LMFDB - Embedded newform 700.2.be.e.443.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(107,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 4]))

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

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

chi := DirichletCharacter("700.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.be (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			443.13
Character	$\chi$	$=$	700.443
Dual form			700.2.be.e.207.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809319 - 1.15974i) q^{2} +(0.551941 + 0.147892i) q^{3} +(-0.690004 - 1.87720i) q^{4} +(0.618214 - 0.520418i) q^{6} +(-2.54158 - 0.735093i) q^{7} +(-2.73551 - 0.719030i) q^{8} +(-2.31531 - 1.33674i) q^{9} +O(q^{10})$	\(q+(0.809319 - 1.15974i) q^{2} +(0.551941 + 0.147892i) q^{3} +(-0.690004 - 1.87720i) q^{4} +(0.618214 - 0.520418i) q^{6} +(-2.54158 - 0.735093i) q^{7} +(-2.73551 - 0.719030i) q^{8} +(-2.31531 - 1.33674i) q^{9} +(3.42960 - 1.98008i) q^{11} +(-0.103218 - 1.13815i) q^{12} +(-2.04987 - 2.04987i) q^{13} +(-2.90947 + 2.35266i) q^{14} +(-3.04779 + 2.59056i) q^{16} +(-0.580528 - 0.155552i) q^{17} +(-3.42410 + 1.60331i) q^{18} +(-1.00269 + 1.73671i) q^{19} +(-1.29409 - 0.781608i) q^{21} +(0.479259 - 5.57997i) q^{22} +(0.640717 + 2.39119i) q^{23} +(-1.40350 - 0.801422i) q^{24} +(-4.03632 + 0.718322i) q^{26} +(-2.29237 - 2.29237i) q^{27} +(0.373784 + 5.27828i) q^{28} -7.25964i q^{29} +(-2.83005 + 1.63393i) q^{31} +(0.537745 + 5.63124i) q^{32} +(2.18578 - 0.585677i) q^{33} +(-0.650233 + 0.547372i) q^{34} +(-0.911768 + 5.26867i) q^{36} +(-2.49187 - 9.29977i) q^{37} +(1.20264 + 2.56841i) q^{38} +(-0.828248 - 1.43457i) q^{39} -3.35439 q^{41} +(-1.95380 + 0.868240i) q^{42} +(3.31777 - 3.31777i) q^{43} +(-6.08345 - 5.07179i) q^{44} +(3.29171 + 1.19217i) q^{46} +(12.1147 - 3.24611i) q^{47} +(-2.06532 + 0.979091i) q^{48} +(5.91928 + 3.73660i) q^{49} +(-0.297413 - 0.171711i) q^{51} +(-2.43360 + 5.26244i) q^{52} +(0.779134 - 2.90777i) q^{53} +(-4.51381 + 0.803298i) q^{54} +(6.42396 + 3.83832i) q^{56} +(-0.810271 + 0.810271i) q^{57} +(-8.41932 - 5.87537i) q^{58} +(7.41735 + 12.8472i) q^{59} +(-2.11676 + 3.66633i) q^{61} +(-0.395476 + 4.60450i) q^{62} +(4.90192 + 5.09941i) q^{63} +(6.96599 + 3.93382i) q^{64} +(1.08976 - 3.00894i) q^{66} +(-0.984566 + 3.67445i) q^{67} +(0.108564 + 1.19710i) q^{68} +1.41455i q^{69} -4.86004i q^{71} +(5.37238 + 5.32145i) q^{72} +(2.53197 - 9.44944i) q^{73} +(-12.8021 - 4.63656i) q^{74} +(3.95201 + 0.683915i) q^{76} +(-10.1722 + 2.51146i) q^{77} +(-2.33405 - 0.200469i) q^{78} +(3.45719 - 5.98803i) q^{79} +(3.08400 + 5.34165i) q^{81} +(-2.71477 + 3.89023i) q^{82} +(5.46792 - 5.46792i) q^{83} +(-0.574310 + 2.96858i) q^{84} +(-1.16262 - 6.53289i) q^{86} +(1.07364 - 4.00690i) q^{87} +(-10.8054 + 2.95054i) q^{88} +(3.35292 + 1.93581i) q^{89} +(3.70307 + 6.71676i) q^{91} +(4.04665 - 2.85269i) q^{92} +(-1.80367 + 0.483291i) q^{93} +(6.03997 - 16.6770i) q^{94} +(-0.536012 + 3.18764i) q^{96} +(-1.11914 + 1.11914i) q^{97} +(9.12407 - 3.84074i) q^{98} -10.5874 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8}+O(q^{10}) $ 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8	$ 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8} - 10 q^{12} - 28 q^{16} - 4 q^{17} + 20 q^{18} + 4 q^{21} + 16 q^{22} - 4 q^{26} - 42 q^{28} + 38 q^{32} + 64 q^{33} + 16 q^{36} + 4 q^{37} - 12 q^{38} - 40 q^{41} - 78 q^{42} - 28 q^{46} - 12 q^{48} - 48 q^{52} + 24 q^{53} + 36 q^{56} + 16 q^{57} - 30 q^{58} - 20 q^{61} - 56 q^{62} + 44 q^{66} + 12 q^{68} - 44 q^{72} + 12 q^{73} + 112 q^{76} - 16 q^{77} - 64 q^{78} - 52 q^{81} + 34 q^{82} + 64 q^{86} - 16 q^{88} - 44 q^{92} - 12 q^{93} - 48 q^{96} + 24 q^{97} + 90 q^{98}+O(q^{100}) $ 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8 - 10 * q^12 - 28 * q^16 - 4 * q^17 + 20 * q^18 + 4 * q^21 + 16 * q^22 - 4 * q^26 - 42 * q^28 + 38 * q^32 + 64 * q^33 + 16 * q^36 + 4 * q^37 - 12 * q^38 - 40 * q^41 - 78 * q^42 - 28 * q^46 - 12 * q^48 - 48 * q^52 + 24 * q^53 + 36 * q^56 + 16 * q^57 - 30 * q^58 - 20 * q^61 - 56 * q^62 + 44 * q^66 + 12 * q^68 - 44 * q^72 + 12 * q^73 + 112 * q^76 - 16 * q^77 - 64 * q^78 - 52 * q^81 + 34 * q^82 + 64 * q^86 - 16 * q^88 - 44 * q^92 - 12 * q^93 - 48 * q^96 + 24 * q^97 + 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.809319	−	1.15974i	0.572275	−	0.820062i
$2$	0.809319	−	1.15974i	0.572275	−	0.820062i
$3$	0.551941	+	0.147892i	0.318663	+	0.0853856i	0.414605	−	0.910001i	$-0.363920\pi$
$3$	0.551941	+	0.147892i	0.318663	+	0.0853856i	−0.0959419	+	0.995387i	$0.530586\pi$
$4$	−0.690004	−	1.87720i	−0.345002	−	0.938602i
$5$		0			0
$5$		0			0
$6$	0.618214	−	0.520418i	0.252385	−	0.212460i
$7$	−2.54158	−	0.735093i	−0.960628	−	0.277839i
$7$	−2.54158	−	0.735093i	−0.960628	−	0.277839i
$8$	−2.73551	−	0.719030i	−0.967148	−	0.254216i
$9$	−2.31531	−	1.33674i	−0.771770	−	0.445581i
$10$		0			0
$11$	3.42960	−	1.98008i	1.03406	−	0.597017i	0.115917	−	0.993259i	$-0.463019\pi$
$11$	3.42960	−	1.98008i	1.03406	−	0.597017i	0.918146	+	0.396242i	$0.129686\pi$
$12$	−0.103218	−	1.13815i	−0.0297965	−	0.328556i
$13$	−2.04987	−	2.04987i	−0.568532	−	0.568532i	0.363185	−	0.931717i	$-0.381689\pi$
$13$	−2.04987	−	2.04987i	−0.568532	−	0.568532i	−0.931717	+	0.363185i	$0.881689\pi$
$14$	−2.90947	+	2.35266i	−0.777588	+	0.628774i
$15$		0			0
$16$	−3.04779	+	2.59056i	−0.761947	+	0.647639i
$17$	−0.580528	−	0.155552i	−0.140799	−	0.0377269i	0.187731	−	0.982220i	$-0.439887\pi$
$17$	−0.580528	−	0.155552i	−0.140799	−	0.0377269i	−0.328530	+	0.944493i	$0.606553\pi$
$18$	−3.42410	+	1.60331i	−0.807069	+	0.377904i
$19$	−1.00269	+	1.73671i	−0.230033	+	0.398428i	−0.957817	−	0.287377i	$-0.907217\pi$
$19$	−1.00269	+	1.73671i	−0.230033	+	0.398428i	0.727785	+	0.685805i	$0.240550\pi$
$20$		0			0
$21$	−1.29409	−	0.781608i	−0.282393	−	0.170561i
$22$	0.479259	−	5.57997i	0.102178	−	1.18965i
$23$	0.640717	+	2.39119i	0.133599	+	0.498597i	1.00000		0.000751542i	$-0.000239223\pi$
$23$	0.640717	+	2.39119i	0.133599	+	0.498597i	−0.866401	+	0.499349i	$0.833573\pi$
$24$	−1.40350	−	0.801422i	−0.286488	−	0.163590i
$25$		0			0
$26$	−4.03632	+	0.718322i	−0.791588	+	0.140874i
$27$	−2.29237	−	2.29237i	−0.441166	−	0.441166i
$28$	0.373784	+	5.27828i	0.0706386	+	0.997502i
$29$		−	7.25964i		−	1.34808i	−0.738694	−	0.674041i	$-0.764557\pi$
$29$		−	7.25964i		−	1.34808i	0.738694	−	0.674041i	$-0.235443\pi$
$30$		0			0
$31$	−2.83005	+	1.63393i	−0.508292	+	0.293462i	−0.732131	−	0.681164i	$-0.761474\pi$
$31$	−2.83005	+	1.63393i	−0.508292	+	0.293462i	0.223840	+	0.974626i	$0.428141\pi$
$32$	0.537745	+	5.63124i	0.0950609	+	0.995471i
$33$	2.18578	−	0.585677i	0.380495	−	0.101953i
$34$	−0.650233	+	0.547372i	−0.111514	+	0.0938735i
$35$		0			0
$36$	−0.911768	+	5.26867i	−0.151961	+	0.878111i
$37$	−2.49187	−	9.29977i	−0.409660	−	1.52887i	−0.795295	−	0.606222i	$-0.792684\pi$
$37$	−2.49187	−	9.29977i	−0.409660	−	1.52887i	0.385635	−	0.922651i	$-0.373982\pi$
$38$	1.20264	+	2.56841i	0.195094	+	0.416651i
$39$	−0.828248	−	1.43457i	−0.132626	−	0.229715i
$40$		0			0
$41$	−3.35439			−0.523868			−0.261934	−	0.965086i	$-0.584360\pi$
$41$	−3.35439			−0.523868			−0.261934	+	0.965086i	$0.584360\pi$
$42$	−1.95380	+	0.868240i	−0.301477	+	0.133972i
$43$	3.31777	−	3.31777i	0.505955	−	0.505955i	−0.407327	−	0.913282i	$-0.633539\pi$
$43$	3.31777	−	3.31777i	0.505955	−	0.505955i	0.913282	+	0.407327i	$0.133539\pi$
$44$	−6.08345	−	5.07179i	−0.917115	−	0.764602i
$45$		0			0
$46$	3.29171	+	1.19217i	0.485336	+	0.175776i
$47$	12.1147	−	3.24611i	1.76710	−	0.473494i	0.778966	−	0.627066i	$-0.215744\pi$
$47$	12.1147	−	3.24611i	1.76710	−	0.473494i	0.988137	+	0.153572i	$0.0490776\pi$
$48$	−2.06532	+	0.979091i	−0.298104	+	0.141320i
$49$	5.91928	+	3.73660i	0.845611	+	0.533799i
$50$		0			0
$51$	−0.297413	−	0.171711i	−0.0416461	−	0.0240444i
$52$	−2.43360	+	5.26244i	−0.337480	+	0.729770i
$53$	0.779134	−	2.90777i	0.107022	−	0.399413i	−0.891544	−	0.452933i	$-0.850378\pi$
$53$	0.779134	−	2.90777i	0.107022	−	0.399413i	0.998567	+	0.0535205i	$0.0170442\pi$
$54$	−4.51381	+	0.803298i	−0.614252	+	0.109315i
$55$		0			0
$56$	6.42396	+	3.83832i	0.858438	+	0.512918i
$57$	−0.810271	+	0.810271i	−0.107323	+	0.107323i
$58$	−8.41932	−	5.87537i	−1.10551	−	0.771474i
$59$	7.41735	+	12.8472i	0.965657	+	1.67257i	0.707839	+	0.706374i	$0.249670\pi$
$59$	7.41735	+	12.8472i	0.965657	+	1.67257i	0.257818	+	0.966193i	$0.416996\pi$
$60$		0			0
$61$	−2.11676	+	3.66633i	−0.271023	+	0.469426i	−0.969124	−	0.246574i	$-0.920695\pi$
$61$	−2.11676	+	3.66633i	−0.271023	+	0.469426i	0.698101	+	0.715999i	$0.254029\pi$
$62$	−0.395476	+	4.60450i	−0.0502255	+	0.584772i
$63$	4.90192	+	5.09941i	0.617584	+	0.642466i
$64$	6.96599	+	3.93382i	0.870749	+	0.491728i
$65$		0			0
