LMFDB - Embedded newform 76.6.i.a.5.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(5,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("76.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.i (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			5.3
Character	$\chi$	$=$	76.5
Dual form			76.6.i.a.61.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.700721 + 3.97399i) q^{3} +(26.7333 + 22.4319i) q^{5} +(-120.347 - 208.448i) q^{7} +(213.044 + 77.5416i) q^{9} +O(q^{10})$	\(q+(-0.700721 + 3.97399i) q^{3} +(26.7333 + 22.4319i) q^{5} +(-120.347 - 208.448i) q^{7} +(213.044 + 77.5416i) q^{9} +(149.931 - 259.689i) q^{11} +(99.2976 + 563.145i) q^{13} +(-107.877 + 90.5193i) q^{15} +(1107.05 - 402.934i) q^{17} +(848.848 - 1324.97i) q^{19} +(912.697 - 332.195i) q^{21} +(3447.47 - 2892.77i) q^{23} +(-331.171 - 1878.17i) q^{25} +(-947.721 + 1641.50i) q^{27} +(-564.107 - 205.318i) q^{29} +(4728.53 + 8190.05i) q^{31} +(926.939 + 777.794i) q^{33} +(1458.60 - 8272.11i) q^{35} -3648.38 q^{37} -2307.51 q^{39} +(3018.09 - 17116.4i) q^{41} +(-6212.74 - 5213.10i) q^{43} +(3955.96 + 6851.92i) q^{45} +(6379.45 + 2321.93i) q^{47} +(-20563.4 + 35616.9i) q^{49} +(825.520 + 4681.75i) q^{51} +(-26931.2 + 22598.0i) q^{53} +(9833.47 - 3579.09i) q^{55} +(4670.62 + 4301.75i) q^{57} +(-40288.0 + 14663.6i) q^{59} +(24770.2 - 20784.7i) q^{61} +(-9475.88 - 53740.4i) q^{63} +(-9977.86 + 17282.2i) q^{65} +(-52628.6 - 19155.2i) q^{67} +(9080.13 + 15727.2i) q^{69} +(54407.3 + 45653.2i) q^{71} +(-1908.02 + 10820.9i) q^{73} +7695.87 q^{75} -72175.3 q^{77} +(11228.7 - 63680.9i) q^{79} +(36343.8 + 30496.0i) q^{81} +(7346.90 + 12725.2i) q^{83} +(38633.7 + 14061.5i) q^{85} +(1211.21 - 2097.88i) q^{87} +(-1672.67 - 9486.17i) q^{89} +(105436. - 88471.3i) q^{91} +(-35860.5 + 13052.2i) q^{93} +(52414.2 - 16379.6i) q^{95} +(8954.07 - 3259.01i) q^{97} +(52078.6 - 43699.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9}+O(q^{10}) $ 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9	$ 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9} - 237 q^{11} + 2049 q^{13} + 2085 q^{15} - 609 q^{17} - 6012 q^{19} + 3591 q^{21} + 14100 q^{23} + 11802 q^{25} - 861 q^{27} - 10575 q^{29} - 6546 q^{31} - 21234 q^{33} - 231 q^{35} + 20052 q^{37} + 72204 q^{39} - 3249 q^{41} - 34677 q^{43} - 34956 q^{45} + 4461 q^{47} - 41139 q^{49} + 12099 q^{51} - 24291 q^{53} - 61767 q^{55} - 64470 q^{57} - 20100 q^{59} + 95490 q^{61} + 86403 q^{63} - 57915 q^{65} - 64452 q^{67} - 99315 q^{69} - 115536 q^{71} - 16362 q^{73} + 236250 q^{75} + 26688 q^{77} + 29799 q^{79} + 180327 q^{81} + 52347 q^{83} + 204618 q^{85} + 69414 q^{87} + 47394 q^{89} - 249384 q^{91} - 462126 q^{93} + 412869 q^{95} - 229974 q^{97} - 692274 q^{99}+O(q^{100}) $ 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9 - 237 * q^11 + 2049 * q^13 + 2085 * q^15 - 609 * q^17 - 6012 * q^19 + 3591 * q^21 + 14100 * q^23 + 11802 * q^25 - 861 * q^27 - 10575 * q^29 - 6546 * q^31 - 21234 * q^33 - 231 * q^35 + 20052 * q^37 + 72204 * q^39 - 3249 * q^41 - 34677 * q^43 - 34956 * q^45 + 4461 * q^47 - 41139 * q^49 + 12099 * q^51 - 24291 * q^53 - 61767 * q^55 - 64470 * q^57 - 20100 * q^59 + 95490 * q^61 + 86403 * q^63 - 57915 * q^65 - 64452 * q^67 - 99315 * q^69 - 115536 * q^71 - 16362 * q^73 + 236250 * q^75 + 26688 * q^77 + 29799 * q^79 + 180327 * q^81 + 52347 * q^83 + 204618 * q^85 + 69414 * q^87 + 47394 * q^89 - 249384 * q^91 - 462126 * q^93 + 412869 * q^95 - 229974 * q^97 - 692274 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.700721	+	3.97399i	−0.0449513	+	0.254931i	−0.998999	−	0.0447219i	$-0.985760\pi$
$3$	−0.700721	+	3.97399i	−0.0449513	+	0.254931i	0.954048	+	0.299653i	$0.0968710\pi$
$4$		0			0
$5$	26.7333	+	22.4319i	0.478220	+	0.401274i	0.849782	−	0.527134i	$-0.176733\pi$
$5$	26.7333	+	22.4319i	0.478220	+	0.401274i	−0.371562	+	0.928408i	$0.621178\pi$
$6$		0			0
$7$	−120.347	−	208.448i	−0.928306	−	1.60787i	−0.786156	−	0.618028i	$-0.787932\pi$
$7$	−120.347	−	208.448i	−0.928306	−	1.60787i	−0.142149	−	0.989845i	$-0.545401\pi$
$8$		0			0
$9$	213.044	+	77.5416i	0.876723	+	0.319101i
$10$		0			0
$11$	149.931	−	259.689i	0.373603	−	0.647100i	−0.616514	−	0.787344i	$-0.711456\pi$
$11$	149.931	−	259.689i	0.373603	−	0.647100i	0.990117	+	0.140244i	$0.0447889\pi$
$12$		0			0
$13$	99.2976	+	563.145i	0.162960	+	0.924191i	0.951143	+	0.308750i	$0.0999108\pi$
$13$	99.2976	+	563.145i	0.162960	+	0.924191i	−0.788183	+	0.615441i	$0.788978\pi$
$14$		0			0
$15$	−107.877	+	90.5193i	−0.123794	+	0.103875i
$16$		0			0
$17$	1107.05	−	402.934i	0.929064	−	0.338152i	0.167226	−	0.985919i	$-0.446519\pi$
$17$	1107.05	−	402.934i	0.929064	−	0.338152i	0.761839	+	0.647767i	$0.224297\pi$
$18$		0			0
$19$	848.848	−	1324.97i	0.539444	−	0.842022i
$19$	848.848	−	1324.97i	0.539444	−	0.842022i
$20$		0			0
$21$	912.697	−	332.195i	0.451626	−	0.164378i
$22$		0			0
$23$	3447.47	−	2892.77i	1.35888	−	1.14024i	0.382555	−	0.923933i	$-0.375044\pi$
$23$	3447.47	−	2892.77i	1.35888	−	1.14024i	0.976326	−	0.216304i	$-0.0694002\pi$
$24$		0			0
$25$	−331.171	−	1878.17i	−0.105975	−	0.601013i
$26$		0			0
$27$	−947.721	+	1641.50i	−0.250191	+	0.433343i
$28$		0			0
$29$	−564.107	−	205.318i	−0.124557	−	0.0453349i	0.278990	−	0.960294i	$-0.410000\pi$
$29$	−564.107	−	205.318i	−0.124557	−	0.0453349i	−0.403546	+	0.914959i	$0.632223\pi$
$30$		0			0
$31$	4728.53	+	8190.05i	0.883734	+	1.53067i	0.847158	+	0.531341i	$0.178312\pi$
$31$	4728.53	+	8190.05i	0.883734	+	1.53067i	0.0365762	+	0.999331i	$0.488355\pi$
$32$		0			0
$33$	926.939	+	777.794i	0.148172	+	0.124331i
$34$		0			0
$35$	1458.60	−	8272.11i	0.201263	−	1.14142i
$36$		0			0
$37$	−3648.38			−0.438122			−0.219061	−	0.975711i	$-0.570299\pi$
$37$	−3648.38			−0.438122			−0.219061	+	0.975711i	$0.570299\pi$
$38$		0			0
$39$	−2307.51			−0.242930
$40$		0			0
$41$	3018.09	−	17116.4i	0.280396	−	1.59021i	−0.440884	−	0.897564i	$-0.645335\pi$
$41$	3018.09	−	17116.4i	0.280396	−	1.59021i	0.721281	−	0.692643i	$-0.243554\pi$
$42$		0			0
$43$	−6212.74	−	5213.10i	−0.512403	−	0.429957i	0.349571	−	0.936910i	$-0.386327\pi$
$43$	−6212.74	−	5213.10i	−0.512403	−	0.429957i	−0.861974	+	0.506953i	$0.830772\pi$
$44$		0			0
$45$	3955.96	+	6851.92i	0.291219	+	0.504407i
$46$		0			0
$47$	6379.45	+	2321.93i	0.421249	+	0.153322i	0.543942	−	0.839123i	$-0.316931\pi$
$47$	6379.45	+	2321.93i	0.421249	+	0.153322i	−0.122694	+	0.992445i	$0.539153\pi$
$48$		0			0
$49$	−20563.4	+	35616.9i	−1.22350	+	2.11917i
$50$		0			0
$51$	825.520	+	4681.75i	0.0444428	+	0.252048i
$52$		0			0
$53$	−26931.2	+	22598.0i	−1.31694	+	1.10504i	−0.329996	+	0.943982i	$0.607048\pi$
$53$	−26931.2	+	22598.0i	−1.31694	+	1.10504i	−0.986944	+	0.161062i	$0.948508\pi$
$54$		0			0
$55$	9833.47	−	3579.09i	0.438329	−	0.159539i
$56$		0			0
$57$	4670.62	+	4301.75i	0.190409	+	0.175371i
$58$		0			0
$59$	−40288.0	+	14663.6i	−1.50676	+	0.548417i	−0.957802	−	0.287429i	$-0.907199\pi$
$59$	−40288.0	+	14663.6i	−1.50676	+	0.548417i	−0.548963	+	0.835847i	$0.684977\pi$
$60$		0			0
$61$	24770.2	−	20784.7i	0.852325	−	0.715185i	−0.107976	−	0.994154i	$-0.534437\pi$
$61$	24770.2	−	20784.7i	0.852325	−	0.715185i	0.960300	+	0.278968i	$0.0899924\pi$
