LMFDB - Embedded newform 950.2.l.l.351.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			351.1
Character	$\chi$	$=$	950.351
Dual form			950.2.l.l.701.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(-2.12694 + 1.78472i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.12694 + 1.78472i) q^{6} +(-0.303737 + 0.526088i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.817727 - 4.63756i) q^{9} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{2} +(-2.12694 + 1.78472i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.12694 + 1.78472i) q^{6} +(-0.303737 + 0.526088i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.817727 - 4.63756i) q^{9} +(-1.15506 - 2.00062i) q^{11} +(1.38826 - 2.40454i) q^{12} +(5.07671 + 4.25986i) q^{13} +(0.570839 + 0.207769i) q^{14} +(0.766044 - 0.642788i) q^{16} +(0.344141 + 1.95172i) q^{17} -4.70910 q^{18} +(4.08792 - 1.51293i) q^{19} +(-0.292887 - 1.66104i) q^{21} +(-1.76966 + 1.48492i) q^{22} +(-4.39211 + 1.59860i) q^{23} +(-2.60908 - 0.949628i) q^{24} +(3.31359 - 5.73930i) q^{26} +(2.37268 + 4.10960i) q^{27} +(0.105487 - 0.598246i) q^{28} +(-0.744297 + 4.22112i) q^{29} +(2.24521 - 3.88881i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(6.02730 + 2.19376i) q^{33} +(1.86231 - 0.677825i) q^{34} +(0.817727 + 4.63756i) q^{36} -0.721909 q^{37} +(-2.19980 - 3.76309i) q^{38} -18.4005 q^{39} +(-9.15679 + 7.68346i) q^{41} +(-1.58495 + 0.576875i) q^{42} +(-11.0333 - 4.01578i) q^{43} +(1.76966 + 1.48492i) q^{44} +(2.33699 + 4.04779i) q^{46} +(-0.863537 + 4.89736i) q^{47} +(-0.482139 + 2.73434i) q^{48} +(3.31549 + 5.74259i) q^{49} +(-4.21524 - 3.53700i) q^{51} +(-6.22751 - 2.26663i) q^{52} +(-5.28731 + 1.92442i) q^{53} +(3.63516 - 3.05026i) q^{54} -0.607475 q^{56} +(-5.99462 + 10.5137i) q^{57} +4.28624 q^{58} +(0.438402 + 2.48630i) q^{59} +(-4.58786 + 1.66984i) q^{61} +(-4.21961 - 1.53581i) q^{62} +(2.19139 + 1.83880i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.11380 - 6.31667i) q^{66} +(0.802437 - 4.55085i) q^{67} +(-0.990914 - 1.71631i) q^{68} +(6.48873 - 11.2388i) q^{69} +(-5.66293 - 2.06114i) q^{71} +(4.42511 - 1.61061i) q^{72} +(0.771436 - 0.647312i) q^{73} +(0.125358 + 0.710942i) q^{74} +(-3.32393 + 2.81983i) q^{76} +1.40334 q^{77} +(3.19522 + 18.1210i) q^{78} +(-2.36071 + 1.98087i) q^{79} +(0.894288 + 0.325494i) q^{81} +(9.15679 + 7.68346i) q^{82} +(-7.56994 + 13.1115i) q^{83} +(0.843335 + 1.46070i) q^{84} +(-2.03886 + 11.5630i) q^{86} +(-5.95043 - 10.3064i) q^{87} +(1.15506 - 2.00062i) q^{88} +(8.62809 + 7.23983i) q^{89} +(-3.78305 + 1.37692i) q^{91} +(3.58048 - 3.00438i) q^{92} +(2.16500 + 12.2783i) q^{93} +4.97291 q^{94} +2.77653 q^{96} +(1.38723 + 7.86738i) q^{97} +(5.07962 - 4.26231i) q^{98} +(-10.2225 + 3.72070i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) $ 30 * q - 12 * q^7 + 15 * q^8	$ 30 q - 12 q^{7} + 15 q^{8} + 6 q^{11} + 6 q^{14} - 30 q^{18} + 24 q^{19} + 24 q^{21} + 3 q^{22} + 3 q^{23} + 3 q^{26} - 18 q^{27} + 3 q^{28} + 12 q^{29} - 30 q^{33} + 24 q^{37} - 12 q^{38} - 24 q^{39} - 3 q^{41} + 12 q^{42} + 6 q^{43} - 3 q^{44} + 48 q^{47} + 15 q^{49} - 90 q^{51} - 18 q^{53} + 18 q^{54} - 24 q^{56} - 42 q^{57} + 36 q^{58} - 18 q^{59} - 60 q^{61} - 24 q^{62} - 21 q^{63} - 15 q^{64} - 78 q^{66} - 30 q^{67} - 12 q^{68} + 24 q^{69} + 30 q^{73} - 9 q^{74} - 3 q^{76} + 78 q^{77} - 6 q^{79} + 60 q^{81} + 3 q^{82} - 42 q^{83} - 6 q^{84} + 12 q^{86} - 54 q^{87} - 6 q^{88} - 30 q^{89} - 6 q^{91} - 6 q^{92} + 72 q^{93} - 78 q^{94} - 42 q^{97} + 6 q^{98} - 99 q^{99}+O(q^{100}) $ 30 * q - 12 * q^7 + 15 * q^8 + 6 * q^11 + 6 * q^14 - 30 * q^18 + 24 * q^19 + 24 * q^21 + 3 * q^22 + 3 * q^23 + 3 * q^26 - 18 * q^27 + 3 * q^28 + 12 * q^29 - 30 * q^33 + 24 * q^37 - 12 * q^38 - 24 * q^39 - 3 * q^41 + 12 * q^42 + 6 * q^43 - 3 * q^44 + 48 * q^47 + 15 * q^49 - 90 * q^51 - 18 * q^53 + 18 * q^54 - 24 * q^56 - 42 * q^57 + 36 * q^58 - 18 * q^59 - 60 * q^61 - 24 * q^62 - 21 * q^63 - 15 * q^64 - 78 * q^66 - 30 * q^67 - 12 * q^68 + 24 * q^69 + 30 * q^73 - 9 * q^74 - 3 * q^76 + 78 * q^77 - 6 * q^79 + 60 * q^81 + 3 * q^82 - 42 * q^83 - 6 * q^84 + 12 * q^86 - 54 * q^87 - 6 * q^88 - 30 * q^89 - 6 * q^91 - 6 * q^92 + 72 * q^93 - 78 * q^94 - 42 * q^97 + 6 * q^98 - 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$	−2.12694	+	1.78472i	−1.22799	+	1.03041i	−0.229624	+	0.973279i	$0.573750\pi$
$3$	−2.12694	+	1.78472i	−1.22799	+	1.03041i	−0.998367	+	0.0571273i	$0.981806\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$		0			0
$5$		0			0
$6$	2.12694	+	1.78472i	0.868321	+	0.728608i
$7$	−0.303737	+	0.526088i	−0.114802	+	0.198843i	−0.917701	−	0.397273i	$-0.869957\pi$
$7$	−0.303737	+	0.526088i	−0.114802	+	0.198843i	0.802899	+	0.596116i	$0.203290\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.817727	−	4.63756i	0.272576	−	1.54585i
$10$		0			0
$11$	−1.15506	−	2.00062i	−0.348264	−	0.603211i	0.637677	−	0.770304i	$-0.279895\pi$
$11$	−1.15506	−	2.00062i	−0.348264	−	0.603211i	−0.985941	+	0.167093i	$0.946562\pi$
$12$	1.38826	−	2.40454i	0.400757	−	0.694132i
$13$	5.07671	+	4.25986i	1.40803	+	1.18147i	0.957401	+	0.288760i	$0.0932430\pi$
$13$	5.07671	+	4.25986i	1.40803	+	1.18147i	0.450624	+	0.892714i	$0.351201\pi$
$14$	0.570839	+	0.207769i	0.152563	+	0.0555285i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.344141	+	1.95172i	0.0834664	+	0.473362i	0.997677	+	0.0681221i	$0.0217007\pi$
$17$	0.344141	+	1.95172i	0.0834664	+	0.473362i	−0.914211	+	0.405239i	$0.867188\pi$
$18$	−4.70910			−1.10995
$19$	4.08792	−	1.51293i	0.937832	−	0.347089i
$19$	4.08792	−	1.51293i	0.937832	−	0.347089i
$20$		0			0
$21$	−0.292887	−	1.66104i	−0.0639132	−	0.362470i
$22$	−1.76966	+	1.48492i	−0.377292	+	0.316586i
$23$	−4.39211	+	1.59860i	−0.915819	+	0.333331i	−0.756574	−	0.653908i	$-0.773128\pi$
$23$	−4.39211	+	1.59860i	−0.915819	+	0.333331i	−0.159245	+	0.987239i	$0.550906\pi$
$24$	−2.60908	−	0.949628i	−0.532577	−	0.193842i
$25$		0			0
$26$	3.31359	−	5.73930i	0.649848	−	1.12557i
$27$	2.37268	+	4.10960i	0.456622	+	0.790893i
$28$	0.105487	−	0.598246i	0.0199351	−	0.113058i
$29$	−0.744297	+	4.22112i	−0.138213	+	0.783842i	0.834356	+	0.551226i	$0.185840\pi$
$29$	−0.744297	+	4.22112i	−0.138213	+	0.783842i	−0.972569	+	0.232616i	$0.925271\pi$
$30$		0			0
$31$	2.24521	−	3.88881i	0.403251	−	0.698451i	−0.590865	−	0.806770i	$-0.701213\pi$
$31$	2.24521	−	3.88881i	0.403251	−	0.698451i	0.994116	+	0.108319i	$0.0345468\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	6.02730	+	2.19376i	1.04922	+	0.381884i
$34$	1.86231	−	0.677825i	0.319383	−	0.116246i
$35$		0			0
$36$	0.817727	+	4.63756i	0.136288	+	0.772926i
$37$	−0.721909			−0.118681			−0.0593406	−	0.998238i	$-0.518900\pi$
$37$	−0.721909			−0.118681			−0.0593406	+	0.998238i	$0.518900\pi$
$38$	−2.19980	−	3.76309i	−0.356855	−	0.610455i
$39$	−18.4005			−2.94644
$40$		0			0
$41$	−9.15679	+	7.68346i	−1.43005	+	1.19995i	−0.484366	+	0.874865i	$0.660950\pi$
$41$	−9.15679	+	7.68346i	−1.43005	+	1.19995i	−0.945683	+	0.325089i	$0.894606\pi$
$42$	−1.58495	+	0.576875i	−0.244563	+	0.0890137i
$43$	−11.0333	−	4.01578i	−1.68256	−	0.612401i	−0.688900	−	0.724856i	$-0.741906\pi$
$43$	−11.0333	−	4.01578i	−1.68256	−	0.612401i	−0.993657	+	0.112455i	$0.964128\pi$
$44$	1.76966	+	1.48492i	0.266786	+	0.223860i
$45$		0			0
$46$	2.33699	+	4.04779i	0.344571	+	0.596815i
$47$	−0.863537	+	4.89736i	−0.125960	+	0.714353i	0.854773	+	0.519001i	$0.173696\pi$
$47$	−0.863537	+	4.89736i	−0.125960	+	0.714353i	−0.980733	+	0.195352i	$0.937415\pi$
$48$	−0.482139	+	2.73434i	−0.0695907	+	0.394669i
$49$	3.31549	+	5.74259i	0.473641	+	0.820370i
$50$		0			0
$51$	−4.21524	−	3.53700i	−0.590251	−	0.495279i
$52$	−6.22751	−	2.26663i	−0.863600	−	0.314325i
$53$	−5.28731	+	1.92442i	−0.726267	+	0.264340i	−0.678584	−	0.734523i	$-0.737406\pi$
$53$	−5.28731	+	1.92442i	−0.726267	+	0.264340i	−0.0476834	+	0.998863i	$0.515184\pi$
$54$	3.63516	−	3.05026i	0.494682	−	0.415088i
$55$		0			0
$56$	−0.607475			−0.0811772
$57$	−5.99462	+	10.5137i	−0.794007	+	1.39257i
$58$	4.28624			0.562811
$59$	0.438402	+	2.48630i	0.0570751	+	0.323689i	0.999955	−	0.00944283i	$-0.00300579\pi$
$59$	0.438402	+	2.48630i	0.0570751	+	0.323689i	−0.942880	+	0.333132i	$0.891895\pi$
$60$		0			0
$61$	−4.58786	+	1.66984i	−0.587415	+	0.213802i	−0.618592	−	0.785712i	$-0.712297\pi$
$61$	−4.58786	+	1.66984i	−0.587415	+	0.213802i	0.0311770	+	0.999514i	$0.490074\pi$
$62$	−4.21961	−	1.53581i	−0.535891	−	0.195048i
