LMFDB - Embedded newform 315.2.cc.a.92.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(92,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("315.92");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.cc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			92.6
Character	$\chi$	$=$	315.92
Dual form			315.2.cc.a.113.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540409 - 2.01684i) q^{2} +(1.29595 - 1.14913i) q^{3} +(-2.04353 + 1.17983i) q^{4} +(-0.0970501 - 2.23396i) q^{5} +(-3.01795 - 1.99273i) q^{6} +(0.965926 - 0.258819i) q^{7} +(0.531022 + 0.531022i) q^{8} +(0.358997 - 2.97844i) q^{9} +O(q^{10})$	\(q+(-0.540409 - 2.01684i) q^{2} +(1.29595 - 1.14913i) q^{3} +(-2.04353 + 1.17983i) q^{4} +(-0.0970501 - 2.23396i) q^{5} +(-3.01795 - 1.99273i) q^{6} +(0.965926 - 0.258819i) q^{7} +(0.531022 + 0.531022i) q^{8} +(0.358997 - 2.97844i) q^{9} +(-4.45308 + 1.40299i) q^{10} +(5.71391 + 3.29893i) q^{11} +(-1.29254 + 3.87730i) q^{12} +(-4.09754 - 1.09793i) q^{13} +(-1.04399 - 1.80825i) q^{14} +(-2.69289 - 2.78359i) q^{15} +(-1.57565 + 2.72911i) q^{16} +(0.882816 - 0.882816i) q^{17} +(-6.20103 + 0.885541i) q^{18} +5.69481i q^{19} +(2.83403 + 4.45067i) q^{20} +(0.954379 - 1.44539i) q^{21} +(3.56554 - 13.3068i) q^{22} +(-0.289368 + 1.07993i) q^{23} +(1.29839 + 0.0779666i) q^{24} +(-4.98116 + 0.433612i) q^{25} +8.85740i q^{26} +(-2.95738 - 4.27246i) q^{27} +(-1.66854 + 1.66854i) q^{28} +(3.06691 - 5.31204i) q^{29} +(-4.15878 + 6.93538i) q^{30} +(2.13262 + 3.69380i) q^{31} +(7.80644 + 2.09173i) q^{32} +(11.1959 - 2.29077i) q^{33} +(-2.25758 - 1.30341i) q^{34} +(-0.671935 - 2.13272i) q^{35} +(2.78045 + 6.51010i) q^{36} +(0.383567 + 0.383567i) q^{37} +(11.4855 - 3.07753i) q^{38} +(-6.57190 + 3.28574i) q^{39} +(1.13475 - 1.23782i) q^{40} +(-4.96575 + 2.86698i) q^{41} +(-3.43087 - 1.14372i) q^{42} +(2.10216 + 7.84536i) q^{43} -15.5687 q^{44} +(-6.68857 - 0.512926i) q^{45} +2.33443 q^{46} +(-1.00549 - 3.75253i) q^{47} +(1.09413 + 5.34743i) q^{48} +(0.866025 - 0.500000i) q^{49} +(3.56639 + 9.81186i) q^{50} +(0.129618 - 2.15856i) q^{51} +(9.66883 - 2.59076i) q^{52} +(0.331638 + 0.331638i) q^{53} +(-7.01866 + 8.27342i) q^{54} +(6.81514 - 13.0848i) q^{55} +(0.650366 + 0.375489i) q^{56} +(6.54408 + 7.38021i) q^{57} +(-12.3709 - 3.31477i) q^{58} +(2.16351 + 3.74731i) q^{59} +(8.78717 + 2.51119i) q^{60} +(6.14599 - 10.6452i) q^{61} +(6.29730 - 6.29730i) q^{62} +(-0.424114 - 2.96987i) q^{63} -10.5721i q^{64} +(-2.05507 + 9.26030i) q^{65} +(-10.6705 - 21.3423i) q^{66} +(0.468161 - 1.74720i) q^{67} +(-0.762486 + 2.84564i) q^{68} +(0.865979 + 1.73207i) q^{69} +(-3.93823 + 2.50773i) q^{70} -12.3908i q^{71} +(1.77225 - 1.39098i) q^{72} +(4.99349 - 4.99349i) q^{73} +(0.566308 - 0.980875i) q^{74} +(-5.95708 + 6.28595i) q^{75} +(-6.71893 - 11.6375i) q^{76} +(6.37304 + 1.70765i) q^{77} +(10.1783 + 11.4788i) q^{78} +(6.24438 + 3.60520i) q^{79} +(6.24964 + 3.25509i) q^{80} +(-8.74224 - 2.13850i) q^{81} +(8.46575 + 8.46575i) q^{82} +(3.92219 - 1.05095i) q^{83} +(-0.244981 + 4.07971i) q^{84} +(-2.05785 - 1.88650i) q^{85} +(14.6868 - 8.47941i) q^{86} +(-2.12966 - 10.4084i) q^{87} +(1.28241 + 4.78601i) q^{88} -14.7775 q^{89} +(2.58008 + 13.7669i) q^{90} -4.24209 q^{91} +(-0.682811 - 2.54829i) q^{92} +(7.00844 + 2.33634i) q^{93} +(-7.02485 + 4.05580i) q^{94} +(12.7220 - 0.552682i) q^{95} +(12.5205 - 6.25984i) q^{96} +(3.39553 - 0.909831i) q^{97} +(-1.47643 - 1.47643i) q^{98} +(11.8769 - 15.8343i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 4 q^{3}+O(q^{10}) $ 144 * q + 4 * q^3	$ 144 q + 4 q^{3} - 12 q^{11} - 16 q^{12} + 16 q^{15} + 72 q^{16} - 64 q^{18} - 48 q^{20} - 4 q^{21} - 24 q^{23} - 12 q^{25} - 32 q^{27} - 20 q^{30} - 60 q^{32} - 16 q^{33} - 16 q^{36} - 24 q^{37} + 72 q^{38} + 48 q^{41} - 40 q^{42} + 40 q^{45} - 48 q^{46} + 12 q^{47} + 104 q^{48} - 76 q^{51} - 24 q^{55} - 4 q^{57} - 92 q^{60} + 8 q^{63} - 72 q^{65} - 80 q^{66} - 12 q^{67} - 64 q^{72} - 108 q^{75} - 24 q^{76} + 72 q^{78} + 32 q^{81} - 96 q^{82} + 120 q^{83} - 48 q^{85} - 144 q^{86} + 116 q^{87} - 48 q^{88} + 252 q^{90} + 24 q^{91} + 156 q^{92} - 44 q^{93} + 120 q^{95} - 96 q^{96} - 60 q^{97}+O(q^{100}) $ 144 * q + 4 * q^3 - 12 * q^11 - 16 * q^12 + 16 * q^15 + 72 * q^16 - 64 * q^18 - 48 * q^20 - 4 * q^21 - 24 * q^23 - 12 * q^25 - 32 * q^27 - 20 * q^30 - 60 * q^32 - 16 * q^33 - 16 * q^36 - 24 * q^37 + 72 * q^38 + 48 * q^41 - 40 * q^42 + 40 * q^45 - 48 * q^46 + 12 * q^47 + 104 * q^48 - 76 * q^51 - 24 * q^55 - 4 * q^57 - 92 * q^60 + 8 * q^63 - 72 * q^65 - 80 * q^66 - 12 * q^67 - 64 * q^72 - 108 * q^75 - 24 * q^76 + 72 * q^78 + 32 * q^81 - 96 * q^82 + 120 * q^83 - 48 * q^85 - 144 * q^86 + 116 * q^87 - 48 * q^88 + 252 * q^90 + 24 * q^91 + 156 * q^92 - 44 * q^93 + 120 * q^95 - 96 * q^96 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.540409	−	2.01684i	−0.382127	−	1.42612i	−0.842646	−	0.538468i	$-0.819003\pi$
$2$	−0.540409	−	2.01684i	−0.382127	−	1.42612i	0.460519	−	0.887650i	$-0.347663\pi$
$3$	1.29595	−	1.14913i	0.748220	−	0.663451i
$3$	1.29595	−	1.14913i	0.748220	−	0.663451i
$4$	−2.04353	+	1.17983i	−1.02177	+	0.589917i
$5$	−0.0970501	−	2.23396i	−0.0434021	−	0.999058i
$5$	−0.0970501	−	2.23396i	−0.0434021	−	0.999058i
$6$	−3.01795	−	1.99273i	−1.23207	−	0.813527i
$7$	0.965926	−	0.258819i	0.365086	−	0.0978244i
$7$	0.965926	−	0.258819i	0.365086	−	0.0978244i
$8$	0.531022	+	0.531022i	0.187745	+	0.187745i
$9$	0.358997	−	2.97844i	0.119666	−	0.992814i
$10$	−4.45308	+	1.40299i	−1.40819	+	0.443664i
$11$	5.71391	+	3.29893i	1.72281	+	0.994664i	0.912987	+	0.407989i	$0.133770\pi$
$11$	5.71391	+	3.29893i	1.72281	+	0.994664i	0.809823	+	0.586675i	$0.199563\pi$
$12$	−1.29254	+	3.87730i	−0.373124	+	1.11928i
$13$	−4.09754	−	1.09793i	−1.13645	−	0.304512i	−0.358929	−	0.933365i	$-0.616858\pi$
$13$	−4.09754	−	1.09793i	−1.13645	−	0.304512i	−0.777524	+	0.628853i	$0.783525\pi$
$14$	−1.04399	−	1.80825i	−0.279018	−	0.483274i
$15$	−2.69289	−	2.78359i	−0.695300	−	0.718719i
$16$	−1.57565	+	2.72911i	−0.393913	+	0.682278i
$17$	0.882816	−	0.882816i	0.214114	−	0.214114i	−0.591898	−	0.806013i	$-0.701621\pi$
$17$	0.882816	−	0.882816i	0.214114	−	0.214114i	0.806013	+	0.591898i	$0.201621\pi$
$18$	−6.20103	+	0.885541i	−1.46160	+	0.208724i
$19$			5.69481i			1.30648i	0.757152	+	0.653239i	$0.226590\pi$
$19$			5.69481i			1.30648i	−0.757152	+	0.653239i	$0.773410\pi$
$20$	2.83403	+	4.45067i	0.633708	+	0.995199i
$21$	0.954379	−	1.44539i	0.208263	−	0.315411i
$22$	3.56554	−	13.3068i	0.760177	−	2.83702i
$23$	−0.289368	+	1.07993i	−0.0603373	+	0.225182i	−0.989510	−	0.144464i	$-0.953854\pi$
$23$	−0.289368	+	1.07993i	−0.0603373	+	0.225182i	0.929173	+	0.369646i	$0.120521\pi$
$24$	1.29839	+	0.0779666i	0.265034	+	0.0159149i
$25$	−4.98116	+	0.433612i	−0.996233	+	0.0867225i
$26$			8.85740i			1.73708i
$27$	−2.95738	−	4.27246i	−0.569147	−	0.822235i
$28$	−1.66854	+	1.66854i	−0.315324	+	0.315324i
$29$	3.06691	−	5.31204i	0.569511	−	0.986422i	−0.427103	−	0.904203i	$-0.640466\pi$
$29$	3.06691	−	5.31204i	0.569511	−	0.986422i	0.996614	−	0.0822191i	$-0.0262007\pi$
$30$	−4.15878	+	6.93538i	−0.759286	+	1.26622i
$31$	2.13262	+	3.69380i	0.383029	+	0.663426i	0.991494	−	0.130155i	$-0.0415475\pi$
$31$	2.13262	+	3.69380i	0.383029	+	0.663426i	−0.608464	+	0.793581i	$0.708214\pi$
$32$	7.80644	+	2.09173i	1.38000	+	0.369769i
$33$	11.1959	−	2.29077i	1.94895	−	0.398772i
$34$	−2.25758	−	1.30341i	−0.387171	−	0.223533i
$35$	−0.671935	−	2.13272i	−0.113578	−	0.360496i
$36$	2.78045	+	6.51010i	0.463408	+	1.08502i
$37$	0.383567	+	0.383567i	0.0630581	+	0.0630581i	0.737933	−	0.674874i	$-0.235802\pi$
$37$	0.383567	+	0.383567i	0.0630581	+	0.0630581i	−0.674874	+	0.737933i	$0.735802\pi$
$38$	11.4855	−	3.07753i	1.86319	−	0.499241i
$39$	−6.57190	+	3.28574i	−1.05235	+	0.526140i
$40$	1.13475	−	1.23782i	0.179419	−	0.195716i
$41$	−4.96575	+	2.86698i	−0.775519	+	0.447746i	−0.834840	−	0.550493i	$-0.814440\pi$
$41$	−4.96575	+	2.86698i	−0.775519	+	0.447746i	0.0593207	+	0.998239i	$0.481107\pi$
$42$	−3.43087	−	1.14372i	−0.529395	−	0.176480i
$43$	2.10216	+	7.84536i	0.320576	+	1.19641i	0.918685	+	0.394991i	$0.129252\pi$
$43$	2.10216	+	7.84536i	0.320576	+	1.19641i	−0.598109	+	0.801415i	$0.704081\pi$
$44$	−15.5687			−2.34708
$45$	−6.68857	−	0.512926i	−0.997072	−	0.0764625i
$46$	2.33443			0.344192
$47$	−1.00549	−	3.75253i	−0.146665	−	0.547362i	−0.999676	−	0.0254682i	$-0.991892\pi$
$47$	−1.00549	−	3.75253i	−0.146665	−	0.547362i	0.853010	−	0.521894i	$-0.174774\pi$
$48$	1.09413	+	5.34743i	0.157924	+	0.771836i
$49$	0.866025	−	0.500000i	0.123718	−	0.0714286i
$50$	3.56639	+	9.81186i	0.504364	+	1.38761i
$51$	0.129618	−	2.15856i	0.0181502	−	0.302259i
$52$	9.66883	−	2.59076i	1.34083	−	0.359273i
$53$	0.331638	+	0.331638i	0.0455540	+	0.0455540i	0.729517	−	0.683963i	$-0.239745\pi$
$53$	0.331638	+	0.331638i	0.0455540	+	0.0455540i	−0.683963	+	0.729517i	$0.739745\pi$
$54$	−7.01866	+	8.27342i	−0.955118	+	1.12587i
$55$	6.81514	−	13.0848i	0.918953	−	1.76436i
$56$	0.650366	+	0.375489i	0.0869088	+	0.0501768i
$57$	6.54408	+	7.38021i	0.866785	+	0.977533i
$58$	−12.3709	−	3.31477i	−1.62438	−	0.435251i
$59$	2.16351	+	3.74731i	0.281665	+	0.487858i	0.971795	−	0.235827i	$-0.0757800\pi$
$59$	2.16351	+	3.74731i	0.281665	+	0.487858i	−0.690130	+	0.723685i	$0.742447\pi$
$60$	8.78717	+	2.51119i	1.13442	+	0.324194i
$61$	6.14599	−	10.6452i	0.786913	−	1.36297i	−0.140936	−	0.990019i	$-0.545011\pi$
$61$	6.14599	−	10.6452i	0.786913	−	1.36297i	0.927849	−	0.372955i	$-0.121656\pi$
