# Properties

 Label 1900.2.i.d.201.2 Level $1900$ Weight $2$ Character 1900.201 Analytic conductor $15.172$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1900 = 2^{2} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1900.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$15.1715763840$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ Defining polynomial: $$x^{8} - x^{7} + 9x^{6} + 2x^{5} + 65x^{4} - 20x^{3} + 25x^{2} + 6x + 4$$ x^8 - x^7 + 9*x^6 + 2*x^5 + 65*x^4 - 20*x^3 + 25*x^2 + 6*x + 4 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$3$$ Twist minimal: no (minimal twist has level 380) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 201.2 Root $$-0.176725 + 0.306096i$$ of defining polynomial Character $$\chi$$ $$=$$ 1900.201 Dual form 1900.2.i.d.501.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.176725 + 0.306096i) q^{3} +4.30507 q^{7} +(1.43754 + 2.48989i) q^{9} +O(q^{10})$$ $$q+(-0.176725 + 0.306096i) q^{3} +4.30507 q^{7} +(1.43754 + 2.48989i) q^{9} +6.01196 q^{11} +(-2.97581 - 5.15425i) q^{13} +(1.93754 - 3.35591i) q^{17} +(4.19835 + 1.17212i) q^{19} +(-0.760812 + 1.31776i) q^{21} +(0.391721 + 0.678480i) q^{23} -2.07654 q^{27} +(-3.98179 - 6.89666i) q^{29} -4.49034 q^{31} +(-1.06246 + 1.84024i) q^{33} +0.988035 q^{37} +2.10360 q^{39} +(-3.15253 + 5.46035i) q^{41} +(-0.785004 + 1.35967i) q^{43} +(-0.630909 - 1.09277i) q^{47} +11.5336 q^{49} +(0.684822 + 1.18615i) q^{51} +(-4.07443 - 7.05712i) q^{53} +(-1.10073 + 1.07796i) q^{57} +(-2.62834 + 4.55242i) q^{59} +(-2.80507 - 4.85852i) q^{61} +(6.18869 + 10.7191i) q^{63} +(3.52162 + 6.09963i) q^{67} -0.276907 q^{69} +(2.90736 - 5.03570i) q^{71} +(-4.62024 + 8.00250i) q^{73} +25.8819 q^{77} +(6.99743 - 12.1199i) q^{79} +(-3.94563 + 6.83404i) q^{81} -6.58197 q^{83} +2.81472 q^{87} +(1.69237 + 2.93126i) q^{89} +(-12.8110 - 22.1894i) q^{91} +(0.793555 - 1.37448i) q^{93} +(-3.69835 + 6.40573i) q^{97} +(8.64242 + 14.9691i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + q^{3} - 5 q^{9}+O(q^{10})$$ 8 * q + q^3 - 5 * q^9 $$8 q + q^{3} - 5 q^{9} + 4 q^{11} - 9 q^{13} - q^{17} + 3 q^{19} + 8 q^{21} - 20 q^{27} + 5 q^{29} - 20 q^{31} - 25 q^{33} + 52 q^{37} - 54 q^{39} - 8 q^{41} - 7 q^{43} - 16 q^{47} + 20 q^{49} + 12 q^{51} - 5 q^{53} - 27 q^{57} + 11 q^{59} + 12 q^{61} + 3 q^{63} + 6 q^{69} + 14 q^{71} + 4 q^{73} + 44 q^{77} + 13 q^{79} - 24 q^{81} - 10 q^{83} + 4 q^{87} + 5 q^{89} - 46 q^{91} + 28 q^{93} + q^{97} + 24 q^{99}+O(q^{100})$$ 8 * q + q^3 - 5 * q^9 + 4 * q^11 - 9 * q^13 - q^17 + 3 * q^19 + 8 * q^21 - 20 * q^27 + 5 * q^29 - 20 * q^31 - 25 * q^33 + 52 * q^37 - 54 * q^39 - 8 * q^41 - 7 * q^43 - 16 * q^47 + 20 * q^49 + 12 * q^51 - 5 * q^53 - 27 * q^57 + 11 * q^59 + 12 * q^61 + 3 * q^63 + 6 * q^69 + 14 * q^71 + 4 * q^73 + 44 * q^77 + 13 * q^79 - 24 * q^81 - 10 * q^83 + 4 * q^87 + 5 * q^89 - 46 * q^91 + 28 * q^93 + q^97 + 24 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$$.

