LMFDB - Embedded newform 1045.2.f.a.626.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(626,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("1045.626");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.f (of order $2$, degree $1$, 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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			626.5
Character	$\chi$	$=$	1045.626
Dual form			1045.2.f.a.626.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.08652 q^{2} +2.80799i q^{3} +2.35358 q^{4} -1.00000 q^{5} -5.85893i q^{6} -0.950248i q^{7} -0.737755 q^{8} -4.88478 q^{9} +O(q^{10})$	\(q-2.08652 q^{2} +2.80799i q^{3} +2.35358 q^{4} -1.00000 q^{5} -5.85893i q^{6} -0.950248i q^{7} -0.737755 q^{8} -4.88478 q^{9} +2.08652 q^{10} +(0.932412 - 3.18286i) q^{11} +6.60882i q^{12} +3.48762 q^{13} +1.98271i q^{14} -2.80799i q^{15} -3.16782 q^{16} -1.26303i q^{17} +10.1922 q^{18} +(-3.21612 + 2.94221i) q^{19} -2.35358 q^{20} +2.66828 q^{21} +(-1.94550 + 6.64112i) q^{22} +4.91539 q^{23} -2.07160i q^{24} +1.00000 q^{25} -7.27700 q^{26} -5.29243i q^{27} -2.23649i q^{28} +4.16032 q^{29} +5.85893i q^{30} +6.79836i q^{31} +8.08524 q^{32} +(8.93743 + 2.61820i) q^{33} +2.63535i q^{34} +0.950248i q^{35} -11.4967 q^{36} +3.59157i q^{37} +(6.71050 - 6.13899i) q^{38} +9.79318i q^{39} +0.737755 q^{40} -3.33055 q^{41} -5.56743 q^{42} +2.02665i q^{43} +(2.19451 - 7.49112i) q^{44} +4.88478 q^{45} -10.2561 q^{46} +9.25227 q^{47} -8.89519i q^{48} +6.09703 q^{49} -2.08652 q^{50} +3.54658 q^{51} +8.20839 q^{52} +3.95431i q^{53} +11.0428i q^{54} +(-0.932412 + 3.18286i) q^{55} +0.701050i q^{56} +(-8.26168 - 9.03081i) q^{57} -8.68061 q^{58} +3.82704i q^{59} -6.60882i q^{60} +3.98693i q^{61} -14.1849i q^{62} +4.64175i q^{63} -10.5344 q^{64} -3.48762 q^{65} +(-18.6482 - 5.46294i) q^{66} -7.67189i q^{67} -2.97265i q^{68} +13.8023i q^{69} -1.98271i q^{70} -8.48153i q^{71} +3.60377 q^{72} +6.81980i q^{73} -7.49390i q^{74} +2.80799i q^{75} +(-7.56939 + 6.92473i) q^{76} +(-3.02451 - 0.886023i) q^{77} -20.4337i q^{78} -14.7309 q^{79} +3.16782 q^{80} +0.206737 q^{81} +6.94927 q^{82} -10.4685i q^{83} +6.28002 q^{84} +1.26303i q^{85} -4.22864i q^{86} +11.6821i q^{87} +(-0.687892 + 2.34817i) q^{88} +4.45627i q^{89} -10.1922 q^{90} -3.31410i q^{91} +11.5688 q^{92} -19.0897 q^{93} -19.3051 q^{94} +(3.21612 - 2.94221i) q^{95} +22.7032i q^{96} +10.0583i q^{97} -12.7216 q^{98} +(-4.55463 + 15.5476i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{4} - 40 q^{5} - 28 q^{9}+O(q^{10}) $ 40 * q + 40 * q^4 - 40 * q^5 - 28 * q^9	$ 40 q + 40 q^{4} - 40 q^{5} - 28 q^{9} - 4 q^{11} + 32 q^{16} - 40 q^{20} - 16 q^{23} + 40 q^{25} + 8 q^{26} + 8 q^{36} + 28 q^{38} - 84 q^{42} - 48 q^{44} + 28 q^{45} + 32 q^{47} - 20 q^{49} + 4 q^{55} - 20 q^{58} + 72 q^{64} + 36 q^{66} + 16 q^{77} - 32 q^{80} + 16 q^{81} + 16 q^{82} - 20 q^{92} - 8 q^{93}+O(q^{100}) $ 40 * q + 40 * q^4 - 40 * q^5 - 28 * q^9 - 4 * q^11 + 32 * q^16 - 40 * q^20 - 16 * q^23 + 40 * q^25 + 8 * q^26 + 8 * q^36 + 28 * q^38 - 84 * q^42 - 48 * q^44 + 28 * q^45 + 32 * q^47 - 20 * q^49 + 4 * q^55 - 20 * q^58 + 72 * q^64 + 36 * q^66 + 16 * q^77 - 32 * q^80 + 16 * q^81 + 16 * q^82 - 20 * q^92 - 8 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.08652			−1.47539			−0.737697	−	0.675131i	$-0.764087\pi$
$2$	−2.08652			−1.47539			−0.737697	+	0.675131i	$0.764087\pi$
$3$			2.80799i			1.62119i	0.585607	+	0.810595i	$0.300856\pi$
$3$			2.80799i			1.62119i	−0.585607	+	0.810595i	$0.699144\pi$
$4$	2.35358			1.17679
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		−	5.85893i		−	2.39190i
$7$		−	0.950248i		−	0.359160i	−0.983743	−	0.179580i	$-0.942526\pi$
$7$		−	0.950248i		−	0.359160i	0.983743	−	0.179580i	$-0.0574739\pi$
$8$	−0.737755			−0.260836
$9$	−4.88478			−1.62826
$10$	2.08652			0.659817
$11$	0.932412	−	3.18286i	0.281133	−	0.959669i
$11$	0.932412	−	3.18286i	0.281133	−	0.959669i
$12$			6.60882i			1.90780i
$13$	3.48762			0.967291			0.483646	−	0.875264i	$-0.339312\pi$
$13$	3.48762			0.967291			0.483646	+	0.875264i	$0.339312\pi$
$14$			1.98271i			0.529903i
$15$		−	2.80799i		−	0.725019i
$16$	−3.16782			−0.791955
$17$		−	1.26303i		−	0.306331i	−0.988201	−	0.153165i	$-0.951053\pi$
$17$		−	1.26303i		−	0.306331i	0.988201	−	0.153165i	$-0.0489467\pi$
$18$	10.1922			2.40233
$19$	−3.21612	+	2.94221i	−0.737828	+	0.674989i
$19$	−3.21612	+	2.94221i	−0.737828	+	0.674989i
$20$	−2.35358			−0.526277
$21$	2.66828			0.582267
$22$	−1.94550	+	6.64112i	−0.414782	+	1.41589i
$23$	4.91539			1.02493			0.512465	−	0.858708i	$-0.328733\pi$
$23$	4.91539			1.02493			0.512465	+	0.858708i	$0.328733\pi$
$24$		−	2.07160i		−	0.422864i
$25$	1.00000			0.200000
$26$	−7.27700			−1.42714
$27$		−	5.29243i		−	1.01853i
$28$		−	2.23649i		−	0.422656i
$29$	4.16032			0.772552			0.386276	−	0.922383i	$-0.373761\pi$
$29$	4.16032			0.772552			0.386276	+	0.922383i	$0.373761\pi$
$30$			5.85893i			1.06969i
$31$			6.79836i			1.22102i	0.792008	+	0.610511i	$0.209036\pi$
$31$			6.79836i			1.22102i	−0.792008	+	0.610511i	$0.790964\pi$
$32$	8.08524			1.42928
$33$	8.93743	+	2.61820i	1.55581	+	0.455770i
$34$			2.63535i			0.451959i
$35$			0.950248i			0.160621i
$36$	−11.4967			−1.91612
$37$			3.59157i			0.590451i	0.955428	+	0.295225i	$0.0953948\pi$
$37$			3.59157i			0.590451i	−0.955428	+	0.295225i	$0.904605\pi$
$38$	6.71050	−	6.13899i	1.08859	−	0.995876i
$39$			9.79318i			1.56816i
$40$	0.737755			0.116649
$41$	−3.33055			−0.520145			−0.260072	−	0.965589i	$-0.583746\pi$
$41$	−3.33055			−0.520145			−0.260072	+	0.965589i	$0.583746\pi$
$42$	−5.56743			−0.859074
$43$			2.02665i			0.309061i	0.987988	+	0.154530i	$0.0493864\pi$
$43$			2.02665i			0.309061i	−0.987988	+	0.154530i	$0.950614\pi$
$44$	2.19451	−	7.49112i	0.330835	−	1.12933i
$45$	4.88478			0.728180
$46$	−10.2561			−1.51218
$47$	9.25227			1.34958			0.674791	−	0.738009i	$-0.264234\pi$
$47$	9.25227			1.34958			0.674791	+	0.738009i	$0.264234\pi$
$48$		−	8.89519i		−	1.28391i
$49$	6.09703			0.871004
$50$	−2.08652			−0.295079
$51$	3.54658			0.496621
$52$	8.20839			1.13830
$53$			3.95431i			0.543167i	0.962415	+	0.271583i	$0.0875473\pi$
$53$			3.95431i			0.543167i	−0.962415	+	0.271583i	$0.912453\pi$
$54$			11.0428i			1.50273i
$55$	−0.932412	+	3.18286i	−0.125726	+	0.429177i
$56$			0.701050i			0.0936817i
$57$	−8.26168	−	9.03081i	−1.09429	−	1.19616i
$58$	−8.68061			−1.13982
$59$			3.82704i			0.498238i	0.968473	+	0.249119i	$0.0801411\pi$
$59$			3.82704i			0.498238i	−0.968473	+	0.249119i	$0.919859\pi$
$60$		−	6.60882i		−	0.853195i
$61$			3.98693i			0.510474i	0.966879	+	0.255237i	$0.0821535\pi$
$61$			3.98693i			0.510474i	−0.966879	+	0.255237i	$0.917847\pi$
$62$		−	14.1849i		−	1.80149i
$63$			4.64175i			0.584806i
$64$	−10.5344			−1.31680
$65$	−3.48762			−0.432586
$66$	−18.6482	−	5.46294i	−2.29543	−	0.672441i