$62$	6.29730	−	6.29730i	0.799758	−	0.799758i
$63$	−0.424114	−	2.96987i	−0.0534333	−	0.374168i
$64$		−	10.5721i		−	1.32151i
$65$	−2.05507	+	9.26030i	−0.254900	+	1.14860i
$66$	−10.6705	−	21.3423i	−1.31344	−	2.62705i
$67$	0.468161	−	1.74720i	0.0571950	−	0.213455i	−0.931414	−	0.363962i	$-0.881424\pi$
$67$	0.468161	−	1.74720i	0.0571950	−	0.213455i	0.988609	+	0.150507i	$0.0480906\pi$
$68$	−0.762486	+	2.84564i	−0.0924650	+	0.345084i
$69$	0.865979	+	1.73207i	0.104252	+	0.208516i
$70$	−3.93823	+	2.50773i	−0.470708	+	0.299730i
$71$		−	12.3908i		−	1.47051i	−0.677788	−	0.735257i	$-0.737061\pi$
$71$		−	12.3908i		−	1.47051i	0.677788	−	0.735257i	$-0.262939\pi$
$72$	1.77225	−	1.39098i	0.208862	−	0.163929i
$73$	4.99349	−	4.99349i	0.584443	−	0.584443i	−0.351678	−	0.936121i	$-0.614389\pi$
$73$	4.99349	−	4.99349i	0.584443	−	0.584443i	0.936121	+	0.351678i	$0.114389\pi$
$74$	0.566308	−	0.980875i	0.0658320	−	0.114024i
$75$	−5.95708	+	6.28595i	−0.687865	+	0.725839i
$76$	−6.71893	−	11.6375i	−0.770714	−	1.33492i
$77$	6.37304	+	1.70765i	0.726275	+	0.194605i
$78$	10.1783	+	11.4788i	1.15247	+	1.29972i
$79$	6.24438	+	3.60520i	0.702548	+	0.405616i	0.808296	−	0.588777i	$-0.200390\pi$
$79$	6.24438	+	3.60520i	0.702548	+	0.405616i	−0.105748	+	0.994393i	$0.533724\pi$
$80$	6.24964	+	3.25509i	0.698731	+	0.363930i
$81$	−8.74224	−	2.13850i	−0.971360	−	0.237611i
$82$	8.46575	+	8.46575i	0.934886	+	0.934886i
$83$	3.92219	−	1.05095i	0.430517	−	0.115357i	−0.0370520	−	0.999313i	$-0.511797\pi$
$83$	3.92219	−	1.05095i	0.430517	−	0.115357i	0.467569	+	0.883957i	$0.345130\pi$
$84$	−0.244981	+	4.07971i	−0.0267296	+	0.445133i
$85$	−2.05785	−	1.88650i	−0.223205	−	0.204619i
$86$	14.6868	−	8.47941i	1.58372	−	0.914359i
$87$	−2.12966	−	10.4084i	−0.228323	−	1.11590i
$88$	1.28241	+	4.78601i	0.136705	+	0.510191i
$89$	−14.7775			−1.56641			−0.783207	−	0.621762i	$-0.786417\pi$
$89$	−14.7775			−1.56641			−0.783207	+	0.621762i	$0.786417\pi$
$90$	2.58008	+	13.7669i	0.271964	+	1.45116i
$91$	−4.24209			−0.444692
$92$	−0.682811	−	2.54829i	−0.0711880	−	0.265677i
$93$	7.00844	+	2.33634i	0.726741	+	0.242267i
$94$	−7.02485	+	4.05580i	−0.724558	+	0.418324i
$95$	12.7220	−	0.552682i	1.30525	−	0.0567040i
$96$	12.5205	−	6.25984i	1.27786	−	0.638892i
$97$	3.39553	−	0.909831i	0.344764	−	0.0923793i	−0.0822820	−	0.996609i	$-0.526221\pi$
$97$	3.39553	−	0.909831i	0.344764	−	0.0923793i	0.427046	+	0.904230i	$0.359554\pi$
$98$	−1.47643	−	1.47643i	−0.149142	−	0.149142i
$99$	11.8769	−	15.8343i	1.19368	−	1.59140i
$100$	9.66757	−	6.76304i	0.966757	−	0.676304i
$101$	−1.57785	−	0.910974i	−0.157002	−	0.0906453i	0.419440	−	0.907783i	$-0.362226\pi$
$101$	−1.57785	−	0.910974i	−0.157002	−	0.0906453i	−0.576443	+	0.817138i	$0.695560\pi$
$102$	−4.42351	+	0.905087i	−0.437992	+	0.0896170i
$103$	−14.1531	−	3.79230i	−1.39454	−	0.373667i	−0.518161	−	0.855283i	$-0.673383\pi$
$103$	−14.1531	−	3.79230i	−1.39454	−	0.373667i	−0.876382	+	0.481616i	$0.840050\pi$
$104$	−1.59286	−	2.75891i	−0.156193	−	0.270533i
$105$	−3.32157	−	1.99177i	−0.324152	−	0.194377i
$106$	0.489640	−	0.848081i	0.0475580	−	0.0823729i
$107$	4.38296	−	4.38296i	0.423717	−	0.423717i	−0.462764	−	0.886481i	$-0.653142\pi$
$107$	4.38296	−	4.38296i	0.423717	−	0.423717i	0.886481	+	0.462764i	$0.153142\pi$
$108$	11.0843	+	5.24170i	1.06659	+	0.504382i
$109$			6.24163i			0.597840i	0.954278	+	0.298920i	$0.0966263\pi$
$109$			6.24163i			0.597840i	−0.954278	+	0.298920i	$0.903374\pi$
$110$	−30.0729	−	6.67386i	−2.86734	−	0.636328i
$111$	0.937854	+	0.0563168i	0.0890172	+	0.00534535i
$112$	−0.815618	+	3.04393i	−0.0770686	+	0.287624i
$113$	−1.47567	+	5.50729i	−0.138820	+	0.518082i	0.861133	+	0.508379i	$0.169755\pi$
$113$	−1.47567	+	5.50729i	−0.138820	+	0.518082i	−0.999953	+	0.00970294i	$0.996911\pi$
$114$	11.3482	−	17.1867i	1.06286	−	1.60968i
$115$	2.44061	+	0.541628i	0.227588	+	0.0505071i
$116$			14.4738i			1.34386i
$117$	−4.74113	+	11.8101i	−0.438318	+	1.09185i
$118$	6.38853	−	6.38853i	0.588111	−	0.588111i
$119$	0.624245	−	1.08122i	0.0572244	−	0.0991156i
$120$	0.0481651	−	2.90813i	0.00439686	−	0.265475i
$121$	16.2659	+	28.1733i	1.47871	+	2.56121i
$122$	−24.7909	−	6.64270i	−2.24446	−	0.601402i
$123$	−3.14085	+	9.42176i	−0.283201	+	0.849532i
$124$	−8.71614	−	5.03227i	−0.782733	−	0.451911i
$125$	1.45210	+	11.0856i	0.129879	+	0.991530i
$126$	−5.76054	+	2.46031i	−0.513190	+	0.219182i
$127$	12.0788	+	12.0788i	1.07182	+	1.07182i	0.997213	+	0.0746024i	$0.0237688\pi$
$127$	12.0788	+	12.0788i	1.07182	+	1.07182i	0.0746024	+	0.997213i	$0.476231\pi$
$128$	−5.70928	+	1.52980i	−0.504634	+	0.135216i
$129$	11.7396	+	7.75158i	1.03362	+	0.682488i
$130$	19.7871	−	0.859612i	1.73544	−	0.0753929i
$131$	−11.2300	+	6.48364i	−0.981169	+	0.566478i	−0.902623	−	0.430433i	$-0.858361\pi$
$131$	−11.2300	+	6.48364i	−0.981169	+	0.566478i	−0.0785458	+	0.996911i	$0.525028\pi$
$132$	−20.1764	+	17.8905i	−1.75613	+	1.55717i
$133$	1.47392	+	5.50076i	0.127805	+	0.476977i
$134$	−3.77682			−0.326267
$135$	−9.25750	+	7.02131i	−0.796758	+	0.604298i
$136$	0.937589			0.0803976
$137$	−0.838372	−	3.12885i	−0.0716269	−	0.267315i	0.920820	−	0.389987i	$-0.127520\pi$
$137$	−0.838372	−	3.12885i	−0.0716269	−	0.267315i	−0.992447	+	0.122672i	$0.960854\pi$
$138$	3.02531	−	2.68256i	0.257532	−	0.228355i
$139$	−4.39699	+	2.53860i	−0.372947	+	0.215321i	−0.674745	−	0.738051i	$-0.735747\pi$
$139$	−4.39699	+	2.53860i	−0.372947	+	0.215321i	0.301798	+	0.953372i	$0.402413\pi$
$140$	3.88938	+	3.56551i	0.328712	+	0.301341i
$141$	−5.61521	−	3.70767i	−0.472886	−	0.312242i
$142$	−24.9902	+	6.69609i	−2.09713	+	0.561924i
$143$	−19.7910	−	19.7910i	−1.65501	−	1.65501i
$144$	7.56285	+	5.67273i	0.630237	+	0.472728i
$145$	−12.1645	−	6.33582i	−1.01021	−	0.526161i
$146$	−12.7696	−	7.37251i	−1.05682	−	0.610154i
$147$	0.547764	−	1.64315i	0.0451788	−	0.135525i
$148$	−1.23638	−	0.331286i	−0.101630	−	0.0272316i
$149$	−0.542242	−	0.939190i	−0.0444222	−	0.0769415i	0.842959	−	0.537977i	$-0.180811\pi$
$149$	−0.542242	−	0.939190i	−0.0444222	−	0.0769415i	−0.887382	+	0.461036i	$0.847478\pi$
$150$	15.8970	+	8.61747i	1.29798	+	0.703613i
$151$	−4.24574	+	7.35383i	−0.345513	+	0.598446i	−0.985447	−	0.169984i	$-0.945628\pi$
$151$	−4.24574	+	7.35383i	−0.345513	+	0.598446i	0.639934	+	0.768430i	$0.278962\pi$
$152$	−3.02407	+	3.02407i	−0.245284	+	0.245284i
$153$	−2.31249	−	2.94634i	−0.186954	−	0.238198i
$154$		−	13.7762i		−	1.11012i
$155$	8.04484	−	5.12267i	0.646177	−	0.411463i
$156$	9.55325	−	14.4683i	0.764872	−	1.15839i
$157$	−4.26699	+	15.9246i	−0.340543	+	1.27092i	0.557191	+	0.830384i	$0.311879\pi$
$157$	−4.26699	+	15.9246i	−0.340543	+	1.27092i	−0.897734	+	0.440538i	$0.854788\pi$
$158$	3.89656	−	14.5422i	0.309994	−	1.15691i
$159$	0.810884	+	0.0486924i	0.0643073	+	0.00386156i
$160$	3.91523	−	17.6423i	0.309526	−	1.39475i
$161$			1.11803i			0.0881131i
$162$	0.411383	+	18.7873i	0.0323213	+	1.47607i
$163$	−12.6620	+	12.6620i	−0.991762	+	0.991762i	−0.999966	−	0.00820445i	$-0.997388\pi$
$163$	−12.6620	+	12.6620i	−0.991762	+	0.991762i	0.00820445	+	0.999966i	$0.497388\pi$
$164$	6.76511	−	11.7175i	0.528266	−	0.914984i
$165$	−6.20405	−	24.7888i	−0.482985	−	1.92981i
$166$	−4.23918	−	7.34248i	−0.329024	−	0.569887i
$167$	−3.16928	−	0.849206i	−0.245246	−	0.0657135i	0.134102	−	0.990968i	$-0.457185\pi$
$167$	−3.16928	−	0.849206i	−0.245246	−	0.0657135i	−0.379348	+	0.925254i	$0.623852\pi$
$168$	1.27433	−	0.260739i	0.0983168	−	0.0201165i
$169$	4.32606	+	2.49765i	0.332774	+	0.192127i
$170$	−2.69267	+	5.16983i	−0.206519	+	0.396508i
$171$	16.9617	+	2.04442i	1.29709	+	0.156340i
$172$	−13.5520	−	13.5520i	−1.03333	−	1.03333i
$173$	2.18122	−	0.584457i	0.165835	−	0.0444355i	−0.174946	−	0.984578i	$-0.555975\pi$
$173$	2.18122	−	0.584457i	0.165835	−	0.0444355i	0.340781	+	0.940143i	$0.389308\pi$
$174$	−19.8412	+	9.91999i	−1.50416	+	0.752033i
$175$	−4.69921	+	1.70806i	−0.355227	+	0.129117i
$176$	−18.0063	+	10.3959i	−1.35727	+	0.783623i
$177$	7.10996	+	2.37019i	0.534417	+	0.178154i
$178$	7.98591	+	29.8038i	0.598569	+	2.23389i
$179$	−0.829493			−0.0619993			−0.0309996	−	0.999519i	$-0.509869\pi$
$179$	−0.829493			−0.0619993			−0.0309996	+	0.999519i	$0.509869\pi$
$180$	14.2735	−	6.84321i	1.06388	−	0.510063i
$181$	−3.68497			−0.273901			−0.136951	−	0.990578i	$-0.543730\pi$
$181$	−3.68497			−0.273901			−0.136951	+	0.990578i	$0.543730\pi$
$182$	2.29246	+	8.55559i	0.169929	+	0.634183i
$183$	−4.26777	−	20.8582i	−0.315482	−	1.54188i
$184$	−0.727129	+	0.419808i	−0.0536047	+	0.0309487i
$185$	0.819649	−	0.894099i	0.0602618	−	0.0657355i
$186$	0.924594	−	15.3974i	0.0677945	−	1.12900i
$187$	7.95668	−	2.13198i	0.581850	−	0.155906i
$188$	6.48210	+	6.48210i	0.472756	+	0.472756i
$189$	−3.96240	−	3.36145i	−0.288222	−	0.244510i
$190$	−7.98975	−	25.3595i	−0.579637	−	1.83977i
$191$	3.32097	+	1.91736i	0.240297	+	0.138735i	0.615313	−	0.788283i	$-0.289030\pi$
$191$	3.32097	+	1.91736i	0.240297	+	0.138735i	−0.375016	+	0.927018i	$0.622363\pi$
$192$	−12.1487	−	13.7009i	−0.876758	−	0.988781i
$193$	0.137282	+	0.0367847i	0.00988179	+	0.00264782i	0.263757	−	0.964589i	$-0.415038\pi$
$193$	0.137282	+	0.0367847i	0.00988179	+	0.00264782i	−0.253875	+	0.967237i	$0.581705\pi$
$194$	−3.66996	−	6.35655i	−0.263488	−	0.456374i
$195$	7.97802	+	14.3625i	0.571318	+	1.02852i
$196$	−1.17983	+	2.04353i	−0.0842738	+	0.145967i
$197$	1.23595	−	1.23595i	0.0880576	−	0.0880576i	−0.661706	−	0.749763i	$-0.730167\pi$
$197$	1.23595	−	1.23595i	0.0880576	−	0.0880576i	0.749763	+	0.661706i	$0.230167\pi$