 $$n$$ $$77$$ $$401$$ $$951$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −0.176725 + 0.306096i −0.102032 + 0.176725i −0.912522 0.409028i $$-0.865868\pi$$
0.810490 + 0.585753i $$0.199201\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 4.30507 1.62716 0.813581 0.581452i $$-0.197515\pi$$
0.813581 + 0.581452i $$0.197515\pi$$
$$8$$ 0 0
$$9$$ 1.43754 + 2.48989i 0.479179 + 0.829962i
$$10$$ 0 0
$$11$$ 6.01196 1.81268 0.906338 0.422554i $$-0.138866\pi$$
0.906338 + 0.422554i $$0.138866\pi$$
$$12$$ 0 0
$$13$$ −2.97581 5.15425i −0.825341 1.42953i −0.901659 0.432448i $$-0.857650\pi$$
0.0763181 0.997084i $$-0.475684\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 1.93754 3.35591i 0.469922 0.813928i −0.529487 0.848318i $$-0.677615\pi$$
0.999408 + 0.0343900i $$0.0109488\pi$$
$$18$$ 0 0
$$19$$ 4.19835 + 1.17212i 0.963167 + 0.268903i
$$20$$ 0 0
$$21$$ −0.760812 + 1.31776i −0.166023 + 0.287560i
$$22$$ 0 0
$$23$$ 0.391721 + 0.678480i 0.0816794 + 0.141473i 0.903971 0.427593i $$-0.140638\pi$$
−0.822292 + 0.569066i $$0.807305\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −2.07654 −0.399631
$$28$$ 0 0
$$29$$ −3.98179 6.89666i −0.739400 1.28068i −0.952766 0.303706i $$-0.901776\pi$$
0.213366 0.976972i $$-0.431557\pi$$
$$30$$ 0 0
$$31$$ −4.49034 −0.806489 −0.403245 0.915092i $$-0.632118\pi$$
−0.403245 + 0.915092i $$0.632118\pi$$
$$32$$ 0 0
$$33$$ −1.06246 + 1.84024i −0.184951 + 0.320345i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0.988035 0.162432 0.0812160 0.996697i $$-0.474120\pi$$
0.0812160 + 0.996697i $$0.474120\pi$$
$$38$$ 0 0
$$39$$ 2.10360 0.336845
$$40$$ 0 0
$$41$$ −3.15253 + 5.46035i −0.492343 + 0.852763i −0.999961 0.00881921i $$-0.997193\pi$$
0.507618 + 0.861582i $$0.330526\pi$$
$$42$$ 0 0
$$43$$ −0.785004 + 1.35967i −0.119712 + 0.207347i −0.919654 0.392731i $$-0.871530\pi$$
0.799942 + 0.600078i $$0.204864\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −0.630909 1.09277i −0.0920275 0.159396i 0.816337 0.577576i $$-0.196001\pi$$
−0.908364 + 0.418180i $$0.862668\pi$$
$$48$$ 0 0
$$49$$ 11.5336 1.64766
$$50$$ 0 0
$$51$$ 0.684822 + 1.18615i 0.0958942 + 0.166094i
$$52$$ 0 0
$$53$$ −4.07443 7.05712i −0.559666 0.969369i −0.997524 0.0703255i $$-0.977596\pi$$
0.437858 0.899044i $$-0.355737\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −1.10073 + 1.07796i −0.145796 + 0.142779i
$$58$$ 0 0
$$59$$ −2.62834 + 4.55242i −0.342181 + 0.592675i −0.984837 0.173480i $$-0.944499\pi$$
0.642657 + 0.766154i $$0.277832\pi$$
$$60$$ 0 0
$$61$$ −2.80507 4.85852i −0.359152 0.622069i 0.628668 0.777674i $$-0.283601\pi$$
−0.987819 + 0.155605i $$0.950267\pi$$
$$62$$ 0 0
$$63$$ 6.18869 + 10.7191i 0.779702 + 1.35048i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 3.52162 + 6.09963i 0.430235 + 0.745189i 0.996893 0.0787642i $$-0.0250974\pi$$
−0.566658 + 0.823953i $$0.691764\pi$$
$$68$$ 0 0
$$69$$ −0.276907 −0.0333357
$$70$$ 0 0
$$71$$ 2.90736 5.03570i 0.345040 0.597628i −0.640321 0.768108i $$-0.721199\pi$$
0.985361 + 0.170480i $$0.0545319\pi$$
$$72$$ 0 0
$$73$$ −4.62024 + 8.00250i −0.540759 + 0.936621i 0.458102 + 0.888900i $$0.348529\pi$$
−0.998861 + 0.0477218i $$0.984804\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 25.8819 2.94952
$$78$$ 0 0
$$79$$ 6.99743 12.1199i 0.787273 1.36360i −0.140359 0.990101i $$-0.544826\pi$$
0.927632 0.373495i $$-0.121841\pi$$
$$80$$ 0 0
$$81$$ −3.94563 + 6.83404i −0.438404 + 0.759338i
$$82$$ 0 0
$$83$$ −6.58197 −0.722465 −0.361233 0.932476i $$-0.617644\pi$$
−0.361233 + 0.932476i $$0.617644\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 2.81472 0.301770
$$88$$ 0 0
$$89$$ 1.69237 + 2.93126i 0.179390 + 0.310713i 0.941672 0.336532i $$-0.109254\pi$$
−0.762281 + 0.647246i $$0.775921\pi$$
$$90$$ 0 0
$$91$$ −12.8110 22.1894i −1.34296 2.32608i
$$92$$ 0 0
$$93$$ 0.793555 1.37448i 0.0822878 0.142527i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −3.69835 + 6.40573i −0.375510 + 0.650403i −0.990403 0.138208i $$-0.955866\pi$$
0.614893 + 0.788611i $$0.289199\pi$$
$$98$$ 0 0
$$99$$ 8.64242 + 14.9691i 0.868596 + 1.50445i
$$100$$ 0 0
$$101$$ 4.90369 + 8.49343i 0.487935 + 0.845128i 0.999904 0.0138759i $$-0.00441699\pi$$
−0.511969 + 0.859004i $$0.671084\pi$$
$$102$$ 0 0