$62$		0			0
$63$	−9475.88	−	53740.4i	−0.300793	−	1.70588i
$64$		0			0
$65$	−9977.86	+	17282.2i	−0.292923	+	0.507358i
$66$		0			0
$67$	−52628.6	−	19155.2i	−1.43230	−	0.521315i	−0.494711	−	0.869057i	$-0.664726\pi$
$67$	−52628.6	−	19155.2i	−1.43230	−	0.521315i	−0.937590	+	0.347742i	$0.886948\pi$
$68$		0			0
$69$	9080.13	+	15727.2i	0.229599	+	0.397676i
$70$		0			0
$71$	54407.3	+	45653.2i	1.28089	+	1.07479i	0.993121	+	0.117094i	$0.0373578\pi$
$71$	54407.3	+	45653.2i	1.28089	+	1.07479i	0.287768	+	0.957700i	$0.407087\pi$
$72$		0			0
$73$	−1908.02	+	10820.9i	−0.0419059	+	0.237660i	−0.998565	−	0.0535494i	$-0.982947\pi$
$73$	−1908.02	+	10820.9i	−0.0419059	+	0.237660i	0.956659	+	0.291209i	$0.0940577\pi$
$74$		0			0
$75$	7695.87			0.157981
$76$		0			0
$77$	−72175.3			−1.38727
$78$		0			0
$79$	11228.7	−	63680.9i	0.202423	−	1.14800i	−0.699021	−	0.715102i	$-0.746380\pi$
$79$	11228.7	−	63680.9i	0.202423	−	1.14800i	0.901444	−	0.432897i	$-0.142508\pi$
$80$		0			0
$81$	36343.8	+	30496.0i	0.615485	+	0.516453i
$82$		0			0
$83$	7346.90	+	12725.2i	0.117060	+	0.202754i	0.918601	−	0.395185i	$-0.129320\pi$
$83$	7346.90	+	12725.2i	0.117060	+	0.202754i	−0.801541	+	0.597939i	$0.795986\pi$
$84$		0			0
$85$	38633.7	+	14061.5i	0.579989	+	0.211099i
$86$		0			0
$87$	1211.21	−	2097.88i	0.0171563	−	0.0297155i
$88$		0			0
$89$	−1672.67	−	9486.17i	−0.0223838	−	0.126945i	0.971568	−	0.236760i	$-0.0760854\pi$
$89$	−1672.67	−	9486.17i	−0.0223838	−	0.126945i	−0.993952	+	0.109815i	$0.964974\pi$
$90$		0			0
$91$	105436.	−	88471.3i	1.33470	−	1.11995i
$92$		0			0
$93$	−35860.5	+	13052.2i	−0.429941	+	0.156486i
$94$		0			0
$95$	52414.2	−	16379.6i	0.595854	−	0.186207i
$96$		0			0
$97$	8954.07	−	3259.01i	0.0966253	−	0.0351687i	−0.293255	−	0.956034i	$-0.594739\pi$
$97$	8954.07	−	3259.01i	0.0966253	−	0.0351687i	0.389880	+	0.920865i	$0.372516\pi$
$98$		0			0
$99$	52078.6	−	43699.1i	0.534037	−	0.448110i
$100$		0			0
$101$	−1301.33	−	7380.20i	−0.0126936	−	0.0719887i	0.977803	−	0.209527i	$-0.0671923\pi$
$101$	−1301.33	−	7380.20i	−0.0126936	−	0.0719887i	−0.990497	+	0.137538i	$0.956081\pi$
$102$		0			0
$103$	1741.78	−	3016.85i	0.0161771	−	0.0280195i	−0.857824	−	0.513944i	$-0.828184\pi$
$103$	1741.78	−	3016.85i	0.0161771	−	0.0280195i	0.874001	+	0.485925i	$0.161517\pi$
$104$		0			0
$105$	31851.2	+	11592.9i	0.281937	+	0.102617i
$106$		0			0
$107$	−36352.1	−	62963.7i	−0.306952	−	0.531656i	0.670742	−	0.741691i	$-0.265976\pi$
$107$	−36352.1	−	62963.7i	−0.306952	−	0.531656i	−0.977694	+	0.210035i	$0.932642\pi$
$108$		0			0
$109$	59109.8	+	49599.0i	0.476533	+	0.399859i	0.849171	−	0.528118i	$-0.177102\pi$
$109$	59109.8	+	49599.0i	0.476533	+	0.399859i	−0.372638	+	0.927977i	$0.621547\pi$
$110$		0			0
$111$	2556.49	−	14498.6i	0.0196942	−	0.111691i
$112$		0			0
$113$	31273.4			0.230398			0.115199	−	0.993342i	$-0.463249\pi$
$113$	31273.4			0.230398			0.115199	+	0.993342i	$0.463249\pi$
$114$		0			0
$115$	157053.			1.10739
$116$		0			0
$117$	−22512.4	+	127674.i	−0.152040	+	0.862260i
$118$		0			0
$119$	−217221.	−	182270.i	−1.40616	−	1.17991i
$120$		0			0
$121$	35566.7	+	61603.4i	0.220841	+	0.382508i
$122$		0			0
$123$	65905.6	+	23987.7i	0.392789	+	0.142964i
$124$		0			0
$125$	87805.4	−	152083.i	0.502628	−	0.870577i
$126$		0			0
$127$	−3109.44	−	17634.5i	−0.0171070	−	0.0970184i	0.975059	−	0.221947i	$-0.0712411\pi$
$127$	−3109.44	−	17634.5i	−0.0171070	−	0.0970184i	−0.992166	+	0.124928i	$0.960130\pi$
$128$		0			0
$129$	25070.2	−	21036.4i	0.132643	−	0.111300i
$130$		0			0
$131$	−121454.	+	44205.7i	−0.618350	+	0.225061i	−0.632153	−	0.774844i	$-0.717829\pi$
$131$	−121454.	+	44205.7i	−0.618350	+	0.225061i	0.0138028	+	0.999905i	$0.495606\pi$
$132$		0			0
$133$	−378344.	−	17483.4i	−1.85463	−	0.0857034i
$134$		0			0
$135$	−62157.7	+	22623.6i	−0.293535	+	0.106838i
$136$		0			0
$137$	−138426.	+	116153.i	−0.630108	+	0.528723i	−0.900963	−	0.433897i	$-0.857138\pi$
$137$	−138426.	+	116153.i	−0.630108	+	0.528723i	0.270854	+	0.962620i	$0.412694\pi$
$138$		0			0
$139$	40788.4	+	231323.i	0.179060	+	1.01550i	0.933352	+	0.358963i	$0.116869\pi$
$139$	40788.4	+	231323.i	0.179060	+	1.01550i	−0.754291	+	0.656540i	$0.772019\pi$
$140$		0			0
$141$	−13697.5	+	23724.8i	−0.0580222	+	0.100497i
$142$		0			0
$143$	161130.	+	58646.6i	0.658926	+	0.239829i
$144$		0			0
$145$	−10474.8	−	18142.8i	−0.0413737	−	0.0716614i
$146$		0			0
$147$	−127132.	−	106676.i	−0.485245	−	0.407169i
$148$		0			0
$149$	−58201.9	+	330079.i	−0.214769	+	1.21802i	0.666538	+	0.745471i	$0.267775\pi$
$149$	−58201.9	+	330079.i	−0.214769	+	1.21802i	−0.881307	+	0.472544i	$0.843336\pi$
$150$		0			0
$151$	−24790.2			−0.0884784			−0.0442392	−	0.999021i	$-0.514086\pi$
$151$	−24790.2			−0.0884784			−0.0442392	+	0.999021i	$0.514086\pi$
$152$		0			0
$153$	267095.			0.922437
$154$		0			0
$155$	−57309.2	+	325017.i	−0.191600	+	1.08662i
$156$		0			0
$157$	175902.	+	147599.i	0.569535	+	0.477897i	0.881492	−	0.472199i	$-0.156540\pi$
$157$	175902.	+	147599.i	0.569535	+	0.477897i	−0.311956	+	0.950096i	$0.600984\pi$
$158$		0			0
$159$	−70932.7	−	122859.i	−0.222512	−	0.385403i
$160$		0			0
$161$	−1.01789e6	−	370480.i	−3.09481	−	1.12642i
$162$		0			0
$163$	166657.	−	288658.i	0.491307	−	0.850969i	−0.508643	−	0.860978i	$-0.669853\pi$
$163$	166657.	−	288658.i	0.491307	−	0.850969i	0.999950	+	0.0100084i	$0.00318584\pi$
$164$		0			0
$165$	7332.73	+	41586.0i	0.0209680	+	0.118915i
$166$		0			0
$167$	−205727.	+	172625.i	−0.570820	+	0.478975i	−0.881918	−	0.471403i	$-0.843748\pi$
$167$	−205727.	+	172625.i	−0.570820	+	0.478975i	0.311098	+	0.950378i	$0.399303\pi$
$168$		0			0
$169$	41629.3	−	15151.8i	0.112120	−	0.0408083i
$170$		0			0
$171$	283582.	−	216456.i	0.741633	−	0.566083i
$172$		0			0
$173$	302110.	−	109959.i	0.767450	−	0.279329i	0.0715203	−	0.997439i	$-0.477215\pi$
$173$	302110.	−	109959.i	0.767450	−	0.279329i	0.695929	+	0.718110i	$0.254993\pi$
$174$		0			0
$175$	−351644.	+	295064.i	−0.867976	+	0.728318i
$176$		0			0
$177$	−30042.4	−	170379.i	−0.0720778	−	0.408773i
$178$		0			0
$179$	−191270.	+	331289.i	−0.446184	+	0.772813i	−0.998134	−	0.0610644i	$-0.980550\pi$
$179$	−191270.	+	331289.i	−0.446184	+	0.772813i	0.551950	+	0.833877i	$0.313884\pi$
$180$		0			0
$181$	323768.	+	117842.i	0.734577	+	0.267364i	0.682101	−	0.731258i	$-0.261066\pi$
$181$	323768.	+	117842.i	0.734577	+	0.267364i	0.0524762	+	0.998622i	$0.483289\pi$
$182$		0			0
$183$	65241.0	+	113001.i	0.144010	+	0.249433i
$184$		0			0
$185$	−97533.2	−	81840.1i	−0.209519	−	0.175807i
$186$		0			0
$187$	61344.4	−	347901.i	0.128283	−	0.727532i
$188$		0			0
$189$	456223.			0.929014
$190$		0			0
$191$	−164121.			−0.325523			−0.162762	−	0.986665i	$-0.552040\pi$
$191$	−164121.			−0.325523			−0.162762	+	0.986665i	$0.552040\pi$
$192$		0			0
$193$	1004.61	−	5697.43i	0.00194135	−	0.0110100i	−0.983822	−	0.179150i	$-0.942665\pi$
$193$	1004.61	−	5697.43i	0.00194135	−	0.0110100i	0.985763	+	0.168140i	$0.0537762\pi$
$194$		0			0
$195$	−61687.3	−	51761.8i	−0.116174	−	0.0974817i
$196$		0			0
$197$	146050.	+	252966.i	0.268124	+	0.464405i	0.968377	−	0.249490i	$-0.0802629\pi$
$197$	146050.	+	252966.i	0.268124	+	0.464405i	−0.700253	+	0.713895i	$0.746930\pi$
$198$		0			0
