LMFDB - Embedded newform 378.3.q.a.197.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,3,Mod(71,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.71"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			197.5
Character	$\chi$	$=$	378.197
Dual form			378.3.q.a.71.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(3.60855 - 2.08340i) q^{5} +(-1.32288 + 2.29129i) q^{7} -2.82843i q^{8} -5.89274 q^{10} +(5.60663 + 3.23699i) q^{11} +(7.36010 + 12.7481i) q^{13} +(3.24037 - 1.87083i) q^{14} +(-2.00000 + 3.46410i) q^{16} -18.6466i q^{17} +15.6987 q^{19} +(7.21710 + 4.16679i) q^{20} +(-4.57780 - 7.92898i) q^{22} +(-17.1145 + 9.88106i) q^{23} +(-3.81892 + 6.61456i) q^{25} -20.8175i q^{26} -5.29150 q^{28} +(9.30724 + 5.37354i) q^{29} +(11.1508 + 19.3137i) q^{31} +(4.89898 - 2.82843i) q^{32} +(-13.1851 + 22.8373i) q^{34} +11.0243i q^{35} +70.8586 q^{37} +(-19.2269 - 11.1006i) q^{38} +(-5.89274 - 10.2065i) q^{40} +(7.29137 - 4.20968i) q^{41} +(24.9486 - 43.2123i) q^{43} +12.9480i q^{44} +27.9479 q^{46} +(62.5123 + 36.0915i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(9.35440 - 5.40077i) q^{50} +(-14.7202 + 25.4961i) q^{52} -80.3093i q^{53} +26.9757 q^{55} +(6.48074 + 3.74166i) q^{56} +(-7.59933 - 13.1624i) q^{58} +(22.8843 - 13.2122i) q^{59} +(32.7902 - 56.7944i) q^{61} -31.5391i q^{62} -8.00000 q^{64} +(53.1186 + 30.6680i) q^{65} +(-11.9038 - 20.6181i) q^{67} +(32.2968 - 18.6466i) q^{68} +(7.79536 - 13.5020i) q^{70} +111.926i q^{71} +13.3109 q^{73} +(-86.7837 - 50.1046i) q^{74} +(15.6987 + 27.1909i) q^{76} +(-14.8338 + 8.56427i) q^{77} +(-59.8755 + 103.707i) q^{79} +16.6672i q^{80} -11.9068 q^{82} +(-10.0716 - 5.81486i) q^{83} +(-38.8482 - 67.2871i) q^{85} +(-61.1114 + 35.2827i) q^{86} +(9.15559 - 15.8580i) q^{88} -83.5516i q^{89} -38.9460 q^{91} +(-34.2290 - 19.7621i) q^{92} +(-51.0411 - 88.4058i) q^{94} +(56.6494 - 32.7065i) q^{95} +(-84.0615 + 145.599i) q^{97} +9.89949i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} - 36 q^{5} - 48 q^{16} + 24 q^{19} - 72 q^{20} + 24 q^{22} + 72 q^{23} + 72 q^{25} + 108 q^{29} - 60 q^{31} - 48 q^{34} - 168 q^{37} - 144 q^{38} - 108 q^{41} + 60 q^{43} + 324 q^{47} - 84 q^{49}+ \cdots + 48 q^{97}+O(q^{100}) $ 24 * q + 24 * q^4 - 36 * q^5 - 48 * q^16 + 24 * q^19 - 72 * q^20 + 24 * q^22 + 72 * q^23 + 72 * q^25 + 108 * q^29 - 60 * q^31 - 48 * q^34 - 168 * q^37 - 144 * q^38 - 108 * q^41 + 60 * q^43 + 324 * q^47 - 84 * q^49 - 144 * q^50 + 264 * q^55 + 432 * q^59 - 192 * q^64 + 180 * q^65 + 72 * q^67 - 72 * q^68 + 24 * q^73 - 288 * q^74 + 24 * q^76 + 12 * q^79 - 288 * q^82 - 756 * q^83 - 156 * q^85 - 360 * q^86 - 48 * q^88 - 168 * q^91 + 144 * q^92 + 936 * q^95 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	3.60855	−	2.08340i	0.721710	−	0.416679i	−0.0936719	−	0.995603i	$-0.529860\pi$
$5$	3.60855	−	2.08340i	0.721710	−	0.416679i	0.815382	+	0.578924i	$0.196527\pi$
$6$		0			0
$7$	−1.32288	+	2.29129i	−0.188982	+	0.327327i
$7$	−1.32288	+	2.29129i	−0.188982	+	0.327327i
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	−5.89274			−0.589274
$11$	5.60663	+	3.23699i	0.509694	+	0.294272i	0.732708	−	0.680543i	$-0.238256\pi$
$11$	5.60663	+	3.23699i	0.509694	+	0.294272i	−0.223014	+	0.974815i	$0.571590\pi$
$12$		0			0
$13$	7.36010	+	12.7481i	0.566162	+	0.980621i	0.996941	+	0.0781633i	$0.0249056\pi$
$13$	7.36010	+	12.7481i	0.566162	+	0.980621i	−0.430779	+	0.902458i	$0.641761\pi$
$14$	3.24037	−	1.87083i	0.231455	−	0.133631i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$		−	18.6466i		−	1.09686i	−0.836197	−	0.548428i	$-0.815226\pi$
$17$		−	18.6466i		−	1.09686i	0.836197	−	0.548428i	$-0.184774\pi$
$18$		0			0
$19$	15.6987			0.826245			0.413123	−	0.910675i	$-0.364438\pi$
$19$	15.6987			0.826245			0.413123	+	0.910675i	$0.364438\pi$
$20$	7.21710	+	4.16679i	0.360855	+	0.208340i
$21$		0			0
$22$	−4.57780	−	7.92898i	−0.208082	−	0.360408i
$23$	−17.1145	+	9.88106i	−0.744109	+	0.429611i	−0.823561	−	0.567227i	$-0.808016\pi$
$23$	−17.1145	+	9.88106i	−0.744109	+	0.429611i	0.0794526	+	0.996839i	$0.474683\pi$
$24$		0			0
$25$	−3.81892	+	6.61456i	−0.152757	+	0.264582i
$26$		−	20.8175i		−	0.800674i
$27$		0			0
$28$	−5.29150			−0.188982
$29$	9.30724	+	5.37354i	0.320939	+	0.185294i	0.651811	−	0.758381i	$-0.274009\pi$
$29$	9.30724	+	5.37354i	0.320939	+	0.185294i	−0.330872	+	0.943676i	$0.607343\pi$
$30$		0			0
$31$	11.1508	+	19.3137i	0.359702	+	0.623022i	0.987911	−	0.155023i	$-0.0495451\pi$
$31$	11.1508	+	19.3137i	0.359702	+	0.623022i	−0.628209	+	0.778044i	$0.716212\pi$
$32$	4.89898	−	2.82843i	0.153093	−	0.0883883i
$33$		0			0
$34$	−13.1851	+	22.8373i	−0.387798	+	0.671685i
$35$			11.0243i			0.314980i
$36$		0			0
$37$	70.8586			1.91510			0.957548	−	0.288273i	$-0.0930810\pi$
$37$	70.8586			1.91510			0.957548	+	0.288273i	$0.0930810\pi$
$38$	−19.2269	−	11.1006i	−0.505970	−	0.292122i
$39$		0			0
$40$	−5.89274	−	10.2065i	−0.147318	−	0.255163i
$41$	7.29137	−	4.20968i	0.177838	−	0.102675i	−0.408438	−	0.912786i	$-0.633926\pi$
$41$	7.29137	−	4.20968i	0.177838	−	0.102675i	0.586277	+	0.810111i	$0.300593\pi$
$42$		0			0
$43$	24.9486	−	43.2123i	0.580201	−	1.00494i	−0.415254	−	0.909705i	$-0.636307\pi$
$43$	24.9486	−	43.2123i	0.580201	−	1.00494i	0.995455	−	0.0952318i	$-0.0303592\pi$
$44$			12.9480i			0.294272i
$45$		0			0
$46$	27.9479			0.607562
$47$	62.5123	+	36.0915i	1.33005	+	0.767904i	0.985307	−	0.170793i	$-0.0546329\pi$
$47$	62.5123	+	36.0915i	1.33005	+	0.767904i	0.344743	+	0.938697i	$0.387966\pi$
$48$		0			0
$49$	−3.50000	−	6.06218i	−0.0714286	−	0.123718i
$50$	9.35440	−	5.40077i	0.187088	−	0.108015i
$51$		0			0
$52$	−14.7202	+	25.4961i	−0.283081	+	0.490310i
$53$		−	80.3093i		−	1.51527i	−0.652679	−	0.757635i	$-0.726355\pi$
$53$		−	80.3093i		−	1.51527i	0.652679	−	0.757635i	$-0.273645\pi$
$54$		0			0
$55$	26.9757			0.490468
$56$	6.48074	+	3.74166i	0.115728	+	0.0668153i
$57$		0			0
$58$	−7.59933	−	13.1624i	−0.131023	−	0.226938i
$59$	22.8843	−	13.2122i	0.387869	−	0.223936i	−0.293368	−	0.956000i	$-0.594776\pi$
$59$	22.8843	−	13.2122i	0.387869	−	0.223936i	0.681236	+	0.732064i	$0.261443\pi$
$60$		0			0
$61$	32.7902	−	56.7944i	0.537545	−	0.931055i	−0.461491	−	0.887145i	$-0.652685\pi$
$61$	32.7902	−	56.7944i	0.537545	−	0.931055i	0.999035	−	0.0439099i	$-0.0139815\pi$
$62$		−	31.5391i		−	0.508695i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	53.1186	+	30.6680i	0.817209	+	0.471816i
$66$		0			0
$67$	−11.9038	−	20.6181i	−0.177669	−	0.307732i	0.763413	−	0.645911i	$-0.223522\pi$
$67$	−11.9038	−	20.6181i	−0.177669	−	0.307732i	−0.941082	+	0.338179i	$0.890189\pi$
$68$	32.2968	−	18.6466i	0.474953	−	0.274214i
$69$		0			0
$70$	7.79536	−	13.5020i	0.111362	−	0.192885i
$71$			111.926i			1.57643i	0.615403	+	0.788213i	$0.288993\pi$
$71$			111.926i			1.57643i	−0.615403	+	0.788213i	$0.711007\pi$
$72$		0			0
$73$	13.3109			0.182342			0.0911709	−	0.995835i	$-0.470939\pi$
$73$	13.3109			0.182342			0.0911709	+	0.995835i	$0.470939\pi$
$74$	−86.7837	−	50.1046i	−1.17275	−	0.677089i
$75$		0			0
$76$	15.6987	+	27.1909i	0.206561	+	0.357775i