$66$	1.08976	−	3.00894i	0.134140	−	0.370375i
$67$	−0.984566	+	3.67445i	−0.120284	+	0.448906i	−0.999628	−	0.0272817i	$-0.991315\pi$
$67$	−0.984566	+	3.67445i	−0.120284	+	0.448906i	0.879344	+	0.476187i	$0.157982\pi$
$68$	0.108564	+	1.19710i	0.0131653	+	0.145170i
$69$			1.41455i			0.170292i
$70$		0			0
$71$		−	4.86004i		−	0.576781i	−0.957513	−	0.288390i	$-0.906880\pi$
$71$		−	4.86004i		−	0.576781i	0.957513	−	0.288390i	$-0.0931201\pi$
$72$	5.37238	+	5.32145i	0.633142	+	0.627139i
$73$	2.53197	−	9.44944i	0.296345	−	1.10597i	−0.643799	−	0.765195i	$-0.722643\pi$
$73$	2.53197	−	9.44944i	0.296345	−	1.10597i	0.940143	−	0.340779i	$-0.110691\pi$
$74$	−12.8021	−	4.63656i	−1.48821	−	0.538990i
$75$		0			0
$76$	3.95201	+	0.683915i	0.453327	+	0.0784504i
$77$	−10.1722	+	2.51146i	−1.15922	+	0.286208i
$78$	−2.33405	−	0.200469i	−0.264279	−	0.0226987i
$79$	3.45719	−	5.98803i	0.388965	−	0.673706i	−0.603346	−	0.797480i	$-0.706166\pi$
$79$	3.45719	−	5.98803i	0.388965	−	0.673706i	0.992311	+	0.123773i	$0.0394995\pi$
$80$		0			0
$81$	3.08400	+	5.34165i	0.342667	+	0.593517i
$82$	−2.71477	+	3.89023i	−0.299796	+	0.429604i
$83$	5.46792	−	5.46792i	0.600182	−	0.600182i	−0.340179	−	0.940361i	$-0.610488\pi$
$83$	5.46792	−	5.46792i	0.600182	−	0.600182i	0.940361	+	0.340179i	$0.110488\pi$
$84$	−0.574310	+	2.96858i	−0.0626624	+	0.323899i
$85$		0			0
$86$	−1.16262	−	6.53289i	−0.125369	−	0.704460i
$87$	1.07364	−	4.00690i	0.115107	−	0.429584i
$88$	−10.8054	+	2.95054i	−1.15186	+	0.314528i
$89$	3.35292	+	1.93581i	0.355409	+	0.205195i	0.667065	−	0.745000i	$-0.267550\pi$
$89$	3.35292	+	1.93581i	0.355409	+	0.205195i	−0.311656	+	0.950195i	$0.600884\pi$
$90$		0			0
$91$	3.70307	+	6.71676i	0.388187	+	0.704108i
$92$	4.04665	−	2.85269i	0.421893	−	0.297413i
$93$	−1.80367	+	0.483291i	−0.187031	+	0.0501149i
$94$	6.03997	−	16.6770i	0.622975	−	1.72010i
$95$		0			0
$96$	−0.536012	+	3.18764i	−0.0547065	+	0.325337i
$97$	−1.11914	+	1.11914i	−0.113632	+	0.113632i	−0.761636	−	0.648005i	$-0.775604\pi$
$97$	−1.11914	+	1.11914i	−0.113632	+	0.113632i	0.648005	+	0.761636i	$0.275604\pi$
$98$	9.12407	−	3.84074i	0.921671	−	0.387973i
$99$	−10.5874			−1.06408
$100$		0			0
$101$	−8.93266	−	15.4718i	−0.888833	−	1.53950i	−0.841257	−	0.540636i	$-0.818184\pi$
$101$	−8.93266	−	15.4718i	−0.888833	−	1.53950i	−0.0475759	−	0.998868i	$-0.515150\pi$
$102$	−0.439843	+	0.205953i	−0.0435509	+	0.0203924i
$103$	2.90309	+	10.8345i	0.286050	+	1.06755i	0.948069	+	0.318066i	$0.103033\pi$
$103$	2.90309	+	10.8345i	0.286050	+	1.06755i	−0.662019	+	0.749487i	$0.730300\pi$
$104$	4.13352	+	7.08135i	0.405325	+	0.694384i
$105$		0			0
$106$	−2.74169	−	3.25691i	−0.266297	−	0.316339i
$107$	−7.59541	+	2.03518i	−0.734276	+	0.196749i	−0.606533	−	0.795059i	$-0.707440\pi$
$107$	−7.59541	+	2.03518i	−0.734276	+	0.196749i	−0.127743	+	0.991807i	$0.540773\pi$
$108$	−2.72150	+	5.88498i	−0.261876	+	0.566283i
$109$	0.350133	−	0.202149i	0.0335366	−	0.0193624i	−0.483138	−	0.875544i	$-0.660503\pi$
$109$	0.350133	−	0.202149i	0.0335366	−	0.0193624i	0.516675	+	0.856182i	$0.327170\pi$
$110$		0			0
$111$		−	5.50146i		−	0.522175i
$112$	9.65050	−	4.34371i	0.911887	−	0.410442i
$113$	3.57217	+	3.57217i	0.336041	+	0.336041i	0.854875	−	0.518834i	$-0.173634\pi$
$113$	3.57217	+	3.57217i	0.336041	+	0.336041i	−0.518834	+	0.854875i	$0.673634\pi$
$114$	0.283937	+	1.59547i	0.0265932	+	0.149430i
$115$		0			0
$116$	−13.6278	+	5.00919i	−1.26531	+	0.465091i
$117$	2.00593	+	7.48624i	0.185448	+	0.692103i
$118$	20.9025	+	1.79530i	1.92423	+	0.165270i
$119$	1.36112	+	0.822090i	0.124773	+	0.0753609i
$120$		0			0
$121$	2.34144	−	4.05549i	0.212858	−	0.368681i
$122$	2.53887	+	5.42213i	0.229858	+	0.490896i
$123$	−1.85143	−	0.496088i	−0.166937	−	0.0447308i
$124$	5.01996	+	4.18516i	0.450806	+	0.375838i
$125$		0			0
$126$	9.88122	−	1.55791i	0.880289	−	0.138789i
$127$	4.80151	+	4.80151i	0.426065	+	0.426065i	0.887286	−	0.461221i	$-0.152588\pi$
$127$	4.80151	+	4.80151i	0.426065	+	0.426065i	−0.461221	+	0.887286i	$0.652588\pi$
$128$	10.1999	−	4.89504i	0.901555	−	0.432664i
$129$	2.32188	−	1.34054i	0.204431	−	0.118028i
$130$		0			0
$131$	13.1564	+	7.59586i	1.14948	+	0.663653i	0.948761	−	0.315996i	$-0.102339\pi$
$131$	13.1564	+	7.59586i	1.14948	+	0.663653i	0.200720	+	0.979649i	$0.435672\pi$
$132$	−2.60763	−	3.69903i	−0.226965	−	0.321959i
$133$	3.82506	−	3.67692i	0.331674	−	0.318829i
$134$	3.46459	+	4.11565i	0.299295	+	0.355538i
$135$		0			0
$136$	1.47619	+	0.842931i	0.126582	+	0.0722807i
$137$	4.42171	+	1.18479i	0.377772	+	0.101224i	0.442708	−	0.896666i	$-0.354018\pi$
$137$	4.42171	+	1.18479i	0.377772	+	0.101224i	−0.0649361	+	0.997889i	$0.520684\pi$
$138$	1.64052	+	1.14483i	0.139650	+	0.0974540i
$139$	11.1198			0.943167			0.471583	−	0.881821i	$-0.343683\pi$
$139$	11.1198			0.943167			0.471583	+	0.881821i	$0.343683\pi$
$140$		0			0
$141$	7.16665			0.603541
$142$	−5.63639	−	3.93332i	−0.472996	−	0.330077i
$143$	−11.0891	−	2.97133i	−0.927321	−	0.248475i
$144$	10.5195	−	1.92383i	0.876624	−	0.160319i
$145$		0			0
$146$	−8.90975	−	10.5841i	−0.737376	−	0.875942i
$147$	2.71448	+	2.93780i	0.223887	+	0.242305i
$148$	−15.7382	+	11.0946i	−1.29367	+	0.911973i
$149$	4.24169	+	2.44894i	0.347493	+	0.200625i	0.663580	−	0.748105i	$-0.269036\pi$
$149$	4.24169	+	2.44894i	0.347493	+	0.200625i	−0.316088	+	0.948730i	$0.602369\pi$
$150$		0			0
$151$	−12.7632	+	7.36881i	−1.03865	+	0.599666i	−0.919451	−	0.393205i	$-0.871366\pi$
$151$	−12.7632	+	7.36881i	−1.03865	+	0.599666i	−0.119200	+	0.992870i	$0.538033\pi$
$152$	3.99161	−	4.02981i	0.323762	−	0.326861i
$153$	1.13617	+	1.13617i	0.0918538	+	0.0918538i
$154$	−5.31987	+	13.8297i	−0.428687	+	1.11443i
$155$		0			0
$156$	−2.12148	+	2.54465i	−0.169854	+	0.203735i
$157$	10.7377	+	2.87717i	0.856964	+	0.229623i	0.660442	−	0.750877i	$-0.270369\pi$
$157$	10.7377	+	2.87717i	0.856964	+	0.229623i	0.196522	+	0.980499i	$0.437035\pi$
$158$	−4.14660	−	8.85568i	−0.329886	−	0.704520i
$159$	0.860073	−	1.48969i	0.0682082	−	0.118140i
$160$		0			0
$161$	0.129310	−	6.54839i	0.0101911	−	0.516085i
$162$	8.69088	+	0.746452i	0.682820	+	0.0586468i
$163$	−4.75254	−	17.7367i	−0.372248	−	1.38925i	−0.857324	−	0.514776i	$-0.827875\pi$
$163$	−4.75254	−	17.7367i	−0.372248	−	1.38925i	0.485077	−	0.874472i	$-0.338792\pi$
$164$	2.31454	+	6.29687i	0.180735	+	0.491703i
$165$		0			0
$166$	−1.91608	−	10.7667i	−0.148717	−	0.835655i
$167$	−13.1233	−	13.1233i	−1.01551	−	1.01551i	−0.999878	−	0.0156336i	$-0.995023\pi$
$167$	−13.1233	−	13.1233i	−1.01551	−	1.01551i	−0.0156336	−	0.999878i	$-0.504977\pi$
$168$	2.97799	+	3.06858i	0.229757	+	0.236746i
$169$		−	4.59606i		−	0.353543i
$170$		0			0
$171$	4.64307	−	2.68068i	0.355064	−	0.204996i
$172$	−8.51740	−	3.93885i	−0.649446	−	0.300335i
$173$	−7.49083	+	2.00716i	−0.569517	+	0.152602i	−0.532075	−	0.846697i	$-0.678588\pi$
$173$	−7.49083	+	2.00716i	−0.569517	+	0.152602i	−0.0374420	+	0.999299i	$0.511921\pi$
$174$	−3.77805	−	4.48801i	−0.286413	−	0.340235i
$175$		0			0
$176$	−5.32318	+	14.9194i	−0.401250	+	1.12460i
$177$	2.19394	+	8.18789i	0.164906	+	0.615439i
$178$	4.95862	−	2.32184i	0.371665	−	0.174029i
$179$	−2.56434	−	4.44157i	−0.191668	−	0.331979i	0.754135	−	0.656719i	$-0.228056\pi$
$179$	−2.56434	−	4.44157i	−0.191668	−	0.331979i	−0.945803	+	0.324741i	$0.894723\pi$
$180$		0			0
$181$	18.1294			1.34755			0.673774	−	0.738938i	$-0.264672\pi$
$181$	18.1294			1.34755			0.673774	+	0.738938i	$0.264672\pi$
$182$	10.7867	+	1.14140i	0.799561	+	0.0846059i
$183$	−1.71055	+	1.71055i	−0.126447	+	0.126447i
$184$	−0.0333491	−	7.00181i	−0.00245853	−	0.516180i
$185$		0			0
$186$	−0.899249	+	2.48292i	−0.0659361	+	0.182057i
$187$	−2.29899	+	0.616011i	−0.168118	+	0.0450472i
$188$	−14.4528	−	20.5018i	−1.05408	−	1.49525i
$189$	4.14114	+	7.51134i	0.301223	+	0.546370i
$190$		0			0
$191$	−13.5825	−	7.84185i	−0.982794	−	0.567416i	−0.0796814	−	0.996820i	$-0.525390\pi$
$191$	−13.5825	−	7.84185i	−0.982794	−	0.567416i	−0.903112	+	0.429404i	$0.858724\pi$
$192$	3.26304	+	3.20145i	0.235489	+	0.231045i
$193$	−2.00899	+	7.49764i	−0.144610	+	0.539692i	0.855162	+	0.518360i	$0.173457\pi$
$193$	−2.00899	+	7.49764i	−0.144610	+	0.539692i	−0.999772	+	0.0213318i	$0.993209\pi$
$194$	0.392173	+	2.20366i	0.0281564	+	0.158214i
$195$		0			0
$196$	2.93002	−	13.6900i	0.209287	−	0.977854i
$197$	−4.22983	+	4.22983i	−0.301363	+	0.301363i	−0.841547	−	0.540184i	$-0.818355\pi$
$197$	−4.22983	+	4.22983i	−0.301363	+	0.301363i	0.540184	+	0.841547i	$0.318355\pi$
$198$	−8.56863	+	12.2787i	−0.608946	+	0.872610i
$199$	−7.04403	−	12.2006i	−0.499338	−	0.864879i	0.500661	−	0.865643i	$-0.333090\pi$
$199$	−7.04403	−	12.2006i	−0.499338	−	0.864879i	−1.00000		0.000763945i	$0.999757\pi$
$200$		0			0
$201$	−1.08685	+	1.88247i	−0.0766601	+	0.132779i
$202$	−25.1727	−	2.16206i	−1.77114	−	0.152122i