$199$	318826.	+	116043.i	0.570717	+	0.207724i	0.611227	−	0.791455i	$-0.290676\pi$
$199$	318826.	+	116043.i	0.570717	+	0.207724i	−0.0405104	+	0.999179i	$0.512898\pi$
$200$		0			0
$201$	113001.	−	195723.i	0.197283	−	0.341705i
$202$		0			0
$203$	25090.7	+	142296.i	0.0427339	+	0.242356i
$204$		0			0
$205$	464638.	−	389877.i	0.772200	−	0.647953i
$206$		0			0
$207$	958773.	−	348965.i	1.55521	−	0.566051i
$208$		0			0
$209$	−216812.	−	419091.i	−0.343334	−	0.663656i
$210$		0			0
$211$	−1.01912e6	+	370928.i	−1.57586	+	0.573566i	−0.974298	−	0.225262i	$-0.927676\pi$
$211$	−1.01912e6	+	370928.i	−1.57586	+	0.573566i	−0.601560	+	0.798828i	$0.705454\pi$
$212$		0			0
$213$	−219549.	+	184224.i	−0.331576	+	0.278225i
$214$		0			0
$215$	−49147.1	−	278727.i	−0.0725106	−	0.411228i
$216$		0			0
$217$	1.13813e6	−	1.97130e6i	1.64075	−	2.84186i
$218$		0			0
$219$	−41665.1	−	15164.9i	−0.0587033	−	0.0213662i
$220$		0			0
$221$	336838.	+	583420.i	0.463917	+	0.803528i
$222$		0			0
$223$	780877.	+	655234.i	1.05153	+	0.882336i	0.993253	−	0.115965i	$-0.0369959\pi$
$223$	780877.	+	655234.i	1.05153	+	0.882336i	0.0582739	+	0.998301i	$0.481440\pi$
$224$		0			0
$225$	75082.0	−	425811.i	0.0988734	−	0.560739i
$226$		0			0
$227$	−514368.			−0.662536			−0.331268	−	0.943537i	$-0.607476\pi$
$227$	−514368.			−0.662536			−0.331268	+	0.943537i	$0.607476\pi$
$228$		0			0
$229$	312694.			0.394031			0.197016	−	0.980400i	$-0.436875\pi$
$229$	312694.			0.394031			0.197016	+	0.980400i	$0.436875\pi$
$230$		0			0
$231$	50574.7	−	286823.i	0.0623596	−	0.353659i
$232$		0			0
$233$	99548.8	+	83531.3i	0.120129	+	0.100800i	0.700873	−	0.713286i	$-0.252794\pi$
$233$	99548.8	+	83531.3i	0.120129	+	0.100800i	−0.580744	+	0.814086i	$0.697238\pi$
$234$		0			0
$235$	118458.	+	205176.i	0.139925	+	0.242358i
$236$		0			0
$237$	245199.	+	89245.0i	0.283561	+	0.103208i
$238$		0			0
$239$	−327393.	+	567061.i	−0.370745	+	0.642148i	−0.989680	−	0.143293i	$-0.954231\pi$
$239$	−327393.	+	567061.i	−0.370745	+	0.642148i	0.618936	+	0.785442i	$0.287564\pi$
$240$		0			0
$241$	174189.	+	987873.i	0.193187	+	1.09562i	0.914978	+	0.403505i	$0.132208\pi$
$241$	174189.	+	987873.i	0.193187	+	1.09562i	−0.721791	+	0.692111i	$0.756681\pi$
$242$		0			0
$243$	−499492.	+	419124.i	−0.542641	+	0.455330i
$244$		0			0
$245$	−1.34868e6	+	490880.i	−1.43547	+	0.522469i
$246$		0			0
$247$	830441.	+	346458.i	0.866096	+	0.361333i
$248$		0			0
$249$	−55717.9	+	20279.6i	−0.0569503	+	0.0207282i
$250$		0			0
$251$	−157086.	+	131811.i	−0.157381	+	0.132058i	−0.718078	−	0.695963i	$-0.754978\pi$
$251$	−157086.	+	131811.i	−0.157381	+	0.132058i	0.560697	+	0.828021i	$0.310533\pi$
$252$		0			0
$253$	−234336.	−	1.32899e6i	−0.230164	−	1.30533i
$254$		0			0
$255$	−82951.8	+	143677.i	−0.0798869	+	0.138368i
$256$		0			0
$257$	−1.27508e6	−	464092.i	−1.20422	−	0.438300i	−0.339525	−	0.940597i	$-0.610266\pi$
$257$	−1.27508e6	−	464092.i	−1.20422	−	0.438300i	−0.864695	+	0.502297i	$0.832488\pi$
$258$		0			0
$259$	439072.	+	760496.i	0.406712	+	0.704445i
$260$		0			0
$261$	−104259.	−	87483.5i	−0.0947352	−	0.0794923i
$262$		0			0
$263$	258032.	−	1.46337e6i	0.230030	−	1.30456i	−0.622802	−	0.782379i	$-0.714006\pi$
$263$	258032.	−	1.46337e6i	0.230030	−	1.30456i	0.852832	−	0.522185i	$-0.174883\pi$
$264$		0			0
$265$	−1.22688e6			−1.07321
$266$		0			0
$267$	38870.0			0.0333685
$268$		0			0
$269$	284877.	−	1.61562e6i	0.240036	−	1.36131i	−0.591709	−	0.806152i	$-0.701546\pi$
$269$	284877.	−	1.61562e6i	0.240036	−	1.36131i	0.831744	−	0.555159i	$-0.187342\pi$
$270$		0			0
$271$	82183.2	+	68959.9i	0.0679767	+	0.0570392i	0.676143	−	0.736770i	$-0.263650\pi$
$271$	82183.2	+	68959.9i	0.0679767	+	0.0570392i	−0.608166	+	0.793810i	$0.708095\pi$
$272$		0			0
$273$	277702.	+	480995.i	0.225514	+	0.390601i
$274$		0			0
$275$	−537391.	−	195594.i	−0.428508	−	0.155964i
$276$		0			0
$277$	−139062.	+	240862.i	−0.108895	+	0.188612i	−0.915323	−	0.402721i	$-0.868065\pi$
$277$	−139062.	+	240862.i	−0.108895	+	0.188612i	0.806428	+	0.591333i	$0.201398\pi$
$278$		0			0
$279$	372314.	+	2.11150e6i	0.286351	+	1.62398i
$280$		0			0
$281$	1.41487e6	−	1.18722e6i	1.06894	−	0.896944i	0.0739801	−	0.997260i	$-0.476430\pi$
$281$	1.41487e6	−	1.18722e6i	1.06894	−	0.896944i	0.994956	+	0.100316i	$0.0319854\pi$
$282$		0			0
$283$	−489193.	+	178052.i	−0.363090	+	0.132154i	−0.517121	−	0.855912i	$-0.672996\pi$
$283$	−489193.	+	178052.i	−0.363090	+	0.132154i	0.154032	+	0.988066i	$0.450774\pi$
$284$		0			0
$285$	28364.7	+	219771.i	0.0206855	+	0.160272i
$286$		0			0
$287$	−3.93110e6	+	1.43080e6i	−2.81714	+	1.02536i
$288$		0			0
$289$	−24464.9	+	20528.5i	−0.0172305	+	0.0144581i
$290$		0			0
$291$	6676.97	+	37867.0i	0.00462218	+	0.0262137i
$292$		0			0
$293$	−1.28637e6	+	2.22806e6i	−0.875383	+	1.51621i	−0.0190290	+	0.999819i	$0.506057\pi$
$293$	−1.28637e6	+	2.22806e6i	−0.875383	+	1.51621i	−0.856354	+	0.516389i	$0.827276\pi$
$294$		0			0
$295$	−1.40596e6	−	511729.i	−0.940630	−	0.342361i
$296$		0			0
$297$	284186.	+	492225.i	0.186944	+	0.323797i
$298$		0			0
$299$	1.97138e6	+	1.65418e6i	1.27524	+	1.07005i
$300$		0			0
$301$	−338973.	+	1.92241e6i	−0.215650	+	1.22301i
$302$		0			0
$303$	30240.7			0.0189228
$304$		0			0
$305$	1.12843e6			0.694584
$306$		0			0
$307$	319871.	−	1.81408e6i	0.193700	−	1.09852i	−0.720559	−	0.693393i	$-0.756115\pi$
$307$	319871.	−	1.81408e6i	0.193700	−	1.09852i	0.914259	−	0.405131i	$-0.132774\pi$
$308$		0			0
$309$	10768.4	+	9035.77i	0.00641587	+	0.00538355i
$310$		0			0
$311$	−366590.	−	634952.i	−0.214921	−	0.372255i	0.738327	−	0.674443i	$-0.235616\pi$
$311$	−366590.	−	634952.i	−0.214921	−	0.372255i	−0.953248	+	0.302188i	$0.902283\pi$
$312$		0			0
$313$	−1.59992e6	−	582324.i	−0.923078	−	0.335973i	−0.163615	−	0.986524i	$-0.552316\pi$
$313$	−1.59992e6	−	582324.i	−0.923078	−	0.335973i	−0.759462	+	0.650551i	$0.774538\pi$
$314$		0			0
$315$	952177.	−	1.64922e6i	0.540681	−	0.936488i
$316$		0			0
$317$	361871.	+	2.05227e6i	0.202258	+	1.14706i	0.901697	+	0.432369i	$0.142322\pi$
$317$	361871.	+	2.05227e6i	0.202258	+	1.14706i	−0.699439	+	0.714692i	$0.746567\pi$
$318$		0			0
$319$	−137896.	+	115709.i	−0.0758709	+	0.0636632i
$320$		0			0
$321$	275689.	−	100343.i	0.149334	−	0.0543530i
$322$		0			0
$323$	405843.	−	1.80884e6i	0.216447	−	0.964706i
$324$		0			0
$325$	1.02480e6	−	372995.i	0.538181	−	0.195882i
$326$		0			0
$327$	−238525.	+	200146.i	−0.123357	+	0.103509i
$328$		0			0
$329$	−283749.	−	1.60922e6i	−0.144525	−	0.819644i
$330$		0			0
$331$	745804.	−	1.29177e6i	0.374158	−	0.648060i	−0.616043	−	0.787713i	$-0.711265\pi$
$331$	745804.	−	1.29177e6i	0.374158	−	0.648060i	0.990201	+	0.139652i	$0.0445985\pi$
$332$		0			0
$333$	−777264.	−	282901.i	−0.384112	−	0.139805i
$334$		0			0
$335$	−977247.	−	1.69264e6i	−0.475765	−	0.824049i
$336$		0			0
$337$	−1.27701e6	−	1.07153e6i	−0.612517	−	0.513962i	0.282925	−	0.959142i	$-0.408695\pi$
$337$	−1.27701e6	−	1.07153e6i	−0.612517	−	0.513962i	−0.895441	+	0.445180i	$0.853140\pi$
$338$		0			0
$339$	−21914.0	+	124280.i	−0.0103567	+	0.0587358i
$340$		0			0
$341$	2.83582e6			1.32066
$342$		0			0
$343$	5.85365e6			2.68653
$344$		0			0
$345$	−110050.	+	624126.i	−0.0497786	+	0.282309i
$346$		0			0