$77$	−14.8338	+	8.56427i	−0.192646	+	0.111224i
$78$		0			0
$79$	−59.8755	+	103.707i	−0.757917	+	1.31275i	0.185994	+	0.982551i	$0.440450\pi$
$79$	−59.8755	+	103.707i	−0.757917	+	1.31275i	−0.943911	+	0.330200i	$0.892884\pi$
$80$			16.6672i			0.208340i
$81$		0			0
$82$	−11.9068			−0.145204
$83$	−10.0716	−	5.81486i	−0.121345	−	0.0700586i	0.438099	−	0.898927i	$-0.355652\pi$
$83$	−10.0716	−	5.81486i	−0.121345	−	0.0700586i	−0.559444	+	0.828868i	$0.688985\pi$
$84$		0			0
$85$	−38.8482	−	67.2871i	−0.457038	−	0.791612i
$86$	−61.1114	+	35.2827i	−0.710598	+	0.410264i
$87$		0			0
$88$	9.15559	−	15.8580i	0.104041	−	0.180204i
$89$		−	83.5516i		−	0.938782i	−0.882990	−	0.469391i	$-0.844473\pi$
$89$		−	83.5516i		−	0.938782i	0.882990	−	0.469391i	$-0.155527\pi$
$90$		0			0
$91$	−38.9460			−0.427978
$92$	−34.2290	−	19.7621i	−0.372054	−	0.214806i
$93$		0			0
$94$	−51.0411	−	88.4058i	−0.542990	−	0.940487i
$95$	56.6494	−	32.7065i	0.596309	−	0.344279i
$96$		0			0
$97$	−84.0615	+	145.599i	−0.866613	+	1.50102i	−0.00117642	+	0.999999i	$0.500374\pi$
$97$	−84.0615	+	145.599i	−0.866613	+	1.50102i	−0.865437	+	0.501018i	$0.832959\pi$
$98$			9.89949i			0.101015i
$99$		0			0
$100$	−15.2757			−0.152757
$101$	19.0956	+	11.0248i	0.189065	+	0.109157i	0.591545	−	0.806272i	$-0.298518\pi$
$101$	19.0956	+	11.0248i	0.189065	+	0.109157i	−0.402480	+	0.915429i	$0.631852\pi$
$102$		0			0
$103$	−63.2562	−	109.563i	−0.614138	−	1.06372i	−0.990535	−	0.137260i	$-0.956170\pi$
$103$	−63.2562	−	109.563i	−0.614138	−	1.06372i	0.376397	−	0.926459i	$-0.377163\pi$
$104$	36.0570	−	20.8175i	0.346702	−	0.200168i
$105$		0			0
$106$	−56.7872	+	98.3584i	−0.535729	+	0.927909i
$107$			39.7026i			0.371053i	0.982639	+	0.185526i	$0.0593990\pi$
$107$			39.7026i			0.371053i	−0.982639	+	0.185526i	$0.940601\pi$
$108$		0			0
$109$	93.2221			0.855249			0.427624	−	0.903957i	$-0.359351\pi$
$109$	93.2221			0.855249			0.427624	+	0.903957i	$0.359351\pi$
$110$	−33.0384	−	19.0747i	−0.300349	−	0.173407i
$111$		0			0
$112$	−5.29150	−	9.16515i	−0.0472456	−	0.0818317i
$113$	−69.6562	+	40.2160i	−0.616427	+	0.355894i	−0.775476	−	0.631376i	$-0.782490\pi$
$113$	−69.6562	+	40.2160i	−0.616427	+	0.355894i	0.159050	+	0.987271i	$0.449157\pi$
$114$		0			0
$115$	−41.1723	+	71.3126i	−0.358020	+	0.620109i
$116$			21.4941i			0.185294i
$117$		0			0
$118$	−37.3698			−0.316693
$119$	42.7247	+	24.6671i	0.359031	+	0.207286i
$120$		0			0
$121$	−39.5438	−	68.4918i	−0.326808	−	0.566048i
$122$	−80.3193	+	46.3724i	−0.658355	+	0.380102i
$123$		0			0
$124$	−22.3015	+	38.6273i	−0.179851	+	0.311511i
$125$			135.995i			1.08796i
$126$		0			0
$127$	−22.5391			−0.177473			−0.0887367	−	0.996055i	$-0.528283\pi$
$127$	−22.5391			−0.177473			−0.0887367	+	0.996055i	$0.528283\pi$
$128$	9.79796	+	5.65685i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−43.3711	−	75.1210i	−0.333624	−	0.577854i
$131$	−205.316	+	118.539i	−1.56729	+	0.904878i	−0.570811	+	0.821081i	$0.693371\pi$
$131$	−205.316	+	118.539i	−1.56729	+	0.904878i	−0.996483	+	0.0837963i	$0.973296\pi$
$132$		0			0
$133$	−20.7674	+	35.9702i	−0.156146	+	0.270452i
$134$			33.6691i			0.251262i
$135$		0			0
$136$	−52.7405			−0.387798
$137$	−168.003	−	96.9965i	−1.22630	−	0.708004i	−0.260045	−	0.965597i	$-0.583737\pi$
$137$	−168.003	−	96.9965i	−1.22630	−	0.708004i	−0.966254	+	0.257593i	$0.917071\pi$
$138$		0			0
$139$	79.4617	+	137.632i	0.571667	+	0.990156i	0.996395	+	0.0848352i	$0.0270364\pi$
$139$	79.4617	+	137.632i	0.571667	+	0.990156i	−0.424728	+	0.905321i	$0.639630\pi$
$140$	−19.0946	+	11.0243i	−0.136390	+	0.0787450i
$141$		0			0
$142$	79.1438	−	137.081i	0.557351	−	0.965360i
$143$			95.2983i			0.666422i
$144$		0			0
$145$	44.7808			0.308833
$146$	−16.3025	−	9.41226i	−0.111661	−	0.0644675i
$147$		0			0
$148$	70.8586	+	122.731i	0.478774	+	0.829261i
$149$	−88.2118	+	50.9291i	−0.592026	+	0.341806i	−0.765898	−	0.642962i	$-0.777705\pi$
$149$	−88.2118	+	50.9291i	−0.592026	+	0.341806i	0.173872	+	0.984768i	$0.444372\pi$
$150$		0			0
$151$	70.2311	−	121.644i	0.465106	−	0.805588i	−0.534100	−	0.845421i	$-0.679349\pi$
$151$	70.2311	−	121.644i	0.465106	−	0.805588i	0.999206	+	0.0398334i	$0.0126827\pi$
$152$		−	44.4025i		−	0.292122i
$153$		0			0
$154$	24.2234			0.157295
$155$	80.4761	+	46.4629i	0.519200	+	0.299760i
$156$		0			0
$157$	−124.454	−	215.560i	−0.792700	−	1.37300i	−0.924290	−	0.381692i	$-0.875342\pi$
$157$	−124.454	−	215.560i	−0.792700	−	1.37300i	0.131590	−	0.991304i	$-0.457992\pi$
$158$	146.664	−	84.6767i	0.928255	−	0.535928i
$159$		0			0
$160$	11.7855	−	20.4130i	0.0736592	−	0.127581i
$161$		−	52.2857i		−	0.324756i
$162$		0			0
$163$	168.569			1.03417			0.517083	−	0.855935i	$-0.327018\pi$
$163$	168.569			1.03417			0.517083	+	0.855935i	$0.327018\pi$
$164$	14.5827	+	8.41935i	0.0889192	+	0.0513375i
$165$		0			0
$166$	8.22346	+	14.2434i	0.0495389	+	0.0858039i
$167$	−252.089	+	145.544i	−1.50952	+	0.871519i	−0.509577	+	0.860425i	$0.670198\pi$
$167$	−252.089	+	145.544i	−1.50952	+	0.871519i	−0.999938	+	0.0110940i	$0.996469\pi$
$168$		0			0
$169$	−23.8422	+	41.2959i	−0.141078	+	0.244354i
$170$			109.879i			0.646349i
$171$		0			0
$172$	99.7945			0.580201
$173$	−119.791	−	69.1612i	−0.692432	−	0.399776i	0.112091	−	0.993698i	$-0.464245\pi$
$173$	−119.791	−	69.1612i	−0.692432	−	0.399776i	−0.804522	+	0.593922i	$0.797579\pi$
$174$		0			0
$175$	−10.1039	−	17.5005i	−0.0577366	−	0.100003i
$176$	−22.4265	+	12.9480i	−0.127423	+	0.0735680i
$177$		0			0
$178$	−59.0799	+	102.329i	−0.331910	+	0.574884i
$179$		−	304.532i		−	1.70130i	−0.525735	−	0.850649i	$-0.676210\pi$
$179$		−	304.532i		−	1.70130i	0.525735	−	0.850649i	$-0.323790\pi$
$180$		0			0
$181$	−260.720			−1.44044			−0.720221	−	0.693745i	$-0.755960\pi$
$181$	−260.720			−1.44044			−0.720221	+	0.693745i	$0.755960\pi$
$182$	47.6989	+	27.5390i	0.262082	+	0.151313i
$183$		0			0
$184$	27.9479	+	48.4071i	0.151891	+	0.263082i
$185$	255.697	−	147.627i	1.38214	−	0.797981i
$186$		0			0
$187$	60.3588	−	104.544i	0.322774	−	0.559061i
$188$			144.366i			0.767904i
$189$		0			0
$190$	−92.5081			−0.486885
$191$	−49.9914	−	28.8626i	−0.261735	−	0.151113i	0.363391	−	0.931637i	$-0.381619\pi$
$191$	−49.9914	−	28.8626i	−0.261735	−	0.151113i	−0.625126	+	0.780524i	$0.714952\pi$
$192$		0			0
$193$	−44.7554	−	77.5186i	−0.231893	−	0.401651i	0.726472	−	0.687196i	$-0.241159\pi$
$193$	−44.7554	−	77.5186i	−0.231893	−	0.401651i	−0.958365	+	0.285545i	$0.907825\pi$
$194$	205.908	−	118.881i	1.06138	−	0.612788i
$195$		0			0
$196$	7.00000	−	12.1244i	0.0357143	−	0.0618590i
$197$			1.87709i			0.00952838i	0.999989	+	0.00476419i	$0.00151650\pi$
$197$			1.87709i			0.00952838i	−0.999989	+	0.00476419i	$0.998484\pi$
$198$		0			0
$199$	−80.1938			−0.402984			−0.201492	−	0.979490i	$-0.564579\pi$
$199$	−80.1938			−0.402984			−0.201492	+	0.979490i	$0.564579\pi$
$200$	18.7088	+	10.8015i	0.0935440	+	0.0540077i
$201$		0			0
$202$	−15.5915	−	27.0052i	−0.0771855	−	0.133689i
$203$	−24.6246	+	14.2170i	−0.121304	+	0.0700347i
$204$		0			0
$205$	17.5409	−	30.3816i	0.0855651	−	0.148203i
$206$			178.916i			0.868523i
$207$		0			0