$63$	2.19139	+	1.83880i	0.276089	+	0.231666i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	1.11380	−	6.31667i	0.137099	−	0.777528i
$67$	0.802437	−	4.55085i	0.0980333	−	0.555975i	−0.895742	−	0.444574i	$-0.853355\pi$
$67$	0.802437	−	4.55085i	0.0980333	−	0.555975i	0.993776	−	0.111401i	$-0.0355337\pi$
$68$	−0.990914	−	1.71631i	−0.120166	−	0.208134i
$69$	6.48873	−	11.2388i	0.781151	−	1.35299i
$70$		0			0
$71$	−5.66293	−	2.06114i	−0.672066	−	0.244612i	−0.0166286	−	0.999862i	$-0.505293\pi$
$71$	−5.66293	−	2.06114i	−0.672066	−	0.244612i	−0.655437	+	0.755250i	$0.727516\pi$
$72$	4.42511	−	1.61061i	0.521504	−	0.189812i
$73$	0.771436	−	0.647312i	0.0902898	−	0.0757621i	−0.596526	−	0.802594i	$-0.703453\pi$
$73$	0.771436	−	0.647312i	0.0902898	−	0.0757621i	0.686815	+	0.726832i	$0.259008\pi$
$74$	0.125358	+	0.710942i	0.0145726	+	0.0826453i
$75$		0			0
$76$	−3.32393	+	2.81983i	−0.381281	+	0.323457i
$77$	1.40334			0.159925
$78$	3.19522	+	18.1210i	0.361787	+	2.05180i
$79$	−2.36071	+	1.98087i	−0.265601	+	0.222865i	−0.765855	−	0.643013i	$-0.777684\pi$
$79$	−2.36071	+	1.98087i	−0.265601	+	0.222865i	0.500255	+	0.865878i	$0.333240\pi$
$80$		0			0
$81$	0.894288	+	0.325494i	0.0993653	+	0.0361660i
$82$	9.15679	+	7.68346i	1.01120	+	0.848496i
$83$	−7.56994	+	13.1115i	−0.830908	+	1.43918i	0.0664104	+	0.997792i	$0.478845\pi$
$83$	−7.56994	+	13.1115i	−0.830908	+	1.43918i	−0.897319	+	0.441383i	$0.854488\pi$
$84$	0.843335	+	1.46070i	0.0920154	+	0.159375i
$85$		0			0
$86$	−2.03886	+	11.5630i	−0.219856	+	1.24687i
$87$	−5.95043	−	10.3064i	−0.637953	−	1.10497i
$88$	1.15506	−	2.00062i	0.123130	−	0.213267i
$89$	8.62809	+	7.23983i	0.914576	+	0.767420i	0.972984	−	0.230873i	$-0.0741581\pi$
$89$	8.62809	+	7.23983i	0.914576	+	0.767420i	−0.0584083	+	0.998293i	$0.518603\pi$
$90$		0			0
$91$	−3.78305	+	1.37692i	−0.396572	+	0.144340i
$92$	3.58048	−	3.00438i	0.373291	−	0.313229i
$93$	2.16500	+	12.2783i	0.224500	+	1.27320i
$94$	4.97291			0.512916
$95$		0			0
$96$	2.77653			0.283378
$97$	1.38723	+	7.86738i	0.140852	+	0.798812i	0.970605	+	0.240680i	$0.0773705\pi$
$97$	1.38723	+	7.86738i	0.140852	+	0.798812i	−0.829752	+	0.558132i	$0.811518\pi$
$98$	5.07962	−	4.26231i	0.513119	−	0.430558i
$99$	−10.2225	+	3.72070i	−1.02740	+	0.373944i
$100$		0			0
$101$	2.46801	+	2.07091i	0.245577	+	0.206063i	0.757265	−	0.653108i	$-0.226535\pi$
$101$	2.46801	+	2.07091i	0.245577	+	0.206063i	−0.511688	+	0.859171i	$0.670980\pi$
$102$	−2.75130	+	4.76539i	−0.272419	+	0.471844i
$103$	1.30838	+	2.26619i	0.128919	+	0.223294i	0.923258	−	0.384181i	$-0.125516\pi$
$103$	1.30838	+	2.26619i	0.128919	+	0.223294i	−0.794339	+	0.607475i	$0.792183\pi$
$104$	−1.15080	+	6.52649i	−0.112845	+	0.639975i
$105$		0			0
$106$	2.81332	+	4.87281i	0.273254	+	0.473289i
$107$	6.31561	−	10.9389i	0.610553	−	1.05751i	−0.380595	−	0.924742i	$-0.624281\pi$
$107$	6.31561	−	10.9389i	0.610553	−	1.05751i	0.991147	−	0.132766i	$-0.0423860\pi$
$108$	−3.63516	−	3.05026i	−0.349793	−	0.293511i
$109$	−14.9133	−	5.42799i	−1.42843	−	0.519907i	−0.491951	−	0.870623i	$-0.663716\pi$
$109$	−14.9133	−	5.42799i	−1.42843	−	0.519907i	−0.936482	+	0.350715i	$0.885938\pi$
$110$		0			0
$111$	1.53546	−	1.28840i	0.145739	−	0.122290i
$112$	0.105487	+	0.598246i	0.00996757	+	0.0565289i
$113$	0.802158			0.0754607			0.0377303	−	0.999288i	$-0.487987\pi$
$113$	0.802158			0.0754607			0.0377303	+	0.999288i	$0.487987\pi$
$114$	11.3949	+	4.07787i	1.06723	+	0.381927i
$115$		0			0
$116$	−0.744297	−	4.22112i	−0.0691063	−	0.391921i
$117$	23.9067	−	20.0601i	2.21018	−	1.85456i
$118$	2.37240	−	0.863483i	0.218397	−	0.0794901i
$119$	−1.13131	−	0.411762i	−0.103707	−	0.0377461i
$120$		0			0
$121$	2.83167	−	4.90459i	0.257424	−	0.445872i
$122$	2.44115	+	4.22819i	0.221011	+	0.382803i
$123$	5.76317	−	32.6845i	0.519647	−	2.94707i
$124$	−0.779752	+	4.42219i	−0.0700238	+	0.397125i
$125$		0			0
$126$	1.43033	−	2.47740i	0.127424	−	0.220705i
$127$	−3.10316	−	2.60386i	−0.275361	−	0.231056i	0.494640	−	0.869098i	$-0.335300\pi$
$127$	−3.10316	−	2.60386i	−0.275361	−	0.231056i	−0.770001	+	0.638042i	$0.779744\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	30.6342	−	11.1499i	2.69719	−	0.981696i
$130$		0			0
$131$	3.37586	+	19.1454i	0.294950	+	1.67275i	0.667405	+	0.744695i	$0.267405\pi$
$131$	3.37586	+	19.1454i	0.294950	+	1.67275i	−0.372455	+	0.928050i	$0.621484\pi$
$132$	−6.41411			−0.558277
$133$	−0.445720	+	2.61014i	−0.0386488	+	0.226328i
$134$	−4.62105			−0.399198
$135$		0			0
$136$	−1.51817	+	1.27389i	−0.130182	+	0.109236i
$137$	−13.0090	+	4.73488i	−1.11143	+	0.404528i	−0.831519	−	0.555497i	$-0.812528\pi$
$137$	−13.0090	+	4.73488i	−1.11143	+	0.404528i	−0.279914	+	0.960025i	$0.590306\pi$
$138$	−12.1948	−	4.43855i	−1.03809	−	0.377835i
$139$	−10.0356	−	8.42083i	−0.851204	−	0.714245i	0.108850	−	0.994058i	$-0.465283\pi$
$139$	−10.0356	−	8.42083i	−0.851204	−	0.714245i	−0.960055	+	0.279813i	$0.909728\pi$
$140$		0			0
$141$	−6.90371	−	11.9576i	−0.581397	−	1.00701i
$142$	−1.04647	+	5.93481i	−0.0878175	+	0.498038i
$143$	2.65848	−	15.0770i	0.222313	−	1.26080i
$144$	−2.35455	−	4.07820i	−0.196212	−	0.339850i
$145$		0			0
$146$	−0.771436	−	0.647312i	−0.0638445	−	0.0535719i
$147$	−17.3008	−	6.29696i	−1.42694	−	0.519364i
$148$	0.678373	−	0.246907i	0.0557619	−	0.0202957i
$149$	−4.43881	+	3.72461i	−0.363642	+	0.305132i	−0.806240	−	0.591588i	$-0.798501\pi$
$149$	−4.43881	+	3.72461i	−0.363642	+	0.305132i	0.442599	+	0.896720i	$0.354057\pi$
$150$		0			0
$151$	18.8185			1.53142			0.765712	−	0.643184i	$-0.222387\pi$
$151$	18.8185			1.53142			0.765712	+	0.643184i	$0.222387\pi$
$152$	3.35419	+	2.78378i	0.272061	+	0.225794i
$153$	9.33263			0.754498
$154$	−0.243688	−	1.38202i	−0.0196369	−	0.111366i
$155$		0			0
$156$	17.2908	−	6.29335i	1.38437	−	0.503871i
$157$	−2.42028	−	0.880908i	−0.193159	−	0.0703041i	0.243629	−	0.969868i	$-0.421662\pi$
$157$	−2.42028	−	0.880908i	−0.193159	−	0.0703041i	−0.436788	+	0.899564i	$0.643884\pi$
$158$	2.36071	+	1.98087i	0.187808	+	0.157590i
$159$	7.81125	−	13.5295i	0.619472	−	1.07296i
$160$		0			0
$161$	0.493044	−	2.79619i	0.0388573	−	0.220371i
$162$	0.165258	−	0.937223i	0.0129839	−	0.0736352i
$163$	−1.51707	−	2.62764i	−0.118826	−	0.205813i	0.800477	−	0.599364i	$-0.204580\pi$
$163$	−1.51707	−	2.62764i	−0.118826	−	0.205813i	−0.919303	+	0.393551i	$0.871246\pi$
$164$	5.97667	−	10.3519i	0.466699	−	0.808347i
$165$		0			0
$166$	14.2268	+	5.17814i	1.10422	+	0.401902i
$167$	5.02408	−	1.82862i	0.388775	−	0.141503i	−0.140235	−	0.990118i	$-0.544786\pi$
$167$	5.02408	−	1.82862i	0.388775	−	0.141503i	0.529010	+	0.848616i	$0.322564\pi$
$168$	1.29206	−	1.08417i	0.0996849	−	0.0836455i
$169$	5.36910	+	30.4497i	0.413008	+	2.34228i
$170$		0			0
$171$	−3.67348	−	20.1951i	−0.280918	−	1.54436i
$172$	11.7414			0.895270
$173$	−3.78707	−	21.4775i	−0.287926	−	1.63291i	−0.694644	−	0.719354i	$-0.744438\pi$
$173$	−3.78707	−	21.4775i	−0.287926	−	1.63291i	0.406718	−	0.913554i	$-0.366673\pi$
$174$	−9.11658	+	7.64972i	−0.691126	+	0.579924i
$175$		0			0
$176$	−2.17080	−	0.790108i	−0.163631	−	0.0595567i
$177$	−5.36980	−	4.50579i	−0.403619	−	0.338676i
$178$	5.63159	−	9.75419i	0.422105	−	0.731108i
$179$	5.82222	+	10.0844i	0.435173	+	0.753742i	0.997310	−	0.0733027i	$-0.0233539\pi$
$179$	5.82222	+	10.0844i	0.435173	+	0.753742i	−0.562137	+	0.827044i	$0.690021\pi$
$180$		0			0
$181$	3.87644	−	21.9844i	0.288133	−	1.63409i	−0.405740	−	0.913988i	$-0.632986\pi$
$181$	3.87644	−	21.9844i	0.288133	−	1.63409i	0.693874	−	0.720097i	$-0.255903\pi$
$182$	2.01292	+	3.48648i	0.149208	+	0.258435i
$183$	6.77791	−	11.7397i	0.501038	−	0.867823i
$184$	−3.58048	−	3.00438i	−0.263957	−	0.221486i
$185$		0			0
$186$	11.7159	−	4.26422i	0.859048	−	0.312668i
$187$	3.50715	−	2.94285i	0.256469	−	0.215203i
$188$	−0.863537	−	4.89736i	−0.0629799	−	0.357177i
$189$	−2.88269			−0.209685
$190$		0			0
$191$	−10.9886			−0.795110			−0.397555	−	0.917578i	$-0.630141\pi$
$191$	−10.9886			−0.795110			−0.397555	+	0.917578i	$0.630141\pi$
$192$	−0.482139	−	2.73434i	−0.0347954	−	0.197334i
$193$	−8.53171	+	7.15896i	−0.614126	+	0.515313i	−0.895951	−	0.444153i	$-0.853505\pi$
$193$	−8.53171	+	7.15896i	−0.614126	+	0.515313i	0.281825	+	0.959466i	$0.409060\pi$
$194$	7.50697	−	2.73231i	0.538969	−	0.196169i
$195$		0			0
$196$	−5.07962	−	4.26231i	−0.362830	−	0.304451i
$197$	−4.37687	+	7.58096i	−0.311839	+	0.540121i	−0.978760	−	0.205007i	$-0.934278\pi$
$197$	−4.37687	+	7.58096i	−0.311839	+	0.540121i	0.666922	+	0.745128i	$0.267612\pi$
$198$	5.43930	+	9.42114i	0.386554	+	0.669531i
$199$	−1.48762	+	8.43669i	−0.105454	+	0.598061i	0.885584	+	0.464480i	$0.153759\pi$