$347$	−1.38558e6	−	1.16264e6i	−0.617745	−	0.518349i	0.279349	−	0.960190i	$-0.409881\pi$
$347$	−1.38558e6	−	1.16264e6i	−0.617745	−	0.518349i	−0.897094	+	0.441840i	$0.854326\pi$
$348$		0			0
$349$	1.76995e6	+	3.06565e6i	0.777855	+	1.34728i	0.933176	+	0.359420i	$0.117026\pi$
$349$	1.76995e6	+	3.06565e6i	0.777855	+	1.34728i	−0.155321	+	0.987864i	$0.549641\pi$
$350$		0			0
$351$	−1.01851e6	−	370707.i	−0.441263	−	0.160606i
$352$		0			0
$353$	−790522.	+	1.36922e6i	−0.337658	+	0.584841i	−0.983992	−	0.178214i	$-0.942968\pi$
$353$	−790522.	+	1.36922e6i	−0.337658	+	0.584841i	0.646334	+	0.763055i	$0.276301\pi$
$354$		0			0
$355$	430400.	+	2.44092e6i	0.181260	+	1.02798i
$356$		0			0
$357$	876551.	−	735514.i	0.364004	−	0.305436i
$358$		0			0
$359$	−3.82457e6	+	1.39203e6i	−1.56620	+	0.570050i	−0.972146	−	0.234376i	$-0.924695\pi$
$359$	−3.82457e6	+	1.39203e6i	−1.56620	+	0.570050i	−0.594053	+	0.804426i	$0.702473\pi$
$360$		0			0
$361$	−1.03501e6	−	2.24940e6i	−0.418001	−	0.908447i
$362$		0			0
$363$	−269733.	+	98174.9i	−0.107440	+	0.0391051i
$364$		0			0
$365$	−293741.	+	246478.i	−0.115407	+	0.0968380i
$366$		0			0
$367$	−455057.	−	2.58076e6i	−0.176360	−	1.00019i	−0.936562	−	0.350502i	$-0.886011\pi$
$367$	−455057.	−	2.58076e6i	−0.176360	−	1.00019i	0.760202	−	0.649687i	$-0.225100\pi$
$368$		0			0
$369$	1.97022e6	−	3.41252e6i	0.753267	−	1.30470i
$370$		0			0
$371$	7.95159e6	+	2.89414e6i	2.99929	+	1.09165i
$372$		0			0
$373$	808978.	+	1.40119e6i	0.301068	+	0.521465i	0.976378	−	0.216069i	$-0.0693235\pi$
$373$	808978.	+	1.40119e6i	0.301068	+	0.521465i	−0.675310	+	0.737534i	$0.735990\pi$
$374$		0			0
$375$	542850.	+	455506.i	0.199343	+	0.167269i
$376$		0			0
$377$	59609.4	−	338062.i	0.0216004	−	0.122502i
$378$		0			0
$379$	1.47041e6			0.525823			0.262911	−	0.964820i	$-0.415317\pi$
$379$	1.47041e6			0.525823			0.262911	+	0.964820i	$0.415317\pi$
$380$		0			0
$381$	72258.1			0.0255020
$382$		0			0
$383$	144063.	−	817022.i	0.0501829	−	0.284601i	−0.949381	−	0.314126i	$-0.898288\pi$
$383$	144063.	−	817022.i	0.0501829	−	0.284601i	0.999564	+	0.0295252i	$0.00939953\pi$
$384$		0			0
$385$	−1.92948e6	−	1.61903e6i	−0.663421	−	0.556676i
$386$		0			0
$387$	−919352.	−	1.59236e6i	−0.312036	−	0.540462i
$388$		0			0
$389$	−2.16056e6	−	786378.i	−0.723922	−	0.263486i	−0.0463321	−	0.998926i	$-0.514753\pi$
$389$	−2.16056e6	−	786378.i	−0.723922	−	0.263486i	−0.677590	+	0.735440i	$0.736975\pi$
$390$		0			0
$391$	2.65094e6	−	4.59156e6i	0.876915	−	1.51886i
$392$		0			0
$393$	−90567.4	−	513633.i	−0.0295795	−	0.167754i
$394$		0			0
$395$	1.72866e6	−	1.45052e6i	0.557465	−	0.467768i
$396$		0			0
$397$	−4.16056e6	+	1.51432e6i	−1.32488	+	0.482216i	−0.905018	−	0.425373i	$-0.860143\pi$
$397$	−4.16056e6	+	1.51432e6i	−1.32488	+	0.482216i	−0.419860	+	0.907589i	$0.637921\pi$
$398$		0			0
$399$	334593.	−	1.49128e6i	0.105217	−	0.468951i
$400$		0			0
$401$	−949863.	+	345722.i	−0.294985	+	0.107366i	−0.485273	−	0.874362i	$-0.661280\pi$
$401$	−949863.	+	345722.i	−0.294985	+	0.107366i	0.190288	+	0.981728i	$0.439058\pi$
$402$		0			0
$403$	−4.14265e6	+	3.47610e6i	−1.27062	+	1.06618i
$404$		0			0
$405$	287505.	+	1.63052e6i	0.0870978	+	0.493956i
$406$		0			0
$407$	−547006.	+	947442.i	−0.163684	+	0.283509i
$408$		0			0
$409$	2.48236e6	+	903507.i	0.733765	+	0.267069i	0.681758	−	0.731578i	$-0.261216\pi$
$409$	2.48236e6	+	903507.i	0.733765	+	0.267069i	0.0520075	+	0.998647i	$0.483438\pi$
$410$		0			0
$411$	−364592.	−	631492.i	−0.106464	−	0.184401i
$412$		0			0
$413$	7.90514e6	+	6.63320e6i	2.28052	+	1.91359i
$414$		0			0
$415$	−89043.6	+	504991.i	−0.0253795	+	0.143934i
$416$		0			0
$417$	−947854.			−0.266932
$418$		0			0
$419$	227006.			0.0631688			0.0315844	−	0.999501i	$-0.489945\pi$
$419$	227006.			0.0631688			0.0315844	+	0.999501i	$0.489945\pi$
$420$		0			0
$421$	−884758.	+	5.01771e6i	−0.243287	+	1.37975i	0.581150	+	0.813797i	$0.302603\pi$
$421$	−884758.	+	5.01771e6i	−0.243287	+	1.37975i	−0.824437	+	0.565954i	$0.808508\pi$
$422$		0			0
$423$	1.17906e6	+	989345.i	0.320393	+	0.268842i
$424$		0			0
$425$	−1.12340e6	−	1.94579e6i	−0.301691	−	0.522544i
$426$		0			0
$427$	−7.31354e6	−	2.66191e6i	−1.94114	−	0.706519i
$428$		0			0
$429$	−345968.	+	599234.i	−0.0907596	+	0.157200i
$430$		0			0
$431$	−55620.7	−	315441.i	−0.0144226	−	0.0817946i	0.976747	−	0.214396i	$-0.0687782\pi$
$431$	−55620.7	−	315441.i	−0.0144226	−	0.0817946i	−0.991169	+	0.132601i	$0.957667\pi$
$432$		0			0
$433$	−521987.	+	437999.i	−0.133795	+	0.112267i	−0.707229	−	0.706984i	$-0.750055\pi$
$433$	−521987.	+	437999.i	−0.133795	+	0.112267i	0.573434	+	0.819252i	$0.305611\pi$
$434$		0			0
$435$	79439.2	−	28913.5i	0.0201285	−	0.00732618i
$436$		0			0
$437$	−906467.	−	7.02334e6i	−0.227064	−	1.75930i
$438$		0			0
$439$	−1.60164e6	+	582948.i	−0.396646	+	0.144367i	−0.532639	−	0.846343i	$-0.678800\pi$
$439$	−1.60164e6	+	582948.i	−0.396646	+	0.144367i	0.135993	+	0.990710i	$0.456577\pi$
$440$		0			0
$441$	−7.14270e6	+	5.99344e6i	−1.74890	+	1.46750i
$442$		0			0
$443$	−604504.	−	3.42832e6i	−0.146349	−	0.829987i	−0.966274	−	0.257516i	$-0.917096\pi$
$443$	−604504.	−	3.42832e6i	−0.146349	−	0.829987i	0.819925	−	0.572471i	$-0.194015\pi$
$444$		0			0
$445$	168077.	−	291118.i	0.0402354	−	0.0696897i
$446$		0			0
$447$	−1.27095e6	−	462587.i	−0.300856	−	0.109503i
$448$		0			0
$449$	1.63439e6	+	2.83085e6i	0.382596	+	0.662675i	0.991432	−	0.130620i	$-0.0416969\pi$
$449$	1.63439e6	+	2.83085e6i	0.382596	+	0.662675i	−0.608837	+	0.793296i	$0.708364\pi$
$450$		0			0
$451$	−3.99244e6	−	3.35005e6i	−0.924265	−	0.775551i
$452$		0			0
$453$	17371.0	−	98515.8i	0.00397722	−	0.0225559i
$454$		0			0
$455$	4.80323e6			1.08769
$456$		0			0
$457$	729058.			0.163295			0.0816473	−	0.996661i	$-0.473982\pi$
$457$	729058.			0.163295			0.0816473	+	0.996661i	$0.473982\pi$
$458$		0			0
$459$	−387760.	+	2.19910e6i	−0.0859076	+	0.487206i
$460$		0			0
$461$	−1.29771e6	−	1.08891e6i	−0.284397	−	0.238637i	0.489418	−	0.872050i	$-0.337209\pi$
$461$	−1.29771e6	−	1.08891e6i	−0.284397	−	0.238637i	−0.773815	+	0.633412i	$0.781654\pi$
$462$		0			0
$463$	−426722.	−	739105.i	−0.0925109	−	0.160234i	0.816056	−	0.577973i	$-0.196156\pi$
$463$	−426722.	−	739105.i	−0.0925109	−	0.160234i	−0.908567	+	0.417739i	$0.862823\pi$
$464$		0			0
$465$	−1.25145e6	−	455492.i	−0.268400	−	0.0976897i
$466$		0			0
$467$	1.46980e6	−	2.54577e6i	0.311865	−	0.540166i	−0.666901	−	0.745146i	$-0.732380\pi$
$467$	1.46980e6	−	2.54577e6i	0.311865	−	0.540166i	0.978766	+	0.204980i	$0.0657129\pi$
$468$		0			0
$469$	2.34084e6	+	1.32756e7i	0.491405	+	2.78690i
$470$		0			0
$471$	−709814.	+	595605.i	−0.147432	+	0.123710i
$472$		0			0
$473$	−2.28527e6	+	831769.i	−0.469661	+	0.170942i
$474$		0			0
$475$	−2.76964e6	−	1.15549e6i	−0.563234	−	0.234980i
$476$		0			0
$477$	−7.48981e6	+	2.72607e6i	−1.50721	+	0.548581i
$478$		0			0
$479$	−1.28875e6	+	1.08139e6i	−0.256643	+	0.215349i	−0.762027	−	0.647546i	$-0.775796\pi$
$479$	−1.28875e6	+	1.08139e6i	−0.256643	+	0.215349i	0.505383	+	0.862895i	$0.331351\pi$
$480$		0			0
$481$	−362275.	−	2.05457e6i	−0.0713963	−	0.404909i
$482$		0			0
$483$	2.18554e6	−	3.78546e6i	0.426275	−	0.738331i
$484$		0			0
$485$	312478.	+	113733.i	0.0603204	+	0.0219548i