$208$	−58.8808			−0.283081
$209$	88.0166	+	50.8164i	0.421132	+	0.243141i
$210$		0			0
$211$	80.5551	+	139.526i	0.381778	+	0.661259i	0.991316	−	0.131498i	$-0.0419786\pi$
$211$	80.5551	+	139.526i	0.381778	+	0.661259i	−0.609539	+	0.792756i	$0.708645\pi$
$212$	139.100	−	80.3093i	0.656131	−	0.378817i
$213$		0			0
$214$	28.0740	−	48.6256i	0.131187	−	0.227222i
$215$		−	207.912i		−	0.967031i
$216$		0			0
$217$	−59.0042			−0.271909
$218$	−114.173	−	65.9180i	−0.523731	−	0.302376i
$219$		0			0
$220$	26.9757	+	46.7234i	0.122617	+	0.212379i
$221$	237.708	−	137.241i	1.07560	−	0.620998i
$222$		0			0
$223$	10.2489	−	17.7515i	0.0459590	−	0.0796033i	−0.842131	−	0.539273i	$-0.818699\pi$
$223$	10.2489	−	17.7515i	0.0459590	−	0.0796033i	0.888090	+	0.459670i	$0.152032\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	113.748			0.503310
$227$	130.615	+	75.4107i	0.575397	+	0.332206i	0.759302	−	0.650738i	$-0.225541\pi$
$227$	130.615	+	75.4107i	0.575397	+	0.332206i	−0.183905	+	0.982944i	$0.558874\pi$
$228$		0			0
$229$	148.880	+	257.868i	0.650133	+	1.12606i	0.983090	+	0.183121i	$0.0586200\pi$
$229$	148.880	+	257.868i	0.650133	+	1.12606i	−0.332958	+	0.942942i	$0.608047\pi$
$230$	100.851	−	58.2265i	0.438484	−	0.253159i
$231$		0			0
$232$	15.1987	−	26.3248i	0.0655115	−	0.113469i
$233$		−	386.415i		−	1.65843i	−0.558928	−	0.829216i	$-0.688787\pi$
$233$		−	386.415i		−	1.65843i	0.558928	−	0.829216i	$-0.311213\pi$
$234$		0			0
$235$	300.772			1.27988
$236$	45.7685	+	26.4245i	0.193934	+	0.111968i
$237$		0			0
$238$	−34.8845	−	60.4218i	−0.146574	−	0.253873i
$239$	180.122	−	103.994i	0.753649	−	0.435119i	−0.0733620	−	0.997305i	$-0.523373\pi$
$239$	180.122	−	103.994i	0.753649	−	0.435119i	0.827011	+	0.562186i	$0.190040\pi$
$240$		0			0
$241$	−161.733	+	280.130i	−0.671092	+	1.16236i	0.306503	+	0.951870i	$0.400841\pi$
$241$	−161.733	+	280.130i	−0.671092	+	1.16236i	−0.977595	+	0.210495i	$0.932492\pi$
$242$			111.847i			0.462176i
$243$		0			0
$244$	131.161			0.537545
$245$	−25.2598	−	14.5838i	−0.103101	−	0.0595256i
$246$		0			0
$247$	115.544	+	200.128i	0.467789	+	0.810234i
$248$	54.6273	−	31.5391i	0.220271	−	0.127174i
$249$		0			0
$250$	96.1631	−	166.559i	0.384652	−	0.666237i
$251$			288.081i			1.14773i	0.818948	+	0.573867i	$0.194558\pi$
$251$			288.081i			1.14773i	−0.818948	+	0.573867i	$0.805442\pi$
$252$		0			0
$253$	−127.940			−0.505690
$254$	27.6047	+	15.9376i	0.108680	+	0.0627463i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	111.683	−	64.4799i	0.434562	−	0.250895i	−0.266726	−	0.963772i	$-0.585942\pi$
$257$	111.683	−	64.4799i	0.434562	−	0.250895i	0.701288	+	0.712878i	$0.252609\pi$
$258$		0			0
$259$	−93.7371	+	162.357i	−0.361919	+	0.626863i
$260$			122.672i			0.471816i
$261$		0			0
$262$	335.279			1.27969
$263$	27.4385	+	15.8417i	0.104329	+	0.0602344i	0.551257	−	0.834336i	$-0.314149\pi$
$263$	27.4385	+	15.8417i	0.104329	+	0.0602344i	−0.446928	+	0.894570i	$0.647482\pi$
$264$		0			0
$265$	−167.316	−	289.800i	−0.631381	−	1.09358i
$266$	50.8695	−	29.3695i	0.191239	−	0.110412i
$267$		0			0
$268$	23.8077	−	41.2361i	0.0888346	−	0.153866i
$269$			154.678i			0.575011i	0.957779	+	0.287505i	$0.0928260\pi$
$269$			154.678i			0.575011i	−0.957779	+	0.287505i	$0.907174\pi$
$270$		0			0
$271$	−170.350			−0.628598			−0.314299	−	0.949324i	$-0.601769\pi$
$271$	−170.350			−0.628598			−0.314299	+	0.949324i	$0.601769\pi$
$272$	64.5936	+	37.2931i	0.237477	+	0.137107i
$273$		0			0
$274$	137.174	+	237.592i	0.500634	+	0.867124i
$275$	−42.8225	+	24.7236i	−0.155718	+	0.0899040i
$276$		0			0
$277$	263.888	−	457.068i	0.952665	−	1.65007i	0.213043	−	0.977043i	$-0.431662\pi$
$277$	263.888	−	457.068i	0.952665	−	1.65007i	0.739622	−	0.673022i	$-0.235004\pi$
$278$		−	224.752i		−	0.808459i
$279$		0			0
$280$	31.1814			0.111362
$281$	349.542	+	201.808i	1.24392	+	0.718179i	0.969890	−	0.243542i	$-0.0783093\pi$
$281$	349.542	+	201.808i	1.24392	+	0.718179i	0.274032	+	0.961721i	$0.411643\pi$
$282$		0			0
$283$	110.981	+	192.224i	0.392158	+	0.679238i	0.992734	−	0.120330i	$-0.0383951\pi$
$283$	110.981	+	192.224i	0.392158	+	0.679238i	−0.600576	+	0.799568i	$0.705062\pi$
$284$	−193.862	+	111.926i	−0.682612	+	0.394106i
$285$		0			0
$286$	67.3861	−	116.716i	0.235616	−	0.408098i
$287$			22.2755i			0.0776150i
$288$		0			0
$289$	−58.6945			−0.203095
$290$	−54.8451	−	31.6648i	−0.189121	−	0.109189i
$291$		0			0
$292$	13.3109	+	23.0552i	0.0455854	+	0.0789563i
$293$	226.579	−	130.815i	0.773306	−	0.446469i	−0.0607464	−	0.998153i	$-0.519348\pi$
$293$	226.579	−	130.815i	0.773306	−	0.446469i	0.834053	+	0.551685i	$0.186015\pi$
$294$		0			0
$295$	55.0526	−	95.3539i	0.186619	−	0.323234i
$296$		−	200.418i		−	0.677089i
$297$		0			0
$298$	144.049			0.483387
$299$	−251.929	−	145.451i	−0.842572	−	0.486459i
$300$		0			0
$301$	66.0079	+	114.329i	0.219295	+	0.379831i
$302$	−172.030	+	99.3217i	−0.569637	+	0.328880i
$303$		0			0
$304$	−31.3973	+	54.3818i	−0.103281	+	0.178887i
$305$		−	273.260i		−	0.895935i
$306$		0			0
$307$	−137.772			−0.448769			−0.224384	−	0.974501i	$-0.572037\pi$
$307$	−137.772			−0.448769			−0.224384	+	0.974501i	$0.572037\pi$
$308$	−29.6675	−	17.1285i	−0.0963231	−	0.0556122i
$309$		0			0
$310$	−65.7084	−	113.810i	−0.211963	−	0.367130i
$311$	−296.994	+	171.469i	−0.954964	+	0.551349i	−0.894619	−	0.446829i	$-0.852553\pi$
$311$	−296.994	+	171.469i	−0.954964	+	0.551349i	−0.0603446	+	0.998178i	$0.519220\pi$
$312$		0			0
$313$	176.129	−	305.064i	0.562711	−	0.974644i	−0.434548	−	0.900649i	$-0.643092\pi$
$313$	176.129	−	305.064i	0.562711	−	0.974644i	0.997259	−	0.0739953i	$-0.0235750\pi$
$314$			352.009i			1.12105i
$315$		0			0
$316$	−239.502			−0.757917
$317$	−128.074	−	73.9438i	−0.404020	−	0.233261i	0.284197	−	0.958766i	$-0.408273\pi$
$317$	−128.074	−	73.9438i	−0.404020	−	0.233261i	−0.688217	+	0.725505i	$0.741606\pi$
$318$		0			0
$319$	34.7882	+	60.2549i	0.109054	+	0.188887i
$320$	−28.8684	+	16.6672i	−0.0902137	+	0.0520849i
$321$		0			0
$322$	−36.9715	+	64.0366i	−0.114818	+	0.198871i
$323$		−	292.726i		−	0.906273i
$324$		0			0
$325$	−112.430			−0.345940
$326$	−206.454	−	119.196i	−0.633295	−	0.365633i
$327$		0			0
$328$	−11.9068	−	20.6231i	−0.0363011	−	0.0628754i
$329$	−165.392	+	95.4892i	−0.502711	+	0.290241i
$330$		0			0
$331$	−280.028	+	485.023i	−0.846006	+	1.46533i	0.0387387	+	0.999249i	$0.487666\pi$
$331$	−280.028	+	485.023i	−0.846006	+	1.46533i	−0.884745	+	0.466076i	$0.845667\pi$
$332$		−	23.2594i		−	0.0700586i
$333$		0			0
$334$	411.660			1.23251
$335$	−85.9112	−	49.6008i	−0.256451	−	0.148062i
$336$		0			0
$337$	11.9600	+	20.7154i	0.0354897	+	0.0614699i	0.883225	−	0.468950i	$-0.155368\pi$
$337$	11.9600	+	20.7154i	0.0354897	+	0.0614699i	−0.847735	+	0.530420i	$0.822034\pi$
$338$	58.4012	−	33.7180i	0.172785	−	0.0997573i
$339$		0			0
$340$	77.6964	−	134.574i	0.228519	−	0.395806i
$341$			144.380i			0.423400i
$342$		0			0
$343$	18.5203			0.0539949
$344$	−122.223	−	70.5654i	−0.355299	−	0.205132i
$345$		0			0
$346$	97.8087	+	169.410i	0.282684	+	0.489623i
$347$	−209.628	+	121.029i	−0.604115	+	0.348786i	−0.770659	−	0.637248i	$-0.780073\pi$