$$103$$ −14.4368 −1.42250 −0.711251 0.702938i $$-0.751871\pi$$
−0.711251 + 0.702938i $$0.751871\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 9.49034 0.917466 0.458733 0.888574i $$-0.348303\pi$$
0.458733 + 0.888574i $$0.348303\pi$$
$$108$$ 0 0
$$109$$ 1.30920 2.26759i 0.125398 0.217196i −0.796490 0.604651i $$-0.793312\pi$$
0.921889 + 0.387455i $$0.126646\pi$$
$$110$$ 0 0
$$111$$ −0.174610 + 0.302434i −0.0165733 + 0.0287058i
$$112$$ 0 0
$$113$$ 13.6705 1.28601 0.643005 0.765862i $$-0.277687\pi$$
0.643005 + 0.765862i $$0.277687\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 8.55567 14.8188i 0.790972 1.37000i
$$118$$ 0 0
$$119$$ 8.34122 14.4474i 0.764639 1.32439i
$$120$$ 0 0
$$121$$ 25.1437 2.28579
$$122$$ 0 0
$$123$$ −1.11426 1.92996i −0.100470 0.174018i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 6.53359 + 11.3165i 0.579762 + 1.00418i 0.995506 + 0.0946960i $$0.0301879\pi$$
−0.415744 + 0.909482i $$0.636479\pi$$
$$128$$ 0 0
$$129$$ −0.277459 0.480574i −0.0244289 0.0423122i
$$130$$ 0 0
$$131$$ 3.75070 6.49640i 0.327700 0.567593i −0.654355 0.756188i $$-0.727060\pi$$
0.982055 + 0.188594i $$0.0603931\pi$$
$$132$$ 0 0
$$133$$ 18.0742 + 5.04606i 1.56723 + 0.437549i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −4.21500 7.30059i −0.360111 0.623731i 0.627867 0.778320i $$-0.283928\pi$$
−0.987979 + 0.154589i $$0.950595\pi$$
$$138$$ 0 0
$$139$$ −4.38961 7.60302i −0.372322 0.644880i 0.617601 0.786492i $$-0.288105\pi$$
−0.989922 + 0.141612i $$0.954771\pi$$
$$140$$ 0 0
$$141$$ 0.445989 0.0375591
$$142$$ 0 0
$$143$$ −17.8905 30.9872i −1.49607 2.59128i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −2.03827 + 3.53039i −0.168114 + 0.291182i
$$148$$ 0 0
$$149$$ 0.915913 1.58641i 0.0750345 0.129964i −0.826067 0.563572i $$-0.809427\pi$$
0.901101 + 0.433609i $$0.142760\pi$$
$$150$$ 0 0
$$151$$ −0.389869 −0.0317271 −0.0158635 0.999874i $$-0.505050\pi$$
−0.0158635 + 0.999874i $$0.505050\pi$$
$$152$$ 0 0
$$153$$ 11.1411 0.900706
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −1.37608 + 2.38344i −0.109823 + 0.190219i −0.915698 0.401866i $$-0.868362\pi$$
0.805875 + 0.592085i $$0.201695\pi$$
$$158$$ 0 0
$$159$$ 2.88021 0.228416
$$160$$ 0 0
$$161$$ 1.68638 + 2.92090i 0.132906 + 0.230199i
$$162$$ 0 0
$$163$$ 15.0953 1.18236 0.591179 0.806540i $$-0.298663\pi$$
0.591179 + 0.806540i $$0.298663\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 1.49402 + 2.58771i 0.115611 + 0.200243i 0.918024 0.396526i $$-0.129784\pi$$
−0.802413 + 0.596769i $$0.796451\pi$$
$$168$$ 0 0
$$169$$ −11.2109 + 19.4178i −0.862374 + 1.49368i
$$170$$ 0 0
$$171$$ 3.11683 + 12.1384i 0.238350 + 0.928245i
$$172$$ 0 0
$$173$$ −11.5945 + 20.0822i −0.881513 + 1.52682i −0.0318535 + 0.999493i $$0.510141\pi$$
−0.849659 + 0.527332i $$0.823192\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −0.928986 1.60905i −0.0698269 0.120944i
$$178$$ 0 0
$$179$$ −13.5091 −1.00972 −0.504860 0.863201i $$-0.668456\pi$$
−0.504860 + 0.863201i $$0.668456\pi$$
$$180$$ 0 0
$$181$$ 10.1559 + 17.5906i 0.754886 + 1.30750i 0.945431 + 0.325822i $$0.105641\pi$$
−0.190546 + 0.981678i $$0.561026\pi$$
$$182$$ 0 0
$$183$$ 1.98290 0.146580
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 11.6484 20.1756i 0.851816 1.47539i
$$188$$ 0 0
$$189$$ −8.93965 −0.650264
$$190$$ 0 0
$$191$$ −7.04838 −0.510003 −0.255002 0.966941i $$-0.582076\pi$$
−0.255002 + 0.966941i $$0.582076\pi$$
$$192$$ 0 0
$$193$$ −11.8892 + 20.5926i −0.855800 + 1.48229i 0.0201010 + 0.999798i $$0.493601\pi$$
−0.875901 + 0.482491i $$0.839732\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −23.7428 −1.69160 −0.845802 0.533497i $$-0.820878\pi$$
−0.845802 + 0.533497i $$0.820878\pi$$
$$198$$ 0 0
$$199$$ 11.4893 + 19.9001i 0.814457 + 1.41068i 0.909717 + 0.415229i $$0.136299\pi$$
−0.0952595 + 0.995452i $$0.530368\pi$$
$$200$$ 0 0
$$201$$ −2.48943 −0.175591
$$202$$ 0 0
$$203$$ −17.1419 29.6906i −1.20312 2.08387i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −1.12623 + 1.95068i −0.0782781 + 0.135582i
$$208$$ 0 0
$$209$$ 25.2403 + 7.04675i 1.74591 + 0.487434i
$$210$$ 0 0
$$211$$ 0.692366 1.19921i 0.0476645 0.0825573i −0.841209 0.540710i $$-0.818156\pi$$
0.888873 + 0.458153i $$0.151489\pi$$
$$212$$ 0 0