$199$	−1.48762	+	8.43669i	−0.105454	+	0.598061i	−0.991038	+	0.133581i	$0.957352\pi$
$200$		0			0
$201$	6.41524	+	11.1115i	0.452496	+	0.783746i
$202$	1.61088	−	2.79013i	0.113341	−	0.196313i
$203$	−1.99461	−	1.67368i	−0.139994	−	0.117469i
$204$	5.17075	+	1.88200i	0.362025	+	0.131766i
$205$		0			0
$206$	2.00456	−	1.68203i	0.139664	−	0.117192i
$207$	3.82205	+	21.6759i	0.265651	+	1.50658i
$208$	6.62717			0.459512
$209$	−7.74859	−	6.43086i	−0.535981	−	0.444832i
$210$		0			0
$211$	3.63481	+	20.6140i	0.250230	+	1.41913i	0.808025	+	0.589148i	$0.200536\pi$
$211$	3.63481	+	20.6140i	0.250230	+	1.41913i	−0.557795	+	0.829979i	$0.688352\pi$
$212$	4.31025	−	3.61673i	0.296029	−	0.248398i
$213$	15.7233	−	5.72280i	1.07734	−	0.392120i
$214$	−11.8695	−	4.32013i	−0.811379	−	0.295318i
$215$		0			0
$216$	−2.37268	+	4.10960i	−0.161440	+	0.279623i
$217$	1.36391	+	2.36235i	0.0925880	+	0.160367i
$218$	−2.75586	+	15.6293i	−0.186651	+	1.05855i
$219$	−0.485532	+	2.75359i	−0.0328092	+	0.186070i
$220$		0			0
$221$	−6.56696	+	11.3743i	−0.441741	+	0.765119i
$222$	−1.53546	−	1.28840i	−0.103053	−	0.0864720i
$223$	9.77507	+	3.55784i	0.654587	+	0.238250i	0.647898	−	0.761727i	$-0.275648\pi$
$223$	9.77507	+	3.55784i	0.654587	+	0.238250i	0.00668955	+	0.999978i	$0.497871\pi$
$224$	0.570839	−	0.207769i	0.0381408	−	0.0138821i
$225$		0			0
$226$	−0.139293	−	0.789971i	−0.00926565	−	0.0525481i
$227$	−6.62347			−0.439615			−0.219807	−	0.975543i	$-0.570543\pi$
$227$	−6.62347			−0.439615			−0.219807	+	0.975543i	$0.570543\pi$
$228$	2.03721	−	11.9299i	0.134918	−	0.790077i
$229$	15.7287			1.03938			0.519692	−	0.854354i	$-0.326047\pi$
$229$	15.7287			1.03938			0.519692	+	0.854354i	$0.326047\pi$
$230$		0			0
$231$	−2.98482	+	2.50457i	−0.196387	+	0.164788i
$232$	−4.02775	+	1.46598i	−0.264435	+	0.0962463i
$233$	17.1225	+	6.23209i	1.12173	+	0.408278i	0.835285	−	0.549817i	$-0.185303\pi$
$233$	17.1225	+	6.23209i	1.12173	+	0.408278i	0.286449	+	0.958095i	$0.407525\pi$
$234$	−23.9067	−	20.0601i	−1.56283	−	1.31137i
$235$		0			0
$236$	−1.26233	−	2.18642i	−0.0821705	−	0.142324i
$237$	1.48580	−	8.42640i	0.0965132	−	0.547353i
$238$	−0.209057	+	1.18562i	−0.0135511	+	0.0768523i
$239$	2.21741	+	3.84067i	0.143432	+	0.248432i	0.928787	−	0.370614i	$-0.120853\pi$
$239$	2.21741	+	3.84067i	0.143432	+	0.248432i	−0.785355	+	0.619046i	$0.787519\pi$
$240$		0			0
$241$	−7.38630	−	6.19784i	−0.475794	−	0.399238i	0.373109	−	0.927788i	$-0.378292\pi$
$241$	−7.38630	−	6.19784i	−0.475794	−	0.399238i	−0.848903	+	0.528549i	$0.822736\pi$
$242$	−5.32180	−	1.93698i	−0.342098	−	0.124513i
$243$	−15.8606	+	5.77277i	−1.01745	+	0.370323i
$244$	3.74006	−	3.13828i	0.239433	−	0.200908i
$245$		0			0
$246$	−33.1888			−2.11604
$247$	27.1980	+	9.73329i	1.73057	+	0.619314i
$248$	4.49041			0.285141
$249$	−7.29952	−	41.3976i	−0.462588	−	2.62347i
$250$		0			0
$251$	−16.5694	+	6.03076i	−1.04585	+	0.380659i	−0.807095	−	0.590421i	$-0.798962\pi$
$251$	−16.5694	+	6.03076i	−1.04585	+	0.380659i	−0.238755	+	0.971080i	$0.576739\pi$
$252$	−2.68814	−	0.978403i	−0.169337	−	0.0616336i
$253$	8.27135	+	6.94049i	0.520016	+	0.436345i
$254$	−2.02545	+	3.50818i	−0.127088	+	0.220123i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	3.69056	−	20.9302i	0.230211	−	1.30559i	−0.622257	−	0.782813i	$-0.713784\pi$
$257$	3.69056	−	20.9302i	0.230211	−	1.30559i	0.852468	−	0.522779i	$-0.175105\pi$
$258$	−16.3001	−	28.2326i	−1.01480	−	1.75768i
$259$	0.219271	−	0.379788i	0.0136248	−	0.0235989i
$260$		0			0
$261$	18.9671	+	6.90344i	1.17403	+	0.427313i
$262$	18.2684	−	6.64914i	1.12862	−	0.410785i
$263$	−2.67179	+	2.24190i	−0.164749	+	0.138241i	−0.721435	−	0.692482i	$-0.756517\pi$
$263$	−2.67179	+	2.24190i	−0.164749	+	0.138241i	0.556686	+	0.830723i	$0.312073\pi$
$264$	1.11380	+	6.31667i	0.0685496	+	0.388764i
$265$		0			0
$266$	2.64788	−	0.0142971i	0.162352	−	0.000876614i
$267$	−31.2725			−1.91385
$268$	0.802437	+	4.55085i	0.0490167	+	0.277987i
$269$	−15.9695	+	13.4000i	−0.973681	+	0.817015i	−0.983124	−	0.182940i	$-0.941438\pi$
$269$	−15.9695	+	13.4000i	−0.973681	+	0.817015i	0.00944341	+	0.999955i	$0.496994\pi$
$270$		0			0
$271$	−24.1420	−	8.78698i	−1.46652	−	0.533771i	−0.519370	−	0.854549i	$-0.673833\pi$
$271$	−24.1420	−	8.78698i	−1.46652	−	0.533771i	−0.947154	+	0.320778i	$0.896056\pi$
$272$	1.51817	+	1.27389i	0.0920525	+	0.0772412i
$273$	5.58892	−	9.68030i	0.338257	−	0.585878i
$274$	6.92194	+	11.9891i	0.418170	+	0.724291i
$275$		0			0
$276$	−2.25351	+	12.7803i	−0.135645	+	0.769284i
$277$	8.87186	+	15.3665i	0.533058	+	0.923284i	0.999255	+	0.0386028i	$0.0122907\pi$
$277$	8.87186	+	15.3665i	0.533058	+	0.923284i	−0.466196	+	0.884681i	$0.654376\pi$
$278$	−6.55024	+	11.3453i	−0.392857	+	0.680449i
$279$	−16.1986	−	13.5923i	−0.969786	−	0.813747i
$280$		0			0
$281$	23.8839	−	8.69302i	1.42479	−	0.518582i	0.489358	−	0.872083i	$-0.337231\pi$
$281$	23.8839	−	8.69302i	1.42479	−	0.518582i	0.935434	+	0.353501i	$0.115009\pi$
$282$	−10.5771	+	8.87523i	−0.629857	+	0.528513i
$283$	2.37789	+	13.4857i	0.141351	+	0.801639i	0.970225	+	0.242205i	$0.0778705\pi$
$283$	2.37789	+	13.4857i	0.141351	+	0.801639i	−0.828875	+	0.559434i	$0.811018\pi$
$284$	6.02636			0.357599
$285$		0			0
$286$	−15.3096			−0.905274
$287$	−1.26092	−	7.15103i	−0.0744297	−	0.422112i
$288$	−3.60738	+	3.02695i	−0.212567	+	0.178365i
$289$	12.2840	−	4.47101i	0.722588	−	0.263001i
$290$		0			0
$291$	−16.9916	−	14.2577i	−0.996066	−	0.835799i
$292$	−0.503519	+	0.872121i	−0.0294662	+	0.0510370i
$293$	−6.44705	−	11.1666i	−0.376641	−	0.652361i	0.613930	−	0.789360i	$-0.289588\pi$
$293$	−6.44705	−	11.1666i	−0.376641	−	0.652361i	−0.990571	+	0.136999i	$0.956254\pi$
$294$	−3.19705	+	18.1314i	−0.186456	+	1.05744i
$295$		0			0
$296$	−0.360954	−	0.625192i	−0.0209801	−	0.0363385i
$297$	5.48118	−	9.49368i	0.318050	−	0.550879i
$298$	4.43881	+	3.72461i	0.257133	+	0.215761i
$299$	−29.1073	−	10.5942i	−1.68332	−	0.612678i
$300$		0			0
$301$	5.46387	−	4.58473i	0.314932	−	0.264259i
$302$	−3.26779	−	18.5326i	−0.188040	−	1.06643i
$303$	−8.94531			−0.513895
$304$	2.15904	−	3.78663i	0.123829	−	0.217178i
$305$		0			0
$306$	−1.62059	−	9.19084i	−0.0926432	−	0.525405i
$307$	−4.47570	+	3.75556i	−0.255442	+	0.214341i	−0.761511	−	0.648152i	$-0.775542\pi$
$307$	−4.47570	+	3.75556i	−0.255442	+	0.214341i	0.506070	+	0.862493i	$0.331098\pi$
$308$	−1.31871	+	0.479971i	−0.0751404	+	0.0273489i
$309$	−6.82736	−	2.48496i	−0.388395	−	0.141364i
$310$		0			0
$311$	2.08305	−	3.60794i	0.118119	−	0.204588i	−0.800903	−	0.598794i	$-0.795647\pi$
$311$	2.08305	−	3.60794i	0.118119	−	0.204588i	0.919022	+	0.394206i	$0.128980\pi$
$312$	−9.20026	−	15.9353i	−0.520862	−	0.902160i
$313$	0.575238	−	3.26234i	0.0325144	−	0.184398i	−0.964225	−	0.265085i	$-0.914600\pi$
$313$	0.575238	−	3.26234i	0.0325144	−	0.184398i	0.996740	+	0.0806864i	$0.0257112\pi$
$314$	−0.447249	+	2.53647i	−0.0252397	+	0.143142i
$315$		0			0
$316$	1.54084	−	2.66882i	0.0866792	−	0.150133i
$317$	−10.6944	−	8.97366i	−0.600657	−	0.504011i	0.291000	−	0.956723i	$-0.406012\pi$
$317$	−10.6944	−	8.97366i	−0.600657	−	0.504011i	−0.891657	+	0.452712i	$0.850457\pi$
$318$	−14.6803	−	5.34321i	−0.823233	−	0.299632i
$319$	9.30459	−	3.38659i	0.520957	−	0.189613i
$320$		0			0
$321$	6.09000	+	34.5381i	0.339910	+	1.92773i
$322$	−2.83933			−0.158230
$323$	4.35963	+	7.45781i	0.242576	+	0.414963i
$324$	−0.951681			−0.0528712
$325$		0			0
$326$	−2.32428	+	1.95031i	−0.128730	+	0.108017i
$327$	41.4071	−	15.0710i	2.28982	−	0.833426i
$328$	−11.2325	−	4.08828i	−0.620209	−	0.225738i
$329$	−2.31416	−	1.94181i	−0.127584	−	0.107055i
$330$		0			0
$331$	9.81952	+	17.0079i	0.539729	+	0.934839i	0.998918	+	0.0465001i	$0.0148068\pi$
$331$	9.81952	+	17.0079i	0.539729	+	0.934839i	−0.459189	+	0.888339i	$0.651860\pi$
$332$	2.62901	−	14.9099i	0.144286	−	0.818285i
$333$	−0.590324	+	3.34789i	−0.0323496	+	0.183463i
$334$	−2.67326	−	4.63022i	−0.146274	−	0.253354i
$335$		0			0
$336$	−1.29206	−	1.08417i	−0.0704879	−	0.0591463i
$337$	20.9949	+	7.64150i	1.14366	+	0.416259i	0.843235	−	0.537545i	$-0.180648\pi$
$337$	20.9949	+	7.64150i	1.14366	+	0.416259i	0.300428	+	0.953805i	$0.402871\pi$
$338$	29.0548	−	10.5751i	1.58037	−	0.575208i
$339$	−1.70614	+	1.43162i	−0.0926650	+	0.0777552i
$340$		0			0
$341$	−10.3734			−0.561751
$342$	−19.2504	+	7.12452i	−1.04094	+	0.385250i
$343$	−8.28047			−0.447103
$344$	−2.03886	−	11.5630i	−0.109928	−	0.623434i
$345$		0			0
$346$	−20.4936	+	7.45907i	−1.10174	+	0.401002i
