\pi$
$318$		0			0
$319$	−2.34936	−	1.97134i	−0.131539	−	0.110374i
$320$		0			0
$321$	−5.63816	−	2.05212i	−0.314691	−	0.114538i
$322$		0			0
$323$	−6.85117	+	24.9851i	−0.381209	+	1.39021i
$324$		0			0
$325$	0.175708	−	0.482753i	0.00974650	−	0.0267783i
$326$		0			0
$327$	9.56418	−	11.3981i	0.528900	−	0.630319i
$328$		0			0
$329$	−0.605189	+	3.43220i	−0.0333652	+	0.189223i
$330$		0			0
$331$	−14.1630	−	24.5310i	−0.778467	−	1.34834i	−0.932825	−	0.360330i	$-0.882664\pi$
$331$	−14.1630	−	24.5310i	−0.778467	−	1.34834i	0.154358	−	0.988015i	$-0.450669\pi$
$332$		0			0
$333$	−2.57532	−	7.07564i	−0.141127	−	0.387743i
$334$		0			0
$335$	11.7442	−	20.3416i	0.641655	−	1.11138i
$336$		0			0
$337$	−8.19506	−	9.76649i	−0.446413	−	0.532015i	0.495169	−	0.868796i	$-0.335106\pi$
$337$	−8.19506	−	9.76649i	−0.446413	−	0.532015i	−0.941583	+	0.336782i	$0.890662\pi$
$338$		0			0
$339$	−8.38919	+	1.47924i	−0.455638	+	0.0803413i
$340$		0			0
$341$			15.6405i			0.846979i
$342$		0			0
$343$			6.16166i			0.332698i
$344$		0			0
$345$	−8.32295	+	1.46756i	−0.448092	+	0.0790108i
$346$		0			0
$347$	−18.1147	−	21.5882i	−0.972447	−	1.15892i	−0.987274	−	0.159027i	$-0.949164\pi$
$347$	−18.1147	−	21.5882i	−0.972447	−	1.15892i	0.0148269	−	0.999890i	$-0.495280\pi$
$348$		0			0
$349$	−12.9067	+	22.3551i	−0.690881	+	1.19664i	0.280668	+	0.959805i	$0.409444\pi$
$349$	−12.9067	+	22.3551i	−0.690881	+	1.19664i	−0.971550	+	0.236837i	$0.923889\pi$
$350$		0			0
$351$	−0.124485	−	0.342020i	−0.00664453	−	0.0182557i
$352$		0			0
$353$	−10.8464	−	18.7865i	−0.577297	−	0.999907i	−0.995788	−	0.0916863i	$-0.970774\pi$
$353$	−10.8464	−	18.7865i	−0.577297	−	0.999907i	0.418491	−	0.908221i	$-0.362559\pi$
$354$		0			0
$355$	2.36097	−	13.3897i	0.125307	−	0.710652i
$356$		0			0
$357$	−1.70574	+	2.03282i	−0.0902772	+	0.107588i
$358$		0			0
$359$	7.33527	−	20.1535i	0.387141	−	1.06366i	−0.581141	−	0.813803i	$-0.697394\pi$
$359$	7.33527	−	20.1535i	0.387141	−	1.06366i	0.968282	−	0.249859i	$-0.0803841\pi$
$360$		0			0
$361$	−18.7486	+	3.08083i	−0.986766	+	0.162149i
$362$		0			0
$363$	−5.21941	−	1.89971i	−0.273948	−	0.0997089i
$364$		0			0
$365$	6.60220	+	5.53990i	0.345575	+	0.289972i
$366$		0			0
$367$	13.4500	+	2.37159i	0.702082	+	0.123796i	0.513283	−	0.858220i	$-0.328429\pi$
$367$	13.4500	+	2.37159i	0.702082	+	0.123796i	0.188800	+	0.982016i	$0.439540\pi$
$368$		0			0
$369$	9.93242	−	5.73448i	0.517061	−	0.298525i
$370$		0			0
$371$	0.738703	−	0.268866i	0.0383516	−	0.0139588i
$372$		0			0
$373$	−7.90848	−	4.56596i	−0.409486	−	0.236417i	0.281083	−	0.959683i	$-0.409306\pi$
$373$	−7.90848	−	4.56596i	−0.409486	−	0.236417i	−0.690569	+	0.723267i	$0.742640\pi$
$374$		0			0
$375$	6.96064	−	5.84067i	0.359446	−	0.301611i
$376$		0			0
$377$	0.0830629	+	0.471073i	0.00427796	+	0.0242615i
$378$		0			0
$379$	35.9154			1.84485			0.922425	−	0.386176i	$-0.126204\pi$
$379$	35.9154			1.84485			0.922425	+	0.386176i	$0.126204\pi$
$380$		0			0
$381$	−13.1506			−0.673728
$382$		0			0
$383$	−1.95512	−	11.0880i	−0.0999019	−	0.566572i	−0.993135	−	0.116977i	$-0.962680\pi$
$383$	−1.95512	−	11.0880i	−0.0999019	−	0.566572i	0.893233	−	0.449595i	$-0.148432\pi$
$384$		0			0
$385$	−2.02094	+	1.69577i	−0.102997	+	0.0864246i
$386$		0			0
$387$	6.09627	+	3.51968i	0.309891	+	0.178915i
$388$		0			0
$389$	18.3919	−	6.69409i	0.932505	−	0.339404i	0.169303	−	0.985564i	$-0.445848\pi$
$389$	18.3919	−	6.69409i	0.932505	−	0.339404i	0.763202	+	0.646160i	$0.223626\pi$
$390$		0			0
$391$	−17.1800	+	9.91890i	−0.868832	+	0.501621i
$392$		0			0
$393$	−4.39053	−	0.774169i	−0.221473	−	0.0390517i
$394$		0			0
$395$	4.93969	+	4.14489i	0.248543	+	0.208552i
$396$		0			0
$397$	−8.54963	−	3.11181i	−0.429094	−	0.156177i	0.118440	−	0.992961i	$-0.462211\pi$
$397$	−8.54963	−	3.11181i	−0.429094	−	0.156177i	−0.547533	+	0.836784i	$0.684433\pi$
$398$		0			0
$399$	−1.87686	−	0.514654i	−0.0939605	−	0.0257649i
$400$		0			0
$401$	0.817734	−	2.24670i	0.0408357	−	0.112195i	−0.917599	−	0.397508i	$-0.869875\pi$
$401$	0.817734	−	2.24670i	0.0408357	−	0.112195i	0.958435	+	0.285313i	$0.0920974\pi$
$402$		0			0
$403$	1.56805	−	1.86873i	0.0781100	−	0.0930879i
$404$		0			0
$405$	−0.439693	+	2.49362i	−0.0218485	+	0.123909i
$406$		0			0
$407$	−8.78564	−	15.2172i	−0.435488	−	0.754288i
$408$		0			0
$409$	−9.90420	−	27.2116i	−0.489731	−	1.34553i	−0.900924	−	0.433977i	$-0.857110\pi$
$409$	−9.90420	−	27.2116i	−0.489731	−	1.34553i	0.411193	−	0.911548i	$-0.365112\pi$
