LMFDB - Embedded newform 76.7.j.a.21.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(13,76)]

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, 5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, 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:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			21.6
Character	$\chi$	$=$	76.21
Dual form			76.7.j.a.29.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99278 - 2.37490i) q^{3} +(187.566 - 68.2686i) q^{5} +(84.5123 + 146.380i) q^{7} +(124.921 + 708.460i) q^{9} +O(q^{10})$	\(q+(1.99278 - 2.37490i) q^{3} +(187.566 - 68.2686i) q^{5} +(84.5123 + 146.380i) q^{7} +(124.921 + 708.460i) q^{9} +(296.296 - 513.200i) q^{11} +(-1333.33 - 1589.00i) q^{13} +(211.647 - 581.496i) q^{15} +(-24.1897 + 137.187i) q^{17} +(6582.58 + 1927.57i) q^{19} +(516.051 + 90.9937i) q^{21} +(18497.1 + 6732.39i) q^{23} +(18551.1 - 15566.2i) q^{25} +(3888.73 + 2245.16i) q^{27} +(-7132.30 + 1257.62i) q^{29} +(17986.2 - 10384.3i) q^{31} +(-628.347 - 1726.37i) q^{33} +(25844.8 + 21686.3i) q^{35} -24794.9i q^{37} -6430.76 q^{39} +(22011.1 - 26231.8i) q^{41} +(43509.8 - 15836.3i) q^{43} +(71796.4 + 124355. i) q^{45} +(-10510.6 - 59608.8i) q^{47} +(44539.9 - 77145.3i) q^{49} +(277.600 + 330.831i) q^{51} +(-86215.4 + 236875. i) q^{53} +(20539.8 - 116487. i) q^{55} +(17695.4 - 11791.8i) q^{57} +(-141003. - 24862.6i) q^{59} +(-220979. - 80429.6i) q^{61} +(-93146.6 + 78159.3i) q^{63} +(-358567. - 207019. i) q^{65} +(-426049. + 75123.9i) q^{67} +(52849.4 - 30512.6i) q^{69} +(112145. + 308115. i) q^{71} +(87636.5 + 73535.7i) q^{73} -75077.1i q^{75} +100163. q^{77} +(130394. - 155397. i) q^{79} +(-479726. + 174606. i) q^{81} +(410905. + 711708. i) q^{83} +(4828.37 + 27383.0i) q^{85} +(-11226.4 + 19444.7i) q^{87} +(-737289. - 878667. i) q^{89} +(119915. - 329463. i) q^{91} +(11180.7 - 63409.2i) q^{93} +(1.36626e6 - 87836.5i) q^{95} +(-1.56717e6 - 276335. i) q^{97} +(400595. + 145805. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9 + 1680 * q^11 - 2940 * q^13 + 2496 * q^15 - 5112 * q^17 - 15792 * q^19 - 32076 * q^21 - 19272 * q^23 + 58896 * q^25 - 124830 * q^27 + 126840 * q^29 + 30780 * q^31 - 274470 * q^33 - 226284 * q^35 + 178968 * q^39 + 83394 * q^41 + 418848 * q^43 - 95472 * q^45 - 498696 * q^47 - 744330 * q^49 + 1334538 * q^51 + 458004 * q^53 - 260136 * q^55 - 981984 * q^57 - 523362 * q^59 - 644172 * q^61 + 926832 * q^63 + 1337220 * q^65 + 1719114 * q^67 + 1333800 * q^69 - 1895220 * q^71 - 1189704 * q^73 + 1337256 * q^77 + 147432 * q^79 + 272130 * q^81 + 442800 * q^83 + 1479096 * q^85 + 1300572 * q^87 - 301596 * q^89 + 661008 * q^91 + 3576 * q^93 - 5709984 * q^95 + 1386630 * q^97 + 3822798 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$1$

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
$3$	1.99278	−	2.37490i	0.0738066	−	0.0879593i	−0.727878	−	0.685707i	$-0.759493\pi$
$3$	1.99278	−	2.37490i	0.0738066	−	0.0879593i	0.801684	+	0.597748i	$0.203938\pi$
$4$		0			0
$5$	187.566	−	68.2686i	1.50053	−	0.546149i	0.544333	−	0.838869i	$-0.316783\pi$
$5$	187.566	−	68.2686i	1.50053	−	0.546149i	0.956198	+	0.292720i	$0.0945605\pi$
$6$		0			0
$7$	84.5123	+	146.380i	0.246391	+	0.426762i	0.962522	−	0.271204i	$-0.0874218\pi$
$7$	84.5123	+	146.380i	0.246391	+	0.426762i	−0.716130	+	0.697966i	$0.754088\pi$
$8$		0			0
$9$	124.921	+	708.460i	0.171359	+	0.971824i
$10$		0			0
$11$	296.296	−	513.200i	0.222612	−	0.385575i	−0.732988	−	0.680241i	$-0.761875\pi$
$11$	296.296	−	513.200i	0.222612	−	0.385575i	0.955600	+	0.294666i	$0.0952084\pi$
$12$		0			0
$13$	−1333.33	−	1589.00i	−0.606887	−	0.723260i	0.371870	−	0.928285i	$-0.378717\pi$
$13$	−1333.33	−	1589.00i	−0.606887	−	0.723260i	−0.978757	+	0.205025i	$0.934272\pi$
$14$		0			0
$15$	211.647	−	581.496i	0.0627103	−	0.172295i
$16$		0			0
$17$	−24.1897	+	137.187i	−0.00492362	+	0.0279232i	−0.987171	−	0.159669i	$-0.948957\pi$
$17$	−24.1897	+	137.187i	−0.00492362	+	0.0279232i	0.982247	+	0.187592i	$0.0600684\pi$
$18$		0			0
$19$	6582.58	+	1927.57i	0.959700	+	0.281028i
$19$	6582.58	+	1927.57i	0.959700	+	0.281028i
$20$		0			0
$21$	516.051	+	90.9937i	0.0557231	+	0.00982548i
$22$		0			0
$23$	18497.1	+	6732.39i	1.52027	+	0.553332i	0.961215	−	0.275801i	$-0.0889431\pi$
$23$	18497.1	+	6732.39i	1.52027	+	0.553332i	0.559052	+	0.829133i	$0.311165\pi$
$24$		0			0
$25$	18551.1	−	15566.2i	1.18727	−	0.996239i
$26$		0			0
$27$	3888.73	+	2245.16i	0.197568	+	0.114066i
$28$		0			0
$29$	−7132.30	+	1257.62i	−0.292439	+	0.0515649i	−0.317943	−	0.948110i	$-0.602992\pi$
$29$	−7132.30	+	1257.62i	−0.292439	+	0.0515649i	0.0255038	+	0.999675i	$0.491881\pi$
$30$		0			0
$31$	17986.2	−	10384.3i	0.603746	−	0.348573i	−0.166768	−	0.985996i	$-0.553333\pi$
$31$	17986.2	−	10384.3i	0.603746	−	0.348573i	0.770514	+	0.637423i	$0.220000\pi$
$32$		0			0
$33$	−628.347	−	1726.37i	−0.0174847	−	0.0480388i
$34$		0			0
$35$	25844.8	+	21686.3i	0.602794	+	0.505804i
$36$		0			0
$37$		−	24794.9i		−	0.489505i	−0.969586	−	0.244752i	$-0.921293\pi$
$37$		−	24794.9i		−	0.489505i	0.969586	−	0.244752i	$-0.0787067\pi$
$38$		0			0
$39$	−6430.76			−0.108410
$40$		0			0
$41$	22011.1	−	26231.8i	0.319367	−	0.380607i	−0.582346	−	0.812941i	$-0.697865\pi$
$41$	22011.1	−	26231.8i	0.319367	−	0.380607i	0.901714	+	0.432334i	$0.142310\pi$
$42$		0			0
$43$	43509.8	−	15836.3i	0.547245	−	0.199181i	−0.0535770	−	0.998564i	$-0.517062\pi$
$43$	43509.8	−	15836.3i	0.547245	−	0.199181i	0.600822	+	0.799383i	$0.294840\pi$
$44$		0			0
$45$	71796.4	+	124355.i	0.787889	+	1.36466i
$46$		0			0
$47$	−10510.6	−	59608.8i	−0.101236	−	0.574139i	−0.992657	−	0.120963i	$-0.961402\pi$
$47$	−10510.6	−	59608.8i	−0.101236	−	0.574139i	0.891421	−	0.453176i	$-0.149709\pi$
$48$		0			0
$49$	44539.9	−	77145.3i	0.378583	−	0.655724i
$50$		0			0
$51$	277.600	+	330.831i	0.00209271	+	0.00249400i
$52$		0			0
$53$	−86215.4	+	236875.i	−0.579105	+	1.59108i	0.210588	+	0.977575i	$0.432462\pi$
$53$	−86215.4	+	236875.i	−0.579105	+	1.59108i	−0.789693	+	0.613502i	$0.789760\pi$
$54$		0			0
$55$	20539.8	−	116487.i	0.123455	−	0.700146i
$56$		0			0
$57$	17695.4	−	11791.8i	0.0955512	−	0.0636728i
$58$		0			0
$59$	−141003.	−	24862.6i	−0.686549	−	0.121057i	−0.180517	−	0.983572i	$-0.557777\pi$
$59$	−141003.	−	24862.6i	−0.686549	−	0.121057i	−0.506032	+	0.862515i	$0.668888\pi$
$60$		0			0
$61$	−220979.	−	80429.6i	−0.973555	−	0.354345i	−0.194224	−	0.980957i	$-0.562219\pi$
$61$	−220979.	−	80429.6i	−0.973555	−	0.354345i	−0.779331	+	0.626612i	$0.784441\pi$
$62$		0			0
$63$	−93146.6	+	78159.3i	−0.372517	+	0.312579i
$64$		0			0
$65$	−358567.	−	207019.i	−1.30566	−	0.753824i
$66$		0			0
$67$	−426049.	+	75123.9i	−1.41656	+	0.249778i	−0.828930	−	0.559352i	$-0.811050\pi$
$67$	−426049.	+	75123.9i	−1.41656	+	0.249778i	−0.587630	+	0.809130i	$0.699939\pi$
$68$		0			0
$69$	52849.4	−	30512.6i	0.160876	−	0.0928820i
$70$		0			0
$71$	112145.	+	308115.i	0.313332	+	0.860872i	0.991978	+	0.126407i	$0.0403445\pi$
$71$	112145.	+	308115.i	0.313332	+	0.860872i	−0.678647	+	0.734465i	$0.737433\pi$
$72$		0			0
$73$	87636.5	+	73535.7i	0.225277	+	0.189030i	0.748439	−	0.663203i	$-0.230804\pi$
