LMFDB - Embedded newform 605.6.a.p.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,6,Mod(1,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("605.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	605.a (trivial)

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:	yes
Analytic conductor:	$97.0322109869$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} - 523 x^{18} + 521 x^{17} + 115018 x^{16} - 115347 x^{15} - 13821739 x^{14} + \cdots - 32708279373824 $ x^20 - x^19 - 523x^18 + 521x^17 + 115018x^16 - 115347x^15 - 13821739x^14 + 14112735x^13 + 987264735x^12 - 1043264932x^11 - 42703408468x^10 + 48021607312x^9 + 1089062915552x^8 - 1362443421632x^7 - 15019635572992x^6 + 22119016261376x^5 + 88321308161536x^4 - 163614980036608x^3 - 51220983567360x^2 + 157475390795776x - 32708279373824
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 11^{8} $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-9.60667$ of defining polynomial
Character	$\chi$	$=$	605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.60667 q^{2} +21.6000 q^{3} +60.2880 q^{4} -25.0000 q^{5} -207.504 q^{6} -51.1649 q^{7} -271.754 q^{8} +223.560 q^{9} +O(q^{10})$	\(q-9.60667 q^{2} +21.6000 q^{3} +60.2880 q^{4} -25.0000 q^{5} -207.504 q^{6} -51.1649 q^{7} -271.754 q^{8} +223.560 q^{9} +240.167 q^{10} +1302.22 q^{12} -495.038 q^{13} +491.524 q^{14} -540.000 q^{15} +681.429 q^{16} -155.804 q^{17} -2147.67 q^{18} +181.439 q^{19} -1507.20 q^{20} -1105.16 q^{21} +3721.18 q^{23} -5869.88 q^{24} +625.000 q^{25} +4755.66 q^{26} -419.903 q^{27} -3084.63 q^{28} -5212.07 q^{29} +5187.60 q^{30} +9044.12 q^{31} +2149.85 q^{32} +1496.75 q^{34} +1279.12 q^{35} +13478.0 q^{36} +14219.8 q^{37} -1743.03 q^{38} -10692.8 q^{39} +6793.84 q^{40} +16623.7 q^{41} +10616.9 q^{42} -8281.23 q^{43} -5589.00 q^{45} -35748.2 q^{46} -15848.0 q^{47} +14718.9 q^{48} -14189.2 q^{49} -6004.17 q^{50} -3365.36 q^{51} -29844.8 q^{52} -5692.80 q^{53} +4033.86 q^{54} +13904.2 q^{56} +3919.09 q^{57} +50070.6 q^{58} -9869.82 q^{59} -32555.5 q^{60} -37029.6 q^{61} -86883.8 q^{62} -11438.4 q^{63} -42458.7 q^{64} +12375.9 q^{65} -980.534 q^{67} -9393.10 q^{68} +80377.6 q^{69} -12288.1 q^{70} -65628.6 q^{71} -60753.2 q^{72} -16324.8 q^{73} -136605. q^{74} +13500.0 q^{75} +10938.6 q^{76} +102722. q^{78} +64020.6 q^{79} -17035.7 q^{80} -63395.0 q^{81} -159698. q^{82} +35522.1 q^{83} -66628.0 q^{84} +3895.09 q^{85} +79555.0 q^{86} -112581. q^{87} -61095.0 q^{89} +53691.7 q^{90} +25328.5 q^{91} +224343. q^{92} +195353. q^{93} +152246. q^{94} -4535.99 q^{95} +46436.9 q^{96} -147482. q^{97} +136310. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9}+O(q^{10}) $ 20 * q + q^2 + 407 * q^4 - 500 * q^5 - 264 * q^6 - 167 * q^7 - 57 * q^8 + 1598 * q^9	\( 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9} - 25 q^{10} - 253 q^{12} - 769 q^{13} - 1045 q^{14} + 6963 q^{16} + 2989 q^{17} - 3775 q^{18} - 5828 q^{19} - 10175 q^{20} - 3310 q^{21} - 695 q^{23} - 16724 q^{24} + 12500 q^{25} - 7384 q^{26} + 5925 q^{27} + 3508 q^{28} - 11268 q^{29} + 6600 q^{30} - 11465 q^{31} + 9062 q^{32} + 1217 q^{34} + 4175 q^{35} + 112083 q^{36} - 3057 q^{37} - 13510 q^{38} - 13459 q^{39} + 1425 q^{40} + 839 q^{41} - 14772 q^{42} - 43671 q^{43} - 39950 q^{45} - 81471 q^{46} + 32245 q^{47} - 104315 q^{48} + 2959 q^{49} + 625 q^{50} - 69047 q^{51} - 42696 q^{52} + 27981 q^{53} - 61212 q^{54} - 28294 q^{56} - 79425 q^{57} + 37274 q^{58} - 56847 q^{59} + 6325 q^{60} - 85616 q^{61} - 38095 q^{62} - 100055 q^{63} - 18233 q^{64} + 19225 q^{65} - 31091 q^{67} + 83972 q^{68} - 48708 q^{69} + 26125 q^{70} - 106431 q^{71} - 350510 q^{72} - 117959 q^{73} - 154757 q^{74} - 451972 q^{76} + 348898 q^{78} - 215138 q^{79} - 174075 q^{80} + 75516 q^{81} - 127864 q^{82} - 66761 q^{83} - 521275 q^{84} - 74725 q^{85} - 32222 q^{86} + 5311 q^{87} + 270560 q^{89} + 94375 q^{90} - 269192 q^{91} - 461663 q^{92} + 9345 q^{93} - 479494 q^{94} + 145700 q^{95} - 1247523 q^{96} + 45338 q^{97} + 420757 q^{98}+O(q^{100}) \) 20 * q + q^2 + 407 * q^4 - 500 * q^5 - 264 * q^6 - 167 * q^7 - 57 * q^8 + 1598 * q^9 - 25 * q^10 - 253 * q^12 - 769 * q^13 - 1045 * q^14 + 6963 * q^16 + 2989 * q^17 - 3775 * q^18 - 5828 * q^19 - 10175 * q^20 - 3310 * q^21 - 695 * q^23 - 16724 * q^24 + 12500 * q^25 - 7384 * q^26 + 5925 * q^27 + 3508 * q^28 - 11268 * q^29 + 6600 * q^30 - 11465 * q^31 + 9062 * q^32 + 1217 * q^34 + 4175 * q^35 + 112083 * q^36 - 3057 * q^37 - 13510 * q^38 - 13459 * q^39 + 1425 * q^40 + 839 * q^41 - 14772 * q^42 - 43671 * q^43 - 39950 * q^45 - 81471 * q^46 + 32245 * q^47 - 104315 * q^48 + 2959 * q^49 + 625 * q^50 - 69047 * q^51 - 42696 * q^52 + 27981 * q^53 - 61212 * q^54 - 28294 * q^56 - 79425 * q^57 + 37274 * q^58 - 56847 * q^59 + 6325 * q^60 - 85616 * q^61 - 38095 * q^62 - 100055 * q^63 - 18233 * q^64 + 19225 * q^65 - 31091 * q^67 + 83972 * q^68 - 48708 * q^69 + 26125 * q^70 - 106431 * q^71 - 350510 * q^72 - 117959 * q^73 - 154757 * q^74 - 451972 * q^76 + 348898 * q^78 - 215138 * q^79 - 174075 * q^80 + 75516 * q^81 - 127864 * q^82 - 66761 * q^83 - 521275 * q^84 - 74725 * q^85 - 32222 * q^86 + 5311 * q^87 + 270560 * q^89 + 94375 * q^90 - 269192 * q^91 - 461663 * q^92 + 9345 * q^93 - 479494 * q^94 + 145700 * q^95 - 1247523 * q^96 + 45338 * q^97 + 420757 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−9.60667	−1.69823	−0.849117	−	0.528204i	$-0.822866\pi$
$2$	−9.60667	−1.69823	−0.849117	+	0.528204i	$0.822866\pi$
$3$	21.6000	1.38564	0.692820	−	0.721110i	$-0.256368\pi$
$3$	21.6000	1.38564	0.692820	+	0.721110i	$0.256368\pi$
$4$	60.2880	1.88400
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−207.504	−2.35314
$7$	−51.1649	−0.394663	−0.197332	−	0.980337i	$-0.563228\pi$
$7$	−51.1649	−0.394663	−0.197332	+	0.980337i	$0.563228\pi$
$8$	−271.754	−1.50124
$9$	223.560	0.920000
$10$	240.167	0.759474
$11$	0	0
$11$	0	0
$12$	1302.22	2.61055
$13$	−495.038	−0.812419	−0.406209	−	0.913780i	$-0.633150\pi$
$13$	−495.038	−0.812419	−0.406209	+	0.913780i	$0.633150\pi$
$14$	491.524	0.670231
$15$	−540.000	−0.619677
$16$	681.429	0.665458
$17$	−155.804	−0.130754	−0.0653771	−	0.997861i	$-0.520825\pi$
$17$	−155.804	−0.130754	−0.0653771	+	0.997861i	$0.520825\pi$
$18$	−2147.67	−1.56238
$19$	181.439	0.115305	0.0576524	−	0.998337i	$-0.481638\pi$