$486$		0			0
$487$	2.28947e6	+	3.96547e6i	0.437433	+	0.757657i	0.997491	−	0.0707969i	$-0.0225542\pi$
$487$	2.28947e6	+	3.96547e6i	0.437433	+	0.757657i	−0.560057	+	0.828454i	$0.689221\pi$
$488$		0			0
$489$	1.03034e6	+	864559.i	0.194854	+	0.163502i
$490$		0			0
$491$	−1.43302e6	+	8.12705e6i	−0.268255	+	1.52135i	0.491348	+	0.870963i	$0.336504\pi$
$491$	−1.43302e6	+	8.12705e6i	−0.268255	+	1.52135i	−0.759603	+	0.650387i	$0.774607\pi$
$492$		0			0
$493$	−707226.			−0.131051
$494$		0			0
$495$	2.37249e6			0.435202
$496$		0			0
$497$	2.96852e6	−	1.68353e7i	0.539075	−	3.05724i
$498$		0			0
$499$	3.48472e6	+	2.92403e6i	0.626494	+	0.525691i	0.899837	−	0.436226i	$-0.143685\pi$
$499$	3.48472e6	+	2.92403e6i	0.626494	+	0.525691i	−0.273343	+	0.961917i	$0.588130\pi$
$500$		0			0
$501$	−541853.	−	938517.i	−0.0964466	−	0.167050i
$502$		0			0
$503$	95513.7	+	34764.1i	0.0168324	+	0.00612649i	0.350423	−	0.936592i	$-0.386038\pi$
$503$	95513.7	+	34764.1i	0.0168324	+	0.00612649i	−0.333590	+	0.942718i	$0.608260\pi$
$504$		0			0
$505$	130763.	−	226488.i	0.0228169	−	0.0395200i
$506$		0			0
$507$	31042.6	+	176051.i	0.00536338	+	0.0304172i
$508$		0			0
$509$	3.38628e6	−	2.84143e6i	0.579333	−	0.486118i	−0.305395	−	0.952226i	$-0.598788\pi$
$509$	3.38628e6	−	2.84143e6i	0.579333	−	0.486118i	0.884728	+	0.466107i	$0.154344\pi$
$510$		0			0
$511$	2.48521e6	−	904544.i	0.421029	−	0.153242i
$512$		0			0
$513$	1.37047e6	+	2.64909e6i	0.229920	+	0.444430i
$514$		0			0
$515$	114237.	−	41578.9i	0.0189797	−	0.00690804i
$516$		0			0
$517$	1.55946e6	−	1.30854e6i	0.256594	−	0.215308i
$518$		0			0
$519$	225281.	+	1.27763e6i	0.0367118	+	0.208203i
$520$		0			0
$521$	1.07798e6	−	1.86711e6i	0.173986	−	0.301353i	−0.765824	−	0.643051i	$-0.777668\pi$
$521$	1.07798e6	−	1.86711e6i	0.173986	−	0.301353i	0.939810	+	0.341697i	$0.111002\pi$
$522$		0			0
$523$	−6.40168e6	−	2.33002e6i	−1.02339	−	0.372483i	−0.224828	−	0.974398i	$-0.572182\pi$
$523$	−6.40168e6	−	2.33002e6i	−1.02339	−	0.372483i	−0.798559	+	0.601916i	$0.794404\pi$
$524$		0			0
$525$	−926176.	−	1.60418e6i	−0.146654	−	0.254013i
$526$		0			0
$527$	8.53477e6	+	7.16153e6i	1.33865	+	1.12326i
$528$		0			0
$529$	2.39928e6	−	1.36070e7i	0.372770	−	2.11408i
$530$		0			0
$531$	−9.72014e6			−1.49602
$532$		0			0
$533$	9.93872e6			1.51535
$534$		0			0
$535$	440584.	−	2.49867e6i	0.0665494	−	0.377420i
$536$		0			0
$537$	−1.18251e6	−	992244.i	−0.176958	−	0.148485i
$538$		0			0
$539$	6.16620e6	+	1.06802e7i	0.914209	+	1.58346i
$540$		0			0
$541$	−5.67837e6	−	2.06676e6i	−0.834124	−	0.303596i	−0.110573	−	0.993868i	$-0.535269\pi$
$541$	−5.67837e6	−	2.06676e6i	−0.834124	−	0.303596i	−0.723550	+	0.690272i	$0.757491\pi$
$542$		0			0
$543$	−695173.	+	1.20408e6i	−0.101180	+	0.175248i
$544$		0			0
$545$	467600.	+	2.65189e6i	0.0674346	+	0.382441i
$546$		0			0
$547$	6.85418e6	−	5.75134e6i	0.979461	−	0.821865i	−0.00454717	−	0.999990i	$-0.501447\pi$
$547$	6.85418e6	−	5.75134e6i	0.979461	−	0.821865i	0.984008	+	0.178124i	$0.0570030\pi$
$548$		0			0
$549$	6.88881e6	−	2.50732e6i	0.975469	−	0.355042i
$550$		0			0
$551$	−750883.	+	573143.i	−0.105364	+	0.0804237i
$552$		0			0
$553$	−1.46255e7	+	5.32323e6i	−2.03375	+	0.740223i
$554$		0			0
$555$	393575.	−	330248.i	0.0542369	−	0.0455102i
$556$		0			0
$557$	−1.10291e6	−	6.25490e6i	−0.150626	−	0.854245i	−0.962676	−	0.270656i	$-0.912759\pi$
$557$	−1.10291e6	−	6.25490e6i	−0.150626	−	0.854245i	0.812050	−	0.583588i	$-0.198352\pi$
$558$		0			0
$559$	2.31882e6	−	4.01632e6i	0.313861	−	0.543624i
$560$		0			0
$561$	1.33957e6	+	487563.i	0.179704	+	0.0654069i
$562$		0			0
$563$	5.70034e6	+	9.87328e6i	0.757931	+	1.31278i	0.943904	+	0.330220i	$0.107123\pi$
$563$	5.70034e6	+	9.87328e6i	0.757931	+	1.31278i	−0.185973	+	0.982555i	$0.559544\pi$
$564$		0			0
$565$	836042.	+	701523.i	0.110181	+	0.0924529i
$566$		0			0
$567$	1.98295e6	−	1.12459e7i	0.259033	−	1.46905i
$568$		0			0
$569$	4.06612e6			0.526501			0.263250	−	0.964728i	$-0.415205\pi$
$569$	4.06612e6			0.526501			0.263250	+	0.964728i	$0.415205\pi$
$570$		0			0
$571$	8.38702e6			1.07651			0.538254	−	0.842782i	$-0.319084\pi$
$571$	8.38702e6			1.07651			0.538254	+	0.842782i	$0.319084\pi$
$572$		0			0
$573$	115003.	−	652216.i	0.0146327	−	0.0829861i
$574$		0			0
$575$	−6.57482e6	−	5.51693e6i	−0.829305	−	0.695869i
$576$		0			0
$577$	3.27046e6	+	5.66461e6i	0.408950	+	0.708321i	0.994772	−	0.102118i	$-0.0325619\pi$
$577$	3.27046e6	+	5.66461e6i	0.408950	+	0.708321i	−0.585823	+	0.810439i	$0.699229\pi$
$578$		0			0
$579$	21937.6	+	7984.62i	0.00271952	+	0.000989823i
$580$		0			0
$581$	1.76836e6	−	3.06288e6i	0.217335	−	0.376435i
$582$		0			0
$583$	1.83060e6	+	1.03819e7i	0.223061	+	1.26504i
$584$		0			0
$585$	−3.46581e6	+	2.90816e6i	−0.418711	+	0.351340i
$586$		0			0
$587$	−9.60492e6	+	3.49590e6i	−1.15053	+	0.418759i	−0.845706	−	0.533649i	$-0.820820\pi$
$587$	−9.60492e6	+	3.49590e6i	−1.15053	+	0.418759i	−0.304825	+	0.952408i	$0.598598\pi$
$588$		0			0
$589$	1.48654e7	+	686937.i	1.76558	+	0.0815884i
$590$		0			0
$591$	−1.10762e6	+	403142.i	−0.130444	+	0.0474777i
$592$		0			0
$593$	1.14454e7	−	9.60387e6i	1.33658	−	1.12153i	0.354093	−	0.935210i	$-0.384790\pi$
$593$	1.14454e7	−	9.60387e6i	1.33658	−	1.12153i	0.982490	−	0.186316i	$-0.0596547\pi$
$594$		0			0
$595$	−1.71837e6	−	9.74538e6i	−0.198987	−	1.12851i
$596$		0			0
$597$	−684561.	+	1.18570e6i	−0.0786098	+	0.136156i
$598$		0			0
$599$	−6.76284e6	−	2.46147e6i	−0.770126	−	0.280303i	−0.0730769	−	0.997326i	$-0.523282\pi$
$599$	−6.76284e6	−	2.46147e6i	−0.770126	−	0.280303i	−0.697049	+	0.717023i	$0.745504\pi$
$600$		0			0
$601$	−3.62349e6	−	6.27606e6i	−0.409204	−	0.708763i	0.585596	−	0.810603i	$-0.300860\pi$
$601$	−3.62349e6	−	6.27606e6i	−0.409204	−	0.708763i	−0.994801	+	0.101840i	$0.967527\pi$
$602$		0			0
$603$	−9.72686e6	−	8.16180e6i	−1.08938	−	0.914098i
$604$		0			0
$605$	−431065.	+	2.44469e6i	−0.0478800	+	0.271541i
$606$		0			0
$607$	−1.01993e7			−1.12357			−0.561784	−	0.827284i	$-0.689885\pi$
$607$	−1.01993e7			−1.12357			−0.561784	+	0.827284i	$0.689885\pi$
$608$		0			0
$609$	−583065.			−0.0637050
$610$		0			0
$611$	−674118.	+	3.82312e6i	−0.0730522	+	0.414299i
$612$		0			0
$613$	3.23263e6	+	2.71250e6i	0.347460	+	0.291554i	0.799769	−	0.600308i	$-0.204955\pi$
$613$	3.23263e6	+	2.71250e6i	0.347460	+	0.291554i	−0.452309	+	0.891861i	$0.649400\pi$
$614$		0			0
$615$	1.22379e6	+	2.11966e6i	0.130472	+	0.225984i
$616$		0			0
$617$	5.60837e6	+	2.04128e6i	0.593094	+	0.215869i	0.621090	−	0.783739i	$-0.286690\pi$
$617$	5.60837e6	+	2.04128e6i	0.593094	+	0.215869i	−0.0279956	+	0.999608i	$0.508912\pi$
$618$		0			0
$619$	1.87908e6	−	3.25466e6i	0.197114	−	0.341412i	−0.750477	−	0.660896i	$-0.770176\pi$
$619$	1.87908e6	−	3.25466e6i	0.197114	−	0.341412i	0.947592	+	0.319484i	$0.103510\pi$
$620$		0			0
$621$	1.48125e6	+	8.40058e6i	0.154134	+	0.874138i
$622$		0			0
$623$	−1.77607e6	+	1.49030e6i	−0.183332	+	0.153834i
$624$		0			0
$625$	158459.	−	57674.3i	0.0162262	−	0.00590585i
$626$		0			0
$627$	1.81739e6	−	567940.i	0.184620	−	0.0576944i
$628$		0			0
$629$	−4.03895e6	+	1.47006e6i	−0.407044	+	0.148152i
$630$		0			0
$631$	−1.21811e7	+	1.02212e7i	−1.21791	+	1.02194i	−0.218975	+	0.975730i	$0.570271\pi$