$347$	−209.628	+	121.029i	−0.604115	+	0.348786i	0.166544	+	0.986034i	$0.446739\pi$
$348$		0			0
$349$	−17.9763	+	31.1358i	−0.0515079	+	0.0892143i	−0.890630	−	0.454729i	$-0.849736\pi$
$349$	−17.9763	+	31.1358i	−0.0515079	+	0.0892143i	0.839122	+	0.543943i	$0.183069\pi$
$350$			28.5782i			0.0816519i
$351$		0			0
$352$	36.6224			0.104041
$353$	−266.093	−	153.629i	−0.753806	−	0.435210i	0.0732617	−	0.997313i	$-0.476659\pi$
$353$	−266.093	−	153.629i	−0.753806	−	0.435210i	−0.827067	+	0.562103i	$0.809992\pi$
$354$		0			0
$355$	233.187	+	403.891i	0.656864	+	1.13772i
$356$	144.716	−	83.5516i	0.406505	−	0.234695i
$357$		0			0
$358$	−215.337	+	372.974i	−0.601499	+	1.04183i
$359$		−	529.049i		−	1.47368i	−0.676070	−	0.736838i	$-0.736318\pi$
$359$		−	529.049i		−	1.47368i	0.676070	−	0.736838i	$-0.263682\pi$
$360$		0			0
$361$	−114.552			−0.317318
$362$	319.316	+	184.357i	0.882087	+	0.509273i
$363$		0			0
$364$	−38.9460	−	67.4564i	−0.106995	−	0.185320i
$365$	48.0332	−	27.7320i	0.131598	−	0.0759780i
$366$		0			0
$367$	169.534	−	293.642i	0.461946	−	0.800115i	−0.537112	−	0.843511i	$-0.680485\pi$
$367$	169.534	−	293.642i	0.461946	−	0.800115i	0.999058	+	0.0433966i	$0.0138179\pi$
$368$		−	79.0485i		−	0.214806i
$369$		0			0
$370$	−417.551			−1.12852
$371$	184.012	+	106.239i	0.495988	+	0.286359i
$372$		0			0
$373$	−247.394	−	428.499i	−0.663255	−	1.14879i	−0.979755	−	0.200199i	$-0.935841\pi$
$373$	−247.394	−	428.499i	−0.663255	−	1.14879i	0.316500	−	0.948593i	$-0.397492\pi$
$374$	−147.848	+	85.3602i	−0.395316	+	0.228236i
$375$		0			0
$376$	102.082	−	176.812i	0.271495	−	0.470244i
$377$			158.199i			0.419626i
$378$		0			0
$379$	−14.4703			−0.0381802			−0.0190901	−	0.999818i	$-0.506077\pi$
$379$	−14.4703			−0.0381802			−0.0190901	+	0.999818i	$0.506077\pi$
$380$	113.299	+	65.4131i	0.298155	+	0.172140i
$381$		0			0
$382$	40.8178	+	70.6985i	0.106853	+	0.185075i
$383$	−258.762	+	149.397i	−0.675620	+	0.390069i	−0.798203	−	0.602389i	$-0.794216\pi$
$383$	−258.762	+	149.397i	−0.675620	+	0.390069i	0.122583	+	0.992458i	$0.460882\pi$
$384$		0			0
$385$	−35.6856	+	61.8092i	−0.0926898	+	0.160543i
$386$			126.587i			0.327947i
$387$		0			0
$388$	−336.246			−0.866613
$389$	77.0026	+	44.4575i	0.197950	+	0.114287i	0.595699	−	0.803208i	$-0.296875\pi$
$389$	77.0026	+	44.4575i	0.197950	+	0.114287i	−0.397749	+	0.917494i	$0.630208\pi$
$390$		0			0
$391$	184.248	+	319.127i	0.471222	+	0.816181i
$392$	−17.1464	+	9.89949i	−0.0437409	+	0.0252538i
$393$		0			0
$394$	1.32730	−	2.29896i	0.00336879	−	0.00583492i
$395$			498.977i			1.26323i
$396$		0			0
$397$	−537.580			−1.35411			−0.677053	−	0.735935i	$-0.736743\pi$
$397$	−537.580			−1.35411			−0.677053	+	0.735935i	$0.736743\pi$
$398$	98.2169	+	56.7056i	0.246776	+	0.142476i
$399$		0			0
$400$	−15.2757	−	26.4582i	−0.0381892	−	0.0661456i
$401$	−151.261	+	87.3304i	−0.377209	+	0.217782i	−0.676603	−	0.736348i	$-0.736549\pi$
$401$	−151.261	+	87.3304i	−0.377209	+	0.217782i	0.299394	+	0.954129i	$0.403215\pi$
$402$		0			0
$403$	−164.141	+	284.301i	−0.407299	+	0.705462i
$404$			44.0993i			0.109157i
$405$		0			0
$406$	40.2119			0.0990440
$407$	397.278	+	229.369i	0.976113	+	0.563559i
$408$		0			0
$409$	−107.632	−	186.423i	−0.263158	−	0.455803i	0.703922	−	0.710278i	$-0.251431\pi$
$409$	−107.632	−	186.423i	−0.263158	−	0.455803i	−0.967079	+	0.254475i	$0.918097\pi$
$410$	−42.9661	+	24.8065i	−0.104795	+	0.0605037i
$411$		0			0
$412$	126.512	−	219.126i	0.307069	−	0.531859i
$413$			69.9125i			0.169280i
$414$		0			0
$415$	−48.4587			−0.116768
$416$	72.1140	+	41.6350i	0.173351	+	0.100084i
$417$		0			0
$418$	−71.8653	−	124.474i	−0.171927	−	0.297785i
$419$	−202.288	+	116.791i	−0.482788	+	0.278738i	−0.721578	−	0.692334i	$-0.756583\pi$
$419$	−202.288	+	116.791i	−0.482788	+	0.278738i	0.238790	+	0.971071i	$0.423249\pi$
$420$		0			0
$421$	407.164	−	705.229i	0.967136	−	1.67513i	0.263372	−	0.964694i	$-0.415165\pi$
$421$	407.164	−	705.229i	0.967136	−	1.67513i	0.703764	−	0.710434i	$-0.251501\pi$
$422$		−	227.844i		−	0.539915i
$423$		0			0
$424$	−227.149			−0.535729
$425$	123.339	+	71.2097i	0.290209	+	0.167552i
$426$		0			0
$427$	86.7548	+	150.264i	0.203173	+	0.351906i
$428$	−68.7670	+	39.7026i	−0.160670	+	0.0927631i
$429$		0			0
$430$	−147.016	+	254.639i	−0.341897	+	0.592183i
$431$			317.979i			0.737770i	0.929475	+	0.368885i	$0.120260\pi$
$431$			317.979i			0.737770i	−0.929475	+	0.368885i	$0.879740\pi$
$432$		0			0
$433$	−344.299			−0.795148			−0.397574	−	0.917570i	$-0.630148\pi$
$433$	−344.299			−0.795148			−0.397574	+	0.917570i	$0.630148\pi$
$434$	72.2651	+	41.7223i	0.166510	+	0.0961343i
$435$		0			0
$436$	93.2221	+	161.465i	0.213812	+	0.370334i
$437$	−268.675	+	155.119i	−0.614816	+	0.354964i
$438$		0			0
$439$	135.682	−	235.008i	0.309071	−	0.535326i	−0.669089	−	0.743183i	$-0.733315\pi$
$439$	135.682	−	235.008i	0.309071	−	0.535326i	0.978159	+	0.207856i	$0.0666487\pi$
$440$		−	76.2989i		−	0.173407i
$441$		0			0
$442$	−388.175			−0.878224
$443$	164.368	+	94.8980i	0.371034	+	0.214217i	0.673910	−	0.738813i	$-0.264613\pi$
$443$	164.368	+	94.8980i	0.371034	+	0.214217i	−0.302876	+	0.953030i	$0.597947\pi$
$444$		0			0
$445$	−174.071	−	301.500i	−0.391171	−	0.677528i
$446$	−25.1045	+	14.4941i	−0.0562881	+	0.0324979i
$447$		0			0
$448$	10.5830	−	18.3303i	0.0236228	−	0.0409159i
$449$		−	601.830i		−	1.34038i	−0.742190	−	0.670190i	$-0.766213\pi$
$449$		−	601.830i		−	1.34038i	0.742190	−	0.670190i	$-0.233787\pi$
$450$		0			0
$451$	54.5067			0.120858
$452$	−139.312	−	80.4321i	−0.308213	−	0.177947i
$453$		0			0
$454$	−106.647	−	184.718i	−0.234905	−	0.406867i
$455$	−140.539	+	81.1400i	−0.308876	+	0.178330i
$456$		0			0
$457$	88.5414	−	153.358i	0.193745	−	0.335576i	−0.752743	−	0.658314i	$-0.771270\pi$
$457$	88.5414	−	153.358i	0.193745	−	0.335576i	0.946488	+	0.322738i	$0.104603\pi$
$458$		−	421.097i		−	0.919426i
$459$		0			0
$460$	−164.689			−0.358020
$461$	−173.407	−	100.117i	−0.376154	−	0.217173i	0.299990	−	0.953942i	$-0.403017\pi$
$461$	−173.407	−	100.117i	−0.376154	−	0.217173i	−0.676144	+	0.736770i	$0.736350\pi$
$462$		0			0
$463$	−237.254	−	410.935i	−0.512427	−	0.887549i	−0.999896	−	0.0144092i	$-0.995413\pi$
$463$	−237.254	−	410.935i	−0.512427	−	0.887549i	0.487469	−	0.873140i	$-0.337920\pi$
$464$	−37.2290	+	21.4941i	−0.0802348	+	0.0463236i
$465$		0			0
$466$	−273.236	+	473.259i	−0.586344	+	1.01558i
$467$		−	253.035i		−	0.541832i	−0.962603	−	0.270916i	$-0.912673\pi$
$467$		−	253.035i		−	0.541832i	0.962603	−	0.270916i	$-0.0873265\pi$
$468$		0			0
$469$	62.9892			0.134305
$470$	−368.369	−	212.678i	−0.783763	−	0.452506i
$471$		0			0
$472$	−37.3698	−	64.7264i	−0.0791734	−	0.137132i
$473$	279.756	−	161.517i	0.591450	−	0.341474i
$474$		0			0
$475$	−59.9519	+	103.840i	−0.126215	+	0.218610i
$476$			98.6684i			0.207286i
$477$		0			0
$478$	−294.138			−0.615352
$479$	633.064	+	365.500i	1.32164	+	0.763048i	0.983990	−	0.178225i	$-0.0570355\pi$
$479$	633.064	+	365.500i	1.32164	+	0.763048i	0.337648	+	0.941273i	$0.390369\pi$
$480$		0			0
$481$	521.526	+	903.310i	1.08425	+	1.87798i