$198$	−38.3535	−	15.3969i	−2.72566	−	1.09421i
$199$		−	1.17156i		−	0.0830496i	−0.999137	−	0.0415248i	$-0.986778\pi$
$199$		−	1.17156i		−	0.0830496i	0.999137	−	0.0415248i	$-0.0132215\pi$
$200$	−2.87536	−	2.41485i	−0.203319	−	0.170756i
$201$	−1.40105	−	2.80227i	−0.0988222	−	0.197657i
$202$	−0.984598	+	3.67457i	−0.0692761	+	0.258542i
$203$	1.58755	−	5.92482i	0.111424	−	0.415841i
$204$	2.28186	+	4.56401i	0.159762	+	0.319545i
$205$	6.88664	+	10.8150i	0.480984	+	0.755355i
$206$			30.5938i			2.13157i
$207$	3.11264	+	1.24956i	0.216344	+	0.0868503i
$208$	9.45268	−	9.45268i	0.655426	−	0.655426i
$209$	−18.7868	+	32.5396i	−1.29951	+	2.25081i
$210$	−2.22206	+	7.77544i	−0.153337	+	0.536556i
$211$	−5.71683	−	9.90184i	−0.393563	−	0.681671i	0.599354	−	0.800484i	$-0.295424\pi$
$211$	−5.71683	−	9.90184i	−0.393563	−	0.681671i	−0.992917	+	0.118813i	$0.962091\pi$
$212$	−1.06899	−	0.286435i	−0.0734186	−	0.0196725i
$213$	−14.2386	−	16.0579i	−0.975615	−	1.10027i
$214$	−11.2083	−	6.47112i	−0.766184	−	0.442357i
$215$	17.3222	−	5.45753i	1.18137	−	0.372201i
$216$	0.698338	−	3.83920i	0.0475159	−	0.261225i
$217$	3.01598	+	3.01598i	0.204738	+	0.204738i
$218$	12.5883	−	3.37304i	0.852590	−	0.228451i
$219$	0.733163	−	12.2095i	0.0495425	−	0.825042i
$220$	1.51095	+	34.7800i	0.101868	+	2.34487i
$221$	−4.58665	+	2.64810i	−0.308531	+	0.178131i
$222$	−0.393244	−	1.92193i	−0.0263928	−	0.128992i
$223$	4.04879	+	15.1103i	0.271127	+	1.01186i	0.958393	+	0.285453i	$0.0921440\pi$
$223$	4.04879	+	15.1103i	0.271127	+	1.01186i	−0.687266	+	0.726406i	$0.741189\pi$
$224$	8.08182			0.539990
$225$	−0.496731	+	14.9918i	−0.0331154	+	0.999452i
$226$	11.9048			0.791893
$227$	1.36311	+	5.08721i	0.0904730	+	0.337650i	0.996294	−	0.0860102i	$-0.0274118\pi$
$227$	1.36311	+	5.08721i	0.0904730	+	0.337650i	−0.905821	+	0.423660i	$0.860745\pi$
$228$	−22.0805	−	7.36077i	−1.46231	−	0.487479i
$229$	12.4745	−	7.20213i	0.824335	−	0.475930i	−0.0275739	−	0.999620i	$-0.508778\pi$
$229$	12.4745	−	7.20213i	0.824335	−	0.475930i	0.851909	+	0.523690i	$0.175445\pi$
$230$	−0.226556	−	5.21502i	−0.0149387	−	0.343868i
$231$	10.2215	−	5.11042i	0.672524	−	0.336241i
$232$	4.44941	−	1.19222i	0.292118	−	0.0782728i
$233$	18.2564	+	18.2564i	1.19602	+	1.19602i	0.975349	+	0.220667i	$0.0708236\pi$
$233$	18.2564	+	18.2564i	1.19602	+	1.19602i	0.220667	+	0.975349i	$0.429176\pi$
$234$	26.3813	+	3.17978i	1.72460	+	0.207869i
$235$	−8.28541	+	2.61040i	−0.540481	+	0.170284i
$236$	−8.84240	−	5.10516i	−0.575591	−	0.332318i
$237$	12.2353	−	2.50344i	0.794767	−	0.162616i
$238$	−2.51800	−	0.674696i	−0.163218	−	0.0437340i
$239$	12.8838	+	22.3154i	0.833386	+	1.44347i	0.895338	+	0.445387i	$0.146934\pi$
$239$	12.8838	+	22.3154i	0.833386	+	1.44347i	−0.0619523	+	0.998079i	$0.519733\pi$
$240$	11.8398	−	2.96321i	0.764254	−	0.191275i
$241$	4.01161	−	6.94831i	0.258410	−	0.447580i	−0.707406	−	0.706808i	$-0.750135\pi$
$241$	4.01161	−	6.94831i	0.258410	−	0.447580i	0.965816	+	0.259228i	$0.0834680\pi$
$242$	48.0307	−	48.0307i	3.08753	−	3.08753i
$243$	−13.7870	+	7.27458i	−0.884434	+	0.466664i
$244$			29.0050i			1.85685i
$245$	−1.20103	−	1.88614i	−0.0767309	−	0.120501i
$246$	20.6995	+	1.24297i	1.31975	+	0.0792491i
$247$	6.25252	−	23.3347i	0.397838	−	1.48475i
$248$	−0.829023	+	3.09396i	−0.0526430	+	0.196466i
$249$	3.87531	−	5.86909i	0.245588	−	0.371939i
$250$	21.5732	−	8.91942i	1.36441	−	0.564114i
$251$		−	19.1985i		−	1.21180i	−0.795541	−	0.605900i	$-0.792813\pi$
$251$		−	19.1985i		−	1.21180i	0.795541	−	0.605900i	$-0.207187\pi$
$252$	4.37064	+	5.56864i	0.275325	+	0.350791i
$253$	−5.21605	+	5.21605i	−0.327930	+	0.327930i
$254$	17.8334	−	30.8883i	1.11897	−	1.93811i
$255$	−4.83472	−	0.0800738i	−0.302762	−	0.00501442i
$256$	−4.40139	−	7.62344i	−0.275087	−	0.476465i
$257$	−10.8449	−	2.90588i	−0.676486	−	0.181264i	−0.0958113	−	0.995400i	$-0.530545\pi$
$257$	−10.8449	−	2.90588i	−0.676486	−	0.181264i	−0.580675	+	0.814136i	$0.697211\pi$
$258$	9.28944	−	27.8660i	0.578335	−	1.73486i
$259$	0.469772	+	0.271223i	0.0291902	+	0.0168530i
$260$	−6.72601	−	21.3484i	−0.417129	−	1.32397i
$261$	−14.7206	−	11.0416i	−0.911183	−	0.683459i
$262$	19.1452	+	19.1452i	1.18280	+	1.18280i
$263$	−0.592659	+	0.158802i	−0.0365449	+	0.00979218i	−0.277045	−	0.960857i	$-0.589355\pi$
$263$	−0.592659	+	0.158802i	−0.0365449	+	0.00979218i	0.240500	+	0.970649i	$0.422689\pi$
$264$	7.16170	+	4.72880i	0.440772	+	0.291038i
$265$	0.708682	−	0.773053i	0.0435340	−	0.0474883i
$266$	10.2976	−	5.94533i	0.631387	−	0.364531i
$267$	−19.1510	+	16.9813i	−1.17202	+	1.03924i
$268$	1.10470	+	4.12281i	0.0674806	+	0.251841i
$269$	−17.0511			−1.03963			−0.519813	−	0.854280i	$-0.673998\pi$
$269$	−17.0511			−1.03963			−0.519813	+	0.854280i	$0.673998\pi$
$270$	19.1637	+	14.8765i	1.16626	+	0.905353i
$271$	10.9584			0.665677			0.332839	−	0.942984i	$-0.391994\pi$
$271$	10.9584			0.665677			0.332839	+	0.942984i	$0.391994\pi$
$272$	1.01829	+	3.80031i	0.0617429	+	0.230428i
$273$	−5.49755	+	4.87471i	−0.332727	+	0.295031i
$274$	−5.85730	+	3.38172i	−0.353853	+	0.204297i
$275$	−29.8924	−	13.9549i	−1.80258	−	0.841511i
$276$	−3.81321	−	2.51782i	−0.229528	−	0.151555i
$277$	−25.0316	+	6.70720i	−1.50400	+	0.402997i	−0.914439	−	0.404724i	$-0.867368\pi$
$277$	−25.0316	+	6.70720i	−1.50400	+	0.402997i	−0.589566	+	0.807720i	$0.700701\pi$
$278$	7.49611	+	7.49611i	0.449587	+	0.449587i
$279$	11.7674	−	5.02582i	0.704494	−	0.300888i
$280$	0.775710	−	1.48933i	0.0463575	−	0.0890047i
$281$	6.39734	+	3.69351i	0.381634	+	0.220336i	0.678529	−	0.734574i	$-0.262618\pi$
$281$	6.39734	+	3.69351i	0.381634	+	0.220336i	−0.296895	+	0.954910i	$0.595951\pi$
$282$	−4.44324	+	13.3286i	−0.264591	+	0.793707i
$283$	−5.81192	−	1.55730i	−0.345483	−	0.0925718i	0.0819054	−	0.996640i	$-0.473899\pi$
$283$	−5.81192	−	1.55730i	−0.345483	−	0.0925718i	−0.427388	+	0.904068i	$0.640566\pi$
$284$	14.6191	+	25.3209i	0.867481	+	1.50252i
$285$	15.8520	−	15.3355i	0.938992	−	0.908395i
$286$	−29.2199	+	50.6104i	−1.72781	+	2.99266i
$287$	−4.05451	+	4.05451i	−0.239330	+	0.239330i
$288$	9.03259	−	22.5001i	0.532250	−	1.32583i
$289$			15.4413i			0.908310i
$290$	−6.20448	+	27.9578i	−0.364340	+	1.64174i
$291$	3.35494	−	5.08101i	0.196670	−	0.297854i
$292$	−4.31287	+	16.0958i	−0.252391	+	0.941937i
$293$	5.11788	−	19.1002i	0.298990	−	1.11584i	−0.639007	−	0.769201i	$-0.720655\pi$
$293$	5.11788	−	19.1002i	0.298990	−	1.11584i	0.937997	−	0.346644i	$-0.112679\pi$
$294$	−3.60999	−	0.216774i	−0.210539	−	0.0126425i
$295$	8.16137	−	5.19687i	0.475174	−	0.302574i
$296$			0.407365i			0.0236776i
$297$	−2.80365	−	34.1686i	−0.162684	−	1.98267i
$298$	−1.60116	+	1.60116i	−0.0927527	+	0.0927527i
$299$	2.37139	−	4.10737i	0.137141	−	0.237535i
$300$	4.75711	−	19.8739i	0.274652	−	1.14742i
$301$	4.06106	+	7.03396i	0.234075	+	0.405431i
$302$	17.1259	+	4.58887i	0.985485	+	0.264060i
$303$	−3.09165	+	0.632579i	−0.177611	+	0.0363407i
$304$	−15.5418	−	8.97304i	−0.891381	−	0.514639i
$305$	−24.3774	−	12.6968i	−1.39584	−	0.727016i
$306$	−4.69260	+	6.25614i	−0.268258	+	0.357640i
$307$	−14.5769	−	14.5769i	−0.831949	−	0.831949i	0.155834	−	0.987783i	$-0.450193\pi$
$307$	−14.5769	−	14.5769i	−0.831949	−	0.831949i	−0.987783	+	0.155834i	$0.950193\pi$
$308$	−15.0383	+	4.02949i	−0.856884	+	0.229601i
$309$	−22.6996	+	11.3491i	−1.29133	+	0.645626i
$310$	−14.6791	−	13.4568i	−0.833716	−	0.764293i
$311$	−3.18899	+	1.84116i	−0.180831	+	0.104403i	−0.587683	−	0.809091i	$-0.699960\pi$
$311$	−3.18899	+	1.84116i	−0.180831	+	0.104403i	0.406852	+	0.913494i	$0.366626\pi$
$312$	−5.23462	−	1.74502i	−0.296352	−	0.0987924i
$313$	−3.61742	−	13.5004i	−0.204469	−	0.763088i	−0.989611	−	0.143772i	$-0.954077\pi$
$313$	−3.61742	−	13.5004i	−0.204469	−	0.763088i	0.785142	−	0.619316i	$-0.212590\pi$
$314$	34.4232			1.94262
$315$	−6.59341	+	1.23568i	−0.371497	+	0.0696226i
$316$	−17.0141			−0.957119
$317$	−2.22410	−	8.30046i	−0.124918	−	0.466200i	0.874919	−	0.484270i	$-0.160915\pi$
$317$	−2.22410	−	8.30046i	−0.124918	−	0.466200i	−0.999837	+	0.0180695i	$0.994248\pi$
$318$	−0.340005	−	1.66173i	−0.0190665	−	0.0931854i
$319$	35.0481	−	20.2350i	1.96232	−	1.13294i
$320$	−23.6176	+	1.02602i	−1.32027	+	0.0573564i
$321$	0.643523	−	10.7167i	0.0359180	−	0.598149i
$322$	2.25488	−	0.604194i	0.125660	−	0.0336704i
$323$	5.02747	+	5.02747i	0.279736	+	0.279736i
$324$	20.3881	−	5.94429i	1.13267	−	0.330239i
$325$	20.8866	+	3.69224i	1.15858	+	0.204809i
$326$	32.3798	+	18.6945i	1.79335	+	1.03539i
$327$	7.17245	+	8.08887i	0.396637	+	0.447315i
$328$	−4.15935	−	1.11449i	−0.229661	−	0.0615376i
$329$	−1.94245	−	3.36442i	−0.107091	−	0.185487i
$330$	−46.6422	+	25.9087i	−2.56757	+	1.42622i
$331$	−2.40825	+	4.17122i	−0.132370	+	0.229271i	−0.924590	−	0.380965i	$-0.875592\pi$
$331$	−2.40825	+	4.17122i	−0.132370	+	0.229271i	0.792220	+	0.610236i	$0.208925\pi$
$332$	−6.77518	+	6.77518i	−0.371836	+	0.371836i
$333$	1.28013	−	1.00473i	0.0701508	−	0.0550591i
$334$			6.85084i			0.374861i
$335$	−3.94861	−	0.876288i	−0.215736	−	0.0478767i
$336$	2.44087	+	4.88204i	0.133160	+	0.266337i
$337$	−3.74310	+	13.9694i	−0.203900	+	0.760964i	0.785882	+	0.618376i	$0.212209\pi$
$337$	−3.74310	+	13.9694i	−0.203900	+	0.760964i	−0.989782	+	0.142588i	$0.954458\pi$
$338$	2.69951	−	10.0747i	0.146834	−	0.547992i
$339$	4.41619	+	8.83294i	0.239855	+	0.479740i
$340$	6.43104	+	1.42719i	0.348772	+	0.0774005i
$341$			28.1414i			1.52394i
$342$	−5.04299	−	35.3137i	−0.272694	−	1.90955i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−3.04977	+	5.28235i	−0.164432	+	0.284805i