$347$	−9.33410	−	3.39734i	−0.501081	−	0.182379i	0.0790992	−	0.996867i	$-0.474796\pi$
$347$	−9.33410	−	3.39734i	−0.501081	−	0.182379i	−0.580180	+	0.814488i	$0.697018\pi$
$348$	9.11658	+	7.64972i	0.488700	+	0.410068i
$349$	2.01817	−	3.49557i	0.108030	−	0.187113i	−0.806942	−	0.590630i	$-0.798879\pi$
$349$	2.01817	−	3.49557i	0.108030	−	0.187113i	0.914972	+	0.403517i	$0.132212\pi$
$350$		0			0
$351$	−5.46094	+	30.9706i	−0.291484	+	1.65309i
$352$	−0.401148	+	2.27503i	−0.0213813	+	0.121259i
$353$	−2.55981	−	4.43373i	−0.136245	−	0.235984i	0.789827	−	0.613329i	$-0.210170\pi$
$353$	−2.55981	−	4.43373i	−0.136245	−	0.235984i	−0.926072	+	0.377346i	$0.876837\pi$
$354$	−3.50489	+	6.07064i	−0.186283	+	0.322651i
$355$		0			0
$356$	−10.5839	−	3.85223i	−0.560947	−	0.204168i
$357$	3.14110	−	1.14327i	0.166245	−	0.0605081i
$358$	8.92015	−	7.48490i	0.471445	−	0.395589i
$359$	4.21056	+	23.8793i	0.222225	+	1.26030i	0.867919	+	0.496705i	$0.165457\pi$
$359$	4.21056	+	23.8793i	0.222225	+	1.26030i	−0.645694	+	0.763596i	$0.723432\pi$
$360$		0			0
$361$	14.4221	−	12.3694i	0.759059	−	0.651022i
$362$	−22.3235			−1.17330
$363$	2.73051	+	15.4855i	0.143315	+	0.812779i
$364$	3.08397	−	2.58776i	0.161644	−	0.135635i
$365$		0			0
$366$	−12.7383	−	4.63637i	−0.665842	−	0.242347i
$367$	26.3703	+	22.1273i	1.37652	+	1.15504i	0.970480	+	0.241183i	$0.0775354\pi$
$367$	26.3703	+	22.1273i	1.37652	+	1.15504i	0.406041	+	0.913855i	$0.366909\pi$
$368$	−2.33699	+	4.04779i	−0.121824	+	0.211006i
$369$	28.1447	+	48.7481i	1.46516	+	2.53772i
$370$		0			0
$371$	0.593536	−	3.36611i	0.0308149	−	0.174760i
$372$	−6.23388	−	10.7974i	−0.323211	−	0.559819i
$373$	−8.34486	+	14.4537i	−0.432080	+	0.748385i	−0.997052	−	0.0767250i	$-0.975554\pi$
$373$	−8.34486	+	14.4537i	−0.432080	+	0.748385i	0.564972	+	0.825110i	$0.308887\pi$
$374$	−3.50715	−	2.94285i	−0.181351	−	0.152171i
$375$		0			0
$376$	−4.67301	+	1.70084i	−0.240992	+	0.0877139i
$377$	−21.7600	+	18.2588i	−1.12070	+	0.940376i
$378$	0.500573	+	2.83889i	0.0257467	+	0.146017i
$379$	22.5678			1.15923			0.579614	−	0.814891i	$-0.303203\pi$
$379$	22.5678			1.15923			0.579614	+	0.814891i	$0.303203\pi$
$380$		0			0
$381$	11.2474			0.576223
$382$	1.90816	+	10.8217i	0.0976299	+	0.553686i
$383$	3.65846	−	3.06981i	0.186938	−	0.156860i	−0.544516	−	0.838751i	$-0.683287\pi$
$383$	3.65846	−	3.06981i	0.186938	−	0.156860i	0.731454	+	0.681891i	$0.238842\pi$
$384$	−2.60908	+	0.949628i	−0.133144	+	0.0484605i
$385$		0			0
$386$	8.53171	+	7.15896i	0.434253	+	0.364381i
$387$	−27.6456	+	47.8836i	−1.40531	+	2.43406i
$388$	−3.99437	−	6.91846i	−0.202784	−	0.351232i
$389$	0.0923756	−	0.523888i	0.00468363	−	0.0265622i	−0.982376	−	0.186913i	$-0.940152\pi$
$389$	0.0923756	−	0.523888i	0.00468363	−	0.0265622i	0.987060	+	0.160351i	$0.0512627\pi$
$390$		0			0
$391$	−4.63152	−	8.02203i	−0.234226	−	0.405692i
$392$	−3.31549	+	5.74259i	−0.167457	+	0.290045i
$393$	−41.3495	−	34.6963i	−2.08580	−	1.75020i
$394$	8.22582	+	2.99395i	0.414411	+	0.150833i
$395$		0			0
$396$	8.33349	−	6.99263i	0.418773	−	0.351393i
$397$	−0.268242	−	1.52128i	−0.0134627	−	0.0763506i	0.977336	−	0.211693i	$-0.0678977\pi$
$397$	−0.268242	−	1.52128i	−0.0134627	−	0.0763506i	−0.990799	+	0.135342i	$0.956787\pi$
$398$	8.56684			0.429417
$399$	−3.71033	−	6.34710i	−0.185749	−	0.317752i
$400$		0			0
$401$	1.24780	+	7.07661i	0.0623120	+	0.353389i	0.999983	+	0.00586419i	$0.00186664\pi$
$401$	1.24780	+	7.07661i	0.0623120	+	0.353389i	−0.937671	+	0.347525i	$0.887022\pi$
$402$	9.82871	−	8.24727i	0.490212	−	0.411336i
$403$	27.9641	−	10.1781i	1.39299	−	0.507007i
$404$	−3.02747	−	1.10191i	−0.150622	−	0.0548220i
$405$		0			0
$406$	−1.30189	+	2.25494i	−0.0646117	+	0.111911i
$407$	0.833849	+	1.44427i	0.0413324	+	0.0715897i
$408$	0.955516	−	5.41900i	0.0473051	−	0.268281i
$409$	2.96990	−	16.8431i	0.146852	−	0.832839i	−0.819009	−	0.573780i	$-0.805476\pi$
$409$	2.96990	−	16.8431i	0.146852	−	0.832839i	0.965861	−	0.259059i	$-0.0834125\pi$
$410$		0			0
$411$	19.2189	−	33.2882i	0.948001	−	1.64199i
$412$	−2.00456	−	1.68203i	−0.0987576	−	0.0828675i
$413$	−1.44117	−	0.524544i	−0.0709155	−	0.0258111i
$414$	20.6829	−	7.52796i	1.01651	−	0.369979i
$415$		0			0
$416$	−1.15080	−	6.52649i	−0.0564224	−	0.319988i
$417$	36.3738			1.78123
$418$	−4.98764	+	8.74758i	−0.243953	+	0.427858i
$419$	−25.4874			−1.24514			−0.622570	−	0.782564i	$-0.713912\pi$
$419$	−25.4874			−1.24514			−0.622570	+	0.782564i	$0.713912\pi$
$420$		0			0
$421$	5.48313	−	4.60089i	0.267231	−	0.224234i	−0.499319	−	0.866418i	$-0.666416\pi$
$421$	5.48313	−	4.60089i	0.267231	−	0.224234i	0.766550	+	0.642185i	$0.221972\pi$
$422$	19.6697	−	7.15917i	0.957504	−	0.348503i
$423$	22.0057	+	8.00940i	1.06995	+	0.389430i
$424$	−4.31025	−	3.61673i	−0.209324	−	0.175644i
$425$		0			0
$426$	−8.36617	−	14.4906i	−0.405342	−	0.702074i
$427$	0.515018	−	2.92081i	0.0249235	−	0.141348i
$428$	−2.19339	+	12.4393i	−0.106021	+	0.601277i
$429$	21.2537	+	36.8125i	1.02614	+	1.77733i
$430$		0			0
$431$	0.571352	+	0.479421i	0.0275211	+	0.0230929i	0.656444	−	0.754374i	$-0.272060\pi$
$431$	0.571352	+	0.479421i	0.0275211	+	0.0230929i	−0.628923	+	0.777467i	$0.716504\pi$
$432$	4.45918	+	1.62301i	0.214542	+	0.0780870i
$433$	−5.59747	+	2.03731i	−0.268997	+	0.0979070i	−0.472997	−	0.881064i	$-0.656828\pi$
$433$	−5.59747	+	2.03731i	−0.268997	+	0.0979070i	0.204000	+	0.978971i	$0.434606\pi$
$434$	2.08962	−	1.75340i	0.100305	−	0.0841661i
$435$		0			0
$436$	15.8704			0.760054
$437$	−15.5360	+	13.1799i	−0.743189	+	0.630479i
$438$	2.79607			0.133601
$439$	−0.256179	−	1.45286i	−0.0122268	−	0.0693414i	0.978084	−	0.208211i	$-0.0667641\pi$
$439$	−0.256179	−	1.45286i	−0.0122268	−	0.0693414i	−0.990311	+	0.138870i	$0.955653\pi$
$440$		0			0
$441$	29.3428	−	10.6799i	1.39727	−	0.508566i
$442$	12.3418	+	4.49206i	0.587042	+	0.213666i
$443$	10.2943	+	8.63791i	0.489095	+	0.410399i	0.853702	−	0.520762i	$-0.174352\pi$
$443$	10.2943	+	8.63791i	0.489095	+	0.410399i	−0.364607	+	0.931162i	$0.618797\pi$
$444$	−1.00220	+	1.73586i	−0.0475623	+	0.0823803i
$445$		0			0
$446$	1.80636	−	10.2444i	0.0855336	−	0.485085i
$447$	2.79373	−	15.8440i	0.132139	−	0.749398i
$448$	−0.303737	−	0.526088i	−0.0143502	−	0.0248553i
$449$	11.9314	−	20.6657i	0.563076	−	0.975276i	−0.434150	−	0.900841i	$-0.642951\pi$
$449$	11.9314	−	20.6657i	0.563076	−	0.975276i	0.997226	−	0.0744357i	$-0.0237155\pi$
$450$		0			0
$451$	25.9484	+	9.44443i	1.22186	+	0.444721i
$452$	−0.753782	+	0.274354i	−0.0354549	+	0.0129045i
$453$	−40.0258	+	33.5856i	−1.88057	+	1.57799i
$454$	1.15015	+	6.52284i	0.0539793	+	0.306132i
$455$		0			0
$456$	−12.1024	+	0.0653466i	−0.566748	+	0.00306014i
$457$	−9.10328			−0.425833			−0.212917	−	0.977070i	$-0.568296\pi$
$457$	−9.10328			−0.425833			−0.212917	+	0.977070i	$0.568296\pi$
$458$	−2.73126	−	15.4898i	−0.127624	−	0.723789i
$459$	−7.20426	+	6.04509i	−0.336266	+	0.282161i
$460$		0			0
$461$	29.1474	+	10.6088i	1.35753	+	0.494101i	0.915290	−	0.402795i	$-0.131961\pi$
$461$	29.1474	+	10.6088i	1.35753	+	0.494101i	0.442242	+	0.896896i	$0.354183\pi$
$462$	2.98482	+	2.50457i	0.138867	+	0.116523i
$463$	−9.67725	+	16.7615i	−0.449740	+	0.778972i	−0.998369	−	0.0570936i	$-0.981817\pi$
$463$	−9.67725	+	16.7615i	−0.449740	+	0.778972i	0.548629	+	0.836066i	$0.315150\pi$
$464$	2.14312	+	3.71199i	0.0994918	+	0.172325i
$465$		0			0
$466$	3.16412	−	17.9446i	0.146575	−	0.831267i
$467$	−8.86564	−	15.3557i	−0.410253	−	0.710579i	0.584664	−	0.811275i	$-0.301226\pi$
$467$	−8.86564	−	15.3557i	−0.410253	−	0.710579i	−0.994917	+	0.100696i	$0.967893\pi$
$468$	−15.6040	+	27.0269i	−0.721296	+	1.24932i
$469$	2.15042	+	1.80442i	0.0992971	+	0.0833202i
$470$		0			0
$471$	6.71996	−	2.44586i	0.309639	−	0.112700i
$472$	−1.93400	+	1.62282i	−0.0890195	+	0.0746962i
$473$	4.71003	+	26.7119i	0.216567	+	1.22821i
$474$	−8.55639			−0.393008
$475$		0			0
$476$	1.20391			0.0551811
$477$	4.60105	+	26.0938i	0.210668	+	1.19475i
$478$	3.39727	−	2.85065i	0.155387	−	0.130386i
$479$	−4.88537	+	1.77813i	−0.223218	+	0.0812447i	−0.451208	−	0.892419i	$-0.649007\pi$
$479$	−4.88537	+	1.77813i	−0.223218	+	0.0812447i	0.227990	+	0.973663i	$0.426785\pi$
$480$		0			0
$481$	−3.66492	−	3.07523i	−0.167106	−	0.140219i
$482$	−4.82107	+	8.35033i	−0.219594	+	0.380347i
$483$	3.94174	+	6.82729i	0.179355	+	0.310652i
$484$	−0.983428	+	5.57730i	−0.0447013	+	0.253514i
$485$		0			0
$486$	8.43922	+	14.6172i	0.382811	+	0.663048i
$487$	−19.0060	+	32.9194i	−0.861244	+	1.49172i	0.00948503	+	0.999955i	$0.496981\pi$
$487$	−19.0060	+	32.9194i	−0.861244	+	1.49172i	−0.870729	+	0.491763i	$0.836353\pi$