$410$		0			0
$411$	−0.458111	+	0.793471i	−0.0225969	+	0.0391391i
$412$		0			0
$413$	−1.73813	−	2.07142i	−0.0855278	−	0.101928i
$414$		0			0
$415$	4.00387	−	0.705990i	0.196542	−	0.0346557i
$416$		0			0
$417$			12.2642i			0.600579i
$418$		0			0
$419$		−	7.56185i		−	0.369420i	−0.982793	−	0.184710i	$-0.940865\pi$
$419$		−	7.56185i		−	0.369420i	0.982793	−	0.184710i	$-0.0591347\pi$
$420$		0			0
$421$	−36.6969	+	6.47065i	−1.78850	+	0.315360i	−0.966985	−	0.254833i	$-0.917980\pi$
$421$	−36.6969	+	6.47065i	−1.78850	+	0.315360i	−0.821511	+	0.570193i	$0.806868\pi$
$422$		0			0
$423$	5.01754	+	5.97967i	0.243961	+	0.290742i
$424$		0			0
$425$	−4.19459	+	7.26525i	−0.203468	+	0.352416i
$426$		0			0
$427$	−1.03549	−	2.84499i	−0.0501110	−	0.137679i
$428$		0			0
$429$	−0.424678	−	0.735564i	−0.0205036	−	0.0355133i
$430$		0			0
$431$	6.28581	−	35.6486i	0.302777	−	1.71713i	−0.331013	−	0.943626i	$-0.607390\pi$
$431$	6.28581	−	35.6486i	0.302777	−	1.71713i	0.633790	−	0.773506i	$-0.281499\pi$
$432$		0			0
$433$	−24.2335	+	28.8804i	−1.16459	+	1.38790i	−0.257865	+	0.966181i	$0.583019\pi$
$433$	−24.2335	+	28.8804i	−1.16459	+	1.38790i	−0.906725	+	0.421723i	$0.861425\pi$
$434$		0			0
$435$	1.13816	−	3.12706i	0.0545704	−	0.149931i
$436$		0			0
$437$	−11.8687	−	8.41415i	−0.567757	−	0.402503i
$438$		0			0
$439$	1.26130	+	0.459074i	0.0601984	+	0.0219104i	0.371944	−	0.928255i	$-0.378691\pi$
$439$	1.26130	+	0.459074i	0.0601984	+	0.0219104i	−0.311745	+	0.950166i	$0.600914\pi$
$440$		0			0
$441$	5.20961	+	4.37138i	0.248077	+	0.208161i
$442$		0			0
$443$	−31.7802	−	5.60370i	−1.50992	−	0.266240i	−0.643459	−	0.765481i	$-0.722501\pi$
$443$	−31.7802	−	5.60370i	−1.50992	−	0.266240i	−0.866463	+	0.499241i	$0.833612\pi$
$444$		0			0
$445$	13.6925	−	7.90539i	0.649088	−	0.374751i
$446$		0			0
$447$	−1.01367	+	0.368946i	−0.0479450	+	0.0174505i
$448$		0			0
$449$	−3.34302	−	1.93009i	−0.157767	−	0.0910866i	0.419038	−	0.907969i	$-0.362367\pi$
$449$	−3.34302	−	1.93009i	−0.157767	−	0.0910866i	−0.576805	+	0.816882i	$0.695701\pi$
$450$		0			0
$451$	20.5023	−	17.2035i	0.965415	−	0.810079i
$452$		0			0
$453$	1.91534	+	10.8625i	0.0899907	+	0.510363i
$454$		0			0
$455$	0.411474			0.0192902
$456$		0			0
$457$	−5.79055			−0.270871			−0.135435	−	0.990786i	$-0.543243\pi$
$457$	−5.79055			−0.270871			−0.135435	+	0.990786i	$0.543243\pi$
$458$		0			0
$459$	1.03209	+	5.85327i	0.0481738	+	0.273207i
$460$		0			0
$461$	−17.5517	+	14.7276i	−0.817464	+	0.685933i	−0.952377	−	0.304924i	$-0.901369\pi$
$461$	−17.5517	+	14.7276i	−0.817464	+	0.685933i	0.134913	+	0.990857i	$0.456924\pi$
$462$		0			0
$463$	−30.3840	−	17.5422i	−1.41207	−	0.815256i	−0.416483	−	0.909144i	$-0.636737\pi$
$463$	−30.3840	−	17.5422i	−1.41207	−	0.815256i	−0.995583	+	0.0938873i	$0.970071\pi$
$464$		0			0
$465$	−15.9474	+	5.80439i	−0.739545	+	0.269172i
$466$		0			0
$467$	−11.6352	+	6.71756i	−0.538411	+	0.310852i	−0.744435	−	0.667695i	$-0.767281\pi$
$467$	−11.6352	+	6.71756i	−0.538411	+	0.310852i	0.206024	+	0.978547i	$0.433948\pi$
$468$		0			0
$469$	4.07873	+	0.719189i	0.188338	+	0.0332091i
$470$		0			0
$471$	4.06805	+	3.41350i	0.187446	+	0.157286i
$472$		0			0
$473$	15.4363	+	5.61835i	0.709761	+	0.258332i
$474$		0			0
$475$	−6.12583	−	0.571962i	−0.281072	−	0.0262434i
$476$		0			0
$477$	0.602196	−	1.65452i	0.0275727	−	0.0757553i
$478$		0			0
$479$	26.1330	−	31.1441i	1.19405	−	1.42301i	0.313149	−	0.949704i	$-0.398616\pi$
$479$	26.1330	−	31.1441i	1.19405	−	1.42301i	0.880898	−	0.473306i	$-0.156939\pi$
$480$		0			0
$481$	−0.475900	+	2.69896i	−0.0216992	+	0.123062i
$482$		0			0
$483$	−0.745100	−	1.29055i	−0.0339032	−	0.0587221i
$484$		0			0
$485$	0.932419	+	2.56180i	0.0423390	+	0.116325i
$486$		0			0
$487$	−16.8935	+	29.2604i	−0.765519	+	1.32592i	0.174453	+	0.984665i	$0.444184\pi$
$487$	−16.8935	+	29.2604i	−0.765519	+	1.32592i	−0.939972	+	0.341252i	$0.889149\pi$
$488$		0			0
$489$	−8.55051	−	10.1901i	−0.386667	−	0.460812i
$490$		0			0
$491$	1.48839	−	0.262443i	0.0671700	−	0.0118439i	−0.139962	−	0.990157i	$-0.544698\pi$
$491$	1.48839	−	0.262443i	0.0671700	−	0.0118439i	0.207132	+	0.978313i	$0.433587\pi$
$492$		0			0
$493$		−	7.81120i		−	0.351799i
$494$		0			0
$495$			5.90885i			0.265583i
$496$		0			0
$497$	2.36097	−	0.416302i	0.105904	−	0.0186737i
$498$		0			0
$499$	11.2827	+	13.4462i	0.505083	+	0.601935i	0.956987	−	0.290132i	$-0.0936992\pi$
$499$	11.2827	+	13.4462i	0.505083	+	0.601935i	−0.451903	+	0.892067i	$0.649255\pi$