$19$	181.439	0.115305	0.0576524	+	0.998337i	$0.481638\pi$
$20$	−1507.20	−0.842551
$21$	−1105.16	−0.546862
$22$	0	0
$23$	3721.18	1.46677	0.733384	−	0.679814i	$-0.237940\pi$
$23$	3721.18	1.46677	0.733384	+	0.679814i	$0.237940\pi$
$24$	−5869.88	−2.08018
$25$	625.000	0.200000
$26$	4755.66	1.37968
$27$	−419.903	−0.110851
$28$	−3084.63	−0.743546
$29$	−5212.07	−1.15084	−0.575420	−	0.817858i	$-0.695161\pi$
$29$	−5212.07	−1.15084	−0.575420	+	0.817858i	$0.695161\pi$
$30$	5187.60	1.05236
$31$	9044.12	1.69029	0.845147	−	0.534534i	$-0.179513\pi$
$31$	9044.12	1.69029	0.845147	+	0.534534i	$0.179513\pi$
$32$	2149.85	0.371137
$33$	0	0
$34$	1496.75	0.222051
$35$	1279.12	0.176499
$36$	13478.0	1.73328
$37$	14219.8	1.70761	0.853804	−	0.520595i	$-0.174290\pi$
$37$	14219.8	1.70761	0.853804	+	0.520595i	$0.174290\pi$
$38$	−1743.03	−0.195815
$39$	−10692.8	−1.12572
$40$	6793.84	0.671375
$41$	16623.7	1.54443	0.772213	−	0.635363i	$-0.219150\pi$
$41$	16623.7	1.54443	0.772213	+	0.635363i	$0.219150\pi$
$42$	10616.9	0.928699
$43$	−8281.23	−0.683005	−0.341502	−	0.939881i	$-0.610936\pi$
$43$	−8281.23	−0.683005	−0.341502	+	0.939881i	$0.610936\pi$
$44$	0	0
$45$	−5589.00	−0.411437
$46$	−35748.2	−2.49092
$47$	−15848.0	−1.04648	−0.523238	−	0.852187i	$-0.675276\pi$
$47$	−15848.0	−1.04648	−0.523238	+	0.852187i	$0.675276\pi$
$48$	14718.9	0.922086
$49$	−14189.2	−0.844241
$50$	−6004.17	−0.339647
$51$	−3365.36	−0.181178
$52$	−29844.8	−1.53060
$53$	−5692.80	−0.278379	−0.139189	−	0.990266i	$-0.544450\pi$
$53$	−5692.80	−0.278379	−0.139189	+	0.990266i	$0.544450\pi$
$54$	4033.86	0.188251
$55$	0	0
$56$	13904.2	0.592485
$57$	3919.09	0.159771
$58$	50070.6	1.95440
$59$	−9869.82	−0.369130	−0.184565	−	0.982820i	$-0.559088\pi$
$59$	−9869.82	−0.369130	−0.184565	+	0.982820i	$0.559088\pi$
$60$	−32555.5	−1.16747
$61$	−37029.6	−1.27416	−0.637080	−	0.770798i	$-0.719858\pi$
$61$	−37029.6	−1.27416	−0.637080	+	0.770798i	$0.719858\pi$
$62$	−86883.8	−2.87051
$63$	−11438.4	−0.363090
$64$	−42458.7	−1.29574
$65$	12375.9	0.363325
$66$	0	0
$67$	−980.534	−0.0266855	−0.0133428	−	0.999911i	$-0.504247\pi$
$67$	−980.534	−0.0266855	−0.0133428	+	0.999911i	$0.504247\pi$
$68$	−9393.10	−0.246341
$69$	80377.6	2.03241
$70$	−12288.1	−0.299736
$71$	−65628.6	−1.54507	−0.772534	−	0.634974i	$-0.781011\pi$
$71$	−65628.6	−1.54507	−0.772534	+	0.634974i	$0.781011\pi$
$72$	−60753.2	−1.38114
$73$	−16324.8	−0.358543	−0.179272	−	0.983800i	$-0.557374\pi$
$73$	−16324.8	−0.358543	−0.179272	+	0.983800i	$0.557374\pi$
$74$	−136605.	−2.89992
$75$	13500.0	0.277128
$76$	10938.6	0.217235
$77$	0	0
$78$	102722.	1.91174
$79$	64020.6	1.15412	0.577062	−	0.816701i	$-0.304199\pi$
$79$	64020.6	1.15412	0.577062	+	0.816701i	$0.304199\pi$
$80$	−17035.7	−0.297602
$81$	−63395.0	−1.07360
$82$	−159698.	−2.62280
$83$	35522.1	0.565982	0.282991	−	0.959123i	$-0.408673\pi$
$83$	35522.1	0.565982	0.282991	+	0.959123i	$0.408673\pi$
$84$	−66628.0	−1.03029
$85$	3895.09	0.0584751
$86$	79555.0	1.15990
$87$	−112581.	−1.59465
$88$	0	0
$89$	−61095.0	−0.817581	−0.408791	−	0.912628i	$-0.634049\pi$
$89$	−61095.0	−0.817581	−0.408791	+	0.912628i	$0.634049\pi$
$90$	53691.7	0.698716
$91$	25328.5	0.320632
$92$	224343.	2.76339
$93$	195353.	2.34214
$94$	152246.	1.77716
$95$	−4535.99	−0.0515659
$96$	46436.9	0.514262
$97$	−147482.	−1.59151	−0.795755	−	0.605618i	$-0.792926\pi$
$97$	−147482.	−1.59151	−0.795755	+	0.605618i	$0.792926\pi$
$98$	136310.	1.43372
$99$	0	0
$100$	37680.0	0.376800
$101$	105949.	1.03346	0.516729	−	0.856149i	$-0.327149\pi$
$101$	105949.	1.03346	0.516729	+	0.856149i	$0.327149\pi$
$102$	32329.9	0.307683
$103$	98780.3	0.917439	0.458720	−	0.888581i	$-0.348308\pi$
$103$	98780.3	0.917439	0.458720	+	0.888581i	$0.348308\pi$
$104$	134528.	1.21964
$105$	27629.0	0.244564
$106$	54688.8	0.472753
$107$	39934.9	0.337205	0.168602	−	0.985684i	$-0.446075\pi$
$107$	39934.9	0.337205	0.168602	+	0.985684i	$0.446075\pi$
$108$	−25315.1	−0.208843
$109$	−241282.	−1.94518	−0.972589	−	0.232531i	$-0.925299\pi$
$109$	−241282.	−1.94518	−0.972589	+	0.232531i	$0.925299\pi$
$110$	0	0
$111$	307147.	2.36613
$112$	−34865.2	−0.262632
$113$	57162.7	0.421130	0.210565	−	0.977580i	$-0.432470\pi$
$113$	57162.7	0.421130	0.210565	+	0.977580i	$0.432470\pi$
$114$	−37649.4	−0.271329
$115$	−93029.6	−0.655959
$116$	−314225.	−2.16818
$117$	−110671.	−0.747425
$118$	94816.0	0.626869
$119$	7971.68	0.0516039
$120$	146747.	0.930285
$121$	0	0
$122$	355731.	2.16382
$123$	359071.	2.14002
$124$	545252.	3.18451
$125$	−15625.0	−0.0894427
$126$	109885.	0.616613
$127$	−153452.	−0.844234	−0.422117	−	0.906541i	$-0.638713\pi$
$127$	−153452.	−0.844234	−0.422117	+	0.906541i	$0.638713\pi$
$128$	339091.	1.82933
$129$	−178875.	−0.946399
$130$	−118892.	−0.617010
$131$	118596.	0.603797	0.301899	−	0.953340i	$-0.402380\pi$
$131$	118596.	0.603797	0.301899	+	0.953340i	$0.402380\pi$
$132$	0	0
$133$	−9283.33	−0.0455066
$134$	9419.66	0.0453183
$135$	10497.6	0.0495740
$136$	42340.2	0.196294
$137$	−158697.	−0.722385	−0.361192	−	0.932491i	$-0.617630\pi$
$137$	−158697.	−0.722385	−0.361192	+	0.932491i	$0.617630\pi$
$138$	−772161.	−3.45152
$139$	271174.	1.19045	0.595224	−	0.803560i	$-0.297063\pi$
$139$	271174.	1.19045	0.595224	+	0.803560i	$0.297063\pi$
$140$	77115.7	0.332524
$141$	−342316.	−1.45004
$142$	630472.	2.62389
$143$	0	0
$144$	152340.	0.612221
$145$	130302.	0.514671
$146$	156827.	0.608890
$147$	−306486.	−1.16981
$148$	857281.	3.21713
$149$	185343.	0.683928	0.341964	−	0.939713i	$-0.388908\pi$
$149$	185343.	0.683928	0.341964	+	0.939713i	$0.388908\pi$
$150$	−129690.	−0.470629
$151$	−428583.	−1.52965	−0.764826	−	0.644237i	$-0.777175\pi$
$151$	−428583.	−1.52965	−0.764826	+	0.644237i	$0.777175\pi$
$152$	−49306.8	−0.173100
$153$	−34831.5	−0.120294
$154$	0	0
$155$	−226103.	−0.755922
$156$	−644649.	−2.12086
$157$	−386924.	−1.25279	−0.626393	−	0.779507i	$-0.715469\pi$
$157$	−386924.	−1.25279	−0.626393	+	0.779507i	$0.715469\pi$
$158$	−615025.	−1.95997
$159$	−122965.	−0.385733
$160$	−53746.4	−0.165977
$161$	−190394.	−0.578880
$162$	609014.	1.82322
$163$	−281850.	−0.830901	−0.415450	−	0.909616i	$-0.636376\pi$
$163$	−281850.	−0.830901	−0.415450	+	0.909616i	$0.636376\pi$
$164$	1.00221e6	2.90970
$165$	0	0
$166$	−341249.	−0.961171
$167$	−525709.	−1.45866	−0.729331	−	0.684161i	$-0.760168\pi$