$73$	87636.5	+	73535.7i	0.225277	+	0.189030i	−0.523163	+	0.852233i	$0.675248\pi$
$74$		0			0
$75$		−	75077.1i		−	0.177961i
$76$		0			0
$77$	100163.			0.219399
$78$		0			0
$79$	130394.	−	155397.i	0.264470	−	0.315183i	−0.617424	−	0.786630i	$-0.711824\pi$
$79$	130394.	−	155397.i	0.264470	−	0.315183i	0.881894	+	0.471447i	$0.156268\pi$
$80$		0			0
$81$	−479726.	+	174606.i	−0.902689	+	0.328552i
$82$		0			0
$83$	410905.	+	711708.i	0.718633	+	1.24471i	0.961542	+	0.274660i	$0.0885652\pi$
$83$	410905.	+	711708.i	0.718633	+	1.24471i	−0.242909	+	0.970049i	$0.578102\pi$
$84$		0			0
$85$	4828.37	+	27383.0i	0.00786219	+	0.0445887i
$86$		0			0
$87$	−11226.4	+	19444.7i	−0.0170483	+	0.0295286i
$88$		0			0
$89$	−737289.	−	878667.i	−1.04585	−	1.24639i	−0.968402	−	0.249394i	$-0.919769\pi$
$89$	−737289.	−	878667.i	−1.04585	−	1.24639i	−0.0774434	−	0.996997i	$-0.524676\pi$
$90$		0			0
$91$	119915.	−	329463.i	0.159128	−	0.437202i
$92$		0			0
$93$	11180.7	−	63409.2i	0.0139002	−	0.0788321i
$94$		0			0
$95$	1.36626e6	−	87836.5i	1.59354	−	0.102448i
$96$		0			0
$97$	−1.56717e6	−	276335.i	−1.71712	−	0.302775i	−0.773500	−	0.633796i	$-0.781496\pi$
$97$	−1.56717e6	−	276335.i	−1.71712	−	0.302775i	−0.943623	+	0.331021i	$0.892607\pi$
$98$		0			0
$99$	400595.	+	145805.i	0.412857	+	0.150268i
$100$		0			0
$101$	−637703.	+	535096.i	−0.618948	+	0.519359i	−0.897473	−	0.441070i	$-0.854599\pi$
$101$	−637703.	+	535096.i	−0.618948	+	0.519359i	0.278525	+	0.960429i	$0.410155\pi$
$102$		0			0
$103$	163845.	+	94595.9i	0.149941	+	0.0865687i	0.573094	−	0.819490i	$-0.305743\pi$
$103$	163845.	+	94595.9i	0.149941	+	0.0865687i	−0.423152	+	0.906059i	$0.639076\pi$
$104$		0			0
$105$	103006.	−	18162.7i	0.0889804	−	0.0156896i
$106$		0			0
$107$	327641.	−	189164.i	0.267453	−	0.154414i	−0.360277	−	0.932845i	$-0.617318\pi$
$107$	327641.	−	189164.i	0.267453	−	0.154414i	0.627729	+	0.778432i	$0.283984\pi$
$108$		0			0
$109$	664905.	+	1.82681e6i	0.513429	+	1.41063i	0.877641	+	0.479318i	$0.159116\pi$
$109$	664905.	+	1.82681e6i	0.513429	+	1.41063i	−0.364213	+	0.931316i	$0.618662\pi$
$110$		0			0
$111$	−58885.4	−	49410.7i	−0.0430565	−	0.0361287i
$112$		0			0
$113$		−	1.99438e6i		−	1.38220i	−0.722758	−	0.691101i	$-0.757126\pi$
$113$		−	1.99438e6i		−	1.38220i	0.722758	−	0.691101i	$-0.242874\pi$
$114$		0			0
$115$	3.92904e6			2.58341
$116$		0			0
$117$	959183.	−	1.14311e6i	0.598886	−	0.713724i
$118$		0			0
$119$	−22125.7	+	8053.08i	−0.0131297	+	0.00477883i
$120$		0			0
$121$	710198.	+	1.23010e6i	0.400888	+	0.694358i
$122$		0			0
$123$	−18434.7	−	104548.i	−0.00990652	−	0.0561827i
$124$		0			0
$125$	857474.	−	1.48519e6i	0.439027	−	0.760417i
$126$		0			0
$127$	1.03813e6	+	1.23720e6i	0.506805	+	0.603987i	0.957408	−	0.288737i	$-0.0932355\pi$
$127$	1.03813e6	+	1.23720e6i	0.506805	+	0.603987i	−0.450603	+	0.892724i	$0.648791\pi$
$128$		0			0
$129$	49095.8	−	134890.i	0.0228705	−	0.0628362i
$130$		0			0
$131$	284582.	−	1.61395e6i	0.126588	−	0.717918i	−0.853763	−	0.520661i	$-0.825685\pi$
$131$	284582.	−	1.61395e6i	0.126588	−	0.717918i	0.980352	−	0.197257i	$-0.0632034\pi$
$132$		0			0
$133$	274152.	+	1.12646e6i	0.116530	+	0.478807i
$134$		0			0
$135$	882668.	+	155638.i	0.358754	+	0.0632579i
$136$		0			0
$137$	−858669.	−	312530.i	−0.333937	−	0.121543i	0.169609	−	0.985511i	$-0.445749\pi$
$137$	−858669.	−	312530.i	−0.333937	−	0.121543i	−0.503546	+	0.863968i	$0.667972\pi$
$138$		0			0
$139$	−3.81921e6	+	3.20470e6i	−1.42210	+	1.19328i	−0.471890	+	0.881657i	$0.656428\pi$
$139$	−3.81921e6	+	3.20470e6i	−1.42210	+	1.19328i	−0.950206	+	0.311623i	$0.899127\pi$
$140$		0			0
$141$	−162510.	−	93825.5i	−0.0579728	−	0.0334706i
$142$		0			0
$143$	−1.21054e6	+	213450.i	−0.413971	+	0.0729943i
$144$		0			0
$145$	−1.25192e6	+	722799.i	−0.410652	+	0.237090i
$146$		0			0
$147$	−94454.4	−	259511.i	−0.0297352	−	0.0816967i
$148$		0			0
$149$	−1.50206e6	−	1.26038e6i	−0.454075	−	0.381014i	0.386870	−	0.922134i	$-0.373556\pi$
$149$	−1.50206e6	−	1.26038e6i	−0.454075	−	0.381014i	−0.840945	+	0.541120i	$0.818001\pi$
$150$		0			0
$151$		−	3.65681e6i		−	1.06212i	−0.847336	−	0.531058i	$-0.821795\pi$
$151$		−	3.65681e6i		−	1.06212i	0.847336	−	0.531058i	$-0.178205\pi$
$152$		0			0
$153$	−100213.			−0.0279802
$154$		0			0
$155$	2.66468e6	−	3.17565e6i	0.715567	−	0.852780i
$156$		0			0
$157$	−2.32443e6	+	846024.i	−0.600645	+	0.218617i	−0.624405	−	0.781101i	$-0.714658\pi$
$157$	−2.32443e6	+	846024.i	−0.600645	+	0.218617i	0.0237599	+	0.999718i	$0.492436\pi$
$158$		0			0
$159$	390746.	+	676792.i	0.0972083	+	0.168370i
$160$		0			0
$161$	577746.	+	3.27656e6i	0.138439	+	0.785129i
$162$		0			0
$163$	−174377.	+	302030.i	−0.0402650	+	0.0697410i	−0.885456	−	0.464724i	$-0.846154\pi$
$163$	−174377.	+	302030.i	−0.0402650	+	0.0697410i	0.845191	+	0.534465i	$0.179487\pi$
$164$		0			0
$165$	−235714.	−	280912.i	−0.0524726	−	0.0625344i
$166$		0			0
$167$	−395539.	+	1.08673e6i	−0.0849259	+	0.233332i	−0.974885	−	0.222708i	$-0.928510\pi$
$167$	−395539.	+	1.08673e6i	−0.0849259	+	0.233332i	0.889959	+	0.456040i	$0.150733\pi$
$168$		0			0
$169$	91010.6	−	516147.i	0.0188552	−	0.106933i
$170$		0			0
$171$	−543305.	+	4.90428e6i	−0.108656	+	0.980816i
$172$		0			0
$173$	−8.62747e6	−	1.52126e6i	−1.66627	−	0.293808i	−0.740545	−	0.672007i	$-0.765433\pi$
$173$	−8.62747e6	−	1.52126e6i	−1.66627	−	0.293808i	−0.925725	+	0.378198i	$0.876544\pi$
$174$		0			0
$175$	3.84637e6	+	1.39997e6i	0.717691	+	0.261218i
$176$		0			0
$177$	−340034.	+	285322.i	−0.0613200	+	0.0514536i
$178$		0			0
$179$	−1.13141e6	−	653219.i	−0.197270	−	0.113894i	0.398112	−	0.917337i	$-0.369666\pi$
$179$	−1.13141e6	−	653219.i	−0.197270	−	0.113894i	−0.595381	+	0.803443i	$0.702999\pi$
$180$		0			0
$181$	−5.35042e6	+	943424.i	−0.902303	+	0.159100i	−0.605506	−	0.795840i	$-0.707029\pi$
$181$	−5.35042e6	+	943424.i	−0.902303	+	0.159100i	−0.296796	+	0.954941i	$0.595918\pi$
$182$		0			0
$183$	−631374.	+	364524.i	−0.103023	+	0.0594802i
$184$		0			0
$185$	−1.69271e6	−	4.65069e6i	−0.267342	−	0.734517i
$186$		0			0
$187$	63236.9	+	53062.1i	0.00967044	+	0.00811446i
$188$		0			0
$189$			758973.i			0.112419i
$190$		0			0
$191$	−6.15444e6			−0.883259			−0.441630	−	0.897197i	$-0.645599\pi$
$191$	−6.15444e6			−0.883259			−0.441630	+	0.897197i	$0.645599\pi$
$192$		0			0
$193$	−3.66851e6	+	4.37196e6i	−0.510291	+	0.608141i	−0.958257	−	0.285910i	$-0.907704\pi$
$193$	−3.66851e6	+	4.37196e6i	−0.510291	+	0.608141i	0.447966	+	0.894051i	$0.352149\pi$
$194$		0			0
$195$	−1.20619e6	+	439019.i	−0.162672	+	0.0592078i
$196$		0			0
$197$	−1.56975e6	−	2.71888e6i	−0.205320	−	0.355624i	0.744915	−	0.667160i	$-0.232490\pi$
$197$	−1.56975e6	−	2.71888e6i	−0.205320	−	0.355624i	−0.950235	+	0.311535i	$0.899157\pi$
$198$		0			0
$199$	−1.40705e6	−	7.97976e6i	−0.178546	−	1.01258i	−0.933971	−	0.357348i	$-0.883681\pi$
$199$	−1.40705e6	−	7.97976e6i	−0.178546	−	1.01258i	0.755426	−	0.655235i	$-0.227430\pi$
$200$		0			0
$201$	−670610.	+	1.16153e6i	−0.0825813	+	0.143035i
$202$		0			0
$203$	−786856.	−	937739.i	−0.0940605	−	0.112097i
$204$		0			0
$205$	2.33774e6	−	6.42288e6i	0.271353	−	0.745535i
$206$		0			0