$500$		0			0
$501$	−2.53209	+	4.38571i	−0.113125	+	0.195939i
$502$		0			0
$503$	−8.82888	−	24.2571i	−0.393660	−	1.08157i	−0.965317	−	0.261080i	$-0.915921\pi$
$503$	−8.82888	−	24.2571i	−0.393660	−	1.08157i	0.571657	−	0.820493i	$-0.306301\pi$
$504$		0			0
$505$	−20.7126	−	35.8753i	−0.921699	−	1.59643i
$506$		0			0
$507$	2.23442	−	12.6720i	0.0992342	−	0.562785i
$508$		0			0
$509$	4.24985	−	5.06477i	0.188371	−	0.224492i	−0.663591	−	0.748096i	$-0.730968\pi$
$509$	4.24985	−	5.06477i	0.188371	−	0.224492i	0.851962	+	0.523604i	$0.175413\pi$
$510$		0			0
$511$	−0.519762	+	1.42804i	−0.0229929	+	0.0631726i
$512$		0			0
$513$	−3.58512	+	2.47929i	−0.158287	+	0.109463i
$514$		0			0
$515$	3.77972	+	1.37570i	0.166554	+	0.0606208i
$516$		0			0
$517$	13.9541	+	11.7089i	0.613700	+	0.514955i
$518$		0			0
$519$	13.2096	+	2.32921i	0.579837	+	0.102241i
$520$		0			0
$521$	34.8252	−	20.1064i	1.52572	−	0.880875i	0.526186	−	0.850369i	$-0.323621\pi$
$521$	34.8252	−	20.1064i	1.52572	−	0.880875i	0.999535	−	0.0305060i	$-0.00971187\pi$
$522$		0			0
$523$	−26.5292	+	9.65582i	−1.16004	+	0.422220i	−0.849111	−	0.528214i	$-0.822862\pi$
$523$	−26.5292	+	9.65582i	−1.16004	+	0.422220i	−0.310928	+	0.950434i	$0.600640\pi$
$524$		0			0
$525$	−0.545759	−	0.315094i	−0.0238189	−	0.0137518i
$526$		0			0
$527$	−30.5159	+	25.6059i	−1.32930	+	1.11541i
$528$		0			0
$529$	2.05943	+	11.6796i	0.0895404	+	0.507809i
$530$		0			0
$531$	−6.05644			−0.262827
$532$		0			0
$533$	−4.17436			−0.180812
$534$		0			0
$535$	−2.63816	−	14.9617i	−0.114057	−	0.646852i
$536$		0			0
$537$	−9.08306	+	7.62159i	−0.391963	+	0.328896i
$538$		0			0
$539$	13.7438	+	7.93496i	0.591985	+	0.341783i
$540$		0			0
$541$	−33.2374	+	12.0974i	−1.42899	+	0.520109i	−0.936641	−	0.350290i	$-0.886083\pi$
$541$	−33.2374	+	12.0974i	−1.42899	+	0.520109i	−0.492347	+	0.870399i	$0.663861\pi$
$542$		0			0
$543$	−17.0706	+	9.85570i	−0.732568	+	0.422949i
$544$		0			0
$545$	37.1031	+	6.54228i	1.58932	+	0.280241i
$546$		0			0
$547$	−15.7044	−	13.1776i	−0.671471	−	0.563431i	0.242029	−	0.970269i	$-0.422187\pi$
$547$	−15.7044	−	13.1776i	−0.671471	−	0.563431i	−0.913500	+	0.406838i	$0.866631\pi$
$548$		0			0
$549$	−6.37211	−	2.31926i	−0.271955	−	0.0989836i
$550$		0			0
$551$	5.20590	−	2.39068i	0.221779	−	0.101847i
$552$		0			0
$553$	−0.388881	+	1.06844i	−0.0165369	+	0.0454347i
$554$		0			0
$555$	12.2554	−	14.6054i	0.520211	−	0.619964i
$556$		0			0
$557$	6.71007	−	38.0547i	0.284315	−	1.61243i	−0.423407	−	0.905939i	$-0.639166\pi$
$557$	6.71007	−	38.0547i	0.284315	−	1.61243i	0.707722	−	0.706491i	$-0.249723\pi$
$558$		0			0
$559$	−1.28106	−	2.21886i	−0.0541830	−	0.0938478i
$560$		0			0
$561$	4.74376	+	13.0334i	0.200282	+	0.550269i
$562$		0			0
$563$	5.28833	−	9.15966i	0.222877	−	0.386034i	−0.732804	−	0.680440i	$-0.761789\pi$
$563$	5.28833	−	9.15966i	0.222877	−	0.386034i	0.955680	+	0.294406i	$0.0951219\pi$
$564$		0			0
$565$	−13.8648	−	16.5235i	−0.583298	−	0.695148i
$566$		0			0
$567$	−0.439693	+	0.0775297i	−0.0184654	+	0.00325594i
$568$		0			0
$569$			6.06920i			0.254434i	0.991875	+	0.127217i	$0.0406045\pi$
$569$			6.06920i			0.254434i	−0.991875	+	0.127217i	$0.959396\pi$
$570$		0			0
$571$			38.8698i			1.62665i	0.581809	+	0.813326i	$0.302345\pi$
$571$			38.8698i			1.62665i	−0.581809	+	0.813326i	$0.697655\pi$
$572$		0			0
$573$	9.31180	−	1.64192i	0.389006	−	0.0685923i
$574$		0			0
$575$	−3.02822	−	3.60889i	−0.126285	−	0.150501i
$576$		0			0
$577$	−22.2319	+	38.5068i	−0.925526	+	1.60306i	−0.134813	+	0.990871i	$0.543043\pi$
$577$	−22.2319	+	38.5068i	−0.925526	+	1.60306i	−0.790713	+	0.612187i	$0.790290\pi$
$578$		0			0
$579$	1.71554	+	4.71340i	0.0712953	+	0.195882i
$580$		0			0
$581$	0.358441	+	0.620838i	0.0148706	+	0.0257567i
$582$		0			0
$583$	0.713478	−	4.04633i	0.0295492	−	0.167582i
$584$		0			0
$585$	0.592396	−	0.705990i	0.0244926	−	0.0291891i
$586$		0			0
$587$	−9.10085	+	25.0044i	−0.375632	+	1.03204i	0.597515	+	0.801858i	$0.296155\pi$
$587$	−9.10085	+	25.0044i	−0.375632	+	1.03204i	−0.973147	+	0.230184i	$0.926067\pi$
$588$		0			0
$589$	−26.4051	−	12.5009i	−1.08800	−	0.515092i
$590$		0			0
$591$	−15.5360	−	5.65463i	−0.639064	−	0.232600i
$592$		0			0
$593$	36.3730	+	30.5206i	1.49366	+	1.25333i	0.889891	+	0.456173i	$0.150780\pi$
$593$	36.3730	+	30.5206i	1.49366	+	1.25333i	0.603771	+	0.797158i	$0.293664\pi$
$594$		0			0
$595$	−6.61721	−	1.16679i	−0.271279	−	0.0478338i