$488$	−3.74006	−	3.13828i	−0.169304	−	0.142063i
$489$	7.91631	+	2.88130i	0.357988	+	0.130297i
$490$		0			0
$491$	16.8331	−	14.1247i	0.759668	−	0.637437i	−0.178372	−	0.983963i	$-0.557083\pi$
$491$	16.8331	−	14.1247i	0.759668	−	0.637437i	0.938040	+	0.346526i	$0.112639\pi$
$492$	5.76317	+	32.6845i	0.259824	+	1.47353i
$493$	−8.49459			−0.382577
$494$	4.86253	−	28.4750i	0.218776	−	1.28115i
$495$		0			0
$496$	−0.779752	−	4.42219i	−0.0350119	−	0.198562i
$497$	2.80438	−	2.35316i	0.125794	−	0.105553i
$498$	−39.5012	+	14.3772i	−1.77009	+	0.644260i
$499$	−3.24801	−	1.18218i	−0.145401	−	0.0529216i	0.268295	−	0.963337i	$-0.413540\pi$
$499$	−3.24801	−	1.18218i	−0.145401	−	0.0529216i	−0.413695	+	0.910415i	$0.635762\pi$
$500$		0			0
$501$	−7.42237	+	12.8559i	−0.331607	+	0.574360i
$502$	8.81639	+	15.2704i	0.393495	+	0.681553i
$503$	−2.09044	+	11.8554i	−0.0932079	+	0.528608i	0.902074	+	0.431582i	$0.142044\pi$
$503$	−2.09044	+	11.8554i	−0.0932079	+	0.528608i	−0.995282	+	0.0970267i	$0.969067\pi$
$504$	−0.496748	+	2.81720i	−0.0221269	+	0.125488i
$505$		0			0
$506$	5.39874	−	9.35090i	0.240003	−	0.415698i
$507$	−65.7638	−	55.1824i	−2.92067	−	2.45074i
$508$	3.80660	+	1.38549i	0.168890	+	0.0614711i
$509$	8.08200	−	2.94161i	0.358228	−	0.130384i	−0.156635	−	0.987656i	$-0.550065\pi$
$509$	8.08200	−	2.94161i	0.358228	−	0.130384i	0.514864	+	0.857272i	$0.327843\pi$
$510$		0			0
$511$	0.106229	+	0.602457i	0.00469931	+	0.0266511i
$512$	−1.00000			−0.0441942
$513$	15.9168	+	13.2100i	0.702746	+	0.583237i
$514$	−21.2531			−0.937435
$515$		0			0
$516$	−24.9732	+	20.9550i	−1.09938	+	0.922492i
$517$	10.7952	−	3.92914i	0.474773	−	0.172803i
$518$	−0.412094	−	0.149990i	−0.0181064	−	0.00659018i
$519$	46.3862	+	38.9227i	2.03613	+	1.70851i
$520$		0			0
$521$	0.867946	+	1.50333i	0.0380254	+	0.0658620i	0.884412	−	0.466707i	$-0.154560\pi$
$521$	0.867946	+	1.50333i	0.0380254	+	0.0658620i	−0.846386	+	0.532569i	$0.821227\pi$
$522$	3.50497	−	19.8777i	0.153408	−	0.870022i
$523$	5.48250	−	31.0928i	0.239733	−	1.35959i	−0.592681	−	0.805437i	$-0.701930\pi$
$523$	5.48250	−	31.0928i	0.239733	−	1.35959i	0.832414	−	0.554155i	$-0.186958\pi$
$524$	−9.72040	−	16.8362i	−0.424638	−	0.735494i
$525$		0			0
$526$	2.67179	+	2.24190i	0.116495	+	0.0977513i
$527$	8.36254	+	3.04371i	0.364278	+	0.132586i
$528$	6.02730	−	2.19376i	0.262304	−	0.0954710i
$529$	−0.883879	+	0.741663i	−0.0384295	+	0.0322462i
$530$		0			0
$531$	11.8889			0.515932
$532$	−0.473880	−	2.60517i	−0.0205453	−	0.112949i
$533$	−79.2168			−3.43126
$534$	5.43041	+	30.7974i	0.234997	+	1.33273i
$535$		0			0
$536$	4.34237	−	1.58049i	0.187562	−	0.0682669i
$537$	−30.3813	−	11.0579i	−1.31105	−	0.477183i
$538$	15.9695	+	13.4000i	0.688496	+	0.577717i
$539$	7.65918	−	13.2661i	0.329904	−	0.571411i
$540$		0			0
$541$	−5.47971	+	31.0770i	−0.235591	+	1.33610i	0.605774	+	0.795637i	$0.292864\pi$
$541$	−5.47971	+	31.0770i	−0.235591	+	1.33610i	−0.841365	+	0.540468i	$0.818247\pi$
$542$	−4.46127	+	25.3011i	−0.191628	+	1.08678i
$543$	30.9909	+	53.6778i	1.32995	+	2.30354i
$544$	0.990914	−	1.71631i	0.0424851	−	0.0735863i
$545$		0			0
$546$	−10.5037	−	3.82305i	−0.449519	−	0.163611i
$547$	17.7748	−	6.46950i	0.759996	−	0.276616i	0.0671901	−	0.997740i	$-0.478597\pi$
$547$	17.7748	−	6.46950i	0.759996	−	0.276616i	0.692806	+	0.721124i	$0.256374\pi$
$548$	10.6050	−	8.89867i	0.453024	−	0.380132i
$549$	3.99238	+	22.6419i	0.170391	+	0.966334i
$550$		0			0
$551$	3.34362	+	18.3817i	0.142443	+	0.783085i
$552$	12.9775			0.552357
$553$	−0.325078	−	1.84361i	−0.0138237	−	0.0783981i
$554$	13.5925	−	11.4054i	0.577489	−	0.484571i
$555$		0			0
$556$	12.3104	+	4.48063i	0.522078	+	0.190021i
$557$	−22.4076	−	18.8022i	−0.949439	−	0.796674i	0.0297637	−	0.999557i	$-0.490525\pi$
$557$	−22.4076	−	18.8022i	−0.949439	−	0.796674i	−0.979203	+	0.202883i	$0.934969\pi$
$558$	−10.5729	+	18.3128i	−0.447587	+	0.775243i
$559$	−38.9060	−	67.3872i	−1.64555	−	2.85017i
$560$		0			0
$561$	−2.20736	+	12.5186i	−0.0931948	+	0.528534i
$562$	−12.7083	−	22.0115i	−0.536069	−	0.928499i
$563$	−2.95443	+	5.11723i	−0.124515	+	0.215665i	−0.921543	−	0.388276i	$-0.873071\pi$
$563$	−2.95443	+	5.11723i	−0.124515	+	0.215665i	0.797029	+	0.603942i	$0.206404\pi$
$564$	10.5771	+	8.87523i	0.445376	+	0.373715i
$565$		0			0
$566$	12.8679	−	4.68352i	0.540877	−	0.196863i
$567$	−0.442867	+	0.371610i	−0.0185987	+	0.0156061i
$568$	−1.04647	−	5.93481i	−0.0439087	−	0.249019i
$569$	20.3117			0.851513			0.425756	−	0.904838i	$-0.360008\pi$
$569$	20.3117			0.851513			0.425756	+	0.904838i	$0.360008\pi$
$570$		0			0
$571$	−40.9170			−1.71232			−0.856162	−	0.516707i	$-0.827158\pi$
$571$	−40.9170			−1.71232			−0.856162	+	0.516707i	$0.827158\pi$
$572$	2.65848	+	15.0770i	0.111157	+	0.630401i
$573$	23.3722	−	19.6116i	0.976388	−	0.819287i
$574$	−6.82343	+	2.48353i	−0.284805	+	0.103660i
$575$		0			0
$576$	3.60738	+	3.02695i	0.150307	+	0.126123i
$577$	1.51218	−	2.61917i	0.0629528	−	0.109038i	−0.832831	−	0.553527i	$-0.813282\pi$
$577$	1.51218	−	2.61917i	0.0629528	−	0.109038i	0.895784	+	0.444489i	$0.146615\pi$
$578$	−6.53618	−	11.3210i	−0.271869	−	0.470891i
$579$	5.36975	−	30.4534i	0.223159	−	1.26560i
$580$		0			0
$581$	−4.59854	−	7.96491i	−0.190780	−	0.330440i
$582$	−11.0905	+	19.2093i	−0.459715	+	0.796251i
$583$	9.95721	+	8.35509i	0.412385	+	0.346032i
$584$	0.946307	+	0.344428i	0.0391585	+	0.0142525i
$585$		0			0
$586$	−9.87746	+	8.28817i	−0.408034	+	0.342381i
$587$	0.867160	+	4.91791i	0.0357915	+	0.202984i	0.997460	−	0.0712317i	$-0.0226930\pi$
$587$	0.867160	+	4.91791i	0.0357915	+	0.202984i	−0.961668	+	0.274215i	$0.911582\pi$
$588$	18.4111			0.759260
$589$	3.29473	−	19.2940i	0.135757	−	0.794994i
$590$		0			0
$591$	−4.22051	−	23.9357i	−0.173609	−	0.984584i
$592$	−0.553014	+	0.464034i	−0.0227288	+	0.0190717i
$593$	31.7591	−	11.5594i	1.30419	−	0.474686i	0.405830	−	0.913948i	$-0.366982\pi$
$593$	31.7591	−	11.5594i	1.30419	−	0.474686i	0.898359	+	0.439262i	$0.144760\pi$
$594$	−10.3012	−	3.74935i	−0.422665	−	0.153838i
$595$		0			0
$596$	2.89723	−	5.01815i	0.118675	−	0.205551i
$597$	−11.8930	−	20.5993i	−0.486749	−	0.843074i
$598$	−5.37881	+	30.5048i	−0.219956	+	1.24743i
$599$	−3.54110	+	20.0826i	−0.144685	+	0.820552i	0.822934	+	0.568137i	$0.192336\pi$
$599$	−3.54110	+	20.0826i	−0.144685	+	0.820552i	−0.967619	+	0.252415i	$0.918775\pi$
$600$		0			0
$601$	4.60806	−	7.98140i	0.187967	−	0.325568i	−0.756605	−	0.653872i	$-0.773144\pi$
$601$	4.60806	−	7.98140i	0.187967	−	0.325568i	0.944572	+	0.328304i	$0.106477\pi$
$602$	−5.46387	−	4.58473i	−0.222691	−	0.186860i
$603$	−20.4486	−	7.44270i	−0.832733	−	0.303090i
$604$	−17.6836	+	6.43629i	−0.719534	+	0.261889i
$605$		0			0
$606$	1.55334	+	8.80941i	0.0631000	+	0.357858i
$607$	45.2100			1.83502			0.917509	−	0.397715i	$-0.130197\pi$
$607$	45.2100			1.83502			0.917509	+	0.397715i	$0.130197\pi$
$608$	−4.10402	−	1.46869i	−0.166440	−	0.0595634i
$609$	7.22947			0.292953
$610$		0			0
$611$	−25.2460	+	21.1839i	−1.02134	+	0.857010i
$612$	−8.76980	+	3.19195i	−0.354498	+	0.129027i
$613$	2.23480	+	0.813401i	0.0902628	+	0.0328530i	0.386757	−	0.922182i	$-0.373595\pi$
$613$	2.23480	+	0.813401i	0.0902628	+	0.0328530i	−0.296494	+	0.955035i	$0.595817\pi$
$614$	4.47570	+	3.75556i	0.180624	+	0.151562i
$615$		0			0
$616$	0.701670	+	1.21533i	0.0282711	+	0.0489670i
$617$	5.47886	−	31.0721i	0.220570	−	1.25092i	−0.650404	−	0.759588i	$-0.725400\pi$
$617$	5.47886	−	31.0721i	0.220570	−	1.25092i	0.870974	−	0.491328i	$-0.163489\pi$
$618$	−1.26165	+	7.15515i	−0.0507508	+	0.287822i
$619$	−0.791136	−	1.37029i	−0.0317984	−	0.0550765i	0.849688	−	0.527285i	$-0.176790\pi$
$619$	−0.791136	−	1.37029i	−0.0317984	−	0.0550765i	−0.881487	+	0.472209i	$0.843457\pi$
$620$		0			0
$621$	−16.9907	−	14.2569i	−0.681813	−	0.572109i
$622$	−3.91485	−	1.42489i	−0.156971	−	0.0571328i
$623$	−6.42946	+	2.34013i	−0.257591	+	0.0937554i
$624$	−14.0956	+	11.8276i	−0.564276	+	0.473484i
$625$		0			0
$626$	−3.31267			−0.132401
$627$	27.9581	−	0.150959i	1.11654	−	0.00602871i
$628$	2.57560			0.102778
$629$	−0.248438	−	1.40896i	−0.00990589	−	0.0561791i
$630$		0			0
$631$	0.422151	−	0.153650i	0.0168056	−	0.00611673i	−0.333604	−	0.942713i	$-0.608265\pi$
$631$	0.422151	−	0.153650i	0.0168056	−	0.00611673i	0.350409	+	0.936597i	$0.386043\pi$
$632$	−2.89584	−	1.05400i	−0.115190	−	0.0419258i
$633$	−44.5212	−	37.3577i	−1.76956	−	1.48484i
$634$	−6.98027	+	12.0902i	−0.277222	+	0.480162i
$635$		0			0
$636$	−2.71282	+	15.3852i	−0.107570	+	0.610061i