$67$		−	7.67189i		−	0.937270i	−0.883392	−	0.468635i	$-0.844746\pi$
$67$		−	7.67189i		−	0.937270i	0.883392	−	0.468635i	$-0.155254\pi$
$68$		−	2.97265i		−	0.360487i
$69$			13.8023i			1.66161i
$70$		−	1.98271i		−	0.236980i
$71$		−	8.48153i		−	1.00657i	−0.864120	−	0.503286i	$-0.832124\pi$
$71$		−	8.48153i		−	1.00657i	0.864120	−	0.503286i	$-0.167876\pi$
$72$	3.60377			0.424708
$73$			6.81980i			0.798197i	0.916908	+	0.399098i	$0.130677\pi$
$73$			6.81980i			0.798197i	−0.916908	+	0.399098i	$0.869323\pi$
$74$		−	7.49390i		−	0.871148i
$75$			2.80799i			0.324238i
$76$	−7.56939	+	6.92473i	−0.868268	+	0.794321i
$77$	−3.02451	−	0.886023i	−0.344675	−	0.100972i
$78$		−	20.4337i		−	2.31366i
$79$	−14.7309			−1.65735			−0.828676	−	0.559728i	$-0.810905\pi$
$79$	−14.7309			−1.65735			−0.828676	+	0.559728i	$0.810905\pi$
$80$	3.16782			0.354173
$81$	0.206737			0.0229708
$82$	6.94927			0.767419
$83$		−	10.4685i		−	1.14906i	−0.818482	−	0.574532i	$-0.805184\pi$
$83$		−	10.4685i		−	1.14906i	0.818482	−	0.574532i	$-0.194816\pi$
$84$	6.28002			0.685206
$85$			1.26303i			0.136995i
$86$		−	4.22864i		−	0.455986i
$87$			11.6821i			1.25245i
$88$	−0.687892	+	2.34817i	−0.0733295	+	0.250316i
$89$			4.45627i			0.472364i	0.971709	+	0.236182i	$0.0758961\pi$
$89$			4.45627i			0.472364i	−0.971709	+	0.236182i	$0.924104\pi$
$90$	−10.1922			−1.07435
$91$		−	3.31410i		−	0.347412i
$92$	11.5688			1.20613
$93$	−19.0897			−1.97951
$94$	−19.3051			−1.99117
$95$	3.21612	−	2.94221i	0.329967	−	0.301864i
$96$			22.7032i			2.31714i
$97$			10.0583i			1.02127i	0.859798	+	0.510635i	$0.170590\pi$
$97$			10.0583i			1.02127i	−0.859798	+	0.510635i	$0.829410\pi$
$98$	−12.7216			−1.28508
$99$	−4.55463	+	15.5476i	−0.457758	+	1.56259i
$100$	2.35358			0.235358
$101$		−	0.514789i		−	0.0512234i	−0.999672	−	0.0256117i	$-0.991847\pi$
$101$		−	0.514789i		−	0.0512234i	0.999672	−	0.0256117i	$-0.00815335\pi$
$102$	−7.40002			−0.732711
$103$			14.7928i			1.45757i	0.684740	+	0.728787i	$0.259916\pi$
$103$			14.7928i			1.45757i	−0.684740	+	0.728787i	$0.740084\pi$
$104$	−2.57301			−0.252304
$105$	−2.66828			−0.260398
$106$		−	8.25077i		−	0.801386i
$107$	−0.507132			−0.0490263			−0.0245131	−	0.999700i	$-0.507804\pi$
$107$	−0.507132			−0.0490263			−0.0245131	+	0.999700i	$0.507804\pi$
$108$		−	12.4562i		−	1.19860i
$109$	5.33073			0.510591			0.255296	−	0.966863i	$-0.417827\pi$
$109$	5.33073			0.510591			0.255296	+	0.966863i	$0.417827\pi$
$110$	1.94550	−	6.64112i	0.185496	−	0.633206i
$111$	−10.0851			−0.957234
$112$			3.01021i			0.284438i
$113$			6.94230i			0.653077i	0.945184	+	0.326538i	$0.105882\pi$
$113$			6.94230i			0.653077i	−0.945184	+	0.326538i	$0.894118\pi$
$114$	17.2382	+	18.8430i	1.61450	+	1.76481i
$115$	−4.91539			−0.458362
$116$	9.79165			0.909132
$117$	−17.0362			−1.57500
$118$		−	7.98521i		−	0.735098i
$119$	−1.20020			−0.110022
$120$			2.07160i			0.189111i
$121$	−9.26121	−	5.93548i	−0.841929	−	0.539589i
$122$		−	8.31882i		−	0.753151i
$123$		−	9.35213i		−	0.843254i
$124$			16.0005i			1.43689i
$125$	−1.00000			−0.0894427
$126$		−	9.68513i		−	0.862820i
$127$	−5.90787			−0.524239			−0.262120	−	0.965035i	$-0.584421\pi$
$127$	−5.90787			−0.524239			−0.262120	+	0.965035i	$0.584421\pi$
$128$	5.80980			0.513519
$129$	−5.69079			−0.501046
$130$	7.27700			0.638235
$131$			5.48750i			0.479445i	0.970841	+	0.239722i	$0.0770564\pi$
$131$			5.48750i			0.479445i	−0.970841	+	0.239722i	$0.922944\pi$
$132$	21.0350	+	6.16215i	1.83086	+	0.536346i
$133$	2.79583	+	3.05611i	0.242429	+	0.264998i
$134$			16.0076i			1.38284i
$135$			5.29243i			0.455500i
$136$			0.931809i			0.0799020i
$137$	18.1170			1.54784			0.773921	−	0.633282i	$-0.218293\pi$
$137$	18.1170			1.54784			0.773921	+	0.633282i	$0.218293\pi$
$138$		−	28.7989i		−	2.45152i
$139$			9.63153i			0.816935i	0.912773	+	0.408468i	$0.133937\pi$
$139$			9.63153i			0.816935i	−0.912773	+	0.408468i	$0.866063\pi$
$140$			2.23649i			0.189018i
$141$			25.9802i			2.18793i
$142$			17.6969i			1.48509i
$143$	3.25190	−	11.1006i	0.271937	−	0.928279i
$144$	15.4741			1.28951
$145$	−4.16032			−0.345496
$146$		−	14.2297i		−	1.17766i
$147$			17.1204i			1.41206i
$148$			8.45306i			0.694837i
$149$			20.0757i			1.64466i	0.569010	+	0.822331i	$0.307327\pi$
$149$			20.0757i			1.64466i	−0.569010	+	0.822331i	$0.692673\pi$
$150$		−	5.85893i		−	0.478379i
$151$	22.4123			1.82389			0.911943	−	0.410318i	$-0.134582\pi$
$151$	22.4123			1.82389			0.911943	+	0.410318i	$0.134582\pi$
$152$	2.37270	−	2.17063i	0.192452	−	0.176061i
$153$			6.16964i			0.498786i
$154$	6.31071	+	1.84871i	0.508531	+	0.148973i
$155$		−	6.79836i		−	0.546057i
$156$			23.0490i			1.84540i
$157$	20.9743			1.67393			0.836966	−	0.547255i	$-0.184327\pi$
$157$	20.9743			1.67393			0.836966	+	0.547255i	$0.184327\pi$
$158$	30.7363			2.44525
$159$	−11.1037			−0.880577
$160$	−8.08524			−0.639194
$161$		−	4.67084i		−	0.368114i
$162$	−0.431362			−0.0338910
$163$	3.09195			0.242180			0.121090	−	0.992642i	$-0.461361\pi$
$163$	3.09195			0.242180			0.121090	+	0.992642i	$0.461361\pi$
$164$	−7.83872			−0.612101
$165$	−8.93743	−	2.61820i	−0.695778	−	0.203827i
$166$			21.8427i			1.69532i
$167$	−6.49141			−0.502320			−0.251160	−	0.967946i	$-0.580812\pi$
$167$	−6.49141			−0.502320			−0.251160	+	0.967946i	$0.580812\pi$
$168$	−1.96854			−0.151876
$169$	−0.836519			−0.0643476
$170$		−	2.63535i		−	0.202122i
$171$	15.7100	−	14.3720i	1.20138	−	1.09906i
$172$			4.76987i			0.363699i
$173$	−10.6352			−0.808579			−0.404290	−	0.914631i	$-0.632481\pi$
$173$	−10.6352			−0.808579			−0.404290	+	0.914631i	$0.632481\pi$
$174$		−	24.3750i		−	1.84787i
$175$		−	0.950248i		−	0.0718320i
$176$	−2.95371	+	10.0827i	−0.222645	+	0.760014i
$177$	−10.7463			−0.807739
$178$		−	9.29812i		−	0.696923i
$179$		−	17.5731i		−	1.31347i	−0.754119	−	0.656737i	$-0.771936\pi$
$179$		−	17.5731i		−	1.31347i	0.754119	−	0.656737i	$-0.228064\pi$
$180$	11.4967			0.856915
$181$		−	15.8579i		−	1.17871i	−0.807875	−	0.589354i	$-0.799382\pi$
$181$		−	15.8579i		−	1.17871i	0.807875	−	0.589354i	$-0.200618\pi$
$182$			6.91495i			0.512570i
$183$	−11.1952			−0.827576
$184$	−3.62635			−0.267338
$185$		−	3.59157i		−	0.264058i
$186$	39.8311			2.92056
$187$	−4.02006	−	1.17767i	−0.293976	−	0.0861196i
$188$	21.7760			1.58817
$189$	−5.02913			−0.365815
$190$	−6.71050	+	6.13899i	−0.486831	+	0.445369i
$191$	−7.01749			−0.507768			−0.253884	−	0.967235i	$-0.581708\pi$
$191$	−7.01749			−0.507768			−0.253884	+	0.967235i	$0.581708\pi$
$192$		−	29.5804i		−	2.13478i
$193$	13.1516			0.946671			0.473335	−	0.880882i	$-0.343050\pi$
$193$	13.1516			0.946671			0.473335	+	0.880882i	$0.343050\pi$
$194$		−	20.9870i		−	1.50678i
$195$		−	9.79318i		−	0.701304i
$196$	14.3498			1.02499
$197$			14.1879i			1.01085i	0.862871	+	0.505423i	$0.168664\pi$
$197$			14.1879i			1.01085i	−0.862871	+	0.505423i	$0.831336\pi$