$207$	−2.45896e6	+	1.39454e7i	−0.277230	+	1.57225i
$208$		0			0
$209$	2.93962e6	−	2.80705e6i	0.321998	−	0.307476i
$210$		0			0
$211$	1.71385e7	+	3.02198e6i	1.82443	+	0.321695i	0.977647	−	0.210251i	$-0.0674282\pi$
$211$	1.71385e7	+	3.02198e6i	1.82443	+	0.321695i	0.846778	+	0.531947i	$0.178539\pi$
$212$		0			0
$213$	955224.	+	347673.i	0.0988477	+	0.0359776i
$214$		0			0
$215$	7.07986e6	−	5.94071e6i	0.712376	−	0.597754i
$216$		0			0
$217$	3.04011e6	+	1.75521e6i	0.297516	+	0.171771i
$218$		0			0
$219$	349280.	−	61587.5i	0.0332538	−	0.00586355i
$220$		0			0
$221$	250243.	−	144478.i	0.0231838	−	0.0133852i
$222$		0			0
$223$	−1.34163e6	−	3.68610e6i	−0.120981	−	0.332393i	0.864388	−	0.502825i	$-0.167706\pi$
$223$	−1.34163e6	−	3.68610e6i	−0.120981	−	0.332393i	−0.985369	+	0.170432i	$0.945484\pi$
$224$		0			0
$225$	1.33455e7	+	1.11982e7i	1.17162	+	0.983104i
$226$		0			0
$227$			6.15202e6i			0.525945i	0.964803	+	0.262973i	$0.0847029\pi$
$227$			6.15202e6i			0.525945i	−0.964803	+	0.262973i	$0.915297\pi$
$228$		0			0
$229$	−728925.			−0.0606983			−0.0303492	−	0.999539i	$-0.509662\pi$
$229$	−728925.			−0.0606983			−0.0303492	+	0.999539i	$0.509662\pi$
$230$		0			0
$231$	199602.	−	237876.i	0.0161931	−	0.0192981i
$232$		0			0
$233$	2.24154e7	−	8.15853e6i	1.77206	−	0.644977i	0.772105	−	0.635495i	$-0.219204\pi$
$233$	2.24154e7	−	8.15853e6i	1.77206	−	0.644977i	0.999955	−	0.00948168i	$-0.00301816\pi$
$234$		0			0
$235$	−6.04085e6	−	1.04631e7i	−0.465473	−	0.806223i
$236$		0			0
$237$	−109207.	−	619345.i	−0.00820364	−	0.0465251i
$238$		0			0
$239$	−3.89577e6	+	6.74766e6i	−0.285364	+	0.494265i	−0.972697	−	0.232077i	$-0.925448\pi$
$239$	−3.89577e6	+	6.74766e6i	−0.285364	+	0.494265i	0.687333	+	0.726342i	$0.258781\pi$
$240$		0			0
$241$	1.08206e7	+	1.28955e7i	0.773040	+	0.921273i	0.998597	−	0.0529569i	$-0.0168646\pi$
$241$	1.08206e7	+	1.28955e7i	0.773040	+	0.921273i	−0.225557	+	0.974230i	$0.572420\pi$
$242$		0			0
$243$	−1.66090e6	+	4.56328e6i	−0.115751	+	0.318023i
$244$		0			0
$245$	3.08758e6	−	1.75105e7i	0.209952	−	1.19070i
$246$		0			0
$247$	−5.71385e6	−	1.30298e7i	−0.379173	−	0.864664i
$248$		0			0
$249$	2.50908e6	+	442419.i	0.162524	+	0.0286573i
$250$		0			0
$251$	−2.65232e7	−	9.65365e6i	−1.67728	−	0.610479i	−0.684344	−	0.729160i	$-0.739911\pi$
$251$	−2.65232e7	−	9.65365e6i	−1.67728	−	0.610479i	−0.992932	+	0.118681i	$0.962133\pi$
$252$		0			0
$253$	8.93568e6	−	7.49792e6i	0.551780	−	0.462998i
$254$		0			0
$255$	74653.9	+	43101.4i	0.00450227	+	0.00259939i
$256$		0			0
$257$	1.62831e7	−	2.87115e6i	0.959262	−	0.169144i	0.327969	−	0.944688i	$-0.393636\pi$
$257$	1.62831e7	−	2.87115e6i	0.959262	−	0.169144i	0.631293	+	0.775545i	$0.282525\pi$
$258$		0			0
$259$	3.62946e6	−	2.09547e6i	0.208902	−	0.120610i
$260$		0			0
$261$	−1.78194e6	−	4.89585e6i	−0.100224	−	0.275363i
$262$		0			0
$263$	−368254.	−	309002.i	−0.0202433	−	0.0169861i	0.632610	−	0.774471i	$-0.281984\pi$
$263$	−368254.	−	309002.i	−0.0202433	−	0.0169861i	−0.652853	+	0.757485i	$0.726428\pi$
$264$		0			0
$265$			5.03156e7i			2.70374i
$266$		0			0
$267$	−3.55600e6			−0.186822
$268$		0			0
$269$	−4.53325e6	+	5.40252e6i	−0.232891	+	0.277549i	−0.869815	−	0.493378i	$-0.835762\pi$
$269$	−4.53325e6	+	5.40252e6i	−0.232891	+	0.277549i	0.636924	+	0.770927i	$0.280206\pi$
$270$		0			0
$271$	1.19906e7	−	4.36420e6i	0.602464	−	0.219279i	−0.0227385	−	0.999741i	$-0.507239\pi$
$271$	1.19906e7	−	4.36420e6i	0.602464	−	0.219279i	0.625203	+	0.780462i	$0.285016\pi$
$272$		0			0
$273$	−543478.	−	941331.i	−0.0267112	−	0.0462652i
$274$		0			0
$275$	−2.49197e6	−	1.41326e7i	−0.119824	−	0.679556i
$276$		0			0
$277$	−7.82226e6	+	1.35485e7i	−0.368038	+	0.637461i	−0.989259	−	0.146175i	$-0.953304\pi$
$277$	−7.82226e6	+	1.35485e7i	−0.368038	+	0.637461i	0.621221	+	0.783636i	$0.286637\pi$
$278$		0			0
$279$	9.60373e6	+	1.14453e7i	0.442209	+	0.527004i
$280$		0			0
$281$	1.02735e7	−	2.82261e7i	0.463018	−	1.27213i	−0.460186	−	0.887823i	$-0.652217\pi$
$281$	1.02735e7	−	2.82261e7i	0.463018	−	1.27213i	0.923204	−	0.384310i	$-0.125561\pi$
$282$		0			0
$283$	−1.38499e6	+	7.85468e6i	−0.0611065	+	0.346552i	0.938891	+	0.344215i	$0.111855\pi$
$283$	−1.38499e6	+	7.85468e6i	−0.0611065	+	0.346552i	−0.999997	+	0.00233709i	$0.999256\pi$
$284$		0			0
$285$	2.51406e6	−	3.41978e6i	0.108603	−	0.147728i
$286$		0			0
$287$	5.70001e6	+	1.00507e6i	0.241118	+	0.0425156i
$288$		0			0
$289$	2.26637e7	+	8.24890e6i	0.938937	+	0.341745i
$290$		0			0
$291$	−3.77930e6	+	3.17121e6i	−0.153367	+	0.128690i
$292$		0			0
$293$	−7.58074e6	−	4.37674e6i	−0.301376	−	0.174000i	0.341685	−	0.939815i	$-0.389002\pi$
$293$	−7.58074e6	−	4.37674e6i	−0.301376	−	0.174000i	−0.643061	+	0.765815i	$0.722336\pi$
$294$		0			0
$295$	−2.81447e7	+	4.96267e6i	−1.09630	+	0.193308i
$296$		0			0
$297$	2.30443e6	−	1.33046e6i	0.0879618	−	0.0507848i
$298$		0			0
$299$	−1.39650e7	−	3.83684e7i	−0.522427	−	1.43536i
$300$		0			0
$301$	5.99522e6	+	5.03059e6i	0.219839	+	0.184467i
$302$		0			0
$303$			2.58081e6i			0.0927744i
$304$		0			0
$305$	−4.69390e7			−1.65437
$306$		0			0
$307$	−3.22650e7	+	3.84519e7i	−1.11511	+	1.32893i	−0.176357	+	0.984326i	$0.556431\pi$
$307$	−3.22650e7	+	3.84519e7i	−1.11511	+	1.32893i	−0.938748	+	0.344605i	$0.888013\pi$
$308$		0			0
$309$	551163.	−	200607.i	0.0186812	−	0.00679940i
$310$		0			0
$311$	−1.83052e7	−	3.17055e7i	−0.608545	−	1.05403i	−0.991480	−	0.130256i	$-0.958420\pi$
$311$	−1.83052e7	−	3.17055e7i	−0.608545	−	1.05403i	0.382935	−	0.923775i	$-0.374913\pi$
$312$		0			0
$313$	4.36773e6	+	2.47706e7i	0.142437	+	0.807800i	0.969389	+	0.245528i	$0.0789614\pi$
$313$	4.36773e6	+	2.47706e7i	0.142437	+	0.807800i	−0.826952	+	0.562272i	$0.809927\pi$
$314$		0			0
$315$	−1.21354e7	+	2.10191e7i	−0.388258	+	0.672483i
$316$		0			0
$317$	−1.48632e7	−	1.77133e7i	−0.466589	−	0.556060i	0.480514	−	0.876987i	$-0.340450\pi$
$317$	−1.48632e7	−	1.77133e7i	−0.466589	−	0.556060i	−0.947104	+	0.320927i	$0.896006\pi$
$318$		0			0
$319$	−1.46787e6	+	4.03293e6i	−0.0452183	+	0.124236i
$320$		0			0
$321$	203671.	−	1.15508e6i	0.00615764	−	0.0349217i
$322$		0			0
$323$	−423668.	+	856416.i	−0.0125724	+	0.0254142i
$324$		0			0
$325$	−4.94695e7	−	8.72282e6i	−1.44108	−	0.254101i
$326$		0			0
$327$	5.66351e6	+	2.06135e6i	0.161973	+	0.0589533i
$328$		0			0
$329$	7.83723e6	−	6.57622e6i	0.220077	−	0.184667i
$330$		0			0
$331$	7.39729e6	+	4.27083e6i	0.203981	+	0.117768i	0.598511	−	0.801115i	$-0.295759\pi$
$331$	7.39729e6	+	4.27083e6i	0.203981	+	0.117768i	−0.394530	+	0.918883i	$0.629093\pi$
$332$		0			0
$333$	1.75662e7	−	3.09739e6i	0.475713	−	0.0838810i
$334$		0			0
$335$	−7.47839e7	+	4.31765e7i	−1.98918	+	1.14845i
$336$		0			0
$337$	−1.66668e7	−	4.57917e7i	−0.435474	−	1.19646i	−0.942406	−	0.334470i	$-0.891443\pi$
$337$	−1.66668e7	−	4.57917e7i	−0.435474	−	1.19646i	0.506932	−	0.861986i	$-0.330779\pi$
$338$		0			0
$339$	−4.73644e6	−	3.97435e6i	−0.121578	−	0.102016i
$340$		0			0
$341$		−	1.23074e7i		−	0.310386i
$342$		0			0
$343$	3.49422e7			0.865901
$344$		0			0
$345$	7.82971e6	−	9.33109e6i	0.190673	−	0.227235i
$346$		0			0
$347$	5.66380e7	−	2.06146e7i	1.35556	−	0.493384i	0.440883	−	0.897565i	$-0.354665\pi$