$596$		0			0
$597$	5.96657	−	3.44480i	0.244195	−	0.140986i
$598$		0			0
$599$	28.8050	−	10.4842i	1.17694	−	0.428371i	0.321820	−	0.946801i	$-0.395705\pi$
$599$	28.8050	−	10.4842i	1.17694	−	0.428371i	0.855120	+	0.518430i	$0.173483\pi$
$600$		0			0
$601$	14.9153	+	8.61138i	0.608410	+	0.351265i	0.772343	−	0.635206i	$-0.219085\pi$
$601$	14.9153	+	8.61138i	0.608410	+	0.351265i	−0.163933	+	0.986471i	$0.552418\pi$
$602$		0			0
$603$	7.10607	−	5.96270i	0.289381	−	0.242820i
$604$		0			0
$605$	−2.44222	−	13.8505i	−0.0992903	−	0.563103i
$606$		0			0
$607$	16.9659			0.688623			0.344311	−	0.938856i	$-0.388112\pi$
$607$	16.9659			0.688623			0.344311	+	0.938856i	$0.388112\pi$
$608$		0			0
$609$	0.586771			0.0237772
$610$		0			0
$611$	−0.493355	−	2.79796i	−0.0199590	−	0.113193i
$612$		0			0
$613$	−34.5069	+	28.9547i	−1.39372	+	1.16947i	−0.429911	+	0.902871i	$0.641455\pi$
$613$	−34.5069	+	28.9547i	−1.39372	+	1.16947i	−0.963808	+	0.266598i	$0.914100\pi$
$614$		0			0
$615$	25.1498	+	14.5202i	1.01414	+	0.585512i
$616$		0			0
$617$	−1.12314	+	0.408790i	−0.0452160	+	0.0164573i	−0.364529	−	0.931192i	$-0.618770\pi$
$617$	−1.12314	+	0.408790i	−0.0452160	+	0.0164573i	0.319313	+	0.947649i	$0.396548\pi$
$618$		0			0
$619$	23.5363	−	13.5887i	0.946002	−	0.546175i	0.0541655	−	0.998532i	$-0.482750\pi$
$619$	23.5363	−	13.5887i	0.946002	−	0.546175i	0.891837	+	0.452357i	$0.149417\pi$
$620$		0			0
$621$	−3.28699	−	0.579585i	−0.131902	−	0.0232579i
$622$		0			0
$623$	2.13563	+	1.79201i	0.0855622	+	0.0717952i
$624$		0			0
$625$	28.2520	+	10.2829i	1.13008	+	0.411315i
$626$		0			0
$627$	−7.23442	+	7.15052i	−0.288915	+	0.285564i
$628$		0			0
$629$	15.3066	−	42.0545i	0.610314	−	1.67682i
$630$		0			0
$631$	−10.1001	+	12.0369i	−0.402080	+	0.479180i	−0.928653	−	0.370950i	$-0.879032\pi$
$631$	−10.1001	+	12.0369i	−0.402080	+	0.479180i	0.526573	+	0.850130i	$0.323477\pi$
$632$		0			0
$633$	3.83750	−	21.7635i	0.152527	−	0.865022i
$634$		0			0
$635$	−16.6493	−	28.8374i	−0.660707	−	1.14438i
$636$		0			0
$637$	−0.846581	−	2.32596i	−0.0335428	−	0.0921580i
$638$		0			0
$639$	2.68479	−	4.65020i	0.106209	−	0.183959i
$640$		0			0
$641$	22.1802	+	26.4333i	0.876066	+	1.04405i	0.998668	+	0.0515983i	$0.0164316\pi$
$641$	22.1802	+	26.4333i	0.876066	+	1.04405i	−0.122602	+	0.992456i	$0.539124\pi$
$642$		0			0
$643$	7.89646	−	1.39236i	0.311406	−	0.0549093i	−0.0157611	−	0.999876i	$-0.505017\pi$
$643$	7.89646	−	1.39236i	0.311406	−	0.0549093i	0.327167	+	0.944967i	$0.393906\pi$
$644$		0			0
$645$			17.8243i			0.701831i
$646$		0			0
$647$		−	47.3299i		−	1.86073i	−0.366633	−	0.930366i	$-0.619490\pi$
$647$		−	47.3299i		−	1.86073i	0.366633	−	0.930366i	$-0.380510\pi$
$648$		0			0
$649$	−13.9185	+	2.45421i	−0.546349	+	0.0963361i
$650$		0			0
$651$	−1.92350	−	2.29233i	−0.0753877	−	0.0898436i
$652$		0			0
$653$	−6.95723	+	12.0503i	−0.272258	+	0.471564i	−0.969440	−	0.245330i	$-0.921104\pi$
$653$	−6.95723	+	12.0503i	−0.272258	+	0.471564i	0.697182	+	0.716894i	$0.254437\pi$
$654$		0			0
$655$	−3.86097	−	10.6079i	−0.150860	−	0.414486i
$656$		0			0
$657$	1.70187	+	2.94772i	0.0663961	+	0.115001i
$658$		0			0
$659$	6.23854	−	35.3805i	0.243019	−	1.37823i	−0.582029	−	0.813168i	$-0.697741\pi$
$659$	6.23854	−	35.3805i	0.243019	−	1.37823i	0.825049	−	0.565062i	$-0.191148\pi$
$660$		0			0
$661$	7.82682	−	9.32764i	0.304428	−	0.362803i	−0.592042	−	0.805907i	$-0.701678\pi$
$661$	7.82682	−	9.32764i	0.304428	−	0.362803i	0.896470	+	0.443104i	$0.146123\pi$
$662$		0			0
$663$	0.739885	−	2.03282i	0.0287348	−	0.0789481i
$664$		0			0
$665$	−1.24763	−	4.76725i	−0.0483809	−	0.184866i
$666$		0			0
$667$	4.12196	+	1.50027i	0.159603	+	0.0580907i
$668$		0			0
$669$	−17.5797	−	14.7511i	−0.679669	−	0.570310i
$670$		0			0
$671$	−15.5838	−	2.74784i	−0.601605	−	0.106079i
$672$		0			0
$673$	18.4029	−	10.6249i	0.709378	−	0.409560i	−0.101453	−	0.994840i	$-0.532349\pi$
$673$	18.4029	−	10.6249i	0.709378	−	0.409560i	0.810831	+	0.585281i	$0.199016\pi$
$674$		0			0
$675$	−1.32635	+	0.482753i	−0.0510513	+	0.0185812i
$676$		0			0
$677$	−9.71806	−	5.61073i	−0.373496	−	0.215638i	0.301489	−	0.953470i	$-0.402516\pi$
$677$	−9.71806	−	5.61073i	−0.373496	−	0.215638i	−0.674984	+	0.737832i	$0.735850\pi$
$678$		0			0
$679$	−0.368241	+	0.308991i	−0.0141318	+	0.0118580i
$680$		0			0
$681$	2.33275	+	13.2297i	0.0893911	+	0.506962i
$682$		0			0
$683$	−36.4867			−1.39612			−0.698062	−	0.716037i	$-0.745954\pi$