$198$	9.50334	−	32.4404i	0.675373	−	2.30544i
$199$	−10.7532			−0.762277			−0.381138	−	0.924518i	$-0.624468\pi$
$199$	−10.7532			−0.762277			−0.381138	+	0.924518i	$0.624468\pi$
$200$	−0.737755			−0.0521671
$201$	21.5425			1.51949
$202$			1.07412i			0.0755747i
$203$		−	3.95334i		−	0.277470i
$204$	8.34716			0.584418
$205$	3.33055			0.232616
$206$		−	30.8655i		−	2.15050i
$207$	−24.0106			−1.66885
$208$	−11.0481			−0.766051
$209$	6.36590	+	12.9798i	0.440339	+	0.897832i
$210$	5.56743			0.384189
$211$	−4.70262			−0.323742			−0.161871	−	0.986812i	$-0.551753\pi$
$211$	−4.70262			−0.323742			−0.161871	+	0.986812i	$0.551753\pi$
$212$			9.30680i			0.639194i
$213$	23.8160			1.63185
$214$	1.05814			0.0723331
$215$		−	2.02665i		−	0.138216i
$216$			3.90452i			0.265669i
$217$	6.46013			0.438542
$218$	−11.1227			−0.753324
$219$	−19.1499			−1.29403
$220$	−2.19451	+	7.49112i	−0.147954	+	0.505051i
$221$		−	4.40498i		−	0.296311i
$222$	21.0428			1.41230
$223$			21.1126i			1.41380i	0.707312	+	0.706901i	$0.249907\pi$
$223$			21.1126i			1.41380i	−0.707312	+	0.706901i	$0.750093\pi$
$224$		−	7.68298i		−	0.513341i
$225$	−4.88478			−0.325652
$226$		−	14.4853i		−	0.963546i
$227$	−15.9318			−1.05743			−0.528716	−	0.848799i	$-0.677326\pi$
$227$	−15.9318			−1.05743			−0.528716	+	0.848799i	$0.677326\pi$
$228$	−19.4445	−	21.2547i	−1.28775	−	1.40763i
$229$	−5.82050			−0.384630			−0.192315	−	0.981333i	$-0.561599\pi$
$229$	−5.82050			−0.384630			−0.192315	+	0.981333i	$0.561599\pi$
$230$	10.2561			0.676265
$231$	2.48794	−	8.49277i	0.163694	−	0.558783i
$232$	−3.06930			−0.201509
$233$		−	12.5412i		−	0.821599i	−0.911726	−	0.410799i	$-0.865250\pi$
$233$		−	12.5412i		−	0.821599i	0.911726	−	0.410799i	$-0.134750\pi$
$234$	35.5465			2.32375
$235$	−9.25227			−0.603551
$236$			9.00725i			0.586322i
$237$		−	41.3641i		−	2.68688i
$238$	2.50424			0.162326
$239$		−	18.9852i		−	1.22805i	−0.789286	−	0.614026i	$-0.789549\pi$
$239$		−	18.9852i		−	1.22805i	0.789286	−	0.614026i	$-0.210451\pi$
$240$			8.89519i			0.574182i
$241$	−15.6024			−1.00504			−0.502520	−	0.864565i	$-0.667594\pi$
$241$	−15.6024			−1.00504			−0.502520	+	0.864565i	$0.667594\pi$
$242$	19.3237	+	12.3845i	1.24218	+	0.796107i
$243$		−	15.2968i		−	0.981289i
$244$			9.38356i			0.600721i
$245$	−6.09703			−0.389525
$246$			19.5134i			1.24413i
$247$	−11.2166	+	10.2613i	−0.713694	+	0.652911i
$248$		−	5.01552i		−	0.318486i
$249$	29.3953			1.86285
$250$	2.08652			0.131963
$251$	4.08182			0.257642			0.128821	−	0.991668i	$-0.458881\pi$
$251$	4.08182			0.257642			0.128821	+	0.991668i	$0.458881\pi$
$252$			10.9247i			0.688194i
$253$	4.58317	−	15.6450i	0.288141	−	0.983592i
$254$	12.3269			0.773460
$255$	−3.54658			−0.222095
$256$	8.94651			0.559157
$257$			22.3096i			1.39163i	0.718220	+	0.695816i	$0.244957\pi$
$257$			22.3096i			1.39163i	−0.718220	+	0.695816i	$0.755043\pi$
$258$	11.8740			0.739241
$259$	3.41289			0.212066
$260$	−8.20839			−0.509063
$261$	−20.3223			−1.25792
$262$		−	11.4498i		−	0.707371i
$263$			14.7638i			0.910374i	0.890396	+	0.455187i	$0.150428\pi$
$263$			14.7638i			0.910374i	−0.890396	+	0.455187i	$0.849572\pi$
$264$	−6.59363	−	1.93159i	−0.405810	−	0.118881i
$265$		−	3.95431i		−	0.242912i
$266$	−5.83356	−	6.37664i	−0.357679	−	0.390977i
$267$	−12.5131			−0.765792
$268$		−	18.0564i		−	1.10297i
$269$		−	21.1294i		−	1.28828i	−0.764906	−	0.644142i	$-0.777215\pi$
$269$		−	21.1294i		−	1.28828i	0.764906	−	0.644142i	$-0.222785\pi$
$270$		−	11.0428i		−	0.672043i
$271$			21.8317i			1.32618i	0.748539	+	0.663090i	$0.230755\pi$
$271$			21.8317i			1.32618i	−0.748539	+	0.663090i	$0.769245\pi$
$272$			4.00106i			0.242600i
$273$	9.30595			0.563222
$274$	−37.8016			−2.28368
$275$	0.932412	−	3.18286i	0.0562266	−	0.191934i
$276$			32.4849i			1.95536i
$277$			9.20960i			0.553351i	0.960963	+	0.276676i	$0.0892328\pi$
$277$			9.20960i			0.553351i	−0.960963	+	0.276676i	$0.910767\pi$
$278$		−	20.0964i		−	1.20530i
$279$		−	33.2085i		−	1.98814i
$280$		−	0.701050i		−	0.0418957i
$281$	30.4292			1.81525			0.907626	−	0.419780i	$-0.137893\pi$
$281$	30.4292			1.81525			0.907626	+	0.419780i	$0.137893\pi$
$282$		−	54.2083i		−	3.22806i
$283$		−	6.01030i		−	0.357276i	−0.983915	−	0.178638i	$-0.942831\pi$
$283$		−	6.01030i		−	0.357276i	0.983915	−	0.178638i	$-0.0571690\pi$
$284$		−	19.9620i		−	1.18452i
$285$	8.26168	+	9.03081i	0.489380	+	0.534939i
$286$	−6.78516	+	23.1617i	−0.401215	+	1.36958i
$287$			3.16485i			0.186815i
$288$	−39.4946			−2.32724
$289$	15.4047			0.906162
$290$	8.68061			0.509743
$291$	−28.2437			−1.65567
$292$			16.0509i			0.939310i
$293$	4.39914			0.257000			0.128500	−	0.991709i	$-0.458984\pi$
$293$	4.39914			0.257000			0.128500	+	0.991709i	$0.458984\pi$
$294$		−	35.7220i		−	2.08335i
$295$		−	3.82704i		−	0.222819i
$296$		−	2.64970i		−	0.154011i
$297$	−16.8451	−	4.93473i	−0.977451	−	0.286342i
$298$		−	41.8883i		−	2.42653i
$299$	17.1430			0.991405
$300$			6.60882i			0.381560i
$301$	1.92582			0.111002
$302$	−46.7637			−2.69095
$303$	1.44552			0.0830429
$304$	10.1881	−	9.32039i	0.584326	−	0.534561i
$305$		−	3.98693i		−	0.228291i
$306$		−	12.8731i		−	0.735906i
$307$	23.5683			1.34512			0.672558	−	0.740045i	$-0.265196\pi$
$307$	23.5683			1.34512			0.672558	+	0.740045i	$0.265196\pi$
$308$	−7.11842	−	2.08533i	−0.405610	−	0.118823i
$309$	−41.5379			−2.36301
$310$			14.1849i			0.805650i
$311$	15.3269			0.869107			0.434554	−	0.900646i	$-0.356906\pi$
$311$	15.3269			0.869107			0.434554	+	0.900646i	$0.356906\pi$
$312$		−	7.22496i		−	0.409033i
$313$	−2.74950			−0.155411			−0.0777054	−	0.996976i	$-0.524759\pi$
$313$	−2.74950			−0.155411			−0.0777054	+	0.996976i	$0.524759\pi$
$314$	−43.7634			−2.46971
$315$		−	4.64175i		−	0.261533i
$316$	−34.6703			−1.95036
$317$		−	31.9622i		−	1.79517i	−0.440837	−	0.897587i	$-0.645318\pi$
$317$		−	31.9622i		−	1.79517i	0.440837	−	0.897587i	$-0.354682\pi$
$318$	23.1680			1.29920
$319$	3.87914	−	13.2417i	0.217190	−	0.741394i
$320$	10.5344			0.588891
$321$		−	1.42402i		−	0.0794809i
$322$			9.74581i			0.543113i
$323$	3.71611	+	4.06206i	0.206770	+	0.226019i
$324$	0.486573			0.0270318
$325$	3.48762			0.193458
$326$	−6.45142			−0.357311
$327$			14.9686i			0.827766i
$328$	2.45713			0.135672
$329$		−	8.79195i		−	0.484716i
$330$	18.6482	+	5.46294i	1.02655	+	0.300725i
$331$			18.4799i			1.01575i	0.861432	+	0.507873i	$0.169568\pi$
$331$			18.4799i			1.01575i	−0.861432	+	0.507873i	$0.830432\pi$
$332$		−	24.6384i		−	1.35221i
$333$		−	17.5440i		−	0.961408i
$334$	13.5445			0.741120
$335$			7.67189i			0.419160i
$336$	−8.45264			−0.461129
$337$	29.1007			1.58522			0.792609	−	0.609730i	$-0.208722\pi$
$337$	29.1007			1.58522			0.792609	+	0.609730i	$0.208722\pi$
$338$	1.74542			0.0949381
$339$	−19.4939			−1.05876
$340$			2.97265i			0.161215i
$341$	21.6382	+	6.33887i	1.17178	+	0.343269i