$203$	−5.33651	+	18.4510i	−0.374550	+	1.29501i
$204$	−0.117121	+	0.676785i	−0.00820011	+	0.0473845i
$205$		0			0
$206$	14.9147	+	5.40172i	1.03916	+	0.376356i
$207$	1.71295	−	6.39282i	0.119058	−	0.444332i
$208$	11.5579	+	0.937263i	0.801395	+	0.0649875i
$209$			7.94162i			0.549333i
$210$		0			0
$211$		−	17.2435i		−	1.18709i	−0.804799	−	0.593547i	$-0.797727\pi$
$211$		−	17.2435i		−	1.18709i	0.804799	−	0.593547i	$-0.202273\pi$
$212$	−5.99608	+	0.543779i	−0.411813	+	0.0373469i
$213$	0.718762	−	2.68246i	0.0492488	−	0.183799i
$214$	−3.78682	+	10.4558i	−0.258862	+	0.714746i
$215$		0			0
$216$	4.62250	+	7.91907i	0.314522	+	0.538824i
$217$	8.39389	−	2.07242i	0.569814	−	0.140685i
$218$	0.0489282	−	0.569667i	0.00331383	−	0.0385827i
$219$	2.79500	−	4.84108i	0.188868	−	0.327130i
$220$		0			0
$221$	0.871146	+	1.50887i	0.0585996	+	0.101498i
$222$	−6.38027	−	4.45244i	−0.428216	−	0.298828i
$223$	11.5356	−	11.5356i	0.772484	−	0.772484i	−0.206056	−	0.978540i	$-0.566063\pi$
$223$	11.5356	−	11.5356i	0.772484	−	0.772484i	0.978540	+	0.206056i	$0.0660630\pi$
$224$	2.77276	−	14.7075i	0.185263	−	0.982689i
$225$		0			0
$226$	7.03382	−	1.25177i	0.467882	−	0.0832664i
$227$	−3.12892	+	11.6773i	−0.207674	+	0.775049i	0.780944	+	0.624601i	$0.214738\pi$
$227$	−3.12892	+	11.6773i	−0.207674	+	0.775049i	−0.988618	+	0.150448i	$0.951928\pi$
$228$	2.08013	+	0.961953i	0.137760	+	0.0637069i
$229$	−1.89994	−	1.09693i	−0.125552	−	0.0724873i	0.435909	−	0.899991i	$-0.356427\pi$
$229$	−1.89994	−	1.09693i	−0.125552	−	0.0724873i	−0.561460	+	0.827504i	$0.689760\pi$
$230$		0			0
$231$	−5.98586	−	0.118202i	−0.393840	−	0.00777710i
$232$	−5.21990	+	19.8588i	−0.342703	+	1.30379i
$233$	1.08868	−	0.291712i	0.0713220	−	0.0191107i	−0.222982	−	0.974823i	$-0.571579\pi$
$233$	1.08868	−	0.291712i	0.0713220	−	0.0191107i	0.294304	+	0.955712i	$0.404912\pi$
$234$	10.3055	+	3.73239i	0.673694	+	0.243994i
$235$		0			0
$236$	18.9989	−	22.7885i	1.23672	−	1.48341i
$237$	2.79375	−	2.79375i	0.181474	−	0.181474i
$238$	2.05499	−	0.913209i	0.133205	−	0.0591946i
$239$	−19.8536			−1.28422			−0.642111	−	0.766612i	$-0.721941\pi$
$239$	−19.8536			−1.28422			−0.642111	+	0.766612i	$0.721941\pi$
$240$		0			0
$241$	4.32744	+	7.49535i	0.278755	+	0.482818i	0.971076	−	0.238772i	$-0.0767449\pi$
$241$	4.32744	+	7.49535i	0.278755	+	0.482818i	−0.692321	+	0.721590i	$0.743412\pi$
$242$	−2.80835	−	5.99765i	−0.180528	−	0.385544i
$243$	3.42939	+	12.7987i	0.219996	+	0.821035i
$244$	8.34302	+	1.44380i	0.534107	+	0.0924299i
$245$		0			0
$246$	−2.07373	+	1.74568i	−0.132216	+	0.111301i
$247$	5.61541	−	1.50464i	0.357300	−	0.0957382i
$248$	8.91646	−	2.43473i	0.566196	−	0.154606i
$249$	3.82663	−	2.20931i	0.242503	−	0.140009i
$250$		0			0
$251$		−	1.55623i		−	0.0982283i	−0.998793	−	0.0491141i	$-0.984360\pi$
$251$		−	1.55623i		−	0.0982283i	0.998793	−	0.0491141i	$-0.0156398\pi$
$252$	6.19029	−	12.7205i	0.389952	−	0.801317i
$253$	6.93215	+	6.93215i	0.435821	+	0.435821i
$254$	9.45447	−	1.68256i	0.593226	−	0.105573i
$255$		0			0
$256$	2.57802	−	15.7909i	0.161126	−	0.986934i
$257$	−4.60489	−	17.1857i	−0.287245	−	1.07201i	−0.947183	−	0.320693i	$-0.896084\pi$
$257$	−4.60489	−	17.1857i	−0.287245	−	1.07201i	0.659938	−	0.751320i	$-0.270582\pi$
$258$	0.324464	−	3.77771i	0.0202003	−	0.235190i
$259$	−0.502910	+	25.4679i	−0.0312493	+	1.58250i
$260$		0			0
$261$	−9.70429	+	16.8083i	−0.600680	+	1.04041i
$262$	19.4570	−	9.11057i	1.20206	−	0.562853i
$263$	−18.5489	−	4.97016i	−1.14377	−	0.306473i	−0.363306	−	0.931670i	$-0.618352\pi$
$263$	−18.5489	−	4.97016i	−1.14377	−	0.306473i	−0.780467	+	0.625197i	$0.785019\pi$
$264$	−6.40032	+	0.0304843i	−0.393913	+	0.00187618i
$265$		0			0
$266$	−1.16858	−	7.41188i	−0.0716504	−	0.454451i
$267$	1.56432	+	1.56432i	0.0957350	+	0.0957350i
$268$	7.57705	−	0.687156i	0.462842	−	0.0419747i
$269$	−12.4257	+	7.17398i	−0.757608	+	0.437405i	−0.828436	−	0.560083i	$-0.810769\pi$
$269$	−12.4257	+	7.17398i	−0.757608	+	0.437405i	0.0708284	+	0.997489i	$0.477436\pi$
$270$		0			0
$271$	17.9057	+	10.3379i	1.08770	+	0.627981i	0.932962	−	0.359975i	$-0.117215\pi$
$271$	17.9057	+	10.3379i	1.08770	+	0.627981i	0.154733	+	0.987956i	$0.450548\pi$
$272$	2.17229	−	1.02980i	0.131715	−	0.0624409i
$273$	1.05052	+	4.25491i	0.0635804	+	0.257519i
$274$	4.95263	−	4.16917i	0.299199	−	0.251869i
$275$		0			0
$276$	2.65540	−	0.976048i	0.159837	−	0.0587512i
$277$	4.70760	+	1.26140i	0.282853	+	0.0757901i	0.397456	−	0.917621i	$-0.369893\pi$
$277$	4.70760	+	1.26140i	0.282853	+	0.0757901i	−0.114604	+	0.993411i	$0.536560\pi$
$278$	8.99945	−	12.8961i	0.539751	−	0.773455i
$279$	8.73658			0.523045
$280$		0			0
$281$	−9.71163			−0.579347			−0.289674	−	0.957125i	$-0.593547\pi$
$281$	−9.71163			−0.579347			−0.289674	+	0.957125i	$0.593547\pi$
$282$	5.80011	−	8.31147i	0.345391	−	0.494941i
$283$	1.36959	+	0.366980i	0.0814136	+	0.0218147i	0.299296	−	0.954160i	$-0.403248\pi$
$283$	1.36959	+	0.366980i	0.0814136	+	0.0218147i	−0.217882	+	0.975975i	$0.569915\pi$
$284$	−9.12328	+	3.35345i	−0.541367	+	0.198991i
$285$		0			0
$286$	−12.4206	+	10.4558i	−0.734447	+	0.618264i
$287$	8.52546	+	2.46579i	0.503242	+	0.145551i
$288$	6.28248	−	13.7569i	0.370199	−	0.810632i
$289$	−14.4096	−	8.31940i	−0.847624	−	0.489376i
$290$		0			0
$291$	−0.783214	+	0.452189i	−0.0459128	+	0.0265078i
$292$	−19.4856	+	1.76713i	−1.14031	+	0.103414i
$293$	6.02648	+	6.02648i	0.352071	+	0.352071i	0.860880	−	0.508809i	$-0.169914\pi$
$293$	6.02648	+	6.02648i	0.352071	+	0.352071i	−0.508809	+	0.860880i	$0.669914\pi$
$294$	5.60397	−	0.770482i	0.326830	−	0.0449354i
$295$		0			0
$296$	0.129701	+	27.2313i	0.00753870	+	1.58279i
$297$	−12.4010	−	3.32283i	−0.719578	−	0.192810i
$298$	6.27302	−	2.93729i	0.363386	−	0.170153i
$299$	3.58824	−	6.21502i	0.207513	−	0.359424i
$300$		0			0
$301$	−10.8712	+	5.99351i	−0.626608	+	0.345460i
$302$	−1.78355	+	20.7657i	−0.102632	+	1.19493i
$303$	−2.64214	−	9.86060i	−0.151787	−	0.566477i
$304$	−1.44306	−	7.89064i	−0.0827651	−	0.452559i
$305$		0			0
$306$	2.23719	−	0.398140i	0.127891	−	0.0227601i
$307$	11.0030	+	11.0030i	0.627975	+	0.627975i	0.947558	−	0.319583i	$-0.103543\pi$
$307$	11.0030	+	11.0030i	0.627975	+	0.627975i	−0.319583	+	0.947558i	$0.603543\pi$
$308$	11.7334	+	17.3623i	0.668570	+	0.989308i
$309$			6.40934i			0.364615i
$310$		0			0
$311$	−21.9956	+	12.6992i	−1.24726	+	0.720104i	−0.970561	−	0.240854i	$-0.922572\pi$
$311$	−21.9956	+	12.6992i	−1.24726	+	0.720104i	−0.276695	+	0.960958i	$0.589239\pi$
$312$	1.23418	+	4.51980i	0.0698717	+	0.255884i
$313$	−25.0624	+	6.71544i	−1.41661	+	0.379579i	−0.884280	−	0.466958i	$-0.845350\pi$
$313$	−25.0624	+	6.71544i	−1.41661	+	0.379579i	−0.532330	+	0.846537i	$0.678683\pi$
$314$	12.0270	−	10.1245i	0.678724	−	0.571356i
$315$		0			0
$316$	−13.6262	−	2.35809i	−0.766536	−	0.132653i
$317$	−0.0554686	−	0.207012i	−0.00311543	−	0.0116269i	0.964351	−	0.264628i	$-0.0852491\pi$
$317$	−0.0554686	−	0.207012i	−0.00311543	−	0.0116269i	−0.967466	+	0.253001i	$0.918582\pi$
$318$	−1.03158	−	2.20310i	−0.0578483	−	0.123544i
$319$	−14.3747	−	24.8977i	−0.804828	−	1.39400i
$320$		0			0
$321$	−4.49321			−0.250786
$322$	−7.48979	−	5.44971i	−0.417390	−	0.303700i
$323$	0.852238	−	0.852238i	0.0474198	−	0.0474198i
$324$	7.89939	−	9.47507i	0.438855	−	0.526393i
$325$		0			0
$326$	−24.4164	−	8.84296i	−1.35230	−	0.489766i
$327$	0.223149	−	0.0597926i	0.0123402	−	0.00330654i
$328$	9.17595	+	2.41191i	0.506657	+	0.133175i
$329$	−33.1766	−	0.655132i	−1.82908	−	0.0361186i
$330$		0			0
$331$	1.84066	+	1.06270i	0.101172	+	0.0584115i	0.549732	−	0.835341i	$-0.314730\pi$
$331$	1.84066	+	1.06270i	0.101172	+	0.0584115i	−0.448560	+	0.893753i	$0.648063\pi$
$332$	−14.0373	−	6.49151i	−0.770396	−	0.356268i
$333$	−6.66198	+	24.8628i	−0.365074	+	1.36248i
$334$	−25.8406	+	4.59871i	−1.41393	+	0.251630i
$335$		0			0
$336$	5.96891	−	0.970238i	0.325631	−	0.0529308i
$337$	22.4528	−	22.4528i	1.22308	−	1.22308i	0.256552	−	0.966530i	$-0.417414\pi$
$337$	22.4528	−	22.4528i	1.22308	−	1.22308i	0.966530	−	0.256552i	$-0.0825865\pi$
$338$	−5.33025	−	3.71968i	−0.289927	−	0.202324i
$339$	1.44333	+	2.49992i	0.0783909	+	0.135777i
$340$		0			0
$341$	−6.47062	+	11.2074i	−0.350404	+	0.606917i
$342$	0.648831	−	7.55429i	0.0350848	−	0.408489i
$343$	−12.2976	−	13.8481i	−0.664007	−	0.747726i
$344$	−11.4613	+	6.69020i	−0.617955	+	0.360711i
$345$		0			0
$346$	−3.73468	+	10.3119i	−0.200778	+	0.554369i
$347$	−4.72717	+	17.6420i	−0.253768	+	0.947074i	0.715004	+	0.699120i	$0.246425\pi$
$347$	−4.72717	+	17.6420i	−0.253768	+	0.947074i	−0.968772	+	0.247954i	$0.920242\pi$
$348$	−8.26258	+	0.749326i	−0.442921	+	0.0401681i
$349$		−	21.6072i		−	1.15661i	−0.815821	−	0.578304i	$-0.803715\pi$
$349$		−	21.6072i		−	1.15661i	0.815821	−	0.578304i	$-0.196285\pi$
$350$		0			0
$351$			9.39811i			0.501634i