$167$	−525709.	−1.45866	−0.729331	+	0.684161i	$0.760168\pi$
$168$	300332.	0.820971
$169$	−126231.	−0.339976
$170$	−37418.9	−0.0993044
$171$	40562.6	0.106081
$172$	−499259.	−1.28678
$173$	−13233.2	−0.0336162	−0.0168081	−	0.999859i	$-0.505350\pi$
$173$	−13233.2	−0.0336162	−0.0168081	+	0.999859i	$0.505350\pi$
$174$	1.08152e6	2.70809
$175$	−31978.0	−0.0789327
$176$	0	0
$177$	−213188.	−0.511481
$178$	586920.	1.38844
$179$	190380.	0.444108	0.222054	−	0.975034i	$-0.428724\pi$
$179$	190380.	0.444108	0.222054	+	0.975034i	$0.428724\pi$
$180$	−336950.	−0.775147
$181$	−418945.	−0.950519	−0.475259	−	0.879846i	$-0.657646\pi$
$181$	−418945.	−0.950519	−0.475259	+	0.879846i	$0.657646\pi$
$182$	−243323.	−0.544508
$183$	−799838.	−1.76553
$184$	−1.01125e6	−2.20197
$185$	−355494.	−0.763665
$186$	−1.87669e6	−3.97750
$187$	0	0
$188$	−955444.	−1.97156
$189$	21484.3	0.0437488
$190$	43575.7	0.0875710
$191$	448722.	0.890008	0.445004	−	0.895529i	$-0.353202\pi$
$191$	448722.	0.890008	0.445004	+	0.895529i	$0.353202\pi$
$192$	−917107.	−1.79542
$193$	414827.	0.801630	0.400815	−	0.916159i	$-0.368727\pi$
$193$	414827.	0.801630	0.400815	+	0.916159i	$0.368727\pi$
$194$	1.41681e6	2.70276
$195$	267320.	0.503437
$196$	−855436.	−1.59055
$197$	216832.	0.398069	0.199035	−	0.979992i	$-0.436219\pi$
$197$	216832.	0.398069	0.199035	+	0.979992i	$0.436219\pi$
$198$	0	0
$199$	−792352.	−1.41836	−0.709178	−	0.705029i	$-0.750934\pi$
$199$	−792352.	−1.41836	−0.709178	+	0.705029i	$0.750934\pi$
$200$	−169846.	−0.300248
$201$	−21179.5	−0.0369765
$202$	−1.01782e6	−1.75505
$203$	266675.	0.454194
$204$	−202891.	−0.341340
$205$	−415592.	−0.690689
$206$	−948949.	−1.55803
$207$	831908.	1.34943
$208$	−337333.	−0.540630
$209$	0	0
$210$	−265423.	−0.415327
$211$	−250508.	−0.387360	−0.193680	−	0.981065i	$-0.562042\pi$
$211$	−250508.	−0.387360	−0.193680	+	0.981065i	$0.562042\pi$
$212$	−343208.	−0.524466
$213$	−1.41758e6	−2.14091
$214$	−383641.	−0.572652
$215$	207031.	0.305449
$216$	114110.	0.166414
$217$	−462741.	−0.667097
$218$	2.31792e6	3.30337
$219$	−352616.	−0.496812
$220$	0	0
$221$	77128.7	0.106227
$222$	−2.95066e6	−4.01824
$223$	248847.	0.335097	0.167548	−	0.985864i	$-0.446415\pi$
$223$	248847.	0.335097	0.167548	+	0.985864i	$0.446415\pi$
$224$	−109997.	−0.146474
$225$	139725.	0.184000
$226$	−549143.	−0.715178
$227$	333096.	0.429047	0.214524	−	0.976719i	$-0.431180\pi$
$227$	333096.	0.429047	0.214524	+	0.976719i	$0.431180\pi$
$228$	236274.	0.301009
$229$	−557350.	−0.702326	−0.351163	−	0.936314i	$-0.614214\pi$
$229$	−557350.	−0.702326	−0.351163	+	0.936314i	$0.614214\pi$
$230$	893704.	1.11397
$231$	0	0
$232$	1.41640e6	1.72769
$233$	−264422.	−0.319086	−0.159543	−	0.987191i	$-0.551002\pi$
$233$	−264422.	−0.319086	−0.159543	+	0.987191i	$0.551002\pi$
$234$	1.06318e6	1.26930
$235$	396200.	0.467998
$236$	−595032.	−0.695441
$237$	1.38285e6	1.59920
$238$	−76581.3	−0.0876355
$239$	−983551.	−1.11379	−0.556893	−	0.830584i	$-0.688007\pi$
$239$	−983551.	−1.11379	−0.556893	+	0.830584i	$0.688007\pi$
$240$	−367972.	−0.412369
$241$	−1.09254e6	−1.21170	−0.605849	−	0.795580i	$-0.707166\pi$
$241$	−1.09254e6	−1.21170	−0.605849	+	0.795580i	$0.707166\pi$
$242$	0	0
$243$	−1.26730e6	−1.37677
$244$	−2.23244e6	−2.40052
$245$	354729.	0.377556
$246$	−3.44948e6	−3.63426
$247$	−89819.4	−0.0936758
$248$	−2.45777e6	−2.53754
$249$	767277.	0.784248
$250$	150104.	0.151895
$251$	−345537.	−0.346187	−0.173093	−	0.984905i	$-0.555376\pi$
$251$	−345537.	−0.346187	−0.173093	+	0.984905i	$0.555376\pi$
$252$	−689600.	−0.684063
$253$	0	0
$254$	1.47416e6	1.43371
$255$	84134.0	0.0810254
$256$	−1.89885e6	−1.81089
$257$	1.51253e6	1.42847	0.714237	−	0.699904i	$-0.246774\pi$
$257$	1.51253e6	1.42847	0.714237	+	0.699904i	$0.246774\pi$
$258$	1.71839e6	1.60721
$259$	−727552.	−0.673930
$260$	746121.	0.684504
$261$	−1.16521e6	−1.05877
$262$	−1.13931e6	−1.02539
$263$	1.00621e6	0.897017	0.448509	−	0.893778i	$-0.351955\pi$
$263$	1.00621e6	0.897017	0.448509	+	0.893778i	$0.351955\pi$
$264$	0	0
$265$	142320.	0.124495
$266$	89181.8	0.0772809
$267$	−1.31965e6	−1.13287
$268$	−59114.5	−0.0502755
$269$	1.04381e6	0.879513	0.439757	−	0.898117i	$-0.355065\pi$
$269$	1.04381e6	0.879513	0.439757	+	0.898117i	$0.355065\pi$
$270$	−100847.	−0.0841883
$271$	59343.8	0.0490853	0.0245427	−	0.999699i	$-0.492187\pi$
$271$	59343.8	0.0490853	0.0245427	+	0.999699i	$0.492187\pi$
$272$	−106169.	−0.0870114
$273$	547097.	0.444281
$274$	1.52455e6	1.22678
$275$	0	0
$276$	4.84581e6	3.82907
$277$	214311.	0.167820	0.0839101	−	0.996473i	$-0.473259\pi$
$277$	214311.	0.167820	0.0839101	+	0.996473i	$0.473259\pi$
$278$	−2.60508e6	−2.02166
$279$	2.02190e6	1.55507
$280$	−347606.	−0.264967
$281$	−246489.	−0.186222	−0.0931110	−	0.995656i	$-0.529681\pi$
$281$	−246489.	−0.186222	−0.0931110	+	0.995656i	$0.529681\pi$
$282$	3.28852e6	2.46251
$283$	−1.00630e6	−0.746895	−0.373447	−	0.927651i	$-0.621824\pi$
$283$	−1.00630e6	−0.746895	−0.373447	+	0.927651i	$0.621824\pi$
$284$	−3.95662e6	−2.91091
$285$	−97977.3	−0.0714518
$286$	0	0
$287$	−850548.	−0.609529
$288$	480622.	0.341446
$289$	−1.39558e6	−0.982903
$290$	−1.25176e6	−0.874033
$291$	−3.18561e6	−2.20526
$292$	−984192.	−0.675496
$293$	747384.	0.508598	0.254299	−	0.967126i	$-0.418155\pi$
$293$	747384.	0.508598	0.254299	+	0.967126i	$0.418155\pi$
$294$	2.94431e6	1.98662
$295$	246745.	0.165080
$296$	−3.86427e6	−2.56353
$297$	0	0
$298$	−1.78053e6	−1.16147
$299$	−1.84213e6	−1.19163
$300$	813888.	0.522110
$301$	423708.	0.269557
$302$	4.11725e6	2.59771
$303$	2.28850e6	1.43200
$304$	123638.	0.0767306
$305$	925739.	0.569822
$306$	334615.	0.204287
$307$	−1.11512e6	−0.675267	−0.337634	−	0.941278i	$-0.609627\pi$
$307$	−1.11512e6	−0.675267	−0.337634	+	0.941278i	$0.609627\pi$
$308$	0	0
$309$	2.13365e6	1.27124
$310$	2.17210e6	1.28373
$311$	−2.08243e6	−1.22087	−0.610436	−	0.792066i	$-0.709006\pi$
$311$	−2.08243e6	−1.22087	−0.610436	+	0.792066i	$0.709006\pi$
$312$	2.90581e6	1.68998
$313$	443548.	0.255906	0.127953	−	0.991780i	$-0.459159\pi$
$313$	443548.	0.255906	0.127953	+	0.991780i	$0.459159\pi$
$314$	3.71705e6	2.12752
$315$	285961.	0.162379
$316$	3.85968e6	2.17437
$317$	921801.	0.515216	0.257608	−	0.966250i	$-0.417066\pi$
$317$	921801.	0.515216	0.257608	+	0.966250i	$0.417066\pi$
$318$	1.18128e6	0.655066
$319$	0	0
$320$	1.06147e6	0.579470