$$213$$ 1.02761 + 1.77987i 0.0704104 + 0.121954i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −19.3312 −1.31229
$$218$$ 0 0
$$219$$ −1.63302 2.82848i −0.110349 0.191131i
$$220$$ 0 0
$$221$$ −23.0629 −1.55138
$$222$$ 0 0
$$223$$ −11.6500 + 20.1783i −0.780139 + 1.35124i 0.151721 + 0.988423i $$0.451519\pi$$
−0.931860 + 0.362818i $$0.881815\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 4.48943 0.297974 0.148987 0.988839i $$-0.452399\pi$$
0.148987 + 0.988839i $$0.452399\pi$$
$$228$$ 0 0
$$229$$ 9.20830 0.608501 0.304251 0.952592i $$-0.401594\pi$$
0.304251 + 0.952592i $$0.401594\pi$$
$$230$$ 0 0
$$231$$ −4.57397 + 7.92236i −0.300945 + 0.521253i
$$232$$ 0 0
$$233$$ −2.16265 + 3.74581i −0.141680 + 0.245396i −0.928129 0.372258i $$-0.878584\pi$$
0.786450 + 0.617654i $$0.211917\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 2.47324 + 4.28378i 0.160654 + 0.278261i
$$238$$ 0 0
$$239$$ −14.8267 −0.959059 −0.479529 0.877526i $$-0.659193\pi$$
−0.479529 + 0.877526i $$0.659193\pi$$
$$240$$ 0 0
$$241$$ −1.44453 2.50199i −0.0930500 0.161167i 0.815743 0.578414i $$-0.196328\pi$$
−0.908793 + 0.417247i $$0.862995\pi$$
$$242$$ 0 0
$$243$$ −4.50940 7.81050i −0.289278 0.501044i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −6.45207 25.1273i −0.410535 1.59881i
$$248$$ 0 0
$$249$$ 1.16320 2.01472i 0.0737147 0.127678i
$$250$$ 0 0
$$251$$ −7.65253 13.2546i −0.483024 0.836621i 0.516786 0.856114i $$-0.327128\pi$$
−0.999810 + 0.0194930i $$0.993795\pi$$
$$252$$ 0 0
$$253$$ 2.35501 + 4.07900i 0.148058 + 0.256445i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 6.54214 + 11.3313i 0.408087 + 0.706828i 0.994675 0.103057i $$-0.0328625\pi$$
−0.586588 + 0.809886i $$0.699529\pi$$
$$258$$ 0 0
$$259$$ 4.25356 0.264303
$$260$$ 0 0
$$261$$ 11.4479 19.8284i 0.708610 1.22735i
$$262$$ 0 0
$$263$$ 9.68980 16.7832i 0.597499 1.03490i −0.395691 0.918384i $$-0.629495\pi$$
0.993189 0.116514i $$-0.0371720\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −1.19633 −0.0732144
$$268$$ 0 0
$$269$$ 0.728523 1.26184i 0.0444188 0.0769357i −0.842961 0.537974i $$-0.819190\pi$$
0.887380 + 0.461039i $$0.152523\pi$$
$$270$$ 0 0
$$271$$ −6.28133 + 10.8796i −0.381563 + 0.660887i −0.991286 0.131728i $$-0.957948\pi$$
0.609722 + 0.792615i $$0.291281\pi$$
$$272$$ 0 0
$$273$$ 9.05612 0.548101
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 4.39448 0.264039 0.132019 0.991247i $$-0.457854\pi$$
0.132019 + 0.991247i $$0.457854\pi$$
$$278$$ 0 0
$$279$$ −6.45503 11.1804i −0.386453 0.669355i
$$280$$ 0 0
$$281$$ −2.16265 3.74581i −0.129013 0.223456i 0.794282 0.607550i $$-0.207847\pi$$
−0.923294 + 0.384093i $$0.874514\pi$$
$$282$$ 0 0
$$283$$ 3.74885 6.49319i 0.222846 0.385980i −0.732825 0.680417i $$-0.761799\pi$$
0.955671 + 0.294437i $$0.0951320\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −13.5719 + 23.5072i −0.801122 + 1.38758i
$$288$$ 0 0
$$289$$ 0.991903 + 1.71803i 0.0583472 + 0.101060i
$$290$$ 0 0
$$291$$ −1.30718 2.26410i −0.0766282 0.132724i
$$292$$ 0 0
$$293$$ 22.2837 1.30183 0.650915 0.759151i $$-0.274385\pi$$
0.650915 + 0.759151i $$0.274385\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −12.4841 −0.724401
$$298$$ 0 0
$$299$$ 2.33137 4.03805i 0.134827 0.233527i
$$300$$ 0 0
$$301$$ −3.37949 + 5.85345i −0.194791 + 0.337387i
$$302$$ 0 0
$$303$$ −3.46641 −0.199140
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −15.1403 + 26.2238i −0.864103 + 1.49667i 0.00383236 + 0.999993i $$0.498780\pi$$
−0.867935 + 0.496677i $$0.834553\pi$$
$$308$$ 0 0
$$309$$ 2.55134 4.41906i 0.145141 0.251391i
$$310$$ 0 0
$$311$$ −5.37224 −0.304632 −0.152316 0.988332i $$-0.548673\pi$$
−0.152316 + 0.988332i $$0.548673\pi$$
$$312$$ 0 0
$$313$$ −2.40369 4.16331i −0.135864 0.235324i 0.790063 0.613026i $$-0.210048\pi$$
−0.925927 + 0.377702i $$0.876714\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −14.8855 25.7824i −0.836052 1.44808i −0.893171 0.449717i $$-0.851525\pi$$
0.0571197 0.998367i $$-0.481808\pi$$
$$318$$ 0 0
$$319$$ −23.9384 41.4625i −1.34029 2.32145i
$$320$$ 0 0
$$321$$ −1.67718 + 2.90496i −0.0936110 + 0.162139i
$$322$$ 0 0
$$323$$ 12.0680 11.8183i 0.671481 0.657586i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0.462735 + 0.801480i 0.0255893 + 0.0443220i