$347$	5.66380e7	−	2.06146e7i	1.35556	−	0.493384i	0.914679	+	0.404180i	$0.132443\pi$
$348$		0			0
$349$	1.92558e7	+	3.33520e7i	0.452986	+	0.784595i	0.998570	−	0.0534611i	$-0.0170253\pi$
$349$	1.92558e7	+	3.33520e7i	0.452986	+	0.784595i	−0.545584	+	0.838056i	$0.683692\pi$
$350$		0			0
$351$	−1.61740e6	−	9.17273e6i	−0.0374021	−	0.212118i
$352$		0			0
$353$	−1.03009e7	+	1.78416e7i	−0.234180	+	0.405612i	−0.959034	−	0.283291i	$-0.908574\pi$
$353$	−1.03009e7	+	1.78416e7i	−0.234180	+	0.405612i	0.724854	+	0.688903i	$0.241907\pi$
$354$		0			0
$355$	4.20692e7	+	5.01361e7i	0.940328	+	1.12064i
$356$		0			0
$357$	−24966.3	+	68594.3i	−0.000548718	+	0.00150759i
$358$		0			0
$359$	9.47367e6	−	5.37278e7i	0.204755	−	1.16122i	−0.693069	−	0.720871i	$-0.743742\pi$
$359$	9.47367e6	−	5.37278e7i	0.204755	−	1.16122i	0.897825	−	0.440353i	$-0.145147\pi$
$360$		0			0
$361$	3.96148e7	+	2.53767e7i	0.842047	+	0.539404i
$362$		0			0
$363$	4.33663e6	+	764665.i	0.0906635	+	0.0159864i
$364$		0			0
$365$	2.14578e7	+	7.81002e6i	0.441273	+	0.160610i
$366$		0			0
$367$	−4.89096e7	+	4.10400e7i	−0.989455	+	0.830251i	−0.985489	−	0.169741i	$-0.945707\pi$
$367$	−4.89096e7	+	4.10400e7i	−0.989455	+	0.830251i	−0.00396620	+	0.999992i	$0.501262\pi$
$368$		0			0
$369$	2.13338e7	+	1.23171e7i	0.424610	+	0.245148i
$370$		0			0
$371$	−4.19599e7	+	7.39866e6i	−0.821698	+	0.144888i
$372$		0			0
$373$	1.18440e7	−	6.83816e6i	0.228230	−	0.131769i	−0.381525	−	0.924359i	$-0.624601\pi$
$373$	1.18440e7	−	6.83816e6i	0.228230	−	0.131769i	0.609755	+	0.792590i	$0.291268\pi$
$374$		0			0
$375$	−1.81842e6	−	4.99607e6i	−0.0344826	−	0.0947403i
$376$		0			0
$377$	1.15081e7	+	9.65642e6i	0.214773	+	0.180216i
$378$		0			0
$379$		−	8.47237e7i		−	1.55628i	−0.628092	−	0.778139i	$-0.716164\pi$
$379$		−	8.47237e7i		−	1.55628i	0.628092	−	0.778139i	$-0.283836\pi$
$380$		0			0
$381$	5.00699e6			0.0905319
$382$		0			0
$383$	5.46108e7	−	6.50826e7i	0.972035	−	1.15843i	−0.0153170	−	0.999883i	$-0.504876\pi$
$383$	5.46108e7	−	6.50826e7i	0.972035	−	1.15843i	0.987352	−	0.158544i	$-0.0506798\pi$
$384$		0			0
$385$	1.87871e7	−	6.83796e6i	0.329214	−	0.119824i
$386$		0			0
$387$	1.66546e7	+	2.88467e7i	0.287344	+	0.497694i
$388$		0			0
$389$	3.07343e6	+	1.74303e7i	0.0522125	+	0.296112i	0.999721	−	0.0236187i	$-0.00751876\pi$
$389$	3.07343e6	+	1.74303e7i	0.0522125	+	0.296112i	−0.947509	+	0.319730i	$0.896408\pi$
$390$		0			0
$391$	−1.37103e6	+	2.37470e6i	−0.0229360	+	0.0397263i
$392$		0			0
$393$	−3.26585e6	−	3.89209e6i	−0.0538046	−	0.0641218i
$394$		0			0
$395$	1.38487e7	−	3.80491e7i	0.224708	−	0.617381i
$396$		0			0
$397$	3.63087e6	−	2.05917e7i	0.0580283	−	0.329095i	−0.941950	−	0.335754i	$-0.891009\pi$
$397$	3.63087e6	−	2.05917e7i	0.0580283	−	0.329095i	0.999978	+	0.00665981i	$0.00211990\pi$
$398$		0			0
$399$	3.22155e6	+	1.59370e6i	0.0507162	+	0.0250892i
$400$		0			0
$401$	1.06512e7	+	1.87810e6i	0.165184	+	0.0291263i	0.255628	−	0.966775i	$-0.417718\pi$
$401$	1.06512e7	+	1.87810e6i	0.165184	+	0.0291263i	−0.0904446	+	0.995901i	$0.528829\pi$
$402$		0			0
$403$	−4.04823e7	−	1.47344e7i	−0.618515	−	0.225121i
$404$		0			0
$405$	−7.80603e7	+	6.55004e7i	−1.17507	+	0.986004i
$406$		0			0
$407$	−1.27247e7	−	7.34663e6i	−0.188741	−	0.108970i
$408$		0			0
$409$	−9.49726e6	+	1.67462e6i	−0.138812	+	0.0244764i	−0.242623	−	0.970121i	$-0.578008\pi$
$409$	−9.49726e6	+	1.67462e6i	−0.138812	+	0.0244764i	0.103810	+	0.994597i	$0.466897\pi$
$410$		0			0
$411$	−2.45337e6	+	1.41645e6i	−0.0353376	+	0.0204022i
$412$		0			0
$413$	−8.27709e6	−	2.27411e7i	−0.117497	−	0.322821i
$414$		0			0
$415$	1.25659e8	+	1.05441e8i	1.75813	+	1.47524i
$416$		0			0
$417$			1.54565e7i			0.213159i
$418$		0			0
$419$	1.08867e8			1.47998			0.739990	−	0.672618i	$-0.234830\pi$
$419$	1.08867e8			1.47998			0.739990	+	0.672618i	$0.234830\pi$
$420$		0			0
$421$	5.75250e7	−	6.85556e7i	0.770922	−	0.918749i	−0.227564	−	0.973763i	$-0.573076\pi$
$421$	5.75250e7	−	6.85556e7i	0.770922	−	0.918749i	0.998486	+	0.0550145i	$0.0175205\pi$
$422$		0			0
$423$	4.09174e7	−	1.48927e7i	0.540614	−	0.196767i
$424$		0			0
$425$	1.68673e6	+	2.92151e6i	0.0219725	+	0.0380575i
$426$		0			0
$427$	−6.90215e6	−	3.91440e7i	−0.0886544	−	0.502784i
$428$		0			0
$429$	−1.90541e6	+	3.30027e6i	−0.0241333	+	0.0418001i
$430$		0			0
$431$	7.13629e7	+	8.50469e7i	0.891334	+	1.06225i	0.997691	+	0.0679223i	$0.0216370\pi$
$431$	7.13629e7	+	8.50469e7i	0.891334	+	1.06225i	−0.106357	+	0.994328i	$0.533919\pi$
$432$		0			0
$433$	3.69492e7	−	1.01517e8i	0.455136	−	1.25048i	−0.473930	−	0.880563i	$-0.657165\pi$
$433$	3.69492e7	−	1.01517e8i	0.455136	−	1.25048i	0.929066	−	0.369914i	$-0.120613\pi$
$434$		0			0
$435$	−778233.	+	4.41358e6i	−0.00945457	+	0.0536195i
$436$		0			0
$437$	1.08781e8	+	7.99709e7i	1.30350	+	0.958269i
$438$		0			0
$439$	−6.72273e7	−	1.18540e7i	−0.794606	−	0.140111i	−0.238414	−	0.971164i	$-0.576627\pi$
$439$	−6.72273e7	−	1.18540e7i	−0.794606	−	0.140111i	−0.556193	+	0.831053i	$0.687738\pi$
$440$		0			0
$441$	6.02183e7	+	2.19177e7i	0.702122	+	0.255551i
$442$		0			0
$443$	−6.33465e7	+	5.31540e7i	−0.728637	+	0.611399i	−0.929760	−	0.368167i	$-0.879985\pi$
$443$	−6.33465e7	+	5.31540e7i	−0.728637	+	0.611399i	0.201123	+	0.979566i	$0.435541\pi$
$444$		0			0
$445$	−1.98276e8	−	1.14475e8i	−2.25004	−	1.29906i
$446$		0			0
$447$	−5.98654e6	+	1.05559e6i	−0.0670275	+	0.0118188i
$448$		0			0
$449$	5.52064e6	−	3.18734e6i	0.0609889	−	0.0352119i	−0.469196	−	0.883094i	$-0.655456\pi$
$449$	5.52064e6	−	3.18734e6i	0.0609889	−	0.0352119i	0.530184	+	0.847882i	$0.322123\pi$
$450$		0			0
$451$	−6.94037e6	−	1.90685e7i	−0.0756576	−	0.207868i
$452$		0			0
$453$	−8.68456e6	−	7.28721e6i	−0.0934229	−	0.0783911i
$454$		0			0
$455$		−	6.99825e7i		−	0.742943i
$456$		0			0
$457$	−1.67794e6			−0.0175803			−0.00879017	−	0.999961i	$-0.502798\pi$
$457$	−1.67794e6			−0.0175803			−0.00879017	+	0.999961i	$0.502798\pi$
$458$		0			0
$459$	−402073.	+	479172.i	−0.00415783	+	0.00495511i
$460$		0			0
$461$	−1.50202e8	+	5.46692e7i	−1.53311	+	0.558008i	−0.964382	−	0.264515i	$-0.914788\pi$
$461$	−1.50202e8	+	5.46692e7i	−1.53311	+	0.558008i	−0.568732	+	0.822523i	$0.692566\pi$
$462$		0			0
$463$	4.22230e7	+	7.31324e7i	0.425408	+	0.736829i	0.996458	−	0.0840863i	$-0.0267971\pi$
$463$	4.22230e7	+	7.31324e7i	0.425408	+	0.736829i	−0.571050	+	0.820915i	$0.693464\pi$
$464$		0			0
$465$	−2.23172e6	−	1.26567e7i	−0.0221963	−	0.125882i
$466$		0			0
$467$	−6.56441e7	+	1.13699e8i	−0.644533	+	1.11636i	0.339876	+	0.940470i	$0.389615\pi$
$467$	−6.56441e7	+	1.13699e8i	−0.644533	+	1.11636i	−0.984409	+	0.175894i	$0.943719\pi$
$468$		0			0
$469$	−4.70030e7	−	5.60159e7i	−0.455624	−	0.542992i
$470$		0			0
$471$	−2.62286e6	+	7.20624e6i	−0.0251022	+	0.0689677i
$472$		0			0
$473$	4.76461e6	−	2.70215e7i	0.0450240	−	0.255344i
$474$		0			0
$475$	1.52119e8	−	6.67074e7i	1.41939	−	0.622434i
$476$		0			0
$477$	−1.78586e8	−	3.14896e7i	−1.64548	−	0.290143i
$478$		0			0
$479$	−5.52120e7	−	2.00955e7i	−0.502374	−	0.182849i	0.0783877	−	0.996923i	$-0.475023\pi$
$479$	−5.52120e7	−	2.00955e7i	−0.502374	−	0.182849i	−0.580761	+	0.814074i	$0.697245\pi$