$352$	12.9946	+	18.2481i	0.692612	+	0.972628i
$353$	−4.39216	+	16.3918i	−0.233771	+	0.872446i	0.744928	+	0.667145i	$0.232484\pi$
$353$	−4.39216	+	16.3918i	−0.233771	+	0.872446i	−0.978699	+	0.205301i	$0.934183\pi$
$354$	11.2714	+	4.08221i	0.599070	+	0.216967i
$355$		0			0
$356$	1.32038	−	7.62983i	0.0699799	−	0.404380i
$357$	0.629675	+	0.655044i	0.0333259	+	0.0346686i
$358$	−7.22645	−	0.620673i	−0.381930	−	0.0328036i
$359$	−4.43990	+	7.69014i	−0.234329	+	0.405870i	−0.959078	−	0.283144i	$-0.908623\pi$
$359$	−4.43990	+	7.69014i	−0.234329	+	0.405870i	0.724748	+	0.689014i	$0.241956\pi$
$360$		0			0
$361$	7.48923	+	12.9717i	0.394170	+	0.682723i
$362$	14.6725	−	21.0254i	0.771168	−	1.10507i
$363$	1.89211	−	1.89211i	0.0993101	−	0.0993101i
$364$	10.0536	−	11.5860i	0.526951	−	0.607272i
$365$		0			0
$366$	0.599415	+	3.36817i	0.0313319	+	0.176057i
$367$	−5.62655	+	20.9986i	−0.293704	+	1.09612i	0.648538	+	0.761182i	$0.275381\pi$
$367$	−5.62655	+	20.9986i	−0.293704	+	1.09612i	−0.942241	+	0.334934i	$0.891286\pi$
$368$	−8.14728	−	5.62802i	−0.424707	−	0.293381i
$369$	7.76645	+	4.48396i	0.404305	+	0.233426i
$370$		0			0
$371$	−4.11771	+	6.81760i	−0.213781	+	0.353952i
$372$	2.15177	+	3.05237i	0.111564	+	0.158258i
$373$	−0.472145	+	0.126511i	−0.0244467	+	0.00655048i	−0.271022	−	0.962573i	$-0.587362\pi$
$373$	−0.472145	+	0.126511i	−0.0244467	+	0.00655048i	0.246575	+	0.969124i	$0.420695\pi$
$374$	−1.14620	+	3.16478i	−0.0592686	+	0.163647i
$375$		0			0
$376$	−35.4738	+	0.168959i	−1.82942	+	0.00871339i
$377$	−14.8813	+	14.8813i	−0.766427	+	0.766427i
$378$	12.0627	+	1.27642i	0.620440	+	0.0656521i
$379$	27.8315			1.42961			0.714805	−	0.699324i	$-0.246516\pi$
$379$	27.8315			1.42961			0.714805	+	0.699324i	$0.246516\pi$
$380$		0			0
$381$	1.94004	+	3.36026i	0.0993915	+	0.172151i
$382$	−20.0871	+	9.40562i	−1.02774	+	0.481233i
$383$	1.33854	+	4.99551i	0.0683964	+	0.255259i	0.991655	−	0.128920i	$-0.0411512\pi$
$383$	1.33854	+	4.99551i	0.0683964	+	0.255259i	−0.923259	+	0.384179i	$0.874484\pi$
$384$	6.35370	−	1.19328i	0.324236	−	0.0608944i
$385$		0			0
$386$	7.06942	+	8.39789i	0.359824	+	0.427441i
$387$	−12.1167	+	3.24665i	−0.615925	+	0.165037i
$388$	2.87307	+	1.32865i	0.145858	+	0.0674518i
$389$	−10.5873	+	6.11259i	−0.536798	+	0.309921i	−0.743780	−	0.668424i	$-0.766969\pi$
$389$	−10.5873	+	6.11259i	−0.536798	+	0.309921i	0.206982	+	0.978345i	$0.433636\pi$
$390$		0			0
$391$		−	1.48782i		−	0.0752422i
$392$	−13.5055	−	14.4776i	−0.682131	−	0.731230i
$393$	6.13820	+	6.13820i	0.309631	+	0.309631i
$394$	1.48223	+	8.32880i	0.0746737	+	0.419599i
$395$		0			0
$396$	7.30538	+	19.8748i	0.367109	+	0.998746i
$397$	4.52602	+	16.8913i	0.227154	+	0.847751i	0.981530	+	0.191308i	$0.0612730\pi$
$397$	4.52602	+	16.8913i	0.227154	+	0.847751i	−0.754376	+	0.656443i	$0.772060\pi$
$398$	−19.8505	−	1.70494i	−0.995013	−	0.0854608i
$399$	2.65499	−	1.46375i	0.132916	−	0.0732789i
$400$		0			0
$401$	15.5612	−	26.9528i	0.777089	−	1.34596i	−0.156524	−	0.987674i	$-0.550029\pi$
$401$	15.5612	−	26.9528i	0.777089	−	1.34596i	0.933613	−	0.358284i	$-0.116638\pi$
$402$	1.30358	+	2.78398i	0.0650165	+	0.138852i
$403$	9.15057	+	2.45189i	0.455823	+	0.122137i
$404$	−22.8802	+	27.4440i	−1.13833	+	1.36539i
$405$		0			0
$406$	17.0794	+	21.1217i	0.847639	+	1.04825i
$407$	−26.9604	−	26.9604i	−1.33638	−	1.33638i
$408$	0.690108	+	0.683566i	0.0341655	+	0.0338415i
$409$	−4.43457	+	2.56030i	−0.219275	+	0.126599i	−0.605615	−	0.795758i	$-0.707073\pi$
$409$	−4.43457	+	2.56030i	−0.219275	+	0.126599i	0.386339	+	0.922357i	$0.373739\pi$
$410$		0			0
$411$	2.26530	+	1.30787i	0.111739	+	0.0645126i
$412$	18.3354	−	12.9255i	0.903319	−	0.636795i
$413$	−9.40791	−	38.1047i	−0.462933	−	1.87501i
$414$	−6.02770	−	7.16041i	−0.296245	−	0.351915i
$415$		0			0
$416$	10.4410	−	12.6456i	0.511912	−	0.620002i
$417$	6.13746	+	1.64453i	0.300553	+	0.0805329i
$418$	9.21023	+	6.42730i	0.450487	+	0.314370i
$419$	−14.0529			−0.686531			−0.343266	−	0.939238i	$-0.611533\pi$
$419$	−14.0529			−0.686531			−0.343266	+	0.939238i	$0.611533\pi$
$420$		0			0
$421$	37.5305			1.82913			0.914563	−	0.404443i	$-0.132535\pi$
$421$	37.5305			1.82913			0.914563	+	0.404443i	$0.132535\pi$
$422$	−19.9981	−	13.9555i	−0.973491	−	0.679345i
$423$	−32.3884	−	8.67844i	−1.57478	−	0.421960i
$424$	−4.22210	+	7.39400i	−0.205043	+	0.359084i
$425$		0			0
$426$	−2.52925	−	3.00454i	−0.122543	−	0.145571i
$427$	8.07501	−	7.76227i	0.390777	−	0.375643i
$428$	9.06132	+	12.8538i	0.437995	+	0.621314i
$429$	−5.68112	−	3.28000i	−0.274287	−	0.158360i
$430$		0			0
$431$	21.0173	−	12.1344i	1.01237	−	0.584492i	0.100485	−	0.994939i	$-0.467961\pi$
$431$	21.0173	−	12.1344i	1.01237	−	0.584492i	0.911885	+	0.410447i	$0.134627\pi$
$432$	12.9252	+	1.04814i	0.621862	+	0.0504287i
$433$	−0.0253628	−	0.0253628i	−0.00121886	−	0.00121886i	0.706497	−	0.707716i	$-0.250274\pi$
$433$	−0.0253628	−	0.0253628i	−0.00121886	−	0.00121886i	−0.707716	+	0.706497i	$0.750274\pi$
$434$	4.38987	−	11.4120i	0.210720	−	0.547793i
$435$		0			0
$436$	−0.621068	−	0.517787i	−0.0297438	−	0.0247975i
$437$	−4.79524	−	1.28488i	−0.229387	−	0.0614641i
$438$	−3.35236	−	7.15946i	−0.160182	−	0.342092i
$439$	7.62951	−	13.2147i	0.364137	−	0.630703i	−0.624500	−	0.781024i	$-0.714697\pi$
$439$	7.62951	−	13.2147i	0.364137	−	0.630703i	0.988637	+	0.150321i	$0.0480307\pi$
$440$		0			0
$441$	−8.71009	−	16.5639i	−0.414766	−	0.788759i
$442$	2.45494	+	0.210852i	0.116769	+	0.0100292i
$443$	3.09446	+	11.5487i	0.147022	+	0.548695i	0.999657	+	0.0261872i	$0.00833660\pi$
$443$	3.09446	+	11.5487i	0.147022	+	0.548695i	−0.852635	+	0.522507i	$0.824997\pi$
$444$	−10.3274	+	3.79603i	−0.490115	+	0.180152i
$445$		0			0
$446$	−4.04235	−	22.7144i	−0.191411	−	1.07556i
$447$	1.97898	+	1.97898i	0.0936027	+	0.0936027i
$448$	−14.8129	−	15.1188i	−0.699844	−	0.714295i
$449$			13.7142i			0.647213i	0.946192	+	0.323607i	$0.104895\pi$
$449$			13.7142i			0.647213i	−0.946192	+	0.323607i	$0.895105\pi$
$450$		0			0
$451$	−11.5042	+	6.64196i	−0.541712	+	0.312758i
$452$	4.24087	−	9.17049i	0.199474	−	0.431344i
$453$	−8.13430	+	2.17958i	−0.382183	+	0.102406i
$454$	11.0104	+	13.0794i	0.516741	+	0.613847i
$455$		0			0
$456$	2.79911	−	1.63389i	0.131080	−	0.0765140i
$457$	3.61073	+	13.4754i	0.168903	+	0.630354i	0.997510	+	0.0705235i	$0.0224670\pi$
$457$	3.61073	+	13.4754i	0.168903	+	0.630354i	−0.828607	+	0.559830i	$0.810866\pi$
$458$	−2.80982	+	1.31567i	−0.131294	+	0.0614774i
$459$	0.974202	+	1.68737i	0.0454718	+	0.0787595i
$460$		0			0
$461$	−27.6588			−1.28820			−0.644100	−	0.764941i	$-0.722768\pi$
$461$	−27.6588			−1.28820			−0.644100	+	0.764941i	$0.722768\pi$
$462$	−4.98155	+	6.84639i	−0.231763	+	0.318523i
$463$	−4.03783	+	4.03783i	−0.187654	+	0.187654i	−0.794681	−	0.607027i	$-0.792362\pi$
$463$	−4.03783	+	4.03783i	−0.187654	+	0.187654i	0.607027	+	0.794681i	$0.292362\pi$
$464$	18.8065	+	22.1259i	0.873071	+	1.02717i
$465$		0			0
$466$	0.542782	−	1.49868i	0.0251439	−	0.0694250i
$467$	11.8626	−	3.17857i	0.548935	−	0.147087i	0.0263172	−	0.999654i	$-0.491622\pi$
$467$	11.8626	−	3.17857i	0.548935	−	0.147087i	0.522618	+	0.852567i	$0.324955\pi$
$468$	12.6691	−	8.93108i	0.585629	−	0.412839i
$469$	5.20342	−	8.61517i	0.240271	−	0.397812i
$470$		0			0
$471$	5.50108	+	3.17605i	0.253477	+	0.146345i
$472$	−11.0527	−	40.4770i	−0.508740	−	1.86310i
$473$	4.80917	−	17.9481i	0.221126	−	0.825253i
$474$	−0.978994	−	5.50107i	−0.0449667	−	0.252672i
$475$		0			0
$476$	0.604056	−	3.12234i	0.0276869	−	0.143112i
$477$	−5.69088	+	5.69088i	−0.260568	+	0.260568i
$478$	−16.0679	+	23.0250i	−0.734928	+	1.05314i
$479$	−12.0422	−	20.8577i	−0.550223	−	0.953014i	−0.998258	−	0.0589981i	$-0.981209\pi$
$479$	−12.0422	−	20.8577i	−0.550223	−	0.953014i	0.448035	−	0.894016i	$-0.352124\pi$
$480$		0			0
$481$	−13.9553	+	24.1713i	−0.636308	+	1.10212i
$482$	12.1950	+	1.04741i	0.555465	+	0.0477084i
$483$	1.03983	−	3.59520i	0.0473138	−	0.163587i
$484$	−9.22859	−	1.59705i	−0.419481	−	0.0725932i
$485$		0			0
$486$	17.6186	+	6.38100i	0.799198	+	0.289448i
$487$	−0.888247	+	3.31498i	−0.0402503	+	0.150216i	−0.983126	−	0.182927i	$-0.941443\pi$
$487$	−0.888247	+	3.31498i	−0.0402503	+	0.150216i	0.942876	+	0.333144i	$0.108109\pi$
$488$	8.42661	−	8.50726i	0.381455	−	0.385106i
$489$		−	10.4925i		−	0.474487i
$490$		0			0
$491$		−	3.54370i		−	0.159925i	−0.996798	−	0.0799626i	$-0.974520\pi$
$491$		−	3.54370i		−	0.159925i	0.996798	−	0.0799626i	$-0.0254801\pi$
$492$	0.346234	+	3.81781i	0.0156094	+	0.172120i
$493$	−1.12925	+	4.21443i	−0.0508590	+	0.189808i
$494$	2.79966	−	7.73016i	0.125963	−	0.347796i
$495$		0			0
$496$	4.39260	−	12.3113i	0.197234	−	0.552792i
$497$	−3.57258	+	12.3522i	−0.160252	+	0.554071i
$498$	0.534740	−	6.22594i	0.0239623	−	0.278991i
$499$	−15.1647	+	26.2660i	−0.678864	+	1.17583i	0.296460	+	0.955045i	$0.404194\pi$