$342$	−32.7793	+	29.9876i	−1.77250	+	1.62154i
$343$		−	12.4454i		−	0.671990i
$344$		−	1.49517i		−	0.0806140i
$345$		−	13.8023i		−	0.743093i
$346$	22.1906			1.19297
$347$			33.5456i			1.80082i	0.435042	+	0.900410i	$0.356734\pi$
$347$			33.5456i			1.80082i	−0.435042	+	0.900410i	$0.643266\pi$
$348$			27.4948i			1.47388i
$349$			9.62017i			0.514956i	0.966284	+	0.257478i	$0.0828915\pi$
$349$			9.62017i			0.514956i	−0.966284	+	0.257478i	$0.917109\pi$
$350$			1.98271i			0.105981i
$351$		−	18.4580i		−	0.985215i
$352$	7.53878	−	25.7342i	0.401818	−	1.37164i
$353$	28.5325			1.51863			0.759317	−	0.650721i	$-0.225533\pi$
$353$	28.5325			1.51863			0.759317	+	0.650721i	$0.225533\pi$
$354$	22.4224			1.19173
$355$			8.48153i			0.450153i
$356$			10.4882i			0.555873i
$357$		−	3.37013i		−	0.178366i
$358$			36.6667i			1.93789i
$359$			6.37196i			0.336299i	0.985761	+	0.168150i	$0.0537792\pi$
$359$			6.37196i			0.336299i	−0.985761	+	0.168150i	$0.946221\pi$
$360$	−3.60377			−0.189935
$361$	1.68680	−	18.9250i	0.0887790	−	0.996051i
$362$			33.0879i			1.73906i
$363$	16.6667	−	26.0054i	0.874777	−	1.36493i
$364$		−	7.80001i		−	0.408831i
$365$		−	6.81980i		−	0.356964i
$366$	23.3591			1.22100
$367$	−28.4067			−1.48282			−0.741409	−	0.671053i	$-0.765842\pi$
$367$	−28.4067			−1.48282			−0.741409	+	0.671053i	$0.765842\pi$
$368$	−15.5711			−0.811697
$369$	16.2690			0.846931
$370$			7.49390i			0.389589i
$371$	3.75758			0.195084
$372$	−44.9291			−2.32947
$373$	12.6887			0.656997			0.328499	−	0.944504i	$-0.393457\pi$
$373$	12.6887			0.656997			0.328499	+	0.944504i	$0.393457\pi$
$374$	8.38795	+	2.45723i	0.433731	+	0.127060i
$375$		−	2.80799i		−	0.145004i
$376$	−6.82590			−0.352019
$377$	14.5096			0.747283
$378$	10.4934			0.539722
$379$			7.43879i			0.382105i	0.981580	+	0.191052i	$0.0611901\pi$
$379$			7.43879i			0.382105i	−0.981580	+	0.191052i	$0.938810\pi$
$380$	7.56939	−	6.92473i	0.388301	−	0.355231i
$381$		−	16.5892i		−	0.849892i
$382$	14.6422			0.749158
$383$		−	3.69512i		−	0.188812i	−0.995534	−	0.0944059i	$-0.969905\pi$
$383$		−	3.69512i		−	0.188812i	0.995534	−	0.0944059i	$-0.0300951\pi$
$384$			16.3138i			0.832512i
$385$	3.02451	+	0.886023i	0.154143	+	0.0451559i
$386$	−27.4411			−1.39671
$387$		−	9.89972i		−	0.503231i
$388$			23.6731i			1.20182i
$389$	−25.9011			−1.31324			−0.656618	−	0.754223i	$-0.728014\pi$
$389$	−25.9011			−1.31324			−0.656618	+	0.754223i	$0.728014\pi$
$390$			20.4337i			1.03470i
$391$		−	6.20830i		−	0.313967i
$392$	−4.49811			−0.227189
$393$	−15.4088			−0.777272
$394$		−	29.6034i		−	1.49140i
$395$	14.7309			0.741190
$396$	−10.7197	+	36.5925i	−0.538685	+	1.83884i
$397$	23.0974			1.15923			0.579613	−	0.814892i	$-0.303204\pi$
$397$	23.0974			1.15923			0.579613	+	0.814892i	$0.303204\pi$
$398$	22.4369			1.12466
$399$	−8.58150	+	7.85065i	−0.429613	+	0.393024i
$400$	−3.16782			−0.158391
$401$		−	7.33323i		−	0.366204i	−0.983094	−	0.183102i	$-0.941386\pi$
$401$		−	7.33323i		−	0.366204i	0.983094	−	0.183102i	$-0.0586139\pi$
$402$	−44.9490			−2.24185
$403$			23.7101i			1.18108i
$404$		−	1.21160i		−	0.0602792i
$405$	−0.206737			−0.0102729
$406$			8.24873i			0.409378i
$407$	11.4315	+	3.34883i	0.566637	+	0.165995i
$408$	−2.61651			−0.129536
$409$	10.4417			0.516310			0.258155	−	0.966104i	$-0.416885\pi$
$409$	10.4417			0.516310			0.258155	+	0.966104i	$0.416885\pi$
$410$	−6.94927			−0.343200
$411$			50.8724i			2.50935i
$412$			34.8160i			1.71526i
$413$	3.63664			0.178947
$414$	50.0987			2.46221
$415$			10.4685i			0.513877i
$416$	28.1982			1.38253
$417$	−27.0452			−1.32441
$418$	−13.2826	−	27.0827i	−0.649673	−	1.32466i
$419$	23.1341			1.13018			0.565088	−	0.825031i	$-0.308842\pi$
$419$	23.1341			1.13018			0.565088	+	0.825031i	$0.308842\pi$
$420$	−6.28002			−0.306434
$421$		−	11.8661i		−	0.578317i	−0.957281	−	0.289159i	$-0.906624\pi$
$421$		−	11.8661i		−	0.578317i	0.957281	−	0.289159i	$-0.0933755\pi$
$422$	9.81213			0.477647
$423$	−45.1953			−2.19747
$424$		−	2.91731i		−	0.141677i
$425$		−	1.26303i		−	0.0612661i
$426$	−49.6927			−2.40762
$427$	3.78857			0.183342
$428$	−1.19358			−0.0576936
$429$	31.1703	+	9.13128i	1.50492	+	0.440863i
$430$			4.22864i			0.203923i
$431$	20.8611			1.00485			0.502423	−	0.864622i	$-0.332442\pi$
$431$	20.8611			1.00485			0.502423	+	0.864622i	$0.332442\pi$
$432$			16.7655i			0.806629i
$433$			34.7817i			1.67150i	0.549110	+	0.835750i	$0.314967\pi$
$433$			34.7817i			1.67150i	−0.549110	+	0.835750i	$0.685033\pi$
$434$	−13.4792			−0.647023
$435$		−	11.6821i		−	0.560115i
$436$	12.5463			0.600859
$437$	−15.8085	+	14.4621i	−0.756221	+	0.691816i
$438$	39.9567			1.90920
$439$	−3.35497			−0.160124			−0.0800621	−	0.996790i	$-0.525512\pi$
$439$	−3.35497			−0.160124			−0.0800621	+	0.996790i	$0.525512\pi$
$440$	0.687892	−	2.34817i	0.0327940	−	0.111945i
$441$	−29.7826			−1.41822
$442$			9.19109i			0.437176i
$443$	−11.9525			−0.567882			−0.283941	−	0.958842i	$-0.591642\pi$
$443$	−11.9525			−0.567882			−0.283941	+	0.958842i	$0.591642\pi$
$444$	−23.7361			−1.12646
$445$		−	4.45627i		−	0.211248i
$446$		−	44.0519i		−	2.08592i
$447$	−56.3721			−2.66631
$448$			10.0103i			0.472942i
$449$			36.3872i			1.71722i	0.512632	+	0.858609i	$0.328671\pi$
$449$			36.3872i			1.71722i	−0.512632	+	0.858609i	$0.671329\pi$
$450$	10.1922			0.480465
$451$	−3.10545	+	10.6007i	−0.146230	+	0.499166i
$452$			16.3393i			0.768535i
$453$			62.9333i			2.95687i
$454$	33.2421			1.56013
$455$			3.31410i			0.155368i
$456$	6.09509	+	6.66252i	0.285429	+	0.312001i
$457$		−	0.115471i		−	0.00540151i	−0.999996	−	0.00270075i	$-0.999140\pi$
$457$		−	0.115471i		−	0.00540151i	0.999996	−	0.00270075i	$-0.000859678\pi$
$458$	12.1446			0.567481
$459$	−6.68452			−0.312007
$460$	−11.5688			−0.539396
$461$		−	11.3135i		−	0.526921i	−0.964670	−	0.263460i	$-0.915136\pi$
$461$		−	11.3135i		−	0.526921i	0.964670	−	0.263460i	$-0.0848638\pi$
$462$	−5.19115	+	17.7204i	−0.241514	+	0.824426i
$463$	−3.86544			−0.179642			−0.0898211	−	0.995958i	$-0.528630\pi$
$463$	−3.86544			−0.179642			−0.0898211	+	0.995958i	$0.528630\pi$
$464$	−13.1791			−0.611826
$465$	19.0897			0.885263
$466$			26.1674i			1.21218i
$467$	−39.4161			−1.82396			−0.911979	−	0.410236i	$-0.865446\pi$
$467$	−39.4161			−1.82396			−0.911979	+	0.410236i	$0.865446\pi$
$468$	−40.0962			−1.85345
$469$	−7.29019			−0.336630
$470$	19.3051			0.890476
$471$			58.8955i			2.71376i
$472$		−	2.82342i		−	0.129958i
$473$	6.45053	+	1.88967i	0.296596	+	0.0868871i
$474$			86.3071i			3.96422i
$475$	−3.21612	+	2.94221i	−0.147566	+	0.134998i
$476$	−2.82476			−0.129473
$477$		−	19.3160i		−	0.884417i
$478$			39.6131i			1.81186i
$479$			32.7400i			1.49593i	0.663739	+	0.747965i	$0.268969\pi$
$479$			32.7400i			1.49593i	−0.663739	+	0.747965i	$0.731031\pi$
$480$		−	22.7032i		−	1.03626i
$481$			12.5260i			0.571138i