$637$	−7.63090	+	43.2770i	−0.302347	+	1.71470i
$638$	−4.95087	−	8.57515i	−0.196007	−	0.339494i
$639$	−14.1894	+	24.5767i	−0.561322	+	0.972239i
$640$		0			0
$641$	−25.1265	−	9.14530i	−0.992437	−	0.361217i	−0.205773	−	0.978600i	$-0.565971\pi$
$641$	−25.1265	−	9.14530i	−0.992437	−	0.361217i	−0.786663	+	0.617382i	$0.788193\pi$
$642$	32.9559	−	11.9950i	1.30066	−	0.473403i
$643$	−9.56530	+	8.02624i	−0.377219	+	0.316524i	−0.811609	−	0.584200i	$-0.801408\pi$
$643$	−9.56530	+	8.02624i	−0.377219	+	0.316524i	0.434391	+	0.900725i	$0.356964\pi$
$644$	0.493044	+	2.79619i	0.0194287	+	0.110185i
$645$		0			0
$646$	6.58746	−	5.58843i	0.259180	−	0.219874i
$647$	22.4225			0.881521			0.440760	−	0.897625i	$-0.354709\pi$
$647$	22.4225			0.881521			0.440760	+	0.897625i	$0.354709\pi$
$648$	0.165258	+	0.937223i	0.00649193	+	0.0368176i
$649$	4.46777	−	3.74891i	0.175375	−	0.147157i
$650$		0			0
$651$	−7.11708	−	2.59041i	−0.278940	−	0.101526i
$652$	2.32428	+	1.95031i	0.0910260	+	0.0763799i
$653$	16.3807	−	28.3722i	0.641027	−	1.11029i	−0.344176	−	0.938905i	$-0.611842\pi$
$653$	16.3807	−	28.3722i	0.641027	−	1.11029i	0.985204	−	0.171387i	$-0.0548248\pi$
$654$	−22.0323	−	38.1610i	−0.861530	−	1.49221i
$655$		0			0
$656$	−2.07567	+	11.7717i	−0.0810415	+	0.459609i
$657$	−2.37112	−	4.10691i	−0.0925063	−	0.160226i
$658$	−1.51046	+	2.61619i	−0.0588838	+	0.101990i
$659$	15.5731	+	13.0674i	0.606643	+	0.509034i	0.893573	−	0.448918i	$-0.148190\pi$
$659$	15.5731	+	13.0674i	0.606643	+	0.509034i	−0.286930	+	0.957951i	$0.592635\pi$
$660$		0			0
$661$	−39.4755	+	14.3679i	−1.53542	+	0.558847i	−0.964941	−	0.262466i	$-0.915464\pi$
$661$	−39.4755	+	14.3679i	−1.53542	+	0.558847i	−0.570478	+	0.821313i	$0.693242\pi$
$662$	15.0444	−	12.6237i	0.584716	−	0.490635i
$663$	−6.33237	−	35.9127i	−0.245929	−	1.39473i
$664$	−15.1399			−0.587541
$665$		0			0
$666$	3.39954			0.131730
$667$	−3.47884	−	19.7295i	−0.134701	−	0.763928i
$668$	−4.09567	+	3.43667i	−0.158466	+	0.132969i
$669$	−27.1407	+	9.87842i	−1.04932	+	0.381922i
$670$		0			0
$671$	8.63999	+	7.24981i	0.333543	+	0.279876i
$672$	−0.843335	+	1.46070i	−0.0325323	+	0.0563477i
$673$	4.51589	+	7.82175i	0.174075	+	0.301506i	0.939841	−	0.341613i	$-0.110973\pi$
$673$	4.51589	+	7.82175i	0.174075	+	0.301506i	−0.765766	+	0.643119i	$0.777640\pi$
$674$	3.87969	−	22.0028i	0.149440	−	0.847517i
$675$		0			0
$676$	−15.4597	−	26.7770i	−0.594604	−	1.02988i
$677$	10.6898	−	18.5152i	0.410842	−	0.711598i	−0.584140	−	0.811653i	$-0.698568\pi$
$677$	10.6898	−	18.5152i	0.410842	−	0.711598i	0.994982	+	0.100054i	$0.0319016\pi$
$678$	1.70614	+	1.43162i	0.0655241	+	0.0549812i
$679$	−4.56029	−	1.65981i	−0.175008	−	0.0636977i
$680$		0			0
$681$	14.0877	−	11.8210i	0.539843	−	0.452982i
$682$	1.80132	+	10.2158i	0.0689762	+	0.391183i
$683$	1.63575			0.0625902			0.0312951	−	0.999510i	$-0.490037\pi$
$683$	1.63575			0.0625902			0.0312951	+	0.999510i	$0.490037\pi$
$684$	10.3591	+	17.7208i	0.396089	+	0.677571i
$685$		0			0
$686$	1.43789	+	8.15467i	0.0548988	+	0.311347i
$687$	−33.4541	+	28.0713i	−1.27635	+	1.07099i
$688$	−11.0333	+	4.01578i	−0.420639	+	0.153100i
$689$	−35.0399	−	12.7535i	−1.33491	−	0.485869i
$690$		0			0
$691$	16.6994	−	28.9242i	0.635275	−	1.10033i	−0.351182	−	0.936307i	$-0.614220\pi$
$691$	16.6994	−	28.9242i	0.635275	−	1.10033i	0.986457	−	0.164022i	$-0.0524467\pi$
$692$	10.9044	+	18.8870i	0.414524	+	0.717977i
$693$	1.14755	−	6.50807i	0.0435918	−	0.247221i
$694$	−1.72487	+	9.78224i	−0.0654753	+	0.371329i
$695$		0			0
$696$	5.95043	−	10.3064i	0.225550	−	0.390665i
$697$	−18.1472	−	15.2273i	−0.687373	−	0.576775i
$698$	−3.79291	−	1.38051i	−0.143564	−	0.0522530i
$699$	−47.5412	+	17.3036i	−1.79817	+	0.654481i
$700$		0			0
$701$	−6.03532	−	34.2280i	−0.227951	−	1.29277i	−0.856963	−	0.515378i	$-0.827651\pi$
$701$	−6.03532	−	34.2280i	−0.227951	−	1.29277i	0.629012	−	0.777396i	$-0.283460\pi$
$702$	31.4483			1.18694
$703$	−2.95110	+	1.09219i	−0.111303	+	0.0411929i
$704$	2.31012			0.0870660
$705$		0			0
$706$	−3.92186	+	3.29083i	−0.147601	+	0.123852i
$707$	−1.83911	+	0.669381i	−0.0691668	+	0.0251747i
$708$	6.58703	+	2.39748i	0.247556	+	0.0901029i
$709$	−7.62641	−	6.39931i	−0.286416	−	0.240331i	0.488248	−	0.872705i	$-0.337636\pi$
$709$	−7.62641	−	6.39931i	−0.286416	−	0.240331i	−0.774663	+	0.632374i	$0.782081\pi$
$710$		0			0
$711$	7.25599	+	12.5677i	0.272121	+	0.471327i
$712$	−1.95583	+	11.0921i	−0.0732978	+	0.415692i
$713$	−3.64455	+	20.6693i	−0.136490	+	0.774071i
$714$	−1.67134	−	2.89485i	−0.0625485	−	0.108337i
$715$		0			0
$716$	−8.92015	−	7.48490i	−0.333362	−	0.279724i
$717$	−11.5708	−	4.21143i	−0.432120	−	0.157279i
$718$	22.7854	−	8.29319i	0.850342	−	0.309499i
$719$	13.9933	−	11.7418i	0.521863	−	0.437895i	−0.343418	−	0.939183i	$-0.611585\pi$
$719$	13.9933	−	11.7418i	0.521863	−	0.437895i	0.865281	+	0.501288i	$0.167140\pi$
$720$		0			0
$721$	−1.58962			−0.0592006
$722$	−14.6859	−	12.0551i	−0.546552	−	0.448644i
$723$	26.7716			0.995648
$724$	3.87644	+	21.9844i	0.144067	+	0.817043i
$725$		0			0
$726$	14.7761	−	5.37806i	0.548393	−	0.199599i
$727$	−5.79850	−	2.11048i	−0.215054	−	0.0782734i	0.232246	−	0.972657i	$-0.425392\pi$
$727$	−5.79850	−	2.11048i	−0.215054	−	0.0782734i	−0.447301	+	0.894384i	$0.647615\pi$
$728$	−3.08397	−	2.58776i	−0.114300	−	0.0959088i
$729$	22.0042	−	38.1124i	0.814971	−	1.41157i
$730$		0			0
$731$	4.04068	−	22.9158i	0.149450	−	0.847573i
$732$	−2.35395	+	13.3499i	−0.0870043	+	0.493426i
$733$	18.1102	+	31.3678i	0.668916	+	1.15860i	0.978207	+	0.207630i	$0.0665749\pi$
$733$	18.1102	+	31.3678i	0.668916	+	1.15860i	−0.309291	+	0.950967i	$0.600092\pi$
$734$	17.2120	−	29.8121i	0.635307	−	1.10038i
$735$		0			0
$736$	4.39211	+	1.59860i	0.161895	+	0.0589251i
$737$	−10.0314	+	3.65113i	−0.369511	+	0.134491i
$738$	43.1202	−	36.1822i	1.58728	−	1.33188i
$739$	−4.14661	−	23.5166i	−0.152536	−	0.865072i	−0.961004	−	0.276533i	$-0.910814\pi$
$739$	−4.14661	−	23.5166i	−0.152536	−	0.865072i	0.808469	−	0.588539i	$-0.200297\pi$
$740$		0			0
$741$	−75.2198	+	27.8386i	−2.76327	+	1.02268i
$742$	−3.41804			−0.125480
$743$	−1.62629	−	9.22315i	−0.0596628	−	0.338365i	0.940335	−	0.340249i	$-0.110511\pi$
$743$	−1.62629	−	9.22315i	−0.0596628	−	0.338365i	−0.999998	+	0.00188425i	$0.999400\pi$
$744$	−9.55085	+	8.01412i	−0.350151	+	0.293812i
$745$		0			0
$746$	15.6832	+	5.70822i	0.574203	+	0.208993i
$747$	54.6153	+	45.8276i	1.99827	+	1.67675i
$748$	−2.28913	+	3.96489i	−0.0836990	+	0.144971i
$749$	3.83657	+	6.64513i	0.140185	+	0.242808i
$750$		0			0
$751$	−5.57634	+	31.6250i	−0.203483	+	1.15401i	0.696325	+	0.717727i	$0.254817\pi$
$751$	−5.57634	+	31.6250i	−0.203483	+	1.15401i	−0.899808	+	0.436285i	$0.856294\pi$
$752$	2.48645	+	4.30667i	0.0906717	+	0.157048i
$753$	24.4789	−	42.3988i	0.892062	−	1.54510i
$754$	21.7600	+	18.2588i	0.792452	+	0.664946i
$755$		0			0
$756$	2.70884	−	0.985937i	0.0985195	−	0.0358582i
$757$	−27.0122	+	22.6659i	−0.981775	+	0.823807i	−0.984356	−	0.176189i	$-0.943623\pi$
$757$	−27.0122	+	22.6659i	−0.981775	+	0.823807i	0.00258109	+	0.999997i	$0.499178\pi$
$758$	−3.91885	−	22.2249i	−0.142339	−	0.807246i
$759$	−29.9795			−1.08819
$760$		0			0
$761$	−6.59530			−0.239079			−0.119540	−	0.992829i	$-0.538142\pi$
$761$	−6.59530			−0.239079			−0.119540	+	0.992829i	$0.538142\pi$
$762$	−1.95309	−	11.0765i	−0.0707531	−	0.401261i
$763$	7.38532	−	6.19702i	0.267367	−	0.224347i
$764$	10.3259	−	3.75834i	0.373580	−	0.135972i
$765$		0			0
$766$	−3.65846	−	3.06981i	−0.132185	−	0.110917i
$767$	−8.36566	+	14.4898i	−0.302067	+	0.523195i
$768$	1.38826	+	2.40454i	0.0500946	+	0.0867665i
$769$	−0.104835	+	0.594549i	−0.00378045	+	0.0214400i	−0.986640	−	0.162918i	$-0.947909\pi$
$769$	−0.104835	+	0.594549i	−0.00378045	+	0.0214400i	0.982859	+	0.184358i	$0.0590205\pi$
$770$		0			0
$771$	29.5049	+	51.1040i	1.06259	+	1.84047i
$772$	5.56868	−	9.64524i	0.200421	−	0.347140i
$773$	3.80193	+	3.19020i	0.136746	+	0.114744i	0.708595	−	0.705615i	$-0.249329\pi$
$773$	3.80193	+	3.19020i	0.136746	+	0.114744i	−0.571849	+	0.820359i	$0.693774\pi$
$774$	51.9567	+	18.9107i	1.86755	+	0.679731i
$775$		0			0
$776$	−6.11974	+	5.13507i	−0.219686	+	0.184338i
$777$	0.211438	+	1.19912i	0.00758529	+	0.0430183i
$778$	−0.531970			−0.0190720
$779$	−25.8077	+	45.2629i	−0.924656	+	1.62171i
$780$		0			0
$781$	2.41746	+	13.7101i	0.0865037	+	0.490587i
$782$	−7.09590	+	5.95417i	−0.253749	+	0.212921i
$783$	−19.1131	+	6.95660i	−0.683047	+	0.248609i
$784$	6.23108	+	2.26793i	0.222538	+	0.0809974i
$785$		0			0
$786$	−26.9889	+	46.7462i	−0.962664	+	1.66738i