$499$	−15.1647	+	26.2660i	−0.678864	+	1.17583i	−0.975323	+	0.220781i	$0.929139\pi$
$500$		0			0
$501$	−5.30246	−	9.18412i	−0.236896	−	0.410316i
$502$	−1.80482	−	1.25949i	−0.0805532	−	0.0562136i
$503$	6.85172	−	6.85172i	0.305503	−	0.305503i	−0.537659	−	0.843162i	$-0.680691\pi$
$503$	6.85172	−	6.85172i	0.305503	−	0.305503i	0.843162	+	0.537659i	$0.180691\pi$
$504$	−9.74260	−	17.4741i	−0.433970	−	0.778358i
$505$		0			0
$506$	13.6498	−	2.42919i	0.606809	−	0.107990i
$507$	0.679722	−	2.53676i	0.0301875	−	0.112661i
$508$	5.70035	−	12.3265i	0.252912	−	0.546899i
$509$	8.23953	+	4.75709i	0.365211	+	0.210854i	0.671364	−	0.741128i	$-0.265709\pi$
$509$	8.23953	+	4.75709i	0.365211	+	0.210854i	−0.306153	+	0.951982i	$0.599042\pi$
$510$		0			0
$511$	−13.3814	+	22.1553i	−0.591960	+	0.980093i
$512$	−16.2270	−	15.7698i	−0.717138	−	0.696931i
$513$	6.27970	−	1.68264i	0.277256	−	0.0742904i
$514$	−23.6578	−	8.56822i	−1.04350	−	0.377928i
$515$		0			0
$516$	−4.11858	−	3.43367i	−0.181310	−	0.151159i
$517$	35.1209	−	35.1209i	1.54461	−	1.54461i
$518$	29.1292	+	21.1949i	1.27986	+	0.931251i
$519$	−4.43134			−0.194514
$520$		0			0
$521$	2.30406	+	3.99075i	0.100943	+	0.174838i	0.912073	−	0.410027i	$-0.134481\pi$
$521$	2.30406	+	3.99075i	0.100943	+	0.174838i	−0.811131	+	0.584865i	$0.801147\pi$
$522$	11.6395	+	24.8578i	0.509445	+	1.08800i
$523$	8.89583	+	33.1997i	0.388987	+	1.45172i	0.831784	+	0.555099i	$0.187320\pi$
$523$	8.89583	+	33.1997i	0.388987	+	1.45172i	−0.442797	+	0.896622i	$0.646014\pi$
$524$	5.18099	−	29.9384i	0.226333	−	1.30787i
$525$		0			0
$526$	−20.7761	+	17.4895i	−0.905880	+	0.762578i
$527$	1.89708	−	0.508322i	0.0826383	−	0.0221429i
$528$	−5.14455	+	7.44740i	−0.223888	+	0.324106i
$529$	14.6113	−	8.43585i	0.635275	−	0.366776i
$530$		0			0
$531$		−	39.6604i		−	1.72112i
$532$	−9.54163	−	4.64332i	−0.413682	−	0.201314i
$533$	6.87606	+	6.87606i	0.297835	+	0.297835i
$534$	3.08025	−	0.548175i	0.133295	−	0.0237218i
$535$		0			0
$536$	5.33533	−	9.34355i	0.230451	−	0.403580i
$537$	−0.758493	−	2.83073i	−0.0327314	−	0.122155i
$538$	−1.73639	+	20.2166i	−0.0748610	+	0.871601i
$539$	27.6995	+	1.09438i	1.19310	+	0.0471384i
$540$		0			0
$541$	7.78637	−	13.4864i	0.334762	−	0.579825i	−0.648677	−	0.761064i	$-0.724677\pi$
$541$	7.78637	−	13.4864i	0.334762	−	0.579825i	0.983439	+	0.181239i	$0.0580107\pi$
$542$	26.4807	−	12.3994i	1.13744	−	0.532599i
$543$	10.0064	+	2.68120i	0.429414	+	0.115061i
$544$	0.563774	−	3.35274i	0.0241716	−	0.143748i
$545$		0			0
$546$	5.78481	+	2.22525i	0.247567	+	0.0952318i
$547$	−6.09970	−	6.09970i	−0.260804	−	0.260804i	0.564577	−	0.825381i	$-0.309039\pi$
$547$	−6.09970	−	6.09970i	−0.260804	−	0.260804i	−0.825381	+	0.564577i	$0.809039\pi$
$548$	−0.826900	−	9.11797i	−0.0353234	−	0.389500i
$549$	9.80190	−	5.65913i	0.418335	−	0.241526i
$550$		0			0
$551$	12.6079	+	7.27916i	0.537114	+	0.310103i
$552$	1.01711	−	3.86952i	0.0432909	−	0.164698i
$553$	−13.1885	+	12.6777i	−0.560832	+	0.539112i
$554$	5.27285	−	4.43873i	0.224022	−	0.188584i
$555$		0			0
$556$	−7.67269	−	20.8741i	−0.325395	−	0.885258i
$557$	−12.5982	−	3.37568i	−0.533804	−	0.143032i	−0.0181595	−	0.999835i	$-0.505781\pi$
$557$	−12.5982	−	3.37568i	−0.533804	−	0.143032i	−0.515644	+	0.856803i	$0.672447\pi$
$558$	7.07068	−	10.1322i	0.299326	−	0.428930i
$559$	−13.6020			−0.575303
$560$		0			0
$561$	−1.36001			−0.0574196
$562$	−7.85981	+	11.2630i	−0.331546	+	0.475100i
$563$	20.1494	+	5.39902i	0.849197	+	0.227542i	0.657071	−	0.753829i	$-0.271795\pi$
$563$	20.1494	+	5.39902i	0.849197	+	0.227542i	0.192126	+	0.981370i	$0.438462\pi$
$564$	−4.94502	−	13.4533i	−0.208223	−	0.566485i
$565$		0			0
$566$	1.53404	−	1.29137i	0.0644804	−	0.0542801i
$567$	−3.91164	−	15.8433i	−0.164274	−	0.665355i
$568$	−3.49451	+	13.2947i	−0.146627	+	0.557832i
$569$	6.92763	+	3.99967i	0.290422	+	0.167675i	0.638132	−	0.769927i	$-0.279707\pi$
$569$	6.92763	+	3.99967i	0.290422	+	0.167675i	−0.347710	+	0.937602i	$0.613041\pi$
$570$		0			0
$571$	28.4622	−	16.4326i	1.19110	−	0.687684i	0.232547	−	0.972585i	$-0.425294\pi$
$571$	28.4622	−	16.4326i	1.19110	−	0.687684i	0.958557	+	0.284901i	$0.0919607\pi$
$572$	2.07377	+	22.8668i	0.0867087	+	0.956109i
$573$	−6.33698	−	6.33698i	−0.264731	−	0.264731i
$574$	9.75949	−	7.89172i	0.407353	−	0.329394i
$575$		0			0
$576$	−10.8699	−	18.4198i	−0.452913	−	0.767490i
$577$	−37.4537	−	10.0357i	−1.55922	−	0.417791i	−0.626802	−	0.779178i	$-0.715637\pi$
$577$	−37.4537	−	10.0357i	−1.55922	−	0.417791i	−0.932416	+	0.361387i	$0.882303\pi$
$578$	−21.3103	+	9.97839i	−0.886393	+	0.415046i
$579$	−2.21768	+	3.84114i	−0.0921638	+	0.159632i
$580$		0			0
$581$	−17.9166	+	9.87773i	−0.743305	+	0.409797i
$582$	−0.109448	+	1.27429i	−0.00453675	+	0.0528211i
$583$	−3.08550	−	11.5152i	−0.127788	−	0.476912i
$584$	−13.7207	+	24.0285i	−0.567765	+	0.994304i
$585$		0			0
$586$	11.8665	−	2.11182i	0.490201	−	0.0872383i
$587$	−6.10922	−	6.10922i	−0.252155	−	0.252155i	0.569699	−	0.821854i	$-0.307060\pi$
$587$	−6.10922	−	6.10922i	−0.252155	−	0.252155i	−0.821854	+	0.569699i	$0.807060\pi$
$588$	3.64184	−	7.12272i	0.150187	−	0.293736i
$589$		−	6.55329i		−	0.270023i
$590$		0			0
$591$	−2.96018	+	1.70906i	−0.121765	+	0.0703013i
$592$	31.6863	+	21.8884i	1.30230	+	0.899608i
$593$	41.4359	−	11.1027i	1.70157	−	0.455934i	0.728236	−	0.685327i	$-0.240341\pi$
$593$	41.4359	−	11.1027i	1.70157	−	0.455934i	0.973334	+	0.229392i	$0.0736739\pi$
$594$	−13.8900	+	11.6927i	−0.569913	+	0.479757i
$595$		0			0
$596$	1.67038	−	9.65229i	0.0684212	−	0.395373i
$597$	−2.08351	−	7.77578i	−0.0852726	−	0.318242i
$598$	−4.30378	−	9.19137i	−0.175995	−	0.375863i
$599$	5.01596	+	8.68789i	0.204946	+	0.354978i	0.950116	−	0.311898i	$-0.100965\pi$
$599$	5.01596	+	8.68789i	0.204946	+	0.354978i	−0.745169	+	0.666875i	$0.767631\pi$
$600$		0			0
$601$	24.3587			0.993613			0.496806	−	0.867861i	$-0.334506\pi$
$601$	24.3587			0.993613			0.496806	+	0.867861i	$0.334506\pi$
$602$	−1.84738	+	17.4585i	−0.0752935	+	0.711556i
$603$	7.19138	−	7.19138i	0.292855	−	0.292855i
$604$	22.6394	+	18.8745i	0.921184	+	0.767994i
$605$		0			0
$606$	−13.5741	−	4.91618i	−0.551410	−	0.199706i
$607$	24.1790	−	6.47873i	0.981394	−	0.262964i	0.267762	−	0.963485i	$-0.413716\pi$
$607$	24.1790	−	6.47873i	0.981394	−	0.262964i	0.713632	+	0.700521i	$0.247049\pi$
$608$	−10.3190	−	4.71247i	−0.418491	−	0.191116i
$609$	−5.67420	+	9.39463i	−0.229930	+	0.380690i
$610$		0			0
$611$	−31.4876	−	18.1794i	−1.27385	−	0.735458i
$612$	1.34886	−	2.91678i	0.0545244	−	0.117904i
$613$	2.42522	−	9.05103i	0.0979535	−	0.365568i	−0.899497	−	0.436927i	$-0.856067\pi$
$613$	2.42522	−	9.05103i	0.0979535	−	0.365568i	0.997451	+	0.0713590i	$0.0227336\pi$
$614$	21.6656	−	3.85571i	0.874353	−	0.155604i
$615$		0			0
$616$	29.6318	+	0.443959i	1.19390	+	0.0178876i
$617$	16.6913	−	16.6913i	0.671965	−	0.671965i	−0.286204	−	0.958169i	$-0.592394\pi$
$617$	16.6913	−	16.6913i	0.671965	−	0.671965i	0.958169	+	0.286204i	$0.0923935\pi$
$618$	7.43318	+	5.18720i	0.299006	+	0.208660i
$619$	14.8926	+	25.7947i	0.598582	+	1.03677i	0.993031	+	0.117857i	$0.0376023\pi$
$619$	14.8926	+	25.7947i	0.598582	+	1.03677i	−0.394448	+	0.918918i	$0.629064\pi$
$620$		0			0
$621$	4.01273	−	6.95024i	0.161025	−	0.278904i
$622$	−3.07371	+	35.7869i	−0.123244	+	1.43492i
$623$	−7.09872	−	7.38472i	−0.284404	−	0.295863i
$624$	6.24065	+	2.22663i	0.249826	+	0.0891367i
$625$		0			0
$626$	−12.4953	+	34.5008i	−0.499412	+	1.37893i
$627$	−1.17450	+	4.38331i	−0.0469051	+	0.175052i
$628$	−2.00805	−	22.1422i	−0.0801301	−	0.883569i
$629$			5.78640i			0.230719i
$630$		0			0
$631$		−	9.29850i		−	0.370167i	−0.982723	−	0.185084i	$-0.940744\pi$
$631$		−	9.29850i		−	0.370167i	0.982723	−	0.185084i	$-0.0592556\pi$
$632$	−13.7627	+	13.8945i	−0.547453	+	0.552693i
$633$	2.55019	−	9.51742i	0.101361	−	0.378284i
$634$	−0.284972	−	0.103209i	−0.0113177	−	0.00409896i
$635$		0			0
$636$	−3.38991	−	0.586639i	−0.134418	−	0.0232618i
$637$	−4.47422	−	19.7933i	−0.177275	−	0.784239i
$638$	−40.5086	−	3.47925i	−1.60375	−	0.137745i
$639$	−6.49663	+	11.2525i	−0.257003	+	0.445142i
$640$		0			0
$641$	1.37174	+	2.37592i	0.0541805	+	0.0938434i	0.891844	−	0.452344i	$-0.149412\pi$
$641$	1.37174	+	2.37592i	0.0541805	+	0.0938434i	−0.837663	+	0.546187i	$0.816079\pi$
$642$	−3.63644	+	5.21096i	−0.143519	+	0.205660i
$643$	−4.45513	+	4.45513i	−0.175693	+	0.175693i	−0.789475	−	0.613782i	$-0.789647\pi$
$643$	−4.45513	+	4.45513i	−0.175693	+	0.175693i	0.613782	+	0.789475i	$0.289647\pi$
$644$	−12.3819	+	4.27568i	−0.487915	+	0.168485i
$645$		0			0
$646$	−0.298644	−	1.67811i	−0.0117500	−	0.0660243i
$647$	5.58856	−	20.8568i	0.219709	−	0.819964i	−0.764747	−	0.644331i	$-0.777136\pi$
$647$	5.58856	−	20.8568i	0.219709	−	0.819964i	0.984456	−	0.175633i	$-0.0561974\pi$
$648$	−4.59551	−	16.8296i	−0.180528	−	0.661130i