$482$	32.5548			1.48283
$483$	13.1156			0.596782
$484$	−21.7970	−	13.9696i	−0.990773	−	0.634983i
$485$		−	10.0583i		−	0.456726i
$486$			31.9171i			1.44779i
$487$		−	26.3250i		−	1.19290i	−0.802651	−	0.596449i	$-0.796578\pi$
$487$		−	26.3250i		−	1.19290i	0.802651	−	0.596449i	$-0.203422\pi$
$488$		−	2.94138i		−	0.133150i
$489$			8.68214i			0.392620i
$490$	12.7216			0.574703
$491$		−	19.7041i		−	0.889232i	−0.895721	−	0.444616i	$-0.853340\pi$
$491$		−	19.7041i		−	0.889232i	0.895721	−	0.444616i	$-0.146660\pi$
$492$		−	22.0110i		−	0.992333i
$493$		−	5.25463i		−	0.236656i
$494$	23.4037	−	21.4105i	1.05298	−	0.963302i
$495$	4.55463	−	15.5476i	0.204715	−	0.698812i
$496$		−	21.5360i		−	0.966993i
$497$	−8.05956			−0.361521
$498$	−61.3340			−2.74844
$499$	−44.2332			−1.98015			−0.990075	−	0.140543i	$-0.955115\pi$
$499$	−44.2332			−1.98015			−0.990075	+	0.140543i	$0.955115\pi$
$500$	−2.35358			−0.105255
$501$		−	18.2278i		−	0.814357i
$502$	−8.51682			−0.380124
$503$			2.95430i			0.131726i	0.997829	+	0.0658629i	$0.0209800\pi$
$503$			2.95430i			0.131726i	−0.997829	+	0.0658629i	$0.979020\pi$
$504$		−	3.42448i		−	0.152538i
$505$			0.514789i			0.0229078i
$506$	−9.56289	+	32.6437i	−0.425122	+	1.45119i
$507$		−	2.34893i		−	0.104320i
$508$	−13.9047			−0.616920
$509$		−	27.9392i		−	1.23838i	−0.785241	−	0.619191i	$-0.787461\pi$
$509$		−	27.9392i		−	1.23838i	0.785241	−	0.619191i	$-0.212539\pi$
$510$	7.40002			0.327679
$511$	6.48050			0.286680
$512$	−30.2867			−1.33850
$513$	15.5715	+	17.0211i	0.687497	+	0.751499i
$514$		−	46.5494i		−	2.05321i
$515$		−	14.7928i		−	0.651847i
$516$	−13.3937			−0.589626
$517$	8.62693	−	29.4487i	0.379412	−	1.29515i
$518$	−7.12107			−0.312882
$519$		−	29.8635i		−	1.31086i
$520$	2.57301			0.112834
$521$			15.8769i			0.695577i	0.937573	+	0.347789i	$0.113067\pi$
$521$			15.8769i			0.695577i	−0.937573	+	0.347789i	$0.886933\pi$
$522$	42.4029			1.85592
$523$	−30.4812			−1.33285			−0.666425	−	0.745572i	$-0.732176\pi$
$523$	−30.4812			−1.33285			−0.666425	+	0.745572i	$0.732176\pi$
$524$			12.9153i			0.564206i
$525$	2.66828			0.116453
$526$		−	30.8050i		−	1.34316i
$527$	8.58656			0.374036
$528$	−28.3122	−	8.29398i	−1.23213	−	0.360949i
$529$	1.16103			0.0504795
$530$			8.25077i			0.358391i
$531$		−	18.6943i		−	0.811261i
$532$	6.58021	+	7.19280i	0.285288	+	0.311847i
$533$	−11.6157			−0.503131
$534$	26.1090			1.12985
$535$	0.507132			0.0219252
$536$			5.65997i			0.244473i
$537$	49.3450			2.12939
$538$			44.0871i			1.90073i
$539$	5.68495	−	19.4060i	0.244868	−	0.835875i
$540$			12.4562i			0.536028i
$541$		−	3.80497i		−	0.163589i	−0.996649	−	0.0817943i	$-0.973935\pi$
$541$		−	3.80497i		−	0.163589i	0.996649	−	0.0817943i	$-0.0260651\pi$
$542$		−	45.5523i		−	1.95664i
$543$	44.5287			1.91091
$544$		−	10.2119i		−	0.437833i
$545$	−5.33073			−0.228343
$546$	−19.4171			−0.830975
$547$	−7.11949			−0.304408			−0.152204	−	0.988349i	$-0.548637\pi$
$547$	−7.11949			−0.304408			−0.152204	+	0.988349i	$0.548637\pi$
$548$	42.6399			1.82149
$549$		−	19.4753i		−	0.831184i
$550$	−1.94550	+	6.64112i	−0.0829564	+	0.283178i
$551$	−13.3801	+	12.2405i	−0.570010	+	0.521465i
$552$		−	10.1827i		−	0.433406i
$553$			13.9980i			0.595255i
$554$		−	19.2161i		−	0.816412i
$555$	10.0851			0.428088
$556$			22.6686i			0.961362i
$557$			35.6661i			1.51122i	0.655021	+	0.755611i	$0.272660\pi$
$557$			35.6661i			1.51122i	−0.655021	+	0.755611i	$0.727340\pi$
$558$			69.2903i			2.93329i
$559$			7.06816i			0.298952i
$560$		−	3.01021i		−	0.127205i
$561$	3.30688	−	11.2883i	0.139616	−	0.476591i
$562$	−63.4912			−2.67821
$563$	−23.1419			−0.975315			−0.487657	−	0.873035i	$-0.662148\pi$
$563$	−23.1419			−0.975315			−0.487657	+	0.873035i	$0.662148\pi$
$564$			61.1466i			2.57473i
$565$		−	6.94230i		−	0.292065i
$566$			12.5406i			0.527123i
$567$		−	0.196452i		−	0.00825020i
$568$			6.25729i			0.262550i
$569$	−40.8965			−1.71447			−0.857236	−	0.514924i	$-0.827820\pi$
$569$	−40.8965			−1.71447			−0.857236	+	0.514924i	$0.827820\pi$
$570$	−17.2382	−	18.8430i	−0.722028	−	0.789246i
$571$		−	25.7532i		−	1.07774i	−0.842390	−	0.538869i	$-0.818852\pi$
$571$		−	25.7532i		−	1.07774i	0.842390	−	0.538869i	$-0.181148\pi$
$572$	7.65361	−	26.1262i	0.320013	−	1.09239i
$573$		−	19.7050i		−	0.823189i
$574$		−	6.60353i		−	0.275626i
$575$	4.91539			0.204986
$576$	51.4582			2.14409
$577$	17.6323			0.734043			0.367022	−	0.930212i	$-0.380377\pi$
$577$	17.6323			0.734043			0.367022	+	0.930212i	$0.380377\pi$
$578$	−32.1424			−1.33695
$579$			36.9294i			1.53473i
$580$	−9.79165			−0.406576
$581$	−9.94764			−0.412697
$582$	58.9311			2.44277
$583$	12.5860	+	3.68705i	0.521260	+	0.152702i
$584$		−	5.03134i		−	0.208198i
$585$	17.0362			0.704362
$586$	−9.17891			−0.379177
$587$	16.5493			0.683065			0.341532	−	0.939870i	$-0.389054\pi$
$587$	16.5493			0.683065			0.341532	+	0.939870i	$0.389054\pi$
$588$			40.2942i			1.66170i
$589$	−20.0022	−	21.8643i	−0.824176	−	0.900903i
$590$			7.98521i			0.328746i
$591$	−39.8394			−1.63878
$592$		−	11.3775i		−	0.467610i
$593$		−	45.0420i		−	1.84965i	−0.380389	−	0.924827i	$-0.624210\pi$
$593$		−	45.0420i		−	1.84965i	0.380389	−	0.924827i	$-0.375790\pi$
$594$	35.1477	+	10.2964i	1.44213	+	0.422468i
$595$	1.20020			0.0492032
$596$			47.2497i			1.93542i
$597$		−	30.1949i		−	1.23580i
$598$	−35.7693			−1.46271
$599$			0.394109i			0.0161029i	0.999968	+	0.00805143i	$0.00256288\pi$
$599$			0.394109i			0.0161029i	−0.999968	+	0.00805143i	$0.997437\pi$
$600$		−	2.07160i		−	0.0845729i
$601$	−11.6008			−0.473209			−0.236604	−	0.971606i	$-0.576034\pi$
$601$	−11.6008			−0.473209			−0.236604	+	0.971606i	$0.576034\pi$
$602$	−4.01826			−0.163772
$603$			37.4755i			1.52612i
$604$	52.7491			2.14633
$605$	9.26121	+	5.93548i	0.376522	+	0.241312i
$606$	−3.01611			−0.122521
$607$	34.0839			1.38342			0.691712	−	0.722174i	$-0.256857\pi$
$607$	34.0839			1.38342			0.691712	+	0.722174i	$0.256857\pi$
$608$	−26.0031	+	23.7885i	−1.05456	+	0.964750i
$609$	11.1009			0.449832
$610$			8.31882i			0.336819i
$611$	32.2684			1.30544
$612$			14.5208i			0.586967i
$613$		−	21.0030i		−	0.848303i	−0.905591	−	0.424151i	$-0.860572\pi$
$613$		−	21.0030i		−	0.848303i	0.905591	−	0.424151i	$-0.139428\pi$
$614$	−49.1759			−1.98458
$615$			9.35213i			0.377114i
$616$	2.23134	+	0.653668i	0.0899034	+	0.0263370i
$617$	47.0050			1.89235			0.946174	−	0.323658i	$-0.104913\pi$
$617$	47.0050			1.89235			0.946174	+	0.323658i	$0.104913\pi$
$618$	86.6697			3.48637
$619$	−6.66187			−0.267763			−0.133882	−	0.990997i	$-0.542744\pi$
$619$	−6.66187			−0.267763			−0.133882	+	0.990997i	$0.542744\pi$
$620$		−	16.0005i		−	0.642595i
$621$		−	26.0144i		−	1.04392i
$622$	−31.9799			−1.28228
$623$	4.23456			0.169654
$624$		−	31.0230i		−	1.24191i
$625$	1.00000			0.0400000
$626$	5.73689			0.229292
$627$	−36.4471	+	17.8754i	−1.45556	+	0.713873i