$$328$$ 0 0
$$329$$ −2.71610 4.70443i −0.149744 0.259364i
$$330$$ 0 0
$$331$$ 30.8042 1.69315 0.846577 0.532266i $$-0.178659\pi$$
0.846577 + 0.532266i $$0.178659\pi$$
$$332$$ 0 0
$$333$$ 1.42034 + 2.46010i 0.0778340 + 0.134812i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −3.32529 + 5.75957i −0.181140 + 0.313744i −0.942269 0.334857i $$-0.891312\pi$$
0.761129 + 0.648601i $$0.224645\pi$$
$$338$$ 0 0
$$339$$ −2.41591 + 4.18448i −0.131214 + 0.227270i
$$340$$ 0 0
$$341$$ −26.9958 −1.46190
$$342$$ 0 0
$$343$$ 19.5174 1.05384
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 7.70534 13.3460i 0.413644 0.716453i −0.581641 0.813446i $$-0.697589\pi$$
0.995285 + 0.0969930i $$0.0309224\pi$$
$$348$$ 0 0
$$349$$ −27.0157 −1.44612 −0.723058 0.690788i $$-0.757264\pi$$
−0.723058 + 0.690788i $$0.757264\pi$$
$$350$$ 0 0
$$351$$ 6.17939 + 10.7030i 0.329832 + 0.571285i
$$352$$ 0 0
$$353$$ −19.7783 −1.05269 −0.526346 0.850270i $$-0.676439\pi$$
−0.526346 + 0.850270i $$0.676439\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 2.94820 + 5.10644i 0.156035 + 0.270261i
$$358$$ 0 0
$$359$$ −17.8408 + 30.9011i −0.941600 + 1.63090i −0.179179 + 0.983816i $$0.557344\pi$$
−0.762420 + 0.647082i $$0.775989\pi$$
$$360$$ 0 0
$$361$$ 16.2523 + 9.84195i 0.855382 + 0.517997i
$$362$$ 0 0
$$363$$ −4.44352 + 7.69640i −0.233224 + 0.403956i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −1.05235 1.82272i −0.0549322 0.0951454i 0.837252 0.546818i $$-0.184161\pi$$
−0.892184 + 0.451672i $$0.850828\pi$$
$$368$$ 0 0
$$369$$ −18.1275 −0.943681
$$370$$ 0 0
$$371$$ −17.5407 30.3813i −0.910667 1.57732i
$$372$$ 0 0
$$373$$ 32.0208 1.65797 0.828987 0.559268i $$-0.188918\pi$$
0.828987 + 0.559268i $$0.188918\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −23.6981 + 41.0463i −1.22051 + 2.11399i
$$378$$ 0 0
$$379$$ −2.24784 −0.115464 −0.0577319 0.998332i $$-0.518387\pi$$
−0.0577319 + 0.998332i $$0.518387\pi$$
$$380$$ 0 0
$$381$$ −4.61859 −0.236617
$$382$$ 0 0
$$383$$ 1.33479 2.31192i 0.0682044 0.118133i −0.829907 0.557902i $$-0.811606\pi$$
0.898111 + 0.439769i $$0.144940\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −4.51389 −0.229454
$$388$$ 0 0
$$389$$ −7.76036 13.4413i −0.393466 0.681503i 0.599438 0.800421i $$-0.295391\pi$$
−0.992904 + 0.118918i $$0.962057\pi$$
$$390$$ 0 0
$$391$$ 3.03589 0.153532
$$392$$ 0 0
$$393$$ 1.32568 + 2.29615i 0.0668719 + 0.115825i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 1.24839 2.16228i 0.0626551 0.108522i −0.832996 0.553278i $$-0.813377\pi$$
0.895651 + 0.444757i $$0.146710\pi$$
$$398$$ 0 0
$$399$$ −4.73873 + 4.64067i −0.237233 + 0.232324i
$$400$$ 0 0
$$401$$ 10.8590 18.8083i 0.542271 0.939242i −0.456502 0.889723i $$-0.650898\pi$$
0.998773 0.0495192i $$-0.0157689\pi$$
$$402$$ 0 0
$$403$$ 13.3624 + 23.1443i 0.665628 + 1.15290i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 5.94003 0.294437
$$408$$ 0 0
$$409$$ −12.1200 20.9924i −0.599294 1.03801i −0.992925 0.118740i $$-0.962115\pi$$
0.393631 0.919269i $$-0.371219\pi$$
$$410$$ 0 0
$$411$$ 2.97958 0.146972
$$412$$ 0 0
$$413$$ −11.3152 + 19.5985i −0.556784 + 0.964377i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 3.10301 0.151955
$$418$$ 0 0
$$419$$ −37.6543 −1.83953 −0.919766 0.392467i $$-0.871622\pi$$
−0.919766 + 0.392467i $$0.871622\pi$$
$$420$$ 0 0
$$421$$ 18.6884 32.3693i 0.910818 1.57758i 0.0979071 0.995196i $$-0.468785\pi$$
0.812911 0.582388i $$-0.197881\pi$$
$$422$$ 0 0
$$423$$ 1.81391 3.14178i 0.0881953 0.152759i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −12.0760 20.9162i −0.584398 1.01221i
$$428$$ 0 0
$$429$$ 12.6467 0.610591
$$430$$ 0 0
$$431$$ −5.41491 9.37889i −0.260827 0.451765i 0.705635 0.708576i $$-0.250662\pi$$
−0.966462 + 0.256810i $$0.917329\pi$$
$$432$$ 0 0
$$433$$ 5.71031 + 9.89055i 0.274420 + 0.475310i 0.969989 0.243150i $$-0.0781808\pi$$
−0.695569 + 0.718460i $$0.744847\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0.849319 + 3.30764i 0.0406284 + 0.158226i
$$438$$ 0 0
$$439$$ −15.0612 + 26.0868i −0.718832 + 1.24505i 0.242631 + 0.970119i $$0.421989\pi$$
−0.961463 + 0.274934i $$0.911344\pi$$
$$440$$ 0 0
$$441$$ 16.5800 + 28.7173i 0.789522 + 1.36749i
$$442$$ 0 0