$649$	50.8771	+	29.3739i	1.99710	+	1.15303i
$650$		0			0
$651$	4.93943	+	0.0975380i	0.193591	+	0.00382282i
$652$	−30.0162	+	21.1599i	−1.17552	+	0.828686i
$653$	28.1634	−	7.54635i	1.10212	−	0.295311i	0.338491	−	0.940970i	$-0.390084\pi$
$653$	28.1634	−	7.54635i	1.10212	−	0.295311i	0.763627	+	0.645658i	$0.223417\pi$
$654$	0.111255	−	0.307187i	0.00435041	−	0.0120119i
$655$		0			0
$656$	10.2235	−	8.68974i	0.399159	−	0.339277i
$657$	−18.4938	+	18.4938i	−0.721511	+	0.721511i
$658$	−27.6102	+	37.9461i	−1.07636	+	1.47929i
$659$	−8.28576			−0.322768			−0.161384	−	0.986892i	$-0.551596\pi$
$659$	−8.28576			−0.322768			−0.161384	+	0.986892i	$0.551596\pi$
$660$		0			0
$661$	−10.4781	−	18.1487i	−0.407553	−	0.705902i	0.587062	−	0.809542i	$-0.300284\pi$
$661$	−10.4781	−	18.1487i	−0.407553	−	0.705902i	−0.994615	+	0.103640i	$0.966951\pi$
$662$	2.72214	−	1.27462i	0.105799	−	0.0495396i
$663$	0.257671	+	0.961643i	0.0100071	+	0.0373471i
$664$	−18.8891	+	11.0259i	−0.733040	+	0.427889i
$665$		0			0
$666$	23.4428	+	27.8482i	0.908391	+	1.07909i
$667$	17.3592	−	4.65138i	0.672150	−	0.180102i
$668$	−15.5800	+	33.6902i	−0.602807	+	1.30351i
$669$	8.07303	−	4.66096i	0.312121	−	0.180203i
$670$		0			0
$671$			16.7654i			0.647221i
$672$	3.70553	−	7.70763i	0.142944	−	0.297328i
$673$	−29.0523	−	29.0523i	−1.11988	−	1.11988i	−0.991758	−	0.128125i	$-0.959104\pi$
$673$	−29.0523	−	29.0523i	−1.11988	−	1.11988i	−0.128125	−	0.991758i	$-0.540896\pi$
$674$	−7.86798	−	44.2110i	−0.303063	−	1.70294i
$675$		0			0
$676$	−8.62775	+	3.17130i	−0.331836	+	0.121973i
$677$	10.1358	+	37.8274i	0.389551	+	1.45383i	0.830866	+	0.556473i	$0.187846\pi$
$677$	10.1358	+	37.8274i	0.389551	+	1.45383i	−0.441314	+	0.897353i	$0.645488\pi$
$678$	4.06738	+	0.349344i	0.156207	+	0.0134165i
$679$	3.66707	−	2.02172i	0.140729	−	0.0775865i
$680$		0			0
$681$	−3.45396	+	5.98243i	−0.132356	+	0.229247i
$682$	7.76095	+	16.5747i	0.297182	+	0.634676i
$683$	11.4729	+	3.07415i	0.438998	+	0.117629i	0.471547	−	0.881841i	$-0.343696\pi$
$683$	11.4729	+	3.07415i	0.438998	+	0.117629i	−0.0325489	+	0.999470i	$0.510362\pi$
$684$	−8.23591	−	6.86631i	−0.314908	−	0.262540i
$685$		0			0
$686$	−26.0129	+	3.05451i	−0.993176	+	0.116622i
$687$	−0.886428	−	0.886428i	−0.0338193	−	0.0338193i
$688$	−1.51698	+	18.7067i	−0.0578345	+	0.713187i
$689$	−7.55767	+	4.36343i	−0.287924	+	0.166233i
$690$		0			0
$691$	−6.84816	−	3.95379i	−0.260516	−	0.150409i	0.364054	−	0.931378i	$-0.381392\pi$
$691$	−6.84816	−	3.95379i	−0.260516	−	0.150409i	−0.624570	+	0.780969i	$0.714726\pi$
$692$	8.93656	+	12.6769i	0.339717	+	0.481902i
$693$	26.9089	+	7.78275i	1.02218	+	0.295642i
$694$	16.6344	+	19.7603i	0.631434	+	0.750092i
$695$		0			0
$696$	−5.81804	+	10.1889i	−0.220532	+	0.386210i
$697$	1.94732	+	0.521782i	0.0737599	+	0.0197639i
$698$	−25.0588	−	17.4871i	−0.948490	−	0.661898i
$699$	0.644031			0.0243595
$700$		0			0
$701$	29.1974			1.10277			0.551386	−	0.834250i	$-0.314099\pi$
$701$	29.1974			1.10277			0.551386	+	0.834250i	$0.314099\pi$
$702$	10.8994	+	7.60607i	0.411371	+	0.287073i
$703$	18.6496	+	4.99713i	0.703381	+	0.188470i
$704$	31.6799	−	0.301784i	1.19398	−	0.0113739i
$705$		0			0
$706$	15.4556	+	18.3600i	0.581678	+	0.690986i
$707$	11.3299	+	45.8892i	0.426103	+	1.72584i
$708$	13.8565	−	9.76814i	0.520759	−	0.367109i
$709$	23.6133	+	13.6331i	0.886816	+	0.512003i	0.872900	−	0.487900i	$-0.162237\pi$
$709$	23.6133	+	13.6331i	0.886816	+	0.512003i	0.0139163	+	0.999903i	$0.495570\pi$
$710$		0			0
$711$	−16.0089	+	9.24277i	−0.600382	+	0.346631i
$712$	−7.78003	−	7.70627i	−0.291569	−	0.288805i
$713$	−5.72029	−	5.72029i	−0.214227	−	0.214227i
$714$	1.26929	−	0.200121i	0.0475020	−	0.00748933i
$715$		0			0
$716$	−6.56833	+	7.87850i	−0.245470	+	0.294433i
$717$	−10.9580	−	2.93619i	−0.409234	−	0.109654i
$718$	5.32528	+	11.3729i	0.198738	+	0.424434i
$719$	17.9745	−	31.1327i	0.670335	−	1.16105i	−0.307474	−	0.951557i	$-0.599484\pi$
$719$	17.9745	−	31.1327i	0.670335	−	1.16105i	0.977809	−	0.209498i	$-0.0671831\pi$
$720$		0			0
$721$	0.585904	−	29.6708i	0.0218202	−	1.10500i
$722$	21.1050	+	1.81269i	0.785448	+	0.0674615i
$723$	1.27999	+	4.77699i	0.0476033	+	0.177658i
$724$	−12.5094	−	34.0326i	−0.464907	−	1.26481i
$725$		0			0
$726$	−0.663039	−	3.72568i	−0.0246077	−	0.138273i
$727$	5.64012	+	5.64012i	0.209180	+	0.209180i	0.803919	−	0.594739i	$-0.202744\pi$
$727$	5.64012	+	5.64012i	0.209180	+	0.209180i	−0.594739	+	0.803919i	$0.702744\pi$
$728$	−5.30022	−	21.0364i	−0.196439	−	0.779659i
$729$		−	10.9327i		−	0.404916i
$730$		0			0
$731$	−2.44214	+	1.40997i	−0.0903260	+	0.0521497i
$732$	4.39133	+	2.03076i	0.162308	+	0.0750591i
$733$	−15.5419	+	4.16444i	−0.574053	+	0.153817i	−0.534155	−	0.845387i	$-0.679370\pi$
$733$	−15.5419	+	4.16444i	−0.574053	+	0.153817i	−0.0398983	+	0.999204i	$0.512703\pi$
$734$	19.7993	+	23.5199i	0.730804	+	0.868136i
$735$		0			0
$736$	−13.1208	+	4.89388i	−0.483640	+	0.180391i
$737$	3.89904	+	14.5514i	0.143623	+	0.536008i
$738$	11.4858	−	5.37812i	0.422797	−	0.197971i
$739$	11.4543	+	19.8395i	0.421355	+	0.729808i	0.996072	−	0.0885439i	$-0.0282214\pi$
$739$	11.4543	+	19.8395i	0.421355	+	0.729808i	−0.574717	+	0.818352i	$0.694888\pi$
$740$		0			0
$741$	3.32190			0.122033
$742$	4.57411	+	10.2931i	0.167921	+	0.377872i
$743$	21.3493	−	21.3493i	0.783229	−	0.783229i	−0.197145	−	0.980374i	$-0.563167\pi$
$743$	21.3493	−	21.3493i	0.783229	−	0.783229i	0.980374	+	0.197145i	$0.0631669\pi$
$744$	5.28144	−	0.0251551i	0.193627	−	0.000922230i
$745$		0			0
$746$	−0.235396	+	0.649954i	−0.00861846	+	0.0237965i
$747$	−19.9691	+	5.35071i	−0.730632	+	0.195772i
$748$	2.74269	+	3.89061i	0.100283	+	0.142255i
$749$	20.8004	+	0.410742i	0.760030	+	0.0150082i
$750$		0			0
$751$	31.7774	+	18.3467i	1.15958	+	0.669481i	0.951202	−	0.308568i	$-0.0998498\pi$
$751$	31.7774	+	18.3467i	1.15958	+	0.669481i	0.208373	+	0.978049i	$0.433183\pi$
$752$	−28.5137	+	41.2772i	−1.03979	+	1.50522i
$753$	0.230154	−	0.858946i	0.00838728	−	0.0313017i
$754$	5.21476	+	29.3023i	0.189910	+	1.06713i
$755$		0			0
$756$	11.2429	−	12.9566i	0.408901	−	0.471228i
$757$	−23.2904	+	23.2904i	−0.846504	+	0.846504i	−0.989695	−	0.143191i	$-0.954264\pi$
$757$	−23.2904	+	23.2904i	−0.846504	+	0.846504i	0.143191	+	0.989695i	$0.454264\pi$
$758$	22.5246	−	32.2774i	0.818130	−	1.17237i
$759$	2.80093	+	4.85135i	0.101667	+	0.176093i
$760$		0			0
$761$	−3.80960	+	6.59842i	−0.138098	+	0.239192i	−0.926777	−	0.375613i	$-0.877432\pi$
$761$	−3.80960	+	6.59842i	−0.138098	+	0.239192i	0.788679	+	0.614806i	$0.210766\pi$
$762$	5.46715	+	0.469568i	0.198054	+	0.0170107i
$763$	−1.03849	+	0.256399i	−0.0375958	+	0.00928226i
$764$	−5.34878	+	30.9080i	−0.193512	+	1.11821i
$765$		0			0
$766$	6.87682	+	2.49060i	0.248470	+	0.0899890i
$767$	11.1305	−	41.5398i	0.401901	−	1.49991i
$768$	3.75827	−	8.33440i	0.135615	−	0.300742i
$769$		−	30.3461i		−	1.09431i	−0.837031	−	0.547155i	$-0.815711\pi$
$769$		−	30.3461i		−	1.09431i	0.837031	−	0.547155i	$-0.184289\pi$
$770$		0			0
$771$		−	10.1665i		−	0.366138i
$772$	15.4608	−	1.40213i	0.556447	−	0.0504637i
$773$	6.78186	−	25.3103i	0.243927	−	0.910347i	−0.729993	−	0.683454i	$-0.760477\pi$
$773$	6.78186	−	25.3103i	0.243927	−	0.910347i	0.973920	−	0.226892i	$-0.0728565\pi$
$774$	−6.04097	+	16.6798i	−0.217138	+	0.599543i
$775$		0			0
$776$	3.86612	−	2.25673i	0.138786	−	0.0810117i
$777$	−4.04408	+	13.9824i	−0.145081	+	0.501616i
$778$	−1.47949	+	17.2256i	−0.0530423	+	0.617568i
$779$	3.36341	−	5.82559i	0.120507	−	0.208724i
$780$		0			0
$781$	−9.62327	−	16.6680i	−0.344348	−	0.596428i
$782$	−1.72549	−	1.20412i	−0.0617032	−	0.0430592i
$783$	−16.6418	+	16.6418i	−0.594728	+	0.594728i
$784$	−27.7206	+	3.94588i	−0.990020	+	0.140924i
$785$		0			0
$786$	12.0865	−	2.15096i	0.431111	−	0.0767224i
$787$	−2.88594	+	10.7705i	−0.102873	+	0.383926i	−0.998095	−	0.0616935i	$-0.980350\pi$
$787$	−2.88594	+	10.7705i	−0.102873	+	0.383926i	0.895222	+	0.445619i	$0.147017\pi$
$788$	10.8589	+	5.02166i	0.386831	+	0.178889i
$789$	−9.50285	−	5.48647i	−0.338310	−	0.195324i
$790$		0			0
$791$	−6.45308	−	11.7048i	−0.229445	−	0.416176i
$792$	28.9620	+	7.61269i	1.02912	+	0.270505i
$793$	11.8546	−	3.17643i	0.420969	−	0.112798i
$794$	23.2526	+	8.42146i	0.825203	+	0.298866i
$795$		0			0
$796$	−18.0426	+	21.6416i	−0.639504	+	0.767065i
$797$	−9.45111	+	9.45111i	−0.334775	+	0.334775i	−0.854397	−	0.519621i	$-0.826073\pi$
$797$	−9.45111	+	9.45111i	−0.334775	+	0.334775i	0.519621	+	0.854397i	$0.326073\pi$
$798$	0.451170	−	4.26374i	0.0159712	−	0.150935i
$799$	−7.53784			−0.266670
$800$		0			0
$801$	−5.17536	−	8.96399i	−0.182863	−	0.316727i
$802$	−18.6643	−	39.8604i	−0.659060	−	1.40752i
$803$	−10.0270	−	37.4213i	−0.353846	−	1.32057i
$804$	4.28371	+	0.741317i	0.151075	+	0.0261442i
$805$		0			0
$806$	10.2493	−	8.62795i	0.361016	−	0.303906i