$345$	3.78533	−	2.10266i	0.203795	−	0.113203i
$346$	−2.35751	−	4.08332i	−0.126740	−	0.219521i
$347$	−34.7998	−	9.32458i	−1.86815	−	0.500570i	−0.999991	−	0.00428706i	$-0.998635\pi$
$347$	−34.7998	−	9.32458i	−1.86815	−	0.500570i	−0.868161	−	0.496283i	$-0.834698\pi$
$348$	16.6323	+	18.7574i	0.891583	+	1.00550i
$349$	4.23695	+	2.44620i	0.226799	+	0.130942i	0.609094	−	0.793098i	$-0.291533\pi$
$349$	4.23695	+	2.44620i	0.226799	+	0.130942i	−0.382296	+	0.924040i	$0.624866\pi$
$350$	5.98437	+	8.55448i	0.319878	+	0.457256i
$351$	7.42710	+	20.7536i	0.396429	+	1.10774i
$352$	37.7049	+	37.7049i	2.00968	+	2.00968i
$353$	6.48053	−	1.73645i	0.344924	−	0.0924221i	−0.0821983	−	0.996616i	$-0.526194\pi$
$353$	6.48053	−	1.73645i	0.344924	−	0.0924221i	0.427122	+	0.904194i	$0.359527\pi$
$354$	0.937988	−	15.6205i	0.0498535	−	0.830220i
$355$	−27.6805	+	1.20253i	−1.46913	+	0.0638235i
$356$	30.1983	−	17.4350i	1.60051	−	0.924053i
$357$	−0.433475	−	2.11856i	−0.0229419	−	0.112126i
$358$	0.448266	+	1.67295i	0.0236916	+	0.0884182i
$359$	12.9145			0.681602			0.340801	−	0.940135i	$-0.389302\pi$
$359$	12.9145			0.681602			0.340801	+	0.940135i	$0.389302\pi$
$360$	−3.27940	−	3.82415i	−0.172840	−	0.201550i
$361$	−13.4308			−0.706886
$362$	1.99139	+	7.43197i	0.104665	+	0.390616i
$363$	53.4546	+	17.8197i	2.80564	+	0.935292i
$364$	8.66884	−	5.00496i	0.454371	−	0.262331i
$365$	−11.6399	−	10.6706i	−0.609259	−	0.558527i
$366$	−39.7612	+	19.8793i	−2.07835	+	1.03911i
$367$	11.9484	−	3.20157i	0.623703	−	0.167121i	0.0668926	−	0.997760i	$-0.478692\pi$
$367$	11.9484	−	3.20157i	0.623703	−	0.167121i	0.556811	+	0.830639i	$0.312025\pi$
$368$	−2.49132	−	2.49132i	−0.129869	−	0.129869i
$369$	6.75643	+	15.8194i	0.351726	+	0.823526i
$370$	−2.24620	−	1.16992i	−0.116774	−	0.0608211i
$371$	0.406172	+	0.234504i	0.0210874	+	0.0121748i
$372$	−17.0785	+	3.49440i	−0.885477	+	0.181176i
$373$	−26.5117	−	7.10379i	−1.37272	−	0.367820i	−0.504251	−	0.863557i	$-0.668231\pi$
$373$	−26.5117	−	7.10379i	−1.37272	−	0.367820i	−0.868473	+	0.495737i	$0.834898\pi$
$374$	−8.59973	−	14.8952i	−0.444681	−	0.770210i
$375$	14.6207	+	12.6978i	0.755010	+	0.655714i
$376$	1.45874	−	2.52661i	0.0752287	−	0.130300i
$377$	−18.3991	+	18.3991i	−0.947600	+	0.947600i
$378$	−4.63818	+	9.80807i	−0.238562	+	0.504473i
$379$		−	33.0150i		−	1.69587i	−0.530101	−	0.847934i	$-0.677846\pi$
$379$		−	33.0150i		−	1.69587i	0.530101	−	0.847934i	$-0.322154\pi$
$380$	−25.3457	+	16.1392i	−1.30021	+	0.827926i
$381$	29.5336	+	1.77345i	1.51305	+	0.0908565i
$382$	2.07232	−	7.73400i	0.106029	−	0.395706i
$383$	2.87375	−	10.7250i	0.146842	−	0.548021i	−0.852825	−	0.522197i	$-0.825113\pi$
$383$	2.87375	−	10.7250i	0.146842	−	0.548021i	0.999667	−	0.0258235i	$-0.00822079\pi$
$384$	−5.64103	+	8.54325i	−0.287868	+	0.435971i
$385$	3.19632	−	14.4029i	0.162900	−	0.734037i
$386$		−	0.296754i		−	0.0151044i
$387$	24.1216	−	3.44470i	1.22617	−	0.175104i
$388$	−5.86543	+	5.86543i	−0.297772	+	0.297772i
$389$	−16.8934	+	29.2602i	−0.856528	+	1.48355i	0.0186931	+	0.999825i	$0.494049\pi$
$389$	−16.8934	+	29.2602i	−0.856528	+	1.48355i	−0.875221	+	0.483724i	$0.839284\pi$
$390$	24.6554	−	23.8520i	1.24847	−	1.20779i
$391$	0.697925	+	1.20884i	0.0352956	+	0.0611337i
$392$	0.725389	+	0.194367i	0.0366377	+	0.00981704i
$393$	−7.10301	+	21.3072i	−0.358299	+	1.07481i
$394$	−3.16062	−	1.82478i	−0.159230	−	0.0919313i
$395$	7.44785	−	14.2996i	0.374742	−	0.719491i
$396$	−5.58913	+	46.3706i	−0.280864	+	2.33021i
$397$	−5.27877	−	5.27877i	−0.264934	−	0.264934i	0.562121	−	0.827055i	$-0.309985\pi$
$397$	−5.27877	−	5.27877i	−0.264934	−	0.264934i	−0.827055	+	0.562121i	$0.809985\pi$
$398$	−2.36284	+	0.633121i	−0.118438	+	0.0317355i
$399$	8.23124	+	5.43501i	0.412077	+	0.272091i
$400$	6.66521	−	14.2774i	0.333260	−	0.713868i
$401$	3.88756	−	2.24448i	0.194135	−	0.112084i	−0.399782	−	0.916610i	$-0.630914\pi$
$401$	3.88756	−	2.24448i	0.194135	−	0.112084i	0.593917	+	0.804526i	$0.297581\pi$
$402$	−4.89458	+	4.34006i	−0.244120	+	0.216462i
$403$	−4.68294	−	17.4770i	−0.233274	−	0.870590i
$404$	4.29919			0.213893
$405$	−3.92889	+	19.7374i	−0.195228	+	0.980758i
$406$	−12.8073			−0.635616
$407$	0.926308	+	3.45703i	0.0459154	+	0.171359i
$408$	1.21507	−	1.07741i	0.0601550	−	0.0533398i
$409$	9.91941	−	5.72697i	0.490483	−	0.283181i	−0.234292	−	0.972166i	$-0.575277\pi$
$409$	9.91941	−	5.72697i	0.490483	−	0.283181i	0.724775	+	0.688986i	$0.241944\pi$
$410$	18.0906	−	19.7338i	0.893429	−	0.974581i
$411$	−4.68194	−	3.09144i	−0.230943	−	0.152490i
$412$	33.3965	−	8.94857i	1.64533	−	0.440864i
$413$	3.05967	+	3.05967i	0.150556	+	0.150556i
$414$	0.838052	−	6.95296i	0.0411880	−	0.341719i
$415$	−2.72843	−	8.66003i	−0.133933	−	0.425104i
$416$	−29.6906	−	17.1419i	−1.45570	−	0.840451i
$417$	−2.78111	+	8.34262i	−0.136192	+	0.408540i
$418$	75.7796	+	20.3051i	3.70650	+	0.993154i
$419$	3.62345	+	6.27600i	0.177017	+	0.306602i	0.940857	−	0.338803i	$-0.110022\pi$
$419$	3.62345	+	6.27600i	0.177017	+	0.306602i	−0.763840	+	0.645405i	$0.776689\pi$
$420$	9.13770	+	0.151341i	0.445874	+	0.00738468i
$421$	3.80452	−	6.58962i	0.185421	−	0.321159i	−0.758297	−	0.651909i	$-0.773968\pi$
$421$	3.80452	−	6.58962i	0.185421	−	0.321159i	0.943718	+	0.330750i	$0.107302\pi$
$422$	−16.8810	+	16.8810i	−0.821752	+	0.821752i
$423$	−11.5376	+	1.64764i	−0.560980	+	0.0801109i
$424$			0.352214i			0.0171050i
$425$	−4.01465	+	4.78025i	−0.194739	+	0.231876i
$426$	−24.6914	+	37.3948i	−1.19630	+	1.81178i
$427$	3.18140	−	11.8731i	0.153959	−	0.574582i
$428$	−3.78556	+	14.1279i	−0.182982	+	0.682898i
$429$	−48.3907	−	2.90579i	−2.33632	−	0.140293i
$430$	−20.3680	−	31.9867i	−0.982234	−	1.54254i
$431$		−	5.17363i		−	0.249205i	−0.992207	−	0.124602i	$-0.960234\pi$
$431$		−	5.17363i		−	0.249205i	0.992207	−	0.124602i	$-0.0397655\pi$
$432$	16.3198	−	1.33909i	0.785188	−	0.0644272i
$433$	12.5698	−	12.5698i	0.604066	−	0.604066i	−0.337323	−	0.941389i	$-0.609522\pi$
$433$	12.5698	−	12.5698i	0.604066	−	0.604066i	0.941389	+	0.337323i	$0.109522\pi$
$434$	4.45287	−	7.71259i	0.213744	−	0.370216i
$435$	−23.0454	+	5.76771i	−1.10494	+	0.276541i
$436$	−7.36408	−	12.7550i	−0.352676	−	0.610852i
$437$	−6.15002	−	1.64789i	−0.294195	−	0.0788294i
$438$	−25.0208	+	5.11946i	−1.19554	+	0.244617i
$439$	10.6098	+	6.12555i	0.506376	+	0.292356i	0.731343	−	0.682010i	$-0.238894\pi$
$439$	10.6098	+	6.12555i	0.506376	+	0.292356i	−0.224967	+	0.974366i	$0.572227\pi$
$440$	10.5673	−	3.32933i	0.503777	−	0.158720i
$441$	−1.17832	−	2.75891i	−0.0561105	−	0.131376i
$442$	7.81945	+	7.81945i	0.371933	+	0.371933i
$443$	4.00839	−	1.07405i	0.190444	−	0.0510294i	−0.162336	−	0.986736i	$-0.551903\pi$
$443$	4.00839	−	1.07405i	0.190444	−	0.0510294i	0.352781	+	0.935706i	$0.385236\pi$
$444$	−1.98298	+	0.991427i	−0.0941081	+	0.0470510i
$445$	1.43416	+	33.0124i	0.0679857	+	1.56494i
$446$	28.2869	−	16.3315i	1.33943	−	0.773317i
$447$	−1.78197	−	0.594041i	−0.0842844	−	0.0280972i
$448$	−2.73626	−	10.2119i	−0.129276	−	0.482465i
$449$	−0.695348			−0.0328155			−0.0164078	−	0.999865i	$-0.505223\pi$
$449$	−0.695348			−0.0328155			−0.0164078	+	0.999865i	$0.505223\pi$
$450$	30.5044	−	7.09987i	1.43799	−	0.334691i
$451$	−37.8318			−1.78143
$452$	−3.48210	−	12.9954i	−0.163784	−	0.611251i
$453$	2.94823	+	14.4091i	0.138520	+	0.677000i
$454$	9.52343	−	5.49835i	0.446956	−	0.258050i
$455$	0.411695	+	9.47666i	0.0193006	+	0.444273i
$456$	−0.444005	+	7.39410i	−0.0207924	+	0.346261i
$457$	−9.65843	+	2.58797i	−0.451802	+	0.121060i	−0.477542	−	0.878609i	$-0.658472\pi$
$457$	−9.65843	+	2.58797i	−0.451802	+	0.121060i	0.0257404	+	0.999669i	$0.491806\pi$
$458$	−21.2668	−	21.2668i	−0.993733	−	0.993733i
$459$	−6.38261	−	1.16098i	−0.297915	−	0.0541897i
$460$	−5.62650	+	1.77268i	−0.262337	+	0.0826519i
$461$	−26.5708	−	15.3407i	−1.23753	−	0.714487i	−0.268940	−	0.963157i	$-0.586673\pi$
$461$	−26.5708	−	15.3407i	−1.23753	−	0.714487i	−0.968588	+	0.248670i	$0.920007\pi$
$462$	−15.8307	−	17.8533i	−0.736509	−	0.830612i
$463$	1.86265	+	0.499096i	0.0865647	+	0.0231949i	0.301841	−	0.953358i	$-0.402399\pi$
$463$	1.86265	+	0.499096i	0.0865647	+	0.0231949i	−0.215277	+	0.976553i	$0.569065\pi$
$464$	9.66477	+	16.7399i	0.448676	+	0.777129i
$465$	4.53913	−	15.8833i	0.210497	−	0.736571i
$466$	26.9542	−	46.6861i	1.24863	−	2.16269i
$467$	17.2824	−	17.2824i	0.799732	−	0.799732i	−0.183321	−	0.983053i	$-0.558685\pi$
$467$	17.2824	−	17.2824i	0.799732	−	0.799732i	0.983053	+	0.183321i	$0.0586847\pi$
$468$	−4.24534	−	29.7281i	−0.196241	−	1.37418i
$469$		−	1.80884i		−	0.0835243i
$470$	9.74226	+	15.2996i	0.449377	+	0.705719i
$471$	12.7696	+	25.5409i	0.588394	+	1.17686i
$472$	−0.841032	+	3.13877i	−0.0387116	+	0.144474i
$473$	−13.8697	+	51.7626i	−0.637731	+	2.38005i
$474$	−11.6611	−	23.3237i	−0.535612	−	1.07129i
$475$	−2.46934	−	28.3668i	−0.113301	−	1.30156i
$476$			2.94602i			0.135031i
$477$	1.10682	−	0.868709i	0.0506779	−	0.0397754i
$478$	38.0440	−	38.0440i	1.74009	−	1.74009i
$479$	−5.84836	+	10.1297i	−0.267218	+	0.462836i	−0.968142	−	0.250400i	$-0.919438\pi$
$479$	−5.84836	+	10.1297i	−0.267218	+	0.462836i	0.700924	+	0.713236i	$0.252771\pi$
$480$	−15.1993	−	27.3627i	−0.693752	−	1.24893i
$481$	−1.15055	−	1.99281i	−0.0524606	−	0.0908645i
$482$	−16.1815	−	4.33582i	−0.737047	−	0.197491i
$483$	1.28476	+	1.44892i	0.0584588	+	0.0659280i
$484$	−66.4796	−	38.3820i	−3.02180	−	1.74464i
$485$	−2.36206	−	7.49719i	−0.107256	−	0.340430i
$486$	22.1222	+	23.8748i	1.00348	+	1.08298i
$487$	−18.0381	−	18.0381i	−0.817383	−	0.817383i	0.168345	−	0.985728i	$-0.446158\pi$