$321$	862594.	0.467244
$322$	1.82905e6	0.983074
$323$	−28269.0	−0.0150766
$324$	−3.82196e6	−2.02266
$325$	−309399.	−0.162484
$326$	2.70764e6	1.41106
$327$	−5.21170e6	−2.69532
$328$	−4.51754e6	−2.31856
$329$	810860.	0.413006
$330$	0	0
$331$	−1.17643e6	−0.590198	−0.295099	−	0.955467i	$-0.595353\pi$
$331$	−1.17643e6	−0.590198	−0.295099	+	0.955467i	$0.595353\pi$
$332$	2.14155e6	1.06631
$333$	3.17897e6	1.57100
$334$	5.05031e6	2.47715
$335$	24513.4	0.0119341
$336$	−753089.	−0.363913
$337$	−2.55043e6	−1.22332	−0.611658	−	0.791122i	$-0.709497\pi$
$337$	−2.55043e6	−1.22332	−0.611658	+	0.791122i	$0.709497\pi$
$338$	1.21266e6	0.577359
$339$	1.23471e6	0.583535
$340$	234828.	0.110167
$341$	0	0
$342$	−389672.	−0.180150
$343$	1.58591e6	0.727854
$344$	2.25045e6	1.02535
$345$	−2.00944e6	−0.908923
$346$	127127.	0.0570882
$347$	−141523.	−0.0630964	−0.0315482	−	0.999502i	$-0.510044\pi$
$347$	−141523.	−0.0630964	−0.0315482	+	0.999502i	$0.510044\pi$
$348$	−6.78727e6	−3.00432
$349$	−3.24678e6	−1.42689	−0.713443	−	0.700713i	$-0.752865\pi$
$349$	−3.24678e6	−1.42689	−0.713443	+	0.700713i	$0.752865\pi$
$350$	307202.	0.134046
$351$	207868.	0.0900573
$352$	0	0
$353$	−1.22912e6	−0.524998	−0.262499	−	0.964932i	$-0.584547\pi$
$353$	−1.22912e6	−0.524998	−0.262499	+	0.964932i	$0.584547\pi$
$354$	2.04803e6	0.868615
$355$	1.64072e6	0.690975
$356$	−3.68330e6	−1.54032
$357$	172188.	0.0715045
$358$	−1.82892e6	−0.754199
$359$	−3.31836e6	−1.35890	−0.679450	−	0.733722i	$-0.737782\pi$
$359$	−3.31836e6	−1.35890	−0.679450	+	0.733722i	$0.737782\pi$
$360$	1.51883e6	0.617665
$361$	−2.44318e6	−0.986705
$362$	4.02467e6	1.61420
$363$	0	0
$364$	1.52701e6	0.604071
$365$	408121.	0.160345
$366$	7.68378e6	2.99828
$367$	3.92084e6	1.51955	0.759773	−	0.650188i	$-0.225310\pi$
$367$	3.92084e6	1.51955	0.759773	+	0.650188i	$0.225310\pi$
$368$	2.53572e6	0.976073
$369$	3.71639e6	1.42087
$370$	3.41511e6	1.29688
$371$	291272.	0.109866
$372$	1.17774e7	4.41259
$373$	−4.99338e6	−1.85833	−0.929163	−	0.369669i	$-0.879471\pi$
$373$	−4.99338e6	−1.85833	−0.929163	+	0.369669i	$0.879471\pi$
$374$	0	0
$375$	−337500.	−0.123935
$376$	4.30675e6	1.57101
$377$	2.58017e6	0.934964
$378$	−206392.	−0.0742957
$379$	−2.42054e6	−0.865592	−0.432796	−	0.901492i	$-0.642473\pi$
$379$	−2.42054e6	−0.865592	−0.432796	+	0.901492i	$0.642473\pi$
$380$	−273466.	−0.0971502
$381$	−3.31456e6	−1.16980
$382$	−4.31072e6	−1.51144
$383$	2.14459e6	0.747046	0.373523	−	0.927621i	$-0.378150\pi$
$383$	2.14459e6	0.747046	0.373523	+	0.927621i	$0.378150\pi$
$384$	7.32436e6	2.53479
$385$	0	0
$386$	−3.98510e6	−1.36136
$387$	−1.85135e6	−0.628364
$388$	−8.89140e6	−2.99841
$389$	−4.64657e6	−1.55689	−0.778446	−	0.627711i	$-0.783992\pi$
$389$	−4.64657e6	−1.55689	−0.778446	+	0.627711i	$0.783992\pi$
$390$	−2.56806e6	−0.854955
$391$	−579775.	−0.191786
$392$	3.85595e6	1.26741
$393$	2.56167e6	0.836646
$394$	−2.08304e6	−0.676015
$395$	−1.60052e6	−0.516140
$396$	0	0
$397$	−3.85949e6	−1.22900	−0.614502	−	0.788915i	$-0.710643\pi$
$397$	−3.85949e6	−1.22900	−0.614502	+	0.788915i	$0.710643\pi$
$398$	7.61186e6	2.40870
$399$	−200520.	−0.0630558
$400$	425893.	0.133092
$401$	−1.86937e6	−0.580543	−0.290271	−	0.956944i	$-0.593746\pi$
$401$	−1.86937e6	−0.580543	−0.290271	+	0.956944i	$0.593746\pi$
$402$	203465.	0.0627948
$403$	−4.47718e6	−1.37323
$404$	6.38745e6	1.94704
$405$	1.58487e6	0.480128
$406$	−2.56186e6	−0.771329
$407$	0	0
$408$	914549.	0.271992
$409$	−398586.	−0.117819	−0.0589094	−	0.998263i	$-0.518762\pi$
$409$	−398586.	−0.117819	−0.0589094	+	0.998263i	$0.518762\pi$
$410$	3.99245e6	1.17295
$411$	−3.42787e6	−1.00097
$412$	5.95527e6	1.72846
$413$	504988.	0.145682
$414$	−7.99186e6	−2.29164
$415$	−888052.	−0.253115
$416$	−1.06426e6	−0.301519
$417$	5.85735e6	1.64953
$418$	0	0
$419$	−5.21213e6	−1.45038	−0.725188	−	0.688551i	$-0.758247\pi$
$419$	−5.21213e6	−1.45038	−0.725188	+	0.688551i	$0.758247\pi$
$420$	1.66570e6	0.460759
$421$	−2.99303e6	−0.823012	−0.411506	−	0.911407i	$-0.634997\pi$
$421$	−2.99303e6	−0.823012	−0.411506	+	0.911407i	$0.634997\pi$
$422$	2.40654e6	0.657828
$423$	−3.54298e6	−0.962758
$424$	1.54704e6	0.417914
$425$	−97377.4	−0.0261508
$426$	1.36182e7	3.63577
$427$	1.89461e6	0.502864
$428$	2.40760e6	0.635294
$429$	0	0
$430$	−1.98887e6	−0.518724
$431$	5.97286e6	1.54878	0.774389	−	0.632710i	$-0.218057\pi$
$431$	5.97286e6	1.54878	0.774389	+	0.632710i	$0.218057\pi$
$432$	−286134.	−0.0737666
$433$	6.75107e6	1.73042	0.865212	−	0.501406i	$-0.167184\pi$
$433$	6.75107e6	1.73042	0.865212	+	0.501406i	$0.167184\pi$
$434$	4.44540e6	1.13289
$435$	2.81452e6	0.713150
$436$	−1.45464e7	−3.66472
$437$	675170.	0.169126
$438$	3.38747e6	0.843703
$439$	5.63681e6	1.39596	0.697979	−	0.716118i	$-0.254083\pi$
$439$	5.63681e6	1.39596	0.697979	+	0.716118i	$0.254083\pi$
$440$	0	0
$441$	−3.17213e6	−0.776702
$442$	−740950.	−0.180399
$443$	3.29575e6	0.797894	0.398947	−	0.916974i	$-0.369376\pi$
$443$	3.29575e6	0.797894	0.398947	+	0.916974i	$0.369376\pi$
$444$	1.85173e7	4.45779
$445$	1.52738e6	0.365633
$446$	−2.39059e6	−0.569073
$447$	4.00341e6	0.947679
$448$	2.17239e6	0.511379
$449$	−287461.	−0.0672920	−0.0336460	−	0.999434i	$-0.510712\pi$
$449$	−287461.	−0.0672920	−0.0336460	+	0.999434i	$0.510712\pi$
$450$	−1.34229e6	−0.312475
$451$	0	0
$452$	3.44622e6	0.793410
$453$	−9.25740e6	−2.11955
$454$	−3.19995e6	−0.728623
$455$	−633214.	−0.143391
$456$	−1.06503e6	−0.239855
$457$	914394.	0.204806	0.102403	−	0.994743i	$-0.467347\pi$
$457$	914394.	0.204806	0.102403	+	0.994743i	$0.467347\pi$
$458$	5.35427e6	1.19271
$459$	65422.4	0.0144942
$460$	−5.60857e6	−1.23583
$461$	−5.16766e6	−1.13251	−0.566255	−	0.824230i	$-0.691608\pi$
$461$	−5.16766e6	−1.13251	−0.566255	+	0.824230i	$0.691608\pi$
$462$	0	0
$463$	8.93306e6	1.93663	0.968317	−	0.249723i	$-0.0803396\pi$
$463$	8.93306e6	1.93663	0.968317	+	0.249723i	$0.0803396\pi$
$464$	−3.55165e6	−0.765836
$465$	−4.88383e6	−1.04744
$466$	2.54021e6	0.541883
$467$	−228487.	−0.0484807	−0.0242403	−	0.999706i	$-0.507717\pi$
$467$	−228487.	−0.0484807	−0.0242403	+	0.999706i	$0.507717\pi$
$468$	−6.67211e6	−1.40815
$469$	50168.9	0.0105318
$470$	−3.80616e6	−0.794771
$471$	−8.35757e6	−1.73591
$472$	2.68216e6	0.554153
$473$	0	0
$474$	−1.32845e7	−2.71582
$475$	113400.	0.0230610
$476$	480597.	0.0972218
$477$	−1.27268e6	−0.256109