$480$		0			0
$481$	−3.93991e7	+	3.30598e7i	−0.354039	+	0.297074i
$482$		0			0
$483$	8.93284e6	+	5.15737e6i	0.0792771	+	0.0457707i
$484$		0			0
$485$	−3.12814e8	+	5.51575e7i	−2.74196	+	0.483481i
$486$		0			0
$487$	−1.20821e8	+	6.97559e7i	−1.04605	+	0.603940i	−0.921542	−	0.388278i	$-0.873070\pi$
$487$	−1.20821e8	+	6.97559e7i	−1.04605	+	0.603940i	−0.124513	+	0.992218i	$0.539737\pi$
$488$		0			0
$489$	369797.	+	1.01601e6i	0.00316255	+	0.00868902i
$490$		0			0
$491$	1.05864e8	+	8.88307e7i	0.894345	+	0.750445i	0.969077	−	0.246759i	$-0.0793656\pi$
$491$	1.05864e8	+	8.88307e7i	0.894345	+	0.750445i	−0.0747319	+	0.997204i	$0.523810\pi$
$492$		0			0
$493$		−	1.00888e6i		−	0.00841973i
$494$		0			0
$495$	8.50920e7			0.701574
$496$		0			0
$497$	−3.56242e7	+	4.24552e7i	−0.290185	+	0.345830i
$498$		0			0
$499$	1.49827e8	−	5.45326e7i	1.20584	−	0.438889i	0.340579	−	0.940216i	$-0.389377\pi$
$499$	1.49827e8	−	5.45326e7i	1.20584	−	0.438889i	0.865258	+	0.501327i	$0.167155\pi$
$500$		0			0
$501$	1.79267e6	+	3.10499e6i	0.0142556	+	0.0246915i
$502$		0			0
$503$	−2.13421e7	−	1.21037e8i	−0.167700	−	0.951073i	−0.946237	−	0.323474i	$-0.895149\pi$
$503$	−2.13421e7	−	1.21037e8i	−0.167700	−	0.951073i	0.778537	−	0.627598i	$-0.215962\pi$
$504$		0			0
$505$	−8.30813e7	+	1.43901e8i	−0.645104	+	1.11735i
$506$		0			0
$507$	−1.04443e6	−	1.24471e6i	−0.00801414	−	0.00955088i
$508$		0			0
$509$	8.96389e7	−	2.46281e8i	0.679740	−	1.86757i	0.234672	−	0.972075i	$-0.424598\pi$
$509$	8.96389e7	−	2.46281e8i	0.679740	−	1.86757i	0.445068	−	0.895497i	$-0.353179\pi$
$510$		0			0
$511$	−3.35777e6	+	1.90429e7i	−0.0251645	+	0.142715i
$512$		0			0
$513$	2.12702e7	+	2.22747e7i	0.157550	+	0.164991i
$514$		0			0
$515$	3.71897e7	+	6.55755e6i	0.272271	+	0.0480087i
$516$		0			0
$517$	−3.37055e7	−	1.22678e7i	−0.243910	−	0.0887759i
$518$		0			0
$519$	−2.08055e7	+	1.74579e7i	−0.148825	+	0.124879i
$520$		0			0
$521$	1.60148e6	+	924617.i	0.0113243	+	0.00653806i	0.505651	−	0.862738i	$-0.331252\pi$
$521$	1.60148e6	+	924617.i	0.0113243	+	0.00653806i	−0.494327	+	0.869276i	$0.664586\pi$
$522$		0			0
$523$	−1.97337e8	+	3.47958e7i	−1.37944	+	0.243233i	−0.813669	−	0.581329i	$-0.802533\pi$
$523$	−1.97337e8	+	3.47958e7i	−1.37944	+	0.243233i	−0.565772	+	0.824562i	$0.691422\pi$
$524$		0			0
$525$	1.09898e7	−	6.34494e6i	0.0759469	−	0.0438480i
$526$		0			0
$527$	989513.	+	2.71866e6i	0.00676067	+	0.0185748i
$528$		0			0
$529$	1.83415e8	+	1.53903e8i	1.23899	+	1.03964i
$530$		0			0
$531$		−	1.03001e8i		−	0.687949i
$532$		0			0
$533$	−7.10305e7			−0.469098
$534$		0			0
$535$	4.85405e7	−	5.78483e7i	0.316988	−	0.377772i
$536$		0			0
$537$	−3.80598e6	+	1.38526e6i	−0.0245778	+	0.00894560i
$538$		0			0
$539$	−2.63940e7	−	4.57157e7i	−0.168554	−	0.291944i
$540$		0			0
$541$	−2.72537e7	−	1.54564e8i	−0.172121	−	0.976147i	−0.941415	−	0.337252i	$-0.890503\pi$
$541$	−2.72537e7	−	1.54564e8i	−0.172121	−	0.976147i	0.769294	−	0.638896i	$-0.220608\pi$
$542$		0			0
$543$	−8.42167e6	+	1.45868e7i	−0.0526016	+	0.0911086i
$544$		0			0
$545$	2.49428e8	+	2.97256e8i	1.54083	+	1.83629i
$546$		0			0
$547$	−8.84055e7	+	2.42892e8i	−0.540154	+	1.48406i	0.306476	+	0.951878i	$0.400850\pi$
$547$	−8.84055e7	+	2.42892e8i	−0.540154	+	1.48406i	−0.846630	+	0.532182i	$0.821372\pi$
$548$		0			0
$549$	2.93764e7	−	1.66602e8i	0.177534	−	1.00684i
$550$		0			0
$551$	−4.93731e7	−	5.46963e6i	−0.295145	−	0.0326966i
$552$		0			0
$553$	3.37669e7	+	5.95401e6i	0.199671	+	0.0352074i
$554$		0			0
$555$	−1.44181e7	−	5.24777e6i	−0.0843393	−	0.0306970i
$556$		0			0
$557$	−8.60018e7	+	7.21641e7i	−0.497671	+	0.417595i	−0.856766	−	0.515706i	$-0.827530\pi$
$557$	−8.60018e7	+	7.21641e7i	−0.497671	+	0.417595i	0.359095	+	0.933301i	$0.383085\pi$
$558$		0			0
$559$	−8.31769e7	−	4.80222e7i	−0.476176	−	0.274920i
$560$		0			0
$561$	252035.	−	44440.5i	0.00142748	−	0.000251704i
$562$		0			0
$563$	−1.23007e8	+	7.10184e7i	−0.689297	+	0.397966i	−0.803349	−	0.595509i	$-0.796950\pi$
$563$	−1.23007e8	+	7.10184e7i	−0.689297	+	0.397966i	0.114052	+	0.993475i	$0.463617\pi$
$564$		0			0
$565$	−1.36153e8	−	3.74078e8i	−0.754888	−	2.07404i
$566$		0			0
$567$	−6.61014e7	−	5.54657e7i	−0.362628	−	0.304281i
$568$		0			0
$569$			1.88963e8i			1.02575i	0.858464	+	0.512874i	$0.171419\pi$
$569$			1.88963e8i			1.02575i	−0.858464	+	0.512874i	$0.828581\pi$
$570$		0			0
$571$	1.89687e7			0.101889			0.0509447	−	0.998701i	$-0.483777\pi$
$571$	1.89687e7			0.101889			0.0509447	+	0.998701i	$0.483777\pi$
$572$		0			0
$573$	−1.22644e7	+	1.46162e7i	−0.0651904	+	0.0776909i
$574$		0			0
$575$	4.47939e8	−	1.63037e8i	2.35622	−	0.857593i
$576$		0			0
$577$	4.57382e7	+	7.92209e7i	0.238096	+	0.412394i	0.960168	−	0.279424i	$-0.0901435\pi$
$577$	4.57382e7	+	7.92209e7i	0.238096	+	0.412394i	−0.722072	+	0.691818i	$0.756810\pi$
$578$		0			0
$579$	3.07244e6	+	1.74247e7i	0.0158288	+	0.0897697i
$580$		0			0
$581$	−6.94530e7	+	1.20296e8i	−0.354130	+	0.613371i
$582$		0			0
$583$	9.60189e7	+	1.14431e8i	0.484564	+	0.577481i
$584$		0			0
$585$	1.01872e8	−	2.79891e8i	0.508847	−	1.39805i
$586$		0			0
$587$	3.96959e7	−	2.25126e8i	0.196260	−	1.11304i	−0.714354	−	0.699785i	$-0.753279\pi$
$587$	3.96959e7	−	2.25126e8i	0.196260	−	1.11304i	0.910614	−	0.413259i	$-0.135610\pi$
$588$		0			0
$589$	1.38412e8	−	3.36861e7i	0.677374	−	0.164856i
$590$		0			0
$591$	−9.58523e6	−	1.69013e6i	−0.0464344	−	0.00818764i
$592$		0			0
$593$	2.76079e8	+	1.00485e8i	1.32394	+	0.481877i	0.904720	−	0.426006i	$-0.140080\pi$
$593$	2.76079e8	+	1.00485e8i	1.32394	+	0.481877i	0.419225	+	0.907883i	$0.362302\pi$
$594$		0			0
$595$	−3.60026e6	+	3.02098e6i	−0.0170916	+	0.0143416i
$596$		0			0
$597$	−2.17551e7	−	1.25603e7i	−0.102244	−	0.0590306i
$598$		0			0
$599$	2.49111e8	−	4.39250e7i	1.15908	−	0.204376i	0.439141	−	0.898418i	$-0.355283\pi$
$599$	2.49111e8	−	4.39250e7i	1.15908	−	0.204376i	0.719935	+	0.694041i	$0.244172\pi$
$600$		0			0
$601$	1.13035e8	−	6.52606e7i	0.520700	−	0.300627i	−0.216521	−	0.976278i	$-0.569471\pi$
$601$	1.13035e8	−	6.52606e7i	0.520700	−	0.300627i	0.737221	+	0.675651i	$0.236138\pi$
$602$		0			0
$603$	−1.06445e8	−	2.92454e8i	−0.485480	−	1.33385i
$604$		0			0
$605$	2.17186e8	+	1.82241e8i	0.980768	+	0.822962i
$606$		0			0
$607$			3.00732e8i			1.34466i	0.740251	+	0.672331i	$0.234707\pi$
$607$			3.00732e8i			1.34466i	−0.740251	+	0.672331i	$0.765293\pi$
$608$		0			0
$609$	−3.79507e6			−0.0168023
$610$		0			0
$611$	−8.07044e7	+	9.61797e7i	−0.353813	+	0.421658i
$612$		0			0
$613$	2.76252e8	−	1.00547e8i	1.19929	−	0.436505i	0.336312	−	0.941751i	$-0.390820\pi$
$613$	2.76252e8	−	1.00547e8i	1.19929	−	0.436505i	0.862975	+	0.505246i	$0.168598\pi$
$614$		0			0
$615$	−1.05951e7	−	1.83513e7i	−0.0455491	−	0.0788934i
$616$		0			0
$617$	7.64889e7	+	4.33790e8i	0.325644	+	1.84682i	0.505111	+	0.863054i	$0.331452\pi$
$617$	7.64889e7	+	4.33790e8i	0.325644	+	1.84682i	−0.179467	+	0.983764i	$0.557437\pi$
$618$		0			0
$619$	−1.92713e7	+	3.33788e7i	−0.0812529	+	0.140734i	−0.903788	−	0.427980i	$-0.859225\pi$
$619$	−1.92713e7	+	3.33788e7i	−0.0812529	+	0.140734i	0.822535	+	0.568714i	$0.192559\pi$
$620$		0			0