$787$	−5.35809	−	9.28049i	−0.190995	−	0.330814i	0.754585	−	0.656202i	$-0.227838\pi$
$787$	−5.35809	−	9.28049i	−0.190995	−	0.330814i	−0.945580	+	0.325389i	$0.894505\pi$
$788$	1.52007	−	8.62075i	0.0541503	−	0.307101i
$789$	1.68159	−	9.53677i	0.0598662	−	0.339518i
$790$		0			0
$791$	−0.243645	+	0.422006i	−0.00866303	+	0.0150048i
$792$	−8.33349	−	6.99263i	−0.296118	−	0.248472i
$793$	−30.4045	−	11.0663i	−1.07970	−	0.392977i
$794$	−1.45158	+	0.528333i	−0.0515148	+	0.0187498i
$795$		0			0
$796$	−1.48762	−	8.43669i	−0.0527272	−	0.299031i
$797$	17.7272			0.627929			0.313964	−	0.949435i	$-0.398343\pi$
$797$	17.7272			0.627929			0.313964	+	0.949435i	$0.398343\pi$
$798$	−5.60638	+	4.75613i	−0.198464	+	0.168365i
$799$	−9.85545			−0.348661
$800$		0			0
$801$	40.6305	−	34.0931i	1.43561	−	1.20462i
$802$	6.75242	−	2.45768i	0.238436	−	0.0867837i
$803$	−2.18608	−	0.795670i	−0.0771452	−	0.0280786i
$804$	−9.82871	−	8.24727i	−0.346632	−	0.290859i
$805$		0			0
$806$	−14.8794	−	25.7718i	−0.524104	−	0.907774i
$807$	10.0510	−	57.0022i	0.353813	−	2.00657i
$808$	−0.559453	+	3.17282i	−0.0196815	+	0.111619i
$809$	−3.00973	−	5.21301i	−0.105816	−	0.183280i	0.808255	−	0.588833i	$-0.200412\pi$
$809$	−3.00973	−	5.21301i	−0.105816	−	0.183280i	−0.914071	+	0.405553i	$0.867079\pi$
$810$		0			0
$811$	−24.3040	−	20.3935i	−0.853431	−	0.716113i	0.107112	−	0.994247i	$-0.465840\pi$
$811$	−24.3040	−	20.3935i	−0.853431	−	0.716113i	−0.960542	+	0.278134i	$0.910284\pi$
$812$	2.44675	+	0.890545i	0.0858642	+	0.0312520i
$813$	67.0310	−	24.3973i	2.35088	−	0.855650i
$814$	1.27753	−	1.07198i	0.0447774	−	0.0375727i
$815$		0			0
$816$	−5.50260			−0.192629
$817$	−51.1786	+	0.276337i	−1.79051	+	0.00966782i
$818$	−17.1030			−0.597991
$819$	3.29204	+	18.6701i	0.115033	+	0.652385i
$820$		0			0
$821$	9.88833	−	3.59906i	0.345105	−	0.125608i	−0.163652	−	0.986518i	$-0.552327\pi$
$821$	9.88833	−	3.59906i	0.345105	−	0.125608i	0.508757	+	0.860910i	$0.330105\pi$
$822$	−36.1198	−	13.1465i	−1.25982	−	0.458538i
$823$	−3.27777	−	2.75038i	−0.114256	−	0.0958720i	0.583870	−	0.811847i	$-0.301538\pi$
$823$	−3.27777	−	2.75038i	−0.114256	−	0.0958720i	−0.698126	+	0.715975i	$0.745982\pi$
$824$	−1.30838	+	2.26619i	−0.0455797	+	0.0789464i
$825$		0			0
$826$	−0.266318	+	1.51036i	−0.00926639	+	0.0525523i
$827$	6.50174	−	36.8732i	0.226088	−	1.28221i	−0.634507	−	0.772917i	$-0.718797\pi$
$827$	6.50174	−	36.8732i	0.226088	−	1.28221i	0.860595	−	0.509290i	$-0.170092\pi$
$828$	−11.0051	−	19.0615i	−0.382455	−	0.662432i
$829$	−21.5719	+	37.3636i	−0.749222	+	1.29769i	0.198974	+	0.980005i	$0.436239\pi$
$829$	−21.5719	+	37.3636i	−0.749222	+	1.29769i	−0.948196	+	0.317686i	$0.897094\pi$
$830$		0			0
$831$	−46.2948	−	16.8499i	−1.60595	−	0.584518i
$832$	−6.22751	+	2.26663i	−0.215900	+	0.0785811i
$833$	−10.0669	+	8.44716i	−0.348799	+	0.292677i
$834$	−6.31625	−	35.8212i	−0.218714	−	1.24039i
$835$		0			0
$836$	9.48078	+	3.39286i	0.327899	+	0.117345i
$837$	21.3086			0.736534
$838$	4.42584	+	25.1002i	0.152888	+	0.867072i
$839$	−3.58248	+	3.00606i	−0.123681	+	0.103781i	−0.702530	−	0.711654i	$-0.747946\pi$
$839$	−3.58248	+	3.00606i	−0.123681	+	0.103781i	0.578849	+	0.815435i	$0.303502\pi$
$840$		0			0
$841$	9.98720	+	3.63505i	0.344386	+	0.125346i
$842$	−5.48313	−	4.60089i	−0.188961	−	0.158557i
$843$	−35.2850	+	61.1155i	−1.21528	+	2.10493i
$844$	−10.4660	−	18.1277i	−0.360255	−	0.623980i
$845$		0			0
$846$	4.06648	−	23.0622i	0.139808	−	0.792893i
$847$	1.72017	+	2.97942i	0.0591056	+	0.102374i
$848$	−2.81332	+	4.87281i	−0.0966097	+	0.167333i
$849$	−29.1257	−	24.4394i	−0.999592	−	0.838757i
$850$		0			0
$851$	3.17071	−	1.15404i	0.108690	−	0.0395601i
$852$	−12.8177	+	10.7553i	−0.439128	+	0.368472i
$853$	−5.53096	−	31.3676i	−0.189376	−	1.07401i	−0.920202	−	0.391443i	$-0.871976\pi$
$853$	−5.53096	−	31.3676i	−0.189376	−	1.07401i	0.730826	−	0.682564i	$-0.239135\pi$
$854$	−2.96587			−0.101490
$855$		0			0
$856$	12.6312			0.431726
$857$	8.70975	+	49.3954i	0.297519	+	1.68732i	0.656783	+	0.754080i	$0.271917\pi$
$857$	8.70975	+	49.3954i	0.297519	+	1.68732i	−0.359263	+	0.933236i	$0.616972\pi$
$858$	32.5626	−	27.3233i	1.11167	−	0.932801i
$859$	20.2461	−	7.36897i	0.690787	−	0.251426i	0.0273150	−	0.999627i	$-0.491304\pi$
$859$	20.2461	−	7.36897i	0.690787	−	0.251426i	0.663472	+	0.748201i	$0.269082\pi$
$860$		0			0
$861$	15.4445	+	12.9594i	0.526346	+	0.441657i
$862$	0.372924	−	0.645923i	0.0127018	−	0.0220002i
$863$	−1.75028	−	3.03157i	−0.0595802	−	0.103196i	0.834697	−	0.550710i	$-0.185643\pi$
$863$	−1.75028	−	3.03157i	−0.0595802	−	0.103196i	−0.894277	+	0.447514i	$0.852310\pi$
$864$	0.824023	−	4.67327i	0.0280338	−	0.158988i
$865$		0			0
$866$	2.97835	+	5.15866i	0.101209	+	0.175298i
$867$	−18.1479	+	31.4330i	−0.616334	+	1.06752i
$868$	−2.08962	−	1.75340i	−0.0709265	−	0.0595144i
$869$	6.68974	+	2.43487i	0.226934	+	0.0825972i
$870$		0			0
$871$	23.4597	−	19.6851i	0.794903	−	0.667003i
$872$	−2.75586	−	15.6293i	−0.0933253	−	0.529274i
$873$	37.6198			1.27324
$874$	15.6774	+	13.0113i	0.530298	+	0.440115i
$875$		0			0
$876$	−0.485532	−	2.75359i	−0.0164046	−	0.0930352i
$877$	34.1406	−	28.6474i	1.15285	−	0.967353i	0.153064	−	0.988216i	$-0.451086\pi$
$877$	34.1406	−	28.6474i	1.15285	−	0.967353i	0.999782	+	0.0208629i	$0.00664136\pi$
$878$	−1.38631	+	0.504574i	−0.0467856	+	0.0170286i
$879$	33.6418	+	12.2446i	1.13471	+	0.413000i
$880$		0			0
$881$	23.1872	−	40.1614i	0.781196	−	1.35307i	−0.150049	−	0.988679i	$-0.547943\pi$
$881$	23.1872	−	40.1614i	0.781196	−	1.35307i	0.931245	−	0.364393i	$-0.118724\pi$
$882$	−15.6130	−	27.0424i	−0.525716	−	0.910566i
$883$	3.54693	−	20.1157i	0.119364	−	0.676946i	−0.865133	−	0.501543i	$-0.832766\pi$
$883$	3.54693	−	20.1157i	0.119364	−	0.676946i	0.984497	−	0.175403i	$-0.0561228\pi$
$884$	2.28068	−	12.9344i	0.0767076	−	0.435030i
$885$		0			0
$886$	6.71910	−	11.6378i	0.225733	−	0.390980i
$887$	27.1687	+	22.7973i	0.912236	+	0.765457i	0.972543	−	0.232723i	$-0.0747635\pi$
$887$	27.1687	+	22.7973i	0.912236	+	0.765457i	−0.0603069	+	0.998180i	$0.519208\pi$
$888$	1.88352	+	0.685545i	0.0632068	+	0.0230054i
$889$	2.31241	−	0.841648i	0.0775557	−	0.0282280i
$890$		0			0
$891$	−0.381765	−	2.16510i	−0.0127896	−	0.0725335i
$892$	−10.4024			−0.348299
$893$	3.87928	+	21.3265i	0.129815	+	0.713663i
$894$	−16.0885			−0.538079
$895$		0			0
$896$	−0.465353	+	0.390477i	−0.0155463	+	0.0130449i
$897$	80.8172	−	29.4150i	2.69841	−	0.982140i
$898$	−22.4236	−	8.16154i	−0.748286	−	0.272354i
$899$	14.7440	+	12.3717i	0.491741	+	0.412620i
$900$		0			0
$901$	−5.57551	−	9.65707i	−0.185747	−	0.321724i
$902$	4.79506	−	27.1941i	0.159658	−	0.905466i
$903$	−3.43889	+	19.5029i	−0.114439	+	0.649017i
$904$	0.401079	+	0.694689i	0.0133397	+	0.0231050i
$905$		0			0
$906$	40.0258	+	33.5856i	1.32977	+	1.11581i
$907$	16.1507	+	5.87837i	0.536275	+	0.195188i	0.595938	−	0.803030i	$-0.296780\pi$
$907$	16.1507	+	5.87837i	0.536275	+	0.195188i	−0.0596630	+	0.998219i	$0.519003\pi$
$908$	6.22402	−	2.26536i	0.206551	−	0.0751786i
$909$	11.6221	−	9.75212i	0.385481	−	0.323457i
$910$		0			0
$911$	−1.09556			−0.0362974			−0.0181487	−	0.999835i	$-0.505777\pi$
$911$	−1.09556			−0.0362974			−0.0181487	+	0.999835i	$0.505777\pi$
$912$	2.16592	+	11.9072i	0.0717207	+	0.394287i
$913$	34.9749			1.15750
$914$	1.58077	+	8.96498i	0.0522871	+	0.296535i
$915$		0			0
$916$	−14.7802	+	5.37954i	−0.488350	+	0.177745i
$917$	−11.0976	−	4.03919i	−0.366474	−	0.133386i
$918$	7.20426	+	6.04509i	0.237776	+	0.199518i
$919$	12.4735	−	21.6048i	0.411464	−	0.712677i	−0.583586	−	0.812052i	$-0.698351\pi$
$919$	12.4735	−	21.6048i	0.411464	−	0.712677i	0.995050	+	0.0993743i	$0.0316841\pi$
$920$		0			0
$921$	2.81695	−	15.9757i	0.0928216	−	0.526417i
$922$	5.38623	−	30.5468i	0.177386	−	1.00601i
$923$	−19.9689	−	34.5871i	−0.657283	−	1.13845i
$924$	1.94821	−	3.37439i	0.0640913	−	0.111009i
$925$		0			0
$926$	18.1873	+	6.61963i	0.597671	+	0.217534i
$927$	11.5795	−	4.21459i	0.380320	−	0.138425i
$928$	3.28345	−	2.75514i	0.107784	−	0.0904419i
$929$	−2.42904	−	13.7758i	−0.0796941	−	0.451968i	−0.998376	−	0.0569694i	$-0.981856\pi$
$929$	−2.42904	−	13.7758i	−0.0796941	−	0.451968i	0.918682	−	0.394998i	$-0.129255\pi$
$930$		0			0
$931$	22.2415	+	18.4591i	0.728937	+	0.604974i
$932$	−18.2214			−0.596862
$933$	2.00864	+	11.3915i	0.0657598	+	0.372942i
$934$	−13.5830	+	11.3975i	−0.444448	+	0.372936i
$935$		0			0
$936$	29.3259	+	10.6738i	0.958548	+	0.348883i
$937$	−0.974977	−	0.818103i	−0.0318511	−	0.0267263i	0.626723	−	0.779242i	$-0.284396\pi$