$631$	−1.21811e7	+	1.02212e7i	−1.21791	+	1.02194i	−0.998932	+	0.0462144i	$0.985284\pi$
$632$		0			0
$633$	−759946.	−	4.30987e6i	−0.0753830	−	0.427518i
$634$		0			0
$635$	312450.	−	541179.i	0.0307501	−	0.0532607i
$636$		0			0
$637$	−2.20994e7	−	8.04351e6i	−2.15790	−	0.785411i
$638$		0			0
$639$	8.05112e6	+	1.39450e7i	0.780018	+	1.35103i
$640$		0			0
$641$	1.11997e7	+	9.39769e6i	1.07662	+	0.903392i	0.995636	−	0.0933234i	$-0.0297490\pi$
$641$	1.11997e7	+	9.39769e6i	1.07662	+	0.903392i	0.0809848	+	0.996715i	$0.474193\pi$
$642$		0			0
$643$	−1.98506e6	+	1.12578e7i	−0.189341	+	1.07381i	0.730908	+	0.682476i	$0.239097\pi$
$643$	−1.98506e6	+	1.12578e7i	−0.189341	+	1.07381i	−0.920249	+	0.391332i	$0.872014\pi$
$644$		0			0
$645$	1.14210e6			0.108094
$646$		0			0
$647$	−7.75738e6			−0.728542			−0.364271	−	0.931293i	$-0.618682\pi$
$647$	−7.75738e6			−0.728542			−0.364271	+	0.931293i	$0.618682\pi$
$648$		0			0
$649$	−2.23245e6	+	1.26609e7i	−0.208051	+	1.17992i
$650$		0			0
$651$	7.03640e6	+	5.90424e6i	0.650726	+	0.546024i
$652$		0			0
$653$	−2.47048e6	−	4.27899e6i	−0.226724	−	0.392698i	0.730111	−	0.683328i	$-0.239468\pi$
$653$	−2.47048e6	−	4.27899e6i	−0.226724	−	0.392698i	−0.956835	+	0.290631i	$0.906135\pi$
$654$		0			0
$655$	−4.23849e6	−	1.54268e6i	−0.386018	−	0.140499i
$656$		0			0
$657$	−1.24556e6	+	2.15737e6i	−0.112577	+	0.194990i
$658$		0			0
$659$	1.49743e6	+	8.49235e6i	0.134318	+	0.761753i	0.975332	+	0.220741i	$0.0708476\pi$
$659$	1.49743e6	+	8.49235e6i	0.134318	+	0.761753i	−0.841015	+	0.541012i	$0.818041\pi$
$660$		0			0
$661$	6.32212e6	−	5.30489e6i	0.562807	−	0.472251i	−0.316443	−	0.948611i	$-0.602489\pi$
$661$	6.32212e6	−	5.30489e6i	0.562807	−	0.472251i	0.879250	+	0.476360i	$0.158044\pi$
$662$		0			0
$663$	−2.55453e6	+	929774.i	−0.225698	+	0.0821474i
$664$		0			0
$665$	−9.72220e6	−	8.95437e6i	−0.852532	−	0.785201i
$666$		0			0
$667$	−2.53868e6	+	924005.i	−0.220950	+	0.0804192i
$668$		0			0
$669$	−3.15107e6	+	2.64406e6i	−0.272203	+	0.228405i
$670$		0			0
$671$	−1.68371e6	−	9.54881e6i	−0.144365	−	0.818734i
$672$		0			0
$673$	−3.01320e6	+	5.21901e6i	−0.256442	+	0.444171i	−0.965286	−	0.261194i	$-0.915884\pi$
$673$	−3.01320e6	+	5.21901e6i	−0.256442	+	0.444171i	0.708844	+	0.705365i	$0.249217\pi$
$674$		0			0
$675$	3.39687e6	+	1.23636e6i	0.286959	+	0.104444i
$676$		0			0
$677$	−9.76511e6	−	1.69137e7i	−0.818852	−	1.41829i	−0.906529	−	0.422144i	$-0.861278\pi$
$677$	−9.76511e6	−	1.69137e7i	−0.818852	−	1.41829i	0.0876769	−	0.996149i	$-0.472056\pi$
$678$		0			0
$679$	−1.75693e6	−	1.47424e6i	−0.146245	−	0.122714i
$680$		0			0
$681$	360429.	−	2.04409e6i	0.0297818	−	0.168901i
$682$		0			0
$683$	1.44509e7			1.18534			0.592670	−	0.805445i	$-0.298074\pi$
$683$	1.44509e7			1.18534			0.592670	+	0.805445i	$0.298074\pi$
$684$		0			0
$685$	−6.30610e6			−0.513493
$686$		0			0
$687$	−219111.	+	1.24264e6i	−0.0177122	+	0.100451i
$688$		0			0
$689$	−1.54001e7	−	1.29222e7i	−1.23588	−	1.03703i
$690$		0			0
$691$	3.31460e6	+	5.74105e6i	0.264080	+	0.457400i	0.967322	−	0.253550i	$-0.0815984\pi$
$691$	3.31460e6	+	5.74105e6i	0.264080	+	0.457400i	−0.703242	+	0.710950i	$0.748265\pi$
$692$		0			0
$693$	−1.53765e7	−	5.59658e6i	−1.21625	−	0.442680i
$694$		0			0
$695$	−4.09860e6	+	7.09898e6i	−0.321865	+	0.557486i
$696$		0			0
$697$	−3.55561e6	−	2.01649e7i	−0.277225	−	1.57222i
$698$		0			0
$699$	−401708.	+	337073.i	−0.0310970	+	0.0260934i
$700$		0			0
$701$	5.21638e6	−	1.89861e6i	0.400935	−	0.145928i	−0.133679	−	0.991025i	$-0.542679\pi$
$701$	5.21638e6	−	1.89861e6i	0.400935	−	0.145928i	0.534614	+	0.845096i	$0.320457\pi$
$702$		0			0
$703$	−3.09692e6	+	4.83401e6i	−0.236342	+	0.368909i
$704$		0			0
$705$	−898373.	+	326981.i	−0.0680744	+	0.0247771i
$706$		0			0
$707$	−1.38177e6	+	1.15944e6i	−0.103965	+	0.0872372i
$708$		0			0
$709$	3.79302e6	+	2.15113e7i	0.283380	+	1.60713i	0.711015	+	0.703177i	$0.248236\pi$
$709$	3.79302e6	+	2.15113e7i	0.283380	+	1.60713i	−0.427634	+	0.903952i	$0.640653\pi$
$710$		0			0
$711$	7.33011e6	−	1.26961e7i	0.543797	−	0.941883i
$712$		0			0
$713$	3.99934e7	+	1.45564e7i	2.94622	+	1.07234i
$714$		0			0
$715$	2.99199e6	+	5.18227e6i	0.218874	+	0.379101i
$716$		0			0
$717$	−2.02408e6	−	1.69841e6i	−0.147038	−	0.123380i
$718$		0			0
$719$	458855.	−	2.60229e6i	0.0331019	−	0.187730i	−0.963773	−	0.266723i	$-0.914059\pi$
$719$	458855.	−	2.60229e6i	0.0331019	−	0.187730i	0.996875	+	0.0789925i	$0.0251703\pi$
$720$		0			0
$721$	−838473.			−0.0600691
$722$		0			0
$723$	−4.04785e6			−0.287991
$724$		0			0
$725$	−198806.	+	1.12748e6i	−0.0140470	+	0.0796645i
$726$		0			0
$727$	5.16742e6	+	4.33598e6i	0.362609	+	0.304265i	0.805829	−	0.592148i	$-0.201720\pi$
$727$	5.16742e6	+	4.33598e6i	0.362609	+	0.304265i	−0.443221	+	0.896412i	$0.646164\pi$
$728$		0			0
$729$	4.44879e6	+	7.70553e6i	0.310044	+	0.537012i
$730$		0			0
$731$	−8.97836e6	−	3.26786e6i	−0.621446	−	0.226188i
$732$		0			0
$733$	1.23506e7	−	2.13918e7i	0.849038	−	1.47058i	−0.0330302	−	0.999454i	$-0.510516\pi$
$733$	1.23506e7	−	2.13918e7i	0.849038	−	1.47058i	0.882068	−	0.471122i	$-0.156151\pi$
$734$		0			0
$735$	−1.00570e6	−	5.70362e6i	−0.0686674	−	0.389432i
$736$		0			0
$737$	−1.28651e7	+	1.07951e7i	−0.872455	+	0.732077i
$738$		0			0
$739$	102865.	−	37439.8i	0.00692877	−	0.00252187i	−0.338553	−	0.940947i	$-0.609938\pi$
$739$	102865.	−	37439.8i	0.00692877	−	0.00252187i	0.345482	+	0.938425i	$0.387715\pi$
$740$		0			0
$741$	−1.95873e6	+	3.05739e6i	−0.131047	+	0.204553i
$742$		0			0
$743$	3.75016e6	−	1.36495e6i	0.249217	−	0.0907075i	−0.214391	−	0.976748i	$-0.568777\pi$
$743$	3.75016e6	−	1.36495e6i	0.249217	−	0.0907075i	0.463608	+	0.886040i	$0.346555\pi$
$744$		0			0
$745$	−8.96024e6	+	7.51853e6i	−0.591465	+	0.496298i
$746$		0			0
$747$	578478.	+	3.28071e6i	0.0379302	+	0.215113i
$748$		0			0
$749$	−8.74975e6	+	1.51550e7i	−0.569890	+	0.987079i
$750$		0			0
$751$	1.64073e7	+	5.97177e6i	1.06154	+	0.386370i	0.813008	−	0.582253i	$-0.197829\pi$
$751$	1.64073e7	+	5.97177e6i	1.06154	+	0.386370i	0.248535	+	0.968623i	$0.420051\pi$
$752$		0			0
$753$	−413740.	−	716619.i	−0.0265913	−	0.0460576i
$754$		0			0
$755$	−662724.	−	556091.i	−0.0423121	−	0.0355041i
$756$		0			0
$757$	−1.25117e6	+	7.09575e6i	−0.0793555	+	0.450048i	0.919077	+	0.394078i	$0.128936\pi$
$757$	−1.25117e6	+	7.09575e6i	−0.0793555	+	0.450048i	−0.998432	+	0.0559694i	$0.982175\pi$
$758$		0			0
$759$	5.44558e6			0.343115
$760$		0			0
$761$	2.13199e7			1.33452			0.667259	−	0.744826i	$-0.267468\pi$
$761$	2.13199e7			1.33452			0.667259	+	0.744826i	$0.267468\pi$
$762$		0			0
$763$	3.22509e6	−	1.82904e7i	0.200554	−	1.13740i
$764$		0			0
$765$	7.14032e6	+	5.99144e6i	0.441128	+	0.370150i
$766$		0			0
$767$	−1.22582e7	−	2.12319e7i	−0.752384	−	1.30317i
$768$		0			0
$769$	1.65198e7	+	6.01272e6i	1.00737	+	0.366653i	0.792423	−	0.609972i	$-0.208819\pi$
$769$	1.65198e7	+	6.01272e6i	1.00737	+	0.366653i	0.214948	+	0.976625i	$0.431042\pi$
$770$		0			0
$771$	2.73777e6	−	4.74196e6i	0.165868	−	0.287291i
$772$		0			0
$773$	−4.47668e6	−	2.53885e7i	−0.269468	−	1.52823i	−0.756003	−	0.654568i	$-0.772851\pi$
$773$	−4.47668e6	−	2.53885e7i	−0.269468	−	1.52823i	0.486536	−	0.873661i	$-0.338260\pi$