$621$	5.68148e7	+	6.77093e7i	0.237239	+	0.282731i
$622$		0			0
$623$	6.63088e7	−	1.82182e8i	0.274225	−	0.753427i
$624$		0			0
$625$	−6.26457e6	+	3.55281e7i	−0.0256597	+	0.145523i
$626$		0			0
$627$	−808450.	−	1.25751e7i	−0.00327983	−	0.0510165i
$628$		0			0
$629$	3.40153e6	+	599782.i	0.0136686	+	0.00241013i
$630$		0			0
$631$	−9.78233e7	−	3.56048e7i	−0.389363	−	0.141716i	0.139918	−	0.990163i	$-0.455316\pi$
$631$	−9.78233e7	−	3.56048e7i	−0.389363	−	0.141716i	−0.529281	+	0.848447i	$0.677538\pi$
$632$		0			0
$633$	4.13302e7	−	3.46802e7i	0.162951	−	0.136732i
$634$		0			0
$635$	2.79180e8	+	1.61185e8i	1.09034	+	0.629510i
$636$		0			0
$637$	−1.81970e8	+	3.20863e7i	−0.704016	+	0.124137i
$638$		0			0
$639$	−2.04278e8	+	1.17940e8i	−0.782924	+	0.452021i
$640$		0			0
$641$	−1.67173e8	−	4.59305e8i	−0.634735	−	1.74392i	−0.667664	−	0.744463i	$-0.732706\pi$
$641$	−1.67173e8	−	4.59305e8i	−0.634735	−	1.74392i	0.0329287	−	0.999458i	$-0.489517\pi$
$642$		0			0
$643$	9.36839e7	+	7.86101e7i	0.352397	+	0.295696i	0.801752	−	0.597657i	$-0.203902\pi$
$643$	9.36839e7	+	7.86101e7i	0.352397	+	0.295696i	−0.449355	+	0.893353i	$0.648346\pi$
$644$		0			0
$645$		−	2.86525e7i		−	0.106778i
$646$		0			0
$647$	−4.29349e8			−1.58525			−0.792625	−	0.609709i	$-0.791286\pi$
$647$	−4.29349e8			−1.58525			−0.792625	+	0.609709i	$0.791286\pi$
$648$		0			0
$649$	−5.45381e7	+	6.49960e7i	−0.199510	+	0.237767i
$650$		0			0
$651$	1.02267e7	−	3.72222e6i	0.0370675	−	0.0134915i
$652$		0			0
$653$	−1.63126e8	−	2.82542e8i	−0.585845	−	1.01471i	−0.994769	−	0.102145i	$-0.967429\pi$
$653$	−1.63126e8	−	2.82542e8i	−0.585845	−	1.01471i	0.408924	−	0.912568i	$-0.365904\pi$
$654$		0			0
$655$	−5.68037e7	−	3.22150e8i	−0.202140	−	1.14640i
$656$		0			0
$657$	−4.11495e7	+	7.12730e7i	−0.145100	+	0.251321i
$658$		0			0
$659$	1.03667e8	+	1.23546e8i	0.362230	+	0.431689i	0.916122	−	0.400900i	$-0.131302\pi$
$659$	1.03667e8	+	1.23546e8i	0.362230	+	0.431689i	−0.553892	+	0.832588i	$0.686858\pi$
$660$		0			0
$661$	1.15617e8	−	3.17654e8i	0.400328	−	1.09989i	−0.561795	−	0.827277i	$-0.689889\pi$
$661$	1.15617e8	−	3.17654e8i	0.400328	−	1.09989i	0.962123	−	0.272616i	$-0.0878889\pi$
$662$		0			0
$663$	155558.	−	882215.i	0.000533768	−	0.00302715i
$664$		0			0
$665$	1.28323e8	+	1.92570e8i	0.436356	+	0.654822i
$666$		0			0
$667$	−1.40394e8	−	2.47552e7i	−0.473118	−	0.0834235i
$668$		0			0
$669$	−1.14277e7	−	4.15934e6i	−0.0381663	−	0.0138914i
$670$		0			0
$671$	−1.06752e8	+	8.95752e7i	−0.353351	+	0.296497i
$672$		0			0
$673$	−1.44013e8	−	8.31457e7i	−0.472449	−	0.272769i	0.244815	−	0.969570i	$-0.421273\pi$
$673$	−1.44013e8	−	8.31457e7i	−0.472449	−	0.272769i	−0.717265	+	0.696801i	$0.754606\pi$
$674$		0			0
$675$	1.07089e8	−	1.88827e7i	0.348203	−	0.0613976i
$676$		0			0
$677$	−4.81415e8	+	2.77945e8i	−1.55151	+	0.895763i	−0.553488	+	0.832857i	$0.686704\pi$
$677$	−4.81415e8	+	2.77945e8i	−1.55151	+	0.895763i	−0.998019	+	0.0629064i	$0.979963\pi$
$678$		0			0
$679$	−9.19955e7	−	2.52756e8i	−0.293871	−	0.807405i
$680$		0			0
$681$	1.46105e7	+	1.22596e7i	0.0462618	+	0.0388182i
$682$		0			0
$683$			3.39407e8i			1.06527i	0.846346	+	0.532634i	$0.178798\pi$
$683$			3.39407e8i			1.06527i	−0.846346	+	0.532634i	$0.821202\pi$
$684$		0			0
$685$	−1.82394e8			−0.567463
$686$		0			0
$687$	−1.45259e6	+	1.73113e6i	−0.00447994	+	0.00533898i
$688$		0			0
$689$	4.91348e8	−	1.78836e8i	1.50221	−	0.546761i
$690$		0			0
$691$	−1.93924e8	−	3.35886e8i	−0.587757	−	1.01802i	−0.994526	−	0.104494i	$-0.966678\pi$
$691$	−1.93924e8	−	3.35886e8i	−0.587757	−	1.01802i	0.406769	−	0.913531i	$-0.366656\pi$
$692$		0			0
$693$	1.25124e7	+	7.09612e7i	0.0375959	+	0.213217i
$694$		0			0
$695$	−4.97575e8	+	8.61825e8i	−1.48219	+	2.56723i
$696$		0			0
$697$	3.06622e6	+	3.65418e6i	0.00905534	+	0.0107917i
$698$		0			0
$699$	2.52932e7	−	6.94925e7i	0.0740580	−	0.203473i
$700$		0			0
$701$	−8.25117e7	+	4.67947e8i	−0.239531	+	1.35845i	0.593327	+	0.804961i	$0.297814\pi$
$701$	−8.25117e7	+	4.67947e8i	−0.239531	+	1.35845i	−0.832858	+	0.553486i	$0.813297\pi$
$702$		0			0
$703$	4.77938e7	−	1.63214e8i	0.137564	−	0.469778i
$704$		0			0
$705$	−3.68868e7	−	6.50414e6i	−0.105270	−	0.0185619i
$706$		0			0
$707$	−1.32221e8	−	4.81244e7i	−0.374146	−	0.136178i
$708$		0			0
$709$	1.86887e8	−	1.56817e8i	0.524374	−	0.440002i	−0.341779	−	0.939780i	$-0.611030\pi$
$709$	1.86887e8	−	1.56817e8i	0.524374	−	0.440002i	0.866153	+	0.499778i	$0.166585\pi$
$710$		0			0
$711$	1.26382e8	+	7.29665e7i	0.351621	+	0.203009i
$712$		0			0
$713$	4.02604e8	−	7.09899e7i	1.11073	−	0.195852i
$714$		0			0
$715$	−2.12484e8	+	1.22678e8i	−0.581311	+	0.335620i
$716$		0			0
$717$	8.26164e6	+	2.26987e7i	0.0224134	+	0.0615804i
$718$		0			0
$719$	−9.71038e7	−	8.14798e7i	−0.261246	−	0.219211i	0.502751	−	0.864431i	$-0.332321\pi$
$719$	−9.71038e7	−	8.14798e7i	−0.261246	−	0.219211i	−0.763997	+	0.645220i	$0.776766\pi$
$720$		0			0
$721$			3.19781e7i			0.0853191i
$722$		0			0
$723$	5.21888e7			0.138090
$724$		0			0
$725$	−1.12736e8	+	1.34353e8i	−0.295834	+	0.352561i
$726$		0			0
$727$	3.26275e8	−	1.18754e8i	0.849143	−	0.309063i	0.119452	−	0.992840i	$-0.461886\pi$
$727$	3.26275e8	−	1.18754e8i	0.849143	−	0.309063i	0.729691	+	0.683777i	$0.239664\pi$
$728$		0			0
$729$	−1.78555e8	−	3.09266e8i	−0.460881	−	0.798269i
$730$		0			0
$731$	1.12004e6	+	6.35205e6i	0.00286735	+	0.0162615i
$732$		0			0
$733$	−3.37119e7	+	5.83907e7i	−0.0855995	+	0.148263i	−0.905647	−	0.424033i	$-0.860614\pi$
$733$	−3.37119e7	+	5.83907e7i	−0.0855995	+	0.148263i	0.820047	+	0.572296i	$0.193947\pi$
$734$		0			0
$735$	−3.54329e7	−	4.22273e7i	−0.0892370	−	0.106349i
$736$		0			0
$737$	−8.76831e7	+	2.40907e8i	−0.219035	+	0.601794i
$738$		0			0
$739$	8.22515e7	−	4.66471e8i	0.203803	−	1.15582i	−0.695510	−	0.718517i	$-0.744821\pi$
$739$	8.22515e7	−	4.66471e8i	0.203803	−	1.15582i	0.899312	−	0.437307i	$-0.144068\pi$
$740$		0			0
$741$	−4.23310e7	−	1.23957e7i	−0.104041	−	0.0304661i
$742$		0			0
$743$	−2.26825e8	−	3.99953e7i	−0.552998	−	0.0975085i	−0.109836	−	0.993950i	$-0.535032\pi$
$743$	−2.26825e8	−	3.99953e7i	−0.552998	−	0.0975085i	−0.443163	+	0.896441i	$0.646144\pi$
$744$		0			0
$745$	−3.67780e8	−	1.33861e8i	−0.889444	−	0.323731i
$746$		0			0
$747$	−4.52886e8	+	3.80017e8i	−1.08649	+	0.911676i
$748$		0			0
$749$	5.53793e7	+	3.19733e7i	0.131796	+	0.0760925i
$750$		0			0
$751$	−7.60461e8	+	1.34090e8i	−1.79538	+	0.316575i	−0.969098	−	0.246676i	$-0.920662\pi$
$751$	−7.60461e8	+	1.34090e8i	−1.79538	+	0.316575i	−0.826286	+	0.563250i	$0.809551\pi$
$752$		0			0
$753$	−7.57813e7	+	4.37524e7i	−0.177491	+	0.102475i
$754$		0			0
$755$	−2.49645e8	−	6.85895e8i	−0.580073	−	1.59374i
$756$		0			0
$757$	4.90420e8	+	4.11511e8i	1.13053	+	0.948623i	0.999088	−	0.0427013i	$-0.0135964\pi$
$757$	4.90420e8	+	4.11511e8i	1.13053	+	0.948623i	0.131437	+	0.991324i	$0.458041\pi$
$758$		0			0
$759$		−	3.61631e7i		−	0.0827065i
$760$		0			0
$761$	3.70113e8			0.839810			0.419905	−	0.907568i	$-0.362063\pi$
$761$	3.70113e8			0.839810			0.419905	+	0.907568i	$0.362063\pi$
$762$		0			0
$763$	−2.11215e8	+	2.51716e8i	−0.475501	+	0.566680i
$764$		0			0
$765$	−1.87966e7	+	6.84140e6i	−0.0419851	+	0.0152813i