$487$	−18.0381	−	18.0381i	−0.817383	−	0.817383i	−0.985728	+	0.168345i	$0.946158\pi$
$488$	8.91647	−	2.38916i	0.403630	−	0.108152i
$489$	−1.85908	+	30.9596i	−0.0840704	+	1.40004i
$490$	−3.15499	+	3.44157i	−0.142528	+	0.155474i
$491$	36.0200	−	20.7962i	1.62556	−	0.938518i	0.640166	−	0.768237i	$-0.278866\pi$
$491$	36.0200	−	20.7962i	1.62556	−	0.938518i	0.985395	−	0.170281i	$-0.0544677\pi$
$492$	−4.69768	−	22.9594i	−0.211788	−	1.03509i
$493$	−1.98204	−	7.39707i	−0.0892666	−	0.333147i
$494$	−50.4412			−2.26946
$495$	−36.5258	−	24.9959i	−1.64171	−	1.12348i
$496$	−13.4411			−0.603521
$497$	−3.20697	−	11.9686i	−0.143852	−	0.536864i
$498$	−13.9313	−	4.64414i	−0.624274	−	0.208109i
$499$	8.08891	−	4.67013i	0.362109	−	0.209064i	−0.307896	−	0.951420i	$-0.599625\pi$
$499$	8.08891	−	4.67013i	0.362109	−	0.209064i	0.670006	+	0.742356i	$0.266292\pi$
$500$	−16.0466	−	20.9406i	−0.717626	−	0.936493i
$501$	−5.08309	+	2.54139i	−0.227096	+	0.113541i
$502$	−38.7203	+	10.3751i	−1.72817	+	0.463062i
$503$	−3.51479	−	3.51479i	−0.156717	−	0.156717i	0.624393	−	0.781110i	$-0.285346\pi$
$503$	−3.51479	−	3.51479i	−0.156717	−	0.156717i	−0.781110	+	0.624393i	$0.785346\pi$
$504$	1.35185	−	1.80228i	0.0602163	−	0.0802799i
$505$	−1.88195	+	3.61327i	−0.0837456	+	0.160789i
$506$	13.3387	+	7.70111i	0.592978	+	0.342356i
$507$	8.47651	−	1.73437i	0.376455	−	0.0770259i
$508$	−38.9342	−	10.4324i	−1.72743	−	0.462863i
$509$	−11.0294	−	19.1035i	−0.488870	−	0.846748i	0.511048	−	0.859552i	$-0.329258\pi$
$509$	−11.0294	−	19.1035i	−0.488870	−	0.846748i	−0.999918	+	0.0128042i	$0.995924\pi$
$510$	2.45123	+	9.79410i	0.108542	+	0.433690i
$511$	3.53093	−	6.11575i	0.156199	−	0.270545i
$512$	−21.3556	+	21.3556i	−0.943794	+	0.943794i
$513$	24.3308	−	16.8417i	1.07423	−	0.743579i
$514$			23.4427i			1.03401i
$515$	−7.09830	+	31.9854i	−0.312788	+	1.40945i
$516$	−33.1359	−	1.98976i	−1.45873	−	0.0875944i
$517$	6.63405	−	24.7586i	0.291765	−	1.08888i
$518$	0.293143	−	1.09402i	0.0128800	−	0.0480687i
$519$	2.15515	−	3.26394i	0.0946006	−	0.143271i
$520$	−6.00871	+	3.82613i	−0.263499	+	0.167787i
$521$		−	1.78035i		−	0.0779987i	−0.999239	−	0.0389993i	$-0.987583\pi$
$521$		−	1.78035i		−	0.0779987i	0.999239	−	0.0389993i	$-0.0124170\pi$
$522$	−14.3140	+	35.6560i	−0.626506	+	1.56062i
$523$	−17.3557	+	17.3557i	−0.758913	+	0.758913i	−0.976124	−	0.217212i	$-0.930304\pi$
$523$	−17.3557	+	17.3557i	−0.758913	+	0.758913i	0.217212	+	0.976124i	$0.430304\pi$
$524$	15.2992	−	26.4990i	0.668350	−	1.15762i
$525$	−4.12718	+	7.61357i	−0.180125	+	0.332283i
$526$	0.640557	+	1.10948i	0.0279296	+	0.0483755i
$527$	5.14365	+	1.37824i	0.224061	+	0.0600370i
$528$	−11.3890	+	34.1642i	−0.495644	+	1.48681i
$529$	18.8361	+	10.8750i	0.818959	+	0.472826i
$530$	−1.94210	−	1.01153i	−0.0843594	−	0.0439380i
$531$	11.9378	−	5.09862i	0.518058	−	0.221261i
$532$	−9.50200	−	9.50200i	−0.411964	−	0.411964i
$533$	23.4951	−	6.29549i	1.01769	−	0.272688i
$534$	44.5978	+	29.4475i	1.92994	+	1.27432i
$535$	−10.2167	−	9.36600i	−0.441708	−	0.404928i
$536$	1.17641	−	0.679198i	0.0508130	−	0.0293369i
$537$	−1.07499	+	0.953197i	−0.0463891	+	0.0411335i
$538$	9.21460	+	34.3893i	0.397269	+	1.48263i
$539$	6.59786			0.284190
$540$	10.6340	−	25.2706i	0.457615	−	1.08747i
$541$	25.0749			1.07805			0.539027	−	0.842289i	$-0.318792\pi$
$541$	25.0749			1.07805			0.539027	+	0.842289i	$0.318792\pi$
$542$	−5.92204	−	22.1014i	−0.254373	−	0.949334i
$543$	−4.77555	+	4.23451i	−0.204938	+	0.181720i
$544$	8.73826	−	5.04504i	0.374650	−	0.216304i
$545$	13.9436	−	0.605751i	0.597276	−	0.0259475i
$546$	12.8024	+	8.45332i	0.547893	+	0.361769i
$547$	21.3223	−	5.71329i	0.911675	−	0.244283i	0.227652	−	0.973743i	$-0.426895\pi$
$547$	21.3223	−	5.71329i	0.911675	−	0.244283i	0.684023	+	0.729460i	$0.260229\pi$
$548$	5.40476	+	5.40476i	0.230880	+	0.230880i
$549$	−29.4996	−	22.1271i	−1.25901	−	0.944360i
$550$	−11.9906	+	67.8294i	−0.511279	+	2.89225i
$551$	30.2511	+	17.4655i	1.28874	+	0.744054i
$552$	−0.459912	+	1.37962i	−0.0195752	+	0.0587205i
$553$	6.96471	+	1.86619i	0.296169	+	0.0793583i
$554$	27.0547	+	46.8600i	1.14944	+	1.99089i
$555$	0.0347906	−	2.10060i	0.00147678	−	0.0891653i
$556$	5.99025	−	10.3754i	0.254043	−	0.440016i
$557$	9.24065	−	9.24065i	0.391539	−	0.391539i	−0.483697	−	0.875236i	$-0.660706\pi$
$557$	9.24065	−	9.24065i	0.391539	−	0.391539i	0.875236	+	0.483697i	$0.160706\pi$
$558$	−16.4954	−	21.0169i	−0.698308	−	0.889715i
$559$		−	34.4547i		−	1.45728i
$560$	6.87917	+	1.52664i	0.290698	+	0.0645125i
$561$	7.86156	−	11.9062i	0.331915	−	0.502681i
$562$	3.99201	−	14.8984i	0.168393	−	0.628451i
$563$	−11.8149	+	44.0938i	−0.497939	+	1.85833i	0.0149674	+	0.999888i	$0.495236\pi$
$563$	−11.8149	+	44.0938i	−0.497939	+	1.85833i	−0.512906	+	0.858445i	$0.671431\pi$
$564$	15.8493	+	0.951726i	0.667375	+	0.0400749i
$565$	12.4463	+	2.76212i	0.523619	+	0.116203i
$566$			12.5633i			0.528073i
$567$	−8.99784	+	0.197024i	−0.377874	+	0.00827425i
$568$	6.57977	−	6.57977i	0.276081	−	0.276081i
$569$	−1.59220	+	2.75778i	−0.0667487	+	0.115612i	−0.897468	−	0.441079i	$-0.854596\pi$
$569$	−1.59220	+	2.75778i	−0.0667487	+	0.115612i	0.830720	+	0.556691i	$0.187929\pi$
$570$	−39.4957	−	23.6834i	−1.65429	−	0.991991i
$571$	10.2284	+	17.7161i	0.428045	+	0.741395i	0.996699	−	0.0811812i	$-0.0258692\pi$
$571$	10.2284	+	17.7161i	0.428045	+	0.741395i	−0.568655	+	0.822576i	$0.692536\pi$
$572$	63.7936	+	17.0934i	2.66734	+	0.714713i
$573$	6.50712	−	1.33141i	0.271839	−	0.0556205i
$574$	10.3684	+	5.98619i	0.432768	+	0.249859i
$575$	0.973114	−	5.50480i	0.0405817	−	0.229566i
$576$	−31.4884	−	3.79535i	−1.31202	−	0.158139i
$577$	7.66993	+	7.66993i	0.319303	+	0.319303i	0.848499	−	0.529196i	$-0.177506\pi$
$577$	7.66993	+	7.66993i	0.319303	+	0.319303i	−0.529196	+	0.848499i	$0.677506\pi$
$578$	31.1425	−	8.34461i	1.29536	−	0.347090i
$579$	0.220182	−	0.110084i	0.00915045	−	0.00457494i
$580$	32.3338	−	1.40468i	1.34259	−	0.0583262i
$581$	3.51654	−	2.03028i	0.145891	−	0.0842301i
$582$	−12.0606	−	4.02054i	−0.499928	−	0.166657i
$583$	0.800901	+	2.98900i	0.0331699	+	0.123792i
$584$	5.30330			0.219452
$585$	26.8435	+	9.44533i	1.10984	+	0.390517i
$586$	−41.2877			−1.70558
$587$	6.84296	+	25.5383i	0.282439	+	1.05408i	0.950690	+	0.310142i	$0.100377\pi$
$587$	6.84296	+	25.5383i	0.282439	+	1.05408i	−0.668251	+	0.743936i	$0.732957\pi$
$588$	0.819274	+	4.00411i	0.0337863	+	0.165127i
$589$	−21.0355	+	12.1448i	−0.866752	+	0.500420i
$590$	−14.8917	−	13.6517i	−0.613083	−	0.562032i
$591$	0.181466	−	3.02200i	0.00746453	−	0.124308i
$592$	−1.65117	+	0.442429i	−0.0678625	+	0.0181837i
$593$	33.2189	+	33.2189i	1.36414	+	1.36414i	0.868570	+	0.495566i	$0.165039\pi$
$593$	33.2189	+	33.2189i	1.36414	+	1.36414i	0.495566	+	0.868570i	$0.334961\pi$
$594$	−67.3974	+	24.1196i	−2.76535	+	0.989637i
$595$	−2.47599	−	1.28961i	−0.101506	−	0.0528687i
$596$	2.21618	+	1.27951i	0.0907781	+	0.0524108i
$597$	−1.34627	−	1.51829i	−0.0550993	−	0.0621393i
$598$	−9.56541	−	2.56304i	−0.391159	−	0.104811i
$599$	−9.59658	−	16.6218i	−0.392106	−	0.679147i	0.600621	−	0.799534i	$-0.294920\pi$
$599$	−9.59658	−	16.6218i	−0.392106	−	0.679147i	−0.992727	+	0.120387i	$0.961587\pi$
$600$	−6.50132	+	0.174635i	−0.265415	+	0.00712945i
$601$	7.37860	−	12.7801i	0.300979	−	0.521311i	−0.675379	−	0.737471i	$-0.736020\pi$
$601$	7.37860	−	12.7801i	0.300979	−	0.521311i	0.976358	+	0.216160i	$0.0693532\pi$
$602$	11.9917	−	11.9917i	0.488745	−	0.488745i
$603$	−5.03587	−	2.02163i	−0.205076	−	0.0823272i
$604$		−	20.0370i		−	0.815296i
$605$	61.3594	−	39.0715i	2.49462	−	1.58848i
$606$	2.94657	+	5.89351i	0.119696	+	0.239407i
$607$	−10.4409	+	38.9658i	−0.423781	+	1.58157i	0.342789	+	0.939412i	$0.388628\pi$
$607$	−10.4409	+	38.9658i	−0.423781	+	1.58157i	−0.766570	+	0.642160i	$0.778038\pi$
$608$	−11.9120	+	44.4562i	−0.483095	+	1.80294i
$609$	−4.75100	−	9.50259i	−0.192520	−	0.385065i
$610$	−12.4336	+	56.0266i	−0.503421	+	2.26845i
$611$			16.4801i			0.666713i
$612$	8.20184	+	3.29260i	0.331540	+	0.133095i
$613$	29.4787	−	29.4787i	1.19064	−	1.19064i	0.213746	−	0.976889i	$-0.431434\pi$
$613$	29.4787	−	29.4787i	1.19064	−	1.19064i	0.976889	−	0.213746i	$-0.0685664\pi$
$614$	−21.5217	+	37.2768i	−0.868547	+	1.50437i
$615$	21.3527	+	6.10216i	0.861023	+	0.246063i
$616$	2.47742	+	4.29102i	0.0998182	+	0.172890i
$617$	−39.8503	−	10.6779i	−1.60431	−	0.429875i	−0.657972	−	0.753042i	$-0.728585\pi$
$617$	−39.8503	−	10.6779i	−1.60431	−	0.429875i	−0.946342	+	0.323168i	$0.895252\pi$
$618$	35.1563	+	39.6482i	1.41419	+	1.59488i
$619$	13.6430	+	7.87682i	0.548360	+	0.316596i	0.748460	−	0.663179i	$-0.230793\pi$
$619$	13.6430	+	7.87682i	0.548360	+	0.316596i	−0.200100	+	0.979775i	$0.564127\pi$
$620$	−10.3960	+	19.9599i	−0.417513	+	0.801609i
$621$	5.46975	−	1.95746i	0.219493	−	0.0785502i
$622$	5.43668	+	5.43668i	0.217991	+	0.217991i
$623$	−14.2740	+	3.82470i	−0.571875	+	0.153233i
$624$	1.38788	−	23.1126i	0.0555596	−	0.925245i
$625$	24.6240	−	4.31979i	0.984958	−	0.172791i
$626$	−25.2732	+	14.5915i	−1.01012	+	0.583194i
$627$	13.0455	+	63.7583i	0.520987	+	2.54626i
$628$	−10.0687	−	37.5768i	−0.401784	−	1.49948i
$629$	0.677238			0.0270033
$630$	6.05530	+	12.6301i	0.241249	+	0.503193i
$631$	−17.7324			−0.705915			−0.352957	−	0.935639i	$-0.614824\pi$
$631$	−17.7324			−0.705915			−0.352957	+	0.935639i	$0.614824\pi$
$632$	1.40147	+	5.23034i	0.0557473	+	0.208052i
$633$	−18.7873	−	6.26295i	−0.746727	−	0.248930i
$634$	−15.5387	+	8.97129i	−0.617122	+	0.356295i