$482$	396.164	−	228.725i	0.821916	−	0.474533i
$483$		0			0
$484$	79.0876	−	136.984i	0.163404	−	0.283024i
$485$			700.533i			1.44440i
$486$		0			0
$487$	638.705			1.31151			0.655754	−	0.754974i	$-0.272351\pi$
$487$	638.705			1.31151			0.655754	+	0.754974i	$0.272351\pi$
$488$	−160.639	−	92.7448i	−0.329178	−	0.190051i
$489$		0			0
$490$	20.6246	+	35.7228i	0.0420910	+	0.0729037i
$491$	−487.319	+	281.354i	−0.992504	+	0.573022i	−0.906022	−	0.423231i	$-0.860896\pi$
$491$	−487.319	+	281.354i	−0.992504	+	0.573022i	−0.0864820	+	0.996253i	$0.527563\pi$
$492$		0			0
$493$	100.198	−	173.548i	0.203241	−	0.352024i
$494$		−	326.807i		−	0.661553i
$495$		0			0
$496$	−89.2060			−0.179851
$497$	−256.455	−	148.064i	−0.516006	−	0.297916i
$498$		0			0
$499$	−379.091	−	656.605i	−0.759701	−	1.31584i	−0.943003	−	0.332785i	$-0.892012\pi$
$499$	−379.091	−	656.605i	−0.759701	−	1.31584i	0.183302	−	0.983057i	$-0.441322\pi$
$500$	−235.550	+	135.995i	−0.471101	+	0.271990i
$501$		0			0
$502$	203.704	−	352.826i	0.405786	−	0.702841i
$503$			367.332i			0.730283i	0.930952	+	0.365142i	$0.118979\pi$
$503$			367.332i			0.730283i	−0.930952	+	0.365142i	$0.881021\pi$
$504$		0			0
$505$	91.8764			0.181933
$506$	156.693	+	90.4670i	0.309671	+	0.178788i
$507$		0			0
$508$	−22.5391	−	39.0389i	−0.0443683	−	0.0768482i
$509$	254.904	−	147.169i	0.500794	−	0.289134i	−0.228247	−	0.973603i	$-0.573299\pi$
$509$	254.904	−	147.169i	0.500794	−	0.289134i	0.729042	+	0.684469i	$0.239966\pi$
$510$		0			0
$511$	−17.6087	+	30.4992i	−0.0344593	+	0.0596853i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	−182.377			−0.354819
$515$	−456.526	−	263.576i	−0.886459	−	0.511797i
$516$		0			0
$517$	233.656	+	404.704i	0.451945	+	0.782792i
$518$	229.608	−	132.564i	0.443259	−	0.255916i
$519$		0			0
$520$	86.7423	−	150.242i	0.166812	−	0.288927i
$521$			53.1458i			0.102007i	0.998698	+	0.0510037i	$0.0162420\pi$
$521$			53.1458i			0.102007i	−0.998698	+	0.0510037i	$0.983758\pi$
$522$		0			0
$523$	−776.112			−1.48396			−0.741981	−	0.670421i	$-0.766113\pi$
$523$	−776.112			−1.48396			−0.741981	+	0.670421i	$0.766113\pi$
$524$	−410.631	−	237.078i	−0.783647	−	0.452439i
$525$		0			0
$526$	−22.4035	−	38.8040i	−0.0425922	−	0.0737718i
$527$	360.134	−	207.923i	0.683365	−	0.394541i
$528$		0			0
$529$	−69.2293	+	119.909i	−0.130868	+	0.226670i
$530$			473.241i			0.892908i
$531$		0			0
$532$	−83.0695			−0.156146
$533$	107.331	+	61.9673i	0.201371	+	0.116261i
$534$		0			0
$535$	82.7163	+	143.269i	0.154610	+	0.267792i
$536$	−58.3167	+	33.6691i	−0.108800	+	0.0628156i
$537$		0			0
$538$	109.374	−	189.441i	0.203297	−	0.352121i
$539$		−	45.3179i		−	0.0840777i
$540$		0			0
$541$	414.383			0.765958			0.382979	−	0.923757i	$-0.374898\pi$
$541$	414.383			0.765958			0.382979	+	0.923757i	$0.374898\pi$
$542$	208.635	+	120.456i	0.384936	+	0.222243i
$543$		0			0
$544$	−52.7405	−	91.3492i	−0.0969494	−	0.167921i
$545$	336.397	−	194.219i	0.617241	−	0.356364i
$546$		0			0
$547$	194.595	−	337.048i	0.355749	−	0.616175i	−0.631497	−	0.775378i	$-0.717559\pi$
$547$	194.595	−	337.048i	0.355749	−	0.616175i	0.987246	+	0.159203i	$0.0508925\pi$
$548$		−	387.986i		−	0.708004i
$549$		0			0
$550$	69.9289			0.127143
$551$	146.111	+	84.3574i	0.265175	+	0.153099i
$552$		0			0
$553$	−158.416	−	274.384i	−0.286466	−	0.496173i
$554$	−646.392	+	373.194i	−1.16677	+	0.673636i
$555$		0			0
$556$	−158.923	+	275.263i	−0.285833	+	0.495078i
$557$			752.828i			1.35158i	0.737096	+	0.675788i	$0.236197\pi$
$557$			752.828i			1.35158i	−0.737096	+	0.675788i	$0.763803\pi$
$558$		0			0
$559$	734.498			1.31395
$560$	−38.1893	−	22.0486i	−0.0681952	−	0.0393725i
$561$		0			0
$562$	−285.400	−	494.327i	−0.507829	−	0.879586i
$563$	574.864	−	331.898i	1.02107	−	0.589517i	0.106659	−	0.994296i	$-0.465985\pi$
$563$	574.864	−	331.898i	1.02107	−	0.589517i	0.914415	+	0.404779i	$0.132651\pi$
$564$		0			0
$565$	−167.572	+	290.243i	−0.296587	+	0.513704i
$566$		−	313.901i		−	0.554596i
$567$		0			0
$568$	316.575			0.557351
$569$	−496.119	−	286.435i	−0.871914	−	0.503400i	−0.00393041	−	0.999992i	$-0.501251\pi$
$569$	−496.119	−	286.435i	−0.871914	−	0.503400i	−0.867984	+	0.496592i	$0.834584\pi$
$570$		0			0
$571$	−179.597	−	311.072i	−0.314531	−	0.544784i	0.664806	−	0.747016i	$-0.268514\pi$
$571$	−179.597	−	311.072i	−0.314531	−	0.544784i	−0.979338	+	0.202231i	$0.935181\pi$
$572$	−165.062	+	95.2983i	−0.288569	+	0.166605i
$573$		0			0
$574$	15.7512	−	27.2818i	0.0274411	−	0.0475293i
$575$		−	150.940i		−	0.262504i
$576$		0			0
$577$	327.352			0.567334			0.283667	−	0.958923i	$-0.408449\pi$
$577$	327.352			0.567334			0.283667	+	0.958923i	$0.408449\pi$
$578$	71.8858	+	41.5033i	0.124370	+	0.0718050i
$579$		0			0
$580$	44.7808	+	77.5627i	0.0772083	+	0.133729i
$581$	26.6470	−	15.3847i	0.0458641	−	0.0264797i
$582$		0			0
$583$	259.960	−	450.265i	0.445901	−	0.772324i
$584$		−	37.6490i		−	0.0644675i
$585$		0			0
$586$	−370.002			−0.631402
$587$	−702.685	−	405.696i	−1.19708	−	0.691134i	−0.237176	−	0.971467i	$-0.576222\pi$
$587$	−702.685	−	405.696i	−1.19708	−	0.691134i	−0.959903	+	0.280333i	$0.909555\pi$
$588$		0			0
$589$	175.052	+	303.199i	0.297202	+	0.514769i
$590$	−134.851	+	77.8562i	−0.228561	+	0.131960i
$591$		0			0
$592$	−141.717	+	245.461i	−0.239387	+	0.414631i
$593$			1078.74i			1.81912i	0.415576	+	0.909559i	$0.363580\pi$
$593$			1078.74i			1.81912i	−0.415576	+	0.909559i	$0.636420\pi$
$594$		0			0
$595$	205.565			0.345488
$596$	−176.424	−	101.858i	−0.296013	−	0.170903i
$597$		0			0
$598$	205.699	+	356.281i	0.343978	+	0.595788i
$599$	−95.0263	+	54.8635i	−0.158642	+	0.0915918i	−0.577219	−	0.816589i	$-0.695862\pi$
$599$	−95.0263	+	54.8635i	−0.158642	+	0.0915918i	0.418578	+	0.908181i	$0.362529\pi$
$600$		0			0
$601$	−402.166	+	696.572i	−0.669161	+	1.15902i	0.308978	+	0.951069i	$0.400013\pi$
$601$	−402.166	+	696.572i	−0.669161	+	1.15902i	−0.978139	+	0.207952i	$0.933320\pi$
$602$		−	186.698i		−	0.310130i
$603$		0			0
$604$	280.924			0.465106
$605$	−285.391	−	164.771i	−0.471721	−	0.272348i
$606$		0			0
$607$	109.545	+	189.738i	0.180470	+	0.312584i	0.942041	−	0.335498i	$-0.108905\pi$
$607$	109.545	+	189.738i	0.180470	+	0.312584i	−0.761571	+	0.648082i	$0.775571\pi$
$608$	76.9074	−	44.4025i	0.126492	−	0.0730305i
$609$		0			0
$610$	−193.224	+	334.674i	−0.316761	+	0.548646i
$611$			1062.55i			1.73903i
$612$		0			0
$613$	897.371			1.46390			0.731951	−	0.681358i	$-0.238610\pi$
$613$	897.371			1.46390			0.731951	+	0.681358i	$0.238610\pi$
$614$	168.736	+	97.4195i	0.274814	+	0.158664i
$615$		0			0
$616$	24.2234	+	41.9562i	0.0393237	+	0.0681107i
$617$	617.603	−	356.573i	1.00098	−	0.577915i	0.0924400	−	0.995718i	$-0.470533\pi$
$617$	617.603	−	356.573i	1.00098	−	0.577915i	0.908537	+	0.417804i	$0.137200\pi$
$618$		0			0
$619$	210.975	−	365.420i	0.340832	−	0.590339i	−0.643755	−	0.765231i	$-0.722625\pi$
$619$	210.975	−	365.420i	0.340832	−	0.590339i	0.984588	+	0.174893i	$0.0559579\pi$
$620$			185.851i			0.299760i
$621$		0			0
$622$	484.989			0.779725
$623$	191.441	+	110.528i	0.307289	+	0.177413i
$624$		0			0