$807$	−7.91923	+	2.12195i	−0.278770	+	0.0746962i
$808$	13.3106	+	48.7461i	0.468267	+	1.71488i
$809$	28.2738	−	16.3239i	0.994055	−	0.573918i	0.0875707	−	0.996158i	$-0.472090\pi$
$809$	28.2738	−	16.3239i	0.994055	−	0.573918i	0.906484	+	0.422241i	$0.138756\pi$
$810$		0			0
$811$			38.0037i			1.33449i	0.744838	+	0.667245i	$0.232527\pi$
$811$			38.0037i			1.33449i	−0.744838	+	0.667245i	$0.767473\pi$
$812$	38.3185	−	2.71354i	1.34471	−	0.0952266i
$813$	8.35402	+	8.35402i	0.292988	+	0.292988i
$814$	−53.0867	+	9.44755i	−1.86069	+	0.331136i
$815$		0			0
$816$	1.35128	−	0.247125i	0.0473042	−	0.00865110i
$817$	2.43530	+	9.08868i	0.0852005	+	0.317973i
$818$	−0.619695	+	7.21506i	−0.0216671	+	0.252269i
$819$	0.404838	−	20.5014i	0.0141462	−	0.716378i
$820$		0			0
$821$	5.78912	−	10.0271i	0.202042	−	0.349947i	−0.747144	−	0.664662i	$-0.768576\pi$
$821$	5.78912	−	10.0271i	0.202042	−	0.349947i	0.949186	+	0.314715i	$0.101909\pi$
$822$	3.35015	−	1.56868i	0.116850	−	0.0547140i
$823$	32.4334	+	8.69051i	1.13056	+	0.302932i	0.775149	−	0.631779i	$-0.217675\pi$
$823$	32.4334	+	8.69051i	1.13056	+	0.302932i	0.355409	+	0.934711i	$0.384341\pi$
$824$	−0.151105	−	31.7252i	−0.00526398	−	1.10520i
$825$		0			0
$826$	−51.8057	−	19.9282i	−1.80255	−	0.693389i
$827$	4.77258	+	4.77258i	0.165959	+	0.165959i	0.785200	−	0.619242i	$-0.212560\pi$
$827$	4.77258	+	4.77258i	0.165959	+	0.165959i	−0.619242	+	0.785200i	$0.712560\pi$
$828$	−13.1826	+	1.19552i	−0.458126	+	0.0415470i
$829$	−29.2731	+	16.9008i	−1.01670	+	0.586989i	−0.913145	−	0.407635i	$-0.866354\pi$
$829$	−29.2731	+	16.9008i	−1.01670	+	0.586989i	−0.103550	+	0.994624i	$0.533020\pi$
$830$		0			0
$831$	2.41177	+	1.39244i	0.0836634	+	0.0483031i
$832$	−6.21555	−	22.3432i	−0.215485	−	0.774611i
$833$	−2.85507	−	3.08996i	−0.0989224	−	0.107061i
$834$	6.87439	−	5.78693i	0.238041	−	0.200385i
$835$		0			0
$836$	14.9080	−	5.47975i	0.515605	−	0.189521i
$837$	10.2331	+	2.74194i	0.353707	+	0.0947755i
$838$	−11.3733	+	16.2978i	−0.392885	+	0.562998i
$839$	−3.12360			−0.107839			−0.0539193	−	0.998545i	$-0.517171\pi$
$839$	−3.12360			−0.107839			−0.0539193	+	0.998545i	$0.517171\pi$
$840$		0			0
$841$	−23.7024			−0.817325
$842$	30.3742	−	43.5258i	1.04676	−	1.50000i
$843$	−5.36025	−	1.43627i	−0.184617	−	0.0494679i
$844$	−32.3696	+	11.8981i	−1.11421	+	0.409550i
$845$		0			0
$846$	−36.2773	+	30.5386i	−1.24724	+	1.04994i
$847$	−8.93212	+	8.58619i	−0.306911	+	0.295025i
$848$	5.15811	+	10.8807i	0.177130	+	0.373643i
$849$	0.701659	+	0.405103i	0.0240809	+	0.0139031i
$850$		0			0
$851$	20.6409	−	11.9171i	0.707562	−	0.408511i
$852$	−5.53147	+	0.501644i	−0.189505	+	0.0171860i
$853$	3.22775	+	3.22775i	0.110516	+	0.110516i	0.760202	−	0.649686i	$-0.225100\pi$
$853$	3.22775	+	3.22775i	0.110516	+	0.110516i	−0.649686	+	0.760202i	$0.725100\pi$
$854$	−2.46697	−	15.6471i	−0.0844181	−	0.535432i
$855$		0			0
$856$	22.2406	−	0.105930i	0.760170	−	0.00362063i
$857$	37.2336	+	9.97671i	1.27187	+	0.340798i	0.830749	−	0.556647i	$-0.187913\pi$
$857$	37.2336	+	9.97671i	1.27187	+	0.340798i	0.441126	+	0.897445i	$0.354579\pi$
$858$	−8.40179	+	3.93407i	−0.286832	+	0.134307i
$859$	−6.97976	+	12.0893i	−0.238146	+	0.412482i	−0.960182	−	0.279374i	$-0.909873\pi$
$859$	−6.97976	+	12.0893i	−0.238146	+	0.412482i	0.722036	+	0.691855i	$0.243206\pi$
$860$		0			0
$861$	4.34088	+	2.62182i	0.147937	+	0.0893513i
$862$	2.93700	−	34.1953i	0.100035	−	1.16470i
$863$	10.7069	+	39.9587i	0.364467	+	1.36021i	0.868142	+	0.496316i	$0.165314\pi$
$863$	10.7069	+	39.9587i	0.364467	+	1.36021i	−0.503675	+	0.863893i	$0.668019\pi$
$864$	11.6762	−	14.1416i	0.397231	−	0.481106i
$865$		0			0
$866$	−0.0499409	+	0.00888771i	−0.00169706	+	0.000302017i
$867$	−6.72289	−	6.72289i	−0.228321	−	0.228321i
$868$	−9.68217	−	14.3271i	−0.328634	−	0.486292i
$869$		−	27.3821i		−	0.928873i
$870$		0			0
$871$	9.55038	−	5.51391i	0.323602	−	0.186832i
$872$	−1.10314	+	0.301224i	−0.0373571	+	0.0102007i
$873$	4.08717	−	1.09515i	0.138330	−	0.0370653i
$874$	−5.37101	+	4.52136i	−0.181677	+	0.152937i
$875$		0			0
$876$	−11.0163	−	1.90642i	−0.372205	−	0.0644118i
$877$	−8.94885	−	33.3976i	−0.302181	−	1.12776i	−0.935345	−	0.353737i	$-0.884911\pi$
$877$	−8.94885	−	33.3976i	−0.302181	−	1.12776i	0.633164	−	0.774018i	$-0.281756\pi$
$878$	−9.15094	−	19.5432i	−0.308829	−	0.659550i
$879$	2.43499	+	4.21753i	0.0821303	+	0.142254i
$880$		0			0
$881$	−9.22163			−0.310685			−0.155342	−	0.987861i	$-0.549648\pi$
$881$	−9.22163			−0.310685			−0.155342	+	0.987861i	$0.549648\pi$
$882$	−26.2591	−	3.30406i	−0.884191	−	0.111253i
$883$	18.1891	−	18.1891i	0.612111	−	0.612111i	−0.331385	−	0.943496i	$-0.607516\pi$
$883$	18.1891	−	18.1891i	0.612111	−	0.612111i	0.943496	+	0.331385i	$0.107516\pi$
$884$	2.23136	−	2.67645i	0.0750488	−	0.0900186i
$885$		0			0
$886$	15.8979	+	5.75780i	0.534101	+	0.193437i
$887$	−19.5218	+	5.23085i	−0.655477	+	0.175635i	−0.571204	−	0.820808i	$-0.693524\pi$
$887$	−19.5218	+	5.23085i	−0.655477	+	0.175635i	−0.0842733	+	0.996443i	$0.526857\pi$
$888$	−3.95571	+	15.0493i	−0.132745	+	0.505020i
$889$	−8.67387	−	15.7330i	−0.290912	−	0.527667i
$890$		0			0
$891$	21.1538	+	12.2132i	0.708679	+	0.409156i
$892$	−29.6144	−	13.6951i	−0.991563	−	0.458546i
$893$	−6.50968	+	24.2944i	−0.217838	+	0.812983i
$894$	3.89674	−	0.693481i	0.130326	−	0.0231935i
$895$		0			0
$896$	−29.5223	+	4.94324i	−0.986270	+	0.165142i
$897$	2.89965	−	2.89965i	0.0968165	−	0.0968165i
$898$	15.9049	+	11.0992i	0.530755	+	0.370384i
$899$	11.8617	+	20.5451i	0.395611	+	0.685219i
$900$		0			0
$901$	−0.904619	+	1.56685i	−0.0301372	+	0.0521992i
$902$	−1.60762	+	18.7174i	−0.0535279	+	0.623221i
$903$	−6.88668	+	1.70029i	−0.229174	+	0.0565822i
$904$	−7.20319	−	12.3402i	−0.239574	−	0.410428i
$905$		0			0
$906$	−4.05550	+	11.1977i	−0.134735	+	0.372018i
$907$	10.9408	−	40.8315i	0.363282	−	1.35579i	−0.506452	−	0.862268i	$-0.669043\pi$
$907$	10.9408	−	40.8315i	0.363282	−	1.35579i	0.869734	−	0.493520i	$-0.164290\pi$
$908$	24.0796	−	2.18376i	0.799110	−	0.0724706i
$909$			47.7627i			1.58419i
$910$		0			0
$911$		−	47.4291i		−	1.57140i	−0.618610	−	0.785698i	$-0.712304\pi$
$911$		−	47.4291i		−	1.57140i	0.618610	−	0.785698i	$-0.287696\pi$
$912$	0.370480	−	4.56859i	0.0122678	−	0.151281i
$913$	7.92585	−	29.5797i	0.262307	−	0.978945i
$914$	18.5503	+	6.71841i	0.613588	+	0.222225i
$915$		0			0
$916$	−0.748196	+	4.32346i	−0.0247211	+	0.142851i
$917$	−27.8544	−	28.9767i	−0.919834	−	0.956894i
$918$	2.74535	+	0.235796i	0.0906101	+	0.00778242i
$919$	15.8502	−	27.4533i	0.522849	−	0.905601i	−0.476797	−	0.879013i	$-0.658202\pi$
$919$	15.8502	−	27.4533i	0.522849	−	0.905601i	0.999646	−	0.0265881i	$-0.00846425\pi$
$920$		0			0
$921$	4.44575	+	7.70027i	0.146493	+	0.253733i
$922$	−22.3848	+	32.0771i	−0.737205	+	1.05640i
$923$	−9.96245	+	9.96245i	−0.327918	+	0.327918i
$924$	3.90838	+	11.3182i	0.128576	+	0.372342i
$925$		0			0
$926$	1.41495	+	7.95074i	0.0464981	+	0.261278i
$927$	7.76138	−	28.9659i	0.254917	−	0.951364i
$928$	40.8808	−	3.90384i	1.34198	−	0.128150i
$929$	−37.2981	−	21.5341i	−1.22371	−	0.706509i	−0.258003	−	0.966144i	$-0.583065\pi$
$929$	−37.2981	−	21.5341i	−1.22371	−	0.706509i	−0.965707	+	0.259635i	$0.916398\pi$
$930$		0			0
$931$	−12.4246	+	6.53341i	−0.407199	+	0.214124i
$932$	−1.29880	−	1.84240i	−0.0425436	−	0.0603498i
$933$	−14.0184	+	3.75622i	−0.458941	+	0.122973i
$934$	5.91430	−	16.3300i	0.193522	−	0.534335i
$935$		0			0
$936$	−0.104408	−	21.9210i	−0.00341268	−	0.716509i
$937$	11.9105	−	11.9105i	0.389100	−	0.389100i	−0.485266	−	0.874366i	$-0.661277\pi$
$937$	11.9105	−	11.9105i	0.389100	−	0.389100i	0.874366	+	0.485266i	$0.161277\pi$
$938$	−5.78015	−	13.0070i	−0.188729	−	0.424695i
$939$	−14.8261			−0.483832
$940$		0			0
$941$	−14.1264	−	24.4676i	−0.460507	−	0.797622i	0.538479	−	0.842639i	$-0.318999\pi$
$941$	−14.1264	−	24.4676i	−0.460507	−	0.797622i	−0.998986	+	0.0450169i	$0.985666\pi$
$942$	8.13554	−	3.80940i	0.265070	−	0.124117i
$943$	−2.14922	−	8.02098i	−0.0699881	−	0.261199i
$944$	−55.8880	−	19.9406i	−1.81900	−	0.649010i
$945$		0			0
$946$	−16.9230	−	20.1031i	−0.550213	−	0.653609i
$947$	−23.9653	+	6.42148i	−0.778767	+	0.208670i	−0.626241	−	0.779629i	$-0.715408\pi$
$947$	−23.9653	+	6.42148i	−0.778767	+	0.208670i	−0.152526	+	0.988299i	$0.548741\pi$
$948$	−7.17214	−	3.31674i	−0.232940	−	0.107723i
$949$	−24.5603	+	14.1799i	−0.797263	+	0.460300i
$950$		0			0
$951$		−	0.122462i		−	0.00397109i
$952$	−3.13223	−	3.22752i	−0.101516	−	0.104604i
$953$	19.4338	+	19.4338i	0.629523	+	0.629523i	0.947948	−	0.318425i	$-0.103154\pi$
$953$	19.4338	+	19.4338i	0.629523	+	0.629523i	−0.318425	+	0.947948i	$0.603154\pi$
$954$	1.99422	+	11.2057i	0.0645651	+	0.362798i
$955$		0			0
$956$	13.6991	+	37.2692i	0.443059	+	1.20537i
$957$	−4.25181	−	15.8680i	−0.137441	−	0.512938i