$635$	25.8112	−	28.1557i	1.02429	−	1.11732i
$636$	−1.71452	+	0.857204i	−0.0679850	+	0.0339903i
$637$	−4.09754	+	1.09793i	−0.162351	+	0.0435017i
$638$	−59.7511	−	59.7511i	−2.36557	−	2.36557i
$639$	−36.9052	−	4.44825i	−1.45995	−	0.175970i
$640$	3.97159	+	12.6058i	0.156991	+	0.498289i
$641$	−30.9950	−	17.8950i	−1.22423	−	0.706808i	−0.258411	−	0.966035i	$-0.583199\pi$
$641$	−30.9950	−	17.8950i	−1.22423	−	0.706808i	−0.965817	+	0.259227i	$0.916532\pi$
$642$	−21.9616	+	4.49354i	−0.866756	+	0.177346i
$643$	−33.4435	−	8.96115i	−1.31888	−	0.353393i	−0.470323	−	0.882494i	$-0.655863\pi$
$643$	−33.4435	−	8.96115i	−1.31888	−	0.353393i	−0.848559	+	0.529101i	$0.822529\pi$
$644$	−1.31909	−	2.28473i	−0.0519794	−	0.0900310i
$645$	16.1774	−	26.9782i	0.636984	−	1.06227i
$646$	7.42268	−	12.8565i	0.292041	−	0.505831i
$647$	−31.6342	+	31.6342i	−1.24367	+	1.24367i	−0.285199	+	0.958468i	$0.592060\pi$
$647$	−31.6342	+	31.6342i	−1.24367	+	1.24367i	−0.958468	+	0.285199i	$0.907940\pi$
$648$	−3.50673	−	5.77791i	−0.137757	−	0.226978i
$649$			28.5491i			1.12065i
$650$	−3.84068	−	44.1202i	−0.150644	−	1.73053i
$651$	7.37432	+	0.442817i	0.289022	+	0.0173554i
$652$	10.9361	−	40.8141i	0.428291	−	1.59841i
$653$	−8.39715	+	31.3386i	−0.328606	+	1.22637i	0.582031	+	0.813166i	$0.302258\pi$
$653$	−8.39715	+	31.3386i	−0.328606	+	1.22637i	−0.910637	+	0.413207i	$0.864409\pi$
$654$	12.4379	−	18.8369i	0.486359	−	0.736583i
$655$	15.5741	+	24.4581i	0.608529	+	0.955658i
$656$		−	18.0694i		−	0.705493i
$657$	−13.0802	−	16.6655i	−0.510306	−	0.650182i
$658$	−5.73577	+	5.73577i	−0.223604	+	0.223604i
$659$	11.1969	−	19.3936i	0.436169	−	0.755466i	−0.561222	−	0.827666i	$-0.689668\pi$
$659$	11.1969	−	19.3936i	0.436169	−	0.755466i	0.997390	+	0.0721994i	$0.0230018\pi$
$660$	41.9249	+	43.3370i	1.63192	+	1.68689i
$661$	13.3298	+	23.0879i	0.518470	+	0.898016i	0.999770	+	0.0214597i	$0.00683137\pi$
$661$	13.3298	+	23.0879i	0.518470	+	0.898016i	−0.481300	+	0.876556i	$0.659835\pi$
$662$	9.71411	+	2.60289i	0.377549	+	0.101164i
$663$	−2.90107	+	8.70248i	−0.112668	+	0.337976i
$664$	2.64085	+	1.52469i	0.102485	+	0.0591696i
$665$	12.1454	−	3.82654i	0.470980	−	0.148387i
$666$	−2.71818	−	2.03885i	−0.105327	−	0.0790038i
$667$	4.84920	+	4.84920i	0.187762	+	0.187762i
$668$	7.47845	−	2.00384i	0.289350	−	0.0775310i
$669$	22.6107	+	14.9296i	0.874181	+	0.577213i
$670$	0.366540	+	8.43726i	0.0141607	+	0.325960i
$671$	70.2353	−	40.5504i	2.71140	−	1.56543i
$672$	10.4737	−	9.28707i	0.404031	−	0.358257i
$673$	1.02959	+	3.84250i	0.0396880	+	0.148117i	0.982927	−	0.183998i	$-0.0589041\pi$
$673$	1.02959	+	3.84250i	0.0396880	+	0.148117i	−0.943239	+	0.332116i	$0.892237\pi$
$674$	30.1969			1.16314
$675$	16.5838	+	19.9995i	0.638309	+	0.769780i
$676$	−11.7873			−0.453356
$677$	−1.32837	−	4.95756i	−0.0510535	−	0.190534i	0.935690	−	0.352824i	$-0.114779\pi$
$677$	−1.32837	−	4.95756i	−0.0510535	−	0.190534i	−0.986743	+	0.162290i	$0.948112\pi$
$678$	15.4280	−	13.6801i	0.592510	−	0.525382i
$679$	3.04435	−	1.75766i	0.116832	−	0.0674527i
$680$	−0.0909931	−	2.09454i	−0.00348943	−	0.0803218i
$681$	7.61240	+	5.02640i	0.291708	+	0.192612i
$682$	56.7566	−	15.2079i	2.17332	−	0.582340i
$683$	11.9468	+	11.9468i	0.457133	+	0.457133i	0.897713	−	0.440580i	$-0.145227\pi$
$683$	11.9468	+	11.9468i	0.457133	+	0.457133i	−0.440580	+	0.897713i	$0.645227\pi$
$684$	−37.0738	+	15.8341i	−1.41755	+	0.605432i
$685$	−6.90835	+	2.17654i	−0.263955	+	0.0831615i
$686$	−1.80825	−	1.04399i	−0.0690391	−	0.0398598i
$687$	7.89014	−	23.6684i	0.301028	−	0.903006i
$688$	−24.7231	−	6.62454i	−0.942560	−	0.252558i
$689$	−0.994785	−	1.72302i	−0.0378983	−	0.0656418i
$690$	−6.28635	−	6.49808i	−0.239317	−	0.247378i
$691$	−21.1397	+	36.6151i	−0.804193	+	1.39290i	0.112642	+	0.993636i	$0.464069\pi$
$691$	−21.1397	+	36.6151i	−0.804193	+	1.39290i	−0.916835	+	0.399267i	$0.869265\pi$
$692$	−3.76784	+	3.76784i	−0.143232	+	0.143232i
$693$	7.37404	−	18.3687i	0.280117	−	0.697769i
$694$			75.2246i			2.85549i
$695$	6.09786	+	9.57632i	0.231305	+	0.363251i
$696$	4.39622	−	6.65801i	0.166638	−	0.252371i
$697$	−1.85283	+	6.91485i	−0.0701809	+	0.261919i
$698$	2.64390	−	9.86718i	0.100073	−	0.373478i
$699$	44.6385	+	2.68047i	1.68838	+	0.101385i
$700$	7.58775	−	9.03475i	0.286790	−	0.341481i
$701$		−	47.9855i		−	1.81239i	−0.422862	−	0.906194i	$-0.638974\pi$
$701$		−	47.9855i		−	1.81239i	0.422862	−	0.906194i	$-0.361026\pi$
$702$	37.8429	−	26.1947i	1.42829	−	0.988654i
$703$	−2.18434	+	2.18434i	−0.0823840	+	0.0823840i
$704$	34.8766	−	60.4080i	1.31446	−	2.27671i
$705$	−7.73783	+	12.9040i	−0.291423	+	0.485992i
$706$	−7.00428	−	12.1318i	−0.263610	−	0.456585i
$707$	−1.75987	−	0.471555i	−0.0661866	−	0.0177346i
$708$	−17.3259	+	3.54502i	−0.651146	+	0.133230i
$709$	−9.93162	−	5.73402i	−0.372990	−	0.215346i	0.301774	−	0.953379i	$-0.402421\pi$
$709$	−9.93162	−	5.73402i	−0.372990	−	0.215346i	−0.674764	+	0.738034i	$0.735755\pi$
$710$	17.3841	+	55.1772i	0.652414	+	2.07076i
$711$	12.9796	−	17.3043i	0.486772	−	0.648961i
$712$	−7.84718	−	7.84718i	−0.294086	−	0.294086i
$713$	−4.60617	+	1.23422i	−0.172503	+	0.0462219i
$714$	−4.03853	+	2.01913i	−0.151138	+	0.0755642i
$715$	−42.2916	+	46.1330i	−1.58162	+	1.72528i
$716$	1.69510	−	0.978664i	0.0633487	−	0.0365744i
$717$	42.3402	+	14.1146i	1.58122	+	0.527119i
$718$	−6.97913	−	26.0465i	−0.260459	−	0.972045i
$719$	−28.4510			−1.06104			−0.530522	−	0.847671i	$-0.678004\pi$
$719$	−28.4510			−1.06104			−0.530522	+	0.847671i	$0.678004\pi$
$720$	11.9387	−	17.4456i	0.444929	−	0.650161i
$721$	−14.6523			−0.545681
$722$	7.25815	+	27.0878i	0.270120	+	1.00810i
$723$	−2.78565	−	13.6146i	−0.103600	−	0.506331i
$724$	7.53035	−	4.34765i	0.279863	−	0.161579i
$725$	−12.9734	+	27.7900i	−0.481820	+	1.03209i
$726$	7.05204	−	117.439i	0.261726	−	4.35857i
$727$	−26.2326	+	7.02899i	−0.972912	+	0.260691i	−0.710057	−	0.704145i	$-0.751331\pi$
$727$	−26.2326	+	7.02899i	−0.972912	+	0.260691i	−0.262855	+	0.964835i	$0.584664\pi$
$728$	−2.25264	−	2.25264i	−0.0834884	−	0.0834884i
$729$	−9.50784	+	25.2706i	−0.352142	+	0.935946i
$730$	−15.2306	+	29.2422i	−0.563711	+	1.08230i
$731$	8.78182	+	5.07019i	0.324808	+	0.187528i
$732$	33.3305	+	37.5891i	1.23193	+	1.38933i
$733$	23.2935	+	6.24146i	0.860364	+	0.230534i	0.661916	−	0.749578i	$-0.269743\pi$
$733$	23.2935	+	6.24146i	0.860364	+	0.230534i	0.198447	+	0.980112i	$0.436410\pi$
$734$	−12.9141	−	22.3679i	−0.476668	−	0.825613i
$735$	−3.72390	−	1.06422i	−0.137358	−	0.0392542i
$736$	−4.51786	+	7.82517i	−0.166531	+	0.288440i
$737$	8.43892	−	8.43892i	0.310852	−	0.310852i
$738$	28.2539	−	22.1756i	1.04004	−	0.816294i
$739$		−	16.7704i		−	0.616907i	−0.951239	−	0.308454i	$-0.900189\pi$
$739$		−	16.7704i		−	0.616907i	0.951239	−	0.308454i	$-0.0998115\pi$
$740$	−0.620090	+	2.79417i	−0.0227950	+	0.102716i
$741$	−18.7117	−	37.4257i	−0.687390	−	1.37487i
$742$	0.253456	−	0.945911i	0.00930466	−	0.0347255i
$743$	7.44545	−	27.7868i	0.273147	−	1.01940i	−0.683926	−	0.729552i	$-0.739729\pi$
$743$	7.44545	−	27.7868i	0.273147	−	1.01940i	0.957073	−	0.289847i	$-0.0936046\pi$
$744$	2.48098	+	4.96228i	0.0909573	+	0.181926i
$745$	−2.04549	+	1.30250i	−0.0749409	+	0.0477197i
$746$			57.3087i			2.09822i
$747$	−1.72214	−	12.0593i	−0.0630096	−	0.441227i
$748$	−13.7443	+	13.7443i	−0.502543	+	0.502543i
$749$	3.09922	−	5.36801i	0.113243	−	0.196143i
$750$	17.7083	−	36.3496i	0.646615	−	1.32730i
$751$	3.29412	+	5.70559i	0.120204	+	0.208200i	0.919848	−	0.392275i	$-0.128312\pi$
$751$	3.29412	+	5.70559i	0.120204	+	0.208200i	−0.799644	+	0.600475i	$0.794978\pi$
$752$	11.8254	+	3.16859i	0.431226	+	0.115547i
$753$	−22.0616	−	24.8804i	−0.803970	−	0.906693i
$754$	47.0509	+	27.1649i	1.71349	+	0.989286i
$755$	16.8402	+	8.77112i	0.612878	+	0.319214i
$756$	12.0632	+	2.19427i	0.438736	+	0.0798047i
$757$	−7.07362	−	7.07362i	−0.257095	−	0.257095i	0.566776	−	0.823872i	$-0.308190\pi$
$757$	−7.07362	−	7.07362i	−0.257095	−	0.257095i	−0.823872	+	0.566776i	$0.808190\pi$
$758$	−66.5859	+	17.8416i	−2.41851	+	0.648038i
$759$	−0.765840	+	12.7537i	−0.0277982	+	0.462929i
$760$	7.04913	+	6.46216i	0.255699	+	0.234407i
$761$	2.36374	−	1.36470i	0.0856854	−	0.0494705i	−0.456545	−	0.889700i	$-0.650913\pi$
$761$	2.36374	−	1.36470i	0.0856854	−	0.0494705i	0.542230	+	0.840230i	$0.317580\pi$
$762$	−12.3835	−	60.5227i	−0.448606	−	2.19251i
$763$	1.61545	+	6.02895i	0.0584833	+	0.218263i
$764$	−9.04866			−0.327369
$765$	−6.35759	+	5.45195i	−0.229859	+	0.197116i
$766$	−23.1835			−0.837654
$767$	−4.75078	−	17.7301i	−0.171541	−	0.640199i
$768$	−14.4643	−	4.82185i	−0.521937	−	0.173994i
$769$	28.5821	−	16.5019i	1.03070	−	0.595073i	0.113513	−	0.993537i	$-0.463790\pi$
$769$	28.5821	−	16.5019i	1.03070	−	0.595073i	0.917184	+	0.398463i	$0.130456\pi$
$770$	−30.7755	+	1.33698i	−1.10907	+	0.0481815i
$771$	−17.3937	+	8.69632i	−0.626420	+	0.313190i
$772$	−0.323940	+	0.0867996i	−0.0116589	+	0.00312398i
$773$	−9.42164	−	9.42164i	−0.338873	−	0.338873i	0.517070	−	0.855943i	$-0.327023\pi$
$773$	−9.42164	−	9.42164i	−0.338873	−	0.338873i	−0.855943	+	0.517070i	$0.827023\pi$
$774$	−19.9829	−	46.7878i	−0.718272	−	1.68175i
$775$	−12.2246	−	17.4747i	−0.439120	−	0.627710i
$776$	2.28624	+	1.31996i	0.0820713	+	0.0473839i
$777$	0.920474	−	0.188337i	0.0330218	−	0.00675654i
$778$	68.1423	+	18.2587i	2.44302	+	0.654605i
$779$	−16.3269	−	28.2790i	−0.584971	−	1.01320i
$780$	−33.2487	−	19.9374i	−1.19049	−	0.713875i
$781$	40.8763	−	70.7998i	1.46267	−	2.53342i
$782$	2.06087	−	2.06087i	0.0736965	−	0.0736965i