$766$		0			0
$767$	1.48497e8	+	2.57204e8i	0.329102	+	0.570022i
$768$		0			0
$769$	−7.42007e7	−	4.20813e8i	−0.163166	−	0.925359i	−0.950935	−	0.309389i	$-0.899875\pi$
$769$	−7.42007e7	−	4.20813e8i	−0.163166	−	0.925359i	0.787770	−	0.615970i	$-0.211236\pi$
$770$		0			0
$771$	2.56299e7	−	4.43923e7i	0.0559221	−	0.0968600i
$772$		0			0
$773$	2.24231e8	+	2.67228e8i	0.485464	+	0.578553i	0.952058	−	0.305919i	$-0.0989635\pi$
$773$	2.24231e8	+	2.67228e8i	0.485464	+	0.578553i	−0.466594	+	0.884472i	$0.654519\pi$
$774$		0			0
$775$	1.72019e8	−	4.72618e8i	0.369548	−	1.01533i
$776$		0			0
$777$	2.25618e6	−	1.27954e7i	0.00480962	−	0.0272767i
$778$		0			0
$779$	1.95454e8	−	1.30245e8i	0.413458	−	0.275518i
$780$		0			0
$781$	1.91353e8	+	3.37407e7i	0.401682	+	0.0708273i
$782$		0			0
$783$	−3.05591e7	−	1.11226e7i	−0.0636584	−	0.0231698i
$784$		0			0
$785$	−3.78228e8	+	3.17371e8i	−0.781889	+	0.656083i
$786$		0			0
$787$	−6.43943e8	−	3.71781e8i	−1.32106	−	0.762716i	−0.337165	−	0.941446i	$-0.609468\pi$
$787$	−6.43943e8	−	3.71781e8i	−1.32106	−	0.762716i	−0.983898	+	0.178730i	$0.942801\pi$
$788$		0			0
$789$	−1.46770e6	+	258795.i	−0.00298817	+	0.000526896i
$790$		0			0
$791$	2.91936e8	−	1.68549e8i	0.589872	−	0.340563i
$792$		0			0
$793$	1.66835e8	+	4.58375e8i	0.334555	+	0.919181i
$794$		0			0
$795$	1.19494e8	+	1.00268e8i	0.237819	+	0.199554i
$796$		0			0
$797$			2.42302e8i			0.478610i	0.970944	+	0.239305i	$0.0769195\pi$
$797$			2.42302e8i			0.478610i	−0.970944	+	0.239305i	$0.923080\pi$
$798$		0			0
$799$	8.43179e6			0.0165303
$800$		0			0
$801$	5.30397e8	−	6.32103e8i	1.03206	−	1.22996i
$802$		0			0
$803$	6.37049e7	−	2.31867e7i	0.123034	−	0.0447808i
$804$		0			0
$805$	3.32052e8	+	5.75131e8i	0.636530	+	1.10250i
$806$		0			0
$807$	3.79668e6	+	2.15320e7i	0.00722410	+	0.0409699i
$808$		0			0
$809$	3.18836e8	−	5.52240e8i	0.602173	−	1.04299i	−0.390318	−	0.920680i	$-0.627635\pi$
$809$	3.18836e8	−	5.52240e8i	0.602173	−	1.04299i	0.992491	−	0.122315i	$-0.0390317\pi$
$810$		0			0
$811$	5.76612e8	+	6.87179e8i	1.08099	+	1.28827i	0.955118	+	0.296224i	$0.0957276\pi$
$811$	5.76612e8	+	6.87179e8i	1.08099	+	1.28827i	0.125869	+	0.992047i	$0.459828\pi$
$812$		0			0
$813$	1.35300e7	−	3.71733e7i	0.0251782	−	0.0691766i
$814$		0			0
$815$	−1.20881e7	+	6.85553e7i	−0.0223299	+	0.126639i
$816$		0			0
$817$	3.16932e8	−	2.03754e7i	0.581166	−	0.0373629i
$818$		0			0
$819$	2.48391e8	+	4.37980e7i	0.452151	+	0.0797264i
$820$		0			0
$821$	2.80064e8	+	1.01935e8i	0.506090	+	0.184202i	0.582431	−	0.812880i	$-0.302101\pi$
$821$	2.80064e8	+	1.01935e8i	0.506090	+	0.184202i	−0.0763409	+	0.997082i	$0.524324\pi$
$822$		0			0
$823$	5.30234e8	−	4.44919e8i	0.951192	−	0.798145i	−0.0283057	−	0.999599i	$-0.509011\pi$
$823$	5.30234e8	−	4.44919e8i	0.951192	−	0.798145i	0.979498	+	0.201454i	$0.0645667\pi$
$824$		0			0
$825$	−3.85296e7	−	2.22451e7i	−0.0686171	−	0.0396161i
$826$		0			0
$827$	−6.69801e7	+	1.18104e7i	−0.118421	+	0.0208808i	−0.232545	−	0.972586i	$-0.574705\pi$
$827$	−6.69801e7	+	1.18104e7i	−0.118421	+	0.0208808i	0.114123	+	0.993467i	$0.463594\pi$
$828$		0			0
$829$	7.36993e8	−	4.25503e8i	1.29360	−	0.746860i	0.314309	−	0.949321i	$-0.398227\pi$
$829$	7.36993e8	−	4.25503e8i	1.29360	−	0.746860i	0.979290	+	0.202461i	$0.0648938\pi$
$830$		0			0
$831$	1.65884e7	+	4.55763e7i	0.0289070	+	0.0794212i
$832$		0			0
$833$	9.50591e6	+	7.97640e6i	0.0164459	+	0.0137998i
$834$		0			0
$835$			2.30838e8i			0.396504i
$836$		0			0
$837$	9.32579e7			0.159041
$838$		0			0
$839$	3.50452e8	−	4.17653e8i	0.593394	−	0.707179i	−0.382861	−	0.923806i	$-0.625061\pi$
$839$	3.50452e8	−	4.17653e8i	0.593394	−	0.707179i	0.976254	+	0.216627i	$0.0695055\pi$
$840$		0			0
$841$	−5.09663e8	+	1.85502e8i	−0.856831	+	0.311861i
$842$		0			0
$843$	−4.65615e7	−	8.06469e7i	−0.0777221	−	0.134619i
$844$		0			0
$845$	−1.81661e7	−	1.03025e8i	−0.0301086	−	0.170755i
$846$		0			0
$847$	−1.20041e8	+	2.07917e8i	−0.197551	+	0.342168i
$848$		0			0
$849$	1.58941e7	+	1.89419e7i	0.0259724	+	0.0309528i
$850$		0			0
$851$	1.66929e8	−	4.58633e8i	0.270859	−	0.744178i
$852$		0			0
$853$	1.31021e8	−	7.43054e8i	0.211102	−	1.19722i	−0.676442	−	0.736496i	$-0.736479\pi$
$853$	1.31021e8	−	7.43054e8i	0.211102	−	1.19722i	0.887544	−	0.460723i	$-0.152410\pi$
$854$		0			0
$855$	2.32903e8	+	9.56970e8i	0.372629	+	1.53109i
$856$		0			0
$857$	−5.69949e8	−	1.00497e8i	−0.905510	−	0.159666i	−0.298546	−	0.954395i	$-0.596502\pi$
$857$	−5.69949e8	−	1.00497e8i	−0.905510	−	0.159666i	−0.606964	+	0.794729i	$0.707613\pi$
$858$		0			0
$859$	8.10346e8	+	2.94942e8i	1.27847	+	0.465325i	0.889926	−	0.456104i	$-0.150756\pi$
$859$	8.10346e8	+	2.94942e8i	1.27847	+	0.465325i	0.388545	+	0.921430i	$0.372978\pi$
$860$		0			0
$861$	1.37458e7	−	1.15341e7i	0.0215358	−	0.0180707i
$862$		0			0
$863$	5.76317e7	+	3.32737e7i	0.0896662	+	0.0517688i	0.544163	−	0.838980i	$-0.316847\pi$
$863$	5.76317e7	+	3.32737e7i	0.0896662	+	0.0517688i	−0.454496	+	0.890749i	$0.650181\pi$
$864$		0			0
$865$	−1.72208e9	+	3.03649e8i	−2.66075	+	0.469162i
$866$		0			0
$867$	6.47540e7	−	3.73857e7i	0.0993595	−	0.0573652i
$868$		0			0
$869$	−4.11147e7	−	1.12962e8i	−0.0626525	−	0.172136i
$870$		0			0
$871$	6.87436e8	+	5.76828e8i	1.04035	+	0.872954i
$872$		0			0
$873$		−	1.14480e9i		−	1.72062i
$874$		0			0
$875$	2.89868e8			0.432690
$876$		0			0
$877$	−2.46555e8	+	2.93833e8i	−0.365524	+	0.435615i	−0.917190	−	0.398451i	$-0.869548\pi$
$877$	−2.46555e8	+	2.93833e8i	−0.365524	+	0.435615i	0.551666	+	0.834065i	$0.313992\pi$
$878$		0			0
$879$	−2.55011e7	+	9.28164e6i	−0.0375484	+	0.0136665i
$880$		0			0
$881$	2.45035e8	+	4.24414e8i	0.358345	+	0.620671i	0.987684	−	0.156459i	$-0.0500079\pi$
$881$	2.45035e8	+	4.24414e8i	0.358345	+	0.620671i	−0.629340	+	0.777130i	$0.716675\pi$
$882$		0			0
$883$	−4.74803e7	−	2.69274e8i	−0.0689655	−	0.391123i	−0.999678	−	0.0253713i	$-0.991923\pi$
$883$	−4.74803e7	−	2.69274e8i	−0.0689655	−	0.391123i	0.930713	−	0.365751i	$-0.119188\pi$
$884$		0			0
$885$	−4.43003e7	+	7.67304e7i	−0.0639112	+	0.110698i
$886$		0			0
$887$	−5.04177e8	−	6.00855e8i	−0.722457	−	0.860991i	0.272410	−	0.962181i	$-0.412179\pi$
$887$	−5.04177e8	−	6.00855e8i	−0.722457	−	0.860991i	−0.994867	+	0.101190i	$0.967735\pi$
$888$		0			0
$889$	−9.33654e7	+	2.56519e8i	−0.132886	+	0.365103i
$890$		0			0
$891$	−5.25332e7	+	2.97930e8i	−0.0742678	+	0.421193i
$892$		0			0
$893$	4.57129e7	−	4.12640e8i	0.0641925	−	0.579451i
$894$		0			0
$895$	−2.56809e8	−	4.52823e7i	−0.358212	−	0.0631625i
$896$		0			0
$897$	−1.18950e8	−	4.32944e7i	−0.164812	−	0.0599866i
$898$		0			0
$899$	−1.15224e8	+	9.66840e7i	−0.158585	+	0.133069i
$900$		0			0
$901$	−3.04106e7	−	1.75575e7i	−0.0415767	−	0.0240043i
$902$		0			0
$903$	2.38943e7	−	4.21321e6i	0.0324512	−	0.00572202i
$904$		0			0
$905$	−9.39153e8	+	5.42220e8i	−1.26704	+	0.731526i
$906$		0			0
$907$	4.04149e8	+	1.11039e9i	0.541651	+	1.48817i	0.844722	+	0.535206i	$0.179766\pi$
$907$	4.04149e8	+	1.11039e9i	0.541651	+	1.48817i	−0.303071	+	0.952968i	$0.598012\pi$
$908$		0			0
$909$	−4.58756e8	−	3.84942e8i	−0.610788	−	0.512512i
$910$		0			0
$911$		−	1.02197e9i		−	1.35171i	−0.737032	−	0.675857i	$-0.763773\pi$