$625$	187.859	+	325.381i	0.300574	+	0.520610i
$626$	−431.425	+	249.083i	−0.689177	+	0.397897i
$627$		0			0
$628$	248.908	−	431.121i	0.396350	−	0.686498i
$629$		−	1321.27i		−	2.10059i
$630$		0			0
$631$	−601.037			−0.952515			−0.476257	−	0.879306i	$-0.658007\pi$
$631$	−601.037			−0.952515			−0.476257	+	0.879306i	$0.658007\pi$
$632$	293.329	+	169.353i	0.464128	+	0.267964i
$633$		0			0
$634$	104.572	+	181.125i	0.164941	+	0.285685i
$635$	−81.3335	+	46.9579i	−0.128084	+	0.0739495i
$636$		0			0
$637$	51.5207	−	89.2365i	0.0808802	−	0.140089i
$638$		−	98.3958i		−	0.154225i
$639$		0			0
$640$	47.1419			0.0736592
$641$	809.038	+	467.098i	1.26215	+	0.728702i	0.973490	−	0.228729i	$-0.0734571\pi$
$641$	809.038	+	467.098i	1.26215	+	0.728702i	0.288660	+	0.957432i	$0.406790\pi$
$642$		0			0
$643$	10.0042	+	17.3277i	0.0155586	+	0.0269482i	0.873700	−	0.486465i	$-0.161714\pi$
$643$	10.0042	+	17.3277i	0.0155586	+	0.0269482i	−0.858141	+	0.513414i	$0.828381\pi$
$644$	90.5614	−	52.2857i	0.140623	−	0.0811889i
$645$		0			0
$646$	−206.989	+	358.515i	−0.320416	+	0.554977i
$647$		−	724.799i		−	1.12025i	−0.828410	−	0.560123i	$-0.810754\pi$
$647$		−	724.799i		−	1.12025i	0.828410	−	0.560123i	$-0.189246\pi$
$648$		0			0
$649$	171.071			0.263592
$650$	137.699	+	79.5004i	0.211844	+	0.122308i
$651$		0			0
$652$	168.569	+	291.970i	0.258541	+	0.447807i
$653$	−68.1776	+	39.3624i	−0.104407	+	0.0602793i	−0.551294	−	0.834311i	$-0.685866\pi$
$653$	−68.1776	+	39.3624i	−0.104407	+	0.0602793i	0.446887	+	0.894590i	$0.352532\pi$
$654$		0			0
$655$	−493.927	+	855.507i	−0.754088	+	1.30612i
$656$			33.6774i			0.0513375i
$657$		0			0
$658$	270.084			0.410462
$659$	822.374	+	474.798i	1.24791	+	0.720483i	0.970693	−	0.240324i	$-0.0772536\pi$
$659$	822.374	+	474.798i	1.24791	+	0.720483i	0.277220	+	0.960806i	$0.410587\pi$
$660$		0			0
$661$	−192.159	−	332.828i	−0.290709	−	0.503523i	0.683269	−	0.730167i	$-0.260558\pi$
$661$	−192.159	−	332.828i	−0.290709	−	0.503523i	−0.973978	+	0.226644i	$0.927224\pi$
$662$	685.926	−	396.019i	1.03614	−	0.598217i
$663$		0			0
$664$	−16.4469	+	28.4869i	−0.0247694	+	0.0429019i
$665$			173.067i			0.260251i
$666$		0			0
$667$	−212.385			−0.318418
$668$	−504.178	−	291.087i	−0.754758	−	0.435760i
$669$		0			0
$670$	70.1462	+	121.497i	0.104696	+	0.181338i
$671$	367.686	−	212.283i	0.547967	−	0.316369i
$672$		0			0
$673$	−99.9437	+	173.108i	−0.148505	+	0.257218i	−0.930675	−	0.365847i	$-0.880779\pi$
$673$	−99.9437	+	173.108i	−0.148505	+	0.257218i	0.782170	+	0.623065i	$0.214113\pi$
$674$		−	33.8281i		−	0.0501900i
$675$		0			0
$676$	−95.3688			−0.141078
$677$	−856.490	−	494.495i	−1.26513	−	0.730420i	−0.291064	−	0.956704i	$-0.594009\pi$
$677$	−856.490	−	494.495i	−1.26513	−	0.730420i	−0.974062	+	0.226283i	$0.927342\pi$
$678$		0			0
$679$	−222.406	−	385.218i	−0.327549	−	0.567331i
$680$	−190.317	+	109.879i	−0.279877	+	0.161587i
$681$		0			0
$682$	102.092	−	176.828i	0.149695	−	0.259279i
$683$		−	472.371i		−	0.691612i	−0.938306	−	0.345806i	$-0.887606\pi$
$683$		−	472.371i		−	0.691612i	0.938306	−	0.345806i	$-0.112394\pi$
$684$		0			0
$685$	−808.329			−1.18004
$686$	−22.6826	−	13.0958i	−0.0330650	−	0.0190901i
$687$		0			0
$688$	99.7945	+	172.849i	0.145050	+	0.251234i
$689$	1023.79	−	591.085i	1.48590	−	0.857888i
$690$		0			0
$691$	−379.591	+	657.471i	−0.549336	+	0.951478i	0.448984	+	0.893540i	$0.351786\pi$
$691$	−379.591	+	657.471i	−0.549336	+	0.951478i	−0.998320	+	0.0579384i	$0.981547\pi$
$692$		−	276.645i		−	0.399776i
$693$		0			0
$694$	342.321			0.493258
$695$	573.483	+	331.100i	0.825155	+	0.476404i
$696$		0			0
$697$	−78.4960	−	135.959i	−0.112620	−	0.195063i
$698$	44.0326	−	25.4223i	0.0630840	−	0.0364216i
$699$		0			0
$700$	20.2078	−	35.0010i	0.0288683	−	0.0500014i
$701$			590.449i			0.842295i	0.906992	+	0.421147i	$0.138372\pi$
$701$			590.449i			0.842295i	−0.906992	+	0.421147i	$0.861628\pi$
$702$		0			0
$703$	1112.38			1.58234
$704$	−44.8531	−	25.8959i	−0.0637117	−	0.0367840i
$705$		0			0
$706$	217.264	+	376.313i	0.307740	+	0.533021i
$707$	−50.5221	+	29.1690i	−0.0714598	+	0.0412574i
$708$		0			0
$709$	−375.204	+	649.872i	−0.529201	+	0.916603i	0.470219	+	0.882550i	$0.344175\pi$
$709$	−375.204	+	649.872i	−0.529201	+	0.916603i	−0.999420	+	0.0340534i	$0.989158\pi$
$710$		−	659.552i		−	0.928946i
$711$		0			0
$712$	−236.320			−0.331910
$713$	−381.679	−	220.362i	−0.535314	−	0.309064i
$714$		0			0
$715$	198.544	+	343.889i	0.277684	+	0.480963i
$716$	527.465	−	304.532i	0.736683	−	0.425324i
$717$		0			0
$718$	−374.094	+	647.951i	−0.521023	+	0.902438i
$719$		−	528.232i		−	0.734676i	−0.930088	−	0.367338i	$-0.880269\pi$
$719$		−	528.232i		−	0.734676i	0.930088	−	0.367338i	$-0.119731\pi$
$720$		0			0
$721$	334.721			0.464245
$722$	140.297	+	81.0005i	0.194317	+	0.112189i
$723$		0			0
$724$	−260.720	−	451.580i	−0.360111	−	0.623730i
$725$	−71.0872	+	41.0422i	−0.0980513	+	0.0566099i
$726$		0			0
$727$	337.899	−	585.259i	0.464786	−	0.805033i	−0.534406	−	0.845228i	$-0.679465\pi$
$727$	337.899	−	585.259i	0.464786	−	0.805033i	0.999192	+	0.0401952i	$0.0127980\pi$
$728$			110.156i			0.151313i
$729$		0			0
$730$	−78.4379			−0.107449
$731$	−805.761	−	465.206i	−1.10227	−	0.636397i
$732$		0			0
$733$	83.9702	+	145.441i	0.114557	+	0.198418i	0.917603	−	0.397499i	$-0.130122\pi$
$733$	83.9702	+	145.441i	0.114557	+	0.198418i	−0.803046	+	0.595918i	$0.796789\pi$
$734$	−415.273	+	239.758i	−0.565766	+	0.326645i
$735$		0			0
$736$	−55.8957	+	96.8142i	−0.0759453	+	0.131541i
$737$		−	154.130i		−	0.209132i
$738$		0			0
$739$	−832.894			−1.12706			−0.563528	−	0.826097i	$-0.690556\pi$
$739$	−832.894			−1.12706			−0.563528	+	0.826097i	$0.690556\pi$
$740$	511.393	+	295.253i	0.691072	+	0.398991i
$741$		0			0
$742$	−150.245	−	260.232i	−0.202486	−	0.350717i
$743$	698.782	−	403.442i	0.940487	−	0.542990i	0.0503738	−	0.998730i	$-0.483959\pi$
$743$	698.782	−	403.442i	0.940487	−	0.542990i	0.890113	+	0.455740i	$0.150625\pi$
$744$		0			0
$745$	−212.211	+	367.560i	−0.284847	+	0.493370i
$746$			699.737i			0.937985i
$747$		0			0
$748$	241.435			0.322774
$749$	−90.9701	−	52.5216i	−0.121455	−	0.0701223i
$750$		0			0
$751$	−203.868	−	353.110i	−0.271462	−	0.470187i	0.697774	−	0.716318i	$-0.254174\pi$
$751$	−203.868	−	353.110i	−0.271462	−	0.470187i	−0.969237	+	0.246131i	$0.920841\pi$
$752$	−250.049	+	144.366i	−0.332512	+	0.191976i
$753$		0			0
$754$	111.864	−	193.754i	0.148360	−	0.256968i
$755$		−	585.277i		−	0.775201i
$756$		0			0
$757$	709.798			0.937646			0.468823	−	0.883292i	$-0.344678\pi$
$757$	709.798			0.937646			0.468823	+	0.883292i	$0.344678\pi$
$758$	17.7224	+	10.2321i	0.0233805	+	0.0134988i
$759$		0			0
$760$	−92.5081	−	160.229i	−0.121721	−	0.210827i
$761$	−454.599	+	262.463i	−0.597370	+	0.344892i	−0.768006	−	0.640442i	$-0.778751\pi$
$761$	−454.599	+	262.463i	−0.597370	+	0.344892i	0.170636	+	0.985334i	$0.445418\pi$
$762$		0			0
$763$	−123.321	+	213.599i	−0.161627	+	0.279946i
$764$		−	115.450i		−	0.151113i
$765$		0			0
$766$	422.557			0.551641
$767$	336.861	+	194.487i	0.439193	+	0.253568i
$768$		0			0