$683$	−36.4867			−1.39612			−0.698062	+	0.716037i	$0.745954\pi$
$684$		0			0
$685$	−2.31996			−0.0886409
$686$		0			0
$687$	3.74257	+	21.2252i	0.142788	+	0.809792i
$688$		0			0
$689$	−0.490915	+	0.411927i	−0.0187024	+	0.0156932i
$690$		0			0
$691$	9.74990	+	5.62911i	0.370904	+	0.214141i	0.673853	−	0.738865i	$-0.264638\pi$
$691$	9.74990	+	5.62911i	0.370904	+	0.214141i	−0.302949	+	0.953007i	$0.597971\pi$
$692$		0			0
$693$	−0.979055	+	0.356347i	−0.0371912	+	0.0135365i
$694$		0			0
$695$	−26.8935	+	15.5270i	−1.02013	+	0.588972i
$696$		0			0
$697$	67.1309	+	11.8370i	2.54277	+	0.448358i
$698$		0			0
$699$	−14.5719	−	12.2273i	−0.551161	−	0.462479i
$700$		0			0
$701$	0.0120217	+	0.00437554i	0.000454053	+	0.000165262i	0.342247	−	0.939610i	$-0.388812\pi$
$701$	0.0120217	+	0.00437554i	0.000454053	+	0.000165262i	−0.341793	+	0.939775i	$0.611034\pi$
$702$		0			0
$703$	32.7126	−	2.66982i	1.23378	−	0.100694i
$704$		0			0
$705$	−6.76011	+	18.5733i	−0.254601	+	0.699510i
$706$		0			0
$707$	4.69517	−	5.59548i	0.176580	−	0.210440i
$708$		0			0
$709$	5.64694	−	32.0254i	0.212075	−	1.20274i	−0.673835	−	0.738882i	$-0.735354\pi$
$709$	5.64694	−	32.0254i	0.212075	−	1.20274i	0.885910	−	0.463856i	$-0.153535\pi$
$710$		0			0
$711$	1.27332	+	2.20545i	0.0477532	+	0.0827109i
$712$		0			0
$713$	−7.65111	−	21.0213i	−0.286536	−	0.787252i
$714$		0			0
$715$	1.07532	−	1.86251i	0.0402148	−	0.0696540i
$716$		0			0
$717$	−10.6309	−	12.6694i	−0.397018	−	0.473147i
$718$		0			0
$719$	50.9876	−	8.99048i	1.90152	−	0.335288i	0.905491	−	0.424366i	$-0.139503\pi$
$719$	50.9876	−	8.99048i	1.90152	−	0.335288i	0.996025	+	0.0890776i	$0.0283919\pi$
$720$		0			0
$721$			0.709238i			0.0264134i
$722$		0			0
$723$			16.4276i			0.610947i
$724$		0			0
$725$	1.82682	−	0.322117i	0.0678463	−	0.0119631i
$726$		0			0
$727$	17.8025	+	21.2162i	0.660257	+	0.786864i	0.987423	−	0.158103i	$-0.0505379\pi$
$727$	17.8025	+	21.2162i	0.660257	+	0.786864i	−0.327165	+	0.944967i	$0.606093\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	14.3097	+	39.3157i	0.529265	+	1.45414i
$732$		0			0
$733$	−22.0608	−	38.2104i	−0.814833	−	1.41133i	−0.909448	−	0.415819i	$-0.863495\pi$
$733$	−22.0608	−	38.2104i	−0.814833	−	1.41133i	0.0946143	−	0.995514i	$-0.469838\pi$
$734$		0			0
$735$	−2.99020	+	16.9583i	−0.110295	+	0.625515i
$736$		0			0
$737$	13.9145	−	16.5826i	0.512546	−	0.610829i
$738$		0			0
$739$	−2.90436	+	7.97967i	−0.106839	+	0.293537i	−0.981579	−	0.191054i	$-0.938809\pi$
$739$	−2.90436	+	7.97967i	−0.106839	+	0.293537i	0.874741	+	0.484591i	$0.161032\pi$
$740$		0			0
$741$	1.58125	−	0.129053i	0.0580887	−	0.00474088i
$742$		0			0
$743$	1.31908	+	0.480105i	0.0483923	+	0.0176133i	0.366103	−	0.930574i	$-0.380692\pi$
$743$	1.31908	+	0.480105i	0.0483923	+	0.0176133i	−0.317711	+	0.948188i	$0.602914\pi$
$744$		0			0
$745$	−2.09240	−	1.75573i	−0.0766595	−	0.0643249i
$746$		0			0
$747$	1.58125	+	0.278817i	0.0578550	+	0.0102014i
$748$		0			0
$749$	2.31996	−	1.33943i	0.0847693	−	0.0489416i
$750$		0			0
$751$	9.12196	−	3.32012i	0.332865	−	0.121153i	−0.170180	−	0.985413i	$-0.554435\pi$
$751$	9.12196	−	3.32012i	0.332865	−	0.121153i	0.503045	+	0.864260i	$0.332213\pi$
$752$		0			0
$753$	−18.9324	−	10.9306i	−0.689936	−	0.398335i
$754$		0			0
$755$	−21.3949	+	17.9524i	−0.778639	+	0.653356i
$756$		0			0
$757$	6.14858	+	34.8704i	0.223474	+	1.26738i	0.865581	+	0.500769i	$0.166950\pi$
$757$	6.14858	+	34.8704i	0.223474	+	1.26738i	−0.642107	+	0.766615i	$0.721939\pi$
$758$		0			0
$759$	−7.78880			−0.282716
$760$		0			0
$761$	3.28817			0.119196			0.0595981	−	0.998222i	$-0.481018\pi$
$761$	3.28817			0.119196			0.0595981	+	0.998222i	$0.481018\pi$
$762$		0			0
$763$	1.15358	+	6.54228i	0.0417624	+	0.236847i
$764$		0			0
$765$	−11.5287	+	9.67372i	−0.416820	+	0.349754i
$766$		0			0
$767$	1.90903	+	1.10218i	0.0689312	+	0.0397975i
$768$		0			0
$769$	21.9443	−	7.98708i	0.791333	−	0.288022i	0.0854429	−	0.996343i	$-0.472769\pi$
$769$	21.9443	−	7.98708i	0.791333	−	0.288022i	0.705890	+	0.708321i	$0.250547\pi$
$770$		0			0
$771$	1.61350	−	0.931556i	0.0581089	−	0.0335492i
$772$		0			0
$773$	23.6550	+	4.17101i	0.850811	+	0.150021i	0.582017	−	0.813177i	$-0.302264\pi$
$773$	23.6550	+	4.17101i	0.850811	+	0.150021i	0.268794	+	0.963198i	$0.413375\pi$
$774$		0			0
$775$	−7.24691	−	6.08088i	−0.260317	−	0.218432i
$776$		0			0
$777$	3.15910	+	1.14982i	0.113332	+	0.0412495i
$778$		0			0
$779$	12.6570	+	48.3633i	0.453486	+	1.73279i