$911$		−	1.02197e9i		−	1.35171i	0.737032	−	0.675857i	$-0.236227\pi$
$912$		0			0
$913$	4.86998e8			0.639905
$914$		0			0
$915$	−9.35390e7	+	1.11475e8i	−0.122104	+	0.145518i
$916$		0			0
$917$	2.60299e8	−	9.47412e7i	0.337571	−	0.122866i
$918$		0			0
$919$	5.53511e8	+	9.58710e8i	0.713148	+	1.23521i	0.963669	+	0.267098i	$0.0860648\pi$
$919$	5.53511e8	+	9.58710e8i	0.713148	+	1.23521i	−0.250521	+	0.968111i	$0.580602\pi$
$920$		0			0
$921$	2.70225e7	+	1.53252e8i	0.0345897	+	0.196168i
$922$		0			0
$923$	3.40070e8	−	5.89018e8i	0.432477	−	0.749072i
$924$		0			0
$925$	−3.85963e8	−	4.59973e8i	−0.487664	−	0.581175i
$926$		0			0
$927$	−4.65498e7	+	1.27894e8i	−0.0584357	+	0.160551i
$928$		0			0
$929$	6.76779e7	−	3.83820e8i	0.0844111	−	0.478719i	−0.913071	−	0.407801i	$-0.866296\pi$
$929$	6.76779e7	−	3.83820e8i	0.0844111	−	0.478719i	0.997482	−	0.0709186i	$-0.0225930\pi$
$930$		0			0
$931$	4.41890e8	−	4.21962e8i	0.547602	−	0.522906i
$932$		0			0
$933$	−1.11776e8	−	1.97091e7i	−0.137627	−	0.0242673i
$934$		0			0
$935$	1.54836e7	+	5.63557e6i	0.0189425	+	0.00689450i
$936$		0			0
$937$	−1.04010e9	+	8.72746e8i	−1.26432	+	1.06089i	−0.269108	+	0.963110i	$0.586729\pi$
$937$	−1.04010e9	+	8.72746e8i	−1.26432	+	1.06089i	−0.995208	+	0.0977770i	$0.968827\pi$
$938$		0			0
$939$	6.75317e7	+	3.89895e7i	0.0815663	+	0.0470923i
$940$		0			0
$941$	−8.31135e7	+	1.46552e7i	−0.0997477	+	0.0175882i	−0.223299	−	0.974750i	$-0.571683\pi$
$941$	−8.31135e7	+	1.46552e7i	−0.0997477	+	0.0175882i	0.123552	+	0.992338i	$0.460572\pi$
$942$		0			0
$943$	5.83744e8	−	3.37025e8i	0.696125	−	0.401908i
$944$		0			0
$945$	5.18140e7	+	1.42358e8i	0.0613977	+	0.168689i
$946$		0			0
$947$	−8.57624e7	−	7.19632e7i	−0.100983	−	0.0847345i	0.590898	−	0.806746i	$-0.298773\pi$
$947$	−8.57624e7	−	7.19632e7i	−0.100983	−	0.0847345i	−0.691881	+	0.722011i	$0.743218\pi$
$948$		0			0
$949$		−	2.37302e8i		−	0.277653i
$950$		0			0
$951$	−7.16864e7			−0.0833480
$952$		0			0
$953$	1.91142e8	−	2.27794e8i	0.220839	−	0.263186i	−0.644237	−	0.764826i	$-0.722825\pi$
$953$	1.91142e8	−	2.27794e8i	0.220839	−	0.263186i	0.865077	+	0.501639i	$0.167270\pi$
$954$		0			0
$955$	−1.15437e9	+	4.20155e8i	−1.32536	+	0.482391i
$956$		0			0
$957$	6.65267e6	+	1.15228e7i	0.00759032	+	0.0131468i
$958$		0			0
$959$	−2.68201e7	−	1.52104e8i	−0.0304091	−	0.172459i
$960$		0			0
$961$	−2.28083e8	+	3.95051e8i	−0.256994	+	0.445126i
$962$		0			0
$963$	1.74944e8	+	2.08490e8i	0.195893	+	0.233457i
$964$		0			0
$965$	−3.89622e8	+	1.07048e9i	−0.433572	+	1.19123i
$966$		0			0
$967$	−1.67980e8	+	9.52663e8i	−0.185771	+	1.05356i	0.739189	+	0.673498i	$0.235209\pi$
$967$	−1.67980e8	+	9.52663e8i	−0.185771	+	1.05356i	−0.924960	+	0.380063i	$0.875902\pi$
$968$		0			0
$969$	1.18963e6	+	2.71282e6i	0.00130749	+	0.00298160i
$970$		0			0
$971$	−3.91361e8	−	6.90075e7i	−0.427484	−	0.0753769i	−0.0442330	−	0.999021i	$-0.514084\pi$
$971$	−3.91361e8	−	6.90075e7i	−0.427484	−	0.0753769i	−0.383251	+	0.923644i	$0.625196\pi$
$972$		0			0
$973$	−7.91872e8	−	2.88218e8i	−0.859640	−	0.312883i
$974$		0			0
$975$	−1.19298e8	+	1.00103e8i	−0.128712	+	0.108002i
$976$		0			0
$977$	−6.01224e8	−	3.47117e8i	−0.644692	−	0.372213i	0.141727	−	0.989906i	$-0.454734\pi$
$977$	−6.01224e8	−	3.47117e8i	−0.644692	−	0.372213i	−0.786420	+	0.617692i	$0.788068\pi$
$978$		0			0
$979$	−6.69388e8	+	1.18031e8i	−0.713394	+	0.125791i
$980$		0			0
$981$	−1.21116e9	+	6.99265e8i	−1.28291	+	0.740687i
$982$		0			0
$983$	−2.33320e8	−	6.41041e8i	−0.245636	−	0.674878i	−0.999834	−	0.0182314i	$-0.994196\pi$
$983$	−2.33320e8	−	6.41041e8i	−0.245636	−	0.674878i	0.754198	−	0.656647i	$-0.228026\pi$
$984$		0			0
$985$	−4.80046e8	−	4.02806e8i	−0.502312	−	0.421490i
$986$		0			0
$987$		−	3.17176e7i		−	0.0329875i
$988$		0			0
$989$	9.11420e8			0.942171
$990$		0			0
$991$	7.36493e8	−	8.77718e8i	0.756741	−	0.901849i	−0.240896	−	0.970551i	$-0.577441\pi$
$991$	7.36493e8	−	8.77718e8i	0.756741	−	0.901849i	0.997637	+	0.0687018i	$0.0218857\pi$
$992$		0			0
$993$	2.48840e7	−	9.05702e6i	0.0254139	−	0.00924992i
$994$		0			0
$995$	−8.08682e8	−	1.40068e9i	−0.820934	−	1.42190i
$996$		0			0
$997$	−1.68767e8	−	9.57124e8i	−0.170295	−	0.965791i	−0.943436	−	0.331556i	$-0.892426\pi$
$997$	−1.68767e8	−	9.57124e8i	−0.170295	−	0.965791i	0.773141	−	0.634235i	$-0.218685\pi$
$998$		0			0
$999$	5.56684e7	−	9.64206e7i	0.0558358	−	0.0967104i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.21.6	✓	60
19.10	odd	18	inner	76.7.j.a.29.6	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.21.6	✓	60	1.1	even	1	trivial
76.7.j.a.29.6	yes	60	19.10	odd	18	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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.99278 - 2.37490i) q^{3} +(187.566 - 68.2686i) q^{5} +(84.5123 + 146.380i) q^{7} +(124.921 + 708.460i) q^{9} +O(q^{10})\)	\(q+(1.99278 - 2.37490i) q^{3} +(187.566 - 68.2686i) q^{5} +(84.5123 + 146.380i) q^{7} +(124.921 + 708.460i) q^{9} +(296.296 - 513.200i) q^{11} +(-1333.33 - 1589.00i) q^{13} +(211.647 - 581.496i) q^{15} +(-24.1897 + 137.187i) q^{17} +(6582.58 + 1927.57i) q^{19} +(516.051 + 90.9937i) q^{21} +(18497.1 + 6732.39i) q^{23} +(18551.1 - 15566.2i) q^{25} +(3888.73 + 2245.16i) q^{27} +(-7132.30 + 1257.62i) q^{29} +(17986.2 - 10384.3i) q^{31} +(-628.347 - 1726.37i) q^{33} +(25844.8 + 21686.3i) q^{35} -24794.9i q^{37} -6430.76 q^{39} +(22011.1 - 26231.8i) q^{41} +(43509.8 - 15836.3i) q^{43} +(71796.4 + 124355. i) q^{45} +(-10510.6 - 59608.8i) q^{47} +(44539.9 - 77145.3i) q^{49} +(277.600 + 330.831i) q^{51} +(-86215.4 + 236875. i) q^{53} +(20539.8 - 116487. i) q^{55} +(17695.4 - 11791.8i) q^{57} +(-141003. - 24862.6i) q^{59} +(-220979. - 80429.6i) q^{61} +(-93146.6 + 78159.3i) q^{63} +(-358567. - 207019. i) q^{65} +(-426049. + 75123.9i) q^{67} +(52849.4 - 30512.6i) q^{69} +(112145. + 308115. i) q^{71} +(87636.5 + 73535.7i) q^{73} -75077.1i q^{75} +100163. q^{77} +(130394. - 155397. i) q^{79} +(-479726. + 174606. i) q^{81} +(410905. + 711708. i) q^{83} +(4828.37 + 27383.0i) q^{85} +(-11226.4 + 19444.7i) q^{87} +(-737289. - 878667. i) q^{89} +(119915. - 329463. i) q^{91} +(11180.7 - 63409.2i) q^{93} +(1.36626e6 - 87836.5i) q^{95} +(-1.56717e6 - 276335. i) q^{97} +(400595. + 145805. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) \) 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9 + 1680 * q^11 - 2940 * q^13 + 2496 * q^15 - 5112 * q^17 - 15792 * q^19 - 32076 * q^21 - 19272 * q^23 + 58896 * q^25 - 124830 * q^27 + 126840 * q^29 + 30780 * q^31 - 274470 * q^33 - 226284 * q^35 + 178968 * q^39 + 83394 * q^41 + 418848 * q^43 - 95472 * q^45 - 498696 * q^47 - 744330 * q^49 + 1334538 * q^51 + 458004 * q^53 - 260136 * q^55 - 981984 * q^57 - 523362 * q^59 - 644172 * q^61 + 926832 * q^63 + 1337220 * q^65 + 1719114 * q^67 + 1333800 * q^69 - 1895220 * q^71 - 1189704 * q^73 + 1337256 * q^77 + 147432 * q^79 + 272130 * q^81 + 442800 * q^83 + 1479096 * q^85 + 1300572 * q^87 - 301596 * q^89 + 661008 * q^91 + 3576 * q^93 - 5709984 * q^95 + 1386630 * q^97 + 3822798 * q^99

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