$478$	9.44864e6	1.89147
$479$	−2.26875e6	−0.451802	−0.225901	−	0.974150i	$-0.572533\pi$
$479$	−2.26875e6	−0.451802	−0.225901	+	0.974150i	$0.572533\pi$
$480$	−1.16092e6	−0.229985
$481$	−7.03932e6	−1.38729
$482$	1.04957e7	2.05775
$483$	−4.11251e6	−0.802120
$484$	0	0
$485$	3.68705e6	0.711745
$486$	1.21745e7	2.33808
$487$	2.81282e6	0.537427	0.268713	−	0.963220i	$-0.413402\pi$
$487$	2.81282e6	0.537427	0.268713	+	0.963220i	$0.413402\pi$
$488$	1.00629e7	1.91282
$489$	−6.08796e6	−1.15133
$490$	−3.40776e6	−0.641179
$491$	7.43285e6	1.39140	0.695700	−	0.718333i	$-0.255094\pi$
$491$	7.43285e6	1.39140	0.695700	+	0.718333i	$0.255094\pi$
$492$	2.16477e7	4.03180
$493$	812060.	0.150477
$494$	862865.	0.159084
$495$	0	0
$496$	6.16293e6	1.12482
$497$	3.35788e6	0.609782
$498$	−7.37097e6	−1.33184
$499$	−3.70564e6	−0.666212	−0.333106	−	0.942889i	$-0.608097\pi$
$499$	−3.70564e6	−0.666212	−0.333106	+	0.942889i	$0.608097\pi$
$500$	−942000.	−0.168510
$501$	−1.13553e7	−2.02118
$502$	3.31946e6	0.587906
$503$	2.90332e6	0.511652	0.255826	−	0.966723i	$-0.417653\pi$
$503$	2.90332e6	0.511652	0.255826	+	0.966723i	$0.417653\pi$
$504$	3.10843e6	0.545086
$505$	−2.64872e6	−0.462177
$506$	0	0
$507$	−2.72658e6	−0.471085
$508$	−9.25131e6	−1.59054
$509$	4.88641e6	0.835979	0.417989	−	0.908452i	$-0.362735\pi$
$509$	4.88641e6	0.835979	0.417989	+	0.908452i	$0.362735\pi$
$510$	−808248.	−0.137600
$511$	835258.	0.141504
$512$	7.39076e6	1.24599
$513$	−76186.9	−0.0127817
$514$	−1.45304e7	−2.42588
$515$	−2.46951e6	−0.410291
$516$	−1.07840e7	−1.78302
$517$	0	0
$518$	6.98935e6	1.14449
$519$	−285836.	−0.0465799
$520$	−3.36321e6	−0.545438
$521$	−9.44242e6	−1.52401	−0.762007	−	0.647568i	$-0.775786\pi$
$521$	−9.44242e6	−1.52401	−0.762007	+	0.647568i	$0.775786\pi$
$522$	1.11938e7	1.79805
$523$	8.67289e6	1.38647	0.693234	−	0.720713i	$-0.256185\pi$
$523$	8.67289e6	1.38647	0.693234	+	0.720713i	$0.256185\pi$
$524$	7.14991e6	1.13755
$525$	−690726.	−0.109372
$526$	−9.66636e6	−1.52335
$527$	−1.40911e6	−0.221013
$528$	0	0
$529$	7.41087e6	1.15141
$530$	−1.36722e6	−0.211421
$531$	−2.20650e6	−0.339600
$532$	−559673.	−0.0857345
$533$	−8.22934e6	−1.25472
$534$	1.26775e7	1.92389
$535$	−998373.	−0.150802
$536$	266464.	0.0400614
$537$	4.11220e6	0.615374
$538$	−1.00276e7	−1.49362
$539$	0	0
$540$	632878.	0.0933975
$541$	5.63676e6	0.828012	0.414006	−	0.910274i	$-0.364129\pi$
$541$	5.63676e6	0.828012	0.414006	+	0.910274i	$0.364129\pi$
$542$	−570096.	−0.0833584
$543$	−9.04922e6	−1.31708
$544$	−334955.	−0.0485277
$545$	6.03206e6	0.869910
$546$	−5.25577e6	−0.754493
$547$	9.08718e6	1.29856	0.649278	−	0.760551i	$-0.275071\pi$
$547$	9.08718e6	1.29856	0.649278	+	0.760551i	$0.275071\pi$
$548$	−9.56756e6	−1.36097
$549$	−8.27833e6	−1.17223
$550$	0	0
$551$	−945675.	−0.132698
$552$	−2.18429e7	−3.05114
$553$	−3.27561e6	−0.455490
$554$	−2.05881e6	−0.284998
$555$	−7.67867e6	−1.05817
$556$	1.63485e7	2.24281
$557$	6.20073e6	0.846846	0.423423	−	0.905932i	$-0.360828\pi$
$557$	6.20073e6	0.846846	0.423423	+	0.905932i	$0.360828\pi$
$558$	−1.94238e7	−2.64087
$559$	4.09952e6	0.554886
$560$	871631.	0.117453
$561$	0	0
$562$	2.36793e6	0.316249
$563$	1.03216e6	0.137239	0.0686193	−	0.997643i	$-0.478141\pi$
$563$	1.03216e6	0.137239	0.0686193	+	0.997643i	$0.478141\pi$
$564$	−2.06376e7	−2.73188
$565$	−1.42907e6	−0.188335
$566$	9.66714e6	1.26840
$567$	3.24360e6	0.423711
$568$	1.78348e7	2.31952
$569$	−1.19045e7	−1.54146	−0.770730	−	0.637162i	$-0.780108\pi$
$569$	−1.19045e7	−1.54146	−0.770730	+	0.637162i	$0.780108\pi$
$570$	941235.	0.121342
$571$	1.10544e7	1.41888	0.709440	−	0.704766i	$-0.248948\pi$
$571$	1.10544e7	1.41888	0.709440	+	0.704766i	$0.248948\pi$
$572$	0	0
$573$	9.69239e6	1.23323
$574$	8.17093e6	1.03512
$575$	2.32574e6	0.293354
$576$	−9.49206e6	−1.19208
$577$	−4.14987e6	−0.518913	−0.259457	−	0.965755i	$-0.583543\pi$
$577$	−4.14987e6	−0.518913	−0.259457	+	0.965755i	$0.583543\pi$
$578$	1.34069e7	1.66920
$579$	8.96027e6	1.11077
$580$	7.85563e6	0.969641
$581$	−1.81748e6	−0.223373
$582$	3.06031e7	3.74505
$583$	0	0
$584$	4.43633e6	0.538260
$585$	2.76677e6	0.334259
$586$	−7.17987e6	−0.863719
$587$	1.37363e6	0.164541	0.0822703	−	0.996610i	$-0.473783\pi$
$587$	1.37363e6	0.164541	0.0822703	+	0.996610i	$0.473783\pi$
$588$	−1.84774e7	−2.20393
$589$	1.64096e6	0.194899
$590$	−2.37040e6	−0.280344
$591$	4.68358e6	0.551581
$592$	9.68976e6	1.13634
$593$	−1.51039e7	−1.76382	−0.881908	−	0.471422i	$-0.843741\pi$
$593$	−1.51039e7	−1.76382	−0.881908	+	0.471422i	$0.843741\pi$
$594$	0	0
$595$	−199292.	−0.0230780
$596$	1.11740e7	1.28852
$597$	−1.71148e7	−1.96533
$598$	1.76967e7	2.02367
$599$	2.36423e6	0.269230	0.134615	−	0.990898i	$-0.457020\pi$
$599$	2.36423e6	0.269230	0.134615	+	0.990898i	$0.457020\pi$
$600$	−3.66867e6	−0.416036
$601$	1.18781e7	1.34141	0.670706	−	0.741723i	$-0.265991\pi$
$601$	1.18781e7	1.34141	0.670706	+	0.741723i	$0.265991\pi$
$602$	−4.07042e6	−0.457771
$603$	−219208.	−0.0245507
$604$	−2.58384e7	−2.88187
$605$	0	0
$606$	−2.19848e7	−2.43188
$607$	−6.69765e6	−0.737820	−0.368910	−	0.929465i	$-0.620269\pi$
$607$	−6.69765e6	−0.737820	−0.368910	+	0.929465i	$0.620269\pi$
$608$	390068.	0.0427939
$609$	5.76018e6	0.629350
$610$	−8.89326e6	−0.967691
$611$	7.84535e6	0.850177
$612$	−2.09992e6	−0.226634
$613$	−193357.	−0.0207830	−0.0103915	−	0.999946i	$-0.503308\pi$
$613$	−193357.	−0.0207830	−0.0103915	+	0.999946i	$0.503308\pi$
$614$	1.07126e7	1.14676
$615$	−8.97678e6	−0.957046
$616$	0	0
$617$	435555.	0.0460607	0.0230303	−	0.999735i	$-0.492669\pi$
$617$	435555.	0.0460607	0.0230303	+	0.999735i	$0.492669\pi$
$618$	−2.04973e7	−2.15887
$619$	2.65030e6	0.278015	0.139008	−	0.990291i	$-0.455609\pi$
$619$	2.65030e6	0.278015	0.139008	+	0.990291i	$0.455609\pi$
$620$	−1.36313e7	−1.42416
$621$	−1.56254e6	−0.162593
$622$	2.00052e7	2.07333
$623$	3.12592e6	0.322669
$624$	−7.28639e6	−0.749120
$625$	390625.	0.0400000
$626$	−4.26102e6	−0.434588
$627$	0	0
$628$	−2.33269e7	−2.36025
$629$	−2.21549e6	−0.223277
$630$	−2.74713e6	−0.275758
$631$	−3.88138e6	−0.388073	−0.194036	−	0.980994i	$-0.562158\pi$
$631$	−3.88138e6	−0.388073	−0.194036	+	0.980994i	$0.562158\pi$
$632$	−1.73978e7	−1.73262
$633$	−5.41097e6	−0.536742
$634$	−8.85543e6	−0.874957
$635$	3.83630e6	0.377553
$636$	−7.41329e6	−0.726722
$637$	7.02417e6	0.685877