$937$	−0.974977	−	0.818103i	−0.0318511	−	0.0267263i	−0.658574	+	0.752516i	$0.728840\pi$
$938$	1.40359	−	2.43108i	0.0458287	−	0.0793777i
$939$	4.59885	+	7.96544i	0.150078	+	0.259942i
$940$		0			0
$941$	3.35170	−	19.0084i	0.109262	−	0.619658i	−0.880170	−	0.474659i	$-0.842571\pi$
$941$	3.35170	−	19.0084i	0.109262	−	0.619658i	0.989432	−	0.144998i	$-0.0463177\pi$
$942$	−3.57562	−	6.19315i	−0.116500	−	0.201784i
$943$	27.9349	−	48.3846i	0.909685	−	1.57562i
$944$	1.93400	+	1.62282i	0.0629463	+	0.0528182i
$945$		0			0
$946$	25.4882	−	9.27694i	0.828692	−	0.301619i
$947$	−0.300798	+	0.252400i	−0.00977463	+	0.00820188i	−0.647662	−	0.761928i	$-0.724253\pi$
$947$	−0.300798	+	0.252400i	−0.00977463	+	0.00820188i	0.637887	+	0.770130i	$0.279809\pi$
$948$	1.48580	+	8.42640i	0.0482566	+	0.273677i
$949$	6.67382			0.216641
$950$		0			0
$951$	38.7618			1.25694
$952$	−0.209057	−	1.18562i	−0.00677557	−	0.0384262i
$953$	19.6441	−	16.4833i	0.636334	−	0.533948i	−0.266556	−	0.963820i	$-0.585886\pi$
$953$	19.6441	−	16.4833i	0.636334	−	0.533948i	0.902890	+	0.429872i	$0.141441\pi$
$954$	24.8985	−	9.06230i	0.806117	−	0.293403i
$955$		0			0
$956$	−3.39727	−	2.85065i	−0.109876	−	0.0921965i
$957$	−13.7462	+	23.8091i	−0.444352	+	0.769640i
$958$	2.59945	+	4.50238i	0.0839844	+	0.145465i
$959$	1.46035	−	8.28204i	0.0471571	−	0.267441i
$960$		0			0
$961$	5.41810	+	9.38442i	0.174777	+	0.302723i
$962$	−2.39211	+	4.14325i	−0.0771247	+	0.133584i
$963$	−45.5656	−	38.2341i	−1.46833	−	1.23208i
$964$	9.06064	+	3.29780i	0.291824	+	0.106215i
$965$		0			0
$966$	6.03909	−	5.06740i	0.194305	−	0.163041i
$967$	−2.46982	−	14.0070i	−0.0794239	−	0.450436i	−0.998421	−	0.0561715i	$-0.982111\pi$
$967$	−2.46982	−	14.0070i	−0.0794239	−	0.450436i	0.918997	−	0.394264i	$-0.129000\pi$
$968$	5.66334			0.182027
$969$	−22.5827	−	8.08163i	−0.725462	−	0.259619i
$970$		0			0
$971$	−0.0425935	−	0.241560i	−0.00136689	−	0.00775201i	0.984117	−	0.177523i	$-0.0568084\pi$
$971$	−0.0425935	−	0.241560i	−0.00136689	−	0.00775201i	−0.985484	+	0.169771i	$0.945697\pi$
$972$	12.9296	−	10.8493i	0.414718	−	0.347990i
$973$	7.47827	−	2.72187i	0.239742	−	0.0872591i
$974$	35.7196	+	13.0009i	1.14453	+	0.416575i
$975$		0			0
$976$	−2.44115	+	4.22819i	−0.0781393	+	0.135341i
$977$	14.6038	+	25.2945i	0.467216	+	0.809241i	0.999298	−	0.0374511i	$-0.0119239\pi$
$977$	14.6038	+	25.2945i	0.467216	+	0.809241i	−0.532083	+	0.846692i	$0.678591\pi$
$978$	1.46288	−	8.29638i	0.0467776	−	0.265289i
$979$	4.51820	−	25.6240i	0.144402	−	0.818947i
$980$		0			0
$981$	−37.3676	+	64.7226i	−1.19306	+	2.06643i
$982$	−16.8331	−	14.1247i	−0.537167	−	0.450736i
$983$	30.4748	+	11.0919i	0.971994	+	0.353777i	0.778722	−	0.627369i	$-0.215868\pi$
$983$	30.4748	+	11.0919i	0.971994	+	0.353777i	0.193271	+	0.981145i	$0.438090\pi$
$984$	31.1872	−	11.3512i	0.994212	−	0.361864i
$985$		0			0
$986$	1.47507	+	8.36554i	0.0469758	+	0.266413i
$987$	8.38765			0.266982
$988$	−28.8868	+	0.155973i	−0.919010	+	0.00496216i
$989$	54.8790			1.74505
$990$		0			0
$991$	26.1090	−	21.9080i	0.829379	−	0.695931i	−0.125770	−	0.992059i	$-0.540140\pi$
$991$	26.1090	−	21.9080i	0.829379	−	0.695931i	0.955148	+	0.296128i	$0.0956956\pi$
$992$	−4.21961	+	1.53581i	−0.133973	+	0.0487621i
$993$	−51.2398	−	18.6498i	−1.62605	−	0.591833i
$994$	−2.80438	−	2.35316i	−0.0889496	−	0.0746376i
$995$		0			0
$996$	21.0181	+	36.4045i	0.665985	+	1.15352i
$997$	3.94587	−	22.3781i	0.124967	−	0.708723i	−0.856361	−	0.516378i	$-0.827280\pi$
$997$	3.94587	−	22.3781i	0.124967	−	0.708723i	0.981327	−	0.192344i	$-0.0616091\pi$
$998$	−0.600208	+	3.40395i	−0.0189993	+	0.107750i
$999$	−1.71286	−	2.96676i	−0.0541925	−	0.0938641i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.l.351.1		30
5.2	odd	4		190.2.p.a.9.10	yes	60
5.3	odd	4		190.2.p.a.9.1	✓	60
5.4	even	2		950.2.l.m.351.5		30
19.17	even	9	inner	950.2.l.l.701.1		30
95.17	odd	36		190.2.p.a.169.1	yes	60
95.74	even	18		950.2.l.m.701.5		30
95.93	odd	36		190.2.p.a.169.10	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.p.a.9.1	✓	60	5.3	odd	4
190.2.p.a.9.10	yes	60	5.2	odd	4
190.2.p.a.169.1	yes	60	95.17	odd	36
190.2.p.a.169.10	yes	60	95.93	odd	36
950.2.l.l.351.1		30	1.1	even	1	trivial
950.2.l.l.701.1		30	19.17	even	9	inner
950.2.l.m.351.5		30	5.4	even	2
950.2.l.m.701.5		30	95.74	even	18

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-2.12694 + 1.78472i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.12694 + 1.78472i) q^{6} +(-0.303737 + 0.526088i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.817727 - 4.63756i) q^{9} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-2.12694 + 1.78472i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.12694 + 1.78472i) q^{6} +(-0.303737 + 0.526088i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.817727 - 4.63756i) q^{9} +(-1.15506 - 2.00062i) q^{11} +(1.38826 - 2.40454i) q^{12} +(5.07671 + 4.25986i) q^{13} +(0.570839 + 0.207769i) q^{14} +(0.766044 - 0.642788i) q^{16} +(0.344141 + 1.95172i) q^{17} -4.70910 q^{18} +(4.08792 - 1.51293i) q^{19} +(-0.292887 - 1.66104i) q^{21} +(-1.76966 + 1.48492i) q^{22} +(-4.39211 + 1.59860i) q^{23} +(-2.60908 - 0.949628i) q^{24} +(3.31359 - 5.73930i) q^{26} +(2.37268 + 4.10960i) q^{27} +(0.105487 - 0.598246i) q^{28} +(-0.744297 + 4.22112i) q^{29} +(2.24521 - 3.88881i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(6.02730 + 2.19376i) q^{33} +(1.86231 - 0.677825i) q^{34} +(0.817727 + 4.63756i) q^{36} -0.721909 q^{37} +(-2.19980 - 3.76309i) q^{38} -18.4005 q^{39} +(-9.15679 + 7.68346i) q^{41} +(-1.58495 + 0.576875i) q^{42} +(-11.0333 - 4.01578i) q^{43} +(1.76966 + 1.48492i) q^{44} +(2.33699 + 4.04779i) q^{46} +(-0.863537 + 4.89736i) q^{47} +(-0.482139 + 2.73434i) q^{48} +(3.31549 + 5.74259i) q^{49} +(-4.21524 - 3.53700i) q^{51} +(-6.22751 - 2.26663i) q^{52} +(-5.28731 + 1.92442i) q^{53} +(3.63516 - 3.05026i) q^{54} -0.607475 q^{56} +(-5.99462 + 10.5137i) q^{57} +4.28624 q^{58} +(0.438402 + 2.48630i) q^{59} +(-4.58786 + 1.66984i) q^{61} +(-4.21961 - 1.53581i) q^{62} +(2.19139 + 1.83880i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.11380 - 6.31667i) q^{66} +(0.802437 - 4.55085i) q^{67} +(-0.990914 - 1.71631i) q^{68} +(6.48873 - 11.2388i) q^{69} +(-5.66293 - 2.06114i) q^{71} +(4.42511 - 1.61061i) q^{72} +(0.771436 - 0.647312i) q^{73} +(0.125358 + 0.710942i) q^{74} +(-3.32393 + 2.81983i) q^{76} +1.40334 q^{77} +(3.19522 + 18.1210i) q^{78} +(-2.36071 + 1.98087i) q^{79} +(0.894288 + 0.325494i) q^{81} +(9.15679 + 7.68346i) q^{82} +(-7.56994 + 13.1115i) q^{83} +(0.843335 + 1.46070i) q^{84} +(-2.03886 + 11.5630i) q^{86} +(-5.95043 - 10.3064i) q^{87} +(1.15506 - 2.00062i) q^{88} +(8.62809 + 7.23983i) q^{89} +(-3.78305 + 1.37692i) q^{91} +(3.58048 - 3.00438i) q^{92} +(2.16500 + 12.2783i) q^{93} +4.97291 q^{94} +2.77653 q^{96} +(1.38723 + 7.86738i) q^{97} +(5.07962 - 4.26231i) q^{98} +(-10.2225 + 3.72070i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) \) 30 * q - 12 * q^7 + 15 * q^8	\( 30 q - 12 q^{7} + 15 q^{8} + 6 q^{11} + 6 q^{14} - 30 q^{18} + 24 q^{19} + 24 q^{21} + 3 q^{22} + 3 q^{23} + 3 q^{26} - 18 q^{27} + 3 q^{28} + 12 q^{29} - 30 q^{33} + 24 q^{37} - 12 q^{38} - 24 q^{39} - 3 q^{41} + 12 q^{42} + 6 q^{43} - 3 q^{44} + 48 q^{47} + 15 q^{49} - 90 q^{51} - 18 q^{53} + 18 q^{54} - 24 q^{56} - 42 q^{57} + 36 q^{58} - 18 q^{59} - 60 q^{61} - 24 q^{62} - 21 q^{63} - 15 q^{64} - 78 q^{66} - 30 q^{67} - 12 q^{68} + 24 q^{69} + 30 q^{73} - 9 q^{74} - 3 q^{76} + 78 q^{77} - 6 q^{79} + 60 q^{81} + 3 q^{82} - 42 q^{83} - 6 q^{84} + 12 q^{86} - 54 q^{87} - 6 q^{88} - 30 q^{89} - 6 q^{91} - 6 q^{92} + 72 q^{93} - 78 q^{94} - 42 q^{97} + 6 q^{98} - 99 q^{99}+O(q^{100}) \) 30 * q - 12 * q^7 + 15 * q^8 + 6 * q^11 + 6 * q^14 - 30 * q^18 + 24 * q^19 + 24 * q^21 + 3 * q^22 + 3 * q^23 + 3 * q^26 - 18 * q^27 + 3 * q^28 + 12 * q^29 - 30 * q^33 + 24 * q^37 - 12 * q^38 - 24 * q^39 - 3 * q^41 + 12 * q^42 + 6 * q^43 - 3 * q^44 + 48 * q^47 + 15 * q^49 - 90 * q^51 - 18 * q^53 + 18 * q^54 - 24 * q^56 - 42 * q^57 + 36 * q^58 - 18 * q^59 - 60 * q^61 - 24 * q^62 - 21 * q^63 - 15 * q^64 - 78 * q^66 - 30 * q^67 - 12 * q^68 + 24 * q^69 + 30 * q^73 - 9 * q^74 - 3 * q^76 + 78 * q^77 - 6 * q^79 + 60 * q^81 + 3 * q^82 - 42 * q^83 - 6 * q^84 + 12 * q^86 - 54 * q^87 - 6 * q^88 - 30 * q^89 - 6 * q^91 - 6 * q^92 + 72 * q^93 - 78 * q^94 - 42 * q^97 + 6 * q^98 - 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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