$769$	164.387	+	284.726i	0.213767	+	0.370255i	0.952890	−	0.303315i	$-0.0980933\pi$
$769$	164.387	+	284.726i	0.213767	+	0.370255i	−0.739123	+	0.673570i	$0.764760\pi$
$770$	87.4114	−	50.4670i	0.113521	−	0.0655416i
$771$		0			0
$772$	89.5108	−	155.037i	0.115947	−	0.200825i
$773$			343.076i			0.443824i	0.975067	+	0.221912i	$0.0712298\pi$
$773$			343.076i			0.443824i	−0.975067	+	0.221912i	$0.928770\pi$
$774$		0			0
$775$	−170.335			−0.219787
$776$	411.815	+	237.762i	0.530690	+	0.306394i
$777$		0			0
$778$	−62.8723	−	108.898i	−0.0808128	−	0.139972i
$779$	114.465	−	66.0863i	0.146938	−	0.0848348i
$780$		0			0
$781$	−362.304	+	627.529i	−0.463898	+	0.803495i
$782$		−	521.132i		−	0.666409i
$783$		0			0
$784$	28.0000			0.0357143
$785$	−898.195	−	518.573i	−1.14420	−	0.660603i
$786$		0			0
$787$	−165.233	−	286.191i	−0.209952	−	0.363648i	0.741747	−	0.670680i	$-0.233998\pi$
$787$	−165.233	−	286.191i	−0.209952	−	0.363648i	−0.951699	+	0.307032i	$0.900664\pi$
$788$	−3.25122	+	1.87709i	−0.00412591	+	0.00238210i
$789$		0			0
$790$	352.830	−	611.120i	0.446621	−	0.773570i
$791$		−	212.803i		−	0.269031i
$792$		0			0
$793$	965.358			1.21735
$794$	658.398	+	380.126i	0.829217	+	0.478749i
$795$		0			0
$796$	−80.1938	−	138.900i	−0.100746	−	0.174497i
$797$	199.933	−	115.431i	0.250856	−	0.144832i	−0.369300	−	0.929310i	$-0.620402\pi$
$797$	199.933	−	115.431i	0.250856	−	0.144832i	0.620156	+	0.784478i	$0.287069\pi$
$798$		0			0
$799$	672.983	−	1165.64i	0.842281	−	1.45887i
$800$			43.2061i			0.0540077i
$801$		0			0
$802$	247.008			0.307990
$803$	74.6296	+	43.0874i	0.0929385	+	0.0536581i
$804$		0			0
$805$	−108.932	−	188.675i	−0.135319	−	0.234379i
$806$	402.062	−	232.131i	0.498837	−	0.288004i
$807$		0			0
$808$	31.1829	−	54.0104i	0.0385927	−	0.0668446i
$809$			1138.49i			1.40729i	0.710554	+	0.703643i	$0.248444\pi$
$809$			1138.49i			1.40729i	−0.710554	+	0.703643i	$0.751556\pi$
$810$		0			0
$811$	1346.08			1.65977			0.829887	−	0.557931i	$-0.188405\pi$
$811$	1346.08			1.65977			0.829887	+	0.557931i	$0.188405\pi$
$812$	−49.2493	−	28.4341i	−0.0606518	−	0.0350173i
$813$		0			0
$814$	−324.376	−	561.836i	−0.398496	−	0.690216i
$815$	608.289	−	351.196i	0.746367	−	0.430915i
$816$		0			0
$817$	391.660	−	678.375i	0.479388	−	0.830325i
$818$			304.428i			0.372161i
$819$		0			0
$820$	70.1634			0.0855651
$821$	−415.276	−	239.760i	−0.505817	−	0.292034i	0.225295	−	0.974291i	$-0.427665\pi$
$821$	−415.276	−	239.760i	−0.505817	−	0.292034i	−0.731113	+	0.682257i	$0.760999\pi$
$822$		0			0
$823$	−623.100	−	1079.24i	−0.757109	−	1.31135i	−0.944319	−	0.329031i	$-0.893278\pi$
$823$	−623.100	−	1079.24i	−0.757109	−	1.31135i	0.187210	−	0.982320i	$-0.440055\pi$
$824$	−309.891	+	178.916i	−0.376081	+	0.217131i
$825$		0			0
$826$	49.4356	−	85.6250i	0.0598494	−	0.103662i
$827$		−	464.446i		−	0.561603i	−0.959766	−	0.280802i	$-0.909400\pi$
$827$		−	464.446i		−	0.561603i	0.959766	−	0.280802i	$-0.0906003\pi$
$828$		0			0
$829$	479.856			0.578837			0.289418	−	0.957203i	$-0.406538\pi$
$829$	479.856			0.578837			0.289418	+	0.957203i	$0.406538\pi$
$830$	59.3495	+	34.2654i	0.0715054	+	0.0412837i
$831$		0			0
$832$	−58.8808	−	101.985i	−0.0707702	−	0.122578i
$833$	−113.039	+	65.2630i	−0.135701	+	0.0783469i
$834$		0			0
$835$	−606.450	+	1050.40i	−0.726288	+	1.25797i
$836$			203.266i			0.243141i
$837$		0			0
$838$	330.335			0.394195
$839$	249.072	+	143.802i	0.296868	+	0.171397i	0.641035	−	0.767512i	$-0.278505\pi$
$839$	249.072	+	143.802i	0.296868	+	0.171397i	−0.344167	+	0.938908i	$0.611839\pi$
$840$		0			0
$841$	−362.750	−	628.302i	−0.431332	−	0.747089i
$842$	−997.344	+	575.817i	−1.18449	+	0.683868i
$843$		0			0
$844$	−161.110	+	279.051i	−0.190889	+	0.330629i
$845$			198.691i			0.235137i
$846$		0			0
$847$	209.246			0.247044
$848$	278.200	+	160.619i	0.328065	+	0.189409i
$849$		0			0
$850$	−100.706	−	174.427i	−0.118477	−	0.205209i
$851$	−1212.71	+	700.158i	−1.42504	+	0.822747i
$852$		0			0
$853$	339.982	−	588.866i	0.398572	−	0.690347i	−0.594978	−	0.803742i	$-0.702839\pi$
$853$	339.982	−	588.866i	0.398572	−	0.690347i	0.993550	+	0.113395i	$0.0361725\pi$
$854$		−	245.380i		−	0.287330i
$855$		0			0
$856$	112.296			0.131187
$857$	−725.061	−	418.614i	−0.846045	−	0.488464i	0.0132695	−	0.999912i	$-0.495776\pi$
$857$	−725.061	−	418.614i	−0.846045	−	0.488464i	−0.859314	+	0.511448i	$0.829109\pi$
$858$		0			0
$859$	−173.311	−	300.184i	−0.201759	−	0.349457i	0.747336	−	0.664446i	$-0.231332\pi$
$859$	−173.311	−	300.184i	−0.201759	−	0.349457i	−0.949095	+	0.314989i	$0.897999\pi$
$860$	360.113	−	207.912i	0.418737	−	0.241758i
$861$		0			0
$862$	224.845	−	389.443i	0.260841	−	0.451790i
$863$			62.3236i			0.0722174i	0.999348	+	0.0361087i	$0.0114962\pi$
$863$			62.3236i			0.0722174i	−0.999348	+	0.0361087i	$0.988504\pi$
$864$		0			0
$865$	−576.361			−0.666313
$866$	421.679	+	243.456i	0.486927	+	0.281127i
$867$		0			0
$868$	−59.0042	−	102.198i	−0.0679772	−	0.117740i
$869$	−671.399	+	387.633i	−0.772612	+	0.446068i
$870$		0			0
$871$	175.227	−	303.502i	0.201179	−	0.348452i
$872$		−	263.672i		−	0.302376i
$873$		0			0
$874$	438.744			0.501995
$875$	−311.604	−	179.905i	−0.356119	−	0.205605i
$876$		0			0
$877$	845.076	+	1463.71i	0.963598	+	1.66900i	0.713334	+	0.700824i	$0.247184\pi$
$877$	845.076	+	1463.71i	0.963598	+	1.66900i	0.250264	+	0.968178i	$0.419483\pi$
$878$	−332.352	+	191.883i	−0.378533	+	0.218546i
$879$		0			0
$880$	−53.9515	+	93.4467i	−0.0613085	+	0.106189i
$881$			1480.43i			1.68040i	0.542280	+	0.840198i	$0.317561\pi$
$881$			1480.43i			1.68040i	−0.542280	+	0.840198i	$0.682439\pi$
$882$		0			0
$883$	−688.171			−0.779356			−0.389678	−	0.920951i	$-0.627414\pi$
$883$	−688.171			−0.779356			−0.389678	+	0.920951i	$0.627414\pi$
$884$	475.416	+	274.481i	0.537800	+	0.310499i
$885$		0			0
$886$	−134.206	−	232.452i	−0.151474	−	0.262361i
$887$	541.722	−	312.763i	0.610735	−	0.352608i	−0.162518	−	0.986706i	$-0.551962\pi$
$887$	541.722	−	312.763i	0.610735	−	0.352608i	0.773253	+	0.634098i	$0.218628\pi$
$888$		0			0
$889$	29.8164	−	51.6436i	0.0335393	−	0.0580918i
$890$			492.347i			0.553199i
$891$		0			0
$892$	40.9954			0.0459590
$893$	981.360	+	566.589i	1.09895	+	0.634478i
$894$		0			0
$895$	−634.461	−	1098.92i	−0.708895	−	1.22784i
$896$	−25.9230	+	14.9666i	−0.0289319	+	0.0167038i
$897$		0			0
$898$	−425.558	+	737.088i	−0.473896	+	0.820811i
$899$			239.676i			0.266603i
$900$		0			0
$901$	−1497.49			−1.66203
$902$	−66.7569	−	38.5421i	−0.0740098	−	0.0427296i
$903$		0			0
$904$	113.748	+	197.018i	0.125828	+	0.217940i
$905$	−940.821	+	543.183i	−1.03958	+	0.600203i
$906$		0			0
$907$	−503.987	+	872.931i	−0.555664	+	0.962438i	0.442188	+	0.896922i	$0.354202\pi$
$907$	−503.987	+	872.931i	−0.555664	+	0.962438i	−0.997852	+	0.0655154i	$0.979131\pi$
$908$			301.643i			0.332206i
$909$		0			0
$910$	229.498			0.252196
$911$	331.886	+	191.614i	0.364309	+	0.210334i	0.670969	−	0.741485i	$-0.265878\pi$
$911$	331.886	+	191.614i	0.364309	+	0.210334i	−0.306660	+	0.951819i	$0.599212\pi$
$912$		0			0
$913$	−37.6453	−	65.2036i	−0.0412325	−	0.0714169i
$914$	−216.881	+	125.217i	−0.237288	+	0.136998i
$915$		0			0