$780$		0			0
$781$	4.28564	−	11.7747i	0.153352	−	0.421332i
$782$		0			0
$783$	0.844770	−	1.00676i	0.0301896	−	0.0359786i
$784$		0			0
$785$	−2.33497	+	13.2423i	−0.0833387	+	0.472637i
$786$		0			0
$787$	−9.58765	−	16.6063i	−0.341763	−	0.591950i	0.642997	−	0.765868i	$-0.277691\pi$
$787$	−9.58765	−	16.6063i	−0.341763	−	0.591950i	−0.984760	+	0.173918i	$0.944357\pi$
$788$		0			0
$789$	−3.98545	−	10.9499i	−0.141886	−	0.389828i
$790$		0			0
$791$	1.90167	−	3.29380i	0.0676157	−	0.117114i
$792$		0			0
$793$	1.58647	+	1.89068i	0.0563371	+	0.0671399i
$794$		0			0
$795$	4.39053	−	0.774169i	0.155716	−	0.0274569i
$796$		0			0
$797$		−	7.63624i		−	0.270490i	−0.990812	−	0.135245i	$-0.956818\pi$
$797$		−	7.63624i		−	0.270490i	0.990812	−	0.135245i	$-0.0431821\pi$
$798$		0			0
$799$			46.3949i			1.64133i
$800$		0			0
$801$	6.14930	−	1.08429i	0.217275	−	0.0383114i
$802$		0			0
$803$	5.10560	+	6.08462i	0.180173	+	0.214721i
$804$		0			0
$805$	1.88666	−	3.26779i	0.0664960	−	0.115174i
$806$		0			0
$807$	−1.95130	−	5.36116i	−0.0686891	−	0.188722i
$808$		0			0
$809$	−4.65389	−	8.06077i	−0.163622	−	0.283401i	0.772543	−	0.634962i	$-0.218984\pi$
$809$	−4.65389	−	8.06077i	−0.163622	−	0.283401i	−0.936165	+	0.351561i	$0.885651\pi$
$810$		0			0
$811$	3.22962	−	18.3161i	0.113407	−	0.643164i	−0.874119	−	0.485711i	$-0.838561\pi$
$811$	3.22962	−	18.3161i	0.113407	−	0.643164i	0.987526	−	0.157453i	$-0.0503283\pi$
$812$		0			0
$813$	−16.7306	+	19.9387i	−0.586766	+	0.699281i
$814$		0			0
$815$	11.5201	−	31.6511i	0.403530	−	1.10869i
$816$		0			0
$817$	−21.8229	+	21.5699i	−0.763488	+	0.754634i
$818$		0			0
$819$	0.152704	+	0.0555796i	0.00533590	+	0.00194211i
$820$		0			0
$821$	−5.56212	−	4.66717i	−0.194119	−	0.162885i	0.540548	−	0.841313i	$-0.318217\pi$
$821$	−5.56212	−	4.66717i	−0.194119	−	0.162885i	−0.734667	+	0.678428i	$0.762662\pi$
$822$		0			0
$823$	−3.18732	−	0.562010i	−0.111103	−	0.0195904i	0.117820	−	0.993035i	$-0.462409\pi$
$823$	−3.18732	−	0.562010i	−0.111103	−	0.0195904i	−0.228923	+	0.973444i	$0.573520\pi$
$824$		0			0
$825$	−2.85251	+	1.64690i	−0.0993117	+	0.0573376i
$826$		0			0
$827$	−45.1207	+	16.4226i	−1.56900	+	0.571069i	−0.972776	−	0.231749i	$-0.925555\pi$
$827$	−45.1207	+	16.4226i	−1.56900	+	0.571069i	−0.596224	+	0.802818i	$0.703333\pi$
$828$		0			0
$829$	−10.1279	−	5.84737i	−0.351758	−	0.203088i	0.313701	−	0.949522i	$-0.398431\pi$
$829$	−10.1279	−	5.84737i	−0.351758	−	0.203088i	−0.665459	+	0.746434i	$0.731764\pi$
$830$		0			0
$831$	−1.97384	+	1.65625i	−0.0684718	+	0.0574546i
$832$		0			0
$833$	7.01889	+	39.8061i	0.243190	+	1.37920i
$834$		0			0
$835$	−12.8229			−0.443756
$836$		0			0
$837$	−6.70233			−0.231667
$838$		0			0
$839$	7.04307	+	39.9432i	0.243154	+	1.37899i	0.824741	+	0.565510i	$0.191321\pi$
$839$	7.04307	+	39.9432i	0.243154	+	1.37899i	−0.581588	+	0.813484i	$0.697568\pi$
$840$		0			0
$841$	20.8922	−	17.5306i	0.720420	−	0.604504i
$842$		0			0
$843$	28.8470	+	16.6549i	0.993545	+	0.573624i
$844$		0			0
$845$	30.6168	−	11.1436i	1.05325	−	0.383352i
$846$		0			0
$847$	2.14765	−	1.23995i	0.0737942	−	0.0426051i
$848$		0			0
$849$	19.9133	+	3.51125i	0.683422	+	0.120506i
$850$		0			0
$851$	19.2522	+	16.1545i	0.659957	+	0.553770i
$852$		0			0
$853$	43.9950	+	16.0129i	1.50636	+	0.548270i	0.957698	−	0.287774i	$-0.0929152\pi$
$853$	43.9950	+	16.0129i	1.50636	+	0.548270i	0.548662	+	0.836044i	$0.315137\pi$
$854$		0			0
$855$	−9.97565	−	4.72275i	−0.341160	−	0.161515i
$856$		0			0
$857$	14.5483	−	39.9711i	0.496960	−	1.36539i	−0.397238	−	0.917715i	$-0.630031\pi$
$857$	14.5483	−	39.9711i	0.496960	−	1.36539i	0.894198	−	0.447671i	$-0.147746\pi$
$858$		0			0
$859$	−0.523938	+	0.624404i	−0.0178765	+	0.0213044i	−0.774909	−	0.632073i	$-0.782204\pi$
$859$	−0.523938	+	0.624404i	−0.0178765	+	0.0213044i	0.757032	+	0.653378i	$0.226649\pi$
$860$		0			0
$861$	−0.889185	+	5.04282i	−0.0303034	+	0.171859i
$862$		0			0
$863$	1.92649	+	3.33678i	0.0655784	+	0.113585i	0.896950	−	0.442131i	$-0.145777\pi$
$863$	1.92649	+	3.33678i	0.0655784	+	0.113585i	−0.831372	+	0.555716i	$0.812444\pi$
$864$		0			0
$865$	11.6163	+	31.9156i	0.394967	+	1.08516i
$866$		0			0
$867$	−9.16297	+	15.8707i	−0.311191	+	0.538998i
$868$		0			0
$869$	3.81996	+	4.55245i	0.129583	+	0.154431i
$870$		0			0
$871$	−3.32501	+	0.586289i	−0.112664	+	0.0198656i
$872$		0			0
$873$			1.07666i			0.0364396i
$874$		0			0
$875$			4.05689i			0.137148i
$876$		0			0