$638$	0	0
$639$	−1.46719e7	−1.42146
$640$	−8.47727e6	−0.818099
$641$	583780.	0.0561182	0.0280591	−	0.999606i	$-0.491067\pi$
$641$	583780.	0.0561182	0.0280591	+	0.999606i	$0.491067\pi$
$642$	−8.28666e6	−0.793491
$643$	−1.17393e7	−1.11973	−0.559866	−	0.828583i	$-0.689147\pi$
$643$	−1.17393e7	−1.11973	−0.559866	+	0.828583i	$0.689147\pi$
$644$	−1.14785e7	−1.09061
$645$	4.47186e6	0.423243
$646$	271570.	0.0256036
$647$	−1.26957e7	−1.19233	−0.596166	−	0.802861i	$-0.703310\pi$
$647$	−1.26957e7	−1.19233	−0.596166	+	0.802861i	$0.703310\pi$
$648$	1.72278e7	1.61173
$649$	0	0
$650$	2.97229e6	0.275935
$651$	−9.99521e6	−0.924357
$652$	−1.69922e7	−1.56542
$653$	3.08242e6	0.282885	0.141442	−	0.989946i	$-0.454826\pi$
$653$	3.08242e6	0.282885	0.141442	+	0.989946i	$0.454826\pi$
$654$	5.00671e7	4.57728
$655$	−2.96489e6	−0.270026
$656$	1.13278e7	1.02775
$657$	−3.64958e6	−0.329860
$658$	−7.78966e6	−0.701381
$659$	−1.00512e6	−0.0901577	−0.0450788	−	0.998983i	$-0.514354\pi$
$659$	−1.00512e6	−0.0901577	−0.0450788	+	0.998983i	$0.514354\pi$
$660$	0	0
$661$	−9.18299e6	−0.817486	−0.408743	−	0.912649i	$-0.634033\pi$
$661$	−9.18299e6	−0.817486	−0.408743	+	0.912649i	$0.634033\pi$
$662$	1.13016e7	1.00229
$663$	1.66598e6	0.147193
$664$	−9.65325e6	−0.849676
$665$	232083.	0.0203512
$666$	−3.05393e7	−2.66793
$667$	−1.93951e7	−1.68802
$668$	−3.16940e7	−2.74812
$669$	5.37509e6	0.464324
$670$	−235492.	−0.0202669
$671$	0	0
$672$	−2.37594e6	−0.202961
$673$	−6.34707e6	−0.540177	−0.270088	−	0.962836i	$-0.587053\pi$
$673$	−6.34707e6	−0.540177	−0.270088	+	0.962836i	$0.587053\pi$
$674$	2.45011e7	2.07748
$675$	−262439.	−0.0221702
$676$	−7.61020e6	−0.640515
$677$	−1.74011e7	−1.45917	−0.729585	−	0.683890i	$-0.760287\pi$
$677$	−1.74011e7	−1.45917	−0.729585	+	0.683890i	$0.760287\pi$
$678$	−1.18615e7	−0.990980
$679$	7.54590e6	0.628111
$680$	−1.05851e6	−0.0877851
$681$	7.19488e6	0.594506
$682$	0	0
$683$	1.57659e7	1.29321	0.646603	−	0.762827i	$-0.276189\pi$
$683$	1.57659e7	1.29321	0.646603	+	0.762827i	$0.276189\pi$
$684$	2.44544e6	0.199856
$685$	3.96744e6	0.323060
$686$	−1.52353e7	−1.23607
$687$	−1.20388e7	−0.973172
$688$	−5.64307e6	−0.454511
$689$	2.81815e6	0.226160
$690$	1.93040e7	1.54357
$691$	−1.70724e7	−1.36019	−0.680096	−	0.733123i	$-0.738062\pi$
$691$	−1.70724e7	−1.36019	−0.680096	+	0.733123i	$0.738062\pi$
$692$	−797801.	−0.0633329
$693$	0	0
$694$	1.35957e6	0.107153
$695$	−6.77934e6	−0.532385
$696$	3.05942e7	2.39395
$697$	−2.59003e6	−0.201940
$698$	3.11907e7	2.42319
$699$	−5.71151e6	−0.442138
$700$	−1.92789e6	−0.148709
$701$	2.53517e7	1.94855	0.974276	−	0.225357i	$-0.0723548\pi$
$701$	2.53517e7	1.94855	0.974276	+	0.225357i	$0.0723548\pi$
$702$	−1.99691e6	−0.152938
$703$	2.58003e6	0.196896
$704$	0	0
$705$	8.55791e6	0.648478
$706$	1.18077e7	0.891569
$707$	−5.42086e6	−0.407868
$708$	−1.28527e7	−0.963631
$709$	1.98460e7	1.48271	0.741357	−	0.671111i	$-0.234183\pi$
$709$	1.98460e7	1.48271	0.741357	+	0.671111i	$0.234183\pi$
$710$	−1.57618e7	−1.17344
$711$	1.43125e7	1.06179
$712$	1.66028e7	1.22739
$713$	3.36548e7	2.47927
$714$	−1.65416e6	−0.121431
$715$	0	0
$716$	1.14776e7	0.836699
$717$	−2.12447e7	−1.54331
$718$	3.18784e7	2.30773
$719$	1.04981e7	0.757339	0.378669	−	0.925532i	$-0.376382\pi$
$719$	1.04981e7	0.757339	0.378669	+	0.925532i	$0.376382\pi$
$720$	−3.80851e6	−0.273794
$721$	−5.05408e6	−0.362080
$722$	2.34708e7	1.67566
$723$	−2.35988e7	−1.67898
$724$	−2.52574e7	−1.79078
$725$	−3.25754e6	−0.230168
$726$	0	0
$727$	9.85512e6	0.691553	0.345777	−	0.938317i	$-0.387615\pi$
$727$	9.85512e6	0.691553	0.345777	+	0.938317i	$0.387615\pi$
$728$	−6.88312e6	−0.481346
$729$	−1.19686e7	−0.834113
$730$	−3.92068e6	−0.272304
$731$	1.29025e6	0.0893057
$732$	−4.82207e7	−3.32626
$733$	−1.97894e7	−1.36042	−0.680209	−	0.733018i	$-0.738111\pi$
$733$	−1.97894e7	−1.36042	−0.680209	+	0.733018i	$0.738111\pi$
$734$	−3.76662e7	−2.58055
$735$	7.66214e6	0.523157
$736$	8.00001e6	0.544372
$737$	0	0
$738$	−3.57021e7	−2.41298
$739$	−2.08020e7	−1.40118	−0.700590	−	0.713564i	$-0.747080\pi$
$739$	−2.08020e7	−1.40118	−0.700590	+	0.713564i	$0.747080\pi$
$740$	−2.14320e7	−1.43875
$741$	−1.94010e6	−0.129801
$742$	−2.79815e6	−0.186578
$743$	2.62440e7	1.74404	0.872022	−	0.489467i	$-0.162809\pi$
$743$	2.62440e7	1.74404	0.872022	+	0.489467i	$0.162809\pi$
$744$	−5.30879e7	−3.51611
$745$	−4.63357e6	−0.305862
$746$	4.79697e7	3.15588
$747$	7.94131e6	0.520704
$748$	0	0
$749$	−2.04327e6	−0.133082
$750$	3.24225e6	0.210472
$751$	−2.00225e6	−0.129544	−0.0647722	−	0.997900i	$-0.520632\pi$
$751$	−2.00225e6	−0.129544	−0.0647722	+	0.997900i	$0.520632\pi$
$752$	−1.07993e7	−0.696386
$753$	−7.46360e6	−0.479690
$754$	−2.47868e7	−1.58779
$755$	1.07146e7	0.684081
$756$	1.29524e6	0.0824227
$757$	2.13409e7	1.35354	0.676772	−	0.736193i	$-0.263378\pi$
$757$	2.13409e7	1.35354	0.676772	+	0.736193i	$0.263378\pi$
$758$	2.32533e7	1.46998
$759$	0	0
$760$	1.23267e6	0.0774128
$761$	7.05190e6	0.441412	0.220706	−	0.975340i	$-0.429164\pi$
$761$	7.05190e6	0.441412	0.220706	+	0.975340i	$0.429164\pi$
$762$	3.18419e7	1.98660
$763$	1.23452e7	0.767690
$764$	2.70526e7	1.67678
$765$	870788.	0.0537971
$766$	−2.06024e7	−1.26866
$767$	4.88593e6	0.299888
$768$	−4.10153e7	−2.50924
$769$	−2.05285e7	−1.25182	−0.625909	−	0.779896i	$-0.715272\pi$
$769$	−2.05285e7	−1.25182	−0.625909	+	0.779896i	$0.715272\pi$
$770$	0	0
$771$	3.26707e7	1.97935
$772$	2.50091e7	1.51027
$773$	7.26401e6	0.437248	0.218624	−	0.975809i	$-0.429843\pi$
$773$	7.26401e6	0.437248	0.218624	+	0.975809i	$0.429843\pi$
$774$	1.77853e7	1.06711
$775$	5.65258e6	0.338059
$776$	4.00788e7	2.38924
$777$	−1.57151e7	−0.933825
$778$	4.46381e7	2.64397
$779$	3.01619e6	0.178080
$780$	1.61162e7	0.948476
$781$	0	0
$782$	5.56970e6	0.325698
$783$	2.18856e6	0.127572
$784$	−9.66890e6	−0.561807
$785$	9.67311e6	0.560263
$786$	−2.46091e7	−1.42082
$787$	5.40354e6	0.310987	0.155493	−	0.987837i	$-0.450303\pi$
$787$	5.40354e6	0.310987	0.155493	+	0.987837i	$0.450303\pi$
$788$	1.30724e7	0.749962
$789$	2.17342e7	1.24294
$790$	1.53756e7	0.876526
$791$	−2.92472e6	−0.166205
$792$	0	0
$793$	1.83310e7	1.03515
$794$	3.70768e7	2.08714
$795$	3.07411e6	0.172505
$796$	−4.77693e7	−2.67218
$797$	1.93872e7	1.08111	0.540554	−	0.841309i	$-0.318215\pi$
$797$	1.93872e7	1.08111	0.540554	+	0.841309i	$0.318215\pi$