$$443$$ −10.3045 17.8479i −0.489582 0.847981i 0.510346 0.859969i $$-0.329517\pi$$
−0.999928 + 0.0119880i $$0.996184\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0.323729 + 0.560715i 0.0153119 + 0.0265209i
$$448$$ 0 0
$$449$$ −3.61436 −0.170572 −0.0852861 0.996357i $$-0.527180\pi$$
−0.0852861 + 0.996357i $$0.527180\pi$$
$$450$$ 0 0
$$451$$ −18.9529 + 32.8274i −0.892458 + 1.54578i
$$452$$ 0 0
$$453$$ 0.0688995 0.119338i 0.00323718 0.00560697i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −5.50452 −0.257491 −0.128745 0.991678i $$-0.541095\pi$$
−0.128745 + 0.991678i $$0.541095\pi$$
$$458$$ 0 0
$$459$$ −4.02338 + 6.96869i −0.187795 + 0.325271i
$$460$$ 0 0
$$461$$ −9.66053 + 16.7325i −0.449936 + 0.779312i −0.998381 0.0568746i $$-0.981886\pi$$
0.548446 + 0.836186i $$0.315220\pi$$
$$462$$ 0 0
$$463$$ −1.05722 −0.0491334 −0.0245667 0.999698i $$-0.507821\pi$$
−0.0245667 + 0.999698i $$0.507821\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −21.9413 −1.01532 −0.507662 0.861556i $$-0.669490\pi$$
−0.507662 + 0.861556i $$0.669490\pi$$
$$468$$ 0 0
$$469$$ 15.1608 + 26.2593i 0.700062 + 1.21254i
$$470$$ 0 0
$$471$$ −0.486375 0.842426i −0.0224110 0.0388169i
$$472$$ 0 0
$$473$$ −4.71942 + 8.17427i −0.216999 + 0.375853i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 11.7143 20.2897i 0.536360 0.929003i
$$478$$ 0 0
$$479$$ 6.60203 + 11.4351i 0.301655 + 0.522481i 0.976511 0.215468i $$-0.0691277\pi$$
−0.674856 + 0.737949i $$0.735794\pi$$
$$480$$ 0 0
$$481$$ −2.94020 5.09258i −0.134062 0.232202i
$$482$$ 0 0
$$483$$ −1.19210 −0.0542426
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −15.5627 −0.705211 −0.352606 0.935772i $$-0.614704\pi$$
−0.352606 + 0.935772i $$0.614704\pi$$
$$488$$ 0 0
$$489$$ −2.66772 + 4.62063i −0.120638 + 0.208952i
$$490$$ 0 0
$$491$$ 14.7978 25.6306i 0.667816 1.15669i −0.310698 0.950509i $$-0.600563\pi$$
0.978514 0.206182i $$-0.0661040\pi$$
$$492$$ 0 0
$$493$$ −30.8595 −1.38984
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 12.5164 21.6790i 0.561437 0.972437i
$$498$$ 0 0
$$499$$ 2.92190 5.06087i 0.130802 0.226556i −0.793184 0.608982i $$-0.791578\pi$$
0.923986 + 0.382426i $$0.124911\pi$$
$$500$$ 0 0
$$501$$ −1.05612 −0.0471840
$$502$$ 0 0
$$503$$ 3.14544 + 5.44807i 0.140248 + 0.242917i 0.927590 0.373600i $$-0.121877\pi$$
−0.787342 + 0.616517i $$0.788543\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −3.96248 6.86321i −0.175980 0.304806i
$$508$$ 0 0
$$509$$ 1.84591 + 3.19720i 0.0818183 + 0.141713i 0.904031 0.427467i $$-0.140594\pi$$
−0.822213 + 0.569180i $$0.807261\pi$$
$$510$$ 0 0
$$511$$ −19.8905 + 34.4513i −0.879902 + 1.52403i
$$512$$ 0 0
$$513$$ −8.71805 2.43396i −0.384911 0.107462i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −3.79300 6.56967i −0.166816 0.288934i
$$518$$ 0 0
$$519$$ −4.09807 7.09806i −0.179885 0.311570i
$$520$$ 0 0
$$521$$ 29.0510 1.27275 0.636373 0.771381i $$-0.280434\pi$$
0.636373 + 0.771381i $$0.280434\pi$$
$$522$$ 0 0
$$523$$ 9.21685 + 15.9640i 0.403025 + 0.698059i 0.994089 0.108565i $$-0.0346256\pi$$
−0.591065 + 0.806624i $$0.701292\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −8.70020 + 15.0692i −0.378987 + 0.656424i
$$528$$ 0 0
$$529$$ 11.1931 19.3870i 0.486657 0.842915i
$$530$$ 0 0
$$531$$ −15.1133 −0.655863
$$532$$ 0 0
$$533$$ 37.5253 1.62540
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 2.38740 4.13510i 0.103024 0.178443i
$$538$$ 0 0
$$539$$ 69.3395 2.98666
$$540$$ 0 0
$$541$$ 21.0875 + 36.5246i 0.906622 + 1.57032i 0.818724 + 0.574187i $$0.194682\pi$$
0.0878981 + 0.996129i $$0.471985\pi$$
$$542$$ 0 0
$$543$$ −7.17923 −0.308090
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 7.87719 + 13.6437i 0.336804 + 0.583362i 0.983830 0.179106i $$-0.0573206\pi$$
−0.647025 + 0.762468i $$0.723987\pi$$
$$548$$ 0 0
$$549$$ 8.06477 13.9686i 0.344196 0.596165i
$$550$$ 0 0
$$551$$ −8.63321 33.6217i −0.367787 1.43233i
$$552$$ 0 0
$$553$$ 30.1244 52.1770i 1.28102 2.21879i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 11.5924 + 20.0786i 0.491185 + 0.850757i 0.999948 0.0101493i $$-0.00323068\pi$$
−0.508764 + 0.860906i $$0.669897\pi$$
$$558$$ 0 0
$$559$$ 9.34408 0.395213
$$560$$ 0 0
$$561$$ 4.11712 + 7.13107i 0.173825 + 0.301074i
$$562$$ 0 0