$916$	−297.761	+	515.737i	−0.325066	+	0.563031i
$917$		−	627.249i		−	0.684023i
$918$		0			0
$919$	−769.956			−0.837819			−0.418910	−	0.908028i	$-0.637588\pi$
$919$	−769.956			−0.837819			−0.418910	+	0.908028i	$0.637588\pi$
$920$	201.702	+	116.453i	0.219242	+	0.126579i
$921$		0			0
$922$	141.586	+	245.234i	0.153564	+	0.265981i
$923$	−1426.84	+	823.788i	−1.54588	+	0.892512i
$924$		0			0
$925$	−270.603	+	468.698i	−0.292544	+	0.506701i
$926$			671.055i			0.724681i
$927$		0			0
$928$	60.7946			0.0655115
$929$	323.085	+	186.533i	0.347778	+	0.200789i	0.663706	−	0.747994i	$-0.268983\pi$
$929$	323.085	+	186.533i	0.347778	+	0.200789i	−0.315928	+	0.948783i	$0.602316\pi$
$930$		0			0
$931$	−54.9453	−	95.1681i	−0.0590175	−	0.102221i
$932$	669.290	−	386.415i	0.718122	−	0.414608i
$933$		0			0
$934$	−178.923	+	309.904i	−0.191566	+	0.331803i
$935$		−	503.005i		−	0.537973i
$936$		0			0
$937$	−987.512			−1.05391			−0.526954	−	0.849894i	$-0.676666\pi$
$937$	−987.512			−1.05391			−0.526954	+	0.849894i	$0.676666\pi$
$938$	−77.1457	−	44.5401i	−0.0822449	−	0.0474841i
$939$		0			0
$940$	300.772	+	520.952i	0.319970	+	0.554204i
$941$	1178.37	−	680.335i	1.25226	−	0.722991i	0.280700	−	0.959795i	$-0.409433\pi$
$941$	1178.37	−	680.335i	1.25226	−	0.722991i	0.971557	+	0.236804i	$0.0761000\pi$
$942$		0			0
$943$	−83.1921	+	144.093i	−0.0882207	+	0.152803i
$944$			105.698i			0.111968i
$945$		0			0
$946$	−456.839			−0.482917
$947$	−1344.82	−	776.431i	−1.42008	−	0.819884i	−0.423776	−	0.905767i	$-0.639296\pi$
$947$	−1344.82	−	776.431i	−1.42008	−	0.819884i	−0.996305	+	0.0858826i	$0.972629\pi$
$948$		0			0
$949$	97.9699	+	169.689i	0.103235	+	0.178808i
$950$	146.852	−	84.7848i	0.154581	−	0.0892472i
$951$		0			0
$952$	69.7691	−	120.844i	0.0732868	−	0.126937i
$953$		−	756.704i		−	0.794023i	−0.917814	−	0.397012i	$-0.870047\pi$
$953$		−	756.704i		−	0.794023i	0.917814	−	0.397012i	$-0.129953\pi$
$954$		0			0
$955$	−240.529			−0.251862
$956$	360.244	+	207.987i	0.376824	+	0.217560i
$957$		0			0
$958$	−516.895	−	895.288i	−0.539556	−	0.934539i
$959$	444.494	−	256.629i	0.463497	−	0.267600i
$960$		0			0
$961$	231.822	−	401.527i	0.241229	−	0.417822i
$962$		−	1475.10i		−	1.53337i
$963$		0			0
$964$	−646.932			−0.671092
$965$	−323.004	−	186.486i	−0.334719	−	0.193250i
$966$		0			0
$967$	49.6997	+	86.0824i	0.0513958	+	0.0890201i	0.890579	−	0.454829i	$-0.150300\pi$
$967$	49.6997	+	86.0824i	0.0513958	+	0.0890201i	−0.839183	+	0.543849i	$0.816966\pi$
$968$	−193.724	+	111.847i	−0.200128	+	0.115544i
$969$		0			0
$970$	495.352	−	857.975i	0.510672	−	0.884510i
$971$		−	24.0392i		−	0.0247571i	−0.999923	−	0.0123786i	$-0.996060\pi$
$971$		−	24.0392i		−	0.0247571i	0.999923	−	0.0123786i	$-0.00394032\pi$
$972$		0			0
$973$	−420.472			−0.432140
$974$	−782.250	−	451.632i	−0.803132	−	0.463688i
$975$		0			0
$976$	131.161	+	227.177i	0.134386	+	0.232764i
$977$	−1101.39	+	635.889i	−1.12732	+	0.650859i	−0.943260	−	0.332056i	$-0.892258\pi$
$977$	−1101.39	+	635.889i	−1.12732	+	0.650859i	−0.184061	+	0.982915i	$0.558924\pi$
$978$		0			0
$979$	270.456	−	468.443i	0.276257	−	0.478491i
$980$		−	58.3351i		−	0.0595256i
$981$		0			0
$982$	795.789			0.810376
$983$	−881.017	−	508.656i	−0.896254	−	0.517452i	−0.0202708	−	0.999795i	$-0.506453\pi$
$983$	−881.017	−	508.656i	−0.896254	−	0.517452i	−0.875983	+	0.482342i	$0.839786\pi$
$984$		0			0
$985$	3.91073	+	6.77358i	0.00397028	+	0.00687673i
$986$	−245.434	+	141.701i	−0.248919	+	0.143713i
$987$		0			0
$988$	−231.088	+	400.255i	−0.233894	+	0.405117i
$989$			986.076i			0.997043i
$990$		0			0
$991$	−1748.26			−1.76414			−0.882070	−	0.471118i	$-0.843851\pi$
$991$	−1748.26			−1.76414			−0.882070	+	0.471118i	$0.843851\pi$
$992$	109.255	+	63.0782i	0.110136	+	0.0635869i
$993$		0			0
$994$	209.395	+	362.682i	0.210659	+	0.364872i
$995$	−289.383	+	167.075i	−0.290837	+	0.167915i
$996$		0			0
$997$	−123.758	+	214.355i	−0.124130	+	0.215000i	−0.921393	−	0.388633i	$-0.872947\pi$
$997$	−123.758	+	214.355i	−0.124130	+	0.215000i	0.797262	+	0.603633i	$0.206281\pi$
$998$			1072.23i			1.07438i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.q.a.197.5		24
3.2	odd	2		126.3.q.a.29.8	✓	24
9.2	odd	6		1134.3.b.c.323.4		24
9.4	even	3		126.3.q.a.113.8	yes	24
9.5	odd	6	inner	378.3.q.a.71.5		24
9.7	even	3		1134.3.b.c.323.21		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.q.a.29.8	✓	24	3.2	odd	2
126.3.q.a.113.8	yes	24	9.4	even	3
378.3.q.a.71.5		24	9.5	odd	6	inner
378.3.q.a.197.5		24	1.1	even	1	trivial
1134.3.b.c.323.4		24	9.2	odd	6
1134.3.b.c.323.21		24	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(3.60855 - 2.08340i) q^{5} +(-1.32288 + 2.29129i) q^{7} -2.82843i q^{8} -5.89274 q^{10} +(5.60663 + 3.23699i) q^{11} +(7.36010 + 12.7481i) q^{13} +(3.24037 - 1.87083i) q^{14} +(-2.00000 + 3.46410i) q^{16} -18.6466i q^{17} +15.6987 q^{19} +(7.21710 + 4.16679i) q^{20} +(-4.57780 - 7.92898i) q^{22} +(-17.1145 + 9.88106i) q^{23} +(-3.81892 + 6.61456i) q^{25} -20.8175i q^{26} -5.29150 q^{28} +(9.30724 + 5.37354i) q^{29} +(11.1508 + 19.3137i) q^{31} +(4.89898 - 2.82843i) q^{32} +(-13.1851 + 22.8373i) q^{34} +11.0243i q^{35} +70.8586 q^{37} +(-19.2269 - 11.1006i) q^{38} +(-5.89274 - 10.2065i) q^{40} +(7.29137 - 4.20968i) q^{41} +(24.9486 - 43.2123i) q^{43} +12.9480i q^{44} +27.9479 q^{46} +(62.5123 + 36.0915i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(9.35440 - 5.40077i) q^{50} +(-14.7202 + 25.4961i) q^{52} -80.3093i q^{53} +26.9757 q^{55} +(6.48074 + 3.74166i) q^{56} +(-7.59933 - 13.1624i) q^{58} +(22.8843 - 13.2122i) q^{59} +(32.7902 - 56.7944i) q^{61} -31.5391i q^{62} -8.00000 q^{64} +(53.1186 + 30.6680i) q^{65} +(-11.9038 - 20.6181i) q^{67} +(32.2968 - 18.6466i) q^{68} +(7.79536 - 13.5020i) q^{70} +111.926i q^{71} +13.3109 q^{73} +(-86.7837 - 50.1046i) q^{74} +(15.6987 + 27.1909i) q^{76} +(-14.8338 + 8.56427i) q^{77} +(-59.8755 + 103.707i) q^{79} +16.6672i q^{80} -11.9068 q^{82} +(-10.0716 - 5.81486i) q^{83} +(-38.8482 - 67.2871i) q^{85} +(-61.1114 + 35.2827i) q^{86} +(9.15559 - 15.8580i) q^{88} -83.5516i q^{89} -38.9460 q^{91} +(-34.2290 - 19.7621i) q^{92} +(-51.0411 - 88.4058i) q^{94} +(56.6494 - 32.7065i) q^{95} +(-84.0615 + 145.599i) q^{97} +9.89949i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} - 36 q^{5} - 48 q^{16} + 24 q^{19} - 72 q^{20} + 24 q^{22} + 72 q^{23} + 72 q^{25} + 108 q^{29} - 60 q^{31} - 48 q^{34} - 168 q^{37} - 144 q^{38} - 108 q^{41} + 60 q^{43} + 324 q^{47} - 84 q^{49}+ \cdots + 48 q^{97}+O(q^{100}) \) 24 * q + 24 * q^4 - 36 * q^5 - 48 * q^16 + 24 * q^19 - 72 * q^20 + 24 * q^22 + 72 * q^23 + 72 * q^25 + 108 * q^29 - 60 * q^31 - 48 * q^34 - 168 * q^37 - 144 * q^38 - 108 * q^41 + 60 * q^43 + 324 * q^47 - 84 * q^49 - 144 * q^50 + 264 * q^55 + 432 * q^59 - 192 * q^64 + 180 * q^65 + 72 * q^67 - 72 * q^68 + 24 * q^73 - 288 * q^74 + 24 * q^76 + 12 * q^79 - 288 * q^82 - 756 * q^83 - 156 * q^85 - 360 * q^86 - 48 * q^88 - 168 * q^91 + 144 * q^92 + 936 * q^95 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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