$783$	−31.7655	+	2.60646i	−1.13521	+	0.0931474i
$784$			3.15131i			0.112547i
$785$	35.9891	+	7.98680i	1.28450	+	0.285061i
$786$	46.8117	+	2.81097i	1.66972	+	0.100264i
$787$	0.359992	−	1.34351i	0.0128323	−	0.0478909i	−0.959213	−	0.282685i	$-0.908775\pi$
$787$	0.359992	−	1.34351i	0.0128323	−	0.0478909i	0.972045	+	0.234794i	$0.0754416\pi$
$788$	−1.06749	+	3.98391i	−0.0380276	+	0.141921i
$789$	−0.585574	+	0.886843i	−0.0208470	+	0.0315725i
$790$	−32.8648	−	7.29345i	−1.16928	−	0.259489i
$791$			5.70157i			0.202724i
$792$	14.7153	−	2.10142i	0.522884	−	0.0746706i
$793$	−36.8711	+	36.8711i	−1.30933	+	1.30933i
$794$	−7.79371	+	13.4991i	−0.276588	+	0.479065i
$795$	0.0300805	−	1.81621i	0.00106685	−	0.0644143i
$796$	1.38224	+	2.39412i	0.0489923	+	0.0848572i
$797$	18.9256	+	5.07111i	0.670381	+	0.179628i	0.577926	−	0.816089i	$-0.303862\pi$
$797$	18.9256	+	5.07111i	0.670381	+	0.179628i	0.0924543	+	0.995717i	$0.470529\pi$
$798$	6.51327	−	19.5382i	0.230567	−	0.691644i
$799$	−4.20045	−	2.42513i	−0.148601	−	0.0857949i
$800$	−39.7922	−	7.03428i	−1.40687	−	0.248699i
$801$	−5.30508	+	44.0140i	−0.187446	+	1.55516i
$802$	−6.62763	−	6.62763i	−0.234030	−	0.234030i
$803$	45.0055	−	12.0592i	1.58821	−	0.425559i
$804$	6.16930	+	4.07353i	0.217574	+	0.143662i
$805$	2.49764	−	0.108505i	0.0880301	−	0.00382430i
$806$	−32.7175	+	18.8894i	−1.15242	+	0.665352i
$807$	−22.0975	+	19.5940i	−0.777869	+	0.689741i
$808$	−0.354127	−	1.32162i	−0.0124582	−	0.0464945i
$809$	32.5959			1.14601			0.573005	−	0.819552i	$-0.305778\pi$
$809$	32.5959			1.14601			0.573005	+	0.819552i	$0.305778\pi$
$810$	41.9302	−	2.74233i	1.47328	−	0.0963555i
$811$	36.6776			1.28792			0.643962	−	0.765057i	$-0.277289\pi$
$811$	36.6776			1.28792			0.643962	+	0.765057i	$0.277289\pi$
$812$	3.74609	+	13.9806i	0.131462	+	0.490623i
$813$	14.2016	−	12.5927i	0.498073	−	0.441644i
$814$	6.47167	−	3.73642i	0.226832	−	0.130962i
$815$	29.5152	+	27.0575i	1.03387	+	0.947783i
$816$	5.68671	+	3.75488i	0.199075	+	0.131447i
$817$	−44.6778	+	11.9714i	−1.56308	+	0.418826i
$818$	−16.9109	−	16.9109i	−0.591276	−	0.591276i
$819$	−1.52290	+	12.6348i	−0.0532143	+	0.441496i
$820$	−26.8330	−	13.9758i	−0.937049	−	0.488056i
$821$	−42.9515	−	24.7981i	−1.49902	−	0.865458i	−0.499018	−	0.866591i	$-0.666306\pi$
$821$	−42.9515	−	24.7981i	−1.49902	−	0.865458i	−0.999999	+	0.00113301i	$0.999639\pi$
$822$	−3.70476	+	11.1134i	−0.129219	+	0.387623i
$823$	8.35299	+	2.23818i	0.291167	+	0.0780180i	0.401446	−	0.915883i	$-0.368508\pi$
$823$	8.35299	+	2.23818i	0.291167	+	0.0780180i	−0.110279	+	0.993901i	$0.535174\pi$
$824$	−5.50179	−	9.52938i	−0.191664	−	0.331972i
$825$	−54.7751	+	16.2654i	−1.90703	+	0.566287i
$826$	4.51737	−	7.82431i	0.157179	−	0.272243i
$827$	−16.5668	+	16.5668i	−0.576085	+	0.576085i	−0.933822	−	0.357737i	$-0.883548\pi$
$827$	−16.5668	+	16.5668i	−0.576085	+	0.576085i	0.357737	+	0.933822i	$0.383548\pi$
$828$	−7.83505	+	1.11889i	−0.272287	+	0.0388840i
$829$		−	49.9138i		−	1.73358i	−0.498675	−	0.866789i	$-0.666180\pi$
$829$		−	49.9138i		−	1.73358i	0.498675	−	0.866789i	$-0.333820\pi$
$830$	−15.9914	+	10.1828i	−0.555069	+	0.353448i
$831$	−24.7324	+	37.4568i	−0.857957	+	1.29936i
$832$	−11.6074	+	43.3196i	−0.402416	+	1.50184i
$833$	0.323133	−	1.20595i	0.0111959	−	0.0417836i
$834$	18.3286	+	1.10061i	0.634669	+	0.0381109i
$835$	−1.58951	+	7.16246i	−0.0550074	+	0.247867i
$836$		−	88.6610i		−	3.06641i
$837$	9.47467	−	20.0355i	0.327492	−	0.692528i
$838$	10.6995	−	10.6995i	0.369608	−	0.369608i
$839$	16.6610	−	28.8577i	0.575201	−	0.996277i	−0.420819	−	0.907145i	$-0.638257\pi$
$839$	16.6610	−	28.8577i	0.575201	−	0.996277i	0.996020	−	0.0891325i	$-0.0284095\pi$
$840$	−0.706155	−	2.82150i	−0.0243647	−	0.0973511i
$841$	−4.31188	−	7.46839i	−0.148685	−	0.257531i
$842$	−15.3462	−	4.11200i	−0.528865	−	0.141709i
$843$	12.5350	−	2.56477i	0.431728	−	0.0883352i
$844$	23.3651	+	13.4898i	0.804258	+	0.464339i
$845$	5.15981	−	9.90665i	0.177503	−	0.340799i
$846$	9.55807	+	22.3791i	0.328613	+	0.769411i
$847$	23.0034	+	23.0034i	0.790406	+	0.790406i
$848$	−1.42762	+	0.382531i	−0.0490248	+	0.0131362i
$849$	−9.32152	+	4.66046i	−0.319914	+	0.159947i
$850$	11.8105	+	5.51359i	0.405098	+	0.189115i
$851$	−0.525219	+	0.303236i	−0.0180043	+	0.0103948i
$852$	48.0427	+	16.0156i	1.64592	+	0.548685i
$853$	−11.1106	−	41.4653i	−0.380419	−	1.41974i	−0.845263	−	0.534351i	$-0.820556\pi$
$853$	−11.1106	−	41.4653i	−0.380419	−	1.41974i	0.464844	−	0.885393i	$-0.346110\pi$
$854$	−25.6654			−0.878253
$855$	2.92102	−	38.0901i	0.0998967	−	1.30265i
$856$	4.65490			0.159101
$857$	−6.85895	−	25.5979i	−0.234297	−	0.874409i	−0.978464	−	0.206416i	$-0.933820\pi$
$857$	−6.85895	−	25.5979i	−0.234297	−	0.874409i	0.744167	−	0.667993i	$-0.232847\pi$
$858$	20.2903	+	99.1663i	0.692698	+	3.38548i
$859$	−9.31118	+	5.37581i	−0.317693	+	0.183420i	−0.650364	−	0.759623i	$-0.725384\pi$
$859$	−9.31118	+	5.37581i	−0.317693	+	0.183420i	0.332671	+	0.943043i	$0.392050\pi$
$860$	−28.9595	+	31.5900i	−0.987511	+	1.07721i
$861$	−0.595299	+	9.91364i	−0.0202877	+	0.337856i
$862$	−10.4344	+	2.79588i	−0.355395	+	0.0952279i
$863$	−29.3248	−	29.3248i	−0.998229	−	0.998229i	0.00176968	−	0.999998i	$-0.499437\pi$
$863$	−29.3248	−	29.3248i	−0.998229	−	0.998229i	−0.999998	+	0.00176968i	$0.999437\pi$
$864$	−14.1498	−	39.5388i	−0.481385	−	1.34514i
$865$	−1.51734	−	4.81605i	−0.0515912	−	0.163751i
$866$	−32.1440	−	18.5584i	−1.09230	−	0.630639i
$867$	17.7440	+	20.0112i	0.602619	+	0.679616i
$868$	−9.72159	−	2.60489i	−0.329972	−	0.0884158i
$869$	23.7866	+	41.1996i	0.806904	+	1.39760i
$870$	24.0865	+	43.3618i	0.816608	+	1.47010i
$871$	−3.83662	+	6.64522i	−0.129999	+	0.225165i
$872$	−3.31444	+	3.31444i	−0.112241	+	0.112241i
$873$	−1.49089	−	10.4400i	−0.0504591	−	0.353341i
$874$			13.2941i			0.449680i
$875$	4.27179	+	10.3321i	0.144413	+	0.349288i
$876$	12.9069	+	25.8155i	0.436085	+	0.872225i
$877$	2.60600	−	9.72572i	0.0879983	−	0.328414i	−0.907867	−	0.419259i	$-0.862290\pi$
$877$	2.60600	−	9.72572i	0.0879983	−	0.328414i	0.995865	+	0.0908446i	$0.0289567\pi$
$878$	6.62060	−	24.7084i	0.223435	−	0.833869i
$879$	−15.3161	−	30.6341i	−0.516598	−	1.03326i
$880$	24.9716	+	39.2164i	0.841793	+	1.32198i
$881$			44.5622i			1.50134i	0.660679	+	0.750669i	$0.270268\pi$
$881$			44.5622i			1.50134i	−0.660679	+	0.750669i	$0.729732\pi$
$882$	−4.92748	+	3.86742i	−0.165917	+	0.130223i
$883$	−8.55117	+	8.55117i	−0.287770	+	0.287770i	−0.836198	−	0.548428i	$-0.815227\pi$
$883$	−8.55117	+	8.55117i	−0.287770	+	0.287770i	0.548428	+	0.836198i	$0.315227\pi$
$884$	6.24864	−	10.8230i	0.210164	−	0.364015i
$885$	4.60488	−	16.1134i	0.154791	−	0.541646i
$886$	−4.33235	−	7.50384i	−0.145548	−	0.252097i
$887$	28.2666	+	7.57402i	0.949100	+	0.254311i	0.699980	−	0.714162i	$-0.253192\pi$
$887$	28.2666	+	7.57402i	0.949100	+	0.254311i	0.249120	+	0.968473i	$0.419859\pi$
$888$	0.468116	+	0.527927i	0.0157089	+	0.0177161i
$889$	14.7934	+	8.54097i	0.496154	+	0.286455i
$890$	65.8055	−	20.7327i	2.20581	−	0.694961i
$891$	−42.8976	−	41.0592i	−1.43712	−	1.37554i
$892$	−26.1014	−	26.1014i	−0.873941	−	0.873941i
$893$	21.3699	−	5.72605i	0.715117	−	0.191615i
$894$	−0.235088	+	3.91497i	−0.00786253	+	0.130936i
$895$	0.0805024	+	1.85306i	0.00269090	+	0.0619408i
$896$	−5.11880	+	2.95534i	−0.171007	+	0.0987310i
$897$	−1.64669	−	8.04801i	−0.0549814	−	0.268715i
$898$	0.375773	+	1.40240i	0.0125397	+	0.0467988i
$899$	26.1622			0.872558
$900$	−16.6727	−	31.2222i	−0.555757	−	1.04074i
$901$	0.585551			0.0195075
$902$	20.4447	+	76.3005i	0.680732	+	2.54053i
$903$	13.3459	+	4.44900i	0.444123	+	0.148054i
$904$	−3.70811	+	2.14088i	−0.123330	+	0.0712045i
$905$	0.357626	+	8.23207i	0.0118879	+	0.273643i
$906$	27.4676	−	13.7329i	0.912550	−	0.456246i
$907$	−44.9405	+	12.0418i	−1.49222	+	0.399840i	−0.910487	−	0.413537i	$-0.864293\pi$
$907$	−44.9405	+	12.0418i	−1.49222	+	0.399840i	−0.581737	+	0.813377i	$0.697627\pi$
$908$	−8.78763	−	8.78763i	−0.291628	−	0.291628i
$909$	−3.27973	+	4.37251i	−0.108782	+	0.145027i
$910$	18.8904	−	5.95160i	0.626210	−	0.197293i
$911$	−40.7473	−	23.5255i	−1.35002	−	0.779434i	−0.361768	−	0.932268i	$-0.617827\pi$
$911$	−40.7473	−	23.5255i	−1.35002	−	0.779434i	−0.988252	+	0.152834i	$0.951160\pi$
$912$	−30.4526	+	6.23086i	−1.00839	+	0.206325i
$913$	25.8781	+	6.93401i	0.856439	+	0.229482i
$914$	10.4390	+	18.0809i	0.345292	+	0.598063i
$915$	−46.1822	+	11.5583i	−1.52674	+	0.382106i
$916$	−16.9946	+	29.4356i	−0.561518	+	0.972578i
$917$	−9.16925	+	9.16925i	−0.302795	+	0.302795i
$918$	1.10773	+	13.5001i	0.0365604	+	0.445569i
$919$		−	33.6436i		−	1.10980i	−0.831917	−	0.554899i	$-0.812757\pi$
$919$		−	33.6436i		−	1.10980i	0.831917	−	0.554899i	$-0.187243\pi$
$920$	1.00840	+	1.58364i	0.0332461	+	0.0522109i
$921$	−35.6418	−	2.14024i	−1.17444	−	0.0705233i
$922$	−16.5805	+	61.8793i	−0.546050	+	2.03789i
$923$	−13.6042	+	50.7717i	−0.447789	+	1.67117i
$924$	−14.8585	+	22.5030i	−0.488808	+	0.740293i
$925$	−2.07693	−	1.74429i	−0.0682890	−	0.0573519i
$926$		−	4.02637i		−	0.132315i
$927$	−16.3761	+	40.7927i	−0.537860	+	1.33981i
$928$	35.0530	−	35.0530i	1.15067	−	1.15067i
$929$	23.1873	−	40.1616i	0.760750	−	1.31766i	−0.181714	−	0.983351i	$-0.558165\pi$
$929$	23.1873	−	40.1616i	0.760750	−	1.31766i	0.942464	−	0.334306i	$-0.108502\pi$
$930$	−34.4870	−	0.571183i	−1.13087	−	0.0187298i
$931$	2.84740	+	4.93185i	0.0933199	+	0.161635i
$932$	−58.8470	−	15.7680i	−1.92760	−	0.516499i
$933$	−2.01705	+	6.05063i	−0.0660351	+	0.198089i
$934$	−44.1952	−	25.5161i	−1.44611	−	0.834913i