$$563$$ 0.970934 0.0409200 0.0204600 0.999791i $$-0.493487\pi$$
0.0204600 + 0.999791i $$0.493487\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −16.9862 + 29.4210i −0.713354 + 1.23556i
$$568$$ 0 0
$$569$$ −30.1395 −1.26351 −0.631757 0.775167i $$-0.717666\pi$$
−0.631757 + 0.775167i $$0.717666\pi$$
$$570$$ 0 0
$$571$$ −31.8976 −1.33487 −0.667436 0.744667i $$-0.732608\pi$$
−0.667436 + 0.744667i $$0.732608\pi$$
$$572$$ 0 0
$$573$$ 1.24562 2.15748i 0.0520367 0.0901302i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −23.2889 −0.969528 −0.484764 0.874645i $$-0.661095\pi$$
−0.484764 + 0.874645i $$0.661095\pi$$
$$578$$ 0 0
$$579$$ −4.20222 7.27845i −0.174638 0.302482i
$$580$$ 0 0
$$581$$ −28.3358 −1.17557
$$582$$ 0 0
$$583$$ −24.4953 42.4271i −1.01449 1.75715i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 4.74059 8.21094i 0.195665 0.338902i −0.751453 0.659786i $$-0.770647\pi$$
0.947118 + 0.320885i $$0.103980\pi$$
$$588$$ 0 0
$$589$$ −18.8520 5.26323i −0.776784 0.216867i
$$590$$ 0 0
$$591$$ 4.19594 7.26758i 0.172598 0.298948i
$$592$$ 0 0
$$593$$ −21.2234 36.7600i −0.871540 1.50955i −0.860403 0.509614i $$-0.829788\pi$$
−0.0111366 0.999938i $$-0.503545\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −8.12180 −0.332403
$$598$$ 0 0
$$599$$ 12.8961 + 22.3368i 0.526922 + 0.912656i 0.999508 + 0.0313711i $$0.00998736\pi$$
−0.472586 + 0.881285i $$0.656679\pi$$
$$600$$ 0 0
$$601$$ 0.206080 0.00840619 0.00420310 0.999991i $$-0.498662\pi$$
0.00420310 + 0.999991i $$0.498662\pi$$
$$602$$ 0 0
$$603$$ −10.1249 + 17.5369i −0.412319 + 0.714157i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −0.100472 −0.00407802 −0.00203901 0.999998i $$-0.500649\pi$$
−0.00203901 + 0.999998i $$0.500649\pi$$
$$608$$ 0 0
$$609$$ 12.1176 0.491029
$$610$$ 0 0
$$611$$ −3.75493 + 6.50373i −0.151908 + 0.263113i
$$612$$ 0 0
$$613$$ −19.7400 + 34.1907i −0.797292 + 1.38095i 0.124081 + 0.992272i $$0.460402\pi$$
−0.921373 + 0.388679i $$0.872932\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −14.1658 24.5359i −0.570294 0.987777i −0.996536 0.0831682i $$-0.973496\pi$$
0.426242 0.904609i $$-0.359837\pi$$
$$618$$ 0 0
$$619$$ −1.39670 −0.0561380 −0.0280690 0.999606i $$-0.508936\pi$$
−0.0280690 + 0.999606i $$0.508936\pi$$
$$620$$ 0 0
$$621$$ −0.813425 1.40889i −0.0326416 0.0565369i
$$622$$ 0 0
$$623$$ 7.28575 + 12.6193i 0.291897 + 0.505581i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ −6.61758 + 6.48063i −0.264281 + 0.258812i
$$628$$ 0 0
$$629$$ 1.91435 3.31576i 0.0763303 0.132208i
$$630$$ 0 0
$$631$$ −4.07397 7.05633i −0.162182 0.280908i 0.773469 0.633834i $$-0.218520\pi$$
−0.935651 + 0.352926i $$0.885187\pi$$
$$632$$ 0 0
$$633$$ 0.244717 + 0.423862i 0.00972661 + 0.0168470i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −34.3217 59.4470i −1.35988 2.35538i
$$638$$ 0 0
$$639$$ 16.7178 0.661344
$$640$$ 0 0
$$641$$ −9.76367 + 16.9112i −0.385642 + 0.667951i −0.991858 0.127349i $$-0.959353\pi$$
0.606216 + 0.795300i $$0.292687\pi$$
$$642$$ 0 0
$$643$$ 21.5945 37.4028i 0.851604 1.47502i −0.0281570 0.999604i $$-0.508964\pi$$
0.879761 0.475417i $$-0.157703\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −27.4390 −1.07874 −0.539370 0.842069i $$-0.681338\pi$$
−0.539370 + 0.842069i $$0.681338\pi$$
$$648$$ 0 0
$$649$$ −15.8015 + 27.3690i −0.620263 + 1.07433i
$$650$$ 0 0
$$651$$ 3.41630 5.91721i 0.133896 0.231914i
$$652$$ 0 0
$$653$$ 3.40515 0.133254 0.0666270 0.997778i $$-0.478776\pi$$
0.0666270 + 0.997778i $$0.478776\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −26.5671 −1.03648
$$658$$ 0 0
$$659$$ −6.09862 10.5631i −0.237569 0.411481i 0.722448 0.691426i $$-0.243017\pi$$
−0.960016 + 0.279945i $$0.909684\pi$$
$$660$$ 0 0
$$661$$ 19.0683 + 33.0272i 0.741670 + 1.28461i 0.951734 + 0.306923i $$0.0992994\pi$$
−0.210064 + 0.977688i $$0.567367\pi$$
$$662$$ 0 0
$$663$$ 4.07580 7.05948i 0.158291 0.274168i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 3.11950 5.40313i 0.120788 0.209210i
$$668$$ 0 0
$$669$$ −4.11768 7.13202i −0.159199 0.275740i
$$670$$ 0 0
$$671$$ −16.8640 29.2092i −0.651026 1.12761i
$$672$$ 0 0
$$673$$ 37.9505 1.46288 0.731442 0.681903i $$-0.238848\pi$$
0.731442 + 0.681903i $$0.238848\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 32.4499 1.24715 0.623575 0.781763i $$-0.285679\pi$$