$798$	1.92633e6	0.107084
$799$	2.46918e6	0.136831
$800$	1.34366e6	0.0742274
$801$	−1.36584e7	−0.752175
$802$	1.79584e7	0.985897
$803$	0	0
$804$	−1.27687e6	−0.0696638
$805$	4.75985e6	0.258883
$806$	4.30108e7	2.33206
$807$	2.25464e7	1.21869
$808$	−2.87920e7	−1.55147
$809$	−3.50579e7	−1.88328	−0.941641	−	0.336620i	$-0.890716\pi$
$809$	−3.50579e7	−1.88328	−0.941641	+	0.336620i	$0.890716\pi$
$810$	−1.52254e7	−0.815371
$811$	−2.26974e7	−1.21178	−0.605890	−	0.795548i	$-0.707183\pi$
$811$	−2.26974e7	−1.21178	−0.605890	+	0.795548i	$0.707183\pi$
$812$	1.60773e7	0.855703
$813$	1.28183e6	0.0680147
$814$	0	0
$815$	7.04625e6	0.371590
$816$	−2.29325e6	−0.120567
$817$	−1.50254e6	−0.0787538
$818$	3.82909e6	0.200084
$819$	5.66245e6	0.294981
$820$	−2.50552e7	−1.30126
$821$	−6.16233e6	−0.319071	−0.159535	−	0.987192i	$-0.551000\pi$
$821$	−6.16233e6	−0.319071	−0.159535	+	0.987192i	$0.551000\pi$
$822$	3.29304e7	1.69987
$823$	2.24064e7	1.15311	0.576557	−	0.817057i	$-0.304396\pi$
$823$	2.24064e7	1.15311	0.576557	+	0.817057i	$0.304396\pi$
$824$	−2.68439e7	−1.37730
$825$	0	0
$826$	−4.85125e6	−0.247402
$827$	−8.77836e6	−0.446323	−0.223162	−	0.974781i	$-0.571638\pi$
$827$	−8.77836e6	−0.446323	−0.223162	+	0.974781i	$0.571638\pi$
$828$	5.01541e7	2.54232
$829$	5.93014e6	0.299695	0.149847	−	0.988709i	$-0.452122\pi$
$829$	5.93014e6	0.299695	0.149847	+	0.988709i	$0.452122\pi$
$830$	8.53121e6	0.429849
$831$	4.62911e6	0.232539
$832$	2.10186e7	1.05268
$833$	2.21072e6	0.110388
$834$	−5.62696e7	−2.80130
$835$	1.31427e7	0.652333
$836$	0	0
$837$	−3.79765e6	−0.187371
$838$	5.00712e7	2.46308
$839$	1.61096e7	0.790097	0.395048	−	0.918660i	$-0.370728\pi$
$839$	1.61096e7	0.790097	0.395048	+	0.918660i	$0.370728\pi$
$840$	−7.50829e6	−0.367149
$841$	6.65450e6	0.324433
$842$	2.87531e7	1.39767
$843$	−5.32415e6	−0.258037
$844$	−1.51026e7	−0.729787
$845$	3.15577e6	0.152042
$846$	3.40362e7	1.63499
$847$	0	0
$848$	−3.87924e6	−0.185250
$849$	−2.17360e7	−1.03493
$850$	935472.	0.0444103
$851$	5.29144e7	2.50467
$852$	−8.54630e7	−4.03347
$853$	−1.69758e7	−0.798838	−0.399419	−	0.916769i	$-0.630788\pi$
$853$	−1.69758e7	−0.798838	−0.399419	+	0.916769i	$0.630788\pi$
$854$	−1.82009e7	−0.853981
$855$	−1.01407e6	−0.0474407
$856$	−1.08525e7	−0.506225
$857$	1.47718e6	0.0687039	0.0343520	−	0.999410i	$-0.489063\pi$
$857$	1.47718e6	0.0687039	0.0343520	+	0.999410i	$0.489063\pi$
$858$	0	0
$859$	3.27516e7	1.51443	0.757216	−	0.653165i	$-0.226559\pi$
$859$	3.27516e7	1.51443	0.757216	+	0.653165i	$0.226559\pi$
$860$	1.24815e7	0.575466
$861$	−1.83718e7	−0.844588
$862$	−5.73793e7	−2.63019
$863$	1.55201e7	0.709364	0.354682	−	0.934987i	$-0.384589\pi$
$863$	1.55201e7	0.709364	0.354682	+	0.934987i	$0.384589\pi$
$864$	−902730.	−0.0411409
$865$	330829.	0.0150336
$866$	−6.48552e7	−2.93867
$867$	−3.01446e7	−1.36195
$868$	−2.78978e7	−1.25681
$869$	0	0
$870$	−2.70381e7	−1.21110
$871$	485401.	0.0216798
$872$	6.55693e7	2.92018
$873$	−3.29711e7	−1.46419
$874$	−6.48613e6	−0.287215
$875$	799451.	0.0352998
$876$	−2.12585e7	−0.935994
$877$	−2.26369e6	−0.0993844	−0.0496922	−	0.998765i	$-0.515824\pi$
$877$	−2.26369e6	−0.0993844	−0.0496922	+	0.998765i	$0.515824\pi$
$878$	−5.41510e7	−2.37066
$879$	1.61435e7	0.704734
$880$	0	0
$881$	−5.99495e6	−0.260223	−0.130112	−	0.991499i	$-0.541534\pi$
$881$	−5.99495e6	−0.260223	−0.130112	+	0.991499i	$0.541534\pi$
$882$	3.04736e7	1.31902
$883$	−2.01988e7	−0.871812	−0.435906	−	0.899992i	$-0.643572\pi$
$883$	−2.01988e7	−0.871812	−0.435906	+	0.899992i	$0.643572\pi$
$884$	4.64994e6	0.200132
$885$	5.32970e6	0.228741
$886$	−3.16612e7	−1.35501
$887$	4.28384e7	1.82820	0.914101	−	0.405487i	$-0.132898\pi$
$887$	4.28384e7	1.82820	0.914101	+	0.405487i	$0.132898\pi$
$888$	−8.34683e7	−3.55213
$889$	7.85134e6	0.333188
$890$	−1.46730e7	−0.620931
$891$	0	0
$892$	1.50025e7	0.631322
$893$	−2.87545e6	−0.120664
$894$	−3.84594e7	−1.60938
$895$	−4.75949e6	−0.198611
$896$	−1.73495e7	−0.721968
$897$	−3.97899e7	−1.65117
$898$	2.76154e6	0.114278
$899$	−4.71386e7	−1.94526
$900$	8.42375e6	0.346656
$901$	886960.	0.0363992
$902$	0	0
$903$	9.15209e6	0.373509
$904$	−1.55342e7	−0.632218
$905$	1.04736e7	0.425085
$906$	8.89327e7	3.59949
$907$	−1.66342e7	−0.671403	−0.335702	−	0.941968i	$-0.608973\pi$
$907$	−1.66342e7	−0.671403	−0.335702	+	0.941968i	$0.608973\pi$
$908$	2.00817e7	0.808326
$909$	2.36859e7	0.950782
$910$	6.08307e6	0.243511
$911$	−2.93595e7	−1.17207	−0.586034	−	0.810286i	$-0.699312\pi$
$911$	−2.93595e7	−1.17207	−0.586034	+	0.810286i	$0.699312\pi$
$912$	2.67058e6	0.106321
$913$	0	0
$914$	−8.78427e6	−0.347809
$915$	1.99960e7	0.789568
$916$	−3.36015e7	−1.32318
$917$	−6.06794e6	−0.238297
$918$	−628491.	−0.0246146
$919$	2.54718e7	0.994880	0.497440	−	0.867498i	$-0.334273\pi$
$919$	2.54718e7	0.994880	0.497440	+	0.867498i	$0.334273\pi$
$920$	2.52811e7	0.984752
$921$	−2.40866e7	−0.935678
$922$	4.96440e7	1.92327
$923$	3.24886e7	1.25524
$924$	0	0
$925$	8.88735e6	0.341522
$926$	−8.58169e7	−3.28886
$927$	2.20833e7	0.844044
$928$	−1.12052e7	−0.427119
$929$	−6.98156e6	−0.265408	−0.132704	−	0.991156i	$-0.542366\pi$
$929$	−6.98156e6	−0.265408	−0.132704	+	0.991156i	$0.542366\pi$
$930$	4.69173e7	1.77879
$931$	−2.57447e6	−0.0973451
$932$	−1.59415e7	−0.601158
$933$	−4.49805e7	−1.69169
$934$	2.19499e6	0.0823315
$935$	0	0
$936$	3.00751e7	1.12207
$937$	−1.40896e7	−0.524263	−0.262131	−	0.965032i	$-0.584425\pi$
$937$	−1.40896e7	−0.524263	−0.262131	+	0.965032i	$0.584425\pi$
$938$	−481956.	−0.0178855
$939$	9.58064e6	0.354593
$940$	2.38861e7	0.881709
$941$	1.21898e7	0.448769	0.224384	−	0.974501i	$-0.427963\pi$
$941$	1.21898e7	0.448769	0.224384	+	0.974501i	$0.427963\pi$
$942$	8.02883e7	2.94799
$943$	6.18597e7	2.26532
$944$	−6.72558e6	−0.245640
$945$	−537107.	−0.0195651
$946$	0	0
$947$	−3.60096e6	−0.130480	−0.0652399	−	0.997870i	$-0.520781\pi$
$947$	−3.60096e6	−0.130480	−0.0652399	+	0.997870i	$0.520781\pi$
$948$	8.33690e7	3.01289
$949$	8.08140e6	0.291287
$950$	−1.08939e6	−0.0391630
$951$	1.99109e7	0.713904
$952$	−2.16633e6	−0.0774699
$953$	−2.06031e7	−0.734853	−0.367427	−	0.930052i	$-0.619761\pi$
$953$	−2.06031e7	−0.734853	−0.367427	+	0.930052i	$0.619761\pi$
$954$	1.22262e7	0.434933
$955$	−1.12180e7	−0.398024
$956$	−5.92963e7	−2.09837
$957$	0	0
$958$	2.17951e7	0.767266
$959$	8.11974e6	0.285099
$960$	2.29277e7	0.802938