$628$	49.3647			1.96987
$629$	4.53628			0.180873
$630$			9.68513i			0.385865i
$631$	35.0854			1.39673			0.698363	−	0.715743i	$-0.253912\pi$
$631$	35.0854			1.39673			0.698363	+	0.715743i	$0.253912\pi$
$632$	10.8678			0.432297
$633$		−	13.2049i		−	0.524847i
$634$			66.6898i			2.64859i
$635$	5.90787			0.234447
$636$	−26.1334			−1.03625
$637$	21.2641			0.842515
$638$	−8.09391	+	27.6292i	−0.320441	+	1.09385i
$639$			41.4304i			1.63896i
$640$	−5.80980			−0.229653
$641$		−	17.1106i		−	0.675830i	−0.941177	−	0.337915i	$-0.890278\pi$
$641$		−	17.1106i		−	0.675830i	0.941177	−	0.337915i	$-0.109722\pi$
$642$			2.97125i			0.117266i
$643$	−2.50261			−0.0986931			−0.0493466	−	0.998782i	$-0.515714\pi$
$643$	−2.50261			−0.0986931			−0.0493466	+	0.998782i	$0.515714\pi$
$644$		−	10.9932i		−	0.433192i
$645$	5.69079			0.224075
$646$	−7.75375	−	8.47559i	−0.305067	−	0.333468i
$647$	15.5165			0.610018			0.305009	−	0.952350i	$-0.401341\pi$
$647$	15.5165			0.610018			0.305009	+	0.952350i	$0.401341\pi$
$648$	−0.152521			−0.00599161
$649$	12.1809	+	3.56838i	0.478144	+	0.140071i
$650$	−7.27700			−0.285427
$651$			18.1399i			0.710960i
$652$	7.27714			0.284995
$653$	18.2898			0.715737			0.357869	−	0.933772i	$-0.383504\pi$
$653$	18.2898			0.715737			0.357869	+	0.933772i	$0.383504\pi$
$654$		−	31.2323i		−	1.22128i
$655$		−	5.48750i		−	0.214414i
$656$	10.5506			0.411931
$657$		−	33.3132i		−	1.29967i
$658$			18.3446i			0.715147i
$659$	−43.1272			−1.68000			−0.840000	−	0.542587i	$-0.817445\pi$
$659$	−43.1272			−1.68000			−0.840000	+	0.542587i	$0.817445\pi$
$660$	−21.0350	−	6.16215i	−0.818785	−	0.239861i
$661$			4.89356i			0.190337i	0.995461	+	0.0951687i	$0.0303390\pi$
$661$			4.89356i			0.190337i	−0.995461	+	0.0951687i	$0.969661\pi$
$662$		−	38.5587i		−	1.49863i
$663$	12.3691			0.480377
$664$			7.72316i			0.299717i
$665$	−2.79583	−	3.05611i	−0.108418	−	0.118511i
$666$			36.6061i			1.41846i
$667$	20.4496			0.791811
$668$	−15.2780			−0.591125
$669$	−59.2838			−2.29204
$670$		−	16.0076i		−	0.618426i
$671$	12.6898	+	3.71746i	0.489886	+	0.143511i
$672$	21.5737			0.832224
$673$	−0.745574			−0.0287398			−0.0143699	−	0.999897i	$-0.504574\pi$
$673$	−0.745574			−0.0287398			−0.0143699	+	0.999897i	$0.504574\pi$
$674$	−60.7194			−2.33882
$675$		−	5.29243i		−	0.203706i
$676$	−1.96882			−0.0757237
$677$	2.57238			0.0988645			0.0494322	−	0.998777i	$-0.484259\pi$
$677$	2.57238			0.0988645			0.0494322	+	0.998777i	$0.484259\pi$
$678$	40.6744			1.56209
$679$	9.55792			0.366799
$680$		−	0.931809i		−	0.0357332i
$681$		−	44.7363i		−	1.71430i
$682$	−45.1487	−	13.2262i	−1.72883	−	0.506458i
$683$		−	10.0637i		−	0.385079i	−0.981289	−	0.192539i	$-0.938328\pi$
$683$		−	10.0637i		−	0.385079i	0.981289	−	0.192539i	$-0.0616723\pi$
$684$	36.9748	−	33.8258i	1.41377	−	1.29336i
$685$	−18.1170			−0.692216
$686$			25.9677i			0.991450i
$687$		−	16.3439i		−	0.623558i
$688$		−	6.42005i		−	0.244762i
$689$			13.7911i			0.525401i
$690$			28.7989i			1.09636i
$691$	35.6112			1.35471			0.677357	−	0.735655i	$-0.263125\pi$
$691$	35.6112			1.35471			0.677357	+	0.735655i	$0.263125\pi$
$692$	−25.0308			−0.951528
$693$	14.7741	+	4.32803i	0.561220	+	0.164408i
$694$		−	69.9936i		−	2.65692i
$695$		−	9.63153i		−	0.365345i
$696$		−	8.61854i		−	0.326685i
$697$			4.20660i			0.159336i
$698$		−	20.0727i		−	0.759763i
$699$	35.2154			1.33197
$700$		−	2.23649i		−	0.0845312i
$701$		−	25.3000i		−	0.955570i	−0.878477	−	0.477785i	$-0.841440\pi$
$701$		−	25.3000i		−	0.955570i	0.878477	−	0.477785i	$-0.158560\pi$
$702$			38.5130i			1.45358i
$703$	−10.5672	−	11.5509i	−0.398548	−	0.435651i
$704$	−9.82241	+	33.5295i	−0.370196	+	1.26369i
$705$		−	25.9802i		−	0.978472i
$706$	−59.5338			−2.24058
$707$	−0.489177			−0.0183974
$708$	−25.2922			−0.950540
$709$	−35.7058			−1.34096			−0.670479	−	0.741928i	$-0.733911\pi$
$709$	−35.7058			−1.34096			−0.670479	+	0.741928i	$0.733911\pi$
$710$		−	17.6969i		−	0.664153i
$711$	71.9571			2.69860
$712$		−	3.28764i		−	0.123209i
$713$			33.4166i			1.25146i
$714$			7.03186i			0.263161i
$715$	−3.25190	+	11.1006i	−0.121614	+	0.415139i
$716$		−	41.3597i		−	1.54568i
$717$	53.3102			1.99091
$718$		−	13.2952i		−	0.496174i
$719$	−37.7536			−1.40797			−0.703987	−	0.710213i	$-0.748599\pi$
$719$	−37.7536			−1.40797			−0.703987	+	0.710213i	$0.748599\pi$
$720$	−15.4741			−0.576686
$721$	14.0568			0.523503
$722$	−3.51955	+	39.4874i	−0.130984	+	1.46957i
$723$		−	43.8114i		−	1.62936i
$724$		−	37.3228i		−	1.38709i
$725$	4.16032			0.154510
$726$	−34.7755	+	54.2608i	−1.29064	+	2.01381i
$727$	−5.16410			−0.191526			−0.0957629	−	0.995404i	$-0.530529\pi$
$727$	−5.16410			−0.191526			−0.0957629	+	0.995404i	$0.530529\pi$
$728$			2.44499i			0.0906175i
$729$	43.5734			1.61383
$730$			14.2297i			0.526664i
$731$	2.55972			0.0946747
$732$	−26.3489			−0.973883
$733$			10.5131i			0.388311i	0.980971	+	0.194156i	$0.0621967\pi$
$733$			10.5131i			0.388311i	−0.980971	+	0.194156i	$0.937803\pi$
$734$	59.2713			2.18774
$735$		−	17.1204i		−	0.631494i
$736$	39.7421			1.46491
$737$	−24.4185	−	7.15336i	−0.899469	−	0.263497i
$738$	−33.9457			−1.24956
$739$		−	49.6200i		−	1.82530i	−0.408742	−	0.912650i	$-0.634032\pi$
$739$		−	49.6200i		−	1.82530i	0.408742	−	0.912650i	$-0.365968\pi$
$740$		−	8.45306i		−	0.310741i
$741$	−28.8136	−	31.4960i	−1.05849	−	1.15703i
$742$	−7.84028			−0.287826
$743$	−38.6120			−1.41654			−0.708269	−	0.705943i	$-0.750524\pi$
$743$	−38.6120			−1.41654			−0.708269	+	0.705943i	$0.750524\pi$
$744$	14.0835			0.516326
$745$		−	20.0757i		−	0.735515i
$746$	−26.4753			−0.969331
$747$			51.1361i			1.87097i
$748$	−9.46154	−	2.77174i	−0.345948	−	0.101345i
$749$			0.481901i			0.0176083i
$750$			5.85893i			0.213938i
$751$		−	6.50018i		−	0.237195i	−0.992942	−	0.118597i	$-0.962160\pi$
$751$		−	6.50018i		−	0.237195i	0.992942	−	0.118597i	$-0.0378398\pi$
$752$	−29.3095			−1.06881
$753$			11.4617i			0.417687i
$754$	−30.2747			−1.10254
$755$	−22.4123			−0.815666
$756$	−11.8365			−0.430488
$757$	26.8511			0.975921			0.487961	−	0.872866i	$-0.337741\pi$
$757$	26.8511			0.975921			0.487961	+	0.872866i	$0.337741\pi$
$758$		−	15.5212i		−	0.563756i
$759$	43.9309	+	12.8695i	1.59459	+	0.467132i
$760$	−2.37270	+	2.17063i	−0.0860670	+	0.0787370i
$761$			34.3608i			1.24558i	0.782389	+	0.622790i	$0.214001\pi$
$761$			34.3608i			1.24558i	−0.782389	+	0.622790i	$0.785999\pi$
$762$			34.6138i			1.25393i
$763$		−	5.06551i		−	0.183384i
$764$	−16.5162			−0.597536
$765$		−	6.16964i		−	0.223064i
$766$			7.70995i			0.278572i
$767$			13.3473i			0.481942i
$768$			25.1217i			0.906500i
$769$		−	17.5008i		−	0.631094i	−0.948910	−	0.315547i	$-0.897812\pi$
$769$		−	17.5008i		−	0.631094i	0.948910	−	0.315547i	$-0.102188\pi$
$770$	−6.31071	−	1.84871i	−0.227422	−	0.0666228i
$771$	−62.6449			−2.25610
$772$	30.9533			1.11403