$877$	4.12196	−	0.726813i	0.139189	−	0.0245427i	−0.103620	−	0.994617i	$-0.533042\pi$
$877$	4.12196	−	0.726813i	0.139189	−	0.0245427i	0.242808	+	0.970074i	$0.421931\pi$
$878$		0			0
$879$	8.68139	+	10.3461i	0.292816	+	0.348964i
$880$		0			0
$881$	−20.5287	+	35.5567i	−0.691629	+	1.19794i	0.279675	+	0.960095i	$0.409773\pi$
$881$	−20.5287	+	35.5567i	−0.691629	+	1.19794i	−0.971304	+	0.237842i	$0.923560\pi$
$882$		0			0
$883$	15.0651	+	41.3909i	0.506979	+	1.39291i	0.884338	+	0.466847i	$0.154610\pi$
$883$	15.0651	+	41.3909i	0.506979	+	1.39291i	−0.377358	+	0.926067i	$0.623168\pi$
$884$		0			0
$885$	−7.66772	−	13.2809i	−0.257748	−	0.446432i
$886$		0			0
$887$	−6.16668	+	34.9730i	−0.207057	+	1.17428i	0.687113	+	0.726550i	$0.258878\pi$
$887$	−6.16668	+	34.9730i	−0.207057	+	1.17428i	−0.894170	+	0.447727i	$0.852234\pi$
$888$		0			0
$889$	3.77409	−	4.49779i	0.126579	−	0.150851i
$890$		0			0
$891$	−0.798133	+	2.19285i	−0.0267385	+	0.0734633i
$892$		0			0
$893$	−30.9206	+	14.1996i	−1.03472	+	0.475170i
$894$		0			0
$895$	−28.2126	−	10.2685i	−0.943043	−	0.343240i
$896$		0			0
$897$	0.930608	+	0.780873i	0.0310721	+	0.0260726i
$898$		0			0
$899$	8.67458	+	1.52956i	0.289314	+	0.0510138i
$900$		0			0
$901$	9.06283	−	5.23243i	0.301927	−	0.174317i
$902$		0			0
$903$	−2.95336	+	1.07494i	−0.0982818	+	0.0357716i
$904$		0			0
$905$	−43.2242	−	24.9555i	−1.43682	−	0.829549i
$906$		0			0
$907$	16.3746	−	13.7400i	0.543711	−	0.456228i	−0.329094	−	0.944297i	$-0.606743\pi$
$907$	16.3746	−	13.7400i	0.543711	−	0.456228i	0.872805	+	0.488070i	$0.162299\pi$
$908$		0			0
$909$	−2.84090	−	16.1115i	−0.0942267	−	0.534386i
$910$		0			0
$911$	−11.9932			−0.397352			−0.198676	−	0.980065i	$-0.563664\pi$
$911$	−11.9932			−0.397352			−0.198676	+	0.980065i	$0.563664\pi$
$912$		0			0
$913$	3.74691			0.124005
$914$		0			0
$915$	−2.98158	−	16.9094i	−0.0985681	−	0.559007i
$916$		0			0
$917$	1.52481	−	1.27947i	0.0503538	−	0.0422519i
$918$		0			0
$919$	23.3219	+	13.4649i	0.769319	+	0.444166i	0.832632	−	0.553827i	$-0.186833\pi$
$919$	23.3219	+	13.4649i	0.769319	+	0.444166i	−0.0633128	+	0.997994i	$0.520167\pi$
$920$		0			0
$921$	8.36484	−	3.04455i	0.275631	−	0.100321i
$922$		0			0
$923$	−1.69253	+	0.977185i	−0.0557104	+	0.0321644i
$924$		0			0
$925$	10.4666	+	1.84554i	0.344139	+	0.0606809i
$926$		0			0
$927$	1.21688	+	1.02108i	0.0399676	+	0.0335368i
$928$		0			0
$929$	22.8192	+	8.30552i	0.748675	+	0.272495i	0.688048	−	0.725665i	$-0.258468\pi$
$929$	22.8192	+	8.30552i	0.748675	+	0.272495i	0.0606269	+	0.998160i	$0.480690\pi$
$930$		0			0
$931$	−24.3812	+	16.8608i	−0.799061	+	0.552591i
$932$		0			0
$933$	−0.640215	+	1.75898i	−0.0209597	+	0.0575863i
$934$		0			0
$935$	−22.5744	+	26.9032i	−0.738263	+	0.879828i
$936$		0			0
$937$	−8.48235	+	48.1058i	−0.277106	+	1.57155i	0.455084	+	0.890449i	$0.349609\pi$
$937$	−8.48235	+	48.1058i	−0.277106	+	1.57155i	−0.732190	+	0.681100i	$0.761502\pi$
$938$		0			0
$939$	7.49613	+	12.9837i	0.244627	+	0.423706i
$940$		0			0
$941$	−9.48111	−	26.0491i	−0.309076	−	0.849178i	−0.992837	−	0.119473i	$-0.961880\pi$
$941$	−9.48111	−	26.0491i	−0.309076	−	0.849178i	0.683762	−	0.729705i	$-0.260343\pi$
$942$		0			0
$943$	−19.1400	+	33.1514i	−0.623283	+	1.07956i
$944$		0			0
$945$	−0.726682	−	0.866025i	−0.0236390	−	0.0281718i
$946$		0			0
$947$	31.5042	−	5.55504i	1.02375	−	0.180514i	0.363525	−	0.931584i	$-0.381573\pi$
$947$	31.5042	−	5.55504i	1.02375	−	0.180514i	0.660223	+	0.751070i	$0.270462\pi$
$948$		0			0
$949$		−	1.23886i		−	0.0402150i
$950$		0			0
$951$			8.51395i			0.276084i
$952$		0			0
$953$	46.3683	−	8.17598i	1.50202	−	0.264846i	0.638679	−	0.769473i	$-0.279481\pi$
$953$	46.3683	−	8.17598i	1.50202	−	0.264846i	0.863337	+	0.504627i	$0.168370\pi$
$954$		0			0
$955$	15.3897	+	18.3407i	0.497997	+	0.593490i
$956$		0			0
$957$	1.53343	−	2.65598i	0.0495689	−	0.0858558i
$958$		0			0
$959$	−0.139910	−	0.384401i	−0.00451794	−	0.0124129i
$960$		0			0
$961$	−6.96064	−	12.0562i	−0.224537	−	0.388909i
$962$		0			0
$963$	1.04189	−	5.90885i	0.0335744	−	0.190410i
$964$		0			0
$965$	−8.16385	+	9.72930i	−0.262804	+	0.313197i
$966$		0			0
$967$	1.58284	−	4.34883i	0.0509008	−	0.139849i	−0.911637	−	0.410996i	$-0.865181\pi$
$967$	1.58284	−	4.34883i	0.0509008	−	0.139849i	0.962538	+	0.271147i	$0.0874031\pi$
$968$		0			0
$969$	−25.7952	−	2.40847i	−0.828661	−	0.0773711i
$970$		0			0
$971$	21.8824	+	7.96453i	0.702239	+	0.255594i	0.668367	−	0.743832i	$-0.266994\pi$