$961$	5.31670e7	1.85709
$962$	6.76244e7	2.35595
$963$	8.92785e6	0.310228
$964$	−6.58670e7	−2.28284
$965$	−1.03707e7	−0.358500
$966$	3.95075e7	1.36219
$967$	−3.32138e7	−1.14223	−0.571114	−	0.820871i	$-0.693489\pi$
$967$	−3.32138e7	−1.14223	−0.571114	+	0.820871i	$0.693489\pi$
$968$	0	0
$969$	−610609.	−0.0208908
$970$	−3.54203e7	−1.20871
$971$	1.24636e7	0.424225	0.212113	−	0.977245i	$-0.431966\pi$
$971$	1.24636e7	0.424225	0.212113	+	0.977245i	$0.431966\pi$
$972$	−7.64027e7	−2.59384
$973$	−1.38746e7	−0.469827
$974$	−2.70218e7	−0.912677
$975$	−6.68301e6	−0.225144
$976$	−2.52330e7	−0.847900
$977$	3.67766e6	0.123264	0.0616318	−	0.998099i	$-0.480370\pi$
$977$	3.67766e6	0.123264	0.0616318	+	0.998099i	$0.480370\pi$
$978$	5.84850e7	1.95523
$979$	0	0
$980$	2.13859e7	0.711316
$981$	−5.39411e7	−1.78956
$982$	−7.14049e7	−2.36292
$983$	4.84009e7	1.59760	0.798802	−	0.601594i	$-0.205467\pi$
$983$	4.84009e7	1.59760	0.798802	+	0.601594i	$0.205467\pi$
$984$	−9.75789e7	−3.21269
$985$	−5.42081e6	−0.178022
$986$	−7.80119e6	−0.255546
$987$	1.75146e7	0.572278
$988$	−5.41503e6	−0.176485
$989$	−3.08160e7	−1.00181
$990$	0	0
$991$	3.43848e7	1.11220	0.556100	−	0.831116i	$-0.312297\pi$
$991$	3.43848e7	1.11220	0.556100	+	0.831116i	$0.312297\pi$
$992$	1.94435e7	0.627330
$993$	−2.54110e7	−0.817802
$994$	−3.22580e7	−1.03555
$995$	1.98088e7	0.634308
$996$	4.62576e7	1.47752
$997$	−2.42849e7	−0.773745	−0.386873	−	0.922133i	$-0.626445\pi$
$997$	−2.42849e7	−0.773745	−0.386873	+	0.922133i	$0.626445\pi$
$998$	3.55989e7	1.13138
$999$	−5.97092e6	−0.189290

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.6.a.p.1.3		20
11.3	even	5		55.6.g.b.31.1	yes	40
11.4	even	5		55.6.g.b.16.1	✓	40
11.10	odd	2		605.6.a.o.1.18		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.g.b.16.1	✓	40	11.4	even	5
55.6.g.b.31.1	yes	40	11.3	even	5
605.6.a.o.1.18		20	11.10	odd	2
605.6.a.p.1.3		20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

\(f(q)\)	\(=\)	\(q-9.60667 q^{2} +21.6000 q^{3} +60.2880 q^{4} -25.0000 q^{5} -207.504 q^{6} -51.1649 q^{7} -271.754 q^{8} +223.560 q^{9} +O(q^{10})\)	\(q-9.60667 q^{2} +21.6000 q^{3} +60.2880 q^{4} -25.0000 q^{5} -207.504 q^{6} -51.1649 q^{7} -271.754 q^{8} +223.560 q^{9} +240.167 q^{10} +1302.22 q^{12} -495.038 q^{13} +491.524 q^{14} -540.000 q^{15} +681.429 q^{16} -155.804 q^{17} -2147.67 q^{18} +181.439 q^{19} -1507.20 q^{20} -1105.16 q^{21} +3721.18 q^{23} -5869.88 q^{24} +625.000 q^{25} +4755.66 q^{26} -419.903 q^{27} -3084.63 q^{28} -5212.07 q^{29} +5187.60 q^{30} +9044.12 q^{31} +2149.85 q^{32} +1496.75 q^{34} +1279.12 q^{35} +13478.0 q^{36} +14219.8 q^{37} -1743.03 q^{38} -10692.8 q^{39} +6793.84 q^{40} +16623.7 q^{41} +10616.9 q^{42} -8281.23 q^{43} -5589.00 q^{45} -35748.2 q^{46} -15848.0 q^{47} +14718.9 q^{48} -14189.2 q^{49} -6004.17 q^{50} -3365.36 q^{51} -29844.8 q^{52} -5692.80 q^{53} +4033.86 q^{54} +13904.2 q^{56} +3919.09 q^{57} +50070.6 q^{58} -9869.82 q^{59} -32555.5 q^{60} -37029.6 q^{61} -86883.8 q^{62} -11438.4 q^{63} -42458.7 q^{64} +12375.9 q^{65} -980.534 q^{67} -9393.10 q^{68} +80377.6 q^{69} -12288.1 q^{70} -65628.6 q^{71} -60753.2 q^{72} -16324.8 q^{73} -136605. q^{74} +13500.0 q^{75} +10938.6 q^{76} +102722. q^{78} +64020.6 q^{79} -17035.7 q^{80} -63395.0 q^{81} -159698. q^{82} +35522.1 q^{83} -66628.0 q^{84} +3895.09 q^{85} +79555.0 q^{86} -112581. q^{87} -61095.0 q^{89} +53691.7 q^{90} +25328.5 q^{91} +224343. q^{92} +195353. q^{93} +152246. q^{94} -4535.99 q^{95} +46436.9 q^{96} -147482. q^{97} +136310. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9}+O(q^{10}) \) 20 * q + q^2 + 407 * q^4 - 500 * q^5 - 264 * q^6 - 167 * q^7 - 57 * q^8 + 1598 * q^9	\( 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9} - 25 q^{10} - 253 q^{12} - 769 q^{13} - 1045 q^{14} + 6963 q^{16} + 2989 q^{17} - 3775 q^{18} - 5828 q^{19} - 10175 q^{20} - 3310 q^{21} - 695 q^{23} - 16724 q^{24} + 12500 q^{25} - 7384 q^{26} + 5925 q^{27} + 3508 q^{28} - 11268 q^{29} + 6600 q^{30} - 11465 q^{31} + 9062 q^{32} + 1217 q^{34} + 4175 q^{35} + 112083 q^{36} - 3057 q^{37} - 13510 q^{38} - 13459 q^{39} + 1425 q^{40} + 839 q^{41} - 14772 q^{42} - 43671 q^{43} - 39950 q^{45} - 81471 q^{46} + 32245 q^{47} - 104315 q^{48} + 2959 q^{49} + 625 q^{50} - 69047 q^{51} - 42696 q^{52} + 27981 q^{53} - 61212 q^{54} - 28294 q^{56} - 79425 q^{57} + 37274 q^{58} - 56847 q^{59} + 6325 q^{60} - 85616 q^{61} - 38095 q^{62} - 100055 q^{63} - 18233 q^{64} + 19225 q^{65} - 31091 q^{67} + 83972 q^{68} - 48708 q^{69} + 26125 q^{70} - 106431 q^{71} - 350510 q^{72} - 117959 q^{73} - 154757 q^{74} - 451972 q^{76} + 348898 q^{78} - 215138 q^{79} - 174075 q^{80} + 75516 q^{81} - 127864 q^{82} - 66761 q^{83} - 521275 q^{84} - 74725 q^{85} - 32222 q^{86} + 5311 q^{87} + 270560 q^{89} + 94375 q^{90} - 269192 q^{91} - 461663 q^{92} + 9345 q^{93} - 479494 q^{94} + 145700 q^{95} - 1247523 q^{96} + 45338 q^{97} + 420757 q^{98}+O(q^{100}) \) 20 * q + q^2 + 407 * q^4 - 500 * q^5 - 264 * q^6 - 167 * q^7 - 57 * q^8 + 1598 * q^9 - 25 * q^10 - 253 * q^12 - 769 * q^13 - 1045 * q^14 + 6963 * q^16 + 2989 * q^17 - 3775 * q^18 - 5828 * q^19 - 10175 * q^20 - 3310 * q^21 - 695 * q^23 - 16724 * q^24 + 12500 * q^25 - 7384 * q^26 + 5925 * q^27 + 3508 * q^28 - 11268 * q^29 + 6600 * q^30 - 11465 * q^31 + 9062 * q^32 + 1217 * q^34 + 4175 * q^35 + 112083 * q^36 - 3057 * q^37 - 13510 * q^38 - 13459 * q^39 + 1425 * q^40 + 839 * q^41 - 14772 * q^42 - 43671 * q^43 - 39950 * q^45 - 81471 * q^46 + 32245 * q^47 - 104315 * q^48 + 2959 * q^49 + 625 * q^50 - 69047 * q^51 - 42696 * q^52 + 27981 * q^53 - 61212 * q^54 - 28294 * q^56 - 79425 * q^57 + 37274 * q^58 - 56847 * q^59 + 6325 * q^60 - 85616 * q^61 - 38095 * q^62 - 100055 * q^63 - 18233 * q^64 + 19225 * q^65 - 31091 * q^67 + 83972 * q^68 - 48708 * q^69 + 26125 * q^70 - 106431 * q^71 - 350510 * q^72 - 117959 * q^73 - 154757 * q^74 - 451972 * q^76 + 348898 * q^78 - 215138 * q^79 - 174075 * q^80 + 75516 * q^81 - 127864 * q^82 - 66761 * q^83 - 521275 * q^84 - 74725 * q^85 - 32222 * q^86 + 5311 * q^87 + 270560 * q^89 + 94375 * q^90 - 269192 * q^91 - 461663 * q^92 + 9345 * q^93 - 479494 * q^94 + 145700 * q^95 - 1247523 * q^96 + 45338 * q^97 + 420757 * q^98

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