$773$			24.8812i			0.894914i	0.894305	+	0.447457i	$0.147670\pi$
$773$			24.8812i			0.894914i	−0.894305	+	0.447457i	$0.852330\pi$
$774$			20.6560i			0.742464i
$775$			6.79836i			0.244204i
$776$		−	7.42059i		−	0.266384i
$777$			9.58333i			0.343800i
$778$	54.0432			1.93754
$779$	10.7114	−	9.79918i	0.383777	−	0.351092i
$780$		−	23.0490i		−	0.825288i
$781$	−26.9955	−	7.90828i	−0.965976	−	0.282981i
$782$			12.9538i			0.463226i
$783$		−	22.0182i		−	0.786867i
$784$	−19.3143			−0.689796
$785$	−20.9743			−0.748605
$786$	32.1508			1.14678
$787$	−28.5417			−1.01740			−0.508700	−	0.860944i	$-0.669874\pi$
$787$	−28.5417			−1.01740			−0.508700	+	0.860944i	$0.669874\pi$
$788$			33.3924i			1.18955i
$789$	−41.4565			−1.47589
$790$	−30.7363			−1.09355
$791$	6.59691			0.234559
$792$	3.36020	−	11.4703i	0.119400	−	0.407579i
$793$			13.9049i			0.493777i
$794$	−48.1933			−1.71031
$795$	11.1037			0.393806
$796$	−25.3086			−0.897040
$797$		−	23.2530i		−	0.823665i	−0.911260	−	0.411832i	$-0.864889\pi$
$797$		−	23.2530i		−	0.823665i	0.911260	−	0.411832i	$-0.135111\pi$
$798$	17.9055	−	16.3806i	0.633848	−	0.579866i
$799$		−	11.6859i		−	0.413418i
$800$	8.08524			0.285856
$801$		−	21.7679i		−	0.769131i
$802$			15.3010i			0.540296i
$803$	21.7065	+	6.35886i	0.766005	+	0.224399i
$804$	50.7021			1.78813
$805$			4.67084i			0.164625i
$806$		−	49.4716i		−	1.74256i
$807$	59.3311			2.08855
$808$			0.379788i			0.0133609i
$809$		−	17.9321i		−	0.630457i	−0.949016	−	0.315229i	$-0.897919\pi$
$809$		−	17.9321i		−	0.630457i	0.949016	−	0.315229i	$-0.102081\pi$
$810$	0.431362			0.0151565
$811$	17.5303			0.615572			0.307786	−	0.951456i	$-0.400412\pi$
$811$	17.5303			0.615572			0.307786	+	0.951456i	$0.400412\pi$
$812$		−	9.30450i		−	0.326524i
$813$	−61.3031			−2.14999
$814$	−23.8521	−	6.98741i	−0.836014	−	0.244909i
$815$	−3.09195			−0.108306
$816$	−11.2349			−0.393301
$817$	−5.96282	−	6.51793i	−0.208613	−	0.228033i
$818$	−21.7869			−0.761761
$819$			16.1887i			0.565678i
$820$	7.83872			0.273740
$821$			16.5134i			0.576322i	0.957582	+	0.288161i	$0.0930439\pi$
$821$			16.5134i			0.576322i	−0.957582	+	0.288161i	$0.906956\pi$
$822$		−	106.146i		−	3.70228i
$823$	−27.2846			−0.951081			−0.475540	−	0.879694i	$-0.657747\pi$
$823$	−27.2846			−0.951081			−0.475540	+	0.879694i	$0.657747\pi$
$824$		−	10.9134i		−	0.380187i
$825$	8.93743	+	2.61820i	0.311161	+	0.0911540i
$826$	−7.58793			−0.264018
$827$	22.9460			0.797909			0.398955	−	0.916971i	$-0.369373\pi$
$827$	22.9460			0.797909			0.398955	+	0.916971i	$0.369373\pi$
$828$	−56.5109			−1.96389
$829$		−	54.0411i		−	1.87693i	−0.345379	−	0.938463i	$-0.612250\pi$
$829$		−	54.0411i		−	1.87693i	0.345379	−	0.938463i	$-0.387750\pi$
$830$		−	21.8427i		−	0.758171i
$831$	−25.8604			−0.897088
$832$	−36.7400			−1.27373
$833$		−	7.70075i		−	0.266815i
$834$	56.4304			1.95403
$835$	6.49141			0.224644
$836$	14.9827	+	30.5490i	0.518186	+	1.05656i
$837$	35.9799			1.24365
$838$	−48.2699			−1.66746
$839$			38.6207i			1.33333i	0.745355	+	0.666667i	$0.232280\pi$
$839$			38.6207i			1.33333i	−0.745355	+	0.666667i	$0.767720\pi$
$840$	1.96854			0.0679210
$841$	−11.6917			−0.403163
$842$			24.7589i			0.853247i
$843$			85.4447i			2.94287i
$844$	−11.0680			−0.380976
$845$	0.836519			0.0287771
$846$	94.3010			3.24214
$847$	−5.64018	+	8.80045i	−0.193799	+	0.302387i
$848$		−	12.5266i		−	0.430164i
$849$	16.8768			0.579212
$850$			2.63535i			0.0903917i
$851$			17.6540i			0.605170i
$852$	56.0529			1.92034
$853$		−	51.7098i		−	1.77051i	−0.465108	−	0.885254i	$-0.653984\pi$
$853$		−	51.7098i		−	1.77051i	0.465108	−	0.885254i	$-0.346016\pi$
$854$	−7.90494			−0.270502
$855$	−15.7100	+	14.3720i	−0.537271	+	0.491514i
$856$	0.374139			0.0127878
$857$	−18.4927			−0.631700			−0.315850	−	0.948809i	$-0.602290\pi$
$857$	−18.4927			−0.631700			−0.315850	+	0.948809i	$0.602290\pi$
$858$	−65.0376	−	19.0526i	−2.22035	−	0.650446i
$859$	16.5866			0.565926			0.282963	−	0.959131i	$-0.408683\pi$
$859$	16.5866			0.565926			0.282963	+	0.959131i	$0.408683\pi$
$860$		−	4.76987i		−	0.162651i
$861$	−8.88685			−0.302863
$862$	−43.5273			−1.48254
$863$		−	19.0806i		−	0.649510i	−0.945798	−	0.324755i	$-0.894718\pi$
$863$		−	19.0806i		−	0.649510i	0.945798	−	0.324755i	$-0.105282\pi$
$864$		−	42.7906i		−	1.45577i
$865$	10.6352			0.361608
$866$		−	72.5728i		−	2.46612i
$867$			43.2563i			1.46906i
$868$	15.2044			0.516072
$869$	−13.7352	+	46.8863i	−0.465936	+	1.59051i
$870$			24.3750i			0.826391i
$871$		−	26.7566i		−	0.906613i
$872$	−3.93277			−0.133180
$873$		−	49.1328i		−	1.66289i
$874$	32.9847	−	30.1755i	1.11572	−	1.02070i
$875$			0.950248i			0.0321242i
$876$	−45.0708			−1.52280
$877$	13.6363			0.460464			0.230232	−	0.973136i	$-0.426051\pi$
$877$	13.6363			0.460464			0.230232	+	0.973136i	$0.426051\pi$
$878$	7.00023			0.236246
$879$			12.3527i			0.416647i
$880$	2.95371	−	10.0827i	0.0995697	−	0.339889i
$881$	5.11244			0.172242			0.0861212	−	0.996285i	$-0.472553\pi$
$881$	5.11244			0.172242			0.0861212	+	0.996285i	$0.472553\pi$
$882$	62.1422			2.09244
$883$	−19.7915			−0.666038			−0.333019	−	0.942920i	$-0.608067\pi$
$883$	−19.7915			−0.666038			−0.333019	+	0.942920i	$0.608067\pi$
$884$		−	10.3675i		−	0.348696i
$885$	10.7463			0.361232
$886$	24.9393			0.837851
$887$	−7.37885			−0.247758			−0.123879	−	0.992297i	$-0.539533\pi$
$887$	−7.37885			−0.247758			−0.123879	+	0.992297i	$0.539533\pi$
$888$	7.44032			0.249681
$889$			5.61395i			0.188286i
$890$			9.29812i			0.311674i
$891$	0.192764	−	0.658016i	0.00645785	−	0.0220444i
$892$			49.6901i			1.66375i
$893$	−29.7564	+	27.2221i	−0.995758	+	0.910953i
$894$	117.622			3.93386
$895$			17.5731i			0.587404i
$896$		−	5.52075i		−	0.184435i
$897$			48.1373i			1.60726i
$898$		−	75.9227i		−	2.53357i
$899$			28.2834i			0.943303i
$900$	−11.4967			−0.383224
$901$	4.99443			0.166389
$902$	6.47959	−	22.1186i	0.215747	−	0.736468i
$903$			5.40766i			0.179956i
$904$		−	5.12172i		−	0.170346i
$905$			15.8579i			0.527134i
$906$		−	131.312i		−	4.36255i
$907$			13.8264i			0.459100i	0.973297	+	0.229550i	$0.0737254\pi$
$907$			13.8264i			0.459100i	−0.973297	+	0.229550i	$0.926275\pi$
$908$	−37.4968			−1.24437
$909$			2.51463i			0.0834050i
$910$		−	6.91495i		−	0.229228i
$911$		−	55.1464i		−	1.82708i	−0.406749	−	0.913540i	$-0.633337\pi$
$911$		−	55.1464i		−	1.82708i	0.406749	−	0.913540i	$-0.366663\pi$
$912$	26.1715	+	28.6080i	0.866625	+	0.947304i
$913$	−33.3197	−	9.76093i	−1.10272	−	0.323039i
$914$			0.240933i			0.00796936i
$915$	11.1952			0.370103
$916$	−13.6990			−0.452628
$917$	5.21448			0.172197
$918$	13.9474			0.460333
$919$		−	44.3304i		−	1.46233i	−0.682203	−	0.731163i	$-0.738978\pi$
$919$		−	44.3304i		−	1.46233i	0.682203	−	0.731163i	$-0.261022\pi$
$920$	3.62635			0.119557
$921$			66.1795i			2.18069i
$922$			23.6058i			0.777416i