$774$		0			0
$775$	1.38163e7	−	1.15933e7i	0.826301	−	0.693349i
$776$		0			0
$777$	−3.32987e6	+	1.21197e6i	−0.197867	+	0.0720178i
$778$		0			0
$779$	−2.01169e7	−	1.85281e7i	−1.18773	−	1.09393i
$780$		0			0
$781$	2.00130e7	−	7.28413e6i	1.17404	−	0.427317i
$782$		0			0
$783$	871646.	−	731398.i	0.0508084	−	0.0426333i
$784$		0			0
$785$	1.39151e6	+	7.89162e6i	0.0805955	+	0.457080i
$786$		0			0
$787$	8.51214e6	−	1.47435e7i	0.489894	−	0.848521i	−0.510039	−	0.860152i	$-0.670369\pi$
$787$	8.51214e6	−	1.47435e7i	0.489894	−	0.848521i	0.999932	+	0.0116305i	$0.00370220\pi$
$788$		0			0
$789$	5.63461e6	+	2.05083e6i	0.322234	+	0.117284i
$790$		0			0
$791$	−3.76367e6	−	6.51887e6i	−0.213880	−	0.370451i
$792$		0			0
$793$	1.41644e7	+	1.18853e7i	0.799862	+	0.671164i
$794$		0			0
$795$	859697.	−	4.87559e6i	0.0482423	−	0.273596i
$796$		0			0
$797$	1.09908e7			0.612889			0.306445	−	0.951888i	$-0.400861\pi$
$797$	1.09908e7			0.612889			0.306445	+	0.951888i	$0.400861\pi$
$798$		0			0
$799$	7.99797e6			0.443213
$800$		0			0
$801$	379221.	−	2.15067e6i	0.0208839	−	0.118438i
$802$		0			0
$803$	2.52399e6	+	2.11788e6i	0.138134	+	0.115908i
$804$		0			0
$805$	−1.89009e7	−	3.27373e7i	−1.02800	−	1.78054i
$806$		0			0
$807$	6.22081e6	+	2.26419e6i	0.336251	+	0.122385i
$808$		0			0
$809$	−1.47698e7	+	2.55820e7i	−0.793420	+	1.37424i	0.130418	+	0.991459i	$0.458368\pi$
$809$	−1.47698e7	+	2.55820e7i	−0.793420	+	1.37424i	−0.923838	+	0.382784i	$0.874965\pi$
$810$		0			0
$811$	514281.	+	2.91663e6i	0.0274567	+	0.155715i	0.995454	−	0.0952474i	$-0.0303642\pi$
$811$	514281.	+	2.91663e6i	0.0274567	+	0.155715i	−0.967997	+	0.250962i	$0.919253\pi$
$812$		0			0
$813$	−331633.	+	278273.i	−0.0175967	+	0.0147654i
$814$		0			0
$815$	1.09304e7	−	3.97835e6i	0.576425	−	0.209802i
$816$		0			0
$817$	−1.21809e7	+	3.80658e6i	−0.638446	+	0.199517i
$818$		0			0
$819$	2.93227e7	−	1.06726e7i	1.52754	−	0.555981i
$820$		0			0
$821$	−911234.	+	764616.i	−0.0471815	+	0.0395900i	−0.666074	−	0.745886i	$-0.732026\pi$
$821$	−911234.	+	764616.i	−0.0471815	+	0.0395900i	0.618892	+	0.785476i	$0.287582\pi$
$822$		0			0
$823$	4.78402e6	+	2.71316e7i	0.246203	+	1.39629i	0.817681	+	0.575671i	$0.195259\pi$
$823$	4.78402e6	+	2.71316e7i	0.246203	+	1.39629i	−0.571478	+	0.820617i	$0.693630\pi$
$824$		0			0
$825$	1.15385e6	−	1.99853e6i	0.0590221	−	0.102229i
$826$		0			0
$827$	−2.46063e7	−	8.95594e6i	−1.25107	−	0.455352i	−0.370307	−	0.928909i	$-0.620748\pi$
$827$	−2.46063e7	−	8.95594e6i	−1.25107	−	0.455352i	−0.880763	+	0.473557i	$0.842970\pi$
$828$		0			0
$829$	823643.	+	1.42659e6i	0.0416249	+	0.0720964i	0.886087	−	0.463518i	$-0.153413\pi$
$829$	823643.	+	1.42659e6i	0.0416249	+	0.0720964i	−0.844462	+	0.535615i	$0.820080\pi$
$830$		0			0
$831$	−859739.	−	721407.i	−0.0431881	−	0.0362391i
$832$		0			0
$833$	−8.41352e6	+	4.77155e7i	−0.420112	+	2.38258i
$834$		0			0
$835$	−9.37206e6			−0.465178
$836$		0			0
$837$	−1.79253e7			−0.884408
$838$		0			0
$839$	−4.91156e6	+	2.78548e7i	−0.240887	+	1.36614i	0.588965	+	0.808158i	$0.299535\pi$
$839$	−4.91156e6	+	2.78548e7i	−0.240887	+	1.36614i	−0.829853	+	0.557982i	$0.811576\pi$
$840$		0			0
$841$	−1.54364e7	−	1.29527e7i	−0.752585	−	0.631494i
$842$		0			0
$843$	3.72656e6	+	6.45459e6i	0.180609	+	0.312824i
$844$		0			0
$845$	1.45277e6	+	528766.i	0.0699932	+	0.0254754i
$846$		0			0
$847$	8.56071e6	−	1.48276e7i	0.410017	−	0.710170i
$848$		0			0
$849$	−364787.	−	2.06881e6i	−0.0173688	−	0.0985034i
$850$		0			0
$851$	−1.25777e7	+	1.05539e7i	−0.595356	+	0.499563i
$852$		0			0
$853$	−8.82811e6	+	3.21317e6i	−0.415427	+	0.151203i	−0.541273	−	0.840847i	$-0.682058\pi$
$853$	−8.82811e6	+	3.21317e6i	−0.415427	+	0.151203i	0.125846	+	0.992050i	$0.459835\pi$
$854$		0			0
$855$	1.24366e7	+	574702.i	0.581818	+	0.0268861i
$856$		0			0
$857$	5.05225e6	−	1.83887e6i	0.234981	−	0.0855261i	−0.221846	−	0.975082i	$-0.571208\pi$
$857$	5.05225e6	−	1.83887e6i	0.234981	−	0.0855261i	0.456827	+	0.889556i	$0.348986\pi$
$858$		0			0
$859$	3.11892e7	−	2.61708e7i	1.44219	−	1.21014i	0.504141	−	0.863621i	$-0.331809\pi$
$859$	3.11892e7	−	2.61708e7i	1.44219	−	1.21014i	0.938044	−	0.346516i	$-0.112635\pi$
$860$		0			0
$861$	−2.93139e6	−	1.66247e7i	−0.134761	−	0.764269i
$862$		0			0
$863$	−1.77322e7	+	3.07130e7i	−0.810465	+	1.40377i	0.102073	+	0.994777i	$0.467452\pi$
$863$	−1.77322e7	+	3.07130e7i	−0.810465	+	1.40377i	−0.912539	+	0.408990i	$0.865881\pi$
$864$		0			0
$865$	1.05430e7	+	3.83733e6i	0.479097	+	0.174377i
$866$		0			0
$867$	−64436.8	−	111608.i	−0.00291129	−	0.00504251i
$868$		0			0
$869$	−1.48537e7	−	1.24637e7i	−0.667243	−	0.559884i
$870$		0			0
$871$	5.56128e6	−	3.15396e7i	0.248387	−	1.40867i
$872$		0			0
$873$	2.16032e6			0.0959360
$874$		0			0
$875$	−4.22686e7			−1.86637
$876$		0			0
$877$	−2.48563e6	+	1.40967e7i	−0.109128	+	0.618898i	0.880362	+	0.474302i	$0.157299\pi$
$877$	−2.48563e6	+	1.40967e7i	−0.109128	+	0.618898i	−0.989491	+	0.144596i	$0.953812\pi$
$878$		0			0
$879$	−7.95291e6	−	6.67328e6i	−0.347179	−	0.291318i
$880$		0			0
$881$	1.72190e6	+	2.98242e6i	0.0747427	+	0.129458i	0.900974	−	0.433872i	$-0.142853\pi$
$881$	1.72190e6	+	2.98242e6i	0.0747427	+	0.129458i	−0.826232	+	0.563331i	$0.809520\pi$
$882$		0			0
$883$	9.80348e6	+	3.56817e6i	0.423134	+	0.154008i	0.544806	−	0.838562i	$-0.316603\pi$
$883$	9.80348e6	+	3.56817e6i	0.423134	+	0.154008i	−0.121672	+	0.992570i	$0.538825\pi$
$884$		0			0
$885$	3.01879e6	−	5.22870e6i	0.129561	−	0.224407i
$886$		0			0
$887$	−700086.	−	3.97039e6i	−0.0298774	−	0.169443i	0.966218	−	0.257726i	$-0.0829732\pi$
$887$	−700086.	−	3.97039e6i	−0.0298774	−	0.169443i	−0.996095	+	0.0882829i	$0.971862\pi$
$888$		0			0
$889$	−3.30166e6	+	2.77042e6i	−0.140113	+	0.117569i
$890$		0			0
$891$	1.33685e7	−	4.86575e6i	0.564144	−	0.205332i
$892$		0			0
$893$	8.49168e6	−	6.48164e6i	0.356340	−	0.271992i
$894$		0			0
$895$	−1.25447e7	+	4.56590e6i	−0.523484	+	0.190532i
$896$		0			0
$897$	−7.95508e6	+	6.67510e6i	−0.330114	+	0.276998i
$898$		0			0
$899$	−985829.	−	5.59092e6i	−0.0406820	−	0.230719i
$900$		0			0
$901$	−2.07088e7	+	3.58686e7i	−0.849850	+	1.47198i
$902$		0			0
$903$	−7.40211e6	−	2.69415e6i	−0.302090	−	0.109952i
$904$		0			0
$905$	6.01197e6	+	1.04130e7i	0.244003	+	0.422626i
$906$		0			0
$907$	−2.62126e7	−	2.19950e7i	−1.05802	−	0.887780i	−0.0641018	−	0.997943i	$-0.520418\pi$
$907$	−2.62126e7	−	2.19950e7i	−1.05802	−	0.887780i	−0.993914	+	0.110163i	$0.964863\pi$
$908$		0			0
$909$	295032.	−	1.67321e6i	0.0118430	−	0.0671647i
$910$		0			0
$911$	−1.66173e7			−0.663383			−0.331691	−	0.943388i	$-0.607619\pi$
$911$	−1.66173e7			−0.663383			−0.331691	+	0.943388i	$0.607619\pi$
$912$		0			0
$913$	4.40612e6			0.174936
$914$		0			0
$915$	−790714.	+	4.48436e6i	−0.0312224	+	0.177071i
$916$		0			0
$917$	2.38313e7	+	1.99968e7i	0.935887	+	0.785303i
$918$		0			0
$919$	1.27834e7	+	2.21414e7i	0.499294	+	0.864802i	1.00000		0.000815476i	$-0.000259574\pi$
$919$	1.27834e7	+	2.21414e7i	0.499294	+	0.864802i	−0.500706	+	0.865617i	$0.666926\pi$
$920$		0			0
$921$	6.98498e6	+	2.54232e6i	0.271341	+	0.0987601i
$922$		0			0
$923$	−2.03068e7	+	3.51725e7i	−0.784581	+	1.35893i
$924$		0			0
$925$	1.20824e6	+	6.85226e6i	0.0464300	+	0.263317i