$935$	−5.53497	−	17.5680i	−0.181013	−	0.574535i
$936$	−8.78909	+	3.75380i	−0.287280	+	0.122697i
$937$	36.6954	+	36.6954i	1.19879	+	1.19879i	0.974530	+	0.224256i	$0.0719951\pi$
$937$	36.6954	+	36.6954i	1.19879	+	1.19879i	0.224256	+	0.974530i	$0.428005\pi$
$938$	−3.64812	+	0.977512i	−0.119115	+	0.0319169i
$939$	−20.2018	−	13.3390i	−0.659259	−	0.435303i
$940$	13.8517	−	15.1098i	0.451792	−	0.492829i
$941$	−16.3526	+	9.44117i	−0.533079	+	0.307773i	−0.742269	−	0.670102i	$-0.766251\pi$
$941$	−16.3526	+	9.44117i	−0.533079	+	0.307773i	0.209190	+	0.977875i	$0.432917\pi$
$942$	44.6109	−	39.5568i	1.45350	−	1.28883i
$943$	−1.65922	−	6.19229i	−0.0540316	−	0.201649i
$944$	−13.6358			−0.443806
$945$	−7.12481	+	9.17808i	−0.231770	+	0.298563i
$946$	111.892			3.63792
$947$	−10.7868	−	40.2570i	−0.350525	−	1.30818i	−0.886023	−	0.463640i	$-0.846543\pi$
$947$	−10.7868	−	40.2570i	−0.350525	−	1.30818i	0.535499	−	0.844536i	$-0.320124\pi$
$948$	−22.0495	+	19.5515i	−0.716136	+	0.635002i
$949$	−25.9435	+	14.9785i	−0.842163	+	0.486223i
$950$	−55.8766	+	20.3099i	−1.81288	+	0.658941i
$951$	−12.4206	−	8.20123i	−0.402767	−	0.265943i
$952$	0.905641	−	0.242666i	0.0293520	−	0.00786484i
$953$	32.3282	+	32.3282i	1.04721	+	1.04721i	0.998829	+	0.0483853i	$0.0154075\pi$
$953$	32.3282	+	32.3282i	1.04721	+	1.04721i	0.0483853	+	0.998829i	$0.484592\pi$
$954$	−2.35018	−	1.76282i	−0.0760899	−	0.0570734i
$955$	3.96101	−	7.60499i	0.128175	−	0.246092i
$956$	−52.6570	−	30.4016i	−1.70305	−	0.983256i
$957$	22.1681	−	66.4986i	0.716591	−	2.14959i
$958$	23.5904	+	6.32102i	0.762170	+	0.204223i
$959$	−1.61961	−	2.80525i	−0.0522999	−	0.0905861i
$960$	−29.4283	+	28.4694i	−0.949796	+	0.918847i
$961$	6.40389	−	11.0919i	0.206577	−	0.357802i
$962$	−3.39741	+	3.39741i	−0.109537	+	0.109537i
$963$	−11.4809	−	14.6279i	−0.369968	−	0.471377i
$964$			18.9321i			0.609762i
$965$	0.0688523	−	0.310253i	0.00221643	−	0.00998740i
$966$	2.22793	−	3.37416i	0.0716824	−	0.108562i
$967$	12.1449	−	45.3252i	0.390552	−	1.45756i	−0.438673	−	0.898647i	$-0.644551\pi$
$967$	12.1449	−	45.3252i	0.390552	−	1.45756i	0.829225	−	0.558914i	$-0.188782\pi$
$968$	−6.32311	+	23.5982i	−0.203232	+	0.758474i
$969$	12.2926	+	0.738152i	0.394895	+	0.0237128i
$970$	−13.8441	+	8.81545i	−0.444508	+	0.283047i
$971$		−	34.3936i		−	1.10374i	−0.833929	−	0.551872i	$-0.813914\pi$
$971$		−	34.3936i		−	1.10374i	0.833929	−	0.551872i	$-0.186086\pi$
$972$	19.5913	−	31.1322i	0.628392	−	0.998565i
$973$	−3.59012	+	3.59012i	−0.115094	+	0.115094i
$974$	−26.6319	+	46.1277i	−0.853340	+	1.47803i
$975$	31.3109	−	19.2165i	1.00275	−	0.615419i
$976$	19.3679	+	33.5462i	0.619951	+	1.07379i
$977$	16.3607	+	4.38383i	0.523424	+	0.140251i	0.510850	−	0.859670i	$-0.329331\pi$
$977$	16.3607	+	4.38383i	0.523424	+	0.140251i	0.0125741	+	0.999921i	$0.495997\pi$
$978$	63.4451	−	12.9814i	2.02875	−	0.415099i
$979$	−84.4374	−	48.7500i	−2.69863	−	1.55806i
$980$	4.67967	+	2.43738i	0.149487	+	0.0778592i
$981$	18.5903	+	2.24072i	0.593544	+	0.0715408i
$982$	−61.4080	−	61.4080i	−1.95961	−	1.95961i
$983$	−43.9617	+	11.7795i	−1.40216	+	0.375708i	−0.879121	−	0.476599i	$-0.841869\pi$
$983$	−43.9617	+	11.7795i	−1.40216	+	0.375708i	−0.523041	+	0.852308i	$0.675203\pi$
$984$	−6.67102	+	3.33530i	−0.212664	+	0.106325i
$985$	−2.88101	−	2.64111i	−0.0917965	−	0.0841527i
$986$	−13.8476	+	7.99489i	−0.440996	+	0.254609i
$987$	−6.38349	−	2.12801i	−0.203189	−	0.0677353i
$988$	14.7539	+	55.0622i	0.469383	+	1.75176i
$989$	−9.08077			−0.288752
$990$	−30.6738	+	87.1745i	−0.974877	+	2.77059i
$991$	14.2781			0.453559			0.226779	−	0.973946i	$-0.427180\pi$
$991$	14.2781			0.453559			0.226779	+	0.973946i	$0.427180\pi$
$992$	8.92172	+	33.2963i	0.283265	+	1.05716i
$993$	1.67229	+	8.17311i	0.0530685	+	0.259366i
$994$	−22.4056	+	12.9359i	−0.710661	+	0.410301i
$995$	−2.61722	+	0.113700i	−0.0829713	+	0.00360453i
$996$	−0.994758	+	16.5659i	−0.0315201	+	0.524911i
$997$	10.6582	−	2.85586i	0.337549	−	0.0904460i	−0.0860630	−	0.996290i	$-0.527429\pi$
$997$	10.6582	−	2.85586i	0.337549	−	0.0904460i	0.423612	+	0.905844i	$0.360762\pi$
$998$	−13.7902	−	13.7902i	−0.436522	−	0.436522i
$999$	0.504423	−	2.77313i	0.0159592	−	0.0877379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.cc.a.92.6	✓	144
3.2	odd	2		945.2.cf.a.197.31		144
5.3	odd	4	inner	315.2.cc.a.218.6	yes	144
9.4	even	3		945.2.cf.a.827.31		144
9.5	odd	6	inner	315.2.cc.a.302.6	yes	144
15.8	even	4		945.2.cf.a.8.31		144
45.13	odd	12		945.2.cf.a.638.31		144
45.23	even	12	inner	315.2.cc.a.113.6	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.cc.a.92.6	✓	144	1.1	even	1	trivial
315.2.cc.a.113.6	yes	144	45.23	even	12	inner
315.2.cc.a.218.6	yes	144	5.3	odd	4	inner
315.2.cc.a.302.6	yes	144	9.5	odd	6	inner
945.2.cf.a.8.31		144	15.8	even	4
945.2.cf.a.197.31		144	3.2	odd	2
945.2.cf.a.638.31		144	45.13	odd	12
945.2.cf.a.827.31		144	9.4	even	3

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.cc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540409 - 2.01684i) q^{2} +(1.29595 - 1.14913i) q^{3} +(-2.04353 + 1.17983i) q^{4} +(-0.0970501 - 2.23396i) q^{5} +(-3.01795 - 1.99273i) q^{6} +(0.965926 - 0.258819i) q^{7} +(0.531022 + 0.531022i) q^{8} +(0.358997 - 2.97844i) q^{9} +O(q^{10})\)	\(q+(-0.540409 - 2.01684i) q^{2} +(1.29595 - 1.14913i) q^{3} +(-2.04353 + 1.17983i) q^{4} +(-0.0970501 - 2.23396i) q^{5} +(-3.01795 - 1.99273i) q^{6} +(0.965926 - 0.258819i) q^{7} +(0.531022 + 0.531022i) q^{8} +(0.358997 - 2.97844i) q^{9} +(-4.45308 + 1.40299i) q^{10} +(5.71391 + 3.29893i) q^{11} +(-1.29254 + 3.87730i) q^{12} +(-4.09754 - 1.09793i) q^{13} +(-1.04399 - 1.80825i) q^{14} +(-2.69289 - 2.78359i) q^{15} +(-1.57565 + 2.72911i) q^{16} +(0.882816 - 0.882816i) q^{17} +(-6.20103 + 0.885541i) q^{18} +5.69481i q^{19} +(2.83403 + 4.45067i) q^{20} +(0.954379 - 1.44539i) q^{21} +(3.56554 - 13.3068i) q^{22} +(-0.289368 + 1.07993i) q^{23} +(1.29839 + 0.0779666i) q^{24} +(-4.98116 + 0.433612i) q^{25} +8.85740i q^{26} +(-2.95738 - 4.27246i) q^{27} +(-1.66854 + 1.66854i) q^{28} +(3.06691 - 5.31204i) q^{29} +(-4.15878 + 6.93538i) q^{30} +(2.13262 + 3.69380i) q^{31} +(7.80644 + 2.09173i) q^{32} +(11.1959 - 2.29077i) q^{33} +(-2.25758 - 1.30341i) q^{34} +(-0.671935 - 2.13272i) q^{35} +(2.78045 + 6.51010i) q^{36} +(0.383567 + 0.383567i) q^{37} +(11.4855 - 3.07753i) q^{38} +(-6.57190 + 3.28574i) q^{39} +(1.13475 - 1.23782i) q^{40} +(-4.96575 + 2.86698i) q^{41} +(-3.43087 - 1.14372i) q^{42} +(2.10216 + 7.84536i) q^{43} -15.5687 q^{44} +(-6.68857 - 0.512926i) q^{45} +2.33443 q^{46} +(-1.00549 - 3.75253i) q^{47} +(1.09413 + 5.34743i) q^{48} +(0.866025 - 0.500000i) q^{49} +(3.56639 + 9.81186i) q^{50} +(0.129618 - 2.15856i) q^{51} +(9.66883 - 2.59076i) q^{52} +(0.331638 + 0.331638i) q^{53} +(-7.01866 + 8.27342i) q^{54} +(6.81514 - 13.0848i) q^{55} +(0.650366 + 0.375489i) q^{56} +(6.54408 + 7.38021i) q^{57} +(-12.3709 - 3.31477i) q^{58} +(2.16351 + 3.74731i) q^{59} +(8.78717 + 2.51119i) q^{60} +(6.14599 - 10.6452i) q^{61} +(6.29730 - 6.29730i) q^{62} +(-0.424114 - 2.96987i) q^{63} -10.5721i q^{64} +(-2.05507 + 9.26030i) q^{65} +(-10.6705 - 21.3423i) q^{66} +(0.468161 - 1.74720i) q^{67} +(-0.762486 + 2.84564i) q^{68} +(0.865979 + 1.73207i) q^{69} +(-3.93823 + 2.50773i) q^{70} -12.3908i q^{71} +(1.77225 - 1.39098i) q^{72} +(4.99349 - 4.99349i) q^{73} +(0.566308 - 0.980875i) q^{74} +(-5.95708 + 6.28595i) q^{75} +(-6.71893 - 11.6375i) q^{76} +(6.37304 + 1.70765i) q^{77} +(10.1783 + 11.4788i) q^{78} +(6.24438 + 3.60520i) q^{79} +(6.24964 + 3.25509i) q^{80} +(-8.74224 - 2.13850i) q^{81} +(8.46575 + 8.46575i) q^{82} +(3.92219 - 1.05095i) q^{83} +(-0.244981 + 4.07971i) q^{84} +(-2.05785 - 1.88650i) q^{85} +(14.6868 - 8.47941i) q^{86} +(-2.12966 - 10.4084i) q^{87} +(1.28241 + 4.78601i) q^{88} -14.7775 q^{89} +(2.58008 + 13.7669i) q^{90} -4.24209 q^{91} +(-0.682811 - 2.54829i) q^{92} +(7.00844 + 2.33634i) q^{93} +(-7.02485 + 4.05580i) q^{94} +(12.7220 - 0.552682i) q^{95} +(12.5205 - 6.25984i) q^{96} +(3.39553 - 0.909831i) q^{97} +(-1.47643 - 1.47643i) q^{98} +(11.8769 - 15.8343i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 4 q^{3}+O(q^{10}) \) 144 * q + 4 * q^3	\( 144 q + 4 q^{3} - 12 q^{11} - 16 q^{12} + 16 q^{15} + 72 q^{16} - 64 q^{18} - 48 q^{20} - 4 q^{21} - 24 q^{23} - 12 q^{25} - 32 q^{27} - 20 q^{30} - 60 q^{32} - 16 q^{33} - 16 q^{36} - 24 q^{37} + 72 q^{38} + 48 q^{41} - 40 q^{42} + 40 q^{45} - 48 q^{46} + 12 q^{47} + 104 q^{48} - 76 q^{51} - 24 q^{55} - 4 q^{57} - 92 q^{60} + 8 q^{63} - 72 q^{65} - 80 q^{66} - 12 q^{67} - 64 q^{72} - 108 q^{75} - 24 q^{76} + 72 q^{78} + 32 q^{81} - 96 q^{82} + 120 q^{83} - 48 q^{85} - 144 q^{86} + 116 q^{87} - 48 q^{88} + 252 q^{90} + 24 q^{91} + 156 q^{92} - 44 q^{93} + 120 q^{95} - 96 q^{96} - 60 q^{97}+O(q^{100}) \) 144 * q + 4 * q^3 - 12 * q^11 - 16 * q^12 + 16 * q^15 + 72 * q^16 - 64 * q^18 - 48 * q^20 - 4 * q^21 - 24 * q^23 - 12 * q^25 - 32 * q^27 - 20 * q^30 - 60 * q^32 - 16 * q^33 - 16 * q^36 - 24 * q^37 + 72 * q^38 + 48 * q^41 - 40 * q^42 + 40 * q^45 - 48 * q^46 + 12 * q^47 + 104 * q^48 - 76 * q^51 - 24 * q^55 - 4 * q^57 - 92 * q^60 + 8 * q^63 - 72 * q^65 - 80 * q^66 - 12 * q^67 - 64 * q^72 - 108 * q^75 - 24 * q^76 + 72 * q^78 + 32 * q^81 - 96 * q^82 + 120 * q^83 - 48 * q^85 - 144 * q^86 + 116 * q^87 - 48 * q^88 + 252 * q^90 + 24 * q^91 + 156 * q^92 - 44 * q^93 + 120 * q^95 - 96 * q^96 - 60 * q^97

Introduction

L-functions

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