$923$		−	29.5803i		−	0.973649i
$924$	5.85557	−	19.9884i	0.192634	−	0.657571i
$925$			3.59157i			0.118090i
$926$	8.06533			0.265043
$927$		−	72.2594i		−	2.37331i
$928$	33.6372			1.10419
$929$	39.0485			1.28114			0.640569	−	0.767901i	$-0.278699\pi$
$929$	39.0485			1.28114			0.640569	+	0.767901i	$0.278699\pi$
$930$	−39.8311			−1.30611
$931$	−19.6087	+	17.9387i	−0.642651	+	0.587918i
$932$		−	29.5166i		−	0.966850i
$933$			43.0376i			1.40899i
$934$	82.2426			2.69106
$935$	4.02006	+	1.17767i	0.131470	+	0.0385139i
$936$	12.5686			0.410817
$937$		−	17.2927i		−	0.564927i	−0.959278	−	0.282464i	$-0.908848\pi$
$937$		−	17.2927i		−	0.564927i	0.959278	−	0.282464i	$-0.0911516\pi$
$938$	15.2112			0.496662
$939$		−	7.72055i		−	0.251951i
$940$	−21.7760			−0.710253
$941$	6.95743			0.226806			0.113403	−	0.993549i	$-0.463825\pi$
$941$	6.95743			0.226806			0.113403	+	0.993549i	$0.463825\pi$
$942$		−	122.887i		−	4.00387i
$943$	−16.3709			−0.533111
$944$		−	12.1234i		−	0.394582i
$945$	5.02913			0.163597
$946$	−13.4592	−	3.94284i	−0.437596	−	0.128193i
$947$	52.2670			1.69845			0.849224	−	0.528032i	$-0.177070\pi$
$947$	52.2670			1.69845			0.849224	+	0.528032i	$0.177070\pi$
$948$		−	97.3537i		−	3.16190i
$949$			23.7848i			0.772089i
$950$	6.71050	−	6.13899i	0.217717	−	0.199175i
$951$	89.7493			2.91032
$952$	0.885450			0.0286976
$953$	−7.08166			−0.229397			−0.114699	−	0.993400i	$-0.536590\pi$
$953$	−7.08166			−0.229397			−0.114699	+	0.993400i	$0.536590\pi$
$954$			40.3032i			1.30486i
$955$	7.01749			0.227081
$956$		−	44.6832i		−	1.44516i
$957$	37.1826	+	10.8926i	1.20194	+	0.352106i
$958$		−	68.3128i		−	2.20709i
$959$		−	17.2157i		−	0.555923i
$960$			29.5804i			0.954705i
$961$	−15.2177			−0.490893
$962$		−	26.1359i		−	0.842654i
$963$	2.47723			0.0798275
$964$	−36.7216			−1.18272
$965$	−13.1516			−0.423364
$966$	−27.3661			−0.880490
$967$			6.99645i			0.224991i	0.993652	+	0.112495i	$0.0358843\pi$
$967$			6.99645i			0.224991i	−0.993652	+	0.112495i	$0.964116\pi$
$968$	6.83250	+	4.37893i	0.219605	+	0.140744i
$969$	−11.4062	+	10.4348i	−0.366420	+	0.335214i
$970$			20.9870i			0.673851i
$971$			7.05574i			0.226429i	0.993571	+	0.113215i	$0.0361148\pi$
$971$			7.05574i			0.226429i	−0.993571	+	0.113215i	$0.963885\pi$
$972$		−	36.0022i		−	1.15477i
$973$	9.15234			0.293410
$974$			54.9277i			1.76000i
$975$			9.79318i			0.313633i
$976$		−	12.6299i		−	0.404272i
$977$		−	19.9660i		−	0.638767i	−0.947625	−	0.319384i	$-0.896524\pi$
$977$		−	19.9660i		−	0.638767i	0.947625	−	0.319384i	$-0.103476\pi$
$978$		−	18.1155i		−	0.579269i
$979$	14.1837	+	4.15508i	0.453313	+	0.132797i
$980$	−14.3498			−0.458389
$981$	−26.0394			−0.831375
$982$			41.1130i			1.31197i
$983$		−	8.39337i		−	0.267707i	−0.991001	−	0.133853i	$-0.957265\pi$
$983$		−	8.39337i		−	0.267707i	0.991001	−	0.133853i	$-0.0427351\pi$
$984$			6.89958i			0.219951i
$985$		−	14.1879i		−	0.452064i
$986$			10.9639i			0.349162i
$987$	24.6877			0.785817
$988$	−26.3991	+	24.1508i	−0.839868	+	0.768340i
$989$			9.96175i			0.316765i
$990$	−9.50334	+	32.4404i	−0.302036	+	1.03102i
$991$		−	41.1976i		−	1.30869i	−0.756198	−	0.654343i	$-0.772945\pi$
$991$		−	41.1976i		−	1.30869i	0.756198	−	0.654343i	$-0.227055\pi$
$992$			54.9663i			1.74518i
$993$	−51.8912			−1.64672
$994$	16.8165			0.533386
$995$	10.7532			0.340901
$996$	69.1842			2.19218
$997$			25.9180i			0.820833i	0.911898	+	0.410416i	$0.134617\pi$
$997$			25.9180i			0.820833i	−0.911898	+	0.410416i	$0.865383\pi$
$998$	92.2936			2.92150
$999$	19.0082			0.601392

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.f.a.626.5	✓	40
11.10	odd	2	inner	1045.2.f.a.626.35	yes	40
19.18	odd	2	inner	1045.2.f.a.626.36	yes	40
209.208	even	2	inner	1045.2.f.a.626.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.f.a.626.5	✓	40	1.1	even	1	trivial
1045.2.f.a.626.6	yes	40	209.208	even	2	inner
1045.2.f.a.626.35	yes	40	11.10	odd	2	inner
1045.2.f.a.626.36	yes	40	19.18	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.08652 q^{2} +2.80799i q^{3} +2.35358 q^{4} -1.00000 q^{5} -5.85893i q^{6} -0.950248i q^{7} -0.737755 q^{8} -4.88478 q^{9} +O(q^{10})\)	\(q-2.08652 q^{2} +2.80799i q^{3} +2.35358 q^{4} -1.00000 q^{5} -5.85893i q^{6} -0.950248i q^{7} -0.737755 q^{8} -4.88478 q^{9} +2.08652 q^{10} +(0.932412 - 3.18286i) q^{11} +6.60882i q^{12} +3.48762 q^{13} +1.98271i q^{14} -2.80799i q^{15} -3.16782 q^{16} -1.26303i q^{17} +10.1922 q^{18} +(-3.21612 + 2.94221i) q^{19} -2.35358 q^{20} +2.66828 q^{21} +(-1.94550 + 6.64112i) q^{22} +4.91539 q^{23} -2.07160i q^{24} +1.00000 q^{25} -7.27700 q^{26} -5.29243i q^{27} -2.23649i q^{28} +4.16032 q^{29} +5.85893i q^{30} +6.79836i q^{31} +8.08524 q^{32} +(8.93743 + 2.61820i) q^{33} +2.63535i q^{34} +0.950248i q^{35} -11.4967 q^{36} +3.59157i q^{37} +(6.71050 - 6.13899i) q^{38} +9.79318i q^{39} +0.737755 q^{40} -3.33055 q^{41} -5.56743 q^{42} +2.02665i q^{43} +(2.19451 - 7.49112i) q^{44} +4.88478 q^{45} -10.2561 q^{46} +9.25227 q^{47} -8.89519i q^{48} +6.09703 q^{49} -2.08652 q^{50} +3.54658 q^{51} +8.20839 q^{52} +3.95431i q^{53} +11.0428i q^{54} +(-0.932412 + 3.18286i) q^{55} +0.701050i q^{56} +(-8.26168 - 9.03081i) q^{57} -8.68061 q^{58} +3.82704i q^{59} -6.60882i q^{60} +3.98693i q^{61} -14.1849i q^{62} +4.64175i q^{63} -10.5344 q^{64} -3.48762 q^{65} +(-18.6482 - 5.46294i) q^{66} -7.67189i q^{67} -2.97265i q^{68} +13.8023i q^{69} -1.98271i q^{70} -8.48153i q^{71} +3.60377 q^{72} +6.81980i q^{73} -7.49390i q^{74} +2.80799i q^{75} +(-7.56939 + 6.92473i) q^{76} +(-3.02451 - 0.886023i) q^{77} -20.4337i q^{78} -14.7309 q^{79} +3.16782 q^{80} +0.206737 q^{81} +6.94927 q^{82} -10.4685i q^{83} +6.28002 q^{84} +1.26303i q^{85} -4.22864i q^{86} +11.6821i q^{87} +(-0.687892 + 2.34817i) q^{88} +4.45627i q^{89} -10.1922 q^{90} -3.31410i q^{91} +11.5688 q^{92} -19.0897 q^{93} -19.3051 q^{94} +(3.21612 - 2.94221i) q^{95} +22.7032i q^{96} +10.0583i q^{97} -12.7216 q^{98} +(-4.55463 + 15.5476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{4} - 40 q^{5} - 28 q^{9}+O(q^{10}) \) 40 * q + 40 * q^4 - 40 * q^5 - 28 * q^9	\( 40 q + 40 q^{4} - 40 q^{5} - 28 q^{9} - 4 q^{11} + 32 q^{16} - 40 q^{20} - 16 q^{23} + 40 q^{25} + 8 q^{26} + 8 q^{36} + 28 q^{38} - 84 q^{42} - 48 q^{44} + 28 q^{45} + 32 q^{47} - 20 q^{49} + 4 q^{55} - 20 q^{58} + 72 q^{64} + 36 q^{66} + 16 q^{77} - 32 q^{80} + 16 q^{81} + 16 q^{82} - 20 q^{92} - 8 q^{93}+O(q^{100}) \) 40 * q + 40 * q^4 - 40 * q^5 - 28 * q^9 - 4 * q^11 + 32 * q^16 - 40 * q^20 - 16 * q^23 + 40 * q^25 + 8 * q^26 + 8 * q^36 + 28 * q^38 - 84 * q^42 - 48 * q^44 + 28 * q^45 + 32 * q^47 - 20 * q^49 + 4 * q^55 - 20 * q^58 + 72 * q^64 + 36 * q^66 + 16 * q^77 - 32 * q^80 + 16 * q^81 + 16 * q^82 - 20 * q^92 - 8 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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