0.623575 + 0.781763i $$0.285679\pi$$
$$678$$ 0 0
$$679$$ −15.9216 + 27.5771i −0.611016 + 1.05831i
$$680$$ 0 0
$$681$$ −0.793394 + 1.37420i −0.0304029 + 0.0526594i
$$682$$ 0 0
$$683$$ −40.5283 −1.55077 −0.775385 0.631488i $$-0.782444\pi$$
−0.775385 + 0.631488i $$0.782444\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −1.62733 + 2.81863i −0.0620867 + 0.107537i
$$688$$ 0 0
$$689$$ −24.2494 + 42.0012i −0.923830 + 1.60012i
$$690$$ 0 0
$$691$$ 1.78657 0.0679642 0.0339821 0.999422i $$-0.489181\pi$$
0.0339821 + 0.999422i $$0.489181\pi$$
$$692$$ 0 0
$$693$$ 37.2062 + 64.4430i 1.41335 + 2.44799i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 12.2163 + 21.1592i 0.462725 + 0.801464i
$$698$$ 0 0
$$699$$ −0.764386 1.32396i −0.0289117 0.0500766i
$$700$$ 0 0
$$701$$ 21.8614 37.8650i 0.825693 1.43014i −0.0756952 0.997131i $$-0.524118\pi$$
0.901388 0.433011i $$-0.142549\pi$$
$$702$$ 0 0
$$703$$ 4.14812 + 1.15810i 0.156449 + 0.0436785i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 21.1107 + 36.5648i 0.793949 + 1.37516i
$$708$$ 0 0
$$709$$ −7.32015 12.6789i −0.274914 0.476165i 0.695199 0.718817i $$-0.255316\pi$$
−0.970113 + 0.242652i $$0.921983\pi$$
$$710$$ 0 0
$$711$$ 40.2363 1.50898
$$712$$ 0 0
$$713$$ −1.75896 3.04661i −0.0658736 0.114096i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 2.62024 4.53840i 0.0978548 0.169489i
$$718$$ 0 0
$$719$$ 11.1778 19.3606i 0.416863 0.722028i −0.578759 0.815499i $$-0.696463\pi$$
0.995622 + 0.0934709i $$0.0297962\pi$$
$$720$$ 0 0
$$721$$ −62.1515 −2.31464
$$722$$ 0 0
$$723$$ 1.02113 0.0379764
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 4.15042 7.18874i 0.153930 0.266615i −0.778739 0.627349i $$-0.784140\pi$$
0.932669 + 0.360733i $$0.117473\pi$$
$$728$$ 0 0
$$729$$ −20.4861 −0.758745
$$730$$ 0 0
$$731$$ 3.04195 + 5.26881i 0.112511 + 0.194874i
$$732$$ 0 0
$$733$$ −35.7912 −1.32198 −0.660989 0.750396i $$-0.729863\pi$$
−0.660989 + 0.750396i $$0.729863\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 21.1719 + 36.6708i 0.779876 + 1.35079i
$$738$$ 0 0
$$739$$ 16.6216 28.7895i 0.611437 1.05904i −0.379561 0.925167i $$-0.623925\pi$$
0.990998 0.133873i $$-0.0427415\pi$$
$$740$$ 0 0
$$741$$ 8.83163 + 2.46567i 0.324438 + 0.0905787i
$$742$$ 0 0
$$743$$ −9.27444 + 16.0638i −0.340246 + 0.589324i −0.984478 0.175506i $$-0.943844\pi$$
0.644232 + 0.764830i $$0.277177\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −9.46183 16.3884i −0.346190 0.599619i
$$748$$ 0 0
$$749$$ 40.8565 1.49287
$$750$$ 0 0
$$751$$ −21.5748 37.3687i −0.787276 1.36360i −0.927630 0.373501i $$-0.878157\pi$$
0.140353 0.990101i $$-0.455176\pi$$
$$752$$ 0 0
$$753$$ 5.40957 0.197136
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 4.77434 8.26940i 0.173526 0.300556i −0.766124 0.642693i $$-0.777817\pi$$
0.939650 + 0.342136i $$0.111151\pi$$
$$758$$ 0 0
$$759$$ −1.66476 −0.0604268
$$760$$ 0 0
$$761$$ 35.8512 1.29960 0.649802 0.760103i $$-0.274852\pi$$
0.649802 + 0.760103i $$0.274852\pi$$
$$762$$ 0 0
$$763$$ 5.63617 9.76214i 0.204043 0.353413i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 31.2857 1.12966
$$768$$ 0 0
$$769$$ 8.93698 + 15.4793i 0.322276 + 0.558198i 0.980957 0.194224i $$-0.0622188\pi$$
−0.658681 + 0.752422i $$0.728886\pi$$
$$770$$ 0 0
$$771$$ −4.62463 −0.166552
$$772$$ 0 0
$$773$$ 0.926769 + 1.60521i 0.0333336 + 0.0577354i 0.882211 0.470854i $$-0.156054\pi$$
−0.848877 + 0.528590i $$0.822721\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −0.751709 + 1.30200i −0.0269674 + 0.0467089i
$$778$$ 0 0
$$779$$ −19.6356 + 19.2293i −0.703519 + 0.688961i
$$780$$ 0 0
$$781$$ 17.4790 30.2744i 0.625446 1.08330i
$$782$$ 0 0
$$783$$ 8.26836 + 14.3212i 0.295487 + 0.511798i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 53.8501 1.91955 0.959774 0.280773i $$-0.0905907\pi$$
0.959774 + 0.280773i $$0.0905907\pi$$
$$788$$ 0 0
$$789$$ 3.42486 + 5.93202i 0.121928 + 0.211186i
$$790$$ 0 0
$$791$$ 58.8523 2.09255
$$792$$ 0 0
$$793$$ −16.6947 + 28.9160i −0.592845 + 1.02684i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 44.2766 1.56836 0.784179 0.620535i $$-0.213085\pi$$
0.784179 + 0.620535i $$0.213085\pi$$
$$798$$ 0 0
$$799$$ −4.88964