$971$	21.8824	+	7.96453i	0.702239	+	0.255594i	0.0338724	+	0.999426i	$0.489216\pi$
$972$		0			0
$973$	−4.19459	−	3.51968i	−0.134472	−	0.112836i
$974$		0			0
$975$	0.505930	+	0.0892091i	0.0162027	+	0.00285698i
$976$		0			0
$977$	37.3717	−	21.5766i	1.19563	−	0.690295i	0.236049	−	0.971741i	$-0.424147\pi$
$977$	37.3717	−	21.5766i	1.19563	−	0.690295i	0.959577	+	0.281446i	$0.0908139\pi$
$978$		0			0
$979$	13.6925	−	4.98367i	0.437615	−	0.159279i
$980$		0			0
$981$	12.8858	+	7.43961i	0.411411	+	0.237528i
$982$		0			0
$983$	−38.0390	+	31.9185i	−1.21325	+	1.01804i	−0.214104	+	0.976811i	$0.568683\pi$
$983$	−38.0390	+	31.9185i	−1.21325	+	1.01804i	−0.999150	+	0.0412304i	$0.986872\pi$
$984$		0			0
$985$	−7.26945	−	41.2271i	−0.231624	−	1.31360i
$986$		0			0
$987$	−3.48515			−0.110933
$988$		0			0
$989$	−23.4953			−0.747106
$990$		0			0
$991$	5.01290	+	28.4296i	0.159240	+	0.903095i	0.954806	+	0.297228i	$0.0960623\pi$
$991$	5.01290	+	28.4296i	0.159240	+	0.903095i	−0.795566	+	0.605866i	$0.792827\pi$
$992$		0			0
$993$	21.6989	−	18.2076i	0.688595	−	0.577800i
$994$		0			0
$995$	15.1079	+	8.72254i	0.478952	+	0.276523i
$996$		0			0
$997$	−25.8999	+	9.42680i	−0.820259	+	0.298550i	−0.717855	−	0.696193i	$-0.754876\pi$
$997$	−25.8999	+	9.42680i	−0.820259	+	0.298550i	−0.102404	+	0.994743i	$0.532653\pi$
$998$		0			0
$999$	6.52094	−	3.76487i	0.206314	−	0.119115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.a.319.1	yes	6
4.3	odd	2		912.2.ci.b.319.1	yes	6
19.14	odd	18		912.2.ci.b.223.1	yes	6
76.71	even	18	inner	912.2.ci.a.223.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.a.223.1	✓	6	76.71	even	18	inner
912.2.ci.a.319.1	yes	6	1.1	even	1	trivial
912.2.ci.b.223.1	yes	6	19.14	odd	18
912.2.ci.b.319.1	yes	6	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{3} +(-1.93969 + 1.62760i) q^{5} +(-0.386659 - 0.223238i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{3} +(-1.93969 + 1.62760i) q^{5} +(-0.386659 - 0.223238i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(-2.02094 + 1.16679i) q^{11} +(0.358441 + 0.0632028i) q^{13} +(-1.93969 - 1.62760i) q^{15} +(-5.58512 - 2.03282i) q^{17} +(-0.354570 - 4.34445i) q^{19} +(0.152704 - 0.419550i) q^{21} +(2.14543 - 2.55682i) q^{23} +(0.245100 - 1.39003i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(0.449493 + 1.23497i) q^{29} +(3.35117 - 5.80439i) q^{31} +(-1.50000 - 1.78763i) q^{33} +(1.11334 - 0.196312i) q^{35} +7.52974i q^{37} +0.363970i q^{39} +(-11.2947 + 1.99157i) q^{41} +(-4.52481 - 5.39246i) q^{43} +(1.26604 - 2.19285i) q^{45} +(-2.66978 - 7.33515i) q^{47} +(-3.40033 - 5.88954i) q^{49} +(1.03209 - 5.85327i) q^{51} +(-1.13176 + 1.34878i) q^{53} +(2.02094 - 5.55250i) q^{55} +(4.21688 - 1.10359i) q^{57} +(5.69119 + 2.07142i) q^{59} +(5.19459 + 4.35878i) q^{61} +(0.439693 + 0.0775297i) q^{63} +(-0.798133 + 0.460802i) q^{65} +(-8.71688 + 3.17269i) q^{67} +(2.89053 + 1.66885i) q^{69} +(-4.11334 + 3.45150i) q^{71} +(-0.591052 - 3.35202i) q^{73} +1.41147 q^{75} +1.04189 q^{77} +(-0.442219 - 2.50795i) q^{79} +(0.766044 - 0.642788i) q^{81} +(-1.39053 - 0.802823i) q^{83} +(14.1420 - 5.14728i) q^{85} +(-1.13816 + 0.657115i) q^{87} +(-6.14930 - 1.08429i) q^{89} +(-0.124485 - 0.104455i) q^{91} +(6.29813 + 2.29233i) q^{93} +(7.75877 + 7.84981i) q^{95} +(0.368241 - 1.01173i) q^{97} +(1.50000 - 1.78763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{5} - 9 q^{7}+O(q^{10}) \) 6 * q - 6 * q^5 - 9 * q^7	\( 6 q - 6 q^{5} - 9 q^{7} - 9 q^{11} - 6 q^{13} - 6 q^{15} - 12 q^{17} - 18 q^{19} + 3 q^{21} - 3 q^{23} - 3 q^{27} - 6 q^{31} - 9 q^{33} - 12 q^{41} + 3 q^{45} - 39 q^{47} - 6 q^{49} - 3 q^{51} - 12 q^{53} + 9 q^{55} + 9 q^{57} - 12 q^{59} + 27 q^{61} - 3 q^{63} + 9 q^{65} - 36 q^{67} - 18 q^{71} - 9 q^{73} - 12 q^{75} + 18 q^{79} + 9 q^{83} + 27 q^{85} + 27 q^{87} + 3 q^{89} + 12 q^{91} + 24 q^{93} + 24 q^{95} - 3 q^{97} + 9 q^{99}+O(q^{100}) \) 6 * q - 6 * q^5 - 9 * q^7 - 9 * q^11 - 6 * q^13 - 6 * q^15 - 12 * q^17 - 18 * q^19 + 3 * q^21 - 3 * q^23 - 3 * q^27 - 6 * q^31 - 9 * q^33 - 12 * q^41 + 3 * q^45 - 39 * q^47 - 6 * q^49 - 3 * q^51 - 12 * q^53 + 9 * q^55 + 9 * q^57 - 12 * q^59 + 27 * q^61 - 3 * q^63 + 9 * q^65 - 36 * q^67 - 18 * q^71 - 9 * q^73 - 12 * q^75 + 18 * q^79 + 9 * q^83 + 27 * q^85 + 27 * q^87 + 3 * q^89 + 12 * q^91 + 24 * q^93 + 24 * q^95 - 3 * q^97 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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