$958$	−33.9356	−	2.91470i	−1.09641	−	0.0941696i
$959$	−10.3672	−	6.26162i	−0.334775	−	0.202198i
$960$		0			0
$961$	−10.1606	+	17.5986i	−0.327760	+	0.567697i
$962$	16.7382	+	35.7469i	0.539661	+	1.15253i
$963$	20.3062	+	5.44104i	0.654359	+	0.175335i
$964$	11.0843	−	13.2953i	0.357003	−	0.428213i
$965$		0			0
$966$	−3.32796	−	4.11560i	−0.107075	−	0.132417i
$967$	34.9483	+	34.9483i	1.12386	+	1.12386i	0.991155	+	0.132706i	$0.0423665\pi$
$967$	34.9483	+	34.9483i	1.12386	+	1.12386i	0.132706	+	0.991155i	$0.457633\pi$
$968$	−9.32104	+	9.41026i	−0.299590	+	0.302457i
$969$	0.596424	−	0.344346i	0.0191599	−	0.0110620i
$970$		0			0
$971$	42.2275	+	24.3801i	1.35515	+	0.782393i	0.988965	−	0.148150i	$-0.0473320\pi$
$971$	42.2275	+	24.3801i	1.35515	+	0.782393i	0.366180	+	0.930544i	$0.380665\pi$
$972$	21.6594	−	15.2688i	0.694726	−	0.489747i
$973$	−28.2618	−	8.17406i	−0.906032	−	0.262048i
$974$	3.12565	+	3.71302i	0.100152	+	0.118973i
$975$		0			0
$976$	−3.04642	−	16.6578i	−0.0975134	−	0.533203i
$977$	−42.7841	−	11.4640i	−1.36879	−	0.366765i	−0.501750	−	0.865012i	$-0.667310\pi$
$977$	−42.7841	−	11.4640i	−1.36879	−	0.366765i	−0.867035	+	0.498248i	$0.833977\pi$
$978$	−12.1686	−	8.49178i	−0.389109	−	0.271537i
$979$	15.3322			0.490020
$980$		0			0
$981$	−1.08089			−0.0345101
$982$	−4.10978	−	2.86799i	−0.131148	−	0.0915212i
$983$	6.04477	+	1.61969i	0.192798	+	0.0516601i	0.353926	−	0.935273i	$-0.384846\pi$
$983$	6.04477	+	1.61969i	0.192798	+	0.0516601i	−0.161128	+	0.986934i	$0.551513\pi$
$984$	4.70789	+	2.68828i	0.150082	+	0.0856993i
$985$		0			0
$986$	3.97373	+	4.72046i	0.126549	+	0.150330i
$987$	−18.2146	−	5.26815i	−0.579778	−	0.167687i
$988$	−6.69918	−	9.50305i	−0.213129	−	0.302332i
$989$	10.0592	+	5.80766i	0.319863	+	0.184673i
$990$		0			0
$991$	−23.9504	+	13.8278i	−0.760809	+	0.439253i	−0.829586	−	0.558379i	$-0.811424\pi$
$991$	−23.9504	+	13.8278i	−0.760809	+	0.439253i	0.0687769	+	0.997632i	$0.478090\pi$
$992$	−10.7229	−	15.0580i	−0.340452	−	0.478093i
$993$	0.858769	+	0.858769i	0.0272522	+	0.0272522i
$994$	11.4340	+	14.1401i	0.362664	+	0.448498i
$995$		0			0
$996$	−6.78771	−	5.65893i	−0.215077	−	0.179310i
$997$	8.67546	+	2.32458i	0.274755	+	0.0736203i	0.393565	−	0.919297i	$-0.371242\pi$
$997$	8.67546	+	2.32458i	0.274755	+	0.0736203i	−0.118811	+	0.992917i	$0.537908\pi$
$998$	18.1887	+	38.8447i	0.575753	+	1.22961i
$999$	−15.6062	+	27.0308i	−0.493759	+	0.855216i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.be.e.443.13		72
4.3	odd	2	inner	700.2.be.e.443.2		72
5.2	odd	4	inner	700.2.be.e.107.16		72
5.3	odd	4		140.2.w.b.107.3	yes	72
5.4	even	2		140.2.w.b.23.6	✓	72
7.4	even	3	inner	700.2.be.e.543.12		72
20.3	even	4		140.2.w.b.107.7	yes	72
20.7	even	4	inner	700.2.be.e.107.12		72
20.19	odd	2		140.2.w.b.23.17	yes	72
28.11	odd	6	inner	700.2.be.e.543.16		72
35.3	even	12		980.2.x.m.67.17		72
35.4	even	6		140.2.w.b.123.7	yes	72
35.9	even	6		980.2.k.k.883.17		36
35.13	even	4		980.2.x.m.667.3		72
35.18	odd	12		140.2.w.b.67.17	yes	72
35.19	odd	6		980.2.k.j.883.17		36
35.23	odd	12		980.2.k.k.687.9		36
35.24	odd	6		980.2.x.m.263.7		72
35.32	odd	12	inner	700.2.be.e.207.2		72
35.33	even	12		980.2.k.j.687.9		36
35.34	odd	2		980.2.x.m.863.6		72
140.3	odd	12		980.2.x.m.67.6		72
140.19	even	6		980.2.k.j.883.9		36
140.23	even	12		980.2.k.k.687.17		36
140.39	odd	6		140.2.w.b.123.3	yes	72
140.59	even	6		980.2.x.m.263.3		72
140.67	even	12	inner	700.2.be.e.207.13		72
140.79	odd	6		980.2.k.k.883.9		36
140.83	odd	4		980.2.x.m.667.7		72
140.103	odd	12		980.2.k.j.687.17		36
140.123	even	12		140.2.w.b.67.6	yes	72
140.139	even	2		980.2.x.m.863.17		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.6	✓	72	5.4	even	2
140.2.w.b.23.17	yes	72	20.19	odd	2
140.2.w.b.67.6	yes	72	140.123	even	12
140.2.w.b.67.17	yes	72	35.18	odd	12
140.2.w.b.107.3	yes	72	5.3	odd	4
140.2.w.b.107.7	yes	72	20.3	even	4
140.2.w.b.123.3	yes	72	140.39	odd	6
140.2.w.b.123.7	yes	72	35.4	even	6
700.2.be.e.107.12		72	20.7	even	4	inner
700.2.be.e.107.16		72	5.2	odd	4	inner
700.2.be.e.207.2		72	35.32	odd	12	inner
700.2.be.e.207.13		72	140.67	even	12	inner
700.2.be.e.443.2		72	4.3	odd	2	inner
700.2.be.e.443.13		72	1.1	even	1	trivial
700.2.be.e.543.12		72	7.4	even	3	inner
700.2.be.e.543.16		72	28.11	odd	6	inner
980.2.k.j.687.9		36	35.33	even	12
980.2.k.j.687.17		36	140.103	odd	12
980.2.k.j.883.9		36	140.19	even	6
980.2.k.j.883.17		36	35.19	odd	6
980.2.k.k.687.9		36	35.23	odd	12
980.2.k.k.687.17		36	140.23	even	12
980.2.k.k.883.9		36	140.79	odd	6
980.2.k.k.883.17		36	35.9	even	6
980.2.x.m.67.6		72	140.3	odd	12
980.2.x.m.67.17		72	35.3	even	12
980.2.x.m.263.3		72	140.59	even	6
980.2.x.m.263.7		72	35.24	odd	6
980.2.x.m.667.3		72	35.13	even	4
980.2.x.m.667.7		72	140.83	odd	4
980.2.x.m.863.6		72	35.34	odd	2
980.2.x.m.863.17		72	140.139	even	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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809319 - 1.15974i) q^{2} +(0.551941 + 0.147892i) q^{3} +(-0.690004 - 1.87720i) q^{4} +(0.618214 - 0.520418i) q^{6} +(-2.54158 - 0.735093i) q^{7} +(-2.73551 - 0.719030i) q^{8} +(-2.31531 - 1.33674i) q^{9} +O(q^{10})\)	\(q+(0.809319 - 1.15974i) q^{2} +(0.551941 + 0.147892i) q^{3} +(-0.690004 - 1.87720i) q^{4} +(0.618214 - 0.520418i) q^{6} +(-2.54158 - 0.735093i) q^{7} +(-2.73551 - 0.719030i) q^{8} +(-2.31531 - 1.33674i) q^{9} +(3.42960 - 1.98008i) q^{11} +(-0.103218 - 1.13815i) q^{12} +(-2.04987 - 2.04987i) q^{13} +(-2.90947 + 2.35266i) q^{14} +(-3.04779 + 2.59056i) q^{16} +(-0.580528 - 0.155552i) q^{17} +(-3.42410 + 1.60331i) q^{18} +(-1.00269 + 1.73671i) q^{19} +(-1.29409 - 0.781608i) q^{21} +(0.479259 - 5.57997i) q^{22} +(0.640717 + 2.39119i) q^{23} +(-1.40350 - 0.801422i) q^{24} +(-4.03632 + 0.718322i) q^{26} +(-2.29237 - 2.29237i) q^{27} +(0.373784 + 5.27828i) q^{28} -7.25964i q^{29} +(-2.83005 + 1.63393i) q^{31} +(0.537745 + 5.63124i) q^{32} +(2.18578 - 0.585677i) q^{33} +(-0.650233 + 0.547372i) q^{34} +(-0.911768 + 5.26867i) q^{36} +(-2.49187 - 9.29977i) q^{37} +(1.20264 + 2.56841i) q^{38} +(-0.828248 - 1.43457i) q^{39} -3.35439 q^{41} +(-1.95380 + 0.868240i) q^{42} +(3.31777 - 3.31777i) q^{43} +(-6.08345 - 5.07179i) q^{44} +(3.29171 + 1.19217i) q^{46} +(12.1147 - 3.24611i) q^{47} +(-2.06532 + 0.979091i) q^{48} +(5.91928 + 3.73660i) q^{49} +(-0.297413 - 0.171711i) q^{51} +(-2.43360 + 5.26244i) q^{52} +(0.779134 - 2.90777i) q^{53} +(-4.51381 + 0.803298i) q^{54} +(6.42396 + 3.83832i) q^{56} +(-0.810271 + 0.810271i) q^{57} +(-8.41932 - 5.87537i) q^{58} +(7.41735 + 12.8472i) q^{59} +(-2.11676 + 3.66633i) q^{61} +(-0.395476 + 4.60450i) q^{62} +(4.90192 + 5.09941i) q^{63} +(6.96599 + 3.93382i) q^{64} +(1.08976 - 3.00894i) q^{66} +(-0.984566 + 3.67445i) q^{67} +(0.108564 + 1.19710i) q^{68} +1.41455i q^{69} -4.86004i q^{71} +(5.37238 + 5.32145i) q^{72} +(2.53197 - 9.44944i) q^{73} +(-12.8021 - 4.63656i) q^{74} +(3.95201 + 0.683915i) q^{76} +(-10.1722 + 2.51146i) q^{77} +(-2.33405 - 0.200469i) q^{78} +(3.45719 - 5.98803i) q^{79} +(3.08400 + 5.34165i) q^{81} +(-2.71477 + 3.89023i) q^{82} +(5.46792 - 5.46792i) q^{83} +(-0.574310 + 2.96858i) q^{84} +(-1.16262 - 6.53289i) q^{86} +(1.07364 - 4.00690i) q^{87} +(-10.8054 + 2.95054i) q^{88} +(3.35292 + 1.93581i) q^{89} +(3.70307 + 6.71676i) q^{91} +(4.04665 - 2.85269i) q^{92} +(-1.80367 + 0.483291i) q^{93} +(6.03997 - 16.6770i) q^{94} +(-0.536012 + 3.18764i) q^{96} +(-1.11914 + 1.11914i) q^{97} +(9.12407 - 3.84074i) q^{98} -10.5874 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8}+O(q^{10}) \) 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8	\( 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8} - 10 q^{12} - 28 q^{16} - 4 q^{17} + 20 q^{18} + 4 q^{21} + 16 q^{22} - 4 q^{26} - 42 q^{28} + 38 q^{32} + 64 q^{33} + 16 q^{36} + 4 q^{37} - 12 q^{38} - 40 q^{41} - 78 q^{42} - 28 q^{46} - 12 q^{48} - 48 q^{52} + 24 q^{53} + 36 q^{56} + 16 q^{57} - 30 q^{58} - 20 q^{61} - 56 q^{62} + 44 q^{66} + 12 q^{68} - 44 q^{72} + 12 q^{73} + 112 q^{76} - 16 q^{77} - 64 q^{78} - 52 q^{81} + 34 q^{82} + 64 q^{86} - 16 q^{88} - 44 q^{92} - 12 q^{93} - 48 q^{96} + 24 q^{97} + 90 q^{98}+O(q^{100}) \) 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8 - 10 * q^12 - 28 * q^16 - 4 * q^17 + 20 * q^18 + 4 * q^21 + 16 * q^22 - 4 * q^26 - 42 * q^28 + 38 * q^32 + 64 * q^33 + 16 * q^36 + 4 * q^37 - 12 * q^38 - 40 * q^41 - 78 * q^42 - 28 * q^46 - 12 * q^48 - 48 * q^52 + 24 * q^53 + 36 * q^56 + 16 * q^57 - 30 * q^58 - 20 * q^61 - 56 * q^62 + 44 * q^66 + 12 * q^68 - 44 * q^72 + 12 * q^73 + 112 * q^76 - 16 * q^77 - 64 * q^78 - 52 * q^81 + 34 * q^82 + 64 * q^86 - 16 * q^88 - 44 * q^92 - 12 * q^93 - 48 * q^96 + 24 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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