$926$		0			0
$927$	605006.	−	507660.i	0.0231239	−	0.0194032i
$928$		0			0
$929$	−4.39625e7	+	1.60010e7i	−1.67126	+	0.608288i	−0.992071	−	0.125678i	$-0.959889\pi$
$929$	−4.39625e7	+	1.60010e7i	−1.67126	+	0.608288i	−0.679186	+	0.733966i	$0.737667\pi$
$930$		0			0
$931$	2.97362e7	+	5.74793e7i	1.12438	+	2.17339i
$932$		0			0
$933$	2.78017e6	−	1.01190e6i	0.104560	−	0.0380569i
$934$		0			0
$935$	9.44403e6	−	7.92448e6i	0.353287	−	0.296443i
$936$		0			0
$937$	3.29478e6	+	1.86856e7i	0.122596	+	0.695278i	0.982707	+	0.185170i	$0.0592836\pi$
$937$	3.29478e6	+	1.86856e7i	0.122596	+	0.695278i	−0.860110	+	0.510108i	$0.829605\pi$
$938$		0			0
$939$	3.43525e6	−	5.95002e6i	0.127143	−	0.220219i
$940$		0			0
$941$	−4.04269e7	−	1.47142e7i	−1.48832	−	0.541704i	−0.535313	−	0.844654i	$-0.679806\pi$
$941$	−4.04269e7	−	1.47142e7i	−1.48832	−	0.541704i	−0.953006	+	0.302950i	$0.902028\pi$
$942$		0			0
$943$	−3.91092e7	−	6.77391e7i	−1.43219	−	2.48062i
$944$		0			0
$945$	1.21963e7	+	1.02339e7i	0.444273	+	0.372789i
$946$		0			0
$947$	3.65216e6	−	2.07124e7i	0.132335	−	0.750509i	−0.844344	−	0.535802i	$-0.820009\pi$
$947$	3.65216e6	−	2.07124e7i	0.132335	−	0.750509i	0.976679	−	0.214707i	$-0.0688796\pi$
$948$		0			0
$949$	−6.28320e6			−0.226472
$950$		0			0
$951$	−8.40927e6			−0.301514
$952$		0			0
$953$	7.15794e6	−	4.05947e7i	0.255303	−	1.44789i	−0.539991	−	0.841671i	$-0.681573\pi$
$953$	7.15794e6	−	4.05947e7i	0.255303	−	1.44789i	0.795294	−	0.606224i	$-0.207316\pi$
$954$		0			0
$955$	−4.38751e6	−	3.68156e6i	−0.155672	−	0.130624i
$956$		0			0
$957$	−363198.	−	629077.i	−0.0128193	−	0.0222036i
$958$		0			0
$959$	4.08709e7	+	1.48758e7i	1.43505	+	0.522317i
$960$		0			0
$961$	−3.04033e7	+	5.26601e7i	−1.06197	+	1.83939i
$962$		0			0
$963$	−2.86228e6	−	1.62328e7i	−0.0994597	−	0.564064i
$964$		0			0
$965$	154661.	−	129776.i	0.00534641	−	0.00448617i
$966$		0			0
$967$	1.98039e7	−	7.20802e6i	0.681057	−	0.247885i	0.0217559	−	0.999763i	$-0.493074\pi$
$967$	1.98039e7	−	7.20802e6i	0.681057	−	0.247885i	0.659301	+	0.751879i	$0.270852\pi$
$968$		0			0
$969$	6.90394e6	+	2.88031e6i	0.236204	+	0.0985438i
$970$		0			0
$971$	−7.27897e6	+	2.64933e6i	−0.247755	+	0.0901753i	−0.462912	−	0.886404i	$-0.653196\pi$
$971$	−7.27897e6	+	2.64933e6i	−0.247755	+	0.0901753i	0.215158	+	0.976579i	$0.430973\pi$
$972$		0			0
$973$	4.33098e7	−	3.63413e7i	1.46658	−	1.23060i
$974$		0			0
$975$	764181.	+	4.33389e6i	0.0257445	+	0.146004i
$976$		0			0
$977$	2.61001e7	−	4.52067e7i	0.874793	−	1.51519i	0.0178105	−	0.999841i	$-0.494330\pi$
$977$	2.61001e7	−	4.52067e7i	0.874793	−	1.51519i	0.856983	−	0.515345i	$-0.172336\pi$
$978$		0			0
$979$	−2.71424e6	−	987901.i	−0.0905088	−	0.0329425i
$980$		0			0
$981$	8.74698e6	+	1.51502e7i	0.290192	+	0.502628i
$982$		0			0
$983$	−2.79197e7	−	2.34274e7i	−0.921566	−	0.773286i	0.0527176	−	0.998609i	$-0.483212\pi$
$983$	−2.79197e7	−	2.34274e7i	−0.921566	−	0.773286i	−0.974284	+	0.225323i	$0.927656\pi$
$984$		0			0
$985$	−1.77011e6	+	1.00388e7i	−0.0581313	+	0.329679i
$986$		0			0
$987$	6.59384e6			0.215450
$988$		0			0
$989$	−3.64986e7			−1.18655
$990$		0			0
$991$	3.60316e6	−	2.04345e7i	0.116546	−	0.660968i	−0.869426	−	0.494062i	$-0.835511\pi$
$991$	3.60316e6	−	2.04345e7i	0.116546	−	0.660968i	0.985973	−	0.166905i	$-0.0533774\pi$
$992$		0			0
$993$	4.61088e6	+	3.86898e6i	0.148392	+	0.124516i
$994$		0			0
$995$	5.92020e6	+	1.02541e7i	0.189574	+	0.328352i
$996$		0			0
$997$	3.67583e7	+	1.33789e7i	1.17116	+	0.426268i	0.853073	−	0.521792i	$-0.174736\pi$
$997$	3.67583e7	+	1.33789e7i	1.17116	+	0.426268i	0.318090	+	0.948060i	$0.396959\pi$
$998$		0			0
$999$	3.45765e6	−	5.98882e6i	0.109614	−	0.189857i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.i.a.5.3	✓	48
19.4	even	9	inner	76.6.i.a.61.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.i.a.5.3	✓	48	1.1	even	1	trivial
76.6.i.a.61.3	yes	48	19.4	even	9	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.700721 + 3.97399i) q^{3} +(26.7333 + 22.4319i) q^{5} +(-120.347 - 208.448i) q^{7} +(213.044 + 77.5416i) q^{9} +O(q^{10})\)	\(q+(-0.700721 + 3.97399i) q^{3} +(26.7333 + 22.4319i) q^{5} +(-120.347 - 208.448i) q^{7} +(213.044 + 77.5416i) q^{9} +(149.931 - 259.689i) q^{11} +(99.2976 + 563.145i) q^{13} +(-107.877 + 90.5193i) q^{15} +(1107.05 - 402.934i) q^{17} +(848.848 - 1324.97i) q^{19} +(912.697 - 332.195i) q^{21} +(3447.47 - 2892.77i) q^{23} +(-331.171 - 1878.17i) q^{25} +(-947.721 + 1641.50i) q^{27} +(-564.107 - 205.318i) q^{29} +(4728.53 + 8190.05i) q^{31} +(926.939 + 777.794i) q^{33} +(1458.60 - 8272.11i) q^{35} -3648.38 q^{37} -2307.51 q^{39} +(3018.09 - 17116.4i) q^{41} +(-6212.74 - 5213.10i) q^{43} +(3955.96 + 6851.92i) q^{45} +(6379.45 + 2321.93i) q^{47} +(-20563.4 + 35616.9i) q^{49} +(825.520 + 4681.75i) q^{51} +(-26931.2 + 22598.0i) q^{53} +(9833.47 - 3579.09i) q^{55} +(4670.62 + 4301.75i) q^{57} +(-40288.0 + 14663.6i) q^{59} +(24770.2 - 20784.7i) q^{61} +(-9475.88 - 53740.4i) q^{63} +(-9977.86 + 17282.2i) q^{65} +(-52628.6 - 19155.2i) q^{67} +(9080.13 + 15727.2i) q^{69} +(54407.3 + 45653.2i) q^{71} +(-1908.02 + 10820.9i) q^{73} +7695.87 q^{75} -72175.3 q^{77} +(11228.7 - 63680.9i) q^{79} +(36343.8 + 30496.0i) q^{81} +(7346.90 + 12725.2i) q^{83} +(38633.7 + 14061.5i) q^{85} +(1211.21 - 2097.88i) q^{87} +(-1672.67 - 9486.17i) q^{89} +(105436. - 88471.3i) q^{91} +(-35860.5 + 13052.2i) q^{93} +(52414.2 - 16379.6i) q^{95} +(8954.07 - 3259.01i) q^{97} +(52078.6 - 43699.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9}+O(q^{10}) \) 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9	\( 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9} - 237 q^{11} + 2049 q^{13} + 2085 q^{15} - 609 q^{17} - 6012 q^{19} + 3591 q^{21} + 14100 q^{23} + 11802 q^{25} - 861 q^{27} - 10575 q^{29} - 6546 q^{31} - 21234 q^{33} - 231 q^{35} + 20052 q^{37} + 72204 q^{39} - 3249 q^{41} - 34677 q^{43} - 34956 q^{45} + 4461 q^{47} - 41139 q^{49} + 12099 q^{51} - 24291 q^{53} - 61767 q^{55} - 64470 q^{57} - 20100 q^{59} + 95490 q^{61} + 86403 q^{63} - 57915 q^{65} - 64452 q^{67} - 99315 q^{69} - 115536 q^{71} - 16362 q^{73} + 236250 q^{75} + 26688 q^{77} + 29799 q^{79} + 180327 q^{81} + 52347 q^{83} + 204618 q^{85} + 69414 q^{87} + 47394 q^{89} - 249384 q^{91} - 462126 q^{93} + 412869 q^{95} - 229974 q^{97} - 692274 q^{99}+O(q^{100}) \) 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9 - 237 * q^11 + 2049 * q^13 + 2085 * q^15 - 609 * q^17 - 6012 * q^19 + 3591 * q^21 + 14100 * q^23 + 11802 * q^25 - 861 * q^27 - 10575 * q^29 - 6546 * q^31 - 21234 * q^33 - 231 * q^35 + 20052 * q^37 + 72204 * q^39 - 3249 * q^41 - 34677 * q^43 - 34956 * q^45 + 4461 * q^47 - 41139 * q^49 + 12099 * q^51 - 24291 * q^53 - 61767 * q^55 - 64470 * q^57 - 20100 * q^59 + 95490 * q^61 + 86403 * q^63 - 57915 * q^65 - 64452 * q^67 - 99315 * q^69 - 115536 * q^71 - 16362 * q^73 + 236250 * q^75 + 26688 * q^77 + 29799 * q^79 + 180327 * q^81 + 52347 * q^83 + 204618 * q^85 + 69414 * q^87 + 47394 * q^89 - 249384 * q^91 - 462126 * q^93 + 412869 * q^95 - 229974 * q^97 - 692274 * q^99

Introduction

L-functions

Modular forms

Varieties

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